diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index a3ec780..4545ab8 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -469,6 +469,25 @@ See source pdf
+
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 1) + source + pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 2) + source + pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 3) + source + pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 4) + source + pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 5) + source + pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 6) + source + pdf


Rich Derivatives



@@ -587,6 +606,25 @@ Mathematica. This test suite shows Axiom's results. source pdf

+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 1) + source + pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 2) + source + pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 3) + source + pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 4) + source + pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 5) + source + pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 6) + source + pdf
+


Rich



diff --git a/src/axiom-website/CATS/rich12a.input.pamphlet b/src/axiom-website/CATS/rich12a.input.pamphlet new file mode 100644 index 0000000..2f89471 --- /dev/null +++ b/src/axiom-website/CATS/rich12a.input.pamphlet @@ -0,0 +1,50704 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 307 matching answers. +\item 0 cases where Axiom answer differs from Rubi +\item 91 cases where Axiom supplied 2 results. +\item 12 cases that Axiom failed to integrate. +\item 31 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12a.output +)spool rich12a.output +)set message test on +)set message auto off +)clear all + + +--S 1 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + A b x)(e x + d) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1457 +r0:=-d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R ((A c + B b)e - 3B c d)m + ((7A c + 7B b)e - 21B c d)m +--R + +--R ((14A c + 14B b)e - 42B c d)m + (8A c + 8B b)e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R (A b e + (- 2A c - 2B b)d e + 3B c d )m +--R + +--R 2 2 2 +--R (8A b e + (- 16A c - 16B b)d e + 24B c d )m +--R + +--R 2 2 2 +--R (19A b e + (- 38A c - 38B b)d e + 57B c d )m + 12A b e +--R + +--R 2 +--R (- 24A c - 24B b)d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 +--R (- A b d e + (A c + B b)d e - B c d )m +--R + +--R 2 2 3 2 +--R (- 9A b d e + (9A c + 9B b)d e - 9B c d )m +--R + +--R 2 2 3 2 +--R (- 26A b d e + (26A c + 26B b)d e - 26B c d )m - 24A b d e +--R + +--R 2 3 +--R (24A c + 24B b)d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R ((A c + B b)e + B c d e )m + ((7A c + 7B b)e + 3B c d e )m +--R + +--R 4 3 4 +--R ((14A c + 14B b)e + 2B c d e )m + (8A c + 8B b)e +--R * +--R 3 +--R x +--R + +--R 4 3 3 +--R (A b e + (A c + B b)d e )m +--R + +--R 4 3 2 2 2 +--R (8A b e + (5A c + 5B b)d e - 3B c d e )m +--R + +--R 4 3 2 2 4 +--R (19A b e + (4A c + 4B b)d e - 3B c d e )m + 12A b e +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 2 2 +--R A b d e m + (7A b d e + (- 2A c - 2B b)d e )m +--R + +--R 3 2 2 3 +--R (12A b d e + (- 8A c - 8B b)d e + 6B c d e)m +--R * +--R x +--R + +--R 2 2 2 2 2 3 2 2 +--R - A b d e m + (- 7A b d e + (2A c + 2B b)d e)m - 12A b d e +--R + +--R 3 4 +--R (8A c + 8B b)d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R ((A c + B b)e + B c d e )m + ((7A c + 7B b)e + 3B c d e )m +--R + +--R 4 3 4 +--R ((14A c + 14B b)e + 2B c d e )m + (8A c + 8B b)e +--R * +--R 3 +--R x +--R + +--R 4 3 3 +--R (A b e + (A c + B b)d e )m +--R + +--R 4 3 2 2 2 +--R (8A b e + (5A c + 5B b)d e - 3B c d e )m +--R + +--R 4 3 2 2 4 +--R (19A b e + (4A c + 4B b)d e - 3B c d e )m + 12A b e +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 2 2 +--R A b d e m + (7A b d e + (- 2A c - 2B b)d e )m +--R + +--R 3 2 2 3 +--R (12A b d e + (- 8A c - 8B b)d e + 6B c d e)m +--R * +--R x +--R + +--R 2 2 2 2 2 3 2 2 +--R - A b d e m + (- 7A b d e + (2A c + 2B b)d e)m - 12A b d e +--R + +--R 3 4 +--R (8A c + 8B b)d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 2 m + 4 +--R (- B c m - 6B c m - 11B c m - 6B c)(e x + d) +--R + +--R 3 2 +--R ((- A c - B b)e + 3B c d)m + ((- 7A c - 7B b)e + 21B c d)m +--R + +--R ((- 14A c - 14B b)e + 42B c d)m + (- 8A c - 8B b)e + 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R (- A b e + (2A c + 2B b)d e - 3B c d )m +--R + +--R 2 2 2 +--R (- 8A b e + (16A c + 16B b)d e - 24B c d )m +--R + +--R 2 2 2 +--R (- 19A b e + (38A c + 38B b)d e - 57B c d )m - 12A b e +--R + +--R 2 +--R (24A c + 24B b)d e - 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 +--R (A b d e + (- A c - B b)d e + B c d )m +--R + +--R 2 2 3 2 +--R (9A b d e + (- 9A c - 9B b)d e + 9B c d )m +--R + +--R 2 2 3 2 +--R (26A b d e + (- 26A c - 26B b)d e + 26B c d )m + 24A b d e +--R + +--R 2 3 +--R (- 24A c - 24B b)d e + 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1457 +t0:=(A+B*x)*(d+e*x)^5*(b*x+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 +--R B c e x + ((A c + B b)e + 5B c d e )x +--R + +--R 5 4 2 3 6 +--R (A b e + (5A c + 5B b)d e + 10B c d e )x +--R + +--R 4 2 3 3 2 5 +--R (5A b d e + (10A c + 10B b)d e + 10B c d e )x +--R + +--R 2 3 3 2 4 4 +--R (10A b d e + (10A c + 10B b)d e + 5B c d e)x +--R + +--R 3 2 4 5 3 4 5 2 +--R (10A b d e + (5A c + 5B b)d e + B c d )x + (5A b d e + (A c + B b)d )x +--R + +--R 5 +--R A b d x +--R Type: Polynomial(Integer) +--E 6 + +--S 7 of 1457 +r0:=-1/6*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^6/e^4+1/7*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^7/e^4-1/8*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^8/e^4+_ + 1/9*B*c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 1 9 5 8 8 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 9 8 8 8 +--R + +--R 1 9 5 5 8 10 2 7 7 +--R (- A b e + (- A c + - B b)d e + -- B c d e )x +--R 7 7 7 7 +--R + +--R 5 8 5 5 2 7 5 3 6 6 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 6 3 3 3 +--R + +--R 2 7 3 6 4 5 5 +--R (2A b d e + (2A c + 2B b)d e + B c d e )x +--R + +--R 5 3 6 5 5 4 5 1 5 4 4 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 2 4 4 4 +--R + +--R 5 4 5 1 1 5 4 3 1 5 4 2 1 7 2 +--R (- A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 3 2 42 +--R + +--R 1 1 8 1 9 +--R (--- A c + --- B b)d e - --- B c d +--R 168 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 7 + +--S 8 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 9 1 1 5 5 4 8 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 9 8 8 8 +--R + +--R 1 5 5 5 4 10 2 3 7 +--R (- A b e + (- A c + - B b)d e + -- B c d e )x +--R 7 7 7 7 +--R + +--R 5 4 5 5 2 3 5 3 2 6 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 6 3 3 3 +--R + +--R 2 3 3 2 4 5 +--R (2A b d e + (2A c + 2B b)d e + B c d e)x +--R + +--R 5 3 2 5 5 4 1 5 4 +--R (- A b d e + (- A c + - B b)d e + - B c d )x +--R 2 4 4 4 +--R + +--R 5 4 1 1 5 3 1 5 2 +--R (- A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 1457 +m0:=a0-r0 +--R +--R +--R 1 7 2 1 1 8 1 9 +--R -- A b d e + (- --- A c - --- B b)d e + --- B c d +--R 42 168 168 504 +--R (4) --------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 9 + +--S 10 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 10 + +)clear all + +--S 11 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 +--R B c e x + ((A c + B b)e + 4B c d e )x +--R + +--R 4 3 2 2 5 +--R (A b e + (4A c + 4B b)d e + 6B c d e )x +--R + +--R 3 2 2 3 4 +--R (4A b d e + (6A c + 6B b)d e + 4B c d e)x +--R + +--R 2 2 3 4 3 3 4 2 +--R (6A b d e + (4A c + 4B b)d e + B c d )x + (4A b d e + (A c + B b)d )x +--R + +--R 4 +--R A b d x +--R Type: Polynomial(Integer) +--E 11 + +--S 12 of 1457 +r0:=-1/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^5/e^4+1/6*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^7/e^4+_ + 1/8*B*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 1 8 4 7 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 8 2 2 7 2 6 6 +--R (- A b e + (- A c + - B b)d e + B c d e )x +--R 6 3 3 +--R + +--R 4 7 6 6 2 6 4 3 5 5 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 3 2 6 3 5 1 4 4 4 +--R (- A b d e + (A c + B b)d e + - B c d e )x +--R 2 4 +--R + +--R 4 3 5 1 1 4 4 3 1 4 4 2 1 6 2 +--R (- A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 3 2 30 +--R + +--R 1 1 7 1 8 +--R (--- A c + --- B b)d e - --- B c d +--R 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 12 + +--S 13 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 8 1 1 4 4 3 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 4 2 2 3 2 2 6 +--R (- A b e + (- A c + - B b)d e + B c d e )x +--R 6 3 3 +--R + +--R 4 3 6 6 2 2 4 3 5 +--R (- A b d e + (- A c + - B b)d e + - B c d e)x +--R 5 5 5 5 +--R + +--R 3 2 2 3 1 4 4 +--R (- A b d e + (A c + B b)d e + - B c d )x +--R 2 4 +--R + +--R 4 3 1 1 4 3 1 4 2 +--R (- A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 1457 +m0:=a0-r0 +--R +--R +--R 1 6 2 1 1 7 1 8 +--R -- A b d e + (- --- A c - --- B b)d e + --- B c d +--R 30 105 105 280 +--R (4) --------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 14 + +--S 15 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 15 + +)clear all + +--S 16 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R (A b e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 2 2 3 3 2 3 2 +--R (3A b d e + (3A c + 3B b)d e + B c d )x + (3A b d e + (A c + B b)d )x +--R + +--R 3 +--R A b d x +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 1457 +r0:=-1/4*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^4/e^4+1/5*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^6/e^4+_ + 1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 1 7 1 6 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 7 3 3 6 3 2 5 5 +--R (- A b e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 3 6 3 3 2 5 1 3 4 4 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 2 5 1 1 3 4 3 1 3 4 2 1 5 2 +--R (A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 2 20 +--R + +--R 1 1 6 1 7 +--R (-- A c + -- B b)d e - --- B c d +--R 60 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 17 + +--S 18 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 7 1 1 3 1 2 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 3 3 3 2 3 2 5 +--R (- A b e + (- A c + - B b)d e + - B c d e)x +--R 5 5 5 5 +--R + +--R 3 2 3 3 2 1 3 4 +--R (- A b d e + (- A c + - B b)d e + - B c d )x +--R 4 4 4 4 +--R + +--R 2 1 1 3 3 1 3 2 +--R (A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 1457 +m0:=a0-r0 +--R +--R +--R 1 5 2 1 1 6 1 7 +--R -- A b d e + (- -- A c - -- B b)d e + --- B c d +--R 20 60 60 140 +--R (4) ------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 19 + +--S 20 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 20 + +)clear all + +--S 21 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 1457 +r0:=1/2*A*b*d^2*x^2+1/3*d*(b*B*d+A*c*d+2*A*b*e)*x^3+1/4*(A*e*(2*c*d+b*e)+_ + B*d*(c*d+2*b*e))*x^4+1/5*e*(2*B*c*d+b*B*e+A*c*e)*x^5+1/6*B*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 1 2 2 5 +--R - B c e x + ((- A c + - B b)e + - B c d e)x +--R 6 5 5 5 +--R + +--R 1 2 1 1 1 2 4 +--R (- A b e + (- A c + - B b)d e + - B c d )x +--R 4 2 2 4 +--R + +--R 2 1 1 2 3 1 2 2 +--R (- A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 6 1 1 2 2 5 +--R - B c e x + ((- A c + - B b)e + - B c d e)x +--R 6 5 5 5 +--R + +--R 1 2 1 1 1 2 4 +--R (- A b e + (- A c + - B b)d e + - B c d )x +--R 4 2 2 4 +--R + +--R 2 1 1 2 3 1 2 2 +--R (- A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 1457 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 1457 +r0:=1/2*A*b*d*x^2+1/3*(b*B*d+A*c*d+A*b*e)*x^3+1/4*(B*c*d+b*B*e+A*c*e)*x^4+_ + 1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 3 1 2 +--R (- A b e + (- A c + - B b)d)x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 3 1 2 +--R (- A b e + (- A c + - B b)d)x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 1457 +t0:=(A+B*x)*(b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + (A c + B b)x + A b x +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 1457 +r0:=1/2*A*b*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 1 3 1 2 +--R (2) - B c x + (- A c + - B b)x + - A b x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 1457 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 1 3 1 2 +--R (3) - B c x + (- A c + - B b)x + - A b x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1457 +r0:=(B*d-A*e)*(c*d-b*e)*x/e^3-1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+_ + 1/3*B*c*x^3/e-d*(B*d-A*e)*(c*d-b*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 2 3 3 3 +--R (- 6A b d e + (6A c + 6B b)d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 +--R ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R (6A b e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 3 +--R (- 6A b d e + (6A c + 6B b)d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 +--R ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R (6A b e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1457 +r0:=-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+d*(B*d-A*e)*_ + (c*d-b*e)/(e^4*(d+e*x))+(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 +--R (2A b e + (- 4A c - 4B b)d e + 6B c d e)x + 2A b d e +--R + +--R 2 3 +--R (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 2 2 3 +--R ((2A c + 2B b)d e - 4B c d e)x + 2A b d e + (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 +--R (2A b e + (- 4A c - 4B b)d e + 6B c d e)x + 2A b d e +--R + +--R 2 3 +--R (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 2 2 3 +--R ((2A c + 2B b)d e - 4B c d e)x + 2A b d e + (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1457 +r0:=B*c*x/e^3+1/2*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^2)+(-B*d*(3*c*d-_ + 2*b*e)+A*e*(2*c*d-b*e))/(e^4*(d+e*x))-(3*B*c*d-b*B*e-A*c*e)*log(d+_ + e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 +--R 2B c e x + 4B c d e x + (- 2A b e + (4A c + 4B b)d e - 4B c d e)x +--R + +--R 2 2 3 +--R - A b d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 +--R 2B c e x + 4B c d e x + (- 2A b e + (4A c + 4B b)d e - 4B c d e)x +--R + +--R 2 2 3 +--R - A b d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1457 +r0:=1/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^3)+1/2*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^2)+(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+_ + B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 2 +--R (- 3A b e + (- 6A c - 6B b)d e + 27B c d e)x - A b d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 2 +--R (- 3A b e + (- 6A c - 6B b)d e + 27B c d e)x - A b d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 1457 +r0:=1/4*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^4)+1/3*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^2)-B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 1 3 3 2 2 +--R - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 2 2 +--R + +--R 1 3 1 1 2 2 1 2 +--R (- - A b e + (- - A c - - B b)d e - B c d e)x - -- A b d e +--R 3 3 3 12 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - - B c d +--R 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 57 + +--S 58 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 12B c e x + ((- 6A c - 6B b)e - 18B c d e )x +--R + +--R 3 2 2 2 +--R (- 4A b e + (- 4A c - 4B b)d e - 12B c d e)x - A b d e +--R + +--R 2 3 +--R (- A c - B b)d e - 3B c d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 1457 +r0:=1/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^5)+1/4*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 3 3 2 +--R + +--R 1 3 1 1 2 1 2 1 2 +--R (- - A b e + (- - A c - - B b)d e - - B c d e)x - -- A b d e +--R 4 6 6 4 20 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - -- B c d +--R 30 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 30B c e x + ((- 20A c - 20B b)e - 30B c d e )x +--R + +--R 3 2 2 2 +--R (- 15A b e + (- 10A c - 10B b)d e - 15B c d e)x - 3A b d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e - 3B c d +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 1457 +r0:=1/6*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^6)+1/5*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^5)+1/4*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 3 4 4 4 +--R + +--R 1 3 1 1 2 1 2 1 2 +--R (- - A b e + (- -- A c - -- B b)d e - -- B c d e)x - -- A b d e +--R 5 10 10 10 30 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - -- B c d +--R 60 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 67 + +--S 68 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 20B c e x + ((- 15A c - 15B b)e - 15B c d e )x +--R + +--R 3 2 2 2 +--R (- 12A b e + (- 6A c - 6B b)d e - 6B c d e)x - 2A b d e +--R + +--R 2 3 +--R (- A c - B b)d e - B c d +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 4 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 m +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )(e x + d) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1457 +r0:=-d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(1+m)/(e^6*(1+m))+d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^6*(2+m))+_ + (A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(4+m)/(e^6*(4+m))-_ + c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*_ + (d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((A c + 2B b c)e - 5B c d)m + ((16A c + 32B b c)e - 80B c d)m +--R + +--R 2 2 3 +--R ((95A c + 190B b c)e - 475B c d)m +--R + +--R 2 2 2 +--R ((260A c + 520B b c)e - 1300B c d)m +--R + +--R 2 2 2 2 +--R ((324A c + 648B b c)e - 1620B c d)m + (144A c + 288B b c)e - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (- 4A c - 8B b c)d e + 10B c d )m +--R + +--R 2 2 2 2 2 4 +--R ((34A b c + 17B b )e + (- 68A c - 136B b c)d e + 170B c d )m +--R + +--R 2 2 2 2 2 3 +--R ((214A b c + 107B b )e + (- 428A c - 856B b c)d e + 1070B c d )m +--R + +--R 2 2 2 2 2 2 +--R ((614A b c + 307B b )e + (- 1228A c - 2456B b c)d e + 3070B c d )m +--R + +--R 2 2 2 2 2 +--R ((792A b c + 396B b )e + (- 1584A c - 3168B b c)d e + 3960B c d )m +--R + +--R 2 2 2 2 2 +--R (360A b c + 180B b )e + (- 720A c - 1440B b c)d e + 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (- 6A b c - 3B b )d e + (6A c + 12B b c)d e - 10B c d )m +--R + +--R 2 3 2 2 2 2 +--R 18A b e + (- 108A b c - 54B b )d e + (108A c + 216B b c)d e +--R + +--R 2 3 +--R - 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 2 2 +--R 121A b e + (- 726A b c - 363B b )d e + (726A c + 1452B b c)d e +--R + +--R 2 3 +--R - 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 +--R 372A b e + (- 2232A b c - 1116B b )d e +--R + +--R 2 2 2 3 +--R (2232A c + 4464B b c)d e - 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 +--R 508A b e + (- 3048A b c - 1524B b )d e +--R + +--R 2 2 2 3 +--R (3048A c + 6096B b c)d e - 5080B c d +--R * +--R m +--R + +--R 2 3 2 2 2 2 +--R 240A b e + (- 1440A b c - 720B b )d e + (1440A c + 2880B b c)d e +--R + +--R 2 3 +--R - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 3 +--R - 2A b d e + (6A b c + 3B b )d e + (- 4A c - 8B b c)d e +--R + +--R 2 4 +--R 5B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 2 2 2 3 +--R - 38A b d e + (114A b c + 57B b )d e + (- 76A c - 152B b c)d e +--R + +--R 2 4 +--R 95B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 2 +--R - 274A b d e + (822A b c + 411B b )d e +--R + +--R 2 3 2 4 +--R (- 548A c - 1096B b c)d e + 685B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 2 +--R - 922A b d e + (2766A b c + 1383B b )d e +--R + +--R 2 3 2 4 +--R (- 1844A c - 3688B b c)d e + 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 +--R - 1404A b d e + (4212A b c + 2106B b )d e +--R + +--R 2 3 2 4 +--R (- 2808A c - 5616B b c)d e + 3510B c d +--R * +--R m +--R + +--R 2 3 2 2 2 +--R - 720A b d e + (2160A b c + 1080B b )d e +--R + +--R 2 3 2 4 +--R (- 1440A c - 2880B b c)d e + 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 2 3 2 2 4 2 5 5 +--R (A b d e + (- 2A b c - B b )d e + (A c + 2B b c)d e - B c d )m +--R + +--R 2 2 3 2 3 2 2 4 +--R 20A b d e + (- 40A b c - 20B b )d e + (20A c + 40B b c)d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 2 3 2 3 2 +--R 155A b d e + (- 310A b c - 155B b )d e +--R + +--R 2 4 2 5 +--R (155A c + 310B b c)d e - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 2 3 2 3 2 +--R 580A b d e + (- 1160A b c - 580B b )d e +--R + +--R 2 4 2 5 +--R (580A c + 1160B b c)d e - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 2 3 2 3 2 +--R 1044A b d e + (- 2088A b c - 1044B b )d e +--R + +--R 2 4 2 5 +--R (1044A c + 2088B b c)d e - 1044B c d +--R * +--R m +--R + +--R 2 2 3 2 3 2 2 4 +--R 720A b d e + (- 1440A b c - 720B b )d e + (720A c + 1440B b c)d e +--R + +--R 2 5 +--R - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 +--R ((A c + 2B b c)e + B c d e )m +--R + +--R 2 6 2 5 4 +--R ((16A c + 32B b c)e + 10B c d e )m +--R + +--R 2 6 2 5 3 +--R ((95A c + 190B b c)e + 35B c d e )m +--R + +--R 2 6 2 5 2 +--R ((260A c + 520B b c)e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R ((324A c + 648B b c)e + 24B c d e )m + (144A c + 288B b c)e +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A b c + B b )e + (A c + 2B b c)d e )m +--R + +--R 2 6 2 5 2 2 4 4 +--R ((34A b c + 17B b )e + (12A c + 24B b c)d e - 5B c d e )m +--R + +--R 2 6 2 5 2 2 4 3 +--R ((214A b c + 107B b )e + (47A c + 94B b c)d e - 30B c d e )m +--R + +--R 2 6 2 5 2 2 4 2 +--R ((614A b c + 307B b )e + (72A c + 144B b c)d e - 55B c d e )m +--R + +--R 2 6 2 5 2 2 4 +--R ((792A b c + 396B b )e + (36A c + 72B b c)d e - 30B c d e )m +--R + +--R 2 6 +--R (360A b c + 180B b )e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 5 +--R (A b e + (2A b c + B b )d e )m +--R + +--R 2 6 2 5 2 2 4 4 +--R (18A b e + (28A b c + 14B b )d e + (- 4A c - 8B b c)d e )m +--R + +--R 2 6 2 5 2 2 4 +--R 121A b e + (130A b c + 65B b )d e + (- 36A c - 72B b c)d e +--R + +--R 2 3 3 +--R 20B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R 372A b e + (224A b c + 112B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 80A c - 160B b c)d e + 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 2 2 4 +--R 508A b e + (120A b c + 60B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 3 3 +--R 40B c d e +--R * +--R m +--R + +--R 2 6 +--R 240A b e +--R * +--R 3 +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A b d e m + (16A b d e + (- 6A b c - 3B b )d e )m +--R + +--R 2 5 2 2 4 2 3 3 3 +--R (89A b d e + (- 72A b c - 36B b )d e + (12A c + 24B b c)d e )m +--R + +--R 2 5 2 2 4 +--R 194A b d e + (- 246A b c - 123B b )d e +--R + +--R 2 3 3 2 4 2 +--R (84A c + 168B b c)d e - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 120A b d e + (- 180A b c - 90B b )d e +--R + +--R 2 3 3 2 4 2 +--R (72A c + 144B b c)d e - 60B c d e +--R * +--R m +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 4 2 3 3 3 +--R - 2A b d e m + (- 30A b d e + (12A b c + 6B b )d e )m +--R + +--R 2 2 4 2 3 3 +--R - 148A b d e + (132A b c + 66B b )d e +--R + +--R 2 4 2 +--R (- 24A c - 48B b c)d e +--R * +--R 2 +--R m +--R + +--R 2 2 4 2 3 3 +--R - 240A b d e + (360A b c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 144A c - 288B b c)d e + 120B c d e +--R * +--R m +--R * +--R x +--R + +--R 2 3 3 3 2 3 3 2 4 2 2 +--R 2A b d e m + (30A b d e + (- 12A b c - 6B b )d e )m +--R + +--R 2 3 3 2 4 2 2 5 +--R (148A b d e + (- 132A b c - 66B b )d e + (24A c + 48B b c)d e)m +--R + +--R 2 3 3 2 4 2 2 5 +--R 240A b d e + (- 360A b c - 180B b )d e + (144A c + 288B b c)d e +--R + +--R 2 6 +--R - 120B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 +--R ((A c + 2B b c)e + B c d e )m +--R + +--R 2 6 2 5 4 +--R ((16A c + 32B b c)e + 10B c d e )m +--R + +--R 2 6 2 5 3 +--R ((95A c + 190B b c)e + 35B c d e )m +--R + +--R 2 6 2 5 2 +--R ((260A c + 520B b c)e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R ((324A c + 648B b c)e + 24B c d e )m + (144A c + 288B b c)e +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A b c + B b )e + (A c + 2B b c)d e )m +--R + +--R 2 6 2 5 2 2 4 4 +--R ((34A b c + 17B b )e + (12A c + 24B b c)d e - 5B c d e )m +--R + +--R 2 6 2 5 2 2 4 3 +--R ((214A b c + 107B b )e + (47A c + 94B b c)d e - 30B c d e )m +--R + +--R 2 6 2 5 2 2 4 2 +--R ((614A b c + 307B b )e + (72A c + 144B b c)d e - 55B c d e )m +--R + +--R 2 6 2 5 2 2 4 +--R ((792A b c + 396B b )e + (36A c + 72B b c)d e - 30B c d e )m +--R + +--R 2 6 +--R (360A b c + 180B b )e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 5 +--R (A b e + (2A b c + B b )d e )m +--R + +--R 2 6 2 5 2 2 4 4 +--R (18A b e + (28A b c + 14B b )d e + (- 4A c - 8B b c)d e )m +--R + +--R 2 6 2 5 +--R 121A b e + (130A b c + 65B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 36A c - 72B b c)d e + 20B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R 372A b e + (224A b c + 112B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 80A c - 160B b c)d e + 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R 508A b e + (120A b c + 60B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 48A c - 96B b c)d e + 40B c d e +--R * +--R m +--R + +--R 2 6 +--R 240A b e +--R * +--R 3 +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A b d e m + (16A b d e + (- 6A b c - 3B b )d e )m +--R + +--R 2 5 2 2 4 +--R 89A b d e + (- 72A b c - 36B b )d e +--R + +--R 2 3 3 +--R (12A c + 24B b c)d e +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 +--R 194A b d e + (- 246A b c - 123B b )d e +--R + +--R 2 3 3 2 4 2 +--R (84A c + 168B b c)d e - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 120A b d e + (- 180A b c - 90B b )d e +--R + +--R 2 3 3 2 4 2 +--R (72A c + 144B b c)d e - 60B c d e +--R * +--R m +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 4 2 3 3 3 +--R - 2A b d e m + (- 30A b d e + (12A b c + 6B b )d e )m +--R + +--R 2 2 4 2 3 3 +--R - 148A b d e + (132A b c + 66B b )d e +--R + +--R 2 4 2 +--R (- 24A c - 48B b c)d e +--R * +--R 2 +--R m +--R + +--R 2 2 4 2 3 3 +--R - 240A b d e + (360A b c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 144A c - 288B b c)d e + 120B c d e +--R * +--R m +--R * +--R x +--R + +--R 2 3 3 3 2 3 3 2 4 2 2 +--R 2A b d e m + (30A b d e + (- 12A b c - 6B b )d e )m +--R + +--R 2 3 3 2 4 2 2 5 +--R (148A b d e + (- 132A b c - 66B b )d e + (24A c + 48B b c)d e)m +--R + +--R 2 3 3 2 4 2 2 5 +--R 240A b d e + (- 360A b c - 180B b )d e + (144A c + 288B b c)d e +--R + +--R 2 6 +--R - 120B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (- B c m - 15B c m - 85B c m - 225B c m - 274B c m - 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((- A c - 2B b c)e + 5B c d)m + ((- 16A c - 32B b c)e + 80B c d)m +--R + +--R 2 2 3 +--R ((- 95A c - 190B b c)e + 475B c d)m +--R + +--R 2 2 2 +--R ((- 260A c - 520B b c)e + 1300B c d)m +--R + +--R 2 2 2 +--R ((- 324A c - 648B b c)e + 1620B c d)m + (- 144A c - 288B b c)e +--R + +--R 2 +--R 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R ((- 2A b c - B b )e + (4A c + 8B b c)d e - 10B c d )m +--R + +--R 2 2 2 2 2 4 +--R ((- 34A b c - 17B b )e + (68A c + 136B b c)d e - 170B c d )m +--R + +--R 2 2 2 2 2 3 +--R ((- 214A b c - 107B b )e + (428A c + 856B b c)d e - 1070B c d )m +--R + +--R 2 2 2 2 2 2 +--R ((- 614A b c - 307B b )e + (1228A c + 2456B b c)d e - 3070B c d )m +--R + +--R 2 2 2 2 2 +--R ((- 792A b c - 396B b )e + (1584A c + 3168B b c)d e - 3960B c d )m +--R + +--R 2 2 2 2 2 +--R (- 360A b c - 180B b )e + (720A c + 1440B b c)d e - 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 +--R - A b e + (6A b c + 3B b )d e + (- 6A c - 12B b c)d e +--R + +--R 2 3 +--R 10B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 2 2 2 +--R - 18A b e + (108A b c + 54B b )d e + (- 108A c - 216B b c)d e +--R + +--R 2 3 +--R 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 +--R - 121A b e + (726A b c + 363B b )d e +--R + +--R 2 2 2 3 +--R (- 726A c - 1452B b c)d e + 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 +--R - 372A b e + (2232A b c + 1116B b )d e +--R + +--R 2 2 2 3 +--R (- 2232A c - 4464B b c)d e + 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 +--R - 508A b e + (3048A b c + 1524B b )d e +--R + +--R 2 2 2 3 +--R (- 3048A c - 6096B b c)d e + 5080B c d +--R * +--R m +--R + +--R 2 3 2 2 2 2 +--R - 240A b e + (1440A b c + 720B b )d e + (- 1440A c - 2880B b c)d e +--R + +--R 2 3 +--R 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 3 +--R 2A b d e + (- 6A b c - 3B b )d e + (4A c + 8B b c)d e +--R + +--R 2 4 +--R - 5B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 2 2 2 3 +--R 38A b d e + (- 114A b c - 57B b )d e + (76A c + 152B b c)d e +--R + +--R 2 4 +--R - 95B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 2 +--R 274A b d e + (- 822A b c - 411B b )d e +--R + +--R 2 3 2 4 +--R (548A c + 1096B b c)d e - 685B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 2 +--R 922A b d e + (- 2766A b c - 1383B b )d e +--R + +--R 2 3 2 4 +--R (1844A c + 3688B b c)d e - 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 +--R 1404A b d e + (- 4212A b c - 2106B b )d e +--R + +--R 2 3 2 4 +--R (2808A c + 5616B b c)d e - 3510B c d +--R * +--R m +--R + +--R 2 3 2 2 2 +--R 720A b d e + (- 2160A b c - 1080B b )d e +--R + +--R 2 3 2 4 +--R (1440A c + 2880B b c)d e - 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 2 3 2 2 4 2 5 5 +--R (- A b d e + (2A b c + B b )d e + (- A c - 2B b c)d e + B c d )m +--R + +--R 2 2 3 2 3 2 2 4 +--R - 20A b d e + (40A b c + 20B b )d e + (- 20A c - 40B b c)d e +--R + +--R 2 5 +--R 20B c d +--R * +--R 4 +--R m +--R + +--R 2 2 3 2 3 2 +--R - 155A b d e + (310A b c + 155B b )d e +--R + +--R 2 4 2 5 +--R (- 155A c - 310B b c)d e + 155B c d +--R * +--R 3 +--R m +--R + +--R 2 2 3 2 3 2 +--R - 580A b d e + (1160A b c + 580B b )d e +--R + +--R 2 4 2 5 +--R (- 580A c - 1160B b c)d e + 580B c d +--R * +--R 2 +--R m +--R + +--R 2 2 3 2 3 2 +--R - 1044A b d e + (2088A b c + 1044B b )d e +--R + +--R 2 4 2 5 +--R (- 1044A c - 2088B b c)d e + 1044B c d +--R * +--R m +--R + +--R 2 2 3 2 3 2 +--R - 720A b d e + (1440A b c + 720B b )d e +--R + +--R 2 4 2 5 +--R (- 720A c - 1440B b c)d e + 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 +--R B c e x + ((A c + 2B b c)e + 4B c d e )x +--R + +--R 2 4 2 3 2 2 2 7 +--R ((2A b c + B b )e + (4A c + 8B b c)d e + 6B c d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 6 +--R (A b e + (8A b c + 4B b )d e + (6A c + 12B b c)d e + 4B c d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 5 +--R (4A b d e + (12A b c + 6B b )d e + (4A c + 8B b c)d e + B c d )x +--R + +--R 2 2 2 2 3 2 4 4 +--R (6A b d e + (8A b c + 4B b )d e + (A c + 2B b c)d )x +--R + +--R 2 3 2 4 3 2 4 2 +--R (4A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 1457 +r0:=-1/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^5/e^6+1/6*d*(c*d-b*e)*(B*d*_ + (5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^6/e^6+1/7*(A*e*(6*c^2*d^2-_ + 6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^7/e^6-1/8*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+_ + b^2*e^2))*(d+e*x)^8/e^6-1/9*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^9/e^6+1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 2 10 4 2 9 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 2 10 1 2 9 3 2 2 8 8 +--R ((- A b c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 8 2 4 +--R + +--R 1 2 10 8 4 2 9 6 2 12 2 8 +--R - A b e + (- A b c + - B b )d e + (- A c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 4 2 3 7 +--R - B c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 2 2 9 2 2 8 2 2 4 3 7 +--R - A b d e + (2A b c + B b )d e + (- A c + - B b c)d e +--R 3 3 3 +--R + +--R 1 2 4 6 +--R - B c d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 6 2 2 8 8 4 2 3 7 1 2 2 4 6 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d e )x +--R 5 5 5 5 5 +--R + +--R 2 3 7 1 1 2 4 6 4 1 2 4 6 3 1 2 7 3 +--R (A b d e + (- A b c + - B b )d e )x + - A b d e x + --- A b d e +--R 2 4 3 105 +--R + +--R 1 1 2 8 2 1 2 1 9 1 2 10 +--R (- --- A b c - --- B b )d e + (--- A c + --- B b c)d e - ---- B c d +--R 140 280 630 315 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 10 1 2 2 4 4 2 3 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 2 4 1 2 3 3 2 2 2 8 +--R ((- A b c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 8 2 4 +--R + +--R 1 2 4 8 4 2 3 6 2 12 2 2 4 2 3 7 +--R (- A b e + (- A b c + - B b )d e + (- A c + -- B b c)d e + - B c d e)x +--R 7 7 7 7 7 7 +--R + +--R 2 2 3 2 2 2 2 2 4 3 1 2 4 6 +--R (- A b d e + (2A b c + B b )d e + (- A c + - B b c)d e + - B c d )x +--R 3 3 3 6 +--R + +--R 6 2 2 2 8 4 2 3 1 2 2 4 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 2 3 1 1 2 4 4 1 2 4 3 +--R (A b d e + (- A b c + - B b )d )x + - A b d x +--R 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 78 + +--S 79 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 7 3 1 1 2 8 2 1 2 1 9 +--R - --- A b d e + (--- A b c + --- B b )d e + (- --- A c - --- B b c)d e +--R 105 140 280 630 315 +--R + +--R 1 2 10 +--R ---- B c d +--R 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 79 + +--S 80 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 80 + +)clear all + +--S 81 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R ((2A b c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (6A b c + 3B b )d e + (3A c + 6B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 3 4 +--R (3A b d e + (6A b c + 3B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 3 2 3 2 +--R (3A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 81 + +--S 82 of 1457 +r0:=1/3*A*b^2*d^3*x^3+1/4*b*d^2*(b*B*d+2*A*c*d+3*A*b*e)*x^4+1/5*d*(A*c^2*_ + d^2+3*b^2*e*(B*d+A*e)+2*b*c*d*(B*d+3*A*e))*x^5+1/6*(A*e*(3*c^2*d^2+_ + 6*b*c*d*e+b^2*e^2)+B*d*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^6+1/7*e*_ + (A*c*e*(3*c*d+2*b*e)+B*(3*c^2*d^2+6*b*c*d*e+b^2*e^2))*x^7+_ + 1/8*c*e^2*(3*B*c*d+2*b*B*e+A*c*e)*x^8+1/9*B*c^2*e^3*x^9 +--R +--R +--R (2) +--R 1 2 3 9 1 2 1 3 3 2 2 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 3 3 2 6 2 3 2 2 7 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d e)x +--R 7 7 7 7 7 +--R + +--R 1 2 3 1 2 2 1 2 2 1 2 3 6 +--R (- A b e + (A b c + - B b )d e + (- A c + B b c)d e + - B c d )x +--R 6 2 2 6 +--R + +--R 3 2 2 6 3 2 2 1 2 2 3 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 3 2 2 1 1 2 3 4 1 2 3 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 82 + +--S 83 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 3 9 1 2 1 3 3 2 2 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 3 3 2 6 2 3 2 2 7 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d e)x +--R 7 7 7 7 7 +--R + +--R 1 2 3 1 2 2 1 2 2 1 2 3 6 +--R (- A b e + (A b c + - B b )d e + (- A c + B b c)d e + - B c d )x +--R 6 2 2 6 +--R + +--R 3 2 2 6 3 2 2 1 2 2 3 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 3 2 2 1 1 2 3 4 1 2 3 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 84 + +--S 85 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +)clear all + +--S 86 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 86 + +--S 87 of 1457 +r0:=1/3*A*b^2*d^2*x^3+1/4*b*d*(b*B*d+2*A*c*d+2*A*b*e)*x^4+1/5*(A*c^2*d^2+_ + b^2*e*(2*B*d+A*e)+2*b*c*d*(B*d+2*A*e))*x^5+1/6*(2*A*c*e*(c*d+b*e)+_ + B*(c^2*d^2+4*b*c*d*e+b^2*e^2))*x^6+1/7*c*e*(A*c*e+2*B*(c*d+b*e))*_ + x^7+1/8*B*c^2*e^2*x^8 +--R +--R +--R (2) +--R 1 2 2 8 1 2 2 2 2 2 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e)x +--R 8 7 7 7 +--R + +--R 1 1 2 2 1 2 2 1 2 2 6 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d )x +--R 3 6 3 3 6 +--R + +--R 1 2 2 4 2 2 1 2 2 2 5 +--R (- A b e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 1 2 1 1 2 2 4 1 2 2 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 2 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 87 + +--S 88 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 8 1 2 2 2 2 2 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e)x +--R 8 7 7 7 +--R + +--R 1 1 2 2 1 2 2 1 2 2 6 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d )x +--R 3 6 3 3 6 +--R + +--R 1 2 2 4 2 2 1 2 2 2 5 +--R (- A b e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 1 2 1 1 2 2 4 1 2 2 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 2 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 88 + +--S 89 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 89 + +--S 90 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 90 + +)clear all + +--S 91 of 1457 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 1457 +r0:=1/3*A*b^2*d*x^3+1/4*b*(b*B*d+2*A*c*d+A*b*e)*x^4+1/5*(A*c^2*d+b^2*B*e+_ + 2*b*c*(B*d+A*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 1 2 1 2 2 5 +--R ((- A b c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 +--R + +--R 1 2 1 1 2 4 1 2 3 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 92 + +--S 93 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 1 2 1 2 2 5 +--R ((- A b c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 +--R + +--R 1 2 1 1 2 4 1 2 3 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 93 + +--S 94 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 94 + +--S 95 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 95 + +)clear all + +--S 96 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R (1) B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R Type: Polynomial(Integer) +--E 96 + +--S 97 of 1457 +r0:=1/3*A*b^2*x^3+1/4*b*(b*B+2*A*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6 +--R +--R +--R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 +--R (2) - B c x + (- A c + - B b c)x + (- A b c + - B b )x + - A b x +--R 6 5 5 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 1457 +a0:=integrate(t0,x) +--R +--R +--R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 +--R (3) - B c x + (- A c + - B b c)x + (- A b c + - B b )x + - A b x +--R 6 5 5 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +)clear all + +--S 101 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 1457 +r0:=d*(B*d-A*e)*(c*d-b*e)^2*x/e^5-1/2*(B*d-A*e)*(c*d-b*e)^2*x^2/e^4-_ + 1/3*(A*c*e*(c*d-2*b*e)-B*(c*d-b*e)^2)*x^3/e^3-1/4*c*(B*c*d-2*b*B*e-_ + A*c*e)*x^4/e^2+1/5*B*c^2*x^5/e-d^2*(B*d-A*e)*(c*d-b*e)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 3 2 3 2 2 4 +--R 60A b d e + (- 120A b c - 60B b )d e + (60A c + 120B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((40A b c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 60A b c - 30B b )d e + (30A c + 60B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 60A b d e + (120A b c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 2 3 2 2 4 +--R 60A b d e + (- 120A b c - 60B b )d e + (60A c + 120B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((40A b c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 60A b c - 30B b )d e + (30A c + 60B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 60A b d e + (120A b c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 1457 +r0:=-(c*d-b*e)*(2*B*d*(2*c*d-b*e)-A*e*(3*c*d-b*e))*x/e^5+1/2*(c*d-b*e)*_ + (3*B*c*d-b*B*e-2*A*c*e)*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x))+d*_ + (c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 4 2 2 3 2 3 2 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 12A b e + (- 36A b c - 18B b )d e + (24A c + 48B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 48A b c - 24B b )d e + (36A c + 72B b c)d e +--R + +--R 2 4 +--R - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 12A b d e + (24A b c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 3 2 3 2 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 12A b e + (- 36A b c - 18B b )d e + (24A c + 48B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 48A b c - 24B b )d e + (36A c + 72B b c)d e +--R + +--R 2 4 +--R - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 12A b d e + (24A b c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 1457 +r0:=-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2-6*b*c*d*e+b^2*e^2))*x/e^5-1/2*c*_ + (3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*(d+e*x)^2)-d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*_ + (2*c*d-b*e))/(e^6*(d+e*x))+(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-_ + B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 +--R 6A b e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e +--R + +--R 2 3 2 +--R - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 72A b c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 6A b d e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((24A b c + 12B b )d e + (- 33A c - 66B b c)d e + 63B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 24A b c - 12B b )d e + (6A c + 12B b c)d e +--R + +--R 2 4 +--R 6B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 9A b d e + (- 30A b c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 2 2 3 +--R 6A b e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e +--R + +--R 2 3 2 +--R - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 72A b c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 6A b d e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((24A b c + 12B b )d e + (- 33A c - 66B b c)d e + 63B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 24A b c - 12B b )d e + (6A c + 12B b c)d e +--R + +--R 2 4 +--R 6B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 9A b d e + (- 30A b c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 1457 +r0:=-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*(d+e*x)^3)-1/2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-_ + 2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^2)+(-A*e*(6*c^2*d^2-6*b*c*d*e+_ + b^2*e^2)+B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*(d+e*x))-_ + (2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 24A c - 48B b c)d e + 60B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e )x +--R + +--R 2 2 3 2 3 2 2 4 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e)x +--R + +--R 2 3 2 2 4 2 5 +--R (12A b c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 6A b e + (36A b c + 18B b )d e + (- 18A c - 36B b c)d e +--R + +--R 2 3 2 +--R - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 6A b d e + (54A b c + 27B b )d e + (- 54A c - 108B b c)d e +--R + +--R 2 4 +--R 81B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 2A b d e + (22A b c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 24A c - 48B b c)d e + 60B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e )x +--R + +--R 2 2 3 2 3 2 2 4 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e)x +--R + +--R 2 3 2 2 4 2 5 +--R (12A b c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 6A b e + (36A b c + 18B b )d e + (- 18A c - 36B b c)d e +--R + +--R 2 3 2 +--R - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 6A b d e + (54A b c + 27B b )d e + (- 54A c - 108B b c)d e +--R + +--R 2 4 +--R 81B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 2A b d e + (22A b c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1457 +r0:=-d^3*(B*d-A*e)*(c*d-b*e)^3*(d+e*x)^(1+m)/(e^8*(1+m))+d^2*(c*d-b*e)^2*_ + (B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^8*(2+m))+_ + 3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-_ + 8*b*c*d*e+2*b^2*e^2))*(d+e*x)^(3+m)/(e^8*(3+m))+(B*d*(35*c^3*d^3-_ + 60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-A*e*(20*c^3*d^3-30*b*c^2*_ + d^2*e+12*b^2*c*d*e^2-b^3*e^3))*(d+e*x)^(4+m)/(e^8*(4+m))+(3*A*c*e*_ + (5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*(35*c^3*d^3-45*b*c^2*d^2*e+15*b^2*_ + c*d*e^2-b^3*e^3))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2-6*b*c*d*e+b^2*e^2))*(d+e*x)^(6+m)/(e^8*(6+m))-c^2*_ + (7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*_ + (d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 2 3 7 3 2 3 6 +--R ((A c + 3B b c )e - 7B c d)m + ((29A c + 87B b c )e - 203B c d)m +--R + +--R 3 2 3 5 +--R ((343A c + 1029B b c )e - 2401B c d)m +--R + 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b c)e + (- 100980A c - 302940B b c )d e +--R + +--R 3 2 +--R 353430B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 3 2 +--R (51432A b c + 51432B b c)e + (- 102864A c - 308592B b c )d e +--R + +--R 3 2 +--R 360024B c d +--R * +--R m +--R + +--R 2 2 2 3 2 +--R (20160A b c + 20160B b c)e + (- 40320A c - 120960B b c )d e +--R + +--R 3 2 +--R 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 3 2 2 2 +--R (3A b c + B b )e + (- 15A b c - 15B b c)d e +--R + +--R 3 2 2 3 3 +--R (15A c + 45B b c )d e - 35B c d +--R * +--R 7 +--R m +--R + +--R 2 3 3 2 2 2 +--R (93A b c + 31B b )e + (- 465A b c - 465B b c)d e +--R + +--R 3 2 2 3 3 +--R (465A c + 1395B b c )d e - 1085B c d +--R * +--R 6 +--R m +--R + +--R 2 3 3 2 2 2 +--R (1173A b c + 391B b )e + (- 5865A b c - 5865B b c)d e +--R + +--R 3 2 2 3 3 +--R (5865A c + 17595B b c )d e - 13685B c d +--R * +--R 5 +--R m +--R + +--R 2 3 3 2 2 2 +--R (7743A b c + 2581B b )e + (- 38715A b c - 38715B b c)d e +--R + +--R 3 2 2 3 3 +--R (38715A c + 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3264B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (6180A b c + 6180B b c)d e + (- 1320A c - 3960B b c )d e +--R + +--R 3 5 3 +--R 840B c d e +--R * +--R 3 +--R m +--R + +--R 3 7 2 3 2 6 +--R 7172A b d e + (- 15600A b c - 5200B b )d e +--R + +--R 2 2 3 5 +--R (11880A b c + 11880B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (- 3120A c - 9360B b c )d e + 2520B c d e +--R * +--R 2 +--R m +--R + +--R 3 7 2 3 2 6 +--R 3360A b d e + (- 8064A b c - 2688B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (6720A b c + 6720B b c)d e + (- 1920A c - 5760B b c )d e +--R + +--R 3 5 3 +--R 1680B c d e +--R * +--R m +--R * +--R 3 +--R x +--R + +--R 3 2 6 6 3 2 6 2 3 3 5 5 +--R - 3A b d e m + (- 81A b d e + (36A b c + 12B b )d e )m +--R + +--R 3 2 6 2 3 3 5 +--R - 831A b d e + (792A b c + 264B b )d e +--R + +--R 2 2 4 4 +--R (- 180A b c - 180B b c)d e +--R * +--R 4 +--R m +--R + +--R 3 2 6 2 3 3 5 +--R - 3951A b d e + (6012A b c + 2004B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (- 2880A b c - 2880B b c)d e + (360A c + 1080B 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5 3 +--R (20160A b c + 20160B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (- 5760A c - 17280B b c )d e + 5040B c d e +--R * +--R m +--R * +--R x +--R + +--R 3 4 4 4 3 4 4 2 3 5 3 3 +--R - 6A b d e m + (- 156A b d e + (72A b c + 24B b )d e )m +--R + +--R 3 4 4 2 3 5 3 +--R - 1506A b d e + (1512A b c + 504B b )d e +--R + +--R 2 2 6 2 +--R (- 360A b c - 360B b c)d e +--R * +--R 2 +--R m +--R + +--R 3 4 4 2 3 5 3 +--R - 6396A b d e + (10512A b c + 3504B b )d e +--R + +--R 2 2 6 2 3 2 7 +--R (- 5400A b c - 5400B b c)d e + (720A c + 2160B b c )d e +--R * +--R m +--R + +--R 3 4 4 2 3 5 3 +--R - 10080A b d e + (24192A b c + 8064B b )d e +--R + +--R 2 2 6 2 3 2 7 +--R (- 20160A b c - 20160B b c)d e + (5760A c + 17280B b c )d e +--R + +--R 3 8 +--R - 5040B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 7 3 6 3 5 3 4 3 3 +--R - B c m - 28B c m - 322B c m - 1960B c m - 6769B c m +--R + +--R 3 2 3 3 +--R - 13132B c m - 13068B c m - 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 2 3 7 +--R 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2 2 2 3 2 +--R (- 25227A b c - 25227B b c)e + (50454A c + 151362B b c )d e +--R + +--R 3 2 +--R - 176589B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 3 2 +--R (- 50490A b c - 50490B b c)e + (100980A c + 302940B b c )d e +--R + +--R 3 2 +--R - 353430B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 3 2 +--R (- 51432A b c - 51432B b c)e + (102864A c + 308592B b c )d e +--R + +--R 3 2 +--R - 360024B c d +--R * +--R m +--R + +--R 2 2 2 3 2 +--R (- 20160A b c - 20160B b c)e + (40320A c + 120960B b c )d e +--R + +--R 3 2 +--R - 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 3 2 2 2 +--R (- 3A b c - B b )e + (15A b c + 15B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 15A c - 45B b c )d e + 35B c d +--R * +--R 7 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 93A b c - 31B b )e + (465A b c + 465B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 465A c - 1395B b c )d e + 1085B c d +--R * +--R 6 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 1173A b c - 391B b )e + (5865A b c + 5865B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 5865A c - 17595B b c )d e + 13685B c d +--R * +--R 5 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 7743A b c - 2581B b )e + (38715A b c + 38715B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 38715A c - 116145B b c )d e + 90335B c d +--R * +--R 4 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 28632A b c - 9544B b )e + (143160A b c + 143160B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 143160A c - 429480B b c )d e + 334040B c d +--R * +--R 3 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 58692A b c - 19564B b )e + (293460A b c + 293460B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 293460A c - 880380B b c )d e + 684740B c d +--R * +--R 2 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 60912A b c - 20304B b )e + (304560A b c + 304560B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 304560A c - 913680B b c )d e + 710640B c d +--R * +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 24192A b c - 8064B b )e + (120960A b c + 120960B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 120960A c - 362880B b c )d e + 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - A b e + (12A b c + 4B b )d e + (- 30A b c - 30B b c)d e +--R + +--R 3 2 3 3 4 +--R (20A c + 60B b c )d e - 35B c d +--R * +--R 7 +--R m +--R + +--R 3 4 2 3 3 +--R - 32A b e + (384A b c + 128B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (- 960A b c - 960B b c)d e + (640A c + 1920B b c )d e +--R + +--R 3 4 +--R - 1120B c d +--R * +--R 6 +--R m +--R + +--R 3 4 2 3 3 +--R - 418A b e + (5016A b c + 1672B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (- 12540A b c - 12540B b c)d e + (8360A c + 25080B b c )d e +--R + +--R 3 4 +--R - 14630B c d +--R * +--R 5 +--R m +--R + +--R 3 4 2 3 3 +--R - 2864A b e + (34368A b c + 11456B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (- 85920A b c - 85920B b c)d e + (57280A c + 171840B b c )d e +--R + +--R 3 4 +--R - 100240B c d +--R * +--R 4 +--R m +--R + +--R 3 4 2 3 3 +--R - 10993A b e + (131916A b c + 43972B b )d e +--R + +--R 2 2 2 2 +--R (- 329790A b c - 329790B b c)d e +--R + +--R 3 2 3 3 4 +--R (219860A c + 659580B b c )d e - 384755B c d +--R * +--R 3 +--R m +--R + +--R 3 4 2 3 3 +--R - 23312A b e + (279744A b c + 93248B b )d e +--R + +--R 2 2 2 2 +--R (- 699360A b c - 699360B b c)d e +--R + +--R 3 2 3 3 4 +--R (466240A c + 1398720B b c )d e - 815920B c d +--R * +--R 2 +--R m +--R + +--R 3 4 2 3 3 +--R - 24876A b e + (298512A b c + 99504B b )d e +--R + +--R 2 2 2 2 +--R (- 746280A b c - 746280B b c)d e +--R + +--R 3 2 3 3 4 +--R (497520A c + 1492560B b c )d e - 870660B c d +--R * +--R m +--R + +--R 3 4 2 3 3 +--R - 10080A b e + (120960A b c + 40320B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (- 302400A b c - 302400B b c)d e + (201600A c + 604800B b c )d e +--R + +--R 3 4 +--R - 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 4 2 3 2 3 2 2 3 2 +--R 3A b d e + (- 18A b c - 6B b )d e + (30A b c + 30B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 15A c - 45B b c )d e + 21B c d +--R * +--R 7 +--R m +--R + +--R 3 4 2 3 2 3 +--R 99A b d e + (- 594A b c - 198B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (990A b c + 990B b c)d e + (- 495A c - 1485B b c )d e +--R + +--R 3 5 +--R 693B c d +--R * +--R 6 +--R m +--R + +--R 3 4 2 3 2 3 +--R 1341A b d e + (- 8046A b c - 2682B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (13410A b c + 13410B b c)d e + (- 6705A c - 20115B b c )d e +--R + +--R 3 5 +--R 9387B c d +--R * +--R 5 +--R m +--R + +--R 3 4 2 3 2 3 +--R 9585A b d e + (- 57510A b c - 19170B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (95850A b c + 95850B b c)d e + (- 47925A c - 143775B b c )d e +--R + +--R 3 5 +--R 67095B c d +--R * +--R 4 +--R m +--R + +--R 3 4 2 3 2 3 +--R 38592A b d e + (- 231552A b c - 77184B b )d e +--R + +--R 2 2 3 2 +--R (385920A b c + 385920B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 192960A c - 578880B b c )d e + 270144B c d +--R * +--R 3 +--R m +--R + +--R 3 4 2 3 2 3 +--R 86076A b d e + (- 516456A b c - 172152B b )d e +--R + +--R 2 2 3 2 +--R (860760A b c + 860760B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 430380A c - 1291140B b c )d e + 602532B c d +--R * +--R 2 +--R m +--R + +--R 3 4 2 3 2 3 +--R 96144A b d e + (- 576864A b c - 192288B b )d e +--R + +--R 2 2 3 2 +--R (961440A b c + 961440B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 480720A c - 1442160B b c )d e + 673008B c d +--R * +--R m +--R + +--R 3 4 2 3 2 3 +--R 40320A b d e + (- 241920A b c - 80640B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (403200A b c + 403200B b c)d e + (- 201600A c - 604800B b c )d e +--R + +--R 3 5 +--R 282240B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 2 4 2 3 3 3 2 2 4 2 +--R - 3A b d e + (12A b c + 4B b )d e + (- 15A b c - 15B b c)d e +--R + +--R 3 2 5 3 6 +--R (6A c + 18B b c )d e - 7B c d +--R * +--R 7 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 102A b d e + (408A b c + 136B b )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (- 510A b c - 510B b c)d e + (204A c + 612B b c )d e - 238B c d +--R * +--R 6 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 1434A b d e + (5736A b c + 1912B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 7170A b c - 7170B b c)d e + (2868A c + 8604B b c )d e +--R + +--R 3 6 +--R - 3346B c d +--R * +--R 5 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 10740A b d e + (42960A b c + 14320B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 53700A b c - 53700B b c)d e + (21480A c + 64440B b c )d e +--R + +--R 3 6 +--R - 25060B c d +--R * +--R 4 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 45867A b d e + (183468A b c + 61156B b )d e +--R + +--R 2 2 4 2 +--R (- 229335A b c - 229335B b c)d e +--R + +--R 3 2 5 3 6 +--R (91734A c + 275202B b c )d e - 107023B c d +--R * +--R 3 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 110118A b d e + (440472A b c + 146824B b )d e +--R + +--R 2 2 4 2 +--R (- 550590A b c - 550590B b c)d e +--R + +--R 3 2 5 3 6 +--R (220236A c + 660708B b c )d e - 256942B c d +--R * +--R 2 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 134136A b d e + (536544A b c + 178848B b )d e +--R + +--R 2 2 4 2 +--R (- 670680A b c - 670680B b c)d e +--R + +--R 3 2 5 3 6 +--R (268272A c + 804816B b c )d e - 312984B c d +--R * +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 60480A b d e + (241920A b c + 80640B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 302400A b c - 302400B b c)d e + (120960A c + 362880B b c )d e +--R + +--R 3 6 +--R - 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R A b d e + (- 3A b c - B b )d e + (3A b c + 3B b c)d e +--R + +--R 3 2 6 3 7 +--R (- A c - 3B b c )d e + B c d +--R * +--R 7 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 35A b d e + (- 105A b c - 35B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (105A b c + 105B b c)d e + (- 35A c - 105B b c )d e + 35B c d +--R * +--R 6 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 511A b d e + (- 1533A b c - 511B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (1533A b c + 1533B b c)d e + (- 511A c - 1533B b c )d e +--R + +--R 3 7 +--R 511B c d +--R * +--R 5 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 4025A b d e + (- 12075A b c - 4025B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (12075A b c + 12075B b c)d e + (- 4025A c - 12075B b c )d e +--R + +--R 3 7 +--R 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 18424A b d e + (- 55272A b c - 18424B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (55272A b c + 55272B b c)d e + (- 18424A c - 55272B b c )d e +--R + +--R 3 7 +--R 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 48860A b d e + (- 146580A b c - 48860B b )d e +--R + +--R 2 2 5 2 +--R (146580A b c + 146580B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48860A c - 146580B b c )d e + 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 69264A b d e + (- 207792A b c - 69264B b )d e +--R + +--R 2 2 5 2 +--R (207792A b c + 207792B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 69264A c - 207792B b c )d e + 69264B c d +--R * +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 40320A b d e + (- 120960A b c - 40320B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (120960A b c + 120960B b c)d e + (- 40320A c - 120960B b c )d e +--R + +--R 3 7 +--R 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 2 4 3 3 10 +--R B c e x + ((A c + 3B b c )e + 4B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 9 +--R ((3A b c + 3B b c)e + (4A c + 12B b c )d e + 6B c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 2 +--R (3A b c + B b )e + (12A b c + 12B b c)d e + (6A c + 18B b c )d e +--R + +--R 3 3 +--R 4B c d e +--R * +--R 8 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (12A b c + 4B b )d e + (18A b c + 18B b c)d e +--R + +--R 3 2 3 3 4 +--R (4A c + 12B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 3 3 2 3 2 2 2 2 3 +--R 4A b d e + (18A b c + 6B b )d e + (12A b c + 12B b c)d e +--R + +--R 3 2 4 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 2 2 2 3 3 2 2 4 5 +--R (6A b d e + (12A b c + 4B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 3 2 3 4 4 3 4 3 +--R (4A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 126 + +--S 127 of 1457 +r0:=1/4*A*b^3*d^4*x^4+1/5*b^2*d^3*(b*B*d+3*A*c*d+4*A*b*e)*x^5+1/6*b*d^2*_ + (3*A*c^2*d^2+2*b^2*e*(2*B*d+3*A*e)+3*b*c*d*(B*d+4*A*e))*x^6+1/7*d*_ + (A*c^3*d^3+2*b^3*e^2*(3*B*d+2*A*e)+6*b^2*c*d*e*(2*B*d+3*A*e)+3*b*_ + c^2*d^2*(B*d+4*A*e))*x^7+1/8*(A*e*(4*c^3*d^3+18*b*c^2*d^2*e+12*_ + b^2*c*d*e^2+b^3*e^3)+B*d*(c^3*d^3+12*b*c^2*d^2*e+18*b^2*c*d*e^2+4*_ + b^3*e^3))*x^8+1/9*e*(3*A*c*e*(2*c^2*d^2+4*b*c*d*e+b^2*e^2)+B*_ + (4*c^3*d^3+18*b*c^2*d^2*e+12*b^2*c*d*e^2+b^3*e^3))*x^9+1/10*c*e^2*_ + (A*c*e*(4*c*d+3*b*e)+3*B*(2*c^2*d^2+4*b*c*d*e+b^2*e^2))*x^10+1/11*_ + c^2*e^3*(4*B*c*d+3*b*B*e+A*c*e)*x^11+1/12*B*c^3*e^4*x^12 +--R +--R +--R (2) +--R 1 3 4 12 1 3 3 2 4 4 3 3 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 2 3 2 4 2 3 6 2 3 3 3 2 2 10 +--R ((-- A b c + -- B b c)e + (- A c + - B b c )d e + - B c d e )x +--R 10 10 5 5 5 +--R + +--R 1 2 1 3 4 4 2 4 2 3 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 3 9 3 3 +--R + +--R 2 3 2 2 2 4 3 3 +--R (- A c + 2B b c )d e + - B c d e +--R 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 4 3 2 1 3 3 9 2 9 2 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 8 2 2 4 4 +--R + +--R 1 3 3 2 3 1 3 4 +--R (- A c + - B b c )d e + - B c d +--R 2 2 8 +--R * +--R 8 +--R x +--R + +--R 4 3 3 18 2 6 3 2 2 12 2 12 2 3 +--R - A b d e + (-- A b c + - B b )d e + (-- A b c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 4 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 2 2 2 3 3 1 2 1 2 4 6 +--R (A b d e + (2A b c + - B b )d e + (- A b c + - B b c)d )x +--R 3 2 2 +--R + +--R 4 3 3 3 2 1 3 4 5 1 3 4 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 12 1 3 3 2 4 4 3 3 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 2 3 2 4 2 3 6 2 3 3 3 2 2 10 +--R ((-- A b c + -- B b c)e + (- A c + - B b c )d e + - B c d e )x +--R 10 10 5 5 5 +--R + +--R 1 2 1 3 4 4 2 4 2 3 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 3 9 3 3 +--R + +--R 2 3 2 2 2 4 3 3 +--R (- A c + 2B b c )d e + - B c d e +--R 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 4 3 2 1 3 3 9 2 9 2 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 8 2 2 4 4 +--R + +--R 1 3 3 2 3 1 3 4 +--R (- A c + - B b c )d e + - B c d +--R 2 2 8 +--R * +--R 8 +--R x +--R + +--R 4 3 3 18 2 6 3 2 2 12 2 12 2 3 +--R - A b d e + (-- A b c + - B b )d e + (-- A b c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 4 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 2 2 2 3 3 1 2 1 2 4 6 +--R (A b d e + (2A b c + - B b )d e + (- A b c + - B b c)d )x +--R 3 2 2 +--R + +--R 4 3 3 3 2 1 3 4 5 1 3 4 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +--S 129 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 129 + +--S 130 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +)clear all + +--S 131 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 2 3 3 2 9 +--R B c e x + ((A c + 3B b c )e + 3B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 8 +--R ((3A b c + 3B b c)e + (3A c + 9B b c )d e + 3B c d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A b c + B b )e + (9A b c + 9B b c)d e + (3A c + 9B b c )d e +--R + +--R 3 3 +--R B c d +--R * +--R 7 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R A b e + (9A b c + 3B b )d e + (9A b c + 9B b c)d e +--R + +--R 3 2 3 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 2 2 3 2 2 2 3 5 +--R (3A b d e + (9A b c + 3B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 2 2 3 3 4 3 3 3 +--R (3A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 131 + +--S 132 of 1457 +r0:=1/4*A*b^3*d^3*x^4+1/5*b^2*d^2*(b*B*d+3*A*c*d+3*A*b*e)*x^5+1/2*b*d*_ + (A*c^2*d^2+b^2*e*(B*d+A*e)+b*c*d*(B*d+3*A*e))*x^6+1/7*(A*c^3*d^3+_ + 9*b^2*c*d*e*(B*d+A*e)+b^3*e^2*(3*B*d+A*e)+3*b*c^2*d^2*(B*d+3*A*e))*_ + x^7+1/8*(3*A*c*e*(c^2*d^2+3*b*c*d*e+b^2*e^2)+B*(c^3*d^3+9*b*c^2*d^2*e+_ + 9*b^2*c*d*e^2+b^3*e^3))*x^8+1/3*c*e*(A*c*e*(c*d+b*e)+B*(c^2*d^2+_ + 3*b*c*d*e+b^2*e^2))*x^9+1/10*c^2*e^2*(A*c*e+3*B*(c*d+b*e))*x^10+_ + 1/11*B*c^3*e^3*x^11 +--R +--R +--R (2) +--R 1 3 3 11 1 3 3 2 3 3 3 2 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 2 1 2 3 1 3 2 2 1 3 2 9 +--R ((- A b c + - B b c)e + (- A c + B b c )d e + - B c d e)x +--R 3 3 3 3 +--R + +--R 3 2 1 3 3 9 2 9 2 2 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 8 8 8 8 +--R + +--R 3 3 9 2 2 1 3 3 +--R (- A c + - B b c )d e + - B c d +--R 8 8 8 +--R * +--R 8 +--R x +--R + +--R 1 3 3 9 2 3 3 2 9 2 9 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 3 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 2 3 2 1 3 2 1 2 1 2 3 6 +--R (- A b d e + (- A b c + - B b )d e + (- A b c + - B b c)d )x +--R 2 2 2 2 2 +--R + +--R 3 3 2 3 2 1 3 3 5 1 3 3 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 3 11 1 3 3 2 3 3 3 2 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 2 1 2 3 1 3 2 2 1 3 2 9 +--R ((- A b c + - B b c)e + (- A c + B b c )d e + - B c d e)x +--R 3 3 3 3 +--R + +--R 3 2 1 3 3 9 2 9 2 2 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 8 8 8 8 +--R + +--R 3 3 9 2 2 1 3 3 +--R (- A c + - B b c )d e + - B c d +--R 8 8 8 +--R * +--R 8 +--R x +--R + +--R 1 3 3 9 2 3 3 2 9 2 9 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 3 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 2 3 2 1 3 2 1 2 1 2 3 6 +--R (- A b d e + (- A b c + - B b )d e + (- A b c + - B b c)d )x +--R 2 2 2 2 2 +--R + +--R 3 3 2 3 2 1 3 3 5 1 3 3 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +--S 134 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +)clear all + +--S 136 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 2 3 8 +--R B c e x + ((A c + 3B b c )e + 2B c d e)x +--R + +--R 2 2 2 3 2 3 2 7 +--R ((3A b c + 3B b c)e + (2A c + 6B b c )d e + B c d )x +--R + +--R 2 3 2 2 2 3 2 2 6 +--R ((3A b c + B b )e + (6A b c + 6B b c)d e + (A c + 3B b c )d )x +--R + +--R 3 2 2 3 2 2 2 5 +--R (A b e + (6A b c + 2B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 2 3 2 4 3 2 3 +--R (2A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 1457 +r0:=1/4*A*b^3*d^2*x^4+1/5*b^2*d*(b*B*d+3*A*c*d+2*A*b*e)*x^5+1/6*b*_ + (3*A*c^2*d^2+b^2*e*(2*B*d+A*e)+3*b*c*d*(B*d+2*A*e))*x^6+1/7*_ + (A*c^3*d^2+b^3*B*e^2+3*b^2*c*e*(2*B*d+A*e)+3*b*c^2*d*(B*d+2*A*e))*x^7+_ + 1/8*c*(A*c*e*(2*c*d+3*b*e)+B*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^8+_ + 1/9*c^2*e*(2*B*c*d+3*b*B*e+A*c*e)*x^9+1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R ((- A b c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 4 4 8 +--R + +--R 3 2 1 3 2 6 2 6 2 1 3 3 2 2 7 +--R ((- A b c + - B b )e + (- A b c + - B b c)d e + (- A c + - B b c )d )x +--R 7 7 7 7 7 7 +--R + +--R 1 3 2 2 1 3 1 2 1 2 2 6 +--R (- A b e + (A b c + - B b )d e + (- A b c + - B b c)d )x +--R 6 3 2 2 +--R + +--R 2 3 3 2 1 3 2 5 1 3 2 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R ((- A b c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 4 4 8 +--R + +--R 3 2 1 3 2 6 2 6 2 1 3 3 2 2 7 +--R ((- A b c + - B b )e + (- A b c + - B b c)d e + (- A c + - B b c )d )x +--R 7 7 7 7 7 7 +--R + +--R 1 3 2 2 1 3 1 2 1 2 2 6 +--R (- A b e + (A b c + - B b )d e + (- A b c + - B b c)d )x +--R 6 3 2 2 +--R + +--R 2 3 3 2 1 3 2 5 1 3 2 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 139 + +--S 140 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +)clear all + +--S 141 of 1457 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 2 3 7 +--R B c e x + ((A c + 3B b c )e + B c d)x +--R + +--R 2 2 3 2 6 +--R ((3A b c + 3B b c)e + (A c + 3B b c )d)x +--R + +--R 2 3 2 2 5 3 2 3 4 +--R ((3A b c + B b )e + (3A b c + 3B b c)d)x + (A b e + (3A b c + B b )d)x +--R + +--R 3 3 +--R A b d x +--R Type: Polynomial(Integer) +--E 141 + +--S 142 of 1457 +r0:=1/4*A*b^3*d*x^4+1/5*b^2*(b*B*d+3*A*c*d+A*b*e)*x^5+1/6*b*(3*A*c^2*d+_ + b^2*B*e+3*b*c*(B*d+A*e))*x^6+1/7*c*(A*c^2*d+3*b^2*B*e+3*b*c*(B*d+_ + A*e))*x^7+1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 2 3 2 1 3 3 2 7 +--R ((- A b c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 +--R + +--R 1 2 1 3 1 2 1 2 6 +--R ((- A b c + - B b )e + (- A b c + - B b c)d)x +--R 2 6 2 2 +--R + +--R 1 3 3 2 1 3 5 1 3 4 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 142 + +--S 143 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 2 3 2 1 3 3 2 7 +--R ((- A b c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 +--R + +--R 1 2 1 3 1 2 1 2 6 +--R ((- A b c + - B b )e + (- A b c + - B b c)d)x +--R 2 6 2 2 +--R + +--R 1 3 3 2 1 3 5 1 3 4 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 143 + +--S 144 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 144 + +--S 145 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 145 + +)clear all + +--S 146 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R Type: Polynomial(Integer) +--E 146 + +--S 147 of 1457 +r0:=1/4*A*b^3*x^4+1/5*b^2*(b*B+3*A*c)*x^5+1/2*b*c*(b*B+A*c)*x^6+_ + 1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8 +--R +--R +--R (2) +--R 1 3 8 1 3 3 2 7 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + (- A b c + - B b c)x +--R 8 7 7 2 2 +--R + +--R 3 2 1 3 5 1 3 4 +--R (- A b c + - B b )x + - A b x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 147 + +--S 148 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 8 1 3 3 2 7 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + (- A b c + - B b c)x +--R 8 7 7 2 2 +--R + +--R 3 2 1 3 5 1 3 4 +--R (- A b c + - B b )x + - A b x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 148 + +--S 149 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 149 + +--S 150 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 150 + +)clear all + +--S 151 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 1457 +r0:=d^2*(B*d-A*e)*(c*d-b*e)^3*x/e^7-1/2*d*(B*d-A*e)*(c*d-b*e)^3*x^2/e^6+_ + 1/3*(B*d-A*e)*(c*d-b*e)^3*x^3/e^5-1/4*(B*(c*d-b*e)^3-A*c*e*(c^2*d^2-_ + 3*b*c*d*e+3*b^2*e^2))*x^4/e^4-1/5*c*(A*c*e*(c*d-3*b*e)-B*(c^2*d^2-_ + 3*b*c*d*e+3*b^2*e^2))*x^5/e^3-1/6*c^2*(B*c*d-3*b*B*e-A*c*e)*x^6/e^2+_ + 1/7*B*c^3*x^7/e-d^3*(B*d-A*e)*(c*d-b*e)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 3 4 2 3 4 3 +--R - 420A b d e + (1260A b c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 1260A b c - 1260B b c)d e + (420A c + 1260B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((252A b c + 252B b c)e + (- 84A c - 252B b c )d e + 84B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (315A b c + 105B b )e + (- 315A b c - 315B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (105A c + 315B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 140A b e + (- 420A b c - 140B b )d e + (420A b c + 420B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 140A c - 420B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 210A b d e + (630A b c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 630A b c - 630B b c)d e + (210A c + 630B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 420A b d e + (- 1260A b c - 420B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1260A b c + 1260B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 4 2 3 4 3 +--R - 420A b d e + (1260A b c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 1260A b c - 1260B b c)d e + (420A c + 1260B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((252A b c + 252B b c)e + (- 84A c - 252B b c )d e + 84B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (315A b c + 105B b )e + (- 315A b c - 315B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (105A c + 315B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 140A b e + (- 420A b c - 140B b )d e + (420A b c + 420B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 140A c - 420B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 210A b d e + (630A b c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 630A b c - 630B b c)d e + (210A c + 630B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 420A b d e + (- 1260A b c - 420B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1260A b c + 1260B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 1457 +r0:=d*(c*d-b*e)^2*(A*e*(5*c*d-2*b*e)-3*B*d*(2*c*d-b*e))*x/e^7+_ + 1/2*(c*d-b*e)^2*(B*d*(5*c*d-2*b*e)-A*e*(4*c*d-b*e))*x^2/e^6-_ + 1/3*(c*d-b*e)^2*(4*B*c*d-b*B*e-3*A*c*e)*x^3/e^5-1/4*c*(A*c*e*_ + (2*c*d-3*b*e)-3*B*(c*d-b*e)^2)*x^4/e^4-1/5*c^2*(2*B*c*d-3*b*B*e-_ + A*c*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*_ + (d+e*x))+d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 5 2 3 3 4 +--R 180A b d e + (- 720A b c - 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (900A b c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 180A b d e + (- 720A b c - 240B b )d e + (900A b c + 900B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 360A c - 1080B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((45A b c + 45B b c)e + (- 18A c - 54B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (60A b c + 20B b )e + (- 75A b c - 75B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (30A c + 90B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 30A b e + (- 120A b c - 40B b )d e + (150A b c + 150B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 60A c - 180B b c )d e + 70B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 90A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 450A b c - 450B b c)d e + (180A c + 540B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (540A b c + 180B b )d e +--R + +--R 2 2 4 3 3 2 5 2 3 6 +--R (- 720A b c - 720B b c)d e + (300A c + 900B b c )d e - 360B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 60A b d e + (- 180A b c - 60B b )d e + (180A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 60A c - 180B b c )d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 5 2 3 3 4 +--R 180A b d e + (- 720A b c - 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (900A b c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 180A b d e + (- 720A b c - 240B b )d e + (900A b c + 900B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 360A c - 1080B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((45A b c + 45B b c)e + (- 18A c - 54B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (60A b c + 20B b )e + (- 75A b c - 75B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (30A c + 90B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 30A b e + (- 120A b c - 40B b )d e + (150A b c + 150B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 60A c - 180B b c )d e + 70B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 90A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 450A b c - 450B b c)d e + (180A c + 540B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (540A b c + 180B b )d e +--R + +--R 2 2 4 3 3 2 5 2 3 6 +--R (- 720A b c - 720B b c)d e + (300A c + 900B b c )d e - 360B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 60A b d e + (- 180A b c - 60B b )d e + (180A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 60A c - 180B b c )d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 1457 +r0:=-(c*d-b*e)*(A*e*(10*c^2*d^2-8*b*c*d*e+b^2*e^2)-3*B*d*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2))*x/e^7+1/2*(c*d-b*e)*(3*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*x^2/e^6+c*(c*d-b*e)*(2*B*c*d-b*B*e-_ + A*c*e)*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*x^4/e^4+1/5*B*c^3*_ + x^5/e^3+1/2*d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*(d+e*x)^2)-d^2*_ + (c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))/(e^8*(d+e*x))+_ + 3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-_ + 8*b*c*d*e+2*b^2*e^2))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 6 2 3 2 5 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 5 2 +--R - 420B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (720A b c + 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1200A b c - 1200B b c)d e + (600A c + 1800B b c )d e +--R + +--R 3 6 +--R - 840B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((20A b c + 20B b c)e + (- 10A c - 30B b c )d e + 14B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (30A b c + 10B b )e + (- 50A b c - 50B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (25A c + 75B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 20A b e + (- 120A b c - 40B b )d e + (200A b c + 200B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 100A c - 300B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 40A b d e + (- 330A b c - 110B b )d e + (630A b c + 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 340A c - 1020B b c )d e + 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R - 40A b d e + (60A b c + 20B b )d e + (60A b c + 60B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 80A c - 240B b c )d e + 160B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 50A b d e + (210A b c + 70B b )d e + (- 270A b c - 270B b c)d e +--R + +--R 3 2 6 3 7 +--R (110A c + 330B b c )d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 3 2 5 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 5 2 +--R - 420B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (720A b c + 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1200A b c - 1200B b c)d e + (600A c + 1800B b c )d e +--R + +--R 3 6 +--R - 840B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((20A b c + 20B b c)e + (- 10A c - 30B b c )d e + 14B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (30A b c + 10B b )e + (- 50A b c - 50B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (25A c + 75B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 20A b e + (- 120A b c - 40B b )d e + (200A b c + 200B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 100A c - 300B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 40A b d e + (- 330A b c - 110B b )d e + (630A b c + 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 340A c - 1020B b c )d e + 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R - 40A b d e + (60A b c + 20B b )d e + (60A b c + 60B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 80A c - 240B b c )d e + 160B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 50A b d e + (210A b c + 70B b )d e + (- 270A b c - 270B b c)d e +--R + +--R 3 2 6 3 7 +--R (110A c + 330B b c )d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1457 +r0:=(A*c*e*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2)-B*(20*c^3*d^3-30*b*c^2*d^2*e+_ + 12*b^2*c*d*e^2-b^3*e^3))*x/e^7-1/2*c*(A*c*e*(4*c*d-3*b*e)-_ + B*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*x^2/e^6-1/3*c^2*(4*B*c*d-_ + 3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*d^3*(B*d-A*e)*_ + (c*d-b*e)^3/(e^8*(d+e*x)^3)-1/2*d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-_ + 3*A*e*(2*c*d-b*e))/(e^8*(d+e*x)^2)-3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-8*b*c*d*e+2*b^2*e^2))/(e^8*_ + (d+e*x))+(B*d*(35*c^3*d^3-60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-_ + A*e*(20*c^3*d^3-30*b*c^2*d^2*e+12*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 3 6 2 2 2 5 +--R 12A b e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 12A b d e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 240A c - 720B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((18A b c + 18B b c)e + (- 12A c - 36B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (36A b c + 12B b )e + (- 90A b c - 90B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (60A c + 180B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 2 5 +--R (108A b c + 36B b )d e + (- 378A b c - 378B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (292A c + 876B b c )d e - 556B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 36A b d e + (- 108A b c - 36B b )d e + (- 54A b c - 54B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (156A c + 468B b c )d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R 54A b d e + (- 324A b c - 108B b )d e + (486A b c + 486B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 204A c - 612B b c )d e + 222B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 22A b d e + (- 156A b c - 52B b )d e + (282A b c + 282B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 148A c - 444B b c )d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 2 3 6 2 2 2 5 +--R 12A b e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 12A b d e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 240A c - 720B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((18A b c + 18B b c)e + (- 12A c - 36B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (36A b c + 12B b )e + (- 90A b c - 90B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (60A c + 180B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 2 5 +--R (108A b c + 36B b )d e + (- 378A b c - 378B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (292A c + 876B b c )d e - 556B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 36A b d e + (- 108A b c - 36B b )d e + (- 54A b c - 54B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (156A c + 468B b c )d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R 54A b d e + (- 324A b c - 108B b )d e + (486A b c + 486B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 204A c - 612B b c )d e + 222B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 22A b d e + (- 156A b c - 52B b )d e + (282A b c + 282B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 148A c - 444B b c )d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1457 +r0:=e*(A*c*e*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)+B*(4*c^3*d^3-6*b*c^2*d^2*e+_ + 4*b^2*c*d*e^2-b^3*e^3))*x/c^4+1/2*e^2*(A*c*e*(4*c*d-b*e)+B*_ + (6*c^2*d^2-4*b*c*d*e+b^2*e^2))*x^2/c^3+1/3*e^3*(4*B*c*d-b*B*e+_ + A*c*e)*x^3/c^2+1/4*B*e^4*x^4/c+A*d^4*log(x)/b+(b*B-A*c)*_ + (c*d-b*e)^4*log(b+c*x)/(b*c^5) +--R +--R +--R (2) +--R 4 5 4 3 2 4 3 +--R (- 12A b c + 12B b )e + (48A b c - 48B b c)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A b c + 72B b c )d e + (48A b c - 48B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 12B b c )d +--R * +--R log(c x + b) +--R + +--R 5 4 4 4 4 4 2 3 4 4 3 3 +--R 12A c d log(x) + 3B b c e x + ((4A b c - 4B b c )e + 16B b c d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 6A b c + 6B b c )e + (24A b c - 24B b c )d e + 36B b c d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A b c - 12B b c)e + (- 48A b c + 48B b c )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A b c - 72B b c )d e + 48B b c d e +--R * +--R x +--R / +--R 5 +--R 12b c +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 4 3 2 4 3 +--R (- 12A b c + 12B b )e + (48A b c - 48B b c)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A b c + 72B b c )d e + (48A b c - 48B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 12B b c )d +--R * +--R log(c x + b) +--R + +--R 5 4 4 4 4 4 2 3 4 4 3 3 +--R 12A c d log(x) + 3B b c e x + ((4A b c - 4B b c )e + 16B b c d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 6A b c + 6B b c )e + (24A b c - 24B b c )d e + 36B b c d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A b c - 12B b c)e + (- 48A b c + 48B b c )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A b c - 72B b c )d e + 48B b c d e +--R * +--R x +--R / +--R 5 +--R 12b c +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1457 +r0:=e*(A*c*e*(3*c*d-b*e)+B*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*x/c^3+_ + 1/2*e^2*(3*B*c*d-b*B*e+A*c*e)*x^2/c^2+1/3*B*e^3*x^3/c+A*d^3*_ + log(x)/b+(b*B-A*c)*(c*d-b*e)^3*log(b+c*x)/(b*c^4) +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (6A b c - 6B b )e + (- 18A b c + 18B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A b c - 18B b c )d e + (- 6A c + 6B b c )d +--R * +--R log(c x + b) +--R + +--R 4 3 3 3 3 3 2 2 3 3 2 2 +--R 6A c d log(x) + 2B b c e x + ((3A b c - 3B b c )e + 9B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 6A b c + 6B b c)e + (18A b c - 18B b c )d e + 18B b c d e)x +--R / +--R 4 +--R 6b c +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 2 3 2 +--R (6A b c - 6B b )e + (- 18A b c + 18B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A b c - 18B b c )d e + (- 6A c + 6B b c )d +--R * +--R log(c x + b) +--R + +--R 4 3 3 3 3 3 2 2 3 3 2 2 +--R 6A c d log(x) + 2B b c e x + ((3A b c - 3B b c )e + 9B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 6A b c + 6B b c)e + (18A b c - 18B b c )d e + 18B b c d e)x +--R / +--R 4 +--R 6b c +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1457 +r0:=e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+A*d^2*log(x)/b+_ + (b*B-A*c)*(c*d-b*e)^2*log(b+c*x)/(b*c^3) +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 2B b )e + (4A b c - 4B b c)d e + (- 2A c + 2B b c )d ) +--R * +--R log(c x + b) +--R + +--R 3 2 2 2 2 2 2 2 2 +--R 2A c d log(x) + B b c e x + ((2A b c - 2B b c)e + 4B b c d e)x +--R / +--R 3 +--R 2b c +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 2B b )e + (4A b c - 4B b c)d e + (- 2A c + 2B b c )d ) +--R * +--R log(c x + b) +--R + +--R 3 2 2 2 2 2 2 2 2 +--R 2A c d log(x) + B b c e x + ((2A b c - 2B b c)e + 4B b c d e)x +--R / +--R 3 +--R 2b c +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1457 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1457 +r0:=B*e*x/c+A*d*log(x)/b+(b*B-A*c)*(c*d-b*e)*log(b+c*x)/(b*c^2) +--R +--R +--R (2) +--R 2 2 2 +--R ((A b c - B b )e + (- A c + B b c)d)log(c x + b) + A c d log(x) + B b c e x +--R ---------------------------------------------------------------------------- +--R 2 +--R b c +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R ((A b c - B b )e + (- A c + B b c)d)log(c x + b) + A c d log(x) + B b c e x +--R ---------------------------------------------------------------------------- +--R 2 +--R b c +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1457 +t0:=(A+B*x)/(b*x+c*x^2) +--R +--R +--R B x + A +--R (1) ---------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1457 +r0:=A*log(x)/b+(b*B-A*c)*log(b+c*x)/(b*c) +--R +--R +--R (- A c + B b)log(c x + b) + A c log(x) +--R (2) -------------------------------------- +--R b c +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (- A c + B b)log(c x + b) + A c log(x) +--R (3) -------------------------------------- +--R b c +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1457 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R 3 2 +--R c e x + (b e + c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1457 +r0:=A*log(x)/(b*d)+(b*B-A*c)*log(b+c*x)/(b*(c*d-b*e))-_ + (B*d-A*e)*log(d+e*x)/(d*(c*d-b*e)) +--R +--R +--R (2) +--R (- A b e + B b d)log(e x + d) + (A c - B b)d log(c x + b) +--R + +--R (A b e - A c d)log(x) +--R / +--R 2 2 +--R b d e - b c d +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (- A b e + B b d)log(e x + d) + (A c - B b)d log(c x + b) +--R + +--R (A b e - A c d)log(x) +--R / +--R 2 2 +--R b d e - b c d +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------ +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1457 +r0:=(B*d-A*e)/(d*(c*d-b*e)*(d+e*x))+A*log(x)/(b*d^2)+c*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^2)-(B*c*d^2-A*e*(2*c*d-b*e))*log(d+e*x)/_ + (d^2*(c*d-b*e)^2) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R (- A b e + 2A b c d e - B b c d e)x - A b d e + 2A b c d e +--R + +--R 3 +--R - B b c d +--R * +--R log(e x + d) +--R + +--R 2 2 2 3 +--R ((- A c + B b c)d e x + (- A c + B b c)d )log(c x + b) +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((A b e - 2A b c d e + A c d e)x + A b d e - 2A b c d e + A c d ) +--R * +--R log(x) +--R + +--R 2 2 2 2 3 +--R A b d e + (- A b c - B b )d e + B b c d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 +--R (- A b e + 2A b c d e - B b c d e)x - A b d e + 2A b c d e +--R + +--R 3 +--R - B b c d +--R * +--R log(e x + d) +--R + +--R 2 2 2 3 +--R ((- A c + B b c)d e x + (- A c + B b c)d )log(c x + b) +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((A b e - 2A b c d e + A c d e)x + A b d e - 2A b c d e + A c d ) +--R * +--R log(x) +--R + +--R 2 2 2 2 3 +--R A b d e + (- A b c - B b )d e + B b c d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1457 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1457 +r0:=1/2*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^2)+(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x))+A*log(x)/(b*d^3)+c^2*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^3)-(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+_ + b^2*e^2))*log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (- 2A b e + 6A b c d e - 6A b c d e + 2B b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 2 4 3 2 3 +--R (- 4A b d e + 12A b c d e - 12A b c d e + 4B b c d e)x - 2A b d e +--R + +--R 2 3 2 2 4 2 5 +--R 6A b c d e - 6A b c d e + 2B b c d +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 3 2 4 +--R (2A c - 2B b c )d e x + (4A c - 4B b c )d e x +--R + +--R 3 2 5 +--R (2A c - 2B b c )d +--R * +--R log(c x + b) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2A b e - 6A b c d e + 6A b c d e - 2A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (4A b d e - 12A b c d e + 12A b c d e - 4A c d e)x + 2A b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 6A b c d e + 6A b c d e - 2A c d +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 2 3 2 2 4 +--R (2A b d e - 6A b c d e + (4A b c + 2B b c)d e - 2B b c d e)x +--R + +--R 3 2 3 2 3 3 2 2 2 4 2 5 +--R 3A b d e + (- 8A b c - B b )d e + (5A b c + 4B b c)d e - 3B b c d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e)x + 2b d e - 6b c d e +--R + +--R 2 2 7 3 8 +--R 6b c d e - 2b c d +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (- 2A b e + 6A b c d e - 6A b c d e + 2B b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 2 4 3 2 3 +--R (- 4A b d e + 12A b c d e - 12A b c d e + 4B b c d e)x - 2A b d e +--R + +--R 2 3 2 2 4 2 5 +--R 6A b c d e - 6A b c d e + 2B b c d +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 3 2 4 +--R (2A c - 2B b c )d e x + (4A c - 4B b c )d e x +--R + +--R 3 2 5 +--R (2A c - 2B b c )d +--R * +--R log(c x + b) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2A b e - 6A b c d e + 6A b c d e - 2A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (4A b d e - 12A b c d e + 12A b c d e - 4A c d e)x + 2A b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 6A b c d e + 6A b c d e - 2A c d +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 2 3 2 2 4 +--R (2A b d e - 6A b c d e + (4A b c + 2B b c)d e - 2B b c d e)x +--R + +--R 3 2 3 2 3 3 2 2 2 4 2 5 +--R 3A b d e + (- 8A b c - B b )d e + (5A b c + 4B b c)d e - 3B b c d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e)x + 2b d e - 6b c d e +--R + +--R 2 2 7 3 8 +--R 6b c d e - 2b c d +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1457 +t0:=(A+B*x)/((d+e*x)^4*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 6 4 3 5 3 2 2 4 +--R c e x + (b e + 4c d e )x + (4b d e + 6c d e )x +--R + +--R 2 2 3 3 3 4 2 4 +--R (6b d e + 4c d e)x + (4b d e + c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1457 +r0:=1/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^3)+1/2*(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x)^2)+(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+_ + b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x))+A*log(x)/(b*d^4)+c^3*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^4)-(B*c^3*d^4-A*e*(4*c^3*d^3-_ + 6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 6A b e + 24A b c d e - 36A b c d e + 24A b c d e +--R + +--R 3 4 3 +--R - 6B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R - 18A b d e + 72A b c d e - 108A b c d e + 72A b c d e +--R + +--R 3 5 2 +--R - 18B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R - 18A b d e + 72A b c d e - 108A b c d e + 72A b c d e +--R + +--R 3 6 +--R - 18B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 3 7 +--R - 6A b d e + 24A b c d e - 36A b c d e + 24A b c d e - 6B b c d +--R * +--R log(e x + d) +--R + +--R 4 3 4 3 3 4 3 5 2 2 +--R (- 6A c + 6B b c )d e x + (- 18A c + 18B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (- 18A c + 18B b c )d e x + (- 6A c + 6B b c )d +--R * +--R log(c x + b) +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (6A b e - 24A b c d e + 36A b c d e - 24A b c d e + 6A c d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R 18A b d e - 72A b c d e + 108A b c d e - 72A b c d e +--R + +--R 4 5 2 +--R 18A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R 18A b d e - 72A b c d e + 108A b c d e - 72A b c d e +--R + +--R 4 6 +--R 18A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 6A b d e - 24A b c d e + 36A b c d e - 24A b c d e + 6A c d +--R * +--R log(x) +--R + +--R 4 6 3 2 5 2 2 3 4 3 2 2 4 3 +--R 6A b d e - 24A b c d e + 36A b c d e + (- 18A b c - 6B b c )d e +--R + +--R 3 5 2 +--R 6B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 15A b d e - 60A b c d e + (87A b c + 3B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 42A b c - 18B b c )d e + 15B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 2 2 3 5 2 +--R 11A b d e + (- 42A b c - 2B b )d e + (57A b c + 9B b c)d e +--R + +--R 3 2 2 6 3 7 +--R (- 26A b c - 18B b c )d e + 11B b c d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (6b d e - 24b c d e + 36b c d e - 24b c d e + 6b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 4 9 2 2 +--R (18b d e - 72b c d e + 108b c d e - 72b c d e + 18b c d e )x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 4 10 +--R (18b d e - 72b c d e + 108b c d e - 72b c d e + 18b c d e)x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 6b d e - 24b c d e + 36b c d e - 24b c d e + 6b c d +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1457 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 1457 +--m0:=a0-r0 +--E 214 + +--S 215 of 1457 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 1457 +r0:=-A*d^4/(b^2*x)+e^3*(4*B*c*d-2*b*B*e+A*c*e)*x/c^3+1/2*B*e^4*x^2/c^2+_ + (b*B-A*c)*(c*d-b*e)^4/(b^2*c^4*(b+c*x))+d^3*(b*B*d-2*A*c*d+_ + 4*A*b*e)*log(x)/b^3+(c*d-b*e)^3*(2*A*c^2*d-3*b^2*B*e-b*c*(B*d-_ + 2*A*e))*log(b+c*x)/(b^3*c^4) +--R +--R +--R (2) +--R 4 2 5 4 3 3 4 2 3 3 3 2 2 +--R (- 4A b c + 6B b c)e + (8A b c - 16B b c )d e + 12B b c d e +--R + +--R 5 3 6 5 4 +--R - 8A b c d e + (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 4 2 2 2 +--R (- 4A b c + 6B b )e + (8A b c - 16B b c)d e + 12B b c d e +--R + +--R 2 4 3 5 2 4 4 +--R - 8A b c d e + (4A b c - 2B b c )d +--R * +--R x +--R * +--R log(c x + b) +--R + +--R 5 3 6 5 4 2 +--R (8A b c d e + (- 4A c + 2B b c )d )x +--R + +--R 2 4 3 5 2 4 4 +--R (8A b c d e + (- 4A b c + 2B b c )d )x +--R * +--R log(x) +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 3 3 +--R B b c e x + ((2A b c - 3B b c )e + 8B b c d e )x +--R + +--R 4 2 5 4 4 2 3 2 +--R ((2A b c - 4B b c)e + 8B b c d e )x +--R + +--R 5 6 4 4 2 5 3 +--R (- 2A b c + 2B b )e + (8A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 12A b c + 12B b c )d e + (8A b c - 8B b c )d e +--R + +--R 5 2 4 4 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 4 4 +--R - 2A b c d +--R / +--R 3 5 2 4 4 +--R 2b c x + 2b c x +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 5 4 3 3 4 2 3 3 3 2 2 +--R (- 4A b c + 6B b c)e + (8A b c - 16B b c )d e + 12B b c d e +--R + +--R 5 3 6 5 4 +--R - 8A b c d e + (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 4 2 2 2 +--R (- 4A b c + 6B b )e + (8A b c - 16B b c)d e + 12B b c d e +--R + +--R 2 4 3 5 2 4 4 +--R - 8A b c d e + (4A b c - 2B b c )d +--R * +--R x +--R * +--R log(c x + b) +--R + +--R 5 3 6 5 4 2 +--R (8A b c d e + (- 4A c + 2B b c )d )x +--R + +--R 2 4 3 5 2 4 4 +--R (8A b c d e + (- 4A b c + 2B b c )d )x +--R * +--R log(x) +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 3 3 +--R B b c e x + ((2A b c - 3B b c )e + 8B b c d e )x +--R + +--R 4 2 5 4 4 2 3 2 +--R ((2A b c - 4B b c)e + 8B b c d e )x +--R + +--R 5 6 4 4 2 5 3 +--R (- 2A b c + 2B b )e + (8A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 12A b c + 12B b c )d e + (8A b c - 8B b c )d e +--R + +--R 5 2 4 4 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 4 4 +--R - 2A b c d +--R / +--R 3 5 2 4 4 +--R 2b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 1457 +r0:=-A*d^3/(b^2*x)+B*e^3*x/c^2+(b*B-A*c)*(c*d-b*e)^3/(b^2*c^3*(b+c*x))+_ + d^2*(b*B*d-2*A*c*d+3*A*b*e)*log(x)/b^3-(c*d-b*e)^2*(b*B*c*d-_ + 2*A*c^2*d+2*b^2*B*e-A*b*c*e)*log(b+c*x)/(b^3*c^3) +--R +--R +--R (2) +--R 3 2 4 3 3 2 2 4 2 +--R (A b c - 2B b c)e + 3B b c d e - 3A b c d e +--R + +--R 5 4 3 +--R (2A c - B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 2 3 2 4 2 3 3 +--R ((A b c - 2B b )e + 3B b c d e - 3A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 4 2 5 4 3 2 +--R (3A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (3A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 3 3 4 3 2 +--R B b c e x + B b c e x +--R + +--R 4 5 3 3 2 4 2 2 3 3 2 2 +--R (A b c - B b )e + (- 3A b c + 3B b c)d e + (3A b c - 3B b c )d e +--R + +--R 4 2 3 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - A b c d +--R / +--R 3 4 2 4 3 +--R b c x + b c x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 3 2 2 4 2 +--R (A b c - 2B b c)e + 3B b c d e - 3A b c d e +--R + +--R 5 4 3 +--R (2A c - B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 2 3 2 4 2 3 3 +--R ((A b c - 2B b )e + 3B b c d e - 3A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 4 2 5 4 3 2 +--R (3A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (3A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 3 3 4 3 2 +--R B b c e x + B b c e x +--R + +--R 4 5 3 3 2 4 2 2 3 3 2 2 +--R (A b c - B b )e + (- 3A b c + 3B b c)d e + (3A b c - 3B b c )d e +--R + +--R 4 2 3 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - A b c d +--R / +--R 3 4 2 4 3 +--R b c x + b c x +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 1457 +r0:=-A*d^2/(b^2*x)+(b*B-A*c)*(c*d-b*e)^2/(b^2*c^2*(b+c*x))+d*_ + (b*B*d-2*A*c*d+2*A*b*e)*log(x)/b^3-(c*d-b*e)*(b*B*c*d-2*A*c^2*d+_ + b^2*B*e)*log(b+c*x)/(b^3*c^2) +--R +--R +--R (2) +--R 3 2 3 4 3 2 2 +--R (B b c e - 2A b c d e + (2A c - B b c )d )x +--R + +--R 4 2 2 2 3 2 2 2 +--R (B b e - 2A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 4 3 2 2 +--R (2A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (2A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((- A b c + B b )e + (2A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 2 2 2 +--R - A b c d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 4 3 2 2 +--R (B b c e - 2A b c d e + (2A c - B b c )d )x +--R + +--R 4 2 2 2 3 2 2 2 +--R (B b e - 2A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 4 3 2 2 +--R (2A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (2A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((- A b c + B b )e + (2A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 2 2 2 +--R - A b c d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1457 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 1457 +r0:=-A*d/(b^2*x)+(b*B-A*c)*(c*d-b*e)/(b^2*c*(b+c*x))+(b*B*d-2*A*c*d+A*b*e)*_ + log(x)/b^3-(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^3 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((- A b c e + (2A c - B b c )d)x + (- A b c e + (2A b c - B b c)d)x) +--R * +--R log(c x + b) +--R + +--R 2 3 2 2 2 2 2 +--R ((A b c e + (- 2A c + B b c )d)x + (A b c e + (- 2A b c + B b c)d)x) +--R * +--R log(x) +--R + +--R 2 3 2 2 2 +--R ((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 +--R ((- A b c e + (2A c - B b c )d)x + (- A b c e + (2A b c - B b c)d)x) +--R * +--R log(c x + b) +--R + +--R 2 3 2 2 2 2 2 +--R ((A b c e + (- 2A c + B b c )d)x + (A b c e + (- 2A b c + B b c)d)x) +--R * +--R log(x) +--R + +--R 2 3 2 2 2 +--R ((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1457 +t0:=(A+B*x)/(b*x+c*x^2)^2 +--R +--R +--R B x + A +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 1457 +r0:=-A/(b^2*x)+(b*B-A*c)/(b^2*(b+c*x))+(b*B-2*A*c)*log(x)/b^3-(b*B-2*A*c)*_ + log(b+c*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R ((2A c - B b c)x + (2A b c - B b )x)log(c x + b) +--R + +--R 2 2 2 2 +--R ((- 2A c + B b c)x + (- 2A b c + B b )x)log(x) + (- 2A b c + B b )x +--R + +--R 2 +--R - A b +--R / +--R 3 2 4 +--R b c x + b x +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R ((2A c - B b c)x + (2A b c - B b )x)log(c x + b) +--R + +--R 2 2 2 2 +--R ((- 2A c + B b c)x + (- 2A b c + B b )x)log(x) + (- 2A b c + B b )x +--R + +--R 2 +--R - A b +--R / +--R 3 2 4 +--R b c x + b x +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1457 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +--R c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 1457 +r0:=-A/(b^2*d*x)+c*(b*B-A*c)/(b^2*(c*d-b*e)*(b+c*x))+(b*B*d-2*A*c*d-A*b*e)*_ + log(x)/(b^3*d^2)+c*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+3*A*e))*log(b+c*x)/_ + (b^3*(c*d-b*e)^2)-e^2*(B*d-A*e)*log(d+e*x)/(d^2*(c*d-b*e)^2) +--R +--R +--R (2) +--R 3 3 3 2 2 4 3 4 2 +--R ((A b c e - B b c d e )x + (A b e - B b d e )x)log(e x + d) +--R + +--R 3 2 2 2 4 3 3 2 +--R ((- 3A b c + 2B b c )d e + (2A c - B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((- 3A b c + 2B b c)d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 3 3 2 3 2 2 2 +--R - A b c e + B b c d e + (3A b c - 2B b c )d e +--R + +--R 4 3 3 +--R (- 2A c + B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 2 2 3 2 3 2 2 3 +--R (- A b e + B b d e + (3A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 2 2 3 +--R (- A b c d e + (3A b c - B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R (b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 4 3 4 2 +--R ((A b c e - B b c d e )x + (A b e - B b d e )x)log(e x + d) +--R + +--R 3 2 2 2 4 3 3 2 +--R ((- 3A b c + 2B b c )d e + (2A c - B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((- 3A b c + 2B b c)d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 3 3 2 3 2 2 2 +--R - A b c e + B b c d e + (3A b c - 2B b c )d e +--R + +--R 4 3 3 +--R (- 2A c + B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 2 2 3 2 3 2 2 3 +--R (- A b e + B b d e + (3A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 2 2 3 +--R (- A b c d e + (3A b c - B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R (b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1457 +r0:=-A/(b^2*d^2*x)+c^2*(b*B-A*c)/(b^2*(c*d-b*e)^2*(b+c*x))+e^2*(B*d-A*e)/_ + (d^2*(c*d-b*e)^2*(d+e*x))+(b*B*d-2*A*c*d-2*A*b*e)*log(x)/(b^3*d^3)+_ + c^2*(2*A*c^2*d+3*b^2*B*e-b*c*(B*d+4*A*e))*log(b+c*x)/(b^3*_ + (c*d-b*e)^3)+e^2*(2*A*e*(2*c*d-b*e)-B*d*(3*c*d-b*e))*log(d+e*x)/_ + (d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 4 5 3 2 4 4 3 2 2 3 3 +--R (2A b c e + (- 4A b c - B b c)d e + 3B b c d e )x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 2A b e + (- 2A b c - B b )d e + (- 4A b c + 2B b c)d e +--R + +--R 3 2 3 2 +--R 3B b c d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R (2A b d e + (- 4A b c - B b )d e + 3B b c d e )x +--R * +--R log(e x + d) +--R + +--R 4 2 3 3 2 5 4 4 3 +--R ((4A b c - 3B b c )d e + (- 2A c + B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (4A b c - 3B b c )d e + (2A b c - 2B b c )d e +--R + +--R 5 4 5 +--R (- 2A c + B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((4A b c - 3B b c )d e + (- 2A b c + B b c )d )x +--R * +--R log(c x + b) +--R + +--R 4 5 3 2 4 4 3 2 2 3 +--R - 2A b c e + (4A b c + B b c)d e - 3B b c d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 4A b c + 3B b c )d e + (2A c - B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 2A b e + (2A b c + B b )d e + (4A b c - 2B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R - 4A b c d e + (- 2A b c + 2B b c )d e + (2A c - B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R - 2A b d e + (4A b c + B b )d e - 3B b c d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (- 4A b c + 3B b c )d e + (2A b c - B b c )d +--R * +--R x +--R * +--R log(x) +--R + +--R 4 4 3 2 4 2 3 2 3 3 2 +--R - 2A b c d e + (4A b c + B b c)d e - 4A b c d e +--R + +--R 4 2 3 4 +--R (2A b c - B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R - 2A b d e + (3A b c + B b )d e - B b c d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (- 3A b c + B b c )d e + (2A b c - B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - A b d e + 3A b c d e - 3A b c d e + A b c d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (b c d e - 3b c d e + 3b c d e - b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (b d e - 2b c d e + 2b c d e - b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (b d e - 3b c d e + 3b c d e - b c d )x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1457 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 1457 +--m0:=a0-r0 +--E 249 + +--S 250 of 1457 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 1457 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1457 +r0:=-A/(b^2*d^3*x)+c^3*(b*B-A*c)/(b^2*(c*d-b*e)^3*(b+c*x))+1/2*e^2*_ + (B*d-A*e)/(d^2*(c*d-b*e)^2*(d+e*x)^2)-e^2*(2*A*e*(2*c*d-b*e)-B*d*_ + (3*c*d-b*e))/(d^3*(c*d-b*e)^3*(d+e*x))+(b*B*d-2*A*c*d-3*A*b*e)*_ + log(x)/(b^3*d^4)+c^3*(2*A*c^2*d+4*b^2*B*e-b*c*(B*d+5*A*e))*log(b+_ + c*x)/(b^3*(c*d-b*e)^4)-e^2*(B*d*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)-_ + A*e*(10*c^2*d^2-10*b*c*d*e+3*b^2*e^2))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 5 7 4 2 5 6 3 3 4 2 2 5 +--R 6A b c e + (- 20A b c - 2B b c)d e + (20A b c + 8B b c )d e +--R + +--R 3 3 3 4 +--R - 12B b c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R 6A b e + (- 8A b c - 2B b )d e + (- 20A b c + 4B b c)d e +--R + +--R 3 3 4 2 3 4 3 3 4 3 +--R (40A b c + 4B b c )d e - 24B b c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R 12A b d e + (- 34A b c - 4B b )d e + (20A b c + 14B b c)d e +--R + +--R 3 3 4 2 4 3 3 3 5 2 +--R (20A b c - 16B b c )d e - 12B b c d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R 6A b d e + (- 20A b c - 2B b )d e + (20A b c + 8B b c)d e +--R + +--R 4 2 5 2 +--R - 12B b c d e +--R * +--R x +--R * +--R log(e x + d) +--R + +--R 5 2 4 4 3 6 5 5 2 4 +--R ((- 10A b c + 8B b c )d e + (4A c - 2B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 10A b c + 8B b c )d e + (- 16A b c + 14B b c )d e +--R + +--R 6 5 6 +--R (8A c - 4B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 20A b c + 16B b c )d e + (- 2A b c + 4B b c )d e +--R + +--R 6 5 7 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((- 10A b c + 8B b c )d e + (4A b c - 2B b c )d )x +--R * +--R log(c x + b) +--R + +--R 5 7 4 2 5 6 +--R - 6A b c e + (20A b c + 2B b c)d e +--R + +--R 3 3 4 2 2 5 3 3 3 4 +--R (- 20A b c - 8B b c )d e + 12B b c d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (10A b c - 8B b c )d e + (- 4A c + 2B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 6A b e + (8A b c + 2B b )d e + (20A b c - 4B b c)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (- 40A b c - 4B b c )d e + (10A b c + 16B b c )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (16A b c - 14B b c )d e + (- 8A c + 4B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R - 12A b d e + (34A b c + 4B b )d e + (- 20A b c - 14B b c)d e +--R + +--R 3 3 4 2 4 3 2 4 3 3 5 2 +--R (- 20A b c + 16B b c )d e + (20A b c - 4B b c )d e +--R + +--R 5 2 4 6 6 5 7 +--R (2A b c - 4B b c )d e + (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R - 6A b d e + (20A b c + 2B b )d e + (- 20A b c - 8B b c)d e +--R + +--R 4 2 5 2 2 4 3 3 6 5 2 4 7 +--R 12B b c d e + (10A b c - 8B b c )d e + (- 4A b c + 2B b c )d +--R * +--R x +--R * +--R log(x) +--R + +--R 5 6 4 2 5 2 5 3 3 4 2 3 4 +--R - 6A b c d e + (20A b c + 2B b c)d e + (- 20A b c - 8B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (10A b c + 4B b c )d e + (- 4A b c + 2B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R - 6A b d e + (11A b c + 2B b )d e + (10A b c - 5B b c)d e +--R + +--R 3 3 4 2 4 3 2 4 3 3 5 2 +--R (- 25A b c - 4B b c )d e + (18A b c + 3B b c )d e +--R + +--R 5 2 4 6 +--R (- 8A b c + 4B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R - 9A b d e + (28A b c + 3B b )d e + (- 25A b c - 10B b c)d e +--R + +--R 3 3 4 2 5 2 2 4 3 3 6 +--R (4A b c + 7B b c )d e + (6A b c - 2B b c )d e +--R + +--R 5 2 4 7 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 2A b d e + 8A b c d e - 12A b c d e + 8A b c d e - 2A b c d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (2b c d e - 8b c d e + 12b c d e - 8b c d e + 2b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3 +--R (2b d e - 4b c d e - 4b c d e + 16b c d e - 14b c d e + 4b c d e)x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2 +--R (4b d e - 14b c d e + 16b c d e - 4b c d e - 4b c d e + 2b c d )x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1457 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 1457 +--m0:=a0-r0 +--E 254 + +--S 255 of 1457 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 1457 +t0:=(A+B*x)*(d+e*x)^5/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1457 +r0:=-1/2*A*d^5/(b^3*x^2)-d^4*(b*B*d-3*A*c*d+5*A*b*e)/(b^4*x)+B*e^5*x/c^3-_ + 1/2*(b*B-A*c)*(c*d-b*e)^5/(b^3*c^4*(b+c*x)^2)-(c*d-b*e)^4*(2*b*B*c*d-_ + 3*A*c^2*d+3*b^2*B*e-2*A*b*c*e)/(b^4*c^4*(b+c*x))+d^3*(6*A*c^2*d^2+_ + 5*b^2*e*(B*d+2*A*e)-3*b*c*d*(B*d+5*A*e))*log(x)/b^5-(c*d-b*e)^3*_ + (6*A*c^3*d^2-3*b^3*B*e^2-3*b*c^2*d*(B*d-A*e)-b^2*c*e*(4*B*d-A*e))*_ + log(b+c*x)/(b^5*c^4) +--R +--R +--R (2) +--R 5 3 6 2 5 5 3 4 2 6 3 2 +--R (2A b c - 6B b c )e + 10B b c d e - 20A b c d e +--R + +--R 7 2 6 4 8 7 5 +--R (30A b c - 10B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 2 7 5 6 2 4 3 5 3 2 +--R (4A b c - 12B b c)e + 20B b c d e - 40A b c d e +--R + +--R 2 6 3 5 4 7 2 6 5 +--R (60A b c - 20B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 7 4 4 4 3 2 +--R (2A b c - 6B b )e + 10B b c d e - 20A b c d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (30A b c - 10B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 6 3 2 7 2 6 4 8 7 5 4 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 5 3 2 2 6 3 5 4 +--R 40A b c d e + (- 60A b c + 20B b c )d e +--R + +--R 7 2 6 5 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 3 2 3 5 4 4 4 2 6 3 5 5 2 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 5 5 6 2 5 4 +--R 2B b c e x + 4B b c e x +--R + +--R 6 2 7 5 5 3 6 2 4 5 3 2 3 +--R (4A b c - 4B b c)e + (- 10A b c + 20B b c )d e - 20B b c d e +--R + +--R 3 5 3 2 2 6 3 5 4 7 2 6 5 +--R 20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 6 2 7 4 +--R (3A b c - 5B b )e + (- 5A b c + 15B b c)d e +--R + +--R 5 3 6 2 2 3 4 4 5 3 3 2 +--R (- 10A b c - 10B b c )d e + (30A b c - 10B b c )d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (- 45A b c + 15B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 5 4 4 5 4 4 5 +--R (- 10A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 6 4 6 5 3 7 4 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 6 2 5 5 3 4 2 6 3 2 +--R (2A b c - 6B b c )e + 10B b c d e - 20A b c d e +--R + +--R 7 2 6 4 8 7 5 +--R (30A b c - 10B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 2 7 5 6 2 4 3 5 3 2 +--R (4A b c - 12B b c)e + 20B b c d e - 40A b c d e +--R + +--R 2 6 3 5 4 7 2 6 5 +--R (60A b c - 20B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 7 4 4 4 3 2 +--R (2A b c - 6B b )e + 10B b c d e - 20A b c d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (30A b c - 10B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 6 3 2 7 2 6 4 8 7 5 4 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 5 3 2 2 6 3 5 4 +--R 40A b c d e + (- 60A b c + 20B b c )d e +--R + +--R 7 2 6 5 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 3 2 3 5 4 4 4 2 6 3 5 5 2 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 5 5 6 2 5 4 +--R 2B b c e x + 4B b c e x +--R + +--R 6 2 7 5 5 3 6 2 4 5 3 2 3 +--R (4A b c - 4B b c)e + (- 10A b c + 20B b c )d e - 20B b c d e +--R + +--R 3 5 3 2 2 6 3 5 4 7 2 6 5 +--R 20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 6 2 7 4 +--R (3A b c - 5B b )e + (- 5A b c + 15B b c)d e +--R + +--R 5 3 6 2 2 3 4 4 5 3 3 2 +--R (- 10A b c - 10B b c )d e + (30A b c - 10B b c )d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (- 45A b c + 15B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 5 4 4 5 4 4 5 +--R (- 10A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 6 4 6 5 3 7 4 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1457 +r0:=-1/2*A*d^4/(b^3*x^2)-d^3*(b*B*d-3*A*c*d+4*A*b*e)/(b^4*x)-1/2*(b*B-_ + A*c)*(c*d-b*e)^4/(b^3*c^3*(b+c*x)^2)+(c*d-b*e)^3*(3*A*c^2*d-2*b^2*_ + B*e-b*c*(2*B*d-A*e))/(b^4*c^3*(b+c*x))+d^2*(6*A*c^2*d^2+2*b^2*e*_ + (2*B*d+3*A*e)-3*b*c*d*(B*d+4*A*e))*log(x)/b^5+(c*d-b*e)^2*(3*b*B*_ + c^2*d^2-6*A*c^3*d^2+2*b^2*B*c*d*e+b^3*B*e^2)*log(b+c*x)/(b^5*c^3) +--R +--R +--R (2) +--R 5 2 4 2 5 2 2 6 2 5 3 +--R 2B b c e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 7 6 4 +--R (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 4 3 4 2 2 2 5 3 4 3 +--R 4B b c e - 24A b c d e + (48A b c - 16B b c )d e +--R + +--R 6 2 5 4 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 4 4 3 2 2 3 4 4 3 3 +--R 2B b e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 2 5 3 4 4 +--R (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 5 2 2 6 2 5 3 7 6 4 4 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 4 2 2 2 5 3 4 3 +--R 24A b c d e + (- 48A b c + 16B b c )d e +--R + +--R 6 2 5 4 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 2 3 4 4 3 3 2 5 3 4 4 2 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 2 6 4 5 2 3 3 4 2 2 +--R (- 2A b c + 4B b c)e - 8B b c d e + 12A b c d e +--R + +--R 2 5 3 4 3 6 2 5 4 +--R (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- A b c + 3B b )e + (- 4A b c - 4B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (18A b c - 6B b c )d e + (- 36A b c + 12B b c )d e +--R + +--R 2 5 3 4 4 +--R (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 3 4 4 3 4 +--R (- 8A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 5 4 6 4 3 7 3 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 2 5 2 2 6 2 5 3 +--R 2B b c e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 7 6 4 +--R (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 4 3 4 2 2 2 5 3 4 3 +--R 4B b c e - 24A b c d e + (48A b c - 16B b c )d e +--R + +--R 6 2 5 4 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 4 4 3 2 2 3 4 4 3 3 +--R 2B b e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 2 5 3 4 4 +--R (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 5 2 2 6 2 5 3 7 6 4 4 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 4 2 2 2 5 3 4 3 +--R 24A b c d e + (- 48A b c + 16B b c )d e +--R + +--R 6 2 5 4 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 2 3 4 4 3 3 2 5 3 4 4 2 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 2 6 4 5 2 3 3 4 2 2 +--R (- 2A b c + 4B b c)e - 8B b c d e + 12A b c d e +--R + +--R 2 5 3 4 3 6 2 5 4 +--R (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- A b c + 3B b )e + (- 4A b c - 4B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (18A b c - 6B b c )d e + (- 36A b c + 12B b c )d e +--R + +--R 2 5 3 4 4 +--R (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 3 4 4 3 4 +--R (- 8A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 5 4 6 4 3 7 3 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1457 +r0:=-1/2*A*d^3/(b^3*x^2)-d^2*(b*B*d-3*A*c*d+3*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)^3/(b^3*c^2*(b+c*x)^2)-(c*d-b*e)^2*(2*b*B*c*d-3*A*c^2*d+_ + b^2*B*e)/(b^4*c^2*(b+c*x))-3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*_ + log(x)/b^5+3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 12A b c d e + (36A b c - 12B b c )d e +--R + +--R 5 2 4 3 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R 12A b c d e + (- 36A b c + 12B b c )d e +--R + +--R 5 2 4 3 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 3 3 2 2 4 3 3 2 +--R - 2B b c e + 6A b c d e + (- 18A b c + 6B b c )d e +--R + +--R 5 2 4 3 +--R (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - B b )e + (9A b c - 3B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 27A b c + 9B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 6A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 12A b c d e + (36A b c - 12B b c )d e +--R + +--R 5 2 4 3 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R 12A b c d e + (- 36A b c + 12B b c )d e +--R + +--R 5 2 4 3 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 3 3 2 2 4 3 3 2 +--R - 2B b c e + 6A b c d e + (- 18A b c + 6B b c )d e +--R + +--R 5 2 4 3 +--R (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - B b )e + (9A b c - 3B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 27A b c + 9B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 6A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1457 +r0:=-1/2*A*d^2/(b^3*x^2)-d*(b*B*d-3*A*c*d+2*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)^2/(b^3*c*(b+c*x)^2)-(c*d-b*e)*(2*b*B*d-3*A*c*d+A*b*e)/_ + (b^4*(b+c*x))+(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*_ + log(x)/b^5-(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*_ + log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 3 2 4 2 3 5 4 2 4 +--R (- 2A b c e + (12A b c - 4B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- 4A b c e + (24A b c - 8B b c )d e + (- 24A b c + 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 2A b c e + (12A b c - 4B b c)d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (4A b c e + (- 24A b c + 8B b c )d e + (24A b c - 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (2A b c e + (- 12A b c + 4B b c)d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A b c - 6B b c )d )x +--R + +--R 4 5 2 3 2 4 2 3 3 2 2 2 +--R ((3A b c - B b )e + (- 18A b c + 6B b c)d e + (18A b c - 9B b c )d )x +--R + +--R 4 3 2 4 2 4 2 +--R (- 4A b c d e + (4A b c - 2B b c)d )x - A b c d +--R / +--R 5 3 4 6 2 3 7 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 2 3 5 4 2 4 +--R (- 2A b c e + (12A b c - 4B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- 4A b c e + (24A b c - 8B b c )d e + (- 24A b c + 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 2A b c e + (12A b c - 4B b c)d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (4A b c e + (- 24A b c + 8B b c )d e + (24A b c - 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (2A b c e + (- 12A b c + 4B b c)d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A b c - 6B b c )d )x +--R + +--R 4 5 2 3 2 4 2 3 3 2 2 2 +--R ((3A b c - B b )e + (- 18A b c + 6B b c)d e + (18A b c - 9B b c )d )x +--R + +--R 4 3 2 4 2 4 2 +--R (- 4A b c d e + (4A b c - 2B b c)d )x - A b c d +--R / +--R 5 3 4 6 2 3 7 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1457 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^3 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1457 +r0:=-1/2*A*d/(b^3*x^2)+(-b*B*d+3*A*c*d-A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)/(b^3*(b+c*x)^2)+(3*A*c^2*d+b^2*B*e-2*b*c*(B*d+A*e))/_ + (b^4*(b+c*x))+(6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(x)/b^5-_ + (6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 3 2 2 4 3 4 +--R ((6A b c - 2B b c )e + (- 12A c + 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((12A b c - 4B b c)e + (- 24A b c + 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((6A b c - 2B b )e + (- 12A b c + 6B b c)d)x +--R * +--R log(c x + b) +--R + +--R 3 2 2 4 3 4 +--R ((- 6A b c + 2B b c )e + (12A c - 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 4B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 6A b c + 2B b )e + (12A b c - 6B b c)d)x +--R * +--R log(x) +--R + +--R 2 2 3 3 2 2 3 +--R ((- 6A b c + 2B b c)e + (12A b c - 6B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 9A b c + 3B b )e + (18A b c - 9B b c)d)x +--R + +--R 4 3 4 4 +--R (- 2A b e + (4A b c - 2B b )d)x - A b d +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 4 3 4 +--R ((6A b c - 2B b c )e + (- 12A c + 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((12A b c - 4B b c)e + (- 24A b c + 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((6A b c - 2B b )e + (- 12A b c + 6B b c)d)x +--R * +--R log(c x + b) +--R + +--R 3 2 2 4 3 4 +--R ((- 6A b c + 2B b c )e + (12A c - 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 4B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 6A b c + 2B b )e + (12A b c - 6B b c)d)x +--R * +--R log(x) +--R + +--R 2 2 3 3 2 2 3 +--R ((- 6A b c + 2B b c)e + (12A b c - 6B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 9A b c + 3B b )e + (18A b c - 9B b c)d)x +--R + +--R 4 3 4 4 +--R (- 2A b e + (4A b c - 2B b )d)x - A b d +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1457 +t0:=(A+B*x)/(b*x+c*x^2)^3 +--R +--R +--R B x + A +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1457 +r0:=-1/2*A/(b^3*x^2)+(-b*B+3*A*c)/(b^4*x)-1/2*c*(b*B-A*c)/(b^3*(b+c*x)^2)-_ + c*(2*b*B-3*A*c)/(b^4*(b+c*x))-3*c*(b*B-2*A*c)*log(x)/b^5+3*c*(b*B-_ + 2*A*c)*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 4 3 4 3 2 2 3 +--R (- 12A c + 6B b c )x + (- 24A b c + 12B b c )x +--R + +--R 2 2 3 2 +--R (- 12A b c + 6B b c)x +--R * +--R log(c x + b) +--R + +--R 4 3 4 3 2 2 3 +--R (12A c - 6B b c )x + (24A b c - 12B b c )x +--R + +--R 2 2 3 2 +--R (12A b c - 6B b c)x +--R * +--R log(x) +--R + +--R 3 2 2 3 2 2 3 2 3 4 4 +--R (12A b c - 6B b c )x + (18A b c - 9B b c)x + (4A b c - 2B b )x - A b +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 3 2 2 3 +--R (- 12A c + 6B b c )x + (- 24A b c + 12B b c )x +--R + +--R 2 2 3 2 +--R (- 12A b c + 6B b c)x +--R * +--R log(c x + b) +--R + +--R 4 3 4 3 2 2 3 +--R (12A c - 6B b c )x + (24A b c - 12B b c )x +--R + +--R 2 2 3 2 +--R (12A b c - 6B b c)x +--R * +--R log(x) +--R + +--R 3 2 2 3 2 2 3 2 3 4 4 +--R (12A b c - 6B b c )x + (18A b c - 9B b c)x + (4A b c - 2B b )x - A b +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1457 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R --------------------------------------------------------------------------- +--R 3 7 2 3 6 2 2 5 3 2 4 3 3 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1457 +r0:=-1/2*A/(b^3*d*x^2)+(-b*B*d+3*A*c*d+A*b*e)/(b^4*d^2*x)-1/2*c^2*(b*B-_ + A*c)/(b^3*(c*d-b*e)*(b+c*x)^2)+c^2*(3*A*c^2*d+3*b^2*B*e-2*b*c*(B*d+_ + 2*A*e))/(b^4*(c*d-b*e)^2*(b+c*x))+(6*A*c^2*d^2-3*b*c*d*(B*d-A*e)-_ + b^2*e*(B*d-A*e))*log(x)/(b^5*d^3)-c^2*(6*A*c^3*d^2-6*b^3*B*e^2-_ + 3*b*c^2*d*(B*d+5*A*e)+2*b^2*c*e*(4*B*d+5*A*e))*log(b+c*x)/(b^5*(c*d-_ + b*e)^3)-e^4*(B*d-A*e)*log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 5 2 5 5 2 4 4 6 5 6 4 3 +--R (- 2A b c e + 2B b c d e )x + (- 4A b c e + 4B b c d e )x +--R + +--R 7 5 7 4 2 +--R (- 2A b e + 2B b d e )x +--R * +--R log(e x + d) +--R + +--R 2 5 3 4 3 2 6 2 5 4 +--R (20A b c - 12B b c )d e + (- 30A b c + 16B b c )d e +--R + +--R 7 6 5 +--R (12A c - 6B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 3 2 2 5 3 4 4 +--R (40A b c - 24B b c )d e + (- 60A b c + 32B b c )d e +--R + +--R 6 2 5 5 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (20A b c - 12B b c )d e + (- 30A b c + 16B b c )d e +--R + +--R 2 5 3 4 5 +--R (12A b c - 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 5 2 5 5 2 4 2 5 3 4 3 2 +--R 2A b c e - 2B b c d e + (- 20A b c + 12B b c )d e +--R + +--R 6 2 5 4 7 6 5 +--R (30A b c - 16B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 5 6 4 3 4 4 3 3 2 +--R 4A b c e - 4B b c d e + (- 40A b c + 24B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (60A b c - 32B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 7 4 4 3 5 2 3 2 +--R 2A b e - 2B b d e + (- 20A b c + 12B b c )d e +--R + +--R 3 4 4 3 4 2 5 3 4 5 +--R (30A b c - 16B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(x) +--R + +--R 5 2 4 5 2 2 3 3 4 4 3 3 2 +--R 2A b c d e - 2B b c d e + (- 20A b c + 12B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (30A b c - 16B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 2 6 2 3 4 3 5 2 3 2 +--R 4A b c d e + (- A b c - 4B b c)d e + (- 30A b c + 19B b c )d e +--R + +--R 3 4 4 3 4 2 5 3 4 5 +--R (45A b c - 24B b c )d e + (- 18A b c + 9B b c )d +--R * +--R 2 +--R x +--R + +--R 7 4 6 7 2 3 5 2 6 3 2 +--R 2A b d e + (- 2A b c - 2B b )d e + (- 6A b c + 6B b c)d e +--R + +--R 4 3 5 2 4 3 4 4 3 5 +--R (10A b c - 6B b c )d e + (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - A b d e + 3A b c d e - 3A b c d e + A b c d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (2b c d e - 6b c d e + 6b c d e - 2b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d )x +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1457 +--a0:=integrate(t0,x) +--E 288 + +--S 289 of 1457 +--m0:=a0-r0 +--E 289 + +--S 290 of 1457 +--d0:=D(m0,x) +--E 290 + +)clear all + +--S 291 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1457 +r0:=-1/2*A/(b^3*d^2*x^2)+(-b*B*d+3*A*c*d+2*A*b*e)/(b^4*d^3*x)-1/2*c^3*(b*B-_ + A*c)/(b^3*(c*d-b*e)^2*(b+c*x)^2)-c^3*(2*b*B*c*d-3*A*c^2*d-4*b^2*B*e+_ + 5*A*b*c*e)/(b^4*(c*d-b*e)^3*(b+c*x))+e^4*(B*d-A*e)/(d^3*(c*d-b*e)^3*_ + (d+e*x))+(6*A*c^2*d^2-b^2*e*(2*B*d-3*A*e)-3*b*c*d*(B*d-2*A*e))*_ + log(x)/(b^5*d^4)-c^3*(6*A*c^3*d^2-10*b^3*B*e^2+5*b^2*c*e*(2*B*d+_ + 3*A*e)-3*b*c^2*d*(B*d+6*A*e))*log(b+c*x)/(b^5*(c*d-b*e)^4)-e^4*_ + (B*d*(5*c*d-2*b*e)-3*A*e*(2*c*d-b*e))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 6 2 7 5 3 6 2 6 5 3 2 5 5 +--R (- 6A b c e + (12A b c + 4B b c )d e - 10B b c d e )x +--R + +--R 7 7 6 2 7 6 +--R - 12A b c e + (18A b c + 8B b c)d e +--R + +--R 5 3 6 2 2 5 5 3 3 4 +--R (12A b c - 16B b c )d e - 10B b c d e +--R * +--R 4 +--R x +--R + +--R 8 7 8 6 6 2 7 2 5 6 2 3 4 3 +--R (- 6A b e + 4B b d e + (24A b c - 2B b c)d e - 20B b c d e )x +--R + +--R 8 6 7 8 2 5 7 3 4 2 +--R (- 6A b d e + (12A b c + 4B b )d e - 10B b c d e )x +--R * +--R log(e x + d) +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 30A b c + 20B b c )d e + (36A b c - 20B b c )d e +--R + +--R 8 7 6 +--R (- 12A c + 6B b c )d e +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 60A b c + 40B b c )d e + (42A b c - 20B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (12A b c - 8B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (- 30A b c + 20B b c )d e + (- 24A b c + 20B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (60A b c - 34B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (- 30A b c + 20B b c )d e + (36A b c - 20B b c )d e +--R + +--R 2 6 3 5 7 +--R (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 6 2 7 5 3 6 2 6 5 3 2 5 +--R 6A b c e + (- 12A b c - 4B b c )d e + 10B b c d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 8 7 6 +--R (12A c - 6B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R 12A b c e + (- 18A b c - 8B b c)d e +--R + +--R 5 3 6 2 2 5 5 3 3 4 +--R (- 12A b c + 16B b c )d e + 10B b c d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (60A b c - 40B b c )d e + (- 42A b c + 20B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (- 12A b c + 8B b c )d e + (12A c - 6B b c )d +--R * +--R 4 +--R x +--R + +--R 8 7 8 6 6 2 7 2 5 6 2 3 4 +--R 6A b e - 4B b d e + (- 24A b c + 2B b c)d e + 20B b c d e +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (30A b c - 20B b c )d e + (24A b c - 20B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 60A b c + 34B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 7 3 4 +--R 6A b d e + (- 12A b c - 4B b )d e + 10B b c d e +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 2 6 3 5 7 +--R (12A b c - 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(x) +--R + +--R 6 2 6 5 3 6 2 2 5 5 3 3 4 +--R 6A b c d e + (- 12A b c - 4B b c )d e + 10B b c d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 7 2 6 6 +--R (12A b c - 6B b c )d e +--R * +--R 4 +--R x +--R + +--R 7 6 6 2 7 2 5 5 3 6 2 3 4 +--R 12A b c d e + (- 21A b c - 8B b c)d e + (- 6A b c + 18B b c )d e +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (45A b c - 25B b c )d e + (- 24A b c + 10B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 18A b c + 11B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 6 2 7 3 4 +--R 6A b d e + (- 6A b c - 4B b )d e + (- 13A b c + 6B b c)d e +--R + +--R 5 3 6 2 4 3 4 4 5 3 5 2 +--R (12A b c + 4B b c )d e + (33A b c - 25B b c )d e +--R + +--R 3 5 4 4 6 2 6 3 5 7 +--R (- 50A b c + 28B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 8 3 4 6 2 7 4 3 +--R 3A b d e + (- 8A b c - 2B b )d e + (2A b c + 8B b c)d e +--R + +--R 5 3 6 2 5 2 4 4 5 3 6 +--R (12A b c - 12B b c )d e + (- 13A b c + 8B b c )d e +--R + +--R 3 5 4 4 7 +--R (4A b c - 2B b c )d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - A b d e + 4A b c d e - 6A b c d e + 4A b c d e - A b c d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (2b c d e - 8b c d e + 12b c d e - 8b c d e + 2b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 5 6 9 4 +--R (4b c d e - 14b c d e + 16b c d e - 4b c d e - 4b c d e + 2b c d )x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 6 5 9 3 +--R (2b d e - 4b c d e - 4b c d e + 16b c d e - 14b c d e + 4b c d )x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )x +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1457 +--a0:=integrate(t0,x) +--E 293 + +--S 294 of 1457 +--m0:=a0-r0 +--E 294 + +--S 295 of 1457 +--d0:=D(m0,x) +--E 295 + +)clear all + +--S 296 of 1457 +t0:=(A+B*x)*(d+e*x)^3*sqrt(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1457 +r0:=1/960*(4*A*c*e*(132*c^2*d^2-132*b*c*d*e+35*b^2*e^2)+B*(64*c^3*d^3-_ + 360*b*c^2*d^2*e+366*b^2*c*d*e^2-105*b^3*e^3))*(b*x+c*x^2)^(3/2)/c^4+_ + 1/20*(2*B*c*d-3*b*B*e+4*A*c*e)*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c^2+_ + 1/6*B*(d+e*x)^3*(b*x+c*x^2)^(3/2)/c-1/160*e*(d*(16*b*B*c*d-40*A*c^2*d-_ + 9*b^2*B*e+12*A*b*c*e)-(28*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-36*b*c*d*e+_ + 21*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/c^3-1/512*b^2*(128*A*c^4*d^3+_ + 21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-28*b^3*c*e^2*(3*B*d+A*e)-_ + 64*b*c^3*d^2*(B*d+3*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+_ + 1/512*b*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-_ + 28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/c^5+_ + 1/256*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-_ + 28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*x*sqrt(b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 5 6 3 4 2 5 2 +--R (420A b c - 315B b )e + (- 1800A b c + 1260B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (2880A b c - 1800B b c )d e + (- 1920A b c + 960B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 3 5 5 4 3 5 2 4 +--R 1280B c e x + ((1536A c + 128B b c )e + 4608B c d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (192A b c - 144B b c )e + (5760A c + 576B b c )d e +--R + +--R 5 2 +--R 5760B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 224A b c + 168B b c )e + (960A b c - 672B b c )d e +--R + +--R 5 4 2 5 3 +--R (7680A c + 960B b c )d e + 2560B c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (280A b c - 210B b c)e + (- 1200A b c + 840B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (1920A b c - 1200B b c )d e + (3840A c + 640B b c )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 420A b c + 315B b )e + (1800A b c - 1260B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 2880A b c + 1800B b c )d e + (1920A b c - 960B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 6 3 4 2 5 2 +--R (420A b c - 315B b )e + (- 1800A b c + 1260B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (2880A b c - 1800B b c )d e + (- 1920A b c + 960B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 5 3 5 5 4 3 5 2 4 +--R 2560B c e x + ((3072A c + 256B b c )e + 9216B c d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (384A b c - 288B b c )e + (11520A c + 1152B b c )d e +--R + +--R 5 2 +--R 11520B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 448A b c + 336B b c )e + (1920A b c - 1344B b c )d e +--R + +--R 5 4 2 5 3 +--R (15360A c + 1920B b c )d e + 5120B c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (560A b c - 420B b c)e + (- 2400A b c + 1680B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (3840A b c - 2400B b c )d e + (7680A c + 1280B b c )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 840A b c + 630B b )e + (3600A b c - 2520B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 5760A b c + 3600B b c )d e + (3840A b c - 1920B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 15360c \|c +--R , +--R +--R 5 6 3 4 2 5 2 +--R (420A b c - 315B b )e + (- 1800A b c + 1260B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (2880A b c - 1800B b c )d e + (- 1920A b c + 960B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 5 3 5 5 4 3 5 2 4 +--R 1280B c e x + ((1536A c + 128B b c )e + 4608B c d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (192A b c - 144B b c )e + (5760A c + 576B b c )d e +--R + +--R 5 2 +--R 5760B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 224A b c + 168B b c )e + (960A b c - 672B b c )d e +--R + +--R 5 4 2 5 3 +--R (7680A c + 960B b c )d e + 2560B c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (280A b c - 210B b c)e + (- 1200A b c + 840B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (1920A b c - 1200B b c )d e + (3840A c + 640B b c )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 420A b c + 315B b )e + (1800A b c - 1260B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 2880A b c + 1800B b c )d e + (1920A b c - 960B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 5 +---+ +--R 7680c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 298 + +--S 299 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 6 3 4 2 5 2 +--R (28A b c - 21B b )e + (- 120A b c + 84B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (192A b c - 120B b c )d e + (- 128A b c + 64B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 5 6 3 4 2 5 2 +--R (- 56A b c + 42B b )e + (240A b c - 168B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 384A b c + 240B b c )d e + (256A b c - 128B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 5 +-+ +--R 1024c \|c +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 6 3 4 2 5 2 +--R (- 28A b c + 21B b )e + (120A b c - 84B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 192A b c + 120B b c )d e + (128A b c - 64B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 6 3 4 2 5 2 +--R (28A b c - 21B b )e + (- 120A b c + 84B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (192A b c - 120B b c )d e + (- 128A b c + 64B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 5 +---+ +-+ +--R 512c \|- c \|c +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 302 + +)clear all + +--S 303 of 1457 +t0:=(A+B*x)*(d+e*x)^2*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R 2 3 2 2 2 2 | 2 +--R (1) (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|c x + b x +--R Type: Expression(Integer) +--E 303 + +--S 304 of 1457 +r0:=1/240*(50*A*c*e*(2*c*d-b*e)+B*(32*c^2*d^2-82*b*c*d*e+35*b^2*e^2))*_ + (b*x+c*x^2)^(3/2)/c^3+1/5*B*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c-1/40*e*_ + ((3*b*B-10*A*c)*d-(4*B*c*d-7*b*B*e+10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/c^2-_ + 1/128*b^2*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-_ + 16*b*c^2*d*(B*d+2*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)+_ + 1/128*b*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*_ + d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/c^4+1/64*(32*A*c^3*d^2-7*b^3*B*e^2+_ + 10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 4 5 2 3 2 4 +--R (- 150A b c + 105B b )e + (480A b c - 300B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 480A b c + 240B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 2 4 4 3 2 4 3 +--R 384B c e x + ((480A c + 48B b c )e + 960B c d e)x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((80A b c - 56B b c )e + (1280A c + 160B b c )d e + 640B c d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 100A b c + 70B b c)e + (320A b c - 200B b c )d e +--R + +--R 4 3 2 +--R (960A c + 160B b c )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (150A b c - 105B b )e + (- 480A b c + 300B b c)d e +--R + +--R 3 2 2 2 +--R (480A b c - 240B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 1920c \|c +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 5 2 3 2 4 +--R (150A b c - 105B b )e + (- 480A b c + 300B b c)d e +--R + +--R 2 3 3 2 2 +--R (480A b c - 240B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 2 4 4 3 2 4 3 +--R 768B c e x + ((960A c + 96B b c )e + 1920B c d e)x +--R + +--R 3 2 2 2 4 3 +--R (160A b c - 112B b c )e + (2560A c + 320B b c )d e +--R + +--R 4 2 +--R 1280B c d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 2 +--R (- 200A b c + 140B b c)e + (640A b c - 400B b c )d e +--R + +--R 4 3 2 +--R (1920A c + 320B b c )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (300A b c - 210B b )e + (- 960A b c + 600B b c)d e +--R + +--R 3 2 2 2 +--R (960A b c - 480B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 3840c \|c +--R , +--R +--R 4 5 2 3 2 4 +--R (- 150A b c + 105B b )e + (480A b c - 300B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 480A b c + 240B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 4 2 4 4 3 2 4 3 +--R 384B c e x + ((480A c + 48B b c )e + 960B c d e)x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((80A b c - 56B b c )e + (1280A c + 160B b c )d e + 640B c d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 100A b c + 70B b c)e + (320A b c - 200B b c )d e +--R + +--R 4 3 2 +--R (960A c + 160B b c )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (150A b c - 105B b )e + (- 480A b c + 300B b c)d e +--R + +--R 3 2 2 2 +--R (480A b c - 240B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 1920c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 305 + +--S 306 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 5 2 3 2 4 +--R (10A b c - 7B b )e + (- 32A b c + 20B b c)d e +--R + +--R 2 3 3 2 2 +--R (32A b c - 16B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 5 2 3 2 4 +--R (20A b c - 14B b )e + (- 64A b c + 40B b c)d e +--R + +--R 2 3 3 2 2 +--R (64A b c - 32B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 256c \|c +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 5 2 3 2 4 +--R (10A b c - 7B b )e + (- 32A b c + 20B b c)d e +--R + +--R 2 3 3 2 2 +--R (32A b c - 16B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 5 2 3 2 4 +--R (- 10A b c + 7B b )e + (32A b c - 20B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 32A b c + 16B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 128c \|- c \|c +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 1457 +t0:=(A+B*x)*(d+e*x)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (1) (B e x + (A e + B d)x + A d)\|c x + b x +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1457 +r0:=1/24*(2*B*c*d-5*b*B*e+8*A*c*e)*(b*x+c*x^2)^(3/2)/c^2+1/4*B*(d+e*x)*_ + (b*x+c*x^2)^(3/2)/c-1/64*b^2*(16*A*c^2*d+5*b^2*B*e-8*b*c*(B*d+A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/64*b*(16*A*c^2*d+5*b^2*B*e-_ + 8*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^3+1/32*(16*A*c^2*d+5*b^2*B*e-_ + 8*b*c*(B*d+A*e))*x*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 3 4 2 2 3 x\|c +--R ((24A b c - 15B b )e + (- 48A b c + 24B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 3 3 2 3 2 +--R 48B c e x + ((64A c + 8B b c )e + 64B c d)x +--R + +--R 2 2 3 2 +--R ((16A b c - 10B b c)e + (96A c + 16B b c )d)x +--R + +--R 2 3 2 2 +--R (- 24A b c + 15B b )e + (48A b c - 24B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 2 3 +--R ((24A b c - 15B b )e + (- 48A b c + 24B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 3 3 2 3 2 +--R 96B c e x + ((128A c + 16B b c )e + 128B c d)x +--R + +--R 2 2 3 2 +--R ((32A b c - 20B b c)e + (192A c + 32B b c )d)x +--R + +--R 2 3 2 2 +--R (- 48A b c + 30B b )e + (96A b c - 48B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 384c \|c +--R , +--R +--R 3 4 2 2 3 +--R ((24A b c - 15B b )e + (- 48A b c + 24B b c)d) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 3 3 2 3 2 +--R 48B c e x + ((64A c + 8B b c )e + 64B c d)x +--R + +--R 2 2 3 2 +--R ((16A b c - 10B b c)e + (96A c + 16B b c )d)x +--R + +--R 2 3 2 2 +--R (- 24A b c + 15B b )e + (48A b c - 24B b c)d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 3 +---+ +--R 192c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 312 + +--S 313 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 +--R ((8A b c - 5B b )e + (- 16A b c + 8B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 3 4 2 2 3 x\|c +--R ((- 16A b c + 10B b )e + (32A b c - 16B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 128c \|c +--R Type: Expression(Integer) +--E 313 + +--S 314 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 3 4 2 2 3 +---+ x\|c +--R ((- 8A b c + 5B b )e + (16A b c - 8B b c)d)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 3 4 2 2 3 +-+ \|- c \|c x + b x +--R ((8A b c - 5B b )e + (- 16A b c + 8B b c)d)\|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 64c \|- c \|c +--R Type: Expression(Integer) +--E 315 + +--S 316 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 316 + +)clear all + +--S 317 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R | 2 +--R (1) (B x + A)\|c x + b x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1457 +r0:=1/3*B*(b*x+c*x^2)^(3/2)/c+1/8*b^2*(b*B-2*A*c)*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/c^(5/2)-1/8*b*(b*B-2*A*c)*sqrt(b*x+c*x^2)/c^2-_ + 1/4*(b*B-2*A*c)*x*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 2 3 x\|c +--R (- 6A b c + 3B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R 2 2 2 2 +-+ | 2 +--R (8B c x + (12A c + 2B b c)x + 6A b c - 3B b )\|c \|c x + b x +--R / +--R 2 +-+ +--R 24c \|c +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 2 3 | 2 +-+ +--R (6A b c - 3B b )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R 2 2 2 2 +-+ | 2 +--R (16B c x + (24A c + 4B b c)x + 12A b c - 6B b )\|c \|c x + b x +--R / +--R 2 +-+ +--R 48c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 2 3 \|- c \|c x + b x +--R (- 6A b c + 3B b )atan(-------------------) +--R c x +--R + +--R +----------+ +--R 2 2 2 2 +---+ | 2 +--R (8B c x + (12A c + 2B b c)x + 6A b c - 3B b )\|- c \|c x + b x +--R / +--R 2 +---+ +--R 24c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 319 + +--S 320 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 2 3 | 2 +-+ +--R (2A b c - B b )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 2 3 x\|c +--R (4A b c - 2B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 2 +-+ +--R 16c \|c +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 3 +---+ x\|c +--R (2A b c - B b )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 2 3 +-+ \|- c \|c x + b x +--R (- 2A b c + B b )\|c atan(-------------------) +--R c x +--R / +--R 2 +---+ +-+ +--R 8c \|- c \|c +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 323 + +)clear all + +--S 324 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R e x + d +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1457 +r0:=-1/4*(4*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-4*b*c*d*e-b^2*e^2))*atanh(x*_ + sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^3)-(B*d-A*e)*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*_ + sqrt(c*d-b*e)/e^3-1/4*(4*B*c*d-b*B*e-4*A*c*e-2*B*c*e*x)*sqrt(b*x+_ + c*x^2)/(c*e^2) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 2 2 x\|c +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ +--R (- 4A c e + 4B c d)\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R 2 2 +-+ | 2 +--R (2B c e x + (4A c + B b)e - 4B c d e)\|c \|c x + b x +--R / +--R 3 +-+ +--R 4c e \|c +--R Type: Expression(Integer) +--E 325 + +--S 326 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R | 2 +-+ +--R (8A c e - 8B c d)\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R 2 2 +-+ | 2 +--R (4B c e x + (8A c + 2B b)e - 8B c d e)\|c \|c x + b x +--R / +--R 3 +-+ +--R 8c e \|c +--R , +--R +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R (16A c e - 16B c d)\|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R +----------+ +--R 2 2 +-+ | 2 +--R (4B c e x + (8A c + 2B b)e - 8B c d e)\|c \|c x + b x +--R / +--R 3 +-+ +--R 8c e \|c +--R , +--R +--R +--------------+ +--R | 2 +---+ +--R (4A c e - 4B c d)\|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R +----------+ +--R 2 2 +---+ | 2 +--R (2B c e x + (4A c + B b)e - 4B c d e)\|- c \|c x + b x +--R / +--R 3 +---+ +--R 4c e \|- c +--R , +--R +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 d\|c x + b x +--R (8A c e - 8B c d)\|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R +----------+ +--R 2 2 +---+ | 2 +--R (2B c e x + (4A c + B b)e - 4B c d e)\|- c \|c x + b x +--R / +--R 3 +---+ +--R 4c e \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 326 + +--S 327 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R | 2 +-+ +--R (8A c e - 8B c d)\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 2 2 +--R ((- 8A b c + 2B b )e + (16A c + 8B b c)d e - 16B c d ) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ +--R (8A c e - 8B c d)\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 3 +-+ +--R 8c e \|c +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 2 2 +--R ((- 8A b c + 2B b )e + (16A c + 8B b c)d e - 16B c d ) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ +--R (8A c e - 8B c d)\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R (16A c e - 16B c d)\|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 3 +-+ +--R 8c e \|c +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1457 +r0:=-(4*B*c*d-b*B*e-2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^3*sqrt(c))+_ + 1/2*(B*d*(4*c*d-3*b*e)-A*e*(2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^3*sqrt(d)*sqrt(c*d-b*e))+_ + (2*B*d-A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)) +--R +--R +--R (2) +--R 2 2 +--R (((4A c + 2B b)e - 8B c d e)x + (4A c + 2B b)d e - 8B c d ) +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 2 2 +--R (- A b e + (2A c + 3B b)d e - 4B c d e)x - A b d e +--R + +--R 2 3 +--R (2A c + 3B b)d e - 4B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R 2 2 +-----------+ +-+ +-+ | 2 +--R (2B e x - 2A e + 4B d e)\|- b e + c d \|c \|d \|c x + b x +--R / +--R 4 3 +-----------+ +-+ +-+ +--R (2e x + 2d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (((2A c + B b)e - 4B c d e)x + (2A c + B b)d e - 4B c d ) +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +-+ +--R \|- b d e + c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 2 2 2 +--R (A b e + (- 2A c - 3B b)d e + 4B c d e)x + A b d e +--R + +--R 2 3 +--R (- 2A c - 3B b)d e + 4B c d +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +----------+ +--R 2 2 | 2 +-+ | 2 +--R (2B e x - 2A e + 4B d e)\|- b d e + c d \|c \|c x + b x +--R / +--R +--------------+ +--R 4 3 | 2 +-+ +--R (2e x + 2d e )\|- b d e + c d \|c +--R , +--R +--R 2 2 +--R (((2A c + B b)e - 4B c d e)x + (2A c + B b)d e - 4B c d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +-+ +--R \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 2 2 2 +--R (- 2A b e + (4A c + 6B b)d e - 8B c d e)x - 2A b d e +--R + +--R 2 3 +--R (4A c + 6B b)d e - 8B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-+ \|b d e - c d \|c x + b x +--R \|c atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +----------+ +--R 2 2 +-+ | 2 | 2 +--R (2B e x - 2A e + 4B d e)\|c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 4 3 +-+ | 2 +--R (2e x + 2d e )\|c \|b d e - c d +--R , +--R +--R 3 2 2 2 +--R (A b e + (- 2A c - 3B b)d e + 4B c d e)x + A b d e +--R + +--R 2 3 +--R (- 2A c - 3B b)d e + 4B c d +--R * +--R +---+ +--R \|- c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 2 +--R (((4A c + 2B b)e - 8B c d e)x + (4A c + 2B b)d e - 8B c d ) +--R * +--R +----------+ +--R +--------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|- b d e + c d atan(-------------------) +--R c x +--R + +--R +--------------+ +----------+ +--R 2 2 | 2 +---+ | 2 +--R (2B e x - 2A e + 4B d e)\|- b d e + c d \|- c \|c x + b x +--R / +--R +--------------+ +--R 4 3 | 2 +---+ +--R (2e x + 2d e )\|- b d e + c d \|- c +--R , +--R +--R 3 2 2 2 +--R (- A b e + (2A c + 3B b)d e - 4B c d e)x - A b d e +--R + +--R 2 3 +--R (2A c + 3B b)d e - 4B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +---+ \|b d e - c d \|c x + b x +--R \|- c atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 2 +--R (((2A c + B b)e - 4B c d e)x + (2A c + B b)d e - 4B c d ) +--R * +--R +----------+ +--R +------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|b d e - c d atan(-------------------) +--R c x +--R + +--R +------------+ +----------+ +--R 2 2 +---+ | 2 | 2 +--R (B e x - A e + 2B d e)\|- c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 4 3 +---+ | 2 +--R (e x + d e )\|- c \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 333 + +--S 334 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R | 2 +-----------+ +-+ +--R ((2A c + B b)e - 4B c d)\|- b d e + c d \|- b e + c d \|d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 +-----------+ +-+ +-+ +--R (A b e + (- 2A c - 3B b)d e + 4B c d )\|- b e + c d \|c \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R | 2 +-----------+ +-+ +--R ((- 4A c - 2B b)e + 8B c d)\|- b d e + c d \|- b e + c d \|d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +--------------+ +--R 2 2 | 2 +-+ +--R (A b e + (- 2A c - 3B b)d e + 4B c d )\|- b d e + c d \|c +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 | 2 +-----------+ +-+ +-+ +--R 2e \|- b d e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R +-----------+ +-+ | 2 +--R ((2A c + B b)e - 4B c d)\|- b e + c d \|d \|b d e - c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +------------+ +--R +-----------+ +-+ | 2 +--R ((- 4A c - 2B b)e + 8B c d)\|- b e + c d \|d \|b d e - c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +------------+ +--R 2 2 +-+ | 2 +--R (A b e + (- 2A c - 3B b)d e + 4B c d )\|c \|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +-+ +--R (- 2A b e + (4A c + 6B b)d e - 8B c d )\|- b e + c d \|c \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 3 +-----------+ +-+ +-+ | 2 +--R 2e \|- b e + c d \|c \|d \|b d e - c d +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 337 + +)clear all + +--S 338 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 338 + +--S 339 of 1457 +r0:=1/2*(B*d-A*e)*(b*x+c*x^2)^(3/2)/(d*(c*d-b*e)*(d+e*x)^2)-1/8*(A*b^2*e^3+_ + B*d*(8*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*e^3*(c*d-b*e)^(3/2))+_ + 2*B*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^3+1/4*(A*b*e^2-B*d*_ + (4*c*d-3*b*e)-2*c*e*(B*d-A*e)*x)*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 3 +--R (16B b d e - 16B c d e )x + (32B b d e - 32B c d e)x + 16B b d e +--R + +--R 4 +--R - 16B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 4 2 3 2 3 2 2 +--R (- A b e - 3B b d e + 12B b c d e - 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (- 2A b d e - 6B b d e + 24B b c d e - 16B c d e)x - A b d e +--R + +--R 2 3 2 4 2 5 +--R - 3B b d e + 12B b c d e - 8B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 3 2 2 3 +--R (2A b e + (- 4A c - 10B b)d e + 12B c d e )x - 2A b d e +--R + +--R 2 2 3 +--R - 6B b d e + 8B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((8b d e - 8c d e )x + (16b d e - 16c d e )x + 8b d e - 8c d e ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 2 3 3 +--R (8B b d e - 8B c d e )x + (16B b d e - 16B c d e)x + 8B b d e +--R + +--R 4 +--R - 8B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R \|- b d e + c d \|c log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 5 2 4 2 3 2 3 2 2 +--R (A b e + 3B b d e - 12B b c d e + 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (2A b d e + 6B b d e - 24B b c d e + 16B c d e)x + A b d e +--R + +--R 2 3 2 4 2 5 +--R 3B b d e - 12B b c d e + 8B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 3 2 2 3 +--R (2A b e + (- 4A c - 10B b)d e + 12B c d e )x - 2A b d e +--R + +--R 2 2 3 +--R - 6B b d e + 8B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((8b d e - 8c d e )x + (16b d e - 16c d e )x + 8b d e - 8c d e ) +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 3 2 2 2 2 2 3 3 +--R (4B b d e - 4B c d e )x + (8B b d e - 8B c d e)x + 4B b d e +--R + +--R 4 +--R - 4B c d +--R * +--R +------------+ +----------+ +--R +-+ | 2 +-+ | 2 +--R \|c \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 5 2 4 2 3 2 3 2 2 +--R (- A b e - 3B b d e + 12B b c d e - 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (- 2A b d e - 6B b d e + 24B b c d e - 16B c d e)x - A b d e +--R + +--R 2 3 2 4 2 5 +--R - 3B b d e + 12B b c d e - 8B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 4 3 2 2 3 2 2 +--R (A b e + (- 2A c - 5B b)d e + 6B c d e )x - A b d e - 3B b d e +--R + +--R 3 +--R 4B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((4b d e - 4c d e )x + (8b d e - 8c d e )x + 4b d e - 4c d e ) +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R , +--R +--R 2 5 2 4 2 3 2 3 2 2 +--R (A b e + 3B b d e - 12B b c d e + 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (2A b d e + 6B b d e - 24B b c d e + 16B c d e)x + A b d e +--R + +--R 2 3 2 4 2 5 +--R 3B b d e - 12B b c d e + 8B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 2 2 2 2 2 3 3 +--R (16B b d e - 16B c d e )x + (32B b d e - 32B c d e)x + 16B b d e +--R + +--R 4 +--R - 16B c d +--R * +--R +----------+ +--R +--------------+ | 2 +--R | 2 +---+ \|c x + b x +--R \|- b d e + c d \|- c atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 4 3 2 2 3 +--R (2A b e + (- 4A c - 10B b)d e + 12B c d e )x - 2A b d e +--R + +--R 2 2 3 +--R - 6B b d e + 8B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((8b d e - 8c d e )x + (16b d e - 16c d e )x + 8b d e - 8c d e ) +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 5 2 4 2 3 2 3 2 2 +--R (- A b e - 3B b d e + 12B b c d e - 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (- 2A b d e - 6B b d e + 24B b c d e - 16B c d e)x - A b d e +--R + +--R 2 3 2 4 2 5 +--R - 3B b d e + 12B b c d e - 8B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 2 2 2 2 2 3 3 +--R (8B b d e - 8B c d e )x + (16B b d e - 16B c d e)x + 8B b d e +--R + +--R 4 +--R - 8B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 \|c x + b x +--R \|- c \|b d e - c d atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 4 3 2 2 3 2 2 +--R (A b e + (- 2A c - 5B b)d e + 6B c d e )x - A b d e - 3B b d e +--R + +--R 3 +--R 4B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((4b d e - 4c d e )x + (8b d e - 8c d e )x + 4b d e - 4c d e ) +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 340 + +--S 341 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +-+ +--R (8B b d e - 8B c d )\|- b d e + c d \|- b e + c d \|c \|d +--R * +--R +----------+ +--R +-+ | 2 +--R log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 3 2 2 2 2 3 +-----------+ +-+ +--R (A b e + 3B b d e - 12B b c d e + 8B c d )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +-+ +--R (- 16B b d e + 16B c d )\|- b d e + c d \|- b e + c d \|c \|d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +--------------+ +--R 2 3 2 2 2 2 3 | 2 +--R (A b e + 3B b d e - 12B b c d e + 8B c d )\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 4 2 3 | 2 +-----------+ +-+ +--R (8b d e - 8c d e )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 2 +-----------+ +-+ +-+ | 2 +--R (8B b d e - 8B c d )\|- b e + c d \|c \|d \|b d e - c d +--R * +--R +----------+ +--R +-+ | 2 +--R log(2\|c \|c x + b x + 2c x + b) +--R + +--R +------------+ +--R 2 +-----------+ +-+ +-+ | 2 +--R (- 16B b d e + 16B c d )\|- b e + c d \|c \|d \|b d e - c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +------------+ +--R 2 3 2 2 2 2 3 | 2 +--R (A b e + 3B b d e - 12B b c d e + 8B c d )\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 2 3 +-----------+ +-+ +--R (- 2A b e - 6B b d e + 24B b c d e - 16B c d )\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 4 2 3 +-----------+ +-+ | 2 +--R (8b d e - 8c d e )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 344 + +)clear all + +--S 345 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 345 + +--S 346 of 1457 +r0:=1/16*b^2*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+1/12*(B*_ + d*(4*c*d-5*b*e)+A*e*(2*c*d-b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*_ + (d+e*x)^2)+1/24*(B*d*(8*c^2*d^2-14*b*c*d*e+3*b^2*e^2)+A*e*(4*c^2*_ + d^2-4*b*c*d*e+3*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*_ + (d+e*x))-1/3*(2*B*d+A*e+3*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)^3) +--R +--R +--R (2) +--R 3 4 2 3 3 3 +--R (- 3A b e + (6A b c - 3B b )d e )x +--R + +--R 3 3 2 3 2 2 2 +--R (- 9A b d e + (18A b c - 9B b )d e )x +--R + +--R 3 2 2 2 3 3 3 3 2 3 4 +--R (- 9A b d e + (18A b c - 9B b )d e)x - 3A b d e + (6A b c - 3B b )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 2 +--R 6A b e + (- 8A b c + 6B b )d e + (8A c - 28B b c)d e +--R + +--R 2 3 +--R 16B c d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 +--R (16A b d e + (- 28A b c - 16B b )d e + (24A c + 4B b c)d )x +--R + +--R 2 2 2 3 +--R - 6A b d e + (12A b c - 6B b )d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (48b d e - 96b c d e + 48c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (144b d e - 288b c d e + 144c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (144b d e - 288b c d e + 144c d e)x + 48b d e - 96b c d e + 48c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 3 3 3 +--R (3A b e + (- 6A b c + 3B b )d e )x +--R + +--R 3 3 2 3 2 2 2 +--R (9A b d e + (- 18A b c + 9B b )d e )x +--R + +--R 3 2 2 2 3 3 3 3 +--R (9A b d e + (- 18A b c + 9B b )d e)x + 3A b d e +--R + +--R 2 3 4 +--R (- 6A b c + 3B b )d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 2 2 2 2 +--R 6A b e + (- 8A b c + 6B b )d e + (8A c - 28B b c)d e +--R + +--R 2 3 +--R 16B c d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 +--R (16A b d e + (- 28A b c - 16B b )d e + (24A c + 4B b c)d )x +--R + +--R 2 2 2 3 +--R - 6A b d e + (12A b c - 6B b )d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (48b d e - 96b c d e + 48c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (144b d e - 288b c d e + 144c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (144b d e - 288b c d e + 144c d e)x + 48b d e - 96b c d e + 48c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 3 4 2 3 3 3 +--R (- 3A b e + (6A b c - 3B b )d e )x +--R + +--R 3 3 2 3 2 2 2 +--R (- 9A b d e + (18A b c - 9B b )d e )x +--R + +--R 3 2 2 2 3 3 3 3 2 3 4 +--R (- 9A b d e + (18A b c - 9B b )d e)x - 3A b d e + (6A b c - 3B b )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 3 2 2 2 2 +--R 3A b e + (- 4A b c + 3B b )d e + (4A c - 14B b c)d e +--R + +--R 2 3 +--R 8B c d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 +--R (8A b d e + (- 14A b c - 8B b )d e + (12A c + 2B b c)d )x +--R + +--R 2 2 2 3 +--R - 3A b d e + (6A b c - 3B b )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (24b d e - 48b c d e + 24c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (72b d e - 144b c d e + 72c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (72b d e - 144b c d e + 72c d e)x + 24b d e - 48b c d e + 24c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 347 + +--S 348 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 3 +-----------+ +-+ +--R (A b e + (- 2A b c + B b )d)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 3 2 3 | 2 +--R (A b e + (- 2A b c + B b )d)\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (16b d e - 32b c d e + 16c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 348 + +--S 349 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 3 2 3 | 2 +--R (A b e + (- 2A b c + B b )d)\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 3 +-----------+ +-+ +--R (- 2A b e + (4A b c - 2B b )d)\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (16b d e - 32b c d e + 16c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1457 +r0:=-1/128*b^2*(16*A*c^2*d^2-8*b*c*d*(B*d+2*A*e)+b^2*e*(3*B*d+5*A*e))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+1/24*(B*d*(2*c*d-3*b*e)+A*e*(2*c*d-_ + b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)^3)+1/96*(B*d*_ + (8*c^2*d^2-16*b*c*d*e+3*b^2*e^2)+A*e*(8*c^2*d^2-8*b*c*d*e+_ + 5*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*(d+e*x)^2)+_ + 1/192*(A*e*(16*c^3*d^3-24*b*c^2*d^2*e+38*b^2*c*d*e^2-15*b^3*e^3)+_ + B*d*(16*c^3*d^3-40*b*c^2*d^2*e+18*b^2*c*d*e^2-9*b^3*e^3))*_ + sqrt(b*x+c*x^2)/(d^3*e^2*(c*d-b*e)^3*(d+e*x))-1/4*(B*d+A*e+_ + 2*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)^4) +--R +--R +--R (2) +--R 4 6 3 4 5 2 2 3 2 4 4 +--R (- 15A b e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d e )x +--R + +--R 4 5 3 4 2 4 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 3 3 +--R (- 192A b c + 96B b c)d e +--R * +--R 3 +--R x +--R + +--R 4 2 4 3 4 3 3 +--R - 90A b d e + (288A b c - 54B b )d e +--R + +--R 2 2 3 4 2 +--R (- 288A b c + 144B b c)d e +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 2 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 5 +--R (- 192A b c + 96B b c)d e +--R * +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 +--R - 15A b d e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 5 2 3 4 2 2 2 3 +--R 30A b e + (- 76A b c + 18B b )d e + (48A b c - 36B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 32A c + 80B b c )d e - 32B c d e +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 3 +--R 110A b d e + (- 280A b c + 66B b )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (208A b c - 184B b c)d e + (- 128A c + 336B b c )d e - 128B c d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 3 2 +--R 146A b d e + (- 396A b c - 66B b )d e +--R + +--R 2 2 4 3 2 5 +--R (352A b c + 188B b c)d e + (- 192A c - 32B b c )d +--R * +--R x +--R + +--R 3 3 2 2 3 4 2 2 5 +--R - 30A b d e + (96A b c - 18B b )d e + (- 96A b c + 48B b c)d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (384b d e - 1152b c d e + 1152b c d e - 384c d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (2304b d e - 6912b c d e + 6912b c d e - 2304c d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e)x + 384b d e +--R + +--R 2 8 2 2 9 3 10 +--R - 1152b c d e + 1152b c d e - 384c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 6 3 4 5 2 2 3 2 4 4 +--R (15A b e + (- 48A b c + 9B b )d e + (48A b c - 24B b c)d e )x +--R + +--R 4 5 3 4 2 4 +--R 60A b d e + (- 192A b c + 36B b )d e +--R + +--R 2 2 3 3 3 +--R (192A b c - 96B b c)d e +--R * +--R 3 +--R x +--R + +--R 4 2 4 3 4 3 3 +--R 90A b d e + (- 288A b c + 54B b )d e +--R + +--R 2 2 3 4 2 +--R (288A b c - 144B b c)d e +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 2 +--R 60A b d e + (- 192A b c + 36B b )d e +--R + +--R 2 2 3 5 +--R (192A b c - 96B b c)d e +--R * +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 +--R 15A b d e + (- 48A b c + 9B b )d e + (48A b c - 24B b c)d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 5 2 3 4 2 2 2 3 +--R 30A b e + (- 76A b c + 18B b )d e + (48A b c - 36B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 32A c + 80B b c )d e - 32B c d e +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 3 +--R 110A b d e + (- 280A b c + 66B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (208A b c - 184B b c)d e + (- 128A c + 336B b c )d e +--R + +--R 3 5 +--R - 128B c d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 3 2 +--R 146A b d e + (- 396A b c - 66B b )d e +--R + +--R 2 2 4 3 2 5 +--R (352A b c + 188B b c)d e + (- 192A c - 32B b c )d +--R * +--R x +--R + +--R 3 3 2 2 3 4 2 2 5 +--R - 30A b d e + (96A b c - 18B b )d e + (- 96A b c + 48B b c)d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (384b d e - 1152b c d e + 1152b c d e - 384c d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (2304b d e - 6912b c d e + 6912b c d e - 2304c d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e)x + 384b d e +--R + +--R 2 8 2 2 9 3 10 +--R - 1152b c d e + 1152b c d e - 384c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 4 6 3 4 5 2 2 3 2 4 4 +--R (- 15A b e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d e )x +--R + +--R 4 5 3 4 2 4 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 3 3 +--R (- 192A b c + 96B b c)d e +--R * +--R 3 +--R x +--R + +--R 4 2 4 3 4 3 3 +--R - 90A b d e + (288A b c - 54B b )d e +--R + +--R 2 2 3 4 2 +--R (- 288A b c + 144B b c)d e +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 2 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 5 +--R (- 192A b c + 96B b c)d e +--R * +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 +--R - 15A b d e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 5 2 3 4 2 2 2 3 +--R 15A b e + (- 38A b c + 9B b )d e + (24A b c - 18B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 16A c + 40B b c )d e - 16B c d e +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 3 +--R 55A b d e + (- 140A b c + 33B b )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (104A b c - 92B b c)d e + (- 64A c + 168B b c )d e - 64B c d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 3 2 +--R 73A b d e + (- 198A b c - 33B b )d e +--R + +--R 2 2 4 3 2 5 +--R (176A b c + 94B b c)d e + (- 96A c - 16B b c )d +--R * +--R x +--R + +--R 3 3 2 2 3 4 2 2 5 +--R - 15A b d e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (192b d e - 576b c d e + 576b c d e - 192c d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (768b d e - 2304b c d e + 2304b c d e - 768c d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (1152b d e - 3456b c d e + 3456b c d e - 1152c d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (768b d e - 2304b c d e + 2304b c d e - 768c d e)x + 192b d e +--R + +--R 2 8 2 2 9 3 10 +--R - 576b c d e + 576b c d e - 192c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 354 + +--S 355 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 2 3 4 2 2 3 2 +--R (5A b e + (- 16A b c + 3B b )d e + (16A b c - 8B b c)d ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 2 3 4 2 2 3 2 +--R (5A b e + (- 16A b c + 3B b )d e + (16A b c - 8B b c)d ) +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +--R (128b d e - 384b c d e + 384b c d e - 128c d )\|- b d e + c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 355 + +--S 356 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 2 3 4 2 2 3 2 +--R (5A b e + (- 16A b c + 3B b )d e + (16A b c - 8B b c)d ) +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 2 3 4 2 2 3 2 +--R (- 10A b e + (32A b c - 6B b )d e + (- 32A b c + 16B b c)d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ +--R (128b d e - 384b c d e + 384b c d e - 128c d )\|- b e + c d \|d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 358 + +)clear all + +--S 359 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1457 +r0:=1/192*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+_ + 2*A*e))*x*(b*x+c*x^2)^(3/2)/c^3+1/840*(98*A*c*e*(2*c*d-b*e)+B*(48*_ + c^2*d^2-146*b*c*d*e+63*b^2*e^2))*(b*x+c*x^2)^(5/2)/c^3+1/7*B*_ + (d+e*x)^2*(b*x+c*x^2)^(5/2)/c-1/84*e*((5*b*B-14*A*c)*d-(4*B*c*d-_ + 9*b*B*e+14*A*c*e)*x)*(b*x+c*x^2)^(5/2)/c^2+1/1024*b^4*(48*A*c^3*d^2-_ + 9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)-1/1024*b^3*(48*A*c^3*d^2-_ + 9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*sqrt(b*x+_ + c*x^2)/c^5+1/1536*b^2*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+_ + A*e)-24*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^4+1/384*b*_ + (48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+_ + 2*A*e))*x^2*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 6 7 2 5 2 6 +--R (1470A b c - 945B b )e + (- 5040A b c + 2940B b c)d e +--R + +--R 4 3 5 2 2 +--R (5040A b c - 2520B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 2 6 6 5 2 6 5 +--R 15360B c e x + ((17920A c + 19200B b c )e + 35840B c d e)x +--R + +--R 5 2 4 2 6 5 +--R (23296A b c + 384B b c )e + (43008A c + 46592B b c )d e +--R + +--R 6 2 +--R 21504B c d +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 2 5 2 4 +--R (672A b c - 432B b c )e + (59136A b c + 1344B b c )d e +--R + +--R 6 5 2 +--R (26880A c + 29568B b c )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 784A b c + 504B b c )e + (2688A b c - 1568B b c )d e +--R + +--R 5 2 4 2 +--R (40320A b c + 1344B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (980A b c - 630B b c)e + (- 3360A b c + 1960B b c )d e +--R + +--R 2 4 3 3 2 +--R (3360A b c - 1680B b c )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 1470A b c + 945B b )e + (5040A b c - 2940B b c)d e +--R + +--R 3 3 4 2 2 +--R (- 5040A b c + 2520B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 107520c \|c +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 7 2 5 2 6 +--R (1470A b c - 945B b )e + (- 5040A b c + 2940B b c)d e +--R + +--R 4 3 5 2 2 +--R (5040A b c - 2520B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 6 2 6 6 5 2 6 5 +--R 30720B c e x + ((35840A c + 38400B b c )e + 71680B c d e)x +--R + +--R 5 2 4 2 6 5 +--R (46592A b c + 768B b c )e + (86016A c + 93184B b c )d e +--R + +--R 6 2 +--R 43008B c d +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 2 5 2 4 +--R (1344A b c - 864B b c )e + (118272A b c + 2688B b c )d e +--R + +--R 6 5 2 +--R (53760A c + 59136B b c )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 1568A b c + 1008B b c )e + (5376A b c - 3136B b c )d e +--R + +--R 5 2 4 2 +--R (80640A b c + 2688B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (1960A b c - 1260B b c)e + (- 6720A b c + 3920B b c )d e +--R + +--R 2 4 3 3 2 +--R (6720A b c - 3360B b c )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 2940A b c + 1890B b )e + (10080A b c - 5880B b c)d e +--R + +--R 3 3 4 2 2 +--R (- 10080A b c + 5040B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 215040c \|c +--R , +--R +--R 6 7 2 5 2 6 +--R (1470A b c - 945B b )e + (- 5040A b c + 2940B b c)d e +--R + +--R 4 3 5 2 2 +--R (5040A b c - 2520B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 6 2 6 6 5 2 6 5 +--R 15360B c e x + ((17920A c + 19200B b c )e + 35840B c d e)x +--R + +--R 5 2 4 2 6 5 +--R (23296A b c + 384B b c )e + (43008A c + 46592B b c )d e +--R + +--R 6 2 +--R 21504B c d +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 2 5 2 4 +--R (672A b c - 432B b c )e + (59136A b c + 1344B b c )d e +--R + +--R 6 5 2 +--R (26880A c + 29568B b c )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 784A b c + 504B b c )e + (2688A b c - 1568B b c )d e +--R + +--R 5 2 4 2 +--R (40320A b c + 1344B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (980A b c - 630B b c)e + (- 3360A b c + 1960B b c )d e +--R + +--R 2 4 3 3 2 +--R (3360A b c - 1680B b c )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 1470A b c + 945B b )e + (5040A b c - 2940B b c)d e +--R + +--R 3 3 4 2 2 +--R (- 5040A b c + 2520B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 5 +---+ +--R 107520c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 361 + +--S 362 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 6 7 2 5 2 6 +--R (14A b c - 9B b )e + (- 48A b c + 28B b c)d e +--R + +--R 4 3 5 2 2 +--R (48A b c - 24B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 6 7 2 5 2 6 +--R (- 28A b c + 18B b )e + (96A b c - 56B b c)d e +--R + +--R 4 3 5 2 2 +--R (- 96A b c + 48B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 5 +-+ +--R 2048c \|c +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 7 2 5 2 6 +--R (- 14A b c + 9B b )e + (48A b c - 28B b c)d e +--R + +--R 4 3 5 2 2 +--R (- 48A b c + 24B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 7 2 5 2 6 +--R (14A b c - 9B b )e + (- 48A b c + 28B b c)d e +--R + +--R 4 3 5 2 2 +--R (48A b c - 24B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 5 +---+ +-+ +--R 1024c \|- c \|c +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 1457 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 4 3 2 +--R (B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x) +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1457 +r0:=1/96*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x*(b*x+c*x^2)^(3/2)/c^2+_ + 1/60*(2*B*c*d-7*b*B*e+12*A*c*e)*(b*x+c*x^2)^(5/2)/c^2+1/6*B*(d+e*x)*_ + (b*x+c*x^2)^(5/2)/c+1/512*b^4*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+_ + A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-1/512*b^3*_ + (24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^4+_ + 1/768*b^2*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x*sqrt(b*x+_ + c*x^2)/c^3+1/192*b*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x^2*_ + sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 5 6 4 2 5 x\|c +--R ((- 180A b c + 105B b )e + (360A b c - 180B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 5 5 4 5 4 +--R 1280B c e x + ((1536A c + 1664B b c )e + 1536B c d)x +--R + +--R 4 2 3 5 4 3 +--R ((2112A b c + 48B b c )e + (1920A c + 2112B b c )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((96A b c - 56B b c )e + (2880A b c + 96B b c )d)x +--R + +--R 3 2 4 2 3 3 2 +--R ((- 120A b c + 70B b c)e + (240A b c - 120B b c )d)x +--R + +--R 4 5 3 2 4 +--R (180A b c - 105B b )e + (- 360A b c + 180B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 6 4 2 5 +--R ((180A b c - 105B b )e + (- 360A b c + 180B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 5 5 5 4 5 4 +--R 2560B c e x + ((3072A c + 3328B b c )e + 3072B c d)x +--R + +--R 4 2 3 5 4 3 +--R ((4224A b c + 96B b c )e + (3840A c + 4224B b c )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((192A b c - 112B b c )e + (5760A b c + 192B b c )d)x +--R + +--R 3 2 4 2 3 3 2 +--R ((- 240A b c + 140B b c)e + (480A b c - 240B b c )d)x +--R + +--R 4 5 3 2 4 +--R (360A b c - 210B b )e + (- 720A b c + 360B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 15360c \|c +--R , +--R +--R 5 6 4 2 5 +--R ((- 180A b c + 105B b )e + (360A b c - 180B b c)d) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 5 5 5 4 5 4 +--R 1280B c e x + ((1536A c + 1664B b c )e + 1536B c d)x +--R + +--R 4 2 3 5 4 3 +--R ((2112A b c + 48B b c )e + (1920A c + 2112B b c )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((96A b c - 56B b c )e + (2880A b c + 96B b c )d)x +--R + +--R 3 2 4 2 3 3 2 +--R ((- 120A b c + 70B b c)e + (240A b c - 120B b c )d)x +--R + +--R 4 5 3 2 4 +--R (180A b c - 105B b )e + (- 360A b c + 180B b c)d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 7680c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 368 + +--S 369 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 6 4 2 5 +--R ((12A b c - 7B b )e + (- 24A b c + 12B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 5 6 4 2 5 x\|c +--R ((24A b c - 14B b )e + (- 48A b c + 24B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 1024c \|c +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 5 6 4 2 5 +---+ x\|c +--R ((12A b c - 7B b )e + (- 24A b c + 12B b c)d)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 5 6 4 2 5 +-+ \|- c \|c x + b x +--R ((- 12A b c + 7B b )e + (24A b c - 12B b c)d)\|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 512c \|- c \|c +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (1) (B c x + (A c + B b)x + A b x)\|c x + b x +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1457 +r0:=-1/8*(b*B-2*A*c)*x*(b*x+c*x^2)^(3/2)/c+1/5*B*(b*x+c*x^2)^(5/2)/c-_ + 3/128*b^4*(b*B-2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+_ + 3/128*b^3*(b*B-2*A*c)*sqrt(b*x+c*x^2)/c^3-1/64*b^2*(b*B-2*A*c)*x*_ + sqrt(b*x+c*x^2)/c^2-1/16*b*(b*B-2*A*c)*x^2*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 4 5 x\|c +--R (30A b c - 15B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 4 4 3 3 3 2 2 2 +--R 128B c x + (160A c + 176B b c )x + (240A b c + 8B b c )x +--R + +--R 2 2 3 3 4 +--R (20A b c - 10B b c)x - 30A b c + 15B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 640c \|c +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 4 5 | 2 +-+ +--R (30A b c - 15B b )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 4 4 3 3 3 2 2 2 +--R 256B c x + (320A c + 352B b c )x + (480A b c + 16B b c )x +--R + +--R 2 2 3 3 4 +--R (40A b c - 20B b c)x - 60A b c + 30B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 1280c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 4 5 \|- c \|c x + b x +--R (30A b c - 15B b )atan(-------------------) +--R c x +--R + +--R 4 4 4 3 3 3 2 2 2 +--R 128B c x + (160A c + 176B b c )x + (240A b c + 8B b c )x +--R + +--R 2 2 3 3 4 +--R (20A b c - 10B b c)x - 30A b c + 15B b +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 3 +---+ +--R 640c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 375 + +--S 376 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 4 5 | 2 +-+ +--R (6A b c - 3B b )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 4 5 x\|c +--R (- 12A b c + 6B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 256c \|c +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 4 5 +---+ x\|c +--R (- 6A b c + 3B b )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 4 5 +-+ \|- c \|c x + b x +--R (6A b c - 3B b )\|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 128c \|- c \|c +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 379 + +)clear all + +--S 380 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1457 +r0:=-1/24*(8*B*c*d-3*b*B*e-8*A*c*e-6*B*c*e*x)*(b*x+c*x^2)^(3/2)/(c*e^2)-_ + 1/64*(8*A*c*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3)-_ + B*(128*c^4*d^4-192*b*c^3*d^3*e+48*b^2*c^2*d^2*e^2+8*b^3*c*d*e^3+_ + 3*b^4*e^4))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^5)-d^(3/2)*_ + (B*d-A*e)*(c*d-b*e)^(3/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^5+1/64*(8*A*c*e*(8*c^2*d^2-_ + 10*b*c*d*e+b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+8*b^2*c*d*e^2+_ + 3*b^3*e^3)-2*c*e*(8*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-8*b*c*d*e-_ + 3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^4) +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 +--R (- 24A b c + 9B b )e + (- 144A b c + 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (576A b c + 144B b c )d e + (- 384A c - 576B b c )d e + 384B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 2 2 3 3 +-----------+ +--R (192A b c d e + (- 192A c - 192B b c )d e + 192B c d )\|- b e + c d +--R * +--R +-+ +-+ (b e - 2c d)x - b d +--R \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 48B c e x + ((64A c + 72B b c )e - 64B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 +--R ((112A b c + 6B b c)e + (- 96A c - 112B b c )d e + 96B c d e )x +--R + +--R 2 3 4 2 2 3 +--R (24A b c - 9B b )e + (- 240A b c - 24B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (192A c + 240B b c )d e - 192B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 5 +-+ +--R 192c e \|c +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 3 3 +--R (- 384A b c d e + (384A c + 384B b c )d e - 384B c d ) +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 3 4 4 2 2 3 3 +--R (24A b c - 9B b )e + (144A b c - 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 576A b c - 144B b c )d e + (384A c + 576B b c )d e - 384B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 96B c e x + ((128A c + 144B b c )e - 128B c d e )x +--R + +--R 2 2 4 3 2 3 +--R (224A b c + 12B b c)e + (- 192A c - 224B b c )d e +--R + +--R 3 2 2 +--R 192B c d e +--R * +--R x +--R + +--R 2 3 4 2 2 3 +--R (48A b c - 18B b )e + (- 480A b c - 48B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (384A c + 480B b c )d e - 384B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 5 +-+ +--R 384c e \|c +--R , +--R +--R 3 4 4 2 2 3 3 +--R (24A b c - 9B b )e + (144A b c - 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 576A b c - 144B b c )d e + (384A c + 576B b c )d e - 384B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 3 2 2 3 3 +-+ +--R (- 768A b c d e + (768A c + 768B b c )d e - 768B c d )\|c +--R * +--R +----------+ +--R +------------+ | 2 +--R | 2 d\|c x + b x +--R \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 96B c e x + ((128A c + 144B b c )e - 128B c d e )x +--R + +--R 2 2 4 3 2 3 +--R (224A b c + 12B b c)e + (- 192A c - 224B b c )d e +--R + +--R 3 2 2 +--R 192B c d e +--R * +--R x +--R + +--R 2 3 4 2 2 3 +--R (48A b c - 18B b )e + (- 480A b c - 48B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (384A c + 480B b c )d e - 384B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 5 +-+ +--R 384c e \|c +--R , +--R +--R 2 2 3 2 2 3 3 +--R (- 192A b c d e + (192A c + 192B b c )d e - 192B c d ) +--R * +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 3 4 4 2 2 3 3 +--R (- 24A b c + 9B b )e + (- 144A b c + 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (576A b c + 144B b c )d e + (- 384A c - 576B b c )d e + 384B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 48B c e x + ((64A c + 72B b c )e - 64B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 +--R ((112A b c + 6B b c)e + (- 96A c - 112B b c )d e + 96B c d e )x +--R + +--R 2 3 4 2 2 3 +--R (24A b c - 9B b )e + (- 240A b c - 24B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (192A c + 240B b c )d e - 192B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 2 5 +---+ +--R 192c e \|- c +--R , +--R +--R 3 4 4 2 2 3 3 +--R (- 24A b c + 9B b )e + (- 144A b c + 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (576A b c + 144B b c )d e + (- 384A c - 576B b c )d e + 384B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 2 3 2 2 3 3 +---+ +--R (- 384A b c d e + (384A c + 384B b c )d e - 384B c d )\|- c +--R * +--R +----------+ +--R +------------+ | 2 +--R | 2 d\|c x + b x +--R \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 48B c e x + ((64A c + 72B b c )e - 64B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 +--R ((112A b c + 6B b c)e + (- 96A c - 112B b c )d e + 96B c d e )x +--R + +--R 2 3 4 2 2 3 +--R (24A b c - 9B b )e + (- 240A b c - 24B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (192A c + 240B b c )d e - 192B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 2 5 +---+ +--R 192c e \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 382 + +--S 383 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 3 2 2 3 3 +--R (- 128A b c d e + (128A c + 128B b c )d e - 128B c d ) +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 3 4 4 2 2 3 3 +--R (8A b c - 3B b )e + (48A b c - 8B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 192A b c - 48B b c )d e + (128A c + 192B b c )d e - 128B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 4 2 2 3 3 +--R (16A b c - 6B b )e + (96A b c - 16B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 384A b c - 96B b c )d e + (256A c + 384B b c )d e - 256B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 2 2 3 3 +-----------+ +--R (- 128A b c d e + (128A c + 128B b c )d e - 128B c d )\|- b e + c d +--R * +--R +-+ +-+ (b e - 2c d)x - b d +--R \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 2 5 +-+ +--R 128c e \|c +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 4 2 2 3 3 +--R (8A b c - 3B b )e + (48A b c - 8B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 192A b c - 48B b c )d e + (128A c + 192B b c )d e - 128B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 4 2 2 3 3 +--R (16A b c - 6B b )e + (96A b c - 16B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 384A b c - 96B b c )d e + (256A c + 384B b c )d e - 256B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 2 2 3 3 +-----------+ +--R (- 128A b c d e + (128A c + 128B b c )d e - 128B c d )\|- b e + c d +--R * +--R +-+ +-+ (b e - 2c d)x - b d +--R \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 3 2 2 3 3 +-+ +--R (- 256A b c d e + (256A c + 256B b c )d e - 256B c d )\|c +--R * +--R +----------+ +--R +------------+ | 2 +--R | 2 d\|c x + b x +--R \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 2 5 +-+ +--R 128c e \|c +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 386 + +)clear all + +--S 387 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1457 +r0:=1/3*(4*B*d-3*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x))+1/8*(4*b*c*e*_ + (4*B*d-3*A*e)*(2*c*d-b*e)-(8*B*c*d-b*B*e-6*A*c*e)*(8*c^2*d^2-_ + 4*b*c*d*e-b^2*e^2))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^5)+_ + 1/2*(B*d*(8*c*d-5*b*e)-3*A*e*(2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-_ + b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-_ + b*e)/e^5-1/8*(6*A*c*e*(4*c*d-3*b*e)-B*(32*c^2*d^2-28*b*c*d*e+_ + b^2*e^2)+2*c*e*(8*B*c*d-b*B*e-6*A*c*e)*x)*sqrt(b*x+c*x^2)/(c*e^4) +--R +--R +--R (2) +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 2 2 2 2 +--R (- 36A b c e + (72A c + 60B b c)d e - 96B c d e)x - 36A b c d e +--R + +--R 2 2 2 3 +--R (72A c + 60B b c)d e - 96B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 4 3 2 4 2 3 2 +--R 8B c e x + ((12A c + 14B b c)e - 16B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((30A b c + 3B b )e + (- 36A c - 46B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (54A b c + 3B b )d e + (- 72A c - 84B b c)d e + 96B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 5 +-+ +--R (24c e x + 24c d e )\|c +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 +--R (72A b c e + (- 144A c - 120B b c)d e + 192B c d e)x +--R + +--R 2 2 2 2 3 +--R 72A b c d e + (- 144A c - 120B b c)d e + 192B c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 4 3 2 4 2 3 2 +--R 16B c e x + ((24A c + 28B b c)e - 32B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((60A b c + 6B b )e + (- 72A c - 92B b c)d e + 96B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (108A b c + 6B b )d e + (- 144A c - 168B b c)d e + 192B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 5 +-+ +--R (48c e x + 48c d e )\|c +--R , +--R +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 2 2 2 2 +--R (144A b c e + (- 288A c - 240B b c)d e + 384B c d e)x +--R + +--R 2 2 2 2 3 +--R 144A b c d e + (- 288A c - 240B b c)d e + 384B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 2 4 3 2 4 2 3 2 +--R 16B c e x + ((24A c + 28B b c)e - 32B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((60A b c + 6B b )e + (- 72A c - 92B b c)d e + 96B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (108A b c + 6B b )d e + (- 144A c - 168B b c)d e + 192B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 5 +-+ +--R (48c e x + 48c d e )\|c +--R , +--R +--R 3 2 2 2 2 2 +--R (36A b c e + (- 72A c - 60B b c)d e + 96B c d e)x + 36A b c d e +--R + +--R 2 2 2 3 +--R (- 72A c - 60B b c)d e + 96B c d +--R * +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 4 3 2 4 2 3 2 +--R 8B c e x + ((12A c + 14B b c)e - 16B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((30A b c + 3B b )e + (- 36A c - 46B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (54A b c + 3B b )d e + (- 72A c - 84B b c)d e + 96B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 6 5 +---+ +--R (24c e x + 24c d e )\|- c +--R , +--R +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 2 2 2 2 +--R (72A b c e + (- 144A c - 120B b c)d e + 192B c d e)x +--R + +--R 2 2 2 2 3 +--R 72A b c d e + (- 144A c - 120B b c)d e + 192B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 d\|c x + b x +--R \|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 2 4 3 2 4 2 3 2 +--R 8B c e x + ((12A c + 14B b c)e - 16B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((30A b c + 3B b )e + (- 36A c - 46B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (54A b c + 3B b )d e + (- 72A c - 84B b c)d e + 96B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 6 5 +---+ +--R (24c e x + 24c d e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 389 + +--S 390 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 2 2 | 2 +-+ +--R (24A b c e + (- 48A c - 40B b c)d e + 64B c d )\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 3 3 2 2 2 +--R (6A b c - B b )e + (- 48A b c - 12B b c)d e +--R + +--R 3 2 2 3 3 +--R (48A c + 72B b c )d e - 64B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 3 2 2 2 +--R (- 12A b c + 2B b )e + (96A b c + 24B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 96A c - 144B b c )d e + 128B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 +-----------+ +-+ +-+ +--R (24A b c e + (- 48A c - 40B b c)d e + 64B c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 5 +-+ +--R 16c e \|c +--R Type: Expression(Integer) +--E 390 + +--S 391 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 +--R (6A b c - B b )e + (- 48A b c - 12B b c)d e +--R + +--R 3 2 2 3 3 +--R (48A c + 72B b c )d e - 64B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 3 2 2 2 +--R (- 12A b c + 2B b )e + (96A b c + 24B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 96A c - 144B b c )d e + 128B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 +-----------+ +-+ +-+ +--R (24A b c e + (- 48A c - 40B b c)d e + 64B c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +--R 2 2 2 2 +-+ | 2 +--R (48A b c e + (- 96A c - 80B b c)d e + 128B c d )\|c \|b d e - c d +--R * +--R +----------+ +--R | 2 +--R d\|c x + b x +--R atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 5 +-+ +--R 16c e \|c +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1457 +r0:=1/2*(2*B*d-A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)-3/4*(4*A*c*e*_ + (2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+b^2*e^2))*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/(e^5*sqrt(c))+3/8*(A*e*(8*c^2*d^2-8*b*c*d*e+_ + b^2*e^2)-B*d*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2))*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^5*_ + sqrt(d)*sqrt(c*d-b*e))-3/4*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+_ + e*(4*B*c*d-b*B*e-2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 +--R ((24A b c + 6B b )e + (- 48A c - 72B b c)d e + 96B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((48A b c + 12B b )d e + (- 96A c - 144B b c)d e + 192B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 2 +--R 48B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 6A b d e + (48A b c + 30B b )d e + (- 48A c - 120B b c)d e +--R + +--R 2 4 +--R 96B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 3A b d e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 5 +--R 48B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 3 4 3 2 +--R 4B c e x + ((8A c + 10B b)e - 16B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 10A b e + (36A c + 38B b)d e - 72B c d e )x - 6A b d e +--R + +--R 2 2 3 +--R (24A c + 24B b)d e - 48B c d e +--R * +--R +----------+ +--R +-----------+ +-+ +-+ | 2 +--R \|- b e + c d \|c \|d \|c x + b x +--R / +--R 7 2 6 2 5 +-----------+ +-+ +-+ +--R (8e x + 16d e x + 8d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 395 + +--S 396 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 2 3 2 2 2 2 +--R ((12A b c + 3B b )e + (- 24A c - 36B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (12A b c + 3B b )d e + (- 24A c - 36B b c)d e + 48B c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +-+ +--R \|- b d e + c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 5 2 4 2 2 3 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 2 +--R 48B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 6A b d e + (48A b c + 30B b )d e +--R + +--R 2 3 2 2 4 +--R (- 48A c - 120B b c)d e + 96B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 3A b d e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 5 +--R 48B c d +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 3 4 3 2 +--R 4B c e x + ((8A c + 10B b)e - 16B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 10A b e + (36A c + 38B b)d e - 72B c d e )x - 6A b d e +--R + +--R 2 2 3 +--R (24A c + 24B b)d e - 48B c d e +--R * +--R +--------------+ +----------+ +--R | 2 +-+ | 2 +--R \|- b d e + c d \|c \|c x + b x +--R / +--R +--------------+ +--R 7 2 6 2 5 | 2 +-+ +--R (8e x + 16d e x + 8d e )\|- b d e + c d \|c +--R , +--R +--R 2 4 2 3 2 2 2 2 +--R ((12A b c + 3B b )e + (- 24A c - 36B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (12A b c + 3B b )d e + (- 24A c - 36B b c)d e + 48B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +-+ +--R \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 5 2 4 2 2 3 +--R - 6A b e + (48A b c + 30B b )d e + (- 48A c - 120B b c)d e +--R + +--R 2 3 2 +--R 96B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 12A b d e + (96A b c + 60B b )d e +--R + +--R 2 3 2 2 4 +--R (- 96A c - 240B b c)d e + 192B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 6A b d e + (48A b c + 30B b )d e + (- 48A c - 120B b c)d e +--R + +--R 2 5 +--R 96B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-+ \|b d e - c d \|c x + b x +--R \|c atan(----------------------------) +--R (b e - c d)x +--R + +--R 4 3 4 3 2 +--R 4B c e x + ((8A c + 10B b)e - 16B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 10A b e + (36A c + 38B b)d e - 72B c d e )x - 6A b d e +--R + +--R 2 2 3 +--R (24A c + 24B b)d e - 48B c d e +--R * +--R +------------+ +----------+ +--R +-+ | 2 | 2 +--R \|c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 7 2 6 2 5 +-+ | 2 +--R (8e x + 16d e x + 8d e )\|c \|b d e - c d +--R , +--R +--R 2 5 2 4 2 2 3 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 2 +--R 48B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 6A b d e + (48A b c + 30B b )d e +--R + +--R 2 3 2 2 4 +--R (- 48A c - 120B b c)d e + 96B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 3A b d e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 5 +--R 48B c d +--R * +--R +---+ +--R \|- c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 4 2 3 2 2 2 2 +--R ((24A b c + 6B b )e + (- 48A c - 72B b c)d e + 96B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((48A b c + 12B b )d e + (- 96A c - 144B b c)d e + 192B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d +--R * +--R +----------+ +--R +--------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|- b d e + c d atan(-------------------) +--R c x +--R + +--R 4 3 4 3 2 +--R 4B c e x + ((8A c + 10B b)e - 16B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 10A b e + (36A c + 38B b)d e - 72B c d e )x - 6A b d e +--R + +--R 2 2 3 +--R (24A c + 24B b)d e - 48B c d e +--R * +--R +--------------+ +----------+ +--R | 2 +---+ | 2 +--R \|- b d e + c d \|- c \|c x + b x +--R / +--R +--------------+ +--R 7 2 6 2 5 | 2 +---+ +--R (8e x + 16d e x + 8d e )\|- b d e + c d \|- c +--R , +--R +--R 2 5 2 4 2 2 3 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 2 +--R 48B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 6A b d e + (48A b c + 30B b )d e +--R + +--R 2 3 2 2 4 +--R (- 48A c - 120B b c)d e + 96B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 3A b d e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 5 +--R 48B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +---+ \|b d e - c d \|c x + b x +--R \|- c atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((12A b c + 3B b )e + (- 24A c - 36B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (12A b c + 3B b )d e + (- 24A c - 36B b c)d e + 48B c d +--R * +--R +----------+ +--R +------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|b d e - c d atan(-------------------) +--R c x +--R + +--R 4 3 4 3 2 +--R 2B c e x + ((4A c + 5B b)e - 8B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 5A b e + (18A c + 19B b)d e - 36B c d e )x - 3A b d e +--R + +--R 2 2 3 +--R (12A c + 12B b)d e - 24B c d e +--R * +--R +------------+ +----------+ +--R +---+ | 2 | 2 +--R \|- c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 7 2 6 2 5 +---+ | 2 +--R (4e x + 8d e x + 4d e )\|- c \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 396 + +--S 397 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 +--R ((12A b c + 3B b )e + (- 24A c - 36B b c)d e + 48B c d ) +--R * +--R +--------------+ +----------+ +--R | 2 +-----------+ +-+ | 2 +-+ +--R \|- b d e + c d \|- b e + c d \|d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 2 2 2 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 +--R 48B c d +--R * +--R +-----------+ +-+ +-+ +--R \|- b e + c d \|c \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 2 2 2 2 +--R ((- 24A b c - 6B b )e + (48A c + 72B b c)d e - 96B c d ) +--R * +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ x\|c +--R \|- b d e + c d \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 2 2 3 +--R (3A b e + (- 24A b c - 15B b )d e + (24A c + 60B b c)d e - 48B c d ) +--R * +--R +--------------+ +--R | 2 +-+ (b e - 2c d)x - b d +--R \|- b d e + c d \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 5 | 2 +-----------+ +-+ +-+ +--R 8e \|- b d e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +--R ((12A b c + 3B b )e + (- 24A c - 36B b c)d e + 48B c d ) +--R * +--R +------------+ +----------+ +--R +-----------+ +-+ | 2 | 2 +-+ +--R \|- b e + c d \|d \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 2 2 +--R ((- 24A b c - 6B b )e + (48A c + 72B b c)d e - 96B c d ) +--R * +--R +------------+ +-+ +--R +-----------+ +-+ | 2 x\|c +--R \|- b e + c d \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 2 2 3 +--R (3A b e + (- 24A b c - 15B b )d e + (24A c + 60B b c)d e - 48B c d ) +--R * +--R +------------+ +--R +-+ | 2 (b e - 2c d)x - b d +--R \|c \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 2 +--R - 6A b e + (48A b c + 30B b )d e + (- 48A c - 120B b c)d e +--R + +--R 2 3 +--R 96B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|c \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 5 +-----------+ +-+ +-+ | 2 +--R 8e \|- b e + c d \|c \|d \|b d e - c d +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1457 +r0:=-1/4*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*(b*x+c*x^2)^(3/2)/(d*e^2*_ + (c*d-b*e)*(d+e*x)^2)+1/3*(4*B*d-A*e+3*B*e*x)*(b*x+c*x^2)^(3/2)/_ + (e^2*(d+e*x)^3)+1/16*(B*d*(64*c^3*d^3-120*b*c^2*d^2*e+60*b^2*c*d*e^2-_ + 5*b^3*e^3)-A*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(3/2)*e^5*(c*d-b*e)^(3/2))-(8*B*c*d-3*b*B*e-2*A*c*e)*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^5-1/8*(A*e*(8*c^2*d^2-_ + 6*b*c*d*e-b^2*e^2)-B*d*(32*c^2*d^2-36*b*c*d*e+5*b^2*e^2)-_ + 2*c*e*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*x)*sqrt(b*x+c*x^2)/_ + (d*e^4*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 5 2 2 4 2 3 3 3 +--R ((96A b c + 144B b )d e + (- 96A c - 528B b c)d e + 384B c d e )x +--R + +--R 2 2 4 2 3 3 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 4 2 +--R 1152B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 5 +--R 1152B c d e +--R * +--R x +--R + +--R 2 4 2 2 5 2 6 +--R (96A b c + 144B b )d e + (- 96A c - 528B b c)d e + 384B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R - 3A b e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 48A c - 360B b c )d e + 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 5 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 6 +--R 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48A c - 360B b c )d e + 192B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 2 2 4 3 +--R (48B b c d e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 6A b e + (- 88A b c - 66B b )d e + (88A c + 412B b c)d e +--R + +--R 2 3 3 +--R - 352B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 16A b d e + (- 92A b c - 80B b )d e +--R + +--R 2 3 3 2 4 2 +--R (120A c + 548B b c)d e - 480B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 6A b d e + (- 36A b c - 30B b )d e + (48A c + 216B b c)d e +--R + +--R 2 5 +--R - 192B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (48b d e - 48c d e )x + (144b d e - 144c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (144b d e - 144c d e )x + 48b d e - 48c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 5 2 2 4 +--R (48A b c + 72B b )d e + (- 48A c - 264B b c)d e +--R + +--R 2 3 3 +--R 192B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R (144A b c + 216B b )d e + (- 144A c - 792B b c)d e +--R + +--R 2 4 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 +--R (144A b c + 216B b )d e + (- 144A c - 792B b c)d e +--R + +--R 2 5 +--R 576B c d e +--R * +--R x +--R + +--R 2 4 2 2 5 2 6 +--R (48A b c + 72B b )d e + (- 48A c - 264B b c)d e + 192B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R \|- b d e + c d \|c log(2\|c \|c x + b x + 2c x + b) +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 3A b e + (18A b c + 15B b )d e + (- 72A b c - 180B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (48A c + 360B b c )d e - 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 9A b d e + (54A b c + 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 216A b c - 540B b c)d e + (144A c + 1080B b c )d e +--R + +--R 3 5 2 +--R - 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 9A b d e + (54A b c + 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 216A b c - 540B b c)d e + (144A c + 1080B b c )d e +--R + +--R 3 6 +--R - 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 3A b d e + (18A b c + 15B b )d e + (- 72A b c - 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (48A c + 360B b c )d e - 192B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 5 2 2 4 3 +--R (48B b c d e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 6A b e + (- 88A b c - 66B b )d e + (88A c + 412B b c)d e +--R + +--R 2 3 3 +--R - 352B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 16A b d e + (- 92A b c - 80B b )d e +--R + +--R 2 3 3 2 4 2 +--R (120A c + 548B b c)d e - 480B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 6A b d e + (- 36A b c - 30B b )d e + (48A c + 216B b c)d e +--R + +--R 2 5 +--R - 192B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (48b d e - 48c d e )x + (144b d e - 144c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (144b d e - 144c d e )x + 48b d e - 48c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 5 2 2 4 2 3 3 3 +--R ((24A b c + 36B b )d e + (- 24A c - 132B b c)d e + 96B c d e )x +--R + +--R 2 2 4 2 3 3 +--R (72A b c + 108B b )d e + (- 72A c - 396B b c)d e +--R + +--R 2 4 2 +--R 288B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R ((72A b c + 108B b )d e + (- 72A c - 396B b c)d e + 288B c d e)x +--R + +--R 2 4 2 2 5 2 6 +--R (24A b c + 36B b )d e + (- 24A c - 132B b c)d e + 96B c d +--R * +--R +------------+ +----------+ +--R +-+ | 2 +-+ | 2 +--R \|c \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 3 7 2 3 6 +--R - 3A b e + (- 18A b c - 15B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (72A b c + 180B b c)d e + (- 48A c - 360B b c )d e +--R + +--R 3 4 3 +--R 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 5 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 6 +--R 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48A c - 360B b c )d e + 192B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 5 2 2 4 3 +--R (24B b c d e - 24B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 3A b e + (- 44A b c - 33B b )d e + (44A c + 206B b c)d e +--R + +--R 2 3 3 +--R - 176B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 8A b d e + (- 46A b c - 40B b )d e +--R + +--R 2 3 3 2 4 2 +--R (60A c + 274B b c)d e - 240B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (24A c + 108B b c)d e +--R + +--R 2 5 +--R - 96B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (24b d e - 24c d e )x + (72b d e - 72c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (72b d e - 72c d e )x + 24b d e - 24c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R , +--R +--R 3 7 2 3 6 2 2 2 5 +--R 3A b e + (18A b c + 15B b )d e + (- 72A b c - 180B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (48A c + 360B b c )d e - 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 9A b d e + (54A b c + 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 216A b c - 540B b c)d e + (144A c + 1080B b c )d e +--R + +--R 3 5 2 +--R - 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 9A b d e + (54A b c + 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 216A b c - 540B b c)d e + (144A c + 1080B b c )d e +--R + +--R 3 6 +--R - 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 3A b d e + (18A b c + 15B b )d e + (- 72A b c - 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (48A c + 360B b c )d e - 192B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 5 2 2 4 +--R (96A b c + 144B b )d e + (- 96A c - 528B b c)d e +--R + +--R 2 3 3 +--R 384B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 4 2 +--R 1152B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 5 +--R 1152B c d e +--R * +--R x +--R + +--R 2 4 2 2 5 2 6 +--R (96A b c + 144B b )d e + (- 96A c - 528B b c)d e + 384B c d +--R * +--R +----------+ +--R +--------------+ | 2 +--R | 2 +---+ \|c x + b x +--R \|- b d e + c d \|- c atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 5 2 2 4 3 +--R (48B b c d e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 6A b e + (- 88A b c - 66B b )d e + (88A c + 412B b c)d e +--R + +--R 2 3 3 +--R - 352B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 16A b d e + (- 92A b c - 80B b )d e +--R + +--R 2 3 3 2 4 2 +--R (120A c + 548B b c)d e - 480B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 6A b d e + (- 36A b c - 30B b )d e + (48A c + 216B b c)d e +--R + +--R 2 5 +--R - 192B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (48b d e - 48c d e )x + (144b d e - 144c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (144b d e - 144c d e )x + 48b d e - 48c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 3 7 2 3 6 +--R - 3A b e + (- 18A b c - 15B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (72A b c + 180B b c)d e + (- 48A c - 360B b c )d e +--R + +--R 3 4 3 +--R 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 5 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 6 +--R 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48A c - 360B b c )d e + 192B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 5 2 2 4 +--R (48A b c + 72B b )d e + (- 48A c - 264B b c)d e +--R + +--R 2 3 3 +--R 192B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R (144A b c + 216B b )d e + (- 144A c - 792B b c)d e +--R + +--R 2 4 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 +--R (144A b c + 216B b )d e + (- 144A c - 792B b c)d e +--R + +--R 2 5 +--R 576B c d e +--R * +--R x +--R + +--R 2 4 2 2 5 2 6 +--R (48A b c + 72B b )d e + (- 48A c - 264B b c)d e + 192B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 \|c x + b x +--R \|- c \|b d e - c d atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 5 2 2 4 3 +--R (24B b c d e - 24B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 3A b e + (- 44A b c - 33B b )d e + (44A c + 206B b c)d e +--R + +--R 2 3 3 +--R - 176B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 8A b d e + (- 46A b c - 40B b )d e +--R + +--R 2 3 3 2 4 2 +--R (60A c + 274B b c)d e - 240B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (24A c + 108B b c)d e +--R + +--R 2 5 +--R - 96B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (24b d e - 24c d e )x + (72b d e - 72c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (72b d e - 72c d e )x + 24b d e - 24c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 403 + +--S 404 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 3 +--R ((16A b c + 24B b )d e + (- 16A c - 88B b c)d e + 64B c d ) +--R * +--R +--------------+ +----------+ +--R | 2 +-----------+ +-+ +-+ +-+ | 2 +--R \|- b d e + c d \|- b e + c d \|c \|d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (6A b c + 5B b )d e + (- 24A b c - 60B b c)d e +--R + +--R 3 2 3 3 4 +--R (16A c + 120B b c )d e - 64B c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 2 2 2 2 3 +--R ((- 32A b c - 48B b )d e + (32A c + 176B b c)d e - 128B c d ) +--R * +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ +-+ x\|c +--R \|- b d e + c d \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (6A b c + 5B b )d e + (- 24A b c - 60B b c)d e +--R + +--R 3 2 3 3 4 +--R (16A c + 120B b c )d e - 64B c d +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 6 2 5 | 2 +-----------+ +-+ +--R (16b d e - 16c d e )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 3 +--R ((16A b c + 24B b )d e + (- 16A c - 88B b c)d e + 64B c d ) +--R * +--R +------------+ +----------+ +--R +-----------+ +-+ +-+ | 2 +-+ | 2 +--R \|- b e + c d \|c \|d \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 2 2 2 2 3 +--R ((- 32A b c - 48B b )d e + (32A c + 176B b c)d e - 128B c d ) +--R * +--R +------------+ +-+ +--R +-----------+ +-+ +-+ | 2 x\|c +--R \|- b e + c d \|c \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (6A b c + 5B b )d e + (- 24A b c - 60B b c)d e +--R + +--R 3 2 3 3 4 +--R (16A c + 120B b c )d e - 64B c d +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A b e + (- 12A b c - 10B b )d e + (48A b c + 120B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 32A c - 240B b c )d e + 128B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 6 2 5 +-----------+ +-+ | 2 +--R (16b d e - 16c d e )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 407 + +)clear all + +--S 408 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1457 +r0:=1/32*(3*A*b^2*e^3+B*d*(16*c^2*d^2-24*b*c*d*e+5*b^2*e^2))*_ + (b*x+c*x^2)^(3/2)/(d^2*e^2*(c*d-b*e)^2*(d+e*x)^2)+1/24*(3*A*b*e^2-_ + B*d*(8*c*d-5*b*e)-6*c*e*(B*d-A*e)*x)*(b*x+c*x^2)^(3/2)/(d*e^2*_ + (c*d-b*e)*(d+e*x)^3)+1/4*(B*d-A*e)*(b*x+c*x^2)^(5/2)/(d*(c*d-b*e)*_ + (d+e*x)^4)+2*B*c^(3/2)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/e^5+_ + 1/128*(3*A*b^4*e^5-B*d*(128*c^4*d^4-320*b*c^3*d^3*e+240*b^2*c^2*_ + d^2*e^2-40*b^3*c*d*e^3-5*b^4*e^4))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*e^5*_ + (c*d-b*e)^(5/2))-1/64*(3*A*b^3*e^4+B*d*(64*c^3*d^3-112*b*c^2*_ + d^2*e+40*b^2*c*d*e^2+5*b^3*e^3)+2*c*e*(3*A*b^2*e^3+B*d*(16*c^2*_ + d^2-24*b*c*d*e+5*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d^2*e^4*_ + (c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 2 6 2 3 5 3 4 4 4 +--R (768B b c d e - 1536B b c d e + 768B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (3072B b c d e - 6144B b c d e + 3072B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (4608B b c d e - 9216B b c d e + 4608B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (3072B b c d e - 6144B b c d e + 3072B c d e)x + 768B b c d e +--R + +--R 2 7 3 8 +--R - 1536B b c d e + 768B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 9 4 8 3 2 7 2 2 3 6 +--R - 9A b e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R - 960B b c d e + 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R - 3840B b c d e + 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R - 54A b d e - 90B b d e - 720B b c d e + 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R - 5760B b c d e + 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 7 2 4 8 +--R - 3840B b c d e + 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R - 9A b d e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 8 4 9 +--R - 960B b c d e + 384B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 18A b e + (12A b c + 30B b )d e + (- 144A b c - 764B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (96A c + 1552B b c )d e - 800B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 66A b d e + (- 264A b c - 146B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (144A b c - 1096B b c)d e + 2960B b c d e - 1664B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 66A b d e + (12A b c - 110B b )d e - 860B b c d e +--R + +--R 2 5 3 3 6 2 +--R 2368B b c d e - 1344B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 3 7 +--R - 18A b d e - 30B b d e - 240B b c d e + 672B b c d e - 384B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (384b d e - 768b c d e + 384c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (1536b d e - 3072b c d e + 1536c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (2304b d e - 4608b c d e + 2304c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (1536b d e - 3072b c d e + 1536c d e )x + 384b d e - 768b c d e +--R + +--R 2 8 5 +--R 384c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 6 2 3 5 3 4 4 4 +--R (384B b c d e - 768B b c d e + 384B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (1536B b c d e - 3072B b c d e + 1536B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (2304B b c d e - 4608B b c d e + 2304B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (1536B b c d e - 3072B b c d e + 1536B c d e)x + 384B b c d e +--R + +--R 2 7 3 8 +--R - 768B b c d e + 384B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R \|- b d e + c d \|c log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 9 4 8 3 2 7 2 2 3 6 +--R 9A b e + 15B b d e + 120B b c d e - 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R 960B b c d e - 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R 36A b d e + 60B b d e + 480B b c d e - 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R 3840B b c d e - 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R 54A b d e + 90B b d e + 720B b c d e - 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R 5760B b c d e - 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R 36A b d e + 60B b d e + 480B b c d e - 2880B b c d e +--R + +--R 3 7 2 4 8 +--R 3840B b c d e - 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R 9A b d e + 15B b d e + 120B b c d e - 720B b c d e +--R + +--R 3 8 4 9 +--R 960B b c d e - 384B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 8 2 3 7 +--R 18A b e + (12A b c + 30B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (- 144A b c - 764B b c)d e + (96A c + 1552B b c )d e +--R + +--R 3 4 4 +--R - 800B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 66A b d e + (- 264A b c - 146B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (144A b c - 1096B b c)d e + 2960B b c d e - 1664B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 66A b d e + (12A b c - 110B b )d e - 860B b c d e +--R + +--R 2 5 3 3 6 2 +--R 2368B b c d e - 1344B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 +--R - 18A b d e - 30B b d e - 240B b c d e + 672B b c d e +--R + +--R 3 7 +--R - 384B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (384b d e - 768b c d e + 384c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (1536b d e - 3072b c d e + 1536c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (2304b d e - 4608b c d e + 2304c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (1536b d e - 3072b c d e + 1536c d e )x + 384b d e - 768b c d e +--R + +--R 2 8 5 +--R 384c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 2 6 2 3 5 3 4 4 4 +--R (192B b c d e - 384B b c d e + 192B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (768B b c d e - 1536B b c d e + 768B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (1152B b c d e - 2304B b c d e + 1152B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (768B b c d e - 1536B b c d e + 768B c d e)x + 192B b c d e +--R + +--R 2 7 3 8 +--R - 384B b c d e + 192B c d +--R * +--R +------------+ +----------+ +--R +-+ | 2 +-+ | 2 +--R \|c \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 9 4 8 3 2 7 2 2 3 6 +--R - 9A b e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R - 960B b c d e + 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R - 3840B b c d e + 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R - 54A b d e - 90B b d e - 720B b c d e + 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R - 5760B b c d e + 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 7 2 4 8 +--R - 3840B b c d e + 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R - 9A b d e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 8 4 9 +--R - 960B b c d e + 384B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 9A b e + (6A b c + 15B b )d e + (- 72A b c - 382B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (48A c + 776B b c )d e - 400B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 33A b d e + (- 132A b c - 73B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (72A b c - 548B b c)d e + 1480B b c d e - 832B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 33A b d e + (6A b c - 55B b )d e - 430B b c d e +--R + +--R 2 5 3 3 6 2 +--R 1184B b c d e - 672B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 3 7 +--R - 9A b d e - 15B b d e - 120B b c d e + 336B b c d e - 192B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (192b d e - 384b c d e + 192c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (768b d e - 1536b c d e + 768c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (1152b d e - 2304b c d e + 1152c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (768b d e - 1536b c d e + 768c d e )x + 192b d e - 384b c d e +--R + +--R 2 8 5 +--R 192c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R , +--R +--R 4 9 4 8 3 2 7 2 2 3 6 +--R 9A b e + 15B b d e + 120B b c d e - 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R 960B b c d e - 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R 36A b d e + 60B b d e + 480B b c d e - 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R 3840B b c d e - 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R 54A b d e + 90B b d e + 720B b c d e - 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R 5760B b c d e - 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R 36A b d e + 60B b d e + 480B b c d e - 2880B b c d e +--R + +--R 3 7 2 4 8 +--R 3840B b c d e - 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R 9A b d e + 15B b d e + 120B b c d e - 720B b c d e +--R + +--R 3 8 4 9 +--R 960B b c d e - 384B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 2 6 2 3 5 3 4 4 4 +--R (768B b c d e - 1536B b c d e + 768B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (3072B b c d e - 6144B b c d e + 3072B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (4608B b c d e - 9216B b c d e + 4608B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (3072B b c d e - 6144B b c d e + 3072B c d e)x + 768B b c d e +--R + +--R 2 7 3 8 +--R - 1536B b c d e + 768B c d +--R * +--R +----------+ +--R +--------------+ | 2 +--R | 2 +---+ \|c x + b x +--R \|- b d e + c d \|- c atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 3 8 2 3 7 +--R 18A b e + (12A b c + 30B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (- 144A b c - 764B b c)d e + (96A c + 1552B b c )d e +--R + +--R 3 4 4 +--R - 800B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 66A b d e + (- 264A b c - 146B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (144A b c - 1096B b c)d e + 2960B b c d e - 1664B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 66A b d e + (12A b c - 110B b )d e - 860B b c d e +--R + +--R 2 5 3 3 6 2 +--R 2368B b c d e - 1344B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 +--R - 18A b d e - 30B b d e - 240B b c d e + 672B b c d e +--R + +--R 3 7 +--R - 384B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (384b d e - 768b c d e + 384c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (1536b d e - 3072b c d e + 1536c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (2304b d e - 4608b c d e + 2304c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (1536b d e - 3072b c d e + 1536c d e )x + 384b d e - 768b c d e +--R + +--R 2 8 5 +--R 384c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 4 9 4 8 3 2 7 2 2 3 6 +--R - 9A b e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R - 960B b c d e + 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R - 3840B b c d e + 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R - 54A b d e - 90B b d e - 720B b c d e + 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R - 5760B b c d e + 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 7 2 4 8 +--R - 3840B b c d e + 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R - 9A b d e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 8 4 9 +--R - 960B b c d e + 384B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 2 6 2 3 5 3 4 4 4 +--R (384B b c d e - 768B b c d e + 384B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (1536B b c d e - 3072B b c d e + 1536B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (2304B b c d e - 4608B b c d e + 2304B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (1536B b c d e - 3072B b c d e + 1536B c d e)x + 384B b c d e +--R + +--R 2 7 3 8 +--R - 768B b c d e + 384B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 \|c x + b x +--R \|- c \|b d e - c d atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 9A b e + (6A b c + 15B b )d e + (- 72A b c - 382B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (48A c + 776B b c )d e - 400B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 33A b d e + (- 132A b c - 73B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (72A b c - 548B b c)d e + 1480B b c d e - 832B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 33A b d e + (6A b c - 55B b )d e - 430B b c d e +--R + +--R 2 5 3 3 6 2 +--R 1184B b c d e - 672B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 3 7 +--R - 9A b d e - 15B b d e - 120B b c d e + 336B b c d e - 192B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (192b d e - 384b c d e + 192c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (768b d e - 1536b c d e + 768c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (1152b d e - 2304b c d e + 1152c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (768b d e - 1536b c d e + 768c d e )x + 192b d e - 384b c d e +--R + +--R 2 8 5 +--R 192c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 410 + +--S 411 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 2 2 3 3 4 | 2 +--R (128B b c d e - 256B b c d e + 128B c d )\|- b d e + c d +--R * +--R +----------+ +--R +-----------+ +-+ +-+ +-+ | 2 +--R \|- b e + c d \|c \|d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 +--R 3A b e + 5B b d e + 40B b c d e - 240B b c d e + 320B b c d e +--R + +--R 4 5 +--R - 128B c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 2 2 2 3 3 4 | 2 +--R (- 256B b c d e + 512B b c d e - 256B c d )\|- b d e + c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 +--R 3A b e + 5B b d e + 40B b c d e - 240B b c d e + 320B b c d e +--R + +--R 4 5 +--R - 128B c d +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 7 3 6 2 4 5 | 2 +-----------+ +-+ +--R (128b d e - 256b c d e + 128c d e )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 3 3 4 +-----------+ +-+ +-+ +--R (128B b c d e - 256B b c d e + 128B c d )\|- b e + c d \|c \|d +--R * +--R +------------+ +----------+ +--R | 2 +-+ | 2 +--R \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 2 2 2 3 3 4 +-----------+ +-+ +-+ +--R (- 256B b c d e + 512B b c d e - 256B c d )\|- b e + c d \|c \|d +--R * +--R +------------+ +-+ +--R | 2 x\|c +--R \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 +--R 3A b e + 5B b d e + 40B b c d e - 240B b c d e + 320B b c d e +--R + +--R 4 5 +--R - 128B c d +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 +--R - 6A b e - 10B b d e - 80B b c d e + 480B b c d e - 640B b c d e +--R + +--R 4 5 +--R 256B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 7 3 6 2 4 5 +-----------+ +-+ | 2 +--R (128b d e - 256b c d e + 128c d e )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1457 +r0:=-1/5*(4*B*d+A*e+5*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^5)-_ + 3/256*b^4*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+_ + 1/80*(A*e*(4*c^2*d^2-4*b*c*d*e-b^2*e^2)+B*d*(16*c^2*d^2-26*b*c*d*e+_ + 11*b^2*e^2))*sqrt(b*x+c*x^2)/(d*e^4*(c*d-b*e)*(d+e*x)^3)+1/320*_ + (A*e*(16*c^3*d^3-24*b*c^2*d^2*e-2*b^2*c*d*e^2+5*b^3*e^3)+B*d*_ + (64*c^3*d^3-136*b*c^2*d^2*e+72*b^2*c*d*e^2+5*b^3*e^3))*_ + sqrt(b*x+c*x^2)/(d^2*e^4*(c*d-b*e)^2*(d+e*x)^2)+1/640*(B*d*_ + (128*c^4*d^4-336*b*c^3*d^3*e+248*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-_ + 15*b^4*e^4)+A*e*(32*c^4*d^4-64*b*c^3*d^3*e+12*b^2*c^2*d^2*e^2+_ + 20*b^3*c*d*e^3-15*b^4*e^4))*sqrt(b*x+c*x^2)/(d^3*e^4*(c*d-b*e)^3*_ + (d+e*x))-3/40*(B*d*(8*c*d-b*e)+A*e*(2*c*d+b*e)+2*e*(8*B*c*d-_ + 5*b*B*e+2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x)^4) +--R +--R +--R (2) +--R 5 6 4 5 5 5 +--R (- 15A b e + (30A b c - 15B b )d e )x +--R + +--R 5 5 4 5 2 4 4 +--R (- 75A b d e + (150A b c - 75B b )d e )x +--R + +--R 5 2 4 4 5 3 3 3 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 3 3 4 5 4 2 2 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 4 2 4 5 5 5 5 +--R (- 75A b d e + (150A b c - 75B b )d e)x - 15A b d e +--R + +--R 4 5 6 +--R (30A b c - 15B b )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 30A b e + (- 40A b c + 30B b )d e + (- 24A b c + 20B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (128A b c - 496B b c )d e + (- 64A c + 672B b c )d e - 256B c d +--R * +--R 4 +--R x +--R + +--R 4 4 3 4 2 3 +--R 140A b d e + (- 188A b c + 140B b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 184A b c - 932B b c)d e + (672A b c + 1024B b c )d e +--R + +--R 4 3 5 +--R (- 320A c - 352B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 4 3 2 +--R 256A b d e + (- 932A b c - 256B b )d e +--R + +--R 2 2 3 4 3 2 2 5 +--R (1336A b c + 92B b c)d e + (- 480A b c - 16B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 +--R (- 140A b d e + (300A b c - 140B b )d e + (- 40A b c + 20B b c)d )x +--R + +--R 4 4 3 4 5 +--R - 30A b d e + (60A b c - 30B b )d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (1280b d e - 3840b c d e + 3840b c d e - 1280c d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e)x + 1280b d e +--R + +--R 2 9 2 2 10 3 11 +--R - 3840b c d e + 3840b c d e - 1280c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 6 4 5 5 5 +--R (15A b e + (- 30A b c + 15B b )d e )x +--R + +--R 5 5 4 5 2 4 4 +--R (75A b d e + (- 150A b c + 75B b )d e )x +--R + +--R 5 2 4 4 5 3 3 3 +--R (150A b d e + (- 300A b c + 150B b )d e )x +--R + +--R 5 3 3 4 5 4 2 2 +--R (150A b d e + (- 300A b c + 150B b )d e )x +--R + +--R 5 4 2 4 5 5 5 5 +--R (75A b d e + (- 150A b c + 75B b )d e)x + 15A b d e +--R + +--R 4 5 6 +--R (- 30A b c + 15B b )d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 5 3 4 4 +--R 30A b e + (- 40A b c + 30B b )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 24A b c + 20B b c)d e + (128A b c - 496B b c )d e +--R + +--R 4 3 4 4 5 +--R (- 64A c + 672B b c )d e - 256B c d +--R * +--R 4 +--R x +--R + +--R 4 4 3 4 2 3 +--R 140A b d e + (- 188A b c + 140B b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 184A b c - 932B b c)d e + (672A b c + 1024B b c )d e +--R + +--R 4 3 5 +--R (- 320A c - 352B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 4 3 2 +--R 256A b d e + (- 932A b c - 256B b )d e +--R + +--R 2 2 3 4 3 2 2 5 +--R (1336A b c + 92B b c)d e + (- 480A b c - 16B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 3 4 4 +--R - 140A b d e + (300A b c - 140B b )d e +--R + +--R 2 2 3 5 +--R (- 40A b c + 20B b c)d +--R * +--R x +--R + +--R 4 4 3 4 5 +--R - 30A b d e + (60A b c - 30B b )d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (1280b d e - 3840b c d e + 3840b c d e - 1280c d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e)x +--R + +--R 3 8 3 2 9 2 2 10 3 11 +--R 1280b d e - 3840b c d e + 3840b c d e - 1280c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 5 6 4 5 5 5 +--R (- 15A b e + (30A b c - 15B b )d e )x +--R + +--R 5 5 4 5 2 4 4 +--R (- 75A b d e + (150A b c - 75B b )d e )x +--R + +--R 5 2 4 4 5 3 3 3 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 3 3 4 5 4 2 2 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 4 2 4 5 5 5 5 +--R (- 75A b d e + (150A b c - 75B b )d e)x - 15A b d e +--R + +--R 4 5 6 +--R (30A b c - 15B b )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 4 5 3 4 4 +--R 15A b e + (- 20A b c + 15B b )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 12A b c + 10B b c)d e + (64A b c - 248B b c )d e +--R + +--R 4 3 4 4 5 +--R (- 32A c + 336B b c )d e - 128B c d +--R * +--R 4 +--R x +--R + +--R 4 4 3 4 2 3 +--R 70A b d e + (- 94A b c + 70B b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 92A b c - 466B b c)d e + (336A b c + 512B b c )d e +--R + +--R 4 3 5 +--R (- 160A c - 176B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 4 3 2 +--R 128A b d e + (- 466A b c - 128B b )d e +--R + +--R 2 2 3 4 3 2 2 5 +--R (668A b c + 46B b c)d e + (- 240A b c - 8B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 +--R (- 70A b d e + (150A b c - 70B b )d e + (- 20A b c + 10B b c)d )x +--R + +--R 4 4 3 4 5 +--R - 15A b d e + (30A b c - 15B b )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (640b d e - 1920b c d e + 1920b c d e - 640c d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (3200b d e - 9600b c d e + 9600b c d e - 3200c d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (3200b d e - 9600b c d e + 9600b c d e - 3200c d e)x + 640b d e +--R + +--R 2 9 2 2 10 3 11 +--R - 1920b c d e + 1920b c d e - 640c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 417 + +--S 418 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 5 +-----------+ +-+ +--R (3A b e + (- 6A b c + 3B b )d)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 5 4 5 | 2 +--R (3A b e + (- 6A b c + 3B b )d)\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +--R (256b d e - 768b c d e + 768b c d e - 256c d )\|- b d e + c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 5 4 5 | 2 +--R (3A b e + (- 6A b c + 3B b )d)\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 4 5 +-----------+ +-+ +--R (- 6A b e + (12A b c - 6B b )d)\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ +--R (256b d e - 768b c d e + 768b c d e - 256c d )\|- b e + c d \|d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 421 + +)clear all + +--S 422 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1457 +r0:=1/768*b*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*_ + (B*d+2*A*e))*x^2*(b*x+c*x^2)^(3/2)/c^3+1/384*(64*A*c^3*d^2-11*b^3*_ + B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*x*(b*x+_ + c*x^2)^(5/2)/c^3+1/2016*(162*A*c*e*(2*c*d-b*e)+B*(64*c^2*d^2-_ + 226*b*c*d*e+99*b^2*e^2))*(b*x+c*x^2)^(7/2)/c^3+1/9*B*(d+e*x)^2*_ + (b*x+c*x^2)^(7/2)/c-1/144*e*((7*b*B-18*A*c)*d-(4*B*c*d-11*b*B*e+_ + 18*A*c*e)*x)*(b*x+c*x^2)^(7/2)/c^2-5/32768*b^6*(64*A*c^3*d^2-_ + 11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(13/2)+5/32768*b^5*(64*A*c^3*_ + d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*_ + sqrt(b*x+c*x^2)/c^6-5/49152*b^4*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*_ + c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^5+_ + 1/12288*b^3*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-_ + 32*b*c^2*d*(B*d+2*A*e))*x^2*sqrt(b*x+c*x^2)/c^4+1/2048*b^2*_ + (64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*_ + (B*d+2*A*e))*x^3*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 8 9 2 7 2 8 +--R (- 5670A b c + 3465B b )e + (20160A b c - 11340B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 20160A b c + 10080B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 8 2 8 8 7 2 8 7 +--R 229376B c e x + ((258048A c + 530432B b c )e + 516096B c d e)x +--R + +--R 7 2 6 2 8 7 +--R (608256A b c + 316416B b c )e + (589824A c + 1216512B b c )d e +--R + +--R 8 2 +--R 294912B c d +--R * +--R 6 +--R x +--R + +--R 2 6 3 5 2 7 2 6 +--R (373248A b c + 1280B b c )e + (1425408A b c + 746496B b c )d e +--R + +--R 8 7 2 +--R (344064A c + 712704B b c )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (2304A b c - 1408B b c )e + (909312A b c + 4608B b c )d e +--R + +--R 7 2 6 2 +--R (860160A b c + 454656B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (- 2592A b c + 1584B b c )e + (9216A b c - 5184B b c )d e +--R + +--R 2 6 3 5 2 +--R (580608A b c + 4608B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (3024A b c - 1848B b c )e + (- 10752A b c + 6048B b c )d e +--R + +--R 3 5 4 4 2 +--R (10752A b c - 5376B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 3780A b c + 2310B b c)e + (13440A b c - 7560B b c )d e +--R + +--R 4 4 5 3 2 +--R (- 13440A b c + 6720B b c )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 +--R (5670A b c - 3465B b )e + (- 20160A b c + 11340B b c)d e +--R + +--R 5 3 6 2 2 +--R (20160A b c - 10080B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 +-+ +--R 2064384c \|c +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 8 9 2 7 2 8 +--R (- 5670A b c + 3465B b )e + (20160A b c - 11340B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 20160A b c + 10080B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 8 2 8 +--R 458752B c e x +--R + +--R 8 7 2 8 7 +--R ((516096A c + 1060864B b c )e + 1032192B c d e)x +--R + +--R 7 2 6 2 +--R (1216512A b c + 632832B b c )e +--R + +--R 8 7 8 2 +--R (1179648A c + 2433024B b c )d e + 589824B c d +--R * +--R 6 +--R x +--R + +--R 2 6 3 5 2 +--R (746496A b c + 2560B b c )e +--R + +--R 7 2 6 +--R (2850816A b c + 1492992B b c )d e +--R + +--R 8 7 2 +--R (688128A c + 1425408B b c )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (4608A b c - 2816B b c )e + (1818624A b c + 9216B b c )d e +--R + +--R 7 2 6 2 +--R (1720320A b c + 909312B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (- 5184A b c + 3168B b c )e + (18432A b c - 10368B b c )d e +--R + +--R 2 6 3 5 2 +--R (1161216A b c + 9216B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (6048A b c - 3696B b c )e + (- 21504A b c + 12096B b c )d e +--R + +--R 3 5 4 4 2 +--R (21504A b c - 10752B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 7560A b c + 4620B b c)e + (26880A b c - 15120B b c )d e +--R + +--R 4 4 5 3 2 +--R (- 26880A b c + 13440B b c )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 +--R (11340A b c - 6930B b )e + (- 40320A b c + 22680B b c)d e +--R + +--R 5 3 6 2 2 +--R (40320A b c - 20160B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 +-+ +--R 4128768c \|c +--R , +--R +--R 8 9 2 7 2 8 +--R (- 5670A b c + 3465B b )e + (20160A b c - 11340B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 20160A b c + 10080B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 8 2 8 8 7 2 8 7 +--R 229376B c e x + ((258048A c + 530432B b c )e + 516096B c d e)x +--R + +--R 7 2 6 2 +--R (608256A b c + 316416B b c )e +--R + +--R 8 7 8 2 +--R (589824A c + 1216512B b c )d e + 294912B c d +--R * +--R 6 +--R x +--R + +--R 2 6 3 5 2 +--R (373248A b c + 1280B b c )e +--R + +--R 7 2 6 8 7 2 +--R (1425408A b c + 746496B b c )d e + (344064A c + 712704B b c )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (2304A b c - 1408B b c )e + (909312A b c + 4608B b c )d e +--R + +--R 7 2 6 2 +--R (860160A b c + 454656B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (- 2592A b c + 1584B b c )e + (9216A b c - 5184B b c )d e +--R + +--R 2 6 3 5 2 +--R (580608A b c + 4608B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (3024A b c - 1848B b c )e + (- 10752A b c + 6048B b c )d e +--R + +--R 3 5 4 4 2 +--R (10752A b c - 5376B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 3780A b c + 2310B b c)e + (13440A b c - 7560B b c )d e +--R + +--R 4 4 5 3 2 +--R (- 13440A b c + 6720B b c )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 +--R (5670A b c - 3465B b )e + (- 20160A b c + 11340B b c)d e +--R + +--R 5 3 6 2 2 +--R (20160A b c - 10080B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 6 +---+ +--R 2064384c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 424 + +--S 425 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 8 9 2 7 2 8 +--R (- 90A b c + 55B b )e + (320A b c - 180B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 320A b c + 160B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 8 9 2 7 2 8 +--R (180A b c - 110B b )e + (- 640A b c + 360B b c)d e +--R + +--R 6 3 7 2 2 +--R (640A b c - 320B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 6 +-+ +--R 65536c \|c +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 8 9 2 7 2 8 +--R (90A b c - 55B b )e + (- 320A b c + 180B b c)d e +--R + +--R 6 3 7 2 2 +--R (320A b c - 160B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 8 9 2 7 2 8 +--R (- 90A b c + 55B b )e + (320A b c - 180B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 320A b c + 160B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 6 +---+ +-+ +--R 32768c \|- c \|c +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 428 + +)clear all + +--S 429 of 1457 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1457 +r0:=1/384*b*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^2*_ + (b*x+c*x^2)^(3/2)/c^2+1/192*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*_ + x*(b*x+c*x^2)^(5/2)/c^2+1/112*(2*B*c*d-9*b*B*e+16*A*c*e)*_ + (b*x+c*x^2)^(7/2)/c^2+1/8*B*(d+e*x)*(b*x+c*x^2)^(7/2)/c-_ + 5/16384*b^6*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*atanh(x*_ + sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+5/16384*b^5*(32*A*c^2*d+9*b^2*B*e-_ + 16*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^5-5/24576*b^4*(32*A*c^2*d+_ + 9*b^2*B*e-16*b*c*(B*d+A*e))*x*sqrt(b*x+c*x^2)/c^4+1/6144*b^3*_ + (32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^2*sqrt(b*x+c*x^2)/c^3+_ + 1/1024*b^2*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^3*_ + sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 7 8 6 2 7 +--R ((1680A b c - 945B b )e + (- 3360A b c + 1680B b c)d) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 7 7 7 6 7 6 +--R 43008B c e x + ((49152A c + 101376B b c )e + 49152B c d)x +--R + +--R 6 2 5 7 6 5 +--R ((118784A b c + 62208B b c )e + (57344A c + 118784B b c )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((75776A b c + 384B b c )e + (143360A b c + 75776B b c )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((768A b c - 432B b c )e + (96768A b c + 768B b c )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((- 896A b c + 504B b c )e + (1792A b c - 896B b c )d)x +--R + +--R 5 2 6 4 3 5 2 +--R ((1120A b c - 630B b c)e + (- 2240A b c + 1120B b c )d)x +--R + +--R 6 7 5 2 6 +--R (- 1680A b c + 945B b )e + (3360A b c - 1680B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 344064c \|c +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 7 8 6 2 7 +--R ((1680A b c - 945B b )e + (- 3360A b c + 1680B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 7 7 7 6 7 6 +--R 86016B c e x + ((98304A c + 202752B b c )e + 98304B c d)x +--R + +--R 6 2 5 7 6 5 +--R ((237568A b c + 124416B b c )e + (114688A c + 237568B b c )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((151552A b c + 768B b c )e + (286720A b c + 151552B b c )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((1536A b c - 864B b c )e + (193536A b c + 1536B b c )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((- 1792A b c + 1008B b c )e + (3584A b c - 1792B b c )d)x +--R + +--R 5 2 6 4 3 5 2 +--R ((2240A b c - 1260B b c)e + (- 4480A b c + 2240B b c )d)x +--R + +--R 6 7 5 2 6 +--R (- 3360A b c + 1890B b )e + (6720A b c - 3360B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 688128c \|c +--R , +--R +--R 7 8 6 2 7 +--R ((1680A b c - 945B b )e + (- 3360A b c + 1680B b c)d) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 7 7 7 6 7 6 +--R 43008B c e x + ((49152A c + 101376B b c )e + 49152B c d)x +--R + +--R 6 2 5 7 6 5 +--R ((118784A b c + 62208B b c )e + (57344A c + 118784B b c )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((75776A b c + 384B b c )e + (143360A b c + 75776B b c )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((768A b c - 432B b c )e + (96768A b c + 768B b c )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((- 896A b c + 504B b c )e + (1792A b c - 896B b c )d)x +--R + +--R 5 2 6 4 3 5 2 +--R ((1120A b c - 630B b c)e + (- 2240A b c + 1120B b c )d)x +--R + +--R 6 7 5 2 6 +--R (- 1680A b c + 945B b )e + (3360A b c - 1680B b c)d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 5 +---+ +--R 344064c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 431 + +--S 432 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 7 8 6 2 7 +--R ((80A b c - 45B b )e + (- 160A b c + 80B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 7 8 6 2 7 x\|c +--R ((- 160A b c + 90B b )e + (320A b c - 160B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 5 +-+ +--R 32768c \|c +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 7 8 6 2 7 +---+ +--R ((- 80A b c + 45B b )e + (160A b c - 80B b c)d)\|- c +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 7 8 6 2 7 +-+ +--R ((80A b c - 45B b )e + (- 160A b c + 80B b c)d)\|c +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R / +--R 5 +---+ +-+ +--R 16384c \|- c \|c +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2) +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1457 +r0:=-1/24*b*(b*B-2*A*c)*x^2*(b*x+c*x^2)^(3/2)/c-1/12*(b*B-2*A*c)*x*_ + (b*x+c*x^2)^(5/2)/c+1/7*B*(b*x+c*x^2)^(7/2)/c+5/1024*b^6*(b*B-_ + 2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-5/1024*b^5*(b*B-_ + 2*A*c)*sqrt(b*x+c*x^2)/c^4+5/1536*b^4*(b*B-2*A*c)*x*sqrt(b*x+_ + c*x^2)/c^3-1/384*b^3*(b*B-2*A*c)*x^2*sqrt(b*x+c*x^2)/c^2-1/64*b^2*_ + (b*B-2*A*c)*x^3*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 6 7 x\|c +--R (- 210A b c + 105B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 6 6 5 5 5 2 4 4 +--R 3072B c x + (3584A c + 7424B b c )x + (8960A b c + 4736B b c )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 +--R (6048A b c + 48B b c )x + (112A b c - 56B b c )x +--R + +--R 4 2 5 5 6 +--R (- 140A b c + 70B b c)x + 210A b c - 105B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 21504c \|c +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 6 7 | 2 +-+ +--R (210A b c - 105B b )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 6 6 6 5 5 +--R 6144B c x + (7168A c + 14848B b c )x +--R + +--R 5 2 4 4 2 4 3 3 3 +--R (17920A b c + 9472B b c )x + (12096A b c + 96B b c )x +--R + +--R 3 3 4 2 2 4 2 5 5 +--R (224A b c - 112B b c )x + (- 280A b c + 140B b c)x + 420A b c +--R + +--R 6 +--R - 210B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 43008c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 6 7 \|- c \|c x + b x +--R (- 210A b c + 105B b )atan(-------------------) +--R c x +--R + +--R 6 6 6 5 5 +--R 3072B c x + (3584A c + 7424B b c )x +--R + +--R 5 2 4 4 2 4 3 3 3 +--R (8960A b c + 4736B b c )x + (6048A b c + 48B b c )x +--R + +--R 3 3 4 2 2 4 2 5 5 +--R (112A b c - 56B b c )x + (- 140A b c + 70B b c)x + 210A b c +--R + +--R 6 +--R - 105B b +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 21504c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 438 + +--S 439 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 6 7 | 2 +-+ +--R (10A b c - 5B b )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 6 7 x\|c +--R (20A b c - 10B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 2048c \|c +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 6 7 +---+ x\|c +--R (10A b c - 5B b )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 6 7 +-+ \|- c \|c x + b x +--R (- 10A b c + 5B b )\|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 1024c \|- c \|c +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x) +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1457 +r0:=1/192*(4*A*c*e*(16*c^2*d^2-22*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-_ + 88*b*c^2*d^2*e+12*b^2*c*d*e^2+5*b^3*e^3)-2*c*e*(12*A*c*e*(2*c*d-_ + b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/_ + (c^2*e^4)-1/60*(12*B*c*d-5*b*B*e-12*A*c*e-10*B*c*e*x)*(b*x+_ + c*x^2)^(5/2)/(c*e^2)-1/512*(4*A*c*e*(256*c^5*d^5-640*b*c^4*d^4*e+_ + 480*b^2*c^3*d^3*e^2-80*b^3*c^2*d^2*e^3-10*b^4*c*d*e^4-3*b^5*e^5)-_ + B*(1024*c^6*d^6-2560*b*c^5*d^5*e+1920*b^2*c^4*d^4*e^2-320*b^3*_ + c^3*d^3*e^3-40*b^4*c^2*d^2*e^4-12*b^5*c*d*e^5-5*b^6*e^6))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(7/2)*e^7)-d^(5/2)*(B*d-A*e)*_ + (c*d-b*e)^(5/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7+1/1536*(3*(4*A*c*e*(128*c^4*d^4-_ + 288*b*c^3*d^3*e+176*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-3*b^4*e^4)-_ + B*(512*c^5*d^5-1152*b*c^4*d^4*e+704*b^2*c^3*d^3*e^2-40*b^3*c^2*_ + d^2*e^3-12*b^4*c*d*e^4-5*b^5*e^5))-2*c*e*(8*b*c*d*e*(2*c*d-b*e)*_ + (12*B*c*d-5*b*B*e-12*A*c*e)+(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2)*_ + (12*A*c*e*(2*c*d-b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2)))*x)*_ + sqrt(b*x+c*x^2)/(c^3*e^6) +--R +--R +--R (2) +--R 5 6 6 4 2 5 5 +--R (180A b c - 75B b )e + (600A b c - 180B b c)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (4800A b c - 600B b c )d e + (- 28800A b c - 4800B b c )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (38400A b c + 28800B b c )d e + (- 15360A c - 38400B b c )d e +--R + +--R 6 6 +--R 15360B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 3 4 2 3 3 2 +--R - 7680A b c d e + (15360A b c + 7680B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 7680A c - 15360B b c )d e + 7680B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 6 5 5 4 6 5 5 4 +--R 1280B c e x + ((1536A c + 3200B b c )e - 1536B c d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (4032A b c + 2160B b c )e + (- 1920A c - 4032B b c )d e +--R + +--R 5 2 4 +--R 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2976A b c + 40B b c )e + (- 5440A b c - 2976B b c )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2560A c + 5440B b c )d e - 2560B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (120A b c - 50B b c)e + (- 4720A b c - 120B b c )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (8320A b c + 4720B b c )d e + (- 3840A c - 8320B b c )d e +--R + +--R 5 4 2 +--R 3840B c d e +--R * +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 180A b c + 75B b )e + (- 600A b c + 180B b c)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (10560A b c + 600B b c )d e + (- 17280A b c - 10560B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (7680A c + 17280B b c )d e - 7680B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 7 +-+ +--R 7680c e \|c +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1457 +--a0:=integrate(t0,x) +--E 445 + +--S 446 of 1457 +--m0:=a0-r0 +--E 446 + +--S 447 of 1457 +--d0:=D(m0,x) +--E 447 + +)clear all + +--S 448 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1457 +r0:=-1/48*(10*A*c*e*(8*c*d-7*b*e)-B*(96*c^2*d^2-92*b*c*d*e+3*b^2*e^2)+_ + 6*c*e*(12*B*c*d-b*B*e-10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(c*e^4)+_ + 1/5*(6*B*d-5*A*e+B*e*x)*(b*x+c*x^2)^(5/2)/(e^2*(d+e*x))+_ + 1/128*(10*A*c*e*(128*c^4*d^4-256*b*c^3*d^3*e+144*b^2*c^2*d^2*e^2-_ + 16*b^3*c*d*e^3-b^4*e^4)-B*(1536*c^5*d^5-3200*b*c^4*d^4*e+_ + 1920*b^2*c^3*d^3*e^2-240*b^3*c^2*d^2*e^3-20*b^4*c*d*e^4-3*b^5*e^5))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^7)+1/2*d^(3/2)*_ + (c*d-b*e)^(3/2)*(B*d*(12*c*d-7*b*e)-5*A*e*(2*c*d-b*e))*atanh(1/2*_ + (b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7-_ + 1/128*(10*A*c*e*(64*c^3*d^3-112*b*c^2*d^2*e+48*b^2*c*d*e^2-b^3*e^3)-_ + B*(768*c^4*d^4-1408*b*c^3*d^3*e+656*b^2*c^2*d^2*e^2-20*b^3*c*d*e^3-_ + 3*b^4*e^4)-2*c*e*(8*b*c*e*(6*B*d-5*A*e)*(2*c*d-b*e)-(12*B*c*d-b*B*e-_ + 10*A*c*e)*(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^6) +--R +--R +--R (2) +--R 4 5 6 3 2 4 5 +--R (- 150A b c + 45B b )e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (21600A b c + 3600B b c )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 38400A b c - 28800B b c )d e + (19200A c + 48000B b c )d e +--R + +--R 5 5 +--R - 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (- 150A b c + 45B b )d e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (21600A b c + 3600B b c )d e + (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (19200A c + 48000B b c )d e - 23040B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 4 3 2 2 2 3 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (9600A c + 18240B b c )d e - 11520B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 4 4 5 +--R (9600A c + 18240B b c )d e - 11520B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 384B c e x + ((480A c + 1008B b c )e - 576B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (1360A b c + 744B b c )e + (- 800A c - 1712B b c )d e +--R + +--R 4 2 4 +--R 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (1180A b c + 30B b c)e + (- 2800A b c - 1616B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (1600A c + 3520B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (150A b c - 45B b )e + (- 4100A b c - 270B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (8800A b c + 5560B b c )d e + (- 4800A c - 11040B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (150A b c - 45B b )d e + (- 7200A b c - 300B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (16800A b c + 9840B b c )d e + (- 9600A c - 21120B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 8 2 7 +-+ +--R (1920c e x + 1920c d e )\|c +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 5 6 3 2 4 5 +--R (150A b c - 45B b )e + (2400A b c - 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (- 21600A b c - 3600B b c )d e +--R + +--R 4 2 3 3 3 +--R (38400A b c + 28800B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (- 19200A c - 48000B b c )d e + 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (150A b c - 45B b )d e + (2400A b c - 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 21600A b c - 3600B b c )d e + (38400A b c + 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (- 19200A c - 48000B b c )d e + 23040B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 4 3 2 2 2 3 +--R 9600A b c d e + (- 28800A b c - 13440B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (19200A c + 36480B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R 9600A b c d e + (- 28800A b c - 13440B b c )d e +--R + +--R 4 3 4 4 5 +--R (19200A c + 36480B b c )d e - 23040B c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 768B c e x + ((960A c + 2016B b c )e - 1152B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (2720A b c + 1488B b c )e + (- 1600A c - 3424B b c )d e +--R + +--R 4 2 4 +--R 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (2360A b c + 60B b c)e + (- 5600A b c - 3232B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (3200A c + 7040B b c )d e - 3840B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (300A b c - 90B b )e + (- 8200A b c - 540B b c)d e +--R + +--R 3 2 2 2 4 +--R (17600A b c + 11120B b c )d e +--R + +--R 4 3 3 3 4 4 2 +--R (- 9600A c - 22080B b c )d e + 11520B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (300A b c - 90B b )d e + (- 14400A b c - 600B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (33600A b c + 19680B b c )d e + (- 19200A c - 42240B b c )d e +--R + +--R 4 5 +--R 23040B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 8 2 7 +-+ +--R (3840c e x + 3840c d e )\|c +--R , +--R +--R 4 5 6 3 2 4 5 +--R (150A b c - 45B b )e + (2400A b c - 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (- 21600A b c - 3600B b c )d e +--R + +--R 4 2 3 3 3 +--R (38400A b c + 28800B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (- 19200A c - 48000B b c )d e + 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (150A b c - 45B b )d e + (2400A b c - 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 21600A b c - 3600B b c )d e + (38400A b c + 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (- 19200A c - 48000B b c )d e + 23040B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 4 3 2 2 2 3 +--R - 19200A b c d e + (57600A b c + 26880B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (- 38400A c - 72960B b c )d e + 46080B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R - 19200A b c d e + (57600A b c + 26880B b c )d e +--R + +--R 4 3 4 4 5 +--R (- 38400A c - 72960B b c )d e + 46080B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 768B c e x + ((960A c + 2016B b c )e - 1152B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (2720A b c + 1488B b c )e + (- 1600A c - 3424B b c )d e +--R + +--R 4 2 4 +--R 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (2360A b c + 60B b c)e + (- 5600A b c - 3232B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (3200A c + 7040B b c )d e - 3840B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (300A b c - 90B b )e + (- 8200A b c - 540B b c)d e +--R + +--R 3 2 2 2 4 +--R (17600A b c + 11120B b c )d e +--R + +--R 4 3 3 3 4 4 2 +--R (- 9600A c - 22080B b c )d e + 11520B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (300A b c - 90B b )d e + (- 14400A b c - 600B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (33600A b c + 19680B b c )d e + (- 19200A c - 42240B b c )d e +--R + +--R 4 5 +--R 23040B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 8 2 7 +-+ +--R (3840c e x + 3840c d e )\|c +--R , +--R +--R 2 2 4 3 2 2 2 3 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (9600A c + 18240B b c )d e - 11520B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 4 4 5 +--R (9600A c + 18240B b c )d e - 11520B c d +--R * +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 4 5 6 3 2 4 5 +--R (- 150A b c + 45B b )e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (21600A b c + 3600B b c )d e +--R + +--R 4 2 3 3 3 +--R (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (19200A c + 48000B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (- 150A b c + 45B b )d e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (21600A b c + 3600B b c )d e + (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (19200A c + 48000B b c )d e - 23040B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 384B c e x + ((480A c + 1008B b c )e - 576B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (1360A b c + 744B b c )e + (- 800A c - 1712B b c )d e +--R + +--R 4 2 4 +--R 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (1180A b c + 30B b c)e + (- 2800A b c - 1616B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (1600A c + 3520B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (150A b c - 45B b )e + (- 4100A b c - 270B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (8800A b c + 5560B b c )d e + (- 4800A c - 11040B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (150A b c - 45B b )d e + (- 7200A b c - 300B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (16800A b c + 9840B b c )d e + (- 9600A c - 21120B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 2 8 2 7 +---+ +--R (1920c e x + 1920c d e )\|- c +--R , +--R +--R 4 5 6 3 2 4 5 +--R (- 150A b c + 45B b )e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (21600A b c + 3600B b c )d e +--R + +--R 4 2 3 3 3 +--R (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (19200A c + 48000B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (- 150A b c + 45B b )d e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (21600A b c + 3600B b c )d e + (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (19200A c + 48000B b c )d e - 23040B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 2 4 3 2 2 2 3 +--R - 9600A b c d e + (28800A b c + 13440B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (- 19200A c - 36480B b c )d e + 23040B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R - 9600A b c d e + (28800A b c + 13440B b c )d e +--R + +--R 4 3 4 4 5 +--R (- 19200A c - 36480B b c )d e + 23040B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 d\|c x + b x +--R \|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 384B c e x + ((480A c + 1008B b c )e - 576B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (1360A b c + 744B b c )e + (- 800A c - 1712B b c )d e +--R + +--R 4 2 4 +--R 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (1180A b c + 30B b c)e + (- 2800A b c - 1616B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (1600A c + 3520B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (150A b c - 45B b )e + (- 4100A b c - 270B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (8800A b c + 5560B b c )d e + (- 4800A c - 11040B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (150A b c - 45B b )d e + (- 7200A b c - 300B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (16800A b c + 9840B b c )d e + (- 9600A c - 21120B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 2 8 2 7 +---+ +--R (1920c e x + 1920c d e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 450 + +--S 451 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 5 5 3 2 4 4 +--R (10A b c - 3B b )e + (160A b c - 20B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 1440A b c - 240B b c )d e + (2560A b c + 1920B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 1280A c - 3200B b c )d e + 1536B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 3 3 2 2 2 2 +--R 640A b c d e + (- 1920A b c - 896B b c )d e +--R + +--R 4 3 3 4 4 +--R (1280A c + 2432B b c )d e - 1536B c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 4 5 5 3 2 4 4 +--R (20A b c - 6B b )e + (320A b c - 40B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 2880A b c - 480B b c )d e + (5120A b c + 3840B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 2560A c - 6400B b c )d e + 3072B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 3 2 2 2 2 +--R - 640A b c d e + (1920A b c + 896B b c )d e +--R + +--R 4 3 3 4 4 +--R (- 1280A c - 2432B b c )d e + 1536B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 2 7 +-+ +--R 256c e \|c +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 5 5 3 2 4 4 +--R (10A b c - 3B b )e + (160A b c - 20B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 1440A b c - 240B b c )d e + (2560A b c + 1920B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 1280A c - 3200B b c )d e + 1536B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 5 5 3 2 4 4 +--R (20A b c - 6B b )e + (320A b c - 40B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 2880A b c - 480B b c )d e + (5120A b c + 3840B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 2560A c - 6400B b c )d e + 3072B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 3 2 2 2 2 +--R - 640A b c d e + (1920A b c + 896B b c )d e +--R + +--R 4 3 3 4 4 +--R (- 1280A c - 2432B b c )d e + 1536B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 3 3 2 2 2 2 +--R - 1280A b c d e + (3840A b c + 1792B b c )d e +--R + +--R 4 3 3 4 4 +--R (- 2560A c - 4864B b c )d e + 3072B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 2 7 +-+ +--R 256c e \|c +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 454 + +)clear all + +--S 455 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1457 +r0:=-5/24*(B*d*(24*c*d-13*b*e)-2*A*e*(8*c*d-3*b*e)+e*(6*B*c*d-b*B*e-_ + 4*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/4*(3*B*d-2*A*e+B*e*x)*_ + (b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)-5/64*(8*A*c*e*(32*c^3*d^3-48*b*c^2*_ + d^2*e+18*b^2*c*d*e^2-b^3*e^3)-B*(384*c^4*d^4-640*b*c^3*d^3*e+288*b^2*_ + c^2*d^2*e^2-24*b^3*c*d*e^3-b^4*e^4))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/_ + (c^(3/2)*e^7)+5/8*(A*e*(16*c^2*d^2-16*b*c*d*e+3*b^2*e^2)-B*d*(24*c^2*_ + d^2-28*b*c*d*e+7*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-b*e)/e^7+5/64*_ + (8*A*c*e*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2)-B*(192*c^3*d^3-272*b*c^2*_ + d^2*e+88*b^2*c*d*e^2-b^3*e^3)-2*c*e*(16*A*c*e*(2*c*d-b*e)-B*(48*c^2*_ + d^2-32*b*c*d*e+b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c*e^6) +--R +--R +--R (2) +--R 3 4 6 2 2 3 5 +--R (120A b c - 15B b )e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (240A b c - 30B b )d e + (- 4320A b c - 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (11520A b c + 8640B b c )d e + (- 7680A c - 19200B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (120A b c - 15B b )d e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 6 +--R 5760B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 2 4 +--R - 360A b c e + (1920A b c + 840B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 1920A c - 3360B b c )d e + 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R - 720A b c d e + (3840A b c + 1680B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 3840A c - 6720B b c )d e + 5760B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R - 360A b c d e + (1920A b c + 840B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 1920A c - 3360B b c )d e + 2880B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 48B c e x + ((64A c + 136B b c )e - 96B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (208A b c + 118B b c)e + (- 160A c - 352B b c )d e +--R + +--R 3 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (264A b c + 15B b )e + (- 880A b c - 556B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (640A c + 1480B b c )d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (960A b c + 30B b )d e + (- 3680A b c - 2090B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 6240B b c )d e - 4320B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (600A b c + 15B b )d e + (- 2400A b c - 1320B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1920A c + 4080B b c )d e - 2880B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 9 2 8 2 7 +-+ +--R (192c e x + 384c d e x + 192c d e )\|c +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 6 2 2 3 5 +--R (- 120A b c + 15B b )e + (2160A b c + 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 5760A b c - 4320B b c )d e + (3840A c + 9600B b c )d e +--R + +--R 4 4 2 +--R - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (- 240A b c + 30B b )d e + (4320A b c + 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (- 11520A b c - 8640B b c )d e + (7680A c + 19200B b c )d e +--R + +--R 4 5 +--R - 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (- 120A b c + 15B b )d e + (2160A b c + 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (- 5760A b c - 4320B b c )d e + (3840A c + 9600B b c )d e +--R + +--R 4 6 +--R - 5760B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 5 2 2 4 +--R - 720A b c e + (3840A b c + 1680B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 3840A c - 6720B b c )d e + 5760B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R - 1440A b c d e + (7680A b c + 3360B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 7680A c - 13440B b c )d e + 11520B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R - 720A b c d e + (3840A b c + 1680B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 3840A c - 6720B b c )d e + 5760B c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 96B c e x + ((128A c + 272B b c )e - 192B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (416A b c + 236B b c)e + (- 320A c - 704B b c )d e +--R + +--R 3 2 4 +--R 480B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (528A b c + 30B b )e + (- 1760A b c - 1112B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (1280A c + 2960B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (1920A b c + 60B b )d e + (- 7360A b c - 4180B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (5760A c + 12480B b c )d e - 8640B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (1200A b c + 30B b )d e + (- 4800A b c - 2640B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (3840A c + 8160B b c )d e - 5760B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 9 2 8 2 7 +-+ +--R (384c e x + 768c d e x + 384c d e )\|c +--R , +--R +--R 3 4 6 2 2 3 5 +--R (- 120A b c + 15B b )e + (2160A b c + 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 5760A b c - 4320B b c )d e + (3840A c + 9600B b c )d e +--R + +--R 4 4 2 +--R - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (- 240A b c + 30B b )d e + (4320A b c + 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (- 11520A b c - 8640B b c )d e + (7680A c + 19200B b c )d e +--R + +--R 4 5 +--R - 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (- 120A b c + 15B b )d e + (2160A b c + 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (- 5760A b c - 4320B b c )d e + (3840A c + 9600B b c )d e +--R + +--R 4 6 +--R - 5760B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 5 2 2 4 +--R 1440A b c e + (- 7680A b c - 3360B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (7680A c + 13440B b c )d e - 11520B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R 2880A b c d e + (- 15360A b c - 6720B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (15360A c + 26880B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R 1440A b c d e + (- 7680A b c - 3360B b c)d e +--R + +--R 3 2 4 3 5 +--R (7680A c + 13440B b c )d e - 11520B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 96B c e x + ((128A c + 272B b c )e - 192B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (416A b c + 236B b c)e + (- 320A c - 704B b c )d e +--R + +--R 3 2 4 +--R 480B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (528A b c + 30B b )e + (- 1760A b c - 1112B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (1280A c + 2960B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (1920A b c + 60B b )d e + (- 7360A b c - 4180B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (5760A c + 12480B b c )d e - 8640B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (1200A b c + 30B b )d e + (- 4800A b c - 2640B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (3840A c + 8160B b c )d e - 5760B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 9 2 8 2 7 +-+ +--R (384c e x + 768c d e x + 384c d e )\|c +--R , +--R +--R 2 5 2 2 4 +--R - 360A b c e + (1920A b c + 840B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 1920A c - 3360B b c )d e + 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R - 720A b c d e + (3840A b c + 1680B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 3840A c - 6720B b c )d e + 5760B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R - 360A b c d e + (1920A b c + 840B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 1920A c - 3360B b c )d e + 2880B c d +--R * +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 3 4 6 2 2 3 5 +--R (120A b c - 15B b )e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (240A b c - 30B b )d e + (- 4320A b c - 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (11520A b c + 8640B b c )d e + (- 7680A c - 19200B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (120A b c - 15B b )d e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 6 +--R 5760B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 48B c e x + ((64A c + 136B b c )e - 96B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (208A b c + 118B b c)e + (- 160A c - 352B b c )d e +--R + +--R 3 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (264A b c + 15B b )e + (- 880A b c - 556B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (640A c + 1480B b c )d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (960A b c + 30B b )d e + (- 3680A b c - 2090B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 6240B b c )d e - 4320B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (600A b c + 15B b )d e + (- 2400A b c - 1320B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1920A c + 4080B b c )d e - 2880B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 9 2 8 2 7 +---+ +--R (192c e x + 384c d e x + 192c d e )\|- c +--R , +--R +--R 3 4 6 2 2 3 5 +--R (120A b c - 15B b )e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (240A b c - 30B b )d e + (- 4320A b c - 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (11520A b c + 8640B b c )d e + (- 7680A c - 19200B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (120A b c - 15B b )d e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 6 +--R 5760B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 5 2 2 4 +--R 720A b c e + (- 3840A b c - 1680B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (3840A c + 6720B b c )d e - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R 1440A b c d e + (- 7680A b c - 3360B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (7680A c + 13440B b c )d e - 11520B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R 720A b c d e + (- 3840A b c - 1680B b c)d e +--R + +--R 3 2 4 3 5 +--R (3840A c + 6720B b c )d e - 5760B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 d\|c x + b x +--R \|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 48B c e x + ((64A c + 136B b c )e - 96B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (208A b c + 118B b c)e + (- 160A c - 352B b c )d e +--R + +--R 3 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (264A b c + 15B b )e + (- 880A b c - 556B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (640A c + 1480B b c )d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (960A b c + 30B b )d e + (- 3680A b c - 2090B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 6240B b c )d e - 4320B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (600A b c + 15B b )d e + (- 2400A b c - 1320B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1920A c + 4080B b c )d e - 2880B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 9 2 8 2 7 +---+ +--R (192c e x + 384c d e x + 192c d e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 457 + +--S 458 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 4 2 2 3 3 +--R (- 40A b c + 5B b )e + (720A b c + 120B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 1920A b c - 1440B b c )d e + (1280A c + 3200B b c )d e +--R + +--R 4 4 +--R - 1920B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 2 2 +--R - 240A b c e + (1280A b c + 560B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 1280A c - 2240B b c )d e + 1920B c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 3 4 4 2 2 3 3 +--R (- 80A b c + 10B b )e + (1440A b c + 240B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 3840A b c - 2880B b c )d e + (2560A c + 6400B b c )d e +--R + +--R 4 4 +--R - 3840B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 +--R 240A b c e + (- 1280A b c - 560B b c)d e +--R + +--R 3 2 2 3 3 +--R (1280A c + 2240B b c )d e - 1920B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 7 +-+ +--R 128c e \|c +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 4 2 2 3 3 +--R (- 40A b c + 5B b )e + (720A b c + 120B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 1920A b c - 1440B b c )d e + (1280A c + 3200B b c )d e +--R + +--R 4 4 +--R - 1920B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 4 2 2 3 3 +--R (- 80A b c + 10B b )e + (1440A b c + 240B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 3840A b c - 2880B b c )d e + (2560A c + 6400B b c )d e +--R + +--R 4 4 +--R - 3840B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 +--R 240A b c e + (- 1280A b c - 560B b c)d e +--R + +--R 3 2 2 3 3 +--R (1280A c + 2240B b c )d e - 1920B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 +--R 480A b c e + (- 2560A b c - 1120B b c)d e +--R + +--R 3 2 2 3 3 +--R (2560A c + 4480B b c )d e - 3840B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 7 +-+ +--R 128c e \|c +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 461 + +)clear all + +--S 462 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1457 +r0:=-5/12*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+e*(4*B*c*d-b*B*e-2*A*c*e)*x)*_ + (b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(2*B*d-A*e+B*e*x)*_ + (b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)+5/8*(2*A*c*e*(16*c^2*d^2-_ + 16*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+24*b^2*c*d*e^2-_ + b^3*e^3))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^7*sqrt(c))+5/16*(B*d*_ + (64*c^3*d^3-112*b*c^2*d^2*e+56*b^2*c*d*e^2-7*b^3*e^3)-A*e*(32*c^3*d^3-_ + 48*b*c^2*d^2*e+18*b^2*c*d*e^2-b^3*e^3))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^7*sqrt(d)*sqrt(c*d-b*e))-_ + 5/8*(A*e*(16*c^2*d^2-12*b*c*d*e+b^2*e^2)-2*B*d*(16*c^2*d^2-_ + 16*b*c*d*e+3*b^2*e^2)+e*(4*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+_ + b^2*e^2))*x)*sqrt(b*x+c*x^2)/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 3 6 2 2 5 +--R (180A b c + 30B b )e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (960A c + 2400B b c )d e - 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (180A b c + 30B b )d e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 5 3 6 +--R (960A c + 2400B b c )d e - 1920B c d +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 7 2 3 6 +--R - 15A b e + (270A b c + 105B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e +--R + +--R 3 4 3 +--R - 960B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 5 2 +--R - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 6 +--R - 2880B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 15A b d e + (270A b c + 105B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e - 960B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 6 5 2 6 2 5 4 +--R 16B c e x + ((24A c + 52B b c)e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 3 +--R ((108A b c + 66B b )e + (- 120A c - 276B b c)d e + 240B c d e )x +--R + +--R 2 6 2 5 +--R - 66A b e + (700A b c + 372B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 880A c - 1840B b c)d e + 1760B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 80A b d e + (920A b c + 470B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 1200A c - 2440B b c)d e + 2400B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 30A b d e + (360A b c + 180B b )d e + (- 480A c - 960B b c)d e +--R + +--R 2 5 +--R 960B c d e +--R * +--R +----------+ +--R +-----------+ +-+ +-+ | 2 +--R \|- b e + c d \|c \|d \|c x + b x +--R / +--R 10 3 9 2 2 8 3 7 +-----------+ +-+ +-+ +--R (48e x + 144d e x + 144d e x + 48d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 6 2 2 5 +--R (90A b c + 15B b )e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (480A c + 1200B b c )d e - 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (90A b c + 15B b )d e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 5 3 6 +--R (480A c + 1200B b c )d e - 960B c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +-+ +--R \|- b d e + c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 7 2 3 6 +--R - 15A b e + (270A b c + 105B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e +--R + +--R 3 4 3 +--R - 960B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 5 2 +--R - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 6 +--R - 2880B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 15A b d e + (270A b c + 105B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e - 960B c d +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 6 5 2 6 2 5 4 +--R 16B c e x + ((24A c + 52B b c)e - 48B c d e )x +--R + +--R 2 6 2 5 +--R (108A b c + 66B b )e + (- 120A c - 276B b c)d e +--R + +--R 2 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 5 +--R - 66A b e + (700A b c + 372B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 880A c - 1840B b c)d e + 1760B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 80A b d e + (920A b c + 470B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 1200A c - 2440B b c)d e + 2400B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 +--R - 30A b d e + (360A b c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 480A c - 960B b c)d e + 960B c d e +--R * +--R +--------------+ +----------+ +--R | 2 +-+ | 2 +--R \|- b d e + c d \|c \|c x + b x +--R / +--R +--------------+ +--R 10 3 9 2 2 8 3 7 | 2 +-+ +--R (48e x + 144d e x + 144d e x + 48d e )\|- b d e + c d \|c +--R , +--R +--R 2 3 6 2 2 5 +--R (90A b c + 15B b )e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (480A c + 1200B b c )d e - 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (90A b c + 15B b )d e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 5 3 6 +--R (480A c + 1200B b c )d e - 960B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +-+ +--R \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 7 2 3 6 +--R - 30A b e + (540A b c + 210B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 1440A b c - 1680B b c)d e + (960A c + 3360B b c )d e +--R + +--R 3 4 3 +--R - 1920B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 90A b d e + (1620A b c + 630B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 4320A b c - 5040B b c)d e + (2880A c + 10080B b c )d e +--R + +--R 3 5 2 +--R - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 90A b d e + (1620A b c + 630B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 4320A b c - 5040B b c)d e + (2880A c + 10080B b c )d e +--R + +--R 3 6 +--R - 5760B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 30A b d e + (540A b c + 210B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (- 1440A b c - 1680B b c)d e + (960A c + 3360B b c )d e +--R + +--R 3 7 +--R - 1920B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-+ \|b d e - c d \|c x + b x +--R \|c atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 6 5 2 6 2 5 4 +--R 16B c e x + ((24A c + 52B b c)e - 48B c d e )x +--R + +--R 2 6 2 5 +--R (108A b c + 66B b )e + (- 120A c - 276B b c)d e +--R + +--R 2 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 5 +--R - 66A b e + (700A b c + 372B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 880A c - 1840B b c)d e + 1760B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 80A b d e + (920A b c + 470B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 1200A c - 2440B b c)d e + 2400B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 +--R - 30A b d e + (360A b c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 480A c - 960B b c)d e + 960B c d e +--R * +--R +------------+ +----------+ +--R +-+ | 2 | 2 +--R \|c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 10 3 9 2 2 8 3 7 +-+ | 2 +--R (48e x + 144d e x + 144d e x + 48d e )\|c \|b d e - c d +--R , +--R +--R 3 7 2 3 6 +--R - 15A b e + (270A b c + 105B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e +--R + +--R 3 4 3 +--R - 960B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 5 2 +--R - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 6 +--R - 2880B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 15A b d e + (270A b c + 105B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e - 960B c d +--R * +--R +---+ +--R \|- c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 6 2 2 5 +--R (180A b c + 30B b )e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (960A c + 2400B b c )d e - 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (180A b c + 30B b )d e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 5 3 6 +--R (960A c + 2400B b c )d e - 1920B c d +--R * +--R +----------+ +--R +--------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|- b d e + c d atan(-------------------) +--R c x +--R + +--R 2 6 5 2 6 2 5 4 +--R 16B c e x + ((24A c + 52B b c)e - 48B c d e )x +--R + +--R 2 6 2 5 +--R (108A b c + 66B b )e + (- 120A c - 276B b c)d e +--R + +--R 2 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 5 +--R - 66A b e + (700A b c + 372B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 880A c - 1840B b c)d e + 1760B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 80A b d e + (920A b c + 470B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 1200A c - 2440B b c)d e + 2400B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 +--R - 30A b d e + (360A b c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 480A c - 960B b c)d e + 960B c d e +--R * +--R +--------------+ +----------+ +--R | 2 +---+ | 2 +--R \|- b d e + c d \|- c \|c x + b x +--R / +--R +--------------+ +--R 10 3 9 2 2 8 3 7 | 2 +---+ +--R (48e x + 144d e x + 144d e x + 48d e )\|- b d e + c d \|- c +--R , +--R +--R 3 7 2 3 6 +--R - 15A b e + (270A b c + 105B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e +--R + +--R 3 4 3 +--R - 960B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 5 2 +--R - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 6 +--R - 2880B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 15A b d e + (270A b c + 105B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e - 960B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +---+ \|b d e - c d \|c x + b x +--R \|- c atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 3 6 2 2 5 +--R (90A b c + 15B b )e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (480A c + 1200B b c )d e - 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (90A b c + 15B b )d e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 5 3 6 +--R (480A c + 1200B b c )d e - 960B c d +--R * +--R +----------+ +--R +------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|b d e - c d atan(-------------------) +--R c x +--R + +--R 2 6 5 2 6 2 5 4 +--R 8B c e x + ((12A c + 26B b c)e - 24B c d e )x +--R + +--R 2 6 2 5 2 2 4 3 +--R ((54A b c + 33B b )e + (- 60A c - 138B b c)d e + 120B c d e )x +--R + +--R 2 6 2 5 +--R - 33A b e + (350A b c + 186B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 440A c - 920B b c)d e + 880B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 40A b d e + (460A b c + 235B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 600A c - 1220B b c)d e + 1200B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 15A b d e + (180A b c + 90B b )d e + (- 240A c - 480B b c)d e +--R + +--R 2 5 +--R 480B c d e +--R * +--R +------------+ +----------+ +--R +---+ | 2 | 2 +--R \|- c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 10 3 9 2 2 8 3 7 +---+ | 2 +--R (24e x + 72d e x + 72d e x + 24d e )\|- c \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 464 + +--S 465 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 +--R (30A b c + 5B b )e + (- 160A b c - 120B b c)d e +--R + +--R 3 2 2 3 3 +--R (160A c + 400B b c )d e - 320B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-----------+ +-+ | 2 +-+ +--R \|- b d e + c d \|- b e + c d \|d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 5A b e + (90A b c + 35B b )d e + (- 240A b c - 280B b c)d e +--R + +--R 3 2 3 3 4 +--R (160A c + 560B b c )d e - 320B c d +--R * +--R +-----------+ +-+ +-+ +--R \|- b e + c d \|c \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 3 2 2 2 +--R (- 60A b c - 10B b )e + (320A b c + 240B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 320A c - 800B b c )d e + 640B c d +--R * +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ x\|c +--R \|- b d e + c d \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 5A b e + (- 90A b c - 35B b )d e + (240A b c + 280B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 160A c - 560B b c )d e + 320B c d +--R * +--R +--------------+ +--R | 2 +-+ (b e - 2c d)x - b d +--R \|- b d e + c d \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 7 | 2 +-----------+ +-+ +-+ +--R 16e \|- b d e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 +--R (30A b c + 5B b )e + (- 160A b c - 120B b c)d e +--R + +--R 3 2 2 3 3 +--R (160A c + 400B b c )d e - 320B c d +--R * +--R +------------+ +----------+ +--R +-----------+ +-+ | 2 | 2 +-+ +--R \|- b e + c d \|d \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 3 2 2 2 +--R (- 60A b c - 10B b )e + (320A b c + 240B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 320A c - 800B b c )d e + 640B c d +--R * +--R +------------+ +-+ +--R +-----------+ +-+ | 2 x\|c +--R \|- b e + c d \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 5A b e + (- 90A b c - 35B b )d e + (240A b c + 280B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 160A c - 560B b c )d e + 320B c d +--R * +--R +------------+ +--R +-+ | 2 (b e - 2c d)x - b d +--R \|c \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A b e + (180A b c + 70B b )d e + (- 480A b c - 560B b c)d e +--R + +--R 3 2 3 3 4 +--R (320A c + 1120B b c )d e - 640B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|c \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 7 +-----------+ +-+ +-+ | 2 +--R 16e \|- b e + c d \|c \|d \|b d e - c d +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1457 +r0:=-5/32*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*d^2-64*b*c*d*e+_ + 17*b^2*e^2))*(b*x+c*x^2)^(3/2)/(d*e^4*(c*d-b*e)*(d+e*x)^2)-5/24*_ + (B*d*(24*c*d-11*b*e)-A*e*(8*c*d-b*e)+6*e*(3*B*c*d-b*B*e-A*c*e)*x)*_ + (b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^3)+1/4*(3*B*d-A*e+2*B*e*x)*(b*x+_ + c*x^2)^(5/2)/(e^2*(d+e*x)^4)+5/128*(A*e*(128*c^4*d^4-256*b*c^3*d^3*e+_ + 144*b^2*c^2*d^2*e^2-16*b^3*c*d*e^3-b^4*e^4)-B*d*(384*c^4*d^4-_ + 896*b*c^3*d^3*e+672*b^2*c^2*d^2*e^2-168*b^3*c*d*e^3+7*b^4*e^4))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(3/2)*e^7*(c*d-b*e)^(3/2))-5/4*(4*A*c*e*(2*c*d-b*e)-_ + B*(24*c^2*d^2-20*b*c*d*e+3*b^2*e^2))*atanh(x*sqrt(c)/sqrt(b*x+_ + c*x^2))*sqrt(c)/e^7-5/64*(B*d*(192*c^3*d^3-304*b*c^2*d^2*e+120*_ + b^2*c*d*e^2-7*b^3*e^3)-A*e*(64*c^3*d^3-80*b*c^2*d^2*e+16*b^2*c*d*_ + e^2+b^3*e^3)-2*c*e*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*_ + d^2-64*b*c*d*e+17*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d*e^6*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 3 7 2 2 2 6 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (3840A c + 21120B b c )d e - 11520B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (11520A b c + 8640B b )d e + (- 34560A b c - 66240B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (23040A c + 126720B b c )d e - 69120B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 7 3 8 +--R (3840A c + 21120B b c )d e - 11520B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 9 3 4 8 +--R - 15A b e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (1920A c + 13440B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 3 6 3 2 2 4 5 +--R (8640A b c + 10080B b c)d e + (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R - 90A b d e + (- 1440A b c - 630B b )d e +--R + +--R 2 2 3 4 5 +--R (12960A b c + 15120B b c)d e +--R + +--R 3 2 2 5 4 4 3 6 3 +--R (- 23040A b c - 60480B b c )d e + (11520A c + 80640B b c )d e +--R + +--R 4 7 2 +--R - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (8640A b c + 10080B b c)d e + (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (1920A c + 13440B b c )d e - 5760B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 7 3 2 6 5 +--R (192B b c d e - 192B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (384A b c + 864B b c)d e + (- 384A c - 2016B b c )d e +--R + +--R 3 3 5 +--R 1152B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 30A b e + (- 1292A b c - 558B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (5232A b c + 8284B b c)d e + (- 4000A c - 19696B b c )d e +--R + +--R 3 4 4 +--R 12000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 146A b d e + (- 2264A b c - 1022B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (10640A b c + 16392B b c)d e + (- 8320A c - 40240B b c )d e +--R + +--R 3 5 3 +--R 24960B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 110A b d e + (- 1740A b c - 770B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (8480A b c + 12860B b c)d e + (- 6720A c - 32160B b c )d e +--R + +--R 3 6 2 +--R 20160B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 30A b d e + (- 480A b c - 210B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (2400A b c + 3600B b c)d e + (- 1920A c - 9120B b c )d e +--R + +--R 3 7 +--R 5760B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (384b d e - 384c d e )x + (1536b d e - 1536c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (2304b d e - 2304c d e )x + (1536b d e - 1536c d e )x + 384b d e +--R + +--R 6 7 +--R - 384c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 7 2 2 2 6 +--R (960A b c + 720B b )d e + (- 2880A b c - 5520B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (1920A c + 10560B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (3840A b c + 2880B b )d e + (- 11520A b c - 22080B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (7680A c + 42240B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (5760A b c + 4320B b )d e + (- 17280A b c - 33120B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (11520A c + 63360B b c )d e - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (3840A b c + 2880B b )d e + (- 11520A b c - 22080B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (7680A c + 42240B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (960A b c + 720B b )d e + (- 2880A b c - 5520B b c)d e +--R + +--R 3 2 7 3 8 +--R (1920A c + 10560B b c )d e - 5760B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R \|- b d e + c d \|c log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 9 3 4 8 +--R 15A b e + (240A b c + 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (- 2160A b c - 2520B b c)d e + (3840A b c + 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (- 1920A c - 13440B b c )d e + 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R 60A b d e + (960A b c + 420B b )d e +--R + +--R 2 2 3 3 6 +--R (- 8640A b c - 10080B b c)d e +--R + +--R 3 2 2 4 5 +--R (15360A b c + 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (- 7680A c - 53760B b c )d e + 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 90A b d e + (1440A b c + 630B b )d e +--R + +--R 2 2 3 4 5 +--R (- 12960A b c - 15120B b c)d e +--R + +--R 3 2 2 5 4 +--R (23040A b c + 60480B b c )d e +--R + +--R 4 3 6 3 4 7 2 +--R (- 11520A c - 80640B b c )d e + 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R 60A b d e + (960A b c + 420B b )d e +--R + +--R 2 2 3 5 4 +--R (- 8640A b c - 10080B b c)d e +--R + +--R 3 2 2 6 3 +--R (15360A b c + 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (- 7680A c - 53760B b c )d e + 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R 15A b d e + (240A b c + 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (- 2160A b c - 2520B b c)d e + (3840A b c + 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (- 1920A c - 13440B b c )d e + 5760B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 7 3 2 6 5 +--R (192B b c d e - 192B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (384A b c + 864B b c)d e + (- 384A c - 2016B b c )d e +--R + +--R 3 3 5 +--R 1152B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 30A b e + (- 1292A b c - 558B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (5232A b c + 8284B b c)d e + (- 4000A c - 19696B b c )d e +--R + +--R 3 4 4 +--R 12000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 146A b d e + (- 2264A b c - 1022B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (10640A b c + 16392B b c)d e + (- 8320A c - 40240B b c )d e +--R + +--R 3 5 3 +--R 24960B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 110A b d e + (- 1740A b c - 770B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (8480A b c + 12860B b c)d e + (- 6720A c - 32160B b c )d e +--R + +--R 3 6 2 +--R 20160B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 30A b d e + (- 480A b c - 210B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (2400A b c + 3600B b c)d e + (- 1920A c - 9120B b c )d e +--R + +--R 3 7 +--R 5760B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (384b d e - 384c d e )x + (1536b d e - 1536c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (2304b d e - 2304c d e )x + (1536b d e - 1536c d e )x + 384b d e +--R + +--R 6 7 +--R - 384c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 3 7 2 2 2 6 +--R (480A b c + 360B b )d e + (- 1440A b c - 2760B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (960A c + 5280B b c )d e - 2880B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (3840A c + 21120B b c )d e - 11520B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (2880A b c + 2160B b )d e + (- 8640A b c - 16560B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (5760A c + 31680B b c )d e - 17280B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (3840A c + 21120B b c )d e - 11520B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (480A b c + 360B b )d e + (- 1440A b c - 2760B b c)d e +--R + +--R 3 2 7 3 8 +--R (960A c + 5280B b c )d e - 2880B c d +--R * +--R +------------+ +----------+ +--R +-+ | 2 +-+ | 2 +--R \|c \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 9 3 4 8 +--R - 15A b e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (1920A c + 13440B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 3 6 +--R (8640A b c + 10080B b c)d e +--R + +--R 3 2 2 4 5 +--R (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R - 90A b d e + (- 1440A b c - 630B b )d e +--R + +--R 2 2 3 4 5 +--R (12960A b c + 15120B b c)d e +--R + +--R 3 2 2 5 4 +--R (- 23040A b c - 60480B b c )d e +--R + +--R 4 3 6 3 4 7 2 +--R (11520A c + 80640B b c )d e - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 5 4 +--R (8640A b c + 10080B b c)d e +--R + +--R 3 2 2 6 3 +--R (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (1920A c + 13440B b c )d e - 5760B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 7 3 2 6 5 +--R (96B b c d e - 96B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (192A b c + 432B b c)d e + (- 192A c - 1008B b c )d e +--R + +--R 3 3 5 +--R 576B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 15A b e + (- 646A b c - 279B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (2616A b c + 4142B b c)d e + (- 2000A c - 9848B b c )d e +--R + +--R 3 4 4 +--R 6000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 73A b d e + (- 1132A b c - 511B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (5320A b c + 8196B b c)d e + (- 4160A c - 20120B b c )d e +--R + +--R 3 5 3 +--R 12480B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 55A b d e + (- 870A b c - 385B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (4240A b c + 6430B b c)d e + (- 3360A c - 16080B b c )d e +--R + +--R 3 6 2 +--R 10080B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (1200A b c + 1800B b c)d e + (- 960A c - 4560B b c )d e +--R + +--R 3 7 +--R 2880B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (192b d e - 192c d e )x + (768b d e - 768c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (1152b d e - 1152c d e )x + (768b d e - 768c d e )x + 192b d e +--R + +--R 6 7 +--R - 192c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R , +--R +--R 4 9 3 4 8 +--R 15A b e + (240A b c + 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (- 2160A b c - 2520B b c)d e + (3840A b c + 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (- 1920A c - 13440B b c )d e + 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R 60A b d e + (960A b c + 420B b )d e +--R + +--R 2 2 3 3 6 +--R (- 8640A b c - 10080B b c)d e +--R + +--R 3 2 2 4 5 +--R (15360A b c + 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (- 7680A c - 53760B b c )d e + 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 90A b d e + (1440A b c + 630B b )d e +--R + +--R 2 2 3 4 5 +--R (- 12960A b c - 15120B b c)d e +--R + +--R 3 2 2 5 4 +--R (23040A b c + 60480B b c )d e +--R + +--R 4 3 6 3 4 7 2 +--R (- 11520A c - 80640B b c )d e + 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R 60A b d e + (960A b c + 420B b )d e +--R + +--R 2 2 3 5 4 +--R (- 8640A b c - 10080B b c)d e +--R + +--R 3 2 2 6 3 +--R (15360A b c + 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (- 7680A c - 53760B b c )d e + 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R 15A b d e + (240A b c + 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (- 2160A b c - 2520B b c)d e + (3840A b c + 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (- 1920A c - 13440B b c )d e + 5760B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 7 2 2 2 6 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (3840A c + 21120B b c )d e - 11520B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (11520A b c + 8640B b )d e + (- 34560A b c - 66240B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (23040A c + 126720B b c )d e - 69120B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 7 3 8 +--R (3840A c + 21120B b c )d e - 11520B c d +--R * +--R +----------+ +--R +--------------+ | 2 +--R | 2 +---+ \|c x + b x +--R \|- b d e + c d \|- c atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 2 7 3 2 6 5 +--R (192B b c d e - 192B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (384A b c + 864B b c)d e + (- 384A c - 2016B b c )d e +--R + +--R 3 3 5 +--R 1152B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 30A b e + (- 1292A b c - 558B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (5232A b c + 8284B b c)d e + (- 4000A c - 19696B b c )d e +--R + +--R 3 4 4 +--R 12000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 146A b d e + (- 2264A b c - 1022B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (10640A b c + 16392B b c)d e + (- 8320A c - 40240B b c )d e +--R + +--R 3 5 3 +--R 24960B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 110A b d e + (- 1740A b c - 770B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (8480A b c + 12860B b c)d e + (- 6720A c - 32160B b c )d e +--R + +--R 3 6 2 +--R 20160B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 30A b d e + (- 480A b c - 210B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (2400A b c + 3600B b c)d e + (- 1920A c - 9120B b c )d e +--R + +--R 3 7 +--R 5760B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (384b d e - 384c d e )x + (1536b d e - 1536c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (2304b d e - 2304c d e )x + (1536b d e - 1536c d e )x + 384b d e +--R + +--R 6 7 +--R - 384c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 4 9 3 4 8 +--R - 15A b e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (1920A c + 13440B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 3 6 +--R (8640A b c + 10080B b c)d e +--R + +--R 3 2 2 4 5 +--R (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R - 90A b d e + (- 1440A b c - 630B b )d e +--R + +--R 2 2 3 4 5 +--R (12960A b c + 15120B b c)d e +--R + +--R 3 2 2 5 4 +--R (- 23040A b c - 60480B b c )d e +--R + +--R 4 3 6 3 4 7 2 +--R (11520A c + 80640B b c )d e - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 5 4 +--R (8640A b c + 10080B b c)d e +--R + +--R 3 2 2 6 3 +--R (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (1920A c + 13440B b c )d e - 5760B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 3 7 2 2 2 6 +--R (960A b c + 720B b )d e + (- 2880A b c - 5520B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (1920A c + 10560B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (3840A b c + 2880B b )d e + (- 11520A b c - 22080B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (7680A c + 42240B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (5760A b c + 4320B b )d e + (- 17280A b c - 33120B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (11520A c + 63360B b c )d e - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (3840A b c + 2880B b )d e + (- 11520A b c - 22080B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (7680A c + 42240B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (960A b c + 720B b )d e + (- 2880A b c - 5520B b c)d e +--R + +--R 3 2 7 3 8 +--R (1920A c + 10560B b c )d e - 5760B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 \|c x + b x +--R \|- c \|b d e - c d atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 2 7 3 2 6 5 +--R (96B b c d e - 96B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (192A b c + 432B b c)d e + (- 192A c - 1008B b c )d e +--R + +--R 3 3 5 +--R 576B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 15A b e + (- 646A b c - 279B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (2616A b c + 4142B b c)d e + (- 2000A c - 9848B b c )d e +--R + +--R 3 4 4 +--R 6000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 73A b d e + (- 1132A b c - 511B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (5320A b c + 8196B b c)d e + (- 4160A c - 20120B b c )d e +--R + +--R 3 5 3 +--R 12480B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 55A b d e + (- 870A b c - 385B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (4240A b c + 6430B b c)d e + (- 3360A c - 16080B b c )d e +--R + +--R 3 6 2 +--R 10080B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (1200A b c + 1800B b c)d e + (- 960A c - 4560B b c )d e +--R + +--R 3 7 +--R 2880B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (192b d e - 192c d e )x + (768b d e - 768c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (1152b d e - 1152c d e )x + (768b d e - 768c d e )x + 192b d e +--R + +--R 6 7 +--R - 192c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 471 + +--S 472 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 2 +--R (320A b c + 240B b )d e + (- 960A b c - 1840B b c)d e +--R + +--R 3 2 3 3 4 +--R (640A c + 3520B b c )d e - 1920B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-----------+ +-+ +-+ +-+ | 2 +--R \|- b d e + c d \|- b e + c d \|c \|d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 5A b e + (80A b c + 35B b )d e + (- 720A b c - 840B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (1280A b c + 3360B b c )d e + (- 640A c - 4480B b c )d e +--R + +--R 4 5 +--R 1920B c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 3 2 2 2 2 +--R (- 640A b c - 480B b )d e + (1920A b c + 3680B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 1280A c - 7040B b c )d e + 3840B c d +--R * +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ +-+ x\|c +--R \|- b d e + c d \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 5A b e + (80A b c + 35B b )d e + (- 720A b c - 840B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (1280A b c + 3360B b c )d e + (- 640A c - 4480B b c )d e +--R + +--R 4 5 +--R 1920B c d +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 8 2 7 | 2 +-----------+ +-+ +--R (128b d e - 128c d e )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 2 +--R (320A b c + 240B b )d e + (- 960A b c - 1840B b c)d e +--R + +--R 3 2 3 3 4 +--R (640A c + 3520B b c )d e - 1920B c d +--R * +--R +------------+ +----------+ +--R +-----------+ +-+ +-+ | 2 +-+ | 2 +--R \|- b e + c d \|c \|d \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 3 3 2 2 2 2 +--R (- 640A b c - 480B b )d e + (1920A b c + 3680B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 1280A c - 7040B b c )d e + 3840B c d +--R * +--R +------------+ +-+ +--R +-----------+ +-+ +-+ | 2 x\|c +--R \|- b e + c d \|c \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 5A b e + (80A b c + 35B b )d e + (- 720A b c - 840B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (1280A b c + 3360B b c )d e + (- 640A c - 4480B b c )d e +--R + +--R 4 5 +--R 1920B c d +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 10A b e + (- 160A b c - 70B b )d e + (1440A b c + 1680B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (- 2560A b c - 6720B b c )d e + (1280A c + 8960B b c )d e +--R + +--R 4 5 +--R - 3840B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 8 2 7 +-----------+ +-+ | 2 +--R (128b d e - 128c d e )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 1457 +t0:=(A+B*x)*(d+e*x)^3/sqrt(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1457 +r0:=1/64*(128*A*c^4*d^3+35*b^4*B*e^3+144*b^2*c^2*d*e*(B*d+A*e)-40*b^3*_ + c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/c^(9/2)+1/192*(8*A*c*e*(52*c^2*d^2-52*b*c*d*e+_ + 15*b^2*e^2)+B*(96*c^3*d^3-352*b*c^2*d^2*e+346*b^2*c*d*e^2-105*_ + b^3*e^3))*sqrt(b*x+c*x^2)/c^4+1/24*(6*B*c*d-7*b*B*e+8*A*c*e)*_ + (d+e*x)^2*sqrt(b*x+c*x^2)/c^2+1/4*B*(d+e*x)^3*sqrt(b*x+c*x^2)/c-_ + 1/96*e*(d*(12*b*B*c*d-48*A*c^2*d-7*b^2*B*e+8*A*b*c*e)-(40*A*c*e*_ + (2*c*d-b*e)+B*(24*c^2*d^2-64*b*c*d*e+35*b^2*e^2))*x)*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (- 120A b c + 105B b )e + (432A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 576A b c + 432B b c )d e + (384A c - 192B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B c e x + ((64A c - 56B b c )e + 192B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 80A b c + 70B b c)e + (288A c - 240B b c )d e + 288B c d e)x +--R + +--R 2 3 3 2 2 2 +--R (120A b c - 105B b )e + (- 432A b c + 360B b c)d e +--R + +--R 3 2 2 3 3 +--R (576A c - 432B b c )d e + 192B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 3 2 2 3 2 +--R (120A b c - 105B b )e + (- 432A b c + 360B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (576A b c - 432B b c )d e + (- 384A c + 192B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 96B c e x + ((128A c - 112B b c )e + 384B c d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 160A b c + 140B b c)e + (576A c - 480B b c )d e +--R + +--R 3 2 +--R 576B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 +--R (240A b c - 210B b )e + (- 864A b c + 720B b c)d e +--R + +--R 3 2 2 3 3 +--R (1152A c - 864B b c )d e + 384B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 384c \|c +--R , +--R +--R 3 4 3 2 2 3 2 +--R (- 120A b c + 105B b )e + (432A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 576A b c + 432B b c )d e + (384A c - 192B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B c e x + ((64A c - 56B b c )e + 192B c d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 80A b c + 70B b c)e + (288A c - 240B b c )d e +--R + +--R 3 2 +--R 288B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 +--R (120A b c - 105B b )e + (- 432A b c + 360B b c)d e +--R + +--R 3 2 2 3 3 +--R (576A c - 432B b c )d e + 192B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 192c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 478 + +--S 479 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 +--R (40A b c - 35B b )e + (- 144A b c + 120B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (192A b c - 144B b c )d e + (- 128A c + 64B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 3 2 2 3 2 +--R (80A b c - 70B b )e + (- 288A b c + 240B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (384A b c - 288B b c )d e + (- 256A c + 128B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 128c \|c +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 3 2 2 3 2 +--R (40A b c - 35B b )e + (- 144A b c + 120B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (192A b c - 144B b c )d e + (- 128A c + 64B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 4 3 2 2 3 2 +--R (- 40A b c + 35B b )e + (144A b c - 120B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 192A b c + 144B b c )d e + (128A c - 64B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 64c \|- c \|c +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 482 + +)clear all + +--S 483 of 1457 +t0:=(A+B*x)*(d+e*x)^2/sqrt(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1457 +r0:=1/8*(16*A*c^3*d^2-5*b^3*B*e^2+6*b^2*c*e*(2*B*d+A*e)-8*b*c^2*d*_ + (B*d+2*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/24*(18*A*c*_ + e*(2*c*d-b*e)+B*(16*c^2*d^2-34*b*c*d*e+15*b^2*e^2))*sqrt(b*x+_ + c*x^2)/c^3+1/3*B*(d+e*x)^2*sqrt(b*x+c*x^2)/c-1/12*e*((b*B-6*A*c)*_ + d-(4*B*c*d-5*b*B*e+6*A*c*e)*x)*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R (18A b c - 15B b )e + (- 48A b c + 36B b c)d e +--R + +--R 3 2 2 +--R (48A c - 24B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 2 2 +--R 8B c e x + ((12A c - 10B b c)e + 24B c d e)x +--R + +--R 2 2 2 2 2 +--R (- 18A b c + 15B b )e + (48A c - 36B b c)d e + 24B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 24c \|c +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 +--R (18A b c - 15B b )e + (- 48A b c + 36B b c)d e +--R + +--R 3 2 2 +--R (48A c - 24B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 2 2 2 +--R 16B c e x + ((24A c - 20B b c)e + 48B c d e)x +--R + +--R 2 2 2 2 2 +--R (- 36A b c + 30B b )e + (96A c - 72B b c)d e + 48B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 48c \|c +--R , +--R +--R 2 3 2 2 2 +--R (18A b c - 15B b )e + (- 48A b c + 36B b c)d e +--R + +--R 3 2 2 +--R (48A c - 24B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 2 2 2 2 2 +--R 8B c e x + ((12A c - 10B b c)e + 24B c d e)x +--R + +--R 2 2 2 2 2 +--R (- 18A b c + 15B b )e + (48A c - 36B b c)d e + 24B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 3 +---+ +--R 24c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 485 + +--S 486 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 2 2 +--R ((6A b c - 5B b )e + (- 16A b c + 12B b c)d e + (16A c - 8B b c )d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 2 2 +--R (- 12A b c + 10B b )e + (32A b c - 24B b c)d e +--R + +--R 3 2 2 +--R (- 32A c + 16B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 16c \|c +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 2 2 2 +--R (- 6A b c + 5B b )e + (16A b c - 12B b c)d e +--R + +--R 3 2 2 +--R (- 16A c + 8B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((6A b c - 5B b )e + (- 16A b c + 12B b c)d e + (16A c - 8B b c )d ) +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 8c \|- c \|c +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 489 + +)clear all + +--S 490 of 1457 +t0:=(A+B*x)*(d+e*x)/sqrt(b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1457 +r0:=1/4*(8*A*c^2*d+3*b^2*B*e-4*b*c*(B*d+A*e))*atanh(x*sqrt(c)/sqrt(b*x+_ + c*x^2))/c^(5/2)+1/4*(2*B*c*d-3*b*B*e+4*A*c*e)*sqrt(b*x+c*x^2)/c^2+_ + 1/2*B*(d+e*x)*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 2 2 x\|c +--R ((- 4A b c + 3B b )e + (8A c - 4B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +-+ | 2 +--R (2B c e x + (4A c - 3B b)e + 4B c d)\|c \|c x + b x +--R / +--R 2 +-+ +--R 4c \|c +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R ((4A b c - 3B b )e + (- 8A c + 4B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R +-+ | 2 +--R (4B c e x + (8A c - 6B b)e + 8B c d)\|c \|c x + b x +--R / +--R 2 +-+ +--R 8c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 2 2 \|- c \|c x + b x +--R ((- 4A b c + 3B b )e + (8A c - 4B b c)d)atan(-------------------) +--R c x +--R + +--R +----------+ +--R +---+ | 2 +--R (2B c e x + (4A c - 3B b)e + 4B c d)\|- c \|c x + b x +--R / +--R 2 +---+ +--R 4c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 492 + +--S 493 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 +--R ((4A b c - 3B b )e + (- 8A c + 4B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 2 2 x\|c +--R ((8A b c - 6B b )e + (- 16A c + 8B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 2 +-+ +--R 8c \|c +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 2 +---+ x\|c +--R ((4A b c - 3B b )e + (- 8A c + 4B b c)d)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 2 2 +-+ \|- c \|c x + b x +--R ((- 4A b c + 3B b )e + (8A c - 4B b c)d)\|c atan(-------------------) +--R c x +--R / +--R 2 +---+ +-+ +--R 4c \|- c \|c +--R Type: Expression(Integer) +--E 495 + +--S 496 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 496 + +)clear all + +--S 497 of 1457 +t0:=(A+B*x)/sqrt(b*x+c*x^2) +--R +--R +--R B x + A +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1457 +r0:=-(b*B-2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+B*sqrt(b*x+c*x^2)/c +--R +--R +--R +-+ +----------+ +--R x\|c +-+ | 2 +--R (2A c - B b)atanh(-------------) + B\|c \|c x + b x +--R +----------+ +--R | 2 +--R \|c x + b x +--R (2) ----------------------------------------------------- +--R +-+ +--R c\|c +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R (2A c - B b)log(2c\|c x + b x + (2c x + b)\|c ) + 2B\|c \|c x + b x +--R [-----------------------------------------------------------------------, +--R +-+ +--R 2c\|c +--R +----------+ +--R +---+ | 2 +----------+ +--R \|- c \|c x + b x +---+ | 2 +--R (2A c - B b)atan(-------------------) + B\|- c \|c x + b x +--R c x +--R ------------------------------------------------------------] +--R +---+ +--R c\|- c +--R Type: Union(List(Expression(Integer)),...) +--E 499 + +--S 500 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R | 2 +-+ +--R (2A c - B b)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R x\|c +--R (- 4A c + 2B b)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R +---+ x\|c +--R (- 2A c + B b)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R (2A c - B b)\|c atan(-------------------) +--R c x +--R / +--R +---+ +-+ +--R c\|- c \|c +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 503 + +)clear all + +--S 504 of 1457 +t0:=(A+B*x)/((d+e*x)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ---------------------- +--R +----------+ +--R | 2 +--R (e x + d)\|c x + b x +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1457 +r0:=2*B*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e*sqrt(c))-(B*d-A*e)*atanh(1/2*_ + (b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/_ + (e*sqrt(d)*sqrt(c*d-b*e)) +--R +--R +--R (2) +--R +-+ +--R +-----------+ +-+ x\|c +--R 2B\|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-+ (b e - 2c d)x - b d +--R (- A e + B d)\|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +-----------+ +-+ +-+ +--R e\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 505 + +--S 506 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +----------+ +--R | 2 | 2 +-+ +--R B\|- b d e + c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R (A e - B d)\|c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R / +--R +--------------+ +--R | 2 +-+ +--R e\|- b d e + c d \|c +--R , +--R +--R +------------+ +----------+ +--R | 2 | 2 +-+ +--R B\|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R +-+ \|b d e - c d \|c x + b x +--R (- 2A e + 2B d)\|c atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R +-+ | 2 +--R e\|c \|b d e - c d +--R , +--R +--R +---+ +--R (A e - B d)\|- c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +----------+ +--R +--------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R 2B\|- b d e + c d atan(-------------------) +--R c x +--R / +--R +--------------+ +--R | 2 +---+ +--R e\|- b d e + c d \|- c +--R , +--R +--R +------------+ +----------+ +--R | 2 | 2 +--R +---+ \|b d e - c d \|c x + b x +--R (- 2A e + 2B d)\|- c atan(----------------------------) +--R (b e - c d)x +--R + +--R +----------+ +--R +------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R 2B\|b d e - c d atan(-------------------) +--R c x +--R / +--R +------------+ +--R +---+ | 2 +--R e\|- c \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 506 + +--S 507 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +----------+ +--R | 2 +-----------+ +-+ | 2 +-+ +--R B\|- b d e + c d \|- b e + c d \|d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-----------+ +-+ +-+ +--R (A e - B d)\|- b e + c d \|c \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ x\|c +--R - 2B\|- b d e + c d \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +--------------+ +--R | 2 +-+ (b e - 2c d)x - b d +--R (A e - B d)\|- b d e + c d \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R | 2 +-----------+ +-+ +-+ +--R e\|- b d e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +----------+ +--R +-----------+ +-+ | 2 | 2 +-+ +--R B\|- b e + c d \|d \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +------------+ +-+ +--R +-----------+ +-+ | 2 x\|c +--R - 2B\|- b e + c d \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +------------+ +--R +-+ | 2 (b e - 2c d)x - b d +--R (A e - B d)\|c \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ +-+ \|b d e - c d \|c x + b x +--R (- 2A e + 2B d)\|- b e + c d \|c \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R +-----------+ +-+ +-+ | 2 +--R e\|- b e + c d \|c \|d \|b d e - c d +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1457 +t0:=(A+B*x)/((d+e*x)^2*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (e x + 2d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1457 +r0:=-1/2*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))+(B*d-A*e)*_ + sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 2 +--R ((- A b e + (2A c - B b)d e)x - A b d e + (2A c - B b)d ) +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +-----------+ +-+ | 2 +--R (2A e - 2B d)\|- b e + c d \|d \|c x + b x +--R / +--R 2 2 2 3 +-----------+ +-+ +--R ((2b d e - 2c d e)x + 2b d e - 2c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R ((A b e + (- 2A c + B b)d e)x + A b d e + (- 2A c + B b)d ) +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +----------+ +--R | 2 | 2 +--R (2A e - 2B d)\|- b d e + c d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 | 2 +--R ((2b d e - 2c d e)x + 2b d e - 2c d )\|- b d e + c d +--R , +--R +--R 2 2 +--R ((- A b e + (2A c - B b)d e)x - A b d e + (2A c - B b)d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R (A e - B d)\|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 2 2 2 3 | 2 +--R ((b d e - c d e)x + b d e - c d )\|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 513 + +--S 514 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R (A b e + (- 2A c + B b)d)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R | 2 +--R (A b e + (- 2A c + B b)d)\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +--R (2b d e - 2c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R | 2 +--R (A b e + (- 2A c + B b)d)\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +-----------+ +-+ +--R (- 2A b e + (4A c - 2B b)d)\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 +-----------+ +-+ | 2 +--R (2b d e - 2c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 517 + +)clear all + +--S 518 of 1457 +t0:=(A+B*x)/((d+e*x)^3*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +----------+ +--R 3 3 2 2 2 3 | 2 +--R (e x + 3d e x + 3d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1457 +r0:=1/8*(8*A*c^2*d^2-4*b*c*d*(B*d+2*A*e)+b^2*e*(B*d+3*A*e))*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*_ + (c*d-b*e)^(5/2))+1/2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ + (d+e*x)^2)-1/4*(3*A*e*(2*c*d-b*e)-B*d*(2*c*d+b*e))*sqrt(b*x+c*x^2)/_ + (d^2*(c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 +--R (- 3A b e + (8A b c - B b )d e + (- 8A c + 4B b c)d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (- 6A b d e + (16A b c - 2B b )d e + (- 16A c + 8B b c)d e)x +--R + +--R 2 2 2 2 3 2 4 +--R - 3A b d e + (8A b c - B b )d e + (- 8A c + 4B b c)d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 2 2 +--R (6A b e + (- 12A c + 2B b)d e + 4B c d e)x + 10A b d e +--R + +--R 2 3 +--R (- 16A c - 2B b)d e + 8B c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (8b d e - 16b c d e + 8c d e )x + (16b d e - 32b c d e + 16c d e)x +--R + +--R 2 4 2 5 2 6 +--R 8b d e - 16b c d e + 8c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 2 3 2 2 2 2 +--R (3A b e + (- 8A b c + B b )d e + (8A c - 4B b c)d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (6A b d e + (- 16A b c + 2B b )d e + (16A c - 8B b c)d e)x +--R + +--R 2 2 2 2 3 2 4 +--R 3A b d e + (- 8A b c + B b )d e + (8A c - 4B b c)d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 2 2 2 +--R (6A b e + (- 12A c + 2B b)d e + 4B c d e)x + 10A b d e +--R + +--R 2 3 +--R (- 16A c - 2B b)d e + 8B c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 +--R (8b d e - 16b c d e + 8c d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (16b d e - 32b c d e + 16c d e)x + 8b d e - 16b c d e + 8c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 4 2 3 2 2 2 2 +--R (- 3A b e + (8A b c - B b )d e + (- 8A c + 4B b c)d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (- 6A b d e + (16A b c - 2B b )d e + (- 16A c + 8B b c)d e)x +--R + +--R 2 2 2 2 3 2 4 +--R - 3A b d e + (8A b c - B b )d e + (- 8A c + 4B b c)d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 2 2 2 +--R (3A b e + (- 6A c + B b)d e + 2B c d e)x + 5A b d e +--R + +--R 2 3 +--R (- 8A c - B b)d e + 4B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (4b d e - 8b c d e + 4c d e )x + (8b d e - 16b c d e + 8c d e)x +--R + +--R 2 4 2 5 2 6 +--R 4b d e - 8b c d e + 4c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 520 + +--S 521 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 +-----------+ +-+ +--R (3A b e + (- 8A b c + B b )d e + (8A c - 4B b c)d )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 2 2 2 2 | 2 +--R (3A b e + (- 8A b c + B b )d e + (8A c - 4B b c)d )\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (8b d e - 16b c d e + 8c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 2 2 2 2 2 | 2 +--R (3A b e + (- 8A b c + B b )d e + (8A c - 4B b c)d )\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 2 2 2 +--R (- 6A b e + (16A b c - 2B b )d e + (- 16A c + 8B b c)d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (8b d e - 16b c d e + 8c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 524 + +)clear all + +--S 525 of 1457 +t0:=(A+B*x)/((d+e*x)^4*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R +----------+ +--R 4 4 3 3 2 2 2 3 4 | 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1457 +r0:=1/16*(16*A*c^3*d^3-8*b*c^2*d^2*(B*d+3*A*e)-b^3*e^2*(B*d+5*A*e)+_ + 2*b^2*c*d*e*(2*B*d+9*A*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+_ + 1/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^3)-_ + 1/12*(5*A*e*(2*c*d-b*e)-B*d*(4*c*d+b*e))*sqrt(b*x+c*x^2)/(d^2*_ + (c*d-b*e)^2*(d+e*x)^2)+1/24*(B*d*(8*c^2*d^2+10*b*c*d*e-3*b^2*e^2)-_ + A*e*(44*c^2*d^2-44*b*c*d*e+15*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*_ + (c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 3 6 2 3 5 2 2 2 4 +--R - 15A b e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 3 3 +--R (48A c - 24B b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 2 4 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 3 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R x +--R + +--R 3 3 3 2 3 4 2 2 2 5 +--R - 15A b d e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 6 +--R (48A c - 24B b c )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 88A b c + 6B b )d e + (88A c - 20B b c)d e +--R + +--R 2 3 2 +--R - 16B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 80A b d e + (- 236A b c + 16B b )d e + (216A c - 28B b c)d e +--R + +--R 2 4 +--R - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 66A b d e + (- 180A b c - 6B b )d e + (144A c + 24B b c)d e +--R + +--R 2 5 +--R - 48B c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (48b d e - 144b c d e + 144b c d e - 48c d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (144b d e - 432b c d e + 432b c d e - 144c d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (144b d e - 432b c d e + 432b c d e - 144c d e)x + 48b d e +--R + +--R 2 7 2 2 8 3 9 +--R - 144b c d e + 144b c d e - 48c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 6 2 3 5 2 2 2 4 +--R 15A b e + (- 54A b c + 3B b )d e + (72A b c - 12B b c)d e +--R + +--R 3 2 3 3 +--R (- 48A c + 24B b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 2 4 +--R 45A b d e + (- 162A b c + 9B b )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (216A b c - 36B b c)d e + (- 144A c + 72B b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 45A b d e + (- 162A b c + 9B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (216A b c - 36B b c)d e + (- 144A c + 72B b c )d e +--R * +--R x +--R + +--R 3 3 3 2 3 4 2 2 2 5 +--R 15A b d e + (- 54A b c + 3B b )d e + (72A b c - 12B b c)d e +--R + +--R 3 2 6 +--R (- 48A c + 24B b c )d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 88A b c + 6B b )d e + (88A c - 20B b c)d e +--R + +--R 2 3 2 +--R - 16B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R 80A b d e + (- 236A b c + 16B b )d e +--R + +--R 2 3 2 2 4 +--R (216A c - 28B b c)d e - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 66A b d e + (- 180A b c - 6B b )d e + (144A c + 24B b c)d e +--R + +--R 2 5 +--R - 48B c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (48b d e - 144b c d e + 144b c d e - 48c d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (144b d e - 432b c d e + 432b c d e - 144c d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (144b d e - 432b c d e + 432b c d e - 144c d e)x + 48b d e +--R + +--R 2 7 2 2 8 3 9 +--R - 144b c d e + 144b c d e - 48c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 3 6 2 3 5 2 2 2 4 +--R - 15A b e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 3 3 +--R (48A c - 24B b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 2 4 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 3 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R x +--R + +--R 3 3 3 2 3 4 2 2 2 5 +--R - 15A b d e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 6 +--R (48A c - 24B b c )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 5 2 4 2 2 3 +--R 15A b e + (- 44A b c + 3B b )d e + (44A c - 10B b c)d e +--R + +--R 2 3 2 +--R - 8B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 40A b d e + (- 118A b c + 8B b )d e + (108A c - 14B b c)d e +--R + +--R 2 4 +--R - 24B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 33A b d e + (- 90A b c - 3B b )d e + (72A c + 12B b c)d e +--R + +--R 2 5 +--R - 24B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (24b d e - 72b c d e + 72b c d e - 24c d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (72b d e - 216b c d e + 216b c d e - 72c d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (72b d e - 216b c d e + 216b c d e - 72c d e)x + 24b d e +--R + +--R 2 7 2 2 8 3 9 +--R - 72b c d e + 72b c d e - 24c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 527 + +--S 528 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 3 2 2 2 2 +--R 5A b e + (- 18A b c + B b )d e + (24A b c - 4B b c)d e +--R + +--R 3 2 3 +--R (- 16A c + 8B b c )d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 3 2 3 2 2 2 2 +--R 5A b e + (- 18A b c + B b )d e + (24A b c - 4B b c)d e +--R + +--R 3 2 3 +--R (- 16A c + 8B b c )d +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +--R (16b d e - 48b c d e + 48b c d e - 16c d )\|- b d e + c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 3 2 2 2 2 +--R 5A b e + (- 18A b c + B b )d e + (24A b c - 4B b c)d e +--R + +--R 3 2 3 +--R (- 16A c + 8B b c )d +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 10A b e + (36A b c - 2B b )d e + (- 48A b c + 8B b c)d e +--R + +--R 3 2 3 +--R (32A c - 16B b c )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ +--R (16b d e - 48b c d e + 48b c d e - 16c d )\|- b e + c d \|d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 531 + +)clear all + +--S 532 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1457 +r0:=3/4*e*(4*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-12*b*c*d*e+5*b^2*e^2))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-2*(A*b-(b*B-2*A*c)*x)*_ + (d+e*x)^3/(b^2*sqrt(b*x+c*x^2))+1/4*e*(32*A*c^3*d^2-15*b^3*B*e^2-_ + 16*b*c^2*d*(B*d+2*A*e)+2*b^2*c*e*(17*B*d+6*A*e))*sqrt(b*x+c*x^2)/_ + (b^2*c^3)-2*(b*B-2*A*c)*e*(d+e*x)^2*sqrt(b*x+c*x^2)/(b^2*c)+_ + 1/2*e^2*(b*(b*B+4*A*c)*d+(8*A*c^2*d+5*b^2*B*e-4*b*c*(B*d+A*e))*x)*_ + sqrt(b*x+c*x^2)/(b^2*c^2) +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 2 2 2 +--R ((- 12A b c + 15B b )e + (24A b c - 36B b c)d e + 24B b c d e) +--R * +--R +----------+ +-+ +--R | 2 x\|c +--R \|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 3 2 2 3 3 2 2 2 2 +--R 2B b c e x + ((4A b c - 5B b c)e + 12B b c d e )x +--R + +--R 3 4 3 2 2 3 2 +--R (12A b c - 15B b )e + (- 24A b c + 36B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (24A b c - 24B b c )d e + (- 16A c + 8B b c )d +--R * +--R x +--R + +--R 3 3 +--R - 8A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 3 +-+ | 2 +--R 4b c \|c \|c x + b x +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 3 2 2 3 2 2 2 2 +--R ((- 12A b c + 15B b )e + (24A b c - 36B b c)d e + 24B b c d e) +--R * +--R +----------+ +----------+ +--R | 2 | 2 +-+ +--R \|c x + b x log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 3 3 2 2 3 3 2 2 2 2 +--R 4B b c e x + ((8A b c - 10B b c)e + 24B b c d e )x +--R + +--R 3 4 3 2 2 3 2 +--R (24A b c - 30B b )e + (- 48A b c + 72B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (48A b c - 48B b c )d e + (- 32A c + 16B b c )d +--R * +--R x +--R + +--R 3 3 +--R - 16A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 3 +-+ | 2 +--R 8b c \|c \|c x + b x +--R , +--R +--R 3 4 3 2 2 3 2 2 2 2 +--R ((- 12A b c + 15B b )e + (24A b c - 36B b c)d e + 24B b c d e) +--R * +--R +----------+ +--R +----------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|c x + b x atan(-------------------) +--R c x +--R + +--R 2 2 3 3 2 2 3 3 2 2 2 2 +--R 2B b c e x + ((4A b c - 5B b c)e + 12B b c d e )x +--R + +--R 3 4 3 2 2 3 2 +--R (12A b c - 15B b )e + (- 24A b c + 36B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (24A b c - 24B b c )d e + (- 16A c + 8B b c )d +--R * +--R x +--R + +--R 3 3 +--R - 8A b c d +--R * +--R +---+ +--R \|- c +--R / +--R +----------+ +--R 2 3 +---+ | 2 +--R 4b c \|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 534 + +--S 535 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 +--R ((- 12A b c + 15B b )e + (24A c - 36B b c)d e + 24B c d e) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 2 2 2 +--R ((24A b c - 30B b )e + (- 48A c + 72B b c)d e - 48B c d e) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 8c \|c +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 2 2 2 2 +---+ +--R ((12A b c - 15B b )e + (- 24A c + 36B b c)d e - 24B c d e)\|- c +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 2 +-+ +--R ((- 12A b c + 15B b )e + (24A c - 36B b c)d e + 24B c d e)\|c +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 4c \|- c \|c +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 538 + +)clear all + +--S 539 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1457 +r0:=e*(4*B*c*d-3*b*B*e+2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-_ + 2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*sqrt(b*x+c*x^2))+e*(8*A*c^2*d+_ + 3*b^2*B*e-4*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/(b^2*c^2)+2*e^2*(A*b-_ + (b*B-2*A*c)*x)*sqrt(b*x+c*x^2)/(b^2*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 2 3 2 2 | 2 x\|c +--R ((2A b c - 3B b )e + 4B b c d e)\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 +--R B b c e x +--R + +--R 2 3 2 2 2 +--R (- 2A b c + 3B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 +--R (- 4A c + 2B b c )d +--R * +--R x +--R + +--R 2 2 +--R - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 2 +-+ | 2 +--R b c \|c \|c x + b x +--R Type: Expression(Integer) +--E 540 + +--S 541 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 2 3 2 2 | 2 +--R ((2A b c - 3B b )e + 4B b c d e)\|c x + b x +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 +--R 2B b c e x +--R + +--R 2 3 2 2 2 +--R (- 4A b c + 6B b )e + (8A b c - 8B b c)d e +--R + +--R 3 2 2 +--R (- 8A c + 4B b c )d +--R * +--R x +--R + +--R 2 2 +--R - 4A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 2 +-+ | 2 +--R 2b c \|c \|c x + b x +--R , +--R +--R +----------+ +--R +----------+ +---+ | 2 +--R 2 3 2 2 | 2 \|- c \|c x + b x +--R ((2A b c - 3B b )e + 4B b c d e)\|c x + b x atan(-------------------) +--R c x +--R + +--R 2 2 2 +--R B b c e x +--R + +--R 2 3 2 2 2 +--R (- 2A b c + 3B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 +--R (- 4A c + 2B b c )d +--R * +--R x +--R + +--R 2 2 +--R - 2A b c d +--R * +--R +---+ +--R \|- c +--R / +--R +----------+ +--R 2 2 +---+ | 2 +--R b c \|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 541 + +--S 542 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 2 | 2 +-+ +--R ((2A c - 3B b)e + 4B c d e)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 2 x\|c +--R ((- 4A c + 6B b)e - 8B c d e)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 2 +-+ +--R 2c \|c +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 +---+ x\|c +--R ((- 2A c + 3B b)e - 4B c d e)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 2 +-+ \|- c \|c x + b x +--R ((2A c - 3B b)e + 4B c d e)\|c atan(-------------------) +--R c x +--R / +--R 2 +---+ +-+ +--R c \|- c \|c +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1457 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1457 +r0:=2*B*e*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)-2*(A*b-(b*B-2*A*c)*x)*_ + (d+e*x)/(b^2*sqrt(b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(b*x+c*x^2)/(b^2*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 2 | 2 x\|c +--R 2B b e\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 +-+ +--R (((2A b c - 2B b )e + (- 4A c + 2B b c)d)x - 2A b c d)\|c +--R / +--R +----------+ +--R 2 +-+ | 2 +--R b c\|c \|c x + b x +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +----------+ +--R 2 | 2 | 2 +-+ +--R B b e\|c x + b x log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 +-+ +--R (((2A b c - 2B b )e + (- 4A c + 2B b c)d)x - 2A b c d)\|c +--R / +--R +----------+ +--R 2 +-+ | 2 +--R b c\|c \|c x + b x +--R , +--R +--R +----------+ +--R +----------+ +---+ | 2 +--R 2 | 2 \|- c \|c x + b x +--R 2B b e\|c x + b x atan(-------------------) +--R c x +--R + +--R 2 2 +---+ +--R (((2A b c - 2B b )e + (- 4A c + 2B b c)d)x - 2A b c d)\|- c +--R / +--R +----------+ +--R 2 +---+ | 2 +--R b c\|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 548 + +--S 549 of 1457 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R | 2 +-+ x\|c +--R B e log(2c\|c x + b x + (2c x + b)\|c ) - 2B e atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (4) --------------------------------------------------------------------- +--R +-+ +--R c\|c +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1457 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R +---+ x\|c +-+ \|- c \|c x + b x +--R - 2B e\|- c atanh(-------------) + 2B e\|c atan(-------------------) +--R +----------+ c x +--R | 2 +--R \|c x + b x +--R (6) -------------------------------------------------------------------- +--R +---+ +-+ +--R c\|- c \|c +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 1457 +t0:=(A+B*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R B x + A +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1457 +r0:=-2*(A*b-(b*B-2*A*c)*x)/(b^2*sqrt(b*x+c*x^2)) +--R +--R +--R (- 4A c + 2B b)x - 2A b +--R (2) ----------------------- +--R +----------+ +--R 2 | 2 +--R b \|c x + b x +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (- 4A c + 2B b)x - 2A b +--R (3) ----------------------- +--R +----------+ +--R 2 | 2 +--R b \|c x + b x +--R Type: Union(Expression(Integer),...) +--E 555 + +--S 556 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 557 + +)clear all + +--S 558 of 1457 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------- +--R +----------+ +--R 3 2 | 2 +--R (c e x + (b e + c d)x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1457 +r0:=-e*(B*d-A*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))-2*(A*b*(c*d-b*e)+_ + c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R +----------+ +--R 2 2 2 | 2 (b e - 2c d)x - b d +--R (A b e - B b d e)\|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +--R ((- 2A b c e + (4A c - 2B b c)d)x - 2A b e + 2A b c d)\|- b e + c d \|d +--R / +--R +----------+ +--R 3 2 2 +-----------+ +-+ | 2 +--R (b d e - b c d )\|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 2 2 2 | 2 +--R (A b e - B b d e)\|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 2 | 2 +--R ((- 2A b c e + (4A c - 2B b c)d)x - 2A b e + 2A b c d)\|- b d e + c d +--R / +--R +--------------+ +----------+ +--R 3 2 2 | 2 | 2 +--R (b d e - b c d )\|- b d e + c d \|c x + b x +--R , +--R +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R 2 2 2 | 2 \|b d e - c d \|c x + b x +--R (2A b e - 2B b d e)\|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +--R 2 2 | 2 +--R ((- 2A b c e + (4A c - 2B b c)d)x - 2A b e + 2A b c d)\|b d e - c d +--R / +--R +------------+ +----------+ +--R 3 2 2 | 2 | 2 +--R (b d e - b c d )\|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 560 + +--S 561 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R (A e - B d e)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 | 2 (b e - 2c d)x - b d +--R (- A e + B d e)\|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +--R (b d e - c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 2 | 2 (b e - 2c d)x - b d +--R (- A e + B d e)\|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 2 +-----------+ +-+ \|b d e - c d \|c x + b x +--R (2A e - 2B d e)\|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 +-----------+ +-+ | 2 +--R (b d e - c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------------------------- +--R +----------+ +--R 2 4 2 3 2 2 2 | 2 +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1457 +r0:=1/2*e*(3*A*e*(2*c*d-b*e)-B*d*(4*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-_ + b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-_ + b*e)^(5/2))-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*_ + (c*d-b*e)*(d+e*x)*sqrt(b*x+c*x^2))-e*(4*A*c^2*d^2-b^2*e*(B*d-_ + 3*A*e)-2*b*c*d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 3 4 2 3 3 2 2 2 3 3 +--R (3A b e + (- 6A b c - B b )d e + 4B b c d e )x + 3A b d e +--R + +--R 2 3 2 2 2 3 +--R (- 6A b c - B b )d e + 4B b c d e +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 3 2 2 2 +--R (- 6A b c e + (8A b c + 2B b c)d e + (- 8A c + 4B b c )d e)x +--R + +--R 3 3 2 3 2 2 2 +--R - 6A b e + (4A b c + 2B b )d e + 4A b c d e +--R + +--R 3 2 3 +--R (- 8A c + 4B b c )d +--R * +--R x +--R + +--R 3 2 2 2 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((2b d e - 4b c d e + 2b c d e)x + 2b d e - 4b c d e + 2b c d ) +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 3 3 2 2 2 3 3 +--R (3A b e + (- 6A b c - B b )d e + 4B b c d e )x + 3A b d e +--R + +--R 2 3 2 2 2 3 +--R (- 6A b c - B b )d e + 4B b c d e +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 2 2 2 3 2 2 2 +--R (- 6A b c e + (8A b c + 2B b c)d e + (- 8A c + 4B b c )d e)x +--R + +--R 3 3 2 3 2 2 2 +--R - 6A b e + (4A b c + 2B b )d e + 4A b c d e +--R + +--R 3 2 3 +--R (- 8A c + 4B b c )d +--R * +--R x +--R + +--R 3 2 2 2 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((2b d e - 4b c d e + 2b c d e)x + 2b d e - 4b c d e + 2b c d ) +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R 3 4 2 3 3 2 2 2 3 3 +--R (3A b e + (- 6A b c - B b )d e + 4B b c d e )x + 3A b d e +--R + +--R 2 3 2 2 2 3 +--R (- 6A b c - B b )d e + 4B b c d e +--R * +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R | 2 \|b d e - c d \|c x + b x +--R \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 3 2 2 2 3 2 2 2 +--R (- 3A b c e + (4A b c + B b c)d e + (- 4A c + 2B b c )d e)x +--R + +--R 3 3 2 3 2 2 2 +--R - 3A b e + (2A b c + B b )d e + 2A b c d e +--R + +--R 3 2 3 +--R (- 4A c + 2B b c )d +--R * +--R x +--R + +--R 3 2 2 2 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 567 + +--S 568 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 +-----------+ +-+ +--R (3A b e + (- 6A c - B b)d e + 4B c d e)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 3 2 2 | 2 +--R (- 3A b e + (6A c + B b)d e - 4B c d e)\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (2b d e - 4b c d e + 2c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 3 2 2 | 2 +--R (- 3A b e + (6A c + B b)d e - 4B c d e)\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 2 +-----------+ +-+ +--R (6A b e + (- 12A c - 2B b)d e + 8B c d e)\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (2b d e - 4b c d e + 2c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 571 + +)clear all + +--S 572 of 1457 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1457 +r0:=-3/8*e*(B*d*(8*c^2*d^2-4*b*c*d*e+b^2*e^2)-A*e*(16*c^2*d^2-16*b*c*d*e+_ + 5*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))-2*(A*b*(c*d-b*e)+_ + c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)^2*sqrt(b*x+_ + c*x^2))-1/2*e*(8*A*c^2*d^2-b^2*e*(B*d-5*A*e)-4*b*c*d*(B*d+2*A*e))*_ + sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^2)-1/4*e*(16*A*c^3*d^3-_ + 2*b^2*c*d*e*(5*B*d-19*A*e)+3*b^3*e^2*(B*d-5*A*e)-8*b*c^2*d^2*_ + (B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 4 6 3 4 5 2 2 3 2 4 +--R 15A b e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 30A b d e + (- 96A b c - 6B b )d e + (96A b c + 24B b c)d e +--R + +--R 2 2 4 2 +--R - 48B b c d e +--R * +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A b d e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 5 +--R - 24B b c d e +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 5 2 2 3 4 +--R - 30A b c e + (76A b c + 6B b c)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 48A b c - 20B b c )d e + (32A c - 16B b c )d e +--R * +--R 3 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 30A b e + (26A b c + 6B b )d e + (80A b c - 10B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (- 80A b c - 24B b c )d e + (64A c - 32B b c )d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 4 2 3 +--R - 50A b d e + (112A b c + 10B b )d e +--R + +--R 2 2 3 3 2 3 4 4 3 5 +--R (- 48A b c - 24B b c)d e - 16A b c d e + (32A c - 16B b c )d +--R * +--R x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 16A b d e + 48A b c d e - 48A b c d e + 16A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (16b d e - 48b c d e + 48b c d e - 16b c d e)x + 8b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 24b c d e + 24b c d e - 8b c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 6 3 4 5 2 2 3 2 4 +--R - 15A b e + (48A b c + 3B b )d e + (- 48A b c - 12B b c)d e +--R + +--R 2 2 3 3 +--R 24B b c d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 4 +--R - 30A b d e + (96A b c + 6B b )d e +--R + +--R 2 2 3 3 3 2 2 4 2 +--R (- 96A b c - 24B b c)d e + 48B b c d e +--R * +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R - 15A b d e + (48A b c + 3B b )d e + (- 48A b c - 12B b c)d e +--R + +--R 2 2 5 +--R 24B b c d e +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 5 2 2 3 4 +--R - 30A b c e + (76A b c + 6B b c)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 48A b c - 20B b c )d e + (32A c - 16B b c )d e +--R * +--R 3 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 30A b e + (26A b c + 6B b )d e + (80A b c - 10B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (- 80A b c - 24B b c )d e + (64A c - 32B b c )d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 4 2 3 +--R - 50A b d e + (112A b c + 10B b )d e +--R + +--R 2 2 3 3 2 3 4 4 3 5 +--R (- 48A b c - 24B b c)d e - 16A b c d e + (32A c - 16B b c )d +--R * +--R x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 16A b d e + 48A b c d e - 48A b c d e + 16A b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (16b d e - 48b c d e + 48b c d e - 16b c d e)x + 8b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 24b c d e + 24b c d e - 8b c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R 4 6 3 4 5 2 2 3 2 4 +--R 15A b e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 30A b d e + (- 96A b c - 6B b )d e + (96A b c + 24B b c)d e +--R + +--R 2 2 4 2 +--R - 48B b c d e +--R * +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A b d e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 5 +--R - 24B b c d e +--R * +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R | 2 \|b d e - c d \|c x + b x +--R \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 5 2 2 3 4 +--R - 15A b c e + (38A b c + 3B b c)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 24A b c - 10B b c )d e + (16A c - 8B b c )d e +--R * +--R 3 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 15A b e + (13A b c + 3B b )d e + (40A b c - 5B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (- 40A b c - 12B b c )d e + (32A c - 16B b c )d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 4 2 3 +--R - 25A b d e + (56A b c + 5B b )d e +--R + +--R 2 2 3 3 2 3 4 4 3 5 +--R (- 24A b c - 12B b c)d e - 8A b c d e + (16A c - 8B b c )d +--R * +--R x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 8A b d e + 24A b c d e - 24A b c d e + 8A b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e)x + 4b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 12b c d e + 12b c d e - 4b c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 574 + +--S 575 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 2 2 +--R - 15A b e + (48A b c + 3B b )d e + (- 48A c - 12B b c)d e +--R + +--R 2 3 +--R 24B c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 4 2 3 2 2 2 +--R - 15A b e + (48A b c + 3B b )d e + (- 48A c - 12B b c)d e +--R + +--R 2 3 +--R 24B c d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +-----------+ +--R (8b d e - 24b c d e + 24b c d e - 8c d )\|- b d e + c d \|- b e + c d +--R * +--R +-+ +--R \|d +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 4 2 3 2 2 2 +--R - 15A b e + (48A b c + 3B b )d e + (- 48A c - 12B b c)d e +--R + +--R 2 3 +--R 24B c d e +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 4 2 3 2 2 2 +--R 30A b e + (- 96A b c - 6B b )d e + (96A c + 24B b c)d e +--R + +--R 2 3 +--R - 48B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ | 2 +--R (8b d e - 24b c d e + 24b c d e - 8c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 578 + +)clear all + +--S 579 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1457 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^4/(b^2*(b*x+c*x^2)^(3/2))+e^3*(8*B*c*d-_ + 5*b*B*e+2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-8/3*_ + (d+e*x)^3*(b*(b*B*d-2*A*c*d+2*A*b*e)-(4*A*c^2*d-b^2*B*e-2*b*c*(B*d+_ + A*e))*x)/(b^4*sqrt(b*x+c*x^2))-1/3*e*(64*A*c^4*d^3-15*b^4*B*e^3-_ + 32*b*c^3*d^2*(B*d+3*A*e)+2*b^3*c*e^2*(11*B*d+3*A*e)+4*b^2*c^2*d*_ + e*(4*B*d+5*A*e))*sqrt(b*x+c*x^2)/(b^4*c^3)-8/3*e*(4*A*c^2*d-b^2*B*e-_ + 2*b*c*(B*d+A*e))*(d+e*x)^2*sqrt(b*x+c*x^2)/(b^4*c)+2/3*e^2*(b*d*_ + (4*b*B*c*d-8*A*c^2*d-b^2*B*e+10*A*b*c*e)-(16*A*c^3*d^2+5*b^3*B*e^2-_ + 2*A*b^2*c*e^2-8*b*c^2*d*(B*d+2*A*e))*x)*sqrt(b*x+c*x^2)/(b^4*c^2) +--R +--R +--R (2) +--R 4 2 5 4 4 2 3 2 +--R ((6A b c - 15B b c)e + 24B b c d e )x +--R + +--R 5 6 4 5 3 +--R ((6A b c - 15B b )e + 24B b c d e )x +--R * +--R +----------+ +-+ +--R | 2 x\|c +--R \|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 2 4 4 +--R 3B b c e x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 8A b c + 20B b c)e + (8A b c - 32B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (24A b c + 12B b c )d e + (- 64A b c + 16B b c )d e +--R + +--R 6 5 4 +--R (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 4 5 3 3 3 2 2 +--R (- 6A b c + 15B b )e - 24B b c d e + 36A b c d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 96A b c + 24B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 4 3 3 4 3 3 4 +--R (- 24A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 4 2 5 3 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 5 4 4 2 3 2 +--R ((6A b c - 15B b c)e + 24B b c d e )x +--R + +--R 5 6 4 5 3 +--R ((6A b c - 15B b )e + 24B b c d e )x +--R * +--R +----------+ +----------+ +--R | 2 | 2 +-+ +--R \|c x + b x log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 2 4 4 +--R 6B b c e x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 16A b c + 40B b c)e + (16A b c - 64B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (48A b c + 24B b c )d e + (- 128A b c + 32B b c )d e +--R + +--R 6 5 4 +--R (64A c - 32B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 4 5 3 3 3 2 2 +--R (- 12A b c + 30B b )e - 48B b c d e + 72A b c d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 192A b c + 48B b c )d e + (96A b c - 48B b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 4 3 3 4 3 3 4 +--R (- 48A b c d e + (24A b c - 12B b c )d )x - 4A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 4 2 5 3 +-+ | 2 +--R (6b c x + 6b c x)\|c \|c x + b x +--R , +--R +--R 4 2 5 4 4 2 3 2 +--R ((6A b c - 15B b c)e + 24B b c d e )x +--R + +--R 5 6 4 5 3 +--R ((6A b c - 15B b )e + 24B b c d e )x +--R * +--R +----------+ +--R +----------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|c x + b x atan(-------------------) +--R c x +--R + +--R 4 2 4 4 +--R 3B b c e x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 8A b c + 20B b c)e + (8A b c - 32B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (24A b c + 12B b c )d e + (- 64A b c + 16B b c )d e +--R + +--R 6 5 4 +--R (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 4 5 3 3 3 2 2 +--R (- 6A b c + 15B b )e - 24B b c d e + 36A b c d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 96A b c + 24B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 4 3 3 4 3 3 4 +--R (- 24A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +---+ +--R \|- c +--R / +--R +----------+ +--R 4 4 2 5 3 +---+ | 2 +--R (3b c x + 3b c x)\|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 581 + +--S 582 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 4 3 | 2 +-+ +--R ((2A c - 5B b)e + 8B c d e )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 4 3 x\|c +--R ((- 4A c + 10B b)e - 16B c d e )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 2c \|c +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 4 3 +---+ x\|c +--R ((- 2A c + 5B b)e - 8B c d e )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 4 3 +-+ \|- c \|c x + b x +--R ((2A c - 5B b)e + 8B c d e )\|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R c \|- c \|c +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1457 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^3/(b^2*(b*x+c*x^2)^(3/2))+2*B*e^3*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-4/3*(d+e*x)^2*(b*(2*b*B*d-_ + 4*A*c*d+3*A*b*e)-(8*A*c^2*d-b^2*B*e-4*b*c*(B*d+A*e))*x)/(b^4*_ + sqrt(b*x+c*x^2))-2/3*e*(32*A*c^3*d^2+3*b^3*B*e^2-16*b*c^2*d*(B*d+_ + 2*A*e)+2*b^2*c*e*(2*B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^4*c^2)+4/3*e^2*_ + (b*(2*b*B*d-4*A*c*d+3*A*b*e)-(8*A*c^2*d-b^2*B*e-4*b*c*(B*d+A*e))*x)*_ + sqrt(b*x+c*x^2)/(b^4*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 4 3 2 5 3 | 2 x\|c +--R (6B b c e x + 6B b e x)\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2A b c - 8B b c)e + (12A b c + 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 12B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 3 2 2 2 3 3 2 2 +--R - 6B b e + 18A b c d e + (- 72A b c + 18B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 3 2 3 3 2 3 +--R (- 18A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 3 2 5 2 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 4 3 2 5 3 | 2 +--R (3B b c e x + 3B b e x)\|c x + b x +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2A b c - 8B b c)e + (12A b c + 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 12B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 3 2 2 2 3 3 2 2 +--R - 6B b e + 18A b c d e + (- 72A b c + 18B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 3 2 3 3 2 3 +--R (- 18A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 3 2 5 2 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R , +--R +--R +----------+ +--R +----------+ +---+ | 2 +--R 4 3 2 5 3 | 2 \|- c \|c x + b x +--R (6B b c e x + 6B b e x)\|c x + b x atan(-------------------) +--R c x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2A b c - 8B b c)e + (12A b c + 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 12B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 3 2 2 2 3 3 2 2 +--R - 6B b e + 18A b c d e + (- 72A b c + 18B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 3 2 3 3 2 3 +--R (- 18A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +---+ +--R \|- c +--R / +--R +----------+ +--R 4 3 2 5 2 +---+ | 2 +--R (3b c x + 3b c x)\|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 588 + +--S 589 of 1457 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R 3 | 2 +-+ 3 x\|c +--R B e log(2c\|c x + b x + (2c x + b)\|c ) - 2B e atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (4) --------------------------------------------------------------------- +--R 2 +-+ +--R c \|c +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1457 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R 3 +---+ x\|c 3 +-+ \|- c \|c x + b x +--R - 2B e \|- c atanh(-------------) + 2B e \|c atan(-------------------) +--R +----------+ c x +--R | 2 +--R \|c x + b x +--R (6) ---------------------------------------------------------------------- +--R 2 +---+ +-+ +--R c \|- c \|c +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 592 + +)clear all + +--S 593 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1457 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*(b*x+c*x^2)^(3/2))-_ + 8/3*(b*B*d-2*A*c*d+A*b*e)*(b*d+(2*c*d-b*e)*x)/(b^4*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 3 +--R ((4A b c + 2B b )e + (- 32A b c + 8B b c)d e + (32A c - 16B b c )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (6A b e + (- 48A b c + 12B b )d e + (48A b c - 24B b c)d )x +--R + +--R 3 2 3 2 3 2 +--R (- 12A b d e + (12A b c - 6B b )d )x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 3 2 2 3 +--R ((4A b c + 2B b )e + (- 32A b c + 8B b c)d e + (32A c - 16B b c )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (6A b e + (- 48A b c + 12B b )d e + (48A b c - 24B b c)d )x +--R + +--R 3 2 3 2 3 2 +--R (- 12A b d e + (12A b c - 6B b )d )x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Union(Expression(Integer),...) +--E 595 + +--S 596 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1457 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1457 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))-_ + 4/3*(b*(2*b*B*d-4*A*c*d+A*b*e)-(8*A*c^2*d+b^2*B*e-_ + 4*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R 2 2 3 2 3 +--R ((- 16A b c + 4B b c)e + (32A c - 16B b c )d)x +--R + +--R 2 3 2 2 2 +--R ((- 24A b c + 6B b )e + (48A b c - 24B b c)d)x +--R + +--R 3 2 3 3 +--R (- 6A b e + (12A b c - 6B b )d)x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 2 3 +--R ((- 16A b c + 4B b c)e + (32A c - 16B b c )d)x +--R + +--R 2 3 2 2 2 +--R ((- 24A b c + 6B b )e + (48A b c - 24B b c)d)x +--R + +--R 3 2 3 3 +--R (- 6A b e + (12A b c - 6B b )d)x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Union(Expression(Integer),...) +--E 600 + +--S 601 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 602 + +)clear all + +--S 603 of 1457 +t0:=(A+B*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R B x + A +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1457 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)/(b^2*(b*x+c*x^2)^(3/2))+8/3*(b*B-2*A*c)/_ + (b^3*sqrt(b*x+c*x^2))-16/3*(b*B-2*A*c)*sqrt(b*x+c*x^2)/(b^4*x) +--R +--R +--R (2) +--R 3 2 3 2 2 2 2 3 3 +--R (32A c - 16B b c )x + (48A b c - 24B b c)x + (12A b c - 6B b )x - 2A b +--R --------------------------------------------------------------------------- +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 2 2 2 3 3 +--R (32A c - 16B b c )x + (48A b c - 24B b c)x + (12A b c - 6B b )x - 2A b +--R --------------------------------------------------------------------------- +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Union(Expression(Integer),...) +--E 605 + +--S 606 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 607 + +)clear all + +--S 608 of 1457 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^(5/2)) +--R +--R +--R B x + A +--R (1) -------------------------------------------------------------------- +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|c x + b x +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1457 +r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ + (b*x+c*x^2)^(3/2))-e^3*(B*d-A*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+_ + 2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+3*b^2*e*(B*d-A*e)-4*b*c*d*(B*d+A*e))+_ + c*(16*A*c^3*d^3-3*b^3*e^2*(B*d-A*e)+2*b^2*c*d*e*(7*B*d+A*e)-_ + 8*b*c^2*d^2*(B*d+3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R +----------+ +--R 4 4 4 3 2 5 4 5 3 | 2 +--R ((- 3A b c e + 3B b c d e )x + (- 3A b e + 3B b d e )x)\|c x + b x +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 3 2 3 3 2 2 4 2 3 2 +--R 6A b c e + (4A b c - 6B b c )d e + (- 48A b c + 28B b c )d e +--R + +--R 5 4 3 +--R (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 4 2 2 3 3 2 2 +--R 12A b c e + (6A b c - 12B b c)d e + (- 72A b c + 42B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 5 2 3 2 4 2 +--R 6A b e - 6B b d e + (- 18A b c + 12B b c)d e +--R + +--R 2 3 3 2 3 +--R (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 4 2 3 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 4 4 4 3 2 5 4 5 3 | 2 +--R ((3A b c e - 3B b c d e )x + (3A b e - 3B b d e )x)\|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 2 3 2 3 3 2 2 +--R 6A b c e + (4A b c - 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 28B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 4 2 +--R 12A b c e + (6A b c - 12B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 72A b c + 42B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 5 2 3 2 4 2 +--R 6A b e - 6B b d e + (- 18A b c + 12B b c)d e +--R + +--R 2 3 3 2 3 +--R (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 4 2 3 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R 4 4 4 3 2 5 4 5 3 +--R ((- 6A b c e + 6B b c d e )x + (- 6A b e + 6B b d e )x) +--R * +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R | 2 \|b d e - c d \|c x + b x +--R \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 2 3 2 3 3 2 2 +--R 6A b c e + (4A b c - 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 28B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 4 2 +--R 12A b c e + (6A b c - 12B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 72A b c + 42B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 5 2 3 2 4 2 +--R 6A b e - 6B b d e + (- 18A b c + 12B b c)d e +--R + +--R 2 3 3 2 3 +--R (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 4 2 3 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 610 + +--S 611 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 3 +-----------+ +-+ +--R (A e - B d e )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 4 3 | 2 (b e - 2c d)x - b d +--R (A e - B d e )\|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (b d e - 2b c d e + c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 4 3 | 2 (b e - 2c d)x - b d +--R (A e - B d e )\|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 4 3 +-----------+ +-+ \|b d e - c d \|c x + b x +--R (- 2A e + 2B d e )\|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (b d e - 2b c d e + c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 614 + +)clear all + +--S 615 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1457 +r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ + (d+e*x)*(b*x+c*x^2)^(3/2))-1/2*e^3*(B*d*(8*c*d-3*b*e)-5*A*e*_ + (2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+2/3*(b*(c*d-b*e)*_ + (8*A*c^2*d^2+b^2*e*(3*B*d-5*A*e)-2*b*c*d*(2*B*d+A*e))+c*(16*A*c^3*d^3-_ + b^3*e^2*(3*B*d-5*A*e)+2*b^2*c*d*e*(8*B*d-A*e)-8*b*c^2*d^2*(B*d+_ + 3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*(d+e*x)*sqrt(b*x+c*x^2))+1/3*e*_ + (32*A*c^4*d^4-2*b^3*c*d*e^2*(9*B*d-10*A*e)+3*b^4*e^3*(3*B*d-5*A*e)+_ + 4*b^2*c^2*d^2*e*(10*B*d+3*A*e)-16*b*c^3*d^3*(B*d+4*A*e))*sqrt(b*x+_ + c*x^2)/(b^4*d^3*(c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 5 4 2 2 4 3 +--R (- 15A b c e + (30A b c + 9B b c)d e - 24B b c d e )x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 15A b e + (15A b c + 9B b )d e + (30A b c - 15B b c)d e +--R + +--R 4 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 6 5 5 6 2 4 5 3 3 +--R (- 15A b d e + (30A b c + 9B b )d e - 24B b c d e )x +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 2 5 3 3 4 2 4 +--R 30A b c e + (- 40A b c - 18B b c )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 24A b c + 36B b c )d e + (128A b c - 80B b c )d e +--R + +--R 6 5 4 +--R (- 64A c + 32B b c )d e +--R * +--R 4 +--R x +--R + +--R 5 5 4 2 5 4 +--R 60A b c e + (- 60A b c - 36B b c)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 76A b c + 60B b c )d e + (168A b c - 84B b c )d e +--R + +--R 5 2 4 4 6 5 5 +--R (32A b c - 32B b c )d e + (- 64A c + 32B b c )d +--R * +--R 3 +--R x +--R + +--R 6 5 6 4 4 2 5 2 3 +--R 30A b e - 18B b d e + (- 84A b c + 12B b c)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (12A b c + 36B b c )d e + (168A b c - 108B b c )d e +--R + +--R 5 2 4 5 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R + +--R 6 4 5 6 2 3 +--R 20A b d e + (- 36A b c - 12B b )d e +--R + +--R 4 2 5 3 2 3 3 4 2 4 +--R (- 12A b c + 36B b c)d e + (52A b c - 36B b c )d e +--R + +--R 2 4 3 3 5 +--R (- 24A b c + 12B b c )d +--R * +--R x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 4A b d e + 12A b c d e - 12A b c d e + 4A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 6 4 2 5 5 4 2 2 4 3 +--R (15A b c e + (- 30A b c - 9B b c)d e + 24B b c d e )x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R 15A b e + (- 15A b c - 9B b )d e + (- 30A b c + 15B b c)d e +--R + +--R 4 2 3 3 +--R 24B b c d e +--R * +--R 2 +--R x +--R + +--R 6 5 5 6 2 4 5 3 3 +--R (15A b d e + (- 30A b c - 9B b )d e + 24B b c d e )x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 2 5 3 3 4 2 4 +--R 30A b c e + (- 40A b c - 18B b c )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 24A b c + 36B b c )d e + (128A b c - 80B b c )d e +--R + +--R 6 5 4 +--R (- 64A c + 32B b c )d e +--R * +--R 4 +--R x +--R + +--R 5 5 4 2 5 4 +--R 60A b c e + (- 60A b c - 36B b c)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 76A b c + 60B b c )d e + (168A b c - 84B b c )d e +--R + +--R 5 2 4 4 6 5 5 +--R (32A b c - 32B b c )d e + (- 64A c + 32B b c )d +--R * +--R 3 +--R x +--R + +--R 6 5 6 4 4 2 5 2 3 +--R 30A b e - 18B b d e + (- 84A b c + 12B b c)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (12A b c + 36B b c )d e + (168A b c - 108B b c )d e +--R + +--R 5 2 4 5 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R + +--R 6 4 5 6 2 3 +--R 20A b d e + (- 36A b c - 12B b )d e +--R + +--R 4 2 5 3 2 3 3 4 2 4 +--R (- 12A b c + 36B b c)d e + (52A b c - 36B b c )d e +--R + +--R 2 4 3 3 5 +--R (- 24A b c + 12B b c )d +--R * +--R x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 4A b d e + 12A b c d e - 12A b c d e + 4A b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R 5 6 4 2 5 5 4 2 2 4 3 +--R (- 15A b c e + (30A b c + 9B b c)d e - 24B b c d e )x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 15A b e + (15A b c + 9B b )d e + (30A b c - 15B b c)d e +--R + +--R 4 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 6 5 5 6 2 4 5 3 3 +--R (- 15A b d e + (30A b c + 9B b )d e - 24B b c d e )x +--R * +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R | 2 \|b d e - c d \|c x + b x +--R \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 4 2 5 3 3 4 2 4 +--R 15A b c e + (- 20A b c - 9B b c )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 12A b c + 18B b c )d e + (64A b c - 40B b c )d e +--R + +--R 6 5 4 +--R (- 32A c + 16B b c )d e +--R * +--R 4 +--R x +--R + +--R 5 5 4 2 5 4 +--R 30A b c e + (- 30A b c - 18B b c)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 38A b c + 30B b c )d e + (84A b c - 42B b c )d e +--R + +--R 5 2 4 4 6 5 5 +--R (16A b c - 16B b c )d e + (- 32A c + 16B b c )d +--R * +--R 3 +--R x +--R + +--R 6 5 6 4 4 2 5 2 3 +--R 15A b e - 9B b d e + (- 42A b c + 6B b c)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (6A b c + 18B b c )d e + (84A b c - 54B b c )d e +--R + +--R 5 2 4 5 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R + +--R 6 4 5 6 2 3 +--R 10A b d e + (- 18A b c - 6B b )d e +--R + +--R 4 2 5 3 2 3 3 4 2 4 +--R (- 6A b c + 18B b c)d e + (26A b c - 18B b c )d e +--R + +--R 2 4 3 3 5 +--R (- 12A b c + 6B b c )d +--R * +--R x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 2A b d e + 6A b c d e - 6A b c d e + 2A b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 617 + +--S 618 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 2 3 +-----------+ +-+ +--R (5A b e + (- 10A c - 3B b)d e + 8B c d e )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 5 4 2 3 | 2 +--R (5A b e + (- 10A c - 3B b)d e + 8B c d e )\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +-----------+ +-+ +--R (2b d e - 6b c d e + 6b c d e - 2c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 5 4 2 3 | 2 +--R (5A b e + (- 10A c - 3B b)d e + 8B c d e )\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 4 2 3 +-----------+ +-+ +--R (- 10A b e + (20A c + 6B b)d e - 16B c d e )\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ | 2 +--R (2b d e - 6b c d e + 6b c d e - 2c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R (A b e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 2 2 3 3 2 3 2 +--R (3A b d e + (3A c + 3B b)d e + B c d )x + (3A b d e + (A c + B b)d )x +--R + +--R 3 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1457 +r0:=-2/9*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(9/2)/e^4+2/11*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^4-2/13*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(13/2)/e^4+2/15*B*c*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 7 7 7 6 6 +--R 858B c e x + ((990A c + 990B b)e + 3036B c d e )x +--R + +--R 7 6 2 5 5 +--R (1170A b e + (3600A c + 3600B b)d e + 3708B c d e )x +--R + +--R 6 2 5 3 4 4 +--R (4420A b d e + (4580A c + 4580B b)d e + 1600B c d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (5980A b d e + (2120A c + 2120B b)d e + 10B c d e )x +--R + +--R 3 4 4 3 5 2 2 +--R (3120A b d e + (30A c + 30B b)d e - 12B c d e )x +--R + +--R 4 3 5 2 6 5 2 +--R (130A b d e + (- 40A c - 40B b)d e + 16B c d e)x - 260A b d e +--R + +--R 6 7 +--R (80A c + 80B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 6 +--R 858B c e x + ((990A c + 990B b)e + 3036B c d e )x +--R + +--R 7 6 2 5 5 +--R (1170A b e + (3600A c + 3600B b)d e + 3708B c d e )x +--R + +--R 6 2 5 3 4 4 +--R (4420A b d e + (4580A c + 4580B b)d e + 1600B c d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (5980A b d e + (2120A c + 2120B b)d e + 10B c d e )x +--R + +--R 3 4 4 3 5 2 2 +--R (3120A b d e + (30A c + 30B b)d e - 12B c d e )x +--R + +--R 4 3 5 2 6 5 2 +--R (130A b d e + (- 40A c - 40B b)d e + 16B c d e)x - 260A b d e +--R + +--R 6 7 +--R (80A c + 80B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Union(Expression(Integer),...) +--E 624 + +--S 625 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 626 + +)clear all + +--S 627 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1457 +r0:=-2/7*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(7/2)/e^4+2/9*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^4-2/11*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(11/2)/e^4+2/13*B*c*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 1386B c e x + ((1638A c + 1638B b)e + 3402B c d e )x +--R + +--R 6 5 2 4 4 +--R (2002A b e + (4186A c + 4186B b)d e + 2226B c d e )x +--R + +--R 5 2 4 3 3 3 +--R (5434A b d e + (2938A c + 2938B b)d e + 30B c d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (4290A b d e + (78A c + 78B b)d e - 36B c d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (286A b d e + (- 104A c - 104B b)d e + 48B c d e)x - 572A b d e +--R + +--R 5 6 +--R (208A c + 208B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 5 +--R 1386B c e x + ((1638A c + 1638B b)e + 3402B c d e )x +--R + +--R 6 5 2 4 4 +--R (2002A b e + (4186A c + 4186B b)d e + 2226B c d e )x +--R + +--R 5 2 4 3 3 3 +--R (5434A b d e + (2938A c + 2938B b)d e + 30B c d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (4290A b d e + (78A c + 78B b)d e - 36B c d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (286A b d e + (- 104A c - 104B b)d e + 48B c d e)x - 572A b d e +--R + +--R 5 6 +--R (208A c + 208B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 629 + +--S 630 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 631 + +)clear all + +--S 632 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R (B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1457 +r0:=-2/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(5/2)/e^4+2/7*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^4-2/9*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(9/2)/e^4+2/11*B*c*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 630B c e x + ((770A c + 770B b)e + 840B c d e )x +--R + +--R 5 4 2 3 3 +--R (990A b e + (1100A c + 1100B b)d e + 30B c d e )x +--R + +--R 4 2 3 3 2 2 +--R (1584A b d e + (66A c + 66B b)d e - 36B c d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (198A b d e + (- 88A c - 88B b)d e + 48B c d e)x - 396A b d e +--R + +--R 4 5 +--R (176A c + 176B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 4 +--R 630B c e x + ((770A c + 770B b)e + 840B c d e )x +--R + +--R 5 4 2 3 3 +--R (990A b e + (1100A c + 1100B b)d e + 30B c d e )x +--R + +--R 4 2 3 3 2 2 +--R (1584A b d e + (66A c + 66B b)d e - 36B c d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (198A b d e + (- 88A c - 88B b)d e + 48B c d e)x - 396A b d e +--R + +--R 4 5 +--R (176A c + 176B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 634 + +--S 635 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)*sqrt(d+e*x) +--R +--R +--R 3 2 +-------+ +--R (1) (B c x + (A c + B b)x + A b x)\|e x + d +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1457 +r0:=-2/3*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(3/2)/e^4+2/5*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^4-2/7*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B c e x + ((90A c + 90B b)e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126A b e + (18A c + 18B b)d e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (42A b d e + (- 24A c - 24B b)d e + 16B c d e)x - 84A b d e +--R + +--R 3 4 +--R (48A c + 48B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 3 +--R 70B c e x + ((90A c + 90B b)e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126A b e + (18A c + 18B b)d e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (42A b d e + (- 24A c - 24B b)d e + 16B c d e)x - 84A b d e +--R + +--R 3 4 +--R (48A c + 48B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 639 + +--S 640 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 641 + +)clear all + +--S 642 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1457 +r0:=2/3*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^4-2/5*(3*B*c*d-_ + b*B*e-A*c*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-2*d*_ + (B*d-A*e)*(c*d-b*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + ((42A c + 42B b)e - 36B c d e )x +--R + +--R 3 2 2 2 +--R (70A b e + (- 56A c - 56B b)d e + 48B c d e)x - 140A b d e +--R + +--R 2 3 +--R (112A c + 112B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B c e x + ((42A c + 42B b)e - 36B c d e )x +--R + +--R 3 2 2 2 +--R (70A b e + (- 56A c - 56B b)d e + 48B c d e)x - 140A b d e +--R + +--R 2 3 +--R (112A c + 112B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 644 + +--S 645 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 646 + +)clear all + +--S 647 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1457 +r0:=-2/3*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+_ + 2*d*(B*d-A*e)*(c*d-b*e)/(e^4*sqrt(d+e*x))+2*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 6B c e x + ((10A c + 10B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (30A b e + (- 40A c - 40B b)d e + 48B c d e)x + 60A b d e +--R + +--R 2 3 +--R (- 80A c - 80B b)d e + 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 6B c e x + ((10A c + 10B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (30A b e + (- 40A c - 40B b)d e + 48B c d e)x + 60A b d e +--R + +--R 2 3 +--R (- 80A c - 80B b)d e + 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 649 + +--S 650 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1457 +r0:=2/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(3/2))+2/3*B*c*(d+e*x)^(3/2)/e^4-_ + 2*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))/(e^4*sqrt(d+e*x))-_ + 2*(3*B*c*d-b*B*e-A*c*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 2B c e x + ((6A c + 6B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (- 6A b e + (24A c + 24B b)d e - 48B c d e)x - 4A b d e +--R + +--R 2 3 +--R (16A c + 16B b)d e - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 2B c e x + ((6A c + 6B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (- 6A b e + (24A c + 24B b)d e - 48B c d e)x - 4A b d e +--R + +--R 2 3 +--R (16A c + 16B b)d e - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 654 + +--S 655 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 656 + +)clear all + +--S 657 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1457 +r0:=2/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(5/2))-2/3*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^(3/2))+2*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + ((- 30A c - 30B b)e + 180B c d e )x +--R + +--R 3 2 2 2 +--R (- 10A b e + (- 40A c - 40B b)d e + 240B c d e)x - 4A b d e +--R + +--R 2 3 +--R (- 16A c - 16B b)d e + 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B c e x + ((- 30A c - 30B b)e + 180B c d e )x +--R + +--R 3 2 2 2 +--R (- 10A b e + (- 40A c - 40B b)d e + 240B c d e)x - 4A b d e +--R + +--R 2 3 +--R (- 16A c - 16B b)d e + 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 659 + +--S 660 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 661 + +)clear all + +--S 662 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R ((2A b c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (6A b c + 3B b )d e + (3A c + 6B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 3 4 +--R (3A b d e + (6A b c + 3B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 3 2 3 2 +--R (3A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1457 +r0:=-2/9*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(9/2)/e^6+2/11*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^6+_ + 2/13*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(15/2)/e^6-2/17*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(17/2)/e^6+2/19*B*c^2*(d+e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 2 9 9 2 9 2 8 8 +--R 218790B c e x + ((244530A c + 489060B b c)e + 746460B c d e )x +--R + +--R 2 9 2 8 +--R (554268A b c + 277134B b )e + (847704A c + 1695408B b c)d e +--R + +--R 2 2 7 +--R 866580B c d e +--R * +--R 7 +--R x +--R + +--R 2 9 2 8 +--R 319770A b e + (1961256A b c + 980628B b )d e +--R + +--R 2 2 7 2 3 6 +--R (1005708A c + 2011416B b c)d e + 345840B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 2 7 +--R 1162800A b d e + (2395368A b c + 1197684B b )d e +--R + +--R 2 3 6 2 4 5 +--R (414504A c + 829008B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 7 2 3 6 +--R 1479340A b d e + (1033600A b c + 516800B b )d e +--R + +--R 2 4 5 2 5 4 +--R (1330A c + 2660B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 4 5 +--R 684760A b d e + (6460A b c + 3230B b )d e +--R + +--R 2 5 4 2 6 3 +--R (- 1520A c - 3040B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 5 2 5 4 +--R 9690A b d e + (- 7752A b c - 3876B b )d e +--R + +--R 2 6 3 2 7 2 +--R (1824A c + 3648B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 4 2 6 3 +--R - 12920A b d e + (10336A b c + 5168B b )d e +--R + +--R 2 7 2 2 8 +--R (- 2432A c - 4864B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 6 3 2 7 2 +--R 25840A b d e + (- 20672A b c - 10336B b )d e +--R + +--R 2 8 2 9 +--R (4864A c + 9728B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 9 2 9 2 8 8 +--R 218790B c e x + ((244530A c + 489060B b c)e + 746460B c d e )x +--R + +--R 2 9 2 8 +--R (554268A b c + 277134B b )e + (847704A c + 1695408B b c)d e +--R + +--R 2 2 7 +--R 866580B c d e +--R * +--R 7 +--R x +--R + +--R 2 9 2 8 +--R 319770A b e + (1961256A b c + 980628B b )d e +--R + +--R 2 2 7 2 3 6 +--R (1005708A c + 2011416B b c)d e + 345840B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 2 7 +--R 1162800A b d e + (2395368A b c + 1197684B b )d e +--R + +--R 2 3 6 2 4 5 +--R (414504A c + 829008B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 7 2 3 6 +--R 1479340A b d e + (1033600A b c + 516800B b )d e +--R + +--R 2 4 5 2 5 4 +--R (1330A c + 2660B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 4 5 +--R 684760A b d e + (6460A b c + 3230B b )d e +--R + +--R 2 5 4 2 6 3 +--R (- 1520A c - 3040B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 5 2 5 4 +--R 9690A b d e + (- 7752A b c - 3876B b )d e +--R + +--R 2 6 3 2 7 2 +--R (1824A c + 3648B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 4 2 6 3 +--R - 12920A b d e + (10336A b c + 5168B b )d e +--R + +--R 2 7 2 2 8 +--R (- 2432A c - 4864B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 6 3 2 7 2 +--R 25840A b d e + (- 20672A b c - 10336B b )d e +--R + +--R 2 8 2 9 +--R (4864A c + 9728B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Union(Expression(Integer),...) +--E 664 + +--S 665 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1457 +r0:=-2/7*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(7/2)/e^6+2/9*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^6+2/11*_ + (A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(15/2)/e^6+2/17*B*c^2*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 2 8 8 2 8 2 7 7 +--R 90090B c e x + ((102102A c + 204204B b c)e + 210210B c d e )x +--R + +--R 2 8 2 7 +--R (235620A b c + 117810B b )e + (243474A c + 486948B b c)d e +--R + +--R 2 2 6 +--R 127050B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 7 +--R 139230A b e + (578340A b c + 289170B b )d e +--R + +--R 2 2 6 2 3 5 +--R (152082A c + 304164B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 2 6 +--R 355810A b d e + (378420A b c + 189210B b )d e +--R + +--R 2 3 5 2 4 4 +--R (1190A c + 2380B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 6 2 3 5 +--R 249730A b d e + (5100A b c + 2550B b )d e +--R + +--R 2 4 4 2 5 3 +--R (- 1360A c - 2720B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 4 4 +--R 6630A b d e + (- 6120A b c - 3060B b )d e +--R + +--R 2 5 3 2 6 2 +--R (1632A c + 3264B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 5 3 +--R - 8840A b d e + (8160A b c + 4080B b )d e +--R + +--R 2 6 2 2 7 +--R (- 2176A c - 4352B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 3 2 6 2 +--R 17680A b d e + (- 16320A b c - 8160B b )d e +--R + +--R 2 7 2 8 +--R (4352A c + 8704B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 8 2 8 2 7 7 +--R 90090B c e x + ((102102A c + 204204B b c)e + 210210B c d e )x +--R + +--R 2 8 2 7 +--R (235620A b c + 117810B b )e + (243474A c + 486948B b c)d e +--R + +--R 2 2 6 +--R 127050B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 7 +--R 139230A b e + (578340A b c + 289170B b )d e +--R + +--R 2 2 6 2 3 5 +--R (152082A c + 304164B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 2 6 +--R 355810A b d e + (378420A b c + 189210B b )d e +--R + +--R 2 3 5 2 4 4 +--R (1190A c + 2380B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 6 2 3 5 +--R 249730A b d e + (5100A b c + 2550B b )d e +--R + +--R 2 4 4 2 5 3 +--R (- 1360A c - 2720B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 4 4 +--R 6630A b d e + (- 6120A b c - 3060B b )d e +--R + +--R 2 5 3 2 6 2 +--R (1632A c + 3264B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 5 3 +--R - 8840A b d e + (8160A b c + 4080B b )d e +--R + +--R 2 6 2 2 7 +--R (- 2176A c - 4352B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 3 2 6 2 +--R 17680A b d e + (- 16320A b c - 8160B b )d e +--R + +--R 2 7 2 8 +--R (4352A c + 8704B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Union(Expression(Integer),...) +--E 669 + +--S 670 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 671 + +)clear all + +--S 672 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1457 +r0:=-2/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(5/2)/e^6+2/7*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^6+2/9*(A*e*_ + (6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^(9/2)/e^6-2/11*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+_ + b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(13/2)/e^6+2/15*B*c^2*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 2 7 7 2 7 2 6 6 +--R 6006B c e x + ((6930A c + 13860B b c)e + 7392B c d e )x +--R + +--R 2 7 2 6 +--R (16380A b c + 8190B b )e + (8820A c + 17640B b c)d e +--R + +--R 2 2 5 +--R 126B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 10010A b e + (21840A b c + 10920B b )d e +--R + +--R 2 2 5 2 3 4 +--R (210A c + 420B b c)d e - 140B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 14300A b d e + (780A b c + 390B b )d e +--R + +--R 2 3 4 2 4 3 +--R (- 240A c - 480B b c)d e + 160B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 858A b d e + (- 936A b c - 468B b )d e + (288A c + 576B b c)d e +--R + +--R 2 5 2 +--R - 192B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 +--R - 1144A b d e + (1248A b c + 624B b )d e +--R + +--R 2 5 2 2 6 +--R (- 384A c - 768B b c)d e + 256B c d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 2288A b d e + (- 2496A b c - 1248B b )d e + (768A c + 1536B b c)d e +--R + +--R 2 7 +--R - 512B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 7 2 7 2 6 6 +--R 6006B c e x + ((6930A c + 13860B b c)e + 7392B c d e )x +--R + +--R 2 7 2 6 +--R (16380A b c + 8190B b )e + (8820A c + 17640B b c)d e +--R + +--R 2 2 5 +--R 126B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 10010A b e + (21840A b c + 10920B b )d e +--R + +--R 2 2 5 2 3 4 +--R (210A c + 420B b c)d e - 140B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 14300A b d e + (780A b c + 390B b )d e +--R + +--R 2 3 4 2 4 3 +--R (- 240A c - 480B b c)d e + 160B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 858A b d e + (- 936A b c - 468B b )d e + (288A c + 576B b c)d e +--R + +--R 2 5 2 +--R - 192B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 +--R - 1144A b d e + (1248A b c + 624B b )d e +--R + +--R 2 5 2 2 6 +--R (- 384A c - 768B b c)d e + 256B c d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 2288A b d e + (- 2496A b c - 1248B b )d e + (768A c + 1536B b c)d e +--R + +--R 2 7 +--R - 512B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 674 + +--S 675 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 676 + +)clear all + +--S 677 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +-------+ +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|e x + d +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1457 +r0:=-2/3*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(3/2)/e^6+2/5*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^6+2/7*(A*e*_ + (6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^(7/2)/e^6-2/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(9/2)/e^6-2/11*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + ((8190A c + 16380B b c)e + 630B c d e )x +--R + +--R 2 6 2 5 +--R (20020A b c + 10010B b )e + (910A c + 1820B b c)d e +--R + +--R 2 2 4 +--R - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 12870A b e + (2860A b c + 1430B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 1040A c - 2080B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 +--R 2574A b d e + (- 3432A b c - 1716B b )d e +--R + +--R 2 3 3 2 4 2 +--R (1248A c + 2496B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R - 3432A b d e + (4576A b c + 2288B b )d e +--R + +--R 2 4 2 2 5 +--R (- 1664A c - 3328B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 6864A b d e + (- 9152A b c - 4576B b )d e + (3328A c + 6656B b c)d e +--R + +--R 2 6 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + ((8190A c + 16380B b c)e + 630B c d e )x +--R + +--R 2 6 2 5 +--R (20020A b c + 10010B b )e + (910A c + 1820B b c)d e +--R + +--R 2 2 4 +--R - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 12870A b e + (2860A b c + 1430B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 1040A c - 2080B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 +--R 2574A b d e + (- 3432A b c - 1716B b )d e +--R + +--R 2 3 3 2 4 2 +--R (1248A c + 2496B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R - 3432A b d e + (4576A b c + 2288B b )d e +--R + +--R 2 4 2 2 5 +--R (- 1664A c - 3328B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 6864A b d e + (- 9152A b c - 4576B b )d e + (3328A c + 6656B b c)d e +--R + +--R 2 6 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 679 + +--S 680 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1457 +r0:=2/3*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^6+_ + 2/5*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(7/2)/e^6-2/9*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(9/2)/e^6+2/11*B*c^2*(d+e*x)^(11/2)/e^6-2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + ((770A c + 1540B b c)e - 700B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A b c + 990B b )e + (- 880A c - 1760B b c)d e + 800B c d e )x +--R + +--R 2 5 2 4 +--R 1386A b e + (- 2376A b c - 1188B b )d e +--R + +--R 2 2 3 2 3 2 +--R (1056A c + 2112B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 1848A b d e + (3168A b c + 1584B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1408A c - 2816B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 3696A b d e + (- 6336A b c - 3168B b )d e + (2816A c + 5632B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + ((770A c + 1540B b c)e - 700B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A b c + 990B b )e + (- 880A c - 1760B b c)d e + 800B c d e )x +--R + +--R 2 5 2 4 +--R 1386A b e + (- 2376A b c - 1188B b )d e +--R + +--R 2 2 3 2 3 2 +--R (1056A c + 2112B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 1848A b d e + (3168A b c + 1584B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1408A c - 2816B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 3696A b d e + (- 6336A b c - 3168B b )d e + (2816A c + 5632B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 684 + +--S 685 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 686 + +)clear all + +--S 687 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1457 +r0:=2/3*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*sqrt(d+e*x))+2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-_ + 2*A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + ((90A c + 180B b c)e - 100B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((252A b c + 126B b )e + (- 144A c - 288B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 504A b c - 252B b )d e + (288A c + 576B b c)d e +--R + +--R 2 3 2 +--R - 320B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 840A b d e + (2016A b c + 1008B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1152A c - 2304B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 1680A b d e + (4032A b c + 2016B b )d e + (- 2304A c - 4608B b c)d e +--R + +--R 2 5 +--R 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + ((90A c + 180B b c)e - 100B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((252A b c + 126B b )e + (- 144A c - 288B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 504A b c - 252B b )d e + (288A c + 576B b c)d e +--R + +--R 2 3 2 +--R - 320B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 840A b d e + (2016A b c + 1008B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1152A c - 2304B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 1680A b d e + (4032A b c + 2016B b )d e + (- 2304A c - 4608B b c)d e +--R + +--R 2 5 +--R 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 689 + +--S 690 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 691 + +)clear all + +--S 692 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1457 +r0:=2/3*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(3/2))-2/3*(2*A*c*e*(2*c*d-_ + b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-_ + 2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*sqrt(d+e*x))+_ + 2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + ((42A c + 84B b c)e - 60B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((140A b c + 70B b )e + (- 112A c - 224B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 840A b c - 420B b )d e + (672A c + 1344B b c)d e +--R + +--R 2 3 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R 840A b d e + (- 3360A b c - 1680B b )d e +--R + +--R 2 3 2 2 4 +--R (2688A c + 5376B b c)d e - 3840B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 560A b d e + (- 2240A b c - 1120B b )d e + (1792A c + 3584B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + ((42A c + 84B b c)e - 60B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((140A b c + 70B b )e + (- 112A c - 224B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 840A b c - 420B b )d e + (672A c + 1344B b c)d e +--R + +--R 2 3 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R 840A b d e + (- 3360A b c - 1680B b )d e +--R + +--R 2 3 2 2 4 +--R (2688A c + 5376B b c)d e - 3840B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 560A b d e + (- 2240A b c - 1120B b )d e + (1792A c + 3584B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 694 + +--S 695 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1457 +r0:=2/5*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(5/2))-2/3*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^(3/2))-2/3*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6-_ + 2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))/(e^6*sqrt(d+e*x))-2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + ((10A c + 20B b c)e - 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((60A b c + 30B b )e + (- 80A c - 160B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 30A b e + (360A b c + 180B b )d e + (- 480A c - 960B b c)d e +--R + +--R 2 3 2 +--R 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 40A b d e + (480A b c + 240B b )d e + (- 640A c - 1280B b c)d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 16A b d e + (192A b c + 96B b )d e + (- 256A c - 512B b c)d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + ((10A c + 20B b c)e - 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((60A b c + 30B b )e + (- 80A c - 160B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 30A b e + (360A b c + 180B b )d e + (- 480A c - 960B b c)d e +--R + +--R 2 3 2 +--R 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 40A b d e + (480A b c + 240B b )d e + (- 640A c - 1280B b c)d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 16A b d e + (192A b c + 96B b )d e + (- 256A c - 512B b c)d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 699 + +--S 700 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 701 + +)clear all + +--S 702 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1457 +r0:=2/3*(B*(c*d-b*e)^2+A*c*e*(2*c*d-b*e))*(d+e*x)^(3/2)/c^3+2/5*_ + (B*c*d-b*B*e+A*c*e)*(d+e*x)^(5/2)/c^2+2/7*B*(d+e*x)^(7/2)/c-_ + 2*A*d^(7/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(7/2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(9/2))+2*(B*(c*d-b*e)^3+_ + A*c*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/c^4 +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (- 210A b c + 210B b )e + (630A b c - 630B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 630A b c + 630B b c )d e + (210A c - 210B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 4 3 +-+ +-+ \|e x + d +--R - 210A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 4 +-+ +--R 105b c \|c +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 3 2 2 3 2 +--R (- 105A b c + 105B b )e + (315A b c - 315B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 315A b c + 315B b c )d e + (105A c - 105B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R +-+ +-------+ +--R 4 3 +-+ - 2\|d \|e x + d + e x + 2d +--R 105A c d \|d log(----------------------------) +--R x +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b c +--R , +--R +--R +-+ +-------+ +--R 4 3 +-+ - 2\|d \|e x + d + e x + 2d +--R 105A c d \|d log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A b c + 210B b )e + (630A b c - 630B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 630A b c + 630B b c )d e + (210A c - 210B b c )d +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b c +--R , +--R +--R 3 4 3 2 2 3 2 +--R (- 105A b c + 105B b )e + (315A b c - 315B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 315A b c + 315B b c )d e + (105A c - 105B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R +-------+ +--R 4 3 +---+ \|e x + d +--R - 210A c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b c +--R , +--R +--R +-------+ +--R 4 3 +---+ \|e x + d +--R - 210A c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A b c + 210B b )e + (630A b c - 630B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 630A b c + 630B b c )d e + (210A c - 210B b c )d +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 704 + +--S 705 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 +--R (- A b c + B b )e + (3A b c - 3B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A b c + 3B b c )d e + (A c - B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-----------------------------------------------) +--R \| c c x + b +--R + +--R +-+ +-------+ +--R 4 3 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d \|c \|d log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (2A b c - 2B b )e + (- 6A b c + 6B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (6A b c - 6B b c )d e + (- 2A c + 2B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 4 3 +-+ +-+ \|e x + d +--R 2A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 4 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 3 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d \|c \|d log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (2A b c - 2B b )e + (- 6A b c + 6B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (6A b c - 6B b c )d e + (- 2A c + 2B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 4 3 +-+ +-+ \|e x + d +--R 2A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 4 3 2 2 3 2 +--R (- 2A b c + 2B b )e + (6A b c - 6B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 6A b c + 6B b c )d e + (2A c - 2B b c )d +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 4 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1457 +r0:=2/3*(B*c*d-b*B*e+A*c*e)*(d+e*x)^(3/2)/c^2+2/5*B*(d+e*x)^(5/2)/c-_ + 2*A*d^(5/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(5/2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(7/2))+2*(B*(c*d-b*e)^2+_ + A*c*e*(2*c*d-b*e))*sqrt(d+e*x)/c^3 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R (30A b c - 30B b )e + (- 60A b c + 60B b c)d e +--R + +--R 3 2 2 +--R (30A c - 30B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 +-+ +-+ \|e x + d +--R - 30A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 +-+ +--R 15b c \|c +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 +--R (- 15A b c + 15B b )e + (30A b c - 30B b c)d e +--R + +--R 3 2 2 +--R (- 15A c + 15B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-------------------------------------------------) +--R \| c c x + b +--R + +--R +-+ +-------+ +--R 3 2 +-+ - 2\|d \|e x + d + e x + 2d +--R 15A c d \|d log(----------------------------) +--R x +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R , +--R +--R +-+ +-------+ +--R 3 2 +-+ - 2\|d \|e x + d + e x + 2d +--R 15A c d \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 +--R (30A b c - 30B b )e + (- 60A b c + 60B b c)d e +--R + +--R 3 2 2 +--R (30A c - 30B b c )d +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R , +--R +--R 2 3 2 2 2 +--R (- 15A b c + 15B b )e + (30A b c - 30B b c)d e +--R + +--R 3 2 2 +--R (- 15A c + 15B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-------------------------------------------------) +--R \| c c x + b +--R + +--R +-------+ +--R 3 2 +---+ \|e x + d +--R - 30A c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R , +--R +--R +-------+ +--R 3 2 +---+ \|e x + d +--R - 30A c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 3 2 2 2 +--R (30A b c - 30B b )e + (- 60A b c + 60B b c)d e +--R + +--R 3 2 2 +--R (30A c - 30B b c )d +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 711 + +--S 712 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 2 2 +--R ((- A b c + B b )e + (2A b c - 2B b c)d e + (- A c + B b c )d ) +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-------------------------------------------------) +--R \| c c x + b +--R + +--R +-+ +-------+ +--R 3 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d \|c \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 2B b )e + (4A b c - 4B b c)d e + (- 2A c + 2B b c )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 +-+ +-+ \|e x + d +--R 2A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d \|c \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 2B b )e + (4A b c - 4B b c)d e + (- 2A c + 2B b c )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 +-+ +-+ \|e x + d +--R 2A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 3 2 2 +--R ((2A b c - 2B b )e + (- 4A b c + 4B b c)d e + (2A c - 2B b c )d ) +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1457 +r0:=2/3*B*(d+e*x)^(3/2)/c-2*A*d^(3/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-_ + 2*(b*B-A*c)*(c*d-b*e)^(3/2)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*c^(5/2))+2*(B*c*d-b*B*e+A*c*e)*sqrt(d+e*x)/c^2 +--R +--R +--R (2) +--R 2 2 +-----------+ +--R ((- 6A b c + 6B b )e + (6A c - 6B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R - 6A c d\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 +-+ +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|c \|e x + d +--R / +--R 2 +-+ +--R 3b c \|c +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 |- b e + c d +--R ((- 3A b c + 3B b )e + (3A c - 3B b c)d) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 +-+ - 2\|d \|e x + d + e x + 2d +--R 3A c d\|d log(----------------------------) +--R x +--R + +--R 2 +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d +--R / +--R 2 +--R 3b c +--R , +--R +--R +-+ +-------+ +--R 2 +-+ - 2\|d \|e x + d + e x + 2d +--R 3A c d\|d log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 |b e - c d \|e x + d +--R ((- 6A b c + 6B b )e + (6A c - 6B b c)d) |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d +--R / +--R 2 +--R 3b c +--R , +--R +--R +-----------+ +--R 2 2 |- b e + c d +--R ((- 3A b c + 3B b )e + (3A c - 3B b c)d) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-------+ +--R 2 +---+ \|e x + d +--R - 6A c d\|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d +--R / +--R 2 +--R 3b c +--R , +--R +--R +-------+ +--R 2 +---+ \|e x + d +--R - 6A c d\|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R +---------+ +-------+ +--R 2 2 |b e - c d \|e x + d +--R ((- 6A b c + 6B b )e + (6A c - 6B b c)d) |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d +--R / +--R 2 +--R 3b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 718 + +--S 719 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 |- b e + c d +-+ +--R ((- A b c + B b )e + (A c - B b c)d) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d\|c \|d log(----------------------------) +--R x +--R + +--R 2 2 +-----------+ +--R ((2A b c - 2B b )e + (- 2A c + 2B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R 2A c d\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 2 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d\|c \|d log(----------------------------) +--R x +--R + +--R 2 2 +-----------+ +--R ((2A b c - 2B b )e + (- 2A c + 2B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R 2A c d\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 2 2 +-+ |b e - c d \|e x + d +--R ((- 2A b c + 2B b )e + (2A c - 2B b c)d)\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 2 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 722 + +)clear all + +--S 723 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1457 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b*c^(3/2))+2*B*sqrt(d+e*x)/c +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R (2A c - 2B b)\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-+ +-+ \|e x + d +-+ +-------+ +--R - 2A c\|c \|d atanh(----------) + 2B b\|c \|e x + d +--R +-+ +--R \|d +--R / +--R +-+ +--R b c\|c +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1457 +--a0:=integrate(t0,x) +--E 725 + +--S 726 of 1457 +--m0a:=a0.1-r0 +--E 726 + +--S 727 of 1457 +--d0a:=D(m0a,x) +--E 727 + +--S 728 of 1457 +--m0b:=a0.2-r0 +--E 728 + +--S 729 of 1457 +--d0b:=D(m0b,x) +--E 729 + +)clear all + +--S 730 of 1457 +t0:=(A+B*x)/((b*x+c*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ---------------------- +--R 2 +-------+ +--R (c x + b x)\|e x + d +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1457 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*sqrt(d))-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b*sqrt(c)*sqrt(c*d-b*e)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R (2A c - 2B b)\|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R - 2A\|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R / +--R +-----------+ +-+ +-+ +--R b\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R A\|- b c e + c d log(-------------------------------) +--R x +--R + +--R +-+ +--R (A c - B b)\|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R / +--R +-------------+ +--R | 2 +-+ +--R b\|- b c e + c d \|d +--R , +--R +--R +-----------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R A\|b c e - c d log(-------------------------------) +--R x +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-+ \|b c e - c d \|e x + d +--R (- 2A c + 2B b)\|d atan(------------------------) +--R b e - c d +--R / +--R +-----------+ +--R +-+ | 2 +--R b\|d \|b c e - c d +--R , +--R +--R +---+ +--R (A c - B b)\|- d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R + +--R +-------------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R - 2A\|- b c e + c d atan(----------------) +--R d +--R / +--R +-------------+ +--R | 2 +---+ +--R b\|- b c e + c d \|- d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R +---+ \|b c e - c d \|e x + d +--R (- 2A c + 2B b)\|- d atan(------------------------) +--R b e - c d +--R + +--R +-----------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R - 2A\|b c e - c d atan(----------------) +--R d +--R / +--R +-----------+ +--R +---+ | 2 +--R b\|- d \|b c e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 732 + +--S 733 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-------------+ +-------+ +-+ +--R | 2 +-----------+ +-+ - 2d\|e x + d + (e x + 2d)\|d +--R A\|- b c e + c d \|- b e + c d \|c log(-------------------------------) +--R x +--R + +--R +-----------+ +-+ +-+ +--R (A c - B b)\|- b e + c d \|c \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R + +--R +-------------+ +-+ +-------+ +--R | 2 +-+ \|c \|e x + d +--R (- 2A c + 2B b)\|- b c e + c d \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------------+ +-------+ +--R | 2 +-----------+ +-+ \|e x + d +--R 2A\|- b c e + c d \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R / +--R +-------------+ +--R | 2 +-----------+ +-+ +-+ +--R b\|- b c e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-------+ +-+ +--R +-----------+ +-+ | 2 - 2d\|e x + d + (e x + 2d)\|d +--R A\|- b e + c d \|c \|b c e - c d log(-------------------------------) +--R x +--R + +--R +-----------+ +-+ +-------+ +--R +-+ | 2 \|c \|e x + d +--R (- 2A c + 2B b)\|d \|b c e - c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-----------+ +-------+ +--R +-----------+ +-+ | 2 \|e x + d +--R 2A\|- b e + c d \|c \|b c e - c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ +-+ \|b c e - c d \|e x + d +--R (- 2A c + 2B b)\|- b e + c d \|c \|d atan(------------------------) +--R b e - c d +--R / +--R +-----------+ +--R +-----------+ +-+ +-+ | 2 +--R b\|- b e + c d \|c \|d \|b c e - c d +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 736 + +)clear all + +--S 737 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------ +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1457 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(3/2))-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b*(c*d-b*e)^(3/2))+_ + 2*(B*d-A*e)/(d*(c*d-b*e)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R (- 2A c + 2B b)d\|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R (- 2A b e + 2A c d)\|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R +-----------+ +-+ +--R (2A b e - 2B b d)\|- b e + c d \|d +--R / +--R 2 2 +-----------+ +-+ +-------+ +--R (b d e - b c d )\|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | c +-+ +-------+ +--R (A c - B b)d |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R (A b e - A c d)\|e x + d log(-------------------------------) +--R x +--R + +--R +-+ +--R (2A b e - 2B b d)\|d +--R / +--R 2 2 +-+ +-------+ +--R (b d e - b c d )\|d \|e x + d +--R , +--R +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R (A b e - A c d)\|e x + d log(-------------------------------) +--R x +--R + +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R (2A c - 2B b)d |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R +-+ +--R (2A b e - 2B b d)\|d +--R / +--R 2 2 +-+ +-------+ +--R (b d e - b c d )\|d \|e x + d +--R , +--R +--R +-----------+ +--R +---+ | c +-------+ +--R (A c - B b)d\|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R (- 2A b e + 2A c d)\|e x + d atan(----------------) +--R d +--R + +--R +---+ +--R (2A b e - 2B b d)\|- d +--R / +--R 2 2 +---+ +-------+ +--R (b d e - b c d )\|- d \|e x + d +--R , +--R +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R (- 2A b e + 2A c d)\|e x + d atan(----------------) +--R d +--R + +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R (2A c - 2B b)d\|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R +---+ +--R (2A b e - 2B b d)\|- d +--R / +--R 2 2 +---+ +-------+ +--R (b d e - b c d )\|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 739 + +--S 740 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | c +-+ +--R (A c - B b)d\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R (A b e - A c d)\|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R (2A c - 2B b)d\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ \|e x + d +--R (2A b e - 2A c d)\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 2 2 +-----------+ +-+ +--R (b d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R (A b e - A c d)\|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R (2A c - 2B b)d\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ \|e x + d +--R (2A b e - 2A c d)\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R +-----------+ | c +-+ c\|e x + d +--R (2A c - 2B b)d\|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 2 2 +-----------+ +-+ +--R (b d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 1457 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------------ +--R 2 4 2 3 2 2 2 +-------+ +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1457 +r0:=2/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(3/2))-2*A*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b*d^(5/2))-2*c^(3/2)*(b*B-A*c)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*(c*d-b*e)^(5/2))+2*(B*c*d^2-A*e*(2*c*d-b*e))/(d^2*_ + (c*d-b*e)^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 3 +-+ +-+ +-------+ +--R ((6A c - 6B b c)d e x + (6A c - 6B b c)d )\|c \|d \|e x + d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 2 2 2 2 2 +--R (- 6A b e + 12A b c d e - 6A c d e)x - 6A b d e + 12A b c d e +--R + +--R 2 3 +--R - 6A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 2 2 2 +--R (3A b e - 6A b c d e + 3A c d e)x + 3A b d e - 6A b c d e +--R + +--R 2 3 +--R 3A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 2 3 | c +-+ +--R ((3A c - 3B b c)d e x + (3A c - 3B b c)d ) |- --------- \|d +--R \| b e - c d +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +-+ +--R \|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +-+ +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d )\|d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 3 2 2 2 2 2 2 +--R (3A b e - 6A b c d e + 3A c d e)x + 3A b d e - 6A b c d e +--R + +--R 2 3 +--R 3A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R +---------+ +--R 2 2 2 3 | c +-+ +--R ((- 6A c + 6B b c)d e x + (- 6A c + 6B b c)d ) |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R +-------+ c\|e x + d +--R \|e x + d atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +-+ +--R \|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +-+ +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d )\|d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +-----------+ +--R 2 2 2 3 +---+ | c +--R ((3A c - 3B b c)d e x + (3A c - 3B b c)d )\|- d |- --------- +--R \| b e - c d +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 3 2 2 2 2 2 2 +--R (- 6A b e + 12A b c d e - 6A c d e)x - 6A b d e + 12A b c d e +--R + +--R 2 3 +--R - 6A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 2 3 2 2 2 2 2 2 +--R (- 6A b e + 12A b c d e - 6A c d e)x - 6A b d e + 12A b c d e +--R + +--R 2 3 +--R - 6A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R +---------+ +--R 2 2 2 3 +---+ | c +--R ((- 6A c + 6B b c)d e x + (- 6A c + 6B b c)d )\|- d |--------- +--R \|b e - c d +--R * +--R +-------+ +--R +-------+ c\|e x + d +--R \|e x + d atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 746 + +--S 747 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 +-----------+ +--R (A b e - 2A b c d e + A c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 +-----------+ | c +-+ +--R (A c - B b c)d \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|c \|e x + d +--R (- 2A c + 2B b c)d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|e x + d +--R (2A b e - 4A b c d e + 2A c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 2 2 2 3 2 4 +-----------+ +-+ +--R (b d e - 2b c d e + b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 +-----------+ +--R (A b e - 2A b c d e + A c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|c \|e x + d +--R (- 2A c + 2B b c)d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|e x + d +--R (2A b e - 4A b c d e + 2A c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 2 +-----------+ | c +-+ +--R (- 2A c + 2B b c)d \|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 3 2 2 2 3 2 4 +-----------+ +-+ +--R (b d e - 2b c d e + b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 1457 +t0:=(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1457 +r0:=2/5*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(5/2))+2/3*(B*c*d^2-A*e*(2*c*d-_ + b*e))/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-2*A*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b*d^(7/2))-2*c^(5/2)*(b*B-A*c)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*(c*d-b*e)^(7/2))+2*(B*c^2*d^3-A*e*(3*c^2*d^2-_ + 3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 2 2 3 2 4 +--R (- 30A c + 30B b c )d e x + (- 60A c + 60B b c )d e x +--R + +--R 3 2 5 +--R (- 30A c + 30B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30A b e + 90A b c d e - 90A b c d e + 30A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (- 60A b d e + 180A b c d e - 180A b c d e + 60A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R - 30A b d e + 90A b c d e - 90A b c d e + 30A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 2 2 3 2 4 +--R (15A c - 15B b c )d e x + (30A c - 30B b c )d e x +--R + +--R 3 2 5 +--R (15A c - 15B b c )d +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15A b e - 45A b c d e + 45A b c d e - 15A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (30A b d e - 90A b c d e + 90A b c d e - 30A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R 15A b d e - 45A b c d e + 45A b c d e - 15A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +-+ +--R \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15A b e - 45A b c d e + 45A b c d e - 15A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (30A b d e - 90A b c d e + 90A b c d e - 30A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R 15A b d e - 45A b c d e + 45A b c d e - 15A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 3 2 3 2 2 3 2 4 +--R (30A c - 30B b c )d e x + (60A c - 60B b c )d e x +--R + +--R 3 2 5 +--R (30A c - 30B b c )d +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +-+ +--R \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 3 2 3 2 2 3 2 4 +--R (15A c - 15B b c )d e x + (30A c - 30B b c )d e x +--R + +--R 3 2 5 +--R (15A c - 15B b c )d +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30A b e + 90A b c d e - 90A b c d e + 30A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (- 60A b d e + 180A b c d e - 180A b c d e + 60A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R - 30A b d e + 90A b c d e - 90A b c d e + 30A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30A b e + 90A b c d e - 90A b c d e + 30A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (- 60A b d e + 180A b c d e - 180A b c d e + 60A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R - 30A b d e + 90A b c d e - 90A b c d e + 30A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 3 2 3 2 2 3 2 4 +--R (30A c - 30B b c )d e x + (60A c - 60B b c )d e x +--R + +--R 3 2 5 +--R (30A c - 30B b c )d +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 753 + +--S 754 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 3 +-----------+ | c +-+ +--R (A c - B b c )d \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (A b e - 3A b c d e + 3A b c d e - A c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 2 3 +-+ +-+ \|c \|e x + d +--R (2A c - 2B b c )d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (2A b e - 6A b c d e + 6A b c d e - 2A c d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R / +--R 4 3 3 3 4 2 2 2 5 3 6 +-----------+ +-+ +--R (b d e - 3b c d e + 3b c d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (A b e - 3A b c d e + 3A b c d e - A c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 2 3 +-+ +-+ \|c \|e x + d +--R (2A c - 2B b c )d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (2A b e - 6A b c d e + 6A b c d e - 2A c d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 3 2 3 +-----------+ | c +-+ +--R (2A c - 2B b c )d \|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 4 3 3 3 4 2 2 2 5 3 6 +-----------+ +-+ +--R (b d e - 3b c d e + 3b c d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 757 + +)clear all + +--S 758 of 1457 +t0:=(A+B*x)/((d+e*x)^(9/2)*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 6 4 3 5 3 2 2 4 +--R c e x + (b e + 4c d e )x + (4b d e + 6c d e )x +--R + +--R 2 2 3 3 3 4 2 4 +--R (6b d e + 4c d e)x + (4b d e + c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1457 +r0:=2/7*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(7/2))+2/5*(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x)^(5/2))+2/3*(B*c^2*d^3-A*e*(3*c^2*d^2-_ + 3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x)^(3/2))-_ + 2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(9/2))-2*c^(7/2)*(b*B-A*c)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*(c*d-b*e)^(9/2))+_ + 2*(B*c^3*d^4-A*e*(4*c^3*d^3-6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))/_ + (d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 3 3 4 3 5 2 2 +--R (210A c - 210B b c )d e x + (630A c - 630B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (630A c - 630B b c )d e x + (210A c - 210B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 210A b e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 4 3 +--R - 210A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R - 630A b d e + 2520A b c d e - 3780A b c d e + 2520A b c d e +--R + +--R 4 5 2 +--R - 630A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R - 630A b d e + 2520A b c d e - 3780A b c d e + 2520A b c d e +--R + +--R 4 6 +--R - 630A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R - 210A b d e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 7 +--R - 210A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 4 10 +--R (315b d e - 1260b c d e + 1890b c d e - 1260b c d e + 315b c d e)x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 105A b e - 420A b c d e + 630A b c d e - 420A b c d e +--R + +--R 4 4 3 +--R 105A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R 315A b d e - 1260A b c d e + 1890A b c d e - 1260A b c d e +--R + +--R 4 5 2 +--R 315A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R 315A b d e - 1260A b c d e + 1890A b c d e - 1260A b c d e +--R + +--R 4 6 +--R 315A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R 105A b d e - 420A b c d e + 630A b c d e - 420A b c d e +--R + +--R 4 7 +--R 105A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 4 3 4 3 3 4 3 5 2 2 +--R (105A c - 105B b c )d e x + (315A c - 315B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (315A c - 315B b c )d e x + (105A c - 105B b c )d +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +-+ +--R \|d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 10 +--R 315b c d e +--R * +--R x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 105A b e - 420A b c d e + 630A b c d e - 420A b c d e +--R + +--R 4 4 3 +--R 105A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R 315A b d e - 1260A b c d e + 1890A b c d e - 1260A b c d e +--R + +--R 4 5 2 +--R 315A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R 315A b d e - 1260A b c d e + 1890A b c d e - 1260A b c d e +--R + +--R 4 6 +--R 315A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R 105A b d e - 420A b c d e + 630A b c d e - 420A b c d e +--R + +--R 4 7 +--R 105A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 4 3 4 3 3 4 3 5 2 2 +--R (- 210A c + 210B b c )d e x + (- 630A c + 630B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (- 630A c + 630B b c )d e x + (- 210A c + 210B b c )d +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +-+ +--R \|d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 10 +--R 315b c d e +--R * +--R x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 4 3 4 3 3 4 3 5 2 2 +--R (105A c - 105B b c )d e x + (315A c - 315B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (315A c - 315B b c )d e x + (105A c - 105B b c )d +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 210A b e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 4 3 +--R - 210A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R - 630A b d e + 2520A b c d e - 3780A b c d e +--R + +--R 3 4 3 4 5 2 +--R 2520A b c d e - 630A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 +--R - 630A b d e + 2520A b c d e - 3780A b c d e +--R + +--R 3 5 2 4 6 +--R 2520A b c d e - 630A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R - 210A b d e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 7 +--R - 210A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 10 +--R 315b c d e +--R * +--R x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 210A b e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 4 3 +--R - 210A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R - 630A b d e + 2520A b c d e - 3780A b c d e +--R + +--R 3 4 3 4 5 2 +--R 2520A b c d e - 630A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 +--R - 630A b d e + 2520A b c d e - 3780A b c d e +--R + +--R 3 5 2 4 6 +--R 2520A b c d e - 630A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R - 210A b d e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 7 +--R - 210A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 4 3 4 3 3 4 3 5 2 2 +--R (- 210A c + 210B b c )d e x + (- 630A c + 630B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (- 630A c + 630B b c )d e x + (- 210A c + 210B b c )d +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 10 +--R 315b c d e +--R * +--R x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 760 + +--S 761 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (A b e - 4A b c d e + 6A b c d e - 4A b c d e + A c d ) +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 4 3 4 +-----------+ | c +-+ +--R (A c - B b c )d \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 4 3 4 +-+ +-+ \|c \|e x + d +--R (- 2A c + 2B b c )d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (2A b e - 8A b c d e + 12A b c d e - 8A b c d e + 2A c d ) +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 +-----------+ +-+ +--R (b d e - 4b c d e + 6b c d e - 4b c d e + b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (A b e - 4A b c d e + 6A b c d e - 4A b c d e + A c d ) +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 4 3 4 +-+ +-+ \|c \|e x + d +--R (- 2A c + 2B b c )d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (2A b e - 8A b c d e + 12A b c d e - 8A b c d e + 2A c d ) +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 4 3 4 +-----------+ | c +-+ +--R (- 2A c + 2B b c )d \|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 +-----------+ +-+ +--R (b d e - 4b c d e + 6b c d e - 4b c d e + b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 764 + +)clear all + +--S 765 of 1457 +t0:=(A+B*x)*(d+e*x)^(9/2)/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 765 + +--S 766 of 1457 +r0:=1/3*e*(6*A*c^3*d^2-7*b^3*B*e^2-3*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ + (12*B*d+5*A*e))*(d+e*x)^(3/2)/(b^2*c^3)+1/5*e*(10*A*c^2*d+7*b^2*B*e-_ + 5*b*c*(B*d+A*e))*(d+e*x)^(5/2)/(b^2*c^2)+(b*B-2*A*c)*(c*d-b*e)*_ + (d+e*x)^(7/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(9/2)/(b*x*(b+c*x))-_ + d^(7/2)*(2*b*B*d-4*A*c*d+9*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/b^3-_ + (c*d-b*e)^(7/2)*(4*A*c^2*d-7*b^2*B*e-b*c*(2*B*d-5*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(9/2))+_ + e*(2*A*c^4*d^3+7*b^4*B*e^3-b*c^3*d^2*(B*d+3*A*e)-b^3*c*e^2*_ + (19*B*d+5*A*e)+b^2*c^2*d*e*(15*B*d+11*A*e))*sqrt(d+e*x)/(b^2*c^4) +--R +--R +--R (2) +--R 4 2 5 4 3 3 4 2 3 +--R (75A b c - 105B b c)e + (- 165A b c + 285B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (45A b c - 225B b c )d e + (105A b c + 15B b c )d e +--R + +--R 6 5 4 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (75A b c - 105B b )e + (- 165A b c + 285B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (45A b c - 225B b c )d e + (105A b c + 15B b c )d e +--R + +--R 5 2 4 4 +--R (- 60A b c + 30B b c )d +--R * +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 3 6 5 4 2 +--R (- 135A b c d e + (60A c - 30B b c )d )x +--R + +--R 2 4 3 5 2 4 4 +--R (- 135A b c d e + (60A b c - 30B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 3 3 +--R 6B b c e x + ((10A b c - 14B b c )e + 42B b c d e )x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 50A b c + 70B b c)e + (130A b c - 218B b c )d e +--R + +--R 3 3 2 2 +--R 216B b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 75A b c + 105B b )e + (190A b c - 320B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 90A b c + 306B b c )d e + (60A b c - 60B b c )d e +--R + +--R 5 2 4 4 +--R (- 30A b c + 15B b c )d +--R * +--R x +--R + +--R 2 4 4 +--R - 15A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 5 2 4 4 +-+ +--R (15b c x + 15b c x)\|c +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1457 +--a0:=integrate(t0,x) +--E 767 + +--S 768 of 1457 +--m0a:=a0.1-r0 +--E 768 + +--S 769 of 1457 +--d0a:=D(m0a,x) +--E 769 + +--S 770 of 1457 +--m0b:=a0.2-r0 +--E 770 + +--S 771 of 1457 +--d0b:=D(m0b,x) +--E 771 + +)clear all + +--S 772 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1457 +r0:=1/3*e*(6*A*c^2*d+5*b^2*B*e-3*b*c*(B*d+A*e))*(d+e*x)^(3/2)/(b^2*c^2)+_ + (b*B-2*A*c)*(c*d-b*e)*(d+e*x)^(5/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(7/2)/_ + (b*x*(b+c*x))-d^(5/2)*(2*b*B*d-4*A*c*d+7*A*b*e)*atanh(sqrt(d+e*x)/_ + sqrt(d))/b^3+(c*d-b*e)^(5/2)*(2*b*B*c*d-4*A*c^2*d+5*b^2*B*e-_ + 3*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(7/2))+_ + e*(2*A*c^3*d^2-5*b^3*B*e^2-b*c^2*d*(B*d+2*A*e)+b^2*c*e*(8*B*d+_ + 3*A*e))*sqrt(d+e*x)/(b^2*c^3) +--R +--R +--R (2) +--R 3 2 4 3 2 3 3 2 2 +--R (- 9A b c + 15B b c)e + (6A b c - 24B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (15A b c + 3B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 9A b c + 15B b )e + (6A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (15A b c + 3B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 2 5 4 3 2 +--R (- 21A b c d e + (12A c - 6B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (- 21A b c d e + (12A b c - 6B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 2B b c e x + ((6A b c - 10B b c)e + 20B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (9A b c - 15B b )e + (- 9A b c + 29B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (9A b c - 9B b c )d e + (- 6A b c + 3B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 3A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 4 2 4 3 +-+ +--R (3b c x + 3b c x)\|c +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 4 3 2 3 3 2 2 +--R (9A b c - 15B b c)e + (- 6A b c + 24B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 15A b c - 3B b c )d e + (12A c - 6B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (9A b c - 15B b )e + (- 6A b c + 24B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 15A b c - 3B b c )d e + (12A b c - 6B b c )d +--R * +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-------------------------------------------------) +--R \| c c x + b +--R + +--R 4 2 5 4 3 2 +--R (21A b c d e + (- 12A c + 6B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (21A b c d e + (- 12A b c + 6B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 4B b c e x + ((12A b c - 20B b c)e + 40B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (18A b c - 30B b )e + (- 18A b c + 58B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (18A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 6A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 6b c x + 6b c x +--R , +--R +--R 4 2 5 4 3 2 +--R (21A b c d e + (- 12A c + 6B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (21A b c d e + (- 12A b c + 6B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 18A b c + 30B b c)e + (12A b c - 48B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (30A b c + 6B b c )d e + (- 24A c + 12B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 18A b c + 30B b )e + (12A b c - 48B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (30A b c + 6B b c )d e + (- 24A b c + 12B b c )d +--R * +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 4B b c e x + ((12A b c - 20B b c)e + 40B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (18A b c - 30B b )e + (- 18A b c + 58B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (18A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 6A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 6b c x + 6b c x +--R , +--R +--R 3 2 4 3 2 3 3 2 2 +--R (9A b c - 15B b c)e + (- 6A b c + 24B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 15A b c - 3B b c )d e + (12A c - 6B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (9A b c - 15B b )e + (- 6A b c + 24B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 15A b c - 3B b c )d e + (12A b c - 6B b c )d +--R * +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-------------------------------------------------) +--R \| c c x + b +--R + +--R 4 2 5 4 3 2 +--R (- 42A b c d e + (24A c - 12B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (- 42A b c d e + (24A b c - 12B b c )d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 4B b c e x + ((12A b c - 20B b c)e + 40B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (18A b c - 30B b )e + (- 18A b c + 58B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (18A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 6A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 6b c x + 6b c x +--R , +--R +--R 4 2 5 4 3 2 +--R (- 21A b c d e + (12A c - 6B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (- 21A b c d e + (12A b c - 6B b c )d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 9A b c + 15B b c)e + (6A b c - 24B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (15A b c + 3B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 9A b c + 15B b )e + (6A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (15A b c + 3B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 2B b c e x + ((6A b c - 10B b c)e + 20B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (9A b c - 15B b )e + (- 9A b c + 29B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (9A b c - 9B b c )d e + (- 6A b c + 3B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 3A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 3b c x + 3b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 774 + +--S 775 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 +--R (3A b c - 5B b )e + (- 2A b c + 8B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 5A b c - B b c )d e + (4A c - 2B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-------------------------------------------------) +--R \| c c x + b +--R + +--R 3 2 4 3 3 +-+ +-+ +--R (7A b c d e + (- 4A c + 2B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (6A b c - 10B b )e + (- 4A b c + 16B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 10A b c - 2B b c )d e + (8A c - 4B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 4 3 3 +-+ +-+ \|e x + d +--R (14A b c d e + (- 8A c + 4B b c )d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 3 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 2 4 3 3 +-+ +-+ +--R (7A b c d e + (- 4A c + 2B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (6A b c - 10B b )e + (- 4A b c + 16B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 10A b c - 2B b c )d e + (8A c - 4B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 4 3 3 +-+ +-+ \|e x + d +--R (14A b c d e + (- 8A c + 4B b c )d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 4 3 2 2 3 2 +--R (- 6A b c + 10B b )e + (4A b c - 16B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (10A b c + 2B b c )d e + (- 8A c + 4B b c )d +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 3 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 778 + +)clear all + +--S 779 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1457 +r0:=(b*B-2*A*c)*(c*d-b*e)*(d+e*x)^(3/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(5/2)/_ + (b*x*(b+c*x))-d^(3/2)*(2*b*B*d-4*A*c*d+5*A*b*e)*atanh(sqrt(d+e*x)/_ + sqrt(d))/b^3-(c*d-b*e)^(3/2)*(4*A*c^2*d-3*b^2*B*e-b*c*(2*B*d-A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(5/2))+e*(2*A*c^2*d+_ + 3*b^2*B*e-b*c*(B*d+A*e))*sqrt(d+e*x)/(b^2*c^2) +--R +--R +--R (2) +--R 2 2 3 2 3 2 2 +--R (A b c - 3B b c)e + (3A b c + B b c )d e +--R + +--R 4 3 2 +--R (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 4 3 2 2 +--R (- 5A b c d e + (4A c - 2B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (- 5A b c d e + (4A b c - 2B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 +--R 2B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- A b c + 3B b )e + (2A b c - 2B b c)d e +--R + +--R 3 2 2 2 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 3 2 4 2 +-+ +--R (b c x + b c x)\|c +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 3 2 2 +--R (A b c - 3B b c)e + (3A b c + B b c )d e +--R + +--R 4 3 2 +--R (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 3 4 3 2 2 +--R (5A b c d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (5A b c d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 2 2 +--R 4B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- 2A b c + 6B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 2 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - 2A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R 2b c x + 2b c x +--R , +--R +--R 3 4 3 2 2 +--R (5A b c d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (5A b c d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 2 3 2 3 2 2 +--R (2A b c - 6B b c)e + (6A b c + 2B b c )d e +--R + +--R 4 3 2 +--R (- 8A c + 4B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 +--R (2A b c - 6B b )e + (6A b c + 2B b c)d e +--R + +--R 3 2 2 2 +--R (- 8A b c + 4B b c )d +--R * +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 2 +--R 4B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- 2A b c + 6B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 2 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - 2A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R 2b c x + 2b c x +--R , +--R +--R 2 2 3 2 3 2 2 +--R (A b c - 3B b c)e + (3A b c + B b c )d e +--R + +--R 4 3 2 +--R (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 3 4 3 2 2 +--R (- 10A b c d e + (8A c - 4B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (- 10A b c d e + (8A b c - 4B b c )d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 2 +--R 4B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- 2A b c + 6B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 2 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - 2A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R 2b c x + 2b c x +--R , +--R +--R 3 4 3 2 2 +--R (- 5A b c d e + (4A c - 2B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (- 5A b c d e + (4A b c - 2B b c )d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 2 3 2 3 2 2 +--R (A b c - 3B b c)e + (3A b c + B b c )d e +--R + +--R 4 3 2 +--R (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 2 +--R 2B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- A b c + 3B b )e + (2A b c - 2B b c)d e +--R + +--R 3 2 2 2 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 781 + +--S 782 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A c + 2B b c )d ) +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 2 +-+ +-+ +--R (5A b c d e + (- 4A c + 2B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 6B b )e + (- 6A b c - 2B b c)d e + (8A c - 4B b c )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 3 2 2 +-+ +-+ \|e x + d +--R (10A b c d e + (- 8A c + 4B b c )d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 2 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 2 2 +-+ +-+ +--R (5A b c d e + (- 4A c + 2B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 6B b )e + (- 6A b c - 2B b c)d e + (8A c - 4B b c )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 3 2 2 +-+ +-+ \|e x + d +--R (10A b c d e + (- 8A c + 4B b c )d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 3 2 2 +--R ((2A b c - 6B b )e + (6A b c + 2B b c)d e + (- 8A c + 4B b c )d ) +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 2 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1457 +r0:=-A*(d+e*x)^(3/2)/(b*x*(b+c*x))-(2*b*B*d-4*A*c*d+3*A*b*e)*_ + atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b^3-(4*A*c^2*d-b^2*B*e-_ + b*c*(2*B*d+A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*_ + sqrt(c*d-b*e)/(b^3*c^(3/2))+(b*B-2*A*c)*(c*d-b*e)*sqrt(d+e*x)/_ + (b^2*c*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 +--R ((A b c + B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((A b c + B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 2 +--R (- 3A b c e + (4A c - 2B b c )d)x +--R + +--R 2 2 2 +--R (- 3A b c e + (4A b c - 2B b c)d)x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 +-+ +-------+ +--R (((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d)\|c \|e x + d +--R / +--R 3 2 2 4 +-+ +--R (b c x + b c x)\|c +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 +--R ((A b c + B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((A b c + B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 2 +--R (3A b c e + (- 4A c + 2B b c )d)x +--R + +--R 2 2 2 +--R (3A b c e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 +-------+ +--R (((2A b c - 2B b )e + (- 4A b c + 2B b c)d)x - 2A b c d)\|e x + d +--R / +--R 3 2 2 4 +--R 2b c x + 2b c x +--R , +--R +--R 2 3 2 2 +--R (3A b c e + (- 4A c + 2B b c )d)x +--R + +--R 2 2 2 +--R (3A b c e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 2 3 2 2 +--R ((2A b c + 2B b c)e + (- 8A c + 4B b c )d)x +--R + +--R 2 3 2 2 +--R ((2A b c + 2B b )e + (- 8A b c + 4B b c)d)x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 3 2 2 2 +-------+ +--R (((2A b c - 2B b )e + (- 4A b c + 2B b c)d)x - 2A b c d)\|e x + d +--R / +--R 3 2 2 4 +--R 2b c x + 2b c x +--R , +--R +--R 2 2 3 2 2 +--R ((A b c + B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((A b c + B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 2 +--R (- 6A b c e + (8A c - 4B b c )d)x +--R + +--R 2 2 2 +--R (- 6A b c e + (8A b c - 4B b c)d)x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 3 2 2 2 +-------+ +--R (((2A b c - 2B b )e + (- 4A b c + 2B b c)d)x - 2A b c d)\|e x + d +--R / +--R 3 2 2 4 +--R 2b c x + 2b c x +--R , +--R +--R 2 3 2 2 +--R (- 3A b c e + (4A c - 2B b c )d)x +--R + +--R 2 2 2 +--R (- 3A b c e + (4A b c - 2B b c)d)x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 2 3 2 2 +--R ((A b c + B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((A b c + B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 3 2 2 2 +-------+ +--R (((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d)\|e x + d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 788 + +--S 789 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 |- b e + c d +-+ +--R ((A b c + B b )e + (- 4A c + 2B b c)d) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (3A b c e + (- 4A c + 2B b c)d)\|c \|d log(----------------------------) +--R x +--R + +--R 2 2 +-----------+ +--R ((- 2A b c - 2B b )e + (8A c - 4B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R (6A b c e + (- 8A c + 4B b c)d)\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 +-+ +--R 2b c\|c +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (3A b c e + (- 4A c + 2B b c)d)\|c \|d log(----------------------------) +--R x +--R + +--R 2 2 +-----------+ +--R ((- 2A b c - 2B b )e + (8A c - 4B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R (6A b c e + (- 8A c + 4B b c)d)\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 2 2 +-+ |b e - c d \|e x + d +--R ((2A b c + 2B b )e + (- 8A c + 4B b c)d)\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 +-+ +--R 2b c\|c +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 792 + +)clear all + +--S 793 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1457 +r0:=-(2*b*B*d-4*A*c*d+A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*sqrt(d))+_ + (2*b*B*c*d-4*A*c^2*d-b^2*B*e+3*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b^3*sqrt(c)*sqrt(c*d-b*e))+(b*B-2*A*c)*sqrt(d+e*x)/_ + (b^2*(b+c*x))-A*sqrt(d+e*x)/(b*x*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 +--R ((3A b c - B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((3A b c - B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 +--R ((- A b c e + (4A c - 2B b c)d)x + (- A b e + (4A b c - 2B b )d)x) +--R * +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 +-----------+ +-+ +-+ +-------+ +--R ((- 2A b c + B b )x - A b )\|- b e + c d \|c \|d \|e x + d +--R / +--R 3 2 4 +-----------+ +-+ +-+ +--R (b c x + b x)\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 +--R ((A b c e + (- 4A c + 2B b c)d)x + (A b e + (- 4A b c + 2B b )d)x) +--R * +--R +-------------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R \|- b c e + c d log(-------------------------------) +--R x +--R + +--R 2 2 3 2 2 +--R ((3A b c - B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((3A b c - B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +--R \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R + +--R +-------------+ +--R 2 2 | 2 +-+ +-------+ +--R ((- 4A b c + 2B b )x - 2A b )\|- b c e + c d \|d \|e x + d +--R / +--R +-------------+ +--R 3 2 4 | 2 +-+ +--R (2b c x + 2b x)\|- b c e + c d \|d +--R , +--R +--R 2 2 2 2 +--R ((A b c e + (- 4A c + 2B b c)d)x + (A b e + (- 4A b c + 2B b )d)x) +--R * +--R +-----------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R \|b c e - c d log(-------------------------------) +--R x +--R + +--R 2 2 3 2 2 +--R ((- 6A b c + 2B b c)e + (8A c - 4B b c )d)x +--R + +--R 2 3 2 2 +--R ((- 6A b c + 2B b )e + (8A b c - 4B b c)d)x +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-+ \|b c e - c d \|e x + d +--R \|d atan(------------------------) +--R b e - c d +--R + +--R +-----------+ +--R 2 2 +-+ | 2 +-------+ +--R ((- 4A b c + 2B b )x - 2A b )\|d \|b c e - c d \|e x + d +--R / +--R +-----------+ +--R 3 2 4 +-+ | 2 +--R (2b c x + 2b x)\|d \|b c e - c d +--R , +--R +--R 2 2 3 2 2 +--R ((3A b c - B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((3A b c - B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +---+ +--R \|- d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 +--R (- 2A b c e + (8A c - 4B b c)d)x +--R + +--R 2 2 +--R (- 2A b e + (8A b c - 4B b )d)x +--R * +--R +-------------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R \|- b c e + c d atan(----------------) +--R d +--R + +--R +-------------+ +--R 2 2 | 2 +---+ +-------+ +--R ((- 4A b c + 2B b )x - 2A b )\|- b c e + c d \|- d \|e x + d +--R / +--R +-------------+ +--R 3 2 4 | 2 +---+ +--R (2b c x + 2b x)\|- b c e + c d \|- d +--R , +--R +--R 2 2 3 2 2 +--R ((- 3A b c + B b c)e + (4A c - 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((- 3A b c + B b )e + (4A b c - 2B b c)d)x +--R * +--R +-----------+ +--R | 2 +-------+ +--R +---+ \|b c e - c d \|e x + d +--R \|- d atan(------------------------) +--R b e - c d +--R + +--R 2 2 2 2 +--R ((- A b c e + (4A c - 2B b c)d)x + (- A b e + (4A b c - 2B b )d)x) +--R * +--R +-----------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R \|b c e - c d atan(----------------) +--R d +--R + +--R +-----------+ +--R 2 2 +---+ | 2 +-------+ +--R ((- 2A b c + B b )x - A b )\|- d \|b c e - c d \|e x + d +--R / +--R +-----------+ +--R 3 2 4 +---+ | 2 +--R (b c x + b x)\|- d \|b c e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 795 + +--S 796 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-------------+ +--R | 2 +-----------+ +-+ +--R (A b e + (- 4A c + 2B b)d)\|- b c e + c d \|- b e + c d \|c +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R 2 2 +-----------+ +-+ +-+ +--R ((3A b c - B b )e + (- 4A c + 2B b c)d)\|- b e + c d \|c \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R + +--R +-------------+ +--R 2 2 | 2 +-+ +--R ((- 6A b c + 2B b )e + (8A c - 4B b c)d)\|- b c e + c d \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------------+ +--R | 2 +-----------+ +-+ +--R (2A b e + (- 8A c + 4B b)d)\|- b c e + c d \|- b e + c d \|c +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R / +--R +-------------+ +--R 3 | 2 +-----------+ +-+ +-+ +--R 2b \|- b c e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R +-----------+ +-+ | 2 +--R (A b e + (- 4A c + 2B b)d)\|- b e + c d \|c \|b c e - c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 +-+ | 2 +--R ((- 6A b c + 2B b )e + (8A c - 4B b c)d)\|d \|b c e - c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-----------+ +--R +-----------+ +-+ | 2 +--R (2A b e + (- 8A c + 4B b)d)\|- b e + c d \|c \|b c e - c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 +-----------+ +-+ +-+ +--R ((- 6A b c + 2B b )e + (8A c - 4B b c)d)\|- b e + c d \|c \|d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|b c e - c d \|e x + d +--R atan(------------------------) +--R b e - c d +--R / +--R +-----------+ +--R 3 +-----------+ +-+ +-+ | 2 +--R 2b \|- b e + c d \|c \|d \|b c e - c d +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 799 + +)clear all + +--S 800 of 1457 +t0:=(A+B*x)/((b*x+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (c x + 2b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1457 +r0:=-(2*b*B*d-4*A*c*d-A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(3/2))+_ + (2*b*B*c*d-4*A*c^2*d-3*b^2*B*e+5*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))*sqrt(c)/(b^3*(c*d-b*e)^(3/2))+c*(b*B*d-2*A*c*d+A*b*e)*_ + sqrt(d+e*x)/(b^2*d*(c*d-b*e)*(b+c*x))-A*sqrt(d+e*x)/(b*d*x*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 2 +--R ((- 5A b c + 3B b c)d e + (4A c - 2B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((- 5A b c + 3B b )d e + (4A b c - 2B b c)d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 3 2 2 2 +--R (A b c e + (3A b c - 2B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (A b e + (3A b c - 2B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 3 2 +-----------+ +-+ +--R ((- A b c e + (2A b c - B b c)d)x - A b e + A b c d)\|- b e + c d \|d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-----------+ +-+ +--R ((b c d e - b c d )x + (b d e - b c d )x)\|- b e + c d \|d +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 2 +--R ((5A b c - 3B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((5A b c - 3B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 2 3 2 2 2 +--R (A b c e + (3A b c - 2B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (A b e + (3A b c - 2B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 2 2 3 2 +-+ +-------+ +--R ((- 2A b c e + (4A b c - 2B b c)d)x - 2A b e + 2A b c d)\|d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-+ +--R ((2b c d e - 2b c d )x + (2b d e - 2b c d )x)\|d +--R , +--R +--R 2 2 2 2 3 2 2 2 +--R (A b c e + (3A b c - 2B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (A b e + (3A b c - 2B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 2 3 2 2 2 +--R ((10A b c - 6B b c)d e + (- 8A c + 4B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((10A b c - 6B b )d e + (- 8A b c + 4B b c)d )x +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 2 2 3 2 +-+ +-------+ +--R ((- 2A b c e + (4A b c - 2B b c)d)x - 2A b e + 2A b c d)\|d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-+ +--R ((2b c d e - 2b c d )x + (2b d e - 2b c d )x)\|d +--R , +--R +--R 2 2 3 2 2 2 +--R ((5A b c - 3B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((5A b c - 3B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-----------+ +--R +---+ | c +--R \|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 2 3 2 2 2 +--R (2A b c e + (6A b c - 4B b c)d e + (- 8A c + 4B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (2A b e + (6A b c - 4B b )d e + (- 8A b c + 4B b c)d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 2 2 3 2 +---+ +-------+ +--R ((- 2A b c e + (4A b c - 2B b c)d)x - 2A b e + 2A b c d)\|- d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +---+ +--R ((2b c d e - 2b c d )x + (2b d e - 2b c d )x)\|- d +--R , +--R +--R 2 2 2 2 3 2 2 2 +--R (A b c e + (3A b c - 2B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (A b e + (3A b c - 2B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 2 3 2 2 2 +--R ((5A b c - 3B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((5A b c - 3B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +---------+ +-------+ +--R +---+ | c c\|e x + d +--R \|- d |--------- atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 2 2 3 2 +---+ +-------+ +--R ((- A b c e + (2A b c - B b c)d)x - A b e + A b c d)\|- d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +---+ +--R ((b c d e - b c d )x + (b d e - b c d )x)\|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 802 + +--S 803 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 +-----------+ +--R ((5A b c - 3B b )d e + (- 4A c + 2B b c)d )\|- b e + c d +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 2 2 +-----------+ +--R (A b e + (3A b c - 2B b )d e + (- 4A c + 2B b c)d )\|- b e + c d +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 2 2 +-+ +-+ +--R ((10A b c - 6B b )d e + (- 8A c + 4B b c)d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 2 +-----------+ +--R (- 2A b e + (- 6A b c + 4B b )d e + (8A c - 4B b c)d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R / +--R 4 3 2 +-----------+ +-+ +--R (2b d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +-----------+ +--R (A b e + (3A b c - 2B b )d e + (- 4A c + 2B b c)d )\|- b e + c d +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 2 2 +-+ +-+ +--R ((10A b c - 6B b )d e + (- 8A c + 4B b c)d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 2 +-----------+ +--R (- 2A b e + (- 6A b c + 4B b )d e + (8A c - 4B b c)d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 2 2 +-----------+ | c +--R ((10A b c - 6B b )d e + (- 8A c + 4B b c)d )\|- b e + c d |--------- +--R \|b e - c d +--R * +--R +-------+ +--R +-+ c\|e x + d +--R \|d atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 4 3 2 +-----------+ +-+ +--R (2b d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1457 +r0:=-(2*b*B*d-4*A*c*d-3*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(5/2))-_ + c^(3/2)*(4*A*c^2*d+5*b^2*B*e-b*c*(2*B*d+7*A*e))*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(5/2))-e*(2*A*c^2*d^2-_ + b^2*e*(2*B*d-3*A*e)-b*c*d*(B*d+2*A*e))/(b^2*d^2*(c*d-b*e)^2*_ + sqrt(d+e*x))+c*(b*B*d-2*A*c*d+A*b*e)/(b^2*d*(c*d-b*e)*(b+c*x)*_ + sqrt(d+e*x))-A/(b*d*x*(b+c*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 2 4 3 3 2 +--R ((7A b c - 5B b c )d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((7A b c - 5B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 2 3 2 3 2 2 2 +--R 3A b c e + (- 2A b c - 2B b c)d e + (- 5A b c + 4B b c )d e +--R + +--R 4 3 3 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 2 3 +--R (4A b c - 2B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 3A b c e + (2A b c + 2B b c)d e + (- 2A b c + B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 3A b e + (A b c + 2B b )d e + A b c d e +--R + +--R 3 2 2 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x) +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 3 2 3 2 2 2 +--R 3A b c e + (- 2A b c - 2B b c)d e + (- 5A b c + 4B b c )d e +--R + +--R 4 3 3 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 2 3 +--R (4A b c - 2B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 3 2 2 2 4 3 3 2 +--R ((7A b c - 5B b c )d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((7A b c - 5B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 6A b c e + (4A b c + 4B b c)d e + (- 4A b c + 2B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 6A b e + (2A b c + 4B b )d e + 2A b c d e +--R + +--R 3 2 2 3 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-+ +--R \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2b c d e - 4b c d e + 2b c d )x + (2b d e - 4b c d e + 2b c d )x) +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 3 3 2 2 3 2 3 2 2 2 +--R 3A b c e + (- 2A b c - 2B b c)d e + (- 5A b c + 4B b c )d e +--R + +--R 4 3 3 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 2 3 +--R (4A b c - 2B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 3 2 2 2 4 3 3 2 +--R ((- 14A b c + 10B b c )d e + (8A c - 4B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((- 14A b c + 10B b c)d e + (8A b c - 4B b c )d )x +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 6A b c e + (4A b c + 4B b c)d e + (- 4A b c + 2B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 6A b e + (2A b c + 4B b )d e + 2A b c d e +--R + +--R 3 2 2 3 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-+ +--R \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2b c d e - 4b c d e + 2b c d )x + (2b d e - 4b c d e + 2b c d )x) +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 3 2 2 2 4 3 3 2 +--R ((7A b c - 5B b c )d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((7A b c - 5B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 2 3 2 +--R 6A b c e + (- 4A b c - 4B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 10A b c + 8B b c )d e + (8A c - 4B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 6A b e + (- 4A b c - 4B b )d e + (- 10A b c + 8B b c)d e +--R + +--R 3 2 2 3 +--R (8A b c - 4B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 6A b c e + (4A b c + 4B b c)d e + (- 4A b c + 2B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 6A b e + (2A b c + 4B b )d e + 2A b c d e +--R + +--R 3 2 2 3 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2b c d e - 4b c d e + 2b c d )x + (2b d e - 4b c d e + 2b c d )x) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 3 3 2 2 3 2 3 2 2 2 +--R 3A b c e + (- 2A b c - 2B b c)d e + (- 5A b c + 4B b c )d e +--R + +--R 4 3 3 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 2 3 +--R (4A b c - 2B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 3 2 2 2 4 3 3 2 +--R ((- 7A b c + 5B b c )d e + (4A c - 2B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((- 7A b c + 5B b c)d e + (4A b c - 2B b c )d )x +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 3A b c e + (2A b c + 2B b c)d e + (- 2A b c + B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 3A b e + (A b c + 2B b )d e + A b c d e +--R + +--R 3 2 2 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 809 + +--S 810 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 3 2 2 2 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 3 +--R (4A c - 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 2 2 2 3 2 3 +-----------+ +--R ((7A b c - 5B b c)d e + (- 4A c + 2B b c )d )\|- b e + c d +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 3 2 3 +-+ +-+ +--R ((- 14A b c + 10B b c)d e + (8A c - 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A b e + (4A b c + 4B b )d e + (10A b c - 8B b c)d e +--R + +--R 3 2 3 +--R (- 8A c + 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 2 2 4 3 3 2 4 +-----------+ +-+ +--R (2b d e - 4b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 3 2 2 2 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 3 +--R (4A c - 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 2 2 2 3 2 3 +-+ +-+ +--R ((- 14A b c + 10B b c)d e + (8A c - 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A b e + (4A b c + 4B b )d e + (10A b c - 8B b c)d e +--R + +--R 3 2 3 +--R (- 8A c + 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 3 2 3 +-----------+ +--R ((- 14A b c + 10B b c)d e + (8A c - 4B b c )d )\|- b e + c d +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 5 2 2 4 3 3 2 4 +-----------+ +-+ +--R (2b d e - 4b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1457 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1457 +r0:=-1/3*e*(6*A*c^2*d^2-b^2*e*(2*B*d-5*A*e)-3*b*c*d*(B*d+2*A*e))/_ + (b^2*d^2*(c*d-b*e)^2*(d+e*x)^(3/2))+c*(b*B*d-2*A*c*d+A*b*e)/_ + (b^2*d*(c*d-b*e)*(b+c*x)*(d+e*x)^(3/2))-A/(b*d*x*(b+c*x)*_ + (d+e*x)^(3/2))-(2*b*B*d-4*A*c*d-5*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^3*d^(7/2))+c^(5/2)*(2*b*B*c*d-4*A*c^2*d-7*b^2*B*e+9*A*b*c*e)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(7/2))-_ + e*(2*A*c^3*d^3-b^2*c*d*e*(6*B*d-11*A*e)+b^3*e^2*(2*B*d-5*A*e)-_ + b*c^2*d^2*(B*d+3*A*e))/(b^2*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 2 3 3 2 5 4 4 3 +--R ((- 27A b c + 21B b c )d e + (12A c - 6B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 27A b c + 21B b c )d e + (- 15A b c + 15B b c )d e +--R + +--R 5 4 5 +--R (12A c - 6B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((- 27A b c + 21B b c )d e + (12A b c - 6B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 5 3 2 4 4 2 3 3 2 2 3 +--R 15A b c e + (- 33A b c - 6B b c)d e + (9A b c + 18B b c )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (21A b c - 18B b c )d e + (- 12A c + 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 15A b e + (- 18A b c - 6B b )d e + (- 24A b c + 12B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R 30A b c d e + (9A b c - 12B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 15A b d e + (- 33A b c - 6B b )d e + (9A b c + 18B b c)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (21A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 5 3 2 4 4 +--R - 15A b c e + (33A b c + 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 9A b c - 18B b c )d e + (6A b c - 3B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 15A b e + (13A b c + 6B b )d e + (35A b c - 10B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 15A b c - 20B b c )d e + (12A b c - 6B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R - 20A b d e + (41A b c + 8B b )d e + (- 9A b c - 20B b c)d e +--R + +--R 2 3 4 4 2 3 5 +--R - 3A b c d e + (6A b c - 3B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 3A b d e + 9A b c d e - 9A b c d e + 3A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 3 3 2 5 4 4 3 +--R ((27A b c - 21B b c )d e + (- 12A c + 6B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (27A b c - 21B b c )d e + (15A b c - 15B b c )d e +--R + +--R 5 4 5 +--R (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((27A b c - 21B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 4 5 3 2 4 4 +--R 15A b c e + (- 33A b c - 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (9A b c + 18B b c )d e + (21A b c - 18B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 15A b e + (- 18A b c - 6B b )d e + (- 24A b c + 12B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R 30A b c d e + (9A b c - 12B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 15A b d e + (- 33A b c - 6B b )d e + (9A b c + 18B b c)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (21A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 4 5 3 2 4 4 +--R - 30A b c e + (66A b c + 12B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 18A b c - 36B b c )d e + (12A b c - 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 30A b e + (26A b c + 12B b )d e + (70A b c - 20B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 30A b c - 40B b c )d e + (24A b c - 12B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 +--R - 40A b d e + (82A b c + 16B b )d e +--R + +--R 3 2 4 3 2 2 3 4 4 2 3 5 +--R (- 18A b c - 40B b c)d e - 6A b c d e + (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6A b d e + 18A b c d e - 18A b c d e + 6A b c d +--R * +--R +-+ +--R \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 4 5 3 2 4 4 +--R 15A b c e + (- 33A b c - 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (9A b c + 18B b c )d e + (21A b c - 18B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 15A b e + (- 18A b c - 6B b )d e + (- 24A b c + 12B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R 30A b c d e + (9A b c - 12B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 15A b d e + (- 33A b c - 6B b )d e + (9A b c + 18B b c)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (21A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 4 2 3 3 2 5 4 4 3 +--R ((54A b c - 42B b c )d e + (- 24A c + 12B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (54A b c - 42B b c )d e + (30A b c - 30B b c )d e +--R + +--R 5 4 5 +--R (- 24A c + 12B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((54A b c - 42B b c )d e + (- 24A b c + 12B b c )d )x +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 5 3 2 4 4 +--R - 30A b c e + (66A b c + 12B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 18A b c - 36B b c )d e + (12A b c - 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 30A b e + (26A b c + 12B b )d e + (70A b c - 20B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 30A b c - 40B b c )d e + (24A b c - 12B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 +--R - 40A b d e + (82A b c + 16B b )d e +--R + +--R 3 2 4 3 2 2 3 4 4 2 3 5 +--R (- 18A b c - 40B b c)d e - 6A b c d e + (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6A b d e + 18A b c d e - 18A b c d e + 6A b c d +--R * +--R +-+ +--R \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 4 2 3 3 2 5 4 4 3 +--R ((27A b c - 21B b c )d e + (- 12A c + 6B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (27A b c - 21B b c )d e + (15A b c - 15B b c )d e +--R + +--R 5 4 5 +--R (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((27A b c - 21B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 4 5 3 2 4 4 +--R 30A b c e + (- 66A b c - 12B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (18A b c + 36B b c )d e + (42A b c - 36B b c )d e +--R + +--R 5 4 4 +--R (- 24A c + 12B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 +--R 30A b e + (- 36A b c - 12B b )d e +--R + +--R 3 2 4 2 3 2 3 3 2 +--R (- 48A b c + 24B b c)d e + 60A b c d e +--R + +--R 4 2 3 4 5 4 5 +--R (18A b c - 24B b c )d e + (- 24A c + 12B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 +--R 30A b d e + (- 66A b c - 12B b )d e +--R + +--R 3 2 4 3 2 2 3 3 2 4 +--R (18A b c + 36B b c)d e + (42A b c - 36B b c )d e +--R + +--R 4 2 3 5 +--R (- 24A b c + 12B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 4 5 3 2 4 4 +--R - 30A b c e + (66A b c + 12B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 18A b c - 36B b c )d e + (12A b c - 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 30A b e + (26A b c + 12B b )d e + (70A b c - 20B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 30A b c - 40B b c )d e + (24A b c - 12B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 +--R - 40A b d e + (82A b c + 16B b )d e +--R + +--R 3 2 4 3 2 2 3 4 4 2 3 5 +--R (- 18A b c - 40B b c)d e - 6A b c d e + (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6A b d e + 18A b c d e - 18A b c d e + 6A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 4 5 3 2 4 4 +--R 15A b c e + (- 33A b c - 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (9A b c + 18B b c )d e + (21A b c - 18B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 15A b e + (- 18A b c - 6B b )d e + (- 24A b c + 12B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R 30A b c d e + (9A b c - 12B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 15A b d e + (- 33A b c - 6B b )d e + (9A b c + 18B b c)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (21A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 4 2 3 3 2 5 4 4 3 +--R ((27A b c - 21B b c )d e + (- 12A c + 6B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (27A b c - 21B b c )d e + (15A b c - 15B b c )d e +--R + +--R 5 4 5 +--R (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((27A b c - 21B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 5 3 2 4 4 +--R - 15A b c e + (33A b c + 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 9A b c - 18B b c )d e + (6A b c - 3B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 15A b e + (13A b c + 6B b )d e + (35A b c - 10B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 15A b c - 20B b c )d e + (12A b c - 6B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 +--R - 20A b d e + (41A b c + 8B b )d e +--R + +--R 3 2 4 3 2 2 3 4 4 2 3 5 +--R (- 9A b c - 20B b c)d e - 3A b c d e + (6A b c - 3B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 3A b d e + 9A b c d e - 9A b c d e + 3A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 816 + +--S 817 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 4 3 4 +-----------+ +--R ((9A b c - 7B b c )d e + (- 4A c + 2B b c )d )\|- b e + c d +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R 5A b e + (- 11A b c - 2B b )d e + (3A b c + 6B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (7A b c - 6B b c )d e + (- 4A c + 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 3 2 2 3 4 3 4 +-+ +-+ +--R ((18A b c - 14B b c )d e + (- 8A c + 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 10A b e + (22A b c + 4B b )d e + (- 6A b c - 12B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 14A b c + 12B b c )d e + (8A c - 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ +--R (2b d e - 6b c d e + 6b c d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 4 3 2 2 3 2 2 +--R 5A b e + (- 11A b c - 2B b )d e + (3A b c + 6B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (7A b c - 6B b c )d e + (- 4A c + 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 3 2 2 3 4 3 4 +-+ +-+ +--R ((18A b c - 14B b c )d e + (- 8A c + 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 10A b e + (22A b c + 4B b )d e + (- 6A b c - 12B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 14A b c + 12B b c )d e + (8A c - 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 3 4 3 4 +-----------+ +--R ((18A b c - 14B b c )d e + (- 8A c + 4B b c )d )\|- b e + c d +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ +--R (2b d e - 6b c d e + 6b c d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 1457 +t0:=(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1457 +r0:=-1/5*e*(10*A*c^2*d^2-b^2*e*(2*B*d-7*A*e)-5*b*c*d*(B*d+2*A*e))/_ + (b^2*d^2*(c*d-b*e)^2*(d+e*x)^(5/2))+c*(b*B*d-2*A*c*d+A*b*e)/_ + (b^2*d*(c*d-b*e)*(b+c*x)*(d+e*x)^(5/2))-A/(b*d*x*(b+c*x)*_ + (d+e*x)^(5/2))-1/3*e*(6*A*c^3*d^3-b^2*c*d*e*(6*B*d-17*A*e)+_ + b^3*e^2*(2*B*d-7*A*e)-3*b*c^2*d^2*(B*d+3*A*e))/(b^2*d^3*_ + (c*d-b*e)^3*(d+e*x)^(3/2))-(2*b*B*d-4*A*c*d-7*A*b*e)*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(9/2))-c^(7/2)*(4*A*c^2*d+9*b^2*B*e-_ + b*c*(2*B*d+11*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^3*(c*d-b*e)^(9/2))-e*(2*A*c^4*d^4-2*b^2*c^2*d^2*e*(6*B*d-13*A*e)-_ + b^4*e^3*(2*B*d-7*A*e)+8*b^3*c*d*e^2*(B*d-3*A*e)-b*c^3*d^3*_ + (B*d+4*A*e))/(b^2*d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 2 4 4 3 6 5 5 2 4 +--R ((165A b c - 135B b c )d e + (- 60A c + 30B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (165A b c - 135B b c )d e + (270A b c - 240B b c )d e +--R + +--R 6 5 6 +--R (- 120A c + 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (330A b c - 270B b c )d e + (45A b c - 75B b c )d e +--R + +--R 6 5 7 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((165A b c - 135B b c )d e + (- 60A b c + 30B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 7 4 2 5 6 +--R 105A b c e + (- 360A b c - 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (390A b c + 120B b c )d e + (- 60A b c - 180B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 135A b c + 120B b c )d e + (60A c - 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 105A b e + (- 150A b c - 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 330A b c + 60B b c)d e + (720A b c + 60B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 255A b c - 240B b c )d e + (- 210A b c + 210B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 210A b d e + (- 615A b c - 60B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (420A b c + 210B b c)d e + (270A b c - 240B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 60B b c )d e + (- 15A b c + 60B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 105A b d e + (- 360A b c - 30B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (390A b c + 120B b c)d e + (- 60A b c - 180B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 135A b c + 120B b c )d e + (60A b c - 30B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 7 4 2 5 6 +--R - 105A b c e + (360A b c + 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 390A b c - 120B b c )d e + (60A b c + 180B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 30A b c + 15B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 105A b e + (115A b c + 30B b )d e + (450A b c - 50B b c)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (- 850A b c - 100B b c )d e + (165A b c + 390B b c )d e +--R + +--R 5 2 4 5 2 +--R (- 90A b c + 45B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 245A b d e + (679A b c + 70B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 358A b c - 234B b c)d e + (- 436A b c + 218B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (135A b c + 216B b c )d e + (- 90A b c + 45B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 161A b d e + (537A b c + 46B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 556A b c - 172B b c)d e + (90A b c + 216B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 15A b c d e + (- 30A b c + 15B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 15A b d e + 60A b c d e - 90A b c d e + 60A b c d e - 15A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (15b c d e - 60b c d e + 90b c d e - 60b c d e + 15b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 15b d e - 30b c d e - 30b c d e + 120b c d e - 105b c d e +--R + +--R 3 5 9 +--R 30b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 30b d e - 105b c d e + 120b c d e - 30b c d e - 30b c d e +--R + +--R 3 5 10 +--R 15b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (15b d e - 60b c d e + 90b c d e - 60b c d e + 15b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 7 4 2 5 6 +--R 105A b c e + (- 360A b c - 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (390A b c + 120B b c )d e + (- 60A b c - 180B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 135A b c + 120B b c )d e + (60A c - 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 105A b e + (- 150A b c - 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 330A b c + 60B b c)d e + (720A b c + 60B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 255A b c - 240B b c )d e + (- 210A b c + 210B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 210A b d e + (- 615A b c - 60B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (420A b c + 210B b c)d e + (270A b c - 240B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 60B b c )d e + (- 15A b c + 60B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 105A b d e + (- 360A b c - 30B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (390A b c + 120B b c)d e + (- 60A b c - 180B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 135A b c + 120B b c )d e + (60A b c - 30B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 5 2 4 4 3 6 5 5 2 4 +--R ((165A b c - 135B b c )d e + (- 60A c + 30B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (165A b c - 135B b c )d e + (270A b c - 240B b c )d e +--R + +--R 6 5 6 +--R (- 120A c + 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (330A b c - 270B b c )d e + (45A b c - 75B b c )d e +--R + +--R 6 5 7 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((165A b c - 135B b c )d e + (- 60A b c + 30B b c )d )x +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 5 7 4 2 5 6 +--R - 210A b c e + (720A b c + 60B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 780A b c - 240B b c )d e + (120A b c + 360B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 60A b c + 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R - 210A b e + (230A b c + 60B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (900A b c - 100B b c)d e + (- 1700A b c - 200B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (330A b c + 780B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 490A b d e + (1358A b c + 140B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 716A b c - 468B b c)d e + (- 872A b c + 436B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (270A b c + 432B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 322A b d e + (1074A b c + 92B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 1112A b c - 344B b c)d e + (180A b c + 432B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 30A b c d e + (- 60A b c + 30B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 +--R - 30A b d e + 120A b c d e - 180A b c d e + 120A b c d e +--R + +--R 2 4 7 +--R - 30A b c d +--R * +--R +-+ +--R \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (30b c d e - 120b c d e + 180b c d e - 120b c d e + 30b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 30b d e - 60b c d e - 60b c d e + 240b c d e - 210b c d e +--R + +--R 3 5 9 +--R 60b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 60b d e - 210b c d e + 240b c d e - 60b c d e - 60b c d e +--R + +--R 3 5 10 +--R 30b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (30b d e - 120b c d e + 180b c d e - 120b c d e + 30b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 5 7 4 2 5 6 +--R 105A b c e + (- 360A b c - 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (390A b c + 120B b c )d e + (- 60A b c - 180B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 135A b c + 120B b c )d e + (60A c - 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 105A b e + (- 150A b c - 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 330A b c + 60B b c)d e + (720A b c + 60B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 255A b c - 240B b c )d e + (- 210A b c + 210B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 210A b d e + (- 615A b c - 60B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (420A b c + 210B b c)d e + (270A b c - 240B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 60B b c )d e + (- 15A b c + 60B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 105A b d e + (- 360A b c - 30B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (390A b c + 120B b c)d e + (- 60A b c - 180B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 135A b c + 120B b c )d e + (60A b c - 30B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 5 2 4 4 3 6 5 5 2 4 +--R ((- 330A b c + 270B b c )d e + (120A c - 60B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 330A b c + 270B b c )d e + (- 540A b c + 480B b c )d e +--R + +--R 6 5 6 +--R (240A c - 120B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 660A b c + 540B b c )d e + (- 90A b c + 150B b c )d e +--R + +--R 6 5 7 +--R (120A c - 60B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((- 330A b c + 270B b c )d e + (120A b c - 60B b c )d )x +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 5 7 4 2 5 6 +--R - 210A b c e + (720A b c + 60B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 780A b c - 240B b c )d e + (120A b c + 360B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 60A b c + 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R - 210A b e + (230A b c + 60B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (900A b c - 100B b c)d e + (- 1700A b c - 200B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (330A b c + 780B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 490A b d e + (1358A b c + 140B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 716A b c - 468B b c)d e + (- 872A b c + 436B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (270A b c + 432B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 322A b d e + (1074A b c + 92B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 1112A b c - 344B b c)d e + (180A b c + 432B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 30A b c d e + (- 60A b c + 30B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 +--R - 30A b d e + 120A b c d e - 180A b c d e + 120A b c d e +--R + +--R 2 4 7 +--R - 30A b c d +--R * +--R +-+ +--R \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (30b c d e - 120b c d e + 180b c d e - 120b c d e + 30b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 30b d e - 60b c d e - 60b c d e + 240b c d e - 210b c d e +--R + +--R 3 5 9 +--R 60b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 60b d e - 210b c d e + 240b c d e - 60b c d e - 60b c d e +--R + +--R 3 5 10 +--R 30b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (30b d e - 120b c d e + 180b c d e - 120b c d e + 30b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 5 2 4 4 3 6 5 5 2 4 +--R ((165A b c - 135B b c )d e + (- 60A c + 30B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (165A b c - 135B b c )d e + (270A b c - 240B b c )d e +--R + +--R 6 5 6 +--R (- 120A c + 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (330A b c - 270B b c )d e + (45A b c - 75B b c )d e +--R + +--R 6 5 7 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((165A b c - 135B b c )d e + (- 60A b c + 30B b c )d )x +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 5 7 4 2 5 6 +--R 210A b c e + (- 720A b c - 60B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (780A b c + 240B b c )d e + (- 120A b c - 360B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 270A b c + 240B b c )d e + (120A c - 60B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 210A b e + (- 300A b c - 60B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 660A b c + 120B b c)d e + (1440A b c + 120B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 510A b c - 480B b c )d e + (- 420A b c + 420B b c )d e +--R + +--R 6 5 6 +--R (240A c - 120B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 420A b d e + (- 1230A b c - 120B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (840A b c + 420B b c)d e + (540A b c - 480B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 660A b c + 120B b c )d e + (- 30A b c + 120B b c )d e +--R + +--R 6 5 7 +--R (120A c - 60B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 210A b d e + (- 720A b c - 60B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (780A b c + 240B b c)d e + (- 120A b c - 360B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 270A b c + 240B b c )d e + (120A b c - 60B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 5 7 4 2 5 6 +--R - 210A b c e + (720A b c + 60B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 780A b c - 240B b c )d e + (120A b c + 360B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 60A b c + 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R - 210A b e + (230A b c + 60B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (900A b c - 100B b c)d e + (- 1700A b c - 200B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (330A b c + 780B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 490A b d e + (1358A b c + 140B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 716A b c - 468B b c)d e + (- 872A b c + 436B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (270A b c + 432B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 322A b d e + (1074A b c + 92B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 1112A b c - 344B b c)d e + (180A b c + 432B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 30A b c d e + (- 60A b c + 30B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 +--R - 30A b d e + 120A b c d e - 180A b c d e + 120A b c d e +--R + +--R 2 4 7 +--R - 30A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (30b c d e - 120b c d e + 180b c d e - 120b c d e + 30b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 30b d e - 60b c d e - 60b c d e + 240b c d e - 210b c d e +--R + +--R 3 5 9 +--R 60b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 60b d e - 210b c d e + 240b c d e - 60b c d e - 60b c d e +--R + +--R 3 5 10 +--R 30b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (30b d e - 120b c d e + 180b c d e - 120b c d e + 30b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 5 7 4 2 5 6 +--R 105A b c e + (- 360A b c - 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (390A b c + 120B b c )d e + (- 60A b c - 180B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 135A b c + 120B b c )d e + (60A c - 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 105A b e + (- 150A b c - 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 330A b c + 60B b c)d e + (720A b c + 60B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 255A b c - 240B b c )d e + (- 210A b c + 210B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 210A b d e + (- 615A b c - 60B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (420A b c + 210B b c)d e + (270A b c - 240B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 60B b c )d e + (- 15A b c + 60B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 105A b d e + (- 360A b c - 30B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (390A b c + 120B b c)d e + (- 60A b c - 180B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 135A b c + 120B b c )d e + (60A b c - 30B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 5 2 4 4 3 6 5 5 2 4 +--R ((- 165A b c + 135B b c )d e + (60A c - 30B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 165A b c + 135B b c )d e + (- 270A b c + 240B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 270B b c )d e + (- 45A b c + 75B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((- 165A b c + 135B b c )d e + (60A b c - 30B b c )d )x +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 5 7 4 2 5 6 +--R - 105A b c e + (360A b c + 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 390A b c - 120B b c )d e + (60A b c + 180B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 30A b c + 15B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R - 105A b e + (115A b c + 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (450A b c - 50B b c)d e + (- 850A b c - 100B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (165A b c + 390B b c )d e + (- 90A b c + 45B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 245A b d e + (679A b c + 70B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 358A b c - 234B b c)d e + (- 436A b c + 218B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (135A b c + 216B b c )d e + (- 90A b c + 45B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 161A b d e + (537A b c + 46B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 556A b c - 172B b c)d e + (90A b c + 216B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 15A b c d e + (- 30A b c + 15B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 15A b d e + 60A b c d e - 90A b c d e + 60A b c d e - 15A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (15b c d e - 60b c d e + 90b c d e - 60b c d e + 15b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 15b d e - 30b c d e - 30b c d e + 120b c d e - 105b c d e +--R + +--R 3 5 9 +--R 30b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 30b d e - 105b c d e + 120b c d e - 30b c d e - 30b c d e +--R + +--R 3 5 10 +--R 15b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (15b d e - 60b c d e + 90b c d e - 60b c d e + 15b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 823 + +--S 824 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 5 4 5 4 3 2 4 2 3 +--R 7A b e + (- 24A b c - 2B b )d e + (26A b c + 8B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 4A b c - 12B b c )d e + (- 9A b c + 8B b c )d e +--R + +--R 5 4 5 +--R (4A c - 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 4 2 3 4 5 4 5 +-----------+ +--R ((11A b c - 9B b c )d e + (- 4A c + 2B b c )d )\|- b e + c d +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 2 3 4 5 4 5 +-+ +-+ +--R ((- 22A b c + 18B b c )d e + (8A c - 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 14A b e + (48A b c + 4B b )d e + (- 52A b c - 16B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (8A b c + 24B b c )d e + (18A b c - 16B b c )d e +--R + +--R 5 4 5 +--R (- 8A c + 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 +-----------+ +-+ +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 5 4 5 4 3 2 4 2 3 +--R 7A b e + (- 24A b c - 2B b )d e + (26A b c + 8B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 4A b c - 12B b c )d e + (- 9A b c + 8B b c )d e +--R + +--R 5 4 5 +--R (4A c - 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 4 2 3 4 5 4 5 +-+ +-+ +--R ((- 22A b c + 18B b c )d e + (8A c - 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 14A b e + (48A b c + 4B b )d e + (- 52A b c - 16B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (8A b c + 24B b c )d e + (18A b c - 16B b c )d e +--R + +--R 5 4 5 +--R (- 8A c + 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 3 4 5 4 5 +-----------+ +--R ((- 22A b c + 18B b c )d e + (8A c - 4B b c )d )\|- b e + c d +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 +-----------+ +-+ +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 827 + +)clear all + +--S 828 of 1457 +t0:=(A+B*x)*(d+e*x)^(9/2)/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1457 +r0:=1/4*(c*d-b*e)*(24*A*c^3*d^2+5*b^3*B*e^2+b^2*c*e*(3*B*d-A*e)-_ + 12*b*c^2*d*(B*d+2*A*e))*(d+e*x)^(3/2)/(b^4*c^2*(b+c*x))-_ + 1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+13*A*b*c*e)*_ + (d+e*x)^(5/2)/(b^3*c*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+9*A*b*e)*_ + (d+e*x)^(7/2)/(b^2*x*(b+c*x)^2)-1/2*A*(d+e*x)^(9/2)/(b*x^2*_ + (b+c*x)^2)-3/4*d^(5/2)*(16*A*c^2*d^2+3*b^2*e*(4*B*d+7*A*e)-_ + 4*b*c*d*(2*B*d+9*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/b^5+_ + 3/4*(c*d-b*e)^(5/2)*(16*A*c^3*d^2-5*b^3*B*e^2-4*b*c^2*d*_ + (2*B*d-A*e)-b^2*c*e*(8*B*d-A*e))*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b^5*c^(7/2))-3/4*e*(8*A*c^4*d^3-5*b^4*B*e^3+_ + b^3*c*e^2*(2*B*d+A*e)+b^2*c^2*d*e*(3*B*d+2*A*e)-4*b*c^3*d^2*_ + (B*d+3*A*e))*sqrt(d+e*x)/(b^4*c^3) +--R +--R +--R (2) +--R 4 3 5 2 4 3 4 4 3 3 +--R (3A b c - 15B b c )e + (6A b c + 6B b c )d e +--R + +--R 2 5 3 4 2 2 6 2 5 3 +--R (27A b c + 9B b c )d e + (- 84A b c + 24B b c )d e +--R + +--R 7 6 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (6A b c - 30B b c)e + (12A b c + 12B b c )d e +--R + +--R 3 4 4 3 2 2 2 5 3 4 3 +--R (54A b c + 18B b c )d e + (- 168A b c + 48B b c )d e +--R + +--R 6 2 5 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (3A b c - 15B b )e + (6A b c + 6B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (27A b c + 9B b c )d e + (- 84A b c + 24B b c )d e +--R + +--R 2 5 3 4 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 5 2 2 6 2 5 3 +--R - 63A b c d e + (108A b c - 36B b c )d e +--R + +--R 7 6 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 2 5 3 4 3 +--R - 126A b c d e + (216A b c - 72B b c )d e +--R + +--R 6 2 5 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 2 3 4 4 3 3 +--R - 63A b c d e + (108A b c - 36B b c )d e +--R + +--R 2 5 3 4 4 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 2 4 4 +--R 8B b c e x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (- 5A b c + 25B b c)e + (3A b c - 19B b c )d e +--R + +--R 3 4 4 3 2 2 2 5 3 4 3 +--R (21A b c + 3B b c )d e + (- 48A b c + 15B b c )d e +--R + +--R 6 2 5 4 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- 3A b c + 15B b )e + (- 5A b c - 11B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (33A b c - 9B b c )d e + (- 73A b c + 23B b c )d e +--R + +--R 2 5 3 4 4 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 3 4 4 3 4 +--R (- 17A b c d e + (8A b c - 4B b c )d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 5 4 6 4 3 7 3 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1457 +--a0:=integrate(t0,x) +--E 830 + +--S 831 of 1457 +--m0:=a0-r0 +--E 831 + +--S 832 of 1457 +--d0:=D(m0,x) +--E 832 + +)clear all + +--S 833 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1457 +r0:=-1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+11*A*b*c*e)*_ + (d+e*x)^(3/2)/(b^3*c*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+7*A*b*e)*_ + (d+e*x)^(5/2)/(b^2*x*(b+c*x)^2)-1/2*A*(d+e*x)^(7/2)/(b*x^2*_ + (b+c*x)^2)-1/4*d^(3/2)*(48*A*c^2*d^2+7*b^2*e*(4*B*d+5*A*e)-_ + 12*b*c*d*(2*B*d+7*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/b^5+1/4*_ + (c*d-b*e)^(3/2)*(48*A*c^3*d^2-3*b^3*B*e^2-12*b*c^2*d*(2*B*d+A*e)-_ + b^2*c*e*(8*B*d+A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^5*c^(5/2))+1/4*(c*d-b*e)*(24*A*c^3*d^2+3*b^3*B*e^2+b^2*c*e*_ + (5*B*d+A*e)-12*b*c^2*d*(B*d+2*A*e))*sqrt(d+e*x)/(b^4*c^2*(b+c*x)) +--R +--R +--R (2) +--R 3 3 4 2 3 2 4 3 3 2 +--R (A b c + 3B b c )e + (11A b c + 5B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c + 6B b c)e + (22A b c + 10B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A b c + 16B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 4 2 5 2 4 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 6 5 3 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 70A b c d e + (168A b c - 56B b c )d e +--R + +--R 5 2 4 3 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 2 4 3 3 3 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (A b c - 5B b c)e + (10A b c + 2B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 36A b c + 11B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - 3B b )e + (16A b c - 4B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 55A b c + 17B b c )d e + (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 13A b c d e + (8A b c - 4B b c )d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 4 2 3 2 4 3 3 2 +--R (A b c + 3B b c )e + (11A b c + 5B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c + 6B b c)e + (22A b c + 10B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A b c + 16B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 4 2 5 2 4 2 +--R 35A b c d e + (- 84A b c + 28B b c )d e +--R + +--R 6 5 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R 70A b c d e + (- 168A b c + 56B b c )d e +--R + +--R 5 2 4 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R 35A b c d e + (- 84A b c + 28B b c )d e +--R + +--R 2 4 3 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c - 10B b c)e + (20A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 22B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 2A b c - 6B b )e + (32A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 34B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 26A b c d e + (16A b c - 8B b c )d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 4 2 5 2 4 2 +--R 35A b c d e + (- 84A b c + 28B b c )d e +--R + +--R 6 5 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R 70A b c d e + (- 168A b c + 56B b c )d e +--R + +--R 5 2 4 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R 35A b c d e + (- 84A b c + 28B b c )d e +--R + +--R 2 4 3 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (2A b c + 6B b c )e + (22A b c + 10B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 120A b c + 32B b c )d e + (96A c - 48B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (4A b c + 12B b c)e + (44A b c + 20B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 240A b c + 64B b c )d e + (192A b c - 96B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (2A b c + 6B b )e + (22A b c + 10B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c - 10B b c)e + (20A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 22B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 2A b c - 6B b )e + (32A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 34B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 26A b c d e + (16A b c - 8B b c )d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 3 3 4 2 3 2 4 3 3 2 +--R (A b c + 3B b c )e + (11A b c + 5B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c + 6B b c)e + (22A b c + 10B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A b c + 16B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 4 2 5 2 4 2 +--R - 70A b c d e + (168A b c - 56B b c )d e +--R + +--R 6 5 3 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 140A b c d e + (336A b c - 112B b c )d e +--R + +--R 5 2 4 3 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R - 70A b c d e + (168A b c - 56B b c )d e +--R + +--R 2 4 3 3 3 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c - 10B b c)e + (20A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 22B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 2A b c - 6B b )e + (32A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 34B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 26A b c d e + (16A b c - 8B b c )d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 4 2 5 2 4 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 6 5 3 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 70A b c d e + (168A b c - 56B b c )d e +--R + +--R 5 2 4 3 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 2 4 3 3 3 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (A b c + 3B b c )e + (11A b c + 5B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c + 6B b c)e + (22A b c + 10B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A b c + 16B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (A b c - 5B b c)e + (10A b c + 2B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 36A b c + 11B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - 3B b )e + (16A b c - 4B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 55A b c + 17B b c )d e + (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 13A b c d e + (8A b c - 4B b c )d )x - 2A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 4b c x + 8b c x + 4b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 835 + +--S 836 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 2 2 3 2 2 2 4 3 3 +-+ +--R (35A b c d e + (- 84A b c + 28B b c )d e + (48A c - 24B b c )d )\|c +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 2A b c - 6B b )e + (- 22A b c - 10B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (120A b c - 32B b c )d e + (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 2 2 2 4 3 3 +--R (70A b c d e + (- 168A b c + 56B b c )d e + (96A c - 48B b c )d ) +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 2 +-+ +--R 8b c \|c +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 3 2 2 2 4 3 3 +-+ +--R (35A b c d e + (- 84A b c + 28B b c )d e + (48A c - 24B b c )d )\|c +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 2A b c - 6B b )e + (- 22A b c - 10B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (120A b c - 32B b c )d e + (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 2 2 2 4 3 3 +--R (70A b c d e + (- 168A b c + 56B b c )d e + (96A c - 48B b c )d ) +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 4 3 2 2 3 2 +--R (2A b c + 6B b )e + (22A b c + 10B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 120A b c + 32B b c )d e + (96A c - 48B b c )d +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 5 2 +-+ +--R 8b c \|c +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 839 + +)clear all + +--S 840 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1457 +r0:=-1/4*(4*b*B*d-8*A*c*d+5*A*b*e)*(d+e*x)^(3/2)/(b^2*x*(b+c*x)^2)-_ + 1/2*A*(d+e*x)^(5/2)/(b*x^2*(b+c*x)^2)-1/4*(48*A*c^2*d^2+5*b^2*e*_ + (4*B*d+3*A*e)-12*b*c*d*(2*B*d+5*A*e))*atanh(sqrt(d+e*x)/sqrt(d))*_ + sqrt(d)/b^5+1/4*(48*A*c^3*d^2+b^3*B*e^2-12*b*c^2*d*(2*B*d+3*A*e)+_ + b^2*c*e*(8*B*d+3*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*_ + sqrt(c*d-b*e)/(b^5*c^(3/2))-1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-_ + 2*b^2*B*e+9*A*b*c*e)*sqrt(d+e*x)/(b^3*c*(b+c*x)^2)+1/4*_ + (24*A*c^3*d^2+b^3*B*e^2-12*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ + (7*B*d+3*A*e))*sqrt(d+e*x)/(b^4*c*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 +--R (3A b c + B b c )e + (- 36A b c + 8B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 72A b c + 16B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (3A b c + B b )e + (- 36A b c + 8B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (- 15A b c e + (60A b c - 20B b c )d e + (- 48A c + 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 +--R - 30A b c e + (120A b c - 40B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 15A b c e + (60A b c - 20B b c)d e + (- 48A b c + 24B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 4 2 2 3 3 2 +--R (3A b c + B b c)e + (- 24A b c + 7B b c )d e +--R + +--R 4 2 3 2 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (5A b c - B b )e + (- 37A b c + 11B b c)d e +--R + +--R 2 3 3 2 2 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 9A b c d e + (8A b c - 4B b c)d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 4 2 3 +--R (3A b c + B b c )e + (- 36A b c + 8B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 72A b c + 16B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (3A b c + B b )e + (- 36A b c + 8B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (15A b c e + (- 60A b c + 20B b c )d e + (48A c - 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 +--R 30A b c e + (- 120A b c + 40B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (15A b c e + (- 60A b c + 20B b c)d e + (48A b c - 24B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 48A b c + 14B b c )d e +--R + +--R 4 2 3 2 +--R (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (10A b c - 2B b )e + (- 74A b c + 22B b c)d e +--R + +--R 2 3 3 2 2 +--R (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 18A b c d e + (16A b c - 8B b c)d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 3 2 4 2 3 5 4 2 4 +--R (15A b c e + (- 60A b c + 20B b c )d e + (48A c - 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 +--R 30A b c e + (- 120A b c + 40B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (15A b c e + (- 60A b c + 20B b c)d e + (48A b c - 24B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 3 3 2 2 4 2 3 +--R (6A b c + 2B b c )e + (- 72A b c + 16B b c )d e +--R + +--R 5 4 2 +--R (96A c - 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (12A b c + 4B b c)e + (- 144A b c + 32B b c )d e +--R + +--R 4 2 3 2 +--R (192A b c - 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (6A b c + 2B b )e + (- 72A b c + 16B b c)d e +--R + +--R 2 3 3 2 2 +--R (96A b c - 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 48A b c + 14B b c )d e +--R + +--R 4 2 3 2 +--R (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (10A b c - 2B b )e + (- 74A b c + 22B b c)d e +--R + +--R 2 3 3 2 2 +--R (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 18A b c d e + (16A b c - 8B b c)d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 3 3 2 2 4 2 3 +--R (3A b c + B b c )e + (- 36A b c + 8B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 72A b c + 16B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (3A b c + B b )e + (- 36A b c + 8B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 4 2 3 +--R - 30A b c e + (120A b c - 40B b c )d e +--R + +--R 5 4 2 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 3 3 2 +--R - 60A b c e + (240A b c - 80B b c )d e +--R + +--R 4 2 3 2 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 30A b c e + (120A b c - 40B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 48A b c + 14B b c )d e +--R + +--R 4 2 3 2 +--R (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (10A b c - 2B b )e + (- 74A b c + 22B b c)d e +--R + +--R 2 3 3 2 2 +--R (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 18A b c d e + (16A b c - 8B b c)d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 3 2 4 2 3 +--R - 15A b c e + (60A b c - 20B b c )d e +--R + +--R 5 4 2 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 3 3 2 +--R - 30A b c e + (120A b c - 40B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 15A b c e + (60A b c - 20B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 3 3 2 2 4 2 3 +--R (3A b c + B b c )e + (- 36A b c + 8B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 72A b c + 16B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (3A b c + B b )e + (- 36A b c + 8B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 4 2 2 3 3 2 +--R (3A b c + B b c)e + (- 24A b c + 7B b c )d e +--R + +--R 4 2 3 2 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (5A b c - B b )e + (- 37A b c + 11B b c)d e +--R + +--R 2 3 3 2 2 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 9A b c d e + (8A b c - 4B b c)d )x - 2A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 4b c x + 8b c x + 4b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 842 + +--S 843 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 2 2 +--R ((3A b c + B b )e + (- 36A b c + 8B b c)d e + (48A c - 24B b c )d ) +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 2 2 2 3 2 2 +-+ +--R (15A b c e + (- 60A b c + 20B b c)d e + (48A c - 24B b c )d )\|c +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 +--R (- 6A b c - 2B b )e + (72A b c - 16B b c)d e +--R + +--R 3 2 2 +--R (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 3 2 2 +-+ +--R (30A b c e + (- 120A b c + 40B b c)d e + (96A c - 48B b c )d )\|c +--R * +--R +-------+ +--R +-+ \|e x + d +--R \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 +-+ +--R 8b c\|c +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 3 2 2 +-+ +--R (15A b c e + (- 60A b c + 20B b c)d e + (48A c - 24B b c )d )\|c +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 +--R (- 6A b c - 2B b )e + (72A b c - 16B b c)d e +--R + +--R 3 2 2 +--R (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 3 2 2 +-+ +--R (30A b c e + (- 120A b c + 40B b c)d e + (96A c - 48B b c )d )\|c +--R * +--R +-------+ +--R +-+ \|e x + d +--R \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 +--R (6A b c + 2B b )e + (- 72A b c + 16B b c)d e +--R + +--R 3 2 2 +--R (96A c - 48B b c )d +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 5 +-+ +--R 8b c\|c +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 846 + +)clear all + +--S 847 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1457 +r0:=-1/2*A*(d+e*x)^(3/2)/(b*x^2*(b+c*x)^2)-3/4*(16*A*c^2*d^2+b^2*e*_ + (4*B*d+A*e)-4*b*c*d*(2*B*d+3*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^5*sqrt(d))+3/4*(16*A*c^3*d^2-b^3*B*e^2-4*b*c^2*d*(2*B*d+5*A*e)+_ + b^2*c*e*(8*B*d+5*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^5*sqrt(c)*sqrt(c*d-b*e))-1/4*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+_ + 7*A*b*c*e)*sqrt(d+e*x)/(b^3*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+3*A*b*e)*_ + sqrt(d+e*x)/(b^2*x*(b+c*x)^2)+3/4*(8*A*c^2*d+b^2*B*e-4*b*c*(B*d+A*e))*_ + sqrt(d+e*x)/(b^4*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 +--R (15A b c - 3B b c )e + (- 60A b c + 24B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (30A b c - 6B b c)e + (- 120A b c + 48B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (15A b c - 3B b )e + (- 60A b c + 24B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 2 2 4 3 2 4 +--R (- 3A b c e + (36A b c - 12B b c )d e + (- 48A c + 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 2 2 3 +--R (- 6A b c e + (72A b c - 24B b c)d e + (- 96A b c + 48B b c )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- 3A b e + (36A b c - 12B b )d e + (- 48A b c + 24B b c)d )x +--R * +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 3B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 19A b c + 5B b )e + (36A b c - 18B b c)d)x +--R + +--R 4 3 4 4 +--R (- 5A b e + (8A b c - 4B b )d)x - 2A b d +--R * +--R +-----------+ +-+ +-+ +-------+ +--R \|- b e + c d \|c \|d \|e x + d +--R / +--R 5 2 4 6 3 7 2 +-----------+ +-+ +-+ +--R (4b c x + 8b c x + 4b x )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 4 2 3 +--R (- 15A b c + 3B b c )e + (60A b c - 24B b c )d e +--R + +--R 5 4 2 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 30A b c + 6B b c)e + (120A b c - 48B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 15A b c + 3B b )e + (60A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +--R \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2b c e - 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(----------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 3 2 2 4 3 2 4 +--R (3A b c e + (- 36A b c + 12B b c )d e + (48A c - 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 2 2 3 +--R (6A b c e + (- 72A b c + 24B b c)d e + (96A b c - 48B b c )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (3A b e + (- 36A b c + 12B b )d e + (48A b c - 24B b c)d )x +--R * +--R +-------------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R \|- b c e + c d log(-------------------------------) +--R x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 24A b c + 6B b c)e + (48A b c - 24B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 38A b c + 10B b )e + (72A b c - 36B b c)d)x +--R + +--R 4 3 4 4 +--R (- 10A b e + (16A b c - 8B b )d)x - 4A b d +--R * +--R +-------------+ +--R | 2 +-+ +-------+ +--R \|- b c e + c d \|d \|e x + d +--R / +--R +-------------+ +--R 5 2 4 6 3 7 2 | 2 +-+ +--R (8b c x + 16b c x + 8b x )\|- b c e + c d \|d +--R , +--R +--R 2 2 2 3 2 2 4 3 2 4 +--R (3A b c e + (- 36A b c + 12B b c )d e + (48A c - 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 2 2 3 +--R (6A b c e + (- 72A b c + 24B b c)d e + (96A b c - 48B b c )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (3A b e + (- 36A b c + 12B b )d e + (48A b c - 24B b c)d )x +--R * +--R +-----------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R \|b c e - c d log(-------------------------------) +--R x +--R + +--R 2 3 3 2 2 4 2 3 +--R (- 30A b c + 6B b c )e + (120A b c - 48B b c )d e +--R + +--R 5 4 2 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 60A b c + 12B b c)e + (240A b c - 96B b c )d e +--R + +--R 4 2 3 2 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 30A b c + 6B b )e + (120A b c - 48B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-+ \|b c e - c d \|e x + d +--R \|d atan(------------------------) +--R b e - c d +--R + +--R 2 2 3 3 2 2 3 +--R ((- 24A b c + 6B b c)e + (48A b c - 24B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 38A b c + 10B b )e + (72A b c - 36B b c)d)x +--R + +--R 4 3 4 4 +--R (- 10A b e + (16A b c - 8B b )d)x - 4A b d +--R * +--R +-----------+ +--R +-+ | 2 +-------+ +--R \|d \|b c e - c d \|e x + d +--R / +--R +-----------+ +--R 5 2 4 6 3 7 2 +-+ | 2 +--R (8b c x + 16b c x + 8b x )\|d \|b c e - c d +--R , +--R +--R 2 3 3 2 2 4 2 3 +--R (- 15A b c + 3B b c )e + (60A b c - 24B b c )d e +--R + +--R 5 4 2 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 30A b c + 6B b c)e + (120A b c - 48B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 15A b c + 3B b )e + (60A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---+ +--R \|- d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2b c e - 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(----------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 3 2 2 +--R - 6A b c e + (72A b c - 24B b c )d e +--R + +--R 4 3 2 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 3 +--R - 12A b c e + (144A b c - 48B b c)d e +--R + +--R 3 2 2 2 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- 6A b e + (72A b c - 24B b )d e + (- 96A b c + 48B b c)d )x +--R * +--R +-------------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R \|- b c e + c d atan(----------------) +--R d +--R + +--R 2 2 3 3 2 2 3 +--R ((- 24A b c + 6B b c)e + (48A b c - 24B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 38A b c + 10B b )e + (72A b c - 36B b c)d)x +--R + +--R 4 3 4 4 +--R (- 10A b e + (16A b c - 8B b )d)x - 4A b d +--R * +--R +-------------+ +--R | 2 +---+ +-------+ +--R \|- b c e + c d \|- d \|e x + d +--R / +--R +-------------+ +--R 5 2 4 6 3 7 2 | 2 +---+ +--R (8b c x + 16b c x + 8b x )\|- b c e + c d \|- d +--R , +--R +--R 2 3 3 2 2 4 2 3 +--R (- 15A b c + 3B b c )e + (60A b c - 24B b c )d e +--R + +--R 5 4 2 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 30A b c + 6B b c)e + (120A b c - 48B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 15A b c + 3B b )e + (60A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R | 2 +-------+ +--R +---+ \|b c e - c d \|e x + d +--R \|- d atan(------------------------) +--R b e - c d +--R + +--R 2 2 2 3 2 2 +--R - 3A b c e + (36A b c - 12B b c )d e +--R + +--R 4 3 2 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 3 +--R - 6A b c e + (72A b c - 24B b c)d e +--R + +--R 3 2 2 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- 3A b e + (36A b c - 12B b )d e + (- 48A b c + 24B b c)d )x +--R * +--R +-----------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R \|b c e - c d atan(----------------) +--R d +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 3B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 19A b c + 5B b )e + (36A b c - 18B b c)d)x +--R + +--R 4 3 4 4 +--R (- 5A b e + (8A b c - 4B b )d)x - 2A b d +--R * +--R +-----------+ +--R +---+ | 2 +-------+ +--R \|- d \|b c e - c d \|e x + d +--R / +--R +-----------+ +--R 5 2 4 6 3 7 2 +---+ | 2 +--R (4b c x + 8b c x + 4b x )\|- d \|b c e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 849 + +--S 850 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 +--R (- 15A b c + 3B b )e + (60A b c - 24B b c)d e +--R + +--R 3 2 2 +--R (- 48A c + 24B b c )d +--R * +--R +-----------+ +-+ +-+ +--R \|- b e + c d \|c \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2b c e - 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(----------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 2 2 +--R (3A b e + (- 36A b c + 12B b )d e + (48A c - 24B b c)d ) +--R * +--R +-------------+ +-------+ +-+ +--R | 2 +-----------+ +-+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b c e + c d \|- b e + c d \|c log(-------------------------------) +--R x +--R + +--R 2 3 2 2 2 +--R (- 30A b c + 6B b )e + (120A b c - 48B b c)d e +--R + +--R 3 2 2 +--R (- 96A c + 48B b c )d +--R * +--R +-------------+ +-+ +-------+ +--R | 2 +-+ \|c \|e x + d +--R \|- b c e + c d \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 2 +--R (6A b e + (- 72A b c + 24B b )d e + (96A c - 48B b c)d ) +--R * +--R +-------------+ +-------+ +--R | 2 +-----------+ +-+ \|e x + d +--R \|- b c e + c d \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R / +--R +-------------+ +--R 5 | 2 +-----------+ +-+ +-+ +--R 8b \|- b c e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +--R (3A b e + (- 36A b c + 12B b )d e + (48A c - 24B b c)d ) +--R * +--R +-----------+ +-------+ +-+ +--R +-----------+ +-+ | 2 - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d \|c \|b c e - c d log(-------------------------------) +--R x +--R + +--R 2 3 2 2 2 +--R (- 30A b c + 6B b )e + (120A b c - 48B b c)d e +--R + +--R 3 2 2 +--R (- 96A c + 48B b c )d +--R * +--R +-----------+ +-+ +-------+ +--R +-+ | 2 \|c \|e x + d +--R \|d \|b c e - c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 2 +--R (6A b e + (- 72A b c + 24B b )d e + (96A c - 48B b c)d ) +--R * +--R +-----------+ +-------+ +--R +-----------+ +-+ | 2 \|e x + d +--R \|- b e + c d \|c \|b c e - c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 +--R (- 30A b c + 6B b )e + (120A b c - 48B b c)d e +--R + +--R 3 2 2 +--R (- 96A c + 48B b c )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ +-+ \|b c e - c d \|e x + d +--R \|- b e + c d \|c \|d atan(------------------------) +--R b e - c d +--R / +--R +-----------+ +--R 5 +-----------+ +-+ +-+ | 2 +--R 8b \|- b e + c d \|c \|d \|b c e - c d +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 853 + +)clear all + +--S 854 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1457 +r0:=-1/4*(48*A*c^2*d^2+b^2*e*(4*B*d-A*e)-12*b*c*d*(2*B*d+A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(3/2))+1/4*(48*A*c^3*d^2-_ + 15*b^3*B*e^2-12*b*c^2*d*(2*B*d+7*A*e)+5*b^2*c*e*(8*B*d+7*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b^5*_ + (c*d-b*e)^(3/2))-1/4*c*(6*b*B*d-12*A*c*d+A*b*e)*sqrt(d+e*x)/_ + (b^3*d*(b+c*x)^2)-1/2*A*sqrt(d+e*x)/(b*x^2*(b+c*x)^2)-_ + 1/4*(4*b*B*d-8*A*c*d+A*b*e)*sqrt(d+e*x)/(b^2*d*x*(b+c*x)^2)+_ + 1/4*c*(24*A*c^2*d^2+b^2*e*(11*B*d+A*e)-12*b*c*d*(B*d+2*A*e))*_ + sqrt(d+e*x)/(b^4*d*(c*d-b*e)*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 2 +--R (- 35A b c + 15B b c )d e + (84A b c - 40B b c )d e +--R + +--R 5 4 3 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (- 70A b c + 30B b c)d e + (168A b c - 80B b c )d e +--R + +--R 4 2 3 3 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (- 35A b c + 15B b )d e + (84A b c - 40B b c)d e +--R + +--R 2 3 3 2 3 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 2 3 2 3 3 2 2 4 2 3 2 +--R A b c e + (11A b c - 4B b c )d e + (- 60A b c + 28B b c )d e +--R + +--R 5 4 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 2 3 3 2 2 +--R 2A b c e + (22A b c - 8B b c)d e + (- 120A b c + 56B b c )d e +--R + +--R 4 2 3 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- A b c e + (24A b c - 11B b c )d e + (- 24A b c + 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 2A b c e + (37A b c - 17B b c)d e + (- 36A b c + 18B b c )d )x +--R + +--R 5 2 4 5 3 2 4 2 5 +--R (- A b e + (9A b c - 4B b )d e + (- 8A b c + 4B b c)d )x - 2A b d e +--R + +--R 4 2 +--R 2A b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 8 7 2 2 +--R ((4b c d e - 4b c d )x + (8b c d e - 8b c d )x + (4b d e - 4b c d )x ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 4 2 3 2 +--R (35A b c - 15B b c )d e + (- 84A b c + 40B b c )d e +--R + +--R 5 4 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (70A b c - 30B b c)d e + (- 168A b c + 80B b c )d e +--R + +--R 4 2 3 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (35A b c - 15B b )d e + (- 84A b c + 40B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 2 3 2 3 3 2 2 +--R A b c e + (11A b c - 4B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 60A b c + 28B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 +--R 2A b c e + (22A b c - 8B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 120A b c + 56B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 3 2 2 2 3 3 2 +--R - 2A b c e + (48A b c - 22B b c )d e +--R + +--R 4 2 3 2 +--R (- 48A b c + 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 4A b c e + (74A b c - 34B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 72A b c + 36B b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R (- 2A b e + (18A b c - 8B b )d e + (- 16A b c + 8B b c)d )x +--R + +--R 5 4 2 +--R - 4A b d e + 4A b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (8b c d e - 8b c d )x + (16b c d e - 16b c d )x +--R + +--R 8 7 2 2 +--R (8b d e - 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 3 2 3 2 3 3 2 2 +--R A b c e + (11A b c - 4B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 60A b c + 28B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 +--R 2A b c e + (22A b c - 8B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 120A b c + 56B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 3 3 2 2 4 2 3 2 +--R (70A b c - 30B b c )d e + (- 168A b c + 80B b c )d e +--R + +--R 5 4 3 +--R (96A c - 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (140A b c - 60B b c)d e + (- 336A b c + 160B b c )d e +--R + +--R 4 2 3 3 +--R (192A b c - 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (70A b c - 30B b )d e + (- 168A b c + 80B b c)d e +--R + +--R 2 3 3 2 3 +--R (96A b c - 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 2 2 2 3 3 2 +--R - 2A b c e + (48A b c - 22B b c )d e +--R + +--R 4 2 3 2 +--R (- 48A b c + 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 4A b c e + (74A b c - 34B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 72A b c + 36B b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R (- 2A b e + (18A b c - 8B b )d e + (- 16A b c + 8B b c)d )x +--R + +--R 5 4 2 +--R - 4A b d e + 4A b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (8b c d e - 8b c d )x + (16b c d e - 16b c d )x +--R + +--R 8 7 2 2 +--R (8b d e - 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 2 3 3 2 2 4 2 3 2 +--R (35A b c - 15B b c )d e + (- 84A b c + 40B b c )d e +--R + +--R 5 4 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (70A b c - 30B b c)d e + (- 168A b c + 80B b c )d e +--R + +--R 4 2 3 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (35A b c - 15B b )d e + (- 84A b c + 40B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R +---+ | c +--R \|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 2 3 2 3 3 2 2 +--R 2A b c e + (22A b c - 8B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 120A b c + 56B b c )d e + (96A c - 48B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 +--R 4A b c e + (44A b c - 16B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 240A b c + 112B b c )d e + (192A b c - 96B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R 2A b e + (22A b c - 8B b )d e + (- 120A b c + 56B b c)d e +--R + +--R 2 3 3 2 3 +--R (96A b c - 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 3 2 2 2 3 3 2 +--R - 2A b c e + (48A b c - 22B b c )d e +--R + +--R 4 2 3 2 +--R (- 48A b c + 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 4A b c e + (74A b c - 34B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 72A b c + 36B b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R (- 2A b e + (18A b c - 8B b )d e + (- 16A b c + 8B b c)d )x +--R + +--R 5 4 2 +--R - 4A b d e + 4A b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (8b c d e - 8b c d )x + (16b c d e - 16b c d )x +--R + +--R 8 7 2 2 +--R (8b d e - 8b c d )x +--R * +--R +---+ +--R \|- d +--R , +--R +--R 3 2 3 2 3 3 2 2 +--R A b c e + (11A b c - 4B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 60A b c + 28B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 +--R 2A b c e + (22A b c - 8B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 120A b c + 56B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 3 3 2 2 4 2 3 2 +--R (35A b c - 15B b c )d e + (- 84A b c + 40B b c )d e +--R + +--R 5 4 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (70A b c - 30B b c)d e + (- 168A b c + 80B b c )d e +--R + +--R 4 2 3 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (35A b c - 15B b )d e + (- 84A b c + 40B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R +---+ | c c\|e x + d +--R \|- d |--------- atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 2 2 2 3 3 2 +--R - A b c e + (24A b c - 11B b c )d e +--R + +--R 4 2 3 2 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 2A b c e + (37A b c - 17B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 36A b c + 18B b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R (- A b e + (9A b c - 4B b )d e + (- 8A b c + 4B b c)d )x +--R + +--R 5 4 2 +--R - 2A b d e + 2A b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (4b c d e - 4b c d )x + (8b c d e - 8b c d )x +--R + +--R 8 7 2 2 +--R (4b d e - 4b c d )x +--R * +--R +---+ +--R \|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 856 + +--S 857 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 +--R (35A b c - 15B b )d e + (- 84A b c + 40B b c)d e +--R + +--R 3 2 3 +--R (48A c - 24B b c )d +--R * +--R +-----------+ +--R +-----------+ | c +-+ +--R \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 3 2 2 2 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 3 2 3 +--R (48A c - 24B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 2 3 2 2 2 2 +--R (70A b c - 30B b )d e + (- 168A b c + 80B b c)d e +--R + +--R 3 2 3 +--R (96A c - 48B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A b e + (- 22A b c + 8B b )d e + (120A b c - 56B b c)d e +--R + +--R 3 2 3 +--R (- 96A c + 48B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 6 5 2 +-----------+ +-+ +--R (8b d e - 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 857 + +--S 858 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 3 2 2 2 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 3 2 3 +--R (48A c - 24B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 2 3 2 2 2 2 +--R (70A b c - 30B b )d e + (- 168A b c + 80B b c)d e +--R + +--R 3 2 3 +--R (96A c - 48B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A b e + (- 22A b c + 8B b )d e + (120A b c - 56B b c)d e +--R + +--R 3 2 3 +--R (- 96A c + 48B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 2 +--R (70A b c - 30B b )d e + (- 168A b c + 80B b c)d e +--R + +--R 3 2 3 +--R (96A c - 48B b c )d +--R * +--R +---------+ +-------+ +--R +-----------+ | c +-+ c\|e x + d +--R \|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 6 5 2 +-----------+ +-+ +--R (8b d e - 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 1457 +t0:=(A+B*x)/((b*x+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R 3 6 2 5 2 4 3 3 +-------+ +--R (c x + 3b c x + 3b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1457 +r0:=-1/4*(48*A*c^2*d^2-b^2*e*(4*B*d-3*A*e)-12*b*c*d*(2*B*d-A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(5/2))+1/4*c^(3/2)*_ + (48*A*c^3*d^2-35*b^3*B*e^2-12*b*c^2*d*(2*B*d+9*A*e)+7*b^2*c*e*_ + (8*B*d+9*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*_ + (c*d-b*e)^(5/2))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-3*A*e)-b*c*d*_ + (6*B*d+7*A*e))*sqrt(d+e*x)/(b^3*d^2*(c*d-b*e)*(b+c*x)^2)-1/2*A*_ + sqrt(d+e*x)/(b*d*x^2*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d-3*A*b*e)*_ + sqrt(d+e*x)/(b^2*d^2*x*(b+c*x)^2)+1/4*c*(24*A*c^3*d^3-b^3*e^2*_ + (4*B*d-3*A*e)-12*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(19*B*d+6*A*e))*_ + sqrt(d+e*x)/(b^4*d^2*(c*d-b*e)^2*(b+c*x)) +--R +--R +--R (2) +--R 2 4 3 3 2 2 5 2 4 3 +--R (63A b c - 35B b c )d e + (- 108A b c + 56B b c )d e +--R + +--R 6 5 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (126A b c - 70B b c )d e + (- 216A b c + 112B b c )d e +--R + +--R 5 2 4 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (63A b c - 35B b c)d e + (- 108A b c + 56B b c )d e +--R + +--R 2 4 3 3 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 2 4 3 3 4 2 3 +--R - 3A b c e + (- 6A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 27A b c + 16B b c )d e + (84A b c - 44B b c )d e +--R + +--R 6 5 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 +--R - 6A b c e + (- 12A b c + 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 54A b c + 32B b c )d e + (168A b c - 88B b c )d e +--R + +--R 5 2 4 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R - 3A b e + (- 6A b c + 4B b )d e + (- 27A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (84A b c - 44B b c )d e + (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 3 3 3 4 2 2 2 4 3 3 2 +--R 3A b c e + (6A b c - 4B b c )d e + (- 36A b c + 19B b c )d e +--R + +--R 5 2 4 3 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 3 3 4 2 2 +--R 6A b c e + (10A b c - 8B b c)d e + (- 55A b c + 29B b c )d e +--R + +--R 2 4 3 3 3 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 3A b e + (2A b c - 4B b )d e + (- 13A b c + 8B b c)d e +--R + +--R 3 3 4 2 3 +--R (8A b c - 4B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (4b c d e - 8b c d e + 4b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 9 2 2 8 3 7 2 4 2 +--R (8b c d e - 16b c d e + 8b c d )x + (4b d e - 8b c d e + 4b c d )x +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 4 3 3 4 2 3 2 4 3 3 2 2 +--R 3A b c e + (6A b c - 4B b c )d e + (27A b c - 16B b c )d e +--R + +--R 5 2 4 3 6 5 4 +--R (- 84A b c + 44B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 3 3 4 2 2 2 +--R 6A b c e + (12A b c - 8B b c)d e + (54A b c - 32B b c )d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 168A b c + 88B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R 3A b e + (6A b c - 4B b )d e + (27A b c - 16B b c)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (- 84A b c + 44B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (63A b c - 35B b c )d e + (- 108A b c + 56B b c )d e +--R + +--R 6 5 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (126A b c - 70B b c )d e + (- 216A b c + 112B b c )d e +--R + +--R 5 2 4 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (63A b c - 35B b c)d e + (- 108A b c + 56B b c )d e +--R + +--R 2 4 3 3 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 2 3 3 3 4 2 2 +--R 6A b c e + (12A b c - 8B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 38B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 +--R 12A b c e + (20A b c - 16B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 58B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 6A b e + (4A b c - 8B b )d e + (- 26A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 +--R (16A b c - 8B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (8b c d e - 16b c d e + 8b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 +--R (16b c d e - 32b c d e + 16b c d )x +--R + +--R 9 2 2 8 3 7 2 4 2 +--R (8b d e - 16b c d e + 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 4 2 4 3 3 4 2 3 2 4 3 3 2 2 +--R 3A b c e + (6A b c - 4B b c )d e + (27A b c - 16B b c )d e +--R + +--R 5 2 4 3 6 5 4 +--R (- 84A b c + 44B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 3 3 4 2 2 2 +--R 6A b c e + (12A b c - 8B b c)d e + (54A b c - 32B b c )d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 168A b c + 88B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R 3A b e + (6A b c - 4B b )d e + (27A b c - 16B b c)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (- 84A b c + 44B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 126A b c + 70B b c )d e + (216A b c - 112B b c )d e +--R + +--R 6 5 4 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 252A b c + 140B b c )d e + (432A b c - 224B b c )d e +--R + +--R 5 2 4 4 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (- 126A b c + 70B b c)d e + (216A b c - 112B b c )d e +--R + +--R 2 4 3 3 4 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 2 3 3 3 4 2 2 +--R 6A b c e + (12A b c - 8B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 38B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 +--R 12A b c e + (20A b c - 16B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 58B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 6A b e + (4A b c - 8B b )d e + (- 26A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 +--R (16A b c - 8B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (8b c d e - 16b c d e + 8b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 +--R (16b c d e - 32b c d e + 16b c d )x +--R + +--R 9 2 2 8 3 7 2 4 2 +--R (8b d e - 16b c d e + 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 2 4 3 3 2 2 5 2 4 3 +--R (63A b c - 35B b c )d e + (- 108A b c + 56B b c )d e +--R + +--R 6 5 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (126A b c - 70B b c )d e + (- 216A b c + 112B b c )d e +--R + +--R 5 2 4 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (63A b c - 35B b c)d e + (- 108A b c + 56B b c )d e +--R + +--R 2 4 3 3 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R +---+ | c +--R \|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 2 4 3 3 4 2 3 +--R - 6A b c e + (- 12A b c + 8B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 54A b c + 32B b c )d e + (168A b c - 88B b c )d e +--R + +--R 6 5 4 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 +--R - 12A b c e + (- 24A b c + 16B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 108A b c + 64B b c )d e + (336A b c - 176B b c )d e +--R + +--R 5 2 4 4 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 +--R - 6A b e + (- 12A b c + 8B b )d e +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (- 54A b c + 32B b c)d e + (168A b c - 88B b c )d e +--R + +--R 2 4 3 3 4 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 4 2 3 3 3 4 2 2 +--R 6A b c e + (12A b c - 8B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 38B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 +--R 12A b c e + (20A b c - 16B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 58B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 6A b e + (4A b c - 8B b )d e + (- 26A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 +--R (16A b c - 8B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (8b c d e - 16b c d e + 8b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 +--R (16b c d e - 32b c d e + 16b c d )x +--R + +--R 9 2 2 8 3 7 2 4 2 +--R (8b d e - 16b c d e + 8b c d )x +--R * +--R +---+ +--R \|- d +--R , +--R +--R 4 2 4 3 3 4 2 3 +--R - 3A b c e + (- 6A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 27A b c + 16B b c )d e + (84A b c - 44B b c )d e +--R + +--R 6 5 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 +--R - 6A b c e + (- 12A b c + 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 54A b c + 32B b c )d e + (168A b c - 88B b c )d e +--R + +--R 5 2 4 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R - 3A b e + (- 6A b c + 4B b )d e + (- 27A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (84A b c - 44B b c )d e + (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 63A b c + 35B b c )d e + (108A b c - 56B b c )d e +--R + +--R 6 5 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 126A b c + 70B b c )d e + (216A b c - 112B b c )d e +--R + +--R 5 2 4 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (- 63A b c + 35B b c)d e + (108A b c - 56B b c )d e +--R + +--R 2 4 3 3 4 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R +---+ | c c\|e x + d +--R \|- d |--------- atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 2 3 3 3 4 2 2 +--R 3A b c e + (6A b c - 4B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 36A b c + 19B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 +--R 6A b c e + (10A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 55A b c + 29B b c )d e + (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 3A b e + (2A b c - 4B b )d e + (- 13A b c + 8B b c)d e +--R + +--R 3 3 4 2 3 +--R (8A b c - 4B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (4b c d e - 8b c d e + 4b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 9 2 2 8 3 7 2 4 2 +--R (8b c d e - 16b c d e + 8b c d )x + (4b d e - 8b c d e + 4b c d )x +--R * +--R +---+ +--R \|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 863 + +--S 864 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 4 3 4 3 2 2 3 2 2 +--R 3A b e + (6A b c - 4B b )d e + (27A b c - 16B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 84A b c + 44B b c )d e + (48A c - 24B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (63A b c - 35B b c)d e + (- 108A b c + 56B b c )d e +--R + +--R 4 3 4 +--R (48A c - 24B b c )d +--R * +--R +-----------+ +--R +-----------+ | c +-+ +--R \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (- 126A b c + 70B b c)d e + (216A b c - 112B b c )d e +--R + +--R 4 3 4 +--R (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R 6A b e + (12A b c - 8B b )d e + (54A b c - 32B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 168A b c + 88B b c )d e + (96A c - 48B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 7 2 2 6 3 5 2 4 +-----------+ +-+ +--R (8b d e - 16b c d e + 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 4 3 2 2 3 2 2 +--R 3A b e + (6A b c - 4B b )d e + (27A b c - 16B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 84A b c + 44B b c )d e + (48A c - 24B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (- 126A b c + 70B b c)d e + (216A b c - 112B b c )d e +--R + +--R 4 3 4 +--R (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R 6A b e + (12A b c - 8B b )d e + (54A b c - 32B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 168A b c + 88B b c )d e + (96A c - 48B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (- 126A b c + 70B b c)d e + (216A b c - 112B b c )d e +--R + +--R 4 3 4 +--R (- 96A c + 48B b c )d +--R * +--R +---------+ +-------+ +--R +-----------+ | c +-+ c\|e x + d +--R \|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 7 2 2 6 3 5 2 4 +-----------+ +-+ +--R (8b d e - 16b c d e + 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 7 2 3 6 2 2 5 3 2 4 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x +--R + +--R 3 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1457 +r0:=-3/4*(16*A*c^2*d^2-b^2*e*(4*B*d-5*A*e)-4*b*c*d*(2*B*d-3*A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(7/2))+3/4*c^(5/2)*(16*A*c^3*d^2-_ + 21*b^3*B*e^2-4*b*c^2*d*(2*B*d+11*A*e)+3*b^2*c*e*(8*B*d+11*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(7/2))+_ + 3/4*e*(8*A*c^4*d^4+b^4*e^3*(4*B*d-5*A*e)-b^3*c*d*e^2*(4*B*d-3*A*e)-_ + 4*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*e*(9*B*d+5*A*e))/(b^4*d^3*_ + (c*d-b*e)^3*sqrt(d+e*x))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-5*A*e)-_ + b*c*d*(6*B*d+5*A*e))/(b^3*d^2*(c*d-b*e)*(b+c*x)^2*sqrt(d+e*x))-_ + 1/2*A/(b*d*x^2*(b+c*x)^2*sqrt(d+e*x))+1/4*(-4*b*B*d+8*A*c*d+_ + 5*A*b*e)/(b^2*d^2*x*(b+c*x)^2*sqrt(d+e*x))+1/4*c*(24*A*c^3*d^3-_ + b^3*e^2*(4*B*d-5*A*e)+b^2*c*d*e*(21*B*d+2*A*e)-12*b*c^2*d^2*(B*d+_ + 3*A*e))/(b^4*d^2*(c*d-b*e)^2*(b+c*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 5 3 4 3 2 6 2 5 4 +--R (- 99A b c + 63B b c )d e + (132A b c - 72B b c )d e +--R + +--R 7 6 5 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 3 2 2 5 3 4 4 +--R (- 198A b c + 126B b c )d e + (264A b c - 144B b c )d e +--R + +--R 6 2 5 5 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (- 99A b c + 63B b c )d e + (132A b c - 72B b c )d e +--R + +--R 2 5 3 4 5 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 2 5 4 3 5 2 4 +--R - 15A b c e + (9A b c + 12B b c )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (15A b c - 12B b c )d e + (51A b c - 36B b c )d e +--R + +--R 6 2 5 4 7 6 5 +--R (- 108A b c + 60B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 6 4 +--R - 30A b c e + (18A b c + 24B b c)d e +--R + +--R 4 3 5 2 2 3 3 4 4 3 3 2 +--R (30A b c - 24B b c )d e + (102A b c - 72B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (- 216A b c + 120B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 6 7 4 5 2 6 2 3 +--R - 15A b e + (9A b c + 12B b )d e + (15A b c - 12B b c)d e +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (51A b c - 36B b c )d e + (- 108A b c + 60B b c )d e +--R + +--R 2 5 3 4 5 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 2 5 4 3 5 2 4 +--R 15A b c e + (- 9A b c - 12B b c )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (- 15A b c + 12B b c )d e + (48A b c - 27B b c )d e +--R + +--R 6 2 5 4 +--R (- 24A b c + 12B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 6 4 +--R 30A b c e + (- 13A b c - 24B b c)d e +--R + +--R 4 3 5 2 2 3 3 4 4 3 3 2 +--R (- 33A b c + 20B b c )d e + (58A b c - 29B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (12A b c - 9B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 6 7 4 5 2 6 2 3 +--R 15A b e + (A b c - 12B b )d e + (- 23A b c + 4B b c)d e +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (- 7A b c + 12B b c )d e + (65A b c - 37B b c )d e +--R + +--R 2 5 3 4 5 +--R (- 36A b c + 18B b c )d +--R * +--R 2 +--R x +--R + +--R 7 4 6 7 2 3 5 2 6 3 2 +--R 5A b d e + (- 7A b c - 4B b )d e + (- 9A b c + 12B b c)d e +--R + +--R 4 3 5 2 4 3 4 4 3 5 +--R (19A b c - 12B b c )d e + (- 8A b c + 4B b c )d +--R * +--R x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - 2A b d e + 6A b c d e - 6A b c d e + 2A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (8b c d e - 24b c d e + 24b c d e - 8b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1457 +--a0:=integrate(t0,x) +--E 870 + +--S 871 of 1457 +--m0a:=a0.1-r0 +--E 871 + +--S 872 of 1457 +--d0a:=D(m0a,x) +--E 872 + +--S 873 of 1457 +--m0b:=a0.2-r0 +--E 873 + +--S 874 of 1457 +--d0b:=D(m0b,x) +--E 874 + +)clear all + +--S 875 of 1457 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1457 +r0:=1/12*e*(72*A*c^4*d^4+5*b^4*e^3*(4*B*d-7*A*e)-9*b^3*c*d*e^2*(4*B*d-_ + 5*A*e)-36*b*c^3*d^3*(B*d+4*A*e)+3*b^2*c^2*d^2*e*(29*B*d+9*A*e))/(b^4*_ + d^3*(c*d-b*e)^3*(d+e*x)^(3/2))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-7*A*e)-_ + 3*b*c*d*(2*B*d+A*e))/(b^3*d^2*(c*d-b*e)*(b+c*x)^2*(d+e*x)^(3/2))-_ + 1/2*A/(b*d*x^2*(b+c*x)^2*(d+e*x)^(3/2))+1/4*(-4*b*B*d+8*A*c*d+7*A*b*e)/_ + (b^2*d^2*x*(b+c*x)^2*(d+e*x)^(3/2))+1/4*c*(24*A*c^3*d^3-b^3*e^2*_ + (4*B*d-7*A*e)+b^2*c*d*e*(23*B*d-2*A*e)-12*b*c^2*d^2*(B*d+3*A*e))/_ + (b^4*d^2*(c*d-b*e)^2*(b+c*x)*(d+e*x)^(3/2))-1/4*(48*A*c^2*d^2-_ + 5*b^2*e*(4*B*d-7*A*e)-12*b*c*d*(2*B*d-5*A*e))*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b^5*d^(9/2))+1/4*c^(7/2)*(48*A*c^3*d^2-99*b^3*B*e^2-_ + 12*b*c^2*d*(2*B*d+13*A*e)+11*b^2*c*e*(8*B*d+13*A*e))*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(9/2))+1/4*e*(24*A*c^5*d^5+_ + 8*b^4*c*d*e^3*(7*B*d-10*A*e)-5*b^5*e^4*(4*B*d-7*A*e)-6*b^3*_ + c^2*d^2*e^2*(4*B*d-3*A*e)+7*b^2*c^3*d^3*e*(5*B*d+4*A*e)-12*b*c^4*d^4*_ + (B*d+5*A*e))/(b^4*d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (429A b c - 297B b c )d e + (- 468A b c + 264B b c )d e +--R + +--R 8 7 6 +--R (144A c - 72B b c )d e +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (858A b c - 594B b c )d e + (- 507A b c + 231B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (- 180A b c + 120B b c )d e + (144A c - 72B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (429A b c - 297B b c )d e + (390A b c - 330B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 792A b c + 456B b c )d e + (288A b c - 144B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (429A b c - 297B b c )d e + (- 468A b c + 264B b c )d e +--R + +--R 2 6 3 5 7 +--R (144A b c - 72B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 6 2 7 5 3 6 2 6 +--R - 105A b c e + (240A b c + 60B b c )d e +--R + +--R 4 4 5 3 2 5 3 5 4 4 3 4 +--R (- 54A b c - 168B b c )d e + (- 84A b c + 72B b c )d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 249A b c + 192B b c )d e + (396A b c - 228B b c )d e +--R + +--R 8 7 6 +--R (- 144A c + 72B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R - 210A b c e + (375A b c + 120B b c)d e +--R + +--R 5 3 6 2 2 5 4 4 5 3 3 4 +--R (132A b c - 276B b c )d e + (- 222A b c - 24B b c )d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 582A b c + 456B b c )d e + (543A b c - 264B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (108A b c - 84B b c )d e + (- 144A c + 72B b c )d +--R * +--R 4 +--R x +--R + +--R 8 7 7 8 6 6 2 7 2 5 +--R - 105A b e + (30A b c + 60B b )d e + (426A b c - 48B b c)d e +--R + +--R 5 3 6 2 3 4 4 4 5 3 4 3 +--R (- 192A b c - 264B b c )d e + (- 417A b c + 336B b c )d e +--R + +--R 3 5 4 4 5 2 2 6 3 5 6 +--R (- 102A b c + 156B b c )d e + (648A b c - 384B b c )d e +--R + +--R 7 2 6 7 +--R (- 288A b c + 144B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 +--R - 105A b d e + (240A b c + 60B b )d e +--R + +--R 6 2 7 3 4 5 3 6 2 4 3 +--R (- 54A b c - 168B b c)d e + (- 84A b c + 72B b c )d e +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (- 249A b c + 192B b c )d e + (396A b c - 228B b c )d e +--R + +--R 2 6 3 5 7 +--R (- 144A b c + 72B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 6 2 7 5 3 6 2 6 +--R 105A b c e + (- 240A b c - 60B b c )d e +--R + +--R 4 4 5 3 2 5 3 5 4 4 3 4 +--R (54A b c + 168B b c )d e + (84A b c - 72B b c )d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 180A b c + 105B b c )d e + (72A b c - 36B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R 210A b c e + (- 340A b c - 120B b c)d e +--R + +--R 5 3 6 2 2 5 4 4 5 3 3 4 +--R (- 212A b c + 256B b c )d e + (240A b c + 80B b c )d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 105A b c + 15B b c )d e + (- 252A b c + 156B b c )d e +--R + +--R 7 2 6 6 +--R (144A b c - 72B b c )d e +--R * +--R 4 +--R x +--R + +--R 8 7 7 8 6 6 2 7 2 5 +--R 105A b e + (40A b c - 60B b )d e + (- 565A b c + 8B b c)d e +--R + +--R 5 3 6 2 3 4 4 4 5 3 4 3 +--R (180A b c + 364B b c )d e + (255A b c - 192B b c )d e +--R + +--R 3 5 4 4 5 2 2 6 3 5 6 +--R (- 438A b c + 234B b c )d e + (36A b c - 3B b c )d e +--R + +--R 7 2 6 7 +--R (72A b c - 36B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 +--R 140A b d e + (- 278A b c - 80B b )d e +--R + +--R 6 2 7 3 4 5 3 6 2 4 3 +--R (- 30A b c + 200B b c)d e + (180A b c - 48B b c )d e +--R + +--R 5 3 5 2 3 5 4 4 6 +--R - 48B b c d e + (- 225A b c + 135B b c )d e +--R + +--R 2 6 3 5 7 +--R (108A b c - 54B b c )d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 8 3 4 6 2 7 4 3 +--R 21A b d e + (- 60A b c - 12B b )d e + (30A b c + 48B b c)d e +--R + +--R 5 3 6 2 5 2 4 4 5 3 6 +--R (60A b c - 72B b c )d e + (- 75A b c + 48B b c )d e +--R + +--R 3 5 4 4 7 +--R (24A b c - 12B b c )d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - 6A b d e + 24A b c d e - 36A b c d e + 24A b c d e - 6A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (12b c d e - 48b c d e + 72b c d e - 48b c d e + 12b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 +--R 24b c d e - 84b c d e + 96b c d e - 24b c d e - 24b c d e +--R + +--R 5 6 9 +--R 12b c d +--R * +--R 4 +--R x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 +--R 12b d e - 24b c d e - 24b c d e + 96b c d e - 84b c d e +--R + +--R 6 5 9 +--R 24b c d +--R * +--R 3 +--R x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (12b d e - 48b c d e + 72b c d e - 48b c d e + 12b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1457 +--a0:=integrate(t0,x) +--E 877 + +--S 878 of 1457 +--m0a:=a0.1-r0 +--E 878 + +--S 879 of 1457 +--d0a:=D(m0a,x) +--E 879 + +--S 880 of 1457 +--m0b:=a0.2-r0 +--E 880 + +--S 881 of 1457 +--d0b:=D(m0b,x) +--E 881 + +)clear all + +--S 882 of 1457 +t0:=(A+B*x)*(d+e*x)^(1/2)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R +-------+ | 2 +--R (1) (B x + A)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1457 +--r0:=2/7*B*(b*x+c*x^2)^(3/2)*sqrt(d+e*x)/c-2/105*(14*A*c*e*(c^2*d^2-_ +-- b*c*d*e+b^2*e^2)-B*(8*c^3*d^3-5*b*c^2*d^2*e-5*b^2*c*d*e^2+8*_ +-- b^3*e^3))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^3*e^(5/2)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/105*(-b)^(3/2)*_ +-- (c*d-b*e)*(7*A*c*e*(c*d-2*b*e)-B*(4*c^2*d^2+b*c*d*e-8*b^2*e^2))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*e^2*sqrt(d+e*x)*sqrt(b*x+_ +-- c*x^2))+2/105*(7*A*c*e*(c*d+b*e)-B*(4*c^2*d^2-2*b*c*d*e+4*b^2*e^2)+_ +-- 3*c*e*(B*c*d-4*b*B*e+7*A*c*e)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^2) +--E 883 + +--S 884 of 1457 +--a0:=integrate(t0,x) +--E 884 + +--S 885 of 1457 +--m0:=a0-r0 +--E 885 + +--S 886 of 1457 +--d0:=D(m0,x) +--E 886 + +)clear all + +--S 887 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1457 +--r0:=-2/15*(5*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^2*e^(5/2)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*(-b)^(3/2)*(c*d-b*e)*(4*B*c*d+_ +-- 2*b*B*e-5*A*c*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*e^2*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(4*B*c*d-b*B*e-5*A*c*e-3*B*c*e*x)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c*e^2) +--E 888 + +--S 889 of 1457 +--a0:=integrate(t0,x) +--E 889 + +--S 890 of 1457 +--m0:=a0-r0 +--E 890 + +--S 891 of 1457 +--d0:=D(m0,x) +--E 891 + +)clear all + +--S 892 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1457 +--r0:=-2/3*(8*B*c*d-b*B*e-6*A*c*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (c*e^(5/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*(-b)^(3/2)*(4*B*c*d-b*B*e-3*A*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+_ +-- e*x)/d)/(c^(3/2)*e^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(4*B*d-_ +-- 3*A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*sqrt(d+e*x)) +--E 893 + +--S 894 of 1457 +--a0:=integrate(t0,x) +--E 894 + +--S 895 of 1457 +--m0:=a0-r0 +--E 895 + +--S 896 of 1457 +--d0:=D(m0,x) +--E 896 + +)clear all + +--S 897 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1457 +--r0:=-2/3*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(e^(5/2)*(c*d-b*e)*sqrt(-d)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(-b)^(3/2)*(4*B*d-A*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*e^2*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*(4*B*d-A*e+3*B*e*x)*sqrt(b*x+c*x^2)/(e^2*_ +-- (d+e*x)^(3/2))-2/3*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*_ +-- sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*sqrt(d+e*x)) +--E 898 + +--S 899 of 1457 +--a0:=integrate(t0,x) +--E 899 + +--S 900 of 1457 +--m0:=a0-r0 +--E 900 + +--S 901 of 1457 +--d0:=D(m0,x) +--E 901 + +)clear all + +--S 902 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1457 +--r0:=-2/15*(2*A*e*(c^2*d^2-b*c*d*e+b^2*e^2)+B*d*(8*c^2*d^2-13*b*c*d*e+_ +-- 3*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(3/2)*e^(5/2)*(c*d-b*e)^2*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(-b)^(3/2)*(B*d*_ +-- (4*c*d-3*b*e)+A*e*(c*d-2*b*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*_ +-- e^2*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*(B*d*(8*c*d-_ +-- 9*b*e)+A*e*(2*c*d-b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+_ +-- e*x)^(3/2))-2/5*(4*B*d+A*e+5*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+_ +-- e*x)^(5/2))+2/15*(2*A*e*(c^2*d^2-b*c*d*e+b^2*e^2)+B*d*(8*c^2*d^2-_ +-- 13*b*c*d*e+3*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 903 + +--S 904 of 1457 +--a0:=integrate(t0,x) +--E 904 + +--S 905 of 1457 +--m0:=a0-r0 +--E 905 + +--S 906 of 1457 +--d0:=D(m0,x) +--E 906 + +)clear all + +--S 907 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(1/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1457 +--r0:=-2/63*(8*B*c*d-3*b*B*e-9*A*c*e-7*B*c*e*x)*(b*x+c*x^2)^(3/2)*_ +-- sqrt(d+e*x)/(c*e^2)-2/315*(18*A*c*e*(8*c^3*d^3-12*b*c^2*d^2*e+_ +-- 2*b^2*c*d*e^2+b^3*e^3)-B*(128*c^4*d^4-184*b*c^3*d^3*e+27*_ +-- b^2*c^2*d^2*e^2+11*b^3*c*d*e^3+8*b^4*e^4))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^3*e^(9/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/315*(-b)^(3/2)*(c*d-b*e)*(9*A*c*e*(8*c^2*d^2-_ +-- 5*b*c*d*e-2*b^2*e^2)-B*(64*c^3*d^3-36*b*c^2*d^2*e-15*b^2*c*d*e^2-_ +-- 8*b^3*e^3))*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*e^4*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/315*(9*A*c*e*(8*c^2*d^2-11*b*c*d*e+b^2*e^2)-_ +-- 2*B*(32*c^3*d^3-42*b*c^2*d^2*e+3*b^2*c*d*e^2+2*b^3*e^3)-3*c*e*_ +-- (9*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-7*b*c*d*e-4*b^2*e^2))*x)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^4) +--E 908 + +--S 909 of 1457 +--a0:=integrate(t0,x) +--E 909 + +--S 910 of 1457 +--m0:=a0-r0 +--E 910 + +--S 911 of 1457 +--d0:=D(m0,x) +--E 911 + +)clear all + +--S 912 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1457 +--r0:=2/7*(8*B*d-7*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+2/35*_ +-- (5*b*c*e*(8*B*d-7*A*e)*(2*c*d-b*e)-(16*B*c*d-b*B*e-14*A*c*e)*_ +-- (8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (c^2*e^(9/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/35*_ +-- (-b)^(3/2)*(c*d-b*e)*(7*A*c*e*(8*c*d-b*e)-2*B*(32*c^2*d^2-6*b*c*d*e-_ +-- b^2*e^2))*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*e^4*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/35*(7*A*c*e*(8*c*d-7*b*e)-B*(64*c^2*d^2-60*b*c*_ +-- d*e+b^2*e^2)+3*c*e*(16*B*c*d-b*B*e-14*A*c*e)*x)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/(c*e^4) +--E 913 + +--S 914 of 1457 +--a0:=integrate(t0,x) +--E 914 + +--S 915 of 1457 +--m0:=a0-r0 +--E 915 + +--S 916 of 1457 +--d0:=D(m0,x) +--E 916 + +)clear all + +--S 917 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1457 +--r0:=2/15*(8*B*d-5*A*e+3*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/15*(40*A*c*e*(2*c*d-b*e)-B*(128*c^2*d^2-88*b*c*d*e+3*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c*e^(9/2)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(-b)^(3/2)*(5*A*c*e*(8*c*d-5*b*e)-_ +-- B*(64*c^2*d^2-52*b*c*d*e+3*b^2*e^2))*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(3/2)*e^4*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/15*(4*B*d*(16*c*d-9*b*e)-5*A*e*(8*c*d-3*b*e)+e*(16*B*c*d-_ +-- 3*b*B*e-10*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*sqrt(d+e*x)) +--E 918 + +--S 919 of 1457 +--a0:=integrate(t0,x) +--E 919 + +--S 920 of 1457 +--m0:=a0-r0 +--E 920 + +--S 921 of 1457 +--d0:=D(m0,x) +--E 921 + +)clear all + +--S 922 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1457 +--r0:=2/15*(8*B*d-3*A*e+5*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 2/15*(3*A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(128*c^2*d^2-_ +-- 168*b*c*d*e+43*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/(e^(9/2)*(c*d-b*e)*_ +-- sqrt(-d)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/15*(-b)^(3/2)*(4*B*d*(16*c*d-7*b*e)-3*A*e*(8*c*d-b*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*e^4*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/15*(4*B*d*(16*c*d-7*b*e)-3*A*e*(8*c*d-b*e)+_ +-- 3*e*(16*B*c*d-5*b*B*e-6*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*_ +-- (d+e*x)^(3/2))-2/15*(3*A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*_ +-- (128*c^2*d^2-168*b*c*d*e+43*b^2*e^2))*sqrt(b*x+c*x^2)/(d*e^4*_ +-- (c*d-b*e)*sqrt(d+e*x)) +--E 923 + +--S 924 of 1457 +--a0:=integrate(t0,x) +--E 924 + +--S 925 of 1457 +--m0:=a0-r0 +--E 925 + +--S 926 of 1457 +--d0:=D(m0,x) +--E 926 + +)clear all + +--S 927 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/sqrt(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1457 +--r0:=2/105*(7*A*c*e*(23*c^2*d^2-23*b*c*d*e+8*b^2*e^2)+B*(15*c^3*d^3-_ +-- 103*b*c^2*d^2*e+128*b^2*c*d*e^2-48*b^3*e^3))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^4*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/105*(c*d-b*e)*(105*A*c^3*d^2-48*b^3*B*e^2+_ +-- 8*b^2*c*e*(13*B*d+7*A*e)-b*c^2*d*(60*B*d+133*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/35*(5*B*c*d-6*b*B*e+7*A*c*e)*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/c^2+2/7*B*(d+e*x)^(5/2)*sqrt(b*x+c*x^2)/c+2/105*_ +-- (28*A*c*e*(2*c*d-b*e)+B*(15*c^2*d^2-43*b*c*d*e+24*b^2*e^2))*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/c^3 +--E 928 + +--S 929 of 1457 +--a0:=integrate(t0,x) +--E 929 + +--S 930 of 1457 +--m0:=a0-r0 +--E 930 + +--S 931 of 1457 +--d0:=D(m0,x) +--E 931 + +)clear all + +--S 932 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1457 +--r0:=2/15*(10*A*c*e*(2*c*d-b*e)+B*(3*c^2*d^2-13*b*c*d*e+8*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^3*sqrt(e)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(c*d-b*e)*(9*b*B*c*d-15*A*c^2*d-_ +-- 8*b^2*B*e+10*A*b*c*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (c^(7/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*B*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/c+2/15*(3*B*c*d-4*b*B*e+5*A*c*e)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/c^2 +--E 933 + +--S 934 of 1457 +--a0:=integrate(t0,x) +--E 934 + +--S 935 of 1457 +--m0:=a0-r0 +--E 935 + +--S 936 of 1457 +--d0:=D(m0,x) +--E 936 + +)clear all + +--S 937 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(b*x+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1457 +--r0:=2/3*(B*c*d-2*b*B*e+3*A*c*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^2*_ +-- sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*(2*b*B-_ +-- 3*A*c)*(c*d-b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (c^(5/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*B*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/c +--E 938 + +--S 939 of 1457 +--a0:=integrate(t0,x) +--E 939 + +--S 940 of 1457 +--m0:=a0-r0 +--E 940 + +--S 941 of 1457 +--d0:=D(m0,x) +--E 941 + +)clear all + +--S 942 of 1457 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------- +--R +----------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1457 +--r0:=2*B*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c*sqrt(e)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(b*B-A*c)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(3/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 943 + +--S 944 of 1457 +--a0:=integrate(t0,x) +--E 944 + +--S 945 of 1457 +--m0:=a0-r0 +--E 945 + +--S 946 of 1457 +--d0:=D(m0,x) +--E 946 + +)clear all + +--S 947 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) -------------------------------- +--R +----------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1457 +--r0:=2*(B*d-A*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((c*d-b*e)*sqrt(-d)*sqrt(e)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*A*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*sqrt(d+e*x)) +--E 948 + +--S 949 of 1457 +--a0:=integrate(t0,x) +--E 949 + +--S 950 of 1457 +--m0:=a0-r0 +--E 950 + +--S 951 of 1457 +--d0:=D(m0,x) +--E 951 + +)clear all + +--S 952 of 1457 +t0:=(A+B*x)/((d+e*x)^(5/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +----------+ +--R 2 2 2 +-------+ | 2 +--R (e x + 2d e x + d )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1457 +--r0:=2/3*(2*A*e*(2*c*d-b*e)-B*d*(c*d+b*e))*(b+c*x)*elliptic_e(asin(_ +-- sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/_ +-- ((-d)^(3/2)*(c*d-b*e)^2*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/3*(b*B*d-3*A*c*d+2*A*b*e)*elliptic_f(asin(_ +-- sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ +-- (d+e*x)^(3/2))-2/3*(2*A*e*(2*c*d-b*e)-B*d*(c*d+b*e))*sqrt(b*x+_ +-- c*x^2)/(d^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 953 + +--S 954 of 1457 +--a0:=integrate(t0,x) +--E 954 + +--S 955 of 1457 +--m0:=a0-r0 +--E 955 + +--S 956 of 1457 +--d0:=D(m0,x) +--E 956 + +)clear all + +--S 957 of 1457 +t0:=(A+B*x)/((d+e*x)^(7/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R +----------+ +--R 3 3 2 2 2 3 +-------+ | 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1457 +--r0:=2/15*(B*d*(3*c^2*d^2+7*b*c*d*e-2*b^2*e^2)-A*e*(23*c^2*d^2-_ +-- 23*b*c*d*e+8*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(5/2)*_ +-- (c*d-b*e)^3*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+_ +-- 2/15*(15*A*c^2*d^2+2*b^2*e*(B*d+4*A*e)-b*c*d*(6*B*d+19*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^3*(c*d-b*e)^2*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*(B*d-A*e)*sqrt(b*x+c*x^2)/_ +-- (d*(c*d-b*e)*(d+e*x)^(5/2))-2/15*(4*A*e*(2*c*d-b*e)-B*d*(3*c*d+_ +-- b*e))*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))+2/15*(B*d*_ +-- (3*c^2*d^2+7*b*c*d*e-2*b^2*e^2)-A*e*(23*c^2*d^2-23*b*c*d*e+_ +-- 8*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 958 + +--S 959 of 1457 +--a0:=integrate(t0,x) +--E 959 + +--S 960 of 1457 +--m0:=a0-r0 +--E 960 + +--S 961 of 1457 +--d0:=D(m0,x) +--E 961 + +)clear all + +--S 962 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1457 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(7/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2/15*(30*A*c^4*d^3+48*b^4*B*e^3-15*b*c^3*d^2*(B*d+3*A*e)-_ +-- 8*b^3*c*e^2*(16*B*d+5*A*e)+b^2*c^2*d*e*(103*B*d+95*A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^4*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*e*(c*d-b*e)*(15*A*c^3*d^2-_ +-- 48*b^3*B*e^2-15*b*c^2*d*(4*B*d+5*A*e)+8*b^2*c*e*(13*B*d+5*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/5*e*(10*A*c^2*d+6*b^2*B*e-5*b*c*(B*d+A*e))*_ +-- (d+e*x)^(3/2)*sqrt(b*x+c*x^2)/(b^2*c^2)-2*(b*B-2*A*c)*e*_ +-- (d+e*x)^(5/2)*sqrt(b*x+c*x^2)/(b^2*c)+2/15*e*(30*A*c^3*d^2-_ +-- 24*b^3*B*e^2-15*b*c^2*d*(B*d+2*A*e)+b^2*c*e*(43*B*d+20*A*e))*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c^3) +--E 963 + +--S 964 of 1457 +--a0:=integrate(t0,x) +--E 964 + +--S 965 of 1457 +--m0:=a0-r0 +--E 965 + +--S 966 of 1457 +--d0:=D(m0,x) +--E 966 + +)clear all + +--S 967 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1457 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(5/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2/3*(6*A*c^3*d^2-8*b^3*B*e^2-3*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ +-- (13*B*d+6*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^3*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(c*d-b*e)*_ +-- (9*b*B*c*d-3*A*c^2*d-8*b^2*B*e+6*A*b*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(7/2)*sqrt(-b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2*(b*B-2*A*c)*e*(d+e*x)^(3/2)*sqrt(b*x+c*x^2)/(b^2*c)+2/3*e*_ +-- (6*A*c^2*d+4*b^2*B*e-3*b*c*(B*d+A*e))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/_ +-- (b^2*c^2) +--E 968 + +--S 969 of 1457 +--a0:=integrate(t0,x) +--E 969 + +--S 970 of 1457 +--m0:=a0-r0 +--E 970 + +--S 971 of 1457 +--d0:=D(m0,x) +--E 971 + +)clear all + +--S 972 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1457 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^2*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(2*b*B-A*c)*e*(c*d-b*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c) +--E 973 + +--S 974 of 1457 +--a0:=integrate(t0,x) +--E 974 + +--S 975 of 1457 +--m0:=a0-r0 +--E 975 + +--S 976 of 1457 +--d0:=D(m0,x) +--E 976 + +)clear all + +--S 977 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1457 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*sqrt(b*x+c*x^2))-_ +-- 2*(b*B-2*A*c)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(b*B-A*c)*e*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(3/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)) +--E 978 + +--S 979 of 1457 +--a0:=integrate(t0,x) +--E 979 + +--S 980 of 1457 +--m0:=a0-r0 +--E 980 + +--S 981 of 1457 +--d0:=D(m0,x) +--E 981 + +)clear all + +--S 982 of 1457 +t0:=(A+B*x)/((b*x+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ----------------------------------- +--R +----------+ +--R 2 +-------+ | 2 +--R (c x + b x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1457 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*d*_ +-- (c*d-b*e)*sqrt(b*x+c*x^2))+2*(b*B*d-2*A*c*d+A*b*e)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^2*(c*d-b*e)*sqrt(-d)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*A*e*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(d*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 983 + +--S 984 of 1457 +--a0:=integrate(t0,x) +--E 984 + +--S 985 of 1457 +--m0:=a0-r0 +--E 985 + +--S 986 of 1457 +--d0:=D(m0,x) +--E 986 + +)clear all + +--S 987 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------- +--R +----------+ +--R 3 2 +-------+ | 2 +--R (c e x + (b e + c d)x + b d x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1457 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*(2*A*c^2*d^2-b^2*e*(B*d-2*A*e)-_ +-- b*c*d*(B*d+2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (b^2*(-d)^(3/2)*(c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*e*(b*B*d+A*c*d-2*A*b*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(d^2*(c*d-b*e)*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2*e*(2*A*c^2*d^2-b^2*e*(B*d-2*A*e)-b*c*d*(B*d+_ +-- 2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 988 + +--S 989 of 1457 +--a0:=integrate(t0,x) +--E 989 + +--S 990 of 1457 +--m0:=a0-r0 +--E 990 + +--S 991 of 1457 +--d0:=D(m0,x) +--E 991 + +)clear all + +--S 992 of 1457 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 4 2 3 2 2 2 +-------+ +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1457 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- (d+e*x)^(3/2)*sqrt(b*x+c*x^2))-2/3*(6*A*c^3*d^3-b^2*c*d*e*(7*B*d-_ +-- 19*A*e)+2*b^3*e^2*(B*d-4*A*e)-3*b*c^2*d^2*(B*d+3*A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^2*(-d)^(5/2)*(c*d-b*e)^3*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(3*A*c^2*d^2+3*b*c*d*(2*B*d-_ +-- 5*A*e)-2*b^2*e*(B*d-4*A*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (d^3*(c*d-b*e)^2*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*e*(6*A*c^2*d^2-b^2*e*(B*d-4*A*e)-3*b*c*d*(B*d+2*A*e))*_ +-- sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-_ +-- 2/3*e*(6*A*c^3*d^3-b^2*c*d*e*(7*B*d-19*A*e)+2*b^3*e^2*(B*d-4*A*e)-_ +-- 3*b*c^2*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*_ +-- sqrt(d+e*x)) +--E 993 + +--S 994 of 1457 +--a0:=integrate(t0,x) +--E 994 + +--S 995 of 1457 +--m0:=a0-r0 +--E 995 + +--S 996 of 1457 +--d0:=D(m0,x) +--E 996 + +)clear all + +--S 997 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1457 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(7/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(d+e*x)^(5/2)*(b*(4*b*B*d-8*A*c*d+7*A*b*e)-(16*A*c^2*d-_ +-- 3*b^2*B*e-8*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^4*d^3-8*b^4*B*e^3+b^3*c*e^2*(5*B*d+2*A*e)-8*b*c^3*d^2*_ +-- (B*d+3*A*e)+b^2*c^2*d*e*(5*B*d+4*A*e))*(b+c*x)*elliptic_e(asin(_ +-- sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(b^4*c^3*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+_ +-- c*x^2))-2/3*e*(c*d-b*e)*(8*A*c^3*d^2+8*b^3*B*e^2-b^2*c*e*(B*d+_ +-- 2*A*e)-b*c^2*d*(4*B*d+5*A*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- ((-b)^(5/2)*c^(7/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*_ +-- (16*A*c^2*d-3*b^2*B*e-8*b*c*(B*d+A*e))*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/(b^4*c)-2/3*e*(16*A*c^3*d^2+4*b^3*B*e^2+b^2*c*e*_ +-- (B*d-A*e)-8*b*c^2*d*(B*d+2*A*e))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^4*c^2) +--E 998 + +--S 999 of 1457 +--a0:=integrate(t0,x) +--E 999 + +--S 1000 of 1457 +--m0:=a0-r0 +--E 1000 + +--S 1001 of 1457 +--d0:=D(m0,x) +--E 1001 + +)clear all + +--S 1002 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1457 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(5/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(d+e*x)^(3/2)*(b*(4*b*B*d-8*A*c*d+5*A*b*e)-(16*A*c^2*d-_ +-- b^2*B*e-8*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^3*d^2+2*b^3*B*e^2+b^2*c*e*(3*B*d+A*e)-8*b*c^2*d*(B*d+_ +-- 2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/_ +-- (b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*c^2*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(c*d-b*e)*_ +-- (8*A*c^2*d-2*b^2*B*e-b*c*(4*B*d+A*e))*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/((-b)^(5/2)*c^(5/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*e*(16*A*c^2*d-b^2*B*e-8*b*c*(B*d+A*e))*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/(b^4*c) +--E 1003 + +--S 1004 of 1457 +--a0:=integrate(t0,x) +--E 1004 + +--S 1005 of 1457 +--m0:=a0-r0 +--E 1005 + +--S 1006 of 1457 +--d0:=D(m0,x) +--E 1006 + +)clear all + +--S 1007 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1457 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(b*(4*b*B*d-8*A*c*d+3*A*b*e)-(16*A*c^2*d+b^2*B*e-8*b*c*_ +-- (B*d+A*e))*x)*sqrt(d+e*x)/(b^4*sqrt(b*x+c*x^2))-2/3*(16*A*c^2*d+_ +-- b^2*B*e-8*b*c*(B*d+A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (b^4*c*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*_ +-- (4*b*B*c*d-8*A*c^2*d-b^2*B*e+5*A*b*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/((-b)^(5/2)*c^(3/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 1008 + +--S 1009 of 1457 +--a0:=integrate(t0,x) +--E 1009 + +--S 1010 of 1457 +--m0:=a0-r0 +--E 1010 + +--S 1011 of 1457 +--d0:=D(m0,x) +--E 1011 + +)clear all + +--S 1012 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1457 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(b*(c*d-b*e)*(4*b*B*d-8*A*c*d+A*b*e)-c*(16*A*c^2*d^2+b^2*e*_ +-- (7*B*d+A*e)-8*b*c*d*(B*d+2*A*e))*x)*sqrt(d+e*x)/(b^4*d*(c*d-b*e)*_ +-- sqrt(b*x+c*x^2))+2/3*(16*A*c^2*d^2+b^2*e*(7*B*d+A*e)-8*b*c*d*_ +-- (B*d+2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*(c*d-b*e)*sqrt(-d)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(4*b*B*d-_ +-- 8*A*c*d+A*b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 1013 + +--S 1014 of 1457 +--a0:=integrate(t0,x) +--E 1014 + +--S 1015 of 1457 +--m0:=a0-r0 +--E 1015 + +--S 1016 of 1457 +--d0:=D(m0,x) +--E 1016 + +)clear all + +--S 1017 of 1457 +t0:=(A+B*x)/((b*x+c*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ---------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 +-------+ | 2 +--R (c x + 2b c x + b x )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1457 +--r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/_ +-- (b^2*d*(c*d-b*e)*(b*x+c*x^2)^(3/2))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+_ +-- b^2*e*(3*B*d-2*A*e)-b*c*d*(4*B*d+5*A*e))+c*(16*A*c^3*d^3-b^3*e^2*_ +-- (3*B*d-2*A*e)-8*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(13*B*d+4*A*e))*x)*_ +-- sqrt(d+e*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^3*d^3-b^3*e^2*(3*B*d-2*A*e)-8*b*c^2*d^2*(B*d+3*A*e)+_ +-- b^2*c*d*e*(13*B*d+4*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*(-d)^(3/2)*_ +-- (c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*_ +-- (8*A*c^2*d^2+b^2*e*(3*B*d-2*A*e)-b*c*d*(4*B*d+5*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d^2*(c*d-b*e)*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 1018 + +--S 1019 of 1457 +--a0:=integrate(t0,x) +--E 1019 + +--S 1020 of 1457 +--m0:=a0-r0 +--E 1020 + +--S 1021 of 1457 +--d0:=D(m0,x) +--E 1021 + +)clear all + +--S 1022 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 5 2 4 2 3 2 2 +-------+ +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1457 +--r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- (b*x+c*x^2)^(3/2)*sqrt(d+e*x))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+b^2*_ +-- e*(3*B*d-4*A*e)-b*c*d*(4*B*d+3*A*e))+c*(16*A*c^3*d^3+15*b^2*B*_ +-- c*d^2*e-b^3*e^2*(3*B*d-4*A*e)-8*b*c^2*d^2*(B*d+3*A*e))*x)/_ +-- (b^4*d^2*(c*d-b*e)^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*_ +-- (16*A*c^4*d^4-b^3*c*d*e^2*(9*B*d-7*A*e)-8*b*c^3*d^3*(B*d+4*A*e)+_ +-- b^2*c^2*d^2*e*(19*B*d+9*A*e)+b^4*(6*B*d*e^3-8*A*e^4))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^4*(-d)^(5/2)*(c*d-b*e)^3*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(8*A*c^3*d^3+3*b^2*c*d*e*_ +-- (2*B*d-A*e)-b*c^2*d^2*(4*B*d+9*A*e)-b^3*(6*B*d*e^2-8*A*e^3))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d^3*(c*d-b*e)^2*_ +-- sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(16*A*c^4*d^4-_ +-- b^3*c*d*e^2*(9*B*d-7*A*e)-8*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*_ +-- e*(19*B*d+9*A*e)+b^4*(6*B*d*e^3-8*A*e^4))*sqrt(b*x+c*x^2)/_ +-- (b^4*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 1023 + +--S 1024 of 1457 +--a0:=integrate(t0,x) +--E 1024 + +--S 1025 of 1457 +--m0:=a0-r0 +--E 1025 + +--S 1026 of 1457 +--d0:=D(m0,x) +--E 1026 + +)clear all + +--S 1027 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + A c x + B a x + A a)(e x + d) +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1457 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(3*B*c*d^2-2*A*_ + c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^4*(2+m))-c*(3*B*d-A*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R (A c e - 3B c d)m + (7A c e - 21B c d)m + (14A c e - 42B c d)m +--R + +--R 8A c e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 2 2 2 +--R (B a e - 2A c d e + 3B c d )m + (8B a e - 16A c d e + 24B c d )m +--R + +--R 2 2 2 2 +--R (19B a e - 38A c d e + 57B c d )m + 12B a e - 24A c d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (A a e - B a d e + A c d e - B c d )m +--R + +--R 3 2 2 3 2 +--R (9A a e - 9B a d e + 9A c d e - 9B c d )m +--R + +--R 3 2 2 3 3 +--R (26A a e - 26B a d e + 26A c d e - 26B c d )m + 24A a e +--R + +--R 2 2 3 +--R - 24B a d e + 24A c d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R (A c e + B c d e )m + (7A c e + 3B c d e )m +--R + +--R 4 3 4 +--R (14A c e + 2B c d e )m + 8A c e +--R * +--R 3 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (B a e + A c d e )m + (8B a e + 5A c d e - 3B c d e )m +--R + +--R 4 3 2 2 4 +--R (19B a e + 4A c d e - 3B c d e )m + 12B a e +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (A a e + B a d e )m + (9A a e + 7B a d e - 2A c d e )m +--R + +--R 4 3 2 2 3 4 +--R (26A a e + 12B a d e - 8A c d e + 6B c d e)m + 24A a e +--R * +--R x +--R + +--R 3 3 3 2 2 2 +--R A a d e m + (9A a d e - B a d e )m +--R + +--R 3 2 2 3 3 2 2 +--R (26A a d e - 7B a d e + 2A c d e)m + 24A a d e - 12B a d e +--R + +--R 3 4 +--R 8A c d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 1029 + +--S 1030 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R (A c e + B c d e )m + (7A c e + 3B c d e )m +--R + +--R 4 3 4 +--R (14A c e + 2B c d e )m + 8A c e +--R * +--R 3 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (B a e + A c d e )m + (8B a e + 5A c d e - 3B c d e )m +--R + +--R 4 3 2 2 4 +--R (19B a e + 4A c d e - 3B c d e )m + 12B a e +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (A a e + B a d e )m + (9A a e + 7B a d e - 2A c d e )m +--R + +--R 4 3 2 2 3 4 +--R (26A a e + 12B a d e - 8A c d e + 6B c d e)m + 24A a e +--R * +--R x +--R + +--R 3 3 3 2 2 2 +--R A a d e m + (9A a d e - B a d e )m +--R + +--R 3 2 2 3 3 2 2 +--R (26A a d e - 7B a d e + 2A c d e)m + 24A a d e - 12B a d e +--R + +--R 3 4 +--R 8A c d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 2 m + 4 +--R (- B c m - 6B c m - 11B c m - 6B c)(e x + d) +--R + +--R 3 2 +--R (- A c e + 3B c d)m + (- 7A c e + 21B c d)m +--R + +--R (- 14A c e + 42B c d)m - 8A c e + 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R (- B a e + 2A c d e - 3B c d )m +--R + +--R 2 2 2 +--R (- 8B a e + 16A c d e - 24B c d )m +--R + +--R 2 2 2 2 +--R (- 19B a e + 38A c d e - 57B c d )m - 12B a e + 24A c d e - 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (- A a e + B a d e - A c d e + B c d )m +--R + +--R 3 2 2 3 2 +--R (- 9A a e + 9B a d e - 9A c d e + 9B c d )m +--R + +--R 3 2 2 3 3 +--R (- 26A a e + 26B a d e - 26A c d e + 26B c d )m - 24A a e +--R + +--R 2 2 3 +--R 24B a d e - 24A c d e + 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1031 + +)clear all + +--S 1032 of 1457 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 5 4 2 3 6 +--R B c e x + (A c e + 5B c d e )x + (B a e + 5A c d e + 10B c d e )x +--R + +--R 5 4 2 3 3 2 5 +--R (A a e + 5B a d e + 10A c d e + 10B c d e )x +--R + +--R 4 2 3 3 2 4 4 +--R (5A a d e + 10B a d e + 10A c d e + 5B c d e)x +--R + +--R 2 3 3 2 4 5 3 +--R (10A a d e + 10B a d e + 5A c d e + B c d )x +--R + +--R 3 2 4 5 2 4 5 5 +--R (10A a d e + 5B a d e + A c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1032 + +--S 1033 of 1457 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^6/e^4+1/7*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^7/e^4-1/8*c*(3*B*d-A*e)*(d+e*x)^8/e^4+1/9*B*_ + c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 1 9 5 8 10 2 7 7 +--R (- B a e + - A c d e + -- B c d e )x +--R 7 7 7 +--R + +--R 1 9 5 8 5 2 7 5 3 6 6 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 6 6 3 3 +--R + +--R 8 2 7 3 6 4 5 5 +--R (A a d e + 2B a d e + 2A c d e + B c d e )x +--R + +--R 5 2 7 5 3 6 5 4 5 1 5 4 4 +--R (- A a d e + - B a d e + - A c d e + - B c d e )x +--R 2 2 4 4 +--R + +--R 10 3 6 5 4 5 1 5 4 3 5 4 5 1 5 4 2 +--R (-- A a d e + - B a d e + - A c d e )x + (- A a d e + - B a d e )x +--R 3 3 3 2 2 +--R + +--R 5 4 1 6 3 1 7 2 1 8 1 9 +--R A a d e x + - A a d e - -- B a d e + --- A c d e - --- B c d +--R 6 42 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1033 + +--S 1034 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 9 1 5 5 4 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 1 5 5 4 10 2 3 7 +--R (- B a e + - A c d e + -- B c d e )x +--R 7 7 7 +--R + +--R 1 5 5 4 5 2 3 5 3 2 6 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 6 6 3 3 +--R + +--R 4 2 3 3 2 4 5 +--R (A a d e + 2B a d e + 2A c d e + B c d e)x +--R + +--R 5 2 3 5 3 2 5 4 1 5 4 +--R (- A a d e + - B a d e + - A c d e + - B c d )x +--R 2 2 4 4 +--R + +--R 10 3 2 5 4 1 5 3 5 4 1 5 2 5 +--R (-- A a d e + - B a d e + - A c d )x + (- A a d e + - B a d )x + A a d x +--R 3 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1034 + +--S 1035 of 1457 +m0:=a0-r0 +--R +--R +--R 1 6 3 1 7 2 1 8 1 9 +--R - - A a d e + -- B a d e - --- A c d e + --- B c d +--R 6 42 168 504 +--R (4) ----------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1035 + +--S 1036 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1036 + +)clear all + +--S 1037 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 4 3 2 2 5 +--R B c e x + (A c e + 4B c d e )x + (B a e + 4A c d e + 6B c d e )x +--R + +--R 4 3 2 2 3 4 +--R (A a e + 4B a d e + 6A c d e + 4B c d e)x +--R + +--R 3 2 2 3 4 3 +--R (4A a d e + 6B a d e + 4A c d e + B c d )x +--R + +--R 2 2 3 4 2 3 4 4 +--R (6A a d e + 4B a d e + A c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1037 + +--S 1038 of 1457 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^5/e^4+1/6*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^6/e^4-1/7*c*(3*B*d-A*e)*(d+e*x)^7/e^4+1/8*B*c*_ + (d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 8 4 7 7 +--R - B c e x + (- A c e + - B c d e )x +--R 8 7 7 +--R + +--R 1 8 2 7 2 6 6 +--R (- B a e + - A c d e + B c d e )x +--R 6 3 +--R + +--R 1 8 4 7 6 2 6 4 3 5 5 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 7 3 2 6 3 5 1 4 4 4 +--R (A a d e + - B a d e + A c d e + - B c d e )x +--R 2 4 +--R + +--R 2 6 4 3 5 1 4 4 3 3 5 1 4 4 2 +--R (2A a d e + - B a d e + - A c d e )x + (2A a d e + - B a d e )x +--R 3 3 2 +--R + +--R 4 4 1 5 3 1 6 2 1 7 1 8 +--R A a d e x + - A a d e - -- B a d e + --- A c d e - --- B c d +--R 5 30 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1038 + +--S 1039 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 8 1 4 4 3 7 +--R - B c e x + (- A c e + - B c d e )x +--R 8 7 7 +--R + +--R 1 4 2 3 2 2 6 +--R (- B a e + - A c d e + B c d e )x +--R 6 3 +--R + +--R 1 4 4 3 6 2 2 4 3 5 +--R (- A a e + - B a d e + - A c d e + - B c d e)x +--R 5 5 5 5 +--R + +--R 3 3 2 2 3 1 4 4 +--R (A a d e + - B a d e + A c d e + - B c d )x +--R 2 4 +--R + +--R 2 2 4 3 1 4 3 3 1 4 2 4 +--R (2A a d e + - B a d e + - A c d )x + (2A a d e + - B a d )x + A a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1039 + +--S 1040 of 1457 +m0:=a0-r0 +--R +--R +--R 1 5 3 1 6 2 1 7 1 8 +--R - - A a d e + -- B a d e - --- A c d e + --- B c d +--R 5 30 105 280 +--R (4) ----------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1040 + +--S 1041 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1041 + +)clear all + +--S 1042 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 3 2 2 4 +--R B c e x + (A c e + 3B c d e )x + (B a e + 3A c d e + 3B c d e)x +--R + +--R 3 2 2 3 3 +--R (A a e + 3B a d e + 3A c d e + B c d )x +--R + +--R 2 2 3 2 2 3 3 +--R (3A a d e + 3B a d e + A c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1042 + +--S 1043 of 1457 +r0:=-1/4*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^4/e^4+1/5*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^5/e^4-1/6*c*(3*B*d-A*e)*(d+e*x)^6/e^4+_ + 1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 7 1 6 6 +--R - B c e x + (- A c e + - B c d e )x +--R 7 6 2 +--R + +--R 1 7 3 6 3 2 5 5 +--R (- B a e + - A c d e + - B c d e )x +--R 5 5 5 +--R + +--R 1 7 3 6 3 2 5 1 3 4 4 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 6 2 5 1 3 4 3 3 2 5 1 3 4 2 +--R (A a d e + B a d e + - A c d e )x + (- A a d e + - B a d e )x +--R 3 2 2 +--R + +--R 3 4 1 4 3 1 5 2 1 6 1 7 +--R A a d e x + - A a d e - -- B a d e + -- A c d e - --- B c d +--R 4 20 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1043 + +--S 1044 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 7 1 3 1 2 6 +--R - B c e x + (- A c e + - B c d e )x +--R 7 6 2 +--R + +--R 1 3 3 2 3 2 5 +--R (- B a e + - A c d e + - B c d e)x +--R 5 5 5 +--R + +--R 1 3 3 2 3 2 1 3 4 +--R (- A a e + - B a d e + - A c d e + - B c d )x +--R 4 4 4 4 +--R + +--R 2 2 1 3 3 3 2 1 3 2 3 +--R (A a d e + B a d e + - A c d )x + (- A a d e + - B a d )x + A a d x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1044 + +--S 1045 of 1457 +m0:=a0-r0 +--R +--R +--R 1 4 3 1 5 2 1 6 1 7 +--R - - A a d e + -- B a d e - -- A c d e + --- B c d +--R 4 20 60 140 +--R (4) ---------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1045 + +--S 1046 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1046 + +)clear all + +--S 1047 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 2 2 3 +--R B c e x + (A c e + 2B c d e)x + (B a e + 2A c d e + B c d )x +--R + +--R 2 2 2 2 2 +--R (A a e + 2B a d e + A c d )x + (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1047 + +--S 1048 of 1457 +r0:=a*A*d^2*x+1/2*a*d*(B*d+2*A*e)*x^2+1/3*(A*c*d^2+2*a*B*d*e+a*A*e^2)*x^3+_ + 1/4*(B*c*d^2+2*A*c*d*e+a*B*e^2)*x^4+1/5*c*e*(2*B*d+A*e)*x^5+_ + 1/6*B*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - B c e x + (- A c e + - B c d e)x + (- B a e + - A c d e + - B c d )x +--R 6 5 5 4 2 4 +--R + +--R 1 2 2 1 2 3 1 2 2 2 +--R (- A a e + - B a d e + - A c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1048 + +--S 1049 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - B c e x + (- A c e + - B c d e)x + (- B a e + - A c d e + - B c d )x +--R 6 5 5 4 2 4 +--R + +--R 1 2 2 1 2 3 1 2 2 2 +--R (- A a e + - B a d e + - A c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1049 + +--S 1050 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1050 + +--S 1051 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1051 + +)clear all + +--S 1052 of 1457 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + (A c e + B c d)x + (B a e + A c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 1052 + +--S 1053 of 1457 +r0:=a*A*d*x+1/2*a*(B*d+A*e)*x^2+1/3*(A*c*d+a*B*e)*x^3+1/4*c*(B*d+A*e)*x^4+_ + 1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 4 1 1 3 +--R - B c e x + (- A c e + - B c d)x + (- B a e + - A c d)x +--R 5 4 4 3 3 +--R + +--R 1 1 2 +--R (- A a e + - B a d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1053 + +--S 1054 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 1 1 4 1 1 3 +--R - B c e x + (- A c e + - B c d)x + (- B a e + - A c d)x +--R 5 4 4 3 3 +--R + +--R 1 1 2 +--R (- A a e + - B a d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1054 + +--S 1055 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1055 + +--S 1056 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1056 + +)clear all + +--S 1057 of 1457 +t0:=(A+B*x)*(a+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + A c x + B a x + A a +--R Type: Polynomial(Integer) +--E 1057 + +--S 1058 of 1457 +r0:=a*A*x+1/2*a*B*x^2+1/3*A*c*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 3 1 2 +--R (2) - B c x + - A c x + - B a x + A a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1058 + +--S 1059 of 1457 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 3 1 2 +--R (3) - B c x + - A c x + - B a x + A a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1059 + +--S 1060 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1060 + +--S 1061 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1061 + +)clear all + +--S 1062 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1062 + +--S 1063 of 1457 +r0:=(B*c*d^2-A*c*d*e+a*B*e^2)*x/e^3-1/2*c*(B*d-A*e)*x^2/e^2+1/3*B*c*x^3/e-_ + (B*d-A*e)*(c*d^2+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 3 3 3 +--R (6A a e - 6B a d e + 6A c d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 3 2 2 +--R (3A c e - 3B c d e )x + (6B a e - 6A c d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 3 3 +--R (6A a e - 6B a d e + 6A c d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 3 2 2 +--R (3A c e - 3B c d e )x + (6B a e - 6A c d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 1064 + +--S 1065 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1066 + +)clear all + +--S 1067 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1067 + +--S 1068 of 1457 +r0:=-c*(2*B*d-A*e)*x/e^3+1/2*B*c*x^2/e^2+(B*d-A*e)*(c*d^2+a*e^2)/_ + (e^4*(d+e*x))+(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((2B a e - 4A c d e + 6B c d e)x + 2B a d e - 4A c d e + 6B c d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 2 2 3 +--R B c e x + (2A c e - 3B c d e )x + (2A c d e - 4B c d e)x - 2A a e +--R + +--R 2 2 3 +--R 2B a d e - 2A c d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 +--R ((2B a e - 4A c d e + 6B c d e)x + 2B a d e - 4A c d e + 6B c d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 2 2 3 +--R B c e x + (2A c e - 3B c d e )x + (2A c d e - 4B c d e)x - 2A a e +--R + +--R 2 2 3 +--R 2B a d e - 2A c d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 1069 + +--S 1070 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1071 + +)clear all + +--S 1072 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1072 + +--S 1073 of 1457 +r0:=B*c*x/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^2)+(-3*B*c*d^2+_ + 2*A*c*d*e-a*B*e^2)/(e^4*(d+e*x))-c*(3*B*d-A*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 +--R (2A c e - 6B c d e )x + (4A c d e - 12B c d e)x + 2A c d e +--R + +--R 3 +--R - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 3 +--R 2B c e x + 4B c d e x + (- 2B a e + 4A c d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R - B a d e + 3A c d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 2 +--R (2A c e - 6B c d e )x + (4A c d e - 12B c d e)x + 2A c d e +--R + +--R 3 +--R - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 3 +--R 2B c e x + 4B c d e x + (- 2B a e + 4A c d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R - B a d e + 3A c d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 1074 + +--S 1075 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1076 + +)clear all + +--S 1077 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1077 + +--S 1078 of 1457 +r0:=1/3*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^2)+c*(3*B*d-A*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 +--R (- 6A c e + 18B c d e )x + (- 3B a e - 6A c d e + 27B c d e)x +--R + +--R 3 2 2 3 +--R - 2A a e - B a d e - 2A c d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 +--R (- 6A c e + 18B c d e )x + (- 3B a e - 6A c d e + 27B c d e)x +--R + +--R 3 2 2 3 +--R - 2A a e - B a d e - 2A c d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 1079 + +--S 1080 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1081 + +)clear all + +--S 1082 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1082 + +--S 1083 of 1457 +r0:=1/4*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^3)+1/2*c*(3*B*d-A*e)/(e^4*(d+e*x)^2)-_ + B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 3 3 2 2 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 1 3 1 2 2 1 3 1 2 +--R (- - B a e - - A c d e - B c d e)x - - A a e - -- B a d e +--R 3 3 4 12 +--R + +--R 1 2 1 3 +--R - -- A c d e - - B c d +--R 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1083 + +--S 1084 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 12B c e x + (- 6A c e - 18B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 4B a e - 4A c d e - 12B c d e)x - 3A a e - B a d e - A c d e +--R + +--R 3 +--R - 3B c d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1084 + +--S 1085 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1086 + +)clear all + +--S 1087 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1087 + +--S 1088 of 1457 +r0:=1/5*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^5)+1/4*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^4)+1/3*c*(3*B*d-A*e)/(e^4*(d+e*x)^3)-_ + 1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 2 +--R + +--R 1 3 1 2 1 2 1 3 1 2 +--R (- - B a e - - A c d e - - B c d e)x - - A a e - -- B a d e +--R 4 6 4 5 20 +--R + +--R 1 2 1 3 +--R - -- A c d e - -- B c d +--R 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1088 + +--S 1089 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 30B c e x + (- 20A c e - 30B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 15B a e - 10A c d e - 15B c d e)x - 12A a e - 3B a d e - 2A c d e +--R + +--R 3 +--R - 3B c d +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 1089 + +--S 1090 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1091 + +)clear all + +--S 1092 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + A c x + B a x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1092 + +--S 1093 of 1457 +r0:=1/6*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^6)+1/5*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^5)+1/4*c*(3*B*d-A*e)/(e^4*(d+e*x)^4)-_ + 1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 +--R - - B c e x + (- - A c e - - B c d e )x +--R 3 4 4 +--R + +--R 1 3 1 2 1 2 1 3 1 2 +--R (- - B a e - -- A c d e - -- B c d e)x - - A a e - -- B a d e +--R 5 10 10 6 30 +--R + +--R 1 2 1 3 +--R - -- A c d e - -- B c d +--R 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1093 + +--S 1094 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 20B c e x + (- 15A c e - 15B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 12B a e - 6A c d e - 6B c d e)x - 10A a e - 2B a d e - A c d e +--R + +--R 3 +--R - B c d +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 4 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 1094 + +--S 1095 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1096 + +)clear all + +--S 1097 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 m +--R (1) (B c x + A c x + 2B a c x + 2A a c x + B a x + A a )(e x + d) +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1457 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))+(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^6*(2+m))-2*c*_ + (5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3+m)/(e^6*_ + (3+m))+2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(4+m)/(e^6*(4+m))-_ + c^2*(5*B*d-A*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 2 2 3 +--R (A c e - 5B c d)m + (16A c e - 80B c d)m + (95A c e - 475B c d)m +--R + +--R 2 2 2 2 2 2 +--R (260A c e - 1300B c d)m + (324A c e - 1620B c d)m + 144A c e +--R + +--R 2 +--R - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 5 +--R (2B a c e - 4A c d e + 10B c d )m +--R + +--R 2 2 2 2 4 +--R (34B a c e - 68A c d e + 170B c d )m +--R + +--R 2 2 2 2 3 +--R (214B a c e - 428A c d e + 1070B c d )m +--R + +--R 2 2 2 2 2 +--R (614B a c e - 1228A c d e + 3070B c d )m +--R + +--R 2 2 2 2 2 2 +--R (792B a c e - 1584A c d e + 3960B c d )m + 360B a c e - 720A c d e +--R + +--R 2 2 +--R 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 5 +--R (2A a c e - 6B a c d e + 6A c d e - 10B c d )m +--R + +--R 3 2 2 2 2 3 4 +--R (36A a c e - 108B a c d e + 108A c d e - 180B c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (242A a c e - 726B a c d e + 726A c d e - 1210B c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (744A a c e - 2232B a c d e + 2232A c d e - 3720B c d )m +--R + +--R 3 2 2 2 2 3 +--R (1016A a c e - 3048B a c d e + 3048A c d e - 5080B c d )m +--R + +--R 3 2 2 2 2 3 +--R 480A a c e - 1440B a c d e + 1440A c d e - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 3 2 2 2 3 2 4 5 +--R (B a e - 4A a c d e + 6B a c d e - 4A c d e + 5B c d )m +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (19B a e - 76A a c d e + 114B a c d e - 76A c d e + 95B c d )m +--R + +--R 2 4 3 2 2 2 3 +--R 137B a e - 548A a c d e + 822B a c d e - 548A c d e +--R + +--R 2 4 +--R 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R 461B a e - 1844A a c d e + 2766B a c d e - 1844A c d e +--R + +--R 2 4 +--R 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R 702B a e - 2808A a c d e + 4212B a c d e - 2808A c d e +--R + +--R 2 4 +--R 3510B c d +--R * +--R m +--R + +--R 2 4 3 2 2 2 3 2 4 +--R 360B a e - 1440A a c d e + 2160B a c d e - 1440A c d e + 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 5 +--R (A a e - B a d e + 2A a c d e - 2B a c d e + A c d e - B c d )m +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R 20A a e - 20B a d e + 40A a c d e - 40B a c d e + 20A c d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 155A a e - 155B a d e + 310A a c d e - 310B a c d e +--R + +--R 2 4 2 5 +--R 155A c d e - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 580A a e - 580B a d e + 1160A a c d e - 1160B a c d e +--R + +--R 2 4 2 5 +--R 580A c d e - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 1044A a e - 1044B a d e + 2088A a c d e - 2088B a c d e +--R + +--R 2 4 2 5 +--R 1044A c d e - 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 720A a e - 720B a d e + 1440A a c d e - 1440B a c d e +--R + +--R 2 4 2 5 +--R 720A c d e - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 2 6 2 5 4 +--R (A c e + B c d e )m + (16A c e + 10B c d e )m +--R + +--R 2 6 2 5 3 2 6 2 5 2 +--R (95A c e + 35B c d e )m + (260A c e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R (324A c e + 24B c d e )m + 144A c e +--R * +--R 5 +--R x +--R + +--R 6 2 5 5 6 2 5 2 2 4 4 +--R (2B a c e + A c d e )m + (34B a c e + 12A c d e - 5B c d e )m +--R + +--R 6 2 5 2 2 4 3 +--R (214B a c e + 47A c d e - 30B c d e )m +--R + +--R 6 2 5 2 2 4 2 +--R (614B a c e + 72A c d e - 55B c d e )m +--R + +--R 6 2 5 2 2 4 6 +--R (792B a c e + 36A c d e - 30B c d e )m + 360B a c e +--R * +--R 4 +--R x +--R + +--R 6 5 5 +--R (2A a c e + 2B a c d e )m +--R + +--R 6 5 2 2 4 4 +--R (36A a c e + 28B a c d e - 4A c d e )m +--R + +--R 6 5 2 2 4 2 3 3 3 +--R (242A a c e + 130B a c d e - 36A c d e + 20B c d e )m +--R + +--R 6 5 2 2 4 2 3 3 2 +--R (744A a c e + 224B a c d e - 80A c d e + 60B c d e )m +--R + +--R 6 5 2 2 4 2 3 3 +--R (1016A a c e + 120B a c d e - 48A c d e + 40B c d e )m +--R + +--R 6 +--R 480A a c e +--R * +--R 3 +--R x +--R + +--R 2 6 5 5 +--R (B a e + 2A a c d e )m +--R + +--R 2 6 5 2 4 4 +--R (19B a e + 32A a c d e - 6B a c d e )m +--R + +--R 2 6 5 2 4 2 3 3 3 +--R (137B a e + 178A a c d e - 72B a c d e + 12A c d e )m +--R + +--R 2 6 5 2 4 2 3 3 +--R 461B a e + 388A a c d e - 246B a c d e + 84A c d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 5 2 4 2 3 3 +--R 702B a e + 240A a c d e - 180B a c d e + 72A c d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R m +--R + +--R 2 6 +--R 360B a e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 5 2 6 2 5 2 4 4 +--R (A a e + B a d e )m + (20A a e + 18B a d e - 4A a c d e )m +--R + +--R 2 6 2 5 2 4 3 3 3 +--R (155A a e + 119B a d e - 60A a c d e + 12B a c d e )m +--R + +--R 2 6 2 5 2 4 3 3 +--R 580A a e + 342B a d e - 296A a c d e + 132B a c d e +--R + +--R 2 4 2 +--R - 24A c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 2 4 3 3 +--R 1044A a e + 360B a d e - 480A a c d e + 360B a c d e +--R + +--R 2 4 2 2 5 +--R - 144A c d e + 120B c d e +--R * +--R m +--R + +--R 2 6 +--R 720A a e +--R * +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A a d e m + (20A a d e - B a d e )m +--R + +--R 2 5 2 2 4 3 3 3 +--R (155A a d e - 18B a d e + 4A a c d e )m +--R + +--R 2 5 2 2 4 3 3 4 2 2 +--R (580A a d e - 119B a d e + 60A a c d e - 12B a c d e )m +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 1044A a d e - 342B a d e + 296A a c d e - 132B a c d e +--R + +--R 2 5 +--R 24A c d e +--R * +--R m +--R + +--R 2 5 2 2 4 3 3 4 2 2 5 +--R 720A a d e - 360B a d e + 480A a c d e - 360B a c d e + 144A c d e +--R + +--R 2 6 +--R - 120B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Union(Expression(Integer),...) +--E 1099 + +--S 1100 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 2 6 2 5 4 +--R (A c e + B c d e )m + (16A c e + 10B c d e )m +--R + +--R 2 6 2 5 3 2 6 2 5 2 +--R (95A c e + 35B c d e )m + (260A c e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R (324A c e + 24B c d e )m + 144A c e +--R * +--R 5 +--R x +--R + +--R 6 2 5 5 +--R (2B a c e + A c d e )m +--R + +--R 6 2 5 2 2 4 4 +--R (34B a c e + 12A c d e - 5B c d e )m +--R + +--R 6 2 5 2 2 4 3 +--R (214B a c e + 47A c d e - 30B c d e )m +--R + +--R 6 2 5 2 2 4 2 +--R (614B a c e + 72A c d e - 55B c d e )m +--R + +--R 6 2 5 2 2 4 6 +--R (792B a c e + 36A c d e - 30B c d e )m + 360B a c e +--R * +--R 4 +--R x +--R + +--R 6 5 5 +--R (2A a c e + 2B a c d e )m +--R + +--R 6 5 2 2 4 4 +--R (36A a c e + 28B a c d e - 4A c d e )m +--R + +--R 6 5 2 2 4 2 3 3 3 +--R (242A a c e + 130B a c d e - 36A c d e + 20B c d e )m +--R + +--R 6 5 2 2 4 2 3 3 2 +--R (744A a c e + 224B a c d e - 80A c d e + 60B c d e )m +--R + +--R 6 5 2 2 4 2 3 3 +--R (1016A a c e + 120B a c d e - 48A c d e + 40B c d e )m +--R + +--R 6 +--R 480A a c e +--R * +--R 3 +--R x +--R + +--R 2 6 5 5 +--R (B a e + 2A a c d e )m +--R + +--R 2 6 5 2 4 4 +--R (19B a e + 32A a c d e - 6B a c d e )m +--R + +--R 2 6 5 2 4 2 3 3 3 +--R (137B a e + 178A a c d e - 72B a c d e + 12A c d e )m +--R + +--R 2 6 5 2 4 2 3 3 +--R 461B a e + 388A a c d e - 246B a c d e + 84A c d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 5 2 4 2 3 3 +--R 702B a e + 240A a c d e - 180B a c d e + 72A c d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R m +--R + +--R 2 6 +--R 360B a e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 5 2 6 2 5 2 4 4 +--R (A a e + B a d e )m + (20A a e + 18B a d e - 4A a c d e )m +--R + +--R 2 6 2 5 2 4 3 3 3 +--R (155A a e + 119B a d e - 60A a c d e + 12B a c d e )m +--R + +--R 2 6 2 5 2 4 3 3 +--R 580A a e + 342B a d e - 296A a c d e + 132B a c d e +--R + +--R 2 4 2 +--R - 24A c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 2 4 3 3 +--R 1044A a e + 360B a d e - 480A a c d e + 360B a c d e +--R + +--R 2 4 2 2 5 +--R - 144A c d e + 120B c d e +--R * +--R m +--R + +--R 2 6 +--R 720A a e +--R * +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A a d e m + (20A a d e - B a d e )m +--R + +--R 2 5 2 2 4 3 3 3 +--R (155A a d e - 18B a d e + 4A a c d e )m +--R + +--R 2 5 2 2 4 3 3 4 2 2 +--R (580A a d e - 119B a d e + 60A a c d e - 12B a c d e )m +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 1044A a d e - 342B a d e + 296A a c d e - 132B a c d e +--R + +--R 2 5 +--R 24A c d e +--R * +--R m +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 720A a d e - 360B a d e + 480A a c d e - 360B a c d e +--R + +--R 2 5 2 6 +--R 144A c d e - 120B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (- B c m - 15B c m - 85B c m - 225B c m - 274B c m - 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R (- A c e + 5B c d)m + (- 16A c e + 80B c d)m +--R + +--R 2 2 3 2 2 2 +--R (- 95A c e + 475B c d)m + (- 260A c e + 1300B c d)m +--R + +--R 2 2 2 2 +--R (- 324A c e + 1620B c d)m - 144A c e + 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 5 +--R (- 2B a c e + 4A c d e - 10B c d )m +--R + +--R 2 2 2 2 4 +--R (- 34B a c e + 68A c d e - 170B c d )m +--R + +--R 2 2 2 2 3 +--R (- 214B a c e + 428A c d e - 1070B c d )m +--R + +--R 2 2 2 2 2 +--R (- 614B a c e + 1228A c d e - 3070B c d )m +--R + +--R 2 2 2 2 2 +--R (- 792B a c e + 1584A c d e - 3960B c d )m - 360B a c e +--R + +--R 2 2 2 +--R 720A c d e - 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 5 +--R (- 2A a c e + 6B a c d e - 6A c d e + 10B c d )m +--R + +--R 3 2 2 2 2 3 4 +--R (- 36A a c e + 108B a c d e - 108A c d e + 180B c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (- 242A a c e + 726B a c d e - 726A c d e + 1210B c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (- 744A a c e + 2232B a c d e - 2232A c d e + 3720B c d )m +--R + +--R 3 2 2 2 2 3 +--R (- 1016A a c e + 3048B a c d e - 3048A c d e + 5080B c d )m +--R + +--R 3 2 2 2 2 3 +--R - 480A a c e + 1440B a c d e - 1440A c d e + 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 3 2 2 2 3 2 4 5 +--R (- B a e + 4A a c d e - 6B a c d e + 4A c d e - 5B c d )m +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (- 19B a e + 76A a c d e - 114B a c d e + 76A c d e - 95B c d )m +--R + +--R 2 4 3 2 2 2 3 +--R - 137B a e + 548A a c d e - 822B a c d e + 548A c d e +--R + +--R 2 4 +--R - 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R - 461B a e + 1844A a c d e - 2766B a c d e + 1844A c d e +--R + +--R 2 4 +--R - 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R - 702B a e + 2808A a c d e - 4212B a c d e + 2808A c d e +--R + +--R 2 4 +--R - 3510B c d +--R * +--R m +--R + +--R 2 4 3 2 2 2 3 +--R - 360B a e + 1440A a c d e - 2160B a c d e + 1440A c d e +--R + +--R 2 4 +--R - 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - A a e + B a d e - 2A a c d e + 2B a c d e - A c d e +--R + +--R 2 5 +--R B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 20A a e + 20B a d e - 40A a c d e + 40B a c d e - 20A c d e +--R + +--R 2 5 +--R 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R - 155A a e + 155B a d e - 310A a c d e + 310B a c d e +--R + +--R 2 4 2 5 +--R - 155A c d e + 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R - 580A a e + 580B a d e - 1160A a c d e + 1160B a c d e +--R + +--R 2 4 2 5 +--R - 580A c d e + 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R - 1044A a e + 1044B a d e - 2088A a c d e + 2088B a c d e +--R + +--R 2 4 2 5 +--R - 1044A c d e + 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R - 720A a e + 720B a d e - 1440A a c d e + 1440B a c d e +--R + +--R 2 4 2 5 +--R - 720A c d e + 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1101 + +)clear all + +--S 1102 of 1457 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 10 2 5 2 4 9 5 2 4 2 2 3 8 +--R B c e x + (A c e + 5B c d e )x + (2B a c e + 5A c d e + 10B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 7 +--R (2A a c e + 10B a c d e + 10A c d e + 10B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 6 +--R (B a e + 10A a c d e + 20B a c d e + 10A c d e + 5B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 5 +--R (A a e + 5B a d e + 20A a c d e + 20B a c d e + 5A c d e + B c d )x +--R + +--R 2 4 2 2 3 3 2 4 2 5 4 +--R (5A a d e + 10B a d e + 20A a c d e + 10B a c d e + A c d )x +--R + +--R 2 2 3 2 3 2 4 5 3 +--R (10A a d e + 10B a d e + 10A a c d e + 2B a c d )x +--R + +--R 2 3 2 2 4 5 2 2 4 2 5 2 5 +--R (10A a d e + 5B a d e + 2A a c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1102 + +--S 1103 of 1457 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^6/e^6+1/7*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^6-1/4*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^8/e^6+2/9*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^9/e^6-1/10*c^2*(5*B*d-A*e)*(d+e*x)^10/e^6+_ + 1/11*B*c^2*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 2 11 11 1 2 11 1 2 10 10 +--R -- B c e x + (-- A c e + - B c d e )x +--R 11 10 2 +--R + +--R 2 11 5 2 10 10 2 2 9 9 +--R (- B a c e + - A c d e + -- B c d e )x +--R 9 9 9 +--R + +--R 1 11 5 10 5 2 2 9 5 2 3 8 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 1 2 11 10 10 20 2 9 10 2 3 8 5 2 4 7 7 +--R (- B a e + -- A a c d e + -- B a c d e + -- A c d e + - B c d e )x +--R 7 7 7 7 7 +--R + +--R 1 2 11 5 2 10 10 2 9 10 3 8 5 2 4 7 +--R - A a e + - B a d e + -- A a c d e + -- B a c d e + - A c d e +--R 6 6 3 3 6 +--R + +--R 1 2 5 6 +--R - B c d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 2 10 2 2 9 3 8 4 7 1 2 5 6 5 +--R (A a d e + 2B a d e + 4A a c d e + 2B a c d e + - A c d e )x +--R 5 +--R + +--R 5 2 2 9 5 2 3 8 5 4 7 1 5 6 4 +--R (- A a d e + - B a d e + - A a c d e + - B a c d e )x +--R 2 2 2 2 +--R + +--R 10 2 3 8 5 2 4 7 2 5 6 3 5 2 4 7 1 2 5 6 2 +--R (-- A a d e + - B a d e + - A a c d e )x + (- A a d e + - B a d e )x +--R 3 3 3 2 2 +--R + +--R 2 5 6 1 2 6 5 1 2 7 4 1 8 3 1 9 2 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 6 42 84 252 +--R + +--R 1 2 10 1 2 11 +--R ---- A c d e - ---- B c d +--R 1260 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1103 + +--S 1104 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 5 11 1 2 5 1 2 4 10 +--R -- B c e x + (-- A c e + - B c d e )x +--R 11 10 2 +--R + +--R 2 5 5 2 4 10 2 2 3 9 +--R (- B a c e + - A c d e + -- B c d e )x +--R 9 9 9 +--R + +--R 1 5 5 4 5 2 2 3 5 2 3 2 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 1 2 5 10 4 20 2 3 10 2 3 2 5 2 4 7 +--R (- B a e + -- A a c d e + -- B a c d e + -- A c d e + - B c d e)x +--R 7 7 7 7 7 +--R + +--R 1 2 5 5 2 4 10 2 3 10 3 2 5 2 4 +--R - A a e + - B a d e + -- A a c d e + -- B a c d e + - A c d e +--R 6 6 3 3 6 +--R + +--R 1 2 5 +--R - B c d +--R 6 +--R * +--R 6 +--R x +--R + +--R 2 4 2 2 3 3 2 4 1 2 5 5 +--R (A a d e + 2B a d e + 4A a c d e + 2B a c d e + - A c d )x +--R 5 +--R + +--R 5 2 2 3 5 2 3 2 5 4 1 5 4 +--R (- A a d e + - B a d e + - A a c d e + - B a c d )x +--R 2 2 2 2 +--R + +--R 10 2 3 2 5 2 4 2 5 3 5 2 4 1 2 5 2 2 5 +--R (-- A a d e + - B a d e + - A a c d )x + (- A a d e + - B a d )x + A a d x +--R 3 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1104 + +--S 1105 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 6 5 1 2 7 4 1 8 3 1 9 2 +--R - - A a d e + -- B a d e - -- A a c d e + --- B a c d e +--R 6 42 84 252 +--R + +--R 1 2 10 1 2 11 +--R - ---- A c d e + ---- B c d +--R 1260 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1105 + +--S 1106 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1106 + +)clear all + +--S 1107 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 4 2 3 2 2 2 7 +--R B c e x + (A c e + 4B c d e )x + (2B a c e + 4A c d e + 6B c d e )x +--R + +--R 4 3 2 2 2 2 3 6 +--R (2A a c e + 8B a c d e + 6A c d e + 4B c d e)x +--R + +--R 2 4 3 2 2 2 3 2 4 5 +--R (B a e + 8A a c d e + 12B a c d e + 4A c d e + B c d )x +--R + +--R 2 4 2 3 2 2 3 2 4 4 +--R (A a e + 4B a d e + 12A a c d e + 8B a c d e + A c d )x +--R + +--R 2 3 2 2 2 3 4 3 +--R (4A a d e + 6B a d e + 8A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 3 4 2 2 3 2 4 2 4 +--R (6A a d e + 4B a d e + 2A a c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1107 + +--S 1108 of 1457 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^5/e^6+1/6*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^6-2/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^7/e^6+1/4*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^8/e^6-1/9*c^2*(5*B*d-A*e)*(d+e*x)^9/e^6+_ + 1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 10 4 2 9 9 +--R -- B c e x + (- A c e + - B c d e )x +--R 10 9 9 +--R + +--R 1 10 1 2 9 3 2 2 8 8 +--R (- B a c e + - A c d e + - B c d e )x +--R 4 2 4 +--R + +--R 2 10 8 9 6 2 2 8 4 2 3 7 7 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 7 7 7 7 +--R + +--R 1 2 10 4 9 2 8 2 2 3 7 1 2 4 6 6 +--R (- B a e + - A a c d e + 2B a c d e + - A c d e + - B c d e )x +--R 6 3 3 6 +--R + +--R 1 2 10 4 2 9 12 2 8 8 3 7 1 2 4 6 5 +--R (- A a e + - B a d e + -- A a c d e + - B a c d e + - A c d e )x +--R 5 5 5 5 5 +--R + +--R 2 9 3 2 2 8 3 7 1 4 6 4 +--R (A a d e + - B a d e + 2A a c d e + - B a c d e )x +--R 2 2 +--R + +--R 2 2 8 4 2 3 7 2 4 6 3 2 3 7 1 2 4 6 2 +--R (2A a d e + - B a d e + - A a c d e )x + (2A a d e + - B a d e )x +--R 3 3 2 +--R + +--R 2 4 6 1 2 5 5 1 2 6 4 2 7 3 1 8 2 +--R A a d e x + - A a d e - -- B a d e + --- A a c d e - --- B a c d e +--R 5 30 105 140 +--R + +--R 1 2 9 1 2 10 +--R --- A c d e - ---- B c d +--R 630 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1108 + +--S 1109 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 10 1 2 4 4 2 3 9 +--R -- B c e x + (- A c e + - B c d e )x +--R 10 9 9 +--R + +--R 1 4 1 2 3 3 2 2 2 8 +--R (- B a c e + - A c d e + - B c d e )x +--R 4 2 4 +--R + +--R 2 4 8 3 6 2 2 2 4 2 3 7 +--R (- A a c e + - B a c d e + - A c d e + - B c d e)x +--R 7 7 7 7 +--R + +--R 1 2 4 4 3 2 2 2 2 3 1 2 4 6 +--R (- B a e + - A a c d e + 2B a c d e + - A c d e + - B c d )x +--R 6 3 3 6 +--R + +--R 1 2 4 4 2 3 12 2 2 8 3 1 2 4 5 +--R (- A a e + - B a d e + -- A a c d e + - B a c d e + - A c d )x +--R 5 5 5 5 5 +--R + +--R 2 3 3 2 2 2 3 1 4 4 +--R (A a d e + - B a d e + 2A a c d e + - B a c d )x +--R 2 2 +--R + +--R 2 2 2 4 2 3 2 4 3 2 3 1 2 4 2 2 4 +--R (2A a d e + - B a d e + - A a c d )x + (2A a d e + - B a d )x + A a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1109 + +--S 1110 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 5 5 1 2 6 4 2 7 3 1 8 2 +--R - - A a d e + -- B a d e - --- A a c d e + --- B a c d e +--R 5 30 105 140 +--R + +--R 1 2 9 1 2 10 +--R - --- A c d e + ---- B c d +--R 630 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1110 + +--S 1111 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1111 + +)clear all + +--S 1112 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 3 2 2 2 2 6 +--R B c e x + (A c e + 3B c d e )x + (2B a c e + 3A c d e + 3B c d e)x +--R + +--R 3 2 2 2 2 3 5 +--R (2A a c e + 6B a c d e + 3A c d e + B c d )x +--R + +--R 2 3 2 2 2 3 4 +--R (B a e + 6A a c d e + 6B a c d e + A c d )x +--R + +--R 2 3 2 2 2 3 3 +--R (A a e + 3B a d e + 6A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 3 2 2 2 2 3 2 3 +--R (3A a d e + 3B a d e + 2A a c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1112 + +--S 1113 of 1457 +r0:=-1/4*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^4/e^6+1/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^5/e^6-1/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^6/e^6+2/7*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^6-1/8*c^2*(5*B*d-A*e)*(d+e*x)^8/e^6+_ + 1/9*B*c^2*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 1 2 9 9 1 2 9 3 2 8 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 2 9 3 2 8 3 2 2 7 7 +--R (- B a c e + - A c d e + - B c d e )x +--R 7 7 7 +--R + +--R 1 9 8 1 2 2 7 1 2 3 6 6 +--R (- A a c e + B a c d e + - A c d e + - B c d e )x +--R 3 2 6 +--R + +--R 1 2 9 6 8 6 2 7 1 2 3 6 5 +--R (- B a e + - A a c d e + - B a c d e + - A c d e )x +--R 5 5 5 5 +--R + +--R 1 2 9 3 2 8 3 2 7 1 3 6 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d e )x +--R 4 4 2 2 +--R + +--R 2 8 2 2 7 2 3 6 3 3 2 2 7 1 2 3 6 2 +--R (A a d e + B a d e + - A a c d e )x + (- A a d e + - B a d e )x +--R 3 2 2 +--R + +--R 2 3 6 1 2 4 5 1 2 5 4 1 6 3 1 7 2 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - -- B a c d e +--R 4 20 30 70 +--R + +--R 1 2 8 1 2 9 +--R --- A c d e - --- B c d +--R 280 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1113 + +--S 1114 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 3 9 1 2 3 3 2 2 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 2 3 3 2 2 3 2 2 7 +--R (- B a c e + - A c d e + - B c d e)x +--R 7 7 7 +--R + +--R 1 3 2 1 2 2 1 2 3 6 +--R (- A a c e + B a c d e + - A c d e + - B c d )x +--R 3 2 6 +--R + +--R 1 2 3 6 2 6 2 1 2 3 5 +--R (- B a e + - A a c d e + - B a c d e + - A c d )x +--R 5 5 5 5 +--R + +--R 1 2 3 3 2 2 3 2 1 3 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d )x +--R 4 4 2 2 +--R + +--R 2 2 2 2 2 3 3 3 2 2 1 2 3 2 2 3 +--R (A a d e + B a d e + - A a c d )x + (- A a d e + - B a d )x + A a d x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1114 + +--S 1115 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 4 5 1 2 5 4 1 6 3 1 7 2 1 2 8 +--R - - A a d e + -- B a d e - -- A a c d e + -- B a c d e - --- A c d e +--R 4 20 30 70 280 +--R + +--R 1 2 9 +--R --- B c d +--R 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1115 + +--S 1116 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1116 + +)clear all + +--S 1117 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 2 2 2 2 5 +--R B c e x + (A c e + 2B c d e)x + (2B a c e + 2A c d e + B c d )x +--R + +--R 2 2 2 4 2 2 2 3 +--R (2A a c e + 4B a c d e + A c d )x + (B a e + 4A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (A a e + 2B a d e + 2A a c d )x + (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1117 + +--S 1118 of 1457 +r0:=a^2*A*d^2*x+1/2*a^2*d*(B*d+2*A*e)*x^2+1/3*a*(2*A*c*d^2+2*a*B*d*e+_ + a*A*e^2)*x^3+1/4*a*(2*B*c*d^2+4*A*c*d*e+a*B*e^2)*x^4+1/5*c*(A*c*d^2+_ + 4*a*B*d*e+2*a*A*e^2)*x^5+1/6*c*(B*c*d^2+2*A*c*d*e+2*a*B*e^2)*x^6+_ + 1/7*c^2*e*(2*B*d+A*e)*x^7+1/8*B*c^2*e^2*x^8 +--R +--R +--R (2) +--R 1 2 2 8 1 2 2 2 2 7 +--R - B c e x + (- A c e + - B c d e)x +--R 8 7 7 +--R + +--R 1 2 1 2 1 2 2 6 +--R (- B a c e + - A c d e + - B c d )x +--R 3 3 6 +--R + +--R 2 2 4 1 2 2 5 +--R (- A a c e + - B a c d e + - A c d )x +--R 5 5 5 +--R + +--R 1 2 2 1 2 4 +--R (- B a e + A a c d e + - B a c d )x +--R 4 2 +--R + +--R 1 2 2 2 2 2 2 3 2 1 2 2 2 2 2 +--R (- A a e + - B a d e + - A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1118 + +--S 1119 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 8 1 2 2 2 2 7 +--R - B c e x + (- A c e + - B c d e)x +--R 8 7 7 +--R + +--R 1 2 1 2 1 2 2 6 +--R (- B a c e + - A c d e + - B c d )x +--R 3 3 6 +--R + +--R 2 2 4 1 2 2 5 +--R (- A a c e + - B a c d e + - A c d )x +--R 5 5 5 +--R + +--R 1 2 2 1 2 4 +--R (- B a e + A a c d e + - B a c d )x +--R 4 2 +--R + +--R 1 2 2 2 2 2 2 3 2 1 2 2 2 2 2 +--R (- A a e + - B a d e + - A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1119 + +--S 1120 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1120 + +--S 1121 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1121 + +)clear all + +--S 1122 of 1457 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 2 4 +--R B c e x + (A c e + B c d)x + (2B a c e + A c d)x +--R + +--R 3 2 2 2 2 2 +--R (2A a c e + 2B a c d)x + (B a e + 2A a c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 1122 + +--S 1123 of 1457 +r0:=a^2*A*d*x+1/2*a^2*(B*d+A*e)*x^2+1/3*a*(2*A*c*d+a*B*e)*x^3+1/2*a*c*_ + (B*d+A*e)*x^4+1/5*c*(A*c*d+2*a*B*e)*x^5+1/6*c^2*(B*d+A*e)*x^6+_ + 1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 2 6 2 1 2 5 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 7 6 6 5 5 +--R + +--R 1 1 4 1 2 2 3 1 2 1 2 2 +--R (- A a c e + - B a c d)x + (- B a e + - A a c d)x + (- A a e + - B a d)x +--R 2 2 3 3 2 2 +--R + +--R 2 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1123 + +--S 1124 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 7 1 2 1 2 6 2 1 2 5 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 7 6 6 5 5 +--R + +--R 1 1 4 1 2 2 3 1 2 1 2 2 +--R (- A a c e + - B a c d)x + (- B a e + - A a c d)x + (- A a e + - B a d)x +--R 2 2 3 3 2 2 +--R + +--R 2 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1124 + +--S 1125 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1125 + +--S 1126 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1126 + +)clear all + +--S 1127 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R (1) B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R Type: Polynomial(Integer) +--E 1127 + +--S 1128 of 1457 +r0:=a^2*A*x+2/3*a*A*c*x^3+1/5*A*c^2*x^5+1/6*B*(a+c*x^2)^3/c +--R +--R +--R (2) +--R 1 3 6 1 3 5 1 2 4 2 2 3 1 2 2 2 1 3 +--R - B c x + - A c x + - B a c x + - A a c x + - B a c x + A a c x + - B a +--R 6 5 2 3 2 6 +--R ----------------------------------------------------------------------------- +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1128 + +--S 1129 of 1457 +a0:=integrate(t0,x) +--R +--R +--R 1 2 6 1 2 5 1 4 2 3 1 2 2 2 +--R (3) - B c x + - A c x + - B a c x + - A a c x + - B a x + A a x +--R 6 5 2 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1129 + +--S 1130 of 1457 +m0:=a0-r0 +--R +--R +--R 1 3 +--R - B a +--R 6 +--R (4) - ------ +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1130 + +--S 1131 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1131 + +)clear all + +--S 1132 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1132 + +--S 1133 of 1457 +r0:=(B*(c*d^2+a*e^2)^2-A*c*d*e*(c*d^2+2*a*e^2))*x/e^5-1/2*c*(B*d-A*e)*_ + (c*d^2+2*a*e^2)*x^2/e^4+1/3*c*(B*c*d^2-A*c*d*e+2*a*B*e^2)*x^3/e^3-_ + 1/4*c^2*(B*d-A*e)*x^4/e^2+1/5*B*c^2*x^5/e-(B*d-A*e)*(c*d^2+a*e^2)^2*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 3 3 2 2 4 +--R 60A a e - 60B a d e + 120A a c d e - 120B a c d e + 60A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + (15A c e - 15B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (40B a c e - 20A c d e + 20B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (60A a c e - 60B a c d e + 30A c d e - 30B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (60B a e - 120A a c d e + 120B a c d e - 60A c d e + 60B c d e)x +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 2 3 3 2 2 4 +--R 60A a e - 60B a d e + 120A a c d e - 120B a c d e + 60A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + (15A c e - 15B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (40B a c e - 20A c d e + 20B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (60A a c e - 60B a c d e + 30A c d e - 30B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (60B a e - 120A a c d e + 120B a c d e - 60A c d e + 60B c d e)x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 1134 + +--S 1135 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1136 + +)clear all + +--S 1137 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1137 + +--S 1138 of 1457 +r0:=-c*(4*B*c*d^3-3*A*c*d^2*e+4*a*B*d*e^2-2*a*A*e^3)*x/e^5+1/2*c*_ + (3*B*c*d^2-2*A*c*d*e+2*a*B*e^2)*x^2/e^4-1/3*c^2*(2*B*d-A*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x))+_ + (c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 4 2 3 2 3 2 2 4 +--R (12B a e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d e)x +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + (4A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 8A c d e + 10B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (24A a c e - 36B a c d e + 24A c d e - 30B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 5 +--R (24A a c d e - 48B a c d e + 36A c d e - 48B c d e)x - 12A a e +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 24A a c d e + 24B a c d e - 12A c d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 2 3 2 3 2 2 4 +--R (12B a e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d e)x +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + (4A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 8A c d e + 10B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (24A a c e - 36B a c d e + 24A c d e - 30B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 5 +--R (24A a c d e - 48B a c d e + 36A c d e - 48B c d e)x - 12A a e +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 24A a c d e + 24B a c d e - 12A c d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1139 + +--S 1140 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1141 + +)clear all + +--S 1142 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^3 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1142 + +--S 1143 of 1457 +r0:=c*(6*B*c*d^2-3*A*c*d*e+2*a*B*e^2)*x/e^5-1/2*c^2*(3*B*d-A*e)*x^2/e^4+_ + 1/3*B*c^2*x^3/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^2)-_ + (c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x))-_ + 2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 4 2 2 3 2 3 2 2 +--R (12A a c e - 36B a c d e + 36A c d e - 60B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (24A a c d e - 72B a c d e + 72A c d e - 120B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R 12A a c d e - 36B a c d e + 36A c d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + (3A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 12A c d e + 20B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (24B a c d e - 33A c d e + 63B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 6B a e + 24A a c d e - 24B a c d e + 6A c d e + 6B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - 3B a d e + 18A a c d e - 30B a c d e + 21A c d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 2 2 3 2 3 2 2 +--R (12A a c e - 36B a c d e + 36A c d e - 60B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (24A a c d e - 72B a c d e + 72A c d e - 120B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R 12A a c d e - 36B a c d e + 36A c d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + (3A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 12A c d e + 20B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (24B a c d e - 33A c d e + 63B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 6B a e + 24A a c d e - 24B a c d e + 6A c d e + 6B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - 3B a d e + 18A a c d e - 30B a c d e + 21A c d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 1144 + +--S 1145 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1146 + +)clear all + +--S 1147 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^4 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1147 + +--S 1148 of 1457 +r0:=-c^2*(4*B*d-A*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*(B*d-A*e)*(c*d^2+_ + a*e^2)^2/(e^6*(d+e*x)^3)-1/2*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+_ + a*B*e^2)/(e^6*(d+e*x)^2)+2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-_ + a*A*e^3)/(e^6*(d+e*x))+2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 2 4 2 2 3 3 +--R (12B a c e - 24A c d e + 60B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (36B a c d e - 72A c d e + 180B c d e )x +--R + +--R 2 3 2 3 2 2 4 3 2 2 4 +--R (36B a c d e - 72A c d e + 180B c d e)x + 12B a c d e - 24A c d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 2 4 2 2 3 3 +--R 3B c e x + (6A c e - 15B c d e )x + (18A c d e - 63B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e + 36B a c d e - 18A c d e - 9B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 3B a e - 12A a c d e + 54B a c d e - 54A c d e + 81B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 2A a e - B a d e - 4A a c d e + 22B a c d e - 26A c d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 2 2 3 3 +--R (12B a c e - 24A c d e + 60B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (36B a c d e - 72A c d e + 180B c d e )x +--R + +--R 2 3 2 3 2 2 4 3 2 2 4 +--R (36B a c d e - 72A c d e + 180B c d e)x + 12B a c d e - 24A c d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 2 4 2 2 3 3 +--R 3B c e x + (6A c e - 15B c d e )x + (18A c d e - 63B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e + 36B a c d e - 18A c d e - 9B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 3B a e - 12A a c d e + 54B a c d e - 54A c d e + 81B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 2A a e - B a d e - 4A a c d e + 22B a c d e - 26A c d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 1149 + +--S 1150 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1151 + +)clear all + +--S 1152 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^5 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1152 + +--S 1153 of 1457 +r0:=B*c^2*x/e^5+1/4*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^4)-1/3*(c*d^2+_ + a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^3)+c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^2)-2*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x))-c^2*(5*B*d-A*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 4 2 4 2 2 3 3 +--R (12A c e - 60B c d e )x + (48A c d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 2 3 2 2 4 2 4 +--R (72A c d e - 360B c d e )x + (48A c d e - 240B c d e)x + 12A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 5 2 4 2 2 3 3 +--R 12B c e x + 48B c d e x + (- 24B a c e + 48A c d e - 48B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e - 36B a c d e + 108A c d e - 252B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 4B a e - 8A a c d e - 24B a c d e + 88A c d e - 248B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - B a d e - 2A a c d e - 6B a c d e + 25A c d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 4 2 4 2 2 3 3 +--R (12A c e - 60B c d e )x + (48A c d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 2 3 2 2 4 2 4 +--R (72A c d e - 360B c d e )x + (48A c d e - 240B c d e)x + 12A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 5 2 4 2 2 3 3 +--R 12B c e x + 48B c d e x + (- 24B a c e + 48A c d e - 48B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e - 36B a c d e + 108A c d e - 252B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 4B a e - 8A a c d e - 24B a c d e + 88A c d e - 248B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - B a d e - 2A a c d e - 6B a c d e + 25A c d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1154 + +--S 1155 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1156 + +)clear all + +--S 1157 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^6 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1157 + +--S 1158 of 1457 +r0:=1/5*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^5)-1/4*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^4)+2/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^3)-c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^2)+c^2*(5*B*d-A*e)/(e^6*(d+e*x))+_ + B*c^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R (- 60A c e + 300B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 60B a c e - 120A c d e + 900B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 40A a c e - 60B a c d e - 120A c d e + 1100B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 15B a e - 20A a c d e - 30B a c d e - 60A c d e + 625B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 12A a e - 3B a d e - 4A a c d e - 6B a c d e - 12A c d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R (- 60A c e + 300B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 60B a c e - 120A c d e + 900B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 40A a c e - 60B a c d e - 120A c d e + 1100B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 15B a e - 20A a c d e - 30B a c d e - 60A c d e + 625B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 12A a e - 3B a d e - 4A a c d e - 6B a c d e - 12A c d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 1159 + +--S 1160 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1161 + +)clear all + +--S 1162 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1162 + +--S 1163 of 1457 +r0:=1/6*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^6)-1/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^5)+1/2*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^4)-2/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^3)+1/2*c^2*(5*B*d-A*e)/_ + (e^6*(d+e*x)^2)-B*c^2/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 5 5 1 2 5 5 2 4 4 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 2 5 2 2 4 10 2 2 3 3 +--R (- - B a c e - - A c d e - -- B c d e )x +--R 3 3 3 +--R + +--R 1 5 1 4 1 2 2 3 5 2 3 2 2 +--R (- - A a c e - - B a c d e - - A c d e - - B c d e )x +--R 2 2 2 2 +--R + +--R 1 2 5 1 4 1 2 3 1 2 3 2 2 4 +--R (- - B a e - - A a c d e - - B a c d e - - A c d e - B c d e)x +--R 5 5 5 5 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - -- A a c d e - -- B a c d e - -- A c d e +--R 6 30 30 30 30 +--R + +--R 1 2 5 +--R - - B c d +--R 6 +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1163 + +--S 1164 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 30B c e x + (- 15A c e - 75B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 20B a c e - 20A c d e - 100B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 15A a c e - 15B a c d e - 15A c d e - 75B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 6B a e - 6A a c d e - 6B a c d e - 6A c d e - 30B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 5A a e - B a d e - A a c d e - B a c d e - A c d e - 5B c d +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 +--R 30e x + 180d e x + 450d e x + 600d e x + 450d e x + 180d e x +--R + +--R 6 6 +--R 30d e +--R Type: Union(Expression(Integer),...) +--E 1164 + +--S 1165 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1166 + +)clear all + +--S 1167 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1167 + +--S 1168 of 1457 +r0:=1/7*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^7)-1/6*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^6)+2/5*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^5)-1/2*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^4)+1/3*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^3)-1/2*B*c^2/(e^6*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 5 2 4 4 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 6 +--R + +--R 1 5 1 2 4 5 2 2 3 3 +--R (- - B a c e - - A c d e - - B c d e )x +--R 2 3 6 +--R + +--R 2 5 3 4 1 2 2 3 1 2 3 2 2 +--R (- - A a c e - -- B a c d e - - A c d e - - B c d e )x +--R 5 10 5 2 +--R + +--R 1 2 5 2 4 1 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - - B c d e)x +--R 6 15 10 15 6 +--R + +--R 1 2 5 1 2 4 2 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - --- A a c d e - -- B a c d e - --- A c d e +--R 7 42 105 70 105 +--R + +--R 1 2 5 +--R - -- B c d +--R 42 +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 6 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1168 + +--S 1169 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 105B c e x + (- 70A c e - 175B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 105B a c e - 70A c d e - 175B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 84A a c e - 63B a c d e - 42A c d e - 105B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 35B a e - 28A a c d e - 21B a c d e - 14A c d e - 35B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 30A a e - 5B a d e - 4A a c d e - 3B a c d e - 2A c d e - 5B c d +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 +--R 210e x + 1470d e x + 4410d e x + 7350d e x + 7350d e x +--R + +--R 5 8 2 6 7 7 6 +--R 4410d e x + 1470d e x + 210d e +--R Type: Union(Expression(Integer),...) +--E 1169 + +--S 1170 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1171 + +)clear all + +--S 1172 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1172 + +--S 1173 of 1457 +r0:=1/8*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^8)-1/7*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^7)+1/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^6)-2/5*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^5)+1/4*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^4)-1/3*B*c^2/(e^6*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 5 2 4 4 +--R - - B c e x + (- - A c e - -- B c d e )x +--R 3 4 12 +--R + +--R 2 5 1 2 4 1 2 2 3 3 +--R (- - B a c e - - A c d e - - B c d e )x +--R 5 5 3 +--R + +--R 1 5 1 4 1 2 2 3 1 2 3 2 2 +--R (- - A a c e - - B a c d e - -- A c d e - - B c d e )x +--R 3 5 10 6 +--R + +--R 1 2 5 2 4 2 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - -- B c d e)x +--R 7 21 35 35 21 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e - --- A c d e +--R 8 56 84 140 280 +--R + +--R 1 2 5 +--R - --- B c d +--R 168 +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 5 9 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 8 2 7 7 8 6 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1173 + +--S 1174 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 280B c e x + (- 210A c e - 350B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 336B a c e - 168A c d e - 280B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 280A a c e - 168B a c d e - 84A c d e - 140B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 120B a e - 80A a c d e - 48B a c d e - 24A c d e - 40B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 105A a e - 15B a d e - 10A a c d e - 6B a c d e - 3A c d e - 5B c d +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 +--R 840e x + 6720d e x + 23520d e x + 47040d e x + 58800d e x +--R + +--R 5 9 3 6 8 2 7 7 8 6 +--R 47040d e x + 23520d e x + 6720d e x + 840d e +--R Type: Union(Expression(Integer),...) +--E 1174 + +--S 1175 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1176 + +)clear all + +--S 1177 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^10 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1177 + +--S 1178 of 1457 +r0:=1/9*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^9)-1/8*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^8)+2/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^7)-1/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^6)+1/5*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^5)-1/4*B*c^2/(e^6*(d+e*x)^4) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 1 2 4 4 +--R - - B c e x + (- - A c e - - B c d e )x +--R 4 5 4 +--R + +--R 1 5 2 2 4 1 2 2 3 3 +--R (- - B a c e - -- A c d e - - B c d e )x +--R 3 15 6 +--R + +--R 2 5 1 4 2 2 2 3 1 2 3 2 2 +--R (- - A a c e - - B a c d e - -- A c d e - -- B c d e )x +--R 7 7 35 14 +--R + +--R 1 2 5 1 4 1 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - -- B c d e)x +--R 8 14 28 70 56 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - --- A a c d e - --- B a c d e - --- A c d e +--R 9 72 126 252 630 +--R + +--R 1 2 5 +--R - --- B c d +--R 504 +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 5 10 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 9 3 7 8 2 8 7 9 6 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1178 + +--S 1179 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 630B c e x + (- 504A c e - 630B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 840B a c e - 336A c d e - 420B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 720A a c e - 360B a c d e - 144A c d e - 180B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 315B a e - 180A a c d e - 90B a c d e - 36A c d e - 45B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 280A a e - 35B a d e - 20A a c d e - 10B a c d e - 4A c d e - 5B c d +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 +--R 2520e x + 22680d e x + 90720d e x + 211680d e x + 317520d e x +--R + +--R 5 10 4 6 9 3 7 8 2 8 7 9 6 +--R 317520d e x + 211680d e x + 90720d e x + 22680d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 1179 + +--S 1180 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1181 + +)clear all + +--S 1182 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1457 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))+(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^8*(2+m))-3*c*(c*d^2+_ + a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3+m)/_ + (e^8*(3+m))-c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*_ + c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(4+m)/(e^8*(4+m))-c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(5+m)/(e^8*(5+m))+_ + 3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(6+m)/(e^8*(6+m))-_ + c^3*(7*B*d-A*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 3 7 3 3 6 +--R (A c e - 7B c d)m + (29A c e - 203B c d)m +--R + +--R 3 3 5 3 3 4 +--R (343A c e - 2401B c d)m + (2135A c e - 14945B c d)m +--R + +--R 3 3 3 3 3 2 +--R (7504A c e - 52528B c d)m + (14756A c e - 103292B c d)m +--R + +--R 3 3 3 3 +--R (14832A c e - 103824B c d)m + 5760A c e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 3 3 2 7 +--R (3B a c e - 6A c d e + 21B c d )m +--R + +--R 2 2 3 3 2 6 +--R (90B a c e - 180A c d e + 630B c d )m +--R + +--R 2 2 3 3 2 5 +--R (1098B a c e - 2196A c d e + 7686B c d )m +--R + +--R 2 2 3 3 2 4 +--R (7020B a c e - 14040A c d e + 49140B c d )m +--R + +--R 2 2 3 3 2 3 +--R (25227B a c e - 50454A c d e + 176589B c d )m +--R + +--R 2 2 3 3 2 2 +--R (50490B a c e - 100980A c d e + 353430B c d )m +--R + +--R 2 2 3 3 2 2 2 +--R (51432B a c e - 102864A c d e + 360024B c d )m + 20160B a c e +--R + +--R 3 3 2 +--R - 40320A c d e + 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 2 2 3 2 3 3 7 +--R (3A a c e - 15B a c d e + 15A c d e - 35B c d )m +--R + +--R 2 3 2 2 3 2 3 3 6 +--R (93A a c e - 465B a c d e + 465A c d e - 1085B c d )m +--R + +--R 2 3 2 2 3 2 3 3 5 +--R (1173A a c e - 5865B a c d e + 5865A c d e - 13685B c d )m +--R + +--R 2 3 2 2 3 2 3 3 4 +--R (7743A a c e - 38715B a c d e + 38715A c d e - 90335B c d )m +--R + +--R 2 3 2 2 3 2 3 3 3 +--R (28632A a c e - 143160B a c d e + 143160A c d e - 334040B c d )m +--R + +--R 2 3 2 2 3 2 3 3 2 +--R (58692A a c e - 293460B a c d e + 293460A c d e - 684740B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R (60912A a c e - 304560B a c d e + 304560A c d e - 710640B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R 24192A a c e - 120960B a c d e + 120960A c d e - 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 4 2 3 2 2 2 3 3 3 4 7 +--R (3B a c e - 12A a c d e + 30B a c d e - 20A c d e + 35B c d )m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 96B a c e - 384A a c d e + 960B a c d e - 640A c d e +--R + +--R 3 4 +--R 1120B c d +--R * +--R 6 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 1254B a c e - 5016A a c d e + 12540B a c d e - 8360A c d e +--R + +--R 3 4 +--R 14630B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 8592B a c e - 34368A a c d e + 85920B a c d e - 57280A c d e +--R + +--R 3 4 +--R 100240B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 32979B a c e - 131916A a c d e + 329790B a c d e +--R + +--R 3 3 3 4 +--R - 219860A c d e + 384755B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 69936B a c e - 279744A a c d e + 699360B a c d e +--R + +--R 3 3 3 4 +--R - 466240A c d e + 815920B c d +--R * +--R 2 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 74628B a c e - 298512A a c d e + 746280B a c d e +--R + +--R 3 3 3 4 +--R - 497520A c d e + 870660B c d +--R * +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 30240B a c e - 120960A a c d e + 302400B a c d e - 201600A c d e +--R + +--R 3 4 +--R 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 +--R 3A a c e - 9B a c d e + 18A a c d e - 30B a c d e + 15A c d e +--R + +--R 3 5 +--R - 21B c d +--R * +--R 7 +--R m +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 99A a c e - 297B a c d e + 594A a c d e - 990B a c d e +--R + +--R 3 4 3 5 +--R 495A c d e - 693B c d +--R * +--R 6 +--R m +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 1341A a c e - 4023B a c d e + 8046A a c d e - 13410B a c d e +--R + +--R 3 4 3 5 +--R 6705A c d e - 9387B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 9585A a c e - 28755B a c d e + 57510A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 95850B a c d e + 47925A c d e - 67095B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 38592A a c e - 115776B a c d e + 231552A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 385920B a c d e + 192960A c d e - 270144B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 86076A a c e - 258228B a c d e + 516456A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 860760B a c d e + 430380A c d e - 602532B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 96144A a c e - 288432B a c d e + 576864A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 961440B a c d e + 480720A c d e - 673008B c d +--R * +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 40320A a c e - 120960B a c d e + 241920A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 403200B a c d e + 201600A c d e - 282240B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 6 2 5 2 2 4 2 3 3 2 4 2 +--R B a e - 6A a c d e + 9B a c d e - 12A a c d e + 15B a c d e +--R + +--R 3 5 3 6 +--R - 6A c d e + 7B c d +--R * +--R 7 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 34B a e - 204A a c d e + 306B a c d e - 408A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 510B a c d e - 204A c d e + 238B c d +--R * +--R 6 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 478B a e - 2868A a c d e + 4302B a c d e - 5736A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 7170B a c d e - 2868A c d e + 3346B c d +--R * +--R 5 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 3580B a e - 21480A a c d e + 32220B a c d e - 42960A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 53700B a c d e - 21480A c d e + 25060B c d +--R * +--R 4 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 15289B a e - 91734A a c d e + 137601B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R - 183468A a c d e + 229335B a c d e - 91734A c d e + 107023B c d +--R * +--R 3 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 36706B a e - 220236A a c d e + 330354B a c d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 440472A a c d e + 550590B a c d e - 220236A c d e +--R + +--R 3 6 +--R 256942B c d +--R * +--R 2 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 44712B a e - 268272A a c d e + 402408B a c d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 536544A a c d e + 670680B a c d e - 268272A c d e +--R + +--R 3 6 +--R 312984B c d +--R * +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 20160B a e - 120960A a c d e + 181440B a c d e - 241920A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 302400B a c d e - 120960A c d e + 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R A a e - B a d e + 3A a c d e - 3B a c d e + 3A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 3B a c d e + A c d e - B c d +--R * +--R 7 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 35A a e - 35B a d e + 105A a c d e - 105B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 105A a c d e - 105B a c d e + 35A c d e - 35B c d +--R * +--R 6 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 511A a e - 511B a d e + 1533A a c d e - 1533B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 1533A a c d e - 1533B a c d e + 511A c d e - 511B c d +--R * +--R 5 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 4025A a e - 4025B a d e + 12075A a c d e - 12075B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 12075A a c d e - 12075B a c d e + 4025A c d e - 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 18424A a e - 18424B a d e + 55272A a c d e - 55272B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 55272A a c d e - 55272B a c d e + 18424A c d e - 18424B c d +--R * +--R 3 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a c d e +--R + +--R 2 3 5 3 4 4 3 5 3 +--R 11880B a c d e - 3120A c d e + 2520B c d e +--R * +--R 2 +--R m +--R + +--R 2 8 2 7 2 2 6 +--R 96144A a c e + 10080B a c d e - 8064A a c d e +--R + +--R 2 3 5 3 4 4 3 5 3 +--R 6720B a c d e - 1920A c d e + 1680B c d e +--R * +--R m +--R + +--R 2 8 +--R 40320A a c e +--R * +--R 3 +--R x +--R + +--R 3 8 2 7 7 +--R (B a e + 3A a c d e )m +--R + +--R 3 8 2 7 2 2 6 6 +--R (34B a e + 93A a c d e - 9B a c d e )m +--R + +--R 3 8 2 7 2 2 6 2 3 5 5 +--R (478B a e + 1155A a c d e - 243B a c d e + 36A a c d e )m +--R + +--R 3 8 2 7 2 2 6 2 3 5 +--R 3580B a e + 7275A a c d e - 2493B a c d e + 792A a c d e +--R + +--R 2 4 4 +--R - 180B a c d e +--R * +--R 4 +--R m +--R + +--R 3 8 2 7 2 2 6 +--R 15289B a e + 24042A a c d e - 11853B a c d e +--R + +--R 2 3 5 2 4 4 3 5 3 +--R 6012A a c d e - 2880B a c d e + 360A c d e +--R * +--R 3 +--R m +--R + +--R 3 8 2 7 2 2 6 +--R 36706B a e + 37992A a c d e - 24714B a c d e +--R + +--R 2 3 5 2 4 4 3 5 3 3 6 2 +--R 17352A a c d e - 12780B a c d e + 3240A c d e - 2520B c d e +--R * +--R 2 +--R m +--R + +--R 3 8 2 7 2 2 6 +--R 44712B a e + 20160A a c d e - 15120B a c d e +--R + +--R 2 3 5 2 4 4 3 5 3 3 6 2 +--R 12096A a c d e - 10080B a c d e + 2880A c d e - 2520B c d e +--R * +--R m +--R + +--R 3 8 +--R 20160B a e +--R * +--R 2 +--R x +--R + +--R 3 8 3 7 7 3 8 3 7 2 2 6 6 +--R (A a e + B a d e )m + (35A a e + 33B a d e - 6A a c d e )m +--R + +--R 3 8 3 7 2 2 6 2 3 5 5 +--R (511A a e + 445B a d e - 180A a c d e + 18B a c d e )m +--R + +--R 3 8 3 7 2 2 6 2 3 5 +--R 4025A a e + 3135B a d e - 2130A a c d e + 468B a c d e +--R + +--R 2 4 4 +--R - 72A a c d e +--R * +--R 4 +--R m +--R + +--R 3 8 3 7 2 2 6 +--R 18424A a e + 12154B a d e - 12420A a c d e +--R + +--R 2 3 5 2 4 4 2 5 3 +--R 4518B a c d e - 1512A a c d e + 360B a c d e +--R * +--R 3 +--R m +--R + +--R 3 8 3 7 2 2 6 +--R 48860A a e + 24552B a d e - 35664A a c d e +--R + +--R 2 3 5 2 4 4 2 5 3 +--R 19188B a c d e - 10512A a c d e + 5400B a c d e +--R + +--R 3 6 2 +--R - 720A c d e +--R * +--R 2 +--R m +--R + +--R 3 8 3 7 2 2 6 +--R 69264A a e + 20160B a d e - 40320A a c d e +--R + +--R 2 3 5 2 4 4 2 5 3 +--R 30240B a c d e - 24192A a c d e + 20160B a c d e +--R + +--R 3 6 2 3 7 +--R - 5760A c d e + 5040B c d e +--R * +--R m +--R + +--R 3 8 +--R 40320A a e +--R * +--R x +--R + +--R 3 7 7 3 7 3 2 6 6 +--R A a d e m + (35A a d e - B a d e )m +--R + +--R 3 7 3 2 6 2 3 5 5 +--R (511A a d e - 33B a d e + 6A a c d e )m +--R + +--R 3 7 3 2 6 2 3 5 2 4 4 4 +--R (4025A a d e - 445B a d e + 180A a c d e - 18B a c d e )m +--R + +--R 3 7 3 2 6 2 3 5 2 4 4 +--R 18424A a d e - 3135B a d e + 2130A a c d e - 468B a c d e +--R + +--R 2 5 3 +--R 72A a c d e +--R * +--R 3 +--R m +--R + +--R 3 7 3 2 6 2 3 5 2 4 4 +--R 48860A a d e - 12154B a d e + 12420A a c d e - 4518B a c d e +--R + +--R 2 5 3 2 6 2 +--R 1512A a c d e - 360B a c d e +--R * +--R 2 +--R m +--R + +--R 3 7 3 2 6 2 3 5 2 4 4 +--R 69264A a d e - 24552B a d e + 35664A a c d e - 19188B a c d e +--R + +--R 2 5 3 2 6 2 3 7 +--R 10512A a c d e - 5400B a c d e + 720A c d e +--R * +--R m +--R + +--R 3 7 3 2 6 2 3 5 2 4 4 +--R 40320A a d e - 20160B a d e + 40320A a c d e - 30240B a c d e +--R + +--R 2 5 3 2 6 2 3 7 3 8 +--R 24192A a c d e - 20160B a c d e + 5760A c d e - 5040B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 7 3 6 3 5 3 4 3 3 +--R - B c m - 28B c m - 322B c m - 1960B c m - 6769B c m +--R + +--R 3 2 3 3 +--R - 13132B c m - 13068B c m - 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 3 7 3 3 6 +--R (- A c e + 7B c d)m + (- 29A c e + 203B c d)m +--R + +--R 3 3 5 3 3 4 +--R (- 343A c e + 2401B c d)m + (- 2135A c e + 14945B c d)m +--R + +--R 3 3 3 3 3 2 +--R (- 7504A c e + 52528B c d)m + (- 14756A c e + 103292B c d)m +--R + +--R 3 3 3 3 +--R (- 14832A c e + 103824B c d)m - 5760A c e + 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 3 3 2 7 +--R (- 3B a c e + 6A c d e - 21B c d )m +--R + +--R 2 2 3 3 2 6 +--R (- 90B a c e + 180A c d e - 630B c d )m +--R + +--R 2 2 3 3 2 5 +--R (- 1098B a c e + 2196A c d e - 7686B c d )m +--R + +--R 2 2 3 3 2 4 +--R (- 7020B a c e + 14040A c d e - 49140B c d )m +--R + +--R 2 2 3 3 2 3 +--R (- 25227B a c e + 50454A c d e - 176589B c d )m +--R + +--R 2 2 3 3 2 2 +--R (- 50490B a c e + 100980A c d e - 353430B c d )m +--R + +--R 2 2 3 3 2 2 2 +--R (- 51432B a c e + 102864A c d e - 360024B c d )m - 20160B a c e +--R + +--R 3 3 2 +--R 40320A c d e - 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 2 2 3 2 3 3 7 +--R (- 3A a c e + 15B a c d e - 15A c d e + 35B c d )m +--R + +--R 2 3 2 2 3 2 3 3 6 +--R (- 93A a c e + 465B a c d e - 465A c d e + 1085B c d )m +--R + +--R 2 3 2 2 3 2 3 3 5 +--R (- 1173A a c e + 5865B a c d e - 5865A c d e + 13685B c d )m +--R + +--R 2 3 2 2 3 2 3 3 4 +--R (- 7743A a c e + 38715B a c d e - 38715A c d e + 90335B c d )m +--R + +--R 2 3 2 2 3 2 3 3 3 +--R (- 28632A a c e + 143160B a c d e - 143160A c d e + 334040B c d )m +--R + +--R 2 3 2 2 3 2 3 3 2 +--R (- 58692A a c e + 293460B a c d e - 293460A c d e + 684740B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R (- 60912A a c e + 304560B a c d e - 304560A c d e + 710640B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R - 24192A a c e + 120960B a c d e - 120960A c d e + 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 4 2 3 2 2 2 3 3 3 4 7 +--R (- 3B a c e + 12A a c d e - 30B a c d e + 20A c d e - 35B c d )m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R - 96B a c e + 384A a c d e - 960B a c d e + 640A c d e +--R + +--R 3 4 +--R - 1120B c d +--R * +--R 6 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R - 1254B a c e + 5016A a c d e - 12540B a c d e + 8360A c d e +--R + +--R 3 4 +--R - 14630B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R - 8592B a c e + 34368A a c d e - 85920B a c d e + 57280A c d e +--R + +--R 3 4 +--R - 100240B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R - 32979B a c e + 131916A a c d e - 329790B a c d e +--R + +--R 3 3 3 4 +--R 219860A c d e - 384755B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R - 69936B a c e + 279744A a c d e - 699360B a c d e +--R + +--R 3 3 3 4 +--R 466240A c d e - 815920B c d +--R * +--R 2 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R - 74628B a c e + 298512A a c d e - 746280B a c d e +--R + +--R 3 3 3 4 +--R 497520A c d e - 870660B c d +--R * +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R - 30240B a c e + 120960A a c d e - 302400B a c d e + 201600A c d e +--R + +--R 3 4 +--R - 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R - 3A a c e + 9B a c d e - 18A a c d e + 30B a c d e +--R + +--R 3 4 3 5 +--R - 15A c d e + 21B c d +--R * +--R 7 +--R m +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R - 99A a c e + 297B a c d e - 594A a c d e + 990B a c d e +--R + +--R 3 4 3 5 +--R - 495A c d e + 693B c d +--R * +--R 6 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 1341A a c e + 4023B a c d e - 8046A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 13410B a c d e - 6705A c d e + 9387B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 9585A a c e + 28755B a c d e - 57510A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 95850B a c d e - 47925A c d e + 67095B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 38592A a c e + 115776B a c d e - 231552A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 385920B a c d e - 192960A c d e + 270144B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 86076A a c e + 258228B a c d e - 516456A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 860760B a c d e - 430380A c d e + 602532B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 96144A a c e + 288432B a c d e - 576864A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 961440B a c d e - 480720A c d e + 673008B c d +--R * +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 40320A a c e + 120960B a c d e - 241920A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 403200B a c d e - 201600A c d e + 282240B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R - B a e + 6A a c d e - 9B a c d e + 12A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R - 15B a c d e + 6A c d e - 7B c d +--R * +--R 7 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R - 34B a e + 204A a c d e - 306B a c d e + 408A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R - 510B a c d e + 204A c d e - 238B c d +--R * +--R 6 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R - 478B a e + 2868A a c d e - 4302B a c d e + 5736A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R - 7170B a c d e + 2868A c d e - 3346B c d +--R * +--R 5 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R - 3580B a e + 21480A a c d e - 32220B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R 42960A a c d e - 53700B a c d e + 21480A c d e - 25060B c d +--R * +--R 4 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R - 15289B a e + 91734A a c d e - 137601B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R 183468A a c d e - 229335B a c d e + 91734A c d e - 107023B c d +--R * +--R 3 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R - 36706B a e + 220236A a c d e - 330354B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R 440472A a c d e - 550590B a c d e + 220236A c d e - 256942B c d +--R * +--R 2 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R - 44712B a e + 268272A a c d e - 402408B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R 536544A a c d e - 670680B a c d e + 268272A c d e - 312984B c d +--R * +--R m +--R + +--R 3 6 2 5 2 2 4 +--R - 20160B a e + 120960A a c d e - 181440B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R 241920A a c d e - 302400B a c d e + 120960A c d e - 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - A a e + B a d e - 3A a c d e + 3B a c d e - 3A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 3B a c d e - A c d e + B c d +--R * +--R 7 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 35A a e + 35B a d e - 105A a c d e + 105B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 105A a c d e + 105B a c d e - 35A c d e + 35B c d +--R * +--R 6 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 511A a e + 511B a d e - 1533A a c d e + 1533B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 1533A a c d e + 1533B a c d e - 511A c d e + 511B c d +--R * +--R 5 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 4025A a e + 4025B a d e - 12075A a c d e + 12075B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 12075A a c d e + 12075B a c d e - 4025A c d e + 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 18424A a e + 18424B a d e - 55272A a c d e + 55272B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 55272A a c d e + 55272B a c d e - 18424A c d e + 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 7 3 6 2 2 5 +--R - 48860A a e + 48860B a d e - 146580A a c d e +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 146580B a c d e - 146580A a c d e + 146580B a c d e +--R + +--R 3 6 3 7 +--R - 48860A c d e + 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 7 3 6 2 2 5 +--R - 69264A a e + 69264B a d e - 207792A a c d e +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 207792B a c d e - 207792A a c d e + 207792B a c d e +--R + +--R 3 6 3 7 +--R - 69264A c d e + 69264B c d +--R * +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 40320A a e + 40320B a d e - 120960A a c d e + 120960B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 120960A a c d e + 120960B a c d e - 40320A c d e + 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1186 + +)clear all + +--S 1187 of 1457 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 5 12 3 5 3 4 11 +--R B c e x + (A c e + 5B c d e )x +--R + +--R 2 5 3 4 3 2 3 10 +--R (3B a c e + 5A c d e + 10B c d e )x +--R + +--R 2 5 2 4 3 2 3 3 3 2 9 +--R (3A a c e + 15B a c d e + 10A c d e + 10B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 3 2 3 4 8 +--R (3B a c e + 15A a c d e + 30B a c d e + 10A c d e + 5B c d e)x +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 +--R 3A a c e + 15B a c d e + 30A a c d e + 30B a c d e + 5A c d e +--R + +--R 3 5 +--R B c d +--R * +--R 7 +--R x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R B a e + 15A a c d e + 30B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R 6 +--R x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R A a e + 5B a d e + 30A a c d e + 30B a c d e + 15A a c d e +--R + +--R 2 5 +--R 3B a c d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 4 +--R (5A a d e + 10B a d e + 30A a c d e + 15B a c d e + 3A a c d )x +--R + +--R 3 2 3 3 3 2 2 4 2 5 3 +--R (10A a d e + 10B a d e + 15A a c d e + 3B a c d )x +--R + +--R 3 3 2 3 4 2 5 2 3 4 3 5 3 5 +--R (10A a d e + 5B a d e + 3A a c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1187 + +--S 1188 of 1457 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^6/e^8+1/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^8-3/8*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^8/e^8-1/9*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))*(d+e*x)^9/e^8-1/10*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*_ + B*d*e^2-3*a*A*e^3)*(d+e*x)^10/e^8+3/11*c^2*(7*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^11/e^8-1/12*c^3*(7*B*d-A*e)*(d+e*x)^12/e^8+1/13*_ + B*c^3*(d+e*x)^13/e^8 +--R +--R +--R (2) +--R 1 3 13 13 1 3 13 5 3 12 12 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 13 12 12 +--R + +--R 3 2 13 5 3 12 10 3 2 11 11 +--R (-- B a c e + -- A c d e + -- B c d e )x +--R 11 11 11 +--R + +--R 3 2 13 3 2 12 3 2 11 3 3 10 10 +--R (-- A a c e + - B a c d e + A c d e + B c d e )x +--R 10 2 +--R + +--R 1 2 13 5 2 12 10 2 2 11 10 3 3 10 +--R - B a c e + - A a c d e + -- B a c d e + -- A c d e +--R 3 3 3 9 +--R + +--R 5 3 4 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 13 15 2 12 15 2 2 11 15 2 3 10 +--R - A a c e + -- B a c d e + -- A a c d e + -- B a c d e +--R 8 8 4 4 +--R + +--R 5 3 4 9 1 3 5 8 +--R - A c d e + - B c d e +--R 8 8 +--R * +--R 8 +--R x +--R + +--R 1 3 13 15 2 12 30 2 2 11 30 2 3 10 +--R - B a e + -- A a c d e + -- B a c d e + -- A a c d e +--R 7 7 7 7 +--R + +--R 15 2 4 9 1 3 5 8 +--R -- B a c d e + - A c d e +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 13 5 3 12 2 2 11 2 3 10 5 2 4 9 +--R - A a e + - B a d e + 5A a c d e + 5B a c d e + - A a c d e +--R 6 6 2 +--R + +--R 1 2 5 8 +--R - B a c d e +--R 2 +--R * +--R 6 +--R x +--R + +--R 3 12 3 2 11 2 3 10 2 4 9 3 2 5 8 5 +--R (A a d e + 2B a d e + 6A a c d e + 3B a c d e + - A a c d e )x +--R 5 +--R + +--R 5 3 2 11 5 3 3 10 15 2 4 9 3 2 5 8 4 +--R (- A a d e + - B a d e + -- A a c d e + - B a c d e )x +--R 2 2 4 4 +--R + +--R 10 3 3 10 5 3 4 9 2 5 8 3 5 3 4 9 1 3 5 8 2 +--R (-- A a d e + - B a d e + A a c d e )x + (- A a d e + - B a d e )x +--R 3 3 2 2 +--R + +--R 3 5 8 1 3 6 7 1 3 7 6 1 2 8 5 1 2 9 4 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 6 42 56 168 +--R + +--R 1 2 10 3 1 2 11 2 1 3 12 1 3 13 +--R --- A a c d e - --- B a c d e + ---- A c d e - ----- B c d +--R 420 924 5544 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1188 + +--S 1189 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 5 13 1 3 5 5 3 4 12 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 13 12 12 +--R + +--R 3 2 5 5 3 4 10 3 2 3 11 +--R (-- B a c e + -- A c d e + -- B c d e )x +--R 11 11 11 +--R + +--R 3 2 5 3 2 4 3 2 3 3 3 2 10 +--R (-- A a c e + - B a c d e + A c d e + B c d e )x +--R 10 2 +--R + +--R 1 2 5 5 2 4 10 2 2 3 10 3 3 2 5 3 4 9 +--R (- B a c e + - A a c d e + -- B a c d e + -- A c d e + - B c d e)x +--R 3 3 3 9 9 +--R + +--R 3 2 5 15 2 4 15 2 2 3 15 2 3 2 5 3 4 +--R - A a c e + -- B a c d e + -- A a c d e + -- B a c d e + - A c d e +--R 8 8 4 4 8 +--R + +--R 1 3 5 +--R - B c d +--R 8 +--R * +--R 8 +--R x +--R + +--R 1 3 5 15 2 4 30 2 2 3 30 2 3 2 15 2 4 +--R - B a e + -- A a c d e + -- B a c d e + -- A a c d e + -- B a c d e +--R 7 7 7 7 7 +--R + +--R 1 3 5 +--R - A c d +--R 7 +--R * +--R 7 +--R x +--R + +--R 1 3 5 5 3 4 2 2 3 2 3 2 5 2 4 +--R - A a e + - B a d e + 5A a c d e + 5B a c d e + - A a c d e +--R 6 6 2 +--R + +--R 1 2 5 +--R - B a c d +--R 2 +--R * +--R 6 +--R x +--R + +--R 3 4 3 2 3 2 3 2 2 4 3 2 5 5 +--R (A a d e + 2B a d e + 6A a c d e + 3B a c d e + - A a c d )x +--R 5 +--R + +--R 5 3 2 3 5 3 3 2 15 2 4 3 2 5 4 +--R (- A a d e + - B a d e + -- A a c d e + - B a c d )x +--R 2 2 4 4 +--R + +--R 10 3 3 2 5 3 4 2 5 3 5 3 4 1 3 5 2 3 5 +--R (-- A a d e + - B a d e + A a c d )x + (- A a d e + - B a d )x + A a d x +--R 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1189 + +--S 1190 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 6 7 1 3 7 6 1 2 8 5 1 2 9 4 +--R - - A a d e + -- B a d e - -- A a c d e + --- B a c d e +--R 6 42 56 168 +--R + +--R 1 2 10 3 1 2 11 2 1 3 12 1 3 13 +--R - --- A a c d e + --- B a c d e - ---- A c d e + ----- B c d +--R 420 924 5544 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1190 + +--S 1191 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1191 + +)clear all + +--S 1192 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 4 3 3 10 2 4 3 3 3 2 2 9 +--R B c e x + (A c e + 4B c d e )x + (3B a c e + 4A c d e + 6B c d e )x +--R + +--R 2 4 2 3 3 2 2 3 3 8 +--R (3A a c e + 12B a c d e + 6A c d e + 4B c d e)x +--R + +--R 2 4 2 3 2 2 2 3 3 3 4 7 +--R (3B a c e + 12A a c d e + 18B a c d e + 4A c d e + B c d )x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 6 +--R (3A a c e + 12B a c d e + 18A a c d e + 12B a c d e + A c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 5 +--R (B a e + 12A a c d e + 18B a c d e + 12A a c d e + 3B a c d )x +--R + +--R 3 4 3 3 2 2 2 2 3 2 4 4 +--R (A a e + 4B a d e + 18A a c d e + 12B a c d e + 3A a c d )x +--R + +--R 3 3 3 2 2 2 3 2 4 3 +--R (4A a d e + 6B a d e + 12A a c d e + 3B a c d )x +--R + +--R 3 2 2 3 3 2 4 2 3 3 3 4 3 4 +--R (6A a d e + 4B a d e + 3A a c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1192 + +--S 1193 of 1457 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^5/e^8+1/6*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^8-3/7*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^7/e^8-1/8*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))*(d+e*x)^8/e^8-1/9*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)*(d+e*x)^9/e^8+3/10*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*_ + (d+e*x)^10/e^8-1/11*c^3*(7*B*d-A*e)*(d+e*x)^11/e^8+1/12*B*c^3*_ + (d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 3 12 12 1 3 12 4 3 11 11 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 12 11 11 +--R + +--R 3 2 12 2 3 11 3 3 2 10 10 +--R (-- B a c e + - A c d e + - B c d e )x +--R 10 5 5 +--R + +--R 1 2 12 4 2 11 2 3 2 10 4 3 3 9 9 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 3 3 3 9 +--R + +--R 3 2 12 3 2 11 9 2 2 10 1 3 3 9 1 3 4 8 8 +--R (- B a c e + - A a c d e + - B a c d e + - A c d e + - B c d e )x +--R 8 2 4 2 8 +--R + +--R 3 2 12 12 2 11 18 2 2 10 12 2 3 9 +--R - A a c e + -- B a c d e + -- A a c d e + -- B a c d e +--R 7 7 7 7 +--R + +--R 1 3 4 8 +--R - A c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 1 3 12 2 11 2 2 10 2 3 9 1 2 4 8 6 +--R (- B a e + 2A a c d e + 3B a c d e + 2A a c d e + - B a c d e )x +--R 6 2 +--R + +--R 1 3 12 4 3 11 18 2 2 10 12 2 3 9 +--R - A a e + - B a d e + -- A a c d e + -- B a c d e +--R 5 5 5 5 +--R + +--R 3 2 4 8 +--R - A a c d e +--R 5 +--R * +--R 5 +--R x +--R + +--R 3 11 3 3 2 10 2 3 9 3 2 4 8 4 +--R (A a d e + - B a d e + 3A a c d e + - B a c d e )x +--R 2 4 +--R + +--R 3 2 10 4 3 3 9 2 4 8 3 3 3 9 1 3 4 8 2 +--R (2A a d e + - B a d e + A a c d e )x + (2A a d e + - B a d e )x +--R 3 2 +--R + +--R 3 4 8 1 3 5 7 1 3 6 6 1 2 7 5 3 2 8 4 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 5 30 35 280 +--R + +--R 1 2 9 3 1 2 10 2 1 3 11 1 3 12 +--R --- A a c d e - --- B a c d e + ---- A c d e - ---- B c d +--R 210 420 2310 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1193 + +--S 1194 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 12 1 3 4 4 3 3 11 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 12 11 11 +--R + +--R 3 2 4 2 3 3 3 3 2 2 10 +--R (-- B a c e + - A c d e + - B c d e )x +--R 10 5 5 +--R + +--R 1 2 4 4 2 3 2 3 2 2 4 3 3 9 +--R (- A a c e + - B a c d e + - A c d e + - B c d e)x +--R 3 3 3 9 +--R + +--R 3 2 4 3 2 3 9 2 2 2 1 3 3 1 3 4 8 +--R (- B a c e + - A a c d e + - B a c d e + - A c d e + - B c d )x +--R 8 2 4 2 8 +--R + +--R 3 2 4 12 2 3 18 2 2 2 12 2 3 1 3 4 7 +--R (- A a c e + -- B a c d e + -- A a c d e + -- B a c d e + - A c d )x +--R 7 7 7 7 7 +--R + +--R 1 3 4 2 3 2 2 2 2 3 1 2 4 6 +--R (- B a e + 2A a c d e + 3B a c d e + 2A a c d e + - B a c d )x +--R 6 2 +--R + +--R 1 3 4 4 3 3 18 2 2 2 12 2 3 3 2 4 5 +--R (- A a e + - B a d e + -- A a c d e + -- B a c d e + - A a c d )x +--R 5 5 5 5 5 +--R + +--R 3 3 3 3 2 2 2 3 3 2 4 4 +--R (A a d e + - B a d e + 3A a c d e + - B a c d )x +--R 2 4 +--R + +--R 3 2 2 4 3 3 2 4 3 3 3 1 3 4 2 3 4 +--R (2A a d e + - B a d e + A a c d )x + (2A a d e + - B a d )x + A a d x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1194 + +--S 1195 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 5 7 1 3 6 6 1 2 7 5 3 2 8 4 +--R - - A a d e + -- B a d e - -- A a c d e + --- B a c d e +--R 5 30 35 280 +--R + +--R 1 2 9 3 1 2 10 2 1 3 11 1 3 12 +--R - --- A a c d e + --- B a c d e - ---- A c d e + ---- B c d +--R 210 420 2310 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1195 + +--S 1196 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1196 + +)clear all + +--S 1197 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 3 3 2 9 2 3 3 2 3 2 8 +--R B c e x + (A c e + 3B c d e )x + (3B a c e + 3A c d e + 3B c d e)x +--R + +--R 2 3 2 2 3 2 3 3 7 +--R (3A a c e + 9B a c d e + 3A c d e + B c d )x +--R + +--R 2 3 2 2 2 2 3 3 6 +--R (3B a c e + 9A a c d e + 9B a c d e + A c d )x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (3A a c e + 9B a c d e + 9A a c d e + 3B a c d )x +--R + +--R 3 3 2 2 2 2 2 3 4 +--R (B a e + 9A a c d e + 9B a c d e + 3A a c d )x +--R + +--R 3 3 3 2 2 2 2 3 3 +--R (A a e + 3B a d e + 9A a c d e + 3B a c d )x +--R + +--R 3 2 3 2 2 3 2 3 2 3 3 3 3 +--R (3A a d e + 3B a d e + 3A a c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1197 + +--S 1198 of 1457 +r0:=a^3*A*d^3*x+1/2*a^3*d^2*(B*d+3*A*e)*x^2+a^2*d*(A*c*d^2+a*B*d*e+_ + a*A*e^2)*x^3+1/4*a^2*(3*B*c*d^3+9*A*c*d^2*e+3*a*B*d*e^2+a*A*e^3)*_ + x^4+1/5*a*(a*B*e*(9*c*d^2+a*e^2)+3*A*c*d*(c*d^2+3*a*e^2))*x^5+_ + 1/2*a*c*(B*c*d^3+3*A*c*d^2*e+3*a*B*d*e^2+a*A*e^3)*x^6+1/7*c*(3*a*_ + B*e*(3*c*d^2+a*e^2)+A*c*d*(c*d^2+9*a*e^2))*x^7+1/8*c^2*(B*c*d^3+3*_ + A*c*d^2*e+9*a*B*d*e^2+3*a*A*e^3)*x^8+1/3*c^2*e*(B*c*d^2+A*c*d*e+_ + a*B*e^2)*x^9+1/10*c^3*e^2*(3*B*d+A*e)*x^10+1/11*B*c^3*e^3*x^11 +--R +--R +--R (2) +--R 1 3 3 11 1 3 3 3 3 2 10 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 11 10 10 +--R + +--R 1 2 3 1 3 2 1 3 2 9 +--R (- B a c e + - A c d e + - B c d e)x +--R 3 3 3 +--R + +--R 3 2 3 9 2 2 3 3 2 1 3 3 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d )x +--R 8 8 8 8 +--R + +--R 3 2 3 9 2 2 9 2 2 1 3 3 7 +--R (- B a c e + - A a c d e + - B a c d e + - A c d )x +--R 7 7 7 7 +--R + +--R 1 2 3 3 2 2 3 2 2 1 2 3 6 +--R (- A a c e + - B a c d e + - A a c d e + - B a c d )x +--R 2 2 2 2 +--R + +--R 1 3 3 9 2 2 9 2 2 3 2 3 5 +--R (- B a e + - A a c d e + - B a c d e + - A a c d )x +--R 5 5 5 5 +--R + +--R 1 3 3 3 3 2 9 2 2 3 2 3 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d )x +--R 4 4 4 4 +--R + +--R 3 2 3 2 2 3 3 3 3 2 1 3 3 2 3 3 +--R (A a d e + B a d e + A a c d )x + (- A a d e + - B a d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1198 + +--S 1199 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 3 11 1 3 3 3 3 2 10 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 11 10 10 +--R + +--R 1 2 3 1 3 2 1 3 2 9 +--R (- B a c e + - A c d e + - B c d e)x +--R 3 3 3 +--R + +--R 3 2 3 9 2 2 3 3 2 1 3 3 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d )x +--R 8 8 8 8 +--R + +--R 3 2 3 9 2 2 9 2 2 1 3 3 7 +--R (- B a c e + - A a c d e + - B a c d e + - A c d )x +--R 7 7 7 7 +--R + +--R 1 2 3 3 2 2 3 2 2 1 2 3 6 +--R (- A a c e + - B a c d e + - A a c d e + - B a c d )x +--R 2 2 2 2 +--R + +--R 1 3 3 9 2 2 9 2 2 3 2 3 5 +--R (- B a e + - A a c d e + - B a c d e + - A a c d )x +--R 5 5 5 5 +--R + +--R 1 3 3 3 3 2 9 2 2 3 2 3 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d )x +--R 4 4 4 4 +--R + +--R 3 2 3 2 2 3 3 3 3 2 1 3 3 2 3 3 +--R (A a d e + B a d e + A a c d )x + (- A a d e + - B a d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1199 + +--S 1200 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1200 + +--S 1201 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1201 + +)clear all + +--S 1202 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 3 8 2 2 3 3 2 7 +--R B c e x + (A c e + 2B c d e)x + (3B a c e + 2A c d e + B c d )x +--R + +--R 2 2 2 3 2 6 +--R (3A a c e + 6B a c d e + A c d )x +--R + +--R 2 2 2 2 2 5 +--R (3B a c e + 6A a c d e + 3B a c d )x +--R + +--R 2 2 2 2 2 4 +--R (3A a c e + 6B a c d e + 3A a c d )x +--R + +--R 3 2 2 2 2 3 3 2 3 2 2 2 +--R (B a e + 6A a c d e + 3B a c d )x + (A a e + 2B a d e + 3A a c d )x +--R + +--R 3 3 2 3 2 +--R (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1202 + +--S 1203 of 1457 +r0:=a^3*A*d^2*x+1/2*a^3*d*(B*d+2*A*e)*x^2+1/3*a^2*(3*A*c*d^2+2*a*B*d*e+_ + a*A*e^2)*x^3+1/4*a^2*(3*B*c*d^2+6*A*c*d*e+a*B*e^2)*x^4+3/5*a*c*_ + (A*c*d^2+2*a*B*d*e+a*A*e^2)*x^5+1/2*a*c*(B*c*d^2+2*A*c*d*e+a*B*_ + e^2)*x^6+1/7*c^2*(A*c*d^2+6*a*B*d*e+3*a*A*e^2)*x^7+1/8*c^2*(B*c*d^2+_ + 2*A*c*d*e+3*a*B*e^2)*x^8+1/9*c^3*e*(2*B*d+A*e)*x^9+1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 2 2 3 9 +--R -- B c e x + (- A c e + - B c d e)x +--R 10 9 9 +--R + +--R 3 2 2 1 3 1 3 2 8 +--R (- B a c e + - A c d e + - B c d )x +--R 8 4 8 +--R + +--R 3 2 2 6 2 1 3 2 7 +--R (- A a c e + - B a c d e + - A c d )x +--R 7 7 7 +--R + +--R 1 2 2 2 1 2 2 6 +--R (- B a c e + A a c d e + - B a c d )x +--R 2 2 +--R + +--R 3 2 2 6 2 3 2 2 5 +--R (- A a c e + - B a c d e + - A a c d )x +--R 5 5 5 +--R + +--R 1 3 2 3 2 3 2 2 4 +--R (- B a e + - A a c d e + - B a c d )x +--R 4 2 4 +--R + +--R 1 3 2 2 3 2 2 3 3 1 3 2 2 3 2 +--R (- A a e + - B a d e + A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1203 + +--S 1204 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 10 1 3 2 2 3 9 +--R -- B c e x + (- A c e + - B c d e)x +--R 10 9 9 +--R + +--R 3 2 2 1 3 1 3 2 8 +--R (- B a c e + - A c d e + - B c d )x +--R 8 4 8 +--R + +--R 3 2 2 6 2 1 3 2 7 +--R (- A a c e + - B a c d e + - A c d )x +--R 7 7 7 +--R + +--R 1 2 2 2 1 2 2 6 +--R (- B a c e + A a c d e + - B a c d )x +--R 2 2 +--R + +--R 3 2 2 6 2 3 2 2 5 +--R (- A a c e + - B a c d e + - A a c d )x +--R 5 5 5 +--R + +--R 1 3 2 3 2 3 2 2 4 +--R (- B a e + - A a c d e + - B a c d )x +--R 4 2 4 +--R + +--R 1 3 2 2 3 2 2 3 3 1 3 2 2 3 2 +--R (- A a e + - B a d e + A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1204 + +--S 1205 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1205 + +--S 1206 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1206 + +)clear all + +--S 1207 of 1457 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 3 7 2 3 6 +--R B c e x + (A c e + B c d)x + (3B a c e + A c d)x +--R + +--R 2 2 5 2 2 4 2 2 3 +--R (3A a c e + 3B a c d)x + (3B a c e + 3A a c d)x + (3A a c e + 3B a c d)x +--R + +--R 3 2 2 3 3 3 +--R (B a e + 3A a c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 1207 + +--S 1208 of 1457 +r0:=a^3*A*d*x+1/2*a^3*(B*d+A*e)*x^2+1/3*a^2*(3*A*c*d+a*B*e)*x^3+3/4*_ + a^2*c*(B*d+A*e)*x^4+3/5*a*c*(A*c*d+a*B*e)*x^5+1/2*a*c^2*(B*d+A*e)*_ + x^6+1/7*c^2*(A*c*d+3*a*B*e)*x^7+1/8*c^3*(B*d+A*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 1 3 8 3 2 1 3 7 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 9 8 8 7 7 +--R + +--R 1 2 1 2 6 3 2 3 2 5 +--R (- A a c e + - B a c d)x + (- B a c e + - A a c d)x +--R 2 2 5 5 +--R + +--R 3 2 3 2 4 1 3 2 3 1 3 1 3 2 +--R (- A a c e + - B a c d)x + (- B a e + A a c d)x + (- A a e + - B a d)x +--R 4 4 3 2 2 +--R + +--R 3 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1208 + +--S 1209 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 9 1 3 1 3 8 3 2 1 3 7 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 9 8 8 7 7 +--R + +--R 1 2 1 2 6 3 2 3 2 5 +--R (- A a c e + - B a c d)x + (- B a c e + - A a c d)x +--R 2 2 5 5 +--R + +--R 3 2 3 2 4 1 3 2 3 1 3 1 3 2 +--R (- A a c e + - B a c d)x + (- B a e + A a c d)x + (- A a e + - B a d)x +--R 4 4 3 2 2 +--R + +--R 3 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1209 + +--S 1210 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1210 + +--S 1211 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1211 + +)clear all + +--S 1212 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R Type: Polynomial(Integer) +--E 1212 + +--S 1213 of 1457 +r0:=a^3*A*x+a^2*A*c*x^3+3/5*a*A*c^2*x^5+1/7*A*c^3*x^7+1/8*B*(a+c*x^2)^4/c +--R +--R +--R (2) +--R 1 4 8 1 4 7 1 3 6 3 3 5 3 2 2 4 2 2 3 +--R - B c x + - A c x + - B a c x + - A a c x + - B a c x + A a c x +--R 8 7 2 5 4 +--R + +--R 1 3 2 3 1 4 +--R - B a c x + A a c x + - B a +--R 2 8 +--R / +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1213 + +--S 1214 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 8 1 3 7 1 2 6 3 2 5 3 2 4 2 3 +--R - B c x + - A c x + - B a c x + - A a c x + - B a c x + A a c x +--R 8 7 2 5 4 +--R + +--R 1 3 2 3 +--R - B a x + A a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1214 + +--S 1215 of 1457 +m0:=a0-r0 +--R +--R +--R 1 4 +--R - B a +--R 8 +--R (4) - ------ +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1215 + +--S 1216 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1216 + +)clear all + +--S 1217 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1217 + +--S 1218 of 1457 +r0:=(B*(c*d^2+a*e^2)^3-A*c*d*e*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4))*x/e^7-_ + 1/2*c*(B*d-A*e)*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4)*x^2/e^6-1/3*c*_ + (A*c*d*e*(c*d^2+3*a*e^2)-B*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4))*_ + x^3/e^5-1/4*c^2*(B*d-A*e)*(c*d^2+3*a*e^2)*x^4/e^4+1/5*c^2*(B*c*_ + d^2-A*c*d*e+3*a*B*e^2)*x^5/e^3-1/6*c^3*(B*d-A*e)*x^6/e^2+1/7*B*_ + c^3*x^7/e-(B*d-A*e)*(c*d^2+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 6 2 2 5 2 3 4 +--R 420A a e - 420B a d e + 1260A a c d e - 1260B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 1260A a c d e - 1260B a c d e + 420A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 60B c e x + (70A c e - 70B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (252B a c e - 84A c d e + 84B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (315A a c e - 315B a c d e + 105A c d e - 105B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 420B a c e - 420A a c d e + 420B a c d e - 140A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 630A a c e - 630B a c d e + 630A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R 210A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 420B a e - 1260A a c d e + 1260B a c d e - 1260A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 1260B a c d e - 420A c d e + 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 3 6 2 2 5 2 3 4 +--R 420A a e - 420B a d e + 1260A a c d e - 1260B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 1260A a c d e - 1260B a c d e + 420A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 60B c e x + (70A c e - 70B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (252B a c e - 84A c d e + 84B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (315A a c e - 315B a c d e + 105A c d e - 105B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 420B a c e - 420A a c d e + 420B a c d e - 140A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 630A a c e - 630B a c d e + 630A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R 210A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 420B a e - 1260A a c d e + 1260B a c d e - 1260A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 1260B a c d e - 420A c d e + 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Union(Expression(Integer),...) +--E 1219 + +--S 1220 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1221 + +)clear all + +--S 1222 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1222 + +--S 1223 of 1457 +r0:=-c*(6*B*d*(c*d^2+a*e^2)^2-A*e*(5*c^2*d^4+9*a*c*d^2*e^2+3*a^2*e^4))*_ + x/e^7-1/2*c*(2*A*c*d*e*(2*c*d^2+3*a*e^2)-B*(5*c^2*d^4+9*a*c*d^2*e^2+_ + 3*a^2*e^4))*x^2/e^6+1/3*c^2*(3*A*e*(c*d^2+a*e^2)-B*(4*c*d^3+_ + 6*a*d*e^2))*x^3/e^5-1/4*c^2*(2*A*c*d*e-3*B*(c*d^2+a*e^2))*x^4/e^4-_ + 1/5*c^3*(2*B*d-A*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+(B*d-A*e)*(c*d^2+_ + a*e^2)^3/(e^8*(d+e*x))+(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+_ + a*B*e^2)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 6 2 2 5 2 3 4 +--R 60B a e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 900B a c d e - 360A c d e + 420B c d e +--R * +--R x +--R + +--R 3 6 2 2 5 2 3 4 2 4 3 +--R 60B a d e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 900B a c d e - 360A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (12A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (45B a c e - 18A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (60A a c e - 75B a c d e + 30A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 3 4 3 3 +--R (90B a c e - 120A a c d e + 150B a c d e - 60A c d e + 70B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 180A a c e - 270B a c d e + 360A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 180A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 180A a c d e - 360B a c d e + 540A a c d e - 720B a c d e +--R + +--R 3 5 2 3 6 +--R 300A c d e - 360B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e + 60B a d e - 180A a c d e + 180B a c d e - 180A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 180B a c d e - 60A c d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 2 6 2 2 5 2 3 4 +--R 60B a e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 900B a c d e - 360A c d e + 420B c d e +--R * +--R x +--R + +--R 3 6 2 2 5 2 3 4 2 4 3 +--R 60B a d e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 900B a c d e - 360A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (12A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (45B a c e - 18A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (60A a c e - 75B a c d e + 30A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 3 4 3 3 +--R (90B a c e - 120A a c d e + 150B a c d e - 60A c d e + 70B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 180A a c e - 270B a c d e + 360A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 180A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 180A a c d e - 360B a c d e + 540A a c d e - 720B a c d e +--R + +--R 3 5 2 3 6 +--R 300A c d e - 360B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e + 60B a d e - 180A a c d e + 180B a c d e - 180A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 180B a c d e - 60A c d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 1224 + +--S 1225 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1226 + +)clear all + +--S 1227 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1227 + +--S 1228 of 1457 +r0:=-c*(A*c*d*e*(10*c*d^2+9*a*e^2)-3*B*(5*c^2*d^4+6*a*c*d^2*e^2+_ + a^2*e^4))*x/e^7-1/2*c^2*(10*B*c*d^3-6*A*c*d^2*e+9*a*B*d*e^2-_ + 3*a*A*e^3)*x^2/e^6+c^2*(2*B*c*d^2-A*c*d*e+a*B*e^2)*x^3/e^5-_ + 1/4*c^3*(3*B*d-A*e)*x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*(B*d-A*e)*_ + (c*d^2+a*e^2)^3/(e^8*(d+e*x)^2)-(c*d^2+a*e^2)^2*(7*B*c*d^2-_ + 6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x))-3*c*(c*d^2+a*e^2)*(7*B*c*d^3-_ + 5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 2 2 5 2 3 4 +--R 60A a c e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 4 3 3 5 2 +--R 300A c d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 120A a c d e - 360B a c d e + 720A a c d e - 1200B a c d e +--R + +--R 3 5 2 3 6 +--R 600A c d e - 840B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 2 5 2 +--R 60A a c d e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 6 3 7 +--R 300A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (5A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (20B a c e - 10A c d e + 14B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30A a c e - 50B a c d e + 25A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 60B a c e - 120A a c d e + 200B a c d e - 100A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 120B a c d e - 330A a c d e + 630B a c d e - 340A c d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 20B a e + 120A a c d e - 120B a c d e + 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 60B a c d e - 80A c d e + 160B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 10B a d e + 90A a c d e - 150B a c d e + 210A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 270B a c d e + 110A c d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 2 6 2 2 5 2 3 4 +--R 60A a c e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 4 3 3 5 2 +--R 300A c d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 120A a c d e - 360B a c d e + 720A a c d e - 1200B a c d e +--R + +--R 3 5 2 3 6 +--R 600A c d e - 840B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 2 5 2 +--R 60A a c d e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 6 3 7 +--R 300A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (5A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (20B a c e - 10A c d e + 14B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30A a c e - 50B a c d e + 25A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 60B a c e - 120A a c d e + 200B a c d e - 100A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 120B a c d e - 330A a c d e + 630B a c d e - 340A c d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 20B a e + 120A a c d e - 120B a c d e + 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 60B a c d e - 80A c d e + 160B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 10B a d e + 90A a c d e - 150B a c d e + 210A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 270B a c d e + 110A c d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 1229 + +--S 1230 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1231 + +)clear all + +--S 1232 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1232 + +--S 1233 of 1457 +r0:=-c^2*(20*B*c*d^3-10*A*c*d^2*e+12*a*B*d*e^2-3*a*A*e^3)*x/e^7+1/2*_ + c^2*(10*B*c*d^2-4*A*c*d*e+3*a*B*e^2)*x^2/e^6-1/3*c^3*(4*B*d-A*e)*_ + x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+_ + e*x)^3)-1/2*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*_ + (d+e*x)^2)+3*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-_ + a*A*e^3)/(e^8*(d+e*x))-c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*_ + d^4+30*a*c*d^2*e^2+3*a^2*e^4))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 2 2 5 3 3 4 +--R 36B a c e - 144A a c d e + 360B a c d e - 240A c d e +--R + +--R 3 4 3 +--R 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 3 5 2 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 3 6 3 7 +--R 36B a c d e - 144A a c d e + 360B a c d e - 240A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 3B c e x + (4A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (18B a c e - 12A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 90B a c d e + 60A c d e - 105B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (108A a c d e - 378B a c d e + 292A c d e - 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 36A a c e + 108B a c d e - 108A a c d e - 54B a c d e +--R + +--R 3 4 3 3 5 2 +--R 156A c d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6B a e - 36A a c d e + 162B a c d e - 324A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 486B a c d e - 204A c d e + 222B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - 2B a d e - 12A a c d e + 66B a c d e - 156A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 282B a c d e - 148A c d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 2 6 2 2 5 3 3 4 +--R 36B a c e - 144A a c d e + 360B a c d e - 240A c d e +--R + +--R 3 4 3 +--R 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 3 5 2 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 3 6 3 7 +--R 36B a c d e - 144A a c d e + 360B a c d e - 240A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 3B c e x + (4A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (18B a c e - 12A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 90B a c d e + 60A c d e - 105B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (108A a c d e - 378B a c d e + 292A c d e - 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 36A a c e + 108B a c d e - 108A a c d e - 54B a c d e +--R + +--R 3 4 3 3 5 2 +--R 156A c d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6B a e - 36A a c d e + 162B a c d e - 324A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 486B a c d e - 204A c d e + 222B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - 2B a d e - 12A a c d e + 66B a c d e - 156A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 282B a c d e - 148A c d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1234 + +--S 1235 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1236 + +)clear all + +--S 1237 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1237 + +--S 1238 of 1457 +r0:=-c^2*(5*A*c*d*e-3*B*(5*c*d^2+a*e^2))*x/e^7-1/2*c^3*(5*B*d-A*e)*_ + x^2/e^6+1/3*B*c^3*x^3/e^5+1/4*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*_ + (d+e*x)^4)-1/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^3)+3/2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*_ + d*e^2-a*A*e^3)/(e^8*(d+e*x)^2)+c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*_ + (35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x))-c^2*(35*B*c*_ + d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 180B a c d e + 180A c d e - 420B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e )x +--R + +--R 2 2 5 2 3 4 3 4 3 3 5 2 2 +--R (216A a c d e - 1080B a c d e + 1080A c d e - 2520B c d e )x +--R + +--R 2 3 4 2 4 3 3 5 2 3 6 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e)x +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 36A a c d e - 180B a c d e + 180A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (6A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (36B a c e - 36A c d e + 84B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (144B a c d e - 204A c d e + 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 36B a c e + 144A a c d e - 144B a c d e - 96A c d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 18A a c e - 54B a c d e + 324A a c d e - 756B a c d e +--R + +--R 3 4 3 3 5 2 +--R 396A c d e - 444B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 4B a e - 12A a c d e - 36B a c d e + 264A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 744B a c d e + 504A c d e - 856B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 3A a e - B a d e - 3A a c d e - 9B a c d e + 75A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 231B a c d e + 171A c d e - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 180B a c d e + 180A c d e - 420B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e )x +--R + +--R 2 2 5 2 3 4 3 4 3 3 5 2 2 +--R (216A a c d e - 1080B a c d e + 1080A c d e - 2520B c d e )x +--R + +--R 2 3 4 2 4 3 3 5 2 3 6 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e)x +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 36A a c d e - 180B a c d e + 180A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (6A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (36B a c e - 36A c d e + 84B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (144B a c d e - 204A c d e + 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 36B a c e + 144A a c d e - 144B a c d e - 96A c d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 18A a c e - 54B a c d e + 324A a c d e - 756B a c d e +--R + +--R 3 4 3 3 5 2 +--R 396A c d e - 444B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 4B a e - 12A a c d e - 36B a c d e + 264A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 744B a c d e + 504A c d e - 856B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 3A a e - B a d e - 3A a c d e - 9B a c d e + 75A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 231B a c d e + 171A c d e - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1239 + +--S 1240 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1240 + +--S 1241 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1241 + +)clear all + +--S 1242 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^6 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1242 + +--S 1243 of 1457 +r0:=-c^3*(6*B*d-A*e)*x/e^7+1/2*B*c^3*x^2/e^6+1/5*(B*d-A*e)*(c*d^2+_ + a*e^2)^3/(e^8*(d+e*x)^5)-1/4*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+_ + a*B*e^2)/(e^8*(d+e*x)^4)+c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+_ + 3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^3)+1/2*c*(4*A*c*d*e*(5*c*d^2+_ + 3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^2)+_ + c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*(d+e*x))+_ + 3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 3 6 3 2 5 5 +--R (60B a c e - 120A c d e + 420B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (300B a c d e - 600A c d e + 2100B c d e )x +--R + +--R 2 2 5 3 3 4 3 4 3 3 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 3 4 3 4 3 3 5 2 2 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 4 3 3 5 2 3 6 2 5 2 +--R (300B a c d e - 600A c d e + 2100B c d e)x + 60B a c d e +--R + +--R 3 6 3 7 +--R - 120A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 3 6 3 2 5 5 +--R 10B c e x + (20A c e - 70B c d e )x + (100A c d e - 500B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 60A a c e + 300B a c d e - 100A c d e - 400B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 30B a c e - 120A a c d e + 900B a c d e - 800A c d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 20A a c e - 30B a c d e - 120A a c d e + 1100B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1200A c d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 5B a e - 10A a c d e - 15B a c d e - 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 625B a c d e - 750A c d e + 1875B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - B a d e - 2A a c d e - 3B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 137B a c d e - 174A c d e + 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 3 6 3 2 5 5 +--R (60B a c e - 120A c d e + 420B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (300B a c d e - 600A c d e + 2100B c d e )x +--R + +--R 2 2 5 3 3 4 3 4 3 3 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 3 4 3 4 3 3 5 2 2 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 4 3 3 5 2 3 6 2 5 2 +--R (300B a c d e - 600A c d e + 2100B c d e)x + 60B a c d e +--R + +--R 3 6 3 7 +--R - 120A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 3 6 3 2 5 5 +--R 10B c e x + (20A c e - 70B c d e )x + (100A c d e - 500B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 60A a c e + 300B a c d e - 100A c d e - 400B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 30B a c e - 120A a c d e + 900B a c d e - 800A c d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 20A a c e - 30B a c d e - 120A a c d e + 1100B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1200A c d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 5B a e - 10A a c d e - 15B a c d e - 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 625B a c d e - 750A c d e + 1875B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - B a d e - 2A a c d e - 3B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 137B a c d e - 174A c d e + 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 1244 + +--S 1245 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1246 + +)clear all + +--S 1247 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^7 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1247 + +--S 1248 of 1457 +r0:=B*c^3*x/e^7+1/6*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^6)-1/5*(c*d^2+_ + a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^5)+3/4*c*(c*d^2+_ + a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^4)+_ + 1/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))/(e^8*(d+e*x)^3)+1/2*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*_ + d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^2)-3*c^2*(7*B*c*d^2-2*A*c*d*e+a*_ + B*e^2)/(e^8*(d+e*x))-c^3*(7*B*d-A*e)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 6 6 3 6 3 2 5 5 +--R (60A c e - 420B c d e )x + (360A c d e - 2520B c d e )x +--R + +--R 3 2 5 3 3 4 4 3 3 4 3 4 3 3 +--R (900A c d e - 6300B c d e )x + (1200A c d e - 8400B c d e )x +--R + +--R 3 4 3 3 5 2 2 3 5 2 3 6 +--R (900A c d e - 6300B c d e )x + (360A c d e - 2520B c d e)x +--R + +--R 3 6 3 7 +--R 60A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 180B a c e + 360A c d e - 360B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 90A a c e - 450B a c d e + 1350A c d e - 4050B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 60B a c e - 120A a c d e - 600B a c d e + 2200A c d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 45A a c e - 45B a c d e - 90A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 1875A c d e - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 12B a e - 18A a c d e - 18B a c d e - 36A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 180B a c d e + 822A c d e - 3594B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 2B a d e - 3A a c d e - 3B a c d e - 6A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e + 147A c d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 3 6 6 3 6 3 2 5 5 +--R (60A c e - 420B c d e )x + (360A c d e - 2520B c d e )x +--R + +--R 3 2 5 3 3 4 4 3 3 4 3 4 3 3 +--R (900A c d e - 6300B c d e )x + (1200A c d e - 8400B c d e )x +--R + +--R 3 4 3 3 5 2 2 3 5 2 3 6 +--R (900A c d e - 6300B c d e )x + (360A c d e - 2520B c d e)x +--R + +--R 3 6 3 7 +--R 60A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 180B a c e + 360A c d e - 360B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 90A a c e - 450B a c d e + 1350A c d e - 4050B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 60B a c e - 120A a c d e - 600B a c d e + 2200A c d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 45A a c e - 45B a c d e - 90A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 1875A c d e - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 12B a e - 18A a c d e - 18B a c d e - 36A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 180B a c d e + 822A c d e - 3594B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 2B a d e - 3A a c d e - 3B a c d e - 6A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e + 147A c d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 1249 + +--S 1250 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1251 + +)clear all + +--S 1252 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^8 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1252 + +--S 1253 of 1457 +r0:=1/7*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^7)-1/6*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^6)+3/5*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^5)+1/4*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^4)+1/3*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^3)-3/2*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^2)+c^3*(7*B*d-A*e)/(e^8*(d+e*x))+B*c^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 3 6 6 +--R (- 420A c e + 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 630B a c e - 1260A c d e + 13230B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 420A a c e - 1050B a c d e - 2100A c d e + 26950B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 315B a c e - 420A a c d e - 1050B a c d e - 2100A c d e +--R + +--R 3 4 3 +--R 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 252A a c e - 189B a c d e - 252A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1260A c d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 70B a e - 84A a c d e - 63B a c d e - 84A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 210B a c d e - 420A c d e + 7203B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e - 10B a d e - 12A a c d e - 9B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e - 60A c d e + 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 3 6 6 +--R (- 420A c e + 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 630B a c e - 1260A c d e + 13230B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 420A a c e - 1050B a c d e - 2100A c d e + 26950B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 315B a c e - 420A a c d e - 1050B a c d e - 2100A c d e +--R + +--R 3 4 3 +--R 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 252A a c e - 189B a c d e - 252A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1260A c d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 70B a e - 84A a c d e - 63B a c d e - 84A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 210B a c d e - 420A c d e + 7203B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e - 10B a d e - 12A a c d e - 9B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e - 60A c d e + 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Union(Expression(Integer),...) +--E 1254 + +--S 1255 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1256 + +)clear all + +--S 1257 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^9 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1257 + +--S 1258 of 1457 +r0:=1/8*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^8)-1/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^7)+1/2*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^6)+1/5*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^5)+1/4*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^4)-c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^8*_ + (d+e*x)^3)+1/2*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^2)-B*c^3/(e^8*(d+e*x)) +--R +--R +--R (2) +--R 3 7 7 1 3 7 7 3 6 6 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 2 7 3 6 3 2 5 5 +--R (- B a c e - A c d e - 7B c d e )x +--R + +--R 3 2 7 5 2 6 5 3 2 5 35 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - -- B c d e )x +--R 4 4 4 4 +--R + +--R 3 2 7 3 2 6 2 2 5 3 3 4 3 4 3 3 +--R (- - B a c e - - A a c d e - B a c d e - A c d e - 7B c d e )x +--R 5 5 +--R + +--R 1 2 7 3 2 6 3 2 2 5 1 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - - B a c d e +--R 2 10 10 2 +--R + +--R 1 3 4 3 7 3 5 2 +--R - - A c d e - - B c d e +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 1 3 7 1 2 6 3 2 2 5 3 2 3 4 +--R - - B a e - - A a c d e - -- B a c d e - -- A a c d e +--R 7 7 35 35 +--R + +--R 1 2 4 3 1 3 5 2 3 6 +--R - - B a c d e - - A c d e - B c d e +--R 7 7 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 3 2 3 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e +--R 8 56 56 280 +--R + +--R 3 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - -- B a c d e - -- A c d e - - B c d +--R 280 56 56 8 +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 10 2 7 9 8 8 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1258 + +--S 1259 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R - 280B c e x + (- 140A c e - 980B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 280B a c e - 280A c d e - 1960B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 210A a c e - 350B a c d e - 350A c d e - 2450B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 168B a c e - 168A a c d e - 280B a c d e - 280A c d e +--R + +--R 3 4 3 +--R - 1960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 140A a c e - 84B a c d e - 84A a c d e - 140B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 140A c d e - 980B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 40B a e - 40A a c d e - 24B a c d e - 24A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 40B a c d e - 40A c d e - 280B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 35A a e - 5B a d e - 5A a c d e - 3B a c d e - 3A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 5B a c d e - 5A c d e - 35B c d +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 +--R 280e x + 2240d e x + 7840d e x + 15680d e x + 19600d e x +--R + +--R 5 11 3 6 10 2 7 9 8 8 +--R 15680d e x + 7840d e x + 2240d e x + 280d e +--R Type: Union(Expression(Integer),...) +--E 1259 + +--S 1260 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1261 + +)clear all + +--S 1262 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^10 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1262 + +--S 1263 of 1457 +r0:=1/9*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^9)-1/8*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^8)+3/7*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^7)+1/6*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))/(e^8*(d+e*x)^6)+1/5*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*_ + d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^5)-3/4*c^2*(7*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)/(e^8*(d+e*x)^4)+1/3*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^3)-_ + 1/2*B*c^3/(e^8*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 7 7 1 3 7 7 3 6 6 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 6 +--R + +--R 3 2 7 1 3 6 7 3 2 5 5 +--R (- - B a c e - - A c d e - - B c d e )x +--R 4 2 4 +--R + +--R 3 2 7 3 2 6 1 3 2 5 7 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - - B c d e )x +--R 5 4 2 4 +--R + +--R 1 2 7 2 2 6 1 2 2 5 1 3 3 4 7 3 4 3 3 +--R (- - B a c e - - A a c d e - - B a c d e - - A c d e - - B c d e )x +--R 2 5 2 3 6 +--R + +--R 3 2 7 3 2 6 6 2 2 5 3 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - -- B a c d e +--R 7 14 35 14 +--R + +--R 1 3 4 3 1 3 5 2 +--R - - A c d e - - B c d e +--R 7 2 +--R * +--R 2 +--R x +--R + +--R 1 3 7 3 2 6 3 2 2 5 3 2 3 4 +--R - - B a e - -- A a c d e - -- B a c d e - -- A a c d e +--R 8 28 56 70 +--R + +--R 3 2 4 3 1 3 5 2 1 3 6 +--R - -- B a c d e - -- A c d e - - B c d e +--R 56 28 8 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 1 2 3 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e +--R 9 72 84 168 +--R + +--R 1 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - --- B a c d e - --- A c d e - -- B c d +--R 210 168 252 72 +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 5 12 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 11 3 7 10 2 8 9 9 8 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1263 + +--S 1264 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R - 1260B c e x + (- 840A c e - 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 1890B a c e - 1260A c d e - 4410B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 1512A a c e - 1890B a c d e - 1260A c d e - 4410B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 1260B a c e - 1008A a c d e - 1260B a c d e - 840A c d e +--R + +--R 3 4 3 +--R - 2940B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 1080A a c e - 540B a c d e - 432A a c d e - 540B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 360A c d e - 1260B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 315B a e - 270A a c d e - 135B a c d e - 108A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 135B a c d e - 90A c d e - 315B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 280A a e - 35B a d e - 30A a c d e - 15B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 15B a c d e - 10A c d e - 35B c d +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 +--R 2520e x + 22680d e x + 90720d e x + 211680d e x + 317520d e x +--R + +--R 5 12 4 6 11 3 7 10 2 8 9 9 8 +--R 317520d e x + 211680d e x + 90720d e x + 22680d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 1264 + +--S 1265 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1266 + +)clear all + +--S 1267 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^11 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1267 + +--S 1268 of 1457 +r0:=1/10*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^10)-1/9*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^9)+3/8*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^8)+1/7*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^7)+1/6*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^6)-3/5*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^5)+1/4*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^4)-1/3*B*c^3/_ + (e^8*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 7 7 1 3 7 7 3 6 6 +--R - - B c e x + (- - A c e - -- B c d e )x +--R 3 4 12 +--R + +--R 3 2 7 3 3 6 7 3 2 5 5 +--R (- - B a c e - -- A c d e - -- B c d e )x +--R 5 10 10 +--R + +--R 1 2 7 1 2 6 1 3 2 5 7 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - -- B c d e )x +--R 2 2 4 12 +--R + +--R 3 2 7 2 2 6 2 2 2 5 1 3 3 4 1 3 4 3 3 +--R (- - B a c e - - A a c d e - - B a c d e - - A c d e - - B c d e )x +--R 7 7 7 7 3 +--R + +--R 3 2 7 9 2 6 3 2 2 5 3 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - -- B a c d e +--R 8 56 28 28 +--R + +--R 3 3 4 3 1 3 5 2 +--R - -- A c d e - - B c d e +--R 56 8 +--R * +--R 2 +--R x +--R + +--R 1 3 7 1 2 6 1 2 2 5 1 2 3 4 +--R - - B a e - -- A a c d e - -- B a c d e - -- A a c d e +--R 9 12 28 42 +--R + +--R 1 2 4 3 1 3 5 2 1 3 6 +--R - -- B a c d e - -- A c d e - -- B c d e +--R 42 84 36 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 1 2 3 4 +--R - -- A a e - -- B a d e - --- A a c d e - --- B a c d e +--R 10 90 120 280 +--R + +--R 1 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - --- B a c d e - --- A c d e - --- B c d +--R 420 420 840 360 +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 5 13 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 12 4 7 11 3 8 10 2 9 9 10 8 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1268 + +--S 1269 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R - 840B c e x + (- 630A c e - 1470B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 1512B a c e - 756A c d e - 1764B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 1260A a c e - 1260B a c d e - 630A c d e - 1470B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 1080B a c e - 720A a c d e - 720B a c d e - 360A c d e +--R + +--R 3 4 3 +--R - 840B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 945A a c e - 405B a c d e - 270A a c d e - 270B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 135A c d e - 315B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 280B a e - 210A a c d e - 90B a c d e - 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 60B a c d e - 30A c d e - 70B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 252A a e - 28B a d e - 21A a c d e - 9B a c d e - 6A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 6B a c d e - 3A c d e - 7B c d +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 +--R 2520e x + 25200d e x + 113400d e x + 302400d e x + 529200d e x +--R + +--R 5 13 5 6 12 4 7 11 3 8 10 2 +--R 635040d e x + 529200d e x + 302400d e x + 113400d e x +--R + +--R 9 9 10 8 +--R 25200d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 1269 + +--S 1270 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1271 + +)clear all + +--S 1272 of 1457 +t0:=(A+B*x)*(d+e*x)^m/(a+c*x^2) +--R +--R +--R m +--R (B x + A)(e x + d) +--R (1) ------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 1272 + +--S 1273 of 1457 +--r0:=-1/2*(d+e*x)^(1+m)*hypergeometric(1,1+m,2+m,(d+e*x)*sqrt(c)/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(A+B*sqrt(-a)/sqrt(c))/((1+m)*sqrt(-a)*_ +-- (e*sqrt(-a)+d*sqrt(c)))-1/2*(d+e*x)^(1+m)*hypergeometric(1,1+m,2+_ +-- m,(d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*B+A*sqrt(-a)*sqrt(c))/_ +-- (a*(1+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c))) +--E 1273 + +--S 1274 of 1457 +--a0:=integrate(t0,x) +--E 1274 + +--S 1275 of 1457 +--m0:=a0-r0 +--E 1275 + +--S 1276 of 1457 +--d0:=D(m0,x) +--E 1276 + +)clear all + +--S 1277 of 1457 +t0:=(A+B*x)*(d+e*x)^(1+m)/(a+c*x^2) +--R +--R +--R m + 1 +--R (B x + A)(e x + d) +--R (1) ----------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1457 +--r0:=-1/2*(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,(d+e*x)*sqrt(c)/(e*_ +-- sqrt(-a)+d*sqrt(c)))*(A+B*sqrt(-a)/sqrt(c))/((2+m)*sqrt(-a)*(e*_ +-- sqrt(-a)+d*sqrt(c)))-1/2*(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,_ +-- (d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*B+A*sqrt(-a)*sqrt(c))/_ +-- (a*(2+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c))) +--E 1278 + +--S 1279 of 1457 +--a0:=integrate(t0,x) +--E 1279 + +--S 1280 of 1457 +--m0:=a0-r0 +--E 1280 + +--S 1281 of 1457 +--d0:=D(m0,x) +--E 1281 + +)clear all + +--S 1282 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1282 + +--S 1283 of 1457 +r0:=e*(4*B*c*d^3+6*A*c*d^2*e-4*a*B*d*e^2-a*A*e^3)*x/c^2+1/2*e^2*(6*B*c*d^2+_ + 4*A*c*d*e-a*B*e^2)*x^2/c^2+1/3*e^3*(4*B*d+A*e)*x^3/c+1/4*B*e^4*x^4/c+_ + 1/2*(4*A*c*d*e*(c*d^2-a*e^2)+B*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*_ + log(a+c*x^2)/c^3-(4*a*B*d*e*(c*d^2-a*e^2)-A*(c^2*d^4-6*a*c*d^2*_ + e^2+a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (12A a c e + 48B a c d e - 72A a c d e - 48B a c d e + 12A c d ) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 2 4 +--R (6B a e - 24A a c d e - 36B a c d e + 24A c d e + 6B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R 3B c e x + (4A c e + 16B c d e )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 6B a c e + 24A c d e + 36B c d e )x +--R + +--R 4 3 2 2 2 2 3 +--R (- 12A a c e - 48B a c d e + 72A c d e + 48B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 +-+ +-+ +--R 12c \|a \|c +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (6A a c e + 24B a c d e - 36A a c d e - 24B a c d e + 6A c d ) +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 4 3 2 2 2 3 2 4 +--R (6B a e - 24A a c d e - 36B a c d e + 24A c d e + 6B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R 3B c e x + (4A c e + 16B c d e )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 6B a c e + 24A c d e + 36B c d e )x +--R + +--R 4 3 2 2 2 2 3 +--R (- 12A a c e - 48B a c d e + 72A c d e + 48B c d e)x +--R * +--R +-----+ +--R \|- a c +--R / +--R 3 +-----+ +--R 12c \|- a c +--R , +--R +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (12A a c e + 48B a c d e - 72A a c d e - 48B a c d e + 12A c d ) +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 4 3 2 2 2 3 2 4 +--R (6B a e - 24A a c d e - 36B a c d e + 24A c d e + 6B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R 3B c e x + (4A c e + 16B c d e )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 6B a c e + 24A c d e + 36B c d e )x +--R + +--R 4 3 2 2 2 2 3 +--R (- 12A a c e - 48B a c d e + 72A c d e + 48B c d e)x +--R * +--R +---+ +--R \|a c +--R / +--R 3 +---+ +--R 12c \|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1284 + +--S 1285 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 2 3 2 4 +-+ +-+ +--R (A a e + 4B a d e - 6A a c d e - 4B a c d e + A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 4 2 3 2 2 3 2 4 +-----+ +--R (- 2A a e - 8B a d e + 12A a c d e + 8B a c d e - 2A c d )\|- a c +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R / +--R 2 +-----+ +-+ +-+ +--R 2c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 4 2 3 2 2 3 2 4 +-+ +-+ +--R (A a e + 4B a d e - 6A a c d e - 4B a c d e + A c d )\|a \|c +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R +-+ +--R 2 4 2 3 2 2 3 2 4 +---+ x\|c +--R (- A a e - 4B a d e + 6A a c d e + 4B a c d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 +-+ +-+ +---+ +--R c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1288 + +)clear all + +--S 1289 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1289 + +--S 1290 of 1457 +r0:=e*(3*B*c*d^2+3*A*c*d*e-a*B*e^2)*x/c^2+1/2*e^2*(3*B*d+A*e)*x^2/c+_ + 1/3*B*e^3*x^3/c+1/2*(B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*_ + log(a+c*x^2)/c^2+(A*c*d*(c*d^2-3*a*e^2)-a*B*e*(3*c*d^2-a*e^2))*_ + atan(x*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R 2 3 2 2 2 3 x\|c +--R (6B a e - 18A a c d e - 18B a c d e + 6A c d )atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 3 2 3 3 +--R (- 3A a e - 9B a d e + 9A c d e + 3B c d )log(c x + a) + 2B c e x +--R + +--R 3 2 2 3 2 2 +--R (3A c e + 9B c d e )x + (- 6B a e + 18A c d e + 18B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 +-+ +-+ +--R 6c \|a \|c +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 3 +--R (3B a e - 9A a c d e - 9B a c d e + 3A c d ) +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 2 2 3 2 +--R (- 3A a e - 9B a d e + 9A c d e + 3B c d )log(c x + a) +--R + +--R 3 3 3 2 2 +--R 2B c e x + (3A c e + 9B c d e )x +--R + +--R 3 2 2 +--R (- 6B a e + 18A c d e + 18B c d e)x +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 +-----+ +--R 6c \|- a c +--R , +--R +--R +---+ +--R 2 3 2 2 2 3 x\|a c +--R (6B a e - 18A a c d e - 18B a c d e + 6A c d )atan(-------) +--R a +--R + +--R 3 2 2 3 2 +--R (- 3A a e - 9B a d e + 9A c d e + 3B c d )log(c x + a) +--R + +--R 3 3 3 2 2 +--R 2B c e x + (3A c e + 9B c d e )x +--R + +--R 3 2 2 +--R (- 6B a e + 18A c d e + 18B c d e)x +--R * +--R +---+ +--R \|a c +--R / +--R 2 +---+ +--R 6c \|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1291 + +--S 1292 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 +-+ +-+ +--R (B a e - 3A a c d e - 3B a c d e + A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 3 2 2 2 3 +-----+ x\|c +--R (- 2B a e + 6A a c d e + 6B a c d e - 2A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 +-----+ +-+ +-+ +--R 2c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 3 2 2 2 3 +-+ +-+ x\|a c +--R (B a e - 3A a c d e - 3B a c d e + A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 3 2 2 2 3 +---+ x\|c +--R (- B a e + 3A a c d e + 3B a c d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 +-+ +-+ +---+ +--R c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1295 + +)clear all + +--S 1296 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1296 + +--S 1297 of 1457 +r0:=e*(2*B*d+A*e)*x/c+1/2*B*e^2*x^2/c+1/2*(B*c*d^2+2*A*c*d*e-a*B*e^2)*_ + log(a+c*x^2)/c^2+(A*c*d^2-2*a*B*d*e-a*A*e^2)*atan(x*sqrt(c)/_ + sqrt(a))/(c^(3/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 x\|c +--R (- 2A a c e - 4B a c d e + 2A c d )atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 +--R (- B a e + 2A c d e + B c d )log(c x + a) + B c e x +--R + +--R 2 +--R (2A c e + 4B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 +-+ +-+ +--R 2c \|a \|c +--R Type: Expression(Integer) +--E 1297 + +--S 1298 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 2 2 (c x - a)\|- a c - 2a c x +--R (A a c e + 2B a c d e - A c d )log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 2 2 2 +--R (- B a e + 2A c d e + B c d )log(c x + a) + B c e x +--R + +--R 2 +--R (2A c e + 4B c d e)x +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 +-----+ +--R 2c \|- a c +--R , +--R +--R +---+ +--R 2 2 2 x\|a c +--R (- 2A a c e - 4B a c d e + 2A c d )atan(-------) +--R a +--R + +--R 2 2 2 2 2 +--R (- B a e + 2A c d e + B c d )log(c x + a) + B c e x +--R + +--R 2 +--R (2A c e + 4B c d e)x +--R * +--R +---+ +--R \|a c +--R / +--R 2 +---+ +--R 2c \|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1298 + +--S 1299 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R 2 2 +-+ +-+ (c x - a)\|- a c - 2a c x +--R (A a e + 2B a d e - A c d )\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 2 +-----+ x\|c +--R (2A a e + 4B a d e - 2A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 2c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1300 + +--S 1301 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 2 +-+ +-+ x\|a c +--R (- A a e - 2B a d e + A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 2 +---+ x\|c +--R (A a e + 2B a d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R / +--R +-+ +-+ +---+ +--R c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1302 + +)clear all + +--S 1303 of 1457 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1303 + +--S 1304 of 1457 +r0:=B*e*x/c+1/2*(B*d+A*e)*log(a+c*x^2)/c+(A*c*d-a*B*e)*atan(x*sqrt(c)/_ + sqrt(a))/(c^(3/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R x\|c 2 +-+ +-+ +--R (- 2B a e + 2A c d)atan(-----) + ((A e + B d)log(c x + a) + 2B e x)\|a \|c +--R +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +-+ +--R 2c\|a \|c +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R (B a e - A c d)log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 +-----+ +--R ((A e + B d)log(c x + a) + 2B e x)\|- a c +--R / +--R +-----+ +--R 2c\|- a c +--R , +--R +---+ +--R x\|a c 2 +---+ +--R (- 2B a e + 2A c d)atan(-------) + ((A e + B d)log(c x + a) + 2B e x)\|a c +--R a +--R ---------------------------------------------------------------------------- +--R +---+ +--R 2c\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1305 + +--S 1306 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c - 2a c x +--R (B a e - A c d)\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R +-----+ x\|c +--R (2B a e - 2A c d)\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 2c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R (- B a e + A c d)\|a \|c atan(-------) + (B a e - A c d)\|a c atan(-----) +--R a +-+ +--R \|a +--R ------------------------------------------------------------------------- +--R +-+ +-+ +---+ +--R c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1309 + +)clear all + +--S 1310 of 1457 +t0:=(A+B*x)/(a+c*x^2) +--R +--R +--R B x + A +--R (1) -------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1310 + +--S 1311 of 1457 +r0:=1/2*B*log(a+c*x^2)/c+A*atan(x*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c)) +--R +--R +--R +-+ +--R x\|c 2 +-+ +-+ +--R 2A c atan(-----) + B log(c x + a)\|a \|c +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R +-+ +-+ +--R 2c\|a \|c +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x 2 +-----+ +--R A c log(---------------------------) + B log(c x + a)\|- a c +--R 2 +--R c x + a +--R [--------------------------------------------------------------, +--R +-----+ +--R 2c\|- a c +--R +---+ +--R x\|a c 2 +---+ +--R 2A c atan(-------) + B log(c x + a)\|a c +--R a +--R ------------------------------------------] +--R +---+ +--R 2c\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1312 + +--S 1313 of 1457 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x\|c +--R A\|a \|c log(---------------------------) - 2A\|- a c atan(-----) +--R 2 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1457 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R A\|a \|c atan(-------) - A\|a c atan(-----) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R \|a \|c \|a c +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1316 + +)clear all + +--S 1317 of 1457 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------- +--R 3 2 +--R c e x + c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1317 + +--S 1318 of 1457 +r0:=-(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)+1/2*(B*d-A*e)*log(a+c*x^2)/_ + (c*d^2+a*e^2)+(A*c*d+a*B*e)*atan(x*sqrt(c)/sqrt(a))/((c*d^2+a*e^2)*_ + sqrt(a)*sqrt(c)) +--R +--R +--R (2) +--R +-+ +--R x\|c +--R (2B a e + 2A c d)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-+ +-+ +--R ((- A e + B d)log(c x + a) + (2A e - 2B d)log(e x + d))\|a \|c +--R / +--R 2 2 +-+ +-+ +--R (2a e + 2c d )\|a \|c +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R (B a e + A c d)log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 +-----+ +--R ((- A e + B d)log(c x + a) + (2A e - 2B d)log(e x + d))\|- a c +--R / +--R 2 2 +-----+ +--R (2a e + 2c d )\|- a c +--R , +--R +--R +---+ +--R x\|a c +--R (2B a e + 2A c d)atan(-------) +--R a +--R + +--R 2 +---+ +--R ((- A e + B d)log(c x + a) + (2A e - 2B d)log(e x + d))\|a c +--R / +--R 2 2 +---+ +--R (2a e + 2c d )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1319 + +--S 1320 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +--R (B a e + A c d)\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R +-----+ x\|c +--R (- 2B a e - 2A c d)\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 2 +-----+ +-+ +-+ +--R (2a e + 2c d )\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1320 + +--S 1321 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R (B a e + A c d)\|a \|c atan(-------) + (- B a e - A c d)\|a c atan(-----) +--R a +-+ +--R \|a +--R ------------------------------------------------------------------------- +--R 2 2 +-+ +-+ +---+ +--R (a e + c d )\|a \|c \|a c +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1323 + +)clear all + +--S 1324 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------ +--R 2 4 3 2 2 2 2 +--R c e x + 2c d e x + (a e + c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1324 + +--S 1325 of 1457 +r0:=(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x))-(B*c*d^2-2*A*c*d*e-a*B*e^2)*_ + log(d+e*x)/(c*d^2+a*e^2)^2+1/2*(B*c*d^2-2*A*c*d*e-a*B*e^2)*_ + log(a+c*x^2)/(c*d^2+a*e^2)^2+(A*c*d^2+2*a*B*d*e-a*A*e^2)*_ + atan(x*sqrt(c)/sqrt(a))*sqrt(c)/((c*d^2+a*e^2)^2*sqrt(a)) +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((- 2A a e + 4B a d e + 2A c d e)x - 2A a d e + 4B a d e + 2A c d ) +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 2 3 +--R ((- B a e - 2A c d e + B c d e)x - B a d e - 2A c d e + B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 2 2 2 +--R (2B a e + 4A c d e - 2B c d e)x + 2B a d e + 4A c d e +--R + +--R 3 +--R - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + 2B a d e - 2A c d e + 2B c d +--R * +--R +-+ +--R \|a +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +-+ +--R ((2a e + 4a c d e + 2c d e)x + 2a d e + 4a c d e + 2c d )\|a +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 3 +--R ((A a e - 2B a d e - A c d e)x + A a d e - 2B a d e - A c d ) +--R * +--R +---+ +--R | c 2 +--R +---+ - 2a x |- - + c x - a +--R | c \| a +--R |- - log(-----------------------) +--R \| a 2 +--R c x + a +--R + +--R 3 2 2 2 2 3 +--R ((- B a e - 2A c d e + B c d e)x - B a d e - 2A c d e + B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 2 2 2 3 +--R ((2B a e + 4A c d e - 2B c d e)x + 2B a d e + 4A c d e - 2B c d ) +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + 2B a d e - 2A c d e + 2B c d +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +--R (2a e + 4a c d e + 2c d e)x + 2a d e + 4a c d e + 2c d +--R , +--R +--R 3 2 2 2 2 3 +--R ((2A a e - 4B a d e - 2A c d e)x + 2A a d e - 4B a d e - 2A c d ) +--R * +--R +-+ +--R |c +--R +-+ a |- +--R |c \|a +--R |- atan(-----) +--R \|a c x +--R + +--R 3 2 2 2 2 3 +--R ((- B a e - 2A c d e + B c d e)x - B a d e - 2A c d e + B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 2 2 2 3 +--R ((2B a e + 4A c d e - 2B c d e)x + 2B a d e + 4A c d e - 2B c d ) +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + 2B a d e - 2A c d e + 2B c d +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +--R (2a e + 4a c d e + 2c d e)x + 2a d e + 4a c d e + 2c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1326 + +--S 1327 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---+ +--R | c 2 +--R +---+ - 2a x |- - + c x - a +--R 2 2 | c +-+ \| a +--R (A a e - 2B a d e - A c d ) |- - \|a log(-----------------------) +--R \| a 2 +--R c x + a +--R + +--R +-+ +--R 2 2 +-+ x\|c +--R (2A a e - 4B a d e - 2A c d )\|c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 4 2 2 2 4 +-+ +--R (2a e + 4a c d e + 2c d )\|a +--R Type: Expression(Integer) +--E 1327 + +--S 1328 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 2 +-+ x\|c +--R (A a e - 2B a d e - A c d )\|c atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R |c +--R +-+ a |- +--R 2 2 +-+ |c \|a +--R (A a e - 2B a d e - A c d )\|a |- atan(-----) +--R \|a c x +--R / +--R 2 4 2 2 2 4 +-+ +--R (a e + 2a c d e + c d )\|a +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1330 + +)clear all + +--S 1331 of 1457 +t0:=(A+B*x)/((d+e*x)^3*(a+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------------- +--R 3 5 2 4 3 2 3 2 3 2 2 3 +--R c e x + 3c d e x + (a e + 3c d e)x + (3a d e + c d )x + 3a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1331 + +--S 1332 of 1457 +r0:=1/2*(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x)^2)+(B*c*d^2-2*A*c*d*e-a*B*e^2)/_ + ((c*d^2+a*e^2)^2*(d+e*x))-c*(B*c*d^3-3*A*c*d^2*e-3*a*B*d*e^2+_ + a*A*e^3)*log(d+e*x)/(c*d^2+a*e^2)^3+1/2*c*(B*c*d^3-3*A*c*d^2*e-_ + 3*a*B*d*e^2+a*A*e^3)*log(a+c*x^2)/(c*d^2+a*e^2)^3+(A*c*d*(c*d^2-_ + 3*a*e^2)+a*B*e*(3*c*d^2-a*e^2))*atan(x*sqrt(c)/sqrt(a))*sqrt(c)/_ + ((c*d^2+a*e^2)^3*sqrt(a)) +--R +--R +--R (2) +--R 2 5 4 2 3 2 3 2 2 +--R (- 2B a e - 6A a c d e + 6B a c d e + 2A c d e )x +--R + +--R 2 4 2 3 3 2 2 4 2 2 3 +--R (- 4B a d e - 12A a c d e + 12B a c d e + 4A c d e)x - 2B a d e +--R + +--R 3 2 4 2 5 +--R - 6A a c d e + 6B a c d e + 2A c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (A a c e - 3B a c d e - 3A c d e + B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 3 +--R (2A a c d e - 6B a c d e - 6A c d e + 2B c d e)x + A a c d e +--R + +--R 3 2 2 4 2 5 +--R - 3B a c d e - 3A c d e + B c d +--R * +--R 2 +--R log(c x + a) +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 2A a c e + 6B a c d e + 6A c d e - 2B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (- 4A a c d e + 12B a c d e + 12A c d e - 4B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R - 2A a c d e + 6B a c d e + 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 4 2 3 2 2 4 2 5 2 4 +--R (- 2B a e - 4A a c d e - 4A c d e + 2B c d e)x - A a e - B a d e +--R + +--R 2 3 3 2 2 4 2 5 +--R - 6A a c d e + 2B a c d e - 5A c d e + 3B c d +--R * +--R +-+ +--R \|a +--R / +--R 3 8 2 2 6 2 4 4 3 6 2 2 +--R (2a e + 6a c d e + 6a c d e + 2c d e )x +--R + +--R 3 7 2 3 5 2 5 3 3 7 3 2 6 2 4 4 +--R (4a d e + 12a c d e + 12a c d e + 4c d e)x + 2a d e + 6a c d e +--R + +--R 2 6 2 3 8 +--R 6a c d e + 2c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 5 4 2 3 2 3 2 2 +--R (B a e + 3A a c d e - 3B a c d e - A c d e )x +--R + +--R 2 4 2 3 3 2 2 4 2 2 3 +--R (2B a d e + 6A a c d e - 6B a c d e - 2A c d e)x + B a d e +--R + +--R 3 2 4 2 5 +--R 3A a c d e - 3B a c d e - A c d +--R * +--R +---+ +--R | c 2 +--R +---+ - 2a x |- - + c x - a +--R | c \| a +--R |- - log(-----------------------) +--R \| a 2 +--R c x + a +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (A a c e - 3B a c d e - 3A c d e + B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 3 +--R (2A a c d e - 6B a c d e - 6A c d e + 2B c d e)x + A a c d e +--R + +--R 3 2 2 4 2 5 +--R - 3B a c d e - 3A c d e + B c d +--R * +--R 2 +--R log(c x + a) +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 2A a c e + 6B a c d e + 6A c d e - 2B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (- 4A a c d e + 12B a c d e + 12A c d e - 4B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R - 2A a c d e + 6B a c d e + 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 4 2 3 2 2 4 2 5 2 4 +--R (- 2B a e - 4A a c d e - 4A c d e + 2B c d e)x - A a e - B a d e +--R + +--R 2 3 3 2 2 4 2 5 +--R - 6A a c d e + 2B a c d e - 5A c d e + 3B c d +--R / +--R 3 8 2 2 6 2 4 4 3 6 2 2 +--R (2a e + 6a c d e + 6a c d e + 2c d e )x +--R + +--R 3 7 2 3 5 2 5 3 3 7 3 2 6 2 4 4 +--R (4a d e + 12a c d e + 12a c d e + 4c d e)x + 2a d e + 6a c d e +--R + +--R 2 6 2 3 8 +--R 6a c d e + 2c d +--R , +--R +--R 2 5 4 2 3 2 3 2 2 +--R (2B a e + 6A a c d e - 6B a c d e - 2A c d e )x +--R + +--R 2 4 2 3 3 2 2 4 2 2 3 +--R (4B a d e + 12A a c d e - 12B a c d e - 4A c d e)x + 2B a d e +--R + +--R 3 2 4 2 5 +--R 6A a c d e - 6B a c d e - 2A c d +--R * +--R +-+ +--R |c +--R +-+ a |- +--R |c \|a +--R |- atan(-----) +--R \|a c x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (A a c e - 3B a c d e - 3A c d e + B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 3 +--R (2A a c d e - 6B a c d e - 6A c d e + 2B c d e)x + A a c d e +--R + +--R 3 2 2 4 2 5 +--R - 3B a c d e - 3A c d e + B c d +--R * +--R 2 +--R log(c x + a) +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 2A a c e + 6B a c d e + 6A c d e - 2B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (- 4A a c d e + 12B a c d e + 12A c d e - 4B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R - 2A a c d e + 6B a c d e + 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 4 2 3 2 2 4 2 5 2 4 +--R (- 2B a e - 4A a c d e - 4A c d e + 2B c d e)x - A a e - B a d e +--R + +--R 2 3 3 2 2 4 2 5 +--R - 6A a c d e + 2B a c d e - 5A c d e + 3B c d +--R / +--R 3 8 2 2 6 2 4 4 3 6 2 2 +--R (2a e + 6a c d e + 6a c d e + 2c d e )x +--R + +--R 3 7 2 3 5 2 5 3 3 7 3 2 6 2 4 4 +--R (4a d e + 12a c d e + 12a c d e + 4c d e)x + 2a d e + 6a c d e +--R + +--R 2 6 2 3 8 +--R 6a c d e + 2c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1333 + +--S 1334 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---+ +--R 2 3 2 2 2 3 | c +-+ +--R (B a e + 3A a c d e - 3B a c d e - A c d ) |- - \|a +--R \| a +--R * +--R +---+ +--R | c 2 +--R - 2a x |- - + c x - a +--R \| a +--R log(-----------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 3 2 2 2 3 +-+ x\|c +--R (2B a e + 6A a c d e - 6B a c d e - 2A c d )\|c atan(-----) +--R +-+ +--R \|a +--R / +--R 3 6 2 2 4 2 4 2 3 6 +-+ +--R (2a e + 6a c d e + 6a c d e + 2c d )\|a +--R Type: Expression(Integer) +--E 1334 + +--S 1335 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 3 2 2 2 3 +-+ x\|c +--R (B a e + 3A a c d e - 3B a c d e - A c d )\|c atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R |c +--R +-+ a |- +--R 2 3 2 2 2 3 +-+ |c \|a +--R (B a e + 3A a c d e - 3B a c d e - A c d )\|a |- atan(-----) +--R \|a c x +--R / +--R 3 6 2 2 4 2 4 2 3 6 +-+ +--R (a e + 3a c d e + 3a c d e + c d )\|a +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1337 + +)clear all + +--S 1338 of 1457 +t0:=(A+B*x)*(d+e*x)^5/(a+c*x^2)^2 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1338 + +--S 1339 of 1457 +r0:=-5/2*e^2*(A*c*d*(2*c*d^2-3*a*e^2)-a*B*e*(6*c*d^2-a*e^2))*x/(a*c^3)-_ + e^3*(5*A*c*d^2-5*a*B*d*e-a*A*e^2)*x^2/(a*c^2)-5/6*e^4*(3*A*c*d-a*B*e)*_ + x^3/(a*c^2)-1/2*A*e^5*x^4/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^5/(a*c*_ + (a+c*x^2))+1/2*(A*c*d*(c^2*d^4+10*a*c*d^2*e^2-15*a^2*e^4)+5*a*B*_ + e*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(3/2)*c^(7/2))+e^2*(5*B*c*d^3+5*A*c*d^2*e-5*a*B*d*e^2-a*A*e^3)*_ + log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 15B a c e - 45A a c d e - 90B a c d e + 30A a c d e +--R + +--R 3 4 4 5 +--R 15B a c d e + 3A c d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 15B a e - 45A a c d e - 90B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 2 3 2 3 2 2 +--R (- 6A a c e - 30B a c d e + 30A a c d e + 30B a c d e )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 +--R - 6A a e - 30B a d e + 30A a c d e + 30B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B a c e x + (3A a c e + 15B a c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (- 10B a c e + 30A a c d e + 60B a c d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 6A a c e + 30B a c d e - 30A a c d e - 30B a c d e +--R + +--R 3 4 +--R 15A c d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 4 2 2 3 2 3 2 +--R - 15B a e + 45A a c d e + 90B a c d e - 30A a c d e +--R + +--R 2 4 3 5 +--R - 15B a c d e + 3A c d +--R * +--R x +--R + +--R 2 5 +--R - 3B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 +-+ +-+ +--R (6a c x + 6a c )\|a \|c +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 15B a c e - 45A a c d e - 90B a c d e + 30A a c d e +--R + +--R 3 4 4 5 +--R 15B a c d e + 3A c d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 15B a e - 45A a c d e - 90B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 5 2 4 2 2 3 2 3 2 2 +--R (- 12A a c e - 60B a c d e + 60A a c d e + 60B a c d e )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 +--R - 12A a e - 60B a d e + 60A a c d e + 60B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 5 2 5 2 4 4 +--R 4B a c e x + (6A a c e + 30B a c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (- 20B a c e + 60A a c d e + 120B a c d e )x +--R + +--R 2 5 2 4 2 +--R (6A a c e + 30B a c d e )x +--R + +--R 3 5 2 4 2 2 3 2 3 2 +--R - 30B a e + 90A a c d e + 180B a c d e - 60A a c d e +--R + +--R 2 4 3 5 +--R - 30B a c d e + 6A c d +--R * +--R x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R - 6A a e - 30B a d e + 60A a c d e + 60B a c d e - 30A a c d e +--R + +--R 2 5 +--R - 6B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 4 2 2 3 +-----+ +--R (12a c x + 12a c )\|- a c +--R , +--R +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 15B a c e - 45A a c d e - 90B a c d e + 30A a c d e +--R + +--R 3 4 4 5 +--R 15B a c d e + 3A c d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 15B a e - 45A a c d e - 90B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 5 2 4 2 2 3 2 3 2 2 +--R (- 6A a c e - 30B a c d e + 30A a c d e + 30B a c d e )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 +--R - 6A a e - 30B a d e + 30A a c d e + 30B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B a c e x + (3A a c e + 15B a c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (- 10B a c e + 30A a c d e + 60B a c d e )x +--R + +--R 2 5 2 4 2 +--R (3A a c e + 15B a c d e )x +--R + +--R 3 5 2 4 2 2 3 2 3 2 +--R - 15B a e + 45A a c d e + 90B a c d e - 30A a c d e +--R + +--R 2 4 3 5 +--R - 15B a c d e + 3A c d +--R * +--R x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R - 3A a e - 15B a d e + 30A a c d e + 30B a c d e - 15A a c d e +--R + +--R 2 5 +--R - 3B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 4 2 2 3 +---+ +--R (6a c x + 6a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1340 + +--S 1341 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 5B a e - 15A a c d e - 30B a c d e + 10A a c d e + 5B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +--R \|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R - 10B a e + 30A a c d e + 60B a c d e - 20A a c d e - 10B a c d e +--R + +--R 3 5 +--R - 2A c d +--R * +--R +-+ +--R +-----+ x\|c +--R \|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R (- 2A a e - 10B a d e + 20A a c d e + 20B a c d e - 10A c d e) +--R * +--R +-----+ +-+ +-+ +--R \|- a c \|a \|c +--R / +--R 3 +-----+ +-+ +-+ +--R 4a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 5B a e - 15A a c d e - 30B a c d e + 10A a c d e + 5B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R +---+ +--R +-+ +-+ x\|a c +--R \|a \|c atan(-------) +--R a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R - 5B a e + 15A a c d e + 30B a c d e - 10A a c d e - 5B a c d e +--R + +--R 3 5 +--R - A c d +--R * +--R +-+ +--R +---+ x\|c +--R \|a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 3 3 2 2 4 +-+ +-+ +--R (- A a e - 5B a d e + 10A a c d e + 10B a c d e - 5A c d e)\|a \|c +--R * +--R +---+ +--R \|a c +--R / +--R 3 +-+ +-+ +---+ +--R 2a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1344 + +)clear all + +--S 1345 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1345 + +--S 1346 of 1457 +r0:=-3/2*e^2*(2*A*c*d^2-4*a*B*d*e-a*A*e^2)*x/(a*c^2)-e^3*(2*A*c*d-a*B*e)*_ + x^2/(a*c^2)-1/2*A*e^4*x^3/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^4/(a*c*_ + (a+c*x^2))+1/2*(4*a*B*d*e*(c*d^2-3*a*e^2)+A*(c^2*d^4+6*a*c*d^2*_ + e^2-3*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(5/2))+e^2*_ + (3*B*c*d^2+2*A*c*d*e-a*B*e^2)*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 2 +--R (- 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A c d )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R - 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (- 2B a c e + 4A a c d e + 6B a c d e )x - 2B a e +--R + +--R 2 3 2 2 2 +--R 4A a c d e + 6B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R B a c e x + (2A a c e + 8B a c d e )x +--R + +--R 2 4 2 3 2 2 2 3 3 2 +--R (2B a c e - 4A a c d e - 6B a c d e + 4A c d e)x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e + A c d )x +--R + +--R 2 4 +--R - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 2 +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e - A c d )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R 3A a c e + 12B a c d e - 6A a c d e - 4B a c d e - A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (- 4B a c e + 8A a c d e + 12B a c d e )x - 4B a e +--R + +--R 2 3 2 2 2 +--R 8A a c d e + 12B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 2 4 2 +--R 2B a c e x + (4A a c e + 16B a c d e )x + 2B a c e x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (6A a c e + 24B a c d e - 12A a c d e - 8B a c d e + 2A c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R - 2B a e + 8A a c d e + 12B a c d e - 8A a c d e - 2B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 4 2 2 3 +-----+ +--R (4a c x + 4a c )\|- a c +--R , +--R +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 2 +--R (- 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A c d )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R - 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (- 2B a c e + 4A a c d e + 6B a c d e )x - 2B a e +--R + +--R 2 3 2 2 2 +--R 4A a c d e + 6B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 2 4 2 +--R B a c e x + (2A a c e + 8B a c d e )x + B a c e x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e + A c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R - B a e + 4A a c d e + 6B a c d e - 4A a c d e - B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 4 2 2 3 +---+ +--R (2a c x + 2a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1347 + +--S 1348 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 2 2 2 3 3 4 +-+ +-+ +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e - A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (6A a c e + 24B a c d e - 12A a c d e - 8B a c d e - 2A c d ) +--R * +--R +-+ +--R +-----+ x\|c +--R \|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 +-----+ +-+ +-+ +--R (- 2B a e + 8A a c d e + 12B a c d e - 8A c d e)\|- a c \|a \|c +--R / +--R 3 +-----+ +-+ +-+ +--R 4a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 4 2 3 2 2 2 2 3 3 4 +-+ +--R (- 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A c d )\|a +--R * +--R +---+ +--R +-+ x\|a c +--R \|c atan(-------) +--R a +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +---+ +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e - A c d )\|a c +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 +-+ +-+ +---+ +--R (- B a e + 4A a c d e + 6B a c d e - 4A c d e)\|a \|c \|a c +--R / +--R 3 +-+ +-+ +---+ +--R 2a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1351 + +)clear all + +--S 1352 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1352 + +--S 1353 of 1457 +r0:=-3/2*e^2*(A*c*d-a*B*e)*x/(a*c^2)-1/2*A*e^3*x^2/(a*c)-1/2*(a*B-A*c*x)*_ + (d+e*x)^3/(a*c*(a+c*x^2))+1/2*(3*a*B*e*(c*d^2-a*e^2)+A*c*d*_ + (c*d^2+3*a*e^2))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(5/2))+1/2*_ + e^2*(3*B*d+A*e)*log(a+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 3B a c e + 3A a c d e + 3B a c d e + A c d )x - 3B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e + 3B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((A a c e + 3B a c d e )x + A a e + 3B a d e )log(c x + a) +--R + +--R 3 3 3 2 2 2 2 +--R 2B a c e x + (- A a c e - 3B a c d e + 3A c d e)x +--R + +--R 2 3 2 2 2 3 3 +--R (3B a e - 3A a c d e - 3B a c d e + A c d )x - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (3B a c e - 3A a c d e - 3B a c d e - A c d )x + 3B a e +--R + +--R 2 2 2 2 2 3 +--R - 3A a c d e - 3B a c d e - A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((2A a c e + 6B a c d e )x + 2A a e + 6B a d e )log(c x + a) +--R + +--R 3 3 2 3 2 2 2 3 +--R 4B a c e x + (6B a e - 6A a c d e - 6B a c d e + 2A c d )x +--R + +--R 2 3 2 2 2 3 +--R 2A a e + 6B a d e - 6A a c d e - 2B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 3 2 2 2 +-----+ +--R (4a c x + 4a c )\|- a c +--R , +--R +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 3B a c e + 3A a c d e + 3B a c d e + A c d )x - 3B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e + 3B a c d e + A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((A a c e + 3B a c d e )x + A a e + 3B a d e )log(c x + a) +--R + +--R 3 3 2 3 2 2 2 3 +--R 2B a c e x + (3B a e - 3A a c d e - 3B a c d e + A c d )x +--R + +--R 2 3 2 2 2 3 +--R A a e + 3B a d e - 3A a c d e - B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 3 2 2 2 +---+ +--R (2a c x + 2a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1354 + +--S 1355 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 +-+ +-+ +--R (3B a e - 3A a c d e - 3B a c d e - A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 3 2 2 2 3 +-----+ x\|c +--R (6B a e - 6A a c d e - 6B a c d e - 2A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 +-----+ +-+ +-+ +--R (2A a e + 6B a d e - 6A c d e)\|- a c \|a \|c +--R / +--R 2 +-----+ +-+ +-+ +--R 4a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1355 + +--S 1356 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 3 2 2 2 3 +-+ +-+ x\|a c +--R (- 3B a e + 3A a c d e + 3B a c d e + A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 3 2 2 2 3 +---+ x\|c +--R (3B a e - 3A a c d e - 3B a c d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 +-+ +-+ +---+ +--R (A a e + 3B a d e - 3A c d e)\|a \|c \|a c +--R / +--R 2 +-+ +-+ +---+ +--R 2a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1357 + +--S 1358 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1358 + +)clear all + +--S 1359 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1359 + +--S 1360 of 1457 +r0:=-1/2*A*e^2*x/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^2/(a*c*(a+c*x^2))+_ + 1/2*(A*c*d^2+2*a*B*d*e+a*A*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*_ + c^(3/2))+1/2*B*e^2*log(a+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 3 2 2 2 2 2 2 2 +--R ((A a c e + 2B a c d e + A c d )x + A a c e + 2B a c d e + A a c d ) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 2 2 2 +--R (B a c e x + B a e )log(c x + a) + (- B a c e + 2A c d e)x +--R + +--R 2 2 2 2 +--R (- A a c e - 2B a c d e + A c d )x - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 2 2 2 2 +--R (A a c e + 2B a c d e + A c d )x + A a c e + 2B a c d e +--R + +--R 2 2 +--R A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 2 2 2 +--R (2B a c e x + 2B a e )log(c x + a) +--R + +--R 2 2 2 2 2 +--R (- 2A a c e - 4B a c d e + 2A c d )x + 2B a e - 4A a c d e +--R + +--R 2 +--R - 2B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 3 2 2 2 +-----+ +--R (4a c x + 4a c )\|- a c +--R , +--R +--R 2 2 2 3 2 2 2 2 2 +--R (A a c e + 2B a c d e + A c d )x + A a c e + 2B a c d e +--R + +--R 2 2 +--R A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 2 2 2 2 +--R (B a c e x + B a e )log(c x + a) +--R + +--R 2 2 2 2 2 2 +--R (- A a c e - 2B a c d e + A c d )x + B a e - 2A a c d e - B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 3 2 2 2 +---+ +--R (2a c x + 2a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1361 + +--S 1362 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R 2 2 2 +-+ +-+ (c x - a)\|- a c + 2a c x +--R (A a c e + 2B a c d e + A c d )\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 2 2 +-----+ x\|c +--R (- 2A a c e - 4B a c d e - 2A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-----+ +-+ +-+ +--R (2B a e - 4A c d e)\|- a c \|a \|c +--R / +--R 2 +-----+ +-+ +-+ +--R 4a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1362 + +--S 1363 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 2 2 +-+ +-+ x\|a c +--R (A a c e + 2B a c d e + A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 2 2 +---+ x\|c +--R (- A a c e - 2B a c d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-+ +-+ +---+ +--R (B a e - 2A c d e)\|a \|c \|a c +--R / +--R 2 +-+ +-+ +---+ +--R 2a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1364 + +--S 1365 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1365 + +)clear all + +--S 1366 of 1457 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1366 + +--S 1367 of 1457 +r0:=-1/2*(a*B-A*c*x)*(d+e*x)/(a*c*(a+c*x^2))+1/2*(A*c*d+a*B*e)*_ + atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(3/2)) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 x\|c +--R ((B a c e + A c d)x + B a e + A a c d)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-+ +-+ +--R (A c e x + (- B a e + A c d)x - B a d)\|a \|c +--R / +--R 2 2 2 +-+ +-+ +--R (2a c x + 2a c)\|a \|c +--R Type: Expression(Integer) +--E 1367 + +--S 1368 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 2 2 (c x - a)\|- a c + 2a c x +--R ((B a c e + A c d)x + B a e + A a c d)log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-----+ +--R ((- 2B a e + 2A c d)x - 2A a e - 2B a d)\|- a c +--R / +--R 2 2 2 +-----+ +--R (4a c x + 4a c)\|- a c +--R , +--R +--R +---+ +--R 2 2 2 x\|a c +--R ((B a c e + A c d)x + B a e + A a c d)atan(-------) +--R a +--R + +--R +---+ +--R ((- B a e + A c d)x - A a e - B a d)\|a c +--R / +--R 2 2 2 +---+ +--R (2a c x + 2a c)\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1368 + +--S 1369 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +--R (B a e + A c d)\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R +-----+ x\|c +-----+ +-+ +-+ +--R (- 2B a e - 2A c d)\|- a c atan(-----) - 2A e\|- a c \|a \|c +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 4a c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1369 + +--S 1370 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1370 + +--S 1371 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R (B a e + A c d)\|a \|c atan(-------) + (- B a e - A c d)\|a c atan(-----) +--R a +-+ +--R \|a +--R + +--R +-+ +-+ +---+ +--R - A e\|a \|c \|a c +--R / +--R +-+ +-+ +---+ +--R 2a c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1371 + +--S 1372 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1372 + +)clear all + +--S 1373 of 1457 +t0:=(A+B*x)/(a+c*x^2)^2 +--R +--R +--R B x + A +--R (1) ------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1373 + +--S 1374 of 1457 +r0:=1/2*(-a*B+A*c*x)/(a*c*(a+c*x^2))+1/2*A*atan(x*sqrt(c)/sqrt(a))/_ + (a^(3/2)*sqrt(c)) +--R +--R +--R +-+ +--R 2 2 x\|c +-+ +-+ +--R (A c x + A a c)atan(-----) + (A c x - B a)\|a \|c +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 2 2 2 +-+ +-+ +--R (2a c x + 2a c)\|a \|c +--R Type: Expression(Integer) +--E 1374 + +--S 1375 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R 2 2 (c x - a)\|- a c + 2a c x +-----+ +--R (A c x + A a c)log(---------------------------) + (2A c x - 2B a)\|- a c +--R 2 +--R c x + a +--R [--------------------------------------------------------------------------, +--R 2 2 2 +-----+ +--R (4a c x + 4a c)\|- a c +--R +---+ +--R 2 2 x\|a c +---+ +--R (A c x + A a c)atan(-------) + (A c x - B a)\|a c +--R a +--R ---------------------------------------------------] +--R 2 2 2 +---+ +--R (2a c x + 2a c)\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1375 + +--S 1376 of 1457 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x\|c +--R A\|a \|c log(---------------------------) - 2A\|- a c atan(-----) +--R 2 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4a\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1376 + +--S 1377 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1377 + +--S 1378 of 1457 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R A\|a \|c atan(-------) - A\|a c atan(-----) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 2a\|a \|c \|a c +--R Type: Expression(Integer) +--E 1378 + +--S 1379 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1379 + +)clear all + +--S 1380 of 1457 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R 2 5 2 4 3 2 2 2 +--R c e x + c d x + 2a c e x + 2a c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1380 + +--S 1381 of 1457 +r0:=1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2))-_ + e^2*(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)^2+1/2*e^2*(B*d-A*e)*log(a+_ + c*x^2)/(c*d^2+a*e^2)^2-1/2*(a*B*e*(c*d^2-a*e^2)-A*c*d*(c*d^2+_ + 3*a*e^2))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*(c*d^2+a*e^2)^2*sqrt(c)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (B a c e + 3A a c d e - B a c d e + A c d )x + B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e - B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((- A a c e + B a c d e )x - A a e + B a d e )log(c x + a) +--R + +--R 3 2 2 2 3 2 2 +--R ((2A a c e - 2B a c d e )x + 2A a e - 2B a d e )log(e x + d) +--R + +--R 2 3 2 2 2 3 2 3 2 2 +--R (B a e + A a c d e + B a c d e + A c d )x + A a e - B a d e +--R + +--R 2 3 +--R A a c d e - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +-+ +-+ +--R ((2a c e + 4a c d e + 2a c d )x + 2a e + 4a c d e + 2a c d )\|a \|c +--R Type: Expression(Integer) +--E 1381 + +--S 1382 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (B a c e + 3A a c d e - B a c d e + A c d )x + B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e - B a c d e + A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((- 2A a c e + 2B a c d e )x - 2A a e + 2B a d e )log(c x + a) +--R + +--R 3 2 2 2 3 2 2 +--R ((4A a c e - 4B a c d e )x + 4A a e - 4B a d e )log(e x + d) +--R + +--R 2 3 2 2 2 3 2 3 +--R (2B a e + 2A a c d e + 2B a c d e + 2A c d )x + 2A a e +--R + +--R 2 2 2 3 +--R - 2B a d e + 2A a c d e - 2B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +-----+ +--R ((4a c e + 8a c d e + 4a c d )x + 4a e + 8a c d e + 4a c d )\|- a c +--R , +--R +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (B a c e + 3A a c d e - B a c d e + A c d )x + B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e - B a c d e + A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((- A a c e + B a c d e )x - A a e + B a d e )log(c x + a) +--R + +--R 3 2 2 2 3 2 2 +--R ((2A a c e - 2B a c d e )x + 2A a e - 2B a d e )log(e x + d) +--R + +--R 2 3 2 2 2 3 2 3 2 2 +--R (B a e + A a c d e + B a c d e + A c d )x + A a e - B a d e +--R + +--R 2 3 +--R A a c d e - B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +---+ +--R ((2a c e + 4a c d e + 2a c d )x + 2a e + 4a c d e + 2a c d )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1382 + +--S 1383 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 +-+ +-+ +--R (B a e + 3A a c d e - B a c d e + A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 3 2 2 2 3 +-----+ x\|c +--R (- 2B a e - 6A a c d e + 2B a c d e - 2A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R 3 4 2 2 2 2 4 +-----+ +-+ +-+ +--R (4a e + 8a c d e + 4a c d )\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1383 + +--S 1384 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1384 + +--S 1385 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 3 2 2 2 3 +-+ +-+ x\|a c +--R (B a e + 3A a c d e - B a c d e + A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 3 2 2 2 3 +---+ x\|c +--R (- B a e - 3A a c d e + B a c d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R / +--R 3 4 2 2 2 2 4 +-+ +-+ +---+ +--R (2a e + 4a c d e + 2a c d )\|a \|c \|a c +--R Type: Expression(Integer) +--E 1385 + +--S 1386 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1386 + +)clear all + +--S 1387 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 5 2 2 2 4 3 +--R c e x + 2c d e x + (2a c e + c d )x + 4a c d e x +--R + +--R 2 2 2 2 2 2 2 +--R (a e + 2a c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1387 + +--S 1388 of 1457 +r0:=1/2*e*(A*c*d^2+4*a*B*d*e-3*a*A*e^2)/(a*(c*d^2+a*e^2)^2*(d+e*x))+_ + 1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(d+e*x)*_ + (a+c*x^2))-e^2*(3*B*c*d^2-4*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+_ + a*e^2)^3+1/2*e^2*(3*B*c*d^2-4*A*c*d*e-a*B*e^2)*log(a+c*x^2)/_ + (c*d^2+a*e^2)^3-1/2*(2*a*B*d*e*(c*d^2-3*a*e^2)-A*(c^2*d^4+6*a*_ + c*d^2*e^2-3*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))*sqrt(c)/(a^(3/2)*_ + (c*d^2+a*e^2)^3) +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 2 3 2 3 4 3 +--R (- 3A a c e + 6B a c d e + 6A a c d e - 2B a c d e + A c d e)x +--R + +--R 2 4 2 2 3 2 3 2 2 4 3 5 2 +--R (- 3A a c d e + 6B a c d e + 6A a c d e - 2B a c d e + A c d )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R (- 3A a e + 6B a d e + 6A a c d e - 2B a c d e + A a c d e)x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 +--R - 3A a d e + 6B a d e + 6A a c d e - 2B a c d e + A a c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 2 3 3 +--R (- B a c e - 4A a c d e + 3B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (- B a c d e - 4A a c d e + 3B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (- B a e - 4A a c d e + 3B a c d e )x - B a d e - 4A a c d e +--R + +--R 2 3 2 +--R 3B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 2 4 2 2 3 3 +--R (2B a c e + 8A a c d e - 6B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (2B a c d e + 8A a c d e - 6B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (2B a e + 8A a c d e - 6B a c d e )x + 2B a d e + 8A a c d e +--R + +--R 2 3 2 +--R - 6B a c d e +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 2 +--R (- 3A a c e + 4B a c d e - 2A a c d e + 4B a c d e + A c d e)x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R B a e + A a c d e + 2B a c d e + 2A a c d e + B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R x +--R + +--R 3 5 3 4 2 3 2 2 4 2 5 +--R - 2A a e + 3B a d e + 2B a c d e + 2A a c d e - B a c d +--R * +--R +-+ +--R \|a +--R / +--R 4 7 3 2 2 5 2 3 4 3 4 6 3 +--R (2a c e + 6a c d e + 6a c d e + 2a c d e)x +--R + +--R 4 6 3 2 3 4 2 3 5 2 4 7 2 +--R (2a c d e + 6a c d e + 6a c d e + 2a c d )x +--R + +--R 5 7 4 2 5 3 2 4 3 2 3 6 5 6 4 3 4 +--R (2a e + 6a c d e + 6a c d e + 2a c d e)x + 2a d e + 6a c d e +--R + +--R 3 2 5 2 2 3 7 +--R 6a c d e + 2a c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1388 + +--S 1389 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 5 2 4 2 2 3 2 3 2 3 4 3 +--R (3A a c e - 6B a c d e - 6A a c d e + 2B a c d e - A c d e)x +--R + +--R 2 4 2 2 3 2 3 2 2 4 3 5 2 +--R (3A a c d e - 6B a c d e - 6A a c d e + 2B a c d e - A c d )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R (3A a e - 6B a d e - 6A a c d e + 2B a c d e - A a c d e)x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 +--R 3A a d e - 6B a d e - 6A a c d e + 2B a c d e - A a c d +--R * +--R +---+ +--R | c 2 +--R +---+ - 2a x |- - + c x - a +--R | c \| a +--R |- - log(-----------------------) +--R \| a 2 +--R c x + a +--R + +--R 2 5 2 4 2 2 3 3 +--R (- 2B a c e - 8A a c d e + 6B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (- 2B a c d e - 8A a c d e + 6B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (- 2B a e - 8A a c d e + 6B a c d e )x - 2B a d e - 8A a c d e +--R + +--R 2 3 2 +--R 6B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 2 4 2 2 3 3 +--R (4B a c e + 16A a c d e - 12B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (4B a c d e + 16A a c d e - 12B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (4B a e + 16A a c d e - 12B a c d e )x + 4B a d e + 16A a c d e +--R + +--R 2 3 2 +--R - 12B a c d e +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 2 +--R (- 6A a c e + 8B a c d e - 4A a c d e + 8B a c d e + 2A c d e)x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 2B a e + 2A a c d e + 4B a c d e + 4A a c d e + 2B a c d e +--R + +--R 3 5 +--R 2A c d +--R * +--R x +--R + +--R 3 5 3 4 2 3 2 2 4 2 5 +--R - 4A a e + 6B a d e + 4B a c d e + 4A a c d e - 2B a c d +--R / +--R 4 7 3 2 2 5 2 3 4 3 4 6 3 +--R (4a c e + 12a c d e + 12a c d e + 4a c d e)x +--R + +--R 4 6 3 2 3 4 2 3 5 2 4 7 2 +--R (4a c d e + 12a c d e + 12a c d e + 4a c d )x +--R + +--R 5 7 4 2 5 3 2 4 3 2 3 6 5 6 4 3 4 +--R (4a e + 12a c d e + 12a c d e + 4a c d e)x + 4a d e + 12a c d e +--R + +--R 3 2 5 2 2 3 7 +--R 12a c d e + 4a c d +--R , +--R +--R 2 5 2 4 2 2 3 2 3 2 3 4 3 +--R (3A a c e - 6B a c d e - 6A a c d e + 2B a c d e - A c d e)x +--R + +--R 2 4 2 2 3 2 3 2 2 4 3 5 2 +--R (3A a c d e - 6B a c d e - 6A a c d e + 2B a c d e - A c d )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R (3A a e - 6B a d e - 6A a c d e + 2B a c d e - A a c d e)x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 +--R 3A a d e - 6B a d e - 6A a c d e + 2B a c d e - A a c d +--R * +--R +-+ +--R |c +--R +-+ a |- +--R |c \|a +--R |- atan(-----) +--R \|a c x +--R + +--R 2 5 2 4 2 2 3 3 +--R (- B a c e - 4A a c d e + 3B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (- B a c d e - 4A a c d e + 3B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (- B a e - 4A a c d e + 3B a c d e )x - B a d e - 4A a c d e +--R + +--R 2 3 2 +--R 3B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 2 4 2 2 3 3 +--R (2B a c e + 8A a c d e - 6B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (2B a c d e + 8A a c d e - 6B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (2B a e + 8A a c d e - 6B a c d e )x + 2B a d e + 8A a c d e +--R + +--R 2 3 2 +--R - 6B a c d e +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 2 +--R (- 3A a c e + 4B a c d e - 2A a c d e + 4B a c d e + A c d e)x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 3 5 +--R (B a e + A a c d e + 2B a c d e + 2A a c d e + B a c d e + A c d )x +--R + +--R 3 5 3 4 2 3 2 2 4 2 5 +--R - 2A a e + 3B a d e + 2B a c d e + 2A a c d e - B a c d +--R / +--R 4 7 3 2 2 5 2 3 4 3 4 6 3 +--R (2a c e + 6a c d e + 6a c d e + 2a c d e)x +--R + +--R 4 6 3 2 3 4 2 3 5 2 4 7 2 +--R (2a c d e + 6a c d e + 6a c d e + 2a c d )x +--R + +--R 5 7 4 2 5 3 2 4 3 2 3 6 5 6 4 3 4 +--R (2a e + 6a c d e + 6a c d e + 2a c d e)x + 2a d e + 6a c d e +--R + +--R 3 2 5 2 2 3 7 +--R 6a c d e + 2a c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1389 + +--S 1390 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---+ +--R 2 4 2 3 2 2 3 2 4 | c +-+ +--R (3A a e - 6B a d e - 6A a c d e + 2B a c d e - A c d ) |- - \|a +--R \| a +--R * +--R +---+ +--R | c 2 +--R - 2a x |- - + c x - a +--R \| a +--R log(-----------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 4 2 3 2 2 3 2 4 +-+ x\|c +--R (6A a e - 12B a d e - 12A a c d e + 4B a c d e - 2A c d )\|c atan(-----) +--R +-+ +--R \|a +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +-+ +--R (4a e + 12a c d e + 12a c d e + 4a c d )\|a +--R Type: Expression(Integer) +--E 1390 + +--S 1391 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1391 + +--S 1392 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 4 2 3 2 2 3 2 4 +-+ x\|c +--R (3A a e - 6B a d e - 6A a c d e + 2B a c d e - A c d )\|c atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R 2 4 2 3 2 2 3 2 4 +-+ |c +--R (3A a e - 6B a d e - 6A a c d e + 2B a c d e - A c d )\|a |- +--R \|a +--R * +--R +-+ +--R |c +--R a |- +--R \|a +--R atan(-----) +--R c x +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +-+ +--R (2a e + 6a c d e + 6a c d e + 2a c d )\|a +--R Type: Expression(Integer) +--E 1392 + +--S 1393 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1393 + +)clear all + +--S 1394 of 1457 +t0:=(A+B*x)*(d+e*x)^5/(a+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1394 + +--S 1395 of 1457 +r0:=-3/8*e^2*(5*a*B*e*(2*c*d^2-a*e^2)+A*c*d*(6*c*d^2+5*a*e^2))*x/(a^2*c^3)-_ + 1/2*e^3*(3*A*c*d^2+5*a*B*d*e+a*A*e^2)*x^2/(a^2*c^2)-1/8*e^4*(3*A*_ + c*d+5*a*B*e)*x^3/(a^2*c^2)-1/4*(a*B-A*c*x)*(d+e*x)^5/(a*c*(a+_ + c*x^2)^2)+1/8*(d+e*x)^4*(2*a*A*e+(3*A*c*d+5*a*B*e)*x)/(a^2*c*(a+_ + c*x^2))+1/8*(5*a*B*e*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4)+A*c*d*_ + (3*c^2*d^4+10*a*c*d^2*e^2+15*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(5/2)*c^(7/2))+1/2*e^4*(5*B*d+A*e)*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R - 15B a c e + 15A a c d e + 30B a c d e + 10A a c d e +--R + +--R 4 4 5 5 +--R 5B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R - 30B a c e + 30A a c d e + 60B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R 10B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R - 15B a e + 15A a c d e + 30B a c d e + 10A a c d e + 5B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (4A a c e + 20B a c d e )x + (8A a c e + 40B a c d e )x +--R + +--R 4 5 4 4 +--R 4A a e + 20B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 5 +--R 8B a c e x +--R + +--R 2 2 5 2 2 4 3 2 3 3 3 2 +--R - 6A a c e - 30B a c d e + 20A a c d e + 20B a c d e +--R + +--R 4 4 +--R 12A c d e +--R * +--R 4 +--R x +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 25B a c e - 25A a c d e - 50B a c d e + 10A a c d e +--R + +--R 3 4 4 5 +--R 5B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 3 4 2 +--R (- 4A a c e - 20B a c d e + 24A a c d e)x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e +--R + +--R 2 2 4 3 5 +--R - 5B a c d e + 5A a c d +--R * +--R x +--R + +--R 2 2 4 2 2 5 +--R 2A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 5 4 3 4 2 4 3 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 1395 + +--S 1396 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R 15B a c e - 15A a c d e - 30B a c d e - 10A a c d e +--R + +--R 4 4 5 5 +--R - 5B a c d e - 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R 30B a c e - 30A a c d e - 60B a c d e - 20A a c d e +--R + +--R 2 3 4 4 5 +--R - 10B a c d e - 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e - 5B a c d e +--R + +--R 2 3 5 +--R - 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (8A a c e + 40B a c d e )x + (16A a c e + 80B a c d e )x +--R + +--R 4 5 4 4 +--R 8A a e + 40B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 5 +--R 16B a c e x +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 50B a c e - 50A a c d e - 100B a c d e + 20A a c d e +--R + +--R 3 4 4 5 +--R 10B a c d e + 6A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (16A a c e + 80B a c d e - 80A a c d e - 80B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 +--R 30B a e - 30A a c d e - 60B a c d e - 20A a c d e +--R + +--R 2 2 4 3 5 +--R - 10B a c d e + 10A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 12A a e + 60B a d e - 40A a c d e - 40B a c d e - 20A a c d e +--R + +--R 2 2 5 +--R - 4B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 5 4 3 4 2 4 3 +-----+ +--R (16a c x + 32a c x + 16a c )\|- a c +--R , +--R +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R - 15B a c e + 15A a c d e + 30B a c d e + 10A a c d e +--R + +--R 4 4 5 5 +--R 5B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R - 30B a c e + 30A a c d e + 60B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R 10B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 +--R - 15B a e + 15A a c d e + 30B a c d e + 10A a c d e +--R + +--R 3 2 4 2 3 5 +--R 5B a c d e + 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (4A a c e + 20B a c d e )x + (8A a c e + 40B a c d e )x +--R + +--R 4 5 4 4 +--R 4A a e + 20B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 5 +--R 8B a c e x +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 25B a c e - 25A a c d e - 50B a c d e + 10A a c d e +--R + +--R 3 4 4 5 +--R 5B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (8A a c e + 40B a c d e - 40A a c d e - 40B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e +--R + +--R 2 2 4 3 5 +--R - 5B a c d e + 5A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 6A a e + 30B a d e - 20A a c d e - 20B a c d e - 10A a c d e +--R + +--R 2 2 5 +--R - 2B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 2 5 4 3 4 2 4 3 +---+ +--R (8a c x + 16a c x + 8a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1396 + +--S 1397 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e - 5B a c d e +--R + +--R 3 5 +--R - 3A c d +--R * +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c - 2a c x +--R \|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 30B a e - 30A a c d e - 60B a c d e - 20A a c d e - 10B a c d e +--R + +--R 3 5 +--R - 6A c d +--R * +--R +-+ +--R +-----+ x\|c +--R \|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R (12A a e + 60B a d e - 40A a c d e - 40B a c d e - 24A c d e) +--R * +--R +-----+ +-+ +-+ +--R \|- a c \|a \|c +--R / +--R 2 3 +-----+ +-+ +-+ +--R 16a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1397 + +--S 1398 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1398 + +--S 1399 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R - 15B a e + 15A a c d e + 30B a c d e + 10A a c d e + 5B a c d e +--R + +--R 3 5 +--R 3A c d +--R * +--R +---+ +--R +-+ +-+ x\|a c +--R \|a \|c atan(-------) +--R a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e - 5B a c d e +--R + +--R 3 5 +--R - 3A c d +--R * +--R +-+ +--R +---+ x\|c +--R \|a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 3 3 2 2 4 +-+ +--R (6A a e + 30B a d e - 20A a c d e - 20B a c d e - 12A c d e)\|a +--R * +--R +-+ +---+ +--R \|c \|a c +--R / +--R 2 3 +-+ +-+ +---+ +--R 8a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1399 + +--S 1400 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1400 + +)clear all + +--S 1401 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1401 + +--S 1402 of 1457 +r0:=-3/8*e^2*(3*A*c*d^2+4*a*B*d*e+a*A*e^2)*x/(a^2*c^2)-1/8*e^3*(3*A*c*d+_ + 4*a*B*e)*x^2/(a^2*c^2)-1/4*(a*B-A*c*x)*(d+e*x)^4/(a*c*(a+c*x^2)^2)+_ + 1/8*(d+e*x)^3*(a*A*e+(3*A*c*d+4*a*B*e)*x)/(a^2*c*(a+c*x^2))+_ + 1/8*(3*A*(c*d^2+a*e^2)^2+4*a*B*d*e*(c*d^2+3*a*e^2))*atan(x*_ + sqrt(c)/sqrt(a))/(a^(5/2)*c^(5/2))+1/2*B*e^4*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 3 4 2 3 3 4 2 2 4 3 5 4 4 +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 2 4 3 2 3 2 3 2 2 2 3 3 4 4 2 +--R (6A a c e + 24B a c d e + 12A a c d e + 8B a c d e + 6A a c d )x +--R + +--R 4 4 4 3 3 2 2 2 3 2 3 2 3 4 +--R 3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 4 4 3 4 2 4 4 2 +--R (4B a c e x + 8B a c e x + 4B a e )log(c x + a) +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 6B a c e + 8A a c d e + 12B a c d e + 9A c d e)x +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 3 +--R (- 5A a c e - 20B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 4 3 3 2 +--R (- 4B a c e + 18A a c d e)x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R (- 3A a c e - 12B a c d e - 6A a c d e - 4B a c d e + 5A a c d )x +--R + +--R 2 2 3 2 2 4 +--R A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 5 4 3 4 2 4 3 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 1402 + +--S 1403 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 4 2 3 3 4 2 2 4 3 5 4 4 +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 2 4 3 2 3 2 3 2 2 2 3 3 +--R 6A a c e + 24B a c d e + 12A a c d e + 8B a c d e +--R + +--R 4 4 +--R 6A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 2 3 2 3 2 3 4 +--R 3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 4 4 3 4 2 4 4 2 +--R (8B a c e x + 16B a c e x + 8B a e )log(c x + a) +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 +--R - 10A a c e - 40B a c d e + 12A a c d e + 8B a c d e +--R + +--R 4 4 +--R 6A c d +--R * +--R 3 +--R x +--R + +--R 3 4 2 2 3 2 2 2 2 2 +--R (16B a c e - 32A a c d e - 48B a c d e )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 6A a c e - 24B a c d e - 12A a c d e - 8B a c d e +--R + +--R 3 4 +--R 10A a c d +--R * +--R x +--R + +--R 4 4 3 3 3 2 2 2 2 3 2 2 4 +--R 12B a e - 16A a c d e - 24B a c d e - 16A a c d e - 4B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 5 4 3 4 2 4 3 +-----+ +--R (16a c x + 32a c x + 16a c )\|- a c +--R , +--R +--R 2 3 4 2 3 3 4 2 2 4 3 5 4 4 +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 2 4 3 2 3 2 3 2 2 2 3 3 +--R 6A a c e + 24B a c d e + 12A a c d e + 8B a c d e +--R + +--R 4 4 +--R 6A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 2 3 2 3 2 3 4 +--R 3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 2 4 4 3 4 2 4 4 2 +--R (4B a c e x + 8B a c e x + 4B a e )log(c x + a) +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 3 +--R (- 5A a c e - 20B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 4 2 2 3 2 2 2 2 2 +--R (8B a c e - 16A a c d e - 24B a c d e )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 3A a c e - 12B a c d e - 6A a c d e - 4B a c d e +--R + +--R 3 4 +--R 5A a c d +--R * +--R x +--R + +--R 4 4 3 3 3 2 2 2 2 3 2 2 4 +--R 6B a e - 8A a c d e - 12B a c d e - 8A a c d e - 2B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 2 5 4 3 4 2 4 3 +---+ +--R (8a c x + 16a c x + 8a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1403 + +--S 1404 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 2 2 2 3 3 4 +-+ +-+ +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (- 6A a c e - 24B a c d e - 12A a c d e - 8B a c d e - 6A c d ) +--R * +--R +-+ +--R +-----+ x\|c +--R \|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 +-----+ +-+ +-+ +--R (12B a e - 16A a c d e - 24B a c d e - 18A c d e)\|- a c \|a \|c +--R / +--R 2 3 +-----+ +-+ +-+ +--R 16a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1404 + +--S 1405 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1405 + +--S 1406 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 4 2 3 2 2 2 2 3 3 4 +-+ +-+ +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )\|a \|c +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +---+ +--R (- 3A a c e - 12B a c d e - 6A a c d e - 4B a c d e - 3A c d )\|a c +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 +-+ +-+ +---+ +--R (6B a e - 8A a c d e - 12B a c d e - 9A c d e)\|a \|c \|a c +--R / +--R 2 3 +-+ +-+ +---+ +--R 8a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1406 + +--S 1407 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1407 + +)clear all + +--S 1408 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1408 + +--S 1409 of 1457 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^3/(a*c*(a+c*x^2)^2)-3/8*(A*c*d+a*B*e)*_ + (a*e-c*d*x)*(d+e*x)/(a^2*c^2*(a+c*x^2))+3/8*(A*c*d+a*B*e)*(c*d^2+_ + a*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(5/2)) +--R +--R +--R (2) +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 6A a c d e + 6B a c d e + 6A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 3A a c d e + 3B a c d e + 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 2 3 2 4 +--R (2A a c e + 3B a c d e + 3A c d e)x +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 5B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 +--R (- 6B a c d e + 6A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 2 +--R (- 3B a e - 3A a c d e - 3B a c d e + 5A a c d )x - 3B a d e +--R + +--R 2 2 2 3 +--R - 3A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 4 4 3 3 2 4 2 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 1409 + +--S 1410 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 6A a c d e + 6B a c d e + 6A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 3A a c d e + 3B a c d e + 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 10B a c e + 6A a c d e + 6B a c d e + 6A c d )x +--R + +--R 2 3 2 2 2 +--R (- 8A a c e - 24B a c d e )x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (- 6B a e - 6A a c d e - 6B a c d e + 10A a c d )x - 4A a e +--R + +--R 3 2 2 2 2 3 +--R - 12B a d e - 12A a c d e - 4B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 4 4 3 3 2 4 2 +-----+ +--R (16a c x + 32a c x + 16a c )\|- a c +--R , +--R +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 6A a c d e + 6B a c d e + 6A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 3A a c d e + 3B a c d e + 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 5B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 2 3 2 2 2 +--R (- 4A a c e - 12B a c d e )x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (- 3B a e - 3A a c d e - 3B a c d e + 5A a c d )x - 2A a e +--R + +--R 3 2 2 2 2 3 +--R - 6B a d e - 6A a c d e - 2B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 2 4 4 3 3 2 4 2 +---+ +--R (8a c x + 16a c x + 8a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1410 + +--S 1411 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 +-+ +-+ +--R (3B a e + 3A a c d e + 3B a c d e + 3A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 3 2 2 2 3 +-----+ x\|c +--R (- 6B a e - 6A a c d e - 6B a c d e - 6A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 +-----+ +-+ +-+ +--R (- 4A a e - 6B a d e - 6A c d e)\|- a c \|a \|c +--R / +--R 2 2 +-----+ +-+ +-+ +--R 16a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1411 + +--S 1412 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1412 + +--S 1413 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 3 2 2 2 3 +-+ +-+ x\|a c +--R (3B a e + 3A a c d e + 3B a c d e + 3A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 3 2 2 2 3 +---+ x\|c +--R (- 3B a e - 3A a c d e - 3B a c d e - 3A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 +-+ +-+ +---+ +--R (- 2A a e - 3B a d e - 3A c d e)\|a \|c \|a c +--R / +--R 2 2 +-+ +-+ +---+ +--R 8a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1413 + +--S 1414 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1414 + +)clear all + +--S 1415 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1415 + +--S 1416 of 1457 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^2/(a*c*(a+c*x^2)^2)-1/8*(a*e-c*d*x)*_ + (3*A*c*d+2*a*B*e+A*c*e*x)/(a^2*c^2*(a+c*x^2))+1/8*(3*A*c*d^2+2*a*_ + B*d*e+a*A*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(3/2)) +--R +--R +--R (2) +--R 3 2 3 4 2 4 +--R (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 3 2 2 3 2 3 +--R (2A a c e + 4B a c d e + 6A a c d )x + A a c e + 2B a c d e +--R + +--R 2 2 2 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 4 2 2 2 3 2 3 +--R A c d e x + (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 4B a c e + 2A a c d e)x + (- A a c e - 2B a c d e + 5A a c d )x +--R + +--R 3 2 2 2 2 +--R - 2B a e - 3A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 4 4 3 3 2 4 2 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 1416 + +--S 1417 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 4 2 4 +--R (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 3 2 2 3 2 3 +--R (2A a c e + 4B a c d e + 6A a c d )x + A a c e + 2B a c d e +--R + +--R 2 2 2 +--R 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 2 3 2 3 2 2 2 +--R (2A a c e + 4B a c d e + 6A c d )x - 8B a c e x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 2A a c e - 4B a c d e + 10A a c d )x - 4B a e - 8A a c d e +--R + +--R 2 2 +--R - 4B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 4 4 3 3 2 4 2 +-----+ +--R (16a c x + 32a c x + 16a c )\|- a c +--R , +--R +--R 3 2 3 4 2 4 +--R (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 3 2 2 3 2 3 +--R (2A a c e + 4B a c d e + 6A a c d )x + A a c e + 2B a c d e +--R + +--R 2 2 2 +--R 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 2 2 3 2 3 2 2 2 +--R (A a c e + 2B a c d e + 3A c d )x - 4B a c e x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- A a c e - 2B a c d e + 5A a c d )x - 2B a e - 4A a c d e +--R + +--R 2 2 +--R - 2B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 2 4 4 3 3 2 4 2 +---+ +--R (8a c x + 16a c x + 8a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1417 + +--S 1418 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R 2 2 +-+ +-+ (c x - a)\|- a c + 2a c x +--R (A a e + 2B a d e + 3A c d )\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 2 +-----+ x\|c +--R (- 2A a e - 4B a d e - 6A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R +-----+ +-+ +-+ +--R - 2A d e\|- a c \|a \|c +--R / +--R 2 +-----+ +-+ +-+ +--R 16a c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1418 + +--S 1419 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1419 + +--S 1420 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 2 +-+ +-+ x\|a c +--R (A a e + 2B a d e + 3A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 2 +---+ x\|c +-+ +-+ +---+ +--R (- A a e - 2B a d e - 3A c d )\|a c atan(-----) - A d e\|a \|c \|a c +--R +-+ +--R \|a +--R / +--R 2 +-+ +-+ +---+ +--R 8a c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1420 + +--S 1421 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1421 + +)clear all + +--S 1422 of 1457 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2)^3 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1422 + +--S 1423 of 1457 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)/(a*c*(a+c*x^2)^2)+1/8*(-2*a*A*e+(3*A*c*d+_ + a*B*e)*x)/(a^2*c*(a+c*x^2))+1/8*(3*A*c*d+a*B*e)*atan(x*sqrt(c)/_ + sqrt(a))/(a^(5/2)*c^(3/2)) +--R +--R +--R (2) +--R 2 3 4 2 2 2 3 2 +--R ((B a c e + 3A c d)x + (2B a c e + 6A a c d)x + B a e + 3A a c d) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 2 2 +-+ +-+ +--R ((B a c e + 3A c d)x + (- B a e + 5A a c d)x - 2A a e - 2B a d)\|a \|c +--R / +--R 2 3 4 3 2 2 4 +-+ +-+ +--R (8a c x + 16a c x + 8a c)\|a \|c +--R Type: Expression(Integer) +--E 1423 + +--S 1424 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 4 2 2 2 3 2 +--R ((B a c e + 3A c d)x + (2B a c e + 6A a c d)x + B a e + 3A a c d) +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 3 2 2 2 +--R ((2B a c e + 6A c d)x + (- 2B a e + 10A a c d)x - 4A a e - 4B a d) +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 3 4 3 2 2 4 +-----+ +--R (16a c x + 32a c x + 16a c)\|- a c +--R , +--R +--R 2 3 4 2 2 2 3 2 +--R ((B a c e + 3A c d)x + (2B a c e + 6A a c d)x + B a e + 3A a c d) +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 3 2 2 2 +---+ +--R ((B a c e + 3A c d)x + (- B a e + 5A a c d)x - 2A a e - 2B a d)\|a c +--R / +--R 2 3 4 3 2 2 4 +---+ +--R (8a c x + 16a c x + 8a c)\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1424 + +--S 1425 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +--R (B a e + 3A c d)\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R +-----+ x\|c +--R (- 2B a e - 6A c d)\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 +-----+ +-+ +-+ +--R 16a c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1425 + +--S 1426 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1426 + +--S 1427 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R (B a e + 3A c d)\|a \|c atan(-------) + (- B a e - 3A c d)\|a c atan(-----) +--R a +-+ +--R \|a +--R --------------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1427 + +--S 1428 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1428 + +)clear all + +--S 1429 of 1457 +t0:=(A+B*x)/(a+c*x^2)^3 +--R +--R +--R B x + A +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1429 + +--S 1430 of 1457 +r0:=1/4*(-a*B+A*c*x)/(a*c*(a+c*x^2)^2)+3/8*A*x/(a^2*(a+c*x^2))+_ + 3/8*A*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*sqrt(c)) +--R +--R +--R (2) +--R +-+ +--R 3 4 2 2 2 x\|c +--R (3A c x + 6A a c x + 3A a c)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 +-+ +-+ +--R (3A c x + 5A a c x - 2B a )\|a \|c +--R / +--R 2 3 4 3 2 2 4 +-+ +-+ +--R (8a c x + 16a c x + 8a c)\|a \|c +--R Type: Expression(Integer) +--E 1430 + +--S 1431 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 3 4 2 2 2 (c x - a)\|- a c + 2a c x +--R (3A c x + 6A a c x + 3A a c)log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 3 2 +-----+ +--R (6A c x + 10A a c x - 4B a )\|- a c +--R / +--R 2 3 4 3 2 2 4 +-----+ +--R (16a c x + 32a c x + 16a c)\|- a c +--R , +--R +--R +---+ +--R 3 4 2 2 2 x\|a c +--R (3A c x + 6A a c x + 3A a c)atan(-------) +--R a +--R + +--R 2 3 2 +---+ +--R (3A c x + 5A a c x - 2B a )\|a c +--R / +--R 2 3 4 3 2 2 4 +---+ +--R (8a c x + 16a c x + 8a c)\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1431 + +--S 1432 of 1457 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x\|c +--R 3A\|a \|c log(---------------------------) - 6A\|- a c atan(-----) +--R 2 +-+ +--R c x + a \|a +--R (4) ------------------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 16a \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1432 + +--S 1433 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1433 + +--S 1434 of 1457 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R 3A\|a \|c atan(-------) - 3A\|a c atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a \|a \|c \|a c +--R Type: Expression(Integer) +--E 1434 + +--S 1435 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1435 + +)clear all + +--S 1436 of 1457 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------------- +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 3 +--R c e x + c d x + 3a c e x + 3a c d x + 3a c e x + 3a c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1436 + +--S 1437 of 1457 +r0:=1/4*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2)^2)+_ + 1/8*(-4*a^2*e^2*(B*d-A*e)-(a*B*e*(c*d^2-3*a*e^2)-A*c*d*(3*c*d^2+7*_ + a*e^2))*x)/(a^2*(c*d^2+a*e^2)^2*(a+c*x^2))-e^4*(B*d-A*e)*log(d+_ + e*x)/(c*d^2+a*e^2)^3+1/2*e^4*(B*d-A*e)*log(a+c*x^2)/(c*d^2+_ + a*e^2)^3-1/8*(a*B*e*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4)-A*c*d*_ + (3*c^2*d^4+10*a*c*d^2*e^2+15*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(5/2)*(c*d^2+a*e^2)^3*sqrt(c)) +--R +--R +--R (2) +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 4 4 +--R 3B a c e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 5 5 +--R 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R 6B a c e + 30A a c d e - 12B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R - 2B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (- 4A a c e + 4B a c d e )x + (- 8A a c e + 8B a c d e )x +--R + +--R 4 5 4 4 +--R - 4A a e + 4B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (8A a c e - 8B a c d e )x + (16A a c e - 16B a c d e )x +--R + +--R 4 5 4 4 +--R 8A a e - 8B a d e +--R * +--R log(e x + d) +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 3 4 +--R 3B a c e + 7A a c d e + 2B a c d e + 10A a c d e - B a c d e +--R + +--R 4 5 +--R 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (4A a c e - 4B a c d e + 4A a c d e - 4B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 5B a e + 9A a c d e + 6B a c d e + 14A a c d e + B a c d e +--R + +--R 3 5 +--R 5A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 6A a e - 6B a d e + 8A a c d e - 8B a c d e + 2A a c d e +--R + +--R 2 2 5 +--R - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 2 6 4 3 2 4 3 4 4 2 2 5 6 4 +--R (8a c e + 24a c d e + 24a c d e + 8a c d )x +--R + +--R 6 6 5 2 2 4 4 3 4 2 3 4 6 2 7 6 6 2 4 +--R (16a c e + 48a c d e + 48a c d e + 16a c d )x + 8a e + 24a c d e +--R + +--R 5 2 4 2 4 3 6 +--R 24a c d e + 8a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R Type: Expression(Integer) +--E 1437 + +--S 1438 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R 3B a c e + 15A a c d e - 6B a c d e + 10A a c d e +--R + +--R 4 4 5 5 +--R - B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R 6B a c e + 30A a c d e - 12B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R - 2B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (- 8A a c e + 8B a c d e )x + (- 16A a c e + 16B a c d e )x +--R + +--R 4 5 4 4 +--R - 8A a e + 8B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (16A a c e - 16B a c d e )x + (32A a c e - 32B a c d e )x +--R + +--R 4 5 4 4 +--R 16A a e - 16B a d e +--R * +--R log(e x + d) +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 6B a c e + 14A a c d e + 4B a c d e + 20A a c d e +--R + +--R 3 4 4 5 +--R - 2B a c d e + 6A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (8A a c e - 8B a c d e + 8A a c d e - 8B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 +--R 10B a e + 18A a c d e + 12B a c d e + 28A a c d e +--R + +--R 2 2 4 3 5 +--R 2B a c d e + 10A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 12A a e - 12B a d e + 16A a c d e - 16B a c d e + 4A a c d e +--R + +--R 2 2 5 +--R - 4B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 5 2 6 4 3 2 4 3 4 4 2 2 5 6 4 +--R (16a c e + 48a c d e + 48a c d e + 16a c d )x +--R + +--R 6 6 5 2 2 4 4 3 4 2 3 4 6 2 7 6 +--R (32a c e + 96a c d e + 96a c d e + 32a c d )x + 16a e +--R + +--R 6 2 4 5 2 4 2 4 3 6 +--R 48a c d e + 48a c d e + 16a c d +--R * +--R +-----+ +--R \|- a c +--R , +--R +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R 3B a c e + 15A a c d e - 6B a c d e + 10A a c d e +--R + +--R 4 4 5 5 +--R - B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R 6B a c e + 30A a c d e - 12B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R - 2B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (- 4A a c e + 4B a c d e )x + (- 8A a c e + 8B a c d e )x +--R + +--R 4 5 4 4 +--R - 4A a e + 4B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (8A a c e - 8B a c d e )x + (16A a c e - 16B a c d e )x +--R + +--R 4 5 4 4 +--R 8A a e - 8B a d e +--R * +--R log(e x + d) +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 3B a c e + 7A a c d e + 2B a c d e + 10A a c d e +--R + +--R 3 4 4 5 +--R - B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (4A a c e - 4B a c d e + 4A a c d e - 4B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 5B a e + 9A a c d e + 6B a c d e + 14A a c d e + B a c d e +--R + +--R 3 5 +--R 5A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 6A a e - 6B a d e + 8A a c d e - 8B a c d e + 2A a c d e +--R + +--R 2 2 5 +--R - 2B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 5 2 6 4 3 2 4 3 4 4 2 2 5 6 4 +--R (8a c e + 24a c d e + 24a c d e + 8a c d )x +--R + +--R 6 6 5 2 2 4 4 3 4 2 3 4 6 2 7 6 +--R (16a c e + 48a c d e + 48a c d e + 16a c d )x + 8a e +--R + +--R 6 2 4 5 2 4 2 4 3 6 +--R 24a c d e + 24a c d e + 8a c d +--R * +--R +---+ +--R \|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1438 + +--S 1439 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 3 5 +--R 3A c d +--R * +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +--R \|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R - 6B a e - 30A a c d e + 12B a c d e - 20A a c d e + 2B a c d e +--R + +--R 3 5 +--R - 6A c d +--R * +--R +-+ +--R +-----+ x\|c +--R \|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R 5 6 4 2 4 3 2 4 2 2 3 6 +-----+ +-+ +-+ +--R (16a e + 48a c d e + 48a c d e + 16a c d )\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1439 + +--S 1440 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1440 + +--S 1441 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 3 5 +--R 3A c d +--R * +--R +---+ +--R +-+ +-+ x\|a c +--R \|a \|c atan(-------) +--R a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R - 3B a e - 15A a c d e + 6B a c d e - 10A a c d e + B a c d e +--R + +--R 3 5 +--R - 3A c d +--R * +--R +-+ +--R +---+ x\|c +--R \|a c atan(-----) +--R +-+ +--R \|a +--R / +--R 5 6 4 2 4 3 2 4 2 2 3 6 +-+ +-+ +---+ +--R (8a e + 24a c d e + 24a c d e + 8a c d )\|a \|c \|a c +--R Type: Expression(Integer) +--E 1441 + +--S 1442 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1442 + +)clear all + +--S 1443 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 3 7 2 2 3 2 6 2 5 +--R c e x + 2c d e x + (3a c e + c d )x + 6a c d e x +--R + +--R 2 2 2 2 4 2 3 3 2 2 2 2 3 3 2 +--R (3a c e + 3a c d )x + 6a c d e x + (a e + 3a c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1443 + +--S 1444 of 1457 +r0:=-1/8*e*(2*a*B*d*e*(c*d^2-11*a*e^2)-3*A*(c^2*d^4+4*a*c*d^2*e^2-_ + 5*a^2*e^4))/(a^2*(c*d^2+a*e^2)^3*(d+e*x))+1/4*(-a*(B*d-A*e)+_ + (A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(d+e*x)*(a+c*x^2)^2)+1/8*(-a*_ + e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)-(2*a*B*e*(c*d^2-2*a*e^2)-3*A*c*d*_ + (c*d^2+3*a*e^2))*x)/(a^2*(c*d^2+a*e^2)^2*(d+e*x)*(a+c*x^2))-e^4*_ + (5*B*c*d^2-6*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+a*e^2)^4+1/2*e^4*_ + (5*B*c*d^2-6*A*c*d*e-a*B*e^2)*log(a+c*x^2)/(c*d^2+a*e^2)^4-1/8*_ + (2*a*B*d*e*(c^2*d^4+10*a*c*d^2*e^2-15*a^2*e^4)-3*A*(c^3*d^6+_ + 5*a*c^2*d^4*e^2+15*a^2*c*d^2*e^4-5*a^3*e^6))*atan(x*sqrt(c)/_ + sqrt(a))*sqrt(c)/(a^(5/2)*(c*d^2+a*e^2)^4) +--R +--R +--R (2) +--R 3 2 7 3 2 6 2 3 2 5 2 3 3 4 +--R - 15A a c e + 30B a c d e + 45A a c d e - 20B a c d e +--R + +--R 4 4 3 4 5 2 5 6 +--R 15A a c d e - 2B a c d e + 3A c d e +--R * +--R 5 +--R x +--R + +--R 3 2 6 3 2 2 5 2 3 3 4 2 3 4 3 +--R - 15A a c d e + 30B a c d e + 45A a c d e - 20B a c d e +--R + +--R 4 5 2 4 6 5 7 +--R 15A a c d e - 2B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 7 4 6 3 2 2 5 3 2 3 4 +--R - 30A a c e + 60B a c d e + 90A a c d e - 40B a c d e +--R + +--R 2 3 4 3 2 3 5 2 4 6 +--R 30A a c d e - 4B a c d e + 6A a c d e +--R * +--R 3 +--R x +--R + +--R 4 6 4 2 5 3 2 3 4 3 2 4 3 +--R - 30A a c d e + 60B a c d e + 90A a c d e - 40B a c d e +--R + +--R 2 3 5 2 2 3 6 4 7 +--R 30A a c d e - 4B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 7 5 6 4 2 5 4 3 4 +--R - 15A a e + 30B a d e + 45A a c d e - 20B a c d e +--R + +--R 3 2 4 3 3 2 5 2 2 3 6 +--R 15A a c d e - 2B a c d e + 3A a c d e +--R * +--R x +--R + +--R 5 6 5 2 5 4 3 4 4 4 3 +--R - 15A a d e + 30B a d e + 45A a c d e - 20B a c d e +--R + +--R 3 2 5 2 3 2 6 2 3 7 +--R 15A a c d e - 2B a c d e + 3A a c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 7 2 3 6 2 3 2 5 5 +--R (- 4B a c e - 24A a c d e + 20B a c d e )x +--R + +--R 3 2 6 2 3 2 5 2 3 3 4 4 +--R (- 4B a c d e - 24A a c d e + 20B a c d e )x +--R + +--R 4 7 3 2 6 3 2 2 5 3 +--R (- 8B a c e - 48A a c d e + 40B a c d e )x +--R + +--R 4 6 3 2 2 5 3 2 3 4 2 +--R (- 8B a c d e - 48A a c d e + 40B a c d e )x +--R + +--R 5 7 4 6 4 2 5 5 6 +--R (- 4B a e - 24A a c d e + 20B a c d e )x - 4B a d e +--R + +--R 4 2 5 4 3 4 +--R - 24A a c d e + 20B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 7 2 3 6 2 3 2 5 5 +--R (8B a c e + 48A a c d e - 40B a c d e )x +--R + +--R 3 2 6 2 3 2 5 2 3 3 4 4 +--R (8B a c d e + 48A a c d e - 40B a c d e )x +--R + +--R 4 7 3 2 6 3 2 2 5 3 +--R (16B a c e + 96A a c d e - 80B a c d e )x +--R + +--R 4 6 3 2 2 5 3 2 3 4 2 +--R (16B a c d e + 96A a c d e - 80B a c d e )x +--R + +--R 5 7 4 6 4 2 5 5 6 +--R (8B a e + 48A a c d e - 40B a c d e )x + 8B a d e +--R + +--R 4 2 5 4 3 4 +--R 48A a c d e - 40B a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 7 3 2 6 2 3 2 5 2 3 3 4 +--R - 15A a c e + 22B a c d e - 3A a c d e + 20B a c d e +--R + +--R 4 4 3 4 5 2 5 6 +--R 15A a c d e - 2B a c d e + 3A c d e +--R * +--R 4 +--R x +--R + +--R 4 7 3 2 6 3 2 2 5 2 3 3 4 +--R 4B a c e + 9A a c d e + 6B a c d e + 21A a c d e +--R + +--R 4 5 2 4 6 5 7 +--R 15A a c d e - 2B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 4 7 4 6 3 2 2 5 3 2 3 4 +--R - 25A a c e + 38B a c d e + 3A a c d e + 28B a c d e +--R + +--R 2 3 4 3 2 3 5 2 4 6 +--R 33A a c d e - 10B a c d e + 5A a c d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 6 4 2 5 3 2 3 4 +--R 6B a e + 11A a c d e + 12B a c d e + 27A a c d e +--R + +--R 3 2 4 3 2 3 5 2 4 7 +--R 6B a c d e + 21A a c d e + 5A a c d +--R * +--R x +--R + +--R 5 7 5 6 4 2 5 4 3 4 3 2 4 3 +--R - 8A a e + 14B a d e + 12A a c d e + 2B a c d e + 24A a c d e +--R + +--R 3 2 5 2 2 3 6 2 3 7 +--R - 14B a c d e + 4A a c d e - 2B a c d +--R * +--R +-+ +--R \|a +--R / +--R 6 2 9 5 3 2 7 4 4 4 5 3 5 6 3 2 6 8 5 +--R (8a c e + 32a c d e + 48a c d e + 32a c d e + 8a c d e)x +--R + +--R 6 2 8 5 3 3 6 4 4 5 4 3 5 7 2 2 6 9 4 +--R (8a c d e + 32a c d e + 48a c d e + 32a c d e + 8a c d )x +--R + +--R 7 9 6 2 2 7 5 3 4 5 4 4 6 3 3 5 8 3 +--R (16a c e + 64a c d e + 96a c d e + 64a c d e + 16a c d e)x +--R + +--R 7 8 6 2 3 6 5 3 5 4 4 4 7 2 3 5 9 2 +--R (16a c d e + 64a c d e + 96a c d e + 64a c d e + 16a c d )x +--R + +--R 8 9 7 2 7 6 2 4 5 5 3 6 3 4 4 8 8 8 +--R (8a e + 32a c d e + 48a c d e + 32a c d e + 8a c d e)x + 8a d e +--R + +--R 7 3 6 6 2 5 4 5 3 7 2 4 4 9 +--R 32a c d e + 48a c d e + 32a c d e + 8a c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1444 + +--S 1445 of 1457 +--a0:=integrate(t0,x) +--E 1445 + +--S 1446 of 1457 +--m0:=a0-r0 +--E 1446 + +--S 1447 of 1457 +--d0:=D(m0,x) +--E 1447 + +)clear all + +--S 1448 of 1457 +t0:=(-11+6*x)/((-1+2*x)*(-1+x^2)) +--R +--R +--R 6x - 11 +--R (1) ----------------- +--R 3 2 +--R 2x - x - 2x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1448 + +--S 1449 of 1457 +r0:=16/3*log(1-2*x)-5/2*log(1-x)-17/6*log(1+x) +--R +--R +--R - 17log(x + 1) - 15log(- x + 1) + 32log(- 2x + 1) +--R (2) ------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1449 + +--S 1450 of 1457 +a0:=integrate(t0,x) +--R +--R +--R 32log(2x - 1) - 17log(x + 1) - 15log(x - 1) +--R (3) ------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1450 + +--S 1451 of 1457 +m0:=a0-r0 +--R +--R +--R 32log(2x - 1) - 15log(x - 1) + 15log(- x + 1) - 32log(- 2x + 1) +--R (4) --------------------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1451 + +--S 1452 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1452 + +)clear all + +--S 1453 of 1457 +t0:=(5-x)*(3+2*x)^4*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (1) (- 16x - 16x + 264x + 864x + 999x + 405)\|3x + 2 +--R Type: Expression(Integer) +--E 1453 + +--S 1454 of 1457 +r0:=8275/162*(2+3*x^2)^(3/2)+923/315*(3+2*x)^2*(2+3*x^2)^(3/2)+29/63*_ + (3+2*x)^3*(2+3*x^2)^(3/2)-1/21*(3+2*x)^4*(2+3*x^2)^(3/2)+1/270*_ + (4583+6132*x)*(2+3*x^2)^(3/2)+2341/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 2341/18*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 12960x - 15120x + 297648x + 1222200x + 1956174x + 1558935x +--R + +--R 1167988 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1474830asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 5670\|3 +--R Type: Expression(Integer) +--E 1454 + +--S 1455 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 6 4 2 +-+ | 2 +--R (4424490x + 70791840x + 157315200x + 83901440)\|2 \|3x + 2 +--R + +--R 6 4 2 +--R - 61942860x - 330361920x - 440482560x - 167802880 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 12 11 10 9 8 +--R 544320x + 635040x - 9598176x - 47945520x - 144961740x +--R + +--R 7 6 5 4 3 +--R - 334732230x - 567653520x - 712511520x - 767612160x - 604661120x +--R + +--R 2 +--R - 322237440x - 177372160x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 14 13 12 11 10 +--R - 116640x - 136080x + 734832x + 8731800x + 56861406x +--R + +--R 9 8 7 6 5 +--R 191070495x + 422782920x + 736469370x + 1052733360x + 1116121440x +--R + +--R 4 3 2 +--R 1009290240x + 737690240x + 322237440x + 177372160x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (17010x + 272160x + 604800x + 322560)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 238140x - 1270080x - 1693440x - 645120)\|3 +--R Type: Union(Expression(Integer),...) +--E 1455 + +--S 1456 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 6 4 2 +-+ | 2 +--R (19910205x + 318563280x + 707918400x + 377556480)\|2 \|3x + 2 +--R + +--R 6 4 2 +--R - 278742870x - 1486628640x - 1982171520x - 755112960 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 6 4 2 +-+ +--R (- 19910205x - 318563280x - 707918400x - 377556480)\|2 +--R * +--R +-+ +--R x\|3 +--R asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +--R (31535676x + 504570816x + 1121268480x + 598009856)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 x\|3 +--R (278742870x + 1486628640x + 1982171520x + 755112960)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 220749732x - 1177331904x - 1569775872x - 598009856)\|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (76545x + 1224720x + 2721600x + 1451520)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 1071630x - 5715360x - 7620480x - 2903040)\|3 +--R Type: Expression(Integer) +--E 1456 + +--S 1457 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1457 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich12b.input.pamphlet b/src/axiom-website/CATS/rich12b.input.pamphlet new file mode 100644 index 0000000..de09257 --- /dev/null +++ b/src/axiom-website/CATS/rich12b.input.pamphlet @@ -0,0 +1,24836 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12b.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 91 matching answers. +\item 0 cases where Axiom answer differs from Rubi +\item 0 cases where Axiom supplied 2 results. +\item 4 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12b.output +)spool rich12b.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(5-x)*(3+2*x)^3*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 4 3 2 | 2 +--R (1) (- 8x + 4x + 126x + 243x + 135)\|3x + 2 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=875/54*(2+3*x^2)^(3/2)+17/30*(3+2*x)^2*(2+3*x^2)^(3/2)-1/18*(3+2*x)^3*_ + (2+3*x^2)^(3/2)+7/90*(91+89*x)*(2+3*x^2)^(3/2)+1022/9*asinh(x*_ + sqrt(3/2))/sqrt(3)+511/9*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 360x + 216x + 8445x + 21918x + 21120x + 14516)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 30660asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 270\|3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 6 4 +--R (551880x + 1962240x + 1308160)\|2 \|3x + 2 - 275940x - 3311280x +--R + +--R 2 +--R - 5886720x - 2616320 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 11 10 9 8 7 6 +--R 3240x - 1944x - 37125x - 220590x - 1033020x - 2539260x +--R + +--R 5 4 3 2 +--R - 3871680x - 5271840x - 4775680x - 2799360x - 1802240x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 11 10 9 8 7 6 +--R - 19440x + 11664x + 373950x + 1232820x + 2973780x + 5705820x +--R + +--R 5 4 3 2 +--R 6946560x + 7371360x + 6127360x + 2799360x + 1802240x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (4860x + 17280x + 11520)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 2430x - 29160x - 51840x - 23040)\|3 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ | 2 6 4 +--R (827820x + 2943360x + 1962240)\|2 \|3x + 2 - 413910x - 4966920x +--R + +--R 2 +--R - 8830080x - 3924480 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (- 827820x - 2943360x - 1962240)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (783864x + 2787072x + 1858048)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 x\|3 +--R (413910x + 4966920x + 8830080x + 3924480)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 195966x - 2351592x - 4180608x - 1858048)\|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (7290x + 25920x + 17280)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 3645x - 43740x - 77760x - 34560)\|3 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(5-x)*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (1) (- 4x + 8x + 51x + 45)\|3x + 2 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=205/54*(2+3*x^2)^(3/2)-1/15*(3+2*x)^2*(2+3*x^2)^(3/2)+1/90*(233+132*x)*_ + (2+3*x^2)^(3/2)+131/3*asinh(x*sqrt(3/2))/sqrt(3)+131/6*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +-+ +--R 4 3 2 +-+ | 2 x\|3 +--R (- 216x + 540x + 4542x + 6255x + 3124)\|3 \|3x + 2 + 11790asinh(-----) +--R +-+ +--R \|2 +--R --------------------------------------------------------------------------- +--R +-+ +--R 270\|3 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (11790x + 94320x + 83840)\|2 \|3x + 2 - 117900x - 314400x +--R + +--R - 167680 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 8 7 6 5 4 3 2 +--R 2160x - 5400x - 39660x - 76950x - 143040x - 174480x - 97920x +--R + +--R - 88960x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 10 9 8 7 6 5 4 +--R - 648x + 1620x + 8010x + 32805x + 119400x + 182790x + 216480x +--R + +--R 3 2 +--R 241200x + 97920x + 88960x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 4 2 +-+ +--R (270x + 2160x + 1920)\|2 \|3 \|3x + 2 + (- 2700x - 7200x - 3840)\|3 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (53055x + 424440x + 377280)\|2 \|3x + 2 - 530550x - 1414800x +--R + +--R - 754560 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (- 53055x - 424440x - 377280)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (28116x + 224928x + 199936)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 4 2 x\|3 +--R (530550x + 1414800x + 754560)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +-+ +--R (- 140580x - 374880x - 199936)\|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (1215x + 9720x + 8640)\|2 \|3 \|3x + 2 +--R + +--R 4 2 +-+ +--R (- 12150x - 32400x - 17280)\|3 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(5-x)*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (1) (- 2x + 7x + 15)\|3x + 2 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=37/36*(2+3*x^2)^(3/2)-1/12*(3+2*x)*(2+3*x^2)^(3/2)+46/3*asinh(x*_ + sqrt(3/2))/sqrt(3)+23/3*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 3 2 +-+ | 2 x\|3 +--R (- 9x + 42x + 132x + 28)\|3 \|3x + 2 + 276asinh(-----) +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------------- +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((1104x + 1472)\|2 \|3x + 2 - 828x - 4416x - 2944) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 7 6 5 4 3 2 +-+ | 2 +--R (27x - 126x - 252x - 756x - 2016x - 672x - 1408x)\|3 \|3x + 2 +--R + +--R 7 6 5 4 3 2 +-+ +-+ +--R (- 108x + 504x + 1368x + 1260x + 3072x + 672x + 1408x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 4 2 +-+ +--R (72x + 96)\|2 \|3 \|3x + 2 + (- 54x - 288x - 192)\|3 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((1656x + 2208)\|2 \|3x + 2 - 1242x - 6624x - 4416) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((- 1656x - 2208)\|2 asinh(-----) + (336x + 448)\|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 4 2 x\|3 4 2 +-+ +-+ +--R (1242x + 6624x + 4416)asinh(-----) + (- 126x - 672x - 448)\|2 \|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 4 2 +-+ +--R (108x + 144)\|2 \|3 \|3x + 2 + (- 81x - 432x - 288)\|3 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(5-x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) (- x + 5)\|3x + 2 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-1/9*(2+3*x^2)^(3/2)+5*asinh(x*sqrt(3/2))/sqrt(3)+_ + 5/2*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 2 +-+ | 2 x\|3 +--R (- 6x + 45x - 4)\|3 \|3x + 2 + 90asinh(-----) +--R +-+ +--R \|2 +--R (2) ------------------------------------------------ +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((30x + 80)\|2 \|3x + 2 - 180x - 160) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 4 3 2 +-+ | 2 +--R (12x - 90x + 16x - 80x)\|3 \|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +-+ +--R (- 6x + 45x - 24x + 150x - 16x + 80x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 2 +-+ +--R (6x + 16)\|2 \|3 \|3x + 2 + (- 36x - 32)\|3 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((135x + 360)\|2 \|3x + 2 - 810x - 720) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((- 135x - 360)\|2 asinh(-----) + (- 12x - 32)\|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 2 x\|3 2 +-+ +-+ +--R (810x + 720)asinh(-----) + (36x + 32)\|2 \|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 2 +-+ +--R (27x + 72)\|2 \|3 \|3x + 2 + (- 162x - 144)\|3 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=-121/8*asinh(x*sqrt(3/2))/sqrt(3)-13/8*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))*sqrt(35)+1/4*(13-x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R +-+ +--+ 9x - 4 +-+ | 2 +--R 13\|3 \|35 atanh(---------------) + (- 2x + 26)\|3 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R - 121asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 8\|3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R | 2 2 +-+ +--R (484\|3x + 2 + (- 363x - 484)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|3 + 3x\|2 )\|3x + 2 + (- 3x - 2)\|2 \|3 - 6x +--R log(-----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R +-+ +--+ | 2 2 +-+ +-+ +--+ +--R (52\|3 \|35 \|3x + 2 + (- 39x - 52)\|2 \|3 \|35 ) +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((- 2x - 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (9x + 4x + 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R 3 2 +-+ +-+ | 2 3 2 +-+ +--R (6x - 78x + 8x)\|2 \|3 \|3x + 2 + (- 24x + 156x - 16x)\|3 +--R / +--R +-------+ +--R +-+ | 2 2 +-+ +-+ +--R 32\|3 \|3x + 2 + (- 24x - 32)\|2 \|3 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | 2 2 +-+ +--R (484\|3x + 2 + (- 363x - 484)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|3 + 3x\|2 )\|3x + 2 + (- 3x - 2)\|2 \|3 - 6x +--R log(-----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R +-+ +--+ | 2 2 +-+ +-+ +--+ +--R (52\|3 \|35 \|3x + 2 + (- 39x - 52)\|2 \|3 \|35 ) +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((- 2x - 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (9x + 4x + 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R +-+ +--+ | 2 2 +-+ +-+ +--+ +--R (- 52\|3 \|35 \|3x + 2 + (39x + 52)\|2 \|3 \|35 ) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +-------+ +--R x\|3 +-+ +-+ | 2 +--R (484asinh(-----) + 104\|2 \|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 2 +-+ x\|3 2 +-+ +--R (- 363x - 484)\|2 asinh(-----) + (- 156x - 208)\|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R +-+ | 2 2 +-+ +-+ +--R 32\|3 \|3x + 2 + (- 24x - 32)\|2 \|3 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=2*asinh(x*sqrt(3/2))*sqrt(3)+19*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)-1/2*(8+x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 9x - 4 +--+ | 2 +--R (- 76x - 114)atanh(---------------) + (- x - 8)\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R +-+ +--+ x\|3 +--R (8x + 12)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R +--+ +--R (4x + 6)\|35 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 3 2 +--R ((456x + 684)\|2 \|3x + 2 - 684x - 1026x - 912x - 1368) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 + 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (- 70x - 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +-+ +-+ +--+ | 2 +--R (48x + 72)\|2 \|3 \|35 \|3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (- 72x - 108x - 96x - 144)\|3 \|35 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|3 + \|2 )\|3x + 2 + x\|2 \|3 - 3x - 2 +--R log(------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 3 2 +-+ +--+ +--R (9x + 72x - 52x)\|35 \|3x + 2 + (30x - 72x + 52x)\|2 \|35 +--R / +--R +-------+ +--R +-+ +--+ | 2 3 2 +--+ +--R (24x + 36)\|2 \|35 \|3x + 2 + (- 36x - 54x - 48x - 72)\|35 +--R Type: Union(Expression(Integer),...) +--E 28 + 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24)\|3 \|35 asinh(-----) + (12x + 16)\|2 \|35 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R 6\|2 \|35 \|3x + 2 + (- 9x - 12)\|35 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^3 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) --------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-13/70*(2+3*x^2)^(3/2)/(3+2*x)^2-1/8*asinh(x*sqrt(3/2))*sqrt(3)-_ + 471/280*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/140*(35+39*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 9x - 4 +--R (1884x + 5652x + 4239)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R +--+ | 2 2 +-+ +--+ x\|3 +--R (374x + 106)\|35 \|3x + 2 + (- 140x - 420x - 315)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 2 +--+ 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Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(5-x)*(3+2*x)^2*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (1) (- 12x + 24x + 145x + 151x + 102x + 90)\|3x + 2 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=397/36*x*(2+3*x^2)^(3/2)+293/135*(2+3*x^2)^(5/2)-1/21*(3+2*x)^2*_ + (2+3*x^2)^(5/2)+1/189*(323+192*x)*(2+3*x^2)^(5/2)+_ + 397/6*asinh(x*sqrt(3/2))/sqrt(3)+397/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 6 5 4 3 2 +-+ +--R (- 2160x + 5040x + 36252x + 48405x + 51216x + 71715x + 17392)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 83370asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 1260\|3 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 6 4 2 +-+ | 2 +--R (750330x + 12005280x + 26678400x + 14228480)\|2 \|3x + 2 +--R + +--R 6 4 2 +--R - 10504620x - 56024640x - 74699520x - 28456960 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 12 11 10 9 8 +--R 272160x - 635040x - 3116232x - 9485910x - 28879200x +--R + +--R 7 6 5 4 3 +--R - 46080090x - 68040000x - 93283680x - 64942080x - 80778880x +--R + +--R 2 +--R - 21934080x - 24478720x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 14 13 12 11 10 +--R - 58320x + 136080x + 6804x + 3574935x + 15000552x +--R + +--R 9 8 7 6 5 +--R 30008475x + 66270960x + 98487270x + 110577600x + 146983200x +--R + +--R 4 3 2 +--R 81392640x + 99137920x + 21934080x + 24478720x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (11340x + 181440x + 403200x + 215040)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 158760x - 846720x - 1128960x - 430080)\|3 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 6 4 2 +-+ | 2 +--R (1125495x + 18007920x + 40017600x + 21342720)\|2 \|3x + 2 +--R + +--R 6 4 2 +--R - 15756930x - 84036960x - 112049280x - 42685440 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 6 4 2 +-+ x\|3 +--R (- 1125495x - 18007920x - 40017600x - 21342720)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +--R (469584x + 7513344x + 16696320x + 8904704)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 x\|3 +--R (15756930x + 84036960x + 112049280x + 42685440)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 3287088x - 17531136x - 23374848x - 8904704)\|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (17010x + 272160x + 604800x + 322560)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 238140x - 1270080x - 1693440x - 645120)\|3 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(5-x)*(3+2*x)*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 4 3 2 | 2 +--R (1) (- 6x + 21x + 41x + 14x + 30)\|3x + 2 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=137/36*x*(2+3*x^2)^(3/2)+19/30*(2+3*x^2)^(5/2)-1/18*(3+2*x)*_ + (2+3*x^2)^(5/2)+137/6*asinh(x*sqrt(3/2))/sqrt(3)+137/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 60x + 252x + 605x + 336x + 1115x + 112)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1370asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 60\|3 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 6 4 +--R (73980x + 263040x + 175360)\|2 \|3x + 2 - 36990x - 443880x +--R + +--R 2 +--R - 789120x - 350720 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 11 10 9 8 7 6 5 +--R 1620x - 6804x + 3105x - 90720x - 191565x - 257040x - 694380x +--R + +--R 4 3 2 +--R - 282240x - 797120x - 107520x - 285440x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 11 10 9 8 7 6 +--R - 9720x + 40824x + 56970x + 226800x + 548370x + 438480x +--R + +--R 5 4 3 2 +--R 1211940x + 362880x + 1011200x + 107520x + 285440x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (3240x + 11520x + 7680)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 1620x - 19440x - 34560x - 15360)\|3 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ | 2 6 4 +--R (36990x + 131520x + 87680)\|2 \|3x + 2 - 18495x - 221940x +--R + +--R 2 +--R - 394560x - 175360 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (- 36990x - 131520x - 87680)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (6048x + 21504x + 14336)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 x\|3 +--R (18495x + 221940x + 394560x + 175360)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 1512x - 18144x - 32256x - 14336)\|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (1620x + 5760x + 3840)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 810x - 9720x - 17280x - 7680)\|3 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(5-x)*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (1) (- 3x + 15x - 2x + 10)\|3x + 2 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=5/4*x*(2+3*x^2)^(3/2)-1/15*(2+3*x^2)^(5/2)+5/2*asinh(x*sqrt(3/2))*_ + sqrt(3)+15/4*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 4 3 2 | 2 +-+ x\|3 +--R (- 36x + 225x - 48x + 375x - 16)\|3x + 2 + 150\|3 asinh(-----) +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------------- +--R 60 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (450x + 3600x + 3200)\|2 \|3 \|3x + 2 +--R + +--R 4 2 +-+ +--R (- 4500x - 12000x - 6400)\|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|3 + \|2 )\|3x + 2 + x\|2 \|3 - 3x - 2 +--R log(------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 8 7 6 5 4 3 2 +--R 1080x - 6750x + 4320x - 29250x + 5760x - 39600x + 2560x +--R + +--R - 16000x +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 10 9 8 7 6 5 4 +--R - 324x + 2025x - 3240x + 20925x - 7920x + 54450x - 7680x +--R + +--R 3 2 +--R 51600x - 2560x + 16000x +--R * +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (180x + 1440x + 1280)\|2 \|3x + 2 - 1800x - 4800x - 2560 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (675x + 5400x + 4800)\|2 \|3 \|3x + 2 +--R + +--R 4 2 +-+ +--R (- 6750x - 18000x - 9600)\|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|3 + \|2 )\|3x + 2 + x\|2 \|3 - 3x - 2 +--R log(------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 4 2 +-+ +-+ x\|3 4 2 +--R ((- 675x - 5400x - 4800)\|2 \|3 asinh(-----) - 144x - 1152x - 1024) +--R +-+ +--R \|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 4 2 +-+ +--R (6750x + 18000x + 9600)\|3 asinh(-----) + (720x + 1920x + 1024)\|2 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (270x + 2160x + 1920)\|2 \|3x + 2 - 2700x - 7200x - 3840 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=1/24*(26-3*x)*(2+3*x^2)^(3/2)-1529/32*asinh(x*sqrt(3/2))*sqrt(3)-_ + 455/32*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+_ + 1/16*(455-123*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R 1365\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R 3 2 | 2 +-+ x\|3 +--R (- 36x + 312x - 762x + 2938)\|3x + 2 - 4587\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 96 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 +--R (36696x + 48928)\|3 \|3x + 2 +--R + +--R 4 2 +-+ +-+ +--R (- 13761x - 73392x - 48928)\|2 \|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (x\|2 \|3 + 2)\|3x + 2 - 2x\|3 + (- 3x - 2)\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (10920x + 14560)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 4095x - 21840x - 14560)\|2 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((- 2x - 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (9x + 4x + 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R 7 6 5 4 3 2 +-+ +--R (108x - 936x + 2862x - 13806x + 12576x - 26832x + 8128x)\|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 7 6 5 4 3 2 +--R - 864x + 7488x - 20016x + 67860x - 37344x + 53664x - 16256x +--R / +--R +-------+ +--R 2 | 2 4 2 +-+ +--R (768x + 1024)\|3x + 2 + (- 288x - 1536x - 1024)\|2 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 +--R (110088x + 146784)\|3 \|3x + 2 +--R + +--R 4 2 +-+ +-+ +--R (- 41283x - 220176x - 146784)\|2 \|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (x\|2 \|3 + 2)\|3x + 2 - 2x\|3 + (- 3x - 2)\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (32760x + 43680)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 12285x - 65520x - 43680)\|2 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((- 2x - 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (9x + 4x + 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (- 32760x - 43680)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (12285x + 65520x + 43680)\|2 \|35 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((110088x + 146784)\|3 asinh(-----) + (70512x + 94016)\|2 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 4 2 +-+ +-+ x\|3 4 2 +--R (- 41283x - 220176x - 146784)\|2 \|3 asinh(-----) - 52884x - 282048x +--R +-+ +--R \|2 +--R + +--R - 188032 +--R / +--R +-------+ +--R 2 | 2 4 2 +-+ +--R (2304x + 3072)\|3x + 2 + (- 864x - 4608x - 3072)\|2 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=-1/6*(21+x)*(2+3*x^2)^(3/2)/(3+2*x)+663/16*asinh(x*sqrt(3/2))*_ + sqrt(3)+193/16*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)-_ + 1/8*(193-63*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R (- 1158x - 1737)\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R 3 2 | 2 +-+ x\|3 +--R (- 24x + 252x - 1198x - 3810)\|3x + 2 + (3978x + 5967)\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 96x + 144 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 2 +--+ | 2 +--R (27792x + 41688x + 37056x + 55584)\|35 \|3x + 2 +--R + +--R 5 4 3 2 +-+ +--+ +--R (- 10422x - 15633x - 55584x - 83376x - 37056x - 55584)\|2 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((2x + 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (- 9x - 4x - 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R 3 2 +-+ | 2 +--R (95472x + 143208x + 127296x + 190944)\|3 \|3x + 2 +--R + +--R 5 4 3 2 +-+ +-+ +--R (- 35802x - 53703x - 190944x - 286416x - 127296x - 190944)\|2 \|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (- x\|2 \|3 + 2)\|3x + 2 + 2x\|3 + (- 3x - 2)\|2 +--R log(------------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R 7 6 5 4 3 2 +-+ +--R (216x - 2268x + 11934x + 22194x - 2688x + 83376x - 42944x)\|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 7 6 5 4 3 2 +--R - 1728x + 18144x - 43992x - 169452x + 69792x - 166752x + 85888x +--R / +--R +-------+ +--R 3 2 | 2 +--R (2304x + 3456x + 3072x + 4608)\|3x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 864x - 1296x - 4608x - 6912x - 3072x - 4608)\|2 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +--+ | 2 +--R (13896x + 18528)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 5211x - 27792x - 18528)\|2 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((2x + 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (- 9x - 4x - 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R 2 +-+ | 2 +--R (47736x + 63648)\|3 \|3x + 2 +--R + +--R 4 2 +-+ +-+ +--R (- 17901x - 95472x - 63648)\|2 \|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (- x\|2 \|3 + 2)\|3x + 2 + 2x\|3 + (- 3x - 2)\|2 +--R log(------------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (13896x + 18528)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 5211x - 27792x - 18528)\|2 \|35 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((- 47736x - 63648)\|3 asinh(-----) + (- 30480x - 40640)\|2 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 4 2 +-+ +-+ x\|3 4 2 +--R (17901x + 95472x + 63648)\|2 \|3 asinh(-----) + 22860x + 121920x +--R +-+ +--R \|2 +--R + +--R 81280 +--R / +--R +-------+ +--R 2 | 2 4 2 +-+ +--R (1152x + 1536)\|3x + 2 + (- 432x - 2304x - 1536)\|2 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^3 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=-1/4*(8+x)*(2+3*x^2)^(3/2)/(3+2*x)^2-111/8*asinh(x*sqrt(3/2))*_ + sqrt(3)-1143/8*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 3/4*(37+12*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 9x - 4 +--R (4572x + 13716x + 10287)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 6x + 96x + 656x + 634)\|35 \|3x + 2 +--R + +--R +-+ +--R 2 +-+ +--+ x\|3 +--R (- 444x - 1332x - 999)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 2 +--+ +--R (32x + 96x + 72)\|35 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 3 2 +-+ | 2 +--R (493776x + 1481328x + 1769364x + 1975104x + 1481328)\|2 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 370332x - 1110996x - 2808351x - 5925312x - 5760720x - 3950208x +--R + +--R - 2962656 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R 4 3 2 +-+ +-+ +--+ +--R (47952x + 143856x + 171828x + 191808x + 143856)\|2 \|3 \|35 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 35964x - 107892x - 272727x - 575424x - 559440x - 383616x +--R + +--R - 287712 +--R * +--R +-+ +--+ 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12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 2 +-+ +-+ +--+ | 2 +--R (11988x + 15984)\|2 \|3 \|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 8991x - 47952x - 31968)\|3 \|35 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (x\|3 + \|2 )\|3x + 2 - x\|2 \|3 - 3x - 2 +--R log(----------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((- 123444x - 164592)\|2 \|3x + 2 + 92583x + 493776x + 329184) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R 2 +-+ +-+ +--+ x\|3 2 +--+ +--R ((11988x + 15984)\|2 \|3 \|35 asinh(-----) + (15216x + 20288)\|35 ) +--R +-+ +--R \|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 4 2 +-+ +--+ x\|3 +--R (- 8991x - 47952x - 31968)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ 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+-+ +--+ | 2 +--R \|2 \|3 \|35 \|3x + 2 +--R + +--R 7 6 5 4 3 +--R - 6735960x - 30311820x - 81392850x - 184396905x - 266444640x +--R + +--R 2 +--R - 229022640x - 161663040x - 80831520 +--R * +--R +-+ +--+ +--R \|3 \|35 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|3 + \|2 )\|3x + 2 + x\|2 \|3 - 3x - 2 +--R log(------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 7 6 5 4 3 +--R 612360x + 11894364x + 15333666x + 25842510x + 34574528x +--R + +--R 2 +--R 11779920x - 20374848x +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 7 6 5 4 3 +--R 1909296x - 27963144x - 46994988x - 34677450x - 19293392x +--R + +--R 2 +--R - 11779920x + 20374848x +--R * +--R +-+ +--+ +--R \|2 \|35 +--R / +--R 5 4 3 2 +--R 4354560x + 19595520x + 35199360x + 40824000x + 39191040x +--R + +--R 19595520 +--R * +--R +-------+ +--R +-+ +--+ | 2 +--R \|2 \|35 \|3x + 2 +--R + +--R 7 6 5 4 3 +--R - 3265920x - 14696640x - 39463200x - 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(198450x + 1058400x + 1411200x + 537600)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +-+ +--R (6048x + 32256x + 43008x + 16384)\|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (1134x + 18144x + 40320x + 21504)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 15876x - 84672x - 112896x - 43008)\|3 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 2x + 3 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=7/96*(130-53*x)*(2+3*x^2)^(3/2)+1/60*(39-5*x)*(2+3*x^2)^(5/2)-_ + 162673/128*asinh(x*sqrt(3/2))/sqrt(3)-15925/128*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+7/64*(2275-691*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +--+ 9x - 4 +--R 238875\|3 \|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 1440x + 11232x - 24180x + 69576x - 160590x + 519142)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R - 2440095asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 1920\|3 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 | 2 +--R (87843420x + 312332160x + 208221440)\|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 21960855x - 263530260x - 468498240x - 208221440)\|2 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|3 + 3x\|2 )\|3x + 2 + (- 3x - 2)\|2 \|3 - 6x +--R log(-----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R 4 2 +-+ +--+ | 2 +--R (8599500x + 30576000x + 20384000)\|3 \|35 \|3x + 2 +--R + +--R 6 4 2 +-+ +-+ +--+ +--R (- 2149875x - 25798500x - 45864000x - 20384000)\|2 \|3 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ 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\|35 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R 4 2 x\|3 +--R (263530260x + 936996480x + 624664320)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +-+ +--R (56067336x + 199350528x + 132900352)\|2 \|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 +-+ x\|3 +--R (- 65882565x - 790590780x - 1405494720x - 624664320)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +--R (- 28033668x - 336404016x - 598051584x - 265800704)\|3 +--R / +--R +-------+ +--R 4 2 +-+ | 2 +--R (207360x + 737280x + 491520)\|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 51840x - 622080x - 1105920x - 491520)\|2 \|3 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=-1/24*(310-153*x)*(2+3*x^2)^(3/2)-1/10*(34+x)*(2+3*x^2)^(5/2)/(3+2*x)+_ + 18543/32*asinh(x*sqrt(3/2))*sqrt(3)+5425/32*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))*sqrt(35)-7/16*(775-243*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R (- 162750x - 244125)\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 432x + 3672x - 10236x + 38916x - 179042x - 531978)\|3x + 2 +--R + +--R +-+ +--R +-+ x\|3 +--R (556290x + 834435)\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 960x + 1440 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 17577000x + 26365500x + 62496000x + 93744000x + 41664000x +--R + +--R 62496000 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 7 6 5 4 3 +--R - 4394250x - 6591375x - 52731000x - 79096500x - 93744000x +--R + +--R 2 +--R - 140616000x - 41664000x - 62496000 +--R * +--R +-+ +--+ +--R \|2 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((2x + 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (- 9x - 4x - 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R 5 4 3 2 +--R 60079320x + 90118980x + 213615360x + 320423040x + 142410240x +--R + +--R 213615360 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 7 6 5 4 +--R - 15019830x - 22529745x - 180237960x - 270356940x +--R + +--R 3 2 +--R - 320423040x - 480634560x - 142410240x - 213615360 +--R * +--R +-+ +-+ +--R \|2 \|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (- x\|2 \|3 + 2)\|3x + 2 + 2x\|3 + (- 3x - 2)\|2 +--R log(------------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R 11 10 9 8 7 6 +--R 11664x - 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+--R 4 2 +-+ +--+ | 2 +--R (25924872960x + 92177326080x + 61451550720)\|2 \|35 \|3x + 2 +--R + +--R 6 4 2 +--+ +--R (- 12962436480x - 155549237760x - 276531978240x - 122903101440)\|35 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^8 +--R +--R +--R (1) +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R / +--R 8 7 6 5 4 3 2 +--R 256x + 3072x + 16128x + 48384x + 90720x + 108864x + 81648x +--R + +--R 34992x + 6561 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=5/84*(11+18*x)*(2+3*x^2)^(3/2)/(3+2*x)^6+1/14*(4+7*x)*_ + (2+3*x^2)^(5/2)/(3+2*x)^7-1107/600250*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)-1/56*(3-55*x)*sqrt(2+3*x^2)/(3+2*x)^5-_ + 193/7840*sqrt(2+3*x^2)/(3+2*x)^4-639/39200*sqrt(2+3*x^2)/(3+2*x)^3-_ + 2007/274400*sqrt(2+3*x^2)/(3+2*x)^2-27351/9604000*sqrt(2+3*x^2)/(3+2*x) 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10 9 8 +--R - 22119425670384000x - 55423831721832000x - 109772744396868000x +--R + +--R 7 6 5 +--R - 173200771124514000x - 220531198822389000x - 230340551884128000x +--R + +--R 4 3 2 +--R - 196280129728368000x - 133002375746688000x - 70312144198464000x +--R + +--R - 27438885540864000x - 5879761187328000 +--R * +--R +--+ +--R \|35 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 6 4 2 +-+ | 2 +--R (65367243x + 1045875888x + 2324168640x + 1239556608)\|2 \|3x + 2 +--R + +--R 6 4 2 +--R - 915141402x - 4880754144x - 6507672192x - 2479113216 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R 6 4 2 +-+ +--R (- 65367243x - 1045875888x - 2324168640x - 1239556608)\|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 6 4 2 +--R 915141402x + 4880754144x + 6507672192x + 2479113216 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 6 4 2 +--+ | 2 +--R (- 40491036x - 647856576x - 1439681280x - 767830016)\|35 \|3x + 2 +--R + +--R 6 4 2 +-+ +--+ +--R (283437252x + 1511665344x + 2015553792x + 767830016)\|2 \|35 +--R / +--R 6 4 2 +-+ +--R (35444162250x + 567106596000x + 1260236880000x + 672126336000)\|2 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 4 2 +--+ +--R (- 496218271500x - 2646497448000x - 3528663264000x - 1344252672000)\|35 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(5-x)*(3+2*x)^4/sqrt(2+3*x^2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=343/3*asinh(x*sqrt(3/2))/sqrt(3)+16660/81*sqrt(2+3*x^2)+_ + 1477/270*(3+2*x)^2*sqrt(2+3*x^2)+19/30*(3+2*x)^3*sqrt(2+3*x^2)-_ + 1/15*(3+2*x)^4*sqrt(2+3*x^2)+49/81*(43+99*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 4 3 2 +-+ | 2 +--R (- 432x - 540x + 12264x + 58860x + 118513)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 46305asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 405\|3 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (15435x + 123480x + 109760)\|2 \|3x + 2 - 154350x - 411600x +--R + +--R - 219520 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 8 7 6 5 4 3 2 +--R 1440x + 1800x - 37040x - 191400x - 423000x - 520640x - 479520x +--R + +--R - 279040x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 10 9 8 7 6 5 4 +--R - 432x - 540x + 8520x + 54180x + 219425x + 503400x + 782640x +--R + +--R 3 2 +--R 729920x + 479520x + 279040x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 4 2 +-+ +--R (135x + 1080x + 960)\|2 \|3 \|3x + 2 + (- 1350x - 3600x - 1920)\|3 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ | 2 4 +--R (416745x + 3333960x + 2963520)\|2 \|3x + 2 - 4167450x +--R + +--R 2 +--R - 11113200x - 5927040 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (- 416745x - 3333960x - 2963520)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (2133234x + 17065872x + 15169664)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 4 2 x\|3 +--R (4167450x + 11113200x + 5927040)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +-+ +--R (- 10666170x - 28443120x - 15169664)\|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (3645x + 29160x + 25920)\|2 \|3 \|3x + 2 +--R + +--R 4 2 +-+ +--R (- 36450x - 97200x - 51840)\|3 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(5-x)*(3+2*x)^3/sqrt(2+3*x^2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=275/3*asinh(x*sqrt(3/2))/sqrt(3)+3305/54*sqrt(2+3*x^2)+_ + 31/36*(3+2*x)^2*sqrt(2+3*x^2)-1/12*(3+2*x)^3*sqrt(2+3*x^2)+_ + 5/54*(148+171*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 3 2 +-+ | 2 x\|3 +--R (- 18x + 12x + 585x + 2171)\|3 \|3x + 2 + 2475asinh(-----) +--R +-+ +--R \|2 +--R (2) -------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((3300x + 4400)\|2 \|3x + 2 - 2475x - 13200x - 8800) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 7 6 5 4 3 2 +-+ | 2 +--R (18x - 12x - 489x - 2235x - 3056x - 5832x - 2080x)\|3 \|3x + 2 +--R + +--R 7 6 5 4 3 2 +-+ +-+ +--R (- 72x + 48x + 2196x + 6609x + 4616x + 5832x + 2080x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 4 2 +-+ +--R (36x + 48)\|2 \|3 \|3x + 2 + (- 27x - 144x - 96)\|3 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((29700x + 39600)\|2 \|3x + 2 - 22275x - 118800x - 79200) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((- 29700x - 39600)\|2 asinh(-----) + (52104x + 69472)\|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 4 2 x\|3 +--R (22275x + 118800x + 79200)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +-+ +--R (- 19539x - 104208x - 69472)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 4 2 +-+ +--R (324x + 432)\|2 \|3 \|3x + 2 + (- 243x - 1296x - 864)\|3 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(5-x)*(3+2*x)^2/sqrt(2+3*x^2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=127/3*asinh(x*sqrt(3/2))/sqrt(3)+359/27*sqrt(2+3*x^2)-_ + 1/9*(3+2*x)^2*sqrt(2+3*x^2)+1/27*(143+72*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 2 +-+ | 2 x\|3 +--R (- 12x + 36x + 475)\|3 \|3x + 2 + 1143asinh(-----) +--R +-+ +--R \|2 +--R (2) ----------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((381x + 1016)\|2 \|3x + 2 - 2286x - 2032) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 4 3 2 +-+ | 2 +--R (24x - 72x - 612x - 64x)\|3 \|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +-+ +--R (- 12x + 36x + 435x + 120x + 612x + 64x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 2 +-+ +--R (9x + 24)\|2 \|3 \|3x + 2 + (- 54x - 48)\|3 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((3429x + 9144)\|2 \|3x + 2 - 20574x - 18288) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((- 3429x - 9144)\|2 asinh(-----) + (2850x + 7600)\|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 2 x\|3 2 +-+ +-+ +--R (20574x + 18288)asinh(-----) + (- 8550x - 7600)\|2 \|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 2 +-+ +--R (81x + 216)\|2 \|3 \|3x + 2 + (- 486x - 432)\|3 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(5-x)*(3+2*x)/sqrt(2+3*x^2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=47/3*asinh(x*sqrt(3/2))/sqrt(3)+17/6*sqrt(2+3*x^2)-_ + 1/6*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R +-+ | 2 x\|3 +--R (- x + 7)\|3 \|3x + 2 + 47asinh(-----) +--R +-+ +--R \|2 +--R (2) ---------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 2 +--R (94\|2 \|3x + 2 - 141x - 188) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R (3x - 21x + 4x)\|3 \|3x + 2 + (- 6x + 21x - 4x)\|2 \|3 +--R / +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +--R 6\|2 \|3 \|3x + 2 + (- 9x - 12)\|3 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-+ | 2 2 +--R (94\|2 \|3x + 2 - 141x - 188) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +-+ +--R +-+ x\|3 +-+ | 2 2 x\|3 +--R (- 94\|2 asinh(-----) + 28\|3 )\|3x + 2 + (141x + 188)asinh(-----) +--R +-+ +-+ +--R \|2 \|2 +--R + +--R 2 +-+ +-+ +--R (- 21x - 28)\|2 \|3 +--R / +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +--R 6\|2 \|3 \|3x + 2 + (- 9x - 12)\|3 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(5-x)/sqrt(2+3*x^2) +--R +--R +--R - x + 5 +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=5*asinh(x*sqrt(3/2))/sqrt(3)-1/3*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R +-+ | 2 x\|3 +--R - \|3 \|3x + 2 + 15asinh(-----) +--R +-+ +--R \|2 +--R (2) --------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 +--R (5\|2 \|3x + 2 - 10) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 2 +-+ +-+ +--R - x \|2 \|3 +--R / +--R +-------+ +--R +-+ +-+ | 2 +-+ +--R \|2 \|3 \|3x + 2 - 2\|3 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-+ | 2 +--R (15\|2 \|3x + 2 - 30) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +-+ +--R +-+ x\|3 +-+ | 2 x\|3 +-+ +-+ +--R (- 15\|2 asinh(-----) - 2\|3 )\|3x + 2 + 30asinh(-----) + 2\|2 \|3 +--R +-+ +-+ +--R \|2 \|2 +--R / +--R +-------+ +--R +-+ +-+ | 2 +-+ +--R 3\|2 \|3 \|3x + 2 - 6\|3 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(5-x)/((3+2*x)*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------ +--R +-------+ +--R | 2 +--R (2x + 3)\|3x + 2 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=-1/2*asinh(x*sqrt(3/2))/sqrt(3)-13/2*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35) +--R +--R +--R +-+ +--R +-+ 9x - 4 +--+ x\|3 +--R 13\|3 atanh(---------------) - \|35 asinh(-----) +--R +-------+ +-+ +--R +--+ | 2 \|2 +--R \|35 \|3x + 2 +--R (2) ------------------------------------------------ +--R +-+ +--+ +--R 2\|3 \|35 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--R 13\|3 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R +--+ (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R \|35 log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R / +--R +-+ +--+ +--R 2\|3 \|35 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--R 13\|3 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R +--+ (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R \|35 log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R +-+ 9x - 4 +--+ x\|3 +--R - 13\|3 atanh(---------------) + \|35 asinh(-----) +--R +-------+ +-+ +--R +--+ | 2 \|2 +--R \|35 \|3x + 2 +--R / +--R +-+ +--+ +--R 2\|3 \|35 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(5-x)/((3+2*x)^2*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------- +--R +-------+ +--R 2 | 2 +--R (4x + 12x + 9)\|3x + 2 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=-41/35*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/35*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R +-------+ +--R 9x - 4 +--+ | 2 +--R (82x + 123)atanh(---------------) - 13\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R (2) ----------------------------------------------------- +--R +--+ +--R (70x + 105)\|35 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 +--R ((246x + 369)\|2 \|3x + 2 - 492x - 738) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +--+ | 2 2 +-+ +--+ +--R - 52x\|35 \|3x + 2 + (- 117x + 52x)\|2 \|35 +--R / +--R +-------+ +--R +-+ +--+ | 2 +--+ +--R (210x + 315)\|2 \|35 \|3x + 2 + (- 420x - 630)\|35 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-+ | 2 +--R (123\|2 \|3x + 2 - 246) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +-------+ +--R +-+ | 2 9x - 4 +--+ | 2 +--R (- 123\|2 \|3x + 2 + 246)atanh(---------------) - 26\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--+ +--R 26\|2 \|35 +--R / +--R +-------+ +--R +-+ +--+ | 2 +--+ +--R 105\|2 \|35 \|3x + 2 - 210\|35 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(5-x)/((3+2*x)^3*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------- +--R +-------+ +--R 3 2 | 2 +--R (8x + 36x + 54x + 27)\|3x + 2 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=-291/1225*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/70*sqrt(2+3*x^2)/(3+2*x)^2-281/2450*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 2 9x - 4 +--+ | 2 +--R (1164x + 3492x + 2619)atanh(---------------) + (- 281x - 649)\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R ----------------------------------------------------------------------------- +--R 2 +--+ +--R (4900x + 14700x + 11025)\|35 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 4 3 +--R (20952x + 62856x + 47142)\|2 \|3x + 2 - 31428x - 94284x +--R + +--R 2 +--R - 112617x - 125712x - 94284 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (7587x + 7139x - 21036x)\|35 \|3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (7788x + 8190x - 7139x + 21036x)\|2 \|35 +--R / +--R +-------+ +--R 2 +-+ +--+ | 2 +--R (88200x + 264600x + 198450)\|2 \|35 \|3x + 2 +--R + +--R 4 3 2 +--+ +--R (- 132300x - 396900x - 474075x - 529200x - 396900)\|35 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-+ | 2 2 +--R (5238\|2 \|3x + 2 - 7857x - 10476) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +-+ | 2 2 9x - 4 +--R (- 5238\|2 \|3x + 2 + 7857x + 10476)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R +--+ | 2 2 +-+ +--+ +--R - 2596\|35 \|3x + 2 + (1947x + 2596)\|2 \|35 +--R / +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R 22050\|2 \|35 \|3x + 2 + (- 33075x - 44100)\|35 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(5-x)/((3+2*x)^4*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------- +--R +-------+ +--R 4 3 2 | 2 +--R (16x + 96x + 216x + 216x + 81)\|3x + 2 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-57/1715*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/105*sqrt(2+3*x^2)/(3+2*x)^3-16/245*sqrt(2+3*x^2)/(3+2*x)^2-_ + 10/343*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 9x - 4 +--R (1368x + 6156x + 9234x + 4617)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (- 600x - 2472x - 2995)\|35 \|3x + 2 +--R / +--R 3 2 +--+ +--R (41160x + 185220x + 277830x + 138915)\|35 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (110808x + 498636x + 1043442x + 1703673x + 1994544x + 997272) +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 664848x - 2991816x - 5078700x - 4903254x - 3989088x - 1994544 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 5 4 3 2 +--+ | 2 +--R (- 143760x - 355320x - 152348x - 495540x - 1519776x)\|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R (- 145800x - 169416x + 726975x + 1292180x + 495540x + 1519776x) +--R * +--R +-+ +--+ +--R \|2 \|35 +--R / +--R 5 4 3 2 +--R 3333960x + 15002820x + 31394790x + 51259635x + 60011280x +--R + +--R 30005640 +--R * +--R +-------+ +--R +-+ +--+ | 2 +--R \|2 \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 20003760x - 90016920x - 152806500x - 147527730x - 120022560x +--R + +--R - 60011280 +--R * +--R +--+ +--R \|35 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((13851x + 36936)\|2 \|3x + 2 - 83106x - 73872) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 2 +-+ | 2 2 +--R ((- 13851x - 36936)\|2 \|3x + 2 + 83106x + 73872) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +--+ | 2 2 +-+ +--+ +--R (- 17970x - 47920)\|35 \|3x + 2 + (53910x + 47920)\|2 \|35 +--R / +--R +-------+ +--R 2 +-+ +--+ | 2 2 +--+ +--R (416745x + 1111320)\|2 \|35 \|3x + 2 + (- 2500470x - 2222640)\|35 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(5-x)/((3+2*x)^5*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------ +--R +-------+ +--R 5 4 3 2 | 2 +--R (32x + 240x + 720x + 1080x + 810x + 243)\|3x + 2 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=27/42875*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 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70x - 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R 7 6 5 4 3 2 +--R 53514x - 10668x - 1001961x - 2593507x - 3171888x - 3168648x +--R + +--R - 3464992x +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 8 7 6 5 4 3 +--R 125136x + 536760x + 1064616x + 2406348x + 4969993x + 5770632x +--R + +--R 2 +--R 3168648x + 3464992x +--R * +--R +-+ +--+ +--R \|2 \|35 +--R / +--R 6 5 4 3 2 +--R 24696000x + 148176000x + 366324000x + 530964000x + 569551500x +--R + +--R 444528000x + 166698000 +--R * +--R +-------+ +--R +-+ +--+ | 2 +--R \|2 \|35 \|3x + 2 +--R + +--R 8 7 6 5 4 +--R - 18522000x - 111132000x - 348831000x - 842751000x - 1493207625x +--R + +--R 3 2 +--R - 1728720000x - 1389150000x - 889056000x - 333396000 +--R * +--R +--+ +--R \|35 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((972x + 1296)\|2 \|3x + 2 - 729x - 3888x - 2592) +--R * +--R log 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Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(5-x)*(3+2*x)^4/(2+3*x^2)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=880/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^4*(2+15*x)/sqrt(2+3*x^2)+_ + 1255/81*sqrt(2+3*x^2)-115/9*(3+2*x)*sqrt(2+3*x^2)-_ + 151/27*(3+2*x)^2*sqrt(2+3*x^2)-5/3*(3+2*x)^3*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R x\|3 | 2 +--R 47520asinh(-----)\|3x + 2 +--R +-+ +--R \|2 +--R + +--R 4 3 2 +-+ +--R (- 288x - 432x + 15024x - 14715x - 33914)\|3 +--R / +--R +-------+ +--R +-+ | 2 +--R 162\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (15840x + 84480x + 56320)\|2 \|3x + 2 - 126720x - 253440x +--R + +--R - 112640 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 6 5 4 3 2 +-+ | 2 +--R (256x + 384x - 24318x + 13592x - 47952x + 17440x)\|3 \|3x + 2 +--R + +--R 8 7 6 5 4 3 2 +--R - 96x - 144x + 4496x - 5673x + 60282x - 26672x + 47952x +--R + +--R - 17440x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 4 2 +-+ +--R (54x + 288x + 192)\|2 \|3 \|3x + 2 + (- 432x - 864x - 384)\|3 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 4 2 +-+ +--R ((570240x + 760320)\|3x + 2 + (- 213840x - 1140480x - 760320)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 2 x\|3 2 +-+ +-+ +--R ((- 570240x - 760320)asinh(-----) + (- 203484x - 271312)\|2 \|3 ) +--R +-+ +--R \|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (213840x + 1140480x + 760320)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (152613x + 813936x + 542624)\|3 +--R / +--R +-------+ +--R 2 +-+ | 2 4 2 +-+ +-+ +--R (1944x + 2592)\|3 \|3x + 2 + (- 729x - 3888x - 2592)\|2 \|3 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(5-x)*(3+2*x)^3/(2+3*x^2)^(3/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=134/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^3*(2+15*x)/sqrt(2+3*x^2)-_ + 109/9*sqrt(2+3*x^2)-17/3*(3+2*x)*sqrt(2+3*x^2)-5/3*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 3 2 +-+ +--R 804asinh(-----)\|3x + 2 + (- 24x + 24x + 411x - 1426)\|3 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------- +--R +-------+ +--R +-+ | 2 +--R 18\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((2412x + 2144)\|2 \|3x + 2 - 2412x - 8040x - 4288) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (24x - 24x - 347x - 2916x - 1096x)\|3 \|3x + 2 +--R + +--R 5 4 3 2 +-+ +-+ +--R (- 72x + 2211x + 1169x + 2916x + 1096x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 4 2 +-+ +--R (54x + 48)\|2 \|3 \|3x + 2 + (- 54x - 180x - 96)\|3 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 2 +-+ +--R ((2412x + 6432)\|3x + 2 + (- 7236x - 6432)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 x\|3 2 +-+ +-+ | 2 +--R ((- 2412x - 6432)asinh(-----) + (- 2139x - 5704)\|2 \|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 2 +-+ x\|3 2 +-+ +--R (7236x + 6432)\|2 asinh(-----) + (12834x + 11408)\|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 2 +-+ | 2 2 +-+ +-+ +--R (54x + 144)\|3 \|3x + 2 + (- 162x - 144)\|2 \|3 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(5-x)*(3+2*x)^2/(2+3*x^2)^(3/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=8/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^2*(2+15*x)/sqrt(2+3*x^2)-_ + 53/9*sqrt(2+3*x^2)-5/3*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 2 +-+ +--R 48asinh(-----)\|3x + 2 + (- 24x + 357x - 338)\|3 +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------- +--R +-------+ +--R +-+ | 2 +--R 18\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((48x + 64)\|2 \|3x + 2 - 192x - 128) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 2 +-+ | 2 4 3 2 +-+ +-+ +--R (- 306x - 476x)\|3 \|3x + 2 + (- 24x + 357x + 306x + 476x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 2 +-+ +--R (18x + 24)\|2 \|3 \|3x + 2 + (- 72x - 48)\|3 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | 2 2 +-+ +--R (96\|3x + 2 + (- 72x - 96)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +-+ +--R x\|3 +-+ +-+ | 2 2 +-+ x\|3 +--R (- 96asinh(-----) - 338\|2 \|3 )\|3x + 2 + (72x + 96)\|2 asinh(-----) +--R +-+ +-+ +--R \|2 \|2 +--R + +--R 2 +-+ +--R (507x + 676)\|3 +--R / +--R +-------+ +--R +-+ | 2 2 +-+ +-+ +--R 36\|3 \|3x + 2 + (- 27x - 36)\|2 \|3 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(5-x)*(3+2*x)/(2+3*x^2)^(3/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-2/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)*(2+15*x)/sqrt(2+3*x^2)-_ + 5/3*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 +-+ +--R - 4asinh(-----)\|3x + 2 + (49x - 14)\|3 +--R +-+ +--R \|2 +--R (2) ------------------------------------------ +--R +-------+ +--R +-+ | 2 +--R 6\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 2 +--R (4\|2 \|3x + 2 - 12x - 8) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R +-+ | 2 2 +-+ +-+ +--R - 49x\|3 \|3x + 2 + (21x + 49x)\|2 \|3 +--R / +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +--R 6\|2 \|3 \|3x + 2 + (- 18x - 12)\|3 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | 2 +-+ +--R (4\|3x + 2 - 4\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +-+ +--R x\|3 +-+ +-+ | 2 +-+ x\|3 +-+ +--R (4asinh(-----) - 7\|2 \|3 )\|3x + 2 - 4\|2 asinh(-----) + 14\|3 +--R +-+ +-+ +--R \|2 \|2 +--R / +--R +-------+ +--R +-+ | 2 +-+ +-+ +--R 6\|3 \|3x + 2 - 6\|2 \|3 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(5-x)/(2+3*x^2)^(3/2) +--R +--R +--R - x + 5 +--R (1) ------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=1/6*(2+15*x)/sqrt(2+3*x^2) +--R +--R +--R 15x + 2 +--R (2) ----------- +--R +-------+ +--R | 2 +--R 6\|3x + 2 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 2 +-+ +--R - 5x\|3x + 2 + (- x + 5x)\|2 +--R (3) -------------------------------- +--R +-------+ +--R +-+ | 2 2 +--R 2\|2 \|3x + 2 - 6x - 4 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R (4) ------------------- +--R +-------+ +--R | 2 +-+ +--R 6\|3x + 2 - 6\|2 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(5-x)/((3+2*x)*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------ +--R +-------+ +--R 3 2 | 2 +--R (6x + 9x + 4x + 6)\|3x + 2 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=-26/35*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R | 2 9x - 4 +--+ +--R 52\|3x + 2 atanh(---------------) + (41x + 26)\|35 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R (2) ---------------------------------------------------- +--R +-------+ +--R +--+ | 2 +--R 70\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 2 +--R (52\|2 \|3x + 2 - 156x - 104) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +--+ | 2 2 +-+ +--+ +--R - 41x\|35 \|3x + 2 + (- 39x + 41x)\|2 \|35 +--R / +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R 70\|2 \|35 \|3x + 2 + (- 210x - 140)\|35 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | 2 +-+ +--R (52\|3x + 2 - 52\|2 ) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +-------+ +--R | 2 +-+ 9x - 4 +-+ +--+ | 2 +--R (- 52\|3x + 2 + 52\|2 )atanh(---------------) + 13\|2 \|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +--+ +--R - 26\|35 +--R / +--R +-------+ +--R +--+ | 2 +-+ +--+ +--R 70\|35 \|3x + 2 - 70\|2 \|35 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(5-x)/((3+2*x)^2*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------- +--R +-------+ +--R 4 3 2 | 2 +--R (12x + 36x + 35x + 24x + 18)\|3x + 2 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=-632/1225*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)*sqrt(2+3*x^2))+19/1225*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R | 2 9x - 4 2 +--+ +--R (2528x + 3792)\|3x + 2 atanh(---------------) + (114x + 1435x + 986)\|35 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R --------------------------------------------------------------------------- +--R +-------+ +--R +--+ | 2 +--R (4900x + 7350)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 2 +-+ | 2 3 +--R (22752x + 34128x + 30336x + 45504)\|2 \|3x + 2 - 91008x +--R + +--R 2 +--R - 136512x - 60672x - 91008 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (5916x + 7506x - 9332x)\|35 \|3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (1026x + 1083x - 7506x + 9332x)\|2 \|35 +--R / +--R +-------+ +--R 3 2 +-+ +--+ | 2 +--R (44100x + 66150x + 58800x + 88200)\|2 \|35 \|3x + 2 +--R + +--R 3 2 +--+ +--R (- 176400x - 264600x - 117600x - 176400)\|35 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | 2 2 +-+ +--R (7584\|3x + 2 + (- 5688x - 7584)\|2 ) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R | 2 2 +-+ 9x - 4 +--R (- 7584\|3x + 2 + (5688x + 7584)\|2 )atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R 986\|2 \|35 \|3x + 2 + (- 1479x - 1972)\|35 +--R / +--R +-------+ +--R +--+ | 2 2 +-+ +--+ +--R 14700\|35 \|3x + 2 + (- 11025x - 14700)\|2 \|35 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(5-x)/((3+2*x)^3*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------- +--R +-------+ +--R 5 4 3 2 | 2 +--R (24x + 108x + 178x + 153x + 108x + 54)\|3x + 2 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=-1962/8575*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^2*sqrt(2+3*x^2))+9/245*sqrt(2+3*x^2)/(3+2*x)^2-_ + 331/8575*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 2 | 2 9x - 4 +--R (15696x + 47088x + 35316)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 3 2 +--+ +--R (- 3972x - 4068x + 7397x + 3658)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 +--R (68600x + 205800x + 154350)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (1271376x + 3814128x + 3990708x + 3390336x + 2542752)\|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 1271376x - 3814128x - 7098516x - 12713760x - 11795544x +--R + +--R - 6780672x - 5085504 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 5 4 3 2 +--+ | 2 +--R (107244x + 241524x + 481329x + 607484x - 181416x)\|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +--+ +--R (- 65844x - 519264x - 697137x - 345267x - 607484x + 181416x)\|2 \|35 +--R / +--R 4 3 2 +-+ +--+ +--R (5556600x + 16669800x + 17441550x + 14817600x + 11113200)\|2 \|35 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 5556600x - 16669800x - 31024350x - 55566000x - 51552900x +--R + +--R - 29635200x - 22226400 +--R * +--R +--+ +--R \|35 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 2 +-+ +--R ((105948x + 282528)\|3x + 2 + (- 317844x - 282528)\|2 ) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 2 | 2 2 +-+ +--R ((- 105948x - 282528)\|3x + 2 + (317844x + 282528)\|2 ) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +-+ +--+ | 2 2 +--+ +--R (5487x + 14632)\|2 \|35 \|3x + 2 + (- 32922x - 29264)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 2 +-+ +--+ +--R (463050x + 1234800)\|35 \|3x + 2 + (- 1389150x - 1234800)\|2 \|35 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(5-x)/((3+2*x)^4*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------- +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (48x + 288x + 680x + 840x + 675x + 432x + 162)\|3x + 2 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=-3312/42875*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^3*sqrt(2+3*x^2))+23/525*sqrt(2+3*x^2)/_ + (3+2*x)^3-27/1225*sqrt(2+3*x^2)/(3+2*x)^2-1051/42875*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 3 2 | 2 9x - 4 +--R (158976x + 715392x + 1073088x + 536544)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 4 3 2 +--+ +--R (- 75672x - 261036x - 237930x - 23349x - 29438)\|35 +--R / +--R +-------+ +--R 3 2 +--+ | 2 +--R (2058000x + 9261000x + 13891500x + 6945750)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 38631168x + 173840256x + 466793280x + 1057528224x +--R + +--R 3 2 +--R 1528077312x + 1313459712x + 927148032x + 463574016 +--R * +--R +-------+ +--R +-+ | 2 +--R 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14617908)\|3x + 2 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 2151936x - 11467872x - 22188792x - 18957672x - 8562487x +--R + +--R - 4197366 +--R * +--R +--+ +--R \|35 +--R / +--R 4 3 2 +--+ +--R (144060000x + 864360000x + 1944810000x + 1944810000x + 729303750)\|35 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 +--R 389810880x + 2338865280x + 6301942560x + 11499420960x +--R + +--R 4 3 2 +--R 16561006956x + 17359577856x + 12746815776x + 7484368896x +--R + +--R 2806638336 +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 10 9 8 7 +--R - 233886528x - 1403319168x - 5184484704x - 15319567584x +--R + +--R 6 5 4 3 +--R - 31459362228x - 44828251200x - 50663503512x - 45945709056x +--R + +--R 2 +--R - 29703589056x - 14968737792x - 5613276672 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ 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2236531500000x - 2527658752500x +--R + +--R 3 2 +--R - 2292282720000x - 1481945220000x - 746807040000x - 280052640000 +--R * +--R +--+ +--R \|35 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 | 2 +--R (4872636x + 38981088x + 34649856)\|3x + 2 +--R + +--R 4 2 +-+ +--R (- 24363180x - 64968480x - 34649856)\|2 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 4 2 | 2 +--R (- 4872636x - 38981088x - 34649856)\|3x + 2 +--R + +--R 4 2 +-+ +--R (24363180x + 64968480x + 34649856)\|2 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 4 2 +-+ +--+ | 2 +--R (- 699561x - 5596488x - 4974656)\|2 \|35 \|3x + 2 +--R + +--R 4 2 +--+ +--R (6995610x + 18654960x + 9949312)\|35 +--R / +--R +-------+ +--R 4 2 +--+ | 2 +--R (243101250x + 1944810000x + 1728720000)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 1215506250x - 3241350000x - 1728720000)\|2 \|35 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(5-x)*(3+2*x)^4/(2+3*x^2)^(5/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=1/18*(3+2*x)^4*(2+15*x)/(2+3*x^2)^(3/2)-16/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 1/18*(3+2*x)^3*(20+37*x)/sqrt(2+3*x^2)-2027/81*sqrt(2+3*x^2)-_ + 19/3*(3+2*x)*sqrt(2+3*x^2)-37/27*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 x\|3 | 2 +--R (- 864x - 576)asinh(-----)\|3x + 2 +--R +-+ +--R \|2 +--R + +--R 4 3 2 +-+ +--R (- 864x + 57285x - 16560x + 33381x - 25342)\|3 +--R / +--R +-------+ +--R 2 +-+ | 2 +--R (486x + 324)\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 6 4 2 +-+ | 2 6 4 +--R (864x + 5184x + 6144x + 2048)\|2 \|3x + 2 - 6912x - 18432x +--R + +--R 2 +--R - 15360x - 4096 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 6 5 4 3 2 +-+ +--R (- 35709x - 152760x - 180846x - 292696x - 143856x - 118688x)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 8 7 6 5 4 3 +--R - 864x + 57285x + 130884x + 338901x + 288738x + 381712x +--R + +--R 2 +--R 143856x + 118688x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (486x + 2916x + 3456x + 1152)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 3888x - 10368x - 8640x - 2304)\|3 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 4 2 +-+ +--R ((6912x + 9216)\|3x + 2 + (- 2592x - 13824x - 9216)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 x\|3 2 +-+ +-+ | 2 +--R ((6912x + 9216)asinh(-----) + (- 152052x - 202736)\|2 \|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (- 2592x - 13824x - 9216)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (114039x + 608208x + 405472)\|3 +--R / +--R +-------+ +--R 2 +-+ | 2 4 2 +-+ +-+ +--R (3888x + 5184)\|3 \|3x + 2 + (- 1458x - 7776x - 5184)\|2 \|3 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(5-x)*(3+2*x)^3/(2+3*x^2)^(5/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=1/18*(3+2*x)^3*(2+15*x)/(2+3*x^2)^(3/2)-8/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 1/18*(3+2*x)^2*(10+39*x)/sqrt(2+3*x^2)-157/27*sqrt(2+3*x^2)-_ + 13/9*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 x\|3 | 2 3 2 +-+ +--R (- 144x - 96)asinh(-----)\|3x + 2 + (4971x - 72x + 3741x - 1490)\|3 +--R +-+ +--R \|2 +--R ------------------------------------------------------------------------- +--R +-------+ +--R 2 +-+ | 2 +--R (162x + 108)\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 6 4 2 +--R ((864x + 1344x + 512)\|2 \|3x + 2 - 864x - 3456x - 3456x - 1024) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 9942x - 13266x - 33994x - 17496x - 19952x)\|3 \|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +-+ +--R (6705x + 29826x + 26388x + 48958x + 17496x + 19952x)\|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (972x + 1512x + 576)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 972x - 3888x - 3888x - 1152)\|3 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 2 +-+ +--R ((288x + 768)\|3x + 2 + (- 864x - 768)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 x\|3 2 +-+ +-+ | 2 +--R ((288x + 768)asinh(-----) + (- 2235x - 5960)\|2 \|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 2 +-+ x\|3 2 +-+ +--R (- 864x - 768)\|2 asinh(-----) + (13410x + 11920)\|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 2 +-+ | 2 2 +-+ +-+ +--R (324x + 864)\|3 \|3x + 2 + (- 972x - 864)\|2 \|3 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(5-x)*(3+2*x)^2/(2+3*x^2)^(5/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=1/18*(3+2*x)^2*(2+15*x)/(2+3*x^2)^(3/2)-41/54*(4-9*x)/sqrt(2+3*x^2) +--R +--R +--R 3 2 +--R 1287x + 72x + 1215x - 274 +--R (2) --------------------------- +--R +-------+ +--R 2 | 2 +--R (162x + 108)\|3x + 2 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 858x - 870x - 3098x - 1224x - 2160x)\|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +--R (411x + 2574x + 1788x + 4718x + 1224x + 2160x)\|2 +--R / +--R +-------+ +--R 4 2 +-+ | 2 6 4 2 +--R (324x + 504x + 192)\|2 \|3x + 2 - 324x - 1296x - 1296x - 384 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R +-------+ +--R 2 +-+ | 2 2 +--R (- 411x - 1096)\|2 \|3x + 2 + 2466x + 2192 +--R (4) ---------------------------------------------- +--R +-------+ +--R 2 | 2 2 +-+ +--R (324x + 864)\|3x + 2 + (- 972x - 864)\|2 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(5-x)*(3+2*x)/(2+3*x^2)^(5/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=1/18*(3+2*x)*(2+15*x)/(2+3*x^2)^(3/2)+1/18*(-10+43*x)/sqrt(2+3*x^2) +--R +--R +--R 3 +--R 129x + 135x - 14 +--R (2) --------------------- +--R +-------+ +--R 2 | 2 +--R (54x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 258x - 126x - 958x - 168x - 720x)\|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +--R (63x + 774x + 252x + 1498x + 168x + 720x)\|2 +--R / +--R +-------+ +--R 4 2 +-+ | 2 6 4 2 +--R (324x + 504x + 192)\|2 \|3x + 2 - 324x - 1296x - 1296x - 384 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R +-------+ +--R 2 +-+ | 2 2 +--R (- 21x - 56)\|2 \|3x + 2 + 126x + 112 +--R (4) --------------------------------------------- +--R +-------+ +--R 2 | 2 2 +-+ +--R (108x + 288)\|3x + 2 + (- 324x - 288)\|2 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(5-x)/(2+3*x^2)^(5/2) +--R +--R +--R - x + 5 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=1/18*(2+15*x)/(2+3*x^2)^(3/2)+5/6*x/sqrt(2+3*x^2) +--R +--R +--R 3 +--R 45x + 45x + 2 +--R (2) --------------------- +--R +-------+ +--R 2 | 2 +--R (54x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 30x + 6x - 110x + 8x - 80x)\|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +--R (- 3x + 90x - 12x + 170x - 8x + 80x)\|2 +--R / +--R +-------+ +--R 4 2 +-+ | 2 6 4 2 +--R (108x + 168x + 64)\|2 \|3x + 2 - 108x - 432x - 432x - 128 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R +-------+ +--R 2 +-+ | 2 2 +--R (3x + 8)\|2 \|3x + 2 - 18x - 16 +--R (4) --------------------------------------------- +--R +-------+ +--R 2 | 2 2 +-+ +--R (108x + 288)\|3x + 2 + (- 324x - 288)\|2 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(5-x)/((3+2*x)*(2+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------- +--R +-------+ +--R 5 4 3 2 | 2 +--R (18x + 27x + 24x + 36x + 8x + 12)\|3x + 2 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=1/210*(26+41*x)/(2+3*x^2)^(3/2)-104/1225*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)+1/7350*(312+2137*x)/sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 2 | 2 9x - 4 +--R (1872x + 1248)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 3 2 +--+ +--R (6411x + 936x + 5709x + 1534)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 +--R (22050x + 14700)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 6 4 +--R (11232x + 17472x + 6656)\|2 \|3x + 2 - 11232x - 44928x +--R + +--R 2 +--R - 44928x - 13312 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 5 4 3 2 +--+ | 2 +--R (- 12822x + 11934x - 45610x + 13416x - 30448x)\|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +--+ +--R (- 6903x + 38466x - 21996x + 68446x - 13416x + 30448x)\|2 \|35 +--R / +--R +-------+ +--R 4 2 +-+ +--+ | 2 +--R (132300x + 205800x + 78400)\|2 \|35 \|3x + 2 +--R + +--R 6 4 2 +--+ +--R (- 132300x - 529200x - 529200x - 156800)\|35 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 2 +-+ +--R ((3744x + 9984)\|3x + 2 + (- 11232x - 9984)\|2 ) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 2 | 2 2 +-+ +--R ((- 3744x - 9984)\|3x + 2 + (11232x + 9984)\|2 ) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +-+ +--+ | 2 2 +--+ +--R (2301x + 6136)\|2 \|35 \|3x + 2 + (- 13806x - 12272)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 2 +-+ +--+ +--R (44100x + 117600)\|35 \|3x + 2 + (- 132300x - 117600)\|2 \|35 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(5-x)/((3+2*x)^2*(2+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------- +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (36x + 108x + 129x + 144x + 124x + 48x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=1/210*(26+41*x)/((3+2*x)*(2+3*x^2)^(3/2))-176/1715*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/1470*(34+507*x)/((3+2*x)*_ + sqrt(2+3*x^2))+277/5145*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 3 2 | 2 9x - 4 +--R (6336x + 9504x + 4224x + 6336)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 4 3 2 +--+ +--R (4986x + 10647x + 7362x + 9107x + 3966)\|35 +--R / +--R +-------+ +--R 3 2 +--+ | 2 +--R (61740x + 92610x + 41160x + 61740)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R 57024x + 85536x + 342144x + 513216x + 405504x + 608256x +--R + +--R 135168x + 202752 +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 7 6 5 4 3 2 +--R - 456192x - 684288x - 1216512x - 1824768x - 1013760x - 1520640x +--R + +--R - 270336x - 405504 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R 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d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 4 +--R 630B c e x + (770A c e + 840B c d e )x +--R + +--R 5 4 2 3 3 +--R (990B a e + 1100A c d e + 30B c d e )x +--R + +--R 5 4 2 3 3 2 2 +--R (1386A a e + 1584B a d e + 66A c d e - 36B c d e )x +--R + +--R 4 2 3 3 2 4 2 3 +--R (2772A a d e + 198B a d e - 88A c d e + 48B c d e)x + 1386A a d e +--R + +--R 3 2 4 5 +--R - 396B a d e + 176A c d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(A+B*x)*(a+c*x^2)*sqrt(d+e*x) +--R +--R +--R 3 2 +-------+ +--R (1) (B c x + A c x + B a x + A a)\|e x + d +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-2/3*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(3/2)/e^4+2/5*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^4-2/7*c*(3*B*d-A*e)*_ + (d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B c e x + (90A c e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126B a e + 18A c d e - 12B c d e )x +--R + +--R 4 3 2 2 3 3 +--R (210A a e + 42B a d e - 24A c d e + 16B c d e)x + 210A a d e +--R + +--R 2 2 3 4 +--R - 84B a d e + 48A c d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 3 +--R 70B c e x + (90A c e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126B a e + 18A c d e - 12B c d e )x +--R + +--R 4 3 2 2 3 3 +--R (210A a e + 42B a d e - 24A c d e + 16B c d e)x + 210A a d e +--R + +--R 2 2 3 4 +--R - 84B a d e + 48A c d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(A+B*x)*(a+c*x^2)/sqrt(d+e*x) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=2/3*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^4-_ + 2/5*c*(3*B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-_ + 2*(B*d-A*e)*(c*d^2+a*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + (42A c e - 36B c d e )x +--R + +--R 3 2 2 3 2 +--R (70B a e - 56A c d e + 48B c d e)x + 210A a e - 140B a d e +--R + +--R 2 3 +--R 112A c d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B c e x + (42A c e - 36B c d e )x +--R + +--R 3 2 2 3 2 +--R (70B a e - 56A c d e + 48B c d e)x + 210A a e - 140B a d e +--R + +--R 2 3 +--R 112A c d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=-2/3*c*(3*B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*sqrt(d+e*x))+2*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 6B c e x + (10A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (30B a e - 40A c d e + 48B c d e)x - 30A a e + 60B a d e - 80A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 6B c e x + (10A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (30B a e - 40A c d e + 48B c d e)x - 30A a e + 60B a d e - 80A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^(3/2))+2/3*B*c*_ + (d+e*x)^(3/2)/e^4-2*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^4*sqrt(d+e*x))-_ + 2*c*(3*B*d-A*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 2B c e x + (6A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 6B a e + 24A c d e - 48B c d e)x - 2A a e - 4B a d e + 16A c d e +--R + +--R 3 +--R - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 2B c e x + (6A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 6B a e + 24A c d e - 48B c d e)x - 2A a e - 4B a d e + 16A c d e +--R + +--R 3 +--R - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^(5/2))-2/3*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^4*(d+e*x)^(3/2))+2*c*(3*B*d-A*e)/_ + (e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + (- 30A c e + 180B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 10B a e - 40A c d e + 240B c d e)x - 6A a e - 4B a d e - 16A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B c e x + (- 30A c e + 180B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 10B a e - 40A c d e + 240B c d e)x - 6A a e - 4B a d e - 16A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(A+B*x)*(a+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +-------+ +--R (1) (B c x + A c x + 2B a c x + 2A a c x + B a x + A a )\|e x + d +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-2/3*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^(3/2)/e^6+2/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^6-4/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(7/2)/e^6+4/9*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(9/2)/e^6-2/11*c^2*(5*B*d-A*e)*_ + (d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + (8190A c e + 630B c d e )x +--R + +--R 6 2 5 2 2 4 4 +--R (20020B a c e + 910A c d e - 700B c d e )x +--R + +--R 6 5 2 2 4 2 3 3 3 +--R (25740A a c e + 2860B a c d e - 1040A c d e + 800B c d e )x +--R + +--R 2 6 5 2 4 2 3 3 +--R 18018B a e + 5148A a c d e - 3432B a c d e + 1248A c d e +--R + +--R 2 4 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 2 4 3 3 +--R 30030A a e + 6006B a d e - 6864A a c d e + 4576B a c d e +--R + +--R 2 4 2 2 5 +--R - 1664A c d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 30030A a d e - 12012B a d e + 13728A a c d e - 9152B a c d e +--R + +--R 2 5 2 6 +--R 3328A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + (8190A c e + 630B c d e )x +--R + +--R 6 2 5 2 2 4 4 +--R (20020B a c e + 910A c d e - 700B c d e )x +--R + +--R 6 5 2 2 4 2 3 3 3 +--R (25740A a c e + 2860B a c d e - 1040A c d e + 800B c d e )x +--R + +--R 2 6 5 2 4 2 3 3 +--R 18018B a e + 5148A a c d e - 3432B a c d e + 1248A c d e +--R + +--R 2 4 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 2 4 3 3 +--R 30030A a e + 6006B a d e - 6864A a c d e + 4576B a c d e +--R + +--R 2 4 2 2 5 +--R - 1664A c d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 30030A a d e - 12012B a d e + 13728A a c d e - 9152B a c d e +--R + +--R 2 5 2 6 +--R 3328A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(A+B*x)*(a+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=2/3*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^6-_ + 4/5*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(5/2)/e^6+_ + 4/7*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(7/2)/e^6-_ + 2/9*c^2*(5*B*d-A*e)*(d+e*x)^(9/2)/e^6+2/11*B*c^2*_ + (d+e*x)^(11/2)/e^6-2*(B*d-A*e)*(c*d^2+a*e^2)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + (770A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (1980B a c e - 880A c d e + 800B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (2772A a c e - 2376B a c d e + 1056A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 2310B a e - 3696A a c d e + 3168B a c d e - 1408A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R 6930A a e - 4620B a d e + 7392A a c d e - 6336B a c d e +--R + +--R 2 4 2 5 +--R 2816A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + (770A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (1980B a c e - 880A c d e + 800B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (2772A a c e - 2376B a c d e + 1056A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 2310B a e - 3696A a c d e + 3168B a c d e - 1408A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R 6930A a e - 4620B a d e + 7392A a c d e - 6336B a c d e +--R + +--R 2 4 2 5 +--R 2816A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-4/3*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3/2)/e^6+_ + 4/5*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^6-_ + 2/7*c^2*(5*B*d-A*e)*(d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*sqrt(d+e*x))+2*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (90A c e - 100B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (252B a c e - 144A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 504B a c d e + 288A c d e - 320B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 630B a e - 1680A a c d e + 2016B a c d e - 1152A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R - 630A a e + 1260B a d e - 3360A a c d e + 4032B a c d e +--R + +--R 2 4 2 5 +--R - 2304A c d e + 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (90A c e - 100B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (252B a c e - 144A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 504B a c d e + 288A c d e - 320B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 630B a e - 1680A a c d e + 2016B a c d e - 1152A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R - 630A a e + 1260B a d e - 3360A a c d e + 4032B a c d e +--R + +--R 2 4 2 5 +--R - 2304A c d e + 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(3/2))+4/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^6-2/5*c^2*(5*B*d-A*e)*_ + (d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-2*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*sqrt(d+e*x))-4*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + (42A c e - 60B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (140B a c e - 112A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 840B a c d e + 672A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 210B a e + 1680A a c d e - 3360B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 3840B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 70A a e - 140B a d e + 1120A a c d e - 2240B a c d e + 1792A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + (42A c e - 60B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (140B a c e - 112A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 840B a c d e + 672A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 210B a e + 1680A a c d e - 3360B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 3840B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 70A a e - 140B a d e + 1120A a c d e - 2240B a c d e + 1792A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(5/2))-2/3*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^(3/2))-2/3*c^2*_ + (5*B*d-A*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6+4*c*_ + (5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*sqrt(d+e*x))+4*c*_ + (5*B*c*d^2-2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + (10A c e - 20B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (60B a c e - 80A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 60A a c e + 360B a c d e - 480A c d e + 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 10B a e - 80A a c d e + 480B a c d e - 640A c d e + 1280B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 6A a e - 4B a d e - 32A a c d e + 192B a c d e - 256A c d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + (10A c e - 20B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (60B a c e - 80A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 60A a c e + 360B a c d e - 480A c d e + 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 10B a e - 80A a c d e + 480B a c d e - 640A c d e + 1280B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 6A a e - 4B a d e - 32A a c d e + 192B a c d e - 256A c d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(9/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=2/7*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(7/2))-2/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^(5/2))+4/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^(3/2))+2/3*B*c^2*_ + (d+e*x)^(3/2)/e^6-4*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*_ + sqrt(d+e*x))-2*c^2*(5*B*d-A*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (210A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 420B a c e + 1680A c d e - 5600B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 140A a c e - 840B a c d e + 3360A c d e - 11200B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 42B a e - 112A a c d e - 672B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 8960B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 30A a e - 12B a d e - 32A a c d e - 192B a c d e + 768A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 9 3 8 2 2 7 3 6 +-------+ +--R (105e x + 315d e x + 315d e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (210A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 420B a c e + 1680A c d e - 5600B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 140A a c e - 840B a c d e + 3360A c d e - 11200B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 42B a e - 112A a c d e - 672B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 8960B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 30A a e - 12B a d e - 32A a c d e - 192B a c d e + 768A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 9 3 8 2 2 7 3 6 +-------+ +--R (105e x + 315d e x + 315d e x + 105d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=2/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^8-_ + 6/5*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*_ + (d+e*x)^(5/2)/e^8-2/7*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+_ + 30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(7/2)/e^8-2/9*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(9/2)/e^8+6/11*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(11/2)/e^8-2/13*c^3*_ + (7*B*d-A*e)*(d+e*x)^(13/2)/e^8+2/15*B*c^3*(d+e*x)^(15/2)/e^8-_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^3*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 6006B c e x + (6930A c e - 6468B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (24570B a c e - 7560A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30030A a c e - 27300B a c d e + 8400A c d e - 7840B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 38610B a c e - 34320A a c d e + 31200B a c d e - 9600A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 54054A a c e - 46332B a c d e + 41184A a c d e - 37440B a c d e +--R + +--R 3 4 3 3 5 2 +--R 11520A c d e - 10752B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 72072A a c d e + 61776B a c d e - 54912A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 49920B a c d e - 15360A c d e + 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 90090A a e - 60060B a d e + 144144A a c d e - 123552B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 109824A a c d e - 99840B a c d e + 30720A c d e - 28672B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 6006B c e x + (6930A c e - 6468B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (24570B a c e - 7560A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30030A a c e - 27300B a c d e + 8400A c d e - 7840B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 38610B a c e - 34320A a c d e + 31200B a c d e - 9600A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 54054A a c e - 46332B a c d e + 41184A a c d e - 37440B a c d e +--R + +--R 3 4 3 3 5 2 +--R 11520A c d e - 10752B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 72072A a c d e + 61776B a c d e - 54912A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 49920B a c d e - 15360A c d e + 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 90090A a e - 60060B a d e + 144144A a c d e - 123552B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 109824A a c d e - 99840B a c d e + 30720A c d e - 28672B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=-2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*_ + (d+e*x)^(3/2)/e^8-2/5*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+_ + 30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(5/2)/e^8-2/7*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(7/2)/e^8+2/3*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(9/2)/e^8-2/11*c^3*_ + (7*B*d-A*e)*(d+e*x)^(11/2)/e^8+2/13*B*c^3*(d+e*x)^(13/2)/e^8+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*sqrt(d+e*x))+2*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 2310B c e x + (2730A c e - 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (10010B a c e - 3640A c d e + 3920B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (12870A a c e - 14300B a c d e + 5200A c d e - 5600B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 18018B a c e - 20592A a c d e + 22880B a c d e - 8320A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 30030A a c e - 36036B a c d e + 41184A a c d e - 45760B a c d e +--R + +--R 3 4 3 3 5 2 +--R 16640A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 120120A a c d e + 144144B a c d e - 164736A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 183040B a c d e - 66560A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 30030A a e + 60060B a d e - 240240A a c d e + 288288B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 329472A a c d e + 366080B a c d e - 133120A c d e + 143360B c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 2310B c e x + (2730A c e - 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (10010B a c e - 3640A c d e + 3920B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (12870A a c e - 14300B a c d e + 5200A c d e - 5600B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 18018B a c e - 20592A a c d e + 22880B a c d e - 8320A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 30030A a c e - 36036B a c d e + 41184A a c d e - 45760B a c d e +--R + +--R 3 4 3 3 5 2 +--R 16640A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 120120A a c d e + 144144B a c d e - 164736A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 183040B a c d e - 66560A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 30030A a e + 60060B a d e - 240240A a c d e + 288288B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 329472A a c d e + 366080B a c d e - 133120A c d e + 143360B c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(3/2))-2/3*c*(4*A*c*d*e*_ + (5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*_ + (d+e*x)^(3/2)/e^8-2/5*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)*(d+e*x)^(5/2)/e^8+6/7*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*_ + (d+e*x)^(7/2)/e^8-2/9*c^3*(7*B*d-A*e)*(d+e*x)^(9/2)/e^8+_ + 2/11*B*c^3*(d+e*x)^(11/2)/e^8-2*(c*d^2+a*e^2)^2*(7*B*c*d^2-_ + 6*A*c*d*e+a*B*e^2)/(e^8*sqrt(d+e*x))-6*c*(c*d^2+a*e^2)*(7*B*c*d^3-_ + 5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 630B c e x + (770A c e - 980B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (2970B a c e - 1320A c d e + 1680B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (4158A a c e - 5940B a c d e + 2640A c d e - 3360B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 6930B a c e - 11088A a c d e + 15840B a c d e - 7040A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 20790A a c e - 41580B a c d e + 66528A a c d e - 95040B a c d e +--R + +--R 3 4 3 3 5 2 +--R 42240A c d e - 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6930B a e + 83160A a c d e - 166320B a c d e + 266112A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 380160B a c d e + 168960A c d e - 215040B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 2310A a e - 4620B a d e + 55440A a c d e - 110880B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 177408A a c d e - 253440B a c d e + 112640A c d e - 143360B c d +--R / +--R 9 8 +-------+ +--R (3465e x + 3465d e )\|e x + d +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 630B c e x + (770A c e - 980B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (2970B a c e - 1320A c d e + 1680B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (4158A a c e - 5940B a c d e + 2640A c d e - 3360B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 6930B a c e - 11088A a c d e + 15840B a c d e - 7040A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 20790A a c e - 41580B a c d e + 66528A a c d e - 95040B a c d e +--R + +--R 3 4 3 3 5 2 +--R 42240A c d e - 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6930B a e + 83160A a c d e - 166320B a c d e + 266112A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 380160B a c d e + 168960A c d e - 215040B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 2310A a e - 4620B a d e + 55440A a c d e - 110880B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 177408A a c d e - 253440B a c d e + 112640A c d e - 143360B c d +--R / +--R 9 8 +-------+ +--R (3465e x + 3465d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(5/2))-2/3*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(3/2))-2/3*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(3/2)/e^8+6/5*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^8-2/7*c^3*(7*B*d-A*e)*_ + (d+e*x)^(7/2)/e^8+2/9*B*c^3*(d+e*x)^(9/2)/e^8+6*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*sqrt(d+e*x))-_ + 2*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 70B c e x + (90A c e - 140B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (378B a c e - 216A c d e + 336B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (630A a c e - 1260B a c d e + 720A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 1890B a c e - 5040A a c d e + 10080B a c d e - 5760A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 1890A a c e + 11340B a c d e - 30240A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 34560A c d e + 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 210B a e - 2520A a c d e + 15120B a c d e - 40320A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 80640B a c d e - 46080A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 126A a e - 84B a d e - 1008A a c d e + 6048B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 16128A a c d e + 32256B a c d e - 18432A c d e + 28672B c d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 70B c e x + (90A c e - 140B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (378B a c e - 216A c d e + 336B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (630A a c e - 1260B a c d e + 720A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 1890B a c e - 5040A a c d e + 10080B a c d e - 5760A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 1890A a c e + 11340B a c d e - 30240A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 34560A c d e + 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 210B a e - 2520A a c d e + 15120B a c d e - 40320A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 80640B a c d e - 46080A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 126A a e - 84B a d e - 1008A a c d e + 6048B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 16128A a c d e + 32256B a c d e - 18432A c d e + 28672B c d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(9/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=2/7*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(7/2))-2/5*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(5/2))+2*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^(3/2))+_ + 2*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^8-2/5*c^3*_ + (7*B*d-A*e)*(d+e*x)^(5/2)/e^8+2/7*B*c^3*(d+e*x)^(7/2)/e^8+2*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))/(e^8*sqrt(d+e*x))-2*c^2*(35*B*c*d^3-15*A*c*d^2*e+_ + 15*a*B*d*e^2-3*a*A*e^3)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (14A c e - 28B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (70B a c e - 56A c d e + 112B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (210A a c e - 700B a c d e + 560A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 210B a c e + 1680A a c d e - 5600B a c d e + 4480A c d e +--R + +--R 3 4 3 +--R - 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 70A a c e - 420B a c d e + 3360A a c d e - 11200B a c d e +--R + +--R 3 4 3 3 5 2 +--R 8960A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 14B a e - 56A a c d e - 336B a c d e + 2688A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 8960B a c d e + 7168A c d e - 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 4B a d e - 16A a c d e - 96B a c d e + 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 2560B a c d e + 2048A c d e - 4096B c d +--R / +--R 11 3 10 2 2 9 3 8 +-------+ +--R (35e x + 105d e x + 105d e x + 35d e )\|e x + d +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (14A c e - 28B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (70B a c e - 56A c d e + 112B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (210A a c e - 700B a c d e + 560A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 210B a c e + 1680A a c d e - 5600B a c d e + 4480A c d e +--R + +--R 3 4 3 +--R - 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 70A a c e - 420B a c d e + 3360A a c d e - 11200B a c d e +--R + +--R 3 4 3 3 5 2 +--R 8960A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 14B a e - 56A a c d e - 336B a c d e + 2688A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 8960B a c d e + 7168A c d e - 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 4B a d e - 16A a c d e - 96B a c d e + 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 2560B a c d e + 2048A c d e - 4096B c d +--R / +--R 11 3 10 2 2 9 3 8 +-------+ +--R (35e x + 105d e x + 105d e x + 35d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(11/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=2/9*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(9/2))-2/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(7/2))+6/5*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^(5/2))+_ + 2/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))/(e^8*(d+e*x)^(3/2))-2/3*c^3*(7*B*d-A*e)*(d+e*x)^(3/2)/_ + e^8+2/5*B*c^3*(d+e*x)^(5/2)/e^8+2*c^2*(35*B*c*d^3-15*A*c*d^2*e+_ + 15*a*B*d*e^2-3*a*A*e^3)/(e^8*sqrt(d+e*x))+6*c^2*(7*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 126B c e x + (210A c e - 588B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (1890B a c e - 2520A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 1890A a c e + 18900B a c d e - 25200A c d e + 70560B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 630B a c e - 5040A a c d e + 50400B a c d e - 67200A c d e +--R + +--R 3 4 3 +--R 188160B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 378A a c e - 756B a c d e - 6048A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 80640A c d e + 225792B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 90B a e - 216A a c d e - 432B a c d e - 3456A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 34560B a c d e - 46080A c d e + 129024B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 70A a e - 20B a d e - 48A a c d e - 96B a c d e - 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 7680B a c d e - 10240A c d e + 28672B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +-------+ +--R (315e x + 1260d e x + 1890d e x + 1260d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 126B c e x + (210A c e - 588B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (1890B a c e - 2520A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 1890A a c e + 18900B a c d e - 25200A c d e + 70560B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 630B a c e - 5040A a c d e + 50400B a c d e - 67200A c d e +--R + +--R 3 4 3 +--R 188160B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 378A a c e - 756B a c d e - 6048A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 80640A c d e + 225792B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 90B a e - 216A a c d e - 432B a c d e - 3456A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 34560B a c d e - 46080A c d e + 129024B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 70A a e - 20B a d e - 48A a c d e - 96B a c d e - 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 7680B a c d e - 10240A c d e + 28672B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +-------+ +--R (315e x + 1260d e x + 1890d e x + 1260d e x + 315d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=2/3*(B*d+A*e)*(d+e*x)^(3/2)/c+2/5*B*(d+e*x)^(5/2)/c+2*(B*c*d^2+_ + 2*A*c*d*e-a*B*e^2)*sqrt(d+e*x)/c^2-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ + sqrt(-a)+d*sqrt(c)))*((-A*c*d*(c*d^2-3*a*e^2)+a*B*e*(3*c*d^2-a*e^2))/_ + sqrt(-a)+(B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*sqrt(c))/(c^(9/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+_ + d*sqrt(c)))*((A*c*d*(c*d^2-3*a*e^2)-a*B*e*(3*c*d^2-a*e^2))/sqrt(-a)+_ + (B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*sqrt(c))/(c^(9/4)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 3 +---+ +-+ 2 3 +--R (15A a e + 45B a d e - 45A c d e - 15B c d )\|- a \|c + 15B a e +--R + +--R 2 2 2 3 +--R - 45A a c d e - 45B a c d e + 15A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 3 +---+ +-+ 2 3 +--R (15A a e + 45B a d e - 45A c d e - 15B c d )\|- a \|c - 15B a e +--R + +--R 2 2 2 3 +--R 45A a c d e + 45B a c d e - 15A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 2 2 +--R (6B c e x + (10A c e + 22B c d e)x - 30B a e + 70A c d e + 46B c d ) +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 15c \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 2 +--R 15c +--R * +--R ROOT +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 2 2 5 +--R (10A a c - 10B a c)d e + 10A B a c d e + (- A c + B a c )d +--R / +--R 4 +--R a c +--R * +--R log +--R 2 7 2 2 7 8 2 +--R (2A a c e + 4B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 2 4 3 3 5 2 7 3 3 4 2 4 3 6 +--R (- A B a c + B a c )e + (2A a c - 12A B a c )d e +--R + +--R 2 3 4 3 4 3 2 5 3 2 5 2 3 4 3 4 +--R (31A B a c - 11B a c )d e + (- 20A a c + 50A B a c )d e +--R + +--R 2 2 5 3 3 4 4 3 3 6 2 2 5 5 2 +--R (- 55A B a c + 15B a c )d e + (10A a c - 32A B a c )d e +--R + +--R 2 6 3 2 5 6 2 6 7 +--R (9A B a c - 5B a c )d e + 2A B a c d +--R * +--R ROOT +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 +--R (10A a c - 10B a c)d e + 10A B a c d e +--R + +--R 2 3 2 2 5 +--R (- A c + B a c )d +--R / +--R 4 +--R a c +--R + +--R 4 4 2 4 6 9 3 4 2 3 5 8 +--R (A a c - B a )e + (10A B a c + 10A B a c)d e +--R + +--R 4 3 3 4 5 2 7 4 2 4 4 4 2 4 5 +--R (- 8A a c + 8B a c)d e + (- 14A a c + 14B a c )d e +--R + +--R 3 2 4 3 3 3 5 4 +--R (- 28A B a c - 28A B a c )d e +--R + +--R 3 5 3 2 4 7 2 4 6 4 2 4 8 +--R (- 16A B a c - 16A B a c )d e + (5A c - 5B a c )d e +--R + +--R 3 6 3 5 9 +--R (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 +--R 15c +--R * +--R ROOT +--R - +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 2 2 5 +--R (10A a c - 10B a c)d e + 10A B a c d e + (- A c + B a c )d +--R / +--R 4 +--R a c +--R * +--R log +--R 2 7 2 2 7 8 2 +--R (2A a c e + 4B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 2 4 3 3 5 2 7 3 3 4 2 4 3 6 +--R (A B a c - B a c )e + (- 2A a c + 12A B a c )d e +--R + +--R 2 3 4 3 4 3 2 5 3 2 5 2 3 4 3 4 +--R (- 31A B a c + 11B a c )d e + (20A a c - 50A B a c )d e +--R + +--R 2 2 5 3 3 4 4 3 3 6 2 2 5 5 2 +--R (55A B a c - 15B a c )d e + (- 10A a c + 32A B a c )d e +--R + +--R 2 6 3 2 5 6 2 6 7 +--R (- 9A B a c + 5B a c )d e - 2A B a c d +--R * +--R ROOT +--R - +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 +--R (10A a c - 10B a c)d e + 10A B a c d e +--R + +--R 2 3 2 2 5 +--R (- A c + B a c )d +--R / +--R 4 +--R a c +--R + +--R 4 4 2 4 6 9 3 4 2 3 5 8 +--R (A a c - B a )e + (10A B a c + 10A B a c)d e +--R + +--R 4 3 3 4 5 2 7 4 2 4 4 4 2 4 5 +--R (- 8A a c + 8B a c)d e + (- 14A a c + 14B a c )d e +--R + +--R 3 2 4 3 3 3 5 4 +--R (- 28A B a c - 28A B a c )d e +--R + +--R 3 5 3 2 4 7 2 4 6 4 2 4 8 +--R (- 16A B a c - 16A B a c )d e + (5A c - 5B a c )d e +--R + +--R 3 6 3 5 9 +--R (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 2 +--R 15c +--R * +--R ROOT +--R - +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 2 2 5 +--R (10A a c - 10B a c)d e + 10A B a c d e + (- A c + B a c )d +--R / +--R 4 +--R a c +--R * +--R log +--R 2 7 2 2 7 8 2 +--R (- 2A a c e - 4B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 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+--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 2 4 3 3 5 2 7 3 3 4 2 4 3 6 +--R (- A B a c + B a c )e + (2A a c - 12A B a c )d e +--R + +--R 2 3 4 3 4 3 2 5 3 2 5 2 3 4 3 4 +--R (31A B a c - 11B a c )d e + (- 20A a c + 50A B a c )d e +--R + +--R 2 2 5 3 3 4 4 3 3 6 2 2 5 5 2 +--R (- 55A B a c + 15B a c )d e + (10A a c - 32A B a c )d e +--R + +--R 2 6 3 2 5 6 2 6 7 +--R (9A B a c - 5B a c )d e + 2A B a c d +--R * +--R ROOT +--R - +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 +--R (- 110A a c + 620A B a c - 110B a c ) +--R * +--R 4 6 +--R d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 +--R (10A a c - 10B a c)d e + 10A B a c d e +--R + +--R 2 3 2 2 5 +--R (- A c + B a c )d +--R / +--R 4 +--R a c +--R + +--R 4 4 2 4 6 9 3 4 2 3 5 8 +--R (A a c - B a )e + (10A B a c + 10A B a c)d e +--R + +--R 4 3 3 4 5 2 7 4 2 4 4 4 2 4 5 +--R (- 8A a c + 8B a c)d e + (- 14A a c + 14B a c )d e +--R + +--R 3 2 4 3 3 3 5 4 +--R (- 28A B a c - 28A B a c )d e +--R + +--R 3 5 3 2 4 7 2 4 6 4 2 4 8 +--R (- 16A B a c - 16A B a c )d e + (5A c - 5B a c )d e +--R + +--R 3 6 3 5 9 +--R (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 +---+4+-+ +--R c \|- a \|c +--R * +--R ROOT +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 2 2 5 +--R (10A a c - 10B a c)d e + 10A B a c d e + (- A c + B a c )d +--R / +--R 4 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 2 7 2 2 7 8 2 +--R (- 2A a c e - 4B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 2 4 3 3 5 2 7 3 3 4 2 4 3 6 +--R (A B a c - B a c )e + (- 2A a c + 12A B a c )d e +--R + +--R 2 3 4 3 4 3 2 5 3 2 5 2 3 4 3 4 +--R (- 31A B a c + 11B a c )d e + (20A a c - 50A B a c )d e +--R + +--R 2 2 5 3 3 4 4 3 3 6 2 2 5 5 2 +--R (55A B a c - 15B a c )d e + (- 10A a c + 32A B a c )d e +--R + +--R 2 6 3 2 5 6 2 6 7 +--R (- 9A B a c + 5B a c )d e - 2A B a c d +--R * +--R ROOT +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 +--R (10A a c - 10B a c)d e + 10A B a c d e +--R + +--R 2 3 2 2 5 +--R (- A c + B a c )d +--R / +--R 4 +--R a c +--R + +--R 4 4 2 4 6 9 3 4 2 3 5 8 +--R (A a c - B a )e + (10A B a c + 10A B a c)d e +--R + +--R 4 3 3 4 5 2 7 4 2 4 4 4 2 4 5 +--R (- 8A a c + 8B a c)d e + (- 14A a c + 14B a c )d e +--R + +--R 3 2 4 3 3 3 5 4 +--R (- 28A B a c - 28A B a c )d e +--R + +--R 3 5 3 2 4 7 2 4 6 4 2 4 8 +--R (- 16A B a c - 16A B a c )d e + (5A c - 5B a c )d e +--R + +--R 3 6 3 5 9 +--R (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 3 +---+ +-+ 2 3 +--R (- 2A a e - 6B a d e + 6A c d e + 2B c d )\|- a \|c - 2B a e +--R + +--R 2 2 2 3 +--R 6A a c d e + 6B a c d e - 2A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 3 +---+ +-+ 2 3 +--R (- 2A a e - 6B a d e + 6A c d e + 2B c d )\|- a \|c + 2B a e +--R + +--R 2 2 2 3 +--R - 6A a c d e - 6B a c d e + 2A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 2c \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=2/3*B*(d+e*x)^(3/2)/c+2*(B*d+A*e)*sqrt(d+e*x)/c-atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2+2*A*c*d*e-_ + a*B*e^2-(A*c*d^2-2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/(c^(7/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*_ + sqrt(-a)+d*sqrt(c)))*(B*c*d^2+2*A*c*d*e-a*B*e^2+(A*c*d^2-2*a*B*d*e-_ + a*A*e^2)*sqrt(c)/sqrt(-a))/(c^(7/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 +-+ +--R (- 3A a e - 6B a d e + 3A c d )\|c +--R + +--R 2 2 +---+ +--R (3B a e - 6A c d e - 3B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 +-+ +--R (3A a e + 6B a d e - 3A c d )\|c +--R + +--R 2 2 +---+ +--R (3B a e - 6A c d e - 3B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ +--R (2B e x + 6A e + 8B d)\|- a \|c \|e x + d \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R 3c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3c +--R * +--R ROOT +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (3A a c - 3B a )d e + 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 3 +--R a c +--R * +--R log +--R 2 5 6 +--R (2B a c e - 2A a c d) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 3 2 3 2 3 2 4 2 2 3 3 3 2 3 +--R (- A a c + A B a c )e + (- 7A B a c + B a c )d e +--R + +--R 3 4 2 2 3 2 2 2 4 3 2 3 3 +--R (3A a c - 9A B a c )d e + (5A B a c - 3B a c )d e +--R + +--R 2 4 4 +--R 2A B a c d +--R * +--R ROOT +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (3A a c - 3B a )d e + 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 3 +--R a c +--R + +--R 4 2 2 4 4 5 3 2 2 3 3 4 +--R (A a c - B a )e + (6A B a c + 6A B a c)d e +--R + +--R 4 3 4 3 2 3 3 3 3 2 2 3 2 +--R (- 2A a c + 2B a c)d e + (4A B a c + 4A B a c )d e +--R + +--R 4 4 4 2 2 4 3 4 3 3 5 +--R (- 3A c + 3B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 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+ +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 3 2 3 2 3 2 4 2 2 3 3 3 2 3 +--R (A a c - A B a c )e + (7A B a c - B a c )d e +--R + +--R 3 4 2 2 3 2 2 2 4 3 2 3 3 +--R (- 3A a c + 9A B a c )d e + (- 5A B a c + 3B a c )d e +--R + +--R 2 4 4 +--R - 2A B a c d +--R * +--R ROOT +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (3A a c - 3B a )d e + 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 3 +--R a c +--R + +--R 4 2 2 4 4 5 3 2 2 3 3 4 +--R (A a c - B a )e + (6A B a c + 6A B a c)d e +--R + +--R 4 3 4 3 2 3 3 3 3 2 2 3 2 +--R (- 2A a c + 2B a c)d e + (4A B a c + 4A B a c )d e +--R + +--R 4 4 4 2 2 4 3 4 3 3 5 +--R (- 3A c + 3B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-+ +--R (2A a e + 4B a d e - 2A c d )\|c +--R + +--R 2 2 +---+ +--R (- 2B a e + 4A c d e + 2B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 +-+ +--R (- 2A a e - 4B a d e + 2A c d )\|c +--R + +--R 2 2 +---+ +--R (- 2B a e + 4A c d e + 2B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R 2c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=2*B*sqrt(d+e*x)/c-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((-A*c*d+a*B*e)/sqrt(-a)+(B*d+A*e)*sqrt(c))/(c^(5/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*_ + sqrt(-a)+d*sqrt(c)))*((A*c*d-a*B*e)/sqrt(-a)+(B*d+A*e)*sqrt(c))/_ + (c^(5/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- A e - B d)\|- a \|c - B a e + A c d)\|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- A e - B d)\|- a \|c + B a e - A c d)\|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R 2B\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R c +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R log +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (- A B a c + B a c)e - 2A B a c d +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R - +--R c +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R log +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (A B a c - B a c)e + 2A B a c d +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R c +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R log +--R - +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (- A B a c + B a c)e - 2A B a c d +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R - +--R c +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R log +--R - +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (A B a c - B a c)e + 2A B a c d +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R +-------+ +--R 4B\|e x + d +--R / +--R 2c +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+4+-+ +--R c\|- a \|c +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (- A B a c + B a c)e - 2A B a c d +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R - +--R +---+4+-+ +--R c\|- a \|c +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (A B a c - B a c)e + 2A B a c d +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R +---+4+-+ +--R c\|- a \|c +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R - +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (- A B a c + B a c)e - 2A B a c d +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R - +--R +---+4+-+ +--R c\|- a \|c +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R - +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (A B a c - B a c)e + 2A B a c d +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((2A e + 2B d)\|- a \|c + 2B a e - 2A c d)\|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((2A e + 2B d)\|- a \|c - 2B a e + 2A c d)\|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 2c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(A+B*x)/((a+c*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) -------------------- +--R 2 +-------+ +--R (c x + a)\|e x + d +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (B+a*A*sqrt(c)/(-a)^(3/2))/(c^(3/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(B+A*sqrt(c)/_ + sqrt(-a))/(c^(3/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (A\|c - B\|- a )\|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (- A\|c - B\|- a )\|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (2B a c e + 2A a c d e + 2B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (- A a c + A B a c)e + (3A B a c - B a c)d e - 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 3 2 3 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 +--R - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (2B a c e + 2A a c d e + 2B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (A a c - A B a c)e + (- 3A B a c + B a c)d e + 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R - +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (- 2B a c e - 2A a c d e - 2B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (- A a c + A B a c)e + (3A B a c - B a c)d e - 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 3 2 3 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 +--R - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (- 2B a c e - 2A a c d e - 2B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (A a c - A B a c)e + (- 3A B a c + B a c)d e + 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +---+4+-+3 +--R \|- a \|c +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (2B a c e + 2A a c d e + 2B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (- A a c + A B a c)e + (3A B a c - B a c)d e - 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R +---+4+-+3 +--R \|- a \|c +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 3 2 3 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 +--R - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (2B a c e + 2A a c d e + 2B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (A a c - A B a c)e + (- 3A B a c + B a c)d e + 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R - +--R +---+4+-+3 +--R \|- a \|c +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (- 2B a c e - 2A a c d e - 2B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (- A a c + A B a c)e + (3A B a c - B a c)d e - 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R +---+4+-+3 +--R \|- a \|c +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 3 2 3 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 +--R - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (- 2B a c e - 2A a c d e - 2B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (A a c - A B a c)e + (- 3A B a c + B a c)d e + 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (- 2A\|c + 2B\|- a )\|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (2A\|c + 2B\|- a )\|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R 3 2 +-------+ +--R (c e x + c d x + a e x + a d)\|e x + d +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=2*(B*d-A*e)/((c*d^2+a*e^2)*sqrt(d+e*x))-atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))*((-A*c*d-a*B*e)/sqrt(-a)+(B*d-A*e)*_ + sqrt(c))/(c^(1/4)*(c*d^2+a*e^2)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*_ + ((A*c*d+a*B*e)/sqrt(-a)+(B*d-A*e)*sqrt(c))/(c^(1/4)*(c*d^2+a*e^2)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ +--R +---+ +-+ +-------+ | +-+ +---+ +--R ((A e - B d)\|- a \|c + B a e + A c d)\|e x + d \|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ +-------+ | +-+ +---+ +--R ((A e - B d)\|- a \|c - B a e - A c d)\|e x + d \|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (- 2A e + 2B d)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R (a e + c d )\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +-------+ +--R (- a e - c d )\|e x + d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R 2A a c e - 4B a c d e + 4A a c d e - 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R - 12B a c d e - 4A a c d e - 4B a c d e - 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (- A B a c + B a )e + (- 2A a c + 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (16A B a c - 4B a c)d e + (6A a c - 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (- 7A B a c + 3B a c )d e + 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-------+ +--R (a e + c d )\|e x + d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R 2A a c e - 4B a c d e + 4A a c d e - 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R - 12B a c d e - 4A a c d e - 4B a c d e - 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (A B a c - B a )e + (2A a c - 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (- 16A B a c + 4B a c)d e + (- 6A a c + 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (7A B a c - 3B a c )d e - 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-------+ +--R (- a e - c d )\|e x + d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R - 2A a c e + 4B a c d e - 4A a c d e + 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R 12B a c d e + 4A a c d e + 4B a c d e + 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (- A B a c + B a )e + (- 2A a c + 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (16A B a c - 4B a c)d e + (6A a c - 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (- 7A B a c + 3B a c )d e + 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-------+ +--R (a e + c d )\|e x + d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R - 2A a c e + 4B a c d e - 4A a c d e + 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R 12B a c d e + 4A a c d e + 4B a c d e + 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (A B a c - B a )e + (2A a c - 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (- 16A B a c + 4B a c)d e + (- 6A a c + 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (7A B a c - 3B a c )d e - 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - 4A e + 4B d +--R / +--R 2 2 +-------+ +--R (2a e + 2c d )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 +---+4+-+ +--R (- a e - c d )\|- a \|c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R 2A a c e - 4B a c d e + 4A a c d e - 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R - 12B a c d e - 4A a c d e - 4B a c d e - 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (- A B a c + B a )e + (- 2A a c + 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (16A B a c - 4B a c)d e + (6A a c - 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (- 7A B a c + 3B a c )d e + 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +---+4+-+ +--R (a e + c d )\|- a \|c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R 2A a c e - 4B a c d e + 4A a c d e - 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R - 12B a c d e - 4A a c d e - 4B a c d e - 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (A B a c - B a )e + (2A a c - 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (- 16A B a c + 4B a c)d e + (- 6A a c + 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (7A B a c - 3B a c )d e - 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +---+4+-+ +--R (- a e - c d )\|- a \|c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R - 2A a c e + 4B a c d e - 4A a c d e + 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R 12B a c d e + 4A a c d e + 4B a c d e + 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (- A B a c + B a )e + (- 2A a c + 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (16A B a c - 4B a c)d e + (6A a c - 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (- 7A B a c + 3B a c )d e + 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +---+4+-+ +--R (a e + c d )\|- a \|c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R - 2A a c e + 4B a c d e - 4A a c d e + 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R 12B a c d e + 4A a c d e + 4B a c d e + 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (A B a c - B a )e + (2A a c - 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (- 16A B a c + 4B a c)d e + (- 6A a c + 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (7A B a c - 3B a c )d e - 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- 2A e + 2B d)\|- a \|c - 2B a e - 2A c d)\|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- 2A e + 2B d)\|- a \|c + 2B a e + 2A c d)\|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (2a e + 2c d )\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------------ +--R 2 4 3 2 2 2 2 +-------+ +--R (c e x + 2c d e x + (a e + c d )x + 2a d e x + a d )\|e x + d +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=2/3*(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x)^(3/2))+2*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2)/((c*d^2+a*e^2)^2*sqrt(d+e*x))-c^(1/4)*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2-(A*c*d^2+2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/((c*d^2+_ + a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))-c^(1/4)*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2+(A*c*d^2+2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/((c*d^2+_ + a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 +--R (- 3A a e + 6B a d e + 3A c d e)x - 3A a d e + 6B a d e +--R + +--R 3 +--R 3A c d +--R * +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 +--R (3B a e + 6A c d e - 3B c d e)x + 3B a d e + 6A c d e +--R + +--R 3 +--R - 3B c d +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ +-------+ | +-+ +---+ \|c \|e x + d +--R \|c \|e x + d \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 +--R (3A a e - 6B a d e - 3A c d e)x + 3A a d e - 6B a d e +--R + +--R 3 +--R - 3A c d +--R * +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 +--R (3B a e + 6A c d e - 3B c d e)x + 3B a d e + 6A c d e +--R + +--R 3 +--R - 3B c d +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ +-------+ | +-+ +---+ \|c \|e x + d +--R \|c \|e x + d \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 3 2 2 3 2 +--R (- 6B a e - 12A c d e + 6B c d e)x - 2A a e - 4B a d e +--R + +--R 2 3 +--R - 14A c d e + 8B c d +--R * +--R +---------------+ +---------------+ +--R +---+ | +-+ +---+ | +-+ +---+ +--R \|- a \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +---+ +--R ((3a e + 6a c d e + 3c d e)x + 3a d e + 6a c d e + 3c d )\|- a +--R * +--R +---------------+ +---------------+ +--R +-------+ | +-+ +---+ | +-+ +---+ +--R \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 3 2 4 2 4 3 2 2 5 +-------+ +--R ((3a e + 6a c d e + 3c d e)x + 3a d e + 6a c d e + 3c d )\|e x + d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R 2a e + 10a c d e + 20a c d e + 20a c d e + 10a c d e +--R + +--R 5 10 +--R 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R 2B a e + 6A a c d e + 4B a c d e + 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 +--R - 10B a c d e + 50A a c d e - 40B a c d e +--R + +--R 4 4 7 6 4 4 8 5 3 5 9 4 3 5 10 3 +--R 40A a c d e - 50B a c d e + 10A a c d e - 28B a c d e +--R + +--R 2 6 11 2 2 6 12 7 13 +--R - 4A a c d e - 6B a c d e - 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (- A a c + A B a c)e + (13A B a c - 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (13A a c - 43A B a c )d e + (- 81A B a c + 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (- 35A a c + 105A B a c )d e + (87A B a c - 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (15A a c - 41A B a c )d e + (- 11A B a c + 5B a c )d e +--R + +--R 2 5 8 +--R 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R 2a e + 10a c d e + 20a c d e + 20a c d e +--R + +--R 2 4 8 2 5 10 +--R 10a c d e + 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 5 2 3 2 4 2 4 3 2 2 5 +--R ((- 3a e - 6a c d e - 3c d e)x - 3a d e - 6a c d e - 3c d ) +--R * +--R +-------+ +--R \|e x + d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e - 10a c d e +--R + +--R 5 10 +--R - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R 2B a e + 6A a c d e + 4B a c d e + 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 +--R - 10B a c d e + 50A a c d e - 40B a c d e +--R + +--R 4 4 7 6 4 4 8 5 3 5 9 4 3 5 10 3 +--R 40A a c d e - 50B a c d e + 10A a c d e - 28B a c d e +--R + +--R 2 6 11 2 2 6 12 7 13 +--R - 4A a c d e - 6B a c d e - 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (A a c - A B a c)e + (- 13A B a c + 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (- 13A a c + 43A B a c )d e + (81A B a c - 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (35A a c - 105A B a c )d e + (- 87A B a c + 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (- 15A a c + 41A B a c )d e + (11A B a c - 5B a c )d e +--R + +--R 2 5 8 +--R - 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e +--R + +--R 2 4 8 2 5 10 +--R - 10a c d e - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 5 2 3 2 4 2 4 3 2 2 5 +-------+ +--R ((3a e + 6a c d e + 3c d e)x + 3a d e + 6a c d e + 3c d )\|e x + d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e - 10a c d e +--R + +--R 5 10 +--R - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R - 2B a e - 6A a c d e - 4B a c d e - 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 4 4 7 6 +--R 10B a c d e - 50A a c d e + 40B a c d e - 40A a c d e +--R + +--R 4 4 8 5 3 5 9 4 3 5 10 3 2 6 11 2 +--R 50B a c d e - 10A a c d e + 28B a c d e + 4A a c d e +--R + +--R 2 6 12 7 13 +--R 6B a c d e + 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (- A a c + A B a c)e + (13A B a c - 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (13A a c - 43A B a c )d e + (- 81A B a c + 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (- 35A a c + 105A B a c )d e + (87A B a c - 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (15A a c - 41A B a c )d e + (- 11A B a c + 5B a c )d e +--R + +--R 2 5 8 +--R 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e +--R + +--R 2 4 8 2 5 10 +--R - 10a c d e - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 5 2 3 2 4 2 4 3 2 2 5 +--R ((- 3a e - 6a c d e - 3c d e)x - 3a d e - 6a c d e - 3c d ) +--R * +--R +-------+ +--R \|e x + d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R 2a e + 10a c d e + 20a c d e + 20a c d e + 10a c d e +--R + +--R 5 10 +--R 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R - 2B a e - 6A a c d e - 4B a c d e - 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 4 4 7 6 +--R 10B a c d e - 50A a c d e + 40B a c d e - 40A a c d e +--R + +--R 4 4 8 5 3 5 9 4 3 5 10 3 2 6 11 2 +--R 50B a c d e - 10A a c d e + 28B a c d e + 4A a c d e +--R + +--R 2 6 12 7 13 +--R 6B a c d e + 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (A a c - A B a c)e + (- 13A B a c + 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (- 13A a c + 43A B a c )d e + (81A B a c - 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (35A a c - 105A B a c )d e + (- 87A B a c + 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (- 15A a c + 41A B a c )d e + (11A B a c - 5B a c )d e +--R + +--R 2 5 8 +--R - 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R 2a e + 10a c d e + 20a c d e + 20a c d e +--R + +--R 2 4 8 2 5 10 +--R 10a c d e + 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 3 2 2 +--R (- 12B a e - 24A c d e + 12B c d e)x - 4A a e - 8B a d e - 28A c d e +--R + +--R 3 +--R 16B c d +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +-------+ +--R ((6a e + 12a c d e + 6c d e)x + 6a d e + 12a c d e + 6c d )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 2 2 2 4 +---+ +--R (a e + 2a c d e + c d )\|- a +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R 2a e + 10a c d e + 20a c d e + 20a c d e + 10a c d e +--R + +--R 5 10 +--R 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R 2B a e + 6A a c d e + 4B a c d e + 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 +--R - 10B a c d e + 50A a c d e - 40B a c d e +--R + +--R 4 4 7 6 4 4 8 5 3 5 9 4 3 5 10 3 +--R 40A a c d e - 50B a c d e + 10A a c d e - 28B a c d e +--R + +--R 2 6 11 2 2 6 12 7 13 +--R - 4A a c d e - 6B a c d e - 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (- A a c + A B a c)e + (13A B a c - 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (13A a c - 43A B a c )d e + (- 81A B a c + 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (- 35A a c + 105A B a c )d e + (87A B a c - 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (15A a c - 41A B a c )d e + (- 11A B a c + 5B a c )d e +--R + +--R 2 5 8 +--R 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R 2a e + 10a c d e + 20a c d e + 20a c d e +--R + +--R 2 4 8 2 5 10 +--R 10a c d e + 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d 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B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R 2B a e + 6A a c d e + 4B a c d e + 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 +--R - 10B a c d e + 50A a c d e - 40B a c d e +--R + +--R 4 4 7 6 4 4 8 5 3 5 9 4 3 5 10 3 +--R 40A a c d e - 50B a c d e + 10A a c d e - 28B a c d e +--R + +--R 2 6 11 2 2 6 12 7 13 +--R - 4A a c d e - 6B a c d e - 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (A a c - A B a c)e + (- 13A B a c + 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (- 13A a c + 43A B a c )d e + (81A B a c - 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (35A a c - 105A B a c )d e + (- 87A B a c + 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (- 15A a c + 41A B a c )d e + (11A B a c - 5B a c )d e +--R + +--R 2 5 8 +--R - 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e +--R + +--R 2 4 8 2 5 10 +--R - 10a c d e - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 2 2 2 4 +---+ +--R (a e + 2a c d e + c d )\|- a +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e - 10a c d e +--R + +--R 5 10 +--R - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R - 2B a e - 6A a c d e - 4B a c d e - 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 4 4 7 6 +--R 10B a c d e - 50A a c d e + 40B a c d e - 40A a c d e +--R + +--R 4 4 8 5 3 5 9 4 3 5 10 3 2 6 11 2 +--R 50B a c d e - 10A a c d e + 28B a c d e + 4A a c d e +--R + +--R 2 6 12 7 13 +--R 6B a c d e + 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (- A a c + A B a c)e + (13A B a c - 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (13A a c - 43A B a c )d e + (- 81A B a c + 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (- 35A a c + 105A B a c )d e + (87A B a c - 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (15A a c - 41A B a c )d e + (- 11A B a c + 5B a c )d e +--R + +--R 2 5 8 +--R 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e +--R + +--R 2 4 8 2 5 10 +--R - 10a c d e - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 2 2 2 4 +---+ +--R (- a e - 2a c d e - c d )\|- a +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R 2a e + 10a c d e + 20a c d e + 20a c d e + 10a c d e +--R + +--R 5 10 +--R 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R - 2B a e - 6A a c d e - 4B a c d e - 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 4 4 7 6 +--R 10B a c d e - 50A a c d e + 40B a c d e - 40A a c d e +--R + +--R 4 4 8 5 3 5 9 4 3 5 10 3 2 6 11 2 +--R 50B a c d e - 10A a c d e + 28B a c d e + 4A a c d e +--R + +--R 2 6 12 7 13 +--R 6B a c d e + 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (A a c - A B a c)e + (- 13A B a c + 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (- 13A a c + 43A B a c )d e + (81A B a c - 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (35A a c - 105A B a c )d e + (- 87A B a c + 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (- 15A a c + 41A B a c )d e + (11A B a c - 5B a c )d e +--R + +--R 2 5 8 +--R - 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R 2a e + 10a c d e + 20a c d e + 20a c d e +--R + +--R 2 4 8 2 5 10 +--R 10a c d e + 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-+ +--R (2A a e - 4B a d e - 2A c d )\|c +--R + +--R 2 2 +---+ +--R (- 2B a e - 4A c d e + 2B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ | +-+ +---+ \|c \|e x + d +--R \|c \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 +-+ +--R (- 2A a e + 4B a d e + 2A c d )\|c +--R + +--R 2 2 +---+ +--R (- 2B a e - 4A c d e + 2B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ | +-+ +---+ \|c \|e x + d +--R \|c \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 4 2 2 2 4 +---+ | +-+ +---+ | +-+ +---+ +--R (2a e + 4a c d e + 2c d )\|- a \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +--d0:=normalize(D(m0,x)) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=-1/2*A*e*(d+e*x)^(3/2)/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^(5/2)/(a*c*_ + (a+c*x^2))-1/2*e*(A*c*d-5*a*B*e)*sqrt(d+e*x)/(a*c^2)-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + ((-5*a*B*e*(c*d^2-a*e^2)-2*A*c*d*(c*d^2+2*a*e^2))/sqrt(-a)+_ + e*(A*c*d^2+10*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a*c^(9/4)*sqrt(-e*_ + sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+_ + d*sqrt(c)))*((5*a*B*e*(c*d^2-a*e^2)+2*A*c*d*(c*d^2+2*a*e^2))/_ + sqrt(-a)+e*(A*c*d^2+10*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a*c^(9/4)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 2 2 +--R (- 3A a c e - 10B a c d e - A c d e)x - 3A a e - 10B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 5B a c e + 4A a c d e + 5B a c d e + 2A c d )x - 5B a e +--R + +--R 2 2 2 2 2 3 +--R 4A a c d e + 5B a c d e + 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 3A a c e - 10B a c d e - A c d e)x - 3A a e - 10B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (5B a c e - 4A a c d e - 5B a c d e - 2A c d )x + 5B a e +--R + +--R 2 2 2 2 2 3 +--R - 4A a c d e - 5B a c d e - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R 8B a c e x + (- 2A a c e - 4B a c d e + 2A c d )x + 10B a e +--R + +--R 2 +--R - 4A a c d e - 2B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 3 2 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c )\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=normalize(D(m0,x)) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=-1/2*(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*(a+c*x^2))-1/2*A*e*sqrt(d+e*x)/(a*c)-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(e*(A*c*d+_ + 3*a*B*e)+a*(2*A*c*d^2+3*a*B*d*e+a*A*e^2)*sqrt(c)/(-a)^(3/2))/(a*_ + c^(7/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(A*c*d+3*a*B*e)+(2*A*c*d^2+_ + 3*a*B*d*e+a*A*e^2)*sqrt(c)/sqrt(-a))/(a*c^(7/4)*sqrt(e*sqrt(-a)+_ + d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (A a c e + 3B a c d e + 2A c d )x + A a e + 3B a d e +--R + +--R 2 +--R 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- 3B a c e - A c d e)x - 3B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R (- A a c e - 3B a c d e - 2A c d )x - A a e - 3B a d e +--R + +--R 2 +--R - 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- 3B a c e - A c d e)x - 3B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---+4+-+3 +-------+ +--R ((- 2B a e + 2A c d)x - 2A a e - 2B a d)\|- a \|c \|e x + d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 2 +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=normalize(D(m0,x)) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=-1/2*(a*B-A*c*x)*sqrt(d+e*x)/(a*c*(a+c*x^2))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*((-2*A*c*d-a*B*e)/sqrt(-a)+_ + A*e*sqrt(c))/(a*c^(5/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*((2*A*c*d+a*B*e)/sqrt(-a)+_ + A*e*sqrt(c))/(a*c^(5/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 +---+ +-+ 2 2 2 +--R (- A c e x - A a e)\|- a \|c + (B a c e + 2A c d)x + B a e +--R + +--R 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 +---+ +-+ 2 2 2 +--R (- A c e x - A a e)\|- a \|c + (- B a c e - 2A c d)x - B a e +--R + +--R - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R (2A c x - 2B a)\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (a c x + a c) +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 4 5 3 +--R 128A a c e + 128B a c d e + 384A a c d e + 128B a c d e +--R + +--R 3 6 4 +--R 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (4A B a c - 4B a c)e + (4A a c - 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R - 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 2 +--R (- a c x - a c) +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 4 5 3 +--R 128A a c e + 128B a c d e + 384A a c d e + 128B a c d e +--R + +--R 3 6 4 +--R 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (- 4A B a c + 4B a c)e + (- 4A a c + 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 2 +--R (a c x + a c) +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 +--R - 128A a c e - 128B a c d e - 384A a c d e +--R + +--R 4 5 3 3 6 4 +--R - 128B a c d e - 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (4A B a c - 4B a c)e + (4A a c - 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R - 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 2 +--R (- a c x - a c) +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 +--R - 128A a c e - 128B a c d e - 384A a c d e +--R + +--R 4 5 3 3 6 4 +--R - 128B a c d e - 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (- 4A B a c + 4B a c)e + (- 4A a c + 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-------+ +--R (A c x - B a)\|e x + d +--R / +--R 2 2 2 +--R 2a c x + 2a c +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+4+-+ +--R 2a c\|- a \|c +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 4 5 3 +--R 128A a c e + 128B a c d e + 384A a c d e + 128B a c d e +--R + +--R 3 6 4 +--R 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (4A B a c - 4B a c)e + (4A a c - 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R - 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +---+4+-+ +--R 2a c\|- a \|c +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 +--R 128A a c e + 128B a c d e + 384A a c d e +--R + +--R 4 5 3 3 6 4 +--R 128B a c d e + 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (- 4A B a c + 4B a c)e + (- 4A a c + 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +---+4+-+ +--R 2a c\|- a \|c +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 +--R - 128A a c e - 128B a c d e - 384A a c d e +--R + +--R 4 5 3 3 6 4 +--R - 128B a c d e - 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (4A B a c - 4B a c)e + (4A a c - 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R - 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +---+4+-+ +--R 2a c\|- a \|c +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 +--R - 128A a c e - 128B a c d e - 384A a c d e +--R + +--R 4 5 3 3 6 4 +--R - 128B a c d e - 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (- 4A B a c + 4B a c)e + (- 4A a c + 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R (A e\|- a \|c - B a e - 2A c d)\|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ 4+-+ +-------+ +--R +---+ +-+ | +-+ +---+ \|c \|e x + d +--R (A e\|- a \|c + B a e + 2A c d)\|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 4a c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +--d0:=normalize(D(m0,x)) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(A+B*x)/((a+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R 2 4 2 2 +-------+ +--R (c x + 2a c x + a )\|e x + d +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=-1/2*(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ + (a+c*x^2))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (e*(A*c*d+a*B*e)-(2*A*c*d^2-a*B*d*e+3*a*A*e^2)*sqrt(c)/sqrt(-a))/_ + (a*c^(3/4)*(c*d^2+a*e^2)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*_ + (e*(A*c*d+a*B*e)+(2*A*c*d^2-a*B*d*e+3*a*A*e^2)*sqrt(c)/sqrt(-a))/_ + (a*c^(3/4)*(c*d^2+a*e^2)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (3A a c e - B a c d e + 2A c d )x + 3A a e - B a d e +--R + +--R 2 +--R 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- B a c e - A c d e)x - B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R (- 3A a c e + B a c d e - 2A c d )x - 3A a e + B a d e +--R + +--R 2 +--R - 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- B a c e - A c d e)x - B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---+4+-+3 +-------+ +--R ((2B a e + 2A c d)x + 2A a e - 2B a d)\|- a \|c \|e x + d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 2 2 2 2 3 2 2 2 +---+4+-+3 | +-+ +---+ +--R ((4a c e + 4a c d )x + 4a e + 4a c d )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=normalize(D(m0,x)) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 3 2 2 2 +-------+ +--R (c e x + c d x + 2a c e x + 2a c d x + a e x + a d)\|e x + d +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=1/2*e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)/(a*(c*d^2+a*e^2)^2*sqrt(d+e*x))+_ + 1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2)*_ + sqrt(d+e*x))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((3*a*B*e*(c*d^2-a*e^2)-2*A*c*d*(c*d^2+4*a*e^2))/_ + sqrt(-a)+e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)*sqrt(c))/(a*c^(1/4)*_ + (c*d^2+a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*((-3*a*B*e*(c*d^2-a*e^2)+_ + 2*A*c*d*(c*d^2+4*a*e^2))/sqrt(-a)+e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)*_ + sqrt(c))/(a*c^(1/4)*(c*d^2+a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 2 2 +--R (5A a c e - 6B a c d e - A c d e)x + 5A a e - 6B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (3B a c e + 8A a c d e - 3B a c d e + 2A c d )x + 3B a e +--R + +--R 2 2 2 2 2 3 +--R 8A a c d e - 3B a c d e + 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R +-------+ | +-+ +---+ \|c \|e x + d +--R \|e x + d \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (5A a c e - 6B a c d e - A c d e)x + 5A a e - 6B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 3B a c e - 8A a c d e + 3B a c d e - 2A c d )x - 3B a e +--R + +--R 2 2 2 2 2 3 +--R - 8A a c d e + 3B a c d e - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R +-------+ | +-+ +---+ \|c \|e x + d +--R \|e x + d \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 3 2 2 2 2 +--R (- 10A a c e + 12B a c d e + 2A c d e)x +--R + +--R 2 3 2 2 2 3 2 3 +--R (2B a e + 2A a c d e + 2B a c d e + 2A c d )x - 8A a e +--R + +--R 2 2 2 3 +--R 10B a d e + 4A a c d e - 2B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +---+ +--R ((4a c e + 8a c d e + 4a c d )x + 4a e + 8a c d e + 4a c d )\|- a +--R * +--R +---------------+ +---------------+ +--R 4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=-1/16*e*(6*A*c*d+7*a*B*e)*(d+e*x)^(3/2)/(a^2*c^2)-1/4*(a*B-A*c*x)*_ + (d+e*x)^(7/2)/(a*c*(a+c*x^2)^2)+1/16*(d+e*x)^(5/2)*(a*A*e+(6*A*c*d+_ + 7*a*B*e)*x)/(a^2*c*(a+c*x^2))-1/16*e*(6*A*c*d^2+7*a*B*d*e+5*a*A*e^2)*_ + sqrt(d+e*x)/(a^2*c^2)-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*(e*(7*a*B*e*(c*d^2+3*a*e^2)+2*A*c*d*(3*c*d^2+4*a*e^2))+_ + a*(14*a*B*d*e*(c*d^2+2*a*e^2)+A*(12*c^2*d^4+19*a*c*d^2*e^2+5*a^2*e^4))*_ + sqrt(c)/(-a)^(3/2))/(a^2*c^(11/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + 1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(7*a*B*_ + e*(c*d^2+3*a*e^2)+2*A*c*d*(3*c*d^2+4*a*e^2))+(14*a*B*d*e*(c*d^2+_ + 2*a*e^2)+A*(12*c^2*d^4+19*a*c*d^2*e^2+5*a^2*e^4))*sqrt(c)/sqrt(-a))/_ + (a^2*c^(11/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 +--R 5A a c e + 28B a c d e + 19A a c d e + 14B a c d e +--R + +--R 4 4 +--R 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R 10A a c e + 56B a c d e + 38A a c d e + 28B a c d e +--R + +--R 3 4 +--R 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R 5A a e + 28B a d e + 19A a c d e + 14B a c d e + 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 21B a c e - 8A a c d e - 7B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 42B a c e - 16A a c d e - 14B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 21B a e - 8A a c d e - 7B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 +--R - 5A a c e - 28B a c d e - 19A a c d e - 14B a c d e +--R + +--R 4 4 +--R - 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 10A a c e - 56B a c d e - 38A a c d e - 28B a c d e +--R + +--R 3 4 +--R - 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R - 5A a e - 28B a d e - 19A a c d e - 14B a c d e - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 21B a c e - 8A a c d e - 7B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 42B a c e - 16A a c d e - 14B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 21B a e - 8A a c d e - 7B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 22B a c e + 16A a c d e + 14B a c d e + 12A c d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 18A a c e - 52B a c d e + 2A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (- 14B a e - 8A a c d e - 10B a c d e + 20A a c d )x - 10A a e +--R + +--R 3 2 2 2 2 3 +--R - 28B a d e - 22A a c d e - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 4 4 3 3 2 4 2 +---+4+-+3 | +-+ +---+ +--R (32a c x + 64a c x + 32a c )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^(5/2)/(a*c*(a+c*x^2)^2)-1/16*(d+e*x)^(3/2)*_ + (a*A*e-(6*A*c*d+5*a*B*e)*x)/(a^2*c*(a+c*x^2))-1/16*e*(6*A*c*d+5*a*B*e)*_ + sqrt(d+e*x)/(a^2*c^2)-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((-5*a*B*e*(2*c*d^2+a*e^2)-3*A*c*d*(4*c*d^2+3*a*e^2))/_ + sqrt(-a)+e*(6*A*c*d^2+5*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a^2*c^(9/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*((5*a*B*e*(2*c*d^2+a*e^2)+3*A*c*d*(4*c*d^2+_ + 3*a*e^2))/sqrt(-a)+e*(6*A*c*d^2+5*a*B*d*e+3*a*A*e^2)*sqrt(c))/_ + (a^2*c^(9/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 3A a c e - 5B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 6A a c e - 10B a c d e - 12A a c d e)x - 3A a e +--R + +--R 3 2 2 2 +--R - 5B a d e - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (5B a c e + 9A a c d e + 10B a c d e + 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (10B a c e + 18A a c d e + 20B a c d e + 24A a c d )x + 5B a e +--R + +--R 3 2 3 2 2 2 3 +--R 9A a c d e + 10B a c d e + 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 3 2 2 3 2 4 +--R (- 3A a c e - 5B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 6A a c e - 10B a c d e - 12A a c d e)x - 3A a e +--R + +--R 3 2 2 2 +--R - 5B a d e - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (- 5B a c e - 9A a c d e - 10B a c d e - 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (- 10B a c e - 18A a c d e - 20B a c d e - 24A a c d )x - 5B a e +--R + +--R 3 2 3 2 2 2 3 +--R - 9A a c d e - 10B a c d e - 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 3 2 3 +--R (6A a c e + 10B a c d e + 12A c d )x +--R + +--R 2 2 2 2 +--R (- 18B a c e + 2A a c d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 2A a c e - 6B a c d e + 20A a c d )x - 10B a e - 14A a c d e +--R + +--R 2 2 +--R - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 4 4 3 3 2 4 2 +---+4+-+ | +-+ +---+ +--R (32a c x + 64a c x + 32a c )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 3 3 2 4 2 +--R (8a c x + 16a c x + 8a c ) +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (196608A a c e + 655360B a c d e + 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (1440A B a c - 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (1728A a c - 9600A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d 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e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (- 196608A a c e - 655360B a c d e - 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (- 1440A B a c + 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (- 1728A a c + 9600A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (3A a c e + 5B a c d e + 6A c d )x + (- 9B a c e + A a c d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- A a c e - 3B a c d e + 10A a c d )x - 5B a e - 7A a c d e +--R + +--R 2 2 +--R - 4B a c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 4 4 3 3 2 4 2 +--R 16a c x + 32a c x + 16a c +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 +---+4+-+ +--R 16a c \|- a \|c +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (196608A a c e + 655360B a c d e + 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (1440A B a c - 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (1728A a c - 9600A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 2 2 +---+4+-+ +--R 16a c \|- a \|c +--R * +--R ROOT +--R - +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (196608A a c e + 655360B a c d e + 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (- 1440A B a c + 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (- 1728A a c + 9600A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R - +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 +--R (540A B c - 1500A B a c)d e +--R + +--R 2 2 2 2 8 +--R - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 +--R - 30A B a e + (- 45A a c - 75B a )d e +--R + +--R 2 2 3 2 2 2 2 3 2 +--R - 240A B a c d e + (- 180A a c - 100B a c)d e +--R + +--R 2 4 2 3 5 +--R - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +---+4+-+ +--R 16a c \|- a \|c +--R * +--R ROOT +--R - +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (- 196608A a c e - 655360B a c d e - 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (1440A B a c - 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (1728A a c - 9600A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R - +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 2 2 +---+4+-+ +--R 16a c \|- a \|c +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (- 196608A a c e - 655360B a c d e - 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (- 1440A B a c + 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (- 1728A a c + 9600A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 +--R - 30A B a e + (- 45A a c - 75B a )d e +--R + +--R 2 2 3 2 2 2 2 3 2 +--R - 240A B a c d e + (- 180A a c - 100B a c)d e +--R + +--R 2 4 2 3 5 +--R - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 +---+ +-+ 2 3 2 +--R (3A a e + 5B a d e + 6A c d e)\|- a \|c - 5B a e - 9A a c d e +--R + +--R 2 2 3 +--R - 10B a c d e - 12A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 +---+ +-+ 2 3 2 +--R (3A a e + 5B a d e + 6A c d e)\|- a \|c + 5B a e + 9A a c d e +--R + +--R 2 2 3 +--R 10B a c d e + 12A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 32a c \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*(a+c*x^2)^2)-3/16*(a*A*e-_ + (2*A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a^2*c*(a+c*x^2))-3/32*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(e*(2*A*c*d+a*B*e)+a*_ + (4*A*c*d^2+2*a*B*d*e+a*A*e^2)*sqrt(c)/(-a)^(3/2))/(a^2*c^(7/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-3/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(2*A*c*d+a*B*e)+(4*A*c*d^2+_ + 2*a*B*d*e+a*A*e^2)*sqrt(c)/sqrt(-a))/(a^2*c^(7/4)*sqrt(e*sqrt(-a)+_ + d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 3 2 4 +--R (3A a c e + 6B a c d e + 12A c d )x +--R + +--R 2 2 2 2 2 2 3 2 3 +--R (6A a c e + 12B a c d e + 24A a c d )x + 3A a e + 6B a d e +--R + +--R 2 2 +--R 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 3 4 2 2 2 2 +--R (- 3B a c e - 6A c d e)x + (- 6B a c e - 12A a c d e)x +--R + +--R 3 2 2 +--R - 3B a e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 3 2 4 +--R (- 3A a c e - 6B a c d e - 12A c d )x +--R + +--R 2 2 2 2 2 2 3 2 3 +--R (- 6A a c e - 12B a c d e - 24A a c d )x - 3A a e - 6B a d e +--R + +--R 2 2 +--R - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 3 4 2 2 2 2 +--R (- 3B a c e - 6A c d e)x + (- 6B a c e - 12A a c d e)x +--R + +--R 3 2 2 +--R - 3B a e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 +--R (6B a c e + 12A c d)x + 2A a c e x + (- 2B a e + 20A a c d)x +--R + +--R 2 2 +--R - 6A a e - 8B a d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 3 4 3 2 2 4 +---+4+-+3 | +-+ +---+ +--R (32a c x + 64a c x + 32a c)\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 4 3 2 2 4 +--R (- 8a c x - 16a c x - 8a c) +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R 65536B a c e + 196608A a c d e + 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R 458752A a c d e + 131072B a c d e + 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (- 288A a c + 288A B a c )e + (288A B a c + 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (- 576A a c + 1152A B a c )d e + 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 4 3 2 2 4 +--R (8a c x + 16a c x + 8a c) +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R 65536B a c e + 196608A a c d e + 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R 458752A a c d e + 131072B a c d e + 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (288A a c - 288A B a c )e + (- 288A B a c - 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (576A a c - 1152A B a c )d e - 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 4 3 2 2 4 +--R (- 8a c x - 16a c x - 8a c) +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R - 65536B a c e - 196608A a c d e - 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R - 458752A a c d e - 131072B a c d e - 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (- 288A a c + 288A B a c )e + (288A B a c + 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (- 576A a c + 1152A B a c )d e + 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 4 3 2 2 4 +--R (8a c x + 16a c x + 8a c) +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R - 65536B a c e - 196608A a c d e - 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R - 458752A a c d e - 131072B a c d e - 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (288A a c - 288A B a c )e + (- 288A B a c - 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (576A a c - 1152A B a c )d e - 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 +--R (3B a c e + 6A c d)x + A a c e x + (- B a e + 10A a c d)x - 3A a e +--R + +--R 2 +--R - 4B a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 3 4 3 2 2 4 +--R 16a c x + 32a c x + 16a c +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 2 +---+4+-+3 +--R 16a c\|- a \|c +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R 65536B a c e + 196608A a c d e + 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R 458752A a c d e + 131072B a c d e + 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 +--R (- 288A a c + 288A B a c )e +--R + +--R 2 4 3 3 5 2 7 +--R (288A B a c + 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (- 576A a c + 1152A B a c )d e + 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 +--R - 18A B a e + (- 45A a c - 27B a )d e +--R + +--R 2 2 3 2 2 2 2 3 2 +--R - 144A B a c d e + (- 180A a c - 36B a c)d e +--R + +--R 2 4 2 3 5 +--R - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 +---+4+-+3 +--R 16a c\|- a \|c +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R 65536B a c e + 196608A a c d e + 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R 458752A a c d e + 131072B a c d e + 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (288A a c - 288A B a c )e + (- 288A B a c - 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (576A a c - 1152A B a c )d e - 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 2 +---+4+-+3 +--R 16a c\|- a \|c +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R - 65536B a c e - 196608A a c d e - 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R - 458752A a c d e - 131072B a c d e - 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 +--R (- 288A a c + 288A B a c )e +--R + +--R 2 4 3 3 5 2 7 +--R (288A B a c + 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (- 576A a c + 1152A B a c )d e + 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 +--R - 18A B a e + (- 45A a c - 27B a )d e +--R + +--R 2 2 3 2 2 2 2 3 2 +--R - 144A B a c d e + (- 180A a c - 36B a c)d e +--R + +--R 2 4 2 3 5 +--R - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 +---+4+-+3 +--R 16a c\|- a \|c +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R - 65536B a c e - 196608A a c d e - 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R - 458752A a c d e - 131072B a c d e - 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (288A a c - 288A B a c )e + (- 288A B a c - 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (576A a c - 1152A B a c )d e - 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-+ 2 +---+ +--R ((- 3A a e - 6B a d e - 12A c d )\|c + (3B a e + 6A c d e)\|- a ) +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 +-+ 2 +---+ +--R ((3A a e + 6B a d e + 12A c d )\|c + (3B a e + 6A c d e)\|- a ) +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R 32a c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=-1/4*(a*B-A*c*x)*sqrt(d+e*x)/(a*c*(a+c*x^2)^2)+1/16*(a*e*(A*c*d+a*B*e)+_ + c*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*x)*sqrt(d+e*x)/(a^2*c*(c*d^2+a*e^2)*_ + (a+c*x^2))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + ((-a*B*e*(2*c*d^2+3*a*e^2)-A*c*d*(12*c*d^2+13*a*e^2))/sqrt(-a)+_ + e*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*sqrt(c))/(a^2*c^(5/4)*(c*d^2+a*e^2)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*((a*B*e*(2*c*d^2+3*a*e^2)+A*c*d*(12*c*d^2+_ + 13*a*e^2))/sqrt(-a)+e*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*sqrt(c))/_ + (a^2*c^(5/4)*(c*d^2+a*e^2)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 5A a c e - B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 +--R (- 10A a c e - 2B a c d e - 12A a c d e)x - 5A a e - B a d e +--R + +--R 2 2 +--R - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 13A a c d e + 2B a c d e + 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 26A a c d e + 4B a c d e + 24A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 13A a c d e + 2B a c d e + 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 3 2 2 3 2 4 +--R (- 5A a c e - B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 +--R (- 10A a c e - 2B a c d e - 12A a c d e)x - 5A a e - B a d e +--R + +--R 2 2 +--R - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (- 3B a c e - 13A a c d e - 2B a c d e - 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (- 6B a c e - 26A a c d e - 4B a c d e - 24A a c d )x - 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R - 13A a c d e - 2B a c d e - 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (10A a c e + 2B a c d e + 12A c d )x + (2B a c e + 2A a c d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R (18A a c e + 2B a c d e + 20A a c d )x - 6B a e + 2A a c d e +--R + +--R 2 2 +--R - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 4 2 2 +--R ((32a c e + 32a c d )x + (64a c e + 64a c d )x + 32a c e + 32a c d ) +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 4 2 2 +--R ((8a c e + 8a c d )x + (16a c e + 16a c d )x + 8a c e + 8a c d ) +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (2048a c e + 6144a c d e + 6144a c d e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R 327680A a c e + 262144B a c d e + 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R 917504B a c d e + 5505024A a c d e + 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R 6422528A a c d e + 655360B a c d e + 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R 131072B a c d e + 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 5 11 12 +--R 62914560a c d e + 25165824a c d e + 4194304a c d +--R + +--R 2 6 2 3 7 11 +--R (2400A B a c - 864B a c)e +--R + +--R 3 5 3 2 6 2 10 +--R (6400A a c - 5952A B a c )d e +--R + +--R 2 5 3 3 6 2 2 9 +--R (- 6912A B a c - 768B a c )d e +--R + +--R 3 4 4 2 5 3 3 8 +--R (10176A a c - 7104A B a c )d e +--R + +--R 2 4 4 3 5 3 4 7 +--R (- 14304A B a c - 160B a c )d e +--R + +--R 3 3 5 2 4 4 5 6 2 3 5 6 5 +--R (4032A a c - 1920A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (2048a c e + 6144a c d e + 6144a c d e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 +--R (- 8a c e - 8a c d )x + (- 16a c e - 16a c d )x - 8a c e +--R + +--R 4 2 2 +--R - 8a c d +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (- 2048a c e - 6144a c d e - 6144a c d e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R 327680A a c e + 262144B a c d e + 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R 917504B a c d e + 5505024A a c d e + 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R 6422528A a c d e + 655360B a c d e + 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R 131072B a c d e + 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 5 11 12 +--R 62914560a c d e + 25165824a c d e + 4194304a c d +--R + +--R 2 6 2 3 7 11 +--R (- 2400A B a c + 864B a c)e +--R + +--R 3 5 3 2 6 2 10 +--R (- 6400A a c + 5952A B a c )d e +--R + +--R 2 5 3 3 6 2 2 9 +--R (6912A B a c + 768B a c )d e +--R + +--R 3 4 4 2 5 3 3 8 +--R (- 10176A a c + 7104A B a c )d e +--R + +--R 2 4 4 3 5 3 4 7 +--R (14304A B a c + 160B a c )d e +--R + +--R 3 3 5 2 4 4 5 6 2 3 5 6 5 +--R (- 4032A a c + 1920A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 +--R - 2048a c e - 6144a c d e - 6144a c d e +--R + +--R 5 5 6 +--R - 2048a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 4 2 2 +--R ((8a c e + 8a c d )x + (16a c e + 16a c d )x + 8a c e + 8a c d ) +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (- 2048a c e - 6144a c d e - 6144a c d e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R - 327680A a c e - 262144B a c d e - 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R - 917504B a c d e - 5505024A a c d e - 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R - 6422528A a c d e - 655360B a c d e - 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R - 131072B a c d e - 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 5 11 12 +--R 62914560a c d e + 25165824a c d e + 4194304a c d +--R + +--R 2 6 2 3 7 11 +--R (2400A B a c - 864B a c)e +--R + +--R 3 5 3 2 6 2 10 +--R (6400A a c - 5952A B a c )d e +--R + +--R 2 5 3 3 6 2 2 9 +--R (- 6912A B a c - 768B a c )d e +--R + +--R 3 4 4 2 5 3 3 8 +--R (10176A a c - 7104A B a c )d e +--R + +--R 2 4 4 3 5 3 4 7 +--R (- 14304A B a c - 160B a c )d e +--R + +--R 3 3 5 2 4 4 5 6 2 3 5 6 5 +--R (4032A a c - 1920A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 +--R - 2048a c e - 6144a c d e - 6144a c d e +--R + +--R 5 5 6 +--R - 2048a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + 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4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 2 2 +---+4+-+ +--R (16a c e + 16a c d )\|- a \|c +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (- 2048a c e - 6144a c d e - 6144a c d e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R - 327680A a c e - 262144B a c d e - 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R - 917504B a c d e - 5505024A a c d e - 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R - 6422528A a c d e - 655360B a c d e - 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R - 131072B a c d e - 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 5 11 12 +--R 62914560a c d e + 25165824a c d e + 4194304a c d +--R + +--R 2 6 2 3 7 11 +--R (2400A B a c - 864B a c)e +--R + +--R 3 5 3 2 6 2 10 +--R (6400A a c - 5952A B a c )d e +--R + +--R 2 5 3 3 6 2 2 9 +--R (- 6912A B a c - 768B a c )d e +--R + +--R 3 4 4 2 5 3 3 8 +--R (10176A a c - 7104A B a c )d e +--R + +--R 2 4 4 3 5 3 4 7 +--R (- 14304A B a c - 160B a c )d e +--R + +--R 3 3 5 2 4 4 5 6 2 3 5 6 5 +--R (4032A a c - 1920A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 +--R - 2048a c e - 6144a c d e - 6144a c d e +--R + +--R 5 5 6 +--R - 2048a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 2 2 +---+4+-+ +--R (- 16a c e - 16a c d )\|- a \|c +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (2048a c e + 6144a c d e + 6144a c d e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R - 327680A a c e - 262144B a c d e - 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R - 917504B a c d e - 5505024A a c d e - 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R - 6422528A a c d e - 655360B a c d e - 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R - 131072B a c d e - 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 5 11 12 +--R 62914560a c d e + 25165824a c d e + 4194304a c d +--R + +--R 2 6 2 3 7 11 +--R (- 2400A B a c + 864B a c)e +--R + +--R 3 5 3 2 6 2 10 +--R (- 6400A a c + 5952A B a c )d e +--R + +--R 2 5 3 3 6 2 2 9 +--R (6912A B a c + 768B a c )d e +--R + +--R 3 4 4 2 5 3 3 8 +--R (- 10176A a c + 7104A B a c )d e +--R + +--R 2 4 4 3 5 3 4 7 +--R (14304A B a c + 160B a c )d e +--R + +--R 3 3 5 2 4 4 5 6 2 3 5 6 5 +--R (- 4032A a c + 1920A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (2048a c e + 6144a c d e + 6144a c d e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 +---+ +-+ 2 3 2 +--R (5A a e + B a d e + 6A c d e)\|- a \|c - 3B a e - 13A a c d e +--R + +--R 2 2 3 +--R - 2B a c d e - 12A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 +---+ +-+ 2 3 2 +--R (5A a e + B a d e + 6A c d e)\|- a \|c + 3B a e + 13A a c d e +--R + +--R 2 2 3 +--R 2B a c d e + 12A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 3 2 2 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (32a c e + 32a c d )\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich12c.input.pamphlet b/src/axiom-website/CATS/rich12c.input.pamphlet new file mode 100644 index 0000000..6f9fc9f --- /dev/null +++ b/src/axiom-website/CATS/rich12c.input.pamphlet @@ -0,0 +1,75902 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12c.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 155 integrals in this file. +\item 155 supplied "optimal results". +\item 211 matching answers. +\item 4 cases where Axiom answer differs from Rubi +\item 35 cases where Axiom supplied 2 results. +\item 26 cases that Axiom failed to integrate. +\item 15 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12c.output +)spool rich12c.output +)set message test on +)set message auto off +)clear all + +--S 1 of 845 +t0:=(A+B*x)/((a+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R 3 6 2 4 2 2 3 +-------+ +--R (c x + 3a c x + 3a c x + a )\|e x + d +--R Type: Expression(Integer) +--E 1 + +--S 2 of 845 +r0:=-1/4*(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ + (a+c*x^2)^2)+1/16*(a*e*(A*c*d^2-6*a*B*d*e+7*a*A*e^2)-(a*B*e*(c*d^2-_ + 5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))*x)*sqrt(d+e*x)/(a^2*(c*d^2+a*e^2)^2*_ + (a+c*x^2))+1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (e*(a*B*e*(c*d^2-5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))-(2*a*B*d*e*(c*d^2+_ + 4*a*e^2)-3*A*(4*c^2*d^4+9*a*c*d^2*e^2+7*a^2*e^4))*sqrt(c)/sqrt(-a))/_ + (a^2*c^(3/4)*(c*d^2+a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))+_ + 1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(a*B*e*_ + (c*d^2-5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))+(2*a*B*d*e*(c*d^2+4*a*e^2)-_ + 3*A*(4*c^2*d^4+9*a*c*d^2*e^2+7*a^2*e^4))*sqrt(c)/sqrt(-a))/(a^2*c^(3/4)*_ + (c*d^2+a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 +--R 21A a c e - 8B a c d e + 27A a c d e - 2B a c d e +--R + +--R 4 4 +--R 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R 42A a c e - 16B a c d e + 54A a c d e - 4B a c d e +--R + +--R 3 4 +--R 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R 21A a e - 8B a d e + 27A a c d e - 2B a c d e + 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 5B a c e - 12A a c d e + B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 10B a c e - 24A a c d e + 2B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 5B a e - 12A a c d e + B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 +--R - 21A a c e + 8B a c d e - 27A a c d e + 2B a c d e +--R + +--R 4 4 +--R - 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 42A a c e + 16B a c d e - 54A a c d e + 4B a c d e +--R + +--R 3 4 +--R - 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R - 21A a e + 8B a d e - 27A a c d e + 2B a c d e - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 5B a c e - 12A a c d e + B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 10B a c e - 24A a c d e + 2B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 5B a e - 12A a c d e + B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (10B a c e + 24A a c d e - 2B a c d e + 12A c d )x +--R + +--R 2 3 2 2 2 2 2 +--R (14A a c e - 12B a c d e + 2A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (18B a e + 32A a c d e + 6B a c d e + 20A a c d )x + 22A a e +--R + +--R 3 2 2 2 2 3 +--R - 20B a d e + 10A a c d e - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 4 2 4 3 3 2 2 2 4 4 4 +--R (32a c e + 64a c d e + 32a c d )x +--R + +--R 5 4 4 2 2 2 3 3 4 2 6 4 5 2 2 4 2 4 +--R (64a c e + 128a c d e + 64a c d )x + 32a e + 64a c d e + 32a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 4 3 3 2 2 2 4 4 4 +--R (- 8a c e - 16a c d e - 8a c d )x +--R + +--R 5 4 4 2 2 2 3 3 4 2 6 4 5 2 2 4 2 4 +--R (- 16a c e - 32a c d e - 16a c d )x - 8a e - 16a c d e - 8a c d +--R * +--R ROOT +--R 10 10 9 2 2 8 8 3 4 6 7 4 6 4 +--R 2048a c e + 10240a c d e + 20480a c d e + 20480a c d e +--R + +--R 6 5 8 2 5 6 10 +--R 10240a c d e + 2048a c d +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 18 +--R (- 194481A a c + 22050A B a c - 625B a )e +--R + +--R 3 4 2 3 5 17 +--R (587412A B a c - 33300A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 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+--R 4194304a c e + 41943040a c d e +--R + +--R 13 5 4 16 12 6 6 14 +--R 188743680a c d e + 503316480a c d e +--R + +--R 11 7 8 12 10 8 10 10 +--R 880803840a c d e + 1056964608a c d e +--R + +--R 9 9 12 8 8 10 14 6 +--R 880803840a c d e + 503316480a c d e +--R + +--R 7 11 16 4 6 12 18 2 +--R 188743680a c d e + 41943040a c d e +--R + +--R 5 13 20 +--R 4194304a c d +--R + +--R 5 9 2 4 2 5 8 +--R - 210A B a e + (- 945A a c + 105B a )d e +--R + +--R 4 2 7 2 3 2 2 4 3 6 +--R 420A B a c d e + (- 1890A a c - 70B a c)d e +--R + +--R 3 2 4 5 2 2 3 2 3 2 5 4 +--R 630A B a c d e + (- 1701A a c - 35B a c )d e +--R + +--R 2 3 6 3 2 4 2 2 3 7 2 +--R 336A B a c d e + (- 756A a c - 4B a c )d e +--R + +--R 4 8 2 5 9 +--R 48A B a c d e - 144A c d +--R / +--R 10 10 9 2 2 8 8 3 4 6 +--R 1024a c e + 5120a c d e + 10240a c d e +--R + +--R 7 4 6 4 6 5 8 2 5 6 10 +--R 10240a c d e + 5120a c d e + 1024a c d +--R + +--R 4 4 2 4 6 13 +--R (194481A a c - 625B a )e +--R + +--R 3 4 2 3 5 12 +--R (- 388962A B a c - 11250A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 11 +--R (388962A a c + 215784A B a c + 3750B a c)d e +--R + +--R 3 3 3 3 4 2 3 10 +--R (- 649188A B a c - 49428A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 9 +--R (339309A a c + 238464A B a c + 1491B a c )d e +--R + +--R 3 2 4 3 3 3 5 8 +--R (- 485514A B a c - 22554A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 7 +--R (144828A a c + 110376A B a c + 140B a c )d e +--R + +--R 3 5 3 2 4 7 6 +--R (- 176904A B a c - 2520A B a c )d e +--R + +--R 4 6 2 2 5 8 5 3 6 9 4 +--R (27216A c + 15120A B a c )d e - 30240A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 2 3 2 2 3 2 4 +-+ +--R (- 21A a e + 8B a d e - 27A a c d e + 2B a c d e - 12A c d )\|c +--R + +--R 2 4 3 2 2 2 3 +---+ +--R (5B a e + 12A a c d e - B a c d e + 6A c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 4 2 3 2 2 3 2 4 +-+ +--R (21A a e - 8B a d e + 27A a c d e - 2B a c d e + 12A c d )\|c +--R + +--R 2 4 3 2 2 2 3 +---+ +--R (5B a e + 12A a c d e - B a c d e + 6A c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +--R 4 4 3 2 2 2 2 4 +---+4+-+3 | +-+ +---+ +--R (32a e + 64a c d e + 32a c d )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 4 + +--S 5 of 845 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 845 +t0:=x*sqrt(1+x)/(1+x^2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (1) --------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 845 +r0:=-atanh(sqrt(1+x)/sqrt(1-%i))*sqrt(1-%i)-atanh(sqrt(1+x)/sqrt(1+%i))*_ + sqrt(1+%i)+2*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R +------+ \|x + 1 +------+ \|x + 1 +-----+ +--R (2) - \|1 - %i atanh(---------) - \|1 + %i atanh(---------) + 2\|x + 1 +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 7 + +--S 8 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(- 2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +--R 2\|2 sin(---)atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 - \|2 cos(---) +--R 8 +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +-----+ +--R 2\|2 sin(---)atan(-----------------------) + 4\|x + 1 +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 + \|2 cos(---) +--R 8 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(- 2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R +-----+ +-----+ +--R +------+ \|x + 1 +------+ \|x + 1 +--R 2\|1 - %i atanh(---------) + 2\|1 + %i atanh(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +--R 2\|2 sin(---)atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 - \|2 cos(---) +--R 8 +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +--R 2\|2 sin(---)atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 + \|2 cos(---) +--R 8 +--R / +--R 2 +--R Type: Expression(Complex(Integer)) +--E 9 + +--S 10 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 %pi 4 3 2 4+-+2 %pi 2 4 3 +--R (- 8x - 8x)cos(---) + (8x + 16x + 8x)\|2 cos(---) - 4x - 12x +--R 8 8 +--R + +--R 2 +--R - 12x - 4x +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 3 2 4+-+2 %pi 4 +--R (- 32x - 32x)cos(---) + (20x + 36x + 20x + 4)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (8x + 32x + 32x - 8)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (- 6x - 26x - 40x - 24x - 2x + 2)\|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 3 2 4+-+2 %pi 6 +--R (- 48x - 48x)cos(---) + (36x + 68x + 36x + 4)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 4 +--R (- 12x - 40x - 40x - 8x + 4)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 6 5 +--R (6x + 34x + 56x + 24x - 14x - 10)\|2 cos(---) - 6x - 36x +--R 8 +--R + +--R 4 3 2 +--R - 78x - 72x - 18x + 12x + 6 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 3 2 4+-+2 %pi 8 +--R (- 32x - 32x)cos(---) + (44x + 92x + 44x - 4)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 6 +--R (- 32x - 96x - 96x - 32x)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (- 4x - 28x - 48x - 16x + 20x + 12)\|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (8x + 56x + 128x + 112x + 8x - 40x - 16)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (- x - 9x - 27x - 35x - 15x + 9x + 11x + 3)\|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (- 8x - 8x)cos(---) + (20x + 44x + 20x - 4)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (- 40x - 140x - 140x - 20x + 20)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (20x + 100x + 160x + 80x - 20x - 20)\|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (- 10x - 70x - 160x - 140x - 10x + 50x + 20)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 7 +--R (x + 11x + 35x + 45x + 15x - 19x - 19x - 5)\|2 cos(---) - x +--R 8 +--R + +--R 6 5 4 3 2 +--R - 5x - 9x - 5x + 5x + 9x + 5x + 1 +--R / +--R 2 %pi 4 3 2 4+-+2 %pi 2 4 +--R (8x + 8)cos(---) + (- 8x - 8x - 8x - 8)\|2 cos(---) + 4x +--R 8 8 +--R + +--R 3 2 +--R 8x + 8x + 8x + 4 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 3 2 4+-+2 %pi 4 +--R (32x + 32)cos(---) + (- 16x - 16x - 16x - 16)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (- 16x - 32x - 32x - 32x - 16)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (8x + 24x + 32x + 32x + 24x + 8)\|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 3 2 4+-+2 %pi 6 +--R (48x + 48)cos(---) + (- 32x - 32x - 32x - 32)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 4 +--R (16x + 32x + 32x + 32x + 16)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 6 +--R (- 16x - 48x - 64x - 64x - 48x - 16)\|2 cos(---) + 12x +--R 8 +--R + +--R 5 4 3 2 +--R 48x + 84x + 96x + 84x + 48x + 12 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 3 2 4+-+2 %pi 8 +--R (32x + 32)cos(---) + (- 48x - 48x - 48x - 48)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 6 +--R (32x + 64x + 64x + 64x + 32)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (16x + 48x + 64x + 64x + 48x + 16)\|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (- 24x - 96x - 168x - 192x - 168x - 96x - 24)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (4x + 20x + 44x + 60x + 60x + 44x + 20x + 4)\|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (8x + 8)cos(---) + (- 24x - 24x - 24x - 24)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (60x + 120x + 120x + 120x + 60)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (- 40x - 120x - 160x - 160x - 120x - 40)\|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (30x + 120x + 210x + 240x + 210x + 120x + 30)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 8 +--R (- 6x - 30x - 66x - 90x - 90x - 66x - 30x - 6)\|2 cos(---) + x +--R 8 +--R + +--R 7 6 5 4 3 2 +--R 6x + 16x + 26x + 30x + 26x + 16x + 6x + 1 +--R * +--R +-----+ +--R \|x + 1 +--R Type: Expression(Complex(Integer)) +--E 10 + +)clear all + +--S 11 of 845 +t0:=(1-x)*sqrt(1+x)/(1+x^2) +--R +--R +--R +-----+ +--R (- x + 1)\|x + 1 +--R (1) ----------------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 845 +r0:=(1-%i)^(3/2)*atanh(sqrt(1+x)/sqrt(1-%i))+(1+%i)^(3/2)*_ + atanh(sqrt(1+x)/sqrt(1+%i))-2*sqrt(1+x) +--R +--R +--R (2) +--R +-----+ +-----+ +--R +------+ \|x + 1 +------+ \|x + 1 +--R (1 - %i)\|1 - %i atanh(---------) + (1 + %i)\|1 + %i atanh(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R + +--R +-----+ +--R - 2\|x + 1 +--R Type: Expression(Complex(Integer)) +--E 12 + +--S 13 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 4+-+ %pi +--R \|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (2\|8 sin(---) - 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi +--R \|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (- 2\|8 sin(---) + 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 2\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 - \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +-----+ +--R - 2\|8 sin(---)atan(---------------------------------------) - 4\|x + 1 +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 + \|8 sin(---) - \|8 cos(---) +--R 8 8 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 4+-+ %pi +--R \|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (2\|8 sin(---) - 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi +--R \|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (- 2\|8 sin(---) + 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R +-----+ +--R +------+ \|x + 1 +--R (- 2 + 2%i)\|1 - %i atanh(---------) +--R +------+ +--R \|1 - %i +--R + +--R +-----+ +--R +------+ \|x + 1 +--R (- 2 - 2%i)\|1 + %i atanh(---------) +--R +------+ +--R \|1 + %i +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 2\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 - \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 2\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 + \|8 sin(---) - \|8 cos(---) +--R 8 8 +--R / +--R 2 +--R Type: Expression(Complex(Integer)) +--E 14 + +--S 15 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 %pi 12 2 %pi %pi 11 +--R (8x - 8)sin(---) + (- 32x + 32)cos(---)sin(---) +--R 8 8 8 +--R + +--R 2 %pi 2 3 2 4+-+2 %pi 10 +--R ((80x - 80)cos(---) + (- 6x - 6x + 10x + 10)\|8 )sin(---) +--R 8 8 +--R + +--R 2 %pi 3 3 2 4+-+2 %pi +--R ((- 160x + 160)cos(---) + (20x + 20x - 44x - 44)\|8 cos(---)) +--R 8 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 2 %pi 4 3 2 4+-+2 %pi 2 +--R (248x - 248)cos(---) + (- 74x - 74x + 134x + 134)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 +--R 4x + 8x - 40x - 88x - 44 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 5 3 2 4+-+2 %pi 3 +--R (- 320x + 320)cos(---) + (144x + 144x - 240x - 240)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi +--R (- 64x - 128x + 192x + 512x + 256)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 3 2 4+-+2 %pi 4 +--R (352x - 352)cos(---) + (- 212x - 212x + 332x + 332)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (224x + 448x - 448x - 1344x - 672)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (x + 3x + 20x + 52x + 51x + 17)\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 7 3 2 4+-+2 %pi 5 +--R (- 320x + 320)cos(---) + (264x + 264x - 376x - 376)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 3 +--R (- 352x - 704x + 768x + 2240x + 1120)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (14x + 42x - 56x - 280x - 294x - 98)\|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 3 2 4+-+2 %pi 6 +--R (248x - 248)cos(---) + (- 236x - 236x + 308x + 308)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 4 +--R (728x + 1456x - 752x - 2960x - 1480)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 4 +--R (- 11x - 33x + 196x + 676x + 687x + 229)\|8 cos(---) - 36x +--R 8 +--R + +--R 3 2 +--R - 144x - 216x - 144x - 36 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 9 3 2 4+-+2 %pi 7 +--R (- 160x + 160)cos(---) + (176x + 176x - 208x - 208)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 5 +--R (- 576x - 1152x + 320x + 1792x + 896)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (140x + 420x + 16x - 1072x - 1212x - 404)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi +--R (32x + 128x + 368x + 832x + 1088x + 704x + 176)cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 3 2 4+-+2 %pi 8 +--R (80x - 80)cos(---) + (- 102x - 102x + 106x + 106)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 6 +--R (416x + 832x - 64x - 960x - 480)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (- 93x - 279x - 132x + 348x + 441x + 147)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (112x + 448x + 184x - 1504x - 2816x - 1952x - 488)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (2x + 10x + 26x + 50x + 70x + 62x + 30x + 6)\|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 11 3 2 4+-+2 %pi 9 +--R (- 32x + 32)cos(---) + (36x + 36x - 28x - 28)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 %pi 7 +--R (- 160x - 320x + 320x + 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (54x + 162x + 104x - 120x - 174x - 58)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 3 +--R (- 64x - 256x - 304x + 64x + 416x + 320x + 80)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi +--R (4x + 20x + 4x - 140x - 340x - 356x - 180x - 36)\|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (8x - 8)cos(---) + (- 10x - 10x + 6x + 6)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (36x + 72x + 24x - 24x - 12)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (- 9x - 27x - 20x + 12x + 21x + 7)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (16x + 64x + 76x - 16x - 104x - 80x - 20)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 6 +--R (- 2x - 10x - 18x - 10x + 10x + 18x + 10x + 2)\|8 cos(---) - 8x +--R 8 +--R + +--R 5 4 3 2 +--R - 48x - 120x - 160x - 120x - 48x - 8 +--R / +--R 2 %pi 12 2 %pi %pi 11 +--R (8x + 8)sin(---) + (- 32x - 32)cos(---)sin(---) +--R 8 8 8 +--R + +--R 2 %pi 2 3 2 4+-+2 %pi 10 +--R ((80x + 80)cos(---) + (- 8x - 8x - 8x - 8)\|8 )sin(---) +--R 8 8 +--R + +--R 2 %pi 3 3 2 4+-+2 %pi +--R ((- 160x - 160)cos(---) + (32x + 32x + 32x + 32)\|8 cos(---)) +--R 8 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 2 %pi 4 +--R (248x + 248)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 2 4 3 2 +--R (- 104x - 104x - 104x - 104)\|8 cos(---) + 24x + 48x + 48x +--R 8 +--R + +--R 48x + 24 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 5 +--R (- 320x - 320)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 3 +--R (192x + 192x + 192x + 192)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi +--R (- 160x - 320x - 320x - 320x - 160)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 +--R (352x + 352)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 4 +--R (- 272x - 272x - 272x - 272)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 2 +--R (448x + 896x + 896x + 896x + 448)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (- 8x - 24x - 32x - 32x - 24x - 8)\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 7 +--R (- 320x - 320)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 5 +--R (320x + 320x + 320x + 320)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (- 736x - 1472x - 1472x - 1472x - 736)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (56x + 168x + 224x + 224x + 168x + 56)\|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 +--R (248x + 248)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 6 +--R (- 272x - 272x - 272x - 272)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (1104x + 2208x + 2208x + 2208x + 1104)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 6 +--R (- 120x - 360x - 480x - 480x - 360x - 120)\|8 cos(---) + 18x +--R 8 +--R + +--R 5 4 3 2 +--R 72x + 126x + 144x + 126x + 72x + 18 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 9 +--R (- 160x - 160)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 7 +--R (192x + 192x + 192x + 192)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (- 736x - 1472x - 1472x - 1472x - 736)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (272x + 816x + 1088x + 1088x + 816x + 272)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi +--R (- 72x - 288x - 504x - 576x - 504x - 288x - 72)cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 +--R (80x + 80)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 8 +--R (- 104x - 104x - 104x - 104)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (448x + 896x + 896x + 896x + 448)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (- 120x - 360x - 480x - 480x - 360x - 120)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (300x + 1200x + 2100x + 2400x + 2100x + 1200x + 300)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (- 2x - 10x - 22x - 30x - 30x - 22x - 10x - 2)\|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 11 3 2 4+-+2 %pi 9 +--R (- 32x - 32)cos(---) + (32x + 32x + 32x + 32)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 7 +--R (- 160x - 320x - 320x - 320x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (56x + 168x + 224x + 224x + 168x + 56)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 3 +--R (- 72x - 288x - 504x - 576x - 504x - 288x - 72)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (20x + 100x + 220x + 300x + 300x + 220x + 100x + 20)\|8 +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (8x + 8)cos(---) + (- 8x - 8x - 8x - 8)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (24x + 48x + 48x + 48x + 24)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (- 8x - 24x - 32x - 32x - 24x - 8)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (18x + 72x + 126x + 144x + 126x + 72x + 18)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 +--R (- 2x - 10x - 22x - 30x - 30x - 22x - 10x - 2)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 4x + 24x + 64x + 104x + 120x + 104x + 64x + 24x + 4 +--R * +--R +-----+ +--R \|x + 1 +--R Type: Expression(Complex(Integer)) +--E 15 + +)clear all + +--S 16 of 845 +t0:=(A+B*x)*sqrt(d+e*x)*sqrt(a+c*x^2) +--R +--R +--R +--------+ +--R +-------+ | 2 +--R (1) (B x + A)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 845 +--r0:=2/7*B*(a+c*x^2)^(3/2)*sqrt(d+e*x)/c-2/105*(4*B*c*d^2-7*A*c*d*e+_ +-- 5*a*B*e^2-3*c*e*(B*d+7*A*e)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/(c*e^2)+_ +-- 4/105*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*_ +-- (4*c^(3/2)*d^3-c*d^2*e*sqrt(-a)-5*a*e^3*sqrt(-a)+8*a*d*e^2*sqrt(c))+_ +-- 7*A*e*sqrt(c)*(c*d^2-3*a*e^2-4*d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*e^3*_ +-- sqrt(a+c*x^2))-4/105*(4*B*c*d^3-7*A*c*d^2*e+8*a*B*d*e^2+21*a*A*e^3)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^4*sqrt(a+c*x^2)) +--E 17 + +--S 18 of 845 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 845 +--m0:=a0-r0 +--E 19 + +--S 20 of 845 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 845 +t0:=(A+B*x)*sqrt(a+c*x^2)/sqrt(d+e*x) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) -------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 21 + +--S 22 of 845 +--r0:=-2/15*(4*B*d-5*A*e-3*B*e*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^2-_ +-- 4/15*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(4*B*c*d^2-_ +-- 5*A*c*d*e+3*a*B*e^2-B*d*e*sqrt(-a)*sqrt(c)+5*A*e^2*sqrt(-a)*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(3/4)*e^3*sqrt(a+c*x^2))-4/15*(4*B*c*d^2-5*A*c*d*e+3*a*B*e^2)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^4*sqrt(a+c*x^2)) +--E 22 + +--S 23 of 845 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 845 +--m0:=a0-r0 +--E 24 + +--S 25 of 845 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 845 +t0:=(A+B*x)*sqrt(a+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) -------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 26 + +--S 27 of 845 +--r0:=2/3*(4*B*d-3*A*e+B*e*x)*sqrt(a+c*x^2)/(e^2*sqrt(d+e*x))+_ +-- 4/3*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*e*_ +-- sqrt(-a)+4*B*d*sqrt(c)-3*A*e*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e^3*sqrt(a+c*x^2))+_ +-- 4/3*c^(1/4)*(4*B*d-3*A*e)*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^4*sqrt(a+c*x^2)) +--E 27 + +--S 28 of 845 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 845 +--m0:=a0-r0 +--E 29 + +--S 30 of 845 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 845 +t0:=(A+B*x)*sqrt(a+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 31 + +--S 32 of 845 +--r0:=2/3*(4*B*d-A*e+3*B*e*x)*sqrt(a+c*x^2)/(e^2*(d+e*x)^(3/2))-_ +-- 4/3*(4*B*c*d^2-A*c*d*e+3*a*B*e^2)*sqrt(a+c*x^2)/(e^2*(c*d^2+a*e^2)*_ +-- sqrt(d+e*x))-4/3*c^(1/4)*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-a)*(4*B*c*d^2-A*c*d*e+3*a*B*e^2-B*d*e*sqrt(-a)*sqrt(c)+A*e^2*_ +-- sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-_ +-- x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*_ +-- sqrt(-a)+d*sqrt(c)))/(e^3*(c*d^2+a*e^2)*sqrt(a+c*x^2))-4/3*c^(1/4)*_ +-- (4*B*c*d^2-A*c*d*e+3*a*B*e^2)*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^4*(c*d^2+a*e^2)*sqrt(a+c*x^2)) +--E 32 + +--S 33 of 845 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 845 +--m0:=a0-r0 +--E 34 + +--S 35 of 845 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 845 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 36 + +--S 37 of 845 +--r0:=-2/63*(8*B*d-9*A*e-7*B*e*x)*(a+c*x^2)^(3/2)*sqrt(d+e*x)/e^2-_ +-- 4/315*(32*B*c*d^3-36*A*c*d^2*e+33*a*B*d*e^2-45*a*A*e^3-3*e*(8*B*c*d^2-_ +-- 9*A*c*d*e+7*a*B*e^2)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^4+8/315*_ +-- elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(9*A*e*_ +-- sqrt(c)*(4*c^(3/2)*d^3+5*(-a)^(3/2)*e^3-c*d^2*e*sqrt(-a)+_ +-- 8*a*d*e^2*sqrt(c))-B*(32*c^2*d^4+57*a*c*d^2*e^2+21*a^2*e^4-8*c^(3/2)*_ +-- d^3*e*sqrt(-a)-12*a*d*e^3*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^5*_ +-- sqrt(a+c*x^2))+8/315*(36*A*c*d*e*(c*d^2+2*a*e^2)-B*(32*c^2*d^4+_ +-- 57*a*c*d^2*e^2+21*a^2*e^4))*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^6*sqrt(a+c*x^2)) +--E 37 + +--S 38 of 845 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 845 +--m0:=a0-r0 +--E 39 + +--S 40 of 845 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 845 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 41 + +--S 42 of 845 +--r0:=2/7*(8*B*d-7*A*e+B*e*x)*(a+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+_ +-- 4/35*(5*a*B*e^2+4*c*d*(8*B*d-7*A*e)-3*c*e*(8*B*d-7*A*e)*x)*_ +-- sqrt(d+e*x)*sqrt(a+c*x^2)/e^4-8/35*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*(32*c^(3/2)*d^3-8*c*d^2*e*_ +-- sqrt(-a)-5*a*e^3*sqrt(-a)+29*a*d*e^2*sqrt(c))+7*A*e*sqrt(c)*(4*c*d^2+_ +-- 3*a*e^2-d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e^5*sqrt(a+c*x^2))+_ +-- 8/35*c^(1/4)*(32*B*c*d^3-28*A*c*d^2*e+29*a*B*d*e^2-21*a*A*e^3)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(e^6*sqrt(a+c*x^2)) +--E 42 + +--S 43 of 845 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 845 +--m0:=a0-r0 +--E 44 + +--S 45 of 845 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 845 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 46 + +--S 47 of 845 +--r0:=2/15*(8*B*d-5*A*e+3*B*e*x)*(a+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 4/15*(9*a*B*e^2+4*c*d*(8*B*d-5*A*e)+c*e*(8*B*d-5*A*e)*x)*_ +-- sqrt(a+c*x^2)/(e^4*sqrt(d+e*x))-8/15*c^(1/4)*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(32*B*c*d^2-20*A*c*d*e+9*a*B*e^2-_ +-- 8*B*d*e*sqrt(-a)*sqrt(c)+5*A*e^2*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^5*_ +-- sqrt(a+c*x^2))-8/15*c^(1/4)*(9*a*B*e^2+4*c*d*(8*B*d-5*A*e))*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(e^6*sqrt(a+c*x^2)) +--E 47 + +--S 48 of 845 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 845 +--m0:=a0-r0 +--E 49 + +--S 50 of 845 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 845 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 51 + +--S 52 of 845 +--r0:=2/15*(8*B*d-3*A*e+5*B*e*x)*(a+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 4/15*(5*a*B*e^2+4*c*d*(8*B*d-3*A*e)+3*c*e*(8*B*d-3*A*e)*x)*_ +-- sqrt(a+c*x^2)/(e^4*(d+e*x)^(3/2))+8/15*c*(32*B*c*d^3-12*A*c*d^2*e+_ +-- 29*a*B*d*e^2-9*a*A*e^3)*sqrt(a+c*x^2)/(e^4*(c*d^2+a*e^2)*sqrt(d+e*x))-_ +-- 8/15*c^(3/4)*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*_ +-- (-B*(32*c^(3/2)*d^3-8*c*d^2*e*sqrt(-a)-5*a*e^3*sqrt(-a)+29*a*d*e^2*_ +-- sqrt(c))+3*A*e*sqrt(c)*(4*c*d^2+3*a*e^2-d*e*sqrt(-a)*sqrt(c)))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (e^5*(c*d^2+a*e^2)*sqrt(a+c*x^2))+8/15*c^(5/4)*(32*B*c*d^3-_ +-- 12*A*c*d^2*e+29*a*B*d*e^2-9*a*A*e^3)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^6*(c*d^2+_ +-- a*e^2)*sqrt(a+c*x^2)) +--E 52 + +--S 53 of 845 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 845 +--m0:=a0-r0 +--E 54 + +--S 55 of 845 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 845 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(a+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------+ +--R | 2 +--R \|c x + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 845 +--r0:=2/5*B*(d+e*x)^(3/2)*sqrt(a+c*x^2)/c+2/15*(3*B*d+5*A*e)*sqrt(d+e*x)*_ +-- sqrt(a+c*x^2)/c-2/15*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- (3*B*(3*(-a)^(3/2)*e^2+c*d^2*sqrt(-a)+4*a*d*e*sqrt(c))-5*A*sqrt(c)*_ +-- (3*c*d^2-a*e^2-4*d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(7/4)*e*sqrt(a+c*x^2))-_ +-- 2/15*(3*B*c*d^2+20*A*c*d*e-9*a*B*e^2)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(7/4)*e^2*_ +-- sqrt(a+c*x^2)) +--E 57 + +--S 58 of 845 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 845 +--m0:=a0-r0 +--E 59 + +--S 60 of 845 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 845 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(a+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +--------+ +--R | 2 +--R \|c x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 845 +--r0:=2/3*B*sqrt(d+e*x)*sqrt(a+c*x^2)/c-2/3*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(-3*A*c*d+a*B*e+B*d*sqrt(-a)*sqrt(c)+3*A*e*_ +-- sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-_ +-- x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*e*sqrt(a+c*x^2))-2/3*(B*d+3*A*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^2*sqrt(a+c*x^2)) +--E 62 + +--S 63 of 845 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 845 +--m0:=a0-r0 +--E 64 + +--S 65 of 845 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 845 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(a+c*x^2)) +--R +--R +--R B x + A +--R (1) --------------------- +--R +--------+ +--R +-------+ | 2 +--R \|e x + d \|c x + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 845 +--r0:=-2*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(B*sqrt(-a)-A*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(3/4)*e*sqrt(a+c*x^2))-2*B*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^2*sqrt(a+c*x^2)) +--E 67 + +--S 68 of 845 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 845 +--m0:=a0-r0 +--E 69 + +--S 70 of 845 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 845 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R +--------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 845 +--r0:=2*(B*d-A*e)*sqrt(a+c*x^2)/((c*d^2+a*e^2)*sqrt(d+e*x))+_ +-- 2*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(A*c*d+a*B*e+B*d*_ +-- sqrt(-a)*sqrt(c)-A*e*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e*(c*d^2+a*e^2)*_ +-- sqrt(a+c*x^2))+2*c^(1/4)*(B*d-A*e)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^2*(c*d^2+_ +-- a*e^2)*sqrt(a+c*x^2)) +--E 72 + +--S 73 of 845 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 845 +--m0:=a0-r0 +--E 74 + +--S 75 of 845 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 845 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------+ +--R 2 | 2 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 845 +--r0:=-(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*sqrt(a+c*x^2))-A*e*sqrt(d+e*x)*_ +-- sqrt(a+c*x^2)/(a*c)+elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- (-A*c*d+3*a*B*e+3*B*d*sqrt(-a)*sqrt(c)+A*e*sqrt(-a)*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(7/4)*sqrt(-a)*sqrt(a+c*x^2))+(A*c*d-3*a*B*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(a*c^(7/4)*e*sqrt(a+c*x^2)) +--E 77 + +--S 78 of 845 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 845 +--m0:=a0-r0 +--E 79 + +--S 80 of 845 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 845 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 845 +--r0:=-(a*B-A*c*x)*sqrt(d+e*x)/(a*c*sqrt(a+c*x^2))+elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(B*sqrt(-a)-A*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*_ +-- sqrt(-a)*sqrt(a+c*x^2))+A*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(a*c^(3/4)*e*sqrt(a+c*x^2)) +--E 82 + +--S 83 of 845 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 845 +--m0:=a0-r0 +--E 84 + +--S 85 of 845 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 845 +t0:=(A+B*x)/((a+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R +--------+ +--R 2 +-------+ | 2 +--R (c x + a)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 845 +--r0:=-(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ +-- sqrt(a+c*x^2))-elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(A*c*d+_ +-- a*B*e+B*d*sqrt(-a)*sqrt(c)-A*e*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*_ +-- (c*d^2+a*e^2)*sqrt(-a)*sqrt(a+c*x^2))+(A*c*d+a*B*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(a*c^(3/4)*e*(c*d^2+a*e^2)*sqrt(a+c*x^2)) +--E 87 + +--S 88 of 845 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 845 +--m0:=a0-r0 +--E 89 + +--S 90 of 845 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 845 +t0:=(-a*e+c*d*x)*(d+e*x)^(-3-2*p)*(a+c*x^2)^p +--R +--R +--R - 2p - 3 2 p +--R (1) (c d x - a e)(e x + d) (c x + a) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 845 +r0:=1/2*(a+c*x^2)^(1+p)/((1+p)*(d+e*x)^(2*(1+p))) +--R +--R +--R 2 p + 1 +--R (c x + a) +--R (2) ----------------------- +--R 2p + 2 +--R (2p + 2)(e x + d) +--R Type: Expression(Integer) +--E 92 + +--S 93 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R 3 2 (- 2p - 3)log(e x + d) p log(c x + a) +--R (c e x + c d x + a e x + a d)%e %e +--R ------------------------------------------------------------------------ +--R 2p + 2 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2p + 2 (- 2p - 3)log(e x + d) +--R (c e x + c d x + a e x + a d)(e x + d) %e +--R * +--R 2 +--R p log(c x + a) +--R %e +--R + +--R 2 p + 1 +--R - (c x + a) +--R / +--R 2p + 2 +--R (2p + 2)(e x + d) +--R Type: Expression(Integer) +--E 94 + +--S 95 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 +--R 2p + 2 2 (- 2p - 3)log(e x + d) p log(c x + a) +--R (c d x - a e)((e x + d) ) %e %e +--R + +--R 2p + 1 2 p + 1 2p + 2 2 p +--R e (e x + d) (c x + a) - c x (e x + d) (c x + a) +--R / +--R 2p + 2 2 +--R ((e x + d) ) +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 845 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 m +--R (1) (2c x + 3b c x + (2a c + b )x + a b)(e x + d) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 845 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(2+m)/(e^4*(2+m))-3*c*(2*c*d-b*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+2*c^2*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 m + 4 +--R (2c m + 12c m + 22c m + 12c )(e x + d) +--R + +--R 2 3 2 2 2 +--R (3b c e - 6c d)m + (21b c e - 42c d)m + (42b c e - 84c d)m +--R + +--R 2 +--R 24b c e - 48c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 3 +--R ((2a c + b )e - 6b c d e + 6c d )m +--R + +--R 2 2 2 2 2 +--R ((16a c + 8b )e - 48b c d e + 48c d )m +--R + +--R 2 2 2 2 2 2 +--R ((38a c + 19b )e - 114b c d e + 114c d )m + (24a c + 12b )e +--R + +--R 2 2 +--R - 72b c d e + 72c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (- 2a c - b )d e + 3b c d e - 2c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (9a b e + (- 18a c - 9b )d e + 27b c d e - 18c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (26a b e + (- 52a c - 26b )d e + 78b c d e - 52c d )m + 24a b e +--R + +--R 2 2 2 2 3 +--R (- 48a c - 24b )d e + 72b c d e - 48c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 97 + +--S 98 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 4 2 2 4 2 4 4 +--R (2c e m + 12c e m + 22c e m + 12c e )x +--R + +--R 4 2 3 3 4 2 3 2 +--R (3b c e + 2c d e )m + (21b c e + 6c d e )m +--R + +--R 4 2 3 4 +--R (42b c e + 4c d e )m + 24b c e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 +--R ((2a c + b )e + 3b c d e )m +--R + +--R 2 4 3 2 2 2 2 +--R ((16a c + 8b )e + 15b c d e - 6c d e )m +--R + +--R 2 4 3 2 2 2 2 4 +--R ((38a c + 19b )e + 12b c d e - 6c d e )m + (24a c + 12b )e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 +--R (a b e + (2a c + b )d e )m +--R + +--R 4 2 3 2 2 2 +--R (9a b e + (14a c + 7b )d e - 6b c d e )m +--R + +--R 4 2 3 2 2 2 3 4 +--R (26a b e + (24a c + 12b )d e - 24b c d e + 12c d e)m + 24a b e +--R * +--R x +--R + +--R 3 3 3 2 2 2 2 +--R a b d e m + (9a b d e + (- 2a c - b )d e )m +--R + +--R 3 2 2 2 3 3 +--R (26a b d e + (- 14a c - 7b )d e + 6b c d e)m + 24a b d e +--R + +--R 2 2 2 3 2 4 +--R (- 24a c - 12b )d e + 24b c d e - 12c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 3 2 4 2 2 4 2 4 4 +--R (2c e m + 12c e m + 22c e m + 12c e )x +--R + +--R 4 2 3 3 4 2 3 2 +--R (3b c e + 2c d e )m + (21b c e + 6c d e )m +--R + +--R 4 2 3 4 +--R (42b c e + 4c d e )m + 24b c e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 +--R ((2a c + b )e + 3b c d e )m +--R + +--R 2 4 3 2 2 2 2 +--R ((16a c + 8b )e + 15b c d e - 6c d e )m +--R + +--R 2 4 3 2 2 2 2 4 +--R ((38a c + 19b )e + 12b c d e - 6c d e )m + (24a c + 12b )e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 +--R (a b e + (2a c + b )d e )m +--R + +--R 4 2 3 2 2 2 +--R (9a b e + (14a c + 7b )d e - 6b c d e )m +--R + +--R 4 2 3 2 2 2 3 4 +--R (26a b e + (24a c + 12b )d e - 24b c d e + 12c d e)m + 24a b e +--R * +--R x +--R + +--R 3 3 3 2 2 2 2 +--R a b d e m + (9a b d e + (- 2a c - b )d e )m +--R + +--R 3 2 2 2 3 3 +--R (26a b d e + (- 14a c - 7b )d e + 6b c d e)m + 24a b d e +--R + +--R 2 2 2 3 2 4 +--R (- 24a c - 12b )d e + 24b c d e - 12c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 3 2 2 2 2 m + 4 +--R (- 2c m - 12c m - 22c m - 12c )(e x + d) +--R + +--R 2 3 2 2 2 +--R (- 3b c e + 6c d)m + (- 21b c e + 42c d)m + (- 42b c e + 84c d)m +--R + +--R 2 +--R - 24b c e + 48c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 3 +--R ((- 2a c - b )e + 6b c d e - 6c d )m +--R + +--R 2 2 2 2 2 +--R ((- 16a c - 8b )e + 48b c d e - 48c d )m +--R + +--R 2 2 2 2 2 2 +--R ((- 38a c - 19b )e + 114b c d e - 114c d )m + (- 24a c - 12b )e +--R + +--R 2 2 +--R 72b c d e - 72c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 3 +--R (- a b e + (2a c + b )d e - 3b c d e + 2c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (- 9a b e + (18a c + 9b )d e - 27b c d e + 18c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (- 26a b e + (52a c + 26b )d e - 78b c d e + 52c d )m - 24a b e +--R + +--R 2 2 2 2 3 +--R (48a c + 24b )d e - 72b c d e + 48c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 99 + +--S 100 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 3 3 2 2 3 3 m log(e x + d) +--R (2c e x + 3b c e x + (2a c + b )e x + a b e )%e +--R + +--R 2 m + 3 2 m + 2 +--R - 2c (e x + d) + (- 3b c e + 6c d)(e x + d) +--R + +--R 2 2 2 2 m + 1 +--R ((- 2a c - b )e + 6b c d e - 6c d )(e x + d) +--R + +--R 3 2 2 2 2 3 m +--R (- a b e + (2a c + b )d e - 3b c d e + 2c d )(e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 845 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 7 4 2 3 6 2 4 3 2 2 2 5 +--R 2c e x + (3b c e + 8c d e )x + ((2a c + b )e + 12b c d e + 12c d e )x +--R + +--R 4 2 3 2 2 2 3 4 +--R (a b e + (8a c + 4b )d e + 18b c d e + 8c d e)x +--R + +--R 3 2 2 2 3 2 4 3 +--R (4a b d e + (12a c + 6b )d e + 12b c d e + 2c d )x +--R + +--R 2 2 2 3 4 2 3 2 4 +--R (6a b d e + (8a c + 4b )d e + 3b c d )x + (4a b d e + (2a c + b )d )x +--R + +--R 4 +--R a b d +--R Type: Polynomial(Integer) +--E 101 + +--S 102 of 845 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4+1/6*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^6/e^4-3/7*c*(2*c*d-b*e)*(d+e*x)^7/e^4+_ + 1/4*c^2*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 2 8 8 3 8 8 2 7 7 +--R - c e x + (- b c e + - c d e )x +--R 4 7 7 +--R + +--R 1 1 2 8 7 2 2 6 6 +--R ((- a c + - b )e + 2b c d e + 2c d e )x +--R 3 6 +--R + +--R 1 8 8 4 2 7 18 2 6 8 2 3 5 5 +--R (- a b e + (- a c + - b )d e + -- b c d e + - c d e )x +--R 5 5 5 5 5 +--R + +--R 7 3 2 2 6 3 5 1 2 4 4 4 +--R (a b d e + (3a c + - b )d e + 3b c d e + - c d e )x +--R 2 2 +--R + +--R 2 6 8 4 2 3 5 4 4 3 +--R (2a b d e + (- a c + - b )d e + b c d e )x +--R 3 3 +--R + +--R 3 5 1 2 4 4 2 4 4 1 5 3 +--R (2a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 5 +--R + +--R 1 1 2 6 2 1 7 1 2 8 +--R (- -- a c - -- b )d e + -- b c d e - --- c d +--R 15 30 35 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 102 + +--S 103 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 8 3 4 8 2 3 7 +--R - c e x + (- b c e + - c d e )x +--R 4 7 7 +--R + +--R 1 1 2 4 3 2 2 2 6 +--R ((- a c + - b )e + 2b c d e + 2c d e )x +--R 3 6 +--R + +--R 1 4 8 4 2 3 18 2 2 8 2 3 5 +--R (- a b e + (- a c + - b )d e + -- b c d e + - c d e)x +--R 5 5 5 5 5 +--R + +--R 3 3 2 2 2 3 1 2 4 4 +--R (a b d e + (3a c + - b )d e + 3b c d e + - c d )x +--R 2 2 +--R + +--R 2 2 8 4 2 3 4 3 3 1 2 4 2 +--R (2a b d e + (- a c + - b )d e + b c d )x + (2a b d e + (a c + - b )d )x +--R 3 3 2 +--R + +--R 4 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 103 + +--S 104 of 845 +m0:=a0-r0 +--R +--R +--R 1 5 3 1 1 2 6 2 1 7 1 2 8 +--R - - a b d e + (-- a c + -- b )d e - -- b c d e + --- c d +--R 5 15 30 35 140 +--R (4) ----------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 104 + +--S 105 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 105 + +)clear all + +--S 106 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R 2c e x + (3b c e + 6c d e )x + ((2a c + b )e + 9b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (6a c + 3b )d e + 9b c d e + 2c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R (3a b d e + (6a c + 3b )d e + 3b c d )x + (3a b d e + (2a c + b )d )x +--R + +--R 3 +--R a b d +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 845 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4+1/5*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^5/e^4-1/2*c*(2*c*d-b*e)*(d+e*x)^6/e^4+_ + 2/7*c^2*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 2 2 7 7 1 7 2 6 6 +--R - c e x + (- b c e + c d e )x +--R 7 2 +--R + +--R 2 1 2 7 9 6 6 2 2 5 5 +--R ((- a c + - b )e + - b c d e + - c d e )x +--R 5 5 5 5 +--R + +--R 1 7 3 3 2 6 9 2 5 1 2 3 4 4 +--R (- a b e + (- a c + - b )d e + - b c d e + - c d e )x +--R 4 2 4 4 2 +--R + +--R 6 2 2 5 3 4 3 +--R (a b d e + (2a c + b )d e + b c d e )x +--R + +--R 3 2 5 1 2 3 4 2 3 4 1 4 3 +--R (- a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 2 4 +--R + +--R 1 1 2 5 2 1 6 1 2 7 +--R (- -- a c - -- b )d e + -- b c d e - -- c d +--R 10 20 20 70 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 107 + +--S 108 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 7 1 3 2 2 6 +--R - c e x + (- b c e + c d e )x +--R 7 2 +--R + +--R 2 1 2 3 9 2 6 2 2 5 +--R ((- a c + - b )e + - b c d e + - c d e)x +--R 5 5 5 5 +--R + +--R 1 3 3 3 2 2 9 2 1 2 3 4 +--R (- a b e + (- a c + - b )d e + - b c d e + - c d )x +--R 4 2 4 4 2 +--R + +--R 2 2 2 3 3 3 2 1 2 3 2 +--R (a b d e + (2a c + b )d e + b c d )x + (- a b d e + (a c + - b )d )x +--R 2 2 +--R + +--R 3 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 845 +m0:=a0-r0 +--R +--R +--R 1 4 3 1 1 2 5 2 1 6 1 2 7 +--R - - a b d e + (-- a c + -- b )d e - -- b c d e + -- c d +--R 4 10 20 20 70 +--R (4) ---------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 109 + +--S 110 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 110 + +)clear all + +--S 111 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x + a b d +--R Type: Polynomial(Integer) +--E 111 + +--S 112 of 845 +r0:=-1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3/e^4+1/4*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^4/e^4-3/5*c*(2*c*d-b*e)*_ + (d+e*x)^5/e^4+1/3*c^2*(d+e*x)^6/e^4 +--R +--R +--R (2) +--R 1 2 6 6 3 6 4 2 5 5 +--R - c e x + (- b c e + - c d e )x +--R 3 5 5 +--R + +--R 1 1 2 6 3 5 1 2 2 4 4 +--R ((- a c + - b )e + - b c d e + - c d e )x +--R 2 4 2 2 +--R + +--R 1 6 4 2 2 5 2 4 3 +--R (- a b e + (- a c + - b )d e + b c d e )x +--R 3 3 3 +--R + +--R 5 1 2 2 4 2 2 4 1 3 3 +--R (a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 3 +--R + +--R 1 1 2 4 2 1 5 1 2 6 +--R (- - a c - -- b )d e + -- b c d e - -- c d +--R 6 12 10 30 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 112 + +--S 113 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 6 3 2 4 2 5 +--R - c e x + (- b c e + - c d e)x +--R 3 5 5 +--R + +--R 1 1 2 2 3 1 2 2 4 +--R ((- a c + - b )e + - b c d e + - c d )x +--R 2 4 2 2 +--R + +--R 1 2 4 2 2 2 3 1 2 2 2 +--R (- a b e + (- a c + - b )d e + b c d )x + (a b d e + (a c + - b )d )x +--R 3 3 3 2 +--R + +--R 2 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 845 +m0:=a0-r0 +--R +--R +--R 1 3 3 1 1 2 4 2 1 5 1 2 6 +--R - - a b d e + (- a c + -- b )d e - -- b c d e + -- c d +--R 3 6 12 10 30 +--R (4) --------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 114 + +--S 115 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 115 + +)clear all + +--S 116 of 845 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R Type: Polynomial(Integer) +--E 116 + +--S 117 of 845 +r0:=a*b*d*x+1/2*(b^2*d+2*a*c*d+a*b*e)*x^2+1/3*(3*b*c*d+b^2*e+2*a*c*e)*x^3+_ + 1/4*c*(2*c*d+3*b*e)*x^4+2/5*c^2*e*x^5 +--R +--R +--R (2) +--R 2 2 5 3 1 2 4 2 1 2 3 +--R - c e x + (- b c e + - c d)x + ((- a c + - b )e + b c d)x +--R 5 4 2 3 3 +--R + +--R 1 1 2 2 +--R (- a b e + (a c + - b )d)x + a b d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 5 3 1 2 4 2 1 2 3 +--R - c e x + (- b c e + - c d)x + ((- a c + - b )e + b c d)x +--R 5 4 2 3 3 +--R + +--R 1 1 2 2 +--R (- a b e + (a c + - b )d)x + a b d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +--S 119 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 119 + +--S 120 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +)clear all + +--S 121 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 +--R (1) 2c x + 3b c x + (2a c + b )x + a b +--R Type: Polynomial(Integer) +--E 121 + +--S 122 of 845 +r0:=1/2*(a+b*x+c*x^2)^2 +--R +--R +--R 1 2 4 3 1 2 2 1 2 +--R (2) - c x + b c x + (a c + - b )x + a b x + - a +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 845 +a0:=integrate(t0,x) +--R +--R +--R 1 2 4 3 1 2 2 +--R (3) - c x + b c x + (a c + - b )x + a b x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +--S 124 of 845 +m0:=a0-r0 +--R +--R +--R 1 2 +--R (4) - - a +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 124 + +--S 125 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +)clear all + +--S 126 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 845 +r0:=(2*c^2*d^2+b^2*e^2-c*e*(3*b*d-2*a*e))*x/e^3-1/2*c*(2*c*d-3*b*e)*x^2/e^2+_ + 2/3*c^2*x^3/e-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R (6a b e + (- 12a c - 6b )d e + 18b c d e - 12c d )log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 4c e x + (9b c e - 6c d e )x + ((12a c + 6b )e - 18b c d e + 12c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 127 + +--S 128 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 +--R (6a b e + (- 12a c - 6b )d e + 18b c d e - 12c d )log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 4c e x + (9b c e - 6c d e )x + ((12a c + 6b )e - 18b c d e + 12c d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 845 +r0:=-c*(4*c*d-3*b*e)*x/e^3+c^2*x^2/e^2+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/_ + (e^4*(d+e*x))+(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 2 +--R ((2a c + b )e - 6b c d e + 6c d e)x + (2a c + b )d e - 6b c d e +--R + +--R 2 3 +--R 6c d +--R * +--R log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 2 2 3 +--R c e x + (3b c e - 3c d e )x + (3b c d e - 4c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (2a c + b )d e - 3b c d e + 2c d +--R / +--R 5 4 +--R e x + d e +--R Type: Expression(Integer) +--E 132 + +--S 133 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 2 +--R ((2a c + b )e - 6b c d e + 6c d e)x + (2a c + b )d e - 6b c d e +--R + +--R 2 3 +--R 6c d +--R * +--R log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 2 2 3 +--R c e x + (3b c e - 3c d e )x + (3b c d e - 4c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (2a c + b )d e - 3b c d e + 2c d +--R / +--R 5 4 +--R e x + d e +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 845 +r0:=2*c^2*x/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x))-3*c*(2*c*d-b*e)*_ + log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 2 2 2 3 +--R ((6b c e - 12c d e )x + (12b c d e - 24c d e)x + 6b c d e - 12c d ) +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 2 3 2 2 2 3 +--R 4c e x + 8c d e x + ((- 4a c - 2b )e + 12b c d e - 8c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (- 2a c - b )d e + 9b c d e - 10c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 137 + +--S 138 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 2 2 2 2 3 +--R ((6b c e - 12c d e )x + (12b c d e - 24c d e)x + 6b c d e - 12c d ) +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 2 3 2 2 2 3 +--R 4c e x + 8c d e x + ((- 4a c - 2b )e + 12b c d e - 8c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (- 2a c - b )d e + 9b c d e - 10c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 845 +r0:=1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+_ + 1/2*(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x)^2)+_ + 3*c*(2*c*d-b*e)/(e^4*(d+e*x))+2*c^2*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 2 2 2 3 +--R (12c e x + 36c d e x + 36c d e x + 12c d )log(e x + d) +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 18b c e + 36c d e )x + ((- 6a c - 3b )e - 18b c d e + 54c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (- 2a c - b )d e - 6b c d e + 22c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 142 + +--S 143 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 2 2 2 3 +--R (12c e x + 36c d e x + 36c d e x + 12c d )log(e x + d) +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 18b c e + 36c d e )x + ((- 6a c - 3b )e - 18b c d e + 54c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (- 2a c - b )d e - 6b c d e + 22c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 845 +r0:=1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+_ + 1/3*(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x)^3)+_ + 3/2*c*(2*c*d-b*e)/(e^4*(d+e*x)^2)-2*c^2/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 3 3 3 3 2 2 2 +--R - 2c e x + (- - b c e - 3c d e )x +--R 2 +--R + +--R 2 1 2 3 2 2 2 1 3 +--R ((- - a c - - b )e - b c d e - 2c d e)x - - a b e +--R 3 3 4 +--R + +--R 1 1 2 2 1 2 1 2 3 +--R (- - a c - -- b )d e - - b c d e - - c d +--R 6 12 4 2 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 147 + +--S 148 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 +--R - 24c e x + (- 18b c e - 36c d e )x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 8a c - 4b )e - 12b c d e - 24c d e)x - 3a b e + (- 2a c - b )d e +--R + +--R 2 2 3 +--R - 3b c d e - 6c d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 845 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 845 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))+_ + 2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(2+m)/(e^6*(2+m))-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(3+m)/(e^6*(3+m))+4*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(4+m)/(e^6*(4+m))-5*c^2*(2*c*d-b*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+2*c^3*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 3 5 3 4 3 3 3 2 3 3 m + 6 +--R (2c m + 30c m + 170c m + 450c m + 548c m + 240c )(e x + d) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R (5b c e - 10c d)m + (80b c e - 160c d)m + (475b c e - 950c d)m +--R + +--R 2 3 2 2 3 2 3 +--R (1300b c e - 2600c d)m + (1620b c e - 3240c d)m + 720b c e - 1440c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 3 2 5 +--R ((4a c + 4b c)e - 20b c d e + 20c d )m +--R + +--R 2 2 2 2 3 2 4 +--R ((68a c + 68b c)e - 340b c d e + 340c d )m +--R + +--R 2 2 2 2 3 2 3 +--R ((428a c + 428b c)e - 2140b c d e + 2140c d )m +--R + +--R 2 2 2 2 3 2 2 +--R ((1228a c + 1228b c)e - 6140b c d e + 6140c d )m +--R + +--R 2 2 2 2 3 2 +--R ((1584a c + 1584b c)e - 7920b c d e + 7920c d )m +--R + +--R 2 2 2 2 3 2 +--R (720a c + 720b c)e - 3600b c d e + 3600c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (- 12a c - 12b c)d e + 30b c d e - 20c d )m +--R + +--R 3 3 2 2 2 2 2 +--R (108a b c + 18b )e + (- 216a c - 216b c)d e + 540b c d e +--R + +--R 3 3 +--R - 360c d +--R * +--R 4 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (726a b c + 121b )e + (- 1452a c - 1452b c)d e + 3630b c d e +--R + +--R 3 3 +--R - 2420c d +--R * +--R 3 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (2232a b c + 372b )e + (- 4464a c - 4464b c)d e + 11160b c d e +--R + +--R 3 3 +--R - 7440c d +--R * +--R 2 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (3048a b c + 508b )e + (- 6096a c - 6096b c)d e + 15240b c d e +--R + +--R 3 3 +--R - 10160c d +--R * +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (1440a b c + 240b )e + (- 2880a c - 2880b c)d e + 7200b c d e +--R + +--R 3 3 +--R - 4800c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (2a c + 2a b )e + (- 12a b c - 2b )d e + (12a c + 12b c)d e +--R + +--R 2 3 3 4 +--R - 20b c d e + 10c d +--R * +--R 5 +--R m +--R + +--R 2 2 4 3 3 +--R (38a c + 38a b )e + (- 228a b c - 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c - 372b )e + (4464a c + 4464b c)d e - 11160b c d e +--R + +--R 3 3 +--R 7440c d +--R * +--R 2 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (- 3048a b c - 508b )e + (6096a c + 6096b c)d e - 15240b c d e +--R + +--R 3 3 +--R 10160c d +--R * +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (- 1440a b c - 240b )e + (2880a c + 2880b c)d e - 7200b c d e +--R + +--R 3 3 +--R 4800c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (- 2a c - 2a b )e + (12a b c + 2b )d e + (- 12a c - 12b c)d e +--R + +--R 2 3 3 4 +--R 20b c d e - 10c d +--R * +--R 5 +--R m +--R + +--R 2 2 4 3 3 +--R (- 38a c - 38a b )e + (228a b c + 38b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 228a c - 228b c)d e + 380b c d e - 190c d +--R * +--R 4 +--R m +--R + +--R 2 2 4 3 3 +--R (- 274a c - 274a b )e + (1644a b c + 274b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 1644a c - 1644b c)d e + 2740b c d e - 1370c d +--R * +--R 3 +--R m +--R + +--R 2 2 4 3 3 +--R (- 922a c - 922a b )e + (5532a b c + 922b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 5532a c - 5532b c)d e + 9220b c d e - 4610c d +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 3 +--R (- 1404a c - 1404a b )e + (8424a b c + 1404b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 8424a c - 8424b c)d e + 14040b c d e - 7020c d +--R * +--R m +--R + +--R 2 2 4 3 3 +--R (- 720a c - 720a b )e + (4320a b c + 720b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 4320a c - 4320b c)d e + 7200b c d e - 3600c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (2a c + 2a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (4a c + 4b c)d e - 5b c d e + 2c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R - 20a b e + (40a c + 40a b )d e + (- 120a b c - 20b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (80a c + 80b c)d e - 100b c d e + 40c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R - 155a b e + (310a c + 310a b )d e + (- 930a b c - 155b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (620a c + 620b c)d e - 775b c d e + 310c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 +--R - 580a b e + (1160a c + 1160a b )d e +--R + +--R 3 2 3 2 2 3 2 +--R (- 3480a b c - 580b )d e + (2320a c + 2320b c)d e +--R + +--R 2 4 3 5 +--R - 2900b c d e + 1160c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R - 1044a b e + (2088a c + 2088a b )d e +--R + +--R 3 2 3 2 2 3 2 +--R (- 6264a b c - 1044b )d e + (4176a c + 4176b c)d e +--R + +--R 2 4 3 5 +--R - 5220b c d e + 2088c d +--R * +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R - 720a b e + (1440a c + 1440a b )d e + (- 4320a b c - 720b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (2880a c + 2880b c)d e - 3600b c d e + 1440c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 154 + +--S 155 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 5 2 5 4 2 2 5 3 3 5 2 +--R 2c e x + 5b c e x + (4a c + 4b c)e x + (6a b c + b )e x +--R + +--R 2 2 5 2 5 +--R (2a c + 2a b )e x + a b e +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 m + 5 2 3 m + 4 +--R - 2c (e x + d) + (- 5b c e + 10c d)(e x + d) +--R + +--R 2 2 2 2 3 2 m + 3 +--R ((- 4a c - 4b c)e + 20b c d e - 20c d )(e x + d) +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((- 6a b c - b )e + (12a c + 12b c)d e - 30b c d e + 20c d ) +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (- 2a c - 2a b )e + (12a b c + 2b )d e + (- 12a c - 12b c)d e +--R + +--R 2 3 3 4 +--R 20b c d e - 10c d +--R * +--R m + 1 +--R (e x + d) +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (2a c + 2a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (4a c + 4b c)d e - 5b c d e + 2c d +--R * +--R m +--R (e x + d) +--R / +--R 5 +--R e +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 845 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 9 2 4 3 3 8 +--R 2c e x + (5b c e + 8c d e )x +--R + +--R 2 2 4 2 3 3 2 2 7 +--R ((4a c + 4b c)e + 20b c d e + 12c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 6 +--R ((6a b c + b )e + (16a c + 16b c)d e + 30b c d e + 8c d e)x +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (2a c + 2a b )e + (24a b c + 4b )d e + (24a c + 24b c)d e +--R + +--R 2 3 3 4 +--R 20b c d e + 2c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 2 3 3 2 2 2 2 3 +--R a b e + (8a c + 8a b )d e + (36a b c + 6b )d e + (16a c + 16b c)d e +--R + +--R 2 4 +--R 5b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 3 +--R 4a b d e + (12a c + 12a b )d e + (24a b c + 4b )d e +--R + +--R 2 2 4 +--R (4a c + 4b c)d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 3 3 4 2 +--R (6a b d e + (8a c + 8a b )d e + (6a b c + b )d )x +--R + +--R 2 3 2 2 4 2 4 +--R (4a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 156 + +--S 157 of 845 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^5/e^6+1/3*(c*d^2-b*d*e+_ + a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^6/e^6-1/7*(2*c*d-_ + b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^7/e^6+1/2*c*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^8/e^6-5/9*c^2*(2*c*d-b*e)*_ + (d+e*x)^9/e^6+1/5*c^3*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 3 10 10 5 2 10 8 3 9 9 +--R - c e x + (- b c e + - c d e )x +--R 5 9 9 +--R + +--R 1 2 1 2 10 5 2 9 3 3 2 8 8 +--R ((- a c + - b c)e + - b c d e + - c d e )x +--R 2 2 2 2 +--R + +--R 6 1 3 10 16 2 16 2 9 30 2 2 8 8 3 3 7 7 +--R ((- a b c + - b )e + (-- a c + -- b c)d e + -- b c d e + - c d e )x +--R 7 7 7 7 7 7 +--R + +--R 1 2 1 2 10 2 3 9 2 2 2 8 +--R (- a c + - a b )e + (4a b c + - b )d e + (4a c + 4b c)d e +--R 3 3 3 +--R + +--R 10 2 3 7 1 3 4 6 +--R -- b c d e + - c d e +--R 3 3 +--R * +--R 6 +--R x +--R + +--R 1 2 10 8 2 8 2 9 36 6 3 2 8 +--R - a b e + (- a c + - a b )d e + (-- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 16 2 16 2 3 7 2 4 6 +--R (-- a c + -- b c)d e + b c d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 2 9 2 2 2 8 3 3 7 2 2 4 6 4 +--R (a b d e + (3a c + 3a b )d e + (6a b c + b )d e + (a c + b c)d e )x +--R + +--R 2 2 8 8 2 8 2 3 7 1 3 4 6 3 +--R (2a b d e + (- a c + - a b )d e + (2a b c + - b )d e )x +--R 3 3 3 +--R + +--R 2 3 7 2 2 4 6 2 2 4 6 1 2 5 5 +--R (2a b d e + (a c + a b )d e )x + a b d e x + - a b d e +--R 5 +--R + +--R 1 2 1 2 6 4 2 1 3 7 3 +--R (- -- a c - -- a b )d e + (-- a b c + --- b )d e +--R 15 15 35 105 +--R + +--R 1 2 1 2 8 2 1 2 9 1 3 10 +--R (- -- a c - -- b c)d e + --- b c d e - --- c d +--R 70 70 126 630 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 157 + +--S 158 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 10 5 2 4 8 3 3 9 +--R - c e x + (- b c e + - c d e )x +--R 5 9 9 +--R + +--R 1 2 1 2 4 5 2 3 3 3 2 2 8 +--R ((- a c + - b c)e + - b c d e + - c d e )x +--R 2 2 2 2 +--R + +--R 6 1 3 4 16 2 16 2 3 30 2 2 2 8 3 3 7 +--R ((- a b c + - b )e + (-- a c + -- b c)d e + -- b c d e + - c d e)x +--R 7 7 7 7 7 7 +--R + +--R 1 2 1 2 4 2 3 3 2 2 2 2 +--R (- a c + - a b )e + (4a b c + - b )d e + (4a c + 4b c)d e +--R 3 3 3 +--R + +--R 10 2 3 1 3 4 +--R -- b c d e + - c d +--R 3 3 +--R * +--R 6 +--R x +--R + +--R 1 2 4 8 2 8 2 3 36 6 3 2 2 +--R - a b e + (- a c + - a b )d e + (-- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 16 2 16 2 3 2 4 +--R (-- a c + -- b c)d e + b c d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 2 3 2 2 2 2 3 3 2 2 4 4 +--R (a b d e + (3a c + 3a b )d e + (6a b c + b )d e + (a c + b c)d )x +--R + +--R 2 2 2 8 2 8 2 3 1 3 4 3 +--R (2a b d e + (- a c + - a b )d e + (2a b c + - b )d )x +--R 3 3 3 +--R + +--R 2 3 2 2 4 2 2 4 +--R (2a b d e + (a c + a b )d )x + a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 158 + +--S 159 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 5 5 1 2 1 2 6 4 2 1 3 7 3 +--R - - a b d e + (-- a c + -- a b )d e + (- -- a b c - --- b )d e +--R 5 15 15 35 105 +--R + +--R 1 2 1 2 8 2 1 2 9 1 3 10 +--R (-- a c + -- b c)d e - --- b c d e + --- c d +--R 70 70 126 630 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 159 + +--S 160 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 3 8 2 3 3 2 7 +--R 2c e x + (5b c e + 6c d e )x +--R + +--R 2 2 3 2 2 3 2 6 +--R ((4a c + 4b c)e + 15b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (12a c + 12b c)d e + 15b c d e + 2c d )x +--R + +--R 2 2 3 3 2 2 2 2 2 3 4 +--R ((2a c + 2a b )e + (18a b c + 3b )d e + (12a c + 12b c)d e + 5b c d )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 3 +--R (a b e + (6a c + 6a b )d e + (18a b c + 3b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 6a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 3 2 3 +--R (3a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 161 + +--S 162 of 845 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4/e^6+2/5*(c*d^2-_ + b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^5/e^6-_ + 1/6*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^6/e^6+4/7*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^7/e^6-5/8*c^2*(2*c*d-b*e)*(d+e*x)^8/e^6+2/9*c^3*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 2 3 9 9 5 2 9 3 3 8 8 +--R - c e x + (- b c e + - c d e )x +--R 9 8 4 +--R + +--R 4 2 4 2 9 15 2 8 6 3 2 7 7 +--R ((- a c + - b c)e + -- b c d e + - c d e )x +--R 7 7 7 7 +--R + +--R 1 3 9 2 2 8 5 2 2 7 1 3 3 6 6 +--R ((a b c + - b )e + (2a c + 2b c)d e + - b c d e + - c d e )x +--R 6 2 3 +--R + +--R 2 2 2 2 9 18 3 3 8 12 2 12 2 2 7 +--R (- a c + - a b )e + (-- a b c + - b )d e + (-- a c + -- b c)d e +--R 5 5 5 5 5 5 +--R + +--R 2 3 6 +--R b c d e +--R * +--R 5 +--R x +--R + +--R 1 2 9 3 2 3 2 8 9 3 3 2 7 +--R - a b e + (- a c + - a b )d e + (- a b c + - b )d e +--R 4 2 2 2 4 +--R + +--R 2 2 3 6 +--R (a c + b c)d e +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 2 7 1 3 3 6 3 +--R (a b d e + (2a c + 2a b )d e + (2a b c + - b )d e )x +--R 3 +--R + +--R 3 2 2 7 2 2 3 6 2 2 3 6 1 2 4 5 +--R (- a b d e + (a c + a b )d e )x + a b d e x + - a b d e +--R 2 4 +--R + +--R 1 2 1 2 5 4 1 1 3 6 3 +--R (- -- a c - -- a b )d e + (-- a b c + -- b )d e +--R 10 10 10 60 +--R + +--R 1 2 1 2 7 2 1 2 8 1 3 9 +--R (- -- a c - -- b c)d e + -- b c d e - --- c d +--R 35 35 56 252 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +--S 163 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 9 5 2 3 3 3 2 8 +--R - c e x + (- b c e + - c d e )x +--R 9 8 4 +--R + +--R 4 2 4 2 3 15 2 2 6 3 2 7 +--R ((- a c + - b c)e + -- b c d e + - c d e)x +--R 7 7 7 7 +--R + +--R 1 3 3 2 2 2 5 2 2 1 3 3 6 +--R ((a b c + - b )e + (2a c + 2b c)d e + - b c d e + - c d )x +--R 6 2 3 +--R + +--R 2 2 2 2 3 18 3 3 2 12 2 12 2 2 +--R (- a c + - a b )e + (-- a b c + - b )d e + (-- a c + -- b c)d e +--R 5 5 5 5 5 5 +--R + +--R 2 3 +--R b c d +--R * +--R 5 +--R x +--R + +--R 1 2 3 3 2 3 2 2 9 3 3 2 2 2 3 4 +--R (- a b e + (- a c + - a b )d e + (- a b c + - b )d e + (a c + b c)d )x +--R 4 2 2 2 4 +--R + +--R 2 2 2 2 2 1 3 3 3 +--R (a b d e + (2a c + 2a b )d e + (2a b c + - b )d )x +--R 3 +--R + +--R 3 2 2 2 2 3 2 2 3 +--R (- a b d e + (a c + a b )d )x + a b d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 163 + +--S 164 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 4 5 1 2 1 2 5 4 1 1 3 6 3 +--R - - a b d e + (-- a c + -- a b )d e + (- -- a b c - -- b )d e +--R 4 10 10 10 60 +--R + +--R 1 2 1 2 7 2 1 2 8 1 3 9 +--R (-- a c + -- b c)d e - -- b c d e + --- c d +--R 35 35 56 252 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 164 + +--S 165 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 166 + +--S 167 of 845 +r0:=a^2*b*d^2*x+a*d*(b^2*d+a*c*d+a*b*e)*x^2+1/3*(b^3*d^2+4*a*b^2*d*e+_ + 4*a^2*c*d*e+a*b*(6*c*d^2+a*e^2))*x^3+1/2*(b^3*d*e+6*a*b*c*d*e+b^2*_ + (2*c*d^2+a*e^2)+a*c*(2*c*d^2+a*e^2))*x^4+1/5*(8*b^2*c*d*e+_ + 8*a*c^2*d*e+b^3*e^2+b*c*(5*c*d^2+6*a*e^2))*x^5+1/3*c*(c^2*d^2+_ + 2*b^2*e^2+c*e*(5*b*d+2*a*e))*x^6+1/7*c^2*e*(4*c*d+5*b*e)*x^7+_ + 1/4*c^3*e^2*x^8 +--R +--R +--R (2) +--R 1 3 2 8 5 2 2 4 3 7 +--R - c e x + (- b c e + - c d e)x +--R 4 7 7 +--R + +--R 2 2 2 2 2 5 2 1 3 2 6 +--R ((- a c + - b c)e + - b c d e + - c d )x +--R 3 3 3 3 +--R + +--R 6 1 3 2 8 2 8 2 2 2 5 +--R ((- a b c + - b )e + (- a c + - b c)d e + b c d )x +--R 5 5 5 5 +--R + +--R 1 2 1 2 2 1 3 2 2 2 4 +--R ((- a c + - a b )e + (3a b c + - b )d e + (a c + b c)d )x +--R 2 2 2 +--R + +--R 1 2 2 4 2 4 2 1 3 2 3 +--R (- a b e + (- a c + - a b )d e + (2a b c + - b )d )x +--R 3 3 3 3 +--R + +--R 2 2 2 2 2 2 2 +--R (a b d e + (a c + a b )d )x + a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 167 + +--S 168 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 8 5 2 2 4 3 7 +--R - c e x + (- b c e + - c d e)x +--R 4 7 7 +--R + +--R 2 2 2 2 2 5 2 1 3 2 6 +--R ((- a c + - b c)e + - b c d e + - c d )x +--R 3 3 3 3 +--R + +--R 6 1 3 2 8 2 8 2 2 2 5 +--R ((- a b c + - b )e + (- a c + - b c)d e + b c d )x +--R 5 5 5 5 +--R + +--R 1 2 1 2 2 1 3 2 2 2 4 +--R ((- a c + - a b )e + (3a b c + - b )d e + (a c + b c)d )x +--R 2 2 2 +--R + +--R 1 2 2 4 2 4 2 1 3 2 3 +--R (- a b e + (- a c + - a b )d e + (2a b c + - b )d )x +--R 3 3 3 3 +--R + +--R 2 2 2 2 2 2 2 +--R (a b d e + (a c + a b )d )x + a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 168 + +--S 169 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 169 + +--S 170 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 170 + +)clear all + +--S 171 of 845 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 2 2 3 2 +--R ((6a b c + b )e + (4a c + 4b c)d)x + ((2a c + 2a b )e + (6a b c + b )d)x +--R + +--R 2 2 2 2 +--R (a b e + (2a c + 2a b )d)x + a b d +--R Type: Polynomial(Integer) +--E 171 + +--S 172 of 845 +r0:=a^2*b*d*x+1/2*a*(2*b^2*d+2*a*c*d+a*b*e)*x^2+1/3*(b^3*d+6*a*b*c*d+_ + 2*a*b^2*e+2*a^2*c*e)*x^3+1/4*(4*b^2*c*d+4*a*c^2*d+b^3*e+6*a*b*c*e)*x^4+_ + 1/5*c*(5*b*c*d+4*b^2*e+4*a*c*e)*x^5+1/6*c^2*(2*c*d+5*b*e)*x^6+2/7*c^3*e*x^7 +--R +--R +--R (2) +--R 2 3 7 5 2 1 3 6 4 2 4 2 2 5 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c)e + b c d)x +--R 7 6 3 5 5 +--R + +--R 3 1 3 2 2 4 +--R ((- a b c + - b )e + (a c + b c)d)x +--R 2 4 +--R + +--R 2 2 2 2 1 3 3 1 2 2 2 2 +--R ((- a c + - a b )e + (2a b c + - b )d)x + (- a b e + (a c + a b )d)x +--R 3 3 3 2 +--R + +--R 2 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 172 + +--S 173 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 7 5 2 1 3 6 4 2 4 2 2 5 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c)e + b c d)x +--R 7 6 3 5 5 +--R + +--R 3 1 3 2 2 4 +--R ((- a b c + - b )e + (a c + b c)d)x +--R 2 4 +--R + +--R 2 2 2 2 1 3 3 1 2 2 2 2 +--R ((- a c + - a b )e + (2a b c + - b )d)x + (- a b e + (a c + a b )d)x +--R 3 3 3 2 +--R + +--R 2 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 173 + +--S 174 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 174 + +--S 175 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 175 + +)clear all + +--S 176 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R Type: Polynomial(Integer) +--E 176 + +--S 177 of 845 +r0:=1/3*(a+b*x+c*x^2)^3 +--R +--R +--R (2) +--R 1 3 6 2 5 2 2 4 1 3 3 2 2 2 +--R - c x + b c x + (a c + b c)x + (2a b c + - b )x + (a c + a b )x +--R 3 3 +--R + +--R 2 1 3 +--R a b x + - a +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 177 + +--S 178 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 6 2 5 2 2 4 1 3 3 2 2 2 2 +--R - c x + b c x + (a c + b c)x + (2a b c + - b )x + (a c + a b )x + a b x +--R 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 178 + +--S 179 of 845 +m0:=a0-r0 +--R +--R +--R 1 3 +--R (4) - - a +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 179 + +--S 180 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 180 + +)clear all + +--S 181 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 845 +r0:=2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*x/e^5-_ + 1/2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^2/e^6+4/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^3/e^6-_ + 5/4*c^2*(2*c*d-b*e)*(d+e*x)^4/e^6+2/5*c^3*(d+e*x)^5/e^6-(2*c*d-b*e)*_ + (c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 2 4 3 2 3 +--R 60a b e + (- 120a c - 120a b )d e + (360a b c + 60b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 240a c - 240b c)d e + 300b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 24c e x + (75b c e - 30c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((80a c + 80b c)e - 100b c d e + 40c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (180a b c + 30b )e + (- 120a c - 120b c)d e + 150b c d e +--R + +--R 3 3 2 +--R - 60c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (120a c + 120a b )e + (- 360a b c - 60b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (240a c + 240b c)d e - 300b c d e + 120c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (180a b c + 30b )d e + (- 280a c - 280b c)d e + 575b c d e - 326c d +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 182 + +--S 183 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 2 4 3 2 3 +--R 60a b e + (- 120a c - 120a b )d e + (360a b c + 60b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 240a c - 240b c)d e + 300b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 24c e x + (75b c e - 30c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((80a c + 80b c)e - 100b c d e + 40c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (180a b c + 30b )e + (- 120a c - 120b c)d e + 150b c d e +--R + +--R 3 3 2 +--R - 60c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (120a c + 120a b )e + (- 360a b c - 60b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (240a c + 240b c)d e - 300b c d e + 120c d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 180a b c - 30b )d e + (280a c + 280b c)d e - 575b c d e + 326c d +--R ----------------------------------------------------------------------- +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 184 + +--S 185 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 845 +r0:=-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*x/e^5+_ + (2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x))+2*c*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^2/e^6-5/3*c^2*(2*c*d-b*e)*_ + (d+e*x)^3/e^6+1/2*c^3*(d+e*x)^4/e^6+2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 5 3 4 +--R (12a c + 12a b )e + (- 72a b c - 12b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (72a c + 72b c)d e - 120b c d e + 60c d e +--R * +--R x +--R + +--R 2 2 4 3 2 3 2 2 3 2 +--R (12a c + 12a b )d e + (- 72a b c - 12b )d e + (72a c + 72b c)d e +--R + +--R 2 4 3 5 +--R - 120b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 3c e x + (10b c e - 5c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 20b c d e + 10c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((36a b c + 6b )e + (- 36a c - 36b c)d e + 60b c d e - 30c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((36a b c + 6b )d e + (- 36a c - 36b c)d e + 40b c d e - 5c d e)x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 6a b e + (12a c + 12a b )d e + (- 36a b c - 6b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (36a c + 36b c)d e - 80b c d e + 55c d +--R / +--R 7 6 +--R 6e x + 6d e +--R Type: Expression(Integer) +--E 187 + +--S 188 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 5 3 4 +--R (12a c + 12a b )e + (- 72a b c - 12b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (72a c + 72b c)d e - 120b c d e + 60c d e +--R * +--R x +--R + +--R 2 2 4 3 2 3 2 2 3 2 +--R (12a c + 12a b )d e + (- 72a b c - 12b )d e + (72a c + 72b c)d e +--R + +--R 2 4 3 5 +--R - 120b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 3c e x + (10b c e - 5c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 20b c d e + 10c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((36a b c + 6b )e + (- 36a c - 36b c)d e + 60b c d e - 30c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((36a b c + 6b )d e + (- 48a c - 48b c)d e + 90b c d e - 48c d e)x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 6a b e + (12a c + 12a b )d e + (- 36a b c - 6b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (24a c + 24b c)d e - 30b c d e + 12c d +--R / +--R 7 6 +--R 6e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 845 +m0:=a0-r0 +--R +--R +--R 2 2 2 2 2 3 3 4 +--R (- 12a c - 12b c)d e + 50b c d e - 43c d +--R (4) ------------------------------------------- +--R 6 +--R 6e +--R Type: Expression(Integer) +--E 189 + +--S 190 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 845 +r0:=c*(12*c^2*d^2+4*b^2*e^2-c*e*(15*b*d-4*a*e))*x/e^5-1/2*c^2*(6*c*d-_ + 5*b*e)*x^2/e^4+2/3*c^3*x^3/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+_ + a*e^2)^2/(e^6*(d+e*x)^2)-2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))/(e^6*(d+e*x))-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 2 2 4 2 2 3 +--R (36a b c + 6b )e + (- 72a c - 72b c)d e + 180b c d e +--R + +--R 3 3 2 +--R - 120c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (72a b c + 12b )d e + (- 144a c - 144b c)d e + 360b c d e +--R + +--R 3 4 +--R - 240c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (36a b c + 6b )d e + (- 72a c - 72b c)d e + 180b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 4c e x + (15b c e - 10c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((24a c + 24b c)e - 60b c d e + 40c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((48a c + 48b c)d e - 165b c d e + 126c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 12a c - 12a b )e + (72a b c + 12b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 30b c d e + 12c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 6a c - 6a b )d e + (54a b c + 9b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 60a c - 60b c)d e + 105b c d e - 54c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 192 + +--S 193 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 2 2 4 2 2 3 +--R (36a b c + 6b )e + (- 72a c - 72b c)d e + 180b c d e +--R + +--R 3 3 2 +--R - 120c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (72a b c + 12b )d e + (- 144a c - 144b c)d e + 360b c d e +--R + +--R 3 4 +--R - 240c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (36a b c + 6b )d e + (- 72a c - 72b c)d e + 180b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 4c e x + (15b c e - 10c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((24a c + 24b c)e - 60b c d e + 40c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((48a c + 48b c)d e - 165b c d e + 126c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 12a c - 12a b )e + (72a b c + 12b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 30b c d e + 12c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 6a c - 6a b )d e + (54a b c + 9b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 60a c - 60b c)d e + 105b c d e - 54c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 845 +r0:=-c^2*(8*c*d-5*b*e)*x/e^5+c^3*x^2/e^4+1/3*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^2/(e^6*(d+e*x)^3)-(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))/(e^6*(d+e*x)^2)+(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))/(e^6*(d+e*x))+4*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 60b c d e + 60c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e )x +--R + +--R 2 2 2 3 2 3 2 3 4 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e)x +--R + +--R 2 2 3 2 2 4 3 5 +--R (12a c + 12b c)d e - 60b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 2 4 3 2 3 3 +--R 3c e x + (15b c e - 15c d e )x + (45b c d e - 63c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 18a b c - 3b )e + (36a c + 36b c)d e - 45b c d e - 9c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 3a c - 3a b )e + (- 18a b c - 3b )d e + (54a c + 54b c)d e +--R + +--R 2 3 2 3 4 +--R - 135b c d e + 81c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (- a c - a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (22a c + 22b c)d e - 65b c d e + 47c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Expression(Integer) +--E 197 + +--S 198 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 60b c d e + 60c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e )x +--R + +--R 2 2 2 3 2 3 2 3 4 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e)x +--R + +--R 2 2 3 2 2 4 3 5 +--R (12a c + 12b c)d e - 60b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 2 4 3 2 3 3 +--R 3c e x + (15b c e - 15c d e )x + (45b c d e - 63c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 18a b c - 3b )e + (36a c + 36b c)d e - 45b c d e - 9c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 3a c - 3a b )e + (- 18a b c - 3b )d e + (54a c + 54b c)d e +--R + +--R 2 3 2 3 4 +--R - 135b c d e + 81c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (- a c - a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (22a c + 22b c)d e - 65b c d e + 47c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 845 +r0:=2*c^3*x/e^5+1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^4)-_ + 2/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/_ + (e^6*(d+e*x)^3)+1/2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-_ + 3*a*e))/(e^6*(d+e*x)^2)-4*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/_ + (e^6*(d+e*x))-5*c^2*(2*c*d-b*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 3 4 4 2 4 3 2 3 3 +--R (60b c e - 120c d e )x + (240b c d e - 480c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 3 4 2 4 +--R (360b c d e - 720c d e )x + (240b c d e - 480c d e)x + 60b c d e +--R + +--R 3 5 +--R - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 3 4 4 2 2 5 2 4 3 2 3 3 +--R 24c e x + 96c d e x + ((- 48a c - 48b c)e + 240b c d e - 96c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 36a b c - 6b )e + (- 72a c - 72b c)d e + 540b c d e +--R + +--R 3 3 2 +--R - 504c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 8a c - 8a b )e + (- 24a b c - 4b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 440b c d e - 496c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 2a c - 2a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12a c - 12b c)d e + 125b c d e - 154c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 202 + +--S 203 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 3 4 4 2 4 3 2 3 3 +--R (60b c e - 120c d e )x + (240b c d e - 480c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 3 4 2 4 +--R (360b c d e - 720c d e )x + (240b c d e - 480c d e)x + 60b c d e +--R + +--R 3 5 +--R - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 3 4 4 2 2 5 2 4 3 2 3 3 +--R 24c e x + 96c d e x + ((- 48a c - 48b c)e + 240b c d e - 96c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 36a b c - 6b )e + (- 72a c - 72b c)d e + 540b c d e +--R + +--R 3 3 2 +--R - 504c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 8a c - 8a b )e + (- 24a b c - 4b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 440b c d e - 496c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 2a c - 2a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12a c - 12b c)d e + 125b c d e - 154c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 845 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 845 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))+_ + (c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(2+m)/(e^8*(2+m))-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(3+m)/(e^8*(3+m))+_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*_ + (7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*_ + (d+e*x)^(4+m)/(e^8*(4+m))-5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^(5+m)/(e^8*(5+m))+3*c^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(6+m)/(e^8*(6+m))-_ + 7*c^3*(2*c*d-b*e)*(d+e*x)^(7+m)/(e^8*(7+m))+2*c^4*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 4 7 4 6 4 5 4 4 4 3 4 2 +--R 2c m + 56c m + 644c m + 3920c m + 13538c m + 26264c m +--R + +--R 4 4 +--R 26136c m + 10080c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 4 7 3 4 6 3 4 5 +--R (7b c e - 14c d)m + (203b c e - 406c d)m + (2401b c e - 4802c d)m +--R + +--R 3 4 4 3 4 3 +--R (14945b c e - 29890c d)m + (52528b c e - 105056c d)m +--R + +--R 3 4 2 3 4 3 +--R (103292b c e - 206584c d)m + (103824b c e - 207648c d)m + 40320b c e +--R + +--R 4 +--R - 80640c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 3 2 2 2 3 4 2 7 +--R ((6a c + 9b c )e - 42b c d e + 42c d )m +--R + +--R 3 2 2 2 3 4 2 6 +--R ((180a c + 270b c )e - 1260b c d e + 1260c d )m +--R + +--R 3 2 2 2 3 4 2 5 +--R ((2196a c + 3294b c )e - 15372b c d e + 15372c d )m +--R + +--R 3 2 2 2 3 4 2 4 +--R ((14040a c + 21060b c )e - 98280b c d e + 98280c d )m +--R + +--R 3 2 2 2 3 4 2 3 +--R ((50454a c + 75681b c )e - 353178b c d e + 353178c d )m +--R + +--R 3 2 2 2 3 4 2 2 +--R ((100980a c + 151470b c )e - 706860b c d e + 706860c d )m +--R + +--R 3 2 2 2 3 4 2 +--R ((102864a c + 154296b c )e - 720048b c d e + 720048c d )m +--R + +--R 3 2 2 2 3 4 2 +--R (40320a c + 60480b c )e - 282240b c d e + 282240c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 3 3 2 2 2 3 2 +--R (15a b c + 5b c)e + (- 30a c - 45b c )d e + 105b c d e +--R + +--R 4 3 +--R - 70c d +--R * +--R 7 +--R m +--R + +--R 2 3 3 3 2 2 2 3 2 +--R (465a b c + 155b c)e + (- 930a c - 1395b c )d e + 3255b c d e +--R + +--R 4 3 +--R - 2170c d +--R * +--R 6 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (5865a b c + 1955b c)e + (- 11730a c - 17595b c )d e +--R + +--R 3 2 4 3 +--R 41055b c d e - 27370c d +--R * +--R 5 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (38715a b c + 12905b c)e + (- 77430a c - 116145b c )d e +--R + +--R 3 2 4 3 +--R 271005b c d e - 180670c d +--R * +--R 4 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (143160a b c + 47720b c)e + (- 286320a c - 429480b c )d e +--R + +--R 3 2 4 3 +--R 1002120b c d e - 668080c d +--R * +--R 3 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (293460a b c + 97820b c)e + (- 586920a c - 880380b c )d e +--R + +--R 3 2 4 3 +--R 2054220b c d e - 1369480c d +--R * +--R 2 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (304560a b c + 101520b c)e + (- 609120a c - 913680b c )d e +--R + +--R 3 2 4 3 +--R 2131920b c d e - 1421280c d +--R * +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (120960a b c + 40320b c)e + (- 241920a c - 362880b c )d e +--R + +--R 3 2 4 3 +--R 846720b c d e - 564480c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c + 12a b c + b )e + (- 60a b c - 20b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (60a c + 90b c )d e - 140b c d e + 70c d +--R * +--R 7 +--R m +--R + +--R 2 2 2 4 4 2 3 3 +--R (192a c + 384a b c + 32b )e + (- 1920a b c - 640b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (1920a c + 2880b c )d e - 4480b c d e + 2240c d +--R * +--R 6 +--R m +--R + +--R 2 2 2 4 4 2 3 3 +--R (2508a c + 5016a b c + 418b )e + (- 25080a b c - 8360b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (25080a c + 37620b c )d e - 58520b c d e + 29260c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 4 4 +--R (17184a c + 34368a b c + 2864b )e +--R + +--R 2 3 3 3 2 2 2 2 +--R (- 171840a b c - 57280b c)d e + (171840a c + 257760b c )d e +--R + +--R 3 3 4 4 +--R - 400960b c d e + 200480c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 4 4 +--R (65958a c + 131916a b c + 10993b )e +--R + +--R 2 3 3 3 2 2 2 2 +--R (- 659580a b c - 219860b c)d e + (659580a c + 989370b c )d e +--R + +--R 3 3 4 4 +--R - 1539020b c d e + 769510c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 4 4 +--R (139872a c + 279744a b c + 23312b )e +--R + +--R 2 3 3 +--R (- 1398720a b c - 466240b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (1398720a c + 2098080b c )d e - 3263680b c d e + 1631840c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 4 4 +--R 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c + 420a b c + 35b )d e + (- 525a b c - 175b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (210a c + 315b c )d e - 245b c d e + 70c d +--R * +--R 6 +--R m +--R + +--R 3 7 3 2 2 6 +--R - 511a b e + (1022a c + 1533a b )d e +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (- 4599a b c - 1533a b )d e + (3066a c + 6132a b c + 511b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 7665a b c - 2555b c)d e + (3066a c + 4599b c )d e +--R + +--R 3 6 4 7 +--R - 3577b c d e + 1022c d +--R * +--R 5 +--R m +--R + +--R 3 7 3 2 2 6 +--R - 4025a b e + (8050a c + 12075a b )d e +--R + +--R 2 3 2 5 +--R (- 36225a b c - 12075a b )d e +--R + +--R 2 2 2 4 3 4 +--R (24150a c + 48300a b c + 4025b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 60375a b c - 20125b c)d e + (24150a c + 36225b c )d e +--R + +--R 3 6 4 7 +--R - 28175b c d e + 8050c d +--R * +--R 4 +--R m +--R + +--R 3 7 3 2 2 6 +--R - 18424a b e + (36848a c + 55272a b )d e +--R + +--R 2 3 2 5 +--R (- 165816a b c - 55272a b )d e +--R + +--R 2 2 2 4 3 4 +--R (110544a c + 221088a b c + 18424b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 276360a b c - 92120b c)d e + (110544a c + 165816b c )d e +--R + +--R 3 6 4 7 +--R - 128968b c d e + 36848c d +--R * +--R 3 +--R m +--R + +--R 3 7 3 2 2 6 +--R - 48860a b e + (97720a c + 146580a b )d e +--R + +--R 2 3 2 5 +--R (- 439740a b c - 146580a b )d e +--R + +--R 2 2 2 4 3 4 +--R (293160a c + 586320a b c + 48860b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 732900a b c - 244300b c)d e + (293160a c + 439740b c )d e +--R + +--R 3 6 4 7 +--R - 342020b c d e + 97720c d +--R * +--R 2 +--R m +--R + +--R 3 7 3 2 2 6 +--R - 69264a b e + (138528a c + 207792a b )d e +--R + +--R 2 3 2 5 +--R (- 623376a b c - 207792a b )d e +--R + +--R 2 2 2 4 3 4 +--R (415584a c + 831168a b c + 69264b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 1038960a b c - 346320b c)d e + (415584a c + 623376b c )d e +--R + +--R 3 6 4 7 +--R - 484848b c d e + 138528c d +--R * +--R m +--R + +--R 3 7 3 2 2 6 +--R - 40320a b e + (80640a c + 120960a b )d e +--R + +--R 2 3 2 5 +--R (- 362880a b c - 120960a b )d e +--R + +--R 2 2 2 4 3 4 +--R (241920a c + 483840a b c + 40320b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 604800a b c - 201600b c)d e + (241920a c + 362880b c )d e +--R + +--R 3 6 4 7 +--R - 282240b c d e + 80640c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 209 + +--S 210 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 7 7 3 7 6 3 2 2 7 5 2 3 7 4 +--R 2c e x + 7b c e x + (6a c + 9b c )e x + (15a b c + 5b c)e x +--R + +--R 2 2 2 4 7 3 2 3 7 2 3 2 2 7 +--R (6a c + 12a b c + b )e x + (9a b c + 3a b )e x + (2a c + 3a b )e x +--R + +--R 3 7 +--R a b e +--R * +--R m log(e x + d) +--R %e +--R + +--R 4 m + 7 3 4 m + 6 +--R - 2c (e x + d) + (- 7b c e + 14c d)(e x + d) +--R + +--R 3 2 2 2 3 4 2 m + 5 +--R ((- 6a c - 9b c )e + 42b c d e - 42c d )(e x + d) +--R + +--R 2 3 3 3 2 2 2 3 2 4 3 +--R ((- 15a b c - 5b c)e + (30a c + 45b c )d e - 105b c d e + 70c d ) +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 6a c - 12a b c - b )e + (60a b c + 20b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 60a c - 90b c )d e + 140b c d e - 70c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 3 5 2 2 2 4 4 +--R (- 9a b c - 3a b )e + (18a c + 36a b c + 3b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 4 5 +--R (- 90a b c - 30b c)d e + (60a c + 90b c )d e - 105b c d e + 42c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 6 2 3 5 +--R (- 2a c - 3a b )e + (18a b c + 6a b )d e +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (- 18a c - 36a b c - 3b )d e + (60a b c + 20b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (- 30a c - 45b c )d e + 42b c d e - 14c d +--R * +--R m + 1 +--R (e x + d) +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - a b e + (2a c + 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (6a c + 12a b c + b )d e + (- 15a b c - 5b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (6a c + 9b c )d e - 7b c d e + 2c d +--R * +--R m +--R (e x + d) +--R / +--R 7 +--R e +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 845 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 4 11 3 4 4 3 10 +--R 2c e x + (7b c e + 8c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 9 +--R ((6a c + 9b c )e + 28b c d e + 12c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 8 +--R ((15a b c + 5b c)e + (24a c + 36b c )d e + 42b c d e + 8c d e)x +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c + 12a b c + b )e + (60a b c + 20b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (36a c + 54b c )d e + 28b c d e + 2c d +--R * +--R 7 +--R x +--R + +--R 2 3 4 2 2 2 4 3 +--R (9a b c + 3a b )e + (24a c + 48a b c + 4b )d e +--R + +--R 2 3 2 2 3 2 2 3 3 4 +--R (90a b c + 30b c)d e + (24a c + 36b c )d e + 7b c d +--R * +--R 6 +--R x +--R + +--R 3 2 2 4 2 3 3 +--R (2a c + 3a b )e + (36a b c + 12a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 3 2 2 4 +--R (36a c + 72a b c + 6b )d e + (60a b c + 20b c)d e + (6a c + 9b c )d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 +--R a b e + (8a c + 12a b )d e + (54a b c + 18a b )d e +--R + +--R 2 2 2 4 3 2 3 4 +--R (24a c + 48a b c + 4b )d e + (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 3 3 2 2 2 2 2 3 3 +--R 4a b d e + (12a c + 18a b )d e + (36a b c + 12a b )d e +--R + +--R 2 2 2 4 4 +--R (6a c + 12a b c + b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 3 2 3 4 2 +--R (6a b d e + (8a c + 12a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 3 2 2 4 3 4 +--R (4a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 845 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^5/e^8+1/6*(c*d^2-b*d*e+_ + a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^6/e^8-_ + 3/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^7/e^8+1/8*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+_ + a^2*e^2))*(d+e*x)^8/e^8-5/9*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^9/e^8+3/10*c^2*(14*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(7*b*d-a*e))*(d+e*x)^10/e^8-7/11*c^3*(2*c*d-b*e)*_ + (d+e*x)^11/e^8+1/6*c^4*(d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 4 12 12 7 3 12 8 4 11 11 +--R - c e x + (-- b c e + -- c d e )x +--R 6 11 11 +--R + +--R 3 3 9 2 2 12 14 3 11 6 4 2 10 10 +--R ((- a c + -- b c )e + -- b c d e + - c d e )x +--R 5 10 5 5 +--R + +--R 5 2 5 3 12 8 3 2 2 11 14 3 2 10 +--R (- a b c + - b c)e + (- a c + 4b c )d e + -- b c d e +--R 3 9 3 3 +--R + +--R 8 4 3 9 +--R - c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 2 3 2 1 4 12 15 2 5 3 11 +--R (- a c + - a b c + - b )e + (-- a b c + - b c)d e +--R 4 2 8 2 2 +--R + +--R 9 3 27 2 2 2 10 7 3 3 9 1 4 4 8 +--R (- a c + -- b c )d e + - b c d e + - c d e +--R 2 4 2 4 +--R * +--R 8 +--R x +--R + +--R 9 2 3 3 12 24 2 2 48 2 4 4 11 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 7 7 7 7 7 +--R + +--R 90 2 30 3 2 10 24 3 36 2 2 3 9 3 4 8 +--R (-- a b c + -- b c)d e + (-- a c + -- b c )d e + b c d e +--R 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 1 2 2 12 2 3 11 +--R (- a c + - a b )e + (6a b c + 2a b )d e +--R 3 2 +--R + +--R 2 2 2 4 2 10 2 10 3 3 9 +--R (6a c + 12a b c + b )d e + (10a b c + -- b c)d e +--R 3 +--R + +--R 3 3 2 2 4 8 +--R (a c + - b c )d e +--R 2 +--R * +--R 6 +--R x +--R + +--R 1 3 12 8 3 12 2 2 11 54 2 18 3 2 10 +--R - a b e + (- a c + -- a b )d e + (-- a b c + -- a b )d e +--R 5 5 5 5 5 +--R + +--R 24 2 2 48 2 4 4 3 9 2 3 4 8 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d e +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 11 3 9 2 2 2 10 2 3 3 9 +--R a b d e + (3a c + - a b )d e + (9a b c + 3a b )d e +--R 2 +--R + +--R 3 2 2 2 1 4 4 8 +--R (- a c + 3a b c + - b )d e +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 2 10 8 3 2 2 3 9 2 3 4 8 3 +--R (2a b d e + (- a c + 4a b )d e + (3a b c + a b )d e )x +--R 3 +--R + +--R 3 3 9 3 3 2 2 4 8 2 3 4 8 1 3 5 7 +--R (2a b d e + (a c + - a b )d e )x + a b d e x + - a b d e +--R 2 5 +--R + +--R 1 3 1 2 2 6 6 3 2 1 3 7 5 +--R (- -- a c - -- a b )d e + (-- a b c + -- a b )d e +--R 15 10 35 35 +--R + +--R 3 2 2 3 2 1 4 8 4 1 2 1 3 9 3 +--R (- --- a c - -- a b c - --- b )d e + (-- a b c + --- b c)d e +--R 140 70 280 42 126 +--R + +--R 1 3 1 2 2 10 2 1 3 11 1 4 12 +--R (- --- a c - --- b c )d e + --- b c d e - ---- c d +--R 210 140 330 1980 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 212 + +--S 213 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 4 12 7 3 4 8 4 3 11 +--R - c e x + (-- b c e + -- c d e )x +--R 6 11 11 +--R + +--R 3 3 9 2 2 4 14 3 3 6 4 2 2 10 +--R ((- a c + -- b c )e + -- b c d e + - c d e )x +--R 5 10 5 5 +--R + +--R 5 2 5 3 4 8 3 2 2 3 14 3 2 2 8 4 3 9 +--R ((- a b c + - b c)e + (- a c + 4b c )d e + -- b c d e + - c d e)x +--R 3 9 3 3 9 +--R + +--R 3 2 2 3 2 1 4 4 15 2 5 3 3 +--R (- a c + - a b c + - b )e + (-- a b c + - b c)d e +--R 4 2 8 2 2 +--R + +--R 9 3 27 2 2 2 2 7 3 3 1 4 4 +--R (- a c + -- b c )d e + - b c d e + - c d +--R 2 4 2 4 +--R * +--R 8 +--R x +--R + +--R 9 2 3 3 4 24 2 2 48 2 4 4 3 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 7 7 7 7 7 +--R + +--R 90 2 30 3 2 2 24 3 36 2 2 3 3 4 +--R (-- a b c + -- b c)d e + (-- a c + -- b c )d e + b c d +--R 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 1 2 2 4 2 3 3 2 2 2 4 2 2 +--R (- a c + - a b )e + (6a b c + 2a b )d e + (6a c + 12a b c + b )d e +--R 3 2 +--R + +--R 2 10 3 3 3 3 2 2 4 +--R (10a b c + -- b c)d e + (a c + - b c )d +--R 3 2 +--R * +--R 6 +--R x +--R + +--R 1 3 4 8 3 12 2 2 3 54 2 18 3 2 2 +--R - a b e + (- a c + -- a b )d e + (-- a b c + -- a b )d e +--R 5 5 5 5 5 +--R + +--R 24 2 2 48 2 4 4 3 2 3 4 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 3 3 9 2 2 2 2 2 3 3 +--R a b d e + (3a c + - a b )d e + (9a b c + 3a b )d e +--R 2 +--R + +--R 3 2 2 2 1 4 4 +--R (- a c + 3a b c + - b )d +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 2 2 8 3 2 2 3 2 3 4 3 +--R (2a b d e + (- a c + 4a b )d e + (3a b c + a b )d )x +--R 3 +--R + +--R 3 3 3 3 2 2 4 2 3 4 +--R (2a b d e + (a c + - a b )d )x + a b d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 5 7 1 3 1 2 2 6 6 3 2 1 3 7 5 +--R - - a b d e + (-- a c + -- a b )d e + (- -- a b c - -- a b )d e +--R 5 15 10 35 35 +--R + +--R 3 2 2 3 2 1 4 8 4 1 2 1 3 9 3 +--R (--- a c + -- a b c + --- b )d e + (- -- a b c - --- b c)d e +--R 140 70 280 42 126 +--R + +--R 1 3 1 2 2 10 2 1 3 11 1 4 12 +--R (--- a c + --- b c )d e - --- b c d e + ---- c d +--R 210 140 330 1980 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 214 + +--S 215 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 3 10 3 3 4 2 9 +--R 2c e x + (7b c e + 6c d e )x +--R + +--R 3 2 2 3 3 2 4 2 8 +--R ((6a c + 9b c )e + 21b c d e + 6c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 4 3 7 +--R ((15a b c + 5b c)e + (18a c + 27b c )d e + 21b c d e + 2c d )x +--R + +--R 2 2 2 4 3 2 3 2 +--R (6a c + 12a b c + b )e + (45a b c + 15b c)d e +--R + +--R 3 2 2 2 3 3 +--R (18a c + 27b c )d e + 7b c d +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 2 2 4 2 +--R (9a b c + 3a b )e + (18a c + 36a b c + 3b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (45a b c + 15b c)d e + (6a c + 9b c )d +--R * +--R 5 +--R x +--R + +--R 3 2 2 3 2 3 2 2 2 2 4 2 +--R (2a c + 3a b )e + (27a b c + 9a b )d e + (18a c + 36a b c + 3b )d e +--R + +--R 2 3 3 +--R (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 3 3 2 2 2 2 3 2 +--R a b e + (6a c + 9a b )d e + (27a b c + 9a b )d e +--R + +--R 2 2 2 4 3 +--R (6a c + 12a b c + b )d +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 9a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 2 3 2 2 3 3 3 +--R (3a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 845 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^4/e^8+1/5*(c*d^2-b*d*e+_ + a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^5/e^8-_ + 1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^6/e^8+1/7*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-_ + 10*a*b*d*e+a^2*e^2))*(d+e*x)^7/e^8-5/8*c*(2*c*d-b*e)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^8/e^8+1/3*c^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^9/e^8-7/10*c^3*(2*c*d-b*e)*_ + (d+e*x)^10/e^8+2/11*c^4*(d+e*x)^11/e^8 +--R +--R +--R (2) +--R 2 4 11 11 7 3 11 3 4 10 10 +--R -- c e x + (-- b c e + - c d e )x +--R 11 10 5 +--R + +--R 2 3 2 2 11 7 3 10 2 4 2 9 9 +--R ((- a c + b c )e + - b c d e + - c d e )x +--R 3 3 3 +--R + +--R 15 2 5 3 11 9 3 27 2 2 10 21 3 2 9 +--R (-- a b c + - b c)e + (- a c + -- b c )d e + -- b c d e +--R 8 8 4 8 8 +--R + +--R 1 4 3 8 +--R - c d e +--R 4 +--R * +--R 8 +--R x +--R + +--R 6 2 2 12 2 1 4 11 45 2 15 3 10 +--R (- a c + -- a b c + - b )e + (-- a b c + -- b c)d e +--R 7 7 7 7 7 +--R + +--R 18 3 27 2 2 2 9 3 3 8 +--R (-- a c + -- b c )d e + b c d e +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 1 3 11 2 2 2 1 4 10 +--R (- a b c + - a b )e + (3a c + 6a b c + - b )d e +--R 2 2 2 +--R + +--R 15 2 5 3 2 9 3 3 2 2 3 8 +--R (-- a b c + - b c)d e + (a c + - b c )d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 2 11 27 2 9 3 10 +--R (- a c + - a b )e + (-- a b c + - a b )d e +--R 5 5 5 5 +--R + +--R 18 2 2 36 2 3 4 2 9 2 3 3 8 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d e +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 11 3 3 9 2 2 10 27 2 9 3 2 9 +--R - a b e + (- a c + - a b )d e + (-- a b c + - a b )d e +--R 4 2 4 4 4 +--R + +--R 3 2 2 2 1 4 3 8 +--R (- a c + 3a b c + - b )d e +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 10 3 2 2 2 9 2 3 3 8 3 +--R (a b d e + (2a c + 3a b )d e + (3a b c + a b )d e )x +--R + +--R 3 3 2 9 3 3 2 2 3 8 2 3 3 8 1 3 4 7 +--R (- a b d e + (a c + - a b )d e )x + a b d e x + - a b d e +--R 2 2 4 +--R + +--R 1 3 3 2 2 5 6 3 2 1 3 6 5 +--R (- -- a c - -- a b )d e + (-- a b c + -- a b )d e +--R 10 20 20 20 +--R + +--R 3 2 2 3 2 1 4 7 4 3 2 1 3 8 3 +--R (- -- a c - -- a b c - --- b )d e + (-- a b c + -- b c)d e +--R 70 35 140 56 56 +--R + +--R 1 3 1 2 2 9 2 1 3 10 1 4 11 +--R (- -- a c - -- b c )d e + --- b c d e - --- c d +--R 84 56 120 660 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 217 + +--S 218 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 11 7 3 3 3 4 2 10 +--R -- c e x + (-- b c e + - c d e )x +--R 11 10 5 +--R + +--R 2 3 2 2 3 7 3 2 2 4 2 9 +--R ((- a c + b c )e + - b c d e + - c d e)x +--R 3 3 3 +--R + +--R 15 2 5 3 3 9 3 27 2 2 2 21 3 2 1 4 3 8 +--R ((-- a b c + - b c)e + (- a c + -- b c )d e + -- b c d e + - c d )x +--R 8 8 4 8 8 4 +--R + +--R 6 2 2 12 2 1 4 3 45 2 15 3 2 +--R (- a c + -- a b c + - b )e + (-- a b c + -- b c)d e +--R 7 7 7 7 7 +--R + +--R 18 3 27 2 2 2 3 3 +--R (-- a c + -- b c )d e + b c d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 1 3 3 2 2 2 1 4 2 +--R (- a b c + - a b )e + (3a c + 6a b c + - b )d e +--R 2 2 2 +--R + +--R 15 2 5 3 2 3 3 2 2 3 +--R (-- a b c + - b c)d e + (a c + - b c )d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 2 3 27 2 9 3 2 +--R (- a c + - a b )e + (-- a b c + - a b )d e +--R 5 5 5 5 +--R + +--R 18 2 2 36 2 3 4 2 2 3 3 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 3 3 3 9 2 2 2 27 2 9 3 2 +--R - a b e + (- a c + - a b )d e + (-- a b c + - a b )d e +--R 4 2 4 4 4 +--R + +--R 3 2 2 2 1 4 3 +--R (- a c + 3a b c + - b )d +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 2 3 2 2 2 2 3 3 3 +--R (a b d e + (2a c + 3a b )d e + (3a b c + a b )d )x +--R + +--R 3 3 2 3 3 2 2 3 2 3 3 +--R (- a b d e + (a c + - a b )d )x + a b d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 4 7 1 3 3 2 2 5 6 3 2 1 3 6 5 +--R - - a b d e + (-- a c + -- a b )d e + (- -- a b c - -- a b )d e +--R 4 10 20 20 20 +--R + +--R 3 2 2 3 2 1 4 7 4 3 2 1 3 8 3 +--R (-- a c + -- a b c + --- b )d e + (- -- a b c - -- b c)d e +--R 70 35 140 56 56 +--R + +--R 1 3 1 2 2 9 2 1 3 10 1 4 11 +--R (-- a c + -- b c )d e - --- b c d e + --- c d +--R 84 56 120 660 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 219 + +--S 220 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 2 9 3 2 4 8 3 2 2 2 3 4 2 7 +--R 2c e x + (7b c e + 4c d e)x + ((6a c + 9b c )e + 14b c d e + 2c d )x +--R + +--R 2 3 2 3 2 2 3 2 6 +--R ((15a b c + 5b c)e + (12a c + 18b c )d e + 7b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 2 2 5 +--R ((6a c + 12a b c + b )e + (30a b c + 10b c)d e + (6a c + 9b c )d )x +--R + +--R 2 3 2 2 2 2 4 2 3 2 4 +--R ((9a b c + 3a b )e + (12a c + 24a b c + 2b )d e + (15a b c + 5b c)d )x +--R + +--R 3 2 2 2 2 3 2 2 2 4 2 3 +--R ((2a c + 3a b )e + (18a b c + 6a b )d e + (6a c + 12a b c + b )d )x +--R + +--R 3 2 3 2 2 2 3 2 2 +--R (a b e + (4a c + 6a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 2 2 2 3 2 +--R (2a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 845 +r0:=a^3*b*d^2*x+1/2*a^2*d*(3*b^2*d+2*a*c*d+2*a*b*e)*x^2+1/3*a*(3*b^3*d^2+_ + 6*a*b^2*d*e+4*a^2*c*d*e+a*b*(9*c*d^2+a*e^2))*x^3+1/4*(b^4*d^2+_ + 6*a*b^3*d*e+18*a^2*b*c*d*e+2*a^2*c*(3*c*d^2+a*e^2)+3*a*b^2*(4*c*d^2+_ + a*e^2))*x^4+1/5*(2*b^4*d*e+24*a*b^2*c*d*e+12*a^2*c^2*d*e+b^3*_ + (5*c*d^2+3*a*e^2)+3*a*b*c*(5*c*d^2+3*a*e^2))*x^5+1/6*(10*b^3*c*d*e+_ + 30*a*b*c^2*d*e+b^4*e^2+6*a*c^2*(c*d^2+a*e^2)+3*b^2*c*(3*c*d^2+_ + 4*a*e^2))*x^6+1/7*c*(18*b^2*c*d*e+12*a*c^2*d*e+5*b^3*e^2+b*c*_ + (7*c*d^2+15*a*e^2))*x^7+1/8*c^2*(2*c^2*d^2+9*b^2*e^2+2*c*e*_ + (7*b*d+3*a*e))*x^8+1/9*c^3*e*(4*c*d+7*b*e)*x^9+1/5*c^4*e^2*x^10 +--R +--R +--R (2) +--R 1 4 2 10 7 3 2 4 4 9 +--R - c e x + (- b c e + - c d e)x +--R 5 9 9 +--R + +--R 3 3 9 2 2 2 7 3 1 4 2 8 +--R ((- a c + - b c )e + - b c d e + - c d )x +--R 4 8 4 4 +--R + +--R 15 2 5 3 2 12 3 18 2 2 3 2 7 +--R ((-- a b c + - b c)e + (-- a c + -- b c )d e + b c d )x +--R 7 7 7 7 +--R + +--R 2 2 2 1 4 2 2 5 3 3 3 2 2 2 6 +--R ((a c + 2a b c + - b )e + (5a b c + - b c)d e + (a c + - b c )d )x +--R 6 3 2 +--R + +--R 9 2 3 3 2 12 2 2 24 2 2 4 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 2 3 2 +--R (3a b c + b c)d +--R * +--R 5 +--R x +--R + +--R 1 3 3 2 2 2 9 2 3 3 3 2 2 2 1 4 2 4 +--R ((- a c + - a b )e + (- a b c + - a b )d e + (- a c + 3a b c + - b )d )x +--R 2 4 2 2 2 4 +--R + +--R 1 3 2 4 3 2 2 2 3 2 3 +--R (- a b e + (- a c + 2a b )d e + (3a b c + a b )d )x +--R 3 3 +--R + +--R 3 3 3 2 2 2 2 3 2 +--R (a b d e + (a c + - a b )d )x + a b d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 2 10 7 3 2 4 4 9 +--R - c e x + (- b c e + - c d e)x +--R 5 9 9 +--R + +--R 3 3 9 2 2 2 7 3 1 4 2 8 +--R ((- a c + - b c )e + - b c d e + - c d )x +--R 4 8 4 4 +--R + +--R 15 2 5 3 2 12 3 18 2 2 3 2 7 +--R ((-- a b c + - b c)e + (-- a c + -- b c )d e + b c d )x +--R 7 7 7 7 +--R + +--R 2 2 2 1 4 2 2 5 3 3 3 2 2 2 6 +--R ((a c + 2a b c + - b )e + (5a b c + - b c)d e + (a c + - b c )d )x +--R 6 3 2 +--R + +--R 9 2 3 3 2 12 2 2 24 2 2 4 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 2 3 2 +--R (3a b c + b c)d +--R * +--R 5 +--R x +--R + +--R 1 3 3 2 2 2 9 2 3 3 3 2 2 2 1 4 2 4 +--R ((- a c + - a b )e + (- a b c + - a b )d e + (- a c + 3a b c + - b )d )x +--R 2 4 2 2 2 4 +--R + +--R 1 3 2 4 3 2 2 2 3 2 3 +--R (- a b e + (- a c + 2a b )d e + (3a b c + a b )d )x +--R 3 3 +--R + +--R 3 3 3 2 2 2 2 3 2 +--R (a b d e + (a c + - a b )d )x + a b d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 845 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 8 3 4 7 3 2 2 3 6 +--R 2c e x + (7b c e + 2c d)x + ((6a c + 9b c )e + 7b c d)x +--R + +--R 2 3 3 2 2 5 +--R ((15a b c + 5b c)e + (6a c + 9b c )d)x +--R + +--R 2 2 2 4 2 3 4 +--R ((6a c + 12a b c + b )e + (15a b c + 5b c)d)x +--R + +--R 2 3 2 2 2 4 3 +--R ((9a b c + 3a b )e + (6a c + 12a b c + b )d)x +--R + +--R 3 2 2 2 3 2 3 3 2 2 3 +--R ((2a c + 3a b )e + (9a b c + 3a b )d)x + (a b e + (2a c + 3a b )d)x + a b d +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 845 +r0:=a^3*b*d*x+1/2*a^2*(3*b^2*d+2*a*c*d+a*b*e)*x^2+1/3*a*(3*b^3*d+_ + 9*a*b*c*d+3*a*b^2*e+2*a^2*c*e)*x^3+1/4*(b^4*d+12*a*b^2*c*d+_ + 6*a^2*c^2*d+3*a*b^3*e+9*a^2*b*c*e)*x^4+1/5*(5*b^3*c*d+15*a*b*c^2*d+_ + b^4*e+12*a*b^2*c*e+6*a^2*c^2*e)*x^5+1/6*c*(9*b^2*c*d+6*a*c^2*d+_ + 5*b^3*e+15*a*b*c*e)*x^6+1/7*c^2*(7*b*c*d+9*b^2*e+6*a*c*e)*x^7+_ + 1/8*c^3*(2*c*d+7*b*e)*x^8+2/9*c^4*e*x^9 +--R +--R +--R (2) +--R 2 4 9 7 3 1 4 8 6 3 9 2 2 3 7 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c )e + b c d)x +--R 9 8 4 7 7 +--R + +--R 5 2 5 3 3 3 2 2 6 +--R ((- a b c + - b c)e + (a c + - b c )d)x +--R 2 6 2 +--R + +--R 6 2 2 12 2 1 4 2 3 5 +--R ((- a c + -- a b c + - b )e + (3a b c + b c)d)x +--R 5 5 5 +--R + +--R 9 2 3 3 3 2 2 2 1 4 4 +--R ((- a b c + - a b )e + (- a c + 3a b c + - b )d)x +--R 4 4 2 4 +--R + +--R 2 3 2 2 2 3 3 1 3 3 3 2 2 2 +--R ((- a c + a b )e + (3a b c + a b )d)x + (- a b e + (a c + - a b )d)x +--R 3 2 2 +--R + +--R 3 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 227 + +--S 228 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 9 7 3 1 4 8 6 3 9 2 2 3 7 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c )e + b c d)x +--R 9 8 4 7 7 +--R + +--R 5 2 5 3 3 3 2 2 6 +--R ((- a b c + - b c)e + (a c + - b c )d)x +--R 2 6 2 +--R + +--R 6 2 2 12 2 1 4 2 3 5 +--R ((- a c + -- a b c + - b )e + (3a b c + b c)d)x +--R 5 5 5 +--R + +--R 9 2 3 3 3 2 2 2 1 4 4 +--R ((- a b c + - a b )e + (- a c + 3a b c + - b )d)x +--R 4 4 2 4 +--R + +--R 2 3 2 2 2 3 3 1 3 3 3 2 2 2 +--R ((- a c + a b )e + (3a b c + a b )d)x + (- a b e + (a c + - a b )d)x +--R 3 2 2 +--R + +--R 3 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 229 + +--S 230 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 230 + +)clear all + +--S 231 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 845 +r0:=1/4*(a+b*x+c*x^2)^4 +--R +--R +--R (2) +--R 1 4 8 3 7 3 3 2 2 6 2 3 5 +--R - c x + b c x + (a c + - b c )x + (3a b c + b c)x +--R 4 2 +--R + +--R 3 2 2 2 1 4 4 2 3 3 3 3 2 2 2 3 +--R (- a c + 3a b c + - b )x + (3a b c + a b )x + (a c + - a b )x + a b x +--R 2 4 2 +--R + +--R 1 4 +--R - a +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 232 + +--S 233 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 8 3 7 3 3 2 2 6 2 3 5 +--R - c x + b c x + (a c + - b c )x + (3a b c + b c)x +--R 4 2 +--R + +--R 3 2 2 2 1 4 4 2 3 3 3 3 2 2 2 3 +--R (- a c + 3a b c + - b )x + (3a b c + a b )x + (a c + - a b )x + a b x +--R 2 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 845 +m0:=a0-r0 +--R +--R +--R 1 4 +--R (4) - - a +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 234 + +--S 235 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 235 + +)clear all + +--S 236 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 845 +r0:=(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*x/e^7-_ + 3/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^2/e^8+1/3*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+_ + a^2*e^2))*(d+e*x)^3/e^8-5/4*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^4/e^8+3/5*c^2*(14*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(7*b*d-a*e))*(d+e*x)^5/e^8-7/6*c^3*(2*c*d-b*e)*(d+e*x)^6/e^8+_ + 2/7*c^4*(d+e*x)^7/e^8-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 2 2 6 2 3 2 5 +--R 420a b e + (- 840a c - 1260a b )d e + (3780a b c + 1260a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 2520a c - 5040a b c - 420b )d e + (6300a b c + 2100b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 2520a c - 3780b c )d e + 2940b c d e - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 120c e x + (490b c e - 140c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((504a c + 756b c )e - 588b c d e + 168c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (1575a b c + 525b c)e + (- 630a c - 945b c )d e + 735b c d e +--R + +--R 4 3 4 +--R - 210c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (840a c + 1680a b c + 140b )e + (- 2100a b c - 700b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (840a c + 1260b c )d e - 980b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (1890a b c + 630a b )e + (- 1260a c - 2520a b c - 210b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (3150a b c + 1050b c)d e + (- 1260a c - 1890b c )d e +--R + +--R 3 4 3 4 5 2 +--R 1470b c d e - 420c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (840a c + 1260a b )e + (- 3780a b c - 1260a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (2520a c + 5040a b c + 420b )d e + (- 6300a b c - 2100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (2520a c + 3780b c )d e - 2940b c d e + 840c d e +--R * +--R x +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (1890a b c + 630a b )d e + (- 2940a c - 5880a b c - 490b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (12075a b c + 4025b c)d e + (- 6846a c - 10269b c )d e + 10437b c d e +--R + +--R 4 7 +--R - 3702c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 237 + +--S 238 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 3 2 2 6 2 3 2 5 +--R 420a b e + (- 840a c - 1260a b )d e + (3780a b c + 1260a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 2520a c - 5040a b c - 420b )d e + (6300a b c + 2100b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 2520a c - 3780b c )d e + 2940b c d e - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 120c e x + (490b c e - 140c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((504a c + 756b c )e - 588b c d e + 168c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (1575a b c + 525b c)e + (- 630a c - 945b c )d e + 735b c d e +--R + +--R 4 3 4 +--R - 210c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (840a c + 1680a b c + 140b )e + (- 2100a b c - 700b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (840a c + 1260b c )d e - 980b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (1890a b c + 630a b )e + (- 1260a c - 2520a b c - 210b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (3150a b c + 1050b c)d e + (- 1260a c - 1890b c )d e +--R + +--R 3 4 3 4 5 2 +--R 1470b c d e - 420c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (840a c + 1260a b )e + (- 3780a b c - 1260a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (2520a c + 5040a b c + 420b )d e + (- 6300a b c - 2100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (2520a c + 3780b c )d e - 2940b c d e + 840c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 5 2 2 2 4 3 4 +--R (- 1890a b c - 630a b )d e + (2940a c + 5880a b c + 490b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (- 12075a b c - 4025b c)d e + (6846a c + 10269b c )d e - 10437b c d e +--R + +--R 4 7 +--R 3702c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 239 + +--S 240 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 845 +r0:=-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*x/e^7+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x))+1/2*_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^2/e^8-_ + 5/3*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^3/e^8+3/4*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^4/e^8-7/5*c^3*(2*c*d-b*e)*(d+e*x)^5/e^8+1/3*c^4*_ + (d+e*x)^6/e^8+(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*_ + (7*b*d-a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 2 7 2 3 6 +--R (120a c + 180a b )e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d e +--R * +--R x +--R + +--R 3 2 2 6 2 3 2 5 +--R (120a c + 180a b )d e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 20c e x + (84b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((90a c + 135b c )e - 126b c d e + 42c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (300a b c + 100b c)e + (- 150a c - 225b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (180a c + 360a b c + 30b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (300a c + 450b c )d e - 420b c d e + 140c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (540a b c + 180a b )e + (- 540a c - 1080a b c - 90b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 3 4 3 +--R (1800a b c + 600b c)d e + (- 900a c - 1350b c )d e + 1260b c d e +--R + +--R 4 5 2 +--R - 420c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (540a b c + 180a b )d e + (- 540a c - 1080a b c - 90b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 3 5 2 +--R (1200a b c + 400b c)d e + (- 150a c - 225b c )d e - 546b c d e +--R + +--R 4 6 +--R 462c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 60a b e + (120a c + 180a b )d e + (- 540a b c - 180a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (540a c + 1080a b c + 90b )d e + (- 2400a b c - 800b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (1650a c + 2475b c )d e - 3066b c d e + 1302c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 242 + +--S 243 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 7 2 3 6 +--R (120a c + 180a b )e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d e +--R * +--R x +--R + +--R 3 2 2 6 2 3 2 5 +--R (120a c + 180a b )d e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 20c e x + (84b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((90a c + 135b c )e - 126b c d e + 42c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (300a b c + 100b c)e + (- 150a c - 225b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (180a c + 360a b c + 30b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (300a c + 450b c )d e - 420b c d e + 140c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (540a b c + 180a b )e + (- 540a c - 1080a b c - 90b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 3 4 3 +--R (1800a b c + 600b c)d e + (- 900a c - 1350b c )d e + 1260b c d e +--R + +--R 4 5 2 +--R - 420c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (540a b c + 180a b )d e + (- 720a c - 1440a b c - 120b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (2700a b c + 900b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 5 2 4 6 +--R 2100b c d e - 720c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 60a b e + (120a c + 180a b )d e + (- 540a b c - 180a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (360a c + 720a b c + 60b )d e + (- 900a b c - 300b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (360a c + 540b c )d e - 420b c d e + 120c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 4 2 4 2 3 3 3 +--R (- 180a c - 360a b c - 30b )d e + (1500a b c + 500b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (- 1290a c - 1935b c )d e + 2646b c d e - 1182c d +--R / +--R 8 +--R 60e +--R Type: Expression(Integer) +--E 244 + +--S 245 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 845 +r0:=(30*c^4*d^4+b^4*e^4-2*c^3*d^2*e*(35*b*d-18*a*e)-3*b^2*c*e^3*_ + (5*b*d-4*a*e)+3*c^2*e^2*(18*b^2*d^2-15*a*b*d*e+2*a^2*e^2))*x/e^7-_ + 1/2*c*(20*c^3*d^3-5*b^3*e^3+3*b*c*e^2*(9*b*d-5*a*e)-6*c^2*d*e*(7*b*d-_ + 3*a*e))*x^2/e^6+c^2*(4*c^2*d^2+3*b^2*e^2-c*e*(7*b*d-2*a*e))*x^3/e^5-_ + 1/4*c^3*(6*c*d-7*b*e)*x^4/e^4+2/5*c^4*x^5/e^3+1/2*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^3/(e^8*(d+e*x)^2)-(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x))-3*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 2 2 2 4 6 +--R (180a b c + 60a b )e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2100b c d e - 840c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (360a b c + 120a b )d e + (- 720a c - 1440a b c - 120b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (3600a b c + 1200b c)d e + (- 2400a c - 3600b c )d e +--R + +--R 3 5 2 4 6 +--R 4200b c d e - 1680c d e +--R * +--R x +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (180a b c + 60a b )d e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e + 2100b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (35b c e - 14c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((40a c + 60b c )e - 70b c d e + 28c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (150a b c + 50b c)e + (- 100a c - 150b c )d e + 175b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (120a c + 240a b c + 20b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (400a c + 600b c )d e - 700b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (240a c + 480a b c + 40b )d e + (- 1650a b c - 550b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1260a c + 1890b c )d e - 2380b c d e + 1000c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 40a c - 60a b )e + (360a b c + 120a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 240a c - 480a b c - 40b )d e + (300a b c + 100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (120a c + 180b c )d e - 560b c d e + 320c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 10a b e + (- 20a c - 30a b )d e + (270a b c + 90a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 300a c - 600a b c - 50b )d e + (1050a b c + 350b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 540a c - 810b c )d e + 770b c d e - 260c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 247 + +--S 248 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 7 2 2 2 4 6 +--R (180a b c + 60a b )e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2100b c d e - 840c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (360a b c + 120a b )d e + (- 720a c - 1440a b c - 120b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (3600a b c + 1200b c)d e + (- 2400a c - 3600b c )d e +--R + +--R 3 5 2 4 6 +--R 4200b c d e - 1680c d e +--R * +--R x +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (180a b c + 60a b )d e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e + 2100b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (35b c e - 14c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((40a c + 60b c )e - 70b c d e + 28c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (150a b c + 50b c)e + (- 100a c - 150b c )d e + 175b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (120a c + 240a b c + 20b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (400a c + 600b c )d e - 700b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (240a c + 480a b c + 40b )d e + (- 1650a b c - 550b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1260a c + 1890b c )d e - 2380b c d e + 1000c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 40a c - 60a b )e + (360a b c + 120a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 240a c - 480a b c - 40b )d e + (300a b c + 100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (120a c + 180b c )d e - 560b c d e + 320c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 10a b e + (- 20a c - 30a b )d e + (270a b c + 90a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 300a c - 600a b c - 50b )d e + (1050a b c + 350b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 540a c - 810b c )d e + 770b c d e - 260c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 845 +r0:=-5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*x/e^7+_ + 1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^3)-1/2*(c*d^2-_ + b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x)^2)+_ + 3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))/(e^8*(d+e*x))+3/2*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^2/e^8-7/3*c^3*(2*c*d-b*e)*(d+e*x)^3/e^8+1/2*c^4*(d+e*x)^4/e^8+_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 2 4 7 2 3 6 +--R (36a c + 72a b c + 6b )e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (360a c + 540b c )d e - 840b c d e + 420c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (36a c + 72a b c + 6b )d e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (360a c + 540b c )d e - 840b c d e + 420c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 3c e x + (14b c e - 7c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((18a c + 27b c )e - 42b c d e + 21c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (90a b c + 30b c)e + (- 90a c - 135b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 105c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 3 3 4 +--R (270a b c + 90b c)d e + (- 360a c - 540b c )d e + 910b c d e +--R + +--R 4 4 3 +--R - 455c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (108a c + 216a b c + 18b )d e +--R + +--R 2 3 2 5 3 4 3 4 5 2 +--R (- 270a b c - 90b c)d e + 210b c d e - 105c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 6a c - 9a b )e + (- 54a b c - 18a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (162a c + 324a b c + 27b )d e + (- 810a b c - 270b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (540a c + 810b c )d e - 1050b c d e + 525c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 2a b e + (- 2a c - 3a b )d e + (- 18a b c - 6a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (66a c + 132a b c + 11b )d e + (- 390a b c - 130b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (300a c + 450b c )d e - 630b c d e + 315c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 252 + +--S 253 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 4 7 2 3 6 +--R (36a c + 72a b c + 6b )e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (360a c + 540b c )d e - 840b c d e + 420c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (36a c + 72a b c + 6b )d e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (360a c + 540b c )d e - 840b c d e + 420c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 3c e x + (14b c e - 7c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((18a c + 27b c )e - 42b c d e + 21c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (90a b c + 30b c)e + (- 90a c - 135b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 105c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 3 3 4 +--R (270a b c + 90b c)d e + (- 378a c - 567b c )d e + 1022b c d e +--R + +--R 4 4 3 +--R - 556c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (108a c + 216a b c + 18b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 3 4 3 +--R (- 270a b c - 90b c)d e + (- 54a c - 81b c )d e + 546b c d e +--R + +--R 4 5 2 +--R - 408c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 6a c - 9a b )e + (- 54a b c - 18a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (162a c + 324a b c + 27b )d e + (- 810a b c - 270b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (486a c + 729b c )d e - 714b c d e + 222c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 2a b e + (- 2a c - 3a b )d e + (- 18a b c - 6a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (66a c + 132a b c + 11b )d e + (- 390a b c - 130b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (282a c + 423b c )d e - 518b c d e + 214c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 845 +m0:=a0-r0 +--R +--R +--R 3 2 2 2 2 3 3 4 4 +--R (- 18a c - 27b c )d e + 112b c d e - 101c d +--R (4) ---------------------------------------------- +--R 8 +--R 6e +--R Type: Expression(Integer) +--E 254 + +--S 255 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 845 +r0:=c^2*(30*c^2*d^2+9*b^2*e^2-c*e*(35*b*d-6*a*e))*x/e^7-1/2*c^3*_ + (10*c*d-7*b*e)*x^2/e^6+2/3*c^4*x^3/e^5+1/4*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^3/(e^8*(d+e*x)^4)-1/3*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x)^3)+3/2*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))/(e^8*(d+e*x)^2)+_ + (-70*c^4*d^4-b^4*e^4+4*b^2*c*e^3*(5*b*d-3*a*e)+20*c^3*d^2*e*(7*b*d-_ + 3*a*e)-6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))/(e^8*(d+e*x))-_ + 5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 3 2 2 6 3 2 5 +--R (180a b c + 60b c)e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 3 4 +--R - 840c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 3 4 4 4 3 +--R 5040b c d e - 3360c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1080a b c + 360b c)d e + (- 2160a c - 3240b c )d e +--R + +--R 3 4 3 4 5 2 +--R 7560b c d e - 5040c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 5 2 4 6 +--R 5040b c d e - 3360c d e +--R * +--R x +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (180a b c + 60b c)d e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (42b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((72a c + 108b c )e - 252b c d e + 168c d e )x +--R + +--R 3 2 2 6 3 2 5 4 3 4 4 +--R ((288a c + 432b c )d e - 1428b c d e + 1112c d e )x +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 72a c - 144a b c - 12b )e + (720a b c + 240b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 288a c - 432b c )d e - 672b c d e + 1088c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (- 108a c - 216a b c - 18b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1620a b c + 540b c)d e + (- 1512a c - 2268b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2772b c d e - 888c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 8a c - 12a b )e + (- 36a b c - 12a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 72a c - 144a b c - 12b )d e + (1320a b c + 440b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 1488a c - 2232b c )d e + 3528b c d e - 1712c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 3a b e + (- 2a c - 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 18a c - 36a b c - 3b )d e + (375a b c + 125b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 462a c - 693b c )d e + 1197b c d e - 638c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 257 + +--S 258 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 7 3 2 2 6 3 2 5 +--R (180a b c + 60b c)e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 3 4 +--R - 840c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 3 4 4 4 3 +--R 5040b c d e - 3360c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1080a b c + 360b c)d e + (- 2160a c - 3240b c )d e +--R + +--R 3 4 3 4 5 2 +--R 7560b c d e - 5040c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 5 2 4 6 +--R 5040b c d e - 3360c d e +--R * +--R x +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (180a b c + 60b c)d e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (42b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((72a c + 108b c )e - 252b c d e + 168c d e )x +--R + +--R 3 2 2 6 3 2 5 4 3 4 4 +--R ((288a c + 432b c )d e - 1428b c d e + 1112c d e )x +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 72a c - 144a b c - 12b )e + (720a b c + 240b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 288a c - 432b c )d e - 672b c d e + 1088c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (- 108a c - 216a b c - 18b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1620a b c + 540b c)d e + (- 1512a c - 2268b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2772b c d e - 888c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 8a c - 12a b )e + (- 36a b c - 12a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 72a c - 144a b c - 12b )d e + (1320a b c + 440b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 1488a c - 2232b c )d e + 3528b c d e - 1712c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 3a b e + (- 2a c - 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 18a c - 36a b c - 3b )d e + (375a b c + 125b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 462a c - 693b c )d e + 1197b c d e - 638c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 845 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 845 +r0:=e*(8*c^3*d^3-b^3*e^3+b*c*e^2*(4*b*d+3*a*e)-2*c^2*d*e*(3*b*d+4*a*e))*_ + x/c^3+1/2*e^2*(12*c^2*d^2+b^2*e^2-2*c*e*(2*b*d+a*e))*x^2/c^2+1/3*e^3*_ + (8*c*d-b*e)*x^3/c+1/2*e^4*x^4+1/2*(2*c^4*d^4+b^4*e^4-4*b^2*c*e^3*_ + (b*d+a*e)-4*c^3*d^2*e*(b*d+3*a*e)+2*c^2*e^2*(3*b^2*d^2+6*a*b*d*e+_ + a^2*e^2))*log(a+b*x+c*x^2)/c^4-e*(2*c*d-b*e)*(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^4 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 12a b c + 6b )e + (24a c - 24b c)d e + 36b c d e - 24c d e) +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c - 12a b c + 3b )e + (36a b c - 12b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 36a c + 18b c )d e - 12b c d e + 6c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3c e x + (- 2b c e + 16c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 2 +--R ((- 6a c + 3b c )e - 12b c d e + 36c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 +--R ((18a b c - 6b c)e + (- 48a c + 24b c )d e - 36b c d e + 48c d e)x +--R / +--R 4 +--R 6c +--R Type: Expression(Integer) +--E 262 + +--S 263 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 2 3 2 2 2 3 3 +--R ((6a b c - 3b )e + (- 12a c + 12b c)d e - 18b c d e + 12c d e) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c - 12a b c + 3b )e + (36a b c - 12b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 36a c + 18b c )d e - 12b c d e + 6c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3c e x + (- 2b c e + 16c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 2 +--R ((- 6a c + 3b c )e - 12b c d e + 36c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 +--R ((18a b c - 6b c)e + (- 48a c + 24b c )d e - 36b c d e + 48c d e)x +--R / +--R 4 +--R 6c +--R , +--R +--R 3 4 2 2 3 2 2 2 3 3 +--R ((12a b c - 6b )e + (- 24a c + 24b c)d e - 36b c d e + 24c d e) +--R * +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b +--R \|4a c - b atan(------------) +--R 2c x + b +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c - 12a b c + 3b )e + (36a b c - 12b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 36a c + 18b c )d e - 12b c d e + 6c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3c e x + (- 2b c e + 16c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 2 +--R ((- 6a c + 3b c )e - 12b c d e + 36c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 +--R ((18a b c - 6b c)e + (- 48a c + 24b c )d e - 36b c d e + 48c d e)x +--R / +--R 4 +--R 6c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 263 + +--S 264 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((2a b c - b )e + (- 4a c + 4b c)d e - 6b c d e + 4c d e) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((4a b c - 2b )e + (- 8a c + 8b c)d e - 12b c d e + 8c d e) +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 +--R 2c +--R Type: Expression(Integer) +--E 264 + +--S 265 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((2a b c - b )e + (- 4a c + 4b c)d e - 6b c d e + 4c d e) +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((2a b c - b )e + (- 4a c + 4b c)d e - 6b c d e + 4c d e) +--R * +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b +--R \|4a c - b atan(------------) +--R 2c x + b +--R / +--R 4 +--R c +--R Type: Expression(Integer) +--E 266 + +--S 267 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 268 + +--S 269 of 845 +r0:=e*(6*c^2*d^2+b^2*e^2-c*e*(3*b*d+2*a*e))*x/c^2+1/2*e^2*(6*c*d-b*e)*x^2/c+_ + 2/3*e^3*x^3+1/2*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(a+b*x+_ + c*x^2)/c^3-e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^3 +--R +--R +--R (2) +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((6a c - 6b )e + 18b c d e - 18c d e)\|- 4a c + b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((9a b c - 3b )e + (- 18a c + 9b c)d e - 9b c d e + 6c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 3 2 3 3 2 2 +--R 4c e x + (- 3b c e + 18c d e )x +--R + +--R 2 2 3 2 2 3 2 +--R ((- 12a c + 6b c)e - 18b c d e + 36c d e)x +--R / +--R 3 +--R 6c +--R Type: Expression(Integer) +--E 269 + +--S 270 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((3a c - 3b )e + 9b c d e - 9c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((9a b c - 3b )e + (- 18a c + 9b c)d e - 9b c d e + 6c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 3 2 3 3 2 2 +--R 4c e x + (- 3b c e + 18c d e )x +--R + +--R 2 2 3 2 2 3 2 +--R ((- 12a c + 6b c)e - 18b c d e + 36c d e)x +--R / +--R 3 +--R 6c +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R 2 3 2 2 2 | 2 \|4a c - b +--R ((- 6a c + 6b )e - 18b c d e + 18c d e)\|4a c - b atan(------------) +--R 2c x + b +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((9a b c - 3b )e + (- 18a c + 9b c)d e - 9b c d e + 6c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 3 2 3 3 2 2 +--R 4c e x + (- 3b c e + 18c d e )x +--R + +--R 2 2 3 2 2 3 2 +--R ((- 12a c + 6b c)e - 18b c d e + 36c d e)x +--R / +--R 3 +--R 6c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 270 + +--S 271 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((a c - b )e + 3b c d e - 3c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((- 2a c + 2b )e - 6b c d e + 6c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 +--R 2c +--R Type: Expression(Integer) +--E 271 + +--S 272 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((- a c + b )e - 3b c d e + 3c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 3 2 2 2 | 2 \|4a c - b +--R ((- a c + b )e - 3b c d e + 3c d e)\|4a c - b atan(------------) +--R 2c x + b +--R / +--R 3 +--R c +--R Type: Expression(Integer) +--E 273 + +--S 274 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 274 + +)clear all + +--S 275 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 275 + +--S 276 of 845 +r0:=e*(4*d-b*e/c)*x+e^2*x^2+1/2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + log(a+b*x+c*x^2)/c^2-e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*_ + sqrt(b^2-4*a*c)/c^2 +--R +--R +--R (2) +--R +-----------+ +--R 2 | 2 2c x + b +--R (2b e - 4c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d )log(c x + b x + a) + 2c e x +--R + +--R 2 2 +--R (- 2b c e + 8c d e)x +--R / +--R 2 +--R 2c +--R Type: Expression(Integer) +--E 276 + +--S 277 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 | 2 +--R (b e - 2c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d )log(c x + b x + a) + 2c e x +--R + +--R 2 2 +--R (- 2b c e + 8c d e)x +--R / +--R 2 +--R 2c +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 \|4a c - b +--R (- 2b e + 4c d e)\|4a c - b atan(------------) +--R 2c x + b +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d )log(c x + b x + a) + 2c e x +--R + +--R 2 2 +--R (- 2b c e + 8c d e)x +--R / +--R 2 +--R 2c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 277 + +--S 278 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 | 2 +--R (b e - 2c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 2c x + b +--R (- 2b e + 4c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 +--R 2c +--R Type: Expression(Integer) +--E 278 + +--S 279 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 | 2 2c x + b +--R (- b e + 2c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 \|4a c - b +--R (- b e + 2c d e)\|4a c - b atan(------------) +--R 2c x + b +--R / +--R 2 +--R c +--R Type: Expression(Integer) +--E 280 + +--S 281 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 281 + +)clear all + +--S 282 of 845 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) ----------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 282 + +--S 283 of 845 +r0:=2*e*x+1/2*(2*c*d-b*e)*log(a+b*x+c*x^2)/c-e*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c +--R +--R +--R (2) +--R +-----------+ +--R | 2 2c x + b +--R - 2e\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R (- b e + 2c d)log(c x + b x + a) + 4c e x +--R / +--R 2c +--R Type: Expression(Integer) +--E 283 + +--S 284 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | 2 +--R e\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 +--R (- b e + 2c d)log(c x + b x + a) + 4c e x +--R / +--R 2c +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b 2 +--R 2e\|4a c - b atan(------------) + (- b e + 2c d)log(c x + b x + a) +--R 2c x + b +--R + +--R 4c e x +--R / +--R 2c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 284 + +--S 285 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R | 2 +--R e\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R | 2 2c x + b +--R 2e\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2c +--R Type: Expression(Integer) +--E 285 + +--S 286 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 845 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +--R +-----------+ +---------+ | 2 +--R | 2 2c x + b | 2 \|4a c - b +--R e\|- 4a c + b atanh(--------------) + e\|4a c - b atan(------------) +--R +-----------+ 2c x + b +--R | 2 +--R \|- 4a c + b +--R (6) ---------------------------------------------------------------------- +--R c +--R Type: Expression(Integer) +--E 287 + +--S 288 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 845 +t0:=(b+2*c*x)/(a+b*x+c*x^2) +--R +--R +--R 2c x + b +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 289 + +--S 290 of 845 +r0:=log(a+b*x+c*x^2) +--R +--R +--R 2 +--R (2) log(c x + b x + a) +--R Type: Expression(Integer) +--E 290 + +--S 291 of 845 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) log(c x + b x + a) +--R Type: Union(Expression(Integer),...) +--E 291 + +--S 292 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 293 + +)clear all + +--S 294 of 845 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------- +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 294 + +--S 295 of 845 +r0:=-(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)+1/2*(2*c*d-b*e)*log(a+b*x+_ + c*x^2)/(c*d^2-b*d*e+a*e^2)+e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-_ + 4*a*c)/(c*d^2-b*d*e+a*e^2) +--R +--R +--R (2) +--R +-----------+ +--R | 2 2c x + b 2 +--R 2e\|- 4a c + b atanh(--------------) + (- b e + 2c d)log(c x + b x + a) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R (2b e - 4c d)log(e x + d) +--R / +--R 2 2 +--R 2a e - 2b d e + 2c d +--R Type: Expression(Integer) +--E 295 + +--S 296 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | 2 +--R e\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 +--R (- b e + 2c d)log(c x + b x + a) + (2b e - 4c d)log(e x + d) +--R / +--R 2 2 +--R 2a e - 2b d e + 2c d +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b 2 +--R - 2e\|4a c - b atan(------------) + (- b e + 2c d)log(c x + b x + a) +--R 2c x + b +--R + +--R (2b e - 4c d)log(e x + d) +--R / +--R 2 2 +--R 2a e - 2b d e + 2c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 296 + +--S 297 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | 2 2 2 2 +--R | 2 (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R e\|- 4a c + b log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R | 2 2c x + b +--R - 2e\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 2 +--R 2a e - 2b d e + 2c d +--R Type: Expression(Integer) +--E 297 + +--S 298 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 298 + +--S 299 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R +-----------+ +---------+ | 2 +--R | 2 2c x + b | 2 \|4a c - b +--R - e\|- 4a c + b atanh(--------------) - e\|4a c - b atan(------------) +--R +-----------+ 2c x + b +--R | 2 +--R \|- 4a c + b +--R ------------------------------------------------------------------------ +--R 2 2 +--R a e - b d e + c d +--R Type: Expression(Integer) +--E 299 + +--S 300 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 845 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 845 +r0:=(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x))-(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2+1/2*(2*c^2*d^2+_ + b^2*e^2-2*c*e*(b*d+a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2+_ + e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/_ + (c*d^2-b*d*e+a*e^2)^2 +--R +--R +--R (2) +--R +-----------+ +--R 3 2 2 2 | 2 +--R ((- 2b e + 4c d e )x - 2b d e + 4c d e)\|- 4a c + b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d e)x + (- 2a c + b )d e +--R + +--R 2 2 3 +--R - 2b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 2 2 2 2 +--R ((4a c - 2b )e + 4b c d e - 4c d e)x + (4a c - 2b )d e + 4b c d e +--R + +--R 2 3 +--R - 4c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (4a c + 2b )d e - 6b c d e + 4c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R Type: Expression(Integer) +--E 302 + +--S 303 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 2 2 2 | 2 +--R ((b e - 2c d e )x + b d e - 2c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d e)x + (- 2a c + b )d e +--R + +--R 2 2 3 +--R - 2b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 2 2 2 +--R ((4a c - 2b )e + 4b c d e - 4c d e)x + (4a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (4a c + 2b )d e - 6b c d e + 4c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R 3 2 2 2 | 2 \|4a c - b +--R ((2b e - 4c d e )x + 2b d e - 4c d e)\|4a c - b atan(------------) +--R 2c x + b +--R + +--R 2 3 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d e)x + (- 2a c + b )d e +--R + +--R 2 2 3 +--R - 2b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 2 2 2 +--R ((4a c - 2b )e + 4b c d e - 4c d e)x + (4a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (4a c + 2b )d e - 6b c d e + 4c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 303 + +--S 304 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 | 2 +--R (b e - 2c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 2c x + b +--R (2b e - 4c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 4 3 2 2 2 3 2 4 +--R 2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R Type: Expression(Integer) +--E 304 + +--S 305 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 | 2 2c x + b +--R (b e - 2c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 \|4a c - b +--R (b e - 2c d e)\|4a c - b atan(------------) +--R 2c x + b +--R / +--R 2 4 3 2 2 2 3 2 4 +--R a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R Type: Expression(Integer) +--E 306 + +--S 307 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 307 + +)clear all + +--S 308 of 845 +t0:=(b+2*c*x)/((d+e*x)^3*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 308 + +--S 309 of 845 +r0:=1/2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))-(2*c*d-b*e)*(c^2*d^2+_ + b^2*e^2-c*e*(b*d+3*a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*(2*c*d-_ + b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+_ + a*e^2)^3+e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/(c*d^2-b*d*e+a*e^2)^3 +--R +--R +--R (2) +--R 2 5 4 2 2 3 2 +--R ((- 2a c + 2b )e - 6b c d e + 6c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 +--R ((- 4a c + 4b )d e - 12b c d e + 12c d e )x + (- 2a c + 2b )d e +--R + +--R 3 2 2 4 +--R - 6b c d e + 6c d e +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((6a b c - 2b )d e + (- 12a c + 6b c)d e - 6b c d e + 4c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (3a b c - b )d e + (- 6a c + 3b c)d e - 3b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((- 12a b c + 4b )d e + (24a c - 12b c)d e + 12b c d e - 8c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 6a b c + 2b )d e + (12a c - 6b c)d e + 6b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 2 2 5 3 4 2 2 3 2 3 2 3 4 2 5 +--R ((- 4a c + 2a b )e - 2b d e + 6b c d e - 8b c d e + 4c d e)x - a b e +--R + +--R 2 2 4 3 2 3 2 2 3 2 +--R (- 2a c + 4a b )d e + (- 6a b c - 3b )d e + (4a c + 10b c)d e +--R + +--R 2 4 3 5 +--R - 13b c d e + 6c d +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R Type: Expression(Integer) +--E 309 + +--S 310 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 5 4 2 2 3 2 +--R ((a c - b )e + 3b c d e - 3c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 +--R ((2a c - 2b )d e + 6b c d e - 6c d e )x + (a c - b )d e +--R + +--R 3 2 2 4 +--R 3b c d e - 3c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((6a b c - 2b )d e + (- 12a c + 6b c)d e - 6b c d e + 4c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (3a b c - b )d e + (- 6a c + 3b c)d e - 3b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 12a b c + 4b )d e + (24a c - 12b c)d e + 12b c d e +--R + +--R 3 4 +--R - 8c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 6a b c + 2b )d e + (12a c - 6b c)d e + 6b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 2 2 5 3 4 2 2 3 2 3 2 3 4 +--R ((- 4a c + 2a b )e - 2b d e + 6b c d e - 8b c d e + 4c d e)x +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (- 2a c + 4a b )d e + (- 6a b c - 3b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (4a c + 10b c)d e - 13b c d e + 6c d +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R , +--R +--R 2 5 4 2 2 3 2 +--R ((2a c - 2b )e + 6b c d e - 6c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 +--R ((4a c - 4b )d e + 12b c d e - 12c d e )x + (2a c - 2b )d e +--R + +--R 3 2 2 4 +--R 6b c d e - 6c d e +--R * +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b +--R \|4a c - b atan(------------) +--R 2c x + b +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((6a b c - 2b )d e + (- 12a c + 6b c)d e - 6b c d e + 4c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (3a b c - b )d e + (- 6a c + 3b c)d e - 3b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 12a b c + 4b )d e + (24a c - 12b c)d e + 12b c d e +--R + +--R 3 4 +--R - 8c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 6a b c + 2b )d e + (12a c - 6b c)d e + 6b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 2 2 5 3 4 2 2 3 2 3 2 3 4 +--R ((- 4a c + 2a b )e - 2b d e + 6b c d e - 8b c d e + 4c d e)x +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (- 2a c + 4a b )d e + (- 6a b c - 3b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (4a c + 10b c)d e - 13b c d e + 6c d +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 310 + +--S 311 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((a c - b )e + 3b c d e - 3c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((2a c - 2b )e + 6b c d e - 6c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R Type: Expression(Integer) +--E 311 + +--S 312 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((a c - b )e + 3b c d e - 3c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 3 2 2 2 | 2 \|4a c - b +--R ((a c - b )e + 3b c d e - 3c d e)\|4a c - b atan(------------) +--R 2c x + b +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R Type: Expression(Integer) +--E 313 + +--S 314 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 314 + +)clear all + +--S 315 of 845 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 315 + +--S 316 of 845 +r0:=4*e^3*(3*c*d-b*e)*x/c^2+2*e^4*x^2/c-(d+e*x)^4/(a+b*x+c*x^2)+_ + 2*e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(a+b*x+c*x^2)/c^3-_ + 4*e*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 3 2 2 +--R (- 12a b c + 4b c)e + (24a c - 12b c )d e + 12b c d e +--R + +--R 4 3 +--R - 8c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 3 3 2 2 2 2 +--R (- 12a b c + 4b )e + (24a b c - 12b c)d e + 12b c d e +--R + +--R 3 3 +--R - 8b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (- 12a b c + 4a b )e + (24a c - 12a b c)d e + 12a b c d e +--R + +--R 3 3 +--R - 8a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 2a c + 2b c)e - 6b c d e + 6c d e )x +--R + +--R 3 4 2 3 2 2 2 +--R ((- 2a b c + 2b )e - 6b c d e + 6b c d e )x +--R + +--R 2 2 4 3 2 2 2 +--R (- 2a c + 2a b )e - 6a b c d e + 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 4 4 2 4 3 3 3 +--R c e x + (- 2b c e + 8c d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((2a c - 4b c)e + 12b c d e - 6c d e )x +--R + +--R 4 2 3 3 3 3 4 +--R (- 4a b c e + 12a c d e - 4c d e)x - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 3 | 2 +--R (c x + b c x + a c )\|- 4a c + b +--R Type: Expression(Integer) +--E 316 + +--S 317 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 4 3 2 2 3 3 2 2 +--R (6a b c - 2b c)e + (- 12a c + 6b c )d e - 6b c d e +--R + +--R 4 3 +--R 4c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 3 3 2 2 2 2 +--R (6a b c - 2b )e + (- 12a b c + 6b c)d e - 6b c d e +--R + +--R 3 3 +--R 4b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 3 3 +--R (6a b c - 2a b )e + (- 12a c + 6a b c)d e - 6a b c d e + 4a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 2a c + 2b c)e - 6b c d e + 6c d e )x +--R + +--R 3 4 2 3 2 2 2 +--R ((- 2a b c + 2b )e - 6b c d e + 6b c d e )x +--R + +--R 2 2 4 3 2 2 2 +--R (- 2a c + 2a b )e - 6a b c d e + 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 4 4 2 4 3 3 3 2 2 4 2 3 2 +--R c e x + (- 2b c e + 8c d e )x + ((a c - 3b c)e + 8b c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 5a b c + b )e + (12a c - 4b c)d e + 6b c d e - 4c d e)x +--R + +--R 2 2 4 3 2 2 2 3 4 +--R (- a c + a b )e - 4a b c d e + 6a c d e - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 3 | 2 +--R (c x + b c x + a c )\|- 4a c + b +--R , +--R +--R 2 3 4 3 2 2 3 3 2 2 +--R (12a b c - 4b c)e + (- 24a c + 12b c )d e - 12b c d e +--R + +--R 4 3 +--R 8c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 3 3 2 2 2 2 +--R (12a b c - 4b )e + (- 24a b c + 12b c)d e - 12b c d e +--R + +--R 3 3 +--R 8b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (12a b c - 4a b )e + (- 24a c + 12a b c)d e - 12a b c d e +--R + +--R 3 3 +--R 8a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 2a c + 2b c)e - 6b c d e + 6c d e )x +--R + +--R 3 4 2 3 2 2 2 +--R ((- 2a b c + 2b )e - 6b c d e + 6b c d e )x +--R + +--R 2 2 4 3 2 2 2 +--R (- 2a c + 2a b )e - 6a b c d e + 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 4 4 2 4 3 3 3 2 2 4 2 3 2 +--R c e x + (- 2b c e + 8c d e )x + ((a c - 3b c)e + 8b c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 5a b c + b )e + (12a c - 4b c)d e + 6b c d e - 4c d e)x +--R + +--R 2 2 4 3 2 2 2 3 4 +--R (- a c + a b )e - 4a b c d e + 6a c d e - c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 4 2 3 3 | 2 +--R (c x + b c x + a c )\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 317 + +--S 318 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((12a b c - 4b )e + (- 24a c + 12b c)d e - 12b c d e + 8c d e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((- a c + b )e - 4b c d e + 6c d e )\|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R c \|- 4a c + b +--R Type: Expression(Integer) +--E 318 + +--S 319 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((12a b c - 4b )e + (- 24a c + 12b c)d e - 12b c d e + 8c d e) +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((12a b c - 4b )e + (- 24a c + 12b c)d e - 12b c d e + 8c d e) +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +-----------+ +---------+ +--R 2 4 3 2 2 2 | 2 | 2 +--R ((- a c + b )e - 4b c d e + 6c d e )\|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 320 + +--S 321 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 322 + +--S 323 of 845 +r0:=3*e^3*x/c-(d+e*x)^3/(a+b*x+c*x^2)+3/2*e^2*(2*c*d-b*e)*_ + log(a+b*x+c*x^2)/c^2-3*e*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 2 3 2 2 +--R ((12a c - 6b c)e + 12b c d e - 12c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((12a b c - 6b )e + 12b c d e - 12b c d e)x + (12a c - 6a b )e +--R + +--R 2 2 2 +--R 12a b c d e - 12a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- 3b c e + 6c d e )x + (- 3b e + 6b c d e )x - 3a b e +--R + +--R 2 +--R 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 3 2 2 2 3 2 2 2 3 +--R 4c e x + (6b c e - 6c d e )x + (6a c e - 6c d e)x - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 | 2 +--R (2c x + 2b c x + 2a c )\|- 4a c + b +--R Type: Expression(Integer) +--E 323 + +--S 324 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 3 2 2 +--R ((6a c - 3b c)e + 6b c d e - 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((6a b c - 3b )e + 6b c d e - 6b c d e)x + (6a c - 3a b )e +--R + +--R 2 2 2 +--R 6a b c d e - 6a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2 2 3 2 3 +--R (- 3b c e + 6c d e )x + (- 3b e + 6b c d e )x - 3a b e +--R + +--R 2 +--R 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 3 2 2 3 2 2 2 +--R 4c e x + 4b c e x + ((6a c - 2b )e + 6b c d e - 6c d e)x +--R + +--R 3 2 2 3 +--R - 2a b e + 6a c d e - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 | 2 +--R (2c x + 2b c x + 2a c )\|- 4a c + b +--R , +--R +--R 2 2 3 2 2 3 2 2 +--R ((- 12a c + 6b c)e - 12b c d e + 12c d e)x +--R + +--R 3 3 2 2 2 2 +--R ((- 12a b c + 6b )e - 12b c d e + 12b c d e)x +--R + +--R 2 2 3 2 2 2 +--R (- 12a c + 6a b )e - 12a b c d e + 12a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- 3b c e + 6c d e )x + (- 3b e + 6b c d e )x - 3a b e +--R + +--R 2 +--R 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 3 2 2 3 2 2 2 +--R 4c e x + 4b c e x + ((6a c - 2b )e + 6b c d e - 6c d e)x +--R + +--R 3 2 2 3 +--R - 2a b e + 6a c d e - 2c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 3 2 2 2 | 2 +--R (2c x + 2b c x + 2a c )\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 324 + +--S 325 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 +--R ((6a c - 3b )e + 6b c d e - 6c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 2c x + b +--R ((- 12a c + 6b )e - 12b c d e + 12c d e)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 2 | 2 +--R (- 2b e + 6c d e )\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 325 + +--S 326 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((- 6a c + 3b )e - 6b c d e + 6c d e)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((- 6a c + 3b )e - 6b c d e + 6c d e)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +-----------+ +---------+ +--R 3 2 | 2 | 2 +--R (- b e + 3c d e )\|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 327 + +--S 328 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 328 + +)clear all + +--S 329 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 329 + +--S 330 of 845 +r0:=-(d+e*x)^2/(a+b*x+c*x^2)+e^2*log(a+b*x+c*x^2)/c-2*e*(2*c*d-b*e)*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R ((2b c e - 4c d e)x + (2b e - 4b c d e)x + 2a b e - 4a c d e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 2 2 +--R ((c e x + b e x + a e )log(c x + b x + a) - c e x - 2c d e x - c d ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (c x + b c x + a c)\|- 4a c + b +--R Type: Expression(Integer) +--E 330 + +--S 331 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R ((b c e - 2c d e)x + (b e - 2b c d e)x + a b e - 2a c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 2 +--R (c e x + b e x + a e )log(c x + b x + a) + (b e - 2c d e)x +--R + +--R 2 2 +--R a e - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (c x + b c x + a c)\|- 4a c + b +--R , +--R +--R 2 2 2 2 2 2 +--R ((- 2b c e + 4c d e)x + (- 2b e + 4b c d e)x - 2a b e + 4a c d e) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 2 2 2 +--R (c e x + b e x + a e )log(c x + b x + a) + (b e - 2c d e)x +--R + +--R 2 2 +--R a e - c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 2 2 | 2 +--R (c x + b c x + a c)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 331 + +--S 332 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +--R (b e - 2c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 2c x + b 2 | 2 +--R (- 2b e + 4c d e)atanh(--------------) + e \|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R c\|- 4a c + b +--R Type: Expression(Integer) +--E 332 + +--S 333 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 333 + +--S 334 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 2 | 2 2c x + b +--R (- 2b e + 4c d e)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (- 2b e + 4c d e)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R e \|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R c\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 334 + +--S 335 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 845 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 845 +r0:=(-d-e*x)/(a+b*x+c*x^2)-2*e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c) +--R +--R +--R (2) +--R +-----------+ +--R 2 2c x + b | 2 +--R (- 2c e x - 2b e x - 2a e)atanh(--------------) + (- e x - d)\|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R ---------------------------------------------------------------------------- +--R +-----------+ +--R 2 | 2 +--R (c x + b x + a)\|- 4a c + b +--R Type: Expression(Integer) +--E 337 + +--S 338 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +--R (c e x + b e x + a e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R | 2 +--R (- e x - d)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R (c x + b x + a)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 (2c x + b)\|4a c - b +--R (2c e x + 2b e x + 2a e)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (- e x - d)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R (c x + b x + a)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 338 + +--S 339 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R 2e atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 339 + +--S 340 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +--S 341 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R | 2 2c x + b +--R 2e\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R 2e\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 341 + +--S 342 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 845 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^2 +--R +--R +--R 2c x + b +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 343 + +--S 344 of 845 +r0:=(-1)/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (2) - -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 344 + +--S 345 of 845 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - -------------- +--R 2 +--R c x + b x + a +--R Type: Union(Expression(Integer),...) +--E 345 + +--S 346 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 347 + +)clear all + +--S 348 of 845 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 348 + +--S 349 of 845 +r0:=(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))-e^2*(2*c*d-b*e)*log(d+e*x)/_ + (c*d^2-b*d*e+a*e^2)^2+1/2*e^2*(2*c*d-b*e)*log(a+b*x+c*x^2)/_ + (c*d^2-b*d*e+a*e^2)^2+e*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 2 3 2 2 +--R ((- 4a c + 2b c)e - 4b c d e + 4c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 4a b c + 2b )e - 4b c d e + 4b c d e)x + (- 4a c + 2a b )e +--R + +--R 2 2 2 +--R - 4a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- b c e + 2c d e )x + (- b e + 2b c d e )x - a b e +--R + +--R 2 +--R 2a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 2 3 2 3 +--R (2b c e - 4c d e )x + (2b e - 4b c d e )x + 2a b e +--R + +--R 2 +--R - 4a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 +--R (2a c e - 2b c d e + 2c d e)x + 2a b e + (- 2a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (2a c e - 4a b c d e + (4a c + 2b c)d e - 4b c d e + 2c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 +--R (2a b e - 4a b d e + (4a b c + 2b )d e - 4b c d e + 2b c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R 2a e - 4a b d e + (4a c + 2a b )d e - 4a b c d e + 2a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 349 + +--S 350 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 3 2 2 +--R ((2a c - b c)e + 2b c d e - 2c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((2a b c - b )e + 2b c d e - 2b c d e)x + (2a c - a b )e +--R + +--R 2 2 2 +--R 2a b c d e - 2a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2 2 3 2 3 +--R (- b c e + 2c d e )x + (- b e + 2b c d e )x - a b e +--R + +--R 2 +--R 2a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 2 3 2 3 +--R (2b c e - 4c d e )x + (2b e - 4b c d e )x + 2a b e +--R + +--R 2 +--R - 4a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 +--R (2a c e - 2b c d e + 2c d e)x + 2a b e + (- 2a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (2a c e - 4a b c d e + (4a c + 2b c)d e - 4b c d e + 2c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 +--R (2a b e - 4a b d e + (4a b c + 2b )d e - 4b c d e + 2b c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R 2a e - 4a b d e + (4a c + 2a b )d e - 4a b c d e + 2a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 2 3 2 2 3 2 2 +--R ((4a c - 2b c)e + 4b c d e - 4c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((4a b c - 2b )e + 4b c d e - 4b c d e)x + (4a c - 2a b )e +--R + +--R 2 2 2 +--R 4a b c d e - 4a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- b c e + 2c d e )x + (- b e + 2b c d e )x - a b e +--R + +--R 2 +--R 2a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 2 3 2 3 +--R (2b c e - 4c d e )x + (2b e - 4b c d e )x + 2a b e +--R + +--R 2 +--R - 4a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 +--R (2a c e - 2b c d e + 2c d e)x + 2a b e + (- 2a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 2c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (2a c e - 4a b c d e + (4a c + 2b c)d e - 4b c d e + 2c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 +--R (2a b e - 4a b d e + (4a b c + 2b )d e - 4b c d e + 2b c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R 2a e - 4a b d e + (4a c + 2a b )d e - 4a b c d e + 2a c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 350 + +--S 351 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 +--R ((2a c - b )e + 2b c d e - 2c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 2c x + b +--R ((4a c - 2b )e + 4b c d e - 4c d e)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 351 + +--S 352 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((2a c - b )e + 2b c d e - 2c d e)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((2a c - b )e + 2b c d e - 2c d e)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (a e - 2a b d e + (2a c + b )d e - 2b c d e + c d )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression(Integer) +--E 353 + +--S 354 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 845 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + ((2a c + b )e + 4b c d e + c d )x +--R + +--R 2 2 2 3 +--R (2a b e + (4a c + 2b )d e + 2b c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (a e + 4a b d e + (2a c + b )d )x + (2a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 355 + +--S 356 of 845 +r0:=2*e^2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))+(-(b^2-4*a*c)*_ + (c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*_ + (a+b*x+c*x^2))-2*e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(d+e*x)/_ + (c*d^2-b*d*e+a*e^2)^3+e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*_ + log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3+2*e*(2*c*d-b*e)*(c^2*d^2+_ + b^2*e^2-c*e*(b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + ((c*d^2-b*d*e+a*e^2)^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 5 3 2 2 4 3 2 3 4 3 2 3 +--R ((6a b c - 2b c)e + (- 12a c + 6b c )d e - 6b c d e + 4c d e )x +--R + +--R 2 4 5 2 3 4 3 2 3 +--R (6a b c - 2b )e + (- 6a b c + 4b c)d e - 12a c d e +--R + +--R 3 3 2 4 4 +--R - 2b c d e + 4c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (6a b c - 2a b )e + (- 12a c + 12a b c - 2b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 +--R (- 18a b c + 6b c)d e + (4a c - 6b c )d e + 4b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 2 3 2 3 2 3 4 +--R (6a b c - 2a b )d e + (- 12a c + 6a b c)d e - 6a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((- a c + b c)e - 3b c d e + 3c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((- a b c + b )e + (- a c - 2b c)d e + 3c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- a c + a b )e + (- 4a b c + b )d e + (3a c - 3b c)d e +--R + +--R 2 3 2 +--R 3b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (- a c + a b )d e - 3a b c d e + 3a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((2a c - 2b c)e + 6b c d e - 6c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((2a b c - 2b )e + (2a c + 4b c)d e - 6c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (2a c - 2a b )e + (8a b c - 2b )d e + (- 6a c + 6b c)d e +--R + +--R 2 3 2 +--R - 6b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (2a c - 2a b )d e + 6a b c d e - 6a c d e +--R * +--R log(e x + d) +--R + +--R 5 2 2 4 2 2 3 3 3 2 2 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (a c - 2a b )e + (2a b c + 2b )d e + (2a c - 5b c)d e +--R + +--R 2 3 2 3 4 +--R 2b c d e + c d e +--R * +--R x +--R + +--R 2 5 2 4 3 2 3 2 2 3 2 +--R - a b e + 3a c d e + (- 2a b c + b )d e + (2a c - 3b c)d e +--R + +--R 2 4 3 5 +--R 3b c d e - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 7 2 6 2 2 2 2 5 2 3 3 4 +--R a c e - 3a b c d e + (3a c + 3a b c)d e + (- 6a b c - b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (3a c + 3b c )d e - 3b c d e + c d e +--R * +--R 3 +--R x +--R + +--R 3 7 3 2 2 6 3 2 5 2 2 2 4 3 4 +--R a b e + (a c - 3a b )d e + 3a b d e + (3a c - 3a b c - b )d e +--R + +--R 2 3 4 3 3 5 2 3 6 4 7 +--R (- 3a b c + 2b c)d e + 3a c d e - 2b c d e + c d +--R * +--R 2 +--R x +--R + +--R 4 7 3 6 3 2 5 2 3 3 4 +--R a e - 2a b d e + 3a c d e + (- 3a b c + 2a b )d e +--R + +--R 2 2 2 4 4 3 3 5 2 3 2 2 6 3 7 +--R (3a c - 3a b c - b )d e + 3b c d e + (a c - 3b c )d e + b c d +--R * +--R x +--R + +--R 4 6 3 2 5 3 2 2 3 4 2 3 4 3 +--R a d e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - a b )d e +--R + +--R 2 2 2 5 2 2 6 3 7 +--R (3a c + 3a b c)d e - 3a b c d e + a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 356 + +--S 357 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 5 3 2 2 4 3 2 3 4 3 2 3 +--R ((3a b c - b c)e + (- 6a c + 3b c )d e - 3b c d e + 2c d e )x +--R + +--R 2 4 5 2 3 4 3 2 3 3 3 2 +--R (3a b c - b )e + (- 3a b c + 2b c)d e - 6a c d e - b c d e +--R + +--R 4 4 +--R 2c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (3a b c - a b )e + (- 6a c + 6a b c - b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 +--R (- 9a b c + 3b c)d e + (2a c - 3b c )d e + 2b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 2 3 2 3 2 3 4 +--R (3a b c - a b )d e + (- 6a c + 3a b c)d e - 3a b c d e + 2a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((- a c + b c)e - 3b c d e + 3c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((- a b c + b )e + (- a c - 2b c)d e + 3c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- a c + a b )e + (- 4a b c + b )d e + (3a c - 3b c)d e +--R + +--R 2 3 2 +--R 3b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (- a c + a b )d e - 3a b c d e + 3a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((2a c - 2b c)e + 6b c d e - 6c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((2a b c - 2b )e + (2a c + 4b c)d e - 6c d e )x +--R + +--R 2 2 5 3 4 +--R (2a c - 2a b )e + (8a b c - 2b )d e +--R + +--R 2 2 2 3 2 3 2 +--R (- 6a c + 6b c)d e - 6b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (2a c - 2a b )d e + 6a b c d e - 6a c d e +--R * +--R log(e x + d) +--R + +--R 5 2 2 4 2 2 3 3 3 2 2 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (a c - 2a b )e + (2a b c + 2b )d e + (2a c - 5b c)d e +--R + +--R 2 3 2 3 4 +--R 2b c d e + c d e +--R * +--R x +--R + +--R 2 5 2 4 3 2 3 2 2 3 2 +--R - a b e + 3a c d e + (- 2a b c + b )d e + (2a c - 3b c)d e +--R + +--R 2 4 3 5 +--R 3b c d e - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 7 2 6 2 2 2 2 5 +--R a c e - 3a b c d e + (3a c + 3a b c)d e +--R + +--R 2 3 3 4 3 2 2 4 3 3 5 2 4 6 +--R (- 6a b c - b c)d e + (3a c + 3b c )d e - 3b c d e + c d e +--R * +--R 3 +--R x +--R + +--R 3 7 3 2 2 6 3 2 5 +--R a b e + (a c - 3a b )d e + 3a b d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 3 5 2 +--R (3a c - 3a b c - b )d e + (- 3a b c + 2b c)d e + 3a c d e +--R + +--R 3 6 4 7 +--R - 2b c d e + c d +--R * +--R 2 +--R x +--R + +--R 4 7 3 6 3 2 5 2 3 3 4 +--R a e - 2a b d e + 3a c d e + (- 3a b c + 2a b )d e +--R + +--R 2 2 2 4 4 3 3 5 2 3 2 2 6 3 7 +--R (3a c - 3a b c - b )d e + 3b c d e + (a c - 3b c )d e + b c d +--R * +--R x +--R + +--R 4 6 3 2 5 3 2 2 3 4 2 3 4 3 +--R a d e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - a b )d e +--R + +--R 2 2 2 5 2 2 6 3 7 +--R (3a c + 3a b c)d e - 3a b c d e + a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 3 5 3 2 2 4 3 2 3 +--R (- 6a b c + 2b c)e + (12a c - 6b c )d e + 6b c d e +--R + +--R 4 3 2 +--R - 4c d e +--R * +--R 3 +--R x +--R + +--R 2 4 5 2 3 4 3 2 3 +--R (- 6a b c + 2b )e + (6a b c - 4b c)d e + 12a c d e +--R + +--R 3 3 2 4 4 +--R 2b c d e - 4c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (- 6a b c + 2a b )e + (12a c - 12a b c + 2b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 +--R (18a b c - 6b c)d e + (- 4a c + 6b c )d e - 4b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 2 3 2 3 2 +--R (- 6a b c + 2a b )d e + (12a c - 6a b c)d e + 6a b c d e +--R + +--R 3 4 +--R - 4a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((- a c + b c)e - 3b c d e + 3c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((- a b c + b )e + (- a c - 2b c)d e + 3c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- a c + a b )e + (- 4a b c + b )d e + (3a c - 3b c)d e +--R + +--R 2 3 2 +--R 3b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (- a c + a b )d e - 3a b c d e + 3a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((2a c - 2b c)e + 6b c d e - 6c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((2a b c - 2b )e + (2a c + 4b c)d e - 6c d e )x +--R + +--R 2 2 5 3 4 +--R (2a c - 2a b )e + (8a b c - 2b )d e +--R + +--R 2 2 2 3 2 3 2 +--R (- 6a c + 6b c)d e - 6b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (2a c - 2a b )d e + 6a b c d e - 6a c d e +--R * +--R log(e x + d) +--R + +--R 5 2 2 4 2 2 3 3 3 2 2 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (a c - 2a b )e + (2a b c + 2b )d e + (2a c - 5b c)d e +--R + +--R 2 3 2 3 4 +--R 2b c d e + c d e +--R * +--R x +--R + +--R 2 5 2 4 3 2 3 2 2 3 2 +--R - a b e + 3a c d e + (- 2a b c + b )d e + (2a c - 3b c)d e +--R + +--R 2 4 3 5 +--R 3b c d e - c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 3 7 2 6 2 2 2 2 5 +--R a c e - 3a b c d e + (3a c + 3a b c)d e +--R + +--R 2 3 3 4 3 2 2 4 3 3 5 2 4 6 +--R (- 6a b c - b c)d e + (3a c + 3b c )d e - 3b c d e + c d e +--R * +--R 3 +--R x +--R + +--R 3 7 3 2 2 6 3 2 5 +--R a b e + (a c - 3a b )d e + 3a b d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 3 5 2 +--R (3a c - 3a b c - b )d e + (- 3a b c + 2b c)d e + 3a c d e +--R + +--R 3 6 4 7 +--R - 2b c d e + c d +--R * +--R 2 +--R x +--R + +--R 4 7 3 6 3 2 5 2 3 3 4 +--R a e - 2a b d e + 3a c d e + (- 3a b c + 2a b )d e +--R + +--R 2 2 2 4 4 3 3 5 2 3 2 2 6 3 7 +--R (3a c - 3a b c - b )d e + 3b c d e + (a c - 3b c )d e + b c d +--R * +--R x +--R + +--R 4 6 3 2 5 3 2 2 3 4 2 3 4 3 +--R a d e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - a b )d e +--R + +--R 2 2 2 5 2 2 6 3 7 +--R (3a c + 3a b c)d e - 3a b c d e + a c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 357 + +--S 358 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 358 + +--S 359 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e) +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e) +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 360 + +--S 361 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 361 + +)clear all + +--S 362 of 845 +t0:=(b+2*c*x)*(d+e*x)^5/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R 2c e x + (b e + 10c d e )x + (5b d e + 20c d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10b d e + 20c d e )x + (10b d e + 10c d e)x + (5b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 362 + +--S 363 of 845 +r0:=5*e^3*(3*c^2*d^2+b^2*e^2-c*e*(2*b*d+3*a*e))*x/(c^2*(b^2-4*a*c))+_ + 5/2*e^4*(2*c*d-b*e)*x^2/(c*(b^2-4*a*c))-1/2*(d+e*x)^5/(a+b*x+c*x^2)^2-_ + 5/2*e*(d+e*x)^3*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+_ + 5*e*(2*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(b*d-3*a*e)-6*a*c^2*e^3*(2*b*d+a*e)+_ + 2*b^2*c*e^3*(b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*(b^2-_ + 4*a*c)^(3/2))+5/2*e^4*(2*c*d-b*e)*log(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (60a c - 60a b c + 10b c )e + (120a b c - 20b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R - 120a c d e + 40b c d e - 20c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (120a b c - 120a b c + 20b c)e + (240a b c - 40b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R - 240a b c d e + 80b c d e - 40b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (120a c - 60a b c - 40a b c + 10b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (240a b c + 80a b c - 20b c)d e + (- 240a c - 120a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (80a b c + 40b c )d e + (- 40a c - 20b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (120a b c - 120a b c + 20a b )e + (240a b c - 40a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R - 240a b c d e + 80a b c d e - 40a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (60a c - 60a b c + 10a b )e + (120a b c - 20a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R - 120a c d e + 40a b c d e - 20a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 20a b c + 5b c )e + (40a c - 10b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 40a b c + 10b c)e + (80a b c - 20b c )d e )x +--R + +--R 2 2 3 5 5 +--R (- 40a b c - 10a b c + 5b )e +--R + +--R 2 3 2 2 4 4 +--R (80a c + 20a b c - 10b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 40a b c + 10a b )e + (80a b c - 20a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 20a b c + 5a b )e + (40a c - 10a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 2 3 5 5 +--R (16a c - 4b c )e x +--R + +--R 3 3 2 5 4 2 3 4 4 2 3 +--R (55a b c - 15b c )e + (- 60a c + 25b c )d e - 30b c d e +--R + +--R 5 3 2 +--R 30c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (50a c + 20a b c - 10b c)e + (- 20a b c + 20b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (- 100a c - 20b c )d e + 40b c d e + 10c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 3 2 3 +--R (65a b c - 20a b c)e + (- 40a c + 40a b c )d e - 90a b c d e +--R + +--R 4 2 3 3 2 4 4 +--R (- 20a c + 20b c )d e + 15b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 5 2 2 4 2 3 2 3 +--R (30a c - 10a b c)e + 20a b c d e - 60a c d e +--R + +--R 4 2 3 4 +--R (- 10a c + 10b c )d e +--R * +--R x +--R + +--R 2 3 3 2 3 4 4 2 3 5 +--R - 10a c d e + 5a b c d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 6 2 5 4 5 3 4 3 2 5 2 4 4 3 2 +--R (8a c - 2b c )x + (16a b c - 4b c )x + (16a c + 4a b c - 2b c )x +--R + +--R 2 4 3 3 3 4 2 2 3 +--R (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 363 + +--S 364 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (30a c - 30a b c + 5b c )e + (60a b c - 10b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R - 60a c d e + 20b c d e - 10c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (60a b c - 60a b c + 10b c)e + (120a b c - 20b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R - 120a b c d e + 40b c d e - 20b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (60a c - 30a b c - 20a b c + 5b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (120a b c + 40a b c - 10b c)d e + (- 120a c - 60a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (40a b c + 20b c )d e + (- 20a c - 10b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (60a b c - 60a b c + 10a b )e + (120a b c - 20a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R - 120a b c d e + 40a b c d e - 20a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (30a c - 30a b c + 5a b )e + (60a b c - 10a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R - 60a c d e + 20a b c d e - 10a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 20a b c + 5b c )e + (40a c - 10b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 40a b c + 10b c)e + (80a b c - 20b c )d e )x +--R + +--R 2 2 3 5 5 +--R (- 40a b c - 10a b c + 5b )e +--R + +--R 2 3 2 2 4 4 +--R (80a c + 20a b c - 10b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 40a b c + 10a b )e + (80a b c - 20a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 20a b c + 5a b )e + (40a c - 10a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 2 3 5 5 3 3 2 5 4 +--R (16a c - 4b c )e x + (32a b c - 8b c )e x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (50a c - 26a b c + 4b c)e + (100a b c - 30b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (- 100a c + 40b c )d e - 20b c d e + 10c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (19a b c - 29a b c + 7b )e + (80a c + 50a b c - 25b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (- 30a b c + 30b c )d e + (- 80a c - 10b c )d e + 15b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 3 4 +--R (30a c - 56a b c + 14a b )e + (140a b c - 50a b c)d e +--R + +--R 2 3 2 2 2 3 3 3 2 4 2 3 4 +--R (- 60a c + 60a b c )d e - 60a b c d e + (- 10a c + 10b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 2 2 2 3 +--R (- 23a b c + 7a b )e + (60a c - 25a b c)d e + 30a b c d e +--R + +--R 2 3 3 2 3 4 4 2 3 5 +--R - 40a c d e + 5a b c d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 6 2 5 4 5 3 4 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 5 2 4 4 3 2 2 4 3 3 3 4 2 2 3 +--R (16a c + 4a b c - 2b c )x + (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (- 60a c + 60a b c - 10b c )e + (- 120a b c + 20b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R 120a c d e - 40b c d e + 20c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 +--R (- 120a b c + 120a b c - 20b c)e +--R + +--R 2 3 4 2 4 4 2 3 2 4 3 2 +--R (- 240a b c + 40b c )d e + 240a b c d e - 80b c d e +--R + +--R 5 4 +--R 40b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 120a c + 60a b c + 40a b c - 10b )e +--R + +--R 2 3 3 2 5 4 +--R (- 240a b c - 80a b c + 20b c)d e +--R + +--R 2 4 2 3 2 3 4 3 3 3 2 +--R (240a c + 120a b c )d e + (- 80a b c - 40b c )d e +--R + +--R 5 2 4 4 +--R (40a c + 20b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 +--R (- 120a b c + 120a b c - 20a b )e +--R + +--R 2 2 2 4 4 2 3 2 3 2 3 3 2 +--R (- 240a b c + 40a b c)d e + 240a b c d e - 80a b c d e +--R + +--R 4 4 +--R 40a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (- 60a c + 60a b c - 10a b )e + (- 120a b c + 20a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R 120a c d e - 40a b c d e + 20a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 20a b c + 5b c )e + (40a c - 10b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 40a b c + 10b c)e + (80a b c - 20b c )d e )x +--R + +--R 2 2 3 5 5 +--R (- 40a b c - 10a b c + 5b )e +--R + +--R 2 3 2 2 4 4 +--R (80a c + 20a b c - 10b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 40a b c + 10a b )e + (80a b c - 20a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 20a b c + 5a b )e + (40a c - 10a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 2 3 5 5 3 3 2 5 4 +--R (16a c - 4b c )e x + (32a b c - 8b c )e x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (50a c - 26a b c + 4b c)e + (100a b c - 30b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (- 100a c + 40b c )d e - 20b c d e + 10c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (19a b c - 29a b c + 7b )e + (80a c + 50a b c - 25b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (- 30a b c + 30b c )d e + (- 80a c - 10b c )d e + 15b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 3 4 +--R (30a c - 56a b c + 14a b )e + (140a b c - 50a b c)d e +--R + +--R 2 3 2 2 2 3 3 3 2 4 2 3 4 +--R (- 60a c + 60a b c )d e - 60a b c d e + (- 10a c + 10b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 2 2 2 3 +--R (- 23a b c + 7a b )e + (60a c - 25a b c)d e + 30a b c d e +--R + +--R 2 3 3 2 3 4 4 2 3 5 +--R - 40a c d e + 5a b c d e + (- 4a c + b c )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 6 2 5 4 5 3 4 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 5 2 4 4 3 2 2 4 3 3 3 4 2 2 3 +--R (16a c + 4a b c - 2b c )x + (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 364 + +--S 365 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 4 5 2 3 4 3 2 3 +--R (30a c - 30a b c + 5b )e + (60a b c - 10b c)d e - 60a c d e +--R + +--R 3 3 2 4 4 +--R 20b c d e - 10c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 4 5 2 3 4 +--R (- 60a c + 60a b c - 10b )e + (- 120a b c + 20b c)d e +--R + +--R 3 2 3 3 3 2 4 4 +--R 120a c d e - 40b c d e + 20c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 +--R ((- 23a b c + 7b )e + (60a c - 25b c)d e + 30b c d e - 30c d e ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 | 2 +--R (8a c - 2b c )\|- 4a c + b +--R Type: Expression(Integer) +--E 365 + +--S 366 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 4 5 2 3 4 +--R (- 60a c + 60a b c - 10b )e + (- 120a b c + 20b c)d e +--R + +--R 3 2 3 3 3 2 4 4 +--R 120a c d e - 40b c d e + 20c d e +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 4 5 2 3 4 +--R (- 60a c + 60a b c - 10b )e + (- 120a b c + 20b c)d e +--R + +--R 3 2 3 3 3 2 4 4 +--R 120a c d e - 40b c d e + 20c d e +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 +--R ((- 23a b c + 7b )e + (60a c - 25b c)d e + 30b c d e - 30c d e ) +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R 4 2 3 | 2 | 2 +--R (8a c - 2b c )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 367 + +--S 368 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 368 + +)clear all + +--S 369 of 845 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 369 + +--S 370 of 845 +r0:=2*e^3*(2*c*d-b*e)*x/(c*(b^2-4*a*c))-1/2*(d+e*x)^4/(a+b*x+c*x^2)^2-_ + 2*e*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+_ + 2*e*(2*c*d-b*e)*(2*c^2*d^2-b^2*e^2-2*c*e*(b*d-3*a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(c^2*(b^2-4*a*c)^(3/2))+e^4*log(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 3 3 2 4 4 3 4 2 2 5 3 4 +--R ((24a b c - 4b c )e - 48a c d e + 24b c d e - 16c d e)x +--R + +--R 2 2 4 4 3 3 2 3 2 2 4 3 3 +--R ((48a b c - 8b c)e - 96a b c d e + 48b c d e - 32b c d e)x +--R + +--R 2 2 3 5 4 2 3 2 2 3 +--R (48a b c + 16a b c - 4b )e + (- 96a c - 48a b c )d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (48a b c + 24b c )d e + (- 32a c - 16b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 2 2 2 2 3 3 +--R ((48a b c - 8a b )e - 96a b c d e + 48a b c d e - 32a b c d e)x +--R + +--R 3 2 3 4 3 2 3 2 2 2 2 2 3 3 +--R (24a b c - 4a b )e - 48a c d e + 24a b c d e - 16a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 4 4 2 3 4 3 +--R (8a c - 2b c )e x + (16a b c - 4b c)e x +--R + +--R 2 2 2 4 4 2 2 3 4 +--R (16a c + 4a b c - 2b )e x + (16a b c - 4a b )e x +--R + +--R 3 2 2 4 +--R (8a c - 2a b )e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 12a c + 5b c )e - 12b c d e + 16c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (- 4a b c + 4b c)e + (- 40a c - 8b c )d e + 20b c d e +--R + +--R 4 3 +--R 8c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 2 3 3 2 2 2 2 +--R (- 8a c + 8a b c)e - 36a b c d e + (- 16a c + 10b c )d e +--R + +--R 3 3 +--R 12b c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 2 2 3 2 2 3 +--R (4a b c e - 24a c d e - 4a b c d e + (- 8a c + 8b c )d e)x +--R + +--R 2 2 2 2 2 3 3 2 2 4 +--R - 8a c d e + 4a b c d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 4 4 3 3 3 2 4 2 3 4 2 2 +--R (8a c - 2b c )x + (16a b c - 4b c )x + (16a c + 4a b c - 2b c )x +--R + +--R 2 3 3 2 3 3 2 2 2 +--R (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 370 + +--S 371 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 4 4 3 4 2 2 5 3 4 +--R ((12a b c - 2b c )e - 24a c d e + 12b c d e - 8c d e)x +--R + +--R 2 2 4 4 3 3 2 3 2 2 4 3 3 +--R ((24a b c - 4b c)e - 48a b c d e + 24b c d e - 16b c d e)x +--R + +--R 2 2 3 5 4 2 3 2 2 3 +--R (24a b c + 8a b c - 2b )e + (- 48a c - 24a b c )d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (24a b c + 12b c )d e + (- 16a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 2 2 2 2 3 3 +--R ((24a b c - 4a b )e - 48a b c d e + 24a b c d e - 16a b c d e)x +--R + +--R 3 2 3 4 3 2 3 2 2 2 2 2 3 3 +--R (12a b c - 2a b )e - 24a c d e + 12a b c d e - 8a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 4 4 2 3 4 3 +--R (8a c - 2b c )e x + (16a b c - 4b c)e x +--R + +--R 2 2 2 4 4 2 2 3 4 +--R (16a c + 4a b c - 2b )e x + (16a b c - 4a b )e x +--R + +--R 3 2 2 4 +--R (8a c - 2a b )e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (20a b c - 6b c)e + (- 40a c + 16b c )d e - 12b c d e +--R + +--R 4 3 +--R 8c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 4 2 3 3 +--R (16a c + 10a b c - 5b )e + (- 12a b c + 12b c)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 48a c - 6b c )d e + 12b c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (28a b c - 10a b )e + (- 24a c + 24a b c)d e - 36a b c d e +--R + +--R 3 2 2 3 +--R (- 8a c + 8b c )d e +--R * +--R x +--R + +--R 3 2 2 4 2 3 2 2 2 2 2 3 +--R (12a c - 5a b )e + 12a b c d e - 24a c d e + 4a b c d e +--R + +--R 3 2 2 4 +--R (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 4 4 3 3 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 4 2 3 4 2 2 2 3 3 2 3 3 2 2 2 +--R (16a c + 4a b c - 2b c )x + (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 3 3 2 4 4 3 4 2 2 5 3 4 +--R ((- 24a b c + 4b c )e + 48a c d e - 24b c d e + 16c d e)x +--R + +--R 2 2 4 4 3 3 2 3 2 2 4 3 3 +--R ((- 48a b c + 8b c)e + 96a b c d e - 48b c d e + 32b c d e)x +--R + +--R 2 2 3 5 4 2 3 2 2 3 +--R (- 48a b c - 16a b c + 4b )e + (96a c + 48a b c )d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (- 48a b c - 24b c )d e + (32a c + 16b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 2 2 2 2 +--R (- 48a b c + 8a b )e + 96a b c d e - 48a b c d e +--R + +--R 3 3 +--R 32a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 3 2 2 2 2 2 3 3 +--R (- 24a b c + 4a b )e + 48a c d e - 24a b c d e + 16a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 2 2 4 4 2 3 4 3 +--R (8a c - 2b c )e x + (16a b c - 4b c)e x +--R + +--R 2 2 2 4 4 2 2 3 4 +--R (16a c + 4a b c - 2b )e x + (16a b c - 4a b )e x +--R + +--R 3 2 2 4 +--R (8a c - 2a b )e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (20a b c - 6b c)e + (- 40a c + 16b c )d e - 12b c d e +--R + +--R 4 3 +--R 8c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 4 2 3 3 +--R (16a c + 10a b c - 5b )e + (- 12a b c + 12b c)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 48a c - 6b c )d e + 12b c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (28a b c - 10a b )e + (- 24a c + 24a b c)d e - 36a b c d e +--R + +--R 3 2 2 3 +--R (- 8a c + 8b c )d e +--R * +--R x +--R + +--R 3 2 2 4 2 3 2 2 2 2 2 3 +--R (12a c - 5a b )e + 12a b c d e - 24a c d e + 4a b c d e +--R + +--R 3 2 2 4 +--R (- 4a c + b c )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 5 2 4 4 4 3 3 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 4 2 3 4 2 2 2 3 3 2 3 3 2 2 2 +--R (16a c + 4a b c - 2b c )x + (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 371 + +--S 372 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 2 3 2 2 2 3 3 +--R ((12a b c - 2b )e - 24a c d e + 12b c d e - 8c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 4 2 3 2 2 2 3 3 +--R ((- 24a b c + 4b )e + 48a c d e - 24b c d e + 16c d e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((12a c - 5b )e + 12b c d e - 16c d e )\|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 | 2 +--R (8a c - 2b c )\|- 4a c + b +--R Type: Expression(Integer) +--E 372 + +--S 373 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 3 4 2 3 2 2 2 3 3 | 2 +--R ((- 24a b c + 4b )e + 48a c d e - 24b c d e + 16c d e)\|4a c - b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 4 2 3 2 2 2 3 3 | 2 +--R ((- 24a b c + 4b )e + 48a c d e - 24b c d e + 16c d e)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +-----------+ +---------+ +--R 2 4 3 2 2 2 | 2 | 2 +--R ((12a c - 5b )e + 12b c d e - 16c d e )\|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R 3 2 2 | 2 | 2 +--R (8a c - 2b c )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 374 + +--S 375 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 845 +r0:=-1/2*(d+e*x)^3/(a+b*x+c*x^2)^2-3/2*e*(d+e*x)*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + ((b^2-4*a*c)*(a+b*x+c*x^2))+6*e*(c*d^2-b*d*e+a*e^2)*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 12a c e + 12b c d e - 12c d e)x +--R + +--R 3 2 2 2 2 3 +--R (- 24a b c e + 24b c d e - 24b c d e)x +--R + +--R 2 2 3 3 2 +--R (- 24a c - 12a b )e + (24a b c + 12b )d e +--R + +--R 2 2 2 +--R (- 24a c - 12b c)d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 3 3 2 2 +--R (- 24a b e + 24a b d e - 24a b c d e)x - 12a e + 12a b d e +--R + +--R 2 2 +--R - 12a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 4 2 3 2 2 2 3 +--R (- 3b c e + 6c d e )x + ((- 10a c - 2b )e + 6b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 +--R (- 9a b e + (- 12a c + 3b )d e + 9b c d e)x +--R + +--R 2 3 2 2 2 2 2 2 +--R (- 6a e - 6a b d e + (- 6a c + 6b )d e)x - 6a d e + 3a b d e +--R + +--R 2 3 +--R (- 4a c + b )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 377 + +--S 378 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 4 2 4 +--R (6a c e - 6b c d e + 6c d e)x +--R + +--R 2 3 2 2 2 3 2 3 +--R (12a b c e - 12b c d e + 12b c d e)x +--R + +--R 2 2 2 3 2 3 2 +--R (12a c + 6a b c)e + (- 12a b c - 6b c)d e +--R + +--R 3 2 2 2 +--R (12a c + 6b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 3 2 2 +--R (12a b c e - 12a b c d e + 12a b c d e)x + 6a c e - 6a b c d e +--R + +--R 2 2 2 +--R 6a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 10a c + 4b c)e - 6b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 3a b c + 3b )e + (- 24a c - 3b c)d e + 9b c d e)x +--R + +--R 2 2 3 2 2 2 2 +--R ((- 6a c + 6a b )e - 18a b c d e + (- 6a c + 6b c)d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R 3a b e - 12a c d e + 3a b c d e + (- 4a c + b c)d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 2 3 4 3 3 2 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 3 2 2 4 2 2 2 3 3 2 2 2 +--R (16a c + 4a b c - 2b c)x + (16a b c - 4a b c)x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 3 3 3 2 4 2 4 +--R (12a c e - 12b c d e + 12c d e)x +--R + +--R 2 3 2 2 2 3 2 3 +--R (24a b c e - 24b c d e + 24b c d e)x +--R + +--R 2 2 2 3 2 3 2 +--R (24a c + 12a b c)e + (- 24a b c - 12b c)d e +--R + +--R 3 2 2 2 +--R (24a c + 12b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 3 +--R (24a b c e - 24a b c d e + 24a b c d e)x + 12a c e +--R + +--R 2 2 2 2 2 +--R - 12a b c d e + 12a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 10a c + 4b c)e - 6b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 3a b c + 3b )e + (- 24a c - 3b c)d e + 9b c d e)x +--R + +--R 2 2 3 2 2 2 2 +--R ((- 6a c + 6a b )e - 18a b c d e + (- 6a c + 6b c)d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R 3a b e - 12a c d e + 3a b c d e + (- 4a c + b c)d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 4 2 3 4 3 3 2 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 3 2 2 4 2 2 2 3 3 2 2 2 +--R (16a c + 4a b c - 2b c)x + (16a b c - 4a b c)x + 8a c - 2a b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 378 + +--S 379 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 2 +--R (6a c e - 6b c d e + 6c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2 2c x + b +--R (12a c e - 12b c d e + 12c d e)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 2 | 2 +--R (3b e - 6c d e )\|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (8a c - 2b c)\|- 4a c + b +--R Type: Expression(Integer) +--E 379 + +--S 380 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 3 2 2 2 | 2 2c x + b +--R (12a c e - 12b c d e + 12c d e)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 2 2 2 | 2 +--R (12a c e - 12b c d e + 12c d e)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +-----------+ +---------+ +--R 3 2 | 2 | 2 +--R (3b e - 6c d e )\|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R 2 2 | 2 | 2 +--R (8a c - 2b c)\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 381 + +--S 382 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 382 + +)clear all + +--S 383 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 383 + +--S 384 of 845 +r0:=-1/2*(d+e*x)^2/(a+b*x+c*x^2)^2-e*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*_ + (a+b*x+c*x^2))+2*e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 2 2 3 4 2 2 2 3 +--R (4b c e - 8c d e)x + (8b c e - 16b c d e)x +--R + +--R 3 2 2 2 2 +--R ((8a b c + 4b )e + (- 16a c - 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (8a b e - 16a b c d e)x + 4a b e - 8a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 2 +--R (- 2b c e + 4c d e)x + ((- 8a c - b )e + 6b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 6a b e + (- 4a c + 4b )d e)x - 4a e + 2a b d e + (- 4a c + b )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 384 + +--S 385 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 4 2 2 2 3 +--R (2b c e - 4c d e)x + (4b c e - 8b c d e)x +--R + +--R 3 2 2 2 2 +--R ((4a b c + 2b )e + (- 8a c - 4b c)d e)x +--R + +--R 2 2 2 2 2 +--R (4a b e - 8a b c d e)x + 2a b e - 4a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 2 2 2 +--R (- 2b c e + 4c d e)x + ((- 8a c - b )e + 6b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 6a b e + (- 4a c + 4b )d e)x - 4a e + 2a b d e + (- 4a c + b )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 2 3 4 2 2 2 3 +--R (- 4b c e + 8c d e)x + (- 8b c e + 16b c d e)x +--R + +--R 3 2 2 2 2 +--R ((- 8a b c - 4b )e + (16a c + 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 8a b e + 16a b c d e)x - 4a b e + 8a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 3 2 2 2 +--R (- 2b c e + 4c d e)x + ((- 8a c - b )e + 6b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 6a b e + (- 4a c + 4b )d e)x - 4a e + 2a b d e + (- 4a c + b )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 385 + +--S 386 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +--R (b e - 2c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2c x + b +--R (- 2b e + 4c d e)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R (4a c - b )\|- 4a c + b +--R Type: Expression(Integer) +--E 386 + +--S 387 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 2 | 2 2c x + b +--R (- 2b e + 4c d e)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (- 2b e + 4c d e)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R (4a c - b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 388 + +--S 389 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 389 + +)clear all + +--S 390 of 845 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 390 + +--S 391 of 845 +r0:=1/2*(-d-e*x)/(a+b*x+c*x^2)^2-1/2*e*(b+2*c*x)/((b^2-4*a*c)*_ + (a+b*x+c*x^2))+2*c*e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 2 +--R (- 4c e x - 8b c e x + (- 8a c - 4b c)e x - 8a b c e x - 4a c e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 2 +--R (2c e x + 3b c e x + (- 2a c + 2b )e x + a b e + (- 4a c + b )d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 391 + +--S 392 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 3 2 2 2 2 +--R (2c e x + 4b c e x + (4a c + 2b c)e x + 4a b c e x + 2a c e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 +--R (2c e x + 3b c e x + (- 2a c + 2b )e x + a b e + (- 4a c + b )d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 3 4 2 3 2 2 2 2 +--R (4c e x + 8b c e x + (8a c + 4b c)e x + 8a b c e x + 4a c e) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 3 2 2 2 +--R (2c e x + 3b c e x + (- 2a c + 2b )e x + a b e + (- 4a c + b )d) +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 392 + +--S 393 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R c e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R 2c e atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R (4a c - b )\|- 4a c + b +--R Type: Expression(Integer) +--E 393 + +--S 394 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R | 2 2c x + b +--R 2c e\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R 2c e\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R (4a c - b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 395 + +--S 396 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 of 845 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 397 + +--S 398 of 845 +r0:=(-1/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 1 +--R - +--R 2 +--R (2) - -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 398 + +--S 399 of 845 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------------------------------------- +--R 2 4 3 2 2 2 +--R 2c x + 4b c x + (4a c + 2b )x + 4a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 401 + +)clear all + +--S 402 of 845 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^3) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 7 2 3 6 2 2 2 5 +--R c e x + (3b c e + c d)x + ((3a c + 3b c)e + 3b c d)x +--R + +--R 3 2 2 4 +--R ((6a b c + b )e + (3a c + 3b c)d)x +--R + +--R 2 2 3 3 2 2 2 2 +--R ((3a c + 3a b )e + (6a b c + b )d)x + (3a b e + (3a c + 3a b )d)x +--R + +--R 3 2 3 +--R (a e + 3a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 402 + +--S 403 of 845 +r0:=1/2*(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)-1/2*e*(3*b^2*c*d*e-8*a*c^2*d*e-_ + 2*b^3*e^2-b*c*(c*d^2-7*a*e^2)-2*c*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*(a+b*x+c*x^2))-e*(2*c^4*d^4-b^4*e^4-_ + 4*c^3*d^2*e*(b*d-3*a*e)-6*a*c^2*e^3*(2*b*d+a*e)+2*b^2*c*e^3*_ + (b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((b^2-4*a*c)^(3/2)*_ + (c*d^2-b*d*e+a*e^2)^3)-e^4*(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+_ + 1/2*e^4*(2*c*d-b*e)*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3 +--R +--R +--R (2) +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (- 12a c + 12a b c - 2b c )e + (- 24a b c + 4b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R 24a c d e - 8b c d e + 4c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (- 24a b c + 24a b c - 4b c)e + (- 48a b c + 8b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R 48a b c d e - 16b c d e + 8b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 24a c + 12a b c + 8a b c - 2b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (- 48a b c - 16a b c + 4b c)d e + (48a c + 24a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (- 16a b c - 8b c )d e + (8a c + 4b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (- 24a b c + 24a b c - 4a b )e + (- 48a b c + 8a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R 48a b c d e - 16a b c d e + 8a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (- 12a c + 12a b c - 2a b )e + (- 24a b c + 4a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R 24a c d e - 8a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 4a b c + b c )e + (8a c - 2b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 8a b c + 2b c)e + (16a b c - 4b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((- 8a b c - 2a b c + b )e + (16a c + 4a b c - 2b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 8a b c + 2a b )e + (16a b c - 4a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 4a b c + a b )e + (8a c - 2a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((8a b c - 2b c )e + (- 16a c + 4b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((16a b c - 4b c)e + (- 32a b c + 8b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((16a b c + 4a b c - 2b )e + (- 32a c - 8a b c + 4b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((16a b c - 4a b )e + (- 32a b c + 8a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (8a b c - 2a b )e + (- 16a c + 4a b c)d e +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 5 3 3 2 4 +--R (6a c - 2a b c )e + (- 4a b c + 2b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (4a c - 4b c )d e + 4b c d e - 2c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 4 +--R (13a b c - 4a b c)e + (- 8a c - 8a b c + 4b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (18a b c - 9b c )d e + (- 8a c + 8b c )d e - 3b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 5 4 +--R (10a c + 4a b c - 2a b )e + (- 20a b c + 2b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (12a c + 12a b c - 6b c)d e + (- 12a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (2a c - 2b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (11a b c - 3a b )e + (- 12a c - 11a b c + 4a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (30a b c - 5a b c - b )d e + (- 16a c - 6a b c + 3b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (11a b c - 3b c )d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 3 3 2 2 6 3 3 2 3 2 5 +--R (8a c - 2a b c )e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 4 +--R (24a c + 18a b c - 6a b c )d e +--R + +--R 2 4 3 3 5 2 3 3 +--R (- 48a b c + 4a b c + 2b c )d e +--R + +--R 2 5 2 4 4 3 4 2 5 3 4 5 +--R (24a c + 18a b c - 6b c )d e + (- 24a b c + 6b c )d e +--R + +--R 6 2 5 6 +--R (8a c - 2b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 6 3 2 2 2 4 5 +--R (16a b c - 4a b c)e + (- 48a b c + 12a b c)d e +--R + +--R 3 3 2 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b c)d e +--R + +--R 2 2 3 4 2 6 3 3 +--R (- 96a b c + 8a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 4 2 2 4 4 3 5 +--R (48a b c + 36a b c - 12b c )d e + (- 48a b c + 12b c )d e +--R + +--R 5 3 4 6 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 6 4 2 3 3 2 5 5 +--R (16a c + 4a b c - 2a b )e + (- 48a b c - 12a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 4 +--R (48a c + 60a b c + 6a b c - 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 96a b c - 40a b c + 8a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 4 2 +--R (48a c + 60a b c + 6a b c - 6b c)d e +--R + +--R 2 4 3 3 5 2 5 2 5 2 4 4 3 6 +--R (- 48a b c - 12a b c + 6b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 3 6 4 2 3 4 5 +--R (16a b c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b )d e +--R + +--R 3 2 2 2 4 6 3 3 +--R (- 96a b c + 8a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 2 3 4 2 5 +--R (48a b c + 36a b c - 12a b c)d e + (- 48a b c + 12a b c )d e +--R + +--R 2 4 3 3 6 +--R (16a b c - 4a b c )d +--R * +--R x +--R + +--R 6 5 2 6 5 4 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 5 2 4 2 3 4 2 4 4 2 3 3 2 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2a b )d e +--R + +--R 4 3 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (24a c + 18a b c - 6a b c)d e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 6 +--R (8a c - 2a b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 403 + +--S 404 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (6a c - 6a b c + b c )e + (12a b c - 2b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R - 12a c d e + 4b c d e - 2c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (12a b c - 12a b c + 2b c)e + (24a b c - 4b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R - 24a b c d e + 8b c d e - 4b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (12a c - 6a b c - 4a b c + b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (24a b c + 8a b c - 2b c)d e + (- 24a c - 12a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (8a b c + 4b c )d e + (- 4a c - 2b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (12a b c - 12a b c + 2a b )e + (24a b c - 4a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R - 24a b c d e + 8a b c d e - 4a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 3 3 2 3 +--R (6a c - 6a b c + a b )e + (12a b c - 2a b c)d e - 12a c d e +--R + +--R 2 3 3 2 2 4 4 +--R 4a b c d e - 2a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 4a b c + b c )e + (8a c - 2b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 8a b c + 2b c)e + (16a b c - 4b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((- 8a b c - 2a b c + b )e + (16a c + 4a b c - 2b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 8a b c + 2a b )e + (16a b c - 4a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 4a b c + a b )e + (8a c - 2a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((8a b c - 2b c )e + (- 16a c + 4b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((16a b c - 4b c)e + (- 32a b c + 8b c )d e )x +--R + +--R 2 2 3 5 5 +--R (16a b c + 4a b c - 2b )e +--R + +--R 2 3 2 2 4 4 +--R (- 32a c - 8a b c + 4b c)d e 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3b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (11a b c - 3b c )d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 3 3 2 2 6 3 3 2 3 2 5 +--R (8a c - 2a b c )e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 4 +--R (24a c + 18a b c - 6a b c )d e +--R + +--R 2 4 3 3 5 2 3 3 +--R (- 48a b c + 4a b c + 2b c )d e +--R + +--R 2 5 2 4 4 3 4 2 5 3 4 5 +--R (24a c + 18a b c - 6b c )d e + (- 24a b c + 6b c )d e +--R + +--R 6 2 5 6 +--R (8a c - 2b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 6 3 2 2 2 4 5 +--R (16a b c - 4a b c)e + (- 48a b c + 12a b c)d e +--R + +--R 3 3 2 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b c)d e +--R + +--R 2 2 3 4 2 6 3 3 +--R (- 96a b c + 8a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 4 2 2 4 4 3 5 +--R (48a b c + 36a b c - 12b c )d e + (- 48a b c + 12b c )d e +--R + +--R 5 3 4 6 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 6 4 2 3 3 2 5 5 +--R (16a c + 4a b c - 2a b )e + (- 48a b c - 12a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 4 +--R (48a c + 60a b c + 6a b c - 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 96a b c - 40a b c + 8a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 4 2 +--R (48a c + 60a b c + 6a b c - 6b c)d e +--R + +--R 2 4 3 3 5 2 5 2 5 2 4 4 3 6 +--R (- 48a b c - 12a b c + 6b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 3 6 4 2 3 4 5 +--R (16a b c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b )d e +--R + +--R 3 2 2 2 4 6 3 3 +--R (- 96a b c + 8a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 2 3 4 2 5 +--R (48a b c + 36a b c - 12a b c)d e + (- 48a b c + 12a b c )d e +--R + +--R 2 4 3 3 6 +--R (16a b c - 4a b c )d +--R * +--R x +--R + +--R 6 5 2 6 5 4 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 5 2 4 2 3 4 2 4 4 2 3 3 2 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2a b )d e +--R + +--R 4 3 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (24a c + 18a b c - 6a b c)d e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 6 +--R (8a c - 2a b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (12a c - 12a b c + 2b c )e + (24a b c - 4b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R - 24a c d e + 8b c d e - 4c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (24a b c - 24a b c + 4b c)e + (48a b c - 8b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R - 48a b c d e + 16b c d e - 8b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (24a c - 12a b c - 8a b c + 2b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (48a b c + 16a b c - 4b c)d e + (- 48a c - 24a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (16a b c + 8b c )d e + (- 8a c - 4b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (24a b c - 24a b c + 4a b )e + (48a b c - 8a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R - 48a b c d e + 16a b c d e - 8a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 3 3 2 3 +--R (12a c - 12a b c + 2a b )e + (24a b c - 4a b c)d e - 24a c d e +--R + +--R 2 3 3 2 2 4 4 +--R 8a b c d e - 4a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 4a b c + b c )e + (8a c - 2b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 8a b c + 2b c)e + (16a b c - 4b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((- 8a b c - 2a b c + b )e + (16a c + 4a b c - 2b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 8a b c + 2a b )e + (16a b c - 4a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 4a b c + a b )e + (8a c - 2a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((8a b c - 2b c )e + (- 16a c + 4b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((16a b c - 4b c)e + (- 32a b c + 8b c )d e )x +--R + +--R 2 2 3 5 5 +--R (16a b c + 4a b c - 2b )e +--R + +--R 2 3 2 2 4 4 +--R (- 32a c - 8a b c + 4b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((16a b c - 4a b )e + (- 32a b c + 8a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (8a b c - 2a b )e + (- 16a c + 4a b c)d e +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 5 3 3 2 4 +--R (6a c - 2a b c )e + (- 4a b c + 2b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (4a c - 4b c )d e + 4b c d e - 2c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 4 +--R (13a b c - 4a b c)e + (- 8a c - 8a b c + 4b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (18a b c - 9b c )d e + (- 8a c + 8b c )d e - 3b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 5 4 +--R (10a c + 4a b c - 2a b )e + (- 20a b c + 2b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (12a c + 12a b c - 6b c)d e + (- 12a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (2a c - 2b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (11a b c - 3a b )e + (- 12a c - 11a b c + 4a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (30a b c - 5a b c - b )d e + (- 16a c - 6a b c + 3b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (11a b c - 3b c )d e + (- 4a c + b c )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 4 3 3 2 2 6 3 3 2 3 2 5 +--R (8a c - 2a b c )e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 4 +--R (24a c + 18a b c - 6a b c )d e +--R + +--R 2 4 3 3 5 2 3 3 +--R (- 48a b c + 4a b c + 2b c )d e +--R + +--R 2 5 2 4 4 3 4 2 5 3 4 5 +--R (24a c + 18a b c - 6b c )d e + (- 24a b c + 6b c )d e +--R + +--R 6 2 5 6 +--R (8a c - 2b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 6 3 2 2 2 4 5 +--R (16a b c - 4a b c)e + (- 48a b c + 12a b c)d e +--R + +--R 3 3 2 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b c)d e +--R + +--R 2 2 3 4 2 6 3 3 +--R (- 96a b c + 8a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 4 2 2 4 4 3 5 +--R (48a b c + 36a b c - 12b c )d e + (- 48a b c + 12b c )d e +--R + +--R 5 3 4 6 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 6 4 2 3 3 2 5 5 +--R (16a c + 4a b c - 2a b )e + (- 48a b c - 12a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 4 +--R (48a c + 60a b c + 6a b c - 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 96a b c - 40a b c + 8a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 4 2 +--R (48a c + 60a b c + 6a b c - 6b c)d e +--R + +--R 2 4 3 3 5 2 5 2 5 2 4 4 3 6 +--R (- 48a b c - 12a b c + 6b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 3 6 4 2 3 4 5 +--R (16a b c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b )d e +--R + +--R 3 2 2 2 4 6 3 3 +--R (- 96a b c + 8a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 2 3 4 2 5 +--R (48a b c + 36a b c - 12a b c)d e + (- 48a b c + 12a b c )d e +--R + +--R 2 4 3 3 6 +--R (16a b c - 4a b c )d +--R * +--R x +--R + +--R 6 5 2 6 5 4 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 5 2 4 2 3 4 2 4 4 2 3 3 2 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2a b )d e +--R + +--R 4 3 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (24a c + 18a b c - 6a b c)d e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 6 +--R (8a c - 2a b c )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 404 + +--S 405 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 4 5 2 3 4 3 2 3 +--R (6a c - 6a b c + b )e + (12a b c - 2b c)d e - 12a c d e +--R + +--R 3 3 2 4 4 +--R 4b c d e - 2c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 4 5 2 3 4 3 2 3 +--R (12a c - 12a b c + 2b )e + (24a b c - 4b c)d e - 24a c d e +--R + +--R 3 3 2 4 4 +--R 8b c d e - 4c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 405 + +--S 406 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 4 5 2 3 4 3 2 3 +--R (6a c - 6a b c + b )e + (12a b c - 2b c)d e - 12a c d e +--R + +--R 3 3 2 4 4 +--R 4b c d e - 2c d e +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 4 5 2 3 4 3 2 3 +--R (6a c - 6a b c + b )e + (12a b c - 2b c)d e - 12a c d e +--R + +--R 3 3 2 4 4 +--R 4b c d e - 2c d e +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 407 + +--S 408 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 845 +t0:=(b+2*c*x)*(d+e*x)^4*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 845 +r0:=1/1680*(128*c^4*d^4+105*b^4*e^4-16*c^3*d^2*e*(16*b*d+93*a*e)-_ + 4*b^2*c*e^3*(109*b*d+101*a*e)+4*c^2*e^2*(141*b^2*d^2+372*a*b*d*e+_ + 16*a^2*e^2))*(a+b*x+c*x^2)^(3/2)/c^4+1/35*(4*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(b*d+2*a*e))*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)/c^2+2/21*(2*c*d-b*e)*_ + (d+e*x)^3*(a+b*x+c*x^2)^(3/2)/c+2/7*(d+e*x)^4*(a+b*x+c*x^2)^(3/2)-_ + 1/280*e*(9*b^3*d*e^2+8*a*c*e*(17*c*d^2-4*a*e^2)-4*b*c*d*(2*c*d^2+_ + 15*a*e^2)-b^2*(22*c*d^2*e-12*a*e^3)-(2*c*d-b*e)*(8*c^2*d^2+_ + 21*b^2*e^2-4*c*e*(2*b*d+19*a*e))*x)*(a+b*x+c*x^2)^(3/2)/c^3-_ + 1/256*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(8*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(2*b*d+a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/_ + c^(11/2)+1/128*(b^2-4*a*c)*e*(2*c*d-b*e)*(8*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(2*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 3 3 2 3 2 5 7 4 +--R (- 6720a b c + 8400a b c - 2940a b c + 315b )e +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (13440a c - 30240a b c + 12600a b c - 1470b c)d e +--R + +--R 2 4 3 3 5 2 2 2 +--R (40320a b c - 20160a b c + 2520b c )d e +--R + +--R 2 5 2 4 4 3 3 +--R (- 26880a c + 13440a b c - 1680b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 6 4 6 5 4 6 3 5 +--R 7680c e x + (5120b c e + 35840c d e )x +--R + +--R 5 2 4 4 5 3 6 2 2 4 +--R ((1536a c - 256b c )e + 25088b c d e + 64512c d e )x +--R + +--R 4 3 3 4 5 2 4 3 +--R (- 1408a b c + 288b c )e + (8960a c - 1344b c )d e +--R + +--R 5 2 2 6 3 +--R 48384b c d e + 53760c d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 4 2 4 +--R (- 2048a c + 1984a b c - 336b c )e +--R + +--R 4 3 3 3 5 2 4 2 2 +--R (- 8064a b c + 1568b c )d e + (21504a c - 2688b c )d e +--R + +--R 5 3 6 4 +--R 44800b c d e + 17920c d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 5 4 +--R (4672a b c - 2912a b c + 420b c)e +--R + +--R 2 4 2 3 4 2 3 +--R (- 13440a c + 12096a b c - 1960b c )d e +--R + +--R 4 3 3 2 2 5 2 4 3 +--R (- 18816a b c + 3360b c )d e + (26880a c - 2240b c )d e +--R + +--R 5 4 +--R 17920b c d +--R * +--R x +--R + +--R 3 3 2 2 2 4 6 4 +--R (4096a c - 10976a b c + 5040a b c - 630b )e +--R + +--R 2 3 3 2 5 3 +--R (36288a b c - 21280a b c + 2940b c)d e +--R + +--R 2 4 2 3 4 2 2 2 +--R (- 43008a c + 33600a b c - 5040b c )d e +--R + +--R 4 3 3 3 5 4 +--R (- 22400a b c + 3360b c )d e + 17920a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 26880c \|c +--R Type: Expression(Integer) +--E 410 + +--S 411 of 845 +--a0:=integrate(t0,x) +--E 411 + +--S 412 of 845 +--m0:=a0-r0 +--E 412 + +--S 413 of 845 +--d0:=D(m0,x) +--E 413 + +)clear all + +--S 414 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 414 + +--S 415 of 845 +r0:=1/480*(2*c*d-b*e)*(32*c^2*d^2+35*b^2*e^2-4*c*e*(8*b*d+27*a*e))*_ + (a+b*x+c*x^2)^(3/2)/c^3+1/10*(2*c*d-b*e)*(d+e*x)^2*_ + (a+b*x+c*x^2)^(3/2)/c+1/3*(d+e*x)^3*(a+b*x+c*x^2)^(3/2)+1/80*e*_ + (3*b^2*d*e-28*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+7*b^2*e^2-4*c*e*_ + (2*b*d+5*a*e))*x)*(a+b*x+c*x^2)^(3/2)/c^2-1/512*(b^2-4*a*c)^2*e*_ + (24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)+1/256*(b^2-4*a*c)*e*(24*c^2*d^2+_ + 7*b^2*e^2-4*c*e*(6*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 3 +--R (960a c - 2160a b c + 900a b c - 105b )e +--R + +--R 2 3 3 2 5 2 +--R (5760a b c - 2880a b c + 360b c)d e +--R + +--R 2 4 2 3 4 2 2 +--R (- 5760a c + 2880a b c - 360b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 5 3 5 4 3 5 2 4 +--R 2560c e x + (1792b c e + 9216c d e )x +--R + +--R 4 2 3 3 4 2 5 2 3 +--R ((640a c - 96b c )e + 6912b c d e + 11520c d e)x +--R + +--R 3 3 2 3 4 2 3 2 +--R (- 576a b c + 112b c )e + (3072a c - 384b c )d e +--R + +--R 4 2 5 3 +--R 9600b c d e + 5120c d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 4 3 3 3 2 2 +--R (- 960a c + 864a b c - 140b c)e + (- 2688a b c + 480b c )d e +--R + +--R 4 2 3 2 4 3 +--R (5760a c - 480b c )d e + 5120b c d +--R * +--R x +--R + +--R 2 2 3 5 3 +--R (2592a b c - 1520a b c + 210b )e +--R + +--R 2 3 2 2 4 2 3 3 2 2 +--R (- 6144a c + 4800a b c - 720b c)d e + (- 4800a b c + 720b c )d e +--R + +--R 4 3 +--R 5120a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 415 + +--S 416 of 845 +--a0:=integrate(t0,x) +--E 416 + +--S 417 of 845 +--m0:=a0-r0 +--E 417 + +--S 418 of 845 +--d0:=D(m0,x) +--E 418 + +)clear all + +--S 419 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R +--------------+ +--R 2 3 2 2 2 2 | 2 +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|c x + b x + a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 845 +r0:=1/60*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*(a+b*x+c*x^2)^(3/2)/c^2+_ + 2/5*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)+1/10*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/c-1/64*(b^2-4*a*c)^2*e*(2*c*d-b*e)*atanh(1/2*(b+_ + 2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+1/32*(b^2-4*a*c)*e*(2*c*d-_ + b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 2 3 5 2 2 3 2 2 4 +--R ((240a b c - 120a b c + 15b )e + (- 480a c + 240a b c - 30b c)d e) +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 4 2 4 3 2 4 3 +--R 384c e x + (288b c e + 960c d e)x +--R + +--R 3 2 2 2 3 4 2 2 +--R ((128a c - 16b c )e + 800b c d e + 640c d )x +--R + +--R 2 3 2 3 2 2 3 2 +--R ((- 112a b c + 20b c)e + (480a c - 40b c )d e + 640b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 +--R (- 256a c + 200a b c - 30b )e + (- 400a b c + 60b c)d e + 640a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 960c \|c +--R Type: Expression(Integer) +--E 420 + +--S 421 of 845 +--a0:=integrate(t0,x) +--E 421 + +--S 422 of 845 +--m0:=a0-r0 +--E 422 + +--S 423 of 845 +--d0:=D(m0,x) +--E 423 + +)clear all + +--S 424 of 845 +t0:=(b+2*c*x)*(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (1) (2c e x + (b e + 2c d)x + b d)\|c x + b x + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 845 +r0:=1/12*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/c+1/2*(d+e*x)*(a+b*x+c*x^2)^(3/2)-_ + 1/64*(b^2-4*a*c)^2*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(5/2)+1/32*(b^2-4*a*c)*e*(b+2*c*x)*_ + sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 4 2c x + b +--R (- 48a c + 24a b c - 3b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 3 2 3 2 2 2 2 +--R 96c e x + (80b c e + 128c d)x + ((48a c - 4b c)e + 128b c d)x +--R + +--R 3 2 +--R (- 40a b c + 6b )e + 128a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 425 + +--S 426 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 384a b c - 96a b c + 24b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 2304a b c - 1728a b c + 240a b )e x +--R + +--R 4 2 3 3 2 5 +--R (9216a b c - 4608a b c + 576a b )e x +--R + +--R 5 2 4 2 3 4 +--R (6144a c - 3072a b c + 384a b )e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (- 768a c - 768a b c + 480a b c - 48a b c - 3b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 1536a b c + 384a b c - 96a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 4608a b c + 3456a b c - 480a b )e x +--R + +--R 5 2 4 3 3 5 +--R (- 12288a b c + 6144a b c - 768a b )e x +--R + +--R 6 2 5 2 4 4 +--R (- 6144a c + 3072a b c - 384a b )e +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 5 2 4 4 3 7 +--R (- 1536a c - 2304a b c - 96b c )e x +--R + +--R 2 4 3 3 5 2 +--R (- 13568a b c - 4992a b c - 80b c )e +--R + +--R 2 5 2 4 4 3 +--R (- 2048a c - 3072a b c - 128b c )d +--R * +--R 6 +--R x +--R + +--R 3 4 2 2 3 4 2 6 +--R (- 13056a c - 26688a b c - 2512a b c + 4b c)e +--R + +--R 2 4 3 3 5 2 +--R (- 18432a b c - 7168a b c - 128b c )d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 5 7 +--R (- 40320a b c - 12960a b c + 24a b c - 6b )e +--R + +--R 3 4 2 2 3 4 2 +--R (- 18432a c - 39936a b c - 4224a b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 2 2 4 6 +--R (- 18432a c - 23808a b c + 1024a b c - 144a b )e +--R + +--R 3 3 2 3 2 +--R (- 61440a b c - 23552a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (- 19968a b c + 3840a b c - 480a b )e +--R + +--R 4 3 3 2 2 +--R (- 24576a c - 43008a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 4 2 +--R ((- 6144a c + 3072a b c - 384a b )e - 24576a b c d)x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 5 3 4 8 +--R (3072a b c + 768b c )e x +--R + +--R 2 5 2 4 4 3 5 3 4 7 +--R ((6144a c + 13312a b c + 1408b c )e + (4096a b c + 1024b c )d)x +--R + +--R 2 4 3 3 5 2 +--R (34304a b c + 17664a b c + 608b c )e +--R + +--R 2 5 2 4 4 3 +--R (8192a c + 18432a b c + 2048b c )d +--R * +--R 6 +--R x +--R + +--R 3 4 2 2 3 4 2 6 +--R (21504a c + 52992a b c + 6848a b c + 16b c)e +--R + +--R 2 4 3 3 5 2 +--R (49152a b c + 26624a b c + 1024b c )d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 5 7 +--R (57984a b c + 21600a b c - 104a b c + 42b )e +--R + +--R 3 4 2 2 3 4 2 +--R (30720a c + 82944a b c + 12160a b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 2 2 4 6 +--R (21504a c + 31488a b c - 2368a b c + 336a b )e +--R + +--R 3 3 2 3 2 +--R (86016a b c + 41984a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (23040a b c - 5376a b c + 672a b )e +--R + +--R 4 3 3 2 2 +--R (24576a c + 55296a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 4 2 +--R ((6144a c - 3072a b c + 384a b )e + 24576a b c d)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 3 2 3 2 3 2 2 2 +--R (6144a b c + 1536b c )x + (12288a c + 15360a b c )x +--R + +--R 2 2 3 2 +--R 36864a b c x + 24576a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 4 2 3 4 2 4 +--R (- 3072a c - 4608a b c - 192b c )x +--R + +--R 2 3 3 2 3 3 3 2 2 2 2 +--R (- 24576a b c - 6144a b c )x + (- 24576a c - 30720a b c )x +--R + +--R 3 2 4 2 +--R - 49152a b c x - 24576a c +--R * +--R +-+ +--R \|c +--R , +--R +--R 3 3 2 3 2 5 7 3 +--R (- 1536a b c + 384a b c + 96a b c - 24b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 3072a c - 2304a b c + 1728a b c - 240a b )e x +--R + +--R 4 2 3 3 2 5 +--R (- 9216a b c + 4608a b c - 576a b )e x +--R + +--R 5 2 4 2 3 4 +--R (- 6144a c + 3072a b c - 384a b )e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (768a c + 768a b c - 480a b c + 48a b c + 3b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (6144a b c - 1536a b c - 384a b c + 96a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (6144a c + 4608a b c - 3456a b c + 480a b )e x +--R + +--R 5 2 4 3 3 5 +--R (12288a b c - 6144a b c + 768a b )e x +--R + +--R 6 2 5 2 4 4 +--R (6144a c - 3072a b c + 384a b )e +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 5 2 4 4 3 7 +--R (- 768a c - 1152a b c - 48b c )e x +--R + +--R 2 4 3 3 5 2 +--R (- 6784a b c - 2496a b c - 40b c )e +--R + +--R 2 5 2 4 4 3 +--R (- 1024a c - 1536a b c - 64b c )d +--R * +--R 6 +--R x +--R + +--R 3 4 2 2 3 4 2 6 +--R (- 6528a c - 13344a b c - 1256a b c + 2b c)e +--R + +--R 2 4 3 3 5 2 +--R (- 9216a b c - 3584a b c - 64b c )d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 5 7 +--R (- 20160a b c - 6480a b c + 12a b c - 3b )e +--R + +--R 3 4 2 2 3 4 2 +--R (- 9216a c - 19968a b c - 2112a b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 2 2 4 6 +--R (- 9216a c - 11904a b c + 512a b c - 72a b )e +--R + +--R 3 3 2 3 2 +--R (- 30720a b c - 11776a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (- 9984a b c + 1920a b c - 240a b )e +--R + +--R 4 3 3 2 2 +--R (- 12288a c - 21504a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 4 2 +--R ((- 3072a c + 1536a b c - 192a b )e - 12288a b c d)x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 5 3 4 8 +--R (1536a b c + 384b c )e x +--R + +--R 2 5 2 4 4 3 5 3 4 7 +--R ((3072a c + 6656a b c + 704b c )e + (2048a b c + 512b c )d)x +--R + +--R 2 4 3 3 5 2 +--R (17152a b c + 8832a b c + 304b c )e +--R + +--R 2 5 2 4 4 3 +--R (4096a c + 9216a b c + 1024b c )d +--R * +--R 6 +--R x +--R + +--R 3 4 2 2 3 4 2 6 +--R (10752a c + 26496a b c + 3424a b c + 8b c)e +--R + +--R 2 4 3 3 5 2 +--R (24576a b c + 13312a b c + 512b c )d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 5 7 +--R (28992a b c + 10800a b c - 52a b c + 21b )e +--R + +--R 3 4 2 2 3 4 2 +--R (15360a c + 41472a b c + 6080a b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 2 2 4 6 +--R (10752a c + 15744a b c - 1184a b c + 168a b )e +--R + +--R 3 3 2 3 2 +--R (43008a b c + 20992a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (11520a b c - 2688a b c + 336a b )e +--R + +--R 4 3 3 2 2 +--R (12288a c + 27648a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 4 2 +--R ((3072a c - 1536a b c + 192a b )e + 12288a b c d)x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (3072a b c + 768b c )x + (6144a c + 7680a b c )x + 18432a b c x +--R + +--R 3 2 +--R 12288a c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 4 2 3 4 2 4 +--R (- 1536a c - 2304a b c - 96b c )x +--R + +--R 2 3 3 2 3 3 3 2 2 2 2 +--R (- 12288a b c - 3072a b c )x + (- 12288a c - 15360a b c )x +--R + +--R 3 2 4 2 +--R - 24576a b c x - 12288a c +--R * +--R +---+ +--R \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 426 + +--S 427 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 384a b c - 96a b c + 24b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 2304a b c - 1728a b c + 240a b )e x +--R + +--R 4 2 3 3 2 5 +--R (9216a b c - 4608a b c + 576a b )e x +--R + +--R 5 2 4 2 3 4 +--R (6144a c - 3072a b c + 384a b )e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (- 768a c - 768a b c + 480a b c - 48a b c - 3b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 1536a b c + 384a b c - 96a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 4608a b c + 3456a b c - 480a b )e x +--R + +--R 5 2 4 3 3 5 +--R (- 12288a b c + 6144a b c - 768a b )e x +--R + +--R 6 2 5 2 4 4 +--R (- 6144a c + 3072a b c - 384a b )e +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 384a b c - 96a b c + 24b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 2304a b c - 1728a b c + 240a b )e x +--R + +--R 4 2 3 3 2 5 +--R (9216a b c - 4608a b c + 576a b )e x +--R + +--R 5 2 4 2 3 4 +--R (6144a c - 3072a b c + 384a b )e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (- 768a c - 768a b c + 480a b c - 48a b c - 3b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 1536a b c + 384a b c - 96a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 4608a b c + 3456a b c - 480a b )e x +--R + +--R 5 2 4 3 3 5 +--R (- 12288a b c + 6144a b c - 768a b )e x +--R + +--R 6 2 5 2 4 4 +--R (- 6144a c + 3072a b c - 384a b )e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 4 6 3 3 2 3 2 3 +--R ((- 1280a b c - 128a b c + 48a b )e + (4096a b c + 1024a b c )d)x +--R + +--R 4 2 3 3 2 5 4 3 3 2 2 2 +--R ((- 2560a b c - 2816a b c + 480a b )e + (8192a c + 10240a b c )d)x +--R + +--R 4 2 3 4 4 2 +--R ((- 7680a b c + 1152a b )e + 24576a b c d)x +--R + +--R 5 4 3 5 2 +--R (- 5120a b c + 768a b )e + 16384a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 +--R (640a b c + 864a b c - 104a b c - 6b )e +--R + +--R 3 4 2 2 3 4 2 +--R (- 2048a c - 3072a b c - 128a b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 4 6 +--R (5120a b c + 512a b c - 192a b )e +--R + +--R 3 3 2 3 2 +--R (- 16384a b c - 4096a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (5120a b c + 5632a b c - 960a b )e +--R + +--R 4 3 3 2 2 +--R (- 16384a c - 20480a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 4 2 5 4 3 +--R ((10240a b c - 1536a b )e - 32768a b c d)x + (5120a b c - 768a b )e +--R + +--R 5 2 +--R - 16384a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 3 2 3 2 3 2 2 2 +--R (6144a b c + 1536b c )x + (12288a c + 15360a b c )x +--R + +--R 2 2 3 2 +--R 36864a b c x + 24576a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 4 2 3 4 2 4 +--R (- 3072a c - 4608a b c - 192b c )x +--R + +--R 2 3 3 2 3 3 3 2 2 2 2 +--R (- 24576a b c - 6144a b c )x + (- 24576a c - 30720a b c )x +--R + +--R 3 2 4 2 +--R - 49152a b c x - 24576a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 427 + +--S 428 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 384a b c - 96a b c + 24b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 2304a b c - 1728a b c + 240a b )e x +--R + +--R 4 2 3 3 2 5 +--R (9216a b c - 4608a b c + 576a b )e x +--R + +--R 5 2 4 2 3 4 +--R (6144a c - 3072a b c + 384a b )e +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (- 768a c - 768a b c + 480a b c - 48a b c - 3b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 1536a b c + 384a b c - 96a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 4608a b c + 3456a b c - 480a b )e x +--R + +--R 5 2 4 3 3 5 +--R (- 12288a b c + 6144a b c - 768a b )e x +--R + +--R 6 2 5 2 4 4 +--R (- 6144a c + 3072a b c - 384a b )e +--R * +--R +---+ +--R \|- c +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 +--R (- 3072a b c + 768a b c + 192a b c - 48b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 6144a c - 4608a b c + 3456a b c - 480a b )e x +--R + +--R 4 2 3 3 2 5 +--R (- 18432a b c + 9216a b c - 1152a b )e x +--R + +--R 5 2 4 2 3 4 +--R (- 12288a c + 6144a b c - 768a b )e +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (1536a c + 1536a b c - 960a b c + 96a b c + 6b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (12288a b c - 3072a b c - 768a b c + 192a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (12288a c + 9216a b c - 6912a b c + 960a b )e x +--R + +--R 5 2 4 3 3 5 +--R (24576a b c - 12288a b c + 1536a b )e x +--R + +--R 6 2 5 2 4 4 +--R (12288a c - 6144a b c + 768a b )e +--R * +--R +-+ +--R \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 2 2 2 4 6 3 3 2 3 2 3 +--R ((- 1280a b c - 128a b c + 48a b )e + (4096a b c + 1024a b c )d)x +--R + +--R 4 2 3 3 2 5 4 3 3 2 2 2 +--R ((- 2560a b c - 2816a b c + 480a b )e + (8192a c + 10240a b c )d)x +--R + +--R 4 2 3 4 4 2 +--R ((- 7680a b c + 1152a b )e + 24576a b c d)x +--R + +--R 5 4 3 5 2 +--R (- 5120a b c + 768a b )e + 16384a c d +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 +--R (640a b c + 864a b c - 104a b c - 6b )e +--R + +--R 3 4 2 2 3 4 2 +--R (- 2048a c - 3072a b c - 128a b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 4 6 +--R (5120a b c + 512a b c - 192a b )e +--R + +--R 3 3 2 3 2 +--R (- 16384a b c - 4096a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (5120a b c + 5632a b c - 960a b )e +--R + +--R 4 3 3 2 2 +--R (- 16384a c - 20480a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 4 2 5 4 3 +--R ((10240a b c - 1536a b )e - 32768a b c d)x + (5120a b c - 768a b )e +--R + +--R 5 2 +--R - 16384a c d +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R / +--R 3 3 2 3 2 3 2 2 2 +--R (6144a b c + 1536b c )x + (12288a c + 15360a b c )x +--R + +--R 2 2 3 2 +--R 36864a b c x + 24576a c +--R * +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R \|- c \|a \|c \|c x + b x + a +--R + +--R 2 4 2 3 4 2 4 +--R (- 3072a c - 4608a b c - 192b c )x +--R + +--R 2 3 3 2 3 3 3 2 2 2 2 +--R (- 24576a b c - 6144a b c )x + (- 24576a c - 30720a b c )x +--R + +--R 3 2 4 2 +--R - 49152a b c x - 24576a c +--R * +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 429 + +--S 430 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R (1) (2c x + b)\|c x + b x + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 845 +r0:=2/3*(a+b*x+c*x^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (2c x + 2b x + 2a)\|c x + b x + a +--R (2) ------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 5 2 2 2 4 4 +--R (- 24a b c - 2b c)x + (- 48a c - 60a b c - 2b )x +--R + +--R 2 3 3 3 2 2 2 3 +--R (- 168a b c - 38a b )x + (- 96a c - 120a b )x - 96a b x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 2 2 6 2 3 5 +--R (16a c + 12b c )x + (96a b c + 24b c)x +--R + +--R 2 2 2 4 4 2 3 3 +--R (96a c + 168a b c + 12b )x + (264a b c + 86a b )x +--R + +--R 3 2 2 2 3 +--R (96a c + 168a b )x + 96a b x +--R * +--R +-+ +--R \|a +--R / +--R +--------------+ +--R 2 2 2 +-+ | 2 +--R ((24a c + 18b )x + 96a b x + 96a )\|a \|c x + b x + a +--R + +--R 3 3 2 2 2 2 3 +--R (- 36a b c - 3b )x + (- 72a c - 54a b )x - 144a b x - 96a +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------------+ +--R 3 2 2 2 3 4 | 2 +--R ((16a c + 12a b )x + 64a b x + 64a )\|c x + b x + a +--R + +--R 2 3 3 3 2 2 2 3 4 +-+ +--R ((- 24a b c - 2a b )x + (- 48a c - 36a b )x - 96a b x - 64a )\|a +--R / +--R +--------------+ +--R 2 2 2 +-+ | 2 +--R ((24a c + 18b )x + 96a b x + 96a )\|a \|c x + b x + a +--R + +--R 3 3 2 2 2 2 3 +--R (- 36a b c - 3b )x + (- 72a c - 54a b )x - 144a b x - 96a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 436 + +--S 437 of 845 +r0:=1/4*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^3*sqrt(c))-(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-_ + b*d*e+a*e^2)/e^3-1/2*(4*c*d-3*b*e-2*c*e*x)*sqrt(a+b*x+c*x^2)/e^2 +--R +--R +--R (2) +--R 2 2 2 2 2c x + b +--R ((4a c + b )e - 8b c d e + 8c d )atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R +-+ | 2 2 +--R (- 4b e + 8c d)\|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +--------------+ +--R 2 2 +-+ | 2 +--R (4c e x + 6b e - 8c d e)\|c \|c x + b x + a +--R / +--R 3 +-+ +--R 4e \|c +--R Type: Expression(Integer) +--E 437 + +--S 438 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 +-+ +-+ +--R ((16b e - 32b c d)x + 32a b e - 64a c d)\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d)x +--R + +--R 2 2 2 +--R (- 32a b e + 64a b c d)x - 32a b e + 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R log +--R +-------------------+ +--R | 2 2 2 +-+ +--R (- 2d x\|a e - b d e + c d + (2d e x + 2d )\|a ) +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2e x + 2d x)\|a \|a e - b d e + c d +--R + +--R 2 2 2 2 2 +--R (- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 2 2 2 3 +--R (- 16a c - 4b c)e x +--R + +--R 3 2 2 2 2 +--R ((- 56a b c - 6b )e + (32a c + 8b c)d e)x +--R + +--R 2 2 2 +--R ((- 32a c - 24a b )e + 32a b c d e)x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 2 4 2 2 2 2 3 +--R 16b c e x + ((32a c + 40b c)e - 32b c d e)x +--R + +--R 3 2 2 2 2 +--R ((72a b c + 18b )e + (- 32a c - 24b c)d e)x +--R + +--R 2 2 2 +--R ((32a c + 24a b )e - 32a b c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 3 +-+ +-+ | 2 +--R (16b e x + 32a e )\|a \|c \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +-+ +--R ((- 16a c - 4b )e x - 32a b e x - 32a e )\|c +--R , +--R +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +---------------------+ +--R 2 | 2 2 +--R ((32b e - 64b c d)x + 64a b e - 128a c d)\|- a e + b d e - c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 32a b c - 8b )e + (64a c + 16b c)d)x +--R + +--R 2 2 2 +--R (- 64a b e + 128a b c d)x - 64a b e + 128a c d +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|c +--R * +--R +--------------+ +--R | 2 +-+ +--R d\|c x + b x + a + (- e x - d)\|a +--R atan(------------------------------------) +--R +---------------------+ +--R | 2 2 +--R x\|- a e + b d e - c d +--R + +--R 2 2 2 3 +--R (- 16a c - 4b c)e x +--R + +--R 3 2 2 2 2 +--R ((- 56a b c - 6b )e + (32a c + 8b c)d e)x +--R + +--R 2 2 2 +--R ((- 32a c - 24a b )e + 32a b c d e)x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 2 4 2 2 2 2 3 +--R 16b c e x + ((32a c + 40b c)e - 32b c d e)x +--R + +--R 3 2 2 2 2 +--R ((72a b c + 18b )e + (- 32a c - 24b c)d e)x +--R + +--R 2 2 2 +--R ((32a c + 24a b )e - 32a b c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 3 +-+ +-+ | 2 +--R (16b e x + 32a e )\|a \|c \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +-+ +--R ((- 16a c - 4b )e x - 32a b e x - 32a e )\|c +--R , +--R +--R 2 +---+ +-+ +--R ((8b e - 16b c d)x + 16a b e - 32a c d)\|- c \|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 8a b c - 2b )e + (16a c + 4b c)d)x +--R + +--R 2 2 2 +--R (- 16a b e + 32a b c d)x - 16a b e + 32a c d +--R * +--R +-------------------+ +--R +---+ | 2 2 +--R \|- c \|a e - b d e + c d +--R * +--R log +--R +-------------------+ +--R | 2 2 2 +-+ +--R (- 2d x\|a e - b d e + c d + (2d e x + 2d )\|a ) +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2e x + 2d x)\|a \|a e - b d e + c d +--R + +--R 2 2 2 2 2 +--R (- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 2 2 3 3 2 2 2 2 +--R (- 8a c - 2b c)e x + ((- 28a b c - 3b )e + (16a c + 4b c)d e)x +--R + +--R 2 2 2 +--R ((- 16a c - 12a b )e + 16a b c d e)x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 2 2 4 2 2 2 2 3 +--R 8b c e x + ((16a c + 20b c)e - 16b c d e)x +--R + +--R 3 2 2 2 2 +--R ((36a b c + 9b )e + (- 16a c - 12b c)d e)x +--R + +--R 2 2 2 +--R ((16a c + 12a b )e - 16a b c d e)x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------------+ +--R 3 3 +---+ +-+ | 2 +--R (8b e x + 16a e )\|- c \|a \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +---+ +--R ((- 8a c - 2b )e x - 16a b e x - 16a e )\|- c +--R , +--R +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R +---------------------+ +--R 2 | 2 2 +--R ((16b e - 32b c d)x + 32a b e - 64a c d)\|- a e + b d e - c d +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d)x +--R + +--R 2 2 2 +--R (- 32a b e + 64a b c d)x - 32a b e + 64a c d +--R * +--R +---------------------+ +--R | 2 2 +---+ +--R \|- a e + b d e - c d \|- c +--R * +--R +--------------+ +--R | 2 +-+ +--R d\|c x + b x + a + (- e x - d)\|a +--R atan(------------------------------------) +--R +---------------------+ +--R | 2 2 +--R x\|- a e + b d e - c d +--R + +--R 2 2 2 3 3 2 2 2 2 +--R (- 8a c - 2b c)e x + ((- 28a b c - 3b )e + (16a c + 4b c)d e)x +--R + +--R 2 2 2 +--R ((- 16a c - 12a b )e + 16a b c d e)x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 2 2 4 2 2 2 2 3 +--R 8b c e x + ((16a c + 20b c)e - 16b c d e)x +--R + +--R 3 2 2 2 2 +--R ((36a b c + 9b )e + (- 16a c - 12b c)d e)x +--R + +--R 2 2 2 +--R ((16a c + 12a b )e - 16a b c d e)x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------------+ +--R 3 3 +---+ +-+ | 2 +--R (8b e x + 16a e )\|- c \|a \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +---+ +--R ((- 8a c - 2b )e x - 16a b e x - 16a e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 438 + +--S 439 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 +-+ +-+ +--R ((16b e - 32b c d)x + 32a b e - 64a c d)\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d)x +--R + +--R 2 2 2 +--R (- 32a b e + 64a b c d)x - 32a b e + 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R log +--R +-------------------+ +--R | 2 2 2 +-+ +--R (- 2d x\|a e - b d e + c d + (2d e x + 2d )\|a ) +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2e x + 2d x)\|a \|a e - b d e + c d +--R + +--R 2 2 2 2 2 +--R (- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R 3 2 2 2 2 +--R ((- 16a b c - 4b )e + 32b c d e - 32b c d )x +--R + +--R 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (16a c + 8a b c + b )e + (- 32a b c - 8b c)d e +--R + +--R 3 2 2 2 +--R (32a c + 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R ((32a b c + 8a b )e - 64a b c d e + 64a b c d )x + (32a c + 8a b )e +--R + +--R 2 2 2 2 +--R - 64a b c d e + 64a c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 +-+ +-+ +--R ((16b e - 32b c d)x + 32a b e - 64a c d)\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d)x +--R + +--R 2 2 2 +--R (- 32a b e + 64a b c d)x - 32a b e + 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +--------------+ +--R 2 2 2 2 2 +-+ | 2 +--R ((24a b e - 32a b c d e)x + 48a b e - 64a c d e)\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 24a b c - 6b )e + (32a c + 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 48a b e + 64a b c d e)x - 48a b e + 64a c d e +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 3 +-+ +-+ | 2 +--R (16b e x + 32a e )\|a \|c \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +-+ +--R ((- 16a c - 4b )e x - 32a b e x - 32a e )\|c +--R Type: Expression(Integer) +--E 439 + +--S 440 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 2 2 2 2 +--R ((- 16a b c - 4b )e + 32b c d e - 32b c d )x +--R + +--R 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (16a c + 8a b c + b )e + (- 32a b c - 8b c)d e +--R + +--R 3 2 2 2 +--R (32a c + 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R ((32a b c + 8a b )e - 64a b c d e + 64a b c d )x + (32a c + 8a b )e +--R + +--R 2 2 2 2 +--R - 64a b c d e + 64a c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 +-+ +-+ +--R ((16b e - 32b c d)x + 32a b e - 64a c d)\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d)x +--R + +--R 2 2 2 +--R (- 32a b e + 64a b c d)x - 32a b e + 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +---------------------+ +--R 2 | 2 2 +--R ((32b e - 64b c d)x + 64a b e - 128a c d)\|- a e + b d e - c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 32a b c - 8b )e + (64a c + 16b c)d)x +--R + +--R 2 2 2 +--R (- 64a b e + 128a b c d)x - 64a b e + 128a c d +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|c +--R * +--R +--------------+ +--R | 2 +-+ +--R d\|c x + b x + a + (- e x - d)\|a +--R atan(------------------------------------) +--R +---------------------+ +--R | 2 2 +--R x\|- a e + b d e - c d +--R + +--R +--------------+ +--R 2 2 2 2 2 +-+ | 2 +--R ((24a b e - 32a b c d e)x + 48a b e - 64a c d e)\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 24a b c - 6b )e + (32a c + 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 48a b e + 64a b c d e)x - 48a b e + 64a c d e +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 3 +-+ +-+ | 2 +--R (16b e x + 32a e )\|a \|c \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +-+ +--R ((- 16a c - 4b )e x - 32a b e x - 32a e )\|c +--R Type: Expression(Integer) +--E 441 + +--S 442 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 443 + +--S 444 of 845 +r0:=-2*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*_ + sqrt(c)/e^3+1/2*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*atanh(1/2*_ + (b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (e^3*sqrt(c*d^2-b*d*e+a*e^2))+(4*c*d-b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/_ + (e^2*(d+e*x)) +--R +--R +--R (2) +--R +-------------------+ +--R 2 2 +-+ | 2 2 +--R ((4b e - 8c d e)x + 4b d e - 8c d )\|c \|a e - b d e + c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 +--R ((- 4a c - b )e + 8b c d e - 8c d e)x + (- 4a c - b )d e +--R + +--R 2 2 3 +--R 8b c d e - 8c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R 2 2 | 2 2 | 2 +--R (4c e x - 2b e + 8c d e)\|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 4 3 | 2 2 +--R (2e x + 2d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 444 + +--S 445 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 2 3 2 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d e)x +--R + +--R 2 2 3 3 2 2 +--R (32a c + 8a b )d e + (- 48a b c + 4b )d e +--R + +--R 2 2 3 2 4 +--R (64a c - 32b c)d e + 32b c d +--R * +--R x +--R + +--R 2 2 2 2 3 2 4 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 2 2 4 2 2 +--R (- 32a b c - 8a b )d e + (- 16a c + 56a b c - b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 32a c - 8a b )d e + (32a b c - 8a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d +--R * +--R x +--R + +--R 3 2 2 2 2 2 3 2 2 4 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 2 2 2 2 +--R (16b d e - 32b c d e)x +--R + +--R 2 2 2 3 2 +--R (32a b d e + (- 64a c + 16b )d e - 32b c d )x + 32a b d e +--R + +--R 3 +--R - 64a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ +-+ | 2 2 | 2 +--R \|a \|c \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((- 16a b c - 4b )d e + (32a c + 8b c)d e)x +--R + +--R 2 2 3 2 2 2 3 2 +--R (- 32a b d e + (48a b c - 4b )d e + (32a c + 8b c)d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 32a b d e + (64a c - 32a b )d e + 64a b c d )x - 32a b d e +--R + +--R 2 3 +--R 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x +--R + +--R - 2a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 2 3 +--R (- 16a c - 4b c)d e x +--R + +--R 2 3 3 2 2 2 2 2 +--R (- 8a b e + (8a b c + 2b )d e + (- 32a c - 8b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (- 16a b e + (32a c + 8a b )d e - 32a b c d e)x +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 4 3 3 2 2 3 +--R 16b c d e x + ((8a b c + 2b )e + 32b c d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R (16a b e + (- 24a b c - 6b )d e + (32a c + 24b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (16a b e + (- 32a c - 8a b )d e + 32a b c d e)x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 4 2 4 2 3 2 3 +-+ +--R (8b d e x + (16a d e + 8b d e )x + 16a d e )\|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 2 3 2 +--R (- 8a c - 2b )d e x + (- 16a b d e + (- 8a c - 2b )d e )x +--R + +--R 2 4 2 3 2 2 3 +--R (- 16a d e - 16a b d e )x - 16a d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R , +--R +--R 3 3 2 2 2 2 3 2 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d e)x +--R + +--R 2 2 3 3 2 2 +--R (32a c + 8a b )d e + (- 48a b c + 4b )d e +--R + +--R 2 2 3 2 4 +--R (64a c - 32b c)d e + 32b c d +--R * +--R x +--R + +--R 2 2 2 2 3 2 4 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 2 2 4 2 2 +--R (- 32a b c - 8a b )d e + (- 16a c + 56a b c - b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 32a c - 8a b )d e + (32a b c - 8a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d +--R * +--R x +--R + +--R 3 2 2 2 2 2 3 2 2 4 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 2 2 2 2 +--R (32b d e - 64b c d e)x +--R + +--R 2 2 2 3 2 +--R (64a b d e + (- 128a c + 32b )d e - 64b c d )x + 64a b d e +--R + +--R 3 +--R - 128a c d +--R * +--R +-------------------+ +--------------+ +--R +---+ +-+ | 2 2 | 2 +--R \|- c \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((- 32a b c - 8b )d e + (64a c + 16b c)d e)x +--R + +--R 2 2 3 2 2 2 3 2 +--R (- 64a b d e + (96a b c - 8b )d e + (64a c + 16b c)d )x +--R + +--R 2 2 2 2 2 3 +--R (- 64a b d e + (128a c - 64a b )d e + 128a b c d )x +--R + +--R 2 2 2 3 +--R - 64a b d e + 128a c d +--R * +--R +-------------------+ +--R +---+ | 2 2 +--R \|- c \|a e - b d e + c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|c x + b x + a - \|a +--R atan(------------------------) +--R +---+ +--R x\|- c +--R + +--R 2 2 2 3 +--R (- 16a c - 4b c)d e x +--R + +--R 2 3 3 2 2 2 2 2 +--R (- 8a b e + (8a b c + 2b )d e + (- 32a c - 8b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (- 16a b e + (32a c + 8a b )d e - 32a b c d e)x +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 4 3 3 2 2 3 +--R 16b c d e x + ((8a b c + 2b )e + 32b c d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R (16a b e + (- 24a b c - 6b )d e + (32a c + 24b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (16a b e + (- 32a c - 8a b )d e + 32a b c d e)x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 4 2 4 2 3 2 3 +-+ +--R (8b d e x + (16a d e + 8b d e )x + 16a d e )\|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 2 3 2 +--R (- 8a c - 2b )d e x + (- 16a b d e + (- 8a c - 2b )d e )x +--R + +--R 2 4 2 3 2 2 3 +--R (- 16a d e - 16a b d e )x - 16a d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R , +--R +--R 2 2 2 2 +--R (8b d e - 16b c d e)x +--R + +--R 2 2 2 3 2 +--R (16a b d e + (- 32a c + 8b )d e - 16b c d )x + 16a b d e +--R + +--R 3 +--R - 32a c d +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ +-+ | 2 +--R \|- a e + b d e - c d \|a \|c \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((- 8a b c - 2b )d e + (16a c + 4b c)d e)x +--R + +--R 2 2 3 2 2 2 3 2 +--R (- 16a b d e + (24a b c - 2b )d e + (16a c + 4b c)d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 16a b d e + (32a c - 16a b )d e + 32a b c d )x - 16a b d e +--R + +--R 2 3 +--R 32a c d +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x +--R + +--R - 2a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 3 2 2 2 2 3 2 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d e)x +--R + +--R 2 2 3 3 2 2 +--R (32a c + 8a b )d e + (- 48a b c + 4b )d e +--R + +--R 2 2 3 2 4 +--R (64a c - 32b c)d e + 32b c d +--R * +--R x +--R + +--R 2 2 2 2 3 2 4 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 2 2 4 2 2 +--R (- 32a b c - 8a b )d e + (- 16a c + 56a b c - b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 32a c - 8a b )d e + (32a b c - 8a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d +--R * +--R x +--R + +--R 3 2 2 2 2 2 3 2 2 4 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 2 2 2 3 +--R (- 8a c - 2b c)d e x +--R + +--R 2 3 3 2 2 2 2 2 +--R (- 4a b e + (4a b c + b )d e + (- 16a c - 4b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (- 8a b e + (16a c + 4a b )d e - 16a b c d e)x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 2 4 3 3 2 2 3 +--R 8b c d e x + ((4a b c + b )e + 16b c d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R (8a b e + (- 12a b c - 3b )d e + (16a c + 12b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (8a b e + (- 16a c - 4a b )d e + 16a b c d e)x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / +--R +---------------------+ +--R 4 2 4 2 3 2 3 | 2 2 +--R (4b d e x + (8a d e + 4b d e )x + 8a d e )\|- a e + b d e - c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 4 3 4 2 2 3 2 +--R (- 4a c - b )d e x + (- 8a b d e + (- 4a c - b )d e )x +--R + +--R 2 4 2 3 2 2 3 +--R (- 8a d e - 8a b d e )x - 8a d e +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R , +--R +--R 3 3 2 2 2 2 3 2 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d e)x +--R + +--R 2 2 3 3 2 2 +--R (32a c + 8a b )d e + (- 48a b c + 4b )d e +--R + +--R 2 2 3 2 4 +--R (64a c - 32b c)d e + 32b c d +--R * +--R x +--R + +--R 2 2 2 2 3 2 4 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 2 2 4 2 2 +--R (- 32a b c - 8a b )d e + (- 16a c + 56a b c - b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 32a c - 8a b )d e + (32a b c - 8a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d +--R * +--R x +--R + +--R 3 2 2 2 2 2 3 2 2 4 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 2 2 2 2 +--R (16b d e - 32b c d e)x +--R + +--R 2 2 2 3 2 +--R (32a b d e + (- 64a c + 16b )d e - 32b c d )x + 32a b d e +--R + +--R 3 +--R - 64a c d +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +---+ +-+ | 2 +--R \|- a e + b d e - c d \|- c \|a \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((- 16a b c - 4b )d e + (32a c + 8b c)d e)x +--R + +--R 2 2 3 2 2 2 3 2 +--R (- 32a b d e + (48a b c - 4b )d e + (32a c + 8b c)d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 32a b d e + (64a c - 32a b )d e + 64a b c d )x - 32a b d e +--R + +--R 2 3 +--R 64a c d +--R * +--R +---------------------+ +--R | 2 2 +---+ +--R \|- a e + b d e - c d \|- c +--R * +--R +--------------+ +--R | 2 +-+ +--R \|c x + b x + a - \|a +--R atan(------------------------) +--R +---+ +--R x\|- c +--R + +--R 2 2 2 3 +--R (- 8a c - 2b c)d e x +--R + +--R 2 3 3 2 2 2 2 2 +--R (- 4a b e + (4a b c + b )d e + (- 16a c - 4b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (- 8a b e + (16a c + 4a b )d e - 16a b c d e)x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 2 4 3 3 2 2 3 +--R 8b c d e x + ((4a b c + b )e + 16b c d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R (8a b e + (- 12a b c - 3b )d e + (16a c + 12b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (8a b e + (- 16a c - 4a b )d e + 16a b c d e)x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / +--R +---------------------+ +--R 4 2 4 2 3 2 3 | 2 2 +--R (4b d e x + (8a d e + 4b d e )x + 8a d e )\|- a e + b d e - c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 4 3 4 2 2 3 2 +--R (- 4a c - b )d e x + (- 8a b d e + (- 4a c - b )d e )x +--R + +--R 2 4 2 3 2 2 3 +--R (- 8a d e - 8a b d e )x - 8a d e +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 445 + +--S 446 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 2 2 3 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d )x +--R + +--R 2 2 2 2 2 3 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R ((- 32a b c - 8a b )d e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 3 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R 2 2 2 +-+ +-+ +--R ((16b d e - 32b c d )x + 32a b d e - 64a c d )\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 16a b c - 4b )d e + (32a c + 8b c)d )x +--R + +--R 2 2 2 2 2 +--R (- 32a b d e + 64a b c d )x - 32a b d e + 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x - 2a +--R log(-------------------------------------------------------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 2 +-+ +-+ +--R ((- 16b d e + 32b c d )x - 32a b d e + 64a c d )\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((16a b c + 4b )d e + (- 32a c - 8b c)d )x +--R + +--R 2 2 2 2 2 +--R (32a b d e - 64a b c d )x + 32a b d e - 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d )x +--R + +--R 2 2 2 2 2 3 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R ((- 32a b c - 8a b )d e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 3 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 8a b e + 32a b c d e)x - 16a b e + 64a c d e) +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((8a b c + 2b )e + (- 32a c - 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (16a b e - 64a b c d e)x + 16a b e - 64a c d e +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 3 3 +-+ | 2 2 | 2 +--R (8b d e x + 16a d e )\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 2 3 2 3 2 3 | 2 2 +--R ((- 8a c - 2b )d e x - 16a b d e x - 16a d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 446 + +--S 447 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 2 2 2 2 3 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d )x +--R + +--R 2 2 2 2 2 3 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R ((- 32a b c - 8a b )d e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 3 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R 2 2 2 +-+ +-+ +--R ((- 16b d e + 32b c d )x - 32a b d e + 64a c d )\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((16a b c + 4b )d e + (- 32a c - 8b c)d )x +--R + +--R 2 2 2 2 2 +--R (32a b d e - 64a b c d )x + 32a b d e - 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d )x +--R + +--R 2 2 2 2 2 3 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R ((- 32a b c - 8a b )d e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 3 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 +---+ +-+ +--R ((32b d e - 64b c d )x + 64a b d e - 128a c d )\|- c \|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 32a b c - 8b )d e + (64a c + 16b c)d )x +--R + +--R 2 2 2 2 2 +--R (- 64a b d e + 128a b c d )x - 64a b d e + 128a c d +--R * +--R +-------------------+ +--R +---+ | 2 2 +--R \|- c \|a e - b d e + c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|c x + b x + a - \|a +--R atan(------------------------) +--R +---+ +--R x\|- c +--R + +--R 2 2 2 2 2 +--R ((- 8a b e + 32a b c d e)x - 16a b e + 64a c d e) +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((8a b c + 2b )e + (- 32a c - 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (16a b e - 64a b c d e)x + 16a b e - 64a c d e +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 3 3 +-+ | 2 2 | 2 +--R (8b d e x + 16a d e )\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 2 3 2 3 2 3 | 2 2 +--R ((- 8a c - 2b )d e x - 16a b d e x - 16a d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 448 + +--S 449 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 449 + +)clear all + +--S 450 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 450 + +--S 451 of 845 +r0:=1/2*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+_ + 2*c^(3/2)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/e^3-_ + 1/8*(2*c*d-b*e)*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*atanh(1/2*_ + (b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (e^3*(c*d^2-b*d*e+a*e^2)^(3/2))-1/4*(8*c^2*d^2-6*b*c*d*e-b^2*e^2+_ + 8*a*c*e^2+2*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-_ + b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 4 3 2 2 2 2 +--R (16a c e - 16b c d e + 16c d e )x +--R + +--R 3 2 2 2 3 2 2 3 2 4 +--R (32a c d e - 32b c d e + 32c d e)x + 16a c d e - 16b c d e + 16c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 12a b c + b )e + (24a c + 6b c)d e - 24b c d e + 16c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 24a b c + 2b )d e + (48a c + 12b c)d e - 48b c d e +--R + +--R 3 4 +--R 32c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 12a b c + b )d e + (24a c + 6b c)d e - 24b c d e + 16c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 2 2 2 4 +--R ((- 16a c - 2b )e + 24b c d e - 24c d e )x - 4a b e +--R + +--R 2 3 2 2 2 3 +--R (- 8a c + 2b )d e + 12b c d e - 16c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 7 6 2 5 2 6 2 5 3 4 +--R (8a e - 8b d e + 8c d e )x + (16a d e - 16b d e + 16c d e )x +--R + +--R 2 5 3 4 4 3 +--R 8a d e - 8b d e + 8c d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 451 + +--S 452 of 845 +--a0:=integrate(t0,x) +--E 452 + +--S 453 of 845 +--m0:=a0-r0 +--E 453 + +--S 454 of 845 +--d0:=D(m0,x) +--E 454 + +)clear all + +--S 455 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 455 + +--S 456 of 845 +r0:=1/16*(b^2-4*a*c)^2*e*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+_ + 1/12*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*sqrt(a+b*x+c*x^2)/_ + (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+1/24*(2*c*d-b*e)*(8*c^2*d^2-_ + 3*b^2*e^2-4*c*e*(2*b*d-5*a*e))*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-_ + b*d*e+a*e^2)^2*(d+e*x))-1/3*(4*c*d+b*e+6*c*e*x)*sqrt(a+b*x+c*x^2)/_ + (e^2*(d+e*x)^3) +--R +--R +--R (2) +--R 2 2 2 4 4 3 2 2 2 4 3 2 +--R (- 48a c + 24a b c - 3b )e x + (- 144a c + 72a b c - 9b )d e x +--R + +--R 2 2 2 4 2 2 2 2 2 4 3 +--R (- 144a c + 72a b c - 9b )d e x + (- 48a c + 24a b c - 3b )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 2 2 2 2 3 3 2 +--R ((- 40a b c + 6b )e + (80a c + 4b c)d e - 48b c d e + 32c d )x +--R + +--R 2 2 3 3 2 2 2 2 +--R (- 48a c - 4a b )e + (32a b c + 16b )d e + (48a c - 60b c)d e +--R + +--R 2 3 +--R 32b c d +--R * +--R x +--R + +--R 2 3 2 2 2 3 2 2 3 +--R - 16a b e + (- 16a c + 28a b )d e + (- 24a b c - 6b )d e + 32a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 2 7 6 2 2 5 3 4 2 4 3 3 +--R (48a e - 96a b d e + (96a c + 48b )d e - 96b c d e + 48c d e )x +--R + +--R 2 6 2 5 2 3 4 4 3 +--R 144a d e - 288a b d e + (288a c + 144b )d e - 288b c d e +--R + +--R 2 5 2 +--R 144c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 2 4 3 5 2 +--R 144a d e - 288a b d e + (288a c + 144b )d e - 288b c d e +--R + +--R 2 6 +--R 144c d e +--R * +--R x +--R + +--R 2 3 4 4 3 2 5 2 6 2 7 +--R 48a d e - 96a b d e + (96a c + 48b )d e - 96b c d e + 48c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 456 + +--S 457 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 4 6 3 4 5 +--R (384a c + 96a b c - 120a b c + 18b )d e x +--R + +--R 3 2 2 3 5 3 4 +--R (1536a b c - 768a b c + 96a b )d e +--R + +--R 3 3 2 2 2 4 6 4 3 +--R (1152a c + 288a b c - 360a b c + 54b )d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 2 2 4 3 4 +--R (1536a c - 768a b c + 96a b )d e +--R + +--R 3 2 2 3 5 4 3 +--R (4608a b c - 2304a b c + 288a b )d e +--R + +--R 3 3 2 2 2 4 6 5 2 +--R (1152a c + 288a b c - 360a b c + 54b )d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 3 +--R (4608a c - 2304a b c + 288a b )d e +--R + +--R 3 2 2 3 5 5 2 +--R (4608a b c - 2304a b c + 288a b )d e +--R + +--R 3 3 2 2 2 4 6 6 +--R (384a c + 96a b c - 120a b c + 18b )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 2 2 4 5 2 +--R (4608a c - 2304a b c + 288a b )d e +--R + +--R 3 2 2 3 5 6 +--R (1536a b c - 768a b c + 96a b )d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 6 +--R (1536a c - 768a b c + 96a b )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 4 6 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 4 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e +--R + +--R 3 3 2 3 2 5 7 4 3 +--R (- 1728a b c + 720a b c - 36a b c - 9b )d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 3 2 5 3 4 +--R (- 2304a b c + 1152a b c - 144a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 3 +--R (- 3456a c - 864a b c + 1080a b c - 162a b )d e +--R + +--R 3 3 2 3 2 5 7 5 2 +--R (- 1728a b c + 720a b c - 36a b c - 9b )d e +--R * +--R 4 +--R x +--R + +--R 5 2 4 2 3 4 3 4 +--R (- 1536a c + 768a b c - 96a b )d e +--R + +--R 4 2 3 3 2 5 4 3 +--R (- 6912a b c + 3456a b c - 432a b )d e +--R + +--R 4 3 3 2 2 2 4 6 5 2 +--R (- 3456a c - 864a b c + 1080a b c - 162a b )d e +--R + +--R 3 3 2 3 2 5 7 6 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 4 3 +--R (- 4608a c + 2304a b c - 288a b )d e +--R + +--R 4 2 3 3 2 5 5 2 +--R (- 6912a b c + 3456a b c - 432a b )d e +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 5 2 +--R (- 4608a c + 2304a b c - 288a b )d e +--R + +--R 4 2 3 3 2 5 6 +--R (- 2304a b c + 1152a b c - 144a b )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 6 +--R (- 1536a c + 768a b c - 96a b )d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 4 3 3 6 4 2 3 2 2 4 5 +--R (- 128a b c - 96a b )e + (- 128a c + 128a b c + 168a b )d e +--R + +--R 3 2 2 3 5 2 4 +--R (- 192a b c - 192a b c - 36a b )d e +--R + +--R 3 3 2 2 2 4 6 3 3 +--R (256a c + 672a b c - 32a b c - 6b )d e +--R + +--R 2 3 3 2 5 4 2 2 3 4 2 5 +--R (- 960a b c - 128a b c - 4b c)d e + (576a b c + 48b c )d e +--R + +--R 4 3 3 6 +--R (- 384a b c - 32b c )d +--R * +--R 5 +--R x +--R + +--R 4 2 6 4 3 3 5 +--R - 512a b e + (- 896a b c + 608a b )d e +--R + +--R 4 2 3 2 2 4 2 4 +--R (- 384a c - 384a b c + 312a b )d e +--R + +--R 3 2 2 3 5 3 3 +--R (1984a b c + 96a b c - 212a b )d e +--R + +--R 3 3 2 2 2 4 6 4 2 +--R (- 1152a c - 1344a b c - 296a b c - 16b )d e +--R + +--R 2 3 3 2 5 5 +--R (576a b c + 1536a b c + 60b c)d e +--R + +--R 2 4 2 3 4 2 6 +--R (- 768a c - 960a b c - 32b c )d +--R * +--R 4 +--R x +--R + +--R 5 6 5 4 2 5 +--R - 512a b e + (- 512a c - 640a b )d e +--R + +--R 4 3 3 2 4 +--R (- 2688a b c + 2208a b )d e +--R + +--R 4 2 3 2 2 4 3 3 +--R (1792a c + 1152a b c - 272a b )d e +--R + +--R 3 2 2 3 5 4 2 +--R (- 1920a b c - 2048a b c - 424a b )d e +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 384a c + 3744a b c + 1176a b c + 6b )d e +--R + +--R 2 3 3 2 6 +--R (- 2688a b c - 608a b c )d +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 2 2 4 3 3 3 3 +--R - 1536a b d e + (- 1536a c + 1152a b )d e + 2304a b d e +--R + +--R 4 2 3 2 2 4 4 2 +--R (768a c - 4224a b c - 1680a b )d e +--R + +--R 3 2 2 3 5 5 +--R (2688a b c + 3264a b c + 72a b )d e +--R + +--R 3 3 2 2 2 6 +--R (- 1536a c - 1920a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 2 3 3 4 3 3 4 2 +--R - 1536a b d e + 3072a b d e + (- 3072a b c - 1536a b )d e +--R + +--R 4 2 3 2 2 4 5 3 2 6 +--R (1536a c + 2304a b c + 96a b )d e - 1536a b c d +--R * +--R x +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 6 3 2 2 3 5 5 +--R (192a b c + 16a b )e + (192a b c - 320a b c - 28a b )d e +--R + +--R 2 2 2 4 6 2 4 +--R (288a b c + 96a b c + 6b )d e +--R + +--R 2 3 3 2 5 3 3 +--R (- 704a b c - 224a b c + 36b c)d e +--R + +--R 2 4 2 3 4 2 4 2 4 3 3 5 +--R (640a c + 512a b c + 24b c )d e + (- 384a b c - 288b c )d e +--R + +--R 5 2 4 6 +--R (256a c + 192b c )d +--R * +--R 6 +--R x +--R + +--R 4 3 3 6 4 2 3 2 2 4 5 +--R (384a b c + 288a b )e + (384a c + 192a b c - 456a b )d e +--R + +--R 3 2 2 3 5 2 4 +--R (1152a b c - 384a b c + 24a b )d e +--R + +--R 3 3 2 2 2 4 6 3 3 +--R (- 1152a c - 1632a b c + 264a b c + 54b )d e +--R + +--R 2 3 3 2 5 4 2 +--R (2304a b c + 864a b c + 120b c)d e +--R + +--R 2 4 2 3 4 2 5 4 3 3 6 +--R (384a c - 2112a b c - 648b c )d e + (1536a b c + 384b c )d +--R * +--R 5 +--R x +--R + +--R 4 2 6 4 3 3 5 +--R 768a b e + (1920a b c - 480a b )d e +--R + +--R 4 2 3 2 2 4 2 4 +--R (1152a c + 576a b c - 1176a b )d e +--R + +--R 3 2 2 3 5 3 3 +--R (- 2880a b c - 1056a b c + 444a b )d e +--R + +--R 3 3 2 2 2 4 6 4 2 +--R (768a c + 3744a b c + 1440a b c + 114b )d e +--R + +--R 2 3 3 2 5 5 +--R (- 1344a b c - 4224a b c - 396b c)d e +--R + +--R 2 4 2 3 4 2 6 +--R (1536a c + 2688a b c + 192b c )d +--R * +--R 4 +--R x +--R + +--R 5 6 5 4 2 5 +--R 512a b e + (512a c + 1408a b )d e +--R + +--R 4 3 3 2 4 +--R (4224a b c - 2976a b )d e +--R + +--R 4 2 3 2 2 4 3 3 +--R (- 1792a c - 2688a b c - 496a b )d e +--R + +--R 3 2 2 3 5 4 2 +--R (3072a b c + 4544a b c + 1072a b )d e +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 384a c - 6048a b c - 2568a b c - 30b )d e +--R + +--R 2 3 3 2 6 +--R (4224a b c + 1376a b c )d +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 2 2 4 3 3 3 3 +--R 1536a b d e + (1536a c - 384a b )d e - 3840a b d e +--R + +--R 4 2 3 2 2 4 4 2 +--R (- 768a c + 5760a b c + 2448a b )d e +--R + +--R 3 2 2 3 5 5 +--R (- 3456a b c - 4416a b c - 120a b )d e +--R + +--R 3 3 2 2 2 6 +--R (1536a c + 2688a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 2 3 3 4 3 3 4 2 +--R 1536a b d e - 3072a b d e + (3072a b c + 1536a b )d e +--R + +--R 4 2 3 2 2 4 5 3 2 6 +--R (- 1536a c - 2304a b c - 96a b )d e + 1536a b c d +--R * +--R x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 3 2 2 3 7 2 3 4 6 +--R (384a c + 288a b )d e + (- 768a b c - 576a b )d e +--R + +--R 2 2 2 4 5 5 2 3 6 4 +--R (768a c + 960a b c + 288b )d e + (- 768a b c - 576b c)d e +--R + +--R 3 2 2 7 3 +--R (384a c + 288b c )d e +--R * +--R 5 +--R x +--R + +--R 3 3 7 3 2 2 4 6 +--R 1536a b d e + (1152a c - 2208a b )d e +--R + +--R 2 3 5 5 2 2 2 4 6 4 +--R (768a b c - 192a b )d e + (2304a c - 192a b c + 864b )d e +--R + +--R 2 3 7 3 3 2 2 8 2 +--R (- 768a b c - 1728b c)d e + (1152a c + 864b c )d e +--R * +--R 4 +--R x +--R + +--R 4 3 7 3 4 6 3 2 2 5 5 +--R 1536a d e + 1536a b d e + (4224a c - 6816a b )d e +--R + +--R 2 3 6 4 2 2 2 4 7 3 +--R (3840a b c + 2880a b )d e + (3840a c - 6336a b c + 864b )d e +--R + +--R 2 3 8 2 3 2 2 9 +--R (2304a b c - 1728b c)d e + (1152a c + 864b c )d e +--R * +--R 3 +--R x +--R + +--R 4 4 6 3 5 5 3 2 2 6 4 +--R 4608a d e - 4608a b d e + (9600a c - 4320a b )d e +--R + +--R 2 3 7 3 +--R (- 768a b c + 4032a b )d e +--R + +--R 2 2 2 4 8 2 2 3 9 +--R (5376a c - 8256a b c + 288b )d e + (3840a b c - 576b c)d e +--R + +--R 3 2 2 10 +--R (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 6 4 3 2 2 7 3 +--R 4608a d e - 7680a b d e + (9216a c + 1536a b )d e +--R + +--R 2 3 8 2 2 2 2 9 +--R (- 6144a b c + 1536a b )d e + (4608a c - 3072a b c)d e +--R + +--R 2 10 +--R 1536a b c d +--R * +--R x +--R + +--R 4 6 4 3 7 3 3 2 2 8 2 +--R 1536a d e - 3072a b d e + (3072a c + 1536a b )d e +--R + +--R 2 9 2 2 10 +--R - 3072a b c d e + 1536a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 3 7 2 2 4 4 6 +--R (- 576a b c - 48a b )d e + (1152a b c + 96a b )d e +--R + +--R 2 2 3 5 5 5 2 2 4 6 4 +--R (- 1152a b c - 672a b c - 48b )d e + (1152a b c + 96b c)d e +--R + +--R 3 3 2 7 3 +--R (- 576a b c - 48b c )d e +--R * +--R 6 +--R x +--R + +--R 4 3 2 3 7 3 2 3 4 6 +--R (- 1152a c - 864a b )d e + (576a b c + 1584a b )d e +--R + +--R 3 2 2 2 4 5 5 +--R (- 2304a c + 576a b c - 576a b )d e +--R + +--R 2 2 3 5 6 4 +--R (- 1152a b c - 288a b c - 144b )d e +--R + +--R 2 3 2 2 4 7 3 +--R (- 1152a c + 2592a b c + 288b c)d e +--R + 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+ 288a b )d e +--R + +--R 3 3 2 2 2 4 6 5 2 +--R (1152a c + 288a b c - 360a b c + 54b )d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 3 +--R (4608a c - 2304a b c + 288a b )d e +--R + +--R 3 2 2 3 5 5 2 +--R (4608a b c - 2304a b c + 288a b )d e +--R + +--R 3 3 2 2 2 4 6 6 +--R (384a c + 96a b c - 120a b c + 18b )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 2 2 4 5 2 +--R (4608a c - 2304a b c + 288a b )d e +--R + +--R 3 2 2 3 5 6 +--R (1536a b c - 768a b c + 96a b )d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 6 +--R (1536a c - 768a b c + 96a b )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 4 6 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 4 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e +--R + +--R 3 3 2 3 2 5 7 4 3 +--R (- 1728a b c + 720a b c - 36a b c - 9b )d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 3 2 5 3 4 +--R (- 2304a b c + 1152a b c - 144a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 3 +--R (- 3456a c - 864a b c + 1080a b c - 162a b )d e +--R + +--R 3 3 2 3 2 5 7 5 2 +--R (- 1728a b c + 720a b c - 36a b c - 9b )d e +--R * +--R 4 +--R x +--R + +--R 5 2 4 2 3 4 3 4 +--R (- 1536a c + 768a b c - 96a b )d e +--R + +--R 4 2 3 3 2 5 4 3 +--R (- 6912a b c + 3456a b c - 432a b )d e +--R + +--R 4 3 3 2 2 2 4 6 5 2 +--R (- 3456a c - 864a b c + 1080a b c - 162a b )d e +--R + +--R 3 3 2 3 2 5 7 6 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 4 3 +--R (- 4608a c + 2304a b c - 288a b )d e +--R + +--R 4 2 3 3 2 5 5 2 +--R (- 6912a b c + 3456a b c - 432a b )d e +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 5 2 +--R (- 4608a c + 2304a b c - 288a b )d e +--R + +--R 4 2 3 3 2 5 6 +--R (- 2304a b c + 1152a b c - 144a b )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 6 +--R (- 1536a c + 768a b c - 96a b )d e +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 4 3 3 6 4 2 3 2 2 4 5 +--R (- 64a b c - 48a b )e + (- 64a c + 64a b c + 84a b )d e +--R + +--R 3 2 2 3 5 2 4 +--R (- 96a b c - 96a b c - 18a b )d e +--R + +--R 3 3 2 2 2 4 6 3 3 +--R (128a c + 336a b c - 16a b c - 3b )d e +--R + +--R 2 3 3 2 5 4 2 2 3 4 2 5 +--R (- 480a b c - 64a b c - 2b c)d e + (288a b c + 24b c )d e +--R + +--R 4 3 3 6 +--R (- 192a b c - 16b c )d +--R * +--R 5 +--R x +--R + +--R 4 2 6 4 3 3 5 +--R - 256a b e + (- 448a b c + 304a b )d e +--R + +--R 4 2 3 2 2 4 2 4 +--R (- 192a c - 192a b c + 156a b )d e +--R + +--R 3 2 2 3 5 3 3 +--R (992a b c + 48a b c - 106a b )d e +--R + +--R 3 3 2 2 2 4 6 4 2 +--R (- 576a c - 672a b c - 148a b c - 8b )d e +--R + +--R 2 3 3 2 5 5 +--R (288a b c + 768a b c + 30b c)d e +--R + +--R 2 4 2 3 4 2 6 +--R (- 384a c - 480a b c - 16b c )d +--R * +--R 4 +--R x +--R + +--R 5 6 5 4 2 5 +--R - 256a b e + (- 256a c - 320a b )d e +--R + +--R 4 3 3 2 4 +--R (- 1344a b c + 1104a b )d e +--R + +--R 4 2 3 2 2 4 3 3 +--R (896a c + 576a b c - 136a b )d e +--R + +--R 3 2 2 3 5 4 2 +--R (- 960a b c - 1024a b c - 212a b )d e +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 192a c + 1872a b c + 588a b c + 3b )d e +--R + +--R 2 3 3 2 6 +--R (- 1344a b c - 304a b c )d +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 2 2 4 3 3 3 3 +--R - 768a b d e + (- 768a c + 576a b )d e + 1152a b d e +--R + +--R 4 2 3 2 2 4 4 2 +--R (384a c - 2112a b c - 840a b )d e +--R + +--R 3 2 2 3 5 5 3 3 2 2 2 6 +--R (1344a b c + 1632a b c + 36a b )d e + (- 768a c - 960a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 2 3 3 4 3 3 4 2 +--R - 768a b d e + 1536a b d e + (- 1536a b c - 768a b )d e +--R + +--R 4 2 3 2 2 4 5 3 2 6 +--R (768a c + 1152a b c + 48a b )d e - 768a b c d +--R * +--R x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 3 2 2 4 6 3 2 2 3 5 5 +--R (96a b c + 8a b )e + (96a b c - 160a b c - 14a b )d e +--R + +--R 2 2 2 4 6 2 4 +--R (144a b c + 48a b c + 3b )d e +--R + +--R 2 3 3 2 5 3 3 +--R (- 352a b c - 112a b c + 18b c)d e +--R + +--R 2 4 2 3 4 2 4 2 4 3 3 5 +--R (320a c + 256a b c + 12b c )d e + (- 192a b c - 144b c )d e +--R + +--R 5 2 4 6 +--R (128a c + 96b c )d +--R * +--R 6 +--R x +--R + +--R 4 3 3 6 4 2 3 2 2 4 5 +--R (192a b c + 144a b )e + (192a c + 96a b c - 228a b )d e +--R + +--R 3 2 2 3 5 2 4 +--R (576a b c - 192a b c + 12a b )d e +--R + +--R 3 3 2 2 2 4 6 3 3 +--R (- 576a c - 816a b c + 132a b c + 27b )d e +--R + +--R 2 3 3 2 5 4 2 +--R (1152a b c + 432a b c + 60b c)d e +--R + +--R 2 4 2 3 4 2 5 4 3 3 6 +--R (192a c - 1056a b c - 324b c )d e + (768a b c + 192b c )d +--R * +--R 5 +--R x +--R + +--R 4 2 6 4 3 3 5 +--R 384a b e + (960a b c - 240a b )d e +--R + +--R 4 2 3 2 2 4 2 4 +--R (576a c + 288a b c - 588a b )d e +--R + +--R 3 2 2 3 5 3 3 +--R (- 1440a b c - 528a b c + 222a b )d e +--R + +--R 3 3 2 2 2 4 6 4 2 +--R (384a c + 1872a b c + 720a b c + 57b )d e +--R + +--R 2 3 3 2 5 5 +--R (- 672a b c - 2112a b c - 198b c)d e +--R + +--R 2 4 2 3 4 2 6 +--R (768a c + 1344a b c + 96b c )d +--R * +--R 4 +--R x +--R + +--R 5 6 5 4 2 5 4 3 3 2 4 +--R 256a b e + (256a c + 704a b )d e + (2112a b c - 1488a b )d e +--R + +--R 4 2 3 2 2 4 3 3 +--R (- 896a c - 1344a b c - 248a b )d e +--R + +--R 3 2 2 3 5 4 2 +--R (1536a b c + 2272a b c + 536a b )d e +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 192a c - 3024a b c - 1284a b c - 15b )d e +--R + +--R 2 3 3 2 6 +--R (2112a b c + 688a b c )d +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 2 2 4 3 3 3 3 +--R 768a b d e + (768a c - 192a b )d e - 1920a b d e +--R + +--R 4 2 3 2 2 4 4 2 +--R (- 384a c + 2880a b c + 1224a b )d e +--R + +--R 3 2 2 3 5 5 3 3 2 2 2 6 +--R (- 1728a b c - 2208a b c - 60a b )d e + (768a c + 1344a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 2 3 3 4 3 3 4 2 +--R 768a b d e - 1536a b d e + (1536a b c + 768a b )d e +--R + +--R 4 2 3 2 2 4 5 3 2 6 +--R (- 768a c - 1152a b c - 48a b )d e + 768a b c d +--R * +--R x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / +--R 3 2 2 3 7 2 3 4 6 +--R (192a c + 144a b )d e + (- 384a b c - 288a b )d e +--R + +--R 2 2 2 4 5 5 2 3 6 4 +--R (384a c + 480a b c + 144b )d e + (- 384a b c - 288b c)d e +--R + +--R 3 2 2 7 3 +--R (192a c + 144b c )d e +--R * +--R 5 +--R x +--R + +--R 3 3 7 3 2 2 4 6 2 3 5 5 +--R 768a b d e + (576a c - 1104a b )d e + (384a b c - 96a b )d e +--R + +--R 2 2 2 4 6 4 2 3 7 3 +--R (1152a c - 96a b c + 432b )d e + (- 384a b c - 864b c)d e +--R + +--R 3 2 2 8 2 +--R (576a c + 432b c )d e +--R * +--R 4 +--R x +--R + +--R 4 3 7 3 4 6 3 2 2 5 5 +--R 768a d e + 768a b d e + (2112a c - 3408a b )d e +--R + +--R 2 3 6 4 2 2 2 4 7 3 +--R (1920a b c + 1440a b )d e + (1920a c - 3168a b c + 432b )d e +--R + +--R 2 3 8 2 3 2 2 9 +--R (1152a b c - 864b c)d e + (576a c + 432b c )d e +--R * +--R 3 +--R x +--R + +--R 4 4 6 3 5 5 3 2 2 6 4 +--R 2304a d e - 2304a b d e + (4800a c - 2160a b )d e +--R + +--R 2 3 7 3 +--R (- 384a b c + 2016a b )d e +--R + +--R 2 2 2 4 8 2 2 3 9 +--R (2688a c - 4128a b c + 144b )d e + (1920a b c - 288b c)d e +--R + +--R 3 2 2 10 +--R (192a c + 144b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 6 4 3 2 2 7 3 +--R 2304a d e - 3840a b d e + (4608a c + 768a b )d e +--R + +--R 2 3 8 2 2 2 2 9 +--R (- 3072a b c + 768a b )d e + (2304a c - 1536a b c)d e +--R + +--R 2 10 +--R 768a b c d +--R * +--R x +--R + +--R 4 6 4 3 7 3 3 2 2 8 2 2 9 +--R 768a d e - 1536a b d e + (1536a c + 768a b )d e - 1536a b c d e +--R + +--R 2 2 10 +--R 768a c d +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 2 3 3 7 2 2 4 4 6 +--R (- 288a b c - 24a b )d e + (576a b c + 48a b )d e +--R + +--R 2 2 3 5 5 5 2 2 4 6 4 +--R (- 576a b c - 336a b c - 24b )d e + (576a b c + 48b c)d e +--R + +--R 3 3 2 7 3 +--R (- 288a b c - 24b c )d e +--R * +--R 6 +--R x +--R + +--R 4 3 2 3 7 3 2 3 4 6 +--R (- 576a c - 432a b )d e + (288a b c + 792a b )d e +--R + +--R 3 2 2 2 4 5 5 +--R (- 1152a c + 288a b c - 288a b )d e +--R + +--R 2 2 3 5 6 4 +--R (- 576a b c - 144a b c - 72b )d e +--R + +--R 2 3 2 2 4 7 3 +--R (- 576a c + 1296a b c + 144b c)d e +--R + +--R 3 3 2 8 2 +--R (- 864a b c - 72b c )d e +--R * +--R 5 +--R x +--R + +--R 4 3 7 4 3 2 4 6 +--R - 1152a b d e + (- 1728a c + 1008a b )d e +--R + +--R 3 2 3 5 5 +--R (288a b c + 1368a b )d e +--R + +--R 3 2 2 2 4 6 4 +--R (- 3456a c - 288a b c - 1152a b )d e +--R + +--R 2 2 3 5 7 3 +--R (576a b c + 1584a b c - 72b )d e +--R + +--R 2 3 2 2 4 8 2 3 3 2 9 +--R (- 1728a c + 432a b c + 144b c)d e + (- 864a b c - 72b c )d e +--R * +--R 4 +--R x +--R + +--R 5 3 7 4 4 6 4 3 2 5 5 +--R - 768a d e - 1920a b d e + (- 3264a c + 4848a b )d e +--R + +--R 3 2 3 6 4 +--R (- 2208a b c - 888a b )d e +--R + +--R 3 2 2 2 4 7 3 +--R (- 4224a c + 3168a b c - 1248a b )d e +--R + +--R 2 2 3 5 8 2 +--R (- 576a b c + 2256a b c - 24b )d e +--R + +--R 2 3 2 2 4 9 3 3 2 10 +--R (- 1728a c - 720a b c + 48b c)d e + (- 288a b c - 24b c )d +--R * +--R 3 +--R x +--R + +--R 5 4 6 4 5 5 4 3 2 6 4 +--R - 2304a d e + 1152a b d e + (- 5184a c + 4176a b )d e +--R + +--R 3 2 3 7 3 +--R (- 1152a b c - 2592a b )d e +--R + +--R 3 2 2 2 4 8 2 +--R (- 3456a c + 5472a b c - 432a b )d e +--R + +--R 2 2 3 9 2 3 2 2 10 +--R (- 2304a b c + 864a b c)d e + (- 576a c - 432a b c )d +--R * +--R 2 +--R x +--R + +--R 5 5 5 4 6 4 4 7 3 +--R - 2304a d e + 3456a b d e - 4608a c d e +--R + +--R 3 2 3 8 2 3 2 2 2 9 +--R (2304a b c - 1152a b )d e + (- 2304a c + 2304a b c)d e +--R + +--R 2 2 10 +--R - 1152a b c d +--R * +--R x +--R + +--R 5 6 4 4 7 3 4 3 2 8 2 +--R - 768a d e + 1536a b d e + (- 1536a c - 768a b )d e +--R + +--R 3 9 3 2 10 +--R 1536a b c d e - 768a c d +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 457 + +--S 458 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 4 6 3 2 +--R (384a c + 96a b c - 120a b c + 18b )d e x +--R + +--R 3 2 2 3 5 3 +--R (1536a b c - 768a b c + 96a b )d e x +--R + +--R 4 2 3 2 2 4 3 +--R (1536a c - 768a b c + 96a b )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e x +--R + +--R 4 2 3 3 2 5 3 +--R (- 2304a b c + 1152a b c - 144a b )d e x +--R + +--R 5 2 4 2 3 4 3 +--R (- 1536a c + 768a b c - 96a b )d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R 3 3 2 2 2 4 6 3 2 +--R (384a c + 96a b c - 120a b c + 18b )d e x +--R + +--R 3 2 2 3 5 3 +--R (1536a b c - 768a b c + 96a b )d e x +--R + +--R 4 2 3 2 2 4 3 +--R (1536a c - 768a b c + 96a b )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e x +--R + +--R 4 2 3 3 2 5 3 +--R (- 2304a b c + 1152a b c - 144a b )d e x +--R + +--R 5 2 4 2 3 4 3 +--R (- 1536a c + 768a b c - 96a b )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 4 3 3 3 4 2 3 2 2 4 2 +--R (- 128a b c - 96a b )e + (- 128a c + 128a b c + 168a b )d e +--R + +--R 3 2 2 3 5 2 3 3 2 2 2 3 +--R (- 192a b c - 192a b c - 36a b )d e + (256a c + 192a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 3 3 2 +--R - 512a b e + (- 512a b c + 896a b )d e +--R + +--R 3 2 2 4 2 3 2 3 +--R (- 768a b c - 192a b )d e + 1024a b c d +--R * +--R x +--R + +--R 5 3 5 4 2 2 4 3 3 2 +--R - 512a b e + (- 512a c + 896a b )d e + (- 768a b c - 192a b )d e +--R + +--R 4 2 3 +--R 1024a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 3 3 2 2 3 5 2 +--R (192a b c + 16a b )e + (192a b c - 320a b c - 28a b )d e +--R + +--R 2 2 2 4 6 2 2 3 3 2 3 +--R (288a b c + 96a b c + 6b )d e + (- 384a b c - 32a b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 3 4 2 3 2 2 4 2 +--R (384a b c + 288a b )e + (384a c - 384a b c - 504a b )d e +--R + +--R 3 2 2 3 5 2 3 3 2 2 2 3 +--R (576a b c + 576a b c + 108a b )d e + (- 768a c - 576a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 3 3 2 3 2 2 4 2 +--R 768a b e + (768a b c - 1344a b )d e + (1152a b c + 288a b )d e +--R + +--R 3 2 3 +--R - 1536a b c d +--R * +--R x +--R + +--R 5 3 5 4 2 2 4 3 3 2 +--R 512a b e + (512a c - 896a b )d e + (768a b c + 192a b )d e +--R + +--R 4 2 3 +--R - 1024a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 3 2 2 3 4 2 3 4 3 +--R (384a c + 288a b )d e + (- 768a b c - 576a b )d e +--R + +--R 2 2 2 4 5 2 2 3 6 +--R (768a c + 960a b c + 288b )d e + (- 768a b c - 576b c)d e +--R + +--R 3 2 2 7 +--R (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 4 2 2 4 3 2 3 5 2 +--R 1536a b d e - 3072a b d e + (3072a b c + 1536a b )d e +--R + +--R 2 6 2 7 +--R - 3072a b c d e + 1536a b c d +--R * +--R x +--R + +--R 4 3 4 3 4 3 3 2 2 5 2 2 6 +--R 1536a d e - 3072a b d e + (3072a c + 1536a b )d e - 3072a b c d e +--R + +--R 2 2 7 +--R 1536a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 3 4 2 2 4 4 3 +--R (- 576a b c - 48a b )d e + (1152a b c + 96a b )d e +--R + +--R 2 2 3 5 5 2 2 2 4 6 +--R (- 1152a b c - 672a b c - 48b )d e + (1152a b c + 96b c)d e +--R + +--R 3 3 2 7 +--R (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 3 2 3 4 3 +--R (- 1152a c - 864a b )d e + (2304a b c + 1728a b )d e +--R + +--R 3 2 2 2 4 5 2 +--R (- 2304a c - 2880a b c - 864a b )d e +--R + +--R 2 2 3 6 2 3 2 2 7 +--R (2304a b c + 1728a b c)d e + (- 1152a c - 864a b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 4 3 2 4 3 3 2 3 5 2 +--R - 2304a b d e + 4608a b d e + (- 4608a b c - 2304a b )d e +--R + +--R 2 2 6 2 2 7 +--R 4608a b c d e - 2304a b c d +--R * +--R x +--R + +--R 5 3 4 4 4 3 4 3 2 5 2 +--R - 1536a d e + 3072a b d e + (- 3072a c - 1536a b )d e +--R + +--R 3 6 3 2 7 +--R 3072a b c d e - 1536a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 458 + +--S 459 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 4 6 3 2 +--R (384a c + 96a b c - 120a b c + 18b )d e x +--R + +--R 3 2 2 3 5 3 +--R (1536a b c - 768a b c + 96a b )d e x +--R + +--R 4 2 3 2 2 4 3 +--R (1536a c - 768a b c + 96a b )d e +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e x +--R + +--R 4 2 3 3 2 5 3 +--R (- 2304a b c + 1152a b c - 144a b )d e x +--R + +--R 5 2 4 2 3 4 3 +--R (- 1536a c + 768a b c - 96a b )d e +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 2 2 4 6 3 2 +--R (768a c + 192a b c - 240a b c + 36b )d e x +--R + +--R 3 2 2 3 5 3 +--R (3072a b c - 1536a b c + 192a b )d e x +--R + +--R 4 2 3 2 2 4 3 +--R (3072a c - 1536a b c + 192a b )d e +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 1152a b c + 480a b c - 24a b c - 6b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (- 2304a c - 576a b c + 720a b c - 108a b )d e x +--R + +--R 4 2 3 3 2 5 3 +--R (- 4608a b c + 2304a b c - 288a b )d e x +--R + +--R 5 2 4 2 3 4 3 +--R (- 3072a c + 1536a b c - 192a b )d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 4 3 3 3 4 2 3 2 2 4 2 +--R (- 128a b c - 96a b )e + (- 128a c + 128a b c + 168a b )d e +--R + +--R 3 2 2 3 5 2 3 3 2 2 2 3 +--R (- 192a b c - 192a b c - 36a b )d e + (256a c + 192a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 3 3 2 +--R - 512a b e + (- 512a b c + 896a b )d e +--R + +--R 3 2 2 4 2 3 2 3 +--R (- 768a b c - 192a b )d e + 1024a b c d +--R * +--R x +--R + +--R 5 3 5 4 2 2 4 3 3 2 +--R - 512a b e + (- 512a c + 896a b )d e + (- 768a b c - 192a b )d e +--R + +--R 4 2 3 +--R 1024a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 | 2 2 | 2 +--R \|- a e + b d e - c d \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 3 3 2 2 3 5 2 +--R (192a b c + 16a b )e + (192a b c - 320a b c - 28a b )d e +--R + +--R 2 2 2 4 6 2 2 3 3 2 3 +--R (288a b c + 96a b c + 6b )d e + (- 384a b c - 32a b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 3 4 2 3 2 2 4 2 +--R (384a b c + 288a b )e + (384a c - 384a b c - 504a b )d e +--R + +--R 3 2 2 3 5 2 3 3 2 2 2 3 +--R (576a b c + 576a b c + 108a b )d e + (- 768a c - 576a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 3 3 2 3 2 2 4 2 +--R 768a b e + (768a b c - 1344a b )d e + (1152a b c + 288a b )d e +--R + +--R 3 2 3 +--R - 1536a b c d +--R * +--R x +--R + +--R 5 3 5 4 2 2 4 3 3 2 +--R 512a b e + (512a c - 896a b )d e + (768a b c + 192a b )d e +--R + +--R 4 2 3 +--R - 1024a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d +--R / +--R 3 2 2 3 4 2 3 4 3 +--R (384a c + 288a b )d e + (- 768a b c - 576a b )d e +--R + +--R 2 2 2 4 5 2 2 3 6 +--R (768a c + 960a b c + 288b )d e + (- 768a b c - 576b c)d e +--R + +--R 3 2 2 7 +--R (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 4 2 2 4 3 2 3 5 2 +--R 1536a b d e - 3072a b d e + (3072a b c + 1536a b )d e +--R + +--R 2 6 2 7 +--R - 3072a b c d e + 1536a b c d +--R * +--R x +--R + +--R 4 3 4 3 4 3 3 2 2 5 2 2 6 +--R 1536a d e - 3072a b d e + (3072a c + 1536a b )d e - 3072a b c d e +--R + +--R 2 2 7 +--R 1536a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 +-+ | 2 2 | 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 3 4 2 2 4 4 3 +--R (- 576a b c - 48a b )d e + (1152a b c + 96a b )d e +--R + +--R 2 2 3 5 5 2 2 2 4 6 +--R (- 1152a b c - 672a b c - 48b )d e + (1152a b c + 96b c)d e +--R + +--R 3 3 2 7 +--R (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 3 2 3 4 3 +--R (- 1152a c - 864a b )d e + (2304a b c + 1728a b )d e +--R + +--R 3 2 2 2 4 5 2 +--R (- 2304a c - 2880a b c - 864a b )d e +--R + +--R 2 2 3 6 2 3 2 2 7 +--R (2304a b c + 1728a b c)d e + (- 1152a c - 864a b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 4 3 2 4 3 3 2 3 5 2 +--R - 2304a b d e + 4608a b d e + (- 4608a b c - 2304a b )d e +--R + +--R 2 2 6 2 2 7 +--R 4608a b c d e - 2304a b c d +--R * +--R x +--R + +--R 5 3 4 4 4 3 4 3 2 5 2 +--R - 1536a d e + 3072a b d e + (- 3072a c - 1536a b )d e +--R + +--R 3 6 3 2 7 +--R 3072a b c d e - 1536a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R Type: Expression(Integer) +--E 460 + +--S 461 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 461 + +)clear all + +--S 462 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 462 + +--S 463 of 845 +r0:=5/128*(b^2-4*a*c)^2*e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (c*d^2-b*d*e+a*e^2)^(7/2)+1/24*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3)+_ + 1/96*(2*c*d-b*e)*(8*c^2*d^2-5*b^2*e^2-4*c*e*(2*b*d-7*a*e))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^2)+_ + 1/192*(32*c^4*d^4-15*b^4*e^4-16*c^3*d^2*e*(4*b*d-9*a*e)+_ + 20*b^2*c*e^3*(b*d+5*a*e)+4*c^2*e^2*(3*b^2*d^2-36*a*b*d*e-32*a^2*e^2))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)^3*(d+e*x))-1/4*(2*c*d+b*e+_ + 4*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^4) +--R +--R +--R (2) +--R 2 2 3 5 6 +--R (240a b c - 120a b c + 15b )e +--R + +--R 2 3 2 2 4 5 +--R (- 480a c + 240a b c - 30b c)d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 5 +--R (960a b c - 480a b c + 60b )d e +--R + +--R 2 3 2 2 4 2 4 +--R (- 1920a c + 960a b c - 120b c)d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 4 +--R (1440a b c - 720a b c + 90b )d e +--R + +--R 2 3 2 2 4 3 3 +--R (- 2880a c + 1440a b c - 180b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 5 3 3 +--R (960a b c - 480a b c + 60b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (- 1920a c + 960a b c - 120b c)d e +--R * +--R x +--R + +--R 2 2 3 5 4 2 2 3 2 2 4 5 +--R (240a b c - 120a b c + 15b )d e + (- 480a c + 240a b c - 30b c)d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 4 5 2 3 4 +--R (- 256a c + 200a b c - 30b )e + (- 288a b c + 40b c)d e +--R + +--R 3 2 2 2 3 3 3 2 4 4 +--R (288a c + 24b c )d e - 128b c d e + 64c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (- 112a b c + 20a b )e + (- 544a c + 704a b c - 110b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 +--R (- 1296a b c + 148b c)d e + (1152a c + 160b c )d e +--R + +--R 3 4 4 5 +--R - 544b c d e + 256c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 5 2 3 4 +--R (- 256a c - 16a b )e + (608a b c + 72a b )d e +--R + +--R 2 2 2 4 2 3 2 3 3 2 +--R (- 1152a c - 120a b c - 146b )d e + (64a b c + 528b c)d e +--R + +--R 3 2 2 4 3 5 +--R (544a c - 728b c )d e + 256b c d +--R * +--R x +--R + +--R 3 5 3 2 2 4 2 3 2 3 +--R - 96a b e + (- 64a c + 272a b )d e + (- 144a b c - 236a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (- 288a c + 528a b c + 30b )d e + (- 368a b c - 60b c)d e +--R + +--R 3 5 +--R 256a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 3 10 2 9 2 2 2 8 +--R 384a e - 1152a b d e + (1152a c + 1152a b )d e +--R + +--R 3 3 7 2 2 4 6 2 5 5 +--R (- 2304a b c - 384b )d e + (1152a c + 1152b c)d e - 1152b c d e +--R + +--R 3 6 4 +--R 384c d e +--R * +--R 4 +--R x +--R + +--R 3 9 2 2 8 2 2 3 7 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 4 6 2 2 5 5 +--R (- 9216a b c - 1536b )d e + (4608a c + 4608b c)d e +--R + +--R 2 6 4 3 7 3 +--R - 4608b c d e + 1536c d e +--R * +--R 3 +--R x +--R + +--R 3 2 8 2 3 7 2 2 4 6 +--R 2304a d e - 6912a b d e + (6912a c + 6912a b )d e +--R + +--R 3 5 5 2 2 6 4 +--R (- 13824a b c - 2304b )d e + (6912a c + 6912b c)d e +--R + +--R 2 7 3 3 8 2 +--R - 6912b c d e + 2304c d e +--R * +--R 2 +--R x +--R + +--R 3 3 7 2 4 6 2 2 5 5 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 6 4 2 2 7 3 +--R (- 9216a b c - 1536b )d e + (4608a c + 4608b c)d e +--R + +--R 2 8 2 3 9 +--R - 4608b c d e + 1536c d e +--R * +--R x +--R + +--R 3 4 6 2 5 5 2 2 6 4 +--R 384a d e - 1152a b d e + (1152a c + 1152a b )d e +--R + +--R 3 7 3 2 2 8 2 2 9 +--R (- 2304a b c - 384b )d e + (1152a c + 1152b c)d e - 1152b c d e +--R + +--R 3 10 +--R 384c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 463 + +--S 464 of 845 +--a0:=integrate(t0,x) +--E 464 + +--S 465 of 845 +--m0:=a0-r0 +--E 465 + +--S 466 of 845 +--d0:=D(m0,x) +--E 466 + +)clear all + +--S 467 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R 2c e x + (3b c e + 6c d e )x + ((2a c + b )e + 9b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (6a c + 3b )d e + 9b c d e + 2c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R (3a b d e + (6a c + 3b )d e + 3b c d )x + (3a b d e + (2a c + b )d )x +--R + +--R 3 +--R a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 845 +r0:=1/1024*(b^2-4*a*c)*e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*_ + (b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+3/2240*(2*c*d-b*e)*(16*c^2*d^2+_ + 21*b^2*e^2-4*c*e*(4*b*d+17*a*e))*(a+b*x+c*x^2)^(5/2)/c^3+3/56*(2*c*d-_ + b*e)*(d+e*x)^2*(a+b*x+c*x^2)^(5/2)/c+1/4*(d+e*x)^3*(a+b*x+c*x^2)^(5/2)+_ + 1/224*e*(5*b^2*d*e-36*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+9*b^2*e^2-_ + 4*c*e*(2*b*d+7*a*e))*x)*(a+b*x+c*x^2)^(5/2)/c^2+3/16384*(b^2-4*a*c)^3*_ + e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)-3/8192*(b^2-4*a*c)^2*e*(32*c^2*_ + d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 4 4 3 2 3 2 4 2 6 8 3 +--R (26880a c - 80640a b c + 50400a b c - 11760a b c + 945b )e +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (215040a b c - 161280a b c + 40320a b c - 3360b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (- 215040a c + 161280a b c - 40320a b c + 3360b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 7 3 7 6 3 7 2 6 +--R 143360c e x + (256000b c e + 491520c d e )x +--R + +--R 6 2 5 3 6 2 7 2 5 +--R ((215040a c + 104960b c )e + 901120b c d e + 573440c d e)x +--R + +--R 5 3 4 3 6 2 5 2 +--R (144384a b c - 768b c )e + (786432a c + 385024b c )d e +--R + +--R 6 2 7 3 +--R 1089536b c d e + 229376c d +--R * +--R 4 +--R x +--R + +--R 2 5 2 4 4 3 3 +--R (17920a c - 6912a b c + 864b c )e +--R + +--R 5 3 4 2 6 2 5 2 +--R (569344a b c - 3072b c )d e + (1003520a c + 494592b c )d e +--R + +--R 6 3 +--R 458752b c d +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 3 +--R (- 22272a b c + 9088a b c - 1008b c )e +--R + +--R 2 5 2 4 4 3 2 +--R (98304a c - 30720a b c + 3584b c )d e +--R + +--R 5 3 4 2 6 2 5 3 +--R (817152a b c - 3584b c )d e + (458752a c + 229376b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (- 26880a c + 38208a b c - 12656a b c + 1260b c)e +--R + +--R 2 4 3 3 5 2 2 +--R (- 116736a b c + 43008a b c - 4480b c )d e +--R + +--R 2 5 2 4 4 3 2 5 3 +--R (215040a c - 43008a b c + 4480b c )d e + 458752a b c d +--R * +--R x +--R + +--R 3 3 2 3 2 5 7 3 +--R (84864a b c - 75488a b c + 21000a b c - 1890b )e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 196608a c + 236544a b c - 71680a b c + 6720b c)d e +--R + +--R 2 4 3 3 5 2 2 2 5 3 +--R (- 236544a b c + 71680a b c - 6720b c )d e + 229376a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 573440c \|c +--R Type: Expression(Integer) +--E 468 + +--S 469 of 845 +--a0:=integrate(t0,x) +--E 469 + +--S 470 of 845 +--m0:=a0-r0 +--E 470 + +--S 471 of 845 +--d0:=D(m0,x) +--E 471 + +)clear all + +--S 472 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x +--R + +--R 2 +--R a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 845 +r0:=1/96*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3+_ + 1/210*(24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*(a+b*x+c*x^2)^(5/2)/c^2+_ + 2/7*(d+e*x)^2*(a+b*x+c*x^2)^(5/2)+1/21*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(5/2)/c+1/512*(b^2-4*a*c)^3*e*(2*c*d-b*e)*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)-1/256*(b^2-4*a*c)^2*e*_ + (2*c*d-b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 3 3 2 3 2 5 7 2 +--R (6720a b c - 5040a b c + 1260a b c - 105b )e +--R + +--R 3 4 2 2 3 4 2 6 +--R (- 13440a c + 10080a b c - 2520a b c + 210b c)d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 6 2 6 5 2 6 5 +--R 15360c e x + (28160b c e + 35840c d e)x +--R + +--R 5 2 4 2 5 6 2 4 +--R ((24576a c + 12032b c )e + 68096b c d e + 21504c d )x +--R + +--R 4 3 3 2 5 2 4 +--R (17792a b c - 96b c )e + (62720a c + 30912b c )d e +--R + +--R 5 2 +--R 43008b c d +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 4 2 2 4 3 3 +--R (3072a c - 960a b c + 112b c )e + (51072a b c - 224b c )d e +--R + +--R 5 2 4 2 +--R (43008a c + 21504b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 5 2 +--R (- 3648a b c + 1344a b c - 140b c)e +--R + +--R 2 4 2 3 4 2 4 2 +--R (13440a c - 2688a b c + 280b c )d e + 43008a b c d +--R * +--R x +--R + +--R 3 3 2 2 2 4 6 2 +--R (- 6144a c + 7392a b c - 2240a b c + 210b )e +--R + +--R 2 3 3 2 5 2 4 2 +--R (- 14784a b c + 4480a b c - 420b c)d e + 21504a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 53760c \|c +--R Type: Expression(Integer) +--E 473 + +--S 474 of 845 +--a0:=integrate(t0,x) +--E 474 + +--S 475 of 845 +--m0:=a0-r0 +--E 475 + +--S 476 of 845 +--d0:=D(m0,x) +--E 476 + +)clear all + +--S 477 of 845 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 845 +r0:=1/96*(b^2-4*a*c)*e*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^2+1/30*(2*c*d-b*e)*_ + (a+b*x+c*x^2)^(5/2)/c+1/3*(d+e*x)*(a+b*x+c*x^2)^(5/2)+1/512*(b^2-4*a*c)^3*_ + e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-1/256*(b^2-_ + 4*a*c)^2*e*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 2c x + b +--R (- 960a c + 720a b c - 180a b c + 15b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 5 5 4 5 4 +--R 2560c e x + (4864b c e + 3072c d)x +--R + +--R 4 2 3 4 3 +--R ((4480a c + 2208b c )e + 6144b c d)x +--R + +--R 3 3 2 4 2 3 2 +--R ((3648a b c - 16b c )e + (6144a c + 3072b c )d)x +--R + +--R 2 3 2 2 4 3 +--R ((960a c - 192a b c + 20b c)e + 6144a b c d)x +--R + +--R 2 2 3 5 2 3 +--R (- 1056a b c + 320a b c - 30b )e + 3072a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 478 + +--S 479 of 845 +--a0:=integrate(t0,x) +--E 479 + +--S 480 of 845 +--m0:=a0-r0 +--E 480 + +--S 481 of 845 +--d0:=D(m0,x) +--E 481 + +)clear all + +--S 482 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (1) (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 845 +r0:=2/5*(a+b*x+c*x^2)^(5/2) +--R +--R +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (2c x + 4b c x + (4a c + 2b )x + 4a b x + 2a )\|c x + b x + a +--R (2) ------------------------------------------------------------------ +--R 5 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 3 5 2 9 +--R (- 160a b c - 80a b c - 2b c )x +--R + +--R 3 4 2 2 3 4 2 6 8 +--R (- 320a c - 1120a b c - 260a b c - 4b c)x +--R + +--R 3 3 2 3 2 5 7 7 +--R (- 2880a b c - 2720a b c - 284a b c - 2b )x +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (- 1920a c - 8320a b c - 2760a b c - 104a b )x +--R + +--R 4 2 3 3 2 5 5 +--R (- 9760a b c - 9680a b c - 1002a b )x +--R + +--R 5 2 4 2 3 4 4 5 4 3 3 +--R (- 3840a c - 15360a b c - 3920a b )x + (- 10880a b c - 7520a b )x +--R + +--R 6 5 2 2 6 +--R (- 2560a c - 7040a b )x - 2560a b x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 5 2 4 4 3 10 2 4 3 3 5 2 9 +--R (64a c + 160a b c + 20b c )x + (960a b c + 800a b c + 60b c )x +--R + +--R 3 4 2 2 3 4 2 6 8 +--R (960a c + 4320a b c + 1500a b c + 60b c)x +--R + +--R 3 3 2 3 2 5 7 7 +--R (7040a b c + 8320a b c + 1240a b c + 20b )x +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (3520a c + 17760a b c + 7260a b c + 380a b )x +--R + +--R 4 2 3 3 2 5 5 +--R (16160a b c + 18640a b c + 2362a b )x +--R + +--R 5 2 4 2 3 4 4 5 4 3 3 +--R (5120a c + 23360a b c + 6960a b )x + (13440a b c + 10720a b )x +--R + +--R 6 5 2 2 6 +--R (2560a c + 8320a b )x + 2560a b x +--R * +--R +-+ +--R \|a +--R / +--R 2 2 2 4 4 2 3 3 +--R (160a c + 400a b c + 50b )x + (1920a b c + 800a b )x +--R + +--R 3 2 2 2 3 4 +--R (1920a c + 3360a b )x + 5120a b x + 2560a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 3 5 5 3 2 2 2 4 4 +--R (- 400a b c - 200a b c - 5b )x + (- 800a c - 2000a b c - 250a b )x +--R + +--R 3 2 3 3 4 3 2 2 4 5 +--R (- 4800a b c - 2000a b )x + (- 3200a c - 5600a b )x - 6400a b x - 2560a +--R Type: Union(Expression(Integer),...) +--E 484 + +--S 485 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 4 2 3 4 4 5 4 3 3 +--R (64a c + 160a b c + 20a b )x + (768a b c + 320a b )x +--R + +--R 6 5 2 2 6 7 +--R (768a c + 1344a b )x + 2048a b x + 1024a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 4 2 3 3 2 5 5 +--R (- 160a b c - 80a b c - 2a b )x +--R + +--R 5 2 4 2 3 4 4 5 4 3 3 +--R (- 320a c - 800a b c - 100a b )x + (- 1920a b c - 800a b )x +--R + +--R 6 5 2 2 6 7 +--R (- 1280a c - 2240a b )x - 2560a b x - 1024a +--R * +--R +-+ +--R \|a +--R / +--R 2 2 2 4 4 2 3 3 +--R (160a c + 400a b c + 50b )x + (1920a b c + 800a b )x +--R + +--R 3 2 2 2 3 4 +--R (1920a c + 3360a b )x + 5120a b x + 2560a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 3 5 5 3 2 2 2 4 4 +--R (- 400a b c - 200a b c - 5b )x + (- 800a c - 2000a b c - 250a b )x +--R + +--R 3 2 3 3 4 3 2 2 4 5 +--R (- 4800a b c - 2000a b )x + (- 3200a c - 5600a b )x - 6400a b x - 2560a +--R Type: Expression(Integer) +--E 485 + +--S 486 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 486 + +)clear all + +--S 487 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 487 + +--S 488 of 845 +r0:=-1/12*(8*c*d-7*b*e-6*c*e*x)*(a+b*x+c*x^2)^(3/2)/e^2+1/64*(128*c^4*d^4-_ + b^4*e^4-8*b^2*c*e^3*(2*b*d-3*a*e)-64*c^3*d^2*e*(4*b*d-3*a*e)+48*c^2*_ + e^2*(3*b^2*d^2-4*a*b*d*e+a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(c^(3/2)*e^5)-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^(3/2)*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/e^5-1/32*(64*c^3*d^3-b^3*e^3+4*b*c*e^2*(12*b*d-_ + 11*a*e)-16*c^2*d*e*(7*b*d-4*a*e)-2*c*e*(16*c^2*d^2+b^2*e^2-_ + 4*c*e*(4*b*d-3*a*e))*x)*sqrt(a+b*x+c*x^2)/(c*e^4) +--R +--R +--R (2) +--R 2 2 2 4 4 2 3 3 +--R (144a c + 72a b c - 3b )e + (- 576a b c - 48b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (576a c + 432b c )d e - 768b c d e + 384c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 2 3 3 +-+ +--R (- 192a b c e + (384a c + 192b c)d e - 576b c d e + 384c d )\|c +--R * +--R +-------------------+ +--R | 2 2 (b e - 2c d)x + 2a e - b d +--R \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 4 3 2 4 3 3 2 +--R 96c e x + (208b c e - 128c d e )x +--R + +--R 2 2 4 2 3 3 2 2 +--R ((240a c + 124b c)e - 320b c d e + 192c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (376a b c + 6b )e + (- 512a c - 288b c)d e + 672b c d e - 384c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 192c e \|c +--R Type: Expression(Integer) +--E 488 + +--S 489 of 845 +--a0:=integrate(t0,x) +--E 489 + +--S 490 of 845 +--m0:=a0-r0 +--E 490 + +--S 491 of 845 +--d0:=D(m0,x) +--E 491 + +)clear all + +--S 492 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 492 + +--S 493 of 845 +r0:=1/3*(8*c*d-3*b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x))-_ + 1/4*(2*c*d-b*e)*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e^5*sqrt(c))+1/2*(16*c^2*d^2+_ + 3*b^2*e^2-4*c*e*(4*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^5+_ + 1/2*(16*c^2*d^2+5*b^2*e^2-4*c*e*(5*b*d-a*e)-4*c*e*(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/e^4 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((36a b c + 3b )e + (- 72a c - 54b c)d e + 144b c d e - 96c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 4 +--R (36a b c + 3b )d e + (- 72a c - 54b c)d e + 144b c d e - 96c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 +--R ((- 24a c - 18b )e + 96b c d e - 96c d e)x + (- 24a c - 18b )d e +--R + +--R 2 2 3 +--R 96b c d e - 96c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 3 2 +--R 8c e x + (20b c e - 16c d e )x +--R + +--R 2 4 3 2 2 2 4 +--R ((32a c + 18b )e - 64b c d e + 48c d e )x - 12a b e +--R + +--R 2 3 2 2 2 3 +--R (56a c + 30b )d e - 120b c d e + 96c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 6 5 +-+ +--R (12e x + 12d e )\|c +--R Type: Expression(Integer) +--E 493 + +--S 494 of 845 +--a0:=integrate(t0,x) +--E 494 + +--S 495 of 845 +--m0:=a0-r0 +--E 495 + +--S 496 of 845 +--d0:=D(m0,x) +--E 496 + +)clear all + +--S 497 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 497 + +--S 498 of 845 +r0:=1/2*(4*c*d-b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)+_ + 3/4*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e^5-3/8*(2*c*d-b*e)*(16*c^2*d^2+_ + b^2*e^2-4*c*e*(4*b*d-3*a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*sqrt(c*d^2-b*d*e+_ + a*e^2))-3/4*(16*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-a*e)+4*c*e*(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 4 3 2 2 2 2 +--R ((24a c + 18b )e - 96b c d e + 96c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 +--R ((48a c + 36b )d e - 192b c d e + 192c d e)x + (24a c + 18b )d e +--R + +--R 3 2 4 +--R - 96b c d e + 96c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 36a b c - 3b )e + (72a c + 54b c)d e - 144b c d e +--R + +--R 3 3 2 +--R 96c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 72a b c - 6b )d e + (144a c + 108b c)d e - 288b c d e +--R + +--R 3 4 +--R 192c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 36a b c - 3b )d e + (72a c + 54b c)d e - 144b c d e + 96c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 3 2 +--R 8c e x + (28b c e - 32c d e )x +--R + +--R 2 4 3 2 2 2 4 +--R ((- 16a c - 10b )e + 112b c d e - 144c d e )x - 4a b e +--R + +--R 2 3 2 2 2 3 +--R (- 8a c - 6b )d e + 72b c d e - 96c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 7 2 6 2 5 | 2 2 +--R (8e x + 16d e x + 8d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 498 + +--S 499 of 845 +--a0:=integrate(t0,x) +--E 499 + +--S 500 of 845 +--m0:=a0-r0 +--E 500 + +--S 501 of 845 +--d0:=D(m0,x) +--E 501 + +)clear all + +--S 502 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 502 + +--S 503 of 845 +r0:=-1/4*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*(a+b*x+c*x^2)^(3/2)/_ + (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+1/3*(8*c*d-b*e+6*c*e*x)*(a+b*x+_ + c*x^2)^(3/2)/(e^2*(d+e*x)^3)-4*c^(3/2)*(2*c*d-b*e)*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/e^5+1/16*(128*c^4*d^4-b^4*e^4-_ + 8*b^2*c*e^3*(2*b*d-3*a*e)-64*c^3*d^2*e*(4*b*d-3*a*e)+48*c^2*e^2*_ + (3*b^2*d^2-4*a*b*d*e+a^2*e^2))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*(c*d^2-b*d*e+_ + a*e^2)^(3/2))+1/8*(64*c^3*d^3+b^3*e^3+4*b*c*e^2*(4*b*d-5*a*e)-_ + 16*c^2*d*e*(5*b*d-4*a*e)+2*c*e*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-_ + 3*a*e))*x)*sqrt(a+b*x+c*x^2)/(e^4*(c*d^2-b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 6 2 2 5 2 2 4 3 3 3 3 +--R (192a b c e + (- 384a c - 192b c)d e + 576b c d e - 384c d e )x +--R + +--R 5 2 2 2 4 2 3 3 +--R 576a b c d e + (- 1152a c - 576b c)d e + 1728b c d e +--R + +--R 3 4 2 +--R - 1152c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 3 2 4 2 +--R 576a b c d e + (- 1152a c - 576b c)d e + 1728b c d e +--R + +--R 3 5 +--R - 1152c d e +--R * +--R x +--R + +--R 3 3 2 2 4 2 2 5 3 6 +--R 192a b c d e + (- 384a c - 192b c)d e + 576b c d e - 384c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 144a c - 72a b c + 3b )e + (576a b c + 48b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 576a c - 432b c )d e + 768b c d e - 384c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (- 432a c - 216a b c + 9b )d e + (1728a b c + 144b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (- 1728a c - 1296b c )d e + 2304b c d e - 1152c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 432a c - 216a b c + 9b )d e + (1728a b c + 144b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 1728a c - 1296b c )d e + 2304b c d e - 1152c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 144a c - 72a b c + 3b )d e + (576a b c + 48b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 576a c - 432b c )d e + 768b c d e - 384c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 6 2 5 3 2 4 3 +--R (96a c e - 96b c d e + 96c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (- 184a b c - 6b )e + (656a c + 220b c)d e - 912b c d e +--R + +--R 3 3 3 +--R 704c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 48a c - 28a b )e + (- 160a b c + 16b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (816a c + 252b c)d e - 1216b c d e + 960c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 16a b e + (- 16a c + 4a b )d e + (- 72a b c + 6b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (320a c + 96b c)d e - 480b c d e + 384c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 10 9 2 8 3 +--R (48a e - 48b d e + 48c d e )x +--R + +--R 9 2 8 3 7 2 +--R (144a d e - 144b d e + 144c d e )x +--R + +--R 2 8 3 7 4 6 3 7 4 6 5 5 +--R (144a d e - 144b d e + 144c d e )x + 48a d e - 48b d e + 48c d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 503 + +--S 504 of 845 +--a0:=integrate(t0,x) +--E 504 + +--S 505 of 845 +--m0:=a0-r0 +--E 505 + +--S 506 of 845 +--d0:=D(m0,x) +--E 506 + +)clear all + +--S 507 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 3 8 2 3 3 2 7 +--R 2c e x + (5b c e + 6c d e )x +--R + +--R 2 2 3 2 2 3 2 6 +--R ((4a c + 4b c)e + 15b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (12a c + 12b c)d e + 15b c d e + 2c d )x +--R + +--R 2 2 3 3 2 2 2 2 +--R (2a c + 2a b )e + (18a b c + 3b )d e + (12a c + 12b c)d e +--R + +--R 2 3 +--R 5b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 3 2 2 2 3 3 +--R (a b e + (6a c + 6a b )d e + (18a b c + 3b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 6a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 3 2 3 +--R (3a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 507 + +--S 508 of 845 +r0:=-1/8192*(b^2-4*a*c)^2*e*(40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*_ + (b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^5+1/2560*(b^2-4*a*c)*e*(40*c^2*d^2+_ + 11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^4+_ + 1/6720*(2*c*d-b*e)*(64*c^2*d^2+99*b^2*e^2-4*c*e*(16*b*d+83*a*e))*_ + (a+b*x+c*x^2)^(7/2)/c^3+1/30*(2*c*d-b*e)*(d+e*x)^2*(a+b*x+_ + c*x^2)^(7/2)/c+1/5*(d+e*x)^3*(a+b*x+c*x^2)^(7/2)+1/480*e*(7*b^2*d*e-_ + 44*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+11*b^2*e^2-4*c*e*(2*b*d+_ + 9*a*e))*x)*(a+b*x+c*x^2)^(7/2)/c^2-3/131072*(b^2-4*a*c)^4*e*_ + (40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(13/2)+3/65536*(b^2-4*a*c)^3*e*_ + (40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^6 +--R +--R +--R (2) +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 322560a c - 1209600a b c + 1008000a b c - 352800a b c +--R + +--R 8 10 +--R 56700a b c - 3465b +--R * +--R 3 +--R e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R 3225600a b c - 3225600a b c + 1209600a b c - 201600a b c +--R + +--R 9 +--R 12600b c +--R * +--R 2 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R - 3225600a c + 3225600a b c - 1209600a b c + 201600a b c +--R + +--R 8 2 +--R - 12600b c +--R * +--R 2 +--R d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 9 3 9 8 3 9 2 8 +--R 2752512c e x + (7798784b c e + 9175040c d e )x +--R + +--R 8 2 7 3 8 2 9 2 7 +--R ((7225344a c + 7196672b c )e + 26378240b c d e + 10321920c d e)x +--R + +--R 7 3 6 3 +--R (12836864a b c + 2119680b c )e +--R + +--R 8 2 7 2 8 2 9 3 +--R (24903680a c + 24821760b c )d e + 30228480b c d e + 3932160c d +--R * +--R 6 +--R x +--R + +--R 2 7 2 6 4 5 3 +--R (5332992a c + 5222400a b c - 2560b c )e +--R + +--R 7 3 6 2 +--R (45465600a b c + 7516160b c )d e +--R + +--R 8 2 7 2 8 3 +--R (29245440a c + 29184000b c )d e + 11796480b c d +--R * +--R 5 +--R x +--R + +--R 2 6 3 5 5 4 3 +--R (3502080a b c - 30720a b c + 2816b c )e +--R + +--R 2 7 2 6 4 5 2 +--R (19660800a c + 19292160a b c - 10240b c )d e +--R + +--R 7 3 6 2 8 2 7 3 +--R (55418880a b c + 9185280b c )d e + (11796480a c + 11796480b c )d +--R * +--R 4 +--R x +--R + +--R 3 6 2 2 5 4 4 6 3 3 +--R (215040a c - 145920a b c + 37760a b c - 3168b c )e +--R + +--R 2 6 3 5 5 4 2 +--R (13946880a b c - 133120a b c + 11520b c )d e +--R + +--R 2 7 2 6 4 5 2 +--R (25374720a c + 25036800a b c - 11520b c )d e +--R + +--R 7 3 6 3 +--R (23592960a b c + 3932160b c )d +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (- 332800a b c + 211200a b c - 47808a b c + 3696b c )e +--R + +--R 3 6 2 2 5 4 4 6 3 2 +--R (1310720a c - 706560a b c + 168960a b c - 13440b c )d e +--R + +--R 2 6 3 5 5 4 2 +--R (20367360a b c - 168960a b c + 13440b c )d e +--R + +--R 2 7 2 6 3 +--R (11796480a c + 11796480a b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R - 322560a c + 634880a b c - 320640a b c + 64512a b c +--R + +--R 8 +--R - 4620b c +--R * +--R 3 +--R e +--R + +--R 3 5 2 3 4 5 3 7 2 2 +--R (- 1914880a b c + 1082880a b c - 228480a b c + 16800b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 2 +--R (3225600a c - 1082880a b c + 228480a b c - 16800b c )d e +--R + +--R 2 6 3 +--R 11796480a b c d +--R * +--R x +--R + +--R 4 4 3 3 3 2 5 2 7 +--R 1149440a b c - 1374720a b c + 576576a b c - 104160a b c +--R + +--R 9 +--R 6930b +--R * +--R 3 +--R e +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R - 2621440a c + 4285440a b c - 1962240a b c + 369600a b c +--R + +--R 8 +--R - 25200b c +--R * +--R 2 +--R d e +--R + +--R 3 5 2 3 4 5 3 7 2 2 +--R (- 4285440a b c + 1962240a b c - 369600a b c + 25200b c )d e +--R + +--R 3 6 3 +--R 3932160a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 6 +-+ +--R 13762560c \|c +--R Type: Expression(Integer) +--E 508 + +--S 509 of 845 +--a0:=integrate(t0,x) +--E 509 + +--S 510 of 845 +--m0:=a0-r0 +--E 510 + +--S 511 of 845 +--d0:=D(m0,x) +--E 511 + +)clear all + +--S 512 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 512 + +--S 513 of 845 +r0:=-5/3072*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+_ + 1/192*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^3+_ + 1/504*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*_ + (a+b*x+c*x^2)^(7/2)/c^2+2/9*(d+e*x)^2*(a+b*x+c*x^2)^(7/2)+_ + 1/36*e*(b*d-2*a*e+(2*c*d-b*e)*x)*(a+b*x+c*x^2)^(7/2)/c-_ + 5/16384*(b^2-4*a*c)^4*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(11/2)+5/8192*(b^2-4*a*c)^3*e*(2*c*d-b*e)*_ + (b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 4 4 3 3 3 2 5 2 7 9 2 +--R (80640a b c - 80640a b c + 30240a b c - 5040a b c + 315b )e +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 +--R (- 161280a c + 161280a b c - 60480a b c + 10080a b c - 630b c)d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 8 2 8 7 2 8 7 +--R 229376c e x + (659456b c e + 516096c d e)x +--R + +--R 7 2 6 2 7 8 2 6 +--R ((622592a c + 620544b c )e + 1511424b c d e + 294912c d )x +--R + +--R 6 3 5 2 7 2 6 +--R (1136640a b c + 187904b c )e + (1462272a c + 1459200b c )d e +--R + +--R 7 2 +--R 884736b c d +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 4 4 2 +--R (491520a c + 482304a b c - 256b c )e +--R + +--R 6 3 5 7 2 6 2 +--R (2770944a b c + 459264b c )d e + (884736a c + 884736b c )d +--R * +--R 4 +--R x +--R + +--R 2 5 3 4 5 3 2 +--R (348672a b c - 3328a b c + 288b c )e +--R + +--R 2 6 2 5 4 4 +--R (1268736a c + 1251840a b c - 576b c )d e +--R + +--R 6 3 5 2 +--R (1769472a b c + 294912b c )d +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (32768a c - 17664a b c + 4224a b c - 336b c )e +--R + +--R 2 5 3 4 5 3 +--R (1018368a b c - 8448a b c + 672b c )d e +--R + +--R 2 6 2 5 2 +--R (884736a c + 884736a b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (- 47872a b c + 27072a b c - 5712a b c + 420b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (161280a c - 54144a b c + 11424a b c - 840b c )d e +--R + +--R 2 5 2 +--R 884736a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 2 4 2 6 8 2 +--R (- 65536a c + 107136a b c - 49056a b c + 9240a b c - 630b )e +--R + +--R 3 4 2 3 3 5 2 7 +--R (- 214272a b c + 98112a b c - 18480a b c + 1260b c)d e +--R + +--R 3 5 2 +--R 294912a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 1032192c \|c +--R Type: Expression(Integer) +--E 513 + +--S 514 of 845 +--a0:=integrate(t0,x) +--E 514 + +--S 515 of 845 +--m0:=a0-r0 +--E 515 + +--S 516 of 845 +--d0:=D(m0,x) +--E 516 + +)clear all + +--S 517 of 845 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 +--R ((6a b c + b )e + (4a c + 4b c)d)x +--R + +--R 2 2 3 2 2 2 2 2 +--R ((2a c + 2a b )e + (6a b c + b )d)x + (a b e + (2a c + 2a b )d)x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 517 + +--S 518 of 845 +r0:=-5/3072*(b^2-4*a*c)^2*e*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3+_ + 1/192*(b^2-4*a*c)*e*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^2+1/56*(2*c*d-b*e)*_ + (a+b*x+c*x^2)^(7/2)/c+1/4*(d+e*x)*(a+b*x+c*x^2)^(7/2)-_ + 5/16384*(b^2-4*a*c)^4*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(9/2)+5/8192*(b^2-4*a*c)^3*e*(b+2*c*x)*_ + sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 4 4 3 2 3 2 4 2 6 8 +--R (- 26880a c + 26880a b c - 10080a b c + 1680a b c - 105b )e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 7 7 6 7 6 +--R 86016c e x + (251904b c e + 98304c d)x +--R + +--R 6 2 5 6 5 +--R ((243712a c + 243200b c )e + 294912b c d)x +--R + +--R 5 3 4 6 2 5 4 +--R ((461824a b c + 76544b c )e + (294912a c + 294912b c )d)x +--R + +--R 2 5 2 4 4 3 +--R (211456a c + 208640a b c - 96b c )e +--R + +--R 5 3 4 +--R (589824a b c + 98304b c )d +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 +--R (169728a b c - 1408a b c + 112b c )e +--R + +--R 2 5 2 4 +--R (294912a c + 294912a b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 3 4 2 6 2 4 +--R ((26880a c - 9024a b c + 1904a b c - 140b c)e + 294912a b c d)x +--R + +--R 3 3 2 3 2 5 7 3 4 +--R (- 35712a b c + 16352a b c - 3080a b c + 210b )e + 98304a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 344064c \|c +--R Type: Expression(Integer) +--E 518 + +--S 519 of 845 +--a0:=integrate(t0,x) +--E 519 + +--S 520 of 845 +--m0:=a0-r0 +--E 520 + +--S 521 of 845 +--d0:=D(m0,x) +--E 521 + +)clear all + +--S 522 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 522 + +--S 523 of 845 +r0:=2/7*(a+b*x+c*x^2)^(7/2) +--R +--R +--R (2) +--R 3 6 2 5 2 2 4 3 3 +--R 2c x + 6b c x + (6a c + 6b c)x + (12a b c + 2b )x +--R + +--R 2 2 2 2 3 +--R (6a c + 6a b )x + 6a b x + 2a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 7 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 3 5 5 4 7 3 13 +--R (- 896a b c - 1120a b c - 168a b c - 2b c )x +--R + +--R 4 6 3 2 5 2 4 4 6 3 8 2 12 +--R (- 1792a c - 12096a b c - 7280a b c - 700a b c - 6b c )x +--R + +--R 4 5 3 3 4 2 5 3 7 2 9 11 +--R (- 29568a b c - 59360a b c - 18760a b c - 1098a b c - 6b c)x +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R - 19712a c - 168000a b c - 141680a b c - 23884a b c +--R + +--R 8 10 +--R - 768a b c - 2b +--R * +--R 10 +--R x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 192640a b c - 451360a b c - 177912a b c - 15014a b c +--R + +--R 9 +--R - 202a b +--R * +--R 9 +--R x +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R - 77056a c - 695744a b c - 626640a b c - 113204a b c +--R + +--R 2 8 +--R - 3730a b +--R * +--R 8 +--R x +--R + +--R 6 3 5 3 2 4 5 3 7 7 +--R (- 515200a b c - 1183392a b c - 435288a b c - 28814a b )x +--R + +--R 7 3 6 2 2 5 4 4 6 6 +--R (- 146944a c - 1233792a b c - 959392a b c - 119784a b )x +--R + +--R 7 2 6 3 5 5 5 +--R (- 666624a b c - 1261568a b c - 298816a b )x +--R + +--R 8 2 7 2 6 4 4 +--R (- 143360a c - 967680a b c - 465920a b )x +--R + +--R 8 7 3 3 9 8 2 2 +--R (- 387072a b c - 448000a b )x + (- 57344a c - 243712a b )x +--R + +--R 9 +--R - 57344a b x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 7 2 2 6 4 5 6 4 14 +--R (256a c + 1344a b c + 560a b c + 28b c )x +--R + +--R 3 6 2 3 5 5 4 7 3 13 +--R (7168a b c + 12544a b c + 3136a b c + 112b c )x +--R + +--R 4 6 3 2 5 2 4 4 6 3 8 2 12 +--R (7168a c + 59136a b c + 47040a b c + 7056a b c + 168b c )x +--R + +--R 4 5 3 3 4 2 5 3 7 2 9 11 +--R (93184a b c + 224000a b c + 90944a b c + 7952a b c + 112b c)x +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 8 +--R 46592a c + 452480a b c + 451360a b c + 96040a b c + 4480a b c +--R + +--R 10 +--R 28b +--R * +--R 10 +--R x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R 408576a b c + 1084160a b c + 501312a b c + 52752a b c +--R + +--R 9 +--R 1008a b +--R * +--R 9 +--R x +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 136192a c + 1356544a b c + 1377600a b c + 290192a b c +--R + +--R 2 8 +--R 11816a b +--R * +--R 8 +--R x +--R + +--R 6 3 5 3 2 4 5 3 7 7 +--R (852096a b c + 2154656a b c + 890904a b c + 68462a b )x +--R + +--R 7 3 6 2 2 5 4 4 6 6 +--R (211456a c + 1927296a b c + 1648864a b c + 231000a b )x +--R + +--R 7 2 6 3 5 5 5 +--R (910336a b c + 1874432a b c + 488768a b )x +--R + +--R 8 2 7 2 6 4 4 +--R (172032a c + 1261568a b c + 663040a b )x +--R + +--R 8 7 3 3 9 8 2 2 9 +--R (444416a b c + 562688a b )x + (57344a c + 272384a b )x + 57344a b x +--R * +--R +-+ +--R \|a +--R / +--R 3 3 2 2 2 4 6 6 +--R (896a c + 4704a b c + 1960a b c + 98b )x +--R + +--R 3 2 2 3 5 5 +--R (21504a b c + 25088a b c + 3136a b )x +--R + +--R 4 2 3 2 2 4 4 4 3 3 3 +--R (21504a c + 96768a b c + 28224a b )x + (143360a b c + 107520a b )x +--R + +--R 5 4 2 2 5 6 +--R (71680a c + 197120a b )x + 172032a b x + 57344a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 7 +--R (- 3136a b c - 3920a b c - 588a b c - 7b )x +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (- 6272a c - 32928a b c - 13720a b c - 686a b )x +--R + +--R 4 2 3 3 2 5 5 +--R (- 75264a b c - 87808a b c - 10976a b )x +--R + +--R 5 2 4 2 3 4 4 +--R (- 50176a c - 225792a b c - 65856a b )x +--R + +--R 5 4 3 3 6 5 2 2 +--R (- 250880a b c - 188160a b )x + (- 100352a c - 275968a b )x +--R + +--R 6 7 +--R - 200704a b x - 57344a +--R Type: Union(Expression(Integer),...) +--E 524 + +--S 525 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 3 6 2 2 5 4 4 6 6 +--R (256a c + 1344a b c + 560a b c + 28a b )x +--R + +--R 7 2 6 3 5 5 5 +--R (6144a b c + 7168a b c + 896a b )x +--R + +--R 8 2 7 2 6 4 4 8 7 3 3 +--R (6144a c + 27648a b c + 8064a b )x + (40960a b c + 30720a b )x +--R + +--R 9 8 2 2 9 10 +--R (20480a c + 56320a b )x + 49152a b x + 16384a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 6 3 5 3 2 4 5 3 7 7 +--R (- 896a b c - 1120a b c - 168a b c - 2a b )x +--R + +--R 7 3 6 2 2 5 4 4 6 6 +--R (- 1792a c - 9408a b c - 3920a b c - 196a b )x +--R + +--R 7 2 6 3 5 5 5 +--R (- 21504a b c - 25088a b c - 3136a b )x +--R + +--R 8 2 7 2 6 4 4 +--R (- 14336a c - 64512a b c - 18816a b )x +--R + +--R 8 7 3 3 9 8 2 2 +--R (- 71680a b c - 53760a b )x + (- 28672a c - 78848a b )x +--R + +--R 9 10 +--R - 57344a b x - 16384a +--R * +--R +-+ +--R \|a +--R / +--R 3 3 2 2 2 4 6 6 +--R (896a c + 4704a b c + 1960a b c + 98b )x +--R + +--R 3 2 2 3 5 5 +--R (21504a b c + 25088a b c + 3136a b )x +--R + +--R 4 2 3 2 2 4 4 4 3 3 3 +--R (21504a c + 96768a b c + 28224a b )x + (143360a b c + 107520a b )x +--R + +--R 5 4 2 2 5 6 +--R (71680a c + 197120a b )x + 172032a b x + 57344a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 7 +--R (- 3136a b c - 3920a b c - 588a b c - 7b )x +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (- 6272a c - 32928a b c - 13720a b c - 686a b )x +--R + +--R 4 2 3 3 2 5 5 +--R (- 75264a b c - 87808a b c - 10976a b )x +--R + +--R 5 2 4 2 3 4 4 +--R (- 50176a c - 225792a b c - 65856a b )x +--R + +--R 5 4 3 3 6 5 2 2 +--R (- 250880a b c - 188160a b )x + (- 100352a c - 275968a b )x +--R + +--R 6 7 +--R - 200704a b x - 57344a +--R Type: Expression(Integer) +--E 525 + +--S 526 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 526 + +)clear all + +--S 527 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R e x + d +--R Type: Expression(Integer) +--E 527 + +--S 528 of 845 +r0:=-1/96*(64*c^3*d^3-b^3*e^3+4*b*c*e^2*(14*b*d-13*a*e)-8*c^2*d*e*_ + (15*b*d-8*a*e)-2*c*e*(24*c^2*d^2+b^2*e^2-4*c*e*(6*b*d-5*a*e))*x)*_ + (a+b*x+c*x^2)^(3/2)/(c*e^4)-1/30*(12*c*d-11*b*e-10*c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/e^2+1/512*(1024*c^6*d^6+b^6*e^6+4*b^4*c*e^5*_ + (2*b*d-5*a*e)-512*c^5*d^4*e*(6*b*d-5*a*e)-320*c^3*e^3*(b*d-a*e)^2*_ + (4*b*d-a*e)+640*c^4*d^2*e^2*(5*b^2*d^2-8*a*b*d*e+3*a^2*e^2)+_ + 40*b^2*c^2*e^4*(3*b^2*d^2-8*a*b*d*e+6*a^2*e^2))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(5/2)*e^7)-(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^(5/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/e^7-1/256*(512*c^5*d^5+b^5*e^5-_ + 128*c^4*d^3*e*(11*b*d-8*a*e)+8*b^3*c*e^4*(b*d-2*a*e)+32*c^3*d*e^2*_ + (40*b^2*d^2-55*a*b*d*e+16*a^2*e^2)-8*b*c^2*e^3*(49*b^2*d^2-_ + 92*a*b*d*e+42*a^2*e^2)-2*c*e*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*_ + (8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/(c^2*e^6) +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 6 +--R (4800a c + 3600a b c - 300a b c + 15b )e +--R + +--R 2 3 3 2 5 5 +--R (- 28800a b c - 4800a b c + 120b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (28800a c + 43200a b c + 1800b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (- 76800a b c - 19200b c )d e + (38400a c + 48000b c )d e +--R + +--R 5 5 6 6 +--R - 46080b c d e + 15360c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 5 2 3 2 2 4 +--R - 7680a b c e + (15360a c + 15360a b c )d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (- 46080a b c - 7680b c )d e + (30720a c + 30720b c )d e +--R + +--R 4 4 5 5 +--R - 38400b c d e + 15360c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 5 6 5 4 6 5 5 4 +--R 2560c e x + (7936b c e - 3072c d e )x +--R + +--R 4 2 3 6 4 5 5 2 4 3 +--R ((8320a c + 8352b c )e - 9984b c d e + 3840c d e )x +--R + +--R 3 3 2 6 4 2 3 5 +--R (18112a b c + 3056b c )e + (- 11264a c - 11392b c )d e +--R + +--R 4 2 4 5 3 3 +--R 13440b c d e - 5120c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 4 6 +--R (10560a c + 10912a b c + 20b c)e +--R + +--R 3 3 2 5 4 2 3 2 4 +--R (- 28544a b c - 4960b c )d e + (17280a c + 17760b c )d e +--R + +--R 4 3 3 5 4 2 +--R - 20480b c d e + 7680c d e +--R * +--R x +--R + +--R 2 2 3 5 6 +--R (17056a b c + 560a b c - 30b )e +--R + +--R 2 3 2 2 4 5 +--R (- 23552a c - 26560a b c - 240b c)d e +--R + +--R 3 3 2 2 4 4 2 3 3 3 +--R (62400a b c + 11760b c )d e + (- 35840a c - 38400b c )d e +--R + +--R 4 4 2 5 5 +--R 42240b c d e - 15360c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 7 +-+ +--R 7680c e \|c +--R Type: Expression(Integer) +--E 528 + +--S 529 of 845 +--a0:=integrate(t0,x) +--E 529 + +--S 530 of 845 +--m0:=a0-r0 +--E 530 + +--S 531 of 845 +--d0:=D(m0,x) +--E 531 + +)clear all + +--S 532 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 532 + +--S 533 of 845 +r0:=1/12*(48*c^2*d^2-66*b*c*d*e+19*b^2*e^2+8*a*c*e^2-18*c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/e^4+1/5*(12*c*d-5*b*e+2*c*e*x)*(a+b*x+c*x^2)^(5/2)/_ + (e^2*(d+e*x))-1/64*(2*c*d-b*e)*(384*c^4*d^4-b^4*e^4-8*b^2*c*e^3*(4*b*d-_ + 5*a*e)-128*c^3*d^2*e*(6*b*d-5*a*e)+16*c^2*e^2*(26*b^2*d^2-40*a*b*d*e+_ + 15*a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*_ + e^7)+1/2*(c*d^2-b*d*e+a*e^2)^(3/2)*(24*c^2*d^2+5*b^2*e^2-4*c*e*_ + (6*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+_ + a*e^2)*sqrt(a+b*x+c*x^2)))/e^7+1/32*(384*c^4*d^4+b^4*e^4-2*b^2*c*e^3*_ + (65*b*d-62*a*e)-32*c^3*d^2*e*(27*b*d-14*a*e)+8*c^2*e^2*(76*b^2*d^2-_ + 67*a*b*d*e+8*a^2*e^2)-2*c*e*(2*c*d-b*e)*(48*c^2*d^2-48*b*c*d*e+_ + b^2*e^2+44*a*c*e^2)*x)*sqrt(a+b*x+c*x^2)/(c*e^6) +--R +--R +--R (2) +--R 2 2 3 5 6 +--R (3600a b c + 600a b c - 15b )e +--R + +--R 2 3 2 2 4 5 +--R (- 7200a c - 10800a b c - 450b c)d e +--R + +--R 3 3 2 2 4 4 2 3 3 3 +--R (28800a b c + 7200b c )d e + (- 19200a c - 24000b c )d e +--R + +--R 4 4 2 5 5 +--R 28800b c d e - 11520c d e +--R * +--R x +--R + +--R 2 2 3 5 5 +--R (3600a b c + 600a b c - 15b )d e +--R + +--R 2 3 2 2 4 2 4 +--R (- 7200a c - 10800a b c - 450b c)d e +--R + +--R 3 3 2 3 3 4 2 3 4 2 +--R (28800a b c + 7200b c )d e + (- 19200a c - 24000b c )d e +--R + +--R 4 5 5 6 +--R 28800b c d e - 11520c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 5 2 3 4 +--R (- 1920a c - 2400a b c)e + (13440a b c + 2400b c)d e +--R + +--R 3 2 2 2 3 3 3 2 4 4 +--R (- 13440a c - 13920b c )d e + 23040b c d e - 11520c d e +--R * +--R x +--R + +--R 2 2 2 4 2 3 2 3 +--R (- 1920a c - 2400a b c)d e + (13440a b c + 2400b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (- 13440a c - 13920b c )d e + 23040b c d e - 11520c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 4 6 5 3 6 4 5 4 +--R 384c e x + (1248b c e - 576c d e )x +--R + +--R 3 2 2 6 3 5 4 2 4 3 +--R ((1408a c + 1424b c )e - 2112b c d e + 960c d e )x +--R + +--R 2 3 6 3 2 2 5 +--R (3568a b c + 620b c)e + (- 2912a c - 3016b c )d e +--R + +--R 3 2 4 4 3 3 +--R 4320b c d e - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 6 2 3 5 +--R (2944a c + 3320a b c + 30b )e + (- 12032a b c - 2320b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (9120a c + 9960b c )d e - 13440b c d e + 5760c d e +--R * +--R x +--R + +--R 2 6 2 2 2 4 5 +--R - 960a b c e + (4864a c + 5240a b c + 30b )d e +--R + +--R 2 3 2 4 3 2 2 3 3 +--R (- 21360a b c - 3900b c)d e + (17280a c + 18240b c )d e +--R + +--R 3 4 2 4 5 +--R - 25920b c d e + 11520c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 8 7 +-+ +--R (960c e x + 960c d e )\|c +--R Type: Expression(Integer) +--E 533 + +--S 534 of 845 +--a0:=integrate(t0,x) +--E 534 + +--S 535 of 845 +--m0:=a0-r0 +--E 535 + +--S 536 of 845 +--d0:=D(m0,x) +--E 536 + +)clear all + +--S 537 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 537 + +--S 538 of 845 +r0:=-5/4*(8*c^2*d^2+b^2*e^2-c*e*(7*b*d-2*a*e)+c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/2*(3*c*d-b*e+c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)+15/64*(128*c^4*d^4+b^4*e^4-_ + 8*b^2*c*e^3*(4*b*d-3*a*e)-128*c^3*d^2*e*(2*b*d-a*e)+16*c^2*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^7*sqrt(c))-15/8*(2*c*d-b*e)*(8*c^2*d^2+b^2*e^2-_ + 4*c*e*(2*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^7-_ + 15/32*(64*c^3*d^3-7*b^3*e^3+4*b*c*e^2*(14*b*d-5*a*e)-16*c^2*d*e*_ + (7*b*d-2*a*e)-2*c*e*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*x)*_ + sqrt(a+b*x+c*x^2)/e^6 +--R +--R +--R (2) +--R 2 2 2 4 6 2 3 5 +--R (240a c + 360a b c + 15b )e + (- 1920a b c - 480b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (1920a c + 2400b c )d e - 3840b c d e + 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 5 2 3 2 4 +--R (480a c + 720a b c + 30b )d e + (- 3840a b c - 960b c)d e +--R + +--R 3 2 2 3 3 3 4 2 4 5 +--R (3840a c + 4800b c )d e - 7680b c d e + 3840c d e +--R * +--R x +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (240a c + 360a b c + 15b )d e + (- 1920a b c - 480b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (1920a c + 2400b c )d e - 3840b c d e + 1920c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 480a b c - 120b )e + (960a c + 1200b c)d e - 2880b c d e +--R + +--R 3 3 2 +--R 1920c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 960a b c - 240b )d e + (1920a c + 2400b c)d e +--R + +--R 2 3 2 3 4 +--R - 5760b c d e + 3840c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 +--R (- 480a b c - 120b )d e + (960a c + 1200b c)d e - 2880b c d e +--R + +--R 3 5 +--R 1920c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 6 5 2 6 3 5 4 +--R 32c e x + (112b c e - 64c d e )x +--R + +--R 2 2 6 2 5 3 2 4 3 +--R ((144a c + 148b c)e - 288b c d e + 160c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (520a b c + 98b )e + (- 608a c - 664b c)d e + 1200b c d e +--R + +--R 3 3 3 +--R - 640c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 128a c - 144a b )e + (1872a b c + 340b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 2480a c - 2620b c)d e + 5120b c d e - 2880c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 32a b e + (- 64a c - 80a b )d e + (1160a b c + 210b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (- 1600a c - 1680b c)d e + 3360b c d e - 1920c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 9 2 8 2 7 +-+ +--R (64e x + 128d e x + 64d e )\|c +--R Type: Expression(Integer) +--E 538 + +--S 539 of 845 +--a0:=integrate(t0,x) +--E 539 + +--S 540 of 845 +--m0:=a0-r0 +--E 540 + +--S 541 of 845 +--d0:=D(m0,x) +--E 541 + +)clear all + +--S 542 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 542 + +--S 543 of 845 +r0:=-5/12*(16*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-a*e)+4*c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(4*c*d-b*e+2*c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)-5/2*(2*c*d-b*e)*(8*c^2*d^2+b^2*e^2-_ + 4*c*e*(2*b*d-a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*_ + sqrt(c)/e^7+5/16*(128*c^4*d^4+b^4*e^4-8*b^2*c*e^3*(4*b*d-3*a*e)-_ + 128*c^3*d^2*e*(2*b*d-a*e)+16*c^2*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2))*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(e^7*sqrt(c*d^2-b*d*e+a*e^2))+5/8*(64*c^3*d^3-_ + b^3*e^3-16*c^2*d*e*(5*b*d-2*a*e)+12*b*c*e^2*(2*b*d-a*e)+2*c*e*_ + (16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 3 6 2 2 5 2 2 4 +--R (480a b c + 120b )e + (- 960a c - 1200b c)d e + 2880b c d e +--R + +--R 3 3 3 +--R - 1920c d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 2 4 +--R (1440a b c + 360b )d e + (- 2880a c - 3600b c)d e +--R + +--R 2 3 3 3 4 2 +--R 8640b c d e - 5760c d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 2 3 3 +--R (1440a b c + 360b )d e + (- 2880a c - 3600b c)d e +--R + +--R 2 4 2 3 5 +--R 8640b c d e - 5760c d e +--R * +--R x +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (480a b c + 120b )d e + (- 960a c - 1200b c)d e + 2880b c d e +--R + +--R 3 6 +--R - 1920c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 240a c - 360a b c - 15b )e + (1920a b c + 480b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 1920a c - 2400b c )d e + 3840b c d e - 1920c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (- 720a c - 1080a b c - 45b )d e + (5760a b c + 1440b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (- 5760a c - 7200b c )d e + 11520b c d e - 5760c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 720a c - 1080a b c - 45b )d e + (5760a b c + 1440b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 5760a c - 7200b c )d e + 11520b c d e - 5760c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 240a c - 360a b c - 15b )d e + (1920a b c + 480b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 1920a c - 2400b c )d e + 3840b c d e - 1920c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 6 5 2 6 3 5 4 +--R 32c e x + (128b c e - 96c d e )x +--R + +--R 2 2 6 2 5 3 2 4 3 +--R ((224a c + 240b c)e - 672b c d e + 480c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (- 328a b c - 66b )e + (1328a c + 1444b c)d e - 4560b c d e +--R + +--R 3 3 3 +--R 3520c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 48a c - 52a b )e + (- 352a b c - 80b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (1680a c + 1860b c)d e - 6080b c d e + 4800c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 16a b e + (- 16a c - 20a b )d e + (- 120a b c - 30b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (640a c + 720b c)d e - 2400b c d e + 1920c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 10 3 9 2 2 8 3 7 | 2 2 +--R (48e x + 144d e x + 144d e x + 48d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 543 + +--S 544 of 845 +--a0:=integrate(t0,x) +--E 544 + +--S 545 of 845 +--m0:=a0-r0 +--E 545 + +--S 546 of 845 +--d0:=D(m0,x) +--E 546 + +)clear all + +--S 547 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 547 + +--S 548 of 845 +r0:=3/64*(b^2-4*a*c)*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+_ + 1/32*(2*c*d-b*e)*(16*c^2*d^2+15*b^2*e^2-4*c*e*(4*b*d+11*a*e))*_ + sqrt(a+b*x+c*x^2)/c^3+1/4*(2*c*d-b*e)*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+_ + 1/2*(d+e*x)^3*sqrt(a+b*x+c*x^2)+1/16*e*(b^2*d*e-20*a*c*d*e+4*b*_ + (c*d^2+a*e^2)+(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*x)*_ + sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 4 3 2 3 2 +--R (48a c - 72a b c + 15b )e + (192a b c - 48b c)d e +--R + +--R 3 2 2 2 +--R (- 192a c + 48b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 32c e x + (- 16b c e + 128c d e )x +--R + +--R 2 2 3 2 2 3 2 3 3 +--R ((- 48a c + 20b c)e - 64b c d e + 192c d e)x + (104a b c - 30b )e +--R + +--R 2 2 2 2 2 3 3 +--R (- 256a c + 96b c)d e - 96b c d e + 128c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 64c \|c +--R Type: Expression(Integer) +--E 548 + +--S 549 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 3 2 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120a b )e +--R + +--R 3 2 3 6 2 3 4 5 2 2 +--R (6144a b c - 384a b c)d e + (- 6144a b c + 384a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (3072a c - 768a b c - 4800a b c + 1200a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (12288a b c + 12288a b c - 3840a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (- 12288a c - 12288a b c + 3840a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (9216a b c - 13824a b c + 2880a b )e +--R + +--R 4 2 2 3 4 2 +--R (36864a b c - 9216a b c)d e +--R + +--R 4 3 3 3 2 2 +--R (- 36864a b c + 9216a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (6144a c - 9216a b c + 1920a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (24576a b c - 6144a b c)d e + (- 24576a c + 6144a b c )d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 3 +--R (- 768a c + 1440a b c - 288a b c - 15b )e +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (- 3072a b c - 3840a b c + 960a b c + 48b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (3072a c + 3840a b c - 960a b c - 48b c )d e +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480a b )e +--R + +--R 3 2 3 6 2 +--R (- 24576a b c + 1536a b c)d e +--R + +--R 3 4 5 2 2 +--R (24576a b c - 1536a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (- 24576a b c - 24576a b c + 7680a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (24576a c + 24576a b c - 7680a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (- 12288a b c + 18432a b c - 3840a b )e +--R + +--R 4 2 2 3 4 2 +--R (- 49152a b c + 12288a b c)d e +--R + +--R 4 3 3 3 2 2 +--R (49152a b c - 12288a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (- 6144a c + 9216a b c - 1920a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (- 24576a b c + 6144a b c)d e + (24576a c - 6144a b c )d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 5 2 4 4 3 3 7 +--R (- 512a c - 768a b c - 32b c )e x +--R + +--R 2 4 3 3 5 2 3 +--R (- 3840a b c - 640a b c + 16b c )e +--R + +--R 2 5 2 4 4 3 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2 +--R \|a \|c \|c x + b x + a +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 1664a b c - 2016a b c + 616a b c + 30a b )e +--R + +--R 4 4 3 2 3 2 4 2 6 2 +--R (4096a c + 4608a b c - 2048a b c - 96a b c)d e +--R + +--R 3 4 2 3 3 5 2 2 +--R (1536a b c + 2304a b c + 96a b c )d e +--R + +--R 3 5 2 2 4 4 3 3 +--R (- 2048a c - 3072a b c - 128a b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 2 3 4 2 6 3 +--R (- 13312a b c + 512a b c + 960a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (32768a b c - 4096a b c - 3072a b c)d e +--R + +--R 3 2 3 2 4 2 2 3 4 2 3 3 3 +--R (12288a b c + 3072a b c )d e + (- 16384a b c - 4096a b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (- 13312a b c - 12800a b c + 4800a b )e +--R + +--R 5 3 4 2 2 3 4 2 +--R (32768a c + 28672a b c - 15360a b c)d e +--R + +--R 4 3 3 3 2 2 4 4 3 2 3 3 +--R (12288a b c + 15360a b c )d e + (- 16384a c - 20480a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 3 5 2 4 3 2 +--R (- 26624a b c + 7680a b )e + (65536a b c - 24576a b c)d e +--R + +--R 4 2 2 2 4 3 3 +--R 24576a b c d e - 32768a b c d +--R * +--R x +--R + +--R 6 5 3 3 6 2 5 2 2 +--R (- 13312a b c + 3840a b )e + (32768a c - 12288a b c)d e +--R + +--R 5 2 2 5 3 3 +--R 12288a b c d e - 16384a c d +--R * +--R +-+ +--R \|c +--R / +--R 2 4 3 3 3 3 4 2 2 3 2 3 3 +--R (2048a b c + 512a b c )x + (4096a c + 5120a b c )x + 12288a b c x +--R + +--R 4 3 +--R 8192a c +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 2 4 3 3 3 +--R (- 1024a c - 1536a b c - 64b c )x + (- 8192a b c - 2048a b c )x +--R + +--R 3 4 2 2 3 2 3 3 4 3 +--R (- 8192a c - 10240a b c )x - 16384a b c x - 8192a c +--R * +--R +-+ +-+ +--R \|a \|c +--R Type: Expression(Integer) +--E 550 + +--S 551 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 551 + +--S 552 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 3 3 2 2 5 7 3 +--R (- 1536a b c + 1920a b c + 96a b c - 120a b )e +--R + +--R 3 2 3 6 2 3 4 5 2 2 +--R (- 6144a b c + 384a b c)d e + (6144a b c - 384a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (- 3072a c + 768a b c + 4800a b c - 1200a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (- 12288a b c - 12288a b c + 3840a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (12288a c + 12288a b c - 3840a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (- 9216a b c + 13824a b c - 2880a b )e +--R + +--R 4 2 2 3 4 2 4 3 3 3 2 2 +--R (- 36864a b c + 9216a b c)d e + (36864a b c - 9216a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (- 6144a c + 9216a b c - 1920a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (- 24576a b c + 6144a b c)d e + (24576a c - 6144a b c )d e +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 3 +--R (768a c - 1440a b c + 288a b c + 15b )e +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (3072a b c + 3840a b c - 960a b c - 48b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (- 3072a c - 3840a b c + 960a b c + 48b c )d e +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (6144a b c - 7680a b c - 384a b c + 480a b )e +--R + +--R 3 2 3 6 2 3 4 5 2 2 +--R (24576a b c - 1536a b c)d e + (- 24576a b c + 1536a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (6144a c - 1536a b c - 9600a b c + 2400a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (24576a b c + 24576a b c - 7680a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (- 24576a c - 24576a b c + 7680a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (12288a b c - 18432a b c + 3840a b )e +--R + +--R 4 2 2 3 4 2 +--R (49152a b c - 12288a b c)d e +--R + +--R 4 3 3 3 2 2 +--R (- 49152a b c + 12288a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (6144a c - 9216a b c + 1920a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (24576a b c - 6144a b c)d e + (- 24576a c + 6144a b c )d e +--R * +--R +---+ +-+ +--R \|- c \|a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (3072a b c - 3840a b c - 192a b c + 240a b )e +--R + +--R 3 2 3 6 2 3 4 5 2 2 +--R (12288a b c - 768a b c)d e + (- 12288a b c + 768a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (6144a c - 1536a b c - 9600a b c + 2400a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (24576a b c + 24576a b c - 7680a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (- 24576a c - 24576a b c + 7680a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (18432a b c - 27648a b c + 5760a b )e +--R + +--R 4 2 2 3 4 2 +--R (73728a b c - 18432a b c)d e +--R + +--R 4 3 3 3 2 2 +--R (- 73728a b c + 18432a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (12288a c - 18432a b c + 3840a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (49152a b c - 12288a b c)d e + (- 49152a c + 12288a b c )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 3 +--R (- 1536a c + 2880a b c - 576a b c - 30b )e +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (- 6144a b c - 7680a b c + 1920a b c + 96b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (6144a c + 7680a b c - 1920a b c - 96b c )d e +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 12288a b c + 15360a b c + 768a b c - 960a b )e +--R + +--R 3 2 3 6 2 3 4 5 2 2 +--R (- 49152a b c + 3072a b c)d e + (49152a b c - 3072a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (- 12288a c + 3072a b c + 19200a b c - 4800a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (- 49152a b c - 49152a b c + 15360a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (49152a c + 49152a b c - 15360a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (- 24576a b c + 36864a b c - 7680a b )e +--R + +--R 4 2 2 3 4 2 +--R (- 98304a b c + 24576a b c)d e +--R + +--R 4 3 3 3 2 2 +--R (98304a b c - 24576a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (- 12288a c + 18432a b c - 3840a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (- 49152a b c + 12288a b c)d e + (49152a c - 12288a b c )d e +--R * +--R +-+ +-+ +--R \|a \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 2 2 2 4 6 3 +--R (3328a b c - 128a b c - 240a b )e +--R + +--R 3 3 2 3 2 5 2 +--R (- 8192a b c + 1024a b c + 768a b c)d e +--R + +--R 2 2 3 4 2 2 2 4 3 3 3 +--R (- 3072a b c - 768a b c )d e + (4096a b c + 1024a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 3 +--R (6656a b c + 6400a b c - 2400a b )e +--R + +--R 4 3 3 2 2 2 4 2 +--R (- 16384a c - 14336a b c + 7680a b c)d e +--R + +--R 3 3 2 3 2 2 3 4 2 2 3 3 +--R (- 6144a b c - 7680a b c )d e + (8192a c + 10240a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 3 4 2 3 3 2 +--R (19968a b c - 5760a b )e + (- 49152a b c + 18432a b c)d e +--R + +--R 3 2 2 2 3 3 3 +--R - 18432a b c d e + 24576a b c d +--R * +--R x +--R + +--R 5 4 3 3 5 2 4 2 2 +--R (13312a b c - 3840a b )e + (- 32768a c + 12288a b c)d e +--R + +--R 4 2 2 4 3 3 +--R - 12288a b c d e + 16384a c d +--R * +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R \|- c \|a \|c \|c x + b x + a +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 1664a b c - 2016a b c + 616a b c + 30a b )e +--R + +--R 4 4 3 2 3 2 4 2 6 2 +--R (4096a c + 4608a b c - 2048a b c - 96a b c)d e +--R + +--R 3 4 2 3 3 5 2 2 +--R (1536a b c + 2304a b c + 96a b c )d e +--R + +--R 3 5 2 2 4 4 3 3 +--R (- 2048a c - 3072a b c - 128a b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 2 3 4 2 6 3 +--R (- 13312a b c + 512a b c + 960a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (32768a b c - 4096a b c - 3072a b c)d e +--R + +--R 3 2 3 2 4 2 2 3 4 2 3 3 3 +--R (12288a b c + 3072a b c )d e + (- 16384a b c - 4096a b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (- 13312a b c - 12800a b c + 4800a b )e +--R + +--R 5 3 4 2 2 3 4 2 +--R (32768a c + 28672a b c - 15360a b c)d e +--R + +--R 4 3 3 3 2 2 4 4 3 2 3 3 +--R (12288a b c + 15360a b c )d e + (- 16384a c - 20480a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 3 5 2 4 3 2 +--R (- 26624a b c + 7680a b )e + (65536a b c - 24576a b c)d e +--R + +--R 4 2 2 2 4 3 3 +--R 24576a b c d e - 32768a b c d +--R * +--R x +--R + +--R 6 5 3 3 6 2 5 2 2 +--R (- 13312a b c + 3840a b )e + (32768a c - 12288a b c)d e +--R + +--R 5 2 2 5 3 3 +--R 12288a b c d e - 16384a c d +--R * +--R +---+ +-+ +--R \|- c \|c +--R / +--R 2 4 3 3 3 3 4 2 2 3 2 3 3 +--R (2048a b c + 512a b c )x + (4096a c + 5120a b c )x + 12288a b c x +--R + +--R 4 3 +--R 8192a c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 2 4 3 3 3 +--R (- 1024a c - 1536a b c - 64b c )x + (- 8192a b c - 2048a b c )x +--R + +--R 3 4 2 2 3 2 3 3 4 3 +--R (- 8192a c - 10240a b c )x - 16384a b c x - 8192a c +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R Type: Expression(Integer) +--E 552 + +--S 553 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 553 + +)clear all + +--S 554 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 554 + +--S 555 of 845 +r0:=1/4*(b^2-4*a*c)*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(5/2)+1/6*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+_ + a*e))*sqrt(a+b*x+c*x^2)/c^2+2/3*(d+e*x)^2*sqrt(a+b*x+c*x^2)+1/3*e*_ + (b*d-2*a*e+(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R 3 2 2 2 2c x + b +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e)atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 2 2 2 2 +--R 8c e x + (- 4b c e + 24c d e)x + (- 16a c + 6b )e - 12b c d e +--R + +--R 2 2 +--R 24c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 +-+ +--R 12c \|c +--R Type: Expression(Integer) +--E 555 + +--S 556 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 5 2 +--R (96a b c + 48a b c - 18b )e +--R + +--R 2 3 2 2 4 +--R (- 192a c - 96a b c + 36b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((384a b c - 96a b )e + (- 768a b c + 192a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (384a b c - 96a b )e + (- 768a c + 192a b c)d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (- 144a b c + 24a b c + 3b )e +--R + +--R 2 3 3 2 5 +--R (288a b c - 48a b c - 6b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (- 288a b c - 144a b c + 54a b )e +--R + +--R 3 3 2 2 2 4 +--R (576a c + 288a b c - 108a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((- 576a b c + 144a b )e + (1152a b c - 288a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (- 384a b c + 96a b )e + (768a c - 192a b c)d e +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 3 2 2 5 +--R (- 96a b c - 8b c )e x +--R + +--R 2 3 2 2 4 2 3 3 2 4 +--R ((- 192a c - 96a b c + 4b c)e + (- 288a b c - 24b c )d e)x +--R + +--R 2 2 3 5 2 +--R (- 96a b c + 16a b c - 6b )e +--R + +--R 2 3 2 2 4 3 3 2 2 +--R (- 576a c - 288a b c + 12b c)d e + (- 288a b c - 24b c )d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R (288a b c - 72a b )e + (- 960a b c + 144a b c)d e +--R + +--R 2 3 2 2 2 +--R (- 384a c - 288a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 2 2 2 2 2 2 +--R ((384a b c - 96a b )e + (- 768a c + 192a b c)d e - 384a b c d )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 4 2 3 2 6 +--R (64a c + 48b c )e x +--R + +--R 3 3 2 2 4 2 3 5 +--R ((288a b c + 24b c )e + (192a c + 144b c )d e)x +--R + +--R 2 3 2 2 4 2 3 3 2 +--R (192a c + 96a b c + 12b c)e + (864a b c + 72b c )d e +--R + +--R 4 2 3 2 +--R (192a c + 144b c )d +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 2 +--R (- 96a b c - 64a b c + 30b )e +--R + +--R 2 3 2 2 4 3 3 2 2 +--R (960a c + 576a b c - 60b c)d e + (672a b c + 120b c )d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R (- 480a b c + 120a b )e + (1344a b c - 240a b c)d e +--R + +--R 2 3 2 2 2 +--R (384a c + 480a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 2 2 2 2 2 2 +--R ((- 384a b c + 96a b )e + (768a c - 192a b c)d e + 384a b c d )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +-+ +-+ | 2 +--R ((96a c + 72b c )x + 384a b c x + 384a c )\|a \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 144a b c - 12b c )x + (- 288a c - 216a b c )x - 576a b c x +--R + +--R 3 2 +--R - 384a c +--R * +--R +-+ +--R \|c +--R , +--R +--R 2 2 3 5 2 +--R (96a b c + 48a b c - 18b )e +--R + +--R 2 3 2 2 4 +--R (- 192a c - 96a b c + 36b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((384a b c - 96a b )e + (- 768a b c + 192a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (384a b c - 96a b )e + (- 768a c + 192a b c)d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (- 144a b c + 24a b c + 3b )e +--R + +--R 2 3 3 2 5 +--R (288a b c - 48a b c - 6b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (- 288a b c - 144a b c + 54a b )e +--R + +--R 3 3 2 2 2 4 +--R (576a c + 288a b c - 108a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((- 576a b c + 144a b )e + (1152a b c - 288a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (- 384a b c + 96a b )e + (768a c - 192a b c)d e +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 3 2 2 5 +--R (- 48a b c - 4b c )e x +--R + +--R 2 3 2 2 4 2 3 3 2 4 +--R ((- 96a c - 48a b c + 2b c)e + (- 144a b c - 12b c )d e)x +--R + +--R 2 2 3 5 2 +--R (- 48a b c + 8a b c - 3b )e +--R + +--R 2 3 2 2 4 3 3 2 2 +--R (- 288a c - 144a b c + 6b c)d e + (- 144a b c - 12b c )d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R (144a b c - 36a b )e + (- 480a b c + 72a b c)d e +--R + +--R 2 3 2 2 2 +--R (- 192a c - 144a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 2 2 2 2 2 2 +--R ((192a b c - 48a b )e + (- 384a c + 96a b c)d e - 192a b c d )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 4 2 3 2 6 +--R (32a c + 24b c )e x +--R + +--R 3 3 2 2 4 2 3 5 +--R ((144a b c + 12b c )e + (96a c + 72b c )d e)x +--R + +--R 2 3 2 2 4 2 3 3 2 +--R (96a c + 48a b c + 6b c)e + (432a b c + 36b c )d e +--R + +--R 4 2 3 2 +--R (96a c + 72b c )d +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 2 +--R (- 48a b c - 32a b c + 15b )e +--R + +--R 2 3 2 2 4 3 3 2 2 +--R (480a c + 288a b c - 30b c)d e + (336a b c + 60b c )d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R (- 240a b c + 60a b )e + (672a b c - 120a b c)d e +--R + +--R 2 3 2 2 2 +--R (192a c + 240a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 2 2 2 2 2 2 +--R ((- 192a b c + 48a b )e + (384a c - 96a b c)d e + 192a b c d )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +---+ +-+ | 2 +--R ((48a c + 36b c )x + 192a b c x + 192a c )\|- c \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 72a b c - 6b c )x + (- 144a c - 108a b c )x - 288a b c x +--R + +--R 3 2 +--R - 192a c +--R * +--R +---+ +--R \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 556 + +--S 557 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 3 5 2 +--R (96a b c + 48a b c - 18b )e +--R + +--R 2 3 2 2 4 +--R (- 192a c - 96a b c + 36b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((384a b c - 96a b )e + (- 768a b c + 192a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (384a b c - 96a b )e + (- 768a c + 192a b c)d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (- 144a b c + 24a b c + 3b )e +--R + +--R 2 3 3 2 5 +--R (288a b c - 48a b c - 6b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (- 288a b c - 144a b c + 54a b )e +--R + +--R 3 3 2 2 2 4 +--R (576a c + 288a b c - 108a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((- 576a b c + 144a b )e + (1152a b c - 288a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (- 384a b c + 96a b )e + (768a c - 192a b c)d e +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 3 5 2 +--R (- 96a b c - 48a b c + 18b )e +--R + +--R 2 3 2 2 4 +--R (192a c + 96a b c - 36b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((- 384a b c + 96a b )e + (768a b c - 192a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (- 384a b c + 96a b )e + (768a c - 192a b c)d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (144a b c - 24a b c - 3b )e +--R + +--R 2 3 3 2 5 +--R (- 288a b c + 48a b c + 6b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (288a b c + 144a b c - 54a b )e +--R + +--R 3 3 2 2 2 4 +--R (- 576a c - 288a b c + 108a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((576a b c - 144a b )e + (- 1152a b c + 288a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (384a b c - 96a b )e + (- 768a c + 192a b c)d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 4 2 2 2 3 +--R (- 128a c - 48a b c + 36a b )e + (- 96a b c - 72a b c)d e +--R + +--R 2 3 2 2 2 +--R (192a c + 144a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 2 2 2 +--R ((- 512a b c + 192a b )e - 384a b c d e + 768a b c d )x +--R + +--R 4 3 2 2 3 3 2 2 +--R (- 512a c + 192a b )e - 384a b c d e + 768a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 2 3 5 2 2 2 4 +--R (192a b c - 56a b c - 6b )e + (144a b c + 12b c)d e +--R + +--R 3 3 2 2 +--R (- 288a b c - 24b c )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 4 2 2 2 3 +--R (384a c + 144a b c - 108a b )e + (288a b c + 216a b c)d e +--R + +--R 2 3 2 2 2 +--R (- 576a c - 432a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 2 2 2 +--R ((768a b c - 288a b )e + 576a b c d e - 1152a b c d )x +--R + +--R 4 3 2 2 3 3 2 2 +--R (512a c - 192a b )e + 384a b c d e - 768a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +-+ +-+ | 2 +--R ((96a c + 72b c )x + 384a b c x + 384a c )\|a \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 144a b c - 12b c )x + (- 288a c - 216a b c )x - 576a b c x +--R + +--R 3 2 +--R - 384a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 557 + +--S 558 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 558 + +--S 559 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 3 5 2 +--R (- 96a b c - 48a b c + 18b )e +--R + +--R 2 3 2 2 4 +--R (192a c + 96a b c - 36b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((- 384a b c + 96a b )e + (768a b c - 192a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (- 384a b c + 96a b )e + (768a c - 192a b c)d e +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (144a b c - 24a b c - 3b )e +--R + +--R 2 3 3 2 5 +--R (- 288a b c + 48a b c + 6b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (288a b c + 144a b c - 54a b )e +--R + +--R 3 3 2 2 2 4 +--R (- 576a c - 288a b c + 108a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((576a b c - 144a b )e + (- 1152a b c + 288a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (384a b c - 96a b )e + (- 768a c + 192a b c)d e +--R * +--R +---+ +--R \|- c +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 3 5 2 +--R (192a b c + 96a b c - 36b )e +--R + +--R 2 3 2 2 4 +--R (- 384a c - 192a b c + 72b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((768a b c - 192a b )e + (- 1536a b c + 384a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (768a b c - 192a b )e + (- 1536a c + 384a b c)d e +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (- 288a b c + 48a b c + 6b )e +--R + +--R 2 3 3 2 5 +--R (576a b c - 96a b c - 12b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (- 576a b c - 288a b c + 108a b )e +--R + +--R 3 3 2 2 2 4 +--R (1152a c + 576a b c - 216a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((- 1152a b c + 288a b )e + (2304a b c - 576a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (- 768a b c + 192a b )e + (1536a c - 384a b c)d e +--R * +--R +-+ +--R \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 2 2 2 4 2 2 2 3 +--R (- 128a c - 48a b c + 36a b )e + (- 96a b c - 72a b c)d e +--R + +--R 2 3 2 2 2 +--R (192a c + 144a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 2 2 2 +--R ((- 512a b c + 192a b )e - 384a b c d e + 768a b c d )x +--R + +--R 4 3 2 2 3 3 2 2 +--R (- 512a c + 192a b )e - 384a b c d e + 768a c d +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 2 2 3 5 2 2 2 4 +--R (192a b c - 56a b c - 6b )e + (144a b c + 12b c)d e +--R + +--R 3 3 2 2 +--R (- 288a b c - 24b c )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 4 2 2 2 3 +--R (384a c + 144a b c - 108a b )e + (288a b c + 216a b c)d e +--R + +--R 2 3 2 2 2 +--R (- 576a c - 432a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 2 2 2 +--R ((768a b c - 288a b )e + 576a b c d e - 1152a b c d )x +--R + +--R 4 3 2 2 3 3 2 2 +--R (512a c - 192a b )e + 384a b c d e - 768a c d +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +-+ +--R ((96a c + 72b c )x + 384a b c x + 384a c )\|- c \|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 144a b c - 12b c )x + (- 288a c - 216a b c )x - 576a b c x +--R + +--R 3 2 +--R - 384a c +--R * +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 559 + +--S 560 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 845 +t0:=(b+2*c*x)*(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) ----------------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 561 + +--S 562 of 845 +r0:=1/4*(b^2-4*a*c)*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/_ + c^(3/2)+1/2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/c+(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R (2) +--R 2 2c x + b +--R (- 4a c + b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R +-+ | 2 +--R (4c e x - 2b e + 8c d)\|c \|c x + b x + a +--R / +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 562 + +--S 563 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R 2 3 3 2 2 | 2 +--R ((16a b c - 4a b )e x + (32a c - 8a b )e)\|c x + b x + a +--R + +--R 2 2 4 2 2 3 +--R (- 16a c + b )e x + (- 32a b c + 8a b )e x +--R + +--R 3 2 2 +--R (- 32a c + 8a b )e +--R * +--R +-+ +--R \|a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 3 3 2 2 2 +--R (- 16a c - 4b c)e x + ((- 24a b c + 2b )e + (- 32a c - 8b c)d)x +--R + +--R 2 2 +--R ((- 32a c + 8a b )e - 32a b c d)x +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 4 2 2 2 2 3 +--R 16a b c e x + ((32a c + 8a b c)e + 32a b c d)x +--R + +--R 2 3 2 2 2 2 +--R ((40a b c - 6a b )e + (32a c + 24a b c)d)x +--R + +--R 3 2 2 2 +--R ((32a c - 8a b )e + 32a b c d)x +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 2 +-+ | 2 +--R (16a b c x + 32a c)\|c \|c x + b x + a +--R + +--R 2 2 2 2 +-+ +-+ +--R ((- 16a c - 4b c)x - 32a b c x - 32a c)\|a \|c +--R , +--R +--R +--------------+ +--R 2 3 3 2 2 | 2 +--R ((- 16a b c + 4a b )e x + (- 32a c + 8a b )e)\|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +-+ +--R ((16a c - b )e x + (32a b c - 8a b )e x + (32a c - 8a b )e)\|a +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 2 3 3 2 2 2 +--R (- 8a c - 2b c)e x + ((- 12a b c + b )e + (- 16a c - 4b c)d)x +--R + +--R 2 2 +--R ((- 16a c + 4a b )e - 16a b c d)x +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 4 2 2 2 2 3 +--R 8a b c e x + ((16a c + 4a b c)e + 16a b c d)x +--R + +--R 2 3 2 2 2 2 +--R ((20a b c - 3a b )e + (16a c + 12a b c)d)x +--R + +--R 3 2 2 2 +--R ((16a c - 4a b )e + 16a b c d)x +--R * +--R +---+ +--R \|- c +--R / +--R +--------------+ +--R 2 +---+ | 2 +--R (8a b c x + 16a c)\|- c \|c x + b x + a +--R + +--R 2 2 2 2 +---+ +-+ +--R ((- 8a c - 2b c)x - 16a b c x - 16a c)\|- c \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 563 + +--S 564 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 3 3 2 2 | 2 +--R ((16a b c - 4a b )e x + (32a c - 8a b )e)\|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +-+ +--R ((- 16a c + b )e x + (- 32a b c + 8a b )e x + (- 32a c + 8a b )e)\|a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +--------------+ +--R 2 3 3 2 2 | 2 +--R ((16a b c - 4a b )e x + (32a c - 8a b )e)\|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +-+ +--R ((- 16a c + b )e x + (- 32a b c + 8a b )e x + (- 32a c + 8a b )e)\|a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R 2 2 2 +-+ +-+ | 2 +--R ((- 8a b e + 32a b c d)x - 16a b e + 64a c d)\|a \|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 2 2 +--R ((8a b c + 2a b )e + (- 32a c - 8a b c)d)x + (16a b e - 64a b c d)x +--R + +--R 3 3 +--R 16a b e - 64a c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 2 +-+ | 2 +--R (16a b c x + 32a c)\|c \|c x + b x + a +--R + +--R 2 2 2 2 +-+ +-+ +--R ((- 16a c - 4b c)x - 32a b c x - 32a c)\|a \|c +--R Type: Expression(Integer) +--E 564 + +--S 565 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 565 + +--S 566 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------------+ +--R 2 3 3 2 2 +---+ | 2 +--R ((16a b c - 4a b )e x + (32a c - 8a b )e)\|- c \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R ((- 16a c + b )e x + (- 32a b c + 8a b )e x + (- 32a c + 8a b )e) +--R * +--R +---+ +-+ +--R \|- c \|a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R 2 3 3 2 2 +-+ | 2 +--R ((- 32a b c + 8a b )e x + (- 64a c + 16a b )e)\|c \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R ((32a c - 2b )e x + (64a b c - 16a b )e x + (64a c - 16a b )e) +--R * +--R +-+ +-+ +--R \|a \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 2 2 +---+ +-+ +-+ +--R ((- 8a b e + 32a b c d)x - 16a b e + 64a c d)\|- c \|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 2 2 +--R ((8a b c + 2a b )e + (- 32a c - 8a b c)d)x + (16a b e - 64a b c d)x +--R + +--R 3 3 +--R 16a b e - 64a c d +--R * +--R +---+ +-+ +--R \|- c \|c +--R / +--R +--------------+ +--R 2 +---+ +-+ | 2 +--R (16a b c x + 32a c)\|- c \|c \|c x + b x + a +--R + +--R 2 2 2 2 +---+ +-+ +-+ +--R ((- 16a c - 4b c)x - 32a b c x - 32a c)\|- c \|a \|c +--R Type: Expression(Integer) +--E 566 + +--S 567 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 845 +t0:=(b+2*c*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2c x + b +--R (1) ----------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 568 + +--S 569 of 845 +r0:=2*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R (2) 2\|c x + b x + a +--R Type: Expression(Integer) +--E 569 + +--S 570 of 845 +a0:=integrate(t0,x) +--R +--R +--R +--------------+ +--R | 2 2 +-+ +--R - 2b x\|c x + b x + a + (4c x + 2b x)\|a +--R (3) -------------------------------------------- +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R Type: Union(Expression(Integer),...) +--E 570 + +--S 571 of 845 +m0:=a0-r0 +--R +--R +--R +--------------+ +--R | 2 +-+ +--R 4a\|c x + b x + a + (- 2b x - 4a)\|a +--R (4) --------------------------------------- +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 572 + +)clear all + +--S 573 of 845 +t0:=(b+2*c*x)/((d+e*x)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) -------------------------- +--R +--------------+ +--R | 2 +--R (e x + d)\|c x + b x + a +--R Type: Expression(Integer) +--E 573 + +--S 574 of 845 +r0:=2*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e-_ + (2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(e*sqrt(c*d^2-b*d*e+a*e^2)) +--R +--R +--R (2) +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R 2\|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R (b e - 2c d)x + 2a e - b d +--R (- b e + 2c d)atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R | 2 2 +--R e\|a e - b d e + c d +--R Type: Expression(Integer) +--E 574 + +--S 575 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (b e - 2c d) +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R +-------------------+ +--R +-+ | 2 2 +--R 2\|c \|a e - b d e + c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x +--R + +--R - 2a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R / +--R +-------------------+ +--R | 2 2 +--R e\|a e - b d e + c d +--R , +--R +--R +---------------------+ +--R | 2 2 +-+ +--R 2\|- a e + b d e - c d \|c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x +--R + +--R - 2a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R (2b e - 4c d) +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R / +--R +---------------------+ +--R | 2 2 +--R e\|- a e + b d e - c d +--R , +--R +--R (b e - 2c d) +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R +--------------+ +--R +-------------------+ | 2 +-+ +--R +---+ | 2 2 \|c x + b x + a - \|a +--R 4\|- c \|a e - b d e + c d atan(------------------------) +--R +---+ +--R x\|- c +--R / +--R +-------------------+ +--R | 2 2 +--R e\|a e - b d e + c d +--R , +--R +--R (2b e - 4c d) +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R +--------------+ +--R +---------------------+ | 2 +-+ +--R | 2 2 +---+ \|c x + b x + a - \|a +--R 4\|- a e + b d e - c d \|- c atan(------------------------) +--R +---+ +--R x\|- c +--R / +--R +---------------------+ +--R | 2 2 +--R e\|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 575 + +--S 576 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R (b e - 2c d) +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R +-------------------+ +--R +-+ | 2 2 +--R 2\|c \|a e - b d e + c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x - 2a +--R log(-------------------------------------------------------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R - 2\|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R (b e - 2c d)x + 2a e - b d +--R (b e - 2c d)atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R | 2 2 +--R e\|a e - b d e + c d +--R Type: Expression(Integer) +--E 576 + +--S 577 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 577 + +--S 578 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R 2\|- a e + b d e - c d \|c \|a e - b d e + c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x - 2a +--R log(-------------------------------------------------------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R - +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R 2\|- a e + b d e - c d \|c \|a e - b d e + c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +--R (b e - 2c d)\|- a e + b d e - c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 +--R (2b e - 4c d)\|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R / +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R e\|- a e + b d e - c d \|a e - b d e + c d +--R Type: Expression(Integer) +--E 578 + +--S 579 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 of 845 +t0:=(b+2*c*x)/((d+e*x)^2*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------- +--R +--------------+ +--R 2 2 2 | 2 +--R (e x + 2d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 580 + +--S 581 of 845 +r0:=-1/2*(b^2-4*a*c)*e*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)+(2*c*d-b*e)*_ + sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 +--R ((- 4a c + b )e x + (- 4a c + b )d e) +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R (- 2b e + 4c d)\|a e - b d e + c d \|c x + b x + a +--R / +--R 3 2 2 2 2 3 +--R ((2a e - 2b d e + 2c d e)x + 2a d e - 2b d e + 2c d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 581 + +--S 582 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R 2 2 2 2 +-+ | 2 +--R ((8a c - 2b )d e x + (8a c - 2b )d e)\|a \|c x + b x + a +--R + +--R 3 2 2 +--R (- 4a b c + b )d e x +--R + +--R 2 2 2 3 2 2 2 2 +--R ((- 8a c + 2a b )d e + (- 4a b c + b )d e)x + (- 8a c + 2a b )d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R +-------------------+ +--R 2 2 2 | 2 2 +--R (- 4a b e + (8a c + 2b )d e - 4b c d )x\|a e - b d e + c d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (2b e - 8b c d e + 8c d )x +--R + +--R 2 2 2 +--R (4a b e + (- 8a c - 2b )d e + 4b c d )x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 3 2 2 3 2 2 3 4 +-+ +--R ((4a d e - 4b d e + 4c d e)x + 4a d e - 4b d e + 4c d )\|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 3 2 +--R (- 2a b d e + 2b d e - 2b c d e)x +--R + +--R 2 3 2 2 2 3 4 2 2 2 +--R (- 4a d e + 2a b d e + (- 4a c + 2b )d e - 2b c d )x - 4a d e +--R + +--R 3 4 +--R 4a b d e - 4a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R , +--R +--R +--------------+ +--R 2 2 2 2 +-+ | 2 +--R ((8a c - 2b )d e x + (8a c - 2b )d e)\|a \|c x + b x + a +--R + +--R 3 2 2 +--R (- 4a b c + b )d e x +--R + +--R 2 2 2 3 2 2 2 2 +--R ((- 8a c + 2a b )d e + (- 4a b c + b )d e)x + (- 8a c + 2a b )d e +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R +---------------------+ +--R 2 2 2 | 2 2 +--R (- 2a b e + (4a c + b )d e - 2b c d )x\|- a e + b d e - c d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (b e - 4b c d e + 4c d )x +--R + +--R 2 2 2 +--R (2a b e + (- 4a c - b )d e + 2b c d )x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / +--R 3 2 2 3 2 2 3 4 +--R ((2a d e - 2b d e + 2c d e)x + 2a d e - 2b d e + 2c d ) +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 2 2 2 3 2 +--R (- a b d e + b d e - b c d e)x +--R + +--R 2 3 2 2 2 3 4 2 2 2 +--R (- 2a d e + a b d e + (- 2a c + b )d e - b c d )x - 2a d e +--R + +--R 3 4 +--R 2a b d e - 2a c d +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 582 + +--S 583 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 +-+ | 2 3 +--R (8a c - 2b )d e\|a \|c x + b x + a + (- 4a b c + b )d e x +--R + +--R 2 2 +--R (- 8a c + 2a b )d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R +--------------+ +--R 2 +-+ | 2 3 +--R (8a c - 2b )d e\|a \|c x + b x + a + (- 4a b c + b )d e x +--R + +--R 2 2 +--R (- 8a c + 2a b )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R (- 4a b e + 8a c d)\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 2 +-+ | 2 2 +--R ((2b e - 4b c d)x + 4a b e - 8a c d)\|a \|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 2 2 3 +-+ | 2 2 | 2 +--R (4a d e - 4b d e + 4c d )\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 3 2 2 2 3 +--R ((- 2a b d e + 2b d e - 2b c d )x - 4a d e + 4a b d e - 4a c d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 583 + +--S 584 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------------------+ +--------------+ +--R 2 | 2 2 +-+ | 2 +--R (8a c - 2b )d e\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R 3 2 2 | 2 2 +--R ((- 4a b c + b )d e x + (- 8a c + 2a b )d e)\|- a e + b d e - c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R 2 +-+ | 2 2 | 2 +--R (16a c - 4b )d e\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 3 2 2 | 2 2 +--R ((- 8a b c + 2b )d e x + (- 16a c + 4a b )d e)\|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R (- 4a b e + 8a c d)\|- a e + b d e - c d \|a e - b d e + c d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R +---------------------+ +--R 2 | 2 2 +-+ +--R ((2b e - 4b c d)x + 4a b e - 8a c d)\|- a e + b d e - c d \|a +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R +---------------------+ +--R 2 2 3 | 2 2 +-+ +--R (4a d e - 4b d e + 4c d )\|- a e + b d e - c d \|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 3 2 2 2 3 +--R ((- 2a b d e + 2b d e - 2b c d )x - 4a d e + 4a b d e - 4a c d ) +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R Type: Expression(Integer) +--E 585 + +--S 586 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 586 + +)clear all + +--S 587 of 845 +t0:=(b+2*c*x)/((d+e*x)^3*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ----------------------------------------------- +--R +--------------+ +--R 3 3 2 2 2 3 | 2 +--R (e x + 3d e x + 3d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 587 + +--S 588 of 845 +r0:=-3/8*(b^2-4*a*c)*e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+_ + 1/2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+_ + 1/4*(4*c^2*d^2+3*b^2*e^2-4*c*e*(b*d+2*a*e))*sqrt(a+b*x+c*x^2)/_ + ((c*d^2-b*d*e+a*e^2)^2*(d+e*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 2 +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e )x +--R + +--R 3 3 2 2 2 2 3 2 2 +--R ((24a b c - 6b )d e + (- 48a c + 12b c)d e )x + (12a b c - 3b )d e +--R + +--R 2 2 3 +--R (- 24a c + 6b c)d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 2 2 2 3 +--R ((- 16a c + 6b )e - 8b c d e + 8c d e)x - 4a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c + 10b )d e - 20b c d e + 16c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 2 6 5 2 2 4 3 3 2 4 2 2 +--R (8a e - 16a b d e + (16a c + 8b )d e - 16b c d e + 8c d e )x +--R + +--R 2 5 2 4 2 3 3 4 2 2 5 +--R (16a d e - 32a b d e + (32a c + 16b )d e - 32b c d e + 16c d e)x +--R + +--R 2 2 4 3 3 2 4 2 5 2 6 +--R 8a d e - 16a b d e + (16a c + 8b )d e - 16b c d e + 8c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 588 + +--S 589 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 4 2 4 2 2 3 3 3 3 +--R ((48a b c - 12a b )d e + (- 96a b c + 24a b c)d e )x +--R + +--R 3 2 3 2 4 +--R (96a b c - 24a b )d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 192a c + 144a b c - 24a b )d e +--R + +--R 2 2 3 4 2 +--R (- 192a b c + 48a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 3 +--R (192a b c - 48a b )d e +--R + +--R 3 2 2 2 4 4 2 +--R (- 384a c + 144a b c - 12a b )d e +--R + +--R 2 2 3 5 +--R (- 96a b c + 24a b c)d e +--R * +--R x +--R + +--R 3 2 3 4 2 3 2 2 2 5 +--R (96a b c - 24a b )d e + (- 192a c + 48a b c)d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 5 2 4 2 3 4 3 3 4 +--R ((- 48a b c + 3b )d e + (96a c - 6b c)d e )x +--R + +--R 2 2 4 2 4 2 2 3 5 3 3 +--R (- 96a b c + 24a b )d e + (96a b c - 48a b c + 6b )d e +--R + +--R 2 3 4 4 2 +--R (192a c - 12b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 4 +--R (- 96a b c + 24a b )d e +--R + +--R 3 2 2 2 4 3 3 +--R (192a c - 240a b c + 48a b )d e +--R + +--R 2 2 3 5 4 2 2 3 4 5 +--R (336a b c - 96a b c + 3b )d e + (96a c - 6b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 3 +--R (- 192a b c + 48a b )d e +--R + +--R 3 2 2 2 4 4 2 2 2 3 5 +--R (384a c - 192a b c + 24a b )d e + (192a b c - 48a b c)d e +--R * +--R x +--R + +--R 3 2 3 4 2 3 2 2 2 5 +--R (- 96a b c + 24a b )d e + (192a c - 48a b c)d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 2 2 2 2 2 2 +--R ((4a e + 4a c d )x + (8a d e + 4a b d )x + 8a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 2 3 2 2 2 3 2 +--R (4a e - 2a b d e + (4a c - 2b )d e + 2b c d )x +--R + +--R 2 2 2 3 +--R (8a d e - 8a b d e + 8a c d )x +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 3 +--R (- 2a b e + (- 4a c + b )d e - 2b c d )x +--R + +--R 2 2 2 2 2 +--R (- 4a e - 4a b d e + (- 8a c - b )d )x +--R + +--R 2 2 2 2 +--R (- 8a d e - 8a b d )x - 8a d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 2a b e + (- 4a c + 2a b )d e + 2a b c d e - 4a c d )x +--R + +--R 3 3 2 2 2 2 2 3 2 +--R (- 4a e - 2a b d e + (- 4a c + 6a b )d e - 6a b c d )x +--R + +--R 3 2 2 2 2 3 +--R (- 8a d e + 8a b d e - 8a c d )x +--R / +--R +--------------+ +--R 2 2 2 | 2 +--R (4a b e x + (8a e + 4a b d)x + 8a d)\|c x + b x + a +--R + +--R 2 3 2 2 +--R (- 4a c - b )e x + (- 8a b e + (- 4a c - b )d)x +--R + +--R 2 2 +--R (- 8a e - 8a b d)x - 8a d +--R * +--R +-+ +--R \|a +--R + +--R 2 2 5 2 3 4 +--R - 16a b e + (- 32a b c + 40a b )d e +--R + +--R 2 2 2 4 2 3 2 3 3 2 +--R (64a c - 88a b c - 6b )d e + (96a b c + 8b c)d e +--R + +--R 3 2 2 4 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 3 2 2 4 2 3 2 3 +--R - 32a b e + (- 64a c + 48a b )d e + (- 80a b c + 36a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (160a c - 128a b c - 10b )d e + (144a b c + 20b c)d e +--R + +--R 3 2 2 5 +--R (- 64a c - 16b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 3 2 +--R - 64a b d e + 128a b d e + (- 224a b c - 40a b )d e +--R + +--R 2 2 2 4 2 5 +--R (192a c + 80a b c)d e - 64a b c d +--R * +--R x +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (16a b c + 4a b )e + (32a c - 32a b c - 10a b )d e +--R + +--R 2 2 3 2 3 2 3 2 2 3 2 +--R (16a b c + 44a b c)d e + (- 64a c - 48a b c )d e +--R + +--R 3 4 +--R 32a b c d e +--R * +--R 4 +--R x +--R + +--R 3 2 5 3 2 3 4 +--R 32a b e + (96a b c - 72a b )d e +--R + +--R 3 2 2 2 4 2 3 2 2 3 3 2 +--R (- 64a c + 64a b c + 4a b )d e + (- 64a b c + 48a b c)d e +--R + +--R 2 3 2 2 4 3 5 +--R (- 64a c - 80a b c )d e + 64a b c d +--R * +--R 3 +--R x +--R + +--R 4 5 4 3 2 4 3 2 3 2 3 +--R 32a b e + (64a c - 16a b )d e + (80a b c - 100a b )d e +--R + +--R 3 2 2 2 4 3 2 +--R (- 160a c + 240a b c + 30a b )d e +--R + +--R 2 2 3 4 2 3 2 2 5 +--R (- 240a b c - 60a b c)d e + (64a c + 48a b c )d +--R * +--R 2 +--R x +--R + +--R 4 4 3 2 2 3 3 2 3 3 2 +--R 64a b d e - 128a b d e + (224a b c + 40a b )d e +--R + +--R 3 2 2 2 4 2 2 5 +--R (- 192a c - 80a b c)d e + 64a b c d +--R * +--R x +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 3 2 6 2 2 3 5 2 3 4 4 2 5 3 +--R 32a b d e - 64a b d e + (64a b c + 32a b )d e - 64a b c d e +--R + +--R 2 6 2 +--R 32a b c d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 3 5 3 2 2 4 4 3 5 3 +--R 64a d e - 64a b d e + (128a c - 64a b )d e + 64a b d e +--R + +--R 2 2 2 6 2 2 7 +--R (64a c - 128a b c)d e + 64a b c d e +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 3 2 2 5 3 +--R 128a d e - 224a b d e + (256a c + 64a b )d e +--R + +--R 2 3 6 2 2 2 2 7 2 8 +--R (- 192a b c + 32a b )d e + (128a c - 64a b c)d e + 32a b c d +--R * +--R x +--R + +--R 4 4 4 3 5 3 3 2 2 6 2 2 7 +--R 64a d e - 128a b d e + (128a c + 64a b )d e - 128a b c d e +--R + +--R 2 2 8 +--R 64a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 6 2 3 3 5 +--R (- 32a c - 8a b )d e + (64a b c + 16a b )d e +--R + +--R 2 2 2 4 4 4 2 3 5 3 +--R (- 64a c - 48a b c - 8b )d e + (64a b c + 16b c)d e +--R + +--R 3 2 2 6 2 +--R (- 32a c - 8b c )d e +--R * +--R 4 +--R x +--R + +--R 3 2 6 3 2 2 3 5 3 4 4 +--R - 64a b d e + (- 64a c + 112a b )d e - 32a b d e +--R + +--R 2 2 2 4 5 3 2 3 6 2 +--R (- 128a c + 32a b c - 16b )d e + (64a b c + 32b c)d e +--R + +--R 3 2 2 7 +--R (- 64a c - 16b c )d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 2 2 4 4 +--R - 64a d e + (- 160a c + 184a b )d e +--R + +--R 2 3 5 3 2 2 2 4 6 2 +--R (- 64a b c - 112a b )d e + (- 128a c + 208a b c - 8b )d e +--R + +--R 2 3 7 3 2 2 8 +--R (- 64a b c + 16b c)d e + (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 3 5 3 +--R - 128a d e + 192a b d e - 256a c d e +--R + +--R 2 3 6 2 2 2 2 7 2 8 +--R (128a b c - 64a b )d e + (- 128a c + 128a b c)d e - 64a b c d +--R * +--R x +--R + +--R 4 4 4 3 5 3 3 2 2 6 2 2 7 +--R - 64a d e + 128a b d e + (- 128a c - 64a b )d e + 128a b c d e +--R + +--R 2 2 8 +--R - 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R , +--R +--R 2 2 4 2 4 2 2 3 3 3 3 +--R ((- 48a b c + 12a b )d e + (96a b c - 24a b c)d e )x +--R + +--R 3 2 3 2 4 +--R (- 96a b c + 24a b )d e +--R + +--R 3 2 2 2 4 3 3 2 2 3 4 2 +--R (192a c - 144a b c + 24a b )d e + (192a b c - 48a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 3 +--R (- 192a b c + 48a b )d e +--R + +--R 3 2 2 2 4 4 2 2 2 3 5 +--R (384a c - 144a b c + 12a b )d e + (96a b c - 24a b c)d e +--R * +--R x +--R + +--R 3 2 3 4 2 3 2 2 2 5 +--R (- 96a b c + 24a b )d e + (192a c - 48a b c)d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 5 2 4 2 3 4 3 3 4 +--R ((48a b c - 3b )d e + (- 96a c + 6b c)d e )x +--R + +--R 2 2 4 2 4 2 2 3 5 3 3 +--R (96a b c - 24a b )d e + (- 96a b c + 48a b c - 6b )d e +--R + +--R 2 3 4 4 2 +--R (- 192a c + 12b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 4 +--R (96a b c - 24a b )d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 192a c + 240a b c - 48a b )d e +--R + +--R 2 2 3 5 4 2 2 3 4 5 +--R (- 336a b c + 96a b c - 3b )d e + (- 96a c + 6b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 3 +--R (192a b c - 48a b )d e +--R + +--R 3 2 2 2 4 4 2 +--R (- 384a c + 192a b c - 24a b )d e +--R + +--R 2 2 3 5 +--R (- 192a b c + 48a b c)d e +--R * +--R x +--R + +--R 3 2 3 4 2 3 2 2 2 5 +--R (96a b c - 24a b )d e + (- 192a c + 48a b c)d e +--R * +--R +-+ +--R \|a +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R d\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +--R (- a e x - a d)\|- a e + b d e - c d +--R / +--R 2 2 +-+ +--R (a e - b d e + c d )x\|a +--R + +--R 2 2 5 2 3 4 +--R - 8a b e + (- 16a b c + 20a b )d e +--R + +--R 2 2 2 4 2 3 2 3 3 2 +--R (32a c - 44a b c - 3b )d e + (48a b c + 4b c)d e +--R + +--R 3 2 2 4 +--R (- 16a c - 4b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 3 2 2 4 2 3 2 3 +--R - 16a b e + (- 32a c + 24a b )d e + (- 40a b c + 18a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (80a c - 64a b c - 5b )d e + (72a b c + 10b c)d e +--R + +--R 3 2 2 5 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 3 2 +--R - 32a b d e + 64a b d e + (- 112a b c - 20a b )d e +--R + +--R 2 2 2 4 2 5 +--R (96a c + 40a b c)d e - 32a b c d +--R * +--R x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (8a b c + 2a b )e + (16a c - 16a b c - 5a b )d e +--R + +--R 2 2 3 2 3 2 3 2 2 3 2 3 4 +--R (8a b c + 22a b c)d e + (- 32a c - 24a b c )d e + 16a b c d e +--R * +--R 4 +--R x +--R + +--R 3 2 5 3 2 3 4 +--R 16a b e + (48a b c - 36a b )d e +--R + +--R 3 2 2 2 4 2 3 2 2 3 3 2 +--R (- 32a c + 32a b c + 2a b )d e + (- 32a b c + 24a b c)d e +--R + +--R 2 3 2 2 4 3 5 +--R (- 32a c - 40a b c )d e + 32a b c d +--R * +--R 3 +--R x +--R + +--R 4 5 4 3 2 4 3 2 3 2 3 +--R 16a b e + (32a c - 8a b )d e + (40a b c - 50a b )d e +--R + +--R 3 2 2 2 4 3 2 2 2 3 4 +--R (- 80a c + 120a b c + 15a b )d e + (- 120a b c - 30a b c)d e +--R + +--R 2 3 2 2 5 +--R (32a c + 24a b c )d +--R * +--R 2 +--R x +--R + +--R 4 4 3 2 2 3 3 2 3 3 2 +--R 32a b d e - 64a b d e + (112a b c + 20a b )d e +--R + +--R 3 2 2 2 4 2 2 5 +--R (- 96a c - 40a b c)d e + 32a b c d +--R * +--R x +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R / +--R 3 2 6 2 2 3 5 2 3 4 4 2 5 3 +--R 16a b d e - 32a b d e + (32a b c + 16a b )d e - 32a b c d e +--R + +--R 2 6 2 +--R 16a b c d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 3 5 3 2 2 4 4 3 5 3 +--R 32a d e - 32a b d e + (64a c - 32a b )d e + 32a b d e +--R + +--R 2 2 2 6 2 2 7 +--R (32a c - 64a b c)d e + 32a b c d e +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 3 2 2 5 3 +--R 64a d e - 112a b d e + (128a c + 32a b )d e +--R + +--R 2 3 6 2 2 2 2 7 2 8 +--R (- 96a b c + 16a b )d e + (64a c - 32a b c)d e + 16a b c d +--R * +--R x +--R + +--R 4 4 4 3 5 3 3 2 2 6 2 2 7 2 2 8 +--R 32a d e - 64a b d e + (64a c + 32a b )d e - 64a b c d e + 32a c d +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 3 2 2 2 6 2 3 3 5 +--R (- 16a c - 4a b )d e + (32a b c + 8a b )d e +--R + +--R 2 2 2 4 4 4 2 3 5 3 +--R (- 32a c - 24a b c - 4b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 6 2 +--R (- 16a c - 4b c )d e +--R * +--R 4 +--R x +--R + +--R 3 2 6 3 2 2 3 5 3 4 4 +--R - 32a b d e + (- 32a c + 56a b )d e - 16a b d e +--R + +--R 2 2 2 4 5 3 2 3 6 2 +--R (- 64a c + 16a b c - 8b )d e + (32a b c + 16b c)d e +--R + +--R 3 2 2 7 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 2 2 4 4 2 3 5 3 +--R - 32a d e + (- 80a c + 92a b )d e + (- 32a b c - 56a b )d e +--R + +--R 2 2 2 4 6 2 2 3 7 +--R (- 64a c + 104a b c - 4b )d e + (- 32a b c + 8b c)d e +--R + +--R 3 2 2 8 +--R (- 16a c - 4b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 3 5 3 2 3 6 2 +--R - 64a d e + 96a b d e - 128a c d e + (64a b c - 32a b )d e +--R + +--R 2 2 2 7 2 8 +--R (- 64a c + 64a b c)d e - 32a b c d +--R * +--R x +--R + +--R 4 4 4 3 5 3 3 2 2 6 2 2 7 +--R - 32a d e + 64a b d e + (- 64a c - 32a b )d e + 64a b c d e +--R + +--R 2 2 8 +--R - 32a c d +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 589 + +--S 590 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 4 2 2 2 2 3 3 +--R ((48a b c - 12a b )d e + (- 96a b c + 24a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (96a b c - 24a b )d e + (- 192a c + 48a b c)d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 5 2 2 2 3 4 3 2 +--R ((- 48a b c + 3b )d e + (96a c - 6b c)d e)x +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((- 96a b c + 24a b )d e + (192a b c - 48a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (- 96a b c + 24a b )d e + (192a c - 48a b c)d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 2 2 2 2 2 2 +--R ((4a e + 4a c d )x + (8a d e + 4a b d )x + 8a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 2 3 2 2 2 3 2 +--R (4a e - 2a b d e + (4a c - 2b )d e + 2b c d )x +--R + +--R 2 2 2 3 +--R (8a d e - 8a b d e + 8a c d )x +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 3 +--R (- 2a b e + (- 4a c + b )d e - 2b c d )x +--R + +--R 2 2 2 2 2 +--R (- 4a e - 4a b d e + (- 8a c - b )d )x +--R + +--R 2 2 2 2 +--R (- 8a d e - 8a b d )x - 8a d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 2a b e + (- 4a c + 2a b )d e + 2a b c d e - 4a c d )x +--R + +--R 3 3 2 2 2 2 2 3 2 +--R (- 4a e - 2a b d e + (- 4a c + 6a b )d e - 6a b c d )x +--R + +--R 3 2 2 2 2 3 +--R (- 8a d e + 8a b d e - 8a c d )x +--R / +--R +--------------+ +--R 2 2 2 | 2 +--R (4a b e x + (8a e + 4a b d)x + 8a d)\|c x + b x + a +--R + +--R 2 3 2 2 +--R (- 4a c - b )e x + (- 8a b e + (- 4a c - b )d)x +--R + +--R 2 2 +--R (- 8a e - 8a b d)x - 8a d +--R * +--R +-+ +--R \|a +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((- 48a b c + 12a b )d e + (96a b c - 24a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (- 96a b c + 24a b )d e + (192a c - 48a b c)d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 5 2 2 2 3 4 3 2 +--R ((48a b c - 3b )d e + (- 96a c + 6b c)d e)x +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((96a b c - 24a b )d e + (- 192a b c + 48a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (96a b c - 24a b )d e + (- 192a c + 48a b c)d e +--R * +--R +-+ +--R \|a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 3 2 3 2 2 2 2 3 +--R (- 16a b e + (- 32a b c + 40a b )d e - 80a b c d e + 64a b c d )x +--R + +--R 3 3 3 2 2 2 2 2 2 2 3 +--R - 32a b e + (- 64a c + 80a b )d e - 160a b c d e + 128a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 3 3 2 2 2 4 2 +--R (16a b c + 4a b )e + (32a c - 32a b c - 10a b )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (80a b c + 20a b c)d e + (- 64a c - 16a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 2 3 2 2 2 2 2 2 3 +--R (32a b e + (64a b c - 80a b )d e + 160a b c d e - 128a b c d )x +--R + +--R 4 3 4 3 2 2 3 2 3 2 3 +--R 32a b e + (64a c - 80a b )d e + 160a b c d e - 128a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 3 2 4 2 2 3 3 2 3 4 2 2 5 +--R 32a b d e - 64a b d e + (64a b c + 32a b )d e - 64a b c d e +--R + +--R 2 6 +--R 32a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 +--R 64a d e - 128a b d e + (128a c + 64a b )d e - 128a b c d e +--R + +--R 2 2 6 +--R 64a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 4 2 3 3 3 +--R (- 32a c - 8a b )d e + (64a b c + 16a b )d e +--R + +--R 2 2 2 4 4 2 2 3 5 +--R (- 64a c - 48a b c - 8b )d e + (64a b c + 16b c)d e +--R + +--R 3 2 2 6 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 2 3 3 2 3 4 2 +--R - 64a b d e + 128a b d e + (- 128a b c - 64a b )d e +--R + +--R 2 5 2 6 +--R 128a b c d e - 64a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 +--R - 64a d e + 128a b d e + (- 128a c - 64a b )d e + 128a b c d e +--R + +--R 2 2 6 +--R - 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R Type: Expression(Integer) +--E 590 + +--S 591 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 591 + +--S 592 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 4 2 2 2 2 3 3 +--R ((- 48a b c + 12a b )d e + (96a b c - 24a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (- 96a b c + 24a b )d e + (192a c - 48a b c)d e +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 2 5 2 2 2 3 4 3 2 +--R ((48a b c - 3b )d e + (- 96a c + 6b c)d e)x +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((96a b c - 24a b )d e + (- 192a b c + 48a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (96a b c - 24a b )d e + (- 192a c + 48a b c)d e +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((- 96a b c + 24a b )d e + (192a b c - 48a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (- 192a b c + 48a b )d e + (384a c - 96a b c)d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 5 2 2 2 3 4 3 2 +--R ((96a b c - 6b )d e + (- 192a c + 12b c)d e)x +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((192a b c - 48a b )d e + (- 384a b c + 96a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (192a b c - 48a b )d e + (- 384a c + 96a b c)d e +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R d\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +--R (- a e x - a d)\|- a e + b d e - c d +--R / +--R 2 2 +-+ +--R (a e - b d e + c d )x\|a +--R + +--R 2 2 3 2 3 2 2 2 2 3 +--R (- 16a b e + (- 32a b c + 40a b )d e - 80a b c d e + 64a b c d )x +--R + +--R 3 3 3 2 2 2 2 2 2 2 3 +--R - 32a b e + (- 64a c + 80a b )d e - 160a b c d e + 128a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 +-+ | 2 2 | 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 3 3 2 2 2 4 2 +--R (16a b c + 4a b )e + (32a c - 32a b c - 10a b )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (80a b c + 20a b c)d e + (- 64a c - 16a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 2 3 2 2 2 2 2 2 3 +--R (32a b e + (64a b c - 80a b )d e + 160a b c d e - 128a b c d )x +--R + +--R 4 3 4 3 2 2 3 2 3 2 3 +--R 32a b e + (64a c - 80a b )d e + 160a b c d e - 128a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R / +--R 3 2 4 2 2 3 3 2 3 4 2 2 5 +--R 32a b d e - 64a b d e + (64a b c + 32a b )d e - 64a b c d e +--R + +--R 2 6 +--R 32a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 +--R 64a d e - 128a b d e + (128a c + 64a b )d e - 128a b c d e +--R + +--R 2 2 6 +--R 64a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 | 2 2 | 2 +--R \|- a e + b d e - c d \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 4 2 3 3 3 +--R (- 32a c - 8a b )d e + (64a b c + 16a b )d e +--R + +--R 2 2 2 4 4 2 2 3 5 +--R (- 64a c - 48a b c - 8b )d e + (64a b c + 16b c)d e +--R + +--R 3 2 2 6 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 2 3 3 2 3 4 2 +--R - 64a b d e + 128a b d e + (- 128a b c - 64a b )d e +--R + +--R 2 5 2 6 +--R 128a b c d e - 64a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 +--R - 64a d e + 128a b d e + (- 128a c - 64a b )d e + 128a b c d e +--R + +--R 2 2 6 +--R - 64a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d +--R Type: Expression(Integer) +--E 592 + +--S 593 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 593 + +)clear all + +--S 594 of 845 +t0:=(b+2*c*x)/((d+e*x)^4*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) --------------------------------------------------------- +--R +--------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 594 + +--S 595 of 845 +r0:=-1/16*(b^2-4*a*c)*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)+1/3*(2*c*d-b*e)*_ + sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^3)+1/12*(8*c^2*d^2+_ + 5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+_ + a*e^2)^2*(d+e*x)^2)+1/24*(2*c*d-b*e)*(8*c^2*d^2+15*b^2*e^2-4*c*e*_ + (2*b*d+13*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^3*(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 4 6 2 3 5 +--R (48a c - 72a b c + 15b )e + (192a b c - 48b c)d e +--R + +--R 3 2 2 2 4 +--R (- 192a c + 48b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 5 2 3 2 4 +--R (144a c - 216a b c + 45b )d e + (576a b c - 144b c)d e +--R + +--R 3 2 2 3 3 +--R (- 576a c + 144b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (144a c - 216a b c + 45b )d e + (576a b c - 144b c)d e +--R + +--R 3 2 2 4 2 +--R (- 576a c + 144b c )d e +--R * +--R x +--R + +--R 2 2 2 4 3 3 2 3 4 2 +--R (48a c - 72a b c + 15b )d e + (192a b c - 48b c)d e +--R + +--R 3 2 2 5 +--R (- 192a c + 48b c )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (104a b c - 30b )e + (- 208a c + 76b c)d e - 48b c d e +--R + +--R 3 3 2 +--R 32c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (- 48a c + 20a b )e + (224a b c - 80b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (- 432a c + 204b c)d e - 160b c d e + 96c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 16a b e + (- 16a c + 52a b )d e + (24a b c - 66b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 160a c + 192b c)d e - 192b c d e + 96c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 3 9 2 8 2 2 2 7 +--R 48a e - 144a b d e + (144a c + 144a b )d e +--R + +--R 3 3 6 2 2 4 5 2 5 4 +--R (- 288a b c - 48b )d e + (144a c + 144b c)d e - 144b c d e +--R + +--R 3 6 3 +--R 48c d e +--R * +--R 3 +--R x +--R + +--R 3 8 2 2 7 2 2 3 6 +--R 144a d e - 432a b d e + (432a c + 432a b )d e +--R + +--R 3 4 5 2 2 5 4 2 6 3 +--R (- 864a b c - 144b )d e + (432a c + 432b c)d e - 432b c d e +--R + +--R 3 7 2 +--R 144c d e +--R * +--R 2 +--R x +--R + +--R 3 2 7 2 3 6 2 2 4 5 +--R 144a d e - 432a b d e + (432a c + 432a b )d e +--R + +--R 3 5 4 2 2 6 3 2 7 2 +--R (- 864a b c - 144b )d e + (432a c + 432b c)d e - 432b c d e +--R + +--R 3 8 +--R 144c d e +--R * +--R x +--R + +--R 3 3 6 2 4 5 2 2 5 4 +--R 48a d e - 144a b d e + (144a c + 144a b )d e +--R + +--R 3 6 3 2 2 7 2 2 8 3 9 +--R (- 288a b c - 48b )d e + (144a c + 144b c)d e - 144b c d e + 48c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 595 + +--S 596 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 4 6 3 6 +--R (384a c - 288a b c - 312a b c + 90b )d e +--R + +--R 2 3 3 2 5 4 5 +--R (1536a b c + 768a b c - 288b c)d e +--R + +--R 2 4 2 3 4 2 5 4 +--R (- 1536a c - 768a b c + 288b c )d e +--R * +--R 5 +--R x +--R + +--R 3 2 2 3 5 3 6 +--R (1536a b c - 2304a b c + 480a b )d e +--R + +--R 3 3 2 2 2 4 6 4 5 +--R (1152a c + 5280a b c - 2472a b c + 270b )d e +--R + +--R 2 3 3 2 5 5 4 +--R (- 1536a b c + 3840a b c - 864b c)d e +--R + +--R 2 4 2 3 4 2 6 3 +--R (- 4608a c - 2304a b c + 864b c )d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 2 2 4 3 6 +--R (1536a c - 2304a b c + 480a b )d e +--R + +--R 3 2 2 3 5 4 5 +--R (10752a b c - 8448a b c + 1440a b )d e +--R + +--R 3 3 2 2 2 4 6 5 4 +--R (- 4992a c + 19104a b c - 5544a b c + 270b )d e +--R + +--R 2 3 3 2 5 6 3 +--R (- 13824a b c + 6912a b c - 864b c)d e +--R + +--R 2 4 2 3 4 2 7 2 +--R (- 4608a c - 2304a b c + 864b c )d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 5 +--R (4608a c - 6912a b c + 1440a b )d e +--R + +--R 3 2 2 3 5 5 4 +--R (23040a b c - 11520a b c + 1440a b )d e +--R + +--R 3 3 2 2 2 4 6 6 3 +--R (- 18048a c + 22752a b c - 4920a b c + 90b )d e +--R + +--R 2 3 3 2 5 7 2 +--R (- 16896a b c + 5376a b c - 288b c)d e +--R + +--R 2 4 2 3 4 2 8 +--R (- 1536a c - 768a b c + 288b c )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 2 2 4 5 4 +--R (4608a c - 6912a b c + 1440a b )d e +--R + +--R 3 2 2 3 5 6 3 +--R (19968a b c - 6912a b c + 480a b )d e +--R + +--R 3 3 2 2 2 4 7 2 +--R (- 18432a c + 10752a b c - 1536a b c)d e +--R + +--R 2 3 3 2 8 +--R (- 6144a b c + 1536a b c )d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 6 3 +--R (1536a c - 2304a b c + 480a b )d e +--R + +--R 3 2 2 3 7 2 3 3 2 2 2 8 +--R (6144a b c - 1536a b c)d e + (- 6144a c + 1536a b c )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 6 +--R (- 576a b c + 816a b c - 108a b c - 15b )d e +--R + +--R 2 2 3 4 2 6 4 5 +--R (- 2304a b c + 384a b c + 48b c)d e +--R + +--R 2 4 3 3 5 2 5 4 +--R (2304a b c - 384a b c - 48b c )d e +--R * +--R 6 +--R x +--R + +--R 4 3 3 2 2 2 4 6 3 6 +--R (- 1152a c + 864a b c + 936a b c - 270a b )d e +--R + +--R 3 3 2 3 2 5 7 4 5 +--R (- 6336a b c + 144a b c + 540a b c - 45b )d e +--R + +--R 3 4 2 2 3 4 2 6 5 4 +--R (4608a c - 4608a b c + 288a b c + 144b c)d e +--R + +--R 2 4 3 3 5 2 6 3 +--R (6912a b c - 1152a b c - 144b c )d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 3 2 5 3 6 +--R (- 2304a b c + 3456a b c - 720a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 5 +--R (- 3456a c - 6624a b c + 5112a b c - 810a b )d e +--R + +--R 3 3 2 3 2 5 7 5 4 +--R (- 6336a b c - 6768a b c + 2268a b c - 45b )d e +--R + +--R 3 4 4 2 6 6 3 +--R (13824a c - 1440a b c + 144b c)d e +--R + +--R 2 4 3 3 5 2 7 2 +--R (6912a b c - 1152a b c - 144b c )d e +--R * +--R 4 +--R x +--R + +--R 5 2 4 2 3 4 3 6 +--R (- 1536a c + 2304a b c - 480a b )d e +--R + +--R 4 2 3 3 2 5 4 5 +--R (- 13056a b c + 11904a b c - 2160a b )d e +--R + +--R 4 3 3 2 2 2 4 6 5 4 +--R (2688a c - 26592a b c + 9720a b c - 810a b )d e +--R + +--R 3 3 2 3 2 5 7 6 3 +--R (13248a b c - 13008a b c + 2484a b c - 15b )d e +--R + +--R 3 4 2 2 3 4 2 6 7 2 +--R (13824a c + 4608a b c - 2208a b c + 48b c)d e +--R + +--R 2 4 3 3 5 2 8 +--R (2304a b c - 384a b c - 48b c )d e +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 4 5 +--R (- 4608a c + 6912a b c - 1440a b )d e +--R + +--R 4 2 3 3 2 5 5 4 +--R (- 25344a b c + 14976a b c - 2160a b )d e +--R + +--R 4 3 3 2 2 2 4 6 6 3 +--R (17280a c - 31392a b c + 7848a b c - 270a b )d e +--R + +--R 3 3 2 3 2 5 7 2 +--R (23040a b c - 9216a b c + 864a b c)d e +--R + +--R 3 4 2 2 3 4 2 8 +--R (4608a c + 2304a b c - 864a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 5 4 +--R (- 4608a c + 6912a b c - 1440a b )d e +--R + +--R 4 2 3 3 2 5 6 3 +--R (- 20736a b c + 8064a b c - 720a b )d e +--R + +--R 4 3 3 2 2 2 4 7 2 +--R (18432a c - 13824a b c + 2304a b c)d e +--R + +--R 3 3 2 3 2 8 +--R (9216a b c - 2304a b c )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 6 3 +--R (- 1536a c + 2304a b c - 480a b )d e +--R + +--R 4 2 3 3 7 2 4 3 3 2 2 8 +--R (- 6144a b c + 1536a b c)d e + (6144a c - 1536a b c )d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (2a d e - 2b d e + 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 +--R (- 2a e + 2b d e - 2c d e)x +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +-+ +--R \|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 4 3 3 8 4 2 3 2 2 4 7 +--R (- 128a b c - 96a b )e + (- 128a c + 320a b c + 312a b )d e +--R + +--R 3 2 2 3 5 2 6 +--R (192a b c - 384a b c - 396a b )d e +--R + +--R 3 3 2 2 2 4 6 3 5 +--R (- 1280a c - 672a b c + 1408a b c + 30b )d e +--R + +--R 2 3 3 2 5 4 4 +--R (960a b c - 1856a b c - 76b c)d e +--R + +--R 2 4 2 3 4 2 5 3 4 3 3 6 2 +--R (768a c + 1152a b c + 48b c )d e + (- 384a b c - 32b c )d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 4 3 3 7 +--R - 512a b e + (- 896a b c + 1376a b )d e +--R + +--R 4 2 3 2 2 4 2 6 +--R (- 384a c + 1728a b c - 1176a b )d e +--R + +--R 3 2 2 3 5 3 5 +--R (- 6464a b c + 3648a b c - 668a b )d e +--R + +--R 3 3 2 2 2 4 6 4 4 +--R (1152a c - 5184a b c + 2824a b c + 80b )d e +--R + +--R 2 3 3 2 5 5 3 +--R (4800a b c - 4608a b c - 204b c)d e +--R + +--R 2 4 2 3 4 2 6 2 +--R (1536a c + 3072a b c + 160b c )d e +--R + +--R 4 3 3 7 +--R (- 1152a b c - 96b c )d e +--R * +--R 4 +--R x +--R + +--R 5 8 5 4 2 7 +--R - 512a b e + (- 512a c + 128a b )d e +--R + +--R 4 3 3 2 6 +--R (- 1152a b c + 2592a b )d e +--R + +--R 4 2 3 2 2 4 3 5 +--R (- 4352a c + 4992a b c - 4304a b )d e +--R + +--R 3 2 2 3 5 4 4 +--R (- 16128a b c + 10912a b c + 200a b )d e +--R + +--R 3 3 2 2 2 4 6 5 3 +--R (9600a c - 11808a b c + 552a b c + 66b )d e +--R + +--R 2 3 3 2 5 6 2 +--R (8832a b c - 2720a b c - 192b c)d e +--R + +--R 2 3 4 2 7 4 3 3 8 +--R (2304a b c + 192b c )d e + (- 1152a b c - 96b c )d +--R * +--R 3 +--R x +--R + +--R 5 7 5 4 2 2 6 3 3 3 5 +--R - 1536a b d e + (- 1536a c + 3456a b )d e - 1152a b d e +--R + +--R 4 2 3 2 2 4 4 4 +--R (- 8448a c + 6912a b c - 3120a b )d e +--R + +--R 3 2 2 3 5 5 3 +--R (- 11904a b c + 9408a b c + 792a b )d e +--R + +--R 3 3 2 2 2 4 6 2 +--R (10752a c - 11904a b c - 2304a b c)d e +--R + +--R 2 3 3 2 7 2 4 2 3 8 +--R (7680a b c + 2304a b c )d e + (- 1536a c - 1152a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 2 3 5 4 3 3 4 4 +--R - 1536a b d e + 4608a b d e + (- 4608a b c - 4608a b )d e +--R + +--R 4 2 3 2 2 4 5 3 +--R (- 1536a c + 11520a b c + 1056a b )d e +--R + +--R 3 2 2 3 6 2 3 3 2 2 2 7 +--R (- 10752a b c - 3072a b c)d e + (6144a c + 3072a b c )d e +--R + +--R 2 3 8 +--R - 1536a b c d +--R * +--R x +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 8 3 2 2 3 5 7 +--R (192a b c + 16a b )e + (192a b c - 608a b c - 52a b )d e +--R + +--R 2 2 2 4 6 2 6 +--R (- 288a b c + 768a b c + 66b )d e +--R + +--R 2 3 3 2 5 3 5 +--R (2752a b c - 1760a b c - 372b c)d e +--R + +--R 2 4 2 3 4 2 4 4 +--R (- 1664a c + 1664a b c + 648b c )d e +--R + +--R 4 3 3 5 3 5 2 4 6 2 +--R (- 1536a b c - 384b c )d e + (256a c + 192b c )d e +--R * +--R 6 +--R x +--R + +--R 4 3 3 8 4 2 3 2 2 4 7 +--R (384a b c + 288a b )e + (384a c - 384a b c - 888a b )d e +--R + +--R 2 3 5 2 6 +--R (- 672a b c + 1032a b )d e +--R + +--R 3 3 2 2 2 4 6 3 5 +--R (3456a c + 1440a b c - 1608a b c + 18b )d e +--R + +--R 2 3 3 2 5 4 4 +--R (3840a b c - 480a b c - 600b c)d e +--R + +--R 2 4 2 3 4 2 5 3 +--R (- 5760a c + 2304a b c + 1512b c )d e +--R + +--R 4 3 3 6 2 5 2 4 7 +--R (- 3456a b c - 1056b c )d e + (768a c + 576b c )d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 4 3 3 7 +--R 768a b e + (1920a b c - 1632a b )d e +--R + +--R 4 2 3 2 2 4 2 6 +--R (1152a c - 3456a b c + 408a b )d e +--R + +--R 3 2 2 3 5 3 5 +--R (8640a b c - 4416a b c + 2388a b )d e +--R + +--R 3 3 2 2 2 4 6 4 4 +--R (3072a c + 7584a b c - 6720a b c - 282b )d e +--R + +--R 2 3 3 2 5 5 3 +--R (- 4032a b c + 7296a b c + 252b c)d e +--R + +--R 2 4 2 3 4 2 6 2 +--R (- 6912a c - 2880a b c + 768b c )d e +--R + +--R 4 3 3 7 5 2 4 8 +--R (- 1152a b c - 864b c )d e + (768a c + 576b c )d +--R * +--R 4 +--R x +--R + +--R 5 8 5 4 2 7 4 3 3 2 6 +--R 512a b e + (512a c + 640a b )d e + (2688a b c - 4512a b )d e +--R + +--R 4 2 3 2 2 4 3 5 +--R (4352a c - 7296a b c + 5456a b )d e +--R + +--R 3 2 2 3 5 4 4 +--R (22656a b c - 12640a b c + 784a b )d e +--R + +--R 3 3 2 2 2 4 6 5 3 +--R (- 8832a c + 11808a b c - 4344a b c - 330b )d e +--R + +--R 2 3 3 2 5 6 2 +--R (- 8832a b c + 8864a b c + 960b c)d e +--R + +--R 2 4 2 3 4 2 7 4 3 3 8 +--R (- 3072a c - 6912a b c - 960b c )d e + (2688a b c + 480b c )d +--R * +--R 3 +--R x +--R + +--R 5 7 5 4 2 2 6 3 3 3 5 +--R 1536a b d e + (1536a c - 2688a b )d e - 1152a b d e +--R + +--R 4 2 3 2 2 4 4 4 +--R (8448a c - 4608a b c + 5424a b )d e +--R + +--R 3 2 2 3 5 5 3 +--R (12672a b c - 15168a b c - 1320a b )d e +--R + +--R 3 3 2 2 2 4 6 2 +--R (- 10752a c + 17280a b c + 3840a b c)d e +--R + +--R 2 3 3 2 7 2 4 2 3 8 +--R (- 10752a b c - 3840a b c )d e + (1536a c + 1920a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 2 3 5 4 3 3 4 4 +--R 1536a b d e - 4608a b d e + (4608a b c + 4608a b )d e +--R + +--R 4 2 3 2 2 4 5 3 +--R (1536a c - 11520a b c - 1056a b )d e +--R + +--R 3 2 2 3 6 2 3 3 2 2 2 7 +--R (10752a b c + 3072a b c)d e + (- 6144a c - 3072a b c )d e +--R + +--R 2 3 8 +--R 1536a b c d +--R * +--R x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 4 3 2 3 9 3 2 3 4 8 +--R (384a c + 288a b )d e + (- 1152a b c - 864a b )d e +--R + +--R 3 2 2 2 4 5 7 +--R (1152a c + 2016a b c + 864a b )d e +--R + +--R 2 2 3 5 6 6 +--R (- 2304a b c - 2112a b c - 288b )d e +--R + +--R 2 3 2 2 4 7 5 +--R (1152a c + 2016a b c + 864b c)d e +--R + +--R 3 3 2 8 4 4 2 3 9 3 +--R (- 1152a b c - 864b c )d e + (384a c + 288b c )d e +--R * +--R 5 +--R x +--R + +--R 4 3 9 4 3 2 4 8 +--R 1536a b d e + (1152a c - 3744a b )d e +--R + +--R 3 2 3 5 7 +--R (1152a b c + 2016a b )d e +--R + +--R 3 2 2 2 4 6 6 +--R (3456a c - 3168a b c + 1056a b )d e +--R + +--R 2 2 3 5 7 5 +--R (- 2304a b c - 1728a b c - 864b )d e +--R + +--R 2 3 2 2 4 8 4 +--R (3456a c + 1440a b c + 2592b c)d e +--R + +--R 3 3 2 9 3 4 2 3 10 2 +--R (- 1920a b c - 2592b c )d e + (1152a c + 864b c )d e +--R * +--R 4 +--R x +--R + +--R 5 3 9 4 3 2 5 7 +--R 1536a d e + (5760a c - 8352a b )d e +--R + +--R 3 2 3 6 6 +--R (1152a b c + 9696a b )d e +--R + +--R 3 2 2 2 4 7 5 +--R (8064a c - 16992a b c - 2016a b )d e +--R + +--R 2 2 3 5 8 4 +--R (2304a b c + 7488a b c - 864b )d e +--R + +--R 2 3 2 2 4 9 3 +--R (4992a c - 7776a b c + 2592b c)d e +--R + +--R 3 3 2 10 2 4 2 3 11 +--R (1152a b c - 2592b c )d e + (1152a c + 864b c )d e +--R * +--R 3 +--R x +--R + +--R 5 4 8 4 5 7 4 3 2 6 6 +--R 4608a d e - 9216a b d e + (14208a c + 288a b )d e +--R + +--R 3 2 3 7 5 +--R (- 14976a b c + 8352a b )d e +--R + +--R 3 2 2 2 4 8 4 +--R (14976a c - 11808a b c - 3744a b )d e +--R + +--R 2 2 3 5 9 3 +--R (- 2304a b c + 11712a b c - 288b )d e +--R + +--R 2 3 2 2 4 10 2 +--R (5760a c - 11808a b c + 864b c)d e +--R + +--R 3 3 2 11 4 2 3 12 +--R (3456a b c - 864b c )d e + (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 5 5 7 4 6 6 4 3 2 7 5 +--R 4608a d e - 12288a b d e + (13824a c + 9216a b )d e +--R + +--R 3 8 4 3 2 2 2 4 9 3 +--R - 23040a b c d e + (13824a c + 4608a b c - 1536a b )d e +--R + +--R 2 2 3 10 2 2 3 2 2 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+--R + +--R 4 2 3 3 2 5 5 4 +--R (25344a b c - 14976a b c + 2160a b )d e +--R + +--R 4 3 3 2 2 2 4 6 6 3 +--R (- 17280a c + 31392a b c - 7848a b c + 270a b )d e +--R + +--R 3 3 2 3 2 5 7 2 +--R (- 23040a b c + 9216a b c - 864a b c)d e +--R + +--R 3 4 2 2 3 4 2 8 +--R (- 4608a c - 2304a b c + 864a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 5 4 +--R (4608a c - 6912a b c + 1440a b )d e +--R + +--R 4 2 3 3 2 5 6 3 +--R (20736a b c - 8064a b c + 720a b )d e +--R + +--R 4 3 3 2 2 2 4 7 2 +--R (- 18432a c + 13824a b c - 2304a b c)d e +--R + +--R 3 3 2 3 2 8 +--R (- 9216a b c + 2304a b c )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 6 3 4 2 3 3 7 2 +--R (1536a c - 2304a b c + 480a b )d e + (6144a b c - 1536a b c)d e +--R + +--R 4 3 3 2 2 8 +--R (- 6144a c + 1536a b c )d e +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 4 3 3 8 4 2 3 2 2 4 7 +--R (- 64a b c - 48a b )e + (- 64a c + 160a b c + 156a b )d e +--R + +--R 3 2 2 3 5 2 6 +--R (96a b c - 192a b c - 198a b )d e +--R + +--R 3 3 2 2 2 4 6 3 5 +--R (- 640a c - 336a b c + 704a b c + 15b )d e +--R + +--R 2 3 3 2 5 4 4 +--R (480a b c - 928a b c - 38b c)d e +--R + +--R 2 4 2 3 4 2 5 3 4 3 3 6 2 +--R (384a c + 576a b c + 24b c )d e + (- 192a b c - 16b c )d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 4 3 3 7 +--R - 256a b e + (- 448a b c + 688a b )d e +--R + +--R 4 2 3 2 2 4 2 6 +--R (- 192a c + 864a b c - 588a b )d e +--R + +--R 3 2 2 3 5 3 5 +--R (- 3232a b c + 1824a b c - 334a b )d e +--R + +--R 3 3 2 2 2 4 6 4 4 +--R (576a c - 2592a b c + 1412a b c + 40b )d e +--R + +--R 2 3 3 2 5 5 3 +--R (2400a b c - 2304a b c - 102b c)d e +--R + +--R 2 4 2 3 4 2 6 2 4 3 3 7 +--R (768a c + 1536a b c + 80b c )d e + (- 576a b c - 48b c )d e +--R * +--R 4 +--R x +--R + +--R 5 8 5 4 2 7 +--R - 256a b e + (- 256a c + 64a b )d e +--R + +--R 4 3 3 2 6 +--R (- 576a b c + 1296a b )d e +--R + +--R 4 2 3 2 2 4 3 5 +--R (- 2176a c + 2496a b c - 2152a b )d e +--R + +--R 3 2 2 3 5 4 4 +--R (- 8064a b c + 5456a b c + 100a b )d e +--R + +--R 3 3 2 2 2 4 6 5 3 +--R (4800a c - 5904a b c + 276a b c + 33b )d e +--R + +--R 2 3 3 2 5 6 2 +--R (4416a b c - 1360a b c - 96b c)d e +--R + +--R 2 3 4 2 7 4 3 3 8 +--R (1152a b c + 96b c )d e + (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 5 7 5 4 2 2 6 3 3 3 5 +--R - 768a b d e + (- 768a c + 1728a b )d e - 576a b d e +--R + +--R 4 2 3 2 2 4 4 4 +--R (- 4224a c + 3456a b c - 1560a b )d e +--R + +--R 3 2 2 3 5 5 3 +--R (- 5952a b c + 4704a b c + 396a b )d e +--R + +--R 3 3 2 2 2 4 6 2 +--R (5376a c - 5952a b c - 1152a b c)d e +--R + +--R 2 3 3 2 7 2 4 2 3 8 +--R (3840a b c + 1152a b c )d e + (- 768a c - 576a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 2 3 5 4 3 3 4 4 +--R - 768a b d e + 2304a b d e + (- 2304a b c - 2304a b )d e +--R + +--R 4 2 3 2 2 4 5 3 +--R (- 768a c + 5760a b c + 528a b )d e +--R + +--R 3 2 2 3 6 2 3 3 2 2 2 7 +--R (- 5376a b c - 1536a b c)d e + (3072a c + 1536a b c )d e +--R + +--R 2 3 8 +--R - 768a b c d +--R * +--R x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 3 2 2 4 8 3 2 2 3 5 7 +--R (96a b c + 8a b )e + (96a b c - 304a b c - 26a b )d e +--R + +--R 2 2 2 4 6 2 6 +--R (- 144a b c + 384a b c + 33b )d e +--R + +--R 2 3 3 2 5 3 5 +--R (1376a b c - 880a b c - 186b c)d e +--R + +--R 2 4 2 3 4 2 4 4 +--R (- 832a c + 832a b c + 324b c )d e +--R + +--R 4 3 3 5 3 5 2 4 6 2 +--R (- 768a b c - 192b c )d e + (128a c + 96b c )d e +--R * +--R 6 +--R x +--R + +--R 4 3 3 8 4 2 3 2 2 4 7 +--R (192a b c + 144a b )e + (192a c - 192a b c - 444a b )d e +--R + +--R 2 3 5 2 6 +--R (- 336a b c + 516a b )d e +--R + +--R 3 3 2 2 2 4 6 3 5 +--R (1728a c + 720a b c - 804a b c + 9b )d e +--R + +--R 2 3 3 2 5 4 4 +--R (1920a b c - 240a b c - 300b c)d e +--R + +--R 2 4 2 3 4 2 5 3 +--R (- 2880a c + 1152a b c + 756b c )d e +--R + +--R 4 3 3 6 2 5 2 4 7 +--R (- 1728a b c - 528b c )d e + (384a c + 288b c )d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 4 3 3 7 +--R 384a b e + (960a b c - 816a b )d e +--R + +--R 4 2 3 2 2 4 2 6 +--R (576a c - 1728a b c + 204a b )d e +--R + +--R 3 2 2 3 5 3 5 +--R (4320a b c - 2208a b c + 1194a b )d e +--R + +--R 3 3 2 2 2 4 6 4 4 +--R (1536a c + 3792a b c - 3360a b c - 141b )d e +--R + +--R 2 3 3 2 5 5 3 +--R (- 2016a b c + 3648a b c + 126b c)d e +--R + +--R 2 4 2 3 4 2 6 2 +--R (- 3456a c - 1440a b c + 384b c )d e +--R + +--R 4 3 3 7 5 2 4 8 +--R (- 576a b c - 432b c )d e + (384a c + 288b c )d +--R * +--R 4 +--R x +--R + +--R 5 8 5 4 2 7 4 3 3 2 6 +--R 256a b e + (256a c + 320a b )d e + (1344a b c - 2256a b )d e +--R + +--R 4 2 3 2 2 4 3 5 +--R (2176a c - 3648a b c + 2728a b )d e +--R + +--R 3 2 2 3 5 4 4 +--R (11328a b c - 6320a b c + 392a b )d e +--R + +--R 3 3 2 2 2 4 6 5 3 +--R (- 4416a c + 5904a b c - 2172a b c - 165b )d e +--R + +--R 2 3 3 2 5 6 2 +--R (- 4416a b c + 4432a b c + 480b c)d e +--R + +--R 2 4 2 3 4 2 7 4 3 3 8 +--R (- 1536a c - 3456a b c - 480b c )d e + (1344a b c + 240b c )d +--R * +--R 3 +--R x +--R + +--R 5 7 5 4 2 2 6 3 3 3 5 +--R 768a b d e + (768a c - 1344a b )d e - 576a b d e +--R + +--R 4 2 3 2 2 4 4 4 +--R (4224a c - 2304a b c + 2712a b )d e +--R + +--R 3 2 2 3 5 5 3 +--R (6336a b c - 7584a b c - 660a b )d e +--R + +--R 3 3 2 2 2 4 6 2 +--R (- 5376a c + 8640a b c + 1920a b c)d e +--R + +--R 2 3 3 2 7 2 4 2 3 8 +--R (- 5376a b c - 1920a b c )d e + (768a c + 960a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 2 3 5 4 3 3 4 4 +--R 768a b d e - 2304a b d e + (2304a b c + 2304a b )d e +--R + +--R 4 2 3 2 2 4 5 3 +--R (768a c - 5760a b c - 528a b )d e +--R + +--R 3 2 2 3 6 2 3 3 2 2 2 7 +--R (5376a b c + 1536a b c)d e + (- 3072a c - 1536a b c )d e +--R + +--R 2 3 8 +--R 768a b c d +--R * +--R x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / 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c - 2496a b )d e +--R + +--R 3 2 2 4 2 3 3 2 2 3 3 2 +--R (- 1152a b c + 3168a b )d e + (7680a b c - 9216a b c)d e +--R + +--R 2 2 2 4 2 3 5 +--R 9216a b c d e - 4608a b c d +--R * +--R x +--R + +--R 5 5 5 4 2 4 4 3 3 2 3 +--R 512a b e + (512a c - 1664a b )d e + (- 768a b c + 2112a b )d e +--R + +--R 4 2 3 2 3 2 3 2 4 3 3 5 +--R (5120a c - 6144a b c)d e + 6144a b c d e - 3072a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 4 3 2 3 6 3 2 3 4 5 +--R (384a c + 288a b )d e + (- 1152a b c - 864a b )d e +--R + +--R 3 2 2 2 4 5 4 +--R (1152a c + 2016a b c + 864a b )d e +--R + +--R 2 2 3 5 6 3 +--R (- 2304a b c - 2112a b c - 288b )d e +--R + +--R 2 3 2 2 4 7 2 +--R (1152a c + 2016a b c + 864b c)d e +--R + +--R 3 3 2 8 4 2 3 9 +--R (- 1152a b c - 864b c )d e + (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 2 4 5 3 2 3 5 4 +--R 1536a b d e - 4608a b d e + (4608a b c + 4608a b )d e +--R + +--R 2 2 4 6 3 2 2 3 7 2 +--R (- 9216a b c - 1536a b )d e + (4608a b c + 4608a b c)d e +--R + +--R 2 2 8 3 9 +--R - 4608a b c d e + 1536a b c d +--R * +--R x +--R + +--R 5 3 6 4 4 5 4 3 2 5 4 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 2 3 6 3 3 2 2 2 7 2 +--R (- 9216a b c - 1536a b )d e + (4608a c + 4608a b c)d e +--R + +--R 2 2 8 2 3 9 +--R - 4608a b c d e + 1536a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 4 3 3 3 6 3 2 2 4 4 5 +--R (- 576a b c - 48a b )d e + (1728a b c + 144a b )d e +--R + +--R 3 2 2 3 5 5 4 +--R (- 1728a b c - 1872a b c - 144a b )d e +--R + +--R 2 2 2 4 6 6 3 +--R (3456a b c + 864a b c + 48b )d e +--R + +--R 2 3 3 2 5 7 2 +--R (- 1728a b c - 1872a b c - 144b c)d e +--R + +--R 2 3 4 2 8 4 3 3 9 +--R (1728a b c + 144b c )d e + (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 5 4 2 3 6 4 3 3 4 5 +--R (- 1152a c - 864a b )d e + (3456a b c + 2592a b )d e +--R + +--R 4 2 3 2 2 4 5 4 +--R (- 3456a c - 6048a b c - 2592a b )d e +--R + +--R 3 2 2 3 5 6 3 +--R (6912a b c + 6336a b c + 864a b )d e +--R + +--R 3 3 2 2 2 4 7 2 +--R (- 3456a c - 6048a b c - 2592a b c)d e +--R + +--R 2 3 3 2 8 2 4 2 3 9 +--R (3456a b c + 2592a b c )d e + (- 1152a c - 864a b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 2 4 5 4 3 3 5 4 +--R - 2304a b d e + 6912a b d e + (- 6912a b c - 6912a b )d e +--R + +--R 3 2 2 4 6 3 3 2 2 3 7 2 +--R (13824a b c + 2304a b )d e + (- 6912a b c - 6912a b c)d e +--R + +--R 2 2 2 8 2 3 9 +--R 6912a b c d e - 2304a b c d +--R * +--R x +--R + +--R 6 3 6 5 4 5 5 4 2 5 4 +--R - 1536a d e + 4608a b d e + (- 4608a c - 4608a b )d e +--R + +--R 4 3 3 6 3 4 2 3 2 7 2 +--R (9216a b c + 1536a b )d e + (- 4608a c - 4608a b c)d e +--R + +--R 3 2 8 3 3 9 +--R 4608a b c d e - 1536a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 597 + +--S 598 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 598 + +--S 599 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 4 6 3 3 +--R (- 384a c + 288a b c + 312a b c - 90b )d e +--R + +--R 2 3 3 2 5 4 2 +--R (- 1536a b c - 768a b c + 288b c)d e +--R + +--R 2 4 2 3 4 2 5 +--R (1536a c + 768a b c - 288b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 3 3 +--R (- 1536a b c + 2304a b c - 480a b )d e +--R + +--R 2 2 2 4 4 2 2 3 3 2 5 +--R (- 6144a b c + 1536a b c)d e + (6144a b c - 1536a b c )d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 3 3 +--R (- 1536a c + 2304a b c - 480a b )d e +--R + +--R 3 2 2 3 4 2 3 3 2 2 2 5 +--R (- 6144a b c + 1536a b c)d e + (6144a c - 1536a b c )d e +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (576a b c - 816a b c + 108a b c + 15b )d e +--R + +--R 2 2 3 4 2 6 4 2 +--R (2304a b c - 384a b c - 48b c)d e +--R + +--R 2 4 3 3 5 2 5 +--R (- 2304a b c + 384a b c + 48b c )d e +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 2 2 4 6 3 3 +--R (1152a c - 864a b c - 936a b c + 270a b )d e +--R + +--R 3 3 2 3 2 5 4 2 +--R (4608a b c + 2304a b c - 864a b c)d e +--R + +--R 3 4 2 2 3 4 2 5 +--R (- 4608a c - 2304a b c + 864a b c )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 3 3 +--R (2304a b c - 3456a b c + 720a b )d e +--R + +--R 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (9216a b c - 2304a b c)d e + (- 9216a b c + 2304a b c )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 3 3 +--R (1536a c - 2304a b c + 480a b )d e +--R + +--R 4 2 3 3 4 2 4 3 3 2 2 5 +--R (6144a b c - 1536a b c)d e + (- 6144a c + 1536a b c )d e +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 2 2 4 6 3 3 +--R (- 768a c + 576a b c + 624a b c - 180b )d e +--R + +--R 2 3 3 2 5 4 2 +--R (- 3072a b c - 1536a b c + 576b c)d e +--R + +--R 2 4 2 3 4 2 5 +--R (3072a c + 1536a b c - 576b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 3 3 +--R (- 3072a b c + 4608a b c - 960a b )d e +--R + +--R 2 2 2 4 4 2 2 3 3 2 5 +--R (- 12288a b c + 3072a b c)d e + (12288a b c - 3072a b c )d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 3 3 +--R (- 3072a c + 4608a b c - 960a b )d e +--R + +--R 3 2 2 3 4 2 3 3 2 2 2 5 +--R (- 12288a b c + 3072a b c)d e + (12288a c - 3072a b c )d e +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (1152a b c - 1632a b c + 216a b c + 30b )d e +--R + +--R 2 2 3 4 2 6 4 2 +--R (4608a b c - 768a b c - 96b c)d e +--R + +--R 2 4 3 3 5 2 5 +--R (- 4608a b c + 768a b c + 96b c )d e +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 2 2 4 6 3 3 +--R (2304a c - 1728a b c - 1872a b c + 540a b )d e +--R + +--R 3 3 2 3 2 5 4 2 +--R (9216a b c + 4608a b c - 1728a b c)d e +--R + +--R 3 4 2 2 3 4 2 5 +--R (- 9216a c - 4608a b c + 1728a b c )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 3 3 +--R (4608a b c - 6912a b c + 1440a b )d e +--R + +--R 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (18432a b c - 4608a b c)d e + (- 18432a b c + 4608a b c )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 3 3 +--R (3072a c - 4608a b c + 960a b )d e +--R + +--R 4 2 3 3 4 2 4 3 3 2 2 5 +--R (12288a b c - 3072a b c)d e + (- 12288a c + 3072a b c )d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 4 3 3 5 4 2 3 2 2 4 4 +--R (- 128a b c - 96a b )e + (- 128a c + 320a b c + 312a b )d e +--R + +--R 3 2 2 3 5 2 3 +--R (192a b c - 384a b c - 396a b )d e +--R + +--R 3 3 2 2 2 4 3 2 +--R (- 1280a c + 576a b c + 1152a b c)d e +--R + +--R 2 3 3 2 4 2 4 2 3 5 +--R (- 1536a b c - 1152a b c )d e + (768a c + 576a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 +--R - 512a b e + (- 512a b c + 1664a b )d e +--R + +--R 3 2 2 4 2 3 3 2 2 3 3 2 +--R (768a b c - 2112a b )d e + (- 5120a b c + 6144a b c)d e +--R + +--R 2 2 2 4 2 3 5 +--R - 6144a b c d e + 3072a b c d +--R * +--R x +--R + +--R 5 5 5 4 2 4 4 3 3 2 3 +--R - 512a b e + (- 512a c + 1664a b )d e + (768a b c - 2112a b )d e +--R + +--R 4 2 3 2 3 2 3 2 4 3 3 5 +--R (- 5120a c + 6144a b c)d e - 6144a b c d e + 3072a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 | 2 2 | 2 +--R \|- a e + b d e - c d \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 5 3 2 2 3 5 4 +--R (192a b c + 16a b )e + (192a b c - 608a b c - 52a b )d e +--R + +--R 2 2 2 4 6 2 3 +--R (- 288a b c + 768a b c + 66b )d e +--R + +--R 2 3 3 2 5 3 2 +--R (1920a b c - 2144a b c - 192b c)d e +--R + +--R 2 3 4 2 4 4 3 3 5 +--R (2304a b c + 192b c )d e + (- 1152a b c - 96b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 5 4 2 3 2 2 4 4 +--R (384a b c + 288a b )e + (384a c - 960a b c - 936a b )d e +--R + +--R 3 2 2 3 5 2 3 +--R (- 576a b c + 1152a b c + 1188a b )d e +--R + +--R 3 3 2 2 2 4 3 2 +--R (3840a c - 1728a b c - 3456a b c)d e +--R + +--R 2 3 3 2 4 2 4 2 3 5 +--R (4608a b c + 3456a b c )d e + (- 2304a c - 1728a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 +--R 768a b e + (768a b c - 2496a b )d e +--R + +--R 3 2 2 4 2 3 3 2 2 3 3 2 +--R (- 1152a b c + 3168a b )d e + (7680a b c - 9216a b c)d e +--R + +--R 2 2 2 4 2 3 5 +--R 9216a b c d e - 4608a b c d +--R * +--R x +--R + +--R 5 5 5 4 2 4 4 3 3 2 3 +--R 512a b e + (512a c - 1664a b )d e + (- 768a b c + 2112a b )d e +--R + +--R 4 2 3 2 3 2 3 2 4 3 3 5 +--R (5120a c - 6144a b c)d e + 6144a b c d e - 3072a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d +--R / +--R 4 3 2 3 6 3 2 3 4 5 +--R (384a c + 288a b )d e + (- 1152a b c - 864a b )d e +--R + +--R 3 2 2 2 4 5 4 +--R (1152a c + 2016a b c + 864a b )d e +--R + +--R 2 2 3 5 6 3 +--R (- 2304a b c - 2112a b c - 288b )d e +--R + +--R 2 3 2 2 4 7 2 +--R (1152a c + 2016a b c + 864b c)d e +--R + +--R 3 3 2 8 4 2 3 9 +--R (- 1152a b c - 864b c )d e + (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 2 4 5 3 2 3 5 4 +--R 1536a b d e - 4608a b d e + (4608a b c + 4608a b )d e +--R + +--R 2 2 4 6 3 2 2 3 7 2 +--R (- 9216a b c - 1536a b )d e + (4608a b c + 4608a b c)d e +--R + +--R 2 2 8 3 9 +--R - 4608a b c d e + 1536a b c d +--R * +--R x +--R + +--R 5 3 6 4 4 5 4 3 2 5 4 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 2 3 6 3 3 2 2 2 7 2 +--R (- 9216a b c - 1536a b )d e + (4608a c + 4608a b c)d e +--R + +--R 2 2 8 2 3 9 +--R - 4608a b c d e + 1536a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 +-+ | 2 2 | 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 4 3 3 3 6 3 2 2 4 4 5 +--R (- 576a b c - 48a b )d e + (1728a b c + 144a b )d e +--R + +--R 3 2 2 3 5 5 4 +--R (- 1728a b c - 1872a b c - 144a b )d e +--R + +--R 2 2 2 4 6 6 3 +--R (3456a b c + 864a b c + 48b )d e +--R + +--R 2 3 3 2 5 7 2 +--R (- 1728a b c - 1872a b c - 144b c)d e +--R + +--R 2 3 4 2 8 4 3 3 9 +--R (1728a b c + 144b c )d e + (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 5 4 2 3 6 4 3 3 4 5 +--R (- 1152a c - 864a b )d e + (3456a b c + 2592a b )d e +--R + +--R 4 2 3 2 2 4 5 4 +--R (- 3456a c - 6048a b c - 2592a b )d e +--R + +--R 3 2 2 3 5 6 3 +--R (6912a b c + 6336a b c + 864a b )d e +--R + +--R 3 3 2 2 2 4 7 2 +--R (- 3456a c - 6048a b c - 2592a b c)d e +--R + +--R 2 3 3 2 8 2 4 2 3 9 +--R (3456a b c + 2592a b c )d e + (- 1152a c - 864a b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 2 4 5 4 3 3 5 4 +--R - 2304a b d e + 6912a b d e + (- 6912a b c - 6912a b )d e +--R + +--R 3 2 2 4 6 3 3 2 2 3 7 2 +--R (13824a b c + 2304a b )d e + (- 6912a b c - 6912a b c)d e +--R + +--R 2 2 2 8 2 3 9 +--R 6912a b c d e - 2304a b c d +--R * +--R x +--R + +--R 6 3 6 5 4 5 5 4 2 5 4 +--R - 1536a d e + 4608a b d e + (- 4608a c - 4608a b )d e +--R + +--R 4 3 3 6 3 4 2 3 2 7 2 +--R (9216a b c + 1536a b )d e + (- 4608a c - 4608a b c)d e +--R + +--R 3 2 8 3 3 9 +--R 4608a b c d e - 1536a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R Type: Expression(Integer) +--E 599 + +--S 600 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 845 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 601 + +--S 602 of 845 +r0:=1/2*e*(2*c*d-b*e)*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-2*(d+e*x)^4/_ + sqrt(a+b*x+c*x^2)+1/3*e^2*(52*c^2*d^2+15*b^2*e^2-4*c*e*(13*b*d+2*a*e))*_ + sqrt(a+b*x+c*x^2)/c^3+8/3*e^2*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+2/3*e^2*_ + (6*c*d^2-e*(b*d+4*a*e)+5*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((36a b c - 15b )e + (- 72a c + 54b c)d e - 72b c d e + 48c d e) +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 4 4 2 4 3 3 3 +--R 4c e x + (- 4b c e + 24c d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 16a c + 10b c)e - 36b c d e + 72c d e )x +--R + +--R 3 4 2 2 3 2 2 2 +--R (- 52a b c + 30b )e + (72a c - 108b c)d e + 144b c d e +--R + +--R 3 3 +--R - 48c d e +--R * +--R x +--R + +--R 2 2 4 3 2 2 2 3 4 +--R (- 32a c + 30a b )e - 108a b c d e + 144a c d e - 12c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 3 +-+ | 2 +--R 6c \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 602 + +--S 603 of 845 +--a0:=integrate(t0,x) +--E 603 + +--S 604 of 845 +--m0a:=a0.1-r0 +--E 604 + +--S 605 of 845 +--d0a:=D(m0a,x) +--E 605 + +--S 606 of 845 +--m0b:=a0.2-r0 +--E 606 + +--S 607 of 845 +--d0b:=D(m0b,x) +--E 607 + +)clear all + +--S 608 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 608 + +--S 609 of 845 +r0:=3/4*e*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-2*(d+e*x)^3/sqrt(a+b*x+c*x^2)+_ + 9/2*e^2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/c^2+3*e^2*(d+e*x)*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R +--------------+ +--R 2 3 2 2 2 | 2 +--R ((- 12a c + 9b )e - 24b c d e + 24c d e)\|c x + b x + a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 3 3 2 2 2 +--R 4c e x + (- 6b c e + 24c d e )x +--R + +--R 2 3 2 2 2 3 2 +--R ((12a c - 18b )e + 48b c d e - 24c d e)x - 18a b e + 48a c d e +--R + +--R 2 3 +--R - 8c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 2 +-+ | 2 +--R 4c \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 609 + +--S 610 of 845 +--a0:=integrate(t0,x) +--E 610 + +--S 611 of 845 +--m0:=a0-r0 +--E 611 + +--S 612 of 845 +--d0:=D(m0,x) +--E 612 + +)clear all + +--S 613 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 613 + +--S 614 of 845 +r0:=2*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-_ + 2*(d+e*x)^2/sqrt(a+b*x+c*x^2)+4*e^2*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R +--------------+ +--R 2 | 2 2c x + b +--R (- 2b e + 4c d e)\|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 2 2 +-+ +--R (2c e x + (4b e - 4c d e)x + 4a e - 2c d )\|c +--R / +--R +--------------+ +--R +-+ | 2 +--R c\|c \|c x + b x + a +--R Type: Expression(Integer) +--E 614 + +--S 615 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 +--R ((8a b c + 2b )e + (- 16a c - 4b c)d e)x +--R + +--R 2 2 2 2 2 +--R (16a b e - 32a b c d e)x + 16a b e - 32a c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 3 +--R (- 8a b c e + 16a b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R ((- 16a b c - 8a b )e + (32a c + 16a b c)d e)x +--R + +--R 2 2 2 2 3 2 3 +--R (- 24a b e + 48a b c d e)x - 16a b e + 32a c d e +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 3 2 2 2 2 2 2 +--R - 8a b c e x + (- 12a b e + 16a b c d e + (- 8a c - 2b c)d )x +--R + +--R 2 2 2 2 +--R (- 16a b e + 32a c d e - 8a b c d )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 2 2 4 +--R (8a c + 2b c)e x +--R + +--R 3 2 2 2 2 2 3 +--R ((16a b c + 4b )e + (- 16a c - 4b c)d e + 8b c d )x +--R + +--R 2 2 2 2 2 2 +--R (20a b e - 32a b c d e + (8a c + 6b c)d )x +--R + +--R 2 2 2 2 +--R (16a b e - 32a c d e + 8a b c d )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 2 2 2 2 +-+ +-+ | 2 +--R ((4a c + b c)x + 8a b c x + 8a c)\|a \|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 3 +-+ +--R (- 4a b c x + (- 8a c - 4a b c)x - 12a b c x - 8a c)\|c +--R , +--R +--R 3 2 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 32a b e + 64a b c d e)x - 32a b e + 64a c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 3 +--R (16a b c e - 32a b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R ((32a b c + 16a b )e + (- 64a c - 32a b c)d e)x +--R + +--R 2 2 2 2 3 2 3 +--R (48a b e - 96a b c d e)x + 32a b e - 64a c d e +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 3 2 2 2 2 2 2 +--R - 8a b c e x + (- 12a b e + 16a b c d e + (- 8a c - 2b c)d )x +--R + +--R 2 2 2 2 +--R (- 16a b e + 32a c d e - 8a b c d )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 2 2 2 4 +--R (8a c + 2b c)e x +--R + +--R 3 2 2 2 2 2 3 +--R ((16a b c + 4b )e + (- 16a c - 4b c)d e + 8b c d )x +--R + +--R 2 2 2 2 2 2 +--R (20a b e - 32a b c d e + (8a c + 6b c)d )x +--R + +--R 2 2 2 2 +--R (16a b e - 32a c d e + 8a b c d )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------------+ +--R 2 2 2 2 +---+ +-+ | 2 +--R ((4a c + b c)x + 8a b c x + 8a c)\|- c \|a \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 3 +---+ +--R (- 4a b c x + (- 8a c - 4a b c)x - 12a b c x - 8a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 615 + +--S 616 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 2 2 2 | 2 +--R ((8a b e - 16a b c d e)x + 16a b e - 32a c d e)\|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 8a b c - 2b )e + (16a c + 4b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 16a b e + 32a b c d e)x - 16a b e + 32a c d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +--------------+ +--R 2 2 2 2 2 | 2 +--R ((8a b e - 16a b c d e)x + 16a b e - 32a c d e)\|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 8a b c - 2b )e + (16a c + 4b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 16a b e + 32a b c d e)x - 16a b e + 32a c d e +--R * +--R +-+ +--R \|a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R 2 2 2 2 2 +-+ +-+ | 2 +--R ((16a b e - 8b c d )x + 32a e - 16a c d )\|a \|c \|c x + b x + a +--R + +--R 2 2 2 2 2 2 2 +--R ((- 16a c - 4a b )e + (8a c + 2b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (- 32a b e + 16a b c d )x - 32a e + 16a c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 2 +-+ | 2 +--R (4a b c x + 8a c)\|c \|c x + b x + a +--R + +--R 2 2 2 2 +-+ +-+ +--R ((- 4a c - b c)x - 8a b c x - 8a c)\|a \|c +--R Type: Expression(Integer) +--E 616 + +--S 617 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 617 + +--S 618 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +---+ +--R ((8a b e - 16a b c d e)x + 16a b e - 32a c d e)\|- c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 8a b c - 2b )e + (16a c + 4b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 16a b e + 32a b c d e)x - 16a b e + 32a c d e +--R * +--R +---+ +-+ +--R \|- c \|a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 2 2 +-+ +--R ((- 16a b e + 32a b c d e)x - 32a b e + 64a c d e)\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((16a b c + 4b )e + (- 32a c - 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (32a b e - 64a b c d e)x + 32a b e - 64a c d e +--R * +--R +-+ +-+ +--R \|a \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 2 2 2 2 +---+ +-+ +-+ +--R ((16a b e - 8b c d )x + 32a e - 16a c d )\|- c \|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 2 2 +--R ((- 16a c - 4a b )e + (8a c + 2b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (- 32a b e + 16a b c d )x - 32a e + 16a c d +--R * +--R +---+ +-+ +--R \|- c \|c +--R / +--R +--------------+ +--R 2 +---+ +-+ | 2 +--R (4a b c x + 8a c)\|- c \|c \|c x + b x + a +--R + +--R 2 2 2 2 +---+ +-+ +-+ +--R ((- 4a c - b c)x - 8a b c x - 8a c)\|- c \|a \|c +--R Type: Expression(Integer) +--E 618 + +--S 619 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 619 + +)clear all + +--S 620 of 845 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 620 + +--S 621 of 845 +r0:=2*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/sqrt(c)-_ + 2*(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 2c x + b +-+ +--R 2e\|c x + b x + a atanh(----------------------) + (- 2e x - 2d)\|c +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R (2) -------------------------------------------------------------------- +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 621 + +--S 622 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R 2 | 2 +--R (2a b e x + 4a e)\|c x + b x + a +--R + +--R 2 2 +-+ +--R (- 4a c e x - 4a b e x - 4a e)\|a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +--------------+ +--R +-+ +-+ | 2 +--R (4a e - 2b d)x\|a \|c \|c x + b x + a +--R + +--R 2 2 +-+ +--R ((- 2a b e + 4a c d)x + (- 4a e + 2a b d)x)\|c +--R / +--R +--------------+ +--R 2 +-+ | 2 2 2 +-+ +-+ +--R (a b x + 2a )\|c \|c x + b x + a + (- 2a c x - 2a b x - 2a )\|a \|c +--R , +--R +--R +--------------+ +--R 2 | 2 +--R (4a b e x + 8a e)\|c x + b x + a +--R + +--R 2 2 +-+ +--R (- 8a c e x - 8a b e x - 8a e)\|a +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R +--------------+ +--R +---+ +-+ | 2 +--R (4a e - 2b d)x\|- c \|a \|c x + b x + a +--R + +--R 2 2 +---+ +--R ((- 2a b e + 4a c d)x + (- 4a e + 2a b d)x)\|- c +--R / +--R +--------------+ +--R 2 +---+ | 2 +--R (a b x + 2a )\|- c \|c x + b x + a +--R + +--R 2 2 +---+ +-+ +--R (- 2a c x - 2a b x - 2a )\|- c \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 622 + +--S 623 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R +-+ | 2 2 +--R (4a e\|a \|c x + b x + a - 2a b e x - 4a e) +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +--------------+ +--R +-+ | 2 2 +--R (- 4a e\|a \|c x + b x + a + 2a b e x + 4a e) +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R +-+ | 2 +-+ +-+ +--R - 4a d\|c \|c x + b x + a + (2b d x + 4a d)\|a \|c +--R / +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R 2a\|a \|c \|c x + b x + a + (- a b x - 2a )\|c +--R Type: Expression(Integer) +--E 623 + +--S 624 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 624 + +--S 625 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------------+ +--R +---+ +-+ | 2 2 +---+ +--R (- 4a e\|- c \|a \|c x + b x + a + (2a b e x + 4a e)\|- c ) +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (8a e\|a \|c \|c x + b x + a + (- 4a b e x - 8a e)\|c ) +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R +--------------+ +--R +---+ +-+ | 2 +---+ +-+ +-+ +--R - 4a d\|- c \|c \|c x + b x + a + (2b d x + 4a d)\|- c \|a \|c +--R / +--R +--------------+ +--R +---+ +-+ +-+ | 2 2 +---+ +-+ +--R 2a\|- c \|a \|c \|c x + b x + a + (- a b x - 2a )\|- c \|c +--R Type: Expression(Integer) +--E 625 + +--S 626 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 626 + +)clear all + +--S 627 of 845 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2c x + b +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 627 + +--S 628 of 845 +r0:=(-2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +--R (2) - ----------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 628 + +--S 629 of 845 +a0:=integrate(t0,x) +--R +--R +--R +--------------+ +--R | 2 2 +-+ +--R - 2b x\|c x + b x + a + (4c x + 2b x)\|a +--R (3) -------------------------------------------------------- +--R +--------------+ +--R +-+ | 2 2 2 +--R (b x + 2a)\|a \|c x + b x + a - 2a c x - 2a b x - 2a +--R Type: Union(Expression(Integer),...) +--E 629 + +--S 630 of 845 +m0:=a0-r0 +--R +--R +--R +--------------+ +--R +-+ | 2 +--R - 4\|a \|c x + b x + a + 2b x + 4a +--R (4) -------------------------------------- +--R +--------------+ +--R | 2 +-+ +--R 2a\|c x + b x + a + (- b x - 2a)\|a +--R Type: Expression(Integer) +--E 630 + +--S 631 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 631 + +)clear all + +--S 632 of 845 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R 2c x + b +--R (1) -------------------------------------------------------------- +--R +--------------+ +--R 3 2 | 2 +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|c x + b x + a +--R Type: Expression(Integer) +--E 632 + +--S 633 of 845 +r0:=-e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)-_ + 2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R +--------------+ +--R 2 | 2 +--R (- b e + 2c d e)\|c x + b x + a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 +--R (2c e x + 2b e - 2c d)\|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 2 2 | 2 2 | 2 +--R (a e - b d e + c d )\|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 633 + +--S 634 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R 2 2 2 2 2 | 2 +--R ((a b e - 2a b c d e)x + 2a b e - 4a c d e)\|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (- 2a b c e + 4a c d e)x + (- 2a b e + 4a b c d e)x +--R + +--R 2 2 2 +--R - 2a b e + 4a c d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 2 2 2 2 2 2 +--R ((4a e + 4a c d )x + (8a d e + 4a b d )x + 8a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 2 3 2 2 2 3 2 +--R (- 4a e + 2a b d e + (- 4a c + 2b )d e - 2b c d )x +--R + +--R 2 2 2 3 +--R (- 8a d e + 8a b d e - 8a c d )x +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 3 +--R (- 2a b e + (- 4a c + b )d e - 2b c d )x +--R + +--R 2 2 2 2 2 +--R (- 4a e - 4a b d e + (- 8a c - b )d )x +--R + +--R 2 2 2 2 +--R (- 8a d e - 8a b d )x - 8a d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (2a b e + (4a c - 2a b )d e - 2a b c d e + 4a c d )x +--R + +--R 3 3 2 2 2 2 2 3 2 +--R (4a e + 2a b d e + (4a c - 6a b )d e + 6a b c d )x +--R + +--R 3 2 2 2 2 3 +--R (8a d e - 8a b d e + 8a c d )x +--R / +--R +--------------+ +--R 2 2 2 | 2 +--R (4a b e x + (8a e + 4a b d)x + 8a d)\|c x + b x + a +--R + +--R 2 3 2 2 +--R (- 4a c - b )e x + (- 8a b e + (- 4a c - b )d)x +--R + +--R 2 2 +--R (- 8a e - 8a b d)x - 8a d +--R * +--R +-+ +--R \|a +--R + +--R +-------------------+ +--------------+ +--R 2 +-+ | 2 2 | 2 +--R ((- 4a c + 2b )e - 2b c d)x\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 2 +--R ((- 2a b c e + 4a c d)x + ((4a c - 2a b )e + 2a b c d)x) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 2 2 2 2 3 2 2 2 2 +--R ((a b e - a b d e + a b c d )x + 2a e - 2a b d e + 2a c d ) +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (- 2a c e + 2a b c d e - 2a c d )x +--R + +--R 2 2 2 2 3 2 2 2 2 +--R (- 2a b e + 2a b d e - 2a b c d )x - 2a e + 2a b d e - 2a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R , +--R +--R +--------------+ +--R 2 2 2 2 2 | 2 +--R ((2a b e - 4a b c d e)x + 4a b e - 8a c d e)\|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (- 4a b c e + 8a c d e)x + (- 4a b e + 8a b c d e)x +--R + +--R 2 2 2 +--R - 4a b e + 8a c d e +--R * +--R +-+ +--R \|a +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R d\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +--R (- a e x - a d)\|- a e + b d e - c d +--R / +--R 2 2 +-+ +--R (a e - b d e + c d )x\|a +--R + +--R +---------------------+ +--R 2 | 2 2 +-+ +--R ((- 4a c + 2b )e - 2b c d)x\|- a e + b d e - c d \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 +--R ((- 2a b c e + 4a c d)x + ((4a c - 2a b )e + 2a b c d)x) +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R / +--R 2 2 2 2 3 2 2 2 2 +--R ((a b e - a b d e + a b c d )x + 2a e - 2a b d e + 2a c d ) +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (- 2a c e + 2a b c d e - 2a c d )x +--R + +--R 2 2 2 2 3 2 2 2 2 +--R (- 2a b e + 2a b d e - 2a b c d )x - 2a e + 2a b d e - 2a c d +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 634 + +--S 635 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 +-+ | 2 2 2 +--R (2a b e - 4a c d e)\|a \|c x + b x + a + (- a b e + 2a b c d e)x +--R + +--R 2 2 2 +--R - 2a b e + 4a c d e +--R * +--R log +--R 2 2 2 2 2 2 2 2 +--R ((4a e + 4a c d )x + (8a d e + 4a b d )x + 8a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 2 3 2 2 2 3 2 +--R (- 4a e + 2a b d e + (- 4a c + 2b )d e - 2b c d )x +--R + +--R 2 2 2 3 +--R (- 8a d e + 8a b d e - 8a c d )x +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 3 +--R (- 2a b e + (- 4a c + b )d e - 2b c d )x +--R + +--R 2 2 2 2 2 +--R (- 4a e - 4a b d e + (- 8a c - b )d )x +--R + +--R 2 2 2 2 +--R (- 8a d e - 8a b d )x - 8a d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (2a b e + (4a c - 2a b )d e - 2a b c d e + 4a c d )x +--R + +--R 3 3 2 2 2 2 2 3 2 +--R (4a e + 2a b d e + (4a c - 6a b )d e + 6a b c d )x +--R + +--R 3 2 2 2 2 3 +--R (8a d e - 8a b d e + 8a c d )x +--R / +--R +--------------+ +--R 2 2 2 | 2 +--R (4a b e x + (8a e + 4a b d)x + 8a d)\|c x + b x + a +--R + +--R 2 3 2 2 +--R (- 4a c - b )e x + (- 8a b e + (- 4a c - b )d)x +--R + +--R 2 2 +--R (- 8a e - 8a b d)x - 8a d +--R * +--R +-+ +--R \|a +--R + +--R +--------------+ +--R 2 +-+ | 2 2 2 +--R (2a b e - 4a c d e)\|a \|c x + b x + a + (- a b e + 2a b c d e)x +--R + +--R 2 2 2 +--R - 2a b e + 4a c d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R (4a b e - 4a c d)\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 2 +-+ | 2 2 +--R ((- 2b e + 2b c d)x - 4a b e + 4a c d)\|a \|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 2 2 2 +-+ | 2 2 | 2 +--R (2a e - 2a b d e + 2a c d )\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 2 3 2 2 2 2 +--R ((- a b e + a b d e - a b c d )x - 2a e + 2a b d e - 2a c d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 635 + +--S 636 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 636 + +--S 637 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------------------+ +--------------+ +--R 2 | 2 2 +-+ | 2 +--R (2a b e - 4a c d e)\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R 2 2 2 2 2 | 2 2 +--R ((- a b e + 2a b c d e)x - 2a b e + 4a c d e)\|- a e + b d e - c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R 2 +-+ | 2 2 | 2 +--R (4a b e - 8a c d e)\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 2 2 2 2 2 | 2 2 +--R ((- 2a b e + 4a b c d e)x - 4a b e + 8a c d e)\|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R d\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +--R (- a e x - a d)\|- a e + b d e - c d +--R / +--R 2 2 +-+ +--R (a e - b d e + c d )x\|a +--R + +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R (4a b e - 4a c d)\|- a e + b d e - c d \|a e - b d e + c d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R +---------------------+ +--R 2 | 2 2 +-+ +--R ((- 2b e + 2b c d)x - 4a b e + 4a c d)\|- a e + b d e - c d \|a +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R +---------------------+ +--R 2 2 2 | 2 2 +-+ +--R (2a e - 2a b d e + 2a c d )\|- a e + b d e - c d \|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 2 3 2 2 2 2 +--R ((- a b e + a b d e - a b c d )x - 2a e + 2a b d e - 2a c d ) +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R Type: Expression(Integer) +--E 637 + +--S 638 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 638 + +)clear all + +--S 639 of 845 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x +--R + +--R 2 2 +--R (2a d e + b d )x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 639 + +--S 640 of 845 +r0:=-1/2*e*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (c*d^2-b*d*e+a*e^2)^(5/2)-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*sqrt(a+b*x+c*x^2))+3*e^2*_ + (2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 4 3 2 2 2 2 3 +--R ((- 4a c + 3b )e - 8b c d e + 8c d e )x + (- 4a c + 3b )d e +--R + +--R 2 2 2 3 +--R - 8b c d e + 8c d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 6b c e + 12c d e )x + ((4a c - 6b )e + 8b c d e + 4c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (8a c - 4b )d e + 8b c d e - 4c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 640 + +--S 641 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 4 4 2 3 2 3 +--R (16a c - 8a b c - 3b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 2 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 4 2 2 2 4 2 3 +--R (32a b c - 24a b )d e + (16a c + 56a b c - 3b )d e +--R + +--R 2 3 3 2 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 3 +--R (32a c - 24a b )d e + (96a b c - 24a b )d e +--R + +--R 2 2 2 3 2 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d e +--R * +--R x +--R + +--R 3 2 2 2 3 2 3 2 2 2 4 +--R (32a c - 24a b )d e + 64a b c d e - 64a c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 3 4 2 2 2 3 3 3 2 4 +--R ((- 16a b c + 12a b c)d e - 32a b c d e + 32a b c d e )x +--R + +--R 3 2 2 2 4 4 2 2 3 2 3 +--R (- 32a c + 8a b c + 12a b )d e + (- 80a b c - 20a b c)d e +--R + +--R 2 3 3 2 3 4 +--R 64a c d e + 32a b c d e +--R * +--R 3 +--R x +--R + +--R 3 2 3 4 3 2 2 2 4 2 3 +--R (- 48a b c + 36a b )d e + (- 32a c - 88a b c + 12a b )d e +--R + +--R 2 2 3 3 2 2 3 2 2 4 +--R (32a b c - 32a b c)d e + (64a c + 32a b c )d e +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 3 2 3 2 3 +--R (- 32a c + 24a b )d e + (- 112a b c + 36a b )d e +--R + +--R 3 2 2 2 3 2 2 2 4 +--R (64a c - 96a b c)d e + 96a b c d e +--R * +--R x +--R + +--R 4 3 2 2 3 3 3 2 3 2 4 +--R (- 32a c + 24a b )d e - 64a b c d e + 64a c d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 2 3 4 2 2 2 4 3 +--R (- 8a b c - 2a b )e + (32a c + 16a b c - 4b )d e +--R + +--R 2 3 2 2 3 2 2 3 +--R (- 16a b c + 8b c)d e + (- 16a c - 4b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R - 16a b e + (88a b c - 10a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 +--R (- 64a c + 24a b c - 4b )d e + (- 16a b c + 8b c)d e +--R + +--R 3 2 2 4 +--R (- 16a c - 4b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 +--R - 16a b e + (32a c + 8a b )d e + (32a b c - 16a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 64a c + 32a b c)d e - 16a b c d +--R * +--R x +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 2 3 3 3 2 2 2 2 +--R 8a b c e + (- 56a b c + 10b c)d e + (48a c - 20b c )d e +--R + +--R 3 3 +--R 16b c d e +--R * +--R 4 +--R x +--R + +--R 2 3 4 2 2 2 4 3 +--R (16a b c + 8a b )e + (- 48a c - 60a b c + 10b )d e +--R + +--R 2 3 2 2 3 2 2 3 3 4 +--R (32a b c - 8b c)d e + (48a c - 12b c )d e + 16b c d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R 24a b e + (- 104a b c + 6a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 +--R (64a c - 40a b c + 12b )d e + (48a b c - 24b c)d e +--R + +--R 3 2 2 4 +--R (16a c + 12b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 +--R 16a b e + (- 32a c - 8a b )d e + (- 32a b c + 16a b )d e +--R + +--R 2 2 2 3 2 4 +--R (64a c - 32a b c)d e + 16a b c d +--R * +--R x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 3 2 2 5 2 3 2 4 +--R (8a c + 2a b )d e + (- 16a b c - 4a b )d e +--R + +--R 2 2 2 4 3 3 2 3 4 2 +--R (16a c + 12a b c + 2b )d e + (- 16a b c - 4b c)d e +--R + +--R 3 2 2 5 +--R (8a c + 2b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 3 2 2 2 4 2 3 3 3 +--R 16a b d e + (8a c - 30a b )d e + (16a b c + 12a b )d e +--R + +--R 2 2 2 4 4 2 3 5 3 2 2 6 +--R (16a c - 20a b c + 2b )d e - 4b c d e + (8a c + 2b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 3 3 4 2 +--R 16a d e - 16a b d e + (32a c - 16a b )d e + 16a b d e +--R + +--R 2 2 2 5 2 6 +--R (16a c - 32a b c)d e + 16a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 2 2 6 +--R 16a d e - 32a b d e + (32a c + 16a b )d e - 32a b c d e + 16a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 5 2 2 2 4 2 2 3 3 3 +--R - 8a b c d e + 16a b c d e + (- 16a b c - 8a b c)d e +--R + +--R 2 2 4 2 3 5 +--R 16a b c d e - 8a b c d e +--R * +--R 4 +--R x +--R + +--R 4 3 2 5 3 2 3 2 4 +--R (- 16a c - 8a b )d e + (24a b c + 16a b )d e +--R + +--R 3 2 2 2 4 3 3 2 2 3 4 2 +--R (- 32a c - 16a b c - 8a b )d e + (16a b c + 8a b c)d e +--R + +--R 2 3 2 2 5 3 6 +--R (- 16a c + 8a b c )d e - 8a b c d +--R * +--R 3 +--R x +--R + +--R 4 5 4 3 2 2 4 3 2 3 3 3 +--R - 24a b d e + (- 16a c + 40a b )d e + (- 16a b c - 8a b )d e +--R + +--R 3 2 2 2 4 4 2 2 2 3 5 +--R (- 32a c + 16a b c - 8a b )d e + (8a b c + 16a b c)d e +--R + +--R 2 3 2 2 6 +--R (- 16a c - 8a b c )d +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 4 3 2 3 3 +--R - 16a d e + 8a b d e + (- 32a c + 32a b )d e +--R + +--R 3 2 3 4 2 3 2 2 2 5 2 2 6 +--R (- 16a b c - 24a b )d e + (- 16a c + 48a b c)d e - 24a b c d +--R * +--R x +--R + +--R 5 2 4 4 3 3 4 3 2 4 2 3 5 +--R - 16a d e + 32a b d e + (- 32a c - 16a b )d e + 32a b c d e +--R + +--R 3 2 6 +--R - 16a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R , +--R +--R 2 2 2 4 4 2 3 2 3 +--R (16a c - 8a b c - 3b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 2 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 4 2 2 2 4 2 3 +--R (32a b c - 24a b )d e + (16a c + 56a b c - 3b )d e 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e + (8a b c + 4a b c)d e +--R + +--R 2 3 2 2 5 3 6 +--R (- 8a c + 4a b c )d e - 4a b c d +--R * +--R 3 +--R x +--R + +--R 4 5 4 3 2 2 4 3 2 3 3 3 +--R - 12a b d e + (- 8a c + 20a b )d e + (- 8a b c - 4a b )d e +--R + +--R 3 2 2 2 4 4 2 2 2 3 5 +--R (- 16a c + 8a b c - 4a b )d e + (4a b c + 8a b c)d e +--R + +--R 2 3 2 2 6 +--R (- 8a c - 4a b c )d +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 4 3 2 3 3 +--R - 8a d e + 4a b d e + (- 16a c + 16a b )d e +--R + +--R 3 2 3 4 2 3 2 2 2 5 2 2 6 +--R (- 8a b c - 12a b )d e + (- 8a c + 24a b c)d e - 12a b c d +--R * +--R x +--R + +--R 5 2 4 4 3 3 4 3 2 4 2 3 5 +--R - 8a d e + 16a b d e + (- 16a c - 8a b )d e + 16a b c d e +--R + +--R 3 2 6 +--R - 8a c d +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 641 + +--S 642 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 2 3 +--R ((16a b c - 12a b )d e + 32a b c d e - 32a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 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+-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 3 2 2 2 4 2 +--R (8a b c + 2a b )e + (- 32a c + 8a b c + 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (- 32a b c - 8b c)d e + (16a c + 4b c )d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 2 2 2 3 +--R (16a b e + (- 64a b c + 32a b )d e - 64a b c d e + 32a b c d )x +--R + +--R 3 3 3 2 2 2 2 2 2 2 3 +--R 16a b e + (- 64a c + 32a b )d e - 64a b c d e + 32a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 3 4 2 2 2 3 2 3 3 2 2 4 +--R 8a b d e - 16a b d e + (16a b c + 8a b )d e - 16a b c d e +--R + +--R 2 5 +--R 8a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 3 2 2 3 2 2 4 2 2 5 +--R 16a d e - 32a b d e + (32a c + 16a b )d e - 32a b c d e + 16a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 2 3 2 3 +--R (- 8a c - 2a b )d e + (16a b c + 4a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (- 16a c - 12a b c - 2b )d e + (16a b c + 4b c)d e +--R + +--R 3 2 2 5 +--R (- 8a c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 3 2 +--R - 16a b d e + 32a b d e + (- 32a b c - 16a b )d e +--R + +--R 2 4 2 5 +--R 32a b c d e - 16a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 3 2 2 3 2 2 4 +--R - 16a d e + 32a b d e + (- 32a c - 16a b )d e + 32a b c d e +--R + +--R 2 2 5 +--R - 16a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R Type: Expression(Integer) +--E 642 + +--S 643 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 643 + +--S 644 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 2 3 +--R ((16a b c - 12a b )d e + 32a b c d e - 32a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (32a c - 24a b )d e + 64a b c d e - 64a c d e +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c + 8a b c + 3b )d e + (- 32a b c - 8b c)d e +--R + +--R 3 2 2 3 +--R (32a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 3 +--R ((- 32a b c + 24a b )d e - 64a b c d e + 64a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (- 32a c + 24a b )d e - 64a b c d e + 64a c d e +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 3 2 2 2 2 3 +--R ((32a b c - 24a b )d e + 64a b c d e - 64a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (64a c - 48a b )d e + 128a b c d e - 128a c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 32a c + 16a b c + 6b )d e + (- 64a b c - 16b c)d e +--R + +--R 3 2 2 3 +--R (64a c + 16b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 3 +--R ((- 64a b c + 48a b )d e - 128a b c d e + 128a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (- 64a c + 48a b )d e - 128a b c d e + 128a c d e +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 2 3 3 2 2 2 2 3 2 3 +--R (- 8a b e + (32a b c - 16b )d e + 32b c d e - 16b c d )x - 16a b e +--R + +--R 2 2 2 2 2 3 +--R (64a c - 32a b )d e + 64a b c d e - 32a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 +-+ | 2 2 | 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 3 2 2 2 4 2 +--R (8a b c + 2a b )e + (- 32a c + 8a b c + 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (- 32a b c - 8b c)d e + (16a c + 4b c )d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 2 2 2 3 +--R (16a b e + (- 64a b c + 32a b )d e - 64a b c d e + 32a b c d )x +--R + +--R 3 3 3 2 2 2 2 2 2 2 3 +--R 16a b e + (- 64a c + 32a b )d e - 64a b c d e + 32a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R / +--R 3 4 2 2 2 3 2 3 3 2 2 4 +--R 8a b d e - 16a b d e + (16a b c + 8a b )d e - 16a b c d e +--R + +--R 2 5 +--R 8a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 3 2 2 3 2 2 4 2 2 5 +--R 16a d e - 32a b d e + (32a c + 16a b )d e - 32a b c d e + 16a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 | 2 2 | 2 +--R \|- a e + b d e - c d \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 2 3 2 3 +--R (- 8a c - 2a b )d e + (16a b c + 4a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (- 16a c - 12a b c - 2b )d e + (16a b c + 4b c)d e +--R + +--R 3 2 2 5 +--R (- 8a c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 3 2 +--R - 16a b d e + 32a b d e + (- 32a b c - 16a b )d e +--R + +--R 2 4 2 5 +--R 32a b c d e - 16a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 3 2 2 3 2 2 4 +--R - 16a d e + 32a b d e + (- 32a c - 16a b )d e + 32a b c d e +--R + +--R 2 2 5 +--R - 16a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d +--R Type: Expression(Integer) +--E 644 + +--S 645 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 845 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 845 +r0:=-2/3*(d+e*x)^4/(a+b*x+c*x^2)^(3/2)+4*e^3*(2*c*d-b*e)*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-_ + 16/3*e*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*_ + sqrt(a+b*x+c*x^2))+8/3*e^2*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*_ + sqrt(a+b*x+c*x^2)/(c^2*(b^2-4*a*c))+16/3*e^3*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/(c*(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 2 +--R ((- 48a b c + 12b c)e + (96a c - 24b c )d e )x +--R + +--R 2 4 4 2 3 3 +--R ((- 48a b c + 12b )e + (96a b c - 24b c)d e )x +--R + +--R 2 3 4 2 2 2 3 +--R (- 48a b c + 12a b )e + (96a c - 24a b c)d e +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 4 4 +--R (24a c - 6b c )e x +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (112a b c - 32b c)e + (- 128a c + 56b c )d e - 48b c d e +--R + +--R 4 3 +--R 32c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 4 2 3 3 +--R (96a c + 48a b c - 24b )e + (- 48a b c + 48b c)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 144a c - 36b c )d e + 48b c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (144a b c - 48a b )e + (- 96a c + 96a b c)d e - 144a b c d e +--R + +--R 2 2 3 +--R 24b c d e +--R * +--R x +--R + +--R 3 2 2 4 2 3 2 2 2 2 2 3 +--R (64a c - 24a b )e + 48a b c d e - 96a c d e + 16a b c d e +--R + +--R 3 2 2 4 +--R (- 8a c + 2b c )d +--R * +--R +-+ +--R \|c +--R / +--R 4 2 3 2 3 3 2 2 3 2 2 +-+ +--R ((12a c - 3b c )x + (12a b c - 3b c )x + 12a c - 3a b c )\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 647 + +--S 648 of 845 +--a0:=integrate(t0,x) +--E 648 + +--S 649 of 845 +--m0:=a0-r0 +--E 649 + +--S 650 of 845 +--d0:=D(m0,x) +--E 650 + +)clear all + +--S 651 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 651 + +--S 652 of 845 +r0:=-2/3*(d+e*x)^3/(a+b*x+c*x^2)^(3/2)+2*e^3*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-4*e*(d+e*x)*(b*d-2*a*e+(2*c*d-_ + b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+4*e^2*(2*c*d-b*e)*sqrt(a+b*x+_ + c*x^2)/(c*(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 3 3 2 2 3 +--R ((24a c - 6b c)e x + (24a b c - 6b )e x + (24a c - 6a b )e ) +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 32a c + 14b c)e - 24b c d e + 24c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 12a b c + 12b )e + (- 72a c - 18b c)d e + 36b c d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R ((- 24a c + 24a b )e - 72a b c d e + 18b c d e)x + 12a b e +--R + +--R 2 2 2 2 2 3 +--R - 48a c d e + 12a b c d e + (- 8a c + 2b c)d +--R * +--R +-+ +--R \|c +--R / +--R 3 2 2 2 2 3 2 2 2 +-+ +--R ((12a c - 3b c )x + (12a b c - 3b c)x + 12a c - 3a b c)\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 652 + +--S 653 of 845 +--a0:=integrate(t0,x) +--E 653 + +--S 654 of 845 +--m0:=a0-r0 +--E 654 + +--S 655 of 845 +--d0:=D(m0,x) +--E 655 + +)clear all + +--S 656 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 656 + +--S 657 of 845 +r0:=-2/3*(d+e*x)^2/(a+b*x+c*x^2)^(3/2)-8/3*e*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + ((b^2-4*a*c)*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 2 3 2 2 2 +--R (- 8b c e + 16c d e)x + ((- 24a c - 6b )e + 24b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 24a b e + 12b d e)x - 16a e + 8a b d e + (- 8a c + 2b )d +--R / +--R +--------------+ +--R 2 2 2 3 2 2 | 2 +--R ((12a c - 3b c)x + (12a b c - 3b )x + 12a c - 3a b )\|c x + b x + a +--R Type: Expression(Integer) +--E 657 + +--S 658 of 845 +--a0:=integrate(t0,x) +--E 658 + +--S 659 of 845 +--m0:=a0-r0 +--E 659 + +--S 660 of 845 +--d0:=D(m0,x) +--E 660 + +)clear all + +--S 661 of 845 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 661 + +--S 662 of 845 +r0:=-2/3*(d+e*x)/(a+b*x+c*x^2)^(3/2)-4/3*e*(b+2*c*x)/((b^2-4*a*c)*_ + sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 2 +--R 8c e x + 12b c e x + 6b e x + 4a b e + (- 8a c + 2b )d +--R ----------------------------------------------------------------------- +--R +--------------+ +--R 2 2 2 3 2 2 | 2 +--R ((12a c - 3b c)x + (12a b c - 3b )x + 12a c - 3a b )\|c x + b x + a +--R Type: Expression(Integer) +--E 662 + +--S 663 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 3 5 +--R ((- 16a c - 4a b c)e + (- 24a b c - 2b c)d)x +--R + +--R 2 3 2 2 2 4 4 +--R ((- 64a b c - 4a b )e + (- 48a c - 60a b c - 2b )d)x +--R + +--R 3 2 2 2 3 3 +--R ((- 64a c - 40a b )e + (- 168a b c - 38a b )d)x +--R + +--R 3 3 2 2 2 3 +--R (- 48a b e + (- 96a c - 120a b )d)x - 96a b d x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 3 2 2 6 +--R (16a b c e + (16a c + 12b c )d)x +--R + +--R 2 2 2 2 3 5 +--R ((48a c + 36a b c)e + (96a b c + 24b c)d)x +--R + +--R 2 3 2 2 2 4 4 +--R ((120a b c + 18a b )e + (96a c + 168a b c + 12b )d)x +--R + +--R 3 2 2 2 3 3 +--R ((64a c + 64a b )e + (264a b c + 86a b )d)x +--R + +--R 3 3 2 2 2 3 +--R (48a b e + (96a c + 168a b )d)x + 96a b d x +--R * +--R +-+ +--R \|a +--R / +--R 2 2 3 5 3 2 2 2 4 4 +--R (36a b c + 3a b c)x + (72a c + 90a b c + 3a b )x +--R + +--R 3 2 3 3 4 3 2 2 4 5 +--R (252a b c + 57a b )x + (168a c + 198a b )x + 240a b x + 96a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 2 2 6 3 2 2 3 5 +--R (- 24a c - 18a b c )x + (- 144a b c - 36a b c)x +--R + +--R 4 2 3 2 2 4 4 4 3 3 3 +--R (- 144a c - 252a b c - 18a b )x + (- 432a b c - 132a b )x +--R + +--R 5 4 2 2 5 6 +--R (- 216a c - 306a b )x - 288a b x - 96a +--R Type: Union(Expression(Integer),...) +--E 663 + +--S 664 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 4 2 +--R ((32a b c + 24a b )e + (- 64a c - 32a b c + 12b )d)x +--R + +--R 2 2 2 3 3 3 2 2 +--R (128a b e + (- 256a b c + 64a b )d)x + 128a b e + (- 256a c + 64a b )d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 5 3 +--R ((- 48a b c - 4a b )e + (96a b c - 16a b c - 2b )d)x +--R + +--R 3 2 3 3 2 2 2 4 2 +--R ((- 96a b c - 72a b )e + (192a c + 96a b c - 36a b )d)x +--R + +--R 3 2 3 2 3 4 4 3 2 +--R (- 192a b e + (384a b c - 96a b )d)x - 128a b e + (256a c - 64a b )d +--R / +--R 4 2 3 2 2 4 2 4 3 3 5 +--R (96a c + 48a b c - 18a b )x + (384a b c - 96a b )x + 384a c +--R + +--R 4 2 +--R - 96a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 2 2 3 5 3 4 2 3 2 2 4 2 +--R (- 144a b c + 24a b c + 3a b )x + (- 288a c - 144a b c + 54a b )x +--R + +--R 4 3 3 5 4 2 +--R (- 576a b c + 144a b )x - 384a c + 96a b +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 664 + +--S 665 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 665 + +)clear all + +--S 666 of 845 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2c x + b +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 666 + +--S 667 of 845 +r0:=(-2/3)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R (2) - ------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (3c x + 3b x + 3a)\|c x + b x + a +--R Type: Expression(Integer) +--E 667 + +--S 668 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 5 2 2 2 4 4 +--R (- 24a b c - 2b c)x + (- 48a c - 60a b c - 2b )x +--R + +--R 2 3 3 3 2 2 2 3 +--R (- 168a b c - 38a b )x + (- 96a c - 120a b )x - 96a b x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 2 2 6 2 3 5 +--R (16a c + 12b c )x + (96a b c + 24b c)x +--R + +--R 2 2 2 4 4 2 3 3 +--R (96a c + 168a b c + 12b )x + (264a b c + 86a b )x +--R + +--R 3 2 2 2 3 +--R (96a c + 168a b )x + 96a b x +--R * +--R +-+ +--R \|a +--R / +--R 2 2 3 5 3 2 2 2 4 4 +--R (36a b c + 3a b c)x + (72a c + 90a b c + 3a b )x +--R + +--R 3 2 3 3 4 3 2 2 4 5 +--R (252a b c + 57a b )x + (168a c + 198a b )x + 240a b x + 96a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 2 2 6 3 2 2 3 5 +--R (- 24a c - 18a b c )x + (- 144a b c - 36a b c)x +--R + +--R 4 2 3 2 2 4 4 4 3 3 3 +--R (- 144a c - 252a b c - 18a b )x + (- 432a b c - 132a b )x +--R + +--R 5 4 2 2 5 6 +--R (- 216a c - 306a b )x - 288a b x - 96a +--R Type: Union(Expression(Integer),...) +--E 668 + +--S 669 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 2 +-+ | 2 +--R ((- 16a c - 12b )x - 64a b x - 64a )\|a \|c x + b x + a +--R + +--R 3 3 2 2 2 2 3 +--R (24a b c + 2b )x + (48a c + 36a b )x + 96a b x + 64a +--R / +--R +--------------+ +--R 3 2 2 2 3 4 | 2 +--R ((24a c + 18a b )x + 96a b x + 96a )\|c x + b x + a +--R + +--R 2 3 3 3 2 2 2 3 4 +-+ +--R ((- 36a b c - 3a b )x + (- 72a c - 54a b )x - 144a b x - 96a )\|a +--R Type: Expression(Integer) +--E 669 + +--S 670 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 670 + +)clear all + +--S 671 of 845 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 671 + +--S 672 of 845 +r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-e^3*(2*c*d-b*e)*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)-2/3*e*(5*b^2*c*d*e-_ + 12*a*c^2*d*e-3*b^3*e^2-2*b*c*(c*d^2-5*a*e^2)-c*(4*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(b*d+2*a*e))*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 2 +--R ((- 12a b c + 3b c)e + (24a c - 6b c )d e )x +--R + +--R 2 4 4 2 3 3 +--R ((- 12a b c + 3b )e + (24a b c - 6b c)d e )x +--R + +--R 2 3 4 2 2 2 3 +--R (- 12a b c + 3a b )e + (24a c - 6a b c)d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 3 3 2 4 2 3 +--R ((16a c - 6b c )e + 8b c d e - 8c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 2 +--R ((36a b c - 12b c)e + (- 24a c + 18b c )d e - 12b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 2 2 2 +--R ((24a c + 12a b c - 6b )e + (- 24a b c + 12b c)d e - 6b c d e)x +--R + +--R 2 3 3 2 2 2 4 2 +--R (28a b c - 8a b )e + (- 32a c + 4a b c + 2b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (12a b c - 4b c)d e + (- 8a c + 2b c )d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 3 2 2 2 4 2 2 3 3 +--R (12a c - 3a b c)e + (- 24a b c + 6a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (24a c + 6a b c - 3b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (12a c - 3b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 2 2 4 3 +--R (12a b c - 3a b )e + (- 24a b c + 6a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (24a b c + 6a b c - 3b )d e + (- 24a b c + 6b c)d e +--R + +--R 3 3 2 4 +--R (12a b c - 3b c )d +--R * +--R x +--R + +--R 4 3 2 4 3 2 3 3 +--R (12a c - 3a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (24a c + 6a b c - 3a b )d e + (- 24a b c + 6a b c)d e +--R + +--R 2 3 2 2 4 +--R (12a c - 3a b c )d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 672 + +--S 673 of 845 +--a0:=integrate(t0,x) +--E 673 + +--S 674 of 845 +--m0:=a0-r0 +--E 674 + +--S 675 of 845 +--d0:=D(m0,x) +--E 675 + +)clear all + +--S 676 of 845 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + ((2a c + b )e + 4b c d e + c d )x +--R + +--R 2 2 2 3 +--R (2a b e + (4a c + 2b )d e + 2b c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (a e + 4a b d e + (2a c + b )d )x + (2a d e + 2a b d )x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 845 +r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(d+e*x)*(a+b*x+c*x^2)^(3/2))-1/2*e^3*(16*c^2*d^2+_ + 5*b^2*e^2-4*c*e*(4*b*d+a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)-_ + 2/3*e*(9*b^2*c*d*e-20*a*c^2*d*e-5*b^3*e^2-4*b*c*(c*d^2-4*a*e^2)-_ + c*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*x)/((b^2-4*a*c)*(c*d^2-_ + b*d*e+a*e^2)^2*(d+e*x)*sqrt(a+b*x+c*x^2))+1/3*e^2*(2*c*d-b*e)*_ + (8*c^2*d^2+15*b^2*e^2-4*c*e*(2*b*d+13*a*e))*sqrt(a+b*x+c*x^2)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)) +--R +--R +--R (2) +--R 2 3 2 2 4 6 3 3 2 5 +--R (- 48a c + 72a b c - 15b c)e + (- 192a b c + 48b c )d e +--R + +--R 4 2 3 2 4 +--R (192a c - 48b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 6 +--R (- 48a b c + 72a b c - 15b )e +--R + +--R 2 3 2 2 4 5 4 2 3 3 3 +--R (- 48a c - 120a b c + 33b c)d e + (192a c - 48b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 6 +--R (- 48a c + 72a b c - 15a b )e +--R + +--R 2 2 3 5 5 +--R (- 240a b c + 120a b c - 15b )d e +--R + +--R 2 3 2 2 4 2 4 3 3 2 3 3 +--R (192a c - 240a b c + 48b c)d e + (192a b c - 48b c )d e +--R * +--R x +--R + +--R 3 2 2 2 4 5 2 2 3 2 4 +--R (- 48a c + 72a b c - 15a b )d e + (- 192a b c + 48a b c)d e +--R + +--R 2 3 2 2 3 3 +--R (192a c - 48a b c )d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 5 4 2 3 4 4 2 3 +--R (- 104a b c + 30b c )e + (208a c - 76b c )d e + 48b c d e +--R + +--R 5 3 2 +--R - 32c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (48a c - 228a b c + 60b c)e + (400a b c - 132b c )d e +--R + +--R 4 2 3 2 3 5 4 +--R (16a c + 44b c )d e - 32c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 5 +--R (- 96a b c - 84a b c + 30b )e +--R + +--R 2 3 2 2 4 4 3 3 2 2 3 +--R (336a c + 12a b c - 36b c)d e + (240a b c - 60b c )d e +--R + +--R 4 2 3 3 2 4 4 +--R (- 144a c + 84b c )d e - 48b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 +--R (64a c - 168a b c + 40a b )e +--R + +--R 2 2 3 5 4 +--R (288a b c - 152a b c + 20b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (48a c + 180a b c - 60b c)d e + (- 112a b c + 60b c )d e +--R + +--R 4 2 3 4 +--R (- 16a c - 20b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (- 24a b c + 6a b )e + (112a c - 132a b c + 28a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (240a b c - 56a b c - 4b )d e + (- 144a c + 12a b c + 12b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (32a b c - 12b c )d e + (- 16a c + 4b c )d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 4 2 3 2 7 3 2 2 3 6 +--R (24a c - 6a b c)e + (- 72a b c + 18a b c)d e +--R + +--R 3 3 2 2 2 4 2 5 +--R (72a c + 54a b c - 18a b c)d e +--R + +--R 2 3 3 2 5 3 4 +--R (- 144a b c + 12a b c + 6b c)d e +--R + +--R 2 4 2 3 4 2 4 3 4 3 3 5 2 +--R (72a c + 54a b c - 18b c )d e + (- 72a b c + 18b c )d e +--R + +--R 5 2 4 6 +--R (24a c - 6b c )d e +--R * +--R 3 +--R x +--R + +--R 4 3 3 7 4 2 3 2 2 4 6 +--R (24a b c - 6a b )e + (24a c - 78a b c + 18a b )d e +--R + +--R 2 3 5 2 5 3 3 2 2 2 4 6 3 4 +--R (72a b c - 18a b )d e + (72a c - 90a b c - 6a b c + 6b )d e +--R + +--R 2 3 3 2 5 4 3 2 4 2 3 5 2 +--R (- 72a b c + 66a b c - 12b c)d e + (72a c - 18a b c )d e +--R + +--R 4 3 3 6 5 2 4 7 +--R (- 48a b c + 12b c )d e + (24a c - 6b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 2 7 4 3 3 6 +--R (24a c - 6a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 2 2 5 3 2 2 3 5 3 4 +--R (72a c - 18a b c)d e + (- 72a b c + 66a b c - 12a b )d e +--R + +--R 3 3 2 2 2 4 6 4 3 3 2 5 5 2 +--R (72a c - 90a b c - 6a b c + 6b )d e + (72a b c - 18b c)d e +--R + +--R 2 4 2 3 4 2 6 4 3 3 7 +--R (24a c - 78a b c + 18b c )d e + (24a b c - 6b c )d +--R * +--R x +--R + +--R 5 4 2 6 4 3 3 2 5 +--R (24a c - 6a b )d e + (- 72a b c + 18a b )d e +--R + +--R 4 2 3 2 2 4 3 4 3 2 2 3 5 4 3 +--R (72a c + 54a b c - 18a b )d e + (- 144a b c + 12a b c + 6a b )d e +--R + +--R 3 3 2 2 2 4 5 2 2 3 3 2 6 +--R (72a c + 54a b c - 18a b c)d e + (- 72a b c + 18a b c )d e +--R + +--R 2 4 2 3 7 +--R (24a c - 6a b c )d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 677 + +--S 678 of 845 +--a0:=integrate(t0,x) +--E 678 + +--S 679 of 845 +--m0:=a0-r0 +--E 679 + +--S 680 of 845 +--d0:=D(m0,x) +--E 680 + +)clear all + +--S 681 of 845 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x +--R + +--R 2 +--R a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 681 + +--S 682 of 845 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(7/2)/e^4+2/9*_ + (6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(9/2)/e^4-6/11*c*_ + (2*c*d-b*e)*(d+e*x)^(11/2)/e^4+4/13*c^2*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 +--R 2772c e x + (4914b c e + 6804c d e )x +--R + +--R 2 6 5 2 2 4 4 +--R ((4004a c + 2002b )e + 12558b c d e + 4452c d e )x +--R + +--R 6 2 5 2 4 2 3 3 3 +--R (2574a b e + (10868a c + 5434b )d e + 8814b c d e + 60c d e )x +--R + +--R 5 2 2 4 3 3 2 4 2 2 +--R (7722a b d e + (8580a c + 4290b )d e + 234b c d e - 72c d e )x +--R + +--R 2 4 2 3 3 4 2 2 5 +--R (7722a b d e + (572a c + 286b )d e - 312b c d e + 96c d e)x +--R + +--R 3 3 2 4 2 5 2 6 +--R 2574a b d e + (- 1144a c - 572b )d e + 624b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 682 + +--S 683 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 6 2 5 5 +--R 2772c e x + (4914b c e + 6804c d e )x +--R + +--R 2 6 5 2 2 4 4 +--R ((4004a c + 2002b )e + 12558b c d e + 4452c d e )x +--R + +--R 6 2 5 2 4 2 3 3 3 +--R (2574a b e + (10868a c + 5434b )d e + 8814b c d e + 60c d e )x +--R + +--R 5 2 2 4 3 3 2 4 2 2 +--R (7722a b d e + (8580a c + 4290b )d e + 234b c d e - 72c d e )x +--R + +--R 2 4 2 3 3 4 2 2 5 +--R (7722a b d e + (572a c + 286b )d e - 312b c d e + 96c d e)x +--R + +--R 3 3 2 4 2 5 2 6 +--R 2574a b d e + (- 1144a c - 572b )d e + 624b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 683 + +--S 684 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 684 + +--S 685 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 685 + +)clear all + +--S 686 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 686 + +--S 687 of 845 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(5/2)/e^4+_ + 2/7*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(7/2)/e^4-_ + 2/3*c*(2*c*d-b*e)*(d+e*x)^(9/2)/e^4+4/11*c^2*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 +--R 420c e x + (770b c e + 560c d e )x +--R + +--R 2 5 4 2 2 3 3 +--R ((660a c + 330b )e + 1100b c d e + 20c d e )x +--R + +--R 5 2 4 2 3 2 3 2 2 +--R (462a b e + (1056a c + 528b )d e + 66b c d e - 24c d e )x +--R + +--R 4 2 2 3 3 2 2 4 +--R (924a b d e + (132a c + 66b )d e - 88b c d e + 32c d e)x +--R + +--R 2 3 2 3 2 4 2 5 +--R 462a b d e + (- 264a c - 132b )d e + 176b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Expression(Integer) +--E 687 + +--S 688 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 5 2 4 4 +--R 420c e x + (770b c e + 560c d e )x +--R + +--R 2 5 4 2 2 3 3 +--R ((660a c + 330b )e + 1100b c d e + 20c d e )x +--R + +--R 5 2 4 2 3 2 3 2 2 +--R (462a b e + (1056a c + 528b )d e + 66b c d e - 24c d e )x +--R + +--R 4 2 2 3 3 2 2 4 +--R (924a b d e + (132a c + 66b )d e - 88b c d e + 32c d e)x +--R + +--R 2 3 2 3 2 4 2 5 +--R 462a b d e + (- 264a c - 132b )d e + 176b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Union(Expression(Integer),...) +--E 688 + +--S 689 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 689 + +--S 690 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)*sqrt(d+e*x) +--R +--R +--R 2 3 2 2 +-------+ +--R (1) (2c x + 3b c x + (2a c + b )x + a b)\|e x + d +--R Type: Expression(Integer) +--E 691 + +--S 692 of 845 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2)/e^4+_ + 2/5*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(5/2)/e^4-_ + 6/7*c*(2*c*d-b*e)*(d+e*x)^(7/2)/e^4+4/9*c^2*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 140c e x + (270b c e + 20c d e )x +--R + +--R 2 4 3 2 2 2 2 +--R ((252a c + 126b )e + 54b c d e - 24c d e )x +--R + +--R 4 2 3 2 2 2 3 3 +--R (210a b e + (84a c + 42b )d e - 72b c d e + 32c d e)x + 210a b d e +--R + +--R 2 2 2 3 2 4 +--R (- 168a c - 84b )d e + 144b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 692 + +--S 693 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 2 3 3 +--R 140c e x + (270b c e + 20c d e )x +--R + +--R 2 4 3 2 2 2 2 +--R ((252a c + 126b )e + 54b c d e - 24c d e )x +--R + +--R 4 2 3 2 2 2 3 3 +--R (210a b e + (84a c + 42b )d e - 72b c d e + 32c d e)x + 210a b d e +--R + +--R 2 2 2 3 2 4 +--R (- 168a c - 84b )d e + 144b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 693 + +--S 694 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 694 + +--S 695 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 695 + +)clear all + +--S 696 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 696 + +--S 697 of 845 +r0:=2/3*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(3/2)/e^4-_ + 6/5*c*(2*c*d-b*e)*(d+e*x)^(5/2)/e^4+4/7*c^2*(d+e*x)^(7/2)/e^4-_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 60c e x + (126b c e - 72c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((140a c + 70b )e - 168b c d e + 96c d e)x + 210a b e +--R + +--R 2 2 2 2 3 +--R (- 280a c - 140b )d e + 336b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 697 + +--S 698 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 +--R 60c e x + (126b c e - 72c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((140a c + 70b )e - 168b c d e + 96c d e)x + 210a b e +--R + +--R 2 2 2 2 3 +--R (- 280a c - 140b )d e + 336b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 698 + +--S 699 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 699 + +--S 700 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 701 + +--S 702 of 845 +r0:=-2*c*(2*c*d-b*e)*(d+e*x)^(3/2)/e^4+4/5*c^2*(d+e*x)^(5/2)/e^4+_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*sqrt(d+e*x))+2*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 4c e x + (10b c e - 8c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((20a c + 10b )e - 40b c d e + 32c d e)x - 10a b e +--R + +--R 2 2 2 2 3 +--R (40a c + 20b )d e - 80b c d e + 64c d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Expression(Integer) +--E 702 + +--S 703 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 +--R 4c e x + (10b c e - 8c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((20a c + 10b )e - 40b c d e + 32c d e)x - 10a b e +--R + +--R 2 2 2 2 3 +--R (40a c + 20b )d e - 80b c d e + 64c d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 706 + +--S 707 of 845 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^(3/2))+_ + 4/3*c^2*(d+e*x)^(3/2)/e^4-2*(6*c^2*d^2+b^2*e^2-2*c*e*_ + (3*b*d-a*e))/(e^4*sqrt(d+e*x))-6*c*(2*c*d-b*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 4c e x + (18b c e - 24c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((- 12a c - 6b )e + 72b c d e - 96c d e)x - 2a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c - 4b )d e + 48b c d e - 64c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 707 + +--S 708 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 +--R 4c e x + (18b c e - 24c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((- 12a c - 6b )e + 72b c d e - 96c d e)x - 2a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c - 4b )d e + 48b c d e - 64c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 709 + +--S 710 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 710 + +)clear all + +--S 711 of 845 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 711 + +--S 712 of 845 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(7/2)/e^6+_ + 4/9*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(9/2)/e^6-2/11*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(11/2)/e^6+8/13*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(13/2)/e^6-2/3*c^2*(2*c*d-b*e)*_ + (d+e*x)^(15/2)/e^6+4/17*c^3*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 3 8 8 2 8 3 7 7 +--R 36036c e x + (102102b c e + 84084c d e )x +--R + +--R 2 2 8 2 7 3 2 6 6 +--R ((94248a c + 94248b c)e + 243474b c d e + 50820c d e )x +--R + +--R 3 8 2 2 7 +--R (167076a b c + 27846b )e + (231336a c + 231336b c)d e +--R + +--R 2 2 6 3 3 5 +--R 152082b c d e + 252c d e +--R * +--R 5 +--R x +--R + +--R 2 2 8 3 7 +--R (68068a c + 68068a b )e + (426972a b c + 71162b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (151368a c + 151368b c)d e + 1190b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 7 +--R 43758a b e + (184756a c + 184756a b )d e +--R + +--R 3 2 6 2 2 3 5 +--R (299676a b c + 49946b )d e + (2040a c + 2040b c)d e +--R + +--R 2 4 4 3 5 3 +--R - 1360b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 2 6 +--R 131274a b d e + (145860a c + 145860a b )d e +--R + +--R 3 3 5 2 2 4 4 +--R (7956a b c + 1326b )d e + (- 2448a c - 2448b c)d e +--R + +--R 2 5 3 3 6 2 +--R 1632b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 2 2 3 5 +--R 131274a b d e + (9724a c + 9724a b )d e +--R + +--R 3 4 4 2 2 5 3 +--R (- 10608a b c - 1768b )d e + (3264a c + 3264b c)d e +--R + +--R 2 6 2 3 7 +--R - 2176b c d e + 512c d e +--R * +--R x +--R + +--R 2 3 5 2 2 4 4 +--R 43758a b d e + (- 19448a c - 19448a b )d e +--R + +--R 3 5 3 2 2 6 2 2 7 +--R (21216a b c + 3536b )d e + (- 6528a c - 6528b c)d e + 4352b c d e +--R + +--R 3 8 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Expression(Integer) +--E 712 + +--S 713 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 8 8 2 8 3 7 7 +--R 36036c e x + (102102b c e + 84084c d e )x +--R + +--R 2 2 8 2 7 3 2 6 6 +--R ((94248a c + 94248b c)e + 243474b c d e + 50820c d e )x +--R + +--R 3 8 2 2 7 +--R (167076a b c + 27846b )e + (231336a c + 231336b c)d e +--R + +--R 2 2 6 3 3 5 +--R 152082b c d e + 252c d e +--R * +--R 5 +--R x +--R + +--R 2 2 8 3 7 +--R (68068a c + 68068a b )e + (426972a b c + 71162b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (151368a c + 151368b c)d e + 1190b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 7 +--R 43758a b e + (184756a c + 184756a b )d e +--R + +--R 3 2 6 2 2 3 5 +--R (299676a b c + 49946b )d e + (2040a c + 2040b c)d e +--R + +--R 2 4 4 3 5 3 +--R - 1360b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 2 6 +--R 131274a b d e + (145860a c + 145860a b )d e +--R + +--R 3 3 5 2 2 4 4 +--R (7956a b c + 1326b )d e + (- 2448a c - 2448b c)d e +--R + +--R 2 5 3 3 6 2 +--R 1632b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 2 2 3 5 +--R 131274a b d e + (9724a c + 9724a b )d e +--R + +--R 3 4 4 2 2 5 3 +--R (- 10608a b c - 1768b )d e + (3264a c + 3264b c)d e +--R + +--R 2 6 2 3 7 +--R - 2176b c d e + 512c d e +--R * +--R x +--R + +--R 2 3 5 2 2 4 4 +--R 43758a b d e + (- 19448a c - 19448a b )d e +--R + +--R 3 5 3 2 2 6 2 2 7 +--R (21216a b c + 3536b )d e + (- 6528a c - 6528b c)d e + 4352b c d e +--R + +--R 3 8 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 714 + +--S 715 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 +--R ((6a b c + b )e + (4a c + 4b c)d)x +--R + +--R 2 2 3 2 2 2 2 2 +--R ((2a c + 2a b )e + (6a b c + b )d)x + (a b e + (2a c + 2a b )d)x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 716 + +--S 717 of 845 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(5/2)/e^6+_ + 4/7*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(7/2)/e^6-2/9*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(9/2)/e^6+8/11*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(11/2)/e^6-10/13*c^2*(2*c*d-b*e)*_ + (d+e*x)^(13/2)/e^6+4/15*c^3*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 3 7 7 2 7 3 6 6 +--R 12012c e x + (34650b c e + 14784c d e )x +--R + +--R 2 2 7 2 6 3 2 5 5 +--R ((32760a c + 32760b c)e + 44100b c d e + 252c d e )x +--R + +--R 3 7 2 2 6 +--R (60060a b c + 10010b )e + (43680a c + 43680b c)d e +--R + +--R 2 2 5 3 3 4 +--R 1050b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 2 7 3 6 +--R (25740a c + 25740a b )e + (85800a b c + 14300b )d e +--R + +--R 2 2 2 5 2 3 4 3 4 3 +--R (1560a c + 1560b c)d e - 1200b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 6 3 2 5 +--R 18018a b e + (41184a c + 41184a b )d e + (5148a b c + 858b )d e +--R + +--R 2 2 3 4 2 4 3 3 5 2 +--R (- 1872a c - 1872b c)d e + 1440b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 2 5 +--R 36036a b d e + (5148a c + 5148a b )d e +--R + +--R 3 3 4 2 2 4 3 +--R (- 6864a b c - 1144b )d e + (2496a c + 2496b c)d e +--R + +--R 2 5 2 3 6 +--R - 1920b c d e + 512c d e +--R * +--R x +--R + +--R 2 2 5 2 2 3 4 +--R 18018a b d e + (- 10296a c - 10296a b )d e +--R + +--R 3 4 3 2 2 5 2 2 6 +--R (13728a b c + 2288b )d e + (- 4992a c - 4992b c)d e + 3840b c d e +--R + +--R 3 7 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 717 + +--S 718 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 2 7 3 6 6 +--R 12012c e x + (34650b c e + 14784c d e )x +--R + +--R 2 2 7 2 6 3 2 5 5 +--R ((32760a c + 32760b c)e + 44100b c d e + 252c d e )x +--R + +--R 3 7 2 2 6 +--R (60060a b c + 10010b )e + (43680a c + 43680b c)d e +--R + +--R 2 2 5 3 3 4 +--R 1050b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 2 7 3 6 +--R (25740a c + 25740a b )e + (85800a b c + 14300b )d e +--R + +--R 2 2 2 5 2 3 4 3 4 3 +--R (1560a c + 1560b c)d e - 1200b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 6 3 2 5 +--R 18018a b e + (41184a c + 41184a b )d e + (5148a b c + 858b )d e +--R + +--R 2 2 3 4 2 4 3 3 5 2 +--R (- 1872a c - 1872b c)d e + 1440b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 2 5 +--R 36036a b d e + (5148a c + 5148a b )d e +--R + +--R 3 3 4 2 2 4 3 +--R (- 6864a b c - 1144b )d e + (2496a c + 2496b c)d e +--R + +--R 2 5 2 3 6 +--R - 1920b c d e + 512c d e +--R * +--R x +--R + +--R 2 2 5 2 2 3 4 +--R 18018a b d e + (- 10296a c - 10296a b )d e +--R + +--R 3 4 3 2 2 5 2 2 6 +--R (13728a b c + 2288b )d e + (- 4992a c - 4992b c)d e + 3840b c d e +--R + +--R 3 7 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 718 + +--S 719 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 719 + +--S 720 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 721 + +--S 722 of 845 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(3/2)/e^6+_ + 4/5*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(5/2)/e^6-2/7*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))*(d+e*x)^(7/2)/e^6+8/9*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(9/2)/e^6-10/11*c^2*(2*c*d-b*e)*_ + (d+e*x)^(11/2)/e^6+4/13*c^3*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 13860c e x + (40950b c e + 1260c d e )x +--R + +--R 2 2 6 2 5 3 2 4 4 +--R ((40040a c + 40040b c)e + 4550b c d e - 1400c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (77220a b c + 12870b )e + (5720a c + 5720b c)d e - 5200b c d e +--R + +--R 3 3 3 +--R 1600c d e +--R * +--R 3 +--R x +--R + +--R 2 2 6 3 5 +--R (36036a c + 36036a b )e + (15444a b c + 2574b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 6864a c - 6864b c)d e + 6240b c d e - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 +--R 30030a b e + (12012a c + 12012a b )d e +--R + +--R 3 2 4 2 2 3 3 +--R (- 20592a b c - 3432b )d e + (9152a c + 9152b c)d e +--R + +--R 2 4 2 3 5 +--R - 8320b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 2 4 +--R 30030a b d e + (- 24024a c - 24024a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (41184a b c + 6864b )d e + (- 18304a c - 18304b c)d e + 16640b c d e +--R + +--R 3 6 +--R - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 722 + +--S 723 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 2 6 3 5 5 +--R 13860c e x + (40950b c e + 1260c d e )x +--R + +--R 2 2 6 2 5 3 2 4 4 +--R ((40040a c + 40040b c)e + 4550b c d e - 1400c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (77220a b c + 12870b )e + (5720a c + 5720b c)d e - 5200b c d e +--R + +--R 3 3 3 +--R 1600c d e +--R * +--R 3 +--R x +--R + +--R 2 2 6 3 5 +--R (36036a c + 36036a b )e + (15444a b c + 2574b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 6864a c - 6864b c)d e + 6240b c d e - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 +--R 30030a b e + (12012a c + 12012a b )d e +--R + +--R 3 2 4 2 2 3 3 +--R (- 20592a b c - 3432b )d e + (9152a c + 9152b c)d e +--R + +--R 2 4 2 3 5 +--R - 8320b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 2 4 +--R 30030a b d e + (- 24024a c - 24024a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (41184a b c + 6864b )d e + (- 18304a c - 18304b c)d e + 16640b c d e +--R + +--R 3 6 +--R - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 723 + +--S 724 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 724 + +--S 725 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 725 + +)clear all + +--S 726 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 726 + +--S 727 of 845 +r0:=4/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(3/2)/e^6-2/5*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(5/2)/e^6+8/7*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(7/2)/e^6-10/9*c^2*(2*c*d-b*e)*_ + (d+e*x)^(9/2)/e^6+4/11*c^3*(d+e*x)^(11/2)/e^6-2*(2*c*d-b*e)*_ + (c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 1260c e x + (3850b c e - 1400c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((3960a c + 3960b c)e - 4400b c d e + 1600c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (8316a b c + 1386b )e + (- 4752a c - 4752b c)d e + 5280b c d e +--R + +--R 3 3 2 +--R - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (4620a c + 4620a b )e + (- 11088a b c - 1848b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (6336a c + 6336b c)d e - 7040b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R 6930a b e + (- 9240a c - 9240a b )d e + (22176a b c + 3696b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12672a c - 12672b c)d e + 14080b c d e - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 727 + +--S 728 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 2 5 3 4 4 +--R 1260c e x + (3850b c e - 1400c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((3960a c + 3960b c)e - 4400b c d e + 1600c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (8316a b c + 1386b )e + (- 4752a c - 4752b c)d e + 5280b c d e +--R + +--R 3 3 2 +--R - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (4620a c + 4620a b )e + (- 11088a b c - 1848b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (6336a c + 6336b c)d e - 7040b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R 6930a b e + (- 9240a c - 9240a b )d e + (22176a b c + 3696b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12672a c - 12672b c)d e + 14080b c d e - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 728 + +--S 729 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 729 + +--S 730 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 730 + +)clear all + +--S 731 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 731 + +--S 732 of 845 +r0:=-2/3*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^(3/2)/e^6+8/5*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(5/2)/e^6-10/7*c^2*(2*c*d-b*e)*(d+e*x)^(7/2)/e^6+4/9*c^3*_ + (d+e*x)^(9/2)/e^6+2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*_ + sqrt(d+e*x))+4*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 140c e x + (450b c e - 200c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((504a c + 504b c)e - 720b c d e + 320c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (1260a b c + 210b )e + (- 1008a c - 1008b c)d e + 1440b c d e +--R + +--R 3 3 2 +--R - 640c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (1260a c + 1260a b )e + (- 5040a b c - 840b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (4032a c + 4032b c)d e - 5760b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 630a b e + (2520a c + 2520a b )d e + (- 10080a b c - 1680b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (8064a c + 8064b c)d e - 11520b c d e + 5120c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 732 + +--S 733 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 2 5 3 4 4 +--R 140c e x + (450b c e - 200c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((504a c + 504b c)e - 720b c d e + 320c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (1260a b c + 210b )e + (- 1008a c - 1008b c)d e + 1440b c d e +--R + +--R 3 3 2 +--R - 640c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (1260a c + 1260a b )e + (- 5040a b c - 840b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (4032a c + 4032b c)d e - 5760b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 630a b e + (2520a c + 2520a b )d e + (- 10080a b c - 1680b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (8064a c + 8064b c)d e - 11520b c d e + 5120c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 733 + +--S 734 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 736 + +--S 737 of 845 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^(3/2))+_ + 8/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(3/2)/e^6-_ + 2*c^2*(2*c*d-b*e)*(d+e*x)^(5/2)/e^6+4/7*c^3*(d+e*x)^(7/2)/e^6-_ + 4*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/(e^6*_ + sqrt(d+e*x))-2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 12c e x + (42b c e - 24c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((56a c + 56b c)e - 112b c d e + 64c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (252a b c + 42b )e + (- 336a c - 336b c)d e + 672b c d e +--R + +--R 3 3 2 +--R - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (- 84a c - 84a b )e + (1008a b c + 168b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (- 1344a c - 1344b c)d e + 2688b c d e - 1536c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 14a b e + (- 56a c - 56a b )d e + (672a b c + 112b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 896a c - 896b c)d e + 1792b c d e - 1024c d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Expression(Integer) +--E 737 + +--S 738 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 2 5 3 4 4 +--R 12c e x + (42b c e - 24c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((56a c + 56b c)e - 112b c d e + 64c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (252a b c + 42b )e + (- 336a c - 336b c)d e + 672b c d e +--R + +--R 3 3 2 +--R - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (- 84a c - 84a b )e + (1008a b c + 168b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (- 1344a c - 1344b c)d e + 2688b c d e - 1536c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 14a b e + (- 56a c - 56a b )d e + (672a b c + 112b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 896a c - 896b c)d e + 1792b c d e - 1024c d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 738 + +--S 739 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 739 + +--S 740 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 740 + +)clear all + +--S 741 of 845 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 2 9 3 2 4 8 +--R 2c e x + (7b c e + 4c d e)x +--R + +--R 3 2 2 2 3 4 2 7 +--R ((6a c + 9b c )e + 14b c d e + 2c d )x +--R + +--R 2 3 2 3 2 2 3 2 6 +--R ((15a b c + 5b c)e + (12a c + 18b c )d e + 7b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 2 2 5 +--R ((6a c + 12a b c + b )e + (30a b c + 10b c)d e + (6a c + 9b c )d )x +--R + +--R 2 3 2 2 2 2 4 +--R (9a b c + 3a b )e + (12a c + 24a b c + 2b )d e +--R + +--R 2 3 2 +--R (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 2 3 2 2 2 4 2 3 +--R ((2a c + 3a b )e + (18a b c + 6a b )d e + (6a c + 12a b c + b )d )x +--R + +--R 3 2 3 2 2 2 3 2 2 +--R (a b e + (4a c + 6a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 2 2 2 3 2 +--R (2a b d e + (2a c + 3a b )d )x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 741 + +--S 742 of 845 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(7/2)/e^8+_ + 2/9*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(9/2)/e^8-6/11*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(11/2)/e^8+2/13*(70*c^4*d^4+_ + b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+_ + 6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(13/2)/e^8-_ + 2/3*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^(15/2)/e^8+6/17*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(17/2)/e^8-14/19*c^3*(2*c*d-b*e)*(d+e*x)^(19/2)/e^8+_ + 4/21*c^4*(d+e*x)^(21/2)/e^8 +--R +--R +--R (2) +--R 4 10 10 3 10 4 9 9 +--R 554268c e x + (2144142b c e + 1254396c d e )x +--R + +--R 3 2 2 10 3 9 4 2 8 8 +--R ((2054052a c + 3081078b c )e + 4918914b c d e + 725868c d e )x +--R + +--R 2 3 10 3 2 2 9 +--R (5819814a b c + 1939938b c)e + (4792788a c + 7189182b c )d e +--R + +--R 3 2 8 4 3 7 +--R 2900898b c d e + 1716c d e +--R * +--R 7 +--R x +--R + +--R 2 2 2 4 10 +--R (2686068a c + 5372136a b c + 447678b )e +--R + +--R 2 3 9 3 2 2 2 8 +--R (13878018a b c + 4626006b c)d e + (2896740a c + 4345110b c )d e +--R + +--R 3 3 7 4 4 6 +--R 9702b c d e - 1848c d e +--R * +--R 6 +--R x +--R + +--R 2 3 10 +--R (4761666a b c + 1587222a b )e +--R + +--R 2 2 2 4 9 +--R (6593076a c + 13186152a b c + 1098846b )d e +--R + +--R 2 3 2 8 3 2 2 3 7 +--R (8668674a b c + 2889558b c)d e + (14364a c + 21546b c )d e +--R + +--R 3 4 6 4 5 5 +--R - 10584b c d e + 2016c d e +--R * +--R 5 +--R x +--R + +--R 3 2 2 10 2 3 9 +--R (1293292a c + 1939938a b )e + (12168702a b c + 4056234a b )d e +--R + +--R 2 2 2 4 2 8 +--R (4313988a c + 8627976a b c + 718998b )d e +--R + +--R 2 3 3 7 3 2 2 4 6 +--R (67830a b c + 22610b c)d e + (- 15960a c - 23940b c )d e +--R + +--R 3 5 5 4 6 4 +--R 11760b c d e - 2240c d e +--R * +--R 4 +--R x +--R + +--R 3 10 3 2 2 9 +--R 831402a b e + (3510364a c + 5265546a b )d e +--R + +--R 2 3 2 8 +--R (8540766a b c + 2846922a b )d e +--R + +--R 2 2 2 4 3 7 +--R (58140a c + 116280a b c + 9690b )d e +--R + +--R 2 3 4 6 3 2 2 5 5 +--R (- 77520a b c - 25840b c)d e + (18240a c + 27360b c )d e +--R + +--R 3 6 4 4 7 3 +--R - 13440b c d e + 2560c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 2 8 +--R 2494206a b d e + (2771340a c + 4157010a b )d e +--R + +--R 2 3 3 7 +--R (226746a b c + 75582a b )d e +--R + +--R 2 2 2 4 4 6 +--R (- 69768a c - 139536a b c - 11628b )d e +--R + +--R 2 3 5 5 3 2 2 6 4 +--R (93024a b c + 31008b c)d e + (- 21888a c - 32832b c )d e +--R + +--R 3 7 3 4 8 2 +--R 16128b c d e - 3072c d e +--R * +--R 2 +--R x +--R + +--R 3 2 8 3 2 2 3 7 +--R 2494206a b d e + (184756a c + 277134a b )d e +--R + +--R 2 3 4 6 +--R (- 302328a b c - 100776a b )d e +--R + +--R 2 2 2 4 5 5 +--R (93024a c + 186048a b c + 15504b )d e +--R + +--R 2 3 6 4 3 2 2 7 3 +--R (- 124032a b c - 41344b c)d e + (29184a c + 43776b c )d e +--R + +--R 3 8 2 4 9 +--R - 21504b c d e + 4096c d e +--R * +--R x +--R + +--R 3 3 7 3 2 2 4 6 +--R 831402a b d e + (- 369512a c - 554268a b )d e +--R + +--R 2 3 5 5 +--R (604656a b c + 201552a b )d e +--R + +--R 2 2 2 4 6 4 +--R (- 186048a c - 372096a b c - 31008b )d e +--R + +--R 2 3 7 3 3 2 2 8 2 +--R (248064a b c + 82688b c)d e + (- 58368a c - 87552b c )d e +--R + +--R 3 9 4 10 +--R 43008b c d e - 8192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Expression(Integer) +--E 742 + +--S 743 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 10 10 3 10 4 9 9 +--R 554268c e x + (2144142b c e + 1254396c d e )x +--R + +--R 3 2 2 10 3 9 4 2 8 8 +--R ((2054052a c + 3081078b c )e + 4918914b c d e + 725868c d e )x +--R + +--R 2 3 10 3 2 2 9 +--R (5819814a b c + 1939938b c)e + (4792788a c + 7189182b c )d e +--R + +--R 3 2 8 4 3 7 +--R 2900898b c d e + 1716c d e +--R * +--R 7 +--R x +--R + +--R 2 2 2 4 10 +--R (2686068a c + 5372136a b c + 447678b )e +--R + +--R 2 3 9 3 2 2 2 8 +--R (13878018a b c + 4626006b c)d e + (2896740a c + 4345110b c )d e +--R + +--R 3 3 7 4 4 6 +--R 9702b c d e - 1848c d e +--R * +--R 6 +--R x +--R + +--R 2 3 10 +--R (4761666a b c + 1587222a b )e +--R + +--R 2 2 2 4 9 +--R (6593076a c + 13186152a b c + 1098846b )d e +--R + +--R 2 3 2 8 3 2 2 3 7 +--R (8668674a b c + 2889558b c)d e + (14364a c + 21546b c )d e +--R + +--R 3 4 6 4 5 5 +--R - 10584b c d e + 2016c d e +--R * +--R 5 +--R x +--R + +--R 3 2 2 10 2 3 9 +--R (1293292a c + 1939938a b )e + (12168702a b c + 4056234a b )d e +--R + +--R 2 2 2 4 2 8 +--R (4313988a c + 8627976a b c + 718998b )d e +--R + +--R 2 3 3 7 3 2 2 4 6 +--R (67830a b c + 22610b c)d e + (- 15960a c - 23940b c )d e +--R + +--R 3 5 5 4 6 4 +--R 11760b c d e - 2240c d e +--R * +--R 4 +--R x +--R + +--R 3 10 3 2 2 9 +--R 831402a b e + (3510364a c + 5265546a b )d e +--R + +--R 2 3 2 8 +--R (8540766a b c + 2846922a b )d e +--R + +--R 2 2 2 4 3 7 +--R (58140a c + 116280a b c + 9690b )d e +--R + +--R 2 3 4 6 3 2 2 5 5 +--R (- 77520a b c - 25840b c)d e + (18240a c + 27360b c )d e +--R + +--R 3 6 4 4 7 3 +--R - 13440b c d e + 2560c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 2 8 +--R 2494206a b d e + (2771340a c + 4157010a b )d e +--R + +--R 2 3 3 7 +--R (226746a b c + 75582a b )d e +--R + +--R 2 2 2 4 4 6 +--R (- 69768a c - 139536a b c - 11628b )d e +--R + +--R 2 3 5 5 3 2 2 6 4 +--R (93024a b c + 31008b c)d e + (- 21888a c - 32832b c )d e +--R + +--R 3 7 3 4 8 2 +--R 16128b c d e - 3072c d e +--R * +--R 2 +--R x +--R + +--R 3 2 8 3 2 2 3 7 +--R 2494206a b d e + (184756a c + 277134a b )d e +--R + +--R 2 3 4 6 +--R (- 302328a b c - 100776a b )d e +--R + +--R 2 2 2 4 5 5 +--R (93024a c + 186048a b c + 15504b )d e +--R + +--R 2 3 6 4 3 2 2 7 3 +--R (- 124032a b c - 41344b c)d e + (29184a c + 43776b c )d e +--R + +--R 3 8 2 4 9 +--R - 21504b c d e + 4096c d e +--R * +--R x +--R + +--R 3 3 7 3 2 2 4 6 +--R 831402a b d e + (- 369512a c - 554268a b )d e +--R + +--R 2 3 5 5 +--R (604656a b c + 201552a b )d e +--R + +--R 2 2 2 4 6 4 +--R (- 186048a c - 372096a b c - 31008b )d e +--R + +--R 2 3 7 3 3 2 2 8 2 +--R (248064a b c + 82688b c)d e + (- 58368a c - 87552b c )d e +--R + +--R 3 9 4 10 +--R 43008b c d e - 8192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Union(Expression(Integer),...) +--E 743 + +--S 744 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 744 + +--S 745 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 745 + +)clear all + +--S 746 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 8 3 4 7 3 2 2 3 6 +--R 2c e x + (7b c e + 2c d)x + ((6a c + 9b c )e + 7b c d)x +--R + +--R 2 3 3 2 2 5 +--R ((15a b c + 5b c)e + (6a c + 9b c )d)x +--R + +--R 2 2 2 4 2 3 4 +--R ((6a c + 12a b c + b )e + (15a b c + 5b c)d)x +--R + +--R 2 3 2 2 2 4 3 +--R ((9a b c + 3a b )e + (6a c + 12a b c + b )d)x +--R + +--R 3 2 2 2 3 2 3 3 2 2 +--R ((2a c + 3a b )e + (9a b c + 3a b )d)x + (a b e + (2a c + 3a b )d)x +--R + +--R 3 +--R a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 746 + +--S 747 of 845 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(5/2)/e^8+_ + 2/7*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(7/2)/e^8-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(9/2)/e^8+2/11*(70*c^4*d^4+_ + b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+_ + 6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(11/2)/e^8-_ + 10/13*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^(13/2)/e^8+2/5*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(15/2)/e^8-14/17*c^3*(2*c*d-b*e)*(d+e*x)^(17/2)/e^8+_ + 4/19*c^4*(d+e*x)^(19/2)/e^8 +--R +--R +--R (2) +--R 4 9 9 3 9 4 8 8 +--R 1021020c e x + (3993990b c e + 1201200c d e )x +--R + +--R 3 2 2 9 3 8 4 2 7 7 +--R ((3879876a c + 5819814b c )e + 4792788b c d e + 12012c d e )x +--R + +--R 2 3 9 3 2 2 8 +--R (11191950a b c + 3730650b c)e + (4775232a c + 7162848b c )d e +--R + +--R 3 2 7 4 3 6 +--R 61446b c d e - 12936c d e +--R * +--R 6 +--R x +--R + +--R 2 2 2 4 9 +--R (5290740a c + 10581480a b c + 881790b )e +--R + +--R 2 3 8 3 2 2 2 7 +--R (14244300a b c + 4748100b c)d e + (81396a c + 122094b c )d e +--R + +--R 3 3 6 4 4 5 +--R - 67032b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 3 9 +--R (9699690a b c + 3233230a b )e +--R + +--R 2 2 2 4 8 +--R (7054320a c + 14108640a b c + 1175720b )d e +--R + +--R 2 3 2 7 3 2 2 3 6 +--R (339150a b c + 113050b c)d e + (- 90440a c - 135660b c )d e +--R + +--R 3 4 5 4 5 4 +--R 74480b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 3 2 2 9 2 3 8 +--R (2771340a c + 4157010a b )e + (13856700a b c + 4618900a b )d e +--R + +--R 2 2 2 4 2 7 +--R (251940a c + 503880a b c + 41990b )d e +--R + +--R 2 3 3 6 3 2 2 4 5 +--R (- 387600a b c - 129200b c)d e + (103360a c + 155040b c )d e +--R + +--R 3 5 4 4 6 3 +--R - 85120b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 8 +--R 1939938a b e + (4434144a c + 6651216a b )d e +--R + +--R 2 3 2 7 +--R (831402a b c + 277134a b )d e +--R + +--R 2 2 2 4 3 6 +--R (- 302328a c - 604656a b c - 50388b )d e +--R + +--R 2 3 4 5 3 2 2 5 4 +--R (465120a b c + 155040b c)d e + (- 124032a c - 186048b c )d e +--R + +--R 3 6 3 4 7 2 +--R 102144b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 2 7 +--R 3879876a b d e + (554268a c + 831402a b )d e +--R + +--R 2 3 3 6 +--R (- 1108536a b c - 369512a b )d e +--R + +--R 2 2 2 4 4 5 +--R (403104a c + 806208a b c + 67184b )d e +--R + +--R 2 3 5 4 3 2 2 6 3 +--R (- 620160a b c - 206720b c)d e + (165376a c + 248064b c )d e +--R + +--R 3 7 2 4 8 +--R - 136192b c d e + 28672c d e +--R * +--R x +--R + +--R 3 2 7 3 2 2 3 6 +--R 1939938a b d e + (- 1108536a c - 1662804a b )d e +--R + +--R 2 3 4 5 +--R (2217072a b c + 739024a b )d e +--R + +--R 2 2 2 4 5 4 +--R (- 806208a c - 1612416a b c - 134368b )d e +--R + +--R 2 3 6 3 3 2 2 7 2 +--R (1240320a b c + 413440b c)d e + (- 330752a c - 496128b c )d e +--R + +--R 3 8 4 9 +--R 272384b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 4849845e +--R Type: Expression(Integer) +--E 747 + +--S 748 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 9 9 3 9 4 8 8 +--R 1021020c e x + (3993990b c e + 1201200c d e )x +--R + +--R 3 2 2 9 3 8 4 2 7 7 +--R ((3879876a c + 5819814b c )e + 4792788b c d e + 12012c d e )x +--R + +--R 2 3 9 3 2 2 8 +--R (11191950a b c + 3730650b c)e + (4775232a c + 7162848b c )d e +--R + +--R 3 2 7 4 3 6 +--R 61446b c d e - 12936c d e +--R * +--R 6 +--R x +--R + +--R 2 2 2 4 9 +--R (5290740a c + 10581480a b c + 881790b )e +--R + +--R 2 3 8 3 2 2 2 7 +--R (14244300a b c + 4748100b c)d e + (81396a c + 122094b c )d e +--R + +--R 3 3 6 4 4 5 +--R - 67032b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 3 9 +--R (9699690a b c + 3233230a b )e +--R + +--R 2 2 2 4 8 +--R (7054320a c + 14108640a b c + 1175720b )d e +--R + +--R 2 3 2 7 3 2 2 3 6 +--R (339150a b c + 113050b c)d e + (- 90440a c - 135660b c )d e +--R + +--R 3 4 5 4 5 4 +--R 74480b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 3 2 2 9 2 3 8 +--R (2771340a c + 4157010a b )e + (13856700a b c + 4618900a b )d e +--R + +--R 2 2 2 4 2 7 +--R (251940a c + 503880a b c + 41990b )d e +--R + +--R 2 3 3 6 3 2 2 4 5 +--R (- 387600a b c - 129200b c)d e + (103360a c + 155040b c )d e +--R + +--R 3 5 4 4 6 3 +--R - 85120b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 8 +--R 1939938a b e + (4434144a c + 6651216a b )d e +--R + +--R 2 3 2 7 +--R (831402a b c + 277134a b )d e +--R + +--R 2 2 2 4 3 6 +--R (- 302328a c - 604656a b c - 50388b )d e +--R + +--R 2 3 4 5 3 2 2 5 4 +--R (465120a b c + 155040b c)d e + (- 124032a c - 186048b c )d e +--R + +--R 3 6 3 4 7 2 +--R 102144b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 2 7 +--R 3879876a b d e + (554268a c + 831402a b )d e +--R + +--R 2 3 3 6 +--R (- 1108536a b c - 369512a b )d e +--R + +--R 2 2 2 4 4 5 +--R (403104a c + 806208a b c + 67184b )d e +--R + +--R 2 3 5 4 3 2 2 6 3 +--R (- 620160a b c - 206720b c)d e + (165376a c + 248064b c )d e +--R + +--R 3 7 2 4 8 +--R - 136192b c d e + 28672c d e +--R * +--R x +--R + +--R 3 2 7 3 2 2 3 6 +--R 1939938a b d e + (- 1108536a c - 1662804a b )d e +--R + +--R 2 3 4 5 +--R (2217072a b c + 739024a b )d e +--R + +--R 2 2 2 4 5 4 +--R (- 806208a c - 1612416a b c - 134368b )d e +--R + +--R 2 3 6 3 3 2 2 7 2 +--R (1240320a b c + 413440b c)d e + (- 330752a c - 496128b c )d e +--R + +--R 3 8 4 9 +--R 272384b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 4849845e +--R Type: Union(Expression(Integer),...) +--E 748 + +--S 749 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 749 + +--S 750 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 751 + +--S 752 of 845 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(3/2)/e^8+_ + 2/5*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(5/2)/e^8-6/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(7/2)/e^8+2/9*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(9/2)/e^8-10/11*c*_ + (2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(11/2)/e^8+_ + 6/13*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(13/2)/e^8-_ + 14/15*c^3*(2*c*d-b*e)*(d+e*x)^(15/2)/e^8+4/17*c^4*(d+e*x)^(17/2)/e^8 +--R +--R +--R (2) +--R 4 8 8 3 8 4 7 7 +--R 180180c e x + (714714b c e + 12012c d e )x +--R + +--R 3 2 2 8 3 7 4 2 6 6 +--R ((706860a c + 1060290b c )e + 54978b c d e - 12936c d e )x +--R + +--R 2 3 8 3 2 2 7 +--R (2088450a b c + 696150b c)e + (64260a c + 96390b c )d e +--R + +--R 3 2 6 4 3 5 +--R - 59976b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 2 2 4 8 +--R (1021020a c + 2042040a b c + 170170b )e +--R + +--R 2 3 7 3 2 2 2 6 +--R (232050a b c + 77350b c)d e + (- 71400a c - 107100b c )d e +--R + +--R 3 3 5 4 4 4 +--R 66640b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 3 8 +--R (1969110a b c + 656370a b )e +--R + +--R 2 2 2 4 7 +--R (145860a c + 291720a b c + 24310b )d e +--R + +--R 2 3 2 6 3 2 2 3 5 +--R (- 265200a b c - 88400b c)d e + (81600a c + 122400b c )d e +--R + +--R 3 4 4 4 5 3 +--R - 76160b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 8 2 3 7 +--R (612612a c + 918918a b )e + (393822a b c + 131274a b )d e +--R + +--R 2 2 2 4 2 6 +--R (- 175032a c - 350064a b c - 29172b )d e +--R + +--R 2 3 3 5 3 2 2 4 4 +--R (318240a b c + 106080b c)d e + (- 97920a c - 146880b c )d e +--R + +--R 3 5 3 4 6 2 +--R 91392b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 7 +--R 510510a b e + (204204a c + 306306a b )d e +--R + +--R 2 3 2 6 +--R (- 525096a b c - 175032a b )d e +--R + +--R 2 2 2 4 3 5 +--R (233376a c + 466752a b c + 38896b )d e +--R + +--R 2 3 4 4 3 2 2 5 3 +--R (- 424320a b c - 141440b c)d e + (130560a c + 195840b c )d e +--R + +--R 3 6 2 4 7 +--R - 121856b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 2 6 +--R 510510a b d e + (- 408408a c - 612612a b )d e +--R + +--R 2 3 3 5 +--R (1050192a b c + 350064a b )d e +--R + +--R 2 2 2 4 4 4 +--R (- 466752a c - 933504a b c - 77792b )d e +--R + +--R 2 3 5 3 3 2 2 6 2 +--R (848640a b c + 282880b c)d e + (- 261120a c - 391680b c )d e +--R + +--R 3 7 4 8 +--R 243712b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Expression(Integer) +--E 752 + +--S 753 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 8 3 8 4 7 7 +--R 180180c e x + (714714b c e + 12012c d e )x +--R + +--R 3 2 2 8 3 7 4 2 6 6 +--R ((706860a c + 1060290b c )e + 54978b c d e - 12936c d e )x +--R + +--R 2 3 8 3 2 2 7 +--R (2088450a b c + 696150b c)e + (64260a c + 96390b c )d e +--R + +--R 3 2 6 4 3 5 +--R - 59976b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 2 2 4 8 +--R (1021020a c + 2042040a b c + 170170b )e +--R + +--R 2 3 7 3 2 2 2 6 +--R (232050a b c + 77350b c)d e + (- 71400a c - 107100b c )d e +--R + +--R 3 3 5 4 4 4 +--R 66640b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 3 8 +--R (1969110a b c + 656370a b )e +--R + +--R 2 2 2 4 7 +--R (145860a c + 291720a b c + 24310b )d e +--R + +--R 2 3 2 6 3 2 2 3 5 +--R (- 265200a b c - 88400b c)d e + (81600a c + 122400b c )d e +--R + +--R 3 4 4 4 5 3 +--R - 76160b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 8 2 3 7 +--R (612612a c + 918918a b )e + (393822a b c + 131274a b )d e +--R + +--R 2 2 2 4 2 6 +--R (- 175032a c - 350064a b c - 29172b )d e +--R + +--R 2 3 3 5 3 2 2 4 4 +--R (318240a b c + 106080b c)d e + (- 97920a c - 146880b c )d e +--R + +--R 3 5 3 4 6 2 +--R 91392b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 7 +--R 510510a b e + (204204a c + 306306a b )d e +--R + +--R 2 3 2 6 +--R (- 525096a b c - 175032a b )d e +--R + +--R 2 2 2 4 3 5 +--R (233376a c + 466752a b c + 38896b )d e +--R + +--R 2 3 4 4 3 2 2 5 3 +--R (- 424320a b c - 141440b c)d e + (130560a c + 195840b c )d e +--R + +--R 3 6 2 4 7 +--R - 121856b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 2 6 +--R 510510a b d e + (- 408408a c - 612612a b )d e +--R + +--R 2 3 3 5 +--R (1050192a b c + 350064a b )d e +--R + +--R 2 2 2 4 4 4 +--R (- 466752a c - 933504a b c - 77792b )d e +--R + +--R 2 3 5 3 3 2 2 6 2 +--R (848640a b c + 282880b c)d e + (- 261120a c - 391680b c )d e +--R + +--R 3 7 4 8 +--R 243712b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Union(Expression(Integer),...) +--E 753 + +--S 754 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 754 + +--S 755 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 756 + +--S 757 of 845 +r0:=2/3*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(3/2)/e^8-6/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5/2)/e^8+2/7*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(7/2)/e^8-10/9*c*(2*c*d-b*e)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(9/2)/e^8+6/11*c^2*_ + (14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(11/2)/e^8-14/13*c^3*_ + (2*c*d-b*e)*(d+e*x)^(13/2)/e^8+4/15*c^4*(d+e*x)^(15/2)/e^8-_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 12012c e x + (48510b c e - 12936c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((49140a c + 73710b c )e - 52920b c d e + 14112c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (150150a b c + 50050b c)e + (- 54600a c - 81900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 58800b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 +--R (77220a c + 154440a b c + 12870b )e +--R + +--R 2 3 6 3 2 2 2 5 +--R (- 171600a b c - 57200b c)d e + (62400a c + 93600b c )d e +--R + +--R 3 3 4 4 4 3 +--R - 67200b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (162162a b c + 54054a b )e +--R + +--R 2 2 2 4 6 +--R (- 92664a c - 185328a b c - 15444b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 74880a c - 112320b c )d e +--R + +--R 3 4 3 4 5 2 +--R 80640b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 216216a b c - 72072a b )d e +--R + +--R 2 2 2 4 2 5 +--R (123552a c + 247104a b c + 20592b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 274560a b c - 91520b c)d e + (99840a c + 149760b c )d e +--R + +--R 3 5 2 4 6 +--R - 107520b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R 90090a b e + (- 120120a c - 180180a b )d e +--R + +--R 2 3 2 5 +--R (432432a b c + 144144a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 247104a c - 494208a b c - 41184b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (549120a b c + 183040b c)d e + (- 199680a c - 299520b c )d e +--R + +--R 3 6 4 7 +--R 215040b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 757 + +--S 758 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 7 3 7 4 6 6 +--R 12012c e x + (48510b c e - 12936c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((49140a c + 73710b c )e - 52920b c d e + 14112c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (150150a b c + 50050b c)e + (- 54600a c - 81900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 58800b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 +--R (77220a c + 154440a b c + 12870b )e +--R + +--R 2 3 6 3 2 2 2 5 +--R (- 171600a b c - 57200b c)d e + (62400a c + 93600b c )d e +--R + +--R 3 3 4 4 4 3 +--R - 67200b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (162162a b c + 54054a b )e +--R + +--R 2 2 2 4 6 +--R (- 92664a c - 185328a b c - 15444b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 74880a c - 112320b c )d e +--R + +--R 3 4 3 4 5 2 +--R 80640b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 216216a b c - 72072a b )d e +--R + +--R 2 2 2 4 2 5 +--R (123552a c + 247104a b c + 20592b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 274560a b c - 91520b c)d e + (99840a c + 149760b c )d e +--R + +--R 3 5 2 4 6 +--R - 107520b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R 90090a b e + (- 120120a c - 180180a b )d e +--R + +--R 2 3 2 5 +--R (432432a b c + 144144a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 247104a c - 494208a b c - 41184b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (549120a b c + 183040b c)d e + (- 199680a c - 299520b c )d e +--R + +--R 3 6 4 7 +--R 215040b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 758 + +--S 759 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 759 + +--S 760 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 760 + +)clear all + +--S 761 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 761 + +--S 762 of 845 +r0:=-2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^(3/2)/e^8+2/5*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(5/2)/e^8-10/7*c*(2*c*d-b*e)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(7/2)/e^8+2/3*c^2*_ + (14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(9/2)/e^8-14/11*c^3*_ + (2*c*d-b*e)*(d+e*x)^(11/2)/e^8+4/13*c^4*(d+e*x)^(13/2)/e^8+_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*sqrt(d+e*x))+2*(c*d^2-_ + b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 4620c e x + (19110b c e - 5880c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((20020a c + 30030b c )e - 25480b c d e + 7840c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (64350a b c + 21450b c)e + (- 28600a c - 42900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 36400b c d e - 11200c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (36036a c + 72072a b c + 6006b )e + (- 102960a b c - 34320b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (45760a c + 68640b c )d e - 58240b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (90090a b c + 30030a b )e +--R + +--R 2 2 2 4 6 +--R (- 72072a c - 144144a b c - 12012b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 91520a c - 137280b c )d e +--R + +--R 3 4 3 4 5 2 +--R 116480b c d e - 35840c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 360360a b c - 120120a b )d e +--R + +--R 2 2 2 4 2 5 +--R (288288a c + 576576a b c + 48048b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 823680a b c - 274560b c)d e + (366080a c + 549120b c )d e +--R + +--R 3 5 2 4 6 +--R - 465920b c d e + 143360c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R - 30030a b e + (120120a c + 180180a b )d e +--R + +--R 2 3 2 5 +--R (- 720720a b c - 240240a b )d e +--R + +--R 2 2 2 4 3 4 +--R (576576a c + 1153152a b c + 96096b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 1647360a b c - 549120b c)d e + (732160a c + 1098240b c )d e +--R + +--R 3 6 4 7 +--R - 931840b c d e + 286720c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Expression(Integer) +--E 762 + +--S 763 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 7 3 7 4 6 6 +--R 4620c e x + (19110b c e - 5880c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((20020a c + 30030b c )e - 25480b c d e + 7840c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (64350a b c + 21450b c)e + (- 28600a c - 42900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 36400b c d e - 11200c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (36036a c + 72072a b c + 6006b )e + (- 102960a b c - 34320b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (45760a c + 68640b c )d e - 58240b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (90090a b c + 30030a b )e +--R + +--R 2 2 2 4 6 +--R (- 72072a c - 144144a b c - 12012b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 91520a c - 137280b c )d e +--R + +--R 3 4 3 4 5 2 +--R 116480b c d e - 35840c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 360360a b c - 120120a b )d e +--R + +--R 2 2 2 4 2 5 +--R (288288a c + 576576a b c + 48048b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 823680a b c - 274560b c)d e + (366080a c + 549120b c )d e +--R + +--R 3 5 2 4 6 +--R - 465920b c d e + 143360c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R - 30030a b e + (120120a c + 180180a b )d e +--R + +--R 2 3 2 5 +--R (- 720720a b c - 240240a b )d e +--R + +--R 2 2 2 4 3 4 +--R (576576a c + 1153152a b c + 96096b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 1647360a b c - 549120b c)d e + (732160a c + 1098240b c )d e +--R + +--R 3 6 4 7 +--R - 931840b c d e + 286720c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 763 + +--S 764 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 764 + +--S 765 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 765 + +)clear all + +--S 766 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 766 + +--S 767 of 845 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^(3/2))+2/3*_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(3/2)/e^8-_ + 2*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5/2)/_ + e^8+6/7*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(7/2)/_ + e^8-14/9*c^3*(2*c*d-b*e)*(d+e*x)^(9/2)/e^8+4/11*c^4*(d+e*x)^(11/2)/_ + e^8-2*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/_ + (e^8*sqrt(d+e*x))-6*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 252c e x + (1078b c e - 392c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((1188a c + 1782b c )e - 1848b c d e + 672c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (4158a b c + 1386b c)e + (- 2376a c - 3564b c )d e + 3696b c d e +--R + +--R 4 3 4 +--R - 1344c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (2772a c + 5544a b c + 462b )e + (- 11088a b c - 3696b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (6336a c + 9504b c )d e - 9856b c d e + 3584c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (12474a b c + 4158a b )e + (- 16632a c - 33264a b c - 2772b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (66528a b c + 22176b c)d e + (- 38016a c - 57024b c )d e +--R + +--R 3 4 3 4 5 2 +--R 59136b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 2772a c - 4158a b )e + (49896a b c + 16632a b )d e +--R + +--R 2 2 2 4 2 5 +--R (- 66528a c - 133056a b c - 11088b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (266112a b c + 88704b c)d e + (- 152064a c - 228096b c )d e +--R + +--R 3 5 2 4 6 +--R 236544b c d e - 86016c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 462a b e + (- 1848a c - 2772a b )d e + (33264a b c + 11088a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 44352a c - 88704a b c - 7392b )d e + (177408a b c + 59136b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 101376a c - 152064b c )d e + 157696b c d e - 57344c d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Expression(Integer) +--E 767 + +--S 768 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 7 3 7 4 6 6 +--R 252c e x + (1078b c e - 392c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((1188a c + 1782b c )e - 1848b c d e + 672c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (4158a b c + 1386b c)e + (- 2376a c - 3564b c )d e + 3696b c d e +--R + +--R 4 3 4 +--R - 1344c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (2772a c + 5544a b c + 462b )e + (- 11088a b c - 3696b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (6336a c + 9504b c )d e - 9856b c d e + 3584c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (12474a b c + 4158a b )e + (- 16632a c - 33264a b c - 2772b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (66528a b c + 22176b c)d e + (- 38016a c - 57024b c )d e +--R + +--R 3 4 3 4 5 2 +--R 59136b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 2772a c - 4158a b )e + (49896a b c + 16632a b )d e +--R + +--R 2 2 2 4 2 5 +--R (- 66528a c - 133056a b c - 11088b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (266112a b c + 88704b c)d e + (- 152064a c - 228096b c )d e +--R + +--R 3 5 2 4 6 +--R 236544b c d e - 86016c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 462a b e + (- 1848a c - 2772a b )d e + (33264a b c + 11088a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 44352a c - 88704a b c - 7392b )d e + (177408a b c + 59136b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 101376a c - 152064b c )d e + 157696b c d e - 57344c d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 768 + +--S 769 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 770 + +)clear all + +--S 771 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 771 + +--S 772 of 845 +r0:=4/3*(d+e*x)^(3/2)+2*(2*c*d-b*e)*sqrt(d+e*x)/c-atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c^2*d^2+b^2*_ + e^2-2*c*e*(b*d+a*e)+e*(2*c*d-b*e)*sqrt(b^2-4*a*c))/(c^(3/2)*sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e)-_ + e*(2*c*d-b*e)*sqrt(b^2-4*a*c))/(c^(3/2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R 2 +-+ | 2 +--R (- 3b e + 6c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((6a c - 3b )e + 6b c d e - 6c d )\|2 +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 +-+ | 2 +--R (3b e - 6c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((6a c - 3b )e + 6b c d e - 6c d )\|2 +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R (4c e x - 6b e + 16c d)\|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R +-+ | | 2 | | 2 +--R 3c\|c \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 772 + +--S 773 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 3c +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R log +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- a b c + b )e + (2a c - 5b c)d e + 9b c d e - 6c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e +--R + +--R 3 3 +--R 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 +--R (4a c - 4a b )e + (8a b c + 4b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 8a c - 16b c)d e + 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3c +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R log +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (a b c - b )e + (- 2a c + 5b c)d e - 9b c d e + 6c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (4a c - 4a b )e + (8a b c + 4b )d e + (- 8a c - 16b c)d e +--R + +--R 2 3 3 4 +--R 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 3c +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R log +--R - +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- a b c + b )e + (2a c - 5b c)d e + 9b c d e - 6c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e +--R + +--R 3 3 +--R 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 +--R (4a c - 4a b )e + (8a b c + 4b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 8a c - 16b c)d e + 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3c +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R log +--R - +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (a b c - b )e + (- 2a c + 5b c)d e - 9b c d e + 6c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (4a c - 4a b )e + (8a b c + 4b )d e + (- 8a c - 16b c)d e +--R + +--R 2 3 3 4 +--R 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-------+ +--R (8c e x - 12b e + 32c d)\|e x + d +--R / +--R 6c +--R Type: Union(Expression(Integer),...) +--E 773 + +--S 774 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R c\|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- a b c + b )e + (2a c - 5b c)d e + 9b c d e - 6c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e +--R + +--R 3 3 +--R 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 +--R (4a c - 4a b )e + (8a b c + 4b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 8a c - 16b c)d e + 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R c\|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (a b c - b )e + (- 2a c + 5b c)d e - 9b c d e + 6c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (4a c - 4a b )e + (8a b c + 4b )d e + (- 8a c - 16b c)d e +--R + +--R 2 3 3 4 +--R 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R c\|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R - +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- a b c + b )e + (2a c - 5b c)d e + 9b c d e - 6c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e +--R + +--R 3 3 +--R 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 +--R (4a c - 4a b )e + (8a b c + 4b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 8a c - 16b c)d e + 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R c\|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R - +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (a b c - b )e + (- 2a c + 5b c)d e - 9b c d e + 6c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (4a c - 4a b )e + (8a b c + 4b )d e + (- 8a c - 16b c)d e +--R + +--R 2 3 3 4 +--R 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 2 +-+ | 2 +--R (2b e - 4c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((- 4a c + 2b )e - 4b c d e + 4c d )\|2 +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 +-+ | 2 +--R (- 2b e + 4c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((- 4a c + 2b )e - 4b c d e + 4c d )\|2 +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R +-+ | | 2 | | 2 +--R 2c\|c \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 774 + +--S 775 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 775 + +)clear all + +--S 776 of 845 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 776 + +--S 777 of 845 +r0:=4*sqrt(d+e*x)-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ + sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))/sqrt(c)-_ + atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ + sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/sqrt(c) +--R +--R +--R (2) +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|2 \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|2 \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-+ +-------+ +--R 4\|c \|e x + d +--R / +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 777 + +--S 778 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +--R |---------------------------------- +--R \| c +--R * +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log( |---------------------------------- + 2\|e x + d ) +--R \| c +--R + +--R - +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +--R |------------------------------------ +--R \| c +--R * +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log( |------------------------------------ + 2\|e x + d ) +--R \| c +--R + +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +--R |------------------------------------ +--R \| c +--R * +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log(- |------------------------------------ + 2\|e x + d ) +--R \| c +--R + +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +--R |---------------------------------- +--R \| c +--R * +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log(- |---------------------------------- + 2\|e x + d ) +--R \| c +--R + +--R +-------+ +--R 8\|e x + d +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 778 + +--S 779 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R +-+ | \| c +--R \|c |---------------------------------- +--R \| c +--R * +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log( |---------------------------------- + 2\|e x + d ) +--R \| c +--R + +--R - +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R +-+ | \| c +--R \|c |------------------------------------ +--R \| c +--R * +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log( |------------------------------------ + 2\|e x + d ) +--R \| c +--R + +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R +-+ | \| c +--R \|c |------------------------------------ +--R \| c +--R * +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log(- |------------------------------------ + 2\|e x + d ) +--R \| c +--R + +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R +-+ | \| c +--R \|c |---------------------------------- +--R \| c +--R * +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log(- |---------------------------------- + 2\|e x + d ) +--R \| c +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R 2\|2 \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R +-+ | | 2 \|2 \|c \|e x + d +--R 2\|2 \|e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-+ +--R 2\|c +--R Type: Expression(Integer) +--E 779 + +--S 780 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 780 + +)clear all + +--S 781 of 845 +t0:=(b+2*c*x)/((a+b*x+c*x^2)*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) -------------------------- +--R 2 +-------+ +--R (c x + b x + a)\|e x + d +--R Type: Expression(Integer) +--E 781 + +--S 782 of 845 +r0:=-2*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ + sqrt(2)*sqrt(c)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))-2*atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*_ + sqrt(c)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))) +--R +--R +--R (2) +--R - +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 782 + +--S 783 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (a e - b d e + c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R b e - 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R - +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (a e - b d e + c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R ROOT +--R 2 2 +--R (- 4a c + b )e +--R / +--R 2 4 3 2 2 2 3 +--R a e - 2a b d e + (2a c + b )d e - 2b c d e +--R + +--R 2 4 +--R c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (- a e + b d e - c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R b e - 2c d +--R * +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R - +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (- a e + b d e - c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R ROOT +--R 2 2 +--R (- 4a c + b )e +--R / +--R 2 4 3 2 2 2 3 +--R a e - 2a b d e + (2a c + b )d e - 2b c d e +--R + +--R 2 4 +--R c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 783 + +--S 784 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (a e - b d e + c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R b e - 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R - +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 2 +--R (a e - b d e + c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R ROOT +--R 2 2 +--R (- 4a c + b )e +--R / +--R 2 4 3 2 2 2 3 +--R a e - 2a b d e + (2a c + b )d e - 2b c d e +--R + +--R 2 4 +--R c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 2 +--R (- a e + b d e - c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R b e - 2c d +--R * +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R - +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (- a e + b d e - c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R ROOT +--R 2 2 +--R (- 4a c + b )e +--R / +--R 2 4 3 2 2 2 3 +--R a e - 2a b d e + (2a c + b )d e - 2b c d e +--R + +--R 2 4 +--R c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 4\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 4\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R 2\|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 784 + +--S 785 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 845 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------------------- +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 786 + +--S 787 of 845 +r0:=2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))+atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b*e*_ + (b+sqrt(b^2-4*a*c))-2*c*(2*a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*_ + (b*e*(b-sqrt(b^2-4*a*c))+2*c*(-2*a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-_ + b*d*e+a*e^2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +-------+ +--R ((b e - 2c d)\|2 \|- 4a c + b + (4a c - b )e\|2 )\|c \|e x + d +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +-------+ +--R ((b e - 2c d)\|2 \|- 4a c + b + (- 4a c + b )e\|2 )\|c \|e x + d +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R (- 2b e + 4c d)\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 2 | 2 +-------+ +--R (a e - b d e + c d )\|- 4a c + b \|e x + d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 787 + +--S 788 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +-------+ +--R (a e - b d e + c d )\|e x + d +--R * +--R ROOT +--R 3 6 2 5 2 2 2 4 +--R 2a e - 6a b d e + (6a c + 6a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (- 12a b c - 2b )d e + (6a c + 6b c)d e - 6b c d e + 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R * +--R log +--R 3 7 3 2 2 6 2 3 2 5 +--R a b e + (- 2a c - 3a b )d e + (9a b c + 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 6a c - 12a b c - b )d e + (15a b c + 5b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 6a c - 9b c )d e + 7b c d e - 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 2 2 2 4 4 2 3 3 +--R (2a c - 3a b c + b )e + (8a b c - 5b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 8a c + 11b c )d e - 12b c d e + 6c 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)d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R * +--R log +--R 3 7 3 2 2 6 2 3 2 5 +--R - a b e + (2a c + 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (6a c + 12a b c + b )d e + (- 15a b c - 5b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (6a c + 9b c )d e - 7b c d e + 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 2 2 2 4 4 2 3 3 +--R (2a c - 3a b c + b )e + (8a b c - 5b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 8a c + 11b c )d e - 12b c d e + 6c d +--R * +--R ROOT +--R 3 6 2 5 2 2 2 4 +--R - 2a e + 6a b d e + (- 6a c - 6a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (12a b c + 2b )d e + (- 6a c - 6b c)d e + 6b c d e +--R + +--R 3 6 +--R - 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 +--R (- 30a b c - 20b c )d e +--R + +--R 5 2 4 10 2 5 11 6 12 +--R (6a c + 15b c )d e - 6b c d e + c d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 6 2 5 2 2 2 4 +--R a e - 3a b d e + (3a c + 3a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (- 6a b c - b )d e + (3a c + 3b c)d e - 3b c d e + c d +--R + +--R 3 2 2 2 3 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d )\|e x + d +--R + +--R 2 2 +-------+ +--R (- a e + b d e - c d )\|e x + d +--R * +--R ROOT +--R 3 6 2 5 2 2 2 4 +--R 2a e - 6a b d e + (6a c + 6a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (- 12a b c - 2b )d e + (6a c + 6b c)d e - 6b c d e + 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R * +--R log +--R 3 7 3 2 2 6 2 3 2 5 +--R - a b e + (2a c + 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (6a c + 12a b c + b )d e + (- 15a b c - 5b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (6a c + 9b c 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e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 2 2 2 4 4 2 3 3 +--R (2a c - 3a b c + b )e + (8a b c - 5b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 8a c + 11b c )d e - 12b c d e + 6c d +--R * +--R ROOT +--R 3 6 2 5 2 2 2 4 +--R - 2a e + 6a b d e + (- 6a c - 6a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (12a b c 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6b c d e + 4c d +--R / +--R 3 6 2 5 2 2 2 4 +--R a e - 3a b d e + (3a c + 3a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (- 6a b c - b )d e + (3a c + 3b c)d e - 3b c d e + c d +--R + +--R 3 2 2 2 3 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (- a e + b d e - c d )\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 6 2 5 2 2 2 4 +--R 2a e - 6a b d e + (6a c + 6a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (- 12a b c - 2b )d e + (6a c + 6b c)d e - 6b c d e + 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R * +--R log +--R 3 7 3 2 2 6 2 3 2 5 +--R - a b e + (2a c + 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (6a c + 12a b c + b )d e + (- 15a b c - 5b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (6a c + 9b c )d e - 7b c d e + 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 2a c + 3a b c - b )e + (- 8a b c + 5b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (8a c - 11b c )d e + 12b c d e - 6c d +--R * +--R ROOT +--R 3 6 2 5 2 2 2 4 +--R 2a e - 6a b d e + (6a c + 6a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (- 12a b c - 2b )d e + (6a c + 6b c)d e - 6b c d e +--R + +--R 3 6 +--R 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 +--R (- 30a b c - 20b c )d e +--R + +--R 5 2 4 10 2 5 11 6 12 +--R (6a c + 15b c )d e - 6b c d e + c d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 6 2 5 2 2 2 4 +--R a e - 3a b d e + (3a c + 3a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (- 6a b c - b )d e + (3a c + 3b c)d e - 3b c d e + c d +--R + +--R 3 2 2 2 3 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d )\|e x + d +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +--R ((- 2b e + 4c d)\|2 \|- 4a c + b + (- 8a c + 2b )e\|2 )\|c +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +--R ((- 2b e + 4c d)\|2 \|- 4a c + b + (8a c - 2b )e\|2 )\|c +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 789 + +--S 790 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +)clear all + +--S 791 of 845 +t0:=(b+2*c*x)/((d+e*x)^(5/2)*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x +--R + +--R 2 2 +--R (2a d e + b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 791 + +--S 792 of 845 +r0:=2/3*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+_ + 2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))/((c*d^2-b*d*e+a*e^2)^2*_ + sqrt(d+e*x))-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b^2*e^2*(b+sqrt(b^2-4*a*c))+_ + 2*c^2*d*(4*a*e+d*sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e+b*d*_ + sqrt(b^2-4*a*c)+a*e*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*_ + sqrt(c)*(b^2*e^2*(b-sqrt(b^2-4*a*c))-2*c^2*d*(-4*a*e+d*_ + sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e-b*d*sqrt(b^2-4*a*c)-_ + a*e*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((6a c - 3b )e + 6b c d e - 6c d e)x + (6a c - 3b )d e +--R + +--R 2 2 3 +--R 6b c d e - 6c d +--R * +--R +-----------+ +--R +-+ | 2 +--R \|2 \|- 4a c + b +--R + +--R 3 3 2 2 2 +--R ((- 12a b c + 3b )e + (24a c - 6b c)d e )x +--R + +--R 3 2 2 2 2 +--R (- 12a b c + 3b )d e + (24a c - 6b c)d e +--R * +--R +-+ +--R \|2 +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 2 2 +--R ((6a c - 3b )e + 6b c d e - 6c d e)x + (6a c - 3b )d e +--R + +--R 2 2 3 +--R 6b c d e - 6c d +--R * +--R +-----------+ +--R +-+ | 2 +--R \|2 \|- 4a c + b +--R + +--R 3 3 2 2 2 +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e )x +--R + +--R 3 2 2 2 2 +--R (12a b c - 3b )d e + (- 24a c + 6b c)d e +--R * +--R +-+ +--R \|2 +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 3 +--R ((- 12a c + 6b )e - 12b c d e + 12c d e)x - 2a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c + 8b )d e - 18b c d e + 16c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (3a e - 6a b d e + (6a c + 3b )d e - 6b c d e + 3c d e)x + 3a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 6a b d e + (6a c + 3b )d e - 6b c d e + 3c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-------+ | | 2 +--R \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 792 + +--S 793 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 2 2 3 3 2 2 4 +--R (- 3a e + 6a b d e + (- 6a c - 3b )d e + 6b c d e - 3c d e)x +--R + +--R 2 4 2 3 2 3 2 4 2 5 +--R - 3a d e + 6a b d e + (- 6a c - 3b )d e + 6b c d e - 3c d +--R * +--R +-------+ +--R \|e x + d +--R * +--R ROOT +--R 5 10 4 9 4 3 2 2 8 +--R 2a e - 10a b d e + (10a c + 20a b )d e +--R + +--R 3 2 3 3 7 3 2 2 2 4 4 6 +--R (- 40a b c - 20a b )d e + (20a c + 60a b c + 10a b )d e +--R + +--R 2 2 3 5 5 5 +--R (- 60a b c - 40a b c - 2b )d e +--R + +--R 2 3 2 2 4 6 4 3 3 2 7 3 +--R (20a c + 60a b c + 10b c)d e + (- 40a b c - 20b c )d e +--R + +--R 4 2 3 8 2 4 9 5 10 +--R (10a c + 20b c )d e - 10b c d e + 2c d +--R * +--R ROOT +--R 5 5 4 2 4 3 4 3 2 6 2 8 +--R - 4a c + 25a b c - 50a b c + 35a b c - 10a b c +--R + +--R 10 +--R b +--R * +--R 10 +--R e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 80a b c + 300a b c - 270a b c + 90a b c +--R + +--R 9 +--R - 10b c +--R * +--R 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 8 2 +--R (80a c - 740a b c + 900a b c - 360a b c + 45b c ) +--R * +--R 2 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 3 7 +--R (880a b c - 1660a b c + 840a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 4 6 +--R (- 440a c + 1830a b c - 1270a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 5 5 +--R (- 1200a b c + 1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 9 2 8 8 2 +--R (400a b c - 100b c )d e + (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 14 +--R (120a c + 1260a b c + 1260a b c + 210a b )d e +--R + +--R 6 3 5 3 2 4 5 3 7 7 13 +--R (- 840a b c - 2520a b c - 1260a b c - 120a b )d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 252a c + 3150a b c + 4200a b c + 1260a b c +--R + +--R 8 10 +--R 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10b c +--R * +--R 11 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 12 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 13 7 +--R (- 840a b c - 2520a b c - 1260a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 14 6 +--R (120a c + 1260a b c + 1260a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 15 5 +--R (- 360a b c - 840a b c - 252b c )d e +--R + +--R 2 8 2 7 4 6 16 4 +--R (45a c + 360a b c + 210b c )d e +--R + +--R 8 3 7 17 3 9 2 8 18 2 +--R (- 90a b c - 120b c )d e + (10a c + 45b c )d e +--R + +--R 9 19 10 20 +--R - 10b c d e + c d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (- 10a b c + 10a b c - 2b )e + (20a c - 40a b c + 10b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (60a b c - 20b c )d e + (- 40a c + 20b c )d e - 10b c d e +--R + +--R 5 5 +--R 4c d +--R / +--R 5 10 4 9 4 3 2 2 8 +--R a e - 5a b d e + (5a c + 10a b )d e +--R + +--R 3 2 3 3 7 3 2 2 2 4 4 6 +--R (- 20a b c - 10a b )d e + (10a c + 30a b c + 5a b )d e +--R + +--R 2 2 3 5 5 5 2 3 2 2 4 6 4 +--R (- 30a b c - 20a b c - b )d e + (10a c + 30a b c + 5b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 4 9 +--R (- 20a b c - 10b c )d e + (5a c + 10b c )d e - 5b c d e +--R + +--R 5 10 +--R c d +--R * +--R log +--R 6 5 2 12 5 4 3 11 +--R (a c - a b )e + (- 2a b c + 5a b )d e +--R + +--R 5 2 4 2 3 4 2 10 +--R (2a c - 10a b c - 10a b )d e +--R + +--R 4 2 3 3 2 5 3 9 +--R (10a b c + 40a b c + 10a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 8 +--R (- 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90a b c - 120b c )d e +--R + +--R 9 2 8 18 2 9 19 10 20 +--R (10a c + 45b c )d e - 10b c d e + c d +--R + +--R 2 2 3 5 5 +--R (- 10a b c + 10a b c - 2b )e +--R + +--R 2 3 2 2 4 4 3 3 2 2 3 +--R (20a c - 40a b c + 10b c)d e + (60a b c - 20b c )d e +--R + +--R 4 2 3 3 2 4 4 5 5 +--R (- 40a c + 20b c )d e - 10b c d e + 4c d +--R / +--R 5 10 4 9 4 3 2 2 8 +--R a e - 5a b d e + (5a c + 10a b )d e +--R + +--R 3 2 3 3 7 3 2 2 2 4 4 6 +--R (- 20a b c - 10a b )d e + (10a c + 30a b c + 5a b )d e +--R + +--R 2 2 3 5 5 5 +--R (- 30a b c - 20a b c - b )d e +--R + +--R 2 3 2 2 4 6 4 +--R (10a c + 30a b c + 5b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 +--R (- 20a b c - 10b c )d e + (5a c + 10b c )d e +--R + +--R 4 9 5 10 +--R - 5b c d e + c d +--R + +--R 2 5 2 4 4 3 4 5 3 4 3 +--R (4a c - 12a b c + 4b c )e + (40a b c - 20b c )d e +--R + +--R 6 2 5 2 2 6 3 7 4 +--R (- 40a c + 40b c )d e - 40b c d e + 20c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 5 4 2 2 3 3 2 2 4 +--R (- 3a e + 6a b d e + (- 6a 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3 7 +--R (880a b c - 1660a b c + 840a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 4 6 +--R (- 440a c + 1830a b c - 1270a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 5 5 +--R (- 1200a b c + 1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 9 2 8 8 2 +--R (400a b c - 100b c )d e + (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 14 +--R (120a c + 1260a b c + 1260a b c + 210a b )d e +--R + +--R 6 3 5 3 2 4 5 3 7 7 13 +--R (- 840a b c - 2520a b c - 1260a b c - 120a b )d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 252a c + 3150a b c + 4200a b c + 1260a b c +--R + +--R 8 10 +--R 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10b c +--R * +--R 11 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 12 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 13 7 +--R (- 840a b c - 2520a b c - 1260a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 14 6 +--R (120a c + 1260a b c + 1260a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 15 5 +--R (- 360a b c - 840a b c - 252b c )d e +--R + +--R 2 8 2 7 4 6 16 4 +--R (45a c + 360a b c + 210b c )d e +--R + +--R 8 3 7 17 3 9 2 8 18 2 +--R (- 90a b c - 120b c )d e + (10a c + 45b c )d e +--R + +--R 9 19 10 20 +--R - 10b c d e + c d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (- 10a b c + 10a b c - 2b )e + (20a c - 40a b c + 10b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (60a b c - 20b c )d e + (- 40a c + 20b c )d e - 10b c d e +--R + +--R 5 5 +--R 4c d +--R / +--R 5 10 4 9 4 3 2 2 8 +--R a e - 5a b d e + (5a c + 10a b )d e +--R + +--R 3 2 3 3 7 3 2 2 2 4 4 6 +--R (- 20a b c - 10a b )d e + (10a c + 30a b c + 5a b )d e +--R + +--R 2 2 3 5 5 5 2 3 2 2 4 6 4 +--R (- 30a b c - 20a b c - b )d e + (10a c + 30a b c + 5b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 4 9 +--R (- 20a b c - 10b c )d e + (5a c + 10b c )d e - 5b c d e +--R + +--R 5 10 +--R c d +--R * +--R log +--R 6 5 2 12 5 4 3 11 +--R (- a c + a b )e + (2a b c - 5a b )d e +--R + +--R 5 2 4 2 3 4 2 10 +--R (- 2a c + 10a b c + 10a b )d e +--R + +--R 4 2 3 3 2 5 3 9 +--R (- 10a b c - 40a b c - 10a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 8 +--R (5a c + 70a b c + 55a b c + 5a b )d e +--R + +--R 3 3 2 3 2 5 7 5 7 +--R (- 60a b c - 130a b c - 34a b c - b )d e +--R + +--R 3 4 2 2 3 4 2 6 6 6 +--R (20a c + 160a b c + 100a b c + 8b c)d e +--R + +--R 2 4 3 3 5 2 7 5 +--R (- 100a b c - 160a b c - 28b c )d e +--R + +--R 2 5 2 4 4 3 8 4 +--R (25a c + 145a b c + 55b c )d e +--R + +--R 5 3 4 9 3 6 2 5 10 2 +--R (- 70a b c - 65b c )d e + (14a c + 46b c )d e +--R + +--R 6 11 7 12 +--R - 18b c d e + 3c d +--R * +--R ROOT +--R 5 5 4 2 4 3 4 3 2 6 2 +--R - 4a c + 25a b c - 50a b c + 35a b c +--R + +--R 8 10 +--R - 10a b c + b +--R * +--R 10 +--R e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 80a b c + 300a b c - 270a b c + 90a b c +--R + +--R 9 +--R - 10b c +--R * +--R 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 80a c - 740a b c + 900a b c - 360a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 2 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 3 7 +--R (880a b c - 1660a b c + 840a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 4 6 +--R (- 440a c + 1830a b c - 1270a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 5 5 +--R (- 1200a b c + 1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 9 2 8 8 2 +--R (400a b c - 100b c )d e + (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 14 +--R (120a c + 1260a b c + 1260a b c + 210a b )d e +--R + +--R 6 3 5 3 2 4 5 3 7 7 13 +--R (- 840a b c - 2520a b c - 1260a b c - 120a b )d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 252a c + 3150a b c + 4200a b c + 1260a b c +--R + +--R 8 10 +--R 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 1260a b c - 4200a b c - 2520a b c +--R + +--R 7 2 9 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65b c )d e - 35b c d e + 10c d +--R * +--R ROOT +--R 5 10 4 9 4 3 2 2 8 +--R - 2a e + 10a b d e + (- 10a c - 20a b )d e +--R + +--R 3 2 3 3 7 +--R (40a b c + 20a b )d e +--R + +--R 3 2 2 2 4 4 6 +--R (- 20a c - 60a b c - 10a b )d e +--R + +--R 2 2 3 5 5 5 +--R (60a b c + 40a b c + 2b )d e +--R + +--R 2 3 2 2 4 6 4 +--R (- 20a c - 60a b c - 10b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 +--R (40a b c + 20b c )d e + (- 10a c - 20b c )d e +--R + +--R 4 9 5 10 +--R 10b c d e - 2c d +--R * +--R ROOT +--R 5 5 4 2 4 3 4 3 2 6 2 +--R - 4a c + 25a b c - 50a b c + 35a b c +--R + +--R 8 10 +--R - 10a b c + b +--R * +--R 10 +--R e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 80a b c + 300a b c - 270a b c +--R + +--R 7 2 9 +--R 90a b c - 10b c +--R * +--R 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 80a c - 740a b c + 900a b c - 360a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 2 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 +--R (880a b c - 1660a b c + 840a b c - 120b c ) +--R * +--R 3 7 +--R d e +--R + +--R 3 7 2 2 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840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 14 +--R (120a c + 1260a b c + 1260a b c + 210a b )d e +--R + +--R 6 3 5 3 2 4 5 3 7 7 13 +--R (- 840a b c - 2520a b c - 1260a b c - 120a b )d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 252a c + 3150a b c + 4200a b c + 1260a b c +--R + +--R 8 10 +--R 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10b c +--R * +--R 11 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 12 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 13 7 +--R (- 840a b c - 2520a b c - 1260a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 14 6 +--R (120a c + 1260a b c + 1260a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 15 5 +--R (- 360a b c - 840a b c - 252b c )d e +--R + +--R 2 8 2 7 4 6 16 4 +--R (45a c + 360a b c + 210b c )d e +--R + +--R 8 3 7 17 3 9 2 8 18 2 +--R (- 90a b c - 120b c )d e + (10a c + 45b c )d e +--R + +--R 9 19 10 20 +--R - 10b c d e + c d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (- 10a b c + 10a b c - 2b )e + (20a c - 40a b c + 10b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (60a b c - 20b c )d e + (- 40a c + 20b c )d e - 10b c d e +--R + +--R 5 5 +--R 4c d +--R / +--R 5 10 4 9 4 3 2 2 8 +--R a e - 5a b d e + (5a c + 10a b )d e +--R + +--R 3 2 3 3 7 3 2 2 2 4 4 6 +--R (- 20a b c - 10a b )d e + (10a c + 30a b c + 5a b )d e +--R + +--R 2 2 3 5 5 5 2 3 2 2 4 6 4 +--R (- 30a b c - 20a b c - b )d e + (10a c + 30a b c + 5b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 4 9 +--R (- 20a b c - 10b c )d e + (5a c + 10b c )d e - 5b c d e +--R + +--R 5 10 +--R c d +--R * +--R log +--R 6 5 2 12 5 4 3 11 +--R (- a c + a b )e + (2a b c - 5a b )d e +--R + +--R 5 2 4 2 3 4 2 10 +--R (- 2a c + 10a b c + 10a b )d e +--R + +--R 4 2 3 3 2 5 3 9 +--R (- 10a b c - 40a b c - 10a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 8 +--R (5a c + 70a b c + 55a b c + 5a b )d e +--R + +--R 3 3 2 3 2 5 7 5 7 +--R (- 60a b c - 130a b c - 34a b c - b )d e +--R + +--R 3 4 2 2 3 4 2 6 6 6 +--R (20a c + 160a b c + 100a b c + 8b c)d e +--R + +--R 2 4 3 3 5 2 7 5 +--R (- 100a b c - 160a b c - 28b c )d e +--R + +--R 2 5 2 4 4 3 8 4 +--R (25a c + 145a b c + 55b c )d e +--R + +--R 5 3 4 9 3 6 2 5 10 2 +--R (- 70a b c - 65b c )d e + (14a c + 46b c )d e +--R + +--R 6 11 7 12 +--R - 18b c d e + 3c d +--R * +--R ROOT +--R 5 5 4 2 4 3 4 3 2 6 2 +--R - 4a c + 25a b c - 50a b c + 35a b c +--R + +--R 8 10 +--R - 10a b c + b +--R * +--R 10 +--R e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 80a b c + 300a b c - 270a b c + 90a b c +--R + +--R 9 +--R - 10b c +--R * +--R 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 80a c - 740a b c + 900a b c - 360a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 2 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 3 7 +--R (880a b c - 1660a b c + 840a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 4 6 +--R (- 440a c + 1830a b c - 1270a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 5 5 +--R (- 1200a b c + 1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 9 2 8 8 2 +--R (400a b c - 100b c )d e + (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 14 +--R (120a c + 1260a b c + 1260a b c + 210a b )d e +--R + +--R 6 3 5 3 2 4 5 3 7 7 13 +--R (- 840a b c - 2520a b c - 1260a b c - 120a b )d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 252a c + 3150a b c + 4200a b c + 1260a b c +--R + +--R 8 10 +--R 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 1260a b c - 4200a b c - 2520a b c +--R + +--R 7 2 9 +--R - 360a b c - 10b c +--R * +--R 11 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 12 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 +--R (- 840a b c - 2520a b c - 1260a b c - 120b c ) +--R * +--R 13 7 +--R d e +--R + +--R 3 7 2 2 6 4 5 6 4 14 6 +--R (120a c + 1260a b c + 1260a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 15 5 +--R (- 360a b c - 840a b c - 252b c )d e +--R + +--R 2 8 2 7 4 6 16 4 +--R (45a c + 360a b c + 210b c )d e +--R + +--R 8 3 7 17 3 9 2 8 18 2 +--R (- 90a b c - 120b c )d e + (10a c + 45b c )d e +--R + +--R 9 19 10 20 +--R - 10b c d e + c d +--R + +--R 3 3 2 3 2 5 7 7 +--R (- 3a b c + 10a b c - 6a b c + b )e +--R + +--R 3 4 2 2 3 4 2 6 6 +--R (6a c - 51a b c + 40a b c - 8b c)d e +--R + +--R 2 4 3 3 5 2 2 5 +--R (93a b c - 109a b c + 28b c )d e +--R + +--R 2 5 2 4 4 3 3 4 +--R (- 62a c + 156a b c - 57b c )d e +--R + +--R 5 3 4 4 3 6 2 5 5 2 6 6 +--R (- 125a b c + 75b c )d e + (50a c - 65b c )d e + 35b c d e +--R + +--R 7 7 +--R - 10c d +--R * +--R ROOT +--R 5 10 4 9 4 3 2 2 8 +--R 2a e - 10a b d e + (10a c + 20a b )d e +--R + +--R 3 2 3 3 7 +--R (- 40a b c - 20a b )d e +--R + +--R 3 2 2 2 4 4 6 +--R (20a c + 60a b c + 10a b )d e +--R + +--R 2 2 3 5 5 5 +--R (- 60a b c - 40a b c - 2b )d e +--R + +--R 2 3 2 2 4 6 4 +--R (20a c + 60a b c + 10b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 +--R (- 40a b c - 20b c )d e + (10a c + 20b c )d e +--R + +--R 4 9 5 10 +--R - 10b c d e + 2c d +--R * +--R ROOT +--R 5 5 4 2 4 3 4 3 2 6 2 +--R - 4a c + 25a b c - 50a b c + 35a b c +--R + +--R 8 10 +--R - 10a b c + b +--R * +--R 10 +--R e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 80a b c + 300a b c - 270a b c +--R + +--R 7 2 9 +--R 90a b c - 10b c +--R * +--R 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 80a c - 740a b c + 900a b c - 360a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 2 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 +--R (880a b c - 1660a b c + 840a b c - 120b c ) +--R * +--R 3 7 +--R d e +--R + +--R 3 7 2 2 6 4 5 +--R - 440a c + 1830a b c - 1270a b c +--R + +--R 6 4 +--R 210b c +--R * +--R 4 6 +--R d e +--R + +--R 2 7 3 6 5 5 5 5 +--R (- 1200a b c + 1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 +--R (400a b c - 100b c )d e +--R + +--R 9 2 8 8 2 +--R (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 +--R (120a c + 1260a b c + 1260a b c + 210a b )d +--R * +--R 14 +--R e +--R + +--R 6 3 5 3 2 4 5 +--R - 840a b c - 2520a b c - 1260a b c +--R + +--R 3 7 +--R - 120a b +--R * +--R 7 13 +--R d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 +--R - 1260a b c - 4200a b c - 2520a b c +--R + +--R 2 7 9 +--R - 360a b c - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 +--R 252a c + 3150a b c + 4200a b c +--R + +--R 2 6 2 8 10 +--R 1260a b c + 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 1260a b c - 4200a b c - 2520a b c +--R + +--R 7 2 9 +--R - 360a b c - 10b c +--R * +--R 11 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 +--R 210a c + 2520a b c + 3150a b c +--R + +--R 6 3 8 2 +--R 840a b c + 45b c +--R * +--R 12 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 +--R - 840a b c - 2520a b c - 1260a b c +--R + +--R 7 3 +--R - 120b c +--R * +--R 13 7 +--R d e +--R + +--R 3 7 2 2 6 4 5 6 4 +--R (120a c + 1260a b c + 1260a b c + 210b c ) +--R * +--R 14 6 +--R d e +--R + +--R 2 7 3 6 5 5 15 5 +--R (- 360a b c - 840a b c - 252b c )d e +--R + +--R 2 8 2 7 4 6 16 4 +--R (45a c + 360a b c + 210b c )d e +--R + +--R 8 3 7 17 3 +--R (- 90a b c - 120b c )d e +--R + +--R 9 2 8 18 2 9 19 10 20 +--R (10a c + 45b c )d e - 10b c d e + c d +--R + +--R 2 2 3 5 5 +--R (- 10a b c + 10a b c - 2b )e +--R + +--R 2 3 2 2 4 4 3 3 2 2 3 +--R (20a c - 40a b c + 10b c)d e + (60a b c - 20b c )d e +--R + +--R 4 2 3 3 2 4 4 5 5 +--R (- 40a c + 20b c )d e - 10b c d e + 4c d +--R / +--R 5 10 4 9 4 3 2 2 8 +--R a e - 5a b d e + (5a c + 10a b )d e +--R + +--R 3 2 3 3 7 3 2 2 2 4 4 6 +--R (- 20a b c - 10a b )d e + (10a c + 30a b c + 5a b )d e +--R + +--R 2 2 3 5 5 5 +--R (- 30a b c - 20a b c - b )d e +--R + +--R 2 3 2 2 4 6 4 +--R (10a c + 30a b c + 5b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 +--R (- 20a b c - 10b c )d e + (5a c + 10b c )d e +--R + +--R 4 9 5 10 +--R - 5b c d e + c d +--R + +--R 2 5 2 4 4 3 4 5 3 4 3 +--R (4a c - 12a b c + 4b c )e + (40a b c - 20b c )d e +--R + +--R 6 2 5 2 2 6 3 7 4 +--R (- 40a c + 40b c )d e - 40b c d e + 20c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 2 2 2 2 +-+ | 2 +--R ((- 4a c + 2b )e - 4b c d e + 4c d )\|2 \|- 4a c + b +--R + +--R 3 2 2 2 +-+ +--R ((8a b c - 2b )e + (- 16a c + 4b c)d e)\|2 +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 2 2 2 +-+ | 2 +--R ((- 4a c + 2b )e - 4b c d e + 4c d )\|2 \|- 4a c + b +--R + +--R 3 2 2 2 +-+ +--R ((- 8a b c + 2b )e + (16a c - 4b c)d e)\|2 +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d )\|- 4a c + b +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 794 + +--S 795 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 795 + +)clear all + +--S 796 of 845 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 796 + +--S 797 of 845 +r0:=-(d+e*x)^(5/2)/(a+b*x+c*x^2)+5*e^2*sqrt(d+e*x)/c-5*e*atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))/sqrt(b^2-4*a*c))/(c^(3/2)*_ + sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-5*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (-2*c^2*d^2-b^2*e^2+2*c*e*(b*d+a*e))/sqrt(b^2-4*a*c))/(c^(3/2)*_ + sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 2 2 3 2 3 +--R (5b c e - 10c d e )x + (5b e - 10b c d e )x + 5a b e +--R + +--R 2 +--R - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((- 10a c + 5b c)e - 10b c d e + 10c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 10a b c + 5b )e - 10b c d e + 10b c d e)x + (- 10a c + 5a b )e +--R + +--R 2 2 2 +--R - 10a b c d e + 10a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 3 +--R (5b c e - 10c d e )x + (5b e - 10b c d e )x + 5a b e +--R + +--R 2 +--R - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((10a c - 5b c)e + 10b c d e - 10c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((10a b c - 5b )e + 10b c d e - 10b c d e)x + (10a c - 5a b )e +--R + +--R 2 2 2 +--R 10a b c d e - 10a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 2 2 2 2 +-+ | 2 +-+ +--R (4c e x + (5b e - 2c d e)x + 5a e - c d )\|2 \|- 4a c + b \|c +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-------+ | | 2 +--R \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 2 +-+ | 2 +-+ +--R (c x + b c x + a c)\|2 \|- 4a c + b \|c +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 797 + +--S 798 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (c x + b c x + a c) +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R log +--R 4 3 3 5 2 4 +--R ((16a b c - 4b c )e + (- 32a c + 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (- 100a c + 125a b c - 25b )e + (- 300a b c + 75b c)d e +--R + +--R 3 2 2 2 4 +--R (300a c - 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +--R (- c x - b c x - a c) +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R log +--R 4 3 3 5 2 4 +--R ((16a b c - 4b c )e + (- 32a c + 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (100a c - 125a b c + 25b )e + (300a b c - 75b c)d e +--R + +--R 3 2 2 2 4 +--R (- 300a c + 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +--R (c x + b c x + a c) +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * 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3 +--R 8a c - 2b c +--R * +--R log +--R 4 3 3 5 2 4 +--R ((- 16a b c + 4b c )e + (32a c - 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (100a c - 125a b c + 25b )e + (300a b c - 75b c)d e +--R + +--R 3 2 2 2 4 +--R (- 300a c + 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 2 2 2 +-------+ +--R (8c e x + (10b e - 4c d e)x + 10a e - 2c d )\|e x + d +--R / +--R 2 2 +--R 2c x + 2b c x + 2a c +--R Type: Union(Expression(Integer),...) +--E 798 + +--S 799 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R c\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 3 3 5 2 4 +--R ((16a b c - 4b c )e + (- 32a c + 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (- 100a c + 125a b c - 25b )e + (- 300a b c + 75b c)d e +--R + +--R 3 2 2 2 4 +--R (300a c - 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R c\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 3 3 5 2 4 +--R ((16a b c - 4b c )e + (- 32a c + 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (100a c - 125a b c + 25b )e + (300a b c - 75b c)d e +--R + +--R 3 2 2 2 4 +--R (- 300a c + 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e +--R + +--R 2 2 3 3 3 2 +--R 75b c d e - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R c\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 3 3 5 2 4 +--R ((- 16a b c + 4b c )e + (32a c - 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (- 100a c + 125a b c - 25b )e + (- 300a b c + 75b c)d e +--R + +--R 3 2 2 2 4 +--R (300a c - 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R c\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 3 3 5 2 4 +--R ((- 16a b c + 4b c )e + (32a c - 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (100a c - 125a b c + 25b )e + (300a b c - 75b c)d e +--R + +--R 3 2 2 2 4 +--R (- 300a c + 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e +--R + +--R 2 2 3 3 3 2 +--R 75b c d e - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 10b e + 20c d e )\|- 4a c + b + (20a c - 10b )e + 20b c d e +--R + +--R 2 2 +--R - 20c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 10b e + 20c d e )\|- 4a c + b + (- 20a c + 10b )e - 20b c d e +--R + +--R 2 2 +--R 20c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R 2c\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 799 + +--S 800 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 800 + +)clear all + +--S 801 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 801 + +--S 802 of 845 +r0:=-(d+e*x)^(3/2)/(a+b*x+c*x^2)-3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ + (sqrt(2)*sqrt(c)*sqrt(b^2-4*a*c))+3*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c)))/(sqrt(2)*sqrt(c)*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R +------------------------------+ +--R | +-----------+ +--R 2 | | 2 +--R (3c e x + 3b e x + 3a e)\|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R | +-----------+ +--R 2 | | 2 +--R (- 3c e x - 3b e x - 3a e)\|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-------+ +--R (- e x - d)\|2 \|- 4a c + b \|c \|e x + d +--R / +--R +-----------+ +--R 2 +-+ | 2 +-+ +--R (c x + b x + a)\|2 \|- 4a c + b \|c +--R Type: Expression(Integer) +--E 802 + +--S 803 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (c x + b x + a) +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R 2 +--R (- c x - b x - a) +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R 2 +--R (c x + b x + a) +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R 2 +--R (- c x - b x - a) +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R +-------+ +--R (- 2e x - 2d)\|e x + d +--R / +--R 2 +--R 2c x + 2b x + 2a +--R Type: Union(Expression(Integer),...) +--E 803 + +--S 804 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-+ | 2 +-+ +--R \|2 \|- 4a c + b \|c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R - +--R +-----------+ +--R +-+ | 2 +-+ +--R \|2 \|- 4a c + b \|c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R \|2 \|- 4a c + b \|c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R - +--R +-----------+ +--R +-+ | 2 +-+ +--R \|2 \|- 4a c + b \|c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R - +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R 6e\|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R 6e\|e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R +-+ | 2 +-+ +--R 2\|2 \|- 4a c + b \|c +--R Type: Expression(Integer) +--E 804 + +--S 805 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 805 + +)clear all + +--S 806 of 845 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^2 +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 806 + +--S 807 of 845 +r0:=-sqrt(d+e*x)/(a+b*x+c*x^2)-e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/(sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/_ + (sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +----------------------------+ +--R | +-----------+ +--R 2 +-+ +-+ | | 2 +--R (c e x + b e x + a e)\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R 2 +-+ +-+ | | 2 +--R (- c e x - b e x - a e)\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-------+ | | 2 +--R \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 +--R (c x + b x + a)\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 807 + +--S 808 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (c x + b x + a) +--R * +--R ROOT +--R 2 2 2 3 2 2 2 +--R ((16a c - 4a b )e + (- 16a b c + 4b )d e + (16a c - 4b c)d ) +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (16a b c - 4a b )e + (- 32a c - 8a b c + 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (48a b c - 12b c)d e + (- 32a c + 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (4a c - b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (16a c - 4a b )e + (- 16a b c + 4b )d e +--R + +--R 2 2 2 +--R (16a c - 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R 2 +--R (- c x - b x - a) +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (16a b c - 4a b )e + (- 32a c - 8a b c + 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (48a b c - 12b c)d e + (- 32a c + 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (- 4a c + b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R 2 +--R (c x + b x + a) +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (- 16a b c + 4a b )e + (32a c + 8a b c - 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (- 48a b c + 12b c)d e + (32a c - 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (4a c - b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R 2 +--R (- c x - b x - a) +--R * +--R ROOT +--R 2 2 2 3 2 2 2 +--R ((16a c - 4a b )e + (- 16a b c + 4b )d e + (16a c - 4b c)d ) +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (- 16a b c + 4a b )e + (32a c + 8a b c - 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (- 48a b c + 12b c)d e + (32a c - 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (- 4a c + b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (16a c - 4a b )e + (- 16a b c + 4b )d e +--R + +--R 2 2 2 +--R (16a c - 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R +-------+ +--R - 2\|e x + d +--R / +--R 2 +--R 2c x + 2b x + 2a +--R Type: Union(Expression(Integer),...) +--E 808 + +--S 809 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 2 3 2 2 2 +--R ((16a c - 4a b )e + (- 16a b c + 4b )d e + (16a c - 4b c)d ) +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (16a b c - 4a b )e + (- 32a c - 8a b c + 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (48a b c - 12b c)d e + (- 32a c + 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (4a c - b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (16a c - 4a b )e + (- 16a b c + 4b )d e +--R + +--R 2 2 2 +--R (16a c - 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (16a b c - 4a b )e + (- 32a c - 8a b c + 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (48a b c - 12b c)d e + (- 32a c + 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (- 4a c + b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 +--R (- 128a b c + 32b c)d e +--R + +--R 3 2 2 4 +--R (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e +--R + +--R 2 2 2 +--R (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (- 16a b c + 4a b )e + (32a c + 8a b c - 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (- 48a b c + 12b c)d e + (32a c - 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (4a c - b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 2 3 +--R (16a c - 4a b )e + (- 16a b c + 4b )d e +--R + +--R 2 2 2 +--R (16a c - 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (- 16a b c + 4a b )e + (32a c + 8a b c - 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (- 48a b c + 12b c)d e + (32a c - 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (- 4a c + b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (16a c - 4a b )e + (- 16a b c + 4b )d e +--R + +--R 2 2 2 +--R (16a c - 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 +--R (- 128a b c + 32b c)d e +--R + +--R 3 2 2 4 +--R (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e +--R + +--R 2 2 2 +--R (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R - +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2e\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2e\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R 2\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 809 + +--S 810 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 810 + +)clear all + +--S 811 of 845 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) -------------------------------------------------------- +--R 2 4 3 2 2 2 +-------+ +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 811 + +--S 812 of 845 +r0:=-((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))+e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(2*c*d-e*(b+_ + sqrt(b^2-4*a*c)))/((c*d^2-e*(b*d-a*e))*sqrt(2)*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(2*c*d-_ + e*(b-sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R 2 2 2 2 | 2 2 2 2 +--R (- c e x - b e x - a e )\|- 4a c + b + (b c e - 2c d e)x +--R + +--R 2 2 2 +--R (b e - 2b c d e)x + a b e - 2a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 2 2 2 | 2 2 2 2 +--R (- c e x - b e x - a e )\|- 4a c + b + (- b c e + 2c d e)x +--R + +--R 2 2 2 +--R (- b e + 2b c d e)x - a b e + 2a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-------+ +--R (c e x + b e - c d)\|2 \|- 4a c + b \|e x + d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (a c e - b c d e + c d )x + (a b e - b d e + b c d )x + a e +--R + +--R 2 +--R - a b d e + a c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 812 + +--S 813 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R (a c e - b c d e + c d )x + (a b e - b d e + b c d )x + a e +--R + +--R 2 +--R - a b d e + a c d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (16a c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (48a c + 36a b c - 12a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 96a b c + 8a b c + 4b 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9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (64a c - 16a b )e + (- 384a b c + 96a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (384a c + 864a b c - 240a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 1920a b c - 800a b c + 320a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (960a c + 3600a b c - 240a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 3840a b c - 2880a b c + 576a b c + 96a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 +--R 1280a c + 5440a b c + 480a b c - 416a b c +--R + +--R 8 +--R - 16b +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 3840a b c - 2880a b c + 576a b c + 96b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (960a c + 3600a b c - 240b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 1920a b c - 800a b c + 320b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (384a c + 864a b c - 240b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 384a b c + 96b c )d e + (64a c - 16b c )d +--R + +--R 2 2 3 5 7 2 3 2 2 4 6 +--R (4a b c - 5a b c + b )e + (- 8a c + 22a b c - 5b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (- 36a b c + 9b c )d e + (24a c - 6b c )d e +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (- 16a c + 4a b )e + (48a b c - 12a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (- 48a c - 36a b c + 12a b )d e +--R + +--R 2 2 3 5 3 3 +--R (96a b c - 8a b c - 4b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (- 48a c - 36a b c + 12b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (48a b c - 12b c )d e + (- 16a c + 4b c )d +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 9 3 2 2 2 8 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 7 4 4 6 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (64a c - 16a b )e + (- 384a b c + 96a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (384a c + 864a b c - 240a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 1920a b c - 800a b c + 320a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (960a c + 3600a b c - 240a b )d e +--R + +--R 4 3 3 3 2 2 5 +--R - 3840a b c - 2880a b c + 576a b c +--R + +--R 7 +--R 96a b +--R * +--R 5 7 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 6 +--R 1280a c + 5440a b c + 480a b c - 416a b c +--R + +--R 8 +--R - 16b +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 3840a b c - 2880a b c + 576a b c +--R + +--R 7 +--R 96b c +--R * +--R 7 5 +--R d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (960a c + 3600a b c - 240b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 1920a b c - 800a b c + 320b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (384a c + 864a b c - 240b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 384a b c + 96b c )d e + (64a c - 16b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 3a b c + b )e + (6a c - 3b c)d e + 3b c d e +--R + +--R 3 3 2 +--R - 2c d e +--R / +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R + +--R 3 2 2 6 3 5 4 2 4 +-------+ +--R ((2a c - 2b c )e + 6b c d e - 6c d e )\|e x + d +--R + +--R +-----------+ +--R 2 2 +-+ | 2 +--R (- a e + b d e - c d )\|2 \|- 4a c + b +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (16a c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (48a c + 36a b c - 12a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 96a b c + 8a b c + 4b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (48a c + 36a b c - 12b c)d e + (- 48a b c + 12b c )d e +--R + +--R 4 2 3 6 +--R (16a c - 4b c )d +--R * +--R ROOT +--R 2 2 2 4 10 2 3 9 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (64a c - 16a b )e + (- 384a b c + 96a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (384a c + 864a b c - 240a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 1920a b c - 800a b c + 320a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (960a c + 3600a b c - 240a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 3840a b c - 2880a b c + 576a b c + 96a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (1280a c + 5440a b c + 480a b c - 416a b c - 16b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 3840a b c - 2880a b c + 576a b c + 96b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (960a c + 3600a b c - 240b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 1920a b c - 800a b c + 320b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (384a c + 864a b c - 240b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 384a b c + 96b c )d e + (64a c - 16b c )d +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 +--R (- 3a b c + b )e + (6a c - 3b c)d e + 3b c d e - 2c d e +--R / +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (- 32a c + 24a b c - 4a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (64a b c - 64a b c + 12a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (- 64a c + 64a b c + 36a b c - 12a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (- 160a b c + 24a b c + 4b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (240a b c + 20a b c - 20b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (- 192a b c - 128a b c + 44b c )d e +--R + +--R 2 5 2 4 4 3 6 2 +--R (64a c + 192a b c - 52b c )d e +--R + +--R 5 3 4 7 6 2 5 8 +--R (- 128a b c + 32b c )d e + (32a c - 8b c )d +--R * +--R ROOT +--R 2 2 2 4 10 2 3 9 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (64a c - 16a b )e + (- 384a b c + 96a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (384a c + 864a b c - 240a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 1920a b c - 800a b c + 320a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (960a c + 3600a b c - 240a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 3840a b c - 2880a b c + 576a b c + 96a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 +--R 1280a c + 5440a b c + 480a b c - 416a b c +--R + +--R 8 +--R - 16b +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 3840a b c - 2880a b c + 576a b c + 96b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (960a c + 3600a b c - 240b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 1920a b c - 800a b c + 320b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (384a c + 864a b c - 240b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 384a b c + 96b c )d e + (64a c - 16b c )d +--R + +--R 2 2 3 5 7 2 3 2 2 4 6 +--R (- 4a b c + 5a b c - b )e + (8a c - 22a b c + 5b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (36a b c - 9b c )d e + (- 24a c + 6b c )d e +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (16a c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (48a c + 36a b c - 12a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 96a b c + 8a b c + 4b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (48a c + 36a b c - 12b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (- 48a b c + 12b c )d e + (16a c - 4b c )d +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 9 3 2 2 2 8 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 7 4 4 6 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (64a c - 16a b )e + (- 384a b c + 96a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (384a c + 864a b c - 240a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 1920a b c - 800a b c + 320a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (960a c + 3600a b c - 240a b )d e +--R + +--R 4 3 3 3 2 2 5 +--R - 3840a b c - 2880a b c + 576a b c +--R + +--R 7 +--R 96a b +--R * +--R 5 7 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 6 +--R 1280a c + 5440a b c + 480a b c - 416a b c +--R + +--R 8 +--R - 16b +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 3840a b c - 2880a b c + 576a b c +--R + +--R 7 +--R 96b c +--R * +--R 7 5 +--R d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (960a c + 3600a b c - 240b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 1920a b c - 800a b c + 320b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (384a c + 864a b c - 240b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 384a b c + 96b c )d e + (64a c - 16b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 3a b c + b )e + (6a c - 3b c)d e + 3b c d e +--R + +--R 3 3 2 +--R - 2c d e +--R / +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R + +--R 3 2 2 6 3 5 4 2 4 +-------+ +--R ((2a c - 2b c )e + 6b c d e - 6c d e )\|e x + d +--R + +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 2 +-+ | | 2 +--R (2e \|- 4a c + b - 2b e + 4c d e)\|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 | 2 2 +-+ +--R (2e \|- 4a c + b + 2b e - 4c d e)\|c +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 2 +-+ | 2 +--R (2a e - 2b d e + 2c d )\|2 \|- 4a c + b +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 814 + +--S 815 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 815 + +)clear all + +--S 816 of 845 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 816 + +--S 817 of 845 +r0:=3*e^2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))+(-(b^2-4*a*c)*_ + (c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ + (a+b*x+c*x^2)*sqrt(d+e*x))+3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(2*c^2*d^2+b*e^2*(b+_ + sqrt(b^2-4*a*c))-2*c*e*(b*d+a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+_ + a*e^2)^2*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-_ + 3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c))))*sqrt(c)*(2*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-_ + 2*c*e*(b*d+a*e-d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(2)*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 2 2 3 2 3 +--R (3b c e - 6c d e )x + (3b e - 6b c d e )x + 3a b e +--R + +--R 2 +--R - 6a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((6a c - 3b c)e + 6b c d e - 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((6a b c - 3b )e + 6b c d e - 6b c d e)x + (6a c - 3a b )e +--R + +--R 2 2 2 +--R 6a b c d e - 6a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 3 +--R (3b c e - 6c d e )x + (3b e - 6b c d e )x + 3a b e +--R + +--R 2 +--R - 6a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((- 6a c + 3b c)e - 6b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 6a b c + 3b )e - 6b c d e + 6b c d e)x + (- 6a c + 3a b )e +--R + +--R 2 2 2 +--R - 6a b c d e + 6a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 3b c e + 6c d e )x + ((a c - 3b )e + 5b c d e + c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (5a c - b )d e + 2b c d e - c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (a c e - 2a b c d e + (2a c + b c)d e - 2b c d e + c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 3 4 +--R (a b e - 2a b d e + (2a b c + b )d e - 2b c d e + b c d )x + a e +--R + +--R 2 3 2 2 2 2 3 2 4 +--R - 2a b d e + (2a c + a b )d e - 2a b c d e + a c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 817 + +--S 818 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (a c e - 2a b c d e + (2a c + b c)d e - 2b c d e + c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 3 4 +--R (a b e - 2a b d e + (2a b c + b )d e - 2b c d e + b c d )x + a e +--R + +--R 2 3 2 2 2 2 3 2 4 +--R - 2a b d e + (2a c + a b )d e - 2a b c d e + a c d +--R * +--R +-------+ +--R \|e x + d +--R * +--R ROOT +--R 6 5 2 10 5 4 3 9 +--R (16a c - 4a b )e + (- 80a b c + 20a b )d e +--R + +--R 5 2 4 2 3 4 2 8 +--R (80a c + 140a b c - 40a b )d e +--R + +--R 4 2 3 3 2 5 3 7 +--R (- 320a b c - 80a b c + 40a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 6 +--R (160a c + 440a b c - 40a b c - 20a b )d e +--R + +--R 3 3 2 3 2 5 7 5 5 +--R (- 480a b c - 200a b c + 64a b c + 4b )d e +--R + +--R 3 4 2 2 3 4 2 6 6 4 +--R (160a c + 440a b c - 40a b c - 20b c)d e +--R + +--R 2 4 3 3 5 2 7 3 +--R (- 320a b c - 80a b c + 40b c )d e +--R + +--R 2 5 2 4 4 3 8 2 5 3 4 9 +--R (80a c + 140a b c - 40b c )d e + (- 80a b c + 20b c )d e +--R + +--R 6 2 5 10 +--R (16a c - 4b c )d +--R * +--R ROOT +--R 4 4 3 2 3 2 4 2 6 8 14 +--R (- 81a c + 486a b c - 891a b c + 486a b c - 81b )e +--R + +--R 3 4 2 3 3 5 2 7 13 +--R (- 1620a b c + 5670a b c - 4050a b c + 810b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 12 +--R (1620a c - 14580a b c + 14580a b c - 3645b c )d e +--R + +--R 2 5 3 4 5 3 3 11 +--R (17820a b c - 29160a b c + 9720b c )d e +--R + +--R 2 6 2 5 4 4 4 10 +--R (- 8910a c + 34830a b c - 17010b c )d e +--R + +--R 6 3 5 5 9 +--R (- 24300a b c + 20250b c )d e +--R + +--R 7 2 6 6 8 7 7 7 8 8 6 +--R (8100a c - 16200b c )d e + 8100b c d e - 2025c d e +--R / +--R 11 10 2 20 10 9 3 19 +--R (64a c - 16a b )e + (- 640a b c + 160a b )d e +--R + +--R 10 2 9 2 8 4 2 18 +--R (640a c + 2720a b c - 720a b )d e +--R + +--R 9 2 8 3 7 5 3 17 +--R (- 5760a b c - 6240a b c + 1920a b )d e +--R + +--R 9 3 8 2 2 7 4 6 6 4 16 +--R (2880a c + 22320a b c + 7680a b c - 3360a b )d e +--R + +--R 8 3 7 3 2 6 5 5 7 +--R (- 23040a b c - 48000a b c - 2688a b c + 4032a b ) +--R * +--R 5 15 +--R d e +--R + +--R 8 4 7 2 3 6 4 2 5 6 +--R 7680a c + 78720a b c + 60480a b c - 6720a b c +--R + +--R 4 8 +--R - 3360a b +--R * +--R 6 14 +--R d e +--R + +--R 7 4 6 3 3 5 5 2 +--R - 53760a b c - 147840a b c - 40320a b c +--R + +--R 4 7 3 9 +--R 12480a b c + 1920a b +--R * +--R 7 13 +--R d e +--R + +--R 7 5 6 2 4 5 4 3 +--R 13440a c + 157920a b 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(640a c + 800a b c - 2160a b c + 32a b c + 112b c ) +--R * +--R 7 6 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 8 5 +--R (- 720a b c + 1860a b c + 492a b c - 228b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 9 4 +--R (160a c - 1000a b c - 960a b c + 300b c )d e +--R + +--R 2 7 3 6 5 5 10 3 +--R (352a b c + 968a b c - 264b c )d e +--R + +--R 2 8 2 7 4 6 11 2 +--R (- 64a c - 592a b c + 152b c )d e +--R + +--R 8 3 7 12 9 2 8 13 +--R (208a b c - 52b c )d e + (- 32a c + 8b c )d +--R * +--R ROOT +--R 4 4 3 2 3 2 4 2 6 +--R - 81a c + 486a b c - 891a b c + 486a b c +--R + +--R 8 +--R - 81b +--R * +--R 14 +--R e +--R + +--R 3 4 2 3 3 5 2 7 +--R (- 1620a b c + 5670a b c - 4050a b c + 810b c)d +--R * +--R 13 +--R e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (1620a c - 14580a b c + 14580a b c - 3645b c )d +--R * +--R 12 +--R e +--R + +--R 2 5 3 4 5 3 3 11 +--R (17820a b c - 29160a b c + 9720b c )d e +--R + +--R 2 6 2 5 4 4 4 10 +--R (- 8910a c + 34830a b c - 17010b c )d e +--R + +--R 6 3 5 5 9 +--R (- 24300a b c + 20250b c )d e +--R + +--R 7 2 6 6 8 7 7 7 8 8 6 +--R (8100a c - 16200b c )d e + 8100b c d e - 2025c d e +--R / +--R 11 10 2 20 10 9 3 19 +--R (64a c - 16a b )e + (- 640a b c + 160a b )d e +--R + +--R 10 2 9 2 8 4 2 18 +--R (640a c + 2720a b c - 720a b )d e +--R + +--R 9 2 8 3 7 5 3 17 +--R (- 5760a b c - 6240a b c + 1920a b )d e +--R + +--R 9 3 8 2 2 7 4 6 6 4 16 +--R (2880a c + 22320a b c + 7680a b c - 3360a b )d e +--R + +--R 8 3 7 3 2 6 5 +--R - 23040a b c - 48000a b c - 2688a b c +--R + +--R 5 7 +--R 4032a b +--R * +--R 5 15 +--R d e +--R + +--R 8 4 7 2 3 6 4 2 5 6 +--R 7680a c + 78720a b c + 60480a b c - 6720a b c +--R + +--R 4 8 +--R - 3360a b +--R * +--R 6 14 +--R d e +--R + +--R 7 4 6 3 3 5 5 2 +--R - 53760a b c - 147840a b c - 40320a b c +--R + +--R 4 7 3 9 +--R 12480a b c + 1920a b +--R * +--R 7 13 +--R d e +--R + +--R 7 5 6 2 4 5 4 3 +--R 13440a c + 157920a b c + 161280a b c +--R + +--R 4 6 2 3 8 2 10 +--R 3360a b c - 10560a b c - 720a b +--R * +--R 8 12 +--R d e +--R + +--R 6 5 5 3 4 4 5 3 +--R - 80640a b c - 248640a b c - 94080a b c +--R + +--R 3 7 2 2 9 11 +--R 17280a b c + 5120a b c + 160a b +--R * +--R 9 11 +--R d e +--R + +--R 6 6 5 2 5 4 4 4 +--R 16128a c + 197568a b c + 218400a b c +--R + +--R 3 6 3 2 8 2 10 12 +--R 13440a b c - 14400a b c - 1376a b c - 16b +--R * +--R 10 10 +--R d e +--R + +--R 5 6 4 3 5 3 5 4 +--R - 80640a b c - 248640a b c - 94080a b c +--R + +--R 2 7 3 9 2 11 +--R 17280a b c + 5120a b c + 160b c +--R * +--R 11 9 +--R d e +--R + +--R 5 7 4 2 6 3 4 5 +--R 13440a c + 157920a b c + 161280a b c +--R + +--R 2 6 4 8 3 10 2 +--R 3360a b c - 10560a b c - 720b c +--R * +--R 12 8 +--R d e +--R + +--R 4 7 3 3 6 2 5 5 +--R - 53760a b c - 147840a b c - 40320a b c +--R + +--R 7 4 9 3 +--R 12480a b c + 1920b c +--R * +--R 13 7 +--R d e +--R + +--R 4 8 3 2 7 2 4 6 6 5 +--R 7680a c + 78720a b c + 60480a b c - 6720a b c +--R + +--R 8 4 +--R - 3360b c +--R * +--R 14 6 +--R d e +--R + +--R 3 8 2 3 7 5 6 +--R - 23040a b c - 48000a b c - 2688a b c +--R + +--R 7 5 +--R 4032b c +--R * +--R 15 5 +--R d e +--R + +--R 3 9 2 2 8 4 7 6 6 16 4 +--R (2880a c + 22320a b c + 7680a b c - 3360b c )d e +--R + +--R 2 9 3 8 5 7 17 3 +--R (- 5760a b c - 6240a b c + 1920b c )d e +--R + +--R 2 10 2 9 4 8 18 2 +--R (640a c + 2720a b c - 720b c )d e +--R + +--R 10 3 9 19 11 2 10 20 +--R (- 640a b c + 160b c )d e + (64a c - 16b c )d +--R + +--R 4 4 3 2 3 2 4 2 6 8 10 +--R (- 36a c + 153a b c - 180a b c + 72a b c - 9b )e +--R + +--R 3 4 2 3 3 5 2 7 9 +--R (- 468a b c + 981a b c - 504a b c + 72b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 8 +--R (468a c - 2241a b c + 1539a b c - 252b c )d e +--R + +--R 2 5 3 4 5 3 3 7 +--R (2520a b c - 2610a b c + 495b c )d e +--R + +--R 2 6 2 5 4 4 4 6 +--R (- 1260a c + 2655a b c - 585b c )d e +--R + +--R 6 3 5 5 5 7 2 6 6 4 +--R (- 1620a b c + 405b c )d e + (540a c - 135b c )d e +--R * +--R ROOT +--R 6 5 2 10 5 4 3 9 +--R (16a c - 4a b )e + (- 80a b c + 20a b )d e +--R + +--R 5 2 4 2 3 4 2 8 +--R (80a c + 140a b c - 40a b )d e +--R + +--R 4 2 3 3 2 5 3 7 +--R (- 320a b c - 80a b c + 40a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 6 +--R (160a c + 440a b c - 40a b c - 20a b )d e +--R + +--R 3 3 2 3 2 5 7 5 5 +--R (- 480a b c - 200a b c + 64a b c + 4b )d e +--R + +--R 3 4 2 2 3 4 2 6 6 4 +--R (160a c + 440a b c - 40a b c - 20b c)d e +--R + +--R 2 4 3 3 5 2 7 3 +--R (- 320a b c - 80a b c + 40b c )d e +--R + +--R 2 5 2 4 4 3 8 2 +--R (80a c + 140a b c - 40b c )d e +--R + +--R 5 3 4 9 6 2 5 10 +--R (- 80a b c + 20b c )d e + (16a c - 4b c )d +--R * +--R ROOT +--R 4 4 3 2 3 2 4 2 6 +--R - 81a c + 486a b c - 891a b c + 486a b c +--R + +--R 8 +--R - 81b +--R * +--R 14 +--R e +--R + +--R 3 4 2 3 3 5 2 +--R - 1620a b c + 5670a b c - 4050a b c +--R + +--R 7 +--R 810b c +--R * +--R 13 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 1620a c - 14580a b c + 14580a b c +--R + +--R 6 2 +--R - 3645b c +--R * +--R 2 12 +--R d e +--R + +--R 2 5 3 4 5 3 3 11 +--R (17820a b c - 29160a b c + 9720b c )d e +--R + +--R 2 6 2 5 4 4 4 10 +--R (- 8910a c + 34830a b c - 17010b c )d e +--R + +--R 6 3 5 5 9 +--R (- 24300a b c + 20250b c )d e +--R + +--R 7 2 6 6 8 7 7 7 +--R (8100a c - 16200b c )d e + 8100b c d e +--R + +--R 8 8 6 +--R - 2025c d e +--R / +--R 11 10 2 20 +--R (64a c - 16a b )e +--R + +--R 10 9 3 19 +--R (- 640a b c + 160a b )d e +--R + +--R 10 2 9 2 8 4 2 18 +--R (640a c + 2720a b c - 720a b )d e +--R + +--R 9 2 8 3 7 5 3 17 +--R (- 5760a b c - 6240a b c + 1920a b )d e +--R + +--R 9 3 8 2 2 7 4 +--R 2880a c + 22320a b c + 7680a b c +--R + +--R 6 6 +--R - 3360a b +--R * +--R 4 16 +--R d e +--R + +--R 8 3 7 3 2 6 5 +--R - 23040a b c - 48000a b c - 2688a b c +--R + +--R 5 7 +--R 4032a b +--R * +--R 5 15 +--R d e +--R + +--R 8 4 7 2 3 6 4 2 +--R 7680a c + 78720a b c + 60480a b c +--R + +--R 5 6 4 8 +--R - 6720a b c - 3360a b +--R * +--R 6 14 +--R d e +--R + +--R 7 4 6 3 3 5 5 2 +--R - 53760a b c - 147840a b c - 40320a b c +--R + +--R 4 7 3 9 +--R 12480a b c + 1920a b +--R * +--R 7 13 +--R d e +--R + +--R 7 5 6 2 4 5 4 3 +--R 13440a c + 157920a b c + 161280a b c +--R + +--R 4 6 2 3 8 2 10 +--R 3360a b c - 10560a b c - 720a b +--R * +--R 8 12 +--R d e +--R + +--R 6 5 5 3 4 4 5 3 +--R - 80640a b c - 248640a b c - 94080a b c +--R + +--R 3 7 2 2 9 11 +--R 17280a b c + 5120a b c + 160a b +--R * +--R 9 11 +--R d e +--R + +--R 6 6 5 2 5 4 4 4 +--R 16128a c + 197568a b c + 218400a b c +--R + +--R 3 6 3 2 8 2 10 12 +--R 13440a b c - 14400a b c - 1376a b c - 16b +--R * +--R 10 10 +--R d e +--R + +--R 5 6 4 3 5 3 5 4 +--R - 80640a b c - 248640a b c - 94080a b c +--R + +--R 2 7 3 9 2 11 +--R 17280a b c + 5120a b c + 160b c +--R * +--R 11 9 +--R d e +--R + +--R 5 7 4 2 6 3 4 5 +--R 13440a c + 157920a b c + 161280a b c +--R + +--R 2 6 4 8 3 10 2 +--R 3360a b c - 10560a b c - 720b c +--R * +--R 12 8 +--R d e +--R + +--R 4 7 3 3 6 2 5 5 +--R - 53760a b c - 147840a b c - 40320a b c +--R + +--R 7 4 9 3 +--R 12480a b c + 1920b c +--R * +--R 13 7 +--R d e +--R + +--R 4 8 3 2 7 2 4 6 +--R 7680a c + 78720a b c + 60480a b c +--R + +--R 6 5 8 4 +--R - 6720a b c - 3360b c +--R * +--R 14 6 +--R d e +--R + +--R 3 8 2 3 7 5 6 +--R - 23040a b c - 48000a b c - 2688a b c +--R + +--R 7 5 +--R 4032b c +--R * +--R 15 5 +--R d e +--R + +--R 3 9 2 2 8 4 7 +--R 2880a c + 22320a b c + 7680a b c +--R + +--R 6 6 +--R - 3360b c +--R * +--R 16 4 +--R d e +--R + +--R 2 9 3 8 5 7 17 3 +--R (- 5760a b c - 6240a b c + 1920b c )d e +--R + +--R 2 10 2 9 4 8 18 2 +--R (640a c + 2720a b c - 720b c )d e +--R + +--R 10 3 9 19 +--R (- 640a b c + 160b c )d e +--R + +--R 11 2 10 20 +--R (64a c - 16b c )d +--R + +--R 2 2 3 5 7 +--R (45a b c - 45a b c + 9b )e +--R + +--R 2 3 2 2 4 6 +--R (- 90a c + 180a b c - 45b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (- 270a b c + 90b c )d e + (180a c - 90b c )d e +--R + +--R 4 4 3 5 5 2 +--R 45b c d e - 18c d e +--R / +--R 6 5 2 10 5 4 3 9 +--R (8a c - 2a b )e + (- 40a b c + 10a b )d e +--R + +--R 5 2 4 2 3 4 2 8 +--R (40a c + 70a b c - 20a b )d e +--R + +--R 4 2 3 3 2 5 3 7 +--R (- 160a b c - 40a b c + 20a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 6 +--R (80a c + 220a b c - 20a b c - 10a b )d e +--R + +--R 3 3 2 3 2 5 7 5 5 +--R (- 240a b c - 100a b c + 32a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 6 4 +--R (80a c + 220a b c - 20a b c - 10b c)d e +--R + +--R 2 4 3 3 5 2 7 3 +--R (- 160a b c - 40a b c + 20b c )d e +--R + +--R 2 5 2 4 4 3 8 2 +--R (40a c + 70a b c - 20b c )d e +--R + +--R 5 3 4 9 6 2 5 10 +--R (- 40a b c + 10b c )d e + (8a c - 2b c )d +--R + +--R 2 5 2 4 4 3 8 5 3 4 7 +--R (54a c - 162a b c + 54b c )e + (540a b c - 270b c )d e +--R + +--R 6 2 5 2 6 6 3 5 7 4 4 +--R (- 540a c + 540b c )d e - 540b c d e + 270c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 6b e + 12c d e )\|- 4a c + b + (- 12a c + 6b )e - 12b c d e +--R + +--R 2 2 +--R 12c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 6b e + 12c d e )\|- 4a c + b + (12a c - 6b )e + 12b c d e +--R + +--R 2 2 +--R - 12c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 4 3 2 2 2 3 2 4 +-+ +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d )\|2 +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 819 + +--S 820 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 845 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 821 + +--S 822 of 845 +r0:=-1/2*(d+e*x)^(7/2)/(a+b*x+c*x^2)^2-7/4*e*(d+e*x)^(3/2)*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+7/4*e^2*(2*c*d-b*e)*_ + sqrt(d+e*x)/(c*(b^2-4*a*c))+7/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c^2*d^2-b^2*e^2-2*c*e*_ + (b*d-3*a*e))+(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))/_ + sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))+7/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(e*(2*c^2*d^2-b^2*e^2-2*c*e*_ + (b*d-3*a*e))-(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))/_ + sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(2*c*d-e*_ + (b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 42a c + 7b c )e + 14b c d e - 14c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 84a b c + 14b c)e + 28b c d e - 28b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 84a c - 28a b c + 7b )e + (28a b c + 14b c)d e +--R + +--R 3 2 2 2 2 +--R (- 28a c - 14b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 84a b c + 14a b )e + 28a b c d e - 28a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 42a c + 7a b )e + 14a b c d e - 14a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (- 56a b c + 7b c )e + (112a c + 14b c )d e - 84b c d e +--R + +--R 5 3 +--R 56c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (- 112a b c + 14b c)e + (224a b c + 28b c )d e - 168b c d e +--R + +--R 4 3 +--R 112b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 +--R (- 112a b c - 42a b c + 7b )e +--R + +--R 2 3 2 2 4 3 3 3 2 2 2 +--R (224a c + 140a b c + 14b c)d e + (- 168a b c - 84b c )d e +--R + +--R 4 2 3 3 +--R (112a c + 56b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 +--R (- 112a b c + 14a b )e + (224a b c + 28a b c)d e +--R + +--R 2 2 2 2 3 3 +--R - 168a b c d e + 112a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 +--R (- 56a b c + 7a b )e + (112a c + 14a b c)d e - 84a b c d e +--R + +--R 2 3 3 +--R 56a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 42a c + 7b c )e + 14b c d e - 14c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 84a b c + 14b c)e + 28b c d e - 28b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 84a c - 28a b c + 7b )e + (28a b c + 14b c)d e +--R + +--R 3 2 2 2 2 +--R (- 28a c - 14b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 84a b c + 14a b )e + 28a b c d e - 28a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 42a c + 7a b )e + 14a b c d e - 14a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (56a b c - 7b c )e + (- 112a c - 14b c )d e + 84b c d e +--R + +--R 5 3 +--R - 56c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (112a b c - 14b c)e + (- 224a b c - 28b c )d e + 168b c d e +--R + +--R 4 3 +--R - 112b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 +--R (112a b c + 42a b c - 7b )e +--R + +--R 2 3 2 2 4 3 3 3 2 2 2 +--R (- 224a c - 140a b c - 14b c)d e + (168a b c + 84b c )d e +--R + +--R 4 2 3 3 +--R (- 112a c - 56b c )d e +--R * +--R 2 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+--R 3 6 2 2 5 4 4 6 3 +--R (4096a c - 3072a b c + 768a b c - 64b c ) +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 +--R (- 216090a c - 36015b c )d e +--R + +--R 3 3 11 4 4 10 +--R 120050b c d e - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 3 5 7 +--R (2940a b c - 735a b c + 49b )e +--R + +--R 2 3 2 2 4 6 +--R (- 5880a c - 1470a b c + 245b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (8820a b c - 245b c )d e + (- 5880a c - 2450b c )d e +--R + +--R 4 4 3 5 5 2 +--R 3920b c d e - 1568c d e +--R / +--R 3 6 2 2 5 4 4 6 3 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 3 2 2 2 4 12 +--R (111132a c - 27783a b c + 1715a b )e +--R + +--R 2 2 3 5 11 +--R (- 222264a b c + 41846a b c - 1715b )d e +--R + +--R 2 3 2 2 4 2 10 +--R (222264a c + 96726a b c - 12348b c)d e +--R + +--R 3 3 2 3 9 4 2 3 4 8 +--R (- 277144a b c + 686b c )d e + (138572a c + 68257b c )d e +--R + +--R 4 5 7 5 6 6 +--R - 82320b c d e + 27440c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((42a c - 7b )e - 14b c d e + 14c d e )\|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (56a b c - 7b )e + (- 112a c - 14b c)d e + 84b c d e - 56c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((42a c - 7b )e - 14b c d e + 14c d e )\|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (- 56a b c + 7b )e + (112a c + 14b c)d e - 84b c d e + 56c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 +-+ | 2 +-+ | | 2 +--R (16a c - 4b c)\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 824 + +--S 825 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 845 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 826 + +--S 827 of 845 +r0:=-1/2*(d+e*x)^(5/2)/(a+b*x+c*x^2)^2-5/4*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + sqrt(d+e*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+5/4*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))/sqrt(b^2-4*a*c))/((b^2-4*a*c)*_ + sqrt(2)*sqrt(c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-5/4*e*_ + atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ + (8*c^2*d^2+b*e^2*(b+sqrt(b^2-4*a*c))-2*c*e*(4*b*d-2*a*e+d*_ + sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(c)*sqrt(2*c*d-e*_ + (b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 3 2 4 2 3 2 2 3 +--R (5b c e - 10c d e )x + (10b c e - 20b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((10a b c + 5b )e + (- 20a c - 10b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (10a b e - 20a b c d e )x + 5a b e - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((20a c + 5b c )e - 40b c d e + 40c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((40a b c + 10b c)e - 80b c d e + 80b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (40a c + 30a b c + 5b )e + (- 80a b c - 40b c)d e +--R + +--R 3 2 2 2 +--R (80a c + 40b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((40a b c + 10a b )e - 80a b c d e + 80a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (20a c + 5a b )e - 40a b c d e + 40a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 3 2 4 2 3 2 2 3 +--R (5b c e - 10c d e )x + (10b c e - 20b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((10a b c + 5b )e + (- 20a c - 10b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (10a b e - 20a b c d e )x + 5a b e - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((- 20a c - 5b c )e + 40b c d e - 40c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((- 40a b c - 10b c)e + 80b c d e - 80b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (- 40a c - 30a b c - 5b )e + (80a b c + 40b c)d e +--R + +--R 3 2 2 2 +--R (- 80a c - 40b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((- 40a b c - 10a b )e + 80a b c d e - 80a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (- 20a c - 5a b )e + 40a b c d e - 40a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 2 2 2 +--R (- 5b c e + 10c d e)x + ((- 18a c - 3b )e + 15b c d e)x +--R + +--R 2 2 2 2 +--R (- 15a b e + (- 6a c + 9b )d e)x - 10a e + 5a b d e +--R + +--R 2 2 +--R (- 8a c + 2b )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-------+ | | 2 +--R \|2 \|- 4a c + b \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c)x + (32a c + 8a b c - 4b )x +--R + +--R 2 3 3 2 2 +--R (32a b c - 8a b )x + 16a c - 4a b +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R \|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 827 + +--S 828 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (32768a b c - 24576a b c + 6144a b c - 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (1600a c - 800a b c + 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R 3 2 2 4 2 3 3 +--R (- 8a c + 2b c )x + (- 16a b c + 4b c)x +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (- 16a c - 4a b c + 2b )x + (- 16a b c + 4a b )x - 8a c + 2a b +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (32768a b c - 24576a b c + 6144a b c - 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (- 1600a c + 800a b c - 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (- 32768a b c + 24576a b c - 6144a b c + 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (1600a c - 800a b c + 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R 3 2 2 4 2 3 3 +--R (- 8a c + 2b c )x + (- 16a b c + 4b c)x +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (- 16a c - 4a b c + 2b )x + (- 16a b c + 4a b )x - 8a c + 2a b +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (- 32768a b c + 24576a b c - 6144a b c + 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (- 1600a c + 800a b c - 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R 2 2 3 2 2 2 +--R (- 5b c e + 10c d e)x + ((- 18a c - 3b )e + 15b c d e)x +--R + +--R 2 2 2 2 +--R (- 15a b e + (- 6a c + 9b )d e)x - 10a e + 5a b d e +--R + +--R 2 2 +--R (- 8a c + 2b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c)x + (32a c + 8a b c - 4b )x +--R + +--R 2 3 3 2 2 +--R (32a b c - 8a b )x + 16a c - 4a b +--R Type: Union(Expression(Integer),...) +--E 828 + +--S 829 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 +-+ | | 2 +--R (8a c - 2b )\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (32768a b c - 24576a b c + 6144a b c - 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (1600a c - 800a b c + 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 +-+ | | 2 +--R (- 8a c + 2b )\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (32768a b c - 24576a b c + 6144a b c - 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (- 1600a c + 800a b c - 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 +-+ | | 2 +--R (8a c - 2b )\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (- 32768a b c + 24576a b c - 6144a b c + 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (1600a c - 800a b c + 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 +-+ | | 2 +--R (- 8a c + 2b )\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (- 32768a b c + 24576a b c - 6144a b c + 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (- 1600a c + 800a b c - 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 5b e + 10c d e )\|- 4a c + b + (- 20a c - 5b )e + 40b c d e +--R + +--R 2 2 +--R - 40c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 5b e + 10c d e )\|- 4a c + b + (20a c + 5b )e - 40b c d e +--R + +--R 2 2 +--R 40c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 +-+ | | 2 +--R (16a c - 4b )\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 829 + +--S 830 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 831 + +--S 832 of 845 +r0:=-1/2*(d+e*x)^(3/2)/(a+b*x+c*x^2)^2-3/4*e*(b+2*c*x)*sqrt(d+e*x)/_ + ((b^2-4*a*c)*(a+b*x+c*x^2))+3/2*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(4*c*d-e*(2*b-_ + sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b-_ + sqrt(b^2-4*a*c))))-3/2*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(4*c*d-e*(2*b+sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 2 4 2 3 2 2 2 2 2 2 +--R (- 6c e x - 12b c e x + (- 12a c - 6b )e x - 12a b e x - 6a e ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 4 2 2 2 3 +--R (- 12b c e + 24c d e)x + (- 24b c e + 48b c d e)x +--R + +--R 3 2 2 2 2 +--R ((- 24a b c - 12b )e + (48a c + 24b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 24a b e + 48a b c d e)x - 12a b e + 24a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 4 2 3 2 2 2 2 2 2 +--R (- 6c e x - 12b c e x + (- 12a c - 6b )e x - 12a b e x - 6a e ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 4 2 2 2 3 +--R (12b c e - 24c d e)x + (24b c e - 48b c d e)x +--R + +--R 3 2 2 2 2 +--R ((24a b c + 12b )e + (- 48a c - 24b c)d e)x +--R + +--R 2 2 2 2 2 +--R (24a b e - 48a b c d e)x + 12a b e - 24a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 +--R (6c e x + 9b c e x + (- 2a c + 5b )e x + 3a b e + (- 8a c + 2b )d) +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c)x + (32a c + 8a b c - 4b )x +--R + +--R 2 3 3 2 2 +--R (32a b c - 8a b )x + 16a c - 4a b +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 832 + +--S 833 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 4096a b c + 3072a b c - 768a b c + 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (4096a c - 3072a b c + 768a b c - 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 6 2 4 +--R (262144a c - 196608a b c + 49152a b c - 4096b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e + 432b c d e +--R + +--R 3 3 2 +--R - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R * +--R log +--R 5 4 4 2 3 2 6 8 4 +--R (32768a c - 16384a b c + 1024a b c - 128a b )e +--R + +--R 4 4 3 3 3 2 5 2 9 3 +--R (- 98304a b c + 65536a b c - 12288a b c + 128b )d e +--R + +--R 4 5 2 4 3 6 2 8 2 2 +--R (98304a c - 36864a b c + 12288a b c - 1152b c)d e +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (- 131072a b c + 98304a b c - 24576a b c + 2048b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 4 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 2 2 3 5 7 +--R (- 288a b c + 144a b c - 18b )e +--R + +--R 2 3 2 2 4 6 +--R (576a c - 288a b c + 36b c)d e +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 4096a b c + 3072a b c - 768a b c + 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (4096a c - 3072a b c + 768a b c - 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 +--R - 524288a b c + 393216a b c +--R + +--R 2 5 7 +--R - 98304a b c + 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 +--R - 524288a b c + 393216a b c +--R + +--R 5 2 7 +--R - 98304a b c + 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 3 5 2 2 4 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e +--R + +--R 2 2 3 3 3 2 +--R 432b c d e - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R + +--R 2 2 8 2 7 3 2 6 +-------+ +--R ((108a c + 81b c)e - 432b c d e + 432c d e )\|e x + d +--R + +--R 3 2 2 4 2 3 3 +--R (- 8a c + 2b c )x + (- 16a b c + 4b c)x +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (- 16a c - 4a b c + 2b )x + (- 16a b c + 4a b )x - 8a c + 2a b +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (4096a b c - 3072a b c + 768a b c - 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 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98304a b c + 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 3 5 2 2 4 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e +--R + +--R 2 2 3 3 3 2 +--R 432b c d e - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R + +--R 2 2 8 2 7 3 2 6 +-------+ +--R ((108a c + 81b c)e - 432b c d e + 432c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 | | 2 +--R (- 4a c + b )\|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (4096a b c - 3072a b c + 768a b c - 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 6 2 4 +--R (262144a c - 196608a b c + 49152a b c - 4096b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e + 432b c d e +--R + +--R 3 3 2 +--R - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 5 4 4 2 3 2 6 8 4 +--R (32768a c - 16384a b c + 1024a b c - 128a b )e +--R + +--R 4 4 3 3 3 2 5 2 9 3 +--R (- 98304a b c + 65536a b c - 12288a b c + 128b )d e +--R + +--R 4 5 2 4 3 6 2 8 2 2 +--R (98304a c - 36864a b c + 12288a b c - 1152b c)d e +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (- 131072a b c + 98304a b c - 24576a b c + 2048b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 4 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 2 2 3 5 7 +--R (288a b c - 144a b c + 18b )e +--R + +--R 2 3 2 2 4 6 +--R (- 576a c + 288a b c - 36b c)d e +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (4096a b c - 3072a b c + 768a b c - 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 +--R - 524288a b c + 393216a b c +--R + +--R 2 5 7 +--R - 98304a b c + 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 +--R - 524288a b c + 393216a b c +--R + +--R 5 2 7 +--R - 98304a b c + 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 3 5 2 2 4 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e +--R + +--R 2 2 3 3 3 2 +--R 432b c d e - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R + +--R 2 2 8 2 7 3 2 6 +-------+ +--R ((108a c + 81b c)e - 432b c d e + 432c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 | | 2 +--R (4a c - b )\|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (4096a b c - 3072a b c + 768a b c - 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 6 2 4 +--R (262144a c - 196608a b c + 49152a b c - 4096b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e + 432b c d e +--R + +--R 3 3 2 +--R - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 5 4 4 2 3 2 6 8 4 +--R (- 32768a c + 16384a b c - 1024a b c + 128a b )e +--R + +--R 4 4 3 3 3 2 5 2 9 3 +--R (98304a b c - 65536a b c + 12288a b c - 128b )d e +--R + +--R 4 5 2 4 3 6 2 8 2 2 +--R (- 98304a c + 36864a b c - 12288a b c + 1152b c)d e +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (131072a b c - 98304a b c + 24576a b c - 2048b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 4 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 2 2 3 5 7 +--R (- 288a b c + 144a b c - 18b )e +--R + +--R 2 3 2 2 4 6 +--R (576a c - 288a b c + 36b c)d e +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (4096a b c - 3072a b c + 768a b c - 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 +--R - 524288a b c + 393216a b c +--R + +--R 2 5 7 +--R - 98304a b c + 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 +--R - 524288a b c + 393216a b c +--R + +--R 5 2 7 +--R - 98304a b c + 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 3 5 2 2 4 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e +--R + +--R 2 2 3 3 3 2 +--R 432b c d e - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R + +--R 2 2 8 2 7 3 2 6 +-------+ +--R ((108a c + 81b c)e - 432b c d e + 432c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 | | 2 +--R (- 4a c + b )\|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 4096a b c + 3072a b c - 768a b c + 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (4096a c - 3072a b c + 768a b c - 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 6 2 4 +--R (262144a c - 196608a b c + 49152a b c - 4096b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e + 432b c d e +--R + +--R 3 3 2 +--R - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 5 4 4 2 3 2 6 8 4 +--R (- 32768a c + 16384a b c - 1024a b c + 128a b )e +--R + +--R 4 4 3 3 3 2 5 2 9 3 +--R (98304a b c - 65536a b c + 12288a b c - 128b )d e +--R + +--R 4 5 2 4 3 6 2 8 2 2 +--R (- 98304a c + 36864a b c - 12288a b c + 1152b c)d e +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (131072a b c - 98304a b c + 24576a b c - 2048b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 4 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 2 2 3 5 7 +--R (288a b c - 144a b c + 18b )e +--R + +--R 2 3 2 2 4 6 +--R (- 576a c + 288a b c - 36b c)d e +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 4096a b c + 3072a b c - 768a b c + 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (4096a c - 3072a b c + 768a b c - 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 +--R - 524288a b c + 393216a b c +--R + +--R 2 5 7 +--R - 98304a b c + 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 +--R - 524288a b c + 393216a b c +--R + +--R 5 2 7 +--R - 98304a b c + 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 3 5 2 2 4 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e +--R + +--R 2 2 3 3 3 2 +--R 432b c d e - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R + +--R 2 2 8 2 7 3 2 6 +-------+ +--R ((108a c + 81b c)e - 432b c d e + 432c d e )\|e x + d +--R + +--R +-----------+ +--R 2 | 2 2 +-+ +--R (3e \|- 4a c + b + 6b e - 12c d e)\|c +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 | 2 2 +-+ +--R (3e \|- 4a c + b - 6b e + 12c d e)\|c +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 | | 2 +--R (8a c - 2b )\|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 834 + +--S 835 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 845 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R +-------+ +--R (2c x + b)\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 836 + +--S 837 of 845 +r0:=-1/2*sqrt(d+e*x)/(a+b*x+c*x^2)^2-1/4*e*(b*c*d-b^2*e+2*a*c*e+_ + c*(2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ + (a+b*x+c*x^2))+1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^2*d^2-b*e^2*(b+sqrt(b^2-4*a*c))-_ + 2*c*e*(4*b*d-6*a*e-d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-_ + e*(b*d-a*e))*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-_ + 1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^2*d^2-b*e^2*(b-sqrt(b^2-4*a*c))-_ + 2*c*e*(4*b*d-6*a*e+d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-_ + b*d*e+a*e^2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 3 2 4 2 3 2 2 3 +--R (b c e - 2c d e )x + (2b c e - 4b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((2a b c + b )e + (- 4a c - 2b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (2a b e - 4a b c d e )x + a b e - 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((12a c - b c )e - 8b c d e + 8c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((24a b c - 2b c)e - 16b c d e + 16b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (24a c + 10a b c - b )e + (- 16a b c - 8b c)d e +--R + +--R 3 2 2 2 +--R (16a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((24a b c - 2a b )e - 16a b c d e + 16a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (12a c - a b )e - 8a b c d e + 8a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 3 2 4 2 3 2 2 3 +--R (b c e - 2c d e )x + (2b c e - 4b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((2a b c + b )e + (- 4a c - 2b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (2a b e - 4a b c d e )x + a b e - 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((- 12a c + b c )e + 8b c d e - 8c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((- 24a b c + 2b c)e + 16b c d e - 16b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (- 24a c - 10a b c + b )e + (16a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 16a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((- 24a b c + 2a b )e + 16a b c d e - 16a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (- 12a c + a b )e + 8a b c d e - 8a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 3 2 2 2 2 2 +--R (- b c e + 2c d e)x + ((2a c - 2b c)e + 3b c d e)x +--R + +--R 3 2 2 2 2 2 2 +--R ((a b c - b )e + (2a c + b c)d e)x + (- 6a c + a b )e +--R + +--R 3 2 2 2 +--R (9a b c - 2b )d e + (- 8a c + 2b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 3 2 2 2 3 3 2 4 2 3 2 4 +--R ((16a c - 4a b c )e + (- 16a b c + 4b c )d e + (16a c - 4b c )d )x +--R + +--R 2 2 3 2 2 2 4 +--R (32a b c - 8a b c)e + (- 32a b c + 8b c)d e +--R + +--R 3 3 2 2 +--R (32a b c - 8b c )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 4 2 2 2 3 5 +--R (32a c + 8a b c - 4a b )e + (- 32a b c - 8a b c + 4b )d e +--R + +--R 2 3 2 2 4 2 +--R (32a c + 8a b c - 4b c)d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 4 2 2 3 2 +--R ((32a b c - 8a b )e + (- 32a b c + 8a b )d e + (32a b c - 8a b c)d )x +--R + +--R 4 3 2 2 3 2 3 3 2 2 2 2 +--R (16a c - 4a b )e + (- 16a b c + 4a b )d e + (16a c - 4a b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 837 + +--S 838 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 3 3 2 4 2 3 2 4 +--R ((8a c - 2a b c )e + (- 8a b c + 2b c )d e + (8a c - 2b c )d )x +--R + +--R 2 2 3 2 2 2 4 +--R (16a b c - 4a b c)e + (- 16a b c + 4b c)d e +--R + +--R 3 3 2 2 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 4 2 2 2 3 5 +--R (16a c + 4a b c - 2a b )e + (- 16a b c - 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 2 +--R (16a c + 4a b c - 2b c)d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 4 +--R (16a b c - 4a b )e + (- 16a b c + 4a b )d e +--R + +--R 2 2 3 2 +--R (16a b c - 4a b c)d +--R * +--R x +--R + +--R 4 3 2 2 3 2 3 3 2 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2a b )d e + (8a c - 2a b c)d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 6 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 5 3 4 3 2 3 5 2 7 5 +--R (- 12288a b c + 9216a b c - 2304a b c + 192a b )d e +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 12288a c + 3072a b c - 6912a b c + 2112a b c +--R + +--R 8 +--R - 192a b +--R * +--R 2 4 +--R d e +--R + +--R 4 4 3 3 3 2 5 2 7 +--R - 24576a b c + 14336a b c - 1536a b c - 384a b c +--R + +--R 9 +--R 64b +--R * +--R 3 3 +--R d e +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R 12288a c + 3072a b c - 6912a b c + 2112a b c +--R + +--R 8 +--R - 192b c +--R * +--R 4 2 +--R d e +--R + +--R 3 5 2 3 4 5 3 7 2 5 +--R (- 12288a b c + 9216a b c - 2304a b c + 192b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 6 +--R (4096a c - 3072a b c + 768a b c - 64b c )d +--R * +--R ROOT +--R 2 2 2 4 14 2 3 13 +--R (- 81a c + 18a b c - b )e + (90a b c - 10b c)d e +--R + +--R 3 2 2 2 12 3 3 11 4 4 10 +--R (- 90a c - 15b c )d e + 50b c d e - 25c d e +--R / +--R 9 3 8 2 2 7 4 6 6 12 +--R (262144a c - 196608a b c + 49152a b c - 4096a b )e +--R + +--R 8 3 7 3 2 6 5 +--R - 1572864a b c + 1179648a b c - 294912a b c +--R + +--R 5 7 +--R 24576a b +--R * +--R 11 +--R d e +--R + +--R 8 4 7 2 3 6 4 2 +--R 1572864a c + 2752512a b c - 2654208a b c +--R + +--R 5 6 4 8 +--R 712704a b c - 61440a b +--R * +--R 2 10 +--R d e +--R + +--R 7 4 6 3 3 5 5 2 +--R - 7864320a b c + 655360a b c + 2457600a b c +--R + +--R 4 7 3 9 +--R - 860160a b c + 81920a b +--R * +--R 3 9 +--R d e +--R + +--R 7 5 6 2 4 5 4 3 +--R 3932160a c + 12779520a b c - 7127040a b c +--R + +--R 4 6 2 3 8 2 10 +--R - 61440a b c + 491520a b c - 61440a b +--R * +--R 4 8 +--R d e +--R + +--R 6 5 5 3 4 4 5 3 +--R - 15728640a b c - 3932160a b c + 7274496a b c +--R + +--R 3 7 2 2 9 11 +--R - 1523712a b c - 49152a b c + 24576a b +--R * +--R 5 7 +--R d e +--R + +--R 6 6 5 2 5 4 4 4 +--R 5242880a c + 19660800a b c - 8847360a b c +--R + +--R 3 6 3 2 8 2 10 +--R - 1294336a b c + 909312a b c - 73728a b c +--R + +--R 12 +--R - 4096b +--R * +--R 6 6 +--R d e +--R + +--R 5 6 4 3 5 3 5 4 +--R - 15728640a b c - 3932160a b c + 7274496a b c +--R + +--R 2 7 3 9 2 11 +--R - 1523712a b c - 49152a b c + 24576b c +--R * +--R 7 5 +--R d e +--R + +--R 5 7 4 2 6 3 4 5 +--R 3932160a c + 12779520a b c - 7127040a b c +--R + +--R 2 6 4 8 3 10 2 +--R - 61440a b c + 491520a b c - 61440b c +--R * +--R 8 4 +--R d e +--R + +--R 4 7 3 3 6 2 5 5 +--R - 7864320a b c + 655360a b c + 2457600a b c +--R + +--R 7 4 9 3 +--R - 860160a b c + 81920b c +--R * +--R 9 3 +--R d e +--R + +--R 4 8 3 2 7 2 4 6 +--R 1572864a c + 2752512a b c - 2654208a b c +--R + +--R 6 5 8 4 +--R 712704a b c - 61440b c +--R * +--R 10 2 +--R d e +--R + +--R 3 8 2 3 7 5 6 +--R - 1572864a b c + 1179648a b c - 294912a b c +--R + +--R 7 5 +--R 24576b c +--R * +--R 11 +--R d e +--R + +--R 3 9 2 2 8 4 7 6 6 12 +--R (262144a c - 196608a b c + 49152a b c - 4096b c )d +--R + +--R 2 2 3 5 7 2 3 2 2 4 6 +--R (60a b c - 15a b c + b )e + (- 120a c - 30a b c + 5b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 4 4 3 +--R (180a b c - 5b c )d e + (- 120a c - 50b c )d e + 80b c d e +--R + +--R 5 5 2 +--R - 32c d e +--R / +--R 6 3 5 2 2 4 4 3 6 6 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 5 3 4 3 2 3 5 2 7 5 +--R (- 6144a b c + 4608a b c - 1152a b c + 96a b )d e +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 2 4 +--R (6144a c + 1536a b c - 3456a b c + 1056a b c - 96a b )d e +--R + +--R 4 4 3 3 3 2 5 2 7 9 3 3 +--R (- 12288a b c + 7168a b c - 768a b c - 192a b c + 32b )d e +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 4 2 +--R (6144a c + 1536a b c - 3456a b c + 1056a b c - 96b c)d e +--R + +--R 3 5 2 3 4 5 3 7 2 5 +--R (- 6144a b c + 4608a b c - 1152a b c + 96b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 6 +--R (2048a c - 1536a b c + 384a b c - 32b c )d +--R * +--R log +--R 7 4 6 3 3 5 5 2 4 7 +--R 65536a b c - 57344a b c + 18432a b c - 2560a b c +--R + +--R 3 9 +--R 128a b +--R * +--R 9 +--R e +--R + +--R 7 5 6 2 4 5 4 3 +--R - 131072a c - 114688a b c + 159744a b c +--R + +--R 4 6 2 3 8 2 10 +--R - 56320a b c + 7936a b c - 384a b +--R * +--R 8 +--R d e +--R + +--R 6 5 5 3 4 4 5 3 +--R 688128a b c - 294912a b c - 61440a b c +--R + +--R 3 7 2 2 9 11 +--R 49152a b c - 8064a b c + 384a b +--R * +--R 2 7 +--R d e +--R + +--R 6 6 5 2 5 4 4 4 +--R - 458752a c - 786432a b c + 696320a b c +--R + +--R 3 6 3 2 8 2 10 12 +--R - 147456a b c - 768a b c + 2560a b c - 128b +--R * +--R 3 6 +--R d e +--R + +--R 5 6 4 3 5 3 5 4 +--R 1474560a b c - 409600a b c - 253952a b c +--R + +--R 2 7 3 9 2 11 +--R 113664a b c - 12416a b c + 128b c +--R * +--R 4 5 +--R d e +--R + +--R 5 7 4 2 6 3 4 5 +--R - 589824a c - 983040a b c + 835584a b c +--R + +--R 2 6 4 8 3 10 2 +--R - 165888a b c - 768a b c + 1920b c +--R * +--R 5 4 +--R d e +--R + +--R 4 7 3 3 6 2 5 5 +--R 1146880a b c - 458752a b c - 86016a b c +--R + +--R 7 4 9 3 +--R 57344a b c - 6272b c +--R * +--R 6 3 +--R d e +--R + +--R 4 8 3 2 7 2 4 6 +--R - 327680a c - 262144a b c + 319488a b c +--R + +--R 6 5 8 4 +--R - 90112a b c + 7936b c +--R * +--R 7 2 +--R d e +--R + +--R 3 8 2 3 7 5 6 7 5 8 +--R (294912a b c - 221184a b c + 55296a b c - 4608b c )d e +--R + +--R 3 9 2 2 8 4 7 6 6 9 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 81a c + 18a b c - b )e +--R + +--R 2 3 13 3 2 2 2 12 +--R (90a b c - 10b c)d e + (- 90a c - 15b c )d e +--R + +--R 3 3 11 4 4 10 +--R 50b c d e - 25c d e +--R / +--R 9 3 8 2 2 7 4 6 6 +--R (262144a c - 196608a b c + 49152a b c - 4096a b ) +--R * +--R 12 +--R e +--R + +--R 8 3 7 3 2 6 5 +--R - 1572864a b c + 1179648a b c - 294912a b c +--R + +--R 5 7 +--R 24576a b +--R * +--R 11 +--R 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2 6 +--R 6144a c + 1536a b c - 3456a b c + 1056a b c +--R + +--R 8 +--R - 96a b +--R * +--R 2 4 +--R d e +--R + +--R 4 4 3 3 3 2 5 2 7 +--R - 12288a b c + 7168a b c - 768a b c - 192a b c +--R + +--R 9 +--R 32b +--R * +--R 3 3 +--R d e +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R 6144a c + 1536a b c - 3456a b c + 1056a b c +--R + +--R 8 +--R - 96b c +--R * +--R 4 2 +--R d e +--R + +--R 3 5 2 3 4 5 3 7 2 5 +--R (- 6144a b c + 4608a b c - 1152a b c + 96b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 6 +--R (2048a c - 1536a b c + 384a b c - 32b c )d +--R + +--R 2 4 2 3 4 2 10 4 3 3 9 +--R (324a c - 81a b c + 5b c )e + (- 324a b c + 41b c )d e +--R + +--R 5 2 4 2 8 5 3 7 6 4 6 +--R (324a c + 39b c )d e - 160b c d e + 80c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- b e + 2c d e )\|- 4a c + b + (- 12a c + b )e + 8b c d e +--R + +--R 2 2 +--R - 8c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- b e + 2c d e )\|- 4a c + b + (12a c - b )e - 8b c d e +--R + +--R 2 2 +--R 8c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 2 2 3 2 2 2 +-+ +--R ((16a c - 4a b )e + (- 16a b c + 4b )d e + (16a c - 4b c)d )\|2 +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 839 + +--S 840 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 845 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 841 + +--S 842 of 845 +r0:=-1/2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)+1/4*e*(5*a*c*e*_ + (2*c*d-b*e)+(c*d-3*b*e)*(b*c*d-b^2*e+2*a*c*e)+c*(2*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(b*d+5*a*e))*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ + (a+b*x+c*x^2))-1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^3*d^3+3*b^2*e^3*(b+_ + sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-16*a*e-d*sqrt(b^2-4*a*c))-2*c*e^2*_ + (b^2*d+8*a*b*e+b*d*sqrt(b^2-4*a*c)+5*a*e*sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))+1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^3*d^3+3*b^2*e^3*_ + (b-sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-16*a*e+d*sqrt(b^2-4*a*c))-_ + 2*c*e^2*(b^2*d+8*a*b*e-b*d*sqrt(b^2-4*a*c)-5*a*e*sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 10a c + 3b c )e - 2b c d e + 2c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 20a b c + 6b c)e - 4b c d e + 4b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 20a c - 4a b c + 3b )e + (- 4a b c - 2b c)d e +--R + +--R 3 2 2 2 2 +--R (4a c + 2b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 20a b c + 6a b )e - 4a b c d e + 4a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 10a c + 3a b )e - 2a b c d e + 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (16a b c - 3b c )e + (- 32a c + 2b c )d e + 12b c d e +--R + +--R 5 3 +--R - 8c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (32a b c - 6b c)e + (- 64a b c + 4b c )d e + 24b c d e +--R + +--R 4 3 +--R - 16b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 2 3 2 2 4 3 +--R (32a b c + 10a b c - 3b )e + (- 64a c - 28a b c + 2b c)d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (24a b c + 12b c )d e + (- 16a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 2 2 2 2 +--R (32a b c - 6a b )e + (- 64a b c + 4a b c)d e + 24a b c d e +--R + +--R 3 3 +--R - 16a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 2 3 3 +--R (16a b c - 3a b )e + (- 32a c + 2a b c)d e + 12a b c d e - 8a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 10a c + 3b c )e - 2b c d e + 2c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 20a b c + 6b c)e - 4b c d e + 4b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 20a c - 4a b c + 3b )e + (- 4a b c - 2b c)d e +--R + +--R 3 2 2 2 2 +--R (4a c + 2b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 20a b c + 6a b )e - 4a b c d e + 4a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 10a c + 3a b )e - 2a b c d e + 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (- 16a b c + 3b c )e + (32a c - 2b c )d e - 12b c d e +--R + +--R 5 3 +--R 8c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (- 32a b c + 6b c)e + (64a b c - 4b c )d e - 24b c d e +--R + +--R 4 3 +--R 16b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 2 3 2 2 4 3 +--R (- 32a b c - 10a b c + 3b )e + (64a c + 28a b c - 2b c)d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (- 24a b c - 12b c )d e + (16a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 2 2 2 2 +--R (- 32a b c + 6a b )e + (64a b c - 4a b c)d e - 24a b c d e +--R + +--R 3 3 +--R 16a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 2 3 3 +--R (- 16a b c + 3a b )e + (32a c - 2a b c)d e - 12a b c d e + 8a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 3 3 2 4 2 3 +--R ((10a c - 3b c )e + 2b c d e - 2c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 2 +--R ((21a b c - 6b c)e + (- 12a c + 6b c )d e - 3b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (18a c + 6a b c - 3b )e + (- 18a b c + 6b c)d e +--R + +--R 3 2 2 2 +--R (6a c - 3b c )d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 4 2 +--R (19a b c - 5a b )e + (- 20a c - 2a b c + 2b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (15a b c - 4b c)d e + (- 8a c + 2b c )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 3 2 2 2 4 2 3 3 2 3 +--R (16a c - 4a b c )e + (- 32a b c + 8a b c )d e +--R + +--R 2 4 2 3 4 2 2 2 4 3 3 3 +--R (32a c + 8a b c - 4b c )d e + (- 32a b c + 8b c )d e +--R + +--R 5 2 4 4 +--R (16a c - 4b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 4 2 2 2 4 3 +--R (32a b c - 8a b c)e + (- 64a b c + 16a b c)d e +--R + +--R 2 3 3 2 5 2 2 2 3 4 2 3 +--R (64a b c + 16a b c - 8b c)d e + (- 64a b c + 16b c )d e +--R + +--R 4 3 3 4 +--R (32a b c - 8b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 3 2 2 3 5 3 +--R (32a c + 8a b c - 4a b )e + (- 64a b c - 16a b c + 8a b )d e +--R + +--R 3 3 2 2 2 6 2 2 2 3 3 2 5 3 +--R (64a c + 48a b c - 4b )d e + (- 64a b c - 16a b c + 8b c)d e +--R + +--R 2 4 2 3 4 2 4 +--R (32a c + 8a b c - 4b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 3 2 2 4 3 +--R (32a b c - 8a b )e + (- 64a b c + 16a b )d e +--R + +--R 3 2 2 3 5 2 2 2 2 2 4 3 +--R (64a b c + 16a b c - 8a b )d e + (- 64a b c + 16a b c)d e +--R + +--R 2 3 3 2 4 +--R (32a b c - 8a b c )d +--R * +--R x +--R + +--R 5 4 2 4 4 3 3 3 +--R (16a c - 4a b )e + (- 32a b c + 8a b )d e +--R + +--R 4 2 3 2 2 4 2 2 3 2 2 3 3 +--R (32a c + 8a b c - 4a b )d e + (- 32a b c + 8a b c)d e +--R + +--R 3 3 2 2 2 4 +--R (16a c - 4a b c )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 842 + +--S 843 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 4 2 3 3 2 3 +--R (8a c - 2a b c )e + (- 16a b c + 4a b c )d e +--R + +--R 2 4 2 3 4 2 2 2 4 3 3 3 +--R (16a c + 4a b c - 2b c )d e + (- 16a b c + 4b c )d e +--R + +--R 5 2 4 4 +--R (8a c - 2b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 4 2 2 2 4 3 +--R (16a b c - 4a b c)e + (- 32a b c + 8a b c)d e +--R + +--R 2 3 3 2 5 2 2 2 3 4 2 3 +--R (32a b c + 8a b c - 4b c)d e + (- 32a b c + 8b c )d e +--R + +--R 4 3 3 4 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 3 2 2 3 5 3 +--R (16a c + 4a b c - 2a b )e + (- 32a b c - 8a b c + 4a b )d e +--R + +--R 3 3 2 2 2 6 2 2 2 3 3 2 5 3 +--R (32a c + 24a b c - 2b )d e + (- 32a b c - 8a b c + 4b c)d e +--R + +--R 2 4 2 3 4 2 4 +--R (16a c + 4a b c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 3 2 2 4 3 +--R (16a b c - 4a b )e + (- 32a b c + 8a b )d e +--R + +--R 3 2 2 3 5 2 2 2 2 2 4 3 +--R (32a b c + 8a b c - 4a b )d e + (- 32a b c + 8a b c)d e +--R + +--R 2 3 3 2 4 +--R (16a b c - 4a b c )d +--R * +--R x +--R + +--R 5 4 2 4 4 3 3 3 +--R (8a c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 4 2 3 2 2 4 2 2 3 2 2 3 3 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 3 3 2 2 2 4 +--R (8a c - 2a b c )d +--R * +--R ROOT +--R 8 3 7 2 2 6 4 5 6 10 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 7 3 6 3 2 5 5 4 7 9 +--R (- 20480a b c + 15360a b c - 3840a b c + 320a b )d e +--R + +--R 7 4 6 2 3 5 4 2 4 6 +--R 20480a c + 25600a b c - 26880a b c + 7360a b c +--R + +--R 3 8 +--R - 640a b +--R * +--R 2 8 +--R d e +--R + +--R 6 4 5 3 3 4 5 2 3 7 +--R - 81920a b c + 20480a b c + 15360a b c - 6400a b c +--R + +--R 2 9 +--R 640a b +--R * +--R 3 7 +--R d e +--R + +--R 6 5 5 2 4 4 4 3 3 6 2 +--R 40960a c + 92160a b c - 64000a b c + 7040a b c +--R + +--R 2 8 10 +--R 1920a b c - 320a b +--R * +--R 4 6 +--R d e +--R + +--R 5 5 4 3 4 3 5 3 2 7 2 +--R - 122880a b c + 10240a b c + 34304a b c - 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92160a b c - 64000a b c +--R + +--R 3 6 2 2 8 10 +--R 7040a b c + 1920a b c - 320a b +--R * +--R 4 6 +--R d e +--R + +--R 5 5 4 3 4 3 5 3 +--R - 122880a b c + 10240a b c + 34304a b c +--R + +--R 2 7 2 9 11 +--R - 10368a b c + 512a b c + 64b +--R * +--R 5 5 +--R d e +--R + +--R 5 6 4 2 5 3 4 4 +--R 40960a c + 92160a b c - 64000a b c +--R + +--R 2 6 3 8 2 10 +--R 7040a b c + 1920a b c - 320b c +--R * +--R 6 4 +--R d e +--R + +--R 4 6 3 3 5 2 5 4 +--R - 81920a b c + 20480a b c + 15360a b c +--R + +--R 7 3 9 2 +--R - 6400a b c + 640b c +--R * +--R 7 3 +--R d e +--R + +--R 4 7 3 2 6 2 4 5 +--R 20480a c + 25600a b c - 26880a b c +--R + +--R 6 4 8 3 +--R 7360a b c - 640b c +--R * +--R 8 2 +--R d e +--R + +--R 3 7 2 3 6 5 5 +--R - 20480a b c + 15360a b c - 3840a b c +--R + +--R 7 4 +--R 320b c +--R * +--R 9 +--R d e +--R + +--R 3 8 2 2 7 4 6 6 5 10 +--R (4096a c - 3072a b c + 768a b c - 64b c )d +--R * +--R ROOT +--R 4 4 3 2 3 2 4 2 +--R - 625a c + 2550a b c - 3051a b c +--R + +--R 6 8 +--R 918a b c - 81b +--R * +--R 18 +--R e +--R + +--R 3 4 2 3 3 5 2 +--R - 7700a b c + 16758a b c - 4914a b c +--R + +--R 7 +--R 378b c +--R * +--R 17 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 7700a c - 38724a b c + 7812a b c +--R + +--R 6 2 +--R - 189b c +--R * +--R 2 16 +--R d e +--R + +--R 2 5 3 4 5 3 3 15 +--R (43932a b c + 4984a b c - 1848b c )d e +--R + +--R 2 6 2 5 4 4 4 14 +--R (- 21966a c - 29442a b c + 3374b c )d e +--R + +--R 6 3 5 5 13 +--R (32340a b c + 490b c )d e +--R + +--R 7 2 6 6 12 7 7 11 +--R (- 10780a c - 5880b c )d e + 4900b c d e +--R + +--R 8 8 10 +--R - 1225c d e +--R / +--R 13 3 12 2 2 11 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 10 6 +--R - 4096a b +--R * +--R 20 +--R e +--R + +--R 12 3 11 3 2 +--R - 2621440a b c + 1966080a b c +--R + +--R 10 5 9 7 +--R - 491520a b c + 40960a b +--R * +--R 19 +--R d e +--R + +--R 12 4 11 2 3 +--R 2621440a c + 9830400a b c +--R + +--R 10 4 2 9 6 8 8 +--R - 8355840a b c + 2170880a b c - 184320a b +--R * +--R 2 18 +--R d e +--R + +--R 11 4 10 3 3 +--R - 23592960a b c - 13762560a b c +--R + +--R 9 5 2 8 7 7 9 +--R 19169280a b c - 5529600a b c + 491520a b +--R * +--R 3 17 +--R d e +--R + +--R 11 5 10 2 4 +--R 11796480a c + 85524480a b c +--R + +--R 9 4 3 8 6 2 +--R - 13516800a b c - 23777280a b c +--R + +--R 7 8 6 10 +--R 8847360a b c - 860160a b +--R * +--R 4 16 +--R d e +--R + +--R 10 5 9 3 4 +--R - 94371840a b c - 149422080a b c +--R + +--R 8 5 3 7 7 2 +--R 81395712a b c + 9732096a b c +--R + +--R 6 9 5 11 +--R - 8945664a b c + 1032192a b +--R * +--R 5 15 +--R d e +--R + +--R 10 6 9 2 5 +--R 31457280a c + 306708480a b c +--R + +--R 8 4 4 7 6 3 +--R 88473600a b c - 131235840a b c +--R + +--R 6 8 2 5 10 4 12 +--R 15482880a b c + 5160960a b c - 860160a b +--R * +--R 6 14 +--R d e +--R + +--R 9 6 8 3 5 +--R - 220200960a b c - 495452160a b c +--R + +--R 7 5 4 6 7 3 +--R 123863040a b c + 95846400a b c +--R + +--R 5 9 2 4 11 3 13 +--R - 28016640a b c - 737280a b c + 491520a b +--R * +--R 7 13 +--R d e +--R + +--R 9 7 8 2 6 +--R 55050240a c + 619315200a b c +--R + +--R 7 4 5 6 6 4 +--R 340623360a b c - 276111360a b c +--R + +--R 5 8 3 4 10 2 +--R - 8847360a b c + 19537920a b c +--R + +--R 3 12 2 14 +--R - 1228800a b c - 184320a b +--R * +--R 8 12 +--R d e +--R + +--R 8 7 7 3 6 +--R - 330301440a b c - 853278720a b c +--R + +--R 6 5 5 5 7 4 +--R 103219200a b c + 199802880a b c +--R + +--R 4 9 3 3 11 2 +--R - 38502400a b c - 5406720a b c +--R + +--R 2 13 15 +--R 983040a b c + 40960a b +--R * +--R 9 11 +--R d e +--R + +--R 8 8 7 2 7 +--R 66060288a c + 776208384a b c +--R + +--R 6 4 6 5 6 5 +--R 494075904a b c - 341655552a b c +--R + +--R 4 8 4 3 10 3 +--R - 30597120a b c + 27295744a b c +--R + +--R 2 12 2 14 16 +--R - 933888a b c - 319488a b c - 4096b +--R * +--R 10 10 +--R d e +--R + +--R 7 8 6 3 7 +--R - 330301440a b c - 853278720a b c +--R + +--R 5 5 6 4 7 5 +--R 103219200a b c + 199802880a b c +--R + +--R 3 9 4 2 11 3 +--R - 38502400a b c - 5406720a b c +--R + +--R 13 2 15 +--R 983040a b c + 40960b c +--R * +--R 11 9 +--R d e +--R + +--R 7 9 6 2 8 +--R 55050240a c + 619315200a b c +--R + +--R 5 4 7 4 6 6 +--R 340623360a b c - 276111360a b c +--R + +--R 3 8 5 2 10 4 +--R - 8847360a b c + 19537920a b c +--R + +--R 12 3 14 2 +--R - 1228800a b c - 184320b c +--R * +--R 12 8 +--R d e +--R + +--R 6 9 5 3 8 +--R - 220200960a b c - 495452160a b c +--R + +--R 4 5 7 3 7 6 +--R 123863040a b c + 95846400a b c +--R + +--R 2 9 5 11 4 13 3 +--R - 28016640a b c - 737280a b c + 491520b c +--R * +--R 13 7 +--R d e +--R + +--R 6 10 5 2 9 +--R 31457280a c + 306708480a b c +--R + +--R 4 4 8 3 6 7 +--R 88473600a b c - 131235840a b c +--R + +--R 2 8 6 10 5 12 4 +--R 15482880a b c + 5160960a b c - 860160b c +--R * +--R 14 6 +--R d e +--R + +--R 5 10 4 3 9 +--R - 94371840a b c - 149422080a b c +--R + +--R 3 5 8 2 7 7 +--R 81395712a b c + 9732096a b c +--R + +--R 9 6 11 5 +--R - 8945664a b c + 1032192b c +--R * +--R 15 5 +--R d e +--R + +--R 5 11 4 2 10 +--R 11796480a c + 85524480a b c +--R + +--R 3 4 9 2 6 8 +--R - 13516800a b c - 23777280a b c +--R + +--R 8 7 10 6 +--R 8847360a b c - 860160b c +--R * +--R 16 4 +--R d e +--R + +--R 4 11 3 3 10 +--R - 23592960a b c - 13762560a b c +--R + +--R 2 5 9 7 8 9 7 +--R 19169280a b c - 5529600a b c + 491520b c +--R * +--R 17 3 +--R d e +--R + +--R 4 12 3 2 11 +--R 2621440a c + 9830400a b c +--R + +--R 2 4 10 6 9 8 8 +--R - 8355840a b c + 2170880a b c - 184320b c +--R * +--R 18 2 +--R d e +--R + +--R 3 12 2 3 11 +--R - 2621440a b c + 1966080a b c +--R + +--R 5 10 7 9 +--R - 491520a b c + 40960b c +--R * +--R 19 +--R d e +--R + +--R 3 13 2 2 12 4 11 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 10 +--R - 4096b c +--R * +--R 20 +--R d +--R + +--R 3 3 2 3 2 5 7 9 +--R (- 420a b c + 385a b c - 105a b c + 9b )e +--R + +--R 3 4 2 2 3 4 2 6 8 +--R (840a c - 1050a b c + 280a b c - 21b c)d e +--R + +--R 2 4 3 3 5 2 2 7 +--R (840a b c - 70a b c - 14b c )d e +--R + +--R 2 5 2 4 4 3 3 6 +--R (- 560a c - 420a b c + 70b c )d e +--R + +--R 5 3 4 4 5 6 2 5 5 4 +--R (700a b c - 35b c )d e + (- 280a c - 98b c )d e +--R + +--R 6 6 3 7 7 2 +--R 112b c d e - 32c d e +--R / +--R 8 3 7 2 2 6 4 5 6 10 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 7 3 6 3 2 5 5 4 7 9 +--R (- 10240a b c + 7680a b c - 1920a b c + 160a b )d e +--R + +--R 7 4 6 2 3 5 4 2 4 6 +--R 10240a c + 12800a b c - 13440a b c + 3680a b c +--R + +--R 3 8 +--R - 320a b +--R * +--R 2 8 +--R d e +--R + +--R 6 4 5 3 3 4 5 2 3 7 +--R - 40960a b c + 10240a b c + 7680a b c - 3200a b c +--R + +--R 2 9 +--R 320a b +--R * +--R 3 7 +--R d e +--R + +--R 6 5 5 2 4 4 4 3 3 6 2 +--R 20480a c + 46080a b c - 32000a b c + 3520a b c +--R + +--R 2 8 10 +--R 960a b c - 160a b +--R * +--R 4 6 +--R d e +--R + +--R 5 5 4 3 4 3 5 3 2 7 2 +--R - 61440a b c + 5120a b c + 17152a b c - 5184a b c +--R + +--R 9 11 +--R 256a b c + 32b +--R * +--R 5 5 +--R d e +--R + +--R 5 6 4 2 5 3 4 4 2 6 3 +--R 20480a c + 46080a b c - 32000a b c + 3520a b c +--R + +--R 8 2 10 +--R 960a b c - 160b c +--R * +--R 6 4 +--R d e +--R + +--R 4 6 3 3 5 2 5 4 7 3 +--R - 40960a b c + 10240a b c + 7680a b c - 3200a b c +--R + +--R 9 2 +--R 320b c +--R * +--R 7 3 +--R d e +--R + +--R 4 7 3 2 6 2 4 5 6 4 +--R 10240a c + 12800a b c - 13440a b c + 3680a b c +--R + +--R 8 3 +--R - 320b c +--R * +--R 8 2 +--R d e +--R + +--R 3 7 2 3 6 5 5 7 4 9 +--R (- 10240a b c + 7680a b c - 1920a b c + 160b c )d e +--R + +--R 3 8 2 2 7 4 6 6 5 10 +--R (2048a c - 1536a b c + 384a b c - 32b c )d +--R + +--R 3 6 2 2 5 4 4 6 3 12 +--R (2500a c - 5625a b c + 1971a b c - 189b c )e +--R + +--R 2 6 3 5 5 4 11 +--R (15000a b c - 4518a b c + 297b c )d e +--R + +--R 2 7 2 6 4 5 2 10 +--R (- 15000a c - 1446a b c + 774b c )d e +--R + +--R 7 3 6 3 9 8 2 7 4 8 +--R (11928a b c - 1582b c )d e + (- 5964a c - 609b c )d e +--R + +--R 8 5 7 9 6 6 +--R 1680b c d e - 560c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((10a c - 3b )e + 2b c d e - 2c d e )\|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (- 16a b c + 3b )e + (32a c - 2b c)d e - 12b c d e + 8c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((10a c - 3b )e + 2b c d e - 2c d e )\|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (16a b c - 3b )e + (- 32a c + 2b c)d e + 12b c d e - 8c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 2 2 4 2 3 3 +--R (16a c - 4a b )e + (- 32a b c + 8a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 3 2 2 4 +--R (32a c + 8a b c - 4b )d e + (- 32a b c + 8b c)d e + (16a c - 4b c )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 844 + +--S 845 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich12d.input.pamphlet b/src/axiom-website/CATS/rich12d.input.pamphlet new file mode 100644 index 0000000..a5bc901 --- /dev/null +++ b/src/axiom-website/CATS/rich12d.input.pamphlet @@ -0,0 +1,68963 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12d.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 129 matching answers. +\item 151 cases where Axiom answer differs from Rubi +\item 52 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 26 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12d.output +)spool rich12d.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1378 +t0:=(b+2*c*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R +-------+ | 2 +--R (1) (2c x + b)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1378 +--r0:=4/7*(a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)-2/105*(8*c^2*d^2+b^2*e^2-_ +-- c*e*(11*b*d-10*a*e)-3*c*e*(2*c*d-b*e)*x)*sqrt(d+e*x)*sqrt(a+b*x+_ +-- c*x^2)/(c*e^2)-1/105*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(5*c*e*(b*d-2*a*e)^2-_ +-- (2*c*d-b*e)*(4*b*c*d^2-b^2*d*e-2*a*c*d*e-a*b*e^2))+(2*c*d-b*e)*_ +-- (4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e^3*sqrt(a+b*x+_ +-- c*x^2))-1/105*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*e^4*sqrt(a+b*x+c*x^2)) +--E 2 + +--S 3 of 1378 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 1378 +--m0:=a0-r0 +--E 4 + +--S 5 of 1378 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 1378 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1378 +--r0:=-2/15*(8*c*d-7*b*e-6*c*e*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/e^2-_ +-- 1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*(2*c*(7*b^2*d*e+4*a*c*d*e-8*b*(c*d^2+a*e^2))+_ +-- (16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e^3*sqrt(2)*sqrt(a+b*x+_ +-- c*x^2))-1/15*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*e^4*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 7 + +--S 8 of 1378 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 1378 +--m0:=a0-r0 +--E 9 + +--S 10 of 1378 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 1378 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1378 +--r0:=2/3*(8*c*d-3*b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*sqrt(d+e*x))-_ +-- 1/3*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(b*e*(b-4*sqrt(b^2-4*a*c))+c*(-4*a*e+_ +-- 8*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^3*sqrt(c)*sqrt(a+b*x+c*x^2))+4/3*(2*c*d-b*e)*elliptic_e(asin(_ +-- sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^4*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 12 + +--S 13 of 1378 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 1378 +--m0:=a0-r0 +--E 14 + +--S 15 of 1378 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 1378 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1378 +--r0:=2/3*(8*c*d-b*e+6*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/3*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*sqrt(a+b*x+c*x^2)/_ +-- (e^2*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(7*b^2*d*e+_ +-- 4*a*c*d*e-8*b*(c*d^2+a*e^2))+(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-_ +-- 3*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^3*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-_ +-- 4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-_ +-- 4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-_ +-- 4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^4*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 17 + +--S 18 of 1378 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 1378 +--m0:=a0-r0 +--E 19 + +--S 20 of 1378 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 1378 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1378 +--r0:=2/15*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*sqrt(a+b*x+c*x^2)/_ +-- (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))-2/5*(8*c*d+b*e+10*c*e*x)*_ +-- sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^(5/2))+4/15*(2*c*d-b*e)*(4*c^2*d^2-_ +-- b^2*e^2-4*c*e*(b*d-2*a*e))*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*_ +-- e^2)^2*sqrt(d+e*x))+1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+_ +-- e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*_ +-- a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*(b^3*d*e^2-4*a*_ +-- c*e*(c*d^2+5*a*e^2)+4*b*c*d*(2*c*d^2+5*a*e^2)-b^2*(11*c*d^2*e-a*e^3))+_ +-- (2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e^3*(c*d^2-b*d*e+a*e^2)^2*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2))+1/15*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-_ +-- 2*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^4*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 22 + +--S 23 of 1378 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 1378 +--m0:=a0-r0 +--E 24 + +--S 25 of 1378 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 1378 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1378 +--r0:=-2/63*(16*c*d-15*b*e-14*c*e*x)*(a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)/e^2-_ +-- 2/315*(128*c^3*d^3-b^3*e^3+3*b*c*e^2*(37*b*d-36*a*e)-12*c^2*d*_ +-- e*(20*b*d-11*a*e)-3*c*e*(32*c^2*d^2+b^2*e^2-4*c*e*(8*b*d-7*a*e))*x)*_ +-- sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*e^4)-1/315*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*((4*b*c*_ +-- d^2-b^2*d*e-2*a*c*d*e-a*b*e^2)*(32*c^2*d^2+b^2*e^2-4*c*e*(8*b*d-_ +-- 7*a*e))+5*c*e*(b*d-2*a*e)*(15*b^2*d*e+4*a*c*d*e-16*b*(c*d^2+a*e^2)))+_ +-- (128*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(64*b*d-57*a*e)-b^2*c*e^3*(7*b*d-_ +-- 15*a*e)+3*c^2*e^2*(45*b^2*d^2-76*a*b*d*e+28*a^2*e^2))*(b-sqrt(b^2-_ +-- 4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e^5*sqrt(a+b*x+_ +-- c*x^2))-1/315*(128*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(64*b*d-57*a*e)-_ +-- b^2*c*e^3*(7*b*d-15*a*e)+3*c^2*e^2*(45*b^2*d^2-76*a*b*d*e+28*a^2*_ +-- e^2))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*e^6*sqrt(a+b*x+c*x^2)) +--E 27 + +--S 28 of 1378 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 1378 +--m0:=a0-r0 +--E 29 + +--S 30 of 1378 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 1378 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1378 +--r0:=2/7*(16*c*d-7*b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+_ +-- 2/35*(128*c^2*d^2+51*b^2*e^2-4*c*e*(44*b*d-5*a*e)-48*c*e*(2*c*d-_ +-- b*e)*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/e^4+1/35*elliptic_f(asin(_ +-- sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- (-2*c*(51*b^3*d*e^2-8*a*c*e*(8*c*d^2+5*a*e^2)+4*b*c*d*(32*c*d^2+_ +-- 45*a*e^2)-2*b^2*(88*c*d^2*e+27*a*e^3))+(2*c*d-b*e)*(128*c^2*d^2+_ +-- 3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e^5*sqrt(2)*sqrt(a+b*x+c*x^2))+_ +-- 1/35*(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*e^6*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 32 + +--S 33 of 1378 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 1378 +--m0:=a0-r0 +--E 34 + +--S 35 of 1378 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 1378 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1378 +--r0:=2/15*(16*c*d-5*b*e+6*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/15*(128*c^2*d^2+15*b^2*e^2-4*c*e*(28*b*d-9*a*e)+16*c*e*(2*c*d-_ +-- b*e)*x)*sqrt(a+b*x+c*x^2)/(e^4*sqrt(d+e*x))-1/15*elliptic_f(_ +-- asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(b^2*e^2*(8*b-23*sqrt(b^2-4*a*c))-64*c^2*d*(-a*e+2*d*_ +-- sqrt(b^2-4*a*c))-4*c*e*(4*b^2*d+8*a*b*e-32*b*d*sqrt(b^2-4*a*c)+_ +-- 9*a*e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^5*sqrt(c)*sqrt(a+b*x+c*x^2))-1/15*(128*c^2*d^2+23*b^2*e^2-_ +-- 4*c*e*(32*b*d-9*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^6*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 37 + +--S 38 of 1378 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 1378 +--m0:=a0-r0 +--E 39 + +--S 40 of 1378 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 1378 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1378 +--r0:=2/15*(16*c*d-3*b*e+10*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 2/15*(128*c^2*d^2+3*b^2*e^2-20*c*e*(4*b*d-a*e)+48*c*e*(2*c*d-b*e)*x)*_ +-- sqrt(a+b*x+c*x^2)/(e^4*(d+e*x)^(3/2))+2/15*(2*c*d-b*e)*(128*c^2*d^2+_ +-- 3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*sqrt(a+b*x+c*x^2)/(e^4*(c*d^2-_ +-- b*d*e+a*e^2)*sqrt(d+e*x))+1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(-2*c*(51*b^3*d*e^2-_ +-- 8*a*c*e*(8*c*d^2+5*a*e^2)+4*b*c*d*(32*c*d^2+45*a*e^2)-2*b^2*(88*c*_ +-- d^2*e+27*a*e^3))+(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-_ +-- 29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^5*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+_ +-- 1/15*(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^6*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 42 + +--S 43 of 1378 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 1378 +--m0:=a0-r0 +--E 44 + +--S 45 of 1378 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1378 +--r0:=2/7*(2*c*d-b*e)*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)/c+4/7*(d+e*x)^(5/2)*_ +-- sqrt(a+b*x+c*x^2)+4/21*(3*c^2*d^2+2*b^2*e^2-c*e*(3*b*d+5*a*e))*_ +-- sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c^2-1/21*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(4*b^3*_ +-- d*e^2+2*a*c*e*(27*c*d^2-5*a*e^2)-b*c*d*(3*c*d^2+25*a*e^2)-b^2*_ +-- (9*c*d^2*e-4*a*e^3))+(2*c*d-b*e)*(3*c^2*d^2+8*b^2*e^2-c*e*(3*b*d+_ +-- 29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(7/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-1/21*(2*c*d-b*e)*(3*c^2*d^2+_ +-- 8*b^2*e^2-c*e*(3*b*d+29*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(7/2)*_ +-- e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 47 + +--S 48 of 1378 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 1378 +--m0:=a0-r0 +--E 49 + +--S 50 of 1378 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1378 +--r0:=4/5*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)+2/5*(2*c*d-b*e)*sqrt(d+e*x)*_ +-- sqrt(a+b*x+c*x^2)/c+1/5*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*_ +-- d*e+a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e*sqrt(a+b*x+c*x^2))-_ +-- 1/5*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- e^2*sqrt(a+b*x+c*x^2)) +--E 52 + +--S 53 of 1378 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 1378 +--m0:=a0-r0 +--E 54 + +--S 55 of 1378 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 1378 +t0:=(b+2*c*x)*sqrt(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1378 +--r0:=4/3*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)+1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(b*e*(b-_ +-- sqrt(b^2-4*a*c))+2*c*(-2*a*e+d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 57 + +--S 58 of 1378 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 1378 +--m0:=a0-r0 +--E 59 + +--S 60 of 1378 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 1378 +t0:=(b+2*c*x)/(sqrt(d+e*x)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) --------------------------- +--R +--------------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1378 +--r0:=elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/(e*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 62 + +--S 63 of 1378 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 1378 +--m0:=a0-r0 +--E 64 + +--S 65 of 1378 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 1378 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------ +--R +--------------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1378 +--r0:=2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+2*d*sqrt(b^2-_ +-- 4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(2*c*d-b*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 67 + +--S 68 of 1378 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 1378 +--m0:=a0-r0 +--E 69 + +--S 70 of 1378 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 1378 +t0:=(b+2*c*x)/((d+e*x)^(5/2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ----------------------------------------------- +--R +--------------+ +--R 2 2 2 +-------+ | 2 +--R (e x + 2d e x + d )\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1378 +--r0:=2/3*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+_ +-- 4/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-_ +-- b*d*e+a*e^2)^2*sqrt(d+e*x))-1/3*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+_ +-- b^2*d*e-8*a*c*d*e+a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*_ +-- sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+_ +-- 2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*(c*d^2-_ +-- b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2))+1/3*(c^2*d^2+b^2*e^2-_ +-- c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 72 + +--S 73 of 1378 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 1378 +--m0:=a0-r0 +--E 74 + +--S 75 of 1378 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1378 +--r0:=-2*(d+e*x)^(7/2)/sqrt(a+b*x+c*x^2)+14/5*e^2*(d+e*x)^(3/2)*_ +-- sqrt(a+b*x+c*x^2)/c+56/15*e^2*(2*c*d-b*e)*sqrt(d+e*x)*sqrt(a+_ +-- b*x+c*x^2)/c^2-7/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(-2*c*(15*c^2*d^3+4*b*e^2*(b*d+a*e)-_ +-- c*d*e*(11*b*d+17*a*e))+e*(23*c^2*d^2+8*b^2*e^2-c*e*(23*b*d+9*a*e))*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(7/2)*sqrt(2)*sqrt(a+b*x+c*x^2))-7/15*(23*c^2*d^2+8*b^2*e^2-_ +-- c*e*(23*b*d+9*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(7/2)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 77 + +--S 78 of 1378 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 1378 +--m0:=a0-r0 +--E 79 + +--S 80 of 1378 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1378 +--r0:=-2*(d+e*x)^(5/2)/sqrt(a+b*x+c*x^2)+10/3*e^2*sqrt(d+e*x)*_ +-- sqrt(a+b*x+c*x^2)/c-5/3*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*(3*c*d^2-e*(b*d+a*e))+_ +-- e*(2*c*d-b*e)*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(5/2)*sqrt(a+b*x+c*x^2))-5/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- sqrt(a+b*x+c*x^2)) +--E 82 + +--S 83 of 1378 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 1378 +--m0:=a0-r0 +--E 84 + +--S 85 of 1378 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1378 +--r0:=-2*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2)+3*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))^(3/2)*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*sqrt(2)*sqrt(a+b*x+c*x^2))-3*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 87 + +--S 88 of 1378 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 1378 +--m0:=a0-r0 +--E 89 + +--S 90 of 1378 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 1378 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1378 +--r0:=-2*sqrt(d+e*x)/sqrt(a+b*x+c*x^2)+elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/(sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 92 + +--S 93 of 1378 +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 1378 +--m0:=a0-r0 +--E 94 + +--S 95 of 1378 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 1378 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------- +--R +--------------+ +--R 2 +-------+ | 2 +--R (c x + b x + a)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1378 +--r0:=-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ +-- (c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2))-elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))^(3/2)*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+_ +-- c*x^2))+elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 97 + +--S 98 of 1378 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 1378 +--m0:=a0-r0 +--E 99 + +--S 100 of 1378 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 1378 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R 2c x + b +--R ------------------------------------------------------------------------ +--R +--------------+ +--R 3 2 +-------+ | 2 +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1378 +--r0:=-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-_ +-- b*d*e+a*e^2)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))+4*e^2*(2*c*d-b*e)*_ +-- sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))-_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(3*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-_ +-- c*e*(3*b*d+a*e-2*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- ((c*d^2-b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2))+(2*c*d-b*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 102 + +--S 103 of 1378 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 1378 +--m0:=a0-r0 +--E 104 + +--S 105 of 1378 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1378 +--r0:=-2/3*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(3/2)-14/3*e*(d+e*x)^(3/2)*(b*d-_ +-- 2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+14/3*e^2*(2*c*d-_ +-- b*e)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*(b^2-4*a*c))+7/3*e*_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*d*e+a*b*e^2)-_ +-- (c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))-_ +-- 7/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- (b^2-4*a*c)*sqrt(a+b*x+c*x^2)) +--E 107 + +--S 108 of 1378 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 1378 +--m0:=a0-r0 +--E 109 + +--S 110 of 1378 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1378 +--r0:=-2/3*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2)-10/3*e*(b*d-2*a*e+(2*c*d-_ +-- b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+5/3*e*_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+2*d*_ +-- sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*(b^2-_ +-- 4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))-5/3*(2*c*d-b*e)*elliptic_e(_ +-- asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*_ +-- (b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 112 + +--S 113 of 1378 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 1378 +--m0:=a0-r0 +--E 114 + +--S 115 of 1378 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1378 +--r0:=-2/3*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2)-2*e*(b+2*c*x)*sqrt(d+e*x)/_ +-- ((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+e*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(sqrt(c)*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2))-_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 117 + +--S 118 of 1378 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 1378 +--m0:=a0-r0 +--E 119 + +--S 120 of 1378 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 1378 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1378 +--r0:=-2/3*sqrt(d+e*x)/(a+b*x+c*x^2)^(3/2)-2/3*e*(b*c*d-b^2*e+2*a*c*e+c*_ +-- (2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(a+b*x+c*x^2))+1/3*e*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+_ +-- 2*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- ((b^2-4*a*c)*(c*d^2-e*(b*d-a*e))*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*(c*d^2-e*(b*d-a*e))*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 122 + +--S 123 of 1378 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 1378 +--m0:=a0-r0 +--E 124 + +--S 125 of 1378 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 1378 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R (1) +--R 2c x + b +--R ------------------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 +-------+ | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1378 +--r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-_ +-- 4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-2/3*e*(3*b^2*c*d*e-_ +-- 8*a*c^2*d*e-2*b^3*e^2-b*c*(c*d^2-7*a*e^2)-2*c*(c^2*d^2+b^2*e^2-_ +-- c*e*(b*d+3*a*e))*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(a+b*x+c*x^2))-1/3*e*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*d*e+_ +-- a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2))+1/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-_ +-- 4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 127 + +--S 128 of 1378 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 1378 +--m0:=a0-r0 +--E 129 + +--S 130 of 1378 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 1378 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 m +--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(e x + d) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1378 +r0:=-(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(b*d-a*e)*(3*b*B*d-_ + 2*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^4*(2+m))-b*(3*b*B*d-A*b*e-2*a*B*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+b^2*B*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 m + 4 +--R (B b m + 6B b m + 11B b m + 6B b )(e x + d) +--R + +--R 2 2 3 2 2 2 +--R ((A b + 2B a b)e - 3B b d)m + ((7A b + 14B a b)e - 21B b d)m +--R + +--R 2 2 2 2 +--R ((14A b + 28B a b)e - 42B b d)m + (8A b + 16B a b)e - 24B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (- 2A b - 4B a b)d e + 3B b d )m +--R + +--R 2 2 2 2 2 2 +--R ((16A a b + 8B a )e + (- 16A b - 32B a b)d e + 24B b d )m +--R + +--R 2 2 2 2 2 +--R ((38A a b + 19B a )e + (- 38A b - 76B a b)d e + 57B b d )m +--R + +--R 2 2 2 2 2 +--R (24A a b + 12B a )e + (- 24A b - 48B a b)d e + 36B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (- 2A a b - B a )d e + (A b + 2B a b)d e - B b d )m +--R + +--R 2 3 2 2 2 2 +--R 9A a e + (- 18A a b - 9B a )d e + (9A b + 18B a b)d e +--R + +--R 2 3 +--R - 9B b d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 2 +--R 26A a e + (- 52A a b - 26B a )d e + (26A b + 52B a b)d e +--R + +--R 2 3 +--R - 26B b d +--R * +--R m +--R + +--R 2 3 2 2 2 2 2 3 +--R 24A a e + (- 48A a b - 24B a )d e + (24A b + 48B a b)d e - 24B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 4 2 2 4 2 4 4 +--R (B b e m + 6B b e m + 11B b e m + 6B b e )x +--R + +--R 2 4 2 3 3 +--R ((A b + 2B a b)e + B b d e )m +--R + +--R 2 4 2 3 2 +--R ((7A b + 14B a b)e + 3B b d e )m +--R + +--R 2 4 2 3 2 4 +--R ((14A b + 28B a b)e + 2B b d e )m + (8A b + 16B a b)e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 3 +--R ((2A a b + B a )e + (A b + 2B a b)d e )m +--R + +--R 2 4 2 3 2 2 2 2 +--R ((16A a b + 8B a )e + (5A b + 10B a b)d e - 3B b d e )m +--R + +--R 2 4 2 3 2 2 2 +--R ((38A a b + 19B a )e + (4A b + 8B a b)d e - 3B b d e )m +--R + +--R 2 4 +--R (24A a b + 12B a )e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 3 +--R (A a e + (2A a b + B a )d e )m +--R + +--R 2 4 2 3 2 2 2 2 +--R (9A a e + (14A a b + 7B a )d e + (- 2A b - 4B a b)d e )m +--R + +--R 2 4 2 3 2 2 2 +--R 26A a e + (24A a b + 12B a )d e + (- 8A b - 16B a b)d e +--R + +--R 2 3 +--R 6B b d e +--R * +--R m +--R + +--R 2 4 +--R 24A a e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 2 2 +--R A a d e m + (9A a d e + (- 2A a b - B a )d e )m +--R + +--R 2 3 2 2 2 2 3 +--R (26A a d e + (- 14A a b - 7B a )d e + (2A b + 4B a b)d e)m +--R + +--R 2 3 2 2 2 2 3 2 4 +--R 24A a d e + (- 24A a b - 12B a )d e + (8A b + 16B a b)d e - 6B b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 3 2 4 2 2 4 2 4 4 +--R (B b e m + 6B b e m + 11B b e m + 6B b e )x +--R + +--R 2 4 2 3 3 +--R ((A b + 2B a b)e + B b d e )m +--R + +--R 2 4 2 3 2 +--R ((7A b + 14B a b)e + 3B b d e )m +--R + +--R 2 4 2 3 2 4 +--R ((14A b + 28B a b)e + 2B b d e )m + (8A b + 16B a b)e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 3 +--R ((2A a b + B a )e + (A b + 2B a b)d e )m +--R + +--R 2 4 2 3 2 2 2 2 +--R ((16A a b + 8B a )e + (5A b + 10B a b)d e - 3B b d e )m +--R + +--R 2 4 2 3 2 2 2 +--R ((38A a b + 19B a )e + (4A b + 8B a b)d e - 3B b d e )m +--R + +--R 2 4 +--R (24A a b + 12B a )e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 3 +--R (A a e + (2A a b + B a )d e )m +--R + +--R 2 4 2 3 2 2 2 2 +--R (9A a e + (14A a b + 7B a )d e + (- 2A b - 4B a b)d e )m +--R + +--R 2 4 2 3 2 2 2 +--R 26A a e + (24A a b + 12B a )d e + (- 8A b - 16B a b)d e +--R + +--R 2 3 +--R 6B b d e +--R * +--R m +--R + +--R 2 4 +--R 24A a e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 2 2 +--R A a d e m + (9A a d e + (- 2A a b - B a )d e )m +--R + +--R 2 3 2 2 2 2 3 +--R (26A a d e + (- 14A a b - 7B a )d e + (2A b + 4B a b)d e)m +--R + +--R 2 3 2 2 2 2 3 2 4 +--R 24A a d e + (- 24A a b - 12B a )d e + (8A b + 16B a b)d e - 6B b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 3 2 2 2 2 m + 4 +--R (- B b m - 6B b m - 11B b m - 6B b )(e x + d) +--R + +--R 2 2 3 2 2 2 +--R ((- A b - 2B a b)e + 3B b d)m + ((- 7A b - 14B a b)e + 21B b d)m +--R + +--R 2 2 2 2 +--R ((- 14A b - 28B a b)e + 42B b d)m + (- 8A b - 16B a b)e + 24B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 2 3 +--R ((- 2A a b - B a )e + (2A b + 4B a b)d e - 3B b d )m +--R + +--R 2 2 2 2 2 2 +--R ((- 16A a b - 8B a )e + (16A b + 32B a b)d e - 24B b d )m +--R + +--R 2 2 2 2 2 +--R ((- 38A a b - 19B a )e + (38A b + 76B a b)d e - 57B b d )m +--R + +--R 2 2 2 2 2 +--R (- 24A a b - 12B a )e + (24A b + 48B a b)d e - 36B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- A a e + (2A a b + B a )d e + (- A b - 2B a b)d e + B b d )m +--R + +--R 2 3 2 2 2 2 +--R - 9A a e + (18A a b + 9B a )d e + (- 9A b - 18B a b)d e +--R + +--R 2 3 +--R 9B b d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 2 +--R - 26A a e + (52A a b + 26B a )d e + (- 26A b - 52B a b)d e +--R + +--R 2 3 +--R 26B b d +--R * +--R m +--R + +--R 2 3 2 2 2 2 +--R - 24A a e + (48A a b + 24B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 24B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1378 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 5 8 2 5 2 4 7 +--R B b e x + ((A b + 2B a b)e + 5B b d e )x +--R + +--R 2 5 2 4 2 2 3 6 +--R ((2A a b + B a )e + (5A b + 10B a b)d e + 10B b d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 5 +--R (A a e + (10A a b + 5B a )d e + (10A b + 20B a b)d e + 10B b d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 4 4 +--R (5A a d e + (20A a b + 10B a )d e + (10A b + 20B a b)d e + 5B b d e)x +--R + +--R 2 2 3 2 3 2 2 4 2 5 3 +--R (10A a d e + (20A a b + 10B a )d e + (5A b + 10B a b)d e + B b d )x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 1378 +r0:=-1/6*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^6/e^4+1/7*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^7/e^4-1/8*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^8/e^4+_ + 1/9*b^2*B*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 2 9 9 1 2 1 9 5 2 8 8 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 9 5 2 10 8 10 2 2 7 7 +--R ((- A a b + - B a )e + (- A b + -- B a b)d e + -- B b d e )x +--R 7 7 7 7 7 +--R + +--R 1 2 9 5 5 2 8 5 2 10 2 7 +--R - A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e +--R 6 3 6 3 3 +--R + +--R 5 2 3 6 +--R - B b d e +--R 3 +--R * +--R 6 +--R x +--R + +--R 2 8 2 2 7 2 3 6 2 4 5 5 +--R (A a d e + (4A a b + 2B a )d e + (2A b + 4B a b)d e + B b d e )x +--R + +--R 5 2 2 7 5 2 3 6 5 2 5 4 5 +--R - A a d e + (5A a b + - B a )d e + (- A b + - B a b)d e +--R 2 2 4 2 +--R + +--R 1 2 5 4 +--R - B b d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 10 2 3 6 10 5 2 4 5 1 2 2 5 4 3 +--R (-- A a d e + (-- A a b + - B a )d e + (- A b + - B a b)d e )x +--R 3 3 3 3 3 +--R + +--R 5 2 4 5 1 2 5 4 2 2 5 4 1 2 6 3 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 1 1 2 7 2 1 2 1 8 1 2 9 +--R (- -- A a b - -- B a )d e + (--- A b + -- B a b)d e - --- B b d +--R 21 42 168 84 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 137 + +--S 138 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 5 9 1 2 1 5 5 2 4 8 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 5 5 2 10 4 10 2 2 3 7 +--R ((- A a b + - B a )e + (- A b + -- B a b)d e + -- B b d e )x +--R 7 7 7 7 7 +--R + +--R 1 2 5 5 5 2 4 5 2 10 2 3 +--R - A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e +--R 6 3 6 3 3 +--R + +--R 5 2 3 2 +--R - B b d e +--R 3 +--R * +--R 6 +--R x +--R + +--R 2 4 2 2 3 2 3 2 2 4 5 +--R (A a d e + (4A a b + 2B a )d e + (2A b + 4B a b)d e + B b d e)x +--R + +--R 5 2 2 3 5 2 3 2 5 2 5 4 1 2 5 4 +--R (- A a d e + (5A a b + - B a )d e + (- A b + - B a b)d e + - B b d )x +--R 2 2 4 2 4 +--R + +--R 10 2 3 2 10 5 2 4 1 2 2 5 3 +--R (-- A a d e + (-- A a b + - B a )d e + (- A b + - B a b)d )x +--R 3 3 3 3 3 +--R + +--R 5 2 4 1 2 5 2 2 5 +--R (- A a d e + (A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 6 3 1 1 2 7 2 1 2 1 8 +--R - - A a d e + (-- A a b + -- B a )d e + (- --- A b - -- B a b)d e +--R 6 21 42 168 84 +--R + +--R 1 2 9 +--R --- B b d +--R 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 139 + +--S 140 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 140 + +)clear all + +--S 141 of 1378 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 7 2 4 2 3 6 +--R B b e x + ((A b + 2B a b)e + 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((2A a b + B a )e + (4A b + 8B a b)d e + 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (A a e + (8A a b + 4B a )d e + (6A b + 12B a b)d e + 4B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 3 +--R (4A a d e + (12A a b + 6B a )d e + (4A b + 8B a b)d e + B b d )x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 141 + +--S 142 of 1378 +r0:=-1/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^5/e^4+1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^6/e^4-1/7*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^7/e^4+_ + 1/8*b^2*B*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 2 8 8 1 2 2 8 4 2 7 7 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 8 7 7 7 +--R + +--R 1 1 2 8 2 2 4 7 2 2 6 6 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + B b d e )x +--R 3 6 3 3 +--R + +--R 1 2 8 8 4 2 7 6 2 12 2 6 +--R - A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e +--R 5 5 5 5 5 +--R + +--R 4 2 3 5 +--R - B b d e +--R 5 +--R * +--R 5 +--R x +--R + +--R 2 7 3 2 2 6 2 3 5 1 2 4 4 4 +--R (A a d e + (3A a b + - B a )d e + (A b + 2B a b)d e + - B b d e )x +--R 2 4 +--R + +--R 2 2 6 8 4 2 3 5 1 2 2 4 4 3 +--R (2A a d e + (- A a b + - B a )d e + (- A b + - B a b)d e )x +--R 3 3 3 3 +--R + +--R 2 3 5 1 2 4 4 2 2 4 4 1 2 5 3 +--R (2A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 5 +--R + +--R 1 1 2 6 2 1 2 2 7 1 2 8 +--R (- -- A a b - -- B a )d e + (--- A b + --- B a b)d e - --- B b d +--R 15 30 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 142 + +--S 143 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 8 1 2 2 4 4 2 3 7 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 8 7 7 7 +--R + +--R 1 1 2 4 2 2 4 3 2 2 2 6 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + B b d e )x +--R 3 6 3 3 +--R + +--R 1 2 4 8 4 2 3 6 2 12 2 2 4 2 3 5 +--R (- A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e + - B b d e)x +--R 5 5 5 5 5 5 +--R + +--R 2 3 3 2 2 2 2 3 1 2 4 4 +--R (A a d e + (3A a b + - B a )d e + (A b + 2B a b)d e + - B b d )x +--R 2 4 +--R + +--R 2 2 2 8 4 2 3 1 2 2 4 3 +--R (2A a d e + (- A a b + - B a )d e + (- A b + - B a b)d )x +--R 3 3 3 3 +--R + +--R 2 3 1 2 4 2 2 4 +--R (2A a d e + (A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 143 + +--S 144 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 5 3 1 1 2 6 2 1 2 2 7 +--R - - A a d e + (-- A a b + -- B a )d e + (- --- A b - --- B a b)d e +--R 5 15 30 105 105 +--R + +--R 1 2 8 +--R --- B b d +--R 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 144 + +--S 145 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 145 + +)clear all + +--S 146 of 1378 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 146 + +--S 147 of 1378 +r0:=-1/4*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^4/e^4+1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^5/e^4-1/6*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^6/e^4+_ + 1/7*b^2*B*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 2 7 7 1 2 1 7 1 2 6 6 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 7 6 3 2 +--R + +--R 2 1 2 7 3 2 6 6 3 2 2 5 5 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + - B b d e )x +--R 5 5 5 5 5 +--R + +--R 1 2 7 3 3 2 6 3 2 3 2 5 +--R - A a e + (- A a b + - B a )d e + (- A b + - B a b)d e +--R 4 2 4 4 2 +--R + +--R 1 2 3 4 +--R - B b d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 1 2 2 3 4 3 +--R (A a d e + (2A a b + B a )d e + (- A b + - B a b)d e )x +--R 3 3 +--R + +--R 3 2 2 5 1 2 3 4 2 2 3 4 1 2 4 3 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 4 +--R + +--R 1 1 2 5 2 1 2 1 6 1 2 7 +--R (- -- A a b - -- B a )d e + (-- A b + -- B a b)d e - --- B b d +--R 10 20 60 30 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 147 + +--S 148 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 3 7 1 2 1 3 1 2 2 6 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 7 6 3 2 +--R + +--R 2 1 2 3 3 2 6 2 3 2 2 5 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + - B b d e)x +--R 5 5 5 5 5 +--R + +--R 1 2 3 3 3 2 2 3 2 3 2 1 2 3 4 +--R (- A a e + (- A a b + - B a )d e + (- A b + - B a b)d e + - B b d )x +--R 4 2 4 4 2 4 +--R + +--R 2 2 2 2 1 2 2 3 3 +--R (A a d e + (2A a b + B a )d e + (- A b + - B a b)d )x +--R 3 3 +--R + +--R 3 2 2 1 2 3 2 2 3 +--R (- A a d e + (A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 148 + +--S 149 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 4 3 1 1 2 5 2 1 2 1 6 +--R - - A a d e + (-- A a b + -- B a )d e + (- -- A b - -- B a b)d e +--R 4 10 20 60 30 +--R + +--R 1 2 7 +--R --- B b d +--R 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 150 + +)clear all + +--S 151 of 1378 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 151 + +--S 152 of 1378 +r0:=1/3*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^3/b^4+1/4*(b*d-a*e)*(b*B*d+2*A*b*e-_ + 3*a*B*e)*(a+b*x)^4/b^4+1/5*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^5/b^4+_ + 1/6*B*e^2*(a+b*x)^6/b^4 +--R +--R +--R (2) +--R 1 6 2 6 1 6 2 5 2 2 6 5 +--R - B b e x + ((- A b + - B a b )e + - B b d e)x +--R 6 5 5 5 +--R + +--R 1 5 1 2 4 2 1 6 5 1 6 2 4 +--R ((- A a b + - B a b )e + (- A b + B a b )d e + - B b d )x +--R 2 4 2 4 +--R + +--R 1 2 4 2 4 5 2 2 4 1 6 2 5 2 3 +--R (- A a b e + (- A a b + - B a b )d e + (- A b + - B a b )d )x +--R 3 3 3 3 3 +--R + +--R 2 4 5 1 2 4 2 2 2 4 2 +--R (A a b d e + (A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 5 1 6 2 1 4 2 1 5 +--R (-- A a b - -- B a )e + (- - A a b + -- B a b)d e +--R 30 60 6 15 +--R + +--R 1 3 3 1 4 2 2 +--R (- A a b - -- B a b )d +--R 3 12 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 152 + +--S 153 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 6 1 2 2 2 2 2 5 +--R - B b e x + ((- A b + - B a b)e + - B b d e)x +--R 6 5 5 5 +--R + +--R 1 1 2 2 1 2 1 2 2 4 +--R ((- A a b + - B a )e + (- A b + B a b)d e + - B b d )x +--R 2 4 2 4 +--R + +--R 1 2 2 4 2 2 1 2 2 2 3 +--R (- A a e + (- A a b + - B a )d e + (- A b + - B a b)d )x +--R 3 3 3 3 3 +--R + +--R 2 1 2 2 2 2 2 +--R (A a d e + (A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 153 + +--S 154 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 5 1 6 2 1 4 2 1 5 +--R (- -- A a b + -- B a )e + (- A a b - -- B a b)d e +--R 30 60 6 15 +--R + +--R 1 3 3 1 4 2 2 +--R (- - A a b + -- B a b )d +--R 3 12 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 154 + +--S 155 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 155 + +)clear all + +--S 156 of 1378 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 156 + +--S 157 of 1378 +r0:=1/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)^3/b^3+1/4*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^4/b^3+1/5*B*e*(a+b*x)^5/b^3 +--R +--R +--R (2) +--R 1 5 5 1 5 1 4 1 5 4 +--R - B b e x + ((- A b + - B a b )e + - B b d)x +--R 5 4 2 4 +--R + +--R 2 4 1 2 3 1 5 2 4 3 +--R ((- A a b + - B a b )e + (- A b + - B a b )d)x +--R 3 3 3 3 +--R + +--R 1 2 3 4 1 2 3 2 2 3 +--R (- A a b e + (A a b + - B a b )d)x + A a b d x +--R 2 2 +--R + +--R 1 4 1 5 1 3 2 1 4 +--R (- -- A a b + -- B a )e + (- A a b - -- B a b)d +--R 12 30 3 12 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 157 + +--S 158 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 5 1 2 1 1 2 4 +--R - B b e x + ((- A b + - B a b)e + - B b d)x +--R 5 4 2 4 +--R + +--R 2 1 2 1 2 2 3 +--R ((- A a b + - B a )e + (- A b + - B a b)d)x +--R 3 3 3 3 +--R + +--R 1 2 1 2 2 2 +--R (- A a e + (A a b + - B a )d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 158 + +--S 159 of 1378 +m0:=a0-r0 +--R +--R +--R 1 4 1 5 1 3 2 1 4 +--R (-- A a b - -- B a )e + (- - A a b + -- B a b)d +--R 12 30 3 12 +--R (4) ------------------------------------------------ +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 159 + +--S 160 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 160 + +)clear all + +--S 161 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 161 + +--S 162 of 1378 +r0:=1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2 +--R +--R +--R (2) +--R 1 4 4 1 4 2 3 3 3 1 2 2 2 2 2 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x + A a b x +--R 4 3 3 2 +--R + +--R 1 3 1 4 +--R - A a b - -- B a +--R 3 12 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +--S 163 of 1378 +a0:=integrate(t0,x) +--R +--R +--R 1 2 4 1 2 2 3 1 2 2 2 +--R (3) - B b x + (- A b + - B a b)x + (A a b + - B a )x + A a x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 163 + +--S 164 of 1378 +m0:=a0-r0 +--R +--R +--R 1 3 1 4 +--R - - A a b + -- B a +--R 3 12 +--R (4) ------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 164 + +--S 165 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 165 + +)clear all + +--S 166 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1378 +r0:=b*(b*d-a*e)*(B*d-A*e)*x/e^3-1/2*(B*d-A*e)*(a+b*x)^2/e^2+_ + 1/3*B*(a+b*x)^3/(b*e)-(b*d-a*e)^2*(B*d-A*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 +--R 6A a b e + (- 12A a b - 6B a b)d e + (6A b + 12B a b )d e +--R + +--R 3 3 +--R - 6B b d +--R * +--R log(e x + d) +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 2B b e x + ((3A b + 6B a b )e - 3B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((12A a b + 6B a b)e + (- 6A b - 12B a b )d e + 6B b d e)x +--R + +--R 2 3 3 2 2 +--R (3A a b + 2B a )e - 3B a b d e +--R / +--R 4 +--R 6b e +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 3 +--R (6A a e + (- 12A a b - 6B a )d e + (6A b + 12B a b)d e - 6B b d ) +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((3A b + 6B a b)e - 3B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((12A a b + 6B a )e + (- 6A b - 12B a b)d e + 6B b d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1378 +m0:=a0-r0 +--R +--R +--R 2 3 2 +--R (- 3A a b - 2B a )e + 3B a b d +--R (4) ------------------------------ +--R 2 +--R 6b e +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1378 +r0:=-b*(2*b*B*d-A*b*e-2*a*B*e)*x/e^3+1/2*b^2*B*x^2/e^2+(b*d-a*e)^2*_ + (B*d-A*e)/(e^4*(d+e*x))+(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 2 +--R ((4A a b + 2B a )e + (- 4A b - 8B a b)d e + 6B b d e)x +--R + +--R 2 2 2 2 2 3 +--R (4A a b + 2B a )d e + (- 4A b - 8B a b)d e + 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 3 2 2 2 +--R B b e x + ((2A b + 4B a b)e - 3B b d e )x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A b + 4B a b)d e - 4B b d e)x - 2A a e + (4A a b + 2B a )d e +--R + +--R 2 2 2 3 +--R (- 2A b - 4B a b)d e + 2B b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 +--R ((4A a b + 2B a )e + (- 4A b - 8B a b)d e + 6B b d e)x +--R + +--R 2 2 2 2 2 3 +--R (4A a b + 2B a )d e + (- 4A b - 8B a b)d e + 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 3 2 2 2 +--R B b e x + ((2A b + 4B a b)e - 3B b d e )x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A b + 4B a b)d e - 4B b d e)x - 2A a e + (4A a b + 2B a )d e +--R + +--R 2 2 2 3 +--R (- 2A b - 4B a b)d e + 2B b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1378 +r0:=b^2*B*x/e^3+1/2*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^2)-(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x))-b*(3*b*B*d-A*b*e-2*a*B*e)*_ + log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R ((2A b + 4B a b)e - 6B b d e )x +--R + +--R 2 2 2 2 2 2 2 3 +--R ((4A b + 8B a b)d e - 12B b d e)x + (2A b + 4B a b)d e - 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 +--R 2B b e x + 4B b d e x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 4A a b - 2B a )e + (4A b + 8B a b)d e - 4B b d e)x - A a e +--R + +--R 2 2 2 2 2 3 +--R (- 2A a b - B a )d e + (3A b + 6B a b)d e - 5B b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 +--R ((2A b + 4B a b)e - 6B b d e )x +--R + +--R 2 2 2 2 2 2 2 3 +--R ((4A b + 8B a b)d e - 12B b d e)x + (2A b + 4B a b)d e - 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 +--R 2B b e x + 4B b d e x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 4A a b - 2B a )e + (4A b + 8B a b)d e - 4B b d e)x - A a e +--R + +--R 2 2 2 2 2 3 +--R (- 2A a b - B a )d e + (3A b + 6B a b)d e - 5B b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1378 +r0:=-1/3*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^3)-1/2*B*(b*d-a*e)^2/_ + (e^4*(d+e*x)^2)+2*b*B*(b*d-a*e)/(e^4*(d+e*x))+b^2*B*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 4 3 3 3 2 3 3 2 2 2 +--R (6B a b e - 6B b d e )x + (18B a b d e - 18B b d e )x +--R + +--R 2 2 2 3 3 2 3 3 4 +--R (18B a b d e - 18B b d e)x + 6B a b d e - 6B b d +--R * +--R log(e x + d) +--R + +--R 3 4 3 3 3 +--R (- 2A b e + 2B b d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 6A a b - 12B a b)e + 30B a b d e - 12B b d e )x +--R + +--R 2 3 4 2 3 2 2 2 3 3 +--R ((- 6A a b - 3B a )e - 9B a b d e + 39B a b d e - 21B b d e)x +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 +--R - 2A a e - B a d e - 3B a b d e + 15B a b d e - 9B b d +--R / +--R 8 7 3 7 2 6 2 2 6 3 5 +--R (6a e - 6b d e )x + (18a d e - 18b d e )x + (18a d e - 18b d e )x +--R + +--R 3 5 4 4 +--R 6a d e - 6b d e +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 2 2 2 3 +--R (6B b e x + 18B b d e x + 18B b d e x + 6B b d )log(e x + d) +--R + +--R 2 3 2 2 2 +--R ((- 6A b - 12B a b)e + 18B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 6A a b - 3B a )e + (- 6A b - 12B a b)d e + 27B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 2A a b - B a )d e + (- 2A b - 4B a b)d e + 11B b d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1378 +m0:=a0-r0 +--R +--R +--R 3 3 +--R A b e - B b d +--R (4) --------------- +--R 5 4 +--R 3a e - 3b d e +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1378 +r0:=-1/4*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^4)+1/12*(3*b*B*d+A*b*e-_ + 4*a*B*e)*(a+b*x)^3/(e*(b*d-a*e)^2*(d+e*x)^3) +--R +--R +--R (2) +--R 1 4 1 3 1 4 4 +--R ((-- A b - - B a b )e + - B b d)x +--R 12 3 4 +--R + +--R 2 2 1 4 2 3 3 +--R (- B a b e + (- A b + - B a b )d)x +--R 3 3 +--R + +--R 1 2 2 3 3 1 2 2 2 +--R ((- - A a b - B a b)e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 2 3 1 4 2 2 1 4 1 3 1 4 +--R ((- - A a b - - B a )e + A a b d)x - - A a e + (- A a b - -- B a )d +--R 3 3 4 3 12 +--R / +--R 2 6 5 2 2 4 4 2 5 2 4 2 3 3 3 +--R (a e - 2a b d e + b d e )x + (4a d e - 8a b d e + 4b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (6a d e - 12a b d e + 6b d e )x + (4a d e - 8a b d e + 4b d e)x +--R + +--R 2 4 2 5 2 6 +--R a d e - 2a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 187 + +--S 188 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R - 12B b e x + ((- 6A b - 12B a b)e - 18B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 8A a b - 4B a )e + (- 4A b - 8B a b)d e - 12B b d e)x - 3A a e +--R + +--R 2 2 2 2 2 3 +--R (- 2A a b - B a )d e + (- A b - 2B a b)d e - 3B b d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1378 +m0:=a0-r0 +--R +--R +--R 4 3 4 +--R (- A b + 4B a b )e - 3B b d +--R (4) ------------------------------ +--R 2 6 5 2 2 4 +--R 12a e - 24a b d e + 12b d e +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1378 +r0:=1/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^5)-1/4*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^4)+1/3*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^3)-_ + 1/2*b^2*B/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 3 3 1 2 2 3 1 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - - B b d e )x +--R 2 3 3 2 +--R + +--R 1 1 2 3 1 2 1 2 1 2 2 +--R ((- - A a b - - B a )e + (- - A b - - B a b)d e - - B b d e)x +--R 2 4 6 3 4 +--R + +--R 1 2 3 1 1 2 2 1 2 1 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A b - -- B a b)d e +--R 5 10 20 30 15 +--R + +--R 1 2 3 +--R - -- B b d +--R 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 192 + +--S 193 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R - 30B b e x + ((- 20A b - 40B a b)e - 30B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 30A a b - 15B a )e + (- 10A b - 20B a b)d e - 15B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 12A a e + (- 6A a b - 3B a )d e + (- 2A b - 4B a b)d e - 3B b d +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1378 +r0:=1/6*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^6)-1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^5)+1/4*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^4)-_ + 1/3*b^2*B/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 3 3 1 2 1 3 1 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - - B b d e )x +--R 3 4 2 4 +--R + +--R 2 1 2 3 1 2 1 2 1 2 2 +--R ((- - A a b - - B a )e + (- -- A b - - B a b)d e - -- B b d e)x +--R 5 5 10 5 10 +--R + +--R 1 2 3 1 1 2 2 1 2 1 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A b - -- B a b)d e +--R 6 15 30 60 30 +--R + +--R 1 2 3 +--R - -- B b d +--R 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 197 + +--S 198 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R - 20B b e x + ((- 15A b - 30B a b)e - 15B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 24A a b - 12B a )e + (- 6A b - 12B a b)d e - 6B b d e)x - 10A a e +--R + +--R 2 2 2 2 2 3 +--R (- 4A a b - 2B a )d e + (- A b - 2B a b)d e - B b d +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 4 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^8 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1378 +r0:=1/7*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^7)-1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^6)+1/5*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^5)-_ + 1/4*b^2*B/(e^4*(d+e*x)^4) +--R +--R +--R (2) +--R 1 2 3 3 1 2 2 3 3 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - -- B b d e )x +--R 4 5 5 20 +--R + +--R 1 1 2 3 1 2 2 2 1 2 2 +--R ((- - A a b - - B a )e + (- -- A b - -- B a b)d e - -- B b d e)x +--R 3 6 15 15 20 +--R + +--R 1 2 3 1 1 2 2 1 2 2 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- --- A b - --- B a b)d e +--R 7 21 42 105 105 +--R + +--R 1 2 3 +--R - --- B b d +--R 140 +--R / +--R 11 7 10 6 2 9 5 3 8 4 4 7 3 5 6 2 6 5 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 4 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 202 + +--S 203 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R - 105B b e x + ((- 84A b - 168B a b)e - 63B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 140A a b - 70B a )e + (- 28A b - 56B a b)d e - 21B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 60A a e + (- 20A a b - 10B a )d e + (- 4A b - 8B a b)d e - 3B b d +--R / +--R 11 7 10 6 2 9 5 3 8 4 4 7 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 6 2 6 5 7 4 +--R 8820d e x + 2940d e x + 420d e +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1378 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1378 +r0:=-(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(1+m)/(e^6*(1+m))+(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^6*(2+m))-2*b*(b*d-a*e)^2*(5*b*B*d-_ + 3*A*b*e-2*a*B*e)*(d+e*x)^(3+m)/(e^6*(3+m))+2*b^2*(b*d-a*e)*(5*b*B*d-_ + 2*A*b*e-3*a*B*e)*(d+e*x)^(4+m)/(e^6*(4+m))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+b^4*B*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 4 5 4 4 4 3 4 2 4 4 +--R (B b m + 15B b m + 85B b m + 225B b m + 274B b m + 120B b ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 4 3 4 5 4 3 4 4 +--R ((A b + 4B a b )e - 5B b d)m + ((16A b + 64B a b )e - 80B b d)m +--R + +--R 4 3 4 3 +--R ((95A b + 380B a b )e - 475B b d)m +--R + +--R 4 3 4 2 +--R ((260A b + 1040B a b )e - 1300B b d)m +--R + +--R 4 3 4 4 3 +--R ((324A b + 1296B a b )e - 1620B b d)m + (144A b + 576B a b )e +--R + +--R 4 +--R - 720B b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (- 4A b - 16B a b )d e + 10B b d )m +--R + +--R 3 2 2 2 4 3 4 2 4 +--R ((68A a b + 102B a b )e + (- 68A b - 272B a b )d e + 170B b d )m +--R + +--R 3 2 2 2 4 3 +--R (428A a b + 642B a b )e + (- 428A b - 1712B a b )d e +--R + +--R 4 2 +--R 1070B b d +--R * +--R 3 +--R m +--R + +--R 3 2 2 2 4 3 +--R (1228A a b + 1842B a b )e + (- 1228A b - 4912B a b )d e +--R + +--R 4 2 +--R 3070B b d +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 4 3 +--R (1584A a b + 2376B a b )e + (- 1584A b - 6336B a b )d e +--R + +--R 4 2 +--R 3960B b d +--R * +--R m +--R + +--R 3 2 2 2 4 3 4 2 +--R (720A a b + 1080B a b )e + (- 720A b - 2880B a b )d e + 1800B b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (- 12A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (6A b + 24B a b )d e - 10B b d +--R * +--R 5 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (108A a b + 72B a b)e + (- 216A a b - 324B a b )d e +--R + +--R 4 3 2 4 3 +--R (108A b + 432B a b )d e - 180B b d +--R * +--R 4 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (726A a b + 484B a b)e + (- 1452A a b - 2178B a b )d e +--R + +--R 4 3 2 4 3 +--R (726A b + 2904B a b )d e - 1210B b d +--R * +--R 3 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (2232A a b + 1488B a b)e + (- 4464A a b - 6696B a b )d e +--R + +--R 4 3 2 4 3 +--R (2232A b + 8928B a b )d e - 3720B b d +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (3048A a b + 2032B a b)e + (- 6096A a b - 9144B a b )d e +--R + +--R 4 3 2 4 3 +--R (3048A b + 12192B a b )d e - 5080B b d +--R * +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (1440A a b + 960B a b)e + (- 2880A a b - 4320B a b )d e +--R + +--R 4 3 2 4 3 +--R (1440A b + 5760B a b )d e - 2400B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (12A a b + 18B a b )d e + (- 4A b - 16B a b )d e + 5B b d +--R * +--R 5 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (76A a b + 19B a )e + (- 228A a b - 152B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (228A a b + 342B a b )d e + (- 76A b - 304B a b )d e + 95B b d +--R * +--R 4 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (548A a b + 137B a )e + (- 1644A a b - 1096B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1644A a b + 2466B a b )d e + (- 548A b - 2192B a b )d e +--R + +--R 4 4 +--R 685B b d +--R * +--R 3 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (1844A a b + 461B a )e + (- 5532A a b - 3688B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (5532A a b + 8298B a b )d e + (- 1844A b - 7376B a b )d e +--R + +--R 4 4 +--R 2305B b d +--R * +--R 2 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (2808A a b + 702B a )e + (- 8424A a b - 5616B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (8424A a b + 12636B a b )d e + (- 2808A b - 11232B a b )d e +--R + +--R 4 4 +--R 3510B b d +--R * +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (1440A a b + 360B a )e + (- 4320A a b - 2880B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (4320A a b + 6480B a b )d e + (- 1440A b - 5760B a b )d e +--R + +--R 4 4 +--R 1800B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (- 4A a b - B a )d e + (6A a b + 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 4A a b - 6B a b )d e + (A b + 4B a b )d e - B b d +--R * +--R 5 +--R m +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 20A a e + (- 80A a b - 20B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 80A a b - 120B a b )d e + (20A b + 80B a b )d e - 20B b d +--R * +--R 4 +--R m +--R + +--R 4 5 3 4 4 +--R 155A a e + (- 620A a b - 155B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (930A a b + 620B a b)d e + (- 620A a b - 930B a b )d e +--R + +--R 4 3 4 4 5 +--R (155A b + 620B a b )d e - 155B b d +--R * +--R 3 +--R m +--R + +--R 4 5 3 4 4 +--R 580A a e + (- 2320A a b - 580B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (3480A a b + 2320B a b)d e + (- 2320A a b - 3480B a b )d e +--R + +--R 4 3 4 4 5 +--R (580A b + 2320B a b )d e - 580B b d +--R * +--R 2 +--R m +--R + +--R 4 5 3 4 4 +--R 1044A a e + (- 4176A a b - 1044B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (6264A a b + 4176B a b)d e + (- 4176A a b - 6264B a b )d e +--R + +--R 4 3 4 4 5 +--R (1044A b + 4176B a b )d e - 1044B b d +--R * +--R m +--R + +--R 4 5 3 4 4 +--R 720A a e + (- 2880A a b - 720B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (4320A a b + 2880B a b)d e + (- 2880A a b - 4320B a b )d e +--R + +--R 4 3 4 4 5 +--R (720A b + 2880B a b )d e - 720B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 5 4 6 4 4 6 3 4 6 2 4 6 +--R B b e m + 15B b e m + 85B b e m + 225B b e m + 274B b e m +--R + +--R 4 6 +--R 120B b e +--R * +--R 6 +--R x +--R + +--R 4 3 6 4 5 5 +--R ((A b + 4B a b )e + B b d e )m +--R + +--R 4 3 6 4 5 4 +--R ((16A b + 64B a b )e + 10B b d e )m +--R + +--R 4 3 6 4 5 3 +--R ((95A b + 380B a b )e + 35B b d e )m +--R + +--R 4 3 6 4 5 2 +--R ((260A b + 1040B a b )e + 50B b d e )m +--R + +--R 4 3 6 4 5 4 3 6 +--R ((324A b + 1296B a b )e + 24B b d e )m + (144A b + 576B a b )e +--R * +--R 5 +--R x +--R + +--R 3 2 2 6 4 3 5 5 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d e )m +--R + +--R 3 2 2 6 4 3 5 4 2 4 4 +--R ((68A a b + 102B a b )e + (12A b + 48B a b )d e - 5B b d e )m +--R + +--R 3 2 2 6 4 3 5 +--R (428A a b + 642B a b )e + (47A b + 188B a b )d e +--R + +--R 4 2 4 +--R - 30B b d e +--R * +--R 3 +--R m +--R + +--R 3 2 2 6 4 3 5 +--R (1228A a b + 1842B a b )e + (72A b + 288B a b )d e +--R + +--R 4 2 4 +--R - 55B b d e +--R * +--R 2 +--R m +--R + +--R 3 2 2 6 4 3 5 +--R (1584A a b + 2376B a b )e + (36A b + 144B a b )d e +--R + +--R 4 2 4 +--R - 30B b d e +--R * +--R m +--R + +--R 3 2 2 6 +--R (720A a b + 1080B a b )e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 3 2 2 5 5 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d e )m +--R + +--R 2 2 3 6 3 2 2 5 +--R (108A a b + 72B a b)e + (56A a b + 84B a b )d e +--R + +--R 4 3 2 4 +--R (- 4A b - 16B a b )d e +--R * +--R 4 +--R m +--R + +--R 2 2 3 6 3 2 2 5 +--R (726A a b + 484B a b)e + (260A a b + 390B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (- 36A b - 144B a b )d e + 20B b d e +--R * +--R 3 +--R m +--R + +--R 2 2 3 6 3 2 2 5 +--R (2232A a b + 1488B a b)e + (448A a b + 672B a b )d e +--R + +--R 4 3 2 4 4 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+ +--R 3 2 2 2 2 4 3 3 +--R (- 8424A a b - 12636B a b )d e + (2808A b + 11232B a b )d e +--R + +--R 4 4 +--R - 3510B b d +--R * +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (- 1440A a b - 360B a )e + (4320A a b + 2880B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 4320A a b - 6480B a b )d e + (1440A b + 5760B a b )d e +--R + +--R 4 4 +--R - 1800B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - A a e + (4A a b + B a )d e + (- 6A a b - 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (4A a b + 6B a b )d e + (- A b - 4B a b )d e + B b d +--R * +--R 5 +--R m +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 20A a e + (80A a b + 20B a )d e + (- 120A a b - 80B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (80A a b + 120B a b )d e + (- 20A b - 80B a b )d e + 20B b d +--R * +--R 4 +--R m +--R + +--R 4 5 3 4 4 +--R - 155A a e + (620A a b + 155B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 930A a b - 620B a b)d e + (620A a b + 930B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 155A b - 620B a b )d e + 155B b d +--R * +--R 3 +--R m +--R + +--R 4 5 3 4 4 +--R - 580A a e + (2320A a b + 580B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 3480A a b - 2320B a b)d e + (2320A a b + 3480B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 580A b - 2320B a b )d e + 580B b d +--R * +--R 2 +--R m +--R + +--R 4 5 3 4 4 +--R - 1044A a e + (4176A a b + 1044B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 6264A a b - 4176B a b)d e + (4176A a b + 6264B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 1044A b - 4176B a b )d e + 1044B b d +--R * +--R m +--R + +--R 4 5 3 4 4 +--R - 720A a e + (2880A a b + 720B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 4320A a b - 2880B a b)d e + (2880A a b + 4320B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 720A b - 2880B a b )d e + 720B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1378 +t0:=(A+B*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 7 12 4 3 7 4 6 11 +--R B b e x + ((A b + 4B a b )e + 7B b d e )x +--R + +--R 3 2 2 7 4 3 6 4 2 5 10 +--R ((4A a b + 6B a b )e + (7A b + 28B a b )d e + 21B b d e )x +--R + +--R 2 2 3 7 3 2 2 6 +--R (6A a b + 4B a b)e + (28A a b + 42B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (21A b + 84B a b )d e + 35B b d e +--R * +--R 9 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (4A a b + B a )e + (42A a b + 28B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 4 4 3 +--R (84A a b + 126B a b )d e + (35A b + 140B a b )d e + 35B b d e +--R * +--R 8 +--R x +--R + +--R 4 7 3 4 6 2 2 3 2 5 +--R A a e + (28A a b + 7B a )d e + (126A a b + 84B a b)d e +--R + +--R 3 2 2 3 4 4 3 4 3 4 5 2 +--R (140A a b + 210B a b )d e + (35A b + 140B a b )d e + 21B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 2 5 2 2 3 3 4 +--R 7A a d e + (84A a b + 21B a )d e + (210A a b + 140B a b)d e +--R + +--R 3 2 2 4 3 4 3 5 2 4 6 +--R (140A a b + 210B a b )d e + (21A b + 84B a b )d e + 7B b d e +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 4 3 4 2 2 3 4 3 +--R 21A a d e + (140A a b + 35B a )d e + (210A a b + 140B a b)d e +--R + +--R 3 2 2 5 2 4 3 6 4 7 +--R (84A a b + 126B a b )d e + (7A b + 28B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 3 4 3 4 4 3 2 2 3 5 2 +--R 35A a d e + (140A a b + 35B a )d e + (126A a b + 84B a b)d e +--R + +--R 3 2 2 6 4 3 7 +--R (28A a b + 42B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 4 3 3 4 5 2 2 2 3 6 +--R 35A a d e + (84A a b + 21B a )d e + (42A a b + 28B a b)d e +--R + +--R 3 2 2 7 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 4 6 2 2 3 7 2 +--R (21A a d e + (28A a b + 7B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 6 3 4 7 4 7 +--R (7A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 1378 +r0:=-1/8*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^8/e^6+1/9*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^9/e^6-1/5*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^10/e^6+2/11*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^11/e^6-1/12*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^12/e^6+_ + 1/13*b^4*B*(d+e*x)^13/e^6 +--R +--R +--R (2) +--R 1 4 13 13 1 4 1 3 13 7 4 12 12 +--R -- B b e x + ((-- A b + - B a b )e + -- B b d e )x +--R 13 12 3 12 +--R + +--R 4 3 6 2 2 13 7 4 28 3 12 +--R (-- A a b + -- B a b )e + (-- A b + -- B a b )d e +--R 11 11 11 11 +--R + +--R 21 4 2 11 +--R -- B b d e +--R 11 +--R * +--R 11 +--R x +--R + +--R 3 2 2 2 3 13 14 3 21 2 2 12 +--R (- A a b + - B a b)e + (-- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 21 4 42 3 2 11 7 4 3 10 +--R (-- A b + -- B a b )d e + - B b d e +--R 10 5 2 +--R * +--R 10 +--R x +--R + +--R 4 3 1 4 13 14 2 2 28 3 12 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 9 9 3 9 +--R + +--R 28 3 2 2 2 11 35 4 140 3 3 10 35 4 4 9 +--R (-- A a b + 14B a b )d e + (-- A b + --- B a b )d e + -- B b d e +--R 3 9 9 9 +--R * +--R 9 +--R x +--R + +--R 1 4 13 7 3 7 4 12 63 2 2 21 3 2 11 +--R - A a e + (- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 8 2 8 4 2 +--R + +--R 35 3 105 2 2 3 10 35 4 35 3 4 9 21 4 5 8 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + -- B b d e +--R 2 4 8 2 8 +--R * +--R 8 +--R x +--R + +--R 4 12 3 4 2 11 2 2 3 3 10 +--R A a d e + (12A a b + 3B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 4 9 4 3 5 8 4 6 7 +--R (20A a b + 30B a b )d e + (3A b + 12B a b )d e + B b d e +--R * +--R 7 +--R x +--R + +--R 7 4 2 11 70 3 35 4 3 10 2 2 70 3 4 9 +--R - A a d e + (-- A a b + -- B a )d e + (35A a b + -- B a b)d e +--R 2 3 6 3 +--R + +--R 3 2 2 5 8 7 4 14 3 6 7 1 4 7 6 +--R (14A a b + 21B a b )d e + (- A b + -- B a b )d e + - B b d e +--R 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 3 10 3 4 4 9 126 2 2 84 3 5 8 +--R 7A a d e + (28A a b + 7B a )d e + (--- A a b + -- B a b)d e +--R 5 5 +--R + +--R 28 3 42 2 2 6 7 1 4 4 3 7 6 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 35 4 4 9 3 21 4 5 8 21 2 2 3 6 7 +--R -- A a d e + (21A a b + -- B a )d e + (-- A a b + 7B a b)d e +--R 4 4 2 +--R + +--R 3 3 2 2 7 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 5 8 28 3 7 4 6 7 2 2 4 3 7 6 3 +--R (7A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d e )x +--R 3 3 3 +--R + +--R 7 4 6 7 3 1 4 7 6 2 4 7 6 1 4 8 5 +--R (- A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 8 +--R + +--R 1 3 1 4 9 4 1 2 2 1 3 10 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 18 72 60 90 +--R + +--R 1 3 1 2 2 11 2 1 4 1 3 12 +--R (- --- A a b - --- B a b )d e + (---- A b + --- B a b )d e +--R 330 220 3960 990 +--R + +--R 1 4 13 +--R - ----- B b d +--R 10296 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 212 + +--S 213 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 7 13 1 4 1 3 7 7 4 6 12 +--R -- B b e x + ((-- A b + - B a b )e + -- B b d e )x +--R 13 12 3 12 +--R + +--R 4 3 6 2 2 7 7 4 28 3 6 21 4 2 5 11 +--R ((-- A a b + -- B a b )e + (-- A b + -- B a b )d e + -- B b d e )x +--R 11 11 11 11 11 +--R + +--R 3 2 2 2 3 7 14 3 21 2 2 6 +--R (- A a b + - B a b)e + (-- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 21 4 42 3 2 5 7 4 3 4 +--R (-- A b + -- B a b )d e + - B b d e +--R 10 5 2 +--R * +--R 10 +--R x +--R + +--R 4 3 1 4 7 14 2 2 28 3 6 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 9 9 3 9 +--R + +--R 28 3 2 2 2 5 35 4 140 3 3 4 35 4 4 3 +--R (-- A a b + 14B a b )d e + (-- A b + --- B a b )d e + -- B b d e +--R 3 9 9 9 +--R * +--R 9 +--R x +--R + +--R 1 4 7 7 3 7 4 6 63 2 2 21 3 2 5 +--R - A a e + (- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 8 2 8 4 2 +--R + +--R 35 3 105 2 2 3 4 35 4 35 3 4 3 21 4 5 2 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + -- B b d e +--R 2 4 8 2 8 +--R * +--R 8 +--R x +--R + +--R 4 6 3 4 2 5 2 2 3 3 4 +--R A a d e + (12A a b + 3B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 4 3 4 3 5 2 4 6 +--R (20A a b + 30B a b )d e + (3A b + 12B a b )d e + B b d e +--R * +--R 7 +--R x +--R + +--R 7 4 2 5 70 3 35 4 3 4 2 2 70 3 4 3 +--R - A a d e + (-- A a b + -- B a )d e + (35A a b + -- B a b)d e +--R 2 3 6 3 +--R + +--R 3 2 2 5 2 7 4 14 3 6 1 4 7 +--R (14A a b + 21B a b )d e + (- A b + -- B a b )d e + - B b d +--R 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 3 4 3 4 4 3 126 2 2 84 3 5 2 +--R 7A a d e + (28A a b + 7B a )d e + (--- A a b + -- B a b)d e +--R 5 5 +--R + +--R 28 3 42 2 2 6 1 4 4 3 7 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 35 4 4 3 3 21 4 5 2 21 2 2 3 6 +--R -- A a d e + (21A a b + -- B a )d e + (-- A a b + 7B a b)d e +--R 4 4 2 +--R + +--R 3 3 2 2 7 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 5 2 28 3 7 4 6 2 2 4 3 7 3 +--R (7A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d )x +--R 3 3 3 +--R + +--R 7 4 6 3 1 4 7 2 4 7 +--R (- A a d e + (2A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 4 8 5 1 3 1 4 9 4 1 2 2 1 3 10 3 +--R - - A a d e + (-- A a b + -- B a )d e + (- -- A a b - -- B a b)d e +--R 8 18 72 60 90 +--R + +--R 1 3 1 2 2 11 2 1 4 1 3 12 +--R (--- A a b + --- B a b )d e + (- ---- A b - --- B a b )d e +--R 330 220 3960 990 +--R + +--R 1 4 13 +--R ----- B b d +--R 10296 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 214 + +--S 215 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 215 + +)clear all + +--S 216 of 1378 +t0:=(A+B*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 11 4 3 6 4 5 10 +--R B b e x + ((A b + 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 6 4 3 5 4 2 4 9 +--R ((4A a b + 6B a b )e + (6A b + 24B a b )d e + 15B b d e )x +--R + +--R 2 2 3 6 3 2 2 5 +--R (6A a b + 4B a b)e + (24A a b + 36B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (15A b + 60B a b )d e + 20B b d e +--R * +--R 8 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (4A a b + B a )e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 4 4 2 +--R (60A a b + 90B a b )d e + (20A b + 80B a b )d e + 15B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 5 2 2 3 2 4 +--R A a e + (24A a b + 6B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 3 3 4 3 4 2 4 5 +--R (80A a b + 120B a b )d e + (15A b + 60B a b )d e + 6B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 6A a d e + (60A a b + 15B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (60A a b + 90B a b )d e + (6A b + 24B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A a d e + (80A a b + 20B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 5 4 3 6 +--R (24A a b + 36B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 4 4 2 2 2 3 5 +--R 20A a d e + (60A a b + 15B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 6 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 2 +--R (15A a d e + (24A a b + 6B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 5 3 4 6 4 6 +--R (6A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 1378 +r0:=-1/7*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^7/e^6+1/8*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^8/e^6-2/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^9/e^6+1/5*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^10/e^6-1/11*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^11/e^6+_ + 1/12*b^4*B*(d+e*x)^12/e^6 +--R +--R +--R (2) +--R 1 4 12 12 1 4 4 3 12 6 4 11 11 +--R -- B b e x + ((-- A b + -- B a b )e + -- B b d e )x +--R 12 11 11 11 +--R + +--R 2 3 3 2 2 12 3 4 12 3 11 3 4 2 10 10 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e )x +--R 5 5 5 5 2 +--R + +--R 2 2 2 4 3 12 8 3 2 2 11 +--R (- A a b + - B a b)e + (- A a b + 4B a b )d e +--R 3 9 3 +--R + +--R 5 4 20 3 2 10 20 4 3 9 +--R (- A b + -- B a b )d e + -- B b d e +--R 3 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 1 4 12 9 2 2 3 11 +--R (- A a b + - B a )e + (- A a b + 3B a b)d e +--R 2 8 2 +--R + +--R 15 3 45 2 2 2 10 5 4 3 3 9 15 4 4 8 +--R (-- A a b + -- B a b )d e + (- A b + 10B a b )d e + -- B b d e +--R 2 4 2 8 +--R * +--R 8 +--R x +--R + +--R 1 4 12 24 3 6 4 11 90 2 2 60 3 2 10 +--R - A a e + (-- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 80 3 120 2 2 3 9 15 4 60 3 4 8 6 4 5 7 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 4 11 3 5 4 2 10 2 2 40 3 3 9 +--R A a d e + (10A a b + - B a )d e + (20A a b + -- B a b)d e +--R 2 3 +--R + +--R 3 2 2 4 8 4 3 5 7 1 4 6 6 +--R (10A a b + 15B a b )d e + (A b + 4B a b )d e + - B b d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 4 2 10 3 4 3 9 2 2 3 4 8 +--R 3A a d e + (16A a b + 4B a )d e + (18A a b + 12B a b)d e +--R + +--R 24 3 36 2 2 5 7 1 4 4 3 6 6 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 3 9 3 15 4 4 8 2 2 3 5 7 +--R 5A a d e + (15A a b + -- B a )d e + (9A a b + 6B a b)d e +--R 4 +--R + +--R 3 3 2 2 6 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 4 8 3 4 5 7 2 2 4 3 6 6 3 +--R (5A a d e + (8A a b + 2B a )d e + (2A a b + - B a b)d e )x +--R 3 +--R + +--R 4 5 7 3 1 4 6 6 2 4 6 6 1 4 7 5 +--R (3A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 7 +--R + +--R 1 3 1 4 8 4 1 2 2 1 3 9 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 14 56 42 63 +--R + +--R 1 3 1 2 2 10 2 1 4 2 3 11 +--R (- --- A a b - --- B a b )d e + (---- A b + ---- B a b )d e +--R 210 140 2310 1155 +--R + +--R 1 4 12 +--R - ---- B b d +--R 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 217 + +--S 218 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 6 12 1 4 4 3 6 6 4 5 11 +--R -- B b e x + ((-- A b + -- B a b )e + -- B b d e )x +--R 12 11 11 11 +--R + +--R 2 3 3 2 2 6 3 4 12 3 5 3 4 2 4 10 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e )x +--R 5 5 5 5 2 +--R + +--R 2 2 2 4 3 6 8 3 2 2 5 +--R (- A a b + - B a b)e + (- A a b + 4B a b )d e +--R 3 9 3 +--R + +--R 5 4 20 3 2 4 20 4 3 3 +--R (- A b + -- B a b )d e + -- B b d e +--R 3 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 1 4 6 9 2 2 3 5 +--R (- A a b + - B a )e + (- A a b + 3B a b)d e +--R 2 8 2 +--R + +--R 15 3 45 2 2 2 4 5 4 3 3 3 15 4 4 2 +--R (-- A a b + -- B a b )d e + (- A b + 10B a b )d e + -- B b d e +--R 2 4 2 8 +--R * +--R 8 +--R x +--R + +--R 1 4 6 24 3 6 4 5 90 2 2 60 3 2 4 +--R - A a e + (-- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 80 3 120 2 2 3 3 15 4 60 3 4 2 6 4 5 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 4 5 3 5 4 2 4 2 2 40 3 3 3 +--R A a d e + (10A a b + - B a )d e + (20A a b + -- B a b)d e +--R 2 3 +--R + +--R 3 2 2 4 2 4 3 5 1 4 6 +--R (10A a b + 15B a b )d e + (A b + 4B a b )d e + - B b d +--R 6 +--R * +--R 6 +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 3A a d e + (16A a b + 4B a )d e + (18A a b + 12B a b)d e +--R + +--R 24 3 36 2 2 5 1 4 4 3 6 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 3 3 3 15 4 4 2 2 2 3 5 +--R 5A a d e + (15A a b + -- B a )d e + (9A a b + 6B a b)d e +--R 4 +--R + +--R 3 3 2 2 6 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 4 2 3 4 5 2 2 4 3 6 3 +--R (5A a d e + (8A a b + 2B a )d e + (2A a b + - B a b)d )x +--R 3 +--R + +--R 4 5 3 1 4 6 2 4 6 +--R (3A a d e + (2A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 4 7 5 1 3 1 4 8 4 1 2 2 1 3 9 3 +--R - - A a d e + (-- A a b + -- B a )d e + (- -- A a b - -- B a b)d e +--R 7 14 56 42 63 +--R + +--R 1 3 1 2 2 10 2 1 4 2 3 11 +--R (--- A a b + --- B a b )d e + (- ---- A b - ---- B a b )d e +--R 210 140 2310 1155 +--R + +--R 1 4 12 +--R ---- B b d +--R 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 219 + +--S 220 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 220 + +)clear all + +--S 221 of 1378 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 10 4 3 5 4 4 9 +--R B b e x + ((A b + 4B a b )e + 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 8 +--R ((4A a b + 6B a b )e + (5A b + 20B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (6A a b + 4B a b)e + (20A a b + 30B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (10A b + 40B a b )d e + 10B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b + B a )e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (40A a b + 60B a b )d e + (10A b + 40B a b )d e + 5B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (20A a b + 5B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (40A a b + 60B a b )d e + (5A b + 20B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R 5A a d e + (40A a b + 10B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 4 4 3 5 +--R (20A a b + 30B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 3 2 2 2 3 4 +--R 10A a d e + (40A a b + 10B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 5 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 2 +--R (10A a d e + (20A a b + 5B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 4 3 4 5 4 5 +--R (5A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 1378 +r0:=-1/6*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^6/e^6+1/7*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^7/e^6-1/4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^8/e^6+2/9*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^9/e^6-1/10*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^10/e^6+_ + 1/11*b^4*B*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 4 11 11 1 4 2 3 11 1 4 10 10 +--R -- B b e x + ((-- A b + - B a b )e + - B b d e )x +--R 11 10 5 2 +--R + +--R 4 3 2 2 2 11 5 4 20 3 10 10 4 2 9 9 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + -- B b d e )x +--R 9 3 9 9 9 +--R + +--R 3 2 2 1 3 11 5 3 15 2 2 10 +--R (- A a b + - B a b)e + (- A a b + -- B a b )d e +--R 4 2 2 4 +--R + +--R 5 4 3 2 9 5 4 3 8 +--R (- A b + 5B a b )d e + - B b d e +--R 4 4 +--R * +--R 8 +--R x +--R + +--R 4 3 1 4 11 30 2 2 20 3 10 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 7 7 7 7 +--R + +--R 40 3 60 2 2 2 9 10 4 40 3 3 8 5 4 4 7 +--R (-- A a b + -- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 4 11 10 3 5 4 10 2 2 20 3 2 9 +--R - A a e + (-- A a b + - B a )d e + (10A a b + -- B a b)d e +--R 6 3 6 3 +--R + +--R 20 3 2 2 3 8 5 4 10 3 4 7 1 4 5 6 +--R (-- A a b + 10B a b )d e + (- A b + -- B a b )d e + - B b d e +--R 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 10 3 4 2 9 2 2 3 3 8 +--R A a d e + (8A a b + 2B a )d e + (12A a b + 8B a b)d e +--R + +--R 3 2 2 4 7 1 4 4 3 5 6 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 4 2 9 3 5 4 3 8 15 2 2 3 4 7 +--R - A a d e + (10A a b + - B a )d e + (-- A a b + 5B a b)d e +--R 2 2 2 +--R + +--R 3 3 2 2 5 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 10 4 3 8 20 3 5 4 4 7 2 2 4 3 5 6 3 +--R (-- A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d e )x +--R 3 3 3 3 +--R + +--R 5 4 4 7 3 1 4 5 6 2 4 5 6 1 4 6 5 +--R (- A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 2 3 1 4 7 4 1 2 2 1 3 8 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 21 42 28 42 +--R + +--R 1 3 1 2 2 9 2 1 4 1 3 10 +--R (- --- A a b - -- B a b )d e + (---- A b + --- B a b )d e +--R 126 84 1260 315 +--R + +--R 1 4 11 +--R - ---- B b d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 222 + +--S 223 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 5 11 1 4 2 3 5 1 4 4 10 +--R -- B b e x + ((-- A b + - B a b )e + - B b d e )x +--R 11 10 5 2 +--R + +--R 4 3 2 2 2 5 5 4 20 3 4 10 4 2 3 9 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + -- B b d e )x +--R 9 3 9 9 9 +--R + +--R 3 2 2 1 3 5 5 3 15 2 2 4 +--R (- A a b + - B a b)e + (- A a b + -- B a b )d e +--R 4 2 2 4 +--R + +--R 5 4 3 2 3 5 4 3 2 +--R (- A b + 5B a b )d e + - B b d e +--R 4 4 +--R * +--R 8 +--R x +--R + +--R 4 3 1 4 5 30 2 2 20 3 4 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 7 7 7 7 +--R + +--R 40 3 60 2 2 2 3 10 4 40 3 3 2 5 4 4 +--R (-- A a b + -- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 4 5 10 3 5 4 4 2 2 20 3 2 3 +--R - A a e + (-- A a b + - B a )d e + (10A a b + -- B a b)d e +--R 6 3 6 3 +--R + +--R 20 3 2 2 3 2 5 4 10 3 4 1 4 5 +--R (-- A a b + 10B a b )d e + (- A b + -- B a b )d e + - B b d +--R 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R A a d e + (8A a b + 2B a )d e + (12A a b + 8B a b)d e +--R + +--R 3 2 2 4 1 4 4 3 5 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 4 2 3 3 5 4 3 2 15 2 2 3 4 +--R - A a d e + (10A a b + - B a )d e + (-- A a b + 5B a b)d e +--R 2 2 2 +--R + +--R 3 3 2 2 5 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 10 4 3 2 20 3 5 4 4 2 2 4 3 5 3 +--R (-- A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d )x +--R 3 3 3 3 +--R + +--R 5 4 4 3 1 4 5 2 4 5 +--R (- A a d e + (2A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 4 6 5 2 3 1 4 7 4 1 2 2 1 3 8 3 +--R - - A a d e + (-- A a b + -- B a )d e + (- -- A a b - -- B a b)d e +--R 6 21 42 28 42 +--R + +--R 1 3 1 2 2 9 2 1 4 1 3 10 +--R (--- A a b + -- B a b )d e + (- ---- A b - --- B a b )d e +--R 126 84 1260 315 +--R + +--R 1 4 11 +--R ---- B b d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 224 + +--S 225 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 225 + +)clear all + +--S 226 of 1378 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 4 9 4 3 4 4 3 8 +--R B b e x + ((A b + 4B a b )e + 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((4A a b + 6B a b )e + (4A b + 16B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (6A a b + 4B a b)e + (16A a b + 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (6A b + 24B a b )d e + 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (24A a b + 36B a b )d e + (4A b + 16B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R A a e + (16A a b + 4B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (16A a b + 24B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 4A a d e + (24A a b + 6B a )d e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 4 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (6A a d e + (16A a b + 4B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (4A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 1378 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^4*(a+b*x)^5/b^6+1/6*(b*d-a*e)^3*(b*B*d+4*A*b*e-_ + 5*a*B*e)*(a+b*x)^6/b^6+2/7*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*_ + (a+b*x)^7/b^6+1/4*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^8/_ + b^6+1/9*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^9/b^6+1/10*B*e^4*_ + (a+b*x)^10/b^6 +--R +--R +--R (2) +--R 1 10 4 10 1 10 4 9 4 4 10 3 9 +--R -- B b e x + ((- A b + - B a b )e + - B b d e )x +--R 10 9 9 9 +--R + +--R 1 9 3 2 8 4 1 10 9 3 3 10 2 2 8 +--R ((- A a b + - B a b )e + (- A b + 2B a b )d e + - B b d e )x +--R 2 4 2 4 +--R + +--R 6 2 8 4 3 7 4 16 9 24 2 8 3 +--R (- A a b + - B a b )e + (-- A a b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 6 10 24 9 2 2 4 10 3 +--R (- A b + -- B a b )d e + - B b d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 2 3 7 1 4 6 4 2 8 8 3 7 3 +--R (- A a b + - B a b )e + (4A a b + - B a b )d e +--R 3 6 3 +--R + +--R 9 2 8 2 2 2 10 8 9 3 1 10 4 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d e + - B b d +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 4 6 4 16 3 7 4 4 6 3 36 2 8 24 3 7 2 2 +--R - A a b e + (-- A a b + - B a b )d e + (-- A a b + -- B a b )d e +--R 5 5 5 5 5 +--R + +--R 16 9 24 2 8 3 1 10 4 9 4 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 6 3 3 7 3 4 6 2 2 2 8 3 7 3 +--R A a b d e + (6A a b + - B a b )d e + (6A a b + 4B a b )d e +--R 2 +--R + +--R 9 3 2 8 4 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 6 2 2 16 3 7 4 4 6 3 2 8 4 3 7 4 3 +--R (2A a b d e + (-- A a b + - B a b )d e + (2A a b + - B a b )d )x +--R 3 3 3 +--R + +--R 4 6 3 3 7 1 4 6 4 2 4 6 4 +--R (2A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 9 1 10 4 1 8 2 2 9 3 +--R (--- A a b - ---- B a )e + (- -- A a b + --- B a b)d e +--R 630 1260 70 315 +--R + +--R 2 7 3 3 8 2 2 2 2 6 4 4 7 3 3 +--R (-- A a b - --- B a b )d e + (- -- A a b + --- B a b )d e +--R 35 140 15 105 +--R + +--R 1 5 5 1 6 4 4 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 227 + +--S 228 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 4 10 1 4 4 3 4 4 4 3 9 +--R -- B b e x + ((- A b + - B a b )e + - B b d e )x +--R 10 9 9 9 +--R + +--R 1 3 3 2 2 4 1 4 3 3 3 4 2 2 8 +--R ((- A a b + - B a b )e + (- A b + 2B a b )d e + - B b d e )x +--R 2 4 2 4 +--R + +--R 6 2 2 4 3 4 16 3 24 2 2 3 +--R (- A a b + - B a b)e + (-- A a b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 6 4 24 3 2 2 4 4 3 +--R (- A b + -- B a b )d e + - B b d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 2 3 1 4 4 2 2 8 3 3 +--R (- A a b + - B a )e + (4A a b + - B a b)d e +--R 3 6 3 +--R + +--R 3 2 2 2 2 2 4 8 3 3 1 4 4 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d e + - B b d +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 4 4 16 3 4 4 3 36 2 2 24 3 2 2 +--R - A a e + (-- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 5 5 5 5 5 +--R + +--R 16 3 24 2 2 3 1 4 4 3 4 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 3 3 3 4 2 2 2 2 3 3 +--R A a d e + (6A a b + - B a )d e + (6A a b + 4B a b)d e +--R 2 +--R + +--R 3 3 2 2 4 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 2 2 16 3 4 4 3 2 2 4 3 4 3 +--R (2A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d )x +--R 3 3 3 +--R + +--R 4 3 3 1 4 4 2 4 4 +--R (2A a d e + (2A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 9 1 10 4 1 8 2 2 9 3 +--R (- --- A a b + ---- B a )e + (-- A a b - --- B a b)d e +--R 630 1260 70 315 +--R + +--R 2 7 3 3 8 2 2 2 2 6 4 4 7 3 3 +--R (- -- A a b + --- B a b )d e + (-- A a b - --- B a b )d e +--R 35 140 15 105 +--R + +--R 1 5 5 1 6 4 4 +--R (- - A a b + -- B a b )d +--R 5 30 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 229 + +--S 230 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 230 + +)clear all + +--S 231 of 1378 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e + (12A a b + 18B a b )d e +--R + +--R 4 3 3 +--R (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 1378 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^3*(a+b*x)^5/b^5+1/6*(b*d-a*e)^2*(b*B*d+3*A*b*e-_ + 4*a*B*e)*(a+b*x)^6/b^5+3/7*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^7/b^5+1/8*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^8/b^5+_ + 1/9*B*e^3*(a+b*x)^9/b^5 +--R +--R +--R (2) +--R 1 9 3 9 1 9 1 8 3 3 9 2 8 +--R - B b e x + ((- A b + - B a b )e + - B b d e )x +--R 9 8 2 8 +--R + +--R 4 8 6 2 7 3 3 9 12 8 2 3 9 2 7 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e)x +--R 7 7 7 7 7 +--R + +--R 2 7 2 3 6 3 8 2 7 2 +--R (A a b + - B a b )e + (2A a b + 3B a b )d e +--R 3 +--R + +--R 1 9 8 2 1 9 3 +--R (- A b + 2B a b )d e + - B b d +--R 2 6 +--R * +--R 6 +--R x +--R + +--R 4 3 6 1 4 5 3 18 2 7 12 3 6 2 +--R (- A a b + - B a b )e + (-- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 12 8 18 2 7 2 1 9 4 8 3 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 4 5 3 3 6 3 4 5 2 9 2 7 3 6 2 +--R - A a b e + (3A a b + - B a b )d e + (- A a b + 3B a b )d e +--R 4 4 2 +--R + +--R 8 3 2 7 3 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 5 2 3 6 4 5 2 2 7 4 3 6 3 3 +--R (A a b d e + (4A a b + B a b )d e + (2A a b + - B a b )d )x +--R 3 +--R + +--R 3 4 5 2 3 6 1 4 5 3 2 4 5 3 +--R (- A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 2 +--R + +--R 1 8 1 9 3 1 7 2 3 8 2 +--R (- --- A a b + --- B a )e + (-- A a b - --- B a b)d e +--R 280 630 35 280 +--R + +--R 1 6 3 1 7 2 2 1 5 4 1 6 3 3 +--R (- -- A a b + -- B a b )d e + (- A a b - -- B a b )d +--R 10 35 5 30 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 232 + +--S 233 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 3 9 1 4 1 3 3 3 4 2 8 +--R - B b e x + ((- A b + - B a b )e + - B b d e )x +--R 9 8 2 8 +--R + +--R 4 3 6 2 2 3 3 4 12 3 2 3 4 2 7 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e)x +--R 7 7 7 7 7 +--R + +--R 2 2 2 3 3 3 2 2 2 1 4 3 2 +--R (A a b + - B a b)e + (2A a b + 3B a b )d e + (- A b + 2B a b )d e +--R 3 2 +--R + +--R 1 4 3 +--R - B b d +--R 6 +--R * +--R 6 +--R x +--R + +--R 4 3 1 4 3 18 2 2 12 3 2 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 5 5 5 5 +--R + +--R 12 3 18 2 2 2 1 4 4 3 3 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 4 3 3 3 4 2 9 2 2 3 2 +--R - A a e + (3A a b + - B a )d e + (- A a b + 3B a b)d e +--R 4 4 2 +--R + +--R 3 3 2 2 3 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 2 3 4 2 2 2 4 3 3 3 +--R (A a d e + (4A a b + B a )d e + (2A a b + - B a b)d )x +--R 3 +--R + +--R 3 4 2 3 1 4 3 2 4 3 +--R (- A a d e + (2A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 8 1 9 3 1 7 2 3 8 2 +--R (--- A a b - --- B a )e + (- -- A a b + --- B a b)d e +--R 280 630 35 280 +--R + +--R 1 6 3 1 7 2 2 1 5 4 1 6 3 3 +--R (-- A a b - -- B a b )d e + (- - A a b + -- B a b )d +--R 10 35 5 30 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 234 + +--S 235 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 235 + +)clear all + +--S 236 of 1378 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 236 + +--S 237 of 1378 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^5/b^4+1/6*(b*d-a*e)*(b*B*d+2*A*b*e-_ + 3*a*B*e)*(a+b*x)^6/b^4+1/7*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^7/b^4+_ + 1/8*B*e^2*(a+b*x)^8/b^4 +--R +--R +--R (2) +--R 1 8 2 8 1 8 4 7 2 2 8 7 +--R - B b e x + ((- A b + - B a b )e + - B b d e)x +--R 8 7 7 7 +--R + +--R 2 7 2 6 2 1 8 4 7 1 8 2 6 +--R ((- A a b + B a b )e + (- A b + - B a b )d e + - B b d )x +--R 3 3 3 6 +--R + +--R 6 2 6 4 3 5 2 8 7 12 2 6 +--R (- A a b + - B a b )e + (- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 1 8 4 7 2 +--R (- A b + - B a b )d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 3 5 1 4 4 2 2 6 3 5 +--R (A a b + - B a b )e + (3A a b + 2B a b )d e +--R 4 +--R + +--R 7 3 2 6 2 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 1 4 4 2 8 3 5 2 4 4 2 6 4 3 5 2 3 +--R (- A a b e + (- A a b + - B a b )d e + (2A a b + - B a b )d )x +--R 3 3 3 3 +--R + +--R 4 4 3 5 1 4 4 2 2 4 4 2 +--R (A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 7 1 8 2 1 6 2 2 7 +--R (--- A a b - --- B a )e + (- -- A a b + --- B a b)d e +--R 105 280 15 105 +--R + +--R 1 5 3 1 6 2 2 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 237 + +--S 238 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 2 8 1 4 4 3 2 2 4 7 +--R - B b e x + ((- A b + - B a b )e + - B b d e)x +--R 8 7 7 7 +--R + +--R 2 3 2 2 2 1 4 4 3 1 4 2 6 +--R ((- A a b + B a b )e + (- A b + - B a b )d e + - B b d )x +--R 3 3 3 6 +--R + +--R 6 2 2 4 3 2 8 3 12 2 2 +--R (- A a b + - B a b)e + (- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 1 4 4 3 2 +--R (- A b + - B a b )d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 3 1 4 2 2 2 3 3 3 2 2 2 4 +--R ((A a b + - B a )e + (3A a b + 2B a b)d e + (A a b + - B a b )d )x +--R 4 2 +--R + +--R 1 4 2 8 3 2 4 2 2 4 3 2 3 +--R (- A a e + (- A a b + - B a )d e + (2A a b + - B a b)d )x +--R 3 3 3 3 +--R + +--R 4 3 1 4 2 2 4 2 +--R (A a d e + (2A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 238 + +--S 239 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 7 1 8 2 1 6 2 2 7 +--R (- --- A a b + --- B a )e + (-- A a b - --- B a b)d e +--R 105 280 15 105 +--R + +--R 1 5 3 1 6 2 2 +--R (- - A a b + -- B a b )d +--R 5 30 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 239 + +--S 240 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 240 + +)clear all + +--S 241 of 1378 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R Type: Polynomial(Integer) +--E 241 + +--S 242 of 1378 +r0:=1/5*(A*b-a*B)*(b*d-a*e)*(a+b*x)^5/b^3+1/6*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^6/b^3+1/7*B*e*(a+b*x)^7/b^3 +--R +--R +--R (2) +--R 1 7 7 1 7 2 6 1 7 6 +--R - B b e x + ((- A b + - B a b )e + - B b d)x +--R 7 6 3 6 +--R + +--R 4 6 6 2 5 1 7 4 6 5 +--R ((- A a b + - B a b )e + (- A b + - B a b )d)x +--R 5 5 5 5 +--R + +--R 3 2 5 3 4 6 3 2 5 4 +--R ((- A a b + B a b )e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 3 4 1 4 3 2 5 4 3 4 3 +--R ((- A a b + - B a b )e + (2A a b + - B a b )d)x +--R 3 3 3 +--R + +--R 1 4 3 3 4 1 4 3 2 4 3 +--R (- A a b e + (2A a b + - B a b )d)x + A a b d x +--R 2 2 +--R + +--R 1 6 1 7 1 5 2 1 6 +--R (- -- A a b + --- B a )e + (- A a b - -- B a b)d +--R 30 105 5 30 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 242 + +--S 243 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 7 1 4 2 3 1 4 6 +--R - B b e x + ((- A b + - B a b )e + - B b d)x +--R 7 6 3 6 +--R + +--R 4 3 6 2 2 1 4 4 3 5 +--R ((- A a b + - B a b )e + (- A b + - B a b )d)x +--R 5 5 5 5 +--R + +--R 3 2 2 3 3 3 2 2 4 +--R ((- A a b + B a b)e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 3 1 4 2 2 4 3 3 +--R ((- A a b + - B a )e + (2A a b + - B a b)d)x +--R 3 3 3 +--R + +--R 1 4 3 1 4 2 4 +--R (- A a e + (2A a b + - B a )d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 243 + +--S 244 of 1378 +m0:=a0-r0 +--R +--R +--R 1 6 1 7 1 5 2 1 6 +--R (-- A a b - --- B a )e + (- - A a b + -- B a b)d +--R 30 105 5 30 +--R (4) ------------------------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 244 + +--S 245 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 245 + +)clear all + +--S 246 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 2 2 3 2 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x + (6A a b + 4B a b)x +--R + +--R 3 4 4 +--R (4A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 246 + +--S 247 of 1378 +r0:=1/5*(A*b-a*B)*(a+b*x)^5/b^2+1/6*B*(a+b*x)^6/b^2 +--R +--R +--R (2) +--R 1 6 6 1 6 4 5 5 5 3 2 4 4 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x +--R 6 5 5 2 +--R + +--R 2 4 4 3 3 3 3 3 1 4 2 2 4 2 1 5 +--R (2A a b + - B a b )x + (2A a b + - B a b )x + A a b x + - A a b +--R 3 2 5 +--R + +--R 1 6 +--R - -- B a +--R 30 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 247 + +--S 248 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 6 1 4 4 3 5 3 3 2 2 4 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x +--R 6 5 5 2 +--R + +--R 2 2 4 3 3 3 1 4 2 4 +--R (2A a b + - B a b)x + (2A a b + - B a )x + A a x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 248 + +--S 249 of 1378 +m0:=a0-r0 +--R +--R +--R 1 5 1 6 +--R - - A a b + -- B a +--R 5 30 +--R (4) ------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 249 + +--S 250 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 250 + +)clear all + +--S 251 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1378 +r0:=b*(b*d-a*e)^3*(B*d-A*e)*x/e^5-1/2*(b*d-a*e)^2*(B*d-A*e)*(a+b*x)^2/e^4+_ + 1/3*(b*d-a*e)*(B*d-A*e)*(a+b*x)^3/e^3-1/4*(B*d-A*e)*(a+b*x)^4/e^2+_ + 1/5*B*(a+b*x)^5/(b*e)-(b*d-a*e)^4*(B*d-A*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 3 2 4 4 +--R 60A a b e + (- 240A a b - 60B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (360A a b + 240B a b )d e + (- 240A a b - 360B a b )d e +--R + +--R 5 4 4 5 5 +--R (60A b + 240B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 5 4 5 5 4 4 +--R 12B b e x + ((15A b + 60B a b )e - 15B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 3 +--R ((80A a b + 120B a b )e + (- 20A b - 80B a b )d e + 20B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (180A a b + 120B a b )e + (- 120A a b - 180B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b + 120B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b + 60B a b)e + (- 360A a b - 240B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (240A a b + 360B a b )d e + (- 60A b - 240B a b )d e + 60B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (65A a b + 12B a )e + (- 80A a b - 65B a b)d e +--R + +--R 2 3 3 2 2 3 2 3 3 2 +--R (30A a b + 80B a b )d e - 30B a b d e +--R / +--R 6 +--R 60b e +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 3 4 4 2 2 3 2 3 +--R 60A a e + (- 240A a b - 60B a )d e + (360A a b + 240B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 240A a b - 360B a b )d e + (60A b + 240B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 12B b e x + ((15A b + 60B a b )e - 15B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((80A a b + 120B a b )e + (- 20A b - 80B a b )d e + 20B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (180A a b + 120B a b)e + (- 120A a b - 180B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (30A b + 120B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (240A a b + 60B a )e + (- 360A a b - 240B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (240A a b + 360B a b )d e + (- 60A b - 240B a b )d e + 60B b d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 3 3 2 4 2 +--R (- 65A a b - 12B a )e + (80A a b + 65B a b)d e +--R + +--R 2 3 3 2 2 2 3 3 +--R (- 30A a b - 80B a b )d e + 30B a b d +--R / +--R 4 +--R 60b e +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1378 +r0:=-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*x/e^5+(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x))+b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^2/e^6-1/3*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^3/e^6+1/4*b^4*_ + B*(d+e*x)^4/e^6+(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 4 5 2 2 3 4 +--R (48A a b + 12B a )e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e +--R + +--R 4 4 +--R 60B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 2 3 +--R (48A a b + 12B a )d e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((4A b + 16B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 8A b - 32B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (72A a b + 48B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (24A b + 96B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (16A b + 64B a b )d e - 5B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 12A a e + (48A a b + 12B a )d e + (- 72A a b - 48B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (72A a b + 108B a b )d e + (- 32A b - 128B a b )d e + 55B b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 5 2 2 3 4 +--R (48A a b + 12B a )e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e +--R + +--R 4 4 +--R 60B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 2 3 +--R (48A a b + 12B a )d e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((4A b + 16B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 8A b - 32B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (72A a b + 48B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (24A b + 96B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 96A a b - 144B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (36A b + 144B a b )d e - 48B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 12A a e + (48A a b + 12B a )d e + (- 72A a b - 48B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (48A a b + 72B a b )d e + (- 12A b - 48B a b )d e + 12B b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1378 +m0:=a0-r0 +--R +--R +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 24A a b - 36B a b )d e + (20A b + 80B a b )d e - 43B b d +--R (4) --------------------------------------------------------------- +--R 6 +--R 12e +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1378 +r0:=2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*x/e^5+1/2*(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x)^2)-(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*_ + (d+e*x))-1/2*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^2/e^6+1/3*b^4*B*_ + (d+e*x)^3/e^6-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 3 5 3 2 2 4 +--R (36A a b + 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (36A b + 144B a b )d e - 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 144A a b - 216B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (72A b + 288B a b )d e - 120B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (36A a b + 24B a b)d e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 4 4 5 +--R (36A b + 144B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 2B b e x + ((3A b + 12B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 12A b - 48B a b )d e + 20B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 4 3 2 2 +--R ((48A a b + 72B a b )d e + (- 30A b - 120B a b )d e + 50B b d e )x +--R + +--R 3 4 5 2 2 3 4 +--R (- 24A a b - 6B a )e + (72A a b + 48B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (12A b + 48B a b )d e - 20B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 12A a b - 3B a )d e + (54A a b + 36B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 60A a b - 90B a b )d e + (24A b + 96B a b )d e - 40B b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 5 3 2 2 4 +--R (36A a b + 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (36A b + 144B a b )d e - 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 144A a b - 216B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (72A b + 288B a b )d e - 120B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (36A a b + 24B a b)d e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 4 4 5 +--R (36A b + 144B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 2B b e x + ((3A b + 12B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 12A b - 48B a b )d e + 20B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 4 3 2 2 +--R ((48A a b + 72B a b )d e + (- 33A b - 132B a b )d e + 63B b d e )x +--R + +--R 3 4 5 2 2 3 4 +--R (- 24A a b - 6B a )e + (72A a b + 48B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (6A b + 24B a b )d e + 6B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 12A a b - 3B a )d e + (54A a b + 36B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 60A a b - 90B a b )d e + (21A b + 84B a b )d e - 27B b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1378 +m0:=a0-r0 +--R +--R +--R 4 3 2 4 3 +--R (- 3A b - 12B a b )d e + 13B b d +--R (4) ---------------------------------- +--R 6 +--R 6e +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1378 +r0:=-b^3*(4*b*B*d-A*b*e-4*a*B*e)*x/e^5+1/2*b^4*B*x^2/e^4+1/3*(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x)^3)-1/2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/_ + (e^6*(d+e*x)^2)+2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*(d+_ + e*x))+2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 24A b - 96B a b )d e + 60B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 3 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 4 +--R 180B b d e +--R * +--R x +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (24A a b + 36B a b )d e + (- 24A b - 96B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((6A b + 24B a b )e - 15B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((18A b + 72B a b )d e - 63B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (72A a b + 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 18A b - 72B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 12A a b - 3B a )e + (- 36A a b - 24B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (108A a b + 162B a b )d e + (- 54A b - 216B a b )d e + 81B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 2A a e + (- 4A a b - B a )d e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (44A a b + 66B a b )d e + (- 26A b - 104B a b )d e + 47B b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 24A b - 96B a b )d e + 60B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 3 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 4 +--R 180B b d e +--R * +--R x +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (24A a b + 36B a b )d e + (- 24A b - 96B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((6A b + 24B a b )e - 15B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((18A b + 72B a b )d e - 63B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (72A a b + 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 18A b - 72B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 12A a b - 3B a )e + (- 36A a b - 24B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (108A a b + 162B a b )d e + (- 54A b - 216B a b )d e + 81B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 2A a e + (- 4A a b - B a )d e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (44A a b + 66B a b )d e + (- 26A b - 104B a b )d e + 47B b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1378 +r0:=b^4*B*x/e^5+1/4*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^4)-1/3*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^3)+b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^2)-2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 3 5 4 4 4 +--R ((12A b + 48B a b )e - 60B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((48A b + 192B a b )d e - 240B b d e )x +--R + +--R 4 3 2 3 4 3 2 2 +--R ((72A b + 288B a b )d e - 360B b d e )x +--R + +--R 4 3 3 2 4 4 4 3 4 +--R ((48A b + 192B a b )d e - 240B b d e)x + (12A b + 48B a b )d e +--R + +--R 4 5 +--R - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 4 4 +--R 12B b e x + 48B b d e x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((- 48A a b - 72B a b )e + (48A b + 192B a b )d e - 48B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (108A b + 432B a b )d e - 252B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 16A a b - 4B a )e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (88A b + 352B a b )d e - 248B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 4A a b - B a )d e + (- 6A a b - 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 12A a b - 18B a b )d e + (25A b + 100B a b )d e - 77B b d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 5 4 4 4 +--R ((12A b + 48B a b )e - 60B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((48A b + 192B a b )d e - 240B b d e )x +--R + +--R 4 3 2 3 4 3 2 2 +--R ((72A b + 288B a b )d e - 360B b d e )x +--R + +--R 4 3 3 2 4 4 4 3 4 +--R ((48A b + 192B a b )d e - 240B b d e)x + (12A b + 48B a b )d e +--R + +--R 4 5 +--R - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 4 4 +--R 12B b e x + 48B b d e x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((- 48A a b - 72B a b )e + (48A b + 192B a b )d e - 48B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (108A b + 432B a b )d e - 252B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 16A a b - 4B a )e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (88A b + 352B a b )d e - 248B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 4A a b - B a )d e + (- 6A a b - 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 12A a b - 18B a b )d e + (25A b + 100B a b )d e - 77B b d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^6 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1378 +r0:=-1/5*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^5)-1/4*B*(b*d-a*e)^4/_ + (e^6*(d+e*x)^4)+4/3*b*B*(b*d-a*e)^3/(e^6*(d+e*x)^3)-3*b^2*B*(b*d-_ + a*e)^2/(e^6*(d+e*x)^2)+4*b^3*B*(b*d-a*e)/(e^6*(d+e*x))+b^4*B*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 6 5 5 5 4 5 5 2 4 4 +--R (60B a b e - 60B b d e )x + (300B a b d e - 300B b d e )x +--R + +--R 4 2 4 5 3 3 3 4 3 3 5 4 2 2 +--R (600B a b d e - 600B b d e )x + (600B a b d e - 600B b d e )x +--R + +--R 4 4 2 5 5 4 5 5 6 +--R (300B a b d e - 300B b d e)x + 60B a b d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 5 6 5 5 5 +--R (- 12A b e + 12B b d e )x +--R + +--R 4 2 3 6 4 5 5 2 4 4 +--R ((- 60A a b - 240B a b )e + 540B a b d e - 240B b d e )x +--R + +--R 2 3 3 2 6 2 3 5 4 2 4 +--R (- 120A a b - 180B a b )e - 300B a b d e + 1380B a b d e +--R + +--R 5 3 3 +--R - 780B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 3 2 5 2 3 2 4 +--R (- 120A a b - 80B a b)e - 100B a b d e - 300B a b d e +--R + +--R 4 3 3 5 4 2 +--R 1580B a b d e - 980B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 4 5 3 2 2 4 2 3 3 3 +--R (- 60A a b - 15B a )e - 25B a b d e - 50B a b d e - 150B a b d e +--R + +--R 4 4 2 5 5 +--R 865B a b d e - 565B b d e +--R * +--R x +--R + +--R 5 6 5 5 4 2 4 3 2 3 3 2 3 4 2 +--R - 12A a e - 3B a d e - 5B a b d e - 10B a b d e - 30B a b d e +--R + +--R 4 5 5 6 +--R 185B a b d e - 125B b d +--R / +--R 12 11 5 11 2 10 4 +--R (60a e - 60b d e )x + (300a d e - 300b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (600a d e - 600b d e )x + (600a d e - 600b d e )x +--R + +--R 4 8 5 7 5 7 6 6 +--R (300a d e - 300b d e )x + 60a d e - 60b d e +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 4 4 4 2 3 3 4 3 2 2 +--R 60B b e x + 300B b d e x + 600B b d e x + 600B b d e x +--R + +--R 4 4 4 5 +--R 300B b d e x + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 4 +--R ((- 60A b - 240B a b )e + 300B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 120A a b - 180B a b )e + (- 120A b - 480B a b )d e +--R + +--R 4 2 3 +--R 900B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 120A a b - 80B a b)e + (- 120A a b - 180B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 120A b - 480B a b )d e + 1100B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 60A a b - 15B a )e + (- 60A a b - 40B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 60A a b - 90B a b )d e + (- 60A b - 240B a b )d e + 625B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 12A a e + (- 12A a b - 3B a )d e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 12A a b - 18B a b )d e + (- 12A b - 48B a b )d e + 137B b d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1378 +m0:=a0-r0 +--R +--R +--R 5 5 +--R A b e - B b d +--R (4) --------------- +--R 7 6 +--R 5a e - 5b d e +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1378 +r0:=-1/6*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^6)+1/30*(5*b*B*d+A*b*e-_ + 6*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^5) +--R +--R +--R (2) +--R 1 6 1 5 1 6 6 +--R ((-- A b - - B a b )e + - B b d)x +--R 30 5 6 +--R + +--R 2 4 1 6 4 5 5 +--R (- B a b e + (- A b + - B a b )d)x +--R 5 5 +--R + +--R 1 2 4 3 3 5 3 2 4 4 +--R ((- - A a b - 2B a b )e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 3 3 4 2 2 4 4 3 3 3 +--R ((- - A a b - 2B a b )e + (2A a b + - B a b )d)x +--R 3 3 +--R + +--R 3 4 2 5 3 3 1 4 2 2 +--R ((- - A a b - B a b)e + (2A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 5 1 6 4 2 1 6 1 5 1 6 +--R ((- - A a b - - B a )e + A a b d)x - - A a e + (- A a b - -- B a )d +--R 5 5 6 5 30 +--R / +--R 2 8 7 2 2 6 6 2 7 2 6 2 3 5 5 +--R (a e - 2a b d e + b d e )x + (6a d e - 12a b d e + 6b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (15a d e - 30a b d e + 15b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (20a d e - 40a b d e + 20b d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 2 5 3 6 2 2 7 +--R (15a d e - 30a b d e + 15b d e )x + (6a d e - 12a b d e + 6b d e)x +--R + +--R 2 6 2 7 2 8 +--R a d e - 2a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 282 + +--S 283 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 30B b e x + ((- 15A b - 60B a b )e - 75B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((- 40A a b - 60B a b )e + (- 20A b - 80B a b )d e - 100B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 45A a b - 30B a b)e + (- 30A a b - 45B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 15A b - 60B a b )d e - 75B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 24A a b - 6B a )e + (- 18A a b - 12B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 12A a b - 18B a b )d e + (- 6A b - 24B a b )d e - 30B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 5A a e + (- 4A a b - B a )d e + (- 3A a b - 2B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 2A a b - 3B a b )d e + (- A b - 4B a b )d e - 5B b d +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 +--R 30e x + 180d e x + 450d e x + 600d e x + 450d e x + 180d e x +--R + +--R 6 6 +--R 30d e +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1378 +m0:=a0-r0 +--R +--R +--R 6 5 6 +--R (- A b + 6B a b )e - 5B b d +--R (4) ------------------------------ +--R 2 8 7 2 2 6 +--R 30a e - 60a b d e + 30b d e +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1378 +r0:=-1/7*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^7)+1/42*(5*b*B*d+2*A*b*e-_ + 7*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^6)+1/210*b*(5*b*B*d+2*A*b*e-_ + 7*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 1 7 1 6 2 1 7 7 +--R ((- --- A b + -- B a b )e - -- B b d e)x +--R 105 30 42 +--R + +--R 1 7 7 6 1 7 2 6 +--R ((- -- A b + -- B a b )d e - - B b d )x +--R 15 30 6 +--R + +--R 1 3 4 2 3 2 5 1 7 4 6 2 5 +--R (- - B a b e + - B a b d e + (- - A b - - B a b )d )x +--R 2 2 5 5 +--R + +--R 1 3 4 4 4 3 2 2 5 19 3 4 +--R (- - A a b - - B a b )e + (A a b + -- B a b )d e +--R 3 3 6 +--R + +--R 6 3 2 5 2 +--R (- A a b - - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 3 3 5 2 2 8 3 4 19 4 3 +--R (- A a b - - B a b )e + (- A a b + -- B a b )d e +--R 2 3 6 +--R + +--R 2 5 4 3 4 2 +--R (- 2A a b - - B a b )d +--R 3 +--R * +--R 3 +--R x +--R + +--R 6 5 2 4 6 2 4 3 3 5 2 +--R (- - A a b - - B a b)e + (3A a b + - B a b )d e +--R 5 5 2 +--R + +--R 3 4 1 4 3 2 +--R (- 2A a b - - B a b )d +--R 2 +--R * +--R 2 +--R x +--R + +--R 2 6 1 7 2 8 5 2 7 6 4 3 2 +--R ((- - A a b - - B a )e + (- A a b + -- B a b)d e - A a b d )x +--R 3 6 5 30 +--R + +--R 1 7 2 1 6 1 7 1 5 2 1 6 2 +--R - - A a e + (- A a b - -- B a )d e + (- - A a b + -- B a b)d +--R 7 3 42 5 30 +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (a e - 3a b d e + 3a b d e - b d e )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (7a d e - 21a b d e + 21a b d e - 7b d e )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (21a d e - 63a b d e + 63a b d e - 21b d e )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (35a d e - 105a b d e + 105a b d e - 35b d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (35a d e - 105a b d e + 105a b d e - 35b d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (21a d e - 63a b d e + 63a b d e - 21b d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 2 8 2 +--R (7a d e - 21a b d e + 21a b d e - 7b d e)x + a d e - 3a b d e +--R + +--R 2 9 3 10 +--R 3a b d e - b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 287 + +--S 288 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 105B b e x + ((- 70A b - 280B a b )e - 175B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 210A a b - 315B a b )e + (- 70A b - 280B a b )d e +--R + +--R 4 2 3 +--R - 175B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 252A a b - 168B a b)e + (- 126A a b - 189B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 42A b - 168B a b )d e - 105B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 140A a b - 35B a )e + (- 84A a b - 56B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 42A a b - 63B a b )d e + (- 14A b - 56B a b )d e - 35B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 30A a e + (- 20A a b - 5B a )d e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 6A a b - 9B a b )d e + (- 2A b - 8B a b )d e - 5B b d +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 +--R 210e x + 1470d e x + 4410d e x + 7350d e x + 7350d e x +--R + +--R 5 8 2 6 7 7 6 +--R 4410d e x + 1470d e x + 210d e +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1378 +m0:=a0-r0 +--R +--R +--R 7 6 7 +--R (2A b - 7B a b )e + 5B b d +--R (4) ----------------------------------------------- +--R 3 9 2 8 2 2 7 3 3 6 +--R 210a e - 630a b d e + 630a b d e - 210b d e +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1378 +r0:=-1/8*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^8)+1/56*(5*b*B*d+3*A*b*e-_ + 8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^7)+1/168*b*(5*b*B*d+3*A*b*e-_ + 8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^3*(d+e*x)^6)+1/840*b^2*(5*b*B*d+_ + 3*A*b*e-8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 1 8 1 7 3 1 8 2 8 +--R ((--- A b - --- B a b )e + --- B b d e )x +--R 280 105 168 +--R + +--R 1 8 8 7 2 1 8 2 7 +--R ((-- A b - --- B a b )d e + -- B b d e)x +--R 35 105 21 +--R + +--R 1 8 4 7 2 1 8 3 6 +--R ((-- A b - -- B a b )d e + - B b d )x +--R 10 15 6 +--R + +--R 1 4 4 3 4 3 5 2 2 6 2 1 8 4 7 3 5 +--R (- - B a b e + - B a b d e - 2B a b d e + (- A b + - B a b )d )x +--R 3 3 5 5 +--R + +--R 1 4 4 5 3 3 3 5 43 4 4 2 +--R (- - A a b - B a b )e + (A a b + -- B a b )d e +--R 4 12 +--R + +--R 3 2 6 13 3 5 2 7 3 2 6 3 +--R (- - A a b - -- B a b )d e + (A a b + - B a b )d +--R 2 3 2 +--R * +--R 4 +--R x +--R + +--R 4 5 3 6 6 2 3 4 4 5 3 2 +--R (- - A a b - - B a b )e + (3A a b + 4B a b )d e +--R 5 5 +--R + +--R 3 5 13 4 4 2 2 6 4 3 5 3 +--R (- 4A a b - -- B a b )d e + (2A a b + - B a b )d +--R 3 3 +--R * +--R 3 +--R x +--R + +--R 6 2 2 7 3 18 5 3 31 6 2 2 +--R (- A a b - - B a b)e + (-- A a b + -- B a b )d e +--R 3 5 15 +--R + +--R 9 4 4 5 3 2 3 5 1 4 4 3 +--R (- - A a b - 2B a b )d e + (2A a b + - B a b )d +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 4 7 1 8 3 6 2 8 7 2 +--R (- - A a b - - B a )e + (2A a b + -- B a b)d e +--R 7 7 21 +--R + +--R 12 5 3 4 6 2 2 4 4 3 +--R (- -- A a b - -- B a b )d e + A a b d +--R 5 15 +--R * +--R x +--R + +--R 1 8 3 3 7 1 8 2 1 6 2 1 7 2 +--R - - A a e + (- A a b - -- B a )d e + (- - A a b + -- B a b)d e +--R 8 7 56 2 21 +--R + +--R 1 5 3 1 6 2 3 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 4 12 3 11 2 2 2 10 3 3 9 4 4 8 8 +--R (a e - 4a b d e + 6a b d e - 4a b d e + b d e )x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 4 5 7 7 +--R (8a d e - 32a b d e + 48a b d e - 32a b d e + 8b d e )x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 4 6 6 6 +--R (28a d e - 112a b d e + 168a b d e - 112a b d e + 28b d e )x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 4 7 5 5 +--R (56a d e - 224a b d e + 336a b d e - 224a b d e + 56b d e )x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 8 4 4 +--R (70a d e - 280a b d e + 420a b d e - 280a b d e + 70b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 8 4 4 9 3 3 +--R (56a d e - 224a b d e + 336a b d e - 224a b d e + 56b d e )x +--R + +--R 4 6 6 3 7 5 2 2 8 4 3 9 3 4 10 2 2 +--R (28a d e - 112a b d e + 168a b d e - 112a b d e + 28b d e )x +--R + +--R 4 7 5 3 8 4 2 2 9 3 3 10 2 4 11 4 8 4 +--R (8a d e - 32a b d e + 48a b d e - 32a b d e + 8b d e)x + a d e +--R + +--R 3 9 3 2 2 10 2 3 11 4 12 +--R - 4a b d e + 6a b d e - 4a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 292 + +--S 293 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 280B b e x + ((- 210A b - 840B a b )e - 350B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 672A a b - 1008B a b )e + (- 168A b - 672B a b )d e +--R + +--R 4 2 3 +--R - 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 840A a b - 560B a b)e + (- 336A a b - 504B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 84A b - 336B a b )d e - 140B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 480A a b - 120B a )e + (- 240A a b - 160B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 96A a b - 144B a b )d e + (- 24A b - 96B a b )d e - 40B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 105A a e + (- 60A a b - 15B a )d e + (- 30A a b - 20B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 12A a b - 18B a b )d e + (- 3A b - 12B a b )d e - 5B b d +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 +--R 840e x + 6720d e x + 23520d e x + 47040d e x + 58800d e x +--R + +--R 5 9 3 6 8 2 7 7 8 6 +--R 47040d e x + 23520d e x + 6720d e x + 840d e +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1378 +m0:=a0-r0 +--R +--R +--R 8 7 8 +--R (- 3A b + 8B a b )e - 5B b d +--R (4) ----------------------------------------------------------------- +--R 4 10 3 9 2 2 2 8 3 3 7 4 4 6 +--R 840a e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d e +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^10 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 1378 +r0:=1/9*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^9)-1/8*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^8)+2/7*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^7)-1/3*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^6)+1/5*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^5)-_ + 1/4*b^4*B/(e^6*(d+e*x)^4) +--R +--R +--R (2) +--R 1 4 5 5 1 4 4 3 5 1 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - - B b d e )x +--R 4 5 5 4 +--R + +--R 2 3 2 2 5 2 4 8 3 4 1 4 2 3 3 +--R ((- - A a b - B a b )e + (- -- A b - -- B a b )d e - - B b d e )x +--R 3 15 15 6 +--R + +--R 6 2 2 4 3 5 2 3 3 2 2 4 +--R (- - A a b - - B a b)e + (- - A a b - - B a b )d e +--R 7 7 7 7 +--R + +--R 2 4 8 3 2 3 1 4 3 2 +--R (- -- A b - -- B a b )d e - -- B b d e +--R 35 35 14 +--R * +--R 2 +--R x +--R + +--R 1 3 1 4 5 3 2 2 1 3 4 +--R (- - A a b - - B a )e + (- -- A a b - - B a b)d e +--R 2 8 14 7 +--R + +--R 1 3 3 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- -- A b - -- B a b )d e +--R 14 28 70 35 +--R + +--R 1 4 4 +--R - -- B b d e +--R 56 +--R * +--R x +--R + +--R 1 4 5 1 3 1 4 4 1 2 2 1 3 2 3 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A a b - -- B a b)d e +--R 9 18 72 42 63 +--R + +--R 1 3 1 2 2 3 2 1 4 2 3 4 1 4 5 +--R (- --- A a b - -- B a b )d e + (- --- A b - --- B a b )d e - --- B b d +--R 126 84 630 315 504 +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 5 10 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 9 3 7 8 2 8 7 9 6 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 297 + +--S 298 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 630B b e x + ((- 504A b - 2016B a b )e - 630B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 1680A a b - 2520B a b )e + (- 336A b - 1344B a b )d e +--R + +--R 4 2 3 +--R - 420B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 2160A a b - 1440B a b)e + (- 720A a b - 1080B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 144A b - 576B a b )d e - 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 1260A a b - 315B a )e + (- 540A a b - 360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 180A a b - 270B a b )d e + (- 36A b - 144B a b )d e - 45B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 280A a e + (- 140A a b - 35B a )d e + (- 60A a b - 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 20A a b - 30B a b )d e + (- 4A b - 16B a b )d e - 5B b d +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 +--R 2520e x + 22680d e x + 90720d e x + 211680d e x + 317520d e x +--R + +--R 5 10 4 6 9 3 7 8 2 8 7 9 6 +--R 317520d e x + 211680d e x + 90720d e x + 22680d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^11 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1378 +r0:=1/10*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^10)-1/9*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^9)+1/4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^8)-2/7*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^7)+1/6*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^6)-_ + 1/5*b^4*B/(e^6*(d+e*x)^5) +--R +--R +--R (2) +--R 1 4 5 5 1 4 2 3 5 1 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - - B b d e )x +--R 5 6 3 6 +--R + +--R 4 3 6 2 2 5 2 4 8 3 4 2 4 2 3 3 +--R ((- - A a b - - B a b )e + (- -- A b - -- B a b )d e - -- B b d e )x +--R 7 7 21 21 21 +--R + +--R 3 2 2 1 3 5 3 3 9 2 2 4 +--R (- - A a b - - B a b)e + (- -- A a b - -- B a b )d e +--R 4 2 14 28 +--R + +--R 1 4 1 3 2 3 1 4 3 2 +--R (- -- A b - - B a b )d e - -- B b d e +--R 28 7 28 +--R * +--R 2 +--R x +--R + +--R 4 3 1 4 5 1 2 2 1 3 4 +--R (- - A a b - - B a )e + (- - A a b - - B a b)d e +--R 9 9 6 9 +--R + +--R 1 3 1 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- --- A b - -- B a b )d e +--R 21 14 126 63 +--R + +--R 1 4 4 +--R - --- B b d e +--R 126 +--R * +--R x +--R + +--R 1 4 5 2 3 1 4 4 1 2 2 1 3 2 3 +--R - -- A a e + (- -- A a b - -- B a )d e + (- -- A a b - -- B a b)d e +--R 10 45 90 60 90 +--R + +--R 1 3 1 2 2 3 2 1 4 1 3 4 +--R (- --- A a b - --- B a b )d e + (- ---- A b - --- B a b )d e +--R 210 140 1260 315 +--R + +--R 1 4 5 +--R - ---- B b d +--R 1260 +--R / +--R 16 10 15 9 2 14 8 3 13 7 4 12 6 5 11 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 10 4 7 9 3 8 8 2 9 7 10 6 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 302 + +--S 303 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 252B b e x + ((- 210A b - 840B a b )e - 210B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 720A a b - 1080B a b )e + (- 120A b - 480B a b )d e +--R + +--R 4 2 3 +--R - 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 945A a b - 630B a b)e + (- 270A a b - 405B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 45A b - 180B a b )d e - 45B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 560A a b - 140B a )e + (- 210A a b - 140B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 60A a b - 90B a b )d e + (- 10A b - 40B a b )d e - 10B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 126A a e + (- 56A a b - 14B a )d e + (- 21A a b - 14B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 6A a b - 9B a b )d e + (- A b - 4B a b )d e - B b d +--R / +--R 16 10 15 9 2 14 8 3 13 7 4 12 6 +--R 1260e x + 12600d e x + 56700d e x + 151200d e x + 264600d e x +--R + +--R 5 11 5 6 10 4 7 9 3 8 8 2 9 7 +--R 317520d e x + 264600d e x + 151200d e x + 56700d e x + 12600d e x +--R + +--R 10 6 +--R 1260d e +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^12 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 1378 +r0:=1/11*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^11)-1/10*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^10)+2/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^9)-1/4*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^8)+1/7*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^7)-_ + 1/6*b^4*B/(e^6*(d+e*x)^6) +--R +--R +--R (2) +--R 1 4 5 5 1 4 4 3 5 5 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - -- B b d e )x +--R 6 7 7 42 +--R + +--R 1 3 3 2 2 5 1 4 2 3 4 5 4 2 3 3 +--R ((- - A a b - - B a b )e + (- -- A b - - B a b )d e - -- B b d e )x +--R 2 4 14 7 84 +--R + +--R 2 2 2 4 3 5 1 3 1 2 2 4 +--R (- - A a b - - B a b)e + (- - A a b - - B a b )d e +--R 3 9 6 4 +--R + +--R 1 4 2 3 2 3 5 4 3 2 +--R (- -- A b - -- B a b )d e - --- B b d e +--R 42 21 252 +--R * +--R 2 +--R x +--R + +--R 2 3 1 4 5 2 2 2 4 3 4 +--R (- - A a b - -- B a )e + (- -- A a b - -- B a b)d e +--R 5 10 15 45 +--R + +--R 1 3 1 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- --- A b - --- B a b )d e +--R 30 20 210 105 +--R + +--R 1 4 4 +--R - --- B b d e +--R 252 +--R * +--R x +--R + +--R 1 4 5 2 3 1 4 4 +--R - -- A a e + (- -- A a b - --- B a )d e +--R 11 55 110 +--R + +--R 2 2 2 4 3 2 3 1 3 1 2 2 3 2 +--R (- --- A a b - --- B a b)d e + (- --- A a b - --- B a b )d e +--R 165 495 330 220 +--R + +--R 1 4 2 3 4 1 4 5 +--R (- ---- A b - ---- B a b )d e - ---- B b d +--R 2310 1155 2772 +--R / +--R 17 11 16 10 2 15 9 3 14 8 4 13 7 5 12 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 11 5 7 10 4 8 9 3 9 8 2 10 7 11 6 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 307 + +--S 308 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 2310B b e x + ((- 1980A b - 7920B a b )e - 1650B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 6930A a b - 10395B a b )e + (- 990A b - 3960B a b )d e +--R + +--R 4 2 3 +--R - 825B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 9240A a b - 6160B a b)e + (- 2310A a b - 3465B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 330A b - 1320B a b )d e - 275B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 5544A a b - 1386B a )e + (- 1848A a b - 1232B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 462A a b - 693B a b )d e + (- 66A b - 264B a b )d e - 55B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 1260A a e + (- 504A a b - 126B a )d e + (- 168A a b - 112B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 42A a b - 63B a b )d e + (- 6A b - 24B a b )d e - 5B b d +--R / +--R 17 11 16 10 2 15 9 3 14 8 +--R 13860e x + 152460d e x + 762300d e x + 2286900d e x +--R + +--R 4 13 7 5 12 6 6 11 5 7 10 4 +--R 4573800d e x + 6403320d e x + 6403320d e x + 4573800d e x +--R + +--R 8 9 3 9 8 2 10 7 11 6 +--R 2286900d e x + 762300d e x + 152460d e x + 13860d e +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1378 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 1378 +r0:=2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*x/b^5-(A*b-a*B)*(b*d-a*e)^4/_ + (b^6*(a+b*x))+e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^2/b^6+_ + 1/3*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^3/b^6+1/4*B*e^4*(a+b*x)^4/b^6+_ + (b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 3 2 4 4 2 3 3 2 3 +--R (- 48A a b + 60B a b)e + (144A a b - 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 144A a b + 216B a b )d e + (48A b - 96B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 60B a )e + (144A a b - 192B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 144A a b + 216B a b )d e + (48A a b - 96B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - 5B a b )e + 16B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 8A a b + 10B a b )e + (24A b - 32B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (24A a b - 30B a b )e + (- 72A a b + 96B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (72A b - 108B a b )d e + 48B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (16A a b - 5B a b)e + (- 72A a b + 64B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 108B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 32A a b + 55B a )e + (72A a b - 128B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A a b + 108B a b )d e + (48A a b - 48B a b )d e +--R + +--R 5 4 4 +--R (- 12A b + 12B a b )d +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 4 2 3 3 2 3 +--R (- 48A a b + 60B a b)e + (144A a b - 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 144A a b + 216B a b )d e + (48A b - 96B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 60B a )e + (144A a b - 192B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 144A a b + 216B a b )d e + (48A a b - 96B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - 5B a b )e + 16B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 8A a b + 10B a b )e + (24A b - 32B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (24A a b - 30B a b )e + (- 72A a b + 96B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (72A b - 108B a b )d e + 48B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (36A a b - 48B a b)e + (- 96A a b + 144B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 144B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 12A a b + 12B a )e + (48A a b - 48B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A a b + 72B a b )d e + (48A a b - 48B a b )d e +--R + +--R 5 4 4 +--R (- 12A b + 12B a b )d +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1378 +m0:=a0-r0 +--R +--R +--R 3 4 4 2 2 3 3 2 2 2 2 +--R (20A a b - 43B a )e + (- 24A a b + 80B a b)d e - 36B a b d e +--R (4) ---------------------------------------------------------------- +--R 6 +--R 12b +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1378 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1378 +r0:=3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*x/b^4-(A*b-a*B)*(b*d-a*e)^3/(b^5*_ + (a+b*x))+1/2*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^2/b^5+1/3*B*e^3*_ + (a+b*x)^3/b^5+(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 24B a b)e + (- 36A a b + 54B a b )d e +--R + +--R 4 3 2 4 3 +--R (18A b - 36B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (18A a b - 24B a )e + (- 36A a b + 54B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A a b - 36B a b )d e + 6B a b d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - 4B a b )e + 9B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 9A a b + 12B a b )e + (18A b - 27B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 9A a b + 8B a b)e + (18A a b - 27B a b )d e + 18B a b d e)x +--R + +--R 3 4 3 2 2 3 2 +--R (9A a b - 16B a )e + (- 18A a b + 27B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A a b - 18B a b )d e + (- 6A b + 6B a b )d +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 24B a b)e + (- 36A a b + 54B a b )d e +--R + +--R 4 3 2 4 3 +--R (18A b - 36B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (18A a b - 24B a )e + (- 36A a b + 54B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A a b - 36B a b )d e + 6B a b d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - 4B a b )e + 9B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 9A a b + 12B a b )e + (18A b - 27B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 18B a b)e + (18A a b - 36B a b )d e + 18B a b d e)x +--R + +--R 3 4 3 2 2 3 2 +--R (6A a b - 6B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A a b - 18B a b )d e + (- 6A b + 6B a b )d +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1378 +m0:=a0-r0 +--R +--R +--R 2 3 3 2 2 +--R (- 3A a b + 10B a )e - 9B a b d e +--R (4) ----------------------------------- +--R 5 +--R 6b +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1378 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 1378 +r0:=e*(2*b*B*d+A*b*e-2*a*B*e)*x/b^3+1/2*B*e^2*x^2/b^2-(A*b-a*B)*_ + (b*d-a*e)^2/(b^4*(a+b*x))+(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((- 4A a b + 6B a b)e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 4A a b + 6B a )e + (4A a b - 8B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((2A a b - 4B a b)e + 4B a b d e)x + (- 2A a b + 2B a )e +--R + +--R 2 2 3 2 2 +--R (4A a b - 4B a b)d e + (- 2A b + 2B a b )d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 +--R ((- 4A a b + 6B a b)e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 4A a b + 6B a )e + (4A a b - 8B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((2A a b - 4B a b)e + 4B a b d e)x + (- 2A a b + 2B a )e +--R + +--R 2 2 3 2 2 +--R (4A a b - 4B a b)d e + (- 2A b + 2B a b )d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 1378 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 1378 +r0:=B*e*x/b^2-(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x))+(b*B*d+A*b*e-2*a*B*e)*_ + log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (((A b - 2B a b)e + B b d)x + (A a b - 2B a )e + B a b d)log(b x + a) +--R + +--R 2 2 2 2 +--R B b e x + B a b e x + (A a b - B a )e + (- A b + B a b)d +--R / +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (((A b - 2B a b)e + B b d)x + (A a b - 2B a )e + B a b d)log(b x + a) +--R + +--R 2 2 2 2 +--R B b e x + B a b e x + (A a b - B a )e + (- A b + B a b)d +--R / +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1378 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R B x + A +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1378 +r0:=(-A*b+a*B)/(b^2*(a+b*x))+B*log(a+b*x)/b^2 +--R +--R +--R (B b x + B a)log(b x + a) - A b + B a +--R (2) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (B b x + B a)log(b x + a) - A b + B a +--R (3) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1378 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (2a b e + b d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 1378 +r0:=(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x))+(B*d-A*e)*log(a+b*x)/(b*d-a*e)^2-_ + (B*d-A*e)*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (2) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(b x + a) + (A a b - B a )e +--R + +--R 2 +--R (- A b + B a b)d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R (a b e - 2a b d e + b d )x + a b e - 2a b d e + a b d +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(b x + a) + (A a b - B a )e +--R + +--R 2 +--R (- A b + B a b)d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R (a b e - 2a b d e + b d )x + a b e - 2a b d e + a b d +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1378 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 1378 +r0:=(-A*b+a*B)/((b*d-a*e)^2*(a+b*x))+(B*d-A*e)/((b*d-a*e)^2*(d+e*x))+_ + (b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^3-(b*B*d-2*A*b*e+a*B*e)*_ + log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 2A b + B a b)e + B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 2A a b + B a )e + (- 2A b + 2B a b)d e + B b d )x +--R + +--R 2 2 +--R (- 2A a b + B a )d e + B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R ((2A b - B a b)e - B b d e)x +--R + +--R 2 2 2 2 2 +--R ((2A a b - B a )e + (2A b - 2B a b)d e - B b d )x +--R + +--R 2 2 +--R (2A a b - B a )d e - B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2A a b + B a )e + 2A b d e - B b d )x - A a e + 2B a d e +--R + +--R 2 2 +--R (A b - 2B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R ((- 2A b + B a b)e + B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 2A a b + B a )e + (- 2A b + 2B a b)d e + B b d )x +--R + +--R 2 2 +--R (- 2A a b + B a )d e + B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R ((2A b - B a b)e - B b d e)x +--R + +--R 2 2 2 2 2 +--R ((2A a b - B a )e + (2A b - 2B a b)d e - B b d )x +--R + +--R 2 2 +--R (2A a b - B a )d e - B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2A a b + B a )e + 2A b d e - B b d )x - A a e + 2B a d e +--R + +--R 2 2 +--R (A b - 2B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1378 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 1378 +r0:=-b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x))+1/2*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^2)+_ + (b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x))+b*(b*B*d-3*A*b*e+2*a*B*e)*_ + log(a+b*x)/(b*d-a*e)^4-b*(b*B*d-3*A*b*e+2*a*B*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((6A b - 4B a b )e - 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (12A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((12A a b - 8B a b)d e + (6A b - 8B a b )d e - 2B b d )x +--R + +--R 2 2 2 2 3 +--R (6A a b - 4B a b)d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((- 6A b + 4B a b )e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 4B a b)e + (- 12A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((- 12A a b + 8B a b)d e + (- 6A b + 8B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 3 +--R (- 6A a b + 4B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (- 6A b + 2B a b )d e + 2B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b - 2B a )e + (6A a b - 5B a b)d e + (- 9A b + 4B a b )d e +--R + +--R 3 3 +--R 3B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - A a e + (6A a b - B a )d e + (- 3A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- 2A b + 5B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 3 +--R ((6A b - 4B a b )e - 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (12A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((12A a b - 8B a b)d e + (6A b - 8B a b )d e - 2B b d )x +--R + +--R 2 2 2 2 3 +--R (6A a b - 4B a b)d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((- 6A b + 4B a b )e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 4B a b)e + (- 12A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((- 12A a b + 8B a b)d e + (- 6A b + 8B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 3 +--R (- 6A a b + 4B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (- 6A b + 2B a b )d e + 2B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b - 2B a )e + (6A a b - 5B a b)d e + (- 9A b + 4B a b )d e +--R + +--R 3 3 +--R 3B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - A a e + (6A a b - B a )d e + (- 3A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- 2A b + 5B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1378 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 1378 +r0:=e^3*(4*b*B*d+A*b*e-4*a*B*e)*x/b^5+1/2*B*e^4*x^2/b^4-1/3*(A*b-a*B)*_ + (b*d-a*e)^4/(b^6*(a+b*x)^3)-1/2*(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)/_ + (b^6*(a+b*x)^2)-2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)/(b^6*(a+b*x))+_ + 2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 24A a b + 60B a b )e + (24A b - 96B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 72A a b + 180B a b )e + (72A a b - 288B a b )d e +--R + +--R 4 2 2 +--R 108B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 72A a b + 180B a b)e + (72A a b - 288B a b )d e +--R + +--R 2 3 2 2 +--R 108B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 3 2 2 2 +--R (- 24A a b + 60B a )e + (24A a b - 96B a b)d e + 36B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((6A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((18A a b - 63B a b )e + 72B a b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 18A a b - 9B a b )e + (72A a b - 72B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 54A a b + 81B a b)e + (108A a b - 216B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 36A a b + 162B a b )d e + (- 12A b - 24B a b )d e - 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 26A a b + 47B a )e + (44A a b - 104B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 12A a b + 66B a b )d e + (- 4A a b - 8B a b )d e +--R + +--R 5 4 4 +--R (- 2A b - B a b )d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 24A a b + 60B a b )e + (24A b - 96B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 72A a b + 180B a b )e + (72A a b - 288B a b )d e +--R + +--R 4 2 2 +--R 108B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 72A a b + 180B a b)e + (72A a b - 288B a b )d e +--R + +--R 2 3 2 2 +--R 108B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 3 2 2 2 +--R (- 24A a b + 60B a )e + (24A a b - 96B a b)d e + 36B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((6A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((18A a b - 63B a b )e + 72B a b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 18A a b - 9B a b )e + (72A a b - 72B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 54A a b + 81B a b)e + (108A a b - 216B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 36A a b + 162B a b )d e + (- 12A b - 24B a b )d e - 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 26A a b + 47B a )e + (44A a b - 104B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 12A a b + 66B a b )d e + (- 4A a b - 8B a b )d e +--R + +--R 5 4 4 +--R (- 2A b - B a b )d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1378 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 1378 +r0:=B*e^3*x/b^4-1/3*(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x)^3)-1/2*(b*d-a*e)^2*_ + (b*B*d+3*A*b*e-4*a*B*e)/(b^5*(a+b*x)^2)-3*e*(b*d-a*e)*(b*B*d+A*b*e-_ + 2*a*B*e)/(b^5*(a+b*x))+e^2*(3*b*B*d+A*b*e-4*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((6A b - 24B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((18A a b - 72B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((18A a b - 72B a b)e + 54B a b d e )x + (6A a b - 24B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 3 +--R 6B b e x + 18B a b e x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((18A a b - 18B a b )e + (- 18A b + 54B a b )d e - 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (27A a b - 54B a b)e + (- 18A a b + 81B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 9A b - 18B a b )d e - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (11A a b - 26B a )e + (- 6A a b + 33B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b - 6B a b )d e + (- 2A b - B a b )d +--R / +--R 8 3 7 2 2 6 3 5 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 3 4 2 3 +--R ((6A b - 24B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((18A a b - 72B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((18A a b - 72B a b)e + 54B a b d e )x + (6A a b - 24B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 3 +--R 6B b e x + 18B a b e x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((18A a b - 18B a b )e + (- 18A b + 54B a b )d e - 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (27A a b - 54B a b)e + (- 18A a b + 81B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 9A b - 18B a b )d e - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (11A a b - 26B a )e + (- 6A a b + 33B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b - 6B a b )d e + (- 2A b - B a b )d +--R / +--R 8 3 7 2 2 6 3 5 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1378 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 1378 +r0:=-1/2*B*(b*d-a*e)^2/(b^4*(a+b*x)^2)-2*B*e*(b*d-a*e)/(b^4*(a+b*x))-_ + 1/3*(A*b-a*B)*(d+e*x)^3/(b*(b*d-a*e)*(a+b*x)^3)+B*e^2*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 4 2 3 2 2 3 3 2 2 +--R (6B a b e - 6B b d e )x + (18B a b e - 18B a b d e )x +--R + +--R 3 3 2 2 2 4 3 3 2 +--R (18B a b e - 18B a b d e )x + 6B a e - 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 3 3 +--R (2A b - 2B a b )e x +--R + +--R 2 2 3 4 3 2 4 2 2 +--R (12B a b e + (6A b - 30B a b )d e + 12B b d e)x +--R + +--R 3 3 2 2 2 4 3 2 4 3 4 3 +--R (21B a b e - 39B a b d e + (6A b + 9B a b )d e + 3B b d )x + 9B a e +--R + +--R 3 2 2 2 2 4 3 3 +--R - 15B a b d e + 3B a b d e + (2A b + B a b )d +--R / +--R 7 8 3 2 6 7 2 3 5 2 6 4 4 +--R (6a b e - 6b d)x + (18a b e - 18a b d)x + (18a b e - 18a b d)x + 6a b e +--R + +--R 3 5 +--R - 6a b d +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 2 2 2 2 3 2 +--R (6B b e x + 18B a b e x + 18B a b e x + 6B a e )log(b x + a) +--R + +--R 3 2 2 3 2 +--R ((- 6A b + 18B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 6A a b + 27B a b)e + (- 6A b - 12B a b )d e - 3B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 2A a b + 11B a )e + (- 2A a b - 4B a b)d e + (- 2A b - B a b )d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 1378 +m0:=a0-r0 +--R +--R +--R 3 +--R (- A b + B a)e +--R (4) --------------- +--R 4 5 +--R 3a b e - 3b d +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 1378 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 1378 +r0:=-1/3*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)^3)+1/2*(-b*B*d-A*b*e+2*a*B*e)/_ + (b^3*(a+b*x)^2)-B*e/(b^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 1 2 1 2 1 1 2 +--R - B b e x + ((- - A b - B a b)e - - B b d)x + (- - A a b - - B a )e +--R 2 2 6 3 +--R + +--R 1 2 1 +--R (- - A b - - B a b)d +--R 3 6 +--R / +--R 6 3 5 2 2 4 3 3 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 367 + +--S 368 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R - 6B b e x + ((- 3A b - 6B a b)e - 3B b d)x + (- A a b - 2B a )e +--R + +--R 2 +--R (- 2A b - B a b)d +--R / +--R 6 3 5 2 2 4 3 3 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 1378 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R B x + A +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 1378 +r0:=1/3*(-A*b+a*B)/(b^2*(a+b*x)^3)-1/2*B/(b^2*(a+b*x)^2) +--R +--R +--R 1 1 1 +--R - - B b x - - A b - - B a +--R 2 3 6 +--R (2) ------------------------------ +--R 5 3 4 2 2 3 3 2 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 372 + +--S 373 of 1378 +a0:=integrate(t0,x) +--R +--R +--R - 3B b x - 2A b - B a +--R (3) ---------------------------------- +--R 5 3 4 2 2 3 3 2 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1378 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 1378 +r0:=1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3)+1/2*(-B*d+A*e)/((b*d-a*e)^2*_ + (a+b*x)^2)+e*(B*d-A*e)/((b*d-a*e)^3*(a+b*x))+e^2*(B*d-A*e)*log(a+b*x)/_ + (b*d-a*e)^4-e^2*(B*d-A*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 4 3 4 2 3 3 3 3 2 2 +--R (6A b e - 6B b d e )x + (18A a b e - 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (18A a b e - 18B a b d e )x + 6A a b e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 2 3 3 3 3 2 2 +--R (- 6A b e + 6B b d e )x + (- 18A a b e + 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (- 18A a b e + 18B a b d e )x - 6A a b e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 4 3 2 4 2 2 +--R (6A a b e + (- 6A b - 6B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 2 2 2 4 3 2 +--R 15A a b e + (- 18A a b - 15B a b )d e + (3A b + 18B a b )d e +--R + +--R 4 3 +--R - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (11A a b - 2B a )e + (- 18A a b - 3B a b)d e + (9A a b + 6B a b )d e +--R + +--R 4 3 3 +--R (- 2A b - B a b )d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 3 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 2 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 7 4 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x + 6a b e +--R + +--R 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 3 3 3 3 2 2 +--R (6A b e - 6B b d e )x + (18A a b e - 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (18A a b e - 18B a b d e )x + 6A a b e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 2 3 3 3 3 2 2 +--R (- 6A b e + 6B b d e )x + (- 18A a b e + 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (- 18A a b e + 18B a b d e )x - 6A a b e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 4 3 2 4 2 2 +--R (6A a b e + (- 6A b - 6B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 2 2 2 4 3 2 +--R 15A a b e + (- 18A a b - 15B a b )d e + (3A b + 18B a b )d e +--R + +--R 4 3 +--R - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (11A a b - 2B a )e + (- 18A a b - 3B a b)d e + (9A a b + 6B a b )d e +--R + +--R 4 3 3 +--R (- 2A b - B a b )d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 3 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 2 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 7 4 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x + 6a b e +--R + +--R 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 1378 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 1378 +r0:=1/3*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^3)+1/2*(-b*B*d+2*A*b*e-a*B*e)/_ + ((b*d-a*e)^3*(a+b*x)^2)+e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(a+b*x))+_ + e^2*(B*d-A*e)/((b*d-a*e)^4*(d+e*x))+e^2*(3*b*B*d-4*A*b*e+a*B*e)*_ + log(a+b*x)/(b*d-a*e)^5-e^2*(3*b*B*d-4*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 24A b + 6B a b )e + 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 72A a b + 18B a b )e + (- 24A b + 60B a b )d e +--R + +--R 4 2 2 +--R 18B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 72A a b + 18B a b)e + (- 72A a b + 72B a b )d e +--R + +--R 3 2 2 +--R 54B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((- 24A a b + 6B a )e + (- 72A a b + 36B a b)d e + 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (- 24A a b + 6B a )d e + 18B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((24A b - 6B a b )e - 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((72A a b - 18B a b )e + (24A b - 60B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 3 2 2 2 +--R ((72A a b - 18B a b)e + (72A a b - 72B a b )d e - 54B a b d e )x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((24A a b - 6B a )e + (72A a b - 36B a b)d e - 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (24A a b - 6B a )d e - 18B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 24A a b + 6B a b )e + (24A b + 12B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 60A a b + 15B a b)e + (48A a b + 33B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 39B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 44A a b + 11B a )e + (12A a b + 30B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (36A a b - 18B a b )d e + (- 4A b - 26B a b )d e + 3B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (- 20A a b + 17B a )d e + (36A a b - 9B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 12A a b - 9B a b )d e + (2A b + B a b )d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 8 5 4 +--R (6a b e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6b d e)x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 18a b e - 84a b d e + 150a b d e - 120a b d e + 30a b d e +--R + +--R 7 5 8 6 +--R 12a b d e - 6b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 18a b e - 72a b d e + 90a b d e - 90a b d e + 72a b d e +--R + +--R 7 6 +--R - 18a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 6a e - 12a b d e - 30a b d e + 120a b d e - 150a b d e +--R + +--R 3 5 5 2 6 6 +--R 84a b d e - 18a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 3 5 6 +--R 6a d e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6a b d +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 4 3 4 +--R ((- 24A b + 6B a b )e + 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 72A a b + 18B a b )e + (- 24A b + 60B a b )d e +--R + +--R 4 2 2 +--R 18B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 72A a b + 18B a b)e + (- 72A a b + 72B a b )d e +--R + +--R 3 2 2 +--R 54B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((- 24A a b + 6B a )e + (- 72A a b + 36B a b)d e + 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (- 24A a b + 6B a )d e + 18B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((24A b - 6B a b )e - 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((72A a b - 18B a b )e + (24A b - 60B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 3 2 2 2 +--R ((72A a b - 18B a b)e + (72A a b - 72B a b )d e - 54B a b d e )x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((24A a b - 6B a )e + (72A a b - 36B a b)d e - 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (24A a b - 6B a )d e - 18B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 24A a b + 6B a b )e + (24A b + 12B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 60A a b + 15B a b)e + (48A a b + 33B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 39B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 44A a b + 11B a )e + (12A a b + 30B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (36A a b - 18B a b )d e + (- 4A b - 26B a b )d e + 3B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (- 20A a b + 17B a )d e + (36A a b - 9B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 12A a b - 9B a b )d e + (2A b + B a b )d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 8 5 4 +--R (6a b e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6b d e)x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 18a b e - 84a b d e + 150a b d e - 120a b d e + 30a b d e +--R + +--R 7 5 8 6 +--R 12a b d e - 6b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 18a b e - 72a b d e + 90a b d e - 90a b d e + 72a b d e +--R + +--R 7 6 +--R - 18a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 6a e - 12a b d e - 30a b d e + 120a b d e - 150a b d e +--R + +--R 3 5 5 2 6 6 +--R 84a b d e - 18a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 3 5 6 +--R 6a d e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6a b d +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 1378 +t0:=(A+B*x)*(d+e*x)^m*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R m | 2 2 2 +--R (1) (B x + A)(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1378 +r0:=(A*b*e*(3+m)-B*(2*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2*(2+m)*(3+m))-(b*d-a*e)*(A*b*e*(3+m)-B*(2*b*d+_ + a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(1+m)*_ + (2+m)*(3+m)*(a+b*x))+B*(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e*(3+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (B b e m + 3B b e m + 2B b e )x +--R + +--R 2 2 2 2 +--R (A b + B a)e m + ((4A b + 4B a)e - 2B b d e)m + (3A b + 3B a)e +--R + +--R - 2B b d e +--R * +--R x +--R + +--R 2 2 2 2 +--R A a e m + (5A a e + (- A b - B a)d e)m + 6A a e + (- 3A b - 3B a)d e +--R + +--R 2 +--R 2B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 3 +--R (B b e m + 3B b e m + 2B b e )x +--R + +--R 3 2 2 3 2 +--R ((A b + B a)e + B b d e )m + ((4A b + 4B a)e + B b d e )m +--R + +--R 3 +--R (3A b + 3B a)e +--R * +--R 2 +--R x +--R + +--R 3 2 2 +--R (A a e + (A b + B a)d e )m +--R + +--R 3 2 2 3 +--R (5A a e + (3A b + 3B a)d e - 2B b d e)m + 6A a e +--R * +--R x +--R + +--R 2 2 2 2 2 +--R A a d e m + (5A a d e + (- A b - B a)d e)m + 6A a d e +--R + +--R 2 3 +--R (- 3A b - 3B a)d e + 2B b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 3 3 3 2 3 3 +--R e m + 6e m + 11e m + 6e +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 3 2 3 4 +--R (B b e m + 3B b e m + 2B b e )x +--R + +--R 2 3 2 2 2 +--R ((A b + 2B a b)e + B b d e )m +--R + +--R 2 3 2 2 2 3 +--R ((4A b + 7B a b)e + B b d e )m + (3A b + 5B a b)e +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d e )m +--R + +--R 2 3 2 2 2 2 +--R ((9A a b + 4B a )e + (3A b + 4B a b)d e - 2B b d e)m +--R + +--R 2 3 +--R (9A a b + 3B a )e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 +--R (A a e + (2A a b + B a )d e )m +--R + +--R 2 3 2 2 2 2 +--R (5A a e + (8A a b + 3B a )d e + (- A b - 3B a b)d e)m +--R + +--R 2 3 2 2 2 2 3 +--R 6A a e + 6A a b d e + (- 3A b - 3B a b)d e + 2B b d +--R * +--R x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R A a d e m + (5A a d e + (- A a b - B a )d e)m + 6A a d e +--R + +--R 2 2 3 +--R (- 3A a b - 3B a )d e + 2B a b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 2 2 2 2 +--R (- B b e m - 3B b e m - 2B b e )x +--R + +--R 2 2 2 +--R (- A b - B a)e m + ((- 4A b - 4B a)e + 2B b d e)m +--R + +--R 2 +--R (- 3A b - 3B a)e + 2B b d e +--R * +--R x +--R + +--R 2 2 2 2 +--R - A a e m + (- 5A a e + (A b + B a)d e)m - 6A a e +--R + +--R 2 +--R (3A b + 3B a)d e - 2B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1378 +t0:=(A+B*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1378 +r0:=-1/42*(2*b*B*d-7*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/210*(b*d-a*e)*(2*b*B*d-7*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/7*B*(a+b*x)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 7 7 7 6 6 +--R 30B b e x + ((35A b + 35B a)e + 140B b d e )x +--R + +--R 7 6 2 5 5 +--R (42A a e + (168A b + 168B a)d e + 252B b d e )x +--R + +--R 6 2 5 3 4 4 +--R (210A a d e + (315A b + 315B a)d e + 210B b d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (420A a d e + (280A b + 280B a)d e + 70B b d e )x +--R + +--R 3 4 4 3 2 4 3 5 2 +--R (420A a d e + (105A b + 105B a)d e )x + 210A a d e x + 42A a d e +--R + +--R 6 7 +--R (- 7A b - 7B a)d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 210b e x + 210a e +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 4 3 6 +--R 30B b e x + ((35A b + 35B a)e + 140B b d e )x +--R + +--R 4 3 2 2 5 +--R (42A a e + (168A b + 168B a)d e + 252B b d e )x +--R + +--R 3 2 2 3 4 +--R (210A a d e + (315A b + 315B a)d e + 210B b d e)x +--R + +--R 2 2 3 4 3 +--R (420A a d e + (280A b + 280B a)d e + 70B b d )x +--R + +--R 3 4 2 4 +--R (420A a d e + (105A b + 105B a)d )x + 210A a d x +--R / +--R 210 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 7 7 6 6 +--R - 30B b e x + ((- 35A b - 35B a)e - 140B b d e )x +--R + +--R 7 6 2 5 5 +--R (- 42A a e + (- 168A b - 168B a)d e - 252B b d e )x +--R + +--R 6 2 5 3 4 4 +--R (- 210A a d e + (- 315A b - 315B a)d e - 210B b d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (- 420A a d e + (- 280A b - 280B a)d e - 70B b d e )x +--R + +--R 3 4 4 3 2 4 3 +--R (- 420A a d e + (- 105A b - 105B a)d e )x - 210A a d e x +--R + +--R 5 2 6 7 +--R - 42A a d e + (7A b + 7B a)d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 7 8 2 7 2 6 7 +--R 30B b e x + ((35A b + 65B a b)e + 140B b d e )x +--R + +--R 2 7 2 6 2 2 5 6 +--R ((77A a b + 35B a )e + (168A b + 308B a b)d e + 252B b d e )x +--R + +--R 2 7 2 6 2 2 5 +--R 42A a e + (378A a b + 168B a )d e + (315A b + 567B a b)d e +--R + +--R 2 3 4 +--R 210B b d e +--R * +--R 5 +--R x +--R + +--R 2 6 2 2 5 2 3 4 +--R 210A a d e + (735A a b + 315B a )d e + (280A b + 490B a b)d e +--R + +--R 2 4 3 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 3 +--R (420A a d e + (700A a b + 280B a )d e + (105A b + 175B a b)d e )x +--R + +--R 2 3 4 2 4 3 2 2 4 3 +--R (420A a d e + (315A a b + 105B a )d e )x + 210A a d e x +--R / +--R 3 3 +--R 210b e x + 210a e +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 6 4 3 5 +--R B b e x + ((A b + B a)e + 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (A a e + (4A b + 4B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (4A a d e + (6A b + 6B a)d e + 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (6A a d e + (4A b + 4B a)d e + B b d )x +--R + +--R 3 4 4 +--R (4A a d e + (A b + B a)d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 7 2 4 2 3 6 +--R - B b e x + ((- A b - 2B a b)e - 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((- 2A a b - B a )e + (- 4A b - 8B a b)d e - 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R - A a e + (- 8A a b - 4B a )d e + (- 6A b - 12B a b)d e +--R + +--R 2 3 +--R - 4B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R - 4A a d e + (- 12A a b - 6B a )d e + (- 4A b - 8B a b)d e +--R + +--R 2 4 +--R - B b d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 3 2 4 2 +--R (- 6A a d e + (- 8A a b - 4B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (- 4A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1378 +t0:=(A+B*x)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1378 +r0:=-1/15*(b*B*d-3*A*b*e+2*a*B*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/60*(b*d-a*e)*(b*B*d-3*A*b*e+2*a*B*e)*(d+e*x)^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/6*B*(a+b*x)*(d+e*x)^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 10B b e x + ((12A b + 12B a)e + 36B b d e )x +--R + +--R 6 5 2 4 4 +--R (15A a e + (45A b + 45B a)d e + 45B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (60A a d e + (60A b + 60B a)d e + 20B b d e )x +--R + +--R 2 4 3 3 2 3 3 4 2 +--R (90A a d e + (30A b + 30B a)d e )x + 60A a d e x + 15A a d e +--R + +--R 5 6 +--R (- 3A b - 3B a)d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 3 2 5 +--R 10B b e x + ((12A b + 12B a)e + 36B b d e )x +--R + +--R 3 2 2 4 +--R (15A a e + (45A b + 45B a)d e + 45B b d e)x +--R + +--R 2 2 3 3 +--R (60A a d e + (60A b + 60B a)d e + 20B b d )x +--R + +--R 2 3 2 3 +--R (90A a d e + (30A b + 30B a)d )x + 60A a d x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 5 +--R - 10B b e x + ((- 12A b - 12B a)e - 36B b d e )x +--R + +--R 6 5 2 4 4 +--R (- 15A a e + (- 45A b - 45B a)d e - 45B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (- 60A a d e + (- 60A b - 60B a)d e - 20B b d e )x +--R + +--R 2 4 3 3 2 3 3 4 2 +--R (- 90A a d e + (- 30A b - 30B a)d e )x - 60A a d e x - 15A a d e +--R + +--R 5 6 +--R (3A b + 3B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 6 7 2 6 2 5 6 +--R 10B b e x + ((12A b + 22B a b)e + 36B b d e )x +--R + +--R 2 6 2 5 2 2 4 5 +--R ((27A a b + 12B a )e + (45A b + 81B a b)d e + 45B b d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 15A a e + (105A a b + 45B a )d e + (60A b + 105B a b)d e +--R + +--R 2 3 3 +--R 20B b d e +--R * +--R 4 +--R x +--R + +--R 2 5 2 2 4 2 3 3 3 +--R (60A a d e + (150A a b + 60B a )d e + (30A b + 50B a b)d e )x +--R + +--R 2 2 4 2 3 3 2 2 3 3 +--R (90A a d e + (90A a b + 30B a )d e )x + 60A a d e x +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 3 2 4 +--R B b e x + ((A b + B a)e + 3B b d e )x +--R + +--R 3 2 2 3 +--R (A a e + (3A b + 3B a)d e + 3B b d e)x +--R + +--R 2 2 3 2 +--R (3A a d e + (3A b + 3B a)d e + B b d )x +--R + +--R 2 3 3 +--R (3A a d e + (A b + B a)d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 6 2 3 2 2 5 +--R - B b e x + ((- A b - 2B a b)e - 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((- 2A a b - B a )e + (- 3A b - 6B a b)d e - 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- A a e + (- 6A a b - 3B a )d e + (- 3A b - 6B a b)d e - B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (- 3A a d e + (- 6A a b - 3B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (- 3A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1378 +t0:=(A+B*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1378 +r0:=-1/20*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/60*(b*d-a*e)*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/5*B*(a+b*x)*(d+e*x)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 12B b e x + ((15A b + 15B a)e + 30B b d e )x +--R + +--R 5 4 2 3 3 +--R (20A a e + (40A b + 40B a)d e + 20B b d e )x +--R + +--R 4 2 3 2 2 3 3 2 +--R (60A a d e + (30A b + 30B a)d e )x + 60A a d e x + 20A a d e +--R + +--R 4 5 +--R (- 5A b - 5B a)d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 +--R 12B b e x + ((15A b + 15B a)e + 30B b d e)x +--R + +--R 2 2 3 +--R (20A a e + (40A b + 40B a)d e + 20B b d )x +--R + +--R 2 2 2 +--R (60A a d e + (30A b + 30B a)d )x + 60A a d x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 4 +--R - 12B b e x + ((- 15A b - 15B a)e - 30B b d e )x +--R + +--R 5 4 2 3 3 +--R (- 20A a e + (- 40A b - 40B a)d e - 20B b d e )x +--R + +--R 4 2 3 2 2 3 3 2 +--R (- 60A a d e + (- 30A b - 30B a)d e )x - 60A a d e x - 20A a d e +--R + +--R 4 5 +--R (5A b + 5B a)d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 5 6 2 5 2 4 5 +--R 12B b e x + ((15A b + 27B a b)e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 4 +--R ((35A a b + 15B a )e + (40A b + 70B a b)d e + 20B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (20A a e + (100A a b + 40B a )d e + (30A b + 50B a b)d e )x +--R + +--R 2 4 2 2 3 2 2 2 3 +--R (60A a d e + (90A a b + 30B a )d e )x + 60A a d e x +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 4 2 3 +--R B b e x + ((A b + B a)e + 2B b d e)x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + B b d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 5 2 2 2 4 +--R - B b e x + ((- A b - 2B a b)e - 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((- 2A a b - B a )e + (- 2A b - 4B a b)d e - B b d )x +--R + +--R 2 2 2 2 2 2 +--R (- A a e + (- 4A a b - 2B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (- 2A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1378 +t0:=(A+B*x)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 | 2 2 2 +--R (1) (B e x + (A e + B d)x + A d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1378 +r0:=1/6*(2*A*b*e-B*(b*d+a*e))*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^3+1/4*(b*d-_ + a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b^3*e)+_ + 1/4*B*(a+b*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 3 3 3 2 3 2 +--R 3B b e x + ((4A b + B a b )e + 4B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((2A a b - B a b)e + (6A b + 2B a b )d)x + (- 2A a b + B a )e +--R + +--R 2 2 +--R (6A a b - 2B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 12b +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 3B b e x + ((4A b + 4B a)e + 4B b d)x + (6A a e + (6A b + 6B a)d)x +--R + +--R 12A a d x +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 +--R - 3B b e x + ((- 4A b - B a b )e - 4B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((- 2A a b + B a b)e + (- 6A b - 2B a b )d)x + (2A a b - B a )e +--R + +--R 2 2 +--R (- 6A a b + 2B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 4 3 4 3 +--R 3B b e x + ((4A b + 4B a b )e + 4B b d)x +--R + +--R 3 4 3 2 3 +--R (6A a b e + (6A b + 6B a b )d)x + 12A a b d x +--R / +--R 3 +--R 12b +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 2 +--R (B b e x + ((A b + B a)e + B b d)x + (A a e + (A b + B a)d)x + A a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 2 3 +--R - B b e x + ((- A b - 2B a b)e - B b d)x +--R + +--R 2 2 2 +--R ((- 2A a b - B a )e + (- A b - 2B a b)d)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (1) (B x + A)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1378 +r0:=1/3*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/b^2 +--R +--R +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R (2B b x + (3A b + B a b)x + 3A a b - B a )\|b x + 2a b x + a +--R (2) ----------------------------------------------------------------- +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1378 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 2B b x + (3A b + 3B a)x + 6A a x +--R (3) ---------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R (- 2B b x + (- 3A b - B a b)x - 3A a b + B a )\|b x + 2a b x + a +--R + +--R 3 3 3 2 2 2 +--R 2B b x + (3A b + 3B a b )x + 6A a b x +--R / +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1378 +r0:=-(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/2*B*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e)+(b*d-a*e)*(B*d-A*e)*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (2A a b e + (- 2A b - 2B a b)d e + 2B b d )log(e x + d) + B b e x +--R + +--R 2 2 2 2 2 +--R ((2A b + 2B a b)e - 2B b d e)x + (2A a b + B a )e - 2B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 3 3 +--R 2b e x + 2a b e +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R (2A a e + (- 2A b - 2B a)d e + 2B b d )log(e x + d) + B b e x +--R + +--R 2 +--R ((2A b + 2B a)e - 2B b d e)x +--R / +--R 3 +--R 2e +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 +--R (- 2A a b e + (2A b + 2B a b)d e - 2B b d )log(e x + d) - B b e x +--R + +--R 2 2 2 2 2 +--R ((- 2A b - 2B a b)e + 2B b d e)x + (- 2A a b - B a )e + 2B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 3 2 2 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + 2A a b e +--R + +--R 2 2 2 2 +--R (- 2A a b - 2B a b)d e + 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b + 3B a b )e - 2B b d e)x +--R + +--R 2 2 2 2 +--R ((2A a b + 2B a b)e - 2B a b d e)x +--R / +--R 2 3 3 +--R 2b e x + 2a b e +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1378 +r0:=(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*(d+e*x))-_ + (2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 +--R (((A b + B a)e - 2B b d e)x + (A b + B a)d e - 2B b d )log(e x + d) +--R + +--R 2 2 2 2 +--R B b e x + ((- A b + B a)e + 2B b d e)x - A a e + 2B a d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (((A b + B a)e - 2B b d e)x + (A b + B a)d e - 2B b d )log(e x + d) +--R + +--R 2 2 2 2 +--R B b e x + B b d e x - A a e + (A b + B a)d e - B b d +--R / +--R 4 3 +--R e x + d e +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 +--R (((- A b - B a)e + 2B b d e)x + (- A b - B a)d e + 2B b d ) +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R - B b e x + ((A b - B a)e - 2B b d e)x + A a e - 2B a d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 2 +--R ((A b + B a b)e - 2B b d e)x +--R + +--R 2 2 2 2 2 2 +--R ((A a b + B a )e + (A b - B a b)d e - 2B b d )x + (A a b + B a )d e +--R + +--R 2 +--R - 2B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 3 2 2 2 +--R B b e x + (B a b e + B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R (- A a b e + (A b + 2B a b)d e - B b d )x - A a e + (A a b + B a )d e +--R + +--R 2 +--R - B a b d +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1378 +r0:=-1/2*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^2)+B*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*_ + (d+e*x))+b*B*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 3 2 2 2 2 2 2 2 +--R (2B a b e - 2B b d e )x + (4B a b d e - 4B b d e)x + 2B a b d e +--R + +--R 2 3 +--R - 2B b d +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- A b e + B b d e )x +--R + +--R 2 3 2 2 2 2 3 2 2 +--R ((- 2A a b - 2B a )e + 6B a b d e - 2B b d e)x - A a e - B a d e +--R + +--R 2 2 3 +--R 4B a b d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 5 3 2 6 5 2 2 4 2 +--R (2a b e - 2b d e )x + (2a e + 2a b d e - 4b d e )x +--R + +--R 2 5 2 4 2 3 3 2 2 4 3 3 +--R (4a d e - 2a b d e - 2b d e )x + 2a d e - 2a b d e +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (2B b e x + 4B b d e x + 2B b d )log(e x + d) +--R + +--R 2 2 2 +--R ((- 2A b - 2B a)e + 4B b d e)x - A a e + (- A b - B a)d e + 3B b d +--R / +--R 5 2 4 2 3 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 2 2 2 2 +--R (- 2B a b e + 2B b d e )x + (- 4B a b d e + 4B b d e)x +--R + +--R 2 2 3 +--R - 2B a b d e + 2B b d +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (A b e - B b d e )x +--R + +--R 2 3 2 2 2 2 3 2 2 +--R ((2A a b + 2B a )e - 6B a b d e + 2B b d e)x + A a e + B a d e +--R + +--R 2 2 3 +--R - 4B a b d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (2B a b e - 2B b d e )x + (2B a b e + 2B a b d e - 4B b d e)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (4B a b d e - 2B a b d e - 2B b d )x + 2B a b d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 2A a b - 2B a b)e + (2A b + 6B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 3 +--R ((- 3A a b - 2B a )e + (2A a b + 5B a b)d e + A b d e - 3B b d )x +--R + +--R 3 3 3 2 2 2 2 2 3 +--R - A a e - B a d e + (A a b + 4B a b)d e - 3B a b d +--R / +--R 6 2 5 3 2 6 5 2 2 4 2 +--R (2a b e - 2b d e )x + (2a e + 2a b d e - 4b d e )x +--R + +--R 2 5 2 4 2 3 3 2 2 4 3 3 +--R (4a d e - 2a b d e - 2b d e )x + 2a d e - 2a b d e +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1378 +r0:=1/3*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^3)+_ + 1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^2) +--R +--R +--R (2) +--R 2 2 2 +--R ((A b - 3B a b)e + 2B b d)x +--R + +--R 2 2 2 2 +--R ((- A a b - 3B a )e + (3A b + B a b)d)x - 2A a e + (3A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 5 4 2 2 3 3 2 4 2 3 2 3 2 2 +--R (6a e - 12a b d e + 6b d e )x + (18a d e - 36a b d e + 18b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (18a d e - 36a b d e + 18b d e)x + 6a d e - 12a b d e + 6b d +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 6B b e x + ((- 3A b - 3B a)e - 6B b d e)x - 2A a e +--R + +--R 2 +--R (- A b - B a)d e - 2B b d +--R / +--R 6 3 5 2 2 4 3 3 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 +--R ((- A b + 3B a b)e - 2B b d e )x +--R + +--R 2 4 2 3 2 4 +--R ((A a b + 3B a )e + (- 3A b - B a b)d e )x + 2A a e +--R + +--R 2 3 +--R (- 3A a b + B a )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 3 2 2 2 +--R (- 6B a b e + 12B a b d e - 6B b d e )x +--R + +--R 2 3 4 2 3 3 2 2 2 +--R (- 3A a b - 3B a )e + 6A a b d e + (- 3A b + 9B a b )d e +--R + +--R 3 3 +--R - 6B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 3 2 3 3 4 +--R - 2A a e + (3A a b - B a )d e + (- A b + 3B a b )d e - 2B b d +--R / +--R 2 8 7 2 2 6 3 2 7 2 6 2 3 5 2 +--R (6a e - 12a b d e + 6b d e )x + (18a d e - 36a b d e + 18b d e )x +--R + +--R 2 2 6 3 5 2 4 4 2 3 5 4 4 2 5 3 +--R (18a d e - 36a b d e + 18b d e )x + 6a d e - 12a b d e + 6b d e +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1378 +r0:=-1/4*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/4*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^3)-1/12*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^3) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a)e - 4B b d e)x - 3A a e +--R + +--R 2 +--R (- A b - B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 5 7 6 4 6 2 5 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 5 3 4 2 3 4 4 3 4 3 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a)e - 4B b d e)x - 3A a e +--R + +--R 2 +--R (- A b - B a)d e - B b d +--R / +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R 6B b e x + ((4A b + 4B a)e + 4B b d e)x + 3A a e + (A b + B a)d e +--R + +--R 2 +--R B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R - 6B b e x + ((- 4A b - 10B a b)e - 4B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 7A a b - 4B a )e + (- A b - 5B a b)d e - B b d )x - 3A a e +--R + +--R 2 2 +--R (- A a b - B a )d e - B a b d +--R / +--R 7 5 7 6 4 6 2 5 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 5 3 4 2 3 4 4 3 4 3 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1378 +r0:=-1/5*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^5)-1/15*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^4)-1/60*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^4) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 20B b e x + ((- 15A b - 15B a)e - 10B b d e)x - 12A a e +--R + +--R 2 +--R (- 3A b - 3B a)d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 6 8 7 5 7 2 6 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 6 3 5 3 3 5 4 4 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 4 5 3 5 3 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 20B b e x + ((- 15A b - 15B a)e - 10B b d e)x - 12A a e +--R + +--R 2 +--R (- 3A b - 3B a)d e - 2B b d +--R / +--R 8 5 7 4 2 6 3 3 5 2 4 4 5 3 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R 20B b e x + ((15A b + 15B a)e + 10B b d e)x + 12A a e +--R + +--R 2 +--R (3A b + 3B a)d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R - 20B b e x + ((- 15A b - 35B a b)e - 10B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 27A a b - 15B a )e + (- 3A b - 13B a b)d e - 2B b d )x - 12A a e +--R + +--R 2 2 +--R (- 3A a b - 3B a )d e - 2B a b d +--R / +--R 8 6 8 7 5 7 2 6 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 6 3 5 3 3 5 4 4 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 4 5 3 5 3 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1378 +r0:=-1/6*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^6)-1/12*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^5)-1/60*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 15B b e x + ((- 12A b - 12B a)e - 6B b d e)x - 10A a e +--R + +--R 2 +--R (- 2A b - 2B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 15B b e x + ((- 12A b - 12B a)e - 6B b d e)x - 10A a e +--R + +--R 2 +--R (- 2A b - 2B a)d e - B b d +--R / +--R 9 6 8 5 2 7 4 3 6 3 4 5 2 5 4 6 3 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R 15B b e x + ((12A b + 12B a)e + 6B b d e)x + 10A a e +--R + +--R 2 +--R (2A b + 2B a)d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R - 15B b e x + ((- 12A b - 27B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 22A a b - 12B a )e + (- 2A b - 8B a b)d e - B b d )x - 10A a e +--R + +--R 2 2 +--R (- 2A a b - 2B a )d e - B a b d +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 1378 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 m +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(e x + d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1378 +r0:=(A*b*e*(5+m)-B*(4*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2*(4+m)*(5+m))+B*(a+b*x)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(b*e*(5+m))+6*(b*d-a*e)^2*(A*b*e*(5+m)-_ + B*(4*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4*_ + (2+m)*(3+m)*(4+m)*(5+m))-6*(b*d-a*e)^3*(A*b*e*(5+m)-B*(4*b*d+a*e*_ + (1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(1+m)*(2+m)*_ + (3+m)*(4+m)*(5+m)*(a+b*x))-3*(b*d-a*e)*(A*b*e*(5+m)-B*(4*b*d+a*e*_ + (1+m)))*(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*_ + (3+m)*(4+m)*(5+m)) +--R +--R +--R (2) +--R 3 4 4 3 4 3 3 4 2 3 4 3 4 4 +--R (B b e m + 10B b e m + 35B b e m + 50B b e m + 24B b e )x +--R + +--R 3 2 4 4 3 2 4 3 3 3 +--R (A b + 3B a b )e m + ((11A b + 33B a b )e - 4B b d e )m +--R + +--R 3 2 4 3 3 2 +--R ((41A b + 123B a b )e - 24B b d e )m +--R + +--R 3 2 4 3 3 3 2 4 +--R ((61A b + 183B a b )e - 44B b d e )m + (30A b + 90B a b )e +--R + +--R 3 3 +--R - 24B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 +--R (3A a b + 3B a b)e m +--R + +--R 2 2 4 3 2 3 3 +--R ((36A a b + 36B a b)e + (- 3A b - 9B a b )d e )m +--R + +--R 2 2 4 3 2 3 +--R (147A a b + 147B a b)e + (- 24A b - 72B a b )d e +--R + +--R 3 2 2 +--R 12B b d e +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 2 3 +--R (234A a b + 234B a b)e + (- 51A b - 153B a b )d e +--R + +--R 3 2 2 +--R 36B b d e +--R * +--R m +--R + +--R 2 2 4 3 2 3 3 2 2 +--R (120A a b + 120B a b)e + (- 30A b - 90B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 +--R (3A a b + B a )e m +--R + +--R 2 3 4 2 2 3 3 +--R ((39A a b + 13B a )e + (- 6A a b - 6B a b)d e )m +--R + +--R 2 3 4 2 2 3 +--R (177A a b + 59B a )e + (- 60A a b - 60B a b)d e +--R + +--R 3 2 2 2 +--R (6A b + 18B a b )d e +--R * +--R 2 +--R m +--R + +--R 2 3 4 2 2 3 +--R (321A a b + 107B a )e + (- 174A a b - 174B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (36A b + 108B a b )d e - 24B b d e +--R * +--R m +--R + +--R 2 3 4 2 2 3 +--R (180A a b + 60B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (30A b + 90B a b )d e - 24B b d e +--R * +--R x +--R + +--R 3 4 4 3 4 2 3 3 3 +--R A a e m + (14A a e + (- 3A a b - B a )d e )m +--R + +--R 3 4 2 3 3 2 2 2 2 2 +--R (71A a e + (- 36A a b - 12B a )d e + (6A a b + 6B a b)d e )m +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 154A a e + (- 141A a b - 47B a )d e + (54A a b + 54B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 18B a b )d e +--R * +--R m +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 120A a e + (- 180A a b - 60B a )d e + (120A a b + 120B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 30A b - 90B a b )d e + 24B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 4 3 5 3 3 5 2 3 5 3 5 5 +--R (B b e m + 10B b e m + 35B b e m + 50B b e m + 24B b e )x +--R + +--R 3 2 5 3 4 4 +--R ((A b + 3B a b )e + B b d e )m +--R + +--R 3 2 5 3 4 3 +--R ((11A b + 33B a b )e + 6B b d e )m +--R + +--R 3 2 5 3 4 2 +--R ((41A b + 123B a b )e + 11B b d e )m +--R + +--R 3 2 5 3 4 3 2 5 +--R ((61A b + 183B a b )e + 6B b d e )m + (30A b + 90B a b )e +--R * +--R 4 +--R x +--R + +--R 2 2 5 3 2 4 4 +--R ((3A a b + 3B a b)e + (A b + 3B a b )d e )m +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((36A a b + 36B a b)e + (8A b + 24B a b )d e - 4B b d e )m +--R + +--R 2 2 5 3 2 4 3 2 3 2 +--R ((147A a b + 147B a b)e + (17A b + 51B a b )d e - 12B b d e )m +--R + +--R 2 2 5 3 2 4 3 2 3 +--R ((234A a b + 234B a b)e + (10A b + 30B a b )d e - 8B b d e )m +--R + +--R 2 2 5 +--R (120A a b + 120B a b)e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 4 4 +--R ((3A a b + B a )e + (3A a b + 3B a b)d e )m +--R + +--R 2 3 5 2 2 4 +--R (39A a b + 13B a )e + (30A a b + 30B a b)d e +--R + +--R 3 2 2 3 +--R (- 3A b - 9B a b )d e +--R * +--R 3 +--R m +--R + +--R 2 3 5 2 2 4 +--R (177A a b + 59B a )e + (87A a b + 87B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 18A b - 54B a b )d e + 12B b d e +--R * +--R 2 +--R m +--R + +--R 2 3 5 2 2 4 +--R (321A a b + 107B a )e + (60A a b + 60B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 15A b - 45B a b )d e + 12B b d e +--R * +--R m +--R + +--R 2 3 5 +--R (180A a b + 60B a )e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 4 +--R (A a e + (3A a b + B a )d e )m +--R + +--R 3 5 2 3 4 2 2 2 3 3 +--R (14A a e + (36A a b + 12B a )d e + (- 6A a b - 6B a b)d e )m +--R + +--R 3 5 2 3 4 2 2 2 3 +--R 71A a e + (141A a b + 47B a )d e + (- 54A a b - 54B a b)d e +--R + +--R 3 2 3 2 +--R (6A b + 18B a b )d e +--R * +--R 2 +--R m +--R + +--R 3 5 2 3 4 +--R 154A a e + (180A a b + 60B a )d e +--R + +--R 2 2 2 3 3 2 3 2 +--R (- 120A a b - 120B a b)d e + (30A b + 90B a b )d e +--R + +--R 3 4 +--R - 24B b d e +--R * +--R m +--R + +--R 3 5 +--R 120A a e +--R * +--R x +--R + +--R 3 4 4 3 4 2 3 2 3 3 +--R A a d e m + (14A a d e + (- 3A a b - B a )d e )m +--R + +--R 3 4 2 3 2 3 2 2 3 2 2 +--R (71A a d e + (- 36A a b - 12B a )d e + (6A a b + 6B a b)d e )m +--R + +--R 3 4 2 3 2 3 2 2 3 2 +--R 154A a d e + (- 141A a b - 47B a )d e + (54A a b + 54B a b)d e +--R + +--R 3 2 4 +--R (- 6A b - 18B a b )d e +--R * +--R m +--R + +--R 3 4 2 3 2 3 2 2 3 2 +--R 120A a d e + (- 180A a b - 60B a )d e + (120A a b + 120B a b)d e +--R + +--R 3 2 4 3 5 +--R (- 30A b - 90B a b )d e + 24B b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R e m + 15e m + 85e m + 225e m + 274e m + 120e +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 4 4 5 3 4 5 2 4 5 4 5 6 +--R (B b e m + 10B b e m + 35B b e m + 50B b e m + 24B b e )x +--R + +--R 4 3 5 4 4 4 +--R ((A b + 4B a b )e + B b d e )m +--R + +--R 4 3 5 4 4 3 +--R ((11A b + 43B a b )e + 6B b d e )m +--R + +--R 4 3 5 4 4 2 +--R ((41A b + 158B a b )e + 11B b d e )m +--R + +--R 4 3 5 4 4 4 3 5 +--R ((61A b + 233B a b )e + 6B b d e )m + (30A b + 114B a b )e +--R * +--R 5 +--R x +--R + +--R 3 2 2 5 4 3 4 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d e )m +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((47A a b + 69B a b )e + (8A b + 30B a b )d e - 4B b d e )m +--R + +--R 3 2 2 5 4 3 4 +--R (188A a b + 270B a b )e + (17A b + 62B a b )d e +--R + +--R 4 2 3 +--R - 12B b d e +--R * +--R 2 +--R m +--R + +--R 3 2 2 5 4 3 4 +--R (295A a b + 417B a b )e + (10A b + 36B a b )d e +--R + +--R 4 2 3 +--R - 8B b d e +--R * +--R m +--R + +--R 3 2 2 5 +--R (150A a b + 210B a b )e +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 3 2 2 4 4 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d e )m +--R + +--R 2 2 3 5 3 2 2 4 +--R (75A a b + 49B a b)e + (38A a b + 54B a b )d e +--R + +--R 4 3 2 3 +--R (- 3A b - 13B a b )d e +--R * +--R 3 +--R m +--R + +--R 2 2 3 5 3 2 2 4 +--R (324A a b + 206B a b)e + (104A a b + 138B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 18A b - 66B a b )d e + 12B b d e +--R * +--R 2 +--R m +--R + +--R 2 2 3 5 3 2 2 4 +--R (555A a b + 341B a b)e + (70A a b + 90B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 15A b - 53B a b )d e + 12B b d e +--R * +--R m +--R + +--R 2 2 3 5 +--R (300A a b + 180B a b)e +--R * +--R 3 +--R x +--R + +--R 3 4 5 2 2 3 4 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d e )m +--R + +--R 3 4 5 2 2 3 4 +--R (53A a b + 13B a )e + (66A a b + 42B a b)d e +--R + +--R 3 2 2 2 3 +--R (- 9A a b - 15B a b )d e +--R * +--R 3 +--R m +--R + +--R 3 4 5 2 2 3 4 +--R (248A a b + 59B a )e + (228A a b + 134B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 72A a b - 108B a b )d e + (6A b + 30B a b )d e +--R * +--R 2 +--R m +--R + +--R 3 4 5 2 2 3 4 +--R (475A a b + 107B a )e + (240A a b + 120B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 135A a b - 165B a b )d e + (30A b + 102B a b )d e +--R + +--R 4 4 +--R - 24B b d e +--R * +--R m +--R + +--R 3 4 5 +--R (300A a b + 60B a )e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 4 4 +--R (A a e + (4A a b + B a )d e )m +--R + +--R 4 5 3 4 4 2 2 3 2 3 3 +--R (14A a e + (50A a b + 12B a )d e + (- 9A a b - 7B a b)d e )m +--R + +--R 4 5 3 4 4 +--R 71A a e + (212A a b + 47B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 90A a b - 66B a b)d e + (12A a b + 24B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 5 3 4 4 +--R 154A a e + (334A a b + 60B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 261A a b - 167B a b)d e + (84A a b + 144B a b )d e +--R + +--R 4 3 4 +--R (- 6A b - 42B a b )d e +--R * +--R m +--R + +--R 4 5 3 4 2 2 3 2 3 +--R 120A a e + 120A a b d e + (- 180A a b - 60B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (120A a b + 120B a b )d e + (- 30A b - 90B a b )d e + 24B b d +--R * +--R x +--R + +--R 4 4 4 4 4 3 4 2 3 3 +--R A a d e m + (14A a d e + (- 3A a b - B a )d e )m +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 2 +--R (71A a d e + (- 36A a b - 12B a )d e + (6A a b + 6B a b)d e )m +--R + +--R 4 4 3 4 2 3 +--R 154A a d e + (- 141A a b - 47B a )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (54A a b + 54B a b)d e + (- 6A a b - 18B a b )d e +--R * +--R m +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R 120A a d e + (- 180A a b - 60B a )d e + (120A a b + 120B a b)d e +--R + +--R 3 2 2 4 3 5 +--R (- 30A a b - 90B a b )d e + 24B a b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 4 4 3 4 3 3 4 2 3 4 3 4 4 +--R (- B b e m - 10B b e m - 35B b e m - 50B b e m - 24B b e )x +--R + +--R 3 2 4 4 3 2 4 3 3 3 +--R (- A b - 3B a b )e m + ((- 11A b - 33B a b )e + 4B b d e )m +--R + +--R 3 2 4 3 3 2 +--R ((- 41A b - 123B a b )e + 24B b d e )m +--R + +--R 3 2 4 3 3 +--R ((- 61A b - 183B a b )e + 44B b d e )m +--R + +--R 3 2 4 3 3 +--R (- 30A b - 90B a b )e + 24B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 +--R (- 3A a b - 3B a b)e m +--R + +--R 2 2 4 3 2 3 3 +--R ((- 36A a b - 36B a b)e + (3A b + 9B a b )d e )m +--R + +--R 2 2 4 3 2 3 +--R (- 147A a b - 147B a b)e + (24A b + 72B a b )d e +--R + +--R 3 2 2 +--R - 12B b d e +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 2 3 +--R (- 234A a b - 234B a b)e + (51A b + 153B a b )d e +--R + +--R 3 2 2 +--R - 36B b d e +--R * +--R m +--R + +--R 2 2 4 3 2 3 3 2 2 +--R (- 120A a b - 120B a b)e + (30A b + 90B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 +--R (- 3A a b - B a )e m +--R + +--R 2 3 4 2 2 3 3 +--R ((- 39A a b - 13B a )e + (6A a b + 6B a b)d e )m +--R + +--R 2 3 4 2 2 3 +--R (- 177A a b - 59B a )e + (60A a b + 60B a b)d e +--R + +--R 3 2 2 2 +--R (- 6A b - 18B a b )d e +--R * +--R 2 +--R m +--R + +--R 2 3 4 2 2 3 +--R (- 321A a b - 107B a )e + (174A a b + 174B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 36A b - 108B a b )d e + 24B b d e +--R * +--R m +--R + +--R 2 3 4 2 2 3 +--R (- 180A a b - 60B a )e + (120A a b + 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 30A b - 90B a b )d e + 24B b d e +--R * +--R x +--R + +--R 3 4 4 3 4 2 3 3 3 +--R - A a e m + (- 14A a e + (3A a b + B a )d e )m +--R + +--R 3 4 2 3 3 2 2 2 2 2 +--R (- 71A a e + (36A a b + 12B a )d e + (- 6A a b - 6B a b)d e )m +--R + +--R 3 4 2 3 3 +--R - 154A a e + (141A a b + 47B a )d e +--R + +--R 2 2 2 2 3 2 3 +--R (- 54A a b - 54B a b)d e + (6A b + 18B a b )d e +--R * +--R m +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 120A a e + (180A a b + 60B a )d e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 3 3 4 +--R (30A b + 90B a b )d e - 24B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 1378 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 5 8 2 5 2 4 7 +--R B b e x + ((A b + 2B a b)e + 5B b d e )x +--R + +--R 2 5 2 4 2 2 3 6 +--R ((2A a b + B a )e + (5A b + 10B a b)d e + 10B b d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 5 +--R (A a e + (10A a b + 5B a )d e + (10A b + 20B a b)d e + 10B b d e )x +--R + +--R 2 4 2 2 3 2 3 2 +--R 5A a d e + (20A a b + 10B a )d e + (10A b + 20B a b)d e +--R + +--R 2 4 +--R 5B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 3 +--R (10A a d e + (20A a b + 10B a )d e + (5A b + 10B a b)d e + B b d )x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1378 +r0:=-1/45*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/10*B*(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-_ + 1/420*(b*d-a*e)^2*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^6*sqrt(a^2+2*a*b*_ + x+b^2*x^2)/(b*e^4)+1/2520*(b*d-a*e)^3*(2*b*B*d-5*A*b*e+3*a*B*e)*_ + (d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))+1/120*(b*d-a*e)*_ + (2*b*B*d-5*A*b*e+3*a*B*e)*(a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 10 10 3 2 10 3 9 9 +--R 252B b e x + ((280A b + 840B a b )e + 1400B b d e )x +--R + +--R 2 2 10 3 2 9 +--R (945A a b + 945B a b)e + (1575A b + 4725B a b )d e +--R + +--R 3 2 8 +--R 3150B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 10 2 2 9 +--R (1080A a b + 360B a )e + (5400A a b + 5400B a b)d e +--R + +--R 3 2 2 8 3 3 7 +--R (3600A b + 10800B a b )d e + 3600B b d e +--R * +--R 7 +--R x +--R + +--R 3 10 2 3 9 +--R 420A a e + (6300A a b + 2100B a )d e +--R + +--R 2 2 2 8 3 2 3 7 +--R (12600A a b + 12600B a b)d e + (4200A b + 12600B a b )d e +--R + +--R 3 4 6 +--R 2100B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 2 8 +--R 2520A a d e + (15120A a b + 5040B a )d e +--R + +--R 2 2 3 7 3 2 4 6 +--R (15120A a b + 15120B a b)d e + (2520A b + 7560B a b )d e +--R + +--R 3 5 5 +--R 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 8 2 3 3 7 +--R 6300A a d e + (18900A a b + 6300B a )d e +--R + +--R 2 2 4 6 3 2 5 5 +--R (9450A a b + 9450B a b)d e + (630A b + 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 3 7 2 3 4 6 +--R 8400A a d e + (12600A a b + 4200B a )d e +--R + +--R 2 2 5 5 +--R (2520A a b + 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 3 5 5 2 3 5 5 +--R (6300A a d e + (3780A a b + 1260B a )d e )x + 2520A a d e x +--R + +--R 3 6 4 2 3 7 3 2 2 8 2 +--R 420A a d e + (- 180A a b - 60B a )d e + (45A a b + 45B a b)d e +--R + +--R 3 2 9 3 10 +--R (- 5A b - 15B a b )d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 10 3 2 5 3 4 9 +--R 252B b e x + ((280A b + 840B a b )e + 1400B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 8 +--R ((945A a b + 945B a b)e + (1575A b + 4725B a b )d e + 3150B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (1080A a b + 360B a )e + (5400A a b + 5400B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (3600A b + 10800B a b )d e + 3600B b d e +--R * +--R 7 +--R x +--R + +--R 3 5 2 3 4 +--R 420A a e + (6300A a b + 2100B a )d e +--R + +--R 2 2 2 3 3 2 3 2 +--R (12600A a b + 12600B a b)d e + (4200A b + 12600B a b )d e +--R + +--R 3 4 +--R 2100B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 2 3 2 3 +--R 2520A a d e + (15120A a b + 5040B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (15120A a b + 15120B a b)d e + (2520A b + 7560B a b )d e + 504B b d +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 3 3 2 +--R 6300A a d e + (18900A a b + 6300B a )d e +--R + +--R 2 2 4 3 2 5 +--R (9450A a b + 9450B a b)d e + (630A b + 1890B a b )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 3 4 +--R 8400A a d e + (12600A a b + 4200B a )d e +--R + +--R 2 2 5 +--R (2520A a b + 2520B a b)d +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 5 2 3 5 +--R (6300A a d e + (3780A a b + 1260B a )d )x + 2520A a d x +--R / +--R 2520 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 10 10 3 2 10 3 9 9 +--R - 252B b e x + ((- 280A b - 840B a b )e - 1400B b d e )x +--R + +--R 2 2 10 3 2 9 +--R (- 945A a b - 945B a b)e + (- 1575A b - 4725B a b )d e +--R + +--R 3 2 8 +--R - 3150B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 10 2 2 9 +--R (- 1080A a b - 360B a )e + (- 5400A a b - 5400B a b)d e +--R + +--R 3 2 2 8 3 3 7 +--R (- 3600A b - 10800B a b )d e - 3600B b d e +--R * +--R 7 +--R x +--R + +--R 3 10 2 3 9 +--R - 420A a e + (- 6300A a b - 2100B a )d e +--R + +--R 2 2 2 8 3 2 3 7 +--R (- 12600A a b - 12600B a b)d e + (- 4200A b - 12600B a b )d e +--R + +--R 3 4 6 +--R - 2100B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 2 8 +--R - 2520A a d e + (- 15120A a b - 5040B a )d e +--R + +--R 2 2 3 7 3 2 4 6 +--R (- 15120A a b - 15120B a b)d e + (- 2520A b - 7560B a b )d e +--R + +--R 3 5 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 8 2 3 3 7 +--R - 6300A a d e + (- 18900A a b - 6300B a )d e +--R + +--R 2 2 4 6 3 2 5 5 +--R (- 9450A a b - 9450B a b)d e + (- 630A b - 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 3 7 2 3 4 6 +--R - 8400A a d e + (- 12600A a b - 4200B a )d e +--R + +--R 2 2 5 5 +--R (- 2520A a b - 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 3 5 5 2 3 5 5 +--R (- 6300A a d e + (- 3780A a b - 1260B a )d e )x - 2520A a d e x +--R + +--R 3 6 4 2 3 7 3 2 2 8 2 +--R - 420A a d e + (180A a b + 60B a )d e + (- 45A a b - 45B a b)d e +--R + +--R 3 2 9 3 10 +--R (5A b + 15B a b )d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 10 11 4 3 10 4 9 10 +--R 252B b e x + ((280A b + 1092B a b )e + 1400B b d e )x +--R + +--R 3 2 2 10 4 3 9 +--R (1225A a b + 1785B a b )e + (1575A b + 6125B a b )d e +--R + +--R 4 2 8 +--R 3150B b d e +--R * +--R 9 +--R x +--R + +--R 2 2 3 10 3 2 2 9 +--R (2025A a b + 1305B a b)e + (6975A a b + 10125B a b )d e +--R + +--R 4 3 2 8 4 3 7 +--R (3600A b + 13950B a b )d e + 3600B b d e +--R * +--R 8 +--R x +--R + +--R 3 4 10 2 2 3 9 +--R (1500A a b + 360B a )e + (11700A a b + 7500B a b)d e +--R + +--R 3 2 2 2 8 4 3 3 7 +--R (16200A a b + 23400B a b )d e + (4200A b + 16200B a b )d e +--R + +--R 4 4 6 +--R 2100B b d e +--R * +--R 7 +--R x +--R + +--R 4 10 3 4 9 +--R 420A a e + (8820A a b + 2100B a )d e +--R + +--R 2 2 3 2 8 3 2 2 3 7 +--R (27720A a b + 17640B a b)d e + (19320A a b + 27720B a b )d e +--R + +--R 4 3 4 6 4 5 5 +--R (2520A b + 9660B a b )d e + 504B b d e +--R * +--R 6 +--R x +--R + +--R 4 9 3 4 2 8 +--R 2520A a d e + (21420A a b + 5040B a )d e +--R + +--R 2 2 3 3 7 3 2 2 4 6 +--R (34020A a b + 21420B a b)d e + (11970A a b + 17010B a b )d e +--R + +--R 4 3 5 5 +--R (630A b + 2394B a b )d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 3 4 3 7 +--R 6300A a d e + (27300A a b + 6300B a )d e +--R + +--R 2 2 3 4 6 3 2 2 5 5 +--R (22050A a b + 13650B a b)d e + (3150A a b + 4410B a b )d e +--R * +--R 4 +--R x +--R + +--R 4 3 7 3 4 4 6 +--R 8400A a d e + (18900A a b + 4200B a )d e +--R + +--R 2 2 3 5 5 +--R (6300A a b + 3780B a b)d e +--R * +--R 3 +--R x +--R + +--R 4 4 6 3 4 5 5 2 4 5 5 +--R (6300A a d e + (6300A a b + 1260B a )d e )x + 2520A a d e x +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 9 3 2 5 3 4 8 +--R B b e x + ((A b + 3B a b )e + 5B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 7 +--R ((3A a b + 3B a b)e + (5A b + 15B a b )d e + 10B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (3A a b + B a )e + (15A a b + 15B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (10A b + 30B a b )d e + 10B b d e +--R * +--R 6 +--R x +--R + +--R 3 5 2 3 4 2 2 2 3 +--R A a e + (15A a b + 5B a )d e + (30A a b + 30B a b)d e +--R + +--R 3 2 3 2 3 4 +--R (10A b + 30B a b )d e + 5B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 2 3 2 2 3 2 +--R 5A a d e + (30A a b + 10B a )d e + (30A a b + 30B a b)d e +--R + +--R 3 2 4 3 5 +--R (5A b + 15B a b )d e + B b d +--R * +--R 4 +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 10A a d e + (30A a b + 10B a )d e + (15A a b + 15B a b)d e +--R + +--R 3 2 5 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 4 2 2 5 2 +--R (10A a d e + (15A a b + 5B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 4 2 3 5 3 5 +--R (5A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 10 4 3 5 4 4 9 +--R - B b e x + ((- A b - 4B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 8 +--R ((- 4A a b - 6B a b )e + (- 5A b - 20B a b )d e - 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 6A a b - 4B a b)e + (- 20A a b - 30B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 10A b - 40B a b )d e - 10B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 4A a b - B a )e + (- 30A a b - 20B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 40A a b - 60B a b )d e + (- 10A b - 40B a b )d e - 5B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - A a e + (- 20A a b - 5B a )d e + (- 60A a b - 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 40A a b - 60B a b )d e + (- 5A b - 20B a b )d e - B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R - 5A a d e + (- 40A a b - 10B a )d e + (- 60A a b - 40B a b)d e +--R + +--R 3 2 2 4 4 3 5 +--R (- 20A a b - 30B a b )d e + (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 3 2 2 2 3 4 +--R - 10A a d e + (- 40A a b - 10B a )d e + (- 30A a b - 20B a b)d e +--R + +--R 3 2 2 5 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 2 +--R (- 10A a d e + (- 20A a b - 5B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 4 3 4 5 4 5 +--R (- 5A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 1378 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 7 2 4 2 3 6 +--R B b e x + ((A b + 2B a b)e + 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((2A a b + B a )e + (4A b + 8B a b)d e + 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (A a e + (8A a b + 4B a )d e + (6A b + 12B a b)d e + 4B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 3 +--R (4A a d e + (12A a b + 6B a )d e + (4A b + 8B a b)d e + B b d )x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1378 +r0:=-1/72*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/9*B*(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-_ + 1/504*(b*d-a*e)^2*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^4)+1/2520*(b*d-a*e)^3*(4*b*B*d-9*A*b*e+5*a*B*e)*_ + (d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))+1/168*(b*d-a*e)*_ + (4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 9 9 3 2 9 3 8 8 +--R 280B b e x + ((315A b + 945B a b )e + 1260B b d e )x +--R + +--R 2 2 9 3 2 8 +--R (1080A a b + 1080B a b)e + (1440A b + 4320B a b )d e +--R + +--R 3 2 7 +--R 2160B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 9 2 2 8 +--R (1260A a b + 420B a )e + (5040A a b + 5040B a b)d e +--R + +--R 3 2 2 7 3 3 6 +--R (2520A b + 7560B a b )d e + 1680B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 8 +--R 504A a e + (6048A a b + 2016B a )d e +--R + +--R 2 2 2 7 3 2 3 6 +--R (9072A a b + 9072B a b)d e + (2016A b + 6048B a b )d e +--R + +--R 3 4 5 +--R 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 2 7 +--R 2520A a d e + (11340A a b + 3780B a )d e +--R + +--R 2 2 3 6 3 2 4 5 +--R (7560A a b + 7560B a b)d e + (630A b + 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 2 7 2 3 3 6 +--R 5040A a d e + (10080A a b + 3360B a )d e +--R + +--R 2 2 4 5 +--R (2520A a b + 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 3 6 2 3 4 5 2 3 4 5 +--R (5040A a d e + (3780A a b + 1260B a )d e )x + 2520A a d e x +--R + +--R 3 5 4 2 3 6 3 2 2 7 2 +--R 504A a d e + (- 252A a b - 84B a )d e + (72A a b + 72B a b)d e +--R + +--R 3 2 8 3 9 +--R (- 9A b - 27B a b )d e + 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 9 3 2 4 3 3 8 +--R 280B b e x + ((315A b + 945B a b )e + 1260B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (1080A a b + 1080B a b)e + (1440A b + 4320B a b )d e +--R + +--R 3 2 2 +--R 2160B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 4 2 2 3 +--R (1260A a b + 420B a )e + (5040A a b + 5040B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (2520A b + 7560B a b )d e + 1680B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 504A a e + (6048A a b + 2016B a )d e + (9072A a b + 9072B a b)d e +--R + +--R 3 2 3 3 4 +--R (2016A b + 6048B a b )d e + 504B b d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 2 +--R 2520A a d e + (11340A a b + 3780B a )d e +--R + +--R 2 2 3 3 2 4 +--R (7560A a b + 7560B a b)d e + (630A b + 1890B a b )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 3 3 +--R 5040A a d e + (10080A a b + 3360B a )d e +--R + +--R 2 2 4 +--R (2520A a b + 2520B a b)d +--R * +--R 3 +--R x +--R + +--R 3 3 2 3 4 2 3 4 +--R (5040A a d e + (3780A a b + 1260B a )d )x + 2520A a d x +--R / +--R 2520 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 9 9 3 2 9 3 8 8 +--R - 280B b e x + ((- 315A b - 945B a b )e - 1260B b d e )x +--R + +--R 2 2 9 3 2 8 +--R (- 1080A a b - 1080B a b)e + (- 1440A b - 4320B a b )d e +--R + +--R 3 2 7 +--R - 2160B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 9 2 2 8 +--R (- 1260A a b - 420B a )e + (- 5040A a b - 5040B a b)d e +--R + +--R 3 2 2 7 3 3 6 +--R (- 2520A b - 7560B a b )d e - 1680B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 8 +--R - 504A a e + (- 6048A a b - 2016B a )d e +--R + +--R 2 2 2 7 3 2 3 6 +--R (- 9072A a b - 9072B a b)d e + (- 2016A b - 6048B a b )d e +--R + +--R 3 4 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 2 7 +--R - 2520A a d e + (- 11340A a b - 3780B a )d e +--R + +--R 2 2 3 6 3 2 4 5 +--R (- 7560A a b - 7560B a b)d e + (- 630A b - 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 2 7 2 3 3 6 +--R - 5040A a d e + (- 10080A a b - 3360B a )d e +--R + +--R 2 2 4 5 +--R (- 2520A a b - 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 3 6 2 3 4 5 2 3 4 5 +--R (- 5040A a d e + (- 3780A a b - 1260B a )d e )x - 2520A a d e x +--R + +--R 3 5 4 2 3 6 3 2 2 7 2 +--R - 504A a d e + (252A a b + 84B a )d e + (- 72A a b - 72B a b)d e +--R + +--R 3 2 8 3 9 +--R (9A b + 27B a b )d e - 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 9 10 4 3 9 4 8 9 +--R 280B b e x + ((315A b + 1225B a b )e + 1260B b d e )x +--R + +--R 3 2 2 9 4 3 8 +--R (1395A a b + 2025B a b )e + (1440A b + 5580B a b )d e +--R + +--R 4 2 7 +--R 2160B b d e +--R * +--R 8 +--R x +--R + +--R 2 2 3 9 3 2 2 8 +--R (2340A a b + 1500B a b)e + (6480A a b + 9360B a b )d e +--R + +--R 4 3 2 7 4 3 6 +--R (2520A b + 9720B a b )d e + 1680B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 9 2 2 3 8 +--R (1764A a b + 420B a )e + (11088A a b + 7056B a b)d e +--R + +--R 3 2 2 2 7 4 3 3 6 +--R (11592A a b + 16632B a b )d e + (2016A b + 7728B a b )d e +--R + +--R 4 4 5 +--R 504B b d e +--R * +--R 6 +--R x +--R + +--R 4 9 3 4 8 +--R 504A a e + (8568A a b + 2016B a )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (20412A a b + 12852B a b)d e + (9576A a b + 13608B a b )d e +--R + +--R 4 3 4 5 +--R (630A b + 2394B a b )d e +--R * +--R 5 +--R x +--R + +--R 4 8 3 4 2 7 +--R 2520A a d e + (16380A a b + 3780B a )d e +--R + +--R 2 2 3 3 6 3 2 2 4 5 +--R (17640A a b + 10920B a b)d e + (3150A a b + 4410B a b )d e +--R * +--R 4 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 5040A a d e + (15120A a b + 3360B a )d e +--R + +--R 2 2 3 4 5 +--R (6300A a b + 3780B a b)d e +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 4 5 2 4 4 5 +--R (5040A a d e + (6300A a b + 1260B a )d e )x + 2520A a d e x +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 8 3 2 4 3 3 7 +--R B b e x + ((A b + 3B a b )e + 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 6 +--R ((3A a b + 3B a b)e + (4A b + 12B a b )d e + 6B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b + B a )e + (12A a b + 12B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (6A b + 18B a b )d e + 4B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A a e + (12A a b + 4B a )d e + (18A a b + 18B a b)d e +--R + +--R 3 2 3 3 4 +--R (4A b + 12B a b )d e + B b d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 3 +--R 4A a d e + (18A a b + 6B a )d e + (12A a b + 12B a b)d e +--R + +--R 3 2 4 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 3 3 2 2 4 2 +--R (6A a d e + (12A a b + 4B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 3 2 3 4 3 4 +--R (4A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 9 4 3 4 4 3 8 +--R - B b e x + ((- A b - 4B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((- 4A a b - 6B a b )e + (- 4A b - 16B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 6A a b - 4B a b)e + (- 16A a b - 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 6A b - 24B a b )d e - 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 4A a b - B a )e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 24A a b - 36B a b )d e + (- 4A b - 16B a b )d e - B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - A a e + (- 16A a b - 4B a )d e + (- 36A a b - 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 16A a b - 24B a b )d e + (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R - 4A a d e + (- 24A a b - 6B a )d e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 4 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (- 6A a d e + (- 16A a b - 4B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (- 4A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 1378 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1378 +r0:=1/14*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/8*B*(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)+_ + 1/70*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^4)-1/280*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))-1/28*(b*d-a*e)*(2*A*b*e-_ + B*(b*d+a*e))*(a+b*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 8 8 3 2 8 3 7 7 +--R 35B b e x + ((40A b + 120B a b )e + 120B b d e )x +--R + +--R 2 2 8 3 2 7 3 2 6 6 +--R ((140A a b + 140B a b)e + (140A b + 420B a b )d e + 140B b d e )x +--R + +--R 2 3 8 2 2 7 +--R (168A a b + 56B a )e + (504A a b + 504B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (168A b + 504B a b )d e + 56B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 70A a e + (630A a b + 210B a )d e + (630A a b + 630B a b)d e +--R + +--R 3 2 3 5 +--R (70A b + 210B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 2 2 3 5 3 +--R (280A a d e + (840A a b + 280B a )d e + (280A a b + 280B a b)d e )x +--R + +--R 3 2 6 2 3 3 5 2 3 3 5 3 4 4 +--R (420A a d e + (420A a b + 140B a )d e )x + 280A a d e x + 70A a d e +--R + +--R 2 3 5 3 2 2 6 2 +--R (- 42A a b - 14B a )d e + (14A a b + 14B a b)d e +--R + +--R 3 2 7 3 8 +--R (- 2A b - 6B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 280b e x + 280a e +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 8 3 2 3 3 2 7 +--R 35B b e x + ((40A b + 120B a b )e + 120B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 6 +--R ((140A a b + 140B a b)e + (140A b + 420B a b )d e + 140B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (168A a b + 56B a )e + (504A a b + 504B a b)d e +--R + +--R 3 2 2 3 3 +--R (168A b + 504B a b )d e + 56B b d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R 70A a e + (630A a b + 210B a )d e + (630A a b + 630B a b)d e +--R + +--R 3 2 3 +--R (70A b + 210B a b )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 2 2 2 3 3 +--R (280A a d e + (840A a b + 280B a )d e + (280A a b + 280B a b)d )x +--R + +--R 3 2 2 3 3 2 3 3 +--R (420A a d e + (420A a b + 140B a )d )x + 280A a d x +--R / +--R 280 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 8 8 3 2 8 3 7 7 +--R - 35B b e x + ((- 40A b - 120B a b )e - 120B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (- 140A a b - 140B a b)e + (- 140A b - 420B a b )d e +--R + +--R 3 2 6 +--R - 140B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (- 168A a b - 56B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (- 168A b - 504B a b )d e - 56B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R - 70A a e + (- 630A a b - 210B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (- 630A a b - 630B a b)d e + (- 70A b - 210B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 280A a d e + (- 840A a b - 280B a )d e +--R + +--R 2 2 3 5 +--R (- 280A a b - 280B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 2 3 3 5 +--R (- 420A a d e + (- 420A a b - 140B a )d e )x - 280A a d e x +--R + +--R 3 4 4 2 3 5 3 2 2 6 2 +--R - 70A a d e + (42A a b + 14B a )d e + (- 14A a b - 14B a b)d e +--R + +--R 3 2 7 3 8 +--R (2A b + 6B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 8 9 4 3 8 4 7 8 +--R 35B b e x + ((40A b + 155B a b )e + 120B b d e )x +--R + +--R 3 2 2 8 4 3 7 4 2 6 7 +--R ((180A a b + 260B a b )e + (140A b + 540B a b )d e + 140B b d e )x +--R + +--R 2 2 3 8 3 2 2 7 +--R (308A a b + 196B a b)e + (644A a b + 924B a b )d e +--R + +--R 4 3 2 6 4 3 5 +--R (168A b + 644B a b )d e + 56B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 8 2 2 3 7 +--R (238A a b + 56B a )e + (1134A a b + 714B a b)d e +--R + +--R 3 2 2 2 6 4 3 3 5 +--R (798A a b + 1134B a b )d e + (70A b + 266B a b )d e +--R * +--R 5 +--R x +--R + +--R 4 8 3 4 7 2 2 3 2 6 +--R 70A a e + (910A a b + 210B a )d e + (1470A a b + 910B a b)d e +--R + +--R 3 2 2 3 5 +--R (350A a b + 490B a b )d e +--R * +--R 4 +--R x +--R + +--R 4 7 3 4 2 6 2 2 3 3 5 3 +--R (280A a d e + (1260A a b + 280B a )d e + (700A a b + 420B a b)d e )x +--R + +--R 4 2 6 3 4 3 5 2 4 3 5 +--R (420A a d e + (700A a b + 140B a )d e )x + 280A a d e x +--R / +--R 5 5 +--R 280b e x + 280a e +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 3 7 3 2 3 3 2 6 +--R B b e x + ((A b + 3B a b )e + 3B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 5 +--R ((3A a b + 3B a b)e + (3A b + 9B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b + B a )e + (9A a b + 9B a b)d e + (3A b + 9B a b )d e +--R + +--R 3 3 +--R B b d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R A a e + (9A a b + 3B a )d e + (9A a b + 9B a b)d e +--R + +--R 3 2 3 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 3 2 +--R (3A a d e + (9A a b + 3B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 2 3 3 3 3 +--R (3A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 8 4 3 3 4 2 7 +--R - B b e x + ((- A b - 4B a b )e - 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((- 4A a b - 6B a b )e + (- 3A b - 12B a b )d e - 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 6A a b - 4B a b)e + (- 12A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 3A b - 12B a b )d e - B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 4A a b - B a )e + (- 18A a b - 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 12A a b - 18B a b )d e + (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R - A a e + (- 12A a b - 3B a )d e + (- 18A a b - 12B a b)d e +--R + +--R 3 2 2 3 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (- 3A a d e + (- 12A a b - 3B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (- 3A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 1378 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 471 + +--S 472 of 1378 +r0:=-1/84*(b*d-a*e)^2*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b^4*e)-1/42*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(d+_ + e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*e)+1/7*B*(a+b*x)*(d+e*x)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-1/105*(b*d-a*e)*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4 +--R +--R +--R (2) +--R 6 2 6 6 5 2 6 5 +--R 60B b e x + ((70A b + 150B a b )e + 140B b d e)x +--R + +--R 5 2 4 2 6 5 6 2 4 +--R ((182A a b + 102B a b )e + (168A b + 364B a b )d e + 84B b d )x +--R + +--R 2 4 3 3 2 5 2 4 +--R (133A a b + 3B a b )e + (462A a b + 266B a b )d e +--R + +--R 6 5 2 +--R (105A b + 231B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (7A a b - 3B a b )e + (378A a b + 14B a b )d e +--R + +--R 5 2 4 2 +--R (315A a b + 189B a b )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (- 7A a b + 3B a b)e + (42A a b - 14B a b )d e +--R + +--R 2 4 3 3 2 +--R (315A a b + 21B a b )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 3 3 4 2 2 +--R (7A a b - 3B a )e + (- 42A a b + 14B a b)d e + (105A a b - 21B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 420b +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 7 3 2 2 3 6 +--R 60B b e x + ((70A b + 210B a b )e + 140B b d e)x +--R + +--R 2 2 2 3 2 3 2 5 +--R ((252A a b + 252B a b)e + (168A b + 504B a b )d e + 84B b d )x +--R + +--R 2 3 2 2 2 +--R (315A a b + 105B a )e + (630A a b + 630B a b)d e +--R + +--R 3 2 2 +--R (105A b + 315B a b )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 2 2 2 3 +--R (140A a e + (840A a b + 280B a )d e + (420A a b + 420B a b)d )x +--R + +--R 3 2 3 2 2 3 2 +--R (420A a d e + (630A a b + 210B a )d )x + 420A a d x +--R / +--R 420 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 2 6 6 5 2 6 5 +--R - 60B b e x + ((- 70A b - 150B a b )e - 140B b d e)x +--R + +--R 5 2 4 2 6 5 +--R (- 182A a b - 102B a b )e + (- 168A b - 364B a b )d e +--R + +--R 6 2 +--R - 84B b d +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 2 5 2 4 +--R (- 133A a b - 3B a b )e + (- 462A a b - 266B a b )d e +--R + +--R 6 5 2 +--R (- 105A b - 231B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 7A a b + 3B a b )e + (- 378A a b - 14B a b )d e +--R + +--R 5 2 4 2 +--R (- 315A a b - 189B a b )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (7A a b - 3B a b)e + (- 42A a b + 14B a b )d e +--R + +--R 2 4 3 3 2 +--R (- 315A a b - 21B a b )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 7A a b + 3B a )e + (42A a b - 14B a b)d e +--R + +--R 3 3 4 2 2 +--R (- 105A a b + 21B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 2 7 7 6 2 7 6 +--R 60B b e x + ((70A b + 210B a b )e + 140B b d e)x +--R + +--R 6 2 5 2 7 6 7 2 5 +--R ((252A a b + 252B a b )e + (168A b + 504B a b )d e + 84B b d )x +--R + +--R 2 5 3 4 2 6 2 5 +--R (315A a b + 105B a b )e + (630A a b + 630B a b )d e +--R + +--R 7 6 2 +--R (105A b + 315B a b )d +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 5 3 4 6 2 5 2 3 +--R (140A a b e + (840A a b + 280B a b )d e + (420A a b + 420B a b )d )x +--R + +--R 3 4 2 5 3 4 2 2 3 4 2 +--R (420A a b d e + (630A a b + 210B a b )d )x + 420A a b d x +--R / +--R 4 +--R 420b +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 2 6 3 2 2 3 5 +--R B b e x + ((A b + 3B a b )e + 2B b d e)x +--R + +--R 2 2 2 3 2 3 2 4 +--R ((3A a b + 3B a b)e + (2A b + 6B a b )d e + B b d )x +--R + +--R 2 3 2 2 2 3 2 2 3 +--R ((3A a b + B a )e + (6A a b + 6B a b)d e + (A b + 3B a b )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (A a e + (6A a b + 2B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 3 2 3 2 +--R (2A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 2 7 4 3 2 4 6 +--R - B b e x + ((- A b - 4B a b )e - 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((- 4A a b - 6B a b )e + (- 2A b - 8B a b )d e - B b d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 6A a b - 4B a b)e + (- 8A a b - 12B a b )d e +--R + +--R 4 3 2 +--R (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 4A a b - B a )e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 2 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- A a e + (- 8A a b - 2B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (- 2A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 1378 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1378 +r0:=-1/12*(b*d-a*e)*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b^3*e)+1/6*B*(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-1/15*(2*b*B*d-3*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b^3 +--R +--R +--R (2) +--R 5 5 5 4 5 4 +--R 10B b e x + ((12A b + 26B a b )e + 12B b d)x +--R + +--R 4 2 3 5 4 3 +--R ((33A a b + 19B a b )e + (15A b + 33B a b )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((27A a b + B a b )e + (45A a b + 27B a b )d)x +--R + +--R 3 2 4 2 3 3 2 4 5 +--R ((3A a b - B a b)e + (45A a b + 3B a b )d)x + (- 3A a b + B a )e +--R + +--R 3 2 4 +--R (15A a b - 3B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 60b +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 3 2 3 5 +--R 10B b e x + ((12A b + 36B a b )e + 12B b d)x +--R + +--R 2 2 3 2 4 +--R ((45A a b + 45B a b)e + (15A b + 45B a b )d)x +--R + +--R 2 3 2 2 3 +--R ((60A a b + 20B a )e + (60A a b + 60B a b)d)x +--R + +--R 3 2 3 2 3 +--R (30A a e + (90A a b + 30B a )d)x + 60A a d x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 5 4 +--R - 10B b e x + ((- 12A b - 26B a b )e - 12B b d)x +--R + +--R 4 2 3 5 4 3 +--R ((- 33A a b - 19B a b )e + (- 15A b - 33B a b )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((- 27A a b - B a b )e + (- 45A a b - 27B a b )d)x +--R + +--R 3 2 4 2 3 3 2 4 5 +--R ((- 3A a b + B a b)e + (- 45A a b - 3B a b )d)x + (3A a b - B a )e +--R + +--R 3 2 4 +--R (- 15A a b + 3B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 6 5 6 5 +--R 10B b e x + ((12A b + 36B a b )e + 12B b d)x +--R + +--R 5 2 4 6 5 4 +--R ((45A a b + 45B a b )e + (15A b + 45B a b )d)x +--R + +--R 2 4 3 3 5 2 4 3 +--R ((60A a b + 20B a b )e + (60A a b + 60B a b )d)x +--R + +--R 3 3 2 4 3 3 2 3 3 +--R (30A a b e + (90A a b + 30B a b )d)x + 60A a b d x +--R / +--R 3 +--R 60b +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 3 2 3 4 +--R B b e x + ((A b + 3B a b )e + B b d)x +--R + +--R 2 2 3 2 3 +--R ((3A a b + 3B a b)e + (A b + 3B a b )d)x +--R + +--R 2 3 2 2 2 +--R ((3A a b + B a )e + (3A a b + 3B a b)d)x +--R + +--R 3 2 3 3 +--R (A a e + (3A a b + B a )d)x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 4 5 +--R - B b e x + ((- A b - 4B a b )e - B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((- 4A a b - 6B a b )e + (- A b - 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 6A a b - 4B a b)e + (- 4A a b - 6B a b )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 4A a b - B a )e + (- 6A a b - 4B a b)d)x +--R + +--R 4 3 4 4 +--R (- A a e + (- 4A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1378 +r0:=1/4*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+_ + 1/5*B*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2 +--R +--R +--R (2) +--R 4 4 4 3 3 3 2 2 2 +--R 4B b x + (5A b + 11B a b )x + (15A a b + 9B a b )x +--R + +--R 2 2 3 3 4 +--R (15A a b + B a b)x + 5A a b - B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 20b +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 3 2 4 2 2 3 +--R 4B b x + (5A b + 15B a b )x + (20A a b + 20B a b)x +--R + +--R 2 3 2 3 +--R (30A a b + 10B a )x + 20A a x +--R / +--R 20 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 3 3 2 2 2 +--R - 4B b x + (- 5A b - 11B a b )x + (- 15A a b - 9B a b )x +--R + +--R 2 2 3 3 4 +--R (- 15A a b - B a b)x - 5A a b + B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 5 5 4 4 4 2 3 3 +--R 4B b x + (5A b + 15B a b )x + (20A a b + 20B a b )x +--R + +--R 2 3 3 2 2 3 2 +--R (30A a b + 10B a b )x + 20A a b x +--R / +--R 2 +--R 20b +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1378 +r0:=-1/3*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/4*B*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-(b*d-a*e)^2*(B*d-A*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^4+1/2*(b*d-a*e)*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^3+(b*d-a*e)^3*(B*d-A*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 3 3 2 2 2 2 +--R 12A a b e + (- 36A a b - 12B a b)d e + (36A a b + 36B a b )d e +--R + +--R 4 3 3 4 4 +--R (- 12A b - 36B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 3B b e x + ((4A b + 12B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((18A a b + 18B a b )e + (- 6A b - 18B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (36A a b + 12B a b)e + (- 36A a b - 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b + 36B a b )d e - 12B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (22A a b + 3B a )e + (- 30A a b - 22B a b)d e +--R + +--R 3 2 2 2 2 3 3 +--R (12A a b + 30B a b )d e - 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 5 5 +--R 12b e x + 12a b e +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 2 3 3 2 2 2 2 +--R 12A a e + (- 36A a b - 12B a )d e + (36A a b + 36B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 12A b - 36B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 3B b e x + ((4A b + 12B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((18A a b + 18B a b)e + (- 6A b - 18B a b )d e + 6B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (36A a b + 12B a )e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (12A b + 36B a b )d e - 12B b d e +--R * +--R x +--R / +--R 5 +--R 12e +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 3 +--R - 12A a b e + (36A a b + 12B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 36A a b - 36B a b )d e + (12A b + 36B a b )d e - 12B b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 4 3 4 4 3 3 +--R - 3B b e x + ((- 4A b - 12B a b )e + 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((- 18A a b - 18B a b )e + (6A b + 18B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 36A a b - 12B a b)e + (36A a b + 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b - 36B a b )d e + 12B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 22A a b - 3B a )e + (30A a b + 22B a b)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 12A a b - 30B a b )d e + 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 4 2 3 3 2 3 +--R 12A a b e + (- 36A a b - 12B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (36A a b + 36B a b )d e + (- 12A b - 36B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 4 3 2 4 3 2 3 3 2 2 2 +--R 12A a b e + (- 36A a b - 12B a b)d e + (36A a b + 36B a b )d e +--R + +--R 4 2 3 3 4 4 +--R (- 12A a b - 36B a b )d e + 12B a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b + 15B a b )e - 4B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((22A a b + 30B a b )e + (- 6A b - 22B a b )d e + 6B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (54A a b + 30B a b )e + (- 42A a b - 54B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (12A b + 42B a b )d e - 12B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (36A a b + 12B a b)e + (- 36A a b - 36B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (12A a b + 36B a b )d e - 12B a b d e +--R * +--R x +--R / +--R 2 5 5 +--R 12b e x + 12a b e +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1378 +r0:=1/3*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*(d+e*x))+_ + (b*d-a*e)*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-_ + 1/2*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-_ + (b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 3 4 2 2 3 +--R (18A a b + 6B a )e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A b + 54B a b )d e - 24B b d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A a b + 6B a )d e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 3 3 4 +--R (18A b + 54B a b )d e - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 2B b e x + ((3A b + 9B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((18A a b + 18B a b)e + (- 9A b - 27B a b )d e + 12B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (9A a b + 11B a )e + (18A a b - 6B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 18A b - 30B a b )d e + 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (27A a b + 17B a )d e + (- 18A a b - 42B a b)d e +--R + +--R 2 3 +--R 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +--R 6b e x + (6a e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 4 2 2 3 +--R (18A a b + 6B a )e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A b + 54B a b )d e - 24B b d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A a b + 6B a )d e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 3 3 4 +--R (18A b + 54B a b )d e - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 2B b e x + ((3A b + 9B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((18A a b + 18B a b)e + (- 9A b - 27B a b )d e + 12B b d e )x +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((18A a b + 18B a b)d e + (- 12A b - 36B a b )d e + 18B b d e)x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (18A a b + 6B a )d e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 3 3 4 +--R (6A b + 18B a b )d e - 6B b d +--R / +--R 6 5 +--R 6e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 4 2 2 3 +--R (- 18A a b - 6B a )e + (36A a b + 36B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 18A b - 54B a b )d e + 24B b d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (- 18A a b - 6B a )d e + (36A a b + 36B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 18A b - 54B a b )d e + 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R - 2B b e x + ((- 3A b - 9B a b )e + 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 18A a b - 18B a b)e + (9A b + 27B a b )d e - 12B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 9A a b - 11B a )e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A b + 30B a b )d e - 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 6A a e + (- 27A a b - 17B a )d e + (18A a b + 42B a b)d e +--R + +--R 2 3 +--R - 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 4 3 2 2 3 +--R (18A a b + 6B a b)e + (- 36A a b - 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (18A b + 54B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (18A a b + 6B a )e + (- 18A a b - 30B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 18A a b + 18B a b )d e + (18A b + 30B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 +--R (18A a b + 6B a )d e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (18A a b + 54B a b )d e - 24B a b d +--R * +--R log(e x + d) +--R + +--R 4 4 5 4 3 4 4 3 4 +--R 2B b e x + ((3A b + 11B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((21A a b + 27B a b )e + (- 9A b - 31B a b )d e + 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (18A a b + 18B a b)e + (9A a b - 9B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b - 24B a b )d e + 18B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 3 3 3 2 2 2 2 +--R - 6A a b e + (36A a b + 24B a b)d e + (- 30A a b - 54B a b )d e +--R + +--R 4 3 3 4 4 +--R (6A b + 36B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (18A a b + 6B a )d e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (6A a b + 18B a b )d e - 6B a b d +--R / +--R 6 2 6 5 5 +--R 6b e x + (6a e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1378 +r0:=-1/2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^2)-(2*b*B*d-A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*_ + (b*d-a*e)*(d+e*x))-3*b*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*_ + x^2)/e^4+3/2*b*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*_ + x^2)/(e^3*(b*d-a*e))+3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 2 4 3 2 3 3 2 2 2 +--R ((6A a b + 6B a b)e + (- 6A b - 18B a b )d e + 12B b d e )x +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((12A a b + 12B a b)d e + (- 12A b - 36B a b )d e + 24B b d e)x +--R + +--R 2 2 2 2 3 2 3 3 4 +--R (6A a b + 6B a b)d e + (- 6A b - 18B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R B b e x + ((2A b + 6B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 3A a b + 3B a b)e + (9A b + 15B a b )d e - 18B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 6A a b - 2B a )e + (6A a b + 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (6A b - 6B a b )d e - 12B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 3 +--R - A a e + (- 3A a b - B a )d e + (6A a b + 12B a b)d e - 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 2 3 3 2 2 2 +--R ((6A a b + 6B a b)e + (- 6A b - 18B a b )d e + 12B b d e )x +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((12A a b + 12B a b)d e + (- 12A b - 36B a b )d e + 24B b d e)x +--R + +--R 2 2 2 2 3 2 3 3 4 +--R (6A a b + 6B a b)d e + (- 6A b - 18B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R B b e x + ((2A b + 6B a b )e - 4B b d e )x +--R + +--R 3 2 3 3 2 2 2 +--R ((4A b + 12B a b )d e - 11B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 6A a b - 2B a )e + (12A a b + 12B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 4A b - 12B a b )d e + 2B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - A a e + (- 3A a b - B a )d e + (9A a b + 9B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 5A b - 15B a b )d e + 7B b d +--R / +--R 7 2 6 2 5 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 6A a b - 6B a b)e + (6A b + 18B a b )d e - 12B b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R (- 12A a b - 12B a b)d e + (12A b + 36B a b )d e +--R + +--R 3 3 +--R - 24B b d e +--R * +--R x +--R + +--R 2 2 2 2 3 2 3 3 4 +--R (- 6A a b - 6B a b)d e + (6A b + 18B a b )d e - 12B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R - B b e x + ((- 2A b - 6B a b )e + 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((3A a b - 3B a b)e + (- 9A b - 15B a b )d e + 18B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (6A a b + 2B a )e + (- 6A a b - 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 6A b + 6B a b )d e + 12B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 3 +--R A a e + (3A a b + B a )d e + (- 6A a b - 12B a b)d e + 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((6A a b + 6B a b )e + (- 6A b - 18B a b )d e + 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (6A a b + 6B a b)e + (6A a b - 6B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b - 24B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (12A a b + 12B a b)d e + (- 6A a b - 30B a b )d e +--R + +--R 4 3 3 4 4 +--R (- 6A b + 6B a b )d e + 12B b d +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 2 3 3 4 +--R (6A a b + 6B a b)d e + (- 6A a b - 18B a b )d e + 12B a b d +--R * +--R log(e x + d) +--R + +--R 4 4 5 4 3 4 4 3 4 +--R B b e x + ((2A b + 7B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((2A a b + 6B a b )e + (4A b + 8B a b )d e - 11B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 6A a b - 2B a b)e + (16A a b + 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 4A b - 23B a b )d e + 2B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 7A a b - 2B a )e + (9A a b + 11B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (5A a b - 3B a b )d e + (- 5A b - 13B a b )d e + 7B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - A a e + (- 3A a b - B a )d e + (9A a b + 9B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 5A a b - 15B a b )d e + 7B a b d +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 500 + +)clear all + +--S 501 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1378 +r0:=-1/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^3)-1/6*(4*b*B*d-A*b*e-3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^2)+b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(b*d-a*e))-1/2*b*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x))-b^2*(4*b*B*d-A*b*e-_ + 3*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 2 4 3 3 3 +--R ((6A b + 18B a b )e - 24B b d e )x +--R + +--R 3 2 3 3 2 2 2 +--R ((18A b + 54B a b )d e - 72B b d e )x +--R + +--R 3 2 2 2 3 3 3 2 3 +--R ((18A b + 54B a b )d e - 72B b d e)x + (6A b + 18B a b )d e +--R + +--R 3 4 +--R - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((- 11A b - 9B a b )e + 44B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 18A a b - 18B a b)e + (- 15A b + 27B a b )d e + 60B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 9A a b - 3B a )e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 6A b + 54B a b )d e + 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (- 3A a b - B a )d e + (- 6A a b - 6B a b)d e +--R + +--R 2 3 +--R 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 6 3 5 3 5 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 3 3 +--R ((6A b + 18B a b )e - 24B b d e )x +--R + +--R 3 2 3 3 2 2 2 +--R ((18A b + 54B a b )d e - 72B b d e )x +--R + +--R 3 2 2 2 3 3 3 2 3 +--R ((18A b + 54B a b )d e - 72B b d e)x + (6A b + 18B a b )d e +--R + +--R 3 4 +--R - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 3 3 +--R 6B b e x + 18B b d e x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 18A a b - 18B a b)e + (18A b + 54B a b )d e - 18B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 9A a b - 3B a )e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (27A b + 81B a b )d e - 54B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (- 3A a b - B a )d e + (- 6A a b - 6B a b)d e +--R + +--R 3 2 3 3 4 +--R (11A b + 33B a b )d e - 26B b d +--R / +--R 8 3 7 2 2 6 3 5 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 4 3 3 3 +--R ((- 6A b - 18B a b )e + 24B b d e )x +--R + +--R 3 2 3 3 2 2 2 +--R ((- 18A b - 54B a b )d e + 72B b d e )x +--R + +--R 3 2 2 2 3 3 +--R ((- 18A b - 54B a b )d e + 72B b d e)x +--R + +--R 3 2 3 3 4 +--R (- 6A b - 18B a b )d e + 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R - 6B b e x + ((11A b + 9B a b )e - 44B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((18A a b + 18B a b)e + (15A b - 27B a b )d e - 60B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (9A a b + 3B a )e + (18A a b + 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (6A b - 54B a b )d e - 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 3 +--R 2A a e + (3A a b + B a )d e + (6A a b + 6B a b)d e - 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 4 3 4 +--R ((6A b + 18B a b )e - 24B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((6A a b + 18B a b )e + (18A b + 30B a b )d e - 72B b d e )x +--R + +--R 3 2 2 3 4 3 2 2 4 3 2 +--R ((18A a b + 54B a b )d e + (18A b - 18B a b )d e - 72B b d e)x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R ((18A a b + 54B a b )d e + (6A b - 54B a b )d e - 24B b d )x +--R + +--R 3 2 2 3 3 4 +--R (6A a b + 18B a b )d e - 24B a b d +--R * +--R log(e x + d) +--R + +--R 4 4 5 3 4 4 3 4 +--R 6B b e x + (6B a b e + 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 18A a b - 18B a b )e + (18A b + 72B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 2 2 3 4 3 2 2 +--R (- 27A a b - 21B a b)e + 36B a b d e + (27A b + 63B a b )d e +--R + +--R 4 3 +--R - 54B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 11A a b - 3B a )e + (- 21A a b - 19B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (21A a b + 75B a b )d e + (11A b - 21B a b )d e - 26B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 2A a e + (- 3A a b - B a )d e + (- 6A a b - 6B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (11A a b + 33B a b )d e - 26B a b d +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 6 3 5 3 5 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 505 + +)clear all + +--S 506 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1378 +r0:=-1/4*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/3*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^3)-_ + 1/2*b*B*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^2)+b^2*B*_ + (b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))+b^3*B*_ + log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 5 4 4 4 3 4 4 2 3 3 +--R (12B a b e - 12B b d e )x + (48B a b d e - 48B b d e )x +--R + +--R 3 2 3 4 3 2 2 3 3 2 4 4 +--R (72B a b d e - 72B b d e )x + (48B a b d e - 48B b d e)x +--R + +--R 3 4 4 5 +--R 12B a b d e - 12B b d +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 4 +--R ((- 3A b - 10B a b )e + 13B b d e )x +--R + +--R 3 2 2 5 3 4 4 2 3 3 +--R ((- 12A a b - 36B a b )e + 44B a b d e + 4B b d e )x +--R + +--R 2 2 3 5 2 2 4 3 2 3 +--R (- 18A a b - 18B a b)e - 36B a b d e + 102B a b d e +--R + +--R 4 3 2 +--R - 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 3 4 2 2 2 3 3 3 2 +--R (- 12A a b - 4B a )e - 8B a b d e - 24B a b d e + 84B a b d e +--R + +--R 4 4 +--R - 36B b d e +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R - 3A a e - B a d e - 2B a b d e - 6B a b d e + 24B a b d e - 12B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 2 9 5 2 10 9 2 2 8 4 +--R (12a b e - 12b d e )x + (12a e + 36a b d e - 48b d e )x +--R + +--R 2 9 2 8 2 3 7 3 +--R (48a d e + 24a b d e - 72b d e )x +--R + +--R 2 2 8 3 7 2 4 6 2 +--R (72a d e - 24a b d e - 48b d e )x +--R + +--R 2 3 7 4 6 2 5 5 2 4 6 5 5 +--R (48a d e - 36a b d e - 12b d e )x + 12a d e - 12a b d e +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 3 3 3 2 2 2 3 3 3 4 +--R (12B b e x + 48B b d e x + 72B b d e x + 48B b d e x + 12B b d ) +--R * +--R log(e x + d) +--R + +--R 3 2 4 3 3 3 +--R ((- 12A b - 36B a b )e + 48B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 18A a b - 18B a b)e + (- 18A b - 54B a b )d e + 108B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 12A a b - 4B a )e + (- 12A a b - 12B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 12A b - 36B a b )d e + 88B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 3A a e + (- 3A a b - B a )d e + (- 3A a b - 3B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 3A b - 9B a b )d e + 25B b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 5 4 4 4 3 4 4 2 3 3 +--R (- 12B a b e + 12B b d e )x + (- 48B a b d e + 48B b d e )x +--R + +--R 3 2 3 4 3 2 2 3 3 2 4 4 +--R (- 72B a b d e + 72B b d e )x + (- 48B a b d e + 48B b d e)x +--R + +--R 3 4 4 5 +--R - 12B a b d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 4 +--R ((3A b + 10B a b )e - 13B b d e )x +--R + +--R 3 2 2 5 3 4 4 2 3 3 +--R ((12A a b + 36B a b )e - 44B a b d e - 4B b d e )x +--R + +--R 2 2 3 5 2 2 4 3 2 3 +--R (18A a b + 18B a b)e + 36B a b d e - 102B a b d e +--R + +--R 4 3 2 +--R 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 3 4 2 2 2 3 3 3 2 +--R (12A a b + 4B a )e + 8B a b d e + 24B a b d e - 84B a b d e +--R + +--R 4 4 +--R 36B b d e +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 3A a e + B a d e + 2B a b d e + 6B a b d e - 24B a b d e + 12B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 5 4 5 +--R (12B a b e - 12B b d e )x +--R + +--R 2 3 5 4 4 5 2 3 4 +--R (12B a b e + 36B a b d e - 48B b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 3 +--R (48B a b d e + 24B a b d e - 72B b d e )x +--R + +--R 2 3 2 3 4 3 2 5 4 2 +--R (72B a b d e - 24B a b d e - 48B b d e)x +--R + +--R 2 3 3 2 4 4 5 5 2 3 4 4 5 +--R (48B a b d e - 36B a b d e - 12B b d )x + 12B a b d e - 12B a b d +--R * +--R log(e x + d) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 12A a b - 36B a b )e + (12A b + 84B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 30A a b - 54B a b )e + (12A a b + 48B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (18A b + 114B a b )d e - 108B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 3 2 4 4 2 3 2 3 +--R (- 30A a b - 22B a b)e - 44B a b d e + (18A a b + 138B a b )d e +--R + +--R 5 4 3 2 5 4 +--R (12A b + 16B a b )d e - 88B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 4 4 3 2 2 3 +--R (- 15A a b - 4B a )e - 9B a b d e - 26B a b d e +--R + +--R 4 2 3 3 2 5 4 4 5 5 +--R (12A a b + 118B a b )d e + (3A b - 54B a b )d e - 25B b d +--R * +--R x +--R + +--R 5 5 5 4 4 2 3 3 2 3 2 +--R - 3A a e - B a d e - 2B a b d e - 6B a b d e +--R + +--R 4 2 3 4 4 5 +--R (3A a b + 34B a b )d e - 25B a b d +--R / +--R 10 2 9 5 2 10 9 2 2 8 4 +--R (12a b e - 12b d e )x + (12a e + 36a b d e - 48b d e )x +--R + +--R 2 9 2 8 2 3 7 3 +--R (48a d e + 24a b d e - 72b d e )x +--R + +--R 2 2 8 3 7 2 4 6 2 +--R (72a d e - 24a b d e - 48b d e )x +--R + +--R 2 3 7 4 6 2 5 5 2 4 6 5 5 +--R (48a d e - 36a b d e - 12b d e )x + 12a d e - 12a b d e +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1378 +r0:=1/4*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*_ + (d+e*x)^4)+1/5*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*_ + (d+e*x)^5) +--R +--R +--R (2) +--R 4 3 4 4 +--R ((A b - 5B a b )e + 4B b d)x +--R + +--R 3 2 2 4 3 3 +--R ((- A a b - 15B a b )e + (5A b + 11B a b )d)x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 9A a b - 15B a b)e + (15A a b + 9B a b )d)x +--R + +--R 3 4 2 2 3 4 3 4 +--R ((- 11A a b - 5B a )e + (15A a b + B a b)d)x - 4A a e + (5A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 7 6 2 2 5 5 +--R (20a e - 40a b d e + 20b d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (100a d e - 200a b d e + 100b d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (100a d e - 200a b d e + 100b d e)x + 20a d e - 40a b d e + 20b d +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 20B b e x + ((- 10A b - 30B a b )e - 40B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 20A a b - 20B a b)e + (- 10A b - 30B a b )d e - 40B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 15A a b - 5B a )e + (- 10A a b - 10B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 5A b - 15B a b )d e - 20B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 4A a e + (- 3A a b - B a )d e + (- 2A a b - 2B a b)d e +--R + +--R 3 2 3 3 4 +--R (- A b - 3B a b )d e - 4B b d +--R / +--R 10 5 9 4 2 8 3 3 7 2 4 6 5 5 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 6 4 5 4 +--R ((- A b + 5B a b )e - 4B b d e )x +--R + +--R 3 2 2 6 4 3 5 3 +--R ((A a b + 15B a b )e + (- 5A b - 11B a b )d e )x +--R + +--R 2 2 3 6 3 2 2 5 2 +--R ((9A a b + 15B a b)e + (- 15A a b - 9B a b )d e )x +--R + +--R 3 4 6 2 2 3 5 4 6 +--R ((11A a b + 5B a )e + (- 15A a b - B a b)d e )x + 4A a e +--R + +--R 3 4 5 +--R (- 5A a b + B a )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 6 4 5 5 2 4 4 +--R (- 20B a b e + 40B a b d e - 20B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 10A a b - 30B a b )e + (20A a b + 20B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 10A b + 50B a b )d e - 40B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 20A a b - 20B a b)e + (30A a b + 10B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (- 10A b + 50B a b )d e - 40B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 5 5 4 4 2 +--R (- 15A a b - 5B a )e + 20A a b d e + (- 5A b + 25B a b )d e +--R + +--R 5 5 +--R - 20B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 5 4 5 5 6 +--R - 4A a e + (5A a b - B a )d e + (- A b + 5B a b )d e - 4B b d +--R / +--R 2 12 11 2 2 10 5 +--R (20a e - 40a b d e + 20b d e )x +--R + +--R 2 11 2 10 2 3 9 4 +--R (100a d e - 200a b d e + 100b d e )x +--R + +--R 2 2 10 3 9 2 4 8 3 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 3 9 4 8 2 5 7 2 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 4 8 5 7 2 6 6 2 5 7 6 6 2 7 5 +--R (100a d e - 200a b d e + 100b d e )x + 20a d e - 40a b d e + 20b d e +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 515 + +)clear all + +--S 516 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1378 +r0:=-1/6*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^6)+1/12*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^5)+1/60*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 5 4 2 5 5 +--R ((- A b + 3B a b )e - 2B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 4 +--R ((A a b - 3B a b )e + (- 6A b + 20B a b )d e - 12B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (- A a b - 27B a b )e + (6A a b + 70B a b )d e +--R + +--R 5 4 2 +--R (- 15A b - 33B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 19A a b - 33B a b)e + (54A a b + 70B a b )d e +--R + +--R 4 2 3 2 +--R (- 45A a b - 27B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 26A a b - 12B a )e + (66A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 +--R (- 45A a b - 3B a b )d +--R * +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R - 10A a e + (24A a b - 2B a )d e + (- 15A a b + 3B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 9 2 8 2 2 7 3 3 6 6 +--R (60a e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 8 2 2 7 2 3 6 3 4 5 5 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e )x +--R + +--R 3 2 7 2 3 6 2 4 5 3 5 4 4 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (1200a d e - 3600a b d e + 3600a b d e - 1200b d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e)x + 60a d e +--R + +--R 2 7 2 2 8 3 9 +--R - 180a b d e + 180a b d e - 60b d +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 30B b e x + ((- 20A b - 60B a b )e - 40B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 45A a b - 45B a b)e + (- 15A b - 45B a b )d e - 30B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 36A a b - 12B a )e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 6A b - 18B a b )d e - 12B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 6A a b - 2B a )d e + (- 3A a b - 3B a b)d e +--R + +--R 3 2 3 3 4 +--R (- A b - 3B a b )d e - 2B b d +--R / +--R 11 6 10 5 2 9 4 3 8 3 4 7 2 5 6 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 5 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 7 5 6 5 +--R ((A b - 3B a b )e + 2B b d e )x +--R + +--R 4 2 3 7 5 4 6 5 2 5 4 +--R ((- A a b + 3B a b )e + (6A b - 20B a b )d e + 12B b d e )x +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (A a b + 27B a b )e + (- 6A a b - 70B a b )d e +--R + +--R 5 4 2 5 +--R (15A b + 33B a b )d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (19A a b + 33B a b)e + (- 54A a b - 70B a b )d e +--R + +--R 4 2 3 2 5 +--R (45A a b + 27B a b )d e +--R * +--R 2 +--R x +--R + +--R 4 5 7 3 2 4 6 +--R (26A a b + 12B a )e + (- 66A a b - 20B a b)d e +--R + +--R 2 3 3 2 2 5 +--R (45A a b + 3B a b )d e +--R * +--R x +--R + +--R 5 7 4 5 6 3 2 4 2 5 +--R 10A a e + (- 24A a b + 2B a )d e + (15A a b - 3B a b)d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 4 +--R (- 30B a b e + 90B a b d e - 90B a b d e + 30B b d e )x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (- 20A a b - 60B a b )e + (60A a b + 140B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 6 4 3 +--R (- 60A a b - 60B a b )d e + (20A b - 60B a b )d e + 40B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (- 45A a b - 45B a b)e + (120A a b + 90B a b )d e +--R + +--R 2 4 3 3 2 5 6 5 4 3 6 5 2 +--R (- 90A a b - 30B a b )d e + (15A b - 45B a b )d e + 30B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 3 3 2 5 +--R (- 36A a b - 12B a )e + (90A a b + 18B a b)d e - 60A a b d e +--R + +--R 6 5 5 2 6 6 +--R (6A b - 18B a b )d e + 12B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 10A a e + (24A a b - 2B a )d e + (- 15A a b + 3B a b)d e +--R + +--R 6 5 6 6 7 +--R (A b - 3B a b )d e + 2B b d +--R / +--R 3 14 2 13 2 2 12 3 3 11 6 +--R (60a e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 13 2 2 12 2 3 11 3 4 10 5 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e )x +--R + +--R 3 2 12 2 3 11 2 4 10 3 5 9 4 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 3 11 2 4 10 2 5 9 3 6 8 3 +--R (1200a d e - 3600a b d e + 3600a b d e - 1200b d e )x +--R + +--R 3 4 10 2 5 9 2 6 8 3 7 7 2 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 5 9 2 6 8 2 7 7 3 8 6 3 6 8 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e )x + 60a d e +--R + +--R 2 7 7 2 8 6 3 9 5 +--R - 180a b d e + 180a b d e - 60b d e +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 520 + +)clear all + +--S 521 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1378 +r0:=-1/7*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^7)+1/42*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^6)+1/84*b*(4*b*B*d+3*A*b*e-_ + 7*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)^3*_ + (d+e*x)^5)+1/420*b*(4*b*B*d+3*A*b*e-7*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 6 5 3 6 2 6 +--R ((3A b - 7B a b )e + 4B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 5 +--R ((- 3A a b + 7B a b )e + (21A b - 53B a b )d e + 28B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (3A a b - 7B a b )e + (- 21A a b + 53B a b )d e +--R + +--R 6 5 2 6 3 +--R (63A b - 175B a b )d e + 84B b d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (- 3A a b - 133B a b )e + (21A a b + 507B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 63A a b - 665B a b )d e + (105A b + 231B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 102A a b - 182B a b)e + (399A a b + 613B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 567A a b - 665B a b )d e + (315A a b + 189B a b )d +--R * +--R 2 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 150A a b - 70B a )e + (546A a b + 206B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 693A a b - 175B a b )d e + (315A a b + 21B a b )d +--R * +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R - 60A a e + (210A a b - 10B a )d e + (- 252A a b + 28B a b)d e +--R + +--R 3 3 4 2 3 +--R (105A a b - 21B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 11 3 10 2 2 2 9 3 3 8 4 4 7 7 +--R (420a e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e )x +--R + +--R 4 10 3 2 9 2 2 3 8 3 4 7 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 5 6 +--R 2940b d e +--R * +--R 6 +--R x +--R + +--R 4 2 9 3 3 8 2 2 4 7 3 5 6 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 6 5 +--R 8820b d e +--R * +--R 5 +--R x +--R + +--R 4 3 8 3 4 7 2 2 5 6 3 6 5 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 7 4 +--R 14700b d e +--R * +--R 4 +--R x +--R + +--R 4 4 7 3 5 6 2 2 6 5 3 7 4 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 8 3 +--R 14700b d e +--R * +--R 3 +--R x +--R + +--R 4 5 6 3 6 5 2 2 7 4 3 8 3 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 9 2 +--R 8820b d e +--R * +--R 2 +--R x +--R + +--R 4 6 5 3 7 4 2 2 8 3 3 9 2 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 10 +--R 2940b d e +--R * +--R x +--R + +--R 4 7 4 3 8 3 2 2 9 2 3 10 4 11 +--R 420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 140B b e x + ((- 105A b - 315B a b )e - 140B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 252A a b - 252B a b)e + (- 63A b - 189B a b )d e - 84B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 210A a b - 70B a )e + (- 84A a b - 84B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 21A b - 63B a b )d e - 28B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 60A a e + (- 30A a b - 10B a )d e + (- 12A a b - 12B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 3A b - 9B a b )d e - 4B b d +--R / +--R 12 7 11 6 2 10 5 3 9 4 4 8 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 7 2 6 6 7 5 +--R 8820d e x + 2940d e x + 420d e +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 8 6 7 6 +--R ((- 3A b + 7B a b )e - 4B b d e )x +--R + +--R 5 2 4 8 6 5 7 6 2 6 5 +--R ((3A a b - 7B a b )e + (- 21A b + 53B a b )d e - 28B b d e )x +--R + +--R 2 4 3 3 8 5 2 4 7 +--R (- 3A a b + 7B a b )e + (21A a b - 53B a b )d e +--R + +--R 6 5 2 6 6 3 5 +--R (- 63A b + 175B a b )d e - 84B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 8 2 4 3 3 7 +--R (3A a b + 133B a b )e + (- 21A a b - 507B a b )d e +--R + +--R 5 2 4 2 6 6 5 3 5 +--R (63A a b + 665B a b )d e + (- 105A b - 231B a b )d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 8 3 3 4 2 7 +--R (102A a b + 182B a b)e + (- 399A a b - 613B a b )d e +--R + +--R 2 4 3 3 2 6 5 2 4 3 5 +--R (567A a b + 665B a b )d e + (- 315A a b - 189B a b )d e +--R * +--R 2 +--R x +--R + +--R 5 6 8 4 2 5 7 +--R (150A a b + 70B a )e + (- 546A a b - 206B a b)d e +--R + +--R 3 3 4 2 2 6 2 4 3 3 3 5 +--R (693A a b + 175B a b )d e + (- 315A a b - 21B a b )d e +--R * +--R x +--R + +--R 6 8 5 6 7 4 2 5 2 6 +--R 60A a e + (- 210A a b + 10B a )d e + (252A a b - 28B a b)d e +--R + +--R 3 3 4 2 3 5 +--R (- 105A a b + 21B a b )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 +--R - 140B a b e + 560B a b d e - 840B a b d e + 560B a b d e +--R + +--R 7 4 4 +--R - 140B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 8 3 4 4 3 7 +--R (- 105A a b - 315B a b )e + (420A a b + 1120B a b )d e +--R + +--R 2 5 3 4 2 6 6 2 5 3 5 +--R (- 630A a b - 1330B a b )d e + (420A a b + 420B a b )d e +--R + +--R 7 6 4 4 7 5 3 +--R (- 105A b + 245B a b )d e - 140B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 8 4 3 5 2 7 +--R (- 252A a b - 252B a b)e + (945A a b + 819B a b )d e +--R + +--R 3 4 4 3 2 6 2 5 3 4 3 5 +--R (- 1260A a b - 840B a b )d e + (630A a b + 210B a b )d e +--R + +--R 7 6 5 3 7 6 2 +--R (- 63A b + 147B a b )d e - 84B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 8 5 2 6 7 +--R (- 210A a b - 70B a )e + (756A a b + 196B a b)d e +--R + +--R 4 3 5 2 2 6 3 4 3 5 +--R (- 945A a b - 147B a b )d e + 420A a b d e +--R + +--R 7 6 6 2 7 7 +--R (- 21A b + 49B a b )d e - 28B b d e +--R * +--R x +--R + +--R 7 8 6 7 7 5 2 6 2 6 +--R - 60A a e + (210A a b - 10B a )d e + (- 252A a b + 28B a b)d e +--R + +--R 4 3 5 2 3 5 7 6 7 7 8 +--R (105A a b - 21B a b )d e + (- 3A b + 7B a b )d e - 4B b d +--R / +--R 4 16 3 15 2 2 2 14 3 3 13 4 4 12 7 +--R (420a e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e )x +--R + +--R 4 15 3 2 14 2 2 3 13 3 4 12 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 5 11 +--R 2940b d e +--R * +--R 6 +--R x +--R + +--R 4 2 14 3 3 13 2 2 4 12 3 5 11 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 6 10 +--R 8820b d e +--R * +--R 5 +--R x +--R + +--R 4 3 13 3 4 12 2 2 5 11 3 6 10 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 7 9 +--R 14700b d e +--R * +--R 4 +--R x +--R + +--R 4 4 12 3 5 11 2 2 6 10 3 7 9 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 8 8 +--R 14700b d e +--R * +--R 3 +--R x +--R + +--R 4 5 11 3 6 10 2 2 7 9 3 8 8 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 9 7 +--R 8820b d e +--R * +--R 2 +--R x +--R + +--R 4 6 10 3 7 9 2 2 8 8 3 9 7 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 10 6 +--R 2940b d e +--R * +--R x +--R + +--R 4 7 9 3 8 8 2 2 9 7 3 10 6 4 11 5 +--R 420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1378 +r0:=-1/8*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^8)-1/14*(b*B*d+A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^7)-1/28*b*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^6)-1/56*b^2*_ + (b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(b*d-a*e)*_ + (d+e*x)^5)-1/280*b^2*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 70B b e x + ((- 56A b - 168B a b )e - 56B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 140A a b - 140B a b)e + (- 28A b - 84B a b )d e - 28B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 120A a b - 40B a )e + (- 40A a b - 40B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 8A b - 24B a b )d e - 8B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 35A a e + (- 15A a b - 5B a )d e + (- 5A a b - 5B a b)d e +--R + +--R 3 2 3 3 4 +--R (- A b - 3B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 9 13 12 8 12 2 11 7 +--R 280b e x + (280a e + 2240b d e )x + (2240a d e + 7840b d e )x +--R + +--R 2 11 3 10 6 3 10 4 9 5 +--R (7840a d e + 15680b d e )x + (15680a d e + 19600b d e )x +--R + +--R 4 9 5 8 4 5 8 6 7 3 +--R (19600a d e + 15680b d e )x + (15680a d e + 7840b d e )x +--R + +--R 6 7 7 6 2 7 6 8 5 8 5 +--R (7840a d e + 2240b d e )x + (2240a d e + 280b d e )x + 280a d e +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 70B b e x + ((- 56A b - 168B a b )e - 56B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 140A a b - 140B a b)e + (- 28A b - 84B a b )d e - 28B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 120A a b - 40B a )e + (- 40A a b - 40B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 8A b - 24B a b )d e - 8B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 35A a e + (- 15A a b - 5B a )d e + (- 5A a b - 5B a b)d e +--R + +--R 3 2 3 3 4 +--R (- A b - 3B a b )d e - B b d +--R / +--R 13 8 12 7 2 11 6 3 10 5 4 9 4 +--R 280e x + 2240d e x + 7840d e x + 15680d e x + 19600d e x +--R + +--R 5 8 3 6 7 2 7 6 8 5 +--R 15680d e x + 7840d e x + 2240d e x + 280d e +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((56A b + 168B a b )e + 56B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((140A a b + 140B a b)e + (28A b + 84B a b )d e + 28B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (120A a b + 40B a )e + (40A a b + 40B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (8A b + 24B a b )d e + 8B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 35A a e + (15A a b + 5B a )d e + (5A a b + 5B a b)d e +--R + +--R 3 2 3 3 4 +--R (A b + 3B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R - 70B b e x + ((- 56A b - 238B a b )e - 56B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 196A a b - 308B a b )e + (- 28A b - 140B a b )d e - 28B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 260A a b - 180B a b)e + (- 68A a b - 124B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 8A b - 52B a b )d e - 8B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 155A a b - 40B a )e + (- 55A a b - 45B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 13A a b - 29B a b )d e + (- A b - 11B a b )d e - B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 35A a e + (- 15A a b - 5B a )d e + (- 5A a b - 5B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- A a b - 3B a b )d e - B a b d +--R / +--R 13 9 13 12 8 12 2 11 7 +--R 280b e x + (280a e + 2240b d e )x + (2240a d e + 7840b d e )x +--R + +--R 2 11 3 10 6 3 10 4 9 5 +--R (7840a d e + 15680b d e )x + (15680a d e + 19600b d e )x +--R + +--R 4 9 5 8 4 5 8 6 7 3 +--R (19600a d e + 15680b d e )x + (15680a d e + 7840b d e )x +--R + +--R 6 7 7 6 2 7 6 8 5 8 5 +--R (7840a d e + 2240b d e )x + (2240a d e + 280b d e )x + 280a d e +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1378 +r0:=-1/9*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^9)-1/72*(4*b*B*d+5*A*b*e-9*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^8)-1/168*b*(4*b*B*d+5*A*b*e-_ + 9*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^7)-_ + 1/420*b^2*(4*b*B*d+5*A*b*e-9*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^6)-1/2520*b^2*(4*b*B*d+5*A*b*e-9*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 504B b e x + ((- 420A b - 1260B a b )e - 336B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 1080A a b - 1080B a b)e + (- 180A b - 540B a b )d e +--R + +--R 3 2 2 +--R - 144B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 945A a b - 315B a )e + (- 270A a b - 270B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 45A b - 135B a b )d e - 36B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 280A a e + (- 105A a b - 35B a )d e + (- 30A a b - 30B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 5A b - 15B a b )d e - 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 10 14 13 9 +--R 2520b e x + (2520a e + 22680b d e )x +--R + +--R 13 2 12 8 2 12 3 11 7 +--R (22680a d e + 90720b d e )x + (90720a d e + 211680b d e )x +--R + +--R 3 11 4 10 6 4 10 5 9 5 +--R (211680a d e + 317520b d e )x + (317520a d e + 317520b d e )x +--R + +--R 5 9 6 8 4 6 8 7 7 3 +--R (317520a d e + 211680b d e )x + (211680a d e + 90720b d e )x +--R + +--R 7 7 8 6 2 8 6 9 5 9 5 +--R (90720a d e + 22680b d e )x + (22680a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 504B b e x + ((- 420A b - 1260B a b )e - 336B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 1080A a b - 1080B a b)e + (- 180A b - 540B a b )d e +--R + +--R 3 2 2 +--R - 144B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 945A a b - 315B a )e + (- 270A a b - 270B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 45A b - 135B a b )d e - 36B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 280A a e + (- 105A a b - 35B a )d e + (- 30A a b - 30B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 5A b - 15B a b )d e - 4B b d +--R / +--R 14 9 13 8 2 12 7 3 11 6 4 10 5 +--R 2520e x + 22680d e x + 90720d e x + 211680d e x + 317520d e x +--R + +--R 5 9 4 6 8 3 7 7 2 8 6 9 5 +--R 317520d e x + 211680d e x + 90720d e x + 22680d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 533 + +--S 534 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R 504B b e x + ((420A b + 1260B a b )e + 336B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (1080A a b + 1080B a b)e + (180A b + 540B a b )d e +--R + +--R 3 2 2 +--R 144B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (945A a b + 315B a )e + (270A a b + 270B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (45A b + 135B a b )d e + 36B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 280A a e + (105A a b + 35B a )d e + (30A a b + 30B a b)d e +--R + +--R 3 2 3 3 4 +--R (5A b + 15B a b )d e + 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R - 504B b e x + ((- 420A b - 1764B a b )e - 336B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1500A a b - 2340B a b )e + (- 180A b - 876B a b )d e +--R + +--R 4 2 2 +--R - 144B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 2025A a b - 1395B a b)e + (- 450A a b - 810B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 45A b - 279B a b )d e - 36B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 1225A a b - 315B a )e + (- 375A a b - 305B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 75A a b - 165B a b )d e + (- 5A b - 51B a b )d e - 4B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 280A a e + (- 105A a b - 35B a )d e + (- 30A a b - 30B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 5A a b - 15B a b )d e - 4B a b d +--R / +--R 14 10 14 13 9 +--R 2520b e x + (2520a e + 22680b d e )x +--R + +--R 13 2 12 8 2 12 3 11 7 +--R (22680a d e + 90720b d e )x + (90720a d e + 211680b d e )x +--R + +--R 3 11 4 10 6 4 10 5 9 5 +--R (211680a d e + 317520b d e )x + (317520a d e + 317520b d e )x +--R + +--R 5 9 6 8 4 6 8 7 7 3 +--R (317520a d e + 211680b d e )x + (211680a d e + 90720b d e )x +--R + +--R 7 7 8 6 2 8 6 9 5 9 5 +--R (90720a d e + 22680b d e )x + (22680a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 535 + +)clear all + +--S 536 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1378 +r0:=-1/10*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^10)-1/45*(2*b*B*d+3*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^9)-1/120*b*(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^8)-_ + 1/360*b^2*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^7)-1/2520*b^2*(2*b*B*d+3*A*b*e-5*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 420B b e x + ((- 360A b - 1080B a b )e - 240B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 945A a b - 945B a b)e + (- 135A b - 405B a b )d e +--R + +--R 3 2 2 +--R - 90B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 840A a b - 280B a )e + (- 210A a b - 210B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 30A b - 90B a b )d e - 20B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 252A a e + (- 84A a b - 28B a )d e + (- 21A a b - 21B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 3A b - 9B a b )d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 15 11 15 14 10 +--R 2520b e x + (2520a e + 25200b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (25200a d e + 113400b d e )x + (113400a d e + 302400b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (302400a d e + 529200b d e )x + (529200a d e + 635040b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (635040a d e + 529200b d e )x + (529200a d e + 302400b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (302400a d e + 113400b d e )x + (113400a d e + 25200b d e )x +--R + +--R 9 6 10 5 10 5 +--R (25200a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 420B b e x + ((- 360A b - 1080B a b )e - 240B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 945A a b - 945B a b)e + (- 135A b - 405B a b )d e - 90B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 840A a b - 280B a )e + (- 210A a b - 210B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 30A b - 90B a b )d e - 20B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 252A a e + (- 84A a b - 28B a )d e + (- 21A a b - 21B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 3A b - 9B a b )d e - 2B b d +--R / +--R 15 10 14 9 2 13 8 3 12 7 4 11 6 +--R 2520e x + 25200d e x + 113400d e x + 302400d e x + 529200d e x +--R + +--R 5 10 5 6 9 4 7 8 3 8 7 2 9 6 +--R 635040d e x + 529200d e x + 302400d e x + 113400d e x + 25200d e x +--R + +--R 10 5 +--R 2520d e +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R 420B b e x + ((360A b + 1080B a b )e + 240B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((945A a b + 945B a b)e + (135A b + 405B a b )d e + 90B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (840A a b + 280B a )e + (210A a b + 210B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (30A b + 90B a b )d e + 20B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 252A a e + (84A a b + 28B a )d e + (21A a b + 21B a b)d e +--R + +--R 3 2 3 3 4 +--R (3A b + 9B a b )d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R - 420B b e x + ((- 360A b - 1500B a b )e - 240B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1305A a b - 2025B a b )e + (- 135A b - 645B a b )d e +--R + +--R 4 2 2 +--R - 90B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 1785A a b - 1225B a b)e + (- 345A a b - 615B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 30A b - 180B a b )d e - 20B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 1092A a b - 280B a )e + (- 294A a b - 238B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 51A a b - 111B a b )d e + (- 3A b - 29B a b )d e - 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 252A a e + (- 84A a b - 28B a )d e + (- 21A a b - 21B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 3A a b - 9B a b )d e - 2B a b d +--R / +--R 15 11 15 14 10 +--R 2520b e x + (2520a e + 25200b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (25200a d e + 113400b d e )x + (113400a d e + 302400b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (302400a d e + 529200b d e )x + (529200a d e + 635040b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (635040a d e + 529200b d e )x + (529200a d e + 302400b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (302400a d e + 113400b d e )x + (113400a d e + 25200b d e )x +--R + +--R 9 6 10 5 10 5 +--R (25200a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1378 +r0:=-1/11*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^11)-1/110*(4*b*B*d+7*A*b*e-11*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^10)-1/330*b*(4*b*B*d+7*A*b*e-_ + 11*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^9)-_ + 1/1155*b^2*(4*b*B*d+7*A*b*e-11*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^8)-1/9240*b^2*(4*b*B*d+7*A*b*e-11*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 1320B b e x + ((- 1155A b - 3465B a b )e - 660B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 3080A a b - 3080B a b)e + (- 385A b - 1155B a b )d e +--R + +--R 3 2 2 +--R - 220B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 2772A a b - 924B a )e + (- 616A a b - 616B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 77A b - 231B a b )d e - 44B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 840A a e + (- 252A a b - 84B a )d e + (- 56A a b - 56B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 7A b - 21B a b )d e - 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 16 12 16 15 11 +--R 9240b e x + (9240a e + 101640b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (101640a d e + 508200b d e )x + (508200a d e + 1524600b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (1524600a d e + 3049200b d e )x + (3049200a d e + 4268880b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (4268880a d e + 4268880b d e )x + (4268880a d e + 3049200b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (3049200a d e + 1524600b d e )x + (1524600a d e + 508200b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (508200a d e + 101640b d e )x + (101640a d e + 9240b d e )x +--R + +--R 11 5 +--R 9240a d e +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 1320B b e x + ((- 1155A b - 3465B a b )e - 660B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 3080A a b - 3080B a b)e + (- 385A b - 1155B a b )d e +--R + +--R 3 2 2 +--R - 220B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 2772A a b - 924B a )e + (- 616A a b - 616B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 77A b - 231B a b )d e - 44B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 840A a e + (- 252A a b - 84B a )d e + (- 56A a b - 56B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 7A b - 21B a b )d e - 4B b d +--R / +--R 16 11 15 10 2 14 9 3 13 8 +--R 9240e x + 101640d e x + 508200d e x + 1524600d e x +--R + +--R 4 12 7 5 11 6 6 10 5 7 9 4 +--R 3049200d e x + 4268880d e x + 4268880d e x + 3049200d e x +--R + +--R 8 8 3 9 7 2 10 6 11 5 +--R 1524600d e x + 508200d e x + 101640d e x + 9240d e +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R 1320B b e x + ((1155A b + 3465B a b )e + 660B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (3080A a b + 3080B a b)e + (385A b + 1155B a b )d e +--R + +--R 3 2 2 +--R 220B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (2772A a b + 924B a )e + (616A a b + 616B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (77A b + 231B a b )d e + 44B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 840A a e + (252A a b + 84B a )d e + (56A a b + 56B a b)d e +--R + +--R 3 2 3 3 4 +--R (7A b + 21B a b )d e + 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R - 1320B b e x + ((- 1155A b - 4785B a b )e - 660B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 4235A a b - 6545B a b )e + (- 385A b - 1815B a b )d e +--R + +--R 4 2 2 +--R - 220B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 5852A a b - 4004B a b)e + (- 1001A a b - 1771B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 77A b - 451B a b )d e - 44B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 3612A a b - 924B a )e + (- 868A a b - 700B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 133A a b - 287B a b )d e + (- 7A b - 65B a b )d e - 4B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 840A a e + (- 252A a b - 84B a )d e + (- 56A a b - 56B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 7A a b - 21B a b )d e - 4B a b d +--R / +--R 16 12 16 15 11 +--R 9240b e x + (9240a e + 101640b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (101640a d e + 508200b d e )x + (508200a d e + 1524600b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (1524600a d e + 3049200b d e )x + (3049200a d e + 4268880b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (4268880a d e + 4268880b d e )x + (4268880a d e + 3049200b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (3049200a d e + 1524600b d e )x + (1524600a d e + 508200b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (508200a d e + 101640b d e )x + (101640a d e + 9240b d e )x +--R + +--R 11 5 +--R 9240a d e +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x +--R + +--R 12 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1378 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R m | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1378 +r0:=20*(b*d-a*e)^2*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4*(4+m)*(5+m)*(6+m)*(7+m))-_ + 5*(b*d-a*e)*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(a+b*x)*(d+e*x)^(1+m)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3*(5+m)*(6+m)*(7+m))+(A*b*e*(7+m)-_ + B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (b*e^2*(6+m)*(7+m))+B*(a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e*(7+m))+120*(b*d-a*e)^4*(A*b*e*(7+m)-B*(6*b*d+_ + a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6*_ + (2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m))-120*(b*d-a*e)^5*(A*b*e*(7+m)-_ + B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^7*(1+m)*(2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)*(a+b*x))-60*(b*d-_ + a*e)^3*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(a+b*x)*(d+e*x)^(1+m)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)) +--R +--R +--R (2) +--R 5 6 6 5 6 5 5 6 4 5 6 3 5 6 2 +--R B b e m + 21B b e m + 175B b e m + 735B b e m + 1624B b e m +--R + +--R 5 6 5 6 +--R 1764B b e m + 720B b e +--R * +--R 6 +--R x +--R + +--R 5 4 6 6 5 4 6 5 5 5 +--R (A b + 5B a b )e m + ((22A b + 110B a b )e - 6B b d e )m +--R + +--R 5 4 6 5 5 4 +--R ((190A b + 950B a b )e - 90B b d e )m +--R + +--R 5 4 6 5 5 3 +--R ((820A b + 4100B a b )e - 510B b d e )m +--R + +--R 5 4 6 5 5 2 +--R ((1849A b + 9245B a b )e - 1350B b d e )m +--R + +--R 5 4 6 5 5 +--R ((2038A b + 10190B a b )e - 1644B b d e )m +--R + +--R 5 4 6 5 5 +--R (840A b + 4200B a b )e - 720B b d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 6 6 +--R (5A a b + 10B a b )e m +--R + +--R 4 2 3 6 5 4 5 5 +--R ((115A a b + 230B a b )e + (- 5A b - 25B a b )d e )m +--R + +--R 4 2 3 6 5 4 5 +--R (1035A a b + 2070B a b )e + (- 85A b - 425B a b )d e +--R + +--R 5 2 4 +--R 30B b d e +--R * +--R 4 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (4625A a b + 9250B a b )e + (- 525A b - 2625B a b )d e +--R + +--R 5 2 4 +--R 300B b d e +--R * +--R 3 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (10720A a b + 21440B a b )e + (- 1475A b - 7375B a b )d e +--R + +--R 5 2 4 +--R 1050B b d e +--R * +--R 2 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (12060A a b + 24120B a b )e + (- 1870A b - 9350B a b )d e +--R + +--R 5 2 4 +--R 1500B b d e +--R * +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (5040A a b + 10080B a b )e + (- 840A b - 4200B a b )d e +--R + +--R 5 2 4 +--R 720B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 6 +--R (10A a b + 10B a b )e m +--R + +--R 2 3 3 2 6 4 2 3 5 5 +--R ((240A a b + 240B a b )e + (- 20A a b - 40B a b )d e )m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2260A a b + 2260B a b )e + (- 380A a b - 760B a b )d e +--R + +--R 5 4 2 4 +--R (20A b + 100B a b )d e +--R * +--R 4 +--R m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (10560A a b + 10560B a b )e + (- 2620A a b - 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b )d e + (- 120A b - 600B a b )d e +--R * +--R m +--R + +--R 5 6 4 5 2 5 +--R 5040A a d e + (- 12600A a b - 2520B a )d e +--R + +--R 3 2 4 3 4 2 3 3 2 4 3 +--R (16800A a b + 8400B a b)d e + (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 5 2 5 4 6 5 7 +--R (5040A a b + 10080B a b )d e + (- 840A b - 4200B a b )d e + 720B b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R e m + 28e m + 322e m + 1960e m + 6769e m + 13132e m + 13068e m +--R + +--R 7 +--R 5040e +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 6 6 7 5 6 7 4 6 7 3 6 7 2 +--R B b e m + 21B b e m + 175B b e m + 735B b e m + 1624B b e m +--R + +--R 6 7 6 7 +--R 1764B b e m + 720B b e +--R * +--R 8 +--R x +--R + +--R 6 5 7 6 6 6 +--R ((A b + 6B a b )e + B b d e )m +--R + +--R 6 5 7 6 6 5 +--R ((22A b + 131B a b )e + 15B b d e )m +--R + +--R 6 5 7 6 6 4 +--R ((190A b + 1125B a b )e + 85B b d e )m +--R + +--R 6 5 7 6 6 3 +--R ((820A b + 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a b + 17640B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 5460A a b - 12180B a b )d e + (840A b + 4560B a b )d e +--R + +--R 6 6 +--R - 720B b d e +--R * +--R m +--R + +--R 5 6 7 +--R (17640A a b + 2520B a )e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 6 6 +--R (A a e + (6A a b + B a )d e )m +--R + +--R 6 7 5 6 6 +--R 27A a e + (152A a b + 25B a )d e +--R + +--R 4 2 5 2 5 +--R (- 25A a b - 11B a b)d e +--R * +--R 5 +--R m +--R + +--R 6 7 5 6 6 +--R 295A a e + (1520A a b + 245B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 565A a b - 245B a b)d e + (80A a b + 70B a b )d e +--R * +--R 4 +--R m +--R + +--R 6 7 5 6 6 +--R 1665A a e + (7540A a b + 1175B a )d e +--R + +--R 4 2 5 2 5 +--R (- 4805A a b - 2035B a b)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (1520A a b + 1300B a b )d e + (- 180A a b - 300B a b )d e +--R * +--R 3 +--R m +--R + +--R 6 7 5 6 6 +--R 5104A a e + (18874A a b + 2754B a )d e +--R + +--R 4 2 5 2 5 +--R (- 18635A a b - 7555B a b)d e +--R + +--R 3 3 4 2 3 4 +--R 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5 4 2 4 +--R (2620A a b + 5240B a b )d e + (- 260A b - 1300B a b )d e +--R + +--R 5 3 3 +--R 120B b d e +--R * +--R 3 +--R m +--R + +--R 2 3 3 2 6 +--R (- 25450A a b - 25450B a b )e +--R + +--R 4 2 3 5 +--R (8020A a b + 16040B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 1060A b - 5300B a b )d e + 720B b d e +--R * +--R 2 +--R m +--R + +--R 2 3 3 2 6 +--R (- 29520A a b - 29520B a b )e +--R + +--R 4 2 3 5 +--R (10800A a b + 21600B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 1660A b - 8300B a b )d e + 1320B b d e +--R * +--R m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 12600A a b - 12600B a b )e + (5040A a b + 10080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 840A b - 4200B a b )d e + 720B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 6 +--R (- 10A a b - 5B a b)e m +--R + +--R 3 2 4 6 2 3 3 2 5 5 +--R ((- 250A a b - 125B a b)e + (30A a b + 30B a b )d e )m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 2470A a b - 1235B a b)e + (630A a b + 630B a b )d e +--R + +--R 4 2 3 2 4 +--R (- 60A a b - 120B a b )d e +--R * +--R 4 +--R m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 12190A a b - 6095B a b)e + (4890A a b + 4890B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 960A a b - 1920B a b )d e + (60A b + 300B a b )d e +--R * +--R 3 +--R m +--R + +--R 3 2 4 6 +--R (- 31120A a b - 15560B a b)e +--R + +--R 2 3 3 2 5 +--R (17010A a b + 17010B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 4980A a b - 9960B a b )d e + (600A b + 3000B a b )d e +--R + +--R 5 4 2 +--R - 360B b d e +--R * +--R 2 +--R m +--R + +--R 3 2 4 6 +--R (- 37960A a b - 18980B a b)e +--R + +--R 2 3 3 2 5 +--R (25320A a b + 25320B a b )d e +--R + +--R 4 2 3 2 4 +--R (- 9120A a b - 18240B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (1380A b + 6900B a b )d e - 1080B b d e +--R * +--R m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 16800A a b - 8400B a b)e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 5040A a b - 10080B a b )d e + (840A b + 4200B a b )d e +--R + +--R 5 4 2 +--R - 720B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 6 +--R (- 5A a b - B a )e m +--R + +--R 4 5 6 3 2 4 5 5 +--R ((- 130A a b - 26B a )e + (20A a b + 10B a b)d e )m +--R + +--R 4 5 6 3 2 4 5 +--R (- 1350A a b - 270B a )e + (460A a b + 230B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 60A a b - 60B a b )d e +--R * +--R 4 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (- 7100A a b - 1420B a )e + (4020A a b + 2010B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 1140A a b - 1140B a b )d e + (120A a b + 240B a b )d e +--R * +--R 3 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (- 19645A a b - 3929B a )e + (16340A a b + 8170B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 7500A a b - 7500B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (1680A a b + 3360B a b )d e + (- 120A b - 600B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (- 26370A a b - 5274B a )e + (29560A a b + 14780B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 19020A a b - 19020B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (6600A a b + 13200B a b )d e + (- 960A b - 4800B a b )d e +--R + +--R 5 5 +--R 720B b d e +--R * +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (- 12600A a b - 2520B a )e + (16800A a b + 8400B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (5040A a b + 10080B a b )d e + (- 840A b - 4200B a b )d e +--R + +--R 5 5 +--R 720B b d e +--R * +--R x +--R + +--R 5 6 6 5 6 4 5 5 5 +--R - A a e m + (- 27A a e + (5A a b + B a )d e )m +--R + +--R 5 6 4 5 5 +--R - 295A a e + (125A a b + 25B a )d e +--R + +--R 3 2 4 2 4 +--R (- 20A a b - 10B a b)d e +--R * +--R 4 +--R m +--R + +--R 5 6 4 5 5 +--R - 1665A a e + (1225A a b + 245B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 440A a b - 220B a b)d e + (60A a b + 60B a b )d e +--R * +--R 3 +--R m +--R + +--R 5 6 4 5 5 +--R - 5104A a e + (5875A a b + 1175B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 3580A a b - 1790B a b)d e + (1080A a b + 1080B a b )d e +--R + +--R 4 2 3 4 2 +--R (- 120A a b - 240B a b )d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 5 5 +--R - 8028A a e + (13770A a b + 2754B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 12760A a b - 6380B a b)d e + (6420A a b + 6420B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 1560A a b - 3120B a b )d e + (120A b + 600B a b )d e +--R * +--R m +--R + +--R 5 6 4 5 5 +--R - 5040A a e + (12600A a b + 2520B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 16800A a b - 8400B a b)d e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 5040A a b - 10080B a b )d e + (840A b + 4200B a b )d e +--R + +--R 5 6 +--R - 720B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m + 13132b e m +--R + +--R 7 7 +--R 13068b e m + 5040b e +--R * +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a e m + 28a e m + 322a e m + 1960a e m + 6769a e m + 13132a e m +--R + +--R 7 7 +--R 13068a e m + 5040a e +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 1378 +t0:=(A+B*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 11 4 3 6 4 5 10 +--R B b e x + ((A b + 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 6 4 3 5 4 2 4 9 +--R ((4A a b + 6B a b )e + (6A b + 24B a b )d e + 15B b d e )x +--R + +--R 2 2 3 6 3 2 2 5 +--R (6A a b + 4B a b)e + (24A a b + 36B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (15A b + 60B a b )d e + 20B b d e +--R * +--R 8 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (4A a b + B a )e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 4 4 2 +--R (60A a b + 90B a b )d e + (20A b + 80B a b )d e + 15B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 5 2 2 3 2 4 +--R A a e + (24A a b + 6B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 3 3 4 3 4 2 4 5 +--R (80A a b + 120B a b )d e + (15A b + 60B a b )d e + 6B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 6A a d e + (60A a b + 15B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (60A a b + 90B a b )d e + (6A b + 24B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A a d e + (80A a b + 20B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 5 4 3 6 +--R (24A a b + 36B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 4 4 2 2 2 3 5 +--R 20A a d e + (60A a b + 15B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 6 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 2 +--R (15A a d e + (24A a b + 6B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 5 3 4 6 4 6 +--R (6A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1378 +r0:=-1/858*(b*d-a*e)^2*(6*b*B*d-13*A*b*e+7*a*B*e)*(d+e*x)^7*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)+5/1716*(b*d-a*e)*(6*b*B*d-13*A*b*e+7*a*B*e)*_ + (a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-1/156*(6*b*B*d-_ + 13*A*b*e+7*a*B*e)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+_ + 1/13*B*(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 1/10296*(b*d-a*e)^4*(6*b*B*d-13*A*b*e+7*a*B*e)*(d+e*x)^7*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^6)+1/72072*(b*d-a*e)^5*(6*b*B*d-13*A*b*e+_ + 7*a*B*e)*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+_ + 1/2574*(b*d-a*e)^3*(6*b*B*d-13*A*b*e+7*a*B*e)*(a+b*x)*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 13 13 5 4 13 5 12 12 +--R 5544B b e x + ((6006A b + 30030B a b )e + 36036B b d e )x +--R + +--R 4 2 3 13 5 4 12 +--R (32760A a b + 65520B a b )e + (39312A b + 196560B a b )d e +--R + +--R 5 2 11 +--R 98280B b d e +--R * +--R 11 +--R x +--R + +--R 2 3 3 2 13 4 2 3 12 +--R (72072A a b + 72072B a b )e + (216216A a b + 432432B a b )d e +--R + +--R 5 4 2 11 5 3 10 +--R (108108A b + 540540B a b )d e + 144144B b d e +--R * +--R 10 +--R x +--R + +--R 3 2 4 13 2 3 3 2 12 +--R (80080A a b + 40040B a b)e + (480480A a b + 480480B a b )d e +--R + +--R 4 2 3 2 11 +--R (600600A a b + 1201200B a b )d e +--R + +--R 5 4 3 10 5 4 9 +--R (160160A b + 800800B a b )d e + 120120B b d e +--R * +--R 9 +--R x +--R + +--R 4 5 13 3 2 4 12 +--R (45045A a b + 9009B a )e + (540540A a b + 270270B a b)d e +--R + +--R 2 3 3 2 2 11 +--R (1351350A a b + 1351350B a b )d e +--R + +--R 4 2 3 3 10 +--R (900900A a b + 1801800B a b )d e +--R + +--R 5 4 4 9 5 5 8 +--R (135135A b + 675675B a b )d e + 54054B b d e +--R * +--R 8 +--R x +--R + +--R 5 13 4 5 12 +--R 10296A a e + (308880A a b + 61776B a )d e +--R + +--R 3 2 4 2 11 +--R (1544400A a b + 772200B a b)d e +--R + +--R 2 3 3 2 3 10 +--R (2059200A a b + 2059200B a b )d e +--R + +--R 4 2 3 4 9 5 4 5 8 +--R (772200A a b + 1544400B a b )d e + (61776A b + 308880B a b )d e +--R + +--R 5 6 7 +--R 10296B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 2 11 +--R 72072A a d e + (900900A a b + 180180B a )d e +--R + +--R 3 2 4 3 10 +--R (2402400A a b + 1201200B a b)d e +--R + +--R 2 3 3 2 4 9 +--R (1801800A a b + 1801800B a b )d e +--R + +--R 4 2 3 5 8 5 4 6 7 +--R (360360A a b + 720720B a b )d e + (12012A b + 60060B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 2 11 4 5 3 10 +--R 216216A a d e + (1441440A a b + 288288B a )d e +--R + +--R 3 2 4 4 9 +--R (2162160A a b + 1081080B a b)d e +--R + +--R 2 3 3 2 5 8 4 2 3 6 7 +--R (864864A a b + 864864B a b )d e + (72072A a b + 144144B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 3 10 4 5 4 9 +--R 360360A a d e + (1351350A a b + 270270B a )d e +--R + +--R 3 2 4 5 8 2 3 3 2 6 7 +--R (1081080A a b + 540540B a b)d e + (180180A a b + 180180B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 4 9 4 5 5 8 +--R 360360A a d e + (720720A a b + 144144B a )d e +--R + +--R 3 2 4 6 7 +--R (240240A a b + 120120B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 5 8 4 5 6 7 2 5 6 7 +--R (216216A a d e + (180180A a b + 36036B a )d e )x + 72072A a d e x +--R + +--R 5 7 6 4 5 8 5 +--R 10296A a d e + (- 6435A a b - 1287B a )d e +--R + +--R 3 2 4 9 4 2 3 3 2 10 3 +--R (2860A a b + 1430B a b)d e + (- 858A a b - 858B a b )d e +--R + +--R 4 2 3 11 2 5 4 12 5 13 +--R (156A a b + 312B a b )d e + (- 13A b - 65B a b )d e + 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 72072b e x + 72072a e +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 13 5 4 6 5 5 12 +--R 5544B b e x + ((6006A b + 30030B a b )e + 36036B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (32760A a b + 65520B a b )e + (39312A b + 196560B a b )d e +--R + +--R 5 2 4 +--R 98280B b d e +--R * +--R 11 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (72072A a b + 72072B a b )e + (216216A a b + 432432B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (108108A b + 540540B a b )d e + 144144B b d e +--R * +--R 10 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (80080A a b + 40040B a b)e + (480480A a b + 480480B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (600600A a b + 1201200B a b )d e + (160160A b + 800800B a b )d e +--R + +--R 5 4 2 +--R 120120B b d e +--R * +--R 9 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (45045A a b + 9009B a )e + (540540A a b + 270270B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (1351350A a b + 1351350B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (900900A a b + 1801800B a b )d e + (135135A b + 675675B a b )d e +--R + +--R 5 5 +--R 54054B b d e +--R * +--R 8 +--R x +--R + +--R 5 6 4 5 5 +--R 10296A a e + (308880A a b + 61776B a )d e +--R + +--R 3 2 4 2 4 +--R (1544400A a b + 772200B a b)d e +--R + +--R 2 3 3 2 3 3 +--R (2059200A a b + 2059200B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (772200A a b + 1544400B a b )d e + (61776A b + 308880B a b )d e +--R + +--R 5 6 +--R 10296B b d +--R * +--R 7 +--R x +--R + +--R 5 5 4 5 2 4 +--R 72072A a d e + (900900A a b + 180180B a )d e +--R + +--R 3 2 4 3 3 +--R (2402400A a b + 1201200B a b)d e +--R + +--R 2 3 3 2 4 2 +--R (1801800A a b + 1801800B a b )d e +--R + +--R 4 2 3 5 5 4 6 +--R (360360A a b + 720720B a b )d e + (12012A b + 60060B a b )d +--R * +--R 6 +--R x +--R + +--R 5 2 4 4 5 3 3 +--R 216216A a d e + (1441440A a b + 288288B a )d e +--R + +--R 3 2 4 4 2 2 3 3 2 5 +--R (2162160A a b + 1081080B a b)d e + (864864A a b + 864864B a b )d e +--R + +--R 4 2 3 6 +--R (72072A a b + 144144B a b )d +--R * +--R 5 +--R x +--R + +--R 5 3 3 4 5 4 2 +--R 360360A a d e + (1351350A a b + 270270B a )d e +--R + +--R 3 2 4 5 2 3 3 2 6 +--R (1081080A a b + 540540B a b)d e + (180180A a b + 180180B a b )d +--R * +--R 4 +--R x +--R + +--R 5 4 2 4 5 5 +--R 360360A a d e + (720720A a b + 144144B a )d e +--R + +--R 3 2 4 6 +--R (240240A a b + 120120B a b)d +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 6 2 5 6 +--R (216216A a d e + (180180A a b + 36036B a )d )x + 72072A a d x +--R / +--R 72072 +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 13 13 +--R - 5544B b e x +--R + +--R 5 4 13 5 12 12 +--R ((- 6006A b - 30030B a b )e - 36036B b d e )x +--R + +--R 4 2 3 13 +--R (- 32760A a b - 65520B a b )e +--R + +--R 5 4 12 5 2 11 +--R (- 39312A b - 196560B a b )d e - 98280B b d e +--R * +--R 11 +--R x +--R + +--R 2 3 3 2 13 +--R (- 72072A a b - 72072B a b )e +--R + +--R 4 2 3 12 +--R (- 216216A a b - 432432B a b )d e +--R + +--R 5 4 2 11 5 3 10 +--R (- 108108A b - 540540B a b )d e - 144144B b d e +--R * +--R 10 +--R x +--R + +--R 3 2 4 13 +--R (- 80080A a b - 40040B a b)e +--R + +--R 2 3 3 2 12 +--R (- 480480A a b - 480480B a b )d e +--R + +--R 4 2 3 2 11 +--R (- 600600A a b - 1201200B a b )d e +--R + +--R 5 4 3 10 5 4 9 +--R (- 160160A b - 800800B a b )d e - 120120B b d e +--R * +--R 9 +--R x +--R + +--R 4 5 13 +--R (- 45045A a b - 9009B a )e +--R + +--R 3 2 4 12 +--R (- 540540A a b - 270270B a b)d e +--R + +--R 2 3 3 2 2 11 +--R (- 1351350A a b - 1351350B a b )d e +--R + +--R 4 2 3 3 10 +--R (- 900900A a b - 1801800B a b )d e +--R + +--R 5 4 4 9 5 5 8 +--R (- 135135A b - 675675B a b )d e - 54054B b d e +--R * +--R 8 +--R x +--R + +--R 5 13 4 5 12 +--R - 10296A a e + (- 308880A a b - 61776B a )d e +--R + +--R 3 2 4 2 11 +--R (- 1544400A a b - 772200B a b)d e +--R + +--R 2 3 3 2 3 10 +--R (- 2059200A a b - 2059200B a b )d e +--R + +--R 4 2 3 4 9 +--R (- 772200A a b - 1544400B a b )d e +--R + +--R 5 4 5 8 5 6 7 +--R (- 61776A b - 308880B a b )d e - 10296B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 2 11 +--R - 72072A a d e + (- 900900A a b - 180180B a )d e +--R + +--R 3 2 4 3 10 +--R (- 2402400A a b - 1201200B a b)d e +--R + +--R 2 3 3 2 4 9 +--R (- 1801800A a b - 1801800B a b )d e +--R + +--R 4 2 3 5 8 +--R (- 360360A a b - 720720B a b )d e +--R + +--R 5 4 6 7 +--R (- 12012A b - 60060B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 2 11 4 5 3 10 +--R - 216216A a d e + (- 1441440A a b - 288288B a )d e +--R + +--R 3 2 4 4 9 +--R (- 2162160A a b - 1081080B a b)d e +--R + +--R 2 3 3 2 5 8 +--R (- 864864A a b - 864864B a b )d e +--R + +--R 4 2 3 6 7 +--R (- 72072A a b - 144144B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 3 10 4 5 4 9 +--R - 360360A a d e + (- 1351350A a b - 270270B a )d e +--R + +--R 3 2 4 5 8 +--R (- 1081080A a b - 540540B a b)d e +--R + +--R 2 3 3 2 6 7 +--R (- 180180A a b - 180180B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 4 9 4 5 5 8 +--R - 360360A a d e + (- 720720A a b - 144144B a )d e +--R + +--R 3 2 4 6 7 +--R (- 240240A a b - 120120B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 5 8 4 5 6 7 2 +--R (- 216216A a d e + (- 180180A a b - 36036B a )d e )x +--R + +--R 5 6 7 5 7 6 4 5 8 5 +--R - 72072A a d e x - 10296A a d e + (6435A a b + 1287B a )d e +--R + +--R 3 2 4 9 4 2 3 3 2 10 3 +--R (- 2860A a b - 1430B a b)d e + (858A a b + 858B a b )d e +--R + +--R 4 2 3 11 2 5 4 12 5 13 +--R (- 156A a b - 312B a b )d e + (13A b + 65B a b )d e - 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 13 14 6 5 13 6 12 13 +--R 5544B b e x + ((6006A b + 35574B a b )e + 36036B b d e )x +--R + +--R 5 2 4 13 6 5 12 +--R (38766A a b + 95550B a b )e + (39312A b + 232596B a b )d e +--R + +--R 6 2 11 +--R 98280B b d e +--R * +--R 12 +--R x +--R + +--R 2 4 3 3 13 5 2 4 12 +--R (104832A a b + 137592B a b )e + (255528A a b + 628992B a b )d e +--R + +--R 6 5 2 11 6 3 10 +--R (108108A b + 638820B a b )d e + 144144B b d e +--R * +--R 11 +--R x +--R + +--R 3 3 4 2 13 2 4 3 3 12 +--R (152152A a b + 112112B a b )e + (696696A a b + 912912B a b )d e +--R + +--R 5 2 4 2 11 +--R (708708A a b + 1741740B a b )d e +--R + +--R 6 5 3 10 6 4 9 +--R (160160A b + 944944B a b )d e + 120120B b d e +--R * +--R 10 +--R x +--R + +--R 4 2 5 13 3 3 4 2 12 +--R (125125A a b + 49049B a b)e + (1021020A a b + 750750B a b )d e +--R + +--R 2 4 3 3 2 11 +--R (1951950A a b + 2552550B a b )d e +--R + +--R 5 2 4 3 10 +--R (1061060A a b + 2602600B a b )d e +--R + +--R 6 5 4 9 6 5 8 +--R (135135A b + 795795B a b )d e + 54054B b d e +--R * +--R 9 +--R x +--R + +--R 5 6 13 4 2 5 12 +--R (55341A a b + 9009B a )e + (849420A a b + 332046B a b)d e +--R + +--R 3 3 4 2 2 11 +--R (2895750A a b + 2123550B a b )d e +--R + +--R 2 4 3 3 3 10 +--R (2960100A a b + 3861000B a b )d e +--R + +--R 5 2 4 4 9 6 5 5 8 +--R (907335A a b + 2220075B a b )d e + (61776A b + 362934B a b )d e +--R + +--R 6 6 7 +--R 10296B b d e +--R * +--R 8 +--R x +--R + +--R 6 13 5 6 12 +--R 10296A a e + (380952A a b + 61776B a )d e +--R + +--R 4 2 5 2 11 +--R (2445300A a b + 952380B a b)d e +--R + +--R 3 3 4 2 3 10 +--R (4461600A a b + 3260400B a b )d e +--R + +--R 2 4 3 3 4 9 +--R (2574000A a b + 3346200B a b )d e +--R + +--R 5 2 4 5 8 6 5 6 7 +--R (422136A a b + 1029600B a b )d e + (12012A b + 70356B a b )d e +--R * +--R 7 +--R x +--R + +--R 6 12 5 6 2 11 +--R 72072A a d e + (1117116A a b + 180180B a )d e +--R + +--R 4 2 5 3 10 +--R (3843840A a b + 1489488B a b)d e +--R + +--R 3 3 4 2 4 9 +--R (3963960A a b + 2882880B a b )d e +--R + +--R 2 4 3 3 5 8 5 2 4 6 7 +--R (1225224A a b + 1585584B a b )d e + (84084A a b + 204204B a b )d e +--R * +--R 6 +--R x +--R + +--R 6 2 11 5 6 3 10 +--R 216216A a d e + (1801800A a b + 288288B a )d e +--R + +--R 4 2 5 4 9 +--R (3513510A a b + 1351350B a b)d e +--R + +--R 3 3 4 2 5 8 2 4 3 3 6 7 +--R (1945944A a b + 1405404B a b )d e + (252252A a b + 324324B a b )d e +--R * +--R 5 +--R x +--R + +--R 6 3 10 5 6 4 9 +--R 360360A a d e + (1711710A a b + 270270B a )d e +--R + +--R 4 2 5 5 8 3 3 4 2 6 7 +--R (1801800A a b + 684684B a b)d e + (420420A a b + 300300B a b )d e +--R * +--R 4 +--R x +--R + +--R 6 4 9 5 6 5 8 +--R 360360A a d e + (936936A a b + 144144B a )d e +--R + +--R 4 2 5 6 7 +--R (420420A a b + 156156B a b)d e +--R * +--R 3 +--R x +--R + +--R 6 5 8 5 6 6 7 2 6 6 7 +--R (216216A a d e + (252252A a b + 36036B a )d e )x + 72072A a d e x +--R / +--R 7 7 +--R 72072b e x + 72072a e +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 12 5 4 6 5 5 11 +--R B b e x + ((A b + 5B a b )e + 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 10 +--R ((5A a b + 10B a b )e + (6A b + 30B a b )d e + 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (10A a b + 10B a b )e + (30A a b + 60B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (15A b + 75B a b )d e + 20B b d e +--R * +--R 9 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (10A a b + 5B a b)e + (60A a b + 60B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (75A a b + 150B a b )d e + (20A b + 100B a b )d e + 15B b d e +--R * +--R 8 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (5A a b + B a )e + (60A a b + 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (150A a b + 150B a b )d e + (100A a b + 200B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (15A b + 75B a b )d e + 6B b d e +--R * +--R 7 +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R A a e + (30A a b + 6B a )d e + (150A a b + 75B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (200A a b + 200B a b )d e + (75A a b + 150B a b )d e +--R + +--R 5 4 5 5 6 +--R (6A b + 30B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 5 5 4 5 2 4 3 2 4 3 3 +--R 6A a d e + (75A a b + 15B a )d e + (200A a b + 100B a b)d e +--R + +--R 2 3 3 2 4 2 4 2 3 5 +--R (150A a b + 150B a b )d e + (30A a b + 60B a b )d e +--R + +--R 5 4 6 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 5 2 4 4 5 3 3 3 2 4 4 2 +--R 15A a d e + (100A a b + 20B a )d e + (150A a b + 75B a b)d e +--R + +--R 2 3 3 2 5 4 2 3 6 +--R (60A a b + 60B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 3 4 5 4 2 3 2 4 5 +--R 20A a d e + (75A a b + 15B a )d e + (60A a b + 30B a b)d e +--R + +--R 2 3 3 2 6 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 4 2 4 5 5 3 2 4 6 2 +--R (15A a d e + (30A a b + 6B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 5 4 5 6 5 6 +--R (6A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 13 6 5 6 6 5 12 +--R - B b e x + ((- A b - 6B a b )e - 6B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 11 +--R ((- 6A a b - 15B a b )e + (- 6A b - 36B a b )d e - 15B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 15A a b - 20B a b )e + (- 36A a b - 90B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 15A b - 90B a b )d e - 20B b d e +--R * +--R 10 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 20A a b - 15B a b )e + (- 90A a b - 120B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (- 90A a b - 225B a b )d e + (- 20A b - 120B a b )d e - 15B b d e +--R * +--R 9 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 15A a b - 6B a b)e + (- 120A a b - 90B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 225A a b - 300B a b )d e + (- 120A a b - 300B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 15A b - 90B a b )d e - 6B b d e +--R * +--R 8 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 6A a b - B a )e + (- 90A a b - 36B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 300A a b - 225B a b )d e + (- 300A a b - 400B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 90A a b - 225B a b )d e + (- 6A b - 36B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - A a e + (- 36A a b - 6B a )d e + (- 225A a b - 90B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 400A a b - 300B a b )d e + (- 225A a b - 300B a b )d e +--R + +--R 5 2 4 5 6 5 6 +--R (- 36A a b - 90B a b )d e + (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 6 5 5 6 2 4 4 2 5 3 3 +--R - 6A a d e + (- 90A a b - 15B a )d e + (- 300A a b - 120B a b)d e +--R + +--R 3 3 4 2 4 2 2 4 3 3 5 +--R (- 300A a b - 225B a b )d e + (- 90A a b - 120B a b )d e +--R + +--R 5 2 4 6 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 6 2 4 5 6 3 3 +--R - 15A a d e + (- 120A a b - 20B a )d e +--R + +--R 4 2 5 4 2 3 3 4 2 5 +--R (- 225A a b - 90B a b)d e + (- 120A a b - 90B a b )d e +--R + +--R 2 4 3 3 6 +--R (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 3 5 6 4 2 4 2 5 5 +--R - 20A a d e + (- 90A a b - 15B a )d e + (- 90A a b - 36B a b)d e +--R + +--R 3 3 4 2 6 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 4 2 5 6 5 4 2 5 6 2 +--R (- 15A a d e + (- 36A a b - 6B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 5 5 6 6 6 6 +--R (- 6A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1378 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 10 4 3 5 4 4 9 +--R B b e x + ((A b + 4B a b )e + 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 8 +--R ((4A a b + 6B a b )e + (5A b + 20B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (6A a b + 4B a b)e + (20A a b + 30B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (10A b + 40B a b )d e + 10B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b + B a )e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (40A a b + 60B a b )d e + (10A b + 40B a b )d e + 5B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (20A a b + 5B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (40A a b + 60B a b )d e + (5A b + 20B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R 5A a d e + (40A a b + 10B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 4 4 3 5 +--R (20A a b + 30B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 3 2 2 2 3 4 +--R 10A a d e + (40A a b + 10B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 5 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 2 +--R (10A a d e + (20A a b + 5B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 4 3 4 5 4 5 +--R (5A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1378 +r0:=1/99*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^6*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)-1/44*(b*d-a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)+1/22*(2*A*b*e-B*(b*d+_ + a*e))*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+1/12*B*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)+1/924*(b*d-a*e)^4*(2*A*b*e-_ + B*(b*d+a*e))*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)-_ + 1/5544*(b*d-a*e)^5*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^7*(a+b*x))-1/264*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*_ + (a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 12 12 5 4 12 5 11 11 +--R 462B b e x + ((504A b + 2520B a b )e + 2520B b d e )x +--R + +--R 4 2 3 12 5 4 11 +--R (2772A a b + 5544B a b )e + (2772A b + 13860B a b )d e +--R + +--R 5 2 10 +--R 5544B b d e +--R * +--R 10 +--R x +--R + +--R 2 3 3 2 12 4 2 3 11 +--R (6160A a b + 6160B a b )e + (15400A a b + 30800B a b )d e +--R + +--R 5 4 2 10 5 3 9 +--R (6160A b + 30800B a b )d e + 6160B b d e +--R * +--R 9 +--R x +--R + +--R 3 2 4 12 2 3 3 2 11 +--R (6930A a b + 3465B a b)e + (34650A a b + 34650B a b )d e +--R + +--R 4 2 3 2 10 5 4 3 9 +--R (34650A a b + 69300B a b )d e + (6930A b + 34650B a b )d e +--R + +--R 5 4 8 +--R 3465B b d e +--R * +--R 8 +--R x +--R + +--R 4 5 12 3 2 4 11 +--R (3960A a b + 792B a )e + (39600A a b + 19800B a b)d e +--R + +--R 2 3 3 2 2 10 4 2 3 3 9 +--R (79200A a b + 79200B a b )d e + (39600A a b + 79200B a b )d e +--R + +--R 5 4 4 8 5 5 7 +--R (3960A b + 19800B a b )d e + 792B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 11 +--R 924A a e + (23100A a b + 4620B a )d e +--R + +--R 3 2 4 2 10 2 3 3 2 3 9 +--R (92400A a b + 46200B a b)d e + (92400A a b + 92400B a b )d e +--R + +--R 4 2 3 4 8 5 4 5 7 +--R (23100A a b + 46200B a b )d e + (924A b + 4620B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 11 4 5 2 10 +--R 5544A a d e + (55440A a b + 11088B a )d e +--R + +--R 3 2 4 3 9 2 3 3 2 4 8 +--R (110880A a b + 55440B a b)d e + (55440A a b + 55440B a b )d e +--R + +--R 4 2 3 5 7 +--R (5544A a b + 11088B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 2 10 4 5 3 9 +--R 13860A a d e + (69300A a b + 13860B a )d e +--R + +--R 3 2 4 4 8 2 3 3 2 5 7 +--R (69300A a b + 34650B a b)d e + (13860A a b + 13860B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 3 9 4 5 4 8 +--R 18480A a d e + (46200A a b + 9240B a )d e +--R + +--R 3 2 4 5 7 +--R (18480A a b + 9240B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 4 8 4 5 5 7 2 5 5 7 +--R (13860A a d e + (13860A a b + 2772B a )d e )x + 5544A a d e x +--R + +--R 5 6 6 4 5 7 5 3 2 4 8 4 +--R 924A a d e + (- 660A a b - 132B a )d e + (330A a b + 165B a b)d e +--R + +--R 2 3 3 2 9 3 4 2 3 10 2 +--R (- 110A a b - 110B a b )d e + (22A a b + 44B a b )d e +--R + +--R 5 4 11 5 12 +--R (- 2A b - 10B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 5544b e x + 5544a e +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 12 5 4 5 5 4 11 +--R 462B b e x + ((504A b + 2520B a b )e + 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (2772A a b + 5544B a b )e + (2772A b + 13860B a b )d e +--R + +--R 5 2 3 +--R 5544B b d e +--R * +--R 10 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (6160A a b + 6160B a b )e + (15400A a b + 30800B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (6160A b + 30800B a b )d e + 6160B b d e +--R * +--R 9 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (6930A a b + 3465B a b)e + (34650A a b + 34650B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (34650A a b + 69300B a b )d e + (6930A b + 34650B a b )d e +--R + +--R 5 4 +--R 3465B b d e +--R * +--R 8 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (3960A a b + 792B a )e + (39600A a b + 19800B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (79200A a b + 79200B a b )d e + (39600A a b + 79200B a b )d e +--R + +--R 5 4 4 5 5 +--R (3960A b + 19800B a b )d e + 792B b d +--R * +--R 7 +--R x +--R + +--R 5 5 4 5 4 +--R 924A a e + (23100A a b + 4620B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (92400A a b + 46200B a b)d e + (92400A a b + 92400B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (23100A a b + 46200B a b )d e + (924A b + 4620B a b )d +--R * +--R 6 +--R x +--R + +--R 5 4 4 5 2 3 +--R 5544A a d e + (55440A a b + 11088B a )d e +--R + +--R 3 2 4 3 2 2 3 3 2 4 +--R (110880A a b + 55440B a b)d e + (55440A a b + 55440B a b )d e +--R + +--R 4 2 3 5 +--R (5544A a b + 11088B a b )d +--R * +--R 5 +--R x +--R + +--R 5 2 3 4 5 3 2 +--R 13860A a d e + (69300A a b + 13860B a )d e +--R + +--R 3 2 4 4 2 3 3 2 5 +--R (69300A a b + 34650B a b)d e + (13860A a b + 13860B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 2 4 5 4 +--R 18480A a d e + (46200A a b + 9240B a )d e +--R + +--R 3 2 4 5 +--R (18480A a b + 9240B a b)d +--R * +--R 3 +--R x +--R + +--R 5 4 4 5 5 2 5 5 +--R (13860A a d e + (13860A a b + 2772B a )d )x + 5544A a d x +--R / +--R 5544 +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 12 12 5 4 12 5 11 11 +--R - 462B b e x + ((- 504A b - 2520B a b )e - 2520B b d e )x +--R + +--R 4 2 3 12 5 4 11 +--R (- 2772A a b - 5544B a b )e + (- 2772A b - 13860B a b )d e +--R + +--R 5 2 10 +--R - 5544B b d e +--R * +--R 10 +--R x +--R + +--R 2 3 3 2 12 +--R (- 6160A a b - 6160B a b )e +--R + +--R 4 2 3 11 +--R (- 15400A a b - 30800B a b )d e +--R + +--R 5 4 2 10 5 3 9 +--R (- 6160A b - 30800B a b )d e - 6160B b d e +--R * +--R 9 +--R x +--R + +--R 3 2 4 12 +--R (- 6930A a b - 3465B a b)e +--R + +--R 2 3 3 2 11 +--R (- 34650A a b - 34650B a b )d e +--R + +--R 4 2 3 2 10 +--R (- 34650A a b - 69300B a b )d e +--R + +--R 5 4 3 9 5 4 8 +--R (- 6930A b - 34650B a b )d e - 3465B b d e +--R * +--R 8 +--R x +--R + +--R 4 5 12 3 2 4 11 +--R (- 3960A a b - 792B a )e + (- 39600A a b - 19800B a b)d e +--R + +--R 2 3 3 2 2 10 +--R (- 79200A a b - 79200B a b )d e +--R + +--R 4 2 3 3 9 +--R (- 39600A a b - 79200B a b )d e +--R + +--R 5 4 4 8 5 5 7 +--R (- 3960A b - 19800B a b )d e - 792B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 11 +--R - 924A a e + (- 23100A a b - 4620B a )d e +--R + +--R 3 2 4 2 10 +--R (- 92400A a b - 46200B a b)d e +--R + +--R 2 3 3 2 3 9 +--R (- 92400A a b - 92400B a b )d e +--R + +--R 4 2 3 4 8 5 4 5 7 +--R (- 23100A a b - 46200B a b )d e + (- 924A b - 4620B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 11 4 5 2 10 +--R - 5544A a d e + (- 55440A a b - 11088B a )d e +--R + +--R 3 2 4 3 9 +--R (- 110880A a b - 55440B a b)d e +--R + +--R 2 3 3 2 4 8 +--R (- 55440A a b - 55440B a b )d e +--R + +--R 4 2 3 5 7 +--R (- 5544A a b - 11088B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 2 10 4 5 3 9 +--R - 13860A a d e + (- 69300A a b - 13860B a )d e +--R + +--R 3 2 4 4 8 +--R (- 69300A a b - 34650B a b)d e +--R + +--R 2 3 3 2 5 7 +--R (- 13860A a b - 13860B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 3 9 4 5 4 8 +--R - 18480A a d e + (- 46200A a b - 9240B a )d e +--R + +--R 3 2 4 5 7 +--R (- 18480A a b - 9240B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 4 8 4 5 5 7 2 5 5 7 +--R (- 13860A a d e + (- 13860A a b - 2772B a )d e )x - 5544A a d e x +--R + +--R 5 6 6 4 5 7 5 +--R - 924A a d e + (660A a b + 132B a )d e +--R + +--R 3 2 4 8 4 2 3 3 2 9 3 +--R (- 330A a b - 165B a b)d e + (110A a b + 110B a b )d e +--R + +--R 4 2 3 10 2 5 4 11 5 12 +--R (- 22A a b - 44B a b )d e + (2A b + 10B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 12 13 6 5 12 6 11 12 +--R 462B b e x + ((504A b + 2982B a b )e + 2520B b d e )x +--R + +--R 5 2 4 12 6 5 11 +--R (3276A a b + 8064B a b )e + (2772A b + 16380B a b )d e +--R + +--R 6 2 10 +--R 5544B b d e +--R * +--R 11 +--R x +--R + +--R 2 4 3 3 12 5 2 4 11 +--R (8932A a b + 11704B a b )e + (18172A a b + 44660B a b )d e +--R + +--R 6 5 2 10 6 3 9 +--R (6160A b + 36344B a b )d e + 6160B b d e +--R * +--R 10 +--R x +--R + +--R 3 3 4 2 12 2 4 3 3 11 +--R (13090A a b + 9625B a b )e + (50050A a b + 65450B a b )d e +--R + +--R 5 2 4 2 10 6 5 3 9 +--R (40810A a b + 100100B a b )d e + (6930A b + 40810B a b )d e +--R + +--R 6 4 8 +--R 3465B b d e +--R * +--R 9 +--R x +--R + +--R 4 2 5 12 3 3 4 2 11 +--R (10890A a b + 4257B a b)e + (74250A a b + 54450B a b )d e +--R + +--R 2 4 3 3 2 10 5 2 4 3 9 +--R (113850A a b + 148500B a b )d e + (46530A a b + 113850B a b )d e +--R + +--R 6 5 4 8 6 5 7 +--R (3960A b + 23265B a b )d e + 792B b d e +--R * +--R 8 +--R x +--R + +--R 5 6 12 4 2 5 11 +--R (4884A a b + 792B a )e + (62700A a b + 24420B a b)d e +--R + +--R 3 3 4 2 2 10 +--R (171600A a b + 125400B a b )d e +--R + +--R 2 4 3 3 3 9 5 2 4 4 8 +--R (132000A a b + 171600B a b )d e + (27060A a b + 66000B a b )d e +--R + +--R 6 5 5 7 +--R (924A b + 5412B a b )d e +--R * +--R 7 +--R x +--R + +--R 6 12 5 6 11 +--R 924A a e + (28644A a b + 4620B a )d e +--R + +--R 4 2 5 2 10 3 3 4 2 3 9 +--R (147840A a b + 57288B a b)d e + (203280A a b + 147840B a b )d e +--R + +--R 2 4 3 3 4 8 5 2 4 5 7 +--R (78540A a b + 101640B a b )d e + (6468A a b + 15708B a b )d e +--R * +--R 6 +--R x +--R + +--R 6 11 5 6 2 10 +--R 5544A a d e + (69300A a b + 11088B a )d e +--R + +--R 4 2 5 3 9 3 3 4 2 4 8 +--R (180180A a b + 69300B a b)d e + (124740A a b + 90090B a b )d e +--R + +--R 2 4 3 3 5 7 +--R (19404A a b + 24948B a b )d e +--R * +--R 5 +--R x +--R + +--R 6 2 10 5 6 3 9 +--R 13860A a d e + (87780A a b + 13860B a )d e +--R + +--R 4 2 5 4 8 3 3 4 2 5 7 +--R (115500A a b + 43890B a b)d e + (32340A a b + 23100B a b )d e +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 6 4 8 +--R 18480A a d e + (60060A a b + 9240B a )d e +--R + +--R 4 2 5 5 7 +--R (32340A a b + 12012B a b)d e +--R * +--R 3 +--R x +--R + +--R 6 4 8 5 6 5 7 2 6 5 7 +--R (13860A a d e + (19404A a b + 2772B a )d e )x + 5544A a d e x +--R / +--R 7 7 +--R 5544b e x + 5544a e +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 5 11 5 4 5 5 4 10 +--R B b e x + ((A b + 5B a b )e + 5B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 9 +--R ((5A a b + 10B a b )e + (5A b + 25B a b )d e + 10B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (10A a b + 10B a b )e + (25A a b + 50B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (10A b + 50B a b )d e + 10B b d e +--R * +--R 8 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (10A a b + 5B a b)e + (50A a b + 50B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (50A a b + 100B a b )d e + (10A b + 50B a b )d e + 5B b d e +--R * +--R 7 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (5A a b + B a )e + (50A a b + 25B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (100A a b + 100B a b )d e + (50A a b + 100B a b )d e +--R + +--R 5 4 4 5 5 +--R (5A b + 25B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R A a e + (25A a b + 5B a )d e + (100A a b + 50B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (100A a b + 100B a b )d e + (25A a b + 50B a b )d e +--R + +--R 5 4 5 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 5A a d e + (50A a b + 10B a )d e + (100A a b + 50B a b)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (50A a b + 50B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 5 3 2 3 2 4 4 +--R 10A a d e + (50A a b + 10B a )d e + (50A a b + 25B a b)d e +--R + +--R 2 3 3 2 5 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 3 2 4 5 4 3 2 4 5 2 +--R (10A a d e + (25A a b + 5B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 4 4 5 5 5 5 +--R (5A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 12 6 5 5 6 4 11 +--R - B b e x + ((- A b - 6B a b )e - 5B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 10 +--R ((- 6A a b - 15B a b )e + (- 5A b - 30B a b )d e - 10B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 15A a b - 20B a b )e + (- 30A a b - 75B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 10A b - 60B a b )d e - 10B b d e +--R * +--R 9 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 20A a b - 15B a b )e + (- 75A a b - 100B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 60A a b - 150B a b )d e + (- 10A b - 60B a b )d e - 5B b d e +--R * +--R 8 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 15A a b - 6B a b)e + (- 100A a b - 75B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 150A a b - 200B a b )d e + (- 60A a b - 150B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 5A b - 30B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 6A a b - B a )e + (- 75A a b - 30B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 200A a b - 150B a b )d e + (- 150A a b - 200B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 30A a b - 75B a b )d e + (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 6 5 5 6 4 4 2 5 2 3 +--R - A a e + (- 30A a b - 5B a )d e + (- 150A a b - 60B a b)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (- 200A a b - 150B a b )d e + (- 75A a b - 100B a b )d e +--R + +--R 5 2 4 5 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 6 4 5 6 2 3 4 2 5 3 2 +--R - 5A a d e + (- 60A a b - 10B a )d e + (- 150A a b - 60B a b)d e +--R + +--R 3 3 4 2 4 2 4 3 3 5 +--R (- 100A a b - 75B a b )d e + (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 2 3 5 6 3 2 4 2 5 4 +--R - 10A a d e + (- 60A a b - 10B a )d e + (- 75A a b - 30B a b)d e +--R + +--R 3 3 4 2 5 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 3 2 5 6 4 4 2 5 5 2 +--R (- 10A a d e + (- 30A a b - 5B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 4 5 6 5 6 5 +--R (- 5A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 1378 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 4 9 4 3 4 4 3 8 +--R B b e x + ((A b + 4B a b )e + 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((4A a b + 6B a b )e + (4A b + 16B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (6A a b + 4B a b)e + (16A a b + 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (6A b + 24B a b )d e + 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (24A a b + 36B a b )d e + (4A b + 16B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R A a e + (16A a b + 4B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (16A a b + 24B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 4A a d e + (24A a b + 6B a )d e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 4 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (6A a d e + (16A a b + 4B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (4A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1378 +r0:=-1/1980*(b*d-a*e)^4*(6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^6*e)-1/660*(b*d-a*e)^2*(6*b*B*d-11*A*b*e+5*a*B*e)*_ + (a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^4*e)-2/495*(b*d-a*e)*_ + (6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^3*e)-1/110*(6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*_ + (d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+1/11*B*(a+b*x)*(d+_ + e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-1/2310*(b*d-a*e)^3*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6 +--R +--R +--R (2) +--R 10 4 10 10 9 4 10 3 9 +--R 1260B b e x + ((1386A b + 5670B a b )e + 5544B b d e )x +--R + +--R 9 2 8 4 10 9 3 +--R (6314A a b + 9730B a b )e + (6160A b + 25256B a b )d e +--R + +--R 10 2 2 +--R 9240B b d e +--R * +--R 8 +--R x +--R + +--R 2 8 3 7 4 9 2 8 3 +--R (11011A a b + 7595B a b )e + (28490A a b + 44044B a b )d e +--R + +--R 10 9 2 2 10 3 +--R (10395A b + 42735B a b )d e + 6930B b d e +--R * +--R 7 +--R x +--R + +--R 3 7 4 6 4 2 8 3 7 3 +--R (8789A a b + 2305B a b )e + (50710A a b + 35156B a b )d e +--R + +--R 9 2 8 2 2 10 9 3 +--R (49005A a b + 76065B a b )d e + (7920A b + 32670B a b )d e +--R + +--R 10 4 +--R 1980B b d +--R * +--R 6 +--R x +--R + +--R 4 6 5 5 4 3 7 4 6 3 +--R (2761A a b + 5B a b )e + (41690A a b + 11044B a b )d e +--R + +--R 2 8 3 7 2 2 9 2 8 3 +--R (89595A a b + 62535B a b )d e + (38280A a b + 59730B a b )d e +--R + +--R 10 9 4 +--R (2310A b + 9570B a b )d +--R * +--R 5 +--R x +--R + +--R 5 5 6 4 4 4 6 5 5 3 +--R (11A a b - 5B a b )e + (13750A a b + 44B a b )d e +--R + +--R 3 7 4 6 2 2 2 8 3 7 3 +--R (76725A a b + 20625B a b )d e + (72600A a b + 51150B a b )d e +--R + +--R 9 2 8 4 +--R (11550A a b + 18150B a b )d +--R * +--R 4 +--R x +--R + +--R 6 4 7 3 4 5 5 6 4 3 +--R (- 11A a b + 5B a b )e + (110A a b - 44B a b )d e +--R + +--R 4 6 5 5 2 2 3 7 4 6 3 +--R (27225A a b + 165B a b )d e + (66000A a b + 18150B a b )d e +--R + +--R 2 8 3 7 4 +--R (23100A a b + 16500B a b )d +--R * +--R 3 +--R x +--R + +--R 7 3 8 2 4 6 4 7 3 3 +--R (11A a b - 5B a b )e + (- 110A a b + 44B a b )d e +--R + +--R 5 5 6 4 2 2 4 6 5 5 3 +--R (495A a b - 165B a b )d e + (26400A a b + 330B a b )d e +--R + +--R 3 7 4 6 4 +--R (23100A a b + 6600B a b )d +--R * +--R 2 +--R x +--R + +--R 8 2 9 4 7 3 8 2 3 +--R (- 11A a b + 5B a b)e + (110A a b - 44B a b )d e +--R + +--R 6 4 7 3 2 2 5 5 6 4 3 +--R (- 495A a b + 165B a b )d e + (1320A a b - 330B a b )d e +--R + +--R 4 6 5 5 4 +--R (11550A a b + 330B a b )d +--R * +--R x +--R + +--R 9 10 4 8 2 9 3 +--R (11A a b - 5B a )e + (- 110A a b + 44B a b)d e +--R + +--R 7 3 8 2 2 2 6 4 7 3 3 +--R (495A a b - 165B a b )d e + (- 1320A a b + 330B a b )d e +--R + +--R 5 5 6 4 4 +--R (2310A a b - 330B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 +--R 13860b +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 11 5 4 4 5 3 10 +--R 1260B b e x + ((1386A b + 6930B a b )e + 5544B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (7700A a b + 15400B a b )e + (6160A b + 30800B a b )d e +--R + +--R 5 2 2 +--R 9240B b d e +--R * +--R 9 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (17325A a b + 17325B a b )e + (34650A a b + 69300B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (10395A b + 51975B a b )d e + 6930B b d e +--R * +--R 8 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (19800A a b + 9900B a b)e + (79200A a b + 79200B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (59400A a b + 118800B a b )d e + (7920A b + 39600B a b )d e +--R + +--R 5 4 +--R 1980B b d +--R * +--R 7 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (11550A a b + 2310B a )e + (92400A a b + 46200B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (138600A a b + 138600B a b )d e + (46200A a b + 92400B a b )d e +--R + +--R 5 4 4 +--R (2310A b + 11550B a b )d +--R * +--R 6 +--R x +--R + +--R 5 4 4 5 3 +--R 2772A a e + (55440A a b + 11088B a )d e +--R + +--R 3 2 4 2 2 2 3 3 2 3 +--R (166320A a b + 83160B a b)d e + (110880A a b + 110880B a b )d e +--R + +--R 4 2 3 4 +--R (13860A a b + 27720B a b )d +--R * +--R 5 +--R x +--R + +--R 5 3 4 5 2 2 +--R 13860A a d e + (103950A a b + 20790B a )d e +--R + +--R 3 2 4 3 2 3 3 2 4 +--R (138600A a b + 69300B a b)d e + (34650A a b + 34650B a b )d +--R * +--R 4 +--R x +--R + +--R 5 2 2 4 5 3 +--R 27720A a d e + (92400A a b + 18480B a )d e +--R + +--R 3 2 4 4 +--R (46200A a b + 23100B a b)d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 4 2 5 4 +--R (27720A a d e + (34650A a b + 6930B a )d )x + 13860A a d x +--R / +--R 13860 +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 10 4 10 10 9 4 10 3 9 +--R - 1260B b e x + ((- 1386A b - 5670B a b )e - 5544B b d e )x +--R + +--R 9 2 8 4 10 9 3 +--R (- 6314A a b - 9730B a b )e + (- 6160A b - 25256B a b )d e +--R + +--R 10 2 2 +--R - 9240B b d e +--R * +--R 8 +--R x +--R + +--R 2 8 3 7 4 +--R (- 11011A a b - 7595B a b )e +--R + +--R 9 2 8 3 +--R (- 28490A a b - 44044B a b )d e +--R + +--R 10 9 2 2 10 3 +--R (- 10395A b - 42735B a b )d e - 6930B b d e +--R * +--R 7 +--R x +--R + +--R 3 7 4 6 4 2 8 3 7 3 +--R (- 8789A a b - 2305B a b )e + (- 50710A a b - 35156B a b )d e +--R + +--R 9 2 8 2 2 +--R (- 49005A a b - 76065B a b )d e +--R + +--R 10 9 3 10 4 +--R (- 7920A b - 32670B a b )d e - 1980B b d +--R * +--R 6 +--R x +--R + +--R 4 6 5 5 4 3 7 4 6 3 +--R (- 2761A a b - 5B a b )e + (- 41690A a b - 11044B a b )d e +--R + +--R 2 8 3 7 2 2 +--R (- 89595A a b - 62535B a b )d e +--R + +--R 9 2 8 3 10 9 4 +--R (- 38280A a b - 59730B a b )d e + (- 2310A b - 9570B a b )d +--R * +--R 5 +--R x +--R + +--R 5 5 6 4 4 4 6 5 5 3 +--R (- 11A a b + 5B a b )e + (- 13750A a b - 44B a b )d e +--R + +--R 3 7 4 6 2 2 +--R (- 76725A a b - 20625B a b )d e +--R + +--R 2 8 3 7 3 9 2 8 4 +--R (- 72600A a b - 51150B a b )d e + (- 11550A a b - 18150B a b )d +--R * +--R 4 +--R x +--R + +--R 6 4 7 3 4 5 5 6 4 3 +--R (11A a b - 5B a b )e + (- 110A a b + 44B a b )d e +--R + +--R 4 6 5 5 2 2 +--R (- 27225A a b - 165B a b )d e +--R + +--R 3 7 4 6 3 2 8 3 7 4 +--R (- 66000A a b - 18150B a b )d e + (- 23100A a b - 16500B a b )d +--R * +--R 3 +--R x +--R + +--R 7 3 8 2 4 6 4 7 3 3 +--R (- 11A a b + 5B a b )e + (110A a b - 44B a b )d e +--R + +--R 5 5 6 4 2 2 4 6 5 5 3 +--R (- 495A a b + 165B a b )d e + (- 26400A a b - 330B a b )d e +--R + +--R 3 7 4 6 4 +--R (- 23100A a b - 6600B a b )d +--R * +--R 2 +--R x +--R + +--R 8 2 9 4 7 3 8 2 3 +--R (11A a b - 5B a b)e + (- 110A a b + 44B a b )d e +--R + +--R 6 4 7 3 2 2 5 5 6 4 3 +--R (495A a b - 165B a b )d e + (- 1320A a b + 330B a b )d e +--R + +--R 4 6 5 5 4 +--R (- 11550A a b - 330B a b )d +--R * +--R x +--R + +--R 9 10 4 8 2 9 3 +--R (- 11A a b + 5B a )e + (110A a b - 44B a b)d e +--R + +--R 7 3 8 2 2 2 6 4 7 3 3 +--R (- 495A a b + 165B a b )d e + (1320A a b - 330B a b )d e +--R + +--R 5 5 6 4 4 +--R (- 2310A a b + 330B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 11 4 11 11 10 4 11 3 10 +--R 1260B b e x + ((1386A b + 6930B a b )e + 5544B b d e )x +--R + +--R 10 2 9 4 11 10 3 +--R (7700A a b + 15400B a b )e + (6160A b + 30800B a b )d e +--R + +--R 11 2 2 +--R 9240B b d e +--R * +--R 9 +--R x +--R + +--R 2 9 3 8 4 10 2 9 3 +--R (17325A a b + 17325B a b )e + (34650A a b + 69300B a b )d e +--R + +--R 11 10 2 2 11 3 +--R (10395A b + 51975B a b )d e + 6930B b d e +--R * +--R 8 +--R x +--R + +--R 3 8 4 7 4 2 9 3 8 3 +--R (19800A a b + 9900B a b )e + (79200A a b + 79200B a b )d e +--R + +--R 10 2 9 2 2 11 10 3 +--R (59400A a b + 118800B a b )d e + (7920A b + 39600B a b )d e +--R + +--R 11 4 +--R 1980B b d +--R * +--R 7 +--R x +--R + +--R 4 7 5 6 4 3 8 4 7 3 +--R (11550A a b + 2310B a b )e + (92400A a b + 46200B a b )d e +--R + +--R 2 9 3 8 2 2 10 2 9 3 +--R (138600A a b + 138600B a b )d e + (46200A a b + 92400B a b )d e +--R + +--R 11 10 4 +--R (2310A b + 11550B a b )d +--R * +--R 6 +--R x +--R + +--R 5 6 4 4 7 5 6 3 +--R 2772A a b e + (55440A a b + 11088B a b )d e +--R + +--R 3 8 4 7 2 2 2 9 3 8 3 +--R (166320A a b + 83160B a b )d e + (110880A a b + 110880B a b )d e +--R + +--R 10 2 9 4 +--R (13860A a b + 27720B a b )d +--R * +--R 5 +--R x +--R + +--R 5 6 3 4 7 5 6 2 2 +--R 13860A a b d e + (103950A a b + 20790B a b )d e +--R + +--R 3 8 4 7 3 2 9 3 8 4 +--R (138600A a b + 69300B a b )d e + (34650A a b + 34650B a b )d +--R * +--R 4 +--R x +--R + +--R 5 6 2 2 4 7 5 6 3 +--R 27720A a b d e + (92400A a b + 18480B a b )d e +--R + +--R 3 8 4 7 4 +--R (46200A a b + 23100B a b )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 7 5 6 4 2 5 6 4 +--R (27720A a b d e + (34650A a b + 6930B a b )d )x + 13860A a b d x +--R / +--R 6 +--R 13860b +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 4 10 5 4 4 5 3 9 +--R B b e x + ((A b + 5B a b )e + 4B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 8 +--R ((5A a b + 10B a b )e + (4A b + 20B a b )d e + 6B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (10A a b + 10B a b )e + (20A a b + 40B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (6A b + 30B a b )d e + 4B b d e +--R * +--R 7 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (10A a b + 5B a b)e + (40A a b + 40B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (30A a b + 60B a b )d e + (4A b + 20B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (5A a b + B a )e + (40A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (60A a b + 60B a b )d e + (20A a b + 40B a b )d e +--R + +--R 5 4 4 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R A a e + (20A a b + 4B a )d e + (60A a b + 30B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (40A a b + 40B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 4 5 2 2 3 2 4 3 +--R 4A a d e + (30A a b + 6B a )d e + (40A a b + 20B a b)d e +--R + +--R 2 3 3 2 4 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 2 4 5 3 3 2 4 4 2 +--R (6A a d e + (20A a b + 4B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 3 4 5 4 5 4 +--R (4A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 4 11 6 5 4 6 3 10 +--R - B b e x + ((- A b - 6B a b )e - 4B b d e )x +--R + +--R 5 2 4 4 6 5 3 6 2 2 9 +--R ((- 6A a b - 15B a b )e + (- 4A b - 24B a b )d e - 6B b d e )x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 15A a b - 20B a b )e + (- 24A a b - 60B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (- 6A b - 36B a b )d e - 4B b d e +--R * +--R 8 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (- 20A a b - 15B a b )e + (- 60A a b - 80B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (- 36A a b - 90B a b )d e + (- 4A b - 24B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 15A a b - 6B a b)e + (- 80A a b - 60B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 90A a b - 120B a b )d e + (- 24A a b - 60B a b )d e +--R + +--R 6 5 4 +--R (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 6A a b - B a )e + (- 60A a b - 24B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 120A a b - 90B a b )d e + (- 60A a b - 80B a b )d e +--R + +--R 5 2 4 4 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R - A a e + (- 24A a b - 4B a )d e + (- 90A a b - 36B a b)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (- 80A a b - 60B a b )d e + (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 5 6 2 2 4 2 5 3 +--R - 4A a d e + (- 36A a b - 6B a )d e + (- 60A a b - 24B a b)d e +--R + +--R 3 3 4 2 4 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 2 5 6 3 4 2 5 4 2 +--R (- 6A a d e + (- 24A a b - 4B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 3 5 6 4 6 4 +--R (- 4A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 565 + +)clear all + +--S 566 of 1378 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1378 +r0:=-1/360*(b*d-a*e)^3*(3*b*B*d-5*A*b*e+2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^5*e)-1/120*(b*d-a*e)*(3*b*B*d-5*A*b*e+2*a*B*e)*_ + (a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^3*e)-1/45*(3*b*B*d-_ + 5*A*b*e+2*a*B*e)*(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+_ + 1/10*B*(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 1/420*(b*d-a*e)^2*(3*b*B*d-5*A*b*e+2*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^5 +--R +--R +--R (2) +--R 9 3 9 9 8 3 9 2 8 +--R 252B b e x + ((280A b + 1148B a b )e + 840B b d e )x +--R + +--R 8 2 7 3 9 8 2 +--R (1295A a b + 2002B a b )e + (945A b + 3885B a b )d e +--R + +--R 9 2 +--R 945B b d e +--R * +--R 7 +--R x +--R + +--R 2 7 3 6 3 8 2 7 2 +--R (2305A a b + 1598B a b )e + (4455A a b + 6915B a b )d e +--R + +--R 9 8 2 9 3 +--R (1080A b + 4455B a b )d e + 360B b d +--R * +--R 6 +--R x +--R + +--R 3 6 4 5 3 2 7 3 6 2 +--R (1895A a b + 502B a b )e + (8145A a b + 5685B a b )d e +--R + +--R 8 2 7 2 9 8 3 +--R (5220A a b + 8145B a b )d e + (420A b + 1740B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 5 4 3 3 6 4 5 2 +--R (625A a b + 2B a b )e + (6975A a b + 1875B a b )d e +--R + +--R 2 7 3 6 2 8 2 7 3 +--R (9900A a b + 6975B a b )d e + (2100A a b + 3300B a b )d +--R * +--R 4 +--R x +--R + +--R 5 4 6 3 3 4 5 5 4 2 +--R (5A a b - 2B a b )e + (2475A a b + 15B a b )d e +--R + +--R 3 6 4 5 2 2 7 3 6 3 +--R (9000A a b + 2475B a b )d e + (4200A a b + 3000B a b )d +--R * +--R 3 +--R x +--R + +--R 6 3 7 2 3 5 4 6 3 2 +--R (- 5A a b + 2B a b )e + (45A a b - 15B a b )d e +--R + +--R 4 5 5 4 2 3 6 4 5 3 +--R (3600A a b + 45B a b )d e + (4200A a b + 1200B a b )d +--R * +--R 2 +--R x +--R + +--R 7 2 8 3 6 3 7 2 2 +--R (5A a b - 2B a b)e + (- 45A a b + 15B a b )d e +--R + +--R 5 4 6 3 2 4 5 5 4 3 +--R (180A a b - 45B a b )d e + (2100A a b + 60B a b )d +--R * +--R x +--R + +--R 8 9 3 7 2 8 2 +--R (- 5A a b + 2B a )e + (45A a b - 15B a b)d e +--R + +--R 6 3 7 2 2 5 4 6 3 3 +--R (- 180A a b + 45B a b )d e + (420A a b - 60B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 2520b +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 10 5 4 3 5 2 9 +--R 252B b e x + ((280A b + 1400B a b )e + 840B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 8 +--R ((1575A a b + 3150B a b )e + (945A b + 4725B a b )d e + 945B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (3600A a b + 3600B a b )e + (5400A a b + 10800B a b )d e +--R + +--R 5 4 2 5 3 +--R (1080A b + 5400B a b )d e + 360B b d +--R * +--R 7 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (4200A a b + 2100B a b)e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (6300A a b + 12600B a b )d e + (420A b + 2100B a b )d +--R * +--R 6 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (2520A a b + 504B a )e + (15120A a b + 7560B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (15120A a b + 15120B a b )d e + (2520A a b + 5040B a b )d +--R * +--R 5 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R 630A a e + (9450A a b + 1890B a )d e + (18900A a b + 9450B a b)d e +--R + +--R 2 3 3 2 3 +--R (6300A a b + 6300B a b )d +--R * +--R 4 +--R x +--R + +--R 5 2 4 5 2 +--R 2520A a d e + (12600A a b + 2520B a )d e +--R + +--R 3 2 4 3 +--R (8400A a b + 4200B a b)d +--R * +--R 3 +--R x +--R + +--R 5 2 4 5 3 2 5 3 +--R (3780A a d e + (6300A a b + 1260B a )d )x + 2520A a d x +--R / +--R 2520 +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 3 9 9 8 3 9 2 8 +--R - 252B b e x + ((- 280A b - 1148B a b )e - 840B b d e )x +--R + +--R 8 2 7 3 9 8 2 +--R (- 1295A a b - 2002B a b )e + (- 945A b - 3885B a b )d e +--R + +--R 9 2 +--R - 945B b d e +--R * +--R 7 +--R x +--R + +--R 2 7 3 6 3 8 2 7 2 +--R (- 2305A a b - 1598B a b )e + (- 4455A a b - 6915B a b )d e +--R + +--R 9 8 2 9 3 +--R (- 1080A b - 4455B a b )d e - 360B b d +--R * +--R 6 +--R x +--R + +--R 3 6 4 5 3 2 7 3 6 2 +--R (- 1895A a b - 502B a b )e + (- 8145A a b - 5685B a b )d e +--R + +--R 8 2 7 2 9 8 3 +--R (- 5220A a b - 8145B a b )d e + (- 420A b - 1740B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 5 4 3 3 6 4 5 2 +--R (- 625A a b - 2B a b )e + (- 6975A a b - 1875B a b )d e +--R + +--R 2 7 3 6 2 8 2 7 3 +--R (- 9900A a b - 6975B a b )d e + (- 2100A a b - 3300B a b )d +--R * +--R 4 +--R x +--R + +--R 5 4 6 3 3 4 5 5 4 2 +--R (- 5A a b + 2B a b )e + (- 2475A a b - 15B a b )d e +--R + +--R 3 6 4 5 2 2 7 3 6 3 +--R (- 9000A a b - 2475B a b )d e + (- 4200A a b - 3000B a b )d +--R * +--R 3 +--R x +--R + +--R 6 3 7 2 3 5 4 6 3 2 +--R (5A a b - 2B a b )e + (- 45A a b + 15B a b )d e +--R + +--R 4 5 5 4 2 3 6 4 5 3 +--R (- 3600A a b - 45B a b )d e + (- 4200A a b - 1200B a b )d +--R * +--R 2 +--R x +--R + +--R 7 2 8 3 6 3 7 2 2 +--R (- 5A a b + 2B a b)e + (45A a b - 15B a b )d e +--R + +--R 5 4 6 3 2 4 5 5 4 3 +--R (- 180A a b + 45B a b )d e + (- 2100A a b - 60B a b )d +--R * +--R x +--R + +--R 8 9 3 7 2 8 2 +--R (5A a b - 2B a )e + (- 45A a b + 15B a b)d e +--R + +--R 6 3 7 2 2 5 4 6 3 3 +--R (180A a b - 45B a b )d e + (- 420A a b + 60B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 10 3 10 10 9 3 10 2 9 +--R 252B b e x + ((280A b + 1400B a b )e + 840B b d e )x +--R + +--R 9 2 8 3 10 9 2 +--R (1575A a b + 3150B a b )e + (945A b + 4725B a b )d e +--R + +--R 10 2 +--R 945B b d e +--R * +--R 8 +--R x +--R + +--R 2 8 3 7 3 9 2 8 2 +--R (3600A a b + 3600B a b )e + (5400A a b + 10800B a b )d e +--R + +--R 10 9 2 10 3 +--R (1080A b + 5400B a b )d e + 360B b d +--R * +--R 7 +--R x +--R + +--R 3 7 4 6 3 2 8 3 7 2 +--R (4200A a b + 2100B a b )e + (12600A a b + 12600B a b )d e +--R + +--R 9 2 8 2 10 9 3 +--R (6300A a b + 12600B a b )d e + (420A b + 2100B a b )d +--R * +--R 6 +--R x +--R + +--R 4 6 5 5 3 3 7 4 6 2 +--R (2520A a b + 504B a b )e + (15120A a b + 7560B a b )d e +--R + +--R 2 8 3 7 2 9 2 8 3 +--R (15120A a b + 15120B a b )d e + (2520A a b + 5040B a b )d +--R * +--R 5 +--R x +--R + +--R 5 5 3 4 6 5 5 2 +--R 630A a b e + (9450A a b + 1890B a b )d e +--R + +--R 3 7 4 6 2 2 8 3 7 3 +--R (18900A a b + 9450B a b )d e + (6300A a b + 6300B a b )d +--R * +--R 4 +--R x +--R + +--R 5 5 2 4 6 5 5 2 +--R 2520A a b d e + (12600A a b + 2520B a b )d e +--R + +--R 3 7 4 6 3 +--R (8400A a b + 4200B a b )d +--R * +--R 3 +--R x +--R + +--R 5 5 2 4 6 5 5 3 2 5 5 3 +--R (3780A a b d e + (6300A a b + 1260B a b )d )x + 2520A a b d x +--R / +--R 5 +--R 2520b +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 3 9 5 4 3 5 2 8 +--R B b e x + ((A b + 5B a b )e + 3B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 7 +--R ((5A a b + 10B a b )e + (3A b + 15B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (10A a b + 10B a b )e + (15A a b + 30B a b )d e +--R + +--R 5 4 2 5 3 +--R (3A b + 15B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (10A a b + 5B a b)e + (30A a b + 30B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (15A a b + 30B a b )d e + (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (5A a b + B a )e + (30A a b + 15B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (30A a b + 30B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A a e + (15A a b + 3B a )d e + (30A a b + 15B a b)d e +--R + +--R 2 3 3 2 3 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 5 2 3 2 4 3 2 +--R (3A a d e + (15A a b + 3B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 2 4 5 3 5 3 +--R (3A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 3 10 6 5 3 6 2 9 +--R - B b e x + ((- A b - 6B a b )e - 3B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 8 +--R ((- 6A a b - 15B a b )e + (- 3A b - 18B a b )d e - 3B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (- 15A a b - 20B a b )e + (- 18A a b - 45B a b )d e +--R + +--R 6 5 2 6 3 +--R (- 3A b - 18B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (- 20A a b - 15B a b )e + (- 45A a b - 60B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 18A a b - 45B a b )d e + (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 15A a b - 6B a b)e + (- 60A a b - 45B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 45A a b - 60B a b )d e + (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 6A a b - B a )e + (- 45A a b - 18B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A a b - 45B a b )d e + (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R - A a e + (- 18A a b - 3B a )d e + (- 45A a b - 18B a b)d e +--R + +--R 3 3 4 2 3 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 2 4 2 5 3 2 +--R (- 3A a d e + (- 18A a b - 3B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 2 5 6 3 6 3 +--R (- 3A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 1378 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1378 +r0:=-1/72*(b*d-a*e)^2*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^4*e)-1/24*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(d+_ + e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+1/9*B*(a+b*x)*(d+e*x)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-1/84*(b*d-a*e)*(2*b*B*d-3*A*b*e+_ + a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4 +--R +--R +--R (2) +--R 8 2 8 8 7 2 8 7 +--R 56B b e x + ((63A b + 259B a b )e + 126B b d e)x +--R + +--R 7 2 6 2 8 7 8 2 6 +--R ((297A a b + 461B a b )e + (144A b + 594B a b )d e + 72B b d )x +--R + +--R 2 6 3 5 2 7 2 6 +--R (543A a b + 379B a b )e + (696A a b + 1086B a b )d e +--R + +--R 8 7 2 +--R (84A b + 348B a b )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (465A a b + 125B a b )e + (1320A a b + 930B a b )d e +--R + +--R 7 2 6 2 +--R (420A a b + 660B a b )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (165A a b + B a b )e + (1200A a b + 330B a b )d e +--R + +--R 2 6 3 5 2 +--R (840A a b + 600B a b )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (3A a b - B a b )e + (480A a b + 6B a b )d e +--R + +--R 3 5 4 4 2 +--R (840A a b + 240B a b )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 3A a b + B a b)e + (24A a b - 6B a b )d e +--R + +--R 4 4 5 3 2 +--R (420A a b + 12B a b )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 5 3 6 2 2 +--R (3A a b - B a )e + (- 24A a b + 6B a b)d e + (84A a b - 12B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 504b +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 9 5 4 2 5 8 +--R 56B b e x + ((63A b + 315B a b )e + 126B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 7 +--R ((360A a b + 720B a b )e + (144A b + 720B a b )d e + 72B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (840A a b + 840B a b )e + (840A a b + 1680B a b )d e +--R + +--R 5 4 2 +--R (84A b + 420B a b )d +--R * +--R 6 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (1008A a b + 504B a b)e + (2016A a b + 2016B a b )d e +--R + +--R 4 2 3 2 +--R (504A a b + 1008B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 2 3 2 4 +--R (630A a b + 126B a )e + (2520A a b + 1260B a b)d e +--R + +--R 2 3 3 2 2 +--R (1260A a b + 1260B a b )d +--R * +--R 4 +--R x +--R + +--R 5 2 4 5 3 2 4 2 3 +--R (168A a e + (1680A a b + 336B a )d e + (1680A a b + 840B a b)d )x +--R + +--R 5 4 5 2 2 5 2 +--R (504A a d e + (1260A a b + 252B a )d )x + 504A a d x +--R / +--R 504 +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 2 8 8 7 2 8 7 +--R - 56B b e x + ((- 63A b - 259B a b )e - 126B b d e)x +--R + +--R 7 2 6 2 8 7 +--R (- 297A a b - 461B a b )e + (- 144A b - 594B a b )d e +--R + +--R 8 2 +--R - 72B b d +--R * +--R 6 +--R x +--R + +--R 2 6 3 5 2 7 2 6 +--R (- 543A a b - 379B a b )e + (- 696A a b - 1086B a b )d e +--R + +--R 8 7 2 +--R (- 84A b - 348B a b )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (- 465A a b - 125B a b )e + (- 1320A a b - 930B a b )d e +--R + +--R 7 2 6 2 +--R (- 420A a b - 660B a b )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (- 165A a b - B a b )e + (- 1200A a b - 330B a b )d e +--R + +--R 2 6 3 5 2 +--R (- 840A a b - 600B a b )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (- 3A a b + B a b )e + (- 480A a b - 6B a b )d e +--R + +--R 3 5 4 4 2 +--R (- 840A a b - 240B a b )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (3A a b - B a b)e + (- 24A a b + 6B a b )d e +--R + +--R 4 4 5 3 2 +--R (- 420A a b - 12B a b )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 +--R (- 3A a b + B a )e + (24A a b - 6B a b)d e +--R + +--R 5 3 6 2 2 +--R (- 84A a b + 12B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 9 2 9 9 8 2 9 8 +--R 56B b e x + ((63A b + 315B a b )e + 126B b d e)x +--R + +--R 8 2 7 2 9 8 9 2 7 +--R ((360A a b + 720B a b )e + (144A b + 720B a b )d e + 72B b d )x +--R + +--R 2 7 3 6 2 8 2 7 +--R (840A a b + 840B a b )e + (840A a b + 1680B a b )d e +--R + +--R 9 8 2 +--R (84A b + 420B a b )d +--R * +--R 6 +--R x +--R + +--R 3 6 4 5 2 2 7 3 6 +--R (1008A a b + 504B a b )e + (2016A a b + 2016B a b )d e +--R + +--R 8 2 7 2 +--R (504A a b + 1008B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 5 4 2 3 6 4 5 +--R (630A a b + 126B a b )e + (2520A a b + 1260B a b )d e +--R + +--R 2 7 3 6 2 +--R (1260A a b + 1260B a b )d +--R * +--R 4 +--R x +--R + +--R 5 4 2 4 5 5 4 +--R 168A a b e + (1680A a b + 336B a b )d e +--R + +--R 3 6 4 5 2 +--R (1680A a b + 840B a b )d +--R * +--R 3 +--R x +--R + +--R 5 4 4 5 5 4 2 2 5 4 2 +--R (504A a b d e + (1260A a b + 252B a b )d )x + 504A a b d x +--R / +--R 4 +--R 504b +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 2 8 5 4 2 5 7 +--R B b e x + ((A b + 5B a b )e + 2B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 6 +--R ((5A a b + 10B a b )e + (2A b + 10B a b )d e + B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (10A a b + 10B a b )e + (10A a b + 20B a b )d e +--R + +--R 5 4 2 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (10A a b + 5B a b)e + (20A a b + 20B a b )d e +--R + +--R 4 2 3 2 +--R (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 4 5 2 3 2 4 +--R (5A a b + B a )e + (20A a b + 10B a b)d e +--R + +--R 2 3 3 2 2 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 5 3 2 4 2 2 +--R (A a e + (10A a b + 2B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 4 5 2 5 2 +--R (2A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 2 9 6 5 2 6 8 +--R - B b e x + ((- A b - 6B a b )e - 2B b d e)x +--R + +--R 5 2 4 2 6 5 6 2 7 +--R ((- 6A a b - 15B a b )e + (- 2A b - 12B a b )d e - B b d )x +--R + +--R 2 4 3 3 2 5 2 4 +--R (- 15A a b - 20B a b )e + (- 12A a b - 30B a b )d e +--R + +--R 6 5 2 +--R (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 20A a b - 15B a b )e + (- 30A a b - 40B a b )d e +--R + +--R 5 2 4 2 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (- 15A a b - 6B a b)e + (- 40A a b - 30B a b )d e +--R + +--R 2 4 3 3 2 +--R (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 6A a b - B a )e + (- 30A a b - 12B a b)d e +--R + +--R 3 3 4 2 2 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 4 2 5 2 2 +--R (- A a e + (- 12A a b - 2B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 5 6 2 6 2 +--R (- 2A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 1378 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1378 +r0:=-1/24*(b*d-a*e)*(3*b*B*d-4*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^3*e)+1/8*B*(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-1/28*(3*b*B*d-4*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^3 +--R +--R +--R (2) +--R 7 7 7 6 7 6 +--R 21B b e x + ((24A b + 99B a b )e + 24B b d)x +--R + +--R 6 2 5 7 6 5 +--R ((116A a b + 181B a b )e + (28A b + 116B a b )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((220A a b + 155B a b )e + (140A a b + 220B a b )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((200A a b + 55B a b )e + (280A a b + 200B a b )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((80A a b + B a b )e + (280A a b + 80B a b )d)x +--R + +--R 5 2 6 4 3 5 2 6 7 +--R ((4A a b - B a b)e + (140A a b + 4B a b )d)x + (- 4A a b + B a )e +--R + +--R 5 2 6 +--R (28A a b - 4B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 168b +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 8 5 4 5 7 +--R 21B b e x + ((24A b + 120B a b )e + 24B b d)x +--R + +--R 4 2 3 5 4 6 +--R ((140A a b + 280B a b )e + (28A b + 140B a b )d)x +--R + +--R 2 3 3 2 4 2 3 5 +--R ((336A a b + 336B a b )e + (168A a b + 336B a b )d)x +--R + +--R 3 2 4 2 3 3 2 4 +--R ((420A a b + 210B a b)e + (420A a b + 420B a b )d)x +--R + +--R 4 5 3 2 4 3 +--R ((280A a b + 56B a )e + (560A a b + 280B a b)d)x +--R + +--R 5 4 5 2 5 +--R (84A a e + (420A a b + 84B a )d)x + 168A a d x +--R / +--R 168 +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 7 7 6 7 6 +--R - 21B b e x + ((- 24A b - 99B a b )e - 24B b d)x +--R + +--R 6 2 5 7 6 5 +--R ((- 116A a b - 181B a b )e + (- 28A b - 116B a b )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((- 220A a b - 155B a b )e + (- 140A a b - 220B a b )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((- 200A a b - 55B a b )e + (- 280A a b - 200B a b )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((- 80A a b - B a b )e + (- 280A a b - 80B a b )d)x +--R + +--R 5 2 6 4 3 5 2 6 7 +--R ((- 4A a b + B a b)e + (- 140A a b - 4B a b )d)x + (4A a b - B a )e +--R + +--R 5 2 6 +--R (- 28A a b + 4B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 8 8 8 7 8 7 +--R 21B b e x + ((24A b + 120B a b )e + 24B b d)x +--R + +--R 7 2 6 8 7 6 +--R ((140A a b + 280B a b )e + (28A b + 140B a b )d)x +--R + +--R 2 6 3 5 7 2 6 5 +--R ((336A a b + 336B a b )e + (168A a b + 336B a b )d)x +--R + +--R 3 5 4 4 2 6 3 5 4 +--R ((420A a b + 210B a b )e + (420A a b + 420B a b )d)x +--R + +--R 4 4 5 3 3 5 4 4 3 +--R ((280A a b + 56B a b )e + (560A a b + 280B a b )d)x +--R + +--R 5 3 4 4 5 3 2 5 3 +--R (84A a b e + (420A a b + 84B a b )d)x + 168A a b d x +--R / +--R 3 +--R 168b +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 7 5 4 5 6 +--R B b e x + ((A b + 5B a b )e + B b d)x +--R + +--R 4 2 3 5 4 5 +--R ((5A a b + 10B a b )e + (A b + 5B a b )d)x +--R + +--R 2 3 3 2 4 2 3 4 +--R ((10A a b + 10B a b )e + (5A a b + 10B a b )d)x +--R + +--R 3 2 4 2 3 3 2 3 +--R ((10A a b + 5B a b)e + (10A a b + 10B a b )d)x +--R + +--R 4 5 3 2 4 2 +--R ((5A a b + B a )e + (10A a b + 5B a b)d)x +--R + +--R 5 4 5 5 +--R (A a e + (5A a b + B a )d)x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 8 6 5 6 7 +--R - B b e x + ((- A b - 6B a b )e - B b d)x +--R + +--R 5 2 4 6 5 6 +--R ((- 6A a b - 15B a b )e + (- A b - 6B a b )d)x +--R + +--R 2 4 3 3 5 2 4 5 +--R ((- 15A a b - 20B a b )e + (- 6A a b - 15B a b )d)x +--R + +--R 3 3 4 2 2 4 3 3 4 +--R ((- 20A a b - 15B a b )e + (- 15A a b - 20B a b )d)x +--R + +--R 4 2 5 3 3 4 2 3 +--R ((- 15A a b - 6B a b)e + (- 20A a b - 15B a b )d)x +--R + +--R 5 6 4 2 5 2 +--R ((- 6A a b - B a )e + (- 15A a b - 6B a b)d)x +--R + +--R 6 5 6 6 +--R (- A a e + (- 6A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1378 +r0:=1/6*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+_ + 1/7*B*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2 +--R +--R +--R (2) +--R 6 6 6 5 5 5 2 4 4 +--R 6B b x + (7A b + 29B a b )x + (35A a b + 55B a b )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 4 2 5 +--R (70A a b + 50B a b )x + (70A a b + 20B a b )x + (35A a b + B a b)x +--R + +--R 5 6 +--R 7A a b - B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 42b +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 5 4 6 4 2 3 5 +--R 6B b x + (7A b + 35B a b )x + (42A a b + 84B a b )x +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (105A a b + 105B a b )x + (140A a b + 70B a b)x +--R + +--R 4 5 2 5 +--R (105A a b + 21B a )x + 42A a x +--R / +--R 42 +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 5 5 2 4 4 +--R - 6B b x + (- 7A b - 29B a b )x + (- 35A a b - 55B a b )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 +--R (- 70A a b - 50B a b )x + (- 70A a b - 20B a b )x +--R + +--R 4 2 5 5 6 +--R (- 35A a b - B a b)x - 7A a b + B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 7 6 6 6 2 5 5 +--R 6B b x + (7A b + 35B a b )x + (42A a b + 84B a b )x +--R + +--R 2 5 3 4 4 3 4 4 3 3 +--R (105A a b + 105B a b )x + (140A a b + 70B a b )x +--R + +--R 4 3 5 2 2 5 2 +--R (105A a b + 21B a b )x + 42A a b x +--R / +--R 2 +--R 42b +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R e x + d +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1378 +r0:=-1/3*(b*d-a*e)^2*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/4*(b*d-a*e)*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/5*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/6*B*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-(b*d-a*e)^4*(B*d-A*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/2*(b*d-a*e)^3*(B*d-A*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+(b*d-a*e)^5*(B*d-A*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 5 +--R 60A a b e + (- 300A a b - 60B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (600A a b + 300B a b )d e + (- 600A a b - 600B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (300A a b + 600B a b )d e + (- 60A b - 300B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 6 5 6 6 5 5 +--R 10B b e x + ((12A b + 60B a b )e - 12B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 4 +--R ((75A a b + 150B a b )e + (- 15A b - 75B a b )d e + 15B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (200A a b + 200B a b )e + (- 100A a b - 200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (20A b + 100B a b )d e - 20B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (300A a b + 150B a b )e + (- 300A a b - 300B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (150A a b + 300B a b )d e + (- 30A b - 150B a b )d e + 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (300A a b + 60B a b)e + (- 600A a b - 300B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (60A b + 300B a b )d e - 60B b d e +--R * +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (137A a b + 10B a )e + (- 385A a b - 137B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (470A a b + 385B a b )d e + (- 270A a b - 470B a b )d e +--R + +--R 5 2 4 4 2 5 5 +--R (60A a b + 270B a b )d e - 60B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 7 7 +--R 60b e x + 60a b e +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 4 5 5 3 2 4 2 4 +--R 60A a e + (- 300A a b - 60B a )d e + (600A a b + 300B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 600A a b - 600B a b )d e + (300A a b + 600B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 60A b - 300B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 10B b e x + ((12A b + 60B a b )e - 12B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((75A a b + 150B a b )e + (- 15A b - 75B a b )d e + 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (200A a b + 200B a b )e + (- 100A a b - 200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (20A b + 100B a b )d e - 20B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (300A a b + 150B a b)e + (- 300A a b - 300B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (150A a b + 300B a b )d e + (- 30A b - 150B a b )d e + 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (300A a b + 60B a )e + (- 600A a b - 300B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (60A b + 300B a b )d e - 60B b d e +--R * +--R x +--R / +--R 7 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 4 2 5 5 +--R - 60A a b e + (300A a b + 60B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 600A a b - 300B a b )d e + (600A a b + 600B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 300A a b - 600B a b )d e + (60A b + 300B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 6 5 6 6 5 5 +--R - 10B b e x + ((- 12A b - 60B a b )e + 12B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 4 +--R ((- 75A a b - 150B a b )e + (15A b + 75B a b )d e - 15B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 200A a b - 200B a b )e + (100A a b + 200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 20A b - 100B a b )d e + 20B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 300A a b - 150B a b )e + (300A a b + 300B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 150A a b - 300B a b )d e + (30A b + 150B a b )d e +--R + +--R 6 4 2 +--R - 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 300A a b - 60B a b)e + (600A a b + 300B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 600A a b - 600B a b )d e + (300A a b + 600B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 60A b - 300B a b )d e + 60B b d e +--R * +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 137A a b - 10B a )e + (385A a b + 137B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 470A a b - 385B a b )d e + (270A a b + 470B a b )d e +--R + +--R 5 2 4 4 2 5 5 +--R (- 60A a b - 270B a b )d e + 60B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 6 4 3 5 2 5 +--R 60A a b e + (- 300A a b - 60B a b )d e +--R + +--R 3 4 4 3 2 4 2 5 3 4 3 3 +--R (600A a b + 300B a b )d e + (- 600A a b - 600B a b )d e +--R + +--R 6 2 5 4 2 7 6 5 7 6 +--R (300A a b + 600B a b )d e + (- 60A b - 300B a b )d e + 60B b d +--R * +--R x +--R + +--R 6 6 5 2 6 5 +--R 60A a b e + (- 300A a b - 60B a b)d e +--R + +--R 4 3 5 2 2 4 3 4 4 3 3 3 +--R (600A a b + 300B a b )d e + (- 600A a b - 600B a b )d e +--R + +--R 2 5 3 4 4 2 6 2 5 5 6 6 +--R (300A a b + 600B a b )d e + (- 60A a b - 300B a b )d e + 60B a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 7 6 6 7 5 6 +--R 10B b e x + ((12A b + 70B a b )e - 12B b d e )x +--R + +--R 6 2 5 6 7 6 5 7 2 4 5 +--R ((87A a b + 210B a b )e + (- 15A b - 87B a b )d e + 15B b d e )x +--R + +--R 2 5 3 4 6 6 2 5 5 +--R (275A a b + 350B a b )e + (- 115A a b - 275B a b )d e +--R + +--R 7 6 2 4 7 3 3 +--R (20A b + 115B a b )d e - 20B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 6 2 5 3 4 5 +--R (500A a b + 350B a b )e + (- 400A a b - 500B a b )d e +--R + +--R 6 2 5 2 4 7 6 3 3 7 4 2 +--R (170A a b + 400B a b )d e + (- 30A b - 170B a b )d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 6 3 4 4 3 5 +--R (600A a b + 210B a b )e + (- 900A a b - 600B a b )d e +--R + +--R 2 5 3 4 2 4 6 2 5 3 3 +--R (750A a b + 900B a b )d e + (- 330A a b - 750B a b )d e +--R + +--R 7 6 4 2 7 5 +--R (60A b + 330B a b )d e - 60B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 6 4 3 5 2 5 +--R (300A a b + 60B a b)e + (- 600A a b - 300B a b )d e +--R + +--R 3 4 4 3 2 4 2 5 3 4 3 3 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 6 2 5 4 2 6 5 +--R (60A a b + 300B a b )d e - 60B a b d e +--R * +--R x +--R / +--R 2 7 7 +--R 60b e x + 60a b e +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1378 +r0:=1/3*(b*d-a*e)*(6*b*B*d-5*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-_ + 1/4*(6*b*B*d-5*A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3+_ + 1/5*(6*b*B*d-5*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x))+_ + (b*d-a*e)^3*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 1/2*(b*d-a*e)^2*(6*b*B*d-5*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^5-(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 5 6 3 2 4 5 +--R (300A a b + 60B a )e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (300A b + 1500B a b )d e - 360B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (300A a b + 60B a )d e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 5 5 6 +--R (300A b + 1500B a b )d e - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 12B b e x + ((15A b + 75B a b )e - 18B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((100A a b + 200B a b )e + (- 25A b - 125B a b )d e + 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (300A a b + 300B a b )e + (- 200A a b - 400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (50A b + 250B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (600A a b + 300B a b)e + (- 900A a b - 900B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (600A a b + 1200B a b )d e + (- 150A b - 750B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (325A a b + 137B a )e + (- 100A a b - 410B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 750A a b - 30B a b )d e + (900A a b + 1080B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 300A b - 1140B a b )d e + 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 60A a e + (625A a b + 197B a )d e + (- 1300A a b - 1010B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (1050A a b + 1770B a b )d e + (- 300A a b - 1320B a b )d e +--R + +--R 4 5 +--R 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +--R 60b e x + (60a e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 6 3 2 4 5 +--R (300A a b + 60B a )e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (300A b + 1500B a b )d e - 360B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (300A a b + 60B a )d e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 5 5 6 +--R (300A b + 1500B a b )d e - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 12B b e x + ((15A b + 75B a b )e - 18B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((100A a b + 200B a b )e + (- 25A b - 125B a b )d e + 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (300A a b + 300B a b )e + (- 200A a b - 400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (50A b + 250B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (600A a b + 300B a b)e + (- 900A a b - 900B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (600A a b + 1200B a b )d e + (- 150A b - 750B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 2 4 +--R (600A a b + 300B a b)d e + (- 1200A a b - 1200B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (900A a b + 1800B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 300B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 60A a e + (300A a b + 60B a )d e + (- 600A a b - 300B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 60B b d +--R / +--R 8 7 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 593 + +--S 594 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 6 3 2 4 5 +--R (- 300A a b - 60B a )e + (1200A a b + 600B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 1800A a b - 1800B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (1200A a b + 2400B a b )d e + (- 300A b - 1500B a b )d e +--R + +--R 5 5 +--R 360B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (- 300A a b - 60B a )d e + (1200A a b + 600B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 1800A a b - 1800B a b )d e + (1200A a b + 2400B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 300A b - 1500B a b )d e + 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R - 12B b e x + ((- 15A b - 75B a b )e + 18B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 100A a b - 200B a b )e + (25A b + 125B a b )d e +--R + +--R 5 2 4 +--R - 30B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 300A a b - 300B a b )e + (200A a b + 400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 50A b - 250B a b )d e + 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 600A a b - 300B a b)e + (900A a b + 900B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 600A a b - 1200B a b )d e + (150A b + 750B a b )d e +--R + +--R 5 4 2 +--R - 180B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 325A a b - 137B a )e + (100A a b + 410B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (750A a b + 30B a b )d e + (- 900A a b - 1080B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (300A b + 1140B a b )d e - 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 60A a e + (- 625A a b - 197B a )d e + (1300A a b + 1010B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 1050A a b - 1770B a b )d e + (300A a b + 1320B a b )d e +--R + +--R 4 5 +--R - 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (300A a b + 60B a b)e + (- 1200A a b - 600B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (300A b + 1500B a b )d e - 360B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (300A a b + 60B a )e + (- 900A a b - 540B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (600A a b + 1200B a b )d e + (600A a b - 600B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (- 900A a b - 900B a b )d e + (300A b + 1140B a b )d e +--R + +--R 6 6 +--R - 360B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 2 4 +--R (300A a b + 60B a )d e + (- 1200A a b - 600B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (300A a b + 1500B a b )d e - 360B a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 12B b e x + ((15A b + 87B a b )e - 18B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((115A a b + 275B a b )e + (- 25A b - 143B a b )d e + 30B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (400A a b + 500B a b )e + (- 225A a b - 525B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (50A b + 280B a b )d e - 60B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (900A a b + 600B a b )e + (- 1100A a b - 1300B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (650A a b + 1450B a b )d e + (- 150A b - 810B a b )d e +--R + +--R 6 4 2 +--R 180B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (600A a b + 300B a b)e + (- 300A a b - 600B a b )d e +--R + +--R 2 4 2 4 5 2 4 3 3 +--R - 600A a b d e + (750A a b + 1050B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 240A b - 1020B a b )d e + 300B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 5 +--R - 60A a b e + (900A a b + 360B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 1800A a b - 1500B a b )d e + (1500A a b + 2400B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 540A a b - 1800B a b )d e + (60A b + 600B a b )d e - 60B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 60A a e + (300A a b + 60B a )d e + (- 600A a b - 300B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (60A a b + 300B a b )d e - 60B a b d +--R / +--R 8 2 8 7 7 +--R 60b e x + (60a e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 595 + +)clear all + +--S 596 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1378 +r0:=-5/3*b*(3*b*B*d-2*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 5/4*b*(3*b*B*d-2*A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e))-1/2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e*(b*d-a*e)*(d+e*x)^2)-(3*b*B*d-2*A*b*e-a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x))-5*b*(b*d-a*e)^2*(3*b*B*d-_ + 2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+5/2*b*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+5*b*_ + (b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 3 2 4 6 2 3 3 2 5 +--R (120A a b + 60B a b)e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 2 4 +--R (240A a b + 120B a b)d e + (- 720A a b - 720B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (720A a b + 1440B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 360B b d e +--R * +--R x +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (120A a b + 60B a b)d e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 3B b e x + ((4A b + 20B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 10A b - 50B a b )d e + 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (120A a b + 120B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (40A b + 200B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (40A a b + 65B a b)e + (240A a b + 60B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 420A a b - 570B a b )d e + (180A b + 720B a b )d e +--R + +--R 5 4 2 +--R - 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 60A a b - 12B a )e + (320A a b + 250B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 240A a b - 600B a b )d e + (- 120A a b + 300B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (120A b + 240B a b )d e - 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 6A a e + (- 30A a b - 6B a )d e + (220A a b + 155B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 300A a b - 480B a b )d e + (120A a b + 510B a b )d e +--R + +--R 4 5 +--R - 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 12b e x + (12a e + 24b d e )x + (24a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 6 2 3 3 2 5 +--R (120A a b + 60B a b)e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 2 4 +--R (240A a b + 120B a b)d e + (- 720A a b - 720B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (720A a b + 1440B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 360B b d e +--R * +--R x +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (120A a b + 60B a b)d e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 3B b e x + ((4A b + 20B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 10A b - 50B a b )d e + 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (120A a b + 120B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (40A b + 200B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 2 4 +--R (240A a b + 240B a b )d e + (- 330A a b - 660B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (126A b + 630B a b )d e - 204B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 60A a b - 12B a )e + (240A a b + 120B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 240A a b - 240B a b )d e + (60A a b + 120B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (12A b + 60B a b )d e - 48B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 6A a e + (- 30A a b - 6B a )d e + (180A a b + 90B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 300A a b - 300B a b )d e + (210A a b + 420B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 54A b - 270B a b )d e + 66B b d +--R / +--R 9 2 8 2 7 +--R 12e x + 24d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 598 + +--S 599 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 4 6 2 3 3 2 5 +--R (- 120A a b - 60B a b)e + (360A a b + 360B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 360A a b - 720B a b )d e + (120A b + 600B a b )d e +--R + +--R 5 4 2 +--R - 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 2 4 +--R (- 240A a b - 120B a b)d e + (720A a b + 720B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 720A a b - 1440B a b )d e + (240A b + 1200B a b )d e +--R + +--R 5 5 +--R - 360B b d e +--R * +--R x +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 120A a b - 60B a b)d e + (360A a b + 360B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 360A a b - 720B a b )d e + (120A b + 600B a b )d e +--R + +--R 5 6 +--R - 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R - 3B b e x + ((- 4A b - 20B a b )e + 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((- 30A a b - 60B a b )e + (10A b + 50B a b )d e - 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 120A a b - 120B a b )e + (120A a b + 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 40A b - 200B a b )d e + 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 40A a b - 65B a b)e + (- 240A a b - 60B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (420A a b + 570B a b )d e + (- 180A b - 720B a b )d e +--R + +--R 5 4 2 +--R 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (60A a b + 12B a )e + (- 320A a b - 250B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (240A a b + 600B a b )d e + (120A a b - 300B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 120A b - 240B a b )d e + 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 6A a e + (30A a b + 6B a )d e + (- 220A a b - 155B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (300A a b + 480B a b )d e + (- 120A a b - 510B a b )d e +--R + +--R 4 5 +--R 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (120A a b + 60B a b )e + (- 360A a b - 360B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e +--R + +--R 6 4 2 +--R 180B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (120A a b + 60B a b)e + (- 120A a b - 240B a b )d e +--R + +--R 2 4 2 4 5 2 4 3 3 +--R - 360A a b d e + (600A a b + 840B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 240A b - 1020B a b )d e + 360B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (240A a b + 120B a b)d e + (- 600A a b - 660B a b )d e +--R + +--R 2 4 3 3 3 3 5 2 4 4 2 +--R (360A a b + 1080B a b )d e + (120A a b - 480B a b )d e +--R + +--R 6 5 5 6 6 +--R (- 120A b - 240B a b )d e + 180B b d +--R * +--R x +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (120A a b + 60B a b)d e + (- 360A a b - 360B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (360A a b + 720B a b )d e + (- 120A a b - 600B a b )d e +--R + +--R 5 6 +--R 180B a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 3B b e x + ((4A b + 23B a b )e - 6B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((34A a b + 80B a b )e + (- 10A b - 56B a b )d e + 15B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (150A a b + 180B a b )e + (- 130A a b - 290B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (40A b + 215B a b )d e - 60B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 5 +--R (120A a b + 120B a b )e + 120A a b d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (- 290A a b - 460B a b )d e + (126A b + 570B a b )d e - 204B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 60A a b - 12B a b)e + (480A a b + 360B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 570A a b - 900B a b )d e + (186A a b + 750B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (12A b - 144B a b )d e - 48B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 66A a b - 12B a )e + (210A a b + 114B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 60A a b - 150B a b )d e + (- 240A a b - 180B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (222A a b + 480B a b )d e + (- 54A b - 318B a b )d e + 66B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 6A a e + (- 30A a b - 6B a )d e + (180A a b + 90B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 300A a b - 300B a b )d e + (210A a b + 420B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- 54A a b - 270B a b )d e + 66B a b d +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 12b e x + (12a e + 24b d e )x + (24a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1378 +r0:=10/3*b^2*(2*b*B*d-A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-_ + a*e))-5/2*b*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x))-1/3*(B*d-A*e)*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^3)-1/2*(2*b*B*d-A*b*e-_ + a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^2)+_ + 10*b^2*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 5*b^2*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-_ + 10*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 2 3 3 2 6 4 2 3 5 +--R (60A a b + 60B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (60A b + 300B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 2 4 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R x +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (60A a b + 60B a b )d e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 120B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 2B b e x + ((3A b + 15B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 15A b - 75B a b )d e + 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 20A a b + 20B a b )e + (160A a b + 200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 110A b - 430B a b )d e + 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (120A a b + 240B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (120A a b - 120B a b )d e + (- 150A b - 390B a b )d e +--R + +--R 5 4 2 +--R 300B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 15A a b - 3B a )e + (- 60A a b - 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (210A a b + 330B a b )d e + (- 60A a b - 480B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b + 60B a b )d e + 120B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 2A a e + (- 5A a b - B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (90A a b + 130B a b )d e + (- 60A a b - 240B a b )d e + 120B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 8 3 7 3 7 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 6 4 2 3 5 +--R (60A a b + 60B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (60A b + 300B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 2 4 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R x +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (60A a b + 60B a b )d e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 120B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 2B b e x + ((3A b + 15B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 15A b - 75B a b )d e + 30B b d e )x +--R + +--R 4 2 3 5 5 4 2 4 5 3 3 3 +--R ((90A a b + 180B a b )d e + (- 63A b - 315B a b )d e + 146B b d e )x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (180A a b + 180B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (- 90A a b - 180B a b )d e + (- 9A b - 45B a b )d e + 78B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 15A a b - 3B a )e + (- 60A a b - 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (270A a b + 270B a b )d e + (- 270A a b - 540B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (81A b + 405B a b )d e - 102B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 2A a e + (- 5A a b - B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (110A a b + 110B a b )d e + (- 130A a b - 260B a b )d e +--R + +--R 5 4 5 5 6 +--R (47A b + 235B a b )d e - 74B b d +--R / +--R 10 3 9 2 2 8 3 7 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 603 + +--S 604 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 3 2 6 4 2 3 5 +--R (- 60A a b - 60B a b )e + (120A a b + 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 60A b - 300B a b )d e + 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 2 4 +--R (- 180A a b - 180B a b )d e + (360A a b + 720B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (- 180A b - 900B a b )d e + 360B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 180A a b - 180B a b )d e + (360A a b + 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 180A b - 900B a b )d e + 360B b d e +--R * +--R x +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 60A a b - 60B a b )d e + (120A a b + 240B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 60A b - 300B a b )d e + 120B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R - 2B b e x + ((- 3A b - 15B a b )e + 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((- 30A a b - 60B a b )e + (15A b + 75B a b )d e - 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (20A a b - 20B a b )e + (- 160A a b - 200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (110A b + 430B a b )d e - 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (60A a b + 30B a b)e + (- 120A a b - 240B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 120A a b + 120B a b )d e + (150A b + 390B a b )d e +--R + +--R 5 4 2 +--R - 300B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (15A a b + 3B a )e + (60A a b + 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 210A a b - 330B a b )d e + (60A a b + 480B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (60A b - 60B a b )d e - 120B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 2A a e + (5A a b + B a )d e + (20A a b + 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 90A a b - 130B a b )d e + (60A a b + 240B a b )d e +--R + +--R 4 5 +--R - 120B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (60A a b + 60B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (60A b + 300B a b )d e - 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (60A a b + 60B a b )e + (60A a b - 60B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 300A a b - 420B a b )d e + (180A b + 780B a b )d e +--R + +--R 6 4 2 +--R - 360B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 2 4 +--R (180A a b + 180B a b )d e + (- 180A a b - 540B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 180A a b + 180B a b )d e + (180A b + 540B a b )d e +--R + +--R 6 5 +--R - 360B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (180A a b + 180B a b )d e + (- 300A a b - 660B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (60A a b + 660B a b )d e + (60A b - 60B a b )d e - 120B b d +--R * +--R x +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (60A a b + 60B a b )d e + (- 120A a b - 240B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (60A a b + 300B a b )d e - 120B a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 2B b e x + ((3A b + 17B a b )e - 6B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((33A a b + 75B a b )e + (- 15A b - 81B a b )d e + 30B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (30A a b + 60B a b )e + (75A a b + 105B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 63A b - 285B a b )d e + 146B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 60A a b - 30B a b )e + (270A a b + 360B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (- 153A a b - 495B a b )d e + (- 9A b + 101B a b )d e + 78B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 75A a b - 33B a b)e + (120A a b + 150B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (180A a b + 90B a b )d e + (- 279A a b - 585B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (81A b + 483B a b )d e - 102B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 17A a b - 3B a )e + (- 65A a b - 31B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (250A a b + 260B a b )d e + (- 160A a b - 430B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 49A a b + 145B a b )d e + (47A b + 133B a b )d e - 74B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 2A a e + (- 5A a b - B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (110A a b + 110B a b )d e + (- 130A a b - 260B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (47A a b + 235B a b )d e - 74B a b d +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 8 3 7 3 7 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 605 + +)clear all + +--S 606 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1378 +r0:=-5/12*b*(3*b*B*d-A*b*e-2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^2)-5/3*b^2*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x))-_ + 1/4*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/6*(3*b*B*d-A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^3)-5*b^3*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^6+5/2*b^3*(3*b*B*d-A*b*e-2*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e))+5*b^3*(b*d-a*e)*(3*b*B*d-_ + A*b*e-2*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 2 3 6 5 4 5 +--R (60A a b + 120B a b )e + (- 60A b - 300B a b )d e +--R + +--R 5 2 4 +--R 180B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 5 5 4 2 4 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 3 3 +--R 720B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 360A b - 1800B a b )d e +--R + +--R 5 4 2 +--R 1080B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 720B b d e +--R * +--R x +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (60A a b + 120B a b )d e + (- 60A b - 300B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 6B b e x + ((12A b + 60B a b )e - 36B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((- 65A a b - 40B a b )e + (125A b + 445B a b )d e - 375B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 120A a b - 120B a b )e + (- 20A a b + 320B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (260A b + 580B a b )d e - 780B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (- 180A a b - 180B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (150A a b + 840B a b )d e + (210A b - 30B a b )d e - 630B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 20A a b - 4B a )e + (- 40A a b - 20B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 120A a b - 120B a b )d e + (180A a b + 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (60A b - 420B a b )d e - 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 3A a e + (- 5A a b - B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (- 30A a b - 30B a b )d e + (60A a b + 210B a b )d e - 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 6 5 4 5 +--R (60A a b + 120B a b )e + (- 60A b - 300B a b )d e +--R + +--R 5 2 4 +--R 180B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 5 5 4 2 4 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 3 3 +--R 720B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 360A b - 1800B a b )d e +--R + +--R 5 4 2 +--R 1080B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 720B b d e +--R * +--R x +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (60A a b + 120B a b )d e + (- 60A b - 300B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 6B b e x + ((12A b + 60B a b )e - 36B b d e )x +--R + +--R 5 4 5 5 2 4 4 +--R ((48A b + 240B a b )d e - 204B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 120A a b - 120B a b )e + (240A a b + 480B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 48A b - 240B a b )d e - 96B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (- 180A a b - 180B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (540A a b + 1080B a b )d e + (- 252A b - 1260B a b )d e +--R + +--R 5 4 2 +--R 396B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 20A a b - 4B a )e + (- 40A a b - 20B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 120A a b - 120B a b )d e + (440A a b + 880B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 248A b - 1240B a b )d e + 504B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 3A a e + (- 5A a b - B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 30A a b - 30B a b )d e + (125A a b + 250B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 77A b - 385B a b )d e + 171B b d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 608 + +--S 609 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 3 6 5 4 5 +--R (- 60A a b - 120B a b )e + (60A b + 300B a b )d e +--R + +--R 5 2 4 +--R - 180B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 5 5 4 2 4 +--R (- 240A a b - 480B a b )d e + (240A b + 1200B a b )d e +--R + +--R 5 3 3 +--R - 720B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 360A a b - 720B a b )d e + (360A b + 1800B a b )d e +--R + +--R 5 4 2 +--R - 1080B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 240A a b - 480B a b )d e + (240A b + 1200B a b )d e +--R + +--R 5 5 +--R - 720B b d e +--R * +--R x +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (- 60A a b - 120B a b )d e + (60A b + 300B a b )d e - 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R - 6B b e x + ((- 12A b - 60B a b )e + 36B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (65A a b + 40B a b )e + (- 125A b - 445B a b )d e +--R + +--R 5 2 4 +--R 375B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (120A a b + 120B a b )e + (20A a b - 320B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 260A b - 580B a b )d e + 780B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (60A a b + 30B a b)e + (180A a b + 180B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 150A a b - 840B a b )d e + (- 210A b + 30B a b )d e +--R + +--R 5 4 2 +--R 630B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (20A a b + 4B a )e + (40A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (120A a b + 120B a b )d e + (- 180A a b - 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b + 420B a b )d e + 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 3A a e + (5A a b + B a )d e + (10A a b + 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (30A a b + 30B a b )d e + (- 60A a b - 210B a b )d e + 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 4 6 6 5 5 +--R (60A a b + 120B a b )e + (- 60A b - 300B a b )d e +--R + +--R 6 2 4 +--R 180B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (60A a b + 120B a b )e + (180A a b + 180B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 240A b - 1020B a b )d e + 720B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 5 2 4 2 4 +--R (240A a b + 480B a b )d e + (120A a b - 480B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 360A b - 1080B a b )d e + 1080B b d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (360A a b + 720B a b )d e + (- 120A a b - 1320B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 240A b - 120B a b )d e + 720B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 3 3 5 2 4 4 2 +--R (240A a b + 480B a b )d e + (- 180A a b - 1080B a b )d e +--R + +--R 6 5 5 6 6 +--R (- 60A b + 420B a b )d e + 180B b d +--R * +--R x +--R + +--R 2 4 3 3 4 2 5 2 4 5 5 6 +--R (60A a b + 120B a b )d e + (- 60A a b - 300B a b )d e + 180B a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 6B b e x + ((12A b + 66B a b )e - 36B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((12A a b + 60B a b )e + (48A b + 204B a b )d e - 204B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 120A a b - 120B a b )e + (288A a b + 720B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 48A b - 444B a b )d e - 96B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 180A a b - 150B a b )e + (60A a b + 300B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (492A a b + 840B a b )d e + (- 252A b - 1356B a b )d e +--R + +--R 6 4 2 +--R 396B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 80A a b - 34B a b)e + (- 220A a b - 200B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (420A a b + 960B a b )d e + (188A a b - 380B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 248A b - 844B a b )d e + 504B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 23A a b - 4B a )e + (- 45A a b - 21B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 130A a b - 125B a b )d e + (410A a b + 850B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 123A a b - 990B a b )d e + (- 77A b + 119B a b )d e + 171B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 3A a e + (- 5A a b - B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 30A a b - 30B a b )d e + (125A a b + 250B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- 77A a b - 385B a b )d e + 171B a b d +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 610 + +)clear all + +--S 611 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^6 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1378 +r0:=-1/12*b*(6*b*B*d-A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e)*(d+e*x)^3)-1/6*b^2*(6*b*B*d-A*b*e-5*a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^2)-1/5*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^5)-_ + 1/20*(6*b*B*d-A*b*e-5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*_ + (b*d-a*e)*(d+e*x)^4)+b^4*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^6*(b*d-a*e))-1/2*b^3*(6*b*B*d-A*b*e-5*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*(d+e*x))-b^4*(6*b*B*d-A*b*e-_ + 5*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 4 6 5 5 5 +--R ((60A b + 300B a b )e - 360B b d e )x +--R + +--R 5 4 5 5 2 4 4 +--R ((300A b + 1500B a b )d e - 1800B b d e )x +--R + +--R 5 4 2 4 5 3 3 3 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 3 3 5 4 2 2 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 4 2 5 5 +--R ((300A b + 1500B a b )d e - 1800B b d e)x +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 60B b e x + ((- 137A b - 325B a b )e + 822B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 300A a b - 600B a b )e + (- 385A b - 125B a b )d e +--R + +--R 5 2 4 +--R 2310B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 300A a b - 300B a b )e + (- 600A a b - 1200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 470A b + 1250B a b )d e + 2820B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 200A a b - 100B a b)e + (- 300A a b - 300B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 600A a b - 1200B a b )d e + (- 270A b + 2250B a b )d e +--R + +--R 5 4 2 +--R 1620B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 75A a b - 15B a )e + (- 100A a b - 50B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 150A a b - 150B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b + 1500B a b )d e + 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 12A a e + (- 15A a b - 3B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (- 30A a b - 30B a b )d e + (- 60A a b - 120B a b )d e + 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 8 5 7 5 7 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 6 5 5 5 +--R ((60A b + 300B a b )e - 360B b d e )x +--R + +--R 5 4 5 5 2 4 4 +--R ((300A b + 1500B a b )d e - 1800B b d e )x +--R + +--R 5 4 2 4 5 3 3 3 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 3 3 5 4 2 2 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 4 2 5 5 5 4 5 +--R ((300A b + 1500B a b )d e - 1800B b d e)x + (60A b + 300B a b )d e +--R + +--R 5 6 +--R - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 5 5 +--R 60B b e x + 300B b d e x +--R + +--R 4 2 3 6 5 4 5 +--R (- 300A a b - 600B a b )e + (300A b + 1500B a b )d e +--R + +--R 5 2 4 +--R - 300B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 300A a b - 300B a b )e + (- 600A a b - 1200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (900A b + 4500B a b )d e - 2400B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 200A a b - 100B a b)e + (- 300A a b - 300B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 600A a b - 1200B a b )d e + (1100A b + 5500B a b )d e +--R + +--R 5 4 2 +--R - 3600B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 75A a b - 15B a )e + (- 100A a b - 50B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 150A a b - 150B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (625A b + 3125B a b )d e - 2250B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 12A a e + (- 15A a b - 3B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 30A a b - 30B a b )d e + (- 60A a b - 120B a b )d e +--R + +--R 5 4 5 5 6 +--R (137A b + 685B a b )d e - 522B b d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 5 7 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 613 + +--S 614 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 6 5 5 5 +--R ((- 60A b - 300B a b )e + 360B b d e )x +--R + +--R 5 4 5 5 2 4 4 +--R ((- 300A b - 1500B a b )d e + 1800B b d e )x +--R + +--R 5 4 2 4 5 3 3 3 +--R ((- 600A b - 3000B a b )d e + 3600B b d e )x +--R + +--R 5 4 3 3 5 4 2 2 +--R ((- 600A b - 3000B a b )d e + 3600B b d e )x +--R + +--R 5 4 4 2 5 5 +--R ((- 300A b - 1500B a b )d e + 1800B b d e)x +--R + +--R 5 4 5 5 6 +--R (- 60A b - 300B a b )d e + 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R - 60B b e x + ((137A b + 325B a b )e - 822B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (300A a b + 600B a b )e + (385A b + 125B a b )d e +--R + +--R 5 2 4 +--R - 2310B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (300A a b + 300B a b )e + (600A a b + 1200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (470A b - 1250B a b )d e - 2820B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (200A a b + 100B a b)e + (300A a b + 300B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (600A a b + 1200B a b )d e + (270A b - 2250B a b )d e +--R + +--R 5 4 2 +--R - 1620B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (75A a b + 15B a )e + (100A a b + 50B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (150A a b + 150B a b )d e + (300A a b + 600B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (60A b - 1500B a b )d e - 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 12A a e + (15A a b + 3B a )d e + (20A a b + 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (30A a b + 30B a b )d e + (60A a b + 120B a b )d e - 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 6 6 5 6 +--R ((60A b + 300B a b )e - 360B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (60A a b + 300B a b )e + (300A b + 1140B a b )d e +--R + +--R 6 2 4 +--R - 1800B b d e +--R * +--R 5 +--R x +--R + +--R 5 2 4 5 6 5 2 4 +--R (300A a b + 1500B a b )d e + (600A b + 1200B a b )d e +--R + +--R 6 3 3 +--R - 3600B b d e +--R * +--R 4 +--R x +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (600A a b + 3000B a b )d e + (600A b - 600B a b )d e +--R + +--R 6 4 2 +--R - 3600B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (600A a b + 3000B a b )d e + (300A b - 2100B a b )d e +--R + +--R 6 5 +--R - 1800B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 2 6 5 5 +--R (300A a b + 1500B a b )d e + (60A b - 1500B a b )d e +--R + +--R 6 6 +--R - 360B b d +--R * +--R x +--R + +--R 5 2 4 5 5 6 +--R (60A a b + 300B a b )d e - 360B a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 5 6 6 5 6 +--R 60B b e x + (60B a b e + 300B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 300A a b - 600B a b )e + (300A b + 1800B a b )d e +--R + +--R 6 2 4 +--R - 300B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 600A a b - 900B a b )e + (- 300A a b + 300B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (900A b + 4200B a b )d e - 2400B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 500A a b - 400B a b )e + (- 900A a b - 1500B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (300A a b + 3300B a b )d e + (1100A b + 3100B a b )d e +--R + +--R 6 4 2 +--R - 3600B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 275A a b - 115B a b)e + (- 400A a b - 350B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 750A a b - 1350B a b )d e + (800A a b + 4900B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (625A b - 475B a b )d e - 2250B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 87A a b - 15B a )e + (- 115A a b - 53B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 170A a b - 160B a b )d e + (- 330A a b - 630B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (565A a b + 3005B a b )d e + (137A b - 1565B a b )d e - 522B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 12A a e + (- 15A a b - 3B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 30A a b - 30B a b )d e + (- 60A a b - 120B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (137A a b + 685B a b )d e - 522B a b d +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 8 5 7 5 7 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^7 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1378 +r0:=-1/4*b*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^4)-_ + 1/3*b^2*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^3)-1/6*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^6)-_ + 1/5*B*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^5)-1/2*b^3*B*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^2)+b^4*B*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))+b^5*B*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 7 6 6 6 5 6 6 2 5 5 +--R (60B a b e - 60B b d e )x + (360B a b d e - 360B b d e )x +--R + +--R 5 2 5 6 3 4 4 5 3 4 6 4 3 3 +--R (900B a b d e - 900B b d e )x + (1200B a b d e - 1200B b d e )x +--R + +--R 5 4 3 6 5 2 2 5 5 2 6 6 +--R (900B a b d e - 900B b d e )x + (360B a b d e - 360B b d e)x +--R + +--R 5 6 6 7 +--R 60B a b d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 6 5 7 6 6 6 +--R ((- 10A b - 77B a b )e + 87B b d e )x +--R + +--R 5 2 4 7 5 6 6 2 5 5 +--R ((- 60A a b - 300B a b )e + 198B a b d e + 162B b d e )x +--R + +--R 2 4 3 3 7 2 4 6 5 2 5 +--R (- 150A a b - 300B a b )e - 450B a b d e + 945B a b d e +--R + +--R 6 3 4 +--R - 45B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 3 3 6 2 4 2 5 +--R (- 200A a b - 200B a b )e - 200B a b d e - 600B a b d e +--R + +--R 5 3 4 6 4 3 +--R 1660B a b d e - 460B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 4 2 6 3 3 2 5 +--R (- 150A a b - 75B a b)e - 75B a b d e - 150B a b d e +--R + +--R 2 4 3 4 5 4 3 6 5 2 +--R - 450B a b d e + 1470B a b d e - 570B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 5 6 4 2 2 5 3 3 3 4 +--R (- 60A a b - 12B a )e - 18B a b d e - 30B a b d e - 60B a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 180B a b d e + 660B a b d e - 300B b d e +--R * +--R x +--R + +--R 6 7 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 10A a e - 2B a d e - 3B a b d e - 5B a b d e - 10B a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R - 30B a b d e + 120B a b d e - 60B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 2 13 7 2 14 13 2 2 12 6 +--R (60a b e - 60b d e )x + (60a e + 300a b d e - 360b d e )x +--R + +--R 2 13 2 12 2 3 11 5 +--R (360a d e + 540a b d e - 900b d e )x +--R + +--R 2 2 12 3 11 2 4 10 4 +--R (900a d e + 300a b d e - 1200b d e )x +--R + +--R 2 3 11 4 10 2 5 9 3 +--R (1200a d e - 300a b d e - 900b d e )x +--R + +--R 2 4 10 5 9 2 6 8 2 +--R (900a d e - 540a b d e - 360b d e )x +--R + +--R 2 5 9 6 8 2 7 7 2 6 8 7 7 +--R (360a d e - 300a b d e - 60b d e )x + 60a d e - 60a b d e +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 5 5 5 2 4 4 5 3 3 3 +--R 60B b e x + 360B b d e x + 900B b d e x + 1200B b d e x +--R + +--R 5 4 2 2 5 5 5 6 +--R 900B b d e x + 360B b d e x + 60B b d +--R * +--R log(e x + d) +--R + +--R 5 4 6 5 5 5 +--R ((- 60A b - 300B a b )e + 360B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 150A a b - 300B a b )e + (- 150A b - 750B a b )d e +--R + +--R 5 2 4 +--R 1350B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 200A a b - 200B a b )e + (- 200A a b - 400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 200A b - 1000B a b )d e + 2200B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 150A a b - 75B a b)e + (- 150A a b - 150B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 150A a b - 300B a b )d e + (- 150A b - 750B a b )d e +--R + +--R 5 4 2 +--R 1875B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 60A a b - 12B a )e + (- 60A a b - 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 60A a b - 60B a b )d e + (- 60A a b - 120B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b - 300B a b )d e + 822B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 10A a e + (- 10A a b - 2B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 10A a b - 10B a b )d e + (- 10A a b - 20B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 10A b - 50B a b )d e + 147B b d +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 5 8 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 7 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 618 + +--S 619 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 7 6 6 6 5 6 6 2 5 5 +--R (- 60B a b e + 60B b d e )x + (- 360B a b d e + 360B b d e )x +--R + +--R 5 2 5 6 3 4 4 +--R (- 900B a b d e + 900B b d e )x +--R + +--R 5 3 4 6 4 3 3 +--R (- 1200B a b d e + 1200B b d e )x +--R + +--R 5 4 3 6 5 2 2 +--R (- 900B a b d e + 900B b d e )x +--R + +--R 5 5 2 6 6 5 6 6 7 +--R (- 360B a b d e + 360B b d e)x - 60B a b d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 6 5 7 6 6 6 +--R ((10A b + 77B a b )e - 87B b d e )x +--R + +--R 5 2 4 7 5 6 6 2 5 5 +--R ((60A a b + 300B a b )e - 198B a b d e - 162B b d e )x +--R + +--R 2 4 3 3 7 2 4 6 5 2 5 +--R (150A a b + 300B a b )e + 450B a b d e - 945B a b d e +--R + +--R 6 3 4 +--R 45B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 3 3 6 2 4 2 5 +--R (200A a b + 200B a b )e + 200B a b d e + 600B a b d e +--R + +--R 5 3 4 6 4 3 +--R - 1660B a b d e + 460B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 4 2 6 3 3 2 5 +--R (150A a b + 75B a b)e + 75B a b d e + 150B a b d e +--R + +--R 2 4 3 4 5 4 3 6 5 2 +--R 450B a b d e - 1470B a b d e + 570B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 5 6 4 2 2 5 3 3 3 4 +--R (60A a b + 12B a )e + 18B a b d e + 30B a b d e + 60B a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 180B a b d e - 660B a b d e + 300B b d e +--R * +--R x +--R + +--R 6 7 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 10A a e + 2B a d e + 3B a b d e + 5B a b d e + 10B a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R 30B a b d e - 120B a b d e + 60B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 7 6 7 +--R (60B a b e - 60B b d e )x +--R + +--R 2 5 7 6 6 7 2 5 6 +--R (60B a b e + 300B a b d e - 360B b d e )x +--R + +--R 2 5 6 6 2 5 7 3 4 5 +--R (360B a b d e + 540B a b d e - 900B b d e )x +--R + +--R 2 5 2 5 6 3 4 7 4 3 4 +--R (900B a b d e + 300B a b d e - 1200B b d e )x +--R + +--R 2 5 3 4 6 4 3 7 5 2 3 +--R (1200B a b d e - 300B a b d e - 900B b d e )x +--R + +--R 2 5 4 3 6 5 2 7 6 2 +--R (900B a b d e - 540B a b d e - 360B b d e)x +--R + +--R 2 5 5 2 6 6 7 7 2 5 6 6 7 +--R (360B a b d e - 300B a b d e - 60B b d )x + 60B a b d e - 60B a b d +--R * +--R log(e x + d) +--R + +--R 6 2 5 7 7 6 6 7 2 5 6 +--R ((- 60A a b - 300B a b )e + (60A b + 660B a b )d e - 360B b d e )x +--R + +--R 2 5 3 4 7 6 2 5 6 +--R (- 210A a b - 600B a b )e + (60A a b + 210B a b )d e +--R + +--R 7 6 2 5 7 3 4 +--R (150A b + 1740B a b )d e - 1350B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 7 3 4 6 +--R (- 350A a b - 500B a b )e - 650B a b d e +--R + +--R 6 2 5 2 5 7 6 3 4 +--R (150A a b + 1500B a b )d e + (200A b + 1850B a b )d e +--R + +--R 7 4 3 +--R - 2200B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 4 3 6 3 4 2 5 +--R (- 350A a b - 275B a b )e - 275B a b d e - 750B a b d e +--R + +--R 6 2 5 3 4 7 6 4 3 7 5 2 +--R (200A a b + 2750B a b )d e + (150A b + 425B a b )d e - 1875B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 7 5 2 6 4 3 2 5 +--R (- 210A a b - 87B a b)e - 93B a b d e - 180B a b d e +--R + +--R 3 4 3 4 6 2 5 4 3 +--R - 510B a b d e + (150A a b + 2445B a b )d e +--R + +--R 7 6 5 2 7 6 +--R (60A b - 753B a b )d e - 822B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 7 6 6 5 2 2 5 4 3 3 4 +--R (- 70A a b - 12B a )e - 20B a b d e - 33B a b d e - 65B a b d e +--R + +--R 3 4 4 3 6 2 5 5 2 +--R - 190B a b d e + (60A a b + 1092B a b )d e +--R + +--R 7 6 6 7 7 +--R (10A b - 625B a b )d e - 147B b d +--R * +--R x +--R + +--R 7 7 7 6 6 2 5 5 2 3 4 4 3 4 3 +--R - 10A a e - 2B a d e - 3B a b d e - 5B a b d e - 10B a b d e +--R + +--R 3 4 5 2 6 2 5 6 6 7 +--R - 30B a b d e + (10A a b + 197B a b )d e - 147B a b d +--R / +--R 14 2 13 7 2 14 13 2 2 12 6 +--R (60a b e - 60b d e )x + (60a e + 300a b d e - 360b d e )x +--R + +--R 2 13 2 12 2 3 11 5 +--R (360a d e + 540a b d e - 900b d e )x +--R + +--R 2 2 12 3 11 2 4 10 4 +--R (900a d e + 300a b d e - 1200b d e )x +--R + +--R 2 3 11 4 10 2 5 9 3 +--R (1200a d e - 300a b d e - 900b d e )x +--R + +--R 2 4 10 5 9 2 6 8 2 +--R (900a d e - 540a b d e - 360b d e )x +--R + +--R 2 5 9 6 8 2 7 7 2 6 8 7 7 +--R (360a d e - 300a b d e - 60b d e )x + 60a d e - 60a b d e +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 620 + +)clear all + +--S 621 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^8 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1378 +r0:=1/6*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*_ + (d+e*x)^6)+1/7*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*_ + (d+e*x)^7) +--R +--R +--R (2) +--R 6 5 6 6 +--R ((A b - 7B a b )e + 6B b d)x +--R + +--R 5 2 4 6 5 5 +--R ((- A a b - 35B a b )e + (7A b + 29B a b )d)x +--R + +--R 2 4 3 3 5 2 4 4 +--R ((- 20A a b - 70B a b )e + (35A a b + 55B a b )d)x +--R + +--R 3 3 4 2 2 4 3 3 3 +--R ((- 50A a b - 70B a b )e + (70A a b + 50B a b )d)x +--R + +--R 4 2 5 3 3 4 2 2 +--R ((- 55A a b - 35B a b)e + (70A a b + 20B a b )d)x +--R + +--R 5 6 4 2 5 6 5 6 +--R ((- 29A a b - 7B a )e + (35A a b + B a b)d)x - 6A a e + (7A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 9 8 2 2 7 7 +--R (42a e - 84a b d e + 42b d e )x +--R + +--R 2 8 2 7 2 3 6 6 +--R (294a d e - 588a b d e + 294b d e )x +--R + +--R 2 2 7 3 6 2 4 5 5 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 3 6 4 5 2 5 4 4 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 4 5 5 4 2 6 3 3 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 5 4 6 3 2 7 2 2 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 6 3 7 2 2 8 2 7 2 8 2 9 +--R (294a d e - 588a b d e + 294b d e)x + 42a d e - 84a b d e + 42b d +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 42B b e x + ((- 21A b - 105B a b )e - 126B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((- 70A a b - 140B a b )e + (- 35A b - 175B a b )d e - 210B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 105A a b - 105B a b )e + (- 70A a b - 140B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 35A b - 175B a b )d e - 210B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 84A a b - 42B a b)e + (- 63A a b - 63B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (- 42A a b - 84B a b )d e + (- 21A b - 105B a b )d e - 126B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 35A a b - 7B a )e + (- 28A a b - 14B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 21A a b - 21B a b )d e + (- 14A a b - 28B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 7A b - 35B a b )d e - 42B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 6A a e + (- 5A a b - B a )d e + (- 4A a b - 2B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 3A a b - 3B a b )d e + (- 2A a b - 4B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - 6B b d +--R / +--R 14 7 13 6 2 12 5 3 11 4 4 10 3 5 9 2 +--R 42e x + 294d e x + 882d e x + 1470d e x + 1470d e x + 882d e x +--R + +--R 6 8 7 7 +--R 294d e x + 42d e +--R Type: Union(Expression(Integer),...) +--E 623 + +--S 624 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 8 6 7 6 +--R ((- A b + 7B a b )e - 6B b d e )x +--R + +--R 5 2 4 8 6 5 7 5 +--R ((A a b + 35B a b )e + (- 7A b - 29B a b )d e )x +--R + +--R 2 4 3 3 8 5 2 4 7 4 +--R ((20A a b + 70B a b )e + (- 35A a b - 55B a b )d e )x +--R + +--R 3 3 4 2 8 2 4 3 3 7 3 +--R ((50A a b + 70B a b )e + (- 70A a b - 50B a b )d e )x +--R + +--R 4 2 5 8 3 3 4 2 7 2 +--R ((55A a b + 35B a b)e + (- 70A a b - 20B a b )d e )x +--R + +--R 5 6 8 4 2 5 7 6 8 +--R ((29A a b + 7B a )e + (- 35A a b - B a b)d e )x + 6A a e +--R + +--R 5 6 7 +--R (- 7A a b + B a )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 5 8 6 7 7 2 6 6 +--R (- 42B a b e + 84B a b d e - 42B b d e )x +--R + +--R 2 5 3 4 8 6 2 5 7 +--R (- 21A a b - 105B a b )e + (42A a b + 84B a b )d e +--R + +--R 7 6 2 6 7 3 5 +--R (- 21A b + 147B a b )d e - 126B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 8 2 5 3 4 7 +--R (- 70A a b - 140B a b )e + (105A a b + 105B a b )d e +--R + +--R 7 6 3 5 7 4 4 +--R (- 35A b + 245B a b )d e - 210B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 8 3 4 4 3 7 +--R (- 105A a b - 105B a b )e + (140A a b + 70B a b )d e +--R + +--R 7 6 4 4 7 5 3 +--R (- 35A b + 245B a b )d e - 210B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 8 4 3 5 2 7 +--R (- 84A a b - 42B a b)e + (105A a b + 21B a b )d e +--R + +--R 7 6 5 3 7 6 2 +--R (- 21A b + 147B a b )d e - 126B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 8 5 2 7 7 6 6 2 +--R (- 35A a b - 7B a )e + 42A a b d e + (- 7A b + 49B a b )d e +--R + +--R 7 7 +--R - 42B b d e +--R * +--R x +--R + +--R 7 8 6 7 7 7 6 7 7 8 +--R - 6A a e + (7A a b - B a )d e + (- A b + 7B a b )d e - 6B b d +--R / +--R 2 16 15 2 2 14 7 +--R (42a e - 84a b d e + 42b d e )x +--R + +--R 2 15 2 14 2 3 13 6 +--R (294a d e - 588a b d e + 294b d e )x +--R + +--R 2 2 14 3 13 2 4 12 5 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 3 13 4 12 2 5 11 4 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 4 12 5 11 2 6 10 3 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 5 11 6 10 2 7 9 2 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 6 10 7 9 2 8 8 2 7 9 8 8 2 9 7 +--R (294a d e - 588a b d e + 294b d e )x + 42a d e - 84a b d e + 42b d e +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 625 + +)clear all + +--S 626 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^9 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1378 +r0:=-1/8*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^8)+1/24*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^7)+1/168*(3*b*B*d+A*b*e-_ + 4*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^7) +--R +--R +--R (2) +--R 7 6 2 7 7 +--R ((- A b + 4B a b )e - 3B b d e)x +--R + +--R 6 2 5 2 7 6 7 2 6 +--R ((A a b - 4B a b )e + (- 8A b + 35B a b )d e - 24B b d )x +--R + +--R 2 5 3 4 2 6 2 5 +--R (- A a b - 80B a b )e + (8A a b + 217B a b )d e +--R + +--R 7 6 2 +--R (- 28A b - 116B a b )d +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 2 2 5 3 4 +--R (- 55A a b - 200B a b )e + (160A a b + 455B a b )d e +--R + +--R 6 2 5 2 +--R (- 140A a b - 220B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 2 3 4 4 3 +--R (- 155A a b - 220B a b )e + (400A a b + 455B a b )d e +--R + +--R 2 5 3 4 2 +--R (- 280A a b - 200B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 6 2 4 3 5 2 +--R (- 181A a b - 116B a b)e + (440A a b + 217B a b )d e +--R + +--R 3 4 4 3 2 +--R (- 280A a b - 80B a b )d +--R * +--R 2 +--R x +--R + +--R 6 7 2 5 2 6 +--R (- 99A a b - 24B a )e + (232A a b + 35B a b)d e +--R + +--R 4 3 5 2 2 +--R (- 140A a b - 4B a b )d +--R * +--R x +--R + +--R 7 2 6 7 5 2 6 2 +--R - 21A a e + (48A a b - 3B a )d e + (- 28A a b + 4B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 11 2 10 2 2 9 3 3 8 8 +--R (168a e - 504a b d e + 504a b d e - 168b d e )x +--R + +--R 3 10 2 2 9 2 3 8 3 4 7 7 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e )x +--R + +--R 3 2 9 2 3 8 2 4 7 3 5 6 6 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (11760a d e - 35280a b d e + 35280a b d e - 11760b d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e)x + 168a d e +--R + +--R 2 9 2 2 10 3 11 +--R - 504a b d e + 504a b d e - 168b d +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 84B b e x + ((- 56A b - 280B a b )e - 168B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 210A a b - 420B a b )e + (- 70A b - 350B a b )d e +--R + +--R 5 2 4 +--R - 210B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 336A a b - 336B a b )e + (- 168A a b - 336B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 56A b - 280B a b )d e - 168B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 280A a b - 140B a b)e + (- 168A a b - 168B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (- 84A a b - 168B a b )d e + (- 28A b - 140B a b )d e - 84B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 120A a b - 24B a )e + (- 80A a b - 40B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 48A a b - 48B a b )d e + (- 24A a b - 48B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 8A b - 40B a b )d e - 24B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 21A a e + (- 15A a b - 3B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 6A a b - 6B a b )d e + (- 3A a b - 6B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - 3B b d +--R / +--R 15 8 14 7 2 13 6 3 12 5 4 11 4 +--R 168e x + 1344d e x + 4704d e x + 9408d e x + 11760d e x +--R + +--R 5 10 3 6 9 2 7 8 8 7 +--R 9408d e x + 4704d e x + 1344d e x + 168d e +--R Type: Union(Expression(Integer),...) +--E 628 + +--S 629 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 6 9 7 8 7 +--R ((A b - 4B a b )e + 3B b d e )x +--R + +--R 6 2 5 9 7 6 8 7 2 7 6 +--R ((- A a b + 4B a b )e + (8A b - 35B a b )d e + 24B b d e )x +--R + +--R 2 5 3 4 9 6 2 5 8 +--R (A a b + 80B a b )e + (- 8A a b - 217B a b )d e +--R + +--R 7 6 2 7 +--R (28A b + 116B a b )d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 9 2 5 3 4 8 +--R (55A a b + 200B a b )e + (- 160A a b - 455B a b )d e +--R + +--R 6 2 5 2 7 +--R (140A a b + 220B a b )d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 9 3 4 4 3 8 +--R (155A a b + 220B a b )e + (- 400A a b - 455B a b )d e +--R + +--R 2 5 3 4 2 7 +--R (280A a b + 200B a b )d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 9 4 3 5 2 8 +--R (181A a b + 116B a b)e + (- 440A a b - 217B a b )d e +--R + +--R 3 4 4 3 2 7 +--R (280A a b + 80B a b )d e +--R * +--R 2 +--R x +--R + +--R 6 7 9 5 2 6 8 +--R (99A a b + 24B a )e + (- 232A a b - 35B a b)d e +--R + +--R 4 3 5 2 2 7 +--R (140A a b + 4B a b )d e +--R * +--R x +--R + +--R 7 9 6 7 8 5 2 6 2 7 +--R 21A a e + (- 48A a b + 3B a )d e + (28A a b - 4B a b)d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 9 2 6 8 7 2 7 8 3 6 6 +--R (- 84B a b e + 252B a b d e - 252B a b d e + 84B b d e )x +--R + +--R 3 5 4 4 9 2 6 3 5 8 +--R (- 56A a b - 280B a b )e + (168A a b + 672B a b )d e +--R + +--R 7 2 6 2 7 8 7 3 6 8 4 5 +--R (- 168A a b - 336B a b )d e + (56A b - 224B a b )d e + 168B b d e +--R * +--R 5 +--R x +--R + +--R 4 4 5 3 9 3 5 4 4 8 +--R (- 210A a b - 420B a b )e + (560A a b + 910B a b )d e +--R + +--R 2 6 3 5 2 7 8 7 4 5 8 5 4 +--R (- 420A a b - 420B a b )d e + (70A b - 280B a b )d e + 210B b d e +--R * +--R 4 +--R x +--R + +--R 5 3 6 2 9 4 4 5 3 8 +--R (- 336A a b - 336B a b )e + (840A a b + 672B a b )d e +--R + +--R 3 5 4 4 2 7 8 7 5 4 8 6 3 +--R (- 560A a b - 280B a b )d e + (56A b - 224B a b )d e + 168B b d e +--R * +--R 3 +--R x +--R + +--R 6 2 7 9 5 3 6 2 8 +--R (- 280A a b - 140B a b)e + (672A a b + 252B a b )d e +--R + +--R 4 4 5 3 2 7 8 7 6 3 8 7 2 +--R (- 420A a b - 84B a b )d e + (28A b - 112B a b )d e + 84B b d e +--R * +--R 2 +--R x +--R + +--R 7 8 9 6 2 7 8 5 3 2 7 +--R (- 120A a b - 24B a )e + (280A a b + 32B a b)d e - 168A a b d e +--R + +--R 8 7 7 2 8 8 +--R (8A b - 32B a b )d e + 24B b d e +--R * +--R x +--R + +--R 8 9 7 8 8 6 2 7 2 7 +--R - 21A a e + (48A a b - 3B a )d e + (- 28A a b + 4B a b)d e +--R + +--R 8 7 8 8 9 +--R (A b - 4B a b )d e + 3B b d +--R / +--R 3 18 2 17 2 2 16 3 3 15 8 +--R (168a e - 504a b d e + 504a b d e - 168b d e )x +--R + +--R 3 17 2 2 16 2 3 15 3 4 14 7 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e )x +--R + +--R 3 2 16 2 3 15 2 4 14 3 5 13 6 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 3 15 2 4 14 2 5 13 3 6 12 5 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 4 14 2 5 13 2 6 12 3 7 11 4 +--R (11760a d e - 35280a b d e + 35280a b d e - 11760b d e )x +--R + +--R 3 5 13 2 6 12 2 7 11 3 8 10 3 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 6 12 2 7 11 2 8 10 3 9 9 2 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 7 11 2 8 10 2 9 9 3 10 8 3 8 10 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e )x + 168a d e +--R + +--R 2 9 9 2 10 8 3 11 7 +--R - 504a b d e + 504a b d e - 168b d e +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^10 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1378 +r0:=-1/9*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^9)+1/24*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^8)+1/72*b*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)^3*_ + (d+e*x)^7)+1/504*b*(2*b*B*d+A*b*e-3*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^7) +--R +--R +--R (2) +--R 8 7 3 8 2 8 +--R ((A b - 3B a b )e + 2B b d e )x +--R + +--R 7 2 6 3 8 7 2 8 2 7 +--R ((- A a b + 3B a b )e + (9A b - 29B a b )d e + 18B b d e)x +--R + +--R 2 6 3 5 3 7 2 6 2 +--R (A a b - 3B a b )e + (- 9A a b + 29B a b )d e +--R + +--R 8 7 2 8 3 +--R (36A b - 126B a b )d e + 72B b d +--R * +--R 6 +--R x +--R + +--R 3 5 4 4 3 2 6 3 5 2 +--R (- A a b - 165B a b )e + (9A a b + 643B a b )d e +--R + +--R 7 2 6 2 8 7 3 +--R (- 36A a b - 882B a b )d e + (84A b + 348B a b )d +--R * +--R 5 +--R x +--R + +--R 4 4 5 3 3 3 5 4 4 2 +--R (- 125A a b - 465B a b )e + (495A a b + 1625B a b )d e +--R + +--R 2 6 3 5 2 7 2 6 3 +--R (- 720A a b - 1890B a b )d e + (420A a b + 660B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 6 2 3 4 4 5 3 2 +--R (- 379A a b - 543B a b )e + (1395A a b + 1777B a b )d e +--R + +--R 3 5 4 4 2 2 6 3 5 3 +--R (- 1800A a b - 1890B a b )d e + (840A a b + 600B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 7 3 5 3 6 2 2 +--R (- 461A a b - 297B a b)e + (1629A a b + 911B a b )d e +--R + +--R 4 4 5 3 2 3 5 4 4 3 +--R (- 1980A a b - 882B a b )d e + (840A a b + 240B a b )d +--R * +--R 2 +--R x +--R + +--R 7 8 3 6 2 7 2 +--R (- 259A a b - 63B a )e + (891A a b + 169B a b)d e +--R + +--R 5 3 6 2 2 4 4 5 3 3 +--R (- 1044A a b - 126B a b )d e + (420A a b + 12B a b )d +--R * +--R x +--R + +--R 8 3 7 8 2 6 2 7 2 +--R - 56A a e + (189A a b - 7B a )d e + (- 216A a b + 18B a b)d e +--R + +--R 5 3 6 2 3 +--R (84A a b - 12B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 13 3 12 2 2 2 11 3 3 10 4 4 9 9 +--R (504a e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d e )x +--R + +--R 4 12 3 2 11 2 2 3 10 3 4 9 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 5 8 +--R 4536b d e +--R * +--R 8 +--R x +--R + +--R 4 2 11 3 3 10 2 2 4 9 3 5 8 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 6 7 +--R 18144b d e +--R * +--R 7 +--R x +--R + +--R 4 3 10 3 4 9 2 2 5 8 3 6 7 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 7 6 +--R 42336b d e +--R * +--R 6 +--R x +--R + +--R 4 4 9 3 5 8 2 2 6 7 3 7 6 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 8 5 +--R 63504b d e +--R * +--R 5 +--R x +--R + +--R 4 5 8 3 6 7 2 2 7 6 3 8 5 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 9 4 +--R 63504b d e +--R * +--R 4 +--R x +--R + +--R 4 6 7 3 7 6 2 2 8 5 3 9 4 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 10 3 +--R 42336b d e +--R * +--R 3 +--R x +--R + +--R 4 7 6 3 8 5 2 2 9 4 3 10 3 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 11 2 +--R 18144b d e +--R * +--R 2 +--R x +--R + +--R 4 8 5 3 9 4 2 2 10 3 3 11 2 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 12 +--R 4536b d e +--R * +--R x +--R + +--R 4 9 4 3 10 3 2 2 11 2 3 12 4 13 +--R 504a d e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 168B b e x + ((- 126A b - 630B a b )e - 252B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 504A a b - 1008B a b )e + (- 126A b - 630B a b )d e +--R + +--R 5 2 4 +--R - 252B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 840A a b - 840B a b )e + (- 336A a b - 672B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 84A b - 420B a b )d e - 168B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 720A a b - 360B a b)e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (- 144A a b - 288B a b )d e + (- 36A b - 180B a b )d e - 72B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 315A a b - 63B a )e + (- 180A a b - 90B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 90A a b - 90B a b )d e + (- 36A a b - 72B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 9A b - 45B a b )d e - 18B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 56A a e + (- 35A a b - 7B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 10A a b - 10B a b )d e + (- 4A a b - 8B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - 2B b d +--R / +--R 16 9 15 8 2 14 7 3 13 6 4 12 5 +--R 504e x + 4536d e x + 18144d e x + 42336d e x + 63504d e x +--R + +--R 5 11 4 6 10 3 7 9 2 8 8 9 7 +--R 63504d e x + 42336d e x + 18144d e x + 4536d e x + 504d e +--R Type: Union(Expression(Integer),...) +--E 633 + +--S 634 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 7 10 8 9 8 +--R ((- A b + 3B a b )e - 2B b d e )x +--R + +--R 7 2 6 10 8 7 9 8 2 8 7 +--R ((A a b - 3B a b )e + (- 9A b + 29B a b )d e - 18B b d e )x +--R + +--R 2 6 3 5 10 7 2 6 9 +--R (- A a b + 3B a b )e + (9A a b - 29B a b )d e +--R + +--R 8 7 2 8 8 3 7 +--R (- 36A b + 126B a b )d e - 72B b d e +--R * +--R 6 +--R x +--R + +--R 3 5 4 4 10 2 6 3 5 9 +--R (A a b + 165B a b )e + (- 9A a b - 643B a b )d e +--R + +--R 7 2 6 2 8 8 7 3 7 +--R (36A a b + 882B a b )d e + (- 84A b - 348B a b )d e +--R * +--R 5 +--R x +--R + +--R 4 4 5 3 10 3 5 4 4 9 +--R (125A a b + 465B a b )e + (- 495A a b - 1625B a b )d e +--R + +--R 2 6 3 5 2 8 7 2 6 3 7 +--R (720A a b + 1890B a b )d e + (- 420A a b - 660B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 3 6 2 10 4 4 5 3 9 +--R (379A a b + 543B a b )e + (- 1395A a b - 1777B a b )d e +--R + +--R 3 5 4 4 2 8 2 6 3 5 3 7 +--R (1800A a b + 1890B a b )d e + (- 840A a b - 600B a b )d e +--R * +--R 3 +--R x +--R + +--R 6 2 7 10 5 3 6 2 9 +--R (461A a b + 297B a b)e + (- 1629A a b - 911B a b )d e +--R + +--R 4 4 5 3 2 8 3 5 4 4 3 7 +--R (1980A a b + 882B a b )d e + (- 840A a b - 240B a b )d e +--R * +--R 2 +--R x +--R + +--R 7 8 10 6 2 7 9 +--R (259A a b + 63B a )e + (- 891A a b - 169B a b)d e +--R + +--R 5 3 6 2 2 8 4 4 5 3 3 7 +--R (1044A a b + 126B a b )d e + (- 420A a b - 12B a b )d e +--R * +--R x +--R + +--R 8 10 7 8 9 6 2 7 2 8 +--R 56A a e + (- 189A a b + 7B a )d e + (216A a b - 18B a b)d e +--R + +--R 5 3 6 2 3 7 +--R (- 84A a b + 12B a b )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 10 3 6 9 2 7 2 8 8 3 7 +--R - 168B a b e + 672B a b d e - 1008B a b d e + 672B a b d e +--R + +--R 9 4 6 +--R - 168B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 5 4 10 3 6 4 5 9 +--R (- 126A a b - 630B a b )e + (504A a b + 2268B a b )d e +--R + +--R 2 7 3 6 2 8 8 2 7 3 7 +--R (- 756A a b - 2772B a b )d e + (504A a b + 1008B a b )d e +--R + +--R 9 8 4 6 9 5 5 +--R (- 126A b + 378B a b )d e - 252B b d e +--R * +--R 5 +--R x +--R + +--R 5 4 6 3 10 4 5 5 4 9 +--R (- 504A a b - 1008B a b )e + (1890A a b + 3402B a b )d e +--R + +--R 3 6 4 5 2 8 2 7 3 6 3 7 +--R (- 2520A a b - 3780B a b )d e + (1260A a b + 1260B a b )d e +--R + +--R 9 8 5 5 9 6 4 +--R (- 126A b + 378B a b )d e - 252B b d e +--R * +--R 4 +--R x +--R + +--R 6 3 7 2 10 5 4 6 3 9 +--R (- 840A a b - 840B a b )e + (3024A a b + 2688B a b )d e +--R + +--R 4 5 5 4 2 8 3 6 4 5 3 7 +--R (- 3780A a b - 2772B a b )d e + (1680A a b + 840B a b )d e +--R + +--R 9 8 6 4 9 7 3 +--R (- 84A b + 252B a b )d e - 168B b d e +--R * +--R 3 +--R x +--R + +--R 7 2 8 10 6 3 7 2 9 +--R (- 720A a b - 360B a b)e + (2520A a b + 1080B a b )d e +--R + +--R 5 4 6 3 2 8 4 5 5 4 3 7 +--R (- 3024A a b - 1008B a b )d e + (1260A a b + 252B a b )d e +--R + +--R 9 8 7 3 9 8 2 +--R (- 36A b + 108B a b )d e - 72B b d e +--R * +--R 2 +--R x +--R + +--R 8 9 10 7 2 8 9 +--R (- 315A a b - 63B a )e + (1080A a b + 162B a b)d e +--R + +--R 6 3 7 2 2 8 5 4 3 7 +--R (- 1260A a b - 108B a b )d e + 504A a b d e +--R + +--R 9 8 8 2 9 9 +--R (- 9A b + 27B a b )d e - 18B b d e +--R * +--R x +--R + +--R 9 10 8 9 9 7 2 8 2 8 +--R - 56A a e + (189A a b - 7B a )d e + (- 216A a b + 18B a b)d e +--R + +--R 6 3 7 2 3 7 9 8 9 9 10 +--R (84A a b - 12B a b )d e + (- A b + 3B a b )d e - 2B b d +--R / +--R 4 20 3 19 2 2 2 18 3 3 17 4 4 16 9 +--R (504a e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d e )x +--R + +--R 4 19 3 2 18 2 2 3 17 3 4 16 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 5 15 +--R 4536b d e +--R * +--R 8 +--R x +--R + +--R 4 2 18 3 3 17 2 2 4 16 3 5 15 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 6 14 +--R 18144b d e +--R * +--R 7 +--R x +--R + +--R 4 3 17 3 4 16 2 2 5 15 3 6 14 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 7 13 +--R 42336b d e +--R * +--R 6 +--R x +--R + +--R 4 4 16 3 5 15 2 2 6 14 3 7 13 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 8 12 +--R 63504b d e +--R * +--R 5 +--R x +--R + +--R 4 5 15 3 6 14 2 2 7 13 3 8 12 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 9 11 +--R 63504b d e +--R * +--R 4 +--R x +--R + +--R 4 6 14 3 7 13 2 2 8 12 3 9 11 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 10 10 +--R 42336b d e +--R * +--R 3 +--R x +--R + +--R 4 7 13 3 8 12 2 2 9 11 3 10 10 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 11 9 +--R 18144b d e +--R * +--R 2 +--R x +--R + +--R 4 8 12 3 9 11 2 2 10 10 3 11 9 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 12 8 +--R 4536b d e +--R * +--R x +--R + +--R 4 9 11 3 10 10 2 2 11 9 3 12 8 4 13 7 +--R 504a d e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d e +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 635 + +)clear all + +--S 636 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^11 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1378 +r0:=-1/10*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^10)+1/45*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^9)+1/120*b*(3*b*B*d+2*A*b*e-_ + 5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)^3*(d+_ + e*x)^8)+1/360*b^2*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^4*(d+e*x)^7)+1/2520*b^2*(3*b*B*d+2*A*b*e-_ + 5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^7) +--R +--R +--R (2) +--R 9 8 4 9 3 9 +--R ((- 2A b + 5B a b )e - 3B b d e )x +--R + +--R 8 2 7 4 9 8 3 9 2 2 8 +--R ((2A a b - 5B a b )e + (- 20A b + 53B a b )d e - 30B b d e )x +--R + +--R 2 7 3 6 4 8 2 7 3 +--R (- 2A a b + 5B a b )e + (20A a b - 53B a b )d e +--R + +--R 9 8 2 2 9 3 +--R (- 90A b + 255B a b )d e - 135B b d e +--R * +--R 7 +--R x +--R + +--R 3 6 4 5 4 2 7 3 6 3 +--R (2A a b - 5B a b )e + (- 20A a b + 53B a b )d e +--R + +--R 8 2 7 2 2 9 8 3 9 4 +--R (90A a b - 255B a b )d e + (- 240A b + 735B a b )d e - 360B b d +--R * +--R 6 +--R x +--R + +--R 4 5 5 4 4 3 6 4 5 3 +--R (- 2A a b - 625B a b )e + (20A a b + 3097B a b )d e +--R + +--R 2 7 3 6 2 2 8 2 7 3 +--R (- 90A a b - 6045B a b )d e + (240A a b + 5565B a b )d e +--R + +--R 9 8 4 +--R (- 420A b - 1740B a b )d +--R * +--R 5 +--R x +--R + +--R 5 4 6 3 4 4 5 5 4 3 +--R (- 502A a b - 1895B a b )e + (2500A a b + 8747B a b )d e +--R + +--R 3 6 4 5 2 2 2 7 3 6 3 +--R (- 4950A a b - 15375B a b )d e + (4800A a b + 12075B a b )d e +--R + +--R 8 2 7 4 +--R (- 2100A a b - 3300B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 7 2 4 5 4 6 3 3 +--R (- 1598A a b - 2305B a b )e + (7580A a b + 10153B a b )d e +--R + +--R 4 5 5 4 2 2 3 6 4 5 3 +--R (- 13950A a b - 16755B a b )d e + (12000A a b + 12075B a b )d e +--R + +--R 2 7 3 6 4 +--R (- 4200A a b - 3000B a b )d +--R * +--R 3 +--R x +--R + +--R 7 2 8 4 6 3 7 2 3 +--R (- 2002A a b - 1295B a b)e + (9220A a b + 5447B a b )d e +--R + +--R 5 4 6 3 2 2 4 5 5 4 3 +--R (- 16290A a b - 8445B a b )d e + (13200A a b + 5565B a b )d e +--R + +--R 3 6 4 5 4 +--R (- 4200A a b - 1200B a b )d +--R * +--R 2 +--R x +--R + +--R 8 9 4 7 2 8 3 +--R (- 1148A a b - 280B a )e + (5180A a b + 1078B a b)d e +--R + +--R 6 3 7 2 2 2 5 4 6 3 3 +--R (- 8910A a b - 1455B a b )d e + (6960A a b + 735B a b )d e +--R + +--R 4 5 5 4 4 +--R (- 2100A a b - 60B a b )d +--R * +--R x +--R + +--R 9 4 8 9 3 7 2 8 2 2 +--R - 252A a e + (1120A a b - 28B a )d e + (- 1890A a b + 105B a b)d e +--R + +--R 6 3 7 2 3 5 4 6 3 4 +--R (1440A a b - 135B a b )d e + (- 420A a b + 60B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 15 4 14 3 2 2 13 2 3 3 12 +--R 2520a e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 4 11 5 5 10 +--R 12600a b d e - 2520b d e +--R * +--R 10 +--R x +--R + +--R 5 14 4 2 13 3 2 3 12 2 3 4 11 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 5 10 5 6 9 +--R 126000a b d e - 25200b d e +--R * +--R 9 +--R x +--R + +--R 5 2 13 4 3 12 3 2 4 11 2 3 5 10 +--R 113400a d e - 567000a b d e + 1134000a b d e - 1134000a b d e +--R + +--R 4 6 9 5 7 8 +--R 567000a b d e - 113400b d e +--R * +--R 8 +--R x +--R + +--R 5 3 12 4 4 11 3 2 5 10 2 3 6 9 +--R 302400a d e - 1512000a b d e + 3024000a b d e - 3024000a b d e +--R + +--R 4 7 8 5 8 7 +--R 1512000a b d e - 302400b d e +--R * +--R 7 +--R x +--R + +--R 5 4 11 4 5 10 3 2 6 9 2 3 7 8 +--R 529200a d e - 2646000a b d e + 5292000a b d e - 5292000a b d e +--R + +--R 4 8 7 5 9 6 +--R 2646000a b d e - 529200b d e +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 2 7 8 2 3 8 7 +--R 635040a d e - 3175200a b d e + 6350400a b d e - 6350400a b d e +--R + +--R 4 9 6 5 10 5 +--R 3175200a b d e - 635040b d e +--R * +--R 5 +--R x +--R + +--R 5 6 9 4 7 8 3 2 8 7 2 3 9 6 +--R 529200a d e - 2646000a b d e + 5292000a b d e - 5292000a b d e +--R + +--R 4 10 5 5 11 4 +--R 2646000a b d e - 529200b d e +--R * +--R 4 +--R x +--R + +--R 5 7 8 4 8 7 3 2 9 6 2 3 10 5 +--R 302400a d e - 1512000a b d e + 3024000a b d e - 3024000a b d e +--R + +--R 4 11 4 5 12 3 +--R 1512000a b d e - 302400b d e +--R * +--R 3 +--R x +--R + +--R 5 8 7 4 9 6 3 2 10 5 2 3 11 4 +--R 113400a d e - 567000a b d e + 1134000a b d e - 1134000a b d e +--R + +--R 4 12 3 5 13 2 +--R 567000a b d e - 113400b d e +--R * +--R 2 +--R x +--R + +--R 5 9 6 4 10 5 3 2 11 4 2 3 12 3 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 13 2 5 14 +--R 126000a b d e - 25200b d e +--R * +--R x +--R + +--R 5 10 5 4 11 4 3 2 12 3 2 3 13 2 +--R 2520a d e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 14 5 15 +--R 12600a b d e - 2520b d +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 630B b e x + ((- 504A b - 2520B a b )e - 756B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 2100A a b - 4200B a b )e + (- 420A b - 2100B a b )d e +--R + +--R 5 2 4 +--R - 630B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 3600A a b - 3600B a b )e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 240A b - 1200B a b )d e - 360B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 3150A a b - 1575B a b)e + (- 1350A a b - 1350B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 450A a b - 900B a b )d e + (- 90A b - 450B a b )d e +--R + +--R 5 4 2 +--R - 135B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 1400A a b - 280B a )e + (- 700A a b - 350B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 300A a b - 300B a b )d e + (- 100A a b - 200B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 20A b - 100B a b )d e - 30B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 252A a e + (- 140A a b - 28B a )d e + (- 70A a b - 35B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 30A a b - 30B a b )d e + (- 10A a b - 20B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 2A b - 10B a b )d e - 3B b d +--R / +--R 17 10 16 9 2 15 8 3 14 7 4 13 6 +--R 2520e x + 25200d e x + 113400d e x + 302400d e x + 529200d e x +--R + +--R 5 12 5 6 11 4 7 10 3 8 9 2 9 8 +--R 635040d e x + 529200d e x + 302400d e x + 113400d e x + 25200d e x +--R + +--R 10 7 +--R 2520d e +--R Type: Union(Expression(Integer),...) +--E 638 + +--S 639 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 8 11 9 10 9 +--R ((2A b - 5B a b )e + 3B b d e )x +--R + +--R 8 2 7 11 9 8 10 9 2 9 8 +--R ((- 2A a b + 5B a b )e + (20A b - 53B a b )d e + 30B b d e )x +--R + +--R 2 7 3 6 11 8 2 7 10 +--R (2A a b - 5B a b )e + (- 20A a b + 53B a b )d e +--R + +--R 9 8 2 9 9 3 8 +--R (90A b - 255B a b )d e + 135B b d e +--R * +--R 7 +--R x +--R + +--R 3 6 4 5 11 2 7 3 6 10 +--R (- 2A a b + 5B a b )e + (20A a b - 53B a b )d e +--R + +--R 8 2 7 2 9 9 8 3 8 +--R (- 90A a b + 255B a b )d e + (240A b - 735B a b )d e +--R + +--R 9 4 7 +--R 360B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 5 4 11 3 6 4 5 10 +--R (2A a b + 625B a b )e + (- 20A a b - 3097B a b )d e +--R + +--R 2 7 3 6 2 9 8 2 7 3 8 +--R (90A a b + 6045B a b )d e + (- 240A a b - 5565B a b )d e +--R + +--R 9 8 4 7 +--R (420A b + 1740B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 4 6 3 11 4 5 5 4 10 +--R (502A a b + 1895B a b )e + (- 2500A a b - 8747B a b )d e +--R + +--R 3 6 4 5 2 9 2 7 3 6 3 8 +--R (4950A a b + 15375B a b )d e + (- 4800A a b - 12075B a b )d e +--R + +--R 8 2 7 4 7 +--R (2100A a b + 3300B a b )d e +--R * +--R 4 +--R x +--R + +--R 6 3 7 2 11 5 4 6 3 10 +--R (1598A a b + 2305B a b )e + (- 7580A a b - 10153B a b )d e +--R + +--R 4 5 5 4 2 9 +--R (13950A a b + 16755B a b )d e +--R + +--R 3 6 4 5 3 8 2 7 3 6 4 7 +--R (- 12000A a b - 12075B a b )d e + (4200A a b + 3000B a b )d e +--R * +--R 3 +--R x +--R + +--R 7 2 8 11 6 3 7 2 10 +--R (2002A a b + 1295B a b)e + (- 9220A a b - 5447B a b )d e +--R + +--R 5 4 6 3 2 9 4 5 5 4 3 8 +--R (16290A a b + 8445B a b )d e + (- 13200A a b - 5565B a b )d e +--R + +--R 3 6 4 5 4 7 +--R (4200A a b + 1200B a b )d e +--R * +--R 2 +--R x +--R + +--R 8 9 11 7 2 8 10 +--R (1148A a b + 280B a )e + (- 5180A a b - 1078B a b)d e +--R + +--R 6 3 7 2 2 9 5 4 6 3 3 8 +--R (8910A a b + 1455B a b )d e + (- 6960A a b - 735B a b )d e +--R + +--R 4 5 5 4 4 7 +--R (2100A a b + 60B a b )d e +--R * +--R x +--R + +--R 9 11 8 9 10 +--R 252A a e + (- 1120A a b + 28B a )d e +--R + +--R 7 2 8 2 9 6 3 7 2 3 8 +--R (1890A a b - 105B a b)d e + (- 1440A a b + 135B a b )d e +--R + +--R 5 4 6 3 4 7 +--R (420A a b - 60B a b )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 5 11 4 6 10 3 7 2 9 2 8 3 8 +--R - 630B a b e + 3150B a b d e - 6300B a b d e + 6300B a b d e +--R + +--R 9 4 7 10 5 6 +--R - 3150B a b d e + 630B b d e +--R * +--R 6 +--R x +--R + +--R 5 5 6 4 11 4 6 5 5 10 +--R (- 504A a b - 2520B a b )e + (2520A a b + 11844B a b )d e +--R + +--R 3 7 4 6 2 9 2 8 3 7 3 8 +--R (- 5040A a b - 21420B a b )d e + (5040A a b + 17640B a b )d e +--R + +--R 9 2 8 4 7 10 9 5 6 +--R (- 2520A a b - 5040B a b )d e + (504A b - 1260B a b )d e +--R + +--R 10 6 5 +--R 756B b d e +--R * +--R 5 +--R x +--R + +--R 6 4 7 3 11 5 5 6 4 10 +--R (- 2100A a b - 4200B a b )e + (10080A a b + 18900B a b )d e +--R + +--R 4 6 5 5 2 9 3 7 4 6 3 8 +--R (- 18900A a b - 32130B a b )d e + (16800A a b + 24150B a b )d e +--R + +--R 2 8 3 7 4 7 10 9 6 5 +--R (- 6300A a b - 6300B a b )d e + (420A b - 1050B a b )d e +--R + +--R 10 7 4 +--R 630B b d e +--R * +--R 4 +--R x +--R + +--R 7 3 8 2 11 6 4 7 3 10 +--R (- 3600A a b - 3600B a b )e + (16800A a b + 15600B a b )d e +--R + +--R 5 5 6 4 2 9 4 6 5 5 3 8 +--R (- 30240A a b - 25200B a b )d e + (25200A a b + 17640B a b )d e +--R + +--R 3 7 4 6 4 7 10 9 7 4 +--R (- 8400A a b - 4200B a b )d e + (240A b - 600B a b )d e +--R + +--R 10 8 3 +--R 360B b d e +--R * +--R 3 +--R x +--R + +--R 8 2 9 11 7 3 8 2 10 +--R (- 3150A a b - 1575B a b)e + (14400A a b + 6525B a b )d e +--R + +--R 6 4 7 3 2 9 5 5 6 4 3 8 +--R (- 25200A a b - 9900B a b )d e + (20160A a b + 6300B a b )d e +--R + +--R 4 6 5 5 4 7 10 9 8 3 +--R (- 6300A a b - 1260B a b )d e + (90A b - 225B a b )d e +--R + +--R 10 9 2 +--R 135B b d e +--R * +--R 2 +--R x +--R + +--R 9 10 11 8 2 9 10 +--R (- 1400A a b - 280B a )e + (6300A a b + 1050B a b)d e +--R + +--R 7 3 8 2 2 9 6 4 7 3 3 8 +--R (- 10800A a b - 1350B a b )d e + (8400A a b + 600B a b )d e +--R + +--R 5 5 4 7 10 9 9 2 10 10 +--R - 2520A a b d e + (20A b - 50B a b )d e + 30B b d e +--R * +--R x +--R + +--R 10 11 9 10 10 +--R - 252A a e + (1120A a b - 28B a )d e +--R + +--R 8 2 9 2 9 7 3 8 2 3 8 +--R (- 1890A a b + 105B a b)d e + (1440A a b - 135B a b )d e +--R + +--R 6 4 7 3 4 7 10 9 10 10 11 +--R (- 420A a b + 60B a b )d e + (2A b - 5B a b )d e + 3B b d +--R / +--R 5 22 4 21 3 2 2 20 2 3 3 19 +--R 2520a e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 4 18 5 5 17 +--R 12600a b d e - 2520b d e +--R * +--R 10 +--R x +--R + +--R 5 21 4 2 20 3 2 3 19 2 3 4 18 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 5 17 5 6 16 +--R 126000a b d e - 25200b d e +--R * +--R 9 +--R x +--R + +--R 5 2 20 4 3 19 3 2 4 18 2 3 5 17 +--R 113400a d e - 567000a b d e + 1134000a b d e - 1134000a b d e +--R + +--R 4 6 16 5 7 15 +--R 567000a b d e - 113400b d e +--R * +--R 8 +--R x +--R + +--R 5 3 19 4 4 18 3 2 5 17 +--R 302400a d e - 1512000a b d e + 3024000a b d e +--R + +--R 2 3 6 16 4 7 15 5 8 14 +--R - 3024000a b d e + 1512000a b d e - 302400b d e +--R * +--R 7 +--R x +--R + +--R 5 4 18 4 5 17 3 2 6 16 +--R 529200a d e - 2646000a b d e + 5292000a b d e +--R + +--R 2 3 7 15 4 8 14 5 9 13 +--R - 5292000a b d e + 2646000a b d e - 529200b d e +--R * +--R 6 +--R x +--R + +--R 5 5 17 4 6 16 3 2 7 15 +--R 635040a d e - 3175200a b d e + 6350400a b d e +--R + +--R 2 3 8 14 4 9 13 5 10 12 +--R - 6350400a b d e + 3175200a b d e - 635040b d e +--R * +--R 5 +--R x +--R + +--R 5 6 16 4 7 15 3 2 8 14 +--R 529200a d e - 2646000a b d e + 5292000a b d e +--R + +--R 2 3 9 13 4 10 12 5 11 11 +--R - 5292000a b d e + 2646000a b d e - 529200b d e +--R * +--R 4 +--R x +--R + +--R 5 7 15 4 8 14 3 2 9 13 +--R 302400a d e - 1512000a b d e + 3024000a b d e +--R + +--R 2 3 10 12 4 11 11 5 12 10 +--R - 3024000a b d e + 1512000a b d e - 302400b d e +--R * +--R 3 +--R x +--R + +--R 5 8 14 4 9 13 3 2 10 12 +--R 113400a d e - 567000a b d e + 1134000a b d e +--R + +--R 2 3 11 11 4 12 10 5 13 9 +--R - 1134000a b d e + 567000a b d e - 113400b d e +--R * +--R 2 +--R x +--R + +--R 5 9 13 4 10 12 3 2 11 11 2 3 12 10 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 13 9 5 14 8 +--R 126000a b d e - 25200b d e +--R * +--R x +--R + +--R 5 10 12 4 11 11 3 2 12 10 2 3 13 9 +--R 2520a d e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 14 8 5 15 7 +--R 12600a b d e - 2520b d e +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 640 + +)clear all + +--S 641 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^12 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1378 +r0:=-1/198*b*(6*b*B*d+5*A*b*e-11*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^9)-1/396*b^2*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^8)-_ + 1/11*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^11)-1/110*(6*b*B*d+5*A*b*e-11*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^10)-1/924*b^3*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*_ + (d+e*x)^7)-1/2310*b^4*(6*b*B*d+5*A*b*e-11*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^6)-1/13860*b^4*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 2772B b e x + ((- 2310A b - 11550B a b )e - 2772B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 9900A a b - 19800B a b )e + (- 1650A b - 8250B a b )d e +--R + +--R 5 2 4 +--R - 1980B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 17325A a b - 17325B a b )e + (- 4950A a b - 9900B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 825A b - 4125B a b )d e - 990B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 15400A a b - 7700B a b)e + (- 5775A a b - 5775B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 1650A a b - 3300B a b )d e + (- 275A b - 1375B a b )d e +--R + +--R 5 4 2 +--R - 330B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 6930A a b - 1386B a )e + (- 3080A a b - 1540B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 1155A a b - 1155B a b )d e + (- 330A a b - 660B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 55A b - 275B a b )d e - 66B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 1260A a e + (- 630A a b - 126B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 280A a b - 140B a b)d e + (- 105A a b - 105B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (- 30A a b - 60B a b )d e + (- 5A b - 25B a b )d e - 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 18 12 18 17 11 +--R 13860b e x + (13860a e + 152460b d e )x +--R + +--R 17 2 16 10 2 16 3 15 9 +--R (152460a d e + 762300b d e )x + (762300a d e + 2286900b d e )x +--R + +--R 3 15 4 14 8 4 14 5 13 7 +--R (2286900a d e + 4573800b d e )x + (4573800a d e + 6403320b d e )x +--R + +--R 5 13 6 12 6 6 12 7 11 5 +--R (6403320a d e + 6403320b d e )x + (6403320a d e + 4573800b d e )x +--R + +--R 7 11 8 10 4 8 10 9 9 3 +--R (4573800a d e + 2286900b d e )x + (2286900a d e + 762300b d e )x +--R + +--R 9 9 10 8 2 10 8 11 7 +--R (762300a d e + 152460b d e )x + (152460a d e + 13860b d e )x +--R + +--R 11 7 +--R 13860a d e +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 2772B b e x + ((- 2310A b - 11550B a b )e - 2772B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 9900A a b - 19800B a b )e + (- 1650A b - 8250B a b )d e +--R + +--R 5 2 4 +--R - 1980B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 17325A a b - 17325B a b )e + (- 4950A a b - 9900B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 825A b - 4125B a b )d e - 990B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 15400A a b - 7700B a b)e + (- 5775A a b - 5775B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 1650A a b - 3300B a b )d e + (- 275A b - 1375B a b )d e +--R + +--R 5 4 2 +--R - 330B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 6930A a b - 1386B a )e + (- 3080A a b - 1540B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 1155A a b - 1155B a b )d e + (- 330A a b - 660B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 55A b - 275B a b )d e - 66B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 1260A a e + (- 630A a b - 126B a )d e + (- 280A a b - 140B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 105A a b - 105B a b )d e + (- 30A a b - 60B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 5A b - 25B a b )d e - 6B b d +--R / +--R 18 11 17 10 2 16 9 3 15 8 +--R 13860e x + 152460d e x + 762300d e x + 2286900d e x +--R + +--R 4 14 7 5 13 6 6 12 5 7 11 4 +--R 4573800d e x + 6403320d e x + 6403320d e x + 4573800d e x +--R + +--R 8 10 3 9 9 2 10 8 11 7 +--R 2286900d e x + 762300d e x + 152460d e x + 13860d e +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R 2772B b e x + ((2310A b + 11550B a b )e + 2772B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (9900A a b + 19800B a b )e + (1650A b + 8250B a b )d e +--R + +--R 5 2 4 +--R 1980B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (17325A a b + 17325B a b )e + (4950A a b + 9900B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (825A b + 4125B a b )d e + 990B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (15400A a b + 7700B a b)e + (5775A a b + 5775B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (1650A a b + 3300B a b )d e + (275A b + 1375B a b )d e +--R + +--R 5 4 2 +--R 330B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (6930A a b + 1386B a )e + (3080A a b + 1540B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1155A a b + 1155B a b )d e + (330A a b + 660B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (55A b + 275B a b )d e + 66B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 1260A a e + (630A a b + 126B a )d e + (280A a b + 140B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (105A a b + 105B a b )d e + (30A a b + 60B a b )d e +--R + +--R 5 4 5 5 6 +--R (5A b + 25B a b )d e + 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R - 2772B b e x + ((- 2310A b - 14322B a b )e - 2772B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 12210A a b - 31350B a b )e + (- 1650A b - 11022B a b )d e +--R + +--R 6 2 4 +--R - 1980B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 27225A a b - 37125B a b )e + (- 6600A a b - 18150B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 825A b - 6105B a b )d e - 990B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 32725A a b - 25025B a b )e + (- 10725A a b - 15675B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 2475A a b - 7425B a b )d e + (- 275A b - 2365B a b )d e +--R + +--R 6 4 2 +--R - 330B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 22330A a b - 9086B a b)e + (- 8855A a b - 7315B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 2805A a b - 4455B a b )d e + (- 605A a b - 2035B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 55A b - 605B a b )d e - 66B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 8190A a b - 1386B a )e + (- 3710A a b - 1666B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 1435A a b - 1295B a b )d e + (- 435A a b - 765B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 85A a b - 335B a b )d e + (- 5A b - 91B a b )d e - 6B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 1260A a e + (- 630A a b - 126B a )d e + (- 280A a b - 140B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 105A a b - 105B a b )d e + (- 30A a b - 60B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- 5A a b - 25B a b )d e - 6B a b d +--R / +--R 18 12 18 17 11 +--R 13860b e x + (13860a e + 152460b d e )x +--R + +--R 17 2 16 10 2 16 3 15 9 +--R (152460a d e + 762300b d e )x + (762300a d e + 2286900b d e )x +--R + +--R 3 15 4 14 8 4 14 5 13 7 +--R (2286900a d e + 4573800b d e )x + (4573800a d e + 6403320b d e )x +--R + +--R 5 13 6 12 6 6 12 7 11 5 +--R (6403320a d e + 6403320b d e )x + (6403320a d e + 4573800b d e )x +--R + +--R 7 11 8 10 4 8 10 9 9 3 +--R (4573800a d e + 2286900b d e )x + (2286900a d e + 762300b d e )x +--R + +--R 9 9 10 8 2 10 8 11 7 +--R (762300a d e + 152460b d e )x + (152460a d e + 13860b d e )x +--R + +--R 11 7 +--R 13860a d e +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x +--R + +--R 12 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^13 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R e x + 13d e x + 78d e x + 286d e x + 715d e x + 1287d e x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 +--R 1716d e x + 1716d e x + 1287d e x + 715d e x + 286d e x + 78d e x +--R + +--R 12 13 +--R 13d e x + d +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1378 +r0:=-1/44*b*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e)*(d+e*x)^10)-1/99*b^2*(b*B*d+A*b*e-2*a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^9)-1/12*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^12)-_ + 1/22*(b*B*d+A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-_ + a*e)*(d+e*x)^11)-1/264*b^3*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*(d+e*x)^8)-1/792*b^4*(b*B*d+A*b*e-_ + 2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^7)-_ + 1/5544*b^4*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*_ + (a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 924B b e x + ((- 792A b - 3960B a b )e - 792B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 3465A a b - 6930B a b )e + (- 495A b - 2475B a b )d e +--R + +--R 5 2 4 +--R - 495B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 6160A a b - 6160B a b )e + (- 1540A a b - 3080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 220A b - 1100B a b )d e - 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 5544A a b - 2772B a b)e + (- 1848A a b - 1848B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 462A a b - 924B a b )d e + (- 66A b - 330B a b )d e +--R + +--R 5 4 2 +--R - 66B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 2520A a b - 504B a )e + (- 1008A a b - 504B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 336A a b - 336B a b )d e + (- 84A a b - 168B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 12A b - 60B a b )d e - 12B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 462A a e + (- 210A a b - 42B a )d e + (- 84A a b - 42B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 28A a b - 28B a b )d e + (- 7A a b - 14B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 19 13 19 18 12 +--R 5544b e x + (5544a e + 66528b d e )x +--R + +--R 18 2 17 11 2 17 3 16 10 +--R (66528a d e + 365904b d e )x + (365904a d e + 1219680b d e )x +--R + +--R 3 16 4 15 9 4 15 5 14 8 +--R (1219680a d e + 2744280b d e )x + (2744280a d e + 4390848b d e )x +--R + +--R 5 14 6 13 7 6 13 7 12 6 +--R (4390848a d e + 5122656b d e )x + (5122656a d e + 4390848b d e )x +--R + +--R 7 12 8 11 5 8 11 9 10 4 +--R (4390848a d e + 2744280b d e )x + (2744280a d e + 1219680b d e )x +--R + +--R 9 10 10 9 3 10 9 11 8 2 +--R (1219680a d e + 365904b d e )x + (365904a d e + 66528b d e )x +--R + +--R 11 8 12 7 12 7 +--R (66528a d e + 5544b d e )x + 5544a d e +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 924B b e x + ((- 792A b - 3960B a b )e - 792B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 3465A a b - 6930B a b )e + (- 495A b - 2475B a b )d e +--R + +--R 5 2 4 +--R - 495B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 6160A a b - 6160B a b )e + (- 1540A a b - 3080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 220A b - 1100B a b )d e - 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 5544A a b - 2772B a b)e + (- 1848A a b - 1848B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (- 462A a b - 924B a b )d e + (- 66A b - 330B a b )d e - 66B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 2520A a b - 504B a )e + (- 1008A a b - 504B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 336A a b - 336B a b )d e + (- 84A a b - 168B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 12A b - 60B a b )d e - 12B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 462A a e + (- 210A a b - 42B a )d e + (- 84A a b - 42B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 28A a b - 28B a b )d e + (- 7A a b - 14B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - B b d +--R / +--R 19 12 18 11 2 17 10 3 16 9 +--R 5544e x + 66528d e x + 365904d e x + 1219680d e x +--R + +--R 4 15 8 5 14 7 6 13 6 7 12 5 +--R 2744280d e x + 4390848d e x + 5122656d e x + 4390848d e x +--R + +--R 8 11 4 9 10 3 10 9 2 11 8 12 7 +--R 2744280d e x + 1219680d e x + 365904d e x + 66528d e x + 5544d e +--R Type: Union(Expression(Integer),...) +--E 648 + +--S 649 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R 924B b e x + ((792A b + 3960B a b )e + 792B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (3465A a b + 6930B a b )e + (495A b + 2475B a b )d e +--R + +--R 5 2 4 +--R 495B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (6160A a b + 6160B a b )e + (1540A a b + 3080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (220A b + 1100B a b )d e + 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (5544A a b + 2772B a b)e + (1848A a b + 1848B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (462A a b + 924B a b )d e + (66A b + 330B a b )d e + 66B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (2520A a b + 504B a )e + (1008A a b + 504B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (336A a b + 336B a b )d e + (84A a b + 168B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (12A b + 60B a b )d e + 12B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 462A a e + (210A a b + 42B a )d e + (84A a b + 42B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (28A a b + 28B a b )d e + (7A a b + 14B a b )d e +--R + +--R 5 4 5 5 6 +--R (A b + 5B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R - 924B b e x + ((- 792A b - 4884B a b )e - 792B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 4257A a b - 10890B a b )e + (- 495A b - 3267B a b )d e +--R + +--R 6 2 4 +--R - 495B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 9625A a b - 13090B a b )e + (- 2035A a b - 5555B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 220A b - 1595B a b )d e - 220B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 11704A a b - 8932B a b )e + (- 3388A a b - 4928B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 682A a b - 2024B a b )d e + (- 66A b - 550B a b )d e +--R + +--R 6 4 2 +--R - 66B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 8064A a b - 3276B a b)e + (- 2856A a b - 2352B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 798A a b - 1260B a b )d e + (- 150A a b - 498B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 12A b - 126B a b )d e - 12B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 2982A a b - 504B a )e + (- 1218A a b - 546B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 420A a b - 378B a b )d e + (- 112A a b - 196B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 19A a b - 74B a b )d e + (- A b - 17B a b )d e - B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 462A a e + (- 210A a b - 42B a )d e + (- 84A a b - 42B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 28A a b - 28B a b )d e + (- 7A a b - 14B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- A a b - 5B a b )d e - B a b d +--R / +--R 19 13 19 18 12 +--R 5544b e x + (5544a e + 66528b d e )x +--R + +--R 18 2 17 11 2 17 3 16 10 +--R (66528a d e + 365904b d e )x + (365904a d e + 1219680b d e )x +--R + +--R 3 16 4 15 9 4 15 5 14 8 +--R (1219680a d e + 2744280b d e )x + (2744280a d e + 4390848b d e )x +--R + +--R 5 14 6 13 7 6 13 7 12 6 +--R (4390848a d e + 5122656b d e )x + (5122656a d e + 4390848b d e )x +--R + +--R 7 12 8 11 5 8 11 9 10 4 +--R (4390848a d e + 2744280b d e )x + (2744280a d e + 1219680b d e )x +--R + +--R 9 10 10 9 3 10 9 11 8 2 +--R (1219680a d e + 365904b d e )x + (365904a d e + 66528b d e )x +--R + +--R 11 8 12 7 12 7 +--R (66528a d e + 5544b d e )x + 5544a d e +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R e x + 13d e x + 78d e x + 286d e x + 715d e x + 1287d e x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 +--R 1716d e x + 1716d e x + 1287d e x + 715d e x + 286d e x +--R + +--R 11 2 2 12 13 +--R 78d e x + 13d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 650 + +)clear all + +--S 651 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^14 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R e x + 14d e x + 91d e x + 364d e x + 1001d e x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002d e x + 3003d e x + 3432d e x + 3003d e x + 2002d e x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001d e x + 364d e x + 91d e x + 14d e x + d +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1378 +r0:=-5/1716*b*(6*b*B*d+7*A*b*e-13*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^11)-1/858*b^2*(6*b*B*d+7*A*b*e-_ + 13*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^10)-_ + 1/13*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^13)-1/156*(6*b*B*d+7*A*b*e-13*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^12)-1/2574*b^3*(6*b*B*d+_ + 7*A*b*e-13*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-_ + a*e)*(d+e*x)^9)-1/9009*b^4*(6*b*B*d+7*A*b*e-13*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^8)-1/72072*b^4*(6*b*B*d+_ + 7*A*b*e-13*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 10296B b e x + ((- 9009A b - 45045B a b )e - 7722B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 40040A a b - 80080B a b )e + (- 5005A b - 25025B a b )d e +--R + +--R 5 2 4 +--R - 4290B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 72072A a b - 72072B a b )e + (- 16016A a b - 32032B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 2002A b - 10010B a b )d e - 1716B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 65520A a b - 32760B a b)e + (- 19656A a b - 19656B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 4368A a b - 8736B a b )d e + (- 546A b - 2730B a b )d e +--R + +--R 5 4 2 +--R - 468B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 30030A a b - 6006B a )e + (- 10920A a b - 5460B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 3276A a b - 3276B a b )d e + (- 728A a b - 1456B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 91A b - 455B a b )d e - 78B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 5544A a e + (- 2310A a b - 462B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 840A a b - 420B a b)d e + (- 252A a b - 252B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (- 56A a b - 112B a b )d e + (- 7A b - 35B a b )d e - 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 20 14 20 19 13 +--R 72072b e x + (72072a e + 936936b d e )x +--R + +--R 19 2 18 12 +--R (936936a d e + 5621616b d e )x +--R + +--R 2 18 3 17 11 +--R (5621616a d e + 20612592b d e )x +--R + +--R 3 17 4 16 10 +--R (20612592a d e + 51531480b d e )x +--R + +--R 4 16 5 15 9 +--R (51531480a d e + 92756664b d e )x +--R + +--R 5 15 6 14 8 +--R (92756664a d e + 123675552b d e )x +--R + +--R 6 14 7 13 7 +--R (123675552a d e + 123675552b d e )x +--R + +--R 7 13 8 12 6 +--R (123675552a d e + 92756664b d e )x +--R + +--R 8 12 9 11 5 +--R (92756664a d e + 51531480b d e )x +--R + +--R 9 11 10 10 4 +--R (51531480a d e + 20612592b d e )x +--R + +--R 10 10 11 9 3 +--R (20612592a d e + 5621616b d e )x +--R + +--R 11 9 12 8 2 12 8 13 7 +--R (5621616a d e + 936936b d e )x + (936936a d e + 72072b d e )x +--R + +--R 13 7 +--R 72072a d e +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 10296B b e x + ((- 9009A b - 45045B a b )e - 7722B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 40040A a b - 80080B a b )e + (- 5005A b - 25025B a b )d e +--R + +--R 5 2 4 +--R - 4290B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 72072A a b - 72072B a b )e + (- 16016A a b - 32032B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 2002A b - 10010B a b )d e - 1716B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 65520A a b - 32760B a b)e + (- 19656A a b - 19656B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 4368A a b - 8736B a b )d e + (- 546A b - 2730B a b )d e +--R + +--R 5 4 2 +--R - 468B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 30030A a b - 6006B a )e + (- 10920A a b - 5460B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 3276A a b - 3276B a b )d e + (- 728A a b - 1456B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 91A b - 455B a b )d e - 78B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 5544A a e + (- 2310A a b - 462B a )d e + (- 840A a b - 420B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 252A a b - 252B a b )d e + (- 56A a b - 112B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 7A b - 35B a b )d e - 6B b d +--R / +--R 20 13 19 12 2 18 11 3 17 10 +--R 72072e x + 936936d e x + 5621616d e x + 20612592d e x +--R + +--R 4 16 9 5 15 8 6 14 7 7 13 6 +--R 51531480d e x + 92756664d e x + 123675552d e x + 123675552d e x +--R + +--R 8 12 5 9 11 4 10 10 3 11 9 2 +--R 92756664d e x + 51531480d e x + 20612592d e x + 5621616d e x +--R + +--R 12 8 13 7 +--R 936936d e x + 72072d e +--R Type: Union(Expression(Integer),...) +--E 653 + +--S 654 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R 10296B b e x + ((9009A b + 45045B a b )e + 7722B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (40040A a b + 80080B a b )e + (5005A b + 25025B a b )d e +--R + +--R 5 2 4 +--R 4290B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (72072A a b + 72072B a b )e + (16016A a b + 32032B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2002A b + 10010B a b )d e + 1716B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (65520A a b + 32760B a b)e + (19656A a b + 19656B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (4368A a b + 8736B a b )d e + (546A b + 2730B a b )d e +--R + +--R 5 4 2 +--R 468B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (30030A a b + 6006B a )e + (10920A a b + 5460B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (3276A a b + 3276B a b )d e + (728A a b + 1456B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (91A b + 455B a b )d e + 78B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 5544A a e + (2310A a b + 462B a )d e + (840A a b + 420B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (252A a b + 252B a b )d e + (56A a b + 112B a b )d e +--R + +--R 5 4 5 5 6 +--R (7A b + 35B a b )d e + 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R - 10296B b e x + ((- 9009A b - 55341B a b )e - 7722B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 49049A a b - 125125B a b )e + (- 5005A b - 32747B a b )d e +--R + +--R 6 2 4 +--R - 4290B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 112112A a b - 152152B a b )e + (- 21021A a b - 57057B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 2002A b - 14300B a b )d e - 1716B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 137592A a b - 104832B a b )e + (- 35672A a b - 51688B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 6370A a b - 18746B a b )d e + (- 546A b - 4446B a b )d e +--R + +--R 6 4 2 +--R - 468B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 95550A a b - 38766B a b)e + (- 30576A a b - 25116B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 7644A a b - 12012B a b )d e + (- 1274A a b - 4186B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 91A b - 923B a b )d e - 78B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 35574A a b - 6006B a )e + (- 13230A a b - 5922B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 4116A a b - 3696B a b )d e + (- 980A a b - 1708B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 147A a b - 567B a b )d e + (- 7A b - 113B a b )d e - 6B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 5544A a e + (- 2310A a b - 462B a )d e + (- 840A a b - 420B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 252A a b - 252B a b )d e + (- 56A a b - 112B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- 7A a b - 35B a b )d e - 6B a b d +--R / +--R 20 14 20 19 13 +--R 72072b e x + (72072a e + 936936b d e )x +--R + +--R 19 2 18 12 +--R (936936a d e + 5621616b d e )x +--R + +--R 2 18 3 17 11 +--R (5621616a d e + 20612592b d e )x +--R + +--R 3 17 4 16 10 +--R (20612592a d e + 51531480b d e )x +--R + +--R 4 16 5 15 9 +--R (51531480a d e + 92756664b d e )x +--R + +--R 5 15 6 14 8 +--R (92756664a d e + 123675552b d e )x +--R + +--R 6 14 7 13 7 +--R (123675552a d e + 123675552b d e )x +--R + +--R 7 13 8 12 6 +--R (123675552a d e + 92756664b d e )x +--R + +--R 8 12 9 11 5 +--R (92756664a d e + 51531480b d e )x +--R + +--R 9 11 10 10 4 +--R (51531480a d e + 20612592b d e )x +--R + +--R 10 10 11 9 3 +--R (20612592a d e + 5621616b d e )x +--R + +--R 11 9 12 8 2 12 8 13 7 +--R (5621616a d e + 936936b d e )x + (936936a d e + 72072b d e )x +--R + +--R 13 7 +--R 72072a d e +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R e x + 14d e x + 91d e x + 364d e x + 1001d e x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002d e x + 3003d e x + 3432d e x + 3003d e x + 2002d e x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001d e x + 364d e x + 91d e x + 14d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 655 + +)clear all + +--S 656 of 1378 +t0:=(A+B*x)*(d+e*x)^3/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1378 +r0:=1/2*(A*b-a*B)*(b*d-a*e)*(a+b*x)*(d+e*x)^2/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+1/3*(A*b-a*B)*(a+b*x)*(d+e*x)^3/(b^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+1/4*B*(a+b*x)*(d+e*x)^4/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*(b*d-a*e)^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+(A*b-a*B)*e*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 2 4 4 2 3 3 2 3 +--R (- 12A a b + 12B a b)e + (36A a b - 36B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 36A a b + 36B a b )d e + (12A a b - 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 2A a b + 2B a b )e + (18A b - 6B a b )d e + 18B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (6A a b - 6B a b )e + (- 18A a b + 18B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 18B a b )d e + 12B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (24A a b - 24B a b)e + (- 60A a b + 60B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (42A a b - 42B a b )d e + (10A b + 2B a b )d e + 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (12A a b - 12B a )e + (- 24A a b + 24B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (6A a b - 6B a b )d e + (10A a b - 10B a b )d e + 3B a b d +--R / +--R +------------------+ +--R 5 | 2 2 2 +--R 12b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 2 3 2 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 3B b e x + ((4A b - 4B a b )e + 12B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 6B a b )e + (18A b - 18B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (12A a b - 12B a b)e + (- 36A a b + 36B a b )d e +--R + +--R 4 3 2 4 3 +--R (36A b - 36B a b )d e + 12B b d +--R * +--R x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 658 + +--S 659 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 2 2 3 3 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 3B b e x + ((4A b - 4B a b )e + 12B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((- 6A a b + 6B a b )e + (18A b - 18B a b )d e + 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 12B a b)e + (- 36A a b + 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (36A b - 36B a b )d e + 12B b d e +--R * +--R x +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A a b - 12B a b)e + (- 36A a b + 36B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (36A a b - 36B a b )d e + (- 12A b + 12B a b )d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (12A a b - 12B a )e + (- 36A a b + 36B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (36A a b - 36B a b )d e + (- 12A a b + 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R - 3B b e x + ((- 4A b + B a b )e - 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((2A a b - 2B a b )e + (- 18A b + 6B a b )d e - 18B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 6A a b + 6B a b )e + (18A a b - 18B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 18B a b )d e - 12B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 24A a b + 24B a b)e + (60A a b - 60B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 42A a b + 42B a b )d e + (- 10A b - 2B a b )d e - 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 12A a b + 12B a )e + (24A a b - 24B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 6A a b + 6B a b )d e + (- 10A a b + 10B a b )d e - 3B a b d +--R / +--R +------------------+ +--R 5 | 2 2 2 +--R 12b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 1378 +t0:=(A+B*x)*(d+e*x)^2/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1378 +r0:=1/2*(A*b-a*B)*(a+b*x)*(d+e*x)^2/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 1/3*B*(a+b*x)*(d+e*x)^3/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*_ + (b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*e*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (6A a b - 6B a b)e + (- 12A a b + 12B a b )d e +--R + +--R 4 3 2 +--R (6A b - 6B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (6A a b - 6B a )e + (- 12A a b + 12B a b)d e +--R + +--R 3 2 2 2 +--R (6A a b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 3A a b + 3B a b )e + (12A b - 6B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 12A a b + 12B a b)e + (18A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 3B a b )d e + 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (- 6A a b + 6B a )e + (6A a b - 6B a b)d e + (3A a b - 3B a b )d e +--R + +--R 3 3 +--R 2B a b d +--R / +--R +------------------+ +--R 4 | 2 2 2 +--R 6b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 3 2 2 +--R ((6A a b - 6B a )e + (- 12A a b + 12B a b)d e + (6A b - 6B a b )d ) +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R 2B b e x + ((3A b - 3B a b )e + 6B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (12A b - 12B a b )d e + 6B b d )x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 663 + +--S 664 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 +--R (6A a b - 6B a )e + (- 12A a b + 12B a b)d e +--R + +--R 3 2 2 +--R (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 2B b e x + ((3A b - 3B a b )e + 6B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 6A a b + 6B a b)e + (12A b - 12B a b )d e + 6B b d e)x +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 6A a b + 6B a b)e + (12A a b - 12B a b )d e +--R + +--R 4 3 2 +--R (- 6A b + 6B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 6A a b + 6B a )e + (12A a b - 12B a b)d e +--R + +--R 3 2 2 2 +--R (- 6A a b + 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R - 2B b e x + ((- 3A b + B a b )e - 6B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((3A a b - 3B a b )e + (- 12A b + 6B a b )d e - 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (12A a b - 12B a b)e + (- 18A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 3A b - 3B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (6A a b - 6B a )e + (- 6A a b + 6B a b)d e + (- 3A a b + 3B a b )d e +--R + +--R 3 3 +--R - 2B a b d +--R / +--R +------------------+ +--R 4 | 2 2 2 +--R 6b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 665 + +)clear all + +--S 666 of 1378 +t0:=(A+B*x)*(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1378 +r0:=1/2*B*(a+b*x)*(d+e*x)^2/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*_ + (b*d-a*e)*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-_ + a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3 +--R +--R +--R (2) +--R 2 2 2 3 2 +--R ((- 2A a b + 2B a b)e + (2A b - 2B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (- 2A a b + 2B a )e + (2A a b - 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - B a b )e + 2B b d e)x +--R + +--R 2 2 2 2 3 2 2 3 2 +--R ((4A a b - 4B a b)e + 2B a b d e + B b d )x + (2A a b - 2B a )e +--R + +--R 2 2 +--R B a b d +--R / +--R +------------------+ +--R 3 | 2 2 2 +--R 2b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R ((- 2A a b + 2B a )e + (2A b - 2B a b)d)log(b x + a) + B b e x +--R + +--R 2 2 +--R ((2A b - 2B a b)e + 2B b d)x +--R / +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 668 + +--S 669 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 +--R ((- 2A a b + 2B a )e + (2A b - 2B a b)d e)log(b x + a) + B b e x +--R + +--R 2 2 2 +--R ((2A b - 2B a b)e + 2B b d e)x +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 3 2 2 3 2 +--R ((2A a b - 2B a b)e + (- 2A b + 2B a b )d e)x + (2A a b - 2B a )e +--R + +--R 2 2 +--R (- 2A a b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R - B b e x + ((- 2A b + B a b )e - 2B b d e)x +--R + +--R 2 2 2 2 3 2 2 3 2 +--R ((- 4A a b + 4B a b)e - 2B a b d e - B b d )x + (- 2A a b + 2B a )e +--R + +--R 2 2 +--R - B a b d +--R / +--R +------------------+ +--R 3 | 2 2 2 +--R 2b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 670 + +)clear all + +--S 671 of 1378 +t0:=(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R B x + A +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1378 +r0:=(A*b-a*B)*(a+b*x)*log(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + B*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2 +--R +--R +--R (2) +--R 2 2 2 2 2 +--R ((A b - B a b)x + A a b - B a )log(b x + a) + B b x + 2B a b x + B a +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (A b - B a)log(b x + a) + B b x +--R (3) ------------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 673 + +--S 674 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R | 2 2 2 +--R ((A b - B a)log(b x + a) + B b x)\|b x + 2a b x + a +--R + +--R 2 2 2 2 2 +--R ((- A b + B a b)x - A a b + B a )log(b x + a) - B b x - 2B a b x - B a +--R / +--R +------------------+ +--R 2 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 1378 +t0:=(A+B*x)/((d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1378 +r0:=(A*b-a*B)*(a+b*x)*log(a+b*x)/(b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (B*d-A*e)*(a+b*x)*log(d+e*x)/(e*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 +--R ((- A b + B a b)e x + (- A a b + B a )e)log(b x + a) +--R / +--R +------------------+ +--R 2 2 | 2 2 2 +--R (a b e - b d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (A b e - B b d)log(e x + d) + (- A b + B a)e log(b x + a) +--R (3) --------------------------------------------------------- +--R 2 2 +--R a b e - b d e +--R Type: Union(Expression(Integer),...) +--E 678 + +--S 679 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R ((A b e - B b d)log(e x + d) + (- A b + B a)e log(b x + a)) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(e x + d) +--R + +--R 2 2 +--R ((A b - B a b)e x + (A a b - B a )e)log(b x + a) +--R / +--R +------------------+ +--R 2 2 | 2 2 2 +--R (a b e - b d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 680 + +)clear all + +--S 681 of 1378 +t0:=(A+B*x)/((d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1378 +r0:=-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (- A b + B a b)e x + ((- A a b + B a )e + (- A b + B a b)d e)x +--R + +--R 2 +--R (- A a b + B a )d e +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 2 2 +--R (A b - B a b)e x + ((A a b - B a )e + (A b - B a b)d e)x +--R + +--R 2 +--R (A a b - B a )d e +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R (- A a b e + (A b + B a b)d e - B b d )x - A a e + (A a b + B a )d e +--R + +--R 2 +--R - B a b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R ((- A b + B a)e x + (- A b + B a)d e)log(e x + d) +--R + +--R 2 2 +--R ((A b - B a)e x + (A b - B a)d e)log(b x + a) - A a e + (A b + B a)d e +--R + +--R 2 +--R - B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R (a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e +--R Type: Union(Expression(Integer),...) +--E 683 + +--S 684 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +--R ((- A b + B a)e x + (- A b + B a)d e)log(e x + d) +--R + +--R 2 2 +--R ((A b - B a)e x + (A b - B a)d e)log(b x + a) - A a e +--R + +--R 2 +--R (A b + B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 2 2 2 +--R (A b - B a b)e x + ((A a b - B a )e + (A b - B a b)d e)x +--R + +--R 2 +--R (A a b - B a )d e +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 2 2 +--R (- A b + B a b)e x + ((- A a b + B a )e + (- A b + B a b)d e)x +--R + +--R 2 +--R (- A a b + B a )d e +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R (A a b e + (- A b - B a b)d e + B b d )x + A a e + (- A a b - B a )d e +--R + +--R 2 +--R B a b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R --------------------------------------------------------------------------- +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 685 + +)clear all + +--S 686 of 1378 +t0:=(A+B*x)/((d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1378 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + b*(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b*(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (A*b-a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 +--R (2A b - 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((2A a b - 2B a b)e + (4A b - 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((4A a b - 4B a b)d e + (2A b - 2B a b )d e)x +--R + +--R 2 2 2 +--R (2A a b - 2B a b)d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 +--R (- 2A b + 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 2A a b + 2B a b)e + (- 4A b + 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 4A a b + 4B a b)d e + (- 2A b + 2B a b )d e)x +--R + +--R 2 2 2 +--R (- 2A a b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 3 2 2 2 +--R (2A b - 2B a b )e x + ((4A a b - 4B a b)e + (2A b - 2B a b )d e )x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (A a b - 2B a )e + (6A a b - 3B a b)d e + (- A b - 2B a b )d e +--R + +--R 3 3 +--R B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R - A a e + (4A a b - B a )d e + (- A a b - 2B a b)d e + B a b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 +--R ((2A b - 2B a b)e x + (4A b - 4B a b)d e x + (2A b - 2B a b)d e) +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- 2A b + 2B a b)e x + (- 4A b + 4B a b)d e x +--R + +--R 2 2 +--R (- 2A b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 2 3 +--R ((2A a b - 2B a )e + (- 2A b + 2B a b)d e )x - A a e +--R + +--R 2 2 2 2 2 3 +--R (4A a b - B a )d e - 3A b d e + B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R Type: Union(Expression(Integer),...) +--E 688 + +--S 689 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 +--R (2A b - 2B a b)e x + (4A b - 4B a b)d e x +--R + +--R 2 2 +--R (2A b - 2B a b)d e +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- 2A b + 2B a b)e x + (- 4A b + 4B a b)d e x +--R + +--R 2 2 +--R (- 2A b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 2 3 +--R ((2A a b - 2B a )e + (- 2A b + 2B a b)d e )x - A a e +--R + +--R 2 2 2 2 2 3 +--R (4A a b - B a )d e - 3A b d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 3 +--R (- 2A b + 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 2A a b + 2B a b)e + (- 4A b + 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 4A a b + 4B a b)d e + (- 2A b + 2B a b )d e)x +--R + +--R 2 2 2 +--R (- 2A a b + 2B a b)d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 +--R (2A b - 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((2A a b - 2B a b)e + (4A b - 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((4A a b - 4B a b)d e + (2A b - 2B a b )d e)x +--R + +--R 2 2 2 +--R (2A a b - 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 +--R (- 2A b + 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 4A a b + 4B a b)e + (- 2A b + 2B a b )d e )x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- A a b + 2B a )e + (- 6A a b + 3B a b)d e + (A b + 2B a b )d e +--R + +--R 3 3 +--R - B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R A a e + (- 4A a b + B a )d e + (A a b + 2B a b)d e - B a b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 1378 +t0:=(A+B*x)/((d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1378 +r0:=-1/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 1/2*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + b^2*(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b^2*(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b*(A*b-a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^4*(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 +--R (- 6A b + 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((- 6A a b + 6B a b )e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((- 18A a b + 18B a b )d e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((- 18A a b + 18B a b )d e + (- 6A b + 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (- 6A a b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 +--R (6A b - 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((6A a b - 6B a b )e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((18A a b - 18B a b )d e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((18A a b - 18B a b )d e + (6A b - 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (6A a b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 +--R (- 6A b + 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((- 12A a b + 12B a b )e + (- 12A b + 12B a b )d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 3A a b + 3B a b)e + (- 30A a b + 30B a b )d e +--R + +--R 4 3 2 2 +--R (- 3A b + 3B a b )d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (A a b - 3B a )e + (- 9A a b + 17B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 21A a b + 9B a b )d e + (5A b + 3B a b )d e - 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (5A a b + 3B a b )d e - 2B a b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4 7 +--R 6a d e - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 3 2 3 2 +--R (- 6A b + 6B a b )e x + (- 18A b + 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (- 18A b + 18B a b )d e x + (- 6A b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 3 2 4 3 3 2 3 2 +--R (6A b - 6B a b )e x + (18A b - 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (18A b - 18B a b )d e x + (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 2 2 4 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (6A b - 6B a b )d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b - 3B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 +--R (15A b - 15B a b )d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 3 3 4 +--R (11A b - 3B a b )d e - 2B b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 4 3 5 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x + 6a d e +--R + +--R 3 4 4 2 2 5 3 3 6 2 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R Type: Union(Expression(Integer),...) +--E 693 + +--S 694 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 4 3 3 2 3 2 +--R (- 6A b + 6B a b )e x + (- 18A b + 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (- 18A b + 18B a b )d e x + (- 6A b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 3 2 4 3 3 2 3 2 +--R (6A b - 6B a b )e x + (18A b - 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (18A b - 18B a b )d e x + (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 2 2 4 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (6A b - 6B a b )d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b - 3B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 +--R (15A b - 15B a b )d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 3 3 4 +--R (11A b - 3B a b )d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 4 +--R (6A b - 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((6A a b - 6B a b )e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((18A a b - 18B a b )d e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((18A a b - 18B a b )d e + (6A b - 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (6A a b - 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 +--R (- 6A b + 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((- 6A a b + 6B a b )e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((- 18A a b + 18B a b )d e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((- 18A a b + 18B a b )d e + (- 6A b + 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (- 6A a b + 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 +--R (6A b - 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((12A a b - 12B a b )e + (12A b - 12B a b )d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (3A a b - 3B a b)e + (30A a b - 30B a b )d e +--R + +--R 4 3 2 2 +--R (3A b - 3B a b )d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- A a b + 3B a )e + (9A a b - 17B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (21A a b - 9B a b )d e + (- 5A b - 3B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R 2A a e + (- 9A a b + B a )d e + (18A a b - 6B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 5A a b - 3B a b )d e + 2B a b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4 7 +--R 6a d e - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 695 + +)clear all + +--S 696 of 1378 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1378 +r0:=-1/6*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^4/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/3*B*(a+b*x)*(d+e*x)^5/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+e*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^2/(b^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-2/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^3/_ + (b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*(a+b*x)*log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2*e^2*(b*d-a*e)*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6 +--R +--R +--R (2) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 90A a b + 150B a b )e + (144A a b - 300B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 156B a b )d e - 4B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 108A a b + 180B a b)e + (144A a b - 312B a b )d e +--R + +--R 2 3 2 2 5 4 3 5 4 +--R 96B a b d e + (- 24A b + 40B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 36A a b + 60B a )e + (36A a b - 84B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (18A a b - 6B a b )d e + (- 12A a b + 32B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R / +--R +------------------+ +--R 7 6 | 2 2 2 +--R (6b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 33A a b + 63B a b )e + (48A a b - 132B a b )d e + 72B a b d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (6A a b + 6B a b)e + (- 48A a b + 24B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (72A a b - 72B a b )d e + (- 24A b + 48B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (21A a b - 27B a )e + (- 60A a b + 84B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (54A a b - 90B a b )d e + (- 12A a b + 36B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 698 + +--S 699 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 33A a b + 63B a b )e + (48A a b - 132B a b )d e +--R + +--R 4 2 2 +--R 72B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (6A a b + 6B a b)e + (- 48A a b + 24B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (72A a b - 72B a b )d e + (- 24A b + 48B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (21A a b - 27B a )e + (- 60A a b + 84B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (54A a b - 90B a b )d e + (- 12A a b + 36B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 36A a b + 60B a b )e + (72A a b - 144B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (- 36A b + 108B a b )d e - 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (- 108A a b + 180B a b )e + (216A a b - 432B a b )d e +--R + +--R 5 2 4 2 2 5 3 +--R (- 108A a b + 324B a b )d e - 72B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 108A a b + 180B a b)e + (216A a b - 432B a b )d e +--R + +--R 2 4 3 3 2 2 2 4 3 +--R (- 108A a b + 324B a b )d e - 72B a b d e +--R * +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 36A a b + 60B a )e + (72A a b - 144B a b)d e +--R + +--R 3 3 4 2 2 2 3 3 3 +--R (- 36A a b + 108B a b )d e - 24B a b d e +--R * +--R log(b x + a) +--R + +--R 6 4 6 6 5 4 6 3 5 +--R - 2B b e x + ((- 3A b + 3B a b )e - 12B b d e )x +--R + +--R 5 2 4 4 6 5 3 6 2 2 4 +--R ((9A a b - 15B a b )e + (- 24A b + 36B a b )d e - 36B b d e )x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (102A a b - 170B a b )e + (- 168A a b + 348B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (36A b - 192B a b )d e + 4B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (198A a b - 330B a b )e + (- 288A a b + 612B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (36A a b - 252B a b )d e + (24A b - 36B a b )d e + 6B b d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (144A a b - 240B a b)e + (- 180A a b + 396B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 18A a b - 90B a b )d e + (36A a b - 72B a b )d e +--R + +--R 6 5 4 +--R (3A b + 9B a b )d +--R * +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (36A a b - 60B a )e + (- 36A a b + 84B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 18A a b + 6B a b )d e + (12A a b - 32B a b )d e +--R + +--R 5 2 4 4 +--R (3A a b + 3B a b )d +--R / +--R +------------------+ +--R 8 2 7 2 6 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 5 +--R - B b e x + ((- A b - B a)e - 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (- A a e + (- 4A b - 4B a)d e - 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (- 4A a d e + (- 6A b - 6B a)d e - 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (- 6A a d e + (- 4A b - 4B a)d e - B b d )x +--R + +--R 3 4 4 +--R (- 4A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 1378 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1378 +r0:=-1/2*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*(d+e*x)^3/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/2*B*(a+b*x)*(d+e*x)^4/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-3/2*(b*B*d+A*b*e-2*a*B*e)*(d+e*x)^2/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*B*d+A*b*e-_ + 2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 24B a b)e + (12A a b - 36B a b )d e + 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((15A a b - 30B a b )e + (- 9A b + 33B a b )d e - 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 36B a b)e + (- 6A a b + 30B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 6B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 3 2 3 2 2 2 +--R (6A a b - 12B a )e + 6B a b d e + (- 3A a b + 6B a b )d e +--R + +--R 4 3 3 +--R (- A b - B a b )d +--R / +--R +------------------+ +--R 6 5 | 2 2 2 +--R (2b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 24B a b)e + (12A a b - 36B a b )d e + 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((4A a b - 11B a b )e + 12B a b d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 4A a b + 2B a b)e + (12A a b - 12B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 12B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (- 5A a b + 7B a )e + (9A a b - 15B a b)d e + (- 3A a b + 9B a b )d e +--R + +--R 4 3 3 +--R (- A b - B a b )d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 12A a b + 24B a b)e + (12A a b - 36B a b )d e +--R + +--R 3 2 +--R 12B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((4A a b - 11B a b )e + 12B a b d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 4A a b + 2B a b)e + (12A a b - 12B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 12B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 5A a b + 7B a )e + (9A a b - 15B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b + 9B a b )d e + (- A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((6A a b - 12B a b )e + (- 6A b + 18B a b )d e - 6B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (18A a b - 36B a b )e + (- 18A a b + 54B a b )d e +--R + +--R 4 2 +--R - 18B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 3 2 +--R ((18A a b - 36B a b)e + (- 18A a b + 54B a b )d e - 18B a b d e)x +--R + +--R 4 5 3 3 2 4 2 3 2 2 +--R (6A a b - 12B a )e + (- 6A a b + 18B a b)d e - 6B a b d e +--R * +--R log(b x + a) +--R + +--R 5 3 5 5 4 3 5 2 4 +--R - B b e x + ((- 2A b + 3B a b )e - 6B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((- 17A a b + 34B a b )e + (9A b - 39B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 33A a b + 66B a b )e + (15A a b - 63B a b )d e +--R + +--R 5 4 2 5 3 +--R (6A b - 3B a b )d e + 2B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 24A a b + 48B a b)e + (6A a b - 36B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (9A a b - 12B a b )d e + (A b + 3B a b )d +--R * +--R x +--R + +--R 4 5 3 4 2 2 3 3 2 2 +--R (- 6A a b + 12B a )e - 6B a b d e + (3A a b - 6B a b )d e +--R + +--R 4 2 3 3 +--R (A a b + B a b )d +--R / +--R +------------------+ +--R 7 2 6 2 5 | 2 2 2 +--R (2b x + 4a b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1378 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1378 +r0:=-1/2*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^2/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+B*(a+b*x)*(d+e*x)^3/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + (2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 2 +--R 2B b e x + (- 3A b + 9B a b )e x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 2A a b + 6B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 2 3 2 2 +--R (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R / +--R +------------------+ +--R 5 4 | 2 2 2 +--R (2b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 2 2 +--R 2B b e x + 4B a b e x +--R + +--R 2 2 2 3 2 3 2 +--R ((4A a b - 4B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (3A a b - 5B a )e + (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 2 2 +--R 2B b e x + 4B a b e x +--R + +--R 2 2 2 3 2 3 2 +--R ((4A a b - 4B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (3A a b - 5B a )e + (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 2 4 3 +--R ((- 2A b + 6B a b )e - 4B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((- 6A a b + 18B a b )e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((- 6A a b + 18B a b)e - 12B a b d e)x + (- 2A a b + 6B a )e +--R + +--R 3 +--R - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 4 4 3 2 3 +--R - 2B b e x + (3A b - 11B a b )e x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((5A a b - 15B a b )e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 +--R ((2A a b - 6B a b)e + (6A a b - 14B a b )d e + (A b + 3B a b )d )x +--R + +--R 2 2 3 3 2 2 2 +--R (2A a b - 6B a b)d e + (A a b + B a b )d +--R / +--R +------------------+ +--R 6 2 5 2 4 | 2 2 2 +--R (2b x + 4a b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 710 + +)clear all + +--S 711 of 1378 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1378 +r0:=-1/2*(A*b-a*B)*(a+b*x)*(d+e*x)^2/(b*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-B*(b*d-a*e)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + B*e*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2)),-1/2*B*(a+_ + b*x)*(d+e*x)^2/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*(B*d-A*e)*(a+_ + b*x)*(d+e*x)^2/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-B*(d+e*x)/_ + (b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e*(a+b*x)*log(a+b*x)/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R [ +--R 2 2 3 2 2 2 2 3 2 +--R (2B a b e - 2B b d e)x + (4B a b e - 4B a b d e)x + 2B a e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 2 2 2 3 2 3 2 +--R (A b - B a b )e x + (2B a b e + (2A b - 6B a b )d e + 2B b d )x +--R + +--R 3 2 2 3 2 2 +--R 2B a e - 4B a b d e + (A b + B a b )d +--R / +--R +------------------+ +--R 4 5 2 3 4 | 2 2 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|b x + 2a b x + a +--R , +--R +--R 2 2 3 2 2 2 2 3 2 +--R (2B a b e - 2B b d e)x + (4B a b e - 4B a b d e)x + 2B a e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 3 2 +--R ((A b - 3B a b )e + 2B b d e)x +--R + +--R 2 2 3 2 3 2 2 +--R (- 2B a b e + (2A b - 2B a b )d e + 2B b d )x - 2B a b d e +--R + +--R 3 2 2 +--R (A b + B a b )d +--R / +--R +------------------+ +--R 4 5 2 3 4 | 2 2 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|b x + 2a b x + a +--R ] +--R Type: Tuple(Expression(Integer)) +--E 712 + +--S 713 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (2B b e x + 4B a b e x + 2B a e)log(b x + a) +--R + +--R 2 2 2 2 +--R ((- 2A b + 4B a b)e - 2B b d)x + (- A a b + 3B a )e + (- A b - B a b)d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 3 2 2 2 2 3 2 +--R (2B a b e - 2B b d e)x + (4B a b e - 4B a b d e)x + 2B a e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 2 3 2 +--R ((- 2A a b + 4B a b)e + (2A b - 6B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 3 2 2 +--R (- A a b + 3B a )e - 4B a b d e + (A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 4 3 2 2 2 3 2 +--R (- 2B a b e + 2B b d e)x + (- 6B a b e + 6B a b d e)x +--R + +--R 3 2 2 2 4 2 3 +--R (- 6B a b e + 6B a b d e)x - 2B a e + 2B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 2 3 +--R (- A b + B a b )e x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((- A a b - B a b )e + (- 2A b + 6B a b )d e - 2B b d )x +--R + +--R 3 2 3 2 2 4 3 2 +--R (- 4B a b e + (- 2A a b + 10B a b )d e + (- A b - 3B a b )d )x +--R + +--R 4 2 3 3 2 2 2 +--R - 2B a e + 4B a b d e + (- A a b - B a b )d +--R / +--R 5 6 2 2 4 5 3 3 2 4 +--R ((2a b e - 2b d)x + (4a b e - 4a b d)x + 2a b e - 2a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 1378 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1378 +r0:=-1/2*(a+b*x)*(A+B*x)^2/((A*b-a*B)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 2 2 2 +--R - B x - 2A B x - A +--R (2) --------------------------------------------------------- +--R +------------------+ +--R 2 2 | 2 2 2 +--R ((2A b - 2B a b)x + 2A a b - 2B a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1378 +a0:=integrate(t0,x) +--R +--R +--R - 2B b x - A b - B a +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 718 + +--S 719 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 2 2 2 2 2 | 2 2 2 2 3 3 +--R ((- 2A B b + 2B a b)x - A b + B a )\|b x + 2a b x + a + B b x +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (2A B b + B a b )x + (A b + 2A B a b )x + A a b +--R / +--R 5 4 2 4 2 3 2 3 3 2 +--R ((2A b - 2B a b )x + (4A a b - 4B a b )x + 2A a b - 2B a b ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 1378 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1378 +r0:=-1/2*(A*b-a*B)*(a+b*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + (-B*d+A*e)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(B*d-A*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + e*(B*d-A*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x - 2A a b e +--R + +--R 2 +--R 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R / +--R 3 2 3 2 3 2 4 2 5 3 4 3 3 2 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x + 2a b e - 6a b d e +--R + +--R 2 3 2 4 3 +--R 6a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x - 2A a b e +--R + +--R 2 +--R 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R / +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 3 4 2 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a b e - 6a b d e +--R + +--R 3 3 2 2 4 3 +--R 6a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 723 + +--S 724 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x +--R + +--R 2 2 2 +--R - 2A a b e + 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 2 4 3 3 2 3 2 +--R (- 2A b e + 2B b d e)x + (- 6A a b e + 6B a b d e)x +--R + +--R 2 2 2 2 2 3 2 3 +--R (- 6A a b e + 6B a b d e)x - 2A a b e + 2B a b d e +--R * +--R log(e x + d) +--R + +--R 4 2 4 3 3 2 3 2 +--R (2A b e - 2B b d e)x + (6A a b e - 6B a b d e)x +--R + +--R 2 2 2 2 2 3 2 3 +--R (6A a b e - 6B a b d e)x + 2A a b e - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 4 3 4 2 2 +--R (- 2A a b e + (2A b + 2B a b )d e - 2B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 +--R ((- 5A a b + B a b)e + (6A a b + 2B a b )d e + (- A b - 3B a b )d )x +--R + +--R 3 4 2 2 2 3 2 2 2 +--R (- 3A a b + B a )e + 4A a b d e + (- A a b - B a b )d +--R / +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 3 4 2 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a b e - 6a b d e +--R + +--R 3 3 2 2 4 3 +--R 6a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 725 + +)clear all + +--S 726 of 1378 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1378 +r0:=1/2*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+(-2*b*B*d+3*A*b*e-a*B*e)/((b*d-a*e)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-e*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/_ + ((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(2*b*B*d-3*A*b*e+a*B*e)*_ + (a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e + (3A b - 5B a b )d e +--R + +--R 3 3 +--R - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (2a e - 6a b d e + 4a b d e + 4a b d e - 6a b d e + 2b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e + (3A b - 5B a b )d e +--R + +--R 3 3 +--R - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 728 + +--S 729 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e +--R + +--R 3 2 2 3 3 +--R (3A b - 5B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 3 4 2 4 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 3 +--R ((18A a b - 6B a b )e + (6A b - 14B a b )d e - 4B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 2 +--R ((18A a b - 6B a b)e + (18A a b - 18B a b )d e - 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R ((6A a b - 2B a )e + (18A a b - 10B a b)d e - 12B a b d e)x +--R + +--R 3 4 2 3 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 3 4 2 4 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 3 +--R ((- 18A a b + 6B a b )e + (- 6A b + 14B a b )d e + 4B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 18A a b + 6B a b)e + (- 18A a b + 18B a b )d e +--R + +--R 3 2 +--R 12B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 18A a b + 10B a b)d e + 12B a b d e)x +--R + +--R 3 4 2 3 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 3 4 3 2 4 2 3 +--R ((6A a b - 2B a b )e + (- 6A b - 2B a b )d e + 4B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (15A a b - 5B a b)e + (- 12A a b - 6B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 3A b + 9B a b )d e + 2B b d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (11A a b - 3B a )e + (- 3A a b - 9B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 9A a b + 9B a b )d e + (A b + 3B a b )d +--R * +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 2A a e + (3A a b - 5B a )d e + (- 6A a b + 4B a b)d e +--R + +--R 3 2 2 3 +--R (A a b + B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 730 + +)clear all + +--S 731 of 1378 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1378 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/2*(b*B*d-2*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-3/2*(b*B*d-2*A*b*e+a*B*e)/_ + ((b*d-a*e)^3*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3*b*e*(b*B*d-_ + 2*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*b*e*(b*B*d-2*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*B*d-2*A*b*e+a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/((b*d-a*e)^5*(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 12B a b )e + (24A b - 24B a b )d e - 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (24A a b - 24B a b )d e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((36A a b - 18B a b )e + (12A b - 24B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (30A a b - 15B a b)e + (48A a b - 39B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 6A b - 21B a b )d e + 3B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R (4A a b - 2B a )e + (48A a b - 26B a b)d e - 24B a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 2B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - A a e + (8A a b - B a )d e + (12A a b - 15B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 8A a b + 3B a b )d e + (A b + B a b )d +--R / +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e +--R + +--R 6 5 2 +--R - 2b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 6 3 3 3 4 2 4 4 3 5 5 2 6 6 2 +--R (2a e - 6a b d e + 20a b d e - 30a b d e + 18a b d e - 4b d e)x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5 6 6 7 +--R (4a d e - 18a b d e + 30a b d e - 20a b d e + 6a b d e - 2b d )x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 12B a b )e + (24A b - 24B a b )d e - 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (24A a b - 24B a b )d e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 4 2 2 3 +--R ((12A a b - 6B a b )e - 12A b d e + 6B b d e )x +--R + +--R 2 2 3 4 2 2 3 4 3 2 2 +--R (18A a b - 9B a b)e - 9B a b d e + (- 18A b + 9B a b )d e +--R + +--R 4 3 +--R 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 3 2 2 +--R (4A a b - 2B a )e + (24A a b - 14B a b)d e - 24A a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 14B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 3 2 2 3 2 2 3 +--R - A a e + (8A a b - B a )d e - 9B a b d e + (- 8A a b + 9B a b )d e +--R + +--R 4 3 4 +--R (A b + B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 733 + +--S 734 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (24A a b - 12B a b )e + (24A b - 24B a b )d e +--R + +--R 4 2 2 +--R - 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (24A a b - 12B a b)d e + (24A a b - 24B a b )d e +--R + +--R 3 3 +--R - 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 4 2 2 3 +--R ((12A a b - 6B a b )e - 12A b d e + 6B b d e )x +--R + +--R 2 2 3 4 2 2 3 4 3 2 2 +--R (18A a b - 9B a b)e - 9B a b d e + (- 18A b + 9B a b )d e +--R + +--R 4 3 +--R 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 3 2 2 +--R (4A a b - 2B a )e + (24A a b - 14B a b)d e - 24A a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 14B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 3 2 2 +--R - A a e + (8A a b - B a )d e - 9B a b d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 8A a b + 9B a b )d e + (A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 4 5 3 5 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 36A a b + 18B a b )e + (- 24A b + 30B a b )d e +--R + +--R 5 2 2 +--R 12B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 36A a b + 18B a b )e + (- 72A a b + 54B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 12A b + 42B a b )d e + 6B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 12A a b + 6B a b)e + (- 72A a b + 42B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (- 36A a b + 54B a b )d e + 18B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 36A a b + 30B a b )d e +--R + +--R 2 3 3 +--R 18B a b d e +--R * +--R x +--R + +--R 3 2 4 2 2 3 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 4 5 3 5 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 4 +--R ((36A a b - 18B a b )e + (24A b - 30B a b )d e - 12B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 18B a b )e + (72A a b - 54B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (12A b - 42B a b )d e - 6B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A a b - 6B a b)e + (72A a b - 42B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (36A a b - 54B a b )d e - 18B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (36A a b - 30B a b )d e - 18B a b d e)x +--R + +--R 3 2 4 2 2 3 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 4 5 3 5 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 4 +--R ((- 48A a b + 24B a b )e + (- 12A b + 30B a b )d e + 6B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 66A a b + 33B a b )e + (- 60A a b + 63B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (6A b + 27B a b )d e - 3B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 34A a b + 17B a b)e + (- 96A a b + 65B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (6A a b + 45B a b )d e + (4A b - 5B a b )d e - 2B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 3A a b + 2B a )e + (- 56A a b + 27B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 12A a b + 39B a b )d e + (12A a b - 5B a b )d e +--R + +--R 5 4 4 +--R (- A b - 3B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R A a e + (- 8A a b + B a )d e + (- 12A a b + 15B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (8A a b - 3B a b )d e + (- A a b - B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e +--R + +--R 7 5 2 +--R - 2b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e +--R + +--R 7 6 +--R - 4b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 18a b d e + 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 1378 +t0:=(A+B*x)*(d+e*x)^5/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1378 +r0:=-1/4*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^5/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/2*B*(a+b*x)*(d+e*x)^6/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-5/6*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^3/_ + (b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/12*(2*b*B*d+A*b*e-3*a*B*e)*_ + (d+e*x)^4/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/2*e^2*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(d+e*x)^2/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+5*e^3*(b*d-a*e)*_ + (2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*log(a+b*x)/(b^7*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+5*e^4*(2*b*B*d+A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7 +--R +--R +--R (2) +--R 5 2 4 5 6 5 4 +--R (- 60A a b + 180B a b )e + (60A b - 300B a b )d e +--R + +--R 6 2 3 +--R 120B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 240A a b + 720B a b )e + (240A a b - 1200B a b )d e +--R + +--R 5 2 3 +--R 480B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 360A a b + 1080B a b )e + (360A a b - 1800B a b )d e +--R + +--R 2 4 2 3 +--R 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 720B a b)e + (240A a b - 1200B a b )d e +--R + +--R 3 3 2 3 +--R 480B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 4 2 2 3 +--R (- 60A a b + 180B a )e + (60A a b - 300B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 6B b e x + ((12A b - 36B a b )e + 60B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((185A a b - 555B a b )e + (- 125A b + 745B a b )d e - 160B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (500A a b - 1500B a b )e + (- 260A a b + 1780B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 120A b - 160B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (570A a b - 1710B a b )e + (- 210A a b + 1770B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 180A a b + 120B a b )d e + (- 60A b - 180B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (300A a b - 900B a b)e + (- 60A a b + 780B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 120A a b + 240B a b )d e + (- 40A a b - 120B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 20A b - 20B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 6 5 5 4 3 3 4 2 2 3 +--R (60A a b - 180B a )e + 120B a b d e + (- 30A a b + 90B a b )d e +--R + +--R 2 4 3 3 3 2 5 2 4 4 +--R (- 10A a b - 30B a b )d e + (- 5A a b - 5B a b )d e +--R + +--R 6 5 5 +--R (- 3A b - B a b )d +--R / +--R +------------------+ +--R 10 3 9 2 2 8 3 7 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 5 6 5 4 +--R (- 60A a b + 180B a b )e + (60A b - 300B a b )d e +--R + +--R 6 2 3 +--R 120B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 240A a b + 720B a b )e + (240A a b - 1200B a b )d e +--R + +--R 5 2 3 +--R 480B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 360A a b + 1080B a b )e + (360A a b - 1800B a b )d e +--R + +--R 2 4 2 3 +--R 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 720B a b)e + (240A a b - 1200B a b )d e +--R + +--R 3 3 2 3 +--R 480B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 4 2 2 3 +--R (- 60A a b + 180B a )e + (60A a b - 300B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 6B b e x + ((12A b - 36B a b )e + 60B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((48A a b - 204B a b )e + 240B a b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 48A a b - 96B a b )e + (240A a b - 240B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 120A b + 480B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 252A a b + 396B a b )e + (540A a b - 1260B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 180A a b + 1080B a b )d e + (- 60A b - 180B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 248A a b + 504B a b)e + (440A a b - 1240B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 120A a b + 880B a b )d e + (- 40A a b - 120B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 20A b - 20B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 77A a b + 171B a )e + (125A a b - 385B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 30A a b + 250B a b )d e + (- 10A a b - 30B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 5A a b - 5B a b )d e + (- 3A b - B a b )d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 738 + +--S 739 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 4 5 6 5 4 +--R (- 60A a b + 180B a b )e + (60A b - 300B a b )d e +--R + +--R 6 2 3 +--R 120B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 240A a b + 720B a b )e + (240A a b - 1200B a b )d e +--R + +--R 5 2 3 +--R 480B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 360A a b + 1080B a b )e + (360A a b - 1800B a b )d e +--R + +--R 2 4 2 3 +--R 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 720B a b)e + (240A a b - 1200B a b )d e +--R + +--R 3 3 2 3 +--R 480B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 4 2 2 3 +--R (- 60A a b + 180B a )e + (60A a b - 300B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 6B b e x + ((12A b - 36B a b )e + 60B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((48A a b - 204B a b )e + 240B a b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 48A a b - 96B a b )e + (240A a b - 240B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 120A b + 480B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 252A a b + 396B a b )e + (540A a b - 1260B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 180A a b + 1080B a b )d e + (- 60A b - 180B a b )d e +--R + +--R 6 4 +--R - 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 248A a b + 504B a b)e + (440A a b - 1240B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 120A a b + 880B a b )d e + (- 40A a b - 120B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 20A b - 20B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 77A a b + 171B a )e + (125A a b - 385B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 30A a b + 250B a b )d e + (- 10A a b - 30B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 5A a b - 5B a b )d e + (- 3A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 2 5 5 7 6 4 +--R (60A a b - 180B a b )e + (- 60A b + 300B a b )d e +--R + +--R 7 2 3 +--R - 120B b d e +--R * +--R 5 +--R x +--R + +--R 2 5 3 4 5 6 2 5 4 +--R (300A a b - 900B a b )e + (- 300A a b + 1500B a b )d e +--R + +--R 6 2 3 +--R - 600B a b d e +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 5 2 5 3 4 4 +--R (600A a b - 1800B a b )e + (- 600A a b + 3000B a b )d e +--R + +--R 2 5 2 3 +--R - 1200B a b d e +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 5 3 4 4 3 4 +--R (600A a b - 1800B a b )e + (- 600A a b + 3000B a b )d e +--R + +--R 3 4 2 3 +--R - 1200B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 4 3 5 2 4 +--R (300A a b - 900B a b)e + (- 300A a b + 1500B a b )d e +--R + +--R 4 3 2 3 +--R - 600B a b d e +--R * +--R x +--R + +--R 6 7 5 5 2 6 4 5 2 2 3 +--R (60A a b - 180B a )e + (- 60A a b + 300B a b)d e - 120B a b d e +--R * +--R log(b x + a) +--R + +--R 7 5 7 7 6 5 7 4 6 +--R - 6B b e x + ((- 12A b + 30B a b )e - 60B b d e )x +--R + +--R 6 2 5 5 7 6 4 7 2 3 5 +--R ((- 197A a b + 591B a b )e + (125A b - 805B a b )d e + 160B b d e )x +--R + +--R 2 5 3 4 5 6 2 5 4 +--R (- 685A a b + 2055B a b )e + (385A a b - 2525B a b )d e +--R + +--R 7 6 2 3 7 3 2 +--R (120A b + 320B a b )d e + 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 5 2 5 3 4 4 +--R (- 1070A a b + 3210B a b )e + (470A a b - 3550B a b )d e +--R + +--R 6 2 5 2 3 7 6 3 2 7 4 +--R (300A a b + 40B a b )d e + (60A b + 300B a b )d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 5 3 4 4 3 4 +--R (- 870A a b + 2610B a b )e + (270A a b - 2550B a b )d e +--R + +--R 2 5 3 4 2 3 6 2 5 3 2 +--R (300A a b - 360B a b )d e + (100A a b + 300B a b )d e +--R + +--R 7 6 4 7 5 +--R (20A b + 50B a b )d e + 4B b d +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 4 3 5 2 4 +--R (- 360A a b + 1080B a b)e + (60A a b - 900B a b )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (150A a b - 330B a b )d e + (50A a b + 150B a b )d e +--R + +--R 6 2 5 4 7 6 5 +--R (25A a b + 25B a b )d e + (3A b + 5B a b )d +--R * +--R x +--R + +--R 6 7 5 6 4 4 3 5 2 2 3 +--R (- 60A a b + 180B a )e - 120B a b d e + (30A a b - 90B a b )d e +--R + +--R 3 4 4 3 3 2 2 5 3 4 4 6 2 5 5 +--R (10A a b + 30B a b )d e + (5A a b + 5B a b )d e + (3A a b + B a b )d +--R / +--R +------------------+ +--R 11 4 10 3 2 9 2 3 8 4 7 | 2 2 2 +--R (12b x + 48a b x + 72a b x + 48a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x +--R + +--R 5 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 7 5 4 6 +--R - B b e x + ((- A b - B a)e - 5B b d e )x +--R + +--R 5 4 2 3 5 +--R (- A a e + (- 5A b - 5B a)d e - 10B b d e )x +--R + +--R 4 2 3 3 2 4 +--R (- 5A a d e + (- 10A b - 10B a)d e - 10B b d e )x +--R + +--R 2 3 3 2 4 3 +--R (- 10A a d e + (- 10A b - 10B a)d e - 5B b d e)x +--R + +--R 3 2 4 5 2 +--R (- 10A a d e + (- 5A b - 5B a)d e - B b d )x +--R + +--R 4 5 5 +--R (- 5A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 740 + +)clear all + +--S 741 of 1378 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1378 +r0:=-1/4*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^4/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+B*(a+b*x)*(d+e*x)^5/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))-_ + 1/2*e*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^2/(b^4*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-1/3*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)^3/(b^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))-e^2*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)/(b^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*_ + log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((12A b - 60B a b )e + 48B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((48A a b - 240B a b )e + 192B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((72A a b - 360B a b )e + 288B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((48A a b - 240B a b)e + 192B a b d e )x + (12A a b - 60B a )e +--R + +--R 4 3 +--R 48B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 12B b e x + ((- 25A b + 125B a b )e - 40B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 52A a b + 260B a b )e + (- 48A b + 32B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 42A a b + 210B a b )e + (- 72A a b + 192B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b - 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 12A a b + 60B a b)e + (- 48A a b + 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 24A a b - 72B a b )d e + (- 16A b - 16B a b )d e - 4B b d +--R * +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (- 12A a b + 60B a b)d e + (- 6A a b - 18B a b )d e +--R + +--R 4 2 3 3 5 4 4 +--R (- 4A a b - 4B a b )d e + (- 3A b - B a b )d +--R / +--R +------------------+ +--R 9 3 8 2 2 7 3 6 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 4 5 3 4 +--R ((12A b - 60B a b )e + 48B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((48A a b - 240B a b )e + 192B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((72A a b - 360B a b )e + 288B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((48A a b - 240B a b)e + 192B a b d e )x + (12A a b - 60B a )e +--R + +--R 4 3 +--R 48B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 4 4 4 +--R 12B b e x + 48B a b e x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((48A a b - 48B a b )e + (- 48A b + 192B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (108A a b - 252B a b )e + (- 72A a b + 432B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b - 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (88A a b - 248B a b)e + (- 48A a b + 352B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 24A a b - 72B a b )d e + (- 16A b - 16B a b )d e - 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 77B a )e + (- 12A a b + 100B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 6A a b - 18B a b )d e + (- 4A a b - 4B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - B a b )d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 743 + +--S 744 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((12A b - 60B a b )e + 48B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((48A a b - 240B a b )e + 192B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((72A a b - 360B a b )e + 288B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((48A a b - 240B a b)e + 192B a b d e )x + (12A a b - 60B a )e +--R + +--R 4 3 +--R 48B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 4 4 4 +--R 12B b e x + 48B a b e x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((48A a b - 48B a b )e + (- 48A b + 192B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (108A a b - 252B a b )e + (- 72A a b + 432B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b - 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (88A a b - 248B a b)e + (- 48A a b + 352B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 24A a b - 72B a b )d e + (- 16A b - 16B a b )d e - 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 77B a )e + (- 12A a b + 100B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 6A a b - 18B a b )d e + (- 4A a b - 4B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 4 6 3 5 +--R ((- 12A b + 60B a b )e - 48B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((- 60A a b + 300B a b )e - 240B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((- 120A a b + 600B a b )e - 480B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((- 120A a b + 600B a b )e - 480B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((- 60A a b + 300B a b)e - 240B a b d e )x + (- 12A a b + 60B a )e +--R + +--R 5 3 +--R - 48B a b d e +--R * +--R log(b x + a) +--R + +--R 6 4 6 6 5 4 6 3 5 +--R - 12B b e x + ((25A b - 137B a b )e + 40B b d e )x +--R + +--R 5 2 4 4 6 5 3 6 2 2 4 +--R ((77A a b - 385B a b )e + (48A b + 8B a b )d e + 72B b d e )x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (94A a b - 470B a b )e + (120A a b - 224B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (36A b + 180B a b )d e + 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (54A a b - 270B a b )e + (120A a b - 384B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (60A a b + 180B a b )d e + (16A b + 40B a b )d e + 4B b d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (12A a b - 60B a b)e + (60A a b - 252B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (30A a b + 90B a b )d e + (20A a b + 20B a b )d e +--R + +--R 6 5 4 +--R (3A b + 5B a b )d +--R * +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 2 +--R (12A a b - 60B a b)d e + (6A a b + 18B a b )d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (4A a b + 4B a b )d e + (3A a b + B a b )d +--R / +--R +------------------+ +--R 10 4 9 3 2 8 2 3 7 4 6 | 2 2 2 +--R (12b x + 48a b x + 72a b x + 48a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 5 +--R - B b e x + ((- A b - B a)e - 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (- A a e + (- 4A b - 4B a)d e - 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (- 4A a d e + (- 6A b - 6B a)d e - 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (- 6A a d e + (- 4A b - 4B a)d e - B b d )x +--R + +--R 3 4 4 +--R (- 4A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 745 + +)clear all + +--S 746 of 1378 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1378 +r0:=-1/4*(A*b-a*B)*(a+b*x)*(d+e*x)^4/(b*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/2*B*e*(a+b*x)*(d+e*x)^2/(b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-1/3*B*(d+e*x)^3/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + B*e^2*(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e^3*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)),-1/4*B*(a+b*x)*_ + (d+e*x)^4/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+1/4*(B*d-A*e)*(a+b*x)*_ + (d+e*x)^4/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-1/2*B*e*(a+b*x)*_ + (d+e*x)^2/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/3*B*(d+e*x)^3/(b^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-B*e^2*(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+B*e^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R [ +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12B a b e - 12B b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 +--R (72B a b e - 72B a b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 5 4 4 3 +--R 12B a e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 4 5 3 4 +--R ((3A b - 25B a b )e + 22B b d e )x +--R + +--R 2 3 4 5 4 3 5 2 2 3 +--R (- 52B a b e + (12A b + 4B a b )d e + 36B b d e )x +--R + +--R 3 2 4 2 3 3 5 4 2 2 5 3 2 +--R (- 42B a b e - 30B a b d e + (18A b + 36B a b )d e + 18B b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 5 4 3 +--R - 12B a b e - 36B a b d e + 24B a b d e + (12A b + 8B a b )d e +--R + +--R 5 4 +--R 4B b d +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 5 4 4 +--R - 12B a b d e + 6B a b d e + 2B a b d e + (3A b + B a b )d +--R / +--R 8 9 3 2 7 8 2 3 6 2 7 +--R (12a b e - 12b d)x + (36a b e - 36a b d)x + (36a b e - 36a b d)x +--R + +--R 4 5 3 6 +--R 12a b e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R , +--R +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12B a b e - 12B b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 +--R (72B a b e - 72B a b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 5 4 4 3 +--R 12B a e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 4 5 3 4 +--R ((3A b - 25B a b )e + 22B b d e )x +--R + +--R 2 3 4 5 4 3 5 2 2 3 +--R (- 52B a b e + (12A b + 4B a b )d e + 36B b d e )x +--R + +--R 3 2 4 2 3 3 5 4 2 2 5 3 2 +--R (- 42B a b e - 30B a b d e + (18A b + 36B a b )d e + 18B b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 5 4 3 +--R - 12B a b e - 36B a b d e + 24B a b d e + (12A b + 8B a b )d e +--R + +--R 5 4 +--R 4B b d +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 5 4 4 +--R - 12B a b d e + 6B a b d e + 2B a b d e + (3A b + B a b )d +--R / +--R 8 9 3 2 7 8 2 3 6 2 7 +--R (12a b e - 12b d)x + (36a b e - 36a b d)x + (36a b e - 36a b d)x +--R + +--R 4 5 3 6 +--R 12a b e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R ] +--R Type: Tuple(Expression(Integer)) +--E 747 + +--S 748 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (12B b e x + 48B a b e x + 72B a b e x + 48B a b e x + 12B a e ) +--R * +--R log(b x + a) +--R + +--R 4 3 3 4 2 3 +--R ((- 12A b + 48B a b )e - 36B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 18A a b + 108B a b )e + (- 18A b - 54B a b )d e - 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 12A a b + 88B a b)e + (- 12A a b - 36B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 12A b - 12B a b )d e - 4B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 3A a b + 25B a )e + (- 3A a b - 9B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b - 3B a b )d e + (- 3A b - B a b )d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 748 + +--S 749 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12B a b e - 12B b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 +--R (72B a b e - 72B a b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 5 4 4 3 +--R 12B a e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 48B a b )e + (12A b - 84B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 2 3 3 +--R (- 18A a b + 108B a b )e - 162B a b d e +--R + +--R 5 4 2 2 5 3 +--R (18A b + 36B a b )d e + 18B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 3 2 3 2 3 2 2 +--R (- 12A a b + 88B a b)e - 124B a b d e + 24B a b d e +--R + +--R 5 4 3 5 4 +--R (12A b + 8B a b )d e + 4B b d +--R * +--R x +--R + +--R 4 5 4 4 3 3 2 2 2 2 3 3 +--R (- 3A a b + 25B a )e - 34B a b d e + 6B a b d e + 2B a b d e +--R + +--R 5 4 4 +--R (3A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 6 3 5 2 4 4 5 3 4 +--R (- 12B a b e + 12B b d e )x + (- 60B a b e + 60B a b d e )x +--R + +--R 3 3 4 2 4 3 3 4 2 4 3 3 3 2 +--R (- 120B a b e + 120B a b d e )x + (- 120B a b e + 120B a b d e )x +--R + +--R 5 4 4 2 3 6 4 5 3 +--R (- 60B a b e + 60B a b d e )x - 12B a e + 12B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 4 6 3 5 +--R ((- 3A b + 25B a b )e - 22B b d e )x +--R + +--R 5 2 4 4 6 5 3 6 2 2 4 +--R ((- 3A a b + 77B a b )e + (- 12A b - 26B a b )d e - 36B b d e )x +--R + +--R 3 3 4 5 2 4 3 6 5 2 2 +--R 94B a b e + (- 12A a b + 26B a b )d e + (- 18A b - 72B a b )d e +--R + +--R 6 3 +--R - 18B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 4 3 3 3 5 2 4 2 2 +--R 54B a b e + 66B a b d e + (- 18A a b - 60B a b )d e +--R + +--R 6 5 3 6 4 +--R (- 12A b - 26B a b )d e - 4B b d +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 3 2 2 5 2 4 3 +--R 12B a b e + 48B a b d e - 30B a b d e + (- 12A a b - 10B a b )d e +--R + +--R 6 5 4 +--R (- 3A b - 5B a b )d +--R * +--R x +--R + +--R 5 3 4 2 2 2 3 3 3 5 2 4 4 +--R 12B a b d e - 6B a b d e - 2B a b d e + (- 3A a b - B a b )d +--R / +--R 9 10 4 2 8 9 3 3 7 2 8 2 +--R (12a b e - 12b d)x + (48a b e - 48a b d)x + (72a b e - 72a b d)x +--R + +--R 4 6 3 7 5 5 4 6 +--R (48a b e - 48a b d)x + 12a b e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 1378 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1378 +r0:=-1/4*(A*b-a*B)*(a+b*x)*(d+e*x)^4/((b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/3*(B*d-A*e)*(d+e*x)^3/((b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 4 3 4 4 3 2 2 3 +--R ((A b + 3B a)e - 4B b d e )x + (4A a e + 8B a d e - 12B b d e )x +--R + +--R 3 2 2 3 2 +--R (12A a d e + (- 6A b + 6B a)d e - 12B b d e)x +--R + +--R 2 2 3 4 3 4 +--R (12A a d e - 8A b d e - 4B b d )x + 4A a d e + (- 3A b - B a)d +--R / +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (12a b e - 24a b d e + 12b d )x + (36a b e - 72a b d e + 36a b d )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (36a b e - 72a b d e + 36a b d )x + 12a e - 24a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 2 3 2 +--R - 12B b e x + ((- 6A b - 18B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 4A a b - 12B a b)e + (- 8A b - 8B a b )d e - 4B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- A a b - 3B a )e + (- 2A a b - 2B a b)d e + (- 3A b - B a b )d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 753 + +--S 754 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 4 4 3 5 2 2 3 +--R (- 12B a b e + 24B a b d e - 12B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 6A a b - 18B a b )e + (12A a b + 24B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 6A b + 6B a b )d e - 12B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 3 2 3 4 2 2 5 3 +--R (- 4A a b - 12B a b)e + 16B a b d e + 12A a b d e - 8A b d e +--R + +--R 5 4 +--R - 4B b d +--R * +--R x +--R + +--R 4 5 4 4 3 4 3 5 4 4 +--R (- A a b - 3B a )e + 4B a b d e + 4A a b d e + (- 3A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 4 6 3 5 +--R ((- A b - 3B a b )e + 4B b d e )x +--R + +--R 5 2 4 4 5 3 6 2 2 4 +--R ((- 5A a b - 3B a b )e - 4B a b d e + 12B b d e )x +--R + +--R 2 4 4 5 2 4 3 6 5 2 2 +--R - 4A a b e + (- 12A a b - 8B a b )d e + (6A b + 6B a b )d e +--R + +--R 6 3 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 5 2 4 2 2 6 5 3 +--R - 12A a b d e + (- 6A a b - 6B a b )d e + (8A b + 12B a b )d e +--R + +--R 6 4 +--R 4B b d +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 5 3 6 5 4 2 4 3 +--R (- 12A a b d e + 4A a b d e + (3A b + 5B a b )d )x - 4A a b d e +--R + +--R 5 2 4 4 +--R (3A a b + B a b )d +--R / +--R 2 8 2 9 10 2 4 +--R (12a b e - 24a b d e + 12b d )x +--R + +--R 3 7 2 2 8 9 2 3 +--R (48a b e - 96a b d e + 48a b d )x +--R + +--R 4 6 2 3 7 2 8 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 5 5 2 4 6 3 7 2 6 4 2 5 5 4 6 2 +--R (48a b e - 96a b d e + 48a b d )x + 12a b e - 24a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 1378 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1378 +r0:=1/4*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)/(b^3*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/2*B*(a+b*x)*(d+e*x)^2/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/3*(2*b*B*d-A*b*e-a*B*e)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a b)e - 4B b d)x + (- A a b - B a )e +--R + +--R 2 +--R (- 3A b - B a b)d +--R / +--R +------------------+ +--R 6 3 5 2 2 4 3 3 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a b)e - 4B b d)x + (- A a b - B a )e +--R + +--R 2 +--R (- 3A b - B a b)d +--R / +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 758 + +--S 759 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a b)e - 4B b d)x + (- A a b - B a )e +--R + +--R 2 +--R (- 3A b - B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 3 3 2 3 2 +--R 6B b e x + ((4A b + 10B a b )e + 4B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((5A a b + 5B a b)e + (3A b + 5B a b )d)x + (A a b + B a )e +--R + +--R 2 2 +--R (3A a b + B a b)d +--R / +--R +------------------+ +--R 7 4 6 3 2 5 2 3 4 4 3 | 2 2 2 +--R (12b x + 48a b x + 72a b x + 48a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 760 + +)clear all + +--S 761 of 1378 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1378 +r0:=-1/4*(A*b-a*B)*(a+b*x)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2))-_ + 1/3*B/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R - 4B b x - 3A b - B a +--R (2) ----------------------------------------------------------- +--R +------------------+ +--R 5 3 4 2 2 3 3 2 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1378 +a0:=integrate(t0,x) +--R +--R +--R - 4B b x - 3A b - B a +--R (3) ----------------------------------------------- +--R 6 4 5 3 2 4 2 3 3 4 2 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 763 + +--S 764 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R | 2 2 2 2 2 +--R (- 4B b x - 3A b - B a)\|b x + 2a b x + a + 4B b x +--R + +--R 2 2 +--R (3A b + 5B a b)x + 3A a b + B a +--R / +--R +------------------+ +--R 6 4 5 3 2 4 2 3 3 4 2 | 2 2 2 +--R (12b x + 48a b x + 72a b x + 48a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R ------------------------------------------------------------------------- +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 765 + +)clear all + +--S 766 of 1378 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1378 +r0:=-1/4*(A*b-a*B)*(a+b*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/3*(-B*d+A*e)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/2*e*(B*d-A*e)*(a+b*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + e^2*(B*d-A*e)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(B*d-A*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*_ + (B*d-A*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 3 4 4 4 4 3 3 +--R (12A b e - 12B b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (72A a b e - 72B a b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 4 4 4 3 +--R 12A a b e - 12B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 3 4 4 4 4 3 3 +--R (- 12A b e + 12B b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (- 72A a b e + 72B a b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 4 4 4 3 +--R - 12A a b e + 12B a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 5 4 3 5 2 2 3 +--R (12A a b e + (- 12A b - 12B a b )d e + 12B b d e )x +--R + +--R 2 3 4 4 2 3 3 5 4 2 2 +--R 42A a b e + (- 48A a b - 42B a b )d e + (6A b + 48B a b )d e +--R + +--R 5 3 +--R - 6B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 2 3 4 2 3 2 2 +--R 52A a b e + (- 72A a b - 52B a b )d e + (24A a b + 72B a b )d e +--R + +--R 5 4 3 5 4 +--R (- 4A b - 24B a b )d e + 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 3B a )e + (- 48A a b - 10B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 5 4 4 +--R (36A a b + 18B a b )d e + (- 16A a b - 6B a b )d e + (3A b + B a b )d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 9 5 +--R - 12b d +--R * +--R 3 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 2 7 4 +--R 36a b e - 180a b d e + 360a b d e - 360a b d e + 180a b d e +--R + +--R 8 5 +--R - 36a b d +--R * +--R 2 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 3 6 4 +--R 36a b e - 180a b d e + 360a b d e - 360a b d e + 180a b d e +--R + +--R 2 7 5 +--R - 36a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 4 5 4 3 6 5 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 5 3 4 4 4 4 3 3 +--R (12A b e - 12B b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (72A a b e - 72B a b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 4 4 4 3 +--R 12A a b e - 12B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 3 4 4 4 4 3 3 +--R (- 12A b e + 12B b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (- 72A a b e + 72B a b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 4 4 4 3 +--R - 12A a b e + 12B a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 5 4 3 5 2 2 3 +--R (12A a b e + (- 12A b - 12B a b )d e + 12B b d e )x +--R + +--R 2 3 4 4 2 3 3 5 4 2 2 +--R 42A a b e + (- 48A a b - 42B a b )d e + (6A b + 48B a b )d e +--R + +--R 5 3 +--R - 6B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 2 3 4 2 3 2 2 +--R 52A a b e + (- 72A a b - 52B a b )d e + (24A a b + 72B a b )d e +--R + +--R 5 4 3 5 4 +--R (- 4A b - 24B a b )d e + 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 3B a )e + (- 48A a b - 10B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 5 4 4 +--R (36A a b + 18B a b )d e + (- 16A a b - 6B a b )d e + (3A b + B a b )d +--R / +--R 5 5 5 4 6 4 3 7 2 3 2 8 3 2 9 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 10 5 +--R - 12b d +--R * +--R 4 +--R x +--R + +--R 6 4 5 5 5 4 4 6 2 3 3 7 3 2 2 8 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 9 5 +--R - 48a b d +--R * +--R 3 +--R x +--R + +--R 7 3 5 6 4 4 5 5 2 3 4 6 3 2 3 7 4 +--R 72a b e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 2 8 5 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 4 2 3 5 5 3 2 4 6 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 7 5 +--R - 48a b d +--R * +--R x +--R + +--R 9 5 8 2 4 7 3 2 3 6 4 3 2 5 5 4 4 6 5 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R Type: Union(Expression(Integer),...) +--E 768 + +--S 769 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 5 3 4 4 4 4 3 3 +--R (12A b e - 12B b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (72A a b e - 72B a b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 4 4 4 3 +--R 12A a b e - 12B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 3 4 4 4 4 3 3 +--R (- 12A b e + 12B b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (- 72A a b e + 72B a b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 4 4 4 3 +--R - 12A a b e + 12B a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 5 4 3 5 2 2 3 +--R (12A a b e + (- 12A b - 12B a b )d e + 12B b d e )x +--R + +--R 2 3 4 4 2 3 3 5 4 2 2 +--R 42A a b e + (- 48A a b - 42B a b )d e + (6A b + 48B a b )d e +--R + +--R 5 3 +--R - 6B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 2 3 +--R 52A a b e + (- 72A a b - 52B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (24A a b + 72B a b )d e + (- 4A b - 24B a b )d e + 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 3B a )e + (- 48A a b - 10B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (36A a b + 18B a b )d e + (- 16A a b - 6B a b )d e +--R + +--R 5 4 4 +--R (3A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 4 6 3 5 5 4 5 3 4 +--R (- 12A b e + 12B b d e )x + (- 60A a b e + 60B a b d e )x +--R + +--R 2 4 4 2 4 3 3 3 3 4 3 3 3 2 +--R (- 120A a b e + 120B a b d e )x + (- 120A a b e + 120B a b d e )x +--R + +--R 4 2 4 4 2 3 5 4 5 3 +--R (- 60A a b e + 60B a b d e )x - 12A a b e + 12B a b d e +--R * +--R log(e x + d) +--R + +--R 6 4 6 3 5 5 4 5 3 4 +--R (12A b e - 12B b d e )x + (60A a b e - 60B a b d e )x +--R + +--R 2 4 4 2 4 3 3 3 3 4 3 3 3 2 +--R (120A a b e - 120B a b d e )x + (120A a b e - 120B a b d e )x +--R + +--R 4 2 4 4 2 3 5 4 5 3 +--R (60A a b e - 60B a b d e )x + 12A a b e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 6 5 3 6 2 2 4 +--R (- 12A a b e + (12A b + 12B a b )d e - 12B b d e )x +--R + +--R 2 4 4 5 2 4 3 6 5 2 2 +--R - 54A a b e + (60A a b + 54B a b )d e + (- 6A b - 60B a b )d e +--R + +--R 6 3 +--R 6B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 3 3 3 +--R - 94A a b e + (120A a b + 94B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (- 30A a b - 120B a b )d e + (4A b + 30B a b )d e - 4B b d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 77A a b + 3B a b)e + (120A a b + 62B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 60A a b - 90B a b )d e + (20A a b + 30B a b )d e +--R + +--R 6 5 4 +--R (- 3A b - 5B a b )d +--R * +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 25A a b + 3B a )e + (48A a b + 10B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 36A a b - 18B a b )d e + (16A a b + 6B a b )d e +--R + +--R 5 2 4 4 +--R (- 3A a b - B a b )d +--R / +--R 5 5 5 4 6 4 3 7 2 3 2 8 3 2 9 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 10 5 +--R - 12b d +--R * +--R 4 +--R x +--R + +--R 6 4 5 5 5 4 4 6 2 3 3 7 3 2 2 8 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 9 5 +--R - 48a b d +--R * +--R 3 +--R x +--R + +--R 7 3 5 6 4 4 5 5 2 3 4 6 3 2 3 7 4 +--R 72a b e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 2 8 5 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 4 2 3 5 5 3 2 4 6 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 7 5 +--R - 48a b d +--R * +--R x +--R + +--R 9 5 8 2 4 7 3 2 3 6 4 3 2 5 5 4 4 6 5 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 6 4 5 5 2 3 4 4 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (10a b e + 10a b d)x + (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 770 + +)clear all + +--S 771 of 1378 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1378 +r0:=1/4*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2))+1/3*(-4*b*B*d+5*A*b*e-a*B*e)/((b*d-a*e)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*e*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)/_ + ((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2*(4*b*B*d-5*A*b*e+_ + a*B*e)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+e^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/_ + ((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((- 60A b + 12B a b )e + 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 240A a b + 48B a b )e + (- 60A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 360A a b + 72B a b )e + (- 240A a b + 336B a b )d e +--R + +--R 4 2 3 +--R 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 240A a b + 48B a b)e + (- 360A a b + 264B a b )d e +--R + +--R 2 3 2 3 +--R 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 60A a b + 12B a )e + (- 240A a b + 96B a b)d e +--R + +--R 3 2 2 3 +--R 192B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 60A a b + 12B a )d e + 48B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 12B a b )e - 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((240A a b - 48B a b )e + (60A b - 204B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (360A a b - 72B a b )e + (240A a b - 336B a b )d e +--R + +--R 4 2 3 +--R - 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b - 48B a b)e + (360A a b - 264B a b )d e +--R + +--R 2 3 2 3 +--R - 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 3 2 2 3 +--R ((60A a b - 12B a )e + (240A a b - 96B a b)d e - 192B a b d e )x +--R + +--R 4 5 4 4 2 3 +--R (60A a b - 12B a )d e - 48B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 12B a b )e + (60A b + 36B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 210A a b + 42B a b )e + (180A a b + 132B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b - 150B a b )d e - 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 260A a b + 52B a b)e + (150A a b + 178B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b - 144B a b )d e + (- 10A b - 94B a b )d e + 8B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 125A a b + 25B a )e + (- 20A a b + 104B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 20B a b )d e + (- 40A a b - 136B a b )d e +--R + +--R 5 4 4 5 5 +--R (5A b + 31B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 12A a e + (- 65A a b + 37B a )d e + (120A a b - 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 60A a b - 36B a b )d e + (20A a b + 8B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - B a b )d +--R / +--R 6 3 7 5 4 6 4 5 2 5 3 6 3 4 2 7 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 8 5 2 9 6 +--R - 72a b d e + 12b d e +--R * +--R 4 +--R x +--R + +--R 7 2 7 6 3 6 5 4 2 5 4 5 3 4 3 6 4 3 +--R 36a b e - 204a b d e + 468a b d e - 540a b d e + 300a b d e +--R + +--R 2 7 5 2 8 6 9 7 +--R - 36a b d e - 36a b d e + 12b d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 4 5 4 3 +--R 36a b e - 180a b d e + 324a b d e - 180a b d e - 180a b d e +--R + +--R 3 6 5 2 2 7 6 8 7 +--R 324a b d e - 180a b d e + 36a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 6 7 2 2 5 6 3 3 4 5 4 4 3 +--R 12a e - 36a b d e - 36a b d e + 300a b d e - 540a b d e +--R + +--R 4 5 5 2 3 6 6 2 7 7 +--R 468a b d e - 204a b d e + 36a b d +--R * +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 4 5 6 3 6 7 +--R - 72a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 5 5 4 5 +--R ((- 60A b + 12B a b )e + 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 240A a b + 48B a b )e + (- 60A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 360A a b + 72B a b )e + (- 240A a b + 336B a b )d e +--R + +--R 4 2 3 +--R 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 240A a b + 48B a b)e + (- 360A a b + 264B a b )d e +--R + +--R 2 3 2 3 +--R 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 60A a b + 12B a )e + (- 240A a b + 96B a b)d e +--R + +--R 3 2 2 3 +--R 192B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 60A a b + 12B a )d e + 48B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 12B a b )e - 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((240A a b - 48B a b )e + (60A b - 204B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (360A a b - 72B a b )e + (240A a b - 336B a b )d e +--R + +--R 4 2 3 +--R - 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b - 48B a b)e + (360A a b - 264B a b )d e +--R + +--R 2 3 2 3 +--R - 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 3 2 2 3 +--R ((60A a b - 12B a )e + (240A a b - 96B a b)d e - 192B a b d e )x +--R + +--R 4 5 4 4 2 3 +--R (60A a b - 12B a )d e - 48B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 12B a b )e + (60A b + 36B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 210A a b + 42B a b )e + (180A a b + 132B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b - 150B a b )d e - 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 260A a b + 52B a b)e + (150A a b + 178B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b - 144B a b )d e + (- 10A b - 94B a b )d e + 8B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 125A a b + 25B a )e + (- 20A a b + 104B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 20B a b )d e + (- 40A a b - 136B a b )d e +--R + +--R 5 4 4 5 5 +--R (5A b + 31B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 12A a e + (- 65A a b + 37B a )d e + (120A a b - 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 60A a b - 36B a b )d e + (20A a b + 8B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - B a b )d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 2 8 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 9 5 2 10 6 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 3 7 4 3 +--R 48a b e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 8 5 2 9 6 10 7 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 4 6 4 3 +--R 72a b e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 3 7 5 2 2 8 6 9 7 +--R 288a b d e - 216a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 5 5 4 3 +--R 48a b e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 4 6 5 2 3 7 6 2 8 7 +--R 792a b d e - 384a b d e + 72a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 6 4 4 3 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 5 5 5 2 4 6 6 3 7 7 +--R 648a b d e - 276a b d e + 48a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 5 5 6 4 6 7 +--R - 72a b d e + 12a b d +--R Type: Union(Expression(Integer),...) +--E 773 + +--S 774 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 5 5 4 5 +--R ((- 60A b + 12B a b )e + 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 240A a b + 48B a b )e + (- 60A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 360A a b + 72B a b )e + (- 240A a b + 336B a b )d e +--R + +--R 4 2 3 +--R 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 240A a b + 48B a b)e + (- 360A a b + 264B a b )d e +--R + +--R 2 3 2 3 +--R 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 60A a b + 12B a )e + (- 240A a b + 96B a b)d e +--R + +--R 3 2 2 3 +--R 192B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 60A a b + 12B a )d e + 48B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 12B a b )e - 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (240A a b - 48B a b )e + (60A b - 204B a b )d e +--R + +--R 5 2 3 +--R - 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (360A a b - 72B a b )e + (240A a b - 336B a b )d e +--R + +--R 4 2 3 +--R - 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b - 48B a b)e + (360A a b - 264B a b )d e +--R + +--R 2 3 2 3 +--R - 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (60A a b - 12B a )e + (240A a b - 96B a b)d e +--R + +--R 3 2 2 3 +--R - 192B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (60A a b - 12B a )d e - 48B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 12B a b )e + (60A b + 36B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 210A a b + 42B a b )e + (180A a b + 132B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b - 150B a b )d e - 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 260A a b + 52B a b)e + (150A a b + 178B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b - 144B a b )d e + (- 10A b - 94B a b )d e + 8B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 125A a b + 25B a )e + (- 20A a b + 104B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 20B a b )d e + (- 40A a b - 136B a b )d e +--R + +--R 5 4 4 5 5 +--R (5A b + 31B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 12A a e + (- 65A a b + 37B a )d e + (120A a b - 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 60A a b - 36B a b )d e + (20A a b + 8B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 5 6 4 6 +--R ((60A b - 12B a b )e - 48B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 5 +--R ((300A a b - 60B a b )e + (60A b - 252B a b )d e - 48B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (600A a b - 120B a b )e + (300A a b - 540B a b )d e +--R + +--R 5 2 3 +--R - 240B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (600A a b - 120B a b )e + (600A a b - 600B a b )d e +--R + +--R 2 4 2 3 +--R - 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (300A a b - 60B a b)e + (600A a b - 360B a b )d e +--R + +--R 3 3 2 3 +--R - 480B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 4 2 2 3 +--R ((60A a b - 12B a )e + (300A a b - 108B a b)d e - 240B a b d e )x +--R + +--R 5 6 4 5 2 3 +--R (60A a b - 12B a )d e - 48B a b d e +--R * +--R log(e x + d) +--R + +--R 6 5 5 6 4 6 +--R ((- 60A b + 12B a b )e + 48B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 300A a b + 60B a b )e + (- 60A b + 252B a b )d e +--R + +--R 6 2 3 +--R 48B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 600A a b + 120B a b )e + (- 300A a b + 540B a b )d e +--R + +--R 5 2 3 +--R 240B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 600A a b + 120B a b )e + (- 600A a b + 600B a b )d e +--R + +--R 2 4 2 3 +--R 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 300A a b + 60B a b)e + (- 600A a b + 360B a b )d e +--R + +--R 3 3 2 3 +--R 480B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 60A a b + 12B a )e + (- 300A a b + 108B a b)d e +--R + +--R 4 2 2 3 +--R 240B a b d e +--R * +--R x +--R + +--R 5 6 4 5 2 3 +--R (- 60A a b + 12B a )d e + 48B a b d e +--R * +--R log(b x + a) +--R + +--R 5 2 4 5 6 5 4 6 2 3 5 +--R ((60A a b - 12B a b )e + (- 60A b - 36B a b )d e + 48B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (270A a b - 54B a b )e + (- 240A a b - 168B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 30A b + 198B a b )d e + 24B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (470A a b - 94B a b )e + (- 330A a b - 310B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 150A a b + 294B a b )d e + (10A b + 118B a b )d e - 8B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (385A a b - 77B a b)e + (- 130A a b - 282B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 300A a b + 164B a b )d e + (50A a b + 230B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 5A b - 39B a b )d e + 4B b d +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (137A a b - 25B a )e + (85A a b - 141B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 300A a b + 28B a b )d e + (100A a b + 172B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 25A a b - 39B a b )d e + (3A b + 5B a b )d +--R * +--R x +--R + +--R 6 5 5 6 4 4 2 5 2 3 +--R 12A a e + (65A a b - 37B a )d e + (- 120A a b + 8B a b)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (60A a b + 36B a b )d e + (- 20A a b - 8B a b )d e +--R + +--R 5 2 4 5 +--R (3A a b + B a b )d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 2 8 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 9 5 2 10 6 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 3 7 4 3 +--R 48a b e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 8 5 2 9 6 10 7 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 4 6 4 3 +--R 72a b e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 3 7 5 2 2 8 6 9 7 +--R 288a b d e - 216a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 5 5 4 3 +--R 48a b e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 4 6 5 2 3 7 6 2 8 7 +--R 792a b d e - 384a b d e + 72a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 6 4 4 3 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 5 5 5 2 4 6 6 3 7 7 +--R 648a b d e - 276a b d e + 48a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 5 5 6 4 6 7 +--R - 72a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 775 + +)clear all + +--S 776 of 1378 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1378 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/4*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-5/12*(2*b*B*d-3*A*b*e+a*B*e)/_ + ((b*d-a*e)^3*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5/6*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)*(a+b*x)/((b*d-a*e)^4*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-5/2*e^2*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^5*(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-5*b*e^3*(2*b*B*d-3*A*b*e+a*B*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^7*sqrt(a^2+2*a*b*x+b^2*x^2))+5*b*e^3*_ + (2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^7*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+5*e^4*(2*b*B*d-3*A*b*e+a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/((b*d-a*e)^7*(d+e*x)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (720A a b - 240B a b )e + (360A b - 600B a b )d e +--R + +--R 6 2 4 +--R - 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (1080A a b - 360B a b )e + (1440A a b - 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (180A b - 1020B a b )d e - 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (720A a b - 240B a b )e + (2160A a b - 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (720A a b - 1680B a b )d e - 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (180A a b - 60B a b)e + (1440A a b - 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (1080A a b - 1320B a b )d e - 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (360A a b - 120B a b)d e + (720A a b - 480B a b )d e +--R + +--R 3 3 3 3 +--R - 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (180A a b - 60B a b)d e - 120B a b d e +--R * +--R log(e x + d) +--R + +--R 6 5 6 6 5 6 +--R ((- 180A b + 60B a b )e + 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 720A a b + 240B a b )e + (- 360A b + 600B a b )d e +--R + +--R 6 2 4 +--R 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 1080A a b + 360B a b )e + (- 1440A a b + 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 180A b + 1020B a b )d e + 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 720A a b + 240B a b )e + (- 2160A a b + 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (- 720A a b + 1680B a b )d e + 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 180A a b + 60B a b)e + (- 1440A a b + 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (- 1080A a b + 1320B a b )d e + 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (- 360A a b + 120B a b)d e + (- 720A a b + 480B a b )d e +--R + +--R 3 3 3 3 +--R 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (- 180A a b + 60B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 6 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((900A a b - 300B a b )e + (180A b - 660B a b )d e - 120B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (1710A a b - 570B a b )e + (1080A a b - 1500B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 90A b - 690B a b )d e + 60B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (1500A a b - 500B a b )e + (2340A a b - 1780B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 180A a b - 1500B a b )d e + (- 60A b + 140B a b )d e +--R + +--R 6 4 2 +--R 40B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (555A a b - 185B a b)e + (2280A a b - 1130B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (90A a b - 1550B a b )d e + (- 240A a b + 20B a b )d e +--R + +--R 6 5 4 2 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b )d e +--R + +--R 3 4 4 3 2 4 2 5 3 4 3 3 +--R (- 510A a b + 2310B a b )d e + (600A a b + 140B a b )d e +--R + +--R 6 2 5 4 2 7 6 5 7 6 +--R (- 75A a b - 375B a b )d e + (6A b + 48B a b )d e - 4B b d +--R * +--R 2 +--R x +--R + +--R 6 7 6 5 2 6 5 +--R (- 30A a b + 12B a )e + (- 1002A a b + 340B a b)d e +--R + +--R 4 3 5 2 2 4 3 4 4 3 3 3 +--R (- 705A a b + 945B a b )d e + (600A a b + 200B a b )d e +--R + +--R 2 5 3 4 4 2 6 2 5 5 +--R (- 150A a b - 280B a b )d e + (30A a b + 48B a b )d e +--R + +--R 7 6 6 +--R (- 3A b - 5B a b )d +--R * +--R x +--R + +--R 7 6 6 7 5 5 2 6 2 4 +--R 6A a e + (- 72A a b + 6B a )d e + (- 285A a b + 185B a b)d e +--R + +--R 4 3 5 2 3 3 3 4 4 3 4 2 +--R (240A a b + 40B a b )d e + (- 90A a b - 60B a b )d e +--R + +--R 2 5 3 4 5 6 2 5 6 +--R (24A a b + 10B a b )d e + (- 3A a b - B a b )d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 3 8 4 5 +--R 12a b e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 2 9 5 4 10 6 3 11 7 2 +--R - 252a b d e + 84a b d e - 12b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 4 7 4 5 +--R 48a b e - 312a b d e + 840a b d e - 1176a b d e + 840a b d e +--R + +--R 3 8 5 4 2 9 6 3 10 7 2 11 8 +--R - 168a b d e - 168a b d e + 120a b d e - 24b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 5 6 4 5 +--R 72a b e - 408a b d e + 852a b d e - 588a b d e - 588a b d e +--R + +--R 4 7 5 4 3 8 6 3 2 9 7 2 10 8 11 9 +--R 1428a b d e - 1092a b d e + 348a b d e - 12a b d e - 12b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 6 5 4 5 +--R 48a b e - 192a b d e + 48a b d e + 1008a b d e - 2352a b d e +--R + +--R 5 6 5 4 4 7 6 3 3 8 7 2 2 9 8 10 9 +--R 2352a b d e - 1008a b d e - 48a b d e + 192a b d e - 48a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5 +--R 12a e + 12a b d e - 348a b d e + 1092a b d e - 1428a b d e +--R + +--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9 +--R 588a b d e + 588a b d e - 852a b d e + 408a b d e - 72a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 7 4 5 4 +--R 24a d e - 120a b d e + 168a b d e + 168a b d e - 840a b d e +--R + +--R 6 5 6 3 5 6 7 2 4 7 8 3 8 9 +--R 1176a b d e - 840a b d e + 312a b d e - 48a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 7 4 6 3 +--R 12a d e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 6 5 7 2 5 6 8 4 7 9 +--R - 252a b d e + 84a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 780 + +)clear all + +--S 781 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1378 +r0:=-2/9*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(9/2)/e^4+2/11*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^4-2/13*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(13/2)/e^4+2/15*b^2*B*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 2 7 7 2 7 2 6 6 +--R 858B b e x + ((990A b + 1980B a b)e + 3036B b d e )x +--R + +--R 2 7 2 6 +--R (2340A a b + 1170B a )e + (3600A b + 7200B a b)d e +--R + +--R 2 2 5 +--R 3708B b d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 1430A a e + (8840A a b + 4420B a )d e +--R + +--R 2 2 5 2 3 4 +--R (4580A b + 9160B a b)d e + 1600B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 5720A a d e + (11960A a b + 5980B a )d e +--R + +--R 2 3 4 2 4 3 +--R (2120A b + 4240B a b)d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 8580A a d e + (6240A a b + 3120B a )d e + (30A b + 60B a b)d e +--R + +--R 2 5 2 +--R - 12B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 5720A a d e + (260A a b + 130B a )d e + (- 40A b - 80B a b)d e +--R + +--R 2 6 +--R 16B b d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 1430A a d e + (- 520A a b - 260B a )d e + (80A b + 160B a b)d e +--R + +--R 2 7 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 7 2 7 2 6 6 +--R 858B b e x + ((990A b + 1980B a b)e + 3036B b d e )x +--R + +--R 2 7 2 6 +--R (2340A a b + 1170B a )e + (3600A b + 7200B a b)d e +--R + +--R 2 2 5 +--R 3708B b d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 1430A a e + (8840A a b + 4420B a )d e +--R + +--R 2 2 5 2 3 4 +--R (4580A b + 9160B a b)d e + 1600B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 5720A a d e + (11960A a b + 5980B a )d e +--R + +--R 2 3 4 2 4 3 +--R (2120A b + 4240B a b)d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 8580A a d e + (6240A a b + 3120B a )d e + (30A b + 60B a b)d e +--R + +--R 2 5 2 +--R - 12B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 5720A a d e + (260A a b + 130B a )d e + (- 40A b - 80B a b)d e +--R + +--R 2 6 +--R 16B b d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 1430A a d e + (- 520A a b - 260B a )d e + (80A b + 160B a b)d e +--R + +--R 2 7 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Union(Expression(Integer),...) +--E 783 + +--S 784 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1378 +r0:=-2/7*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(7/2)/e^4+2/9*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^4-2/11*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(11/2)/e^4+2/13*b^2*B*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 1386B b e x + ((1638A b + 3276B a b)e + 3402B b d e )x +--R + +--R 2 6 2 5 +--R (4004A a b + 2002B a )e + (4186A b + 8372B a b)d e +--R + +--R 2 2 4 +--R 2226B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 2574A a e + (10868A a b + 5434B a )d e +--R + +--R 2 2 4 2 3 3 +--R (2938A b + 5876B a b)d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 7722A a d e + (8580A a b + 4290B a )d e + (78A b + 156B a b)d e +--R + +--R 2 4 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R 7722A a d e + (572A a b + 286B a )d e +--R + +--R 2 4 2 2 5 +--R (- 104A b - 208B a b)d e + 48B b d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 2574A a d e + (- 1144A a b - 572B a )d e + (208A b + 416B a b)d e +--R + +--R 2 6 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 6 2 5 5 +--R 1386B b e x + ((1638A b + 3276B a b)e + 3402B b d e )x +--R + +--R 2 6 2 5 +--R (4004A a b + 2002B a )e + (4186A b + 8372B a b)d e +--R + +--R 2 2 4 +--R 2226B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 2574A a e + (10868A a b + 5434B a )d e +--R + +--R 2 2 4 2 3 3 +--R (2938A b + 5876B a b)d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 7722A a d e + (8580A a b + 4290B a )d e + (78A b + 156B a b)d e +--R + +--R 2 4 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R 7722A a d e + (572A a b + 286B a )d e +--R + +--R 2 4 2 2 5 +--R (- 104A b - 208B a b)d e + 48B b d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 2574A a d e + (- 1144A a b - 572B a )d e + (208A b + 416B a b)d e +--R + +--R 2 6 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 788 + +--S 789 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +)clear all + +--S 791 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1378 +r0:=-2/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^4-2/9*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(9/2)/e^4+2/11*b^2*B*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B b e x + ((770A b + 1540B a b)e + 840B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A a b + 990B a )e + (1100A b + 2200B a b)d e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 1386A a e + (3168A a b + 1584B a )d e + (66A b + 132B a b)d e +--R + +--R 2 3 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 2772A a d e + (396A a b + 198B a )d e + (- 88A b - 176B a b)d e +--R + +--R 2 4 +--R 48B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 1386A a d e + (- 792A a b - 396B a )d e + (176A b + 352B a b)d e +--R + +--R 2 5 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 630B b e x + ((770A b + 1540B a b)e + 840B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A a b + 990B a )e + (1100A b + 2200B a b)d e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 1386A a e + (3168A a b + 1584B a )d e + (66A b + 132B a b)d e +--R + +--R 2 3 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 2772A a d e + (396A a b + 198B a )d e + (- 88A b - 176B a b)d e +--R + +--R 2 4 +--R 48B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 1386A a d e + (- 792A a b - 396B a )d e + (176A b + 352B a b)d e +--R + +--R 2 5 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 793 + +--S 794 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 795 + +)clear all + +--S 796 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1378 +r0:=-2/3*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^4-2/7*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(7/2)/e^4+2/9*b^2*B*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 2 4 4 2 4 2 3 3 +--R 70B b e x + ((90A b + 180B a b)e + 10B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((252A a b + 126B a )e + (18A b + 36B a b)d e - 12B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 210A a e + (84A a b + 42B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 16B b d e +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 210A a d e + (- 168A a b - 84B a )d e + (48A b + 96B a b)d e +--R + +--R 2 4 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 2 4 2 3 3 +--R 70B b e x + ((90A b + 180B a b)e + 10B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((252A a b + 126B a )e + (18A b + 36B a b)d e - 12B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 210A a e + (84A a b + 42B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 16B b d e +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 210A a d e + (- 168A a b - 84B a )d e + (48A b + 96B a b)d e +--R + +--R 2 4 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 798 + +--S 799 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 800 + +)clear all + +--S 801 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1378 +r0:=2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^4-2/5*b*_ + (3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^4+2/7*b^2*B*(d+e*x)^(7/2)/e^4-_ + 2*(b*d-a*e)^2*(B*d-A*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((42A b + 84B a b)e - 36B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((140A a b + 70B a )e + (- 56A b - 112B a b)d e + 48B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 210A a e + (- 280A a b - 140B a )d e + (112A b + 224B a b)d e +--R + +--R 2 3 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((42A b + 84B a b)e - 36B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((140A a b + 70B a )e + (- 56A b - 112B a b)d e + 48B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 210A a e + (- 280A a b - 140B a )d e + (112A b + 224B a b)d e +--R + +--R 2 3 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 803 + +--S 804 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 805 + +)clear all + +--S 806 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1378 +r0:=-2/3*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^4+2/5*b^2*B*_ + (d+e*x)^(5/2)/e^4+2*(b*d-a*e)^2*(B*d-A*e)/(e^4*sqrt(d+e*x))+_ + 2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((10A b + 20B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((60A a b + 30B a )e + (- 40A b - 80B a b)d e + 48B b d e)x - 30A a e +--R + +--R 2 2 2 2 2 3 +--R (120A a b + 60B a )d e + (- 80A b - 160B a b)d e + 96B b d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((10A b + 20B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((60A a b + 30B a )e + (- 40A b - 80B a b)d e + 48B b d e)x - 30A a e +--R + +--R 2 2 2 2 2 3 +--R (120A a b + 60B a )d e + (- 80A b - 160B a b)d e + 96B b d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 808 + +--S 809 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 810 + +)clear all + +--S 811 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1378 +r0:=2/3*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(3/2))+2/3*b^2*B*_ + (d+e*x)^(3/2)/e^4-2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*_ + sqrt(d+e*x))-2*b*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((6A b + 12B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12A a b - 6B a )e + (24A b + 48B a b)d e - 48B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 8A a b - 4B a )d e + (16A b + 32B a b)d e - 32B b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((6A b + 12B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12A a b - 6B a )e + (24A b + 48B a b)d e - 48B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 8A a b - 4B a )d e + (16A b + 32B a b)d e - 32B b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 813 + +--S 814 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 815 + +)clear all + +--S 816 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1378 +r0:=2/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(5/2))-2/3*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^(3/2))+2*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)/(e^4*sqrt(d+e*x))+2*b^2*B*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((- 30A b - 60B a b)e + 180B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 20A a b - 10B a )e + (- 40A b - 80B a b)d e + 240B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 6A a e + (- 8A a b - 4B a )d e + (- 16A b - 32B a b)d e + 96B b d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((- 30A b - 60B a b)e + 180B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 20A a b - 10B a )e + (- 40A b - 80B a b)d e + 240B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 6A a e + (- 8A a b - 4B a )d e + (- 16A b - 32B a b)d e + 96B b d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 818 + +--S 819 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1378 +r0:=-2/9*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(9/2)/e^6+2/11*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^6-4/13*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^6+4/15*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^6-2/17*b^3*(5*b*B*d-_ + A*b*e-4*a*B*e)*(d+e*x)^(17/2)/e^6+2/19*b^4*B*(d+e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 4 9 9 4 3 9 4 8 8 +--R 218790B b e x + ((244530A b + 978120B a b )e + 746460B b d e )x +--R + +--R 3 2 2 9 +--R (1108536A a b + 1662804B a b )e +--R + +--R 4 3 8 4 2 7 +--R (847704A b + 3390816B a b )d e + 866580B b d e +--R * +--R 7 +--R x +--R + +--R 2 2 3 9 +--R (1918620A a b + 1279080B a b)e +--R + +--R 3 2 2 8 +--R (3922512A a b + 5883768B a b )d e +--R + +--R 4 3 2 7 4 3 6 +--R (1005708A b + 4022832B a b )d e + 345840B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 9 2 2 3 8 +--R (1511640A a b + 377910B a )e + (6976800A a b + 4651200B a b)d e +--R + +--R 3 2 2 2 7 +--R (4790736A a b + 7186104B a b )d e +--R + +--R 4 3 3 6 4 4 5 +--R (414504A b + 1658016B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 4 9 3 4 8 +--R 461890A a e + (5710640A a b + 1427660B a )d e +--R + +--R 2 2 3 2 7 +--R (8876040A a b + 5917360B a b)d e +--R + +--R 3 2 2 3 6 4 3 4 5 +--R (2067200A a b + 3100800B a b )d e + (1330A b + 5320B a b )d e +--R + +--R 4 5 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R 1847560A a d e + (7726160A a b + 1931540B a )d e +--R + +--R 2 2 3 3 6 +--R (4108560A a b + 2739040B a b)d e +--R + +--R 3 2 2 4 5 4 3 5 4 +--R (12920A a b + 19380B a b )d e + (- 1520A b - 6080B a b )d e +--R + +--R 4 6 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 2771340A a d e + (4031040A a b + 1007760B a )d e +--R + +--R 2 2 3 4 5 3 2 2 5 4 +--R (58140A a b + 38760B a b)d e + (- 15504A a b - 23256B a b )d e +--R + +--R 4 3 6 3 4 7 2 +--R (1824A b + 7296B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R 1847560A a d e + (167960A a b + 41990B a )d e +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (- 77520A a b - 51680B a b)d e + (20672A a b + 31008B a b )d e +--R + +--R 4 3 7 2 4 8 +--R (- 2432A b - 9728B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R 461890A a d e + (- 335920A a b - 83980B a )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (155040A a b + 103360B a b)d e + (- 41344A a b - 62016B a b )d e +--R + +--R 4 3 8 4 9 +--R (4864A b + 19456B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 9 9 4 3 9 4 8 8 +--R 218790B b e x + ((244530A b + 978120B a b )e + 746460B b d e )x +--R + +--R 3 2 2 9 +--R (1108536A a b + 1662804B a b )e +--R + +--R 4 3 8 4 2 7 +--R (847704A b + 3390816B a b )d e + 866580B b d e +--R * +--R 7 +--R x +--R + +--R 2 2 3 9 +--R (1918620A a b + 1279080B a b)e +--R + +--R 3 2 2 8 +--R (3922512A a b + 5883768B a b )d e +--R + +--R 4 3 2 7 4 3 6 +--R (1005708A b + 4022832B a b )d e + 345840B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 9 2 2 3 8 +--R (1511640A a b + 377910B a )e + (6976800A a b + 4651200B a b)d e +--R + +--R 3 2 2 2 7 +--R (4790736A a b + 7186104B a b )d e +--R + +--R 4 3 3 6 4 4 5 +--R (414504A b + 1658016B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 4 9 3 4 8 +--R 461890A a e + (5710640A a b + 1427660B a )d e +--R + +--R 2 2 3 2 7 +--R (8876040A a b + 5917360B a b)d e +--R + +--R 3 2 2 3 6 4 3 4 5 +--R (2067200A a b + 3100800B a b )d e + (1330A b + 5320B a b )d e +--R + +--R 4 5 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R 1847560A a d e + (7726160A a b + 1931540B a )d e +--R + +--R 2 2 3 3 6 +--R (4108560A a b + 2739040B a b)d e +--R + +--R 3 2 2 4 5 4 3 5 4 +--R (12920A a b + 19380B a b )d e + (- 1520A b - 6080B a b )d e +--R + +--R 4 6 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 2771340A a d e + (4031040A a b + 1007760B a )d e +--R + +--R 2 2 3 4 5 3 2 2 5 4 +--R (58140A a b + 38760B a b)d e + (- 15504A a b - 23256B a b )d e +--R + +--R 4 3 6 3 4 7 2 +--R (1824A b + 7296B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R 1847560A a d e + (167960A a b + 41990B a )d e +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (- 77520A a b - 51680B a b)d e + (20672A a b + 31008B a b )d e +--R + +--R 4 3 7 2 4 8 +--R (- 2432A b - 9728B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R 461890A a d e + (- 335920A a b - 83980B a )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (155040A a b + 103360B a b)d e + (- 41344A a b - 62016B a b )d e +--R + +--R 4 3 8 4 9 +--R (4864A b + 19456B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Union(Expression(Integer),...) +--E 823 + +--S 824 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1378 +r0:=-2/7*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(7/2)/e^6+2/9*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^6-4/11*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(11/2)/e^6+4/13*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(13/2)/e^6-2/15*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(15/2)/e^6+2/17*b^4*B*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 4 8 8 4 3 8 4 7 7 +--R 90090B b e x + ((102102A b + 408408B a b )e + 210210B b d e )x +--R + +--R 3 2 2 8 4 3 7 +--R (471240A a b + 706860B a b )e + (243474A b + 973896B a b )d e +--R + +--R 4 2 6 +--R 127050B b d e +--R * +--R 6 +--R x +--R + +--R 2 2 3 8 +--R (835380A a b + 556920B a b)e +--R + +--R 3 2 2 7 +--R (1156680A a b + 1735020B a b )d e +--R + +--R 4 3 2 6 4 3 5 +--R (152082A b + 608328B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 8 2 2 3 7 +--R (680680A a b + 170170B a )e + (2134860A a b + 1423240B a b)d e +--R + +--R 3 2 2 2 6 4 3 3 5 +--R (756840A a b + 1135260B a b )d e + (1190A b + 4760B a b )d e +--R + +--R 4 4 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 7 +--R 218790A a e + (1847560A a b + 461890B a )d e +--R + +--R 2 2 3 2 6 3 2 2 3 5 +--R (1498380A a b + 998920B a b)d e + (10200A a b + 15300B a b )d e +--R + +--R 4 3 4 4 4 5 3 +--R (- 1360A b - 5440B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 2 6 +--R 656370A a d e + (1458600A a b + 364650B a )d e +--R + +--R 2 2 3 3 5 3 2 2 4 4 +--R (39780A a b + 26520B a b)d e + (- 12240A a b - 18360B a b )d e +--R + +--R 4 3 5 3 4 6 2 +--R (1632A b + 6528B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 6 3 4 3 5 +--R 656370A a d e + (97240A a b + 24310B a )d e +--R + +--R 2 2 3 4 4 3 2 2 5 3 +--R (- 53040A a b - 35360B a b)d e + (16320A a b + 24480B a b )d e +--R + +--R 4 3 6 2 4 7 +--R (- 2176A b - 8704B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 3 5 3 4 4 4 +--R 218790A a d e + (- 194480A a b - 48620B a )d e +--R + +--R 2 2 3 5 3 3 2 2 6 2 +--R (106080A a b + 70720B a b)d e + (- 32640A a b - 48960B a b )d e +--R + +--R 4 3 7 4 8 +--R (4352A b + 17408B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 8 4 3 8 4 7 7 +--R 90090B b e x + ((102102A b + 408408B a b )e + 210210B b d e )x +--R + +--R 3 2 2 8 4 3 7 +--R (471240A a b + 706860B a b )e + (243474A b + 973896B a b )d e +--R + +--R 4 2 6 +--R 127050B b d e +--R * +--R 6 +--R x +--R + +--R 2 2 3 8 +--R (835380A a b + 556920B a b)e +--R + +--R 3 2 2 7 +--R (1156680A a b + 1735020B a b )d e +--R + +--R 4 3 2 6 4 3 5 +--R (152082A b + 608328B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 8 2 2 3 7 +--R (680680A a b + 170170B a )e + (2134860A a b + 1423240B a b)d e +--R + +--R 3 2 2 2 6 4 3 3 5 +--R (756840A a b + 1135260B a b )d e + (1190A b + 4760B a b )d e +--R + +--R 4 4 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 7 +--R 218790A a e + (1847560A a b + 461890B a )d e +--R + +--R 2 2 3 2 6 3 2 2 3 5 +--R (1498380A a b + 998920B a b)d e + (10200A a b + 15300B a b )d e +--R + +--R 4 3 4 4 4 5 3 +--R (- 1360A b - 5440B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 2 6 +--R 656370A a d e + (1458600A a b + 364650B a )d e +--R + +--R 2 2 3 3 5 3 2 2 4 4 +--R (39780A a b + 26520B a b)d e + (- 12240A a b - 18360B a b )d e +--R + +--R 4 3 5 3 4 6 2 +--R (1632A b + 6528B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 6 3 4 3 5 +--R 656370A a d e + (97240A a b + 24310B a )d e +--R + +--R 2 2 3 4 4 3 2 2 5 3 +--R (- 53040A a b - 35360B a b)d e + (16320A a b + 24480B a b )d e +--R + +--R 4 3 6 2 4 7 +--R (- 2176A b - 8704B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 3 5 3 4 4 4 +--R 218790A a d e + (- 194480A a b - 48620B a )d e +--R + +--R 2 2 3 5 3 3 2 2 6 2 +--R (106080A a b + 70720B a b)d e + (- 32640A a b - 48960B a b )d e +--R + +--R 4 3 7 4 8 +--R (4352A b + 17408B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Union(Expression(Integer),...) +--E 828 + +--S 829 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1378 +r0:=-2/5*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(5/2)/e^6+2/7*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^6-4/9*b*(b*d-a*e)^2*(5*b*B*d-_ + 3*A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^6+4/11*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-_ + 3*a*B*e)*(d+e*x)^(11/2)/e^6-2/13*b^3*(5*b*B*d-A*b*e-4*a*B*e)*_ + (d+e*x)^(13/2)/e^6+2/15*b^4*B*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 4 7 7 4 3 7 4 6 6 +--R 6006B b e x + ((6930A b + 27720B a b )e + 7392B b d e )x +--R + +--R 3 2 2 7 4 3 6 +--R (32760A a b + 49140B a b )e + (8820A b + 35280B a b )d e +--R + +--R 4 2 5 +--R 126B b d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 3 2 2 6 +--R (60060A a b + 40040B a b)e + (43680A a b + 65520B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (210A b + 840B a b )d e - 140B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (51480A a b + 12870B a )e + (85800A a b + 57200B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 +--R (1560A a b + 2340B a b )d e + (- 240A b - 960B a b )d e +--R + +--R 4 4 3 +--R 160B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 6 +--R 18018A a e + (82368A a b + 20592B a )d e +--R + +--R 2 2 3 2 5 3 2 2 3 4 +--R (5148A a b + 3432B a b)d e + (- 1872A a b - 2808B a b )d e +--R + +--R 4 3 4 3 4 5 2 +--R (288A b + 1152B a b )d e - 192B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 2 5 +--R 36036A a d e + (10296A a b + 2574B a )d e +--R + +--R 2 2 3 3 4 3 2 2 4 3 +--R (- 6864A a b - 4576B a b)d e + (2496A a b + 3744B a b )d e +--R + +--R 4 3 5 2 4 6 +--R (- 384A b - 1536B a b )d e + 256B b d e +--R * +--R x +--R + +--R 4 2 5 3 4 3 4 +--R 18018A a d e + (- 20592A a b - 5148B a )d e +--R + +--R 2 2 3 4 3 3 2 2 5 2 +--R (13728A a b + 9152B a b)d e + (- 4992A a b - 7488B a b )d e +--R + +--R 4 3 6 4 7 +--R (768A b + 3072B a b )d e - 512B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 7 4 3 7 4 6 6 +--R 6006B b e x + ((6930A b + 27720B a b )e + 7392B b d e )x +--R + +--R 3 2 2 7 4 3 6 +--R (32760A a b + 49140B a b )e + (8820A b + 35280B a b )d e +--R + +--R 4 2 5 +--R 126B b d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 3 2 2 6 +--R (60060A a b + 40040B a b)e + (43680A a b + 65520B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (210A b + 840B a b )d e - 140B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (51480A a b + 12870B a )e + (85800A a b + 57200B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 +--R (1560A a b + 2340B a b )d e + (- 240A b - 960B a b )d e +--R + +--R 4 4 3 +--R 160B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 6 +--R 18018A a e + (82368A a b + 20592B a )d e +--R + +--R 2 2 3 2 5 3 2 2 3 4 +--R (5148A a b + 3432B a b)d e + (- 1872A a b - 2808B a b )d e +--R + +--R 4 3 4 3 4 5 2 +--R (288A b + 1152B a b )d e - 192B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 2 5 +--R 36036A a d e + (10296A a b + 2574B a )d e +--R + +--R 2 2 3 3 4 3 2 2 4 3 +--R (- 6864A a b - 4576B a b)d e + (2496A a b + 3744B a b )d e +--R + +--R 4 3 5 2 4 6 +--R (- 384A b - 1536B a b )d e + 256B b d e +--R * +--R x +--R + +--R 4 2 5 3 4 3 4 +--R 18018A a d e + (- 20592A a b - 5148B a )d e +--R + +--R 2 2 3 4 3 3 2 2 5 2 +--R (13728A a b + 9152B a b)d e + (- 4992A a b - 7488B a b )d e +--R + +--R 4 3 6 4 7 +--R (768A b + 3072B a b )d e - 512B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 833 + +--S 834 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1378 +r0:=-2/3*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(3/2)/e^6+2/5*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^6-4/7*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^6+4/9*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^6-2/11*b^3*_ + (5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(11/2)/e^6+2/13*b^4*B*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 4 6 6 4 3 6 4 5 5 +--R 6930B b e x + ((8190A b + 32760B a b )e + 630B b d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (40040A a b + 60060B a b )e + (910A b + 3640B a b )d e +--R + +--R 4 2 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (77220A a b + 51480B a b)e + (5720A a b + 8580B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (- 1040A b - 4160B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (72072A a b + 18018B a )e + (15444A a b + 10296B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 6864A a b - 10296B a b )d e + (1248A b + 4992B a b )d e +--R + +--R 4 4 2 +--R - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 5 +--R 30030A a e + (24024A a b + 6006B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 20592A a b - 13728B a b)d e + (9152A a b + 13728B a b )d e +--R + +--R 4 3 4 2 4 5 +--R (- 1664A b - 6656B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 2 4 +--R 30030A a d e + (- 48048A a b - 12012B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (41184A a b + 27456B a b)d e + (- 18304A a b - 27456B a b )d e +--R + +--R 4 3 5 4 6 +--R (3328A b + 13312B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 6 4 3 6 4 5 5 +--R 6930B b e x + ((8190A b + 32760B a b )e + 630B b d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (40040A a b + 60060B a b )e + (910A b + 3640B a b )d e +--R + +--R 4 2 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (77220A a b + 51480B a b)e + (5720A a b + 8580B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (- 1040A b - 4160B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (72072A a b + 18018B a )e + (15444A a b + 10296B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 6864A a b - 10296B a b )d e + (1248A b + 4992B a b )d e +--R + +--R 4 4 2 +--R - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 5 +--R 30030A a e + (24024A a b + 6006B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 20592A a b - 13728B a b)d e + (9152A a b + 13728B a b )d e +--R + +--R 4 3 4 2 4 5 +--R (- 1664A b - 6656B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 2 4 +--R 30030A a d e + (- 48048A a b - 12012B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (41184A a b + 27456B a b)d e + (- 18304A a b - 27456B a b )d e +--R + +--R 4 3 5 4 6 +--R (3328A b + 13312B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 838 + +--S 839 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1378 +r0:=2/3*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^6-4/5*b*_ + (b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^6+4/7*b^2*_ + (b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^6-2/9*b^3*_ + (5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(9/2)/e^6+2/11*b^4*B*(d+e*x)^(11/2)/e^6-_ + 2*(b*d-a*e)^4*(B*d-A*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 630B b e x + ((770A b + 3080B a b )e - 700B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (3960A a b + 5940B a b )e + (- 880A b - 3520B a b )d e +--R + +--R 4 2 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (8316A a b + 5544B a b)e + (- 4752A a b - 7128B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (1056A b + 4224B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (9240A a b + 2310B a )e + (- 11088A a b - 7392B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (6336A a b + 9504B a b )d e + (- 1408A b - 5632B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R 6930A a e + (- 18480A a b - 4620B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (22176A a b + 14784B a b)d e + (- 12672A a b - 19008B a b )d e +--R + +--R 4 3 4 4 5 +--R (2816A b + 11264B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R 630B b e x + ((770A b + 3080B a b )e - 700B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (3960A a b + 5940B a b )e + (- 880A b - 3520B a b )d e +--R + +--R 4 2 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (8316A a b + 5544B a b)e + (- 4752A a b - 7128B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (1056A b + 4224B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (9240A a b + 2310B a )e + (- 11088A a b - 7392B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (6336A a b + 9504B a b )d e + (- 1408A b - 5632B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R 6930A a e + (- 18480A a b - 4620B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (22176A a b + 14784B a b)d e + (- 12672A a b - 19008B a b )d e +--R + +--R 4 3 4 4 5 +--R (2816A b + 11264B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 843 + +--S 844 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +)clear all + +--S 846 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1378 +r0:=-4/3*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^6+_ + 4/5*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^6-_ + 2/7*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(7/2)/e^6+2/9*b^4*B*_ + (d+e*x)^(9/2)/e^6+2*(b*d-a*e)^4*(B*d-A*e)/(e^6*sqrt(d+e*x))+_ + 2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 70B b e x + ((90A b + 360B a b )e - 100B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((504A a b + 756B a b )e + (- 144A b - 576B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1008A a b - 1512B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (288A b + 1152B a b )d e - 320B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (2520A a b + 630B a )e + (- 5040A a b - 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (4032A a b + 6048B a b )d e + (- 1152A b - 4608B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R - 630A a e + (5040A a b + 1260B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 10080A a b - 6720B a b)d e + (8064A a b + 12096B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 2304A b - 9216B a b )d e + 2560B b d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R 70B b e x + ((90A b + 360B a b )e - 100B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((504A a b + 756B a b )e + (- 144A b - 576B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1008A a b - 1512B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (288A b + 1152B a b )d e - 320B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (2520A a b + 630B a )e + (- 5040A a b - 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (4032A a b + 6048B a b )d e + (- 1152A b - 4608B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R - 630A a e + (5040A a b + 1260B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 10080A a b - 6720B a b)d e + (8064A a b + 12096B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 2304A b - 9216B a b )d e + 2560B b d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 848 + +--S 849 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1378 +r0:=2/3*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^(3/2))+4/3*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^6-2/5*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(5/2)/e^6+2/7*b^4*B*(d+e*x)^(7/2)/e^6-2*(b*d-_ + a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*sqrt(d+e*x))-4*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 30B b e x + ((42A b + 168B a b )e - 60B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((280A a b + 420B a b )e + (- 112A b - 448B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1680A a b - 2520B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (672A b + 2688B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 840A a b - 210B a )e + (5040A a b + 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 6720A a b - 10080B a b )d e + (2688A b + 10752B a b )d e +--R + +--R 4 4 +--R - 3840B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 70A a e + (- 560A a b - 140B a )d e + (3360A a b + 2240B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 4480A a b - 6720B a b )d e + (1792A b + 7168B a b )d e - 2560B b d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R 30B b e x + ((42A b + 168B a b )e - 60B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((280A a b + 420B a b )e + (- 112A b - 448B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1680A a b - 2520B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (672A b + 2688B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 840A a b - 210B a )e + (5040A a b + 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 6720A a b - 10080B a b )d e + (2688A b + 10752B a b )d e +--R + +--R 4 4 +--R - 3840B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 70A a e + (- 560A a b - 140B a )d e + (3360A a b + 2240B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 4480A a b - 6720B a b )d e + (1792A b + 7168B a b )d e - 2560B b d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 853 + +--S 854 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 855 + +)clear all + +--S 856 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1378 +r0:=2/5*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^(5/2))-2/3*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^(3/2))-2/3*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(3/2)/e^6+2/5*b^4*B*(d+e*x)^(5/2)/e^6+4*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*sqrt(d+e*x))+4*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 6B b e x + ((10A b + 40B a b )e - 20B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((120A a b + 180B a b )e + (- 80A b - 320B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 180A a b - 120B a b)e + (720A a b + 1080B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 480A b - 1920B a b )d e + 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 40A a b - 10B a )e + (- 240A a b - 160B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (960A a b + 1440B a b )d e + (- 640A b - 2560B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 6A a e + (- 16A a b - 4B a )d e + (- 96A a b - 64B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (384A a b + 576B a b )d e + (- 256A b - 1024B a b )d e + 512B b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 857 + +--S 858 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R 6B b e x + ((10A b + 40B a b )e - 20B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((120A a b + 180B a b )e + (- 80A b - 320B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 180A a b - 120B a b)e + (720A a b + 1080B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 480A b - 1920B a b )d e + 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 40A a b - 10B a )e + (- 240A a b - 160B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (960A a b + 1440B a b )d e + (- 640A b - 2560B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 6A a e + (- 16A a b - 4B a )d e + (- 96A a b - 64B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (384A a b + 576B a b )d e + (- 256A b - 1024B a b )d e + 512B b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 858 + +--S 859 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 6 3 10 6 5 3 6 2 9 +--R B b e x + ((A b + 6B a b )e + 3B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 8 +--R ((6A a b + 15B a b )e + (3A b + 18B a b )d e + 3B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (15A a b + 20B a b )e + (18A a b + 45B a b )d e +--R + +--R 6 5 2 6 3 +--R (3A b + 18B a b )d e + B b d +--R * +--R 7 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (20A a b + 15B a b )e + (45A a b + 60B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (18A a b + 45B a b )d e + (A b + 6B a b )d +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (15A a b + 6B a b)e + (60A a b + 45B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (45A a b + 60B a b )d e + (6A a b + 15B a b )d +--R * +--R 5 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (6A a b + B a )e + (45A a b + 18B a b)d e +--R + +--R 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5 2 4 8 3 +--R (247296A a b + 618240B a b )d e +--R + +--R 6 5 9 2 6 10 +--R (- 23552A b - 141312B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 4 7 5 6 5 6 +--R 14872858A a d e + (- 16224936A a b - 2704156B a )d e +--R + +--R 4 2 5 6 5 +--R (12480720A a b + 4992288B a b)d e +--R + +--R 3 3 4 2 7 4 +--R (- 6656384A a b - 4992288B a b )d e +--R + +--R 2 4 3 3 8 3 +--R (2349312A a b + 3132416B a b )d e +--R + +--R 5 2 4 9 2 6 5 10 +--R (- 494592A a b - 1236480B a b )d e + (47104A b + 282624B a b )d e +--R + +--R 6 11 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 66927861e +--R Type: Union(Expression(Integer),...) +--E 863 + +--S 864 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +)clear all + +--S 866 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 6 2 9 6 5 2 6 8 +--R B b e x + ((A b + 6B a b 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875 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 875 + +)clear all + +--S 876 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1378 +r0:=-2/3*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(3/2)/e^8+2/5*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^8-6/7*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^8+10/9*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^8-10/11*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(11/2)/e^8+6/13*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(13/2)/e^8-2/15*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(15/2)/e^8+2/17*b^6*B*(d+e*x)^(17/2)/e^8 +--R +--R 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)d e +--R + +--R 6 5 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 5 6 8 4 2 5 7 +--R (1837836A a b + 306306B a )e + (656370A a b + 262548B a b)d e +--R + +--R 3 3 4 2 2 6 +--R (- 583440A a b - 437580B a b )d e +--R + +--R 2 4 3 3 3 5 +--R (318240A a b + 424320B a b )d e +--R + +--R 5 2 4 4 4 6 5 5 3 +--R (- 97920A a b - 244800B a b )d e + (13056A b + 78336B a b )d e +--R + +--R 6 6 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 6 8 5 6 7 +--R 510510A a e + (612612A a b + 102102B a )d e +--R + +--R 4 2 5 2 6 +--R (- 875160A a b - 350064B a b)d e +--R + +--R 3 3 4 2 3 5 +--R (777920A a b + 583440B a b )d e +--R + +--R 2 4 3 3 4 4 +--R (- 424320A a b - 565760B a b )d e +--R + +--R 5 2 4 5 3 +--R (130560A a b + 326400B a b )d e +--R + +--R 6 5 6 2 6 7 +--R (- 17408A b - 104448B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 2 6 +--R 510510A a d e + (- 1225224A a b - 204204B a )d e +--R + +--R 4 2 5 3 5 +--R (1750320A a b + 700128B a b)d e +--R + +--R 3 3 4 2 4 4 +--R (- 1555840A a b - 1166880B a b )d e +--R + +--R 2 4 3 3 5 3 +--R (848640A a b + 1131520B a b )d e +--R + +--R 5 2 4 6 2 6 5 7 +--R (- 261120A a b - 652800B a b )d e + (34816A b + 208896B a b )d e +--R + +--R 6 8 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 8 8 6 5 8 6 7 7 +--R 90090B b e x + ((102102A b + 612612B a b )e + 6006B b d e )x +--R + +--R 5 2 4 8 6 5 7 +--R (706860A a b + 1767150B a b )e + (7854A b + 47124B a b )d e +--R + +--R 6 2 6 +--R - 6468B b d e +--R * +--R 6 +--R x +--R + +--R 2 4 3 3 8 +--R (2088450A a b + 2784600B a b )e +--R + +--R 5 2 4 7 6 5 2 6 +--R (64260A a b + 160650B a b )d e + (- 8568A b - 51408B a b )d e +--R + +--R 6 3 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 3 3 4 2 8 +--R (3403400A a b + 2552550B a b )e +--R + +--R 2 4 3 3 7 +--R (232050A a b + 309400B a b )d e +--R + +--R 5 2 4 2 6 6 5 3 5 +--R (- 71400A a b - 178500B a b )d e + (9520A b + 57120B a b )d e +--R + +--R 6 4 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 5 8 +--R (3281850A a b + 1312740B a b)e +--R + +--R 3 3 4 2 7 +--R (486200A a b + 364650B a b )d e +--R + +--R 2 4 3 3 2 6 +--R (- 265200A a b - 353600B a b )d e +--R + +--R 5 2 4 3 5 6 5 4 4 +--R (81600A a b + 204000B a b )d e + (- 10880A b - 65280B a b )d e +--R + +--R 6 5 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 5 6 8 4 2 5 7 +--R (1837836A a b + 306306B a )e + (656370A a b + 262548B a b)d e +--R + +--R 3 3 4 2 2 6 +--R (- 583440A a b - 437580B a b )d e +--R + +--R 2 4 3 3 3 5 +--R (318240A a b + 424320B a b )d e +--R + +--R 5 2 4 4 4 6 5 5 3 +--R (- 97920A a b - 244800B a b )d e + (13056A b + 78336B a b )d e +--R + +--R 6 6 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 6 8 5 6 7 +--R 510510A a e + (612612A a b + 102102B a )d e +--R + +--R 4 2 5 2 6 +--R (- 875160A a b - 350064B a b)d e +--R + +--R 3 3 4 2 3 5 +--R (777920A a b + 583440B a b )d e +--R + +--R 2 4 3 3 4 4 +--R (- 424320A a b - 565760B a b )d e +--R + +--R 5 2 4 5 3 +--R (130560A a b + 326400B a b )d e +--R + +--R 6 5 6 2 6 7 +--R (- 17408A b - 104448B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 2 6 +--R 510510A a d e + (- 1225224A a b - 204204B a )d e +--R + +--R 4 2 5 3 5 +--R (1750320A a b + 700128B a b)d e +--R + +--R 3 3 4 2 4 4 +--R (- 1555840A a b - 1166880B a b )d e +--R + +--R 2 4 3 3 5 3 +--R (848640A a b + 1131520B a b )d e +--R + +--R 5 2 4 6 2 6 5 7 +--R (- 261120A a b - 652800B a b )d e + (34816A b + 208896B a b )d e +--R + +--R 6 8 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Union(Expression(Integer),...) +--E 878 + +--S 879 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 880 + +)clear all + +--S 881 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1378 +r0:=2/3*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^8-6/5*b*_ + (b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^8+10/7*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^8-10/9*b^3*_ + (b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(9/2)/e^8+6/11*b^4*_ + (b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(11/2)/e^8-2/13*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(13/2)/e^8+2/15*b^6*B*_ + (d+e*x)^(15/2)/e^8-2*(b*d-a*e)^6*(B*d-A*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 6006B b e x + ((6930A b + 41580B a b )e - 6468B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (49140A a b + 122850B a b )e + (- 7560A b - 45360B a b )d e +--R + +--R 6 2 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 +--R (150150A a b + 200200B a b )e +--R + +--R 5 2 4 6 6 5 2 5 +--R (- 54600A a b - 136500B a b )d e + (8400A b + 50400B a b )d e +--R + +--R 6 3 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 +--R (257400A a b + 193050B a b )e +--R + +--R 2 4 3 3 6 +--R (- 171600A a b - 228800B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (62400A a b + 156000B a b )d e + (- 9600A b - 57600B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 +--R (270270A a b + 108108B a b)e +--R + +--R 3 3 4 2 6 +--R (- 308880A a b - 231660B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (205920A a b + 274560B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (- 74880A a b - 187200B a b )d e + (11520A b + 69120B a b )d e +--R + +--R 6 5 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (180180A a b + 30030B a )e + (- 360360A a b - 144144B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (411840A a b + 308880B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 274560A a b - 366080B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (99840A a b + 249600B a b )d e + (- 15360A b - 92160B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R 90090A a e + (- 360360A a b - 60060B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (720720A a b + 288288B a b)d e + (- 823680A a b - 617760B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (549120A a b + 732160B a b )d e + (- 199680A a b - 499200B a b )d e +--R + +--R 6 5 6 6 7 +--R (30720A b + 184320B a b )d e - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 6 5 7 6 6 6 +--R 6006B b e x + ((6930A b + 41580B a b )e - 6468B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (49140A a b + 122850B a b )e + (- 7560A b - 45360B a b )d e +--R + +--R 6 2 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 +--R (150150A a b + 200200B a b )e +--R + +--R 5 2 4 6 6 5 2 5 +--R (- 54600A a b - 136500B a b )d e + (8400A b + 50400B a b )d e +--R + +--R 6 3 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 +--R (257400A a b + 193050B a b )e +--R + +--R 2 4 3 3 6 +--R (- 171600A a b - 228800B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (62400A a b + 156000B a b )d e + (- 9600A b - 57600B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 +--R (270270A a b + 108108B a b)e +--R + +--R 3 3 4 2 6 +--R (- 308880A a b - 231660B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (205920A a b + 274560B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (- 74880A a b - 187200B a b )d e + (11520A b + 69120B a b )d e +--R + +--R 6 5 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (180180A a b + 30030B a )e + (- 360360A a b - 144144B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (411840A a b + 308880B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 274560A a b - 366080B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (99840A a b + 249600B a b )d e + (- 15360A b - 92160B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R 90090A a e + (- 360360A a b - 60060B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (720720A a b + 288288B a b)d e + (- 823680A a b - 617760B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (549120A a b + 732160B a b )d e + (- 199680A a b - 499200B a b )d e +--R + +--R 6 5 6 6 7 +--R (30720A b + 184320B a b )d e - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 883 + +--S 884 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1378 +r0:=-2*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^8+2*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^8-10/7*b^3*_ + (b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(7/2)/e^8+2/3*b^4*_ + (b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(9/2)/e^8-2/11*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(11/2)/e^8+2/13*b^6*B*_ + (d+e*x)^(13/2)/e^8+2*(b*d-a*e)^6*(B*d-A*e)/(e^8*sqrt(d+e*x))+_ + 2*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 462B b e x + ((546A b + 3276B a b )e - 588B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (4004A a b + 10010B a b )e + (- 728A b - 4368B a b )d e +--R + +--R 6 2 5 +--R 784B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (12870A a b + 17160B a b )e + (- 5720A a b - 14300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (1040A b + 6240B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (24024A a b + 18018B a b )e + (- 20592A a b - 27456B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (9152A a b + 22880B a b )d e + (- 1664A b - 9984B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (30030A a b + 12012B a b)e + (- 48048A a b - 36036B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (41184A a b + 54912B a b )d e + (- 18304A a b - 45760B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (3328A b + 19968B a b )d e - 3584B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (36036A a b + 6006B a )e + (- 120120A a b - 48048B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (192192A a b + 144144B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 164736A a b - 219648B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (73216A a b + 183040B a b )d e + (- 13312A b - 79872B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 6006A a e + (72072A a b + 12012B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 240240A a b - 96096B a b)d e + (384384A a b + 288288B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 329472A a b - 439296B a b )d e + (146432A a b + 366080B a b )d e +--R + +--R 6 5 6 6 7 +--R (- 26624A b - 159744B a b )d e + 28672B b d +--R / +--R 8 +-------+ +--R 3003e \|e x + d +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 6 5 7 6 6 6 +--R 462B b e x + ((546A b + 3276B a b )e - 588B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (4004A a b + 10010B a b )e + (- 728A b - 4368B a b )d e +--R + +--R 6 2 5 +--R 784B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (12870A a b + 17160B a b )e + (- 5720A a b - 14300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (1040A b + 6240B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (24024A a b + 18018B a b )e + (- 20592A a b - 27456B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (9152A a b + 22880B a b )d e + (- 1664A b - 9984B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (30030A a b + 12012B a b)e + (- 48048A a b - 36036B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (41184A a b + 54912B a b )d e + (- 18304A a b - 45760B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (3328A b + 19968B a b )d e - 3584B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (36036A a b + 6006B a )e + (- 120120A a b - 48048B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (192192A a b + 144144B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 164736A a b - 219648B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (73216A a b + 183040B a b )d e + (- 13312A b - 79872B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 6006A a e + (72072A a b + 12012B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 240240A a b - 96096B a b)d e + (384384A a b + 288288B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 329472A a b - 439296B a b )d e + (146432A a b + 366080B a b )d e +--R + +--R 6 5 6 6 7 +--R (- 26624A b - 159744B a b )d e + 28672B b d +--R / +--R 8 +-------+ +--R 3003e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 888 + +--S 889 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1378 +r0:=2/3*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^(3/2))+10/3*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^8-2*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(5/2)/e^8+6/7*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(7/2)/e^8-2/9*b^5*(7*b*B*d-A*b*e-_ + 6*a*B*e)*(d+e*x)^(9/2)/e^8+2/11*b^6*B*(d+e*x)^(11/2)/e^8-2*_ + (b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*sqrt(d+e*x))-6*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 126B b e x + ((154A b + 924B a b )e - 196B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (1188A a b + 2970B a b )e + (- 264A b - 1584B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (4158A a b + 5544B a b )e + (- 2376A a b - 5940B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (528A b + 3168B a b )d e - 672B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (9240A a b + 6930B a b )e + (- 11088A a b - 14784B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (6336A a b + 15840B a b )d e + (- 1408A b - 8448B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (20790A a b + 8316B a b)e + (- 55440A a b - 41580B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (66528A a b + 88704B a b )d e + (- 38016A a b - 95040B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (8448A b + 50688B a b )d e - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 8316A a b - 1386B a )e + (83160A a b + 33264B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (- 221760A a b - 166320B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (266112A a b + 354816B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 152064A a b - 380160B a b )d e + (33792A b + 202752B a b )d e +--R + +--R 6 6 +--R - 43008B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 462A a e + (- 5544A a b - 924B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (55440A a b + 22176B a b)d e + (- 147840A a b - 110880B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (177408A a b + 236544B a b )d e + (- 101376A a b - 253440B a b )d e +--R + +--R 6 5 6 6 7 +--R (22528A b + 135168B a b )d e - 28672B b d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 6 5 7 6 6 6 +--R 126B b e x + ((154A b + 924B a b )e - 196B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (1188A a b + 2970B a b )e + (- 264A b - 1584B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (4158A a b + 5544B a b )e + (- 2376A a b - 5940B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (528A b + 3168B a b )d e - 672B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (9240A a b + 6930B a b )e + (- 11088A a b - 14784B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (6336A a b + 15840B a b )d e + (- 1408A b - 8448B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (20790A a b + 8316B a b)e + (- 55440A a b - 41580B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (66528A a b + 88704B a b )d e + (- 38016A a b - 95040B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (8448A b + 50688B a b )d e - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 8316A a b - 1386B a )e + (83160A a b + 33264B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (- 221760A a b - 166320B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (266112A a b + 354816B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 152064A a b - 380160B a b )d e + (33792A b + 202752B a b )d e +--R + +--R 6 6 +--R - 43008B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 462A a e + (- 5544A a b - 924B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (55440A a b + 22176B a b)d e + (- 147840A a b - 110880B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (177408A a b + 236544B a b )d e + (- 101376A a b - 253440B a b )d e +--R + +--R 6 5 6 6 7 +--R (22528A b + 135168B a b )d e - 28672B b d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 893 + +--S 894 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 895 + +)clear all + +--S 896 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1378 +r0:=2/5*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^(5/2))-2/3*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^(3/2))-10/3*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(3/2)/e^8+6/5*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(5/2)/e^8-2/7*b^5*(7*b*B*d-_ + A*b*e-6*a*B*e)*(d+e*x)^(7/2)/e^8+2/9*b^6*B*(d+e*x)^(9/2)/e^8+6*b*_ + (b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*sqrt(d+e*x))+10*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 70B b e x + ((90A b + 540B a b )e - 140B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (756A a b + 1890B a b )e + (- 216A b - 1296B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (3150A a b + 4200B a b )e + (- 2520A a b - 6300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (720A b + 4320B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (12600A a b + 9450B a b )e + (- 25200A a b - 33600B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (20160A a b + 50400B a b )d e + (- 5760A b - 34560B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (- 9450A a b - 3780B a b)e + (75600A a b + 56700B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (- 151200A a b - 201600B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (120960A a b + 302400B a b )d e + (- 34560A b - 207360B a b )d e +--R + +--R 6 5 2 +--R 53760B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 1260A a b - 210B a )e + (- 12600A a b - 5040B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (100800A a b + 75600B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 201600A a b - 268800B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (161280A a b + 403200B a b )d e + (- 46080A b - 276480B a b )d e +--R + +--R 6 6 +--R 71680B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 126A a e + (- 504A a b - 84B a )d e + (- 5040A a b - 2016B a b)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (40320A a b + 30240B a b )d e + (- 80640A a b - 107520B a b )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (64512A a b + 161280B a b )d e + (- 18432A b - 110592B a b )d e +--R + +--R 6 7 +--R 28672B b d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 6 5 7 6 6 6 +--R 70B b e x + ((90A b + 540B a b )e - 140B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (756A a b + 1890B a b )e + (- 216A b - 1296B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (3150A a b + 4200B a b )e + (- 2520A a b - 6300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (720A b + 4320B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (12600A a b + 9450B a b )e + (- 25200A a b - 33600B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (20160A a b + 50400B a b )d e + (- 5760A b - 34560B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (- 9450A a b - 3780B a b)e + (75600A a b + 56700B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (- 151200A a b - 201600B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (120960A a b + 302400B a b )d e + (- 34560A b - 207360B a b )d e +--R + +--R 6 5 2 +--R 53760B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 1260A a b - 210B a )e + (- 12600A a b - 5040B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (100800A a b + 75600B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 201600A a b - 268800B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (161280A a b + 403200B a b )d e + (- 46080A b - 276480B a b )d e +--R + +--R 6 6 +--R 71680B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 126A a e + (- 504A a b - 84B a )d e + (- 5040A a b - 2016B a b)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (40320A a b + 30240B a b )d e + (- 80640A a b - 107520B a b )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (64512A a b + 161280B a b )d e + (- 18432A b - 110592B a b )d e +--R + +--R 6 7 +--R 28672B b d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 898 + +--S 899 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +)clear all + +--S 901 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1378 +r0:=1/3*(b*d-a*e)*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+_ + 1/5*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/b^3+1/7*(2*b*B*d+7*A*b*e-_ + 9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(9/2)/(b*_ + (b*d-a*e)*(a+b*x))-(b*d-a*e)^(5/2)*(2*b*B*d+7*A*b*e-9*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+(b*d-a*e)^2*_ + (2*b*B*d+7*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (- 735A a b + 945B a b)e + (1470A a b - 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 735A b + 1365B a b )d e - 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 735A a b + 945B a )e + (1470A a b - 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 735A a b + 1365B a b )d e - 210B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 54B a b )e + 132B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 98A a b + 126B a b )e + (224A b - 316B a b )d e +--R + +--R 4 2 +--R 244B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (490A a b - 630B a b)e + (- 1176A a b + 1652B a b )d e +--R + +--R 4 3 2 4 3 +--R (812A b - 1380B a b )d e + 352B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1715A a b + 2415B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (1127A a b - 1939B a b )d e + (- 105A b + 457B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 5 +-+ +--R (105b x + 105a b )\|b +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 3 3 2 2 2 +--R (735A a b - 945B a b)e + (- 1470A a b + 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (735A b - 1365B a b )d e + 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1470A a b + 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (735A a b - 1365B a b )d e + 210B a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 60B b e x + ((84A b - 108B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 196A a b + 252B a b )e + (448A b - 632B a b )d e +--R + +--R 4 2 +--R 488B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (980A a b - 1260B a b)e + (- 2352A a b + 3304B a b )d e +--R + +--R 4 3 2 4 3 +--R (1624A b - 2760B a b )d e + 704B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (1470A a b - 1890B a )e + (- 3430A a b + 4830B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (2254A a b - 3878B a b )d e + (- 210A b + 914B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 5 +--R 210b x + 210a b +--R , +--R +--R 2 2 3 3 3 2 2 2 +--R (- 735A a b + 945B a b)e + (1470A a b - 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 735A b + 1365B a b )d e - 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 735A a b + 945B a )e + (1470A a b - 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 735A a b + 1365B a b )d e - 210B a b d +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 54B a b )e + 132B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 98A a b + 126B a b )e + (224A b - 316B a b )d e +--R + +--R 4 2 +--R 244B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (490A a b - 630B a b)e + (- 1176A a b + 1652B a b )d e +--R + +--R 4 3 2 4 3 +--R (812A b - 1380B a b )d e + 352B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1715A a b + 2415B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (1127A a b - 1939B a b )d e + (- 105A b + 457B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 5 +--R 105b x + 105a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 903 + +--S 904 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 +--R (7A a b - 9B a )e + (- 14A a b + 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (7A b - 13B a b )d e + 2B b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 18B a )e + (- 28A a b + 40B a b)d e +--R + +--R 3 2 2 3 3 +--R (14A b - 26B a b )d e + 4B b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 +--R (7A a b - 9B a )e + (- 14A a b + 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (7A b - 13B a b )d e + 2B b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 3 2 2 2 +--R (- 7A a b + 9B a )e + (14A a b - 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 7A b + 13B a b )d e - 2B b d +--R * +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 907 + +)clear all + +--S 908 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1378 +r0:=1/3*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/b^3+1/5*(2*b*B*d+5*A*b*e-_ + 7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(7/2)/(b*_ + (b*d-a*e)*(a+b*x))-(b*d-a*e)^(3/2)*(2*b*B*d+5*A*b*e-7*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+(b*d-a*e)*(2*b*B*d+_ + 5*A*b*e-7*a*B*e)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 14B a b )e + 22B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 50A a b + 70B a b)e + (70A b - 118B a b )d e + 46B b d )x +--R + +--R 2 3 2 2 2 +--R (- 75A a b + 105B a )e + (100A a b - 170B a b)d e +--R + +--R 3 2 2 +--R (- 15A b + 61B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 5 4 +-+ +--R (15b x + 15a b )\|b +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R 12B b e x + ((20A b - 28B a b )e + 44B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 100A a b + 140B a b)e + (140A b - 236B a b )d e + 92B b d )x +--R + +--R 2 3 2 2 2 +--R (- 150A a b + 210B a )e + (200A a b - 340B a b)d e +--R + +--R 3 2 2 +--R (- 30A b + 122B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 30b x + 30a b +--R , +--R +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 14B a b )e + 22B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 50A a b + 70B a b)e + (70A b - 118B a b )d e + 46B b d )x +--R + +--R 2 3 2 2 2 +--R (- 75A a b + 105B a )e + (100A a b - 170B a b)d e +--R + +--R 3 2 2 +--R (- 15A b + 61B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 15b x + 15a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 910 + +--S 911 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 2 |- a e + b d +--R ((5A a b - 7B a )e + (- 5A b + 9B a b)d e - 2B b d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R +-+ \| b +--R \|b log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 +--R ((- 10A a b + 14B a )e + (10A b - 18B a b)d e + 4B b d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +-----------+ +--R ((- 5A a b + 7B a )e + (5A b - 9B a b)d e + 2B b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 2 2 2 +-+ |a e - b d +--R ((5A a b - 7B a )e + (- 5A b + 9B a b)d e - 2B b d )\|b |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 914 + +)clear all + +--S 915 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1378 +r0:=1/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e))-_ + (A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+_ + (2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (((- 9A b + 15B a b)e - 6B b d)x + (- 9A a b + 15B a )e - 6B a b d) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 10B a b)e + 8B b d)x + (9A a b - 15B a )e +--R + +--R 2 +--R (- 3A b + 11B a b)d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((9A b - 15B a b)e + 6B b d)x + (9A a b - 15B a )e + 6B a b d) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 2 2 2 2 +--R 4B b e x + ((12A b - 20B a b)e + 16B b d)x + (18A a b - 30B a )e +--R + +--R 2 +--R (- 6A b + 22B a b)d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +--R 2 2 2 +--R (((- 9A b + 15B a b)e - 6B b d)x + (- 9A a b + 15B a )e - 6B a b d) +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 10B a b)e + 8B b d)x + (9A a b - 15B a )e +--R + +--R 2 +--R (- 3A b + 11B a b)d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 3b x + 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 917 + +--S 918 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- a e + b d +-+ +--R ((3A b - 5B a)e + 2B b d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R ((6A b - 10B a)e + 4B b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R ((3A b - 5B a)e + 2B b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R ((- 3A b + 5B a)e - 2B b d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 921 + +)clear all + +--S 922 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1378 +r0:=-(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+A*b*e-3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))+_ + (2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)) +--R +--R +--R (2) +--R 2 2 2 +--R (((- A b + 3B a b)e - 2B b d)x + (- A a b + 3B a )e - 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (2B b x - A b + 3B a)\|- a e + b d \|b \|e x + d +--R / +--R 3 2 +-----------+ +-+ +--R (b x + a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((A b - 3B a b)e + 2B b d)x + (A a b - 3B a )e + 2B a b d) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (4B b x - 2A b + 6B a)\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 3 2 | 2 +--R (2b x + 2a b )\|- a b e + b d +--R , +--R +--R 2 2 2 +--R (((A b - 3B a b)e + 2B b d)x + (A a b - 3B a )e + 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (2B b x - A b + 3B a)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 3 2 | 2 +--R (b x + a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 924 + +--S 925 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R ((A b - 3B a)e + 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((2A b - 6B a)e + 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R 2b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((A b - 3B a)e + 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b - 3B a)e + 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 928 + +)clear all + +--S 929 of 1378 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1378 +r0:=-(2*b*B*d-A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(3/2)*(b*d-a*e)^(3/2))-(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 +--R (((- A b - B a b)e + 2B b d)x + (- A a b - B a )e + 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (A b - B a)\|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 2 +-----------+ +-+ +--R ((a b e - b d)x + a b e - a b d)\|- a e + b d \|b +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((A b + B a b)e - 2B b d)x + (A a b + B a )e - 2B a b d) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (2A b - 2B a)\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 2 3 2 2 | 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|- a b e + b d +--R , +--R +--R 2 2 2 +--R (((A b + B a b)e - 2B b d)x + (A a b + B a )e - 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (A b - B a)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 2 3 2 2 | 2 +--R ((a b e - b d)x + a b e - a b d)\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 931 + +--S 932 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R ((A b + B a)e - 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((2A b + 2B a)e - 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R (2a b e - 2b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((A b + B a)e - 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b + B a)e - 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R (a b e - b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 935 + +)clear all + +--S 936 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1378 +r0:=-(2*b*B*d-3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(5/2)*sqrt(b))+(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^2*_ + sqrt(d+e*x))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 +-------+ +--R (((3A b - B a b)e - 2B b d)x + (3A a b - B a )e - 2B a b d)\|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R (((- 3A b + B a)e + 2B b d)x - 2A a e + (- A b + 3B a)d)\|- a e + b d \|b +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-----------+ +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((3A b - B a b)e - 2B b d)x + (3A a b - B a )e - 2B a b d) +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R (((- 6A b + 2B a)e + 4B b d)x - 4A a e + (- 2A b + 6B a)d) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +--R ((2a b e - 4a b d e + 2b d )x + 2a e - 4a b d e + 2a b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 2 2 2 +--R (((- 3A b + B a b)e + 2B b d)x + (- 3A a b + B a )e + 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +--R (((- 3A b + B a)e + 2B b d)x - 2A a e + (- A b + 3B a)d)\|a b e - b d +--R / +--R +-----------+ +--R 2 2 2 3 2 3 2 2 2 2 | 2 +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|a b e - b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 938 + +--S 939 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R ((3A b - B a)e - 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((- 6A b + 2B a)e + 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 2 | 2 +-----------+ +-+ +--R (2a e - 4a b d e + 2b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((- 3A b + B a)e + 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((- 3A b + B a)e + 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 2 +-----------+ +-+ | 2 +--R (a e - 2a b d e + b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 942 + +)clear all + +--S 943 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1378 +r0:=1/3*(2*b*B*d-5*A*b*e+3*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+(-A*b+a*B)/_ + (b*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2))-(2*b*B*d-5*A*b*e+3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(7/2)+_ + (2*b*B*d-5*A*b*e+3*a*B*e)/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 15A b + 9B a b)e + 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 15A a b + 9B a )e + (- 15A b + 15B a b)d e + 6B b d )x +--R + +--R 2 2 +--R (- 15A a b + 9B a )d e + 6B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((10A a b - 6B a )e + (20A b - 16B a b)d e - 8B b d )x - 2A a e +--R + +--R 2 2 2 +--R (14A a b - 4B a )d e + (3A b - 11B a b)d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((15A a b - 9B a )e + (15A b - 15B a b)d e - 6B b d )x +--R + +--R 2 2 +--R (15A a b - 9B a )d e - 6B a b d +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R ((30A b - 18B a b)e - 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((20A a b - 12B a )e + (40A b - 32B a b)d e - 16B b d )x - 4A a e +--R + +--R 2 2 2 +--R (28A a b - 8B a )d e + (6A b - 22B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b e - 18a b d e + 18a b d e - 6b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (6a e - 12a b d e + 12a b d e - 6b d )x + 6a d e - 18a b d e +--R + +--R 2 2 3 3 4 +--R 18a b d e - 6a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((15A a b - 9B a )e + (15A b - 15B a b)d e - 6B b d )x +--R + +--R 2 2 +--R (15A a b - 9B a )d e - 6B a b d +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((10A a b - 6B a )e + (20A b - 16B a b)d e - 8B b d )x - 2A a e +--R + +--R 2 2 2 +--R (14A a b - 4B a )d e + (3A b - 11B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 945 + +--S 946 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R ((5A b - 3B a)e - 2B b d)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R ((10A b - 6B a)e - 4B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (2a e - 6a b d e + 6a b d e - 2b d )\|- a e + b d +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R ((5A b - 3B a)e - 2B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R +-----------+ | b +--R ((5A b - 3B a)e - 2B b d)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 949 + +)clear all + +--S 950 of 1378 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1378 +r0:=1/5*(2*b*B*d-7*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+_ + (-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(5/2))+1/3*(2*b*B*d-7*A*b*e+_ + 5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2))-b^(3/2)*(2*b*B*d-7*A*b*e+_ + 5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+_ + b*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((105A b - 75B a b )e - 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((105A a b - 75B a b)e + (210A b - 180B a b )d e - 60B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((210A a b - 150B a b)d e + (105A b - 135B a b )d e - 30B b d )x +--R + +--R 2 2 2 2 3 +--R (105A a b - 75B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 70A a b + 50B a b)e + (- 245A b + 195B a b )d e +--R + +--R 3 2 +--R 70B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 10B a )e + (- 168A a b + 116B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 161A b + 163B a b )d e + 46B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (32A a b - 4B a )d e + (- 116A a b + 48B a b)d e +--R + +--R 3 2 3 +--R (- 15A b + 61B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 3 2 3 +--R ((105A b - 75B a b )e - 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((105A a b - 75B a b)e + (210A b - 180B a b )d e - 60B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((210A a b - 150B a b)d e + (105A b - 135B a b )d e - 30B b d )x +--R + +--R 2 2 2 2 3 +--R (105A a b - 75B a b)d e - 30B a b d +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 3 +--R ((- 210A b + 150B a b )e + 60B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 140A a b + 100B a b)e + (- 490A b + 390B a b )d e +--R + +--R 3 2 +--R 140B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (28A a b - 20B a )e + (- 336A a b + 232B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 322A b + 326B a b )d e + 92B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 12A a e + (64A a b - 8B a )d e + (- 232A a b + 96B a b)d e +--R + +--R 3 2 3 +--R (- 30A b + 122B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (30a b e - 120a b d e + 180a b d e - 120a b d e + 30b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 30a e - 60a b d e - 60a b d e + 240a b d e - 210a b d e +--R + +--R 5 5 +--R 60b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 60a d e - 210a b d e + 240a b d e - 60a b d e - 60a b d e +--R + +--R 5 6 +--R 30b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 30a d e - 120a b d e + 180a b d e - 120a b d e + 30a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 105A a b + 75B a b)e + (- 210A b + 180B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 3 2 2 +--R (- 210A a b + 150B a b)d e + (- 105A b + 135B a b )d e +--R + +--R 3 3 +--R 30B b d +--R * +--R x +--R + +--R 2 2 2 2 3 +--R (- 105A a b + 75B a b)d e + 30B a b d +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 70A a b + 50B a b)e + (- 245A b + 195B a b )d e + 70B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 10B a )e + (- 168A a b + 116B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 161A b + 163B a b )d e + 46B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (32A a b - 4B a )d e + (- 116A a b + 48B a b)d e +--R + +--R 3 2 3 +--R (- 15A b + 61B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 952 + +--S 953 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 +-----------+ | b +--R ((7A b - 5B a b)e - 2B b d)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R ((- 14A b + 10B a b)e + 4B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (2a e - 8a b d e + 12a b d e - 8a b d e + 2b d )\|- a e + b d +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R ((- 7A b + 5B a b)e + 2B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 +-----------+ | b +--R ((- 7A b + 5B a b)e + 2B b d)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (a e - 4a b d e + 6a b d e - 4a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 956 + +)clear all + +--S 957 of 1378 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1378 +r0:=7/8*e^2*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(3/2)/b^5+21/40*e^2*_ + (6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*(b*d-a*e))-3/8*e*_ + (6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(7/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/12*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(9/2)/(b^2*(b*d-a*e)*_ + (a+b*x)^2)-1/3*(A*b-a*B)*(d+e*x)^(11/2)/(b*(b*d-a*e)*(a+b*x)^3)-_ + 21/8*e^2*(b*d-a*e)^(3/2)*(6*b*B*d+5*A*b*e-11*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(13/2)+21/8*e^2*(b*d-a*e)*(6*b*B*d+_ + 5*A*b*e-11*a*B*e)*sqrt(d+e*x)/b^6 +--R +--R +--R (2) +--R 4 2 3 4 5 4 3 +--R (1575A a b - 3465B a b )e + (- 1575A b + 5355B a b )d e +--R + +--R 5 2 2 +--R - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4725A a b - 10395B a b )e + (- 4725A a b + 16065B a b )d e +--R + +--R 4 2 2 +--R - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (4725A a b - 10395B a b)e + (- 4725A a b + 16065B a b )d e +--R + +--R 2 3 2 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (1575A a b - 3465B a )e + (- 1575A a b + 5355B a b)d e +--R + +--R 3 2 2 2 +--R - 1890B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 48B b e x + ((80A b - 176B a b )e + 336B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 720A a b + 1584B a b )e + (1040A b - 3152B a b )d e +--R + +--R 5 2 2 +--R 1728B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 3465A a b + 7623B a b )e + (4770A a b - 14652B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 825A b + 7539B a b )d e - 510B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 4200A a b + 9240B a b)e + (5670A a b - 17514B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 900A a b + 8784B a b )d e + (- 250A b - 530B a b )d e +--R + +--R 5 4 +--R - 60B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 1575A a b + 3465B a )e + (2100A a b - 6510B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 315A a b + 3213B a b )d e + (- 90A a b - 180B a b )d e +--R + +--R 5 4 4 +--R (- 40A b - 20B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 9 3 8 2 2 7 3 6 +-+ +--R (120b x + 360a b x + 360a b x + 120a b )\|b +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 3 4 5 4 3 +--R (- 1575A a b + 3465B a b )e + (1575A b - 5355B a b )d e +--R + +--R 5 2 2 +--R 1890B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 4725A a b + 10395B a b )e + (4725A a b - 16065B a b )d e +--R + +--R 4 2 2 +--R 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 4725A a b + 10395B a b)e + (4725A a b - 16065B a b )d e +--R + +--R 2 3 2 2 +--R 5670B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 1575A a b + 3465B a )e + (1575A a b - 5355B a b)d e +--R + +--R 3 2 2 2 +--R 1890B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 96B b e x + ((160A b - 352B a b )e + 672B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 1440A a b + 3168B a b )e + (2080A b - 6304B a b )d e +--R + +--R 5 2 2 +--R 3456B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 6930A a b + 15246B a b )e + (9540A a b - 29304B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1650A b + 15078B a b )d e - 1020B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 8400A a b + 18480B a b)e + (11340A a b - 35028B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 1800A a b + 17568B a b )d e + (- 500A b - 1060B a b )d e +--R + +--R 5 4 +--R - 120B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 3150A a b + 6930B a )e + (4200A a b - 13020B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 630A a b + 6426B a b )d e + (- 180A a b - 360B a b )d e +--R + +--R 5 4 4 +--R (- 80A b - 40B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 9 3 8 2 2 7 3 6 +--R 240b x + 720a b x + 720a b x + 240a b +--R , +--R +--R 4 2 3 4 5 4 3 +--R (1575A a b - 3465B a b )e + (- 1575A b + 5355B a b )d e +--R + +--R 5 2 2 +--R - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4725A a b - 10395B a b )e + (- 4725A a b + 16065B a b )d e +--R + +--R 4 2 2 +--R - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (4725A a b - 10395B a b)e + (- 4725A a b + 16065B a b )d e +--R + +--R 2 3 2 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (1575A a b - 3465B a )e + (- 1575A a b + 5355B a b)d e +--R + +--R 3 2 2 2 +--R - 1890B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 48B b e x + ((80A b - 176B a b )e + 336B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 720A a b + 1584B a b )e + (1040A b - 3152B a b )d e +--R + +--R 5 2 2 +--R 1728B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 3465A a b + 7623B a b )e + (4770A a b - 14652B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 825A b + 7539B a b )d e - 510B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 4200A a b + 9240B a b)e + (5670A a b - 17514B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 900A a b + 8784B a b )d e + (- 250A b - 530B a b )d e +--R + +--R 5 4 +--R - 60B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 1575A a b + 3465B a )e + (2100A a b - 6510B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 315A a b + 3213B a b )d e + (- 90A a b - 180B a b )d e +--R + +--R 5 4 4 +--R (- 40A b - 20B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 9 3 8 2 2 7 3 6 +--R 120b x + 360a b x + 360a b x + 120a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 959 + +--S 960 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 2 2 +--R ((- 105A a b + 231B a )e + (105A b - 357B a b)d e + 126B b d e ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 4 2 3 2 2 2 +--R ((- 210A a b + 462B a )e + (210A b - 714B a b)d e + 252B b d e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 4 2 3 2 2 2 +--R ((- 105A a b + 231B a )e + (105A b - 357B a b)d e + 126B b d e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 4 2 3 2 2 2 +-+ +--R ((105A a b - 231B a )e + (- 105A b + 357B a b)d e - 126B b d e )\|b +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 6 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 963 + +)clear all + +--S 964 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1378 +r0:=35/24*e^2*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e))-_ + 7/8*e*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(5/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/4*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^3)-35/8*e^2*(2*b*B*d+_ + A*b*e-3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-_ + a*e)/b^(11/2)+35/8*e^2*(2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 105A b + 315B a b )e - 210B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 315A a b + 945B a b )e - 630B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 315A a b + 945B a b)e - 630B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 105A a b + 315B a )e - 210B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 16B b e x + ((48A b - 144B a b )e + 160B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (231A a b - 693B a b )e + (- 87A b + 723B a b )d e +--R + +--R 4 2 +--R - 78B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (280A a b - 840B a b)e + (- 98A a b + 854B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 38A b - 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (105A a b - 315B a )e + (- 35A a b + 315B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 14A a b - 28B a b )d e + (- 8A b - 4B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +-+ +--R (24b x + 72a b x + 72a b x + 24a b )\|b +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((- 105A b + 315B a b )e - 210B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 315A a b + 945B a b )e - 630B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 315A a b + 945B a b)e - 630B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 105A a b + 315B a )e - 210B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 32B b e x + ((96A b - 288B a b )e + 320B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (462A a b - 1386B a b )e + (- 174A b + 1446B a b )d e +--R + +--R 4 2 +--R - 156B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (560A a b - 1680B a b)e + (- 196A a b + 1708B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 76A b - 164B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 630B a )e + (- 70A a b + 630B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 28A a b - 56B a b )d e + (- 16A b - 8B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +--R 48b x + 144a b x + 144a b x + 48a b +--R , +--R +--R 4 3 3 4 2 3 +--R ((- 105A b + 315B a b )e - 210B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 315A a b + 945B a b )e - 630B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 315A a b + 945B a b)e - 630B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 105A a b + 315B a )e - 210B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 16B b e x + ((48A b - 144B a b )e + 160B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (231A a b - 693B a b )e + (- 87A b + 723B a b )d e +--R + +--R 4 2 +--R - 78B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (280A a b - 840B a b)e + (- 98A a b + 854B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 38A b - 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (105A a b - 315B a )e + (- 35A a b + 315B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 14A a b - 28B a b )d e + (- 8A b - 4B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +--R 24b x + 72a b x + 72a b x + 24a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 966 + +--S 967 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 |- a e + b d +-+ +--R ((- 35A b + 105B a)e - 70B b d e ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 2 +-----------+ \|b \|e x + d +--R ((70A b - 210B a)e + 140B b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 +-----------+ \|b \|e x + d +--R ((35A b - 105B a)e + 70B b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 3 2 +-+ |a e - b d \|e x + d +--R ((- 35A b + 105B a)e - 70B b d e )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1378 +r0:=-5/24*e*(6*b*B*d+A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/12*(6*b*B*d+A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^3)-5/8*e^2*_ + (6*b*B*d+A*b*e-7*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(9/2)*sqrt(b*d-a*e))+5/8*e^2*(6*b*B*d+A*b*e-7*a*B*e)*sqrt(d+e*x)/_ + (b^4*(b*d-a*e)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 15A b + 105B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 45A a b + 315B a b )e - 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 45A a b + 315B a b)e - 270B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 15A a b + 105B a )e - 90B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 48B b e x + ((- 33A b + 231B a b )e - 54B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 40A a b + 280B a b)e + (- 26A b - 58B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (- 15A a b + 105B a )e + (- 10A a b - 20B a b)d e +--R + +--R 3 2 2 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 3 6 2 2 5 3 4 +-----------+ +-+ +--R (24b x + 72a b x + 72a b x + 24a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((15A b - 105B a b )e + 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((45A a b - 315B a b )e + 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((45A a b - 315B a b)e + 270B a b d e )x + (15A a b - 105B a )e +--R + +--R 3 2 +--R 90B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R 96B b e x + ((- 66A b + 462B a b )e - 108B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 80A a b + 560B a b)e + (- 52A b - 116B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (- 30A a b + 210B a )e + (- 20A a b - 40B a b)d e +--R + +--R 3 2 2 +--R (- 16A b - 8B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 7 3 6 2 2 5 3 4 | 2 +--R (48b x + 144a b x + 144a b x + 48a b )\|- a b e + b d +--R , +--R +--R 4 3 3 4 2 3 +--R ((15A b - 105B a b )e + 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((45A a b - 315B a b )e + 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((45A a b - 315B a b)e + 270B a b d e )x + (15A a b - 105B a )e +--R + +--R 3 2 +--R 90B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 48B b e x + ((- 33A b + 231B a b )e - 54B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 40A a b + 280B a b)e + (- 26A b - 58B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (- 15A a b + 105B a )e + (- 10A a b - 20B a b)d e +--R + +--R 3 2 2 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 7 3 6 2 2 5 3 4 | 2 +--R (24b x + 72a b x + 72a b x + 24a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 973 + +--S 974 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R ((5A b - 35B a)e + 30B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((10A b - 70B a)e + 60B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 4 | 2 +-----------+ +-+ +--R 16b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +--S 976 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((5A b - 35B a)e + 30B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 +-----------+ +-+ +--R ((5A b - 35B a)e + 30B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 4 +-----------+ +-+ | 2 +--R 8b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 977 + +)clear all + +--S 978 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1378 +r0:=-1/12*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^3)-1/8*e^2*(6*b*B*d-_ + A*b*e-5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*_ + (b*d-a*e)^(3/2))-1/8*e*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*_ + (b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 3A b - 15B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 9A a b - 45B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 9A a b - 45B a b)e + 54B a b d e )x + (- 3A a b - 15B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b - 33B a b )e + 30B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 8A a b - 40B a b)e + (14A b + 22B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 15B a )e + (- 2A a b + 8B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 6 7 3 2 5 6 2 3 4 2 5 +--R (24a b e - 24b d)x + (72a b e - 72a b d)x + (72a b e - 72a b d)x +--R + +--R 4 3 3 4 +--R 24a b e - 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((3A b + 15B a b )e - 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((9A a b + 45B a b )e - 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((9A a b + 45B a b)e - 54B a b d e )x + (3A a b + 15B a )e +--R + +--R 3 2 +--R - 18B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 2 3 2 +--R ((6A b - 66B a b )e + 60B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 16A a b - 80B a b)e + (28A b + 44B a b )d e + 24B b d )x +--R + +--R 2 3 2 2 2 +--R (- 6A a b - 30B a )e + (- 4A a b + 16B a b)d e +--R + +--R 3 2 2 +--R (16A b + 8B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 6 7 3 2 5 6 2 +--R (48a b e - 48b d)x + (144a b e - 144a b d)x +--R + +--R 3 4 2 5 4 3 3 4 +--R (144a b e - 144a b d)x + 48a b e - 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 3 3 4 2 3 +--R ((3A b + 15B a b )e - 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((9A a b + 45B a b )e - 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((9A a b + 45B a b)e - 54B a b d e )x + (3A a b + 15B a )e +--R + +--R 3 2 +--R - 18B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 2 2 3 2 +--R ((3A b - 33B a b )e + 30B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 8A a b - 40B a b)e + (14A b + 22B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 15B a )e + (- 2A a b + 8B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 6 7 3 2 5 6 2 3 4 2 5 +--R (24a b e - 24b d)x + (72a b e - 72a b d)x + (72a b e - 72a b d)x +--R + +--R 4 3 3 4 +--R 24a b e - 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 980 + +--S 981 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R ((A b + 5B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((2A b + 10B a)e - 12B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 4 | 2 +-----------+ +-+ +--R (16a b e - 16b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((A b + 5B a)e - 6B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 +-----------+ +-+ +--R ((A b + 5B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 3 4 +-----------+ +-+ | 2 +--R (8a b e - 8b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 984 + +)clear all + +--S 985 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1378 +r0:=-1/3*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^3)+1/8*e^2*(2*b*B*d-_ + A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*_ + (b*d-a*e)^(5/2))-1/4*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^2*_ + (b*d-a*e)*(a+b*x)^2)-1/8*e*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 3A b - 3B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 9A a b - 9B a b )e + 18B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 9A a b - 9B a b)e + 18B a b d e )x + (- 3A a b - 3B a )e +--R + +--R 3 2 +--R 6B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b + 3B a b )e - 6B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((8A a b - 8B a b)e + (- 2A b + 14B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 3B a )e + (14A a b + 4B a b)d e + (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 5 2 6 7 2 3 +--R (24a b e - 48a b d e + 24b d )x +--R + +--R 3 4 2 2 5 6 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 2 2 4 3 3 4 2 +--R (72a b e - 144a b d e + 72a b d )x + 24a b e - 48a b d e + 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((3A b + 3B a b )e - 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((9A a b + 9B a b )e - 18B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((9A a b + 9B a b)e - 18B a b d e )x + (3A a b + 3B a )e +--R + +--R 3 2 +--R - 6B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 2 3 2 +--R ((6A b + 6B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((16A a b - 16B a b)e + (- 4A b + 28B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (- 6A a b - 6B a )e + (28A a b + 8B a b)d e +--R + +--R 3 2 2 +--R (- 16A b - 8B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 5 2 6 7 2 3 +--R (48a b e - 96a b d e + 48b d )x +--R + +--R 3 4 2 2 5 6 2 2 +--R (144a b e - 288a b d e + 144a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 2 2 4 3 3 4 2 +--R (144a b e - 288a b d e + 144a b d )x + 48a b e - 96a b d e + 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 3 3 4 2 3 +--R ((3A b + 3B a b )e - 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((9A a b + 9B a b )e - 18B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((9A a b + 9B a b)e - 18B a b d e )x + (3A a b + 3B a )e +--R + +--R 3 2 +--R - 6B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 2 2 3 2 +--R ((3A b + 3B a b )e - 6B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((8A a b - 8B a b)e + (- 2A b + 14B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 3B a )e + (14A a b + 4B a b)d e + (- 8A b - 4B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 5 2 6 7 2 3 +--R (24a b e - 48a b d e + 24b d )x +--R + +--R 3 4 2 2 5 6 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 2 2 4 3 3 4 2 +--R (72a b e - 144a b d e + 72a b d )x + 24a b e - 48a b d e + 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 987 + +--S 988 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R ((A b + B a)e - 2B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((2A b + 2B a)e - 4B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 3 4 2 | 2 +-----------+ +-+ +--R (16a b e - 32a b d e + 16b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((A b + B a)e - 2B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 3 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b + B a)e - 2B b d e )\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 3 4 2 +-----------+ +-+ | 2 +--R (8a b e - 16a b d e + 8b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 990 + +--S 991 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 991 + +)clear all + +--S 992 of 1378 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1378 +r0:=-1/8*e^2*(6*b*B*d-5*A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(7/2))-1/3*(A*b-a*B)*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^3)-1/12*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*(a+b*x)^2)+1/8*e*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 15A b - 3B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 45A a b - 9B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 45A a b - 9B a b)e + 54B a b d e )x + (- 15A a b - 3B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((15A b + 3B a b )e - 18B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((40A a b + 8B a b)e + (- 10A b - 50B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (33A a b - 3B a )e + (- 26A a b - 16B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 6 3 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x + 24a b e +--R + +--R 5 2 2 4 3 2 3 4 3 +--R - 72a b d e + 72a b d e - 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((15A b + 3B a b )e - 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((45A a b + 9B a b )e - 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((45A a b + 9B a b)e - 54B a b d e )x + (15A a b + 3B a )e +--R + +--R 3 2 +--R - 18B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 2 3 2 +--R ((30A b + 6B a b )e - 36B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((80A a b + 16B a b)e + (- 20A b - 100B a b )d e + 24B b d )x +--R + +--R 2 3 2 2 2 +--R (66A a b - 6B a )e + (- 52A a b - 32B a b)d e +--R + +--R 3 2 2 +--R (16A b + 8B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (48a b e - 144a b d e + 144a b d e - 48b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 2 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 6 3 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x + 48a b e +--R + +--R 5 2 2 4 3 2 3 4 3 +--R - 144a b d e + 144a b d e - 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 3 3 4 2 3 +--R ((15A b + 3B a b )e - 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((45A a b + 9B a b )e - 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((45A a b + 9B a b)e - 54B a b d e )x + (15A a b + 3B a )e +--R + +--R 3 2 +--R - 18B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 2 2 3 2 +--R ((15A b + 3B a b )e - 18B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((40A a b + 8B a b)e + (- 10A b - 50B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (33A a b - 3B a )e + (- 26A a b - 16B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 6 3 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x + 24a b e +--R + +--R 5 2 2 4 3 2 3 4 3 +--R - 72a b d e + 72a b d e - 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 994 + +--S 995 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R ((5A b + B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((10A b + 2B a)e - 12B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 3 2 2 2 3 2 4 3 | 2 +--R (16a b e - 48a b d e + 48a b d e - 16b d )\|- a b e + b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((5A b + B a)e - 6B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 +-----------+ +-+ +--R ((5A b + B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 3 3 2 2 2 3 2 4 3 +-----------+ +-+ | 2 +--R (8a b e - 24a b d e + 24a b d e - 8b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 998 + +)clear all + +--S 999 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1378 +r0:=-5/8*e^2*(6*b*B*d-7*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(b))+5/8*e^2*(6*b*B*d-7*A*b*e+_ + a*B*e)/(b*(b*d-a*e)^4*sqrt(d+e*x))+1/3*(-A*b+a*B)/(b*(b*d-a*e)*_ + (a+b*x)^3*sqrt(d+e*x))+1/12*(-6*b*B*d+7*A*b*e-a*B*e)/(b*(b*d-a*e)^2*_ + (a+b*x)^2*sqrt(d+e*x))+5/24*e*(6*b*B*d-7*A*b*e+a*B*e)/(b*(b*d-a*e)^3*_ + (a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((105A b - 15B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((315A a b - 45B a b )e - 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((315A a b - 45B a b)e - 270B a b d e )x + (105A a b - 15B a )e +--R + +--R 3 2 +--R - 90B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 15B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 280A a b + 40B a b)e + (- 35A b + 245B a b )d e +--R + +--R 3 2 +--R 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 231A a b + 33B a )e + (- 98A a b + 212B a b)d e +--R + +--R 3 2 2 3 3 +--R (14A b + 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 48A a e + (- 87A a b + 81B a )d e + (38A a b + 28B a b)d e +--R + +--R 3 2 3 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((105A b - 15B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((315A a b - 45B a b )e - 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((315A a b - 45B a b)e - 270B a b d e )x + (105A a b - 15B a )e +--R + +--R 3 2 +--R - 90B a b d e +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 3 +--R ((- 210A b + 30B a b )e + 180B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 560A a b + 80B a b)e + (- 70A b + 490B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 462A a b + 66B a )e + (- 196A a b + 424B a b)d e +--R + +--R 3 2 2 3 3 +--R (28A b + 164B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 96A a e + (- 174A a b + 162B a )d e + (76A a b + 56B a b)d e +--R + +--R 3 2 3 +--R (- 16A b - 8B a b )d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (48a b e - 192a b d e + 288a b d e - 192a b d e + 48b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 48a e - 192a b d e + 288a b d e - 192a b d e + 48a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 4 3 3 4 2 3 +--R ((- 105A b + 15B a b )e + 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 315A a b + 45B a b )e + 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 315A a b + 45B a b)e + 270B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 105A a b + 15B a )e + 90B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 15B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 280A a b + 40B a b)e + (- 35A b + 245B a b )d e +--R + +--R 3 2 +--R 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 231A a b + 33B a )e + (- 98A a b + 212B a b)d e +--R + +--R 3 2 2 3 3 +--R (14A b + 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 48A a e + (- 87A a b + 81B a )d e + (38A a b + 28B a b)d e +--R + +--R 3 2 3 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1001 + +--S 1002 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R ((35A b - 5B a)e - 30B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((- 70A b + 10B a)e + 60B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 4 4 3 3 2 2 2 2 3 3 4 4 | 2 +--R (16a e - 64a b d e + 96a b d e - 64a b d e + 16b d )\|- a b e + b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((- 35A b + 5B a)e + 30B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 +-----------+ +-+ +--R ((- 35A b + 5B a)e + 30B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +-+ +--R (8a e - 32a b d e + 48a b d e - 32a b d e + 8b d )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1378 +r0:=35/24*e^2*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(3/2))+_ + 1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(3/2))+1/4*(-2*b*B*d+_ + 3*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(3/2))+7/8*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(3/2))-35/8*e^2*(2*b*B*d-_ + 3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-_ + a*e)^(11/2)+35/8*e^2*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 315A b + 105B a b )e + 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 945A a b + 315B a b )e + (- 315A b + 735B a b )d e +--R + +--R 4 2 2 +--R 210B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 945A a b + 315B a b)e + (- 945A a b + 945B a b )d e +--R + +--R 3 2 2 +--R 630B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 315A a b + 105B a )e + (- 945A a b + 525B a b)d e +--R + +--R 2 2 2 2 +--R 630B a b d e +--R * +--R x +--R + +--R 3 4 3 3 2 2 +--R (- 315A a b + 105B a )d e + 210B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((315A b - 105B a b )e - 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (840A a b - 280B a b )e + (420A b - 700B a b )d e +--R + +--R 4 2 2 +--R - 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (693A a b - 231B a b)e + (1134A a b - 840B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (63A b - 777B a b )d e - 42B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 48B a )e + (954A a b - 414B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (180A a b - 696B a b )d e + (- 18A b - 114B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 16A a e + (208A a b - 32B a )d e + (165A a b - 247B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 50A a b - 40B a b )d e + (8A b + 4B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 8 5 +--R - 24b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b e - 336a b d e + 600a b d e - 480a b d e + 120a b d e +--R + +--R 7 5 8 6 +--R 48a b d e - 24b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b e - 288a b d e + 360a b d e - 360a b d e + 288a b d e +--R + +--R 7 6 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a e - 48a b d e - 120a b d e + 480a b d e - 600a b d e +--R + +--R 3 5 5 2 6 6 +--R 336a b d e - 72a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 3 5 6 +--R - 24a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 4 4 3 4 +--R ((315A b - 105B a b )e - 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (945A a b - 315B a b )e + (315A b - 735B a b )d e +--R + +--R 4 2 2 +--R - 210B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 315B a b)e + (945A a b - 945B a b )d e +--R + +--R 3 2 2 +--R - 630B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (315A a b - 105B a )e + (945A a b - 525B a b)d e +--R + +--R 2 2 2 2 +--R - 630B a b d e +--R * +--R x +--R + +--R 3 4 3 3 2 2 +--R (315A a b - 105B a )d e - 210B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 4 3 4 +--R ((630A b - 210B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1680A a b - 560B a b )e + (840A b - 1400B a b )d e +--R + +--R 4 2 2 +--R - 560B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (1386A a b - 462B a b)e + (2268A a b - 1680B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (126A b - 1554B a b )d e - 84B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (288A a b - 96B a )e + (1908A a b - 828B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (360A a b - 1392B a b )d e + (- 36A b - 228B a b )d e + 24B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 32A a e + (416A a b - 64B a )d e + (330A a b - 494B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 100A a b - 80B a b )d e + (16A b + 8B a b )d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 +--R 144a b e - 672a b d e + 1200a b d e - 960a b d e +--R + +--R 2 6 4 2 7 5 8 6 +--R 240a b d e + 96a b d e - 48b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 144a b e - 576a b d e + 720a b d e - 720a b d e + 576a b d e +--R + +--R 7 6 +--R - 144a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 48a e - 96a b d e - 240a b d e + 960a b d e - 1200a b d e +--R + +--R 3 5 5 2 6 6 +--R 672a b d e - 144a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 5 6 +--R - 48a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 3 4 4 3 4 +--R ((315A b - 105B a b )e - 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (945A a b - 315B a b )e + (315A b - 735B a b )d e +--R + +--R 4 2 2 +--R - 210B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 315B a b)e + (945A a b - 945B a b )d e +--R + +--R 3 2 2 +--R - 630B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (315A a b - 105B a )e + (945A a b - 525B a b)d e +--R + +--R 2 2 2 2 +--R - 630B a b d e +--R * +--R x +--R + +--R 3 4 3 3 2 2 +--R (315A a b - 105B a )d e - 210B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((315A b - 105B a b )e - 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((840A a b - 280B a b )e + (420A b - 700B a b )d e - 280B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (693A a b - 231B a b)e + (1134A a b - 840B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (63A b - 777B a b )d e - 42B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 48B a )e + (954A a b - 414B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (180A a b - 696B a b )d e + (- 18A b - 114B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 16A a e + (208A a b - 32B a )d e + (165A a b - 247B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 50A a b - 40B a b )d e + (8A b + 4B a b )d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 8 5 +--R - 24b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b e - 336a b d e + 600a b d e - 480a b d e + 120a b d e +--R + +--R 7 5 8 6 +--R 48a b d e - 24b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b e - 288a b d e + 360a b d e - 360a b d e + 288a b d e +--R + +--R 7 6 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a e - 48a b d e - 120a b d e + 480a b d e - 600a b d e +--R + +--R 3 5 5 2 6 6 +--R 336a b d e - 72a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 3 5 6 +--R - 24a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1008 + +--S 1009 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 +-----------+ | b +--R ((105A b - 35B a)e - 70B b d e )\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 2 +-+ \|b \|e x + d +--R ((210A b - 70B a)e - 140B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (16a e - 80a b d e + 160a b d e - 160a b d e + 80a b d e - 16b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 +-+ \|b \|e x + d +--R ((105A b - 35B a)e - 70B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 3 2 +-----------+ | b +--R ((105A b - 35B a)e - 70B b d e )\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (8a e - 40a b d e + 80a b d e - 80a b d e + 40a b d e - 8b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1012 + +)clear all + +--S 1013 of 1378 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1378 +r0:=21/40*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(5/2))+_ + 1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(5/2))+1/12*(-6*b*B*d+_ + 11*A*b*e-5*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(5/2))+3/8*e*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(5/2))+7/8*e^2*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)/((b*d-a*e)^5*(d+e*x)^(3/2))-21/8*b^(3/2)*e^2*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b*d-a*e)^(13/2)+21/8*b*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/((b*d-a*e)^6*_ + sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((3465A b - 1575B a b )e - 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (10395A a b - 4725B a b )e + (6930A b - 8820B a b )d e +--R + +--R 5 2 3 +--R - 3780B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (10395A a b - 4725B a b )e + (20790A a b - 15120B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (3465A b - 12915B a b )d e - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (3465A a b - 1575B a b)e + (20790A a b - 11340B a b )d e +--R + +--R 4 2 3 2 3 4 3 2 +--R (10395A a b - 16065B a b )d e - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 2 3 +--R (6930A a b - 3150B a b)d e + (10395A a b - 8505B a b )d e +--R + +--R 2 3 3 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 2 3 2 +--R (3465A a b - 1575B a b)d e - 1890B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 1575B a b )e + 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 9240A a b + 4200B a b )e + (- 8085A b + 8715B a b )d e +--R + +--R 5 2 3 +--R 4410B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 7623A a b + 3465B a b )e + (- 21714A a b + 14028B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 5313A b + 14259B a b )d e + 2898B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 1584A a b + 720B a b)e + (- 18117A a b + 9099B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 14454A a b + 16452B a b )d e + (- 495A b + 8109B a b )d e +--R + +--R 5 4 +--R 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (176A a b - 80B a )e + (- 3872A a b + 1664B a b)d e +--R + +--R 2 3 3 2 2 3 +--R (- 12309A a b + 7707B a b )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 1430A a b + 7364B a b )d e + (110A b + 730B a b )d e +--R + +--R 5 5 +--R - 60B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 48A a e + (416A a b - 32B a )d e + (- 2768A a b + 704B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 1335A a b + 2553B a b )d e + (310A a b + 260B a b )d e +--R + +--R 5 4 5 +--R (- 40A b - 20B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 120a b e - 720a b d e + 1800a b d e - 2400a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 1800a b d e - 720a b d e + 120b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 360a b e - 1920a b d e + 3960a b d e - 3600a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 600a b d e + 1440a b d e - 1080a b d e + 240b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 360a b e - 1440a b d e + 1200a b d e + 2880a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 7200a b d e + 6240a b d e - 2160a b d e + 120b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 4 5 5 3 +--R 120a e - 2160a b d e + 6240a b d e - 7200a b d e + 2880a b d e +--R + +--R 3 6 6 2 2 7 7 8 8 +--R 1200a b d e - 1440a b d e + 360a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 +--R 240a d e - 1080a b d e + 1440a b d e + 600a b d e +--R + +--R 5 4 5 3 4 5 6 2 3 6 7 2 7 8 +--R - 3600a b d e + 3960a b d e - 1920a b d e + 360a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 120a d e - 720a b d e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 5 7 3 6 8 +--R - 720a b d e + 120a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 5 5 4 5 +--R ((3465A b - 1575B a b )e - 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (10395A a b - 4725B a b )e + (6930A b - 8820B a b )d e +--R + +--R 5 2 3 +--R - 3780B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (10395A a b - 4725B a b )e + (20790A a b - 15120B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (3465A b - 12915B a b )d e - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (3465A a b - 1575B a b)e + (20790A a b - 11340B a b )d e +--R + +--R 4 2 3 2 3 4 3 2 +--R (10395A a b - 16065B a b )d e - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 2 3 +--R (6930A a b - 3150B a b)d e + (10395A a b - 8505B a b )d e +--R + +--R 2 3 3 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 2 3 2 +--R (3465A a b - 1575B a b)d e - 1890B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 5 5 4 5 +--R ((- 6930A b + 3150B a b )e + 3780B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 18480A a b + 8400B a b )e + (- 16170A b + 17430B a b )d e +--R + +--R 5 2 3 +--R 8820B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 15246A a b + 6930B a b )e + (- 43428A a b + 28056B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 10626A b + 28518B a b )d e + 5796B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 3168A a b + 1440B a b)e + (- 36234A a b + 18198B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 28908A a b + 32904B a b )d e + (- 990A b + 16218B a b )d e +--R + +--R 5 4 +--R 540B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (352A a b - 160B a )e + (- 7744A a b + 3328B a b)d e +--R + +--R 2 3 3 2 2 3 +--R (- 24618A a b + 15414B a b )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 2860A a b + 14728B a b )d e + (220A b + 1460B a b )d e +--R + +--R 5 5 +--R - 120B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 96A a e + (832A a b - 64B a )d e + (- 5536A a b + 1408B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 2670A a b + 5106B a b )d e + (620A a b + 520B a b )d e +--R + +--R 5 4 5 +--R (- 80A b - 40B a b )d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 240a b e - 1440a b d e + 3600a b d e - 4800a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 3600a b d e - 1440a b d e + 240b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 720a b e - 3840a b d e + 7920a b d e - 7200a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 1200a b d e + 2880a b d e - 2160a b d e + 480b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 720a b e - 2880a b d e + 2400a b d e + 5760a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 14400a b d e + 12480a b d e - 4320a b d e + 240b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 +--R 240a e - 4320a b d e + 12480a b d e - 14400a b d e +--R + +--R 4 5 5 3 3 6 6 2 2 7 7 8 8 +--R 5760a b d e + 2400a b d e - 2880a b d e + 720a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 +--R 480a d e - 2160a b d e + 2880a b d e + 1200a b d e +--R + +--R 5 4 5 3 4 5 6 2 3 6 7 2 7 8 +--R - 7200a b d e + 7920a b d e - 3840a b d e + 720a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 240a d e - 1440a b d e + 3600a b d e - 4800a b d e + 3600a b d e +--R + +--R 4 5 7 3 6 8 +--R - 1440a b d e + 240a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 5 4 5 5 4 5 +--R ((- 3465A b + 1575B a b )e + 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 10395A a b + 4725B a b )e + (- 6930A b + 8820B a b )d e +--R + +--R 5 2 3 +--R 3780B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 +--R (- 10395A a b + 4725B a b )e +--R + +--R 4 2 3 4 +--R (- 20790A a b + 15120B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 3465A b + 12915B a b )d e + 1890B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 +--R (- 3465A a b + 1575B a b)e +--R + +--R 2 3 3 2 4 +--R (- 20790A a b + 11340B a b )d e +--R + +--R 4 2 3 2 3 4 3 2 +--R (- 10395A a b + 16065B a b )d e + 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 +--R (- 6930A a b + 3150B a b)d e +--R + +--R 2 3 3 2 2 3 2 3 3 2 +--R (- 10395A a b + 8505B a b )d e + 5670B a b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 2 3 2 +--R (- 3465A a b + 1575B a b)d e + 1890B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 1575B a b )e + 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 9240A a b + 4200B a b )e + (- 8085A b + 8715B a b )d e +--R + +--R 5 2 3 +--R 4410B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 7623A a b + 3465B a b )e + (- 21714A a b + 14028B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 5313A b + 14259B a b )d e + 2898B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 1584A a b + 720B a b)e + (- 18117A a b + 9099B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 14454A a b + 16452B a b )d e + (- 495A b + 8109B a b )d e +--R + +--R 5 4 +--R 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (176A a b - 80B a )e + (- 3872A a b + 1664B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 12309A a b + 7707B a b )d e + (- 1430A a b + 7364B a b )d e +--R + +--R 5 4 4 5 5 +--R (110A b + 730B a b )d e - 60B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 48A a e + (416A a b - 32B a )d e + (- 2768A a b + 704B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 1335A a b + 2553B a b )d e + (310A a b + 260B a b )d e +--R + +--R 5 4 5 +--R (- 40A b - 20B a b )d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 120a b e - 720a b d e + 1800a b d e - 2400a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 1800a b d e - 720a b d e + 120b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 360a b e - 1920a b d e + 3960a b d e - 3600a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 600a b d e + 1440a b d e - 1080a b d e + 240b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 360a b e - 1440a b d e + 1200a b d e + 2880a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 7200a b d e + 6240a b d e - 2160a b d e + 120b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 +--R 120a e - 2160a b d e + 6240a b d e - 7200a b d e +--R + +--R 4 5 5 3 3 6 6 2 2 7 7 8 8 +--R 2880a b d e + 1200a b d e - 1440a b d e + 360a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 +--R 240a d e - 1080a b d e + 1440a b d e + 600a b d e +--R + +--R 5 4 5 3 4 5 6 2 3 6 7 2 7 8 +--R - 3600a b d e + 3960a b d e - 1920a b d e + 360a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 120a d e - 720a b d e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 5 7 3 6 8 +--R - 720a b d e + 120a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1015 + +--S 1016 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 3 2 2 +-----------+ | b +--R ((231A b - 105B a b)e - 126B b d e )\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 3 2 2 +-+ \|b \|e x + d +--R ((- 462A b + 210B a b)e + 252B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 16a e - 96a b d e + 240a b d e - 320a b d e + 240a b d e +--R + +--R 5 5 6 6 +--R - 96a b d e + 16b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 3 2 2 +-+ \|b \|e x + d +--R ((- 231A b + 105B a b)e + 126B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 3 2 2 +-----------+ | b +--R ((- 231A b + 105B a b)e + 126B b d e )\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 8a e - 48a b d e + 120a b d e - 160a b d e + 120a b d e +--R + +--R 5 5 6 6 +--R - 48a b d e + 8b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1019 + +)clear all + +--S 1020 of 1378 +t0:=(A+B*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1378 +r0:=77/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(3/2)/(b^6*(b*d-a*e))-_ + 231/640*e^3*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(5/2)/(b^5*(b*d-a*e)*_ + (a+b*x))-33/320*e^2*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(7/2)/(b^4*_ + (b*d-a*e)*(a+b*x)^2)-11/240*e*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(9/2)/_ + (b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d+3*A*b*e-13*a*B*e)*_ + (d+e*x)^(11/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(13/2)/_ + (b*(b*d-a*e)*(a+b*x)^5)-231/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(15/2)+_ + 231/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*sqrt(d+e*x)/b^7 +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 10395A b + 45045B a b )e - 34650B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 51975A a b + 225225B a b )e - 173250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 51975A a b + 225225B a b)e - 173250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 10395A a b + 45045B a )e - 34650B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 1280B b e x + ((3840A b - 16640B a b )e + 20480B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (31845A a b - 137995B a b )e + (- 12645A b + 160945B a b )d e +--R + +--R 6 2 3 +--R - 22950B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (78210A a b - 338910B a b )e +--R + +--R 5 2 4 4 +--R (- 29040A a b + 386540B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 10770A b - 50130B a b )d e - 10300B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (88704A a b - 384384B a b )e +--R + +--R 2 4 3 3 4 +--R (- 31482A a b + 432102B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 12078A a b - 52602B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 6744A b - 11036B a b )d e - 3280B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (48510A a b - 210210B a b)e +--R + +--R 3 3 4 2 4 +--R (- 16632A a b + 233772B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 6534A a b - 27126B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3696A a b - 5764B a b )d e + (- 2448A b - 1712B a b )d e +--R + +--R 6 5 +--R - 480B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (10395A a b - 45045B a )e + (- 3465A a b + 49665B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 1386A a b - 5544B a b )d e + (- 792A a b - 1188B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 528A a b - 352B a b )d e + (- 384A b - 96B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 +--R 1920b x + 9600a b x + 19200a b x + 19200a b x + 9600a b x +--R + +--R 5 7 +--R 1920a b +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((- 10395A b + 45045B a b )e - 34650B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 51975A a b + 225225B a b )e - 173250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 51975A a b + 225225B a b)e - 173250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 10395A a b + 45045B a )e - 34650B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 2560B b e x + ((7680A b - 33280B a b )e + 40960B b d e )x +--R + +--R 5 2 4 5 +--R (63690A a b - 275990B a b )e +--R + +--R 6 5 4 6 2 3 +--R (- 25290A b + 321890B a b )d e - 45900B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (156420A a b - 677820B a b )e +--R + +--R 5 2 4 4 +--R (- 58080A a b + 773080B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 21540A b - 100260B a b )d e - 20600B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (177408A a b - 768768B a b )e +--R + +--R 2 4 3 3 4 +--R (- 62964A a b + 864204B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 24156A a b - 105204B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 13488A b - 22072B a b )d e - 6560B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (97020A a b - 420420B a b)e +--R + +--R 3 3 4 2 4 +--R (- 33264A a b + 467544B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 13068A a b - 54252B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 7392A a b - 11528B a b )d e + (- 4896A b - 3424B a b )d e +--R + +--R 6 5 +--R - 960B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (20790A a b - 90090B a )e + (- 6930A a b + 99330B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 2772A a b - 11088B a b )d e + (- 1584A a b - 2376B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 1056A a b - 704B a b )d e + (- 768A b - 192B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 +--R 3840b x + 19200a b x + 38400a b x + 38400a b x + 19200a b x +--R + +--R 5 7 +--R 3840a b +--R , +--R +--R 6 5 5 6 4 5 +--R ((- 10395A b + 45045B a b )e - 34650B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 51975A a b + 225225B a b )e - 173250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 51975A a b + 225225B a b)e - 173250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 10395A a b + 45045B a )e - 34650B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 1280B b e x + ((3840A b - 16640B a b )e + 20480B b d e )x +--R + +--R 5 2 4 5 +--R (31845A a b - 137995B a b )e +--R + +--R 6 5 4 6 2 3 +--R (- 12645A b + 160945B a b )d e - 22950B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (78210A a b - 338910B a b )e +--R + +--R 5 2 4 4 +--R (- 29040A a b + 386540B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 10770A b - 50130B a b )d e - 10300B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (88704A a b - 384384B a b )e +--R + +--R 2 4 3 3 4 +--R (- 31482A a b + 432102B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 12078A a b - 52602B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 6744A b - 11036B a b )d e - 3280B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (48510A a b - 210210B a b)e +--R + +--R 3 3 4 2 4 +--R (- 16632A a b + 233772B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 6534A a b - 27126B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3696A a b - 5764B a b )d e + (- 2448A b - 1712B a b )d e +--R + +--R 6 5 +--R - 480B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (10395A a b - 45045B a )e + (- 3465A a b + 49665B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 1386A a b - 5544B a b )d e + (- 792A a b - 1188B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 528A a b - 352B a b )d e + (- 384A b - 96B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 +--R 1920b x + 9600a b x + 19200a b x + 19200a b x + 9600a b x +--R + +--R 5 7 +--R 1920a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1022 + +--S 1023 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 5 4 |- a e + b d +-+ +--R ((- 693A b + 3003B a)e - 2310B b d e ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 5 4 +-----------+ \|b \|e x + d +--R ((1386A b - 6006B a)e + 4620B b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 +-+ +--R 256b \|b +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 5 4 +-----------+ \|b \|e x + d +--R ((693A b - 3003B a)e + 2310B b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 5 4 +-+ |a e - b d \|e x + d +--R ((- 693A b + 3003B a)e - 2310B b d e )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 7 +-+ +--R 128b \|b +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1026 + +)clear all + +--S 1027 of 1378 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1378 +r0:=-21/128*e^3*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(3/2)/(b^5*(b*d-a*e)*_ + (a+b*x))-21/320*e^2*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*_ + (b*d-a*e)*(a+b*x)^2)-3/80*e*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(7/2)/_ + (b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d+A*b*e-11*a*B*e)*_ + (d+e*x)^(9/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(11/2)/_ + (b*(b*d-a*e)*(a+b*x)^5)-63/128*e^4*(10*b*B*d+A*b*e-11*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(13/2)*sqrt(b*d-a*e))+_ + 63/128*e^4*(10*b*B*d+A*b*e-11*a*B*e)*sqrt(d+e*x)/(b^6*(b*d-a*e)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 315A b + 3465B a b )e - 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 1575A a b + 17325B a b )e - 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 3150A a b + 34650B a b )e - 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 3150A a b + 34650B a b )e - 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 1575A a b + 17325B a b)e - 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 315A a b + 3465B a )e - 3150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 1280B b e x + ((- 965A b + 10615B a b )e - 3250B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 2370A a b + 26070B a b )e + (- 1490A b - 7310B a b )d e +--R + +--R 5 2 2 +--R - 2100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 2688A a b + 29568B a b )e + (- 1734A a b - 7806B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1368A b - 2292B a b )d e - 880B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 1470A a b + 16170B a b)e + (- 966A a b - 4074B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 768A a b - 1212B a b )d e + (- 656A b - 464B a b )d e +--R + +--R 5 4 +--R - 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 315A a b + 3465B a )e + (- 210A a b - 840B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 168A a b - 252B a b )d e + (- 144A a b - 96B a b )d e +--R + +--R 5 4 4 +--R (- 128A b - 32B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R (640b x + 3200a b x + 6400a b x + 6400a b x + 3200a b x + 640a b ) +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((315A b - 3465B a b )e + 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((1575A a b - 17325B a b )e + 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((3150A a b - 34650B a b )e + 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((3150A a b - 34650B a b )e + 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((1575A a b - 17325B a b)e + 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (315A a b - 3465B a )e + 3150B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2560B b e x + ((- 1930A b + 21230B a b )e - 6500B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 4740A a b + 52140B a b )e + (- 2980A b - 14620B a b )d e +--R + +--R 5 2 2 +--R - 4200B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 +--R (- 5376A a b + 59136B a b )e +--R + +--R 4 2 3 3 +--R (- 3468A a b - 15612B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 2736A b - 4584B a b )d e - 1760B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 2940A a b + 32340B a b)e + (- 1932A a b - 8148B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 1536A a b - 2424B a b )d e + (- 1312A b - 928B a b )d e +--R + +--R 5 4 +--R - 320B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 630A a b + 6930B a )e + (- 420A a b - 1680B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 336A a b - 504B a b )d e + (- 288A a b - 192B a b )d e +--R + +--R 5 4 4 +--R (- 256A b - 64B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 +--R 1280b x + 6400a b x + 12800a b x + 12800a b x + 6400a b x +--R + +--R 5 6 +--R 1280a b +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 6 5 5 6 4 5 +--R ((315A b - 3465B a b )e + 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((1575A a b - 17325B a b )e + 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((3150A a b - 34650B a b )e + 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((3150A a b - 34650B a b )e + 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((1575A a b - 17325B a b)e + 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (315A a b - 3465B a )e + 3150B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 1280B b e x + ((- 965A b + 10615B a b )e - 3250B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 2370A a b + 26070B a b )e + (- 1490A b - 7310B a b )d e +--R + +--R 5 2 2 +--R - 2100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 +--R (- 2688A a b + 29568B a b )e +--R + +--R 4 2 3 3 5 4 2 2 +--R (- 1734A a b - 7806B a b )d e + (- 1368A b - 2292B a b )d e +--R + +--R 5 3 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 1470A a b + 16170B a b)e + (- 966A a b - 4074B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 768A a b - 1212B a b )d e + (- 656A b - 464B a b )d e +--R + +--R 5 4 +--R - 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 315A a b + 3465B a )e + (- 210A a b - 840B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 168A a b - 252B a b )d e + (- 144A a b - 96B a b )d e +--R + +--R 5 4 4 +--R (- 128A b - 32B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 +--R 640b x + 3200a b x + 6400a b x + 6400a b x + 3200a b x +--R + +--R 5 6 +--R 640a b +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1029 + +--S 1030 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((63A b - 693B a)e + 630B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((126A b - 1386B a)e + 1260B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 6 | 2 +-----------+ +-+ +--R 256b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((63A b - 693B a)e + 630B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((63A b - 693B a)e + 630B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 6 +-----------+ +-+ | 2 +--R 128b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1033 + +)clear all + +--S 1034 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1378 +r0:=-7/192*e^2*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e)*_ + (a+b*x)^2)-7/240*e*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(5/2)/(b^3*_ + (b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(7/2)/_ + (b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*_ + (a+b*x)^5)-7/128*e^4*(10*b*B*d-A*b*e-9*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(11/2)*(b*d-a*e)^(3/2))-_ + 7/128*e^3*(10*b*B*d-A*b*e-9*a*B*e)*sqrt(d+e*x)/(b^5*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 105A b - 945B a b )e + 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 525A a b - 4725B a b )e + 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 1050A a b - 9450B a b )e + 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 1050A a b - 9450B a b )e + 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 525A a b - 4725B a b)e + 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 105A a b - 945B a )e + 1050B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b - 2895B a b )e + 2790B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 790A a b - 7110B a b )e + (1210A b + 3430B a b )d e +--R + +--R 5 2 2 +--R 3260B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 896A a b - 8064B a b )e + (- 578A a b + 3758B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (2104A b + 1676B a b )d e + 2000B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 490A a b - 4410B a b)e + (- 322A a b + 2002B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 256A a b + 916B a b )d e + (1488A b + 592B a b )d e +--R + +--R 5 4 +--R 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 945B a )e + (- 70A a b + 420B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 56A a b + 196B a b )d e + (- 48A a b + 128B a b )d e +--R + +--R 5 4 4 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 10 11 5 2 9 10 4 +--R (1920a b e - 1920b d)x + (9600a b e - 9600a b d)x +--R + +--R 3 8 2 9 3 4 7 3 8 2 +--R (19200a b e - 19200a b d)x + (19200a b e - 19200a b d)x +--R + +--R 5 6 4 7 6 5 5 6 +--R (9600a b e - 9600a b d)x + 1920a b e - 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((105A b + 945B a b )e - 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((525A a b + 4725B a b )e - 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((1050A a b + 9450B a b )e - 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((1050A a b + 9450B a b )e - 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((525A a b + 4725B a b)e - 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (105A a b + 945B a )e - 1050B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 4 5 3 4 +--R ((210A b - 5790B a b )e + 5580B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 1580A a b - 14220B a b )e + (2420A b + 6860B a b )d e +--R + +--R 5 2 2 +--R 6520B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 +--R (- 1792A a b - 16128B a b )e +--R + +--R 4 2 3 3 5 4 2 2 +--R (- 1156A a b + 7516B a b )d e + (4208A b + 3352B a b )d e +--R + +--R 5 3 +--R 4000B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 980A a b - 8820B a b)e + (- 644A a b + 4004B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 512A a b + 1832B a b )d e + (2976A b + 1184B a b )d e +--R + +--R 5 4 +--R 960B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 210A a b - 1890B a )e + (- 140A a b + 840B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 112A a b + 392B a b )d e + (- 96A a b + 256B a b )d e +--R + +--R 5 4 4 +--R (768A b + 192B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 10 11 5 2 9 10 4 +--R (3840a b e - 3840b d)x + (19200a b e - 19200a b d)x +--R + +--R 3 8 2 9 3 4 7 3 8 2 +--R (38400a b e - 38400a b d)x + (38400a b e - 38400a b d)x +--R + +--R 5 6 4 7 6 5 5 6 +--R (19200a b e - 19200a b d)x + 3840a b e - 3840a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 6 5 5 6 4 5 +--R ((105A b + 945B a b )e - 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((525A a b + 4725B a b )e - 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((1050A a b + 9450B a b )e - 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((1050A a b + 9450B a b )e - 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((525A a b + 4725B a b)e - 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (105A a b + 945B a )e - 1050B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b - 2895B a b )e + 2790B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 790A a b - 7110B a b )e + (1210A b + 3430B a b )d e +--R + +--R 5 2 2 +--R 3260B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 896A a b - 8064B a b )e + (- 578A a b + 3758B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (2104A b + 1676B a b )d e + 2000B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 490A a b - 4410B a b)e + (- 322A a b + 2002B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 256A a b + 916B a b )d e + (1488A b + 592B a b )d e +--R + +--R 5 4 +--R 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 945B a )e + (- 70A a b + 420B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 56A a b + 196B a b )d e + (- 48A a b + 128B a b )d e +--R + +--R 5 4 4 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 10 11 5 2 9 10 4 +--R (1920a b e - 1920b d)x + (9600a b e - 9600a b d)x +--R + +--R 3 8 2 9 3 4 7 3 8 2 +--R (19200a b e - 19200a b d)x + (19200a b e - 19200a b d)x +--R + +--R 5 6 4 7 6 5 5 6 +--R (9600a b e - 9600a b d)x + 1920a b e - 1920a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1036 + +--S 1037 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((7A b + 63B a)e - 70B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((14A b + 126B a)e - 140B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 5 6 | 2 +-----------+ +-+ +--R (256a b e - 256b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((7A b + 63B a)e - 70B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((7A b + 63B a)e - 70B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 5 6 +-----------+ +-+ | 2 +--R (128a b e - 128b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1040 + +)clear all + +--S 1041 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1378 +r0:=-1/48*e*(10*b*B*d-3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*_ + (a+b*x)^3)-1/40*(10*b*B*d-3*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-_ + a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^5)+_ + 1/128*e^4*(10*b*B*d-3*A*b*e-7*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(9/2)*(b*d-a*e)^(5/2))-1/64*e^2*(10*b*B*d-_ + 3*A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)*(a+b*x)^2)-_ + 1/128*e^3*(10*b*B*d-3*A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 45A b - 105B a b )e + 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 225A a b - 525B a b )e + 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 450A a b - 1050B a b )e + 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 450A a b - 1050B a b )e + 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 225A a b - 525B a b)e + 750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 45A a b - 105B a )e + 150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((45A b + 105B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (210A a b - 790B a b )e + (- 30A b + 1790B a b )d e +--R + +--R 5 2 2 +--R - 1180B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 384A a b - 896B a b )e + (1398A a b + 702B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 744A b + 1284B a b )d e - 1360B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 210A a b - 490B a b)e + (- 138A a b + 378B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (1536A a b + 204B a b )d e + (- 1008A b + 208B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 45A a b - 105B a )e + (- 30A a b + 80B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 24A a b + 44B a b )d e + (528A a b + 32B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 9 2 10 11 2 5 +--R (1920a b e - 3840a b d e + 1920b d )x +--R + +--R 3 8 2 2 9 10 2 4 +--R (9600a b e - 19200a b d e + 9600a b d )x +--R + +--R 4 7 2 3 8 2 9 2 3 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 5 6 2 4 7 3 8 2 2 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 6 5 2 5 6 4 7 2 7 4 2 6 5 +--R (9600a b e - 19200a b d e + 9600a b d )x + 1920a b e - 3840a b d e +--R + +--R 5 6 2 +--R 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((45A b + 105B a b )e - 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((225A a b + 525B a b )e - 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((450A a b + 1050B a b )e - 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((450A a b + 1050B a b )e - 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((225A a b + 525B a b)e - 750B a b d e )x + (45A a b + 105B a )e +--R + +--R 5 4 +--R - 150B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 4 5 3 4 +--R ((90A b + 210B a b )e - 300B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (420A a b - 1580B a b )e + (- 60A b + 3580B a b )d e +--R + +--R 5 2 2 +--R - 2360B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 768A a b - 1792B a b )e + (2796A a b + 1404B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1488A b + 2568B a b )d e - 2720B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 420A a b - 980B a b)e + (- 276A a b + 756B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (3072A a b + 408B a b )d e + (- 2016A b + 416B a b )d e +--R + +--R 5 4 +--R - 960B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 90A a b - 210B a )e + (- 60A a b + 160B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 48A a b + 88B a b )d e + (1056A a b + 64B a b )d e +--R + +--R 5 4 4 +--R (- 768A b - 192B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 9 2 10 11 2 5 +--R (3840a b e - 7680a b d e + 3840b d )x +--R + +--R 3 8 2 2 9 10 2 4 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 4 7 2 3 8 2 9 2 3 +--R (38400a b e - 76800a b d e + 38400a b d )x +--R + +--R 5 6 2 4 7 3 8 2 2 +--R (38400a b e - 76800a b d e + 38400a b d )x +--R + +--R 6 5 2 5 6 4 7 2 7 4 2 +--R (19200a b e - 38400a b d e + 19200a b d )x + 3840a b e +--R + +--R 6 5 5 6 2 +--R - 7680a b d e + 3840a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 6 5 5 6 4 5 +--R ((45A b + 105B a b )e - 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((225A a b + 525B a b )e - 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((450A a b + 1050B a b )e - 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((450A a b + 1050B a b )e - 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((225A a b + 525B a b)e - 750B a b d e )x + (45A a b + 105B a )e +--R + +--R 5 4 +--R - 150B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 5 4 4 5 3 4 +--R ((45A b + 105B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (210A a b - 790B a b )e + (- 30A b + 1790B a b )d e +--R + +--R 5 2 2 +--R - 1180B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 384A a b - 896B a b )e + (1398A a b + 702B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 744A b + 1284B a b )d e - 1360B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 210A a b - 490B a b)e + (- 138A a b + 378B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (1536A a b + 204B a b )d e + (- 1008A b + 208B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 45A a b - 105B a )e + (- 30A a b + 80B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 24A a b + 44B a b )d e + (528A a b + 32B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 9 2 10 11 2 5 +--R (1920a b e - 3840a b d e + 1920b d )x +--R + +--R 3 8 2 2 9 10 2 4 +--R (9600a b e - 19200a b d e + 9600a b d )x +--R + +--R 4 7 2 3 8 2 9 2 3 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 5 6 2 4 7 3 8 2 2 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 6 5 2 5 6 4 7 2 7 4 2 6 5 +--R (9600a b e - 19200a b d e + 9600a b d )x + 1920a b e - 3840a b d e +--R + +--R 5 6 2 +--R 1920a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1043 + +--S 1044 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((3A b + 7B a)e - 10B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((6A b + 14B a)e - 20B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 4 2 5 6 2 | 2 +-----------+ +-+ +--R (256a b e - 512a b d e + 256b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((3A b + 7B a)e - 10B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((3A b + 7B a)e - 10B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 4 2 5 6 2 +-----------+ +-+ | 2 +--R (128a b e - 256a b d e + 128b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1047 + +)clear all + +--S 1048 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1378 +r0:=-1/8*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-_ + 1/5*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^5)-3/128*e^4*(2*b*B*d-_ + A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-_ + a*e)^(7/2))-1/16*e*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)*_ + (a+b*x)^3)-1/64*e^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)^2*_ + (a+b*x)^2)+3/128*e^3*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*_ + (b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 15A b - 15B a b )e + 30B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 75A a b - 75B a b )e + 150B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 150A a b - 150B a b )e + 300B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 150A a b - 150B a b )e + 300B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((- 75A a b - 75B a b)e + 150B a b d e )x + (- 15A a b - 15B a )e +--R + +--R 5 4 +--R 30B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((15A b + 15B a b )e - 30B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((70A a b + 70B a b )e + (- 10A b - 150B a b )d e + 20B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (128A a b - 128B a b )e + (- 46A a b + 466B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (8A b - 668B a b )d e + 240B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 70A a b - 70B a b)e + (466A a b + 94B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 512A a b + 92B a b )d e + (176A b - 336B a b )d e + 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 15A a b - 15B a )e + (- 10A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (248A a b + 12B a b )d e + (- 336A a b - 64B a b )d e +--R + +--R 5 4 4 +--R (128A b + 32B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 8 3 2 9 2 10 2 11 3 5 +--R (640a b e - 1920a b d e + 1920a b d e - 640b d )x +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 4 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x +--R + +--R 5 6 3 4 7 2 3 8 2 2 9 3 3 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 6 5 3 5 6 2 4 7 2 3 8 3 2 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 7 4 3 6 5 2 5 6 2 4 7 3 8 3 3 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x + 640a b e +--R + +--R 7 4 2 6 5 2 5 6 3 +--R - 1920a b d e + 1920a b d e - 640a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((15A b + 15B a b )e - 30B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((75A a b + 75B a b )e - 150B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((150A a b + 150B a b )e - 300B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((150A a b + 150B a b )e - 300B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((75A a b + 75B a b)e - 150B a b d e )x + (15A a b + 15B a )e +--R + +--R 5 4 +--R - 30B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 4 5 3 4 +--R ((30A b + 30B a b )e - 60B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (140A a b + 140B a b )e + (- 20A b - 300B a b )d e +--R + +--R 5 2 2 +--R 40B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (256A a b - 256B a b )e + (- 92A a b + 932B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (16A b - 1336B a b )d e + 480B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 140A a b - 140B a b)e + (932A a b + 188B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 1024A a b + 184B a b )d e + (352A b - 672B a b )d e +--R + +--R 5 4 +--R 320B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 30A a b - 30B a )e + (- 20A a b + 40B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (496A a b + 24B a b )d e + (- 672A a b - 128B a b )d e +--R + +--R 5 4 4 +--R (256A b + 64B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 3 8 3 2 9 2 10 2 11 3 5 +--R (1280a b e - 3840a b d e + 3840a b d e - 1280b d )x +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 4 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 5 6 3 4 7 2 3 8 2 2 9 3 3 +--R (12800a b e - 38400a b d e + 38400a b d e - 12800a b d )x +--R + +--R 6 5 3 5 6 2 4 7 2 3 8 3 2 +--R (12800a b e - 38400a b d e + 38400a b d e - 12800a b d )x +--R + +--R 7 4 3 6 5 2 5 6 2 4 7 3 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 8 3 3 7 4 2 6 5 2 5 6 3 +--R 1280a b e - 3840a b d e + 3840a b d e - 1280a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 6 5 5 6 4 5 +--R ((15A b + 15B a b )e - 30B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((75A a b + 75B a b )e - 150B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((150A a b + 150B a b )e - 300B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((150A a b + 150B a b )e - 300B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((75A a b + 75B a b)e - 150B a b d e )x + (15A a b + 15B a )e +--R + +--R 5 4 +--R - 30B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 5 4 4 5 3 4 +--R ((15A b + 15B a b )e - 30B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (70A a b + 70B a b )e + (- 10A b - 150B a b )d e +--R + +--R 5 2 2 +--R 20B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (128A a b - 128B a b )e + (- 46A a b + 466B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (8A b - 668B a b )d e + 240B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 70A a b - 70B a b)e + (466A a b + 94B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 512A a b + 92B a b )d e + (176A b - 336B a b )d e +--R + +--R 5 4 +--R 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 15A a b - 15B a )e + (- 10A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (248A a b + 12B a b )d e + (- 336A a b - 64B a b )d e +--R + +--R 5 4 4 +--R (128A b + 32B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 3 8 3 2 9 2 10 2 11 3 5 +--R (640a b e - 1920a b d e + 1920a b d e - 640b d )x +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 4 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x +--R + +--R 5 6 3 4 7 2 3 8 2 2 9 3 3 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 6 5 3 5 6 2 4 7 2 3 8 3 2 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 7 4 3 6 5 2 5 6 2 4 7 3 8 3 3 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x + 640a b e +--R + +--R 7 4 2 6 5 2 5 6 3 +--R - 1920a b d e + 1920a b d e - 640a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1050 + +--S 1051 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((3A b + 3B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((6A b + 6B a)e - 12B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 3 3 2 4 2 5 2 6 3 | 2 +--R (256a b e - 768a b d e + 768a b d e - 256b d )\|- a b e + b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((3A b + 3B a)e - 6B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((3A b + 3B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R 3 3 3 2 4 2 5 2 6 3 +-----------+ +-+ +--R (128a b e - 384a b d e + 384a b d e - 128b d )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1054 + +)clear all + +--S 1055 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1378 +r0:=-1/5*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^5)+1/128*e^4*_ + (10*b*B*d-7*A*b*e-3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(5/2)*(b*d-a*e)^(9/2))-1/40*(10*b*B*d-7*A*b*e-3*a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)*(a+b*x)^4)-1/240*e*(10*b*B*d-7*A*b*e-3*a*B*e)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x)^3)+1/192*e^2*(10*b*B*d-7*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^3*(a+b*x)^2)-1/128*e^3*(10*b*B*d-_ + 7*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^4*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 105A b - 45B a b )e + 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 525A a b - 225B a b )e + 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 1050A a b - 450B a b )e + 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 1050A a b - 450B a b )e + 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 525A a b - 225B a b)e + 750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 105A a b - 45B a )e + 150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b + 45B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (490A a b + 210B a b )e + (- 70A b - 730B a b )d e +--R + +--R 5 2 2 +--R 100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (896A a b + 384B a b )e + (- 322A a b - 1418B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (56A b + 484B a b )d e - 80B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (790A a b - 210B a b)e + (- 578A a b + 818B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (256A a b - 2356B a b )d e + (- 48A b + 1808B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 45B a )e + (1210A a b + 120B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 2104A a b - 436B a b )d e + (1488A a b + 352B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 7 4 3 8 3 2 9 2 2 10 3 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e +--R + +--R 11 4 +--R 1920b d +--R * +--R 5 +--R x +--R + +--R 5 6 4 4 7 3 3 8 2 2 2 9 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 10 4 +--R 9600a b d +--R * +--R 4 +--R x +--R + +--R 6 5 4 5 6 3 4 7 2 2 3 8 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 2 9 4 +--R 19200a b d +--R * +--R 3 +--R x +--R + +--R 7 4 4 6 5 3 5 6 2 2 4 7 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 3 8 4 +--R 19200a b d +--R * +--R 2 +--R x +--R + +--R 8 3 4 7 4 3 6 5 2 2 5 6 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 4 7 4 +--R 9600a b d +--R * +--R x +--R + +--R 9 2 4 8 3 3 7 4 2 2 6 5 3 5 6 4 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e + 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((105A b + 45B a b )e - 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((525A a b + 225B a b )e - 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((1050A a b + 450B a b )e - 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((1050A a b + 450B a b )e - 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((525A a b + 225B a b)e - 750B a b d e )x + (105A a b + 45B a )e +--R + +--R 5 4 +--R - 150B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 4 5 3 4 +--R ((210A b + 90B a b )e - 300B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (980A a b + 420B a b )e + (- 140A b - 1460B a b )d e +--R + +--R 5 2 2 +--R 200B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (1792A a b + 768B a b )e + (- 644A a b - 2836B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (112A b + 968B a b )d e - 160B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (1580A a b - 420B a b)e + (- 1156A a b + 1636B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (512A a b - 4712B a b )d e + (- 96A b + 3616B a b )d e +--R + +--R 5 4 +--R - 960B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 210A a b - 90B a )e + (2420A a b + 240B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 4208A a b - 872B a b )d e + (2976A a b + 704B a b )d e +--R + +--R 5 4 4 +--R (- 768A b - 192B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 4 7 4 3 8 3 2 9 2 2 10 3 +--R 3840a b e - 15360a b d e + 23040a b d e - 15360a b d e +--R + +--R 11 4 +--R 3840b d +--R * +--R 5 +--R x +--R + +--R 5 6 4 4 7 3 3 8 2 2 2 9 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 10 4 +--R 19200a b d +--R * +--R 4 +--R x +--R + +--R 6 5 4 5 6 3 4 7 2 2 3 8 3 +--R 38400a b e - 153600a b d e + 230400a b d e - 153600a b d e +--R + +--R 2 9 4 +--R 38400a b d +--R * +--R 3 +--R x +--R + +--R 7 4 4 6 5 3 5 6 2 2 4 7 3 +--R 38400a b e - 153600a b d e + 230400a b d e - 153600a b d e +--R + +--R 3 8 4 +--R 38400a b d +--R * +--R 2 +--R x +--R + +--R 8 3 4 7 4 3 6 5 2 2 5 6 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 4 7 4 +--R 19200a b d +--R * +--R x +--R + +--R 9 2 4 8 3 3 7 4 2 2 6 5 3 5 6 4 +--R 3840a b e - 15360a b d e + 23040a b d e - 15360a b d e + 3840a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 6 5 5 6 4 5 +--R ((105A b + 45B a b )e - 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((525A a b + 225B a b )e - 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((1050A a b + 450B a b )e - 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((1050A a b + 450B a b )e - 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((525A a b + 225B a b)e - 750B a b d e )x + (105A a b + 45B a )e +--R + +--R 5 4 +--R - 150B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b + 45B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (490A a b + 210B a 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57600a b d e - 38400a b d e +--R + +--R 10 4 +--R 9600a b d +--R * +--R 4 +--R x +--R + +--R 6 5 4 5 6 3 4 7 2 2 3 8 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 2 9 4 +--R 19200a b d +--R * +--R 3 +--R x +--R + +--R 7 4 4 6 5 3 5 6 2 2 4 7 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 3 8 4 +--R 19200a b d +--R * +--R 2 +--R x +--R + +--R 8 3 4 7 4 3 6 5 2 2 5 6 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 4 7 4 +--R 9600a b d +--R * +--R x +--R + +--R 9 2 4 8 3 3 7 4 2 2 6 5 3 5 6 4 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e + 1920a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1057 + +--S 1058 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((7A b + 3B a)e - 10B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((14A b + 6B a)e - 20B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 +--R (256a b e - 1024a b d e + 1536a b d e - 1024a b d e + 256b d ) +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((7A b + 3B a)e - 10B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((7A b + 3B a)e - 10B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e 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2 +--R 1920a b e - 9600a b d e + 19200a b d e - 19200a b d e +--R + +--R 6 5 4 5 6 5 +--R 9600a b d e - 1920a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1064 + +--S 1065 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((63A b + 7B a)e - 70B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((126A b + 14B a)e - 140B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e + 1280a b d e +--R + +--R 6 5 +--R - 256b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((63A b + 7B a)e - 70B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((63A b + 7B a)e - 70B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 128a b e - 640a b d e + 1280a b d e - 1280a b d e + 640a b d e +--R + +--R 6 5 +--R - 128b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1068 + +)clear all + +--S 1069 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 7 5 6 6 2 4 5 5 +--R b e x + (6a b e + b d)x + (15a b e + 6a b d)x +--R + +--R 3 3 2 4 4 4 2 3 3 3 5 4 2 2 +--R (20a b e + 15a b d)x + (15a b e + 20a b d)x + (6a b e + 15a b d)x +--R + +--R 6 5 6 +--R (a e + 6a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1378 +r0:=-63/128*e^4*(10*b*B*d-11*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/((b*d-a*e)^(13/2)*sqrt(b))+63/128*e^4*(10*b*B*d-_ + 11*A*b*e+a*B*e)/(b*(b*d-a*e)^6*sqrt(d+e*x))+1/5*(-A*b+a*B)/(b*(b*d-_ + a*e)*(a+b*x)^5*sqrt(d+e*x))+1/40*(-10*b*B*d+11*A*b*e-a*B*e)/(b*(b*d-_ + a*e)^2*(a+b*x)^4*sqrt(d+e*x))+3/80*e*(10*b*B*d-11*A*b*e+a*B*e)/(b*_ + (b*d-a*e)^3*(a+b*x)^3*sqrt(d+e*x))-21/320*e^2*(10*b*B*d-11*A*b*e+_ + a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*sqrt(d+e*x))+21/128*e^3*(10*b*B*d-_ + 11*A*b*e+a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((3465A b - 315B a b )e - 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((17325A a b - 1575B a b )e - 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((34650A a b - 3150B a b )e - 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((34650A a b - 3150B a b )e - 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((17325A a b - 1575B a b)e - 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (3465A a b - 315B a )e - 3150B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 315B a b )e + 3150B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 16170A a b + 1470B a b )e + (- 1155A b + 14805B a b )d e +--R + +--R 5 2 3 +--R 1050B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 29568A a b + 2688B a b )e + (- 5544A a b + 27384B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (462A b + 4998B a b )d e - 420B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 26070A a b + 2370B a b)e + (- 10494A a b + 24654B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2178A a b + 9342B a b )d e + (- 264A b - 1956B a b )d e +--R + +--R 5 4 +--R 240B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 10615A a b + 965B a )e + (- 9680A a b + 10530B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (4026A a b + 8434B a b )d e + (- 1232A a b - 3548B a b )d e +--R + +--R 5 4 4 5 5 +--R (176A b + 1104B a b )d e - 160B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 1280A a e + (- 4215A a b + 2245B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (3590A a b + 1760B a b)d e + (- 2248A a b - 732B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (816A a b + 224B a b )d e + (- 128A b - 32B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 6 5 6 5 6 5 4 7 2 4 3 8 3 3 +--R 640a b e - 3840a b d e + 9600a b d e - 12800a b d e +--R + +--R 2 9 4 2 10 5 11 6 +--R 9600a b d e - 3840a b d e + 640b d +--R * +--R 5 +--R x +--R + +--R 7 4 6 6 5 5 5 6 2 4 4 7 3 3 +--R 3200a b e - 19200a b d e + 48000a b d e - 64000a b d e +--R + +--R 3 8 4 2 2 9 5 10 6 +--R 48000a b d e - 19200a b d e + 3200a b d +--R * +--R 4 +--R x +--R + +--R 8 3 6 7 4 5 6 5 2 4 5 6 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 4 7 4 2 3 8 5 2 9 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 3 +--R x +--R + +--R 9 2 6 8 3 5 7 4 2 4 6 5 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 5 6 4 2 4 7 5 3 8 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 2 +--R x +--R + +--R 10 6 9 2 5 8 3 2 4 7 4 3 3 +--R 3200a b e - 19200a b d e + 48000a b d e - 64000a b d e +--R + +--R 6 5 4 2 5 6 5 4 7 6 +--R 48000a b d e - 19200a b d e + 3200a b d +--R * +--R x +--R + +--R 11 6 10 5 9 2 2 4 8 3 3 3 7 4 4 2 +--R 640a e - 3840a b d e + 9600a b d e - 12800a b d e + 9600a b d e +--R + +--R 6 5 5 5 6 6 +--R - 3840a b d e + 640a b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((3465A b - 315B a b )e - 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((17325A a b - 1575B a b )e - 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((34650A a b - 3150B a b )e - 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((34650A a b - 3150B a b )e - 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((17325A a b - 1575B a b)e - 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (3465A a b - 315B a )e - 3150B a b d e +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 5 5 4 5 +--R ((- 6930A b + 630B a b )e + 6300B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 32340A a b + 2940B a b )e + (- 2310A b + 29610B a b )d e +--R + +--R 5 2 3 +--R 2100B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 +--R (- 59136A a b + 5376B a b )e +--R + +--R 4 2 3 4 5 4 2 3 +--R (- 11088A a b + 54768B a b )d e + (924A b + 9996B a b )d e +--R + +--R 5 3 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 +--R (- 52140A a b + 4740B a b)e +--R + +--R 2 3 3 2 4 +--R (- 20988A a b + 49308B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (4356A a b + 18684B a b )d e + (- 528A b - 3912B a b )d e +--R + +--R 5 4 +--R 480B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 21230A a b + 1930B a )e + (- 19360A a b + 21060B a b)d e +--R + +--R 2 3 3 2 2 3 +--R (8052A a b + 16868B a b )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 2464A a b - 7096B a b )d e + (352A b + 2208B a b )d e +--R + +--R 5 5 +--R - 320B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 2560A a e + (- 8430A a b + 4490B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (7180A a b + 3520B a b)d e + (- 4496A a b - 1464B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (1632A a b + 448B a b )d e + (- 256A b - 64B a b )d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 5 6 5 6 5 4 7 2 4 3 8 3 3 +--R 1280a b e - 7680a b d e + 19200a b d e - 25600a b d e +--R + +--R 2 9 4 2 10 5 11 6 +--R 19200a b d e - 7680a b d e + 1280b d +--R * +--R 5 +--R x +--R + +--R 7 4 6 6 5 5 5 6 2 4 4 7 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 3 8 4 2 2 9 5 10 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 4 +--R x +--R + +--R 8 3 6 7 4 5 6 5 2 4 5 6 3 3 +--R 12800a b e - 76800a b d e + 192000a b d e - 256000a b d e +--R + +--R 4 7 4 2 3 8 5 2 9 6 +--R 192000a b d e - 76800a b d e + 12800a b d +--R * +--R 3 +--R x +--R + +--R 9 2 6 8 3 5 7 4 2 4 6 5 3 3 +--R 12800a b e - 76800a b d e + 192000a b d e - 256000a b d e +--R + +--R 5 6 4 2 4 7 5 3 8 6 +--R 192000a b d e - 76800a b d e + 12800a b d +--R * +--R 2 +--R x +--R + +--R 10 6 9 2 5 8 3 2 4 7 4 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 6 5 4 2 5 6 5 4 7 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R x +--R + +--R 11 6 10 5 9 2 2 4 8 3 3 3 +--R 1280a e - 7680a b d e + 19200a b d e - 25600a b d e +--R + +--R 7 4 4 2 6 5 5 5 6 6 +--R 19200a b d e - 7680a b d e + 1280a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 6 5 5 6 4 5 +--R ((- 3465A b + 315B a b )e + 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 17325A a b + 1575B a b )e + 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 34650A a b + 3150B a b )e + 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 34650A a b + 3150B a b )e + 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 17325A a b + 1575B a b)e + 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 3465A a b + 315B a )e + 3150B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 315B a b )e + 3150B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 16170A a b + 1470B a b )e + (- 1155A b + 14805B a b )d e +--R + +--R 5 2 3 +--R 1050B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 +--R (- 29568A a b + 2688B a b )e +--R + +--R 4 2 3 4 5 4 2 3 +--R (- 5544A a b + 27384B a b )d e + (462A b + 4998B a b )d e +--R + +--R 5 3 2 +--R - 420B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 +--R (- 26070A a b + 2370B a b)e +--R + +--R 2 3 3 2 4 +--R (- 10494A a b + 24654B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2178A a b + 9342B a b )d e + (- 264A b - 1956B a b )d e +--R + +--R 5 4 +--R 240B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 10615A a b + 965B a )e + (- 9680A a b + 10530B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (4026A a b + 8434B a b )d e + (- 1232A a b - 3548B a b )d e +--R + +--R 5 4 4 5 5 +--R (176A b + 1104B a b )d e - 160B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 1280A a e + (- 4215A a b + 2245B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (3590A a b + 1760B a b)d e + (- 2248A a b - 732B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (816A a b + 224B a b )d e + (- 128A b - 32B a b )d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R / +--R 6 5 6 5 6 5 4 7 2 4 3 8 3 3 +--R 640a b e - 3840a b d e + 9600a b d e - 12800a b d e +--R + +--R 2 9 4 2 10 5 11 6 +--R 9600a b d e - 3840a b d e + 640b d +--R * +--R 5 +--R x +--R + +--R 7 4 6 6 5 5 5 6 2 4 4 7 3 3 +--R 3200a b e - 19200a b d e + 48000a b d e - 64000a b d e +--R + +--R 3 8 4 2 2 9 5 10 6 +--R 48000a b d e - 19200a b d e + 3200a b d +--R * +--R 4 +--R x +--R + +--R 8 3 6 7 4 5 6 5 2 4 5 6 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 4 7 4 2 3 8 5 2 9 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 3 +--R x +--R + +--R 9 2 6 8 3 5 7 4 2 4 6 5 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 5 6 4 2 4 7 5 3 8 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 2 +--R x +--R + +--R 10 6 9 2 5 8 3 2 4 7 4 3 3 +--R 3200a b e - 19200a b d e + 48000a b d e - 64000a b d e +--R + +--R 6 5 4 2 5 6 5 4 7 6 +--R 48000a b d e - 19200a b d e + 3200a b d +--R * +--R x +--R + +--R 11 6 10 5 9 2 2 4 8 3 3 3 +--R 640a e - 3840a b d e + 9600a b d e - 12800a b d e +--R + +--R 7 4 4 2 6 5 5 5 6 6 +--R 9600a b d e - 3840a b d e + 640a b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1071 + +--S 1072 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((693A b - 63B a)e - 630B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R 5 4 | 2 +--R ((- 1386A b + 126B a)e + 1260B b d e )\|- a b e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 256a e - 1536a b d e + 3840a b d e - 5120a b d e + 3840a b d e +--R + +--R 5 5 6 6 +--R - 1536a b d e + 256b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((- 693A b + 63B a)e + 630B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((- 693A b + 63B a)e + 630B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 128a e - 768a b d e + 1920a b d e - 2560a b d e + 1920a b d e +--R + +--R 5 5 6 6 +--R - 768a b d e + 128b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1075 + +)clear all + +--S 1076 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 2 8 5 2 6 7 2 4 2 5 6 2 6 +--R b e x + (6a b e + 2b d e)x + (15a b e + 12a b d e + b d )x +--R + +--R 3 3 2 2 4 5 2 5 +--R (20a b e + 30a b d e + 6a b d )x +--R + +--R 4 2 2 3 3 2 4 2 4 +--R (15a b e + 40a b d e + 15a b d )x +--R + +--R 5 2 4 2 3 3 2 3 6 2 5 4 2 2 2 +--R (6a b e + 30a b d e + 20a b d )x + (a e + 12a b d e + 15a b d )x +--R + +--R 6 5 2 6 2 +--R (2a d e + 6a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1378 +r0:=77/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^6*(d+e*x)^(3/2))+_ + 1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*(d+e*x)^(3/2))+1/40*(-10*b*B*d+_ + 13*A*b*e-3*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*(d+e*x)^(3/2))+11/240*e*_ + (10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*(d+e*x)^(3/2))-_ + 33/320*e^2*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*_ + (d+e*x)^(3/2))+231/640*e^3*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^5*_ + (a+b*x)*(d+e*x)^(3/2))-231/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(15/2)+_ + 231/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)/((b*d-a*e)^7*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((- 45045A b + 10395B a b )e + 34650B b d e )x +--R + +--R 5 2 4 6 +--R (- 225225A a b + 51975B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 45045A b + 183645B a b )d e + 34650B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 450450A a b + 103950B a b )e +--R + +--R 5 2 4 5 5 2 4 +--R (- 225225A a b + 398475B a b )d e + 173250B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 450450A a b + 103950B a b )e +--R + +--R 2 4 3 3 5 2 4 2 4 +--R (- 450450A a b + 450450B a b )d e + 346500B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 225225A a b + 51975B a b)e +--R + +--R 3 3 4 2 5 3 3 2 4 +--R (- 450450A a b + 277200B a b )d e + 346500B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 45045A a b + 10395B a )e + (- 225225A a b + 86625B a b)d e +--R + +--R 4 2 2 4 +--R 173250B a b d e +--R * +--R x +--R + +--R 5 6 5 5 2 4 +--R (- 45045A a b + 10395B a )d e + 34650B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 6 +--R ((45045A b - 10395B a b )e - 34650B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (210210A a b - 48510B a b )e + (60060A b - 175560B a b )d e +--R + +--R 6 2 4 +--R - 46200B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (384384A a b - 88704B a b )e +--R + +--R 5 2 4 5 6 5 2 4 +--R (282282A a b - 360822B a b )d e + (9009A b - 219219B a b )d e +--R + +--R 6 3 3 +--R - 6930B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (338910A a b - 78210B a b )e +--R + +--R 2 4 3 3 5 +--R (520806A a b - 380886B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (43758A a b - 410718B a b )d e + (- 2574A b - 33066B a b )d e +--R + +--R 6 4 2 +--R 1980B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (137995A a b - 31845B a b)e + (464750A a b - 213400B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (84084A a b - 376904B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 12298A a b - 61842B a b )d e + (1144A b + 9196B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (16640A a b - 3840B a )e + (192790A a b - 57290B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (79170A a b - 166570B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 23114A a b - 55566B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (5408A a b + 16532B a b )d e + (- 624A b - 4016B a b )d e +--R + +--R 6 6 +--R 480B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 1280A a e + (24320A a b - 2560B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (35595A a b - 33125B a b)d e + (- 21070A a b - 12180B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (10024A a b + 3556B a b )d e + (- 2928A a b - 832B a b )d e +--R + +--R 6 5 6 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 5 8 6 6 7 5 7 2 6 4 8 3 5 +--R 1920a b e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 3 9 4 4 2 10 5 3 11 6 2 12 7 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920b d e +--R * +--R 6 +--R x +--R + +--R 8 4 8 7 5 7 6 6 2 6 5 7 3 5 +--R 9600a b e - 65280a b d e + 188160a b d e - 295680a b d e +--R + +--R 4 8 4 4 3 9 5 3 2 10 6 2 11 7 +--R 268800a b d e - 134400a b d e + 26880a b d e + 3840a b d e +--R + +--R 12 8 +--R - 1920b d +--R * +--R 5 +--R x +--R + +--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5 +--R 19200a b e - 124800a b d e + 336000a b d e - 470400a b d e +--R + +--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7 +--R 336000a b d e - 67200a b d e - 67200a b d e + 48000a b d e +--R + +--R 11 8 +--R - 9600a b d +--R * +--R 4 +--R x +--R + +--R 10 2 8 9 3 7 8 4 2 6 7 5 3 5 +--R 19200a b e - 115200a b d e + 268800a b d e - 268800a b d e +--R + +--R 5 7 5 3 4 8 6 2 3 9 7 2 10 8 +--R 268800a b d e - 268800a b d e + 115200a b d e - 19200a b d +--R * +--R 3 +--R x +--R + +--R 11 8 10 2 7 9 3 2 6 8 4 3 5 +--R 9600a b e - 48000a b d e + 67200a b d e + 67200a b d e +--R + +--R 7 5 4 4 6 6 5 3 5 7 6 2 4 8 7 +--R - 336000a b d e + 470400a b d e - 336000a b d e + 124800a b d e +--R + +--R 3 9 8 +--R - 19200a b d +--R * +--R 2 +--R x +--R + +--R 12 8 11 7 10 2 2 6 9 3 3 5 +--R 1920a e - 3840a b d e - 26880a b d e + 134400a b d e +--R + +--R 8 4 4 4 7 5 5 3 6 6 6 2 5 7 7 +--R - 268800a b d e + 295680a b d e - 188160a b d e + 65280a b d e +--R + +--R 4 8 8 +--R - 9600a b d +--R * +--R x +--R + +--R 12 7 11 2 6 10 2 3 5 9 3 4 4 +--R 1920a d e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 8 4 5 3 7 5 6 2 6 6 7 5 7 8 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 6 6 5 6 +--R ((45045A b - 10395B a b )e - 34650B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (225225A a b - 51975B a b )e + (45045A b - 183645B a b )d e +--R + +--R 6 2 4 +--R - 34650B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (450450A a b - 103950B a b )e +--R + +--R 5 2 4 5 5 2 4 +--R (225225A a b - 398475B a b )d e - 173250B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (450450A a b - 103950B a b )e +--R + +--R 2 4 3 3 5 2 4 2 4 +--R (450450A a b - 450450B a b )d e - 346500B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (225225A a b - 51975B a b)e +--R + +--R 3 3 4 2 5 3 3 2 4 +--R (450450A a b - 277200B a b )d e - 346500B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (45045A a b - 10395B a )e + (225225A a b - 86625B a b)d e +--R + +--R 4 2 2 4 +--R - 173250B a b d e +--R * +--R x +--R + +--R 5 6 5 5 2 4 +--R (45045A a b - 10395B a )d e - 34650B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 6 5 6 6 5 6 +--R ((90090A b - 20790B a b )e - 69300B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (420420A a b - 97020B a b )e + (120120A b - 351120B a b )d e +--R + +--R 6 2 4 +--R - 92400B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (768768A a b - 177408B a b )e + (564564A a b - 721644B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (18018A b - 438438B a b )d e - 13860B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (677820A a b - 156420B a b )e +--R + +--R 2 4 3 3 5 +--R (1041612A a b - 761772B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (87516A a b - 821436B a b )d e + (- 5148A b - 66132B a b )d e +--R + +--R 6 4 2 +--R 3960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (275990A a b - 63690B a b)e + (929500A a b - 426800B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (168168A a b - 753808B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 24596A a b - 123684B a b )d e + (2288A b + 18392B a b )d e +--R + +--R 6 5 +--R - 1760B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (33280A a b - 7680B a )e + (385580A a b - 114580B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (158340A a b - 333140B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 46228A a b - 111132B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (10816A a b + 33064B a b )d e + (- 1248A b - 8032B a b )d e +--R + +--R 6 6 +--R 960B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 2560A a e + (48640A a b - 5120B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (71190A a b - 66250B a b)d e + (- 42140A a b - 24360B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (20048A a b + 7112B a b )d e + (- 5856A a b - 1664B a b )d e +--R + +--R 6 5 6 +--R (768A b + 192B a b )d +--R / +--R 7 5 8 6 6 7 5 7 2 6 4 8 3 5 +--R 3840a b e - 26880a b d e + 80640a b d e - 134400a b d e +--R + +--R 3 9 4 4 2 10 5 3 11 6 2 12 7 +--R 134400a b d e - 80640a b d e + 26880a b d e - 3840b d e +--R * +--R 6 +--R x +--R + +--R 8 4 8 7 5 7 6 6 2 6 5 7 3 5 +--R 19200a b e - 130560a b d e + 376320a b d e - 591360a b d e +--R + +--R 4 8 4 4 3 9 5 3 2 10 6 2 11 7 +--R 537600a b d e - 268800a b d e + 53760a b d e + 7680a b d e +--R + +--R 12 8 +--R - 3840b d +--R * +--R 5 +--R x +--R + +--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5 +--R 38400a b e - 249600a b d e + 672000a b d e - 940800a b d e +--R + +--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7 +--R 672000a b d e - 134400a b d e - 134400a b d e + 96000a b d e +--R + +--R 11 8 +--R - 19200a b d +--R * +--R 4 +--R x +--R + +--R 10 2 8 9 3 7 8 4 2 6 7 5 3 5 +--R 38400a b e - 230400a b d e + 537600a b d e - 537600a b d e +--R + +--R 5 7 5 3 4 8 6 2 3 9 7 2 10 8 +--R 537600a b d e - 537600a b d e + 230400a b d e - 38400a b d +--R * +--R 3 +--R x +--R + +--R 11 8 10 2 7 9 3 2 6 8 4 3 5 +--R 19200a b e - 96000a b d e + 134400a b d e + 134400a b d e +--R + +--R 7 5 4 4 6 6 5 3 5 7 6 2 +--R - 672000a b d e + 940800a b d e - 672000a b d e +--R + +--R 4 8 7 3 9 8 +--R 249600a b d e - 38400a b d +--R * +--R 2 +--R x +--R + +--R 12 8 11 7 10 2 2 6 9 3 3 5 +--R 3840a e - 7680a b d e - 53760a b d e + 268800a b d e +--R + +--R 8 4 4 4 7 5 5 3 6 6 6 2 +--R - 537600a b d e + 591360a b d e - 376320a b d e +--R + +--R 5 7 7 4 8 8 +--R 130560a b d e - 19200a b d +--R * +--R x +--R + +--R 12 7 11 2 6 10 2 3 5 9 3 4 4 +--R 3840a d e - 26880a b d e + 80640a b d e - 134400a b d e +--R + +--R 8 4 5 3 7 5 6 2 6 6 7 5 7 8 +--R 134400a b d e - 80640a b d e + 26880a b d e - 3840a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 6 5 6 6 5 6 +--R ((45045A b - 10395B a b )e - 34650B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (225225A a b - 51975B a b )e + (45045A b - 183645B a b )d e +--R + +--R 6 2 4 +--R - 34650B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (450450A a b - 103950B a b )e +--R + +--R 5 2 4 5 5 2 4 +--R (225225A a b - 398475B a b )d e - 173250B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (450450A a b - 103950B a b )e +--R + +--R 2 4 3 3 5 2 4 2 4 +--R (450450A a b - 450450B a b )d e - 346500B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (225225A a b - 51975B a b)e +--R + +--R 3 3 4 2 5 3 3 2 4 +--R (450450A a b - 277200B a b )d e - 346500B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (45045A a b - 10395B a )e + (225225A a b - 86625B a b)d e +--R + +--R 4 2 2 4 +--R - 173250B a b d e +--R * +--R x +--R + +--R 5 6 5 5 2 4 +--R (45045A a b - 10395B a )d e - 34650B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 6 5 6 6 5 6 +--R ((45045A b - 10395B a b )e - 34650B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (210210A a b - 48510B a b )e + (60060A b - 175560B a b )d e +--R + +--R 6 2 4 +--R - 46200B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (384384A a b - 88704B a b )e + (282282A a b - 360822B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (9009A b - 219219B a b )d e - 6930B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (338910A a b - 78210B a b )e + (520806A a b - 380886B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (43758A a b - 410718B a b )d e + (- 2574A b - 33066B a b )d e +--R + +--R 6 4 2 +--R 1980B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (137995A a b - 31845B a b)e + (464750A a b - 213400B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (84084A a b - 376904B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 12298A a b - 61842B a b )d e + (1144A b + 9196B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (16640A a b - 3840B a )e + (192790A a b - 57290B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (79170A a b - 166570B a b )d e +--R + +--R 2 4 3 3 3 3 5 2 4 4 2 +--R (- 23114A a b - 55566B a b )d e + (5408A a b + 16532B a b )d e +--R + +--R 6 5 5 6 6 +--R (- 624A b - 4016B a b )d e + 480B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 1280A a e + (24320A a b - 2560B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (35595A a b - 33125B a b)d e + (- 21070A a b - 12180B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (10024A a b + 3556B a b )d e + (- 2928A a b - 832B a b )d e +--R + +--R 6 5 6 +--R (384A b + 96B a b )d +--R / +--R 7 5 8 6 6 7 5 7 2 6 4 8 3 5 +--R 1920a b e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 3 9 4 4 2 10 5 3 11 6 2 12 7 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920b d e +--R * +--R 6 +--R x +--R + +--R 8 4 8 7 5 7 6 6 2 6 5 7 3 5 +--R 9600a b e - 65280a b d e + 188160a b d e - 295680a b d e +--R + +--R 4 8 4 4 3 9 5 3 2 10 6 2 11 7 +--R 268800a b d e - 134400a b d e + 26880a b d e + 3840a b d e +--R + +--R 12 8 +--R - 1920b d +--R * +--R 5 +--R x +--R + +--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5 +--R 19200a b e - 124800a b d e + 336000a b d e - 470400a b d e +--R + +--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7 +--R 336000a b d e - 67200a b d e - 67200a b d e + 48000a b d e +--R + +--R 11 8 +--R - 9600a b d +--R * +--R 4 +--R x +--R + +--R 10 2 8 9 3 7 8 4 2 6 7 5 3 5 +--R 19200a b e - 115200a b d e + 268800a b d e - 268800a b d e +--R + +--R 5 7 5 3 4 8 6 2 3 9 7 2 10 8 +--R 268800a b d e - 268800a b d e + 115200a b d e - 19200a b d +--R * +--R 3 +--R x +--R + +--R 11 8 10 2 7 9 3 2 6 8 4 3 5 +--R 9600a b e - 48000a b d e + 67200a b d e + 67200a b d e +--R + +--R 7 5 4 4 6 6 5 3 5 7 6 2 +--R - 336000a b d e + 470400a b d e - 336000a b d e +--R + +--R 4 8 7 3 9 8 +--R 124800a b d e - 19200a b d +--R * +--R 2 +--R x +--R + +--R 12 8 11 7 10 2 2 6 9 3 3 5 +--R 1920a e - 3840a b d e - 26880a b d e + 134400a b d e +--R + +--R 8 4 4 4 7 5 5 3 6 6 6 2 5 7 7 +--R - 268800a b d e + 295680a b d e - 188160a b d e + 65280a b d e +--R + +--R 4 8 8 +--R - 9600a b d +--R * +--R x +--R + +--R 12 7 11 2 6 10 2 3 5 9 3 4 4 +--R 1920a d e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 8 4 5 3 7 5 6 2 6 6 7 5 7 8 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1078 + +--S 1079 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 5 4 +-----------+ | b +--R ((3003A b - 693B a)e - 2310B b d e )\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 5 4 +-+ \|b \|e x + d +--R ((6006A b - 1386B a)e - 4620B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 256a e - 1792a b d e + 5376a b d e - 8960a b d e + 8960a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 5376a b d e + 1792a b d e - 256b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 5 4 +-+ \|b \|e x + d +--R ((3003A b - 693B a)e - 2310B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 5 4 +-----------+ | b +--R ((3003A b - 693B a)e - 2310B b d e )\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 128a e - 896a b d e + 2688a b d e - 4480a b d e + 4480a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 2688a b d e + 896a b d e - 128b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1082 + +)clear all + +--S 1083 of 1378 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 3 9 5 3 6 2 8 2 4 3 5 2 6 2 7 +--R b e x + (6a b e + 3b d e )x + (15a b e + 18a b d e + 3b d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (20a b e + 45a b d e + 18a b d e + b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (15a b e + 60a b d e + 45a b d e + 6a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (6a b e + 45a b d e + 60a b d e + 15a b d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (a e + 18a b d e + 45a b d e + 20a b d )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (3a d e + 18a b d e + 15a b d )x + (3a d e + 6a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1378 +r0:=3003/640*e^4*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^6*(d+e*x)^(5/2))+_ + 1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*(d+e*x)^(5/2))+1/8*(-2*b*B*d+_ + 3*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*(d+e*x)^(5/2))+13/48*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*(d+e*x)^(5/2))-143/192*e^2*_ + (2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*(d+e*x)^(5/2))+_ + 429/128*e^3*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*_ + (d+e*x)^(5/2))+1001/128*e^4*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^7*_ + (d+e*x)^(3/2))-3003/128*b^(3/2)*e^4*(2*b*B*d-3*A*b*e+a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(17/2)+_ + 3003/128*b*e^4*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^8*sqrt(d+e*x)) +--R +--R +--R (2) +--R 7 6 7 7 6 7 +--R ((135135A b - 45045B a b )e - 90090B b d e )x +--R + +--R 6 2 5 7 7 6 6 +--R (675675A a b - 225225B a b )e + (270270A b - 540540B a b )d e +--R + +--R 7 2 5 +--R - 180180B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 7 +--R (1351350A a b - 450450B a b )e +--R + +--R 6 2 5 6 +--R (1351350A a b - 1351350B a b )d e +--R + +--R 7 6 2 5 7 3 4 +--R (135135A b - 945945B a b )d e - 90090B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 7 +--R (1351350A a b - 450450B a b )e +--R + +--R 2 5 3 4 6 +--R (2702700A a b - 1801800B a b )d e +--R + +--R 6 2 5 2 5 6 3 4 +--R (675675A a b - 2027025B a b )d e - 450450B a b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 +--R (675675A a b - 225225B a b )e +--R + +--R 3 4 4 3 6 +--R (2702700A a b - 1351350B a b )d e +--R + +--R 2 5 3 4 2 5 2 5 3 4 +--R (1351350A a b - 2252250B a b )d e - 900900B a b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 7 +--R (135135A a b - 45045B a b)e +--R + +--R 4 3 5 2 6 +--R (1351350A a b - 540540B a b )d e +--R + +--R 3 4 4 3 2 5 3 4 3 4 +--R (1351350A a b - 1351350B a b )d e - 900900B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 6 +--R (270270A a b - 90090B a b)d e +--R + +--R 4 3 5 2 2 5 4 3 3 4 +--R (675675A a b - 405405B a b )d e - 450450B a b d e +--R * +--R x +--R + +--R 5 2 6 2 5 5 2 3 4 +--R (135135A a b - 45045B a b)d e - 90090B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 7 6 7 7 6 7 +--R ((- 135135A b + 45045B a b )e + 90090B b d e )x +--R + +--R 6 2 5 7 +--R (- 630630A a b + 210210B a b )e +--R + +--R 7 6 6 7 2 5 +--R (- 315315A b + 525525B a b )d e + 210210B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 7 +--R (- 1153152A a b + 384384B a b )e +--R + +--R 6 2 5 6 +--R (- 1477476A a b + 1261260B a b )d e +--R + +--R 7 6 2 5 7 3 4 +--R (- 207207A b + 1054053B a b )d e + 138138B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 7 +--R (- 1016730A a b + 338910B a b )e +--R + +--R 2 5 3 4 6 +--R (- 2715570A a b + 1583010B a b )d e +--R + +--R 6 2 5 2 5 +--R (- 978120A a b + 2136420B a b )d e +--R + +--R 7 6 3 4 7 4 3 +--R (- 19305A b + 658515B a b )d e + 12870B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 +--R (- 413985A a b + 137995B a b )e +--R + +--R 3 4 4 3 6 +--R (- 2410980A a b + 1079650B a b )d e +--R + +--R 2 5 3 4 2 5 +--R (- 1814670A a b + 2212210B a b )d e +--R + +--R 6 2 5 3 4 +--R (- 94380A a b + 1241240B a b )d e +--R + +--R 7 6 4 3 7 5 2 +--R (4290A b + 61490B a b )d e - 2860B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 7 +--R (- 49920A a b + 16640B a b)e +--R + +--R 4 3 5 2 6 +--R (- 992355A a b + 364065B a b )d e +--R + +--R 3 4 4 3 2 5 +--R (- 1631760A a b + 1205490B a b )d e +--R + +--R 2 5 3 4 3 4 +--R (- 182910A a b + 1148810B a b )d e +--R + +--R 6 2 5 4 3 7 6 5 2 +--R (20670A a b + 115050B a b )d e + (- 1560A b - 13260B a b )d e +--R + +--R 7 6 +--R 1040B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 7 5 2 6 6 +--R (3840A a b - 1280B a )e + (- 122880A a b + 38400B a b)d e +--R + +--R 4 3 5 2 2 5 +--R (- 685155A a b + 310305B a b )d e +--R + +--R 3 4 4 3 3 4 +--R (- 174300A a b + 514870B a b )d e +--R + +--R 2 5 3 4 4 3 +--R (39270A a b + 103110B a b )d e +--R + +--R 6 2 5 5 2 7 6 6 +--R (- 7440A a b - 23700B a b )d e + (720A b + 4720B a b )d e +--R + +--R 7 7 +--R - 480B b d +--R * +--R x +--R + +--R 7 7 6 7 6 +--R - 768A a e + (9216A a b - 512B a )d e +--R + +--R 5 2 6 2 5 4 3 5 2 3 4 +--R (- 89088A a b + 16384B a b)d e + (- 79905A a b + 100363B a b )d e +--R + +--R 3 4 4 3 4 3 2 5 3 4 5 2 +--R (36330A a b + 23240B a b )d e + (- 13944A a b - 5236B a b )d e +--R + +--R 6 2 5 6 7 6 7 +--R (3408A a b + 992B a b )d e + (- 384A b - 96B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 8 5 10 7 6 9 6 7 2 8 5 8 3 7 +--R 1920a b e - 15360a b d e + 53760a b d e - 107520a b d e +--R + +--R 4 9 4 6 3 10 5 5 2 11 6 4 12 7 3 +--R 134400a b d e - 107520a b d e + 53760a b d e - 15360a b d e +--R + +--R 13 8 2 +--R 1920b d e +--R * +--R 7 +--R x +--R + +--R 9 4 10 8 5 9 7 6 2 8 6 7 3 7 +--R 9600a b e - 72960a b d e + 238080a b d e - 430080a b d e +--R + +--R 5 8 4 6 4 9 5 5 3 10 6 4 2 11 7 3 +--R 456960a b d e - 268800a b d e + 53760a b d e + 30720a b d e +--R + +--R 12 8 2 13 9 +--R - 21120a b d e + 3840b d e +--R * +--R 6 +--R x +--R + +--R 10 3 10 9 4 9 8 5 2 8 7 6 3 7 +--R 19200a b e - 134400a b d e + 385920a b d e - 552960a b d e +--R + +--R 6 7 4 6 5 8 5 5 4 9 6 4 3 10 7 3 +--R 322560a b d e + 161280a b d e - 403200a b d e + 276480a b d e +--R + +--R 2 11 8 2 12 9 13 10 +--R - 80640a b d e + 3840a b d e + 1920b d +--R * +--R 5 +--R x +--R + +--R 11 2 10 10 3 9 9 4 2 8 8 5 3 7 +--R 19200a b e - 115200a b d e + 240000a b d e - 76800a b d e +--R + +--R 7 6 4 6 6 7 5 5 5 8 6 4 +--R - 537600a b d e + 1075200a b d e - 940800a b d e +--R + +--R 4 9 7 3 3 10 8 2 2 11 9 12 10 +--R 384000a b d e - 19200a b d e - 38400a b d e + 9600a b d +--R * +--R 4 +--R x +--R + +--R 12 10 11 2 9 10 3 2 8 9 4 3 7 +--R 9600a b e - 38400a b d e - 19200a b d e + 384000a b d e +--R + +--R 8 5 4 6 7 6 5 5 6 7 6 4 5 8 7 3 +--R - 940800a b d e + 1075200a b d e - 537600a b d e - 76800a b d e +--R + +--R 4 9 8 2 3 10 9 2 11 10 +--R 240000a b d e - 115200a b d e + 19200a b d +--R * +--R 3 +--R x +--R + +--R 13 10 12 9 11 2 2 8 10 3 3 7 +--R 1920a e + 3840a b d e - 80640a b d e + 276480a b d e +--R + +--R 9 4 4 6 8 5 5 5 7 6 6 4 6 7 7 3 +--R - 403200a b d e + 161280a b d e + 322560a b d e - 552960a b d e +--R + +--R 5 8 8 2 4 9 9 3 10 10 +--R 385920a b d e - 134400a b d e + 19200a b d +--R * +--R 2 +--R x +--R + +--R 13 9 12 2 8 11 2 3 7 10 3 4 6 +--R 3840a d e - 21120a b d e + 30720a b d e + 53760a b d e +--R + +--R 9 4 5 5 8 5 6 4 7 6 7 3 6 7 8 2 +--R - 268800a b d e + 456960a b d e - 430080a b d e + 238080a b d e +--R + +--R 5 8 9 4 9 10 +--R - 72960a b d e + 9600a b d +--R * +--R x +--R + +--R 13 2 8 12 3 7 11 2 4 6 10 3 5 5 +--R 1920a d e - 15360a b d e + 53760a b d e - 107520a b d e +--R + +--R 9 4 6 4 8 5 7 3 7 6 8 2 6 7 9 +--R 134400a b d e - 107520a b d e + 53760a b d e - 15360a b d e +--R + +--R 5 8 10 +--R 1920a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1378 +a0:=integrate(t0,x) +--R +--R 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* +--R 2 +--R x +--R + +--R 13 9 12 2 8 11 2 3 7 10 3 4 6 +--R 3840a d e - 21120a b d e + 30720a b d e + 53760a b d e +--R + +--R 9 4 5 5 8 5 6 4 7 6 7 3 +--R - 268800a b d e + 456960a b d e - 430080a b d e +--R + +--R 6 7 8 2 5 8 9 4 9 10 +--R 238080a b d e - 72960a b d e + 9600a b d +--R * +--R x +--R + +--R 13 2 8 12 3 7 11 2 4 6 10 3 5 5 +--R 1920a d e - 15360a b d e + 53760a b d e - 107520a b d e +--R + +--R 9 4 6 4 8 5 7 3 7 6 8 2 6 7 9 +--R 134400a b d e - 107520a b d e + 53760a b d e - 15360a b d e +--R + +--R 5 8 10 +--R 1920a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1085 + +--S 1086 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 5 2 4 +-----------+ | b +--R ((9009A b - 3003B a b)e - 6006B b d e )\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R 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+--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R 128a e - 1024a b d e + 3584a b d e - 7168a b d e + 8960a b d e +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R - 7168a b d e + 3584a b d e - 1024a b d e + 128b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1089 + +)clear all + +--S 1090 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1378 +r0:=-2/143*(4*b*B*d-13*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/1287*(b*d-a*e)*(4*b*B*d-13*A*b*e+9*a*B*e)*_ + (d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+_ + 2/13*B*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 198B b e x + ((234A b + 234B a)e + 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (286A a e + (884A b + 884B a)d e + 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (1144A a d e + (1196A b + 1196B a)d e + 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (1716A a d e + (624A b + 624B a)d e + 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (1144A a d e + (26A b + 26B a)d e - 8B b d e)x + 286A a d e +--R + +--R 5 6 +--R (- 52A b - 52B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 5 +--R 198B b e x + ((234A b + 234B a)e + 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (286A a e + (884A b + 884B a)d e + 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (1144A a d e + (1196A b + 1196B a)d e + 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (1716A a d e + (624A b + 624B a)d e + 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (1144A a d e + (26A b + 26B a)d e - 8B b d e)x + 286A a d e +--R + +--R 5 6 +--R (- 52A b - 52B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 1287e +--R Type: Union(Expression(Integer),...) +--E 1092 + +--S 1093 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 5 +--R - 198B b e x + ((- 234A b - 234B a)e - 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (- 286A a e + (- 884A b - 884B a)d e - 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (- 1144A a d e + (- 1196A b - 1196B a)d e - 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (- 1716A a d e + (- 624A b - 624B a)d e - 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (- 1144A a d e + (- 26A b - 26B a)d e + 8B b d e)x - 286A a d e +--R + +--R 5 6 +--R (52A b + 52B a)d e - 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 2 6 7 2 6 2 5 6 +--R 198B b e x + ((234A b + 432B a b)e + 720B b d e )x +--R + +--R 2 6 2 5 2 2 4 5 +--R ((520A a b + 234B a )e + (884A b + 1604B a b)d e + 916B b d e )x +--R + +--R 2 6 2 5 +--R 286A a e + (2028A a b + 884B a )d e +--R + +--R 2 2 4 2 3 3 +--R (1196A b + 2112B a b)d e + 424B b d e +--R * +--R 4 +--R x +--R + +--R 2 5 2 2 4 +--R 1144A a d e + (2912A a b + 1196B a )d e +--R + +--R 2 3 3 2 4 2 +--R (624A b + 1048B a b)d e + 6B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R 1716A a d e + (1768A a b + 624B a )d e + (26A b + 32B a b)d e +--R + +--R 2 5 +--R - 8B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 1144A a d e + (312A a b + 26B a )d e + (- 52A b - 60B a b)d e +--R + +--R 2 6 +--R 16B b d +--R * +--R x +--R + +--R 2 4 2 2 5 6 +--R 286A a d e + (- 52A a b - 52B a )d e + 16B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 6 4 3 5 +--R B b e x + ((A b + B a)e + 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (A a e + (4A b + 4B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (4A a d e + (6A b + 6B a)d e + 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (6A a d e + (4A b + 4B a)d e + B b d )x +--R + +--R 3 4 4 +--R (4A a d e + (A b + B a)d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 7 2 4 2 3 6 +--R - B b e x + ((- A b - 2B a b)e - 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((- 2A a b - B a )e + (- 4A b - 8B a b)d e - 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R - A a e + (- 8A a b - 4B a )d e + (- 6A b - 12B a b)d e +--R + +--R 2 3 +--R - 4B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R - 4A a d e + (- 12A a b - 6B a )d e + (- 4A b - 8B a b)d e +--R + +--R 2 4 +--R - B b d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 3 2 4 2 +--R (- 6A a d e + (- 8A a b - 4B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (- 4A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1094 + +)clear all + +--S 1095 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1378 +r0:=-2/99*(4*b*B*d-11*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/693*(b*d-a*e)*(4*b*B*d-11*A*b*e+7*a*B*e)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/11*B*_ + (a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 126B b e x + ((154A b + 154B a)e + 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (198A a e + (418A b + 418B a)d e + 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (594A a d e + (330A b + 330B a)d e + 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (594A a d e + (22A b + 22B a)d e - 8B b d e)x + 198A a d e +--R + +--R 4 5 +--R (- 44A b - 44B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 4 +--R 126B b e x + ((154A b + 154B a)e + 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (198A a e + (418A b + 418B a)d e + 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (594A a d e + (330A b + 330B a)d e + 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (594A a d e + (22A b + 22B a)d e - 8B b d e)x + 198A a d e +--R + +--R 4 5 +--R (- 44A b - 44B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 693e +--R Type: Union(Expression(Integer),...) +--E 1097 + +--S 1098 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 4 +--R - 126B b e x + ((- 154A b - 154B a)e - 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (- 198A a e + (- 418A b - 418B a)d e - 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (- 594A a d e + (- 330A b - 330B a)d e - 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (- 594A a d e + (- 22A b - 22B a)d e + 8B b d e)x - 198A a d e +--R + +--R 4 5 +--R (44A b + 44B a)d e - 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 2 5 6 2 5 2 4 5 +--R 126B b e x + ((154A b + 280B a b)e + 322B b d e )x +--R + +--R 2 5 2 4 2 2 3 4 +--R ((352A a b + 154B a )e + (418A b + 740B a b)d e + 226B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 198A a e + (1012A a b + 418B a )d e + (330A b + 556B a b)d e +--R + +--R 2 3 2 +--R 6B b d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 594A a d e + (924A a b + 330B a )d e + (22A b + 28B a b)d e +--R + +--R 2 4 +--R - 8B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 594A a d e + (220A a b + 22B a )d e + (- 44A b - 52B a b)d e +--R + +--R 2 5 +--R 16B b d +--R * +--R x +--R + +--R 2 3 2 2 4 5 +--R 198A a d e + (- 44A a b - 44B a )d e + 16B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 3 2 4 +--R B b e x + ((A b + B a)e + 3B b d e )x +--R + +--R 3 2 2 3 +--R (A a e + (3A b + 3B a)d e + 3B b d e)x +--R + +--R 2 2 3 2 +--R (3A a d e + (3A b + 3B a)d e + B b d )x +--R + +--R 2 3 3 +--R (3A a d e + (A b + B a)d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 6 2 3 2 2 5 +--R - B b e x + ((- A b - 2B a b)e - 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((- 2A a b - B a )e + (- 3A b - 6B a b)d e - 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- A a e + (- 6A a b - 3B a )d e + (- 3A b - 6B a b)d e - B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (- 3A a d e + (- 6A a b - 3B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (- 3A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1099 + +)clear all + +--S 1100 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (1) (B e x + (A e + B d)x + A d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1378 +r0:=-2/63*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/315*(b*d-a*e)*(4*b*B*d-9*A*b*e+5*a*B*e)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/9*B*_ + (a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B b e x + ((90A b + 90B a)e + 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (126A a e + (144A b + 144B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (252A a d e + (18A b + 18B a)d e - 8B b d e)x + 126A a d e +--R + +--R 3 4 +--R (- 36A b - 36B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 3 +--R 70B b e x + ((90A b + 90B a)e + 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (126A a e + (144A b + 144B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (252A a d e + (18A b + 18B a)d e - 8B b d e)x + 126A a d e +--R + +--R 3 4 +--R (- 36A b - 36B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 1102 + +--S 1103 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 3 +--R - 70B b e x + ((- 90A b - 90B a)e - 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (- 126A a e + (- 144A b - 144B a)d e - 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 252A a d e + (- 18A b - 18B a)d e + 8B b d e)x - 126A a d e +--R + +--R 3 4 +--R (36A b + 36B a)d e - 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 2 4 5 2 4 2 3 4 +--R 70B b e x + ((90A b + 160B a b)e + 100B b d e )x +--R + +--R 2 4 2 3 2 2 2 3 +--R ((216A a b + 90B a )e + (144A b + 244B a b)d e + 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 126A a e + (396A a b + 144B a )d e + (18A b + 24B a b)d e +--R + +--R 2 3 +--R - 8B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 252A a d e + (144A a b + 18B a )d e + (- 36A b - 44B a b)d e +--R + +--R 2 4 +--R 16B b d +--R * +--R x +--R + +--R 2 2 2 2 3 4 +--R 126A a d e + (- 36A a b - 36B a )d e + 16B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 4 2 3 +--R B b e x + ((A b + B a)e + 2B b d e)x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + B b d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 5 2 2 2 4 +--R - B b e x + ((- A b - 2B a b)e - 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((- 2A a b - B a )e + (- 2A b - 4B a b)d e - B b d )x +--R + +--R 2 2 2 2 2 2 +--R (- A a e + (- 4A a b - 2B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (- 2A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1104 + +)clear all + +--S 1105 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R +-------+ | 2 2 2 +--R (1) (B x + A)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1378 +r0:=-2/35*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/105*(b*d-a*e)*(4*b*B*d-7*A*b*e+3*a*B*e)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/7*B*_ + (a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B b e x + ((42A b + 42B a)e + 6B b d e )x +--R + +--R 3 2 2 2 +--R (70A a e + (14A b + 14B a)d e - 8B b d e)x + 70A a d e +--R + +--R 2 3 +--R (- 28A b - 28B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B b e x + ((42A b + 42B a)e + 6B b d e )x +--R + +--R 3 2 2 2 +--R (70A a e + (14A b + 14B a)d e - 8B b d e)x + 70A a d e +--R + +--R 2 3 +--R (- 28A b - 28B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 1107 + +--S 1108 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 2 +--R - 30B b e x + ((- 42A b - 42B a)e - 6B b d e )x +--R + +--R 3 2 2 2 +--R (- 70A a e + (- 14A b - 14B a)d e + 8B b d e)x - 70A a d e +--R + +--R 2 3 +--R (28A b + 28B a)d e - 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 2 3 4 2 3 2 2 3 +--R 30B b e x + ((42A b + 72B a b)e + 6B b d e )x +--R + +--R 2 3 2 2 2 2 2 +--R ((112A a b + 42B a )e + (14A b + 20B a b)d e - 8B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 70A a e + (84A a b + 14B a )d e + (- 28A b - 36B a b)d e +--R + +--R 2 3 +--R 16B b d +--R * +--R x +--R + +--R 2 2 2 2 3 +--R 70A a d e + (- 28A a b - 28B a )d e + 16B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 2 +--R (B b e x + ((A b + B a)e + B b d)x + (A a e + (A b + B a)d)x + A a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 2 3 +--R - B b e x + ((- A b - 2B a b)e - B b d)x +--R + +--R 2 2 2 +--R ((- 2A a b - B a )e + (- A b - 2B a b)d)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1109 + +)clear all + +--S 1110 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1378 +r0:=-2/15*(4*b*B*d-5*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/15*(b*d-a*e)*(4*b*B*d-5*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/5*B*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 2 2 2 2 +--R 6B b e x + ((10A b + 10B a)e - 8B b d e)x + 30A a e +--R + +--R 2 +--R (- 20A b - 20B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R 6B b e x + ((10A b + 10B a)e - 8B b d e)x + 30A a e +--R + +--R 2 +--R (- 20A b - 20B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15e +--R Type: Union(Expression(Integer),...) +--E 1112 + +--S 1113 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R - 6B b e x + ((- 10A b - 10B a)e + 8B b d e)x - 30A a e +--R + +--R 2 +--R (20A b + 20B a)d e - 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R 6B b e x + ((10A b + 16B a b)e - 8B b d e)x +--R + +--R 2 2 2 2 2 +--R ((40A a b + 10B a )e + (- 20A b - 28B a b)d e + 16B b d )x +--R + +--R 2 2 2 2 +--R 30A a e + (- 20A a b - 20B a )d e + 16B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1114 + +)clear all + +--S 1115 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1378 +r0:=-2*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+2/3*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^2*(b*d-a*e))-4/3*(4*b*B*d-3*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R 2B b e x + ((6A b + 6B a)e - 8B b d e)x - 6A a e +--R + +--R 2 +--R (12A b + 12B a)d e - 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R 2B b e x + ((6A b + 6B a)e - 8B b d e)x - 6A a e + (12A b + 12B a)d e +--R + +--R 2 +--R - 16B b d +--R / +--R 3 +-------+ +--R 3e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1117 + +--S 1118 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R - 2B b e x + ((- 6A b - 6B a)e + 8B b d e)x + 6A a e +--R + +--R 2 +--R (- 12A b - 12B a)d e + 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R 2B b e x + ((6A b + 8B a b)e - 8B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R (6B a e + (12A b + 4B a b)d e - 16B b d )x - 6A a e +--R + +--R 2 2 +--R (12A a b + 12B a )d e - 16B a b d +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))+2/3*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^2*(b*d-a*e)*sqrt(d+e*x))+4/3*(4*b*B*d-A*b*e-3*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R 6B b e x + ((- 6A b - 6B a)e + 24B b d e)x - 2A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e + 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R 6B b e x + ((- 6A b - 6B a)e + 24B b d e)x - 2A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e + 16B b d +--R / +--R 4 3 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R - 6B b e x + ((6A b + 6B a)e - 24B b d e)x + 2A a e +--R + +--R 2 +--R (4A b + 4B a)d e - 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R 6B b e x + (- 6A b e + 24B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 8A a b - 6B a )e + (- 4A b + 20B a b)d e + 16B b d )x - 2A a e +--R + +--R 2 2 +--R (- 4A a b - 4B a )d e + 16B a b d +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1378 +r0:=-2/5*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/5*(4*b*B*d+A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/15*(4*b*B*d+A*b*e-5*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 30B b e x + ((- 10A b - 10B a)e - 40B b d e)x - 6A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e - 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 30B b e x + ((- 10A b - 10B a)e - 40B b d e)x - 6A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e - 16B b d +--R / +--R 5 2 4 2 3 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R 30B b e x + ((10A b + 10B a)e + 40B b d e)x + 6A a e +--R + +--R 2 +--R (4A b + 4B a)d e + 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R - 30B b e x + ((- 10A b - 40B a b)e - 40B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 16A a b - 10B a )e + (- 4A b - 44B a b)d e - 16B b d )x - 6A a e +--R + +--R 2 2 +--R (- 4A a b - 4B a )d e - 16B a b d +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1378 +r0:=-2/255*(8*b*B*d-17*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/17*B*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/12155*(b*d-a*e)^2*(8*b*B*d-17*A*b*e+_ + 9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/109395*_ + (b*d-a*e)^3*(8*b*B*d-17*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5*(a+b*x))+4/1105*(b*d-a*e)*(8*b*B*d-17*A*b*e+_ + 9*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 8 8 3 2 8 3 7 7 +--R 12870B b e x + ((14586A b + 43758B a b )e + 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (50490A a b + 50490B a b)e + (51612A b + 154836B a b )d e +--R + +--R 3 2 6 +--R 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (59670A a b + 19890B a )e + (183600A a b + 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (63036A b + 189108B a b )d e + 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R 24310A a e + (225420A a b + 75140B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (233580A a b + 233580B a b)d e + (27200A b + 81600B a b )d e +--R + +--R 3 4 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R 97240A a d e + (304980A a b + 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (108120A a b + 108120B a b)d e + (170A b + 510B a b )d e +--R + +--R 3 5 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R 145860A a d e + (159120A a b + 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (1530A a b + 1530B a b)d e + (- 204A b - 612B a b )d e +--R + +--R 3 6 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R 97240A a d e + (6630A a b + 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (- 2040A a b - 2040B a b)d e + (272A b + 816B a b )d e +--R + +--R 3 7 +--R - 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (4080A a b + 4080B a b)d e + (- 544A b - 1632B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 109395b e x + 109395a e +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 8 8 3 2 8 3 7 7 +--R 12870B b e x + ((14586A b + 43758B a b )e + 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (50490A a b + 50490B a b)e + (51612A b + 154836B a b )d e +--R + +--R 3 2 6 +--R 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (59670A a b + 19890B a )e + (183600A a b + 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (63036A b + 189108B a b )d e + 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R 24310A a e + (225420A a b + 75140B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (233580A a b + 233580B a b)d e + (27200A b + 81600B a b )d e +--R + +--R 3 4 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R 97240A a d e + (304980A a b + 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (108120A a b + 108120B a b)d e + (170A b + 510B a b )d e +--R + +--R 3 5 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R 145860A a d e + (159120A a b + 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (1530A a b + 1530B a b)d e + (- 204A b - 612B a b )d e +--R + +--R 3 6 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R 97240A a d e + (6630A a b + 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (- 2040A a b - 2040B a b)d e + (272A b + 816B a b )d e +--R + +--R 3 7 +--R - 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (4080A a b + 4080B a b)d e + (- 544A b - 1632B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 109395e +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 8 8 3 2 8 3 7 7 +--R - 12870B b e x + ((- 14586A b - 43758B a b )e - 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (- 50490A a b - 50490B a b)e + (- 51612A b - 154836B a b )d e +--R + +--R 3 2 6 +--R - 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (- 59670A a b - 19890B a )e + (- 183600A a b - 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (- 63036A b - 189108B a b )d e - 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R - 24310A a e + (- 225420A a b - 75140B a )d e +--R + +--R 2 2 2 6 +--R (- 233580A a b - 233580B a b)d e +--R + +--R 3 2 3 5 3 4 4 +--R (- 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8 9 4 3 8 4 7 8 +--R 12870B b e x + ((14586A b + 56628B a b )e + 44616B b d e )x +--R + +--R 3 2 2 8 4 3 7 +--R (65076A a b + 94248B a b )e + (51612A b + 199452B a b )d e +--R + +--R 4 2 6 +--R 52932B b d e +--R * +--R 7 +--R x +--R + +--R 2 2 3 8 3 2 2 7 +--R (110160A a b + 70380B a b)e + (235212A a b + 338436B a b )d e +--R + +--R 4 3 2 6 4 3 5 +--R (63036A b + 242040B a b )d e + 21816B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 8 2 2 3 7 +--R (83980A a b + 19890B a )e + (409020A a b + 258740B a b)d e +--R + +--R 3 2 2 2 6 +--R (296616A a b + 422688B a b )d e +--R + +--R 4 3 3 5 4 4 4 +--R (27200A b + 103416B a b )d e + 70B b d e +--R * +--R 5 +--R x +--R + +--R 4 8 3 4 7 +--R 24310A a e + (322660A a b + 75140B a )d e +--R + +--R 2 2 3 2 6 +--R (538560A a b + 335240B a b)d e +--R + +--R 3 2 2 3 5 4 3 4 4 +--R (135320A a b + 189720B a b )d e + (170A b + 580B a b )d e +--R + +--R 4 5 3 +--R - 80B b d e +--R * +--R 4 +--R x +--R + +--R 4 7 3 4 2 6 +--R 97240A a d e + (450840A a b + 101660B a )d e +--R + +--R 2 2 3 3 5 3 2 2 4 4 +--R (267240A a b + 161160B a b)d e + (1700A a b + 2040B a b )d e +--R + +--R 4 3 5 3 4 6 2 +--R (- 204A b - 692B a b )d e + 96B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 4 3 5 +--R 145860A a d e + (256360A a b + 53040B a )d e +--R + +--R 2 2 3 4 4 3 2 2 5 3 +--R (8160A a b + 3740B a b)d e + (- 2244A a b - 2652B a b )d e +--R + +--R 4 3 6 2 4 7 +--R (272A b + 912B a b )d e - 128B b d e +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 4 +--R 97240A a d e + (30940A a b + 2210B a )d e +--R + +--R 2 2 3 5 3 3 2 2 6 2 +--R (- 15300A a b - 6460B a b)d e + (4352A a b + 4896B a b )d e +--R + +--R 4 3 7 4 8 +--R (- 544A b - 1760B a b )d e + 256B b d +--R * +--R x +--R + +--R 4 4 4 3 4 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 3 6 2 3 2 2 7 +--R (4080A a b + 4080B a b)d e + (- 544A a b - 1632B a b )d e +--R + +--R 3 8 +--R 256B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 109395b e x + 109395a e +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 8 3 2 4 3 3 7 +--R B b e x + ((A b + 3B a b )e + 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 6 +--R ((3A a b + 3B a b)e + (4A b + 12B a b )d e + 6B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b + B a )e + (12A a b + 12B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (6A b + 18B a b )d e + 4B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A a e + (12A a b + 4B a )d e + (18A a b + 18B a b)d e +--R + +--R 3 2 3 3 4 +--R (4A b + 12B a b )d e + B b d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 3 +--R 4A a d e + (18A a b + 6B a )d e + (12A a b + 12B a b)d e +--R + +--R 3 2 4 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 3 3 2 2 4 2 +--R (6A a d e + (12A a b + 4B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 3 2 3 4 3 4 +--R (4A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 9 4 3 4 4 3 8 +--R - B b e x + ((- A b - 4B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((- 4A a b - 6B a b )e + (- 4A b - 16B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 6A a b - 4B a b)e + (- 16A a b - 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 6A b - 24B a b )d e - 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 4A a b - B a )e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 24A a b - 36B a b )d e + (- 4A b - 16B a b )d e - B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - A a e + (- 16A a b - 4B a )d e + (- 36A a b - 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 16A a b - 24B a b )d e + (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R - 4A a d e + (- 24A a b - 6B a )d e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 4 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (- 6A a d e + (- 16A a b - 4B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (- 4A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1378 +r0:=-2/195*(8*b*B*d-15*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/15*B*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/6435*(b*d-a*e)^2*(8*b*B*d-15*A*b*e+7*a*B*e)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/45045*(b*d-a*e)^3*_ + (8*b*B*d-15*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/715*(b*d-a*e)*(8*b*B*d-15*A*b*e+7*a*B*e)*(a+b*x)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 7 7 3 2 7 3 6 6 +--R 6006B b e x + ((6930A b + 20790B a b )e + 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (24570A a b + 24570B a b)e + (17010A b + 51030B a b )d e +--R + +--R 3 2 5 +--R 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (30030A a b + 10010B a )e + (62790A a b + 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (11130A b + 33390B a b )d e + 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R 12870A a e + (81510A a b + 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (44070A a b + 44070B a b)d e + (150A b + 450B a b )d e +--R + +--R 3 4 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 38610A a d e + (64350A a b + 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1170A a b + 1170B a b)d e + (- 180A b - 540B a b )d e +--R + +--R 3 5 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 38610A a d e + (4290A a b + 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1560A a b - 1560B a b)d e + (240A b + 720B a b )d e +--R + +--R 3 6 +--R - 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (3120A a b + 3120B a b)d e + (- 480A b - 1440B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 2 7 3 6 6 +--R 6006B b e x + ((6930A b + 20790B a b )e + 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (24570A a b + 24570B a b)e + (17010A b + 51030B a b )d e +--R + +--R 3 2 5 +--R 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (30030A a b + 10010B a )e + (62790A a b + 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (11130A b + 33390B a b )d e + 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R 12870A a e + (81510A a b + 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (44070A a b + 44070B a b)d e + (150A b + 450B a b )d e +--R + +--R 3 4 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 38610A a d e + (64350A a b + 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1170A a b + 1170B a b)d e + (- 180A b - 540B a b )d e +--R + +--R 3 5 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 38610A a d e + (4290A a b + 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1560A a b - 1560B a b)d e + (240A b + 720B a b )d e +--R + +--R 3 6 +--R - 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (3120A a b + 3120B a b)d e + (- 480A b - 1440B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 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+--R - 38610A a d e + (- 4290A a b - 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1560A a b + 1560B a b)d e + (- 240A b - 720B a b )d e +--R + +--R 3 6 +--R 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 12870A a d e + (8580A a b + 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 3120A a b - 3120B a b)d e + (480A b + 1440B a b )d e - 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 4 7 8 4 3 7 4 6 7 +--R 6006B b e x + ((6930A b + 26796B a b )e + 14322B b d e )x +--R + +--R 3 2 2 7 4 3 6 +--R (31500A a b + 45360B a b )e + (17010A b + 65352B a b )d e +--R + +--R 4 2 5 +--R 8946B b d e +--R * +--R 6 +--R x +--R + +--R 2 2 3 7 3 2 2 6 +--R (54600A a b + 34580B a b)e + (79800A a b + 113820B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (11130A b + 42336B a b )d e + 70B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (42900A a b + 10010B a )e + (144300A a b + 89960B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 +--R (55200A a b + 77460B a b )d e + (150A b + 520B a b )d e +--R + +--R 4 4 3 +--R - 80B b d e +--R * +--R 4 +--R x +--R + +--R 4 7 3 4 6 +--R 12870A a e + (120120A a b + 27170B a )d e +--R + +--R 2 2 3 2 5 3 2 2 3 4 +--R (108420A a b + 65520B a b)d e + (1320A a b + 1620B a b )d e +--R + +--R 4 3 4 3 4 5 2 +--R (- 180A b - 620B a b )d e + 96B b d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 4 2 5 +--R 38610A a d e + (102960A a b + 21450B a )d e +--R + +--R 2 2 3 3 4 3 2 2 4 3 +--R (5460A a b + 2600B a b)d e + (- 1740A a b - 2100B a b )d e +--R + +--R 4 3 5 2 4 6 +--R (240A b + 816B a b )d e - 128B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 4 3 4 +--R 38610A a d e + (17160A a b + 1430B a )d e +--R + +--R 2 2 3 4 3 3 2 2 5 2 +--R (- 10140A a b - 4420B a b)d e + (3360A a b + 3840B a b )d e +--R + +--R 4 3 6 4 7 +--R (- 480A b - 1568B a b )d e + 256B b d +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (3120A a b + 3120B a b)d e + (- 480A a b - 1440B a b )d e +--R + +--R 3 7 +--R 256B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 3 7 3 2 3 3 2 6 +--R B b e x + ((A b + 3B a b )e + 3B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 5 +--R ((3A a b + 3B a b)e + (3A b + 9B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b + B a )e + (9A a b + 9B a b)d e + (3A b + 9B a b )d e +--R + +--R 3 3 +--R B b d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R A a e + (9A a b + 3B a )d e + (9A a b + 9B a b)d e +--R + +--R 3 2 3 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 3 2 +--R (3A a d e + (9A a b + 3B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 2 3 3 3 3 +--R (3A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 8 4 3 3 4 2 7 +--R - B b e x + ((- A b - 4B a b )e - 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((- 4A a b - 6B a b )e + (- 3A b - 12B a b )d e - 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 6A a b - 4B a b)e + (- 12A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 3A b - 12B a b )d e - B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 4A a b - B a )e + (- 18A a b - 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 12A a b - 18B a b )d e + (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R - A a e + (- 12A a b - 3B a )d e + (- 18A a b - 12B a b)d e +--R + +--R 3 2 2 3 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (- 3A a d e + (- 12A a b - 3B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (- 3A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1139 + +)clear all + +--S 1140 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1378 +r0:=-2/143*(8*b*B*d-13*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/13*B*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/3003*(b*d-a*e)^2*(8*b*B*d-13*A*b*e+5*a*B*e)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/15015*(b*d-a*e)^3*_ + (8*b*B*d-13*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/429*(b*d-a*e)*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 6 6 3 2 6 3 5 5 +--R 2310B b e x + ((2730A b + 8190B a b )e + 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (10010A a b + 10010B a b)e + (3640A b + 10920B a b )d e +--R + +--R 3 2 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (12870A a b + 4290B a )e + (14300A a b + 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (130A b + 390B a b )d e - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R 6006A a e + (20592A a b + 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 3 4 2 +--R (858A a b + 858B a b)d e + (- 156A b - 468B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R 12012A a d e + (2574A a b + 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 1144A a b - 1144B a b)d e + (208A b + 624B a b )d e +--R + +--R 3 5 +--R - 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (2288A a b + 2288B a b)d e + (- 416A b - 1248B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 3 2 6 3 5 5 +--R 2310B b e x + ((2730A b + 8190B a b )e + 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (10010A a b + 10010B a b)e + (3640A b + 10920B a b )d e +--R + +--R 3 2 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (12870A a b + 4290B a )e + (14300A a b + 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (130A b + 390B a b )d e - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R 6006A a e + (20592A a b + 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 3 4 2 +--R (858A a b + 858B a b)d e + (- 156A b - 468B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R 12012A a d e + (2574A a b + 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 1144A a b - 1144B a b)d e + (208A b + 624B a b )d e +--R + +--R 3 5 +--R - 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (2288A a b + 2288B a b)d e + (- 416A b - 1248B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 15015e +--R Type: Union(Expression(Integer),...) +--E 1142 + +--S 1143 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 6 6 3 2 6 3 5 5 +--R - 2310B b e x + ((- 2730A b - 8190B a b )e - 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (- 10010A a b - 10010B a b)e + (- 3640A b - 10920B a b )d e +--R + +--R 3 2 4 +--R - 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (- 12870A a b - 4290B a )e + (- 14300A a b - 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (- 130A b - 390B a b )d e + 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R - 6006A a e + (- 20592A a b - 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 +--R (- 858A a b - 858B a b)d e + (156A b + 468B a b )d e +--R + +--R 3 4 2 +--R - 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R - 12012A a d e + (- 2574A a b - 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (1144A a b + 1144B a b)d e + (- 208A b - 624B a b )d e +--R + +--R 3 5 +--R 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R - 6006A a d e + (5148A a b + 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (- 2288A a b - 2288B a b)d e + (416A b + 1248B a b )d e - 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 4 6 7 4 3 6 4 5 6 +--R 2310B b e x + ((2730A b + 10500B a b )e + 2940B b d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (12740A a b + 18200B a b )e + (3640A b + 13860B a b )d e +--R + +--R 4 2 4 +--R 70B b d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (22880A a b + 14300B a b)e + (17940A a b + 25220B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (130A b + 460B a b )d e - 80B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (18876A a b + 4290B a )e + (34892A a b + 21164B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (988A a b + 1248B a b )d e + (- 156A b - 548B a b )d e +--R + +--R 4 4 2 +--R 96B b d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 4 5 +--R 6006A a e + (32604A a b + 6864B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (3432A a b + 1716B a b)d e + (- 1300A a b - 1612B a b )d e +--R + +--R 4 3 4 2 4 5 +--R (208A b + 720B a b )d e - 128B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 4 +--R 12012A a d e + (8580A a b + 858B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (- 6292A a b - 2860B a b)d e + (2496A a b + 2912B a b )d e +--R + +--R 4 3 5 4 6 +--R (- 416A b - 1376B a b )d e + 256B b d +--R * +--R x +--R + +--R 4 2 4 3 4 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 3 4 2 3 2 2 5 +--R (2288A a b + 2288B a b)d e + (- 416A a b - 1248B a b )d e +--R + +--R 3 6 +--R 256B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 2 6 3 2 2 3 5 +--R B b e x + ((A b + 3B a b )e + 2B b d e)x +--R + +--R 2 2 2 3 2 3 2 4 +--R ((3A a b + 3B a b)e + (2A b + 6B a b )d e + B b d )x +--R + +--R 2 3 2 2 2 3 2 2 3 +--R ((3A a b + B a )e + (6A a b + 6B a b)d e + (A b + 3B a b )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (A a e + (6A a b + 2B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 3 2 3 2 +--R (2A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 2 7 4 3 2 4 6 +--R - B b e x + ((- A b - 4B a b )e - 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((- 4A a b - 6B a b )e + (- 2A b - 8B a b )d e - B b d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 6A a b - 4B a b)e + (- 8A a b - 12B a b )d e +--R + +--R 4 3 2 +--R (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 4A a b - B a )e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 2 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- A a e + (- 8A a b - 2B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (- 2A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1144 + +)clear all + +--S 1145 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1378 +r0:=-2/99*(8*b*B*d-11*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/11*B*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/1155*(b*d-a*e)^2*(8*b*B*d-11*A*b*e+3*a*B*e)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/3465*(b*d-a*e)^3*_ + (8*b*B*d-11*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/231*(b*d-a*e)*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 5 5 3 2 5 3 4 4 +--R 630B b e x + ((770A b + 2310B a b )e + 70B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((2970A a b + 2970B a b)e + (110A b + 330B a b )d e - 80B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (4158A a b + 1386B a )e + (594A a b + 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 132A b - 396B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R 2310A a e + (1386A a b + 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R (- 792A a b - 792B a b)d e + (176A b + 528B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (1584A a b + 1584B a b)d e + (- 352A b - 1056B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 3 2 5 3 4 4 +--R 630B b e x + ((770A b + 2310B a b )e + 70B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((2970A a b + 2970B a b)e + (110A b + 330B a b )d e - 80B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (4158A a b + 1386B a )e + (594A a b + 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 132A b - 396B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R 2310A a e + (1386A a b + 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R (- 792A a b - 792B a b)d e + (176A b + 528B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (1584A a b + 1584B a b)d e + (- 352A b - 1056B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 1147 + +--S 1148 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 5 5 3 2 5 3 4 4 +--R - 630B b e x + ((- 770A b - 2310B a b )e - 70B b d e )x +--R + +--R 2 2 5 3 2 4 +--R (- 2970A a b - 2970B a b)e + (- 110A b - 330B a b )d e +--R + +--R 3 2 3 +--R 80B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 4 +--R (- 4158A a b - 1386B a )e + (- 594A a b - 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (132A b + 396B a b )d e - 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R - 2310A a e + (- 1386A a b - 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 +--R (792A a b + 792B a b)d e + (- 176A b - 528B a b )d e +--R + +--R 3 4 +--R 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R - 2310A a d e + (2772A a b + 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (- 1584A a b - 1584B a b)d e + (352A b + 1056B a b )d e - 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 4 5 6 4 3 5 4 4 5 +--R 630B b e x + ((770A b + 2940B a b )e + 70B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (3740A a b + 5280B a b )e + (110A b + 400B a b )d e +--R + +--R 4 2 3 +--R - 80B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (7128A a b + 4356B a b)e + (704A a b + 924B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 132A b - 476B a b )d e + 96B b d e +--R * +--R 3 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (6468A a b + 1386B a )e + (1980A a b + 1056B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 924A a b - 1188B a b )d e + (176A b + 624B a b )d e +--R + +--R 4 4 +--R - 128B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 4 +--R 2310A a e + (3696A a b + 462B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 3564A a b - 1716B a b)d e + (1760A a b + 2112B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 352A b - 1184B a b )d e + 256B b d +--R * +--R x +--R + +--R 4 4 3 4 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (1584A a b + 1584B a b)d e + (- 352A a b - 1056B a b )d e +--R + +--R 3 5 +--R 256B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 3 2 3 4 +--R B b e x + ((A b + 3B a b )e + B b d)x +--R + +--R 2 2 3 2 3 +--R ((3A a b + 3B a b)e + (A b + 3B a b )d)x +--R + +--R 2 3 2 2 2 +--R ((3A a b + B a )e + (3A a b + 3B a b)d)x +--R + +--R 3 2 3 3 +--R (A a e + (3A a b + B a )d)x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 4 5 +--R - B b e x + ((- A b - 4B a b )e - B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((- 4A a b - 6B a b )e + (- A b - 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 6A a b - 4B a b)e + (- 4A a b - 6B a b )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 4A a b - B a )e + (- 6A a b - 4B a b)d)x +--R + +--R 4 3 4 4 +--R (- A a e + (- 4A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1149 + +)clear all + +--S 1150 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1378 +r0:=-2/63*(8*b*B*d-9*A*b*e+a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(b*e^2)+2/9*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(b*e)-16/315*(b*d-a*e)^2*(8*b*B*d-9*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/315*(b*d-a*e)^3*_ + (8*b*B*d-9*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/105*(b*d-a*e)*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((90A b + 270B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((378A a b + 378B a b)e + (- 108A b - 324B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (630A a b + 210B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (144A b + 432B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 630A a e + (- 1260A a b - 420B a )d e + (1008A a b + 1008B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 288A b - 864B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((90A b + 270B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((378A a b + 378B a b)e + (- 108A b - 324B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (630A a b + 210B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (144A b + 432B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 630A a e + (- 1260A a b - 420B a )d e + (1008A a b + 1008B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 288A b - 864B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 1152 + +--S 1153 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R - 70B b e x + ((- 90A b - 270B a b )e + 80B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 378A a b - 378B a b)e + (108A b + 324B a b )d e +--R + +--R 3 2 2 +--R - 96B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 630A a b - 210B a )e + (504A a b + 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 144A b - 432B a b )d e + 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 +--R - 630A a e + (1260A a b + 420B a )d e +--R + +--R 2 2 2 2 3 2 3 3 4 +--R (- 1008A a b - 1008B a b)d e + (288A b + 864B a b )d e - 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R 70B b e x + ((90A b + 340B a b )e - 80B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (468A a b + 648B a b )e + (- 108A b - 404B a b )d e +--R + +--R 4 2 2 +--R 96B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (1008A a b + 588B a b)e + (- 612A a b - 828B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (144A b + 528B a b )d e - 128B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (1260A a b + 210B a )e + (- 1764A a b - 924B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1152A a b + 1440B a b )d e + (- 288A b - 992B a b )d e +--R + +--R 4 4 +--R 256B b d +--R * +--R x +--R + +--R 4 4 3 4 3 +--R 630A a e + (- 1260A a b - 420B a )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (1008A a b + 1008B a b)d e + (- 288A a b - 864B a b )d e +--R + +--R 3 4 +--R 256B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1154 + +)clear all + +--S 1155 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1378 +r0:=-2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+2/7*(8*b*B*d-7*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(e^2*(b*d-a*e))+16/35*(b*d-a*e)*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-32/35*(b*d-a*e)^2*(8*b*B*d-_ + 7*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-_ + 12/35*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^3 +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((14A b + 42B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((70A a b + 70B a b)e + (- 28A b - 84B a b )d e + 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (210A a b + 70B a )e + (- 280A a b - 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (112A b + 336B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (224A b + 672B a b )d e - 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((14A b + 42B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((70A a b + 70B a b)e + (- 28A b - 84B a b )d e + 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (210A a b + 70B a )e + (- 280A a b - 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (112A b + 336B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (224A b + 672B a b )d e - 256B b d +--R / +--R 5 +-------+ +--R 35e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1157 + +--S 1158 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R - 10B b e x + ((- 14A b - 42B a b )e + 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 70A a b - 70B a b)e + (28A b + 84B a b )d e - 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 210A a b - 70B a )e + (280A a b + 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 112A b - 336B a b )d e + 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 70A a e + (- 420A a b - 140B a )d e + (560A a b + 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 224A b - 672B a b )d e + 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R 10B b e x + ((14A b + 52B a b )e - 16B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((84A a b + 112B a b )e + (- 28A b - 100B a b )d e + 32B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (280A a b + 140B a b)e + (- 308A a b - 364B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (112A b + 368B a b )d e - 128B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (140A a b + 70B a )e + (140A a b - 140B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 448A a b - 224B a b )d e + (224A b + 544B a b )d e - 256B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (224A a b + 672B a b )d e - 256B a b d +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1159 + +)clear all + +--S 1160 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))-2/3*(8*b*B*d-5*A*b*e-3*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*sqrt(d+e*x))-16/15*b*(8*b*B*d-5*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+32/15*b*(b*d-a*e)*_ + (8*b*B*d-5*A*b*e-3*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x))+4/5*b*(8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((10A b + 30B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((90A a b + 90B a b)e + (- 60A b - 180B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 90A a b - 30B a )e + (360A a b + 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 160A b - 480B a b )d e + 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((10A b + 30B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((90A a b + 90B a b)e + (- 60A b - 180B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 90A a b - 30B a )e + (360A a b + 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 160A b - 480B a b )d e + 256B b d +--R / +--R 6 5 +-------+ +--R (15e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1162 + +--S 1163 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R - 6B b e x + ((- 10A b - 30B a b )e + 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (60A b + 180B a b )d e - 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (90A a b + 30B a )e + (- 360A a b - 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 10A a e + (60A a b + 20B a )d e + (- 240A a b - 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (160A b + 480B a b )d e - 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R 6B b e x + ((10A b + 36B a b )e - 16B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((100A a b + 120B a b )e + (- 60A b - 196B a b )d e + 96B b d e )x +--R + +--R 3 4 3 2 2 3 +--R 60B a b e + (300A a b + 180B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 240A b - 624B a b )d e + 384B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R (- 100A a b - 30B a )e + (300A a b + 340B a b)d e - 480B a b d e +--R + +--R 4 3 3 4 4 +--R (- 160A b - 96B a b )d e + 256B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 160A a b - 480B a b )d e + 256B a b d +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1164 + +)clear all + +--S 1165 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1378 +r0:=-2/5*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/15*(8*b*B*d-3*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/5*b*(8*b*B*d-_ + 3*A*b*e-5*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*_ + sqrt(d+e*x))+16/15*b^2*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(b*d-a*e))-32/15*b^2*(8*b*B*d-3*A*b*e-_ + 5*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((30A b + 90B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (180A b + 540B a b )d e - 480B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 30A a b - 10B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (96A b + 288B a b )d e - 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((30A b + 90B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (180A b + 540B a b )d e - 480B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 30A a b - 10B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (96A b + 288B a b )d e - 256B b d +--R / +--R 7 2 6 2 5 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1167 + +--S 1168 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R - 10B b e x + ((- 30A b - 90B a b )e + 80B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (90A a b + 90B a b)e + (- 180A b - 540B a b )d e +--R + +--R 3 2 2 +--R 480B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (30A a b + 10B a )e + (120A a b + 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 6A a e + (12A a b + 4B a )d e + (48A a b + 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 96A b - 288B a b )d e + 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R 10B b e x + ((30A b + 100B a b )e - 80B b d e )x +--R + +--R 3 4 4 3 3 4 2 2 3 +--R (- 60A a b e + (180A b + 460B a b )d e - 480B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 120A a b - 100B a b)e + (60A a b + 420B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (240A b + 240B a b )d e - 640B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 36A a b - 10B a )e + (- 132A a b - 124B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (192A a b + 672B a b )d e + (96A b - 352B a b )d e - 256B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (96A a b + 288B a b )d e - 256B a b d +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1378 +r0:=-32/6783*(b*d-a*e)^2*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+20/2261*(b*d-a*e)*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-_ + 2/133*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/21*B*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/323323*(b*d-a*e)^4*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/2909907*(b*d-a*e)^5*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/29393*(b*d-a*e)^3*_ + (4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 10 10 5 4 10 5 9 9 +--R 277134B b e x + ((306306A b + 1531530B a b )e + 933504B b d e )x +--R + +--R 4 2 3 10 +--R (1711710A a b + 3423420B a b )e +--R + +--R 5 4 9 5 2 8 +--R (1045044A b + 5225220B a b )d e + 1065636B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 3 2 10 +--R (3879876A a b + 3879876B a b )e +--R + +--R 4 2 3 9 +--R (5933928A a b + 11867856B a b )d e +--R + +--R 5 4 2 8 5 3 7 +--R (1213212A b + 6066060B a b )d e + 415272B b d e +--R * +--R 7 +--R x +--R + +--R 3 2 4 10 +--R (4476780A a b + 2238390B a b)e +--R + +--R 2 3 3 2 9 +--R (13728792A a b + 13728792B a b )d e +--R + +--R 4 2 3 2 8 +--R (7039956A a b + 14079912B a b )d e +--R + +--R 5 4 3 7 5 4 6 +--R (484176A b + 2420880B a b )d e + 462B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 10 +--R (2645370A a b + 529074B a )e +--R + +--R 3 2 4 9 +--R (16279200A a b + 8139600B a b)d e +--R + +--R 2 3 3 2 2 8 +--R (16767576A a b + 16767576B a b )d e +--R + +--R 4 2 3 3 7 5 4 4 6 +--R (2901528A a b + 5803056B a b )d e + (882A b + 4410B a b )d e +--R + +--R 5 5 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 5 10 4 5 9 +--R 646646A a e + (9993620A a b + 1998724B a )d e +--R + +--R 3 2 4 2 8 +--R (20710760A a b + 10355380B a b)d e +--R + +--R 2 3 3 2 3 7 +--R (7235200A a b + 7235200B a b )d e +--R + +--R 4 2 3 4 6 5 4 5 5 +--R (9310A a b + 18620B a b )d e + (- 980A b - 4900B a b )d e +--R + +--R 5 6 4 +--R 560B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 2 8 +--R 2586584A a d e + (13520780A a b + 2704156B a )d e +--R + +--R 3 2 4 3 7 +--R (9586640A a b + 4793320B a b)d e +--R + +--R 2 3 3 2 4 6 4 2 3 5 5 +--R (45220A a b + 45220B a b )d e + (- 10640A a b - 21280B a b )d e +--R + +--R 5 4 6 4 5 7 3 +--R (1120A b + 5600B a b )d e - 640B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 8 4 5 3 7 +--R 3879876A a d e + (7054320A a b + 1410864B a )d e +--R + +--R 3 2 4 4 6 2 3 3 2 5 5 +--R (135660A a b + 67830B a b)d e + (- 54264A a b - 54264B a b )d e +--R + +--R 4 2 3 6 4 5 4 7 3 +--R (12768A a b + 25536B a b )d e + (- 1344A b - 6720B a b )d e +--R + +--R 5 8 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 3 7 4 5 4 6 +--R 2586584A a d e + (293930A a b + 58786B a )d e +--R + +--R 3 2 4 5 5 2 3 3 2 6 4 +--R (- 180880A a b - 90440B a b)d e + (72352A a b + 72352B a b )d e +--R + +--R 4 2 3 7 3 5 4 8 2 +--R (- 17024A a b - 34048B a b )d e + (1792A b + 8960B a b )d e +--R + +--R 5 9 +--R - 1024B b d e +--R * +--R x +--R + +--R 5 4 6 4 5 5 5 +--R 646646A a d e + (- 587860A a b - 117572B a )d e +--R + +--R 3 2 4 6 4 2 3 3 2 7 3 +--R (361760A a b + 180880B a b)d e + (- 144704A a b - 144704B a b )d e +--R + +--R 4 2 3 8 2 5 4 9 +--R (34048A a b + 68096B a b )d e + (- 3584A b - 17920B a b )d e +--R + +--R 5 10 +--R 2048B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 2909907b e x + 2909907a e +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 10 5 4 10 5 9 9 +--R 277134B b e x + ((306306A b + 1531530B a b )e + 933504B b d e )x +--R + +--R 4 2 3 10 +--R (1711710A a b + 3423420B a b )e +--R + +--R 5 4 9 5 2 8 +--R (1045044A b + 5225220B a b )d e + 1065636B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 3 2 10 +--R (3879876A a b + 3879876B a b )e +--R + +--R 4 2 3 9 +--R (5933928A a b + 11867856B a b )d e +--R + +--R 5 4 2 8 5 3 7 +--R (1213212A b + 6066060B a b )d e + 415272B b d e +--R * +--R 7 +--R x +--R + +--R 3 2 4 10 +--R (4476780A a b + 2238390B a b)e +--R + +--R 2 3 3 2 9 +--R (13728792A a b + 13728792B a b )d e +--R + +--R 4 2 3 2 8 +--R (7039956A a b + 14079912B a b )d e +--R + +--R 5 4 3 7 5 4 6 +--R (484176A b + 2420880B a b )d e + 462B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 10 +--R (2645370A a b + 529074B a )e +--R + +--R 3 2 4 9 +--R (16279200A a b + 8139600B a b)d e +--R + +--R 2 3 3 2 2 8 +--R (16767576A a b + 16767576B a b )d e +--R + +--R 4 2 3 3 7 5 4 4 6 +--R (2901528A a b + 5803056B a b )d e + (882A b + 4410B a b )d e +--R + +--R 5 5 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 5 10 4 5 9 +--R 646646A a e + (9993620A a b + 1998724B a )d e +--R + +--R 3 2 4 2 8 +--R (20710760A a b + 10355380B a b)d e +--R + +--R 2 3 3 2 3 7 +--R (7235200A a b + 7235200B a b )d e +--R + +--R 4 2 3 4 6 5 4 5 5 +--R (9310A a b + 18620B a b )d e + (- 980A b - 4900B a b )d e +--R + +--R 5 6 4 +--R 560B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 2 8 +--R 2586584A a d e + (13520780A a b + 2704156B a )d e +--R + +--R 3 2 4 3 7 +--R (9586640A a b + 4793320B a b)d e +--R + +--R 2 3 3 2 4 6 4 2 3 5 5 +--R (45220A a b + 45220B a b )d e + (- 10640A a b - 21280B a b )d e +--R + +--R 5 4 6 4 5 7 3 +--R (1120A b + 5600B a b )d e - 640B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 8 4 5 3 7 +--R 3879876A a d e + (7054320A a b + 1410864B a )d e +--R + +--R 3 2 4 4 6 2 3 3 2 5 5 +--R (135660A a b + 67830B a b)d e + (- 54264A a b - 54264B a b )d e +--R + +--R 4 2 3 6 4 5 4 7 3 +--R (12768A a b + 25536B a b )d e + (- 1344A b - 6720B a b )d e +--R + +--R 5 8 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 3 7 4 5 4 6 +--R 2586584A a d e + (293930A a b + 58786B a )d e +--R + +--R 3 2 4 5 5 2 3 3 2 6 4 +--R (- 180880A a b - 90440B a b)d e + (72352A a b + 72352B a b )d e +--R + +--R 4 2 3 7 3 5 4 8 2 +--R (- 17024A a b - 34048B a b )d e + (1792A b + 8960B a b )d e +--R + +--R 5 9 +--R - 1024B b d e +--R * +--R x +--R + +--R 5 4 6 4 5 5 5 +--R 646646A a d e + (- 587860A a b - 117572B a )d e +--R + +--R 3 2 4 6 4 2 3 3 2 7 3 +--R (361760A a b + 180880B a b)d e + (- 144704A a b - 144704B a b )d e +--R + +--R 4 2 3 8 2 5 4 9 +--R (34048A a b + 68096B a b )d e + (- 3584A b - 17920B a b )d e +--R + +--R 5 10 +--R 2048B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 2909907e +--R Type: Union(Expression(Integer),...) +--E 1172 + +--S 1173 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 10 10 +--R - 277134B b e x +--R + +--R 5 4 10 5 9 9 +--R ((- 306306A b - 1531530B a b )e - 933504B b d e )x +--R + +--R 4 2 3 10 +--R (- 1711710A a b - 3423420B a b )e +--R + +--R 5 4 9 5 2 8 +--R (- 1045044A b - 5225220B a b )d e - 1065636B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 3 2 10 +--R (- 3879876A a b - 3879876B a b )e +--R + +--R 4 2 3 9 +--R (- 5933928A a b - 11867856B a b )d e +--R + +--R 5 4 2 8 5 3 7 +--R (- 1213212A b - 6066060B a b )d e - 415272B b d e +--R * +--R 7 +--R x +--R + +--R 3 2 4 10 +--R (- 4476780A a b - 2238390B a b)e +--R + +--R 2 3 3 2 9 +--R (- 13728792A a b - 13728792B a b )d e +--R + +--R 4 2 3 2 8 +--R (- 7039956A a b - 14079912B a b )d e +--R + +--R 5 4 3 7 5 4 6 +--R (- 484176A b - 2420880B a b )d e - 462B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 10 +--R (- 2645370A a b - 529074B a )e +--R + +--R 3 2 4 9 +--R (- 16279200A a b - 8139600B a b)d e +--R + +--R 2 3 3 2 2 8 +--R (- 16767576A a b - 16767576B a b )d e +--R + +--R 4 2 3 3 7 +--R (- 2901528A a b - 5803056B a b )d e +--R + +--R 5 4 4 6 5 5 5 +--R (- 882A b - 4410B a b )d e + 504B b d e +--R * +--R 5 +--R x +--R + +--R 5 10 4 5 9 +--R - 646646A a e + (- 9993620A a b - 1998724B a )d e +--R + +--R 3 2 4 2 8 +--R (- 20710760A a b - 10355380B a b)d e +--R + +--R 2 3 3 2 3 7 +--R (- 7235200A a b - 7235200B a b )d e +--R + +--R 4 2 3 4 6 5 4 5 5 +--R (- 9310A a b - 18620B a b )d e + (980A b + 4900B a b )d e +--R + +--R 5 6 4 +--R - 560B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 2 8 +--R - 2586584A a d e + (- 13520780A a b - 2704156B a )d e +--R + +--R 3 2 4 3 7 +--R (- 9586640A a b - 4793320B a b)d e +--R + +--R 2 3 3 2 4 6 +--R (- 45220A a b - 45220B a b )d e +--R + +--R 4 2 3 5 5 5 4 6 4 +--R (10640A a b + 21280B a b )d e + (- 1120A b - 5600B a b )d e +--R + +--R 5 7 3 +--R 640B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 8 4 5 3 7 +--R - 3879876A a d e + (- 7054320A a b - 1410864B a )d e +--R + +--R 3 2 4 4 6 +--R (- 135660A a b - 67830B a b)d e +--R + +--R 2 3 3 2 5 5 +--R (54264A a b + 54264B a b )d e +--R + +--R 4 2 3 6 4 5 4 7 3 +--R (- 12768A a b - 25536B a b )d e + (1344A b + 6720B a b )d e +--R + +--R 5 8 2 +--R - 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 3 7 4 5 4 6 +--R - 2586584A a d e + (- 293930A a b - 58786B a )d e +--R + +--R 3 2 4 5 5 +--R (180880A a b + 90440B a b)d e +--R + +--R 2 3 3 2 6 4 +--R (- 72352A a b - 72352B a b )d e +--R + +--R 4 2 3 7 3 5 4 8 2 +--R (17024A a b + 34048B a b )d e + (- 1792A b - 8960B a b )d e +--R + +--R 5 9 +--R 1024B b d e +--R * +--R x +--R + +--R 5 4 6 4 5 5 5 +--R - 646646A a d e + (587860A a b + 117572B a )d e +--R + +--R 3 2 4 6 4 +--R (- 361760A a b - 180880B a b)d e +--R + +--R 2 3 3 2 7 3 4 2 3 8 2 +--R (144704A a b + 144704B a b )d e + (- 34048A a b - 68096B a b )d e +--R + +--R 5 4 9 5 10 +--R (3584A b + 17920B a b )d e - 2048B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 6 10 11 +--R 277134B b e x +--R + +--R 6 5 10 6 9 10 +--R ((306306A b + 1808664B a b )e + 933504B b d e )x +--R + +--R 5 2 4 10 +--R (2018016A a b + 4954950B a b )e +--R + +--R 6 5 9 6 2 8 +--R (1045044A b + 6158724B a b )d e + 1065636B b d e +--R * +--R 9 +--R x +--R + +--R 2 4 3 3 10 +--R (5591586A a b + 7303296B a b )e +--R + +--R 5 2 4 9 +--R (6978972A a b + 17093076B a b )d e +--R + +--R 6 5 2 8 6 3 7 +--R (1213212A b + 7131696B a b )d e + 415272B b d e +--R * +--R 8 +--R x +--R + +--R 3 3 4 2 10 +--R (8356656A a b + 6118266B a b )e +--R + +--R 2 4 3 3 9 +--R (19662720A a b + 25596648B a b )d e +--R + +--R 5 2 4 2 8 +--R (8253168A a b + 20145972B a b )d e +--R + +--R 6 5 3 7 6 4 6 +--R (484176A b + 2836152B a b )d e + 462B b d e +--R * +--R 7 +--R x +--R + +--R 4 2 5 10 +--R (7122150A a b + 2767464B a b)e +--R + +--R 3 3 4 2 9 +--R (30007992A a b + 21868392B a b )d e +--R + +--R 2 4 3 3 2 8 +--R (23807532A a b + 30847488B a b )d e +--R + +--R 5 2 4 3 7 6 5 4 6 +--R (3385704A a b + 8223936B a b )d e + (882A b + 4872B a b )d e +--R + +--R 6 5 5 +--R - 504B b d e +--R * +--R 6 +--R x +--R + +--R 5 6 10 +--R (3292016A a b + 529074B a )e +--R + +--R 4 2 5 9 +--R (26272820A a b + 10138324B a b)d e +--R + +--R 3 3 4 2 2 8 +--R (37478336A a b + 27122956B a b )d e +--R + +--R 2 4 3 3 3 7 +--R (10136728A a b + 13038256B a b )d e +--R + +--R 5 2 4 4 6 6 5 5 5 +--R (10192A a b + 23030B a b )d e + (- 980A b - 5404B a b )d e +--R + +--R 6 6 4 +--R 560B b d e +--R * +--R 5 +--R x +--R + +--R 6 10 5 6 9 +--R 646646A a e + (12580204A a b + 1998724B a )d e +--R + +--R 4 2 5 2 8 +--R (34231540A a b + 13059536B a b)d e +--R + +--R 3 3 4 2 3 7 +--R (16821840A a b + 12028520B a b )d e +--R + +--R 2 4 3 3 4 6 +--R (54530A a b + 63840B a b )d e +--R + +--R 5 2 4 5 5 6 5 6 4 +--R (- 11620A a b - 26180B a b )d e + (1120A b + 6160B a b )d e +--R + +--R 6 7 3 +--R - 640B b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 6 2 8 +--R 2586584A a d e + (17400656A a b + 2704156B a )d e +--R + +--R 4 2 5 3 7 +--R (16640960A a b + 6204184B a b)d e +--R + +--R 3 3 4 2 4 6 +--R (180880A a b + 113050B a b )d e +--R + +--R 2 4 3 3 5 5 +--R (- 64904A a b - 75544B a b )d e +--R + +--R 5 2 4 6 4 6 5 7 3 +--R (13888A a b + 31136B a b )d e + (- 1344A b - 7360B a b )d e +--R + +--R 6 8 2 +--R 768B b d e +--R * +--R 3 +--R x +--R + +--R 6 2 8 5 6 3 7 +--R 3879876A a d e + (9640904A a b + 1410864B a )d e +--R + +--R 4 2 5 4 6 +--R (429590A a b + 126616B a b)d e +--R + +--R 3 3 4 2 5 5 +--R (- 235144A a b - 144704B a b )d e +--R + +--R 2 4 3 3 6 4 +--R (85120A a b + 97888B a b )d e +--R + +--R 5 2 4 7 3 6 5 8 2 +--R (- 18368A a b - 40768B a b )d e + (1792A b + 9728B a b )d e +--R + +--R 6 9 +--R - 1024B b d e +--R * +--R 2 +--R x +--R + +--R 6 3 7 5 6 4 6 +--R 2586584A a d e + (940576A a b + 58786B a )d e +--R + +--R 4 2 5 5 5 +--R (- 768740A a b - 208012B a b)d e +--R + +--R 3 3 4 2 6 4 +--R (434112A a b + 253232B a b )d e +--R + +--R 2 4 3 3 7 3 +--R (- 161728A a b - 178752B a b )d e +--R + +--R 5 2 4 8 2 6 5 9 +--R (35840A a b + 77056B a b )d e + (- 3584A b - 18944B a b )d e +--R + +--R 6 10 +--R 2048B b d +--R * +--R x +--R + +--R 6 4 6 5 6 5 5 +--R 646646A a d e + (- 587860A a b - 117572B a )d e +--R + +--R 4 2 5 6 4 +--R (361760A a b + 180880B a b)d e +--R + +--R 3 3 4 2 7 3 2 4 3 3 8 2 +--R (- 144704A a b - 144704B a b )d e + (34048A a b + 68096B a b )d e +--R + +--R 5 2 4 9 5 10 +--R (- 3584A a b - 17920B a b )d e + 2048B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 2909907b e x + 2909907a e +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 4 10 5 4 4 5 3 9 +--R B b e x + ((A b + 5B a b )e + 4B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 8 +--R ((5A a b + 10B a b )e + (4A b + 20B a b )d e + 6B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (10A a b + 10B a b )e + (20A a b + 40B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (6A b + 30B a b )d e + 4B b d e +--R * +--R 7 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (10A a b + 5B a b)e + (40A a b + 40B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (30A a b + 60B a b )d e + (4A b + 20B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (5A a b + B a )e + (40A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (60A a b + 60B a b )d e + (20A a b + 40B a b )d e +--R + +--R 5 4 4 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R A a e + (20A a b + 4B a )d e + (60A a b + 30B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (40A a b + 40B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 4 5 2 2 3 2 4 3 +--R 4A a d e + (30A a b + 6B a )d e + (40A a b + 20B a b)d e +--R + +--R 2 3 3 2 4 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 2 4 5 3 3 2 4 4 2 +--R (6A a d e + (20A a b + 4B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 3 4 5 4 5 4 +--R (4A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 4 11 6 5 4 6 3 10 +--R - B b e x + ((- A b - 6B a b )e - 4B b d e )x +--R + +--R 5 2 4 4 6 5 3 6 2 2 9 +--R ((- 6A a b - 15B a b )e + (- 4A b - 24B a b )d e - 6B b d e )x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 15A a b - 20B a b )e + (- 24A a b - 60B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (- 6A b - 36B a b )d e - 4B b d e +--R * +--R 8 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (- 20A a b - 15B a b )e + (- 60A a b - 80B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (- 36A a b - 90B a b )d e + (- 4A b - 24B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 15A a b - 6B a b)e + (- 80A a b - 60B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 90A a b - 120B a b )d e + (- 24A a b - 60B a b )d e +--R + +--R 6 5 4 +--R (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 6A a b - B a )e + (- 60A a b - 24B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 120A a b - 90B a b )d e + (- 60A a b - 80B a b )d e +--R + +--R 5 2 4 4 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R - A a e + (- 24A a b - 4B a )d e + (- 90A a b - 36B a b)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (- 80A a b - 60B a b )d e + (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 5 6 2 2 4 2 5 3 +--R - 4A a d e + (- 36A a b - 6B a )d e + (- 60A a b - 24B a b)d e +--R + +--R 3 3 4 2 4 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 2 5 6 3 4 2 5 4 2 +--R (- 6A a d e + (- 24A a b - 4B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 3 5 6 4 6 4 +--R (- 4A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1378 +r0:=-32/12597*(b*d-a*e)^2*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+4/969*(b*d-a*e)*(12*b*B*d-19*A*b*e+_ + 7*a*B*e)*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-_ + 2/323*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/19*B*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/415701*(b*d-a*e)^4*(12*b*B*d-19*A*b*e+_ + 7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/2909907*(b*d-a*e)^5*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/46189*(b*d-a*e)^3*_ + (12*b*B*d-19*A*b*e+7*a*B*e)*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 9 9 5 4 9 5 8 8 +--R 306306B b e x + ((342342A b + 1711710B a b )e + 702702B b d e )x +--R + +--R 4 2 3 9 +--R (1939938A a b + 3879876B a b )e +--R + +--R 5 4 8 5 2 7 +--R (798798A b + 3993990B a b )d e + 414414B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 3 2 9 +--R (4476780A a b + 4476780B a b )e +--R + +--R 4 2 3 8 +--R (4626006A a b + 9252012B a b )d e +--R + +--R 5 4 2 7 5 3 6 +--R (482790A b + 2413950B a b )d e + 1386B b d e +--R * +--R 6 +--R x +--R + +--R 3 2 4 9 +--R (5290740A a b + 2645370B a b)e +--R + +--R 2 3 3 2 8 +--R (10988460A a b + 10988460B a b )d e +--R + +--R 4 2 3 2 7 5 4 3 6 +--R (2889558A a b + 5779116B a b )d e + (2394A b + 11970B a b )d e +--R + +--R 5 4 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 4 5 9 3 2 4 8 +--R (3233230A a b + 646646B a )e + (13520780A a b + 6760390B a b)d e +--R + +--R 2 3 3 2 2 7 +--R (7189980A a b + 7189980B a b )d e +--R + +--R 4 2 3 3 6 5 4 4 5 +--R (22610A a b + 45220B a b )d e + (- 2660A b - 13300B a b )d e +--R + +--R 5 5 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 8 +--R 831402A a e + (8775910A a b + 1755182B a )d e +--R + +--R 3 2 4 2 7 +--R (9489740A a b + 4744870B a b)d e +--R + +--R 2 3 3 2 3 6 4 2 3 4 5 +--R (96900A a b + 96900B a b )d e + (- 25840A a b - 51680B a b )d e +--R + +--R 5 4 5 4 5 6 3 +--R (3040A b + 15200B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 2 7 +--R 2494206A a d e + (6928350A a b + 1385670B a )d e +--R + +--R 3 2 4 3 6 +--R (251940A a b + 125970B a b)d e +--R + +--R 2 3 3 2 4 5 +--R (- 116280A a b - 116280B a b )d e +--R + +--R 4 2 3 5 4 5 4 6 3 +--R (31008A a b + 62016B a b )d e + (- 3648A b - 18240B a b )d e +--R + +--R 5 7 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 7 4 5 3 6 +--R 2494206A a d e + (461890A a b + 92378B a )d e +--R + +--R 3 2 4 4 5 +--R (- 335920A a b - 167960B a b)d e +--R + +--R 2 3 3 2 5 4 +--R (155040A a b + 155040B a b )d e +--R + +--R 4 2 3 6 3 5 4 7 2 +--R (- 41344A a b - 82688B a b )d e + (4864A b + 24320B a b )d e +--R + +--R 5 8 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 3 6 4 5 4 5 +--R 831402A a d e + (- 923780A a b - 184756B a )d e +--R + +--R 3 2 4 5 4 2 3 3 2 6 3 +--R (671840A a b + 335920B a b)d e + (- 310080A a b - 310080B a b )d e +--R + +--R 4 2 3 7 2 5 4 8 +--R (82688A a b + 165376B a b )d e + (- 9728A b - 48640B a b )d e +--R + +--R 5 9 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 2909907b e x + 2909907a e +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 9 9 5 4 9 5 8 8 +--R 306306B b e x + ((342342A b + 1711710B a b )e + 702702B b d e )x +--R + +--R 4 2 3 9 +--R (1939938A a b + 3879876B a b )e +--R + +--R 5 4 8 5 2 7 +--R (798798A b + 3993990B a b )d e + 414414B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 3 2 9 +--R (4476780A a b + 4476780B a b )e +--R + +--R 4 2 3 8 +--R (4626006A a b + 9252012B a b )d e +--R + +--R 5 4 2 7 5 3 6 +--R (482790A b + 2413950B a b )d e + 1386B b d e +--R * +--R 6 +--R x +--R + +--R 3 2 4 9 +--R (5290740A a b + 2645370B a b)e +--R + +--R 2 3 3 2 8 +--R (10988460A a b + 10988460B a b )d e +--R + +--R 4 2 3 2 7 5 4 3 6 +--R (2889558A a b + 5779116B a b )d e + (2394A b + 11970B a b )d e +--R + +--R 5 4 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 4 5 9 3 2 4 8 +--R (3233230A a b + 646646B a )e + (13520780A a b + 6760390B a b)d e +--R + +--R 2 3 3 2 2 7 +--R (7189980A a b + 7189980B a b )d e +--R + +--R 4 2 3 3 6 5 4 4 5 +--R (22610A a b + 45220B a b )d e + (- 2660A b - 13300B a b )d e +--R + +--R 5 5 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 8 +--R 831402A a e + (8775910A a b + 1755182B a )d e +--R + +--R 3 2 4 2 7 +--R (9489740A a b + 4744870B a b)d e +--R + +--R 2 3 3 2 3 6 4 2 3 4 5 +--R (96900A a b + 96900B a b )d e + (- 25840A a b - 51680B a b )d e +--R + +--R 5 4 5 4 5 6 3 +--R (3040A b + 15200B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 2 7 +--R 2494206A a d e + (6928350A a b + 1385670B a )d e +--R + +--R 3 2 4 3 6 +--R (251940A a b + 125970B a b)d e +--R + +--R 2 3 3 2 4 5 +--R (- 116280A a b - 116280B a b )d e +--R + +--R 4 2 3 5 4 5 4 6 3 +--R (31008A a b + 62016B a b )d e + (- 3648A b - 18240B a b )d e +--R + +--R 5 7 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 7 4 5 3 6 +--R 2494206A a d e + (461890A a b + 92378B a )d e +--R + +--R 3 2 4 4 5 +--R (- 335920A a b - 167960B a b)d e +--R + +--R 2 3 3 2 5 4 +--R (155040A a b + 155040B a b )d e +--R + +--R 4 2 3 6 3 5 4 7 2 +--R (- 41344A a b - 82688B a b )d e + (4864A b + 24320B a b )d e +--R + +--R 5 8 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 3 6 4 5 4 5 +--R 831402A a d e + (- 923780A a b - 184756B a )d e +--R + +--R 3 2 4 5 4 2 3 3 2 6 3 +--R (671840A a b + 335920B a b)d e + (- 310080A a b - 310080B a b )d e +--R + +--R 4 2 3 7 2 5 4 8 +--R (82688A a b + 165376B a b )d e + (- 9728A b - 48640B a b )d e +--R + +--R 5 9 +--R 6144B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 2909907e +--R Type: Union(Expression(Integer),...) +--E 1177 + +--S 1178 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 9 9 +--R - 306306B b e x +--R + +--R 5 4 9 5 8 8 +--R ((- 342342A b - 1711710B a b )e - 702702B b d e )x +--R + +--R 4 2 3 9 +--R (- 1939938A a b - 3879876B a b )e +--R + +--R 5 4 8 5 2 7 +--R (- 798798A b - 3993990B a b )d e - 414414B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 3 2 9 +--R (- 4476780A a b - 4476780B a b )e +--R + +--R 4 2 3 8 +--R (- 4626006A a b - 9252012B a b )d e +--R + +--R 5 4 2 7 5 3 6 +--R (- 482790A b - 2413950B a b )d e - 1386B b d e +--R * +--R 6 +--R x +--R + +--R 3 2 4 9 +--R (- 5290740A a b - 2645370B a b)e +--R + +--R 2 3 3 2 8 +--R (- 10988460A a b - 10988460B a b )d e +--R + +--R 4 2 3 2 7 +--R (- 2889558A a b - 5779116B a b )d e +--R + +--R 5 4 3 6 5 4 5 +--R (- 2394A b - 11970B a b )d e + 1512B b d e +--R * +--R 5 +--R x +--R + +--R 4 5 9 +--R (- 3233230A a b - 646646B a )e +--R + +--R 3 2 4 8 +--R (- 13520780A a b - 6760390B a b)d e +--R + +--R 2 3 3 2 2 7 +--R (- 7189980A a b - 7189980B a b )d e +--R + +--R 4 2 3 3 6 5 4 4 5 +--R (- 22610A a b - 45220B a b )d e + (2660A b + 13300B a b )d e +--R + +--R 5 5 4 +--R - 1680B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 8 +--R - 831402A a e + (- 8775910A a b - 1755182B a )d e +--R + +--R 3 2 4 2 7 +--R (- 9489740A a b - 4744870B a b)d e +--R + +--R 2 3 3 2 3 6 +--R (- 96900A a b - 96900B a b )d e +--R + +--R 4 2 3 4 5 5 4 5 4 +--R (25840A a b + 51680B a b )d e + (- 3040A b - 15200B a b )d e +--R + +--R 5 6 3 +--R 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 2 7 +--R - 2494206A a d e + (- 6928350A a b - 1385670B a )d e +--R + +--R 3 2 4 3 6 +--R (- 251940A a b - 125970B a b)d e +--R + +--R 2 3 3 2 4 5 +--R (116280A a b + 116280B a b )d e +--R + +--R 4 2 3 5 4 5 4 6 3 +--R (- 31008A a b - 62016B a b )d e + (3648A b + 18240B a b )d e +--R + +--R 5 7 2 +--R - 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 7 4 5 3 6 +--R - 2494206A a d e + (- 461890A a b - 92378B a )d e +--R + +--R 3 2 4 4 5 +--R (335920A a b + 167960B a b)d e +--R + +--R 2 3 3 2 5 4 +--R (- 155040A a b - 155040B a b )d e +--R + +--R 4 2 3 6 3 5 4 7 2 +--R (41344A a b + 82688B a b )d e + (- 4864A b - 24320B a b )d e +--R + +--R 5 8 +--R 3072B b d e +--R * +--R x +--R + +--R 5 3 6 4 5 4 5 +--R - 831402A a d e + (923780A a b + 184756B a )d e +--R + +--R 3 2 4 5 4 +--R (- 671840A a b - 335920B a b)d e +--R + +--R 2 3 3 2 6 3 +--R (310080A a b + 310080B a b )d e +--R + +--R 4 2 3 7 2 5 4 8 +--R (- 82688A a b - 165376B a b )d e + (9728A b + 48640B a b )d e +--R + +--R 5 9 +--R - 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 6 9 10 6 5 9 6 8 9 +--R 306306B b e x + ((342342A b + 2018016B a b )e + 702702B b d e )x +--R + +--R 5 2 4 9 +--R (2282280A a b + 5591586B a b )e +--R + +--R 6 5 8 6 2 7 +--R (798798A b + 4696692B a b )d e + 414414B b d e +--R * +--R 8 +--R x +--R + +--R 2 4 3 3 9 +--R (6416718A a b + 8356656B a b )e +--R + +--R 5 2 4 8 +--R (5424804A a b + 13246002B a b )d e +--R + +--R 6 5 2 7 6 3 6 +--R (482790A b + 2828364B a b )d e + 1386B b d e +--R * +--R 7 +--R x +--R + +--R 3 3 4 2 9 +--R (9767520A a b + 7122150B a b )e +--R + +--R 2 4 3 3 8 +--R (15614466A a b + 20240472B a b )d e +--R + +--R 5 2 4 2 7 +--R (3372348A a b + 8193066B a b )d e +--R + +--R 6 5 3 6 6 4 5 +--R (2394A b + 13356B a b )d e - 1512B b d e +--R * +--R 6 +--R x +--R + +--R 4 2 5 9 +--R (8523970A a b + 3292016B a b)e +--R + +--R 3 3 4 2 8 +--R (24509240A a b + 17748850B a b )d e +--R + +--R 2 4 3 3 2 7 +--R (10079538A a b + 12969096B a b )d e +--R + +--R 5 2 4 3 6 6 5 4 5 +--R (25004A a b + 57190B a b )d e + (- 2660A b - 14812B a b )d e +--R + +--R 6 5 4 +--R 1680B b d e +--R * +--R 5 +--R x +--R + +--R 5 6 9 +--R (4064632A a b + 646646B a )e +--R + +--R 4 2 5 8 +--R (22296690A a b + 8515572B a b)d e +--R + +--R 3 3 4 2 2 7 +--R (16679720A a b + 11934850B a b )d e +--R + +--R 2 4 3 3 3 6 +--R (119510A a b + 142120B a b )d e +--R + +--R 5 2 4 4 5 6 5 5 4 +--R (- 28500A a b - 64980B a b )d e + (3040A b + 16880B a b )d e +--R + +--R 6 6 3 +--R - 1920B b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 6 8 +--R 831402A a e + (11270116A a b + 1755182B a )d e +--R + +--R 4 2 5 2 7 +--R (16418090A a b + 6130540B a b)d e +--R + +--R 3 3 4 2 3 6 +--R (348840A a b + 222870B a b )d e +--R + +--R 2 4 3 3 4 5 +--R (- 142120A a b - 167960B a b )d e +--R + +--R 5 2 4 5 4 6 5 6 3 +--R (34048A a b + 77216B a b )d e + (- 3648A b - 20160B a b )d e +--R + +--R 6 7 2 +--R 2304B b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 6 2 7 +--R 2494206A a d e + (9422556A a b + 1385670B a )d e +--R + +--R 4 2 5 3 6 +--R (713830A a b + 218348B a b)d e +--R + +--R 3 3 4 2 4 5 +--R (- 452200A a b - 284240B a b )d e +--R + +--R 2 4 3 3 5 4 +--R (186048A a b + 217056B a b )d e +--R + +--R 5 2 4 6 3 6 5 7 2 +--R (- 44992A a b - 100928B a b )d e + (4864A b + 26624B a b )d e +--R + +--R 6 8 +--R - 3072B b d e +--R * +--R 2 +--R x +--R + +--R 6 2 7 5 6 3 6 +--R 2494206A a d e + (1293292A a b + 92378B a )d e +--R + +--R 4 2 5 4 5 +--R (- 1259700A a b - 352716B a b)d e +--R + +--R 3 3 4 2 5 4 +--R (826880A a b + 490960B a b )d e +--R + +--R 2 4 3 3 6 3 +--R (- 351424A a b - 392768B a b )d e +--R + +--R 5 2 4 7 2 6 5 8 +--R (87552A a b + 189696B a b )d e + (- 9728A b - 51712B a b )d e +--R + +--R 6 9 +--R 6144B b d +--R * +--R x +--R + +--R 6 3 6 5 6 4 5 +--R 831402A a d e + (- 923780A a b - 184756B a )d e +--R + +--R 4 2 5 5 4 +--R (671840A a b + 335920B a b)d e +--R + +--R 3 3 4 2 6 3 +--R (- 310080A a b - 310080B a b )d e +--R + +--R 2 4 3 3 7 2 5 2 4 8 +--R (82688A a b + 165376B a b )d e + (- 9728A a b - 48640B a b )d e +--R + +--R 5 9 +--R 6144B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 2909907b e x + 2909907a e +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 3 9 5 4 3 5 2 8 +--R B b e x + ((A b + 5B a b )e + 3B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 7 +--R ((5A a b + 10B a b )e + (3A b + 15B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (10A a b + 10B a b )e + (15A a b + 30B a b )d e +--R + +--R 5 4 2 5 3 +--R (3A b + 15B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (10A a b + 5B a b)e + (30A a b + 30B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (15A a b + 30B a b )d e + (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (5A a b + B a )e + (30A a b + 15B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (30A a b + 30B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A a e + (15A a b + 3B a )d e + (30A a b + 15B a b)d e +--R + +--R 2 3 3 2 3 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 5 2 3 2 4 3 2 +--R (3A a d e + (15A a b + 3B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 2 4 5 3 5 3 +--R (3A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 3 10 6 5 3 6 2 9 +--R - B b e x + ((- A b - 6B a b )e - 3B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 8 +--R ((- 6A a b - 15B a b )e + (- 3A b - 18B a b )d e - 3B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (- 15A a b - 20B a b )e + (- 18A a b - 45B a b )d e +--R + +--R 6 5 2 6 3 +--R (- 3A b - 18B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (- 20A a b - 15B a b )e + (- 45A a b - 60B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 18A a b - 45B a b )d e + (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 15A a b - 6B a b)e + (- 60A a b - 45B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 45A a b - 60B a b )d e + (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 6A a b - B a )e + (- 45A a b - 18B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A a b - 45B a b )d e + (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R - A a e + (- 18A a b - 3B a )d e + (- 45A a b - 18B a b)d e +--R + +--R 3 3 4 2 3 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 2 4 2 5 3 2 +--R (- 3A a d e + (- 18A a b - 3B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 2 5 6 3 6 3 +--R (- 3A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1179 + +)clear all + +--S 1180 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1378 +r0:=-32/7293*(b*d-a*e)^2*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+4/663*(b*d-a*e)*(12*b*B*d-_ + 17*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^3)-2/255*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/17*B*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/153153*(b*d-a*e)^4*(12*b*B*d-17*A*b*e+_ + 5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/765765*(b*d-a*e)^5*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/21879*(b*d-a*e)^3*_ + (12*b*B*d-17*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 8 8 5 4 8 5 7 7 +--R 90090B b e x + ((102102A b + 510510B a b )e + 108108B b d e )x +--R + +--R 4 2 3 8 5 4 7 +--R (589050A a b + 1178100B a b )e + (125664A b + 628320B a b )d e +--R + +--R 5 2 6 +--R 1386B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 8 +--R (1392300A a b + 1392300B a b )e +--R + +--R 4 2 3 7 5 4 2 6 +--R (749700A a b + 1499400B a b )d e + (2142A b + 10710B a b )d e +--R + +--R 5 3 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 4 8 +--R (1701700A a b + 850850B a b)e +--R + +--R 2 3 3 2 7 +--R (1856400A a b + 1856400B a b )d e +--R + +--R 4 2 3 2 6 5 4 3 5 +--R (17850A a b + 35700B a b )d e + (- 2380A b - 11900B a b )d e +--R + +--R 5 4 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 4 5 8 3 2 4 7 +--R (1093950A a b + 218790B a )e + (2431000A a b + 1215500B a b)d e +--R + +--R 2 3 3 2 2 6 4 2 3 3 5 +--R (66300A a b + 66300B a b )d e + (- 20400A a b - 40800B a b )d e +--R + +--R 5 4 4 4 5 5 3 +--R (2720A b + 13600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 7 +--R 306306A a e + (1750320A a b + 350064B a )d e +--R + +--R 3 2 4 2 6 2 3 3 2 3 5 +--R (145860A a b + 72930B a b)d e + (- 79560A a b - 79560B a b )d e +--R + +--R 4 2 3 4 4 5 4 5 3 +--R (24480A a b + 48960B a b )d e + (- 3264A b - 16320B a b )d e +--R + +--R 5 6 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 2 6 +--R 612612A a d e + (218790A a b + 43758B a )d e +--R + +--R 3 2 4 3 5 +--R (- 194480A a b - 97240B a b)d e +--R + +--R 2 3 3 2 4 4 +--R (106080A a b + 106080B a b )d e +--R + +--R 4 2 3 5 3 5 4 6 2 +--R (- 32640A a b - 65280B a b )d e + (4352A b + 21760B a b )d e +--R + +--R 5 7 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 2 6 4 5 3 5 +--R 306306A a d e + (- 437580A a b - 87516B a )d e +--R + +--R 3 2 4 4 4 2 3 3 2 5 3 +--R (388960A a b + 194480B a b)d e + (- 212160A a b - 212160B a b )d e +--R + +--R 4 2 3 6 2 5 4 7 +--R (65280A a b + 130560B a b )d e + (- 8704A b - 43520B a b )d e +--R + +--R 5 8 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 765765b e x + 765765a e +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 8 8 5 4 8 5 7 7 +--R 90090B b e x + ((102102A b + 510510B a b )e + 108108B b d e )x +--R + +--R 4 2 3 8 5 4 7 +--R (589050A a b + 1178100B a b )e + (125664A b + 628320B a b )d e +--R + +--R 5 2 6 +--R 1386B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 8 +--R (1392300A a b + 1392300B a b )e +--R + +--R 4 2 3 7 5 4 2 6 +--R (749700A a b + 1499400B a b )d e + (2142A b + 10710B a b )d e +--R + +--R 5 3 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 4 8 +--R (1701700A a b + 850850B a b)e +--R + +--R 2 3 3 2 7 +--R (1856400A a b + 1856400B a b )d e +--R + +--R 4 2 3 2 6 5 4 3 5 +--R (17850A a b + 35700B a b )d e + (- 2380A b - 11900B a b )d e +--R + +--R 5 4 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 4 5 8 3 2 4 7 +--R (1093950A a b + 218790B a )e + (2431000A a b + 1215500B a b)d e +--R + +--R 2 3 3 2 2 6 4 2 3 3 5 +--R (66300A a b + 66300B a b )d e + (- 20400A a b - 40800B a b )d e +--R + +--R 5 4 4 4 5 5 3 +--R (2720A b + 13600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 7 +--R 306306A a e + (1750320A a b + 350064B a )d e +--R + +--R 3 2 4 2 6 2 3 3 2 3 5 +--R (145860A a b + 72930B a b)d e + (- 79560A a b - 79560B a b )d e +--R + +--R 4 2 3 4 4 5 4 5 3 +--R (24480A a b + 48960B a b )d e + (- 3264A b - 16320B a b )d e +--R + +--R 5 6 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 2 6 +--R 612612A a d e + (218790A a b + 43758B a )d e +--R + +--R 3 2 4 3 5 +--R (- 194480A a b - 97240B a b)d e +--R + +--R 2 3 3 2 4 4 +--R (106080A a b + 106080B a b )d e +--R + +--R 4 2 3 5 3 5 4 6 2 +--R (- 32640A a b - 65280B a b )d e + (4352A b + 21760B a b )d e +--R + +--R 5 7 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 2 6 4 5 3 5 +--R 306306A a d e + (- 437580A a b - 87516B a )d e +--R + +--R 3 2 4 4 4 2 3 3 2 5 3 +--R (388960A a b + 194480B a b)d e + (- 212160A a b - 212160B a b )d e +--R + +--R 4 2 3 6 2 5 4 7 +--R (65280A a b + 130560B a b )d e + (- 8704A b - 43520B a b )d e +--R + +--R 5 8 +--R 6144B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 765765e +--R Type: Union(Expression(Integer),...) +--E 1182 + +--S 1183 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 8 8 +--R - 90090B b e x +--R + +--R 5 4 8 5 7 7 +--R ((- 102102A b - 510510B a b )e - 108108B b d e )x +--R + +--R 4 2 3 8 +--R (- 589050A a b - 1178100B a b )e +--R + +--R 5 4 7 5 2 6 +--R (- 125664A b - 628320B a b )d e - 1386B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 8 +--R (- 1392300A a b - 1392300B a b )e +--R + +--R 4 2 3 7 +--R (- 749700A a b - 1499400B a b )d e +--R + +--R 5 4 2 6 5 3 5 +--R (- 2142A b - 10710B a b )d e + 1512B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 4 8 +--R (- 1701700A a b - 850850B a b)e +--R + +--R 2 3 3 2 7 +--R (- 1856400A a b - 1856400B a b )d e +--R + +--R 4 2 3 2 6 5 4 3 5 +--R (- 17850A a b - 35700B a b )d e + (2380A b + 11900B a b )d e +--R + +--R 5 4 4 +--R - 1680B b d e +--R * +--R 4 +--R x +--R + +--R 4 5 8 +--R (- 1093950A a b - 218790B a )e +--R + +--R 3 2 4 7 +--R (- 2431000A a b - 1215500B a b)d e +--R + +--R 2 3 3 2 2 6 +--R (- 66300A a b - 66300B a b )d e +--R + +--R 4 2 3 3 5 5 4 4 4 +--R (20400A a b + 40800B a b )d e + (- 2720A b - 13600B a b )d e +--R + +--R 5 5 3 +--R 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 7 +--R - 306306A a e + (- 1750320A a b - 350064B a )d e +--R + +--R 3 2 4 2 6 +--R (- 145860A a b - 72930B a b)d e +--R + +--R 2 3 3 2 3 5 +--R (79560A a b + 79560B a b )d e +--R + +--R 4 2 3 4 4 5 4 5 3 +--R (- 24480A a b - 48960B a b )d e + (3264A b + 16320B a b )d e +--R + +--R 5 6 2 +--R - 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 2 6 +--R - 612612A a d e + (- 218790A a b - 43758B a )d e +--R + +--R 3 2 4 3 5 +--R (194480A a b + 97240B a b)d e +--R + +--R 2 3 3 2 4 4 +--R (- 106080A a b - 106080B a b )d e +--R + +--R 4 2 3 5 3 5 4 6 2 +--R (32640A a b + 65280B a b )d e + (- 4352A b - 21760B a b )d e +--R + +--R 5 7 +--R 3072B b d e +--R * +--R x +--R + +--R 5 2 6 4 5 3 5 +--R - 306306A a d e + (437580A a b + 87516B a )d e +--R + +--R 3 2 4 4 4 +--R (- 388960A a b - 194480B a b)d e +--R + +--R 2 3 3 2 5 3 +--R (212160A a b + 212160B a b )d e +--R + +--R 4 2 3 6 2 5 4 7 +--R (- 65280A a b - 130560B a b )d e + (8704A b + 43520B a b )d e +--R + +--R 5 8 +--R - 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 6 8 9 6 5 8 6 7 8 +--R 90090B b e x + ((102102A b + 600600B a b )e + 108108B b d e )x +--R + +--R 5 2 4 8 +--R (691152A a b + 1688610B a b )e +--R + +--R 6 5 7 6 2 6 +--R (125664A b + 736428B a b )d e + 1386B b d e +--R * +--R 7 +--R x +--R + +--R 2 4 3 3 8 +--R (1981350A a b + 2570400B a b )e +--R + +--R 5 2 4 7 6 5 2 6 +--R (875364A a b + 2127720B a b )d e + (2142A b + 12096B a b )d e +--R + +--R 6 3 5 +--R - 1512B b d e +--R * +--R 6 +--R x +--R + +--R 3 3 4 2 8 +--R (3094000A a b + 2243150B a b )e +--R + +--R 2 4 3 3 7 +--R (2606100A a b + 3355800B a b )d e +--R + +--R 5 2 4 2 6 6 5 3 5 +--R (19992A a b + 46410B a b )d e + (- 2380A b - 13412B a b )d e +--R + +--R 6 4 4 +--R 1680B b d e +--R * +--R 5 +--R x +--R + +--R 4 2 5 8 +--R (2795650A a b + 1069640B a b)e +--R + +--R 3 3 4 2 7 +--R (4287400A a b + 3071900B a b )d e +--R + +--R 2 4 3 3 2 6 +--R (84150A a b + 102000B a b )d e +--R + +--R 5 2 4 3 5 6 5 4 4 +--R (- 22780A a b - 52700B a b )d e + (2720A b + 15280B a b )d e +--R + +--R 6 5 3 +--R - 1920B b d e +--R * +--R 4 +--R x +--R + +--R 5 6 8 +--R (1400256A a b + 218790B a )e +--R + +--R 4 2 5 7 +--R (4181320A a b + 1565564B a b)d e +--R + +--R 3 3 4 2 2 6 +--R (212160A a b + 139230B a b )d e +--R + +--R 2 4 3 3 3 5 +--R (- 99960A a b - 120360B a b )d e +--R + +--R 5 2 4 4 4 6 5 5 3 +--R (27200A a b + 62560B a b )d e + (- 3264A b - 18240B a b )d e +--R + +--R 6 6 2 +--R 2304B b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 6 7 +--R 306306A a e + (2362932A a b + 350064B a )d e +--R + +--R 4 2 5 2 6 +--R (364650A a b + 116688B a b)d e +--R + +--R 3 3 4 2 3 5 +--R (- 274040A a b - 176800B a b )d e +--R + +--R 2 4 3 3 4 4 +--R (130560A a b + 155040B a b )d e +--R + +--R 5 2 4 5 3 6 5 6 2 +--R (- 35904A a b - 81600B a b )d e + (4352A b + 24064B a b )d e +--R + +--R 6 7 +--R - 3072B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 2 6 +--R 612612A a d e + (525096A a b + 43758B a )d e +--R + +--R 4 2 5 3 5 +--R (- 632060A a b - 184756B a b)d e +--R + +--R 3 3 4 2 4 4 +--R (495040A a b + 300560B a b )d e +--R + +--R 2 4 3 3 5 3 +--R (- 244800A a b - 277440B a b )d e +--R + +--R 5 2 4 6 2 6 5 7 +--R (69632A a b + 152320B a b )d e + (- 8704A b - 46592B a b )d e +--R + +--R 6 8 +--R 6144B b d +--R * +--R x +--R + +--R 6 2 6 5 6 3 5 +--R 306306A a d e + (- 437580A a b - 87516B a )d e +--R + +--R 4 2 5 4 4 +--R (388960A a b + 194480B a b)d e +--R + +--R 3 3 4 2 5 3 +--R (- 212160A a b - 212160B a b )d e +--R + +--R 2 4 3 3 6 2 5 2 4 7 +--R (65280A a b + 130560B a b )d e + (- 8704A a b - 43520B a b )d e +--R + +--R 5 8 +--R 6144B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 765765b e x + 765765a e +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 2 8 5 4 2 5 7 +--R B b e x + ((A b + 5B a b )e + 2B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 6 +--R ((5A a b + 10B a b )e + (2A b + 10B a b )d e + B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (10A a b + 10B a b )e + (10A a b + 20B a b )d e +--R + +--R 5 4 2 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (10A a b + 5B a b)e + (20A a b + 20B a b )d e +--R + +--R 4 2 3 2 +--R (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 4 5 2 3 2 4 +--R (5A a b + B a )e + (20A a b + 10B a b)d e +--R + +--R 2 3 3 2 2 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 5 3 2 4 2 2 +--R (A a e + (10A a b + 2B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 4 5 2 5 2 +--R (2A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 2 9 6 5 2 6 8 +--R - B b e x + ((- A b - 6B a b )e - 2B b d e)x +--R + +--R 5 2 4 2 6 5 6 2 7 +--R ((- 6A a b - 15B a b )e + (- 2A b - 12B a b )d e - B b d )x +--R + +--R 2 4 3 3 2 5 2 4 +--R (- 15A a b - 20B a b )e + (- 12A a b - 30B a b )d e +--R + +--R 6 5 2 +--R (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 20A a b - 15B a b )e + (- 30A a b - 40B a b )d e +--R + +--R 5 2 4 2 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (- 15A a b - 6B a b)e + (- 40A a b - 30B a b )d e +--R + +--R 2 4 3 3 2 +--R (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 6A a b - B a )e + (- 30A a b - 12B a b)d e +--R + +--R 3 3 4 2 2 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 4 2 5 2 2 +--R (- A a e + (- 12A a b - 2B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 5 6 2 6 2 +--R (- 2A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1184 + +)clear all + +--S 1185 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1378 +r0:=-32/1287*(b*d-a*e)^2*(4*b*B*d-5*A*b*e+a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)+4/143*(b*d-a*e)*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-2/65*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+_ + 2/15*B*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 256/15015*(b*d-a*e)^4*(4*b*B*d-5*A*b*e+a*B*e)*(d+e*x)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+512/45045*(b*d-a*e)^5*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*_ + (a+b*x))+64/3003*(b*d-a*e)^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 7 7 5 4 7 5 6 6 +--R 6006B b e x + ((6930A b + 34650B a b )e + 462B b d e )x +--R + +--R 4 2 3 7 5 4 6 +--R (40950A a b + 81900B a b )e + (630A b + 3150B a b )d e +--R + +--R 5 2 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (100100A a b + 100100B a b )e + (4550A a b + 9100B a b )d e +--R + +--R 5 4 2 5 5 3 4 +--R (- 700A b - 3500B a b )d e + 560B b d e +--R * +--R 4 +--R x +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (128700A a b + 64350B a b)e + (14300A a b + 14300B a b )d e +--R + +--R 4 2 3 2 5 5 4 3 4 +--R (- 5200A a b - 10400B a b )d e + (800A b + 4000B a b )d e +--R + +--R 5 4 3 +--R - 640B b d e +--R * +--R 3 +--R x +--R + +--R 4 5 7 3 2 4 6 +--R (90090A a b + 18018B a )e + (25740A a b + 12870B a b)d e +--R + +--R 2 3 3 2 2 5 4 2 3 3 4 +--R (- 17160A a b - 17160B a b )d e + (6240A a b + 12480B a b )d e +--R + +--R 5 4 4 3 5 5 2 +--R (- 960A b - 4800B a b )d e + 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 6 +--R 30030A a e + (30030A a b + 6006B a )d e +--R + +--R 3 2 4 2 5 2 3 3 2 3 4 +--R (- 34320A a b - 17160B a b)d e + (22880A a b + 22880B a b )d e +--R + +--R 4 2 3 4 3 5 4 5 2 +--R (- 8320A a b - 16640B a b )d e + (1280A b + 6400B a b )d e +--R + +--R 5 6 +--R - 1024B b d e +--R * +--R x +--R + +--R 5 6 4 5 2 5 +--R 30030A a d e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 3 4 2 3 3 2 4 3 +--R (68640A a b + 34320B a b)d e + (- 45760A a b - 45760B a b )d e +--R + +--R 4 2 3 5 2 5 4 6 +--R (16640A a b + 33280B a b )d e + (- 2560A b - 12800B a b )d e +--R + +--R 5 7 +--R 2048B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 7 5 4 7 5 6 6 +--R 6006B b e x + ((6930A b + 34650B a b )e + 462B b d e )x +--R + +--R 4 2 3 7 5 4 6 +--R (40950A a b + 81900B a b )e + (630A b + 3150B a b )d e +--R + +--R 5 2 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (100100A a b + 100100B a b )e + (4550A a b + 9100B a b )d e +--R + +--R 5 4 2 5 5 3 4 +--R (- 700A b - 3500B a b )d e + 560B b d e +--R * +--R 4 +--R x +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (128700A a b + 64350B a b)e + (14300A a b + 14300B a b )d e +--R + +--R 4 2 3 2 5 5 4 3 4 +--R (- 5200A a b - 10400B a b )d e + (800A b + 4000B a b )d e +--R + +--R 5 4 3 +--R - 640B b d e +--R * +--R 3 +--R x +--R + +--R 4 5 7 3 2 4 6 +--R (90090A a b + 18018B a )e + (25740A a b + 12870B a b)d e +--R + +--R 2 3 3 2 2 5 4 2 3 3 4 +--R (- 17160A a b - 17160B a b )d e + (6240A a b + 12480B a b )d e +--R + +--R 5 4 4 3 5 5 2 +--R (- 960A b - 4800B a b )d e + 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 6 +--R 30030A a e + (30030A a b + 6006B a )d e +--R + +--R 3 2 4 2 5 2 3 3 2 3 4 +--R (- 34320A a b - 17160B a b)d e + (22880A a b + 22880B a b )d e +--R + +--R 4 2 3 4 3 5 4 5 2 +--R (- 8320A a b - 16640B a b )d e + (1280A b + 6400B a b )d e +--R + +--R 5 6 +--R - 1024B b d e +--R * +--R x +--R + +--R 5 6 4 5 2 5 +--R 30030A a d e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 3 4 2 3 3 2 4 3 +--R (68640A a b + 34320B a b)d e + (- 45760A a b - 45760B a b )d e +--R + +--R 4 2 3 5 2 5 4 6 +--R (16640A a b + 33280B a b )d e + (- 2560A b - 12800B a b )d e +--R + +--R 5 7 +--R 2048B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 7 7 5 4 7 5 6 6 +--R - 6006B b e x + ((- 6930A b - 34650B a b )e - 462B b d e )x +--R + +--R 4 2 3 7 5 4 6 +--R (- 40950A a b - 81900B a b )e + (- 630A b - 3150B a b )d e +--R + +--R 5 2 5 +--R 504B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 7 +--R (- 100100A a b - 100100B a b )e +--R + +--R 4 2 3 6 5 4 2 5 +--R (- 4550A a b - 9100B a b )d e + (700A b + 3500B a b )d e +--R + +--R 5 3 4 +--R - 560B b d e +--R * +--R 4 +--R x +--R + +--R 3 2 4 7 +--R (- 128700A a b - 64350B a b)e +--R + +--R 2 3 3 2 6 +--R (- 14300A a b - 14300B a b )d e +--R + +--R 4 2 3 2 5 5 4 3 4 +--R (5200A a b + 10400B a b )d e + (- 800A b - 4000B a b )d e +--R + +--R 5 4 3 +--R 640B b d e +--R * +--R 3 +--R x +--R + +--R 4 5 7 3 2 4 6 +--R (- 90090A a b - 18018B a )e + (- 25740A a b - 12870B a b)d e +--R + +--R 2 3 3 2 2 5 +--R (17160A a b + 17160B a b )d e +--R + +--R 4 2 3 3 4 5 4 4 3 +--R (- 6240A a b - 12480B a b )d e + (960A b + 4800B a b )d e +--R + +--R 5 5 2 +--R - 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 6 +--R - 30030A a e + (- 30030A a b - 6006B a )d e +--R + +--R 3 2 4 2 5 +--R (34320A a b + 17160B a b)d e +--R + +--R 2 3 3 2 3 4 +--R (- 22880A a b - 22880B a b )d e +--R + +--R 4 2 3 4 3 5 4 5 2 +--R (8320A a b + 16640B a b )d e + (- 1280A b - 6400B a b )d e +--R + +--R 5 6 +--R 1024B b d e +--R * +--R x +--R + +--R 5 6 4 5 2 5 +--R - 30030A a d e + (60060A a b + 12012B a )d e +--R + +--R 3 2 4 3 4 2 3 3 2 4 3 +--R (- 68640A a b - 34320B a b)d e + (45760A a b + 45760B a b )d e +--R + +--R 4 2 3 5 2 5 4 6 +--R (- 16640A a b - 33280B a b )d e + (2560A b + 12800B a b )d e +--R + +--R 5 7 +--R - 2048B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 6 7 8 6 5 7 6 6 7 +--R 6006B b e x + ((6930A b + 40656B a b )e + 462B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (47880A a b + 116550B a b )e + (630A b + 3612B a b )d e +--R + +--R 6 2 5 +--R - 504B b d e +--R * +--R 6 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (141050A a b + 182000B a b )e + (5180A a b + 12250B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (- 700A b - 4004B a b )d e + 560B b d e +--R * +--R 5 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (228800A a b + 164450B a b )e + (18850A a b + 23400B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (- 5900A a b - 13900B a b )d e + (800A b + 4560B a b )d e +--R + +--R 6 4 3 +--R - 640B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (218790A a b + 82368B a b)e + (40040A a b + 27170B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (- 22360A a b - 27560B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (7040A a b + 16480B a b )d e + (- 960A b - 5440B a b )d e +--R + +--R 6 5 2 +--R 768B b d e +--R * +--R 3 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (120120A a b + 18018B a )e + (55770A a b + 18876B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (- 51480A a b - 34320B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (29120A a b + 35360B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 9280A a b - 21440B a b )d e + (1280A b + 7168B a b )d e +--R + +--R 6 6 +--R - 1024B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 6 +--R 30030A a e + (60060A a b + 6006B a )d e +--R + +--R 4 2 5 2 5 +--R (- 94380A a b - 29172B a b)d e +--R + +--R 3 3 4 2 3 4 +--R (91520A a b + 57200B a b )d e +--R + +--R 2 4 3 3 4 3 +--R (- 54080A a b - 62400B a b )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (17920A a b + 39680B a b )d e + (- 2560A b - 13824B a b )d e +--R + +--R 6 7 +--R 2048B b d +--R * +--R x +--R + +--R 6 6 5 6 2 5 +--R 30030A a d e + (- 60060A a b - 12012B a )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (68640A a b + 34320B a b)d e + (- 45760A a b - 45760B a b )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (16640A a b + 33280B a b )d e + (- 2560A a b - 12800B a b )d e +--R + +--R 5 7 +--R 2048B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 7 5 4 5 6 +--R B b e x + ((A b + 5B a b )e + B b d)x +--R + +--R 4 2 3 5 4 5 +--R ((5A a b + 10B a b )e + (A b + 5B a b )d)x +--R + +--R 2 3 3 2 4 2 3 4 +--R ((10A a b + 10B a b )e + (5A a b + 10B a b )d)x +--R + +--R 3 2 4 2 3 3 2 3 +--R ((10A a b + 5B a b)e + (10A a b + 10B a b )d)x +--R + +--R 4 5 3 2 4 2 +--R ((5A a b + B a )e + (10A a b + 5B a b)d)x +--R + +--R 5 4 5 5 +--R (A a e + (5A a b + B a )d)x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 8 6 5 6 7 +--R - B b e x + ((- A b - 6B a b )e - B b d)x +--R + +--R 5 2 4 6 5 6 +--R ((- 6A a b - 15B a b )e + (- A b - 6B a b )d)x +--R + +--R 2 4 3 3 5 2 4 5 +--R ((- 15A a b - 20B a b )e + (- 6A a b - 15B a b )d)x +--R + +--R 3 3 4 2 2 4 3 3 4 +--R ((- 20A a b - 15B a b )e + (- 15A a b - 20B a b )d)x +--R + +--R 4 2 5 3 3 4 2 3 +--R ((- 15A a b - 6B a b)e + (- 20A a b - 15B a b )d)x +--R + +--R 5 6 4 2 5 2 +--R ((- 6A a b - B a )e + (- 15A a b - 6B a b)d)x +--R + +--R 6 5 6 6 +--R (- A a e + (- 6A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1378 +r0:=-160/9009*(b*d-a*e)^2*(12*b*B*d-13*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x)/(b*e^4)+20/1287*(b*d-a*e)*(12*b*B*d-_ + 13*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/_ + (b*e^3)-2/143*(12*b*B*d-13*A*b*e+a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x)/(b*e^2)+2/13*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x)/(b*e)-256/9009*(b*d-a*e)^4*(12*b*B*d-13*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+512/9009*(b*d-a*e)^5*_ + (12*b*B*d-13*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^7*(a+b*x))+64/3003*(b*d-a*e)^3*(12*b*B*d-13*A*b*e+a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 1386B b e x + ((1638A b + 8190B a b )e - 1512B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (10010A a b + 20020B a b )e + (- 1820A b - 9100B a b )d e +--R + +--R 5 2 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (25740A a b + 25740B a b )e + (- 11440A a b - 22880B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2080A b + 10400B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (36036A a b + 18018B a b)e + (- 30888A a b - 30888B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (13728A a b + 27456B a b )d e + (- 2496A b - 12480B a b )d e +--R + +--R 5 4 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (30030A a b + 6006B a )e + (- 48048A a b - 24024B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (41184A a b + 41184B a b )d e + (- 18304A a b - 36608B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (3328A b + 16640B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R 18018A a e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (96096A a b + 48048B a b)d e + (- 82368A a b - 82368B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (36608A a b + 73216B a b )d e + (- 6656A b - 33280B a b )d e +--R + +--R 5 6 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 9009b e x + 9009a e +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R 1386B b e x + ((1638A b + 8190B a b )e - 1512B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (10010A a b + 20020B a b )e + (- 1820A b - 9100B a b )d e +--R + +--R 5 2 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (25740A a b + 25740B a b )e + (- 11440A a b - 22880B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2080A b + 10400B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (36036A a b + 18018B a b)e + (- 30888A a b - 30888B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (13728A a b + 27456B a b )d e + (- 2496A b - 12480B a b )d e +--R + +--R 5 4 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (30030A a b + 6006B a )e + (- 48048A a b - 24024B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (41184A a b + 41184B a b )d e + (- 18304A a b - 36608B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (3328A b + 16640B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R 18018A a e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (96096A a b + 48048B a b)d e + (- 82368A a b - 82368B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (36608A a b + 73216B a b )d e + (- 6656A b - 33280B a b )d e +--R + +--R 5 6 +--R 6144B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R - 1386B b e x + ((- 1638A b - 8190B a b )e + 1512B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 10010A a b - 20020B a b )e + (1820A b + 9100B a b )d e +--R + +--R 5 2 4 +--R - 1680B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 25740A a b - 25740B a b )e + (11440A a b + 22880B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 2080A b - 10400B a b )d e + 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 36036A a b - 18018B a b)e + (30888A a b + 30888B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 13728A a b - 27456B a b )d e + (2496A b + 12480B a b )d e +--R + +--R 5 4 2 +--R - 2304B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 30030A a b - 6006B a )e + (48048A a b + 24024B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 41184A a b - 41184B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (18304A a b + 36608B a b )d e + (- 3328A b - 16640B a b )d e +--R + +--R 5 5 +--R 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 18018A a e + (60060A a b + 12012B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 96096A a b - 48048B a b)d e + (82368A a b + 82368B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 36608A a b - 73216B a b )d e + (6656A b + 33280B a b )d e +--R + +--R 5 6 +--R - 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 1386B b e x + ((1638A b + 9576B a b )e - 1512B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (11648A a b + 28210B a b )e + (- 1820A b - 10612B a b )d e +--R + +--R 6 2 4 +--R 1680B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (35750A a b + 45760B a b )e + (- 13260A a b - 31980B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (2080A b + 12080B a b )d e - 1920B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (61776A a b + 43758B a b )e + (- 42328A a b - 53768B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (15808A a b + 37856B a b )d e + (- 2496A b - 14400B a b )d e +--R + +--R 6 4 2 +--R 2304B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (66066A a b + 24024B a b)e + (- 78936A a b - 54912B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (54912A a b + 68640B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 20800A a b - 49088B a b )d e + (3328A b + 18944B a b )d e +--R + +--R 6 5 +--R - 3072B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (48048A a b + 6006B a )e + (- 108108A a b - 36036B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (137280A a b + 89232B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 100672A a b - 118976B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (39936A a b + 89856B a b )d e + (- 6656A b - 36352B a b )d e +--R + +--R 6 6 +--R 6144B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R 18018A a e + (- 60060A a b - 12012B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (96096A a b + 48048B a b)d e + (- 82368A a b - 82368B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (36608A a b + 73216B a b )d e + (- 6656A a b - 33280B a b )d e +--R + +--R 5 6 +--R 6144B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 9009b e x + 9009a e +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1378 +r0:=-2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+160/693*(b*d-a*e)*(12*b*B*d-11*A*b*e-a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4-20/99*(12*b*B*d-11*A*b*e-_ + a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3+2/11*_ + (12*b*B*d-11*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/_ + (e^2*(b*d-a*e))+256/693*(b*d-a*e)^3*(12*b*B*d-11*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-512/693*(b*d-a*e)^4*_ + (12*b*B*d-11*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x))-64/231*(b*d-a*e)^2*(12*b*B*d-11*A*b*e-a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 126B b e x + ((154A b + 770B a b )e - 168B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (990A a b + 1980B a b )e + (- 220A b - 1100B a b )d e +--R + +--R 5 2 4 +--R 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2772A a b + 2772B a b )e + (- 1584A a b - 3168B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (352A b + 1760B a b )d e - 384B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (4620A a b + 2310B a b)e + (- 5544A a b - 5544B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (3168A a b + 6336B a b )d e + (- 704A b - 3520B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (6930A a b + 1386B a )e + (- 18480A a b - 9240B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (22176A a b + 22176B a b )d e + (- 12672A a b - 25344B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (2816A b + 14080B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 1386A a e + (13860A a b + 2772B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 36960A a b - 18480B a b)d e + (44352A a b + 44352B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 25344A a b - 50688B a b )d e + (5632A b + 28160B a b )d e +--R + +--R 5 6 +--R - 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +-------+ +--R (693b e x + 693a e )\|e x + d +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R 126B b e x + ((154A b + 770B a b )e - 168B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (990A a b + 1980B a b )e + (- 220A b - 1100B a b )d e +--R + +--R 5 2 4 +--R 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2772A a b + 2772B a b )e + (- 1584A a b - 3168B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (352A b + 1760B a b )d e - 384B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (4620A a b + 2310B a b)e + (- 5544A a b - 5544B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (3168A a b + 6336B a b )d e + (- 704A b - 3520B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (6930A a b + 1386B a )e + (- 18480A a b - 9240B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (22176A a b + 22176B a b )d e + (- 12672A a b - 25344B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (2816A b + 14080B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 1386A a e + (13860A a b + 2772B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 36960A a b - 18480B a b)d e + (44352A a b + 44352B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 25344A a b - 50688B a b )d e + (5632A b + 28160B a b )d e +--R + +--R 5 6 +--R - 6144B b d +--R / +--R 7 +-------+ +--R 693e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R - 126B b e x + ((- 154A b - 770B a b )e + 168B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 990A a b - 1980B a b )e + (220A b + 1100B a b )d e +--R + +--R 5 2 4 +--R - 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 2772A a b - 2772B a b )e + (1584A a b + 3168B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 352A b - 1760B a b )d e + 384B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 4620A a b - 2310B a b)e + (5544A a b + 5544B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 3168A a b - 6336B a b )d e + (704A b + 3520B a b )d e +--R + +--R 5 4 2 +--R - 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 6930A a b - 1386B a )e + (18480A a b + 9240B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 22176A a b - 22176B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (12672A a b + 25344B a b )d e + (- 2816A b - 14080B a b )d e +--R + +--R 5 5 +--R 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R 1386A a e + (- 13860A a b - 2772B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (36960A a b + 18480B a b)d e + (- 44352A a b - 44352B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (25344A a b + 50688B a b )d e + (- 5632A b - 28160B a b )d e +--R + +--R 5 6 +--R 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 126B b e x + ((154A b + 896B a b )e - 168B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (1144A a b + 2750B a b )e + (- 220A b - 1268B a b )d e +--R + +--R 6 2 4 +--R 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (3762A a b + 4752B a b )e + (- 1804A a b - 4268B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (352A b + 2000B a b )d e - 384B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (7392A a b + 5082B a b )e + (- 7128A a b - 8712B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (3520A a b + 8096B a b )d e + (- 704A b - 3904B a b )d e +--R + +--R 6 4 2 +--R 768B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (11550A a b + 3696B a b)e + (- 24024A a b - 14784B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (25344A a b + 28512B a b )d e + (- 13376A a b - 28864B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (2816A b + 14848B a b )d e - 3072B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (5544A a b + 1386B a )e + (- 4620A a b - 6468B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 14784A a b + 3696B a b )d e + (31680A a b + 19008B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (- 22528A a b - 36608B a b )d e + (5632A b + 25088B a b )d e +--R + +--R 6 6 +--R - 6144B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 1386A a e + (13860A a b + 2772B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 36960A a b - 18480B a b)d e + (44352A a b + 44352B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (- 25344A a b - 50688B a b )d e + (5632A a b + 28160B a b )d e +--R + +--R 5 6 +--R - 6144B a b d +--R / +--R 7 7 +-------+ +--R (693b e x + 693a e )\|e x + d +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))-2*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(b*d-a*e)*sqrt(d+e*x))-160/63*b*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+20/9*b*(4*b*B*d-3*A*b*e-a*B*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/(e^3*(b*d-a*e))-_ + 256/63*b*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^6+512/63*b*(b*d-a*e)^3*(4*b*B*d-3*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+64/21*b*(b*d-_ + a*e)*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 14B b e x + ((18A b + 90B a b )e - 24B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((126A a b + 252B a b )e + (- 36A b - 180B a b )d e + 48B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (420A a b + 420B a b )e + (- 336A a b - 672B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (96A b + 480B a b )d e - 128B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (1260A a b + 630B a b)e + (- 2520A a b - 2520B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (2016A a b + 4032B a b )d e + (- 576A b - 2880B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 630A a b - 126B a )e + (5040A a b + 2520B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 10080A a b - 10080B a b )d e + (8064A a b + 16128B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 2304A b - 11520B a b )d e + 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 420A a b - 84B a )d e + (3360A a b + 1680B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 6720A a b - 6720B a b )d e + (5376A a b + 10752B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 1536A b - 7680B a b )d e + 2048B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R 14B b e x + ((18A b + 90B a b )e - 24B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((126A a b + 252B a b )e + (- 36A b - 180B a b )d e + 48B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (420A a b + 420B a b )e + (- 336A a b - 672B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (96A b + 480B a b )d e - 128B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (1260A a b + 630B a b)e + (- 2520A a b - 2520B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (2016A a b + 4032B a b )d e + (- 576A b - 2880B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 630A a b - 126B a )e + (5040A a b + 2520B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 10080A a b - 10080B a b )d e + (8064A a b + 16128B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 2304A b - 11520B a b )d e + 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 420A a b - 84B a )d e + (3360A a b + 1680B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 6720A a b - 6720B a b )d e + (5376A a b + 10752B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 1536A b - 7680B a b )d e + 2048B b d +--R / +--R 8 7 +-------+ +--R (63e x + 63d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R - 14B b e x + ((- 18A b - 90B a b )e + 24B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 126A a b - 252B a b )e + (36A b + 180B a b )d e +--R + +--R 5 2 4 +--R - 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 420A a b - 420B a b )e + (336A a b + 672B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 96A b - 480B a b )d e + 128B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 1260A a b - 630B a b)e + (2520A a b + 2520B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 2016A a b - 4032B a b )d e + (576A b + 2880B a b )d e +--R + +--R 5 4 2 +--R - 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (630A a b + 126B a )e + (- 5040A a b - 2520B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (10080A a b + 10080B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 8064A a b - 16128B a b )d e + (2304A b + 11520B a b )d e +--R + +--R 5 5 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 42A a e + (420A a b + 84B a )d e + (- 3360A a b - 1680B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (6720A a b + 6720B a b )d e + (- 5376A a b - 10752B a b )d e +--R + +--R 5 4 5 5 6 +--R (1536A b + 7680B a b )d e - 2048B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 14B b e x + ((18A b + 104B a b )e - 24B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((144A a b + 342B a b )e + (- 36A b - 204B a b )d e + 48B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (546A a b + 672B a b )e + (- 372A a b - 852B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (96A b + 528B a b )d e - 128B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (1680A a b + 1050B a b )e + (- 2856A a b - 3192B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (2112A a b + 4512B a b )d e + (- 576A b - 3008B a b )d e +--R + +--R 6 4 2 +--R 768B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 5 +--R (630A a b + 504B a b)e + 2520A a b d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 8064A a b - 6048B a b )d e + (7488A a b + 13248B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 2304A b - 10752B a b )d e + 3072B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 672A a b - 126B a )e + (4620A a b + 2436B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 6720A a b - 8400B a b )d e + (1344A a b + 9408B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (3072A a b - 768B a b )d e + (- 1536A b - 4608B a b )d e +--R + +--R 6 6 +--R 2048B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 42A a e + (- 420A a b - 84B a )d e + (3360A a b + 1680B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 6720A a b - 6720B a b )d e + (5376A a b + 10752B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- 1536A a b - 7680B a b )d e + 2048B a b d +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1378 +r0:=-2/5*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/15*(12*b*B*d-7*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/3*b*(12*b*B*d-_ + 7*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*_ + sqrt(d+e*x))+32/21*b^2*(12*b*B*d-7*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x)/(e^4*(b*d-a*e))+256/105*b^2*(b*d-a*e)*_ + (12*b*B*d-7*A*b*e-5*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 512/105*b^2*(b*d-a*e)^2*(12*b*B*d-7*A*b*e-5*a*B*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-64/35*b^2*(12*b*B*d-7*A*b*_ + e-5*a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 30B b e x + ((42A b + 210B a b )e - 72B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (350A a b + 700B a b )e + (- 140A b - 700B a b )d e +--R + +--R 5 2 4 +--R 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2100A a b + 2100B a b )e + (- 2800A a b - 5600B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (1120A b + 5600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 2100A a b - 1050B a b)e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 16800A a b - 33600B a b )d e + (6720A b + 33600B a b )d e +--R + +--R 5 4 2 +--R - 11520B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 350A a b - 70B a )e + (- 2800A a b - 1400B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (16800A a b + 16800B a b )d e + (- 22400A a b - 44800B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (8960A b + 44800B a b )d e - 15360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 140A a b - 28B a )d e + (- 1120A a b - 560B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (6720A a b + 6720B a b )d e + (- 8960A a b - 17920B a b )d e +--R + +--R 5 4 5 5 6 +--R (3584A b + 17920B a b )d e - 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 +--R 105b e x + (105a e + 210b d e )x + (210a d e + 105b d e )x +--R + +--R 2 7 +--R 105a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R 30B b e x + ((42A b + 210B a b )e - 72B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((350A a b + 700B a b )e + (- 140A b - 700B a b )d e + 240B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2100A a b + 2100B a b )e + (- 2800A a b - 5600B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (1120A b + 5600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 2100A a b - 1050B a b)e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 16800A a b - 33600B a b )d e + (6720A b + 33600B a b )d e +--R + +--R 5 4 2 +--R - 11520B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 350A a b - 70B a )e + (- 2800A a b - 1400B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (16800A a b + 16800B a b )d e + (- 22400A a b - 44800B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (8960A b + 44800B a b )d e - 15360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 140A a b - 28B a )d e + (- 1120A a b - 560B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (6720A a b + 6720B a b )d e + (- 8960A a b - 17920B a b )d e +--R + +--R 5 4 5 5 6 +--R (3584A b + 17920B a b )d e - 6144B b d +--R / +--R 9 2 8 2 7 +-------+ +--R (105e x + 210d e x + 105d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R - 30B b e x + ((- 42A b - 210B a b )e + 72B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 350A a b - 700B a b )e + (140A b + 700B a b )d e +--R + +--R 5 2 4 +--R - 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 2100A a b - 2100B a b )e + (2800A a b + 5600B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 1120A b - 5600B a b )d e + 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (2100A a b + 1050B a b)e + (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (16800A a b + 33600B a b )d e + (- 6720A b - 33600B a b )d e +--R + +--R 5 4 2 +--R 11520B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (350A a b + 70B a )e + (2800A a b + 1400B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 16800A a b - 16800B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (22400A a b + 44800B a b )d e + (- 8960A b - 44800B a b )d e +--R + +--R 5 5 +--R 15360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 42A a e + (140A a b + 28B a )d e + (1120A a b + 560B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 6720A a b - 6720B a b )d e + (8960A a b + 17920B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 3584A b - 17920B a b )d e + 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 30B b e x + ((42A b + 240B a b )e - 72B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((392A a b + 910B a b )e + (- 140A b - 772B a b )d e + 240B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (2450A a b + 2800B a b )e + (- 2940A a b - 6300B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (1120A b + 5840B a b )d e - 1920B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 6 2 4 3 3 5 +--R 1050B a b e + (9800A a b + 7000B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 15680A a b - 28000B a b )d e + (6720A b + 31680B a b )d e +--R + +--R 6 4 2 +--R - 11520B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 2450A a b - 1120B a b)e + (9800A a b + 11200B a b )d e +--R + +--R 3 3 2 4 5 2 4 3 3 +--R - 16800B a b d e + (- 15680A a b - 11200B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (8960A b + 33280B a b )d e - 15360B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 392A a b - 70B a )e + (- 2940A a b - 1428B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (15680A a b + 16240B a b )d e + (- 15680A a b - 38080B a b )d e +--R + +--R 2 4 4 2 6 5 5 6 6 +--R 26880B a b d e + (3584A b + 2560B a b )d e - 6144B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 42A a e + (- 140A a b - 28B a )d e + (- 1120A a b - 560B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (6720A a b + 6720B a b )d e + (- 8960A a b - 17920B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (3584A a b + 17920B a b )d e - 6144B a b d +--R / +--R 9 3 9 8 2 8 2 7 +--R 105b e x + (105a e + 210b d e )x + (210a d e + 105b d e )x +--R + +--R 2 7 +--R 105a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1210 + +--S 1211 of 1378 +r0:=2/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/5*(A*b-a*B)*(a+b*x)*(d+e*x)^(5/2)/(b^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/7*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(b*d-a*e)^(5/2)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (- 210A a b + 210B a b)e + (420A a b - 420B a b )d e +--R + +--R 4 3 2 +--R (- 210A b + 210B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 2 +--R (- 210A a b + 210B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 12B a b )e + 90B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 28A a b + 28B a b )e + (154A b - 64B a b )d e + 90B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (140A a b - 140B a b)e + (- 336A a b + 336B a b )d e +--R + +--R 4 3 2 4 3 +--R (322A b - 232B a b )d e + 30B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (322A a b - 322B a b )d e + 30B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 105b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 2 +--R (- 105A a b + 105B a )e + (210A a b - 210B a b)d e +--R + +--R 3 2 2 +--R (- 105A b + 105B a b )d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b e +--R , +--R +--R 2 3 3 2 2 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 +--R (- 210A b + 210B a b )d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1212 + +--S 1213 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 +--R (- 105A a b + 105B a )e + (210A a b - 210B a b)d e +--R + +--R 3 2 2 +--R (- 105A b + 105B a b )d e +--R * +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 3 3 3 2 2 2 +--R (210A a b - 210B a b)e + (- 420A a b + 420B a b )d e +--R + +--R 4 3 2 +--R (210A b - 210B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 210B a )e + (- 420A a b + 420B a b)d e +--R + +--R 3 2 2 2 +--R (210A a b - 210B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R - 30B b e x + ((- 42A b + 12B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((28A a b - 28B a b )e + (- 154A b + 64B a b )d e - 90B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 140A a b + 140B a b)e + (336A a b - 336B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 322A b + 232B a b )d e - 30B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 210B a )e + (490A a b - 490B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 322A a b + 322B a b )d e - 30B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 105b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 +--R 2B b e x + (2A b e + 6B b d e )x + (6A b d e + 6B b d e)x +--R + +--R 2 3 3 +--R (6A b d e + 2B b d )x + 2A b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 4 5 4 3 4 +--R B b e x + ((A b - B a)e + 5B b d e )x +--R + +--R 4 3 2 2 3 +--R (- A a e + (5A b - 3B a)d e + 9B b d e )x +--R + +--R 3 2 2 3 2 +--R (- 3A a d e + (9A b - 3B a)d e + 7B b d e)x +--R + +--R 2 2 3 4 3 4 +--R (- 3A a d e + (7A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 5 2 3 2 2 4 +--R - 2B b e x + ((- 2A b - 2B a b)e - 6B b d e )x +--R + +--R 3 2 2 2 2 3 +--R (- 2A a b e + (- 6A b - 6B a b)d e - 6B b d e)x +--R + +--R 2 2 2 2 3 2 +--R (- 6A a b d e + (- 6A b - 6B a b)d e - 2B b d )x +--R + +--R 2 2 3 3 +--R (- 6A a b d e + (- 2A b - 2B a b)d )x - 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 4 6 2 4 2 3 5 +--R - B b e x + (- A b e - 5B b d e )x +--R + +--R 2 4 2 3 2 2 2 4 +--R (B a e + (- 5A b - 2B a b)d e - 9B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 3 +--R (A a e + (- 2A a b + 3B a )d e + (- 9A b - 6B a b)d e - 7B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 2 +--R (3A a d e + (- 6A a b + 3B a )d e + (- 7A b - 6B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 3 2 4 2 3 +--R (3A a d e + (- 6A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 4 +--R - 2A a b d +--R / +--R 2 2 2 2 +-------+ +--R (b e x + 2b d x - a e + 2a b d)\|e x + d +--R + +--R +-----------+ +--R 2 2 2 |- a e + b d +--R (2b e x + (2a b e + 2b d)x + 2a b d) |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 3 3 3 2 2 2 +--R (210A a b - 210B a b)e + (- 420A a b + 420B a b )d e +--R + +--R 4 3 2 +--R (210A b - 210B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 210B a )e + (- 420A a b + 420B a b)d e +--R + +--R 3 2 2 2 +--R (210A a b - 210B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 3 2 2 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 +--R (- 210A b + 210B a b )d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R - 30B b e x + ((- 42A b + 12B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((28A a b - 28B a b )e + (- 154A b + 64B a b )d e - 90B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 140A a b + 140B a b)e + (336A a b - 336B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 322A b + 232B a b )d e - 30B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 210B a )e + (490A a b - 490B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 322A a b + 322B a b )d e - 30B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 105b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1216 + +)clear all + +--S 1217 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1217 + +--S 1218 of 1378 +r0:=2/3*(A*b-a*B)*(a+b*x)*(d+e*x)^(3/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2/5*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(b*d-a*e)^(3/2)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (b*d-a*e)*(a+b*x)*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 3 2 +--R ((30A a b - 30B a b)e + (- 30A b + 30B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (30A a b - 30B a )e + (- 30A a b + 30B a b)d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 4B a b )e + 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 20A a b + 20B a b)e + (40A b - 28B a b )d e + 6B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A a b - 40B a b)d e + 6B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 15b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 |- a e + b d +--R ((- 15A a b + 15B a )e + (15A b - 15B a b)d e) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b e +--R , +--R +--R +---------+ +--R 2 2 2 |a e - b d +--R ((30A a b - 30B a )e + (- 30A b + 30B a b)d e) |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1219 + +--S 1220 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 |- a e + b d +-+ +--R ((- 15A a b + 15B a )e + (15A b - 15B a b)d e) |----------- \|b +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 3 2 +--R ((- 30A a b + 30B a b)e + (30A b - 30B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (- 30A a b + 30B a )e + (30A a b - 30B a b)d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R - 6B b e x + ((- 10A b + 4B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((20A a b - 20B a b)e + (- 40A b + 28B a b )d e - 6B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (30A a b - 30B a )e + (- 40A a b + 40B a b)d e - 6B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 15b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 3 2 2 2 +--R - 2B b e x + (- 2A b e - 4B b d e)x + (- 4A b d e - 2B b d )x +--R + +--R 2 +--R - 2A b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 3 4 3 2 3 +--R B b e x + ((A b - B a)e + 4B b d e )x +--R + +--R 3 2 2 2 +--R (- A a e + (4A b - 2B a)d e + 5B b d e)x +--R + +--R 2 2 3 2 3 +--R (- 2A a d e + (5A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 4 2 2 2 3 +--R 2B b e x + ((2A b + 2B a b)e + 4B b d e)x +--R + +--R 2 2 2 2 2 +--R (2A a b e + (4A b + 4B a b)d e + 2B b d )x +--R + +--R 2 2 2 +--R (4A a b d e + (2A b + 2B a b)d )x + 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 3 5 2 3 2 2 4 +--R - B b e x + (- A b e - 4B b d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (B a e + (- 4A b - 2B a b)d e - 5B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 2 +--R (A a e + (- 2A a b + 2B a )d e + (- 5A b - 4B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (2A a d e + (- 4A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 3 +--R - 2A a b d +--R / +--R 2 2 2 2 +-------+ +--R (b e x + 2b d x - a e + 2a b d)\|e x + d +--R + +--R +-----------+ +--R 2 2 2 |- a e + b d +--R (- 2b e x + (- 2a b e - 2b d)x - 2a b d) |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 3 2 +--R ((- 30A a b + 30B a b)e + (30A b - 30B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (- 30A a b + 30B a )e + (30A a b - 30B a b)d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 2 +-+ |a e - b d +--R ((30A a b - 30B a )e + (- 30A b + 30B a b)d e)\|b |--------- +--R \| b +--R * +--R +------------------+ +-------+ +--R | 2 2 2 \|e x + d +--R \|b x + 2a b x + a atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R - 6B b e x + ((- 10A b + 4B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((20A a b - 20B a b)e + (- 40A b + 28B a b )d e - 6B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (30A a b - 30B a )e + (- 40A a b + 40B a b)d e - 6B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 15b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1223 + +)clear all + +--S 1224 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1378 +r0:=2/3*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b*d-a*e)/(b^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (a+b*x)*sqrt(d+e*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 +-----------+ +--R ((- 6A b + 6B a b)e x + (- 6A a b + 6B a )e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 4B a b)e + 2B b d)x + (6A a b - 6B a )e +--R + +--R 2B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R 3b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a e + b d +--R (3A b - 3B a)e |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|e x + d +--R / +--R 2 +--R 3b e +--R , +--R +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R (- 6A b + 6B a)e |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +-------+ +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|e x + d +--R / +--R 2 +--R 3b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1226 + +--S 1227 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R (3A b - 3B a)e |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 +-----------+ +--R ((6A b - 6B a b)e x + (6A a b - 6B a )e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|b \|e x + d \|b x + 2a b x + a +--R + +--R 2 2 2 2 2 +--R - 2B b e x + ((- 6A b + 4B a b)e - 2B b d)x + (- 6A a b + 6B a )e +--R + +--R - 2B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R 3b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +-----------+ +--R 2 |- a e + b d +-------+ +--R (- 2B b e x + (- 2A b e - 2B b d)x - 2A b d) |----------- \|e x + d +--R \| b +--R + +--R 2 3 2 2 +--R B b e x + ((A b - B a)e + 3B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (3A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 2 +--R 2B b e x + ((2A b + 2B a b)e + 2B b d)x +--R + +--R 2 +--R (2A a b e + (2A b + 2B a b)d)x + 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 2 4 2 2 2 3 +--R - B b e x + (- A b e - 3B b d e)x +--R + +--R 2 2 2 2 2 2 +--R (B a e + (- 3A b - 2B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (- 2A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 2 +--R - 2A a b d +--R / +--R 2 2 2 2 +-------+ +--R (b e x + 2b d x - a e + 2a b d)\|e x + d +--R + +--R +-----------+ +--R 2 2 2 |- a e + b d +--R (- 2b e x + (- 2a b e - 2b d)x - 2a b d) |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 +-----------+ +--R ((6A b - 6B a b)e x + (6A a b - 6B a )e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R (- 6A b + 6B a)e\|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|b \|e x + d \|b x + 2a b x + a +--R + +--R 2 2 2 2 2 +--R - 2B b e x + ((- 6A b + 4B a b)e - 2B b d)x + (- 6A a b + 6B a )e +--R + +--R - 2B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R 3b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1230 + +)clear all + +--S 1231 of 1378 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1378 +r0:=-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(3/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*B*(a+b*x)*_ + sqrt(d+e*x)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 \|b \|e x + d +--R ((- 2A b + 2B a b)e x + (- 2A a b + 2B a )e)atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (2B b x + 2B a)\|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R b e\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (A b - B a)e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R 2B\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R | 2 +--R b e\|- a b e + b d +--R , +--R +-----------+ +--R | 2 +-------+ +-----------+ +--R \|a b e - b d \|e x + d | 2 +-------+ +--R (2A b - 2B a)e atan(------------------------) + 2B\|a b e - b d \|e x + d +--R a e - b d +--R --------------------------------------------------------------------------] +--R +-----------+ +--R | 2 +--R b e\|a b e - b d +--R Type: Union(List(Expression(Integer)),...) +--E 1233 + +--S 1234 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (A b - B a)e\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R 2 2 | 2 +--R ((2A b - 2B a b)e x + (2A a b - 2B a )e)\|- a b e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R 2B\|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R (- 2B b x - 2B a)\|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R b e\|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 +-------+ +--R ((2B a b e - 2B b d)x + 2A a b e - 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 +--R (- 2B a b e + 2B b d)x +--R + +--R 2 2 3 2 2 2 +--R ((- 2A a b - 2B a b)e + (2A b + 2B a b )d)x - 2A a b e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R +-------------+ +--R 2 2 2 2 | 2 +-------+ +--R (b e x + 2b d x - a e + 2a b d)\|- a b e + b d \|e x + d +--R + +--R 2 2 3 2 2 2 3 2 2 2 2 +--R (2a b e - 2b d e)x + (2a b e - 2b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 2 | 2 +--R ((2A b - 2B a b)e x + (2A a b - 2B a )e)\|a b e - b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (2A b - 2B a)e\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R 2B\|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R (- 2B b x - 2B a)\|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R b e\|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (7) -------------------------------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1237 + +)clear all + +--S 1238 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1378 +r0:=-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(3/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*(B*d-A*e)*_ + (a+b*x)/(e*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 +-------+ \|b \|e x + d +--R ((2A b - 2B a b)e x + (2A a b - 2B a )e)\|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R ((- 2A b e + 2B b d)x - 2A a e + 2B a d)\|- a e + b d \|b +--R / +--R +------------------+ +--R 2 +-----------+ +-+ +-------+ | 2 2 2 +--R (a e - b d e)\|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R (A b - B a)e\|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +--R (- 2A e + 2B d)\|- a b e + b d +--R / +--R +-------------+ +--R 2 | 2 +-------+ +--R (a e - b d e)\|- a b e + b d \|e x + d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R (- 2A b + 2B a)e\|e x + d atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +--R (- 2A e + 2B d)\|a b e - b d +--R / +--R +-----------+ +--R 2 | 2 +-------+ +--R (a e - b d e)\|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1240 + +--S 1241 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R (A b - B a)e\|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R 2 2 | 2 +-------+ +--R ((- 2A b + 2B a b)e x + (- 2A a b + 2B a )e)\|- a b e + b d \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R (- 2A e + 2B d)\|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R + +--R +-------------+ +--R | 2 +-----------+ +-+ +--R ((2A b e - 2B b d)x + 2A a e - 2B a d)\|- a b e + b d \|- a e + b d \|b +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +-------+ +--R (a e - b d e)\|- a b e + b d \|- a e + b d \|b \|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 +-------+ +--R ((- 2B a b e + 2B b d)x - 2A a b e + 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 2 3 2 +--R (2B a b e - 2B b d)x + ((2A a b + 2B a b)e + (- 2A b - 2B a b )d)x +--R + +--R 2 2 +--R 2A a b e - 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (b e x + 3b d e x + (- a e + 2a b d e + 2b d )x - a d e + 2a b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (- 2a b e + 2b d e )x + (- 2a b e - 2a b d e + 4b d e)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (- 4a b d e + 2a b d e + 2b d )x - 2a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 2 | 2 +-------+ +--R ((- 2A b + 2B a b)e x + (- 2A a b + 2B a )e)\|a b e - b d \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R (- 2A b + 2B a)e\|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R (- 2A e + 2B d)\|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R + +--R +-----------+ +--R +-----------+ +-+ | 2 +--R ((2A b e - 2B b d)x + 2A a e - 2B a d)\|- a e + b d \|b \|a b e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +-------+ +--R (a e - b d e)\|- a e + b d \|b \|a b e - b d \|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (7) -------------------------------------------------------------- +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))*sqrt(b)/((b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-_ + a*B)*(a+b*x)/((b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 +--R (- 6A b + 6B a b)e x +--R + +--R 2 2 2 2 +--R ((- 6A a b + 6B a )e + (- 6A b + 6B a b)d e)x + (- 6A a b + 6B a )d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +--R (6A b - 6B a b)e x +--R + +--R 2 2 2 2 2 2 2 +--R ((4A a b - 6B a )e + (8A b - 4B a b)d e - 2B b d )x - 2A a e +--R + +--R 2 2 +--R (8A a b - 4B a )d e - 2B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e) +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 | b +-------+ +--R ((3A b - 3B a)e x + (3A b - 3B a)d e) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R (6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e)\|e x + d +--R , +--R +--R +---------+ +--R 2 | b +-------+ +--R ((6A b - 6B a)e x + (6A b - 6B a)d e) |--------- \|e x + d +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 +--R (6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e)\|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1247 + +--S 1248 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R ((3A b - 3B a)e x + (3A b - 3B a)d e)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 +--R (6A b - 6B a b)e x + ((6A a b - 6B a )e + (6A b - 6B a b)d e)x +--R + +--R 2 +--R (6A a b - 6B a )d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +-----------+ +--R ((6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d )\|- a e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 +--R (- 6A b + 6B a b)e x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 4A a b + 6B a )e + (- 8A b + 4B a b)d e + 2B b d )x + 2A a e +--R + +--R 2 2 +--R (- 8A a b + 4B a )d e + 2B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e) +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 2 +--R (6A b - 6B a b)e x + ((6A a b - 6B a )e + (6A b - 6B a b)d e)x +--R + +--R 2 +--R (6A a b - 6B a )d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 +-----------+ | b +--R ((6A b - 6B a)e x + (6A b - 6B a)d e)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +------------------+ +-------+ +--R +-------+ | 2 2 2 b\|e x + d +--R \|e x + d \|b x + 2a b x + a atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 +-----------+ +--R ((6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d )\|- a e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 +--R (- 6A b + 6B a b)e x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 4A a b + 6B a )e + (- 8A b + 4B a b)d e + 2B b d )x + 2A a e +--R + +--R 2 2 +--R (- 8A a b + 4B a )d e + 2B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e) +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1251 + +)clear all + +--S 1252 of 1378 +t0:=(A+B*x)/((d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 1378 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/3*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-2*b^(3/2)*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2*b*(A*b-a*B)*(a+b*x)/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 +--R (30A b - 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((30A a b - 30B a b)e + (60A b - 60B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((60A a b - 60B a b)d e + (30A b - 30B a b )d e)x +--R + +--R 2 2 2 +--R (30A a b - 30B a b)d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 +--R (- 30A b + 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 20A a b + 20B a b)e + (- 70A b + 70B a b )d e )x +--R + +--R 2 3 3 2 2 2 +--R (4A a b - 10B a )e + (- 48A a b + 66B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 46A b + 28B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (22A a b - 4B a )d e + (- 46A a b + 28B a b)d e +--R + +--R 2 3 +--R 6B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 +--R (15A b - 15B a b)e x + (30A b - 30B a b)d e x +--R + +--R 2 2 +--R (15A b - 15B a b)d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 3 2 2 2 +--R (- 30A b + 30B a b)e x + (- 60A b + 60B a b)d e x +--R + +--R 2 2 +--R (- 30A b + 30B a b)d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1254 + +--S 1255 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 +--R (15A b - 15B a b)e x + (30A b - 30B a b)d e x +--R + +--R 2 2 +--R (15A b - 15B a b)d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 +--R (- 30A b + 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 30A a b + 30B a b)e + (- 60A b + 60B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 60A a b + 60B a b)d e + (- 30A b + 30B a b )d e)x +--R + +--R 2 2 2 +--R (- 30A a b + 30B a b)d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 3 2 3 3 +--R (30A b - 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((20A a b - 20B a b)e + (70A b - 70B a b )d e )x +--R + +--R 2 3 3 2 2 2 +--R (- 4A a b + 10B a )e + (48A a b - 66B a b)d e +--R + +--R 3 2 2 3 3 +--R (46A b - 28B a b )d e - 6B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R 6A a e + (- 22A a b + 4B a )d e + (46A a b - 28B a b)d e - 6B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 2 3 3 +--R (- 30A b + 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 30A a b + 30B a b)e + (- 60A b + 60B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 60A a b + 60B a b)d e + (- 30A b + 30B a b )d e)x +--R + +--R 2 2 2 +--R (- 30A a b + 30B a b)d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 2 2 +--R (- 30A b + 30B a b)e x + (- 60A b + 60B a b)d e x +--R + +--R 2 2 +--R (- 30A b + 30B a b)d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 3 2 3 3 +--R (30A b - 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((20A a b - 20B a b)e + (70A b - 70B a b )d e )x +--R + +--R 2 3 3 2 2 2 +--R (- 4A a b + 10B a )e + (48A a b - 66B a b)d e +--R + +--R 3 2 2 3 3 +--R (46A b - 28B a b )d e - 6B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R 6A a e + (- 22A a b + 4B a )d e + (46A a b - 28B a b)d e - 6B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1258 + +)clear all + +--S 1259 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 1378 +r0:=-1/10*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*(d+e*x)^(7/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+2/5*B*(a+b*x)*(d+e*x)^(9/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+7/12*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-7/20*(4*b*B*d+5*A*b*e-_ + 9*a*B*e)*(d+e*x)^(5/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*e*(b*d-_ + a*e)^(3/2)*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/(b^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*e*(b*d-_ + a*e)*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 5 +-+ | 2 2 2 +--R (60b x + 60a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 4 3 2 +--R (- 525A a b + 945B a b )e + (525A b - 1365B a b )d e +--R + +--R 4 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1050A a b + 1890B a b)e + (1050A a b - 2730B a b )d e +--R + +--R 3 2 +--R 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 525A a b + 945B a )e + (525A a b - 1365B a b)d e + 420B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 48B b e x + ((80A b - 144B a b )e + 256B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 560A a b + 1008B a b )e + (800A b - 1888B a b )d e +--R + +--R 4 2 +--R 928B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1750A a b + 3150B a b)e + (2380A a b - 5684B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 390A b + 2606B a b )d e - 120B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 1050A a b + 1890B a )e + (1400A a b - 3360B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 210A a b + 1498B a b )d e + (- 60A b - 60B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 120b x + 240a b x + 120a b +--R , +--R +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 60b x + 120a b x + 60a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1261 + +--S 1262 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 4 3 2 +--R (- 525A a b + 945B a b )e + (525A b - 1365B a b )d e +--R + +--R 4 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1050A a b + 1890B a b)e + (1050A a b - 2730B a b )d e +--R + +--R 3 2 +--R 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 525A a b + 945B a )e + (525A a b - 1365B a b)d e + 420B a b d e +--R * +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 4 2 3 3 5 4 2 +--R (- 1050A a b + 1890B a b )e + (1050A b - 2730B a b )d e +--R + +--R 5 2 +--R 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 3150A a b + 5670B a b )e + (3150A a b - 8190B a b )d e +--R + +--R 4 2 +--R 2520B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 3150A a b + 5670B a b)e + (3150A a b - 8190B a b )d e +--R + +--R 2 3 2 +--R 2520B a b d e +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 1050A a b + 1890B a )e + (1050A a b - 2730B a b)d e +--R + +--R 3 2 2 +--R 840B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 48B b e x + ((80A b - 144B a b )e + 256B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 560A a b + 1008B a b )e + (800A b - 1888B a b )d e +--R + +--R 4 2 +--R 928B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1750A a b + 3150B a b)e + (2380A a b - 5684B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 390A b + 2606B a b )d e - 120B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 1050A a b + 1890B a )e + (1400A a b - 3360B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 210A a b + 1498B a b )d e + (- 60A b - 60B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 3 5 5 4 3 5 2 4 +--R - 48B b e x + ((- 80A b + 96B a b )e - 256B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (480A a b - 864B a b )e + (- 800A b + 1632B a b )d e +--R + +--R 5 2 +--R - 928B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (2310A a b - 4158B a b )e + (- 3180A a b + 7572B a b )d e +--R + +--R 5 4 2 5 3 +--R (390A b - 3534B a b )d e + 120B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2800A a b - 5040B a b)e + (- 3780A a b + 9044B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (600A a b - 4104B a b )d e + (60A b + 180B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (1050A a b - 1890B a )e + (- 1400A a b + 3360B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (210A a b - 1498B a b )d e + (60A a b + 60B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 7 2 6 2 5 +-+ | 2 2 2 +--R (120b x + 240a b x + 120a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 4 5 4 3 4 +--R - 2B b e x + (- 2A b e - 8B b d e )x +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 8A b d e - 12B b d e )x + (- 12A b d e - 8B b d e)x +--R + +--R 3 4 4 +--R (- 8A b d e - 2B b d )x - 2A b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 5 6 5 4 5 +--R B b e x + ((A b - B a)e + 6B b d e )x +--R + +--R 5 4 2 3 4 +--R (- A a e + (6A b - 4B a)d e + 14B b d e )x +--R + +--R 4 2 3 3 2 3 +--R (- 4A a d e + (14A b - 6B a)d e + 16B b d e )x +--R + +--R 2 3 3 2 4 2 +--R (- 6A a d e + (16A b - 4B a)d e + 9B b d e)x +--R + +--R 3 2 4 5 4 5 +--R (- 4A a d e + (9A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 6 2 4 2 3 5 +--R 2B b e x + ((2A b + 2B a b)e + 8B b d e )x +--R + +--R 4 2 3 2 2 2 4 +--R (2A a b e + (8A b + 8B a b)d e + 12B b d e )x +--R + +--R 3 2 2 2 2 3 3 +--R (8A a b d e + (12A b + 12B a b)d e + 8B b d e)x +--R + +--R 2 2 2 3 2 4 2 +--R (12A a b d e + (8A b + 8B a b)d e + 2B b d )x +--R + +--R 3 2 4 4 +--R (8A a b d e + (2A b + 2B a b)d )x + 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 5 7 2 5 2 4 6 +--R - B b e x + (- A b e - 6B b d e )x +--R + +--R 2 5 2 4 2 2 3 5 +--R (B a e + (- 6A b - 2B a b)d e - 14B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (- 2A a b + 4B a )d e + (- 14A b - 8B a b)d e +--R + +--R 2 3 2 +--R - 16B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 4A a d e + (- 8A a b + 6B a )d e + (- 16A b - 12B a b)d e +--R + +--R 2 4 +--R - 9B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 2 +--R (6A a d e + (- 12A a b + 4B a )d e + (- 9A b - 8B a b)d e - 2B b d )x +--R + +--R 2 3 2 2 4 2 5 2 4 +--R (4A a d e + (- 8A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 5 +--R - 2A a b d +--R / +--R 4 4 3 4 3 3 2 3 2 2 4 +--R b e x + (2a b e + 2b d)x + 6a b d x + (- 2a b e + 6a b d)x - a e +--R + +--R 3 +--R 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 4 4 3 4 3 2 2 3 2 +--R - 2b e x + (- 6a b e - 2b d)x + (- 6a b e - 6a b d)x +--R + +--R 3 2 2 3 +--R (- 2a b e - 6a b d)x - 2a b d +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 2 3 3 5 4 2 +--R (- 525A a b + 945B a b )e + (525A b - 1365B a b )d e +--R + +--R 5 2 +--R 420B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 1575A a b + 2835B a b )e + (1575A a b - 4095B a b )d e +--R + +--R 4 2 +--R 1260B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 1575A a b + 2835B a b)e + (1575A a b - 4095B a b )d e +--R + +--R 2 3 2 +--R 1260B a b d e +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 3 2 2 +--R (- 525A a b + 945B a )e + (525A a b - 1365B a b)d e + 420B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 3 5 5 4 3 5 2 4 +--R - 24B b e x + ((- 40A b + 48B a b )e - 128B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (240A a b - 432B a b )e + (- 400A b + 816B a b )d e +--R + +--R 5 2 +--R - 464B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (1155A a b - 2079B a b )e + (- 1590A a b + 3786B a b )d e +--R + +--R 5 4 2 5 3 +--R (195A b - 1767B a b )d e + 60B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (1400A a b - 2520B a b)e + (- 1890A a b + 4522B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (300A a b - 2052B a b )d e + (30A b + 90B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (525A a b - 945B a )e + (- 700A a b + 1680B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (105A a b - 749B a b )d e + (30A a b + 30B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 7 2 6 2 5 +-+ | 2 2 2 +--R (60b x + 120a b x + 60a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 5 +--R - B b e x + ((- A b - B a)e - 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (- A a e + (- 4A b - 4B a)d e - 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (- 4A a d e + (- 6A b - 6B a)d e - 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (- 6A a d e + (- 4A b - 4B a)d e - B b d )x +--R + +--R 3 4 4 +--R (- 4A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1265 + +)clear all + +--S 1266 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1378 +r0:=-1/6*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*(d+e*x)^(5/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+2/3*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))-5/12*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/_ + (b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/_ + (b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*_ + (a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x + (- 45A a b + 105B a )e +--R + +--R 2 +--R - 60B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 5 4 +-+ | 2 2 2 +--R (12b x + 12a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1267 + +--S 1268 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x +--R + +--R 2 3 2 2 +--R (- 45A a b + 105B a )e - 60B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R 16B b e x + ((48A b - 112B a b )e + 112B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((150A a b - 350B a b)e + (- 54A b + 326B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (90A a b - 210B a )e + (- 30A a b + 190B a b)d e +--R + +--R 3 2 2 +--R (- 12A b - 12B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 24b x + 48a b x + 24a b +--R , +--R +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x +--R + +--R 2 3 2 2 +--R (- 45A a b + 105B a )e - 60B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 12b x + 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1268 + +--S 1269 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x + (- 45A a b + 105B a )e +--R + +--R 2 +--R - 60B a b d e +--R * +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((90A b - 210B a b )e + 120B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((270A a b - 630B a b )e + 360B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((270A a b - 630B a b)e + 360B a b d e)x + (90A a b - 210B a )e +--R + +--R 3 +--R 120B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 16B b e x + ((48A b - 112B a b )e + 112B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((150A a b - 350B a b)e + (- 54A b + 326B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (90A a b - 210B a )e + (- 30A a b + 190B a b)d e +--R + +--R 3 2 2 +--R (- 12A b - 12B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 2 4 4 3 2 4 3 +--R - 16B b e x + ((- 48A b + 96B a b )e - 112B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((- 198A a b + 462B a b )e + (54A b - 438B a b )d e + 24B b d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 240A a b + 560B a b)e + (84A a b - 516B a b )d e +--R + +--R 4 3 2 +--R (12A b + 36B a b )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 90A a b + 210B a )e + (30A a b - 190B a b)d e +--R + +--R 3 2 2 2 +--R (12A a b + 12B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 2 5 2 4 +-+ | 2 2 2 +--R (24b x + 48a b x + 24a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 +--R 2B b e x + (2A b e + 6B b d e )x + (6A b d e + 6B b d e)x +--R + +--R 2 3 3 +--R (6A b d e + 2B b d )x + 2A b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 4 5 4 3 4 +--R B b e x + ((A b - B a)e + 5B b d e )x +--R + +--R 4 3 2 2 3 +--R (- A a e + (5A b - 3B a)d e + 9B b d e )x +--R + +--R 3 2 2 3 2 +--R (- 3A a d e + (9A b - 3B a)d e + 7B b d e)x +--R + +--R 2 2 3 4 3 4 +--R (- 3A a d e + (7A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 5 2 3 2 2 4 +--R - 2B b e x + ((- 2A b - 2B a b)e - 6B b d e )x +--R + +--R 3 2 2 2 2 3 +--R (- 2A a b e + (- 6A b - 6B a b)d e - 6B b d e)x +--R + +--R 2 2 2 2 3 2 +--R (- 6A a b d e + (- 6A b - 6B a b)d e - 2B b d )x +--R + +--R 2 2 3 3 +--R (- 6A a b d e + (- 2A b - 2B a b)d )x - 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 4 6 2 4 2 3 5 +--R - B b e x + (- A b e - 5B b d e )x +--R + +--R 2 4 2 3 2 2 2 4 +--R (B a e + (- 5A b - 2B a b)d e - 9B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 3 +--R (A a e + (- 2A a b + 3B a )d e + (- 9A b - 6B a b)d e - 7B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 2 +--R (3A a d e + (- 6A a b + 3B a )d e + (- 7A b - 6B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 3 2 4 2 3 +--R (3A a d e + (- 6A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 4 +--R - 2A a b d +--R / +--R 4 4 3 4 3 3 2 3 2 2 4 +--R b e x + (2a b e + 2b d)x + 6a b d x + (- 2a b e + 6a b d)x - a e +--R + +--R 3 +--R 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 4 4 3 4 3 2 2 3 2 +--R 2b e x + (6a b e + 2b d)x + (6a b e + 6a b d)x +--R + +--R 3 2 2 3 +--R (2a b e + 6a b d)x + 2a b d +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 2 4 3 +--R ((45A b - 105B a b )e + 60B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((135A a b - 315B a b )e + 180B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((135A a b - 315B a b)e + 180B a b d e)x + (45A a b - 105B a )e +--R + +--R 3 +--R 60B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x + (- 45A a b + 105B a )e +--R + +--R 2 +--R - 60B a b d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 2 4 4 3 2 4 3 +--R - 8B b e x + ((- 24A b + 48B a b )e - 56B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((- 99A a b + 231B a b )e + (27A b - 219B a b )d e + 12B b d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 120A a b + 280B a b)e + (42A a b - 258B a b )d e +--R + +--R 4 3 2 +--R (6A b + 18B a b )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 45A a b + 105B a )e + (15A a b - 95B a b)d e +--R + +--R 3 2 2 2 +--R (6A a b + 6B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 2 5 2 4 +-+ | 2 2 2 +--R (12b x + 24a b x + 12a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1272 + +)clear all + +--S 1273 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1378 +r0:=-1/2*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+2*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-3/4*(4*b*B*d+A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 3A b + 15B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b + 30B a b)e - 24B a b d e)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 4 3 +-----------+ +-+ | 2 2 2 +--R (4b x + 4a b )\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R 16B b e x + ((- 10A b + 50B a b)e - 8B b d)x +--R + +--R 2 2 +--R (- 6A a b + 30B a )e + (- 4A b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 5 2 4 2 3 | 2 +--R (8b x + 16a b x + 8a b )\|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 5 2 4 2 3 | 2 +--R (4b x + 8a b x + 4a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1275 + +--S 1276 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((6A b - 30B a b )e + 24B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((18A a b - 90B a b )e + 72B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((18A a b - 90B a b)e + 72B a b d e)x + (6A a b - 30B a )e +--R + +--R 3 +--R 24B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 16B b e x + ((- 10A b + 50B a b)e - 8B b d)x + (- 6A a b + 30B a )e +--R + +--R 2 +--R (- 4A b - 4B a b)d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 3 3 2 3 2 +--R - 16B b e x + ((10A b - 66B a b )e + 8B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((16A a b - 80B a b)e + (4A b + 12B a b )d)x + (6A a b - 30B a )e +--R + +--R 2 2 +--R (4A a b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +--R 5 2 4 2 3 | 2 +-----------+ +-+ +--R (8b x + 16a b x + 8a b )\|- a b e + b d \|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 3 2 2 3 +--R (2B a b e - 2B b d e )x +--R + +--R 3 2 2 2 2 2 +--R (2A a b e + (- 2A b + 4B a b)d e - 4B b d e)x +--R + +--R 2 2 2 2 3 2 +--R (4A a b d e + (- 4A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 3 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 4 3 2 3 +--R B b e x + ((A b - B a)e + 4B b d e )x +--R + +--R 3 2 2 2 +--R (- A a e + (4A b - 2B a)d e + 5B b d e)x +--R + +--R 2 2 3 2 3 +--R (- 2A a d e + (5A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 3 2 4 +--R (- 2B a b e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 3 +--R ((- 2A a b - 2B a b)e + (2A b - 2B a b )d e + 4B b d e)x +--R + +--R 2 3 2 2 2 3 2 2 +--R - 2A a b e + (- 2A a b - 4B a b)d e + (4A b + 2B a b )d e +--R + +--R 3 3 +--R 2B b d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 2 3 +--R (- 4A a b d e + (2A a b - 2B a b)d e + (2A b + 2B a b )d )x +--R + +--R 2 2 2 3 +--R - 2A a b d e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 5 2 3 2 2 4 +--R - B b e x + (- A b e - 4B b d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (B a e + (- 4A b - 2B a b)d e - 5B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 2 +--R (A a e + (- 2A a b + 2B a )d e + (- 5A b - 4B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (2A a d e + (- 4A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 3 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 4 4 3 4 3 3 2 3 2 2 4 +--R b e x + (2a b e + 2b d)x + 6a b d x + (- 2a b e + 6a b d)x - a e +--R + +--R 3 +--R 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (2a b e - 2b d e)x + (6a b e - 4a b d e - 2b d )x +--R + +--R 3 2 2 4 2 2 4 2 3 2 2 3 2 4 +--R (6a b e - 6a b d )x + (2a b e + 4a b d e - 6a b d )x + 2a b d e +--R + +--R 3 2 2 +--R - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 2 4 3 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((9A a b - 45B a b )e + 36B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((9A a b - 45B a b)e + 36B a b d e)x + (3A a b - 15B a )e +--R + +--R 3 +--R 12B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 3 3 2 3 2 +--R - 8B b e x + ((5A b - 33B a b )e + 4B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((8A a b - 40B a b)e + (2A b + 6B a b )d)x + (3A a b - 15B a )e +--R + +--R 2 2 +--R (2A a b + 2B a b)d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 5 2 4 2 3 +-----------+ +-+ | 2 +--R (4b x + 8a b x + 4a b )\|- a e + b d \|b \|a b e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1378 +r0:=-2*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/2*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-1/4*e*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 2A a b - 6B a b)e + 8B a b d e)x + (- A a b - 3B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e + (2A b + 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 3 4 2 2 3 +-----------+ +-+ | 2 2 2 +--R ((4a b e - 4b d)x + 4a b e - 4a b d)\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R ((2A b - 10B a b)e + 8B b d)x + (- 2A a b - 6B a )e +--R + +--R 2 +--R (4A b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +--R ((8a b e - 8b d)x + (16a b e - 16a b d)x + 8a b e - 8a b d) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 +--R ((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e +--R + +--R 2 +--R (2A b + 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 4 5 2 2 3 4 3 2 2 3 | 2 +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1282 + +--S 1283 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((2A b + 6B a b )e - 8B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((6A a b + 18B a b )e - 24B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((6A a b + 18B a b)e - 24B a b d e)x + (2A a b + 6B a )e +--R + +--R 3 +--R - 8B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +--R ((2A b - 10B a b)e + 8B b d)x + (- 2A a b - 6B a )e +--R + +--R 2 +--R (4A b + 4B a b)d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 +--R ((- 2A b + 10B a b )e - 8B b d)x +--R + +--R 2 3 2 2 3 +--R (16B a b e + (- 4A b - 12B a b )d)x + (2A a b + 6B a )e +--R + +--R 2 2 +--R (- 4A a b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +--R ((8a b e - 8b d)x + (16a b e - 16a b d)x + 8a b e - 8a b d) +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 2 +--R (2B a b e - 2B b d e)x +--R + +--R 2 2 2 2 +--R (2A a b e + (- 2A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 2 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 +--R B b e x + ((A b - B a)e + 3B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (3A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 3 +--R (- 2B a b e + 2B b d e)x +--R + +--R 2 2 2 3 3 2 2 +--R ((- 2A a b - 2B a b)e + 2A b d e + 2B b d )x +--R + +--R 2 2 2 3 2 2 2 +--R (- 2A a b e - 2B a b d e + (2A b + 2B a b )d )x - 2A a b d e +--R + +--R 2 2 +--R 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 4 2 2 2 3 +--R - B b e x + (- A b e - 3B b d e)x +--R + +--R 2 2 2 2 2 2 +--R (B a e + (- 3A b - 2B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (- 2A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 2 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 4 4 3 4 3 3 2 3 2 2 4 +--R b e x + (2a b e + 2b d)x + 6a b d x + (- 2a b e + 6a b d)x - a e +--R + +--R 3 +--R 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (2a b e - 2b d e)x + (6a b e - 4a b d e - 2b d )x +--R + +--R 3 2 2 4 2 2 4 2 3 2 2 3 2 4 +--R (6a b e - 6a b d )x + (2a b e + 4a b d e - 6a b d )x + 2a b d e +--R + +--R 3 2 2 +--R - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 2 4 3 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((3A a b + 9B a b )e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 3 +--R ((3A a b + 9B a b)e - 12B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 +--R (((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e + (2A b + 2B a b)d) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R ((- A b + 5B a b )e - 4B b d)x + (8B a b e + (- 2A b - 6B a b )d)x +--R + +--R 2 3 2 2 +--R (A a b + 3B a )e + (- 2A a b - 2B a b)d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +-----------+ +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|- a e + b d +--R * +--R +-----------+ +------------------+ +--R +-+ | 2 | 2 2 2 +--R \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1286 + +)clear all + +--S 1287 of 1378 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1378 +r0:=-2/3*B*(a+b*x)*sqrt(d+e*x)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/6*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/4*e*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 3A b - B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b - 2B a b)e + 8B a b d e)x + (- 3A a b - B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((3A b + B a b)e - 4B b d)x + (5A a b - B a )e + (- 2A b - 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R ((4a b e - 8a b d e + 4b d )x + 4a b e - 8a b d e + 4a b d ) +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R ((6A b + 2B a b)e - 8B b d)x + (10A a b - 2B a )e +--R + +--R 2 +--R (- 4A b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (8a b e - 16a b d e + 8b d )x + (16a b e - 32a b d e + 16a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 8a b e - 16a b d e + 8a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 +--R ((3A b + B a b)e - 4B b d)x + (5A a b - B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 4a b e - 8a b d e + 4a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1289 + +--S 1290 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((6A b + 2B a b )e - 8B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((18A a b + 6B a b )e - 24B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((18A a b + 6B a b)e - 24B a b d e)x + (6A a b + 2B a )e +--R + +--R 3 +--R - 8B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +--R ((6A b + 2B a b)e - 8B b d)x + (10A a b - 2B a )e +--R + +--R 2 +--R (- 4A b - 4B a b)d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 +--R ((- 6A b - 2B a b )e + 8B b d)x +--R + +--R 2 3 2 2 3 +--R (- 16A a b e + (4A b + 12B a b )d)x + (- 10A a b + 2B a )e +--R + +--R 2 2 +--R (4A a b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (8a b e - 16a b d e + 8b d )x + (16a b e - 32a b d e + 16a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 8a b e - 16a b d e + 8a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (5) +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((6A b + 2B a b )e - 8B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((18A a b + 6B a b )e - 24B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((18A a b + 6B a b)e - 24B a b d e)x + (6A a b + 2B a )e +--R + +--R 3 +--R - 8B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +--R ((6A b + 2B a b)e - 8B b d)x + (10A a b - 2B a )e +--R + +--R 2 +--R (- 4A b - 4B a b)d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 +--R ((- 6A b - 2B a b )e + 8B b d)x +--R + +--R 2 3 2 2 3 +--R (- 16A a b e + (4A b + 12B a b )d)x + (- 10A a b + 2B a )e +--R + +--R 2 2 +--R (4A a b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (8a b e - 16a b d e + 8b d )x + (16a b e - 32a b d e + 16a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 8a b e - 16a b d e + 8a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (6) +--R 2 2 +-------+ +--R ((2B a b e - 2B b d)x + 2A a b e - 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 +--R (- 2B a b e + 2B b d)x +--R + +--R 2 2 3 2 2 2 +--R ((- 2A a b - 2B a b)e + (2A b + 2B a b )d)x - 2A a b e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 4 4 3 4 3 3 2 3 2 2 4 +--R b e x + (2a b e + 2b d)x + 6a b d x + (- 2a b e + 6a b d)x - a e +--R + +--R 3 +--R 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (2a b e - 2b d e)x + (6a b e - 4a b d e - 2b d )x +--R + +--R 3 2 2 4 2 2 4 2 3 2 2 3 2 4 +--R (6a b e - 6a b d )x + (2a b e + 4a b d e - 6a b d )x + 2a b d e +--R + +--R 3 2 2 +--R - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (7) +--R 4 3 2 4 3 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((9A a b + 3B a b )e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 3 +--R ((9A a b + 3B a b)e - 12B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 +--R (((3A b + B a b)e - 4B b d)x + (5A a b - B a )e + (- 2A b - 2B a b)d) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R ((- 3A b - B a b )e + 4B b d)x + (- 8A a b e + (2A b + 6B a b )d)x +--R + +--R 2 3 2 2 +--R (- 5A a b + B a )e + (2A a b + 2B a b)d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 4a b e - 8a b d e + 4a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (8) -------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1295 + +--S 1296 of 1378 +r0:=-2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x))+1/2*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/(e*_ + (b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+3/4*e*(4*b*B*d-5*A*b*e+_ + a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-_ + a*e)^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-3/4*(4*b*B*d-5*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x - 8A a e +--R + +--R 2 2 2 +--R (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x + 4a e - 12a b d e +--R + +--R 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R ((- 30A b + 6B a b)e + 24B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 50A a b + 10B a )e + (- 10A b + 42B a b)d e + 8B b d )x +--R + +--R 2 2 2 2 2 +--R - 16A a e + (- 18A a b + 26B a )d e + (4A b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (8a b e - 24a b d e + 24a b d e - 8b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (16a b e - 48a b d e + 48a b d e - 16a b d )x + 8a e - 24a b d e +--R + +--R 3 2 2 2 3 3 +--R 24a b d e - 8a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 3 2 2 3 2 +--R ((- 15A b + 3B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 30A a b + 6B a b)e + 24B a b d e)x + (- 15A a b + 3B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x +--R + +--R 2 2 2 2 2 +--R - 8A a e + (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1297 + +--S 1298 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((- 30A b + 6B a b )e + 24B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((- 90A a b + 18B a b )e + 72B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((- 90A a b + 18B a b)e + 72B a b d e)x + (- 30A a b + 6B a )e +--R + +--R 3 +--R 24B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 +-------+ \|b \|e x + d +--R \|- a b e + b d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((- 30A b + 6B a b)e + 24B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 50A a b + 10B a )e + (- 10A b + 42B a b)d e + 8B b d )x +--R + +--R 2 2 2 2 2 +--R - 16A a e + (- 18A a b + 26B a )d e + (4A b + 4B a b)d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R + +--R 3 2 2 3 3 +--R ((30A b - 6B a b )e - 24B b d e)x +--R + +--R 2 2 2 3 2 3 2 2 +--R ((80A a b - 16B a b)e + (10A b - 66B a b )d e - 8B b d )x +--R + +--R 2 3 2 2 2 +--R (66A a b - 10B a )e + (28A a b - 68B a b)d e +--R + +--R 3 2 2 +--R (- 4A b - 12B a b )d +--R * +--R x +--R + +--R 3 2 2 3 2 2 2 +--R 16A a e + (18A a b - 26B a )d e + (- 4A a b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (8a b e - 24a b d e + 24a b d e - 8b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (16a b e - 48a b d e + 48a b d e - 16a b d )x + 8a e - 24a b d e +--R + +--R 3 2 2 2 3 3 +--R 24a b d e - 8a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 +-------+ +--R ((- 2B a b e + 2B b d)x - 2A a b e + 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 2 3 2 +--R (2B a b e - 2B b d)x + ((2A a b + 2B a b)e + (- 2A b - 2B a b )d)x +--R + +--R 2 2 +--R 2A a b e - 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 4 2 5 3 2 4 4 3 4 2 3 +--R b e x + (2a b e + 3b d e)x + (8a b d e + 2b d )x +--R + +--R 3 2 2 2 3 2 2 4 2 2 2 2 4 +--R (- 2a b e + 6a b d e + 6a b d )x + (- a e + 6a b d )x - a d e +--R + +--R 3 2 +--R 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 4 3 5 2 5 2 3 3 4 2 5 2 4 +--R (- 2a b e + 2b d e )x + (- 6a b e + 2a b d e + 4b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (- 6a b e - 6a b d e + 10a b d e + 2b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 2 +--R (- 2a b e - 10a b d e + 6a b d e + 6a b d )x +--R + +--R 4 2 3 2 2 2 3 3 4 2 3 2 3 +--R (- 4a b d e - 2a b d e + 6a b d )x - 2a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 2 4 3 +--R ((- 15A b + 3B a b )e + 12B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((- 45A a b + 9B a b )e + 36B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((- 45A a b + 9B a b)e + 36B a b d e)x + (- 15A a b + 3B a )e +--R + +--R 3 +--R 12B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 +-------+ \|b \|e x + d +--R \|a b e - b d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((- 15A b + 3B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 30A a b + 6B a b)e + 24B a b d e)x + (- 15A a b + 3B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x - 8A a e +--R + +--R 2 2 2 +--R (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R + +--R 3 2 2 3 3 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 2 +--R ((40A a b - 8B a b)e + (5A b - 33B a b )d e - 4B b d )x +--R + +--R 2 3 2 2 2 +--R (33A a b - 5B a )e + (14A a b - 34B a b)d e +--R + +--R 3 2 2 +--R (- 2A b - 6B a b )d +--R * +--R x +--R + +--R 3 2 2 3 2 2 2 +--R 8A a e + (9A a b - 13B a )d e + (- 2A a b - 2B a b)d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1300 + +--S 1301 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1301 + +)clear all + +--S 1302 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1302 + +--S 1303 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/6*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))+5/4*e*(4*b*B*d-_ + 7*A*b*e+3*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b)/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/12*(4*b*B*d-_ + 7*A*b*e+3*a*B*e)/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 105A b + 45B a b )e + 60B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 210A a b + 90B a b)e + (- 105A b + 165B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 105A a b + 45B a )e + (- 210A a b + 150B a b)d e +--R + +--R 2 2 +--R 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (- 105A a b + 45B a )d e + 60B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (12a e - 36a b d e + 24a b d e + 24a b d e - 36a b d e + 12b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (105A a b - 45B a )e + (210A a b - 150B a b)d e +--R + +--R 2 2 +--R - 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 3 +--R ((210A b - 90B a b )e - 120B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((350A a b - 150B a b)e + (280A b - 320B a b )d e - 160B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (112A a b - 48B a )e + (476A a b - 268B a b)d e +--R + +--R 3 2 2 3 3 +--R (42A b - 290B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 16A a e + (160A a b - 32B a )d e + (78A a b - 166B a b)d e +--R + +--R 3 2 3 +--R (- 12A b - 12B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 48a b e - 168a b d e + 192a b d e - 48a b d e - 48a b d e +--R + +--R 6 5 +--R 24b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 24a e - 48a b d e - 48a b d e + 192a b d e - 168a b d e +--R + +--R 5 5 +--R 48a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 24a d e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (105A a b - 45B a )e + (210A a b - 150B a b)d e +--R + +--R 2 2 +--R - 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e +--R + +--R 5 5 +--R 24a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1304 + +--S 1305 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((105A a b - 45B a )e + (210A a b - 150B a b)d e - 120B a b d e)x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 3 3 4 2 4 +--R ((210A b - 90B a b )e - 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (630A a b - 270B a b )e + (210A b - 450B a b )d e +--R + +--R 4 2 +--R - 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (630A a b - 270B a b)e + (630A a b - 630B a b )d e +--R + +--R 3 2 +--R - 360B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R ((210A a b - 90B a )e + (630A a b - 390B a b)d e - 360B a b d e)x +--R + +--R 3 4 2 3 2 +--R (210A a b - 90B a )d e - 120B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((210A b - 90B a b )e - 120B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((350A a b - 150B a b)e + (280A b - 320B a b )d e - 160B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (112A a b - 48B a )e + (476A a b - 268B a b)d e +--R + +--R 3 2 2 3 3 +--R (42A b - 290B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 16A a e + (160A a b - 32B a )d e + (78A a b - 166B a b)d e +--R + +--R 3 2 3 +--R (- 12A b - 12B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 3 4 2 4 +--R ((- 210A b + 90B a b )e + 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 560A a b + 240B a b )e + (- 280A b + 440B a b )d e +--R + +--R 4 2 +--R 160B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 462A a b + 198B a b)e + (- 756A a b + 588B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 42A b + 450B a b )d e + 24B b d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 96A a b + 48B a )e + (- 636A a b + 300B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 120A a b + 456B a b )d e + (12A b + 36B a b )d +--R * +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 16A a e + (- 160A a b + 32B a )d e + (- 78A a b + 166B a b)d e +--R + +--R 3 2 2 3 +--R (12A a b + 12B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 48a b e - 168a b d e + 192a b d e - 48a b d e - 48a b d e +--R + +--R 6 5 +--R 24b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 24a e - 48a b d e - 48a b d e + 192a b d e - 168a b d e +--R + +--R 5 5 +--R 48a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 24a d e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1305 + +--S 1306 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 3 4 2 4 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 3 +--R ((315A a b - 135B a b )e + (105A b - 225B a b )d e - 60B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (315A a b - 135B a b)e + (315A a b - 315B a b )d e +--R + +--R 3 2 +--R - 180B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R ((105A a b - 45B a )e + (315A a b - 195B a b)d e - 180B a b d e)x +--R + +--R 3 4 2 3 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((105A a b - 45B a )e + (210A a b - 150B a b)d e - 120B a b d e)x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 3 4 2 4 +--R ((- 105A b + 45B a b )e + 60B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 120B a b )e + (- 140A b + 220B a b )d e +--R + +--R 4 2 +--R 80B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 231A a b + 99B a b)e + (- 378A a b + 294B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 21A b + 225B a b )d e + 12B b d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 48A a b + 24B a )e + (- 318A a b + 150B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 60A a b + 228B a b )d e + (6A b + 18B a b )d +--R * +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 8A a e + (- 80A a b + 16B a )d e + (- 39A a b + 83B a b)d e +--R + +--R 3 2 2 3 +--R (6A a b + 6B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e + 24a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1308 + +)clear all + +--S 1309 of 1378 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 1378 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/10*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-7/20*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-7/12*e*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^4*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*b^(3/2)*e*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*b*e*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 5 2 +--R - 60b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 6 3 3 3 4 2 4 4 3 5 5 2 +--R 60a e - 180a b d e + 600a b d e - 900a b d e + 540a b d e +--R + +--R 6 6 +--R - 120b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5 6 +--R 120a d e - 540a b d e + 900a b d e - 600a b d e + 180a b d e +--R + +--R 6 7 +--R - 60b d +--R * +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 5 7 +--R - 60a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 4 3 4 +--R ((- 1890A b + 1050B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3150A a b + 1750B a b )e + (- 4410A b + 3850B a b )d e +--R + +--R 4 2 2 +--R 1960B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 1008A a b + 560B a b)e + (- 7434A a b + 4578B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 2898A b + 4914B a b )d e + 1288B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 80B a )e + (- 2448A a b + 1296B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 4986A a b + 3858B a b )d e + (- 270A b + 2366B a b )d e +--R + +--R 4 4 +--R 120B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 48A a e + (336A a b - 32B a )d e + (- 1728A a b + 544B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 510A a b + 1318B a b )d e + (60A b + 60B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 120a b e - 600a b d e + 1200a b d e - 1200a b d e +--R + +--R 6 4 3 7 5 2 +--R 600a b d e - 120b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 +--R 240a b e - 960a b d e + 1200a b d e - 1200a b d e +--R + +--R 6 5 2 7 6 +--R 960a b d e - 240b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 120a e - 120a b d e - 1080a b d e + 3000a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 3000a b d e + 1080a b d e + 120a b d e - 120b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 +--R 240a d e - 960a b d e + 1200a b d e - 1200a b d e +--R + +--R 2 5 6 6 7 +--R 960a b d e - 240a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 120a d e - 600a b d e + 1200a b d e - 1200a b d e + 600a b d e +--R + +--R 2 5 7 +--R - 120a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1890A a b + 1050B a b )e + (- 1890A b + 1890B a b )d e +--R + +--R 4 2 2 +--R 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 945A a b + 525B a b)e + (- 3780A a b + 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 945A b + 2205B a b )d e + 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 +--R (- 1890A a b + 1050B a b)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 1890A a b + 1890B a b )d e + 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 945A a b + 525B a b)d e + 420B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 7 5 2 +--R - 60b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 120a b e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 7 6 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 60a e - 60a b d e - 540a b d e + 1500a b d e - 1500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 540a b d e + 60a b d e - 60b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 120a d e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 6 7 +--R - 120a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 2 5 7 +--R - 60a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1311 + +--S 1312 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 4 5 3 5 +--R ((- 1890A b + 1050B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 5670A a b + 3150B a b )e + (- 3780A b + 4620B a b )d e +--R + +--R 5 2 2 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 5670A a b + 3150B a b )e + (- 11340A a b + 8820B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1890A b + 6090B a b )d e + 840B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 1890A a b + 1050B a b)e + (- 11340A a b + 7140B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (- 5670A a b + 8190B a b )d e + 2520B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (- 3780A a b + 2100B a b)d e + (- 5670A a b + 4830B a b )d e +--R + +--R 2 3 3 +--R 2520B a b d e +--R * +--R x +--R + +--R 3 2 4 2 2 3 2 3 +--R (- 1890A a b + 1050B a b)d e + 840B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 1890A b + 1050B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3150A a b + 1750B a b )e + (- 4410A b + 3850B a b )d e +--R + +--R 4 2 2 +--R 1960B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 1008A a b + 560B a b)e + (- 7434A a b + 4578B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 2898A b + 4914B a b )d e + 1288B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 80B a )e + (- 2448A a b + 1296B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 4986A a b + 3858B a b )d e + (- 270A b + 2366B a b )d e +--R + +--R 4 4 +--R 120B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 48A a e + (336A a b - 32B a )d e + (- 1728A a b + 544B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 510A a b + 1318B a b )d e + (60A b + 60B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 5 4 4 5 3 5 +--R ((1890A b - 1050B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (5040A a b - 2800B a b )e + (4410A b - 4690B a b )d e +--R + +--R 5 2 2 +--R - 1960B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4158A a b - 2310B a b )e + (11844A a b - 8428B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (2898A b - 6874B a b )d e - 1288B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (864A a b - 480B a b)e + (9882A a b - 5874B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (7884A a b - 8772B a b )d e + (270A b - 3654B a b )d e +--R + +--R 5 4 +--R - 120B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 96A a b + 80B a )e + (2112A a b - 1264B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (6714A a b - 4402B a b )d e + (780A a b - 3684B a b )d e +--R + +--R 5 4 4 +--R (- 60A b - 180B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R 48A a e + (- 336A a b + 32B a )d e + (1728A a b - 544B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (510A a b - 1318B a b )d e + (- 60A a b - 60B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 120a b e - 600a b d e + 1200a b d e - 1200a b d e + 600a b d e +--R + +--R 7 5 2 +--R - 120b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 240a b e - 960a b d e + 1200a b d e - 1200a b d e + 960a b d e +--R + +--R 7 6 +--R - 240b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 120a e - 120a b d e - 1080a b d e + 3000a b d e - 3000a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 1080a b d e + 120a b d e - 120b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 240a d e - 960a b d e + 1200a b d e - 1200a b d e + 960a b d e +--R + +--R 6 7 +--R - 240a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 120a d e - 600a b d e + 1200a b d e - 1200a b d e + 600a b d e +--R + +--R 2 5 7 +--R - 120a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 4 4 5 3 5 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 2835A a b + 1575B a b )e + (- 1890A b + 2310B a b )d e +--R + +--R 5 2 2 +--R 840B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 2835A a b + 1575B a b )e + (- 5670A a b + 4410B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 945A b + 3045B a b )d e + 420B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 945A a b + 525B a b)e + (- 5670A a b + 3570B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (- 2835A a b + 4095B a b )d e + 1260B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (- 1890A a b + 1050B a b)d e + (- 2835A a b + 2415B a b )d e +--R + +--R 2 3 3 +--R 1260B a b d e +--R * +--R x +--R + +--R 3 2 4 2 2 3 2 3 +--R (- 945A a b + 525B a b)d e + 420B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1890A a b + 1050B a b )e + (- 1890A b + 1890B a b )d e +--R + +--R 4 2 2 +--R 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 945A a b + 525B a b)e + (- 3780A a b + 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 945A b + 2205B a b )d e + 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 1890A a b + 1050B a b)d e + (- 1890A a b + 1890B a b )d e +--R + +--R 3 3 +--R 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 945A a b + 525B a b)d e + 420B a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 5 4 4 5 3 5 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (2520A a b - 1400B a b )e + (2205A b - 2345B a b )d e +--R + +--R 5 2 2 +--R - 980B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (2079A a b - 1155B a b )e + (5922A a b - 4214B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (1449A b - 3437B a b )d e - 644B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (432A a b - 240B a b)e + (4941A a b - 2937B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (3942A a b - 4386B a b )d e + (135A b - 1827B a b )d e +--R + +--R 5 4 +--R - 60B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 40B a )e + (1056A a b - 632B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (3357A a b - 2201B a b )d e + (390A a b - 1842B a b )d e +--R + +--R 5 4 4 +--R (- 30A b - 90B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R 24A a e + (- 168A a b + 16B a )d e + (864A a b - 272B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (255A a b - 659B a b )d e + (- 30A a b - 30B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 7 5 2 +--R - 60b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 120a b e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 7 6 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 60a e - 60a b d e - 540a b d e + 1500a b d e - 1500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 540a b d e + 60a b d e - 60b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 120a d e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 6 7 +--R - 120a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 2 5 7 +--R - 60a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1315 + +)clear all + +--S 1316 of 1378 +t0:=(A+B*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1378 +r0:=-1/20*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*(d+e*x)^(11/2)/(b^2*e*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))+2/5*B*(a+b*x)*(d+e*x)^(13/2)/(b*e*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-33/160*e*(8*b*B*d+5*A*b*e-13*a*B*e)*_ + (a+b*x)*(d+e*x)^(7/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-11/120*_ + (8*b*B*d+5*A*b*e-13*a*B*e)*(d+e*x)^(9/2)/(b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+77/64*e^3*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*(d+_ + e*x)^(3/2)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))-231/320*e^2*(8*b*B*d+_ + 5*A*b*e-13*a*B*e)*(d+e*x)^(5/2)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 231/64*e^3*(b*d-a*e)^(3/2)*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(15/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+231/64*e^3*(b*d-a*e)*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*_ + sqrt(d+e*x)/(b^7*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 2 4 5 6 5 4 +--R (17325A a b - 45045B a b )e + (- 17325A b + 72765B a b )d e +--R + +--R 6 2 3 +--R - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (69300A a b - 180180B a b )e +--R + +--R 5 2 4 4 5 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (103950A a b - 270270B a b )e +--R + +--R 2 4 3 3 4 2 4 2 3 +--R (- 103950A a b + 436590B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (69300A a b - 180180B a b)e +--R + +--R 3 3 4 2 4 3 3 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (17325A a b - 45045B a )e + (- 17325A a b + 72765B a b)d e +--R + +--R 4 2 2 3 +--R - 27720B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 384B b e x + ((640A b - 1664B a b )e + 3328B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 7040A a b + 18304B a b )e + (10240A b - 37888B a b )d e +--R + +--R 6 2 3 +--R 22144B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (- 46035A a b + 119691B a b )e +--R + +--R 5 2 4 4 +--R (63910A a b - 239822B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 11475A b + 132091B a b )d e - 10680B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (- 84315A a b + 219219B a b )e +--R + +--R 2 4 3 3 4 +--R (114840A a b - 433488B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 18975A a b + 233079B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 5150A b - 16970B a b )d e - 2480B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 63525A a b + 165165B a b)e +--R + +--R 3 3 4 2 4 +--R (85470A a b - 323862B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 13365A a b + 171501B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3740A a b - 11660B a b )d e + (- 1640A b - 1720B a b )d e +--R + +--R 6 5 +--R - 320B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 17325A a b + 45045B a )e + (23100A a b - 87780B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 3465A a b + 45969B a b )d e + (- 990A a b - 2970B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 440A a b - 440B a b )d e + (- 240A b - 80B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 10 3 9 2 2 8 3 7 +-+ | 2 2 2 +--R (960b x + 2880a b x + 2880a b x + 960a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 2 4 5 6 5 4 +--R (- 17325A a b + 45045B a b )e + (17325A b - 72765B a b )d e +--R + +--R 6 2 3 +--R 27720B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (- 69300A a b + 180180B a b )e +--R + +--R 5 2 4 4 5 2 3 +--R (69300A a b - 291060B a b )d e + 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (- 103950A a b + 270270B a b )e +--R + +--R 2 4 3 3 4 2 4 2 3 +--R (103950A a b - 436590B a b )d e + 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 69300A a b + 180180B a b)e +--R + +--R 3 3 4 2 4 3 3 2 3 +--R (69300A a b - 291060B a b )d e + 110880B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 17325A a b + 45045B a )e + (17325A a b - 72765B a b)d e +--R + +--R 4 2 2 3 +--R 27720B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b 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+--R +--R (6) +--R 6 2 5 5 7 6 4 +--R (- 17325A a b + 45045B a b )e + (17325A b - 72765B a b )d e +--R + +--R 7 2 3 +--R 27720B b d e +--R * +--R 5 +--R x +--R + +--R 2 5 3 4 5 +--R (- 86625A a b + 225225B a b )e +--R + +--R 6 2 5 4 6 2 3 +--R (86625A a b - 363825B a b )d e + 138600B a b d e +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 5 +--R (- 173250A a b + 450450B a b )e +--R + +--R 2 5 3 4 4 2 5 2 3 +--R (173250A a b - 727650B a b )d e + 277200B a b d e +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 5 +--R (- 173250A a b + 450450B a b )e +--R + +--R 3 4 4 3 4 3 4 2 3 +--R (173250A a b - 727650B a b )d e + 277200B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 +--R (- 86625A a b + 225225B a b)e +--R + +--R 4 3 5 2 4 4 3 2 3 +--R (86625A a b - 363825B a b )d e + 138600B a b d e +--R * +--R x +--R + +--R 6 7 5 5 2 6 4 +--R (- 17325A a b + 45045B a )e + (17325A a b - 72765B a b)d e +--R + +--R 5 2 2 3 +--R 27720B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 2 4 5 6 5 4 +--R (17325A a b - 45045B a b )e + (- 17325A b + 72765B a b )d e +--R + +--R 6 2 3 +--R - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (69300A a b - 180180B a b )e +--R + +--R 5 2 4 4 5 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (103950A a b - 270270B a b )e +--R + +--R 2 4 3 3 4 2 4 2 3 +--R (- 103950A a b + 436590B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (69300A a b - 180180B a b)e +--R + +--R 3 3 4 2 4 3 3 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (17325A a b - 45045B a )e + (- 17325A a b + 72765B a b)d e +--R + +--R 4 2 2 3 +--R - 27720B a b d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 384B b e x + ((640A b - 1664B a b )e + 3328B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 7040A a b + 18304B a b )e + (10240A b - 37888B a b )d e +--R + +--R 6 2 3 +--R 22144B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (- 46035A a b + 119691B a b )e +--R + +--R 5 2 4 4 +--R (63910A a b - 239822B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 11475A b + 132091B a b )d e - 10680B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (- 84315A a b + 219219B a b )e +--R + +--R 2 4 3 3 4 +--R (114840A a b - 433488B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 18975A a b + 233079B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 5150A b - 16970B a b )d e - 2480B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 63525A a b + 165165B a b)e +--R + +--R 3 3 4 2 4 +--R (85470A a b - 323862B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 13365A a b + 171501B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3740A a b - 11660B a b )d e + (- 1640A b - 1720B a b )d e +--R + +--R 6 5 +--R - 320B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 17325A a b + 45045B a )e + (23100A a b - 87780B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 3465A a b + 45969B a b )d e + (- 990A a b - 2970B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 440A a b - 440B a b )d e + (- 240A b - 80B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 7 5 7 7 6 5 7 4 6 +--R - 384B b e x + ((- 640A b + 1280B a b )e - 3328B b d e )x +--R + +--R 6 2 5 5 7 6 4 +--R (6400A a b - 16640B a b )e + (- 10240A b + 34560B a b )d e +--R + +--R 7 2 3 +--R - 22144B b d e +--R * +--R 5 +--R x +--R + +--R 2 5 3 4 5 +--R (53075A a b - 137995B a b )e +--R + +--R 6 2 5 4 +--R (- 74150A a b + 277710B a b )d e +--R + +--R 7 6 2 3 7 3 2 +--R (11475A b - 154235B a b )d e + 10680B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 5 +--R (130350A a b - 338910B a b )e +--R + +--R 2 5 3 4 4 +--R (- 178750A a b + 673310B a b )d e +--R + +--R 6 2 5 2 3 7 6 3 2 +--R (30450A a b - 365170B a b )d e + (5150A b + 27650B a b )d e +--R + +--R 7 4 +--R 2480B b d e +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 5 +--R (147840A a b - 384384B a b )e +--R + +--R 3 4 4 3 4 +--R (- 200310A a b + 757350B a b )d e +--R + +--R 2 5 3 4 2 3 6 2 5 3 2 +--R (32340A a b - 404580B a b )d e + (8890A a b + 28630B a b )d e +--R + +--R 7 6 4 7 5 +--R (1640A b + 4200B a b )d e + 320B b d +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 +--R (80850A a b - 210210B a b)e +--R + +--R 4 3 5 2 4 +--R (- 108570A a b + 411642B a b )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (16830A a b - 217470B a b )d e + (4730A a b + 14630B a b )d e +--R + +--R 6 2 5 4 7 6 5 +--R (2080A a b + 2160B a b )d e + (240A b + 400B a b )d +--R * +--R x +--R + +--R 6 7 5 5 2 6 4 +--R (17325A a b - 45045B a )e + (- 23100A a b + 87780B a b)d e +--R + +--R 4 3 5 2 2 3 3 4 4 3 3 2 +--R (3465A a b - 45969B a b )d e + (990A a b + 2970B a b )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (440A a b + 440B a b )d e + (240A a b + 80B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +-+ +--R (960b x + 3840a b x + 5760a b x + 3840a b x + 960a b )\|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 6 7 6 5 6 5 2 4 5 +--R B e x + (A e + 6B d e )x + (6A d e + 15B d e )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (15A d e + 20B d e )x + (20A d e + 15B d e )x +--R + +--R 4 2 5 2 5 6 6 +--R (15A d e + 6B d e)x + (6A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 8 6 5 7 +--R - B b e x + ((- A b - B a)e - 6B b d e )x +--R + +--R 6 5 2 4 6 +--R (- A a e + (- 6A b - 6B a)d e - 15B b d e )x +--R + +--R 5 2 4 3 3 5 +--R (- 6A a d e + (- 15A b - 15B a)d e - 20B b d e )x +--R + +--R 2 4 3 3 4 2 4 +--R (- 15A a d e + (- 20A b - 20B a)d e - 15B b d e )x +--R + +--R 3 3 4 2 5 3 +--R (- 20A a d e + (- 15A b - 15B a)d e - 6B b d e)x +--R + +--R 4 2 5 6 2 +--R (- 15A a d e + (- 6A b - 6B a)d e - B b d )x +--R + +--R 5 6 6 +--R (- 6A a d e + (- A b - B a)d )x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1322 + +)clear all + +--S 1323 of 1378 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1323 + +--S 1324 of 1378 +r0:=-1/12*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*(d+e*x)^(9/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2))+2/3*B*(a+b*x)*(d+e*x)^(11/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-7/32*e*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*(d+_ + e*x)^(5/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/8*(8*b*B*d+3*A*b*e-_ + 11*a*B*e)*(d+e*x)^(7/2)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 35/64*e^2*(8*b*B*d+3*A*b*e-11*a*B*e)*(d+e*x)^(3/2)/(b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-105/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(13/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+105/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*_ + (a+b*x)*sqrt(d+e*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 128B b e x + ((384A b - 1408B a b )e + 1664B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (2511A a b - 9207B a b )e + (- 975A b + 10271B a b )d e +--R + +--R 5 2 2 +--R - 1320B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4599A a b - 16863B a b )e + (- 1665A a b + 18369B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 630A b - 2130B a b )d e - 400B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (3465A a b - 12705B a b)e + (- 1197A a b + 13629B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 468A a b - 1476B a b )d e + (- 264A b - 280B a b )d e +--R + +--R 5 4 +--R - 64B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (945A a b - 3465B a )e + (- 315A a b + 3675B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 126A a b - 378B a b )d e + (- 72A a b - 72B a b )d e +--R + +--R 5 4 4 +--R (- 48A b - 16B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 9 3 8 2 2 7 3 6 +-+ | 2 2 2 +--R (192b x + 576a b x + 576a b x + 192a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 256B b e x + ((768A b - 2816B a b )e + 3328B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (5022A a b - 18414B a b )e + (- 1950A b + 20542B a b )d e +--R + +--R 5 2 2 +--R - 2640B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (9198A a b - 33726B a b )e + (- 3330A a b + 36738B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1260A b - 4260B a b )d e - 800B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (6930A a b - 25410B a b)e + (- 2394A a b + 27258B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 936A a b - 2952B a b )d e + (- 528A b - 560B a b )d e +--R + +--R 5 4 +--R - 128B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (1890A a b - 6930B a )e + (- 630A a b + 7350B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 252A a b - 756B a b )d e + (- 144A a b - 144B a b )d e +--R + +--R 5 4 4 +--R (- 96A b - 32B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 384b x + 1536a b x + 2304a b x + 1536a b x + 384a b +--R , +--R +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 128B b e x + ((384A b - 1408B a b )e + 1664B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (2511A a b - 9207B a b )e + (- 975A b + 10271B a b )d e +--R + +--R 5 2 2 +--R - 1320B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4599A a b - 16863B a b )e + (- 1665A a b + 18369B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 630A b - 2130B a b )d e - 400B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (3465A a b - 12705B a b)e + (- 1197A a b + 13629B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 468A a b - 1476B a b )d e + (- 264A b - 280B a b )d e +--R + +--R 5 4 +--R - 64B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (945A a b - 3465B a )e + (- 315A a b + 3675B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 126A a b - 378B a b )d e + (- 72A a b - 72B a b )d e +--R + +--R 5 4 4 +--R (- 48A b - 16B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 192b x + 768a b x + 1152a b x + 768a b x + 192a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1325 + +--S 1326 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((1890A b - 6930B a b )e + 5040B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((9450A a b - 34650B a b )e + 25200B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((18900A a b - 69300B a b )e + 50400B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((18900A a b - 69300B a b )e + 50400B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((9450A a b - 34650B a b)e + 25200B a b d e )x +--R + +--R 5 6 4 5 3 +--R (1890A a b - 6930B a )e + 5040B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 256B b e x + ((768A b - 2816B a b )e + 3328B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (5022A a b - 18414B a b )e + (- 1950A b + 20542B a b )d e +--R + +--R 5 2 2 +--R - 2640B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (9198A a b - 33726B a b )e + (- 3330A a b + 36738B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1260A b - 4260B a b )d e - 800B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (6930A a b - 25410B a b)e + (- 2394A a b + 27258B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 936A a b - 2952B a b )d e + (- 528A b - 560B a b )d e +--R + +--R 5 4 +--R - 128B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (1890A a b - 6930B a )e + (- 630A a b + 7350B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 252A a b - 756B a b )d e + (- 144A a b - 144B a b )d e +--R + +--R 5 4 4 +--R (- 96A b - 32B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 6 4 6 6 5 4 6 3 5 +--R - 256B b e x + ((- 768A b + 2560B a b )e - 3328B b d e )x +--R + +--R 5 2 4 4 6 5 3 +--R (- 5790A a b + 21230B a b )e + (1950A b - 23870B a b )d e +--R + +--R 6 2 2 +--R 2640B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 14220A a b + 52140B a b )e + (5280A a b - 57280B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (1260A b + 6900B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (- 16128A a b + 59136B a b )e + (5724A a b - 63996B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 +--R (2196A a b + 7212B a b )d e + (528A b + 1360B a b )d e +--R + +--R 6 4 +--R 128B b d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 8820A a b + 32340B a b)e + (3024A a b - 34608B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (1188A a b + 3708B a b )d e + (672A a b + 704B a b )d e +--R + +--R 6 5 4 +--R (96A b + 160B a b )d +--R * +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 1890A a b + 6930B a )e + (630A a b - 7350B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (252A a b + 756B a b )d e + (144A a b + 144B a b )d e +--R + +--R 5 2 4 4 +--R (96A a b + 32B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +-+ +--R (384b x + 1536a b x + 2304a b x + 1536a b x + 384a b )\|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 +--R 2B b e x + (2A b e + 10B b d e )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (10A b d e + 20B b d e )x + (20A b d e + 20B b d e )x +--R + +--R 3 2 4 2 4 5 5 +--R (20A b d e + 10B b d e)x + (10A b d e + 2B b d )x + 2A b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 6 7 6 5 6 +--R B b e x + ((A b - B a)e + 7B b d e )x +--R + +--R 6 5 2 4 5 +--R (- A a e + (7A b - 5B a)d e + 20B b d e )x +--R + +--R 5 2 4 3 3 4 +--R (- 5A a d e + (20A b - 10B a)d e + 30B b d e )x +--R + +--R 2 4 3 3 4 2 3 +--R (- 10A a d e + (30A b - 10B a)d e + 25B b d e )x +--R + +--R 3 3 4 2 5 2 +--R (- 10A a d e + (25A b - 5B a)d e + 11B b d e)x +--R + +--R 4 2 5 6 5 6 +--R (- 5A a d e + (11A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 5 7 2 5 2 4 6 +--R - 2B b e x + ((- 2A b - 2B a b)e - 10B b d e )x +--R + +--R 5 2 4 2 2 3 5 +--R (- 2A a b e + (- 10A b - 10B a b)d e - 20B b d e )x +--R + +--R 4 2 2 3 2 3 2 4 +--R (- 10A a b d e + (- 20A b - 20B a b)d e - 20B b d e )x +--R + +--R 2 3 2 3 2 2 4 3 +--R (- 20A a b d e + (- 20A b - 20B a b)d e - 10B b d e)x +--R + +--R 3 2 2 4 2 5 2 +--R (- 20A a b d e + (- 10A b - 10B a b)d e - 2B b d )x +--R + +--R 4 2 5 5 +--R (- 10A a b d e + (- 2A b - 2B a b)d )x - 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 6 8 2 6 2 5 7 +--R - B b e x + (- A b e - 7B b d e )x +--R + +--R 2 6 2 5 2 2 4 6 +--R (B a e + (- 7A b - 2B a b)d e - 20B b d e )x +--R + +--R 2 6 2 5 2 2 4 +--R A a e + (- 2A a b + 5B a )d e + (- 20A b - 10B a b)d e +--R + +--R 2 3 3 +--R - 30B b d e +--R * +--R 5 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 5A a d e + (- 10A a b + 10B a )d e + (- 30A b - 20B a b)d e +--R + +--R 2 4 2 +--R - 25B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R 10A a d e + (- 20A a b + 10B a )d e + (- 25A b - 20B a b)d e +--R + +--R 2 5 +--R - 11B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 10A a d e + (- 20A a b + 5B a )d e + (- 11A b - 10B a b)d e +--R + +--R 2 6 +--R - 2B b d +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 5 2 6 2 5 +--R (5A a d e + (- 10A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 6 +--R - 2A a b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 6 6 5 6 5 2 4 5 4 +--R 2b e x + (10a b e + 2b d)x + (20a b e + 10a b d)x +--R + +--R 3 3 2 4 3 4 2 3 3 2 5 4 2 +--R (20a b e + 20a b d)x + (10a b e + 20a b d)x + (2a b e + 10a b d)x +--R + +--R 5 +--R 2a b d +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1327 + +--S 1328 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((945A b - 3465B a b )e + 2520B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((4725A a b - 17325B a b )e + 12600B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((9450A a b - 34650B a b )e + 25200B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((9450A a b - 34650B a b )e + 25200B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((4725A a b - 17325B a b)e + 12600B a b d e )x +--R + +--R 5 6 4 5 3 +--R (945A a b - 3465B a )e + 2520B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 128B b e x + ((384A b - 1408B a b )e + 1664B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (2511A a b - 9207B a b )e + (- 975A b + 10271B a b )d e +--R + +--R 5 2 2 +--R - 1320B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4599A a b - 16863B a b )e + (- 1665A a b + 18369B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 630A b - 2130B a b )d e - 400B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (3465A a b - 12705B a b)e + (- 1197A a b + 13629B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 468A a b - 1476B a b )d e + (- 264A b - 280B a b )d e +--R + +--R 5 4 +--R - 64B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (945A a b - 3465B a )e + (- 315A a b + 3675B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 126A a b - 378B a b )d e + (- 72A a b - 72B a b )d e +--R + +--R 5 4 4 +--R (- 48A b - 16B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 6 4 6 6 5 4 6 3 5 +--R - 128B b e x + ((- 384A b + 1280B a b )e - 1664B b d e )x +--R + +--R 5 2 4 4 6 5 3 +--R (- 2895A a b + 10615B a b )e + (975A b - 11935B a b )d e +--R + +--R 6 2 2 +--R 1320B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 7110A a b + 26070B a b )e + (2640A a b - 28640B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (630A b + 3450B a b )d e + 400B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (- 8064A a b + 29568B a b )e + (2862A a b - 31998B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (1098A a b + 3606B a b )d e + (264A b + 680B a b )d e + 64B b d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 4410A a b + 16170B a b)e + (1512A a b - 17304B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (594A a b + 1854B a b )d e + (336A a b + 352B a b )d e +--R + +--R 6 5 4 +--R (48A b + 80B a b )d +--R * +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 945A a b + 3465B a )e + (315A a b - 3675B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (126A a b + 378B a b )d e + (72A a b + 72B a b )d e +--R + +--R 5 2 4 4 +--R (48A a b + 16B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x +--R + +--R 5 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 7 5 4 6 +--R - B b e x + ((- A b - B a)e - 5B b d e )x +--R + +--R 5 4 2 3 5 +--R (- A a e + (- 5A b - 5B a)d e - 10B b d e )x +--R + +--R 4 2 3 3 2 4 +--R (- 5A a d e + (- 10A b - 10B a)d e - 10B b d e )x +--R + +--R 2 3 3 2 4 3 +--R (- 10A a d e + (- 10A b - 10B a)d e - 5B b d e)x +--R + +--R 3 2 4 5 2 +--R (- 10A a d e + (- 5A b - 5B a)d e - B b d )x +--R + +--R 4 5 5 +--R (- 5A a d e + (- A b - B a)d )x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1329 + +)clear all + +--S 1330 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1330 + +--S 1331 of 1378 +r0:=-1/4*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*(d+e*x)^(7/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+2*B*(a+b*x)*(d+e*x)^(9/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-35/96*e*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*(d+_ + e*x)^(3/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-7/24*(8*b*B*d+A*b*e-_ + 9*a*B*e)*(d+e*x)^(5/2)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-35/64*e^3*_ + (8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))/(b^(11/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*_ + (8*b*B*d+A*b*e-9*a*B*e)*sqrt(d+e*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 105A b + 945B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 420A a b + 3780B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 630A a b + 5670B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 420A a b + 3780B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 105A a b + 945B a )e - 840B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 384B b e x + ((- 279A b + 2511B a b )e - 696B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 511A a b + 4599B a b )e + (- 326A b - 1154B a b )d e +--R + +--R 4 2 +--R - 304B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 385A a b + 3465B a b)e + (- 252A a b - 812B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 200A b - 216B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 105A a b + 945B a )e + (- 70A a b - 210B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 56A a b - 56B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +-----------+ +-+ +--R (192b x + 576a b x + 576a b x + 192a b )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((105A b - 945B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b - 3780B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b - 5670B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((420A a b - 3780B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (105A a b - 945B a )e + 840B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 768B b e x + ((- 558A b + 5022B a b )e - 1392B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 1022A a b + 9198B a b )e + (- 652A b - 2308B a b )d e +--R + +--R 4 2 +--R - 608B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 770A a b + 6930B a b)e + (- 504A a b - 1624B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 400A b - 432B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 1890B a )e + (- 140A a b - 420B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 112A a b - 112B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 9 4 8 3 2 7 2 3 6 4 5 | 2 +--R (384b x + 1536a b x + 2304a b x + 1536a b x + 384a b )\|- a b e + b d +--R , +--R +--R 5 4 4 5 3 4 +--R ((105A b - 945B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b - 3780B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b - 5670B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((420A a b - 3780B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (105A a b - 945B a )e + 840B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 384B b e x + ((- 279A b + 2511B a b )e - 696B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 511A a b + 4599B a b )e + (- 326A b - 1154B a b )d e +--R + +--R 4 2 +--R - 304B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 385A a b + 3465B a b)e + (- 252A a b - 812B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 200A b - 216B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 105A a b + 945B a )e + (- 70A a b - 210B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 56A a b - 56B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 9 4 8 3 2 7 2 3 6 4 5 | 2 +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1332 + +--S 1333 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((105A b - 945B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b - 3780B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b - 5670B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((420A a b - 3780B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (105A a b - 945B a )e + 840B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((210A b - 1890B a b )e + 1680B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((1050A a b - 9450B a b )e + 8400B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((2100A a b - 18900B a b )e + 16800B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((2100A a b - 18900B a b )e + 16800B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((1050A a b - 9450B a b)e + 8400B a b d e )x +--R + +--R 5 6 4 5 3 +--R (210A a b - 1890B a )e + 1680B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 768B b e x + ((- 558A b + 5022B a b )e - 1392B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 1022A a b + 9198B a b )e + (- 652A b - 2308B a b )d e +--R + +--R 4 2 +--R - 608B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 770A a b + 6930B a b)e + (- 504A a b - 1624B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 400A b - 432B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 1890B a )e + (- 140A a b - 420B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 112A a b - 112B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 3 5 5 4 3 5 2 4 +--R - 768B b e x + ((558A b - 5790B a b )e + 1392B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (1580A a b - 14220B a b )e + (652A b + 3700B a b )d e +--R + +--R 5 2 +--R 608B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (1792A a b - 16128B a b )e + (1156A a b + 3932B a b )d e +--R + +--R 5 4 2 5 3 +--R (400A b + 1040B a b )d e + 128B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (980A a b - 8820B a b)e + (644A a b + 2044B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (512A a b + 544B a b )d e + (96A b + 160B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (210A a b - 1890B a )e + (140A a b + 420B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (112A a b + 112B a b )d e + (96A a b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +--R 9 4 8 3 2 7 2 3 6 4 5 | 2 +--R (384b x + 1536a b x + 2304a b x + 1536a b x + 384a b )\|- a b e + b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 5 2 4 5 +--R (2B a b e - 2B b d e )x +--R + +--R 5 2 4 2 2 3 4 +--R (2A a b e + (- 2A b + 8B a b)d e - 8B b d e )x +--R + +--R 4 2 2 3 2 3 2 3 +--R (8A a b d e + (- 8A b + 12B a b)d e - 12B b d e )x +--R + +--R 2 3 2 3 2 2 4 2 +--R (12A a b d e + (- 12A b + 8B a b)d e - 8B b d e)x +--R + +--R 3 2 2 4 2 5 4 +--R (8A a b d e + (- 8A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 5 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 5 6 5 4 5 +--R B b e x + ((A b - B a)e + 6B b d e )x +--R + +--R 5 4 2 3 4 +--R (- A a e + (6A b - 4B a)d e + 14B b d e )x +--R + +--R 4 2 3 3 2 3 +--R (- 4A a d e + (14A b - 6B a)d e + 16B b d e )x +--R + +--R 2 3 3 2 4 2 +--R (- 6A a d e + (16A b - 4B a)d e + 9B b d e)x +--R + +--R 3 2 4 5 4 5 +--R (- 4A a d e + (9A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 5 3 4 6 +--R (- 2B a b e + 2B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 5 +--R ((- 2A a b - 2B a b)e + (2A b - 6B a b )d e + 8B b d e )x +--R + +--R 2 5 2 2 4 3 2 2 3 +--R - 2A a b e + (- 6A a b - 8B a b)d e + (8A b - 4B a b )d e +--R + +--R 3 3 2 +--R 12B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 2 2 2 3 +--R - 8A a b d e + (- 4A a b - 12B a b)d e +--R + +--R 3 2 3 2 3 4 +--R (12A b + 4B a b )d e + 8B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 2 3 2 3 2 4 +--R - 12A a b d e + (4A a b - 8B a b)d e + (8A b + 6B a b )d e +--R + +--R 3 5 +--R 2B b d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 4 3 2 5 +--R (- 8A a b d e + (6A a b - 2B a b)d e + (2A b + 2B a b )d )x +--R + +--R 2 4 2 5 +--R - 2A a b d e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 5 7 2 5 2 4 6 +--R - B b e x + (- A b e - 6B b d e )x +--R + +--R 2 5 2 4 2 2 3 5 +--R (B a e + (- 6A b - 2B a b)d e - 14B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (- 2A a b + 4B a )d e + (- 14A b - 8B a b)d e +--R + +--R 2 3 2 +--R - 16B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 4A a d e + (- 8A a b + 6B a )d e + (- 16A b - 12B a b)d e +--R + +--R 2 4 +--R - 9B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 6A a d e + (- 12A a b + 4B a )d e + (- 9A b - 8B a b)d e +--R + +--R 2 5 +--R - 2B b d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 4 2 5 2 4 +--R (4A a d e + (- 8A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 5 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 2 7 6 2 5 2 6 7 2 5 +--R (2a b e - 2b d e)x + (10a b e - 8a b d e - 2b d )x +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 2 5 2 3 +--R (20a b e - 10a b d e - 10a b d )x + (20a b e - 20a b d )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (10a b e + 10a b d e - 20a b d )x + (2a b e + 8a b d e - 10a b d )x +--R + +--R 6 5 2 2 +--R 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1334 + +--S 1335 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((105A b - 945B a b )e + 840B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((525A a b - 4725B a b )e + 4200B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((1050A a b - 9450B a b )e + 8400B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((1050A a b - 9450B a b )e + 8400B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((525A a b - 4725B a b)e + 4200B a b d e )x +--R + +--R 5 6 4 5 3 +--R (105A a b - 945B a )e + 840B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b - 945B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b - 3780B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b - 5670B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((420A a b - 3780B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (105A a b - 945B a )e + 840B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 384B b e x + ((- 279A b + 2511B a b )e - 696B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 511A a b + 4599B a b )e + (- 326A b - 1154B a b )d e +--R + +--R 4 2 +--R - 304B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 385A a b + 3465B a b)e + (- 252A a b - 812B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 200A b - 216B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 105A a b + 945B a )e + (- 70A a b - 210B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 56A a b - 56B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 5 3 5 5 4 3 5 2 4 +--R - 384B b e x + ((279A b - 2895B a b )e + 696B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (790A a b - 7110B a b )e + (326A b + 1850B a b )d e +--R + +--R 5 2 +--R 304B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (896A a b - 8064B a b )e + (578A a b + 1966B a b )d e +--R + +--R 5 4 2 5 3 +--R (200A b + 520B a b )d e + 64B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (490A a b - 4410B a b)e + (322A a b + 1022B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (256A a b + 272B a b )d e + (48A b + 80B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (105A a b - 945B a )e + (70A a b + 210B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (56A a b + 56B a b )d e + (48A a b + 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +-----------+ +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|- a e + b d \|b +--R * +--R +-----------+ +------------------+ +--R | 2 | 2 2 2 +--R \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 5 +--R - B b e x + ((- A b - B a)e - 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (- A a e + (- 4A b - 4B a)d e - 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (- 4A a d e + (- 6A b - 6B a)d e - 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (- 6A a d e + (- 4A b - 4B a)d e - B b d )x +--R + +--R 3 4 4 +--R (- 4A a d e + (- A b - B a)d )x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1336 + +)clear all + +--S 1337 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1337 + +--S 1338 of 1378 +r0:=1/4*(8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*(d+e*x)^(5/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-2*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+5/24*(8*b*B*d-A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+5/32*e*(8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/64*e^3*_ + (8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))/(b^(9/2)*(b*d-a*e)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^2*_ + (8*b*B*d-A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 15A b - 105B a b )e + 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 60A a b - 420B a b )e + 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 90A a b - 630B a b )e + 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 60A a b - 420B a b)e + 480B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 15A a b - 105B a )e + 120B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b - 279B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 73A a b - 511B a b )e + (118A b + 258B a b )d e +--R + +--R 4 2 +--R 208B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 55A a b - 385B a b)e + (- 36A a b + 188B a b )d e +--R + +--R 4 3 2 4 3 +--R (136A b + 88B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 105B a )e + (- 10A a b + 50B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 8A a b + 24B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 8 3 2 6 7 2 +--R (192a b e - 192b d)x + (576a b e - 576a b d)x +--R + +--R 3 5 2 6 4 4 3 5 +--R (576a b e - 576a b d)x + 192a b e - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((15A b + 105B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 420B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 630B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 420B a b)e - 480B a b d e )x + (15A a b + 105B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 3 4 2 3 +--R ((30A b - 558B a b )e + 528B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 146A a b - 1022B a b )e + (236A b + 516B a b )d e +--R + +--R 4 2 +--R 416B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 110A a b - 770B a b)e + (- 72A a b + 376B a b )d e +--R + +--R 4 3 2 4 3 +--R (272A b + 176B a b )d e + 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 30A a b - 210B a )e + (- 20A a b + 100B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 16A a b + 48B a b )d e + (96A b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 8 9 4 2 7 8 3 +--R (384a b e - 384b d)x + (1536a b e - 1536a b d)x +--R + +--R 3 6 2 7 2 4 5 3 6 5 4 +--R (2304a b e - 2304a b d)x + (1536a b e - 1536a b d)x + 384a b e +--R + +--R 4 5 +--R - 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 5 4 4 5 3 4 +--R ((15A b + 105B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 420B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 630B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 420B a b)e - 480B a b d e )x + (15A a b + 105B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b - 279B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 73A a b - 511B a b )e + (118A b + 258B a b )d e +--R + +--R 4 2 +--R 208B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 55A a b - 385B a b)e + (- 36A a b + 188B a b )d e +--R + +--R 4 3 2 4 3 +--R (136A b + 88B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 105B a )e + (- 10A a b + 50B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 8A a b + 24B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 8 9 4 2 7 8 3 +--R (192a b e - 192b d)x + (768a b e - 768a b d)x +--R + +--R 3 6 2 7 2 4 5 3 6 5 4 +--R (1152a b e - 1152a b d)x + (768a b e - 768a b d)x + 192a b e +--R + +--R 4 5 +--R - 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1339 + +--S 1340 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((15A b + 105B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 420B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 630B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 420B a b)e - 480B a b d e )x + (15A a b + 105B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((30A b + 210B a b )e - 240B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((150A a b + 1050B a b )e - 1200B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((300A a b + 2100B a b )e - 2400B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((300A a b + 2100B a b )e - 2400B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((150A a b + 1050B a b)e - 1200B a b d e )x + (30A a b + 210B a )e +--R + +--R 5 3 +--R - 240B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((30A b - 558B a b )e + 528B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 146A a b - 1022B a b )e + (236A b + 516B a b )d e +--R + +--R 4 2 +--R 416B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 110A a b - 770B a b)e + (- 72A a b + 376B a b )d e +--R + +--R 4 3 2 4 3 +--R (272A b + 176B a b )d e + 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 30A a b - 210B a )e + (- 20A a b + 100B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 16A a b + 48B a b )d e + (96A b + 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 30A b + 558B a b )e - 528B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (116A a b + 1580B a b )e + (- 236A b - 1044B a b )d e +--R + +--R 5 2 +--R - 416B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (256A a b + 1792B a b )e + (- 164A a b - 892B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 272A b - 592B a b )d e - 128B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (140A a b + 980B a b)e + (92A a b - 476B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 256A a b - 224B a b )d e + (- 96A b - 160B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (30A a b + 210B a )e + (20A a b - 100B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (16A a b - 48B a b )d e + (- 96A a b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 8 9 4 2 7 8 3 +--R (384a b e - 384b d)x + (1536a b e - 1536a b d)x +--R + +--R 3 6 2 7 2 4 5 3 6 5 4 +--R (2304a b e - 2304a b d)x + (1536a b e - 1536a b d)x + 384a b e +--R + +--R 4 5 +--R - 384a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 4 2 3 4 +--R (2B a b e - 2B b d e )x +--R + +--R 4 2 3 2 2 2 3 +--R (2A a b e + (- 2A b + 6B a b)d e - 6B b d e )x +--R + +--R 3 2 2 2 2 3 2 +--R (6A a b d e + (- 6A b + 6B a b)d e - 6B b d e)x +--R + +--R 2 2 2 3 2 4 3 +--R (6A a b d e + (- 6A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 4 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 4 5 4 3 4 +--R B b e x + ((A b - B a)e + 5B b d e )x +--R + +--R 4 3 2 2 3 +--R (- A a e + (5A b - 3B a)d e + 9B b d e )x +--R + +--R 3 2 2 3 2 +--R (- 3A a d e + (9A b - 3B a)d e + 7B b d e)x +--R + +--R 2 2 3 4 3 4 +--R (- 3A a d e + (7A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 3 3 5 +--R (- 2B a b e + 2B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 4 +--R ((- 2A a b - 2B a b)e + (2A b - 4B a b )d e + 6B b d e )x +--R + +--R 2 4 2 2 3 3 2 2 3 3 3 +--R (- 2A a b e + (- 4A a b - 6B a b)d e + 6A b d e + 6B b d e)x +--R + +--R 2 3 2 2 2 3 2 3 3 4 2 +--R (- 6A a b d e - 6B a b d e + (6A b + 4B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 2 3 3 2 4 +--R (- 6A a b d e + (4A a b - 2B a b)d e + (2A b + 2B a b )d )x +--R + +--R 2 3 2 4 +--R - 2A a b d e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 6 2 4 2 3 5 +--R - B b e x + (- A b e - 5B b d e )x +--R + +--R 2 4 2 3 2 2 2 4 +--R (B a e + (- 5A b - 2B a b)d e - 9B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R A a e + (- 2A a b + 3B a )d e + (- 9A b - 6B a b)d e +--R + +--R 2 3 +--R - 7B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 3A a d e + (- 6A a b + 3B a )d e + (- 7A b - 6B a b)d e +--R + +--R 2 4 +--R - 2B b d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 3 2 4 2 3 +--R (3A a d e + (- 6A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 4 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 2 7 6 2 5 2 6 7 2 5 +--R (2a b e - 2b d e)x + (10a b e - 8a b d e - 2b d )x +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 2 5 2 3 +--R (20a b e - 10a b d e - 10a b d )x + (20a b e - 20a b d )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (10a b e + 10a b d e - 20a b d )x + (2a b e + 8a b d e - 10a b d )x +--R + +--R 6 5 2 2 +--R 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((15A b + 105B a b )e - 120B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((75A a b + 525B a b )e - 600B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((150A a b + 1050B a b )e - 1200B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((150A a b + 1050B a b )e - 1200B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((75A a b + 525B a b)e - 600B a b d e )x + (15A a b + 105B a )e +--R + +--R 5 3 +--R - 120B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((15A b + 105B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 420B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 630B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 420B a b)e - 480B a b d e )x + (15A a b + 105B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b - 279B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 73A a b - 511B a b )e + (118A b + 258B a b )d e +--R + +--R 4 2 +--R 208B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 55A a b - 385B a b)e + (- 36A a b + 188B a b )d e +--R + +--R 4 3 2 4 3 +--R (136A b + 88B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 105B a )e + (- 10A a b + 50B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 8A a b + 24B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 15A b + 279B a b )e - 264B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (58A a b + 790B a b )e + (- 118A b - 522B a b )d e +--R + +--R 5 2 +--R - 208B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (128A a b + 896B a b )e + (- 82A a b - 446B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 136A b - 296B a b )d e - 64B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (70A a b + 490B a b)e + (46A a b - 238B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 128A a b - 112B a b )d e + (- 48A b - 80B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (15A a b + 105B a )e + (10A a b - 50B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (8A a b - 24B a b )d e + (- 48A a b - 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 8 9 4 2 7 8 3 +--R (192a b e - 192b d)x + (768a b e - 768a b d)x +--R + +--R 3 6 2 7 2 4 5 3 6 5 4 4 5 +--R (1152a b e - 1152a b d)x + (768a b e - 768a b d)x + 192a b e - 192a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1343 + +)clear all + +--S 1344 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1344 + +--S 1345 of 1378 +r0:=1/12*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-2/3*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/24*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/96*e*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+_ + b*x)*sqrt(d+e*x)/(b^3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/64*e^3*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-1/64*e^2*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*(b*d-_ + a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 9A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 36A a b - 60B a b )e + 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 54A a b - 90B a b )e + 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((- 36A a b - 60B a b)e + 96B a b d e )x + (- 9A a b - 15B a )e +--R + +--R 4 3 +--R 24B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((33A a b - 73B a b )e + (- 6A b + 158B a b )d e - 112B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 33A a b - 55B a b)e + (132A a b + 52B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 72A b + 40B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 9A a b - 15B a )e + (- 6A a b + 14B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (72A a b + 8B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 6 2 7 8 2 3 +--R (192a b e - 384a b d e + 192b d )x +--R + +--R 3 5 2 2 6 7 2 2 +--R (576a b e - 1152a b d e + 576a b d )x +--R + +--R 4 4 2 3 5 2 6 2 5 3 2 4 4 +--R (576a b e - 1152a b d e + 576a b d )x + 192a b e - 384a b d e +--R + +--R 3 5 2 +--R 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((36A a b + 60B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((54A a b + 90B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((36A a b + 60B a b)e - 96B a b d e )x + (9A a b + 15B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 3 4 2 3 +--R ((18A b + 30B a b )e - 48B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (66A a b - 146B a b )e + (- 12A b + 316B a b )d e +--R + +--R 4 2 +--R - 224B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 66A a b - 110B a b)e + (264A a b + 104B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 144A b + 80B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 18A a b - 30B a )e + (- 12A a b + 28B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (144A a b + 16B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 7 2 8 9 2 4 +--R (384a b e - 768a b d e + 384b d )x +--R + +--R 3 6 2 2 7 8 2 3 +--R (1536a b e - 3072a b d e + 1536a b d )x +--R + +--R 4 5 2 3 6 2 7 2 2 +--R (2304a b e - 4608a b d e + 2304a b d )x +--R + +--R 5 4 2 4 5 3 6 2 6 3 2 5 4 +--R (1536a b e - 3072a b d e + 1536a b d )x + 384a b e - 768a b d e +--R + +--R 4 5 2 +--R 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 5 4 4 5 3 4 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((36A a b + 60B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((54A a b + 90B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((36A a b + 60B a b)e - 96B a b d e )x + (9A a b + 15B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (33A a b - 73B a b )e + (- 6A b + 158B a b )d e +--R + +--R 4 2 +--R - 112B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 33A a b - 55B a b)e + (132A a b + 52B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 72A b + 40B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 9A a b - 15B a )e + (- 6A a b + 14B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (72A a b + 8B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 7 2 8 9 2 4 +--R (192a b e - 384a b d e + 192b d )x +--R + +--R 3 6 2 2 7 8 2 3 +--R (768a b e - 1536a b d e + 768a b d )x +--R + +--R 4 5 2 3 6 2 7 2 2 +--R (1152a b e - 2304a b d e + 1152a b d )x +--R + +--R 5 4 2 4 5 3 6 2 6 3 2 5 4 +--R (768a b e - 1536a b d e + 768a b d )x + 192a b e - 384a b d e +--R + +--R 4 5 2 +--R 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1346 + +--S 1347 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((36A a b + 60B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((54A a b + 90B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((36A a b + 60B a b)e - 96B a b d e )x + (9A a b + 15B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((18A b + 30B a b )e - 48B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((90A a b + 150B a b )e - 240B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((180A a b + 300B a b )e - 480B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((180A a b + 300B a b )e - 480B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((90A a b + 150B a b)e - 240B a b d e )x + (18A a b + 30B a )e +--R + +--R 5 3 +--R - 48B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((18A b + 30B a b )e - 48B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (66A a b - 146B a b )e + (- 12A b + 316B a b )d e +--R + +--R 4 2 +--R - 224B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 66A a b - 110B a b)e + (264A a b + 104B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 144A b + 80B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 18A a b - 30B a )e + (- 12A a b + 28B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (144A a b + 16B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 18A b - 30B a b )e + 48B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (- 84A a b + 116B a b )e + (12A b - 268B a b )d e +--R + +--R 5 2 +--R 224B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 3 4 2 3 2 +--R 256B a b e + (- 252A a b - 420B a b )d e +--R + +--R 5 4 2 5 3 +--R (144A b + 144B a b )d e + 128B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (84A a b + 140B a b)e + (- 252A a b - 132B a b )d e +--R + +--R 2 3 2 5 4 3 +--R - 96B a b d e + (96A b + 160B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (18A a b + 30B a )e + (12A a b - 28B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 144A a b - 16B a b )d e + (96A a b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 2 7 2 8 9 2 4 +--R (384a b e - 768a b d e + 384b d )x +--R + +--R 3 6 2 2 7 8 2 3 +--R (1536a b e - 3072a b d e + 1536a b d )x +--R + +--R 4 5 2 3 6 2 7 2 2 +--R (2304a b e - 4608a b d e + 2304a b d )x +--R + +--R 5 4 2 4 5 3 6 2 6 3 2 5 4 +--R (1536a b e - 3072a b d e + 1536a b d )x + 384a b e - 768a b d e +--R + +--R 4 5 2 +--R 384a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 3 2 2 3 +--R (2B a b e - 2B b d e )x +--R + +--R 3 2 2 2 2 2 +--R (2A a b e + (- 2A b + 4B a b)d e - 4B b d e)x +--R + +--R 2 2 2 2 3 2 +--R (4A a b d e + (- 4A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 3 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 4 3 2 3 +--R B b e x + ((A b - B a)e + 4B b d e )x +--R + +--R 3 2 2 2 +--R (- A a e + (4A b - 2B a)d e + 5B b d e)x +--R + +--R 2 2 3 2 3 +--R (- 2A a d e + (5A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 3 2 4 +--R (- 2B a b e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 3 +--R ((- 2A a b - 2B a b)e + (2A b - 2B a b )d e + 4B b d e)x +--R + +--R 2 3 2 2 2 3 2 2 +--R - 2A a b e + (- 2A a b - 4B a b)d e + (4A b + 2B a b )d e +--R + +--R 3 3 +--R 2B b d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 2 3 +--R (- 4A a b d e + (2A a b - 2B a b)d e + (2A b + 2B a b )d )x +--R + +--R 2 2 2 3 +--R - 2A a b d e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 5 2 3 2 2 4 +--R - B b e x + (- A b e - 4B b d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (B a e + (- 4A b - 2B a b)d e - 5B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 2 +--R (A a e + (- 2A a b + 2B a )d e + (- 5A b - 4B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (2A a d e + (- 4A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 3 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 2 7 6 2 5 2 6 7 2 5 +--R (2a b e - 2b d e)x + (10a b e - 8a b d e - 2b d )x +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 2 5 2 3 +--R (20a b e - 10a b d e - 10a b d )x + (20a b e - 20a b d )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (10a b e + 10a b d e - 20a b d )x + (2a b e + 8a b d e - 10a b d )x +--R + +--R 6 5 2 2 +--R 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((45A a b + 75B a b )e - 120B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((90A a b + 150B a b )e - 240B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((90A a b + 150B a b )e - 240B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((45A a b + 75B a b)e - 120B a b d e )x + (9A a b + 15B a )e +--R + +--R 5 3 +--R - 24B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((36A a b + 60B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((54A a b + 90B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((36A a b + 60B a b)e - 96B a b d e )x + (9A a b + 15B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((33A a b - 73B a b )e + (- 6A b + 158B a b )d e - 112B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 33A a b - 55B a b)e + (132A a b + 52B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 72A b + 40B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 9A a b - 15B a )e + (- 6A a b + 14B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (72A a b + 8B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 9A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((- 42A a b + 58B a b )e + (6A b - 134B a b )d e + 112B b d e)x +--R + +--R 3 2 3 4 2 3 2 +--R 128B a b e + (- 126A a b - 210B a b )d e +--R + +--R 5 4 2 5 3 +--R (72A b + 72B a b )d e + 64B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (42A a b + 70B a b)e + (- 126A a b - 66B a b )d e +--R + +--R 2 3 2 5 4 3 +--R - 48B a b d e + (48A b + 80B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (9A a b + 15B a )e + (6A a b - 14B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 72A a b - 8B a b )d e + (48A a b + 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 2 7 2 8 9 2 4 +--R (192a b e - 384a b d e + 192b d )x +--R + +--R 3 6 2 2 7 8 2 3 +--R (768a b e - 1536a b d e + 768a b d )x +--R + +--R 4 5 2 3 6 2 7 2 2 +--R (1152a b e - 2304a b d e + 1152a b d )x +--R + +--R 5 4 2 4 5 3 6 2 6 3 2 5 4 +--R (768a b e - 1536a b d e + 768a b d )x + 192a b e - 384a b d e +--R + +--R 4 5 2 +--R 192a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1350 + +)clear all + +--S 1351 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1378 +r0:=-2/5*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/20*(8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-1/24*(8*b*B*d-5*A*b*e-3*a*B*e)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/96*e*_ + (8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-1/64*e^3*(8*b*B*d-5*A*b*e-3*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-_ + a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/64*e^2*(8*b*B*d-5*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 15A b - 9B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 60A a b - 36B a b )e + 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 90A a b - 54B a b )e + 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((- 60A a b - 36B a b)e + 96B a b d e )x + (- 15A a b - 9B a )e +--R + +--R 4 3 +--R 24B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((55A a b + 33B a b )e + (- 10A b - 94B a b )d e + 16B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (73A a b - 33B a b)e + (- 36A a b + 92B a b )d e +--R + +--R 4 3 2 4 3 +--R (8A b - 168B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 9B a )e + (118A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 136A a b - 40B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 3 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 2 +--R (576a b e - 1728a b d e + 1728a b d e - 576a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 6 2 3 +--R (576a b e - 1728a b d e + 1728a b d e - 576a b d )x + 192a b e +--R + +--R 5 3 2 4 4 2 3 5 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1352 + +--S 1353 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 36B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 54B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 36B a b)e - 96B a b d e )x + (15A a b + 9B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 3 4 2 3 +--R ((30A b + 18B a b )e - 48B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (110A a b + 66B a b )e + (- 20A b - 188B a b )d e +--R + +--R 4 2 +--R 32B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (146A a b - 66B a b)e + (- 72A a b + 184B a b )d e +--R + +--R 4 3 2 4 3 +--R (16A b - 336B a b )d e + 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 30A a b - 18B a )e + (236A a b + 36B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 272A a b - 80B a b )d e + (96A b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 3 6 3 2 7 2 8 2 9 3 4 +--R (384a b e - 1152a b d e + 1152a b d e - 384b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 2 +--R (2304a b e - 6912a b d e + 6912a b d e - 2304a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 7 2 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x + 384a b e +--R + +--R 6 3 2 5 4 2 4 5 3 +--R - 1152a b d e + 1152a b d e - 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 5 4 4 5 3 4 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 36B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 54B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 36B a b)e - 96B a b d e )x + (15A a b + 9B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((55A a b + 33B a b )e + (- 10A b - 94B a b )d e + 16B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (73A a b - 33B a b)e + (- 36A a b + 92B a b )d e +--R + +--R 4 3 2 4 3 +--R (8A b - 168B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 9B a )e + (118A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 136A a b - 40B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 3 6 3 2 7 2 8 2 9 3 4 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 2 +--R (1152a b e - 3456a b d e + 3456a b d e - 1152a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 7 2 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x + 192a b e +--R + +--R 6 3 2 5 4 2 4 5 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1353 + +--S 1354 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 36B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 54B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 36B a b)e - 96B a b d e )x + (15A a b + 9B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((30A b + 18B a b )e - 48B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((150A a b + 90B a b )e - 240B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((300A a b + 180B a b )e - 480B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((300A a b + 180B a b )e - 480B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((150A a b + 90B a b)e - 240B a b d e )x + (30A a b + 18B a )e +--R + +--R 5 3 +--R - 48B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((30A b + 18B a b )e - 48B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((110A a b + 66B a b )e + (- 20A b - 188B a b )d e + 32B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (146A a b - 66B a b)e + (- 72A a b + 184B a b )d e +--R + +--R 4 3 2 4 3 +--R (16A b - 336B a b )d e + 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 30A a b - 18B a )e + (236A a b + 36B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 272A a b - 80B a b )d e + (96A b + 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 30A b - 18B a b )e + 48B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((- 140A a b - 84B a b )e + (20A b + 236B a b )d e - 32B b d e)x +--R + +--R 2 3 3 4 2 3 2 +--R - 256A a b e + (92A a b + 4B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 16A b + 304B a b )d e - 128B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 116A a b + 84B a b)e + (- 164A a b - 220B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (256A a b + 416B a b )d e + (- 96A b - 160B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (30A a b + 18B a )e + (- 236A a b - 36B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (272A a b + 80B a b )d e + (- 96A a b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 3 6 3 2 7 2 8 2 9 3 4 +--R (384a b e - 1152a b d e + 1152a b d e - 384b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 2 +--R (2304a b e - 6912a b d e + 6912a b d e - 2304a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 7 2 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x + 384a b e +--R + +--R 6 3 2 5 4 2 4 5 3 +--R - 1152a b d e + 1152a b d e - 384a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1354 + +--S 1355 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 2 +--R (2B a b e - 2B b d e)x +--R + +--R 2 2 2 2 +--R (2A a b e + (- 2A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 2 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 +--R B b e x + ((A b - B a)e + 3B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (3A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 3 +--R (- 2B a b e + 2B b d e)x +--R + +--R 2 2 2 3 3 2 2 +--R ((- 2A a b - 2B a b)e + 2A b d e + 2B b d )x +--R + +--R 2 2 2 3 2 2 2 +--R (- 2A a b e - 2B a b d e + (2A b + 2B a b )d )x - 2A a b d e +--R + +--R 2 2 +--R 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 4 2 2 2 3 +--R - B b e x + (- A b e - 3B b d e)x +--R + +--R 2 2 2 2 2 2 +--R (B a e + (- 3A b - 2B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (- 2A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 2 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 2 7 6 2 5 2 6 7 2 5 +--R (2a b e - 2b d e)x + (10a b e - 8a b d e - 2b d )x +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 2 5 2 3 +--R (20a b e - 10a b d e - 10a b d )x + (20a b e - 20a b d )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (10a b e + 10a b d e - 20a b d )x + (2a b e + 8a b d e - 10a b d )x +--R + +--R 6 5 2 2 +--R 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1355 + +--S 1356 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((75A a b + 45B a b )e - 120B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((150A a b + 90B a b )e - 240B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((150A a b + 90B a b )e - 240B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((75A a b + 45B a b)e - 120B a b d e )x + (15A a b + 9B a )e +--R + +--R 5 3 +--R - 24B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 36B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 54B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 36B a b)e - 96B a b d e )x + (15A a b + 9B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((55A a b + 33B a b )e + (- 10A b - 94B a b )d e + 16B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (73A a b - 33B a b)e + (- 36A a b + 92B a b )d e +--R + +--R 4 3 2 4 3 +--R (8A b - 168B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 9B a )e + (118A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 136A a b - 40B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 15A b - 9B a b )e + 24B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((- 70A a b - 42B a b )e + (10A b + 118B a b )d e - 16B b d e)x +--R + +--R 2 3 3 4 2 3 2 +--R - 128A a b e + (46A a b + 2B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 8A b + 152B a b )d e - 64B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 58A a b + 42B a b)e + (- 82A a b - 110B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (128A a b + 208B a b )d e + (- 48A b - 80B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (15A a b + 9B a )e + (- 118A a b - 18B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (136A a b + 40B a b )d e + (- 48A a b - 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 3 6 3 2 7 2 8 2 9 3 4 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 2 +--R (1152a b e - 3456a b d e + 3456a b d e - 1152a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 7 2 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x + 192a b e +--R + +--R 6 3 2 5 4 2 4 5 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1357 + +)clear all + +--S 1358 of 1378 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1358 + +--S 1359 of 1378 +r0:=-2/7*B*(a+b*x)*sqrt(d+e*x)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/28*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-1/24*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5/96*e*_ + (8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+5/64*e^3*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^2*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 105A b - 15B a b )e + 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 420A a b - 60B a b )e + 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 630A a b - 90B a b )e + 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 420A a b - 60B a b)e + 480B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 105A a b - 15B a )e + 120B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((385A a b + 55B a b )e + (- 70A b - 450B a b )d e + 80B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (511A a b + 73B a b)e + (- 252A a b - 620B a b )d e +--R + +--R 4 3 2 4 3 +--R (56A b + 296B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (279A a b - 15B a )e + (- 326A a b - 146B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (200A a b + 72B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 3 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 2 +--R (576a b e - 2304a b d e + 3456a b d e - 2304a b d e + 576a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 +--R (576a b e - 2304a b d e + 3456a b d e - 2304a b d e + 576a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R 192a b e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1359 + +--S 1360 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b + 60B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b + 90B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((420A a b + 60B a b)e - 480B a b d e )x + (105A a b + 15B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 3 4 2 3 +--R ((210A b + 30B a b )e - 240B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (770A a b + 110B a b )e + (- 140A b - 900B a b )d e +--R + +--R 4 2 +--R 160B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1022A a b + 146B a b)e + (- 504A a b - 1240B a b )d e +--R + +--R 4 3 2 4 3 +--R (112A b + 592B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (558A a b - 30B a )e + (- 652A a b - 292B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (400A a b + 144B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 4 +--R (384a b e - 1536a b d e + 2304a b d e - 1536a b d e + 384b d )x +--R + +--R 5 4 4 4 5 3 3 6 2 2 2 7 3 +--R 1536a b e - 6144a b d e + 9216a b d e - 6144a b d e +--R + +--R 8 4 +--R 1536a b d +--R * +--R 3 +--R x +--R + +--R 6 3 4 5 4 3 4 5 2 2 3 6 3 +--R 2304a b e - 9216a b d e + 13824a b d e - 9216a b d e +--R + +--R 2 7 4 +--R 2304a b d +--R * +--R 2 +--R x +--R + +--R 7 2 4 6 3 3 5 4 2 2 4 5 3 +--R 1536a b e - 6144a b d e + 9216a b d e - 6144a b d e +--R + +--R 3 6 4 +--R 1536a b d +--R * +--R x +--R + +--R 8 4 7 2 3 6 3 2 2 5 4 3 4 5 4 +--R 384a b e - 1536a b d e + 2304a b d e - 1536a b d e + 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 5 4 4 5 3 4 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b + 60B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b + 90B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((420A a b + 60B a b)e - 480B a b d e )x + (105A a b + 15B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (385A a b + 55B a b )e + (- 70A b - 450B a b )d e +--R + +--R 4 2 +--R 80B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (511A a b + 73B a b)e + (- 252A a b - 620B a b )d e +--R + +--R 4 3 2 4 3 +--R (56A b + 296B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (279A a b - 15B a )e + (- 326A a b - 146B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (200A a b + 72B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 4 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 4 4 4 5 3 3 6 2 2 2 7 3 8 4 3 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 6 3 4 5 4 3 4 5 2 2 3 6 3 +--R 1152a b e - 4608a b d e + 6912a b d e - 4608a b d e +--R + +--R 2 7 4 +--R 1152a b d +--R * +--R 2 +--R x +--R + +--R 7 2 4 6 3 3 5 4 2 2 4 5 3 3 6 4 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 8 4 7 2 3 6 3 2 2 5 4 3 4 5 4 +--R 192a b e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1360 + +--S 1361 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b + 60B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b + 90B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((420A a b + 60B a b)e - 480B a b d e )x + (105A a b + 15B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((210A b + 30B a b )e - 240B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((1050A a b + 150B a b )e - 1200B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((2100A a b + 300B a b )e - 2400B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((2100A a b + 300B a b )e - 2400B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((1050A a b + 150B a b)e - 1200B a b d e )x + (210A a b + 30B a )e +--R + +--R 5 3 +--R - 240B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((210A b + 30B a b )e - 240B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (770A a b + 110B a b )e + (- 140A b - 900B a b )d e +--R + +--R 4 2 +--R 160B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1022A a b + 146B a b)e + (- 504A a b - 1240B a b )d e +--R + +--R 4 3 2 4 3 +--R (112A b + 592B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (558A a b - 30B a )e + (- 652A a b - 292B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (400A a b + 144B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 210A b - 30B a b )e + 240B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (- 980A a b - 140B a b )e + (140A b + 1140B a b )d e +--R + +--R 5 2 +--R - 160B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 1792A a b - 256B a b )e + (644A a b + 2140B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 112A b - 752B a b )d e + 128B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 1580A a b - 116B a b)e + (1156A a b + 1532B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 512A a b - 736B a b )d e + (96A b + 160B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 558A a b + 30B a )e + (652A a b + 292B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 400A a b - 144B a b )d e + (96A a b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 4 +--R (384a b e - 1536a b d e + 2304a b d e - 1536a b d e + 384b d )x +--R + +--R 5 4 4 4 5 3 3 6 2 2 2 7 3 8 4 3 +--R (1536a b e - 6144a b d e + 9216a b d e - 6144a b d e + 1536a b d )x +--R + +--R 6 3 4 5 4 3 4 5 2 2 3 6 3 +--R 2304a b e - 9216a b d e + 13824a b d e - 9216a b d e +--R + +--R 2 7 4 +--R 2304a b d +--R * +--R 2 +--R x +--R + +--R 7 2 4 6 3 3 5 4 2 2 4 5 3 3 6 4 +--R (1536a b e - 6144a b d e + 9216a b d e - 6144a b d e + 1536a b d )x +--R + +--R 8 4 7 2 3 6 3 2 2 5 4 3 4 5 4 +--R 384a b e - 1536a b d e + 2304a b d e - 1536a b d e + 384a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 +-------+ +--R ((2B a b e - 2B b d)x + 2A a b e - 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 +--R (- 2B a b e + 2B b d)x +--R + +--R 2 2 3 2 2 2 +--R ((- 2A a b - 2B a b)e + (2A b + 2B a b )d)x - 2A a b e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 2 7 6 2 5 2 6 7 2 5 +--R (2a b e - 2b d e)x + (10a b e - 8a b d e - 2b d )x +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 2 5 2 3 +--R (20a b e - 10a b d e - 10a b d )x + (20a b e - 20a b d )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (10a b e + 10a b d e - 20a b d )x + (2a b e + 8a b d e - 10a b d )x +--R + +--R 6 5 2 2 +--R 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1362 + +--S 1363 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((525A a b + 75B a b )e - 600B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((1050A a b + 150B a b )e - 1200B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((1050A a b + 150B a b )e - 1200B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((525A a b + 75B a b)e - 600B a b d e )x + (105A a b + 15B a )e +--R + +--R 5 3 +--R - 120B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b + 60B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b + 90B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((420A a b + 60B a b)e - 480B a b d e )x + (105A a b + 15B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((385A a b + 55B a b )e + (- 70A b - 450B a b )d e + 80B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (511A a b + 73B a b)e + (- 252A a b - 620B a b )d e +--R + +--R 4 3 2 4 3 +--R (56A b + 296B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (279A a b - 15B a )e + (- 326A a b - 146B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (200A a b + 72B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 105A b - 15B a b )e + 120B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((- 490A a b - 70B a b )e + (70A b + 570B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 896A a b - 128B a b )e + (322A a b + 1070B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 56A b - 376B a b )d e + 64B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 790A a b - 58B a b)e + (578A a b + 766B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 256A a b - 368B a b )d e + (48A b + 80B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 279A a b + 15B a )e + (326A a b + 146B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 200A a b - 72B a b )d e + (48A a b + 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 4 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 4 4 4 5 3 3 6 2 2 2 7 3 8 4 3 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 6 3 4 5 4 3 4 5 2 2 3 6 3 2 7 4 2 +--R (1152a b e - 4608a b d e + 6912a b d e - 4608a b d e + 1152a b d )x +--R + +--R 7 2 4 6 3 3 5 4 2 2 4 5 3 3 6 4 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 8 4 7 2 3 6 3 2 2 5 4 3 4 5 4 +--R 192a b e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1364 + +)clear all + +--S 1365 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1365 + +--S 1366 of 1378 +r0:=-2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x))+1/4*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/(e*_ + (b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2))-7/24*(8*b*B*d-9*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/96*e*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^4*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+35/64*e^3*(8*b*B*d-9*A*b*e+a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(11/2)*_ + sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*(8*b*B*d-9*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((945A b - 105B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((3780A a b - 420B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((5670A a b - 630B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((3780A a b - 420B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (945A a b - 105B a )e - 840B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3465A a b + 385B a b )e + (- 315A b + 3115B a b )d e +--R + +--R 4 2 2 +--R 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 4599A a b + 511B a b)e + (- 1197A a b + 4221B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (126A b + 1050B a b )d e - 112B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 2511A a b + 279B a )e + (- 1665A a b + 2417B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (468A a b + 1428B a b )d e + (- 72A b - 408B a b )d e + 64B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 384A a e + (- 975A a b + 663B a )d e + (630A a b + 370B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 264A a b - 104B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 5 3 5 4 4 4 3 5 2 3 2 6 3 2 7 4 +--R 192a b e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 8 5 +--R - 192b d +--R * +--R 3 +--R x +--R + +--R 6 2 5 5 3 4 4 4 2 3 3 5 3 2 +--R 576a b e - 2880a b d e + 5760a b d e - 5760a b d e +--R + +--R 2 6 4 7 5 +--R 2880a b d e - 576a b d +--R * +--R 2 +--R x +--R + +--R 7 5 6 2 4 5 3 2 3 4 4 3 2 +--R 576a b e - 2880a b d e + 5760a b d e - 5760a b d e +--R + +--R 3 5 4 2 6 5 +--R 2880a b d e - 576a b d +--R * +--R x +--R + +--R 8 5 7 4 6 2 2 3 5 3 3 2 4 4 4 +--R 192a e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 3 5 5 +--R - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((945A b - 105B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((3780A a b - 420B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((5670A a b - 630B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((3780A a b - 420B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (945A a b - 105B a )e - 840B a b d e +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 4 3 4 +--R ((- 1890A b + 210B a b )e + 1680B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 6930A a b + 770B a b )e + (- 630A b + 6230B a b )d e +--R + +--R 4 2 2 +--R 560B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 9198A a b + 1022B a b)e + (- 2394A a b + 8442B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (252A b + 2100B a b )d e - 224B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 5022A a b + 558B a )e + (- 3330A a b + 4834B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (936A a b + 2856B a b )d e + (- 144A b - 816B a b )d e +--R + +--R 4 4 +--R 128B b d +--R * +--R x +--R + +--R 4 4 3 4 3 +--R - 768A a e + (- 1950A a b + 1326B a )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (1260A a b + 740B a b)d e + (- 528A a b - 208B a b )d e +--R + +--R 4 3 4 +--R (96A b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 +--R 384a b e - 1920a b d e + 3840a b d e - 3840a b d e +--R + +--R 8 4 9 5 +--R 1920a b d e - 384b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 1536a b e - 7680a b d e + 15360a b d e - 15360a b d e +--R + +--R 2 7 4 8 5 +--R 7680a b d e - 1536a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 2304a b e - 11520a b d e + 23040a b d e - 23040a b d e +--R + +--R 3 6 4 2 7 5 +--R 11520a b d e - 2304a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 1536a b e - 7680a b d e + 15360a b d e - 15360a b d e +--R + +--R 4 5 4 3 6 5 +--R 7680a b d e - 1536a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 384a e - 1920a b d e + 3840a b d e - 3840a b d e + 1920a b d e +--R + +--R 4 5 5 +--R - 384a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 5 4 4 5 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 420B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 630B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 420B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 105B a )e + 840B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3465A a b + 385B a b )e + (- 315A b + 3115B a b )d e +--R + +--R 4 2 2 +--R 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 4599A a b + 511B a b)e + (- 1197A a b + 4221B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (126A b + 1050B a b )d e - 112B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 2511A a b + 279B a )e + (- 1665A a b + 2417B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (468A a b + 1428B a b )d e + (- 72A b - 408B a b )d e +--R + +--R 4 4 +--R 64B b d +--R * +--R x +--R + +--R 4 4 3 4 3 +--R - 384A a e + (- 975A a b + 663B a )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (630A a b + 370B a b)d e + (- 264A a b - 104B a b )d e +--R + +--R 4 3 4 +--R (48A b + 16B a b )d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 +--R 192a b e - 960a b d e + 1920a b d e - 1920a b d e +--R + +--R 8 4 9 5 +--R 960a b d e - 192b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 768a b e - 3840a b d e + 7680a b d e - 7680a b d e +--R + +--R 2 7 4 8 5 +--R 3840a b d e - 768a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 1152a b e - 5760a b d e + 11520a b d e - 11520a b d e +--R + +--R 3 6 4 2 7 5 +--R 5760a b d e - 1152a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 768a b e - 3840a b d e + 7680a b d e - 7680a b d e +--R + +--R 4 5 4 3 6 5 +--R 3840a b d e - 768a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 192a e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 4 5 5 +--R - 192a b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1367 + +--S 1368 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((945A b - 105B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((3780A a b - 420B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((5670A a b - 630B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((3780A a b - 420B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (945A a b - 105B a )e - 840B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((- 1890A b + 210B a b )e + 1680B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((- 9450A a b + 1050B a b )e + 8400B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((- 18900A a b + 2100B a b )e + 16800B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((- 18900A a b + 2100B a b )e + 16800B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((- 9450A a b + 1050B a b)e + 8400B a b d e )x +--R + +--R 5 6 4 5 3 +--R (- 1890A a b + 210B a )e + 1680B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 +-------+ \|b \|e x + d +--R \|- a b e + b d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 1890A b + 210B a b )e + 1680B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 6930A a b + 770B a b )e + (- 630A b + 6230B a b )d e +--R + +--R 4 2 2 +--R 560B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 9198A a b + 1022B a b)e + (- 2394A a b + 8442B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (252A b + 2100B a b )d e - 224B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 5022A a b + 558B a )e + (- 3330A a b + 4834B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (936A a b + 2856B a b )d e + (- 144A b - 816B a b )d e +--R + +--R 4 4 +--R 128B b d +--R * +--R x +--R + +--R 4 4 3 4 3 +--R - 768A a e + (- 1950A a b + 1326B a )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (1260A a b + 740B a b)d e + (- 528A a b - 208B a b )d e +--R + +--R 4 3 4 +--R (96A b + 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R + +--R 5 4 4 5 3 5 +--R ((1890A b - 210B a b )e - 1680B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (8820A a b - 980B a b )e + (630A b - 7910B a b )d e +--R + +--R 5 2 2 +--R - 560B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (16128A a b - 1792B a b )e + (3024A a b - 14672B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 252A b - 2660B a b )d e + 224B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (14220A a b - 1580B a b)e + (5724A a b - 13276B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 1188A a b - 4956B a b )d e + (144A b + 1040B a b )d e +--R + +--R 5 4 +--R - 128B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (5790A a b - 558B a )e + (5280A a b - 6160B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 2196A a b - 3596B a b )d e + (672A a b + 1024B a b )d e +--R + +--R 5 4 4 +--R (- 96A b - 160B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 +--R 768A a e + (1950A a b - 1326B a )d e +--R + +--R 3 2 4 2 2 2 3 3 2 3 +--R (- 1260A a b - 740B a b)d e + (528A a b + 208B a b )d e +--R + +--R 4 2 3 4 +--R (- 96A a b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 +--R 384a b e - 1920a b d e + 3840a b d e - 3840a b d e +--R + +--R 8 4 9 5 +--R 1920a b d e - 384b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 1536a b e - 7680a b d e + 15360a b d e - 15360a b d e +--R + +--R 2 7 4 8 5 +--R 7680a b d e - 1536a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 2304a b e - 11520a b d e + 23040a b d e - 23040a b d e +--R + +--R 3 6 4 2 7 5 +--R 11520a b d e - 2304a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 1536a b e - 7680a b d e + 15360a b d e - 15360a b d e +--R + +--R 4 5 4 3 6 5 +--R 7680a b d e - 1536a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 384a e - 1920a b d e + 3840a b d e - 3840a b d e + 1920a b d e +--R + +--R 4 5 5 +--R - 384a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 +-------+ +--R ((- 2B a b e + 2B b d)x - 2A a b e + 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 2 3 2 +--R (2B a b e - 2B b d)x + ((2A a b + 2B a b)e + (- 2A b - 2B a b )d)x +--R + +--R 2 2 +--R 2A a b e - 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 2 7 5 2 6 6 2 4 2 5 6 2 5 +--R b e x + (4a b e + 3b d e)x + (5a b e + 14a b d e + 2b d )x +--R + +--R 2 4 5 2 4 4 2 2 3 3 2 4 2 3 +--R (25a b d e + 10a b d )x + (- 5a b e + 20a b d e + 20a b d )x +--R + +--R 5 2 4 2 3 3 2 2 +--R (- 4a b e + 5a b d e + 20a b d )x +--R + +--R 6 2 5 4 2 2 6 5 2 +--R (- a e - 2a b d e + 10a b d )x - a d e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 3 7 2 7 2 5 3 6 2 7 2 6 +--R (- 2a b e + 2b d e )x + (- 10a b e + 6a b d e + 4b d e)x +--R + +--R 3 4 3 6 2 7 3 5 +--R (- 20a b e + 18a b d e + 2b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 4 +--R (- 20a b e - 20a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 3 +--R (- 10a b e - 30a b d e + 20a b d e + 20a b d )x +--R + +--R 6 3 5 2 2 3 4 3 2 +--R (- 2a b e - 18a b d e + 20a b d )x +--R + +--R 6 2 5 2 2 4 3 3 6 2 5 2 3 +--R (- 4a b d e - 6a b d e + 10a b d )x - 2a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1369 + +--S 1370 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((- 4725A a b + 525B a b )e + 4200B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((- 9450A a b + 1050B a b )e + 8400B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((- 9450A a b + 1050B a b )e + 8400B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((- 4725A a b + 525B a b)e + 4200B a b d e )x +--R + +--R 5 6 4 5 3 +--R (- 945A a b + 105B a )e + 840B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 +-------+ \|b \|e x + d +--R \|a b e - b d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 420B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 630B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 420B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 105B a )e + 840B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3465A a b + 385B a b )e + (- 315A b + 3115B a b )d e +--R + +--R 4 2 2 +--R 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 4599A a b + 511B a b)e + (- 1197A a b + 4221B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (126A b + 1050B a b )d e - 112B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 2511A a b + 279B a )e + (- 1665A a b + 2417B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (468A a b + 1428B a b )d e + (- 72A b - 408B a b )d e + 64B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 384A a e + (- 975A a b + 663B a )d e + (630A a b + 370B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 264A a b - 104B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R + +--R 5 4 4 5 3 5 +--R ((945A b - 105B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (4410A a b - 490B a b )e + (315A b - 3955B a b )d e +--R + +--R 5 2 2 +--R - 280B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (8064A a b - 896B a b )e + (1512A a b - 7336B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 126A b - 1330B a b )d e + 112B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (7110A a b - 790B a b)e + (2862A a b - 6638B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 594A a b - 2478B a b )d e + (72A b + 520B a b )d e - 64B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (2895A a b - 279B a )e + (2640A a b - 3080B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 1098A a b - 1798B a b )d e + (336A a b + 512B a b )d e +--R + +--R 5 4 4 +--R (- 48A b - 80B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R 384A a e + (975A a b - 663B a )d e + (- 630A a b - 370B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (264A a b + 104B a b )d e + (- 48A a b - 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 192a b e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 9 5 +--R - 192b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 768a b e - 3840a b d e + 7680a b d e - 7680a b d e +--R + +--R 2 7 4 8 5 +--R 3840a b d e - 768a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 1152a b e - 5760a b d e + 11520a b d e - 11520a b d e +--R + +--R 3 6 4 2 7 5 +--R 5760a b d e - 1152a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 768a b e - 3840a b d e + 7680a b d e - 7680a b d e +--R + +--R 4 5 4 3 6 5 +--R 3840a b d e - 768a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 192a e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 4 5 5 +--R - 192a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1370 + +--S 1371 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 6 4 5 5 2 3 4 4 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (10a b e + 10a b d)x + (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1371 + +)clear all + +--S 1372 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1372 + +--S 1373 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/12*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x))+1/8*(-8*b*B*d+11*A*b*e-_ + 3*a*B*e)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))+_ + 7/32*e*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x))+105/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-_ + a*e)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*(8*b*B*d-11*A*b*e+_ + 3*a*B*e)/((b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 105/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^6*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((- 3465A b + 945B a b )e + 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 13860A a b + 3780B a b )e + (- 3465A b + 11025B a b )d e +--R + +--R 5 2 3 +--R 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 +--R (- 20790A a b + 5670B a b )e +--R + +--R 4 2 3 4 4 2 3 +--R (- 13860A a b + 18900B a b )d e + 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 13860A a b + 3780B a b)e + (- 20790A a b + 15750B a b )d e +--R + +--R 2 3 2 3 +--R 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 3465A a b + 945B a )e + (- 13860A a b + 6300B a b)d e +--R + +--R 3 2 2 3 +--R 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 3465A a b + 945B a )d e + 2520B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (12705A a b - 3465B a b )e + (4620A b - 10500B a b )d e +--R + +--R 5 2 3 +--R - 3360B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (16863A a b - 4599B a b )e + (17094A a b - 16926B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (693A b - 12621B a b )d e - 504B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (9207A a b - 2511B a b)e + (22968A a b - 12960B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2673A a b - 17433B a b )d e + (- 198A b - 1890B a b )d e +--R + +--R 5 4 +--R 144B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (1408A a b - 384B a )e + (12782A a b - 4510B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (3795A a b - 10331B a b )d e + (- 748A a b - 2556B a b )d e +--R + +--R 5 4 4 5 5 +--R (88A b + 520B a b )d e - 64B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 128A a e + (2048A a b - 256B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (2295A a b - 2639B a b)d e + (- 1030A a b - 690B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (328A a b + 136B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 7 5 4 6 4 5 2 5 3 6 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 7 4 3 8 5 2 9 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 4 +--R x +--R + +--R 7 2 7 6 3 6 5 4 2 5 4 5 3 4 +--R 576a b e - 3264a b d e + 7488a b d e - 8640a b d e +--R + +--R 3 6 4 3 2 7 5 2 8 6 9 7 +--R 4800a b d e - 576a b d e - 576a b d e + 192b d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 +--R 576a b e - 2880a b d e + 5184a b d e - 2880a b d e +--R + +--R 4 5 4 3 3 6 5 2 2 7 6 8 7 +--R - 2880a b d e + 5184a b d e - 2880a b d e + 576a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 6 7 2 2 5 6 3 3 4 5 4 4 3 +--R 192a e - 576a b d e - 576a b d e + 4800a b d e - 8640a b d e +--R + +--R 4 5 5 2 3 6 6 2 7 7 +--R 7488a b d e - 3264a b d e + 576a b d +--R * +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e + 2880a b d e +--R + +--R 4 5 6 3 6 7 +--R - 1152a b d e + 192a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1373 + +--S 1374 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (13860A a b - 3780B a b )e + (3465A b - 11025B a b )d e +--R + +--R 5 2 3 +--R - 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (20790A a b - 5670B a b )e + (13860A a b - 18900B a b )d e +--R + +--R 4 2 3 +--R - 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (13860A a b - 3780B a b)e + (20790A a b - 15750B a b )d e +--R + +--R 2 3 2 3 +--R - 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (3465A a b - 945B a )e + (13860A a b - 6300B a b)d e +--R + +--R 3 2 2 3 +--R - 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (3465A a b - 945B a )d e - 2520B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 5 4 5 5 4 5 +--R ((6930A b - 1890B a b )e - 5040B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (25410A a b - 6930B a b )e + (9240A b - 21000B a b )d e +--R + +--R 5 2 3 +--R - 6720B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (33726A a b - 9198B a b )e + (34188A a b - 33852B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (1386A b - 25242B a b )d e - 1008B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (18414A a b - 5022B a b)e + (45936A a b - 25920B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (5346A a b - 34866B a b )d e + (- 396A b - 3780B a b )d e +--R + +--R 5 4 +--R 288B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (2816A a b - 768B a )e + (25564A a b - 9020B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (7590A a b - 20662B a b )d e + (- 1496A a b - 5112B a b )d e +--R + +--R 5 4 4 5 5 +--R (176A b + 1040B a b )d e - 128B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 256A a e + (4096A a b - 512B a )d e + (4590A a b - 5278B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 2060A a b - 1380B a b )d e + (656A a b + 272B a b )d e +--R + +--R 5 4 5 +--R (- 96A b - 32B a b )d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 384a b e - 2304a b d e + 5760a b d e - 7680a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 5760a b d e - 2304a b d e + 384b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 1536a b e - 8832a b d e + 20736a b d e - 24960a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 15360a b d e - 3456a b d e - 768a b d e + 384b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 2304a b e - 12288a b d e + 25344a b d e - 23040a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 3840a b d e + 9216a b d e - 6912a b d e + 1536a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 1536a b e - 6912a b d e + 9216a b d e + 3840a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 23040a b d e + 25344a b d e - 12288a b d e + 2304a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 384a e - 768a b d e - 3456a b d e + 15360a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 24960a b d e + 20736a b d e - 8832a b d e + 1536a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 +--R 384a d e - 2304a b d e + 5760a b d e - 7680a b d e +--R + +--R 6 4 5 2 5 5 6 4 6 7 +--R 5760a b d e - 2304a b d e + 384a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (13860A a b - 3780B a b )e + (3465A b - 11025B a b )d e +--R + +--R 5 2 3 +--R - 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (20790A a b - 5670B a b )e + (13860A a b - 18900B a b )d e +--R + +--R 4 2 3 +--R - 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (13860A a b - 3780B a b)e + (20790A a b - 15750B a b )d e +--R + +--R 2 3 2 3 +--R - 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (3465A a b - 945B a )e + (13860A a b - 6300B a b)d e +--R + +--R 3 2 2 3 +--R - 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (3465A a b - 945B a )d e - 2520B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (12705A a b - 3465B a b )e + (4620A b - 10500B a b )d e +--R + +--R 5 2 3 +--R - 3360B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (16863A a b - 4599B a b )e + (17094A a b - 16926B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (693A b - 12621B a b )d e - 504B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (9207A a b - 2511B a b)e + (22968A a b - 12960B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2673A a b - 17433B a b )d e + (- 198A b - 1890B a b )d e +--R + +--R 5 4 +--R 144B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (1408A a b - 384B a )e + (12782A a b - 4510B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (3795A a b - 10331B a b )d e + (- 748A a b - 2556B a b )d e +--R + +--R 5 4 4 5 5 +--R (88A b + 520B a b )d e - 64B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 128A a e + (2048A a b - 256B a )d e + (2295A a b - 2639B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 1030A a b - 690B a b )d e + (328A a b + 136B a b )d e +--R + +--R 5 4 5 +--R (- 48A b - 16B a b )d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 768a b e - 4416a b d e + 10368a b d e - 12480a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 7680a b d e - 1728a b d e - 384a b d e + 192b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 1152a b e - 6144a b d e + 12672a b d e - 11520a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 1920a b d e + 4608a b d e - 3456a b d e + 768a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 768a b e - 3456a b d e + 4608a b d e + 1920a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 11520a b d e + 12672a b d e - 6144a b d e + 1152a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 192a e - 384a b d e - 1728a b d e + 7680a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 12480a b d e + 10368a b d e - 4416a b d e + 768a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 6 4 5 2 5 5 6 4 6 7 +--R 2880a b d e - 1152a b d e + 192a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1374 + +--S 1375 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (13860A a b - 3780B a b )e + (3465A b - 11025B a b )d e +--R + +--R 5 2 3 +--R - 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (20790A a b - 5670B a b )e + (13860A a b - 18900B a b )d e +--R + +--R 4 2 3 +--R - 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (13860A a b - 3780B a b)e + (20790A a b - 15750B a b )d e +--R + +--R 2 3 2 3 +--R - 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (3465A a b - 945B a )e + (13860A a b - 6300B a b)d e +--R + +--R 3 2 2 3 +--R - 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (3465A a b - 945B a )d e - 2520B a b d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 6 5 5 6 4 6 +--R ((6930A b - 1890B a b )e - 5040B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (34650A a b - 9450B a b )e + (6930A b - 27090B a b )d e +--R + +--R 6 2 3 +--R - 5040B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (69300A a b - 18900B a b )e + (34650A a b - 59850B a b )d e +--R + +--R 5 2 3 +--R - 25200B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (69300A a b - 18900B a b )e + (69300A a b - 69300B a b )d e +--R + +--R 2 4 2 3 +--R - 50400B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (34650A a b - 9450B a b)e + (69300A a b - 44100B a b )d e +--R + +--R 3 3 2 3 +--R - 50400B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (6930A a b - 1890B a )e + (34650A a b - 14490B a b)d e +--R + +--R 4 2 2 3 +--R - 25200B a b d e +--R * +--R x +--R + +--R 5 6 4 5 2 3 +--R (6930A a b - 1890B a )d e - 5040B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((6930A b - 1890B a b )e - 5040B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (25410A a b - 6930B a b )e + (9240A b - 21000B a b )d e +--R + +--R 5 2 3 +--R - 6720B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (33726A a b - 9198B a b )e + (34188A a b - 33852B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (1386A b - 25242B a b )d e - 1008B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (18414A a b - 5022B a b)e + (45936A a b - 25920B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (5346A a b - 34866B a b )d e + (- 396A b - 3780B a b )d e +--R + +--R 5 4 +--R 288B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (2816A a b - 768B a )e + (25564A a b - 9020B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (7590A a b - 20662B a b )d e + (- 1496A a b - 5112B a b )d e +--R + +--R 5 4 4 5 5 +--R (176A b + 1040B a b )d e - 128B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 256A a e + (4096A a b - 512B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (4590A a b - 5278B a b)d e + (- 2060A a b - 1380B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (656A a b + 272B a b )d e + (- 96A b - 32B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 6 5 5 6 4 6 +--R ((- 6930A b + 1890B a b )e + 5040B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 32340A a b + 8820B a b )e + (- 9240A b + 26040B a b )d e +--R + +--R 6 2 3 +--R 6720B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 +--R (- 59136A a b + 16128B a b )e +--R + +--R 5 2 4 4 +--R (- 43428A a b + 54852B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 1386A b + 31962B a b )d e + 1008B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 +--R (- 52140A a b + 14220B a b )e +--R + +--R 2 4 3 3 4 +--R (- 80124A a b + 59772B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 6732A a b + 60108B a b )d e + (396A b + 4788B a b )d e +--R + +--R 6 4 +--R - 288B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 21230A a b + 5790B a b)e + (- 71500A a b + 34940B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 12936A a b + 55528B a b )d e + (1892A a b + 8892B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 176A b - 1328B a b )d e + 128B b d +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 2560A a b + 768B a )e + (- 29660A a b + 9532B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 12180A a b + 25940B a b )d e + (3556A a b + 6492B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 832A a b - 1312B a b )d e + (96A b + 160B a b )d +--R * +--R x +--R + +--R 6 5 5 6 4 +--R 256A a e + (- 4096A a b + 512B a )d e +--R + +--R 4 2 5 2 3 3 3 4 2 3 2 +--R (- 4590A a b + 5278B a b)d e + (2060A a b + 1380B a b )d e +--R + +--R 2 4 3 3 4 5 2 4 5 +--R (- 656A a b - 272B a b )d e + (96A a b + 32B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 384a b e - 2304a b d e + 5760a b d e - 7680a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 5760a b d e - 2304a b d e + 384b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 1536a b e - 8832a b d e + 20736a b d e - 24960a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 15360a b d e - 3456a b d e - 768a b d e + 384b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 2304a b e - 12288a b d e + 25344a b d e - 23040a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 3840a b d e + 9216a b d e - 6912a b d e + 1536a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 1536a b e - 6912a b d e + 9216a b d e + 3840a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 23040a b d e + 25344a b d e - 12288a b d e + 2304a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 384a e - 768a b d e - 3456a b d e + 15360a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 24960a b d e + 20736a b d e - 8832a b d e + 1536a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 384a d e - 2304a b d e + 5760a b d e - 7680a b d e + 5760a b d e +--R + +--R 5 5 6 4 6 7 +--R - 2304a b d e + 384a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1375 + +--S 1376 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1376 + +--S 1377 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 5 6 4 6 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (17325A a b - 4725B a b )e + (3465A b - 13545B a b )d e +--R + +--R 6 2 3 +--R - 2520B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (34650A a b - 9450B a b )e + (17325A a b - 29925B a b )d e +--R + +--R 5 2 3 +--R - 12600B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (34650A a b - 9450B a b )e + (34650A a b - 34650B a b )d e +--R + +--R 2 4 2 3 +--R - 25200B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (17325A a b - 4725B a b)e + (34650A a b - 22050B a b )d e +--R + +--R 3 3 2 3 +--R - 25200B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (3465A a b - 945B a )e + (17325A a b - 7245B a b)d e +--R + +--R 4 2 2 3 +--R - 12600B a b d e +--R * +--R x +--R + +--R 5 6 4 5 2 3 +--R (3465A a b - 945B a )d e - 2520B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (13860A a b - 3780B a b )e + (3465A b - 11025B a b )d e +--R + +--R 5 2 3 +--R - 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (20790A a b - 5670B a b )e + (13860A a b - 18900B a b )d e +--R + +--R 4 2 3 +--R - 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (13860A a b - 3780B a b)e + (20790A a b - 15750B a b )d e +--R + +--R 2 3 2 3 +--R - 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (3465A a b - 945B a )e + (13860A a b - 6300B a b)d e +--R + +--R 3 2 2 3 +--R - 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (3465A a b - 945B a )d e - 2520B a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (12705A a b - 3465B a b )e + (4620A b - 10500B a b )d e +--R + +--R 5 2 3 +--R - 3360B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (16863A a b - 4599B a b )e + (17094A a b - 16926B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (693A b - 12621B a b )d e - 504B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (9207A a b - 2511B a b)e + (22968A a b - 12960B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2673A a b - 17433B a b )d e + (- 198A b - 1890B a b )d e +--R + +--R 5 4 +--R 144B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (1408A a b - 384B a )e + (12782A a b - 4510B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (3795A a b - 10331B a b )d e + (- 748A a b - 2556B a b )d e +--R + +--R 5 4 4 5 5 +--R (88A b + 520B a b )d e - 64B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 128A a e + (2048A a b - 256B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (2295A a b - 2639B a b)d e + (- 1030A a b - 690B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (328A a b + 136B a b )d e + (- 48A b - 16B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 6 5 5 6 4 6 +--R ((- 3465A b + 945B a b )e + 2520B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 16170A a b + 4410B a b )e + (- 4620A b + 13020B a b )d e +--R + +--R 6 2 3 +--R 3360B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 +--R (- 29568A a b + 8064B a b )e +--R + +--R 5 2 4 4 6 5 2 3 +--R (- 21714A a b + 27426B a b )d e + (- 693A b + 15981B a b )d e +--R + +--R 6 3 2 +--R 504B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 +--R (- 26070A a b + 7110B a b )e +--R + +--R 2 4 3 3 4 +--R (- 40062A a b + 29886B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 3366A a b + 30054B a b )d e + (198A b + 2394B a b )d e +--R + +--R 6 4 +--R - 144B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 10615A a b + 2895B a b)e + (- 35750A a b + 17470B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 6468A a b + 27764B a b )d e + (946A a b + 4446B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 88A b - 664B a b )d e + 64B b d +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 1280A a b + 384B a )e + (- 14830A a b + 4766B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 6090A a b + 12970B a b )d e + (1778A a b + 3246B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 416A a b - 656B a b )d e + (48A b + 80B a b )d +--R * +--R x +--R + +--R 6 5 5 6 4 +--R 128A a e + (- 2048A a b + 256B a )d e +--R + +--R 4 2 5 2 3 3 3 4 2 3 2 +--R (- 2295A a b + 2639B a b)d e + (1030A a b + 690B a b )d e +--R + +--R 2 4 3 3 4 5 2 4 5 +--R (- 328A a b - 136B a b )d e + (48A a b + 16B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 768a b e - 4416a b d e + 10368a b d e - 12480a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 7680a b d e - 1728a b d e - 384a b d e + 192b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 1152a b e - 6144a b d e + 12672a b d e - 11520a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 1920a b d e + 4608a b d e - 3456a b d e + 768a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 768a b e - 3456a b d e + 4608a b d e + 1920a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 11520a b d e + 12672a b d e - 6144a b d e + 1152a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 192a e - 384a b d e - 1728a b d e + 7680a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 12480a b d e + 10368a b d e - 4416a b d e + 768a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e + 2880a b d e +--R + +--R 5 5 6 4 6 7 +--R - 1152a b d e + 192a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1377 + +--S 1378 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1378 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich12e.input.pamphlet b/src/axiom-website/CATS/rich12e.input.pamphlet new file mode 100644 index 0000000..15e31d2 --- /dev/null +++ b/src/axiom-website/CATS/rich12e.input.pamphlet @@ -0,0 +1,46858 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12e.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 138 matching answers. +\item 157 cases where Axiom answer differs from Rubi +\item 39 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12e.output +)spool rich12e.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1353 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1353 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/20*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-11/120*(8*b*B*d-13*A*b*e+_ + 5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 33/160*e*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-231/320*e^2*(8*b*B*d-13*A*b*e+5*a*B*e)/_ + ((b*d-a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-77/64*e^3*(8*b*B*d-_ + 13*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+231/64*b^(3/2)*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(15/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-231/64*b*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/_ + ((b*d-a*e)^7*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((45045A b - 17325B a b )e - 27720B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (180180A a b - 69300B a b )e + (90090A b - 145530B a b )d e +--R + +--R 6 2 4 +--R - 55440B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (270270A a b - 103950B a b )e +--R + +--R 5 2 4 5 +--R (360360A a b - 304920B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (45045A b - 239085B a b )d e - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (180180A a b - 69300B a b )e +--R + +--R 2 4 3 3 5 +--R (540540A a b - 318780B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (180180A a b - 401940B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (45045A a b - 17325B a b)e + (360360A a b - 166320B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (270270A a b - 325710B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (90090A a b - 34650B a b)d e +--R + +--R 3 3 4 2 2 4 3 3 3 3 +--R (180180A a b - 124740B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (45045A a b - 17325B a b)d e - 27720B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 165165A a b + 63525B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 105105A b + 142065B a b )d e + 64680B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 219219A a b + 84315B a b )e +--R + +--R 5 2 4 5 +--R (- 387387A a b + 283899B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 69069A b + 264957B a b )d e + 42504B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 119691A a b + 46035B a b )e +--R + +--R 2 4 3 3 5 +--R (- 517803A a b + 272811B a b )d e +--R + +--R 5 2 4 2 4 +--R (- 256971A a b + 417483B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 6435A b + 160611B a b )d e + 3960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 18304A a b + 7040B a b)e +--R + +--R 3 3 4 2 5 +--R (- 285857A a b + 121209B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (- 347919A a b + 309727B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 25025A a b + 223729B a b )d e + (1430A b + 14850B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (1664A a b - 640B a )e + (- 44928A a b + 16256B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (- 196001A a b + 103033B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 35945A a b + 134441B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (5460A a b + 20020B a b )d e + (- 520A b - 3160B a b )d e +--R + +--R 6 6 +--R 320B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 384A a e + (3968A a b - 256B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 32384A a b + 6912B a b)d e + (- 22155A a b + 33619B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (7630A a b + 5530B a b )d e + (- 1960A a b - 840B a b )d e +--R + +--R 6 5 6 +--R (240A b + 80B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 3 9 6 4 8 5 5 2 7 4 6 3 6 +--R 960a b e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 3 7 4 5 2 8 5 4 9 6 3 10 7 2 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960b d e +--R * +--R 5 +--R x +--R + +--R 8 2 9 7 3 8 6 4 2 7 5 5 3 6 +--R 2880a b e - 18240a b d e + 47040a b d e - 60480a b d e +--R + +--R 4 6 4 5 3 7 5 4 2 8 6 3 9 7 2 +--R 33600a b d e + 6720a b d e - 20160a b d e + 10560a b d e +--R + +--R 10 8 +--R - 1920b d e +--R * +--R 4 +--R x +--R + +--R 9 9 8 2 8 7 3 2 7 6 4 3 6 +--R 2880a b e - 14400a b d e + 21120a b d e + 13440a b d e +--R + +--R 5 5 4 5 4 6 5 4 3 7 6 3 2 8 7 2 +--R - 80640a b d e + 107520a b d e - 67200a b d e + 17280a b d e +--R + +--R 9 8 10 9 +--R 960a b d e - 960b d +--R * +--R 3 +--R x +--R + +--R 10 9 9 8 8 2 2 7 7 3 3 6 +--R 960a e - 960a b d e - 17280a b d e + 67200a b d e +--R + +--R 6 4 4 5 5 5 5 4 4 6 6 3 3 7 7 2 +--R - 107520a b d e + 80640a b d e - 13440a b d e - 21120a b d e +--R + +--R 2 8 8 9 9 +--R 14400a b d e - 2880a b d +--R * +--R 2 +--R x +--R + +--R 10 8 9 2 7 8 2 3 6 7 3 4 5 +--R 1920a d e - 10560a b d e + 20160a b d e - 6720a b d e +--R + +--R 6 4 5 4 5 5 6 3 4 6 7 2 3 7 8 +--R - 33600a b d e + 60480a b d e - 47040a b d e + 18240a b d e +--R + +--R 2 8 9 +--R - 2880a b d +--R * +--R x +--R + +--R 10 2 7 9 3 6 8 2 4 5 7 3 5 4 +--R 960a d e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 6 4 6 3 5 5 7 2 4 6 8 3 7 9 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 6 6 5 6 +--R ((45045A b - 17325B a b )e - 27720B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (180180A a b - 69300B a b )e + (90090A b - 145530B a b )d e +--R + +--R 6 2 4 +--R - 55440B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (270270A a b - 103950B a b )e +--R + +--R 5 2 4 5 +--R (360360A a b - 304920B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (45045A b - 239085B a b )d e - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (180180A a b - 69300B a b )e +--R + +--R 2 4 3 3 5 +--R (540540A a b - 318780B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (180180A a b - 401940B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (45045A a b - 17325B a b)e +--R + +--R 3 3 4 2 5 +--R (360360A a b - 166320B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (270270A a b - 325710B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (90090A a b - 34650B a b)d e +--R + +--R 3 3 4 2 2 4 3 3 3 3 +--R (180180A a b - 124740B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (45045A a b - 17325B a b)d e - 27720B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 6 6 5 6 +--R ((- 90090A b + 34650B a b )e + 55440B b d e )x +--R + +--R 5 2 4 6 +--R (- 330330A a b + 127050B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 210210A b + 284130B a b )d e + 129360B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 438438A a b + 168630B a b )e +--R + +--R 5 2 4 5 +--R (- 774774A a b + 567798B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 138138A b + 529914B a b )d e + 85008B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 239382A a b + 92070B a b )e +--R + +--R 2 4 3 3 5 +--R (- 1035606A a b + 545622B a b )d e +--R + +--R 5 2 4 2 4 +--R (- 513942A a b + 834966B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 12870A b + 321222B a b )d e + 7920B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 36608A a b + 14080B a b)e +--R + +--R 3 3 4 2 5 +--R (- 571714A a b + 242418B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (- 695838A a b + 619454B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 50050A a b + 447458B a b )d e + (2860A b + 29700B a b )d e +--R + +--R 6 5 +--R - 1760B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (3328A a b - 1280B a )e + (- 89856A a b + 32512B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (- 392002A a b + 206066B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 71890A a b + 268882B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (10920A a b + 40040B a b )d e + (- 1040A b - 6320B a b )d e +--R + +--R 6 6 +--R 640B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 768A a e + (7936A a b - 512B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 64768A a b + 13824B a b)d e + (- 44310A a b + 67238B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (15260A a b + 11060B a b )d e + (- 3920A a b - 1680B a b )d e +--R + +--R 6 5 6 +--R (480A b + 160B a b )d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 +--R 1920a b e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 3 8 4 5 2 9 5 4 10 6 3 11 7 2 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 +--R 7680a b e - 49920a b d e + 134400a b d e - 188160a b d e +--R + +--R 4 7 4 5 3 8 5 4 2 9 6 3 10 7 2 +--R 134400a b d e - 26880a b d e - 26880a b d e + 19200a b d e +--R + +--R 11 8 +--R - 3840b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 +--R 11520a b e - 65280a b d e + 136320a b d e - 94080a b d e +--R + +--R 5 6 4 5 4 7 5 4 3 8 6 3 2 9 7 2 +--R - 94080a b d e + 228480a b d e - 174720a b d e + 55680a b d e +--R + +--R 10 8 11 9 +--R - 1920a b d e - 1920b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 +--R 7680a b e - 30720a b d e + 7680a b d e + 161280a b d e +--R + +--R 6 5 4 5 5 6 5 4 4 7 6 3 3 8 7 2 +--R - 376320a b d e + 376320a b d e - 161280a b d e - 7680a b d e +--R + +--R 2 9 8 10 9 +--R 30720a b d e - 7680a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 +--R 1920a e + 1920a b d e - 55680a b d e + 174720a b d e +--R + +--R 7 4 4 5 6 5 5 4 5 6 6 3 4 7 7 2 +--R - 228480a b d e + 94080a b d e + 94080a b d e - 136320a b d e +--R + +--R 3 8 8 2 9 9 +--R 65280a b d e - 11520a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 +--R 3840a d e - 19200a b d e + 26880a b d e + 26880a b d e +--R + +--R 7 4 5 4 6 5 6 3 5 6 7 2 4 7 8 +--R - 134400a b d e + 188160a b d e - 134400a b d e + 49920a b d e +--R + +--R 3 8 9 +--R - 7680a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 +--R 1920a d e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 7 4 6 3 6 5 7 2 5 6 8 4 7 9 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 180180A a b + 69300B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 90090A b + 145530B a b )d e + 55440B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 270270A a b + 103950B a b )e +--R + +--R 5 2 4 5 +--R (- 360360A a b + 304920B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 45045A b + 239085B a b )d e + 27720B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 180180A a b + 69300B a b )e +--R + +--R 2 4 3 3 5 +--R (- 540540A a b + 318780B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (- 180180A a b + 401940B a b )d e + 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 45045A a b + 17325B a b)e +--R + +--R 3 3 4 2 5 +--R (- 360360A a b + 166320B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (- 270270A a b + 325710B a b )d e + 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 90090A a b + 34650B a b)d e +--R + +--R 3 3 4 2 2 4 3 3 3 3 +--R (- 180180A a b + 124740B a b )d e + 110880B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (- 45045A a b + 17325B a b)d e + 27720B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 165165A a b + 63525B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 105105A b + 142065B a b )d e + 64680B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 219219A a b + 84315B a b )e +--R + +--R 5 2 4 5 +--R (- 387387A a b + 283899B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 69069A b + 264957B a b )d e + 42504B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 119691A a b + 46035B a b )e +--R + +--R 2 4 3 3 5 +--R (- 517803A a b + 272811B a b )d e +--R + +--R 5 2 4 2 4 +--R (- 256971A a b + 417483B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 6435A b + 160611B a b )d e + 3960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 18304A a b + 7040B a b)e + (- 285857A a b + 121209B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (- 347919A a b + 309727B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 25025A a b + 223729B a b )d e + (1430A b + 14850B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (1664A a b - 640B a )e + (- 44928A a b + 16256B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (- 196001A a b + 103033B a b )d e +--R + +--R 2 4 3 3 3 3 5 2 4 4 2 +--R (- 35945A a b + 134441B a b )d e + (5460A a b + 20020B a b )d e +--R + +--R 6 5 5 6 6 +--R (- 520A b - 3160B a b )d e + 320B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 384A a e + (3968A a b - 256B a )d e +--R + +--R 4 2 5 2 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(- 90090A b + 173250B a b )d e + 55440B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 6 +--R (- 450450A a b + 173250B a b )e +--R + +--R 6 2 5 5 +--R (- 450450A a b + 450450B a b )d e +--R + +--R 7 6 2 4 7 3 3 +--R (- 45045A b + 294525B a b )d e + 27720B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 6 +--R (- 450450A a b + 173250B a b )e +--R + +--R 2 5 3 4 5 +--R (- 900900A a b + 623700B a b )d e +--R + +--R 6 2 5 2 4 6 3 3 +--R (- 225225A a b + 641025B a b )d e + 138600B a b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 6 +--R (- 225225A a b + 86625B a b )e +--R + +--R 3 4 4 3 5 +--R (- 900900A a b + 485100B a b )d e +--R + +--R 2 5 3 4 2 4 2 5 3 3 +--R (- 450450A a b + 727650B a b )d e + 277200B a b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 6 +--R (- 45045A a b + 17325B a b)e +--R + +--R 4 3 5 2 5 +--R (- 450450A a b + 200970B a b )d e +--R + +--R 3 4 4 3 2 4 3 4 3 3 +--R (- 450450A a b + 450450B a b )d e + 277200B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 +--R (- 90090A a b + 34650B a b)d e +--R + +--R 4 3 5 2 2 4 4 3 3 3 +--R (- 225225A a b + 142065B a b )d e + 138600B a b d e +--R * +--R x +--R + +--R 5 2 6 2 4 5 2 3 3 +--R (- 45045A a b + 17325B a b)d e + 27720B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 180180A a b + 69300B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 90090A b + 145530B a b )d e + 55440B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 270270A a b + 103950B a b )e +--R + +--R 5 2 4 5 +--R (- 360360A a b + 304920B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 45045A b + 239085B a b )d e + 27720B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 180180A a b + 69300B a b )e +--R + +--R 2 4 3 3 5 +--R (- 540540A a b + 318780B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (- 180180A a b + 401940B a b )d e + 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 45045A a b + 17325B a b)e +--R + +--R 3 3 4 2 5 +--R (- 360360A a b + 166320B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (- 270270A a b + 325710B a b )d e + 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 90090A a b + 34650B a b)d e +--R + +--R 3 3 4 2 2 4 3 3 3 3 +--R (- 180180A a b + 124740B a b )d e + 110880B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (- 45045A a b + 17325B a b)d e + 27720B a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 165165A a b + 63525B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 105105A b + 142065B a b )d e + 64680B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 219219A a b + 84315B a b )e +--R + +--R 5 2 4 5 +--R (- 387387A a b + 283899B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 69069A b + 264957B a b )d e + 42504B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 119691A a b + 46035B a b )e +--R + +--R 2 4 3 3 5 +--R (- 517803A a b + 272811B a b )d e +--R + +--R 5 2 4 2 4 +--R (- 256971A a b + 417483B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 6435A b + 160611B a b )d e + 3960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 18304A a b + 7040B a b)e +--R + +--R 3 3 4 2 5 +--R (- 285857A a b + 121209B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (- 347919A a b + 309727B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 25025A a b + 223729B a b )d e + (1430A b + 14850B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (1664A a b - 640B a )e + (- 44928A a b + 16256B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (- 196001A a b + 103033B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 35945A a b + 134441B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (5460A a b + 20020B a b )d e + (- 520A b - 3160B a b )d e +--R + +--R 6 6 +--R 320B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 384A a e + (3968A a b - 256B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 32384A a b + 6912B a b)d e + (- 22155A a b + 33619B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (7630A a b + 5530B a b )d e + (- 1960A a b - 840B a b )d e +--R + +--R 6 5 6 +--R (240A b + 80B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 7 6 6 7 5 7 +--R ((45045A b - 17325B a b )e - 27720B b d e )x +--R + +--R 6 2 5 6 7 6 5 +--R (210210A a b - 80850B a b )e + (105105A b - 169785B a b )d e +--R + +--R 7 2 4 +--R - 64680B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 6 +--R (384384A a b - 147840B a b )e +--R + +--R 6 2 5 5 +--R (492492A a b - 425964B a b )d e +--R + +--R 7 6 2 4 7 3 3 +--R (69069A b - 329637B a b )d e - 42504B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 6 +--R (338910A a b - 130350B a b )e +--R + +--R 2 5 3 4 5 +--R (905190A a b - 556710B a b )d e +--R + +--R 6 2 5 2 4 7 6 3 3 +--R (326040A a b - 682440B a b )d e + (6435A b - 203115B a b )d e +--R + +--R 7 4 2 +--R - 3960B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 6 +--R (137995A a b - 53075B a b )e +--R + +--R 3 4 4 3 5 +--R (803660A a b - 394020B a b )d e +--R + +--R 2 5 3 4 2 4 +--R (604890A a b - 727210B a b )d e +--R + +--R 6 2 5 3 3 7 6 4 2 +--R (31460A a b - 384340B a b )d e + (- 1430A b - 18810B a b )d e +--R + +--R 7 5 +--R 880B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 6 4 3 5 2 5 +--R (16640A a b - 6400B a b)e + (330785A a b - 137465B a b )d e +--R + +--R 3 4 4 3 2 4 +--R (543920A a b - 412760B a b )d e +--R + +--R 2 5 3 4 3 3 +--R (60970A a b - 358170B a b )d e +--R + +--R 6 2 5 4 2 7 6 5 +--R (- 6890A a b - 34870B a b )d e + (520A b + 4040B a b )d e +--R + +--R 7 6 +--R - 320B b d +--R * +--R 2 +--R x +--R + +--R 6 7 6 5 2 6 5 +--R (- 1280A a b + 640B a )e + (40960A a b - 16000B a b)d e +--R + +--R 4 3 5 2 2 4 +--R (228385A a b - 109945B a b )d e +--R + +--R 3 4 4 3 3 3 +--R (58100A a b - 168060B a b )d e +--R + +--R 2 5 3 4 4 2 6 2 5 5 +--R (- 13090A a b - 25550B a b )d e + (2480A a b + 4000B a b )d e +--R + +--R 7 6 6 +--R (- 240A b - 400B a b )d +--R * +--R x +--R + +--R 7 6 6 7 5 +--R 384A a e + (- 3968A a b + 256B a )d e +--R + +--R 5 2 6 2 4 4 3 5 2 3 3 +--R (32384A a b - 6912B a b)d e + (22155A a b - 33619B a b )d e +--R + +--R 3 4 4 3 4 2 2 5 3 4 5 +--R (- 7630A a b - 5530B a b )d e + (1960A a b + 840B a b )d e +--R + +--R 6 2 5 6 +--R (- 240A a b - 80B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 +--R 960a b e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 3 8 4 5 2 9 5 4 10 6 3 11 7 2 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 +--R 3840a b e - 24960a b d e + 67200a b d e - 94080a b d e +--R + +--R 4 7 4 5 3 8 5 4 2 9 6 3 10 7 2 +--R 67200a b d e - 13440a b d e - 13440a b d e + 9600a b d e +--R + +--R 11 8 +--R - 1920b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 +--R 5760a b e - 32640a b d e + 68160a b d e - 47040a b d e +--R + +--R 5 6 4 5 4 7 5 4 3 8 6 3 2 9 7 2 +--R - 47040a b d e + 114240a b d e - 87360a b d e + 27840a b d e +--R + +--R 10 8 11 9 +--R - 960a b d e - 960b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 +--R 3840a b e - 15360a b d e + 3840a b d e + 80640a b d e +--R + +--R 6 5 4 5 5 6 5 4 4 7 6 3 3 8 7 2 +--R - 188160a b d e + 188160a b d e - 80640a b d e - 3840a b d e +--R + +--R 2 9 8 10 9 +--R 15360a b d e - 3840a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 +--R 960a e + 960a b d e - 27840a b d e + 87360a b d e +--R + +--R 7 4 4 5 6 5 5 4 5 6 6 3 4 7 7 2 +--R - 114240a b d e + 47040a b d e + 47040a b d e - 68160a b d e +--R + +--R 3 8 8 2 9 9 +--R 32640a b d e - 5760a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 +--R 1920a d e - 9600a b d e + 13440a b d e + 13440a b d e +--R + +--R 7 4 5 4 6 5 6 3 5 6 7 2 4 7 8 +--R - 67200a b d e + 94080a b d e - 67200a b d e + 24960a b d e +--R + +--R 3 8 9 +--R - 3840a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 +--R 960a d e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 7 4 6 3 6 5 7 2 5 6 8 4 7 9 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 7 + +)clear all + +--S 8 of 1353 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 m +--R (1) (b x + 3a b x + 3a b x + a )(e x + d) +--R Type: Expression(Integer) +--E 8 + +--S 9 of 1353 +r0:=-(b*d-a*e)^3*(d+e*x)^(1+m)/(e^4*(1+m))+3*b*(b*d-a*e)^2*_ + (d+e*x)^(2+m)/(e^4*(2+m))-3*b^2*(b*d-a*e)*(d+e*x)^(3+m)/(e^4*(3+m))+_ + b^3*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 4 +--R (b m + 6b m + 11b m + 6b )(e x + d) +--R + +--R 2 3 3 2 3 2 2 3 +--R (3a b e - 3b d)m + (21a b e - 21b d)m + (42a b e - 42b d)m +--R + +--R 2 3 +--R 24a b e - 24b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 3 2 2 +--R (3a b e - 6a b d e + 3b d )m + (24a b e - 48a b d e + 24b d )m +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (57a b e - 114a b d e + 57b d )m + 36a b e - 72a b d e + 36b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e - 3a b d e + 3a b d e - b d )m +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (9a e - 27a b d e + 27a b d e - 9b d )m +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (26a e - 78a b d e + 78a b d e - 26b d )m + 24a e - 72a b d e +--R + +--R 2 2 3 3 +--R 72a b d e - 24b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 3 4 2 3 4 3 4 4 +--R (b e m + 6b e m + 11b e m + 6b e )x +--R + +--R 2 4 3 3 3 2 4 3 3 2 +--R (3a b e + b d e )m + (21a b e + 3b d e )m +--R + +--R 2 4 3 3 2 4 +--R (42a b e + 2b d e )m + 24a b e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 3 2 4 2 3 3 2 2 2 +--R (3a b e + 3a b d e )m + (24a b e + 15a b d e - 3b d e )m +--R + +--R 2 4 2 3 3 2 2 2 4 +--R (57a b e + 12a b d e - 3b d e )m + 36a b e +--R * +--R 2 +--R x +--R + +--R 3 4 2 3 3 3 4 2 3 2 2 2 2 +--R (a e + 3a b d e )m + (9a e + 21a b d e - 6a b d e )m +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 +--R (26a e + 36a b d e - 24a b d e + 6b d e)m + 24a e +--R * +--R x +--R + +--R 3 3 3 3 3 2 2 2 2 +--R a d e m + (9a d e - 3a b d e )m +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (26a d e - 21a b d e + 6a b d e)m + 24a d e - 36a b d e + 24a b d e +--R + +--R 3 4 +--R - 6b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 10 + +--S 11 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 3 3 4 2 3 4 3 4 4 +--R (b e m + 6b e m + 11b e m + 6b e )x +--R + +--R 2 4 3 3 3 2 4 3 3 2 +--R (3a b e + b d e )m + (21a b e + 3b d e )m +--R + +--R 2 4 3 3 2 4 +--R (42a b e + 2b d e )m + 24a b e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 3 2 4 2 3 3 2 2 2 +--R (3a b e + 3a b d e )m + (24a b e + 15a b d e - 3b d e )m +--R + +--R 2 4 2 3 3 2 2 2 4 +--R (57a b e + 12a b d e - 3b d e )m + 36a b e +--R * +--R 2 +--R x +--R + +--R 3 4 2 3 3 3 4 2 3 2 2 2 2 +--R (a e + 3a b d e )m + (9a e + 21a b d e - 6a b d e )m +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 +--R (26a e + 36a b d e - 24a b d e + 6b d e)m + 24a e +--R * +--R x +--R + +--R 3 3 3 3 3 2 2 2 2 +--R a d e m + (9a d e - 3a b d e )m +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 +--R (26a d e - 21a b d e + 6a b d e)m + 24a d e - 36a b d e +--R + +--R 2 3 3 4 +--R 24a b d e - 6b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 3 3 2 3 3 m + 4 +--R (- b m - 6b m - 11b m - 6b )(e x + d) +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 3a b e + 3b d)m + (- 21a b e + 21b d)m + (- 42a b e + 42b d)m +--R + +--R 2 3 +--R - 24a b e + 24b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 +--R (- 3a b e + 6a b d e - 3b d )m +--R + +--R 2 2 2 3 2 2 +--R (- 24a b e + 48a b d e - 24b d )m +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (- 57a b e + 114a b d e - 57b d )m - 36a b e + 72a b d e - 36b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a e + 3a b d e - 3a b d e + b d )m +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 9a e + 27a b d e - 27a b d e + 9b d )m +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 26a e + 78a b d e - 78a b d e + 26b d )m - 24a e + 72a b d e +--R + +--R 2 2 3 3 +--R - 72a b d e + 24b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 1353 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 5 8 2 5 3 4 7 2 5 2 4 3 2 3 6 +--R b e x + (3a b e + 5b d e )x + (3a b e + 15a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 5 +--R (a e + 15a b d e + 30a b d e + 10b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 4 +--R (5a d e + 30a b d e + 30a b d e + 5b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (10a d e + 30a b d e + 15a b d e + b d )x +--R + +--R 3 3 2 2 4 2 5 2 3 4 2 5 3 5 +--R (10a d e + 15a b d e + 3a b d )x + (5a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 13 + +--S 14 of 1353 +r0:=-1/6*(b*d-a*e)^3*(d+e*x)^6/e^4+3/7*b*(b*d-a*e)^2*(d+e*x)^7/e^4-_ + 3/8*b^2*(b*d-a*e)*(d+e*x)^8/e^4+1/9*b^3*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 3 9 9 3 2 9 5 3 8 8 +--R - b e x + (- a b e + - b d e )x +--R 9 8 8 +--R + +--R 3 2 9 15 2 8 10 3 2 7 7 +--R (- a b e + -- a b d e + -- b d e )x +--R 7 7 7 +--R + +--R 1 3 9 5 2 8 2 2 7 5 3 3 6 6 +--R (- a e + - a b d e + 5a b d e + - b d e )x +--R 6 2 3 +--R + +--R 3 8 2 2 7 2 3 6 3 4 5 5 +--R (a d e + 6a b d e + 6a b d e + b d e )x +--R + +--R 5 3 2 7 15 2 3 6 15 2 4 5 1 3 5 4 4 +--R (- a d e + -- a b d e + -- a b d e + - b d e )x +--R 2 2 4 4 +--R + +--R 10 3 3 6 2 4 5 2 5 4 3 5 3 4 5 3 2 5 4 2 +--R (-- a d e + 5a b d e + a b d e )x + (- a d e + - a b d e )x +--R 3 2 2 +--R + +--R 3 5 4 1 3 6 3 1 2 7 2 1 2 8 1 3 9 +--R a d e x + - a d e - -- a b d e + -- a b d e - --- b d +--R 6 14 56 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 14 + +--S 15 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 5 9 3 2 5 5 3 4 8 3 2 5 15 2 4 10 3 2 3 7 +--R - b e x + (- a b e + - b d e )x + (- a b e + -- a b d e + -- b d e )x +--R 9 8 8 7 7 7 +--R + +--R 1 3 5 5 2 4 2 2 3 5 3 3 2 6 +--R (- a e + - a b d e + 5a b d e + - b d e )x +--R 6 2 3 +--R + +--R 3 4 2 2 3 2 3 2 3 4 5 +--R (a d e + 6a b d e + 6a b d e + b d e)x +--R + +--R 5 3 2 3 15 2 3 2 15 2 4 1 3 5 4 +--R (- a d e + -- a b d e + -- a b d e + - b d )x +--R 2 2 4 4 +--R + +--R 10 3 3 2 2 4 2 5 3 5 3 4 3 2 5 2 3 5 +--R (-- a d e + 5a b d e + a b d )x + (- a d e + - a b d )x + a d x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 15 + +--S 16 of 1353 +m0:=a0-r0 +--R +--R +--R 1 3 6 3 1 2 7 2 1 2 8 1 3 9 +--R - - a d e + -- a b d e - -- a b d e + --- b d +--R 6 14 56 504 +--R (4) ------------------------------------------------ +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 16 + +--S 17 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 17 + +)clear all + +--S 18 of 1353 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 18 + +--S 19 of 1353 +r0:=-1/5*(b*d-a*e)^3*(d+e*x)^5/e^4+1/2*b*(b*d-a*e)^2*(d+e*x)^6/e^4-_ + 3/7*b^2*(b*d-a*e)*(d+e*x)^7/e^4+1/8*b^3*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 3 8 8 3 2 8 4 3 7 7 1 2 8 2 7 3 2 6 6 +--R - b e x + (- a b e + - b d e )x + (- a b e + 2a b d e + b d e )x +--R 8 7 7 2 +--R + +--R 1 3 8 12 2 7 18 2 2 6 4 3 3 5 5 +--R (- a e + -- a b d e + -- a b d e + - b d e )x +--R 5 5 5 5 +--R + +--R 3 7 9 2 2 6 2 3 5 1 3 4 4 4 +--R (a d e + - a b d e + 3a b d e + - b d e )x +--R 2 4 +--R + +--R 3 2 6 2 3 5 2 4 4 3 3 3 5 3 2 4 4 2 3 4 4 +--R (2a d e + 4a b d e + a b d e )x + (2a d e + - a b d e )x + a d e x +--R 2 +--R + +--R 1 3 5 3 1 2 6 2 1 2 7 1 3 8 +--R - a d e - -- a b d e + -- a b d e - --- b d +--R 5 10 35 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 19 + +--S 20 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 8 3 2 4 4 3 3 7 1 2 4 2 3 3 2 2 6 +--R - b e x + (- a b e + - b d e )x + (- a b e + 2a b d e + b d e )x +--R 8 7 7 2 +--R + +--R 1 3 4 12 2 3 18 2 2 2 4 3 3 5 +--R (- a e + -- a b d e + -- a b d e + - b d e)x +--R 5 5 5 5 +--R + +--R 3 3 9 2 2 2 2 3 1 3 4 4 +--R (a d e + - a b d e + 3a b d e + - b d )x +--R 2 4 +--R + +--R 3 2 2 2 3 2 4 3 3 3 3 2 4 2 3 4 +--R (2a d e + 4a b d e + a b d )x + (2a d e + - a b d )x + a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +--S 21 of 1353 +m0:=a0-r0 +--R +--R +--R 1 3 5 3 1 2 6 2 1 2 7 1 3 8 +--R - - a d e + -- a b d e - -- a b d e + --- b d +--R 5 10 35 280 +--R (4) ------------------------------------------------ +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 21 + +--S 22 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 22 + +)clear all + +--S 23 of 1353 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 23 + +--S 24 of 1353 +r0:=1/4*(b*d-a*e)^3*(a+b*x)^4/b^4+3/5*e*(b*d-a*e)^2*(a+b*x)^5/b^4+_ + 1/2*e^2*(b*d-a*e)*(a+b*x)^6/b^4+1/7*e^3*(a+b*x)^7/b^4 +--R +--R +--R (2) +--R 1 7 3 7 1 6 3 1 7 2 6 3 2 5 3 9 6 2 3 7 2 5 +--R - b e x + (- a b e + - b d e )x + (- a b e + - a b d e + - b d e)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 4 3 9 2 5 2 9 6 2 1 7 3 4 +--R (- a b e + - a b d e + - a b d e + - b d )x +--R 4 4 4 4 +--R + +--R 3 4 2 2 5 2 6 3 3 3 3 4 2 3 2 5 3 2 3 4 3 +--R (a b d e + 3a b d e + a b d )x + (- a b d e + - a b d )x + a b d x +--R 2 2 +--R + +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R - --- a e + -- a b d e - -- a b d e + - a b d +--R 140 20 20 4 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 24 + +--S 25 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 3 7 1 2 3 1 3 2 6 3 2 3 9 2 2 3 3 2 5 +--R - b e x + (- a b e + - b d e )x + (- a b e + - a b d e + - b d e)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 3 9 2 2 9 2 2 1 3 3 4 +--R (- a e + - a b d e + - a b d e + - b d )x +--R 4 4 4 4 +--R + +--R 3 2 2 2 2 3 3 3 3 2 3 2 3 2 3 3 +--R (a d e + 3a b d e + a b d )x + (- a d e + - a b d )x + a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +--S 26 of 1353 +m0:=a0-r0 +--R +--R +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R --- a e - -- a b d e + -- a b d e - - a b d +--R 140 20 20 4 +--R (4) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 26 + +--S 27 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 27 + +)clear all + +--S 28 of 1353 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 28 + +--S 29 of 1353 +r0:=1/4*(b*d-a*e)^2*(a+b*x)^4/b^3+2/5*e*(b*d-a*e)*(a+b*x)^5/b^3+_ + 1/6*e^2*(a+b*x)^6/b^3 +--R +--R +--R (2) +--R 1 6 2 6 3 5 2 2 6 5 3 2 4 2 3 5 1 6 2 4 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 3 2 2 4 5 2 3 3 3 3 2 4 2 2 3 3 2 +--R (- a b e + 2a b d e + a b d )x + (a b d e + - a b d )x + a b d x +--R 3 2 +--R + +--R 1 6 2 1 5 1 4 2 2 +--R -- a e - -- a b d e + - a b d +--R 60 10 4 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 29 + +--S 30 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 6 3 2 2 2 3 5 3 2 2 3 2 1 3 2 4 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 2 2 2 2 3 3 3 2 2 2 3 2 +--R (- a e + 2a b d e + a b d )x + (a d e + - a b d )x + a d x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +--S 31 of 1353 +m0:=a0-r0 +--R +--R +--R 1 6 2 1 5 1 4 2 2 +--R - -- a e + -- a b d e - - a b d +--R 60 10 4 +--R (4) --------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 31 + +--S 32 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 32 + +)clear all + +--S 33 of 1353 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d +--R Type: Polynomial(Integer) +--E 33 + +--S 34 of 1353 +r0:=1/4*(b*d-a*e)*(a+b*x)^4/b^2+1/5*e*(a+b*x)^5/b^2 +--R +--R +--R (2) +--R 1 5 5 3 4 1 5 4 2 3 4 3 +--R - b e x + (- a b e + - b d)x + (a b e + a b d)x +--R 5 4 4 +--R + +--R 1 3 2 3 2 3 2 3 2 1 5 1 4 +--R (- a b e + - a b d)x + a b d x - -- a e + - a b d +--R 2 2 20 4 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 34 + +--S 35 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 5 3 2 1 3 4 2 2 3 1 3 3 2 2 +--R - b e x + (- a b e + - b d)x + (a b e + a b d)x + (- a e + - a b d)x +--R 5 4 4 2 2 +--R + +--R 3 +--R a d x +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +--S 36 of 1353 +m0:=a0-r0 +--R +--R +--R 1 5 1 4 +--R -- a e - - a b d +--R 20 4 +--R (4) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 36 + +--S 37 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 37 + +)clear all + +--S 38 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 38 + +--S 39 of 1353 +r0:=1/4*(a+b*x)^4/b +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - b x + a b x + - a b x + a b x + - a +--R 4 2 4 +--R (2) ----------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 39 + +--S 40 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 3 4 2 3 3 2 2 3 +--R (3) - b x + a b x + - a b x + a x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +--S 41 of 1353 +m0:=a0-r0 +--R +--R +--R 1 4 +--R - a +--R 4 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 41 + +--S 42 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 42 + +)clear all + +--S 43 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 43 + +--S 44 of 1353 +r0:=b*(b*d-a*e)^2*x/e^3-1/2*(b*d-a*e)*(a+b*x)^2/e^2+1/3*(a+b*x)^3/e-_ + (b*d-a*e)^3*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a e - 18a b d e + 18a b d e - 6b d )log(e x + d) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (9a b e - 3b d e )x + (18a b e - 18a b d e + 6b d e)x + 5a e +--R + +--R 2 2 +--R - 3a b d e +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a e - 18a b d e + 18a b d e - 6b d )log(e x + d) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (9a b e - 3b d e )x + (18a b e - 18a b d e + 6b d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 45 + +--S 46 of 1353 +m0:=a0-r0 +--R +--R +--R 3 2 +--R - 5a e + 3a b d +--R (4) --------------- +--R 2 +--R 6e +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 47 + +)clear all + +--S 48 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 48 + +--S 49 of 1353 +r0:=-b^2*(2*b*d-3*a*e)*x/e^3+1/2*b^3*x^2/e^2+(b*d-a*e)^3/(e^4*(d+e*x))+_ + 3*b*(b*d-a*e)^2*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b e - 12a b d e + 6b d e)x + 6a b d e - 12a b d e + 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 3 3 +--R b e x + (6a b e - 3b d e )x + (6a b d e - 4b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 6a b d e + 2b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b e - 12a b d e + 6b d e)x + 6a b d e - 12a b d e + 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 3 3 +--R b e x + (6a b e - 3b d e )x + (6a b d e - 4b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 6a b d e + 2b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 50 + +--S 51 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 52 + +)clear all + +--S 53 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 53 + +--S 54 of 1353 +r0:=b^3*x/e^3+1/2*(b*d-a*e)^3/(e^4*(d+e*x)^2)-3*b*(b*d-a*e)^2/(e^4*(d+e*x))-_ + 3*b^2*(b*d-a*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 2 3 2 2 2 3 3 +--R ((6a b e - 6b d e )x + (12a b d e - 12b d e)x + 6a b d e - 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 3 2 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4b d e x + (- 6a b e + 12a b d e - 4b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 9a b d e - 5b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 2 3 2 2 2 3 3 +--R ((6a b e - 6b d e )x + (12a b d e - 12b d e)x + 6a b d e - 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 3 2 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4b d e x + (- 6a b e + 12a b d e - 4b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 9a b d e - 5b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 55 + +--S 56 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 58 + +--S 59 of 1353 +r0:=1/3*(b*d-a*e)^3/(e^4*(d+e*x)^3)-3/2*b*(b*d-a*e)^2/(e^4*(d+e*x)^2)+_ + 3*b^2*(b*d-a*e)/(e^4*(d+e*x))+b^3*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(e x + d) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 18a b e + 18b d e )x + (- 9a b e - 18a b d e + 27b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e - 6a b d e + 11b d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(e x + d) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 18a b e + 18b d e )x + (- 9a b e - 18a b d e + 27b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e - 6a b d e + 11b d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 60 + +--S 61 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 62 + +)clear all + +--S 63 of 1353 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 m +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )(e x + d) +--R Type: Expression(Integer) +--E 63 + +--S 64 of 1353 +r0:=-(b*d-a*e)^5*(d+e*x)^(1+m)/(e^6*(1+m))+5*b*(b*d-a*e)^4*(d+e*x)^(2+m)/_ + (e^6*(2+m))-10*b^2*(b*d-a*e)^3*(d+e*x)^(3+m)/(e^6*(3+m))+10*b^3*_ + (b*d-a*e)^2*(d+e*x)^(4+m)/(e^6*(4+m))-5*b^4*(b*d-a*e)*(d+e*x)^(5+m)/_ + (e^6*(5+m))+b^5*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 5 5 5 4 5 3 5 2 5 5 m + 6 +--R (b m + 15b m + 85b m + 225b m + 274b m + 120b )(e x + d) +--R + +--R 4 5 5 4 5 4 4 5 3 +--R (5a b e - 5b d)m + (80a b e - 80b d)m + (475a b e - 475b d)m +--R + +--R 4 5 2 4 5 4 5 +--R (1300a b e - 1300b d)m + (1620a b e - 1620b d)m + 720a b e - 720b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 3 2 4 5 2 5 +--R (10a b e - 20a b d e + 10b d )m +--R + +--R 2 3 2 4 5 2 4 +--R (170a b e - 340a b d e + 170b d )m +--R + +--R 2 3 2 4 5 2 3 +--R (1070a b e - 2140a b d e + 1070b d )m +--R + +--R 2 3 2 4 5 2 2 +--R (3070a b e - 6140a b d e + 3070b d )m +--R + +--R 2 3 2 4 5 2 2 3 2 4 +--R (3960a b e - 7920a b d e + 3960b d )m + 1800a b e - 3600a b d e +--R + +--R 5 2 +--R 1800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e - 30a b d e + 30a b d e - 10b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (180a b e - 540a b d e + 540a b d e - 180b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (1210a b e - 3630a b d e + 3630a b d e - 1210b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (3720a b e - 11160a b d e + 11160a b d e - 3720b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 2 3 +--R (5080a b e - 15240a b d e + 15240a b d e - 5080b d )m + 2400a b e +--R + +--R 2 3 2 4 2 5 3 +--R - 7200a b d e + 7200a b d e - 2400b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e - 20a b d e + 30a b d e - 20a b d e + 5b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 4 +--R (95a b e - 380a b d e + 570a b d e - 380a b d e + 95b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (685a b e - 2740a b d e + 4110a b d e - 2740a b d e + 685b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 2305a b e - 9220a b d e + 13830a b d e - 9220a b d e +--R + +--R 5 4 +--R 2305b d +--R * +--R 2 +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 3510a b e - 14040a b d e + 21060a b d e - 14040a b d e +--R + +--R 5 4 +--R 3510b d +--R * +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R 1800a b e - 7200a b d e + 10800a b d e - 7200a b d e + 1800b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e - 5a b d e + 10a b d e - 10a b d e + 5a b d e - b d )m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 20a e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 5 5 +--R - 20b d +--R * +--R 4 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 155a e - 775a b d e + 1550a b d e - 1550a b d e + 775a b d e +--R + +--R 5 5 +--R - 155b d +--R * +--R 3 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R 580a e - 2900a b d e + 5800a b d e - 5800a b d e +--R + +--R 4 4 5 5 +--R 2900a b d e - 580b d +--R * +--R 2 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R 1044a e - 5220a b d e + 10440a b d e - 10440a b d e +--R + +--R 4 4 5 5 +--R 5220a b d e - 1044b d +--R * +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 720a e - 3600a b d e + 7200a b d e - 7200a b d e + 3600a b d e +--R + +--R 5 5 +--R - 720b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 5 6 4 5 6 3 5 6 2 5 6 5 6 6 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x +--R + +--R 4 6 5 5 5 4 6 5 5 4 +--R (5a b e + b d e )m + (80a b e + 10b d e )m +--R + +--R 4 6 5 5 3 4 6 5 5 2 +--R (475a b e + 35b d e )m + (1300a b e + 50b d e )m +--R + +--R 4 6 5 5 4 6 +--R (1620a b e + 24b d e )m + 720a b e +--R * +--R 5 +--R x +--R + +--R 2 3 6 4 5 5 2 3 6 4 5 5 2 4 4 +--R (10a b e + 5a b d e )m + (170a b e + 60a b d e - 5b d e )m +--R + +--R 2 3 6 4 5 5 2 4 3 +--R (1070a b e + 235a b d e - 30b d e )m +--R + +--R 2 3 6 4 5 5 2 4 2 +--R (3070a b e + 360a b d e - 55b d e )m +--R + +--R 2 3 6 4 5 5 2 4 2 3 6 +--R (3960a b e + 180a b d e - 30b d e )m + 1800a b e +--R * +--R 4 +--R x +--R + +--R 3 2 6 2 3 5 5 +--R (10a b e + 10a b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 4 +--R (180a b e + 140a b d e - 20a b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (1210a b e + 650a b d e - 180a b d e + 20b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 2 +--R (3720a b e + 1120a b d e - 400a b d e + 60b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 2 6 +--R (5080a b e + 600a b d e - 240a b d e + 40b d e )m + 2400a b e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 5 4 6 3 2 5 2 3 2 4 4 +--R (5a b e + 10a b d e )m + (95a b e + 160a b d e - 30a b d e )m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 3 +--R (685a b e + 890a b d e - 360a b d e + 60a b d e )m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 2305a b e + 1940a b d e - 1230a b d e + 420a b d e +--R + +--R 5 4 2 +--R - 60b d e +--R * +--R 2 +--R m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 +--R (3510a b e + 1200a b d e - 900a b d e + 360a b d e - 60b d e )m +--R + +--R 4 6 +--R 1800a b e +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 5 5 6 4 5 3 2 2 4 4 +--R (a e + 5a b d e )m + (20a e + 90a b d e - 20a b d e )m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 3 +--R (155a e + 595a b d e - 300a b d e + 60a b d e )m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 580a e + 1710a b d e - 1480a b d e + 660a b d e +--R + +--R 4 4 2 +--R - 120a b d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 1044a e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 4 2 5 5 +--R - 720a b d e + 120b d e +--R * +--R m +--R + +--R 5 6 +--R 720a e +--R * +--R x +--R + +--R 5 5 5 5 5 4 2 4 4 +--R a d e m + (20a d e - 5a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 3 +--R (155a d e - 90a b d e + 20a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 2 +--R (580a d e - 595a b d e + 300a b d e - 60a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R (1044a d e - 1710a b d e + 1480a b d e - 660a b d e + 120a b d e)m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 720a d e - 1800a b d e + 2400a b d e - 1800a b d e + 720a b d e +--R + +--R 5 6 +--R - 120b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Union(Expression(Integer),...) +--E 65 + +--S 66 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 5 5 6 4 5 6 3 5 6 2 5 6 5 6 6 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x +--R + +--R 4 6 5 5 5 4 6 5 5 4 +--R (5a b e + b d e )m + (80a b e + 10b d e )m +--R + +--R 4 6 5 5 3 4 6 5 5 2 +--R (475a b e + 35b d e )m + (1300a b e + 50b d e )m +--R + +--R 4 6 5 5 4 6 +--R (1620a b e + 24b d e )m + 720a b e +--R * +--R 5 +--R x +--R + +--R 2 3 6 4 5 5 2 3 6 4 5 5 2 4 4 +--R (10a b e + 5a b d e )m + (170a b e + 60a b d e - 5b d e )m +--R + +--R 2 3 6 4 5 5 2 4 3 +--R (1070a b e + 235a b d e - 30b d e )m +--R + +--R 2 3 6 4 5 5 2 4 2 +--R (3070a b e + 360a b d e - 55b d e )m +--R + +--R 2 3 6 4 5 5 2 4 2 3 6 +--R (3960a b e + 180a b d e - 30b d e )m + 1800a b e +--R * +--R 4 +--R x +--R + +--R 3 2 6 2 3 5 5 +--R (10a b e + 10a b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 4 +--R (180a b e + 140a b d e - 20a b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (1210a b e + 650a b d e - 180a b d e + 20b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 2 +--R (3720a b e + 1120a b d e - 400a b d e + 60b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 2 6 +--R (5080a b e + 600a b d e - 240a b d e + 40b d e )m + 2400a b e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 5 +--R (5a b e + 10a b d e )m +--R + +--R 4 6 3 2 5 2 3 2 4 4 +--R (95a b e + 160a b d e - 30a b d e )m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 3 +--R (685a b e + 890a b d e - 360a b d e + 60a b d e )m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 2305a b e + 1940a b d e - 1230a b d e + 420a b d e +--R + +--R 5 4 2 +--R - 60b d e +--R * +--R 2 +--R m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 3510a b e + 1200a b d e - 900a b d e + 360a b d e +--R + +--R 5 4 2 +--R - 60b d e +--R * +--R m +--R + +--R 4 6 +--R 1800a b e +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 5 5 6 4 5 3 2 2 4 4 +--R (a e + 5a b d e )m + (20a e + 90a b d e - 20a b d e )m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 3 +--R (155a e + 595a b d e - 300a b d e + 60a b d e )m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 580a e + 1710a b d e - 1480a b d e + 660a b d e +--R + +--R 4 4 2 +--R - 120a b d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 1044a e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 4 2 5 5 +--R - 720a b d e + 120b d e +--R * +--R m +--R + +--R 5 6 +--R 720a e +--R * +--R x +--R + +--R 5 5 5 5 5 4 2 4 4 +--R a d e m + (20a d e - 5a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 3 +--R (155a d e - 90a b d e + 20a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 2 +--R (580a d e - 595a b d e + 300a b d e - 60a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 +--R 1044a d e - 1710a b d e + 1480a b d e - 660a b d e +--R + +--R 4 5 +--R 120a b d e +--R * +--R m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 720a d e - 1800a b d e + 2400a b d e - 1800a b d e + 720a b d e +--R + +--R 5 6 +--R - 120b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 6 +--R (- b m - 15b m - 85b m - 225b m - 274b m - 120b )(e x + d) +--R + +--R 4 5 5 4 5 4 4 5 3 +--R (- 5a b e + 5b d)m + (- 80a b e + 80b d)m + (- 475a b e + 475b d)m +--R + +--R 4 5 2 4 5 4 +--R (- 1300a b e + 1300b d)m + (- 1620a b e + 1620b d)m - 720a b e +--R + +--R 5 +--R 720b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 3 2 4 5 2 5 +--R (- 10a b e + 20a b d e - 10b d )m +--R + +--R 2 3 2 4 5 2 4 +--R (- 170a b e + 340a b d e - 170b d )m +--R + +--R 2 3 2 4 5 2 3 +--R (- 1070a b e + 2140a b d e - 1070b d )m +--R + +--R 2 3 2 4 5 2 2 +--R (- 3070a b e + 6140a b d e - 3070b d )m +--R + +--R 2 3 2 4 5 2 2 3 2 4 +--R (- 3960a b e + 7920a b d e - 3960b d )m - 1800a b e + 3600a b d e +--R + +--R 5 2 +--R - 1800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 10a b e + 30a b d e - 30a b d e + 10b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (- 180a b e + 540a b d e - 540a b d e + 180b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (- 1210a b e + 3630a b d e - 3630a b d e + 1210b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 3720a b e + 11160a b d e - 11160a b d e + 3720b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 +--R (- 5080a b e + 15240a b d e - 15240a b d e + 5080b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 +--R - 2400a b e + 7200a b d e - 7200a b d e + 2400b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (- 5a b e + 20a b d e - 30a b d e + 20a b d e - 5b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 4 +--R (- 95a b e + 380a b d e - 570a b d e + 380a b d e - 95b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (- 685a b e + 2740a b d e - 4110a b d e + 2740a b d e - 685b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R - 2305a b e + 9220a b d e - 13830a b d e + 9220a b d e +--R + +--R 5 4 +--R - 2305b d +--R * +--R 2 +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R - 3510a b e + 14040a b d e - 21060a b d e + 14040a b d e +--R + +--R 5 4 +--R - 3510b d +--R * +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R - 1800a b e + 7200a b d e - 10800a b d e + 7200a b d e - 1800b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (- a e + 5a b d e - 10a b d e + 10a b d e - 5a b d e + b d )m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 20a e + 100a b d e - 200a b d e + 200a b d e - 100a b d e +--R + +--R 5 5 +--R 20b d +--R * +--R 4 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R - 155a e + 775a b d e - 1550a b d e + 1550a b d e +--R + +--R 4 4 5 5 +--R - 775a b d e + 155b d +--R * +--R 3 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R - 580a e + 2900a b d e - 5800a b d e + 5800a b d e +--R + +--R 4 4 5 5 +--R - 2900a b d e + 580b d +--R * +--R 2 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R - 1044a e + 5220a b d e - 10440a b d e + 10440a b d e +--R + +--R 4 4 5 5 +--R - 5220a b d e + 1044b d +--R * +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 720a e + 3600a b d e - 7200a b d e + 7200a b d e - 3600a b d e +--R + +--R 5 5 +--R 720b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 67 + +)clear all + +--S 68 of 1353 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 11 4 6 5 5 10 2 3 6 4 5 5 2 4 9 +--R b e x + (5a b e + 6b d e )x + (10a b e + 30a b d e + 15b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 8 +--R (10a b e + 60a b d e + 75a b d e + 20b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 7 +--R (5a b e + 60a b d e + 150a b d e + 100a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 6 +--R (a e + 30a b d e + 150a b d e + 200a b d e + 75a b d e + 6b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 5 +--R (6a d e + 75a b d e + 200a b d e + 150a b d e + 30a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 4 +--R (15a d e + 100a b d e + 150a b d e + 60a b d e + 5a b d )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 3 +--R (20a d e + 75a b d e + 60a b d e + 10a b d )x +--R + +--R 5 4 2 4 5 3 2 6 2 5 5 4 6 5 6 +--R (15a d e + 30a b d e + 10a b d )x + (6a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 68 + +--S 69 of 1353 +r0:=-1/7*(b*d-a*e)^5*(d+e*x)^7/e^6+5/8*b*(b*d-a*e)^4*(d+e*x)^8/e^6-_ + 10/9*b^2*(b*d-a*e)^3*(d+e*x)^9/e^6+b^3*(b*d-a*e)^2*(d+e*x)^10/e^6-_ + 5/11*b^4*(b*d-a*e)*(d+e*x)^11/e^6+1/12*b^5*(d+e*x)^12/e^6 +--R +--R +--R (2) +--R 1 5 12 12 5 4 12 6 5 11 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 2 3 12 4 11 3 5 2 10 10 +--R (a b e + 3a b d e + - b d e )x +--R 2 +--R + +--R 10 3 2 12 20 2 3 11 25 4 2 10 20 5 3 9 9 +--R (-- a b e + -- a b d e + -- a b d e + -- b d e )x +--R 9 3 3 9 +--R + +--R 5 4 12 15 3 2 11 75 2 3 2 10 25 4 3 9 15 5 4 8 8 +--R (- a b e + -- a b d e + -- a b d e + -- a b d e + -- b d e )x +--R 8 2 4 2 8 +--R + +--R 1 5 12 30 4 11 150 3 2 2 10 200 2 3 3 9 75 4 4 8 +--R - a e + -- a b d e + --- a b d e + --- a b d e + -- a b d e +--R 7 7 7 7 7 +--R + +--R 6 5 5 7 +--R - b d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 5 11 25 4 2 10 100 3 2 3 9 2 3 4 8 4 5 7 +--R a d e + -- a b d e + --- a b d e + 25a b d e + 5a b d e +--R 2 3 +--R + +--R 1 5 6 6 +--R - b d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 2 4 8 2 3 5 7 4 6 6 5 +--R (3a d e + 20a b d e + 30a b d e + 12a b d e + a b d e )x +--R + +--R 5 3 9 75 4 4 8 3 2 5 7 5 2 3 6 6 4 +--R (5a d e + -- a b d e + 15a b d e + - a b d e )x +--R 4 2 +--R + +--R 5 4 8 4 5 7 10 3 2 6 6 3 5 5 7 5 4 6 6 2 +--R (5a d e + 10a b d e + -- a b d e )x + (3a d e + - a b d e )x +--R 3 2 +--R + +--R 5 6 6 1 5 7 5 5 4 8 4 5 3 2 9 3 1 2 3 10 2 +--R a d e x + - a d e - -- a b d e + --- a b d e - -- a b d e +--R 7 56 126 84 +--R + +--R 1 4 11 1 5 12 +--R --- a b d e - ---- b d +--R 462 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 69 + +--S 70 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 6 12 5 4 6 6 5 5 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 2 3 6 4 5 3 5 2 4 10 +--R (a b e + 3a b d e + - b d e )x +--R 2 +--R + +--R 10 3 2 6 20 2 3 5 25 4 2 4 20 5 3 3 9 +--R (-- a b e + -- a b d e + -- a b d e + -- b d e )x +--R 9 3 3 9 +--R + +--R 5 4 6 15 3 2 5 75 2 3 2 4 25 4 3 3 15 5 4 2 8 +--R (- a b e + -- a b d e + -- a b d e + -- a b d e + -- b d e )x +--R 8 2 4 2 8 +--R + +--R 1 5 6 30 4 5 150 3 2 2 4 200 2 3 3 3 75 4 4 2 +--R - a e + -- a b d e + --- a b d e + --- a b d e + -- a b d e +--R 7 7 7 7 7 +--R + +--R 6 5 5 +--R - b d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 5 5 25 4 2 4 100 3 2 3 3 2 3 4 2 4 5 1 5 6 6 +--R (a d e + -- a b d e + --- a b d e + 25a b d e + 5a b d e + - b d )x +--R 2 3 6 +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 5 +--R (3a d e + 20a b d e + 30a b d e + 12a b d e + a b d )x +--R + +--R 5 3 3 75 4 4 2 3 2 5 5 2 3 6 4 +--R (5a d e + -- a b d e + 15a b d e + - a b d )x +--R 4 2 +--R + +--R 5 4 2 4 5 10 3 2 6 3 5 5 5 4 6 2 5 6 +--R (5a d e + 10a b d e + -- a b d )x + (3a d e + - a b d )x + a d x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 70 + +--S 71 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 5 7 5 5 4 8 4 5 3 2 9 3 1 2 3 10 2 1 4 11 +--R - - a d e + -- a b d e - --- a b d e + -- a b d e - --- a b d e +--R 7 56 126 84 462 +--R + +--R 1 5 12 +--R ---- b d +--R 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 71 + +--S 72 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 72 + +)clear all + +--S 73 of 1353 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 5 10 4 5 5 4 9 2 3 5 4 4 5 2 3 8 +--R b e x + (5a b e + 5b d e )x + (10a b e + 25a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 7 +--R (10a b e + 50a b d e + 50a b d e + 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 6 +--R (5a b e + 50a b d e + 100a b d e + 50a b d e + 5b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e + 25a b d e + 100a b d e + 100a b d e + 25a b d e + b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4 +--R (5a d e + 50a b d e + 100a b d e + 50a b d e + 5a b d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 3 +--R (10a d e + 50a b d e + 50a b d e + 10a b d )x +--R + +--R 5 3 2 4 4 3 2 5 2 5 4 4 5 5 5 +--R (10a d e + 25a b d e + 10a b d )x + (5a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 73 + +--S 74 of 1353 +r0:=1/6*(b*d-a*e)^5*(a+b*x)^6/b^6+5/7*e*(b*d-a*e)^4*(a+b*x)^7/b^6+_ + 5/4*e^2*(b*d-a*e)^3*(a+b*x)^8/b^6+10/9*e^3*(b*d-a*e)^2*(a+b*x)^9/b^6+_ + 1/2*e^4*(b*d-a*e)*(a+b*x)^10/b^6+1/11*e^5*(a+b*x)^11/b^6 +--R +--R +--R (2) +--R 1 11 5 11 1 10 5 1 11 4 10 +--R -- b e x + (- a b e + - b d e )x +--R 11 2 2 +--R + +--R 10 2 9 5 25 10 4 10 11 2 3 9 +--R (-- a b e + -- a b d e + -- b d e )x +--R 9 9 9 +--R + +--R 5 3 8 5 25 2 9 4 25 10 2 3 5 11 3 2 8 +--R (- a b e + -- a b d e + -- a b d e + - b d e )x +--R 4 4 4 4 +--R + +--R 5 4 7 5 50 3 8 4 100 2 9 2 3 50 10 3 2 5 11 4 7 +--R (- a b e + -- a b d e + --- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 7 +--R + +--R 1 5 6 5 25 4 7 4 50 3 8 2 3 50 2 9 3 2 25 10 4 +--R - a b e + -- a b d e + -- a b d e + -- a b d e + -- a b d e +--R 6 6 3 3 6 +--R + +--R 1 11 5 +--R - b d +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 6 4 4 7 2 3 3 8 3 2 2 9 4 10 5 5 +--R (a b d e + 10a b d e + 20a b d e + 10a b d e + a b d )x +--R + +--R 5 5 6 2 3 25 4 7 3 2 25 3 8 4 5 2 9 5 4 +--R (- a b d e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 10 5 6 3 2 25 4 7 4 10 3 8 5 3 5 5 6 4 5 4 7 5 2 +--R (-- a b d e + -- a b d e + -- a b d )x + (- a b d e + - a b d )x +--R 3 3 3 2 2 +--R + +--R 5 6 5 1 11 5 1 10 4 5 9 2 2 3 5 8 3 3 2 +--R a b d x - ---- a e + --- a b d e - --- a b d e + -- a b d e +--R 2772 252 252 84 +--R + +--R 5 7 4 4 1 6 5 5 +--R - -- a b d e + - a b d +--R 42 6 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 74 + +--S 75 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 5 11 1 4 5 1 5 4 10 +--R -- b e x + (- a b e + - b d e )x +--R 11 2 2 +--R + +--R 10 2 3 5 25 4 4 10 5 2 3 9 +--R (-- a b e + -- a b d e + -- b d e )x +--R 9 9 9 +--R + +--R 5 3 2 5 25 2 3 4 25 4 2 3 5 5 3 2 8 +--R (- a b e + -- a b d e + -- a b d e + - b d e )x +--R 4 4 4 4 +--R + +--R 5 4 5 50 3 2 4 100 2 3 2 3 50 4 3 2 5 5 4 7 +--R (- a b e + -- a b d e + --- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 7 +--R + +--R 1 5 5 25 4 4 50 3 2 2 3 50 2 3 3 2 25 4 4 1 5 5 6 +--R (- a e + -- a b d e + -- a b d e + -- a b d e + -- a b d e + - b d )x +--R 6 6 3 3 6 6 +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 5 +--R (a d e + 10a b d e + 20a b d e + 10a b d e + a b d )x +--R + +--R 5 5 2 3 25 4 3 2 25 3 2 4 5 2 3 5 4 +--R (- a d e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 10 5 3 2 25 4 4 10 3 2 5 3 5 5 4 5 4 5 2 5 5 +--R (-- a d e + -- a b d e + -- a b d )x + (- a d e + - a b d )x + a d x +--R 3 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 75 + +--S 76 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 11 5 1 10 4 5 9 2 2 3 5 8 3 3 2 5 7 4 4 +--R ---- a e - --- a b d e + --- a b d e - -- a b d e + -- a b d e +--R 2772 252 252 84 42 +--R + +--R 1 6 5 5 +--R - - a b d +--R 6 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 76 + +--S 77 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +)clear all + +--S 78 of 1353 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 78 + +--S 79 of 1353 +r0:=1/6*(b*d-a*e)^4*(a+b*x)^6/b^5+4/7*e*(b*d-a*e)^3*(a+b*x)^7/b^5+3/4*e^2*_ + (b*d-a*e)^2*(a+b*x)^8/b^5+4/9*e^3*(b*d-a*e)*(a+b*x)^9/b^5+1/10*e^4*_ + (a+b*x)^10/b^5 +--R +--R +--R (2) +--R 1 10 4 10 5 9 4 4 10 3 9 +--R -- b e x + (- a b e + - b d e )x +--R 10 9 9 +--R + +--R 5 2 8 4 5 9 3 3 10 2 2 8 +--R (- a b e + - a b d e + - b d e )x +--R 4 2 4 +--R + +--R 10 3 7 4 40 2 8 3 30 9 2 2 4 10 3 7 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 +--R + +--R 5 4 6 4 20 3 7 3 2 8 2 2 10 9 3 1 10 4 6 +--R (- a b e + -- a b d e + 10a b d e + -- a b d e + - b d )x +--R 6 3 3 6 +--R + +--R 1 5 5 4 4 6 3 3 7 2 2 2 8 3 9 4 5 +--R (- a b e + 4a b d e + 12a b d e + 8a b d e + a b d )x +--R 5 +--R + +--R 5 5 3 15 4 6 2 2 3 7 3 5 2 8 4 4 +--R (a b d e + -- a b d e + 10a b d e + - a b d )x +--R 2 2 +--R + +--R 5 5 2 2 20 4 6 3 10 3 7 4 3 5 5 3 5 4 6 4 2 +--R (2a b d e + -- a b d e + -- a b d )x + (2a b d e + - a b d )x +--R 3 3 2 +--R + +--R 5 5 4 1 10 4 1 9 3 1 8 2 2 2 2 7 3 3 1 6 4 4 +--R a b d x + ---- a e - --- a b d e + -- a b d e - -- a b d e + - a b d +--R 1260 126 28 21 6 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 79 + +--S 80 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 4 10 5 4 4 4 5 3 9 5 2 3 4 5 4 3 3 5 2 2 8 +--R -- b e x + (- a b e + - b d e )x + (- a b e + - a b d e + - b d e )x +--R 10 9 9 4 2 4 +--R + +--R 10 3 2 4 40 2 3 3 30 4 2 2 4 5 3 7 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 +--R + +--R 5 4 4 20 3 2 3 2 3 2 2 10 4 3 1 5 4 6 +--R (- a b e + -- a b d e + 10a b d e + -- a b d e + - b d )x +--R 6 3 3 6 +--R + +--R 1 5 4 4 3 3 2 2 2 2 3 3 4 4 5 +--R (- a e + 4a b d e + 12a b d e + 8a b d e + a b d )x +--R 5 +--R + +--R 5 3 15 4 2 2 3 2 3 5 2 3 4 4 +--R (a d e + -- a b d e + 10a b d e + - a b d )x +--R 2 2 +--R + +--R 5 2 2 20 4 3 10 3 2 4 3 5 3 5 4 4 2 5 4 +--R (2a d e + -- a b d e + -- a b d )x + (2a d e + - a b d )x + a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +--S 81 of 1353 +m0:=a0-r0 +--R +--R +--R 1 10 4 1 9 3 1 8 2 2 2 2 7 3 3 1 6 4 4 +--R - ---- a e + --- a b d e - -- a b d e + -- a b d e - - a b d +--R 1260 126 28 21 6 +--R (4) ----------------------------------------------------------------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 81 + +--S 82 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 82 + +)clear all + +--S 83 of 1353 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 83 + +--S 84 of 1353 +r0:=1/6*(b*d-a*e)^3*(a+b*x)^6/b^4+3/7*e*(b*d-a*e)^2*(a+b*x)^7/b^4+_ + 3/8*e^2*(b*d-a*e)*(a+b*x)^8/b^4+1/9*e^3*(a+b*x)^9/b^4 +--R +--R +--R (2) +--R 1 9 3 9 5 8 3 3 9 2 8 +--R - b e x + (- a b e + - b d e )x +--R 9 8 8 +--R + +--R 10 2 7 3 15 8 2 3 9 2 7 +--R (-- a b e + -- a b d e + - b d e)x +--R 7 7 7 +--R + +--R 5 3 6 3 2 7 2 5 8 2 1 9 3 6 +--R (- a b e + 5a b d e + - a b d e + - b d )x +--R 3 2 6 +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (a b e + 6a b d e + 6a b d e + a b d )x +--R + +--R 1 5 4 3 15 4 5 2 15 3 6 2 5 2 7 3 4 +--R (- a b e + -- a b d e + -- a b d e + - a b d )x +--R 4 4 2 2 +--R + +--R 5 4 2 4 5 2 10 3 6 3 3 3 5 4 2 5 4 5 3 2 5 4 3 +--R (a b d e + 5a b d e + -- a b d )x + (- a b d e + - a b d )x + a b d x +--R 3 2 2 +--R + +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R - --- a e + -- a b d e - -- a b d e + - a b d +--R 504 56 14 6 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 84 + +--S 85 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 3 9 5 4 3 3 5 2 8 10 2 3 3 15 4 2 3 5 2 7 +--R - b e x + (- a b e + - b d e )x + (-- a b e + -- a b d e + - b d e)x +--R 9 8 8 7 7 7 +--R + +--R 5 3 2 3 2 3 2 5 4 2 1 5 3 6 +--R (- a b e + 5a b d e + - a b d e + - b d )x +--R 3 2 6 +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 +--R (a b e + 6a b d e + 6a b d e + a b d )x +--R + +--R 1 5 3 15 4 2 15 3 2 2 5 2 3 3 4 +--R (- a e + -- a b d e + -- a b d e + - a b d )x +--R 4 4 2 2 +--R + +--R 5 2 4 2 10 3 2 3 3 3 5 2 5 4 3 2 5 3 +--R (a d e + 5a b d e + -- a b d )x + (- a d e + - a b d )x + a d x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +--S 86 of 1353 +m0:=a0-r0 +--R +--R +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R --- a e - -- a b d e + -- a b d e - - a b d +--R 504 56 14 6 +--R (4) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 86 + +--S 87 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +)clear all + +--S 88 of 1353 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 88 + +--S 89 of 1353 +r0:=1/6*(b*d-a*e)^2*(a+b*x)^6/b^3+2/7*e*(b*d-a*e)*(a+b*x)^7/b^3+_ + 1/8*e^2*(a+b*x)^8/b^3 +--R +--R +--R (2) +--R 1 8 2 8 5 7 2 2 8 7 5 2 6 2 5 7 1 8 2 6 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 8 7 7 3 3 6 +--R + +--R 3 5 2 2 6 7 2 5 5 4 4 2 3 5 5 2 6 2 4 +--R (2a b e + 4a b d e + a b d )x + (- a b e + 5a b d e + - a b d )x +--R 4 2 +--R + +--R 1 5 3 2 10 4 4 10 3 5 2 3 5 3 5 4 4 2 2 5 3 2 +--R (- a b e + -- a b d e + -- a b d )x + (a b d e + - a b d )x + a b d x +--R 3 3 3 2 +--R + +--R 1 8 2 1 7 1 6 2 2 +--R --- a e - -- a b d e + - a b d +--R 168 21 6 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 2 8 5 4 2 2 5 7 5 2 3 2 5 4 1 5 2 6 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 8 7 7 3 3 6 +--R + +--R 3 2 2 2 3 4 2 5 5 4 2 3 2 5 2 3 2 4 +--R (2a b e + 4a b d e + a b d )x + (- a b e + 5a b d e + - a b d )x +--R 4 2 +--R + +--R 1 5 2 10 4 10 3 2 2 3 5 5 4 2 2 5 2 +--R (- a e + -- a b d e + -- a b d )x + (a d e + - a b d )x + a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 90 + +--S 91 of 1353 +m0:=a0-r0 +--R +--R +--R 1 8 2 1 7 1 6 2 2 +--R - --- a e + -- a b d e - - a b d +--R 168 21 6 +--R (4) ---------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 91 + +--S 92 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +)clear all + +--S 93 of 1353 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R Type: Polynomial(Integer) +--E 93 + +--S 94 of 1353 +r0:=1/6*(b*d-a*e)*(a+b*x)^6/b^2+1/7*e*(a+b*x)^7/b^2 +--R +--R +--R (2) +--R 1 7 7 5 6 1 7 6 2 5 6 5 +--R - b e x + (- a b e + - b d)x + (2a b e + a b d)x +--R 7 6 6 +--R + +--R 5 3 4 5 2 5 4 5 4 3 10 3 4 3 1 5 2 5 4 3 2 +--R (- a b e + - a b d)x + (- a b e + -- a b d)x + (- a b e + - a b d)x +--R 2 2 3 3 2 2 +--R + +--R 5 2 1 7 1 6 +--R a b d x - -- a e + - a b d +--R 42 6 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 94 + +--S 95 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 7 5 4 1 5 6 2 3 4 5 5 3 2 5 2 3 4 +--R - b e x + (- a b e + - b d)x + (2a b e + a b d)x + (- a b e + - a b d)x +--R 7 6 6 2 2 +--R + +--R 5 4 10 3 2 3 1 5 5 4 2 5 +--R (- a b e + -- a b d)x + (- a e + - a b d)x + a d x +--R 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 95 + +--S 96 of 1353 +m0:=a0-r0 +--R +--R +--R 1 7 1 6 +--R -- a e - - a b d +--R 42 6 +--R (4) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 96 + +--S 97 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 97 + +)clear all + +--S 98 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Polynomial(Integer) +--E 98 + +--S 99 of 1353 +r0:=1/6*(a+b*x)^6/b +--R +--R +--R 1 6 6 5 5 5 2 4 4 10 3 3 3 5 4 2 2 5 1 6 +--R - b x + a b x + - a b x + -- a b x + - a b x + a b x + - a +--R 6 2 3 2 6 +--R (2) ---------------------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 99 + +--S 100 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 5 6 4 5 5 2 3 4 10 3 2 3 5 4 2 5 +--R (3) - b x + a b x + - a b x + -- a b x + - a b x + a x +--R 6 2 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +--S 101 of 1353 +m0:=a0-r0 +--R +--R +--R 1 6 +--R - a +--R 6 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 101 + +--S 102 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 102 + +)clear all + +--S 103 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 103 + +--S 104 of 1353 +r0:=b*(b*d-a*e)^4*x/e^5-1/2*(b*d-a*e)^3*(a+b*x)^2/e^4+1/3*(b*d-a*e)^2*_ + (a+b*x)^3/e^3-1/4*(b*d-a*e)*(a+b*x)^4/e^2+1/5*(a+b*x)^5/e-(b*d-a*e)^5*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 5 5 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b e x + (75a b e - 15b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b e - 100a b d e + 20b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b e - 300a b d e + 150a b d e - 30b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (300a b e - 600a b d e + 600a b d e - 300a b d e + 60b d e)x + 77a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 +--R - 145a b d e + 110a b d e - 30a b d e +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 5 5 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b e x + (75a b e - 15b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b e - 100a b d e + 20b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b e - 300a b d e + 150a b d e - 30b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (300a b e - 600a b d e + 600a b d e - 300a b d e + 60b d e)x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 105 + +--S 106 of 1353 +m0:=a0-r0 +--R +--R +--R 5 3 4 2 3 2 2 2 3 3 +--R - 77a e + 145a b d e - 110a b d e + 30a b d +--R (4) ---------------------------------------------- +--R 4 +--R 60e +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 107 + +)clear all + +--S 108 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 108 + +--S 109 of 1353 +r0:=-10*b^2*(b*d-a*e)^3*x/e^5+(b*d-a*e)^5/(e^6*(d+e*x))+5*b^3*(b*d-a*e)^2*_ + (d+e*x)^2/e^6-5/3*b^4*(b*d-a*e)*(d+e*x)^3/e^6+1/4*b^5*(d+e*x)^4/e^6+_ + 5*b*(b*d-a*e)^4*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b e x + (20a b e - 5b d e )x + (60a b e - 40a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b e - 180a b d e + 120a b d e - 30b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 5 5 4 4 +--R (120a b d e - 180a b d e + 80a b d e - 5b d e)x - 12a e + 60a b d e +--R + +--R 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 120a b d e + 180a b d e - 160a b d e + 55b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b e x + (20a b e - 5b d e )x + (60a b e - 40a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b e - 180a b d e + 120a b d e - 30b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (120a b d e - 240a b d e + 180a b d e - 48b d e)x - 12a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e - 120a b d e + 120a b d e - 60a b d e + 12b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 110 + +--S 111 of 1353 +m0:=a0-r0 +--R +--R +--R 2 3 2 2 4 3 5 4 +--R - 60a b d e + 100a b d e - 43b d +--R (4) ---------------------------------- +--R 6 +--R 12e +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 112 + +)clear all + +--S 113 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 113 + +--S 114 of 1353 +r0:=10*b^3*(b*d-a*e)^2*x/e^5+1/2*(b*d-a*e)^5/(e^6*(d+e*x)^2)-_ + 5*b*(b*d-a*e)^4/(e^6*(d+e*x))-5/2*b^4*(b*d-a*e)*(d+e*x)^2/e^6+_ + 1/3*b^5*(d+e*x)^3/e^6-10*b^2*(b*d-a*e)^3*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b d e - 360a b d e + 360a b d e - 120b d e)x + 60a b d e +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b e x + (15a b e - 5b d e )x + (60a b e - 60a b d e + 20b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (120a b d e - 150a b d e + 50b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b e + 120a b d e - 120a b d e + 60a b d e - 20b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b d e + 90a b d e - 150a b d e + 120a b d e - 40b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b d e - 360a b d e + 360a b d e - 120b d e)x + 60a b d e +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b e x + (15a b e - 5b d e )x + (60a b e - 60a b d e + 20b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (120a b d e - 165a b d e + 63b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b e + 120a b d e - 120a b d e + 30a b d e + 6b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b d e + 90a b d e - 150a b d e + 105a b d e - 27b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 115 + +--S 116 of 1353 +m0:=a0-r0 +--R +--R +--R 4 2 5 3 +--R - 15a b d e + 13b d +--R (4) -------------------- +--R 6 +--R 6e +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^4 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 of 1353 +r0:=-b^4*(4*b*d-5*a*e)*x/e^5+1/2*b^5*x^2/e^4+1/3*(b*d-a*e)^5/(e^6*(d+e*x)^3)-_ + 5/2*b*(b*d-a*e)^4/(e^6*(d+e*x)^2)+10*b^2*(b*d-a*e)^3/(e^6*(d+e*x))+_ + 10*b^3*(b*d-a*e)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e - 360a b d e + 180b d e )x +--R + +--R 2 3 2 3 4 3 2 5 4 2 3 3 2 4 4 +--R (180a b d e - 360a b d e + 180b d e)x + 60a b d e - 120a b d e +--R + +--R 5 5 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 4 4 5 2 3 3 +--R 3b e x + (30a b e - 15b d e )x + (90a b d e - 63b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 60a b e + 180a b d e - 90a b d e - 9b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 15a b e - 60a b d e + 270a b d e - 270a b d e + 81b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 5a b d e - 20a b d e + 110a b d e - 130a b d e + 47b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e - 360a b d e + 180b d e )x +--R + +--R 2 3 2 3 4 3 2 5 4 2 3 3 2 4 4 +--R (180a b d e - 360a b d e + 180b d e)x + 60a b d e - 120a b d e +--R + +--R 5 5 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 4 4 5 2 3 3 +--R 3b e x + (30a b e - 15b d e )x + (90a b d e - 63b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 60a b e + 180a b d e - 90a b d e - 9b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 15a b e - 60a b d e + 270a b d e - 270a b d e + 81b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 5a b d e - 20a b d e + 110a b d e - 130a b d e + 47b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 120 + +--S 121 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 122 + +)clear all + +--S 123 of 1353 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 123 + +--S 124 of 1353 +r0:=-(b*d-a*e)^7*(d+e*x)^(1+m)/(e^8*(1+m))+7*b*(b*d-a*e)^6*(d+e*x)^(2+m)/_ + (e^8*(2+m))-21*b^2*(b*d-a*e)^5*(d+e*x)^(3+m)/(e^8*(3+m))+35*b^3*_ + (b*d-a*e)^4*(d+e*x)^(4+m)/(e^8*(4+m))-35*b^4*(b*d-a*e)^3*(d+e*x)^(5+m)/_ + (e^8*(5+m))+21*b^5*(b*d-a*e)^2*(d+e*x)^(6+m)/(e^8*(6+m))-7*b^6*(b*d-_ + a*e)*(d+e*x)^(7+m)/(e^8*(7+m))+b^7*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R b m + 28b m + 322b m + 1960b m + 6769b m + 13132b m + 13068b m +--R + +--R 7 +--R 5040b +--R * +--R m + 8 +--R (e x + d) +--R + +--R 6 7 7 6 7 6 6 7 5 +--R (7a b e - 7b d)m + (203a b e - 203b d)m + (2401a b e - 2401b d)m +--R + +--R 6 7 4 6 7 3 +--R (14945a b e - 14945b d)m + (52528a b e - 52528b d)m +--R + +--R 6 7 2 6 7 6 +--R (103292a b e - 103292b d)m + (103824a b e - 103824b d)m + 40320a b e +--R + +--R 7 +--R - 40320b d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 5 2 6 7 2 7 +--R (21a b e - 42a b d e + 21b d )m +--R + +--R 2 5 2 6 7 2 6 +--R (630a b e - 1260a b d e + 630b d )m +--R + +--R 2 5 2 6 7 2 5 +--R (7686a b e - 15372a b d e + 7686b d )m +--R + +--R 2 5 2 6 7 2 4 +--R (49140a b e - 98280a b d e + 49140b d )m +--R + +--R 2 5 2 6 7 2 3 +--R (176589a b e - 353178a b d e + 176589b d )m +--R + +--R 2 5 2 6 7 2 2 +--R (353430a b e - 706860a b d e + 353430b d )m +--R + +--R 2 5 2 6 7 2 2 5 2 +--R (360024a b e - 720048a b d e + 360024b d )m + 141120a b e +--R + +--R 6 7 2 +--R - 282240a b d e + 141120b d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e - 105a b d e + 105a b d e - 35b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 6 +--R (1085a b e - 3255a b d e + 3255a b d e - 1085b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 5 +--R (13685a b e - 41055a b d e + 41055a b d e - 13685b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (90335a b e - 271005a b d e + 271005a b d e - 90335b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (334040a b e - 1002120a b d e + 1002120a b d e - 334040b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 2 +--R (684740a b e - 2054220a b d e + 2054220a b d e - 684740b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R (710640a b e - 2131920a b d e + 2131920a b d e - 710640b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R 282240a b e - 846720a b d e + 846720a b d e - 282240b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (35a b e - 140a b d e + 210a b d e - 140a b d e + 35b d )m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 6 +--R (1120a b e - 4480a b d e + 6720a b d e - 4480a b d e + 1120b d )m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 14630a b e - 58520a b d e + 87780a b d e - 58520a b d e +--R + +--R 7 4 +--R 14630b d +--R * +--R 5 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 100240a b e - 400960a b d e + 601440a b d e - 400960a b d e +--R + +--R 7 4 +--R 100240b d +--R * +--R 4 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 384755a b e - 1539020a b d e + 2308530a b d e - 1539020a b d e +--R + +--R 7 4 +--R 384755b d +--R * +--R 3 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 815920a b e - 3263680a b d e + 4895520a b d e - 3263680a b d e +--R + +--R 7 4 +--R 815920b d +--R * +--R 2 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 870660a b e - 3482640a b d e + 5223960a b d e - 3482640a b d e +--R + +--R 7 4 +--R 870660b d +--R * +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 352800a b e - 1411200a b d e + 2116800a b d e - 1411200a b d e +--R + +--R 7 4 +--R 352800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R 21a b e - 105a b d e + 210a b d e - 210a b d e + 105a b d e +--R + +--R 7 5 +--R - 21b d +--R * +--R 7 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 693a b e - 3465a b d e + 6930a b d e - 6930a b d e +--R + +--R 6 4 7 5 +--R 3465a b d e - 693b d +--R * +--R 6 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 9387a b e - 46935a b d e + 93870a b d e - 93870a b d e +--R + +--R 6 4 7 5 +--R 46935a b d e - 9387b d +--R * +--R 5 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 67095a b e - 335475a b d e + 670950a b d e - 670950a b d e +--R + +--R 6 4 7 5 +--R 335475a b d e - 67095b d +--R * +--R 4 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 270144a b e - 1350720a b d e + 2701440a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 2701440a b d e + 1350720a b d e - 270144b d +--R * +--R 3 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 602532a b e - 3012660a b d e + 6025320a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 6025320a b d e + 3012660a b d e - 602532b d +--R * +--R 2 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 673008a b e - 3365040a b d e + 6730080a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 6730080a b d e + 3365040a b d e - 673008b d +--R * +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 282240a b e - 1411200a b d e + 2822400a b d e - 2822400a b d e +--R + +--R 6 4 7 5 +--R 1411200a b d e - 282240b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 7a b e - 42a b d e + 105a b d e - 140a b d e + 105a b d e +--R + +--R 6 5 7 6 +--R - 42a b d e + 7b d +--R * +--R 7 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 238a b e - 1428a b d e + 3570a b d e - 4760a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 3570a b d e - 1428a b d e + 238b d +--R * +--R 6 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 3346a b e - 20076a b d e + 50190a b d e - 66920a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 50190a b d e - 20076a b d e + 3346b d +--R * +--R 5 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 25060a b e - 150360a b d e + 375900a b d e - 501200a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 375900a b d e - 150360a b d e + 25060b d +--R * +--R 4 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 107023a b e - 642138a b d e + 1605345a b d e - 2140460a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 1605345a b d e - 642138a b d e + 107023b d +--R * +--R 3 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R 256942a b e - 1541652a b d e + 3854130a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R - 5138840a b d e + 3854130a b d e - 1541652a b d e + 256942b d +--R * +--R 2 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R 312984a b e - 1877904a b d e + 4694760a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R - 6259680a b d e + 4694760a b d e - 1877904a b d e + 312984b d +--R * +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 141120a b e - 846720a b d e + 2116800a b d e - 2822400a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 2116800a b d e - 846720a b d e + 141120b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R a e - 7a b d e + 21a b d e - 35a b d e + 35a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 21a b d e + 7a b d e - b d +--R * +--R 7 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 35a e - 245a b d e + 735a b d e - 1225a b d e + 1225a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 735a b d e + 245a b d e - 35b d +--R * +--R 6 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 511a e - 3577a b d e + 10731a b d e - 17885a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 17885a b d e - 10731a b d e + 3577a b d e - 511b d +--R * +--R 5 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 4025a e - 28175a b d e + 84525a b d e - 140875a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 140875a b d e - 84525a b d e + 28175a b d e - 4025b d +--R * +--R 4 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 18424a e - 128968a b d e + 386904a b d e - 644840a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 644840a b d e - 386904a b d e + 128968a b d e - 18424b d +--R * +--R 3 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 48860a e - 342020a b d e + 1026060a b d e - 1710100a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 1710100a b d e - 1026060a b d e + 342020a b d e - 48860b d +--R * +--R 2 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 69264a e - 484848a b d e + 1454544a b d e - 2424240a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 2424240a b d e - 1454544a b d e + 484848a b d e - 69264b d +--R * +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 40320a e - 282240a b d e + 846720a b d e - 1411200a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 1411200a b d e - 846720a b d e + 282240a b d e - 40320b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 8 7 7 8 6 7 8 5 7 8 4 7 8 3 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m +--R + +--R 7 8 2 7 8 7 8 +--R 13132b e m + 13068b e m + 5040b e +--R * +--R 8 +--R x +--R + +--R 6 8 7 7 7 6 8 7 7 6 +--R (7a b e + b d e )m + (203a b e + 21b d e )m +--R + +--R 6 8 7 7 5 6 8 7 7 4 +--R (2401a b e + 175b d e )m + (14945a b e + 735b d e )m +--R + +--R 6 8 7 7 3 6 8 7 7 2 +--R (52528a b e + 1624b d e )m + (103292a b e + 1764b d e )m +--R + +--R 6 8 7 7 6 8 +--R (103824a b e + 720b d e )m + 40320a b e +--R * +--R 7 +--R x +--R + +--R 2 5 8 6 7 7 2 5 8 6 7 7 2 6 6 +--R (21a b e + 7a b d e )m + (630a b e + 161a b d e - 7b d e )m +--R + +--R 2 5 8 6 7 7 2 6 5 +--R (7686a b e + 1435a b d e - 105b d e )m +--R + +--R 2 5 8 6 7 7 2 6 4 +--R (49140a b e + 6335a b d e - 595b d e )m +--R + +--R 2 5 8 6 7 7 2 6 3 +--R (176589a b e + 14518a b d e - 1575b d e )m +--R + +--R 2 5 8 6 7 7 2 6 2 +--R (353430a b e + 16184a b d e - 1918b d e )m +--R + +--R 2 5 8 6 7 7 2 6 2 5 8 +--R (360024a b e + 6720a b d e - 840b d e )m + 141120a b e +--R * +--R 6 +--R x +--R + +--R 3 4 8 2 5 7 7 +--R (35a b e + 21a b d e )m +--R + +--R 3 4 8 2 5 7 6 2 6 6 +--R (1085a b e + 525a b d e - 42a b d e )m +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 5 +--R (13685a b e + 5061a b d e - 756a b d e + 42b d e )m +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 4 +--R (90335a b e + 23835a b d e - 4830a b d e + 420b d e )m +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 3 +--R 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282240a b d e + 141120a b d e - 40320a b d e + 5040b d e +--R * +--R m +--R + +--R 7 8 +--R 40320a e +--R * +--R x +--R + +--R 7 7 7 7 7 6 2 6 6 +--R a d e m + (35a d e - 7a b d e )m +--R + +--R 7 7 6 2 6 5 2 3 5 5 +--R (511a d e - 231a b d e + 42a b d e )m +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 4 +--R (4025a d e - 3115a b d e + 1260a b d e - 210a b d e )m +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 18424a d e - 21945a b d e + 14910a b d e - 5460a b d e +--R + +--R 3 4 5 3 +--R 840a b d e +--R * +--R 3 +--R m +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 48860a d e - 85078a b d e + 86940a b d e - 52710a b d e +--R + +--R 3 4 5 3 2 5 6 2 +--R 17640a b d e - 2520a b d e +--R * +--R 2 +--R m +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 69264a d e - 171864a b d e + 249648a b d e - 223860a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 +--R 122640a b d e - 37800a b d e + 5040a b d e +--R * +--R m +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 40320a d e - 141120a b d e + 282240a b d e - 352800a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 +--R 282240a b d e - 141120a b d e + 40320a b d e - 5040b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R - b m - 28b m - 322b m - 1960b m - 6769b m - 13132b m +--R + +--R 7 7 +--R - 13068b m - 5040b +--R * +--R m + 8 +--R (e x + d) +--R + +--R 6 7 7 6 7 6 +--R (- 7a b e + 7b d)m + (- 203a b e + 203b d)m +--R + +--R 6 7 5 6 7 4 +--R (- 2401a b e + 2401b d)m + (- 14945a b e + 14945b d)m +--R + +--R 6 7 3 6 7 2 +--R (- 52528a b e + 52528b d)m + (- 103292a b e + 103292b d)m +--R + +--R 6 7 6 7 +--R (- 103824a b e + 103824b d)m - 40320a b e + 40320b d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 5 2 6 7 2 7 +--R (- 21a b e + 42a b d e - 21b d )m +--R + +--R 2 5 2 6 7 2 6 +--R (- 630a b e + 1260a b d e - 630b d )m +--R + +--R 2 5 2 6 7 2 5 +--R (- 7686a b e + 15372a b d e - 7686b d )m +--R + +--R 2 5 2 6 7 2 4 +--R (- 49140a b e + 98280a b d e - 49140b d )m +--R + +--R 2 5 2 6 7 2 3 +--R (- 176589a b e + 353178a b d e - 176589b d )m +--R + +--R 2 5 2 6 7 2 2 +--R (- 353430a b e + 706860a b d e - 353430b d )m +--R + +--R 2 5 2 6 7 2 2 5 2 +--R (- 360024a b e + 720048a b d e - 360024b d )m - 141120a b e +--R + +--R 6 7 2 +--R 282240a b d e - 141120b d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (- 35a b e + 105a b d e - 105a b d e + 35b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 6 +--R (- 1085a b e + 3255a b d e - 3255a b d e + 1085b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 5 +--R (- 13685a b e + 41055a b d e - 41055a b d e + 13685b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 90335a b e + 271005a b d e - 271005a b d e + 90335b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (- 334040a b e + 1002120a b d e - 1002120a b d e + 334040b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 2 +--R (- 684740a b e + 2054220a b d e - 2054220a b d e + 684740b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R (- 710640a b e + 2131920a b d e - 2131920a b d e + 710640b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R - 282240a b e + 846720a b d e - 846720a b d e + 282240b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (- 35a b e + 140a b d e - 210a b d e + 140a b d e - 35b d )m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R - 1120a b e + 4480a b d e - 6720a b d e + 4480a b d e +--R + +--R 7 4 +--R - 1120b d +--R * +--R 6 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R - 14630a b e + 58520a b d e - 87780a b d e + 58520a b d e +--R + +--R 7 4 +--R - 14630b d +--R * +--R 5 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R - 100240a b e + 400960a b d e - 601440a b d e + 400960a b d e +--R + +--R 7 4 +--R - 100240b d +--R * +--R 4 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 +--R - 384755a b e + 1539020a b d e - 2308530a b d e +--R + +--R 6 3 7 4 +--R 1539020a b d e - 384755b d +--R * +--R 3 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 +--R - 815920a b e + 3263680a b d e - 4895520a b d e +--R + +--R 6 3 7 4 +--R 3263680a b d e - 815920b d +--R * +--R 2 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 +--R - 870660a b e + 3482640a b d e - 5223960a b d e +--R + +--R 6 3 7 4 +--R 3482640a b d e - 870660b d +--R * +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R - 352800a b e + 1411200a b d e - 2116800a b d e + 1411200a b d e +--R + +--R 7 4 +--R - 352800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R - 21a b e + 105a b d e - 210a b d e + 210a b d e - 105a b d e +--R + +--R 7 5 +--R 21b d +--R * +--R 7 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R - 693a b e + 3465a b d e - 6930a b d e + 6930a b d e +--R + +--R 6 4 7 5 +--R - 3465a b d e + 693b d +--R * +--R 6 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R - 9387a b e + 46935a b d e - 93870a b d e + 93870a b d e +--R + +--R 6 4 7 5 +--R - 46935a b d e + 9387b d +--R * +--R 5 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R - 67095a b e + 335475a b d e - 670950a b d e + 670950a b d e +--R + +--R 6 4 7 5 +--R - 335475a b d e + 67095b d +--R * +--R 4 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R - 270144a b e + 1350720a b d e - 2701440a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R 2701440a b d e - 1350720a b d e + 270144b d +--R * +--R 3 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R - 602532a b e + 3012660a b d e - 6025320a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R 6025320a b d e - 3012660a b d e + 602532b d +--R * +--R 2 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R - 673008a b e + 3365040a b d e - 6730080a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R 6730080a b d e - 3365040a b d e + 673008b d +--R * +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R - 282240a b e + 1411200a b d e - 2822400a b d e + 2822400a b d e +--R + +--R 6 4 7 5 +--R - 1411200a b d e + 282240b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 7a b e + 42a b d e - 105a b d e + 140a b d e - 105a b d e +--R + +--R 6 5 7 6 +--R 42a b d e - 7b d +--R * +--R 7 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 238a b e + 1428a b d e - 3570a b d e + 4760a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 3570a b d e + 1428a b d e - 238b d +--R * +--R 6 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 3346a b e + 20076a b d e - 50190a b d e + 66920a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 50190a b d e + 20076a b d e - 3346b d +--R * +--R 5 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 25060a b e + 150360a b d e - 375900a b d e + 501200a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 375900a b d e + 150360a b d e - 25060b d +--R * +--R 4 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R - 107023a b e + 642138a b d e - 1605345a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R 2140460a b d e - 1605345a b d e + 642138a b d e - 107023b d +--R * +--R 3 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R - 256942a b e + 1541652a b d e - 3854130a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R 5138840a b d e - 3854130a b d e + 1541652a b d e - 256942b d +--R * +--R 2 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R - 312984a b e + 1877904a b d e - 4694760a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R 6259680a b d e - 4694760a b d e + 1877904a b d e - 312984b d +--R * +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 141120a b e + 846720a b d e - 2116800a b d e + 2822400a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 2116800a b d e + 846720a b d e - 141120b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - a e + 7a b d e - 21a b d e + 35a b d e - 35a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 21a b d e - 7a b d e + b d +--R * +--R 7 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 35a e + 245a b d e - 735a b d e + 1225a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 1225a b d e + 735a b d e - 245a b d e + 35b d +--R * +--R 6 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 511a e + 3577a b d e - 10731a b d e + 17885a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 17885a b d e + 10731a b d e - 3577a b d e + 511b d +--R * +--R 5 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 4025a e + 28175a b d e - 84525a b d e + 140875a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 140875a b d e + 84525a b d e - 28175a b d e + 4025b d +--R * +--R 4 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 18424a e + 128968a b d e - 386904a b d e + 644840a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 644840a b d e + 386904a b d e - 128968a b d e + 18424b d +--R * +--R 3 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 48860a e + 342020a b d e - 1026060a b d e + 1710100a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 1710100a b d e + 1026060a b d e - 342020a b d e + 48860b d +--R * +--R 2 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 69264a e + 484848a b d e - 1454544a b d e + 2424240a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 2424240a b d e + 1454544a b d e - 484848a b d e + 69264b d +--R * +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 40320a e + 282240a b d e - 846720a b d e + 1411200a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 1411200a b d e + 846720a b d e - 282240a b d e + 40320b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 127 + +)clear all + +--S 128 of 1353 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 6 13 6 6 7 5 12 2 5 6 6 5 7 2 4 11 +--R b e x + (7a b e + 6b d e )x + (21a b e + 42a b d e + 15b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 10 +--R (35a b e + 126a b d e + 105a b d e + 20b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 9 +--R (35a b e + 210a b d e + 315a b d e + 140a b d e + 15b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 21a b e + 210a b d e + 525a b d e + 420a b d e + 105a b d e +--R + +--R 7 5 +--R 6b d e +--R * +--R 8 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 7a b e + 126a b d e + 525a b d e + 700a b d e + 315a b d e +--R + +--R 6 5 7 6 +--R 42a b d e + b d +--R * +--R 7 +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R a e + 42a b d e + 315a b d e + 700a b d e + 525a b d e +--R + +--R 2 5 5 6 6 +--R 126a b d e + 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 +--R 6a d e + 105a b d e + 420a b d e + 525a b d e + 210a b d e +--R + +--R 2 5 6 +--R 21a b d +--R * +--R 5 +--R x +--R + +--R 7 2 4 6 3 3 5 2 4 2 4 3 5 3 4 6 4 +--R (15a d e + 140a b d e + 315a b d e + 210a b d e + 35a b d )x +--R + +--R 7 3 3 6 4 2 5 2 5 4 3 6 3 +--R (20a d e + 105a b d e + 126a b d e + 35a b d )x +--R + +--R 7 4 2 6 5 5 2 6 2 7 5 6 6 7 6 +--R (15a d e + 42a b d e + 21a b d )x + (6a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 128 + +--S 129 of 1353 +r0:=1/8*(b*d-a*e)^6*(a+b*x)^8/b^7+2/3*e*(b*d-a*e)^5*(a+b*x)^9/b^7+_ + 3/2*e^2*(b*d-a*e)^4*(a+b*x)^10/b^7+20/11*e^3*(b*d-a*e)^3*(a+b*x)^11/b^7+_ + 5/4*e^4*(b*d-a*e)^2*(a+b*x)^12/b^7+6/13*e^5*(b*d-a*e)*(a+b*x)^13/b^7+_ + 1/14*e^6*(a+b*x)^14/b^7 +--R +--R +--R (2) +--R 1 14 6 14 7 13 6 6 14 5 13 +--R -- b e x + (-- a b e + -- b d e )x +--R 14 13 13 +--R + +--R 7 2 12 6 7 13 5 5 14 2 4 12 +--R (- a b e + - a b d e + - b d e )x +--R 4 2 4 +--R + +--R 35 3 11 6 126 2 12 5 105 13 2 4 20 14 3 3 11 +--R (-- a b e + --- a b d e + --- a b d e + -- b d e )x +--R 11 11 11 11 +--R + +--R 7 4 10 6 3 11 5 63 2 12 2 4 13 3 3 3 14 4 2 10 +--R (- a b e + 21a b d e + -- a b d e + 14a b d e + - b d e )x +--R 2 2 2 +--R + +--R 7 5 9 6 70 4 10 5 175 3 11 2 4 140 2 12 3 3 +--R - a b e + -- a b d e + --- a b d e + --- a b d e +--R 3 3 3 3 +--R + +--R 35 13 4 2 2 14 5 +--R -- a b d e + - b d e +--R 3 3 +--R * +--R 9 +--R x +--R + +--R 7 6 8 6 63 5 9 5 525 4 10 2 4 175 3 11 3 3 +--R - a b e + -- a b d e + --- a b d e + --- a b d e +--R 8 4 8 2 +--R + +--R 315 2 12 4 2 21 13 5 1 14 6 +--R --- a b d e + -- a b d e + - b d +--R 8 4 8 +--R * +--R 8 +--R x +--R + +--R 1 7 7 6 6 8 5 5 9 2 4 4 10 3 3 3 11 4 2 +--R - a b e + 6a b d e + 45a b d e + 100a b d e + 75a b d e +--R 7 +--R + +--R 2 12 5 13 6 +--R 18a b d e + a b d +--R * +--R 7 +--R x +--R + +--R 7 7 5 35 6 8 2 4 5 9 3 3 175 4 10 4 2 3 11 5 +--R a b d e + -- a b d e + 70a b d e + --- a b d e + 35a b d e +--R 2 2 +--R + +--R 7 2 12 6 +--R - a b d +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 7 2 4 6 8 3 3 5 9 4 2 4 10 5 3 11 6 5 +--R (3a b d e + 28a b d e + 63a b d e + 42a b d e + 7a b d )x +--R + +--R 7 7 3 3 105 6 8 4 2 63 5 9 5 35 4 10 6 4 +--R (5a b d e + --- a b d e + -- a b d e + -- a b d )x +--R 4 2 4 +--R + +--R 7 7 4 2 6 8 5 5 9 6 3 7 7 5 7 6 8 6 2 7 7 6 +--R (5a b d e + 14a b d e + 7a b d )x + (3a b d e + - a b d )x + a b d x +--R 2 +--R + +--R 1 14 6 1 13 5 1 12 2 2 4 1 11 3 3 3 +--R ----- a e - ---- a b d e + --- a b d e - -- a b d e +--R 24024 1716 264 66 +--R + +--R 1 10 4 4 2 1 9 5 5 1 8 6 6 +--R -- a b d e - -- a b d e + - a b d +--R 24 12 8 +--R / +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 129 + +--S 130 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 6 14 7 6 6 6 7 5 13 +--R -- b e x + (-- a b e + -- b d e )x +--R 14 13 13 +--R + +--R 7 2 5 6 7 6 5 5 7 2 4 12 +--R (- a b e + - a b d e + - b d e )x +--R 4 2 4 +--R + +--R 35 3 4 6 126 2 5 5 105 6 2 4 20 7 3 3 11 +--R (-- a b e + --- a b d e + --- a b d e + -- b d e )x +--R 11 11 11 11 +--R + +--R 7 4 3 6 3 4 5 63 2 5 2 4 6 3 3 3 7 4 2 10 +--R (- a b e + 21a b d e + -- a b d e + 14a b d e + - b d e )x +--R 2 2 2 +--R + +--R 7 5 2 6 70 4 3 5 175 3 4 2 4 140 2 5 3 3 35 6 4 2 +--R - a b e + -- a b d e + --- a b d e + --- a b d e + -- a b d e +--R 3 3 3 3 3 +--R + +--R 2 7 5 +--R - b d e +--R 3 +--R * +--R 9 +--R x +--R + +--R 7 6 6 63 5 2 5 525 4 3 2 4 175 3 4 3 3 315 2 5 4 2 +--R - a b e + -- a b d e + --- a b d e + --- a b d e + --- a b d e +--R 8 4 8 2 8 +--R + +--R 21 6 5 1 7 6 +--R -- a b d e + - b d +--R 4 8 +--R * +--R 8 +--R x +--R + +--R 1 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R - a e + 6a b d e + 45a b d e + 100a b d e + 75a b d e + 18a b d e +--R 7 +--R + +--R 6 6 +--R a b d +--R * +--R 7 +--R x +--R + +--R 7 5 35 6 2 4 5 2 3 3 175 4 3 4 2 3 4 5 7 2 5 6 6 +--R (a d e + -- a b d e + 70a b d e + --- a b d e + 35a b d e + - a b d )x +--R 2 2 2 +--R + +--R 7 2 4 6 3 3 5 2 4 2 4 3 5 3 4 6 5 +--R (3a d e + 28a b d e + 63a b d e + 42a b d e + 7a b d )x +--R + +--R 7 3 3 105 6 4 2 63 5 2 5 35 4 3 6 4 +--R (5a d e + --- a b d e + -- a b d e + -- a b d )x +--R 4 2 4 +--R + +--R 7 4 2 6 5 5 2 6 3 7 5 7 6 6 2 7 6 +--R (5a d e + 14a b d e + 7a b d )x + (3a d e + - a b d )x + a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +--S 131 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 14 6 1 13 5 1 12 2 2 4 1 11 3 3 3 +--R - ----- a e + ---- a b d e - --- a b d e + -- a b d e +--R 24024 1716 264 66 +--R + +--R 1 10 4 4 2 1 9 5 5 1 8 6 6 +--R - -- a b d e + -- a b d e - - a b d +--R 24 12 8 +--R / +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 131 + +--S 132 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 132 + +)clear all + +--S 133 of 1353 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 5 12 6 5 7 4 11 2 5 5 6 4 7 2 3 10 +--R b e x + (7a b e + 5b d e )x + (21a b e + 35a b d e + 10b d e )x +--R + +--R 3 4 5 2 5 4 6 2 3 7 3 2 9 +--R (35a b e + 105a b d e + 70a b d e + 10b d e )x +--R + +--R 4 3 5 3 4 4 2 5 2 3 6 3 2 7 4 8 +--R (35a b e + 175a b d e + 210a b d e + 70a b d e + 5b d e)x +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 7 5 7 +--R (21a b e + 175a b d e + 350a b d e + 210a b d e + 35a b d e + b d )x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 7a b e + 105a b d e + 350a b d e + 350a b d e + 105a b d e +--R + +--R 6 5 +--R 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 5 +--R (a e + 35a b d e + 210a b d e + 350a b d e + 175a b d e + 21a b d )x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 4 +--R (5a d e + 70a b d e + 210a b d e + 175a b d e + 35a b d )x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 3 +--R (10a d e + 70a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 2 6 4 5 2 5 2 7 4 6 5 7 5 +--R (10a d e + 35a b d e + 21a b d )x + (5a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 133 + +--S 134 of 1353 +r0:=1/8*(b*d-a*e)^5*(a+b*x)^8/b^6+5/9*e*(b*d-a*e)^4*(a+b*x)^9/b^6+e^2*_ + (b*d-a*e)^3*(a+b*x)^10/b^6+10/11*e^3*(b*d-a*e)^2*(a+b*x)^11/b^6+_ + 5/12*e^4*(b*d-a*e)*(a+b*x)^12/b^6+1/13*e^5*(a+b*x)^13/b^6 +--R +--R +--R (2) +--R 1 13 5 13 7 12 5 5 13 4 12 +--R -- b e x + (-- a b e + -- b d e )x +--R 13 12 12 +--R + +--R 21 2 11 5 35 12 4 10 13 2 3 11 +--R (-- a b e + -- a b d e + -- b d e )x +--R 11 11 11 +--R + +--R 7 3 10 5 21 2 11 4 12 2 3 13 3 2 10 +--R (- a b e + -- a b d e + 7a b d e + b d e )x +--R 2 2 +--R + +--R 35 4 9 5 175 3 10 4 70 2 11 2 3 70 12 3 2 5 13 4 9 +--R (-- a b e + --- a b d e + -- a b d e + -- a b d e + - b d e)x +--R 9 9 3 9 9 +--R + +--R 21 5 8 5 175 4 9 4 175 3 10 2 3 105 2 11 3 2 +--R -- a b e + --- a b d e + --- a b d e + --- a b d e +--R 8 8 4 4 +--R + +--R 35 12 4 1 13 5 +--R -- a b d e + - b d +--R 8 8 +--R * +--R 8 +--R x +--R + +--R 6 7 5 5 8 4 4 9 2 3 3 10 3 2 2 11 4 12 5 7 +--R (a b e + 15a b d e + 50a b d e + 50a b d e + 15a b d e + a b d )x +--R + +--R 1 7 6 5 35 6 7 4 5 8 2 3 175 4 9 3 2 175 3 10 4 +--R - a b e + -- a b d e + 35a b d e + --- a b d e + --- a b d e +--R 6 6 3 6 +--R + +--R 7 2 11 5 +--R - a b d +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 6 4 6 7 2 3 5 8 3 2 4 9 4 3 10 5 5 +--R (a b d e + 14a b d e + 42a b d e + 35a b d e + 7a b d )x +--R + +--R 5 7 6 2 3 35 6 7 3 2 105 5 8 4 35 4 9 5 4 +--R (- a b d e + -- a b d e + --- a b d e + -- a b d )x +--R 2 2 4 4 +--R + +--R 10 7 6 3 2 35 6 7 4 5 8 5 3 5 7 6 4 7 6 7 5 2 +--R (-- a b d e + -- a b d e + 7a b d )x + (- a b d e + - a b d )x +--R 3 3 2 2 +--R + +--R 7 6 5 1 13 5 1 12 4 1 11 2 2 3 1 10 3 3 2 +--R a b d x - ----- a e + --- a b d e - --- a b d e + -- a b d e +--R 10296 792 132 36 +--R + +--R 5 9 4 4 1 8 5 5 +--R - -- a b d e + - a b d +--R 72 8 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 134 + +--S 135 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 5 13 7 6 5 5 7 4 12 +--R -- b e x + (-- a b e + -- b d e )x +--R 13 12 12 +--R + +--R 21 2 5 5 35 6 4 10 7 2 3 11 +--R (-- a b e + -- a b d e + -- b d e )x +--R 11 11 11 +--R + +--R 7 3 4 5 21 2 5 4 6 2 3 7 3 2 10 +--R (- a b e + -- a b d e + 7a b d e + b d e )x +--R 2 2 +--R + +--R 35 4 3 5 175 3 4 4 70 2 5 2 3 70 6 3 2 5 7 4 9 +--R (-- a b e + --- a b d e + -- a b d e + -- a b d e + - b d e)x +--R 9 9 3 9 9 +--R + +--R 21 5 2 5 175 4 3 4 175 3 4 2 3 105 2 5 3 2 35 6 4 +--R -- a b e + --- a b d e + --- a b d e + --- a b d e + -- a b d e +--R 8 8 4 4 8 +--R + +--R 1 7 5 +--R - b d +--R 8 +--R * +--R 8 +--R x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 6 5 7 +--R (a b e + 15a b d e + 50a b d e + 50a b d e + 15a b d e + a b d )x +--R + +--R 1 7 5 35 6 4 5 2 2 3 175 4 3 3 2 175 3 4 4 +--R - a e + -- a b d e + 35a b d e + --- a b d e + --- a b d e +--R 6 6 3 6 +--R + +--R 7 2 5 5 +--R - a b d +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 5 +--R (a d e + 14a b d e + 42a b d e + 35a b d e + 7a b d )x +--R + +--R 5 7 2 3 35 6 3 2 105 5 2 4 35 4 3 5 4 +--R (- a d e + -- a b d e + --- a b d e + -- a b d )x +--R 2 2 4 4 +--R + +--R 10 7 3 2 35 6 4 5 2 5 3 5 7 4 7 6 5 2 7 5 +--R (-- a d e + -- a b d e + 7a b d )x + (- a d e + - a b d )x + a d x +--R 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +--S 136 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 13 5 1 12 4 1 11 2 2 3 1 10 3 3 2 5 9 4 4 +--R ----- a e - --- a b d e + --- a b d e - -- a b d e + -- a b d e +--R 10296 792 132 36 72 +--R + +--R 1 8 5 5 +--R - - a b d +--R 8 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 136 + +--S 137 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 137 + +)clear all + +--S 138 of 1353 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 4 11 6 4 7 3 10 2 5 4 6 3 7 2 2 9 +--R b e x + (7a b e + 4b d e )x + (21a b e + 28a b d e + 6b d e )x +--R + +--R 3 4 4 2 5 3 6 2 2 7 3 8 +--R (35a b e + 84a b d e + 42a b d e + 4b d e)x +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (35a b e + 140a b d e + 126a b d e + 28a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 6 +--R (21a b e + 140a b d e + 210a b d e + 84a b d e + 7a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 5 +--R (7a b e + 84a b d e + 210a b d e + 140a b d e + 21a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 4 +--R (a e + 28a b d e + 126a b d e + 140a b d e + 35a b d )x +--R + +--R 7 3 6 2 2 5 2 3 4 3 4 3 +--R (4a d e + 42a b d e + 84a b d e + 35a b d )x +--R + +--R 7 2 2 6 3 5 2 4 2 7 3 6 4 7 4 +--R (6a d e + 28a b d e + 21a b d )x + (4a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 138 + +--S 139 of 1353 +r0:=1/8*(b*d-a*e)^4*(a+b*x)^8/b^5+4/9*e*(b*d-a*e)^3*(a+b*x)^9/b^5+3/5*e^2*_ + (b*d-a*e)^2*(a+b*x)^10/b^5+4/11*e^3*(b*d-a*e)*(a+b*x)^11/b^5+1/12*e^4*_ + (a+b*x)^12/b^5 +--R +--R +--R (2) +--R 1 12 4 12 7 11 4 4 12 3 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 21 2 10 4 14 11 3 3 12 2 2 10 +--R (-- a b e + -- a b d e + - b d e )x +--R 10 5 5 +--R + +--R 35 3 9 4 28 2 10 3 14 11 2 2 4 12 3 9 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 9 3 3 9 +--R + +--R 35 4 8 4 35 3 9 3 63 2 10 2 2 7 11 3 1 12 4 8 +--R (-- a b e + -- a b d e + -- a b d e + - a b d e + - b d )x +--R 8 2 4 2 8 +--R + +--R 5 7 4 4 8 3 3 9 2 2 2 10 3 11 4 7 +--R (3a b e + 20a b d e + 30a b d e + 12a b d e + a b d )x +--R + +--R 7 6 6 4 5 7 3 4 8 2 2 70 3 9 3 7 2 10 4 6 +--R (- a b e + 14a b d e + 35a b d e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 1 7 5 4 28 6 6 3 126 5 7 2 2 4 8 3 3 9 4 5 +--R (- a b e + -- a b d e + --- a b d e + 28a b d e + 7a b d )x +--R 5 5 5 +--R + +--R 7 5 3 21 6 6 2 2 5 7 3 35 4 8 4 4 +--R (a b d e + -- a b d e + 21a b d e + -- a b d )x +--R 2 4 +--R + +--R 7 5 2 2 28 6 6 3 5 7 4 3 7 5 3 7 6 6 4 2 7 5 4 +--R (2a b d e + -- a b d e + 7a b d )x + (2a b d e + - a b d )x + a b d x +--R 3 2 +--R + +--R 1 12 4 1 11 3 1 10 2 2 2 1 9 3 3 1 8 4 4 +--R ---- a e - --- a b d e + -- a b d e - -- a b d e + - a b d +--R 3960 330 60 18 8 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 139 + +--S 140 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 4 12 7 6 4 4 7 3 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 21 2 5 4 14 6 3 3 7 2 2 10 +--R (-- a b e + -- a b d e + - b d e )x +--R 10 5 5 +--R + +--R 35 3 4 4 28 2 5 3 14 6 2 2 4 7 3 9 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 9 3 3 9 +--R + +--R 35 4 3 4 35 3 4 3 63 2 5 2 2 7 6 3 1 7 4 8 +--R (-- a b e + -- a b d e + -- a b d e + - a b d e + - b d )x +--R 8 2 4 2 8 +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 7 +--R (3a b e + 20a b d e + 30a b d e + 12a b d e + a b d )x +--R + +--R 7 6 4 5 2 3 4 3 2 2 70 3 4 3 7 2 5 4 6 +--R (- a b e + 14a b d e + 35a b d e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 1 7 4 28 6 3 126 5 2 2 2 4 3 3 3 4 4 5 +--R (- a e + -- a b d e + --- a b d e + 28a b d e + 7a b d )x +--R 5 5 5 +--R + +--R 7 3 21 6 2 2 5 2 3 35 4 3 4 4 +--R (a d e + -- a b d e + 21a b d e + -- a b d )x +--R 2 4 +--R + +--R 7 2 2 28 6 3 5 2 4 3 7 3 7 6 4 2 7 4 +--R (2a d e + -- a b d e + 7a b d )x + (2a d e + - a b d )x + a d x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +--S 141 of 1353 +m0:=a0-r0 +--R +--R +--R 1 12 4 1 11 3 1 10 2 2 2 1 9 3 3 1 8 4 4 +--R - ---- a e + --- a b d e - -- a b d e + -- a b d e - - a b d +--R 3960 330 60 18 8 +--R (4) ------------------------------------------------------------------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 141 + +--S 142 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 142 + +)clear all + +--S 143 of 1353 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 3 10 6 3 7 2 9 2 5 3 6 2 7 2 8 +--R b e x + (7a b e + 3b d e )x + (21a b e + 21a b d e + 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e + 63a b d e + 21a b d e + b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (35a b e + 105a b d e + 63a b d e + 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (21a b e + 105a b d e + 105a b d e + 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (7a b e + 63a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (a e + 21a b d e + 63a b d e + 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (3a d e + 21a b d e + 21a b d )x + (3a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 143 + +--S 144 of 1353 +r0:=1/8*(b*d-a*e)^3*(a+b*x)^8/b^4+1/3*e*(b*d-a*e)^2*(a+b*x)^9/b^4+3/10*e^2*_ + (b*d-a*e)*(a+b*x)^10/b^4+1/11*e^3*(a+b*x)^11/b^4 +--R +--R +--R (2) +--R 1 11 3 11 7 10 3 3 11 2 10 +--R -- b e x + (-- a b e + -- b d e )x +--R 11 10 10 +--R + +--R 7 2 9 3 7 10 2 1 11 2 9 +--R (- a b e + - a b d e + - b d e)x +--R 3 3 3 +--R + +--R 35 3 8 3 63 2 9 2 21 10 2 1 11 3 8 +--R (-- a b e + -- a b d e + -- a b d e + - b d )x +--R 8 8 8 8 +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 7 +--R (5a b e + 15a b d e + 9a b d e + a b d )x +--R + +--R 7 5 6 3 35 4 7 2 35 3 8 2 7 2 9 3 6 +--R (- a b e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 7 6 5 3 63 5 6 2 4 7 2 3 8 3 5 +--R (- a b e + -- a b d e + 21a b d e + 7a b d )x +--R 5 5 +--R + +--R 1 7 4 3 21 6 5 2 63 5 6 2 35 4 7 3 4 +--R (- a b e + -- a b d e + -- a b d e + -- a b d )x +--R 4 4 4 4 +--R + +--R 7 4 2 6 5 2 5 6 3 3 3 7 4 2 7 6 5 3 2 7 4 3 +--R (a b d e + 7a b d e + 7a b d )x + (- a b d e + - a b d )x + a b d x +--R 2 2 +--R + +--R 1 11 3 1 10 2 1 9 2 2 1 8 3 3 +--R - ---- a e + --- a b d e - -- a b d e + - a b d +--R 1320 120 24 8 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 144 + +--S 145 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 3 11 7 6 3 3 7 2 10 +--R -- b e x + (-- a b e + -- b d e )x +--R 11 10 10 +--R + +--R 7 2 5 3 7 6 2 1 7 2 9 +--R (- a b e + - a b d e + - b d e)x +--R 3 3 3 +--R + +--R 35 3 4 3 63 2 5 2 21 6 2 1 7 3 8 +--R (-- a b e + -- a b d e + -- a b d e + - b d )x +--R 8 8 8 8 +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 7 +--R (5a b e + 15a b d e + 9a b d e + a b d )x +--R + +--R 7 5 2 3 35 4 3 2 35 3 4 2 7 2 5 3 6 +--R (- a b e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 7 6 3 63 5 2 2 4 3 2 3 4 3 5 +--R (- a b e + -- a b d e + 21a b d e + 7a b d )x +--R 5 5 +--R + +--R 1 7 3 21 6 2 63 5 2 2 35 4 3 3 4 +--R (- a e + -- a b d e + -- a b d e + -- a b d )x +--R 4 4 4 4 +--R + +--R 7 2 6 2 5 2 3 3 3 7 2 7 6 3 2 7 3 +--R (a d e + 7a b d e + 7a b d )x + (- a d e + - a b d )x + a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 145 + +--S 146 of 1353 +m0:=a0-r0 +--R +--R +--R 1 11 3 1 10 2 1 9 2 2 1 8 3 3 +--R ---- a e - --- a b d e + -- a b d e - - a b d +--R 1320 120 24 8 +--R (4) -------------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 146 + +--S 147 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 147 + +)clear all + +--S 148 of 1353 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R b e x + (7a b e + 2b d e)x + (21a b e + 14a b d e + b d )x +--R + +--R 3 4 2 2 5 6 2 6 4 3 2 3 4 2 5 2 5 +--R (35a b e + 42a b d e + 7a b d )x + (35a b e + 70a b d e + 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 6 2 5 2 4 3 2 3 +--R (21a b e + 70a b d e + 35a b d )x + (7a b e + 42a b d e + 35a b d )x +--R + +--R 7 2 6 5 2 2 2 7 6 2 7 2 +--R (a e + 14a b d e + 21a b d )x + (2a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 148 + +--S 149 of 1353 +r0:=1/8*(b*d-a*e)^2*(a+b*x)^8/b^3+2/9*e*(b*d-a*e)*(a+b*x)^9/b^3+1/10*e^2*_ + (a+b*x)^10/b^3 +--R +--R +--R (2) +--R 1 10 2 10 7 9 2 2 10 9 +--R -- b e x + (- a b e + - b d e)x +--R 10 9 9 +--R + +--R 21 2 8 2 7 9 1 10 2 8 3 7 2 2 8 9 2 7 +--R (-- a b e + - a b d e + - b d )x + (5a b e + 6a b d e + a b d )x +--R 8 4 8 +--R + +--R 35 4 6 2 35 3 7 7 2 8 2 6 +--R (-- a b e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 21 5 5 2 4 6 3 7 2 5 +--R (-- a b e + 14a b d e + 7a b d )x +--R 5 +--R + +--R 7 6 4 2 21 5 5 35 4 6 2 4 +--R (- a b e + -- a b d e + -- a b d )x +--R 4 2 4 +--R + +--R 1 7 3 2 14 6 4 5 5 2 3 7 3 7 6 4 2 2 7 3 2 +--R (- a b e + -- a b d e + 7a b d )x + (a b d e + - a b d )x + a b d x +--R 3 3 2 +--R + +--R 1 10 2 1 9 1 8 2 2 +--R --- a e - -- a b d e + - a b d +--R 360 36 8 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 2 10 7 6 2 2 7 9 21 2 5 2 7 6 1 7 2 8 +--R -- b e x + (- a b e + - b d e)x + (-- a b e + - a b d e + - b d )x +--R 10 9 9 8 4 8 +--R + +--R 3 4 2 2 5 6 2 7 35 4 3 2 35 3 4 7 2 5 2 6 +--R (5a b e + 6a b d e + a b d )x + (-- a b e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 21 5 2 2 4 3 3 4 2 5 7 6 2 21 5 2 35 4 3 2 4 +--R (-- a b e + 14a b d e + 7a b d )x + (- a b e + -- a b d e + -- a b d )x +--R 5 4 2 4 +--R + +--R 1 7 2 14 6 5 2 2 3 7 7 6 2 2 7 2 +--R (- a e + -- a b d e + 7a b d )x + (a d e + - a b d )x + a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 150 + +--S 151 of 1353 +m0:=a0-r0 +--R +--R +--R 1 10 2 1 9 1 8 2 2 +--R - --- a e + -- a b d e - - a b d +--R 360 36 8 +--R (4) ----------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 151 + +--S 152 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 152 + +)clear all + +--S 153 of 1353 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 8 6 7 7 2 5 6 6 3 4 2 5 5 +--R b e x + (7a b e + b d)x + (21a b e + 7a b d)x + (35a b e + 21a b d)x +--R + +--R 4 3 3 4 4 5 2 4 3 3 6 5 2 2 +--R (35a b e + 35a b d)x + (21a b e + 35a b d)x + (7a b e + 21a b d)x +--R + +--R 7 6 7 +--R (a e + 7a b d)x + a d +--R Type: Polynomial(Integer) +--E 153 + +--S 154 of 1353 +r0:=1/8*(b*d-a*e)*(a+b*x)^8/b^2+1/9*e*(a+b*x)^9/b^2 +--R +--R +--R (2) +--R 1 9 9 7 8 1 9 8 2 7 8 7 +--R - b e x + (- a b e + - b d)x + (3a b e + a b d)x +--R 9 8 8 +--R + +--R 35 3 6 7 2 7 6 4 5 3 6 5 21 5 4 35 4 5 4 +--R (-- a b e + - a b d)x + (7a b e + 7a b d)x + (-- a b e + -- a b d)x +--R 6 2 4 4 +--R + +--R 7 6 3 5 4 3 1 7 2 7 6 3 2 7 2 1 9 1 8 +--R (- a b e + 7a b d)x + (- a b e + - a b d)x + a b d x - -- a e + - a b d +--R 3 2 2 72 8 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 154 + +--S 155 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 9 7 6 1 7 8 2 5 6 7 +--R - b e x + (- a b e + - b d)x + (3a b e + a b d)x +--R 9 8 8 +--R + +--R 35 3 4 7 2 5 6 4 3 3 4 5 21 5 2 35 4 3 4 +--R (-- a b e + - a b d)x + (7a b e + 7a b d)x + (-- a b e + -- a b d)x +--R 6 2 4 4 +--R + +--R 7 6 5 2 3 1 7 7 6 2 7 +--R (- a b e + 7a b d)x + (- a e + - a b d)x + a d x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 155 + +--S 156 of 1353 +m0:=a0-r0 +--R +--R +--R 1 9 1 8 +--R -- a e - - a b d +--R 72 8 +--R (4) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 156 + +--S 157 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 157 + +)clear all + +--S 158 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Polynomial(Integer) +--E 158 + +--S 159 of 1353 +r0:=1/8*(a+b*x)^8/b +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - b x + a b x + - a b x + 7a b x + -- a b x + 7a b x + - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R a b x + - a +--R 8 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 159 + +--S 160 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 8 6 7 7 2 5 6 3 4 5 35 4 3 4 5 2 3 7 6 2 7 +--R - b x + a b x + - a b x + 7a b x + -- a b x + 7a b x + - a b x + a x +--R 8 2 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 160 + +--S 161 of 1353 +m0:=a0-r0 +--R +--R +--R 1 8 +--R - a +--R 8 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 161 + +--S 162 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +)clear all + +--S 163 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 of 1353 +r0:=b*(b*d-a*e)^6*x/e^7-1/2*(b*d-a*e)^5*(a+b*x)^2/e^6+1/3*(b*d-a*e)^4*_ + (a+b*x)^3/e^5-1/4*(b*d-a*e)^3*(a+b*x)^4/e^4+1/5*(b*d-a*e)^2*(a+b*x)^5/e^3-_ + 1/6*(b*d-a*e)*(a+b*x)^6/e^2+1/7*(a+b*x)^7/e-(b*d-a*e)^7*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a e - 2940a b d e + 8820a b d e - 14700a b d e + 14700a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 8820a b d e + 2940a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b e x + (490a b e - 70b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (1764a b e - 588a b d e + 84b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (3675a b e - 2205a b d e + 735a b d e - 105b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (4900a b e - 4900a b d e + 2940a b d e - 980a b d e + 140b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4410a b e - 7350a b d e + 7350a b d e - 4410a b d e +--R + +--R 6 4 3 7 5 2 +--R 1470a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 2940a b e - 8820a b d e + 14700a b d e - 14700a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 8820a b d e - 2940a b d e + 420b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 669a e - 2163a b d e + 3339a b d e - 2765a b d e + 1190a b d e +--R + +--R 2 5 5 2 +--R - 210a b d e +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a e - 2940a b d e + 8820a b d e - 14700a b d e + 14700a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 8820a b d e + 2940a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b e x + (490a b e - 70b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (1764a b e - 588a b d e + 84b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (3675a b e - 2205a b d e + 735a b d e - 105b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (4900a b e - 4900a b d e + 2940a b d e - 980a b d e + 140b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4410a b e - 7350a b d e + 7350a b d e - 4410a b d e +--R + +--R 6 4 3 7 5 2 +--R 1470a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 2940a b e - 8820a b d e + 14700a b d e - 14700a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 8820a b d e - 2940a b d e + 420b d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Union(Expression(Integer),...) +--E 165 + +--S 166 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R - 669a e + 2163a b d e - 3339a b d e + 2765a b d e - 1190a b d e +--R + +--R 2 5 5 +--R 210a b d +--R / +--R 6 +--R 420e +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 167 + +)clear all + +--S 168 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 168 + +--S 169 of 1353 +r0:=-21*b^2*(b*d-a*e)^5*x/e^7+(b*d-a*e)^7/(e^8*(d+e*x))+35/2*b^3*_ + (b*d-a*e)^4*(d+e*x)^2/e^8-35/3*b^4*(b*d-a*e)^3*(d+e*x)^3/e^8+_ + 21/4*b^5*(b*d-a*e)^2*(d+e*x)^4/e^8-7/5*b^6*(b*d-a*e)*(d+e*x)^5/e^8+_ + 1/6*b^7*(d+e*x)^6/e^8+7*b*(b*d-a*e)^6*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b d e - 2520a b d e + 420b d e +--R * +--R x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a b d e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 6300a b d e - 2520a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (84a b e - 14b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (315a b e - 126a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (700a b e - 525a b d e + 210a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1050a b e - 1400a b d e + 1050a b d e - 420a b d e + 70b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b e - 3150a b d e + 4200a b d e - 3150a b d e +--R + +--R 6 4 3 7 5 2 +--R 1260a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 1260a b d e - 3150a b d e + 2800a b d e - 525a b d e +--R + +--R 6 5 2 7 6 +--R - 546a b d e + 231b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a e + 420a b d e - 1260a b d e + 3150a b d e - 5600a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 5775a b d e - 3066a b d e + 651b d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b d e - 2520a b d e + 420b d e +--R * +--R x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a b d e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 6300a b d e - 2520a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (84a b e - 14b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (315a b e - 126a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (700a b e - 525a b d e + 210a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1050a b e - 1400a b d e + 1050a b d e - 420a b d e + 70b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b e - 3150a b d e + 4200a b d e - 3150a b d e +--R + +--R 6 4 3 7 5 2 +--R 1260a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 1260a b d e - 4200a b d e + 6300a b d e - 5040a b d e +--R + +--R 6 5 2 7 6 +--R 2100a b d e - 360b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a e + 420a b d e - 1260a b d e + 2100a b d e - 2100a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 1260a b d e - 420a b d e + 60b d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 170 + +--S 171 of 1353 +m0:=a0-r0 +--R +--R +--R 4 3 2 4 3 4 3 3 2 5 4 2 6 5 7 6 +--R - 1050a b d e + 3500a b d e - 4515a b d e + 2646a b d e - 591b d +--R (4) -------------------------------------------------------------------- +--R 8 +--R 60e +--R Type: Expression(Integer) +--E 171 + +--S 172 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 172 + +)clear all + +--S 173 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 173 + +--S 174 of 1353 +r0:=35*b^3*(b*d-a*e)^4*x/e^7+1/2*(b*d-a*e)^7/(e^8*(d+e*x)^2)-_ + 7*b*(b*d-a*e)^6/(e^8*(d+e*x))-35/2*b^4*(b*d-a*e)^3*(d+e*x)^2/e^8+_ + 7*b^5*(b*d-a*e)^2*(d+e*x)^3/e^8-7/4*b^6*(b*d-a*e)*(d+e*x)^4/e^8+_ + 1/5*b^7*(d+e*x)^5/e^8-21*b^2*(b*d-a*e)^5*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 420a b e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 4 3 7 5 2 +--R 2100a b d e - 420b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 840a b d e - 4200a b d e + 8400a b d e - 8400a b d e +--R + +--R 6 5 2 7 6 +--R 4200a b d e - 840b d e +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 420a b d e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 6 7 7 +--R 2100a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 4b e x + (35a b e - 7b d e )x + (140a b e - 70a b d e + 14b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (350a b e - 350a b d e + 175a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (700a b e - 1400a b d e + 1400a b d e - 700a b d e + 140b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (1400a b d e - 3500a b d e + 3500a b d e - 1575a b d e + 259b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 140a b e + 840a b d e - 1400a b d e + 1400a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 1400a b d e + 1050a b d e - 322b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a e - 70a b d e + 630a b d e - 1750a b d e + 2800a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 2800a b d e + 1575a b d e - 371b d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 420a b e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 4 3 7 5 2 +--R 2100a b d e - 420b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 840a b d e - 4200a b d e + 8400a b d e - 8400a b d e +--R + +--R 6 5 2 7 6 +--R 4200a b d e - 840b d e +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 420a b d e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 6 7 7 +--R 2100a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 4b e x + (35a b e - 7b d e )x + (140a b e - 70a b d e + 14b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (350a b e - 350a b d e + 175a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (700a b e - 1400a b d e + 1400a b d e - 700a b d e + 140b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (1400a b d e - 3850a b d e + 4410a b d e - 2380a b d e + 500b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 140a b e + 840a b d e - 1400a b d e + 700a b d e + 420a b d e +--R + +--R 6 5 2 7 6 +--R - 560a b d e + 160b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a e - 70a b d e + 630a b d e - 1750a b d e + 2450a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1890a b d e + 770a b d e - 130b d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 175 + +--S 176 of 1353 +m0:=a0-r0 +--R +--R +--R 3 4 2 3 2 5 3 2 6 4 7 5 +--R - 350a b d e + 910a b d e - 805a b d e + 241b d +--R (4) -------------------------------------------------- +--R 8 +--R 20e +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 178 + +--S 179 of 1353 +r0:=-35*b^4*(b*d-a*e)^3*x/e^7+1/3*(b*d-a*e)^7/(e^8*(d+e*x)^3)-_ + 7/2*b*(b*d-a*e)^6/(e^8*(d+e*x)^2)+21*b^2*(b*d-a*e)^5/(e^8*(d+e*x))+_ + 21/2*b^5*(b*d-a*e)^2*(d+e*x)^2/e^8-7/3*b^6*(b*d-a*e)*(d+e*x)^3/e^8+_ + 1/4*b^7*(d+e*x)^4/e^8+35*b^3*(b*d-a*e)^4*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b e - 1680a b d e + 2520a b d e - 1680a b d e +--R + +--R 7 4 3 +--R 420b d e +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 5 2 +--R 1260b d e +--R * +--R 2 +--R x +--R + +--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 6 +--R 1260b d e +--R * +--R x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 3b e x + (28a b e - 7b d e )x + (126a b e - 84a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b e - 630a b d e + 420a b d e - 105b d e )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1260a b d e - 2520a b d e + 1820a b d e - 455b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 6 4 3 7 5 2 2 +--R (- 252a b e + 1260a b d e - 1260a b d e + 420a b d e - 105b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 42a b e - 252a b d e + 1890a b d e - 3780a b d e + 3780a b d e +--R + +--R 6 5 2 7 6 +--R - 2100a b d e + 525b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e - 14a b d e - 84a b d e + 770a b d e - 1820a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 2100a b d e - 1260a b d e + 315b d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b e - 1680a b d e + 2520a b d e - 1680a b d e +--R + +--R 7 4 3 +--R 420b d e +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 5 2 +--R 1260b d e +--R * +--R 2 +--R x +--R + +--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 6 +--R 1260b d e +--R * +--R x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 3b e x + (28a b e - 7b d e )x + (126a b e - 84a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b e - 630a b d e + 420a b d e - 105b d e )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1260a b d e - 2646a b d e + 2044a b d e - 556b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 252a b e + 1260a b d e - 1260a b d e - 378a b d e +--R + +--R 6 4 3 7 5 2 +--R 1092a b d e - 408b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 42a b e - 252a b d e + 1890a b d e - 3780a b d e + 3402a b d e +--R + +--R 6 5 2 7 6 +--R - 1428a b d e + 222b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e - 14a b d e - 84a b d e + 770a b d e - 1820a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 1974a b d e - 1036a b d e + 214b d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 180 + +--S 181 of 1353 +m0:=a0-r0 +--R +--R +--R 2 5 2 2 6 3 7 4 +--R - 126a b d e + 224a b d e - 101b d +--R (4) ------------------------------------ +--R 8 +--R 12e +--R Type: Expression(Integer) +--E 181 + +--S 182 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 182 + +)clear all + +--S 183 of 1353 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 183 + +--S 184 of 1353 +r0:=e*(b*d-a*e)^3*x/b^4+1/2*(b*d-a*e)^2*(d+e*x)^2/b^3+1/3*(b*d-a*e)*_ + (d+e*x)^3/b^2+1/4*(d+e*x)^4/b+(b*d-a*e)^4*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (- 4a b e + 16b d e )x + (6a b e - 24a b d e + 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 2 2 2 3 3 +--R (- 12a b e + 48a b d e - 72a b d e + 48b d e)x + 6a b d e - 16a b d e +--R + +--R 4 4 +--R 13b d +--R / +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (- 4a b e + 16b d e )x + (6a b e - 24a b d e + 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 +--R (- 12a b e + 48a b d e - 72a b d e + 48b d e)x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 185 + +--S 186 of 1353 +m0:=a0-r0 +--R +--R +--R 2 2 2 3 2 4 +--R - 6a d e + 16a b d e - 13b d +--R (4) ------------------------------ +--R 3 +--R 12b +--R Type: Expression(Integer) +--E 186 + +--S 187 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 187 + +)clear all + +--S 188 of 1353 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 188 + +--S 189 of 1353 +r0:=e*(b*d-a*e)^2*x/b^3+1/2*(b*d-a*e)*(d+e*x)^2/b^2+1/3*(d+e*x)^3/b+_ + (b*d-a*e)^3*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (- 6a e + 18a b d e - 18a b d e + 6b d )log(b x + a) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 2 2 +--R (- 3a b e + 9b d e )x + (6a b e - 18a b d e + 18b d e)x - 3a b d e +--R + +--R 3 3 +--R 5b d +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (- 6a e + 18a b d e - 18a b d e + 6b d )log(b x + a) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (- 3a b e + 9b d e )x + (6a b e - 18a b d e + 18b d e)x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 190 + +--S 191 of 1353 +m0:=a0-r0 +--R +--R +--R 2 3 +--R 3a d e - 5b d +--R (4) -------------- +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 1353 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------ +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 193 + +--S 194 of 1353 +r0:=e*(b*d-a*e)*x/b^2+1/2*(d+e*x)^2/b+(b*d-a*e)^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(b x + a) + b e x + (- 2a b e + 4b d e)x +--R + +--R 2 2 +--R b d +--R / +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(b x + a) + b e x + (- 2a b e + 4b d e)x +--R ----------------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 195 + +--S 196 of 1353 +m0:=a0-r0 +--R +--R +--R 2 +--R d +--R (4) - -- +--R 2b +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 197 + +)clear all + +--S 198 of 1353 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R e x + d +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 198 + +--S 199 of 1353 +r0:=e*x/b+(b*d-a*e)*log(a+b*x)/b^2 +--R +--R +--R (- a e + b d)log(b x + a) + b e x +--R (2) --------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (- a e + b d)log(b x + a) + b e x +--R (3) --------------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 200 + +--S 201 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 202 + +)clear all + +--S 203 of 1353 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 1 +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 203 + +--S 204 of 1353 +r0:=log(a+b*x)/b +--R +--R +--R log(b x + a) +--R (2) ------------ +--R b +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1353 +a0:=integrate(t0,x) +--R +--R +--R log(b x + a) +--R (3) ------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 205 + +--S 206 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 1353 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--R b e x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 208 + +--S 209 of 1353 +r0:=log(a+b*x)/(b*d-a*e)-log(d+e*x)/(b*d-a*e) +--R +--R +--R log(e x + d) - log(b x + a) +--R (2) --------------------------- +--R a e - b d +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1353 +a0:=integrate(t0,x) +--R +--R +--R log(e x + d) - log(b x + a) +--R (3) --------------------------- +--R a e - b d +--R Type: Union(Expression(Integer),...) +--E 210 + +--S 211 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 212 + +)clear all + +--S 213 of 1353 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (a e + 2b d e)x + (2a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 213 + +--S 214 of 1353 +r0:=1/((b*d-a*e)*(d+e*x))+b*log(a+b*x)/(b*d-a*e)^2-b*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (- b e x - b d)log(e x + d) + (b e x + b d)log(b x + a) - a e + b d +--R (2) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a e - 2a b d e + b d e)x + a d e - 2a b d e + b d +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (- b e x - b d)log(e x + d) + (b e x + b d)log(b x + a) - a e + b d +--R (3) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a e - 2a b d e + b d e)x + a d e - 2a b d e + b d +--R Type: Union(Expression(Integer),...) +--E 215 + +--S 216 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 217 + +)clear all + +--S 218 of 1353 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 218 + +--S 219 of 1353 +r0:=1/2/((b*d-a*e)*(d+e*x)^2)+b/((b*d-a*e)^2*(d+e*x))+b^2*log(a+b*x)/_ + (b*d-a*e)^3-b^2*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4b d e x - 2b d )log(b x + a) + (2a b e - 2b d e)x - a e +--R + +--R 2 2 +--R 4a b d e - 3b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a d e - 12a b d e + 12a b d e - 4b d e)x + 2a d e - 6a b d e +--R + +--R 2 4 3 5 +--R 6a b d e - 2b d +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4b d e x - 2b d )log(b x + a) + (2a b e - 2b d e)x - a e +--R + +--R 2 2 +--R 4a b d e - 3b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a d e - 12a b d e + 12a b d e - 4b d e)x + 2a d e - 6a b d e +--R + +--R 2 4 3 5 +--R 6a b d e - 2b d +--R Type: Union(Expression(Integer),...) +--E 220 + +--S 221 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 1353 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 223 + +--S 224 of 1353 +r0:=1/3/((b*d-a*e)*(d+e*x)^3)+1/2*b/((b*d-a*e)^2*(d+e*x)^2)+_ + b^2/((b*d-a*e)^3*(d+e*x))+b^3*log(a+b*x)/(b*d-a*e)^4-_ + b^3*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 3 3 3 2 2 3 2 3 3 +--R (- 6b e x - 18b d e x - 18b d e x - 6b d )log(e x + d) +--R + +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (3a b e - 18a b d e + 15b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 18a b d e + 11b d +--R / +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4 3 4 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e)x + 6a d e +--R + +--R 3 4 3 2 2 5 2 3 6 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 3 2 2 3 2 3 3 +--R (- 6b e x - 18b d e x - 18b d e x - 6b d )log(e x + d) +--R + +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (3a b e - 18a b d e + 15b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 18a b d e + 11b d +--R / +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4 3 4 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e)x + 6a d e +--R + +--R 3 4 3 2 2 5 2 3 6 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d +--R Type: Union(Expression(Integer),...) +--E 225 + +--S 226 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 227 + +)clear all + +--S 228 of 1353 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 228 + +--S 229 of 1353 +r0:=e^3*(4*b*d-3*a*e)*x/b^4+1/2*e^4*x^2/b^3-1/2*(b*d-a*e)^4/(b^5*(a+b*x)^2)-_ + 4*e*(b*d-a*e)^3/(b^5*(a+b*x))+6*e^2*(b*d-a*e)^2*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (24a b e - 48a b d e + 24a b d e )x + 12a e - 24a b d e +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R b e x + (- 4a b e + 8b d e )x + (- 11a b e + 16a b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (2a b e - 16a b d e + 24a b d e - 8b d e)x + 7a e - 20a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 4a b d e - b d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (24a b e - 48a b d e + 24a b d e )x + 12a e - 24a b d e +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R b e x + (- 4a b e + 8b d e )x + (- 11a b e + 16a b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (2a b e - 16a b d e + 24a b d e - 8b d e)x + 7a e - 20a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 4a b d e - b d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 230 + +--S 231 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 232 + +)clear all + +--S 233 of 1353 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 233 + +--S 234 of 1353 +r0:=e^3*x/b^3-1/2*(b*d-a*e)^3/(b^4*(a+b*x)^2)-3*e*(b*d-a*e)^2/(b^4*(a+b*x))+_ + 3*e^2*(b*d-a*e)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b e + 6b d e )x + (- 12a b e + 12a b d e )x - 6a e +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4a b e x + (- 4a b e + 12a b d e - 6b d e)x - 5a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 3a b d e - b d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b e + 6b d e )x + (- 12a b e + 12a b d e )x - 6a e +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4a b e x + (- 4a b e + 12a b d e - 6b d e)x - 5a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 3a b d e - b d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 235 + +--S 236 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 1353 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 238 + +--S 239 of 1353 +r0:=-1/2*(b*d-a*e)^2/(b^3*(a+b*x)^2)-2*e*(b*d-a*e)/(b^3*(a+b*x))+_ + e^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(b x + a) + (4a b e - 4b d e)x + 3a e +--R + +--R 2 2 +--R - 2a b d e - b d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(b x + a) + (4a b e - 4b d e)x + 3a e +--R + +--R 2 2 +--R - 2a b d e - b d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 240 + +--S 241 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 242 + +)clear all + +--S 243 of 1353 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 243 + +--S 244 of 1353 +r0:=-1/2*(d+e*x)^2/((b*d-a*e)*(a+b*x)^2) +--R +--R +--R 1 2 2 1 2 +--R - e x + d e x + - d +--R 2 2 +--R (2) -------------------------------------------------- +--R 2 3 2 2 2 3 2 +--R (a b e - b d)x + (2a b e - 2a b d)x + a e - a b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 244 + +--S 245 of 1353 +a0:=integrate(t0,x) +--R +--R +--R - 2b e x - a e - b d +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 245 + +--S 246 of 1353 +m0:=a0-r0 +--R +--R +--R 2 +--R e +--R (4) - ------------- +--R 2 3 +--R 2a b e - 2b d +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 247 + +)clear all + +--S 248 of 1353 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 1 +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 248 + +--S 249 of 1353 +r0:=(-1/2)/(b*(a+b*x)^2) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ------------------- +--R 3 2 2 2 +--R b x + 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 249 + +--S 250 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------------------- +--R 3 2 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 250 + +--S 251 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 1353 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 253 + +--S 254 of 1353 +r0:=(-1/2)/((b*d-a*e)*(a+b*x)^2)+e/((b*d-a*e)^2*(a+b*x))+_ + e^2*log(a+b*x)/(b*d-a*e)^3-e^2*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4a b e x - 2a e )log(b x + a) + (2a b e - 2b d e)x + 3a e +--R + +--R 2 2 +--R - 4a b d e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a e - 6a b d e +--R + +--R 3 2 2 2 3 3 +--R 6a b d e - 2a b d +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4a b e x - 2a e )log(b x + a) + (2a b e - 2b d e)x + 3a e +--R + +--R 2 2 +--R - 4a b d e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a e - 6a b d e +--R + +--R 3 2 2 2 3 3 +--R 6a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 255 + +--S 256 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 257 + +)clear all + +--S 258 of 1353 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 258 + +--S 259 of 1353 +r0:=-1/2*b/((b*d-a*e)^2*(a+b*x)^2)+2*b*e/((b*d-a*e)^3*(a+b*x))+_ + e^2/((b*d-a*e)^3*(d+e*x))+3*b*e^2*log(a+b*x)/(b*d-a*e)^4-_ + 3*b*e^2*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R - 6b e x + (- 12a b e - 6b d e )x + (- 6a b e - 12a b d e )x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 6b e x + (12a b e + 6b d e )x + (6a b e + 12a b d e )x +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (- 9a b e + 6a b d e + 3b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 6a b d e - b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R - 6b e x + (- 12a b e - 6b d e )x + (- 6a b e - 12a b d e )x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 6b e x + (12a b e + 6b d e )x + (6a b e + 12a b d e )x +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (- 9a b e + 6a b d e + 3b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 6a b d e - b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 260 + +--S 261 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 262 + +)clear all + +--S 263 of 1353 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 263 + +--S 264 of 1353 +r0:=-1/2*b^2/((b*d-a*e)^3*(a+b*x)^2)+3*b^2*e/((b*d-a*e)^4*(a+b*x))+_ + 1/2*e^2/((b*d-a*e)^3*(d+e*x)^2)+3*b*e^2/((b*d-a*e)^4*(d+e*x))+_ + 6*b^2*e^2*log(a+b*x)/(b*d-a*e)^5-6*b^2*e^2*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 12b e x + (24a b e + 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b e + 48a b d e + 12b d e )x + (24a b d e + 24a b d e )x +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b e x + (- 24a b e - 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b e - 48a b d e - 12b d e )x + (- 24a b d e - 24a b d e )x +--R + +--R 2 2 2 2 +--R - 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b e - 12b d e )x + (18a b e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b e + 24a b d e - 24a b d e - 4b d e)x - a e + 8a b d e +--R + +--R 3 3 4 4 +--R - 8a b d e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 12b e x + (24a b e + 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b e + 48a b d e + 12b d e )x + (24a b d e + 24a b d e )x +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b e x + (- 24a b e - 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b e - 48a b d e - 12b d e )x + (- 24a b d e - 24a b d e )x +--R + +--R 2 2 2 2 +--R - 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b e - 12b d e )x + (18a b e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b e + 24a b d e - 24a b d e - 4b d e)x - a e + 8a b d e +--R + +--R 3 3 4 4 +--R - 8a b d e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 265 + +--S 266 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 1353 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 268 + +--S 269 of 1353 +r0:=-1/2*b^3/((b*d-a*e)^4*(a+b*x)^2)+4*b^3*e/((b*d-a*e)^5*(a+b*x))+_ + 1/3*e^2/((b*d-a*e)^3*(d+e*x)^3)+3/2*b*e^2/((b*d-a*e)^4*(d+e*x)^2)+_ + 6*b^2*e^2/((b*d-a*e)^5*(d+e*x))+10*b^3*e^2*log(a+b*x)/(b*d-a*e)^6-_ + 10*b^3*e^2*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 120a b e - 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 60a b e - 360a b d e - 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (- 180a b d e - 360a b d e - 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (- 180a b d e - 120a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (120a b e + 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e + 360a b d e + 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e + 360a b d e + 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (180a b d e + 120a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 90a b e - 60a b d e + 150b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 20a b e - 210a b d e + 120a b d e + 110b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (5a b e - 60a b d e - 120a b d e + 160a b d e + 15b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 15a b d e - 60a b d e + 20a b d e + 30a b d e - 3b d +--R / +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 4 8 6 3 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 12a b e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 198a b d e - 96a b d e + 18b d e +--R * +--R 4 +--R x +--R + +--R 8 9 6 2 2 7 5 3 3 6 4 4 4 5 3 5 5 4 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 2 6 6 3 7 7 2 8 8 +--R 60a b d e - 72a b d e + 18b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4 +--R 18a d e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 5 6 3 2 6 7 2 8 9 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 2 7 7 3 6 6 2 4 5 5 3 5 4 4 4 6 3 +--R 18a d e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 3 5 7 2 2 6 8 7 9 +--R 72a b d e - 54a b d e + 12a b d +--R * +--R x +--R + +--R 8 3 6 7 4 5 6 2 5 4 5 3 6 3 4 4 7 2 3 5 8 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 2 6 9 +--R 6a b d +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 120a b e - 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 60a b e - 360a b d e - 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (- 180a b d e - 360a b d e - 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (- 180a b d e - 120a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (120a b e + 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e + 360a b d e + 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e + 360a b d e + 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (180a b d e + 120a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 90a b e - 60a b d e + 150b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 20a b e - 210a b d e + 120a b d e + 110b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (5a b e - 60a b d e - 120a b d e + 160a b d e + 15b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 15a b d e - 60a b d e + 20a b d e + 30a b d e - 3b d +--R / +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 4 8 6 3 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 12a b e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 198a b d e - 96a b d e + 18b d e +--R * +--R 4 +--R x +--R + +--R 8 9 6 2 2 7 5 3 3 6 4 4 4 5 3 5 5 4 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 2 6 6 3 7 7 2 8 8 +--R 60a b d e - 72a b d e + 18b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4 +--R 18a d e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 5 6 3 2 6 7 2 8 9 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 2 7 7 3 6 6 2 4 5 5 3 5 4 4 4 6 3 +--R 18a d e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 3 5 7 2 2 6 8 7 9 +--R 72a b d e - 54a b d e + 12a b d +--R * +--R x +--R + +--R 8 3 6 7 4 5 6 2 5 4 5 3 6 3 4 4 7 2 3 5 8 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 2 6 9 +--R 6a b d +--R Type: Union(Expression(Integer),...) +--E 270 + +--S 271 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 272 + +)clear all + +--S 273 of 1353 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 273 + +--S 274 of 1353 +r0:=-1/4*(b*d-a*e)^4/(b^5*(a+b*x)^4)-4/3*e*(b*d-a*e)^3/(b^5*(a+b*x)^3)-_ + 3*e^2*(b*d-a*e)^2/(b^5*(a+b*x)^2)-4*e^3*(b*d-a*e)/(b^5*(a+b*x))+_ + e^4*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (48a b e - 48b d e )x + (108a b e - 72a b d e - 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (88a b e - 48a b d e - 24a b d e - 16b d e)x + 25a e - 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 4a b d e - 3b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (48a b e - 48b d e )x + (108a b e - 72a b d e - 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (88a b e - 48a b d e - 24a b d e - 16b d e)x + 25a e - 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 4a b d e - 3b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 275 + +--S 276 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 277 + +)clear all + +--S 278 of 1353 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 278 + +--S 279 of 1353 +r0:=-1/4*(d+e*x)^4/((b*d-a*e)*(a+b*x)^4) +--R +--R +--R (2) +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - e x + d e x + - d e x + d e x + - d +--R 4 2 4 +--R / +--R 4 5 4 2 3 4 3 3 2 2 3 2 +--R (a b e - b d)x + (4a b e - 4a b d)x + (6a b e - 6a b d)x +--R + +--R 4 3 2 5 4 +--R (4a b e - 4a b d)x + a e - a b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 279 + +--S 280 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R - 4b e x + (- 6a b e - 6b d e )x + (- 4a b e - 4a b d e - 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - a e - a b d e - a b d e - b d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 4b x + 16a b x + 24a b x + 16a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 280 + +--S 281 of 1353 +m0:=a0-r0 +--R +--R +--R 4 +--R e +--R (4) - ------------- +--R 4 5 +--R 4a b e - 4b d +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 1353 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 283 + +--S 284 of 1353 +r0:=-1/4*(b*d-a*e)^2/(b^3*(a+b*x)^4)-2/3*e*(b*d-a*e)/(b^3*(a+b*x)^3)-_ + 1/2*e^2/(b^3*(a+b*x)^2) +--R +--R +--R 1 2 2 2 1 2 2 2 1 2 2 1 1 2 2 +--R - - b e x + (- - a b e - - b d e)x - -- a e - - a b d e - - b d +--R 2 3 3 12 6 4 +--R (2) ------------------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 284 + +--S 285 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 6b e x + (- 4a b e - 8b d e)x - a e - 2a b d e - 3b d +--R (3) ----------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 285 + +--S 286 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 287 + +)clear all + +--S 288 of 1353 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 288 + +--S 289 of 1353 +r0:=1/4*(-b*d+a*e)/(b^2*(a+b*x)^4)-1/3*e/(b^2*(a+b*x)^3) +--R +--R +--R 1 1 1 +--R - - b e x - -- a e - - b d +--R 3 12 4 +--R (2) ---------------------------------------- +--R 6 4 5 3 2 4 2 3 3 4 2 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 289 + +--S 290 of 1353 +a0:=integrate(t0,x) +--R +--R +--R - 4b e x - a e - 3b d +--R (3) ----------------------------------------------- +--R 6 4 5 3 2 4 2 3 3 4 2 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 290 + +--S 291 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 292 + +)clear all + +--S 293 of 1353 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 293 + +--S 294 of 1353 +r0:=(-1/4)/(b*(a+b*x)^4) +--R +--R +--R 1 +--R - +--R 4 +--R (2) - --------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 294 + +--S 295 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - -------------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R 4b x + 16a b x + 24a b x + 16a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 295 + +--S 296 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 1353 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 298 + +--S 299 of 1353 +r0:=(-1/4)/((b*d-a*e)*(a+b*x)^4)+1/3*e/((b*d-a*e)^2*(a+b*x)^3)-_ + 1/2*e^2/((b*d-a*e)^3*(a+b*x)^2)+e^3/((b*d-a*e)^4*(a+b*x))+_ + e^4*log(a+b*x)/(b*d-a*e)^5-e^4*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(e x + d) +--R + +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 12b e x - 48a b e x - 72a b e x - 48a b e x - 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (42a b e - 48a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (52a b e - 72a b d e + 24a b d e - 4b d e)x + 25a e - 48a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 36a b d e - 16a b d e + 3b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 9 5 +--R - 12b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 2 7 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 3 6 4 +--R 72a b e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 2 7 5 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 4 5 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 6 5 +--R - 48a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 4 5 5 +--R 12a e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(e x + d) +--R + +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 12b e x - 48a b e x - 72a b e x - 48a b e x - 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (42a b e - 48a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (52a b e - 72a b d e + 24a b d e - 4b d e)x + 25a e - 48a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 36a b d e - 16a b d e + 3b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 9 5 +--R - 12b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 2 7 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 3 6 4 +--R 72a b e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 2 7 5 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 4 5 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 6 5 +--R - 48a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 4 5 5 +--R 12a e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R Type: Union(Expression(Integer),...) +--E 300 + +--S 301 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 302 + +)clear all + +--S 303 of 1353 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 303 + +--S 304 of 1353 +r0:=-1/4*b/((b*d-a*e)^2*(a+b*x)^4)+2/3*b*e/((b*d-a*e)^3*(a+b*x)^3)-_ + 3/2*b*e^2/((b*d-a*e)^4*(a+b*x)^2)+4*b*e^3/((b*d-a*e)^5*(a+b*x))+_ + e^4/((b*d-a*e)^5*(d+e*x))+5*b*e^4*log(a+b*x)/(b*d-a*e)^6-_ + 5*b*e^4*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 240a b e - 60b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (- 360a b e - 240a b d e )x + (- 240a b e - 360a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (- 60a b e - 240a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 3 +--R 60b e x + (240a b e + 60b d e )x + (360a b e + 240a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 4 4 +--R (240a b e + 360a b d e )x + (60a b e + 240a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 210a b e + 180a b d e + 30b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 260a b e + 150a b d e + 120a b d e - 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 125a b e - 20a b d e + 180a b d e - 40a b d e + 5b d e)x - 12a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 65a b d e + 120a b d e - 60a b d e + 20a b d e - 3b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 2 8 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 9 5 2 10 6 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 3 7 4 3 +--R 48a b e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 8 5 2 9 6 10 7 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 4 6 4 3 +--R 72a b e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 3 7 5 2 2 8 6 9 7 +--R 288a b d e - 216a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 5 5 4 3 +--R 48a b e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 4 6 5 2 3 7 6 2 8 7 +--R 792a b d e - 384a b d e + 72a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 6 4 4 3 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 5 5 5 2 4 6 6 3 7 7 +--R 648a b d e - 276a b d e + 48a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 5 5 6 4 6 7 +--R - 72a b d e + 12a b d +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 240a b e - 60b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (- 360a b e - 240a b d e )x + (- 240a b e - 360a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (- 60a b e - 240a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 3 +--R 60b e x + (240a b e + 60b d e )x + (360a b e + 240a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 4 4 +--R (240a b e + 360a b d e )x + (60a b e + 240a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 210a b e + 180a b d e + 30b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 260a b e + 150a b d e + 120a b d e - 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 125a b e - 20a b d e + 180a b d e - 40a b d e + 5b d e)x - 12a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 65a b d e + 120a b d e - 60a b d e + 20a b d e - 3b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 2 8 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 9 5 2 10 6 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 3 7 4 3 +--R 48a b e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 8 5 2 9 6 10 7 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 4 6 4 3 +--R 72a b e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 3 7 5 2 2 8 6 9 7 +--R 288a b d e - 216a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 5 5 4 3 +--R 48a b e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 4 6 5 2 3 7 6 2 8 7 +--R 792a b d e - 384a b d e + 72a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 6 4 4 3 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 5 5 5 2 4 6 6 3 7 7 +--R 648a b d e - 276a b d e + 48a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 5 5 6 4 6 7 +--R - 72a b d e + 12a b d +--R Type: Union(Expression(Integer),...) +--E 305 + +--S 306 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 307 + +)clear all + +--S 308 of 1353 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 308 + +--S 309 of 1353 +r0:=-1/4*b^2/((b*d-a*e)^3*(a+b*x)^4)+b^2*e/((b*d-a*e)^4*(a+b*x)^3)-_ + 3*b^2*e^2/((b*d-a*e)^5*(a+b*x)^2)+10*b^2*e^3/((b*d-a*e)^6*(a+b*x))+_ + 1/2*e^4/((b*d-a*e)^5*(d+e*x)^2)+5*b*e^4/((b*d-a*e)^6*(d+e*x))+_ + 15*b^2*e^4*log(a+b*x)/(b*d-a*e)^7-15*b^2*e^4*log(d+e*x)/(b*d-a*e)^7 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 60b e x + (240a b e + 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (360a b e + 480a b d e + 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (240a b e + 720a b d e + 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (60a b e + 480a b d e + 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (120a b d e + 240a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 60b e x + (- 240a b e - 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 360a b e - 480a b d e - 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (- 240a b e - 720a b d e - 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (- 60a b e - 480a b d e - 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (- 120a b d e - 240a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (210a b e - 120a b d e - 90b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (260a b e + 60a b d e - 300a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (125a b e + 280a b d e - 330a b d e - 80a b d e + 5b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 12a b e + 190a b d e - 100a b d e - 120a b d e + 20a b d e +--R + +--R 6 5 +--R - 2b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e + 24a b d e + 35a b d e - 80a b d e + 30a b d e - 8a b d e +--R + +--R 6 6 +--R b d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 3 8 4 5 +--R 4a b e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 2 9 5 4 10 6 3 11 7 2 +--R - 84a b d e + 28a b d e - 4b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 4 7 4 5 +--R 16a b e - 104a b d e + 280a b d e - 392a b d e + 280a b d e +--R + +--R 3 8 5 4 2 9 6 3 10 7 2 11 8 +--R - 56a b d e - 56a b d e + 40a b d e - 8b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 5 6 4 5 +--R 24a b e - 136a b d e + 284a b d e - 196a b d e - 196a b d e +--R + +--R 4 7 5 4 3 8 6 3 2 9 7 2 10 8 11 9 +--R 476a b d e - 364a b d e + 116a b d e - 4a b d e - 4b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 6 5 4 5 +--R 16a b e - 64a b d e + 16a b d e + 336a b d e - 784a b d e +--R + +--R 5 6 5 4 4 7 6 3 3 8 7 2 2 9 8 10 9 +--R 784a b d e - 336a b d e - 16a b d e + 64a b d e - 16a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5 +--R 4a e + 4a b d e - 116a b d e + 364a b d e - 476a b d e +--R + +--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9 +--R 196a b d e + 196a b d e - 284a b d e + 136a b d e - 24a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 7 4 5 4 +--R 8a d e - 40a b d e + 56a b d e + 56a b d e - 280a b d e +--R + +--R 6 5 6 3 5 6 7 2 4 7 8 3 8 9 +--R 392a b d e - 280a b d e + 104a b d e - 16a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 7 4 6 3 +--R 4a d e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 6 5 7 2 5 6 8 4 7 9 +--R - 84a b d e + 28a b d e - 4a b d +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 60b e x + (240a b e + 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (360a b e + 480a b d e + 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (240a b e + 720a b d e + 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (60a b e + 480a b d e + 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (120a b d e + 240a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 60b e x + (- 240a b e - 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 360a b e - 480a b d e - 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (- 240a b e - 720a b d e - 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (- 60a b e - 480a b d e - 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (- 120a b d e - 240a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (210a b e - 120a b d e - 90b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (260a b e + 60a b d e - 300a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (125a b e + 280a b d e - 330a b d e - 80a b d e + 5b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 12a b e + 190a b d e - 100a b d e - 120a b d e + 20a b d e +--R + +--R 6 5 +--R - 2b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e + 24a b d e + 35a b d e - 80a b d e + 30a b d e - 8a b d e +--R + +--R 6 6 +--R b d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 3 8 4 5 +--R 4a b e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 2 9 5 4 10 6 3 11 7 2 +--R - 84a b d e + 28a b d e - 4b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 4 7 4 5 +--R 16a b e - 104a b d e + 280a b d e - 392a b d e + 280a b d e +--R + +--R 3 8 5 4 2 9 6 3 10 7 2 11 8 +--R - 56a b d e - 56a b d e + 40a b d e - 8b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 5 6 4 5 +--R 24a b e - 136a b d e + 284a b d e - 196a b d e - 196a b d e +--R + +--R 4 7 5 4 3 8 6 3 2 9 7 2 10 8 11 9 +--R 476a b d e - 364a b d e + 116a b d e - 4a b d e - 4b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 6 5 4 5 +--R 16a b e - 64a b d e + 16a b d e + 336a b d e - 784a b d e +--R + +--R 5 6 5 4 4 7 6 3 3 8 7 2 2 9 8 10 9 +--R 784a b d e - 336a b d e - 16a b d e + 64a b d e - 16a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5 +--R 4a e + 4a b d e - 116a b d e + 364a b d e - 476a b d e +--R + +--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9 +--R 196a b d e + 196a b d e - 284a b d e + 136a b d e - 24a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 7 4 5 4 +--R 8a d e - 40a b d e + 56a b d e + 56a b d e - 280a b d e +--R + +--R 6 5 6 3 5 6 7 2 4 7 8 3 8 9 +--R 392a b d e - 280a b d e + 104a b d e - 16a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 7 4 6 3 +--R 4a d e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 6 5 7 2 5 6 8 4 7 9 +--R - 84a b d e + 28a b d e - 4a b d +--R Type: Union(Expression(Integer),...) +--E 310 + +--S 311 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 1353 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 313 + +--S 314 of 1353 +r0:=-1/4*b^3/((b*d-a*e)^4*(a+b*x)^4)+4/3*b^3*e/((b*d-a*e)^5*(a+b*x)^3)-_ + 5*b^3*e^2/((b*d-a*e)^6*(a+b*x)^2)+20*b^3*e^3/((b*d-a*e)^7*(a+b*x))+_ + 1/3*e^4/((b*d-a*e)^5*(d+e*x)^3)+5/2*b*e^4/((b*d-a*e)^6*(d+e*x)^2)+_ + 15*b^2*e^4/((b*d-a*e)^7*(d+e*x))+35*b^3*e^4*log(a+b*x)/(b*d-a*e)^8-_ + 35*b^3*e^4*log(d+e*x)/(b*d-a*e)^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R - 420b e x + (- 1680a b e - 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 2520a b e - 5040a b d e - 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1680a b e - 7560a b d e - 5040a b d e - 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (- 420a b e - 5040a b d e - 7560a b d e - 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (- 1260a b d e - 5040a b d e - 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (- 1260a b d e - 1680a b d e )x - 420a b d e +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 420b e x + (1680a b e + 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2520a b e + 5040a b d e + 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1680a b e + 7560a b d e + 5040a b d e + 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (420a b e + 5040a b d e + 7560a b d e + 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (1260a b d e + 5040a b d e + 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (1260a b d e + 1680a b d e )x + 420a b d e +--R * +--R log(b x + a) +--R + +--R 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R (- 420a b e + 420b d e )x + (- 1470a b e + 420a b d e + 1050b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1820a b e - 1890a b d e + 2940a b d e + 770b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 875a b e - 3780a b d e + 1890a b d e + 2660a b d e + 105b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 84a b e - 2205a b d e - 1260a b d e + 3150a b d e + 420a b d e +--R + +--R 7 5 2 +--R - 21b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 14a b e - 252a b d e - 1575a b d e + 1260a b d e + 630a b d e +--R + +--R 6 5 2 7 6 +--R - 84a b d e + 7b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e + 42a b d e - 252a b d e - 105a b d e + 420a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 126a b d e + 28a b d e - 3b d +--R / +--R 8 4 11 7 5 10 6 6 2 9 5 7 3 8 4 8 4 7 +--R 12a b e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 3 9 5 6 2 10 6 5 11 7 4 12 8 3 +--R - 672a b d e + 336a b d e - 96a b d e + 12b d e +--R * +--R 7 +--R x +--R + +--R 9 3 11 8 4 10 7 5 2 9 6 6 3 8 5 7 4 7 +--R 48a b e - 348a b d e + 1056a b d e - 1680a b d e + 1344a b d e +--R + +--R 4 8 5 6 3 9 6 5 2 10 7 4 11 8 3 12 9 2 +--R - 168a b d e - 672a b d e + 624a b d e - 240a b d e + 36b d e +--R * +--R 6 +--R x +--R + +--R 10 2 11 9 3 10 8 4 2 9 7 5 3 8 6 6 4 7 +--R 72a b e - 432a b d e + 900a b d e - 288a b d e - 2016a b d e +--R + +--R 5 7 5 6 4 8 6 5 3 9 7 4 2 10 8 3 +--R 4032a b d e - 3528a b d e + 1440a b d e - 72a b d e +--R + +--R 11 9 2 12 10 +--R - 144a b d e + 36b d e +--R * +--R 5 +--R x +--R + +--R 11 11 10 2 10 9 3 2 9 8 4 3 8 +--R 48a b e - 168a b d e - 240a b d e + 2220a b d e +--R + +--R 7 5 4 7 6 6 5 6 5 7 6 5 4 8 7 4 +--R - 4800a b d e + 4704a b d e - 1344a b d e - 1560a b d e +--R + +--R 3 9 8 3 2 10 9 2 11 10 12 11 +--R 1680a b d e - 600a b d e + 48a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 12 11 11 10 10 2 2 9 9 3 3 8 8 4 4 7 +--R 12a e + 48a b d e - 600a b d e + 1680a b d e - 1560a b d e +--R + +--R 7 5 5 6 6 6 6 5 5 7 7 4 4 8 8 3 +--R - 1344a b d e + 4704a b d e - 4800a b d e + 2220a b d e +--R + +--R 3 9 9 2 2 10 10 11 11 +--R - 240a b d e - 168a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 12 10 11 2 9 10 2 3 8 9 3 4 7 8 4 5 6 +--R 36a d e - 144a b d e - 72a b d e + 1440a b d e - 3528a b d e +--R + +--R 7 5 6 5 6 6 7 4 5 7 8 3 4 8 9 2 3 9 10 +--R 4032a b d e - 2016a b d e - 288a b d e + 900a b d e - 432a b d e +--R + +--R 2 10 11 +--R 72a b d +--R * +--R 2 +--R x +--R + +--R 12 2 9 11 3 8 10 2 4 7 9 3 5 6 8 4 6 5 +--R 36a d e - 240a b d e + 624a b d e - 672a b d e - 168a b d e +--R + +--R 7 5 7 4 6 6 8 3 5 7 9 2 4 8 10 3 9 11 +--R 1344a b d e - 1680a b d e + 1056a b d e - 348a b d e + 48a b d +--R * +--R x +--R + +--R 12 3 8 11 4 7 10 2 5 6 9 3 6 5 8 4 7 4 +--R 12a d e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 7 5 8 3 6 6 9 2 5 7 10 4 8 11 +--R - 672a b d e + 336a b d e - 96a b d e + 12a b d +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R - 420b e x + (- 1680a b e - 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 2520a b e - 5040a b d e - 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1680a b e - 7560a b d e - 5040a b d e - 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (- 420a b e - 5040a b d e - 7560a b d e - 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (- 1260a b d e - 5040a b d e - 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (- 1260a b d e - 1680a b d e )x - 420a b d e +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 420b e x + (1680a b e + 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2520a b e + 5040a b d e + 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1680a b e + 7560a b d e + 5040a b d e + 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (420a b e + 5040a b d e + 7560a b d e + 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (1260a b d e + 5040a b d e + 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (1260a b d e + 1680a b d e )x + 420a b d e +--R * +--R log(b x + a) +--R + +--R 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R (- 420a b e + 420b d e )x + (- 1470a b e + 420a b d e + 1050b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1820a b e - 1890a b d e + 2940a b d e + 770b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 875a b e - 3780a b d e + 1890a b d e + 2660a b d e + 105b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 84a b e - 2205a b d e - 1260a b d e + 3150a b d e + 420a b d e +--R + +--R 7 5 2 +--R - 21b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 14a b e - 252a b d e - 1575a b d e + 1260a b d e + 630a b d e +--R + +--R 6 5 2 7 6 +--R - 84a b d e + 7b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e + 42a b d e - 252a b d e - 105a b d e + 420a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 126a b d e + 28a b d e - 3b d +--R / +--R 8 4 11 7 5 10 6 6 2 9 5 7 3 8 4 8 4 7 +--R 12a b e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 3 9 5 6 2 10 6 5 11 7 4 12 8 3 +--R - 672a b d e + 336a b d e - 96a b d e + 12b d e +--R * +--R 7 +--R x +--R + +--R 9 3 11 8 4 10 7 5 2 9 6 6 3 8 5 7 4 7 +--R 48a b e - 348a b d e + 1056a b d e - 1680a b d e + 1344a b d e +--R + +--R 4 8 5 6 3 9 6 5 2 10 7 4 11 8 3 12 9 2 +--R - 168a b d e - 672a b d e + 624a b d e - 240a b d e + 36b d e +--R * +--R 6 +--R x +--R + +--R 10 2 11 9 3 10 8 4 2 9 7 5 3 8 6 6 4 7 +--R 72a b e - 432a b d e + 900a b d e - 288a b d e - 2016a b d e +--R + +--R 5 7 5 6 4 8 6 5 3 9 7 4 2 10 8 3 +--R 4032a b d e - 3528a b d e + 1440a b d e - 72a b d e +--R + +--R 11 9 2 12 10 +--R - 144a b d e + 36b d e +--R * +--R 5 +--R x +--R + +--R 11 11 10 2 10 9 3 2 9 8 4 3 8 +--R 48a b e - 168a b d e - 240a b d e + 2220a b d e +--R + +--R 7 5 4 7 6 6 5 6 5 7 6 5 4 8 7 4 +--R - 4800a b d e + 4704a b d e - 1344a b d e - 1560a b d e +--R + +--R 3 9 8 3 2 10 9 2 11 10 12 11 +--R 1680a b d e - 600a b d e + 48a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 12 11 11 10 10 2 2 9 9 3 3 8 8 4 4 7 +--R 12a e + 48a b d e - 600a b d e + 1680a b d e - 1560a b d e +--R + +--R 7 5 5 6 6 6 6 5 5 7 7 4 4 8 8 3 +--R - 1344a b d e + 4704a b d e - 4800a b d e + 2220a b d e +--R + +--R 3 9 9 2 2 10 10 11 11 +--R - 240a b d e - 168a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 12 10 11 2 9 10 2 3 8 9 3 4 7 8 4 5 6 +--R 36a d e - 144a b d e - 72a b d e + 1440a b d e - 3528a b d e +--R + +--R 7 5 6 5 6 6 7 4 5 7 8 3 4 8 9 2 3 9 10 +--R 4032a b d e - 2016a b d e - 288a b d e + 900a b d e - 432a b d e +--R + +--R 2 10 11 +--R 72a b d +--R * +--R 2 +--R x +--R + +--R 12 2 9 11 3 8 10 2 4 7 9 3 5 6 8 4 6 5 +--R 36a d e - 240a b d e + 624a b d e - 672a b d e - 168a b d e +--R + +--R 7 5 7 4 6 6 8 3 5 7 9 2 4 8 10 3 9 11 +--R 1344a b d e - 1680a b d e + 1056a b d e - 348a b d e + 48a b d +--R * +--R x +--R + +--R 12 3 8 11 4 7 10 2 5 6 9 3 6 5 8 4 7 4 +--R 12a d e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 7 5 8 3 6 6 9 2 5 7 10 4 8 11 +--R - 672a b d e + 336a b d e - 96a b d e + 12a b d +--R Type: Union(Expression(Integer),...) +--E 315 + +--S 316 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 317 + +)clear all + +--S 318 of 1353 +t0:=(a+b*x)*(d+e*x)^m*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R m | 2 2 2 +--R (1) (b x + a)(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1353 +r0:=-2*(b*d-a*e)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(2+m)*(3+m))+_ + 2*(b*d-a*e)^2*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(1+m)*_ + (2+m)*(3+m)*(a+b*x))+(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e*(3+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (b e m + 3b e m + 2b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a b e m + (8a b e - 2b d e)m + 6a b e - 2b d e)x + a e m +--R + +--R 2 2 2 2 2 2 +--R (5a e - 2a b d e)m + 6a e - 6a b d e + 2b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 3 3 +--R (b e m + 3b e m + 2b e )x +--R + +--R 3 2 2 2 3 2 2 3 2 +--R ((2a b e + b d e )m + (8a b e + b d e )m + 6a b e )x +--R + +--R 2 3 2 2 2 3 2 2 2 2 3 +--R ((a e + 2a b d e )m + (5a e + 6a b d e - 2b d e)m + 6a e )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 3 +--R a d e m + (5a d e - 2a b d e)m + 6a d e - 6a b d e + 2b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 3 3 3 2 3 3 +--R e m + 6e m + 11e m + 6e +--R Type: Union(Expression(Integer),...) +--E 320 + +--S 321 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 3 3 3 3 4 +--R (b e m + 3b e m + 2b e )x +--R + +--R 2 3 3 2 2 2 3 3 2 2 3 3 +--R ((3a b e + b d e )m + (11a b e + b d e )m + 8a b e )x +--R + +--R 2 3 2 2 2 2 3 2 2 3 2 +--R (3a b e + 3a b d e )m + (13a b e + 7a b d e - 2b d e)m +--R + +--R 2 3 +--R 12a b e +--R * +--R 2 +--R x +--R + +--R 3 3 2 2 2 3 3 2 2 2 2 3 3 +--R (a e + 3a b d e )m + (5a e + 11a b d e - 4a b d e)m + 6a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 6a b d e + 2b d +--R * +--R x +--R + +--R 3 2 2 3 2 2 2 3 2 2 2 2 3 +--R a d e m + (5a d e - 2a b d e)m + 6a d e - 6a b d e + 2a b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 2 2 2 2 2 2 2 +--R (- b e m - 3b e m - 2b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 2a b e m + (- 8a b e + 2b d e)m - 6a b e + 2b d e)x - a e m +--R + +--R 2 2 2 2 2 2 +--R (- 5a e + 2a b d e)m - 6a e + 6a b d e - 2b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x +--R + +--R 3 +--R - a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 322 + +)clear all + +--S 323 of 1353 +t0:=(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b e x + (a e + 5b d e )x + (5a d e + 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a d e + 10b d e )x + (10a d e + 5b d e)x + (5a d e + b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1353 +r0:=-1/28*(b*d-a*e)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 1/168*(b*d-a*e)^2*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 1/8*(a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 8 8 8 2 7 7 +--R 21b e x + (48a b e + 120b d e )x +--R + +--R 2 8 7 2 2 6 6 +--R (28a e + 280a b d e + 280b d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (168a d e + 672a b d e + 336b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (420a d e + 840a b d e + 210b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 2 4 4 5 3 2 +--R (560a d e + 560a b d e + 56b d e )x + (420a d e + 168a b d e )x +--R + +--R 2 5 3 2 6 2 7 2 8 +--R 168a d e x + 28a d e - 8a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 168b e x + 168a e +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 8 5 2 4 7 +--R 21b e x + (48a b e + 120b d e )x +--R + +--R 2 5 4 2 2 3 6 +--R (28a e + 280a b d e + 280b d e )x +--R + +--R 2 4 2 3 2 3 2 5 +--R (168a d e + 672a b d e + 336b d e )x +--R + +--R 2 2 3 3 2 2 4 4 +--R (420a d e + 840a b d e + 210b d e)x +--R + +--R 2 3 2 4 2 5 3 2 4 5 2 2 5 +--R (560a d e + 560a b d e + 56b d )x + (420a d e + 168a b d )x + 168a d x +--R / +--R 168 +--R Type: Union(Expression(Integer),...) +--E 325 + +--S 326 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 8 8 8 2 7 7 +--R - 21b e x + (- 48a b e - 120b d e )x +--R + +--R 2 8 7 2 2 6 6 +--R (- 28a e - 280a b d e - 280b d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (- 168a d e - 672a b d e - 336b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (- 420a d e - 840a b d e - 210b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (- 560a d e - 560a b d e - 56b d e )x +--R + +--R 2 4 4 5 3 2 2 5 3 2 6 2 7 2 8 +--R (- 420a d e - 168a b d e )x - 168a d e x - 28a d e + 8a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 8 9 2 8 3 7 8 +--R 21b e x + (69a b e + 120b d e )x +--R + +--R 2 8 2 7 3 2 6 7 +--R (76a b e + 400a b d e + 280b d e )x +--R + +--R 3 8 2 7 2 2 6 3 3 5 6 +--R (28a e + 448a b d e + 952a b d e + 336b d e )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 5 +--R (168a d e + 1092a b d e + 1176a b d e + 210b d e )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 4 +--R (420a d e + 1400a b d e + 770a b d e + 56b d e )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 3 4 4 2 5 3 2 +--R (560a d e + 980a b d e + 224a b d e )x + (420a d e + 336a b d e )x +--R + +--R 3 5 3 +--R 168a d e x +--R / +--R 3 3 +--R 168b e x + 168a e +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 5 7 5 2 4 6 2 5 4 2 2 3 5 +--R b e x + (2a b e + 5b d e )x + (a e + 10a b d e + 10b d e )x +--R + +--R 2 4 2 3 2 3 2 4 +--R (5a d e + 20a b d e + 10b d e )x +--R + +--R 2 2 3 3 2 2 4 3 2 3 2 4 2 5 2 +--R (10a d e + 20a b d e + 5b d e)x + (10a d e + 10a b d e + b d )x +--R + +--R 2 4 5 2 5 +--R (5a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 8 2 5 3 4 7 +--R - b e x + (- 3a b e - 5b d e )x +--R + +--R 2 5 2 4 3 2 3 6 +--R (- 3a b e - 15a b d e - 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 5 +--R (- a e - 15a b d e - 30a b d e - 10b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 4 +--R (- 5a d e - 30a b d e - 30a b d e - 5b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (- 10a d e - 30a b d e - 15a b d e - b d )x +--R + +--R 3 3 2 2 4 2 5 2 3 4 2 5 3 5 +--R (- 10a d e - 15a b d e - 3a b d )x + (- 5a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 1353 +t0:=(a+b*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1353 +r0:=-1/21*(b*d-a*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 1/105*(b*d-a*e)^2*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 1/7*(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 7 7 7 2 6 6 +--R 15b e x + (35a b e + 70b d e )x +--R + +--R 2 7 6 2 2 5 5 +--R (21a e + 168a b d e + 126b d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (105a d e + 315a b d e + 105b d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 2 3 4 4 3 2 +--R (210a d e + 280a b d e + 35b d e )x + (210a d e + 105a b d e )x +--R + +--R 2 4 3 2 5 2 6 2 7 +--R 105a d e x + 21a d e - 7a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 7 4 2 3 6 2 4 3 2 2 2 5 +--R 15b e x + (35a b e + 70b d e )x + (21a e + 168a b d e + 126b d e )x +--R + +--R 2 3 2 2 2 3 4 +--R (105a d e + 315a b d e + 105b d e)x +--R + +--R 2 2 2 3 2 4 3 2 3 4 2 2 4 +--R (210a d e + 280a b d e + 35b d )x + (210a d e + 105a b d )x + 105a d x +--R / +--R 105 +--R Type: Union(Expression(Integer),...) +--E 330 + +--S 331 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 7 7 7 2 6 6 +--R - 15b e x + (- 35a b e - 70b d e )x +--R + +--R 2 7 6 2 2 5 5 +--R (- 21a e - 168a b d e - 126b d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (- 105a d e - 315a b d e - 105b d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 +--R (- 210a d e - 280a b d e - 35b d e )x +--R + +--R 2 3 4 4 3 2 2 4 3 2 5 2 6 2 7 +--R (- 210a d e - 105a b d e )x - 105a d e x - 21a d e + 7a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 7 8 2 7 3 6 7 +--R 15b e x + (50a b e + 70b d e )x +--R + +--R 2 7 2 6 3 2 5 6 +--R (56a b e + 238a b d e + 126b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 5 +--R (21a e + 273a b d e + 441a b d e + 105b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 4 +--R (105a d e + 525a b d e + 385a b d e + 35b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 3 3 4 2 4 3 2 +--R (210a d e + 490a b d e + 140a b d e )x + (210a d e + 210a b d e )x +--R + +--R 3 4 3 +--R 105a d e x +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 4 6 4 2 3 5 2 4 3 2 2 2 4 +--R b e x + (2a b e + 4b d e )x + (a e + 8a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 3 2 2 2 3 2 4 2 +--R (4a d e + 12a b d e + 4b d e)x + (6a d e + 8a b d e + b d )x +--R + +--R 2 3 4 2 4 +--R (4a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R - b e x + (- 3a b e - 4b d e )x + (- 3a b e - 12a b d e - 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (- a e - 12a b d e - 18a b d e - 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (- 4a d e - 18a b d e - 12a b d e - b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (- 6a d e - 12a b d e - 3a b d )x + (- 4a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 332 + +)clear all + +--S 333 of 1353 +t0:=(a+b*x)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1353 +r0:=-1/15*(b*d-a*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/60*(b*d-_ + a*e)^2*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+1/6*(a+b*x)*_ + (d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 2 6 5 2 2 4 4 +--R 10b e x + (24a b e + 36b d e )x + (15a e + 90a b d e + 45b d e )x +--R + +--R 2 5 2 4 2 3 3 3 2 2 4 3 3 2 +--R (60a d e + 120a b d e + 20b d e )x + (90a d e + 60a b d e )x +--R + +--R 2 3 3 2 4 2 5 2 6 +--R 60a d e x + 15a d e - 6a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R 10b e x + (24a b e + 36b d e )x + (15a e + 90a b d e + 45b d e)x +--R + +--R 2 2 2 2 3 3 2 2 3 2 2 3 +--R (60a d e + 120a b d e + 20b d )x + (90a d e + 60a b d )x + 60a d x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 335 + +--S 336 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 6 6 6 2 5 5 +--R - 10b e x + (- 24a b e - 36b d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (- 15a e - 90a b d e - 45b d e )x +--R + +--R 2 5 2 4 2 3 3 3 2 2 4 3 3 2 +--R (- 60a d e - 120a b d e - 20b d e )x + (- 90a d e - 60a b d e )x +--R + +--R 2 3 3 2 4 2 5 2 6 +--R - 60a d e x - 15a d e + 6a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 6 7 2 6 3 5 6 +--R 10b e x + (34a b e + 36b d e )x +--R + +--R 2 6 2 5 3 2 4 5 +--R (39a b e + 126a b d e + 45b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 4 +--R (15a e + 150a b d e + 165a b d e + 20b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 3 2 4 2 3 3 2 +--R (60a d e + 210a b d e + 80a b d e )x + (90a d e + 120a b d e )x +--R + +--R 3 3 3 +--R 60a d e x +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R - b e x + (- 3a b e - 3b d e )x + (- 3a b e - 9a b d e - 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a e - 9a b d e - 9a b d e - b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 3a d e - 9a b d e - 3a b d )x + (- 3a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 337 + +)clear all + +--S 338 of 1353 +t0:=(a+b*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 1353 +r0:=1/30*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^3+1/10*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/5*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/b +--R +--R +--R (2) +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R 6b e x + (9a b e + 15b d e)x + (a b e + 25a b d e + 10b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- a b e + 5a b d e + 20a b d )x + a e - 5a b d e + 10a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 30b +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 6b e x + (15a b e + 15b d e)x + (10a e + 40a b d e + 10b d )x +--R + +--R 2 2 2 2 2 +--R (30a d e + 30a b d )x + 30a d x +--R / +--R 30 +--R Type: Union(Expression(Integer),...) +--E 340 + +--S 341 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 4 3 2 4 3 +--R - 6b e x + (- 9a b e - 15b d e)x +--R + +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (- a b e - 25a b d e - 10b d )x + (a b e - 5a b d e - 20a b d )x +--R + +--R 4 2 3 2 2 2 +--R - a e + 5a b d e - 10a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 6b e x + (15a b e + 15b d e)x + (10a b e + 40a b d e + 10b d )x +--R + +--R 2 3 4 2 2 2 3 2 +--R (30a b d e + 30a b d )x + 30a b d x +--R / +--R 3 +--R 30b +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - b e x + (- 3a b e - 2b d e)x + (- 3a b e - 6a b d e - b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- a e - 6a b d e - 3a b d )x + (- 2a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 1353 +t0:=(a+b*x)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 | 2 2 2 +--R (1) (b e x + (a e + b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1353 +r0:=1/12*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/4*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/b +--R +--R +--R (2) +--R 3 3 2 3 2 2 2 3 2 +--R (3b e x + (5a b e + 4b d)x + (a b e + 8a b d)x - a e + 4a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 12b +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 3 2 2 2 +--R 3b e x + (8a b e + 4b d)x + (6a e + 12a b d)x + 12a d x +--R (3) ---------------------------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 345 + +--S 346 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 3 2 2 2 3 2 +--R (- 3b e x + (- 5a b e - 4b d)x + (- a b e - 8a b d)x + a e - 4a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 3 4 3 2 2 3 2 2 2 +--R 3b e x + (8a b e + 4b d)x + (6a b e + 12a b d)x + 12a b d x +--R / +--R 2 +--R 12b +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + 2a b x + a +--R + +--R 3 4 2 3 3 2 2 2 3 2 +--R - b e x + (- 3a b e - b d)x + (- 3a b e - 3a b d)x + (- a e - 3a b d)x +--R + +--R 3 +--R - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 347 + +)clear all + +--S 348 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (1) (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 348 + +--S 349 of 1353 +r0:=1/3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b +--R +--R +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R (2) ----------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 +--R b x + 3a b x + 3a x +--R (3) --------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 350 + +--S 351 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 +--R (- b x - 2a b x - a )\|b x + 2a b x + a + b x + 3a b x + 3a b x +--R (4) --------------------------------------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 352 + +)clear all + +--S 353 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1353 +r0:=-(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e+(b*d-a*e)^2*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(e x + d) + b e x + (4a b e - 2b d e)x +--R + +--R 2 2 +--R 3a e - 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 2b e x + 2a e +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(e x + d) + b e x + (4a b e - 2b d e)x +--R (3) --------------------------------------------------------------------- +--R 3 +--R 2e +--R Type: Union(Expression(Integer),...) +--E 355 + +--S 356 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 +--R (- 2a e + 4a b d e - 2b d )log(e x + d) - b e x +--R + +--R 2 2 2 2 +--R (- 4a b e + 2b d e)x - 3a e + 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((2a b e - 4a b d e + 2b d )x + 2a e - 4a b d e + 2a b d )log(e x + d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 +--R b e x + (5a b e - 2b d e)x + (4a b e - 2a b d e)x +--R / +--R 3 3 +--R 2b e x + 2a e +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1353 +r0:=2*b*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2-(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e*(d+e*x))-2*b*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((2a b e - 2b d e)x + 2a b d e - 2b d )log(e x + d) + b e x +--R + +--R 2 2 2 +--R 2b d e x - a e + 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 +--R ((2a b e - 2b d e)x + 2a b d e - 2b d )log(e x + d) + b e x + b d e x +--R + +--R 2 2 2 2 +--R - a e + 2a b d e - b d +--R / +--R 4 3 +--R e x + d e +--R Type: Union(Expression(Integer),...) +--E 360 + +--S 361 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 +--R ((- 2a b e + 2b d e)x - 2a b d e + 2b d )log(e x + d) - b e x +--R + +--R 2 2 2 +--R - 2b d e x + a e - 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 3 2 2 2 2 +--R ((2a b e - 2b d e)x + (2a b e - 2b d )x + 2a b d e - 2a b d ) +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 3 2 +--R b e x + (a b e + b d e)x + (- a b e + 3a b d e - b d )x - a e +--R + +--R 2 2 2 +--R 2a b d e - a b d +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 362 + +)clear all + +--S 363 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1353 +r0:=-1/2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^2)+b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x))+b^2*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) - b e x +--R + +--R 2 2 2 2 2 2 +--R (- 4a b e + 2b d e)x - a e - 2a b d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) + (- 4a b e + 4b d e)x - a e +--R + +--R 2 2 +--R - 2a b d e + 3b d +--R / +--R 5 2 4 2 3 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 365 + +--S 366 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4b d e x - 2b d )log(e x + d) + b e x +--R + +--R 2 2 2 2 2 2 +--R (4a b e - 2b d e)x + a e + 2a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 3 2 2 2 +--R (2b e x + (2a b e + 4b d e)x + (4a b d e + 2b d )x + 2a b d ) +--R * +--R log(e x + d) +--R + +--R 2 2 3 2 2 2 2 3 2 3 2 +--R (- 4a b e + 4b d e)x + (- 5a b e + 2a b d e + 3b d )x - a e +--R + +--R 2 2 2 +--R - 2a b d e + 3a b d +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 367 + +)clear all + +--S 368 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1353 +r0:=1/3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^3) +--R +--R +--R (2) +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (- b x - 2a b x - a )\|b x + 2a b x + a +--R / +--R 4 3 3 3 2 2 2 2 2 3 +--R (3a e - 3b d e )x + (9a d e - 9b d e )x + (9a d e - 9b d e)x +--R + +--R 3 4 +--R 3a d e - 3b d +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 3b e x + (- 3a b e - 3b d e)x - a e - a b d e - b d +--R (3) --------------------------------------------------------- +--R 6 3 5 2 2 4 3 3 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 370 + +--S 371 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 3 2 3 2 3 | 2 2 2 2 3 3 2 2 +--R (b e x + 2a b e x + a e )\|b x + 2a b x + a + (- 3a b e + 3b d e )x +--R + +--R 2 3 3 2 3 3 3 3 +--R (- 3a b e + 3b d e)x - a e + b d +--R / +--R 7 6 3 6 2 5 2 2 5 3 4 +--R (3a e - 3b d e )x + (9a d e - 9b d e )x + (9a d e - 9b d e )x +--R + +--R 3 4 4 3 +--R 3a d e - 3b d e +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1353 +r0:=1/4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^4)+_ + 1/12*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^3) +--R +--R +--R (2) +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (- a b e + 4b d)x + (- 5a b e + 8a b d)x - 3a e + 4a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 6 5 2 2 4 4 2 5 2 4 2 3 3 3 +--R (12a e - 24a b d e + 12b d e )x + (48a d e - 96a b d e + 48b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (72a d e - 144a b d e + 72b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (48a d e - 96a b d e + 48b d e)x + 12a d e - 24a b d e + 12b d +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 6b e x + (- 8a b e - 4b d e)x - 3a e - 2a b d e - b d +--R (3) ----------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 375 + +--S 376 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 3 2 4 3 3 2 2 4 2 3 3 4 +--R - b e x + (a b e - 4b d e )x + (5a b e - 8a b d e )x + 3a e +--R + +--R 2 3 +--R - 4a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 4 3 3 4 2 2 2 3 4 2 2 3 4 3 +--R (- 6a b e + 12a b d e - 6b d e )x + (- 8a b e + 12a b d e - 4b d e)x +--R + +--R 4 4 3 3 4 4 +--R - 3a e + 4a b d e - b d +--R / +--R 2 9 8 2 2 7 4 2 8 2 7 2 3 6 3 +--R (12a e - 24a b d e + 12b d e )x + (48a d e - 96a b d e + 48b d e )x +--R + +--R 2 2 7 3 6 2 4 5 2 +--R (72a d e - 144a b d e + 72b d e )x +--R + +--R 2 3 6 4 5 2 5 4 2 4 5 5 4 2 6 3 +--R (48a d e - 96a b d e + 48b d e )x + 12a d e - 24a b d e + 12b d e +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------- +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 377 + +)clear all + +--S 378 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1353 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^5)+_ + 1/10*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^4)+_ + 1/30*b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^3*(d+e*x)^3) +--R +--R +--R (2) +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R - b e x + (a b e - 5b d e)x + (- a b e + 5a b d e - 10b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- 9a b e + 25a b d e - 20a b d )x - 6a e + 15a b d e - 10a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 8 2 7 2 2 6 3 3 5 5 +--R (30a e - 90a b d e + 90a b d e - 30b d e )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 4 +--R (150a d e - 450a b d e + 450a b d e - 150b d e )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 3 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 6 2 2 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 4 4 2 5 3 2 6 2 3 7 3 5 3 +--R (150a d e - 450a b d e + 450a b d e - 150b d e)x + 30a d e +--R + +--R 2 6 2 2 7 3 8 +--R - 90a b d e + 90a b d e - 30b d +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 10b e x + (- 15a b e - 5b d e)x - 6a e - 3a b d e - b d +--R (3) -------------------------------------------------------------- +--R 8 5 7 4 2 6 3 3 5 2 4 4 5 3 +--R 30e x + 150d e x + 300d e x + 300d e x + 150d e x + 30d e +--R Type: Union(Expression(Integer),...) +--E 380 + +--S 381 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 4 3 5 4 4 3 2 2 5 3 4 4 2 3 2 +--R b e x + (- a b e + 5b d e )x + (a b e - 5a b d e + 10b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 5 3 4 2 2 2 3 +--R (9a b e - 25a b d e + 20a b d e )x + 6a e - 15a b d e + 10a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 10a b e + 30a b d e - 30a b d e + 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 5 4 5 5 4 4 +--R (- 15a b e + 40a b d e - 30a b d e + 5b d e)x - 6a e + 15a b d e +--R + +--R 3 2 2 3 5 5 +--R - 10a b d e + b d +--R / +--R 3 11 2 10 2 2 9 3 3 8 5 +--R (30a e - 90a b d e + 90a b d e - 30b d e )x +--R + +--R 3 10 2 2 9 2 3 8 3 4 7 4 +--R (150a d e - 450a b d e + 450a b d e - 150b d e )x +--R + +--R 3 2 9 2 3 8 2 4 7 3 5 6 3 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 3 8 2 4 7 2 5 6 3 6 5 2 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 3 5 6 +--R (150a d e - 450a b d e + 450a b d e - 150b d e )x + 30a d e +--R + +--R 2 6 5 2 7 4 3 8 3 +--R - 90a b d e + 90a b d e - 30b d e +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 382 + +)clear all + +--S 383 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1353 +r0:=-1/6*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^6)-_ + 1/12*b*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^5)-1/60*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 15b e x + (- 24a b e - 6b d e)x - 10a e - 4a b d e - b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R - 15b e x + (- 24a b e - 6b d e)x - 10a e - 4a b d e - b d +--R --------------------------------------------------------------------------- +--R 9 6 8 5 2 7 4 3 6 3 4 5 2 5 4 6 3 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 385 + +--S 386 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (24a b e + 6b d e)x + 10a e + 4a b d e + b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 15b e x + (- 39a b e - 6b d e)x + (- 34a b e - 10a b d e - b d )x +--R + +--R 3 2 2 2 2 +--R - 10a e - 4a b d e - a b d +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1353 +r0:=-1/7*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^7)-_ + 2/35*b*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^6)-1/105*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 21b e x + (- 35a b e - 7b d e)x - 15a e - 5a b d e - b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 8 10 9 7 9 2 8 6 +--R 105b e x + (105a e + 735b d e )x + (735a d e + 2205b d e )x +--R + +--R 2 8 3 7 5 3 7 4 6 4 +--R (2205a d e + 3675b d e )x + (3675a d e + 3675b d e )x +--R + +--R 4 6 5 5 3 5 5 6 4 2 +--R (3675a d e + 2205b d e )x + (2205a d e + 735b d e )x +--R + +--R 6 4 7 3 7 3 +--R (735a d e + 105b d e )x + 105a d e +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R - 21b e x + (- 35a b e - 7b d e)x - 15a e - 5a b d e - b d +--R / +--R 10 7 9 6 2 8 5 3 7 4 4 6 3 5 5 2 +--R 105e x + 735d e x + 2205d e x + 3675d e x + 3675d e x + 2205d e x +--R + +--R 6 4 7 3 +--R 735d e x + 105d e +--R Type: Union(Expression(Integer),...) +--E 390 + +--S 391 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (21b e x + (35a b e + 7b d e)x + 15a e + 5a b d e + b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 21b e x + (- 56a b e - 7b d e)x + (- 50a b e - 12a b d e - b d )x +--R + +--R 3 2 2 2 2 +--R - 15a e - 5a b d e - a b d +--R / +--R 10 8 10 9 7 9 2 8 6 +--R 105b e x + (105a e + 735b d e )x + (735a d e + 2205b d e )x +--R + +--R 2 8 3 7 5 3 7 4 6 4 +--R (2205a d e + 3675b d e )x + (3675a d e + 3675b d e )x +--R + +--R 4 6 5 5 3 5 5 6 4 2 +--R (3675a d e + 2205b d e )x + (2205a d e + 735b d e )x +--R + +--R 6 4 7 3 7 3 +--R (735a d e + 105b d e )x + 105a d e +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 392 + +)clear all + +--S 393 of 1353 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 m | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 393 + +--S 394 of 1353 +r0:=-4*(b*d-a*e)*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(4+m)*(5+m))+_ + (a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(5+m))-_ + 24*(b*d-a*e)^3*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(2+m)*_ + (3+m)*(4+m)*(5+m))+24*(b*d-a*e)^4*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(1+m)*(2+m)*(3+m)*(4+m)*(5+m)*(a+b*x))+12*(b*d-a*e)^2*_ + (a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(3+m)*(4+m)*(5+m)) +--R +--R +--R (2) +--R 4 4 4 4 4 3 4 4 2 4 4 4 4 4 +--R (b e m + 10b e m + 35b e m + 50b e m + 24b e )x +--R + +--R 3 4 4 3 4 4 3 3 3 4 4 3 2 +--R 4a b e m + (44a b e - 4b d e )m + (164a b e - 24b d e )m +--R + +--R 3 4 4 3 3 4 4 3 +--R (244a b e - 44b d e )m + 120a b e - 24b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 2 2 4 3 3 3 +--R 6a b e m + (72a b e - 12a b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (294a b e - 96a b d e + 12b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 2 4 3 3 +--R (468a b e - 204a b d e + 36b d e )m + 240a b e - 120a b d e +--R + +--R 4 2 2 +--R 24b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 4 2 2 3 3 +--R 4a b e m + (52a b e - 12a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 2 +--R (236a b e - 120a b d e + 24a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 4 +--R (428a b e - 348a b d e + 144a b d e - 24b d e)m + 240a b e +--R + +--R 2 2 3 3 2 2 4 3 +--R - 240a b d e + 120a b d e - 24b d e +--R * +--R x +--R + +--R 4 4 4 4 4 3 3 3 4 4 3 3 2 2 2 2 2 +--R a e m + (14a e - 4a b d e )m + (71a e - 48a b d e + 12a b d e )m +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (154a e - 188a b d e + 108a b d e - 24a b d e)m + 120a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 240a b d e + 240a b d e - 120a b d e + 24b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 4 4 5 3 4 5 2 4 5 4 5 5 +--R (b e m + 10b e m + 35b e m + 50b e m + 24b e )x +--R + +--R 3 5 4 4 4 3 5 4 4 3 +--R (4a b e + b d e )m + (44a b e + 6b d e )m +--R + +--R 3 5 4 4 2 3 5 4 4 3 5 +--R (164a b e + 11b d e )m + (244a b e + 6b d e )m + 120a b e +--R * +--R 4 +--R x +--R + +--R 2 2 5 3 4 4 2 2 5 3 4 4 2 3 3 +--R (6a b e + 4a b d e )m + (72a b e + 32a b d e - 4b d e )m +--R + +--R 2 2 5 3 4 4 2 3 2 +--R (294a b e + 68a b d e - 12b d e )m +--R + +--R 2 2 5 3 4 4 2 3 2 2 5 +--R (468a b e + 40a b d e - 8b d e )m + 240a b e +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 4 4 3 5 2 2 4 3 2 3 3 +--R (4a b e + 6a b d e )m + (52a b e + 60a b d e - 12a b d e )m +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (236a b e + 174a b d e - 72a b d e + 12b d e )m +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 5 +--R (428a b e + 120a b d e - 60a b d e + 12b d e )m + 240a b e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 4 4 5 3 4 2 2 2 3 3 +--R (a e + 4a b d e )m + (14a e + 48a b d e - 12a b d e )m +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 2 +--R (71a e + 188a b d e - 108a b d e + 24a b d e )m +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (154a e + 240a b d e - 240a b d e + 120a b d e - 24b d e)m +--R + +--R 4 5 +--R 120a e +--R * +--R x +--R + +--R 4 4 4 4 4 3 2 3 3 +--R a d e m + (14a d e - 4a b d e )m +--R + +--R 4 4 3 2 3 2 2 3 2 2 +--R (71a d e - 48a b d e + 12a b d e )m +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 4 +--R (154a d e - 188a b d e + 108a b d e - 24a b d e)m + 120a d e +--R + +--R 3 2 3 2 2 3 2 3 4 4 5 +--R - 240a b d e + 240a b d e - 120a b d e + 24b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R e m + 15e m + 85e m + 225e m + 274e m + 120e +--R Type: Union(Expression(Integer),...) +--E 395 + +--S 396 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 4 5 5 3 5 5 2 5 5 5 5 6 +--R (b e m + 10b e m + 35b e m + 50b e m + 24b e )x +--R + +--R 4 5 5 4 4 4 5 5 4 3 +--R (5a b e + b d e )m + (54a b e + 6b d e )m +--R + +--R 4 5 5 4 2 4 5 5 4 4 5 +--R (199a b e + 11b d e )m + (294a b e + 6b d e )m + 144a b e +--R * +--R 5 +--R x +--R + +--R 2 3 5 4 4 4 2 3 5 4 4 5 2 3 3 +--R (10a b e + 5a b d e )m + (116a b e + 38a b d e - 4b d e )m +--R + +--R 2 3 5 4 4 5 2 3 2 +--R (458a b e + 79a b d e - 12b d e )m +--R + +--R 2 3 5 4 4 5 2 3 2 3 5 +--R (712a b e + 46a b d e - 8b d e )m + 360a b e +--R * +--R 4 +--R x +--R + +--R 3 2 5 2 3 4 4 +--R (10a b e + 10a b d e )m +--R + +--R 3 2 5 2 3 4 4 2 3 3 +--R (124a b e + 92a b d e - 16a b d e )m +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (530a b e + 242a b d e - 84a b d e + 12b d e )m +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 2 5 +--R (896a b e + 160a b d e - 68a b d e + 12b d e )m + 480a b e +--R * +--R 3 +--R x +--R + +--R 4 5 3 2 4 4 +--R (5a b e + 10a b d e )m +--R + +--R 4 5 3 2 4 2 3 2 3 3 +--R (66a b e + 108a b d e - 24a b d e )m +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 2 +--R (307a b e + 362a b d e - 180a b d e + 36a b d e )m +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (582a b e + 360a b d e - 300a b d e + 132a b d e - 24b d e)m +--R + +--R 4 5 +--R 360a b e +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 5 5 4 4 3 2 2 3 3 +--R (a e + 5a b d e )m + (14a e + 62a b d e - 16a b d e )m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 2 +--R (71a e + 259a b d e - 156a b d e + 36a b d e )m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R (154a e + 394a b d e - 428a b d e + 228a b d e - 48a b d e)m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 120a e + 120a b d e - 240a b d e + 240a b d e - 120a b d e +--R + +--R 5 5 +--R 24b d +--R * +--R x +--R + +--R 5 4 4 5 4 4 2 3 3 +--R a d e m + (14a d e - 4a b d e )m +--R + +--R 5 4 4 2 3 3 2 3 2 2 +--R (71a d e - 48a b d e + 12a b d e )m +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 5 4 +--R (154a d e - 188a b d e + 108a b d e - 24a b d e)m + 120a d e +--R + +--R 4 2 3 3 2 3 2 2 3 4 4 5 +--R - 240a b d e + 240a b d e - 120a b d e + 24a b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 4 4 4 4 4 3 4 4 2 4 4 4 4 4 +--R (- b e m - 10b e m - 35b e m - 50b e m - 24b e )x +--R + +--R 3 4 4 3 4 4 3 3 +--R - 4a b e m + (- 44a b e + 4b d e )m +--R + +--R 3 4 4 3 2 3 4 4 3 +--R (- 164a b e + 24b d e )m + (- 244a b e + 44b d e )m +--R + +--R 3 4 4 3 +--R - 120a b e + 24b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 2 2 4 3 3 3 +--R - 6a b e m + (- 72a b e + 12a b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 294a b e + 96a b d e - 12b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 2 4 3 3 +--R (- 468a b e + 204a b d e - 36b d e )m - 240a b e + 120a b d e +--R + +--R 4 2 2 +--R - 24b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 4 2 2 3 3 +--R - 4a b e m + (- 52a b e + 12a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 2 +--R (- 236a b e + 120a b d e - 24a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 4 +--R (- 428a b e + 348a b d e - 144a b d e + 24b d e)m - 240a b e +--R + +--R 2 2 3 3 2 2 4 3 +--R 240a b d e - 120a b d e + 24b d e +--R * +--R x +--R + +--R 4 4 4 4 4 3 3 3 +--R - a e m + (- 14a e + 4a b d e )m +--R + +--R 4 4 3 3 2 2 2 2 2 +--R (- 71a e + 48a b d e - 12a b d e )m +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 154a e + 188a b d e - 108a b d e + 24a b d e)m - 120a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 240a b d e - 240a b d e + 120a b d e - 24b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 397 + +)clear all + +--S 398 of 1353 +t0:=(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 7 10 2 7 3 6 9 2 7 2 6 3 2 5 8 +--R b e x + (3a b e + 7b d e )x + (3a b e + 21a b d e + 21b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 7 +--R (a e + 21a b d e + 63a b d e + 35b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 6 +--R (7a d e + 63a b d e + 105a b d e + 35b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 5 +--R (21a d e + 105a b d e + 105a b d e + 21b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 4 +--R (35a d e + 105a b d e + 63a b d e + 7b d e)x +--R + +--R 3 4 3 2 5 2 2 6 3 7 3 +--R (35a d e + 63a b d e + 21a b d e + b d )x +--R + +--R 3 5 2 2 6 2 7 2 3 6 2 7 3 7 +--R (21a d e + 21a b d e + 3a b d )x + (7a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1353 +r0:=-1/33*(b*d-a*e)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/12*(a+b*x)*_ + (d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/495*(b*d-a*e)^3*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/3960*(b*d-a*e)^4*(d+e*x)^8*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/110*(b*d-a*e)^2*(a+b*x)*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 12 12 3 12 4 11 11 +--R 330b e x + (1440a b e + 2520b d e )x +--R + +--R 2 2 12 3 11 4 2 10 10 +--R (2376a b e + 11088a b d e + 8316b d e )x +--R + +--R 3 12 2 2 11 3 2 10 4 3 9 9 +--R (1760a b e + 18480a b d e + 36960a b d e + 15400b d e )x +--R + +--R 4 12 3 11 2 2 2 10 3 3 9 +--R 495a e + 13860a b d e + 62370a b d e + 69300a b d e +--R + +--R 4 4 8 +--R 17325b d e +--R * +--R 8 +--R x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 +--R 3960a d e + 47520a b d e + 118800a b d e + 79200a b d e +--R + +--R 4 5 7 +--R 11880b d e +--R * +--R 7 +--R x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 +--R 13860a d e + 92400a b d e + 138600a b d e + 55440a b d e +--R + +--R 4 6 6 +--R 4620b d e +--R * +--R 6 +--R x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 +--R 27720a d e + 110880a b d e + 99792a b d e + 22176a b d e +--R + +--R 4 7 5 +--R 792b d e +--R * +--R 5 +--R x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 +--R (34650a d e + 83160a b d e + 41580a b d e + 3960a b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 +--R (27720a d e + 36960a b d e + 7920a b d e )x +--R + +--R 4 6 6 3 7 5 2 4 7 5 4 8 4 3 9 3 +--R (13860a d e + 7920a b d e )x + 3960a d e x + 495a d e - 220a b d e +--R + +--R 2 2 10 2 3 11 4 12 +--R 66a b d e - 12a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 3960b e x + 3960a e +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 12 3 7 4 6 11 +--R 330b e x + (1440a b e + 2520b d e )x +--R + +--R 2 2 7 3 6 4 2 5 10 +--R (2376a b e + 11088a b d e + 8316b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 9 +--R (1760a b e + 18480a b d e + 36960a b d e + 15400b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 8 +--R (495a e + 13860a b d e + 62370a b d e + 69300a b d e + 17325b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R 3960a d e + 47520a b d e + 118800a b d e + 79200a b d e +--R + +--R 4 5 2 +--R 11880b d e +--R * +--R 7 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R 13860a d e + 92400a b d e + 138600a b d e + 55440a b d e +--R + +--R 4 6 +--R 4620b d e +--R * +--R 6 +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 5 +--R (27720a d e + 110880a b d e + 99792a b d e + 22176a b d e + 792b d )x +--R + +--R 4 4 3 3 5 2 2 2 6 3 7 4 +--R (34650a d e + 83160a b d e + 41580a b d e + 3960a b d )x +--R + +--R 4 5 2 3 6 2 2 7 3 4 6 3 7 2 +--R (27720a d e + 36960a b d e + 7920a b d )x + (13860a d e + 7920a b d )x +--R + +--R 4 7 +--R 3960a d x +--R / +--R 3960 +--R Type: Union(Expression(Integer),...) +--E 400 + +--S 401 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 12 12 3 12 4 11 11 +--R - 330b e x + (- 1440a b e - 2520b d e )x +--R + +--R 2 2 12 3 11 4 2 10 10 +--R (- 2376a b e - 11088a b d e - 8316b d e )x +--R + +--R 3 12 2 2 11 3 2 10 4 3 9 9 +--R (- 1760a b e - 18480a b d e - 36960a b d e - 15400b d e )x +--R + +--R 4 12 3 11 2 2 2 10 3 3 9 +--R - 495a e - 13860a b d e - 62370a b d e - 69300a b d e +--R + +--R 4 4 8 +--R - 17325b d e +--R * +--R 8 +--R x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 +--R - 3960a d e - 47520a b d e - 118800a b d e - 79200a b d e +--R + +--R 4 5 7 +--R - 11880b d e +--R * +--R 7 +--R x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 +--R - 13860a d e - 92400a b d e - 138600a b d e - 55440a b d e +--R + +--R 4 6 6 +--R - 4620b d e +--R * +--R 6 +--R x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 +--R - 27720a d e - 110880a b d e - 99792a b d e - 22176a b d e +--R + +--R 4 7 5 +--R - 792b d e +--R * +--R 5 +--R x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 +--R (- 34650a d e - 83160a b d e - 41580a b d e - 3960a b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 +--R (- 27720a d e - 36960a b d e - 7920a b d e )x +--R + +--R 4 6 6 3 7 5 2 4 7 5 4 8 4 +--R (- 13860a d e - 7920a b d e )x - 3960a d e x - 495a d e +--R + +--R 3 9 3 2 2 10 2 3 11 4 12 +--R 220a b d e - 66a b d e + 12a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 12 13 4 12 5 11 12 +--R 330b e x + (1770a b e + 2520b d e )x +--R + +--R 2 3 12 4 11 5 2 10 11 +--R (3816a b e + 13608a b d e + 8316b d e )x +--R + +--R 3 2 12 2 3 11 4 2 10 5 3 9 10 +--R (4136a b e + 29568a b d e + 45276a b d e + 15400b d e )x +--R + +--R 4 12 3 2 11 2 3 2 10 4 3 9 +--R 2255a b e + 32340a b d e + 99330a b d e + 84700a b d e +--R + +--R 5 4 8 +--R 17325b d e +--R * +--R 9 +--R x +--R + +--R 5 12 4 11 3 2 2 10 2 3 3 9 +--R 495a e + 17820a b d e + 109890a b d e + 188100a b d e +--R + +--R 4 4 8 5 5 7 +--R 96525a b d e + 11880b d e +--R * +--R 8 +--R x +--R + +--R 5 11 4 2 10 3 2 3 9 2 3 4 8 +--R 3960a d e + 61380a b d e + 211200a b d e + 217800a b d e +--R + +--R 4 5 7 5 6 6 +--R 67320a b d e + 4620b d e +--R * +--R 7 +--R x +--R + +--R 5 2 10 4 3 9 3 2 4 8 2 3 5 7 +--R 13860a d e + 120120a b d e + 249480a b d e + 155232a b d e +--R + +--R 4 6 6 5 7 5 +--R 26796a b d e + 792b d e +--R * +--R 6 +--R x +--R + +--R 5 3 9 4 4 8 3 2 5 7 2 3 6 6 +--R 27720a d e + 145530a b d e + 182952a b d e + 63756a b d e +--R + +--R 4 7 5 +--R 4752a b d e +--R * +--R 5 +--R x +--R + +--R 5 4 8 4 5 7 3 2 6 6 2 3 7 5 4 +--R (34650a d e + 110880a b d e + 78540a b d e + 11880a b d e )x +--R + +--R 5 5 7 4 6 6 3 2 7 5 3 +--R (27720a d e + 50820a b d e + 15840a b d e )x +--R + +--R 5 6 6 4 7 5 2 5 7 5 +--R (13860a d e + 11880a b d e )x + 3960a d e x +--R / +--R 5 5 +--R 3960b e x + 3960a e +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 7 11 3 7 4 6 10 +--R b e x + (4a b e + 7b d e )x +--R + +--R 2 2 7 3 6 4 2 5 9 +--R (6a b e + 28a b d e + 21b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 8 +--R (4a b e + 42a b d e + 84a b d e + 35b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 7 +--R (a e + 28a b d e + 126a b d e + 140a b d e + 35b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6 +--R (7a d e + 84a b d e + 210a b d e + 140a b d e + 21b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 5 +--R (21a d e + 140a b d e + 210a b d e + 84a b d e + 7b d e)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 4 +--R (35a d e + 140a b d e + 126a b d e + 28a b d e + b d )x +--R + +--R 4 4 3 3 5 2 2 2 6 3 7 3 +--R (35a d e + 84a b d e + 42a b d e + 4a b d )x +--R + +--R 4 5 2 3 6 2 2 7 2 4 6 3 7 4 7 +--R (21a d e + 28a b d e + 6a b d )x + (7a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 7 12 4 7 5 6 11 +--R - b e x + (- 5a b e - 7b d e )x +--R + +--R 2 3 7 4 6 5 2 5 10 +--R (- 10a b e - 35a b d e - 21b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 9 +--R (- 10a b e - 70a b d e - 105a b d e - 35b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 8 +--R (- 5a b e - 70a b d e - 210a b d e - 175a b d e - 35b d e )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 +--R - a e - 35a b d e - 210a b d e - 350a b d e - 175a b d e +--R + +--R 5 5 2 +--R - 21b d e +--R * +--R 7 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 +--R - 7a d e - 105a b d e - 350a b d e - 350a b d e - 105a b d e +--R + +--R 5 6 +--R - 7b d e +--R * +--R 6 +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 +--R - 21a d e - 175a b d e - 350a b d e - 210a b d e - 35a b d e +--R + +--R 5 7 +--R - b d +--R * +--R 5 +--R x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 4 +--R (- 35a d e - 175a b d e - 210a b d e - 70a b d e - 5a b d )x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 3 +--R (- 35a d e - 105a b d e - 70a b d e - 10a b d )x +--R + +--R 5 5 2 4 6 3 2 7 2 5 6 4 7 5 7 +--R (- 21a d e - 35a b d e - 10a b d )x + (- 7a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 1353 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 6 9 2 6 3 5 8 2 6 2 5 3 2 4 7 +--R b e x + (3a b e + 6b d e )x + (3a b e + 18a b d e + 15b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 6 +--R (a e + 18a b d e + 45a b d e + 20b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 5 +--R (6a d e + 45a b d e + 60a b d e + 15b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 4 +--R (15a d e + 60a b d e + 45a b d e + 6b d e)x +--R + +--R 3 3 3 2 4 2 2 5 3 6 3 +--R (20a d e + 45a b d e + 18a b d e + b d )x +--R + +--R 3 4 2 2 5 2 6 2 3 5 2 6 3 6 +--R (15a d e + 18a b d e + 3a b d )x + (6a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1353 +r0:=-2/55*(b*d-a*e)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/11*(a+b*x)*_ + (d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/330*(b*d-a*e)^3*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/2310*(b*d-a*e)^4*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/165*(b*d-a*e)^2*(a+b*x)*_ + (d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 11 11 3 11 4 10 10 +--R 210b e x + (924a b e + 1386b d e )x +--R + +--R 2 2 11 3 10 4 2 9 9 +--R (1540a b e + 6160a b d e + 3850b d e )x +--R + +--R 3 11 2 2 10 3 2 9 4 3 8 8 +--R (1155a b e + 10395a b d e + 17325a b d e + 5775b d e )x +--R + +--R 4 11 3 10 2 2 2 9 3 3 8 +--R 330a e + 7920a b d e + 29700a b d e + 26400a b d e +--R + +--R 4 4 7 +--R 4950b d e +--R * +--R 7 +--R x +--R + +--R 4 10 3 2 9 2 2 3 8 3 4 7 +--R 2310a d e + 23100a b d e + 46200a b d e + 23100a b d e +--R + +--R 4 5 6 +--R 2310b d e +--R * +--R 6 +--R x +--R + +--R 4 2 9 3 3 8 2 2 4 7 3 5 6 +--R 6930a d e + 36960a b d e + 41580a b d e + 11088a b d e +--R + +--R 4 6 5 +--R 462b d e +--R * +--R 5 +--R x +--R + +--R 4 3 8 3 4 7 2 2 5 6 3 6 5 4 +--R (11550a d e + 34650a b d e + 20790a b d e + 2310a b d e )x +--R + +--R 4 4 7 3 5 6 2 2 6 5 3 +--R (11550a d e + 18480a b d e + 4620a b d e )x +--R + +--R 4 5 6 3 6 5 2 4 6 5 4 7 4 3 8 3 +--R (6930a d e + 4620a b d e )x + 2310a d e x + 330a d e - 165a b d e +--R + +--R 2 2 9 2 3 10 4 11 +--R 55a b d e - 11a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2310b e x + 2310a e +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 11 3 6 4 5 10 +--R 210b e x + (924a b e + 1386b d e )x +--R + +--R 2 2 6 3 5 4 2 4 9 +--R (1540a b e + 6160a b d e + 3850b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 8 +--R (1155a b e + 10395a b d e + 17325a b d e + 5775b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 7 +--R (330a e + 7920a b d e + 29700a b d e + 26400a b d e + 4950b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 +--R 2310a d e + 23100a b d e + 46200a b d e + 23100a b d e +--R + +--R 4 5 +--R 2310b d e +--R * +--R 6 +--R x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 5 +--R (6930a d e + 36960a b d e + 41580a b d e + 11088a b d e + 462b d )x +--R + +--R 4 3 3 3 4 2 2 2 5 3 6 4 +--R (11550a d e + 34650a b d e + 20790a b d e + 2310a b d )x +--R + +--R 4 4 2 3 5 2 2 6 3 4 5 3 6 2 +--R (11550a d e + 18480a b d e + 4620a b d )x + (6930a d e + 4620a b d )x +--R + +--R 4 6 +--R 2310a d x +--R / +--R 2310 +--R Type: Union(Expression(Integer),...) +--E 405 + +--S 406 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 11 11 3 11 4 10 10 +--R - 210b e x + (- 924a b e - 1386b d e )x +--R + +--R 2 2 11 3 10 4 2 9 9 +--R (- 1540a b e - 6160a b d e - 3850b d e )x +--R + +--R 3 11 2 2 10 3 2 9 4 3 8 8 +--R (- 1155a b e - 10395a b d e - 17325a b d e - 5775b d e )x +--R + +--R 4 11 3 10 2 2 2 9 3 3 8 +--R - 330a e - 7920a b d e - 29700a b d e - 26400a b d e +--R + +--R 4 4 7 +--R - 4950b d e +--R * +--R 7 +--R x +--R + +--R 4 10 3 2 9 2 2 3 8 3 4 7 +--R - 2310a d e - 23100a b d e - 46200a b d e - 23100a b d e +--R + +--R 4 5 6 +--R - 2310b d e +--R * +--R 6 +--R x +--R + +--R 4 2 9 3 3 8 2 2 4 7 3 5 6 +--R - 6930a d e - 36960a b d e - 41580a b d e - 11088a b d e +--R + +--R 4 6 5 +--R - 462b d e +--R * +--R 5 +--R x +--R + +--R 4 3 8 3 4 7 2 2 5 6 3 6 5 4 +--R (- 11550a d e - 34650a b d e - 20790a b d e - 2310a b d e )x +--R + +--R 4 4 7 3 5 6 2 2 6 5 3 +--R (- 11550a d e - 18480a b d e - 4620a b d e )x +--R + +--R 4 5 6 3 6 5 2 4 6 5 4 7 4 +--R (- 6930a d e - 4620a b d e )x - 2310a d e x - 330a d e +--R + +--R 3 8 3 2 2 9 2 3 10 4 11 +--R 165a b d e - 55a b d e + 11a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 11 12 4 11 5 10 11 +--R 210b e x + (1134a b e + 1386b d e )x +--R + +--R 2 3 11 4 10 5 2 9 10 +--R (2464a b e + 7546a b d e + 3850b d e )x +--R + +--R 3 2 11 2 3 10 4 2 9 5 3 8 9 +--R (2695a b e + 16555a b d e + 21175a b d e + 5775b d e )x +--R + +--R 4 11 3 2 10 2 3 2 9 4 3 8 +--R 1485a b e + 18315a b d e + 47025a b d e + 32175a b d e +--R + +--R 5 4 7 +--R 4950b d e +--R * +--R 8 +--R x +--R + +--R 5 11 4 10 3 2 2 9 2 3 3 8 +--R 330a e + 10230a b d e + 52800a b d e + 72600a b d e +--R + +--R 4 4 7 5 5 6 +--R 28050a b d e + 2310b d e +--R * +--R 7 +--R x +--R + +--R 5 10 4 2 9 3 2 3 8 2 3 4 7 +--R 2310a d e + 30030a b d e + 83160a b d e + 64680a b d e +--R + +--R 4 5 6 5 6 5 +--R 13398a b d e + 462b d e +--R * +--R 6 +--R x +--R + +--R 5 2 9 4 3 8 3 2 4 7 2 3 5 6 +--R 6930a d e + 48510a b d e + 76230a b d e + 31878a b d e +--R + +--R 4 6 5 +--R 2772a b d e +--R * +--R 5 +--R x +--R + +--R 5 3 8 4 4 7 3 2 5 6 2 3 6 5 4 +--R (11550a d e + 46200a b d e + 39270a b d e + 6930a b d e )x +--R + +--R 5 4 7 4 5 6 3 2 6 5 3 +--R (11550a d e + 25410a b d e + 9240a b d e )x +--R + +--R 5 5 6 4 6 5 2 5 6 5 +--R (6930a d e + 6930a b d e )x + 2310a d e x +--R / +--R 5 5 +--R 2310b e x + 2310a e +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 6 10 3 6 4 5 9 2 2 6 3 5 4 2 4 8 +--R b e x + (4a b e + 6b d e )x + (6a b e + 24a b d e + 15b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 7 +--R (4a b e + 36a b d e + 60a b d e + 20b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 6 +--R (a e + 24a b d e + 90a b d e + 80a b d e + 15b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 5 +--R (6a d e + 60a b d e + 120a b d e + 60a b d e + 6b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4 +--R (15a d e + 80a b d e + 90a b d e + 24a b d e + b d )x +--R + +--R 4 3 3 3 4 2 2 2 5 3 6 3 +--R (20a d e + 60a b d e + 36a b d e + 4a b d )x +--R + +--R 4 4 2 3 5 2 2 6 2 4 5 3 6 4 6 +--R (15a d e + 24a b d e + 6a b d )x + (6a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 6 11 4 6 5 5 10 +--R - b e x + (- 5a b e - 6b d e )x +--R + +--R 2 3 6 4 5 5 2 4 9 +--R (- 10a b e - 30a b d e - 15b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 8 +--R (- 10a b e - 60a b d e - 75a b d e - 20b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 7 +--R (- 5a b e - 60a b d e - 150a b d e - 100a b d e - 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 6 +--R (- a e - 30a b d e - 150a b d e - 200a b d e - 75a b d e - 6b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 5 +--R (- 6a d e - 75a b d e - 200a b d e - 150a b d e - 30a b d e - b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 4 +--R (- 15a d e - 100a b d e - 150a b d e - 60a b d e - 5a b d )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 3 +--R (- 20a d e - 75a b d e - 60a b d e - 10a b d )x +--R + +--R 5 4 2 4 5 3 2 6 2 5 5 4 6 5 6 +--R (- 15a d e - 30a b d e - 10a b d )x + (- 6a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 407 + +)clear all + +--S 408 of 1353 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 5 8 2 5 3 4 7 2 5 2 4 3 2 3 6 +--R b e x + (3a b e + 5b d e )x + (3a b e + 15a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 5 +--R (a e + 15a b d e + 30a b d e + 10b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 4 +--R (5a d e + 30a b d e + 30a b d e + 5b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (10a d e + 30a b d e + 15a b d e + b d )x +--R + +--R 3 3 2 2 4 2 5 2 3 4 2 5 3 5 +--R (10a d e + 15a b d e + 3a b d )x + (5a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1353 +r0:=-2/45*(b*d-a*e)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/10*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/210*(b*d-a*e)^3*(d+e*x)^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/1260*(b*d-a*e)^4*(d+e*x)^6*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/60*(b*d-a*e)^2*(a+b*x)*(d+e*x)^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 10 10 3 10 4 9 9 +--R 126b e x + (560a b e + 700b d e )x +--R + +--R 2 2 10 3 9 4 2 8 8 +--R (945a b e + 3150a b d e + 1575b d e )x +--R + +--R 3 10 2 2 9 3 2 8 4 3 7 7 +--R (720a b e + 5400a b d e + 7200a b d e + 1800b d e )x +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 4 4 6 6 +--R (210a e + 4200a b d e + 12600a b d e + 8400a b d e + 1050b d e )x +--R + +--R 4 9 3 2 8 2 2 3 7 3 4 6 +--R 1260a d e + 10080a b d e + 15120a b d e + 5040a b d e +--R + +--R 4 5 5 +--R 252b d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 3 3 7 2 2 4 6 3 5 5 4 +--R (3150a d e + 12600a b d e + 9450a b d e + 1260a b d e )x +--R + +--R 4 3 7 3 4 6 2 2 5 5 3 +--R (4200a d e + 8400a b d e + 2520a b d e )x +--R + +--R 4 4 6 3 5 5 2 4 5 5 4 6 4 3 7 3 +--R (3150a d e + 2520a b d e )x + 1260a d e x + 210a d e - 120a b d e +--R + +--R 2 2 8 2 3 9 4 10 +--R 45a b d e - 10a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 1260b e x + 1260a e +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 10 3 5 4 4 9 +--R 126b e x + (560a b e + 700b d e )x +--R + +--R 2 2 5 3 4 4 2 3 8 +--R (945a b e + 3150a b d e + 1575b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 7 +--R (720a b e + 5400a b d e + 7200a b d e + 1800b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 6 +--R (210a e + 4200a b d e + 12600a b d e + 8400a b d e + 1050b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 5 +--R (1260a d e + 10080a b d e + 15120a b d e + 5040a b d e + 252b d )x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 4 +--R (3150a d e + 12600a b d e + 9450a b d e + 1260a b d )x +--R + +--R 4 3 2 3 4 2 2 5 3 4 4 3 5 2 +--R (4200a d e + 8400a b d e + 2520a b d )x + (3150a d e + 2520a b d )x +--R + +--R 4 5 +--R 1260a d x +--R / +--R 1260 +--R Type: Union(Expression(Integer),...) +--E 410 + +--S 411 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 10 10 3 10 4 9 9 +--R - 126b e x + (- 560a b e - 700b d e )x +--R + +--R 2 2 10 3 9 4 2 8 8 +--R (- 945a b e - 3150a b d e - 1575b d e )x +--R + +--R 3 10 2 2 9 3 2 8 4 3 7 7 +--R (- 720a b e - 5400a b d e - 7200a b d e - 1800b d e )x +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 +--R - 210a e - 4200a b d e - 12600a b d e - 8400a b d e +--R + +--R 4 4 6 +--R - 1050b d e +--R * +--R 6 +--R x +--R + +--R 4 9 3 2 8 2 2 3 7 3 4 6 +--R - 1260a d e - 10080a b d e - 15120a b d e - 5040a b d e +--R + +--R 4 5 5 +--R - 252b d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 3 3 7 2 2 4 6 3 5 5 4 +--R (- 3150a d e - 12600a b d e - 9450a b d e - 1260a b d e )x +--R + +--R 4 3 7 3 4 6 2 2 5 5 3 +--R (- 4200a d e - 8400a b d e - 2520a b d e )x +--R + +--R 4 4 6 3 5 5 2 4 5 5 4 6 4 +--R (- 3150a d e - 2520a b d e )x - 1260a d e x - 210a d e +--R + +--R 3 7 3 2 2 8 2 3 9 4 10 +--R 120a b d e - 45a b d e + 10a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 10 11 4 10 5 9 10 +--R 126b e x + (686a b e + 700b d e )x +--R + +--R 2 3 10 4 9 5 2 8 9 +--R (1505a b e + 3850a b d e + 1575b d e )x +--R + +--R 3 2 10 2 3 9 4 2 8 5 3 7 8 +--R (1665a b e + 8550a b d e + 8775a b d e + 1800b d e )x +--R + +--R 4 10 3 2 9 2 3 2 8 4 3 7 +--R 930a b e + 9600a b d e + 19800a b d e + 10200a b d e +--R + +--R 5 4 6 +--R 1050b d e +--R * +--R 7 +--R x +--R + +--R 5 10 4 9 3 2 2 8 2 3 3 7 +--R 210a e + 5460a b d e + 22680a b d e + 23520a b d e +--R + +--R 4 4 6 5 5 5 +--R 6090a b d e + 252b d e +--R * +--R 6 +--R x +--R + +--R 5 9 4 2 8 3 2 3 7 2 3 4 6 +--R 1260a d e + 13230a b d e + 27720a b d e + 14490a b d e +--R + +--R 4 5 5 +--R 1512a b d e +--R * +--R 5 +--R x +--R + +--R 5 2 8 4 3 7 3 2 4 6 2 3 5 5 4 +--R (3150a d e + 16800a b d e + 17850a b d e + 3780a b d e )x +--R + +--R 5 3 7 4 4 6 3 2 5 5 3 +--R (4200a d e + 11550a b d e + 5040a b d e )x +--R + +--R 5 4 6 4 5 5 2 5 5 5 +--R (3150a d e + 3780a b d e )x + 1260a d e x +--R / +--R 5 5 +--R 1260b e x + 1260a e +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 5 9 3 5 4 4 8 2 2 5 3 4 4 2 3 7 +--R b e x + (4a b e + 5b d e )x + (6a b e + 20a b d e + 10b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 6 +--R (4a b e + 30a b d e + 40a b d e + 10b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 5 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 +--R (5a d e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 3 +--R (10a d e + 40a b d e + 30a b d e + 4a b d )x +--R + +--R 4 3 2 3 4 2 2 5 2 4 4 3 5 4 5 +--R (10a d e + 20a b d e + 6a b d )x + (5a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 5 10 4 5 5 4 9 +--R - b e x + (- 5a b e - 5b d e )x +--R + +--R 2 3 5 4 4 5 2 3 8 +--R (- 10a b e - 25a b d e - 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 7 +--R (- 10a b e - 50a b d e - 50a b d e - 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 6 +--R (- 5a b e - 50a b d e - 100a b d e - 50a b d e - 5b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (- a e - 25a b d e - 100a b d e - 100a b d e - 25a b d e - b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4 +--R (- 5a d e - 50a b d e - 100a b d e - 50a b d e - 5a b d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 3 +--R (- 10a d e - 50a b d e - 50a b d e - 10a b d )x +--R + +--R 5 3 2 4 4 3 2 5 2 5 4 4 5 5 5 +--R (- 10a d e - 25a b d e - 10a b d )x + (- 5a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 412 + +)clear all + +--S 413 of 1353 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1353 +r0:=1/630*(b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^5+1/126*(b*d-a*e)^3*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4+1/42*(b*d-a*e)^2*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+1/18*(b*d-a*e)*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/b^2+1/9*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 8 4 8 7 4 8 3 7 +--R 70b e x + (245a b e + 315b d e )x +--R + +--R 2 6 4 7 3 8 2 2 6 +--R (295a b e + 1125a b d e + 540b d e )x +--R + +--R 3 5 4 2 6 3 7 2 2 8 3 5 +--R (125a b e + 1395a b d e + 1980a b d e + 420b d e)x +--R + +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (a b e + 621a b d e + 2556a b d e + 1596a b d e + 126b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (- a b e + 9a b d e + 1224a b d e + 2184a b d e + 504a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (a b e - 9a b d e + 36a b d e + 1176a b d e + 756a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 8 4 +--R (- a b e + 9a b d e - 36a b d e + 84a b d e + 504a b d )x + a e +--R + +--R 7 3 6 2 2 2 5 3 3 4 4 4 +--R - 9a b d e + 36a b d e - 84a b d e + 126a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 630b +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 9 3 4 4 3 8 +--R 70b e x + (315a b e + 315b d e )x +--R + +--R 2 2 4 3 3 4 2 2 7 +--R (540a b e + 1440a b d e + 540b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 6 +--R (420a b e + 2520a b d e + 2520a b d e + 420b d e)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 5 +--R (126a e + 2016a b d e + 4536a b d e + 2016a b d e + 126b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R (630a d e + 3780a b d e + 3780a b d e + 630a b d )x +--R + +--R 4 2 2 3 3 2 2 4 3 4 3 3 4 2 +--R (1260a d e + 3360a b d e + 1260a b d )x + (1260a d e + 1260a b d )x +--R + +--R 4 4 +--R 630a d x +--R / +--R 630 +--R Type: Union(Expression(Integer),...) +--E 415 + +--S 416 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 4 8 7 4 8 3 7 +--R - 70b e x + (- 245a b e - 315b d e )x +--R + +--R 2 6 4 7 3 8 2 2 6 +--R (- 295a b e - 1125a b d e - 540b d e )x +--R + +--R 3 5 4 2 6 3 7 2 2 8 3 5 +--R (- 125a b e - 1395a b d e - 1980a b d e - 420b d e)x +--R + +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (- a b e - 621a b d e - 2556a b d e - 1596a b d e - 126b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (a b e - 9a b d e - 1224a b d e - 2184a b d e - 504a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (- a b e + 9a b d e - 36a b d e - 1176a b d e - 756a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 8 4 +--R (a b e - 9a b d e + 36a b d e - 84a b d e - 504a b d )x - a e +--R + +--R 7 3 6 2 2 2 5 3 3 4 4 4 +--R 9a b d e - 36a b d e + 84a b d e - 126a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 9 4 9 8 4 9 3 8 +--R 70b e x + (315a b e + 315b d e )x +--R + +--R 2 7 4 8 3 9 2 2 7 +--R (540a b e + 1440a b d e + 540b d e )x +--R + +--R 3 6 4 2 7 3 8 2 2 9 3 6 +--R (420a b e + 2520a b d e + 2520a b d e + 420b d e)x +--R + +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 5 +--R (126a b e + 2016a b d e + 4536a b d e + 2016a b d e + 126b d )x +--R + +--R 4 5 3 3 6 2 2 2 7 3 8 4 4 +--R (630a b d e + 3780a b d e + 3780a b d e + 630a b d )x +--R + +--R 4 5 2 2 3 6 3 2 7 4 3 +--R (1260a b d e + 3360a b d e + 1260a b d )x +--R + +--R 4 5 3 3 6 4 2 4 5 4 +--R (1260a b d e + 1260a b d )x + 630a b d x +--R / +--R 5 +--R 630b +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 4 8 3 4 4 3 7 2 2 4 3 3 4 2 2 6 +--R b e x + (4a b e + 4b d e )x + (6a b e + 16a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 5 +--R (4a b e + 24a b d e + 24a b d e + 4b d e)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 16a b d e + 36a b d e + 16a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 24a b d e + 24a b d e + 4a b d )x +--R + +--R 4 2 2 3 3 2 2 4 2 4 3 3 4 4 4 +--R (6a d e + 16a b d e + 6a b d )x + (4a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 9 4 4 5 3 8 +--R - b e x + (- 5a b e - 4b d e )x +--R + +--R 2 3 4 4 3 5 2 2 7 +--R (- 10a b e - 20a b d e - 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (- 10a b e - 40a b d e - 30a b d e - 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (- 5a b e - 40a b d e - 60a b d e - 20a b d e - b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (- a e - 20a b d e - 60a b d e - 40a b d e - 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (- 4a d e - 30a b d e - 40a b d e - 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (- 6a d e - 20a b d e - 10a b d )x + (- 4a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 1353 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1353 +r0:=1/280*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4+1/56*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+3/56*(b*d-a*e)*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/8*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 7 3 7 6 3 7 2 6 +--R 35b e x + (125a b e + 120b d e )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (155a b e + 440a b d e + 140b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (69a b e + 568a b d e + 532a b d e + 56b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (a b e + 272a b d e + 728a b d e + 224a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- a b e + 8a b d e + 392a b d e + 336a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 6 2 +--R (a b e - 8a b d e + 28a b d e + 224a b d )x - a e + 8a b d e +--R + +--R 5 2 2 4 3 3 +--R - 28a b d e + 56a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 280b +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 8 3 3 4 2 7 +--R 35b e x + (160a b e + 120b d e )x +--R + +--R 2 2 3 3 2 4 2 6 +--R (280a b e + 560a b d e + 140b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 5 +--R (224a b e + 1008a b d e + 672a b d e + 56b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 +--R (70a e + 840a b d e + 1260a b d e + 280a b d )x +--R + +--R 4 2 3 2 2 2 3 3 4 2 3 3 2 +--R (280a d e + 1120a b d e + 560a b d )x + (420a d e + 560a b d )x +--R + +--R 4 3 +--R 280a d x +--R / +--R 280 +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 3 7 6 3 7 2 6 +--R - 35b e x + (- 125a b e - 120b d e )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (- 155a b e - 440a b d e - 140b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 69a b e - 568a b d e - 532a b d e - 56b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (- a b e - 272a b d e - 728a b d e - 224a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (a b e - 8a b d e - 392a b d e - 336a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 6 2 +--R (- a b e + 8a b d e - 28a b d e - 224a b d )x + a e - 8a b d e +--R + +--R 5 2 2 4 3 3 +--R 28a b d e - 56a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 8 3 8 7 3 8 2 7 +--R 35b e x + (160a b e + 120b d e )x +--R + +--R 2 6 3 7 2 8 2 6 +--R (280a b e + 560a b d e + 140b d e)x +--R + +--R 3 5 3 2 6 2 7 2 8 3 5 +--R (224a b e + 1008a b d e + 672a b d e + 56b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 4 +--R (70a b e + 840a b d e + 1260a b d e + 280a b d )x +--R + +--R 4 4 2 3 5 2 2 6 3 3 4 4 2 3 5 3 2 +--R (280a b d e + 1120a b d e + 560a b d )x + (420a b d e + 560a b d )x +--R + +--R 4 4 3 +--R 280a b d x +--R / +--R 4 +--R 280b +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R - b e x + (- 5a b e - 3b d e )x + (- 10a b e - 15a b d e - 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 10a b e - 30a b d e - 15a b d e - b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 5a b e - 30a b d e - 30a b d e - 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- a e - 15a b d e - 30a b d e - 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 3a d e - 15a b d e - 10a b d )x + (- 3a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 422 + +)clear all + +--S 423 of 1353 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1353 +r0:=1/105*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+1/21*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/7*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 15b e x + (55a b e + 35b d e)x + (71a b e + 133a b d e + 21b d )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (34a b e + 182a b d e + 84a b d )x +--R + +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (a b e + 98a b d e + 126a b d )x + (- a b e + 7a b d e + 84a b d )x +--R + +--R 6 2 5 4 2 2 +--R a e - 7a b d e + 21a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 105b +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 7 3 2 4 6 2 2 2 3 4 2 5 +--R 15b e x + (70a b e + 35b d e)x + (126a b e + 168a b d e + 21b d )x +--R + +--R 3 2 2 2 3 2 4 +--R (105a b e + 315a b d e + 105a b d )x +--R + +--R 4 2 3 2 2 2 3 4 3 2 2 4 2 +--R (35a e + 280a b d e + 210a b d )x + (105a d e + 210a b d )x + 105a d x +--R / +--R 105 +--R Type: Union(Expression(Integer),...) +--E 425 + +--S 426 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 2 6 5 2 6 5 +--R - 15b e x + (- 55a b e - 35b d e)x +--R + +--R 2 4 2 5 6 2 4 +--R (- 71a b e - 133a b d e - 21b d )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 34a b e - 182a b d e - 84a b d )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- a b e - 98a b d e - 126a b d )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (a b e - 7a b d e - 84a b d )x - a e + 7a b d e - 21a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 2 7 6 2 7 6 2 5 2 6 7 2 5 +--R 15b e x + (70a b e + 35b d e)x + (126a b e + 168a b d e + 21b d )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (105a b e + 315a b d e + 105a b d )x +--R + +--R 4 3 2 3 4 2 5 2 3 4 3 3 4 2 2 +--R (35a b e + 280a b d e + 210a b d )x + (105a b d e + 210a b d )x +--R + +--R 4 3 2 +--R 105a b d x +--R / +--R 3 +--R 105b +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R - b e x + (- 5a b e - 2b d e)x + (- 10a b e - 10a b d e - b d )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 10a b e - 20a b d e - 5a b d )x +--R + +--R 4 2 3 2 2 3 2 3 5 2 4 3 2 2 2 +--R (- 5a b e - 20a b d e - 10a b d )x + (- a e - 10a b d e - 10a b d )x +--R + +--R 5 4 2 5 2 +--R (- 2a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 427 + +)clear all + +--S 428 of 1353 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1353 +r0:=1/30*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/6*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 5 5 4 5 4 2 3 4 3 +--R 5b e x + (19a b e + 6b d)x + (26a b e + 24a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (14a b e + 36a b d)x + (a b e + 24a b d)x - a e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 30b +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 3 4 5 2 2 3 4 +--R 5b e x + (24a b e + 6b d)x + (45a b e + 30a b d)x +--R + +--R 3 2 2 3 4 3 2 4 +--R (40a b e + 60a b d)x + (15a e + 60a b d)x + 30a d x +--R / +--R 30 +--R Type: Union(Expression(Integer),...) +--E 430 + +--S 431 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 4 5 4 2 3 4 3 +--R - 5b e x + (- 19a b e - 6b d)x + (- 26a b e - 24a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 14a b e - 36a b d)x + (- a b e - 24a b d)x + a e - 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 5 6 5 2 4 5 4 +--R 5b e x + (24a b e + 6b d)x + (45a b e + 30a b d)x +--R + +--R 3 3 2 4 3 4 2 3 3 2 4 2 +--R (40a b e + 60a b d)x + (15a b e + 60a b d)x + 30a b d x +--R / +--R 2 +--R 30b +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 6 4 5 5 2 3 4 4 +--R - b e x + (- 5a b e - b d)x + (- 10a b e - 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (- 10a b e - 10a b d)x + (- 5a b e - 10a b d)x + (- a e - 5a b d)x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1353 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R (2) ------------------------------------------------------------- +--R 5b +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 4 5 3 4 2 2 3 3 2 4 +--R b x + 5a b x + 10a b x + 10a b x + 5a x +--R (3) ------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 435 + +--S 436 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (- b x - 4a b x - 6a b x - 4a b x - a )\|b x + 2a b x + a + b x +--R + +--R 4 4 2 3 3 3 2 2 4 +--R 5a b x + 10a b x + 10a b x + 5a b x +--R / +--R 5b +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 437 + +)clear all + +--S 438 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1353 +r0:=-1/3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/4*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/e-(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/2*(b*d-_ + a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3+(b*d-a*e)^4*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (16a b e - 4b d e )x + (36a b e - 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (48a b e - 72a b d e + 48a b d e - 12b d e)x + 25a e - 52a b d e +--R + +--R 2 2 2 2 3 3 +--R 42a b d e - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 12b e x + 12a e +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (16a b e - 4b d e )x + (36a b e - 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 +--R (48a b e - 72a b d e + 48a b d e - 12b d e)x +--R / +--R 5 +--R 12e +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 12a e + 48a b d e - 72a b d e + 48a b d e - 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 3b e x + (- 16a b e + 4b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 36a b e + 24a b d e - 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 48a b e + 72a b d e - 48a b d e + 12b d e)x - 25a e +--R + +--R 3 3 2 2 2 2 3 3 +--R 52a b d e - 42a b d e + 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d )x + 12a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R 3b e x + (19a b e - 4b d e )x + (52a b e - 28a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (84a b e - 96a b d e + 54a b d e - 12b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R (48a b e - 72a b d e + 48a b d e - 12a b d e)x +--R / +--R 5 5 +--R 12b e x + 12a e +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1353 +r0:=4/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2-(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(d+e*x))+4*b*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^4-2*b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-_ + 4*b*(b*d-a*e)^3*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b e - 36a b d e + 36a b d e - 12b d e)x + 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b d e + 36a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (6a b e - 2b d e )x + (18a b e - 18a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (10a b e + 6a b d e - 24a b d e + 12b d e)x - 3a e + 22a b d e +--R + +--R 2 2 2 2 3 3 +--R - 30a b d e + 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +--R 3b e x + (3a e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b e - 36a b d e + 36a b d e - 12b d e)x + 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b d e + 36a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (6a b e - 2b d e )x + (18a b e - 18a b d e + 6b d e )x +--R + +--R 2 2 3 3 2 2 4 3 4 4 3 3 2 2 2 2 +--R (18a b d e - 24a b d e + 9b d e)x - 3a e + 12a b d e - 18a b d e +--R + +--R 3 3 4 4 +--R 12a b d e - 3b d +--R / +--R 6 5 +--R 3e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 445 + +--S 446 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (- 12a b e + 36a b d e - 36a b d e + 12b d e)x - 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 36a b d e - 36a b d e + 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - b e x + (- 6a b e + 2b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 18a b e + 18a b d e - 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 10a b e - 6a b d e + 24a b d e - 12b d e)x + 3a e - 22a b d e +--R + +--R 2 2 2 2 3 3 +--R 30a b d e - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (12a b e - 36a b d e + 36a b d e - 12b d e)x +--R + +--R 4 4 3 2 3 4 3 5 4 4 3 +--R (12a b e - 24a b d e + 24a b d e - 12b d )x + 12a b d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R - 36a b d e + 36a b d e - 12a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R b e x + (7a b e - 2b d e )x + (24a b e - 20a b d e + 6b d e )x +--R + +--R 3 2 4 4 2 2 5 3 2 +--R (18a b e - 18a b d e + 9b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 3a b e + 30a b d e - 42a b d e + 21a b d e - 3b d )x - 3a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R 12a b d e - 18a b d e + 12a b d e - 3a b d +--R / +--R 6 2 6 5 5 +--R 3b e x + (3a e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1353 +r0:=-1/2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^2)-_ + 2*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x))-6*b^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+3*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + e^3+6*b^2*(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 +--R (24a b d e - 48a b d e + 24b d e)x + 12a b d e - 24a b d e +--R + +--R 4 4 +--R 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R b e x + (8a b e - 4b d e )x + (24a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 4 3 4 4 3 3 2 2 2 2 +--R (- 8a b e + 24a b d e - 12b d e)x - a e - 4a b d e + 18a b d e +--R + +--R 3 3 +--R - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 4 4 +--R (24a b d e - 48a b d e + 24b d e)x + 12a b d e - 24a b d e + 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R b e x + (8a b e - 4b d e )x + (16a b d e - 11b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 8a b e + 24a b d e - 16a b d e + 2b d e)x - a e - 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 20a b d e + 7b d +--R / +--R 7 2 6 2 5 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 450 + +--S 451 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 4 3 3 4 2 2 2 +--R (- 12a b e + 24a b d e - 12b d e )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 +--R (- 24a b d e + 48a b d e - 24b d e)x - 12a b d e + 24a b d e +--R + +--R 4 4 +--R - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R - b e x + (- 8a b e + 4b d e )x + (- 24a b d e + 18b d e )x +--R + +--R 3 4 2 2 3 4 3 4 4 3 3 2 2 2 2 +--R (8a b e - 24a b d e + 12b d e)x + a e + 4a b d e - 18a b d e +--R + +--R 3 3 +--R 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 3 2 4 4 2 2 5 3 2 +--R (12a b e - 36a b d e + 24b d e)x +--R + +--R 3 2 3 2 3 2 2 5 4 3 2 2 2 2 3 3 4 4 +--R (24a b d e - 36a b d e + 12b d )x + 12a b d e - 24a b d e + 12a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R b e x + (9a b e - 4b d e )x + (8a b e + 12a b d e - 11b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 8a b e + 40a b d e - 27a b d e + 2b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 9a b e + 20a b d e + 2a b d e - 18a b d e + 7b d )x - a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 4a b d e + 18a b d e - 20a b d e + 7a b d +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 452 + +)clear all + +--S 453 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1353 +r0:=-1/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^3)-_ + 2/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^2)+4*b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^4-2*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+_ + e*x))-4*b^3*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 4 3 3 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (36a b d e - 36b d e )x +--R + +--R 3 2 2 4 3 3 3 4 4 +--R (36a b d e - 36b d e)x + 12a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3b e x + (- 10a b e + 22b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 18a b e + 6a b d e + 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 6a b e - 18a b d e + 24a b d e + 12b d e)x - a e - 2a b d e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e + 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 6 3 5 3 5 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 3 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (36a b d e - 36b d e )x +--R + +--R 3 2 2 4 3 3 3 4 4 +--R (36a b d e - 36b d e)x + 12a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + 9b d e x + (- 18a b e + 36a b d e - 9b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 6a b e - 18a b d e + 54a b d e - 27b d e)x - a e - 2a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e + 22a b d e - 13b d +--R / +--R 8 3 7 2 2 6 3 5 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 455 + +--S 456 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 3 3 3 4 2 2 2 +--R (- 12a b e + 12b d e )x + (- 36a b d e + 36b d e )x +--R + +--R 3 2 2 4 3 3 3 4 4 +--R (- 36a b d e + 36b d e)x - 12a b d e + 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 3b e x + (10a b e - 22b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (18a b e - 6a b d e - 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (6a b e + 18a b d e - 24a b d e - 12b d e)x + a e + 2a b d e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R (12a b e - 12b d e )x + (12a b e + 24a b d e - 36b d e )x +--R + +--R 2 3 3 5 3 2 2 3 2 2 4 3 5 4 +--R (36a b d e - 36b d e)x + (36a b d e - 24a b d e - 12b d )x +--R + +--R 2 3 3 4 4 +--R 12a b d e - 12a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R 3b e x + (3a b e + 9b d e )x + (- 18a b e + 45a b d e - 9b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 24a b e + 18a b d e + 45a b d e - 27b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 7a b e - 20a b d e + 48a b d e - 5a b d e - 13b d )x - a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 2a b d e - 6a b d e + 22a b d e - 13a b d +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 6 3 5 3 5 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 457 + +)clear all + +--S 458 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1353 +r0:=-1/4*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^4)-1/3*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^3)-1/2*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^3*(d+e*x)^2)+b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x)*(d+e*x))+b^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 4 3 3 4 2 2 2 4 3 4 4 +--R (12b e x + 48b d e x + 72b d e x + 48b d e x + 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 13b e x + (- 48a b e - 4b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 36a b e - 72a b d e + 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 16a b e - 24a b d e - 48a b d e + 36b d e)x - 3a e - 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 12a b d e + 12b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 4 3 3 4 2 2 2 4 3 4 4 +--R (12b e x + 48b d e x + 72b d e x + 48b d e x + 12b d )log(e x + d) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (- 48a b e + 48b d e )x + (- 36a b e - 72a b d e + 108b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 16a b e - 24a b d e - 48a b d e + 88b d e)x - 3a e - 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 12a b d e + 25b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 460 + +--S 461 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 4 3 3 4 2 2 2 4 3 4 4 +--R (- 12b e x - 48b d e x - 72b d e x - 48b d e x - 12b d ) +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R 13b e x + (48a b e + 4b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (36a b e + 72a b d e - 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (16a b e + 24a b d e + 48a b d e - 36b d e)x + 3a e + 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 6a b d e + 12a b d e - 12b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 4 3 5 2 2 3 +--R 12b e x + (12a b e + 48b d e )x + (48a b d e + 72b d e )x +--R + +--R 4 2 2 5 3 2 4 3 5 4 4 4 +--R (72a b d e + 48b d e)x + (48a b d e + 12b d )x + 12a b d +--R * +--R log(e x + d) +--R + +--R 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R (- 48a b e + 48b d e )x + (- 84a b e - 24a b d e + 108b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 52a b e - 96a b d e + 60a b d e + 88b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 19a b e - 28a b d e - 54a b d e + 76a b d e + 25b d )x - 3a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 4a b d e - 6a b d e - 12a b d e + 25a b d +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1353 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^5) +--R +--R +--R (2) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (- b x - 4a b x - 6a b x - 4a b x - a )\|b x + 2a b x + a +--R / +--R 6 5 5 5 2 4 4 2 4 3 3 3 +--R (5a e - 5b d e )x + (25a d e - 25b d e )x + (50a d e - 50b d e )x +--R + +--R 3 3 4 2 2 4 2 5 5 6 +--R (50a d e - 50b d e )x + (25a d e - 25b d e)x + 5a d e - 5b d +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 5b e x + (- 10a b e - 10b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 10a b e - 10a b d e - 10b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 5a b e - 5a b d e - 5a b d e - 5b d e)x - a e - a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - a b d e - a b d e - b d +--R / +--R 10 5 9 4 2 8 3 3 7 2 4 6 5 5 +--R 5e x + 25d e x + 50d e x + 50d e x + 25d e x + 5d e +--R Type: Union(Expression(Integer),...) +--E 465 + +--S 466 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 4 5 4 3 5 3 2 2 5 2 3 5 4 5 | 2 2 2 +--R (b e x + 4a b e x + 6a b e x + 4a b e x + a e )\|b x + 2a b x + a +--R + +--R 4 5 5 4 4 2 3 5 5 2 3 3 +--R (- 5a b e + 5b d e )x + (- 10a b e + 10b d e )x +--R + +--R 3 2 5 5 3 2 2 4 5 5 4 5 5 5 5 +--R (- 10a b e + 10b d e )x + (- 5a b e + 5b d e)x - a e + b d +--R / +--R 11 10 5 10 2 9 4 +--R (5a e - 5b d e )x + (25a d e - 25b d e )x +--R + +--R 2 9 3 8 3 3 8 4 7 2 +--R (50a d e - 50b d e )x + (50a d e - 50b d e )x +--R + +--R 4 7 5 6 5 6 6 5 +--R (25a d e - 25b d e )x + 5a d e - 5b d e +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 467 + +)clear all + +--S 468 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1353 +r0:=1/6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^6)+_ + 1/30*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^5) +--R +--R +--R (2) +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (- a b e + 6b d)x + (- 14a b e + 24a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 26a b e + 36a b d)x + (- 19a b e + 24a b d)x - 5a e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 8 7 2 2 6 6 +--R (30a e - 60a b d e + 30b d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (180a d e - 360a b d e + 180b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (600a d e - 1200a b d e + 600b d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 5 3 6 2 2 7 2 6 2 7 2 8 +--R (180a d e - 360a b d e + 180b d e)x + 30a d e - 60a b d e + 30b d +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 15b e x + (- 40a b e - 20b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 45a b e - 30a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 24a b e - 18a b d e - 12a b d e - 6b d e)x - 5a e - 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 3a b d e - 2a b d e - b d +--R / +--R 11 6 10 5 2 9 4 3 8 3 4 7 2 5 6 +--R 30e x + 180d e x + 450d e x + 600d e x + 450d e x + 180d e x +--R + +--R 6 5 +--R 30d e +--R Type: Union(Expression(Integer),...) +--E 470 + +--S 471 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 5 4 6 5 5 4 2 3 6 4 5 3 +--R - b e x + (a b e - 6b d e )x + (14a b e - 24a b d e )x +--R + +--R 3 2 6 2 3 5 2 4 6 3 2 5 5 6 +--R (26a b e - 36a b d e )x + (19a b e - 24a b d e )x + 5a e +--R + +--R 4 5 +--R - 6a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 15a b e + 30a b d e - 15b d e )x +--R + +--R 3 3 6 2 4 5 6 3 3 3 +--R (- 40a b e + 60a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 6 4 2 2 +--R (- 45a b e + 60a b d e - 15b d e )x +--R + +--R 5 6 4 2 5 6 5 6 6 5 5 6 6 +--R (- 24a b e + 30a b d e - 6b d e)x - 5a e + 6a b d e - b d +--R / +--R 2 13 12 2 2 11 6 +--R (30a e - 60a b d e + 30b d e )x +--R + +--R 2 12 2 11 2 3 10 5 +--R (180a d e - 360a b d e + 180b d e )x +--R + +--R 2 2 11 3 10 2 4 9 4 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (600a d e - 1200a b d e + 600b d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 2 8 5 +--R (180a d e - 360a b d e + 180b d e )x + 30a d e - 60a b d e + 30b d e +--R Type: Expression(Integer) +--E 471 + +--S 472 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 472 + +)clear all + +--S 473 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1353 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^7)+_ + 1/21*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^6)+_ + 1/105*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R - b e x + (a b e - 7b d e)x + (- a b e + 7a b d e - 21b d )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 34a b e + 98a b d e - 84a b d )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 71a b e + 182a b d e - 126a b d )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 55a b e + 133a b d e - 84a b d )x - 15a e + 35a b d e - 21a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (105a e - 315a b d e + 315a b d e - 105b d e )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e)x + 105a d e +--R + +--R 2 8 2 2 9 3 10 +--R - 315a b d e + 315a b d e - 105b d +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 35b e x + (- 105a b e - 35b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 126a b e - 63a b d e - 21b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 70a b e - 42a b d e - 21a b d e - 7b d e)x - 15a e - 10a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 3a b d e - b d +--R / +--R 12 7 11 6 2 10 5 3 9 4 4 8 3 +--R 105e x + 735d e x + 2205d e x + 3675d e x + 3675d e x +--R + +--R 5 7 2 6 6 7 5 +--R 2205d e x + 735d e x + 105d e +--R Type: Union(Expression(Integer),...) +--E 475 + +--S 476 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 6 5 7 6 6 5 2 4 7 5 6 6 2 5 4 +--R b e x + (- a b e + 7b d e )x + (a b e - 7a b d e + 21b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 3 +--R (34a b e - 98a b d e + 84a b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 2 +--R (71a b e - 182a b d e + 126a b d e )x +--R + +--R 5 7 4 2 6 3 3 2 5 6 7 5 6 +--R (55a b e - 133a b d e + 84a b d e )x + 15a e - 35a b d e +--R + +--R 4 2 2 5 +--R 21a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 35a b e + 105a b d e - 105a b d e + 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 7 4 3 3 +--R (- 105a b e + 280a b d e - 210a b d e + 35b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 7 5 2 2 +--R (- 126a b e + 315a b d e - 210a b d e + 21b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 7 6 7 7 6 6 +--R (- 70a b e + 168a b d e - 105a b d e + 7b d e)x - 15a e + 35a b d e +--R + +--R 5 2 2 5 7 7 +--R - 21a b d e + b d +--R / +--R 3 15 2 14 2 2 13 3 3 12 7 +--R (105a e - 315a b d e + 315a b d e - 105b d e )x +--R + +--R 3 14 2 2 13 2 3 12 3 4 11 6 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e )x +--R + +--R 3 2 13 2 3 12 2 4 11 3 5 10 5 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 3 12 2 4 11 2 5 10 3 6 9 4 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 4 11 2 5 10 2 6 9 3 7 8 3 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 5 10 2 6 9 2 7 8 3 8 7 2 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 6 9 2 7 8 2 8 7 3 9 6 3 7 8 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e )x + 105a d e +--R + +--R 2 8 7 2 9 6 3 10 5 +--R - 315a b d e + 315a b d e - 105b d e +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1353 +r0:=1/8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^8)+_ + 3/56*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^7)+_ + 1/56*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^6)+_ + 1/280*b^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 7 3 7 6 3 7 2 6 2 5 3 6 2 7 2 5 +--R b e x + (- a b e + 8b d e )x + (a b e - 8a b d e + 28b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- a b e + 8a b d e - 28a b d e + 56b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (- 69a b e + 272a b d e - 392a b d e + 224a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 155a b e + 568a b d e - 728a b d e + 336a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (- 125a b e + 440a b d e - 532a b d e + 224a b d )x - 35a e +--R + +--R 6 2 5 2 2 4 3 3 +--R 120a b d e - 140a b d e + 56a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 12 3 11 2 2 2 10 3 3 9 4 4 8 8 +--R (280a e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d e )x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 +--R 2240a d e - 8960a b d e + 13440a b d e - 8960a b d e +--R + +--R 4 5 7 +--R 2240b d e +--R * +--R 7 +--R x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 6 6 +--R 7840b d e +--R * +--R 6 +--R x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 7 5 +--R 15680b d e +--R * +--R 5 +--R x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 +--R 19600a d e - 78400a b d e + 117600a b d e - 78400a b d e +--R + +--R 4 8 4 +--R 19600b d e +--R * +--R 4 +--R x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 8 4 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 9 3 +--R 15680b d e +--R * +--R 3 +--R x +--R + +--R 4 6 6 3 7 5 2 2 8 4 3 9 3 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 10 2 +--R 7840b d e +--R * +--R 2 +--R x +--R + +--R 4 7 5 3 8 4 2 2 9 3 3 10 2 4 11 +--R (2240a d e - 8960a b d e + 13440a b d e - 8960a b d e + 2240b d e)x +--R + +--R 4 8 4 3 9 3 2 2 10 2 3 11 4 12 +--R 280a d e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 70b e x + (- 224a b e - 56b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 280a b e - 112a b d e - 28b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 160a b e - 80a b d e - 32a b d e - 8b d e)x - 35a e - 20a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 10a b d e - 4a b d e - b d +--R / +--R 13 8 12 7 2 11 6 3 10 5 4 9 4 +--R 280e x + 2240d e x + 7840d e x + 15680d e x + 19600d e x +--R + +--R 5 8 3 6 7 2 7 6 8 5 +--R 15680d e x + 7840d e x + 2240d e x + 280d e +--R Type: Union(Expression(Integer),...) +--E 480 + +--S 481 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 8 7 6 8 7 7 6 2 5 8 6 7 7 2 6 5 +--R - b e x + (a b e - 8b d e )x + (- a b e + 8a b d e - 28b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 4 +--R (a b e - 8a b d e + 28a b d e - 56b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 3 +--R (69a b e - 272a b d e + 392a b d e - 224a b d e )x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 2 +--R (155a b e - 568a b d e + 728a b d e - 336a b d e )x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 7 8 +--R (125a b e - 440a b d e + 532a b d e - 224a b d e )x + 35a e +--R + +--R 6 7 5 2 2 6 4 3 3 5 +--R - 120a b d e + 140a b d e - 56a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 8 4 4 4 +--R (- 70a b e + 280a b d e - 420a b d e + 280a b d e - 70b d e )x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 8 5 3 3 +--R (- 224a b e + 840a b d e - 1120a b d e + 560a b d e - 56b d e )x +--R + +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 8 6 2 2 +--R (- 280a b e + 1008a b d e - 1260a b d e + 560a b d e - 28b d e )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 8 7 +--R (- 160a b e + 560a b d e - 672a b d e + 280a b d e - 8b d e)x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 8 8 +--R - 35a e + 120a b d e - 140a b d e + 56a b d e - b d +--R / +--R 4 17 3 16 2 2 2 15 3 3 14 4 4 13 8 +--R (280a e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d e )x +--R + +--R 4 16 3 2 15 2 2 3 14 3 4 13 +--R 2240a d e - 8960a b d e + 13440a b d e - 8960a b d e +--R + +--R 4 5 12 +--R 2240b d e +--R * +--R 7 +--R x +--R + +--R 4 2 15 3 3 14 2 2 4 13 3 5 12 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 6 11 +--R 7840b d e +--R * +--R 6 +--R x +--R + +--R 4 3 14 3 4 13 2 2 5 12 3 6 11 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 7 10 +--R 15680b d e +--R * +--R 5 +--R x +--R + +--R 4 4 13 3 5 12 2 2 6 11 3 7 10 +--R 19600a d e - 78400a b d e + 117600a b d e - 78400a b d e +--R + +--R 4 8 9 +--R 19600b d e +--R * +--R 4 +--R x +--R + +--R 4 5 12 3 6 11 2 2 7 10 3 8 9 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 9 8 +--R 15680b d e +--R * +--R 3 +--R x +--R + +--R 4 6 11 3 7 10 2 2 8 9 3 9 8 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 10 7 +--R 7840b d e +--R * +--R 2 +--R x +--R + +--R 4 7 10 3 8 9 2 2 9 8 3 10 7 +--R 2240a d e - 8960a b d e + 13440a b d e - 8960a b d e +--R + +--R 4 11 6 +--R 2240b d e +--R * +--R x +--R + +--R 4 8 9 3 9 8 2 2 10 7 3 11 6 4 12 5 +--R 280a d e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d e +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 482 + +)clear all + +--S 483 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1353 +r0:=1/9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^9)+_ + 1/18*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^8)+_ + 1/42*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^7)+_ + 1/126*b^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^6)+_ + 1/630*b^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^5*(d+e*x)^5) +--R +--R +--R (2) +--R 8 4 8 7 4 8 3 7 2 6 4 7 3 8 2 2 6 +--R - b e x + (a b e - 9b d e )x + (- a b e + 9a b d e - 36b d e )x +--R + +--R 3 5 4 2 6 3 7 2 2 8 3 5 +--R (a b e - 9a b d e + 36a b d e - 84b d e)x +--R + +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (- a b e + 9a b d e - 36a b d e + 84a b d e - 126b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (- 125a b e + 621a b d e - 1224a b d e + 1176a b d e - 504a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (- 295a b e + 1395a b d e - 2556a b d e + 2184a b d e - 756a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (- 245a b e + 1125a b d e - 1980a b d e + 1596a b d e - 504a b d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R - 70a e + 315a b d e - 540a b d e + 420a b d e - 126a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 14 4 13 3 2 2 12 2 3 3 11 +--R 630a e - 3150a b d e + 6300a b d e - 6300a b d e +--R + +--R 4 4 10 5 5 9 +--R 3150a b d e - 630b d e +--R * +--R 9 +--R x +--R + +--R 5 13 4 2 12 3 2 3 11 2 3 4 10 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 5 9 5 6 8 +--R 28350a b d e - 5670b d e +--R * +--R 8 +--R x +--R + +--R 5 2 12 4 3 11 3 2 4 10 2 3 5 9 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 6 8 5 7 7 +--R 113400a b d e - 22680b d e +--R * +--R 7 +--R x +--R + +--R 5 3 11 4 4 10 3 2 5 9 2 3 6 8 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 7 7 5 8 6 +--R 264600a b d e - 52920b d e +--R * +--R 6 +--R x +--R + +--R 5 4 10 4 5 9 3 2 6 8 2 3 7 7 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 8 6 5 9 5 +--R 396900a b d e - 79380b d e +--R * +--R 5 +--R x +--R + +--R 5 5 9 4 6 8 3 2 7 7 2 3 8 6 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 9 5 5 10 4 +--R 396900a b d e - 79380b d e +--R * +--R 4 +--R x +--R + +--R 5 6 8 4 7 7 3 2 8 6 2 3 9 5 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 10 4 5 11 3 +--R 264600a b d e - 52920b d e +--R * +--R 3 +--R x +--R + +--R 5 7 7 4 8 6 3 2 9 5 2 3 10 4 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 11 3 5 12 2 +--R 113400a b d e - 22680b d e +--R * +--R 2 +--R x +--R + +--R 5 8 6 4 9 5 3 2 10 4 2 3 11 3 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 12 2 5 13 +--R 28350a b d e - 5670b d e +--R * +--R x +--R + +--R 5 9 5 4 10 4 3 2 11 3 2 3 12 2 4 13 +--R 630a d e - 3150a b d e + 6300a b d e - 6300a b d e + 3150a b d e +--R + +--R 5 14 +--R - 630b d +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 126b e x + (- 420a b e - 84b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 540a b e - 180a b d e - 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 315a b e - 135a b d e - 45a b d e - 9b d e)x - 70a e - 35a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 15a b d e - 5a b d e - b d +--R / +--R 14 9 13 8 2 12 7 3 11 6 4 10 5 +--R 630e x + 5670d e x + 22680d e x + 52920d e x + 79380d e x +--R + +--R 5 9 4 6 8 3 7 7 2 8 6 9 5 +--R 79380d e x + 52920d e x + 22680d e x + 5670d e x + 630d e +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 9 8 7 9 8 8 7 2 6 9 7 8 8 2 7 6 +--R b e x + (- a b e + 9b d e )x + (a b e - 9a b d e + 36b d e )x +--R + +--R 3 5 9 2 6 8 7 2 7 8 3 6 5 +--R (- a b e + 9a b d e - 36a b d e + 84b d e )x +--R + +--R 4 4 9 3 5 8 2 6 2 7 7 3 6 8 4 5 4 +--R (a b e - 9a b d e + 36a b d e - 84a b d e + 126b d e )x +--R + +--R 5 3 9 4 4 8 3 5 2 7 2 6 3 6 +--R 125a b e - 621a b d e + 1224a b d e - 1176a b d e +--R + +--R 7 4 5 +--R 504a b d e +--R * +--R 3 +--R x +--R + +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 +--R 295a b e - 1395a b d e + 2556a b d e - 2184a b d e +--R + +--R 2 6 4 5 +--R 756a b d e +--R * +--R 2 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 +--R 245a b e - 1125a b d e + 1980a b d e - 1596a b d e +--R + +--R 3 5 4 5 +--R 504a b d e +--R * +--R x +--R + +--R 8 9 7 8 6 2 2 7 5 3 3 6 4 4 4 5 +--R 70a e - 315a b d e + 540a b d e - 420a b d e + 126a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 +--R - 126a b e + 630a b d e - 1260a b d e + 1260a b d e - 630a b d e +--R + +--R 9 5 4 +--R 126b d e +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 5 2 7 3 6 3 6 +--R - 420a b e + 2016a b d e - 3780a b d e + 3360a b d e +--R + +--R 2 7 4 5 9 6 3 +--R - 1260a b d e + 84b d e +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 +--R - 540a b e + 2520a b d e - 4536a b d e + 3780a b d e +--R + +--R 3 6 4 5 9 7 2 +--R - 1260a b d e + 36b d e +--R * +--R 2 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 +--R - 315a b e + 1440a b d e - 2520a b d e + 2016a b d e +--R + +--R 4 5 4 5 9 8 +--R - 630a b d e + 9b d e +--R * +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 9 9 +--R - 70a e + 315a b d e - 540a b d e + 420a b d e - 126a b d e + b d +--R / +--R 5 19 4 18 3 2 2 17 2 3 3 16 +--R 630a e - 3150a b d e + 6300a b d e - 6300a b d e +--R + +--R 4 4 15 5 5 14 +--R 3150a b d e - 630b d e +--R * +--R 9 +--R x +--R + +--R 5 18 4 2 17 3 2 3 16 2 3 4 15 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 5 14 5 6 13 +--R 28350a b d e - 5670b d e +--R * +--R 8 +--R x +--R + +--R 5 2 17 4 3 16 3 2 4 15 2 3 5 14 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 6 13 5 7 12 +--R 113400a b d e - 22680b d e +--R * +--R 7 +--R x +--R + +--R 5 3 16 4 4 15 3 2 5 14 2 3 6 13 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 7 12 5 8 11 +--R 264600a b d e - 52920b d e +--R * +--R 6 +--R x +--R + +--R 5 4 15 4 5 14 3 2 6 13 2 3 7 12 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 8 11 5 9 10 +--R 396900a b d e - 79380b d e +--R * +--R 5 +--R x +--R + +--R 5 5 14 4 6 13 3 2 7 12 2 3 8 11 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 9 10 5 10 9 +--R 396900a b d e - 79380b d e +--R * +--R 4 +--R x +--R + +--R 5 6 13 4 7 12 3 2 8 11 2 3 9 10 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 10 9 5 11 8 +--R 264600a b d e - 52920b d e +--R * +--R 3 +--R x +--R + +--R 5 7 12 4 8 11 3 2 9 10 2 3 10 9 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 11 8 5 12 7 +--R 113400a b d e - 22680b d e +--R * +--R 2 +--R x +--R + +--R 5 8 11 4 9 10 3 2 10 9 2 3 11 8 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 12 7 5 13 6 +--R 28350a b d e - 5670b d e +--R * +--R x +--R + +--R 5 9 10 4 10 9 3 2 11 8 2 3 12 7 +--R 630a d e - 3150a b d e + 6300a b d e - 6300a b d e +--R + +--R 4 13 6 5 14 5 +--R 3150a b d e - 630b d e +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 487 + +)clear all + +--S 488 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1353 +r0:=-1/10*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^10)-_ + 2/45*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^9)-1/60*b^2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^8)-1/180*b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(d+e*x)^7)-1/1260*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 210b e x + (- 720a b e - 120b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 945a b e - 270a b d e - 45b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 560a b e - 210a b d e - 60a b d e - 10b d e)x - 126a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 56a b d e - 21a b d e - 6a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 15 11 15 14 10 +--R 1260b e x + (1260a e + 12600b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (12600a d e + 56700b d e )x + (56700a d e + 151200b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (151200a d e + 264600b d e )x + (264600a d e + 317520b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (317520a d e + 264600b d e )x + (264600a d e + 151200b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (151200a d e + 56700b d e )x + (56700a d e + 12600b d e )x +--R + +--R 9 6 10 5 10 5 +--R (12600a d e + 1260b d e )x + 1260a d e +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 210b e x + (- 720a b e - 120b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 945a b e - 270a b d e - 45b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 560a b e - 210a b d e - 60a b d e - 10b d e)x - 126a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 56a b d e - 21a b d e - 6a b d e - b d +--R / +--R 15 10 14 9 2 13 8 3 12 7 4 11 6 +--R 1260e x + 12600d e x + 56700d e x + 151200d e x + 264600d e x +--R + +--R 5 10 5 6 9 4 7 8 3 8 7 2 9 6 +--R 317520d e x + 264600d e x + 151200d e x + 56700d e x + 12600d e x +--R + +--R 10 5 +--R 1260d e +--R Type: Union(Expression(Integer),...) +--E 490 + +--S 491 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R 210b e x + (720a b e + 120b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (945a b e + 270a b d e + 45b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (560a b e + 210a b d e + 60a b d e + 10b d e)x + 126a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 56a b d e + 21a b d e + 6a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 210b e x + (- 930a b e - 120b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 1665a b e - 390a b d e - 45b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 1505a b e - 480a b d e - 105a b d e - 10b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 686a b e - 266a b d e - 81a b d e - 16a b d e - b d )x - 126a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 56a b d e - 21a b d e - 6a b d e - a b d +--R / +--R 15 11 15 14 10 +--R 1260b e x + (1260a e + 12600b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (12600a d e + 56700b d e )x + (56700a d e + 151200b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (151200a d e + 264600b d e )x + (264600a d e + 317520b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (317520a d e + 264600b d e )x + (264600a d e + 151200b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (151200a d e + 56700b d e )x + (56700a d e + 12600b d e )x +--R + +--R 9 6 10 5 10 5 +--R (12600a d e + 1260b d e )x + 1260a d e +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1353 +r0:=-1/11*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^11)-_ + 2/55*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^10)-2/165*b^2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^9)-4/1155*b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(d+e*x)^8)-1/2310*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 330b e x + (- 1155a b e - 165b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1540a b e - 385a b d e - 55b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 924a b e - 308a b d e - 77a b d e - 11b d e)x - 210a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 84a b d e - 28a b d e - 7a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 16 12 16 15 11 +--R 2310b e x + (2310a e + 25410b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (25410a d e + 127050b d e )x + (127050a d e + 381150b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (381150a d e + 762300b d e )x + (762300a d e + 1067220b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (1067220a d e + 1067220b d e )x + (1067220a d e + 762300b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (762300a d e + 381150b d e )x + (381150a d e + 127050b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (127050a d e + 25410b d e )x + (25410a d e + 2310b d e )x +--R + +--R 11 5 +--R 2310a d e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 330b e x + (- 1155a b e - 165b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1540a b e - 385a b d e - 55b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 924a b e - 308a b d e - 77a b d e - 11b d e)x - 210a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 84a b d e - 28a b d e - 7a b d e - b d +--R / +--R 16 11 15 10 2 14 9 3 13 8 +--R 2310e x + 25410d e x + 127050d e x + 381150d e x +--R + +--R 4 12 7 5 11 6 6 10 5 7 9 4 +--R 762300d e x + 1067220d e x + 1067220d e x + 762300d e x +--R + +--R 8 8 3 9 7 2 10 6 11 5 +--R 381150d e x + 127050d e x + 25410d e x + 2310d e +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R 330b e x + (1155a b e + 165b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1540a b e + 385a b d e + 55b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (924a b e + 308a b d e + 77a b d e + 11b d e)x + 210a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 84a b d e + 28a b d e + 7a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 330b e x + (- 1485a b e - 165b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 2695a b e - 550a b d e - 55b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 2464a b e - 693a b d e - 132a b d e - 11b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 1134a b e - 392a b d e - 105a b d e - 18a b d e - b d )x - 210a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 84a b d e - 28a b d e - 7a b d e - a b d +--R / +--R 16 12 16 15 11 +--R 2310b e x + (2310a e + 25410b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (25410a d e + 127050b d e )x + (127050a d e + 381150b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (381150a d e + 762300b d e )x + (762300a d e + 1067220b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (1067220a d e + 1067220b d e )x + (1067220a d e + 762300b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (762300a d e + 381150b d e )x + (381150a d e + 127050b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (127050a d e + 25410b d e )x + (25410a d e + 2310b d e )x +--R + +--R 11 5 +--R 2310a d e +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x +--R + +--R 12 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 1353 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 m +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )(e x + d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1353 +r0:=-120*(b*d-a*e)^3*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(4+m)*_ + (5+m)*(6+m)*(7+m))+30*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(5+m)*(6+m)*(7+m))-6*(b*d-a*e)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(6+m)*(7+m))+(a+b*x)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(7+m))-720*(b*d-a*e)^5*(d+e*x)^(1+m)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m))+_ + 720*(b*d-a*e)^6*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(1+m)*_ + (2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)*(a+b*x))+360*(b*d-a*e)^4*(a+b*x)*_ + (d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)) +--R +--R +--R (2) +--R 6 6 6 6 6 5 6 6 4 6 6 3 6 6 2 6 6 +--R b e m + 21b e m + 175b e m + 735b e m + 1624b e m + 1764b e m +--R + +--R 6 6 +--R 720b e +--R * +--R 6 +--R x +--R + +--R 5 6 6 5 6 6 5 5 5 6 6 5 4 +--R 6a b e m + (132a b e - 6b d e )m + (1140a b e - 90b d e )m +--R + +--R 5 6 6 5 3 5 6 6 5 2 +--R (4920a b e - 510b d e )m + (11094a b e - 1350b d e )m +--R + +--R 5 6 6 5 5 6 6 5 +--R (12228a b e - 1644b d e )m + 5040a b e - 720b d e +--R * +--R 5 +--R x +--R + +--R 2 4 6 6 2 4 6 5 5 5 +--R 15a b e m + (345a b e - 30a b d e )m +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (3105a b e - 510a b d e + 30b d e )m +--R + +--R 2 4 6 5 5 6 2 4 3 +--R (13875a b e - 3150a b d e + 300b d e )m +--R + +--R 2 4 6 5 5 6 2 4 2 +--R (32160a b e - 8850a b d e + 1050b d e )m +--R + +--R 2 4 6 5 5 6 2 4 2 4 6 +--R (36180a b e - 11220a b d e + 1500b d e )m + 15120a b e +--R + +--R 5 5 6 2 4 +--R - 5040a b d e + 720b d e +--R * 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d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 31644a b e + 44340a b d e - 38040a b d e + 19800a b d e +--R + +--R 5 4 2 6 5 +--R - 5760a b d e + 720b d e +--R * +--R m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 15120a b e + 25200a b d e - 25200a b d e + 15120a b d e +--R + +--R 5 4 2 6 5 +--R - 5040a b d e + 720b d e +--R * +--R x +--R + +--R 6 6 6 6 6 5 5 5 +--R - a e m + (- 27a e + 6a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 4 +--R (- 295a e + 150a b d e - 30a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 3 +--R (- 1665a e + 1470a b d e - 660a b d e + 120a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 5104a e + 7050a b d e - 5370a b d e + 2160a b d e +--R + +--R 2 4 4 2 +--R - 360a b d e +--R * +--R 2 +--R m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 8028a e + 16524a b d e - 19140a b d e + 12840a b d e +--R + +--R 2 4 4 2 5 5 +--R - 4680a b d e + 720a b d e +--R * +--R m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 5040a e + 15120a b d e - 25200a b d e + 25200a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 15120a b d e + 5040a b d e - 720b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m + 13132b e m +--R + +--R 7 7 +--R 13068b e m + 5040b e +--R * +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a e m + 28a e m + 322a e m + 1960a e m + 6769a e m + 13132a e m +--R + +--R 7 7 +--R 13068a e m + 5040a e +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x +--R + +--R 7 +--R - a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 502 + +)clear all + +--S 503 of 1353 +t0:=(a+b*x)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 9 14 4 9 5 8 13 2 3 9 4 8 5 2 7 12 +--R b e x + (5a b e + 9b d e )x + (10a b e + 45a b d e + 36b d e )x +--R + +--R 3 2 9 2 3 8 4 2 7 5 3 6 11 +--R (10a b e + 90a b d e + 180a b d e + 84b d e )x +--R + +--R 4 9 3 2 8 2 3 2 7 4 3 6 5 4 5 10 +--R (5a b e + 90a b d e + 360a b d e + 420a b d e + 126b d e )x +--R + +--R 5 9 4 8 3 2 2 7 2 3 3 6 4 4 5 +--R a e + 45a b d e + 360a b d e + 840a b d e + 630a b d e +--R + +--R 5 5 4 +--R 126b d e +--R * +--R 9 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 4 5 4 +--R 9a d e + 180a b d e + 840a b d e + 1260a b d e + 630a b d e +--R + +--R 5 6 3 +--R 84b d e +--R * +--R 8 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 4 6 3 +--R 36a d e + 420a b d e + 1260a b d e + 1260a b d e + 420a b d e +--R + +--R 5 7 2 +--R 36b d e +--R * +--R 7 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 4 7 2 +--R 84a d e + 630a b d e + 1260a b d e + 840a b d e + 180a b d e +--R + +--R 5 8 +--R 9b d e +--R * +--R 6 +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 4 8 +--R 126a d e + 630a b d e + 840a b d e + 360a b d e + 45a b d e +--R + +--R 5 9 +--R b d +--R * +--R 5 +--R x +--R + +--R 5 5 4 4 6 3 3 2 7 2 2 3 8 4 9 4 +--R (126a d e + 420a b d e + 360a b d e + 90a b d e + 5a b d )x +--R + +--R 5 6 3 4 7 2 3 2 8 2 3 9 3 +--R (84a d e + 180a b d e + 90a b d e + 10a b d )x +--R + +--R 5 7 2 4 8 3 2 9 2 5 8 4 9 5 9 +--R (36a d e + 45a b d e + 10a b d )x + (9a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1353 +r0:=-1/364*(b*d-a*e)^3*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/112*(b*d-a*e)^2*(a+b*x)*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/40*(b*d-a*e)*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/16*(a+b*x)*_ + (d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/8008*(b*d-a*e)^5*(d+e*x)^10*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/80080*(b*d-a*e)^6*(d+e*x)^10*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/1456*(b*d-a*e)^4*(a+b*x)*(d+e*x)^10*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 16 16 5 16 6 15 15 +--R 5005b e x + (32032a b e + 48048b d e )x +--R + +--R 2 4 16 5 15 6 2 14 14 +--R (85800a b e + 308880a b d e + 205920b d e )x +--R + +--R 3 3 16 2 4 15 5 2 14 6 3 13 13 +--R (123200a b e + 831600a b d e + 1330560a b d e + 517440b d e )x +--R + +--R 4 2 16 3 3 15 2 4 2 14 +--R 100100a b e + 1201200a b d e + 3603600a b d e +--R + +--R 5 3 13 6 4 12 +--R 3363360a b d e + 840840b d e +--R * +--R 12 +--R x +--R + +--R 5 16 4 2 15 3 3 2 14 +--R 43680a b e + 982800a b d e + 5241600a b d e +--R + +--R 2 4 3 13 5 4 12 6 5 11 +--R 9172800a b d e + 5503680a b d e + 917280b d e +--R * +--R 11 +--R x +--R + +--R 6 16 5 15 4 2 2 14 3 3 3 13 +--R 8008a e + 432432a b d e + 4324320a b d e + 13453440a b d e +--R + +--R 2 4 4 12 5 5 11 6 6 10 +--R 15135120a b d e + 6054048a b d e + 672672b d e +--R * +--R 10 +--R x +--R + +--R 6 15 5 2 14 4 2 3 13 +--R 80080a d e + 1921920a b d e + 11211200a b d e +--R + +--R 3 3 4 12 2 4 5 11 5 6 10 +--R 22422400a b d e + 16816800a b d e + 4484480a b d e +--R + +--R 6 7 9 +--R 320320b d e +--R * +--R 9 +--R x +--R + +--R 6 2 14 5 3 13 4 2 4 12 +--R 360360a d e + 5045040a b d e + 18918900a b d e +--R + +--R 3 3 5 11 2 4 6 10 5 7 9 6 8 8 +--R 25225200a b d e + 12612600a b d e + 2162160a b d e + 90090b d e +--R * +--R 8 +--R x +--R + +--R 6 3 13 5 4 12 4 2 5 11 +--R 960960a d e + 8648640a b d e + 21621600a b d e +--R + +--R 3 3 6 10 2 4 7 9 5 8 8 6 9 7 +--R 19219200a b d e + 6177600a b d e + 617760a b d e + 11440b d e +--R * +--R 7 +--R x +--R + +--R 6 4 12 5 5 11 4 2 6 10 +--R 1681680a d e + 10090080a b d e + 16816800a b d e +--R + +--R 3 3 7 9 2 4 8 8 5 9 7 +--R 9609600a b d e + 1801800a b d e + 80080a b d e +--R * +--R 6 +--R x +--R + +--R 6 5 11 5 6 10 4 2 7 9 +--R 2018016a d e + 8072064a b d e + 8648640a b d e +--R + +--R 3 3 8 8 2 4 9 7 +--R 2882880a b d e + 240240a b d e +--R * +--R 5 +--R x +--R + +--R 6 6 10 5 7 9 4 2 8 8 3 3 9 7 4 +--R (1681680a d e + 4324320a b d e + 2702700a b d e + 400400a b d e )x +--R + +--R 6 7 9 5 8 8 4 2 9 7 3 +--R (960960a d e + 1441440a b d e + 400400a b d e )x +--R + +--R 6 8 8 5 9 7 2 6 9 7 6 10 6 +--R (360360a d e + 240240a b d e )x + 80080a d e x + 8008a d e +--R + +--R 5 11 5 4 2 12 4 3 3 13 3 2 4 14 2 +--R - 4368a b d e + 1820a b d e - 560a b d e + 120a b d e +--R + +--R 5 15 6 16 +--R - 16a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 80080b e x + 80080a e +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 9 16 5 9 6 8 15 +--R 5005b e x + (32032a b e + 48048b d e )x +--R + +--R 2 4 9 5 8 6 2 7 14 +--R (85800a b e + 308880a b d e + 205920b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 13 +--R (123200a b e + 831600a b d e + 1330560a b d e + 517440b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 5 3 6 +--R 100100a b e + 1201200a b d e + 3603600a b d e + 3363360a b d e +--R + +--R 6 4 5 +--R 840840b d e +--R * +--R 12 +--R x +--R + +--R 5 9 4 2 8 3 3 2 7 2 4 3 6 +--R 43680a b e + 982800a b d e + 5241600a b d e + 9172800a b d e +--R + +--R 5 4 5 6 5 4 +--R 5503680a b d e + 917280b d e +--R * +--R 11 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 +--R 8008a e + 432432a b d e + 4324320a b d e + 13453440a b d e +--R + +--R 2 4 4 5 5 5 4 6 6 3 +--R 15135120a b d e + 6054048a b d e + 672672b d e +--R * +--R 10 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R 80080a d e + 1921920a b d e + 11211200a b d e + 22422400a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R 16816800a b d e + 4484480a b d e + 320320b d e +--R * +--R 9 +--R x +--R + +--R 6 2 7 5 3 6 4 2 4 5 3 3 5 4 +--R 360360a d e + 5045040a b d e + 18918900a b d e + 25225200a b d e +--R + +--R 2 4 6 3 5 7 2 6 8 +--R 12612600a b d e + 2162160a b d e + 90090b d e +--R * +--R 8 +--R x +--R + +--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 +--R 960960a d e + 8648640a b d e + 21621600a b d e + 19219200a b d e +--R + +--R 2 4 7 2 5 8 6 9 +--R 6177600a b d e + 617760a b d e + 11440b d +--R * +--R 7 +--R x +--R + +--R 6 4 5 5 5 4 4 2 6 3 3 3 7 2 +--R 1681680a d e + 10090080a b d e + 16816800a b d e + 9609600a b d e +--R + +--R 2 4 8 5 9 +--R 1801800a b d e + 80080a b d +--R * +--R 6 +--R x +--R + +--R 6 5 4 5 6 3 4 2 7 2 3 3 8 +--R 2018016a d e + 8072064a b d e + 8648640a b d e + 2882880a b d e +--R + +--R 2 4 9 +--R 240240a b d +--R * +--R 5 +--R x +--R + +--R 6 6 3 5 7 2 4 2 8 3 3 9 4 +--R (1681680a d e + 4324320a b d e + 2702700a b d e + 400400a b d )x +--R + +--R 6 7 2 5 8 4 2 9 3 +--R (960960a d e + 1441440a b d e + 400400a b d )x +--R + +--R 6 8 5 9 2 6 9 +--R (360360a d e + 240240a b d )x + 80080a d x +--R / +--R 80080 +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 16 16 5 16 6 15 15 +--R - 5005b e x + (- 32032a b e - 48048b d e )x +--R + +--R 2 4 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8339760a b d e +--R + +--R 6 8 8 7 9 7 +--R 707850a b d e + 11440b d e +--R * +--R 8 +--R x +--R + +--R 7 3 13 6 4 12 5 2 5 11 +--R 960960a d e + 10330320a b d e + 31711680a b d e +--R + +--R 4 3 6 10 3 4 7 9 2 5 8 8 6 9 7 +--R 36036000a b d e + 15787200a b d e + 2419560a b d e + 91520a b d e +--R * +--R 7 +--R x +--R + +--R 7 4 12 6 5 11 5 2 6 10 +--R 1681680a d e + 12108096a b d e + 24888864a b d e +--R + +--R 4 3 7 9 3 4 8 8 2 5 9 7 +--R 18258240a b d e + 4684680a b d e + 320320a b d e +--R * +--R 6 +--R x +--R + +--R 7 5 11 6 6 10 5 2 7 9 +--R 2018016a d e + 9753744a b d e + 12972960a b d e +--R + +--R 4 3 8 8 3 4 9 7 +--R 5585580a b d e + 640640a b d e +--R * +--R 5 +--R x +--R + +--R 7 6 10 6 7 9 5 2 8 8 4 3 9 7 4 +--R (1681680a d e + 5285280a b d e + 4144140a b d e + 800800a b d e )x +--R + +--R 7 7 9 6 8 8 5 2 9 7 3 +--R (960960a d e + 1801800a b d e + 640640a b d e )x +--R + +--R 7 8 8 6 9 7 2 7 9 7 +--R (360360a d e + 320320a b d e )x + 80080a d e x +--R / +--R 7 7 +--R 80080b e x + 80080a e +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 9 15 5 9 6 8 14 +--R b e x + (6a b e + 9b d e )x +--R + +--R 2 4 9 5 8 6 2 7 13 +--R (15a b e + 54a b d e + 36b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 12 +--R (20a b e + 135a b d e + 216a b d e + 84b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 5 3 6 6 4 5 11 +--R (15a b e + 180a b d e + 540a b d e + 504a b d e + 126b d e )x +--R + +--R 5 9 4 2 8 3 3 2 7 2 4 3 6 5 4 5 +--R 6a b e + 135a b d e + 720a b d e + 1260a b d e + 756a b d e +--R + +--R 6 5 4 +--R 126b d e +--R * +--R 10 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 2 4 4 5 +--R a e + 54a b d e + 540a b d e + 1680a b d e + 1890a b d e +--R + +--R 5 5 4 6 6 3 +--R 756a b d e + 84b d e +--R * +--R 9 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R 9a d e + 216a b d e + 1260a b d e + 2520a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R 1890a b d e + 504a b d e + 36b d e +--R * +--R 8 +--R x +--R + +--R 6 2 7 5 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- 63a b d e - 36b d e )x +--R + +--R 3 4 9 2 5 8 6 2 7 7 3 6 13 +--R (- 35a b e - 189a b d e - 252a b d e - 84b d e )x +--R + +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 7 4 5 12 +--R (- 35a b e - 315a b d e - 756a b d e - 588a b d e - 126b d e )x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 6 4 5 +--R - 21a b e - 315a b d e - 1260a b d e - 1764a b d e - 882a b d e +--R + +--R 7 5 4 +--R - 126b d e +--R * +--R 11 +--R x +--R + +--R 6 9 5 2 8 4 3 2 7 3 4 3 6 2 5 4 5 +--R - 7a b e - 189a b d e - 1260a b d e - 2940a b d e - 2646a b d e +--R + +--R 6 5 4 7 6 3 +--R - 882a b d e - 84b d e +--R * +--R 10 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 3 4 4 5 +--R - a e - 63a b d e - 756a b d e - 2940a b d e - 4410a b d e +--R + +--R 2 5 5 4 6 6 3 7 7 2 +--R - 2646a b d e - 588a b d e - 36b d e +--R * +--R 9 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 3 4 5 4 +--R - 9a d e - 252a b d e - 1764a b d e - 4410a b d e - 4410a b d e +--R + +--R 2 5 6 3 6 7 2 7 8 +--R - 1764a b d e - 252a b d e - 9b d e +--R * +--R 8 +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 +--R - 36a d e - 588a b d e - 2646a b d e - 4410a b d e - 2940a b d e +--R + +--R 2 5 7 2 6 8 7 9 +--R - 756a b d e - 63a b d e - b d +--R * +--R 7 +--R x +--R + +--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2 +--R - 84a d e - 882a b d e - 2646a b d e - 2940a b d e - 1260a b d e +--R + +--R 2 5 8 6 9 +--R - 189a b d e - 7a b d +--R * +--R 6 +--R x +--R + +--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8 +--R - 126a d e - 882a b d e - 1764a b d e - 1260a b d e - 315a b d e +--R + +--R 2 5 9 +--R - 21a b d +--R * +--R 5 +--R x +--R + +--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9 4 +--R (- 126a d e - 588a b d e - 756a b d e - 315a b d e - 35a b d )x +--R + +--R 7 6 3 6 7 2 5 2 8 4 3 9 3 +--R (- 84a d e - 252a b d e - 189a b d e - 35a b d )x +--R + +--R 7 7 2 6 8 5 2 9 2 7 8 6 9 7 9 +--R (- 36a d e - 63a b d e - 21a b d )x + (- 9a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 1353 +t0:=(a+b*x)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 8 13 4 8 5 7 12 2 3 8 4 7 5 2 6 11 +--R b e x + (5a b e + 8b d e )x + (10a b e + 40a b d e + 28b d e )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 10 +--R (10a b e + 80a b d e + 140a b d e + 56b d e )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 5 4 4 9 +--R (5a b e + 80a b d e + 280a b d e + 280a b d e + 70b d e )x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 4 4 4 +--R a e + 40a b d e + 280a b d e + 560a b d e + 350a b d e +--R + +--R 5 5 3 +--R 56b d e +--R * +--R 8 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 4 5 3 +--R 8a d e + 140a b d e + 560a b d e + 700a b d e + 280a b d e +--R + +--R 5 6 2 +--R 28b d e +--R * +--R 7 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 4 6 2 +--R 28a d e + 280a b d e + 700a b d e + 560a b d e + 140a b d e +--R + +--R 5 7 +--R 8b d e +--R * +--R 6 +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 4 7 5 8 5 +--R (56a d e + 350a b d e + 560a b d e + 280a b d e + 40a b d e + b d )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 4 +--R (70a d e + 280a b d e + 280a b d e + 80a b d e + 5a b d )x +--R + +--R 5 5 3 4 6 2 3 2 7 2 3 8 3 +--R (56a d e + 140a b d e + 80a b d e + 10a b d )x +--R + +--R 5 6 2 4 7 3 2 8 2 5 7 4 8 5 8 +--R (28a d e + 40a b d e + 10a b d )x + (8a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1353 +r0:=-1/273*(b*d-a*e)^3*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/91*(b*d-a*e)^2*(a+b*x)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/35*(b*d-a*e)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/15*(a+b*x)*_ + (d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/5005*(b*d-a*e)^5*(d+e*x)^9*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/45045*(b*d-a*e)^6*(d+e*x)^9*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/1001*(b*d-a*e)^4*(a+b*x)*(d+e*x)^9*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 15 15 5 15 6 14 14 +--R 3003b e x + (19305a b e + 25740b d e )x +--R + +--R 2 4 15 5 14 6 2 13 13 +--R (51975a b e + 166320a b d e + 97020b d e )x +--R + +--R 3 3 15 2 4 14 5 2 13 6 3 12 12 +--R (75075a b e + 450450a b d e + 630630a b d e + 210210b d e )x +--R + +--R 4 2 15 3 3 14 2 4 2 13 +--R 61425a b e + 655200a b d e + 1719900a b d e +--R + +--R 5 3 12 6 4 11 +--R 1375920a b d e + 286650b d e +--R * +--R 11 +--R x +--R + +--R 5 15 4 2 14 3 3 2 13 +--R 27027a b e + 540540a b d e + 2522520a b d e +--R + +--R 2 4 3 12 5 4 11 6 5 10 +--R 3783780a b d e + 1891890a b d e + 252252b d e +--R * +--R 10 +--R x +--R + +--R 6 15 5 14 4 2 2 13 3 3 3 12 +--R 5005a e + 240240a b d e + 2102100a b d e + 5605600a b d e +--R + +--R 2 4 4 11 5 5 10 6 6 9 +--R 5255250a b d e + 1681680a b d e + 140140b d e +--R * +--R 9 +--R x +--R + +--R 6 14 5 2 13 4 2 3 12 +--R 45045a d e + 945945a b d e + 4729725a b d e +--R + +--R 3 3 4 11 2 4 5 10 5 6 9 6 7 8 +--R 7882875a b d e + 4729725a b d e + 945945a b d e + 45045b d e +--R * +--R 8 +--R x +--R + +--R 6 2 13 5 3 12 4 2 4 11 +--R 180180a d e + 2162160a b d e + 6756750a b d e +--R + +--R 3 3 5 10 2 4 6 9 5 7 8 6 8 7 +--R 7207200a b d e + 2702700a b d e + 308880a b d e + 6435b d e +--R * +--R 7 +--R x +--R + +--R 6 3 12 5 4 11 4 2 5 10 +--R 420420a d e + 3153150a b d e + 6306300a b d e +--R + +--R 3 3 6 9 2 4 7 8 5 8 7 +--R 4204200a b d e + 900900a b d e + 45045a b d e +--R * +--R 6 +--R x +--R + +--R 6 4 11 5 5 10 4 2 6 9 +--R 630630a d e + 3027024a b d e + 3783780a b d e +--R + +--R 3 3 7 8 2 4 8 7 +--R 1441440a b d e + 135135a b d e +--R * +--R 5 +--R x +--R + +--R 6 5 10 5 6 9 4 2 7 8 3 3 8 7 4 +--R (630630a d e + 1891890a b d e + 1351350a b d e + 225225a b d e )x +--R + +--R 6 6 9 5 7 8 4 2 8 7 3 +--R (420420a d e + 720720a b d e + 225225a b d e )x +--R + +--R 6 7 8 5 8 7 2 6 8 7 6 9 6 +--R (180180a d e + 135135a b d e )x + 45045a d e x + 5005a d e +--R + +--R 5 10 5 4 2 11 4 3 3 12 3 2 4 13 2 +--R - 3003a b d e + 1365a b d e - 455a b d e + 105a b d e +--R + +--R 5 14 6 15 +--R - 15a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 8 15 5 8 6 7 14 +--R 3003b e x + (19305a b e + 25740b d e )x +--R + +--R 2 4 8 5 7 6 2 6 13 +--R (51975a b e + 166320a b d e + 97020b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 12 +--R (75075a b e + 450450a b d e + 630630a b d e + 210210b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 +--R 61425a b e + 655200a b d e + 1719900a b d e + 1375920a b d e +--R + +--R 6 4 4 +--R 286650b d e +--R * +--R 11 +--R x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 +--R 27027a b e + 540540a b d e + 2522520a b d e + 3783780a b d e +--R + +--R 5 4 4 6 5 3 +--R 1891890a b d e + 252252b d e +--R * +--R 10 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 +--R 5005a e + 240240a b d e + 2102100a b d e + 5605600a b d e +--R + +--R 2 4 4 4 5 5 3 6 6 2 +--R 5255250a b d e + 1681680a b d e + 140140b d e +--R * +--R 9 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 +--R 45045a d e + 945945a b d e + 4729725a b d e + 7882875a b d e +--R + +--R 2 4 5 3 5 6 2 6 7 +--R 4729725a b d e + 945945a b d e + 45045b d e +--R * +--R 8 +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R 180180a d e + 2162160a b d e + 6756750a b d e + 7207200a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R 2702700a b d e + 308880a b d e + 6435b d +--R * +--R 7 +--R x +--R + +--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 +--R 420420a d e + 3153150a b d e + 6306300a b d e + 4204200a b d e +--R + +--R 2 4 7 5 8 +--R 900900a b d e + 45045a b d +--R * +--R 6 +--R x +--R + +--R 6 4 4 5 5 3 4 2 6 2 3 3 7 +--R 630630a d e + 3027024a b d e + 3783780a b d e + 1441440a b d e +--R + +--R 2 4 8 +--R 135135a b d +--R * +--R 5 +--R x +--R + +--R 6 5 3 5 6 2 4 2 7 3 3 8 4 +--R (630630a d e + 1891890a b d e + 1351350a b d e + 225225a b d )x +--R + +--R 6 6 2 5 7 4 2 8 3 +--R (420420a d e + 720720a b d e + 225225a b d )x +--R + +--R 6 7 5 8 2 6 8 +--R (180180a d e + 135135a b d )x + 45045a d x +--R / +--R 45045 +--R Type: Union(Expression(Integer),...) +--E 510 + +--S 511 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 15 15 5 15 6 14 14 +--R - 3003b e x + (- 19305a b e - 25740b d e )x +--R + +--R 2 4 15 5 14 6 2 13 13 +--R (- 51975a b e - 166320a b d e - 97020b d e )x +--R + +--R 3 3 15 2 4 14 5 2 13 +--R - 75075a b e - 450450a b d e - 630630a b d e +--R + +--R 6 3 12 +--R - 210210b d e +--R * +--R 12 +--R x +--R + +--R 4 2 15 3 3 14 2 4 2 13 +--R - 61425a b e - 655200a b d e - 1719900a b d e +--R + +--R 5 3 12 6 4 11 +--R - 1375920a b d e - 286650b d e +--R * +--R 11 +--R x +--R + +--R 5 15 4 2 14 3 3 2 13 +--R - 27027a b e - 540540a b d e - 2522520a b d e +--R + +--R 2 4 3 12 5 4 11 6 5 10 +--R - 3783780a b d e - 1891890a b d e - 252252b d e +--R * +--R 10 +--R x +--R + +--R 6 15 5 14 4 2 2 13 +--R - 5005a e - 240240a b d e - 2102100a b d e +--R + +--R 3 3 3 12 2 4 4 11 5 5 10 +--R - 5605600a b d e - 5255250a b d e - 1681680a b d e +--R + +--R 6 6 9 +--R 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x +--R + +--R 6 6 9 5 7 8 4 2 8 7 3 +--R (- 420420a d e - 720720a b d e - 225225a b d e )x +--R + +--R 6 7 8 5 8 7 2 6 8 7 6 9 6 +--R (- 180180a d e - 135135a b d e )x - 45045a d e x - 5005a d e +--R + +--R 5 10 5 4 2 11 4 3 3 12 3 2 4 13 2 +--R 3003a b d e - 1365a b d e + 455a b d e - 105a b d e +--R + +--R 5 14 6 15 +--R 15a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 15 16 6 15 7 14 15 +--R 3003b e x + (22308a b e + 25740b d e )x +--R + +--R 2 5 15 6 14 7 2 13 14 +--R (71280a b e + 192060a b d e + 97020b d e )x +--R + +--R 3 4 15 2 5 14 6 2 13 7 3 12 13 +--R (127050a b e + 616770a b d e + 727650a b d e + 210210b d e )x +--R + +--R 4 3 15 3 4 14 2 5 2 13 +--R 136500a b e + 1105650a b d e + 2350530a b d e +--R + +--R 6 3 12 7 4 11 +--R 1586130a b d e + 286650b d e +--R * +--R 12 +--R x +--R + +--R 5 2 15 4 3 14 3 4 2 13 2 5 3 12 +--R 88452a b e + 1195740a b d e + 4242420a b d e + 5159700a b d e +--R + +--R 6 4 11 7 5 10 +--R 2178540a b d e + 252252b d e +--R * +--R 11 +--R x +--R + +--R 6 15 5 2 14 4 3 2 13 3 4 3 12 +--R 32032a b e + 780780a b d e + 4624620a b d e + 9389380a b d e +--R + +--R 2 5 4 11 6 5 10 7 6 9 +--R 7147140a b d e + 1933932a b d e + 140140b d e +--R * +--R 10 +--R x +--R + +--R 7 15 6 14 5 2 2 13 4 3 3 12 +--R 5005a e + 285285a b d e + 3048045a b d e + 10335325a b d e +--R + +--R 3 4 4 11 2 5 5 10 6 6 9 7 7 8 +--R 13138125a b d e + 6411405a b d e + 1086085a b d e + 45045b d e +--R * +--R 9 +--R x +--R + +--R 7 14 6 2 13 5 2 3 12 +--R 45045a d e + 1126125a b d e + 6891885a b d e +--R + +--R 4 3 4 11 3 4 5 10 2 5 6 9 +--R 14639625a b d e + 11936925a b d e + 3648645a b d e +--R + +--R 6 7 8 7 8 7 +--R 353925a b d e + 6435b d e +--R * +--R 8 +--R x +--R + +--R 7 2 13 6 3 12 5 2 4 11 +--R 180180a d e + 2582580a b d e + 9909900a b d e +--R + +--R 4 3 5 10 3 4 6 9 2 5 7 8 6 8 7 +--R 13513500a b d e + 6906900a b d e + 1209780a b d e + 51480a b d e +--R * +--R 7 +--R x +--R + +--R 7 3 12 6 4 11 5 2 5 10 4 3 6 9 +--R 420420a d e + 3783780a b d e + 9333324a b d e + 7987980a b d e +--R + +--R 3 4 7 8 2 5 8 7 +--R 2342340a b d e + 180180a b d e +--R * +--R 6 +--R x +--R + +--R 7 4 11 6 5 10 5 2 6 9 4 3 7 8 +--R 630630a d e + 3657654a b d e + 5675670a b d e + 2792790a b d e +--R + +--R 3 4 8 7 +--R 360360a b d e +--R * +--R 5 +--R x +--R + +--R 7 5 10 6 6 9 5 2 7 8 4 3 8 7 4 +--R (630630a d e + 2312310a b d e + 2072070a b d e + 450450a b d e )x +--R + +--R 7 6 9 6 7 8 5 2 8 7 3 +--R (420420a d e + 900900a b d e + 360360a b d e )x +--R + +--R 7 7 8 6 8 7 2 7 8 7 +--R (180180a d e + 180180a b d e )x + 45045a d e x +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 8 14 5 8 6 7 13 +--R b e x + (6a b e + 8b d e )x +--R + +--R 2 4 8 5 7 6 2 6 12 +--R (15a b e + 48a b d e + 28b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 11 +--R (20a b e + 120a b d e + 168a b d e + 56b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 6 4 4 10 +--R (15a b e + 160a b d e + 420a b d e + 336a b d e + 70b d e )x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 +--R 6a b e + 120a b d e + 560a b d e + 840a b d e + 420a b d e +--R + +--R 6 5 3 +--R 56b d e +--R * +--R 9 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 2 4 4 4 +--R a e + 48a b d e + 420a b d e + 1120a b d e + 1050a b d e +--R + +--R 5 5 3 6 6 2 +--R 336a b d e + 28b d e +--R * +--R 8 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 +--R 8a d e + 168a b d e + 840a b d e + 1400a b d e + 840a b d e +--R + +--R 5 6 2 6 7 +--R 168a b d e + 8b d e +--R * +--R 7 +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R 28a d e + 336a b d e + 1050a b d e + 1120a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R 420a b d e + 48a b d e + b d +--R * +--R 6 +--R x +--R + +--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7 +--R 56a d e + 420a b d e + 840a b d e + 560a b d e + 120a b d e +--R + +--R 5 8 +--R 6a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8 4 +--R (70a d e + 336a b d e + 420a b d e + 160a b d e + 15a b d )x +--R + +--R 6 5 3 5 6 2 4 2 7 3 3 8 3 +--R (56a d e + 168a b d e + 120a b d e + 20a b d )x +--R + +--R 6 6 2 5 7 4 2 8 2 6 7 5 8 6 8 +--R (28a d e + 48a b d e + 15a b d )x + (8a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 8 15 6 8 7 7 14 +--R - b e x + (- 7a b e - 8b d e )x +--R + +--R 2 5 8 6 7 7 2 6 13 +--R (- 21a b e - 56a b d e - 28b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 12 +--R (- 35a b e - 168a b d e - 196a b d e - 56b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 7 4 4 11 +--R (- 35a b e - 280a b d e - 588a b d e - 392a b d e - 70b d e )x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 6 4 4 +--R - 21a b e - 280a b d e - 980a b d e - 1176a b d e - 490a b d e +--R + +--R 7 5 3 +--R - 56b d e +--R * +--R 10 +--R x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 2 5 4 4 +--R - 7a b e - 168a b d e - 980a b d e - 1960a b d e - 1470a b d e +--R + +--R 6 5 3 7 6 2 +--R - 392a b d e - 28b d e +--R * +--R 9 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 3 4 4 4 +--R - a e - 56a b d e - 588a b d e - 1960a b d e - 2450a b d e +--R + +--R 2 5 5 3 6 6 2 7 7 +--R - 1176a b d e - 196a b d e - 8b d e +--R * +--R 8 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 3 4 5 3 +--R - 8a d e - 196a b d e - 1176a b d e - 2450a b d e - 1960a b d e +--R + +--R 2 5 6 2 6 7 7 8 +--R - 588a b d e - 56a b d e - b d +--R * +--R 7 +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 4 3 5 3 3 4 6 2 +--R - 28a d e - 392a b d e - 1470a b d e - 1960a b d e - 980a b d e +--R + +--R 2 5 7 6 8 +--R - 168a b d e - 7a b d +--R * +--R 6 +--R x +--R + +--R 7 3 5 6 4 4 5 2 5 3 4 3 6 2 3 4 7 +--R - 56a d e - 490a b d e - 1176a b d e - 980a b d e - 280a b d e +--R + +--R 2 5 8 +--R - 21a b d +--R * +--R 5 +--R x +--R + +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 4 +--R (- 70a d e - 392a b d e - 588a b d e - 280a b d e - 35a b d )x +--R + +--R 7 5 3 6 6 2 5 2 7 4 3 8 3 +--R (- 56a d e - 196a b d e - 168a b d e - 35a b d )x +--R + +--R 7 6 2 6 7 5 2 8 2 7 7 6 8 7 8 +--R (- 28a d e - 56a b d e - 21a b d )x + (- 8a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 512 + +)clear all + +--S 513 of 1353 +t0:=(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 7 12 4 7 5 6 11 2 3 7 4 6 5 2 5 10 +--R b e x + (5a b e + 7b d e )x + (10a b e + 35a b d e + 21b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 9 +--R (10a b e + 70a b d e + 105a b d e + 35b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 8 +--R (5a b e + 70a b d e + 210a b d e + 175a b d e + 35b d e )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 +--R a e + 35a b d e + 210a b d e + 350a b d e + 175a b d e +--R + +--R 5 5 2 +--R 21b d e +--R * +--R 7 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 +--R 7a d e + 105a b d e + 350a b d e + 350a b d e + 105a b d e +--R + +--R 5 6 +--R 7b d e +--R * +--R 6 +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 5 7 5 +--R (21a d e + 175a b d e + 350a b d e + 210a b d e + 35a b d e + b d )x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 4 +--R (35a d e + 175a b d e + 210a b d e + 70a b d e + 5a b d )x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 3 +--R (35a d e + 105a b d e + 70a b d e + 10a b d )x +--R + +--R 5 5 2 4 6 3 2 7 2 5 6 4 7 5 7 +--R (21a d e + 35a b d e + 10a b d )x + (7a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1353 +r0:=-5/1001*(b*d-a*e)^3*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 5/364*(b*d-a*e)^2*(a+b*x)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 3/91*(b*d-a*e)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/14*(a+b*x)*_ + (d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/3003*(b*d-a*e)^5*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/24024*(b*d-a*e)^6*(d+e*x)^8*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+3/2002*(b*d-a*e)^4*(a+b*x)*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 14 14 5 14 6 13 13 +--R 1716b e x + (11088a b e + 12936b d e )x +--R + +--R 2 4 14 5 13 6 2 12 12 +--R (30030a b e + 84084a b d e + 42042b d e )x +--R + +--R 3 3 14 2 4 13 5 2 12 6 3 11 11 +--R (43680a b e + 229320a b d e + 275184a b d e + 76440b d e )x +--R + +--R 4 2 14 3 3 13 2 4 2 12 5 3 11 +--R 36036a b e + 336336a b d e + 756756a b d e + 504504a b d e +--R + +--R 6 4 10 +--R 84084b d e +--R * +--R 10 +--R x +--R + +--R 5 14 4 2 13 3 3 2 12 +--R 16016a b e + 280280a b d e + 1121120a b d e +--R + +--R 2 4 3 11 5 4 10 6 5 9 +--R 1401400a b d e + 560560a b d e + 56056b d e +--R * +--R 9 +--R x +--R + +--R 6 14 5 13 4 2 2 12 3 3 3 11 +--R 3003a e + 126126a b d e + 945945a b d e + 2102100a b d e +--R + +--R 2 4 4 10 5 5 9 6 6 8 +--R 1576575a b d e + 378378a b d e + 21021b d e +--R * +--R 8 +--R x +--R + +--R 6 13 5 2 12 4 2 3 11 +--R 24024a d e + 432432a b d e + 1801800a b d e +--R + +--R 3 3 4 10 2 4 5 9 5 6 8 6 7 7 +--R 2402400a b d e + 1081080a b d e + 144144a b d e + 3432b d e +--R * +--R 7 +--R x +--R + +--R 6 2 12 5 3 11 4 2 4 10 3 3 5 9 +--R 84084a d e + 840840a b d e + 2102100a b d e + 1681680a b d e +--R + +--R 2 4 6 8 5 7 7 +--R 420420a b d e + 24024a b d e +--R * +--R 6 +--R x +--R + +--R 6 3 11 5 4 10 4 2 5 9 3 3 6 8 +--R 168168a d e + 1009008a b d e + 1513512a b d e + 672672a b d e +--R + +--R 2 4 7 7 +--R 72072a b d e +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 2 6 8 3 3 7 7 4 +--R (210210a d e + 756756a b d e + 630630a b d e + 120120a b d e )x +--R + +--R 6 5 9 5 6 8 4 2 7 7 3 +--R (168168a d e + 336336a b d e + 120120a b d e )x +--R + +--R 6 6 8 5 7 7 2 6 7 7 6 8 6 +--R (84084a d e + 72072a b d e )x + 24024a d e x + 3003a d e +--R + +--R 5 9 5 4 2 10 4 3 3 11 3 2 4 12 2 +--R - 2002a b d e + 1001a b d e - 364a b d e + 91a b d e +--R + +--R 5 13 6 14 +--R - 14a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 24024b e x + 24024a e +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 14 5 7 6 6 13 +--R 1716b e x + (11088a b e + 12936b d e )x +--R + +--R 2 4 7 5 6 6 2 5 12 +--R (30030a b e + 84084a b d e + 42042b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 11 +--R (43680a b e + 229320a b d e + 275184a b d e + 76440b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 +--R 36036a b e + 336336a b d e + 756756a b d e + 504504a b d e +--R + +--R 6 4 3 +--R 84084b d e +--R * +--R 10 +--R x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 16016a b e + 280280a b d e + 1121120a b d e + 1401400a b d e +--R + +--R 5 4 3 6 5 2 +--R 560560a b d e + 56056b d e +--R * +--R 9 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 3003a e + 126126a b d e + 945945a b d e + 2102100a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 1576575a b d e + 378378a b d e + 21021b d e +--R * +--R 8 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 24024a d e + 432432a b d e + 1801800a b d e + 2402400a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R 1081080a b d e + 144144a b d e + 3432b d +--R * +--R 7 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 +--R 84084a d e + 840840a b d e + 2102100a b d e + 1681680a b d e +--R + +--R 2 4 6 5 7 +--R 420420a b d e + 24024a b d +--R * +--R 6 +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 +--R 168168a d e + 1009008a b d e + 1513512a b d e + 672672a b d e +--R + +--R 2 4 7 +--R 72072a b d +--R * +--R 5 +--R x +--R + +--R 6 4 3 5 5 2 4 2 6 3 3 7 4 +--R (210210a d e + 756756a b d e + 630630a b d e + 120120a b d )x +--R + +--R 6 5 2 5 6 4 2 7 3 +--R (168168a d e + 336336a b d e + 120120a b d )x +--R + +--R 6 6 5 7 2 6 7 +--R (84084a d e + 72072a b d )x + 24024a d x +--R / +--R 24024 +--R Type: Union(Expression(Integer),...) +--E 515 + +--S 516 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 14 14 5 14 6 13 13 +--R - 1716b e x + (- 11088a b e - 12936b d e )x +--R + +--R 2 4 14 5 13 6 2 12 12 +--R (- 30030a b e - 84084a b d e - 42042b d e )x +--R + +--R 3 3 14 2 4 13 5 2 12 6 3 11 +--R (- 43680a b e - 229320a b d e - 275184a b d e - 76440b d e ) +--R * +--R 11 +--R x +--R + +--R 4 2 14 3 3 13 2 4 2 12 +--R - 36036a b e - 336336a b d e - 756756a b d e +--R + +--R 5 3 11 6 4 10 +--R - 504504a b d e - 84084b d e +--R * +--R 10 +--R x +--R + +--R 5 14 4 2 13 3 3 2 12 +--R - 16016a b e - 280280a b d e - 1121120a b d e +--R + +--R 2 4 3 11 5 4 10 6 5 9 +--R - 1401400a b d e - 560560a b d e - 56056b d e +--R * +--R 9 +--R x +--R + +--R 6 14 5 13 4 2 2 12 +--R - 3003a e - 126126a b d e - 945945a b d e +--R + +--R 3 3 3 11 2 4 4 10 5 5 9 +--R - 2102100a b d e - 1576575a b d e - 378378a b d e +--R + +--R 6 6 8 +--R - 21021b d e +--R * +--R 8 +--R x +--R + +--R 6 13 5 2 12 4 2 3 11 +--R - 24024a d e - 432432a b d e - 1801800a b d e +--R + +--R 3 3 4 10 2 4 5 9 5 6 8 6 7 7 +--R - 2402400a b d e - 1081080a b d e - 144144a b d e - 3432b d e +--R * +--R 7 +--R x +--R + +--R 6 2 12 5 3 11 4 2 4 10 +--R - 84084a d e - 840840a b d e - 2102100a b d e +--R + +--R 3 3 5 9 2 4 6 8 5 7 7 +--R - 1681680a b d e - 420420a b d e - 24024a b d e +--R * +--R 6 +--R x +--R + +--R 6 3 11 5 4 10 4 2 5 9 +--R - 168168a d e - 1009008a b d e - 1513512a b d e +--R + +--R 3 3 6 8 2 4 7 7 +--R - 672672a b d e - 72072a b d e +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 2 6 8 +--R - 210210a d e - 756756a b d e - 630630a b d e +--R + +--R 3 3 7 7 +--R - 120120a b d e +--R * +--R 4 +--R x +--R + +--R 6 5 9 5 6 8 4 2 7 7 3 +--R (- 168168a d e - 336336a b d e - 120120a b d e )x +--R + +--R 6 6 8 5 7 7 2 6 7 7 6 8 6 +--R (- 84084a d e - 72072a b d e )x - 24024a d e x - 3003a d e +--R + +--R 5 9 5 4 2 10 4 3 3 11 3 2 4 12 2 +--R 2002a b d e - 1001a b d e + 364a b d e - 91a b d e +--R + +--R 5 13 6 14 +--R 14a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 14 15 6 14 7 13 14 +--R 1716b e x + (12804a b e + 12936b d e )x +--R + +--R 2 5 14 6 13 7 2 12 13 +--R (41118a b e + 97020a b d e + 42042b d e )x +--R + +--R 3 4 14 2 5 13 6 2 12 7 3 11 12 +--R (73710a b e + 313404a b d e + 317226a b d e + 76440b d e )x +--R + +--R 4 3 14 3 4 13 2 5 2 12 6 3 11 +--R 79716a b e + 565656a b d e + 1031940a b d e + 580944a b d e +--R + +--R 7 4 10 +--R 84084b d e +--R * +--R 11 +--R x +--R + +--R 5 2 14 4 3 13 3 4 2 12 2 5 3 11 +--R 52052a b e + 616616a b d e + 1877876a b d e + 1905904a b d e +--R + +--R 6 4 10 7 5 9 +--R 644644a b d e + 56056b d e +--R * +--R 10 +--R x +--R + +--R 6 14 5 2 13 4 3 2 12 3 4 3 11 +--R 19019a b e + 406406a b d e + 2067065a b d e + 3503500a b d e +--R + +--R 2 5 4 10 6 5 9 7 6 8 +--R 2137135a b d e + 434434a b d e + 21021b d e +--R * +--R 9 +--R x +--R + +--R 7 14 6 13 5 2 2 12 4 3 3 11 +--R 3003a e + 150150a b d e + 1378377a b d e + 3903900a b d e +--R + +--R 3 4 4 10 2 5 5 9 6 6 8 7 7 7 +--R 3978975a b d e + 1459458a b d e + 165165a b d e + 3432b d e +--R * +--R 8 +--R x +--R + +--R 7 13 6 2 12 5 2 3 11 4 3 4 10 +--R 24024a d e + 516516a b d e + 2642640a b d e + 4504500a b d e +--R + +--R 3 4 5 9 2 5 6 8 6 7 7 +--R 2762760a b d e + 564564a b d e + 27456a b d e +--R * +--R 7 +--R x +--R + +--R 7 2 12 6 3 11 5 2 4 10 4 3 5 9 +--R 84084a d e + 1009008a b d e + 3111108a b d e + 3195192a b d e +--R + +--R 3 4 6 8 2 5 7 7 +--R 1093092a b d e + 96096a b d e +--R * +--R 6 +--R x +--R + +--R 7 3 11 6 4 10 5 2 5 9 4 3 6 8 +--R 168168a d e + 1219218a b d e + 2270268a b d e + 1303302a b d e +--R + +--R 3 4 7 7 +--R 192192a b d e +--R * +--R 5 +--R x +--R + +--R 7 4 10 6 5 9 5 2 6 8 4 3 7 7 4 +--R (210210a d e + 924924a b d e + 966966a b d e + 240240a b d e )x +--R + +--R 7 5 9 6 6 8 5 2 7 7 3 +--R (168168a d e + 420420a b d e + 192192a b d e )x +--R + +--R 7 6 8 6 7 7 2 7 7 7 +--R (84084a d e + 96096a b d e )x + 24024a d e x +--R / +--R 7 7 +--R 24024b e x + 24024a e +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 7 13 5 7 6 6 12 +--R b e x + (6a b e + 7b d e )x +--R + +--R 2 4 7 5 6 6 2 5 11 +--R (15a b e + 42a b d e + 21b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 10 +--R (20a b e + 105a b d e + 126a b d e + 35b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 6 4 3 9 +--R (15a b e + 140a b d e + 315a b d e + 210a b d e + 35b d e )x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 6a b e + 105a b d e + 420a b d e + 525a b d e + 210a b d e +--R + +--R 6 5 2 +--R 21b d e +--R * +--R 8 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R a e + 42a b d e + 315a b d e + 700a b d e + 525a b d e +--R + +--R 5 5 2 6 6 +--R 126a b d e + 7b d e +--R * +--R 7 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R 7a d e + 126a b d e + 525a b d e + 700a b d e + 315a b d e +--R + +--R 5 6 6 7 +--R 42a b d e + b d +--R * +--R 6 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R 21a d e + 210a b d e + 525a b d e + 420a b d e + 105a b d e +--R + +--R 5 7 +--R 6a b d +--R * +--R 5 +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 4 +--R (35a d e + 210a b d e + 315a b d e + 140a b d e + 15a b d )x +--R + +--R 6 4 3 5 5 2 4 2 6 3 3 7 3 +--R (35a d e + 126a b d e + 105a b d e + 20a b d )x +--R + +--R 6 5 2 5 6 4 2 7 2 6 6 5 7 6 7 +--R (21a d e + 42a b d e + 15a b d )x + (7a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 14 6 7 7 6 13 +--R - b e x + (- 7a b e - 7b d e )x +--R + +--R 2 5 7 6 6 7 2 5 12 +--R (- 21a b e - 49a b d e - 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 11 +--R (- 35a b e - 147a b d e - 147a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 10 +--R (- 35a b e - 245a b d e - 441a b d e - 245a b d e - 35b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 21a b e - 245a b d e - 735a b d e - 735a b d e - 245a b d e +--R + +--R 7 5 2 +--R - 21b d e +--R * +--R 9 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 7a b e - 147a b d e - 735a b d e - 1225a b d e - 735a b d e +--R + +--R 6 5 2 7 6 +--R - 147a b d e - 7b d e +--R * +--R 8 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - a e - 49a b d e - 441a b d e - 1225a b d e - 1225a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 441a b d e - 49a b d e - b d +--R * +--R 7 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 +--R - 7a d e - 147a b d e - 735a b d e - 1225a b d e - 735a b d e +--R + +--R 2 5 6 6 7 +--R - 147a b d e - 7a b d +--R * +--R 6 +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R - 21a d e - 245a b d e - 735a b d e - 735a b d e - 245a b d e +--R + +--R 2 5 7 +--R - 21a b d +--R * +--R 5 +--R x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 4 +--R (- 35a d e - 245a b d e - 441a b d e - 245a b d e - 35a b d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 3 +--R (- 35a d e - 147a b d e - 147a b d e - 35a b d )x +--R + +--R 7 5 2 6 6 5 2 7 2 7 6 6 7 7 7 +--R (- 21a d e - 49a b d e - 21a b d )x + (- 7a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 517 + +)clear all + +--S 518 of 1353 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 11 4 6 5 5 10 2 3 6 4 5 5 2 4 9 +--R b e x + (5a b e + 6b d e )x + (10a b e + 30a b d e + 15b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 8 +--R (10a b e + 60a b d e + 75a b d e + 20b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 7 +--R (5a b e + 60a b d e + 150a b d e + 100a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 6 +--R (a e + 30a b d e + 150a b d e + 200a b d e + 75a b d e + 6b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 5 +--R (6a d e + 75a b d e + 200a b d e + 150a b d e + 30a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 4 +--R (15a d e + 100a b d e + 150a b d e + 60a b d e + 5a b d )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 3 +--R (20a d e + 75a b d e + 60a b d e + 10a b d )x +--R + +--R 5 4 2 4 5 3 2 6 2 5 5 4 6 5 6 +--R (15a d e + 30a b d e + 10a b d )x + (6a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1353 +r0:=1/12012*(b*d-a*e)^6*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^7+1/1716*(b*d-a*e)^5*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6+1/429*(b*d-a*e)^4*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/143*(b*d-a*e)^3*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^4+5/286*(b*d-a*e)^2*(d+e*x)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^3+1/26*(b*d-a*e)*(d+e*x)^5*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/13*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 12 6 12 11 6 12 5 11 +--R 924b e x + (5082a b e + 6006b d e )x +--R + +--R 2 10 6 11 5 12 2 4 10 +--R (11298a b e + 33306a b d e + 16380b d e )x +--R + +--R 3 9 6 2 10 5 11 2 4 12 3 3 9 +--R (12726a b e + 74802a b d e + 91728a b d e + 24024b d e )x +--R + +--R 4 8 6 3 9 5 2 10 2 4 11 3 3 +--R 7294a b e + 85358a b d e + 208572a b d e + 136136a b d e +--R + +--R 12 4 2 +--R 20020b d e +--R * +--R 8 +--R x +--R + +--R 5 7 6 4 8 5 3 9 2 4 2 10 3 3 +--R 1715a b e + 49777a b d e + 241878a b d e + 314314a b d e +--R + +--R 11 4 2 12 5 +--R 115115a b d e + 9009b d e +--R * +--R 7 +--R x +--R + +--R 6 6 6 5 7 5 4 8 2 4 3 9 3 3 +--R a b e + 11999a b d e + 144222a b d e + 372086a b d e +--R + +--R 2 10 4 2 11 5 12 6 +--R 270985a b d e + 52767a b d e + 1716b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 6 6 5 5 7 2 4 4 8 3 3 +--R - a b e + 13a b d e + 35958a b d e + 228514a b d e +--R + +--R 3 9 4 2 2 10 5 11 6 +--R 329615a b d e + 127413a b d e + 10296a b d +--R * +--R 5 +--R x +--R + +--R 8 4 6 7 5 5 6 6 2 4 5 7 3 3 4 8 4 2 +--R a b e - 13a b d e + 78a b d e + 59774a b d e + 210925a b d e +--R + +--R 3 9 5 2 10 6 +--R 160875a b d e + 25740a b d +--R * +--R 4 +--R x +--R + +--R 9 3 6 8 4 5 7 5 2 4 6 6 3 3 5 7 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e + 59345a b d e +--R + +--R 4 8 5 3 9 6 +--R 109395a b d e + 34320a b d +--R * +--R 3 +--R x +--R + +--R 10 2 6 9 3 5 8 4 2 4 7 5 3 3 6 6 4 2 +--R a b e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 5 7 5 4 8 6 +--R 34749a b d e + 25740a b d +--R * +--R 2 +--R x +--R + +--R 11 6 10 2 5 9 3 2 4 8 4 3 3 7 5 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e - 715a b d e +--R + +--R 6 6 5 5 7 6 +--R 1287a b d e + 10296a b d +--R * +--R x +--R + +--R 12 6 11 5 10 2 2 4 9 3 3 3 8 4 4 2 +--R a e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 7 5 5 6 6 6 +--R - 1287a b d e + 1716a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 +--R 12012b +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 13 5 6 6 5 12 +--R 924b e x + (6006a b e + 6006b d e )x +--R + +--R 2 4 6 5 5 6 2 4 11 +--R (16380a b e + 39312a b d e + 16380b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 10 +--R (24024a b e + 108108a b d e + 108108a b d e + 24024b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 20020a b e + 160160a b d e + 300300a b d e + 160160a b d e +--R + +--R 6 4 2 +--R 20020b d e +--R * +--R 9 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 9009a b e + 135135a b d e + 450450a b d e + 450450a b d e +--R + +--R 5 4 2 6 5 +--R 135135a b d e + 9009b d e +--R * +--R 8 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 1716a e + 61776a b d e + 386100a b d e + 686400a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 386100a b d e + 61776a b d e + 1716b d +--R * +--R 7 +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 +--R 12012a d e + 180180a b d e + 600600a b d e + 600600a b d e +--R + +--R 2 4 5 5 6 +--R 180180a b d e + 12012a b d +--R * +--R 6 +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 +--R 36036a d e + 288288a b d e + 540540a b d e + 288288a b d e +--R + +--R 2 4 6 +--R 36036a b d +--R * +--R 5 +--R x +--R + +--R 6 3 3 5 4 2 4 2 5 3 3 6 4 +--R (60060a d e + 270270a b d e + 270270a b d e + 60060a b d )x +--R + +--R 6 4 2 5 5 4 2 6 3 +--R (60060a d e + 144144a b d e + 60060a b d )x +--R + +--R 6 5 5 6 2 6 6 +--R (36036a d e + 36036a b d )x + 12012a d x +--R / +--R 12012 +--R Type: Union(Expression(Integer),...) +--E 520 + +--S 521 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 12 6 12 11 6 12 5 11 +--R - 924b e x + (- 5082a b e - 6006b d e )x +--R + +--R 2 10 6 11 5 12 2 4 10 +--R (- 11298a b e - 33306a b d e - 16380b d e )x +--R + +--R 3 9 6 2 10 5 11 2 4 12 3 3 9 +--R (- 12726a b e - 74802a b d e - 91728a b d e - 24024b d e )x +--R + +--R 4 8 6 3 9 5 2 10 2 4 11 3 3 +--R - 7294a b e - 85358a b d e - 208572a b d e - 136136a b d e +--R + +--R 12 4 2 +--R - 20020b d e +--R * +--R 8 +--R x +--R + +--R 5 7 6 4 8 5 3 9 2 4 2 10 3 3 +--R - 1715a b e - 49777a b d e - 241878a b d e - 314314a b d e +--R + +--R 11 4 2 12 5 +--R - 115115a b d e - 9009b d e +--R * +--R 7 +--R x +--R + +--R 6 6 6 5 7 5 4 8 2 4 3 9 3 3 +--R - a b e - 11999a b d e - 144222a b d e - 372086a b d e +--R + +--R 2 10 4 2 11 5 12 6 +--R - 270985a b d e - 52767a b d e - 1716b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 6 6 5 5 7 2 4 4 8 3 3 +--R a b e - 13a b d e - 35958a b d e - 228514a b d e +--R + +--R 3 9 4 2 2 10 5 11 6 +--R - 329615a b d e - 127413a b d e - 10296a b d +--R * +--R 5 +--R x +--R + +--R 8 4 6 7 5 5 6 6 2 4 5 7 3 3 +--R - a b e + 13a b d e - 78a b d e - 59774a b d e +--R + +--R 4 8 4 2 3 9 5 2 10 6 +--R - 210925a b d e - 160875a b d e - 25740a b d +--R * +--R 4 +--R x +--R + +--R 9 3 6 8 4 5 7 5 2 4 6 6 3 3 5 7 4 2 +--R a b e - 13a b d e + 78a b d e - 286a b d e - 59345a b d e +--R + +--R 4 8 5 3 9 6 +--R - 109395a b d e - 34320a b d +--R * +--R 3 +--R x +--R + +--R 10 2 6 9 3 5 8 4 2 4 7 5 3 3 6 6 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e - 715a b d e +--R + +--R 5 7 5 4 8 6 +--R - 34749a b d e - 25740a b d +--R * +--R 2 +--R x +--R + +--R 11 6 10 2 5 9 3 2 4 8 4 3 3 7 5 4 2 +--R a b e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 6 6 5 5 7 6 +--R - 1287a b d e - 10296a b d +--R * +--R x +--R + +--R 12 6 11 5 10 2 2 4 9 3 3 3 8 4 4 2 +--R - a e + 13a b d e - 78a b d e + 286a b d e - 715a b d e +--R + +--R 7 5 5 6 6 6 +--R 1287a b d e - 1716a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 13 6 13 12 6 13 5 12 +--R 924b e x + (6006a b e + 6006b d e )x +--R + +--R 2 11 6 12 5 13 2 4 11 +--R (16380a b e + 39312a b d e + 16380b d e )x +--R + +--R 3 10 6 2 11 5 12 2 4 13 3 3 10 +--R (24024a b e + 108108a b d e + 108108a b d e + 24024b d e )x +--R + +--R 4 9 6 3 10 5 2 11 2 4 12 3 3 +--R 20020a b e + 160160a b d e + 300300a b d e + 160160a b d e +--R + +--R 13 4 2 +--R 20020b d e +--R * +--R 9 +--R x +--R + +--R 5 8 6 4 9 5 3 10 2 4 2 11 3 3 +--R 9009a b e + 135135a b d e + 450450a b d e + 450450a b d e +--R + +--R 12 4 2 13 5 +--R 135135a b d e + 9009b d e +--R * +--R 8 +--R x +--R + +--R 6 7 6 5 8 5 4 9 2 4 3 10 3 3 +--R 1716a b e + 61776a b d e + 386100a b d e + 686400a b d e +--R + +--R 2 11 4 2 12 5 13 6 +--R 386100a b d e + 61776a b d e + 1716b d +--R * +--R 7 +--R x +--R + +--R 6 7 5 5 8 2 4 4 9 3 3 3 10 4 2 +--R 12012a b d e + 180180a b d e + 600600a b d e + 600600a b d e +--R + +--R 2 11 5 12 6 +--R 180180a b d e + 12012a b d +--R * +--R 6 +--R x +--R + +--R 6 7 2 4 5 8 3 3 4 9 4 2 3 10 5 +--R 36036a b d e + 288288a b d e + 540540a b d e + 288288a b d e +--R + +--R 2 11 6 +--R 36036a b d +--R * +--R 5 +--R x +--R + +--R 6 7 3 3 5 8 4 2 4 9 5 3 10 6 4 +--R (60060a b d e + 270270a b d e + 270270a b d e + 60060a b d )x +--R + +--R 6 7 4 2 5 8 5 4 9 6 3 +--R (60060a b d e + 144144a b d e + 60060a b d )x +--R + +--R 6 7 5 5 8 6 2 6 7 6 +--R (36036a b d e + 36036a b d )x + 12012a b d x +--R / +--R 7 +--R 12012b +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 12 5 6 6 5 11 +--R b e x + (6a b e + 6b d e )x +--R + +--R 2 4 6 5 5 6 2 4 10 +--R (15a b e + 36a b d e + 15b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 9 +--R (20a b e + 90a b d e + 90a b d e + 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 8 +--R (15a b e + 120a b d e + 225a b d e + 120a b d e + 15b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 6a b e + 90a b d e + 300a b d e + 300a b d e + 90a b d e +--R + +--R 6 5 +--R 6b d e +--R * +--R 7 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R a e + 36a b d e + 225a b d e + 400a b d e + 225a b d e +--R + +--R 5 5 6 6 +--R 36a b d e + b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R 6a d e + 90a b d e + 300a b d e + 300a b d e + 90a b d e +--R + +--R 5 6 +--R 6a b d +--R * +--R 5 +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 4 +--R (15a d e + 120a b d e + 225a b d e + 120a b d e + 15a b d )x +--R + +--R 6 3 3 5 4 2 4 2 5 3 3 6 3 +--R (20a d e + 90a b d e + 90a b d e + 20a b d )x +--R + +--R 6 4 2 5 5 4 2 6 2 6 5 5 6 6 6 +--R (15a d e + 36a b d e + 15a b d )x + (6a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 13 6 6 7 5 12 +--R - b e x + (- 7a b e - 6b d e )x +--R + +--R 2 5 6 6 5 7 2 4 11 +--R (- 21a b e - 42a b d e - 15b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 10 +--R (- 35a b e - 126a b d e - 105a b d e - 20b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 9 +--R (- 35a b e - 210a b d e - 315a b d e - 140a b d e - 15b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 21a b e - 210a b d e - 525a b d e - 420a b d e - 105a b d e +--R + +--R 7 5 +--R - 6b d e +--R * +--R 8 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 7a b e - 126a b d e - 525a b d e - 700a b d e - 315a b d e +--R + +--R 6 5 7 6 +--R - 42a b d e - b d +--R * +--R 7 +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - a e - 42a b d e - 315a b d e - 700a b d e - 525a b d e +--R + +--R 2 5 5 6 6 +--R - 126a b d e - 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 +--R - 6a d e - 105a b d e - 420a b d e - 525a b d e - 210a b d e +--R + +--R 2 5 6 +--R - 21a b d +--R * +--R 5 +--R x +--R + +--R 7 2 4 6 3 3 5 2 4 2 4 3 5 3 4 6 4 +--R (- 15a d e - 140a b d e - 315a b d e - 210a b d e - 35a b d )x +--R + +--R 7 3 3 6 4 2 5 2 5 4 3 6 3 +--R (- 20a d e - 105a b d e - 126a b d e - 35a b d )x +--R + +--R 7 4 2 6 5 5 2 6 2 7 5 6 6 7 6 +--R (- 15a d e - 42a b d e - 21a b d )x + (- 6a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 522 + +)clear all + +--S 523 of 1353 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 5 10 4 5 5 4 9 2 3 5 4 4 5 2 3 8 +--R b e x + (5a b e + 5b d e )x + (10a b e + 25a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 7 +--R (10a b e + 50a b d e + 50a b d e + 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 6 +--R (5a b e + 50a b d e + 100a b d e + 50a b d e + 5b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e + 25a b d e + 100a b d e + 100a b d e + 25a b d e + b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4 +--R (5a d e + 50a b d e + 100a b d e + 50a b d e + 5a b d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 3 +--R (10a d e + 50a b d e + 50a b d e + 10a b d )x +--R + +--R 5 3 2 4 4 3 2 5 2 5 4 4 5 5 5 +--R (10a d e + 25a b d e + 10a b d )x + (5a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1353 +r0:=1/5544*(b*d-a*e)^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6+1/792*(b*d-a*e)^4*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/198*(b*d-a*e)^3*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+1/66*(b*d-a*e)^2*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^3+5/132*(b*d-a*e)*(d+e*x)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/12*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 11 5 11 10 5 11 4 10 +--R 462b e x + (2562a b e + 2520b d e )x +--R + +--R 2 9 5 10 4 11 2 3 9 +--R (5754a b e + 14112a b d e + 5544b d e )x +--R + +--R 3 8 5 2 9 4 10 2 3 11 3 2 8 +--R (6566a b e + 32088a b d e + 31416a b d e + 6160b d e )x +--R + +--R 4 7 5 3 8 4 2 9 2 3 10 3 2 +--R 3829a b e + 37212a b d e + 72534a b d e + 35420a b d e +--R + +--R 11 4 +--R 3465b d e +--R * +--R 7 +--R x +--R + +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 +--R 923a b e + 22188a b d e + 85866a b d e + 83380a b d e +--R + +--R 10 4 11 5 +--R 20295a b d e + 792b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R a b e + 5532a b d e + 52734a b d e + 101420a b d e +--R + +--R 2 9 4 10 5 +--R 49005a b d e + 4752a b d +--R * +--R 5 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R - a b e + 12a b d e + 13794a b d e + 64900a b d e +--R + +--R 3 8 4 2 9 5 +--R 61875a b d e + 11880a b d +--R * +--R 4 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 4 7 4 +--R a b e - 12a b d e + 66a b d e + 18260a b d e + 42075a b d e +--R + +--R 3 8 5 +--R 15840a b d +--R * +--R 3 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 5 6 4 +--R - a b e + 12a b d e - 66a b d e + 220a b d e + 13365a b d e +--R + +--R 4 7 5 +--R 11880a b d +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 6 5 4 +--R a b e - 12a b d e + 66a b d e - 220a b d e + 495a b d e +--R + +--R 5 6 5 +--R 4752a b d +--R * +--R x +--R + +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 6 5 5 +--R - a e + 12a b d e - 66a b d e + 220a b d e - 495a b d e + 792a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 +--R 5544b +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 12 5 5 6 4 11 +--R 462b e x + (3024a b e + 2520b d e )x +--R + +--R 2 4 5 5 4 6 2 3 10 +--R (8316a b e + 16632a b d e + 5544b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 9 +--R (12320a b e + 46200a b d e + 36960a b d e + 6160b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 +--R 10395a b e + 69300a b d e + 103950a b d e + 41580a b d e +--R + +--R 6 4 +--R 3465b d e +--R * +--R 8 +--R x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 +--R 4752a b e + 59400a b d e + 158400a b d e + 118800a b d e +--R + +--R 5 4 6 5 +--R 23760a b d e + 792b d +--R * +--R 7 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 +--R 924a e + 27720a b d e + 138600a b d e + 184800a b d e +--R + +--R 2 4 4 5 5 +--R 69300a b d e + 5544a b d +--R * +--R 6 +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 +--R 5544a d e + 66528a b d e + 166320a b d e + 110880a b d e +--R + +--R 2 4 5 +--R 16632a b d +--R * +--R 5 +--R x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 4 +--R (13860a d e + 83160a b d e + 103950a b d e + 27720a b d )x +--R + +--R 6 3 2 5 4 4 2 5 3 +--R (18480a d e + 55440a b d e + 27720a b d )x +--R + +--R 6 4 5 5 2 6 5 +--R (13860a d e + 16632a b d )x + 5544a d x +--R / +--R 5544 +--R Type: Union(Expression(Integer),...) +--E 525 + +--S 526 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 11 5 11 10 5 11 4 10 +--R - 462b e x + (- 2562a b e - 2520b d e )x +--R + +--R 2 9 5 10 4 11 2 3 9 +--R (- 5754a b e - 14112a b d e - 5544b d e )x +--R + +--R 3 8 5 2 9 4 10 2 3 11 3 2 8 +--R (- 6566a b e - 32088a b d e - 31416a b d e - 6160b d e )x +--R + +--R 4 7 5 3 8 4 2 9 2 3 10 3 2 +--R - 3829a b e - 37212a b d e - 72534a b d e - 35420a b d e +--R + +--R 11 4 +--R - 3465b d e +--R * +--R 7 +--R x +--R + +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 +--R - 923a b e - 22188a b d e - 85866a b d e - 83380a b d e +--R + +--R 10 4 11 5 +--R - 20295a b d e - 792b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R - a b e - 5532a b d e - 52734a b d e - 101420a b d e +--R + +--R 2 9 4 10 5 +--R - 49005a b d e - 4752a b d +--R * +--R 5 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R a b e - 12a b d e - 13794a b d e - 64900a b d e +--R + +--R 3 8 4 2 9 5 +--R - 61875a b d e - 11880a b d +--R * +--R 4 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 4 7 4 +--R - a b e + 12a b d e - 66a b d e - 18260a b d e - 42075a b d e +--R + +--R 3 8 5 +--R - 15840a b d +--R * +--R 3 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 5 6 4 +--R a b e - 12a b d e + 66a b d e - 220a b d e - 13365a b d e +--R + +--R 4 7 5 +--R - 11880a b d +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 6 5 4 +--R - a b e + 12a b d e - 66a b d e + 220a b d e - 495a b d e +--R + +--R 5 6 5 +--R - 4752a b d +--R * +--R x +--R + +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 6 5 5 +--R a e - 12a b d e + 66a b d e - 220a b d e + 495a b d e - 792a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 12 5 12 11 5 12 4 11 +--R 462b e x + (3024a b e + 2520b d e )x +--R + +--R 2 10 5 11 4 12 2 3 10 +--R (8316a b e + 16632a b d e + 5544b d e )x +--R + +--R 3 9 5 2 10 4 11 2 3 12 3 2 9 +--R (12320a b e + 46200a b d e + 36960a b d e + 6160b d e )x +--R + +--R 4 8 5 3 9 4 2 10 2 3 11 3 2 +--R 10395a b e + 69300a b d e + 103950a b d e + 41580a b d e +--R + +--R 12 4 +--R 3465b d e +--R * +--R 8 +--R x +--R + +--R 5 7 5 4 8 4 3 9 2 3 2 10 3 2 +--R 4752a b e + 59400a b d e + 158400a b d e + 118800a b d e +--R + +--R 11 4 12 5 +--R 23760a b d e + 792b d +--R * +--R 7 +--R x +--R + +--R 6 6 5 5 7 4 4 8 2 3 3 9 3 2 +--R 924a b e + 27720a b d e + 138600a b d e + 184800a b d e +--R + +--R 2 10 4 11 5 +--R 69300a b d e + 5544a b d +--R * +--R 6 +--R x +--R + +--R 6 6 4 5 7 2 3 4 8 3 2 3 9 4 +--R 5544a b d e + 66528a b d e + 166320a b d e + 110880a b d e +--R + +--R 2 10 5 +--R 16632a b d +--R * +--R 5 +--R x +--R + +--R 6 6 2 3 5 7 3 2 4 8 4 3 9 5 4 +--R (13860a b d e + 83160a b d e + 103950a b d e + 27720a b d )x +--R + +--R 6 6 3 2 5 7 4 4 8 5 3 +--R (18480a b d e + 55440a b d e + 27720a b d )x +--R + +--R 6 6 4 5 7 5 2 6 6 5 +--R (13860a b d e + 16632a b d )x + 5544a b d x +--R / +--R 6 +--R 5544b +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 5 11 5 5 6 4 10 +--R b e x + (6a b e + 5b d e )x +--R + +--R 2 4 5 5 4 6 2 3 9 +--R (15a b e + 30a b d e + 10b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 8 +--R (20a b e + 75a b d e + 60a b d e + 10b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 7 +--R (15a b e + 100a b d e + 150a b d e + 60a b d e + 5b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 6a b e + 75a b d e + 200a b d e + 150a b d e + 30a b d e +--R + +--R 6 5 +--R b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R a e + 30a b d e + 150a b d e + 200a b d e + 75a b d e +--R + +--R 5 5 +--R 6a b d +--R * +--R 5 +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 4 +--R (5a d e + 60a b d e + 150a b d e + 100a b d e + 15a b d )x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 3 +--R (10a d e + 60a b d e + 75a b d e + 20a b d )x +--R + +--R 6 3 2 5 4 4 2 5 2 6 4 5 5 6 5 +--R (10a d e + 30a b d e + 15a b d )x + (5a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 5 12 6 5 7 4 11 +--R - b e x + (- 7a b e - 5b d e )x +--R + +--R 2 5 5 6 4 7 2 3 10 +--R (- 21a b e - 35a b d e - 10b d e )x +--R + +--R 3 4 5 2 5 4 6 2 3 7 3 2 9 +--R (- 35a b e - 105a b d e - 70a b d e - 10b d e )x +--R + +--R 4 3 5 3 4 4 2 5 2 3 6 3 2 7 4 8 +--R (- 35a b e - 175a b d e - 210a b d e - 70a b d e - 5b d e)x +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R - 21a b e - 175a b d e - 350a b d e - 210a b d e - 35a b d e +--R + +--R 7 5 +--R - b d +--R * +--R 7 +--R x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R - 7a b e - 105a b d e - 350a b d e - 350a b d e - 105a b d e +--R + +--R 6 5 +--R - 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R - a e - 35a b d e - 210a b d e - 350a b d e - 175a b d e +--R + +--R 2 5 5 +--R - 21a b d +--R * +--R 5 +--R x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 4 +--R (- 5a d e - 70a b d e - 210a b d e - 175a b d e - 35a b d )x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 3 +--R (- 10a d e - 70a b d e - 105a b d e - 35a b d )x +--R + +--R 7 3 2 6 4 5 2 5 2 7 4 6 5 7 5 +--R (- 10a d e - 35a b d e - 21a b d )x + (- 5a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 527 + +)clear all + +--S 528 of 1353 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1353 +r0:=1/2310*(b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/330*(b*d-a*e)^3*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+2/165*(b*d-a*e)^2*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+2/55*(b*d-a*e)*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/11*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 10 4 10 9 4 10 3 9 +--R 210b e x + (1176a b e + 924b d e )x +--R + +--R 2 8 4 9 3 10 2 2 8 +--R (2674a b e + 5236a b d e + 1540b d e )x +--R + +--R 3 7 4 2 8 3 9 2 2 10 3 7 +--R (3101a b e + 12089a b d e + 8855a b d e + 1155b d e)x +--R + +--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 6 +--R (1849a b e + 14311a b d e + 20845a b d e + 6765a b d e + 330b d )x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R 461a b e + 8789a b d e + 25355a b d e + 16335a b d e +--R + +--R 9 4 +--R 1980a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 2 8 4 4 +--R (a b e + 2299a b d e + 16225a b d e + 20625a b d e + 4950a b d )x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 3 7 4 3 +--R (- a b e + 11a b d e + 4565a b d e + 14025a b d e + 6600a b d )x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 4 6 4 2 +--R (a b e - 11a b d e + 55a b d e + 4455a b d e + 4950a b d )x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 5 5 4 10 4 +--R (- a b e + 11a b d e - 55a b d e + 165a b d e + 1980a b d )x + a e +--R + +--R 9 3 8 2 2 2 7 3 3 6 4 4 +--R - 11a b d e + 55a b d e - 165a b d e + 330a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 2310b +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 4 11 5 4 6 3 10 +--R 210b e x + (1386a b e + 924b d e )x +--R + +--R 2 4 4 5 3 6 2 2 9 +--R (3850a b e + 6160a b d e + 1540b d e )x +--R + +--R 3 3 4 2 4 3 5 2 2 6 3 8 +--R (5775a b e + 17325a b d e + 10395a b d e + 1155b d e)x +--R + +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 7 +--R (4950a b e + 26400a b d e + 29700a b d e + 7920a b d e + 330b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 +--R 2310a b e + 23100a b d e + 46200a b d e + 23100a b d e +--R + +--R 5 4 +--R 2310a b d +--R * +--R 6 +--R x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 5 +--R (462a e + 11088a b d e + 41580a b d e + 36960a b d e + 6930a b d )x +--R + +--R 6 3 5 2 2 4 2 3 3 3 4 4 +--R (2310a d e + 20790a b d e + 34650a b d e + 11550a b d )x +--R + +--R 6 2 2 5 3 4 2 4 3 6 3 5 4 2 +--R (4620a d e + 18480a b d e + 11550a b d )x + (4620a d e + 6930a b d )x +--R + +--R 6 4 +--R 2310a d x +--R / +--R 2310 +--R Type: Union(Expression(Integer),...) +--E 530 + +--S 531 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 10 4 10 9 4 10 3 9 +--R - 210b e x + (- 1176a b e - 924b d e )x +--R + +--R 2 8 4 9 3 10 2 2 8 +--R (- 2674a b e - 5236a b d e - 1540b d e )x +--R + +--R 3 7 4 2 8 3 9 2 2 10 3 7 +--R (- 3101a b e - 12089a b d e - 8855a b d e - 1155b d e)x +--R + +--R 4 6 4 3 7 3 2 8 2 2 9 3 +--R - 1849a b e - 14311a b d e - 20845a b d e - 6765a b d e +--R + +--R 10 4 +--R - 330b d +--R * +--R 6 +--R x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R - 461a b e - 8789a b d e - 25355a b d e - 16335a b d e +--R + +--R 9 4 +--R - 1980a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 +--R - a b e - 2299a b d e - 16225a b d e - 20625a b d e +--R + +--R 2 8 4 +--R - 4950a b d +--R * +--R 4 +--R x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 3 7 4 3 +--R (a b e - 11a b d e - 4565a b d e - 14025a b d e - 6600a b d )x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 4 6 4 2 +--R (- a b e + 11a b d e - 55a b d e - 4455a b d e - 4950a b d )x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 5 5 4 10 4 +--R (a b e - 11a b d e + 55a b d e - 165a b d e - 1980a b d )x - a e +--R + +--R 9 3 8 2 2 2 7 3 3 6 4 4 +--R 11a b d e - 55a b d e + 165a b d e - 330a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 11 4 11 10 4 11 3 10 +--R 210b e x + (1386a b e + 924b d e )x +--R + +--R 2 9 4 10 3 11 2 2 9 +--R (3850a b e + 6160a b d e + 1540b d e )x +--R + +--R 3 8 4 2 9 3 10 2 2 11 3 8 +--R (5775a b e + 17325a b d e + 10395a b d e + 1155b d e)x +--R + +--R 4 7 4 3 8 3 2 9 2 2 10 3 11 4 7 +--R (4950a b e + 26400a b d e + 29700a b d e + 7920a b d e + 330b d )x +--R + +--R 5 6 4 4 7 3 3 8 2 2 2 9 3 +--R 2310a b e + 23100a b d e + 46200a b d e + 23100a b d e +--R + +--R 10 4 +--R 2310a b d +--R * +--R 6 +--R x +--R + +--R 6 5 4 5 6 3 4 7 2 2 3 8 3 2 9 4 5 +--R (462a b e + 11088a b d e + 41580a b d e + 36960a b d e + 6930a b d )x +--R + +--R 6 5 3 5 6 2 2 4 7 3 3 8 4 4 +--R (2310a b d e + 20790a b d e + 34650a b d e + 11550a b d )x +--R + +--R 6 5 2 2 5 6 3 4 7 4 3 +--R (4620a b d e + 18480a b d e + 11550a b d )x +--R + +--R 6 5 3 5 6 4 2 6 5 4 +--R (4620a b d e + 6930a b d )x + 2310a b d x +--R / +--R 5 +--R 2310b +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 4 10 5 4 6 3 9 2 4 4 5 3 6 2 2 8 +--R b e x + (6a b e + 4b d e )x + (15a b e + 24a b d e + 6b d e )x +--R + +--R 3 3 4 2 4 3 5 2 2 6 3 7 +--R (20a b e + 60a b d e + 36a b d e + 4b d e)x +--R + +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 6 +--R (15a b e + 80a b d e + 90a b d e + 24a b d e + b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 5 +--R (6a b e + 60a b d e + 120a b d e + 60a b d e + 6a b d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 4 +--R (a e + 24a b d e + 90a b d e + 80a b d e + 15a b d )x +--R + +--R 6 3 5 2 2 4 2 3 3 3 4 3 +--R (4a d e + 36a b d e + 60a b d e + 20a b d )x +--R + +--R 6 2 2 5 3 4 2 4 2 6 3 5 4 6 4 +--R (6a d e + 24a b d e + 15a b d )x + (4a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 4 11 6 4 7 3 10 +--R - b e x + (- 7a b e - 4b d e )x +--R + +--R 2 5 4 6 3 7 2 2 9 +--R (- 21a b e - 28a b d e - 6b d e )x +--R + +--R 3 4 4 2 5 3 6 2 2 7 3 8 +--R (- 35a b e - 84a b d e - 42a b d e - 4b d e)x +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (- 35a b e - 140a b d e - 126a b d e - 28a b d e - b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 6 +--R (- 21a b e - 140a b d e - 210a b d e - 84a b d e - 7a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 5 +--R (- 7a b e - 84a b d e - 210a b d e - 140a b d e - 21a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 4 +--R (- a e - 28a b d e - 126a b d e - 140a b d e - 35a b d )x +--R + +--R 7 3 6 2 2 5 2 3 4 3 4 3 +--R (- 4a d e - 42a b d e - 84a b d e - 35a b d )x +--R + +--R 7 2 2 6 3 5 2 4 2 7 3 6 4 7 4 +--R (- 6a d e - 28a b d e - 21a b d )x + (- 4a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 532 + +)clear all + +--S 533 of 1353 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1353 +r0:=1/840*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+1/120*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+1/30*(b*d-a*e)*(d+e*x)^2*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^2+1/10*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 9 3 9 8 3 9 2 8 +--R 84b e x + (476a b e + 280b d e )x +--R + +--R 2 7 3 8 2 9 2 7 +--R (1099a b e + 1610a b d e + 315b d e)x +--R + +--R 3 6 3 2 7 2 8 2 9 3 6 +--R (1301a b e + 3790a b d e + 1845a b d e + 120b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (799a b e + 4610a b d e + 4455a b d e + 720a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 4 +--R (209a b e + 2950a b d e + 5625a b d e + 1800a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (a b e + 830a b d e + 3825a b d e + 2400a b d )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (- a b e + 10a b d e + 1215a b d e + 1800a b d )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 8 2 +--R (a b e - 10a b d e + 45a b d e + 720a b d )x - a e + 10a b d e +--R + +--R 7 2 2 6 3 3 +--R - 45a b d e + 120a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 840b +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3 10 5 3 6 2 9 +--R 84b e x + (560a b e + 280b d e )x +--R + +--R 2 4 3 5 2 6 2 8 +--R (1575a b e + 1890a b d e + 315b d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 7 +--R (2400a b e + 5400a b d e + 2160a b d e + 120b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 6 +--R (2100a b e + 8400a b d e + 6300a b d e + 840a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 5 +--R (1008a b e + 7560a b d e + 10080a b d e + 2520a b d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 4 +--R (210a e + 3780a b d e + 9450a b d e + 4200a b d )x +--R + +--R 6 2 5 2 4 2 3 3 6 2 5 3 2 +--R (840a d e + 5040a b d e + 4200a b d )x + (1260a d e + 2520a b d )x +--R + +--R 6 3 +--R 840a d x +--R / +--R 840 +--R Type: Union(Expression(Integer),...) +--E 535 + +--S 536 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 3 9 8 3 9 2 8 +--R - 84b e x + (- 476a b e - 280b d e )x +--R + +--R 2 7 3 8 2 9 2 7 +--R (- 1099a b e - 1610a b d e - 315b d e)x +--R + +--R 3 6 3 2 7 2 8 2 9 3 6 +--R (- 1301a b e - 3790a b d e - 1845a b d e - 120b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (- 799a b e - 4610a b d e - 4455a b d e - 720a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 4 +--R (- 209a b e - 2950a b d e - 5625a b d e - 1800a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (- a b e - 830a b d e - 3825a b d e - 2400a b d )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (a b e - 10a b d e - 1215a b d e - 1800a b d )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 8 2 +--R (- a b e + 10a b d e - 45a b d e - 720a b d )x + a e - 10a b d e +--R + +--R 7 2 2 6 3 3 +--R 45a b d e - 120a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 10 3 10 9 3 10 2 9 +--R 84b e x + (560a b e + 280b d e )x +--R + +--R 2 8 3 9 2 10 2 8 +--R (1575a b e + 1890a b d e + 315b d e)x +--R + +--R 3 7 3 2 8 2 9 2 10 3 7 +--R (2400a b e + 5400a b d e + 2160a b d e + 120b d )x +--R + +--R 4 6 3 3 7 2 2 8 2 9 3 6 +--R (2100a b e + 8400a b d e + 6300a b d e + 840a b d )x +--R + +--R 5 5 3 4 6 2 3 7 2 2 8 3 5 +--R (1008a b e + 7560a b d e + 10080a b d e + 2520a b d )x +--R + +--R 6 4 3 5 5 2 4 6 2 3 7 3 4 +--R (210a b e + 3780a b d e + 9450a b d e + 4200a b d )x +--R + +--R 6 4 2 5 5 2 4 6 3 3 6 4 2 5 5 3 2 +--R (840a b d e + 5040a b d e + 4200a b d )x + (1260a b d e + 2520a b d )x +--R + +--R 6 4 3 +--R 840a b d x +--R / +--R 4 +--R 840b +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 3 9 5 3 6 2 8 2 4 3 5 2 6 2 7 +--R b e x + (6a b e + 3b d e )x + (15a b e + 18a b d e + 3b d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (20a b e + 45a b d e + 18a b d e + b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (15a b e + 60a b d e + 45a b d e + 6a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (6a b e + 45a b d e + 60a b d e + 15a b d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (a e + 18a b d e + 45a b d e + 20a b d )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (3a d e + 18a b d e + 15a b d )x + (3a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 3 10 6 3 7 2 9 +--R - b e x + (- 7a b e - 3b d e )x +--R + +--R 2 5 3 6 2 7 2 8 +--R (- 21a b e - 21a b d e - 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (- 35a b e - 63a b d e - 21a b d e - b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (- 35a b e - 105a b d e - 63a b d e - 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (- 21a b e - 105a b d e - 105a b d e - 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (- 7a b e - 63a b d e - 105a b d e - 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (- a e - 21a b d e - 63a b d e - 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (- 3a d e - 21a b d e - 21a b d )x + (- 3a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1353 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1353 +r0:=1/252*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+1/36*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2+1/9*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 8 2 8 7 2 8 7 +--R 28b e x + (161a b e + 63b d e)x +--R + +--R 2 6 2 7 8 2 6 +--R (379a b e + 369a b d e + 36b d )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (461a b e + 891a b d e + 216a b d )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (295a b e + 1125a b d e + 540a b d )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (83a b e + 765a b d e + 720a b d )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (a b e + 243a b d e + 540a b d )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- a b e + 9a b d e + 216a b d )x + a e - 9a b d e + 36a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 252b +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 9 5 2 6 8 2 4 2 5 6 2 7 +--R 28b e x + (189a b e + 63b d e)x + (540a b e + 432a b d e + 36b d )x +--R + +--R 3 3 2 2 4 5 2 6 +--R (840a b e + 1260a b d e + 252a b d )x +--R + +--R 4 2 2 3 3 2 4 2 5 +--R (756a b e + 2016a b d e + 756a b d )x +--R + +--R 5 2 4 2 3 3 2 4 +--R (378a b e + 1890a b d e + 1260a b d )x +--R + +--R 6 2 5 4 2 2 3 6 5 2 2 6 2 +--R (84a e + 1008a b d e + 1260a b d )x + (252a d e + 756a b d )x + 252a d x +--R / +--R 252 +--R Type: Union(Expression(Integer),...) +--E 540 + +--S 541 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 2 8 7 2 8 7 +--R - 28b e x + (- 161a b e - 63b d e)x +--R + +--R 2 6 2 7 8 2 6 +--R (- 379a b e - 369a b d e - 36b d )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 461a b e - 891a b d e - 216a b d )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 295a b e - 1125a b d e - 540a b d )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 83a b e - 765a b d e - 720a b d )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- a b e - 243a b d e - 540a b d )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (a b e - 9a b d e - 216a b d )x - a e + 9a b d e - 36a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 9 2 9 8 2 9 8 2 7 2 8 9 2 7 +--R 28b e x + (189a b e + 63b d e)x + (540a b e + 432a b d e + 36b d )x +--R + +--R 3 6 2 2 7 8 2 6 +--R (840a b e + 1260a b d e + 252a b d )x +--R + +--R 4 5 2 3 6 2 7 2 5 +--R (756a b e + 2016a b d e + 756a b d )x +--R + +--R 5 4 2 4 5 3 6 2 4 +--R (378a b e + 1890a b d e + 1260a b d )x +--R + +--R 6 3 2 5 4 4 5 2 3 6 3 5 4 2 2 +--R (84a b e + 1008a b d e + 1260a b d )x + (252a b d e + 756a b d )x +--R + +--R 6 3 2 +--R 252a b d x +--R / +--R 3 +--R 252b +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 2 8 5 2 6 7 2 4 2 5 6 2 6 +--R b e x + (6a b e + 2b d e)x + (15a b e + 12a b d e + b d )x +--R + +--R 3 3 2 2 4 5 2 5 +--R (20a b e + 30a b d e + 6a b d )x +--R + +--R 4 2 2 3 3 2 4 2 4 +--R (15a b e + 40a b d e + 15a b d )x +--R + +--R 5 2 4 2 3 3 2 3 6 2 5 4 2 2 2 +--R (6a b e + 30a b d e + 20a b d )x + (a e + 12a b d e + 15a b d )x +--R + +--R 6 5 2 6 2 +--R (2a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R - b e x + (- 7a b e - 2b d e)x + (- 21a b e - 14a b d e - b d )x +--R + +--R 3 4 2 2 5 6 2 6 +--R (- 35a b e - 42a b d e - 7a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 +--R (- 35a b e - 70a b d e - 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 +--R (- 21a b e - 70a b d e - 35a b d )x +--R + +--R 6 2 5 2 4 3 2 3 7 2 6 5 2 2 2 +--R (- 7a b e - 42a b d e - 35a b d )x + (- a e - 14a b d e - 21a b d )x +--R + +--R 7 6 2 7 2 +--R (- 2a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 542 + +)clear all + +--S 543 of 1353 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1353 +r0:=1/56*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2+1/8*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 7 7 6 7 6 2 5 6 5 +--R 7b e x + (41a b e + 8b d)x + (99a b e + 48a b d)x +--R + +--R 3 4 2 5 4 4 3 3 4 3 +--R (125a b e + 120a b d)x + (85a b e + 160a b d)x +--R + +--R 5 2 4 3 2 6 5 2 7 6 +--R (27a b e + 120a b d)x + (a b e + 48a b d)x - a e + 8a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 56b +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 8 5 6 7 2 4 5 6 +--R 7b e x + (48a b e + 8b d)x + (140a b e + 56a b d)x +--R + +--R 3 3 2 4 5 4 2 3 3 4 +--R (224a b e + 168a b d)x + (210a b e + 280a b d)x +--R + +--R 5 4 2 3 6 5 2 6 +--R (112a b e + 280a b d)x + (28a e + 168a b d)x + 56a d x +--R / +--R 56 +--R Type: Union(Expression(Integer),...) +--E 545 + +--S 546 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 7 6 7 6 2 5 6 5 +--R - 7b e x + (- 41a b e - 8b d)x + (- 99a b e - 48a b d)x +--R + +--R 3 4 2 5 4 4 3 3 4 3 +--R (- 125a b e - 120a b d)x + (- 85a b e - 160a b d)x +--R + +--R 5 2 4 3 2 6 5 2 7 6 +--R (- 27a b e - 120a b d)x + (- a b e - 48a b d)x + a e - 8a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 8 8 7 8 7 2 6 7 6 +--R 7b e x + (48a b e + 8b d)x + (140a b e + 56a b d)x +--R + +--R 3 5 2 6 5 4 4 3 5 4 +--R (224a b e + 168a b d)x + (210a b e + 280a b d)x +--R + +--R 5 3 4 4 3 6 2 5 3 2 6 2 +--R (112a b e + 280a b d)x + (28a b e + 168a b d)x + 56a b d x +--R / +--R 2 +--R 56b +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 7 5 6 6 2 4 5 5 +--R b e x + (6a b e + b d)x + (15a b e + 6a b d)x +--R + +--R 3 3 2 4 4 4 2 3 3 3 5 4 2 2 +--R (20a b e + 15a b d)x + (15a b e + 20a b d)x + (6a b e + 15a b d)x +--R + +--R 6 5 6 +--R (a e + 6a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 8 6 7 7 2 5 6 6 +--R - b e x + (- 7a b e - b d)x + (- 21a b e - 7a b d)x +--R + +--R 3 4 2 5 5 4 3 3 4 4 +--R (- 35a b e - 21a b d)x + (- 35a b e - 35a b d)x +--R + +--R 5 2 4 3 3 6 5 2 2 7 6 7 +--R (- 21a b e - 35a b d)x + (- 7a b e - 21a b d)x + (- a e - 7a b d)x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 547 + +)clear all + +--S 548 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1353 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7b +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 6 7 5 6 2 4 5 3 3 4 4 2 3 5 2 6 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a x +--R (3) ----------------------------------------------------------------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 550 + +--S 551 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- b x - 6a b x - 15a b x - 20a b x - 15a b x - 6a b x - a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R / +--R 7b +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1353 +r0:=-1/3*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+1/4*(b*d-a*e)^2*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-1/5*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/e^2+1/6*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-(b*d-_ + a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/2*(b*d-a*e)^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+(b*d-a*e)^6*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 60a e - 360a b d e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 5 5 6 6 +--R - 360a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (72a b e - 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (225a b e - 90a b d e + 15b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b e - 300a b d e + 120a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (450a b e - 600a b d e + 450a b d e - 180a b d e + 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 360a b e - 900a b d e + 1200a b d e - 900a b d e + 360a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 147a e - 522a b d e + 855a b d e - 740a b d e + 330a b d e +--R + +--R 5 5 +--R - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 60a e - 360a b d e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 5 5 6 6 +--R - 360a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (72a b e - 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (225a b e - 90a b d e + 15b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b e - 300a b d e + 120a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (450a b e - 600a b d e + 450a b d e - 180a b d e + 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 360a b e - 900a b d e + 1200a b d e - 900a b d e + 360a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R / +--R 7 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 555 + +--S 556 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 60a e + 360a b d e - 900a b d e + 1200a b d e - 900a b d e +--R + +--R 5 5 6 6 +--R 360a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 10b e x + (- 72a b e + 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 225a b e + 90a b d e - 15b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 400a b e + 300a b d e - 120a b d e + 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 450a b e + 600a b d e - 450a b d e + 180a b d e - 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 360a b e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 5 4 2 6 5 +--R - 360a b d e + 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 147a e + 522a b d e - 855a b d e + 740a b d e - 330a b d e +--R + +--R 5 5 +--R 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 60a b e - 360a b d e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 6 5 7 6 +--R - 360a b d e + 60b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R 60a e - 360a b d e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 2 5 5 6 6 +--R - 360a b d e + 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 +--R 10b e x + (82a b e - 12b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (297a b e - 102a b d e + 15b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (625a b e - 390a b d e + 135a b d e - 20b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (850a b e - 900a b d e + 570a b d e - 200a b d e + 30b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 810a b e - 1500a b d e + 1650a b d e - 1080a b d e + 390a b d e +--R + +--R 7 5 +--R - 60b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 360a b e - 900a b d e + 1200a b d e - 900a b d e + 360a b d e +--R + +--R 6 5 +--R - 60a b d e +--R * +--R x +--R / +--R 7 7 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 557 + +)clear all + +--S 558 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1353 +r0:=2*b*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-3/2*b*(b*d-a*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3+6/5*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/e^2-(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x))+_ + 6*b*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-3*b*(b*d-a*e)^3*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-6*b*(b*d-a*e)^5*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e +--R + +--R 5 4 2 6 5 +--R 300a b d e - 60b d e +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 60a b d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 6 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 2b e x + (15a b e - 3b d e )x + (50a b e - 25a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b e - 100a b d e + 50a b d e - 10b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (150a b e - 300a b d e + 300a b d e - 150a b d e + 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 77a b e - 85a b d e - 130a b d e + 330a b d e - 240a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e + 137a b d e - 385a b d e + 470a b d e - 270a b d e +--R + +--R 5 5 +--R 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +--R 10b e x + (10a e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 60a b d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 6 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 2b e x + (15a b e - 3b d e )x + (50a b e - 25a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b e - 100a b d e + 50a b d e - 10b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (150a b e - 300a b d e + 300a b d e - 150a b d e + 30b d e )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (150a b d e - 400a b d e + 450a b d e - 240a b d e + 50b d e)x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e + 60a b d e - 150a b d e + 200a b d e - 150a b d e +--R + +--R 5 5 6 6 +--R 60a b d e - 10b d +--R / +--R 8 7 +--R 10e x + 10d e +--R Type: Union(Expression(Integer),...) +--E 560 + +--S 561 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 60a b e + 300a b d e - 600a b d e + 600a b d e +--R + +--R 5 4 2 6 5 +--R - 300a b d e + 60b d e +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 60a b d e + 300a b d e - 600a b d e + 600a b d e +--R + +--R 5 5 6 6 +--R - 300a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 2b e x + (- 15a b e + 3b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 50a b e + 25a b d e - 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 100a b e + 100a b d e - 50a b d e + 10b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 150a b e + 300a b d e - 300a b d e + 150a b d e - 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 77a b e + 85a b d e + 130a b d e - 330a b d e + 240a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 10a e - 137a b d e + 385a b d e - 470a b d e + 270a b d e +--R + +--R 5 5 +--R - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 7 5 +--R - 60b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 2 5 4 2 6 5 +--R 60a b e - 240a b d e + 300a b d e - 300a b d e + 240a b d e +--R + +--R 7 6 +--R - 60b d +--R * +--R x +--R + +--R 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R 60a b d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 6 +--R - 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R 2b e x + (17a b e - 3b d e )x + (65a b e - 28a b d e + 5b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (150a b e - 125a b d e + 55a b d e - 10b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (250a b e - 400a b d e + 350a b d e - 160a b d e + 30b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 150a b e - 150a b d e - 100a b d e + 300a b d e - 210a b d e +--R + +--R 7 5 +--R 50b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 10a b e + 210a b d e - 550a b d e + 650a b d e - 390a b d e +--R + +--R 6 5 7 6 +--R 110a b d e - 10b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 10a e + 60a b d e - 150a b d e + 200a b d e - 150a b d e +--R + +--R 2 5 5 6 6 +--R 60a b d e - 10a b d +--R / +--R 8 2 8 7 7 +--R 10b e x + (10a e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 562 + +)clear all + +--S 563 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1353 +r0:=-5*b^2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+15/4*b^2*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-1/2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(d+e*x)^2)-3*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(d+e*x))-15*b^2*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+_ + 15/2*b^2*(b*d-a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+_ + 15*b^2*(b*d-a*e)^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b d e - 480a b d e + 720a b d e - 480a b d e + 120b d e)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (8a b e - 2b d e )x + (30a b e - 20a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b e - 120a b d e + 80a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (35a b e + 100a b d e - 330a b d e + 300a b d e - 90b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b e + 190a b d e - 280a b d e + 60a b d e + 120a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a e - 12a b d e + 125a b d e - 260a b d e + 210a b d e +--R + +--R 5 5 +--R - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 4b e x + (4a e + 8b d e )x + (8a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b d e - 480a b d e + 720a b d e - 480a b d e + 120b d e)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (8a b e - 2b d e )x + (30a b e - 20a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b e - 120a b d e + 80a b d e - 20b d e )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (160a b d e - 330a b d e + 252a b d e - 68b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b e + 120a b d e - 160a b d e + 60a b d e + 24a b d e +--R + +--R 6 5 +--R - 16b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a e - 12a b d e + 90a b d e - 200a b d e + 210a b d e +--R + +--R 5 5 6 6 +--R - 108a b d e + 22b d +--R / +--R 9 2 8 2 7 +--R 4e x + 8d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 565 + +--S 566 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 60a b e + 240a b d e - 360a b d e + 240a b d e +--R + +--R 6 4 2 +--R - 60b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 120a b d e + 480a b d e - 720a b d e + 480a b d e +--R + +--R 6 5 +--R - 120b d e +--R * +--R x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R - 60a b d e + 240a b d e - 360a b d e + 240a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - b e x + (- 8a b e + 2b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 30a b e + 20a b d e - 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 80a b e + 120a b d e - 80a b d e + 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 35a b e - 100a b d e + 330a b d e - 300a b d e + 90b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 24a b e - 190a b d e + 280a b d e - 60a b d e - 120a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 2a e + 12a b d e - 125a b d e + 260a b d e - 210a b d e +--R + +--R 5 5 +--R 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 60a b e - 120a b d e - 120a b d e + 480a b d e - 420a b d e +--R + +--R 7 5 +--R 120b d e +--R * +--R 2 +--R x +--R + +--R 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 120a b d e - 420a b d e + 480a b d e - 120a b d e +--R + +--R 6 5 7 6 +--R - 120a b d e + 60b d +--R * +--R x +--R + +--R 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 6 6 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R b e x + (9a b e - 2b d e )x + (38a b e - 22a b d e + 5b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (110a b e - 140a b d e + 85a b d e - 20b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (80a b e + 40a b d e - 250a b d e + 232a b d e - 68b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 24a b e + 280a b d e - 490a b d e + 312a b d e - 44a b d e +--R + +--R 7 5 +--R - 16b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 26a b e + 108a b d e - 70a b d e - 140a b d e + 234a b d e +--R + +--R 6 5 7 6 +--R - 124a b d e + 22b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 2a e - 12a b d e + 90a b d e - 200a b d e + 210a b d e +--R + +--R 2 5 5 6 6 +--R - 108a b d e + 22a b d +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 4b e x + (4a e + 8b d e )x + (8a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1353 +r0:=20/3*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-5*b^2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(d+e*x))-1/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e*(d+e*x)^3)-b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^2)+20*b^3*_ + (b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-10*b^3*(b*d-a*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-20*b^3*(b*d-a*e)^3*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e )x +--R + +--R 3 3 2 4 2 4 3 3 5 4 2 6 5 3 3 3 3 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e)x + 60a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (9a b e - 3b d e )x + (45a b e - 45a b d e + 15b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (180a b d e - 270a b d e + 110b d e )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 2 +--R (- 45a b e + 180a b d e - 270a b d e + 150b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 6 5 6 6 +--R (- 9a b e - 45a b d e + 270a b d e - 270a b d e + 60b d e)x - a e +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 3a b d e - 15a b d e + 110a b d e - 150a b d e + 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 8 3 7 3 7 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e )x +--R + +--R 3 3 2 4 2 4 3 3 5 4 2 6 5 3 3 3 3 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e)x + 60a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (9a b e - 3b d e )x + (45a b e - 45a b d e + 15b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (135a b d e - 189a b d e + 73b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 45a b e + 180a b d e - 135a b d e - 27a b d e + 39b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 9a b e - 45a b d e + 270a b d e - 405a b d e + 243a b d e +--R + +--R 6 5 +--R - 51b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - a e - 3a b d e - 15a b d e + 110a b d e - 195a b d e + 141a b d e +--R + +--R 6 6 +--R - 37b d +--R / +--R 10 3 9 2 2 8 3 7 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 570 + +--S 571 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 60a b e + 180a b d e - 180a b d e + 60b d e )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 180a b d e + 540a b d e - 540a b d e + 180b d e )x +--R + +--R 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (- 180a b d e + 540a b d e - 540a b d e + 180b d e)x +--R + +--R 3 3 3 3 2 4 4 2 5 5 6 6 +--R - 60a b d e + 180a b d e - 180a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - b e x + (- 9a b e + 3b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 45a b e + 45a b d e - 15b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (- 180a b d e + 270a b d e - 110b d e )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 2 +--R (45a b e - 180a b d e + 270a b d e - 150b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 6 5 6 6 +--R (9a b e + 45a b d e - 270a b d e + 270a b d e - 60b d e)x + a e +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 3a b d e + 15a b d e - 110a b d e + 150a b d e - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 4 3 6 2 5 2 4 6 3 3 7 4 2 3 +--R (60a b e - 360a b d e + 480a b d e - 180b d e )x +--R + +--R 4 3 5 3 4 2 4 6 4 2 7 5 2 +--R (180a b d e - 360a b d e + 360a b d e - 180b d e)x +--R + +--R 4 3 2 4 3 4 3 3 2 5 4 2 7 6 4 3 3 3 +--R (180a b d e - 480a b d e + 360a b d e - 60b d )x + 60a b d e +--R + +--R 3 4 4 2 2 5 5 6 6 +--R - 180a b d e + 180a b d e - 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R b e x + (10a b e - 3b d e )x + (54a b e - 48a b d e + 15b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (45a b e + 90a b d e - 174a b d e + 73b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (- 45a b e + 315a b d e - 324a b d e + 46a b d e + 39b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 54a b e + 135a b d e + 135a b d e - 432a b d e + 282a b d e +--R + +--R 7 5 +--R - 51b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 10a b e - 48a b d e + 255a b d e - 295a b d e + 48a b d e +--R + +--R 6 5 7 6 +--R 90a b d e - 37b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R - a e - 3a b d e - 15a b d e + 110a b d e - 195a b d e + 141a b d e +--R + +--R 6 6 +--R - 37a b d +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 8 3 7 3 7 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 572 + +)clear all + +--S 573 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1353 +r0:=-5/4*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^2)-_ + 5*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x))-1/4*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^4)-1/2*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^3)-15*b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6+15/2*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+_ + 15*b^4*(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 2 4 6 5 5 6 2 4 4 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (240a b d e - 480a b d e + 240b d e )x +--R + +--R 2 4 2 4 5 3 3 6 4 2 2 +--R (360a b d e - 720a b d e + 360b d e )x +--R + +--R 2 4 3 3 5 4 2 6 5 2 4 4 2 5 5 +--R (240a b d e - 480a b d e + 240b d e)x + 60a b d e - 120a b d e +--R + +--R 6 6 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 2b e x + (24a b e - 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 35a b e + 190a b d e - 125b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 80a b e + 100a b d e + 280a b d e - 260b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 30a b e - 120a b d e + 330a b d e + 60a b d e - 210b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 8a b e - 20a b d e - 80a b d e + 300a b d e - 120a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - a e - 2a b d e - 5a b d e - 20a b d e + 90a b d e - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 4b e x + (4a e + 16b d e )x + (16a d e + 24b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (24a d e + 16b d e )x + (16a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 6 5 5 6 2 4 4 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (240a b d e - 480a b d e + 240b d e )x +--R + +--R 2 4 2 4 5 3 3 6 4 2 2 +--R (360a b d e - 720a b d e + 360b d e )x +--R + +--R 2 4 3 3 5 4 2 6 5 2 4 4 2 5 5 +--R (240a b d e - 480a b d e + 240b d e)x + 60a b d e - 120a b d e +--R + +--R 6 6 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 5 5 6 2 4 4 +--R 2b e x + (24a b e - 12b d e )x + (96a b d e - 68b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 80a b e + 240a b d e - 96a b d e - 32b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 30a b e - 120a b d e + 540a b d e - 504a b d e + 132b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 8a b e - 20a b d e - 80a b d e + 440a b d e - 496a b d e +--R + +--R 6 5 +--R 168b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - a e - 2a b d e - 5a b d e - 20a b d e + 125a b d e - 154a b d e +--R + +--R 6 6 +--R 57b d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +--R 4e x + 16d e x + 24d e x + 16d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 575 + +--S 576 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 6 5 5 6 2 4 4 +--R (- 60a b e + 120a b d e - 60b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (- 240a b d e + 480a b d e - 240b d e )x +--R + +--R 2 4 2 4 5 3 3 6 4 2 2 +--R (- 360a b d e + 720a b d e - 360b d e )x +--R + +--R 2 4 3 3 5 4 2 6 5 2 4 4 2 +--R (- 240a b d e + 480a b d e - 240b d e)x - 60a b d e +--R + +--R 5 5 6 6 +--R 120a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 2b e x + (- 24a b e + 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (35a b e - 190a b d e + 125b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b e - 100a b d e - 280a b d e + 260b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (30a b e + 120a b d e - 330a b d e - 60a b d e + 210b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 8a b e + 20a b d e + 80a b d e - 300a b d e + 120a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R a e + 2a b d e + 5a b d e + 20a b d e - 90a b d e + 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (60a b e + 120a b d e - 420a b d e + 240b d e )x +--R + +--R 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (240a b d e - 120a b d e - 480a b d e + 360b d e )x +--R + +--R 3 4 2 4 2 5 3 3 6 4 2 7 5 2 +--R (360a b d e - 480a b d e - 120a b d e + 240b d e)x +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 3 4 4 2 +--R (240a b d e - 420a b d e + 120a b d e + 60b d )x + 60a b d e +--R + +--R 2 5 5 6 6 +--R - 120a b d e + 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R 2b e x + (26a b e - 12b d e )x + (24a b e + 84a b d e - 68b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 80a b e + 336a b d e - 164a b d e - 32b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (- 110a b e + 120a b d e + 444a b d e - 536a b d e + 132b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 38a b e - 140a b d e + 460a b d e - 64a b d e - 364a b d e +--R + +--R 7 5 +--R 168b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 9a b e - 22a b d e - 85a b d e + 420a b d e - 371a b d e +--R + +--R 6 5 7 6 +--R 14a b d e + 57b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R - a e - 2a b d e - 5a b d e - 20a b d e + 125a b d e - 154a b d e +--R + +--R 6 6 +--R 57a b d +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 4b e x + (4a e + 16b d e )x + (16a d e + 24b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (24a d e + 16b d e )x + (16a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 577 + +)clear all + +--S 578 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^6 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1353 +r0:=-1/2*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^3)-_ + b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^2)-1/5*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^5)-3/10*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^4)+6*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 3*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x))-_ + 6*b^5*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 6 5 5 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (300a b d e - 300b d e )x +--R + +--R 5 2 4 6 3 3 3 5 3 3 6 4 2 2 +--R (600a b d e - 600b d e )x + (600a b d e - 600b d e )x +--R + +--R 5 4 2 6 5 5 5 6 6 +--R (300a b d e - 300b d e)x + 60a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (- 77a b e + 137b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 150a b e - 85a b d e + 385b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 100a b e - 300a b d e + 130a b d e + 470b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 50a b e - 100a b d e - 300a b d e + 330a b d e + 270b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 15a b e - 25a b d e - 50a b d e - 150a b d e + 240a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e - 3a b d e - 5a b d e - 10a b d e - 30a b d e + 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 10b e x + (10a e + 50b d e )x + (50a d e + 100b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (100a d e + 100b d e )x + (100a d e + 50b d e )x +--R + +--R 4 8 5 7 5 7 +--R (50a d e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 5 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (300a b d e - 300b d e )x +--R + +--R 5 2 4 6 3 3 3 5 3 3 6 4 2 2 +--R (600a b d e - 600b d e )x + (600a b d e - 600b d e )x +--R + +--R 5 4 2 6 5 5 5 6 6 +--R (300a b d e - 300b d e)x + 60a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 10b e x + 50b d e x + (- 150a b e + 300a b d e - 50b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 100a b e - 300a b d e + 900a b d e - 400b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 50a b e - 100a b d e - 300a b d e + 1100a b d e - 600b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 15a b e - 25a b d e - 50a b d e - 150a b d e + 625a b d e +--R + +--R 6 5 +--R - 375b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e - 3a b d e - 5a b d e - 10a b d e - 30a b d e + 137a b d e +--R + +--R 6 6 +--R - 87b d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 5 7 +--R 10e x + 50d e x + 100d e x + 100d e x + 50d e x + 10d e +--R Type: Union(Expression(Integer),...) +--E 580 + +--S 581 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 5 5 5 6 2 4 4 +--R (- 60a b e + 60b d e )x + (- 300a b d e + 300b d e )x +--R + +--R 5 2 4 6 3 3 3 5 3 3 6 4 2 2 +--R (- 600a b d e + 600b d e )x + (- 600a b d e + 600b d e )x +--R + +--R 5 4 2 6 5 5 5 6 6 +--R (- 300a b d e + 300b d e)x - 60a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 10b e x + (77a b e - 137b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (150a b e + 85a b d e - 385b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b e + 300a b d e - 130a b d e - 470b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (50a b e + 100a b d e + 300a b d e - 330a b d e - 270b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 15a b e + 25a b d e + 50a b d e + 150a b d e - 240a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 2a e + 3a b d e + 5a b d e + 10a b d e + 30a b d e - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R (60a b e - 60b d e )x + (60a b e + 240a b d e - 300b d e )x +--R + +--R 2 5 5 6 2 4 7 3 3 4 +--R (300a b d e + 300a b d e - 600b d e )x +--R + +--R 2 5 2 4 7 4 2 3 +--R (600a b d e - 600b d e )x +--R + +--R 2 5 3 3 6 4 2 7 5 2 +--R (600a b d e - 300a b d e - 300b d e)x +--R + +--R 2 5 4 2 6 5 7 6 2 5 5 6 6 +--R (300a b d e - 240a b d e - 60b d )x + 60a b d e - 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 +--R 10b e x + (10a b e + 50b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 150a b e + 350a b d e - 50b d e )x +--R + +--R 3 4 6 6 2 4 7 3 3 4 +--R (- 250a b e + 850a b d e - 400b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (- 150a b e - 400a b d e + 600a b d e + 700a b d e - 600b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 65a b e - 125a b d e - 350a b d e + 950a b d e + 25a b d e +--R + +--R 7 5 +--R - 375b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 17a b e - 28a b d e - 55a b d e - 160a b d e + 595a b d e +--R + +--R 6 5 7 6 +--R - 238a b d e - 87b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R - 2a e - 3a b d e - 5a b d e - 10a b d e - 30a b d e + 137a b d e +--R + +--R 6 6 +--R - 87a b d +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 10b e x + (10a e + 50b d e )x + (50a d e + 100b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (100a d e + 100b d e )x + (100a d e + 50b d e )x +--R + +--R 4 8 5 7 5 7 +--R (50a d e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1353 +r0:=-1/4*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^4)-_ + 1/3*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^3)-1/6*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^6)-1/5*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^5)-1/2*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^2)+b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x))+b^6*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 6 6 5 5 6 2 4 4 6 3 3 3 6 4 2 2 +--R 60b e x + 360b d e x + 900b d e x + 1200b d e x + 900b d e x +--R + +--R 6 5 6 6 +--R 360b d e x + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 87b e x + (- 360a b e - 162b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 450a b e - 900a b d e + 45b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 400a b e - 600a b d e - 1200a b d e + 460b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 225a b e - 300a b d e - 450a b d e - 900a b d e + 570b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 72a b e - 90a b d e - 120a b d e - 180a b d e - 360a b d e +--R + +--R 6 5 +--R 300b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e - 12a b d e - 15a b d e - 20a b d e - 30a b d e +--R + +--R 5 5 6 6 +--R - 60a b d e + 60b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 7 13 12 6 12 2 11 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 11 3 10 4 3 10 4 9 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 9 5 8 2 5 8 6 7 6 7 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 6 5 5 6 2 4 4 6 3 3 3 6 4 2 2 +--R 60b e x + 360b d e x + 900b d e x + 1200b d e x + 900b d e x +--R + +--R 6 5 6 6 +--R 360b d e x + 60b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R (- 360a b e + 360b d e )x + (- 450a b e - 900a b d e + 1350b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 400a b e - 600a b d e - 1200a b d e + 2200b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 225a b e - 300a b d e - 450a b d e - 900a b d e + 1875b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 72a b e - 90a b d e - 120a b d e - 180a b d e - 360a b d e +--R + +--R 6 5 +--R 822b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 10a e - 12a b d e - 15a b d e - 20a b d e - 30a b d e - 60a b d e +--R + +--R 6 6 +--R 147b d +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 5 8 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 7 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 585 + +--S 586 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 6 5 5 6 2 4 4 6 3 3 3 +--R - 60b e x - 360b d e x - 900b d e x - 1200b d e x +--R + +--R 6 4 2 2 6 5 6 6 +--R - 900b d e x - 360b d e x - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 87b e x + (360a b e + 162b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (450a b e + 900a b d e - 45b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b e + 600a b d e + 1200a b d e - 460b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (225a b e + 300a b d e + 450a b d e + 900a b d e - 570b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 72a b e + 90a b d e + 120a b d e + 180a b d e + 360a b d e +--R + +--R 6 5 +--R - 300b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 10a e + 12a b d e + 15a b d e + 20a b d e + 30a b d e +--R + +--R 5 5 6 6 +--R 60a b d e - 60b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 6 5 7 2 4 5 +--R 60b e x + (60a b e + 360b d e )x + (360a b d e + 900b d e )x +--R + +--R 6 2 4 7 3 3 4 6 3 3 7 4 2 3 +--R (900a b d e + 1200b d e )x + (1200a b d e + 900b d e )x +--R + +--R 6 4 2 7 5 2 6 5 7 6 6 6 +--R (900a b d e + 360b d e)x + (360a b d e + 60b d )x + 60a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R (- 360a b e + 360b d e )x + (- 810a b e - 540a b d e + 1350b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 850a b e - 1500a b d e + 150a b d e + 2200b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (- 625a b e - 900a b d e - 1650a b d e + 1300a b d e + 1875b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 297a b e - 390a b d e - 570a b d e - 1080a b d e + 1515a b d e +--R + +--R 7 5 +--R 822b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 82a b e - 102a b d e - 135a b d e - 200a b d e - 390a b d e +--R + +--R 6 5 7 6 +--R 762a b d e + 147b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R - 10a e - 12a b d e - 15a b d e - 20a b d e - 30a b d e - 60a b d e +--R + +--R 6 6 +--R 147a b d +--R / +--R 13 7 13 12 6 12 2 11 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 11 3 10 4 3 10 4 9 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 9 5 8 2 5 8 6 7 6 7 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 587 + +)clear all + +--S 588 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1353 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^7) +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- b x - 6a b x - 15a b x - 20a b x - 15a b x - 6a b x - a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 7 7 7 2 6 6 2 6 3 5 5 +--R (7a e - 7b d e )x + (49a d e - 49b d e )x + (147a d e - 147b d e )x +--R + +--R 3 5 4 4 4 4 4 5 3 3 +--R (245a d e - 245b d e )x + (245a d e - 245b d e )x +--R + +--R 5 3 6 2 2 6 2 7 7 8 +--R (147a d e - 147b d e )x + (49a d e - 49b d e)x + 7a d e - 7b d +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 7b e x + (- 21a b e - 21b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 35a b e - 35a b d e - 35b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 35a b e - 35a b d e - 35a b d e - 35b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 21a b e - 21a b d e - 21a b d e - 21a b d e - 21b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (- 7a b e - 7a b d e - 7a b d e - 7a b d e - 7a b d e - 7b d e)x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R - a e - a b d e - a b d e - a b d e - a b d e - a b d e - b d +--R / +--R 14 7 13 6 2 12 5 3 11 4 4 10 3 5 9 2 +--R 7e x + 49d e x + 147d e x + 245d e x + 245d e x + 147d e x +--R + +--R 6 8 7 7 +--R 49d e x + 7d e +--R Type: Union(Expression(Integer),...) +--E 590 + +--S 591 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 6 5 7 5 2 4 7 4 3 3 7 3 4 2 7 2 5 7 +--R b e x + 6a b e x + 15a b e x + 20a b e x + 15a b e x + 6a b e x +--R + +--R 6 7 +--R a e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 7 6 6 2 5 7 7 2 5 5 +--R (- 7a b e + 7b d e )x + (- 21a b e + 21b d e )x +--R + +--R 3 4 7 7 3 4 4 4 3 7 7 4 3 3 +--R (- 35a b e + 35b d e )x + (- 35a b e + 35b d e )x +--R + +--R 5 2 7 7 5 2 2 6 7 7 6 7 7 7 7 +--R (- 21a b e + 21b d e )x + (- 7a b e + 7b d e)x - a e + b d +--R / +--R 15 14 7 14 2 13 6 +--R (7a e - 7b d e )x + (49a d e - 49b d e )x +--R + +--R 2 13 3 12 5 3 12 4 11 4 +--R (147a d e - 147b d e )x + (245a d e - 245b d e )x +--R + +--R 4 11 5 10 3 5 10 6 9 2 +--R (245a d e - 245b d e )x + (147a d e - 147b d e )x +--R + +--R 6 9 7 8 7 8 8 7 +--R (49a d e - 49b d e )x + 7a d e - 7b d e +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 592 + +)clear all + +--S 593 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1353 +r0:=1/8*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^8)+_ + 1/56*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^7) +--R +--R +--R (2) +--R 7 7 6 7 6 2 5 6 5 +--R b e x + (- a b e + 8b d)x + (- 27a b e + 48a b d)x +--R + +--R 3 4 2 5 4 4 3 3 4 3 +--R (- 85a b e + 120a b d)x + (- 125a b e + 160a b d)x +--R + +--R 5 2 4 3 2 6 5 2 7 6 +--R (- 99a b e + 120a b d)x + (- 41a b e + 48a b d)x - 7a e + 8a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 10 9 2 2 8 8 +--R (56a e - 112a b d e + 56b d e )x +--R + +--R 2 9 2 8 2 3 7 7 +--R (448a d e - 896a b d e + 448b d e )x +--R + +--R 2 2 8 3 7 2 4 6 6 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 3 7 4 6 2 5 5 5 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 4 6 5 5 2 6 4 4 +--R (3920a d e - 7840a b d e + 3920b d e )x +--R + +--R 2 5 5 6 4 2 7 3 3 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 6 4 7 3 2 8 2 2 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 7 3 8 2 2 9 2 8 2 9 2 10 +--R (448a d e - 896a b d e + 448b d e)x + 56a d e - 112a b d e + 56b d +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 28b e x + (- 112a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 210a b e - 140a b d e - 70b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 224a b e - 168a b d e - 112a b d e - 56b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 140a b e - 112a b d e - 84a b d e - 56a b d e - 28b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 48a b e - 40a b d e - 32a b d e - 24a b d e - 16a b d e +--R + +--R 6 5 +--R - 8b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R - 7a e - 6a b d e - 5a b d e - 4a b d e - 3a b d e - 2a b d e - b d +--R / +--R 15 8 14 7 2 13 6 3 12 5 4 11 4 +--R 56e x + 448d e x + 1568d e x + 3136d e x + 3920d e x +--R + +--R 5 10 3 6 9 2 7 8 8 7 +--R 3136d e x + 1568d e x + 448d e x + 56d e +--R Type: Union(Expression(Integer),...) +--E 595 + +--S 596 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 8 7 6 8 7 7 6 2 5 8 6 7 5 +--R - b e x + (a b e - 8b d e )x + (27a b e - 48a b d e )x +--R + +--R 3 4 8 2 5 7 4 4 3 8 3 4 7 3 +--R (85a b e - 120a b d e )x + (125a b e - 160a b d e )x +--R + +--R 5 2 8 4 3 7 2 6 8 5 2 7 7 8 +--R (99a b e - 120a b d e )x + (41a b e - 48a b d e )x + 7a e +--R + +--R 6 7 +--R - 8a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 6 8 7 7 8 2 6 6 +--R (- 28a b e + 56a b d e - 28b d e )x +--R + +--R 3 5 8 2 6 7 8 3 5 5 +--R (- 112a b e + 168a b d e - 56b d e )x +--R + +--R 4 4 8 3 5 7 8 4 4 4 +--R (- 210a b e + 280a b d e - 70b d e )x +--R + +--R 5 3 8 4 4 7 8 5 3 3 +--R (- 224a b e + 280a b d e - 56b d e )x +--R + +--R 6 2 8 5 3 7 8 6 2 2 +--R (- 140a b e + 168a b d e - 28b d e )x +--R + +--R 7 8 6 2 7 8 7 8 8 7 7 8 8 +--R (- 48a b e + 56a b d e - 8b d e)x - 7a e + 8a b d e - b d +--R / +--R 2 17 16 2 2 15 8 +--R (56a e - 112a b d e + 56b d e )x +--R + +--R 2 16 2 15 2 3 14 7 +--R (448a d e - 896a b d e + 448b d e )x +--R + +--R 2 2 15 3 14 2 4 13 6 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 3 14 4 13 2 5 12 5 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 4 13 5 12 2 6 11 4 +--R (3920a d e - 7840a b d e + 3920b d e )x +--R + +--R 2 5 12 6 11 2 7 10 3 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 6 11 7 10 2 8 9 2 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 7 10 8 9 2 9 8 2 8 9 9 8 +--R (448a d e - 896a b d e + 448b d e )x + 56a d e - 112a b d e +--R + +--R 2 10 7 +--R 56b d e +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1353 +r0:=1/9*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^9)+_ + 1/36*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^8)+_ + 1/252*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^7) +--R +--R +--R (2) +--R 8 2 8 7 2 8 7 2 6 2 7 8 2 6 +--R - b e x + (a b e - 9b d e)x + (- a b e + 9a b d e - 36b d )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 83a b e + 243a b d e - 216a b d )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 295a b e + 765a b d e - 540a b d )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 461a b e + 1125a b d e - 720a b d )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 379a b e + 891a b d e - 540a b d )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 161a b e + 369a b d e - 216a b d )x - 28a e + 63a b d e - 36a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 12 2 11 2 2 10 3 3 9 9 +--R (252a e - 756a b d e + 756a b d e - 252b d e )x +--R + +--R 3 11 2 2 10 2 3 9 3 4 8 8 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e )x +--R + +--R 3 2 10 2 3 9 2 4 8 3 5 7 7 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 3 9 2 4 8 2 5 7 3 6 6 6 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 4 8 2 5 7 2 6 6 3 7 5 5 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 5 7 2 6 6 2 7 5 3 8 4 4 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 6 6 2 7 5 2 8 4 3 9 3 3 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 7 5 2 8 4 2 9 3 3 10 2 2 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 8 4 2 9 3 2 10 2 3 11 3 9 3 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e)x + 252a d e +--R + +--R 2 10 2 2 11 3 12 +--R - 756a b d e + 756a b d e - 252b d +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 84b e x + (- 378a b e - 126b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 756a b e - 378a b d e - 126b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 840a b e - 504a b d e - 252a b d e - 84b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 540a b e - 360a b d e - 216a b d e - 108a b d e - 36b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 189a b e - 135a b d e - 90a b d e - 54a b d e - 27a b d e +--R + +--R 6 5 +--R - 9b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 28a e - 21a b d e - 15a b d e - 10a b d e - 6a b d e - 3a b d e +--R + +--R 6 6 +--R - b d +--R / +--R 16 9 15 8 2 14 7 3 13 6 4 12 5 +--R 252e x + 2268d e x + 9072d e x + 21168d e x + 31752d e x +--R + +--R 5 11 4 6 10 3 7 9 2 8 8 9 7 +--R 31752d e x + 21168d e x + 9072d e x + 2268d e x + 252d e +--R Type: Union(Expression(Integer),...) +--E 600 + +--S 601 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 9 8 7 9 8 8 7 2 6 9 7 8 8 2 7 6 +--R b e x + (- a b e + 9b d e )x + (a b e - 9a b d e + 36b d e )x +--R + +--R 3 5 9 2 6 8 7 2 7 5 +--R (83a b e - 243a b d e + 216a b d e )x +--R + +--R 4 4 9 3 5 8 2 6 2 7 4 +--R (295a b e - 765a b d e + 540a b d e )x +--R + +--R 5 3 9 4 4 8 3 5 2 7 3 +--R (461a b e - 1125a b d e + 720a b d e )x +--R + +--R 6 2 9 5 3 8 4 4 2 7 2 +--R (379a b e - 891a b d e + 540a b d e )x +--R + +--R 7 9 6 2 8 5 3 2 7 8 9 7 8 +--R (161a b e - 369a b d e + 216a b d e )x + 28a e - 63a b d e +--R + +--R 6 2 2 7 +--R 36a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 6 9 2 7 8 8 2 7 9 3 6 6 +--R (- 84a b e + 252a b d e - 252a b d e + 84b d e )x +--R + +--R 4 5 9 3 6 8 2 7 2 7 9 4 5 5 +--R (- 378a b e + 1008a b d e - 756a b d e + 126b d e )x +--R + +--R 5 4 9 4 5 8 3 6 2 7 9 5 4 4 +--R (- 756a b e + 1890a b d e - 1260a b d e + 126b d e )x +--R + +--R 6 3 9 5 4 8 4 5 2 7 9 6 3 3 +--R (- 840a b e + 2016a b d e - 1260a b d e + 84b d e )x +--R + +--R 7 2 9 6 3 8 5 4 2 7 9 7 2 2 +--R (- 540a b e + 1260a b d e - 756a b d e + 36b d e )x +--R + +--R 8 9 7 2 8 6 3 2 7 9 8 9 9 8 8 +--R (- 189a b e + 432a b d e - 252a b d e + 9b d e)x - 28a e + 63a b d e +--R + +--R 7 2 2 7 9 9 +--R - 36a b d e + b d +--R / +--R 3 19 2 18 2 2 17 3 3 16 9 +--R (252a e - 756a b d e + 756a b d e - 252b d e )x +--R + +--R 3 18 2 2 17 2 3 16 3 4 15 8 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e )x +--R + +--R 3 2 17 2 3 16 2 4 15 3 5 14 7 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 3 16 2 4 15 2 5 14 3 6 13 6 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 4 15 2 5 14 2 6 13 3 7 12 5 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 5 14 2 6 13 2 7 12 3 8 11 4 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 6 13 2 7 12 2 8 11 3 9 10 3 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 7 12 2 8 11 2 9 10 3 10 9 2 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 8 11 2 9 10 2 10 9 3 11 8 3 9 10 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e )x + 252a d e +--R + +--R 2 10 9 2 11 8 3 12 7 +--R - 756a b d e + 756a b d e - 252b d e +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 602 + +)clear all + +--S 603 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1353 +r0:=1/10*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^10)+_ + 1/30*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^9)+_ + 1/120*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^8)+_ + 1/840*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^7) +--R +--R +--R (2) +--R 9 3 9 8 3 9 2 8 2 7 3 8 2 9 2 7 +--R b e x + (- a b e + 10b d e )x + (a b e - 10a b d e + 45b d e)x +--R + +--R 3 6 3 2 7 2 8 2 9 3 6 +--R (- a b e + 10a b d e - 45a b d e + 120b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (- 209a b e + 830a b d e - 1215a b d e + 720a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 4 +--R (- 799a b e + 2950a b d e - 3825a b d e + 1800a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (- 1301a b e + 4610a b d e - 5625a b d e + 2400a b d )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (- 1099a b e + 3790a b d e - 4455a b d e + 1800a b d )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 +--R (- 476a b e + 1610a b d e - 1845a b d e + 720a b d )x - 84a e +--R + +--R 8 2 7 2 2 6 3 3 +--R 280a b d e - 315a b d e + 120a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 14 3 13 2 2 2 12 3 3 11 4 4 10 +--R (840a e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d e ) +--R * +--R 10 +--R x +--R + +--R 4 13 3 2 12 2 2 3 11 3 4 10 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 5 9 +--R 8400b d e +--R * +--R 9 +--R x +--R + +--R 4 2 12 3 3 11 2 2 4 10 3 5 9 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 6 8 +--R 37800b d e +--R * +--R 8 +--R x +--R + +--R 4 3 11 3 4 10 2 2 5 9 3 6 8 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 7 7 +--R 100800b d e +--R * +--R 7 +--R x +--R + +--R 4 4 10 3 5 9 2 2 6 8 3 7 7 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 8 6 +--R 176400b d e +--R * +--R 6 +--R x +--R + +--R 4 5 9 3 6 8 2 2 7 7 3 8 6 +--R 211680a d e - 846720a b d e + 1270080a b d e - 846720a b d e +--R + +--R 4 9 5 +--R 211680b d e +--R * +--R 5 +--R x +--R + +--R 4 6 8 3 7 7 2 2 8 6 3 9 5 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 10 4 +--R 176400b d e +--R * +--R 4 +--R x +--R + +--R 4 7 7 3 8 6 2 2 9 5 3 10 4 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 11 3 +--R 100800b d e +--R * +--R 3 +--R x +--R + +--R 4 8 6 3 9 5 2 2 10 4 3 11 3 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 12 2 +--R 37800b d e +--R * +--R 2 +--R x +--R + +--R 4 9 5 3 10 4 2 2 11 3 3 12 2 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 13 +--R 8400b d e +--R * +--R x +--R + +--R 4 10 4 3 11 3 2 2 12 2 3 13 4 14 +--R 840a d e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 210b e x + (- 1008a b e - 252b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 2100a b e - 840a b d e - 210b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 2400a b e - 1200a b d e - 480a b d e - 120b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 1575a b e - 900a b d e - 450a b d e - 180a b d e - 45b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 560a b e - 350a b d e - 200a b d e - 100a b d e - 40a b d e +--R + +--R 6 5 +--R - 10b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 84a e - 56a b d e - 35a b d e - 20a b d e - 10a b d e - 4a b d e +--R + +--R 6 6 +--R - b d +--R / +--R 17 10 16 9 2 15 8 3 14 7 4 13 6 +--R 840e x + 8400d e x + 37800d e x + 100800d e x + 176400d e x +--R + +--R 5 12 5 6 11 4 7 10 3 8 9 2 9 8 +--R 211680d e x + 176400d e x + 100800d e x + 37800d e x + 8400d e x +--R + +--R 10 7 +--R 840d e +--R Type: Union(Expression(Integer),...) +--E 605 + +--S 606 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 10 9 8 10 9 9 8 +--R - b e x + (a b e - 10b d e )x +--R + +--R 2 7 10 8 9 9 2 8 7 +--R (- a b e + 10a b d e - 45b d e )x +--R + +--R 3 6 10 2 7 9 8 2 8 9 3 7 6 +--R (a b e - 10a b d e + 45a b d e - 120b d e )x +--R + +--R 4 5 10 3 6 9 2 7 2 8 8 3 7 5 +--R (209a b e - 830a b d e + 1215a b d e - 720a b d e )x +--R + +--R 5 4 10 4 5 9 3 6 2 8 2 7 3 7 4 +--R (799a b e - 2950a b d e + 3825a b d e - 1800a b d e )x +--R + +--R 6 3 10 5 4 9 4 5 2 8 3 6 3 7 3 +--R (1301a b e - 4610a b d e + 5625a b d e - 2400a b d e )x +--R + +--R 7 2 10 6 3 9 5 4 2 8 4 5 3 7 2 +--R (1099a b e - 3790a b d e + 4455a b d e - 1800a b d e )x +--R + +--R 8 10 7 2 9 6 3 2 8 5 4 3 7 9 10 +--R (476a b e - 1610a b d e + 1845a b d e - 720a b d e )x + 84a e +--R + +--R 8 9 7 2 2 8 6 3 3 7 +--R - 280a b d e + 315a b d e - 120a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (- 210a b e + 840a b d e - 1260a b d e + 840a b d e - 210b d e )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 1008a b e + 3780a b d e - 5040a b d e + 2520a b d e +--R + +--R 10 5 5 +--R - 252b d e +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 2100a b e + 7560a b d e - 9450a b d e + 4200a b d e +--R + +--R 10 6 4 +--R - 210b d e +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 2400a b e + 8400a b d e - 10080a b d e + 4200a b d e +--R + +--R 10 7 3 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 1575a b e + 5400a b d e - 6300a b d e + 2520a b d e +--R + +--R 10 8 2 +--R - 45b d e +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 10 9 +--R (- 560a b e + 1890a b d e - 2160a b d e + 840a b d e - 10b d e)x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 10 10 +--R - 84a e + 280a b d e - 315a b d e + 120a b d e - b d +--R / +--R 4 21 3 20 2 2 2 19 3 3 18 4 4 17 +--R (840a e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d e ) +--R * +--R 10 +--R x +--R + +--R 4 20 3 2 19 2 2 3 18 3 4 17 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 5 16 +--R 8400b d e +--R * +--R 9 +--R x +--R + +--R 4 2 19 3 3 18 2 2 4 17 3 5 16 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 6 15 +--R 37800b d e +--R * +--R 8 +--R x +--R + +--R 4 3 18 3 4 17 2 2 5 16 3 6 15 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 7 14 +--R 100800b d e +--R * +--R 7 +--R x +--R + +--R 4 4 17 3 5 16 2 2 6 15 3 7 14 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 8 13 +--R 176400b d e +--R * +--R 6 +--R x +--R + +--R 4 5 16 3 6 15 2 2 7 14 3 8 13 +--R 211680a d e - 846720a b d e + 1270080a b d e - 846720a b d e +--R + +--R 4 9 12 +--R 211680b d e +--R * +--R 5 +--R x +--R + +--R 4 6 15 3 7 14 2 2 8 13 3 9 12 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 10 11 +--R 176400b d e +--R * +--R 4 +--R x +--R + +--R 4 7 14 3 8 13 2 2 9 12 3 10 11 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 11 10 +--R 100800b d e +--R * +--R 3 +--R x +--R + +--R 4 8 13 3 9 12 2 2 10 11 3 11 10 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 12 9 +--R 37800b d e +--R * +--R 2 +--R x +--R + +--R 4 9 12 3 10 11 2 2 11 10 3 12 9 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 13 8 +--R 8400b d e +--R * +--R x +--R + +--R 4 10 11 3 11 10 2 2 12 9 3 13 8 4 14 7 +--R 840a d e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d e +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 607 + +)clear all + +--S 608 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1353 +r0:=1/11*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^11)+_ + 2/55*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^10)+_ + 2/165*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^9)+_ + 1/330*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^8)+_ + 1/2310*b^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^7) +--R +--R +--R (2) +--R 10 4 10 9 4 10 3 9 +--R - b e x + (a b e - 11b d e )x +--R + +--R 2 8 4 9 3 10 2 2 8 +--R (- a b e + 11a b d e - 55b d e )x +--R + +--R 3 7 4 2 8 3 9 2 2 10 3 7 +--R (a b e - 11a b d e + 55a b d e - 165b d e)x +--R + +--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 6 +--R (- a b e + 11a b d e - 55a b d e + 165a b d e - 330b d )x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R - 461a b e + 2299a b d e - 4565a b d e + 4455a b d e +--R + +--R 9 4 +--R - 1980a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 +--R - 1849a b e + 8789a b d e - 16225a b d e + 14025a b d e +--R + +--R 2 8 4 +--R - 4950a b d +--R * +--R 4 +--R x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 +--R - 3101a b e + 14311a b d e - 25355a b d e + 20625a b d e +--R + +--R 3 7 4 +--R - 6600a b d +--R * +--R 3 +--R x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 +--R - 2674a b e + 12089a b d e - 20845a b d e + 16335a b d e +--R + +--R 4 6 4 +--R - 4950a b d +--R * +--R 2 +--R x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 +--R - 1176a b e + 5236a b d e - 8855a b d e + 6765a b d e +--R + +--R 5 5 4 +--R - 1980a b d +--R * +--R x +--R + +--R 10 4 9 3 8 2 2 2 7 3 3 6 4 4 +--R - 210a e + 924a b d e - 1540a b d e + 1155a b d e - 330a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 16 4 15 3 2 2 14 2 3 3 13 +--R 2310a e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 4 12 5 5 11 +--R 11550a b d e - 2310b d e +--R * +--R 11 +--R x +--R + +--R 5 15 4 2 14 3 2 3 13 2 3 4 12 +--R 25410a d e - 127050a b d e + 254100a b d e - 254100a b d e +--R + +--R 4 5 11 5 6 10 +--R 127050a b d e - 25410b d e +--R * +--R 10 +--R x +--R + +--R 5 2 14 4 3 13 3 2 4 12 2 3 5 11 +--R 127050a d e - 635250a b d e + 1270500a b d e - 1270500a b d e +--R + +--R 4 6 10 5 7 9 +--R 635250a b d e - 127050b d e +--R * +--R 9 +--R x +--R + +--R 5 3 13 4 4 12 3 2 5 11 +--R 381150a d e - 1905750a b d e + 3811500a b d e +--R + +--R 2 3 6 10 4 7 9 5 8 8 +--R - 3811500a b d e + 1905750a b d e - 381150b d e +--R * +--R 8 +--R x +--R + +--R 5 4 12 4 5 11 3 2 6 10 2 3 7 9 +--R 762300a d e - 3811500a b d e + 7623000a b d e - 7623000a b d e +--R + +--R 4 8 8 5 9 7 +--R 3811500a b d e - 762300b d e +--R * +--R 7 +--R x +--R + +--R 5 5 11 4 6 10 3 2 7 9 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 8 8 4 9 7 5 10 6 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 6 +--R x +--R + +--R 5 6 10 4 7 9 3 2 8 8 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 9 7 4 10 6 5 11 5 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 5 +--R x +--R + +--R 5 7 9 4 8 8 3 2 9 7 2 3 10 6 +--R 762300a d e - 3811500a b d e + 7623000a b d e - 7623000a b d e +--R + +--R 4 11 5 5 12 4 +--R 3811500a b d e - 762300b d e +--R * +--R 4 +--R x +--R + +--R 5 8 8 4 9 7 3 2 10 6 2 3 11 5 +--R 381150a d e - 1905750a b d e + 3811500a b d e - 3811500a b d e +--R + +--R 4 12 4 5 13 3 +--R 1905750a b d e - 381150b d e +--R * +--R 3 +--R x +--R + +--R 5 9 7 4 10 6 3 2 11 5 2 3 12 4 +--R 127050a d e - 635250a b d e + 1270500a b d e - 1270500a b d e +--R + +--R 4 13 3 5 14 2 +--R 635250a b d e - 127050b d e +--R * +--R 2 +--R x +--R + +--R 5 10 6 4 11 5 3 2 12 4 2 3 13 3 +--R 25410a d e - 127050a b d e + 254100a b d e - 254100a b d e +--R + +--R 4 14 2 5 15 +--R 127050a b d e - 25410b d e +--R * +--R x +--R + +--R 5 11 5 4 12 4 3 2 13 3 2 3 14 2 +--R 2310a d e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 15 5 16 +--R 11550a b d e - 2310b d +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 462b e x + (- 2310a b e - 462b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 4950a b e - 1650a b d e - 330b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 5775a b e - 2475a b d e - 825a b d e - 165b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 3850a b e - 1925a b d e - 825a b d e - 275a b d e - 55b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 1386a b e - 770a b d e - 385a b d e - 165a b d e - 55a b d e +--R + +--R 6 5 +--R - 11b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 210a e - 126a b d e - 70a b d e - 35a b d e - 15a b d e - 5a b d e +--R + +--R 6 6 +--R - b d +--R / +--R 18 11 17 10 2 16 9 3 15 8 +--R 2310e x + 25410d e x + 127050d e x + 381150d e x +--R + +--R 4 14 7 5 13 6 6 12 5 7 11 4 +--R 762300d e x + 1067220d e x + 1067220d e x + 762300d e x +--R + +--R 8 10 3 9 9 2 10 8 11 7 +--R 381150d e x + 127050d e x + 25410d e x + 2310d e +--R Type: Union(Expression(Integer),...) +--E 610 + +--S 611 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 10 11 10 9 11 10 10 9 +--R b e x + (- a b e + 11b d e )x +--R + +--R 2 8 11 9 10 10 2 9 8 +--R (a b e - 11a b d e + 55b d e )x +--R + +--R 3 7 11 2 8 10 9 2 9 10 3 8 7 +--R (- a b e + 11a b d e - 55a b d e + 165b d e )x +--R + +--R 4 6 11 3 7 10 2 8 2 9 9 3 8 10 4 7 6 +--R (a b e - 11a b d e + 55a b d e - 165a b d e + 330b d e )x +--R + +--R 5 5 11 4 6 10 3 7 2 9 2 8 3 8 +--R 461a b e - 2299a b d e + 4565a b d e - 4455a b d e +--R + +--R 9 4 7 +--R 1980a b d e +--R * +--R 5 +--R x +--R + +--R 6 4 11 5 5 10 4 6 2 9 3 7 3 8 +--R 1849a b e - 8789a b d e + 16225a b d e - 14025a b d e +--R + +--R 2 8 4 7 +--R 4950a b d e +--R * +--R 4 +--R x +--R + +--R 7 3 11 6 4 10 5 5 2 9 4 6 3 8 +--R 3101a b e - 14311a b d e + 25355a b d e - 20625a b d e +--R + +--R 3 7 4 7 +--R 6600a b d e +--R * +--R 3 +--R x +--R + +--R 8 2 11 7 3 10 6 4 2 9 5 5 3 8 +--R 2674a b e - 12089a b d e + 20845a b d e - 16335a b d e +--R + +--R 4 6 4 7 +--R 4950a b d e +--R * +--R 2 +--R x +--R + +--R 9 11 8 2 10 7 3 2 9 6 4 3 8 +--R 1176a b e - 5236a b d e + 8855a b d e - 6765a b d e +--R + +--R 5 5 4 7 +--R 1980a b d e +--R * +--R x +--R + +--R 10 11 9 10 8 2 2 9 7 3 3 8 6 4 4 7 +--R 210a e - 924a b d e + 1540a b d e - 1155a b d e + 330a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 6 11 4 7 10 3 8 2 9 2 9 3 8 +--R - 462a b e + 2310a b d e - 4620a b d e + 4620a b d e +--R + +--R 10 4 7 11 5 6 +--R - 2310a b d e + 462b d e +--R * +--R 6 +--R x +--R + +--R 6 5 11 5 6 10 4 7 2 9 3 8 3 8 +--R - 2310a b e + 11088a b d e - 20790a b d e + 18480a b d e +--R + +--R 2 9 4 7 11 6 5 +--R - 6930a b d e + 462b d e +--R * +--R 5 +--R x +--R + +--R 7 4 11 6 5 10 5 6 2 9 4 7 3 8 +--R - 4950a b e + 23100a b d e - 41580a b d e + 34650a b d e +--R + +--R 3 8 4 7 11 7 4 +--R - 11550a b d e + 330b d e +--R * +--R 4 +--R x +--R + +--R 8 3 11 7 4 10 6 5 2 9 5 6 3 8 +--R - 5775a b e + 26400a b d e - 46200a b d e + 36960a b d e +--R + +--R 4 7 4 7 11 8 3 +--R - 11550a b d e + 165b d e +--R * +--R 3 +--R x +--R + +--R 9 2 11 8 3 10 7 4 2 9 6 5 3 8 +--R - 3850a b e + 17325a b d e - 29700a b d e + 23100a b d e +--R + +--R 5 6 4 7 11 9 2 +--R - 6930a b d e + 55b d e +--R * +--R 2 +--R x +--R + +--R 10 11 9 2 10 8 3 2 9 7 4 3 8 +--R - 1386a b e + 6160a b d e - 10395a b d e + 7920a b d e +--R + +--R 6 5 4 7 11 10 +--R - 2310a b d e + 11b d e +--R * +--R x +--R + +--R 11 11 10 10 9 2 2 9 8 3 3 8 7 4 4 7 +--R - 210a e + 924a b d e - 1540a b d e + 1155a b d e - 330a b d e +--R + +--R 11 11 +--R b d +--R / +--R 5 23 4 22 3 2 2 21 2 3 3 20 +--R 2310a e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 4 19 5 5 18 +--R 11550a b d e - 2310b d e +--R * +--R 11 +--R x +--R + +--R 5 22 4 2 21 3 2 3 20 2 3 4 19 +--R 25410a d e - 127050a b d e + 254100a b d e - 254100a b d e +--R + +--R 4 5 18 5 6 17 +--R 127050a b d e - 25410b d e +--R * +--R 10 +--R x +--R + +--R 5 2 21 4 3 20 3 2 4 19 2 3 5 18 +--R 127050a d e - 635250a b d e + 1270500a b d e - 1270500a b d e +--R + +--R 4 6 17 5 7 16 +--R 635250a b d e - 127050b d e +--R * +--R 9 +--R x +--R + +--R 5 3 20 4 4 19 3 2 5 18 +--R 381150a d e - 1905750a b d e + 3811500a b d e +--R + +--R 2 3 6 17 4 7 16 5 8 15 +--R - 3811500a b d e + 1905750a b d e - 381150b d e +--R * +--R 8 +--R x +--R + +--R 5 4 19 4 5 18 3 2 6 17 +--R 762300a d e - 3811500a b d e + 7623000a b d e +--R + +--R 2 3 7 16 4 8 15 5 9 14 +--R - 7623000a b d e + 3811500a b d e - 762300b d e +--R * +--R 7 +--R x +--R + +--R 5 5 18 4 6 17 3 2 7 16 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 8 15 4 9 14 5 10 13 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 6 +--R x +--R + +--R 5 6 17 4 7 16 3 2 8 15 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 9 14 4 10 13 5 11 12 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 5 +--R x +--R + +--R 5 7 16 4 8 15 3 2 9 14 +--R 762300a d e - 3811500a b d e + 7623000a b d e +--R + +--R 2 3 10 13 4 11 12 5 12 11 +--R - 7623000a b d e + 3811500a b d e - 762300b d e +--R * +--R 4 +--R x +--R + +--R 5 8 15 4 9 14 3 2 10 13 +--R 381150a d e - 1905750a b d e + 3811500a b d e +--R + +--R 2 3 11 12 4 12 11 5 13 10 +--R - 3811500a b d e + 1905750a b d e - 381150b d e +--R * +--R 3 +--R x +--R + +--R 5 9 14 4 10 13 3 2 11 12 +--R 127050a d e - 635250a b d e + 1270500a b d e +--R + +--R 2 3 12 11 4 13 10 5 14 9 +--R - 1270500a b d e + 635250a b d e - 127050b d e +--R * +--R 2 +--R x +--R + +--R 5 10 13 4 11 12 3 2 12 11 +--R 25410a d e - 127050a b d e + 254100a b d e +--R + +--R 2 3 13 10 4 14 9 5 15 8 +--R - 254100a b d e + 127050a b d e - 25410b d e +--R * +--R x +--R + +--R 5 11 12 4 12 11 3 2 13 10 2 3 14 9 +--R 2310a d e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 15 8 5 16 7 +--R 11550a b d e - 2310b d e +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x +--R + +--R 12 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^13 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R e x + 13d e x + 78d e x + 286d e x + 715d e x + 1287d e x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 +--R 1716d e x + 1716d e x + 1287d e x + 715d e x + 286d e x + 78d e x +--R + +--R 12 13 +--R 13d e x + d +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1353 +r0:=1/12*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^12)+_ + 5/132*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^11)+_ + 1/66*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^10)+_ + 1/198*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^9)+_ + 1/792*b^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^8)+_ + 1/5544*b^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^6*(d+e*x)^7) +--R +--R +--R (2) +--R 11 5 11 10 5 11 4 10 +--R b e x + (- a b e + 12b d e )x +--R + +--R 2 9 5 10 4 11 2 3 9 +--R (a b e - 12a b d e + 66b d e )x +--R + +--R 3 8 5 2 9 4 10 2 3 11 3 2 8 +--R (- a b e + 12a b d e - 66a b d e + 220b d e )x +--R + +--R 4 7 5 3 8 4 2 9 2 3 10 3 2 11 4 7 +--R (a b e - 12a b d e + 66a b d e - 220a b d e + 495b d e)x +--R + +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 10 4 +--R - a b e + 12a b d e - 66a b d e + 220a b d e - 495a b d e +--R + +--R 11 5 +--R 792b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R - 923a b e + 5532a b d e - 13794a b d e + 18260a b d e +--R + +--R 2 9 4 10 5 +--R - 13365a b d e + 4752a b d +--R * +--R 5 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R - 3829a b e + 22188a b d e - 52734a b d e + 64900a b d e +--R + +--R 3 8 4 2 9 5 +--R - 42075a b d e + 11880a b d +--R * +--R 4 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 +--R - 6566a b e + 37212a b d e - 85866a b d e + 101420a b d e +--R + +--R 4 7 4 3 8 5 +--R - 61875a b d e + 15840a b d +--R * +--R 3 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 +--R - 5754a b e + 32088a b d e - 72534a b d e + 83380a b d e +--R + +--R 5 6 4 4 7 5 +--R - 49005a b d e + 11880a b d +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 +--R - 2562a b e + 14112a b d e - 31416a b d e + 35420a b d e +--R + +--R 6 5 4 5 6 5 +--R - 20295a b d e + 4752a b d +--R * +--R x +--R + +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 +--R - 462a e + 2520a b d e - 5544a b d e + 6160a b d e - 3465a b d e +--R + +--R 6 5 5 +--R 792a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x 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324648324a b d e +--R + +--R 4 3 8 19 3 4 9 18 2 5 10 17 +--R - 541080540a b d e + 541080540a b d e - 324648324a b d e +--R + +--R 6 11 16 7 12 15 +--R 108216108a b d e - 15459444b d e +--R * +--R 8 +--R x +--R + +--R 7 6 21 6 7 20 5 2 8 19 +--R 20612592a d e - 144288144a b d e + 432864432a b d e +--R + +--R 4 3 9 18 3 4 10 17 2 5 11 16 +--R - 721440720a b d e + 721440720a b d e - 432864432a b d e +--R + +--R 6 12 15 7 13 14 +--R 144288144a b d e - 20612592b d e +--R * +--R 7 +--R x +--R + +--R 7 7 20 6 8 19 5 2 9 18 +--R 20612592a d e - 144288144a b d e + 432864432a b d e +--R + +--R 4 3 10 17 3 4 11 16 2 5 12 15 +--R - 721440720a b d e + 721440720a b d e - 432864432a b d e +--R + +--R 6 13 14 7 14 13 +--R 144288144a b d e - 20612592b d e +--R * +--R 6 +--R x +--R + +--R 7 8 19 6 9 18 5 2 10 17 +--R 15459444a d e - 108216108a b d e + 324648324a b d e +--R + +--R 4 3 11 16 3 4 12 15 2 5 13 14 +--R - 541080540a b d e + 541080540a b d e - 324648324a b d e +--R + +--R 6 14 13 7 15 12 +--R 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4 16 11 2 5 17 10 +--R - 5465460a b d e + 5465460a b d e - 3279276a b d e +--R + +--R 6 18 9 7 19 8 +--R 1093092a b d e - 156156b d e +--R * +--R x +--R + +--R 7 13 14 6 14 13 5 2 15 12 4 3 16 11 +--R 12012a d e - 84084a b d e + 252252a b d e - 420420a b d e +--R + +--R 3 4 17 10 2 5 18 9 6 19 8 7 20 7 +--R 420420a b d e - 252252a b d e + 84084a b d e - 12012b d e +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R e x + 14d e x + 91d e x + 364d e x + 1001d e x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002d e x + 3003d e x + 3432d e x + 3003d e x + 2002d e x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001d e x + 364d e x + 91d e x + 14d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 622 + +)clear all + +--S 623 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^15 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 15 15 14 14 2 13 13 3 12 12 4 11 11 +--R e x + 15d e x + 105d e x + 455d e x + 1365d e x +--R + +--R 5 10 10 6 9 9 7 8 8 8 7 7 9 6 6 +--R 3003d e x + 5005d e x + 6435d e x + 6435d e x + 5005d e x +--R + +--R 10 5 5 11 4 4 12 3 3 13 2 2 14 15 +--R 3003d e x + 1365d e x + 455d e x + 105d e x + 15d e x + d +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1353 +r0:=-5/364*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^12)-_ + 5/1001*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^11)-1/14*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^14)-3/91*b*(a^2+2*a*b*x+_ + 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| 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 21 15 21 20 14 +--R 24024b e x + (24024a e + 336336b d e )x +--R + +--R 20 2 19 13 +--R (336336a d e + 2186184b d e )x +--R + +--R 2 19 3 18 12 +--R (2186184a d e + 8744736b d e )x +--R + +--R 3 18 4 17 11 +--R (8744736a d e + 24048024b d e )x +--R + +--R 4 17 5 16 10 +--R (24048024a d e + 48096048b d e )x +--R + +--R 5 16 6 15 9 +--R (48096048a d e + 72144072b d e )x +--R + +--R 6 15 7 14 8 +--R (72144072a d e + 82450368b d e )x +--R + +--R 7 14 8 13 7 +--R (82450368a d e + 72144072b d e )x +--R + +--R 8 13 9 12 6 +--R (72144072a d e + 48096048b d e )x +--R + +--R 9 12 10 11 5 +--R (48096048a d e + 24048024b d e )x +--R + +--R 10 11 11 10 4 +--R (24048024a d e + 8744736b d e )x +--R + +--R 11 10 12 9 3 12 9 13 8 2 +--R (8744736a d e + 2186184b d e )x + (2186184a d e + 336336b d e )x +--R + +--R 13 8 14 7 14 7 +--R (336336a d e + 24024b d e )x + 24024a d e +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 3003b e x + (- 16016a b e - 2002b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 36036a b e - 8008a b d e - 1001b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 43680a b e - 13104a b d e - 2912a b d e - 364b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 30030a b e - 10920a b d e - 3276a b d e - 728a b d e - 91b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 11088a b e - 4620a b d e - 1680a b d e - 504a b d e +--R + +--R 5 4 2 6 5 +--R - 112a b d e - 14b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 1716a e - 792a b d e - 330a b d e - 120a b d e - 36a b d e +--R + +--R 5 5 6 6 +--R - 8a b d e - b d +--R / +--R 21 14 20 13 2 19 12 3 18 11 +--R 24024e x + 336336d e x + 2186184d e x + 8744736d e x +--R + +--R 4 17 10 5 16 9 6 15 8 7 14 7 +--R 24048024d e x + 48096048d e x + 72144072d e x + 82450368d e x +--R + +--R 8 13 6 9 12 5 10 11 4 11 10 3 +--R 72144072d e x + 48096048d e x + 24048024d e x + 8744736d e x +--R + +--R 12 9 2 13 8 14 7 +--R 2186184d e x + 336336d e x + 24024d e +--R Type: Union(Expression(Integer),...) +--E 625 + +--S 626 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R 3003b e x + (16016a b e + 2002b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (36036a b e + 8008a b d e + 1001b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (43680a b e + 13104a b d e + 2912a b d e + 364b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 30030a b e + 10920a b d e + 3276a b d e + 728a b d e +--R + +--R 6 4 2 +--R 91b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 11088a b e + 4620a b d e + 1680a b d e + 504a b d e +--R + +--R 5 4 2 6 5 +--R 112a b d e + 14b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 1716a e + 792a b d e + 330a b d e + 120a b d e + 36a b d e +--R + +--R 5 5 6 6 +--R 8a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R - 3003b e x + (- 19019a b e - 2002b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 52052a b e - 10010a b d e - 1001b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 79716a b e - 21112a b d e - 3913a b d e - 364b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 73710a b e - 24024a b d e - 6188a b d e - 1092a b d e +--R + +--R 7 4 2 +--R - 91b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 41118a b e - 15540a b d e - 4956a b d e - 1232a b d e +--R + +--R 6 4 2 7 5 +--R - 203a b d e - 14b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 12804a b e - 5412a b d e - 2010a b d e - 624a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 148a b d e - 22a b d e - b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 1716a e - 792a b d e - 330a b d e - 120a b d e - 36a b d e +--R + +--R 2 5 5 6 6 +--R - 8a b d e - a b d +--R / +--R 21 15 21 20 14 +--R 24024b e x + (24024a e + 336336b d e )x +--R + +--R 20 2 19 13 +--R (336336a d e + 2186184b d e )x +--R + +--R 2 19 3 18 12 +--R (2186184a d e + 8744736b d e )x +--R + +--R 3 18 4 17 11 +--R (8744736a d e + 24048024b d e )x +--R + +--R 4 17 5 16 10 +--R (24048024a d e + 48096048b d e )x +--R + +--R 5 16 6 15 9 +--R (48096048a d e + 72144072b d e )x +--R + +--R 6 15 7 14 8 +--R (72144072a d e + 82450368b d e )x +--R + +--R 7 14 8 13 7 +--R (82450368a d e + 72144072b d e )x +--R + +--R 8 13 9 12 6 +--R (72144072a d e + 48096048b d e )x +--R + +--R 9 12 10 11 5 +--R (48096048a d e + 24048024b d e )x +--R + +--R 10 11 11 10 4 +--R (24048024a d e + 8744736b d e )x +--R + +--R 11 10 12 9 3 12 9 13 8 2 +--R (8744736a d e + 2186184b d e )x + (2186184a d e + 336336b d e )x +--R + +--R 13 8 14 7 14 7 +--R (336336a d e + 24024b d e )x + 24024a d e +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 15 15 14 14 2 13 13 3 12 12 4 11 11 +--R e x + 15d e x + 105d e x + 455d e x + 1365d e x +--R + +--R 5 10 10 6 9 9 7 8 8 8 7 7 9 6 6 +--R 3003d e x + 5005d e x + 6435d e x + 6435d e x + 5005d e x +--R + +--R 10 5 5 11 4 4 12 3 3 13 2 2 14 15 +--R 3003d e x + 1365d e x + 455d e x + 105d e x + 15d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^16 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 16 16 15 15 2 14 14 3 13 13 4 12 12 +--R e x + 16d e x + 120d e x + 560d e x + 1820d e x +--R + +--R 5 11 11 6 10 10 7 9 9 8 8 8 9 7 7 +--R 4368d e x + 8008d e x + 11440d e x + 12870d e x + 11440d e x +--R + +--R 10 6 6 11 5 5 12 4 4 13 3 3 14 2 2 +--R 8008d e x + 4368d e x + 1820d e x + 560d e x + 120d e x +--R + +--R 15 16 +--R 16d e x + d +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1353 +r0:=-1/91*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^13)-_ + 1/273*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^12)-1/15*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^15)-1/35*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^14)-1/1001*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^11)-2/9009*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^6*(d+e*x)^10)-1/45045*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x)^10) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 5005b e x + (- 27027a b e - 3003b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 61425a b e - 12285a b d e - 1365b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 75075a b e - 20475a b d e - 4095a b d e - 455b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 51975a b e - 17325a b d e - 4725a b d e - 945a b d e +--R + +--R 6 4 2 +--R - 105b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 19305a b e - 7425a b d e - 2475a b d e - 675a b d e +--R + +--R 5 4 2 6 5 +--R - 135a b d e - 15b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 3003a e - 1287a b d e - 495a b d e - 165a b d e - 45a b d e +--R + +--R 5 5 6 6 +--R - 9a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 22 16 22 21 15 +--R 45045b e x + (45045a e + 675675b d e )x +--R + +--R 21 2 20 14 +--R (675675a d e + 4729725b d e )x +--R + +--R 2 20 3 19 13 +--R (4729725a d e + 20495475b d e )x +--R + +--R 3 19 4 18 12 +--R (20495475a d e + 61486425b d e )x +--R + +--R 4 18 5 17 11 +--R (61486425a d e + 135270135b d e )x +--R + +--R 5 17 6 16 10 +--R (135270135a d e + 225450225b d e )x +--R + +--R 6 16 7 15 9 +--R (225450225a d e + 289864575b d e )x +--R + +--R 7 15 8 14 8 +--R (289864575a d e + 289864575b d e )x +--R + +--R 8 14 9 13 7 +--R (289864575a d e + 225450225b d e )x +--R + +--R 9 13 10 12 6 +--R (225450225a d e + 135270135b d e )x +--R + +--R 10 12 11 11 5 +--R (135270135a d e + 61486425b d e )x +--R + +--R 11 11 12 10 4 +--R (61486425a d e + 20495475b d e )x +--R + +--R 12 10 13 9 3 +--R (20495475a d e + 4729725b d e )x +--R + +--R 13 9 14 8 2 14 8 15 7 +--R (4729725a d e + 675675b d e )x + (675675a d e + 45045b d e )x +--R + +--R 15 7 +--R 45045a d e +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 5005b e x + (- 27027a b e - 3003b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 61425a b e - 12285a b d e - 1365b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 75075a b e - 20475a b d e - 4095a b d e - 455b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 51975a b e - 17325a b d e - 4725a b d e - 945a b d e +--R + +--R 6 4 2 +--R - 105b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 19305a b e - 7425a b d e - 2475a b d e - 675a b d e +--R + +--R 5 4 2 6 5 +--R - 135a b d e - 15b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 3003a e - 1287a b d e - 495a b d e - 165a b d e - 45a b d e +--R + +--R 5 5 6 6 +--R - 9a b d e - b d +--R / +--R 22 15 21 14 2 20 13 3 19 12 +--R 45045e x + 675675d e x + 4729725d e x + 20495475d e x +--R + +--R 4 18 11 5 17 10 6 16 9 +--R 61486425d e x + 135270135d e x + 225450225d e x +--R + +--R 7 15 8 8 14 7 9 13 6 +--R 289864575d e x + 289864575d e x + 225450225d e x +--R + +--R 10 12 5 11 11 4 12 10 3 13 9 2 +--R 135270135d e x + 61486425d e x + 20495475d e x + 4729725d e x +--R + +--R 14 8 15 7 +--R 675675d e x + 45045d e +--R Type: Union(Expression(Integer),...) +--E 630 + +--S 631 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R 5005b e x + (27027a b e + 3003b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (61425a b e + 12285a b d e + 1365b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (75075a b e + 20475a b d e + 4095a b d e + 455b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 51975a b e + 17325a b d e + 4725a b d e + 945a b d e +--R + +--R 6 4 2 +--R 105b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 19305a b e + 7425a b d e + 2475a b d e + 675a b d e +--R + +--R 5 4 2 6 5 +--R 135a b d e + 15b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 3003a e + 1287a b d e + 495a b d e + 165a b d e + 45a b d e +--R + +--R 5 5 6 6 +--R 9a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R - 5005b e x + (- 32032a b e - 3003b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 88452a b e - 15288a b d e - 1365b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 136500a b e - 32760a b d e - 5460a b d e - 455b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 127050a b e - 37800a b d e - 8820a b d e - 1400a b d e +--R + +--R 7 4 2 +--R - 105b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 71280a b e - 24750a b d e - 7200a b d e - 1620a b d e +--R + +--R 6 4 2 7 5 +--R - 240a b d e - 15b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 22308a b e - 8712a b d e - 2970a b d e - 840a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 180a b d e - 24a b d e - b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 3003a e - 1287a b d e - 495a b d e - 165a b d e - 45a b d e +--R + +--R 2 5 5 6 6 +--R - 9a b d e - a b d +--R / +--R 22 16 22 21 15 +--R 45045b e x + (45045a e + 675675b d e )x +--R + +--R 21 2 20 14 +--R (675675a d e + 4729725b d e )x +--R + +--R 2 20 3 19 13 +--R (4729725a d e + 20495475b d e )x +--R + +--R 3 19 4 18 12 +--R (20495475a d e + 61486425b d e )x +--R + +--R 4 18 5 17 11 +--R (61486425a d e + 135270135b d e )x +--R + +--R 5 17 6 16 10 +--R (135270135a d e + 225450225b d e )x +--R + +--R 6 16 7 15 9 +--R (225450225a d e + 289864575b d e )x +--R + +--R 7 15 8 14 8 +--R (289864575a d e + 289864575b d e )x +--R + +--R 8 14 9 13 7 +--R (289864575a d e + 225450225b d e )x +--R + +--R 9 13 10 12 6 +--R (225450225a d e + 135270135b d e )x +--R + +--R 10 12 11 11 5 +--R (135270135a d e + 61486425b d e )x +--R + +--R 11 11 12 10 4 +--R (61486425a d e + 20495475b d e )x +--R + +--R 12 10 13 9 3 +--R (20495475a d e + 4729725b d e )x +--R + +--R 13 9 14 8 2 14 8 15 7 +--R (4729725a d e + 675675b d e )x + (675675a d e + 45045b d e )x +--R + +--R 15 7 +--R 45045a d e +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 16 16 15 15 2 14 14 3 13 13 4 12 12 +--R e x + 16d e x + 120d e x + 560d e x + 1820d e x +--R + +--R 5 11 11 6 10 10 7 9 9 8 8 8 9 7 7 +--R 4368d e x + 8008d e x + 11440d e x + 12870d e x + 11440d e x +--R + +--R 10 6 6 11 5 5 12 4 4 13 3 3 14 2 2 +--R 8008d e x + 4368d e x + 1820d e x + 560d e x + 120d e x +--R + +--R 15 16 +--R 16d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 632 + +)clear all + +--S 633 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^17 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 17 17 16 16 2 15 15 3 14 14 4 13 13 +--R e x + 17d e x + 136d e x + 680d e x + 2380d e x +--R + +--R 5 12 12 6 11 11 7 10 10 8 9 9 9 8 8 +--R 6188d e x + 12376d e x + 19448d e x + 24310d e x + 24310d e x +--R + +--R 10 7 7 11 6 6 12 5 5 13 4 4 14 3 3 +--R 19448d e x + 12376d e x + 6188d e x + 2380d e x + 680d e x +--R + +--R 15 2 2 16 17 +--R 136d e x + 17d e x + d +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1353 +r0:=-1/112*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^14)-_ + 1/364*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^13)-1/16*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^16)-1/40*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^15)-1/1456*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^12)-1/7280*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^6*(d+e*x)^11)-1/80080*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x)^11) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 8008b e x + (- 43680a b e - 4368b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 100100a b e - 18200a b d e - 1820b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 123200a b e - 30800a b d e - 5600a b d e - 560b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 85800a b e - 26400a b d e - 6600a b d e - 1200a b d e +--R + +--R 6 4 2 +--R - 120b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 32032a b e - 11440a b d e - 3520a b d e - 880a b d e +--R + +--R 5 4 2 6 5 +--R - 160a b d e - 16b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 5005a e - 2002a b d e - 715a b d e - 220a b d e - 55a b d e +--R + +--R 5 5 6 6 +--R - 10a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 23 17 23 22 16 +--R 80080b e x + (80080a e + 1281280b d e )x +--R + +--R 22 2 21 15 +--R (1281280a d e + 9609600b d e )x +--R + +--R 2 21 3 20 14 +--R (9609600a d e + 44844800b d e )x +--R + +--R 3 20 4 19 13 +--R (44844800a d e + 145745600b d e )x +--R + +--R 4 19 5 18 12 +--R (145745600a d e + 349789440b d e )x +--R + +--R 5 18 6 17 11 +--R (349789440a d e + 641280640b d e )x +--R + +--R 6 17 7 16 10 +--R (641280640a d e + 916115200b d e )x +--R + +--R 7 16 8 15 9 +--R (916115200a d e + 1030629600b d e )x +--R + +--R 8 15 9 14 8 +--R (1030629600a d e + 916115200b d e )x +--R + +--R 9 14 10 13 7 +--R (916115200a d e + 641280640b d e )x +--R + +--R 10 13 11 12 6 +--R (641280640a d e + 349789440b d e )x +--R + +--R 11 12 12 11 5 +--R (349789440a d e + 145745600b d e )x +--R + +--R 12 11 13 10 4 +--R (145745600a d e + 44844800b d e )x +--R + +--R 13 10 14 9 3 +--R (44844800a d e + 9609600b d e )x +--R + +--R 14 9 15 8 2 15 8 16 7 +--R (9609600a d e + 1281280b d e )x + (1281280a d e + 80080b d e )x +--R + +--R 16 7 +--R 80080a d e +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 8008b e x + (- 43680a b e - 4368b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 100100a b e - 18200a b d e - 1820b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 123200a b e - 30800a b d e - 5600a b d e - 560b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 85800a b e - 26400a b d e - 6600a b d e - 1200a b d e +--R + +--R 6 4 2 +--R - 120b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 32032a b e - 11440a b d e - 3520a b d e - 880a b d e +--R + +--R 5 4 2 6 5 +--R - 160a b d e - 16b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 5005a e - 2002a b d e - 715a b d e - 220a b d e - 55a b d e +--R + +--R 5 5 6 6 +--R - 10a b d e - b d +--R / +--R 23 16 22 15 2 21 14 3 20 13 +--R 80080e x + 1281280d e x + 9609600d e x + 44844800d e x +--R + +--R 4 19 12 5 18 11 6 17 10 +--R 145745600d e x + 349789440d e x + 641280640d e x +--R + +--R 7 16 9 8 15 8 9 14 7 +--R 916115200d e x + 1030629600d e x + 916115200d e x +--R + +--R 10 13 6 11 12 5 12 11 4 +--R 641280640d e x + 349789440d e x + 145745600d e x +--R + +--R 13 10 3 14 9 2 15 8 16 7 +--R 44844800d e x + 9609600d e x + 1281280d e x + 80080d e +--R Type: Union(Expression(Integer),...) +--E 635 + +--S 636 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R 8008b e x + (43680a b e + 4368b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (100100a b e + 18200a b d e + 1820b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (123200a b e + 30800a b d e + 5600a b d e + 560b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 85800a b e + 26400a b d e + 6600a b d e + 1200a b d e +--R + +--R 6 4 2 +--R 120b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 32032a b e + 11440a b d e + 3520a b d e + 880a b d e +--R + +--R 5 4 2 6 5 +--R 160a b d e + 16b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 5005a e + 2002a b d e + 715a b d e + 220a b d e + 55a b d e +--R + +--R 5 5 6 6 +--R 10a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R - 8008b e x + (- 51688a b e - 4368b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 143780a b e - 22568a b d e - 1820b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 223300a b e - 49000a b d e - 7420a b d e - 560b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 209000a b e - 57200a b d e - 12200a b d e - 1760a b d e +--R + +--R 7 4 2 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 117832a b e - 37840a b d e - 10120a b d e - 2080a b d e +--R + +--R 6 4 2 7 5 +--R - 280a b d e - 16b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 37037a b e - 13442a b d e - 4235a b d e - 1100a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 215a b d e - 26a b d e - b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 5005a e - 2002a b d e - 715a b d e - 220a b d e - 55a b d e +--R + +--R 2 5 5 6 6 +--R - 10a b d e - a b d +--R / +--R 23 17 23 22 16 +--R 80080b e x + (80080a e + 1281280b d e )x +--R + +--R 22 2 21 15 +--R (1281280a d e + 9609600b d e )x +--R + +--R 2 21 3 20 14 +--R (9609600a d e + 44844800b d e )x +--R + +--R 3 20 4 19 13 +--R (44844800a d e + 145745600b d e )x +--R + +--R 4 19 5 18 12 +--R (145745600a d e + 349789440b d e )x +--R + +--R 5 18 6 17 11 +--R (349789440a d e + 641280640b d e )x +--R + +--R 6 17 7 16 10 +--R (641280640a d e + 916115200b d e )x +--R + +--R 7 16 8 15 9 +--R (916115200a d e + 1030629600b d e )x +--R + +--R 8 15 9 14 8 +--R (1030629600a d e + 916115200b d e )x +--R + +--R 9 14 10 13 7 +--R (916115200a d e + 641280640b d e )x +--R + +--R 10 13 11 12 6 +--R (641280640a d e + 349789440b d e )x +--R + +--R 11 12 12 11 5 +--R (349789440a d e + 145745600b d e )x +--R + +--R 12 11 13 10 4 +--R (145745600a d e + 44844800b d e )x +--R + +--R 13 10 14 9 3 +--R (44844800a d e + 9609600b d e )x +--R + +--R 14 9 15 8 2 15 8 16 7 +--R (9609600a d e + 1281280b d e )x + (1281280a d e + 80080b d e )x +--R + +--R 16 7 +--R 80080a d e +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 17 17 16 16 2 15 15 3 14 14 4 13 13 +--R e x + 17d e x + 136d e x + 680d e x + 2380d e x +--R + +--R 5 12 12 6 11 11 7 10 10 8 9 9 +--R 6188d e x + 12376d e x + 19448d e x + 24310d e x +--R + +--R 9 8 8 10 7 7 11 6 6 12 5 5 13 4 4 +--R 24310d e x + 19448d e x + 12376d e x + 6188d e x + 2380d e x +--R + +--R 14 3 3 15 2 2 16 17 +--R 680d e x + 136d e x + 17d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 637 + +)clear all + +--S 638 of 1353 +t0:=(a+b*x)*(d+e*x)^m/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R m +--R (b x + a)(e x + d) +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1353 +r0:=(a+b*x)*(d+e*x)^(1+m)/(e*(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R m + 1 +--R (b x + a)(e x + d) +--R (2) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e m + e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1353 +a0:=integrate(t0,x) +--R +--R +--R m log(e x + d) +--R (e x + d)%e +--R (3) ------------------------- +--R e m + e +--R Type: Union(Expression(Integer),...) +--E 640 + +--S 641 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R | 2 2 2 m log(e x + d) m + 1 +--R (e x + d)\|b x + 2a b x + a %e + (- b x - a)(e x + d) +--R -------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (e m + e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 m log(e x + d) +--R (\|b x + 2a b x + a - b x - a)%e +--R (5) ------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 1353 +t0:=(a+b*x)*(d+e*x)^4/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1353 +r0:=1/5*(a+b*x)*(d+e*x)^5/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 6 5 4 5 4 2 3 4 +--R b e x + (a e + 5b d e )x + (5a d e + 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a d e + 10b d e )x + (10a d e + 5b d e)x + (5a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 4 5 3 4 2 2 3 3 2 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d x +--R (3) ------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 645 + +--S 646 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x)\|b x + 2a b x + a +--R + +--R 5 6 5 4 5 4 2 3 4 +--R - b e x + (- a e - 5b d e )x + (- 5a d e - 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (- 10a d e - 10b d e )x + (- 10a d e - 5b d e)x + (- 5a d e - b d )x +--R + +--R 5 +--R - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 647 + +)clear all + +--S 648 of 1353 +t0:=(a+b*x)*(d+e*x)^3/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1353 +r0:=1/4*(a+b*x)*(d+e*x)^4/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 4e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 3 4 2 3 2 2 3 +--R e x + 4d e x + 6d e x + 4d x +--R (3) ------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 650 + +--S 651 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x)\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 4e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 652 + +)clear all + +--S 653 of 1353 +t0:=(a+b*x)*(d+e*x)^2/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R b e x + (a e + 2b d e)x + (2a d e + b d )x + a d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1353 +r0:=1/3*(a+b*x)*(d+e*x)^3/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 +--R e x + 3d e x + 3d x +--R (3) --------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 655 + +--S 656 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 3 3 2 2 2 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x)\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1353 +t0:=(a+b*x)*(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R b e x + (a e + b d)x + a d +--R (1) --------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1353 +r0:=d*x*(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2)+1/2*e*x^2*(a+b*x)/_ + sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 2 +--R b e x + (a e + 2b d)x + 2a d x +--R (2) -------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 2\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R e x + 2d x +--R (3) ----------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 660 + +--S 661 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 | 2 2 2 3 2 +--R (e x + 2d x)\|b x + 2a b x + a - b e x + (- a e - 2b d)x - 2a d x +--R ----------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 2\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 662 + +)clear all + +--S 663 of 1353 +t0:=(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R b x + a +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1353 +r0:=sqrt(a^2+2*a*b*x+b^2*x^2)/b +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (2) --------------------- +--R b +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) x +--R Type: Union(Expression(Integer),...) +--E 665 + +--S 666 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x +--R (4) ----------------------------- +--R b +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 667 + +)clear all + +--S 668 of 1353 +t0:=(a+b*x)/((d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1353 +r0:=(a+b*x)*log(d+e*x)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b x + a)log(e x + d) +--R (2) ---------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1353 +a0:=integrate(t0,x) +--R +--R +--R log(e x + d) +--R (3) ------------ +--R e +--R Type: Union(Expression(Integer),...) +--E 670 + +--S 671 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R log(e x + d)\|b x + 2a b x + a + (- b x - a)log(e x + d) +--R (4) ----------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 1353 +t0:=(a+b*x)/((d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1353 +r0:=(-a-b*x)/(e*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) -------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (e x + d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------- +--R 2 +--R e x + d e +--R Type: Union(Expression(Integer),...) +--E 675 + +--S 676 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) --------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (e x + d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 677 + +)clear all + +--S 678 of 1353 +t0:=(a+b*x)/((d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1353 +r0:=1/2*(-a-b*x)/(e*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) -------------------------------------------- +--R +------------------+ +--R 3 2 2 2 | 2 2 2 +--R (2e x + 4d e x + 2d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------------------- +--R 3 2 2 2 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 680 + +--S 681 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) -------------------------------------------- +--R +------------------+ +--R 3 2 2 2 | 2 2 2 +--R (2e x + 4d e x + 2d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 682 + +)clear all + +--S 683 of 1353 +t0:=(a+b*x)/((d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1353 +r0:=1/3*(-a-b*x)/(e*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) ------------------------------------------------------ +--R +------------------+ +--R 4 3 3 2 2 2 3 | 2 2 2 +--R (3e x + 9d e x + 9d e x + 3d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------------------------- +--R 4 3 3 2 2 2 3 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 685 + +--S 686 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) ------------------------------------------------------ +--R +------------------+ +--R 4 3 3 2 2 2 3 | 2 2 2 +--R (3e x + 9d e x + 9d e x + 3d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 1353 +t0:=(a+b*x)/((d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R b x + a +--R ------------------------------------------------------------------------- +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1353 +r0:=1/4*(-a-b*x)/(e*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R 5 4 4 3 2 3 2 3 2 4 | 2 2 2 +--R (4e x + 16d e x + 24d e x + 16d e x + 4d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - -------------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R 4e x + 16d e x + 24d e x + 16d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 690 + +--S 691 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) ------------------------------------------------------------------- +--R +------------------+ +--R 5 4 4 3 2 3 2 3 2 4 | 2 2 2 +--R (4e x + 16d e x + 24d e x + 16d e x + 4d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R ------------------------------------------------------------------------- +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 692 + +)clear all + +--S 693 of 1353 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1353 +r0:=2*e*(b*d-a*e)*(a+b*x)*(d+e*x)^2/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 4/3*e*(a+b*x)*(d+e*x)^3/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^4/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+4*e*(b*d-a*e)^3*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^2*(b*d-a*e)^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 12a b e + 36a b d e - 36a b d e + 12b d e)x - 12a e +--R + +--R 3 3 2 2 2 2 3 3 +--R 36a b d e - 36a b d e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (- 2a b e + 6b d e )x + (6a b e - 18a b d e + 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (24a b e - 60a b d e + 42a b d e - 2b d e)x + 12a e - 24a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 6a b d e + 10a b d e - 3b d +--R / +--R +------------------+ +--R 5 | 2 2 2 +--R 3b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 12a b e + 36a b d e - 36a b d e + 12b d e)x - 12a e +--R + +--R 3 3 2 2 2 2 3 3 +--R 36a b d e - 36a b d e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (- 2a b e + 6b d e )x + (6a b e - 18a b d e + 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 2 2 2 2 +--R (9a b e - 24a b d e + 18a b d e )x - 3a e + 12a b d e - 18a b d e +--R + +--R 3 3 4 4 +--R 12a b d e - 3b d +--R / +--R 6 5 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 695 + +--S 696 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 12a b e + 36a b d e - 36a b d e + 12b d e)x - 12a e +--R + +--R 3 3 2 2 2 2 3 3 +--R 36a b d e - 36a b d e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 +--R b e x + (- 2a b e + 6b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (6a b e - 18a b d e + 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (9a b e - 24a b d e + 18a b d e )x - 3a e + 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 18a b d e + 12a b d e - 3b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (12a b e - 36a b d e + 36a b d e - 12b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (24a b e - 72a b d e + 72a b d e - 24a b d e)x + 12a e +--R + +--R 4 3 3 2 2 2 2 3 3 +--R - 36a b d e + 36a b d e - 12a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R - b e x + (a b e - 6b d e )x + (- 4a b e + 12a b d e - 18b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 30a b e + 78a b d e - 60a b d e + 2b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 36a b e + 84a b d e - 48a b d e - 8a b d e + 3b d )x - 12a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R 24a b d e - 6a b d e - 10a b d e + 3a b d +--R / +--R +------------------+ +--R 6 5 | 2 2 2 +--R (3b x + 3a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 697 + +)clear all + +--S 698 of 1353 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1353 +r0:=3/2*e*(a+b*x)*(d+e*x)^2/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-(d+e*x)^3/_ + (b*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/_ + (b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b e - 12a b d e + 6b d e)x + 6a e - 12a b d e + 6a b d e) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R b e x + (- 3a b e + 6b d e )x + (- 12a b e + 18a b d e - 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 6a e + 6a b d e + 3a b d e - 2b d +--R / +--R +------------------+ +--R 4 | 2 2 2 +--R 2b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b e - 12a b d e + 6b d e)x + 6a e - 12a b d e + 6a b d e) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 3 +--R b e x + (- 3a b e + 6b d e )x + (- 4a b e + 6a b d e )x + 2a e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e + 6a b d e - 2b d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 700 + +--S 701 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b e - 12a b d e + 6b d e)x + 6a e - 12a b d e + 6a b d e) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 3 +--R b e x + (- 3a b e + 6b d e )x + (- 4a b e + 6a b d e )x + 2a e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e + 6a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 6a b e + 12a b d e - 6b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (- 12a b e + 24a b d e - 12a b d e)x - 6a e + 12a b d e - 6a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R - b e x + (2a b e - 6b d e )x + (15a b e - 24a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 4 3 4 3 3 2 2 2 2 3 3 +--R (18a b e - 24a b d e + 2b d )x + 6a e - 6a b d e - 3a b d e + 2a b d +--R / +--R +------------------+ +--R 5 4 | 2 2 2 +--R (2b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 1353 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1353 +r0:=-(d+e*x)^2/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)*(a+b*x)*_ + log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((- 2a b e + 2b d e)x - 2a e + 2a b d e)log(b x + a) + b e x +--R + +--R 2 2 2 2 2 2 +--R (4a b e - 2b d e)x + 2a e - b d +--R / +--R +------------------+ +--R 3 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 +--R ((- 2a b e + 2b d e)x - 2a e + 2a b d e)log(b x + a) + b e x + a b e x +--R + +--R 2 2 2 2 +--R - a e + 2a b d e - b d +--R / +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 705 + +--S 706 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 +--R ((- 2a b e + 2b d e)x - 2a e + 2a b d e)log(b x + a) + b e x +--R + +--R 2 2 2 2 2 +--R a b e x - a e + 2a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 3 2 2 +--R ((2a b e - 2b d e)x + (4a b e - 4a b d e)x + 2a e - 2a b d e) +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - b e x + (- 5a b e + 2b d e)x + (- 6a b e + 2a b d e + b d )x +--R + +--R 3 2 2 2 +--R - 2a e + a b d +--R / +--R +------------------+ +--R 4 3 | 2 2 2 +--R (b x + a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 707 + +)clear all + +--S 708 of 1353 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1353 +r0:=(-d-e*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(a+b*x)*log(a+b*x)/_ + (b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b e x + a e)log(b x + a) - b e x - b d +--R (2) --------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (b e x + a e)log(b x + a) + a e - b d +--R (3) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 710 + +--S 711 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R | 2 2 2 +--R ((b e x + a e)log(b x + a) + a e - b d)\|b x + 2a b x + a +--R + +--R 2 2 2 2 2 2 +--R (- b e x - 2a b e x - a e)log(b x + a) + b e x + (a b e + b d)x + a b d +--R / +--R +------------------+ +--R 3 2 | 2 2 2 +--R (b x + a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 712 + +)clear all + +--S 713 of 1353 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1353 +r0:=(-1)/(b*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (2) - ---------------------- +--R +------------------+ +--R | 2 2 2 +--R b\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------- +--R 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 715 + +--S 716 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) --------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (b x + a b)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 1353 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1353 +r0:=(-1)/((b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(a+b*x)*log(a+b*x)/_ + ((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(a+b*x)*log(d+e*x)/_ + ((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b e x + a e)log(e x + d) + (- b e x - a e)log(b x + a) + a e - b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R (a e - 2a b d e + b d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (b e x + a e)log(e x + d) + (- b e x - a e)log(b x + a) + a e - b d +--R (3) ------------------------------------------------------------------- +--R 2 2 2 3 2 3 2 2 2 2 +--R (a b e - 2a b d e + b d )x + a e - 2a b d e + a b d +--R Type: Union(Expression(Integer),...) +--E 720 + +--S 721 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R ((b e x + a e)log(e x + d) + (- b e x - a e)log(b x + a) + a e - b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 +--R (- b e x - 2a b e x - a e)log(e x + d) +--R + +--R 2 2 2 2 2 +--R (b e x + 2a b e x + a e)log(b x + a) + (- a b e + b d)x - a e + a b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 722 + +)clear all + +--S 723 of 1353 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1353 +r0:=-2*b/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/((b*d-a*e)*(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-2*b*e*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+2*b*e*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (- 2b e x + (- 2a b e - 2b d e)x - 2a b d e)log(e x + d) +--R + +--R 2 2 2 2 2 +--R (2b e x + (2a b e + 2b d e)x + 2a b d e)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b e + 2b d e)x - a e + b d +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 2 3 +--R (a e - 3a b d e + 3a b d e - b d e)x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (- 2b e x + (- 2a b e - 2b d e)x - 2a b d e)log(e x + d) +--R + +--R 2 2 2 2 2 +--R (2b e x + (2a b e + 2b d e)x + 2a b d e)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b e + 2b d e)x - a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Union(Expression(Integer),...) +--E 725 + +--S 726 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 +--R (- 2b e x + (- 2a b e - 2b d e)x - 2a b d e)log(e x + d) +--R + +--R 2 2 2 2 2 +--R (2b e x + (2a b e + 2b d e)x + 2a b d e)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b e + 2b d e)x - a e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 2 +--R (2b e x + (4a b e + 2b d e)x + (2a b e + 4a b d e)x + 2a b d e) +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 +--R - 2b e x + (- 4a b e - 2b d e)x + (- 2a b e - 4a b d e)x +--R + +--R 2 +--R - 2a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 2 2 2 3 2 3 2 2 2 +--R (2a b e - 2b d e)x + (3a b e - 2a b d e - b d )x + a e - a b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 727 + +)clear all + +--S 728 of 1353 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1353 +r0:=-3*b^2/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2/((b*d-a*e)*(d+e*x)^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+3/2*b/((b*d-a*e)^2*(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-3*b^2*e*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*b^2*e*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 2 2 2 +--R (6b e x + (6a b e + 12b d e )x + (12a b d e + 6b d e)x + 6a b d e) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b e x + (- 6a b e - 12b d e )x + (- 12a b d e - 6b d e)x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (3a b e + 6a b d e - 9b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 3a b d e - 2b d +--R / +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (2a e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4 2 4 +--R (4a d e - 16a b d e + 24a b d e - 16a b d e + 4b d e)x + 2a d e +--R + +--R 3 3 3 2 2 4 2 3 5 4 6 +--R - 8a b d e + 12a b d e - 8a b d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 2 3 2 2 2 +--R (6b e x + (6a b e + 12b d e )x + (12a b d e + 6b d e)x + 6a b d e) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b e x + (- 6a b e - 12b d e )x + (- 12a b d e - 6b d e)x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (3a b e + 6a b d e - 9b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 3a b d e - 2b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 730 + +--S 731 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R 6b e x + (6a b e + 12b d e )x + (12a b d e + 6b d e)x +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b e x + (- 6a b e - 12b d e )x + (- 12a b d e - 6b d e)x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (3a b e + 6a b d e - 9b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 3a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 6b e x + (- 12a b e - 12b d e )x +--R + +--R 2 2 3 3 2 4 2 2 2 2 2 3 2 +--R (- 6a b e - 24a b d e - 6b d e)x + (- 12a b d e - 12a b d e)x +--R + +--R 2 2 2 +--R - 6a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R 6b e x + (12a b e + 12b d e )x + (6a b e + 24a b d e + 6b d e)x +--R + +--R 2 2 2 3 2 2 2 2 +--R (12a b d e + 12a b d e)x + 6a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 4 2 3 2 2 3 4 2 2 +--R (- 6a b e + 6b d e )x + (- 9a b e + 9b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (- 2a b e - 12a b d e + 12a b d e + 2b d )x + a e - 6a b d e +--R + +--R 2 2 2 3 3 +--R 3a b d e + 2a b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 732 + +)clear all + +--S 733 of 1353 +t0:=(a+b*x)*(d+e*x)^5/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1353 +r0:=-5/6*e*(a+b*x)*(d+e*x)^4/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^5/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5*e^3*(a+b*x)*_ + (d+e*x)^2/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-10/3*e^2*(d+e*x)^3/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10*e^3*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10*e^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6 +--R +--R +--R (2) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (180a b e - 360a b d e + 180a b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 5 5 4 4 +--R (180a b e - 360a b d e + 180a b d e )x + 60a e - 120a b d e +--R + +--R 3 2 2 3 +--R 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 5 5 4 5 5 4 4 +--R 3b e x + (- 15a b e + 30b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 170a b e + 280a b d e - 80b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 330a b e + 480a b d e - 60a b d e - 60b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 240a b e + 300a b d e + 30a b d e - 60a b d e - 15b d e)x - 60a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e + 30a b d e - 20a b d e - 5a b d e - 2b d +--R / +--R +------------------+ +--R 8 2 7 2 6 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (180a b e - 360a b d e + 180a b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 5 5 4 4 +--R (180a b e - 360a b d e + 180a b d e )x + 60a e - 120a b d e +--R + +--R 3 2 2 3 +--R 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 3 +--R 3b e x + (- 15a b e + 30b d e )x + (- 63a b e + 90a b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 9a b e - 90a b d e + 180a b d e - 60b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (81a b e - 270a b d e + 270a b d e - 60a b d e - 15b d e)x + 47a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 130a b d e + 110a b d e - 20a b d e - 5a b d e - 2b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 735 + +--S 736 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (180a b e - 360a b d e + 180a b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 5 5 4 4 +--R (180a b e - 360a b d e + 180a b d e )x + 60a e - 120a b d e +--R + +--R 3 2 2 3 +--R 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 3 +--R 3b e x + (- 15a b e + 30b d e )x + (- 63a b e + 90a b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 9a b e - 90a b d e + 180a b d e - 60b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (81a b e - 270a b d e + 270a b d e - 60a b d e - 15b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 47a e - 130a b d e + 110a b d e - 20a b d e - 5a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (- 60a b e + 120a b d e - 60b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 3 +--R (- 240a b e + 480a b d e - 240a b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 2 +--R (- 360a b e + 720a b d e - 360a b d e )x +--R + +--R 5 5 4 2 4 3 3 2 3 6 5 5 4 +--R (- 240a b e + 480a b d e - 240a b d e )x - 60a e + 120a b d e +--R + +--R 4 2 2 3 +--R - 60a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 5 5 6 4 5 +--R - 3b e x + (12a b e - 30b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (185a b e - 310a b d e + 80b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 3 +--R (500a b e - 760a b d e + 140a b d e + 60b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 2 +--R (570a b e - 780a b d e + 30a b d e + 120a b d e + 15b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 +--R (300a b e - 360a b d e - 60a b d e + 80a b d e + 20a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R 60a e - 60a b d e - 30a b d e + 20a b d e + 5a b d e + 2a b d +--R / +--R +------------------+ +--R 9 3 8 2 2 7 3 6 | 2 2 2 +--R (6b x + 18a b x + 18a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R + +--R 5 6 5 4 5 4 2 3 4 +--R - b e x + (- a e - 5b d e )x + (- 5a d e - 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (- 10a d e - 10b d e )x + (- 10a d e - 5b d e)x + (- 5a d e - b d )x +--R + +--R 5 +--R - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 737 + +)clear all + +--S 738 of 1353 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1353 +r0:=-2/3*e*(a+b*x)*(d+e*x)^3/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^4/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-2*e^2*(d+e*x)^2/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^3*(b*d-a*e)*(a+b*x)*log(a+b*x)/(b^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 4 4 3 3 2 2 4 3 3 2 +--R (- 12a b e + 12b d e )x + (- 36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 4 4 3 3 +--R (- 36a b e + 36a b d e )x - 12a e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (34a b e - 22b d e )x + (66a b e - 30a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 2 2 2 2 +--R (48a b e - 12a b d e - 18a b d e - 6b d e)x + 12a e - 6a b d e +--R + +--R 3 3 4 4 +--R - 2a b d e - b d +--R / +--R +------------------+ +--R 7 2 6 2 5 | 2 2 2 +--R (3b x + 6a b x + 3a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 3 2 2 4 3 3 2 +--R (- 12a b e + 12b d e )x + (- 36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 4 4 3 3 +--R (- 36a b e + 36a b d e )x - 12a e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + 9a b e x + (- 9a b e + 36a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 27a b e + 54a b d e - 18a b d e - 6b d e)x - 13a e + 22a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 2a b d e - b d +--R / +--R 8 3 7 2 2 6 3 5 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 740 + +--S 741 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 3 2 2 4 3 3 2 +--R (- 12a b e + 12b d e )x + (- 36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 4 4 3 3 +--R (- 36a b e + 36a b d e )x - 12a e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + 9a b e x + (- 9a b e + 36a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 27a b e + 54a b d e - 18a b d e - 6b d e)x - 13a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 22a b d e - 6a b d e - 2a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12a b e - 12b d e )x + (48a b e - 48a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 5 4 +--R (72a b e - 72a b d e )x + (48a b e - 48a b d e )x + 12a e +--R + +--R 4 3 +--R - 12a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 4 4 5 3 4 +--R - 3b e x + (- 37a b e + 22b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 100a b e + 52a b d e + 18b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 114a b e + 42a b d e + 36a b d e + 6b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 60a b e + 12a b d e + 24a b d e + 8a b d e + b d )x - 12a e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R 6a b d e + 2a b d e + a b d +--R / +--R +------------------+ +--R 8 3 7 2 2 6 3 5 | 2 2 2 +--R (3b x + 9a b x + 9a b x + 3a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 742 + +)clear all + +--S 743 of 1353 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1353 +r0:=-1/2*e*(a+b*x)*(d+e*x)^2/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^3/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2*(d+e*x)/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(b x + a) - 11b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (- 15a b e - 18b d e )x + (- 6a b e - 18a b d e - 9b d e)x +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e - 3a b d e - 2b d +--R / +--R +------------------+ +--R 6 2 5 2 4 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (18a b e - 18b d e )x + (27a b e - 18a b d e - 9b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e - 3a b d e - 2b d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 745 + +--S 746 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (18a b e - 18b d e )x + (27a b e - 18a b d e - 9b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e - 3a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (- 6b e x - 24a b e x - 36a b e x - 24a b e x - 6a e )log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R 11b e x + (26a b e + 18b d e )x + (21a b e + 36a b d e + 9b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (6a b e + 24a b d e + 12a b d e + 2b d )x + 6a b d e + 3a b d e +--R + +--R 3 3 +--R 2a b d +--R / +--R +------------------+ +--R 7 3 6 2 2 5 3 4 | 2 2 2 +--R (6b x + 18a b x + 18a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 747 + +)clear all + +--S 748 of 1353 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1353 +r0:=-1/3*(d+e*x)^3/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R ----------------------------------------------------------------------------- +--R +------------------+ +--R 2 3 2 2 2 3 2 | 2 2 2 +--R ((3a b e - 3b d)x + (6a b e - 6a b d)x + 3a e - 3a b d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 3b e x + (- 3a b e - 3b d e)x - a e - a b d e - b d +--R (3) --------------------------------------------------------- +--R 6 3 5 2 2 4 3 3 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 750 + +--S 751 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 3 3 2 3 3 3 3 +--R ((- 3a b e + 3b d e )x + (- 3a b e + 3b d e)x - a e + b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 3 2 4 2 2 +--R - b e x + (- a b e - 3b d e )x + (- 3a b d e - 3b d e)x +--R + +--R 3 2 4 3 3 3 +--R (- 3a b d e - b d )x - a b d +--R / +--R 6 7 3 2 5 6 2 3 4 2 5 4 3 +--R (3a b e - 3b d)x + (9a b e - 9a b d)x + (9a b e - 9a b d)x + 3a b e +--R + +--R 3 4 +--R - 3a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 752 + +)clear all + +--S 753 of 1353 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1353 +r0:=-1/6*e*(a+b*x)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/3*(-d-e*x)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R - 3b e x - a e - 2b d +--R (2) ---------------------------------------------- +--R +------------------+ +--R 4 2 3 2 2 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1353 +a0:=integrate(t0,x) +--R +--R +--R - 3b e x - a e - 2b d +--R (3) ---------------------------------- +--R 5 3 4 2 2 3 3 2 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 755 + +--S 756 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R | 2 2 2 2 2 2 +--R (- 3b e x - a e - 2b d)\|b x + 2a b x + a + 3b e x + (4a b e + 2b d)x +--R + +--R 2 +--R a e + 2a b d +--R / +--R +------------------+ +--R 5 3 4 2 2 3 3 2 | 2 2 2 +--R (6b x + 18a b x + 18a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 757 + +)clear all + +--S 758 of 1353 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 1 +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1353 +r0:=(-1/3)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (2) - -------------------------------------------- +--R +------------------+ +--R 3 2 2 2 | 2 2 2 +--R (3b x + 6a b x + 3a b)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------------------------- +--R 4 3 3 2 2 2 3 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 760 + +--S 761 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) ------------------------------------------------------ +--R +------------------+ +--R 4 3 3 2 2 2 3 | 2 2 2 +--R (3b x + 9a b x + 9a b x + 3a b)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 762 + +)clear all + +--S 763 of 1353 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1353 +r0:=(-1/3)/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*e*(a+b*x)/_ + ((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(e x + d) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (- 6b e x - 18a b e x - 18a b e x - 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (15a b e - 18a b d e + 3b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 18a b d e + 9a b d e - 2b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 6 4 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12a b d )x + 6a e +--R + +--R 5 3 4 2 2 2 3 3 3 2 4 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(e x + d) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (- 6b e x - 18a b e x - 18a b e x - 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (15a b e - 18a b d e + 3b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 18a b d e + 9a b d e - 2b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 7 4 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x + 6a e +--R + +--R 6 3 5 2 2 2 4 3 3 3 4 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R Type: Union(Expression(Integer),...) +--E 765 + +--S 766 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(e x + d) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (- 6b e x - 18a b e x - 18a b e x - 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (15a b e - 18a b d e + 3b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 18a b d e + 9a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (- 6b e x - 24a b e x - 36a b e x - 24a b e x - 6a e )log(e x + d) +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (6b e x + 24a b e x + 36a b e x + 24a b e x + 6a e )log(b x + a) +--R + +--R 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R (- 6a b e + 6b d e )x + (- 21a b e + 24a b d e - 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (- 26a b e + 36a b d e - 12a b d e + 2b d )x - 11a e + 18a b d e +--R + +--R 2 2 2 3 3 +--R - 9a b d e + 2a b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 7 4 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x + 6a e +--R + +--R 6 3 5 2 2 2 4 3 3 3 4 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 767 + +)clear all + +--S 768 of 1353 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1353 +r0:=-4/3*b/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+2*b*e*(a+b*x)/_ + ((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/((b*d-a*e)*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-4*b*e^2/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-4*b*e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+4*b*e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R - 12b e x + (- 36a b e - 12b d e )x + (- 36a b e - 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (- 12a b e - 36a b d e )x - 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 12b e x + (36a b e + 12b d e )x + (36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (12a b e + 36a b d e )x + 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (- 12a b e + 12b d e )x + (- 30a b e + 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 22a b e + 6a b d e + 18a b d e - 2b d e)x - 3a e - 10a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 6a b d e + b d +--R / +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 3a b e - 15a b d e + 30a b d e - 30a b d e + 15a b d e +--R + +--R 7 5 +--R - 3b d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 6 5 7 6 2 +--R (6a b e - 27a b d e + 45a b d e - 30a b d e + 9a b d e - 3b d )x +--R + +--R 7 6 6 5 4 3 3 3 3 4 4 2 2 5 5 6 6 +--R (3a e - 9a b d e + 30a b d e - 45a b d e + 27a b d e - 6a b d )x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 2 5 6 +--R 3a d e - 15a b d e + 30a b d e - 30a b d e + 15a b d e - 3a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R - 12b e x + (- 36a b e - 12b d e )x + (- 36a b e - 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (- 12a b e - 36a b d e )x - 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 12b e x + (36a b e + 12b d e )x + (36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (12a b e + 36a b d e )x + 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (- 12a b e + 12b d e )x + (- 30a b e + 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 22a b e + 6a b d e + 18a b d e - 2b d e)x - 3a e - 10a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 6a b d e + b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 8 5 4 +--R (3a b e - 15a b d e + 30a b d e - 30a b d e + 15a b d e - 3b d e)x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 9a b e - 42a b d e + 75a b d e - 60a b d e + 15a b d e +--R + +--R 7 5 8 6 +--R 6a b d e - 3b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 7 6 2 +--R (9a b e - 36a b d e + 45a b d e - 45a b d e + 36a b d e - 9a b d )x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5 +--R 3a e - 6a b d e - 15a b d e + 60a b d e - 75a b d e + 42a b d e +--R + +--R 2 6 6 +--R - 9a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 3 5 6 +--R 3a d e - 15a b d e + 30a b d e - 30a b d e + 15a b d e - 3a b d +--R Type: Union(Expression(Integer),...) +--E 770 + +--S 771 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 12b e x + (- 36a b e - 12b d e )x +--R + +--R 2 2 4 3 3 2 3 4 2 2 3 +--R (- 36a b e - 36a b d e )x + (- 12a b e - 36a b d e )x +--R + +--R 3 3 +--R - 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 12b e x + (36a b e + 12b d e )x + (36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (12a b e + 36a b d e )x + 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (- 12a b e + 12b d e )x + (- 30a b e + 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 22a b e + 6a b d e + 18a b d e - 2b d e)x - 3a e - 10a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 6a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 3 +--R 12b e x + (48a b e + 12b d e )x + (72a b e + 48a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 4 3 +--R (48a b e + 72a b d e )x + (12a b e + 48a b d e )x + 12a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 3 +--R - 12b e x + (- 48a b e - 12b d e )x + (- 72a b e - 48a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 4 3 +--R (- 48a b e - 72a b d e )x + (- 12a b e - 48a b d e )x - 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R (12a b e - 12b d e )x + (42a b e - 36a b d e - 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (52a b e - 30a b d e - 24a b d e + 2b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (25a b e + 4a b d e - 36a b d e + 8a b d e - b d )x + 3a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R 10a b d e - 18a b d e + 6a b d e - a b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 3a b e - 15a b d e + 30a b d e - 30a b d e + 15a b d e +--R + +--R 8 5 +--R - 3b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 9a b e - 42a b d e + 75a b d e - 60a b d e + 15a b d e +--R + +--R 7 5 8 6 +--R 6a b d e - 3b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 9a b e - 36a b d e + 45a b d e - 45a b d e + 36a b d e +--R + +--R 7 6 +--R - 9a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 3a e - 6a b d e - 15a b d e + 60a b d e - 75a b d e +--R + +--R 3 5 5 2 6 6 +--R 42a b d e - 9a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 3 5 6 +--R 3a d e - 15a b d e + 30a b d e - 30a b d e + 15a b d e - 3a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 772 + +)clear all + +--S 773 of 1353 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1353 +r0:=-10/3*b^2/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5*b^2*e*(a+b*x)/_ + ((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2/((b*d-a*e)*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+5/2*b/((b*d-a*e)^2*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-10*b^2*e^2/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 10*b^2*e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 10*b^2*e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (180a b e + 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (180a b e + 360a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (60a b e + 360a b d e + 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (120a b d e + 180a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 180a b e - 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 180a b e - 360a b d e - 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (- 60a b e - 360a b d e - 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (- 120a b d e - 180a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (60a b e - 60b d e )x + (150a b e - 60a b d e - 90b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (110a b e + 120a b d e - 210a b d e - 20b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (15a b e + 160a b d e - 120a b d e - 60a b d e + 5b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 30a b d e + 20a b d e - 60a b d e + 15a b d e - 2b d +--R / +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 2 6 4 4 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 3 8 6 2 +--R - 36a b d e + 6b d e +--R * +--R 4 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R 12a b e - 60a b d e + 108a b d e - 60a b d e - 60a b d e +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 108a b d e - 60a b d e + 12b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R 6a e - 12a b d e - 48a b d e + 204a b d e - 300a b d e +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R 204a b d e - 48a b d e - 12a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R 12a d e - 60a b d e + 108a b d e - 60a b d e - 60a b d e +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 108a b d e - 60a b d e + 12a b d +--R * +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 3 5 7 2 6 8 +--R - 36a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (180a b e + 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (180a b e + 360a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (60a b e + 360a b d e + 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (120a b d e + 180a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 180a b e - 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 180a b e - 360a b d e - 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (- 60a b e - 360a b d e - 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (- 120a b d e - 180a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (60a b e - 60b d e )x + (150a b e - 60a b d e - 90b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (110a b e + 120a b d e - 210a b d e - 20b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (15a b e + 160a b d e - 120a b d e - 60a b d e + 5b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 30a b d e + 20a b d e - 60a b d e + 15a b d e - 2b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 2 7 4 4 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 8 5 3 9 6 2 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 3 6 4 4 +--R 18a b e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 2 7 5 3 8 6 2 9 7 +--R 72a b d e - 54a b d e + 12b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 4 5 4 4 +--R 18a b e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 6 5 3 2 7 6 2 9 8 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 4 5 5 3 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 3 6 6 2 2 7 7 8 8 +--R 60a b d e - 72a b d e + 18a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 5 4 5 3 +--R 12a d e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 4 5 6 2 3 6 7 2 7 8 +--R 198a b d e - 96a b d e + 18a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 4 5 7 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 3 6 8 +--R 6a b d +--R Type: Union(Expression(Integer),...) +--E 775 + +--S 776 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (180a b e + 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (180a b e + 360a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (60a b e + 360a b d e + 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (120a b d e + 180a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 180a b e - 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 180a b e - 360a b d e - 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (- 60a b e - 360a b d e - 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (- 120a b d e - 180a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (60a b e - 60b d e )x + (150a b e - 60a b d e - 90b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (110a b e + 120a b d e - 210a b d e - 20b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (15a b e + 160a b d e - 120a b d e - 60a b d e + 5b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 30a b d e + 20a b d e - 60a b d e + 15a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 6 5 5 6 4 5 +--R - 60b e x + (- 240a b e - 120b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (- 360a b e - 480a b d e - 60b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 3 +--R (- 240a b e - 720a b d e - 240a b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 2 +--R (- 60a b e - 480a b d e - 360a b d e )x +--R + +--R 4 2 4 3 3 2 3 4 2 2 3 +--R (- 120a b d e - 240a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 6 5 6 5 5 6 4 5 +--R 60b e x + (240a b e + 120b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (360a b e + 480a b d e + 60b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 3 +--R (240a b e + 720a b d e + 240a b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 2 +--R (60a b e + 480a b d e + 360a b d e )x +--R + +--R 4 2 4 3 3 2 3 4 2 2 3 +--R (120a b d e + 240a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 5 6 4 5 2 4 5 5 4 6 2 3 4 +--R (- 60a b e + 60b d e )x + (- 210a b e + 120a b d e + 90b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 3 +--R (- 260a b e - 60a b d e + 300a b d e + 20b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 2 +--R (- 125a b e - 280a b d e + 330a b d e + 80a b d e - 5b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R - 12a b e - 190a b d e + 100a b d e + 120a b d e - 20a b d e +--R + +--R 6 5 +--R 2b d +--R * +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R 3a e - 30a b d e - 20a b d e + 60a b d e - 15a b d e + 2a b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 2 7 4 4 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 8 5 3 9 6 2 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 3 6 4 4 +--R 18a b e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 2 7 5 3 8 6 2 9 7 +--R 72a b d e - 54a b d e + 12b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 4 5 4 4 +--R 18a b e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 6 5 3 2 7 6 2 9 8 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 4 5 5 3 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 3 6 6 2 2 7 7 8 8 +--R 60a b d e - 72a b d e + 18a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 5 4 5 3 +--R 12a d e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 4 5 6 2 3 6 7 2 7 8 +--R 198a b d e - 96a b d e + 18a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 4 5 7 3 6 8 +--R - 36a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 777 + +)clear all + +--S 778 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1353 +r0:=-2/9*(b*d-a*e)^3*(d+e*x)^(9/2)/e^4+6/11*b*(b*d-a*e)^2*(d+e*x)^(11/2)/e^4-_ + 6/13*b^2*(b*d-a*e)*(d+e*x)^(13/2)/e^4+2/15*b^3*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 3 7 7 2 7 3 6 6 +--R 858b e x + (2970a b e + 3036b d e )x +--R + +--R 2 7 2 6 3 2 5 5 +--R (3510a b e + 10800a b d e + 3708b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (1430a e + 13260a b d e + 13740a b d e + 1600b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (5720a d e + 17940a b d e + 6360a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (8580a d e + 9360a b d e + 90a b d e - 12b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 3 4 3 +--R (5720a d e + 390a b d e - 120a b d e + 16b d e)x + 1430a d e +--R + +--R 2 5 2 2 6 3 7 +--R - 780a b d e + 240a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 2 7 3 6 6 +--R 858b e x + (2970a b e + 3036b d e )x +--R + +--R 2 7 2 6 3 2 5 5 +--R (3510a b e + 10800a b d e + 3708b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (1430a e + 13260a b d e + 13740a b d e + 1600b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (5720a d e + 17940a b d e + 6360a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (8580a d e + 9360a b d e + 90a b d e - 12b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 3 4 3 +--R (5720a d e + 390a b d e - 120a b d e + 16b d e)x + 1430a d e +--R + +--R 2 5 2 2 6 3 7 +--R - 780a b d e + 240a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Union(Expression(Integer),...) +--E 780 + +--S 781 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 782 + +)clear all + +--S 783 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1353 +r0:=-2/7*(b*d-a*e)^3*(d+e*x)^(7/2)/e^4+2/3*b*(b*d-a*e)^2*(d+e*x)^(9/2)/e^4-_ + 6/11*b^2*(b*d-a*e)*(d+e*x)^(11/2)/e^4+2/13*b^3*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 462b e x + (1638a b e + 1134b d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (2002a b e + 4186a b d e + 742b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (858a e + 5434a b d e + 2938a b d e + 10b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (2574a d e + 4290a b d e + 78a b d e - 12b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (2574a d e + 286a b d e - 104a b d e + 16b d e)x + 858a d e +--R + +--R 2 4 2 2 5 3 6 +--R - 572a b d e + 208a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3003e +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 2 6 3 5 5 +--R 462b e x + (1638a b e + 1134b d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (2002a b e + 4186a b d e + 742b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (858a e + 5434a b d e + 2938a b d e + 10b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (2574a d e + 4290a b d e + 78a b d e - 12b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (2574a d e + 286a b d e - 104a b d e + 16b d e)x + 858a d e +--R + +--R 2 4 2 2 5 3 6 +--R - 572a b d e + 208a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3003e +--R Type: Union(Expression(Integer),...) +--E 785 + +--S 786 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 787 + +)clear all + +--S 788 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1353 +r0:=-2/5*(b*d-a*e)^3*(d+e*x)^(5/2)/e^4+6/7*b*(b*d-a*e)^2*(d+e*x)^(7/2)/e^4-_ + 2/3*b^2*(b*d-a*e)*(d+e*x)^(9/2)/e^4+2/11*b^3*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 210b e x + (770a b e + 280b d e )x +--R + +--R 2 5 2 4 3 2 3 3 +--R (990a b e + 1100a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (462a e + 1584a b d e + 66a b d e - 12b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (924a d e + 198a b d e - 88a b d e + 16b d e)x + 462a d e +--R + +--R 2 3 2 2 4 3 5 +--R - 396a b d e + 176a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 2 5 3 4 4 +--R 210b e x + (770a b e + 280b d e )x +--R + +--R 2 5 2 4 3 2 3 3 +--R (990a b e + 1100a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (462a e + 1584a b d e + 66a b d e - 12b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (924a d e + 198a b d e - 88a b d e + 16b d e)x + 462a d e +--R + +--R 2 3 2 2 4 3 5 +--R - 396a b d e + 176a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Union(Expression(Integer),...) +--E 790 + +--S 791 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 792 + +)clear all + +--S 793 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (1) (b x + 3a b x + 3a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1353 +r0:=-2/3*(b*d-a*e)^3*(d+e*x)^(3/2)/e^4+6/5*b*(b*d-a*e)^2*(d+e*x)^(5/2)/e^4-_ + 6/7*b^2*(b*d-a*e)*(d+e*x)^(7/2)/e^4+2/9*b^3*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 3 4 4 2 4 3 3 3 +--R 70b e x + (270a b e + 10b d e )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (378a b e + 54a b d e - 12b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 +--R (210a e + 126a b d e - 72a b d e + 16b d e)x + 210a d e +--R + +--R 2 2 2 2 3 3 4 +--R - 252a b d e + 144a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 2 4 3 3 3 +--R 70b e x + (270a b e + 10b d e )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (378a b e + 54a b d e - 12b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 +--R (210a e + 126a b d e - 72a b d e + 16b d e)x + 210a d e +--R + +--R 2 2 2 2 3 3 4 +--R - 252a b d e + 144a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 795 + +--S 796 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 797 + +)clear all + +--S 798 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1353 +r0:=2*b*(b*d-a*e)^2*(d+e*x)^(3/2)/e^4-6/5*b^2*(b*d-a*e)*(d+e*x)^(5/2)/e^4+_ + 2/7*b^3*(d+e*x)^(7/2)/e^4-2*(b*d-a*e)^3*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 10b e x + (42a b e - 12b d e )x + (70a b e - 56a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R 70a e - 140a b d e + 112a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 35e +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 10b e x + (42a b e - 12b d e )x + (70a b e - 56a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R 70a e - 140a b d e + 112a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 35e +--R Type: Union(Expression(Integer),...) +--E 800 + +--S 801 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 802 + +)clear all + +--S 803 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1353 +r0:=-2*b^2*(b*d-a*e)*(d+e*x)^(3/2)/e^4+2/5*b^3*(d+e*x)^(5/2)/e^4+_ + 2*(b*d-a*e)^3/(e^4*sqrt(d+e*x))+6*b*(b*d-a*e)^2*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (10a b e - 4b d e )x + (30a b e - 40a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 10a e + 60a b d e - 80a b d e + 32b d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (10a b e - 4b d e )x + (30a b e - 40a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 10a e + 60a b d e - 80a b d e + 32b d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 805 + +--S 806 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 807 + +)clear all + +--S 808 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1353 +r0:=2/3*(b*d-a*e)^3/(e^4*(d+e*x)^(3/2))+2/3*b^3*(d+e*x)^(3/2)/e^4-_ + 6*b*(b*d-a*e)^2/(e^4*sqrt(d+e*x))-6*b^2*(b*d-a*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (18a b e - 12b d e )x + (- 18a b e + 72a b d e - 48b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a e - 12a b d e + 48a b d e - 32b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (18a b e - 12b d e )x + (- 18a b e + 72a b d e - 48b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a e - 12a b d e + 48a b d e - 32b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 810 + +--S 811 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 812 + +)clear all + +--S 813 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1353 +r0:=2/5*(b*d-a*e)^3/(e^4*(d+e*x)^(5/2))-2*b*(b*d-a*e)^2/(e^4*(d+e*x)^(3/2))+_ + 6*b^2*(b*d-a*e)/(e^4*sqrt(d+e*x))+2*b^3*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R 10b e x + (- 30a b e + 60b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 10a b e - 40a b d e + 80b d e)x - 2a e - 4a b d e - 16a b d e +--R + +--R 3 3 +--R 32b d +--R / +--R 6 2 5 2 4 +-------+ +--R (5e x + 10d e x + 5d e )\|e x + d +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 +--R 10b e x + (- 30a b e + 60b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 10a b e - 40a b d e + 80b d e)x - 2a e - 4a b d e - 16a b d e +--R + +--R 3 3 +--R 32b d +--R / +--R 6 2 5 2 4 +-------+ +--R (5e x + 10d e x + 5d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 815 + +--S 816 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 817 + +)clear all + +--S 818 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1353 +r0:=-2/9*(b*d-a*e)^5*(d+e*x)^(9/2)/e^6+10/11*b*(b*d-a*e)^4*(d+e*x)^(11/2)/_ + e^6-20/13*b^2*(b*d-a*e)^3*(d+e*x)^(13/2)/e^6+4/3*b^3*(b*d-a*e)^2*(d+_ + e*x)^(15/2)/e^6-10/17*b^4*(b*d-a*e)*(d+e*x)^(17/2)/e^6+2/19*b^5*(d+_ + e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 5 9 9 4 9 5 8 8 +--R 43758b e x + (244530a b e + 149292b d e )x +--R + +--R 2 3 9 4 8 5 2 7 7 +--R (554268a b e + 847704a b d e + 173316b d e )x +--R + +--R 3 2 9 2 3 8 4 2 7 5 3 6 6 +--R (639540a b e + 1961256a b d e + 1005708a b d e + 69168b d e )x +--R + +--R 4 9 3 2 8 2 3 2 7 4 3 6 +--R 377910a b e + 2325600a b d e + 2395368a b d e + 414504a b d e +--R + +--R 5 4 5 +--R 126b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 8 3 2 2 7 2 3 3 6 +--R 92378a e + 1427660a b d e + 2958680a b d e + 1033600a b d e +--R + +--R 4 4 5 5 5 4 +--R 1330a b d e - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 +--R 369512a d e + 1931540a b d e + 1369520a b d e + 6460a b d e +--R + +--R 4 5 4 5 6 3 +--R - 1520a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 +--R 554268a d e + 1007760a b d e + 19380a b d e - 7752a b d e +--R + +--R 4 6 3 5 7 2 +--R 1824a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 +--R 369512a d e + 41990a b d e - 25840a b d e + 10336a b d e +--R + +--R 4 7 2 5 8 +--R - 2432a b d e + 256b d e +--R * +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 +--R 92378a d e - 83980a b d e + 51680a b d e - 20672a b d e +--R + +--R 4 8 5 9 +--R 4864a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 415701e +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 9 9 4 9 5 8 8 +--R 43758b e x + (244530a b e + 149292b d e )x +--R + +--R 2 3 9 4 8 5 2 7 7 +--R (554268a b e + 847704a b d e + 173316b d e )x +--R + +--R 3 2 9 2 3 8 4 2 7 5 3 6 6 +--R (639540a b e + 1961256a b d e + 1005708a b d e + 69168b d e )x +--R + +--R 4 9 3 2 8 2 3 2 7 4 3 6 +--R 377910a b e + 2325600a b d e + 2395368a b d e + 414504a b d e +--R + +--R 5 4 5 +--R 126b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 8 3 2 2 7 2 3 3 6 +--R 92378a e + 1427660a b d e + 2958680a b d e + 1033600a b d e +--R + +--R 4 4 5 5 5 4 +--R 1330a b d e - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 +--R 369512a d e + 1931540a b d e + 1369520a b d e + 6460a b d e +--R + +--R 4 5 4 5 6 3 +--R - 1520a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 +--R 554268a d e + 1007760a b d e + 19380a b d e - 7752a b d e +--R + +--R 4 6 3 5 7 2 +--R 1824a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 +--R 369512a d e + 41990a b d e - 25840a b d e + 10336a b d e +--R + +--R 4 7 2 5 8 +--R - 2432a b d e + 256b d e +--R * +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 +--R 92378a d e - 83980a b d e + 51680a b d e - 20672a b d e +--R + +--R 4 8 5 9 +--R 4864a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 415701e +--R Type: Union(Expression(Integer),...) +--E 820 + +--S 821 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 822 + +)clear all + +--S 823 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1353 +r0:=-2/7*(b*d-a*e)^5*(d+e*x)^(7/2)/e^6+10/9*b*(b*d-a*e)^4*(d+e*x)^(9/2)/e^6-_ + 20/11*b^2*(b*d-a*e)^3*(d+e*x)^(11/2)/e^6+20/13*b^3*(b*d-a*e)^2*(d+_ + e*x)^(13/2)/e^6-2/3*b^4*(b*d-a*e)*(d+e*x)^(15/2)/e^6+2/17*b^5*(d+_ + e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 5 8 8 4 8 5 7 7 +--R 18018b e x + (102102a b e + 42042b d e )x +--R + +--R 2 3 8 4 7 5 2 6 6 +--R (235620a b e + 243474a b d e + 25410b d e )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 5 +--R (278460a b e + 578340a b d e + 152082a b d e + 126b d e )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 +--R 170170a b e + 711620a b d e + 378420a b d e + 1190a b d e +--R + +--R 5 4 4 +--R - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 +--R 43758a e + 461890a b d e + 499460a b d e + 5100a b d e +--R + +--R 4 4 4 5 5 3 +--R - 1360a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 +--R 131274a d e + 364650a b d e + 13260a b d e - 6120a b d e +--R + +--R 4 5 3 5 6 2 +--R 1632a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 +--R 131274a d e + 24310a b d e - 17680a b d e + 8160a b d e +--R + +--R 4 6 2 5 7 +--R - 2176a b d e + 256b d e +--R * +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 +--R 43758a d e - 48620a b d e + 35360a b d e - 16320a b d e +--R + +--R 4 7 5 8 +--R 4352a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 8 8 4 8 5 7 7 +--R 18018b e x + (102102a b e + 42042b d e )x +--R + +--R 2 3 8 4 7 5 2 6 6 +--R (235620a b e + 243474a b d e + 25410b d e )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 5 +--R (278460a b e + 578340a b d e + 152082a b d e + 126b d e )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 +--R 170170a b e + 711620a b d e + 378420a b d e + 1190a b d e +--R + +--R 5 4 4 +--R - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 +--R 43758a e + 461890a b d e + 499460a b d e + 5100a b d e +--R + +--R 4 4 4 5 5 3 +--R - 1360a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 +--R 131274a d e + 364650a b d e + 13260a b d e - 6120a b d e +--R + +--R 4 5 3 5 6 2 +--R 1632a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 +--R 131274a d e + 24310a b d e - 17680a b d e + 8160a b d e +--R + +--R 4 6 2 5 7 +--R - 2176a b d e + 256b d e +--R * +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 +--R 43758a d e - 48620a b d e + 35360a b d e - 16320a b d e +--R + +--R 4 7 5 8 +--R 4352a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Union(Expression(Integer),...) +--E 825 + +--S 826 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 827 + +)clear all + +--S 828 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1353 +r0:=-2/5*(b*d-a*e)^5*(d+e*x)^(5/2)/e^6+10/7*b*(b*d-a*e)^4*(d+e*x)^(7/2)/e^6-_ + 20/9*b^2*(b*d-a*e)^3*(d+e*x)^(9/2)/e^6+20/11*b^3*(b*d-a*e)^2*(d+_ + e*x)^(11/2)/e^6-10/13*b^4*(b*d-a*e)*(d+e*x)^(13/2)/e^6+2/15*b^5*(d+_ + e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 5 7 7 4 7 5 6 6 +--R 6006b e x + (34650a b e + 7392b d e )x +--R + +--R 2 3 7 4 6 5 2 5 5 +--R (81900a b e + 44100a b d e + 126b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (100100a b e + 109200a b d e + 1050a b d e - 140b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 +--R 64350a b e + 143000a b d e + 3900a b d e - 1200a b d e +--R + +--R 5 4 3 +--R 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 18018a e + 102960a b d e + 8580a b d e - 4680a b d e +--R + +--R 4 4 3 5 5 2 +--R 1440a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 +--R 36036a d e + 12870a b d e - 11440a b d e + 6240a b d e +--R + +--R 4 5 2 5 6 +--R - 1920a b d e + 256b d e +--R * +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 +--R 18018a d e - 25740a b d e + 22880a b d e - 12480a b d e +--R + +--R 4 6 5 7 +--R 3840a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 7 4 7 5 6 6 +--R 6006b e x + (34650a b e + 7392b d e )x +--R + +--R 2 3 7 4 6 5 2 5 5 +--R (81900a b e + 44100a b d e + 126b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (100100a b e + 109200a b d e + 1050a b d e - 140b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 +--R 64350a b e + 143000a b d e + 3900a b d e - 1200a b d e +--R + +--R 5 4 3 +--R 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 18018a e + 102960a b d e + 8580a b d e - 4680a b d e +--R + +--R 4 4 3 5 5 2 +--R 1440a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 +--R 36036a d e + 12870a b d e - 11440a b d e + 6240a b d e +--R + +--R 4 5 2 5 6 +--R - 1920a b d e + 256b d e +--R * +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 +--R 18018a d e - 25740a b d e + 22880a b d e - 12480a b d e +--R + +--R 4 6 5 7 +--R 3840a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 830 + +--S 831 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 832 + +)clear all + +--S 833 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1353 +r0:=-2/3*(b*d-a*e)^5*(d+e*x)^(3/2)/e^6+2*b*(b*d-a*e)^4*(d+e*x)^(5/2)/e^6-_ + 20/7*b^2*(b*d-a*e)^3*(d+e*x)^(7/2)/e^6+20/9*b^3*(b*d-a*e)^2*(d+_ + e*x)^(9/2)/e^6-10/11*b^4*(b*d-a*e)*(d+e*x)^(11/2)/e^6+2/13*b^5*(d+_ + e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 5 6 6 4 6 5 5 5 +--R 1386b e x + (8190a b e + 126b d e )x +--R + +--R 2 3 6 4 5 5 2 4 4 +--R (20020a b e + 910a b d e - 140b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (25740a b e + 2860a b d e - 1040a b d e + 160b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 18018a b e + 5148a b d e - 3432a b d e + 1248a b d e +--R + +--R 5 4 2 +--R - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 6006a e + 6006a b d e - 6864a b d e + 4576a b d e +--R + +--R 4 4 2 5 5 +--R - 1664a b d e + 256b d e +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 6006a d e - 12012a b d e + 13728a b d e - 9152a b d e + 3328a b d e +--R + +--R 5 6 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 9009e +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 4 6 5 5 5 +--R 1386b e x + (8190a b e + 126b d e )x +--R + +--R 2 3 6 4 5 5 2 4 4 +--R (20020a b e + 910a b d e - 140b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (25740a b e + 2860a b d e - 1040a b d e + 160b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 18018a b e + 5148a b d e - 3432a b d e + 1248a b d e +--R + +--R 5 4 2 +--R - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 6006a e + 6006a b d e - 6864a b d e + 4576a b d e +--R + +--R 4 4 2 5 5 +--R - 1664a b d e + 256b d e +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 6006a d e - 12012a b d e + 13728a b d e - 9152a b d e + 3328a b d e +--R + +--R 5 6 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 835 + +--S 836 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 837 + +)clear all + +--S 838 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1353 +r0:=10/3*b*(b*d-a*e)^4*(d+e*x)^(3/2)/e^6-4*b^2*(b*d-a*e)^3*(d+e*x)^(5/2)/e^6+_ + 20/7*b^3*(b*d-a*e)^2*(d+e*x)^(7/2)/e^6-10/9*b^4*(b*d-a*e)*_ + (d+e*x)^(9/2)/e^6+2/11*b^5*(d+e*x)^(11/2)/e^6-2*(b*d-a*e)^5*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 126b e x + (770a b e - 140b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (1980a b e - 880a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (2772a b e - 2376a b d e + 1056a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 1386a e - 4620a b d e + 7392a b d e - 6336a b d e + 2816a b d e +--R + +--R 5 5 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 693e +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 126b e x + (770a b e - 140b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (1980a b e - 880a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (2772a b e - 2376a b d e + 1056a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 1386a e - 4620a b d e + 7392a b d e - 6336a b d e + 2816a b d e +--R + +--R 5 5 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 693e +--R Type: Union(Expression(Integer),...) +--E 840 + +--S 841 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 842 + +)clear all + +--S 843 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1353 +r0:=-20/3*b^2*(b*d-a*e)^3*(d+e*x)^(3/2)/e^6+4*b^3*(b*d-a*e)^2*_ + (d+e*x)^(5/2)/e^6-10/7*b^4*(b*d-a*e)*(d+e*x)^(7/2)/e^6+2/9*b^5*_ + (d+e*x)^(9/2)/e^6+2*(b*d-a*e)^5/(e^6*sqrt(d+e*x))+10*b*(b*d-a*e)^4*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 14b e x + (90a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (252a b e - 144a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 504a b d e + 288a b d e - 64b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (630a b e - 1680a b d e + 2016a b d e - 1152a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 126a e + 1260a b d e - 3360a b d e + 4032a b d e - 2304a b d e +--R + +--R 5 5 +--R 512b d +--R / +--R 6 +-------+ +--R 63e \|e x + d +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 14b e x + (90a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (252a b e - 144a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 504a b d e + 288a b d e - 64b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (630a b e - 1680a b d e + 2016a b d e - 1152a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 126a e + 1260a b d e - 3360a b d e + 4032a b d e - 2304a b d e +--R + +--R 5 5 +--R 512b d +--R / +--R 6 +-------+ +--R 63e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 845 + +--S 846 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1353 +r0:=2/3*(b*d-a*e)^5/(e^6*(d+e*x)^(3/2))+20/3*b^3*(b*d-a*e)^2*_ + (d+e*x)^(3/2)/e^6-2*b^4*(b*d-a*e)*(d+e*x)^(5/2)/e^6+2/7*b^5*_ + (d+e*x)^(7/2)/e^6-10*b*(b*d-a*e)^4/(e^6*sqrt(d+e*x))-20*b^2*_ + (b*d-a*e)^3*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (42a b e - 12b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 840a b d e + 672a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b e + 1680a b d e - 3360a b d e + 2688a b d e - 768b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 14a e - 140a b d e + 1120a b d e - 2240a b d e + 1792a b d e +--R + +--R 5 5 +--R - 512b d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (42a b e - 12b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 840a b d e + 672a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b e + 1680a b d e - 3360a b d e + 2688a b d e - 768b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 14a e - 140a b d e + 1120a b d e - 2240a b d e + 1792a b d e +--R + +--R 5 5 +--R - 512b d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 850 + +--S 851 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 852 + +)clear all + +--S 853 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1353 +r0:=2/5*(b*d-a*e)^5/(e^6*(d+e*x)^(5/2))-10/3*b*(b*d-a*e)^4/(e^6*_ + (d+e*x)^(3/2))-10/3*b^4*(b*d-a*e)*(d+e*x)^(3/2)/e^6+2/5*b^5*_ + (d+e*x)^(5/2)/e^6+20*b^2*(b*d-a*e)^3/(e^6*sqrt(d+e*x))+20*b^3*_ + (b*d-a*e)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (50a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (300a b e - 400a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 300a b e + 1800a b d e - 2400a b d e + 960b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 50a b e - 400a b d e + 2400a b d e - 3200a b d e + 1280b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 6a e - 20a b d e - 160a b d e + 960a b d e - 1280a b d e + 512b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (50a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (300a b e - 400a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 300a b e + 1800a b d e - 2400a b d e + 960b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 50a b e - 400a b d e + 2400a b d e - 3200a b d e + 1280b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 6a e - 20a b d e - 160a b d e + 960a b d e - 1280a b d e + 512b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 855 + +--S 856 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 857 + +)clear all + +--S 858 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 3 10 6 3 7 2 9 2 5 3 6 2 7 2 8 +--R b e x + (7a b e + 3b d e )x + (21a b e + 21a b d e + 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e + 63a b d e + 21a b d e + b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (35a b e + 105a b d e + 63a b d e + 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (21a b e + 105a b d e + 105a b d e + 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (7a b e + 63a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (a e + 21a b d e + 63a b d e + 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (3a d e + 21a b d e + 21a b d )x + (3a d e + 7a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1353 +r0:=-2/9*(b*d-a*e)^7*(d+e*x)^(9/2)/e^8+14/11*b*(b*d-a*e)^6*_ + (d+e*x)^(11/2)/e^8-42/13*b^2*(b*d-a*e)^5*(d+e*x)^(13/2)/e^8+_ + 14/3*b^3*(b*d-a*e)^4*(d+e*x)^(15/2)/e^8-70/17*b^4*(b*d-a*e)^3*_ + (d+e*x)^(17/2)/e^8+42/19*b^5*(b*d-a*e)^2*(d+e*x)^(19/2)/e^8-_ + 2/3*b^6*(b*d-a*e)*(d+e*x)^(21/2)/e^8+2/23*b^7*(d+e*x)^(23/2)/e^8 +--R +--R +--R (2) +--R 7 11 11 6 11 7 10 10 +--R 831402b e x + (6374082a b e + 2771340b d e )x +--R + +--R 2 5 11 6 10 7 2 9 9 +--R (21135114a b e + 21470592a b d e + 3121404b d e )x +--R + +--R 3 4 11 2 5 10 6 2 9 +--R 39369330a b e + 72108036a b d e + 24509628a b d e +--R + +--R 7 3 8 +--R 1194336b d e +--R * +--R 8 +--R x +--R + +--R 4 3 11 3 4 10 2 5 2 9 +--R 44618574a b e + 136480344a b d e + 83711628a b d e +--R + +--R 6 3 8 7 4 7 +--R 9551256a b d e + 858b d e +--R * +--R 7 +--R x +--R + +--R 5 2 11 4 3 10 3 4 2 9 +--R 30889782a b e + 157881108a b d e + 161918988a b d e +--R + +--R 2 5 3 8 6 4 7 7 5 6 +--R 33408144a b d e + 10626a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 6 11 5 2 10 4 3 2 9 +--R 12168702a b e + 112326480a b d e + 192827124a b d e +--R + +--R 3 4 3 8 2 5 4 7 6 5 6 7 6 5 +--R 66735144a b d e + 60858a b d e - 11592a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 7 11 6 10 5 2 2 9 +--R 2124694a e + 45970652a b d e + 142904244a b d e +--R + +--R 4 3 3 8 3 4 4 7 2 5 5 6 6 6 5 +--R 83204800a b d e + 214130a b d e - 67620a b d e + 12880a b d e +--R + +--R 7 7 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 2 9 5 2 3 8 +--R 8498776a d e + 62195588a b d e + 66147816a b d e +--R + +--R 4 3 4 7 3 4 5 6 2 5 6 5 6 7 4 +--R 520030a b d e - 244720a b d e + 77280a b d e - 14720a b d e +--R + +--R 7 8 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 2 4 7 4 3 5 6 +--R 12748164a d e + 32449872a b d e + 936054a b d e - 624036a b d e +--R + +--R 3 4 6 5 2 5 7 4 6 8 3 7 9 2 +--R 293664a b d e - 92736a b d e + 17664a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 3 8 6 4 7 5 2 5 6 4 3 6 5 +--R 8498776a d e + 1352078a b d e - 1248072a b d e + 832048a b d e +--R + +--R 3 4 7 4 2 5 8 3 6 9 2 7 10 +--R - 391552a b d e + 123648a b d e - 23552a b d e + 2048b d e +--R * +--R x +--R + +--R 7 4 7 6 5 6 5 2 6 5 4 3 7 4 +--R 2124694a d e - 2704156a b d e + 2496144a b d e - 1664096a b d e +--R + +--R 3 4 8 3 2 5 9 2 6 10 7 11 +--R 783104a b d e - 247296a b d e + 47104a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 9561123e +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 11 11 6 11 7 10 10 +--R 831402b e x + (6374082a b e + 2771340b d e )x +--R + +--R 2 5 11 6 10 7 2 9 9 +--R (21135114a b e + 21470592a b d e + 3121404b d e )x +--R + +--R 3 4 11 2 5 10 6 2 9 +--R 39369330a b e + 72108036a b d e + 24509628a b d e +--R + +--R 7 3 8 +--R 1194336b d e +--R * +--R 8 +--R x +--R + +--R 4 3 11 3 4 10 2 5 2 9 +--R 44618574a b e + 136480344a b d e + 83711628a b d e +--R + +--R 6 3 8 7 4 7 +--R 9551256a b d e + 858b d e +--R * +--R 7 +--R x +--R + +--R 5 2 11 4 3 10 3 4 2 9 +--R 30889782a b e + 157881108a b d e + 161918988a b d e +--R + +--R 2 5 3 8 6 4 7 7 5 6 +--R 33408144a b d e + 10626a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 6 11 5 2 10 4 3 2 9 +--R 12168702a b e + 112326480a b d e + 192827124a b d e +--R + +--R 3 4 3 8 2 5 4 7 6 5 6 7 6 5 +--R 66735144a b d e + 60858a b d e - 11592a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 7 11 6 10 5 2 2 9 +--R 2124694a e + 45970652a b d e + 142904244a b d e +--R + +--R 4 3 3 8 3 4 4 7 2 5 5 6 6 6 5 +--R 83204800a b d e + 214130a b d e - 67620a b d e + 12880a b d e +--R + +--R 7 7 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 2 9 5 2 3 8 +--R 8498776a d e + 62195588a b d e + 66147816a b d e +--R + +--R 4 3 4 7 3 4 5 6 2 5 6 5 6 7 4 +--R 520030a b d e - 244720a b d e + 77280a b d e - 14720a b d e +--R + +--R 7 8 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 2 4 7 4 3 5 6 +--R 12748164a d e + 32449872a b d e + 936054a b d e - 624036a b d e +--R + +--R 3 4 6 5 2 5 7 4 6 8 3 7 9 2 +--R 293664a b d e - 92736a b d e + 17664a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 3 8 6 4 7 5 2 5 6 4 3 6 5 +--R 8498776a d e + 1352078a b d e - 1248072a b d e + 832048a b d e +--R + +--R 3 4 7 4 2 5 8 3 6 9 2 7 10 +--R - 391552a b d e + 123648a b d e - 23552a b d e + 2048b d e +--R * +--R x +--R + +--R 7 4 7 6 5 6 5 2 6 5 4 3 7 4 +--R 2124694a d e - 2704156a b d e + 2496144a b d e - 1664096a b d e +--R + +--R 3 4 8 3 2 5 9 2 6 10 7 11 +--R 783104a b d e - 247296a b d e + 47104a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 9561123e +--R Type: Union(Expression(Integer),...) +--E 860 + +--S 861 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 862 + +)clear all + +--S 863 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R b e x + (7a b e + 2b d e)x + (21a b e + 14a b d e + b d )x +--R + +--R 3 4 2 2 5 6 2 6 4 3 2 3 4 2 5 2 5 +--R (35a b e + 42a b d e + 7a b d )x + (35a b e + 70a b d e + 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 6 2 5 2 4 3 2 3 +--R (21a b e + 70a b d e + 35a b d )x + (7a b e + 42a b d e + 35a b d )x +--R + +--R 7 2 6 5 2 2 2 7 6 2 7 2 +--R (a e + 14a b d e + 21a b d )x + (2a d e + 7a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1353 +r0:=-2/7*(b*d-a*e)^7*(d+e*x)^(7/2)/e^8+14/9*b*(b*d-a*e)^6*_ + (d+e*x)^(9/2)/e^8-42/11*b^2*(b*d-a*e)^5*(d+e*x)^(11/2)/e^8+_ + 70/13*b^3*(b*d-a*e)^4*(d+e*x)^(13/2)/e^8-14/3*b^4*(b*d-a*e)^3*_ + (d+e*x)^(15/2)/e^8+42/17*b^5*(b*d-a*e)^2*(d+e*x)^(17/2)/e^8-_ + 14/19*b^6*(b*d-a*e)*(d+e*x)^(19/2)/e^8+2/21*b^7*(d+e*x)^(21/2)/e^8 +--R +--R +--R (2) +--R 7 10 10 6 10 7 9 9 +--R 277134b e x + (2144142a b e + 627198b d e )x +--R + +--R 2 5 10 6 9 7 2 8 8 +--R (7189182a b e + 4918914a b d e + 362934b d e )x +--R + +--R 3 4 10 2 5 9 6 2 8 7 3 7 7 +--R (13579566a b e + 16774758a b d e + 2900898a b d e + 858b d e )x +--R + +--R 4 3 10 3 4 9 2 5 2 8 +--R 15668730a b e + 32382042a b d e + 10138590a b d e +--R + +--R 6 3 7 7 4 6 +--R 9702a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 4 2 8 +--R 11110554a b e + 38459610a b d e + 20226906a b d e +--R + +--R 2 5 3 7 6 4 6 7 5 5 +--R 50274a b d e - 10584a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 6 10 5 2 9 4 3 2 8 +--R 4526522a b e + 28393638a b d e + 25164930a b d e +--R + +--R 3 4 3 7 2 5 4 6 6 5 5 7 6 4 +--R 158270a b d e - 55860a b d e + 11760a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 +--R 831402a e + 12286274a b d e + 19928454a b d e + 339150a b d e +--R + +--R 3 4 4 6 2 5 5 5 6 6 4 7 7 3 +--R - 180880a b d e + 63840a b d e - 13440a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 +--R 2494206a d e + 9699690a b d e + 529074a b d e - 406980a b d e +--R + +--R 3 4 5 5 2 5 6 4 6 7 3 7 8 2 +--R 217056a b d e - 76608a b d e + 16128a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 +--R 2494206a d e + 646646a b d e - 705432a b d e + 542640a b d e +--R + +--R 3 4 6 4 2 5 7 3 6 8 2 7 9 +--R - 289408a b d e + 102144a b d e - 21504a b d e + 2048b d e +--R * +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 +--R 831402a d e - 1293292a b d e + 1410864a b d e - 1085280a b d e +--R + +--R 3 4 7 3 2 5 8 2 6 9 7 10 +--R 578816a b d e - 204288a b d e + 43008a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 10 10 6 10 7 9 9 +--R 277134b e x + (2144142a b e + 627198b d e )x +--R + +--R 2 5 10 6 9 7 2 8 8 +--R (7189182a b e + 4918914a b d e + 362934b d e )x +--R + +--R 3 4 10 2 5 9 6 2 8 7 3 7 7 +--R (13579566a b e + 16774758a b d e + 2900898a b d e + 858b d e )x +--R + +--R 4 3 10 3 4 9 2 5 2 8 +--R 15668730a b e + 32382042a b d e + 10138590a b d e +--R + +--R 6 3 7 7 4 6 +--R 9702a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 4 2 8 +--R 11110554a b e + 38459610a b d e + 20226906a b d e +--R + +--R 2 5 3 7 6 4 6 7 5 5 +--R 50274a b d e - 10584a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 6 10 5 2 9 4 3 2 8 +--R 4526522a b e + 28393638a b d e + 25164930a b d e +--R + +--R 3 4 3 7 2 5 4 6 6 5 5 7 6 4 +--R 158270a b d e - 55860a b d e + 11760a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 +--R 831402a e + 12286274a b d e + 19928454a b d e + 339150a b d e +--R + +--R 3 4 4 6 2 5 5 5 6 6 4 7 7 3 +--R - 180880a b d e + 63840a b d e - 13440a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 +--R 2494206a d e + 9699690a b d e + 529074a b d e - 406980a b d e +--R + +--R 3 4 5 5 2 5 6 4 6 7 3 7 8 2 +--R 217056a b d e - 76608a b d e + 16128a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 +--R 2494206a d e + 646646a b d e - 705432a b d e + 542640a b d e +--R + +--R 3 4 6 4 2 5 7 3 6 8 2 7 9 +--R - 289408a b d e + 102144a b d e - 21504a b d e + 2048b d e +--R * +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 +--R 831402a d e - 1293292a b d e + 1410864a b d e - 1085280a b d e +--R + +--R 3 4 7 3 2 5 8 2 6 9 7 10 +--R 578816a b d e - 204288a b d e + 43008a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Union(Expression(Integer),...) +--E 865 + +--S 866 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 8 6 7 7 2 5 6 6 3 4 2 5 5 +--R b e x + (7a b e + b d)x + (21a b e + 7a b d)x + (35a b e + 21a b d)x +--R + +--R 4 3 3 4 4 5 2 4 3 3 6 5 2 2 +--R (35a b e + 35a b d)x + (21a b e + 35a b d)x + (7a b e + 21a b d)x +--R + +--R 7 6 7 +--R (a e + 7a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1353 +r0:=-2/5*(b*d-a*e)^7*(d+e*x)^(5/2)/e^8+2*b*(b*d-a*e)^6*(d+e*x)^(7/2)/e^8-_ + 14/3*b^2*(b*d-a*e)^5*(d+e*x)^(9/2)/e^8+70/11*b^3*(b*d-a*e)^4*_ + (d+e*x)^(11/2)/e^8-70/13*b^4*(b*d-a*e)^3*(d+e*x)^(13/2)/e^8+_ + 14/5*b^5*(b*d-a*e)^2*(d+e*x)^(15/2)/e^8-14/17*b^6*(b*d-a*e)*_ + (d+e*x)^(17/2)/e^8+2/19*b^7*(d+e*x)^(19/2)/e^8 +--R +--R +--R (2) +--R 7 9 9 6 9 7 8 8 +--R 72930b e x + (570570a b e + 85800b d e )x +--R + +--R 2 5 9 6 8 7 2 7 7 +--R (1939938a b e + 684684a b d e + 858b d e )x +--R + +--R 3 4 9 2 5 8 6 2 7 7 3 6 6 +--R (3730650a b e + 2387616a b d e + 8778a b d e - 924b d e )x +--R + +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 +--R 4408950a b e + 4748100a b d e + 40698a b d e - 9576a b d e +--R + +--R 7 4 5 +--R 1008b d e +--R * +--R 5 +--R x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 +--R 3233230a b e + 5878600a b d e + 113050a b d e - 45220a b d e +--R + +--R 6 4 5 7 5 4 +--R 10640a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 2 8 4 3 2 7 3 4 3 6 +--R 1385670a b e + 4618900a b d e + 209950a b d e - 129200a b d e +--R + +--R 2 5 4 5 6 5 4 7 6 3 +--R 51680a b d e - 12160a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 +--R 277134a e + 2217072a b d e + 277134a b d e - 251940a b d e +--R + +--R 3 4 4 5 2 5 5 4 6 6 3 7 7 2 +--R 155040a b d e - 62016a b d e + 14592a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 +--R 554268a d e + 277134a b d e - 369512a b d e + 335920a b d e +--R + +--R 3 4 5 4 2 5 6 3 6 7 2 7 8 +--R - 206720a b d e + 82688a b d e - 19456a b d e + 2048b d e +--R * +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 +--R 277134a d e - 554268a b d e + 739024a b d e - 671840a b d e +--R + +--R 3 4 6 3 2 5 7 2 6 8 7 9 +--R 413440a b d e - 165376a b d e + 38912a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 692835e +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 9 9 6 9 7 8 8 +--R 72930b e x + (570570a b e + 85800b d e )x +--R + +--R 2 5 9 6 8 7 2 7 7 +--R (1939938a b e + 684684a b d e + 858b d e )x +--R + +--R 3 4 9 2 5 8 6 2 7 7 3 6 6 +--R (3730650a b e + 2387616a b d e + 8778a b d e - 924b d e )x +--R + +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 +--R 4408950a b e + 4748100a b d e + 40698a b d e - 9576a b d e +--R + +--R 7 4 5 +--R 1008b d e +--R * +--R 5 +--R x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 +--R 3233230a b e + 5878600a b d e + 113050a b d e - 45220a b d e +--R + +--R 6 4 5 7 5 4 +--R 10640a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 2 8 4 3 2 7 3 4 3 6 +--R 1385670a b e + 4618900a b d e + 209950a b d e - 129200a b d e +--R + +--R 2 5 4 5 6 5 4 7 6 3 +--R 51680a b d e - 12160a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 +--R 277134a e + 2217072a b d e + 277134a b d e - 251940a b d e +--R + +--R 3 4 4 5 2 5 5 4 6 6 3 7 7 2 +--R 155040a b d e - 62016a b d e + 14592a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 +--R 554268a d e + 277134a b d e - 369512a b d e + 335920a b d e +--R + +--R 3 4 5 4 2 5 6 3 6 7 2 7 8 +--R - 206720a b d e + 82688a b d e - 19456a b d e + 2048b d e +--R * +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 +--R 277134a d e - 554268a b d e + 739024a b d e - 671840a b d e +--R + +--R 3 4 6 3 2 5 7 2 6 8 7 9 +--R 413440a b d e - 165376a b d e + 38912a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 692835e +--R Type: Union(Expression(Integer),...) +--E 870 + +--S 871 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 872 + +)clear all + +--S 873 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1353 +r0:=-2/3*(b*d-a*e)^7*(d+e*x)^(3/2)/e^8+14/5*b*(b*d-a*e)^6*(d+e*x)^(5/2)/e^8-_ + 6*b^2*(b*d-a*e)^5*(d+e*x)^(7/2)/e^8+70/9*b^3*(b*d-a*e)^4*_ + (d+e*x)^(9/2)/e^8-70/11*b^4*(b*d-a*e)^3*(d+e*x)^(11/2)/e^8+42/13*b^5*_ + (b*d-a*e)^2*(d+e*x)^(13/2)/e^8-14/15*b^6*(b*d-a*e)*(d+e*x)^(15/2)/e^8+_ + 2/17*b^7*(d+e*x)^(17/2)/e^8 +--R +--R +--R (2) +--R 7 8 8 6 8 7 7 7 +--R 12870b e x + (102102a b e + 858b d e )x +--R + +--R 2 5 8 6 7 7 2 6 6 +--R (353430a b e + 7854a b d e - 924b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 5 +--R (696150a b e + 32130a b d e - 8568a b d e + 1008b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 +--R 850850a b e + 77350a b d e - 35700a b d e + 9520a b d e +--R + +--R 7 4 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 +--R 656370a b e + 121550a b d e - 88400a b d e + 40800a b d e +--R + +--R 6 4 4 7 5 3 +--R - 10880a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 +--R 306306a b e + 131274a b d e - 145860a b d e + 106080a b d e +--R + +--R 2 5 4 4 6 5 3 7 6 2 +--R - 48960a b d e + 13056a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 +--R 72930a e + 102102a b d e - 175032a b d e + 194480a b d e +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 +--R - 141440a b d e + 65280a b d e - 17408a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 72930a d e - 204204a b d e + 350064a b d e - 388960a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 +--R 282880a b d e - 130560a b d e + 34816a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 109395e +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 8 8 6 8 7 7 7 +--R 12870b e x + (102102a b e + 858b d e )x +--R + +--R 2 5 8 6 7 7 2 6 6 +--R (353430a b e + 7854a b d e - 924b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 5 +--R (696150a b e + 32130a b d e - 8568a b d e + 1008b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 +--R 850850a b e + 77350a b d e - 35700a b d e + 9520a b d e +--R + +--R 7 4 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 +--R 656370a b e + 121550a b d e - 88400a b d e + 40800a b d e +--R + +--R 6 4 4 7 5 3 +--R - 10880a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 +--R 306306a b e + 131274a b d e - 145860a b d e + 106080a b d e +--R + +--R 2 5 4 4 6 5 3 7 6 2 +--R - 48960a b d e + 13056a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 +--R 72930a e + 102102a b d e - 175032a b d e + 194480a b d e +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 +--R - 141440a b d e + 65280a b d e - 17408a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 72930a d e - 204204a b d e + 350064a b d e - 388960a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 +--R 282880a b d e - 130560a b d e + 34816a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 109395e +--R Type: Union(Expression(Integer),...) +--E 875 + +--S 876 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 877 + +)clear all + +--S 878 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1353 +r0:=14/3*b*(b*d-a*e)^6*(d+e*x)^(3/2)/e^8-42/5*b^2*(b*d-a*e)^5*_ + (d+e*x)^(5/2)/e^8+10*b^3*(b*d-a*e)^4*(d+e*x)^(7/2)/e^8-70/9*b^4*_ + (b*d-a*e)^3*(d+e*x)^(9/2)/e^8+42/11*b^5*(b*d-a*e)^2*(d+e*x)^(11/2)/e^8-_ + 14/13*b^6*(b*d-a*e)*(d+e*x)^(13/2)/e^8+2/15*b^7*(d+e*x)^(15/2)/e^8-_ + 2*(b*d-a*e)^7*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 858b e x + (6930a b e - 924b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (24570a b e - 7560a b d e + 1008b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (50050a b e - 27300a b d e + 8400a b d e - 1120b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 64350a b e - 57200a b d e + 31200a b d e - 9600a b d e +--R + +--R 7 4 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 54054a b e - 77220a b d e + 68640a b d e - 37440a b d e +--R + +--R 6 4 3 7 5 2 +--R 11520a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 30030a b e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 49920a b d e - 15360a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 12870a e - 60060a b d e + 144144a b d e - 205920a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 183040a b d e - 99840a b d e + 30720a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 6435e +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R 858b e x + (6930a b e - 924b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (24570a b e - 7560a b d e + 1008b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (50050a b e - 27300a b d e + 8400a b d e - 1120b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 64350a b e - 57200a b d e + 31200a b d e - 9600a b d e +--R + +--R 7 4 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 54054a b e - 77220a b d e + 68640a b d e - 37440a b d e +--R + +--R 6 4 3 7 5 2 +--R 11520a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 30030a b e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 49920a b d e - 15360a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 12870a e - 60060a b d e + 144144a b d e - 205920a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 183040a b d e - 99840a b d e + 30720a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 6435e +--R Type: Union(Expression(Integer),...) +--E 880 + +--S 881 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 882 + +)clear all + +--S 883 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1353 +r0:=-14*b^2*(b*d-a*e)^5*(d+e*x)^(3/2)/e^8+14*b^3*(b*d-a*e)^4*_ + (d+e*x)^(5/2)/e^8-10*b^4*(b*d-a*e)^3*(d+e*x)^(7/2)/e^8+14/3*b^5*_ + (b*d-a*e)^2*(d+e*x)^(9/2)/e^8-14/11*b^6*(b*d-a*e)*(d+e*x)^(11/2)/e^8+_ + 2/13*b^7*(d+e*x)^(13/2)/e^8+2*(b*d-a*e)^7/(e^8*sqrt(d+e*x))+_ + 14*b*(b*d-a*e)^6*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 66b e x + (546a b e - 84b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2002a b e - 728a b d e + 112b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (4290a b e - 2860a b d e + 1040a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (6006a b e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 6006a b e - 12012a b d e + 13728a b d e - 9152a b d e +--R + +--R 6 4 3 7 5 2 +--R 3328a b d e - 512b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 6006a b e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 36608a b d e - 13312a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 858a e + 12012a b d e - 48048a b d e + 96096a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 109824a b d e + 73216a b d e - 26624a b d e + 4096b d +--R / +--R 8 +-------+ +--R 429e \|e x + d +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R 66b e x + (546a b e - 84b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2002a b e - 728a b d e + 112b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (4290a b e - 2860a b d e + 1040a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (6006a b e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 6006a b e - 12012a b d e + 13728a b d e - 9152a b d e +--R + +--R 6 4 3 7 5 2 +--R 3328a b d e - 512b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 6006a b e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 36608a b d e - 13312a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 858a e + 12012a b d e - 48048a b d e + 96096a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 109824a b d e + 73216a b d e - 26624a b d e + 4096b d +--R / +--R 8 +-------+ +--R 429e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 885 + +--S 886 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 887 + +)clear all + +--S 888 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1353 +r0:=2/3*(b*d-a*e)^7/(e^8*(d+e*x)^(3/2))+70/3*b^3*(b*d-a*e)^4*_ + (d+e*x)^(3/2)/e^8-14*b^4*(b*d-a*e)^3*(d+e*x)^(5/2)/e^8+6*b^5*_ + (b*d-a*e)^2*(d+e*x)^(7/2)/e^8-14/9*b^6*(b*d-a*e)*(d+e*x)^(9/2)/e^8+_ + 2/11*b^7*(d+e*x)^(11/2)/e^8-14*b*(b*d-a*e)^6/(e^8*sqrt(d+e*x))-_ + 42*b^2*(b*d-a*e)^5*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 18b e x + (154a b e - 28b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (594a b e - 264a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1386a b e - 1188a b d e + 528a b d e - 96b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4158a b e - 13860a b d e + 22176a b d e - 19008a b d e +--R + +--R 6 4 3 7 5 2 +--R 8448a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 1386a b e + 16632a b d e - 55440a b d e + 88704a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 76032a b d e + 33792a b d e - 6144b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 66a e - 924a b d e + 11088a b d e - 36960a b d e + 59136a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 50688a b d e + 22528a b d e - 4096b d +--R / +--R 9 8 +-------+ +--R (99e x + 99d e )\|e x + d +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R 18b e x + (154a b e - 28b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (594a b e - 264a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1386a b e - 1188a b d e + 528a b d e - 96b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4158a b e - 13860a b d e + 22176a b d e - 19008a b d e +--R + +--R 6 4 3 7 5 2 +--R 8448a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 1386a b e + 16632a b d e - 55440a b d e + 88704a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 76032a b d e + 33792a b d e - 6144b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 66a e - 924a b d e + 11088a b d e - 36960a b d e + 59136a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 50688a b d e + 22528a b d e - 4096b d +--R / +--R 9 8 +-------+ +--R (99e x + 99d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 890 + +--S 891 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 892 + +)clear all + +--S 893 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1353 +r0:=2/5*(b*d-a*e)^7/(e^8*(d+e*x)^(5/2))-14/3*b*(b*d-a*e)^6/(e^8*_ + (d+e*x)^(3/2))-70/3*b^4*(b*d-a*e)^3*(d+e*x)^(3/2)/e^8+42/5*b^5*_ + (b*d-a*e)^2*(d+e*x)^(5/2)/e^8-2*b^6*(b*d-a*e)*(d+e*x)^(7/2)/e^8+_ + 2/9*b^7*(d+e*x)^(9/2)/e^8+42*b^2*(b*d-a*e)^5/(e^8*sqrt(d+e*x))+_ + 70*b^3*(b*d-a*e)^4*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (90a b e - 20b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1050a b e - 1260a b d e + 720a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (3150a b e - 8400a b d e + 10080a b d e - 5760a b d e + 1280b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1890a b e + 18900a b d e - 50400a b d e + 60480a b d e +--R + +--R 6 4 3 7 5 2 +--R - 34560a b d e + 7680b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 210a b e - 2520a b d e + 25200a b d e - 67200a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 80640a b d e - 46080a b d e + 10240b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 18a e - 84a b d e - 1008a b d e + 10080a b d e - 26880a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 32256a b d e - 18432a b d e + 4096b d +--R / +--R 10 2 9 2 8 +-------+ +--R (45e x + 90d e x + 45d e )\|e x + d +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (90a b e - 20b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1050a b e - 1260a b d e + 720a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (3150a b e - 8400a b d e + 10080a b d e - 5760a b d e + 1280b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1890a b e + 18900a b d e - 50400a b d e + 60480a b d e +--R + +--R 6 4 3 7 5 2 +--R - 34560a b d e + 7680b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 210a b e - 2520a b d e + 25200a b d e - 67200a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 80640a b d e - 46080a b d e + 10240b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 18a e - 84a b d e - 1008a b d e + 10080a b d e - 26880a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 32256a b d e - 18432a b d e + 4096b d +--R / +--R 10 2 9 2 8 +-------+ +--R (45e x + 90d e x + 45d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 895 + +--S 896 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 897 + +)clear all + +--S 898 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1353 +r0:=2/3*(b*d-a*e)^2*(d+e*x)^(3/2)/b^3+2/5*(b*d-a*e)*(d+e*x)^(5/2)/b^2+_ + 2/7*(d+e*x)^(7/2)/b-2*(b*d-a*e)^(7/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/b^(9/2)+2*(b*d-a*e)^3*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (210a e - 630a b d e + 630a b d e - 210b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (- 42a b e + 132b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 224a b d e + 244b d e)x - 210a e + 700a b d e +--R + +--R 2 2 3 3 +--R - 812a b d e + 352b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 +-+ +--R 105b \|b +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 2 2 2 2 3 3 |- a e + b d +--R (105a e - 315a b d e + 315a b d e - 105b d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (- 42a b e + 132b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 224a b d e + 244b d e)x - 210a e + 700a b d e +--R + +--R 2 2 3 3 +--R - 812a b d e + 352b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b +--R , +--R +--R +---------+ +--R 3 3 2 2 2 2 3 3 |a e - b d +--R (210a e - 630a b d e + 630a b d e - 210b d ) |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (- 42a b e + 132b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 224a b d e + 244b d e)x - 210a e + 700a b d e +--R + +--R 2 2 3 3 +--R - 812a b d e + 352b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 900 + +--S 901 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 2 2 2 2 3 3 |- a e + b d +-+ +--R (a e - 3a b d e + 3a b d e - b d ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|b \|e x + d +--R (- 2a e + 6a b d e - 6a b d e + 2b d )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (- 2a e + 6a b d e - 6a b d e + 2b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 3 3 2 2 2 2 3 3 +-+ |a e - b d \|e x + d +--R (2a e - 6a b d e + 6a b d e - 2b d )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 904 + +)clear all + +--S 905 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R b x + a +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1353 +r0:=2/3*(b*d-a*e)*(d+e*x)^(3/2)/b^2+2/5*(d+e*x)^(5/2)/b-2*(b*d-a*e)^(5/2)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(7/2)+2*(b*d-a*e)^2*_ + sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|e x + d +--R (- 30a e + 60a b d e - 30b d )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (6b e x + (- 10a b e + 22b d e)x + 30a e - 70a b d e + 46b d )\|b +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a e + b d +--R (15a e - 30a b d e + 15b d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 10a b e + 22b d e)x + 30a e - 70a b d e + 46b d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b +--R , +--R +--R +---------+ +-------+ +--R 2 2 2 2 |a e - b d \|e x + d +--R (- 30a e + 60a b d e - 30b d ) |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 10a b e + 22b d e)x + 30a e - 70a b d e + 46b d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 907 + +--S 908 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a e + b d +-+ +--R (a e - 2a b d e + b d ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|e x + d +--R (2a e - 4a b d e + 2b d )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|e x + d +--R (2a e - 4a b d e + 2b d )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a e - b d \|e x + d +--R (- 2a e + 4a b d e - 2b d )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 911 + +)clear all + +--S 912 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------- +--R b x + a +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1353 +r0:=2/3*(d+e*x)^(3/2)/b-2*(b*d-a*e)^(3/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/b^(5/2)+2*(b*d-a*e)*sqrt(d+e*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (6a e - 6b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-+ +-------+ +--R (2b e x - 6a e + 8b d)\|b \|e x + d +--R / +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a e + b d +--R (3a e - 3b d) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R (2b e x - 6a e + 8b d)\|e x + d +--R / +--R 2 +--R 3b +--R , +--R +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R (6a e - 6b d) |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +-------+ +--R (2b e x - 6a e + 8b d)\|e x + d +--R / +--R 2 +--R 3b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 914 + +--S 915 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- a e + b d +-+ +--R (a e - b d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (- 2a e + 2b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (- 2a e + 2b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R (2a e - 2b d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 918 + +)clear all + +--S 919 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ---------- +--R b x + a +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1353 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(3/2)+_ + 2*sqrt(d+e*x)/b +--R +--R +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +-+ +-------+ +--R - 2\|- a e + b d atanh(--------------) + 2\|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) -------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R +-------+ +--R 2\|e x + d +--R / +--R b +--R , +--R +---------+ +-------+ +--R |a e - b d \|e x + d +-------+ +--R - 2 |--------- atan(------------ + 2\|e x + d +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R -----------------------------------------------] +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 921 + +--S 922 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R 2\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +---------+ +-------+ +--R +-----------+ \|b \|e x + d +-+ |a e - b d \|e x + d +--R 2\|- a e + b d atanh(--------------) - 2\|b |--------- atan(------------) +--R +-----------+ \| b +---------+ +--R \|- a e + b d |a e - b d +--R |--------- +--R \| b +--R -------------------------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 925 + +)clear all + +--S 926 of 1353 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|e x + d +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1353 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(sqrt(b)*sqrt(b*d-a*e)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +--R 2atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R (2) - ---------------------- +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R [---------------------------------------------------------------------, +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R 2atan(------------------------) +--R a e - b d +--R -------------------------------] +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R Type: Union(List(Expression(Integer)),...) +--E 928 + +--S 929 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R 2\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R 2\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R 2\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 932 + +)clear all + +--S 933 of 1353 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) --------------------------------------- +--R 2 +-------+ +--R (b e x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1353 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(3/2)+_ + 2/((b*d-a*e)*sqrt(d+e*x)) +--R +--R +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +-----------+ +--R 2\|b \|e x + d atanh(--------------) - 2\|- a e + b d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------ +--R +-----------+ +-------+ +--R (a e - b d)\|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R - 2 +--R / +--R +-------+ +--R (a e - b d)\|e x + d +--R , +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R - 2 |--------- \|e x + d atan(----------------------- - 2 +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R ----------------------------------------------------------] +--R +-------+ +--R (a e - b d)\|e x + d +--R Type: Union(List(Expression(Integer)),...) +--E 935 + +--S 936 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R - 2\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-----------+ +--R (a e - b d)\|- a e + b d +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R - 2\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-----------+ | b b\|e x + d +--R - 2\|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R +-----------+ +--R (a e - b d)\|- a e + b d +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 939 + +)clear all + +--S 940 of 1353 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1353 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2))-2*b^(3/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b*d-a*e)^(5/2)+2*b/((b*d-a*e)^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R (- 6b e x - 6b d)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R (6b e x - 2a e + 8b d)\|- a e + b d +--R / +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e)x + 3a d e - 6a b d e + 3b d ) +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | b +-------+ +--R (3b e x + 3b d) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 6b e x - 2a e + 8b d +--R / +--R 2 3 2 2 2 2 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e)x + 3a d e - 6a b d e + 3b d )\|e x + d +--R , +--R +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R (6b e x + 6b d) |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 6b e x - 2a e + 8b d +--R / +--R 2 3 2 2 2 2 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e)x + 3a d e - 6a b d e + 3b d )\|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 942 + +--S 943 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R b\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R 2b\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 2 2 2 +-----------+ +--R (a e - 2a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R 2b\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-----------+ | b b\|e x + d +--R 2b\|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 2 2 2 2 +-----------+ +--R (a e - 2a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 946 + +)clear all + +--S 947 of 1353 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1353 +r0:=2/5/((b*d-a*e)*(d+e*x)^(5/2))+2/3*b/((b*d-a*e)^2*(d+e*x)^(3/2))-_ + 2*b^(5/2)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(7/2)+_ + 2*b^2/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-+ +-------+ \|b \|e x + d +--R (30b e x + 60b d e x + 30b d )\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 30b e x + (10a b e - 70b d e)x - 6a e + 22a b d e - 46b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (30a d e - 90a b d e + 90a b d e - 30b d e)x + 15a d e - 45a b d e +--R + +--R 2 4 3 5 +--R 45a b d e - 15b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 2 | b +-------+ +--R (15b e x + 30b d e x + 15b d ) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R - 30b e x + (10a b e - 70b d e)x - 6a e + 22a b d e - 46b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30a d e - 90a b d e + 90a b d e - 30b d e)x + 15a d e +--R + +--R 2 3 2 2 4 3 5 +--R - 45a b d e + 45a b d e - 15b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +---------+ +--R 2 2 2 2 2 2 | b +-------+ +--R (- 30b e x - 60b d e x - 30b d ) |--------- \|e x + d +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R - 30b e x + (10a b e - 70b d e)x - 6a e + 22a b d e - 46b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30a d e - 90a b d e + 90a b d e - 30b d e)x + 15a d e +--R + +--R 2 3 2 2 4 3 5 +--R - 45a b d e + 45a b d e - 15b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 949 + +--S 950 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R b \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R - 2b \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R - 2b \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-----------+ | b b\|e x + d +--R - 2b \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 953 + +)clear all + +--S 954 of 1353 +t0:=(a+b*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1353 +r0:=21/4*e^2*(b*d-a*e)*(d+e*x)^(3/2)/b^4+63/20*e^2*(d+e*x)^(5/2)/b^3-_ + 9/4*e*(d+e*x)^(7/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(9/2)/(b*(a+b*x)^2)-_ + 63/4*e^2*(b*d-a*e)^(5/2)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + b^(11/2)+63/4*e^2*(b*d-a*e)^2*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (- 315a b e + 630a b d e - 315b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (- 630a b e + 1260a b d e - 630a b d e )x - 315a e + 630a b d e +--R + +--R 2 2 2 2 +--R - 315a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 8b e x + (- 24a b e + 56b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (168a b e - 408a b d e + 288b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (525a b e - 1239a b d e + 831a b d e - 85b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 735a b d e + 483a b d e - 45a b d e - 10b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 7 2 6 2 5 +-+ +--R (20b x + 40a b x + 20a b )\|b +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 4 3 3 4 2 2 2 +--R (315a b e - 630a b d e + 315b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (630a b e - 1260a b d e + 630a b d e )x + 315a e - 630a b d e +--R + +--R 2 2 2 2 +--R 315a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 16b e x + (- 48a b e + 112b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (336a b e - 816a b d e + 576b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1050a b e - 2478a b d e + 1662a b d e - 170b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1470a b d e + 966a b d e - 90a b d e - 20b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 40b x + 80a b x + 40a b +--R , +--R +--R 2 2 4 3 3 4 2 2 2 +--R (- 315a b e + 630a b d e - 315b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (- 630a b e + 1260a b d e - 630a b d e )x - 315a e + 630a b d e +--R + +--R 2 2 2 2 +--R - 315a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 4 4 3 4 4 3 3 +--R 8b e x + (- 24a b e + 56b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (168a b e - 408a b d e + 288b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (525a b e - 1239a b d e + 831a b d e - 85b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 735a b d e + 483a b d e - 45a b d e - 10b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 20b x + 40a b x + 20a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 956 + +--S 957 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 4 3 2 2 2 |- a e + b d +-+ +--R (63a e - 126a b d e + 63b d e ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 4 3 2 2 2 +-----------+ \|b \|e x + d +--R (126a e - 252a b d e + 126b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 4 3 2 2 2 +-----------+ \|b \|e x + d +--R (63a e - 126a b d e + 63b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 4 3 2 2 2 +-+ |a e - b d \|e x + d +--R (- 63a e + 126a b d e - 63b d e )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1353 +r0:=35/12*e^2*(d+e*x)^(3/2)/b^3-7/4*e*(d+e*x)^(5/2)/(b^2*(a+b*x))-_ + 1/2*(d+e*x)^(7/2)/(b*(a+b*x)^2)-35/4*e^2*(b*d-a*e)^(3/2)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+35/4*e^2*(b*d-a*e)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (105a b e - 105b d e )x + (210a b e - 210a b d e )x + 105a e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 8b e x + (- 56a b e + 80b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 175a b e + 238a b d e - 39b d e)x - 105a e + 140a b d e +--R + +--R 2 2 3 3 +--R - 21a b d e - 6b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 2 5 2 4 +-+ +--R (12b x + 24a b x + 12a b )\|b +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (105a b e - 105b d e )x + (210a b e - 210a b d e )x + 105a e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 16b e x + (- 112a b e + 160b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 350a b e + 476a b d e - 78b d e)x - 210a e + 280a b d e +--R + +--R 2 2 3 3 +--R - 42a b d e - 12b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 24b x + 48a b x + 24a b +--R , +--R +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (105a b e - 105b d e )x + (210a b e - 210a b d e )x + 105a e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 8b e x + (- 56a b e + 80b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 175a b e + 238a b d e - 39b d e)x - 105a e + 140a b d e +--R + +--R 2 2 3 3 +--R - 21a b d e - 6b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 12b x + 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 963 + +--S 964 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 |- a e + b d +-+ +--R (35a e - 35b d e ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 2 +-----------+ \|b \|e x + d +--R (- 70a e + 70b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 +-----------+ \|b \|e x + d +--R (- 35a e + 35b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 3 2 +-+ |a e - b d \|e x + d +--R (35a e - 35b d e )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 967 + +)clear all + +--S 968 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1353 +r0:=-5/4*e*(d+e*x)^(3/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(5/2)/(b*(a+b*x)^2)-_ + 15/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+_ + 15/4*e^2*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-----------+ \|b \|e x + d +--R (- 15b e x - 30a b e x - 15a e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-------+ +--R (8b e x + (25a b e - 9b d e)x + 15a e - 5a b d e - 2b d )\|b \|e x + d +--R / +--R 5 2 4 2 3 +-+ +--R (4b x + 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 2 |- a e + b d +--R (15b e x + 30a b e x + 15a e ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (16b e x + (50a b e - 18b d e)x + 30a e - 10a b d e - 4b d )\|e x + d +--R / +--R 5 2 4 2 3 +--R 8b x + 16a b x + 8a b +--R , +--R +--R +---------+ +-------+ +--R 2 2 2 2 2 2 |a e - b d \|e x + d +--R (- 15b e x - 30a b e x - 15a e ) |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (8b e x + (25a b e - 9b d e)x + 15a e - 5a b d e - 2b d )\|e x + d +--R / +--R 5 2 4 2 3 +--R 4b x + 8a b x + 4a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 970 + +--S 971 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 |- a e + b d +-+ +--R 15e |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-----------+ \|b \|e x + d +--R 30e \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-----------+ \|b \|e x + d +--R 15e \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-+ |a e - b d \|e x + d +--R - 15e \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 974 + +)clear all + +--S 975 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 975 + +--S 976 of 1353 +r0:=-1/2*(d+e*x)^(3/2)/(b*(a+b*x)^2)-3/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))-3/4*e*sqrt(d+e*x)/(b^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- 3b e x - 6a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (- 5b e x - 3a e - 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 4 2 3 2 2 +-----------+ +-+ +--R (4b x + 8a b x + 4a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R (3b e x + 6a b e x + 3a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (- 10b e x - 6a e - 4b d)\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 4 2 3 2 2 | 2 +--R (8b x + 16a b x + 8a b )\|- a b e + b d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 2 2 2 2 2 2 \|a b e - b d \|e x + d +--R (3b e x + 6a b e x + 3a e )atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (- 5b e x - 3a e - 2b d)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 4 2 3 2 2 | 2 +--R (4b x + 8a b x + 4a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 977 + +--S 978 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R 3e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R 6e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R 8b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R 3e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R 3e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R 4b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 981 + +)clear all + +--S 982 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1353 +r0:=1/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + (b*d-a*e)^(3/2))-1/2*sqrt(d+e*x)/(b*(a+b*x)^2)-1/4*e*_ + sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- b e x - 2a b e x - a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (b e x - a e + 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 3 4 2 2 2 3 3 2 2 +-----------+ +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|- a e + b d +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R (b e x + 2a b e x + a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (2b e x - 2a e + 4b d)\|- a b e + b d \|e x + d +--R / +--R 3 4 2 2 2 3 3 2 2 +--R ((8a b e - 8b d)x + (16a b e - 16a b d)x + 8a b e - 8a b d) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 2 2 2 2 2 2 \|a b e - b d \|e x + d +--R (b e x + 2a b e x + a e )atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (b e x - a e + 2b d)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 3 4 2 2 2 3 3 2 2 | 2 +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 984 + +--S 985 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R 2e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R (8a b e - 8b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R (4a b e - 4b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 988 + +)clear all + +--S 989 of 1353 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1353 +r0:=-3/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(5/2)*_ + sqrt(b))-1/2*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^2)+3/4*e*sqrt(d+e*x)/_ + ((b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- 3b e x - 6a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (3b e x + 5a e - 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 2 +--R 4a e - 8a b d e + 4a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 990 + +--S 991 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R (3b e x + 6a b e x + 3a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (6b e x + 10a e - 4b d)\|- a b e + b d \|e x + d +--R / +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (8a b e - 16a b d e + 8b d )x + (16a b e - 32a b d e + 16a b d )x +--R + +--R 4 2 3 2 2 2 +--R 8a e - 16a b d e + 8a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 2 2 2 2 2 2 \|a b e - b d \|e x + d +--R (3b e x + 6a b e x + 3a e )atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (3b e x + 5a e - 2b d)\|a b e - b d \|e x + d +--R / +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 2 +--R 4a e - 8a b d e + 4a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 991 + +--S 992 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R 3e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R 6e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 2 | 2 +-----------+ +-+ +--R (8a e - 16a b d e + 8b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R 3e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R 3e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 2 +-----------+ +-+ | 2 +--R (4a e - 8a b d e + 4b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 1353 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1353 +r0:=-15/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/_ + (b*d-a*e)^(7/2)+15/4*e^2/((b*d-a*e)^3*sqrt(d+e*x))+(-1/2)/((b*d-a*e)*_ + (a+b*x)^2*sqrt(d+e*x))+5/4*e/((b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-+ +-------+ \|b \|e x + d +--R (15b e x + 30a b e x + 15a e )\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 15b e x + (- 25a b e - 5b d e)x - 8a e - 9a b d e + 2b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 2 | b +-------+ +--R (15b e x + 30a b e x + 15a e ) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R - 30b e x + (- 50a b e - 10b d e)x - 16a e - 18a b d e + 4b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (8a b e - 24a b d e + 24a b d e - 8b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (16a b e - 48a b d e + 48a b d e - 16a b d )x + 8a e - 24a b d e +--R + +--R 3 2 2 2 3 3 +--R 24a b d e - 8a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +---------+ +--R 2 2 2 2 2 2 | b +-------+ +--R (- 15b e x - 30a b e x - 15a e ) |--------- \|e x + d +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R - 15b e x + (- 25a b e - 5b d e)x - 8a e - 9a b d e + 2b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 998 + +--S 999 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R 15e \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R - 30e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (8a e - 24a b d e + 24a b d e - 8b d )\|- a e + b d +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R - 15e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-----------+ | b b\|e x + d +--R - 15e \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (4a e - 12a b d e + 12a b d e - 4b d )\|- a e + b d +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1002 + +)clear all + +--S 1003 of 1353 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1353 +r0:=35/12*e^2/((b*d-a*e)^3*(d+e*x)^(3/2))+(-1/2)/((b*d-a*e)*(a+b*x)^2*_ + (d+e*x)^(3/2))+7/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2))-35/4*b^(3/2)*_ + e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+35/4*b*_ + e^2/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 210a b e - 105b d e )x +--R + +--R 2 3 2 2 2 2 +--R (- 105a b e - 210a b d e )x - 105a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (175a b e + 140b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (56a b e + 238a b d e + 21b d e)x - 8a e + 80a b d e + 39a b d e +--R + +--R 3 3 +--R - 6b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e + 24a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 105b e x + (210a b e + 105b d e )x + (105a b e + 210a b d e )x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 210b e x + (350a b e + 280b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (112a b e + 476a b d e + 42b d e)x - 16a e + 160a b d e + 78a b d e +--R + +--R 3 3 +--R - 12b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 48a b e - 168a b d e + 192a b d e - 48a b d e - 48a b d e +--R + +--R 6 5 +--R 24b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 24a e - 48a b d e - 48a b d e + 192a b d e - 168a b d e +--R + +--R 5 5 +--R 48a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 24a d e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 105b e x + (210a b e + 105b d e )x + (105a b e + 210a b d e )x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (175a b e + 140b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (56a b e + 238a b d e + 21b d e)x - 8a e + 80a b d e + 39a b d e +--R + +--R 3 3 +--R - 6b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e +--R + +--R 5 5 +--R 24a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1005 + +--S 1006 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R 35b e \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R 70b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (8a e - 32a b d e + 48a b d e - 32a b d e + 8b d )\|- a e + b d +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R 35b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-----------+ | b b\|e x + d +--R 35b e \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (4a e - 16a b d e + 24a b d e - 16a b d e + 4b d )\|- a e + b d +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1009 + +)clear all + +--S 1010 of 1353 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1353 +r0:=63/20*e^2/((b*d-a*e)^3*(d+e*x)^(5/2))+(-1/2)/((b*d-a*e)*(a+b*x)^2*_ + (d+e*x)^(5/2))+9/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2))+21/4*b*_ + e^2/((b*d-a*e)^4*(d+e*x)^(3/2))-63/4*b^(5/2)*e^2*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(11/2)+63/4*b^2*e^2/((b*d-a*e)^5*_ + sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (630a b e + 630b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (315a b e + 1260a b d e + 315b d e )x +--R + +--R 2 2 3 3 2 2 2 2 2 2 +--R (630a b d e + 630a b d e )x + 315a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 525a b e - 735b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 168a b e - 1239a b d e - 483b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (24a b e - 408a b d e - 831a b d e - 45b d e)x - 8a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 56a b d e - 288a b d e - 85a b d e + 10b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 20a b e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 7 5 2 +--R - 20b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 40a b e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 7 6 +--R - 40b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 20a e - 20a b d e - 180a b d e + 500a b d e - 500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 180a b d e + 20a b d e - 20b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 40a d e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 6 7 +--R - 40a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 20a d e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 2 5 7 +--R - 20a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (630a b e + 630b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (315a b e + 1260a b d e + 315b d e )x +--R + +--R 2 2 3 3 2 2 2 2 2 2 +--R (630a b d e + 630a b d e )x + 315a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R - 630b e x + (- 1050a b e - 1470b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 336a b e - 2478a b d e - 966b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (48a b e - 816a b d e - 1662a b d e - 90b d e)x - 16a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 112a b d e - 576a b d e - 170a b d e + 20b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 40a b e - 200a b d e + 400a b d e - 400a b d e + 200a b d e +--R + +--R 7 5 2 +--R - 40b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 80a b e - 320a b d e + 400a b d e - 400a b d e + 320a b d e +--R + +--R 7 6 +--R - 80b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 40a e - 40a b d e - 360a b d e + 1000a b d e - 1000a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 360a b d e + 40a b d e - 40b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 80a d e - 320a b d e + 400a b d e - 400a b d e + 320a b d e +--R + +--R 6 7 +--R - 80a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 40a d e - 200a b d e + 400a b d e - 400a b d e + 200a b d e +--R + +--R 2 5 7 +--R - 40a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 630a b e - 630b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 315a b e - 1260a b d e - 315b d e )x +--R + +--R 2 2 3 3 2 2 2 2 2 2 +--R (- 630a b d e - 630a b d e )x - 315a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 525a b e - 735b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 168a b e - 1239a b d e - 483b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (24a b e - 408a b d e - 831a b d e - 45b d e)x - 8a e + 56a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 288a b d e - 85a b d e + 10b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 20a b e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 7 5 2 +--R - 20b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 40a b e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 7 6 +--R - 40b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 20a e - 20a b d e - 180a b d e + 500a b d e - 500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 180a b d e + 20a b d e - 20b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 40a d e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 6 7 +--R - 40a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 20a d e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 2 5 7 +--R - 20a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1012 + +--S 1013 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 +-----------+ | b +--R 63b e \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R - 126b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (8a e - 40a b d e + 80a b d e - 80a b d e + 40a b d e - 8b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R - 63b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 2 +-----------+ | b b\|e x + d +--R - 63b e \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (4a e - 20a b d e + 40a b d e - 40a b d e + 20a b d e - 4b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1016 + +)clear all + +--S 1017 of 1353 +t0:=(a+b*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1353 +r0:=385/64*e^4*(d+e*x)^(3/2)/b^5-231/64*e^3*(d+e*x)^(5/2)/(b^4*(a+b*x))-_ + 33/32*e^2*(d+e*x)^(7/2)/(b^3*(a+b*x)^2)-11/24*e*(d+e*x)^(9/2)/(b^2*_ + (a+b*x)^3)-1/4*(d+e*x)^(11/2)/(b*(a+b*x)^4)-1155/64*e^4*(b*d-a*e)^(3/2)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(13/2)+1155/64*e^4*(b*d-_ + a*e)*sqrt(d+e*x)/b^6 +--R +--R +--R (2) +--R 4 5 5 4 4 2 3 5 4 4 3 +--R (3465a b e - 3465b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 +--R (20790a b e - 20790a b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 5 5 4 4 +--R 3465a e - 3465a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R 128b e x + (- 1408a b e + 2048b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 9207a b e + 12782a b d e - 2295b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 16863a b e + 22968a b d e - 3795a b d e - 1030b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 +--R - 12705a b e + 17094a b d e - 2673a b d e - 748a b d e +--R + +--R 5 4 +--R - 328b d e +--R * +--R x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 3465a e + 4620a b d e - 693a b d e - 198a b d e - 88a b d e +--R + +--R 5 5 +--R - 48b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|b +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 5 5 4 4 2 3 5 4 4 3 +--R (3465a b e - 3465b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 +--R (20790a b e - 20790a b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 5 5 4 4 +--R 3465a e - 3465a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 5 5 5 4 5 5 4 4 +--R 256b e x + (- 2816a b e + 4096b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 18414a b e + 25564a b d e - 4590b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 33726a b e + 45936a b d e - 7590a b d e - 2060b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 +--R - 25410a b e + 34188a b d e - 5346a b d e - 1496a b d e +--R + +--R 5 4 +--R - 656b d e +--R * +--R x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 6930a e + 9240a b d e - 1386a b d e - 396a b d e - 176a b d e +--R + +--R 5 5 +--R - 96b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 384b x + 1536a b x + 2304a b x + 1536a b x + 384a b +--R , +--R +--R 4 5 5 4 4 2 3 5 4 4 3 +--R (3465a b e - 3465b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 +--R (20790a b e - 20790a b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 5 5 4 4 +--R 3465a e - 3465a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 5 5 5 4 5 5 4 4 +--R 128b e x + (- 1408a b e + 2048b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 9207a b e + 12782a b d e - 2295b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 16863a b e + 22968a b d e - 3795a b d e - 1030b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 +--R - 12705a b e + 17094a b d e - 2673a b d e - 748a b d e +--R + +--R 5 4 +--R - 328b d e +--R * +--R x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 3465a e + 4620a b d e - 693a b d e - 198a b d e - 88a b d e +--R + +--R 5 5 +--R - 48b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 192b x + 768a b x + 1152a b x + 768a b x + 192a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1019 + +--S 1020 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 5 4 |- a e + b d +-+ +--R (1155a e - 1155b d e ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 5 4 +-----------+ \|b \|e x + d +--R (- 2310a e + 2310b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 +-+ +--R 128b \|b +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 5 4 +-----------+ \|b \|e x + d +--R (- 1155a e + 1155b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 5 4 +-+ |a e - b d \|e x + d +--R (1155a e - 1155b d e )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 6 +-+ +--R 64b \|b +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1023 + +)clear all + +--S 1024 of 1353 +t0:=(a+b*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1353 +r0:=-105/64*e^3*(d+e*x)^(3/2)/(b^4*(a+b*x))-21/32*e^2*(d+e*x)^(5/2)/_ + (b^3*(a+b*x)^2)-3/8*e*(d+e*x)^(7/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(9/2)/_ + (b*(a+b*x)^4)-315/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b*d-a*e)/b^(11/2)+315/64*e^4*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 315b e x - 1260a b e x - 1890a b e x - 1260a b e x - 315a e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 128b e x + (837a b e - 325b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1533a b e - 555a b d e - 210b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1155a b e - 399a b d e - 156a b d e - 88b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 105a b d e - 42a b d e - 24a b d e - 16b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +-+ +--R (64b x + 256a b x + 384a b x + 256a b x + 64a b )\|b +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (315b e x + 1260a b e x + 1890a b e x + 1260a b e x + 315a e ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 256b e x + (1674a b e - 650b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (3066a b e - 1110a b d e - 420b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (2310a b e - 798a b d e - 312a b d e - 176b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 210a b d e - 84a b d e - 48a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 128b x + 512a b x + 768a b x + 512a b x + 128a b +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 315b e x - 1260a b e x - 1890a b e x - 1260a b e x - 315a e ) +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 4 4 3 4 4 3 3 +--R 128b e x + (837a b e - 325b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1533a b e - 555a b d e - 210b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1155a b e - 399a b d e - 156a b d e - 88b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 105a b d e - 42a b d e - 24a b d e - 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 64b x + 256a b x + 384a b x + 256a b x + 64a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1026 + +--S 1027 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 |- a e + b d +-+ +--R 315e |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 4 +-----------+ \|b \|e x + d +--R 630e \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 128b \|b +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 +-----------+ \|b \|e x + d +--R 315e \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 4 +-+ |a e - b d \|e x + d +--R - 315e \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R 64b \|b +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1030 + +)clear all + +--S 1031 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1353 +r0:=-35/96*e^2*(d+e*x)^(3/2)/(b^3*(a+b*x)^2)-7/24*e*(d+e*x)^(5/2)/_ + (b^2*(a+b*x)^3)-1/4*(d+e*x)^(7/2)/(b*(a+b*x)^4)-35/64*e^4*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(b*d-a*e))-_ + 35/64*e^3*sqrt(d+e*x)/(b^4*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 105b e x - 420a b e x - 630a b e x - 420a b e x - 105a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 279b e x + (- 511a b e - 326b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 385a b e - 252a b d e - 200b d e)x - 105a e - 70a b d e +--R + +--R 2 2 3 3 +--R - 56a b d e - 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +-----------+ +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (105b e x + 420a b e x + 630a b e x + 420a b e x + 105a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R - 558b e x + (- 1022a b e - 652b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 770a b e - 504a b d e - 400b d e)x - 210a e - 140a b d e +--R + +--R 2 2 3 3 +--R - 112a b d e - 96b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 8 4 7 3 2 6 2 3 5 4 4 | 2 +--R (384b x + 1536a b x + 2304a b x + 1536a b x + 384a b )\|- a b e + b d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (105b e x + 420a b e x + 630a b e x + 420a b e x + 105a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 279b e x + (- 511a b e - 326b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 385a b e - 252a b d e - 200b d e)x - 105a e - 70a b d e +--R + +--R 2 2 3 3 +--R - 56a b d e - 48b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 8 4 7 3 2 6 2 3 5 4 4 | 2 +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1033 + +--S 1034 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 35e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 70e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 4 | 2 +-----------+ +-+ +--R 128b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 35e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b e - b d \|e x + d +--R 35e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 4 +-----------+ +-+ | 2 +--R 64b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1037 + +)clear all + +--S 1038 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1353 +r0:=-5/24*e*(d+e*x)^(3/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(5/2)/(b*(a+b*x)^4)+_ + 5/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*_ + (b*d-a*e)^(3/2))-5/32*e^2*sqrt(d+e*x)/(b^3*(a+b*x)^2)-5/64*e^3*_ + sqrt(d+e*x)/(b^3*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 15b e x - 60a b e x - 90a b e x - 60a b e x - 15a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (- 73a b e + 118b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 55a b e - 36a b d e + 136b d e)x - 15a e - 10a b d e +--R + +--R 2 2 3 3 +--R - 8a b d e + 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 8 4 2 6 7 3 +--R (192a b e - 192b d)x + (768a b e - 768a b d)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 4 4 +--R (1152a b e - 1152a b d)x + (768a b e - 768a b d)x + 192a b e - 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (- 146a b e + 236b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 110a b e - 72a b d e + 272b d e)x - 30a e - 20a b d e +--R + +--R 2 2 3 3 +--R - 16a b d e + 96b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 7 8 4 2 6 7 3 +--R (384a b e - 384b d)x + (1536a b e - 1536a b d)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 +--R (2304a b e - 2304a b d)x + (1536a b e - 1536a b d)x + 384a b e +--R + +--R 4 4 +--R - 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (- 73a b e + 118b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 55a b e - 36a b d e + 136b d e)x - 15a e - 10a b d e +--R + +--R 2 2 3 3 +--R - 8a b d e + 48b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 7 8 4 2 6 7 3 +--R (192a b e - 192b d)x + (768a b e - 768a b d)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 +--R (1152a b e - 1152a b d)x + (768a b e - 768a b d)x + 192a b e +--R + +--R 4 4 +--R - 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1040 + +--S 1041 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 5e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 10e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 4 | 2 +-----------+ +-+ +--R (128a b e - 128b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 5e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b e - b d \|e x + d +--R 5e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 3 4 +-----------+ +-+ | 2 +--R (64a b e - 64b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1353 +r0:=-1/4*(d+e*x)^(3/2)/(b*(a+b*x)^4)-3/64*e^4*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(5/2))-1/8*e*_ + sqrt(d+e*x)/(b^2*(a+b*x)^3)-1/32*e^2*sqrt(d+e*x)/(b^2*(b*d-a*e)*_ + (a+b*x)^2)+3/64*e^3*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 3b e x - 12a b e x - 18a b e x - 12a b e x - 3a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 3b e x + (11a b e - 2b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 11a b e + 44a b d e - 24b d e)x - 3a e - 2a b d e + 24a b d e +--R + +--R 3 3 +--R - 16b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 6 2 7 8 2 4 +--R (64a b e - 128a b d e + 64b d )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (256a b e - 512a b d e + 256a b d )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (384a b e - 768a b d e + 384a b d )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 4 4 2 +--R (256a b e - 512a b d e + 256a b d )x + 64a b e - 128a b d e + 64a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (3b e x + 12a b e x + 18a b e x + 12a b e x + 3a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b e x + (22a b e - 4b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 22a b e + 88a b d e - 48b d e)x - 6a e - 4a b d e +--R + +--R 2 2 3 3 +--R 48a b d e - 32b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 6 2 7 8 2 4 +--R (128a b e - 256a b d e + 128b d )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (512a b e - 1024a b d e + 512a b d )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (768a b e - 1536a b d e + 768a b d )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 +--R (512a b e - 1024a b d e + 512a b d )x + 128a b e - 256a b d e +--R + +--R 4 4 2 +--R 128a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (3b e x + 12a b e x + 18a b e x + 12a b e x + 3a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 3b e x + (11a b e - 2b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 11a b e + 44a b d e - 24b d e)x - 3a e - 2a b d e +--R + +--R 2 2 3 3 +--R 24a b d e - 16b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 6 2 7 8 2 4 +--R (64a b e - 128a b d e + 64b d )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (256a b e - 512a b d e + 256a b d )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (384a b e - 768a b d e + 384a b d )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 +--R (256a b e - 512a b d e + 256a b d )x + 64a b e - 128a b d e +--R + +--R 4 4 2 +--R 64a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1047 + +--S 1048 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 3e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 6e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 3 4 2 | 2 +-----------+ +-+ +--R (128a b e - 256a b d e + 128b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 3e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b e - b d \|e x + d +--R 3e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 3 4 2 +-----------+ +-+ | 2 +--R (64a b e - 128a b d e + 64b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1051 + +)clear all + +--S 1052 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R \|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1353 +r0:=5/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + (b*d-a*e)^(7/2))-1/4*sqrt(d+e*x)/(b*(a+b*x)^4)-1/24*e*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^3)+5/96*e^2*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x)^2)-_ + 5/64*e^3*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 15b e x - 60a b e x - 90a b e x - 60a b e x - 15a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (55a b e - 10b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (73a b e - 36a b d e + 8b d e)x - 15a e + 118a b d e - 136a b d e +--R + +--R 3 3 +--R 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (1152a b e - 3456a b d e + 3456a b d e - 1152a b d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x + 192a b e +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (110a b e - 20b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (146a b e - 72a b d e + 16b d e)x - 30a e + 236a b d e +--R + +--R 2 2 3 3 +--R - 272a b d e + 96b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (384a b e - 1152a b d e + 1152a b d e - 384b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (2304a b e - 6912a b d e + 6912a b d e - 2304a b d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x + 384a b e +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 1152a b d e + 1152a b d e - 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (55a b e - 10b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (73a b e - 36a b d e + 8b d e)x - 15a e + 118a b d e +--R + +--R 2 2 3 3 +--R - 136a b d e + 48b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (1152a b e - 3456a b d e + 3456a b d e - 1152a b d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x + 192a b e +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1054 + +--S 1055 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 5e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 10e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 3 2 2 2 3 2 4 3 | 2 +--R (128a b e - 384a b d e + 384a b d e - 128b d )\|- a b e + b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 5e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b e - b d \|e x + d +--R 5e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R 3 3 2 2 2 3 2 4 3 +-----------+ +-+ +--R (64a b e - 192a b d e + 192a b d e - 64b d )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1058 + +)clear all + +--S 1059 of 1353 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1353 +r0:=-35/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*_ + sqrt(b))-1/4*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^4)+7/24*e*sqrt(d+e*x)/_ + ((b*d-a*e)^2*(a+b*x)^3)-35/96*e^2*sqrt(d+e*x)/((b*d-a*e)^3*(a+b*x)^2)+_ + 35/64*e^3*sqrt(d+e*x)/((b*d-a*e)^4*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 105b e x - 420a b e x - 630a b e x - 420a b e x - 105a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (385a b e - 70b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (511a b e - 252a b d e + 56b d e)x + 279a e - 326a b d e +--R + +--R 2 2 3 3 +--R 200a b d e - 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (1152a b e - 4608a b d e + 6912a b d e - 4608a b d e + 1152a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 192a e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (105b e x + 420a b e x + 630a b e x + 420a b e x + 105a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 210b e x + (770a b e - 140b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (1022a b e - 504a b d e + 112b d e)x + 558a e - 652a b d e +--R + +--R 2 2 3 3 +--R 400a b d e - 96b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (384a b e - 1536a b d e + 2304a b d e - 1536a b d e + 384b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 +--R 1536a b e - 6144a b d e + 9216a b d e - 6144a b d e +--R + +--R 7 4 +--R 1536a b d +--R * +--R 3 +--R x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 +--R 2304a b e - 9216a b d e + 13824a b d e - 9216a b d e +--R + +--R 2 6 4 +--R 2304a b d +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 +--R 1536a b e - 6144a b d e + 9216a b d e - 6144a b d e +--R + +--R 3 5 4 +--R 1536a b d +--R * +--R x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 384a e - 1536a b d e + 2304a b d e - 1536a b d e + 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (105b e x + 420a b e x + 630a b e x + 420a b e x + 105a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (385a b e - 70b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (511a b e - 252a b d e + 56b d e)x + 279a e - 326a b d e +--R + +--R 2 2 3 3 +--R 200a b d e - 48b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 +--R 1152a b e - 4608a b d e + 6912a b d e - 4608a b d e +--R + +--R 2 6 4 +--R 1152a b d +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 192a e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1061 + +--S 1062 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 35e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 70e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (128a e - 512a b d e + 768a b d e - 512a b d e + 128b d ) +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 35e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b e - b d \|e x + d +--R 35e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (64a e - 256a b d e + 384a b d e - 256a b d e + 64b d )\|- a e + b d +--R * +--R +-----------+ +--R +-+ | 2 +--R \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1065 + +)clear all + +--S 1066 of 1353 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 6 4 5 5 2 3 4 4 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (10a b e + 10a b d)x + (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1353 +r0:=-315/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-_ + a*e)^(11/2)+315/64*e^4/((b*d-a*e)^5*sqrt(d+e*x))+(-1/4)/((b*d-a*e)*_ + (a+b*x)^4*sqrt(d+e*x))+3/8*e/((b*d-a*e)^2*(a+b*x)^3*sqrt(d+e*x))-_ + 21/32*e^2/((b*d-a*e)^3*(a+b*x)^2*sqrt(d+e*x))+105/64*e^3/((b*d-a*e)^4*_ + (a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +-+ +--R (315b e x + 1260a b e x + 1890a b e x + 1260a b e x + 315a e )\|b +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 1155a b e - 105b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1533a b e - 399a b d e + 42b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 837a b e - 555a b d e + 156a b d e - 24b d e)x - 128a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 325a b d e + 210a b d e - 88a b d e + 16b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 64a b e - 320a b d e + 640a b d e - 640a b d e + 320a b d e +--R + +--R 9 5 +--R - 64b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 2 7 4 8 5 +--R 1280a b d e - 256a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 384a b e - 1920a b d e + 3840a b d e - 3840a b d e +--R + +--R 3 6 4 2 7 5 +--R 1920a b d e - 384a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 4 5 4 3 6 5 +--R 1280a b d e - 256a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 4 5 5 +--R 64a e - 320a b d e + 640a b d e - 640a b d e + 320a b d e - 64a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (315b e x + 1260a b e x + 1890a b e x + 1260a b e x + 315a e ) +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R - 630b e x + (- 2310a b e - 210b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 3066a b e - 798a b d e + 84b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 1674a b e - 1110a b d e + 312a b d e - 48b d e)x - 256a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 650a b d e + 420a b d e - 176a b d e + 32b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 +--R 128a b e - 640a b d e + 1280a b d e - 1280a b d e +--R + +--R 8 4 9 5 +--R 640a b d e - 128b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 512a b e - 2560a b d e + 5120a b d e - 5120a b d e +--R + +--R 2 7 4 8 5 +--R 2560a b d e - 512a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 768a b e - 3840a b d e + 7680a b d e - 7680a b d e +--R + +--R 3 6 4 2 7 5 +--R 3840a b d e - 768a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 512a b e - 2560a b d e + 5120a b d e - 5120a b d e +--R + +--R 4 5 4 3 6 5 +--R 2560a b d e - 512a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 128a e - 640a b d e + 1280a b d e - 1280a b d e + 640a b d e +--R + +--R 4 5 5 +--R - 128a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 315b e x - 1260a b e x - 1890a b e x - 1260a b e x - 315a e ) +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 1155a b e - 105b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1533a b e - 399a b d e + 42b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 837a b e - 555a b d e + 156a b d e - 24b d e)x - 128a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 325a b d e + 210a b d e - 88a b d e + 16b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 64a b e - 320a b d e + 640a b d e - 640a b d e + 320a b d e +--R + +--R 9 5 +--R - 64b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 2 7 4 8 5 +--R 1280a b d e - 256a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 384a b e - 1920a b d e + 3840a b d e - 3840a b d e +--R + +--R 3 6 4 2 7 5 +--R 1920a b d e - 384a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 4 5 4 3 6 5 +--R 1280a b d e - 256a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 64a e - 320a b d e + 640a b d e - 640a b d e + 320a b d e +--R + +--R 4 5 5 +--R - 64a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1068 + +--S 1069 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 +-----------+ | b +--R 315e \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 4 +-+ \|b \|e x + d +--R - 630e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 128a e - 640a b d e + 1280a b d e - 1280a b d e + 640a b d e +--R + +--R 5 5 +--R - 128b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 +-+ \|b \|e x + d +--R - 315e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 4 +-----------+ | b b\|e x + d +--R - 315e \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (64a e - 320a b d e + 640a b d e - 640a b d e + 320a b d e - 64b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1072 + +)clear all + +--S 1073 of 1353 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1353 +r0:=385/64*e^4/((b*d-a*e)^5*(d+e*x)^(3/2))+(-1/4)/((b*d-a*e)*(a+b*x)^4*_ + (d+e*x)^(3/2))+11/24*e/((b*d-a*e)^2*(a+b*x)^3*(d+e*x)^(3/2))-_ + 33/32*e^2/((b*d-a*e)^3*(a+b*x)^2*(d+e*x)^(3/2))+231/64*e^3/((b*d-a*e)^4*_ + (a+b*x)*(d+e*x)^(3/2))-1155/64*b^(3/2)*e^4*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b*d-a*e)^(13/2)+1155/64*b*e^4/((b*d-a*e)^6*sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 3465b e x + (- 13860a b e - 3465b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (- 20790a b e - 13860a b d e )x + (- 13860a b e - 20790a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (- 3465a b e - 13860a b d e )x - 3465a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (12705a b e + 4620b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (16863a b e + 17094a b d e + 693b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (9207a b e + 22968a b d e + 2673a b d e - 198b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (1408a b e + 12782a b d e + 3795a b d e - 748a b d e + 88b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 128a e + 2048a b d e + 2295a b d e - 1030a b d e + 328a b d e +--R + +--R 5 5 +--R - 48b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 768a b e - 4416a b d e + 10368a b d e - 12480a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 7680a b d e - 1728a b d e - 384a b d e + 192b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 1152a b e - 6144a b d e + 12672a b d e - 11520a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 1920a b d e + 4608a b d e - 3456a b d e + 768a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 768a b e - 3456a b d e + 4608a b d e + 1920a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 11520a b d e + 12672a b d e - 6144a b d e + 1152a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 192a e - 384a b d e - 1728a b d e + 7680a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 12480a b d e + 10368a b d e - 4416a b d e + 768a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e + 2880a b d e +--R + +--R 5 5 6 4 6 7 +--R - 1152a b d e + 192a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (13860a b e + 3465b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (20790a b e + 13860a b d e )x + (13860a b e + 20790a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (3465a b e + 13860a b d e )x + 3465a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 5 5 5 4 5 5 4 4 +--R 6930b e x + (25410a b e + 9240b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (33726a b e + 34188a b d e + 1386b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (18414a b e + 45936a b d e + 5346a b d e - 396b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2816a b e + 25564a b d e + 7590a b d e - 1496a b d e + 176b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 256a e + 4096a b d e + 4590a b d e - 2060a b d e + 656a b d e +--R + +--R 5 5 +--R - 96b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 384a b e - 2304a b d e + 5760a b d e - 7680a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 5760a b d e - 2304a b d e + 384b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 1536a b e - 8832a b d e + 20736a b d e - 24960a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 15360a b d e - 3456a b d e - 768a b d e + 384b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 2304a b e - 12288a b d e + 25344a b d e - 23040a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 3840a b d e + 9216a b d e - 6912a b d e + 1536a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 1536a b e - 6912a b d e + 9216a b d e + 3840a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 23040a b d e + 25344a b d e - 12288a b d e + 2304a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 384a e - 768a b d e - 3456a b d e + 15360a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 24960a b d e + 20736a b d e - 8832a b d e + 1536a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 +--R 384a d e - 2304a b d e + 5760a b d e - 7680a b d e +--R + +--R 6 4 5 2 5 5 6 4 6 7 +--R 5760a b d e - 2304a b d e + 384a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (13860a b e + 3465b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (20790a b e + 13860a b d e )x + (13860a b e + 20790a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (3465a b e + 13860a b d e )x + 3465a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (12705a b e + 4620b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (16863a b e + 17094a b d e + 693b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (9207a b e + 22968a b d e + 2673a b d e - 198b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (1408a b e + 12782a b d e + 3795a b d e - 748a b d e + 88b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 128a e + 2048a b d e + 2295a b d e - 1030a b d e + 328a b d e +--R + +--R 5 5 +--R - 48b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 768a b e - 4416a b d e + 10368a b d e - 12480a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 7680a b d e - 1728a b d e - 384a b d e + 192b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 1152a b e - 6144a b d e + 12672a b d e - 11520a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 1920a b d e + 4608a b d e - 3456a b d e + 768a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 768a b e - 3456a b d e + 4608a b d e + 1920a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 11520a b d e + 12672a b d e - 6144a b d e + 1152a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 192a e - 384a b d e - 1728a b d e + 7680a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 12480a b d e + 10368a b d e - 4416a b d e + 768a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 6 4 5 2 5 5 6 4 6 7 +--R 2880a b d e - 1152a b d e + 192a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1075 + +--S 1076 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 +-----------+ | b +--R 1155b e \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 4 +-+ \|b \|e x + d +--R 2310b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 128a e - 768a b d e + 1920a b d e - 2560a b d e + 1920a b d e +--R + +--R 5 5 6 6 +--R - 768a b d e + 128b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 +-+ \|b \|e x + d +--R 1155b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 4 +-----------+ | b b\|e x + d +--R 1155b e \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 64a e - 384a b d e + 960a b d e - 1280a b d e + 960a b d e +--R + +--R 5 5 6 6 +--R - 384a b d e + 64b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1079 + +)clear all + +--S 1080 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1353 +r0:=-8/143*(b*d-a*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/1287*(b*d-a*e)^2*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+_ + b*x))+2/13*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 +--R 198b e x + (468a b e + 720b d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (286a e + 1768a b d e + 916b d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (1144a d e + 2392a b d e + 424b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (1716a d e + 1248a b d e + 6b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (1144a d e + 52a b d e - 8b d e)x + 286a d e - 104a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 6 2 5 5 +--R 198b e x + (468a b e + 720b d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (286a e + 1768a b d e + 916b d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (1144a d e + 2392a b d e + 424b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (1716a d e + 1248a b d e + 6b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (1144a d e + 52a b d e - 8b d e)x + 286a d e - 104a b d e + 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 1287e +--R Type: Union(Expression(Integer),...) +--E 1082 + +--S 1083 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 6 6 6 2 5 5 +--R - 198b e x + (- 468a b e - 720b d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (- 286a e - 1768a b d e - 916b d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (- 1144a d e - 2392a b d e - 424b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (- 1716a d e - 1248a b d e - 6b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (- 1144a d e - 52a b d e + 8b d e)x - 286a d e + 104a b d e - 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 6 7 2 6 3 5 6 +--R 198b e x + (666a b e + 720b d e )x +--R + +--R 2 6 2 5 3 2 4 5 +--R (754a b e + 2488a b d e + 916b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 4 +--R (286a e + 2912a b d e + 3308a b d e + 424b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 +--R (1144a d e + 4108a b d e + 1672a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 2 +--R (1716a d e + 2392a b d e + 58a b d e - 8b d e)x +--R + +--R 3 3 3 2 4 2 2 5 3 6 3 4 2 +--R (1144a d e + 338a b d e - 112a b d e + 16b d )x + 286a d e +--R + +--R 2 5 2 6 +--R - 104a b d e + 16a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 4 6 4 2 3 5 2 4 3 2 2 2 4 +--R b e x + (2a b e + 4b d e )x + (a e + 8a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 3 2 2 2 3 2 4 2 +--R (4a d e + 12a b d e + 4b d e)x + (6a d e + 8a b d e + b d )x +--R + +--R 2 3 4 2 4 +--R (4a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R - b e x + (- 3a b e - 4b d e )x + (- 3a b e - 12a b d e - 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (- a e - 12a b d e - 18a b d e - 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (- 4a d e - 18a b d e - 12a b d e - b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (- 6a d e - 12a b d e - 3a b d )x + (- 4a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1084 + +)clear all + +--S 1085 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1353 +r0:=-8/99*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/693*(b*d-a*e)^2*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+_ + b*x))+2/11*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 +--R 126b e x + (308a b e + 322b d e )x +--R + +--R 2 5 4 2 2 3 3 +--R (198a e + 836a b d e + 226b d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (594a d e + 660a b d e + 6b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (594a d e + 44a b d e - 8b d e)x + 198a d e - 88a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 5 2 4 4 +--R 126b e x + (308a b e + 322b d e )x +--R + +--R 2 5 4 2 2 3 3 +--R (198a e + 836a b d e + 226b d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (594a d e + 660a b d e + 6b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (594a d e + 44a b d e - 8b d e)x + 198a d e - 88a b d e + 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 693e +--R Type: Union(Expression(Integer),...) +--E 1087 + +--S 1088 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5 5 5 2 4 4 +--R - 126b e x + (- 308a b e - 322b d e )x +--R + +--R 2 5 4 2 2 3 3 +--R (- 198a e - 836a b d e - 226b d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (- 594a d e - 660a b d e - 6b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (- 594a d e - 44a b d e + 8b d e)x - 198a d e + 88a b d e - 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 5 6 2 5 3 4 5 +--R 126b e x + (434a b e + 322b d e )x +--R + +--R 2 5 2 4 3 2 3 4 +--R (506a b e + 1158a b d e + 226b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 3 +--R (198a e + 1430a b d e + 886a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 2 +--R (594a d e + 1254a b d e + 50a b d e - 8b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 3 2 +--R (594a d e + 242a b d e - 96a b d e + 16b d )x + 198a d e +--R + +--R 2 4 2 5 +--R - 88a b d e + 16a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R - b e x + (- 3a b e - 3b d e )x + (- 3a b e - 9a b d e - 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a e - 9a b d e - 9a b d e - b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 3a d e - 9a b d e - 3a b d )x + (- 3a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1089 + +)clear all + +--S 1090 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (1) (b e x + (a e + b d)x + a d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1353 +r0:=-8/63*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/315*(b*d-a*e)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 2/9*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 70b e x + (180a b e + 100b d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (126a e + 288a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (252a d e + 36a b d e - 8b d e)x + 126a d e - 72a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 2 3 3 +--R 70b e x + (180a b e + 100b d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (126a e + 288a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (252a d e + 36a b d e - 8b d e)x + 126a d e - 72a b d e + 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 1092 + +--S 1093 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 4 4 2 3 3 +--R - 70b e x + (- 180a b e - 100b d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (- 126a e - 288a b d e - 6b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 252a d e - 36a b d e + 8b d e)x - 126a d e + 72a b d e - 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 4 5 2 4 3 3 4 +--R 70b e x + (250a b e + 100b d e )x +--R + +--R 2 4 2 3 3 2 2 3 +--R (306a b e + 388a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 2 +--R (126a e + 540a b d e + 42a b d e - 8b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 +--R (252a d e + 162a b d e - 80a b d e + 16b d )x + 126a d e +--R + +--R 2 3 2 4 +--R - 72a b d e + 16a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - b e x + (- 3a b e - 2b d e)x + (- 3a b e - 6a b d e - b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- a e - 6a b d e - 3a b d )x + (- 2a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1094 + +)clear all + +--S 1095 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R +-------+ | 2 2 2 +--R (1) (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1353 +r0:=-8/35*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/105*(b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 2/7*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 30b e x + (84a b e + 6b d e )x + (70a e + 28a b d e - 8b d e)x +--R + +--R 2 2 2 2 3 +--R 70a d e - 56a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 30b e x + (84a b e + 6b d e )x + (70a e + 28a b d e - 8b d e)x +--R + +--R 2 2 2 2 3 +--R 70a d e - 56a b d e + 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 1097 + +--S 1098 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 3 3 2 2 2 +--R - 30b e x + (- 84a b e - 6b d e )x +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R (- 70a e - 28a b d e + 8b d e)x - 70a d e + 56a b d e - 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 3 4 2 3 3 2 3 +--R 30b e x + (114a b e + 6b d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (154a b e + 34a b d e - 8b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 +--R (70a e + 98a b d e - 64a b d e + 16b d )x + 70a d e - 56a b d e +--R + +--R 2 3 +--R 16a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + 2a b x + a +--R + +--R 3 4 2 3 3 2 2 2 3 2 +--R - b e x + (- 3a b e - b d)x + (- 3a b e - 3a b d)x + (- a e - 3a b d)x +--R + +--R 3 +--R - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1099 + +)clear all + +--S 1100 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1353 +r0:=-8/15*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+16/15*(b*d-_ + a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/5*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (6b e x + (20a b e - 8b d e)x + 30a e - 40a b d e + 16b d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (6b e x + (20a b e - 8b d e)x + 30a e - 40a b d e + 16b d )\|e x + d +--R ------------------------------------------------------------------------ +--R 3 +--R 15e +--R Type: Union(Expression(Integer),...) +--E 1102 + +--S 1103 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (- 6b e x + (- 20a b e + 8b d e)x - 30a e + 40a b d e - 16b d ) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R 6b e x + (26a b e - 8b d e)x + (50a b e - 48a b d e + 16b d )x +--R + +--R 3 2 2 2 2 +--R 30a e - 40a b d e + 16a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1104 + +)clear all + +--S 1105 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1353 +r0:=-2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*sqrt(d+e*x))+8/3*b*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^2-16/3*b*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2b e x + (12a b e - 8b d e)x - 6a e + 24a b d e - 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R 2b e x + (12a b e - 8b d e)x - 6a e + 24a b d e - 16b d +--R (3) ----------------------------------------------------------- +--R 3 +-------+ +--R 3e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1107 + +--S 1108 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (- 2b e x + (- 12a b e + 8b d e)x + 6a e - 24a b d e + 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 3 2 +--R 2b e x + (14a b e - 8b d e)x + (6a b e + 16a b d e - 16b d )x - 6a e +--R + +--R 2 2 2 +--R 24a b d e - 16a b d +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1109 + +)clear all + +--S 1110 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1353 +r0:=-2/3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^(3/2))+8/3*b*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*sqrt(d+e*x))+16/3*b*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 12a b e + 24b d e)x - 2a e - 8a b d e + 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R 6b e x + (- 12a b e + 24b d e)x - 2a e - 8a b d e + 16b d +--R (3) ------------------------------------------------------------- +--R 4 3 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1112 + +--S 1113 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (- 6b e x + (12a b e - 24b d e)x + 2a e + 8a b d e - 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R 6b e x + (- 6a b e + 24b d e)x + (- 14a b e + 16a b d e + 16b d )x +--R + +--R 3 2 2 2 2 +--R - 2a e - 8a b d e + 16a b d +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1114 + +)clear all + +--S 1115 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1353 +r0:=-2/5*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^(5/2))-8/5*b*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^(3/2))-16/15*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 30b e x + (- 20a b e - 40b d e)x - 6a e - 8a b d e - 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 30b e x + (- 20a b e - 40b d e)x - 6a e - 8a b d e - 16b d +--R (3) ---------------------------------------------------------------- +--R 5 2 4 2 3 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1117 + +--S 1118 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (30b e x + (20a b e + 40b d e)x + 6a e + 8a b d e + 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 30b e x + (- 50a b e - 40b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 26a b e - 48a b d e - 16b d )x - 6a e - 8a b d e - 16a b d +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1353 +r0:=-16/195*(b*d-a*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/15*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/6435*(b*d-_ + a*e)^3*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/45045*(b*d-_ + a*e)^4*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/715*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 6006b e x + (27720a b e + 14322b d e )x +--R + +--R 2 2 7 3 6 4 2 5 5 +--R (49140a b e + 68040a b d e + 8946b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 4 +--R (40040a b e + 125580a b d e + 44520a b d e + 70b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (12870a e + 108680a b d e + 88140a b d e + 600a b d e - 80b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (38610a d e + 85800a b d e + 2340a b d e - 720a b d e + 96b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 +--R (38610a d e + 5720a b d e - 3120a b d e + 960a b d e - 128b d e)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 12870a d e - 11440a b d e + 6240a b d e - 1920a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 7 3 7 4 6 6 +--R 6006b e x + (27720a b e + 14322b d e )x +--R + +--R 2 2 7 3 6 4 2 5 5 +--R (49140a b e + 68040a b d e + 8946b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 4 +--R (40040a b e + 125580a b d e + 44520a b d e + 70b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (12870a e + 108680a b d e + 88140a b d e + 600a b d e - 80b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (38610a d e + 85800a b d e + 2340a b d e - 720a b d e + 96b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 +--R (38610a d e + 5720a b d e - 3120a b d e + 960a b d e - 128b d e)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 12870a d e - 11440a b d e + 6240a b d e - 1920a b d e + 256b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 7 7 3 7 4 6 6 +--R - 6006b e x + (- 27720a b e - 14322b d e )x +--R + +--R 2 2 7 3 6 4 2 5 5 +--R (- 49140a b e - 68040a b d e - 8946b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 4 +--R (- 40040a b e - 125580a b d e - 44520a b d e - 70b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 12870a e - 108680a b d e - 88140a b d e - 600a b d e +--R + +--R 4 4 3 +--R 80b d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R - 38610a d e - 85800a b d e - 2340a b d e + 720a b d e +--R + +--R 4 5 2 +--R - 96b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R - 38610a d e - 5720a b d e + 3120a b d e - 960a b d e +--R + +--R 4 6 +--R 128b d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R - 12870a d e + 11440a b d e - 6240a b d e + 1920a b d e - 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 5 7 8 4 7 5 6 7 +--R 6006b e x + (33726a b e + 14322b d e )x +--R + +--R 2 3 7 4 6 5 2 5 6 +--R (76860a b e + 82362a b d e + 8946b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 5 +--R (89180a b e + 193620a b d e + 53466a b d e + 70b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 +--R 52910a b e + 234260a b d e + 132660a b d e + 670a b d e +--R + +--R 5 4 3 +--R - 80b d e +--R * +--R 4 +--R x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 12870a e + 147290a b d e + 173940a b d e + 2940a b d e +--R + +--R 4 4 3 5 5 2 +--R - 800a b d e + 96b d e +--R * +--R 3 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 +--R 38610a d e + 124410a b d e + 8060a b d e - 3840a b d e +--R + +--R 4 5 2 5 6 +--R 1056a b d e - 128b d e +--R * +--R 2 +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 +--R 38610a d e + 18590a b d e - 14560a b d e + 7200a b d e +--R + +--R 4 6 5 7 +--R - 2048a b d e + 256b d +--R * +--R x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 +--R 12870a d e - 11440a b d e + 6240a b d e - 1920a b d e + 256a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R - b e x + (- 5a b e - 3b d e )x + (- 10a b e - 15a b d e - 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 10a b e - 30a b d e - 15a b d e - b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 5a b e - 30a b d e - 30a b d e - 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- a e - 15a b d e - 30a b d e - 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 3a d e - 15a b d e - 10a b d )x + (- 3a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1353 +r0:=-16/143*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/13*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/3003*_ + (b*d-a*e)^3*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/15015*_ + (b*d-a*e)^4*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/429*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 6 6 3 6 4 5 5 +--R 2310b e x + (10920a b e + 2940b d e )x +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (20020a b e + 14560a b d e + 70b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (17160a b e + 28600a b d e + 520a b d e - 80b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (6006a e + 27456a b d e + 1716a b d e - 624a b d e + 96b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (12012a d e + 3432a b d e - 2288a b d e + 832a b d e - 128b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 6006a d e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 6 3 6 4 5 5 +--R 2310b e x + (10920a b e + 2940b d e )x +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (20020a b e + 14560a b d e + 70b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (17160a b e + 28600a b d e + 520a b d e - 80b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (6006a e + 27456a b d e + 1716a b d e - 624a b d e + 96b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (12012a d e + 3432a b d e - 2288a b d e + 832a b d e - 128b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 6006a d e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 15015e +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 6 6 3 6 4 5 5 +--R - 2310b e x + (- 10920a b e - 2940b d e )x +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (- 20020a b e - 14560a b d e - 70b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (- 17160a b e - 28600a b d e - 520a b d e + 80b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 +--R - 6006a e - 27456a b d e - 1716a b d e + 624a b d e +--R + +--R 4 4 2 +--R - 96b d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 +--R - 12012a d e - 3432a b d e + 2288a b d e - 832a b d e +--R + +--R 4 5 +--R 128b d e +--R * +--R x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R - 6006a d e + 6864a b d e - 4576a b d e + 1664a b d e - 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 5 6 7 4 6 5 5 6 +--R 2310b e x + (13230a b e + 2940b d e )x +--R + +--R 2 3 6 4 5 5 2 4 5 +--R (30940a b e + 17500a b d e + 70b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 4 +--R (37180a b e + 43160a b d e + 590a b d e - 80b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 23166a b e + 56056a b d e + 2236a b d e - 704a b d e +--R + +--R 5 4 2 +--R 96b d e +--R * +--R 3 +--R x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 6006a e + 39468a b d e + 5148a b d e - 2912a b d e +--R + +--R 4 4 2 5 5 +--R 928a b d e - 128b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 +--R 12012a d e + 9438a b d e - 9152a b d e + 5408a b d e +--R + +--R 4 5 5 6 +--R - 1792a b d e + 256b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 6006a d e - 6864a b d e + 4576a b d e - 1664a b d e + 256a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R - b e x + (- 5a b e - 2b d e)x + (- 10a b e - 10a b d e - b d )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 10a b e - 20a b d e - 5a b d )x +--R + +--R 4 2 3 2 2 3 2 3 5 2 4 3 2 2 2 +--R (- 5a b e - 20a b d e - 10a b d )x + (- a e - 10a b d e - 10a b d )x +--R + +--R 5 4 2 5 2 +--R (- 2a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1353 +r0:=-16/99*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/11*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/1155*_ + (b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/3465*_ + (b*d-a*e)^4*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/231*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 5 5 3 5 4 4 4 +--R 630b e x + (3080a b e + 70b d e )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (5940a b e + 440a b d e - 80b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (5544a b e + 1188a b d e - 528a b d e + 96b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (2310a e + 1848a b d e - 1584a b d e + 704a b d e - 128b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 2310a d e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 3 5 4 4 4 +--R 630b e x + (3080a b e + 70b d e )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (5940a b e + 440a b d e - 80b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (5544a b e + 1188a b d e - 528a b d e + 96b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (2310a e + 1848a b d e - 1584a b d e + 704a b d e - 128b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 2310a d e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 5 3 5 4 4 4 +--R - 630b e x + (- 3080a b e - 70b d e )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (- 5940a b e - 440a b d e + 80b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (- 5544a b e - 1188a b d e + 528a b d e - 96b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (- 2310a e - 1848a b d e + 1584a b d e - 704a b d e + 128b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R - 2310a d e + 3696a b d e - 3168a b d e + 1408a b d e - 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 5 5 6 4 5 5 4 5 +--R 630b e x + (3710a b e + 70b d e )x +--R + +--R 2 3 5 4 4 5 2 3 4 +--R (9020a b e + 510a b d e - 80b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (11484a b e + 1628a b d e - 608a b d e + 96b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (7854a b e + 3036a b d e - 2112a b d e + 800a b d e - 128b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R 2310a e + 4158a b d e - 5280a b d e + 3872a b d e +--R + +--R 4 4 5 5 +--R - 1536a b d e + 256b d +--R * +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 2310a d e - 3696a b d e + 3168a b d e - 1408a b d e + 256a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 6 4 5 5 2 3 4 4 +--R - b e x + (- 5a b e - b d)x + (- 10a b e - 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (- 10a b e - 10a b d)x + (- 5a b e - 10a b d)x + (- a e - 5a b d)x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1353 +r0:=-16/63*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^2+_ + 2/9*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e-_ + 128/315*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+_ + 256/315*(b*d-a*e)^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/105*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (360a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (756a b e - 432a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1680a b d e + 2016a b d e - 1152a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (360a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (756a b e - 432a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1680a b d e + 2016a b d e - 1152a b d e + 256b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 1137 + +--S 1138 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 70b e x + (- 360a b e + 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 756a b e + 432a b d e - 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 840a b e + 1008a b d e - 576a b d e + 128b d e)x - 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 1680a b d e - 2016a b d e + 1152a b d e - 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 70b e x + (430a b e - 80b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (1116a b e - 512a b d e + 96b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (1596a b e - 1440a b d e + 672a b d e - 128b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (1470a b e - 2688a b d e + 2592a b d e - 1280a b d e + 256b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 630a e - 1680a b d e + 2016a b d e - 1152a b d e + 256a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1139 + +)clear all + +--S 1140 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1353 +r0:=-2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*sqrt(d+e*x))+16/7*b*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^2+128/35*b*(b*d-a*e)^2*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-256/35*b*(b*d-a*e)^3*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-96/35*b*(b*d-a*e)*_ + (a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (56a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (280a b e - 560a b d e + 448a b d e - 128b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 560a b d e - 1120a b d e + 896a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (56a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (280a b e - 560a b d e + 448a b d e - 128b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 560a b d e - 1120a b d e + 896a b d e - 256b d +--R / +--R 5 +-------+ +--R 35e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1142 + +--S 1143 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 10b e x + (- 56a b e + 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 140a b e + 112a b d e - 32b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 280a b e + 560a b d e - 448a b d e + 128b d e)x + 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 560a b d e + 1120a b d e - 896a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 10b e x + (66a b e - 16b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (196a b e - 128a b d e + 32b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (420a b e - 672a b d e + 480a b d e - 128b d e)x +--R + +--R 4 4 2 3 2 2 4 3 5 4 5 4 4 3 +--R (210a b e - 672a b d e + 768a b d e - 256b d )x - 70a e + 560a b d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R - 1120a b d e + 896a b d e - 256a b d +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1144 + +)clear all + +--S 1145 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1353 +r0:=-2/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(3/2))-_ + 16/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*sqrt(d+e*x))-_ + 128/15*b^2*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+_ + 256/15*b^2*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*_ + (a+b*x))+32/5*b^2*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 6b e x + (40a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (180a b e - 240a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 120a b e + 720a b d e - 960a b d e + 384b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e + 480a b d e - 640a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 6b e x + (40a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (180a b e - 240a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 120a b e + 720a b d e - 960a b d e + 384b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e + 480a b d e - 640a b d e + 256b d +--R / +--R 6 5 +-------+ +--R (15e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1147 + +--S 1148 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 6b e x + (- 40a b e + 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 180a b e + 240a b d e - 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (120a b e - 720a b d e + 960a b d e - 384b d e)x + 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 80a b d e - 480a b d e + 640a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 6b e x + (46a b e - 16b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (220a b e - 256a b d e + 96b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (60a b e + 480a b d e - 864a b d e + 384b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 130a b e + 640a b d e - 480a b d e - 256a b d e + 256b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R - 10a e - 80a b d e + 480a b d e - 640a b d e + 256a b d +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1149 + +)clear all + +--S 1150 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1353 +r0:=-2/5*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(5/2))-_ + 16/15*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-32/5*b^2*_ + (a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*sqrt(d+e*x))+128/15*b^3*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-256/15*b^3*(b*d-a*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (120a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 180a b e + 720a b d e - 480b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 40a b e - 240a b d e + 960a b d e - 640b d e)x - 6a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 96a b d e + 384a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (120a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 180a b e + 720a b d e - 480b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 40a b e - 240a b d e + 960a b d e - 640b d e)x - 6a e - 16a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 96a b d e + 384a b d e - 256b d +--R / +--R 7 2 6 2 5 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1152 + +--S 1153 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 10b e x + (- 120a b e + 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (180a b e - 720a b d e + 480b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (40a b e + 240a b d e - 960a b d e + 640b d e)x + 6a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 16a b d e + 96a b d e - 384a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 10b e x + (130a b e - 80b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 60a b e + 640a b d e - 480b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 220a b e + 480a b d e + 480a b d e - 640b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 46a b e - 256a b d e + 864a b d e - 256a b d e - 256b d )x - 6a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 96a b d e + 384a b d e - 256a b d +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1154 + +)clear all + +--S 1155 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(9/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1353 +r0:=-2/7*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(7/2))-_ + 16/35*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ + 32/35*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(3/2))+_ + 128/35*b^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*sqrt(d+e*x))+_ + 256/35*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (- 280a b e + 560b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 140a b e - 560a b d e + 1120b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 56a b e - 112a b d e - 448a b d e + 896b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 32a b d e - 128a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 6 3 5 3 5 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (- 280a b e + 560b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 140a b e - 560a b d e + 1120b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 56a b e - 112a b d e - 448a b d e + 896b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 32a b d e - 128a b d e + 256b d +--R / +--R 8 3 7 2 2 6 3 5 +-------+ +--R (35e x + 105d e x + 105d e x + 35d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1157 + +--S 1158 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 70b e x + (280a b e - 560b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (140a b e + 560a b d e - 1120b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (56a b e + 112a b d e + 448a b d e - 896b d e)x + 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 16a b d e + 32a b d e + 128a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 5 2 2 3 +--R 70b e x + (- 210a b e + 560b d e )x + (- 420a b e + 1120b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 196a b e - 672a b d e + 672a b d e + 896b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 66a b e - 128a b d e - 480a b d e + 768a b d e + 256b d )x - 10a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 32a b d e - 128a b d e + 256a b d +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 6 3 5 3 5 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1159 + +)clear all + +--S 1160 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(11/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1353 +r0:=-2/9*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(9/2))-_ + 16/63*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(7/2))-_ + 32/105*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(5/2))-_ + 128/105*b^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(d+e*x)^(3/2))-_ + 256/315*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 630b e x + (- 840a b e - 1680b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 756a b e - 1008a b d e - 2016b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 360a b e - 432a b d e - 576a b d e - 1152b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e - 96a b d e - 128a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 315b e x + (315a e + 1260b d e )x + (1260a d e + 1890b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (1890a d e + 1260b d e )x + (1260a d e + 315b d e )x + 315a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 630b e x + (- 840a b e - 1680b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 756a b e - 1008a b d e - 2016b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 360a b e - 432a b d e - 576a b d e - 1152b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e - 96a b d e - 128a b d e - 256b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +-------+ +--R (315e x + 1260d e x + 1890d e x + 1260d e x + 315d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1162 + +--S 1163 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R 630b e x + (840a b e + 1680b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (756a b e + 1008a b d e + 2016b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (360a b e + 432a b d e + 576a b d e + 1152b d e)x + 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 80a b d e + 96a b d e + 128a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 630b e x + (- 1470a b e - 1680b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 1596a b e - 2688a b d e - 2016b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 1116a b e - 1440a b d e - 2592a b d e - 1152b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 430a b e - 512a b d e - 672a b d e - 1280a b d e - 256b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R - 70a e - 80a b d e - 96a b d e - 128a b d e - 256a b d +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 315b e x + (315a e + 1260b d e )x + (1260a d e + 1890b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (1890a d e + 1260b d e )x + (1260a d e + 315b d e )x + 315a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1164 + +)clear all + +--S 1165 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1353 +r0:=-2/11*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(11/2))-_ + 16/99*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(9/2))-32/231*b^2*_ + (a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(7/2))-128/693*b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(d+e*x)^(5/2))-256/3465*b^3*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 2310b e x + (- 5544a b e - 3696b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 5940a b e - 4752a b d e - 3168b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 3080a b e - 2640a b d e - 2112a b d e - 1408b d e)x - 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 560a b d e - 480a b d e - 384a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 6 10 9 5 +--R 3465b e x + (3465a e + 17325b d e )x +--R + +--R 9 2 8 4 2 8 3 7 3 +--R (17325a d e + 34650b d e )x + (34650a d e + 34650b d e )x +--R + +--R 3 7 4 6 2 4 6 5 5 5 5 +--R (34650a d e + 17325b d e )x + (17325a d e + 3465b d e )x + 3465a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 2310b e x + (- 5544a b e - 3696b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 5940a b e - 4752a b d e - 3168b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 3080a b e - 2640a b d e - 2112a b d e - 1408b d e)x - 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 560a b d e - 480a b d e - 384a b d e - 256b d +--R / +--R 10 5 9 4 2 8 3 3 7 2 4 6 +--R 3465e x + 17325d e x + 34650d e x + 34650d e x + 17325d e x +--R + +--R 5 5 +--R 3465d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1167 + +--S 1168 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R 2310b e x + (5544a b e + 3696b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (5940a b e + 4752a b d e + 3168b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (3080a b e + 2640a b d e + 2112a b d e + 1408b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 560a b d e + 480a b d e + 384a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 2310b e x + (- 7854a b e - 3696b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 11484a b e - 8448a b d e - 3168b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 9020a b e - 7392a b d e - 5280a b d e - 1408b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 3710a b e - 3200a b d e - 2592a b d e - 1792a b d e - 256b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R - 630a e - 560a b d e - 480a b d e - 384a b d e - 256a b d +--R / +--R 10 6 10 9 5 +--R 3465b e x + (3465a e + 17325b d e )x +--R + +--R 9 2 8 4 2 8 3 7 3 +--R (17325a d e + 34650b d e )x + (34650a d e + 34650b d e )x +--R + +--R 3 7 4 6 2 4 6 5 5 5 5 +--R (34650a d e + 17325b d e )x + (17325a d e + 3465b d e )x + 3465a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1353 +r0:=-128/4199*(b*d-a*e)^3*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/323*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 24/323*(b*d-a*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/19*_ + (a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/138567*(b*d-_ + a*e)^5*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/969969*(b*d-_ + a*e)^6*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+768/46189*_ + (b*d-a*e)^4*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 9 9 5 9 6 8 8 +--R 102102b e x + (684684a b e + 234234b d e )x +--R + +--R 2 4 9 5 8 6 2 7 7 +--R (1939938a b e + 1597596a b d e + 138138b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 6 +--R (2984520a b e + 4626006a b d e + 965580a b d e + 462b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 5 3 6 +--R 2645370a b e + 7325640a b d e + 2889558a b d e + 4788a b d e +--R + +--R 6 4 5 +--R - 504b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 2 8 3 3 2 7 2 4 3 6 +--R 1293292a b e + 6760390a b d e + 4793320a b d e + 22610a b d e +--R + +--R 5 4 5 6 5 4 +--R - 5320a b d e + 560b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 +--R 277134a e + 3510364a b d e + 4744870a b d e + 64600a b d e +--R + +--R 2 4 4 5 5 5 4 6 6 3 +--R - 25840a b d e + 6080a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R 831402a d e + 2771340a b d e + 125970a b d e - 77520a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R 31008a b d e - 7296a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 2 7 5 3 6 4 2 4 5 3 3 5 4 +--R 831402a d e + 184756a b d e - 167960a b d e + 103360a b d e +--R + +--R 2 4 6 3 5 7 2 6 8 +--R - 41344a b d e + 9728a b d e - 1024b d e +--R * +--R x +--R + +--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 +--R 277134a d e - 369512a b d e + 335920a b d e - 206720a b d e +--R + +--R 2 4 7 2 5 8 6 9 +--R 82688a b d e - 19456a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 969969b e x + 969969a e +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 9 9 5 9 6 8 8 +--R 102102b e x + (684684a b e + 234234b d e )x +--R + +--R 2 4 9 5 8 6 2 7 7 +--R (1939938a b e + 1597596a b d e + 138138b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 6 +--R (2984520a b e + 4626006a b d e + 965580a b d e + 462b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 5 3 6 +--R 2645370a b e + 7325640a b d e + 2889558a b d e + 4788a b d e +--R + +--R 6 4 5 +--R - 504b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 2 8 3 3 2 7 2 4 3 6 +--R 1293292a b e + 6760390a b d e + 4793320a b d e + 22610a b d e +--R + +--R 5 4 5 6 5 4 +--R - 5320a b d e + 560b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 +--R 277134a e + 3510364a b d e + 4744870a b d e + 64600a b d e +--R + +--R 2 4 4 5 5 5 4 6 6 3 +--R - 25840a b d e + 6080a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R 831402a d e + 2771340a b d e + 125970a b d e - 77520a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R 31008a b d e - 7296a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 2 7 5 3 6 4 2 4 5 3 3 5 4 +--R 831402a d e + 184756a b d e - 167960a b d e + 103360a b d e +--R + +--R 2 4 6 3 5 7 2 6 8 +--R - 41344a b d e + 9728a b d e - 1024b d e +--R * +--R x +--R + +--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 +--R 277134a d e - 369512a b d e + 335920a b d e - 206720a b d e +--R + +--R 2 4 7 2 5 8 6 9 +--R 82688a b d e - 19456a b d e + 2048b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 969969e +--R Type: Union(Expression(Integer),...) +--E 1172 + +--S 1173 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 9 9 5 9 6 8 8 +--R - 102102b e x + (- 684684a b e - 234234b d e )x +--R + +--R 2 4 9 5 8 6 2 7 7 +--R (- 1939938a b e - 1597596a b d e - 138138b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 6 +--R (- 2984520a b e - 4626006a b d e - 965580a b d e - 462b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 +--R - 2645370a b e - 7325640a b d e - 2889558a b d e +--R + +--R 5 3 6 6 4 5 +--R - 4788a b d e + 504b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 2 8 3 3 2 7 +--R - 1293292a b e - 6760390a b d e - 4793320a b d e +--R + +--R 2 4 3 6 5 4 5 6 5 4 +--R - 22610a b d e + 5320a b d e - 560b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 +--R - 277134a e - 3510364a b d e - 4744870a b d e - 64600a b d e +--R + +--R 2 4 4 5 5 5 4 6 6 3 +--R 25840a b d e - 6080a b d e + 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R - 831402a d e - 2771340a b d e - 125970a b d e + 77520a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R - 31008a b d e + 7296a b d e - 768b d e +--R * +--R 2 +--R x +--R + +--R 6 2 7 5 3 6 4 2 4 5 3 3 5 4 +--R - 831402a d e - 184756a b d e + 167960a b d e - 103360a b d e +--R + +--R 2 4 6 3 5 7 2 6 8 +--R 41344a b d e - 9728a b d e + 1024b d e +--R * +--R x +--R + +--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 +--R - 277134a d e + 369512a b d e - 335920a b d e + 206720a b d e +--R + +--R 2 4 7 2 5 8 6 9 +--R - 82688a b d e + 19456a b d e - 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 7 9 10 6 9 7 8 9 +--R 102102b e x + (786786a b e + 234234b d e )x +--R + +--R 2 5 9 6 8 7 2 7 8 +--R (2624622a b e + 1831830a b d e + 138138b d e )x +--R + +--R 3 4 9 2 5 8 6 2 7 7 3 6 7 +--R (4924458a b e + 6223602a b d e + 1103718a b d e + 462b d e )x +--R + +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 +--R 5629890a b e + 11951646a b d e + 3855138a b d e + 5250a b d e +--R + +--R 7 4 5 +--R - 504b d e +--R * +--R 6 +--R x +--R + +--R 5 2 9 4 3 8 3 4 2 7 +--R 3938662a b e + 14086030a b d e + 7682878a b d e +--R + +--R 2 5 3 6 6 4 5 7 5 4 +--R 27398a b d e - 5824a b d e + 560b d e +--R * +--R 5 +--R x +--R + +--R 6 9 5 2 8 4 3 2 7 +--R 1570426a b e + 10270754a b d e + 9538190a b d e +--R + +--R 3 4 3 6 2 5 4 5 6 5 4 7 6 3 +--R 87210a b d e - 31160a b d e + 6640a b d e - 640b d e +--R * +--R 4 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 +--R 277134a e + 4341766a b d e + 7516210a b d e + 190570a b d e +--R + +--R 3 4 4 5 2 5 5 4 6 6 3 7 7 2 +--R - 103360a b d e + 37088a b d e - 7936a b d e + 768b d e +--R * +--R 3 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 +--R 831402a d e + 3602742a b d e + 310726a b d e - 245480a b d e +--R + +--R 3 4 5 4 2 5 6 3 6 7 2 7 8 +--R 134368a b d e - 48640a b d e + 10496a b d e - 1024b d e +--R * +--R 2 +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 +--R 831402a d e + 461890a b d e - 537472a b d e + 439280a b d e +--R + +--R 3 4 6 3 2 5 7 2 6 8 7 9 +--R - 248064a b d e + 92416a b d e - 20480a b d e + 2048b d +--R * +--R x +--R + +--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 +--R 277134a d e - 369512a b d e + 335920a b d e - 206720a b d e +--R + +--R 3 4 7 2 2 5 8 6 9 +--R 82688a b d e - 19456a b d e + 2048a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 969969b e x + 969969a e +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 3 9 5 3 6 2 8 2 4 3 5 2 6 2 7 +--R b e x + (6a b e + 3b d e )x + (15a b e + 18a b d e + 3b d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (20a b e + 45a b d e + 18a b d e + b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (15a b e + 60a b d e + 45a b d e + 6a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (6a b e + 45a b d e + 60a b d e + 15a b d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (a e + 18a b d e + 45a b d e + 20a b d )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (3a d e + 18a b d e + 15a b d )x + (3a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 3 10 6 3 7 2 9 +--R - b e x + (- 7a b e - 3b d e )x +--R + +--R 2 5 3 6 2 7 2 8 +--R (- 21a b e - 21a b d e - 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (- 35a b e - 63a b d e - 21a b d e - b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (- 35a b e - 105a b d e - 63a b d e - 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (- 21a b e - 105a b d e - 105a b d e - 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (- 7a b e - 63a b d e - 105a b d e - 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (- a e - 21a b d e - 63a b d e - 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (- 3a d e - 21a b d e - 21a b d )x + (- 3a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1353 +r0:=-128/2431*(b*d-a*e)^3*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/221*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 8/85*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/17*(a+_ + b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/51051*(b*d-a*e)^5*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/255255*(b*d-a*e)^6*(d+_ + e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/7293*(b*d-a*e)^4*_ + (a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 8 8 5 8 6 7 7 +--R 30030b e x + (204204a b e + 36036b d e )x +--R + +--R 2 4 8 5 7 6 2 6 6 +--R (589050a b e + 251328a b d e + 462b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (928200a b e + 749700a b d e + 4284a b d e - 504b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 +--R 850850a b e + 1237600a b d e + 17850a b d e - 4760a b d e +--R + +--R 6 4 4 +--R 560b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 +--R 437580a b e + 1215500a b d e + 44200a b d e - 20400a b d e +--R + +--R 5 4 4 6 5 3 +--R 5440a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 +--R 102102a e + 700128a b d e + 72930a b d e - 53040a b d e +--R + +--R 2 4 4 4 5 5 3 6 6 2 +--R 24480a b d e - 6528a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 +--R 204204a d e + 87516a b d e - 97240a b d e + 70720a b d e +--R + +--R 2 4 5 3 5 6 2 6 7 +--R - 32640a b d e + 8704a b d e - 1024b d e +--R * +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R 102102a d e - 175032a b d e + 194480a b d e - 141440a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R 65280a b d e - 17408a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 255255b e x + 255255a e +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 8 8 5 8 6 7 7 +--R 30030b e x + (204204a b e + 36036b d e )x +--R + +--R 2 4 8 5 7 6 2 6 6 +--R (589050a b e + 251328a b d e + 462b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (928200a b e + 749700a b d e + 4284a b d e - 504b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 +--R 850850a b e + 1237600a b d e + 17850a b d e - 4760a b d e +--R + +--R 6 4 4 +--R 560b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 +--R 437580a b e + 1215500a b d e + 44200a b d e - 20400a b d e +--R + +--R 5 4 4 6 5 3 +--R 5440a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 +--R 102102a e + 700128a b d e + 72930a b d e - 53040a b d e +--R + +--R 2 4 4 4 5 5 3 6 6 2 +--R 24480a b d e - 6528a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 +--R 204204a d e + 87516a b d e - 97240a b d e + 70720a b d e +--R + +--R 2 4 5 3 5 6 2 6 7 +--R - 32640a b d e + 8704a b d e - 1024b d e +--R * +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R 102102a d e - 175032a b d e + 194480a b d e - 141440a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R 65280a b d e - 17408a b d e + 2048b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 255255e +--R Type: Union(Expression(Integer),...) +--E 1177 + +--S 1178 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 8 8 5 8 6 7 7 +--R - 30030b e x + (- 204204a b e - 36036b d e )x +--R + +--R 2 4 8 5 7 6 2 6 6 +--R (- 589050a b e - 251328a b d e - 462b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (- 928200a b e - 749700a b d e - 4284a b d e + 504b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 +--R - 850850a b e - 1237600a b d e - 17850a b d e + 4760a b d e +--R + +--R 6 4 4 +--R - 560b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 +--R - 437580a b e - 1215500a b d e - 44200a b d e + 20400a b d e +--R + +--R 5 4 4 6 5 3 +--R - 5440a b d e + 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 +--R - 102102a e - 700128a b d e - 72930a b d e + 53040a b d e +--R + +--R 2 4 4 4 5 5 3 6 6 2 +--R - 24480a b d e + 6528a b d e - 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 +--R - 204204a d e - 87516a b d e + 97240a b d e - 70720a b d e +--R + +--R 2 4 5 3 5 6 2 6 7 +--R 32640a b d e - 8704a b d e + 1024b d e +--R * +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R - 102102a d e + 175032a b d e - 194480a b d e + 141440a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R - 65280a b d e + 17408a b d e - 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 7 8 9 6 8 7 7 8 +--R 30030b e x + (234234a b e + 36036b d e )x +--R + +--R 2 5 8 6 7 7 2 6 7 +--R (793254a b e + 287364a b d e + 462b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 6 +--R (1517250a b e + 1001028a b d e + 4746a b d e - 504b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 +--R 1779050a b e + 1987300a b d e + 22134a b d e - 5264a b d e +--R + +--R 7 4 4 +--R 560b d e +--R * +--R 5 +--R x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 +--R 1288430a b e + 2453100a b d e + 62050a b d e - 25160a b d e +--R + +--R 6 4 4 7 5 3 +--R 6000a b d e - 640b d e +--R * +--R 4 +--R x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 +--R 539682a b e + 1915628a b d e + 117130a b d e - 73440a b d e +--R + +--R 2 5 4 4 6 5 3 7 6 2 +--R 29920a b d e - 7168a b d e + 768b d e +--R * +--R 3 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 +--R 102102a e + 904332a b d e + 160446a b d e - 150280a b d e +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 +--R 95200a b d e - 39168a b d e + 9472a b d e - 1024b d e +--R * +--R 2 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 204204a d e + 189618a b d e - 272272a b d e + 265200a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 +--R - 174080a b d e + 73984a b d e - 18432a b d e + 2048b d +--R * +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 4 3 5 3 +--R 102102a d e - 175032a b d e + 194480a b d e - 141440a b d e +--R + +--R 3 4 6 2 2 5 7 6 8 +--R 65280a b d e - 17408a b d e + 2048a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 255255b e x + 255255a e +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 2 8 5 2 6 7 2 4 2 5 6 2 6 +--R b e x + (6a b e + 2b d e)x + (15a b e + 12a b d e + b d )x +--R + +--R 3 3 2 2 4 5 2 5 +--R (20a b e + 30a b d e + 6a b d )x +--R + +--R 4 2 2 3 3 2 4 2 4 +--R (15a b e + 40a b d e + 15a b d )x +--R + +--R 5 2 4 2 3 3 2 3 6 2 5 4 2 2 2 +--R (6a b e + 30a b d e + 20a b d )x + (a e + 12a b d e + 15a b d )x +--R + +--R 6 5 2 6 2 +--R (2a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R - b e x + (- 7a b e - 2b d e)x + (- 21a b e - 14a b d e - b d )x +--R + +--R 3 4 2 2 5 6 2 6 +--R (- 35a b e - 42a b d e - 7a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 +--R (- 35a b e - 70a b d e - 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 +--R (- 21a b e - 70a b d e - 35a b d )x +--R + +--R 6 2 5 2 4 3 2 3 7 2 6 5 2 2 2 +--R (- 7a b e - 42a b d e - 35a b d )x + (- a e - 14a b d e - 21a b d )x +--R + +--R 7 6 2 7 2 +--R (- 2a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1179 + +)clear all + +--S 1180 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1353 +r0:=-128/1287*(b*d-a*e)^3*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/143*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 8/65*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/15*(a+_ + b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/15015*(b*d-_ + a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/45045*(b*d-_ + a*e)^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+_ + 256/3003*(b*d-a*e)^4*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 7 7 5 7 6 6 6 +--R 6006b e x + (41580a b e + 462b d e )x +--R + +--R 2 4 7 5 6 6 2 5 5 +--R (122850a b e + 3780a b d e - 504b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 4 +--R (200200a b e + 13650a b d e - 4200a b d e + 560b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 +--R 193050a b e + 28600a b d e - 15600a b d e + 4800a b d e +--R + +--R 6 4 3 +--R - 640b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 108108a b e + 38610a b d e - 34320a b d e + 18720a b d e +--R + +--R 5 4 3 6 5 2 +--R - 5760a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 30030a e + 36036a b d e - 51480a b d e + 45760a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 24960a b d e + 7680a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 30030a d e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R 49920a b d e - 15360a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 5 7 6 6 6 +--R 6006b e x + (41580a b e + 462b d e )x +--R + +--R 2 4 7 5 6 6 2 5 5 +--R (122850a b e + 3780a b d e - 504b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 4 +--R (200200a b e + 13650a b d e - 4200a b d e + 560b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 +--R 193050a b e + 28600a b d e - 15600a b d e + 4800a b d e +--R + +--R 6 4 3 +--R - 640b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 108108a b e + 38610a b d e - 34320a b d e + 18720a b d e +--R + +--R 5 4 3 6 5 2 +--R - 5760a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 30030a e + 36036a b d e - 51480a b d e + 45760a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 24960a b d e + 7680a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 30030a d e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R 49920a b d e - 15360a b d e + 2048b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 1182 + +--S 1183 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 7 5 7 6 6 6 +--R - 6006b e x + (- 41580a b e - 462b d e )x +--R + +--R 2 4 7 5 6 6 2 5 5 +--R (- 122850a b e - 3780a b d e + 504b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 4 +--R (- 200200a b e - 13650a b d e + 4200a b d e - 560b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 +--R - 193050a b e - 28600a b d e + 15600a b d e - 4800a b d e +--R + +--R 6 4 3 +--R 640b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R - 108108a b e - 38610a b d e + 34320a b d e - 18720a b d e +--R + +--R 5 4 3 6 5 2 +--R 5760a b d e - 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 30030a e - 36036a b d e + 51480a b d e - 45760a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 24960a b d e - 7680a b d e + 1024b d e +--R * +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 30030a d e + 72072a b d e - 102960a b d e + 91520a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R - 49920a b d e + 15360a b d e - 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 7 7 8 6 7 7 6 7 +--R 6006b e x + (47586a b e + 462b d e )x +--R + +--R 2 5 7 6 6 7 2 5 6 +--R (164430a b e + 4242a b d e - 504b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 5 +--R (323050a b e + 17430a b d e - 4704a b d e + 560b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 393250a b e + 42250a b d e - 19800a b d e + 5360a b d e +--R + +--R 7 4 3 +--R - 640b d e +--R * +--R 4 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 301158a b e + 67210a b d e - 49920a b d e + 23520a b d e +--R + +--R 6 4 3 7 5 2 +--R - 6400a b d e + 768b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 138138a b e + 74646a b d e - 85800a b d e + 64480a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 30720a b d e + 8448a b d e - 1024b d e +--R * +--R 2 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 30030a e + 66066a b d e - 123552a b d e + 148720a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 116480a b d e + 57600a b d e - 16384a b d e + 2048b d +--R * +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 +--R 30030a d e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 3 4 5 2 2 5 6 6 7 +--R 49920a b d e - 15360a b d e + 2048a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 7 5 6 6 2 4 5 5 +--R b e x + (6a b e + b d)x + (15a b e + 6a b d)x +--R + +--R 3 3 2 4 4 4 2 3 3 3 5 4 2 2 +--R (20a b e + 15a b d)x + (15a b e + 20a b d)x + (6a b e + 15a b d)x +--R + +--R 6 5 6 +--R (a e + 6a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 8 6 7 7 2 5 6 6 +--R - b e x + (- 7a b e - b d)x + (- 21a b e - 7a b d)x +--R + +--R 3 4 2 5 5 4 3 3 4 4 +--R (- 35a b e - 21a b d)x + (- 35a b e - 35a b d)x +--R + +--R 5 2 4 3 3 6 5 2 2 7 6 7 +--R (- 21a b e - 35a b d)x + (- 7a b e - 21a b d)x + (- a e - 7a b d)x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1184 + +)clear all + +--S 1185 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1353 +r0:=-640/3003*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+_ + 80/429*(b*d-a*e)^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3-_ + 24/143*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e^2+2/13*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e-1024/3003*(b*d-a*e)^5*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/3003*(b*d-a*e)^6*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/1001*(b*d-_ + a*e)^4*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (3276a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (10010a b e - 3640a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (17160a b e - 11440a b d e + 4160a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 18018a b e - 20592a b d e + 13728a b d e - 4992a b d e +--R + +--R 6 4 2 +--R 768b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 12012a b e - 24024a b d e + 27456a b d e - 18304a b d e +--R + +--R 5 4 2 6 5 +--R 6656a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 6006a e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 36608a b d e - 13312a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 3003b e x + 3003a e +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (3276a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (10010a b e - 3640a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (17160a b e - 11440a b d e + 4160a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 18018a b e - 20592a b d e + 13728a b d e - 4992a b d e +--R + +--R 6 4 2 +--R 768b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 12012a b e - 24024a b d e + 27456a b d e - 18304a b d e +--R + +--R 5 4 2 6 5 +--R 6656a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 6006a e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 36608a b d e - 13312a b d e + 2048b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 3003e +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 462b e x + (- 3276a b e + 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 10010a b e + 3640a b d e - 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 17160a b e + 11440a b d e - 4160a b d e + 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 18018a b e + 20592a b d e - 13728a b d e + 4992a b d e +--R + +--R 6 4 2 +--R - 768b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 12012a b e + 24024a b d e - 27456a b d e + 18304a b d e +--R + +--R 5 4 2 6 5 +--R - 6656a b d e + 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 6006a e + 24024a b d e - 48048a b d e + 54912a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 36608a b d e + 13312a b d e - 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 462b e x + (3738a b e - 504b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (13286a b e - 4144a b d e + 560b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (27170a b e - 15080a b d e + 4720a b d e - 640b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R 35178a b e - 32032a b d e + 17888a b d e - 5632a b d e +--R + +--R 7 4 2 +--R 768b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R 30030a b e - 44616a b d e + 41184a b d e - 23296a b d e +--R + +--R 6 4 2 7 5 +--R 7424a b d e - 1024b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 18018a b e - 48048a b d e + 75504a b d e - 73216a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 43264a b d e - 14336a b d e + 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 +--R 6006a e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 3 4 4 2 2 5 5 6 6 +--R 36608a b d e - 13312a b d e + 2048a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 3003b e x + 3003a e +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1353 +r0:=-2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*sqrt(d+e*x))+640/231*b*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4-80/33*b*(b*d-a*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3+24/11*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e^2+1024/231*b*(b*d-a*e)^4*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-2048/231*b*(b*d-a*e)^5*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-256/77*b*(b*d-a*e)^3*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (308a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (990a b e - 440a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1848a b e - 1584a b d e + 704a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 2772a b e - 9240a b d e + 14784a b d e - 12672a b d e +--R + +--R 5 4 2 6 5 +--R 5632a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 462a e + 5544a b d e - 18480a b d e + 29568a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 25344a b d e + 11264a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +-------+ +--R (231b e x + 231a e )\|e x + d +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (308a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (990a b e - 440a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1848a b e - 1584a b d e + 704a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 2772a b e - 9240a b d e + 14784a b d e - 12672a b d e +--R + +--R 5 4 2 6 5 +--R 5632a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 462a e + 5544a b d e - 18480a b d e + 29568a b d e - 25344a b d e +--R + +--R 5 5 6 6 +--R 11264a b d e - 2048b d +--R / +--R 7 +-------+ +--R 231e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 42b e x + (- 308a b e + 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 990a b e + 440a b d e - 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1848a b e + 1584a b d e - 704a b d e + 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 2310a b e + 3696a b d e - 3168a b d e + 1408a b d e +--R + +--R 6 4 2 +--R - 256b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 2772a b e + 9240a b d e - 14784a b d e + 12672a b d e +--R + +--R 5 4 2 6 5 +--R - 5632a b d e + 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 462a e - 5544a b d e + 18480a b d e - 29568a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 25344a b d e - 11264a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 42b e x + (350a b e - 56b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (1298a b e - 496a b d e + 80b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (2838a b e - 2024a b d e + 784a b d e - 128b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (4158a b e - 5280a b d e + 3872a b d e - 1536a b d e + 256b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R 5082a b e - 12936a b d e + 17952a b d e - 14080a b d e +--R + +--R 6 4 2 7 5 +--R 5888a b d e - 1024b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 2310a b e - 3696a b d e - 3696a b d e + 16896a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 19712a b d e + 10240a b d e - 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 462a e + 5544a b d e - 18480a b d e + 29568a b d e - 25344a b d e +--R + +--R 2 5 5 6 6 +--R 11264a b d e - 2048a b d +--R / +--R 7 7 +-------+ +--R (231b e x + 231a e )\|e x + d +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1353 +r0:=-2/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(3/2))-8*b*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*sqrt(d+e*x))-640/63*b^2*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+80/9*b^2*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3-1024/63*b^2*(b*d-a*e)^3*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/63*b^2*(b*d-a*e)^4*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/21*b^2*(b*d-a*e)^2*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (108a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (1890a b e - 5040a b d e + 6048a b d e - 3456a b d e + 768b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 756a b e + 7560a b d e - 20160a b d e + 24192a b d e +--R + +--R 5 4 2 6 5 +--R - 13824a b d e + 3072b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 504a b d e + 5040a b d e - 13440a b d e + 16128a b d e +--R + +--R 5 5 6 6 +--R - 9216a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (108a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (1890a b e - 5040a b d e + 6048a b d e - 3456a b d e + 768b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 756a b e + 7560a b d e - 20160a b d e + 24192a b d e +--R + +--R 5 4 2 6 5 +--R - 13824a b d e + 3072b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 504a b d e + 5040a b d e - 13440a b d e + 16128a b d e +--R + +--R 5 5 6 6 +--R - 9216a b d e + 2048b d +--R / +--R 8 7 +-------+ +--R (63e x + 63d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 14b e x + (- 108a b e + 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 378a b e + 216a b d e - 48b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 840a b e + 1008a b d e - 576a b d e + 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1890a b e + 5040a b d e - 6048a b d e + 3456a b d e +--R + +--R 6 4 2 +--R - 768b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 756a b e - 7560a b d e + 20160a b d e - 24192a b d e +--R + +--R 5 4 2 6 5 +--R 13824a b d e - 3072b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 42a e + 504a b d e - 5040a b d e + 13440a b d e - 16128a b d e +--R + +--R 5 5 6 6 +--R 9216a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 14b e x + (122a b e - 24b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (486a b e - 240a b d e + 48b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (1218a b e - 1224a b d e + 624a b d e - 128b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (2730a b e - 6048a b d e + 6624a b d e - 3584a b d e + 768b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R 1134a b e + 2520a b d e - 14112a b d e + 20736a b d e +--R + +--R 6 4 2 7 5 +--R - 13056a b d e + 3072b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 798a b e + 7056a b d e - 15120a b d e + 10752a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 2304a b d e - 6144a b d e + 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 42a e - 504a b d e + 5040a b d e - 13440a b d e + 16128a b d e +--R + +--R 2 5 5 6 6 +--R - 9216a b d e + 2048a b d +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1353 +r0:=-2/5*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(5/2))-8/5*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(3/2))-16*b^2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*sqrt(d+e*x))+128/7*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/e^4+1024/35*b^3*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6-2048/35*b^3*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x))-768/35*b^3*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (84a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (350a b e - 280a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1400a b e - 2800a b d e + 2240a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1050a b e + 8400a b d e - 16800a b d e + 13440a b d e +--R + +--R 6 4 2 +--R - 3840b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 140a b e - 1400a b d e + 11200a b d e - 22400a b d e +--R + +--R 5 4 2 6 5 +--R 17920a b d e - 5120b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 56a b d e - 560a b d e + 4480a b d e - 8960a b d e +--R + +--R 5 5 6 6 +--R 7168a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R (35b e x + (35a e + 70b d e )x + (70a d e + 35b d e )x + 35a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (84a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (350a b e - 280a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1400a b e - 2800a b d e + 2240a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1050a b e + 8400a b d e - 16800a b d e + 13440a b d e +--R + +--R 6 4 2 +--R - 3840b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 140a b e - 1400a b d e + 11200a b d e - 22400a b d e +--R + +--R 5 4 2 6 5 +--R 17920a b d e - 5120b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 56a b d e - 560a b d e + 4480a b d e - 8960a b d e +--R + +--R 5 5 6 6 +--R 7168a b d e - 2048b d +--R / +--R 9 2 8 2 7 +-------+ +--R (35e x + 70d e x + 35d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 10b e x + (- 84a b e + 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 350a b e + 280a b d e - 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1400a b e + 2800a b d e - 2240a b d e + 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 1050a b e - 8400a b d e + 16800a b d e - 13440a b d e +--R + +--R 6 4 2 +--R 3840b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 140a b e + 1400a b d e - 11200a b d e + 22400a b d e +--R + +--R 5 4 2 6 5 +--R - 17920a b d e + 5120b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 14a e + 56a b d e + 560a b d e - 4480a b d e + 8960a b d e +--R + +--R 5 5 6 6 +--R - 7168a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 10b e x + (94a b e - 24b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (434a b e - 304a b d e + 80b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (1750a b e - 3080a b d e + 2320a b d e - 640b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (350a b e + 5600a b d e - 14560a b d e + 12800a b d e - 3840b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 1190a b e + 7000a b d e - 5600a b d e - 8960a b d e +--R + +--R 6 4 2 7 5 +--R 14080a b d e - 5120b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 154a b e - 1456a b d e + 10640a b d e - 17920a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 8960a b d e + 2048a b d e - 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 14a e - 56a b d e - 560a b d e + 4480a b d e - 8960a b d e +--R + +--R 2 5 5 6 6 +--R 7168a b d e - 2048a b d +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R (35b e x + (35a e + 70b d e )x + (70a d e + 35b d e )x + 35a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(9/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1353 +r0:=-16/7*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(3/2))-_ + 2/7*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(7/2))-24/35*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(5/2))-128/7*b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^4*sqrt(d+e*x))-1024/35*b^4*(b*d-a*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/35*b^4*(b*d-a*e)^2*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+768/35*b^4*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (140a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (1050a b e - 1400a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1400a b e + 8400a b d e - 11200a b d e + 4480b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 350a b e - 2800a b d e + 16800a b d e - 22400a b d e +--R + +--R 6 4 2 +--R 8960b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 84a b e - 280a b d e - 2240a b d e + 13440a b d e +--R + +--R 5 4 2 6 5 +--R - 17920a b d e + 7168b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e - 24a b d e - 80a b d e - 640a b d e + 3840a b d e +--R + +--R 5 5 6 6 +--R - 5120a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 8 3 7 3 7 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (140a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (1050a b e - 1400a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1400a b e + 8400a b d e - 11200a b d e + 4480b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 350a b e - 2800a b d e + 16800a b d e - 22400a b d e +--R + +--R 6 4 2 +--R 8960b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 84a b e - 280a b d e - 2240a b d e + 13440a b d e +--R + +--R 5 4 2 6 5 +--R - 17920a b d e + 7168b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e - 24a b d e - 80a b d e - 640a b d e + 3840a b d e +--R + +--R 5 5 6 6 +--R - 5120a b d e + 2048b d +--R / +--R 10 3 9 2 2 8 3 7 +-------+ +--R (35e x + 105d e x + 105d e x + 35d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 14b e x + (- 140a b e + 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1050a b e + 1400a b d e - 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1400a b e - 8400a b d e + 11200a b d e - 4480b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 350a b e + 2800a b d e - 16800a b d e + 22400a b d e +--R + +--R 6 4 2 +--R - 8960b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 84a b e + 280a b d e + 2240a b d e - 13440a b d e +--R + +--R 5 4 2 6 5 +--R 17920a b d e - 7168b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 10a e + 24a b d e + 80a b d e + 640a b d e - 3840a b d e +--R + +--R 5 5 6 6 +--R 5120a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 14b e x + (154a b e - 56b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (1190a b e - 1456a b d e + 560b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 350a b e + 7000a b d e - 10640a b d e + 4480b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 1750a b e + 5600a b d e + 5600a b d e - 17920a b d e +--R + +--R 7 4 2 +--R 8960b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 434a b e - 3080a b d e + 14560a b d e - 8960a b d e +--R + +--R 6 4 2 7 5 +--R - 8960a b d e + 7168b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 94a b e - 304a b d e - 2320a b d e + 12800a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 14080a b d e + 2048a b d e + 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 10a e - 24a b d e - 80a b d e - 640a b d e + 3840a b d e +--R + +--R 2 5 5 6 6 +--R - 5120a b d e + 2048a b d +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 8 3 7 3 7 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(11/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1210 + +--S 1211 of 1353 +r0:=-16/21*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(5/2))-_ + 128/63*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(3/2))-2/9*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(9/2))-8/21*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^(7/2))-256/21*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*sqrt(d+e*x))+1024/63*b^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6-2048/63*b^5*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (756a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1890a b e + 7560a b d e - 5040b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 840a b e - 5040a b d e + 20160a b d e - 13440b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 378a b e - 1008a b d e - 6048a b d e + 24192a b d e +--R + +--R 6 4 2 +--R - 16128b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 108a b e - 216a b d e - 576a b d e - 3456a b d e +--R + +--R 5 4 2 6 5 +--R 13824a b d e - 9216b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 24a b d e - 48a b d e - 128a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R 3072a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 63b e x + (63a e + 252b d e )x + (252a d e + 378b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (378a d e + 252b d e )x + (252a d e + 63b d e )x + 63a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (756a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1890a b e + 7560a b d e - 5040b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 840a b e - 5040a b d e + 20160a b d e - 13440b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 378a b e - 1008a b d e - 6048a b d e + 24192a b d e +--R + +--R 6 4 2 +--R - 16128b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 108a b e - 216a b d e - 576a b d e - 3456a b d e +--R + +--R 5 4 2 6 5 +--R 13824a b d e - 9216b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 24a b d e - 48a b d e - 128a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R 3072a b d e - 2048b d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +-------+ +--R (63e x + 252d e x + 378d e x + 252d e x + 63d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1212 + +--S 1213 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 42b e x + (- 756a b e + 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (1890a b e - 7560a b d e + 5040b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (840a b e + 5040a b d e - 20160a b d e + 13440b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 378a b e + 1008a b d e + 6048a b d e - 24192a b d e +--R + +--R 6 4 2 +--R 16128b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 108a b e + 216a b d e + 576a b d e + 3456a b d e +--R + +--R 5 4 2 6 5 +--R - 13824a b d e + 9216b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 14a e + 24a b d e + 48a b d e + 128a b d e + 768a b d e +--R + +--R 5 5 6 6 +--R - 3072a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 42b e x + (798a b e - 504b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 1134a b e + 7056a b d e - 5040b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 2730a b e + 2520a b d e + 15120a b d e - 13440b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 1218a b e - 6048a b d e + 14112a b d e + 10752a b d e +--R + +--R 7 4 2 +--R - 16128b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 486a b e - 1224a b d e - 6624a b d e + 20736a b d e +--R + +--R 6 4 2 7 5 +--R - 2304a b d e - 9216b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 122a b e - 240a b d e - 624a b d e - 3584a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 13056a b d e - 6144a b d e - 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 14a e - 24a b d e - 48a b d e - 128a b d e - 768a b d e +--R + +--R 2 5 5 6 6 +--R 3072a b d e - 2048a b d +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 63b e x + (63a e + 252b d e )x + (252a d e + 378b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (378a d e + 252b d e )x + (252a d e + 63b d e )x + 63a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1353 +r0:=-80/231*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(7/2))-_ + 128/231*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(5/2))-2/11*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(11/2))-8/33*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(9/2))-256/231*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(3/2))+1024/231*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*sqrt(d+e*x))+2048/231*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (- 2772a b e + 5544b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 2310a b e - 9240a b d e + 18480b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1848a b e - 3696a b d e - 14784a b d e + 29568b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 990a b e - 1584a b d e - 3168a b d e - 12672a b d e +--R + +--R 6 4 2 +--R 25344b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 308a b e - 440a b d e - 704a b d e - 1408a b d e +--R + +--R 5 4 2 6 5 +--R - 5632a b d e + 11264b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 56a b d e - 80a b d e - 128a b d e - 256a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 231b e x + (231a e + 1155b d e )x + (1155a d e + 2310b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (2310a d e + 2310b d e )x + (2310a d e + 1155b d e )x +--R + +--R 4 8 5 7 5 7 +--R (1155a d e + 231b d e )x + 231a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (- 2772a b e + 5544b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 2310a b e - 9240a b d e + 18480b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1848a b e - 3696a b d e - 14784a b d e + 29568b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 990a b e - 1584a b d e - 3168a b d e - 12672a b d e +--R + +--R 6 4 2 +--R 25344b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 308a b e - 440a b d e - 704a b d e - 1408a b d e - 5632a b d e +--R + +--R 6 5 +--R 11264b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 56a b d e - 80a b d e - 128a b d e - 256a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e + 2048b d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 5 7 +--R (231e x + 1155d e x + 2310d e x + 2310d e x + 1155d e x + 231d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 462b e x + (2772a b e - 5544b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (2310a b e + 9240a b d e - 18480b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1848a b e + 3696a b d e + 14784a b d e - 29568b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 990a b e + 1584a b d e + 3168a b d e + 12672a b d e +--R + +--R 6 4 2 +--R - 25344b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 308a b e + 440a b d e + 704a b d e + 1408a b d e +--R + +--R 5 4 2 6 5 +--R 5632a b d e - 11264b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 42a e + 56a b d e + 80a b d e + 128a b d e + 256a b d e +--R + +--R 5 5 6 6 +--R 1024a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 462b e x + (- 2310a b e + 5544b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 5082a b e - 3696a b d e + 18480b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 4158a b e - 12936a b d e + 3696a b d e + 29568b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 2838a b e - 5280a b d e - 17952a b d e + 16896a b d e +--R + +--R 7 4 2 +--R 25344b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 1298a b e - 2024a b d e - 3872a b d e - 14080a b d e +--R + +--R 6 4 2 7 5 +--R 19712a b d e + 11264b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 350a b e - 496a b d e - 784a b d e - 1536a b d e - 5888a b d e +--R + +--R 6 5 7 6 +--R 10240a b d e + 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 42a e - 56a b d e - 80a b d e - 128a b d e - 256a b d e +--R + +--R 2 5 5 6 6 +--R - 1024a b d e + 2048a b d +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 231b e x + (231a e + 1155b d e )x + (1155a d e + 2310b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (2310a d e + 2310b d e )x + (2310a d e + 1155b d e )x +--R + +--R 4 8 5 7 5 7 +--R (1155a d e + 231b d e )x + 231a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(15/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1353 +r0:=-80/429*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(9/2))-_ + 640/3003*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(7/2))-2/13*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(13/2))-24/143*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(11/2))-256/1001*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(5/2))-1024/1001*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(d+e*x)^(3/2))-2048/3003*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 6006b e x + (- 12012a b e - 24024b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 18018a b e - 24024a b d e - 48048b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 17160a b e - 20592a b d e - 27456a b d e - 54912b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 10010a b e - 11440a b d e - 13728a b d e - 18304a b d e +--R + +--R 6 4 2 +--R - 36608b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 3276a b e - 3640a b d e - 4160a b d e - 4992a b d e +--R + +--R 5 4 2 6 5 +--R - 6656a b d e - 13312b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 462a e - 504a b d e - 560a b d e - 640a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 7 13 12 6 +--R 3003b e x + (3003a e + 18018b d e )x +--R + +--R 12 2 11 5 2 11 3 10 4 +--R (18018a d e + 45045b d e )x + (45045a d e + 60060b d e )x +--R + +--R 3 10 4 9 3 4 9 5 8 2 +--R (60060a d e + 45045b d e )x + (45045a d e + 18018b d e )x +--R + +--R 5 8 6 7 6 7 +--R (18018a d e + 3003b d e )x + 3003a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 6006b e x + (- 12012a b e - 24024b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 18018a b e - 24024a b d e - 48048b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 17160a b e - 20592a b d e - 27456a b d e - 54912b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 10010a b e - 11440a b d e - 13728a b d e - 18304a b d e +--R + +--R 6 4 2 +--R - 36608b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 3276a b e - 3640a b d e - 4160a b d e - 4992a b d e +--R + +--R 5 4 2 6 5 +--R - 6656a b d e - 13312b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 462a e - 504a b d e - 560a b d e - 640a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e - 2048b d +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 +--R 3003e x + 18018d e x + 45045d e x + 60060d e x + 45045d e x +--R + +--R 5 8 6 7 +--R 18018d e x + 3003d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R 6006b e x + (12012a b e + 24024b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (18018a b e + 24024a b d e + 48048b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (17160a b e + 20592a b d e + 27456a b d e + 54912b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 10010a b e + 11440a b d e + 13728a b d e + 18304a b d e +--R + +--R 6 4 2 +--R 36608b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 3276a b e + 3640a b d e + 4160a b d e + 4992a b d e +--R + +--R 5 4 2 6 5 +--R 6656a b d e + 13312b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 462a e + 504a b d e + 560a b d e + 640a b d e + 768a b d e +--R + +--R 5 5 6 6 +--R 1024a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R - 6006b e x + (- 18018a b e - 24024b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 30030a b e - 48048a b d e - 48048b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 35178a b e - 44616a b d e - 75504a b d e - 54912b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 27170a b e - 32032a b d e - 41184a b d e - 73216a b d e +--R + +--R 7 4 2 +--R - 36608b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 13286a b e - 15080a b d e - 17888a b d e - 23296a b d e +--R + +--R 6 4 2 7 5 +--R - 43264a b d e - 13312b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 3738a b e - 4144a b d e - 4720a b d e - 5632a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 7424a b d e - 14336a b d e - 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 462a e - 504a b d e - 560a b d e - 640a b d e - 768a b d e +--R + +--R 2 5 5 6 6 +--R - 1024a b d e - 2048a b d +--R / +--R 13 7 13 12 6 +--R 3003b e x + (3003a e + 18018b d e )x +--R + +--R 12 2 11 5 2 11 3 10 4 +--R (18018a d e + 45045b d e )x + (45045a d e + 60060b d e )x +--R + +--R 3 10 4 9 3 4 9 5 8 2 +--R (60060a d e + 45045b d e )x + (45045a d e + 18018b d e )x +--R + +--R 5 8 6 7 6 7 +--R (18018a d e + 3003b d e )x + 3003a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(17/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1353 +r0:=-16/143*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(11/2))-_ + 128/1287*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(9/2))-2/15*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(15/2))-8/65*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(13/2))-256/3003*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(7/2))-1024/9009*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(d+e*x)^(5/2))-2048/45045*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 30030b e x + (- 108108a b e - 72072b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 193050a b e - 154440a b d e - 102960b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 200200a b e - 171600a b d e - 137280a b d e - 91520b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 122850a b e - 109200a b d e - 93600a b d e - 74880a b d e +--R + +--R 6 4 2 +--R - 49920b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 41580a b e - 37800a b d e - 33600a b d e - 28800a b d e +--R + +--R 5 4 2 6 5 +--R - 23040a b d e - 15360b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 6006a e - 5544a b d e - 5040a b d e - 4480a b d e - 3840a b d e +--R + +--R 5 5 6 6 +--R - 3072a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 8 14 13 7 +--R 45045b e x + (45045a e + 315315b d e )x +--R + +--R 13 2 12 6 2 12 3 11 5 +--R (315315a d e + 945945b d e )x + (945945a d e + 1576575b d e )x +--R + +--R 3 11 4 10 4 4 10 5 9 3 +--R (1576575a d e + 1576575b d e )x + (1576575a d e + 945945b d e )x +--R + +--R 5 9 6 8 2 6 8 7 7 +--R (945945a d e + 315315b d e )x + (315315a d e + 45045b d e )x +--R + +--R 7 7 +--R 45045a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 30030b e x + (- 108108a b e - 72072b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 193050a b e - 154440a b d e - 102960b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 200200a b e - 171600a b d e - 137280a b d e - 91520b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 122850a b e - 109200a b d e - 93600a b d e - 74880a b d e +--R + +--R 6 4 2 +--R - 49920b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 41580a b e - 37800a b d e - 33600a b d e - 28800a b d e +--R + +--R 5 4 2 6 5 +--R - 23040a b d e - 15360b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 6006a e - 5544a b d e - 5040a b d e - 4480a b d e - 3840a b d e +--R + +--R 5 5 6 6 +--R - 3072a b d e - 2048b d +--R / +--R 14 7 13 6 2 12 5 3 11 4 +--R 45045e x + 315315d e x + 945945d e x + 1576575d e x +--R + +--R 4 10 3 5 9 2 6 8 7 7 +--R 1576575d e x + 945945d e x + 315315d e x + 45045d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R 30030b e x + (108108a b e + 72072b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (193050a b e + 154440a b d e + 102960b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (200200a b e + 171600a b d e + 137280a b d e + 91520b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 122850a b e + 109200a b d e + 93600a b d e + 74880a b d e +--R + +--R 6 4 2 +--R 49920b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 41580a b e + 37800a b d e + 33600a b d e + 28800a b d e +--R + +--R 5 4 2 6 5 +--R 23040a b d e + 15360b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 6006a e + 5544a b d e + 5040a b d e + 4480a b d e + 3840a b d e +--R + +--R 5 5 6 6 +--R 3072a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R - 30030b e x + (- 138138a b e - 72072b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 301158a b e - 226512a b d e - 102960b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 393250a b e - 326040a b d e - 240240a b d e - 91520b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 323050a b e - 280800a b d e - 230880a b d e - 166400a b d e +--R + +--R 7 4 2 +--R - 49920b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 164430a b e - 147000a b d e - 127200a b d e - 103680a b d e +--R + +--R 6 4 2 7 5 +--R - 72960a b d e - 15360b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 47586a b e - 43344a b d e - 38640a b d e - 33280a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 26880a b d e - 18432a b d e - 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 6006a e - 5544a b d e - 5040a b d e - 4480a b d e - 3840a b d e +--R + +--R 2 5 5 6 6 +--R - 3072a b d e - 2048a b d +--R / +--R 14 8 14 13 7 +--R 45045b e x + (45045a e + 315315b d e )x +--R + +--R 13 2 12 6 2 12 3 11 5 +--R (315315a d e + 945945b d e )x + (945945a d e + 1576575b d e )x +--R + +--R 3 11 4 10 4 4 10 5 9 3 +--R (1576575a d e + 1576575b d e )x + (1576575a d e + 945945b d e )x +--R + +--R 5 9 6 8 2 6 8 7 7 +--R (945945a d e + 315315b d e )x + (315315a d e + 45045b d e )x +--R + +--R 7 7 +--R 45045a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1353 +r0:=2/9*(a+b*x)*(d+e*x)^(9/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 5 4 3 4 3 2 2 3 +--R 2b e x + (2a e + 8b d e )x + (8a d e + 12b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (12a d e + 8b d e)x + (8a d e + 2b d )x + 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 9e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (2e x + 8d e x + 12d e x + 8d e x + 2d )\|e x + d +--R (3) ----------------------------------------------------- +--R 9e +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (2e x + 8d e x + 12d e x + 8d e x + 2d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - 2b e x + (- 2a e - 8b d e )x + (- 8a d e - 12b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 12a d e - 8b d e)x + (- 8a d e - 2b d )x - 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 9e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1353 +r0:=2/7*(a+b*x)*(d+e*x)^(7/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 4 3 2 3 2 2 2 +--R 2b e x + (2a e + 6b d e )x + (6a d e + 6b d e)x +--R + +--R 2 3 3 +--R (6a d e + 2b d )x + 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 7e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (2e x + 6d e x + 6d e x + 2d )\|e x + d +--R (3) ------------------------------------------ +--R 7e +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (2e x + 6d e x + 6d e x + 2d )\|e x + d \|b x + 2a b x + a +--R + +--R 3 4 3 2 3 2 2 2 +--R - 2b e x + (- 2a e - 6b d e )x + (- 6a d e - 6b d e)x +--R + +--R 2 3 3 +--R (- 6a d e - 2b d )x - 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 7e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (b e x + (a e + b d)x + a d)\|e x + d +--R (1) --------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1240 + +--S 1241 of 1353 +r0:=2/5*(a+b*x)*(d+e*x)^(5/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2b e x + (2a e + 4b d e)x + (4a d e + 2b d )x + 2a d )\|e x + d +--R (2) -------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +-------+ +--R (2e x + 4d e x + 2d )\|e x + d +--R (3) -------------------------------- +--R 5e +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (2e x + 4d e x + 2d )\|e x + d \|b x + 2a b x + a +--R + +--R 2 3 2 2 2 2 +-------+ +--R (- 2b e x + (- 2a e - 4b d e)x + (- 4a d e - 2b d )x - 2a d )\|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (b x + a)\|e x + d +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1353 +r0:=2/3*(a+b*x)*(d+e*x)^(3/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 2 +-------+ +--R (2b e x + (2a e + 2b d)x + 2a d)\|e x + d +--R (2) ------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1353 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R (2e x + 2d)\|e x + d +--R (3) --------------------- +--R 3e +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R +-------+ | 2 2 2 +--R (2e x + 2d)\|e x + d \|b x + 2a b x + a +--R + +--R 2 +-------+ +--R (- 2b e x + (- 2a e - 2b d)x - 2a d)\|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1353 +t0:=(a+b*x)/(sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1353 +r0:=2*(a+b*x)*sqrt(d+e*x)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R +-------+ +--R (2b x + 2a)\|e x + d +--R (2) ---------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1353 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2\|e x + d +--R (3) ----------- +--R e +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R +-------+ | 2 2 2 +-------+ +--R 2\|e x + d \|b x + 2a b x + a + (- 2b x - 2a)\|e x + d +--R (4) ---------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1353 +t0:=(a+b*x)/((d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1353 +r0:=-2*(a+b*x)/(e*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) -------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R e\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - ----------- +--R +-------+ +--R e\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - 2\|b x + 2a b x + a + 2b x + 2a +--R (4) ------------------------------------ +--R +------------------+ +--R +-------+ | 2 2 2 +--R e\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1353 +t0:=(a+b*x)/((d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1353 +r0:=-2/3*(a+b*x)/(e*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) -------------------------------------------- +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (3e x + 3d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - ----------------------- +--R 2 +-------+ +--R (3e x + 3d e)\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - 2\|b x + 2a b x + a + 2b x + 2a +--R (4) -------------------------------------------- +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (3e x + 3d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1353 +t0:=(a+b*x)/((d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1353 +r0:=-2/5*(a+b*x)/(e*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) ------------------------------------------------------- +--R +------------------+ +--R 3 2 2 2 +-------+ | 2 2 2 +--R (5e x + 10d e x + 5d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - ---------------------------------- +--R 3 2 2 2 +-------+ +--R (5e x + 10d e x + 5d e)\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - 2\|b x + 2a b x + a + 2b x + 2a +--R (4) ------------------------------------------------------- +--R +------------------+ +--R 3 2 2 2 +-------+ | 2 2 2 +--R (5e x + 10d e x + 5d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1353 +r0:=7/3*e*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 7/5*e*(a+b*x)*(d+e*x)^(5/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^(7/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-7*e*(b*d-a*e)^(5/2)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+7*e*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 105a b e + 210a b d e - 105b d e)x - 105a e + 210a b d e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b e x + (- 14a b e + 32b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 168a b d e + 116b d e)x + 105a e - 245a b d e +--R + +--R 2 2 3 3 +--R 161a b d e - 15b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 15b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 3 2 3 3 2 2 +--R (105a b e - 210a b d e + 105b d e)x + 105a e - 210a b d e +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 12b e x + (- 28a b e + 64b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (140a b e - 336a b d e + 232b d e)x + 210a e - 490a b d e +--R + +--R 2 2 3 3 +--R 322a b d e - 30b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 30b x + 30a b +--R , +--R +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 105a b e + 210a b d e - 105b d e)x - 105a e + 210a b d e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b e x + (- 14a b e + 32b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 168a b d e + 116b d e)x + 105a e - 245a b d e +--R + +--R 2 2 3 3 +--R 161a b d e - 15b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 15b x + 15a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1272 + +--S 1273 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 3 2 3 3 2 2 +--R (105a b e - 210a b d e + 105b d e)x + 105a e - 210a b d e +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 3 3 2 4 2 2 +--R (210a b e - 420a b d e + 210b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 +--R (420a b e - 840a b d e + 420a b d e)x + 210a e - 420a b d e +--R + +--R 2 2 2 +--R 210a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 12b e x + (- 28a b e + 64b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (140a b e - 336a b d e + 232b d e)x + 210a e - 490a b d e +--R + +--R 2 2 3 3 +--R 322a b d e - 30b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 12b e x + (16a b e - 64b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 112a b e + 272a b d e - 232b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 350a b e + 826a b d e - 554a b d e + 30b d )x - 210a e +--R + +--R 3 2 2 2 2 3 3 +--R 490a b d e - 322a b d e + 30a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 5 4 +-+ | 2 2 2 +--R (30b x + 30a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b e x - 8b d e x - 12b d e x - 8b d e x - 2b d ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 5 5 5 4 4 4 2 3 3 +--R b e x + (- a e + 6b d e )x + (- 4a d e + 14b d e )x +--R + +--R 2 3 3 2 2 3 2 4 4 5 +--R (- 6a d e + 16b d e )x + (- 4a d e + 9b d e)x - a d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 5 4 2 3 4 3 2 2 2 3 +--R 2b e x + (2a b e + 8b d e )x + (8a b d e + 12b d e )x +--R + +--R 2 2 2 3 2 3 2 4 4 +--R (12a b d e + 8b d e)x + (8a b d e + 2b d )x + 2a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 5 6 2 4 5 2 5 4 2 2 3 4 +--R - b e x - 6b d e x + (a e - 2a b d e - 14b d e )x +--R + +--R 2 4 2 3 2 3 2 3 2 2 3 3 2 2 4 2 +--R (4a d e - 8a b d e - 16b d e )x + (6a d e - 12a b d e - 9b d e)x +--R + +--R 2 3 2 4 2 5 2 4 5 +--R (4a d e - 8a b d e - 2b d )x + a d e - 2a b d +--R / +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (a b e + 2b d)x + (- a b e + 4a b d)x - a e + 2a b d) +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 2 3 2 2 2 2 +--R (- 2b e x + (- 4a b e - 2b d)x + (- 2a b e - 4a b d)x - 2a b d) +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 3 3 2 4 2 2 +--R (105a b e - 210a b d e + 105b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 +--R (210a b e - 420a b d e + 210a b d e)x + 105a e - 210a b d e +--R + +--R 2 2 2 +--R 105a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 105a b e + 210a b d e - 105b d e)x - 105a e + 210a b d e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b e x + (- 14a b e + 32b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 168a b d e + 116b d e)x + 105a e - 245a b d e +--R + +--R 2 2 3 3 +--R 161a b d e - 15b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 6b e x + (8a b e - 32b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 56a b e + 136a b d e - 116b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 175a b e + 413a b d e - 277a b d e + 15b d )x - 105a e +--R + +--R 3 2 2 2 2 3 3 +--R 245a b d e - 161a b d e + 15a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 5 4 +-+ | 2 2 2 +--R (15b x + 15a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1275 + +--S 1276 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1276 + +)clear all + +--S 1277 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1353 +r0:=5/3*e*(a+b*x)*(d+e*x)^(3/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^(5/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-5*e*(b*d-a*e)^(3/2)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+5*e*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 +-----------+ +--R ((15a b e - 15b d e)x + 15a e - 15a b d e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (2b e x + (- 10a b e + 14b d e)x - 15a e + 20a b d e - 3b d )\|b +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 3b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a e + b d +--R ((15a b e - 15b d e)x + 15a e - 15a b d e) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4b e x + (- 20a b e + 28b d e)x - 30a e + 40a b d e - 6b d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +--R +---------+ +--R 2 2 2 2 |a e - b d +--R ((15a b e - 15b d e)x + 15a e - 15a b d e) |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2b e x + (- 10a b e + 14b d e)x - 15a e + 20a b d e - 3b d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 3b x + 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1279 + +--S 1280 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a e + b d +-+ +--R ((15a b e - 15b d e)x + 15a e - 15a b d e) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +------------------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R | 2 2 2 \| b +--R \|b x + 2a b x + a log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 3 2 2 2 2 3 2 +--R (- 30a b e + 30b d e)x + (- 60a b e + 60a b d e)x - 30a e +--R + +--R 2 +--R 30a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (4b e x + (- 20a b e + 28b d e)x - 30a e + 40a b d e - 6b d )\|b +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 4b e x + (16a b e - 28b d e)x + (50a b e - 68a b d e + 6b d )x +--R + +--R 3 2 2 2 2 +--R 30a e - 40a b d e + 6a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 3 +-+ | 2 2 2 +--R (6b x + 6a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +-----------+ +--R 3 3 2 2 2 3 |- a e + b d +-------+ +--R (2b e x + 6b d e x + 6b d e x + 2b d ) |----------- \|e x + d +--R \| b +--R + +--R 4 4 4 3 3 3 2 2 2 +--R b e x + (- a e + 5b d e )x + (- 3a d e + 9b d e )x +--R + +--R 2 2 3 3 4 +--R (- 3a d e + 7b d e)x - a d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 4 3 2 2 3 2 2 2 2 +--R - 2b e x + (- 2a b e - 6b d e )x + (- 6a b d e - 6b d e)x +--R + +--R 2 2 3 3 +--R (- 6a b d e - 2b d )x - 2a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 4 5 2 3 4 2 4 3 2 2 2 3 +--R - b e x - 5b d e x + (a e - 2a b d e - 9b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 2 3 2 4 2 3 +--R (3a d e - 6a b d e - 7b d e)x + (3a d e - 6a b d e - 2b d )x + a d e +--R + +--R 4 +--R - 2a b d +--R / +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (a b e + 2b d)x + (- a b e + 4a b d)x - a e + 2a b d) +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 3 3 2 3 2 2 2 2 |- a e + b d +--R (2b e x + (4a b e + 2b d)x + (2a b e + 4a b d)x + 2a b d) |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 3 2 2 2 2 3 2 +--R (- 15a b e + 15b d e)x + (- 30a b e + 30a b d e)x - 15a e +--R + +--R 2 +--R 15a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 2 2 +-+ |a e - b d +--R ((15a b e - 15b d e)x + 15a e - 15a b d e)\|b |--------- +--R \| b +--R * +--R +------------------+ +-------+ +--R | 2 2 2 \|e x + d +--R \|b x + 2a b x + a atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (2b e x + (- 10a b e + 14b d e)x - 15a e + 20a b d e - 3b d )\|b +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 2b e x + (8a b e - 14b d e)x + (25a b e - 34a b d e + 3b d )x +--R + +--R 3 2 2 2 2 +--R 15a e - 20a b d e + 3a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 3 +-+ | 2 2 2 +--R (3b x + 3a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1283 + +)clear all + +--S 1284 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1353 +r0:=-(d+e*x)^(3/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-3*e*(a+b*x)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*e*(a+b*x)*sqrt(d+e*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (- 3b e x - 3a e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-+ +-------+ +--R (2b e x + 3a e - b d)\|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a e + b d +--R (3b e x + 3a e) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R (4b e x + 6a e - 2b d)\|e x + d +--R / +--R 3 2 +--R 2b x + 2a b +--R , +--R +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R (- 3b e x - 3a e) |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +-------+ +--R (2b e x + 3a e - b d)\|e x + d +--R / +--R 3 2 +--R b x + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1286 + +--S 1287 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R (3b e x + 3a e) |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 +-----------+ \|b \|e x + d +--R (6b e x + 12a b e x + 6a e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R (4b e x + 6a e - 2b d)\|b \|e x + d \|b x + 2a b x + a +--R + +--R 2 2 2 2 +-+ +-------+ +--R (- 4b e x + (- 10a b e + 2b d)x - 6a e + 2a b d)\|b \|e x + d +--R / +--R +------------------+ +--R 3 2 +-+ | 2 2 2 +--R (2b x + 2a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +-----------+ +--R 2 2 2 |- a e + b d +-------+ 3 3 +--R (- 2b e x - 4b d e x - 2b d ) |----------- \|e x + d + b e x +--R \| b +--R + +--R 3 2 2 2 2 2 3 +--R (- a e + 4b d e )x + (- 2a d e + 5b d e)x - a d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 2 2 +--R (2b e x + (2a b e + 4b d e)x + (4a b d e + 2b d )x + 2a b d ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 3 4 2 2 3 2 3 2 2 2 2 +--R - b e x - 4b d e x + (a e - 2a b d e - 5b d e)x +--R + +--R 2 2 2 2 3 2 2 3 +--R (2a d e - 4a b d e - 2b d )x + a d e - 2a b d +--R / +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (a b e + 2b d)x + (- a b e + 4a b d)x - a e + 2a b d) +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 2 3 2 2 2 2 +--R (- 2b e x + (- 4a b e - 2b d)x + (- 2a b e - 4a b d)x - 2a b d) +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 +-----------+ \|b \|e x + d +--R (3b e x + 6a b e x + 3a e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R (- 3b e x - 3a e)\|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R (2b e x + 3a e - b d)\|b \|e x + d \|b x + 2a b x + a +--R + +--R 2 2 2 2 +-+ +-------+ +--R (- 2b e x + (- 5a b e + b d)x - 3a e + a b d)\|b \|e x + d +--R / +--R +------------------+ +--R 3 2 +-+ | 2 2 2 +--R (b x + a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1290 + +)clear all + +--S 1291 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1353 +r0:=-e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-sqrt(d+e*x)/(b*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +-----------+ +-+ +-------+ +--R (- b e x - a e)atanh(--------------) - \|- a e + b d \|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R b\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (b e x + a e) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 2 | 2 +--R (2b x + 2a b)\|- a b e + b d +--R , +--R +-----------+ +--R | 2 +-------+ +-----------+ +--R \|a b e - b d \|e x + d | 2 +-------+ +--R (b e x + a e)atan(------------------------) - \|a b e - b d \|e x + d +--R a e - b d +--R ----------------------------------------------------------------------] +--R +-----------+ +--R 2 | 2 +--R (b x + a b)\|a b e - b d +--R Type: Union(List(Expression(Integer)),...) +--E 1293 + +--S 1294 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (b e x + a e)\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 2 2 | 2 \|b \|e x + d +--R (2b e x + 4a b e x + 2a e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R - 2\|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R (2b x + 2a)\|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +------------------+ +--R 2 | 2 +-----------+ +-+ | 2 2 2 +--R (2b x + 2a b)\|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 2 2 +-------+ +--R ((2a b e - 2b d e)x + 2a b d e - 2b d )\|e x + d +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +--R (b e x + (- a e + 3b d e)x - a d e + 2b d )\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 3 2 2 2 2 +--R ((- 2a b e + 2b d e)x + (- 2a b e + 2b d )x - 2a b d e + 2a b d ) +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (- b e x - 3b d e x + (a e - 2a b d e - 2b d )x + a d e - 2a b d ) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (a b e + 2b d)x + (- a b e + 4a b d)x - a e + 2a b d) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (2a b e - 2b d e)x + (4a b e - 2a b d e - 2b d )x +--R + +--R 3 2 2 2 3 2 3 2 2 2 +--R (2a b e + 2a b d e - 4a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1295 + +--S 1296 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 2 2 | 2 \|b \|e x + d +--R (b e x + 2a b e x + a e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (b e x + a e)\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R - \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R (b x + a)\|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R +-----------+ +------------------+ +--R 2 +-----------+ +-+ | 2 | 2 2 2 +--R (b x + a b)\|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R (7) -------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1297 + +)clear all + +--S 1298 of 1353 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1353 +r0:=e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(3/2)*_ + sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-sqrt(d+e*x)/((b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +-----------+ +-+ +-------+ +--R (- b e x - a e)atanh(--------------) + \|- a e + b d \|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (a e - b d)\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (b e x + a e) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R 2\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 2 2 | 2 +--R ((2a b e - 2b d)x + 2a e - 2a b d)\|- a b e + b d +--R , +--R +-----------+ +--R | 2 +-------+ +-----------+ +--R \|a b e - b d \|e x + d | 2 +-------+ +--R (b e x + a e)atan(------------------------) + \|a b e - b d \|e x + d +--R a e - b d +--R ----------------------------------------------------------------------] +--R +-----------+ +--R 2 2 | 2 +--R ((a b e - b d)x + a e - a b d)\|a b e - b d +--R Type: Union(List(Expression(Integer)),...) +--E 1300 + +--S 1301 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (b e x + a e)\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 2 2 | 2 \|b \|e x + d +--R (2b e x + 4a b e x + 2a e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R 2\|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R (- 2b x - 2a)\|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +--R 2 2 | 2 +-----------+ +-+ +--R ((2a b e - 2b d)x + 2a e - 2a b d)\|- a b e + b d \|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +-------------+ +--R 2 +-------+ | 2 +--R ((2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 +-------+ +--R ((- 2a b e + 2b d)x - 2a b e + 2a b d)\|e x + d +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +--R (- b e x - 2b d x + a e - 2a b d)\|- a b e + b d +--R / +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (a b e + 2b d)x + (- a b e + 4a b d)x - a e + 2a b d) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (2a b e - 2b d e)x + (4a b e - 2a b d e - 2b d )x +--R + +--R 3 2 2 2 3 2 3 2 2 2 +--R (2a b e + 2a b d e - 4a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1302 + +--S 1303 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 2 2 | 2 \|b \|e x + d +--R (b e x + 2a b e x + a e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (b e x + a e)\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R (- b x - a)\|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 2 2 +-----------+ +-+ | 2 +--R ((a b e - b d)x + a e - a b d)\|- a e + b d \|b \|a b e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (7) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1304 + +)clear all + +--S 1305 of 1353 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------ +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1305 + +--S 1306 of 1353 +r0:=3*e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-_ + a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2/((b*d-a*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-3*b*sqrt(d+e*x)/((b*d-a*e)^2*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R (3b e x + 3a e)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R (- 3b e x - 2a e - b d)\|- a e + b d +--R / +--R +------------------+ +--R 2 2 2 2 +-----------+ +-------+ | 2 2 2 +--R (a e - 2a b d e + b d )\|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | b +-------+ +--R (3b e x + 3a e) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R - 6b e x - 4a e - 2b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-------+ +--R ((2a b e - 4a b d e + 2b d )x + 2a e - 4a b d e + 2a b d )\|e x + d +--R , +--R +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R (- 3b e x - 3a e) |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R - 3b e x - 2a e - b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-------+ +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1307 + +--S 1308 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +-------+ +--R (3b e x + 3a e)\|- a e + b d |- --------- \|e x + d +--R \| a e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 +-+ +-------+ \|b \|e x + d +--R (- 6b e x - 12a b e x - 6a e)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-----------+ | 2 2 2 +--R (- 6b e x - 4a e - 2b d)\|- a e + b d \|b x + 2a b x + a +--R + +--R 2 2 2 2 +-----------+ +--R (6b e x + (10a b e + 2b d)x + 4a e + 2a b d)\|- a e + b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +--R ((2a b e - 4a b d e + 2b d )x + 2a e - 4a b d e + 2a b d ) +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 +-+ +-------+ \|b \|e x + d +--R (- 3b e x - 6a b e x - 3a e)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R +-----------+ | b +-------+ +--R (- 3b e x - 3a e)\|- a e + b d |--------- \|e x + d +--R \|a e - b d +--R * +--R +------------------+ +-------+ +--R | 2 2 2 b\|e x + d +--R \|b x + 2a b x + a atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R +------------------+ +--R +-----------+ | 2 2 2 +--R (- 3b e x - 2a e - b d)\|- a e + b d \|b x + 2a b x + a +--R + +--R 2 2 2 2 +-----------+ +--R (3b e x + (5a b e + b d)x + 2a e + a b d)\|- a e + b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-----------+ +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|- a e + b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1311 + +)clear all + +--S 1312 of 1353 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1353 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5*b^(3/2)*e*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10/3*b/((b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-5*b^2*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +-+ +-------+ +--R (- 15b e x + (- 15a b e - 15b d e)x - 15a b d e)\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (10a b e + 20b d e)x - 2a e + 14a b d e + 3b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a e - 9a b d e + 9a b d e - 3b d e)x + 3a d e - 9a b d e +--R + +--R 2 3 3 4 +--R 9a b d e - 3b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 | b +--R (15b e x + (15a b e + 15b d e)x + 15a b d e) |- --------- +--R \| a e - b d +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R 30b e x + (20a b e + 40b d e)x - 4a e + 28a b d e + 6b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b e - 18a b d e + 18a b d e - 6b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (6a e - 12a b d e + 12a b d e - 6b d )x + 6a d e - 18a b d e +--R + +--R 2 2 3 3 4 +--R 18a b d e - 6a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +---------+ +--R 2 2 2 2 2 | b +-------+ +--R (15b e x + (15a b e + 15b d e)x + 15a b d e) |--------- \|e x + d +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R 15b e x + (10a b e + 20b d e)x - 2a e + 14a b d e + 3b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1314 + +--S 1315 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 +-----------+ +--R (15b e x + (15a b e + 15b d e)x + 15a b d e)\|- a e + b d +--R * +--R +-----------+ +------------------+ +--R | b +-------+ | 2 2 2 +--R |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 +--R 30b e x + (60a b e + 30b d e)x + (30a b e + 60a b d e)x +--R + +--R 2 +--R 30a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (30b e x + (20a b e + 40b d e)x - 4a e + 28a b d e + 6b d ) +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 30b e x + (- 50a b e - 40b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 16a b e - 68a b d e - 6b d )x + 4a e - 28a b d e - 6a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b e - 18a b d e + 18a b d e - 6b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (6a e - 12a b d e + 12a b d e - 6b d )x + 6a d e - 18a b d e +--R + +--R 2 2 3 3 4 +--R 18a b d e - 6a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 2 3 2 2 3 2 2 2 2 +--R 15b e x + (30a b e + 15b d e)x + (15a b e + 30a b d e)x +--R + +--R 2 +--R 15a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +-----------+ +--R (15b e x + (15a b e + 15b d e)x + 15a b d e)\|- a e + b d +--R * +--R +---------+ +------------------+ +-------+ +--R | b +-------+ | 2 2 2 b\|e x + d +--R |--------- \|e x + d \|b x + 2a b x + a atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (10a b e + 20b d e)x - 2a e + 14a b d e + 3b d ) +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 15b e x + (- 25a b e - 20b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 8a b e - 34a b d e - 3b d )x + 2a e - 14a b d e - 3a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1318 + +)clear all + +--S 1319 of 1353 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 1353 +r0:=2/5/((b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+14/15*b/((b*d-_ + a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7*b^(5/2)*e*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+14/3*b^2/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-7*b^3*sqrt(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R 105b e x + (105a b e + 210b d e )x + (210a b d e + 105b d e)x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 70a b e - 245b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (14a b e - 168a b d e - 161b d e)x - 6a e + 32a b d e +--R + +--R 2 2 3 3 +--R - 116a b d e - 15b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (15a e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (30a d e - 120a b d e + 180a b d e - 120a b d e + 30b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1320 + +--S 1321 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R 105b e x + (105a b e + 210b d e )x + (210a b d e + 105b d e)x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R - 210b e x + (- 140a b e - 490b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (28a b e - 336a b d e - 322b d e)x - 12a e + 64a b d e - 232a b d e +--R + +--R 3 3 +--R - 30b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (30a b e - 120a b d e + 180a b d e - 120a b d e + 30b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 30a e - 60a b d e - 60a b d e + 240a b d e - 210a b d e +--R + +--R 5 5 +--R 60b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 60a d e - 210a b d e + 240a b d e - 60a b d e - 60a b d e +--R + +--R 5 6 +--R 30b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 30a d e - 120a b d e + 180a b d e - 120a b d e + 30a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 105a b e - 210b d e )x +--R + +--R 2 2 3 2 2 2 +--R (- 210a b d e - 105b d e)x - 105a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 70a b e - 245b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (14a b e - 168a b d e - 161b d e)x - 6a e + 32a b d e - 116a b d e +--R + +--R 3 3 +--R - 15b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1321 + +--S 1322 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R 105b e x + (105a b e + 210b d e )x + (210a b d e + 105b d e)x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 210b e x + (- 420a b e - 420b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 210a b e - 840a b d e - 210b d e)x +--R + +--R 2 2 2 3 2 2 2 2 +--R (- 420a b d e - 420a b d e)x - 210a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 210b e x + (- 140a b e - 490b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (28a b e - 336a b d e - 322b d e)x - 12a e + 64a b d e +--R + +--R 2 2 3 3 +--R - 232a b d e - 30b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R 210b e x + (350a b e + 490b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (112a b e + 826a b d e + 322b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 16a b e + 272a b d e + 554a b d e + 30b d )x + 12a e +--R + +--R 3 2 2 2 2 3 3 +--R - 64a b d e + 232a b d e + 30a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (30a b e - 120a b d e + 180a b d e - 120a b d e + 30b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 30a e - 60a b d e - 60a b d e + 240a b d e - 210a b d e +--R + +--R 5 5 +--R 60b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 60a d e - 210a b d e + 240a b d e - 60a b d e - 60a b d e +--R + +--R 5 6 +--R 30b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 30a d e - 120a b d e + 180a b d e - 120a b d e + 30a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1323 + +--S 1324 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 4 3 3 4 2 3 +--R - 105b e x + (- 210a b e - 210b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 105a b e - 420a b d e - 105b d e)x +--R + +--R 2 2 2 3 2 2 2 2 +--R (- 210a b d e - 210a b d e)x - 105a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 105a b e - 210b d e )x +--R + +--R 2 2 3 2 2 2 +--R (- 210a b d e - 105b d e)x - 105a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 70a b e - 245b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (14a b e - 168a b d e - 161b d e)x - 6a e + 32a b d e +--R + +--R 2 2 3 3 +--R - 116a b d e - 15b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R 105b e x + (175a b e + 245b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (56a b e + 413a b d e + 161b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (- 8a b e + 136a b d e + 277a b d e + 15b d )x + 6a e - 32a b d e +--R + +--R 2 2 2 3 3 +--R 116a b d e + 15a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1325 + +)clear all + +--S 1326 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1353 +r0:=-7/12*e*(a+b*x)*(d+e*x)^(5/2)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^(7/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-35/24*e^2*_ + (d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-35/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+35/8*e^3*(a+b*x)*sqrt(d+e*x)/(b^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +--R (- 105b e x - 315a b e x - 315a b e x - 105a e )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b e x + (231a b e - 87b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (280a b e - 98a b d e - 38b d e)x + 105a e - 35a b d e +--R + +--R 2 2 3 3 +--R - 14a b d e - 8b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 2 5 2 4 +-+ | 2 2 2 +--R (24b x + 48a b x + 24a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1327 + +--S 1328 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 3 2 3 2 2 3 3 3 |- a e + b d +--R (105b e x + 315a b e x + 315a b e x + 105a e ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 96b e x + (462a b e - 174b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (560a b e - 196a b d e - 76b d e)x + 210a e - 70a b d e +--R + +--R 2 2 3 3 +--R - 28a b d e - 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 3 6 2 2 5 3 4 +--R 48b x + 144a b x + 144a b x + 48a b +--R , +--R +--R +---------+ +--R 3 3 3 2 3 2 2 3 3 3 |a e - b d +--R (- 105b e x - 315a b e x - 315a b e x - 105a e ) |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b e x + (231a b e - 87b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (280a b e - 98a b d e - 38b d e)x + 105a e - 35a b d e +--R + +--R 2 2 3 3 +--R - 14a b d e - 8b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 3 6 2 2 5 3 4 +--R 24b x + 72a b x + 72a b x + 24a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1328 + +--S 1329 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 3 2 3 2 2 3 3 3 |- a e + b d +-+ +--R (105b e x + 315a b e x + 315a b e x + 105a e ) |----------- \|b +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (210b e x + 840a b e x + 1260a b e x + 840a b e x + 210a e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 96b e x + (462a b e - 174b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (560a b e - 196a b d e - 76b d e)x + 210a e - 70a b d e +--R + +--R 2 2 3 3 +--R - 28a b d e - 16b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 96b e x + (- 558a b e + 174b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 1022a b e + 370a b d e + 76b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 770a b e + 266a b d e + 104a b d e + 16b d )x - 210a e +--R + +--R 3 2 2 2 2 3 3 +--R 70a b d e + 28a b d e + 16a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 7 3 6 2 2 5 3 4 +-+ | 2 2 2 +--R (48b x + 144a b x + 144a b x + 48a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b e x - 8b d e x - 12b d e x - 8b d e x - 2b d ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 5 5 5 4 4 4 2 3 3 +--R b e x + (- a e + 6b d e )x + (- 4a d e + 14b d e )x +--R + +--R 2 3 3 2 2 3 2 4 4 5 +--R (- 6a d e + 16b d e )x + (- 4a d e + 9b d e)x - a d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 5 4 2 3 4 3 2 2 2 3 +--R 2b e x + (2a b e + 8b d e )x + (8a b d e + 12b d e )x +--R + +--R 2 2 2 3 2 3 2 4 4 +--R (12a b d e + 8b d e)x + (8a b d e + 2b d )x + 2a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 5 6 2 4 5 2 5 4 2 2 3 4 +--R - b e x - 6b d e x + (a e - 2a b d e - 14b d e )x +--R + +--R 2 4 2 3 2 3 2 3 2 2 3 3 2 2 4 2 +--R (4a d e - 8a b d e - 16b d e )x + (6a d e - 12a b d e - 9b d e)x +--R + +--R 2 3 2 4 2 5 2 4 5 +--R (4a d e - 8a b d e - 2b d )x + a d e - 2a b d +--R / +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (3a b e + 2b d)x + (2a b e + 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 2a b e + 12a b d)x + (- 3a b e + 8a b d)x - a e + 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 5 5 4 5 4 2 3 4 3 +--R - 2b e x + (- 8a b e - 2b d)x + (- 12a b e - 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 4 +--R (- 8a b e - 12a b d)x + (- 2a b e - 8a b d)x - 2a b d +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1330 + +--S 1331 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (105b e x + 420a b e x + 630a b e x + 420a b e x + 105a e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 3 3 3 2 3 2 2 3 3 3 +-+ |a e - b d +--R (- 105b e x - 315a b e x - 315a b e x - 105a e )\|b |--------- +--R \| b +--R * +--R +------------------+ +-------+ +--R | 2 2 2 \|e x + d +--R \|b x + 2a b x + a atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b e x + (231a b e - 87b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (280a b e - 98a b d e - 38b d e)x + 105a e - 35a b d e +--R + +--R 2 2 3 3 +--R - 14a b d e - 8b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 48b e x + (- 279a b e + 87b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 511a b e + 185a b d e + 38b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 385a b e + 133a b d e + 52a b d e + 8b d )x - 105a e +--R + +--R 3 2 2 2 2 3 3 +--R 35a b d e + 14a b d e + 8a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 7 3 6 2 2 5 3 4 +-+ | 2 2 2 +--R (24b x + 72a b x + 72a b x + 24a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1332 + +)clear all + +--S 1333 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1353 +r0:=-5/12*e*(a+b*x)*(d+e*x)^(3/2)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^(5/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-5/8*e^2*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 15b e x - 45a b e x - 45a b e x - 15a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 33b e x + (- 40a b e - 26b d e)x - 15a e - 10a b d e - 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 5 2 4 2 3 +-----------+ +-+ | 2 2 2 +--R (24b x + 48a b x + 24a b )\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1334 + +--S 1335 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b e x + 45a b e x + 45a b e x + 15a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 66b e x + (- 80a b e - 52b d e)x - 30a e - 20a b d e - 16b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 6 3 5 2 2 4 3 3 | 2 +--R (48b x + 144a b x + 144a b x + 48a b )\|- a b e + b d +--R , +--R +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b e x + 45a b e x + 45a b e x + 15a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 33b e x + (- 40a b e - 26b d e)x - 15a e - 10a b d e - 8b d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 6 3 5 2 2 4 3 3 | 2 +--R (24b x + 72a b x + 72a b x + 24a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1335 + +--S 1336 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (15b e x + 45a b e x + 45a b e x + 15a e )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (30b e x + 120a b e x + 180a b e x + 120a b e x + 30a e ) +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 66b e x + (- 80a b e - 52b d e)x - 30a e - 20a b d e - 16b d ) +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R 66b e x + (146a b e + 52b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (110a b e + 72a b d e + 16b d )x + 30a e + 20a b d e + 16a b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +--R 6 3 5 2 2 4 3 3 | 2 +-----------+ +--R (48b x + 144a b x + 144a b x + 48a b )\|- a b e + b d \|- a e + b d +--R * +--R +------------------+ +--R +-+ | 2 2 2 +--R \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 4 2 3 3 3 2 2 2 2 +--R (2a b e - 2b d e )x + (6a b d e - 6b d e )x +--R + +--R 2 2 2 3 3 2 4 +--R (6a b d e - 6b d e)x + 2a b d e - 2b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 4 4 4 3 3 3 2 2 2 +--R b e x + (- a e + 5b d e )x + (- 3a d e + 9b d e )x +--R + +--R 2 2 3 3 4 +--R (- 3a d e + 7b d e)x - a d e + 2b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 3 3 4 2 4 2 3 3 2 2 3 +--R (- 2a b e + 2b d e )x + (- 2a b e - 4a b d e + 6b d e )x +--R + +--R 2 3 3 3 2 2 2 2 2 3 3 4 +--R (- 6a b d e + 6b d e)x + (- 6a b d e + 4a b d e + 2b d )x +--R + +--R 2 3 2 4 +--R - 2a b d e + 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 5 2 3 4 2 4 3 2 2 2 3 +--R - b e x - 5b d e x + (a e - 2a b d e - 9b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +--R (3a d e - 6a b d e - 7b d e)x + (3a d e - 6a b d e - 2b d )x +--R + +--R 2 3 4 +--R a d e - 2a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (3a b e + 2b d)x + (2a b e + 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 2a b e + 12a b d)x + (- 3a b e + 8a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (2a b e - 2b d e)x + (8a b e - 6a b d e - 2b d )x +--R + +--R 3 3 2 2 4 5 2 3 4 2 2 3 3 2 4 2 2 +--R (12a b e - 4a b d e - 8a b d )x + (8a b e + 4a b d e - 12a b d )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (2a b e + 6a b d e - 8a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1337 + +--S 1338 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e )\|a b e - b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (15b e x + 45a b e x + 45a b e x + 15a e )\|- a e + b d \|b +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R | 2 2 2 \|a b e - b d \|e x + d +--R \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 33b e x + (- 40a b e - 26b d e)x - 15a e - 10a b d e - 8b d ) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R 33b e x + (73a b e + 26b d e)x + (55a b e + 36a b d e + 8b d )x +--R + +--R 3 2 2 2 2 +--R 15a e + 10a b d e + 8a b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 6 3 5 2 2 4 3 3 +-----------+ +-+ | 2 +--R (24b x + 72a b x + 72a b x + 24a b )\|- a e + b d \|b \|a b e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1339 + +)clear all + +--S 1340 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1353 +r0:=-1/3*(d+e*x)^(3/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/4*e*(a+b*x)*_ + (d+e*x)^(3/2)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/8*e^3*(a+_ + b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+1/8*e^2*sqrt(d+e*x)/(b^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 3b e x - 9a b e x - 9a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (- 8a b e + 14b d e)x - 3a e - 2a b d e + 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +--R ((24a b e - 24b d)x + (48a b e - 48a b d)x + 24a b e - 24a b d) +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (3b e x + 9a b e x + 9a b e x + 3a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 16a b e + 28b d e)x - 6a e - 4a b d e + 16b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 5 6 3 2 4 5 2 +--R (48a b e - 48b d)x + (144a b e - 144a b d)x +--R + +--R 3 3 2 4 4 2 3 3 +--R (144a b e - 144a b d)x + 48a b e - 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|a b e - b d \|e x + d +--R (3b e x + 9a b e x + 9a b e x + 3a e )atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (- 8a b e + 14b d e)x - 3a e - 2a b d e + 8b d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 5 6 3 2 4 5 2 3 3 2 4 +--R (24a b e - 24b d)x + (72a b e - 72a b d)x + (72a b e - 72a b d)x +--R + +--R 4 2 3 3 +--R 24a b e - 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1342 + +--S 1343 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (3b e x + 9a b e x + 9a b e x + 3a e )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (6b e x + 24a b e x + 36a b e x + 24a b e x + 6a e )\|- a b e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 16a b e + 28b d e)x - 6a e - 4a b d e + 16b d ) +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 6b e x + (10a b e - 28b d e)x + (22a b e - 24a b d e - 16b d )x +--R + +--R 3 2 2 2 2 +--R 6a e + 4a b d e - 16a b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 5 6 3 2 4 5 2 3 3 2 4 +--R (48a b e - 48b d)x + (144a b e - 144a b d)x + (144a b e - 144a b d)x +--R + +--R 4 2 3 3 +--R 48a b e - 48a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 3 2 2 2 2 2 2 2 2 3 +--R ((2a b e - 2b d e )x + (4a b d e - 4b d e)x + 2a b d e - 2b d ) +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 3 2 2 2 2 2 +--R b e x + (- a e + 4b d e )x + (- 2a d e + 5b d e)x - a d e +--R + +--R 3 +--R 2b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (- 2a b e + 2b d e )x + (- 2a b e - 2a b d e + 4b d e)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (- 4a b d e + 2a b d e + 2b d )x - 2a b d e + 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 4 2 2 3 2 3 2 2 2 2 +--R - b e x - 4b d e x + (a e - 2a b d e - 5b d e)x +--R + +--R 2 2 2 2 3 2 2 3 +--R (2a d e - 4a b d e - 2b d )x + a d e - 2a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (3a b e + 2b d)x + (2a b e + 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 2a b e + 12a b d)x + (- 3a b e + 8a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (2a b e - 2b d e)x + (8a b e - 6a b d e - 2b d )x +--R + +--R 3 3 2 2 4 5 2 3 4 2 2 3 3 2 4 2 2 +--R (12a b e - 4a b d e - 8a b d )x + (8a b e + 4a b d e - 12a b d )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (2a b e + 6a b d e - 8a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1344 + +--S 1345 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (3b e x + 12a b e x + 18a b e x + 12a b e x + 3a e )\|a b e - b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (3b e x + 9a b e x + 9a b e x + 3a e )\|- a e + b d \|b +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R | 2 2 2 \|a b e - b d \|e x + d +--R \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (- 8a b e + 14b d e)x - 3a e - 2a b d e + 8b d ) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 3b e x + (5a b e - 14b d e)x + (11a b e - 12a b d e - 8b d )x +--R + +--R 3 2 2 2 2 +--R 3a e + 2a b d e - 8a b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 5 6 3 2 4 5 2 3 3 2 4 +--R (24a b e - 24b d)x + (72a b e - 72a b d)x + (72a b e - 72a b d)x +--R + +--R 4 2 3 3 +--R 24a b e - 24a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1346 + +)clear all + +--S 1347 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1353 +r0:=-1/3*sqrt(d+e*x)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/12*e*(a+b*x)*_ + sqrt(d+e*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+1/8*e^2*sqrt(d+e*x)/(b*(b*d-a*e)^2*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 3b e x - 9a b e x - 9a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (8a b e - 2b d e)x - 3a e + 14a b d e - 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (24a b e - 48a b d e + 24b d )x + (48a b e - 96a b d e + 48a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 24a b e - 48a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (3b e x + 9a b e x + 9a b e x + 3a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (16a b e - 4b d e)x - 6a e + 28a b d e - 16b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 4 2 5 6 2 3 +--R (48a b e - 96a b d e + 48b d )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (144a b e - 288a b d e + 144a b d )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (144a b e - 288a b d e + 144a b d )x + 48a b e - 96a b d e + 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|a b e - b d \|e x + d +--R (3b e x + 9a b e x + 9a b e x + 3a e )atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (8a b e - 2b d e)x - 3a e + 14a b d e - 8b d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 4 2 5 6 2 3 +--R (24a b e - 48a b d e + 24b d )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (72a b e - 144a b d e + 72a b d )x + 24a b e - 48a b d e + 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1349 + +--S 1350 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (3b e x + 9a b e x + 9a b e x + 3a e )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (6b e x + 24a b e x + 36a b e x + 24a b e x + 6a e )\|- a b e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (16a b e - 4b d e)x - 6a e + 28a b d e - 16b d ) +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 6b e x + (- 22a b e + 4b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 10a b e - 24a b d e + 16b d )x + 6a e - 28a b d e + 16a b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 2 4 2 5 6 2 3 +--R (48a b e - 96a b d e + 48b d )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (144a b e - 288a b d e + 144a b d )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (144a b e - 288a b d e + 144a b d )x + 48a b e - 96a b d e + 48a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 2 2 +-------+ +--R ((2a b e - 2b d e)x + 2a b d e - 2b d )\|e x + d +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +--R (b e x + (- a e + 3b d e)x - a d e + 2b d )\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 3 2 2 2 2 +--R ((- 2a b e + 2b d e)x + (- 2a b e + 2b d )x - 2a b d e + 2a b d ) +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (- b e x - 3b d e x + (a e - 2a b d e - 2b d )x + a d e - 2a b d ) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (3a b e + 2b d)x + (2a b e + 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 2a b e + 12a b d)x + (- 3a b e + 8a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (2a b e - 2b d e)x + (8a b e - 6a b d e - 2b d )x +--R + +--R 3 3 2 2 4 5 2 3 4 2 2 3 3 2 4 2 2 +--R (12a b e - 4a b d e - 8a b d )x + (8a b e + 4a b d e - 12a b d )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (2a b e + 6a b d e - 8a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (3b e x + 12a b e x + 18a b e x + 12a b e x + 3a e )\|a b e - b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (3b e x + 9a b e x + 9a b e x + 3a e )\|- a e + b d \|b +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R | 2 2 2 \|a b e - b d \|e x + d +--R \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (8a b e - 2b d e)x - 3a e + 14a b d e - 8b d ) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 3b e x + (- 11a b e + 2b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 5a b e - 12a b d e + 8b d )x + 3a e - 14a b d e + 8a b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 2 4 2 5 6 2 3 +--R (24a b e - 48a b d e + 24b d )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (72a b e - 144a b d e + 72a b d )x + 24a b e - 48a b d e + 24a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1352 + +--S 1353 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1353 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich12f.input.pamphlet b/src/axiom-website/CATS/rich12f.input.pamphlet new file mode 100644 index 0000000..f085ca0 --- /dev/null +++ b/src/axiom-website/CATS/rich12f.input.pamphlet @@ -0,0 +1,49316 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12f.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 345 integrals in this file. +\item 345 supplied "optimal results". +\item 275 matching answers. +\item 14 cases where Axiom answer differs from Rubi +\item 13 cases where Axiom supplied 2 results. +\item 9 cases that Axiom failed to integrate. +\item 59 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12f.output +)spool rich12f.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1751 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1751 +r0:=-1/3*sqrt(d+e*x)/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 5/12*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 5/8*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 5/8*e^2*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 15b e x - 45a b e x - 45a b e x - 15a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (40a b e - 10b d e)x + 33a e - 26a b d e + 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (48a b e - 144a b d e + 144a b d e - 48a b d )x + 24a e - 72a b d e +--R + +--R 3 2 2 2 3 3 +--R 72a b d e - 24a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b e x + 45a b e x + 45a b e x + 15a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (30b e x + (80a b e - 20b d e)x + 66a e - 52a b d e + 16b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (48a b e - 144a b d e + 144a b d e - 48b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x + 48a e +--R + +--R 5 2 4 2 2 3 3 3 +--R - 144a b d e + 144a b d e - 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b e x + 45a b e x + 45a b e x + 15a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (40a b e - 10b d e)x + 33a e - 26a b d e + 8b d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x + 24a e +--R + +--R 5 2 4 2 2 3 3 3 +--R - 72a b d e + 72a b d e - 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 3 + +--S 4 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (15b e x + 45a b e x + 45a b e x + 15a e )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (30b e x + 120a b e x + 180a b e x + 120a b e x + 30a e ) +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (30b e x + (80a b e - 20b d e)x + 66a e - 52a b d e + 16b d ) +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 30b e x + (- 110a b e + 20b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 146a b e + 72a b d e - 16b d )x - 66a e + 52a b d e - 16a b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (48a b e - 144a b d e + 144a b d e - 48b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x + 48a e +--R + +--R 5 2 4 2 2 3 3 3 +--R - 144a b d e + 144a b d e - 48a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +-------------+ +--R 2 +-------+ | 2 +--R ((2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 +-------+ +--R ((- 2a b e + 2b d)x - 2a b e + 2a b d)\|e x + d +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +--R (- b e x - 2b d x + a e - 2a b d)\|- a b e + b d +--R / +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (3a b e + 2b d)x + (2a b e + 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 2a b e + 12a b d)x + (- 3a b e + 8a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (2a b e - 2b d e)x + (8a b e - 6a b d e - 2b d )x +--R + +--R 3 3 2 2 4 5 2 3 4 2 2 3 3 2 4 2 2 +--R (12a b e - 4a b d e - 8a b d )x + (8a b e + 4a b d e - 12a b d )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (2a b e + 6a b d e - 8a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 5 + +--S 6 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e )\|a b e - b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (15b e x + 45a b e x + 45a b e x + 15a e )\|- a e + b d \|b +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R | 2 2 2 \|a b e - b d \|e x + d +--R \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (40a b e - 10b d e)x + 33a e - 26a b d e + 8b d ) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 15b e x + (- 55a b e + 10b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 73a b e + 36a b d e - 8b d )x - 33a e + 26a b d e - 8a b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x + 24a e - 72a b d e +--R + +--R 4 2 2 3 3 3 +--R 72a b d e - 24a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 7 + +)clear all + +--S 8 of 1751 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 8 + +--S 9 of 1751 +r0:=2/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))-_ + 7/3*b*sqrt(d+e*x)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/12*b*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/8*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b)/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 35/8*b*e^2*sqrt(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-+ +-------+ +--R (105b e x + 315a b e x + 315a b e x + 105a e )\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 280a b e - 35b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 231a b e - 98a b d e + 14b d e)x - 48a e - 87a b d e +--R + +--R 2 2 3 3 +--R 38a b d e - 8b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 +--R (48a b e - 192a b d e + 288a b d e - 192a b d e + 48a b d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 3 2 3 2 2 3 3 3 | b +--R (105b e x + 315a b e x + 315a b e x + 105a e ) |- --------- +--R \| a e - b d +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R - 210b e x + (- 560a b e - 70b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 462a b e - 196a b d e + 28b d e)x - 96a e - 174a b d e +--R + +--R 2 2 3 3 +--R 76a b d e - 16b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (48a b e - 192a b d e + 288a b d e - 192a b d e + 48b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 48a e - 192a b d e + 288a b d e - 192a b d e + 48a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +---------+ +--R 3 3 3 2 3 2 2 3 3 3 | b +--R (- 105b e x - 315a b e x - 315a b e x - 105a e ) |--------- +--R \|a e - b d +--R * +--R +-------+ +--R +-------+ b\|e x + d +--R \|e x + d atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 280a b e - 35b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 231a b e - 98a b d e + 14b d e)x - 48a e - 87a b d e + 38a b d e +--R + +--R 3 3 +--R - 8b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 10 + +--S 11 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +--R (105b e x + 315a b e x + 315a b e x + 105a e )\|- a e + b d +--R * +--R +-----------+ +------------------+ +--R | b +-------+ | 2 2 2 +--R |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +-+ +--R (- 210b e x - 840a b e x - 1260a b e x - 840a b e x - 210a e )\|b +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 210b e x + (- 560a b e - 70b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 462a b e - 196a b d e + 28b d e)x - 96a e - 174a b d e +--R + +--R 2 2 3 3 +--R 76a b d e - 16b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R 210b e x + (770a b e + 70b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (1022a b e + 266a b d e - 28b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (558a b e + 370a b d e - 104a b d e + 16b d )x + 96a e +--R + +--R 3 2 2 2 2 3 3 +--R 174a b d e - 76a b d e + 16a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (48a b e - 192a b d e + 288a b d e - 192a b d e + 48b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 48a e - 192a b d e + 288a b d e - 192a b d e + 48a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +-+ +--R (- 105b e x - 420a b e x - 630a b e x - 420a b e x - 105a e )\|b +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +--R (- 105b e x - 315a b e x - 315a b e x - 105a e )\|- a e + b d +--R * +--R +---------+ +------------------+ +-------+ +--R | b +-------+ | 2 2 2 b\|e x + d +--R |--------- \|e x + d \|b x + 2a b x + a atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 280a b e - 35b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 231a b e - 98a b d e + 14b d e)x - 48a e - 87a b d e +--R + +--R 2 2 3 3 +--R 38a b d e - 8b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R 105b e x + (385a b e + 35b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (511a b e + 133a b d e - 14b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (279a b e + 185a b d e - 52a b d e + 8b d )x + 48a e + 87a b d e +--R + +--R 2 2 2 3 3 +--R - 38a b d e + 8a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 13 + +--S 14 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 14 + +)clear all + +--S 15 of 1751 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 15 + +--S 16 of 1751 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 6*b/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))-_ + 7*b^2*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/4*b^2*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 105/8*b^(3/2)*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 105/8*b^2*e^2*sqrt(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 945a b e - 315b d e )x +--R + +--R 2 2 4 3 3 2 3 4 2 2 3 +--R (- 945a b e - 945a b d e )x + (- 315a b e - 945a b d e )x +--R + +--R 3 3 +--R - 315a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (840a b e + 420b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (693a b e + 1134a b d e + 63b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (144a b e + 954a b d e + 180a b d e - 18b d e)x - 16a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 208a b d e + 165a b d e - 50a b d e + 8b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 7 5 +--R - 24b d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 6 5 +--R 48a b e - 216a b d e + 360a b d e - 240a b d e + 72a b d e +--R + +--R 7 6 +--R - 24b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 5 4 3 3 3 3 4 4 2 2 5 5 +--R 24a e - 72a b d e + 240a b d e - 360a b d e + 216a b d e +--R + +--R 6 6 +--R - 48a b d +--R * +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 2 5 6 +--R - 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 315b e x + (945a b e + 315b d e )x + (945a b e + 945a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (315a b e + 945a b d e )x + 315a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 630b e x + (1680a b e + 840b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1386a b e + 2268a b d e + 126b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (288a b e + 1908a b d e + 360a b d e - 36b d e)x - 32a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 416a b d e + 330a b d e - 100a b d e + 16b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 +--R 144a b e - 672a b d e + 1200a b d e - 960a b d e +--R + +--R 2 6 4 2 7 5 8 6 +--R 240a b d e + 96a b d e - 48b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 144a b e - 576a b d e + 720a b d e - 720a b d e + 576a b d e +--R + +--R 7 6 +--R - 144a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 48a e - 96a b d e - 240a b d e + 960a b d e - 1200a b d e +--R + +--R 3 5 5 2 6 6 +--R 672a b d e - 144a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 5 6 +--R - 48a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 315b e x + (945a b e + 315b d e )x + (945a b e + 945a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (315a b e + 945a b d e )x + 315a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (840a b e + 420b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (693a b e + 1134a b d e + 63b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (144a b e + 954a b d e + 180a b d e - 18b d e)x - 16a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 208a b d e + 165a b d e - 50a b d e + 8b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 8 5 +--R - 24b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b e - 336a b d e + 600a b d e - 480a b d e + 120a b d e +--R + +--R 7 5 8 6 +--R 48a b d e - 24b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b e - 288a b d e + 360a b d e - 360a b d e + 288a b d e +--R + +--R 7 6 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a e - 48a b d e - 120a b d e + 480a b d e - 600a b d e +--R + +--R 3 5 5 2 6 6 +--R 336a b d e - 72a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 3 5 6 +--R - 24a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 17 + +--S 18 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 315b e x + (945a b e + 315b d e )x + (945a b e + 945a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (315a b e + 945a b d e )x + 315a b d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 630b e x + (2520a b e + 630b d e )x +--R + +--R 2 3 4 4 3 3 3 2 4 2 3 3 2 +--R (3780a b e + 2520a b d e )x + (2520a b e + 3780a b d e )x +--R + +--R 4 4 3 2 3 4 3 +--R (630a b e + 2520a b d e )x + 630a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 630b e x + (1680a b e + 840b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1386a b e + 2268a b d e + 126b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (288a b e + 1908a b d e + 360a b d e - 36b d e)x - 32a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 416a b d e + 330a b d e - 100a b d e + 16b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 630b e x + (- 2310a b e - 840b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 3066a b e - 3108a b d e - 126b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 1674a b e - 4176a b d e - 486a b d e + 36b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 256a b e - 2324a b d e - 690a b d e + 136a b d e - 16b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 32a e - 416a b d e - 330a b d e + 100a b d e - 16a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 144a b e - 672a b d e + 1200a b d e - 960a b d e + 240a b d e +--R + +--R 7 5 8 6 +--R 96a b d e - 48b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 144a b e - 576a b d e + 720a b d e - 720a b d e + 576a b d e +--R + +--R 7 6 +--R - 144a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 48a e - 96a b d e - 240a b d e + 960a b d e - 1200a b d e +--R + +--R 3 5 5 2 6 6 +--R 672a b d e - 144a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 5 6 +--R - 48a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 18 + +--S 19 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 4 5 4 4 5 3 4 +--R 315b e x + (1260a b e + 315b d e )x +--R + +--R 2 3 4 4 3 3 3 2 4 2 3 3 2 +--R (1890a b e + 1260a b d e )x + (1260a b e + 1890a b d e )x +--R + +--R 4 4 3 2 3 4 3 +--R (315a b e + 1260a b d e )x + 315a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 315b e x + (945a b e + 315b d e )x + (945a b e + 945a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (315a b e + 945a b d e )x + 315a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (840a b e + 420b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (693a b e + 1134a b d e + 63b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (144a b e + 954a b d e + 180a b d e - 18b d e)x - 16a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 208a b d e + 165a b d e - 50a b d e + 8b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 315b e x + (- 1155a b e - 420b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 1533a b e - 1554a b d e - 63b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 837a b e - 2088a b d e - 243a b d e + 18b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 128a b e - 1162a b d e - 345a b d e + 68a b d e - 8b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 16a e - 208a b d e - 165a b d e + 50a b d e - 8a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 8 5 +--R - 24b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b e - 336a b d e + 600a b d e - 480a b d e + 120a b d e +--R + +--R 7 5 8 6 +--R 48a b d e - 24b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b e - 288a b d e + 360a b d e - 360a b d e + 288a b d e +--R + +--R 7 6 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a e - 48a b d e - 120a b d e + 480a b d e - 600a b d e +--R + +--R 3 5 5 2 6 6 +--R 336a b d e - 72a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 3 5 6 +--R - 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 20 + +--S 21 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 of 1751 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 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4 2 3 5 3 2 2 +--R (- 3168a b e - 36234a b d e - 28908a b d e - 990b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (352a b e - 7744a b d e - 24618a b d e - 2860a b d e + 220b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 96a e + 832a b d e - 5536a b d e - 2670a b d e + 620a b d e +--R + +--R 5 5 +--R - 80b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 6 5 6 5 5 6 4 5 +--R 6930b e x + (25410a b e + 16170b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (33726a b e + 59598a b d e + 10626b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 3 +--R (18414a b e + 79662a b d e + 39534a b d e + 990b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 +--R 2816a b e + 43978a b d e + 53526a b d e + 3850a b d e +--R + +--R 6 4 +--R - 220b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 +--R - 256a b e + 6912a b d e + 30154a b d e + 5530a b d e +--R + +--R 5 4 6 5 +--R - 840a b d e + 80b d +--R * +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 96a e - 832a b d e + 5536a b d e + 2670a b d e - 620a b d e +--R + +--R 5 5 +--R 80a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 240a b e - 1440a b d e + 3600a b d e - 4800a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 3600a b d e - 1440a b d e + 240b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 720a b e - 3840a b d e + 7920a b d e - 7200a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 1200a b d e + 2880a b d e - 2160a b d e + 480b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 720a b e - 2880a b d e + 2400a b d e + 5760a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 14400a b d e + 12480a b d e - 4320a b d e + 240b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 +--R 240a e - 4320a b d e + 12480a b d e - 14400a b d e +--R + +--R 4 5 5 3 3 6 6 2 2 7 7 8 8 +--R 5760a b d e + 2400a b d e - 2880a b d e + 720a b d +--R * +--R 2 +--R x +--R + +--R 9 7 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4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 6 5 5 6 4 5 +--R - 3465b e x + (- 13860a b e - 6930b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (- 20790a b e - 27720a b d e - 3465b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 3 +--R (- 13860a b e - 41580a b d e - 13860a b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 2 +--R (- 3465a b e - 27720a b d e - 20790a b d e )x +--R + +--R 4 2 4 3 3 2 3 4 2 2 3 +--R (- 6930a b d e - 13860a b d e )x - 3465a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R - 3465b e x + (- 10395a b e - 6930b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 10395a b e - 20790a b d e - 3465b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (- 3465a b e - 20790a b d e - 10395a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (- 6930a b d e - 10395a b d e )x - 3465a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 5 5 5 4 5 5 4 4 +--R - 3465b e x + (- 9240a b e - 8085b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 7623a b e - 21714a b d e - 5313b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 1584a b e - 18117a b d e - 14454a b d e - 495b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (176a b e - 3872a b d e - 12309a b d e - 1430a b d e + 110b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 48a e + 416a b d e - 2768a b d e - 1335a b d e + 310a b d e +--R + +--R 5 5 +--R - 40b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 6 5 6 5 5 6 4 5 +--R 3465b e x + (12705a b e + 8085b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (16863a b e + 29799a b d e + 5313b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 3 +--R (9207a b e + 39831a b d e + 19767a b d e + 495b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 +--R 1408a b e + 21989a b d e + 26763a b d e + 1925a b d e +--R + +--R 6 4 +--R - 110b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 +--R - 128a b e + 3456a b d e + 15077a b d e + 2765a b d e +--R + +--R 5 4 6 5 +--R - 420a b d e + 40b d +--R * +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 48a e - 416a b d e + 2768a b d e + 1335a b d e - 310a b d e +--R + +--R 5 5 +--R 40a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 120a b e - 720a b d e + 1800a b d e - 2400a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 1800a b d e - 720a b d e + 120b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 360a b e - 1920a b d e + 3960a b d e - 3600a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 600a b d e + 1440a b d e - 1080a b d e + 240b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 360a b e - 1440a b d e + 1200a b d e + 2880a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 7200a b d e + 6240a b d e - 2160a b d e + 120b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 4 5 5 3 +--R 120a e - 2160a b d e + 6240a b d e - 7200a b d e + 2880a b d e +--R + +--R 3 6 6 2 2 7 7 8 8 +--R 1200a b d e - 1440a b d e + 360a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 +--R 240a d e - 1080a b d e + 1440a b d e + 600a b d e +--R + +--R 5 4 5 3 4 5 6 2 3 6 7 2 7 8 +--R - 3600a b d e + 3960a b d e - 1920a b d e + 360a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 120a d e - 720a b d e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 5 7 3 6 8 +--R - 720a b d e + 120a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 28 + +)clear all + +--S 29 of 1751 +t0:=(a+b*x)*(d+e*x)^(-3-2*p)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R - 2p - 3 2 2 2 p +--R (1) (b x + a)(e x + d) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1751 +r0:=1/2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/((b*d-a*e)*(1+p)*(d+e*x)^(2*(1+p))) +--R +--R +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R (2) - --------------------------------------------- +--R 2p + 2 +--R ((2a e - 2b d)p + 2a e - 2b d)(e x + d) +--R Type: Expression(Integer) +--E 30 + +--S 31 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 +--R (- b e x + (- 2a b e - b d)x + (- a e - 2a b d)x - a d) +--R * +--R 2 2 2 +--R (- 2p - 3)log(e x + d) p log(b x + 2a b x + a ) +--R %e %e +--R / +--R (2a e - 2b d)p + 2a e - 2b d +--R Type: Union(Expression(Integer),...) +--E 31 + +--S 32 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 +--R (- b e x + (- 2a b e - b d)x + (- a e - 2a b d)x - a d) +--R * +--R 2 2 2 +--R 2p + 2 (- 2p - 3)log(e x + d) p log(b x + 2a b x + a ) +--R (e x + d) %e %e +--R + +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 2p + 2 +--R ((2a e - 2b d)p + 2a e - 2b d)(e x + d) +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 of 1751 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R 2 2 2 p +--R (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1751 +r0:=3/2*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^4*(1+p)*(2+p)*(3+2*p)*_ + (5+2*p))+3*(b*d-a*e)^2*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^3*(2+p)*_ + (3+2*p)*(5+2*p))+3/2*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/_ + (b^2*(2+p)*(5+2*p))+(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(5+2*p)) +--R +--R +--R (2) +--R 3 3 3 3 3 2 3 3 3 3 3 +--R (4b e p + 18b e p + 26b e p + 12b e )x +--R + +--R 3 2 3 2 3 3 2 2 2 3 3 2 +--R 12b d e p + (- 6a b e + 60b d e )p + (- 15a b e + 93b d e )p +--R + +--R 2 3 3 2 +--R - 9a b e + 45b d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 3 2 2 +--R 12b d e p + (- 12a b d e + 66b d e)p +--R + +--R 2 3 2 2 3 2 2 3 2 2 3 2 +--R (6a b e - 42a b d e + 114b d e)p + 6a b e - 30a b d e + 60b d e +--R * +--R x +--R + +--R 3 3 3 2 2 3 3 2 2 2 2 2 3 3 +--R 4b d p + (- 6a b d e + 24b d )p + (6a b d e - 27a b d e + 47b d )p +--R + +--R 3 3 2 2 2 2 3 3 +--R - 3a e + 15a b d e - 30a b d e + 30b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 4 4 4 3 4 2 4 4 +--R 8b p + 56b p + 142b p + 154b p + 60b +--R Type: Expression(Integer) +--E 35 + +--S 36 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 3 5 3 2 5 3 5 3 5 +--R (4b e p + 18b e p + 26b e p + 12b e )x +--R + +--R 4 3 5 2 3 4 3 5 2 2 +--R (8a b e + 12b d e )p + (30a b e + 60b d e )p +--R + +--R 4 3 5 2 4 3 5 2 +--R (37a b e + 93b d e )p + 15a b e + 45b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 4 2 5 2 3 +--R (4a b e + 24a b d e + 12b d e)p +--R + +--R 2 3 3 4 2 5 2 2 +--R (6a b e + 108a b d e + 66b d e)p +--R + +--R 2 3 3 4 2 5 2 4 2 5 2 +--R (2a b e + 144a b d e + 114b d e)p + 60a b d e + 60b d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 4 2 5 3 3 +--R (12a b d e + 24a b d e + 4b d )p +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 6a b e + 36a b d e + 126a b d e + 24b d )p +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 2 5 3 +--R (- 3a b e + 15a b d e + 201a b d e + 47b d )p + 90a b d e + 30b d +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 3 3 3 2 2 2 3 2 4 3 2 +--R (12a b d e + 8a b d )p + (- 12a b d e + 54a b d e + 48a b d )p +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 3 +--R (6a b e - 30a b d e + 60a b d e + 94a b d )p + 60a b d +--R * +--R x +--R + +--R 2 3 3 3 3 2 2 2 3 3 2 +--R 4a b d p + (- 6a b d e + 24a b d )p +--R + +--R 4 2 3 2 2 2 3 3 5 3 4 2 3 2 2 +--R (6a b d e - 27a b d e + 47a b d )p - 3a e + 15a b d e - 30a b d e +--R + +--R 2 3 3 +--R 30a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R 8b p + 56b p + 142b p + 154b p + 60b +--R Type: Union(Expression(Integer),...) +--E 36 + +--S 37 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 3 3 5 3 2 5 3 5 3 5 +--R (4b e p + 18b e p + 26b e p + 12b e )x +--R + +--R 4 3 5 2 3 4 3 5 2 2 +--R (8a b e + 12b d e )p + (30a b e + 60b d e )p +--R + +--R 4 3 5 2 4 3 5 2 +--R (37a b e + 93b d e )p + 15a b e + 45b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 4 2 5 2 3 +--R (4a b e + 24a b d e + 12b d e)p +--R + +--R 2 3 3 4 2 5 2 2 +--R (6a b e + 108a b d e + 66b d e)p +--R + +--R 2 3 3 4 2 5 2 4 2 5 2 +--R (2a b e + 144a b d e + 114b d e)p + 60a b d e + 60b d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 4 2 5 3 3 +--R (12a b d e + 24a b d e + 4b d )p +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 6a b e + 36a b d e + 126a b d e + 24b d )p +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 2 +--R (- 3a b e + 15a b d e + 201a b d e + 47b d )p + 90a b d e +--R + +--R 5 3 +--R 30b d +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 3 3 3 2 2 2 3 2 4 3 2 +--R (12a b d e + 8a b d )p + (- 12a b d e + 54a b d e + 48a b d )p +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 3 +--R (6a b e - 30a b d e + 60a b d e + 94a b d )p + 60a b d +--R * +--R x +--R + +--R 2 3 3 3 3 2 2 2 3 3 2 +--R 4a b d p + (- 6a b d e + 24a b d )p +--R + +--R 4 2 3 2 2 2 3 3 5 3 4 2 3 2 2 +--R (6a b d e - 27a b d e + 47a b d )p - 3a e + 15a b d e - 30a b d e +--R + +--R 2 3 3 +--R 30a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R + +--R 3 3 3 3 3 2 3 3 3 3 3 +--R (- 4b e p - 18b e p - 26b e p - 12b e )x +--R + +--R 3 2 3 2 3 3 2 2 2 3 3 2 +--R - 12b d e p + (6a b e - 60b d e )p + (15a b e - 93b d e )p +--R + +--R 2 3 3 2 +--R 9a b e - 45b d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 3 2 2 +--R - 12b d e p + (12a b d e - 66b d e)p +--R + +--R 2 3 2 2 3 2 2 3 2 2 +--R (- 6a b e + 42a b d e - 114b d e)p - 6a b e + 30a b d e +--R + +--R 3 2 +--R - 60b d e +--R * +--R x +--R + +--R 3 3 3 2 2 3 3 2 +--R - 4b d p + (6a b d e - 24b d )p +--R + +--R 2 2 2 2 3 3 3 3 2 2 2 2 +--R (- 6a b d e + 27a b d e - 47b d )p + 3a e - 15a b d e + 30a b d e +--R + +--R 3 3 +--R - 30b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 4 4 4 3 4 2 4 4 +--R 8b p + 56b p + 142b p + 154b p + 60b +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 38 + +)clear all + +--S 39 of 1751 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R (1) +--R 2 3 2 2 2 2 2 2 2 p +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1751 +r0:=1/2*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^3*(1+p)*(2+p)*(3+2*p))+_ + (b*d-a*e)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^2*(2+p)*(3+2*p))+_ + 1/2*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(2+p)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (2b e p + 5b e p + 3b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4b d e p + (- 2a b e + 12b d e)p - 2a b e + 8b d e)x + 2b d p +--R + +--R 2 2 2 2 2 2 +--R (- 2a b d e + 7b d )p + a e - 4a b d e + 6b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 3 3 3 2 3 3 +--R 4b p + 18b p + 26b p + 12b +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 2 4 2 4 2 4 +--R (2b e p + 5b e p + 3b e )x +--R + +--R 3 2 4 2 3 2 4 3 2 4 3 +--R ((4a b e + 4b d e)p + (8a b e + 12b d e)p + 4a b e + 8b d e)x +--R + +--R 2 2 2 3 4 2 2 2 2 2 3 4 2 +--R (2a b e + 8a b d e + 2b d )p + (a b e + 22a b d e + 7b d )p +--R + +--R 3 4 2 +--R 12a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 3 2 2 2 3 2 +--R (4a b d e + 4a b d )p + (- 2a b e + 8a b d e + 14a b d )p +--R + +--R 3 2 +--R 12a b d +--R * +--R x +--R + +--R 2 2 2 2 3 2 2 2 4 2 3 2 2 2 +--R 2a b d p + (- 2a b d e + 7a b d )p + a e - 4a b d e + 6a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R / +--R 3 3 3 2 3 3 +--R 4b p + 18b p + 26b p + 12b +--R Type: Union(Expression(Integer),...) +--E 41 + +--S 42 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 2 4 2 4 2 4 +--R (2b e p + 5b e p + 3b e )x +--R + +--R 3 2 4 2 3 2 4 3 2 4 3 +--R ((4a b e + 4b d e)p + (8a b e + 12b d e)p + 4a b e + 8b d e)x +--R + +--R 2 2 2 3 4 2 2 2 2 2 3 4 2 +--R (2a b e + 8a b d e + 2b d )p + (a b e + 22a b d e + 7b d )p +--R + +--R 3 4 2 +--R 12a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 3 2 2 2 3 2 +--R (4a b d e + 4a b d )p + (- 2a b e + 8a b d e + 14a b d )p +--R + +--R 3 2 +--R 12a b d +--R * +--R x +--R + +--R 2 2 2 2 3 2 2 2 4 2 3 2 2 2 +--R 2a b d p + (- 2a b d e + 7a b d )p + a e - 4a b d e + 6a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 2b e p - 5b e p - 3b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 4b d e p + (2a b e - 12b d e)p + 2a b e - 8b d e)x - 2b d p +--R + +--R 2 2 2 2 2 2 +--R (2a b d e - 7b d )p - a e + 4a b d e - 6b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 3 3 3 2 3 3 +--R 4b p + 18b p + 26b p + 12b +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 43 + +)clear all + +--S 44 of 1751 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R 2 2 2 2 p +--R (1) (b e x + (a e + b d)x + a d)(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1751 +r0:=1/2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^2*(1+p)*(3+2*p))+(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(3+2*p)) +--R +--R +--R 2 2 2 p + 1 +--R ((2b e p + 2b e)x + 2b d p - a e + 3b d)(b x + 2a b x + a ) +--R (2) ----------------------------------------------------------------- +--R 2 2 2 2 +--R 4b p + 10b p + 6b +--R Type: Expression(Integer) +--E 45 + +--S 46 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 3 2 +--R (2b e p + 2b e)x + ((4a b e + 2b d)p + 3a b e + 3b d)x +--R + +--R 2 2 2 2 3 2 +--R ((2a b e + 4a b d)p + 6a b d)x + 2a b d p - a e + 3a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R / +--R 2 2 2 2 +--R 4b p + 10b p + 6b +--R Type: Union(Expression(Integer),...) +--E 46 + +--S 47 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 3 2 +--R (2b e p + 2b e)x + ((4a b e + 2b d)p + 3a b e + 3b d)x +--R + +--R 2 2 2 2 3 2 +--R ((2a b e + 4a b d)p + 6a b d)x + 2a b d p - a e + 3a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R + +--R 2 2 2 p + 1 +--R ((- 2b e p - 2b e)x - 2b d p + a e - 3b d)(b x + 2a b x + a ) +--R / +--R 2 2 2 2 +--R 4b p + 10b p + 6b +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 48 + +)clear all + +--S 49 of 1751 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R 2 2 2 p +--R (1) (b x + a)(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1751 +r0:=1/2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(1+p)) +--R +--R +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R (2) ------------------------- +--R 2b p + 2b +--R Type: Expression(Integer) +--E 50 + +--S 51 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2 2 2 p log(b x + 2a b x + a ) +--R (b x + 2a b x + a )%e +--R (3) ----------------------------------------------- +--R 2b p + 2b +--R Type: Union(Expression(Integer),...) +--E 51 + +--S 52 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 +--R 2 2 2 p log(b x + 2a b x + a ) 2 2 2 p + 1 +--R (b x + 2a b x + a )%e - (b x + 2a b x + a ) +--R --------------------------------------------------------------------------- +--R 2b p + 2b +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 53 + +)clear all + +--S 54 of 1751 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p/(d+e*x) +--R +--R +--R 2 2 2 p +--R (b x + a)(b x + 2a b x + a ) +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1751 +--r0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p/(e*(1+2*p))-(a+b*x)*_ +-- (a^2+2*a*b*x+b^2*x^2)^p*hypergeometric(1,1+2*p,2*(1+p),_ +-- -e*(a+b*x)/(b*d-a*e))/(e*(1+2*p)) +--E 55 + +--S 56 of 1751 +--a0:=integrate(t0,x) +--E 56 + +--S 57 of 1751 +--m0:=a0-r0 +--E 57 + +--S 58 of 1751 +--d0:=D(m0,x) +--E 58 + +)clear all + +--S 59 of 1751 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R * +--R m +--R (b c x + a c) +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1751 +r0:=(A*b-a*B)*(a*c+b*c*x)^(7+m)/(b^2*c^7*(7+m))+B*(a*c+b*c*x)^(8+m)/_ + (b^2*c^8*(8+m)) +--R +--R +--R (2) +--R m + 8 +--R (B m + 7B)(b c x + a c) +--R + +--R m + 7 +--R ((A b - B a)c m + (8A b - 8B a)c)(b c x + a c) +--R / +--R 2 8 2 2 8 2 8 +--R b c m + 15b c m + 56b c +--R Type: Expression(Integer) +--E 60 + +--S 61 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 8 8 7 8 7 7 +--R (B b m + 7B b )x + ((A b + 7B a b )m + 8A b + 48B a b )x +--R + +--R 7 2 6 7 2 6 6 +--R ((7A a b + 21B a b )m + 56A a b + 140B a b )x +--R + +--R 2 6 3 5 2 6 3 5 5 +--R ((21A a b + 35B a b )m + 168A a b + 224B a b )x +--R + +--R 3 5 4 4 3 5 4 4 4 +--R ((35A a b + 35B a b )m + 280A a b + 210B a b )x +--R + +--R 4 4 5 3 4 4 5 3 3 +--R ((35A a b + 21B a b )m + 280A a b + 112B a b )x +--R + +--R 5 3 6 2 5 3 6 2 2 +--R ((21A a b + 7B a b )m + 168A a b + 28B a b )x +--R + +--R 6 2 7 6 2 7 7 8 +--R ((7A a b + B a b)m + 56A a b )x + A a b m + 8A a b - B a +--R * +--R m log(b c x + a c) +--R %e +--R / +--R 2 2 2 2 +--R b m + 15b m + 56b +--R Type: Union(Expression(Integer),...) +--E 61 + +--S 62 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8 8 8 8 +--R (B b c m + 7B b c )x +--R + +--R 8 7 8 8 7 8 7 +--R ((A b + 7B a b )c m + (8A b + 48B a b )c )x +--R + +--R 7 2 6 8 7 2 6 8 6 +--R ((7A a b + 21B a b )c m + (56A a b + 140B a b )c )x +--R + +--R 2 6 3 5 8 2 6 3 5 8 5 +--R ((21A a b + 35B a b )c m + (168A a b + 224B a b )c )x +--R + +--R 3 5 4 4 8 3 5 4 4 8 4 +--R ((35A a b + 35B a b )c m + (280A a b + 210B a b )c )x +--R + +--R 4 4 5 3 8 4 4 5 3 8 3 +--R ((35A a b + 21B a b )c m + (280A a b + 112B a b )c )x +--R + +--R 5 3 6 2 8 5 3 6 2 8 2 +--R ((21A a b + 7B a b )c m + (168A a b + 28B a b )c )x +--R + +--R 6 2 7 8 6 2 8 7 8 7 8 8 +--R ((7A a b + B a b)c m + 56A a b c )x + A a b c m + (8A a b - B a )c +--R * +--R m log(b c x + a c) +--R %e +--R + +--R m + 8 +--R (- B m - 7B)(b c x + a c) +--R + +--R m + 7 +--R ((- A b + B a)c m + (- 8A b + 8B a)c)(b c x + a c) +--R / +--R 2 8 2 2 8 2 8 +--R b c m + 15b c m + 56b c +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 1751 +t0:=(A+B*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R m +--R (B x + A)(b c x + a c) +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1751 +r0:=-(A*b-a*B)*c^5*(a*c+b*c*x)^(-5+m)/(b^2*(5-m))-B*c^4*(a*c+b*c*x)^(-4+m)/_ + (b^2*(4-m)) +--R +--R +--R (2) +--R 4 4 m - 4 +--R (B c m - 5B c )(b c x + a c) +--R + +--R 5 5 m - 5 +--R ((A b - B a)c m + (- 4A b + 4B a)c )(b c x + a c) +--R / +--R 2 2 2 2 +--R b m - 9b m + 20b +--R Type: Expression(Integer) +--E 65 + +--S 66 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R m log(b c x + a c) +--R ((B b m - 5B b)x + A b m - 4A b - B a)%e +--R / +--R 7 2 7 7 5 6 2 6 6 4 +--R (b m - 9b m + 20b )x + (5a b m - 45a b m + 100a b )x +--R + +--R 2 5 2 2 5 2 5 3 3 4 2 3 4 3 4 2 +--R (10a b m - 90a b m + 200a b )x + (10a b m - 90a b m + 200a b )x +--R + +--R 4 3 2 4 3 4 3 5 2 2 5 2 5 2 +--R (5a b m - 45a b m + 100a b )x + a b m - 9a b m + 20a b +--R Type: Union(Expression(Integer),...) +--E 66 + +--S 67 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R m log(b c x + a c) +--R ((B b m - 5B b)x + A b m - 4A b - B a)%e +--R + +--R 5 4 5 4 5 4 4 4 4 4 +--R (- B b c m + 5B b c )x + (- 5B a b c m + 25B a b c )x +--R + +--R 2 3 4 2 3 4 3 3 2 4 3 2 4 2 +--R (- 10B a b c m + 50B a b c )x + (- 10B a b c m + 50B a b c )x +--R + +--R 4 4 4 4 5 4 5 4 +--R (- 5B a b c m + 25B a b c )x - B a c m + 5B a c +--R * +--R m - 4 +--R (b c x + a c) +--R + +--R 6 5 5 6 5 5 5 +--R ((- A b + B a b )c m + (4A b - 4B a b )c )x +--R + +--R 5 2 4 5 5 2 4 5 4 +--R ((- 5A a b + 5B a b )c m + (20A a b - 20B a b )c )x +--R + +--R 2 4 3 3 5 2 4 3 3 5 3 +--R ((- 10A a b + 10B a b )c m + (40A a b - 40B a b )c )x +--R + +--R 3 3 4 2 5 3 3 4 2 5 2 +--R ((- 10A a b + 10B a b )c m + (40A a b - 40B a b )c )x +--R + +--R 4 2 5 5 4 2 5 5 +--R ((- 5A a b + 5B a b)c m + (20A a b - 20B a b)c )x +--R + +--R 5 6 5 5 6 5 +--R (- A a b + B a )c m + (4A a b - 4B a )c +--R * +--R m - 5 +--R (b c x + a c) +--R / +--R 7 2 7 7 5 6 2 6 6 4 +--R (b m - 9b m + 20b )x + (5a b m - 45a b m + 100a b )x +--R + +--R 2 5 2 2 5 2 5 3 3 4 2 3 4 3 4 2 +--R (10a b m - 90a b m + 200a b )x + (10a b m - 90a b m + 200a b )x +--R + +--R 4 3 2 4 3 4 3 5 2 2 5 2 5 2 +--R (5a b m - 45a b m + 100a b )x + a b m - 9a b m + 20a b +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 68 + +)clear all + +--S 69 of 1751 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 m +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(b c x + a c) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1751 +r0:=(A*b-a*B)*(a*c+b*c*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*c*(4+m))+_ + B*(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*c^2*(5+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R ((B b m + 4B b )x + (2B a b m + 8B a b)x + B a m + 4B a ) +--R * +--R m + 2 +--R (b c x + a c) +--R + +--R 3 2 3 2 2 +--R ((A b - B a b )c m + (5A b - 5B a b )c)x +--R + +--R 2 2 2 2 +--R ((2A a b - 2B a b)c m + (10A a b - 10B a b)c)x +--R + +--R 2 3 2 3 +--R (A a b - B a )c m + (5A a b - 5B a )c +--R * +--R m + 1 +--R (b c x + a c) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 2 2 2 2 +--R b c m + 9b c m + 20b c +--R Type: Expression(Integer) +--E 70 + +--S 71 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 5 4 5 4 4 +--R (B b m + 4B b )x + ((A b + 4B a b )m + 5A b + 15B a b )x +--R + +--R 4 2 3 4 2 3 3 +--R ((4A a b + 6B a b )m + 20A a b + 20B a b )x +--R + +--R 2 3 3 2 2 3 3 2 2 +--R ((6A a b + 4B a b )m + 30A a b + 10B a b )x +--R + +--R 3 2 4 3 2 4 4 5 +--R ((4A a b + B a b)m + 20A a b )x + A a b m + 5A a b - B a +--R * +--R m log(b c x + a c) +--R %e +--R / +--R 2 2 2 2 +--R b m + 9b m + 20b +--R Type: Union(Expression(Integer),...) +--E 71 + +--S 72 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 5 2 5 +--R (B b c m + 4B b c )x +--R + +--R 5 4 2 5 4 2 4 +--R ((A b + 4B a b )c m + (5A b + 15B a b )c )x +--R + +--R 4 2 3 2 4 2 3 2 3 +--R ((4A a b + 6B a b )c m + (20A a b + 20B a b )c )x +--R + +--R 2 3 3 2 2 2 3 3 2 2 2 +--R ((6A a b + 4B a b )c m + (30A a b + 10B a b )c )x +--R + +--R 3 2 4 2 3 2 2 4 2 4 5 2 +--R ((4A a b + B a b)c m + 20A a b c )x + A a b c m + (5A a b - B a )c +--R * +--R m log(b c x + a c) +--R %e +--R + +--R 2 2 2 2 2 +--R ((- B b m - 4B b )x + (- 2B a b m - 8B a b)x - B a m - 4B a ) +--R * +--R m + 2 +--R (b c x + a c) +--R + +--R 3 2 3 2 2 +--R ((- A b + B a b )c m + (- 5A b + 5B a b )c)x +--R + +--R 2 2 2 2 +--R ((- 2A a b + 2B a b)c m + (- 10A a b + 10B a b)c)x +--R + +--R 2 3 2 3 +--R (- A a b + B a )c m + (- 5A a b + 5B a )c +--R * +--R m + 1 +--R (b c x + a c) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 2 2 2 2 +--R b c m + 9b c m + 20b c +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R * +--R m log(b c x + a c) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 73 + +)clear all + +--S 74 of 1751 +t0:=(A+B*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R m +--R (B x + A)(b c x + a c) +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1751 +r0:=-(A*b-a*B)*(a*c+b*c*x)^(1+m)/(b^2*c*(2-m)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + B*(a*c+b*c*x)^(2+m)/(b^2*c^2*(1-m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R m + 2 +--R (B m - 2B)(b c x + a c) +--R + +--R m + 1 +--R ((A b - B a)c m + (- A b + B a)c)(b c x + a c) +--R / +--R 4 2 2 4 2 4 2 2 3 2 2 3 2 3 2 +--R (b c m - 3b c m + 2b c )x + (2a b c m - 6a b c m + 4a b c )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R a b c m - 3a b c m + 2a b c +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 75 + +--S 76 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R m log(b c x + a c) +--R ((B b m - 2B b)x + A b m - A b - B a)%e +--R ----------------------------------------------------------------------------- +--R 4 2 4 4 2 3 2 3 3 2 2 2 2 2 2 2 +--R (b m - 3b m + 2b )x + (2a b m - 6a b m + 4a b )x + a b m - 3a b m + 2a b +--R Type: Union(Expression(Integer),...) +--E 76 + +--S 77 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R ((B b c m - 2B b c )x + A b c m + (- A b - B a)c )\|b x + 2a b x + a +--R * +--R m log(b c x + a c) +--R %e +--R + +--R m + 2 +--R (- B m + 2B)(b c x + a c) +--R + +--R m + 1 +--R ((- A b + B a)c m + (A b - B a)c)(b c x + a c) +--R / +--R 4 2 2 4 2 4 2 2 3 2 2 3 2 3 2 +--R (b c m - 3b c m + 2b c )x + (2a b c m - 6a b c m + 4a b c )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R a b c m - 3a b c m + 2a b c +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R ((B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a) +--R * +--R m log(b c x + a c) +--R %e +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 1751 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R m 2 2 2 p +--R (1) (B x + A)(b c x + a c) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1751 +r0:=(A*b-a*B)*(a*c+b*c*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*c*(1+m+2*p))+_ + B*(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*c^2*(2+m+2*p)) +--R +--R +--R (2) +--R m + 2 +--R (2B p + B m + B)(b c x + a c) +--R + +--R m + 1 +--R ((2A b - 2B a)c p + (A b - B a)c m + (2A b - 2B a)c)(b c x + a c) +--R * +--R 2 2 2 p +--R (b x + 2a b x + a ) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +--R 4b c p + (4b c m + 6b c )p + b c m + 3b c m + 2b c +--R Type: Expression(Integer) +--E 80 + +--S 81 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R (2B b p + B b m + B b )x +--R + +--R 2 2 2 +--R ((2A b + 2B a b)p + (A b + B a b)m + 2A b )x + 2A a b p + A a b m +--R + +--R 2 +--R 2A a b - B a +--R * +--R 1 +--R 2p log(b c x + a c) + p log(--) +--R 2 +--R m log(b c x + a c) c +--R %e %e +--R / +--R 2 2 2 2 2 2 2 2 +--R 4b p + (4b m + 6b )p + b m + 3b m + 2b +--R Type: Union(Expression(Integer),...) +--E 81 + +--S 82 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 +--R (2B b c p + B b c m + B b c )x +--R + +--R 2 2 2 2 2 2 2 +--R ((2A b + 2B a b)c p + (A b + B a b)c m + 2A b c )x + 2A a b c p +--R + +--R 2 2 2 +--R A a b c m + (2A a b - B a )c +--R * +--R 1 +--R 2p log(b c x + a c) + p log(--) +--R 2 +--R m log(b c x + a c) c +--R %e %e +--R + +--R m + 2 +--R (- 2B p - B m - B)(b c x + a c) +--R + +--R ((- 2A b + 2B a)c p + (- A b + B a)c m + (- 2A b + 2B a)c) +--R * +--R m + 1 +--R (b c x + a c) +--R * +--R 2 2 2 p +--R (b x + 2a b x + a ) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +--R 4b c p + (4b c m + 6b c )p + b c m + 3b c m + 2b c +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 83 + +)clear all + +--S 84 of 1751 +t0:=(a+b*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R m 2 2 2 p +--R (1) (b x + a)(b c x + a c) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1751 +r0:=(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b*c^2*(2+m+2*p)) +--R +--R +--R m + 2 2 2 2 p +--R (b c x + a c) (b x + 2a b x + a ) +--R (2) --------------------------------------- +--R 2 2 2 +--R 2b c p + b c m + 2b c +--R Type: Expression(Integer) +--E 85 + +--S 86 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 +--R 2p log(b c x + a c) + p log(--) +--R 2 +--R 2 2 2 m log(b c x + a c) c +--R (b x + 2a b x + a )%e %e +--R ------------------------------------------------------------------------- +--R 2b p + b m + 2b +--R Type: Union(Expression(Integer),...) +--E 86 + +--S 87 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 m log(b c x + a c) +--R (b c x + 2a b c x + a c )%e +--R * +--R 1 +--R 2p log(b c x + a c) + p log(--) +--R 2 +--R c +--R %e +--R + +--R m + 2 2 2 2 p +--R - (b c x + a c) (b x + 2a b x + a ) +--R / +--R 2 2 2 +--R 2b c p + b c m + 2b c +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 88 + +)clear all + +--S 89 of 1751 +t0:=(a+b*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R m +--R (b c x + a c) +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1751 +r0:=(a*c+b*c*x)^(8+m)/(b*c^8*(8+m)) +--R +--R +--R m + 8 +--R (b c x + a c) +--R (2) ------------------ +--R 8 8 +--R b c m + 8b c +--R Type: Expression(Integer) +--E 90 + +--S 91 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 8 +--R 8a b x + a +--R * +--R m log(b c x + a c) +--R %e +--R / +--R b m + 8b +--R Type: Union(Expression(Integer),...) +--E 91 + +--S 92 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8 8 7 8 7 2 6 8 6 3 5 8 5 4 4 8 4 +--R b c x + 8a b c x + 28a b c x + 56a b c x + 70a b c x +--R + +--R 5 3 8 3 6 2 8 2 7 8 8 8 +--R 56a b c x + 28a b c x + 8a b c x + a c +--R * +--R m log(b c x + a c) +--R %e +--R + +--R m + 8 +--R - (b c x + a c) +--R / +--R 8 8 +--R b c m + 8b c +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 1751 +t0:=(a+b*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R m +--R (b c x + a c) +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1751 +r0:=-c^4*(a*c+b*c*x)^(-4+m)/(b*(4-m)) +--R +--R +--R 4 m - 4 +--R c (b c x + a c) +--R (2) -------------------- +--R b m - 4b +--R Type: Expression(Integer) +--E 95 + +--S 96 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R m log(b c x + a c) +--R %e +--R / +--R 5 5 4 4 4 3 2 3 2 3 2 +--R (b m - 4b )x + (4a b m - 16a b )x + (6a b m - 24a b )x +--R + +--R 3 2 3 2 4 4 +--R (4a b m - 16a b )x + a b m - 4a b +--R Type: Union(Expression(Integer),...) +--E 96 + +--S 97 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R m log(b c x + a c) +--R %e +--R + +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 m - 4 +--R (- b c x - 4a b c x - 6a b c x - 4a b c x - a c )(b c x + a c) +--R / +--R 5 5 4 4 4 3 2 3 2 3 2 +--R (b m - 4b )x + (4a b m - 16a b )x + (6a b m - 24a b )x +--R + +--R 3 2 3 2 4 4 +--R (4a b m - 16a b )x + a b m - 4a b +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 98 + +)clear all + +--S 99 of 1751 +t0:=x*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (c x + b x + a x)(e x + d) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1751 +r0:=-d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(3*c*d^2-_ + e*(2*b*d-a*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*c*d-b*e)*(d+e*x)^(3+m)/_ + (e^4*(3+m))+c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (c m + 6c m + 11c m + 6c)(e x + d) +--R + +--R 3 2 +--R ((b e - 3c d)m + (7b e - 21c d)m + (14b e - 42c d)m + 8b e - 24c d) +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 2 2 2 +--R (a e - 2b d e + 3c d )m + (8a e - 16b d e + 24c d )m +--R + +--R 2 2 2 2 +--R (19a e - 38b d e + 57c d )m + 12a e - 24b d e + 36c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 2 2 3 2 +--R (- a d e + b d e - c d )m + (- 9a d e + 9b d e - 9c d )m +--R + +--R 2 2 3 2 2 3 +--R (- 26a d e + 26b d e - 26c d )m - 24a d e + 24b d e - 24c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 100 + +--S 101 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (c e m + 6c e m + 11c e m + 6c e )x +--R + +--R 4 3 3 4 3 2 4 3 +--R (b e + c d e )m + (7b e + 3c d e )m + (14b e + 2c d e )m +--R + +--R 4 +--R 8b e +--R * +--R 3 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (a e + b d e )m + (8a e + 5b d e - 3c d e )m +--R + +--R 4 3 2 2 4 +--R (19a e + 4b d e - 3c d e )m + 12a e +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 2 2 3 2 2 3 +--R (a d e m + (7a d e - 2b d e )m + (12a d e - 8b d e + 6c d e)m)x +--R + +--R 2 2 2 2 2 3 2 2 3 4 +--R - a d e m + (- 7a d e + 2b d e)m - 12a d e + 8b d e - 6c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 101 + +--S 102 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (c e m + 6c e m + 11c e m + 6c e )x +--R + +--R 4 3 3 4 3 2 4 3 +--R (b e + c d e )m + (7b e + 3c d e )m + (14b e + 2c d e )m +--R + +--R 4 +--R 8b e +--R * +--R 3 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (a e + b d e )m + (8a e + 5b d e - 3c d e )m +--R + +--R 4 3 2 2 4 +--R (19a e + 4b d e - 3c d e )m + 12a e +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 2 2 3 2 2 3 +--R (a d e m + (7a d e - 2b d e )m + (12a d e - 8b d e + 6c d e)m)x +--R + +--R 2 2 2 2 2 3 2 2 3 4 +--R - a d e m + (- 7a d e + 2b d e)m - 12a d e + 8b d e - 6c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 2 m + 4 +--R (- c m - 6c m - 11c m - 6c)(e x + d) +--R + +--R 3 2 +--R (- b e + 3c d)m + (- 7b e + 21c d)m + (- 14b e + 42c d)m - 8b e +--R + +--R 24c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 2 2 2 +--R (- a e + 2b d e - 3c d )m + (- 8a e + 16b d e - 24c d )m +--R + +--R 2 2 2 2 +--R (- 19a e + 38b d e - 57c d )m - 12a e + 24b d e - 36c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 2 2 3 2 +--R (a d e - b d e + c d )m + (9a d e - 9b d e + 9c d )m +--R + +--R 2 2 3 2 2 3 +--R (26a d e - 26b d e + 26c d )m + 24a d e - 24b d e + 24c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 103 + +)clear all + +--S 104 of 1751 +t0:=x*(d+e*x)^5*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 5 4 2 3 6 +--R c e x + (b e + 5c d e )x + (a e + 5b d e + 10c d e )x +--R + +--R 4 2 3 3 2 5 2 3 3 2 4 4 +--R (5a d e + 10b d e + 10c d e )x + (10a d e + 10b d e + 5c d e)x +--R + +--R 3 2 4 5 3 4 5 2 5 +--R (10a d e + 5b d e + c d )x + (5a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 104 + +--S 105 of 1751 +r0:=-1/6*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^6/e^4+1/7*(3*c*d^2-e*(2*b*d-a*e))*_ + (d+e*x)^7/e^4-1/8*(3*c*d-b*e)*(d+e*x)^8/e^4+1/9*c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 1 9 5 8 10 2 7 7 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + -- c d e )x +--R 9 8 8 7 7 7 +--R + +--R 5 8 5 2 7 5 3 6 6 2 7 3 6 4 5 5 +--R (- a d e + - b d e + - c d e )x + (2a d e + 2b d e + c d e )x +--R 6 3 3 +--R + +--R 5 3 6 5 4 5 1 5 4 4 5 4 5 1 5 4 3 1 5 4 2 +--R (- a d e + - b d e + - c d e )x + (- a d e + - b d e )x + - a d e x +--R 2 4 4 3 3 2 +--R + +--R 1 7 2 1 8 1 9 +--R - -- a d e + --- b d e - --- c d +--R 42 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 105 + +--S 106 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 9 1 5 5 4 8 1 5 5 4 10 2 3 7 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + -- c d e )x +--R 9 8 8 7 7 7 +--R + +--R 5 4 5 2 3 5 3 2 6 2 3 3 2 4 5 +--R (- a d e + - b d e + - c d e )x + (2a d e + 2b d e + c d e)x +--R 6 3 3 +--R + +--R 5 3 2 5 4 1 5 4 5 4 1 5 3 1 5 2 +--R (- a d e + - b d e + - c d )x + (- a d e + - b d )x + - a d x +--R 2 4 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 106 + +--S 107 of 1751 +m0:=a0-r0 +--R +--R +--R 1 7 2 1 8 1 9 +--R -- a d e - --- b d e + --- c d +--R 42 168 504 +--R (4) -------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 107 + +--S 108 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 108 + +)clear all + +--S 109 of 1751 +t0:=x*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 4 3 2 2 5 +--R c e x + (b e + 4c d e )x + (a e + 4b d e + 6c d e )x +--R + +--R 3 2 2 3 4 2 2 3 4 3 +--R (4a d e + 6b d e + 4c d e)x + (6a d e + 4b d e + c d )x +--R + +--R 3 4 2 4 +--R (4a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 109 + +--S 110 of 1751 +r0:=-1/5*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4+1/6*(3*c*d^2-e*(2*b*d-a*e))*_ + (d+e*x)^6/e^4-1/7*(3*c*d-b*e)*(d+e*x)^7/e^4+1/8*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 8 4 7 7 1 8 2 7 2 6 6 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + c d e )x +--R 8 7 7 6 3 +--R + +--R 4 7 6 2 6 4 3 5 5 3 2 6 3 5 1 4 4 4 +--R (- a d e + - b d e + - c d e )x + (- a d e + b d e + - c d e )x +--R 5 5 5 2 4 +--R + +--R 4 3 5 1 4 4 3 1 4 4 2 1 6 2 1 7 1 8 +--R (- a d e + - b d e )x + - a d e x - -- a d e + --- b d e - --- c d +--R 3 3 2 30 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 110 + +--S 111 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 8 1 4 4 3 7 1 4 2 3 2 2 6 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + c d e )x +--R 8 7 7 6 3 +--R + +--R 4 3 6 2 2 4 3 5 3 2 2 3 1 4 4 +--R (- a d e + - b d e + - c d e)x + (- a d e + b d e + - c d )x +--R 5 5 5 2 4 +--R + +--R 4 3 1 4 3 1 4 2 +--R (- a d e + - b d )x + - a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 111 + +--S 112 of 1751 +m0:=a0-r0 +--R +--R +--R 1 6 2 1 7 1 8 +--R -- a d e - --- b d e + --- c d +--R 30 105 280 +--R (4) -------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 112 + +--S 113 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 113 + +)clear all + +--S 114 of 1751 +t0:=x*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 3 2 2 4 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 3 2 3 2 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 114 + +--S 115 of 1751 +r0:=1/2*a*d^3*x^2+1/3*d^2*(b*d+3*a*e)*x^3+1/4*d*(c*d^2+3*e*(b*d+a*e))*x^4+_ + 1/5*e*(3*c*d^2+e*(3*b*d+a*e))*x^5+1/6*e^2*(3*c*d+b*e)*x^6+1/7*c*e^3*x^7 +--R +--R +--R (2) +--R 1 3 7 1 3 1 2 6 1 3 3 2 3 2 5 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + - c d e)x +--R 7 6 2 5 5 5 +--R + +--R 3 2 3 2 1 3 4 2 1 3 3 1 3 2 +--R (- a d e + - b d e + - c d )x + (a d e + - b d )x + - a d x +--R 4 4 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 115 + +--S 116 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 7 1 3 1 2 6 1 3 3 2 3 2 5 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + - c d e)x +--R 7 6 2 5 5 5 +--R + +--R 3 2 3 2 1 3 4 2 1 3 3 1 3 2 +--R (- a d e + - b d e + - c d )x + (a d e + - b d )x + - a d x +--R 4 4 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 116 + +--S 117 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +)clear all + +--S 119 of 1751 +t0:=x*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 2 2 3 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d x +--R Type: Polynomial(Integer) +--E 119 + +--S 120 of 1751 +r0:=1/2*a*d^2*x^2+1/3*d*(b*d+2*a*e)*x^3+1/4*(c*d^2+e*(2*b*d+a*e))*x^4+_ + 1/5*e*(2*c*d+b*e)*x^5+1/6*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - c e x + (- b e + - c d e)x + (- a e + - b d e + - c d )x +--R 6 5 5 4 2 4 +--R + +--R 2 1 2 3 1 2 2 +--R (- a d e + - b d )x + - a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +--S 121 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - c e x + (- b e + - c d e)x + (- a e + - b d e + - c d )x +--R 6 5 5 4 2 4 +--R + +--R 2 1 2 3 1 2 2 +--R (- a d e + - b d )x + - a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 121 + +--S 122 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +)clear all + +--S 124 of 1751 +t0:=x*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R 4 3 2 +--R (1) c e x + (b e + c d)x + (a e + b d)x + a d x +--R Type: Polynomial(Integer) +--E 124 + +--S 125 of 1751 +r0:=1/2*a*d*x^2+1/3*(b*d+a*e)*x^3+1/4*(c*d+b*e)*x^4+1/5*c*e*x^5 +--R +--R +--R 1 5 1 1 4 1 1 3 1 2 +--R (2) - c e x + (- b e + - c d)x + (- a e + - b d)x + - a d x +--R 5 4 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +--S 126 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 1 5 1 1 4 1 1 3 1 2 +--R (3) - c e x + (- b e + - c d)x + (- a e + - b d)x + - a d x +--R 5 4 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 126 + +--S 127 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +)clear all + +--S 129 of 1751 +t0:=x*(a+b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) c x + b x + a x +--R Type: Polynomial(Integer) +--E 129 + +--S 130 of 1751 +r0:=1/2*a*x^2+1/3*b*x^3+1/4*c*x^4 +--R +--R +--R 1 4 1 3 1 2 +--R (2) - c x + - b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +--S 131 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 3 1 2 +--R (3) - c x + - b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 131 + +--S 132 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +)clear all + +--S 134 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ----------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 134 + +--S 135 of 1751 +r0:=(c*d^2-b*d*e+a*e^2)*x/e^3-1/2*(c*d-b*e)*x^2/e^2+1/3*c*x^3/e-_ + d*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 2 3 3 3 3 2 2 +--R (- 6a d e + 6b d e - 6c d )log(e x + d) + 2c e x + (3b e - 3c d e )x +--R + +--R 3 2 2 +--R (6a e - 6b d e + 6c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 135 + +--S 136 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 3 3 2 2 +--R (- 6a d e + 6b d e - 6c d )log(e x + d) + 2c e x + (3b e - 3c d e )x +--R + +--R 3 2 2 +--R (6a e - 6b d e + 6c d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 136 + +--S 137 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 139 + +--S 140 of 1751 +r0:=-(2*c*d-b*e)*x/e^3+1/2*c*x^2/e^2+d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))+_ + (3*c*d^2-e*(2*b*d-a*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((2a e - 4b d e + 6c d e)x + 2a d e - 4b d e + 6c d )log(e x + d) +--R + +--R 3 3 3 2 2 2 2 2 2 +--R c e x + (2b e - 3c d e )x + (2b d e - 4c d e)x + 2a d e - 2b d e +--R + +--R 3 +--R 2c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 140 + +--S 141 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 +--R ((2a e - 4b d e + 6c d e)x + 2a d e - 4b d e + 6c d )log(e x + d) +--R + +--R 3 3 3 2 2 2 2 2 2 +--R c e x + (2b e - 3c d e )x + (2b d e - 4c d e)x + 2a d e - 2b d e +--R + +--R 3 +--R 2c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 141 + +--S 142 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 143 + +)clear all + +--S 144 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 144 + +--S 145 of 1751 +r0:=c*x/e^3+1/2*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (-3*c*d^2+e*(2*b*d-a*e))/(e^4*(d+e*x))-(3*c*d-b*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 +--R ((2b e - 6c d e )x + (4b d e - 12c d e)x + 2b d e - 6c d )log(e x + d) +--R + +--R 3 3 2 2 3 2 2 2 2 +--R 2c e x + 4c d e x + (- 2a e + 4b d e - 4c d e)x - a d e + 3b d e +--R + +--R 3 +--R - 5c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 145 + +--S 146 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 2 3 +--R ((2b e - 6c d e )x + (4b d e - 12c d e)x + 2b d e - 6c d )log(e x + d) +--R + +--R 3 3 2 2 3 2 2 2 2 +--R 2c e x + 4c d e x + (- 2a e + 4b d e - 4c d e)x - a d e + 3b d e +--R + +--R 3 +--R - 5c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 146 + +--S 147 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 148 + +)clear all + +--S 149 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 149 + +--S 150 of 1751 +r0:=1/3*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-3*c*d^2+_ + e*(2*b*d-a*e))/(e^4*(d+e*x)^2)+(3*c*d-b*e)/(e^4*(d+e*x))+c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6c e x + 18c d e x + 18c d e x + 6c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 2 2 +--R (- 6b e + 18c d e )x + (- 3a e - 6b d e + 27c d e)x - a d e - 2b d e +--R + +--R 3 +--R 11c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 150 + +--S 151 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (6c e x + 18c d e x + 18c d e x + 6c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 2 2 +--R (- 6b e + 18c d e )x + (- 3a e - 6b d e + 27c d e)x - a d e - 2b d e +--R + +--R 3 +--R 11c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 151 + +--S 152 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 154 + +--S 155 of 1751 +r0:=1/4*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^3)+1/2*(3*c*d-b*e)/(e^4*(d+e*x)^2)-c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 3 3 2 2 1 3 1 2 2 +--R - c e x + (- - b e - - c d e )x + (- - a e - - b d e - c d e)x +--R 2 2 3 3 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - - c d +--R 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 155 + +--S 156 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 3 2 2 +--R - 12c e x + (- 6b e - 18c d e )x + (- 4a e - 4b d e - 12c d e)x +--R + +--R 2 2 3 +--R - a d e - b d e - 3c d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 156 + +--S 157 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 158 + +)clear all + +--S 159 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 159 + +--S 160 of 1751 +r0:=1/5*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^5)+1/4*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^4)+1/3*(3*c*d-b*e)/(e^4*(d+e*x)^3)-1/2*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 1 3 1 2 1 2 +--R - - c e x + (- - b e - - c d e )x + (- - a e - - b d e - - c d e)x +--R 2 3 2 4 6 4 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - -- c d +--R 20 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 160 + +--S 161 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 3 2 2 +--R - 30c e x + (- 20b e - 30c d e )x + (- 15a e - 10b d e - 15c d e)x +--R + +--R 2 2 3 +--R - 3a d e - 2b d e - 3c d +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 161 + +--S 162 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 163 + +)clear all + +--S 164 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R c x + b x + a x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 164 + +--S 165 of 1751 +r0:=1/6*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^6)+1/5*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^5)+1/4*(3*c*d-b*e)/(e^4*(d+e*x)^4)-1/3*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 1 3 1 2 1 2 +--R - - c e x + (- - b e - - c d e )x + (- - a e - -- b d e - -- c d e)x +--R 3 4 4 5 10 10 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - -- c d +--R 30 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 165 + +--S 166 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 3 2 2 +--R - 20c e x + (- 15b e - 15c d e )x + (- 12a e - 6b d e - 6c d e)x +--R + +--R 2 2 3 +--R - 2a d e - b d e - c d +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 4 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 166 + +--S 167 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 1751 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + (A b + B a)x + A a)(e x + d) +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1751 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))-_ + (A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^(2+m)/(e^4*(2+m))-_ + (3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3+m)/(e^4*(3+m))+_ + B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R ((A c + B b)e - 3B c d)m + ((7A c + 7B b)e - 21B c d)m +--R + +--R ((14A c + 14B b)e - 42B c d)m + (8A c + 8B b)e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R ((A b + B a)e + (- 2A c - 2B b)d e + 3B c d )m +--R + +--R 2 2 2 +--R ((8A b + 8B a)e + (- 16A c - 16B b)d e + 24B c d )m +--R + +--R 2 2 +--R ((19A b + 19B a)e + (- 38A c - 38B b)d e + 57B c d )m +--R + +--R 2 2 +--R (12A b + 12B a)e + (- 24A c - 24B b)d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (A a e + (- A b - B a)d e + (A c + B b)d e - B c d )m +--R + +--R 3 2 2 3 2 +--R (9A a e + (- 9A b - 9B a)d e + (9A c + 9B b)d e - 9B c d )m +--R + +--R 3 2 2 3 +--R (26A a e + (- 26A b - 26B a)d e + (26A c + 26B b)d e - 26B c d )m +--R + +--R 3 2 2 3 +--R 24A a e + (- 24A b - 24B a)d e + (24A c + 24B b)d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R ((A c + B b)e + B c d e )m + ((7A c + 7B b)e + 3B c d e )m +--R + +--R 4 3 4 +--R ((14A c + 14B b)e + 2B c d e )m + (8A c + 8B b)e +--R * +--R 3 +--R x +--R + +--R 4 3 3 +--R ((A b + B a)e + (A c + B b)d e )m +--R + +--R 4 3 2 2 2 +--R ((8A b + 8B a)e + (5A c + 5B b)d e - 3B c d e )m +--R + +--R 4 3 2 2 +--R ((19A b + 19B a)e + (4A c + 4B b)d e - 3B c d e )m +--R + +--R 4 +--R (12A b + 12B a)e +--R * +--R 2 +--R x +--R + +--R 4 3 3 +--R (A a e + (A b + B a)d e )m +--R + +--R 4 3 2 2 2 +--R (9A a e + (7A b + 7B a)d e + (- 2A c - 2B b)d e )m +--R + +--R 4 3 2 2 3 +--R (26A a e + (12A b + 12B a)d e + (- 8A c - 8B b)d e + 6B c d e)m +--R + +--R 4 +--R 24A a e +--R * +--R x +--R + +--R 3 3 3 2 2 2 +--R A a d e m + (9A a d e + (- A b - B a)d e )m +--R + +--R 3 2 2 3 3 +--R (26A a d e + (- 7A b - 7B a)d e + (2A c + 2B b)d e)m + 24A a d e +--R + +--R 2 2 3 4 +--R (- 12A b - 12B a)d e + (8A c + 8B b)d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 171 + +--S 172 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R ((A c + B b)e + B c d e )m + ((7A c + 7B b)e + 3B c d e )m +--R + +--R 4 3 4 +--R ((14A c + 14B b)e + 2B c d e )m + (8A c + 8B b)e +--R * +--R 3 +--R x +--R + +--R 4 3 3 +--R ((A b + B a)e + (A c + B b)d e )m +--R + +--R 4 3 2 2 2 +--R ((8A b + 8B a)e + (5A c + 5B b)d e - 3B c d e )m +--R + +--R 4 3 2 2 +--R ((19A b + 19B a)e + (4A c + 4B b)d e - 3B c d e )m +--R + +--R 4 +--R (12A b + 12B a)e +--R * +--R 2 +--R x +--R + +--R 4 3 3 +--R (A a e + (A b + B a)d e )m +--R + +--R 4 3 2 2 2 +--R (9A a e + (7A b + 7B a)d e + (- 2A c - 2B b)d e )m +--R + +--R 4 3 2 2 +--R 26A a e + (12A b + 12B a)d e + (- 8A c - 8B b)d e +--R + +--R 3 +--R 6B c d e +--R * +--R m +--R + +--R 4 +--R 24A a e +--R * +--R x +--R + +--R 3 3 3 2 2 2 +--R A a d e m + (9A a d e + (- A b - B a)d e )m +--R + +--R 3 2 2 3 3 +--R (26A a d e + (- 7A b - 7B a)d e + (2A c + 2B b)d e)m + 24A a d e +--R + +--R 2 2 3 4 +--R (- 12A b - 12B a)d e + (8A c + 8B b)d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 2 m + 4 +--R (- B c m - 6B c m - 11B c m - 6B c)(e x + d) +--R + +--R 3 2 +--R ((- A c - B b)e + 3B c d)m + ((- 7A c - 7B b)e + 21B c d)m +--R + +--R ((- 14A c - 14B b)e + 42B c d)m + (- 8A c - 8B b)e + 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R ((- A b - B a)e + (2A c + 2B b)d e - 3B c d )m +--R + +--R 2 2 2 +--R ((- 8A b - 8B a)e + (16A c + 16B b)d e - 24B c d )m +--R + +--R 2 2 +--R ((- 19A b - 19B a)e + (38A c + 38B b)d e - 57B c d )m +--R + +--R 2 2 +--R (- 12A b - 12B a)e + (24A c + 24B b)d e - 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (- A a e + (A b + B a)d e + (- A c - B b)d e + B c d )m +--R + +--R 3 2 2 3 2 +--R (- 9A a e + (9A b + 9B a)d e + (- 9A c - 9B b)d e + 9B c d )m +--R + +--R 3 2 2 3 +--R (- 26A a e + (26A b + 26B a)d e + (- 26A c - 26B b)d e + 26B c d )m +--R + +--R 3 2 2 3 +--R - 24A a e + (24A b + 24B a)d e + (- 24A c - 24B b)d e + 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 173 + +)clear all + +--S 174 of 1751 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 +--R B c e x + ((A c + B b)e + 4B c d e )x +--R + +--R 4 3 2 2 5 +--R ((A b + B a)e + (4A c + 4B b)d e + 6B c d e )x +--R + +--R 4 3 2 2 3 4 +--R (A a e + (4A b + 4B a)d e + (6A c + 6B b)d e + 4B c d e)x +--R + +--R 3 2 2 3 4 3 +--R (4A a d e + (6A b + 6B a)d e + (4A c + 4B b)d e + B c d )x +--R + +--R 2 2 3 4 2 +--R (6A a d e + (4A b + 4B a)d e + (A c + B b)d )x +--R + +--R 3 4 4 +--R (4A a d e + (A b + B a)d )x + A a d +--R Type: Polynomial(Integer) +--E 174 + +--S 175 of 1751 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4-1/6*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^7/e^4+1/8*B*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 1 8 4 7 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 1 8 2 2 7 2 6 6 +--R ((- A b + - B a)e + (- A c + - B b)d e + B c d e )x +--R 6 6 3 3 +--R + +--R 1 8 4 4 7 6 6 2 6 4 3 5 5 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 5 5 +--R + +--R 7 3 3 2 6 3 5 1 4 4 4 +--R (A a d e + (- A b + - B a)d e + (A c + B b)d e + - B c d e )x +--R 2 2 4 +--R + +--R 2 6 4 4 3 5 1 1 4 4 3 +--R (2A a d e + (- A b + - B a)d e + (- A c + - B b)d e )x +--R 3 3 3 3 +--R + +--R 3 5 1 1 4 4 2 4 4 1 5 3 +--R (2A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 5 +--R + +--R 1 1 6 2 1 1 7 1 8 +--R (- -- A b - -- B a)d e + (--- A c + --- B b)d e - --- B c d +--R 30 30 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 175 + +--S 176 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 8 1 1 4 4 3 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 1 4 2 2 3 2 2 6 +--R ((- A b + - B a)e + (- A c + - B b)d e + B c d e )x +--R 6 6 3 3 +--R + +--R 1 4 4 4 3 6 6 2 2 4 3 5 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d e)x +--R 5 5 5 5 5 5 +--R + +--R 3 3 3 2 2 3 1 4 4 +--R (A a d e + (- A b + - B a)d e + (A c + B b)d e + - B c d )x +--R 2 2 4 +--R + +--R 2 2 4 4 3 1 1 4 3 +--R (2A a d e + (- A b + - B a)d e + (- A c + - B b)d )x +--R 3 3 3 3 +--R + +--R 3 1 1 4 2 4 +--R (2A a d e + (- A b + - B a)d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 176 + +--S 177 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 5 3 1 1 6 2 1 1 7 1 8 +--R - - A a d e + (-- A b + -- B a)d e + (- --- A c - --- B b)d e + --- B c d +--R 5 30 30 105 105 280 +--R ---------------------------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 177 + +--S 178 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 178 + +)clear all + +--S 179 of 1751 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R ((A b + B a)e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 3 2 2 3 3 +--R (A a e + (3A b + 3B a)d e + (3A c + 3B b)d e + B c d )x +--R + +--R 2 2 3 2 +--R (3A a d e + (3A b + 3B a)d e + (A c + B b)d )x +--R + +--R 2 3 3 +--R (3A a d e + (A b + B a)d )x + A a d +--R Type: Polynomial(Integer) +--E 179 + +--S 180 of 1751 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4-1/5*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^6/e^4+1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 1 7 1 6 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 1 7 3 3 6 3 2 5 5 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 5 +--R + +--R 1 7 3 3 6 3 3 2 5 1 3 4 4 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d e )x +--R 4 4 4 4 4 4 +--R + +--R 6 2 5 1 1 3 4 3 +--R (A a d e + (A b + B a)d e + (- A c + - B b)d e )x +--R 3 3 +--R + +--R 3 2 5 1 1 3 4 2 3 4 1 4 3 +--R (- A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 2 4 +--R + +--R 1 1 5 2 1 1 6 1 7 +--R (- -- A b - -- B a)d e + (-- A c + -- B b)d e - --- B c d +--R 20 20 60 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 180 + +--S 181 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 7 1 1 3 1 2 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 1 3 3 3 2 3 2 5 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d e)x +--R 5 5 5 5 5 +--R + +--R 1 3 3 3 2 3 3 2 1 3 4 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d )x +--R 4 4 4 4 4 4 +--R + +--R 2 2 1 1 3 3 +--R (A a d e + (A b + B a)d e + (- A c + - B b)d )x +--R 3 3 +--R + +--R 3 2 1 1 3 2 3 +--R (- A a d e + (- A b + - B a)d )x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 181 + +--S 182 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 4 3 1 1 5 2 1 1 6 1 7 +--R - - A a d e + (-- A b + -- B a)d e + (- -- A c - -- B b)d e + --- B c d +--R 4 20 20 60 60 140 +--R -------------------------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 182 + +--S 183 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 183 + +)clear all + +--S 184 of 1751 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 +--R ((A b + B a)e + (2A c + 2B b)d e + B c d )x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + (A c + B b)d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R Type: Polynomial(Integer) +--E 184 + +--S 185 of 1751 +r0:=-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3/e^4-1/4*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^4/e^4-1/5*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^5/e^4+1/6*B*c*(d+e*x)^6/e^4 +--R +--R +--R (2) +--R 1 6 6 1 1 6 2 5 5 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 6 5 5 5 +--R + +--R 1 1 6 1 1 5 1 2 4 4 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d e )x +--R 4 4 2 2 4 +--R + +--R 1 6 2 2 5 1 1 2 4 3 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e )x +--R 3 3 3 3 3 +--R + +--R 5 1 1 2 4 2 2 4 1 3 3 +--R (A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 3 +--R + +--R 1 1 4 2 1 1 5 1 6 +--R (- -- A b - -- B a)d e + (-- A c + -- B b)d e - -- B c d +--R 12 12 30 30 60 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 185 + +--S 186 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 6 1 1 2 2 5 +--R - B c e x + ((- A c + - B b)e + - B c d e)x +--R 6 5 5 5 +--R + +--R 1 1 2 1 1 1 2 4 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d )x +--R 4 4 2 2 4 +--R + +--R 1 2 2 2 1 1 2 3 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d )x +--R 3 3 3 3 3 +--R + +--R 1 1 2 2 2 +--R (A a d e + (- A b + - B a)d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 186 + +--S 187 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 3 1 1 4 2 1 1 5 1 6 +--R - - A a d e + (-- A b + -- B a)d e + (- -- A c - -- B b)d e + -- B c d +--R 3 12 12 30 30 60 +--R ------------------------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 187 + +--S 188 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 188 + +)clear all + +--S 189 of 1751 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + ((A c + B b)e + B c d)x + ((A b + B a)e + (A c + B b)d)x +--R + +--R (A a e + (A b + B a)d)x + A a d +--R Type: Polynomial(Integer) +--E 189 + +--S 190 of 1751 +r0:=a*A*d*x+1/2*(A*b*d+a*B*d+a*A*e)*x^2+1/3*(b*B*d+A*c*d+A*b*e+a*B*e)*x^3+_ + 1/4*(B*c*d+b*B*e+A*c*e)*x^4+1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 1 3 1 1 1 2 +--R ((- A b + - B a)e + (- A c + - B b)d)x + (- A a e + (- A b + - B a)d)x +--R 3 3 3 3 2 2 2 +--R + +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 190 + +--S 191 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 1 3 1 1 1 2 +--R ((- A b + - B a)e + (- A c + - B b)d)x + (- A a e + (- A b + - B a)d)x +--R 3 3 3 3 2 2 2 +--R + +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 191 + +--S 192 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 192 + +--S 193 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +)clear all + +--S 194 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + (A c + B b)x + (A b + B a)x + A a +--R Type: Polynomial(Integer) +--E 194 + +--S 195 of 1751 +r0:=a*A*x+1/2*(A*b+a*B)*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 1 3 1 1 2 +--R (2) - B c x + (- A c + - B b)x + (- A b + - B a)x + A a x +--R 4 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 195 + +--S 196 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 1 3 1 1 2 +--R (3) - B c x + (- A c + - B b)x + (- A b + - B a)x + A a x +--R 4 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 196 + +--S 197 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +)clear all + +--S 199 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 199 + +--S 200 of 1751 +r0:=-(A*e*(c*d-b*e)-B*(c*d^2-e*(b*d-a*e)))*x/e^3-_ + 1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+1/3*B*c*x^3/e-_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 3 +--R (6A a e + (- 6A b - 6B a)d e + (6A c + 6B b)d e - 6B c d )log(e x + d) +--R + +--R 3 3 3 2 2 +--R 2B c e x + ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R ((6A b + 6B a)e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 200 + +--S 201 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 +--R (6A a e + (- 6A b - 6B a)d e + (6A c + 6B b)d e - 6B c d )log(e x + d) +--R + +--R 3 3 3 2 2 +--R 2B c e x + ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R ((6A b + 6B a)e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 201 + +--S 202 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 203 + +)clear all + +--S 204 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 204 + +--S 205 of 1751 +r0:=-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))-(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 +--R ((2A b + 2B a)e + (- 4A c - 4B b)d e + 6B c d e)x +--R + +--R 2 2 3 +--R (2A b + 2B a)d e + (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 3 2 +--R ((2A c + 2B b)d e - 4B c d e)x - 2A a e + (2A b + 2B a)d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 205 + +--S 206 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 +--R ((2A b + 2B a)e + (- 4A c - 4B b)d e + 6B c d e)x +--R + +--R 2 2 3 +--R (2A b + 2B a)d e + (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 3 2 +--R ((2A c + 2B b)d e - 4B c d e)x - 2A a e + (2A b + 2B a)d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 206 + +--S 207 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 208 + +)clear all + +--S 209 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 209 + +--S 210 of 1751 +r0:=B*c*x/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x))-_ + (3*B*c*d-b*B*e-A*c*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 +--R 2B c e x + 4B c d e x +--R + +--R 3 2 2 3 +--R ((- 2A b - 2B a)e + (4A c + 4B b)d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 210 + +--S 211 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 +--R 2B c e x + 4B c d e x +--R + +--R 3 2 2 3 +--R ((- 2A b - 2B a)e + (4A c + 4B b)d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 211 + +--S 212 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 214 + +--S 215 of 1751 +r0:=1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+_ + 1/2*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^2)+_ + (3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 3 +--R ((- 3A b - 3B a)e + (- 6A c - 6B b)d e + 27B c d e)x - 2A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 3 +--R ((- 3A b - 3B a)e + (- 6A c - 6B b)d e + 27B c d e)x - 2A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 216 + +--S 217 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 218 + +)clear all + +--S 219 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 219 + +--S 220 of 1751 +r0:=1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^2)-B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 1 3 3 2 2 +--R - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 2 2 +--R + +--R 1 1 3 1 1 2 2 1 3 +--R ((- - A b - - B a)e + (- - A c - - B b)d e - B c d e)x - - A a e +--R 3 3 3 3 4 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - - B c d +--R 12 12 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 220 + +--S 221 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 12B c e x + ((- 6A c - 6B b)e - 18B c d e )x +--R + +--R 3 2 2 3 +--R ((- 4A b - 4B a)e + (- 4A c - 4B b)d e - 12B c d e)x - 3A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (- A c - B b)d e - 3B c d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 221 + +--S 222 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 223 + +)clear all + +--S 224 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 224 + +--S 225 of 1751 +r0:=1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^5)+1/4*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 3 3 2 +--R + +--R 1 1 3 1 1 2 1 2 1 3 +--R ((- - A b - - B a)e + (- - A c - - B b)d e - - B c d e)x - - A a e +--R 4 4 6 6 4 5 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - -- B c d +--R 20 20 30 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 225 + +--S 226 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 30B c e x + ((- 20A c - 20B b)e - 30B c d e )x +--R + +--R 3 2 2 3 +--R ((- 15A b - 15B a)e + (- 10A c - 10B b)d e - 15B c d e)x - 12A a e +--R + +--R 2 2 3 +--R (- 3A b - 3B a)d e + (- 2A c - 2B b)d e - 3B c d +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 226 + +--S 227 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 229 + +--S 230 of 1751 +r0:=1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^6)+1/5*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^5)+1/4*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 3 4 4 4 +--R + +--R 1 1 3 1 1 2 1 2 1 3 +--R ((- - A b - - B a)e + (- -- A c - -- B b)d e - -- B c d e)x - - A a e +--R 5 5 10 10 10 6 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - -- B c d +--R 30 30 60 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 230 + +--S 231 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 20B c e x + ((- 15A c - 15B b)e - 15B c d e )x +--R + +--R 3 2 2 3 +--R ((- 12A b - 12B a)e + (- 6A c - 6B b)d e - 6B c d e)x - 10A a e +--R + +--R 2 2 3 +--R (- 2A b - 2B a)d e + (- A c - B b)d e - B c d +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 4 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 231 + +--S 232 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 233 + +)clear all + +--S 234 of 1751 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1751 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))-_ + (c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^(2+m)/(e^6*(2+m))-(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^(4+m)/(e^6*(4+m))-c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((A c + 2B b c)e - 5B c d)m + ((16A c + 32B b c)e - 80B c d)m +--R + +--R 2 2 3 +--R ((95A c + 190B b c)e - 475B c d)m +--R + +--R 2 2 2 +--R ((260A c + 520B b c)e - 1300B c d)m +--R + +--R 2 2 2 2 +--R ((324A c + 648B b c)e - 1620B c d)m + (144A c + 288B b c)e - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R (((2A b + 2B a)c + B b )e + (- 4A c - 8B b c)d e + 10B c d )m +--R + +--R 2 2 2 +--R ((34A b + 34B a)c + 17B b )e + (- 68A c - 136B b c)d e +--R + +--R 2 2 +--R 170B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 +--R ((214A b + 214B a)c + 107B b )e + (- 428A c - 856B b c)d e +--R + +--R 2 2 +--R 1070B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 +--R ((614A b + 614B a)c + 307B b )e + (- 1228A c - 2456B b c)d e +--R + +--R 2 2 +--R 3070B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 +--R ((792A b + 792B a)c + 396B b )e + (- 1584A c - 3168B b c)d e +--R + +--R 2 2 +--R 3960B c d +--R * +--R m +--R + +--R 2 2 2 +--R ((360A b + 360B a)c + 180B b )e + (- 720A c - 1440B b c)d e +--R + +--R 2 2 +--R 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 +--R (2A a c + A b + 2B a b)e + ((- 6A b - 6B a)c - 3B b )d e +--R + +--R 2 2 2 3 +--R (6A c + 12B b c)d e - 10B c d +--R * +--R 5 +--R m +--R + +--R 2 3 +--R (36A a c + 18A b + 36B a b)e +--R + +--R 2 2 2 2 +--R ((- 108A b - 108B a)c - 54B b )d e + (108A c + 216B b c)d e +--R + +--R 2 3 +--R - 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 +--R (242A a c + 121A b + 242B a b)e +--R + +--R 2 2 2 2 +--R ((- 726A b - 726B a)c - 363B b )d e + (726A c + 1452B b c)d e +--R + +--R 2 3 +--R - 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 +--R (744A a c + 372A b + 744B a b)e +--R + +--R 2 2 +--R ((- 2232A b - 2232B a)c - 1116B b )d e +--R + +--R 2 2 2 3 +--R (2232A c + 4464B b c)d e - 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 +--R (1016A a c + 508A b + 1016B a b)e +--R + +--R 2 2 +--R ((- 3048A b - 3048B a)c - 1524B b )d e +--R + +--R 2 2 2 3 +--R (3048A c + 6096B b c)d e - 5080B c d +--R * +--R m +--R + +--R 2 3 +--R (480A a c + 240A b + 480B a b)e +--R + +--R 2 2 2 2 +--R ((- 1440A b - 1440B a)c - 720B b )d e + (1440A c + 2880B b c)d e +--R + +--R 2 3 +--R - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 2 3 +--R (2A a b + B a )e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 2 2 2 3 2 4 +--R ((6A b + 6B a)c + 3B b )d e + (- 4A c - 8B b c)d e + 5B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 +--R (38A a b + 19B a )e + (- 76A a c - 38A b - 76B a b)d e +--R + +--R 2 2 2 2 3 +--R ((114A b + 114B a)c + 57B b )d e + (- 76A c - 152B b c)d e +--R + +--R 2 4 +--R 95B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 +--R (274A a b + 137B a )e + (- 548A a c - 274A b - 548B a b)d e +--R + +--R 2 2 2 2 3 +--R ((822A b + 822B a)c + 411B b )d e + (- 548A c - 1096B b c)d e +--R + +--R 2 4 +--R 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 +--R (922A a b + 461B a )e + (- 1844A a c - 922A b - 1844B a b)d e +--R + +--R 2 2 2 +--R ((2766A b + 2766B a)c + 1383B b )d e +--R + +--R 2 3 2 4 +--R (- 1844A c - 3688B b c)d e + 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 +--R (1404A a b + 702B a )e +--R + +--R 2 3 +--R (- 2808A a c - 1404A b - 2808B a b)d e +--R + +--R 2 2 2 +--R ((4212A b + 4212B a)c + 2106B b )d e +--R + +--R 2 3 2 4 +--R (- 2808A c - 5616B b c)d e + 3510B c d +--R * +--R m +--R + +--R 2 4 2 3 +--R (720A a b + 360B a )e + (- 1440A a c - 720A b - 1440B a b)d e +--R + +--R 2 2 2 2 3 +--R ((2160A b + 2160B a)c + 1080B b )d e + (- 1440A c - 2880B b c)d e +--R + +--R 2 4 +--R 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (- 2A a b - B a )d e + (2A a c + A b + 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 2A b - 2B a)c - B b )d e + (A c + 2B b c)d e - B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 +--R 20A a e + (- 40A a b - 20B a )d e +--R + +--R 2 2 3 +--R (40A a c + 20A b + 40B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 40A b - 40B a)c - 20B b )d e + (20A c + 40B b c)d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 +--R 155A a e + (- 310A a b - 155B a )d e +--R + +--R 2 2 3 +--R (310A a c + 155A b + 310B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 310A b - 310B a)c - 155B b )d e + (155A c + 310B b c)d e +--R + +--R 2 5 +--R - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 +--R 580A a e + (- 1160A a b - 580B a )d e +--R + +--R 2 2 3 +--R (1160A a c + 580A b + 1160B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 1160A b - 1160B a)c - 580B b )d e + (580A c + 1160B b c)d e +--R + +--R 2 5 +--R - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 +--R 1044A a e + (- 2088A a b - 1044B a )d e +--R + +--R 2 2 3 +--R (2088A a c + 1044A b + 2088B a b)d e +--R + +--R 2 3 2 +--R ((- 2088A b - 2088B a)c - 1044B b )d e +--R + +--R 2 4 2 5 +--R (1044A c + 2088B b c)d e - 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 +--R 720A a e + (- 1440A a b - 720B a )d e +--R + +--R 2 2 3 +--R (1440A a c + 720A b + 1440B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 1440A b - 1440B a)c - 720B b )d e + (720A c + 1440B b c)d e +--R + +--R 2 5 +--R - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 235 + +--S 236 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 +--R ((A c + 2B b c)e + B c d e )m +--R + +--R 2 6 2 5 4 +--R ((16A c + 32B b c)e + 10B c d e )m +--R + +--R 2 6 2 5 3 +--R ((95A c + 190B b c)e + 35B c d e )m +--R + +--R 2 6 2 5 2 +--R ((260A c + 520B b c)e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R ((324A c + 648B b c)e + 24B c d e )m + (144A c + 288B b c)e +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 5 +--R (((2A b + 2B a)c + B b )e + (A c + 2B b c)d e )m +--R + +--R 2 6 2 5 +--R ((34A b + 34B a)c + 17B b )e + (12A c + 24B b c)d e +--R + +--R 2 2 4 +--R - 5B c d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R ((214A b + 214B a)c + 107B b )e + (47A c + 94B b c)d e +--R + +--R 2 2 4 +--R - 30B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R ((614A b + 614B a)c + 307B b )e + (72A c + 144B b c)d e +--R + +--R 2 2 4 +--R - 55B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R ((792A b + 792B a)c + 396B b )e + (36A c + 72B b c)d e +--R + +--R 2 2 4 +--R - 30B c d e +--R * +--R m +--R + +--R 2 6 +--R ((360A b + 360B a)c + 180B b )e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A a c + A b + 2B a b)e + ((2A b + 2B a)c + B b )d e )m +--R + +--R 2 6 +--R (36A a c + 18A b + 36B a b)e +--R + +--R 2 5 2 2 4 +--R ((28A b + 28B a)c + 14B b )d e + (- 4A c - 8B b c)d e +--R * +--R 4 +--R m +--R + +--R 2 6 +--R (242A a c + 121A b + 242B a b)e +--R + +--R 2 5 2 2 4 +--R ((130A b + 130B a)c + 65B b )d e + (- 36A c - 72B b c)d e +--R + +--R 2 3 3 +--R 20B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 +--R (744A a c + 372A b + 744B a b)e +--R + +--R 2 5 2 2 4 +--R ((224A b + 224B a)c + 112B b )d e + (- 80A c - 160B b c)d e +--R + +--R 2 3 3 +--R 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 +--R (1016A a c + 508A b + 1016B a b)e +--R + +--R 2 5 2 2 4 +--R ((120A b + 120B a)c + 60B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 3 3 +--R 40B c d e +--R * +--R m +--R + +--R 2 6 +--R (480A a c + 240A b + 480B a b)e +--R * +--R 3 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A a b + B a )e + (2A a c + A b + 2B a b)d e )m +--R + +--R 2 6 2 5 +--R (38A a b + 19B a )e + (32A a c + 16A b + 32B a b)d e +--R + +--R 2 2 4 +--R ((- 6A b - 6B a)c - 3B b )d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R (274A a b + 137B a )e + (178A a c + 89A b + 178B a b)d e +--R + +--R 2 2 4 2 3 3 +--R ((- 72A b - 72B a)c - 36B b )d e + (12A c + 24B b c)d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R (922A a b + 461B a )e + (388A a c + 194A b + 388B a b)d e +--R + +--R 2 2 4 2 3 3 +--R ((- 246A b - 246B a)c - 123B b )d e + (84A c + 168B b c)d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R (1404A a b + 702B a )e + (240A a c + 120A b + 240B a b)d e +--R + +--R 2 2 4 2 3 3 +--R ((- 180A b - 180B a)c - 90B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R m +--R + +--R 2 6 +--R (720A a b + 360B a )e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 5 +--R (A a e + (2A a b + B a )d e )m +--R + +--R 2 6 2 5 +--R 20A a e + (36A a b + 18B a )d e +--R + +--R 2 2 4 +--R (- 4A a c - 2A b - 4B a b)d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R 155A a e + (238A a b + 119B a )d e +--R + +--R 2 2 4 +--R (- 60A a c - 30A b - 60B a b)d e +--R + +--R 2 3 3 +--R ((12A b + 12B a)c + 6B b )d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R 580A a e + (684A a b + 342B a )d e +--R + +--R 2 2 4 +--R (- 296A a c - 148A b - 296B a b)d e +--R + +--R 2 3 3 2 4 2 +--R ((132A b + 132B a)c + 66B b )d e + (- 24A c - 48B b c)d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R 1044A a e + (720A a b + 360B a )d e +--R + +--R 2 2 4 +--R (- 480A a c - 240A b - 480B a b)d e +--R + +--R 2 3 3 2 4 2 +--R ((360A b + 360B a)c + 180B b )d e + (- 144A c - 288B b c)d e +--R + +--R 2 5 +--R 120B c d e +--R * +--R m +--R + +--R 2 6 +--R 720A a e +--R * +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A a d e m + (20A a d e + (- 2A a b - B a )d e )m +--R + +--R 2 5 2 2 4 +--R 155A a d e + (- 36A a b - 18B a )d e +--R + +--R 2 3 3 +--R (4A a c + 2A b + 4B a b)d e +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 +--R 580A a d e + (- 238A a b - 119B a )d e +--R + +--R 2 3 3 2 4 2 +--R (60A a c + 30A b + 60B a b)d e + ((- 12A b - 12B a)c - 6B b )d e +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 1044A a d e + (- 684A a b - 342B a )d e +--R + +--R 2 3 3 +--R (296A a c + 148A b + 296B a b)d e +--R + +--R 2 4 2 2 5 +--R ((- 132A b - 132B a)c - 66B b )d e + (24A c + 48B b c)d e +--R * +--R m +--R + +--R 2 5 2 2 4 +--R 720A a d e + (- 720A a b - 360B a )d e +--R + +--R 2 3 3 +--R (480A a c + 240A b + 480B a b)d e +--R + +--R 2 4 2 2 5 +--R ((- 360A b - 360B a)c - 180B b )d e + (144A c + 288B b c)d e +--R + +--R 2 6 +--R - 120B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Union(Expression(Integer),...) +--E 236 + +--S 237 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 +--R ((A c + 2B b c)e + B c d e )m +--R + +--R 2 6 2 5 4 +--R ((16A c + 32B b c)e + 10B c d e )m +--R + +--R 2 6 2 5 3 +--R ((95A c + 190B b c)e + 35B c d e )m +--R + +--R 2 6 2 5 2 +--R ((260A c + 520B b c)e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R ((324A c + 648B b c)e + 24B c d e )m + (144A c + 288B b c)e +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 5 +--R (((2A b + 2B a)c + B b )e + (A c + 2B b c)d e )m +--R + +--R 2 6 2 5 +--R ((34A b + 34B a)c + 17B b )e + (12A c + 24B b c)d e +--R + +--R 2 2 4 +--R - 5B c d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R ((214A b + 214B a)c + 107B b )e + (47A c + 94B b c)d e +--R + +--R 2 2 4 +--R - 30B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R ((614A b + 614B a)c + 307B b )e + (72A c + 144B b c)d e +--R + +--R 2 2 4 +--R - 55B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R ((792A b + 792B a)c + 396B b )e + (36A c + 72B b c)d e +--R + +--R 2 2 4 +--R - 30B c d e +--R * +--R m +--R + +--R 2 6 +--R ((360A b + 360B a)c + 180B b )e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A a c + A b + 2B a b)e + ((2A b + 2B a)c + B b )d e )m +--R + +--R 2 6 +--R (36A a c + 18A b + 36B a b)e +--R + +--R 2 5 2 2 4 +--R ((28A b + 28B a)c + 14B b )d e + (- 4A c - 8B b c)d e +--R * +--R 4 +--R m +--R + +--R 2 6 +--R (242A a c + 121A b + 242B a b)e +--R + +--R 2 5 2 2 4 +--R ((130A b + 130B a)c + 65B b )d e + (- 36A c - 72B b c)d e +--R + +--R 2 3 3 +--R 20B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 +--R (744A a c + 372A b + 744B a b)e +--R + +--R 2 5 +--R ((224A b + 224B a)c + 112B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 80A c - 160B b c)d e + 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 +--R (1016A a c + 508A b + 1016B a b)e +--R + +--R 2 5 2 2 4 +--R ((120A b + 120B a)c + 60B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 3 3 +--R 40B c d e +--R * +--R m +--R + +--R 2 6 +--R (480A a c + 240A b + 480B a b)e +--R * +--R 3 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A a b + B a )e + (2A a c + A b + 2B a b)d e )m +--R + +--R 2 6 2 5 +--R (38A a b + 19B a )e + (32A a c + 16A b + 32B a b)d e +--R + +--R 2 2 4 +--R ((- 6A b - 6B a)c - 3B b )d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R (274A a b + 137B a )e + (178A a c + 89A b + 178B a b)d e +--R + +--R 2 2 4 2 3 3 +--R ((- 72A b - 72B a)c - 36B b )d e + (12A c + 24B b c)d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R (922A a b + 461B a )e + (388A a c + 194A b + 388B a b)d e +--R + +--R 2 2 4 +--R ((- 246A b - 246B a)c - 123B b )d e +--R + +--R 2 3 3 2 4 2 +--R (84A c + 168B b c)d e - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R (1404A a b + 702B a )e + (240A a c + 120A b + 240B a b)d e +--R + +--R 2 2 4 2 3 3 +--R ((- 180A b - 180B a)c - 90B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R m +--R + +--R 2 6 +--R (720A a b + 360B a )e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 5 +--R (A a e + (2A a b + B a )d e )m +--R + +--R 2 6 2 5 +--R 20A a e + (36A a b + 18B a )d e +--R + +--R 2 2 4 +--R (- 4A a c - 2A b - 4B a b)d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R 155A a e + (238A a b + 119B a )d e +--R + +--R 2 2 4 +--R (- 60A a c - 30A b - 60B a b)d e +--R + +--R 2 3 3 +--R ((12A b + 12B a)c + 6B b )d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R 580A a e + (684A a b + 342B a )d e +--R + +--R 2 2 4 +--R (- 296A a c - 148A b - 296B a b)d e +--R + +--R 2 3 3 2 4 2 +--R ((132A b + 132B a)c + 66B b )d e + (- 24A c - 48B b c)d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R 1044A a e + (720A a b + 360B a )d e +--R + +--R 2 2 4 +--R (- 480A a c - 240A b - 480B a b)d e +--R + +--R 2 3 3 +--R ((360A b + 360B a)c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 144A c - 288B b c)d e + 120B c d e +--R * +--R m +--R + +--R 2 6 +--R 720A a e +--R * +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A a d e m + (20A a d e + (- 2A a b - B a )d e )m +--R + +--R 2 5 2 2 4 +--R 155A a d e + (- 36A a b - 18B a )d e +--R + +--R 2 3 3 +--R (4A a c + 2A b + 4B a b)d e +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 +--R 580A a d e + (- 238A a b - 119B a )d e +--R + +--R 2 3 3 2 4 2 +--R (60A a c + 30A b + 60B a b)d e + ((- 12A b - 12B a)c - 6B b )d e +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 1044A a d e + (- 684A a b - 342B a )d e +--R + +--R 2 3 3 +--R (296A a c + 148A b + 296B a b)d e +--R + +--R 2 4 2 2 5 +--R ((- 132A b - 132B a)c - 66B b )d e + (24A c + 48B b c)d e +--R * +--R m +--R + +--R 2 5 2 2 4 +--R 720A a d e + (- 720A a b - 360B a )d e +--R + +--R 2 3 3 +--R (480A a c + 240A b + 480B a b)d e +--R + +--R 2 4 2 2 5 +--R ((- 360A b - 360B a)c - 180B b )d e + (144A c + 288B b c)d e +--R + +--R 2 6 +--R - 120B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (- B c m - 15B c m - 85B c m - 225B c m - 274B c m - 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((- A c - 2B b c)e + 5B c d)m + ((- 16A c - 32B b c)e + 80B c d)m +--R + +--R 2 2 3 +--R ((- 95A c - 190B b c)e + 475B c d)m +--R + +--R 2 2 2 +--R ((- 260A c - 520B b c)e + 1300B c d)m +--R + +--R 2 2 2 +--R ((- 324A c - 648B b c)e + 1620B c d)m + (- 144A c - 288B b c)e +--R + +--R 2 +--R 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R (((- 2A b - 2B a)c - B b )e + (4A c + 8B b c)d e - 10B c d )m +--R + +--R 2 2 2 +--R ((- 34A b - 34B a)c - 17B b )e + (68A c + 136B b c)d e +--R + +--R 2 2 +--R - 170B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 +--R ((- 214A b - 214B a)c - 107B b )e + (428A c + 856B b c)d e +--R + +--R 2 2 +--R - 1070B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 +--R ((- 614A b - 614B a)c - 307B b )e + (1228A c + 2456B b c)d e +--R + +--R 2 2 +--R - 3070B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 +--R ((- 792A b - 792B a)c - 396B b )e + (1584A c + 3168B b c)d e +--R + +--R 2 2 +--R - 3960B c d +--R * +--R m +--R + +--R 2 2 2 +--R ((- 360A b - 360B a)c - 180B b )e + (720A c + 1440B b c)d e +--R + +--R 2 2 +--R - 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 +--R (- 2A a c - A b - 2B a b)e + ((6A b + 6B a)c + 3B b )d e +--R + +--R 2 2 2 3 +--R (- 6A c - 12B b c)d e + 10B c d +--R * +--R 5 +--R m +--R + +--R 2 3 +--R (- 36A a c - 18A b - 36B a b)e +--R + +--R 2 2 2 2 +--R ((108A b + 108B a)c + 54B b )d e + (- 108A c - 216B b c)d e +--R + +--R 2 3 +--R 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 +--R (- 242A a c - 121A b - 242B a b)e +--R + +--R 2 2 2 2 +--R ((726A b + 726B a)c + 363B b )d e + (- 726A c - 1452B b c)d e +--R + +--R 2 3 +--R 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 +--R (- 744A a c - 372A b - 744B a b)e +--R + +--R 2 2 +--R ((2232A b + 2232B a)c + 1116B b )d e +--R + +--R 2 2 2 3 +--R (- 2232A c - 4464B b c)d e + 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 +--R (- 1016A a c - 508A b - 1016B a b)e +--R + +--R 2 2 +--R ((3048A b + 3048B a)c + 1524B b )d e +--R + +--R 2 2 2 3 +--R (- 3048A c - 6096B b c)d e + 5080B c d +--R * +--R m +--R + +--R 2 3 +--R (- 480A a c - 240A b - 480B a b)e +--R + +--R 2 2 2 2 +--R ((1440A b + 1440B a)c + 720B b )d e + (- 1440A c - 2880B b c)d e +--R + +--R 2 3 +--R 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 2 3 +--R (- 2A a b - B a )e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 2 2 2 3 2 4 +--R ((- 6A b - 6B a)c - 3B b )d e + (4A c + 8B b c)d e - 5B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 +--R (- 38A a b - 19B a )e + (76A a c + 38A b + 76B a b)d e +--R + +--R 2 2 2 2 3 +--R ((- 114A b - 114B a)c - 57B b )d e + (76A c + 152B b c)d e +--R + +--R 2 4 +--R - 95B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 +--R (- 274A a b - 137B a )e + (548A a c + 274A b + 548B a b)d e +--R + +--R 2 2 2 2 3 +--R ((- 822A b - 822B a)c - 411B b )d e + (548A c + 1096B b c)d e +--R + +--R 2 4 +--R - 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 +--R (- 922A a b - 461B a )e + (1844A a c + 922A b + 1844B a b)d e +--R + +--R 2 2 2 +--R ((- 2766A b - 2766B a)c - 1383B b )d e +--R + +--R 2 3 2 4 +--R (1844A c + 3688B b c)d e - 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 +--R (- 1404A a b - 702B a )e +--R + +--R 2 3 +--R (2808A a c + 1404A b + 2808B a b)d e +--R + +--R 2 2 2 +--R ((- 4212A b - 4212B a)c - 2106B b )d e +--R + +--R 2 3 2 4 +--R (2808A c + 5616B b c)d e - 3510B c d +--R * +--R m +--R + +--R 2 4 2 3 +--R (- 720A a b - 360B a )e + (1440A a c + 720A b + 1440B a b)d e +--R + +--R 2 2 2 2 3 +--R ((- 2160A b - 2160B a)c - 1080B b )d e + (1440A c + 2880B b c)d e +--R + +--R 2 4 +--R - 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 +--R - A a e + (2A a b + B a )d e + (- 2A a c - A b - 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((2A b + 2B a)c + B b )d e + (- A c - 2B b c)d e + B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 +--R - 20A a e + (40A a b + 20B a )d e +--R + +--R 2 2 3 +--R (- 40A a c - 20A b - 40B a b)d e +--R + +--R 2 3 2 2 4 +--R ((40A b + 40B a)c + 20B b )d e + (- 20A c - 40B b c)d e +--R + +--R 2 5 +--R 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 +--R - 155A a e + (310A a b + 155B a )d e +--R + +--R 2 2 3 +--R (- 310A a c - 155A b - 310B a b)d e +--R + +--R 2 3 2 2 4 +--R ((310A b + 310B a)c + 155B b )d e + (- 155A c - 310B b c)d e +--R + +--R 2 5 +--R 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 +--R - 580A a e + (1160A a b + 580B a )d e +--R + +--R 2 2 3 +--R (- 1160A a c - 580A b - 1160B a b)d e +--R + +--R 2 3 2 2 4 +--R ((1160A b + 1160B a)c + 580B b )d e + (- 580A c - 1160B b c)d e +--R + +--R 2 5 +--R 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 +--R - 1044A a e + (2088A a b + 1044B a )d e +--R + +--R 2 2 3 +--R (- 2088A a c - 1044A b - 2088B a b)d e +--R + +--R 2 3 2 +--R ((2088A b + 2088B a)c + 1044B b )d e +--R + +--R 2 4 2 5 +--R (- 1044A c - 2088B b c)d e + 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 +--R - 720A a e + (1440A a b + 720B a )d e +--R + +--R 2 2 3 +--R (- 1440A a c - 720A b - 1440B a b)d e +--R + +--R 2 3 2 2 4 +--R ((1440A b + 1440B a)c + 720B b )d e + (- 720A c - 1440B b c)d e +--R + +--R 2 5 +--R 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 238 + +)clear all + +--S 239 of 1751 +t0:=(A+B*x)*(d+e*x)^5*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 10 2 5 2 4 9 +--R B c e x + ((A c + 2B b c)e + 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 8 +--R (((2A b + 2B a)c + B b )e + (5A c + 10B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 +--R (2A a c + A b + 2B a b)e + ((10A b + 10B a)c + 5B b )d e +--R + +--R 2 2 3 2 3 2 +--R (10A c + 20B b c)d e + 10B c d e +--R * +--R 7 +--R x +--R + +--R 2 5 2 4 +--R (2A a b + B a )e + (10A a c + 5A b + 10B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((20A b + 20B a)c + 10B b )d e + (10A c + 20B b c)d e + 5B c d e +--R * +--R 6 +--R x +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (10A a b + 5B a )d e + (20A a c + 10A b + 20B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((20A b + 20B a)c + 10B b )d e + (5A c + 10B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 5A a d e + (20A a b + 10B a )d e + (20A a c + 10A b + 20B a b)d e +--R + +--R 2 4 2 5 +--R ((10A b + 10B a)c + 5B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 10A a d e + (20A a b + 10B a )d e + (10A a c + 5A b + 10B a b)d e +--R + +--R 2 5 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 239 + +--S 240 of 1751 +r0:=-1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^6/e^6-_ + 1/7*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-_ + e*(3*b*d-a*e)))*(d+e*x)^7/e^6-1/8*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^8/e^6-1/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^9/e^6-1/10*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^10/e^6+1/11*B*c^2*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 2 11 11 1 2 1 11 1 2 10 10 +--R -- B c e x + ((-- A c + - B b c)e + - B c d e )x +--R 11 10 5 2 +--R + +--R 2 2 1 2 11 5 2 10 10 +--R ((- A b + - B a)c + - B b )e + (- A c + -- B b c)d e +--R 9 9 9 9 9 +--R + +--R 10 2 2 9 +--R -- B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 1 1 2 1 11 5 5 5 2 10 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 4 8 4 4 4 8 +--R + +--R 5 2 5 2 9 5 2 3 8 +--R (- A c + - B b c)d e + - B c d e +--R 4 2 4 +--R * +--R 8 +--R x +--R + +--R 2 1 2 11 10 5 2 10 10 +--R (- A a b + - B a )e + (-- A a c + - A b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 20 20 10 2 2 9 10 2 20 3 8 +--R ((-- A b + -- B a)c + -- B b )d e + (-- A c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 5 2 4 7 +--R - B c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 1 2 11 5 5 2 10 +--R - A a e + (- A a b + - B a )d e +--R 6 3 6 +--R + +--R 10 5 2 10 2 9 +--R (-- A a c + - A b + -- B a b)d e +--R 3 3 3 +--R + +--R 10 10 5 2 3 8 5 2 5 4 7 1 2 5 6 +--R ((-- A b + -- B a)c + - B b )d e + (- A c + - B b c)d e + - B c d e +--R 3 3 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 2 10 2 2 9 2 3 8 +--R A a d e + (4A a b + 2B a )d e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 4 7 1 2 2 5 6 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 2 2 9 5 2 3 8 5 5 2 5 4 7 +--R - A a d e + (5A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 2 2 2 4 2 +--R + +--R 1 1 1 2 5 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 10 2 3 8 10 5 2 4 7 +--R -- A a d e + (-- A a b + - B a )d e +--R 3 3 3 +--R + +--R 2 1 2 2 5 6 +--R (- A a c + - A b + - B a b)d e +--R 3 3 3 +--R * +--R 3 +--R x +--R + +--R 5 2 4 7 1 2 5 6 2 2 5 6 1 2 6 5 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 1 1 2 7 4 1 1 2 1 8 3 +--R (- -- A a b - -- B a )d e + (-- A a c + --- A b + -- B a b)d e +--R 21 42 84 168 84 +--R + +--R 1 1 1 2 9 2 1 2 1 10 +--R ((- --- A b - --- B a)c - --- B b )d e + (---- A c + --- B b c)d e +--R 252 252 504 1260 630 +--R + +--R 1 2 11 +--R - ---- B c d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 240 + +--S 241 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 5 11 1 2 1 5 1 2 4 10 +--R -- B c e x + ((-- A c + - B b c)e + - B c d e )x +--R 11 10 5 2 +--R + +--R 2 2 1 2 5 5 2 10 4 10 2 2 3 9 +--R (((- A b + - B a)c + - B b )e + (- A c + -- B b c)d e + -- B c d e )x +--R 9 9 9 9 9 9 +--R + +--R 1 1 2 1 5 5 5 5 2 4 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 4 8 4 4 4 8 +--R + +--R 5 2 5 2 3 5 2 3 2 +--R (- A c + - B b c)d e + - B c d e +--R 4 2 4 +--R * +--R 8 +--R x +--R + +--R 2 1 2 5 10 5 2 10 4 +--R (- A a b + - B a )e + (-- A a c + - A b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 20 20 10 2 2 3 10 2 20 3 2 5 2 4 +--R ((-- A b + -- B a)c + -- B b )d e + (-- A c + -- B b c)d e + - B c d e +--R 7 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 5 5 5 2 4 10 5 2 10 2 3 +--R - A a e + (- A a b + - B a )d e + (-- A a c + - A b + -- B a b)d e +--R 6 3 6 3 3 3 +--R + +--R 10 10 5 2 3 2 5 2 5 4 1 2 5 +--R ((-- A b + -- B a)c + - B b )d e + (- A c + - B b c)d e + - B c d +--R 3 3 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R A a d e + (4A a b + 2B a )d e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 4 1 2 2 5 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 2 2 3 5 2 3 2 5 5 2 5 4 +--R - A a d e + (5A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 2 2 2 4 2 +--R + +--R 1 1 1 2 5 +--R ((- A b + - B a)c + - B b )d +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 10 2 3 2 10 5 2 4 2 1 2 2 5 3 +--R (-- A a d e + (-- A a b + - B a )d e + (- A a c + - A b + - B a b)d )x +--R 3 3 3 3 3 3 +--R + +--R 5 2 4 1 2 5 2 2 5 +--R (- A a d e + (A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 241 + +--S 242 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 6 5 1 1 2 7 4 +--R - - A a d e + (-- A a b + -- B a )d e +--R 6 21 42 +--R + +--R 1 1 2 1 8 3 +--R (- -- A a c - --- A b - -- B a b)d e +--R 84 168 84 +--R + +--R 1 1 1 2 9 2 1 2 1 10 +--R ((--- A b + --- B a)c + --- B b )d e + (- ---- A c - --- B b c)d e +--R 252 252 504 1260 630 +--R + +--R 1 2 11 +--R ---- B c d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 242 + +--S 243 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 243 + +)clear all + +--S 244 of 1751 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 +--R B c e x + ((A c + 2B b c)e + 4B c d e )x +--R + +--R 2 4 2 3 2 2 2 7 +--R (((2A b + 2B a)c + B b )e + (4A c + 8B b c)d e + 6B c d e )x +--R + +--R 2 4 2 3 +--R (2A a c + A b + 2B a b)e + ((8A b + 8B a)c + 4B b )d e +--R + +--R 2 2 2 2 3 +--R (6A c + 12B b c)d e + 4B c d e +--R * +--R 6 +--R x +--R + +--R 2 4 2 3 +--R (2A a b + B a )e + (8A a c + 4A b + 8B a b)d e +--R + +--R 2 2 2 2 3 2 4 +--R ((12A b + 12B a)c + 6B b )d e + (4A c + 8B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 3 2 2 2 +--R A a e + (8A a b + 4B a )d e + (12A a c + 6A b + 12B a b)d e +--R + +--R 2 3 2 4 +--R ((8A b + 8B a)c + 4B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 4A a d e + (12A a b + 6B a )d e + (8A a c + 4A b + 8B a b)d e +--R + +--R 2 4 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 244 + +--S 245 of 1751 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^5/e^6-_ + 1/6*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^7/e^6-_ + 1/8*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*_ + (d+e*x)^8/e^6-1/9*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^9/e^6+_ + 1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 2 10 4 2 9 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 1 2 10 1 2 9 3 2 2 8 8 +--R (((- A b + - B a)c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 4 8 2 4 +--R + +--R 2 1 2 2 10 8 8 4 2 9 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 7 7 7 7 7 7 +--R + +--R 6 2 12 2 8 4 2 3 7 +--R (- A c + -- B b c)d e + - B c d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 1 2 10 4 2 2 4 9 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 3 6 3 3 3 +--R + +--R 2 2 8 2 2 4 3 7 1 2 4 6 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d e + - B c d e +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 2 10 8 4 2 9 +--R - A a e + (- A a b + - B a )d e +--R 5 5 5 +--R + +--R 12 6 2 12 2 8 8 8 4 2 3 7 +--R (-- A a c + - A b + -- B a b)d e + ((- A b + - B a)c + - B b )d e +--R 5 5 5 5 5 5 +--R + +--R 1 2 2 4 6 +--R (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 2 9 3 2 2 8 2 3 7 +--R A a d e + (3A a b + - B a )d e + (2A a c + A b + 2B a b)d e +--R 2 +--R + +--R 1 1 1 2 4 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 2 8 8 4 2 3 7 2 1 2 2 4 6 3 +--R (2A a d e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 3 3 +--R + +--R 2 3 7 1 2 4 6 2 2 4 6 1 2 5 5 +--R (2A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 5 +--R + +--R 1 1 2 6 4 2 1 2 2 7 3 +--R (- -- A a b - -- B a )d e + (--- A a c + --- A b + --- B a b)d e +--R 15 30 105 105 105 +--R + +--R 1 1 1 2 8 2 1 2 1 9 +--R ((- --- A b - --- B a)c - --- B b )d e + (--- A c + --- B b c)d e +--R 140 140 280 630 315 +--R + +--R 1 2 10 +--R - ---- B c d +--R 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 245 + +--S 246 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 10 1 2 2 4 4 2 3 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 1 2 4 1 2 3 3 2 2 2 8 +--R (((- A b + - B a)c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 4 8 2 4 +--R + +--R 2 1 2 2 4 8 8 4 2 3 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 7 7 7 7 7 7 +--R + +--R 6 2 12 2 2 4 2 3 +--R (- A c + -- B b c)d e + - B c d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 1 2 4 4 2 2 4 3 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 3 6 3 3 3 +--R + +--R 2 2 2 2 2 4 3 1 2 4 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d e + - B c d +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 2 4 8 4 2 3 12 6 2 12 2 2 +--R - A a e + (- A a b + - B a )d e + (-- A a c + - A b + -- B a b)d e +--R 5 5 5 5 5 5 +--R + +--R 8 8 4 2 3 1 2 2 4 +--R ((- A b + - B a)c + - B b )d e + (- A c + - B b c)d +--R 5 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 2 2 2 3 +--R A a d e + (3A a b + - B a )d e + (2A a c + A b + 2B a b)d e +--R 2 +--R + +--R 1 1 1 2 4 +--R ((- A b + - B a)c + - B b )d +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 2 2 8 4 2 3 2 1 2 2 4 3 +--R (2A a d e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d )x +--R 3 3 3 3 3 +--R + +--R 2 3 1 2 4 2 2 4 +--R (2A a d e + (A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 246 + +--S 247 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 5 5 1 1 2 6 4 +--R - - A a d e + (-- A a b + -- B a )d e +--R 5 15 30 +--R + +--R 2 1 2 2 7 3 +--R (- --- A a c - --- A b - --- B a b)d e +--R 105 105 105 +--R + +--R 1 1 1 2 8 2 1 2 1 9 +--R ((--- A b + --- B a)c + --- B b )d e + (- --- A c - --- B b c)d e +--R 140 140 280 630 315 +--R + +--R 1 2 10 +--R ---- B c d +--R 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 247 + +--S 248 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 248 + +)clear all + +--S 249 of 1751 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R (((2A b + 2B a)c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 +--R (2A a c + A b + 2B a b)e + ((6A b + 6B a)c + 3B b )d e +--R + +--R 2 2 2 3 +--R (3A c + 6B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 3 2 2 +--R (2A a b + B a )e + (6A a c + 3A b + 6B a b)d e +--R + +--R 2 2 2 3 +--R ((6A b + 6B a)c + 3B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 +--R A a e + (6A a b + 3B a )d e + (6A a c + 3A b + 6B a b)d e +--R + +--R 2 3 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 249 + +--S 250 of 1751 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4/e^6-_ + 1/5*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^5/e^6-1/6*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^7/e^6-1/8*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^8/e^6+1/9*B*c^2*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 1 2 9 9 1 2 1 9 3 2 8 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 2 1 2 9 3 2 6 8 3 2 2 7 7 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d e )x +--R 7 7 7 7 7 7 +--R + +--R 1 1 2 1 9 1 2 8 +--R (- A a c + - A b + - B a b)e + ((A b + B a)c + - B b )d e +--R 3 6 3 2 +--R + +--R 1 2 2 7 1 2 3 6 +--R (- A c + B b c)d e + - B c d e +--R 2 6 +--R * +--R 6 +--R x +--R + +--R 2 1 2 9 6 3 2 6 8 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 6 6 3 2 2 7 1 2 2 3 6 +--R ((- A b + - B a)c + - B b )d e + (- A c + - B b c)d e +--R 5 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 2 9 3 3 2 8 3 3 2 3 2 7 +--R - A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 4 2 4 2 4 2 +--R + +--R 1 1 1 2 3 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 7 2 1 2 2 3 6 3 +--R (A a d e + (2A a b + B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 +--R + +--R 3 2 2 7 1 2 3 6 2 2 3 6 1 2 4 5 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 4 +--R + +--R 1 1 2 5 4 1 1 2 1 6 3 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A b + -- B a b)d e +--R 10 20 30 60 30 +--R + +--R 1 1 1 2 7 2 1 2 1 8 +--R ((- -- A b - -- B a)c - --- B b )d e + (--- A c + --- B b c)d e +--R 70 70 140 280 140 +--R + +--R 1 2 9 +--R - --- B c d +--R 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 250 + +--S 251 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 3 9 1 2 1 3 3 2 2 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 2 1 2 3 3 2 6 2 3 2 2 7 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d e)x +--R 7 7 7 7 7 7 +--R + +--R 1 1 2 1 3 1 2 2 +--R (- A a c + - A b + - B a b)e + ((A b + B a)c + - B b )d e +--R 3 6 3 2 +--R + +--R 1 2 2 1 2 3 +--R (- A c + B b c)d e + - B c d +--R 2 6 +--R * +--R 6 +--R x +--R + +--R 2 1 2 3 6 3 2 6 2 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 6 6 3 2 2 1 2 2 3 +--R ((- A b + - B a)c + - B b )d e + (- A c + - B b c)d +--R 5 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 2 3 3 3 2 2 3 3 2 3 2 +--R - A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 4 2 4 2 4 2 +--R + +--R 1 1 1 2 3 +--R ((- A b + - B a)c + - B b )d +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 2 2 2 2 1 2 2 3 3 +--R (A a d e + (2A a b + B a )d e + (- A a c + - A b + - B a b)d )x +--R 3 3 3 +--R + +--R 3 2 2 1 2 3 2 2 3 +--R (- A a d e + (A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 251 + +--S 252 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 4 5 1 1 2 5 4 +--R - - A a d e + (-- A a b + -- B a )d e +--R 4 10 20 +--R + +--R 1 1 2 1 6 3 +--R (- -- A a c - -- A b - -- B a b)d e +--R 30 60 30 +--R + +--R 1 1 1 2 7 2 1 2 1 8 +--R ((-- A b + -- B a)c + --- B b )d e + (- --- A c - --- B b c)d e +--R 70 70 140 280 140 +--R + +--R 1 2 9 +--R --- B c d +--R 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 252 + +--S 253 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 253 + +)clear all + +--S 254 of 1751 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R (((2A b + 2B a)c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 +--R (2A a c + A b + 2B a b)e + ((4A b + 4B a)c + 2B b )d e +--R + +--R 2 2 +--R (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 2 2 +--R (2A a b + B a )e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 2 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 254 + +--S 255 of 1751 +r0:=-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^3/e^6-1/4*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*(d+e*x)^4/e^6-_ + 1/5*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^5/e^6-_ + 1/6*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^7/e^6+_ + 1/8*B*c^2*(d+e*x)^8/e^6 +--R +--R +--R (2) +--R 1 2 8 8 1 2 2 8 2 2 7 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 1 1 2 8 1 2 2 7 1 2 2 6 6 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d e )x +--R 3 3 6 3 3 6 +--R + +--R 2 1 2 2 8 4 4 2 2 7 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 5 5 5 5 5 5 +--R + +--R 1 2 2 2 6 +--R (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 1 1 2 8 1 2 7 +--R (- A a b + - B a )e + (A a c + - A b + B a b)d e +--R 2 4 2 +--R + +--R 1 1 1 2 2 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 1 2 8 4 2 2 7 2 1 2 2 2 6 3 +--R (- A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 3 3 3 +--R + +--R 2 7 1 2 2 6 2 2 2 6 1 2 3 5 +--R (A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 3 +--R + +--R 1 1 2 4 4 1 1 2 1 5 3 +--R (- - A a b - -- B a )d e + (-- A a c + -- A b + -- B a b)d e +--R 6 12 15 30 15 +--R + +--R 1 1 1 2 6 2 1 2 2 7 +--R ((- -- A b - -- B a)c - -- B b )d e + (--- A c + --- B b c)d e +--R 30 30 60 105 105 +--R + +--R 1 2 8 +--R - --- B c d +--R 168 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 255 + +--S 256 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 8 1 2 2 2 2 2 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e)x +--R 8 7 7 7 +--R + +--R 1 1 1 2 2 1 2 2 1 2 2 6 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d )x +--R 3 3 6 3 3 6 +--R + +--R 2 1 2 2 2 4 4 2 2 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 5 5 5 5 5 5 +--R + +--R 1 2 2 2 +--R (- A c + - B b c)d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 1 1 2 2 1 2 +--R (- A a b + - B a )e + (A a c + - A b + B a b)d e +--R 2 4 2 +--R + +--R 1 1 1 2 2 +--R ((- A b + - B a)c + - B b )d +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 1 2 2 4 2 2 2 1 2 2 2 3 +--R (- A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d )x +--R 3 3 3 3 3 3 +--R + +--R 2 1 2 2 2 2 2 +--R (A a d e + (A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 256 + +--S 257 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 3 5 1 1 2 4 4 +--R - - A a d e + (- A a b + -- B a )d e +--R 3 6 12 +--R + +--R 1 1 2 1 5 3 +--R (- -- A a c - -- A b - -- B a b)d e +--R 15 30 15 +--R + +--R 1 1 1 2 6 2 1 2 2 7 +--R ((-- A b + -- B a)c + -- B b )d e + (- --- A c - --- B b c)d e +--R 30 30 60 105 105 +--R + +--R 1 2 8 +--R --- B c d +--R 168 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 257 + +--S 258 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 258 + +)clear all + +--S 259 of 1751 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 +--R (((2A b + 2B a)c + B b )e + (A c + 2B b c)d)x +--R + +--R 2 2 3 +--R ((2A a c + A b + 2B a b)e + ((2A b + 2B a)c + B b )d)x +--R + +--R 2 2 2 +--R ((2A a b + B a )e + (2A a c + A b + 2B a b)d)x +--R + +--R 2 2 2 +--R (A a e + (2A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 259 + +--S 260 of 1751 +r0:=a^2*A*d*x+1/2*a*(2*A*b*d+a*B*d+a*A*e)*x^2+1/3*(a*B*(2*b*d+a*e)+_ + A*(b^2*d+2*a*c*d+2*a*b*e))*x^3+1/4*(b^2*(B*d+A*e)+2*a*c*(B*d+A*e)+_ + 2*b*(A*c*d+a*B*e))*x^4+1/5*(b^2*B*e+2*b*c*(B*d+A*e)+_ + c*(A*c*d+2*a*B*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 2 1 2 1 2 2 5 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 5 +--R + +--R 1 1 2 1 1 1 1 2 4 +--R ((- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d)x +--R 2 4 2 2 2 4 +--R + +--R 2 1 2 2 1 2 2 3 +--R ((- A a b + - B a )e + (- A a c + - A b + - B a b)d)x +--R 3 3 3 3 3 +--R + +--R 1 2 1 2 2 2 +--R (- A a e + (A a b + - B a )d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 260 + +--S 261 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 2 1 2 1 2 2 5 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 5 +--R + +--R 1 1 2 1 1 1 1 2 4 +--R ((- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d)x +--R 2 4 2 2 2 4 +--R + +--R 2 1 2 2 1 2 2 3 +--R ((- A a b + - B a )e + (- A a c + - A b + - B a b)d)x +--R 3 3 3 3 3 +--R + +--R 1 2 1 2 2 2 +--R (- A a e + (A a b + - B a )d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 261 + +--S 262 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 262 + +--S 263 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 263 + +)clear all + +--S 264 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 264 + +--S 265 of 1751 +r0:=a^2*A*x+1/2*a*(2*A*b+a*B)*x^2+1/3*(2*a*b*B+A*(b^2+2*a*c))*x^3+_ + 1/4*(b^2*B+2*A*b*c+2*a*B*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 1 1 2 4 +--R - B c x + (- A c + - B b c)x + ((- A b + - B a)c + - B b )x +--R 6 5 5 2 2 4 +--R + +--R 2 1 2 2 3 1 2 2 2 +--R (- A a c + - A b + - B a b)x + (A a b + - B a )x + A a x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 265 + +--S 266 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 6 1 2 2 5 1 1 1 2 4 +--R - B c x + (- A c + - B b c)x + ((- A b + - B a)c + - B b )x +--R 6 5 5 2 2 4 +--R + +--R 2 1 2 2 3 1 2 2 2 +--R (- A a c + - A b + - B a b)x + (A a b + - B a )x + A a x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 266 + +--S 267 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 267 + +--S 268 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 268 + +)clear all + +--S 269 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 269 + +--S 270 of 1751 +r0:=-(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + x/e^5-1/2*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^2/e^6-1/3*(2*A*c*e*_ + (2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*(d+e*x)^3/e^6-_ + 1/4*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^4/e^6+1/5*B*c^2*(d+e*x)^5/e^6-_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R 60A a e + (- 120A a b - 60B a )d e +--R + +--R 2 2 3 +--R (120A a c + 60A b + 120B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 120A b - 120B a)c - 60B b )d e + (60A c + 120B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((40A b + 40B a)c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 +--R (60A a c + 30A b + 60B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (30A c + 60B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (120A a b + 60B a )e + (- 120A a c - 60A b - 120B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((120A b + 120B a)c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 +--R (60A a c + 30A b + 60B a b)d e + ((- 140A b - 140B a)c - 70B b )d e +--R + +--R 2 4 2 5 +--R (115A c + 230B b c)d e - 163B c d +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 270 + +--S 271 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 +--R 60A a e + (- 120A a b - 60B a )d e +--R + +--R 2 2 3 +--R (120A a c + 60A b + 120B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 120A b - 120B a)c - 60B b )d e + (60A c + 120B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((40A b + 40B a)c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 +--R (60A a c + 30A b + 60B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (30A c + 60B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (120A a b + 60B a )e + (- 120A a c - 60A b - 120B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((120A b + 120B a)c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 271 + +--S 272 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 3 2 3 2 +--R (- 60A a c - 30A b - 60B a b)d e + ((140A b + 140B a)c + 70B b )d e +--R + +--R 2 4 2 5 +--R (- 115A c - 230B b c)d e + 163B c d +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 274 + +--S 275 of 1751 +r0:=-(2*B*(2*c*d-b*e)*(c*d^2-e*(b*d-a*e))-A*e*(3*c^2*d^2+b^2*e^2-_ + 2*c*e*(2*b*d-a*e)))*x/e^5-1/2*(2*A*c*e*(c*d-b*e)-B*(3*c^2*d^2+b^2*e^2-_ + 2*c*e*(2*b*d-a*e)))*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x))-_ + (c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R (24A a b + 12B a )e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 4 2 2 3 +--R (24A a b + 12B a )d e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 +--R (24A a c + 12A b + 24B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (24A c + 48B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R (24A a c + 12A b + 24B a b)d e + ((- 48A b - 48B a)c - 24B b )d e +--R + +--R 2 3 2 2 4 +--R (36A c + 72B b c)d e - 48B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (24A a b + 12B a )d e + (- 24A a c - 12A b - 24B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((24A b + 24B a)c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 +--R (24A a b + 12B a )e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 4 2 2 3 +--R (24A a b + 12B a )d e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 +--R (24A a c + 12A b + 24B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (24A c + 48B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R (24A a c + 12A b + 24B a b)d e + ((- 48A b - 48B a)c - 24B b )d e +--R + +--R 2 3 2 2 4 +--R (36A c + 72B b c)d e - 48B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (24A a b + 12B a )d e + (- 24A a c - 12A b - 24B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((24A b + 24B a)c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 276 + +--S 277 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 278 + +)clear all + +--S 279 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 279 + +--S 280 of 1751 +r0:=-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*x/e^5-_ + 1/2*c*(3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^2)+(c*d^2-b*d*e+a*e^2)*(2*A*e*_ + (2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x))-(B*(10*c^2*d^3+_ + b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-_ + 2*c*e*(3*b*d-a*e)))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R (12A a c + 6A b + 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (36A c + 72B b c)d e - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 +--R (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 72A b - 72B a)c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 +--R (12A a c + 6A b + 12B a b)d e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 4 2 5 +--R (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 +--R ((24A b + 24B a)c + 12B b )d e + (- 33A c - 66B b c)d e +--R + +--R 2 3 2 +--R 63B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 12A a b - 6B a )e + (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((- 24A b - 24B a)c - 12B b )d e + (6A c + 12B b c)d e + 6B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 6A a b - 3B a )d e + (18A a c + 9A b + 18B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 30A b - 30B a)c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 280 + +--S 281 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 +--R (12A a c + 6A b + 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (36A c + 72B b c)d e - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 +--R (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 72A b - 72B a)c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 +--R (12A a c + 6A b + 12B a b)d e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 4 2 5 +--R (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 +--R ((24A b + 24B a)c + 12B b )d e + (- 33A c - 66B b c)d e +--R + +--R 2 3 2 +--R 63B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 12A a b - 6B a )e + (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((- 24A b - 24B a)c - 12B b )d e + (6A c + 12B b c)d e + 6B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 6A a b - 3B a )d e + (18A a c + 9A b + 18B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 30A b - 30B a)c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 281 + +--S 282 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 283 + +)clear all + +--S 284 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 284 + +--S 285 of 1751 +r0:=-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^3)+1/2*(c*d^2-b*d*e+a*e^2)*(2*A*e*_ + (2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^2)+(B*(10*c^2*d^3+_ + b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-_ + 2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(4*b*d-a*e)))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R ((12A b + 12B a)c + 6B b )e + (- 24A c - 48B b c)d e +--R + +--R 2 2 3 +--R 60B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 2 3 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 3 2 +--R 180B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 4 +--R 180B c d e +--R * +--R x +--R + +--R 2 3 2 2 4 2 5 +--R ((12A b + 12B a)c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((36A b + 36B a)c + 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 18A c - 36B b c)d e - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 6A a b - 3B a )e + (- 12A a c - 6A b - 12B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((54A b + 54B a)c + 27B b )d e + (- 54A c - 108B b c)d e + 81B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 2A a e + (- 2A a b - B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((22A b + 22B a)c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 285 + +--S 286 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 +--R ((12A b + 12B a)c + 6B b )e + (- 24A c - 48B b c)d e +--R + +--R 2 2 3 +--R 60B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 2 3 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 3 2 +--R 180B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 4 +--R 180B c d e +--R * +--R x +--R + +--R 2 3 2 2 4 2 5 +--R ((12A b + 12B a)c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((36A b + 36B a)c + 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 18A c - 36B b c)d e - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 6A a b - 3B a )e + (- 12A a c - 6A b - 12B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((54A b + 54B a)c + 27B b )d e + (- 54A c - 108B b c)d e + 81B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 2A a e + (- 2A a b - B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((22A b + 22B a)c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 286 + +--S 287 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 289 + +--S 290 of 1751 +r0:=B*c^2*x/e^5+1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^4)+_ + 1/3*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/_ + (e^6*(d+e*x)^3)+1/2*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-_ + a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^2)+_ + (2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*_ + (d+e*x))-c*(5*B*c*d-2*b*B*e-A*c*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 4 +--R ((12A c + 24B b c)e - 60B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((48A c + 96B b c)d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 +--R ((72A c + 144B b c)d e - 360B c d e )x +--R + +--R 2 3 2 2 4 2 4 +--R ((48A c + 96B b c)d e - 240B c d e)x + (12A c + 24B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 +--R 12B c e x + 48B c d e x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((- 24A b - 24B a)c - 12B b )e + (48A c + 96B b c)d e - 48B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (108A c + 216B b c)d e - 252B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 8A a b - 4B a )e + (- 8A a c - 4A b - 8B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 24A b - 24B a)c - 12B b )d e + (88A c + 176B b c)d e +--R + +--R 2 4 +--R - 248B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 2A a b - B a )d e + (- 2A a c - A b - 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (25A c + 50B b c)d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 4 +--R ((12A c + 24B b c)e - 60B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((48A c + 96B b c)d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 +--R ((72A c + 144B b c)d e - 360B c d e )x +--R + +--R 2 3 2 2 4 2 4 +--R ((48A c + 96B b c)d e - 240B c d e)x + (12A c + 24B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 +--R 12B c e x + 48B c d e x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((- 24A b - 24B a)c - 12B b )e + (48A c + 96B b c)d e - 48B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (108A c + 216B b c)d e - 252B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 8A a b - 4B a )e + (- 8A a c - 4A b - 8B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 24A b - 24B a)c - 12B b )d e + (88A c + 176B b c)d e +--R + +--R 2 4 +--R - 248B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 2A a b - B a )d e + (- 2A a c - A b - 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (25A c + 50B b c)d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 291 + +--S 292 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 293 + +)clear all + +--S 294 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^6 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 294 + +--S 295 of 1751 +r0:=1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^5)+1/4*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^4)+_ + 1/3*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^3)+_ + 1/2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^2)+c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x))+B*c^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R ((- 60A c - 120B b c)e + 300B c d e )x +--R + +--R 2 5 2 4 +--R ((- 60A b - 60B a)c - 30B b )e + (- 120A c - 240B b c)d e +--R + +--R 2 2 3 +--R 900B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 4 +--R (- 40A a c - 20A b - 40B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 120A c - 240B b c)d e + 1100B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 30A a b - 15B a )e + (- 20A a c - 10A b - 20B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 30A b - 30B a)c - 15B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 625B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (- 6A a b - 3B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (- 12A c - 24B b c)d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R ((- 60A c - 120B b c)e + 300B c d e )x +--R + +--R 2 5 2 4 +--R ((- 60A b - 60B a)c - 30B b )e + (- 120A c - 240B b c)d e +--R + +--R 2 2 3 +--R 900B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 4 +--R (- 40A a c - 20A b - 40B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 120A c - 240B b c)d e + 1100B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 30A a b - 15B a )e + (- 20A a c - 10A b - 20B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 30A b - 30B a)c - 15B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 625B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (- 6A a b - 3B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (- 12A c - 24B b c)d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 296 + +--S 297 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 298 + +)clear all + +--S 299 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 299 + +--S 300 of 1751 +r0:=1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^6)+1/5*(c*d^2-_ + b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+_ + e*x)^5)+1/4*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^4)+_ + 1/3*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^3)+1/2*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^2)-_ + B*c^2/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 5 5 1 2 5 5 2 4 4 +--R - B c e x + ((- - A c - B b c)e - - B c d e )x +--R 2 2 +--R + +--R 2 2 1 2 5 2 2 4 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 3 3 3 3 3 +--R + +--R 10 2 2 3 +--R - -- B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 1 1 2 1 5 1 1 1 2 4 +--R (- - A a c - - A b - - B a b)e + ((- - A b - - B a)c - - B b )d e +--R 2 4 2 2 2 4 +--R + +--R 1 2 2 3 5 2 3 2 +--R (- - A c - B b c)d e - - B c d e +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 2 1 2 5 1 1 2 1 4 +--R (- - A a b - - B a )e + (- - A a c - -- A b - - B a b)d e +--R 5 5 5 10 5 +--R + +--R 1 1 1 2 2 3 1 2 2 3 2 2 4 +--R ((- - A b - - B a)c - -- B b )d e + (- - A c - - B b c)d e - B c d e +--R 5 5 10 5 5 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 6 15 30 +--R + +--R 1 1 2 1 2 3 +--R (- -- A a c - -- A b - -- B a b)d e +--R 30 60 30 +--R + +--R 1 1 1 2 3 2 1 2 1 4 1 2 5 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e - - B c d +--R 30 30 60 30 15 6 +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 300 + +--S 301 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 60B c e x + ((- 30A c - 60B b c)e - 150B c d e )x +--R + +--R 2 5 2 4 +--R ((- 40A b - 40B a)c - 20B b )e + (- 40A c - 80B b c)d e +--R + +--R 2 2 3 +--R - 200B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 4 +--R (- 30A a c - 15A b - 30B a b)e + ((- 30A b - 30B a)c - 15B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 30A c - 60B b c)d e - 150B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 24A a b - 12B a )e + (- 12A a c - 6A b - 12B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((- 12A b - 12B a)c - 6B b )d e + (- 12A c - 24B b c)d e - 60B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 10A a e + (- 4A a b - 2B a )d e + (- 2A a c - A b - 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 2A b - 2B a)c - B b )d e + (- 2A c - 4B b c)d e - 10B c d +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 6 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 301 + +--S 302 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 304 + +--S 305 of 1751 +r0:=1/7*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^7)+1/6*(c*d^2-_ + b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*_ + (d+e*x)^6)+1/5*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^5)+_ + 1/4*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^4)+1/3*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^3)-_ + 1/2*B*c^2/(e^6*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 5 5 1 2 2 5 5 2 4 4 +--R - - B c e x + ((- - A c - - B b c)e - - B c d e )x +--R 2 3 3 6 +--R + +--R 1 1 1 2 5 1 2 2 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 2 2 4 3 3 +--R + +--R 5 2 2 3 +--R - - B c d e +--R 6 +--R * +--R 3 +--R x +--R + +--R 2 1 2 2 5 +--R (- - A a c - - A b - - B a b)e +--R 5 5 5 +--R + +--R 3 3 3 2 4 1 2 2 2 3 +--R ((- -- A b - -- B a)c - -- B b )d e + (- - A c - - B b c)d e +--R 10 10 20 5 5 +--R + +--R 1 2 3 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 1 1 2 5 2 1 2 2 4 +--R (- - A a b - - B a )e + (- -- A a c - -- A b - -- B a b)d e +--R 3 6 15 15 15 +--R + +--R 1 1 1 2 2 3 1 2 2 3 2 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e +--R 10 10 20 15 15 +--R + +--R 1 2 4 +--R - - B c d e +--R 6 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 7 21 42 +--R + +--R 2 1 2 2 2 3 +--R (- --- A a c - --- A b - --- B a b)d e +--R 105 105 105 +--R + +--R 1 1 1 2 3 2 1 2 2 4 +--R ((- -- A b - -- B a)c - --- B b )d e + (- --- A c - --- B b c)d e +--R 70 70 140 105 105 +--R + +--R 1 2 5 +--R - -- B c d +--R 42 +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 6 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 305 + +--S 306 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 210B c e x + ((- 140A c - 280B b c)e - 350B c d e )x +--R + +--R 2 5 2 4 +--R ((- 210A b - 210B a)c - 105B b )e + (- 140A c - 280B b c)d e +--R + +--R 2 2 3 +--R - 350B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 +--R (- 168A a c - 84A b - 168B a b)e +--R + +--R 2 4 2 2 3 +--R ((- 126A b - 126B a)c - 63B b )d e + (- 84A c - 168B b c)d e +--R + +--R 2 3 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 140A a b - 70B a )e + (- 56A a c - 28A b - 56B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 42A b - 42B a)c - 21B b )d e + (- 28A c - 56B b c)d e +--R + +--R 2 4 +--R - 70B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 60A a e + (- 20A a b - 10B a )d e + (- 8A a c - 4A b - 8B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (- 4A c - 8B b c)d e - 10B c d +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 8 2 6 7 7 6 +--R 8820d e x + 2940d e x + 420d e +--R Type: Union(Expression(Integer),...) +--E 306 + +--S 307 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 308 + +)clear all + +--S 309 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 309 + +--S 310 of 1751 +r0:=1/8*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^8)+1/7*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^7)+_ + 1/6*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*_ + d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^6)+1/5*(2*A*c*e*(2*c*d-_ + b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*(d+e*x)^5)+_ + 1/4*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^4)-1/3*B*c^2/(e^6*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 5 5 1 2 1 5 5 2 4 4 +--R - - B c e x + ((- - A c - - B b c)e - -- B c d e )x +--R 3 4 2 12 +--R + +--R 2 2 1 2 5 1 2 2 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 5 5 5 5 5 +--R + +--R 1 2 2 3 +--R - - B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 1 1 2 1 5 1 1 1 2 4 +--R (- - A a c - - A b - - B a b)e + ((- - A b - - B a)c - -- B b )d e +--R 3 6 3 5 5 10 +--R + +--R 1 2 1 2 3 1 2 3 2 +--R (- -- A c - - B b c)d e - - B c d e +--R 10 5 6 +--R * +--R 2 +--R x +--R + +--R 2 1 2 5 2 1 2 2 4 +--R (- - A a b - - B a )e + (- -- A a c - -- A b - -- B a b)d e +--R 7 7 21 21 21 +--R + +--R 2 2 1 2 2 3 1 2 2 3 2 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e +--R 35 35 35 35 35 +--R + +--R 1 2 4 +--R - -- B c d e +--R 21 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 8 28 56 +--R + +--R 1 1 2 1 2 3 +--R (- -- A a c - --- A b - -- B a b)d e +--R 84 168 84 +--R + +--R 1 1 1 2 3 2 1 2 1 4 +--R ((- --- A b - --- B a)c - --- B b )d e + (- --- A c - --- B b c)d e +--R 140 140 280 280 140 +--R + +--R 1 2 5 +--R - --- B c d +--R 168 +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 5 9 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 8 2 7 7 8 6 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 310 + +--S 311 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 280B c e x + ((- 210A c - 420B b c)e - 350B c d e )x +--R + +--R 2 5 2 4 +--R ((- 336A b - 336B a)c - 168B b )e + (- 168A c - 336B b c)d e +--R + +--R 2 2 3 +--R - 280B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 +--R (- 280A a c - 140A b - 280B a b)e +--R + +--R 2 4 2 2 3 +--R ((- 168A b - 168B a)c - 84B b )d e + (- 84A c - 168B b c)d e +--R + +--R 2 3 2 +--R - 140B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 240A a b - 120B a )e + (- 80A a c - 40A b - 80B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 48A b - 48B a)c - 24B b )d e + (- 24A c - 48B b c)d e +--R + +--R 2 4 +--R - 40B c d e +--R * +--R x +--R + +--R 2 5 2 4 +--R - 105A a e + (- 30A a b - 15B a )d e +--R + +--R 2 2 3 2 3 2 +--R (- 10A a c - 5A b - 10B a b)d e + ((- 6A b - 6B a)c - 3B b )d e +--R + +--R 2 4 2 5 +--R (- 3A c - 6B b c)d e - 5B c d +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 +--R 840e x + 6720d e x + 23520d e x + 47040d e x + 58800d e x +--R + +--R 5 9 3 6 8 2 7 7 8 6 +--R 47040d e x + 23520d e x + 6720d e x + 840d e +--R Type: Union(Expression(Integer),...) +--E 311 + +--S 312 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 313 + +)clear all + +--S 314 of 1751 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1751 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))-_ + (c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*_ + (d+e*x)^(2+m)/(e^8*(2+m))-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*(d+e*x)^(3+m)/(e^8*(3+m))-(A*e*(2*c*d-b*e)*_ + (10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*_ + (4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+_ + a^2*e^2)))*(d+e*x)^(4+m)/(e^8*(4+m))-(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*_ + (5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^(6+m)/(e^8*(6+m))-_ + c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*_ + (d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 2 3 7 3 2 3 6 +--R ((A c + 3B b c )e - 7B c d)m + ((29A c + 87B b c )e - 203B c d)m +--R + +--R 3 2 3 5 +--R ((343A c + 1029B b c )e - 2401B c d)m +--R + +--R 3 2 3 4 +--R ((2135A c + 6405B b c )e - 14945B c d)m +--R + +--R 3 2 3 3 +--R ((7504A c + 22512B b c )e - 52528B c d)m +--R + +--R 3 2 3 2 +--R ((14756A c + 44268B b c )e - 103292B c d)m +--R + +--R 3 2 3 +--R ((14832A c + 44496B b c )e - 103824B c d)m +--R + +--R 3 2 3 +--R (5760A c + 17280B b c )e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 7 +--R (((3A b + 3B a)c + 3B b c)e + (- 6A c - 18B b c )d e + 21B c d )m +--R + +--R 2 2 2 3 2 +--R ((90A b + 90B a)c + 90B b c)e + (- 180A c - 540B b c )d e +--R + +--R 3 2 +--R 630B c d +--R * +--R 6 +--R m +--R + +--R 2 2 2 +--R ((1098A b + 1098B a)c + 1098B b c)e +--R + +--R 3 2 3 2 +--R (- 2196A c - 6588B b c )d e + 7686B c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 +--R ((7020A b + 7020B a)c + 7020B b c)e +--R + +--R 3 2 3 2 +--R (- 14040A c - 42120B b c )d e + 49140B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 +--R ((25227A b + 25227B a)c + 25227B b c)e +--R + +--R 3 2 3 2 +--R (- 50454A c - 151362B b c )d e + 176589B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 +--R ((50490A b + 50490B a)c + 50490B b c)e +--R + +--R 3 2 3 2 +--R (- 100980A c - 302940B b c )d e + 353430B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 +--R ((51432A b + 51432B a)c + 51432B b c)e +--R + +--R 3 2 3 2 +--R (- 102864A c - 308592B b c )d e + 360024B c d +--R * +--R m +--R + +--R 2 2 2 +--R ((20160A b + 20160B a)c + 20160B b c)e +--R + +--R 3 2 3 2 +--R (- 40320A c - 120960B b c )d e + 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 3 3 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 2 3 2 2 +--R ((- 15A b - 15B a)c - 15B b c)d e + (15A c + 45B b c )d e +--R + +--R 3 3 +--R - 35B c d +--R * +--R 7 +--R m +--R + +--R 2 2 3 3 +--R (93A a c + (93A b + 186B a b)c + 31B b )e +--R + +--R 2 2 2 +--R ((- 465A b - 465B a)c - 465B b c)d e +--R + +--R 3 2 2 3 3 +--R (465A c + 1395B b c )d e - 1085B c d +--R * +--R 6 +--R m +--R + +--R 2 2 3 3 +--R (1173A a c + (1173A b + 2346B a b)c + 391B b )e +--R + +--R 2 2 2 +--R ((- 5865A b - 5865B a)c - 5865B b c)d e +--R + +--R 3 2 2 3 3 +--R (5865A c + 17595B b c )d e - 13685B c d +--R * +--R 5 +--R m +--R + +--R 2 2 3 3 +--R (7743A a c + (7743A b + 15486B a b)c + 2581B b )e +--R + +--R 2 2 2 +--R ((- 38715A b - 38715B a)c - 38715B b c)d e +--R + +--R 3 2 2 3 3 +--R (38715A c + 116145B b c )d e - 90335B c d +--R * +--R 4 +--R m +--R + +--R 2 2 3 3 +--R (28632A a c + (28632A b + 57264B a b)c + 9544B b )e +--R + +--R 2 2 2 +--R ((- 143160A b - 143160B a)c - 143160B b c)d e +--R + +--R 3 2 2 3 3 +--R (143160A c + 429480B b c )d e - 334040B c d +--R * +--R 3 +--R m +--R + +--R 2 2 3 3 +--R (58692A a c + (58692A b + 117384B a b)c + 19564B b )e +--R + +--R 2 2 2 +--R ((- 293460A b - 293460B a)c - 293460B b c)d e +--R + +--R 3 2 2 3 3 +--R (293460A c + 880380B b c )d e - 684740B c d +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 +--R (60912A a c + (60912A b + 121824B a b)c + 20304B b )e +--R + +--R 2 2 2 +--R ((- 304560A b - 304560B a)c - 304560B b c)d e +--R + +--R 3 2 2 3 3 +--R (304560A c + 913680B b c )d e - 710640B c d +--R * +--R m +--R + +--R 2 2 3 3 +--R (24192A a c + (24192A b + 48384B a b)c + 8064B b )e +--R + +--R 2 2 2 +--R ((- 120960A b - 120960B a)c - 120960B b c)d e +--R + +--R 3 2 2 3 3 +--R (120960A c + 362880B b c )d e - 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R ((30A b + 30B a)c + 30B b c)d e + (- 20A c - 60B b c )d e +--R + +--R 3 4 +--R 35B c d +--R * +--R 7 +--R m +--R + +--R 2 3 2 4 +--R ((192A a b + 96B a )c + 32A b + 96B a b )e +--R + +--R 2 2 3 3 +--R (- 384A a c + (- 384A b - 768B a b)c - 128B b )d e +--R + +--R 2 2 2 2 +--R ((960A b + 960B a)c + 960B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 640A c - 1920B b c )d e + 1120B c d +--R * +--R 6 +--R m +--R + +--R 2 3 2 4 +--R ((2508A a b + 1254B a )c + 418A b + 1254B a b )e +--R + +--R 2 2 3 3 +--R (- 5016A a c + (- 5016A b - 10032B a b)c - 1672B b )d e +--R + +--R 2 2 2 2 +--R ((12540A b + 12540B a)c + 12540B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 8360A c - 25080B b c )d e + 14630B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 4 +--R ((17184A a b + 8592B a )c + 2864A b + 8592B a b )e +--R + +--R 2 2 3 3 +--R (- 34368A a c + (- 34368A b - 68736B a b)c - 11456B b )d e +--R + +--R 2 2 2 2 +--R ((85920A b + 85920B a)c + 85920B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 57280A c - 171840B b c )d e + 100240B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 4 +--R ((65958A a b + 32979B a )c + 10993A b + 32979B a b )e +--R + +--R 2 2 3 3 +--R (- 131916A a c + (- 131916A b - 263832B a b)c - 43972B b )d e +--R + +--R 2 2 2 2 +--R ((329790A b + 329790B a)c + 329790B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 219860A c - 659580B b c )d e + 384755B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 4 +--R ((139872A a b + 69936B a )c + 23312A b + 69936B a b )e +--R + +--R 2 2 3 3 +--R (- 279744A a c + (- 279744A b - 559488B a b)c - 93248B b )d e +--R + +--R 2 2 2 2 +--R ((699360A b + 699360B a)c + 699360B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 466240A c - 1398720B b c )d e + 815920B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 4 +--R ((149256A a b + 74628B a )c + 24876A b + 74628B a b )e +--R + +--R 2 2 3 3 +--R (- 298512A a c + (- 298512A b - 597024B a b)c - 99504B b )d e +--R + +--R 2 2 2 2 +--R ((746280A b + 746280B a)c + 746280B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 497520A c - 1492560B b c )d e + 870660B c d +--R * +--R m +--R + +--R 2 3 2 4 +--R ((60480A a b + 30240B a )c + 10080A b + 30240B a b )e +--R + +--R 2 2 3 3 +--R (- 120960A a c + (- 120960A b - 241920B a b)c - 40320B b )d e +--R + +--R 2 2 2 2 +--R ((302400A b + 302400B a)c + 302400B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 201600A c - 604800B b c )d e + 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 2 5 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 2 3 +--R (18A a c + (18A b + 36B a b)c + 6B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R ((- 30A b - 30B a)c - 30B b c)d e + (15A c + 45B b c )d e +--R + +--R 3 5 +--R - 21B c d +--R * +--R 7 +--R m +--R + +--R 2 2 2 5 +--R (99A a c + 99A a b + 99B a b)e +--R + +--R 2 3 2 4 +--R ((- 594A a b - 297B a )c - 99A b - 297B a b )d e +--R + +--R 2 2 3 2 3 +--R (594A a c + (594A b + 1188B a b)c + 198B b )d e +--R + +--R 2 2 3 2 +--R ((- 990A b - 990B a)c - 990B b c)d e +--R + +--R 3 2 4 3 5 +--R (495A c + 1485B b c )d e - 693B c d +--R * +--R 6 +--R m +--R + +--R 2 2 2 5 +--R (1341A a c + 1341A a b + 1341B a b)e +--R + +--R 2 3 2 4 +--R ((- 8046A a b - 4023B a )c - 1341A b - 4023B a b )d e +--R + +--R 2 2 3 2 3 +--R (8046A a c + (8046A b + 16092B a b)c + 2682B b )d e +--R + +--R 2 2 3 2 +--R ((- 13410A b - 13410B a)c - 13410B b c)d e +--R + +--R 3 2 4 3 5 +--R (6705A c + 20115B b c )d e - 9387B c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 5 +--R (9585A a c + 9585A a b + 9585B a b)e +--R + +--R 2 3 2 4 +--R ((- 57510A a b - 28755B a )c - 9585A b - 28755B a b )d e +--R + +--R 2 2 3 2 3 +--R (57510A a c + (57510A b + 115020B a b)c + 19170B b )d e +--R + +--R 2 2 3 2 +--R ((- 95850A b - 95850B a)c - 95850B b c)d e +--R + +--R 3 2 4 3 5 +--R (47925A c + 143775B b c )d e - 67095B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 5 +--R (38592A a c + 38592A a b + 38592B a b)e +--R + +--R 2 3 2 4 +--R ((- 231552A a b - 115776B a )c - 38592A b - 115776B a b )d e +--R + +--R 2 2 3 2 3 +--R (231552A a c + (231552A b + 463104B a b)c + 77184B b )d e +--R + +--R 2 2 3 2 +--R ((- 385920A b - 385920B a)c - 385920B b c)d e +--R + +--R 3 2 4 3 5 +--R (192960A c + 578880B b c )d e - 270144B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 5 +--R (86076A a c + 86076A a b + 86076B a b)e +--R + +--R 2 3 2 4 +--R ((- 516456A a b - 258228B a )c - 86076A b - 258228B a b )d e +--R + +--R 2 2 3 2 3 +--R (516456A a c + (516456A b + 1032912B a b)c + 172152B b )d e +--R + +--R 2 2 3 2 +--R ((- 860760A b - 860760B a)c - 860760B b c)d e +--R + +--R 3 2 4 3 5 +--R (430380A c + 1291140B b c )d e - 602532B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 5 +--R 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2 2 3 2 +--R ((990A b + 990B a)c + 990B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 495A c - 1485B b c )d e + 693B c d +--R * +--R 6 +--R m +--R + +--R 2 2 2 5 +--R (- 1341A a c - 1341A a b - 1341B a b)e +--R + +--R 2 3 2 4 +--R ((8046A a b + 4023B a )c + 1341A b + 4023B a b )d e +--R + +--R 2 2 3 2 3 +--R (- 8046A a c + (- 8046A b - 16092B a b)c - 2682B b )d e +--R + +--R 2 2 3 2 +--R ((13410A b + 13410B a)c + 13410B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 6705A c - 20115B b c )d e + 9387B c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 5 +--R (- 9585A a c - 9585A a b - 9585B a b)e +--R + +--R 2 3 2 4 +--R ((57510A a b + 28755B a )c + 9585A b + 28755B a b )d e +--R + +--R 2 2 3 2 3 +--R (- 57510A a c + (- 57510A b - 115020B a b)c - 19170B b )d e +--R + +--R 2 2 3 2 +--R ((95850A b + 95850B a)c + 95850B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 47925A c - 143775B b c )d e + 67095B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 5 +--R (- 38592A a c - 38592A a b - 38592B a b)e +--R + +--R 2 3 2 4 +--R ((231552A a b + 115776B a )c + 38592A b + 115776B a b )d e +--R + +--R 2 2 3 2 3 +--R (- 231552A a c + (- 231552A b - 463104B a b)c - 77184B b )d e +--R + +--R 2 2 3 2 +--R ((385920A b + 385920B a)c + 385920B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 192960A c - 578880B b c )d e + 270144B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 5 +--R (- 86076A a c - 86076A a b - 86076B a b)e +--R + +--R 2 3 2 4 +--R ((516456A a b + 258228B a )c + 86076A b + 258228B a b )d e +--R + +--R 2 2 3 +--R (- 516456A a c + (- 516456A b - 1032912B a b)c - 172152B b ) +--R * +--R 2 3 +--R d e +--R + +--R 2 2 3 2 +--R ((860760A b + 860760B a)c + 860760B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 430380A c - 1291140B b c )d e + 602532B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 5 +--R (- 96144A a c - 96144A a b - 96144B a b)e +--R + +--R 2 3 2 4 +--R ((576864A a b + 288432B a )c + 96144A b + 288432B a b )d e +--R + +--R 2 2 3 +--R (- 576864A a c + (- 576864A b - 1153728B a b)c - 192288B b ) +--R * +--R 2 3 +--R d e +--R 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c)d e +--R + +--R 3 2 5 3 6 +--R (220236A c + 660708B b c )d e - 256942B c d +--R * +--R 2 +--R m +--R + +--R 2 3 6 +--R (- 134136A a b - 44712B a )e +--R + +--R 2 2 2 5 +--R (268272A a c + 268272A a b + 268272B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 804816A a b - 402408B a )c - 134136A b - 402408B a b )d e +--R + +--R 2 2 3 3 3 +--R (536544A a c + (536544A b + 1073088B a b)c + 178848B b )d e +--R + +--R 2 2 4 2 +--R ((- 670680A b - 670680B a)c - 670680B b c)d e +--R + +--R 3 2 5 3 6 +--R (268272A c + 804816B b c )d e - 312984B c d +--R * +--R m +--R + +--R 2 3 6 +--R (- 60480A a b - 20160B a )e +--R + +--R 2 2 2 5 +--R (120960A a c + 120960A a b + 120960B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 362880A a b - 181440B a )c - 60480A b - 181440B a b )d e +--R + +--R 2 2 3 3 3 +--R (241920A a c + (241920A b + 483840B a b)c + 80640B b )d e +--R + +--R 2 2 4 2 +--R ((- 302400A b - 302400B a)c - 302400B b c)d e +--R + +--R 3 2 5 3 6 +--R (120960A c + 362880B b c )d e - 141120B c d +--R * +--R 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b + 1533B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 1533A a c + (- 1533A b - 3066B a b)c - 511B b )d e +--R + +--R 2 2 5 2 +--R ((1533A b + 1533B a)c + 1533B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 511A c - 1533B b c )d e + 511B c d +--R * +--R 5 +--R m +--R + +--R 3 7 2 3 6 +--R - 4025A a e + (12075A a b + 4025B a )d e +--R + +--R 2 2 2 2 5 +--R (- 12075A a c - 12075A a b - 12075B a b)d e +--R + +--R 2 3 2 3 4 +--R ((24150A a b + 12075B a )c + 4025A b + 12075B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12075A a c + (- 12075A b - 24150B a b)c - 4025B b )d e +--R + +--R 2 2 5 2 +--R ((12075A b + 12075B a)c + 12075B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 4025A c - 12075B b c )d e + 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 7 2 3 6 +--R - 18424A a e + (55272A a b + 18424B a )d e +--R + +--R 2 2 2 2 5 +--R (- 55272A a c - 55272A a b - 55272B a b)d e +--R + +--R 2 3 2 3 4 +--R ((110544A a b + 55272B a )c + 18424A b + 55272B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 55272A a c + (- 55272A b - 110544B a b)c - 18424B b )d e +--R + +--R 2 2 5 2 +--R ((55272A b + 55272B a)c + 55272B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 18424A c - 55272B b c )d e + 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 7 2 3 6 +--R - 48860A a e + (146580A a b + 48860B a )d e +--R + +--R 2 2 2 2 5 +--R (- 146580A a c - 146580A a b - 146580B a b)d e +--R + +--R 2 3 2 3 4 +--R ((293160A a b + 146580B a )c + 48860A b + 146580B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 146580A a c + (- 146580A b - 293160B a b)c - 48860B b )d e +--R + +--R 2 2 5 2 +--R ((146580A b + 146580B a)c + 146580B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48860A c - 146580B b c )d e + 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 7 2 3 6 +--R - 69264A a e + (207792A a b + 69264B a )d e +--R + +--R 2 2 2 2 5 +--R (- 207792A a c - 207792A a b - 207792B a b)d e +--R + +--R 2 3 2 3 4 +--R ((415584A a b + 207792B a )c + 69264A b + 207792B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 207792A a c + (- 207792A b - 415584B a b)c - 69264B b )d e +--R + +--R 2 2 5 2 +--R ((207792A b + 207792B a)c + 207792B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 69264A c - 207792B b c )d e + 69264B c d +--R * +--R m +--R + +--R 3 7 2 3 6 +--R - 40320A a e + (120960A a b + 40320B a )d e +--R + +--R 2 2 2 2 5 +--R (- 120960A a c - 120960A a b - 120960B a b)d e +--R + +--R 2 3 2 3 4 +--R ((241920A a b + 120960B a )c + 40320A b + 120960B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 120960A a c + (- 120960A b - 241920B a b)c - 40320B b )d e +--R + +--R 2 2 5 2 +--R ((120960A b + 120960B a)c + 120960B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 40320A c - 120960B b c )d e + 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 of 1751 +t0:=(A+B*x)*(d+e*x)^5*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 5 12 3 2 5 3 4 11 +--R B c e x + ((A c + 3B b c )e + 5B c d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 10 +--R (((3A b + 3B a)c + 3B b c)e + (5A c + 15B b c )d e + 10B c d e )x +--R + +--R 2 2 3 5 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 4 3 2 2 3 3 3 2 +--R ((15A b + 15B a)c + 15B b c)d e + (10A c + 30B b c )d e + 10B c d e +--R * +--R 9 +--R x +--R + +--R 2 3 2 5 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 4 +--R (15A a c + (15A b + 30B a b)c + 5B b )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R ((30A b + 30B a)c + 30B b c)d e + (10A c + 30B b c )d e + 5B c d e +--R * +--R 8 +--R x +--R + +--R 2 2 2 5 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 4 +--R ((30A a b + 15B a )c + 5A b + 15B a b )d e +--R + +--R 2 2 3 2 3 +--R (30A a c + (30A b + 60B a b)c + 10B b )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R ((30A b + 30B a)c + 30B b c)d e + (5A c + 15B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (3A a b + B a )e + (15A a c + 15A a b + 15B a b)d e +--R + +--R 2 3 2 2 3 +--R ((60A a b + 30B a )c + 10A b + 30B a b )d e +--R + +--R 2 2 3 3 2 +--R (30A a c + (30A b + 60B a b)c + 10B b )d e +--R + +--R 2 2 4 3 2 5 +--R ((15A b + 15B a)c + 15B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 5 2 3 4 2 2 2 2 3 +--R A a e + (15A a b + 5B a )d e + (30A a c + 30A a b + 30B a b)d e +--R + +--R 2 3 2 3 2 +--R ((60A a b + 30B a )c + 10A b + 30B a b )d e +--R + +--R 2 2 3 4 +--R (15A a c + (15A b + 30B a b)c + 5B b )d e +--R + +--R 2 2 5 +--R ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 2 3 2 2 2 3 2 +--R 5A a d e + (30A a b + 10B a )d e + (30A a c + 30A a b + 30B a b)d e +--R + +--R 2 3 2 4 +--R ((30A a b + 15B a )c + 5A b + 15B a b )d e +--R + +--R 2 2 3 5 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 2 4 +--R 10A a d e + (30A a b + 10B a )d e + (15A a c + 15A a b + 15B a b)d e +--R + +--R 2 3 2 5 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 4 2 2 2 5 2 +--R (10A a d e + (15A a b + 5B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 4 2 3 5 3 5 +--R (5A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 319 + +--S 320 of 1751 +r0:=-1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^6/e^8-_ + 1/7*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-_ + e*(4*b*d-a*e)))*(d+e*x)^7/e^8-3/8*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*(d+e*x)^8/e^8-1/9*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*_ + (d+e*x)^9/e^8-1/10*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + (d+e*x)^10/e^8-3/11*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-_ + c*e*(6*b*d-a*e)))*(d+e*x)^11/e^8-1/12*c^2*(7*B*c*d-3*b*B*e-A*c*e)*_ + (d+e*x)^12/e^8+1/13*B*c^3*(d+e*x)^13/e^8 +--R +--R +--R (2) +--R 1 3 13 13 1 3 1 2 13 5 3 12 12 +--R -- B c e x + ((-- A c + - B b c )e + -- B c d e )x +--R 13 12 4 12 +--R + +--R 3 3 2 3 2 13 5 3 15 2 12 +--R ((-- A b + -- B a)c + -- B b c)e + (-- A c + -- B b c )d e +--R 11 11 11 11 11 +--R + +--R 10 3 2 11 +--R -- B c d e +--R 11 +--R * +--R 11 +--R x +--R + +--R 3 2 3 2 3 1 3 13 +--R (-- A a c + (-- A b + - B a b)c + -- B b )e +--R 10 10 5 10 +--R + +--R 3 3 2 3 2 12 3 2 2 11 3 3 10 +--R ((- A b + - B a)c + - B b c)d e + (A c + 3B b c )d e + B c d e +--R 2 2 2 +--R * +--R 10 +--R x +--R + +--R 2 1 2 1 3 1 2 13 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 3 3 9 3 +--R + +--R 5 2 5 2 10 5 3 12 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 3 3 3 9 +--R + +--R 10 10 2 10 2 2 11 10 3 10 2 3 10 +--R ((-- A b + -- B a)c + -- B b c)d e + (-- A c + -- B b c )d e +--R 3 3 3 9 3 +--R + +--R 5 3 4 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 3 2 3 2 13 +--R (- A a c + - A a b + - B a b)e +--R 8 8 8 +--R + +--R 15 15 2 5 3 15 2 12 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 4 8 8 8 +--R + +--R 15 2 15 2 15 5 3 2 11 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 4 4 2 4 +--R + +--R 15 15 2 15 2 3 10 5 3 15 2 4 9 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + -- B b c )d e +--R 4 4 4 8 8 +--R + +--R 1 3 5 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 3 2 1 3 13 15 2 15 2 15 2 12 +--R (- A a b + - B a )e + (-- A a c + -- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 60 30 2 10 3 30 2 2 11 +--R ((-- A a b + -- B a )c + -- A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 30 2 30 2 60 10 3 3 10 +--R (-- A a c + (-- A b + -- B a b)c + -- B b )d e +--R 7 7 7 7 +--R + +--R 15 15 2 15 2 4 9 1 3 3 2 5 8 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 13 5 2 5 3 12 +--R - A a e + (- A a b + - B a )d e +--R 6 2 6 +--R + +--R 2 2 2 2 11 +--R (5A a c + 5A a b + 5B a b)d e +--R + +--R 2 5 3 2 3 10 +--R ((10A a b + 5B a )c + - A b + 5B a b )d e +--R 3 +--R + +--R 5 2 5 2 5 3 4 9 +--R (- A a c + (- A b + 5B a b)c + - B b )d e +--R 2 2 6 +--R + +--R 1 1 2 1 2 5 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 12 2 3 2 11 2 2 2 3 10 +--R A a d e + (6A a b + 2B a )d e + (6A a c + 6A a b + 6B a b)d e +--R + +--R 2 3 2 4 9 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 3 2 3 2 6 1 3 5 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 5 3 2 11 15 2 5 3 3 10 +--R - A a d e + (-- A a b + - B a )d e +--R 2 2 2 +--R + +--R 15 2 15 2 15 2 4 9 +--R (-- A a c + -- A a b + -- B a b)d e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 5 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 10 3 3 10 2 5 3 4 9 2 2 2 5 8 3 +--R (-- A a d e + (5A a b + - B a )d e + (A a c + A a b + B a b)d e )x +--R 3 3 +--R + +--R 5 3 4 9 3 2 1 3 5 8 2 3 5 8 1 3 6 7 +--R (- A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 2 6 +--R + +--R 1 2 1 3 7 6 1 2 1 2 1 2 8 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 14 42 56 56 56 +--R + +--R 1 1 2 1 3 1 2 9 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 84 168 504 168 +--R + +--R 1 2 1 2 1 1 3 10 3 +--R (--- A a c + (--- A b + --- B a b)c + ---- B b )d e +--R 420 420 210 1260 +--R + +--R 1 1 2 1 2 11 2 +--R ((- --- A b - --- B a)c - --- B b c)d e +--R 924 924 924 +--R + +--R 1 3 1 2 12 1 3 13 +--R (---- A c + ---- B b c )d e - ----- B c d +--R 5544 1848 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 320 + +--S 321 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 5 13 1 3 1 2 5 5 3 4 12 +--R -- B c e x + ((-- A c + - B b c )e + -- B c d e )x +--R 13 12 4 12 +--R + +--R 3 3 2 3 2 5 5 3 15 2 4 +--R ((-- A b + -- B a)c + -- B b c)e + (-- A c + -- B b c )d e +--R 11 11 11 11 11 +--R + +--R 10 3 2 3 +--R -- B c d e +--R 11 +--R * +--R 11 +--R x +--R + +--R 3 2 3 2 3 1 3 5 +--R (-- A a c + (-- A b + - B a b)c + -- B b )e +--R 10 10 5 10 +--R + +--R 3 3 2 3 2 4 3 2 2 3 3 3 2 +--R ((- A b + - B a)c + - B b c)d e + (A c + 3B b c )d e + B c d e +--R 2 2 2 +--R * +--R 10 +--R x +--R + +--R 2 1 2 1 3 1 2 5 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 3 3 9 3 +--R + +--R 5 2 5 2 10 5 3 4 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 3 3 3 9 +--R + +--R 10 10 2 10 2 2 3 10 3 10 2 3 2 +--R ((-- A b + -- B a)c + -- B b c)d e + (-- A c + -- B b c )d e +--R 3 3 3 9 3 +--R + +--R 5 3 4 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 3 2 3 2 5 +--R (- A a c + - A a b + - B a b)e +--R 8 8 8 +--R + +--R 15 15 2 5 3 15 2 4 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 4 8 8 8 +--R + +--R 15 2 15 2 15 5 3 2 3 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 4 4 2 4 +--R + +--R 15 15 2 15 2 3 2 5 3 15 2 4 1 3 5 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + -- B b c )d e + - B c d +--R 4 4 4 8 8 8 +--R * +--R 8 +--R x +--R + +--R 3 2 1 3 5 15 2 15 2 15 2 4 +--R (- A a b + - B a )e + (-- A a c + -- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 60 30 2 10 3 30 2 2 3 +--R ((-- A a b + -- B a )c + -- A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 30 2 30 2 60 10 3 3 2 +--R (-- A a c + (-- A b + -- B a b)c + -- B b )d e +--R 7 7 7 7 +--R + +--R 15 15 2 15 2 4 1 3 3 2 5 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 5 5 2 5 3 4 2 2 2 2 3 +--R - A a e + (- A a b + - B a )d e + (5A a c + 5A a b + 5B a b)d e +--R 6 2 6 +--R + +--R 2 5 3 2 3 2 +--R ((10A a b + 5B a )c + - A b + 5B a b )d e +--R 3 +--R + +--R 5 2 5 2 5 3 4 +--R (- A a c + (- A b + 5B a b)c + - B b )d e +--R 2 2 6 +--R + +--R 1 1 2 1 2 5 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 4 2 3 2 3 2 2 2 3 2 +--R A a d e + (6A a b + 2B a )d e + (6A a c + 6A a b + 6B a b)d e +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 3 2 3 2 6 1 3 5 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 5 3 2 3 15 2 5 3 3 2 +--R - A a d e + (-- A a b + - B a )d e +--R 2 2 2 +--R + +--R 15 2 15 2 15 2 4 +--R (-- A a c + -- A a b + -- B a b)d e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 5 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 10 3 3 2 2 5 3 4 2 2 2 5 3 +--R (-- A a d e + (5A a b + - B a )d e + (A a c + A a b + B a b)d )x +--R 3 3 +--R + +--R 5 3 4 3 2 1 3 5 2 3 5 +--R (- A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 321 + +--S 322 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 6 7 1 2 1 3 7 6 +--R - - A a d e + (-- A a b + -- B a )d e +--R 6 14 42 +--R + +--R 1 2 1 2 1 2 8 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 56 56 56 +--R + +--R 1 1 2 1 3 1 2 9 4 +--R ((-- A a b + --- B a )c + --- A b + --- B a b )d e +--R 84 168 504 168 +--R + +--R 1 2 1 2 1 1 3 10 3 +--R (- --- A a c + (- --- A b - --- B a b)c - ---- B b )d e +--R 420 420 210 1260 +--R + +--R 1 1 2 1 2 11 2 +--R ((--- A b + --- B a)c + --- B b c)d e +--R 924 924 924 +--R + +--R 1 3 1 2 12 1 3 13 +--R (- ---- A c - ---- B b c )d e + ----- B c d +--R 5544 1848 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 322 + +--S 323 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 323 + +)clear all + +--S 324 of 1751 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 2 4 3 3 10 +--R B c e x + ((A c + 3B b c )e + 4B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 9 +--R (((3A b + 3B a)c + 3B b c)e + (4A c + 12B b c )d e + 6B c d e )x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((12A b + 12B a)c + 12B b c)d e + (6A c + 18B b c )d e + 4B c d e +--R * +--R 8 +--R x +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 3 +--R (12A a c + (12A b + 24B a b)c + 4B b )d e +--R + +--R 2 2 2 2 3 2 3 3 4 +--R ((18A b + 18B a)c + 18B b c)d e + (4A c + 12B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 2 2 4 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 3 +--R ((24A a b + 12B a )c + 4A b + 12B a b )d e +--R + +--R 2 2 3 2 2 +--R (18A a c + (18A b + 36B a b)c + 6B b )d e +--R + +--R 2 2 3 3 2 4 +--R ((12A b + 12B a)c + 12B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 3 4 2 2 2 3 +--R (3A a b + B a )e + (12A a c + 12A a b + 12B a b)d e +--R + +--R 2 3 2 2 2 +--R ((36A a b + 18B a )c + 6A b + 18B a b )d e +--R + +--R 2 2 3 3 +--R (12A a c + (12A b + 24B a b)c + 4B b )d e +--R + +--R 2 2 4 +--R ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 +--R A a e + (12A a b + 4B a )d e + (18A a c + 18A a b + 18B a b)d e +--R + +--R 2 3 2 3 +--R ((24A a b + 12B a )c + 4A b + 12B a b )d e +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R 4A a d e + (18A a b + 6B a )d e + (12A a c + 12A a b + 12B a b)d e +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 3 3 2 2 2 4 2 +--R (6A a d e + (12A a b + 4B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 3 2 3 4 3 4 +--R (4A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 324 + +--S 325 of 1751 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^5/e^8-1/6*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^6/e^8-_ + 3/7*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^7/e^8-_ + 1/8*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^8/e^8-1/9*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*_ + d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^9/e^8-3/10*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^10/e^8-1/11*c^2*(7*B*c*d-_ + 3*b*B*e-A*c*e)*(d+e*x)^11/e^8+1/12*B*c^3*(d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 3 12 12 1 3 3 2 12 4 3 11 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 3 2 3 2 12 2 3 6 2 11 +--R ((-- A b + -- B a)c + -- B b c)e + (- A c + - B b c )d e +--R 10 10 10 5 5 +--R + +--R 3 3 2 10 +--R - B c d e +--R 5 +--R * +--R 10 +--R x +--R + +--R 1 2 1 2 2 1 3 12 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 3 3 3 9 +--R + +--R 4 4 2 4 2 11 2 3 2 2 10 +--R ((- A b + - B a)c + - B b c)d e + (- A c + 2B b c )d e +--R 3 3 3 3 +--R + +--R 4 3 3 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 3 2 1 3 3 2 12 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 4 8 8 8 +--R + +--R 3 2 3 2 1 3 11 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 9 9 2 9 2 2 10 1 3 3 2 3 9 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 4 4 4 2 2 +--R + +--R 1 3 4 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 3 2 3 2 3 2 12 +--R (- A a c + - A a b + - B a b)e +--R 7 7 7 +--R + +--R 24 12 2 4 3 12 2 11 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 18 2 18 2 36 6 3 2 10 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 12 12 2 12 2 3 9 1 3 3 2 4 8 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 12 2 2 2 11 +--R (- A a b + - B a )e + (2A a c + 2A a b + 2B a b)d e +--R 2 6 +--R + +--R 2 3 2 2 10 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 2 2 2 3 3 9 +--R (2A a c + (2A b + 4B a b)c + - B b )d e +--R 3 +--R + +--R 1 1 2 1 2 4 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 1 3 12 12 2 4 3 11 +--R - A a e + (-- A a b + - B a )d e +--R 5 5 5 +--R + +--R 18 2 18 2 18 2 2 10 +--R (-- A a c + -- A a b + -- B a b)d e +--R 5 5 5 +--R + +--R 24 12 2 4 3 12 2 3 9 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 4 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 11 9 2 3 3 2 10 2 2 2 3 9 +--R A a d e + (- A a b + - B a )d e + (3A a c + 3A a b + 3B a b)d e +--R 2 2 +--R + +--R 3 3 2 1 3 3 2 4 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 2 10 2 4 3 3 9 2 2 2 4 8 3 +--R (2A a d e + (4A a b + - B a )d e + (A a c + A a b + B a b)d e )x +--R 3 +--R + +--R 3 3 9 3 2 1 3 4 8 2 3 4 8 1 3 5 7 +--R (2A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 5 +--R + +--R 1 2 1 3 6 6 1 2 1 2 1 2 7 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 10 30 35 35 35 +--R + +--R 3 3 2 1 3 3 2 8 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 280 280 +--R + +--R 1 2 1 2 1 1 3 9 3 +--R (--- A a c + (--- A b + --- B a b)c + --- B b )d e +--R 210 210 105 630 +--R + +--R 1 1 2 1 2 10 2 1 3 1 2 11 +--R ((- --- A b - --- B a)c - --- B b c)d e + (---- A c + --- B b c )d e +--R 420 420 420 2310 770 +--R + +--R 1 3 12 +--R - ---- B c d +--R 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 325 + +--S 326 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 12 1 3 3 2 4 4 3 3 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 3 2 3 2 4 2 3 6 2 3 +--R ((-- A b + -- B a)c + -- B b c)e + (- A c + - B b c )d e +--R 10 10 10 5 5 +--R + +--R 3 3 2 2 +--R - B c d e +--R 5 +--R * +--R 10 +--R x +--R + +--R 1 2 1 2 2 1 3 4 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 3 3 3 9 +--R + +--R 4 4 2 4 2 3 2 3 2 2 2 4 3 3 +--R ((- A b + - B a)c + - B b c)d e + (- A c + 2B b c )d e + - B c d e +--R 3 3 3 3 9 +--R * +--R 9 +--R x +--R + +--R 3 3 2 1 3 3 2 4 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 4 8 8 8 +--R + +--R 3 2 3 2 1 3 3 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 9 9 2 9 2 2 2 1 3 3 2 3 1 3 4 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e + - B c d +--R 4 4 4 2 2 8 +--R * +--R 8 +--R x +--R + +--R 3 2 3 2 3 2 4 +--R (- A a c + - A a b + - B a b)e +--R 7 7 7 +--R + +--R 24 12 2 4 3 12 2 3 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 18 2 18 2 36 6 3 2 2 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 12 12 2 12 2 3 1 3 3 2 4 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 4 2 2 2 3 +--R (- A a b + - B a )e + (2A a c + 2A a b + 2B a b)d e +--R 2 6 +--R + +--R 2 3 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 2 2 2 3 3 +--R (2A a c + (2A b + 4B a b)c + - B b )d e +--R 3 +--R + +--R 1 1 2 1 2 4 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 1 3 4 12 2 4 3 3 +--R - A a e + (-- A a b + - B a )d e +--R 5 5 5 +--R + +--R 18 2 18 2 18 2 2 2 +--R (-- A a c + -- A a b + -- B a b)d e +--R 5 5 5 +--R + +--R 24 12 2 4 3 12 2 3 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 4 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 3 9 2 3 3 2 2 2 2 2 3 +--R A a d e + (- A a b + - B a )d e + (3A a c + 3A a b + 3B a b)d e +--R 2 2 +--R + +--R 3 3 2 1 3 3 2 4 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 4 3 3 2 2 2 4 3 +--R (2A a d e + (4A a b + - B a )d e + (A a c + A a b + B a b)d )x +--R 3 +--R + +--R 3 3 3 2 1 3 4 2 3 4 +--R (2A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 326 + +--S 327 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 5 7 1 2 1 3 6 6 +--R - - A a d e + (-- A a b + -- B a )d e +--R 5 10 30 +--R + +--R 1 2 1 2 1 2 7 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 35 35 35 +--R + +--R 3 3 2 1 3 3 2 8 4 +--R ((--- A a b + --- B a )c + --- A b + --- B a b )d e +--R 140 280 280 280 +--R + +--R 1 2 1 2 1 1 3 9 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 210 210 105 630 +--R + +--R 1 1 2 1 2 10 2 1 3 1 2 11 +--R ((--- A b + --- B a)c + --- B b c)d e + (- ---- A c - --- B b c )d e +--R 420 420 420 2310 770 +--R + +--R 1 3 12 +--R ---- B c d +--R 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 327 + +--S 328 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 328 + +)clear all + +--S 329 of 1751 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 2 3 3 2 9 +--R B c e x + ((A c + 3B b c )e + 3B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 8 +--R (((3A b + 3B a)c + 3B b c)e + (3A c + 9B b c )d e + 3B c d e)x +--R + +--R 2 2 3 3 2 2 2 +--R (3A a c + (3A b + 6B a b)c + B b )e + ((9A b + 9B a)c + 9B b c)d e +--R + +--R 3 2 2 3 3 +--R (3A c + 9B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 3 2 3 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 2 +--R (9A a c + (9A b + 18B a b)c + 3B b )d e +--R + +--R 2 2 2 3 2 3 +--R ((9A b + 9B a)c + 9B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 2 2 3 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 2 +--R ((18A a b + 9B a )c + 3A b + 9B a b )d e +--R + +--R 2 2 3 2 2 2 3 +--R (9A a c + (9A b + 18B a b)c + 3B b )d e + ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (3A a b + B a )e + (9A a c + 9A a b + 9B a b)d e +--R + +--R 2 3 2 2 +--R ((18A a b + 9B a )c + 3A b + 9B a b )d e +--R + +--R 2 2 3 3 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 +--R A a e + (9A a b + 3B a )d e + (9A a c + 9A a b + 9B a b)d e +--R + +--R 2 3 2 3 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 2 3 2 +--R (3A a d e + (9A a b + 3B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 2 2 3 3 3 3 +--R (3A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 329 + +--S 330 of 1751 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^4/e^8-1/5*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^5/e^8-_ + 1/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^6/e^8-_ + 1/7*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^7/e^8-1/8*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^8/e^8-1/3*c*(A*c*e*(2*c*d-_ + b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^9/e^8-1/10*c^2*_ + (7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^10/e^8+1/11*B*c^3*(d+e*x)^11/e^8 +--R +--R +--R (2) +--R 1 3 11 11 1 3 3 2 11 3 3 10 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 1 2 1 2 11 1 3 2 10 +--R ((- A b + - B a)c + - B b c)e + (- A c + B b c )d e +--R 3 3 3 3 +--R + +--R 1 3 2 9 +--R - B c d e +--R 3 +--R * +--R 9 +--R x +--R + +--R 3 2 3 2 3 1 3 11 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 8 8 4 8 +--R + +--R 9 9 2 9 2 10 3 3 9 2 2 9 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 8 8 8 8 8 +--R + +--R 1 3 3 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 6 3 2 1 3 3 2 11 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 7 7 7 7 +--R + +--R 9 2 9 2 18 3 3 10 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 9 9 2 9 2 2 9 1 3 3 2 3 8 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 2 1 2 11 +--R (- A a c + - A a b + - B a b)e +--R 2 2 2 +--R + +--R 3 2 1 3 3 2 10 +--R ((3A a b + - B a )c + - A b + - B a b )d e +--R 2 2 2 +--R + +--R 3 2 3 2 1 3 2 9 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 1 1 2 1 2 3 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 1 3 11 9 2 9 2 9 2 10 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 18 9 2 3 3 9 2 2 9 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 3 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 11 9 2 3 3 10 +--R - A a e + (- A a b + - B a )d e +--R 4 4 4 +--R + +--R 9 2 9 2 9 2 2 9 +--R (- A a c + - A a b + - B a b)d e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 3 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 10 2 3 2 9 2 2 2 3 8 3 +--R (A a d e + (3A a b + B a )d e + (A a c + A a b + B a b)d e )x +--R + +--R 3 3 2 9 3 2 1 3 3 8 2 3 3 8 1 3 4 7 +--R (- A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 2 4 +--R + +--R 3 2 1 3 5 6 1 2 1 2 1 2 6 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 20 20 20 20 20 +--R + +--R 3 3 2 1 3 3 2 7 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 70 140 140 140 +--R + +--R 3 2 3 2 3 1 3 8 3 +--R (--- A a c + (--- A b + --- B a b)c + --- B b )d e +--R 280 280 140 280 +--R + +--R 1 1 2 1 2 9 2 1 3 1 2 10 +--R ((- --- A b - --- B a)c - --- B b c)d e + (--- A c + --- B b c )d e +--R 168 168 168 840 280 +--R + +--R 1 3 11 +--R - ---- B c d +--R 1320 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 330 + +--S 331 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 3 11 1 3 3 2 3 3 3 2 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 1 2 1 2 3 1 3 2 2 1 3 2 9 +--R (((- A b + - B a)c + - B b c)e + (- A c + B b c )d e + - B c d e)x +--R 3 3 3 3 3 +--R + +--R 3 2 3 2 3 1 3 3 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 8 8 4 8 +--R + +--R 9 9 2 9 2 2 3 3 9 2 2 1 3 3 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e + - B c d +--R 8 8 8 8 8 8 +--R * +--R 8 +--R x +--R + +--R 6 3 2 1 3 3 2 3 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 7 7 7 7 +--R + +--R 9 2 9 2 18 3 3 2 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 9 9 2 9 2 2 1 3 3 2 3 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 2 1 2 3 +--R (- A a c + - A a b + - B a b)e +--R 2 2 2 +--R + +--R 3 2 1 3 3 2 2 +--R ((3A a b + - B a )c + - A b + - B a b )d e +--R 2 2 2 +--R + +--R 3 2 3 2 1 3 2 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 1 1 2 1 2 3 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 1 3 3 9 2 9 2 9 2 2 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 18 9 2 3 3 9 2 2 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 3 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 3 9 2 3 3 2 9 2 9 2 9 2 2 +--R - A a e + (- A a b + - B a )d e + (- A a c + - A a b + - B a b)d e +--R 4 4 4 4 4 4 +--R + +--R 3 3 2 1 3 3 2 3 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 2 2 2 2 3 3 +--R (A a d e + (3A a b + B a )d e + (A a c + A a b + B a b)d )x +--R + +--R 3 3 2 3 2 1 3 3 2 3 3 +--R (- A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 331 + +--S 332 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 4 7 3 2 1 3 5 6 +--R - - A a d e + (-- A a b + -- B a )d e +--R 4 20 20 +--R + +--R 1 2 1 2 1 2 6 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 20 20 20 +--R + +--R 3 3 2 1 3 3 2 7 4 +--R ((-- A a b + --- B a )c + --- A b + --- B a b )d e +--R 70 140 140 140 +--R + +--R 3 2 3 2 3 1 3 8 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 280 280 140 280 +--R + +--R 1 1 2 1 2 9 2 1 3 1 2 10 +--R ((--- A b + --- B a)c + --- B b c)d e + (- --- A c - --- B b c )d e +--R 168 168 168 840 280 +--R + +--R 1 3 11 +--R ---- B c d +--R 1320 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 332 + +--S 333 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 333 + +)clear all + +--S 334 of 1751 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 2 3 8 +--R B c e x + ((A c + 3B b c )e + 2B c d e)x +--R + +--R 2 2 2 3 2 3 2 7 +--R (((3A b + 3B a)c + 3B b c)e + (2A c + 6B b c )d e + B c d )x +--R + +--R 2 2 3 2 2 2 +--R (3A a c + (3A b + 6B a b)c + B b )e + ((6A b + 6B a)c + 6B b c)d e +--R + +--R 3 2 2 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 3 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 2 2 2 +--R (6A a c + (6A b + 12B a b)c + 2B b )d e + ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 2 2 2 2 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 +--R ((12A a b + 6B a )c + 2A b + 6B a b )d e +--R + +--R 2 2 3 2 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 +--R (3A a b + B a )e + (6A a c + 6A a b + 6B a b)d e +--R + +--R 2 3 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (A a e + (6A a b + 2B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 2 3 2 3 2 +--R (2A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 334 + +--S 335 of 1751 +r0:=a^3*A*d^2*x+1/2*a^2*d*(3*A*b*d+a*B*d+2*a*A*e)*x^2+1/3*a*(a*B*d*_ + (3*b*d+2*a*e)+A*(3*b^2*d^2+6*a*b*d*e+a*(3*c*d^2+a*e^2)))*x^3+1/4*(A*_ + (b^3*d^2+6*a*b^2*d*e+6*a^2*c*d*e+3*a*b*(2*c*d^2+a*e^2))+a*B*_ + (3*b^2*d^2+6*a*b*d*e+a*(3*c*d^2+a*e^2)))*x^4+1/5*(b^3*d*(B*d+2*A*e)+_ + 3*b^2*(A*c*d^2+2*a*B*d*e+a*A*e^2)+3*a*c*(A*c*d^2+2*a*B*d*e+a*A*e^2)+_ + 3*a*b*(2*B*c*d^2+4*A*c*d*e+a*B*e^2))*x^5+1/6*(b^3*e*(2*B*d+A*e)+_ + 3*b*c*(A*c*d^2+4*a*B*d*e+2*a*A*e^2)+3*b^2*(B*c*d^2+2*A*c*d*e+a*B*e^2)+_ + 3*a*c*(B*c*d^2+2*A*c*d*e+a*B*e^2))*x^6+1/7*(b^3*B*e^2+3*b^2*c*e*_ + (2*B*d+A*e)+c^2*(A*c*d^2+6*a*B*d*e+3*a*A*e^2)+3*b*c*(B*c*d^2+2*A*c*d*e+_ + 2*a*B*e^2))*x^7+1/8*c*(A*c*e*(2*c*d+3*b*e)+B*(c^2*d^2+3*b^2*e^2+_ + 3*c*e*(2*b*d+a*e)))*x^8+1/9*c^2*e*(2*B*c*d+3*b*B*e+A*c*e)*x^9+_ + 1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 8 4 4 8 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 7 7 7 7 +--R + +--R 6 6 2 6 2 1 3 3 2 2 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 1 2 2 +--R ((A a b + - B a )c + - A b + - B a b )e +--R 2 6 2 +--R + +--R 2 2 1 3 1 1 2 1 2 2 +--R (A a c + (A b + 2B a b)c + - B b )d e + ((- A b + - B a)c + - B b c)d +--R 3 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 3 2 3 2 2 +--R (- A a c + - A a b + - B a b)e +--R 5 5 5 +--R + +--R 12 6 2 2 3 6 2 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 1 3 2 3 2 3 2 3 2 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 4 4 2 2 2 +--R + +--R 3 3 2 1 3 3 2 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 1 3 2 2 2 3 2 2 2 2 3 +--R (- A a e + (2A a b + - B a )d e + (A a c + A a b + B a b)d )x +--R 3 3 +--R + +--R 3 3 2 1 3 2 2 3 2 +--R (A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 335 + +--S 336 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 8 4 4 8 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 7 7 7 7 +--R + +--R 6 6 2 6 2 1 3 3 2 2 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 1 2 2 +--R ((A a b + - B a )c + - A b + - B a b )e +--R 2 6 2 +--R + +--R 2 2 1 3 1 1 2 1 2 2 +--R (A a c + (A b + 2B a b)c + - B b )d e + ((- A b + - B a)c + - B b c)d +--R 3 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 3 2 3 2 2 +--R (- A a c + - A a b + - B a b)e +--R 5 5 5 +--R + +--R 12 6 2 2 3 6 2 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 1 3 2 3 2 3 2 3 2 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 4 4 2 2 2 +--R + +--R 3 3 2 1 3 3 2 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 1 3 2 2 2 3 2 2 2 2 3 +--R (- A a e + (2A a b + - B a )d e + (A a c + A a b + B a b)d )x +--R 3 3 +--R + +--R 3 3 2 1 3 2 2 3 2 +--R (A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 336 + +--S 337 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 337 + +--S 338 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 338 + +)clear all + +--S 339 of 1751 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 2 3 7 +--R B c e x + ((A c + 3B b c )e + B c d)x +--R + +--R 2 2 3 2 6 +--R (((3A b + 3B a)c + 3B b c)e + (A c + 3B b c )d)x +--R + +--R 2 2 3 2 2 5 +--R ((3A a c + (3A b + 6B a b)c + B b )e + ((3A b + 3B a)c + 3B b c)d)x +--R + +--R 2 3 2 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 2 2 2 2 3 2 3 +--R ((3A a c + 3A a b + 3B a b)e + ((6A a b + 3B a )c + A b + 3B a b )d)x +--R + +--R 2 3 2 2 2 2 +--R ((3A a b + B a )e + (3A a c + 3A a b + 3B a b)d)x +--R + +--R 3 2 3 3 +--R (A a e + (3A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 339 + +--S 340 of 1751 +r0:=a^3*A*d*x+1/2*a^2*(3*A*b*d+a*B*d+a*A*e)*x^2+1/3*a*(a*B*(3*b*d+a*e)+_ + 3*A*(b^2*d+a*c*d+a*b*e))*x^3+1/4*(3*a*B*(b^2*d+a*c*d+a*b*e)+A*(b^3*d+_ + 6*a*b*c*d+3*a*b^2*e+3*a^2*c*e))*x^4+1/5*(b^3*(B*d+A*e)+6*a*b*c*(B*d+_ + A*e)+3*b^2*(A*c*d+a*B*e)+3*a*c*(A*c*d+a*B*e))*x^5+1/6*(b^3*B*e+_ + 3*b^2*c*(B*d+A*e)+3*a*c^2*(B*d+A*e)+3*b*c*(A*c*d+2*a*B*e))*x^6+_ + 1/7*c*(3*b^2*B*e+3*b*c*(B*d+A*e)+c*(A*c*d+3*a*B*e))*x^7+_ + 1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 3 2 3 2 1 3 3 2 7 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 7 +--R + +--R 1 2 1 2 1 3 +--R (- A a c + (- A b + B a b)c + - B b )e +--R 2 2 6 +--R + +--R 1 1 2 1 2 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 6 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 3 2 +--R (- A a c + - A a b + - B a b)e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 2 1 3 2 2 2 3 +--R ((A a b + - B a )e + (A a c + A a b + B a b)d)x +--R 3 +--R + +--R 1 3 3 2 1 3 2 3 +--R (- A a e + (- A a b + - B a )d)x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 340 + +--S 341 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 3 2 3 2 1 3 3 2 7 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 7 +--R + +--R 1 2 1 2 1 3 +--R (- A a c + (- A b + B a b)c + - B b )e +--R 2 2 6 +--R + +--R 1 1 2 1 2 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 6 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 3 2 +--R (- A a c + - A a b + - B a b)e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 2 1 3 2 2 2 3 +--R ((A a b + - B a )e + (A a c + A a b + B a b)d)x +--R 3 +--R + +--R 1 3 3 2 1 3 2 3 +--R (- A a e + (- A a b + - B a )d)x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 341 + +--S 342 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 342 + +--S 343 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 343 + +)clear all + +--S 344 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 344 + +--S 345 of 1751 +r0:=a^3*A*x+1/2*a^2*(3*A*b+a*B)*x^2+a*(a*b*B+A*(b^2+a*c))*x^3+_ + 1/4*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^4+1/5*(b^3*B+3*A*b^2*c+_ + 6*a*b*B*c+3*a*A*c^2)*x^5+1/2*c*(b^2*B+A*b*c+a*B*c)*x^6+_ + 1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8 +--R +--R +--R (2) +--R 1 3 8 1 3 3 2 7 1 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + ((- A b + - B a)c + - B b c)x +--R 8 7 7 2 2 2 +--R + +--R 3 2 3 2 6 1 3 5 +--R (- A a c + (- A b + - B a b)c + - B b )x +--R 5 5 5 5 +--R + +--R 3 3 2 1 3 3 2 4 2 2 2 3 +--R ((- A a b + - B a )c + - A b + - B a b )x + (A a c + A a b + B a b)x +--R 2 4 4 4 +--R + +--R 3 2 1 3 2 3 +--R (- A a b + - B a )x + A a x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 345 + +--S 346 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 8 1 3 3 2 7 1 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + ((- A b + - B a)c + - B b c)x +--R 8 7 7 2 2 2 +--R + +--R 3 2 3 2 6 1 3 5 +--R (- A a c + (- A b + - B a b)c + - B b )x +--R 5 5 5 5 +--R + +--R 3 3 2 1 3 3 2 4 2 2 2 3 +--R ((- A a b + - B a )c + - A b + - B a b )x + (A a c + A a b + B a b)x +--R 2 4 4 4 +--R + +--R 3 2 1 3 2 3 +--R (- A a b + - B a )x + A a x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 346 + +--S 347 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 347 + +--S 348 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 348 + +)clear all + +--S 349 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 349 + +--S 350 of 1751 +r0:=-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*_ + (4*b*d-a*e)))*x/e^7-3/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*_ + (8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))*(d+e*x)^2/e^8-1/3*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^3/e^8-_ + 1/4*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^4/e^8-_ + 3/5*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*_ + (d+e*x)^5/e^8-1/6*c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^6/e^8+1/7*B*c^3*_ + (d+e*x)^7/e^8-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 3 6 +--R 420A a e + (- 1260A a b - 420B a )d e +--R + +--R 2 2 2 2 5 +--R (1260A a c + 1260A a b + 1260B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 2520A a b - 1260B a )c - 420A b - 1260B a b )d e +--R + +--R 2 2 3 4 3 +--R (1260A a c + (1260A b + 2520B a b)c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 1260A b - 1260B a)c - 1260B b c)d e + (420A c + 1260B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((252A b + 252B a)c + 252B b c)e + (- 84A c - 252B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (315A a c + (315A b + 630B a b)c + 105B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 315A b - 315B a)c - 315B b c)d e + (105A c + 315B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((840A a b + 420B a )c + 140A b + 420B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((420A b + 420B a)c + 420B b c)d e + (- 140A c - 420B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (630A a c + 630A a b + 630B a b)e +--R + +--R 2 3 2 6 +--R ((- 1260A a b - 630B a )c - 210A b - 630B a b )d e +--R + +--R 2 2 3 2 5 +--R (630A a c + (630A b + 1260B a b)c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 630A b - 630B a)c - 630B b c)d e + (210A c + 630B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (1260A a b + 420B a )e + (- 1260A a c - 1260A a b - 1260B a b)d e +--R + +--R 2 3 2 2 5 +--R ((2520A a b + 1260B a )c + 420A b + 1260B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 1260A a c + (- 1260A b - 2520B a b)c - 420B b )d e +--R + +--R 2 2 4 3 +--R ((1260A b + 1260B a)c + 1260B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 420A c - 1260B b c )d e + 420B c d e +--R * +--R x +--R + +--R 2 2 2 2 5 +--R (630A a c + 630A a b + 630B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 2940A a b - 1470B a )c - 490A b - 1470B a b )d e +--R + +--R 2 2 3 4 3 +--R (2415A a c + (2415A b + 4830B a b)c + 805B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 3423A b - 3423B a)c - 3423B b c)d e + (1491A c + 4473B b c )d e +--R + +--R 3 7 +--R - 1851B c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 2 3 6 +--R 420A a e + (- 1260A a b - 420B a )d e +--R + +--R 2 2 2 2 5 +--R (1260A a c + 1260A a b + 1260B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 2520A a b - 1260B a )c - 420A b - 1260B a b )d e +--R + +--R 2 2 3 4 3 +--R (1260A a c + (1260A b + 2520B a b)c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 1260A b - 1260B a)c - 1260B b c)d e + (420A c + 1260B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((252A b + 252B a)c + 252B b c)e + (- 84A c - 252B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (315A a c + (315A b + 630B a b)c + 105B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 315A b - 315B a)c - 315B b c)d e + (105A c + 315B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((840A a b + 420B a )c + 140A b + 420B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((420A b + 420B a)c + 420B b c)d e + (- 140A c - 420B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (630A a c + 630A a b + 630B a b)e +--R + +--R 2 3 2 6 +--R ((- 1260A a b - 630B a )c - 210A b - 630B a b )d e +--R + +--R 2 2 3 2 5 +--R (630A a c + (630A b + 1260B a b)c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 630A b - 630B a)c - 630B b c)d e + (210A c + 630B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (1260A a b + 420B a )e + (- 1260A a c - 1260A a b - 1260B a b)d e +--R + +--R 2 3 2 2 5 +--R ((2520A a b + 1260B a )c + 420A b + 1260B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 1260A a c + (- 1260A b - 2520B a b)c - 420B b )d e +--R + +--R 2 2 4 3 +--R ((1260A b + 1260B a)c + 1260B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 420A c - 1260B b c )d e + 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Union(Expression(Integer),...) +--E 351 + +--S 352 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 5 +--R (- 630A a c - 630A a b - 630B a b)d e +--R + +--R 2 3 2 3 4 +--R ((2940A a b + 1470B a )c + 490A b + 1470B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 2415A a c + (- 2415A b - 4830B a b)c - 805B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((3423A b + 3423B a)c + 3423B b c)d e + (- 1491A c - 4473B b c )d e +--R + +--R 3 7 +--R 1851B c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 353 + +)clear all + +--S 354 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 354 + +--S 355 of 1751 +r0:=-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*_ + (2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*x/e^7+(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x))-1/2*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*_ + (d+e*x)^2/e^8-1/3*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + (d+e*x)^3/e^8-3/4*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))*(d+e*x)^4/e^8-1/5*c^2*(7*B*c*d-3*b*B*e-A*c*e)*_ + (d+e*x)^5/e^8+1/6*B*c^3*(d+e*x)^6/e^8-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*_ + (2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 2 2 2 6 +--R (180A a b + 60B a )e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 2 5 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 4 3 +--R ((900A b + 900B a)c + 900B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 360A c - 1080B b c )d e + 420B c d e +--R * +--R x +--R + +--R 2 3 6 2 2 2 2 5 +--R (180A a b + 60B a )d e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 3 4 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((900A b + 900B a)c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((45A b + 45B a)c + 45B b c)e + (- 18A c - 54B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (60A a c + (60A b + 120B a b)c + 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 75A b - 75B a)c - 75B b c)d e + (30A c + 90B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((180A a b + 90B a )c + 30A b + 90B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((150A b + 150B a)c + 150B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 4 3 +--R 70B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (180A a c + 180A a b + 180B a b)e +--R + +--R 2 3 2 6 +--R ((- 540A a b - 270B a )c - 90A b - 270B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (180A a c + 180A a b + 180B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 540A a b - 270B a )c - 90A b - 270B a b )d e +--R + +--R 2 2 3 3 4 +--R (240A a c + (240A b + 480B a b)c + 80B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 75A b - 75B a)c - 75B b c)d e + (- 78A c - 234B b c )d e +--R + +--R 3 6 +--R 231B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (180A a b + 60B a )d e +--R + +--R 2 2 2 2 5 +--R (- 180A a c - 180A a b - 180B a b)d e +--R + +--R 2 3 2 3 4 +--R ((540A a b + 270B a )c + 90A b + 270B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 480A a c + (- 480A b - 960B a b)c - 160B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((825A b + 825B a)c + 825B b c)d e + (- 438A c - 1314B b c )d e +--R + +--R 3 7 +--R 651B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 355 + +--S 356 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 7 2 2 2 6 +--R (180A a b + 60B a )e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 2 5 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 4 3 +--R ((900A b + 900B a)c + 900B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 360A c - 1080B b c )d e + 420B c d e +--R * +--R x +--R + +--R 2 3 6 2 2 2 2 5 +--R (180A a b + 60B a )d e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 3 4 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((900A b + 900B a)c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((45A b + 45B a)c + 45B b c)e + (- 18A c - 54B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (60A a c + (60A b + 120B a b)c + 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 75A b - 75B a)c - 75B b c)d e + (30A c + 90B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((180A a b + 90B a )c + 30A b + 90B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((150A b + 150B a)c + 150B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 4 3 +--R 70B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (180A a c + 180A a b + 180B a b)e +--R + +--R 2 3 2 6 +--R ((- 540A a b - 270B a )c - 90A b - 270B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (180A a c + 180A a b + 180B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 720A a b - 360B a )c - 120A b - 360B a b )d e +--R + +--R 2 2 3 3 4 +--R (540A a c + (540A b + 1080B a b)c + 180B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 720A b - 720B a)c - 720B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 6 +--R - 360B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (180A a b + 60B a )d e +--R + +--R 2 2 2 2 5 +--R (- 180A a c - 180A a b - 180B a b)d e +--R + +--R 2 3 2 3 4 +--R ((360A a b + 180B a )c + 60A b + 180B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 180A a c + (- 180A b - 360B a b)c - 60B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((180A b + 180B a)c + 180B b c)d e + (- 60A c - 180B b c )d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 356 + +--S 357 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 4 +--R ((- 180A a b - 90B a )c - 30A b - 90B a b )d e +--R + +--R 2 2 3 3 3 +--R (300A a c + (300A b + 600B a b)c + 100B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R ((- 645A b - 645B a)c - 645B b c)d e + (378A c + 1134B b c )d e +--R + +--R 3 6 +--R - 591B c d +--R / +--R 8 +--R 60e +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 358 + +)clear all + +--S 359 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 359 + +--S 360 of 1751 +r0:=-(A*e*(10*c^3*d^3-b^3*e^3+3*b*c*e^2*(3*b*d-2*a*e)-9*c^2*d*e*(2*b*d-a*e))-_ + 3*B*(5*c^3*d^4-2*c^2*d^2*e*(5*b*d-3*a*e)-b^2*e^3*(b*d-a*e)+c*e^2*_ + (6*b^2*d^2-6*a*b*d*e+a^2*e^2)))*x/e^7-1/2*(B*(10*c^3*d^3-b^3*e^3+_ + 3*b*c*e^2*(3*b*d-2*a*e)-9*c^2*d*e*(2*b*d-a*e))-3*A*c*e*(2*c^2*d^2+_ + b^2*e^2-c*e*(3*b*d-a*e)))*x^2/e^6-c*(A*c*e*(c*d-b*e)-B*(2*c^2*d^2+_ + b^2*e^2-c*e*(3*b*d-a*e)))*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*_ + x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*_ + (d+e*x)^2)+(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-_ + e*(4*b*d-a*e)))/(e^8*(d+e*x))-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 2 7 +--R (60A a c + 60A a b + 60B a b)e +--R + +--R 2 3 2 6 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (300A c + 900B b c )d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 720A a b - 360B a )c - 120A b - 360B a b )d e +--R + +--R 2 2 3 3 4 +--R (720A a c + (720A b + 1440B a b)c + 240B b )d e +--R + +--R 2 2 4 3 +--R ((- 1200A b - 1200B a)c - 1200B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (600A c + 1800B b c )d e - 840B c d e +--R * +--R x +--R + +--R 2 2 2 2 5 +--R (60A a c + 60A a b + 60B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 4 3 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 600A b - 600B a)c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((20A b + 20B a)c + 20B b c)e + (- 10A c - 30B b c )d e +--R + +--R 3 2 5 +--R 14B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (30A a c + (30A b + 60B a b)c + 10B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 50A b - 50B a)c - 50B b c)d e + (25A c + 75B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((120A a b + 60B a )c + 20A b + 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((200A b + 200B a)c + 200B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((240A a b + 120B a )c + 40A b + 120B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 330A a c + (- 330A b - 660B a b)c - 110B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((630A b + 630B a)c + 630B b c)d e + (- 340A c - 1020B b c )d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 60A a b - 20B a )e + (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 240A a b - 120B a )c - 40A b - 120B a b )d e +--R + +--R 2 2 3 3 4 +--R (60A a c + (60A b + 120B a b)c + 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((60A b + 60B a)c + 60B b c)d e + (- 80A c - 240B b c )d e +--R + +--R 3 6 +--R 160B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 10A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (90A a c + 90A a b + 90B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 300A a b - 150B a )c - 50A b - 150B a b )d e +--R + +--R 2 2 3 4 3 +--R (210A a c + (210A b + 420B a b)c + 70B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 270A b - 270B a)c - 270B b c)d e + (110A c + 330B b c )d e +--R + +--R 3 7 +--R - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 7 +--R (60A a c + 60A a b + 60B a b)e +--R + +--R 2 3 2 6 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (300A c + 900B b c )d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 720A a b - 360B a )c - 120A b - 360B a b )d e +--R + +--R 2 2 3 3 4 +--R (720A a c + (720A b + 1440B a b)c + 240B b )d e +--R + +--R 2 2 4 3 +--R ((- 1200A b - 1200B a)c - 1200B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (600A c + 1800B b c )d e - 840B c d e +--R * +--R x +--R + +--R 2 2 2 2 5 +--R (60A a c + 60A a b + 60B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 4 3 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 600A b - 600B a)c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((20A b + 20B a)c + 20B b c)e + (- 10A c - 30B b c )d e +--R + +--R 3 2 5 +--R 14B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (30A a c + (30A b + 60B a b)c + 10B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 50A b - 50B a)c - 50B b c)d e + (25A c + 75B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((120A a b + 60B a )c + 20A b + 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((200A b + 200B a)c + 200B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((240A a b + 120B a )c + 40A b + 120B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 330A a c + (- 330A b - 660B a b)c - 110B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((630A b + 630B a)c + 630B b c)d e + (- 340A c - 1020B b c )d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 60A a b - 20B a )e + (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 240A a b - 120B a )c - 40A b - 120B a b )d e +--R + +--R 2 2 3 3 4 +--R (60A a c + (60A b + 120B a b)c + 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((60A b + 60B a)c + 60B b c)d e + (- 80A c - 240B b c )d e +--R + +--R 3 6 +--R 160B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 10A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (90A a c + 90A a b + 90B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 300A a b - 150B a )c - 50A b - 150B a b )d e +--R + +--R 2 2 3 4 3 +--R (210A a c + (210A b + 420B a b)c + 70B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 270A b - 270B a)c - 270B b c)d e + (110A c + 330B b c )d e +--R + +--R 3 7 +--R - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 361 + +--S 362 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 364 + +--S 365 of 1751 +r0:=-(B*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + A*c*e*(10*c^2*d^2+3*b^2*e^2-3*c*e*(4*b*d-a*e)))*x/e^7-1/2*c*(A*c*e*_ + (4*c*d-3*b*e)-B*(10*c^2*d^2+3*b^2*e^2-3*c*e*(4*b*d-a*e)))*x^2/e^6-_ + 1/3*c^2*(4*B*c*d-3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+_ + 1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^3)+1/2*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^2)+3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x))-(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+_ + 3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 2 7 +--R ((72A a b + 36B a )c + 12A b + 36B a b )e +--R + +--R 2 2 3 6 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 2 5 +--R ((360A b + 360B a)c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 3 4 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 5 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 4 3 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R x +--R + +--R 2 3 2 3 4 +--R ((72A a b + 36B a )c + 12A b + 36B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((360A b + 360B a)c + 360B b c)d e + (- 240A c - 720B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((18A b + 18B a)c + 18B b c)e + (- 12A c - 36B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 90A b - 90B a)c - 90B b c)d e + (60A c + 180B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (108A a c + (108A b + 216B a b)c + 36B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 378A b - 378B a)c - 378B b c)d e + (292A c + 876B b c )d e +--R + +--R 3 4 3 +--R - 556B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 36A a c - 36A a b - 36B a b)e +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 108A a c + (- 108A b - 216B a b)c - 36B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 54A b - 54B a)c - 54B b c)d e + (156A c + 468B b c )d e +--R + +--R 3 5 2 +--R - 408B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 18A a b - 6B a )e + (- 36A a c - 36A a b - 36B a b)d e +--R + +--R 2 3 2 2 5 +--R ((324A a b + 162B a )c + 54A b + 162B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 324A a c + (- 324A b - 648B a b)c - 108B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((486A b + 486B a)c + 486B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 6 +--R 222B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 6A a b - 2B a )d e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((132A a b + 66B a )c + 22A b + 66B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 156A a c + (- 156A b - 312B a b)c - 52B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((282A b + 282B a)c + 282B b c)d e + (- 148A c - 444B b c )d e +--R + +--R 3 7 +--R 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 7 +--R ((72A a b + 36B a )c + 12A b + 36B a b )e +--R + +--R 2 2 3 6 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 2 5 +--R ((360A b + 360B a)c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 3 4 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 5 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 4 3 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R x +--R + +--R 2 3 2 3 4 +--R ((72A a b + 36B a )c + 12A b + 36B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((360A b + 360B a)c + 360B b c)d e + (- 240A c - 720B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((18A b + 18B a)c + 18B b c)e + (- 12A c - 36B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 90A b - 90B a)c - 90B b c)d e + (60A c + 180B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (108A a c + (108A b + 216B a b)c + 36B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 378A b - 378B a)c - 378B b c)d e + (292A c + 876B b c )d e +--R + +--R 3 4 3 +--R - 556B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 36A a c - 36A a b - 36B a b)e +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 108A a c + (- 108A b - 216B a b)c - 36B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 54A b - 54B a)c - 54B b c)d e + (156A c + 468B b c )d e +--R + +--R 3 5 2 +--R - 408B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 18A a b - 6B a )e + (- 36A a c - 36A a b - 36B a b)d e +--R + +--R 2 3 2 2 5 +--R ((324A a b + 162B a )c + 54A b + 162B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 324A a c + (- 324A b - 648B a b)c - 108B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((486A b + 486B a)c + 486B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 6 +--R 222B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 6A a b - 2B a )d e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((132A a b + 66B a )c + 22A b + 66B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 156A a c + (- 156A b - 312B a b)c - 52B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((282A b + 282B a)c + 282B b c)d e + (- 148A c - 444B b c )d e +--R + +--R 3 7 +--R 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 366 + +--S 367 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 368 + +)clear all + +--S 369 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 369 + +--S 370 of 1751 +r0:=-c*(A*c*e*(5*c*d-3*b*e)-3*B*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*x/e^7-_ + 1/2*c^2*(5*B*c*d-3*b*B*e-A*c*e)*x^2/e^6+1/3*B*c^3*x^3/e^5+1/4*_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^4)+1/3*_ + (c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/_ + (e^8*(d+e*x)^3)+3/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*_ + (8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))/(e^8*(d+e*x)^2)+(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/_ + (e^8*(d+e*x))-(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (180A c + 540B b c )d e - 420B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 5 +--R (216A a c + (216A b + 432B a b)c + 72B b )d e +--R + +--R 2 2 3 4 +--R ((- 1080A b - 1080B a)c - 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (1080A c + 3240B b c )d e - 2520B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 4 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 4 3 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R x +--R + +--R 2 2 3 4 3 +--R (36A a c + (36A b + 72B a b)c + 12B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((6A c + 18B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((36A b + 36B a)c + 36B b c)e + (- 36A c - 108B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 3 2 2 5 +--R ((144A b + 144B a)c + 144B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 3 4 +--R 556B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )e +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 144A b - 144B a)c - 144B b c)d e + (- 96A c - 288B b c )d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 18A a c - 18A a b - 18B a b)e +--R + +--R 2 3 2 6 +--R ((- 108A a b - 54B a )c - 18A b - 54B a b )d e +--R + +--R 2 2 3 2 5 +--R (324A a c + (324A b + 648B a b)c + 108B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 756A b - 756B a)c - 756B b c)d e + (396A c + 1188B b c )d e +--R + +--R 3 5 2 +--R - 444B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 12A a b - 4B a )e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )d e +--R + +--R 2 2 3 3 4 +--R (264A a c + (264A b + 528B a b)c + 88B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 744A b - 744B a)c - 744B b c)d e + (504A c + 1512B b c )d e +--R + +--R 3 6 +--R - 856B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 3A a e + (- 3A a b - B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (75A a c + (75A b + 150B a b)c + 25B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 231A b - 231B a)c - 231B b c)d e + (171A c + 513B b c )d e +--R + +--R 3 7 +--R - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (180A c + 540B b c )d e - 420B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 5 +--R (216A a c + (216A b + 432B a b)c + 72B b )d e +--R + +--R 2 2 3 4 +--R ((- 1080A b - 1080B a)c - 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (1080A c + 3240B b c )d e - 2520B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 4 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 4 3 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R x +--R + +--R 2 2 3 4 3 +--R (36A a c + (36A b + 72B a b)c + 12B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((6A c + 18B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((36A b + 36B a)c + 36B b c)e + (- 36A c - 108B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 3 2 2 5 +--R ((144A b + 144B a)c + 144B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 3 4 +--R 556B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )e +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 144A b - 144B a)c - 144B b c)d e + (- 96A c - 288B b c )d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 18A a c - 18A a b - 18B a b)e +--R + +--R 2 3 2 6 +--R ((- 108A a b - 54B a )c - 18A b - 54B a b )d e +--R + +--R 2 2 3 2 5 +--R (324A a c + (324A b + 648B a b)c + 108B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 756A b - 756B a)c - 756B b c)d e + (396A c + 1188B b c )d e +--R + +--R 3 5 2 +--R - 444B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 12A a b - 4B a )e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )d e +--R + +--R 2 2 3 3 4 +--R (264A a c + (264A b + 528B a b)c + 88B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 744A b - 744B a)c - 744B b c)d e + (504A c + 1512B b c )d e +--R + +--R 3 6 +--R - 856B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 3A a e + (- 3A a b - B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (75A a c + (75A b + 150B a b)c + 25B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 231A b - 231B a)c - 231B b c)d e + (171A c + 513B b c )d e +--R + +--R 3 7 +--R - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 371 + +--S 372 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 373 + +)clear all + +--S 374 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^6 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 374 + +--S 375 of 1751 +r0:=-c^2*(6*B*c*d-3*b*B*e-A*c*e)*x/e^7+1/2*B*c^3*x^2/e^6+1/5*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^5)+1/4*(c*d^2-b*d*e+a*e^2)^2*_ + (3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^4)+_ + (c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*_ + (2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^3)+_ + 1/2*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+_ + 3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^2)+_ + (B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-_ + 3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x))-_ + 3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 7 3 2 6 +--R ((60A b + 60B a)c + 60B b c)e + (- 120A c - 360B b c )d e +--R + +--R 3 2 5 +--R 420B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 5 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 3 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 2 6 +--R ((60A b + 60B a)c + 60B b c)d e + (- 120A c - 360B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((20A c + 60B b c )e - 70B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((100A c + 300B b c )d e - 500B c d e )x +--R + +--R 2 2 3 7 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((300A b + 300B a)c + 300B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 3 4 +--R - 400B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((900A b + 900B a)c + 900B b c)d e + (- 800A c - 2400B b c )d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 20A a c - 20A a b - 20B a b)e +--R + +--R 2 3 2 6 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 3 4 +--R ((1100A b + 1100B a)c + 1100B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 15A a b - 5B a )e + (- 10A a c - 10A a b - 10B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 30A a b - 15B a )c - 5A b - 15B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((625A b + 625B a)c + 625B b c)d e + (- 750A c - 2250B b c )d e +--R + +--R 3 6 +--R 1875B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 3A a b - B a )d e + (- 2A a c - 2A a b - 2B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((137A b + 137B a)c + 137B b c)d e + (- 174A c - 522B b c )d e +--R + +--R 3 7 +--R 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 7 3 2 6 +--R ((60A b + 60B a)c + 60B b c)e + (- 120A c - 360B b c )d e +--R + +--R 3 2 5 +--R 420B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 5 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 3 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 2 6 +--R ((60A b + 60B a)c + 60B b c)d e + (- 120A c - 360B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((20A c + 60B b c )e - 70B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((100A c + 300B b c )d e - 500B c d e )x +--R + +--R 2 2 3 7 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((300A b + 300B a)c + 300B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 3 4 +--R - 400B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((900A b + 900B a)c + 900B b c)d e + (- 800A c - 2400B b c )d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 20A a c - 20A a b - 20B a b)e +--R + +--R 2 3 2 6 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 3 4 +--R ((1100A b + 1100B a)c + 1100B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 15A a b - 5B a )e + (- 10A a c - 10A a b - 10B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 30A a b - 15B a )c - 5A b - 15B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((625A b + 625B a)c + 625B b c)d e + (- 750A c - 2250B b c )d e +--R + +--R 3 6 +--R 1875B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 3A a b - B a )d e + (- 2A a c - 2A a b - 2B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((137A b + 137B a)c + 137B b c)d e + (- 174A c - 522B b c )d e +--R + +--R 3 7 +--R 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 376 + +--S 377 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^7 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 379 + +--S 380 of 1751 +r0:=B*c^3*x/e^7+1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^6)+_ + 1/5*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-_ + a*e)))/(e^8*(d+e*x)^5)+3/4*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^4)+1/3*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/_ + (e^8*(d+e*x)^3)+1/2*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/_ + (e^8*(d+e*x)^2)+3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x))-c^2*(7*B*c*d-3*b*B*e-A*c*e)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 7 3 6 6 +--R ((60A c + 180B b c )e - 420B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((360A c + 1080B b c )d e - 2520B c d e )x +--R + +--R 3 2 2 5 3 3 4 4 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 3 4 3 4 3 3 +--R ((1200A c + 3600B b c )d e - 8400B c d e )x +--R + +--R 3 2 4 3 3 5 2 2 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 5 2 3 6 3 2 6 +--R ((360A c + 1080B b c )d e - 2520B c d e)x + (60A c + 180B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 2 7 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)e + (360A c + 1080B b c )d e +--R + +--R 3 2 5 +--R - 360B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1350A c + 4050B b c )d e +--R + +--R 3 3 4 +--R - 4050B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 120A a b - 60B a )c - 20A b - 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e + (2200A c + 6600B b c )d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 45A a c - 45A a b - 45B a b)e +--R + +--R 2 3 2 6 +--R ((- 90A a b - 45B a )c - 15A b - 45B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1875A c + 5625B b c )d e +--R + +--R 3 5 2 +--R - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 36A a b - 12B a )e + (- 18A a c - 18A a b - 18B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 36A a b - 18B a )c - 6A b - 18B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 36A a c + (- 36A b - 72B a b)c - 12B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 180A b - 180B a)c - 180B b c)d e + (822A c + 2466B b c )d e +--R + +--R 3 6 +--R - 3594B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 10A a e + (- 6A a b - 2B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 6A a c + (- 6A b - 12B a b)c - 2B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 30A b - 30B a)c - 30B b c)d e + (147A c + 441B b c )d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 7 3 6 6 +--R ((60A c + 180B b c )e - 420B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((360A c + 1080B b c )d e - 2520B c d e )x +--R + +--R 3 2 2 5 3 3 4 4 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 3 4 3 4 3 3 +--R ((1200A c + 3600B b c )d e - 8400B c d e )x +--R + +--R 3 2 4 3 3 5 2 2 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 5 2 3 6 3 2 6 +--R ((360A c + 1080B b c )d e - 2520B c d e)x + (60A c + 180B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 2 7 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)e + (360A c + 1080B b c )d e +--R + +--R 3 2 5 +--R - 360B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1350A c + 4050B b c )d e +--R + +--R 3 3 4 +--R - 4050B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 120A a b - 60B a )c - 20A b - 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e + (2200A c + 6600B b c )d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 45A a c - 45A a b - 45B a b)e +--R + +--R 2 3 2 6 +--R ((- 90A a b - 45B a )c - 15A b - 45B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1875A c + 5625B b c )d e +--R + +--R 3 5 2 +--R - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 36A a b - 12B a )e + (- 18A a c - 18A a b - 18B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 36A a b - 18B a )c - 6A b - 18B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 36A a c + (- 36A b - 72B a b)c - 12B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 180A b - 180B a)c - 180B b c)d e + (822A c + 2466B b c )d e +--R + +--R 3 6 +--R - 3594B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 10A a e + (- 6A a b - 2B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 6A a c + (- 6A b - 12B a b)c - 2B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 30A b - 30B a)c - 30B b c)d e + (147A c + 441B b c )d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 383 + +)clear all + +--S 384 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^8 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 384 + +--S 385 of 1751 +r0:=1/7*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^7)+1/6*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+3/5*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^5)+1/4*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^4)+_ + 1/3*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^3)+3/2*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x)^2)+c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*_ + (d+e*x))+B*c^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 2 7 3 6 6 +--R ((- 420A c - 1260B b c )e + 2940B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((- 630A b - 630B a)c - 630B b c)e + (- 1260A c - 3780B b c )d e +--R + +--R 3 2 5 +--R 13230B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )e +--R + +--R 2 2 6 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 2100A c - 6300B b c )d e + 26950B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 630A a b - 315B a )c - 105A b - 315B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 2100A c - 6300B b c )d e + 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 252A a c - 252A a b - 252B a b)e +--R + +--R 2 3 2 6 +--R ((- 378A a b - 189B a )c - 63A b - 189B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 252A a c + (- 252A b - 504B a b)c - 84B b )d e +--R + +--R 2 2 3 4 +--R ((- 630A b - 630B a)c - 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1260A c - 3780B b c )d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 210A a b - 70B a )e + (- 84A a c - 84A a b - 84B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 126A a b - 63B a )c - 21A b - 63B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 84A a c + (- 84A b - 168B a b)c - 28B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 210A b - 210B a)c - 210B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 7203B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 30A b - 30B a)c - 30B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 7 +--R 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 2 7 3 6 6 +--R ((- 420A c - 1260B b c )e + 2940B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((- 630A b - 630B a)c - 630B b c)e + (- 1260A c - 3780B b c )d e +--R + +--R 3 2 5 +--R 13230B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )e +--R + +--R 2 2 6 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 2100A c - 6300B b c )d e + 26950B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 630A a b - 315B a )c - 105A b - 315B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 2100A c - 6300B b c )d e + 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 252A a c - 252A a b - 252B a b)e +--R + +--R 2 3 2 6 +--R ((- 378A a b - 189B a )c - 63A b - 189B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 252A a c + (- 252A b - 504B a b)c - 84B b )d e +--R + +--R 2 2 3 4 +--R ((- 630A b - 630B a)c - 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1260A c - 3780B b c )d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 210A a b - 70B a )e + (- 84A a c - 84A a b - 84B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 126A a b - 63B a )c - 21A b - 63B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 84A a c + (- 84A b - 168B a b)c - 28B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 210A b - 210B a)c - 210B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 7203B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 30A b - 30B a)c - 30B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 7 +--R 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 388 + +)clear all + +--S 389 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^9 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 389 + +--S 390 of 1751 +r0:=1/8*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^8)+1/7*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^7)+1/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+1/5*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^5)+_ + 1/4*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-_ + a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^4)+c*_ + (A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*_ + (d+e*x)^3)+1/2*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^2)-B*c^3/_ + (e^8*(d+e*x)) +--R +--R +--R (2) +--R 3 7 7 1 3 3 2 7 7 3 6 6 +--R - B c e x + ((- - A c - - B b c )e - - B c d e )x +--R 2 2 2 +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R (((- A b - B a)c - B b c)e + (- A c - 3B b c )d e - 7B c d e )x +--R + +--R 3 2 3 2 3 1 3 7 +--R (- - A a c + (- - A b - - B a b)c - - B b )e +--R 4 4 2 4 +--R + +--R 5 5 2 5 2 6 5 3 15 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - -- B b c )d e +--R 4 4 4 4 4 +--R + +--R 35 3 3 4 +--R - -- B c d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 6 3 2 1 3 3 2 7 +--R ((- - A a b - - B a )c - - A b - - B a b )e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 6 +--R (- - A a c + (- - A b - - B a b)c - - B b )d e +--R 5 5 5 5 +--R + +--R 2 2 2 5 3 2 3 4 3 4 3 +--R ((- A b - B a)c - B b c)d e + (- A c - 3B b c )d e - 7B c d e +--R * +--R 3 +--R x +--R + +--R 1 2 1 2 1 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 2 2 2 +--R + +--R 3 3 2 1 3 3 2 6 +--R ((- - A a b - -- B a )c - -- A b - -- B a b )d e +--R 5 10 10 10 +--R + +--R 3 2 3 2 3 1 3 2 5 +--R (- -- A a c + (- -- A b - - B a b)c - -- B b )d e +--R 10 10 5 10 +--R + +--R 1 1 2 1 2 3 4 1 3 3 2 4 3 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 2 2 2 2 2 +--R + +--R 7 3 5 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 3 2 1 3 7 1 2 1 2 1 2 6 +--R (- - A a b - - B a )e + (- - A a c - - A a b - - B a b)d e +--R 7 7 7 7 7 +--R + +--R 6 3 2 1 3 3 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 35 35 35 35 +--R + +--R 3 2 3 2 6 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 35 35 35 35 +--R + +--R 1 1 2 1 2 4 3 1 3 3 2 5 2 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 7 7 7 7 7 +--R + +--R 3 6 +--R - B c d e +--R * +--R x +--R + +--R 1 3 7 3 2 1 3 6 +--R - - A a e + (- -- A a b - -- B a )d e +--R 8 56 56 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 56 56 56 +--R + +--R 3 3 2 1 3 3 2 3 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 280 280 +--R + +--R 3 2 3 2 3 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 280 280 140 280 +--R + +--R 1 1 2 1 2 5 2 1 3 3 2 6 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 56 56 56 56 56 +--R + +--R 1 3 7 +--R - - B c d +--R 8 +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 10 2 7 9 8 8 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 390 + +--S 391 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 2 7 3 6 6 +--R - 280B c e x + ((- 140A c - 420B b c )e - 980B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((- 280A b - 280B a)c - 280B b c)e + (- 280A c - 840B b c )d e +--R + +--R 3 2 5 +--R - 1960B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 210A a c + (- 210A b - 420B a b)c - 70B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 350A b - 350B a)c - 350B b c)d e + (- 350A c - 1050B b c )d e +--R + +--R 3 3 4 +--R - 2450B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 336A a b - 168B a )c - 56A b - 168B a b )e +--R + +--R 2 2 3 6 +--R (- 168A a c + (- 168A b - 336B a b)c - 56B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 280A b - 280B a)c - 280B b c)d e + (- 280A c - 840B b c )d e +--R + +--R 3 4 3 +--R - 1960B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 140A a c - 140A a b - 140B a b)e +--R + +--R 2 3 2 6 +--R ((- 168A a b - 84B a )c - 28A b - 84B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 84A a c + (- 84A b - 168B a b)c - 28B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 140A b - 140B a)c - 140B b c)d e + (- 140A c - 420B b c )d e +--R + +--R 3 5 2 +--R - 980B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 120A a b - 40B a )e + (- 40A a c - 40A a b - 40B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 48A a b - 24B a )c - 8A b - 24B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 24A a c + (- 24A b - 48B a b)c - 8B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 40A b - 40B a)c - 40B b c)d e + (- 40A c - 120B b c )d e +--R + +--R 3 6 +--R - 280B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 35A a e + (- 15A a b - 5B a )d e + (- 5A a c - 5A a b - 5B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 3A a c + (- 3A b - 6B a b)c - B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 5A b - 5B a)c - 5B b c)d e + (- 5A c - 15B b c )d e - 35B c d +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 +--R 280e x + 2240d e x + 7840d e x + 15680d e x + 19600d e x +--R + +--R 5 11 3 6 10 2 7 9 8 8 +--R 15680d e x + 7840d e x + 2240d e x + 280d e +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^10 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 394 + +--S 395 of 1751 +r0:=1/9*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^9)+1/8*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^8)+_ + 3/7*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^7)+_ + 1/6*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^6)+1/5*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^5)+3/4*c*(A*c*e*_ + (2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*(d+e*x)^4)+_ + 1/3*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^3)-1/2*B*c^3/(e^8*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 7 7 1 3 2 7 7 3 6 6 +--R - - B c e x + ((- - A c - B b c )e - - B c d e )x +--R 2 3 6 +--R + +--R 3 3 2 3 2 7 1 3 3 2 6 +--R ((- - A b - - B a)c - - B b c)e + (- - A c - - B b c )d e +--R 4 4 4 2 2 +--R + +--R 7 3 2 5 +--R - - B c d e +--R 4 +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 6 1 3 7 +--R (- - A a c + (- - A b - - B a b)c - - B b )e +--R 5 5 5 5 +--R + +--R 3 3 2 3 2 6 1 3 3 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 4 4 4 2 2 +--R + +--R 7 3 3 4 +--R - - B c d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 1 2 1 3 1 2 7 +--R ((- A a b - - B a )c - - A b - - B a b )e +--R 2 6 2 +--R + +--R 2 2 2 2 4 2 3 6 +--R (- - A a c + (- - A b - - B a b)c - -- B b )d e +--R 5 5 5 15 +--R + +--R 1 1 2 1 2 2 5 1 3 2 3 4 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - B b c )d e +--R 2 2 2 3 +--R + +--R 7 3 4 3 +--R - - B c d e +--R 6 +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 3 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 7 7 7 +--R + +--R 3 3 2 1 3 3 2 6 +--R ((- - A a b - -- B a )c - -- A b - -- B a b )d e +--R 7 14 14 14 +--R + +--R 6 2 6 2 12 2 3 2 5 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 35 35 35 35 +--R + +--R 3 3 2 3 2 3 4 1 3 3 2 4 3 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- - A c - - B b c )d e +--R 14 14 14 7 7 +--R + +--R 1 3 5 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 3 2 1 3 7 3 2 3 2 3 2 6 +--R (- - A a b - - B a )e + (- -- A a c - -- A a b - -- B a b)d e +--R 8 8 28 28 28 +--R + +--R 3 3 2 1 3 3 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 28 56 56 56 +--R + +--R 3 2 3 2 3 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 70 70 35 70 +--R + +--R 3 3 2 3 2 4 3 1 3 3 2 5 2 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 56 56 56 28 28 +--R + +--R 1 3 6 +--R - - B c d e +--R 8 +--R * +--R x +--R + +--R 1 3 7 1 2 1 3 6 +--R - - A a e + (- -- A a b - -- B a )d e +--R 9 24 72 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 84 84 84 +--R + +--R 1 1 2 1 3 1 2 3 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 84 168 504 168 +--R + +--R 1 2 1 2 1 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 210 210 105 630 +--R + +--R 1 1 2 1 2 5 2 1 3 1 2 6 +--R ((- --- A b - --- B a)c - --- B b c)d e + (- --- A c - -- B b c )d e +--R 168 168 168 252 84 +--R + +--R 1 3 7 +--R - -- B c d +--R 72 +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 5 12 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 11 3 7 10 2 8 9 9 8 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 395 + +--S 396 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 2 7 3 6 6 +--R - 1260B c e x + ((- 840A c - 2520B b c )e - 2940B c d e )x +--R + +--R 2 2 7 +--R ((- 1890A b - 1890B a)c - 1890B b c)e +--R + +--R 3 2 6 3 2 5 +--R (- 1260A c - 3780B b c )d e - 4410B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 1512A a c + (- 1512A b - 3024B a b)c - 504B b )e +--R + +--R 2 2 6 +--R ((- 1890A b - 1890B a)c - 1890B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 1260A c - 3780B b c )d e - 4410B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 2520A a b - 1260B a )c - 420A b - 1260B a b )e +--R + +--R 2 2 3 6 +--R (- 1008A a c + (- 1008A b - 2016B a b)c - 336B b )d e +--R + +--R 2 2 2 5 +--R ((- 1260A b - 1260B a)c - 1260B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 840A c - 2520B b c )d e - 2940B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 1080A a c - 1080A a b - 1080B a b)e +--R + +--R 2 3 2 6 +--R ((- 1080A a b - 540B a )c - 180A b - 540B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 540A b - 540B a)c - 540B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 5 2 +--R - 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 945A a b - 315B a )e + (- 270A a c - 270A a b - 270B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 270A a b - 135B a )c - 45A b - 135B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 108A a c + (- 108A b - 216B a b)c - 36B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 135A b - 135B a)c - 135B b c)d e + (- 90A c - 270B b c )d e +--R + +--R 3 6 +--R - 315B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 280A a e + (- 105A a b - 35B a )d e +--R + +--R 2 2 2 2 5 +--R (- 30A a c - 30A a b - 30B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 30A a b - 15B a )c - 5A b - 15B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 15A b - 15B a)c - 15B b c)d e + (- 10A c - 30B b c )d e - 35B c d +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 +--R 2520e x + 22680d e x + 90720d e x + 211680d e x + 317520d e x +--R + +--R 5 12 4 6 11 3 7 10 2 8 9 9 8 +--R 317520d e x + 211680d e x + 90720d e x + 22680d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 398 + +)clear all + +--S 399 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^11 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 399 + +--S 400 of 1751 +r0:=1/10*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^10)+1/9*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^9)+3/8*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^8)+1/7*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^7)+_ + 1/6*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+3/5*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x)^5)+1/4*c^2*(7*B*c*d-3*b*B*e-A*c*e)/_ + (e^8*(d+e*x)^4)-1/3*B*c^3/(e^8*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 7 7 1 3 3 2 7 7 3 6 6 +--R - - B c e x + ((- - A c - - B b c )e - -- B c d e )x +--R 3 4 4 12 +--R + +--R 3 3 2 3 2 7 3 3 9 2 6 +--R ((- - A b - - B a)c - - B b c)e + (- -- A c - -- B b c )d e +--R 5 5 5 10 10 +--R + +--R 7 3 2 5 +--R - -- B c d e +--R 10 +--R * +--R 5 +--R x +--R + +--R 1 2 1 2 1 3 7 +--R (- - A a c + (- - A b - B a b)c - - B b )e +--R 2 2 6 +--R + +--R 1 1 2 1 2 6 1 3 3 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 2 2 2 4 4 +--R + +--R 7 3 3 4 +--R - -- B c d e +--R 12 +--R * +--R 4 +--R x +--R + +--R 6 3 2 1 3 3 2 7 +--R ((- - A a b - - B a )c - - A b - - B a b )e +--R 7 7 7 7 +--R + +--R 2 2 2 2 4 2 3 6 +--R (- - A a c + (- - A b - - B a b)c - -- B b )d e +--R 7 7 7 21 +--R + +--R 2 2 2 2 2 2 5 1 3 3 2 3 4 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 7 7 7 7 7 +--R + +--R 1 3 4 3 +--R - - B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 3 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 8 8 8 +--R + +--R 9 9 2 3 3 9 2 6 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 28 56 56 56 +--R + +--R 3 2 3 2 3 1 3 2 5 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 28 28 14 28 +--R + +--R 3 3 2 3 2 3 4 3 3 9 2 4 3 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 28 28 28 56 56 +--R + +--R 1 3 5 2 +--R - - B c d e +--R 8 +--R * +--R 2 +--R x +--R + +--R 1 2 1 3 7 1 2 1 2 1 2 6 +--R (- - A a b - - B a )e + (- -- A a c - -- A a b - -- B a b)d e +--R 3 9 12 12 12 +--R + +--R 1 1 2 1 3 1 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 14 28 84 28 +--R + +--R 1 2 1 2 1 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - --- B b )d e +--R 42 42 21 126 +--R + +--R 1 1 2 1 2 4 3 1 3 1 2 5 2 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 42 42 42 84 28 +--R + +--R 1 3 6 +--R - -- B c d e +--R 36 +--R * +--R x +--R + +--R 1 3 7 1 2 1 3 6 +--R - -- A a e + (- -- A a b - -- B a )d e +--R 10 30 90 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- --- A a c - --- A a b - --- B a b)d e +--R 120 120 120 +--R + +--R 1 1 2 1 3 1 2 3 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 840 280 +--R + +--R 1 2 1 2 1 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - ---- B b )d e +--R 420 420 210 1260 +--R + +--R 1 1 2 1 2 5 2 1 3 1 2 6 +--R ((- --- A b - --- B a)c - --- B b c)d e + (- --- A c - --- B b c )d e +--R 420 420 420 840 280 +--R + +--R 1 3 7 +--R - --- B c d +--R 360 +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 5 13 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 12 4 7 11 3 8 10 2 9 9 10 8 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 400 + +--S 401 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 2 7 3 6 6 +--R - 840B c e x + ((- 630A c - 1890B b c )e - 1470B c d e )x +--R + +--R 2 2 7 +--R ((- 1512A b - 1512B a)c - 1512B b c)e +--R + +--R 3 2 6 3 2 5 +--R (- 756A c - 2268B b c )d e - 1764B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 1260A a c + (- 1260A b - 2520B a b)c - 420B b )e +--R + +--R 2 2 6 +--R ((- 1260A b - 1260B a)c - 1260B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 630A c - 1890B b c )d e - 1470B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 2160A a b - 1080B a )c - 360A b - 1080B a b )e +--R + +--R 2 2 3 6 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 720A b - 720B a)c - 720B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 4 3 +--R - 840B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 945A a c - 945A a b - 945B a b)e +--R + +--R 2 3 2 6 +--R ((- 810A a b - 405B a )c - 135A b - 405B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 270A a c + (- 270A b - 540B a b)c - 90B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 270A b - 270B a)c - 270B b c)d e + (- 135A c - 405B b c )d e +--R + +--R 3 5 2 +--R - 315B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 840A a b - 280B a )e + (- 210A a c - 210A a b - 210B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 180A a b - 90B a )c - 30A b - 90B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 60A b - 60B a)c - 60B b c)d e + (- 30A c - 90B b c )d e +--R + +--R 3 6 +--R - 70B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 252A a e + (- 84A a b - 28B a )d e +--R + +--R 2 2 2 2 5 +--R (- 21A a c - 21A a b - 21B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 6A a c + (- 6A b - 12B a b)c - 2B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 6A b - 6B a)c - 6B b c)d e + (- 3A c - 9B b c )d e - 7B c d +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 +--R 2520e x + 25200d e x + 113400d e x + 302400d e x + 529200d e x +--R + +--R 5 13 5 6 12 4 7 11 3 8 10 2 +--R 635040d e x + 529200d e x + 302400d e x + 113400d e x +--R + +--R 9 9 10 8 +--R 25200d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 403 + +)clear all + +--S 404 of 1751 +t0:=(e*x)^m*(A+B*x) +--R +--R +--R m +--R (1) (B x + A)(e x) +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1751 +r0:=A*(e*x)^(1+m)/(e*(1+m))+B*(e*x)^(2+m)/(e^2*(2+m)) +--R +--R +--R m + 2 m + 1 +--R (B m + B)(e x) + (A e m + 2A e)(e x) +--R (2) ---------------------------------------------- +--R 2 2 2 2 +--R e m + 3e m + 2e +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 2 m log(e x) +--R ((B m + B)x + (A m + 2A)x)%e +--R (3) --------------------------------------- +--R 2 +--R m + 3m + 2 +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 m log(e x) m + 2 +--R ((B e m + B e )x + (A e m + 2A e )x)%e + (- B m - B)(e x) +--R + +--R m + 1 +--R (- A e m - 2A e)(e x) +--R / +--R 2 2 2 2 +--R e m + 3e m + 2e +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 1751 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + (A b + B a)x + A a)(e x) +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1751 +r0:=a*A*(e*x)^(1+m)/(e*(1+m))+(A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+(b*B+A*c)*_ + (e*x)^(3+m)/(e^3*(3+m))+B*c*(e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x) +--R + +--R 3 2 +--R (A c + B b)e m + (7A c + 7B b)e m + (14A c + 14B b)e m +--R + +--R (8A c + 8B b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 2 2 2 +--R (A b + B a)e m + (8A b + 8B a)e m + (19A b + 19B a)e m +--R + +--R 2 +--R (12A b + 12B a)e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 3 3 2 3 3 m + 1 +--R (A a e m + 9A a e m + 26A a e m + 24A a e )(e x) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 +--R (B c m + 6B c m + 11B c m + 6B c)x +--R + +--R 3 2 3 +--R ((A c + B b)m + (7A c + 7B b)m + (14A c + 14B b)m + 8A c + 8B b)x +--R + +--R 3 2 2 +--R ((A b + B a)m + (8A b + 8B a)m + (19A b + 19B a)m + 12A b + 12B a)x +--R + +--R 3 2 +--R (A a m + 9A a m + 26A a m + 24A a)x +--R * +--R m log(e x) +--R %e +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 4 2 4 +--R (A c + B b)e m + (7A c + 7B b)e m + (14A c + 14B b)e m +--R + +--R 4 +--R (8A c + 8B b)e +--R * +--R 3 +--R x +--R + +--R 4 3 4 2 4 +--R (A b + B a)e m + (8A b + 8B a)e m + (19A b + 19B a)e m +--R + +--R 4 +--R (12A b + 12B a)e +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 4 4 +--R (A a e m + 9A a e m + 26A a e m + 24A a e )x +--R * +--R m log(e x) +--R %e +--R + +--R 3 2 m + 4 +--R (- B c m - 6B c m - 11B c m - 6B c)(e x) +--R + +--R 3 2 +--R (- A c - B b)e m + (- 7A c - 7B b)e m + (- 14A c - 14B b)e m +--R + +--R (- 8A c - 8B b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 2 2 2 +--R (- A b - B a)e m + (- 8A b - 8B a)e m + (- 19A b - 19B a)e m +--R + +--R 2 +--R (- 12A b - 12B a)e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- A a e m - 9A a e m - 26A a e m - 24A a e )(e x) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 413 + +)clear all + +--S 414 of 1751 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R * +--R m +--R (e x) +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1751 +r0:=a^2*A*(e*x)^(1+m)/(e*(1+m))+a*(2*A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+_ + (2*a*b*B+A*(b^2+2*a*c))*(e*x)^(3+m)/(e^3*(3+m))+(b^2*B+2*A*b*c+2*a*B*c)*_ + (e*x)^(4+m)/(e^4*(4+m))+c*(2*b*B+A*c)*(e*x)^(5+m)/(e^5*(5+m))+_ + B*c^2*(e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 m + 6 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c )(e x) +--R + +--R 2 5 2 4 +--R (A c + 2B b c)e m + (16A c + 32B b c)e m +--R + +--R 2 3 2 2 +--R (95A c + 190B b c)e m + (260A c + 520B b c)e m +--R + +--R 2 2 +--R (324A c + 648B b c)e m + (144A c + 288B b c)e +--R * +--R m + 5 +--R (e x) +--R + +--R 2 2 5 2 2 4 +--R ((2A b + 2B a)c + B b )e m + ((34A b + 34B a)c + 17B b )e m +--R + +--R 2 2 3 +--R ((214A b + 214B a)c + 107B b )e m +--R + +--R 2 2 2 +--R ((614A b + 614B a)c + 307B b )e m +--R + +--R 2 2 2 2 +--R ((792A b + 792B a)c + 396B b )e m + ((360A b + 360B a)c + 180B b )e +--R * +--R m + 4 +--R (e x) +--R + +--R 2 3 5 2 3 4 +--R (2A a c + A b + 2B a b)e m + (36A a c + 18A b + 36B a b)e m +--R + +--R 2 3 3 +--R (242A a c + 121A b + 242B a b)e m +--R + +--R 2 3 2 +--R (744A a c + 372A b + 744B a b)e m +--R + +--R 2 3 +--R (1016A a c + 508A b + 1016B a b)e m +--R + +--R 2 3 +--R (480A a c + 240A b + 480B a b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 4 5 2 4 4 +--R (2A a b + B a )e m + (38A a b + 19B a )e m +--R + +--R 2 4 3 2 4 2 +--R (274A a b + 137B a )e m + (922A a b + 461B a )e m +--R + +--R 2 4 2 4 +--R (1404A a b + 702B a )e m + (720A a b + 360B a )e +--R * +--R m + 2 +--R (e x) +--R + +--R 2 5 5 2 5 4 2 5 3 2 5 2 2 5 +--R A a e m + 20A a e m + 155A a e m + 580A a e m + 1044A a e m +--R + +--R 2 5 +--R 720A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 2 3 2 2 2 2 6 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c )x +--R + +--R 2 5 2 4 2 3 +--R (A c + 2B b c)m + (16A c + 32B b c)m + (95A c + 190B b c)m +--R + +--R 2 2 2 2 +--R (260A c + 520B b c)m + (324A c + 648B b c)m + 144A c + 288B b c +--R * +--R 5 +--R x +--R + +--R 2 5 2 4 +--R ((2A b + 2B a)c + B b )m + ((34A b + 34B a)c + 17B b )m +--R + +--R 2 3 2 2 +--R ((214A b + 214B a)c + 107B b )m + ((614A b + 614B a)c + 307B b )m +--R + +--R 2 2 +--R ((792A b + 792B a)c + 396B b )m + (360A b + 360B a)c + 180B b +--R * +--R 4 +--R x +--R + +--R 2 5 2 4 +--R (2A a c + A b + 2B a b)m + (36A a c + 18A b + 36B a b)m +--R + +--R 2 3 +--R (242A a c + 121A b + 242B a b)m +--R + +--R 2 2 +--R (744A a c + 372A b + 744B a b)m +--R + +--R 2 2 +--R (1016A a c + 508A b + 1016B a b)m + 480A a c + 240A b + 480B a b +--R * +--R 3 +--R x +--R + +--R 2 5 2 4 2 3 +--R (2A a b + B a )m + (38A a b + 19B a )m + (274A a b + 137B a )m +--R + +--R 2 2 2 2 +--R (922A a b + 461B a )m + (1404A a b + 702B a )m + 720A a b + 360B a +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (A a m + 20A a m + 155A a m + 580A a m + 1044A a m + 720A a )x +--R * +--R m log(e x) 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3 +--R (242A a c + 121A b + 242B a b)e m +--R + +--R 2 6 2 +--R (744A a c + 372A b + 744B a b)e m +--R + +--R 2 6 +--R (1016A a c + 508A b + 1016B a b)e m +--R + +--R 2 6 +--R (480A a c + 240A b + 480B a b)e +--R * +--R 3 +--R x +--R + +--R 2 6 5 2 6 4 +--R (2A a b + B a )e m + (38A a b + 19B a )e m +--R + +--R 2 6 3 2 6 2 +--R (274A a b + 137B a )e m + (922A a b + 461B a )e m +--R + +--R 2 6 2 6 +--R (1404A a b + 702B a )e m + (720A a b + 360B a )e +--R * +--R 2 +--R x +--R + +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R A a e m + 20A a e m + 155A a e m + 580A a e m + 1044A a e m +--R + +--R 2 6 +--R 720A a e +--R * +--R x +--R * +--R m log(e x) +--R %e +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (- B c m - 15B c m - 85B c m - 225B c m - 274B c m - 120B c ) +--R * +--R m + 6 +--R (e x) +--R + +--R 2 5 2 4 +--R (- A c - 2B b c)e m + (- 16A c - 32B b c)e m +--R + +--R 2 3 2 2 +--R (- 95A c - 190B b c)e m + (- 260A c - 520B b c)e m +--R + +--R 2 2 +--R (- 324A c - 648B b c)e m + (- 144A c - 288B b c)e 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+--R + +--R 2 5 5 2 5 4 2 5 3 2 5 2 2 5 +--R - A a e m - 20A a e m - 155A a e m - 580A a e m - 1044A a e m +--R + +--R 2 5 +--R - 720A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 418 + +)clear all + +--S 419 of 1751 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R m +--R (e x) +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1751 +r0:=a^3*A*(e*x)^(1+m)/(e*(1+m))+a^2*(3*A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+_ + 3*a*(a*b*B+A*(b^2+a*c))*(e*x)^(3+m)/(e^3*(3+m))+(3*a*B*(b^2+a*c)+A*_ + (b^3+6*a*b*c))*(e*x)^(4+m)/(e^4*(4+m))+(b^3*B+3*A*b^2*c+6*a*b*B*c+_ + 3*a*A*c^2)*(e*x)^(5+m)/(e^5*(5+m))+3*c*(b^2*B+A*b*c+a*B*c)*_ + (e*x)^(6+m)/(e^6*(6+m))+c^2*(3*b*B+A*c)*(e*x)^(7+m)/(e^7*(7+m))+_ + B*c^3*(e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x) +--R + +--R 3 2 7 3 2 6 +--R (A c + 3B b c )e m + (29A c + 87B b c )e m +--R + +--R 3 2 5 3 2 4 +--R (343A c + 1029B b c )e m + (2135A c + 6405B b c )e m +--R + +--R 3 2 3 3 2 2 +--R (7504A c + 22512B b c )e m + (14756A c + 44268B b c )e m +--R + +--R 3 2 3 2 +--R (14832A c + 44496B b c )e m + (5760A c + 17280B b c )e +--R * +--R m + 7 +--R (e x) +--R + +--R 2 2 2 7 2 2 2 6 +--R ((3A b + 3B a)c + 3B b c)e m + ((90A b + 90B a)c + 90B b c)e m +--R + +--R 2 2 2 5 +--R ((1098A b + 1098B a)c + 1098B b c)e m 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+ 86076B a b)e m +--R + +--R 2 2 2 5 +--R (96144A a c + 96144A a b + 96144B a b)e m +--R + +--R 2 2 2 5 +--R (40320A a c + 40320A a b + 40320B a b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 6 7 2 3 6 6 +--R (3A a b + B a )e m + (102A a b + 34B a )e m +--R + +--R 2 3 6 5 2 3 6 4 +--R (1434A a b + 478B a )e m + (10740A a b + 3580B a )e m +--R + +--R 2 3 6 3 2 3 6 2 +--R (45867A a b + 15289B a )e m + (110118A a b + 36706B a )e m +--R + +--R 2 3 6 2 3 6 +--R (134136A a b + 44712B a )e m + (60480A a b + 20160B a )e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 7 7 3 7 6 3 7 5 3 7 4 3 7 3 +--R A a e m + 35A a e m + 511A a e m + 4025A a e m + 18424A a e m +--R + +--R 3 7 2 3 7 3 7 +--R 48860A a e m + 69264A a e m + 40320A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1751 +a0:=integrate(t0,x) +--R +--R 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+--R 3 7 3 6 3 5 3 4 3 3 +--R A a m + 35A a m + 511A a m + 4025A a m + 18424A a m +--R + +--R 3 2 3 3 +--R 48860A a m + 69264A a m + 40320A a +--R * +--R x +--R * +--R m log(e x) +--R %e +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 8 7 3 8 6 3 8 5 3 8 4 3 8 3 +--R B c e m + 28B c e m + 322B c e m + 1960B c e m + 6769B c e m +--R + +--R 3 8 2 3 8 3 8 +--R 13132B c e m + 13068B c e m + 5040B c e +--R * +--R 8 +--R x +--R + +--R 3 2 8 7 3 2 8 6 +--R (A c + 3B b c )e m + (29A c + 87B b c )e m +--R + +--R 3 2 8 5 3 2 8 4 +--R (343A c + 1029B b c )e m + (2135A c + 6405B b c )e m +--R + +--R 3 2 8 3 3 2 8 2 +--R (7504A c + 22512B b c )e m + (14756A c + 44268B b c )e m +--R + +--R 3 2 8 3 2 8 +--R (14832A c + 44496B b c )e m + (5760A c + 17280B b c )e +--R * +--R 7 +--R x +--R + +--R 2 2 8 7 +--R ((3A b + 3B a)c + 3B b c)e m +--R + +--R 2 2 8 6 +--R ((90A b + 90B a)c + 90B b c)e m +--R + +--R 2 2 8 5 +--R ((1098A b + 1098B a)c + 1098B b c)e m +--R + +--R 2 2 8 4 +--R ((7020A b + 7020B a)c + 7020B b c)e m +--R + +--R 2 2 8 3 +--R ((25227A b + 25227B a)c + 25227B b c)e m +--R + +--R 2 2 8 2 +--R ((50490A b + 50490B a)c + 50490B b c)e m +--R + +--R 2 2 8 +--R ((51432A b + 51432B a)c + 51432B b c)e m +--R + +--R 2 2 8 +--R ((20160A b + 20160B a)c + 20160B b c)e +--R * +--R 6 +--R x +--R + +--R 2 2 3 8 7 +--R (3A a c + (3A b + 6B a b)c + B b )e m +--R + +--R 2 2 3 8 6 +--R (93A a c + (93A b + 186B a b)c + 31B b )e m +--R + +--R 2 2 3 8 5 +--R (1173A a c + (1173A b + 2346B a b)c + 391B b )e m +--R + +--R 2 2 3 8 4 +--R (7743A a c + (7743A b + 15486B a b)c + 2581B b )e m +--R + +--R 2 2 3 8 3 +--R (28632A a c + (28632A b + 57264B a b)c + 9544B b )e m +--R + +--R 2 2 3 8 2 +--R (58692A a c + (58692A b + 117384B a b)c + 19564B b )e m +--R + +--R 2 2 3 8 +--R (60912A a c + (60912A b + 121824B a b)c + 20304B b )e m +--R + +--R 2 2 3 8 +--R (24192A a c + (24192A b + 48384B a b)c + 8064B b )e +--R * +--R 5 +--R x +--R + +--R 2 3 2 8 7 +--R ((6A a b + 3B a )c + A b + 3B a b )e m +--R + +--R 2 3 2 8 6 +--R ((192A a b + 96B a )c + 32A b + 96B a b )e m +--R + +--R 2 3 2 8 5 +--R ((2508A a b + 1254B a )c + 418A b + 1254B a b )e m +--R + +--R 2 3 2 8 4 +--R ((17184A a b + 8592B a )c + 2864A b + 8592B a b )e m +--R + +--R 2 3 2 8 3 +--R ((65958A a b + 32979B a )c + 10993A b + 32979B a b )e m +--R + +--R 2 3 2 8 2 +--R ((139872A a b + 69936B a )c + 23312A b + 69936B a b )e m +--R + +--R 2 3 2 8 +--R ((149256A a b + 74628B a )c + 24876A b + 74628B a b )e m +--R + +--R 2 3 2 8 +--R ((60480A a b + 30240B a )c + 10080A b + 30240B a b )e +--R * +--R 4 +--R x +--R + +--R 2 2 2 8 7 +--R (3A a c + 3A a b + 3B a b)e m +--R + +--R 2 2 2 8 6 +--R (99A a c + 99A a b + 99B a b)e m +--R + +--R 2 2 2 8 5 +--R (1341A a c + 1341A a b + 1341B a b)e m +--R + +--R 2 2 2 8 4 +--R (9585A a c + 9585A a b + 9585B a b)e m +--R + +--R 2 2 2 8 3 +--R (38592A a c + 38592A a b + 38592B a b)e m +--R + +--R 2 2 2 8 2 +--R (86076A a c + 86076A a b + 86076B a b)e m +--R + +--R 2 2 2 8 +--R (96144A a c + 96144A a b + 96144B a b)e m +--R + +--R 2 2 2 8 +--R (40320A a c + 40320A a b + 40320B a b)e +--R * +--R 3 +--R x +--R + +--R 2 3 8 7 2 3 8 6 +--R (3A a b + B a )e m + (102A a b + 34B a )e m +--R + +--R 2 3 8 5 2 3 8 4 +--R (1434A a b + 478B a )e m + (10740A a b + 3580B a )e m +--R + +--R 2 3 8 3 2 3 8 2 +--R (45867A a b + 15289B a )e m + (110118A a b + 36706B a )e m +--R + +--R 2 3 8 2 3 8 +--R (134136A a b + 44712B a )e m + (60480A a b + 20160B a )e +--R * +--R 2 +--R x +--R + +--R 3 8 7 3 8 6 3 8 5 3 8 4 +--R A a e m + 35A a e m + 511A a e m + 4025A a e m +--R + +--R 3 8 3 3 8 2 3 8 3 8 +--R 18424A a e m + 48860A a e m + 69264A a e m + 40320A a e +--R * +--R x +--R * +--R m log(e x) +--R %e +--R + +--R 3 7 3 6 3 5 3 4 3 3 +--R - B c m - 28B c m - 322B c m - 1960B c m - 6769B c m +--R + +--R 3 2 3 3 +--R - 13132B c m - 13068B c m - 5040B c +--R * +--R m + 8 +--R (e x) +--R + +--R 3 2 7 3 2 6 +--R (- A c - 3B b c )e m + (- 29A c - 87B b c )e m +--R + +--R 3 2 5 3 2 4 +--R (- 343A c - 1029B b c )e m + (- 2135A c - 6405B b c )e m +--R + +--R 3 2 3 3 2 2 +--R (- 7504A c - 22512B b c )e m + (- 14756A c - 44268B b c )e m +--R + +--R 3 2 3 2 +--R (- 14832A c - 44496B b c )e m + (- 5760A c - 17280B b c )e +--R * +--R m + 7 +--R (e x) +--R + +--R 2 2 2 7 +--R ((- 3A b - 3B a)c - 3B b c)e m +--R + +--R 2 2 2 6 +--R ((- 90A b - 90B a)c - 90B b c)e m +--R + +--R 2 2 2 5 +--R ((- 1098A b - 1098B a)c - 1098B b c)e m +--R + +--R 2 2 2 4 +--R ((- 7020A b - 7020B a)c - 7020B b c)e m +--R + +--R 2 2 2 3 +--R ((- 25227A b - 25227B a)c - 25227B b c)e m +--R + +--R 2 2 2 2 +--R ((- 50490A b - 50490B a)c - 50490B b c)e m +--R + +--R 2 2 2 +--R ((- 51432A b - 51432B a)c - 51432B b c)e m +--R + +--R 2 2 2 +--R ((- 20160A b - 20160B a)c - 20160B b c)e +--R * +--R m + 6 +--R (e x) +--R + +--R 2 2 3 3 7 +--R (- 3A a c + (- 3A b - 6B a b)c - B b )e m +--R + +--R 2 2 3 3 6 +--R (- 93A a c + (- 93A b - 186B a b)c - 31B b )e m +--R + +--R 2 2 3 3 5 +--R (- 1173A a c + (- 1173A b - 2346B a b)c - 391B b )e m +--R + +--R 2 2 3 3 4 +--R (- 7743A a c + (- 7743A b - 15486B a b)c - 2581B b )e m +--R + +--R 2 2 3 3 3 +--R (- 28632A a c + (- 28632A b - 57264B a b)c - 9544B b )e m +--R + +--R 2 2 3 3 2 +--R (- 58692A a c + (- 58692A b - 117384B a b)c - 19564B b )e m +--R + +--R 2 2 3 3 +--R (- 60912A a c + (- 60912A b - 121824B a b)c - 20304B b )e m +--R + +--R 2 2 3 3 +--R (- 24192A a c + (- 24192A b - 48384B a b)c - 8064B b )e +--R * +--R m + 5 +--R (e x) +--R + +--R 2 3 2 4 7 +--R ((- 6A a b - 3B a )c - A b - 3B a b )e m +--R + +--R 2 3 2 4 6 +--R ((- 192A a b - 96B a )c - 32A b - 96B a b )e m +--R + +--R 2 3 2 4 5 +--R ((- 2508A a b - 1254B a )c - 418A b - 1254B a b )e m +--R + +--R 2 3 2 4 4 +--R ((- 17184A a b - 8592B a )c - 2864A b - 8592B a b )e m +--R + +--R 2 3 2 4 3 +--R ((- 65958A a b - 32979B a )c - 10993A b - 32979B a b )e m +--R + +--R 2 3 2 4 2 +--R ((- 139872A a b - 69936B a )c - 23312A b - 69936B a b )e m +--R + +--R 2 3 2 4 +--R ((- 149256A a b - 74628B a )c - 24876A b - 74628B a b )e m +--R + +--R 2 3 2 4 +--R ((- 60480A a b - 30240B a )c - 10080A b - 30240B a b )e +--R * +--R m + 4 +--R (e x) +--R + +--R 2 2 2 5 7 +--R (- 3A a c - 3A a b - 3B a b)e m +--R + +--R 2 2 2 5 6 +--R (- 99A a c - 99A a b - 99B a b)e m +--R + +--R 2 2 2 5 5 +--R (- 1341A a c - 1341A a b - 1341B a b)e m +--R + +--R 2 2 2 5 4 +--R (- 9585A a c - 9585A a b - 9585B a b)e m +--R + +--R 2 2 2 5 3 +--R (- 38592A a c - 38592A a b - 38592B a b)e m +--R + +--R 2 2 2 5 2 +--R (- 86076A a c - 86076A a b - 86076B a b)e m +--R + +--R 2 2 2 5 +--R (- 96144A a c - 96144A a b - 96144B a b)e m +--R + +--R 2 2 2 5 +--R (- 40320A a c - 40320A a b - 40320B a b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 6 7 2 3 6 6 +--R (- 3A a b - B a )e m + (- 102A a b - 34B a )e m +--R + +--R 2 3 6 5 2 3 6 4 +--R (- 1434A a b - 478B a )e m + (- 10740A a b - 3580B a )e m +--R + +--R 2 3 6 3 2 3 6 2 +--R (- 45867A a b - 15289B a )e m + (- 110118A a b - 36706B a )e m +--R + +--R 2 3 6 2 3 6 +--R (- 134136A a b - 44712B a )e m + (- 60480A a b - 20160B a )e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 7 7 3 7 6 3 7 5 3 7 4 3 7 3 +--R - A a e m - 35A a e m - 511A a e m - 4025A a e m - 18424A a e m +--R + +--R 3 7 2 3 7 3 7 +--R - 48860A a e m - 69264A a e m - 40320A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 1751 +t0:=(A+B*x)*(d+e*x)^m/(a+b*x+c*x^2) +--R +--R +--R m +--R (B x + A)(e x + d) +--R (1) ------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1751 +--r0:=-(d+e*x)^(1+m)*hypergeometric(1,1+m,2+m,2*c*(d+e*x)/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/((1+m)*_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))-(d+e*x)^(1+m)*hypergeometric(1,1+m,_ +-- 2+m,2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(B+(b*B-2*A*c)/_ +-- sqrt(b^2-4*a*c))/((1+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--E 425 + +--S 426 of 1751 +--a0:=integrate(t0,x) +--E 426 + +--S 427 of 1751 +--m0:=a0-r0 +--E 427 + +--S 428 of 1751 +--d0:=D(m0,x) +--E 428 + +)clear all + +--S 429 of 1751 +t0:=(A+B*x)*(d+e*x)^(1+m)/(a+b*x+c*x^2) +--R +--R +--R m + 1 +--R (B x + A)(e x + d) +--R (1) ----------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1751 +--r0:=-(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,2*c*(d+e*x)/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/((2+m)*_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))-(d+e*x)^(2+m)*_ +-- hypergeometric(1,2+m,3+m,2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- (B+(b*B-2*A*c)/sqrt(b^2-4*a*c))/((2+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--E 430 + +--S 431 of 1751 +--a0:=integrate(t0,x) +--E 431 + +--S 432 of 1751 +--m0:=a0-r0 +--E 432 + +--S 433 of 1751 +--d0:=D(m0,x) +--E 433 + +)clear all + +--S 434 of 1751 +t0:=(A+B*x)*(d+e*x)^2/(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 434 + +--S 435 of 1751 +r0:=e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+1/2*(A*c*e*(2*c*d-b*e)+_ + B*(c^2*d^2+b^2*e^2-c*e*(2*b*d+a*e)))*log(a+b*x+c*x^2)/c^3+(b^3*B*e^2-_ + b^2*c*e*(2*B*d+A*e)-2*c^2*(A*c*d^2-2*a*B*d*e-a*A*e^2)+b*c*(B*c*d^2+_ + 2*A*c*d*e-3*a*B*e^2))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-_ + 4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 +--R (4A a c + (- 2A b - 6B a b)c + 2B b )e +--R + +--R 2 2 3 2 2 +--R ((4A b + 8B a)c - 4B b c)d e + (- 4A c + 2B b c )d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 +--R (((- A b - B a)c + B b )e + (2A c - 2B b c)d e + B c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 2 2 2 2 +--R B c e x + ((2A c - 2B b c)e + 4B c d e)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 435 + +--S 436 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 +--R (2A a c + (- A b - 3B a b)c + B b )e +--R + +--R 2 2 3 2 2 +--R ((2A b + 4B a)c - 2B b c)d e + (- 2A c + B b c )d +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 +--R (((- A b - B a)c + B b )e + (2A c - 2B b c)d e + B c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 2 2 2 2 +--R B c e x + ((2A c - 2B b c)e + 4B c d e)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R 2 2 3 2 +--R (- 4A a c + (2A b + 6B a b)c - 2B b )e +--R + +--R 2 2 3 2 2 +--R ((- 4A b - 8B a)c + 4B b c)d e + (4A c - 2B b c )d +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 2 2 +--R (((- A b - B a)c + B b )e + (2A c - 2B b c)d e + B c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 2 2 2 2 +--R B c e x + ((2A c - 2B b c)e + 4B c d e)x +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 3 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 436 + +--S 437 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 3 2 +--R (2A a c + (- A b - 3B a b)c + B b )e +--R + +--R 2 2 3 2 2 +--R ((2A b + 4B a)c - 2B b c)d e + (- 2A c + B b c )d +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 2 +--R (- 4A a c + (2A b + 6B a b)c - 2B b )e +--R + +--R 2 2 3 2 2 +--R ((- 4A b - 8B a)c + 4B b c)d e + (4A c - 2B b c )d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 3 2 +--R (- 2A a c + (A b + 3B a b)c - B b )e +--R + +--R 2 2 3 2 2 +--R ((- 2A b - 4B a)c + 2B b c)d e + (2A c - B b c )d +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 +--R (- 2A a c + (A b + 3B a b)c - B b )e +--R + +--R 2 2 3 2 2 +--R ((- 2A b - 4B a)c + 2B b c)d e + (2A c - B b c )d +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1751 +t0:=(A+B*x)*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 1751 +r0:=B*e*x/c+1/2*(B*c*d-b*B*e+A*c*e)*log(a+b*x+c*x^2)/c^2-(b^2*B*e-b*c*_ + (B*d+A*e)+2*c*(A*c*d-a*B*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (c^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2c x + b +--R (((2A b + 4B a)c - 2B b )e + (- 4A c + 2B b c)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R (((A c - B b)e + B c d)log(c x + b x + a) + 2B c e x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (((A b + 2B a)c - B b )e + (- 2A c + B b c)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R (((A c - B b)e + B c d)log(c x + b x + a) + 2B c e x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R 2 2 +--R (((- 2A b - 4B a)c + 2B b )e + (4A c - 2B b c)d) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (((A c - B b)e + B c d)log(c x + b x + a) + 2B c e x)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 443 + +--S 444 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 +--R (((A b + 2B a)c - B b )e + (- 2A c + B b c)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2c x + b +--R (((- 2A b - 4B a)c + 2B b )e + (4A c - 2B b c)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 2 2 | 2 +--R (((- A b - 2B a)c + B b )e + (2A c - B b c)d)\|4a c - b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 2 | 2 +--R (((- A b - 2B a)c + B b )e + (2A c - B b c)d)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 1751 +t0:=(A+B*x)/(a+b*x+c*x^2) +--R +--R +--R B x + A +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 448 + +--S 449 of 1751 +r0:=1/2*B*log(a+b*x+c*x^2)/c+(b*B-2*A*c)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (c*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R +-----------+ +--R 2c x + b 2 | 2 +--R (- 4A c + 2B b)atanh(--------------) + B log(c x + b x + a)\|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R -------------------------------------------------------------------------- +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (2A c - B b) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R B log(c x + b x + a)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R (4A c - 2B b)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R B log(c x + b x + a)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2c\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 450 + +--S 451 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R (2A c - B b) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R (4A c - 2B b)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R | 2 2c x + b +--R (2A c - B b)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R (2A c - B b)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R c\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 454 + +)clear all + +--S 455 of 1751 +t0:=(A+B*x)/((d+e*x)*(a+b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 455 + +--S 456 of 1751 +r0:=-(B*d-A*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)+1/2*(B*d-A*e)*_ + log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)+(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2c x + b +--R ((2A b - 4B a)e + (- 4A c + 2B b)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R ((- A e + B d)log(c x + b x + a) + (2A e - 2B d)log(e x + d)) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R ((A b - 2B a)e + (- 2A c + B b)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 +--R ((- A e + B d)log(c x + b x + a) + (2A e - 2B d)log(e x + d)) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R ((- 2A b + 4B a)e + (4A c - 2B b)d)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 +--R ((- A e + B d)log(c x + b x + a) + (2A e - 2B d)log(e x + d)) +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 2 2 | 2 +--R (2a e - 2b d e + 2c d )\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 457 + +--S 458 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R ((A b - 2B a)e + (- 2A c + B b)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R ((- 2A b + 4B a)e + (4A c - 2B b)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R | 2 2c x + b +--R ((- A b + 2B a)e + (2A c - B b)d)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R ((- A b + 2B a)e + (2A c - B b)d)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 2 | 2 | 2 +--R (a e - b d e + c d )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 461 + +)clear all + +--S 462 of 1751 +t0:=(A+B*x)/((d+e*x)^2*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R Type: Fraction(Polynomial(Integer)) +--E 462 + +--S 463 of 1751 +r0:=(B*d-A*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x))+(A*e*(2*c*d-b*e)-_ + B*(c*d^2-a*e^2))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2-1/2*(A*e*(2*c*d-b*e)-_ + B*(c*d^2-a*e^2))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2-(A*b^2*e^2+_ + 2*c*(A*c*d^2+2*a*B*d*e-a*A*e^2)-b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 2 +--R (4A a c - 2A b + 2B a b)e + (4A b - 8B a)c d e +--R + +--R 2 2 +--R (- 4A c + 2B b c)d e +--R * +--R x +--R + +--R 2 2 2 +--R (4A a c - 2A b + 2B a b)d e + (4A b - 8B a)c d e +--R + +--R 2 3 +--R (- 4A c + 2B b c)d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 +--R ((A b - B a)e - 2A c d e + B c d e)x + (A b - B a)d e +--R + +--R 2 3 +--R - 2A c d e + B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 +--R ((- 2A b + 2B a)e + 4A c d e - 2B c d e)x + (- 2A b + 2B a)d e +--R + +--R 2 3 +--R 4A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + (2A b + 2B a)d e + (- 2A c - 2B b)d e + 2B c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 +--R (2A a c - A b + B a b)e + (2A b - 4B a)c d e +--R + +--R 2 2 +--R (- 2A c + B b c)d e +--R * +--R x +--R + +--R 2 2 2 +--R (2A a c - A b + B a b)d e + (2A b - 4B a)c d e +--R + +--R 2 3 +--R (- 2A c + B b c)d +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2 +--R ((A b - B a)e - 2A c d e + B c d e)x + (A b - B a)d e +--R + +--R 2 3 +--R - 2A c d e + B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 +--R ((- 2A b + 2B a)e + 4A c d e - 2B c d e)x +--R + +--R 2 2 3 +--R (- 2A b + 2B a)d e + 4A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + (2A b + 2B a)d e + (- 2A c - 2B b)d e + 2B c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 5 4 2 2 3 3 2 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x +--R + +--R 2 4 2 3 2 3 2 4 2 5 +--R 2a d e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 3 2 +--R (- 4A a c + 2A b - 2B a b)e + (- 4A b + 8B a)c d e +--R + +--R 2 2 +--R (4A c - 2B b c)d e +--R * +--R x +--R + +--R 2 2 2 +--R (- 4A a c + 2A b - 2B a b)d e + (- 4A b + 8B a)c d e +--R + +--R 2 3 +--R (4A c - 2B b c)d +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 2 2 2 +--R ((A b - B a)e - 2A c d e + B c d e)x + (A b - B a)d e +--R + +--R 2 3 +--R - 2A c d e + B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 +--R ((- 2A b + 2B a)e + 4A c d e - 2B c d e)x +--R + +--R 2 2 3 +--R (- 2A b + 2B a)d e + 4A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + (2A b + 2B a)d e + (- 2A c - 2B b)d e + 2B c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 2 5 4 2 2 3 3 2 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x +--R + +--R 2 4 2 3 2 3 2 4 2 5 +--R 2a d e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 464 + +--S 465 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R ((2A a c - A b + B a b)e + (2A b - 4B a)c d e + (- 2A c + B b c)d ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 +--R (- 4A a c + 2A b - 2B a b)e + (- 4A b + 8B a)c d e +--R + +--R 2 2 +--R (4A c - 2B b c)d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 +--R (- 2A a c + A b - B a b)e + (- 2A b + 4B a)c d e +--R + +--R 2 2 +--R (2A c - B b c)d +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 +--R (- 2A a c + A b - B a b)e + (- 2A b + 4B a)c d e +--R + +--R 2 2 +--R (2A c - B b c)d +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (a e - 2a b d e + (2a c + b )d e - 2b c d e + c d )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1751 +t0:=(A+B*x)/((d+e*x)^3*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 469 + +--S 470 of 1751 +r0:=1/2*(B*d-A*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+(-A*e*(2*c*d-b*e)+_ + B*(c*d^2-a*e^2))/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))-(B*(c^2*d^3-_ + 3*a*c*d*e^2+a*b*e^3)-A*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*_ + log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*(B*(c^2*d^3-3*a*c*d*e^2+a*b*e^3)-_ + A*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*log(a+b*x+c*x^2)/(c*d^2-_ + b*d*e+a*e^2)^3+(A*b^3*e^3-b^2*e^2*(3*A*c*d+a*B*e)+b*c*(B*c*d^3+_ + 3*A*c*d^2*e+3*a*B*d*e^2-3*a*A*e^3)-2*c*(A*c*d*(c*d^2-3*a*e^2)+_ + a*B*e*(3*c*d^2-a*e^2)))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + ((c*d^2-b*d*e+a*e^2)^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 2 5 +--R ((- 6A a b + 4B a )c + 2A b - 2B a b )e +--R + +--R 2 2 4 2 2 3 +--R (12A a c + (- 6A b + 6B a b)c)d e + (6A b - 12B a)c d e +--R + +--R 3 2 3 2 +--R (- 4A c + 2B b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 +--R ((- 12A a b + 8B a )c + 4A b - 4B a b )d e +--R + +--R 2 2 2 3 2 3 2 +--R (24A a c + (- 12A b + 12B a b)c)d e + (12A b - 24B a)c d e +--R + +--R 3 2 4 +--R (- 8A c + 4B b c )d e +--R * +--R x +--R + +--R 2 3 2 2 3 +--R ((- 6A a b + 4B a )c + 2A b - 2B a b )d e +--R + +--R 2 2 3 2 2 4 +--R (12A a c + (- 6A b + 6B a b)c)d e + (6A b - 12B a)c d e +--R + +--R 3 2 5 +--R (- 4A c + 2B b c )d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 5 4 2 2 3 +--R (A a c - A b + B a b)e + (3A b - 3B a)c d e - 3A c d e +--R + +--R 2 3 2 +--R B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 +--R (2A a c - 2A b + 2B a b)d e + (6A b - 6B a)c d e +--R + +--R 2 3 2 2 4 +--R - 6A c d e + 2B c d e +--R * +--R x +--R + +--R 2 2 3 3 2 2 4 +--R (A a c - A b + B a b)d e + (3A b - 3B a)c d e - 3A c d e +--R + +--R 2 5 +--R B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 5 4 +--R (- 2A a c + 2A b - 2B a b)e + (- 6A b + 6B a)c d e +--R + +--R 2 2 3 2 3 2 +--R 6A c d e - 2B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 +--R (- 4A a c + 4A b - 4B a b)d e + (- 12A b + 12B a)c d e +--R + +--R 2 3 2 2 4 +--R 12A c d e - 4B c d e +--R * +--R x +--R + +--R 2 2 3 3 2 +--R (- 2A a c + 2A b - 2B a b)d e + (- 6A b + 6B a)c d e +--R + +--R 2 4 2 5 +--R 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 +--R (2A a b - 2B a )e + (- 4A a c - 2A b + 2B a b)d e +--R + +--R 2 3 2 3 2 2 4 +--R 6A b c d e + (- 4A c - 2B b c)d e + 2B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - A a e + (4A a b - B a )d e + (- 6A a c - 3A b )d e +--R + +--R 2 3 2 2 4 2 5 +--R ((8A b + 2B a)c + B b )d e + (- 5A c - 4B b c)d e + 3B c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1751 +--a0:=integrate(t0,x) +--E 471 + +--S 472 of 1751 +--m0a:=a0.1-r0 +--E 472 + +--S 473 of 1751 +--d0a:=D(m0a,x) +--E 473 + +--S 474 of 1751 +--m0b:=a0.2-r0 +--E 474 + +--S 475 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (4) 0 +--R Type: Polynomial(Integer) +--E 475 + +)clear all + +--S 476 of 1751 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 1751 +r0:=11576/81*x+1156/27*x^2+32/27*x^3-4/3*x^4-6*log(1+x)+10625/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R 10625log(3x + 2) - 1458log(x + 1) - 324x + 288x + 10404x + 34728x +--R (2) -------------------------------------------------------------------- +--R 243 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 10625log(3x + 2) - 1458log(x + 1) - 324x + 288x + 10404x + 34728x +--R (3) -------------------------------------------------------------------- +--R 243 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1751 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 1751 +r0:=922/27*x+26/9*x^2-8/9*x^3-6*log(1+x)+2125/81*log(2+3*x) +--R +--R +--R 3 2 +--R 2125log(3x + 2) - 486log(x + 1) - 72x + 234x + 2766x +--R (2) ------------------------------------------------------ +--R 81 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 2125log(3x + 2) - 486log(x + 1) - 72x + 234x + 2766x +--R (3) ------------------------------------------------------ +--R 81 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1751 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 1751 +r0:=44/9*x-2/3*x^2-6*log(1+x)+425/27*log(2+3*x) +--R +--R +--R 2 +--R 425log(3x + 2) - 162log(x + 1) - 18x + 132x +--R (2) -------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 425log(3x + 2) - 162log(x + 1) - 18x + 132x +--R (3) -------------------------------------------- +--R 27 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 1751 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1751 +r0:=-2/3*x-6*log(1+x)+85/9*log(2+3*x) +--R +--R +--R 85log(3x + 2) - 54log(x + 1) - 6x +--R (2) --------------------------------- +--R 9 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 85log(3x + 2) - 54log(x + 1) - 6x +--R (3) --------------------------------- +--R 9 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1751 +t0:=(5-x)/(2+5*x+3*x^2) +--R +--R +--R - x + 5 +--R (1) ------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 1751 +r0:=-6*log(1+x)+17/3*log(2+3*x) +--R +--R +--R 17log(3x + 2) - 18log(x + 1) +--R (2) ---------------------------- +--R 3 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 17log(3x + 2) - 18log(x + 1) +--R (3) ---------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)clear all + +--S 501 of 1751 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) -------------------- +--R 3 2 +--R 6x + 19x + 19x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 501 + +--S 502 of 1751 +r0:=-6*log(1+x)+13/5*log(3+2*x)+17/5*log(2+3*x) +--R +--R +--R 17log(3x + 2) + 13log(2x + 3) - 30log(x + 1) +--R (2) -------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 17log(3x + 2) + 13log(2x + 3) - 30log(x + 1) +--R (3) -------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 505 + +)clear all + +--S 506 of 1751 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------- +--R 4 3 2 +--R 12x + 56x + 95x + 69x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 506 + +--S 507 of 1751 +r0:=(-13/5)/(3+2*x)-6*log(1+x)+99/25*log(3+2*x)+51/25*log(2+3*x) +--R +--R +--R (2) +--R (102x + 153)log(3x + 2) + (198x + 297)log(2x + 3) +--R + +--R (- 300x - 450)log(x + 1) - 65 +--R / +--R 50x + 75 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (102x + 153)log(3x + 2) + (198x + 297)log(2x + 3) +--R + +--R (- 300x - 450)log(x + 1) - 65 +--R / +--R 50x + 75 +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1751 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 24x + 148x + 358x + 423x + 243x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 511 + +--S 512 of 1751 +r0:=(-13/10)/(3+2*x)^2+(-99/25)/(3+2*x)-6*log(1+x)+597/125*log(3+2*x)+_ + 153/125*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (1224x + 3672x + 2754)log(3x + 2) + (4776x + 14328x + 10746)log(2x + 3) +--R + +--R 2 +--R (- 6000x - 18000x - 13500)log(x + 1) - 1980x - 3295 +--R / +--R 2 +--R 1000x + 3000x + 2250 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (1224x + 3672x + 2754)log(3x + 2) + (4776x + 14328x + 10746)log(2x + 3) +--R + +--R 2 +--R (- 6000x - 18000x - 13500)log(x + 1) - 1980x - 3295 +--R / +--R 2 +--R 1000x + 3000x + 2250 +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 515 + +)clear all + +--S 516 of 1751 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------- +--R 6 5 4 3 2 +--R 48x + 368x + 1160x + 1920x + 1755x + 837x + 162 +--R Type: Fraction(Polynomial(Integer)) +--E 516 + +--S 517 of 1751 +r0:=(-13/15)/(3+2*x)^3+(-99/50)/(3+2*x)^2+(-597/125)/(3+2*x)-6*log(1+x)+_ + 3291/625*log(3+2*x)+459/625*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (22032x + 99144x + 148716x + 74358)log(3x + 2) +--R + +--R 3 2 +--R (157968x + 710856x + 1066284x + 533142)log(2x + 3) +--R + +--R 3 2 2 +--R (- 180000x - 810000x - 1215000x - 607500)log(x + 1) - 71640x - 229770x +--R + +--R - 186715 +--R / +--R 3 2 +--R 30000x + 135000x + 202500x + 101250 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (22032x + 99144x + 148716x + 74358)log(3x + 2) +--R + +--R 3 2 +--R (157968x + 710856x + 1066284x + 533142)log(2x + 3) +--R + +--R 3 2 2 +--R (- 180000x - 810000x - 1215000x - 607500)log(x + 1) - 71640x - 229770x +--R + +--R - 186715 +--R / +--R 3 2 +--R 30000x + 135000x + 202500x + 101250 +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 520 + +)clear all + +--S 521 of 1751 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^2 +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 521 + +--S 522 of 1751 +r0:=15496/9*x+2888/3*x^2+560/3*x^3-(3+2*x)^4*(29+35*x)/(2+5*x+3*x^2)+_ + 83*log(1+x)-1625/27*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 4875x - 8125x - 3250)log(3x + 2) + (6723x + 11205x + 4482)log(x + 1) +--R + +--R 4 3 2 +--R - 72x + 216x - 88824x - 152697x - 63423 +--R / +--R 2 +--R 81x + 135x + 54 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 14625x - 24375x - 9750)log(3x + 2) +--R + +--R 2 4 3 2 +--R (20169x + 33615x + 13446)log(x + 1) - 216x + 648x + 1536x - 11411x +--R + +--R - 11597 +--R / +--R 2 +--R 243x + 405x + 162 +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 1751 +m0:=a0-r0 +--R +--R +--R 89336 +--R (4) ----- +--R 81 +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1751 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^2 +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 526 + +--S 527 of 1751 +r0:=3068/9*x+280/3*x^2-(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)+71*log(1+x)-_ + 1825/27*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 5475x - 9125x - 3650)log(3x + 2) + (5751x + 9585x + 3834)log(x + 1) +--R + +--R 3 2 +--R - 72x - 28158x - 49389x - 21141 +--R / +--R 2 +--R 81x + 135x + 54 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 5475x - 9125x - 3650)log(3x + 2) + (5751x + 9585x + 3834)log(x + 1) +--R + +--R 3 2 +--R - 72x - 120x - 2659x - 2449 +--R / +--R 2 +--R 81x + 135x + 54 +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1751 +m0:=a0-r0 +--R +--R +--R 9346 +--R (4) ---- +--R 27 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1751 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^2 +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 531 + +--S 532 of 1751 +r0:=140/3*x-(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)+59*log(1+x)-535/9*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 1605x - 2675x - 1070)log(3x + 2) + (1593x + 2655x + 1062)log(x + 1) +--R + +--R 2 +--R - 2724x - 5127x - 2349 +--R / +--R 2 +--R 27x + 45x + 18 +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 1605x - 2675x - 1070)log(3x + 2) + (1593x + 2655x + 1062)log(x + 1) +--R + +--R - 587x - 533 +--R / +--R 2 +--R 27x + 45x + 18 +--R Type: Union(Expression(Integer),...) +--E 533 + +--S 534 of 1751 +m0:=a0-r0 +--R +--R +--R 908 +--R (4) --- +--R 9 +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +)clear all + +--S 536 of 1751 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^2 +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 536 + +--S 537 of 1751 +r0:=-(3+2*x)*(29+35*x)/(2+5*x+3*x^2)+94*atanh(5+6*x) +--R +--R +--R 2 2 +--R (282x + 470x + 188)atanh(6x + 5) - 70x - 163x - 87 +--R (2) ---------------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 423x - 705x - 282)log(3x + 2) + (423x + 705x + 282)log(x + 1) - 139x +--R + +--R - 121 +--R / +--R 2 +--R 9x + 15x + 6 +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 1751 +m0:=a0-r0 +--R +--R +--R - 141log(3x + 2) + 141log(x + 1) - 282atanh(6x + 5) + 70 +--R (4) -------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1751 +t0:=(5-x)/(2+5*x+3*x^2)^2 +--R +--R +--R - x + 5 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 541 + +--S 542 of 1751 +r0:=(-29-35*x)/(2+5*x+3*x^2)+70*atanh(5+6*x) +--R +--R +--R 2 +--R (210x + 350x + 140)atanh(6x + 5) - 35x - 29 +--R (2) -------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 105x - 175x - 70)log(3x + 2) + (105x + 175x + 70)log(x + 1) - 35x - 29 +--R --------------------------------------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 1751 +m0:=a0-r0 +--R +--R +--R (4) - 35log(3x + 2) + 35log(x + 1) - 70atanh(6x + 5) +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1751 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R 5 4 3 2 +--R 18x + 87x + 164x + 151x + 68x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 1751 +r0:=-3/5*(37+47*x)/(2+5*x+3*x^2)+23*log(1+x)+52/25*log(3+2*x)-627/25*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 1881x - 3135x - 1254)log(3x + 2) + (156x + 260x + 104)log(2x + 3) +--R + +--R 2 +--R (1725x + 2875x + 1150)log(x + 1) - 705x - 555 +--R / +--R 2 +--R 75x + 125x + 50 +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 1881x - 3135x - 1254)log(3x + 2) + (156x + 260x + 104)log(2x + 3) +--R + +--R 2 +--R (1725x + 2875x + 1150)log(x + 1) - 705x - 555 +--R / +--R 2 +--R 75x + 125x + 50 +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 1751 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------ +--R 6 5 4 3 2 +--R 36x + 228x + 589x + 794x + 589x + 228x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 1751 +r0:=(-454/25)/(3+2*x)-3/5*(37+47*x)/((3+2*x)*(2+5*x+3*x^2))+11*log(1+x)+_ + 812/125*log(3+2*x)-2187/125*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (- 13122x - 41553x - 41553x - 13122)log(3x + 2) +--R + +--R 3 2 +--R (4872x + 15428x + 15428x + 4872)log(2x + 3) +--R + +--R 3 2 2 +--R (8250x + 26125x + 26125x + 8250)log(x + 1) - 6810x - 14875x - 7315 +--R / +--R 3 2 +--R 750x + 2375x + 2375x + 750 +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 13122x - 41553x - 41553x - 13122)log(3x + 2) +--R + +--R 3 2 +--R (4872x + 15428x + 15428x + 4872)log(2x + 3) +--R + +--R 3 2 2 +--R (8250x + 26125x + 26125x + 8250)log(x + 1) - 6810x - 14875x - 7315 +--R / +--R 3 2 +--R 750x + 2375x + 2375x + 750 +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1751 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 1751 +r0:=(-428/25)/(3+2*x)^2+(-2618/125)/(3+2*x)-3/5*(37+47*x)/((3+2*x)^2*_ + (2+5*x+3*x^2))-log(1+x)+8104/625*log(3+2*x)-7479/625*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 89748x - 418824x - 710505x - 516051x - 134622)log(3x + 2) +--R + +--R 4 3 2 +--R (97248x + 453824x + 769880x + 559176x + 145872)log(2x + 3) +--R + +--R 4 3 2 3 +--R (- 7500x - 35000x - 59375x - 43125x - 11250)log(x + 1) - 78540x +--R + +--R 2 +--R - 280810x - 319835x - 113815 +--R / +--R 4 3 2 +--R 7500x + 35000x + 59375x + 43125x + 11250 +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 89748x - 418824x - 710505x - 516051x - 134622)log(3x + 2) +--R + +--R 4 3 2 +--R (97248x + 453824x + 769880x + 559176x + 145872)log(2x + 3) +--R + +--R 4 3 2 3 +--R (- 7500x - 35000x - 59375x - 43125x - 11250)log(x + 1) - 78540x +--R + +--R 2 +--R - 280810x - 319835x - 113815 +--R / +--R 4 3 2 +--R 7500x + 35000x + 59375x + 43125x + 11250 +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 1751 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^2) +--R +--R +--R (1) +--R - x + 5 +--R ---------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 144x + 1344x + 5416x + 12296x + 17185x + 15126x + 8181x + 2484x + 324 +--R Type: Fraction(Polynomial(Integer)) +--E 561 + +--S 562 of 1751 +r0:=(-1258/75)/(3+2*x)^3+(-2212/125)/(3+2*x)^2+(-16522/625)/(3+2*x)-_ + 3/5*(37+47*x)/((3+2*x)^3*(2+5*x+3*x^2))-13*log(1+x)+65816/3125*_ + log(3+2*x)-25191/3125*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 1813752x - 11184804x - 27055134x - 31967379x - 18364239x +--R + +--R - 4080942 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 4738752x + 29222304x + 70686384x + 83520504x + 47979864x +--R + +--R 10662192 +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 2925000x - 18037500x - 43631250x - 51553125x - 29615625x +--R + +--R - 6581250 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R - 2973960x - 14873880x - 27167700x - 21302995x - 5978965 +--R / +--R 5 4 3 2 +--R 225000x + 1387500x + 3356250x + 3965625x + 2278125x + 506250 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 1813752x - 11184804x - 27055134x - 31967379x - 18364239x +--R + +--R - 4080942 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 4738752x + 29222304x + 70686384x + 83520504x + 47979864x +--R + +--R 10662192 +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 2925000x - 18037500x - 43631250x - 51553125x - 29615625x +--R + +--R - 6581250 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R - 2973960x - 14873880x - 27167700x - 21302995x - 5978965 +--R / +--R 5 4 3 2 +--R 225000x + 1387500x + 3356250x + 3965625x + 2278125x + 506250 +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 565 + +)clear all + +--S 566 of 1751 +t0:=(5-x)*(3+2*x)^5/(2+5*x+3*x^2)^3 +--R +--R +--R 6 5 4 3 2 +--R - 32x - 80x + 480x + 2520x + 4590x + 3807x + 1215 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 566 + +--S 567 of 1751 +r0:=-182920/9*x-34760/3*x^2-6800/3*x^3-1/2*(3+2*x)^5*(29+35*x)/_ + (2+5*x+3*x^2)^2+5/2*(3+2*x)^4*(137+170*x)/(2+5*x+3*x^2)-_ + 1085*log(1+x)+29375/27*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (528750x + 1762500x + 2173750x + 1175000x + 235000)log(3x + 2) +--R + +--R 4 3 2 +--R (- 527310x - 1757700x - 2167830x - 1171800x - 234360)log(x + 1) +--R + +--R 5 4 3 2 +--R - 576x + 6126120x + 20591850x + 25603665x + 13944270x + 2805921 +--R / +--R 4 3 2 +--R 486x + 1620x + 1998x + 1080x + 216 +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1586250x + 5287500x + 6521250x + 3525000x + 705000)log(3x + 2) +--R + +--R 4 3 2 +--R (- 1581930x - 5273100x - 6503490x - 3515400x - 703080)log(x + 1) +--R + +--R 5 4 3 2 +--R - 1728x - 5760x + 495150x + 1231835x + 979210x + 247043 +--R / +--R 4 3 2 +--R 1458x + 4860x + 5994x + 3240x + 648 +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 1751 +m0:=a0-r0 +--R +--R +--R 1021340 +--R (4) - ------- +--R 81 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 1751 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^3 +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 of 1751 +r0:=-36892/9*x-3392/3*x^2-1/2*(3+2*x)^4*(29+35*x)/(2+5*x+3*x^2)^2+_ + 1/2*(3+2*x)^3*(695+848*x)/(2+5*x+3*x^2)-883*log(1+x)+23825/27*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (428850x + 1429500x + 1763050x + 953000x + 190600)log(3x + 2) +--R + +--R 4 3 2 +--R (- 429138x - 1430460x - 1764234x - 953640x - 190728)log(x + 1) +--R + +--R 4 3 2 +--R 1971108x + 6712446x + 8456811x + 4665198x + 949887 +--R / +--R 4 3 2 +--R 486x + 1620x + 1998x + 1080x + 216 +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (428850x + 1429500x + 1763050x + 953000x + 190600)log(3x + 2) +--R + +--R 4 3 2 +--R (- 429138x - 1430460x - 1764234x - 953640x - 190728)log(x + 1) +--R + +--R 3 2 +--R 142086x + 353367x + 284958x + 73839 +--R / +--R 4 3 2 +--R 486x + 1620x + 1998x + 1080x + 216 +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 1751 +m0:=a0-r0 +--R +--R +--R 36502 +--R (4) - ----- +--R 9 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 1751 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^3 +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 1751 +r0:=-1/2*(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)^2+141/2*(3+2*x)*(7+8*x)/_ + (2+5*x+3*x^2)-1410*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 4 +--R (- 25380x - 84600x - 104340x - 56400x - 11280)atanh(6x + 5) + 6488x +--R + +--R 3 2 +--R 25862x + 37251x + 23010x + 5139 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (114210x + 380700x + 469530x + 253800x + 50760)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 114210x - 380700x - 469530x - 253800x - 50760)log(x + 1) + 38118x +--R + +--R 2 +--R 95203x + 77330x + 20299 +--R / +--R 4 3 2 +--R 162x + 540x + 666x + 360x + 72 +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 1751 +m0:=a0-r0 +--R +--R +--R 6345log(3x + 2) - 6345log(x + 1) + 12690atanh(6x + 5) - 3244 +--R (4) ------------------------------------------------------------ +--R 9 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 1751 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^3 +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 581 + +--S 582 of 1751 +r0:=-1/2*(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)^2+1/2*(7+8*x)*(199+70*x)/_ + (2+5*x+3*x^2)-1102*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 4 +--R (- 19836x - 66120x - 81548x - 44080x - 8816)atanh(6x + 5) + 1680x +--R + +--R 3 2 +--R 8906x + 15173x + 10466x + 2525 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (29754x + 99180x + 122322x + 66120x + 13224)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 29754x - 99180x - 122322x - 66120x - 13224)log(x + 1) + 9918x +--R + +--R 2 +--R 24799x + 20198x + 5335 +--R / +--R 4 3 2 +--R 54x + 180x + 222x + 120x + 24 +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 1751 +m0:=a0-r0 +--R +--R +--R 1653log(3x + 2) - 1653log(x + 1) + 3306atanh(6x + 5) - 280 +--R (4) ---------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1751 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^3 +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 1751 +r0:=-1/2*(3+2*x)*(29+35*x)/(2+5*x+3*x^2)^2+1/2*(725+842*x)/(2+5*x+3*x^2)-_ + 842*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (- 15156x - 50520x - 62308x - 33680x - 6736)atanh(6x + 5) + 2526x +--R + +--R 2 +--R 6315x + 5146x + 1363 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (7578x + 25260x + 31154x + 16840x + 3368)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 7578x - 25260x - 31154x - 16840x - 3368)log(x + 1) + 2526x +--R + +--R 2 +--R 6315x + 5146x + 1363 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 421log(3x + 2) - 421log(x + 1) + 842atanh(6x + 5) +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1751 +t0:=(5-x)/(2+5*x+3*x^2)^3 +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 591 + +--S 592 of 1751 +r0:=1/2*(-29-35*x)/(2+5*x+3*x^2)^2+105/2*(5+6*x)/(2+5*x+3*x^2)-630*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (- 11340x - 37800x - 46620x - 25200x - 5040)atanh(6x + 5) + 1890x +--R + +--R 2 +--R 4725x + 3850x + 1021 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (5670x + 18900x + 23310x + 12600x + 2520)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 5670x - 18900x - 23310x - 12600x - 2520)log(x + 1) + 1890x +--R + +--R 2 +--R 4725x + 3850x + 1021 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Union(Expression(Integer),...) +--E 593 + +--S 594 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 315log(3x + 2) - 315log(x + 1) + 630atanh(6x + 5) +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +)clear all + +--S 596 of 1751 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 54x + 351x + 963x + 1447x + 1287x + 678x + 196x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 596 + +--S 597 of 1751 +r0:=-3/10*(37+47*x)/(2+5*x+3*x^2)^2+1/50*(9587+11442*x)/(2+5*x+3*x^2)-_ + 233*log(1+x)+208/125*log(3+2*x)+28917/125*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (520506x + 1735020x + 2139858x + 1156680x + 231336)log(3x + 2) +--R + +--R 4 3 2 +--R (3744x + 12480x + 15392x + 8320x + 1664)log(2x + 3) +--R + +--R 4 3 2 +--R (- 524250x - 1747500x - 2155250x - 1165000x - 233000)log(x + 1) +--R + +--R 3 2 +--R 171630x + 429855x + 350570x + 93095 +--R / +--R 4 3 2 +--R 2250x + 7500x + 9250x + 5000x + 1000 +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (520506x + 1735020x + 2139858x + 1156680x + 231336)log(3x + 2) +--R + +--R 4 3 2 +--R (3744x + 12480x + 15392x + 8320x + 1664)log(2x + 3) +--R + +--R 4 3 2 +--R (- 524250x - 1747500x - 2155250x - 1165000x - 233000)log(x + 1) +--R + +--R 3 2 +--R 171630x + 429855x + 350570x + 93095 +--R / +--R 4 3 2 +--R 2250x + 7500x + 9250x + 5000x + 1000 +--R Type: Union(Expression(Integer),...) +--E 598 + +--S 599 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 1751 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 108x + 864x + 2979x + 5783x + 6915x + 5217x + 2426x + 636x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 601 + +--S 602 of 1751 +r0:=12946/125/(3+2*x)-3/10*(37+47*x)/((3+2*x)*(2+5*x+3*x^2)^2)+_ + 1/50*(9293+10848*x)/((3+2*x)*(2+5*x+3*x^2))-175*log(1+x)+_ + 4912/625*log(3+2*x)+104463/625*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3760668x + 18176562x + 34263864x + 31547826x + 14206968x +--R + +--R 2507112 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (176832x + 854688x + 1611136x + 1483424x + 668032x + 117888) +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 3937500x - 19031250x - 35875000x - 33031250x - 14875000x +--R + +--R - 2625000 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R 1165140x + 4697400x + 6842995x + 4275600x + 968615 +--R / +--R 5 4 3 2 +--R 22500x + 108750x + 205000x + 188750x + 85000x + 15000 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 3760668x + 18176562x + 34263864x + 31547826x + 14206968x +--R + +--R 2507112 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (176832x + 854688x + 1611136x + 1483424x + 668032x + 117888) +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 3937500x - 19031250x - 35875000x - 33031250x - 14875000x +--R + +--R - 2625000 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R 1165140x + 4697400x + 6842995x + 4275600x + 968615 +--R / +--R 5 4 3 2 +--R 22500x + 108750x + 205000x + 188750x + 85000x + 15000 +--R Type: Union(Expression(Integer),...) +--E 603 + +--S 604 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 605 + +)clear all + +--S 606 of 1751 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 9 8 7 6 5 4 3 2 +--R 216x + 2052x + 8550x + 20503x + 31179x + 31179x + 20503x + 8550x +--R + +--R 2052x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 606 + +--S 607 of 1751 +r0:=11856/125/(3+2*x)^2+35886/625/(3+2*x)-3/10*(37+47*x)/((3+2*x)^2*_ + (2+5*x+3*x^2)^2)+1/50*(8999+10254*x)/((3+2*x)^2*(2+5*x+3*x^2))-_ + 141*log(1+x)+68592/3125*log(3+2*x)+372033/3125*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 26786376x + 169647048x + 438254874x + 590788404x + 438254874x +--R + +--R 169647048x + 26786376 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R 4938624x + 31277952x + 80801376x + 108924096x + 80801376x +--R + +--R 31277952x + 4938624 +--R * +--R log(2x + 3) +--R + +--R 6 5 4 3 2 +--R - 31725000x - 200925000x - 519056250x - 699712500x - 519056250x +--R + +--R - 200925000x - 31725000 +--R * +--R log(x + 1) +--R + +--R 5 4 3 2 +--R 6459480x + 36556020x + 80482290x + 85904835x + 44358230x + 8857895 +--R / +--R 6 5 4 3 2 +--R 225000x + 1425000x + 3681250x + 4962500x + 3681250x + 1425000x +--R + +--R 225000 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 26786376x + 169647048x + 438254874x + 590788404x + 438254874x +--R + +--R 169647048x + 26786376 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R 4938624x + 31277952x + 80801376x + 108924096x + 80801376x +--R + +--R 31277952x + 4938624 +--R * +--R log(2x + 3) +--R + +--R 6 5 4 3 2 +--R - 31725000x - 200925000x - 519056250x - 699712500x - 519056250x +--R + +--R - 200925000x - 31725000 +--R * +--R log(x + 1) +--R + +--R 5 4 3 2 +--R 6459480x + 36556020x + 80482290x + 85904835x + 44358230x + 8857895 +--R / +--R 6 5 4 3 2 +--R 225000x + 1425000x + 3681250x + 4962500x + 3681250x + 1425000x +--R + +--R 225000 +--R Type: Union(Expression(Integer),...) +--E 608 + +--S 609 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 610 + +)clear all + +--S 611 of 1751 +t0:=x/((-1+x)^3*(3+5*x+4*x^2)^2) +--R +--R +--R x +--R (1) ----------------------------------------------- +--R 7 6 5 4 3 2 +--R 16x - 8x - 23x - 13x + 26x + 14x - 3x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 611 + +--S 612 of 1751 +r0:=(-21/736)/(1-x)^2+(-97/4416)/(1-x)+1/276*(39+44*x)/((1-x)^2*_ + (3+5*x+4*x^2))+11/2304*log(1-x)-11/4608*log(3+5*x+4*x^2)+_ + 6023/52992*atan((5+8*x)/sqrt(23))/sqrt(23) +--R +--R +--R (2) +--R 4 3 2 +--+ 2 +--R (- 1012x + 759x + 759x + 253x - 759)\|23 log(4x + 5x + 3) +--R + +--R 4 3 2 +--+ +--R (2024x - 1518x - 1518x - 506x + 1518)\|23 log(- x + 1) +--R + +--R +--+ +--R 4 3 2 (8x + 5)\|23 +--R (48184x - 36138x - 36138x - 12046x + 36138)atan(-------------) +--R 23 +--R + +--R 3 2 +--+ +--R (9312x - 9768x - 2880x - 1080)\|23 +--R / +--R 4 3 2 +--+ +--R (423936x - 317952x - 317952x - 105984x + 317952)\|23 +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--+ 2 +--R (- 1012x + 759x + 759x + 253x - 759)\|23 log(4x + 5x + 3) +--R + +--R 4 3 2 +--+ +--R (2024x - 1518x - 1518x - 506x + 1518)\|23 log(x - 1) +--R + +--R +--+ +--R 4 3 2 (8x + 5)\|23 +--R (48184x - 36138x - 36138x - 12046x + 36138)atan(-------------) +--R 23 +--R + +--R 3 2 +--+ +--R (9312x - 9768x - 2880x - 1080)\|23 +--R / +--R 4 3 2 +--+ +--R (423936x - 317952x - 317952x - 105984x + 317952)\|23 +--R Type: Union(Expression(Integer),...) +--E 613 + +--S 614 of 1751 +m0:=a0-r0 +--R +--R +--R 11log(x - 1) - 11log(- x + 1) +--R (4) ----------------------------- +--R 2304 +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 1751 +t0:=(x^2+x^3)/(-2+x+x^2) +--R +--R +--R 3 2 +--R x + x +--R (1) ---------- +--R 2 +--R x + x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 616 + +--S 617 of 1751 +r0:=1/2*x^2+2/3*log(1-x)+4/3*log(2+x) +--R +--R +--R 2 +--R 8log(x + 2) + 4log(- x + 1) + 3x +--R (2) --------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 8log(x + 2) + 4log(x - 1) + 3x +--R (3) ------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 618 + +--S 619 of 1751 +m0:=a0-r0 +--R +--R +--R 2log(x - 1) - 2log(- x + 1) +--R (4) 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(2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 7 6 5 4 3 +--R 4148064x - 4657872x - 114284804x - 339936502x - 427075232x +--R + +--R 2 +--R - 246418304x - 53656576x +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 8 7 6 5 4 +--R - 5080320x + 1471104x + 144794208x + 532838896x + 868175930x +--R + +--R 3 2 +--R 733421344x + 313489024x + 53656576x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (3386880x + 8239104x + 6635520x + 1769472)\|2 \|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 8296128x - 27095040x - 32956416x - 17694720x - 3538944)\|3 +--R Type: Union(Expression(Integer),...) +--E 638 + +--S 639 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R 3 2 +-+ | 2 +--R (1095640x + 2665312x + 2146560x + 572416)\|2 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R - 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17694720x - 3538944)\|3 +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 640 + +)clear all + +--S 641 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 +--R (1) (- x + 5)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1751 +r0:=-1/9*(2+5*x+3*x^2)^(3/2)-35/144*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)+35/72*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 6x + 5 2 +-+ | 2 +--R - 35atanh(--------------------) + (- 48x + 340x + 318)\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R -------------------------------------------------------------------------- +--R +-+ +--R 144\|3 +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 2 +-+ | 2 3 2 +--R (6930x + 11200x + 4480)\|2 \|3x + 5x + 2 - 16975x - 41580x +--R + +--R - 33600x - 8960 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R 5 4 3 2 +-+ | 2 +--R (23280x - 107876x - 512070x - 565968x - 188800x)\|3 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +-+ +-+ +--R (- 28512x + 108360x + 737652x + 1213630x + 801968x + 188800x)\|2 \|3 +--R / +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (28512x + 46080x + 18432)\|2 \|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 69840x - 171072x - 138240x - 36864)\|3 +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R 2 +-+ | 2 3 2 +--R (6930x + 11200x + 4480)\|2 \|3x + 5x + 2 - 16975x - 41580x +--R + +--R - 33600x - 8960 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R 2 +-+ | 2 3 2 +--R (6930x + 11200x + 4480)\|2 \|3x + 5x + 2 - 16975x - 41580x +--R + +--R - 33600x - 8960 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 2 +-+ | 2 +--R (125928x + 203520x + 81408)\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ +--R (- 154230x - 377784x - 305280x - 81408)\|2 \|3 +--R / +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (28512x + 46080x + 18432)\|2 \|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 69840x - 171072x - 138240x - 36864)\|3 +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2x + 3 +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1751 +r0:=-311/48*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 13/8*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+_ + 1/24*(73-6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +-+ +-+ 8x + 7 +--R - 311atanh(--------------------) + 78\|3 \|5 atanh(--------------------) +--R +------------+ +------------+ +--R +-+ | 2 +-+ | 2 +--R 2\|3 \|3x + 5x + 2 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (- 12x + 146)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 48\|3 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R +-+ | 2 2 +--R ((6220x + 4976)\|2 \|3x + 5x + 2 - 15239x - 24880x - 9952) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ +-+ +-+ | 2 +--R (1560x + 1248)\|2 \|3 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +-+ +--R (- 3822x - 6240x - 2496)\|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (- 6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (4x + 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (588x - 6194x - 5456x)\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 720x + 6984x + 13014x + 5456x)\|2 \|3 +--R / +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R (960x + 768)\|2 \|3 \|3x + 5x + 2 + (- 2352x - 3840x - 1536)\|3 +--R Type: Union(Expression(Integer),...) +--E 648 + +--S 649 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 2 +--R ((6220x + 4976)\|2 \|3x + 5x + 2 - 15239x - 24880x - 9952) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ +-+ +-+ | 2 +--R (1560x + 1248)\|2 \|3 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +-+ +--R (- 3822x - 6240x - 2496)\|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (- 6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (4x + 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R +-+ | 2 2 +--R ((6220x + 4976)\|2 \|3x + 5x + 2 - 15239x - 24880x - 9952) +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ +-+ | 2 +--R (- 1560x - 1248)\|2 \|3 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +-+ +--R (3822x + 6240x + 2496)\|3 \|5 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R (5840x + 4672)\|3 \|3x + 5x + 2 + (- 7154x - 11680x - 4672)\|2 \|3 +--R / +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R (960x + 768)\|2 \|3 \|3x + 5x + 2 + (- 2352x - 3840x - 1536)\|3 +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 650 + +)clear all + +--S 651 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1751 +r0:=43/8*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 57/8*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/2*(8+x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-+ 6x + 5 +--R (86x + 129)\|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ 8x + 7 +--R (- 114x - 171)\|3 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (- 4x - 32)\|3 \|5 \|3x + 5x + 2 +--R / +--R +-+ +-+ +--R (16x + 24)\|3 \|5 +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (6840x + 15732x + 8208)\|2 \|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 16758x - 52497x - 51984x - 16416)\|3 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 + 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (- 20x - 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (5160x + 11868x + 6192)\|2 \|5 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 12642x - 39603x - 39216x - 12384)\|5 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (588x + 3104x + 2176x)\|3 \|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +-+ +--R (- 720x - 4400x - 5824x - 2176x)\|2 \|3 \|5 +--R / +--R +------------+ +--R 2 +-+ +-+ +-+ | 2 +--R (960x + 2208x + 1152)\|2 \|3 \|5 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ +--R (- 2352x - 7368x - 7296x - 2304)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 653 + +--S 654 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ +-+ | 2 +--R (3420x + 2736)\|2 \|3 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (- 8379x - 13680x - 5472)\|3 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 + 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (- 20x - 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (2580x + 2064)\|2 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (- 6321x - 10320x - 4128)\|5 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (- 2580x - 2064)\|2 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (6321x + 10320x + 4128)\|5 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (3420x + 2736)\|2 \|3 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (- 8379x - 13680x - 5472)\|3 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (- 1280x - 1024)\|3 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +-+ +-+ +--R (1568x + 2560x + 1024)\|2 \|3 \|5 +--R / +--R +------------+ +--R +-+ +-+ +-+ | 2 2 +-+ +-+ +--R (480x + 384)\|2 \|3 \|5 \|3x + 5x + 2 + (- 1176x - 1920x - 768)\|3 \|5 +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 655 + +)clear all + +--S 656 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^3 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1751 +r0:=-13/10*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/8*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+27/80*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3/40*(25+26*x)*sqrt(2+5*x+3*x^2)/_ + (3+2*x) +--R +--R +--R (2) +--R 2 +-+ +-+ 6x + 5 +--R (- 40x - 120x - 90)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 2 8x + 7 +--R (108x + 324x + 243)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (248x + 242)\|5 \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (320x + 960x + 720)\|5 +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 3 2 +-+ | 2 4 +--R (19440x + 73872x + 90396x + 34992)\|2 \|3x + 5x + 2 - 47628x +--R + +--R 3 2 +--R - 220644x - 371547x - 268272x - 69984 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 3 2 +-+ +-+ +-+ | 2 +--R (7200x + 27360x + 33480x + 12960)\|2 \|3 \|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 17640x - 81720x - 137610x - 99360x - 25920)\|3 \|5 +--R * +--R +------------+ +--R +-+ +-+ | 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+------------+ +--R 3 2 | 2 +--R (1) (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1751 +r0:=35/144*(5+6*x)*(2+5*x+3*x^2)^(3/2)-1/15*(2+5*x+3*x^2)^(5/2)+_ + 35/2304*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 35/1152*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 175atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (- 6912x + 27360x + 97584x + 86140x + 23178)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 11520\|3 +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (3395350x + 11032000x + 13372800x + 7168000x + 1433600)\|2 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 8316875x - 33953500x - 55160000x - 44576000x - 17920000x +--R + +--R - 2867200 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 9 8 7 6 +--R 328492800x + 40782240x - 7767404400x - 29890298540x +--R + +--R 5 4 3 2 +--R - 54834244450x - 58293938720x - 36765872000x - 12781112320x +--R + +--R - 1886003200x +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 10 9 8 7 +--R - 402319872x - 385214400x + 9477053280x + 44531601000x +--R + +--R 6 5 4 3 +--R 97535832740x + 126958985650x + 103925540960x + 52683324800x +--R + +--R 2 +--R 15138616320x + 1886003200x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R 4 3 2 +-+ +--R (223511040x + 726220800x + 880312320x + 471859200x + 94371840)\|2 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 547488000x - 2235110400x - 3631104000x - 2934374400x +--R + +--R - 1179648000x - 188743680 +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 2 +-+ +--R (3395350x + 11032000x + 13372800x + 7168000x + 1433600)\|2 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 8316875x - 33953500x - 55160000x - 44576000x - 17920000x +--R + +--R - 2867200 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 4 3 2 +-+ +--R (- 3395350x - 11032000x - 13372800x - 7168000x - 1433600)\|2 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R 8316875x + 33953500x + 55160000x + 44576000x + 17920000x + 2867200 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R (899399112x + 2922282240x + 3542340096x + 1898741760x + 379748352) +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 1101534450x - 4496995560x - 7305705600x - 5903900160x +--R + +--R - 2373427200x - 379748352 +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R 4 3 2 +-+ +--R (223511040x + 726220800x + 880312320x + 471859200x + 94371840)\|2 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 547488000x - 2235110400x - 3631104000x - 2934374400x +--R + +--R - 1179648000x - 188743680 +--R * +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1751 +r0:=1/48*(47-6*x)*(2+5*x+3*x^2)^(3/2)-2011/256*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+65/32*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+1/128*(175-414*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 6033atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R 1560\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 288x + 1776x + 1084x + 2554)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 768\|3 +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 3 2 +-+ | 2 +--R (11824680x + 28765344x + 23166720x + 6177792)\|2 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R - 28964433x - 94597440x - 115061376x - 61777920x - 12355584 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 3 2 +-+ +-+ +-+ +--R (3057600x + 7438080x + 5990400x + 1597440)\|2 \|3 \|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 7489560x - 24460800x - 29752320x - 15974400x - 3194880)\|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (- 6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (4x + 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R 7 6 5 4 3 +--R 1382688x - 4010736x - 27559228x - 60181626x - 68305504x +--R + +--R 2 +--R - 39092352x - 8758272x +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 8 7 6 5 4 +--R - 1693440x + 3500928x + 37869984x + 101746832x + 144683990x +--R + +--R 3 2 +--R 116897248x + 50040192x + 8758272x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (1505280x + 3661824x + 2949120x + 786432)\|2 \|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 3687168x - 12042240x - 14647296x - 7864320x - 1572864)\|3 +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R 3 2 +-+ | 2 +--R (11824680x + 28765344x + 23166720x + 6177792)\|2 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R - 28964433x - 94597440x - 115061376x - 61777920x - 12355584 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 3 2 +-+ +-+ +-+ +--R (3057600x + 7438080x + 5990400x + 1597440)\|2 \|3 \|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 7489560x - 24460800x - 29752320x - 15974400x - 3194880)\|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (- 6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (4x + 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (11824680x + 28765344x + 23166720x + 6177792)\|2 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R - 28964433x - 94597440x - 115061376x - 61777920x - 12355584 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ +-+ +--R (- 3057600x - 7438080x - 5990400x - 1597440)\|2 \|3 \|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (7489560x + 24460800x + 29752320x + 15974400x + 3194880)\|3 \|5 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (10011680x + 24354944x + 19614720x + 5230592)\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 12261754x - 40046720x - 48709888x - 26152960x - 5230592)\|2 \|3 +--R / +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (1505280x + 3661824x + 2949120x + 786432)\|2 \|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 3687168x - 12042240x - 14647296x - 7864320x - 1572864)\|3 +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 710 + +)clear all + +--S 711 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1751 +r0:=-1/6*(21+x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)+3743/192*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-161/32*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)-1/96*(361-726*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R (7486x + 11229)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R (- 1932x - 2898)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 96x + 728x - 512x - 3510)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R (384x + 576)\|3 +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +-+ +--R (3786720x + 14891856x + 21236544x + 13106688x + 2967552)\|2 \|3 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 9275532x - 44207058x - 82287744x - 75054336x - 33632256x +--R + +--R - 5935104 +--R * +--R +-+ +-+ +--R \|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (- 4x - 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R 4 3 2 +-+ +--R (14672560x + 57702088x + 82286112x + 50785024x + 11498496)\|2 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 35940286x - 171290909x - 318843712x - 290816128x - 130316288x +--R + +--R - 22996992 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 7 6 5 4 3 +--R 460896x - 1989848x - 7126016x + 2805494x + 21470112x +--R + +--R 2 +--R 19252096x + 5241856x +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 8 7 6 5 4 +--R - 564480x + 1966656x + 10766272x + 3796564x - 29246266x +--R + +--R 3 2 +--R - 45371424x - 25804416x - 5241856x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R 4 3 2 +-+ +-+ +--R (752640x + 2959872x + 4220928x + 2605056x + 589824)\|2 \|3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 1843584x - 8786496x - 16355328x - 14917632x - 6684672x +--R + +--R - 1179648 +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 +-+ +-+ +-+ +--R (1893360x + 4605888x + 3709440x + 989184)\|2 \|3 \|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 4637766x - 15146880x - 18423552x - 9891840x - 1978368)\|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (- 4x - 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (7336280x + 17846624x + 14373120x + 3832832)\|2 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R - 17970143x - 58690240x - 71386496x - 38328320x - 7665664 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 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22314240x + 11980800x + 2396160)\|2 \|3 +--R / +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (376320x + 915456x + 737280x + 196608)\|2 \|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 921792x - 3010560x - 3661824x - 1966080x - 393216)\|3 +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1751 +r0:=-1/4*(8+x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-343/64*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+1329/64*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3/16*(93+43*x)*sqrt(2+5*x+3*x^2)/_ + (3+2*x) +--R +--R +--R (2) +--R 2 +-+ +-+ 6x + 5 +--R (- 1372x - 4116x - 3087)\|3 \|5 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1751 +r0:=35/6*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 1/3*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 6x + 5 +-+ | 2 +--R 35atanh(--------------------) - 2\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ---------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R +-+ | 2 +--R (70\|2 \|3x + 5x + 2 - 175x - 140) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R 10x\|3 \|3x + 5x + 2 + (- 12x - 10x)\|2 \|3 +--R / +--R +------------+ +--R +-+ +-+ | 2 +-+ +--R 12\|2 \|3 \|3x + 5x + 2 + (- 30x - 24)\|3 +--R Type: Union(Expression(Integer),...) +--E 833 + +--S 834 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 +--R (70\|2 \|3x + 5x + 2 - 175x - 140) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ | 2 6x + 5 +--R (- 70\|2 \|3x + 5x + 2 + 175x + 140)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +-+ +-+ +--R - 8\|3 \|3x + 5x + 2 + (10x + 8)\|2 \|3 +--R / +--R +------------+ +--R +-+ +-+ | 2 +-+ +--R 12\|2 \|3 \|3x + 5x + 2 + (- 30x - 24)\|3 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 1751 +t0:=(5-x)/((3+2*x)*sqrt(2+5*x+3*x^2)) +--R +--R +--R 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13\|3 atanh(--------------------) +--R +------------+ +------------+ +--R +-+ | 2 +-+ | 2 +--R 2\|3 \|3x + 5x + 2 2\|5 \|3x + 5x + 2 +--R / +--R +-+ +-+ +--R 2\|3 \|5 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 1751 +t0:=(5-x)/((3+2*x)^2*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------ +--R +------------+ +--R 2 | 2 +--R (4x + 12x + 9)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1751 +r0:=47/10*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/5*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R +------------+ +--R 8x + 7 +-+ | 2 +--R (94x + 141)atanh(--------------------) - 26\|5 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R (2) -------------------------------------------------------------- +--R +-+ +--R (20x + 30)\|5 +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R +-+ | 2 2 +--R ((564x + 846)\|2 \|3x + 5x + 2 - 1410x - 3243x - 1692) +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R 182x\|5 \|3x + 5x + 2 + (- 208x - 182x)\|2 \|5 +--R / +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R (120x + 180)\|2 \|5 \|3x + 5x + 2 + (- 300x - 690x - 360)\|5 +--R Type: Union(Expression(Integer),...) +--E 843 + +--S 844 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 +--R (282\|2 \|3x + 5x + 2 - 705x - 564) +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R +-+ | 2 8x + 7 +--R (- 282\|2 \|3x + 5x + 2 + 705x + 564)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +-+ +-+ +--R - 104\|5 \|3x + 5x + 2 + (130x + 104)\|2 \|5 +--R / +--R +------------+ +--R +-+ +-+ | 2 +-+ +--R 60\|2 \|5 \|3x + 5x + 2 + (- 150x - 120)\|5 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +)clear all + +--S 846 of 1751 +t0:=(5-x)/((3+2*x)^3*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R +------------+ +--R 3 2 | 2 +--R (8x + 36x + 54x + 27)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1751 +r0:=389/100*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/10*sqrt(2+5*x+3*x^2)/(3+2*x)^2-73/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 8x + 7 +--R (1556x + 4668x + 3501)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (- 584x - 1006)\|5 \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (400x + 1200x + 900)\|5 +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 3 2 | 2 +--R (560160x + 2128608x + 2604744x + 1008288)\|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 686196x - 3178908x - 5353029x - 3865104x - 1008288)\|2 +--R * +--R log +--R +------------+ +--R 2 +-+ 2 +-+ | 2 +--R ((280x + 552x + 288)\|5 + (- 230x - 240x)\|2 )\|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ 3 2 +--R (- 344x - 961x - 912x - 288)\|2 \|5 + 560x + 1060x + 480x +--R / +--R +------------+ +--R 2 | 2 +--R (80x + 184x + 96)\|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 98x - 307x - 304x - 96)\|2 +--R + +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (96584x + 252478x + 144048x)\|2 \|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 236368x - 815360x - 865076x - 288096x)\|5 +--R / +--R +------------+ +--R 3 2 +-+ | 2 +--R (144000x + 547200x + 669600x + 259200)\|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 176400x - 817200x - 1376100x - 993600x - 259200)\|2 \|5 +--R Type: Union(Expression(Integer),...) +--E 848 + +--S 849 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R | 2 +--R (140040x + 112032)\|3x + 5x + 2 +--R + +--R 2 +-+ +--R (- 171549x - 280080x - 112032)\|2 +--R * +--R log +--R +------------+ +--R 2 +-+ 2 +-+ | 2 +--R ((280x + 552x + 288)\|5 + (- 230x - 240x)\|2 )\|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ 3 2 +--R (- 344x - 961x - 912x - 288)\|2 \|5 + 560x + 1060x + 480x +--R / +--R +------------+ +--R 2 | 2 +--R (80x + 184x + 96)\|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 98x - 307x - 304x - 96)\|2 +--R + +--R +------------+ +--R | 2 +--R (- 140040x - 112032)\|3x + 5x + 2 +--R + +--R 2 +-+ +--R (171549x + 280080x + 112032)\|2 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R (- 40240x - 32192)\|2 \|5 \|3x + 5x + 2 + (98588x + 160960x + 64384)\|5 +--R / +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R (36000x + 28800)\|5 \|3x + 5x + 2 + (- 44100x - 72000x - 28800)\|2 \|5 +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 1751 +t0:=(5-x)/((3+2*x)^4*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------ +--R +------------+ +--R 4 3 2 | 2 +--R (16x + 96x + 216x + 216x + 81)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1751 +r0:=331/100*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/15*sqrt(2+5*x+3*x^2)/(3+2*x)^3-49/30*sqrt(2+5*x+3*x^2)/(3+2*x)^2-_ + 72/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 8x + 7 +--R (7944x + 35748x + 53622x + 26811)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 2 +-+ | 2 +--R (- 3456x - 11348x - 9506)\|5 \|3x + 5x + 2 +--R / +--R 3 2 +-+ +--R (2400x + 10800x + 16200x + 8100)\|5 +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 42468624x + 259744968x + 622980396x + 730170774x + 416964672x +--R + +--R 92658816 +--R * +--R +------------+ +--R +-+ | 2 +--R \|2 \|3x + 5x + 2 +--R + +--R 6 5 4 3 +--R - 104026680x - 722931804x - 2054741418x - 3052566405x +--R + +--R 2 +--R - 2496962052x - 1065576384x - 185317632 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R 5 4 3 2 +-+ +--R (15141312x + 75268460x + 136296206x + 105169680x + 29158272x)\|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R - 18544048x - 107637840x - 243491160x - 266847110x - 141617520x +--R + +--R - 29158272x +--R * +--R +-+ +-+ +--R \|2 \|5 +--R / +--R 5 4 3 2 +--R 12830400x + 78472800x + 188211600x + 220595400x + 125971200x +--R + +--R 27993600 +--R * +--R +------------+ +--R +-+ +-+ | 2 +--R \|2 \|5 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R - 31428000x - 218408400x - 620767800x - 922225500x - 754369200x +--R + +--R - 321926400x - 55987200 +--R * +--R +-+ +--R \|5 +--R Type: Union(Expression(Integer),...) +--E 853 + +--S 854 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R 2 +-+ | 2 3 +--R (5308578x + 8579520x + 3431808)\|2 \|3x + 5x + 2 - 13003335x +--R + +--R 2 +--R - 31851468x - 25738560x - 6863616 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R 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log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R 2 +-+ | 2 3 2 +--R (- 48906x - 79040x - 31616)\|2 \|3x + 5x + 2 + 119795x + 293436x +--R + +--R 237120x + 63232 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 2 +-+ | 2 +--R (- 312444x - 504960x - 201984)\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ +--R (382665x + 937332x + 757440x + 201984)\|2 \|3 +--R / +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (1782x + 2880x + 1152)\|2 \|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 4365x - 10692x - 8640x - 2304)\|3 +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 875 + +)clear all + +--S 876 of 1751 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1751 +r0:=2*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-2*(3+2*x)^2*_ + (29+35*x)/sqrt(2+5*x+3*x^2)+184/3*sqrt(2+5*x+3*x^2)+140/3*(3+2*x)*_ + sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R +-+ | 2 6x + 5 2 +--R 6\|3 \|3x + 5x + 2 atanh(--------------------) - 4x - 398x - 358 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ------------------------------------------------------------------ +--R +------------+ +--R | 2 +--R 3\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (294x + 480x + 192)\|2 \|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 720x - 1776x - 1440x - 384)\|3 +--R * +--R +------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|3 + 2\|2 )\|3x + 5x + 2 + 2x\|2 \|3 - 6x - 5x - 4 +--R log(-------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R 3 2 | 2 +--R (160x - 1494x - 1584x)\|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 196x + 1658x + 3474x + 1584x)\|2 +--R / +--R +------------+ +--R 2 +-+ | 2 3 2 +--R (147x + 240x + 96)\|2 \|3x + 5x + 2 - 360x - 888x - 720x - 192 +--R Type: Union(Expression(Integer),...) +--E 878 + +--S 879 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R ((240x + 192)\|3 \|3x + 5x + 2 + (- 294x - 480x - 192)\|2 \|3 ) +--R * +--R +------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|3 + 2\|2 )\|3x + 5x + 2 + 2x\|2 \|3 - 6x - 5x - 4 +--R log(-------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R ((- 240x - 192)\|3 \|3x + 5x + 2 + (294x + 480x + 192)\|2 \|3 ) +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 2 +--R (- 7160x - 5728)\|2 \|3x + 5x + 2 + 17542x + 28640x + 11456 +--R / +--R +------------+ +--R | 2 2 +-+ +--R (120x + 96)\|3x + 5x + 2 + (- 147x - 240x - 96)\|2 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 880 + +)clear all + +--S 881 of 1751 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1751 +r0:=-2/3*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 2*(3+2*x)*(29+35*x)/sqrt(2+5*x+3*x^2)+140/3*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 6x + 5 +-+ +--R - 2\|3x + 5x + 2 atanh(--------------------) + (- 278x - 242)\|3 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ------------------------------------------------------------------ +--R +------------+ +--R +-+ | 2 +--R 3\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R | 2 2 +-+ +--R ((10x + 8)\|3x + 5x + 2 + (- 12x - 20x - 8)\|2 ) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R - 49x\|2 \|3 \|3x + 5x + 2 + (62x + 98x)\|3 +--R / +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R (15x + 12)\|3 \|3x + 5x + 2 + (- 18x - 30x - 12)\|2 \|3 +--R Type: Union(Expression(Integer),...) +--E 883 + +--S 884 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 +--R (4\|2 \|3x + 5x + 2 - 10x - 8) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ | 2 6x + 5 +--R (4\|2 \|3x + 5x + 2 - 10x - 8)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +-+ +-+ +--R - 484\|3 \|3x + 5x + 2 + (605x + 484)\|2 \|3 +--R / +--R +------------+ +--R +-+ +-+ | 2 +-+ +--R 6\|2 \|3 \|3x + 5x + 2 + (- 15x - 12)\|3 +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 1751 +t0:=(5-x)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R - x + 5 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1751 +r0:=-2*(29+35*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R - 70x - 58 +--R (2) --------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1751 +a0:=integrate(t0,x) +--R +--R +--R +------------+ +--R | 2 2 +-+ +--R - 10x\|3x + 5x + 2 + (- 2x + 10x)\|2 +--R (3) -------------------------------------------- +--R +------------+ +--R +-+ | 2 2 +--R (5x + 4)\|2 \|3x + 5x + 2 - 12x - 20x - 8 +--R Type: Union(Expression(Integer),...) +--E 888 + +--S 889 of 1751 +m0:=a0-r0 +--R +--R +--R +------------+ +--R +-+ | 2 +--R - 116\|2 \|3x + 5x + 2 + 290x + 232 +--R (4) ------------------------------------- +--R +------------+ +--R | 2 +-+ +--R 4\|3x + 5x + 2 + (- 5x - 4)\|2 +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 1751 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------- +--R +------------+ +--R 3 2 | 2 +--R (6x + 19x + 19x + 6)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1751 +r0:=26/5*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 8x + 7 +-+ +--R 26\|3x + 5x + 2 atanh(--------------------) + (- 282x - 222)\|5 +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R (2) ----------------------------------------------------------------- +--R +------------+ +--R +-+ | 2 +--R 5\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R | 2 2 +-+ +--R ((130x + 104)\|3x + 5x + 2 + (- 156x - 260x - 104)\|2 ) +--R * +--R log +--R +------------+ +--R 2 +-+ 2 +-+ | 2 +--R ((280x + 552x + 288)\|5 + (- 230x - 240x)\|2 )\|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ 3 2 +--R (- 344x - 961x - 912x - 288)\|2 \|5 + 560x + 1060x + 480x +--R / +--R +------------+ +--R 2 | 2 +--R (80x + 184x + 96)\|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 98x - 307x - 304x - 96)\|2 +--R + +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R 9x\|2 \|5 \|3x + 5x + 2 + (- 78x - 18x)\|5 +--R / +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R (25x + 20)\|5 \|3x + 5x + 2 + (- 30x - 50x - 20)\|2 \|5 +--R Type: Union(Expression(Integer),...) +--E 893 + +--S 894 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 +--R (52\|2 \|3x + 5x + 2 - 130x - 104) +--R * +--R log +--R +------------+ +--R 2 +-+ 2 +-+ | 2 +--R ((280x + 552x + 288)\|5 + (- 230x - 240x)\|2 )\|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ 3 2 +--R (- 344x - 961x - 912x - 288)\|2 \|5 + 560x + 1060x + 480x +--R / +--R +------------+ +--R 2 | 2 +--R (80x + 184x + 96)\|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 98x - 307x - 304x - 96)\|2 +--R + +--R +------------+ +--R +-+ | 2 8x + 7 +--R (- 52\|2 \|3x + 5x + 2 + 130x + 104)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +-+ +-+ +--R - 444\|5 \|3x + 5x + 2 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Expression(Integer) +--E 897 + +--S 898 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 3 2 +-+ | 2 4 +--R (88788x + 278142x + 275424x + 86976)\|2 \|3x + 5x + 2 - 217440x +--R + +--R 3 2 +--R - 862512x - 1239408x - 768288x - 173952 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (31604x + 62974x + 26992x)\|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 38856x - 109478x - 96714x - 26992x)\|2 \|5 +--R / +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (7350x + 23025x + 22800x + 7200)\|2 \|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 18000x - 71400x - 102600x - 63600x - 14400)\|5 +--R Type: Union(Expression(Integer),...) +--E 898 + +--S 899 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R | 2 2 +-+ +--R ((36240x + 28992)\|3x + 5x + 2 + (- 44394x - 72480x - 28992)\|2 ) +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R | 2 2 +-+ +--R ((- 36240x - 28992)\|3x + 5x + 2 + (44394x + 72480x + 28992)\|2 ) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (- 56440x - 45152)\|2 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (138278x + 225760x + 90304)\|5 +--R / +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R (3000x + 2400)\|5 \|3x + 5x + 2 + (- 3675x - 6000x - 2400)\|2 \|5 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +)clear all + +--S 901 of 1751 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 | 2 +--R (24x + 148x + 358x + 423x + 243x + 54)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1751 +r0:=483/25*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/((3+2*x)^2*sqrt(2+5*x+3*x^2))-166/5*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2-864/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R 2 | 2 8x + 7 +--R (1932x + 5796x + 4347)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 5184x - 18906x - 21976x - 7954)\|5 +--R / +--R +------------+ +--R 2 +-+ | 2 +--R (100x + 300x + 225)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 8433180x + 45956484x + 97637967x + 101006892x + 50912064x +--R + +--R 10015488 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4 3 2 +--R - 20592x - 30096x + 447048x + 2029120x + 3733305x + 3496257x +--R + +--R 1636821x + 301887 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 6435 +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2) +--R +--R +--R 5 4 3 2 +------+ +--R (1) (- 12x + 4x + 185x + 406x + 327x + 90)\|2x + 3 +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1751 +r0:=65/56*(3+2*x)^(7/2)-109/72*(3+2*x)^(9/2)+47/88*(3+2*x)^(11/2)-_ + 3/104*(3+2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 16632x + 4284x + 375242x + 1116057x + 1364067x + 758349x +--R + +--R 157383 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 9009 +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 16632x + 4284x + 375242x + 1116057x + 1364067x + 758349x +--R + +--R 157383 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 9009 +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +------+ +--R (1) (- 6x + 11x + 76x + 89x + 30)\|2x + 3 +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1751 +r0:=13/8*(3+2*x)^(5/2)-109/56*(3+2*x)^(7/2)+47/72*(3+2*x)^(9/2)-_ + 3/88*(3+2*x)^(11/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 756x + 1568x + 15627x + 28143x + 19251x + 4617)\|2x + 3 +--R (2) --------------------------------------------------------------- +--R 693 +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +------+ +--R (- 756x + 1568x + 15627x + 28143x + 19251x + 4617)\|2x + 3 +--R (3) --------------------------------------------------------------- +--R 693 +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)*sqrt(3+2*x) +--R +--R +--R 3 2 +------+ +--R (1) (- 3x + 10x + 23x + 10)\|2x + 3 +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1751 +r0:=65/24*(3+2*x)^(3/2)-109/40*(3+2*x)^(5/2)+47/56*(3+2*x)^(7/2)-_ + 1/24*(3+2*x)^(9/2) +--R +--R +--R 4 3 2 +------+ +--R (- 70x + 285x + 1083x + 949x + 303)\|2x + 3 +--R (2) ----------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +------+ +--R (- 70x + 285x + 1083x + 949x + 303)\|2x + 3 +--R (3) ----------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)/sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ----------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1751 +r0:=-109/24*(3+2*x)^(3/2)+47/40*(3+2*x)^(5/2)-3/56*(3+2*x)^(7/2)+_ + 65/8*sqrt(3+2*x) +--R +--R +--R 3 2 +------+ +--R (- 45x + 291x + 223x + 381)\|2x + 3 +--R (2) -------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +------+ +--R (- 45x + 291x + 223x + 381)\|2x + 3 +--R (3) -------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(3/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ----------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1751 +r0:=47/24*(3+2*x)^(3/2)-3/40*(3+2*x)^(5/2)+(-65/8)/sqrt(3+2*x)-_ + 109/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 9x + 77x - 117x - 501 +--R (2) ------------------------- +--R +------+ +--R 15\|2x + 3 +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 9x + 77x - 117x - 501 +--R (3) ------------------------- +--R +------+ +--R 15\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 988 + +--S 989 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(5/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ------------------------ +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1751 +r0:=(-65/24)/(3+2*x)^(3/2)-1/8*(3+2*x)^(3/2)+109/8/sqrt(3+2*x)+_ + 47/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 3x + 57x + 273x + 263 +--R (2) ------------------------- +--R +------+ +--R (6x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 3x + 57x + 273x + 263 +--R (3) ------------------------- +--R +------+ +--R (6x + 9)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(7/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1751 +r0:=(-13/8)/(3+2*x)^(5/2)+109/24/(3+2*x)^(3/2)+(-47/8)/sqrt(3+2*x)-_ + 3/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 9x - 111x - 245x - 153 +--R (2) -------------------------- +--R 2 +------+ +--R (12x + 36x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 9x - 111x - 245x - 153 +--R (3) -------------------------- +--R 2 +------+ +--R (12x + 36x + 27)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 998 + +--S 999 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1000 + +)clear all + +--S 1001 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 72x - 204x + 958x + 5955x + 13215x + 15577x + 10359x + 3672x +--R + +--R 540 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1751 +r0:=325/288*(3+2*x)^(9/2)-1065/352*(3+2*x)^(11/2)+651/208*(3+2*x)^(13/2)-_ + 359/240*(3+2*x)^(15/2)+165/544*(3+2*x)^(17/2)-9/608*(3+2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R - 15752880x - 51274080x + 262729896x + 1939330008x + 5196312621x +--R + +--R 4 3 2 +--R 7690154020x + 6844462215x + 3651616134x + 1077299892x + 135278424 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 2078505 +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 +--R - 15752880x - 51274080x + 262729896x + 1939330008x + 5196312621x +--R + +--R 4 3 2 +--R 7690154020x + 6844462215x + 3651616134x + 1077299892x + 135278424 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 2078505 +--R Type: Union(Expression(Integer),...) +--E 1003 + +--S 1004 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^2 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +------+ +--R (- 36x - 48x + 551x + 2151x + 3381x + 2717x + 1104x + 180)\|2x + 3 +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1751 +r0:=325/224*(3+2*x)^(7/2)-355/96*(3+2*x)^(9/2)+651/176*(3+2*x)^(11/2)-_ + 359/208*(3+2*x)^(13/2)+11/32*(3+2*x)^(15/2)-9/544*(3+2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 216216x - 348348x + 4324782x + 20560239x + 40692820x +--R + +--R 3 2 +--R 43843941x + 26848368x + 8789688x + 1198476 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 51051 +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R - 216216x - 348348x + 4324782x + 20560239x + 40692820x +--R + +--R 3 2 +--R 43843941x + 26848368x + 8789688x + 1198476 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 51051 +--R Type: Union(Expression(Integer),...) +--E 1008 + +--S 1009 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1010 + +)clear all + +--S 1011 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^2 +--R +--R +--R 6 5 4 3 2 +------+ +--R (1) (- 18x + 3x + 271x + 669x + 687x + 328x + 60)\|2x + 3 +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1751 +r0:=65/32*(3+2*x)^(5/2)-1065/224*(3+2*x)^(7/2)+217/48*(3+2*x)^(9/2)-_ + 359/176*(3+2*x)^(11/2)+165/416*(3+2*x)^(13/2)-3/160*(3+2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 36036x + 2772x + 747579x + 2342620x + 3236325x + 2333766x +--R + +--R 857988x + 128736 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15015 +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 36036x + 2772x + 747579x + 2342620x + 3236325x + 2333766x +--R + +--R 857988x + 128736 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15015 +--R Type: Union(Expression(Integer),...) +--E 1013 + +--S 1014 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1015 + +)clear all + +--S 1016 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^2*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +------+ +--R (1) (- 9x + 15x + 113x + 165x + 96x + 20)\|2x + 3 +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1751 +r0:=325/96*(3+2*x)^(3/2)-213/32*(3+2*x)^(5/2)+93/16*(3+2*x)^(7/2)-_ + 359/144*(3+2*x)^(9/2)+15/32*(3+2*x)^(11/2)-9/416*(3+2*x)^(13/2) +--R +--R +--R 6 5 4 3 2 +------+ +--R (- 162x + 297x + 3028x + 5991x + 5292x + 2208x + 396)\|2x + 3 +--R (2) ------------------------------------------------------------------- +--R 117 +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 6 5 4 3 2 +------+ +--R (- 162x + 297x + 3028x + 5991x + 5292x + 2208x + 396)\|2x + 3 +--R (3) ------------------------------------------------------------------- +--R 117 +--R Type: Union(Expression(Integer),...) +--E 1018 + +--S 1019 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^2/sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1751 +r0:=-355/32*(3+2*x)^(3/2)+651/80*(3+2*x)^(5/2)-359/112*(3+2*x)^(7/2)+_ + 55/96*(3+2*x)^(9/2)-9/352*(3+2*x)^(11/2)+325/32*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +------+ +--R (- 945x + 3500x + 12645x + 15354x + 6252x + 4344)\|2x + 3 +--R (2) -------------------------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +------+ +--R (- 945x + 3500x + 12645x + 15354x + 6252x + 4344)\|2x + 3 +--R (3) -------------------------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 1023 + +--S 1024 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1025 + +)clear all + +--S 1026 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1751 +r0:=217/16*(3+2*x)^(3/2)-359/80*(3+2*x)^(5/2)+165/224*(3+2*x)^(7/2)-_ + 1/32*(3+2*x)^(9/2)+(-325/32)/sqrt(3+2*x)-1065/32*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 35x + 150x + 431x + 632x - 432x - 1996 +--R (2) -------------------------------------------- +--R +------+ +--R 35\|2x + 3 +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 35x + 150x + 431x + 632x - 432x - 1996 +--R (3) -------------------------------------------- +--R +------+ +--R 35\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1028 + +--S 1029 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1030 + +)clear all + +--S 1031 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(5/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1751 +r0:=(-325/96)/(3+2*x)^(3/2)-359/48*(3+2*x)^(3/2)+33/32*(3+2*x)^(5/2)-_ + 9/224*(3+2*x)^(7/2)+1065/32/sqrt(3+2*x)+651/16*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 27x + 144x + 215x + 1530x + 7164x + 7024 +--R (2) ---------------------------------------------- +--R +------+ +--R (42x + 63)\|2x + 3 +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 27x + 144x + 215x + 1530x + 7164x + 7024 +--R (3) ---------------------------------------------- +--R +------+ +--R (42x + 63)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1033 + +--S 1034 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1035 + +)clear all + +--S 1036 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(7/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1751 +r0:=(-65/32)/(3+2*x)^(5/2)+355/32/(3+2*x)^(3/2)+55/32*(3+2*x)^(3/2)-_ + 9/160*(3+2*x)^(5/2)+(-651/16)/sqrt(3+2*x)-359/16*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 9x + 70x - 275x - 3300x - 6760x - 4076 +--R (2) -------------------------------------------- +--R 2 +------+ +--R (20x + 60x + 45)\|2x + 3 +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 9x + 70x - 275x - 3300x - 6760x - 4076 +--R (3) -------------------------------------------- +--R 2 +------+ +--R (20x + 60x + 45)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1038 + +--S 1039 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1040 + +)clear all + +--S 1041 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 216x - 972x + 1710x + 22247x + 71336x + 124716x + 135392x +--R + +--R 3 2 +--R 93965x + 40698x + 10044x + 1080 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1751 +r0:=1625/1152*(3+2*x)^(9/2)-7925/1408*(3+2*x)^(11/2)+_ + 16005/1664*(3+2*x)^(13/2)-17201/1920*(3+2*x)^(15/2)+_ + 10475/2176*(3+2*x)^(17/2)-3519/2432*(3+2*x)^(19/2)+_ + 27/128*(3+2*x)^(21/2)-27/2944*(3+2*x)^(23/2) +--R +--R +--R (2) +--R 11 10 9 8 +--R - 897914160x - 4489570800x + 8356902840x + 126274674240x +--R + +--R 7 6 5 4 +--R 465368338149x + 952484547267x + 1244240822034x + 1081998930520x +--R + +--R 3 2 +--R 626194644675x + 232269229971x + 50041179918x + 4766652846 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 47805615 +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 10 9 8 +--R - 897914160x - 4489570800x + 8356902840x + 126274674240x +--R + +--R 7 6 5 4 +--R 465368338149x + 952484547267x + 1244240822034x + 1081998930520x +--R + +--R 3 2 +--R 626194644675x + 232269229971x + 50041179918x + 4766652846 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 47805615 +--R Type: Union(Expression(Integer),...) +--E 1043 + +--S 1044 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1045 + +)clear all + +--S 1046 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 108x - 324x + 1341x + 9112x + 22000x + 29358x + 23659x + 11494x +--R + +--R 3108x + 360 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1751 +r0:=1625/896*(3+2*x)^(7/2)-7925/1152*(3+2*x)^(9/2)+_ + 1455/128*(3+2*x)^(11/2)-17201/1664*(3+2*x)^(13/2)+_ + 2095/384*(3+2*x)^(15/2)-207/128*(3+2*x)^(17/2)+_ + 567/2432*(3+2*x)^(19/2)-9/896*(3+2*x)^(21/2) +--R +--R +--R (2) +--R 10 9 8 7 6 +--R - 160056x - 543348x + 2428218x + 19193889x + 54383679x +--R + +--R 5 4 3 2 +--R 87436314x + 88365578x + 57400347x + 23339691x + 5418846x + 549342 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15561 +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 7 6 +--R - 160056x - 543348x + 2428218x + 19193889x + 54383679x +--R + +--R 5 4 3 2 +--R 87436314x + 88365578x + 57400347x + 23339691x + 5418846x + 549342 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15561 +--R Type: Union(Expression(Integer),...) +--E 1048 + +--S 1049 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1050 + +)clear all + +--S 1051 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (- 54x - 81x + 792x + 3368x + 5948x + 5757x + 3194x + 956x + 120) +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1751 +r0:=325/128*(3+2*x)^(5/2)-7925/896*(3+2*x)^(7/2)+_ + 5335/384*(3+2*x)^(9/2)-17201/1408*(3+2*x)^(11/2)+_ + 10475/1664*(3+2*x)^(13/2)-1173/640*(3+2*x)^(15/2)+_ + 567/2176*(3+2*x)^(17/2)-27/2432*(3+2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R - 27567540x - 48648600x + 511413903x + 2573238129x + 5488936698x +--R + +--R 4 3 2 +--R 6671966560x + 4954126305x + 2231396337x + 561646746x + 61003962 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 4849845 +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 +--R - 27567540x - 48648600x + 511413903x + 2573238129x + 5488936698x +--R + +--R 4 3 2 +--R 6671966560x + 4954126305x + 2231396337x + 561646746x + 61003962 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 4849845 +--R Type: Union(Expression(Integer),...) +--E 1053 + +--S 1054 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1055 + +)clear all + +--S 1056 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^3*sqrt(3+2*x) +--R +--R +--R 7 5 4 3 2 +------+ +--R (1) (- 27x + 396x + 1090x + 1339x + 870x + 292x + 40)\|2x + 3 +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1751 +r0:=1625/384*(3+2*x)^(3/2)-1585/128*(3+2*x)^(5/2)+_ + 16005/896*(3+2*x)^(7/2)-17201/1152*(3+2*x)^(9/2)+_ + 10475/1408*(3+2*x)^(11/2)-3519/1664*(3+2*x)^(13/2)+_ + 189/640*(3+2*x)^(15/2)-27/2176*(3+2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 2432430x - 243243x + 47045691x + 157479462x + 243619810x +--R + +--R 3 2 +--R 212153055x + 107295183x + 29433414x + 3591558 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 765765 +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R - 2432430x - 243243x + 47045691x + 157479462x + 243619810x +--R + +--R 3 2 +--R 212153055x + 107295183x + 29433414x + 3591558 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 765765 +--R Type: Union(Expression(Integer),...) +--E 1058 + +--S 1059 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1060 + +)clear all + +--S 1061 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^3/sqrt(3+2*x) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1061 + +--S 1062 of 1751 +r0:=-7925/384*(3+2*x)^(3/2)+3201/128*(3+2*x)^(5/2)-17201/896*(3+2*x)^(7/2)+_ + 10475/1152*(3+2*x)^(9/2)-3519/1408*(3+2*x)^(11/2)+567/1664*(3+2*x)^(13/2)-_ + 9/640*(3+2*x)^(15/2)+1625/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 81081x + 130977x + 1407294x + 3109960x + 3285105x + 1924641x +--R + +--R 535098x + 196506 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 45045 +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 81081x + 130977x + 1407294x + 3109960x + 3285105x + 1924641x +--R + +--R 535098x + 196506 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 45045 +--R Type: Union(Expression(Integer),...) +--E 1063 + +--S 1064 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1065 + +)clear all + +--S 1066 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(3/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1751 +r0:=5335/128*(3+2*x)^(3/2)-17201/640*(3+2*x)^(5/2)+10475/896*(3+2*x)^(7/2)-_ + 391/128*(3+2*x)^(9/2)+567/1408*(3+2*x)^(11/2)-27/1664*(3+2*x)^(13/2)+_ + (-1625/128)/sqrt(3+2*x)-7925/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 10395x + 19845x + 180530x + 392500x + 398339x + 256433x - 77138x +--R + +--R - 431614 +--R / +--R +------+ +--R 5005\|2x + 3 +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 10395x + 19845x + 180530x + 392500x + 398339x + 256433x - 77138x +--R + +--R - 431614 +--R / +--R +------+ +--R 5005\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1068 + +--S 1069 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1070 + +)clear all + +--S 1071 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(5/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1751 +r0:=(-1625/384)/(3+2*x)^(3/2)-17201/384*(3+2*x)^(3/2)+2095/128*(3+2*x)^(5/2)-_ + 3519/896*(3+2*x)^(7/2)+63/128*(3+2*x)^(9/2)-27/1408*(3+2*x)^(11/2)+_ + 7925/128/sqrt(3+2*x)+16005/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 567x + 1323x + 9666x + 21360x + 17663x + 42003x + 184566x + 181486 +--R -------------------------------------------------------------------------- +--R +------+ +--R (462x + 693)\|2x + 3 +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 567x + 1323x + 9666x + 21360x + 17663x + 42003x + 184566x + 181486 +--R -------------------------------------------------------------------------- +--R +------+ +--R (462x + 693)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1073 + +--S 1074 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1075 + +)clear all + +--S 1076 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(7/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1751 +r0:=(-325/128)/(3+2*x)^(5/2)+7925/384/(3+2*x)^(3/2)+10475/384*(3+2*x)^(3/2)-_ + 3519/640*(3+2*x)^(5/2)+81/128*(3+2*x)^(7/2)-3/128*(3+2*x)^(9/2)+_ + (-16005/128)/sqrt(3+2*x)-17201/128*sqrt(3+2*x) +--R +--R +--R 7 6 5 4 3 2 +--R - 45x + 135x + 702x + 1940x - 3195x - 41805x - 85070x - 51162 +--R (2) ------------------------------------------------------------------- +--R 2 +------+ +--R (60x + 180x + 135)\|2x + 3 +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 7 6 5 4 3 2 +--R - 45x + 135x + 702x + 1940x - 3195x - 41805x - 85070x - 51162 +--R (3) ------------------------------------------------------------------- +--R 2 +------+ +--R (60x + 180x + 135)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1078 + +--S 1079 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +)clear all + +--S 1081 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1751 +r0:=526/81*(3+2*x)^(3/2)+62/45*(3+2*x)^(5/2)-2/21*(3+2*x)^(7/2)+_ + 12*atanh(sqrt(3+2*x))-4250/81*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+_ + 3278/81*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 34020\|3 atanh(\|2x + 3 ) - 148750\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (- 2160x + 5904x + 69112x + 197824)\|3 \|2x + 3 +--R / +--R +-+ +--R 2835\|3 +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +------+ +--R 17010\|3 log(\|2x + 3 + 1) - 17010\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +--R 74375\|5 log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (- 2160x + 5904x + 69112x + 197824)\|3 \|2x + 3 +--R / +--R +-+ +--R 2835\|3 +--R Type: Union(Expression(Integer),...) +--E 1083 + +--S 1084 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 486\|3 log(\|2x + 3 + 1) - 486\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 2125\|5 log(-------------------------------) - 972\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 4250\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1751 +r0:=62/27*(3+2*x)^(3/2)-2/15*(3+2*x)^(5/2)+12*atanh(sqrt(3+2*x))-_ + 850/27*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+526/27*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 1620\|3 atanh(\|2x + 3 ) - 4250\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +------+ +--R (- 72x + 404x + 3398)\|3 \|2x + 3 +--R / +--R +-+ +--R 135\|3 +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +------+ +--R 810\|3 log(\|2x + 3 + 1) - 810\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +--R 2125\|5 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +--R (- 72x + 404x + 3398)\|3 \|2x + 3 +--R / +--R +-+ +--R 135\|3 +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 162\|3 log(\|2x + 3 + 1) - 162\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 425\|5 log(-------------------------------) - 324\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 850\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1751 +r0:=-2/9*(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-170/9*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(5/3)+62/9*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 108\|3 atanh(\|2x + 3 ) - 170\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +------+ +--R (- 4x + 56)\|3 \|2x + 3 +--R / +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +------+ +--R 54\|3 log(\|2x + 3 + 1) - 54\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 85\|5 log(-------------------------------) + (- 4x + 56)\|3 \|2x + 3 +--R 3x + 2 +--R / +--R +-+ +--R 9\|3 +--R Type: Union(Expression(Integer),...) +--E 1093 + +--S 1094 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 54\|3 log(\|2x + 3 + 1) - 54\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 85\|5 log(-------------------------------) - 108\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 170\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 1751 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ------------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1751 +r0:=12*atanh(sqrt(3+2*x))-34/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-_ + 2/3*sqrt(3+2*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +-+ +------+ +--R 36\|3 atanh(\|2x + 3 ) - 34\|5 atanh(-------------) - 2\|3 \|2x + 3 +--R +-+ +--R \|5 +--R (2) -------------------------------------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +------+ +--R 18\|3 log(\|2x + 3 + 1) - 18\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 17\|5 log(-------------------------------) - 2\|3 \|2x + 3 +--R 3x + 2 +--R / +--R +-+ +--R 3\|3 +--R Type: Union(Expression(Integer),...) +--E 1098 + +--S 1099 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 18\|3 log(\|2x + 3 + 1) - 18\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 17\|5 log(-------------------------------) - 36\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 34\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1100 + +)clear all + +--S 1101 of 1751 +t0:=(5-x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) ----------------------- +--R 2 +------+ +--R (3x + 5x + 2)\|2x + 3 +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1751 +r0:=12*atanh(sqrt(3+2*x))-34*atanh(sqrt(3/5)*sqrt(3+2*x))/sqrt(15) +--R +--R +--R +-+ +------+ +--R +--+ +------+ \|3 \|2x + 3 +--R 12\|15 atanh(\|2x + 3 ) - 34atanh(-------------) +--R +-+ +--R \|5 +--R (2) ------------------------------------------------ +--R +--+ +--R \|15 +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +------+ +--+ +------+ +--R 6\|15 log(\|2x + 3 + 1) - 6\|15 log(\|2x + 3 - 1) +--R + +--R +------+ +--+ +--R - 15\|2x + 3 + (3x + 7)\|15 +--R 17log(-----------------------------) +--R 3x + 2 +--R / +--R +--+ +--R \|15 +--R Type: Union(Expression(Integer),...) +--E 1103 + +--S 1104 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +------+ +--+ +------+ +--R 6\|15 log(\|2x + 3 + 1) - 6\|15 log(\|2x + 3 - 1) +--R + +--R +------+ +--+ +--R - 15\|2x + 3 + (3x + 7)\|15 +--+ +------+ +--R 17log(-----------------------------) - 12\|15 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R \|3 \|2x + 3 +--R 34atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +--+ +--R \|15 +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-+ +-+ +--+ +------+ +--+ +-+ +-+ +--R (17\|3 \|5 \|15 - 255)\|2x + 3 + (51x + 119)\|15 + (- 51x - 119)\|3 \|5 +--R --------------------------------------------------------------------------- +--R 2 +--+ +------+ 2 +--R (9x + 27x + 14)\|15 \|2x + 3 - 90x - 195x - 90 +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------- +--R 3 2 +------+ +--R (6x + 19x + 19x + 6)\|2x + 3 +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1751 +r0:=12*atanh(sqrt(3+2*x))-34/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-26/5)/sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +------+ +-+ +------+ \|3 \|2x + 3 +--R 60\|5 \|2x + 3 atanh(\|2x + 3 ) - 34\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +--R - 26\|5 +--R / +--R +-+ +------+ +--R 5\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +------+ +-+ +------+ +------+ +--R 30\|5 \|2x + 3 log(\|2x + 3 + 1) - 30\|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ +------+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +--R 17\|3 \|2x + 3 log(-------------------------------) - 26\|5 +--R 3x + 2 +--R / +--R +-+ +------+ +--R 5\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1108 + +--S 1109 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 30\|5 log(\|2x + 3 + 1) - 30\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 17\|3 log(-------------------------------) - 60\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 34\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 5\|5 +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1110 + +)clear all + +--S 1111 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------- +--R 4 3 2 +------+ +--R (12x + 56x + 95x + 69x + 18)\|2x + 3 +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1751 +r0:=(-26/15)/(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-102/25*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(3/5)+(-198/25)/sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +------+ +--R (1800x + 2700)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +-+ +--R (- 612x - 918)\|3 \|2x + 3 atanh(-------------) + (- 1188x - 1912)\|5 +--R +-+ +--R \|5 +--R / +--R +-+ +------+ +--R (150x + 225)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1112 + +--S 1113 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +------+ +--R (900x + 1350)\|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R +-+ +------+ +------+ +--R (- 900x - 1350)\|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ +------+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R (306x + 459)\|3 \|2x + 3 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--R (- 1188x - 1912)\|5 +--R / +--R +-+ +------+ +--R (150x + 225)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1113 + +--S 1114 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 150\|5 log(\|2x + 3 + 1) - 150\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 51\|3 log(-------------------------------) - 300\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 102\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1115 + +)clear all + +--S 1116 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------- +--R 5 4 3 2 +------+ +--R (24x + 148x + 358x + 423x + 243x + 54)\|2x + 3 +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1751 +r0:=(-26/25)/(3+2*x)^(5/2)+(-66/25)/(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-_ + 306/125*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-1194/125)/sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +------+ +--R (6000x + 18000x + 13500)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ +------+ \|3 \|2x + 3 +--R (- 1224x - 3672x - 2754)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +--R (- 4776x - 14988x - 11866)\|5 +--R / +--R 2 +-+ +------+ +--R (500x + 1500x + 1125)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +------+ +------+ +--R (3000x + 9000x + 6750)\|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +------+ +--R (- 3000x - 9000x - 6750)\|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R 2 +-+ +------+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R (612x + 1836x + 1377)\|3 \|2x + 3 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--R (- 4776x - 14988x - 11866)\|5 +--R / +--R 2 +-+ +------+ +--R (500x + 1500x + 1125)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1118 + +--S 1119 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 750\|5 log(\|2x + 3 + 1) - 750\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 153\|3 log(-------------------------------) - 1500\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 306\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 125\|5 +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1120 + +)clear all + +--S 1121 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1751 +r0:=826/27*(3+2*x)^(3/2)+70/3*(3+2*x)^(5/2)-(3+2*x)^(7/2)*(29+35*x)/_ + (2+5*x+3*x^2)-154*atanh(sqrt(3+2*x))+2800/27*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(5/3)+1358/27*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 12474x - 20790x - 8316)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (8400x + 14000x + 5600)\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (- 48x + 400x - 1843x - 2129)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (81x + 135x + 54)\|3 +--R Type: Expression(Integer) +--E 1122 + +--S 1123 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +--R 2 +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +--R (4200x + 7000x + 2800)\|5 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +--R (- 6237x - 10395x - 4158)\|3 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +--R (6237x + 10395x + 4158)\|3 log(\|2x + 3 - 1) +--R + +--R 3 2 +-+ +------+ +--R (- 48x + 400x - 1843x - 2129)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (81x + 135x + 54)\|3 +--R Type: Union(Expression(Integer),...) +--E 1123 + +--S 1124 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 1400\|5 log(-----------------------------) - 2079\|3 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 2079\|3 log(\|2x + 3 - 1) + 4158\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 2800\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1125 + +)clear all + +--S 1126 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1751 +r0:=70/3*(3+2*x)^(3/2)-(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)-_ + 130*atanh(sqrt(3+2*x))+100*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+_ + 30*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 1170x - 1950x - 780)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (900x + 1500x + 600)\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +------+ +--R (- 8x - 209x - 183)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Expression(Integer) +--E 1127 + +--S 1128 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +--R 2 +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +--R (450x + 750x + 300)\|5 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +--R (- 585x - 975x - 390)\|3 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +--R (585x + 975x + 390)\|3 log(\|2x + 3 - 1) +--R + +--R 2 +-+ +------+ +--R (- 8x - 209x - 183)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Union(Expression(Integer),...) +--E 1128 + +--S 1129 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 50\|5 log(-----------------------------) - 65\|3 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 65\|3 log(\|2x + 3 - 1) + 130\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 100\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1751 +r0:=-(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)-106*atanh(sqrt(3+2*x))+_ + 248/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+70/3*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 954x - 1590x - 636)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +-+ +------+ +--R (744x + 1240x + 496)\|5 atanh(-------------) + (- 139x - 121)\|3 \|2x + 3 +--R +-+ +--R \|5 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +--R 2 +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +--R (372x + 620x + 248)\|5 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +--R (- 477x - 795x - 318)\|3 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +-+ +------+ +--R (477x + 795x + 318)\|3 log(\|2x + 3 - 1) + (- 139x - 121)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 124\|5 log(-----------------------------) - 159\|3 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 159\|3 log(\|2x + 3 - 1) + 318\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 248\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 1751 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2 +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1751 +r0:=-82*atanh(sqrt(3+2*x))+316*atanh(sqrt(3/5)*sqrt(3+2*x))/sqrt(15)-_ + (29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 2 +--+ +------+ +--R (- 246x - 410x - 164)\|15 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 \|3 \|2x + 3 +--+ +------+ +--R (948x + 1580x + 632)atanh(-------------) + (- 35x - 29)\|15 \|2x + 3 +--R +-+ +--R \|5 +--R / +--R 2 +--+ +--R (3x + 5x + 2)\|15 +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--+ +------+ +--R (- 123x - 205x - 82)\|15 log(\|2x + 3 + 1) +--R + +--R 2 +--+ +------+ +--R (123x + 205x + 82)\|15 log(\|2x + 3 - 1) +--R + +--R +------+ +--+ +--R 2 15\|2x + 3 + (3x + 7)\|15 +--R (474x + 790x + 316)log(---------------------------) +--R 3x + 2 +--R + +--R +--+ +------+ +--R (- 35x - 29)\|15 \|2x + 3 +--R / +--R 2 +--+ +--R (3x + 5x + 2)\|15 +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +------+ +--+ +------+ +--R - 41\|15 log(\|2x + 3 + 1) + 41\|15 log(\|2x + 3 - 1) +--R + +--R +------+ +--+ +--R 15\|2x + 3 + (3x + 7)\|15 +--+ +------+ +--R 158log(---------------------------) + 82\|15 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R \|3 \|2x + 3 +--R - 316atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +--+ +--R \|15 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-+ +-+ +--+ +------+ +--+ +--R (158\|3 \|5 \|15 - 2370)\|2x + 3 + (- 474x - 1106)\|15 +--R + +--R +-+ +-+ +--R (474x + 1106)\|3 \|5 +--R / +--R 2 +--+ +------+ 2 +--R (9x + 27x + 14)\|15 \|2x + 3 + 90x + 195x + 90 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 1751 +t0:=(5-x)/((2+5*x+3*x^2)^2*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R 4 3 2 +------+ +--R (9x + 30x + 37x + 20x + 4)\|2x + 3 +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1751 +r0:=-58*atanh(sqrt(3+2*x))+384/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 3/5*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 870x - 1450x - 580)\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (1152x + 1920x + 768)\|3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +------+ +--R (- 141x - 111)\|5 \|2x + 3 +--R / +--R 2 +-+ +--R (15x + 25x + 10)\|5 +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +--R 2 +-+ 5\|3 \|2x + 3 + (3x + 7)\|5 +--R (576x + 960x + 384)\|3 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +--R (- 435x - 725x - 290)\|5 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +-+ +------+ +--R (435x + 725x + 290)\|5 log(\|2x + 3 - 1) + (- 141x - 111)\|5 \|2x + 3 +--R / +--R 2 +-+ +--R (15x + 25x + 10)\|5 +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 192\|3 log(-----------------------------) - 145\|5 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 145\|5 log(\|2x + 3 - 1) + 290\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 384\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 5\|5 +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +------+ +--R (18x + 87x + 164x + 151x + 68x + 12)\|2x + 3 +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1751 +r0:=-34*atanh(sqrt(3+2*x))+1356/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-506/25)/sqrt(3+2*x)-3/5*(37+47*x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R (2) +--R 2 +-+ +------+ +------+ +--R (- 2550x - 4250x - 1700)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ +------+ \|3 \|2x + 3 +--R (4068x + 6780x + 2712)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +--R (- 1518x - 3235x - 1567)\|5 +--R / +--R 2 +-+ +------+ +--R (75x + 125x + 50)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +--R 2 +-+ +------+ 5\|3 \|2x + 3 + (3x + 7)\|5 +--R (2034x + 3390x + 1356)\|3 \|2x + 3 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +------+ +--R (- 1275x - 2125x - 850)\|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +------+ +--R (1275x + 2125x + 850)\|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R 2 +-+ +--R (- 1518x - 3235x - 1567)\|5 +--R / +--R 2 +-+ +------+ +--R (75x + 125x + 50)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1148 + +--S 1149 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 678\|3 log(-----------------------------) - 425\|5 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 425\|5 log(\|2x + 3 - 1) + 850\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 1356\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1150 + +)clear all + +--S 1151 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (36x + 228x + 589x + 794x + 589x + 228x + 36)\|2x + 3 +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1751 +r0:=(-262/15)/(3+2*x)^(3/2)-3/5*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2))-_ + 10*atanh(sqrt(3+2*x))+936/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-686/25)/sqrt(3+2*x) +--R +--R +--R (2) +--R 3 2 +-+ +------+ +------+ +--R (- 4500x - 14250x - 14250x - 4500)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 3 2 +-+ +------+ \|3 \|2x + 3 +--R (16848x + 53352x + 53352x + 16848)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +--R (- 12348x - 43032x - 47767x - 16633)\|5 +--R / +--R 3 2 +-+ +------+ +--R (450x + 1425x + 1425x + 450)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +------+ +--R (8424x + 26676x + 26676x + 8424)\|3 \|2x + 3 +--R * +--R +-+ +------+ +-+ +--R 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +------+ +--R (- 2250x - 7125x - 7125x - 2250)\|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R 3 2 +-+ +------+ +------+ +--R (2250x + 7125x + 7125x + 2250)\|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R 3 2 +-+ +--R (- 12348x - 43032x - 47767x - 16633)\|5 +--R / +--R 3 2 +-+ +------+ +--R (450x + 1425x + 1425x + 450)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1153 + +--S 1154 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 468\|3 log(-----------------------------) - 125\|5 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 125\|5 log(\|2x + 3 - 1) + 250\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 936\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1155 + +)clear all + +--S 1156 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^2) +--R +--R +--R (1) +--R - x + 5 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +------+ +--R (72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108)\|2x + 3 +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1751 +r0:=(-2114/125)/(3+2*x)^(5/2)+(-7042/375)/(3+2*x)^(3/2)-3/5*(37+47*x)/_ + ((3+2*x)^(5/2)*(2+5*x+3*x^2))+14*atanh(sqrt(3+2*x))+_ + 15876/625*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-24626/625)/sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (315000x + 1470000x + 2493750x + 1811250x + 472500)\|5 \|2x + 3 +--R * +--R +------+ +--R atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +------+ +--R (571536x + 2667168x + 4524660x + 3286332x + 857304)\|3 \|2x + 3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +--R (- 886536x - 4348428x - 7782530x - 5977997x - 1646109)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (22500x + 105000x + 178125x + 129375x + 33750)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (285768x + 1333584x + 2262330x + 1643166x + 428652)\|3 \|2x + 3 +--R * +--R +-+ +------+ +-+ +--R 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +------+ +--R (157500x + 735000x + 1246875x + 905625x + 236250)\|5 \|2x + 3 +--R * +--R +------+ +--R log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 157500x - 735000x - 1246875x - 905625x - 236250)\|5 \|2x + 3 +--R * +--R +------+ +--R log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (- 886536x - 4348428x - 7782530x - 5977997x - 1646109)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (22500x + 105000x + 178125x + 129375x + 33750)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1158 + +--S 1159 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 7938\|3 log(-----------------------------) + 4375\|5 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R - 4375\|5 log(\|2x + 3 - 1) - 8750\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 15876\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 1751 +t0:=(5-x)*(3+2*x)^(9/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 5 4 3 2 +------+ +--R (- 16x - 16x + 264x + 864x + 999x + 405)\|2x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1751 +r0:=-3151/9*(3+2*x)^(3/2)-283*(3+2*x)^(5/2)-1/2*(3+2*x)^(9/2)*(29+35*x)/_ + (2+5*x+3*x^2)^2+3/2*(3+2*x)^(7/2)*(230+283*x)/(2+5*x+3*x^2)+_ + 1962*atanh(sqrt(3+2*x))-13675/9*atanh(sqrt(3/5)*sqrt(3+2*x))*_ + sqrt(5/3)-3983/9*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (317844x + 1059480x + 1306692x + 706320x + 141264)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 246150x - 820500x - 1011950x - 547000x - 109400)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +------+ +--R (- 192x + 45083x + 112467x + 90465x + 23327)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (162x + 540x + 666x + 360x + 72)\|3 +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (158922x + 529740x + 653346x + 353160x + 70632)\|3 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +--R (- 158922x - 529740x - 653346x - 353160x - 70632)\|3 +--R * +--R +------+ +--R log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (123075x + 410250x + 505975x + 273500x + 54700)\|5 +--R * +--R +-+ +------+ +-+ +--R - 3\|5 \|2x + 3 + (3x + 7)\|3 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +------+ +--R (- 192x + 45083x + 112467x + 90465x + 23327)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (162x + 540x + 666x + 360x + 72)\|3 +--R Type: Union(Expression(Integer),...) +--E 1163 + +--S 1164 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 17658\|3 log(\|2x + 3 + 1) - 17658\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 13675\|5 log(-------------------------------) - 35316\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 27350\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1165 + +)clear all + +--S 1166 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1751 +r0:=-847/3*(3+2*x)^(3/2)-1/2*(3+2*x)^(7/2)*(29+35*x)/(2+5*x+3*x^2)^2+_ + 7/2*(3+2*x)^(5/2)*(100+121*x)/(2+5*x+3*x^2)+1582*atanh(sqrt(3+2*x))-_ + 1225*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-357*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (85428x + 284760x + 351204x + 189840x + 37968)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 66150x - 220500x - 271950x - 147000x - 29400)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (12443x + 30979x + 25073x + 6555)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (42714x + 142380x + 175602x + 94920x + 18984)\|3 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 42714x - 142380x - 175602x - 94920x - 18984)\|3 log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (33075x + 110250x + 135975x + 73500x + 14700)\|5 +--R * +--R +-+ +------+ +-+ +--R - 3\|5 \|2x + 3 + (3x + 7)\|3 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (12443x + 30979x + 25073x + 6555)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Union(Expression(Integer),...) +--E 1168 + +--S 1169 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 1582\|3 log(\|2x + 3 + 1) - 1582\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 1225\|5 log(-------------------------------) - 3164\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 2450\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 2\|3 +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1170 + +)clear all + +--S 1171 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1751 +r0:=-1/2*(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)^2+5/2*(3+2*x)^(3/2)*_ + (142+169*x)/(2+5*x+3*x^2)+1250*atanh(sqrt(3+2*x))-_ + 2905/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-845/3*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (67500x + 225000x + 277500x + 150000x + 30000)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 52290x - 174300x - 214970x - 116200x - 23240)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (9825x + 24497x + 19891x + 5237)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (33750x + 112500x + 138750x + 75000x + 15000)\|3 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 33750x - 112500x - 138750x - 75000x - 15000)\|3 log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (26145x + 87150x + 107485x + 58100x + 11620)\|5 +--R * +--R +-+ +------+ +-+ +--R - 3\|5 \|2x + 3 + (3x + 7)\|3 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (9825x + 24497x + 19891x + 5237)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Union(Expression(Integer),...) +--E 1173 + +--S 1174 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 3750\|3 log(\|2x + 3 + 1) - 3750\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 2905\|5 log(-------------------------------) - 7500\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 5810\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1175 + +)clear all + +--S 1176 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1751 +r0:=-1/2*(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)^2+966*atanh(sqrt(3+2*x))-_ + 1247*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+3/2*(240+281*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (17388x + 57960x + 71484x + 38640x + 7728)\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 4 3 2 +-+ \|3 \|2x + 3 +--R (- 22446x - 74820x - 92278x - 49880x - 9976)\|3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (2529x + 6305x + 5123x + 1353)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (18x + 60x + 74x + 40x + 8)\|5 +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (8694x + 28980x + 35742x + 19320x + 3864)\|5 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 8694x - 28980x - 35742x - 19320x - 3864)\|5 log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (11223x + 37410x + 46139x + 24940x + 4988)\|3 +--R * +--R +-+ +------+ +-+ +--R - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (2529x + 6305x + 5123x + 1353)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (18x + 60x + 74x + 40x + 8)\|5 +--R Type: Union(Expression(Integer),...) +--E 1178 + +--S 1179 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 966\|5 log(\|2x + 3 + 1) - 966\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 1247\|3 log(-------------------------------) - 1932\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 2494\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 2\|5 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1180 + +)clear all + +--S 1181 of 1751 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^3 +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1751 +r0:=730*atanh(sqrt(3+2*x))-4713/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 1/2*(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+3/10*(878+1063*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (65700x + 219000x + 270100x + 146000x + 29200)\|5 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 84834x - 282780x - 348762x - 188520x - 37704)\|3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (9567x + 23847x + 19373x + 5123)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (90x + 300x + 370x + 200x + 40)\|5 +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (32850x + 109500x + 135050x + 73000x + 14600)\|5 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 32850x - 109500x - 135050x - 73000x - 14600)\|5 log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (42417x + 141390x + 174381x + 94260x + 18852)\|3 +--R * +--R +-+ +------+ +-+ +--R - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (9567x + 23847x + 19373x + 5123)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (90x + 300x + 370x + 200x + 40)\|5 +--R Type: Union(Expression(Integer),...) +--E 1183 + +--S 1184 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 3650\|5 log(\|2x + 3 + 1) - 3650\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 4713\|3 log(-------------------------------) - 7300\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 9426\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 10\|5 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 1751 +t0:=(5-x)/((2+5*x+3*x^2)^3*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (27x + 135x + 279x + 305x + 186x + 60x + 8)\|2x + 3 +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1751 +r0:=542*atanh(sqrt(3+2*x))-17463/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 3/10*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+1/50*(9734+11739*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (243900x + 813000x + 1002700x + 542000x + 108400)\|5 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 314334x - 1047780x - 1292262x - 698520x - 139704)\|3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (35217x + 87897x + 71443x + 18913)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (121950x + 406500x + 501350x + 271000x + 54200)\|5 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +--R (- 121950x - 406500x - 501350x - 271000x - 54200)\|5 +--R * +--R +------+ +--R log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (157167x + 523890x + 646131x + 349260x + 69852)\|3 +--R * +--R +-+ +------+ +-+ +--R - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (35217x + 87897x + 71443x + 18913)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 +--R Type: Union(Expression(Integer),...) +--E 1188 + +--S 1189 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 13550\|5 log(\|2x + 3 + 1) - 13550\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 17463\|3 log(-------------------------------) - 27100\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 34926\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 50\|5 +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +------+ +--R (54x + 351x + 963x + 1447x + 1287x + 678x + 196x + 24)\|2x + 3 +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1751 +r0:=402*atanh(sqrt(3+2*x))-12717/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + 2667/25/sqrt(3+2*x)-3/10*(37+47*x)/((2+5*x+3*x^2)^2*sqrt(3+2*x))+_ + 1/10*(1888+2229*x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (180900x + 603000x + 743700x + 402000x + 80400)\|5 \|2x + 3 +--R * +--R +------+ +--R atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +------+ +--R (- 228906x - 763020x - 941058x - 508680x - 101736)\|3 \|2x + 3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +--R (48006x + 193455x + 281403x + 175465x + 39661)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (90450x + 301500x + 371850x + 201000x + 40200)\|5 \|2x + 3 +--R * +--R +------+ +--R log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 90450x - 301500x - 371850x - 201000x - 40200)\|5 \|2x + 3 +--R * +--R +------+ +--R log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +------+ +--R (114453x + 381510x + 470529x + 254340x + 50868)\|3 \|2x + 3 +--R * +--R +-+ +------+ +-+ +--R - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--R (48006x + 193455x + 281403x + 175465x + 39661)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 10050\|5 log(\|2x + 3 + 1) - 10050\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 12717\|3 log(-------------------------------) - 20100\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 25434\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 50\|5 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 8 7 6 5 4 3 2 +--R (108x + 864x + 2979x + 5783x + 6915x + 5217x + 2426x + 636x + 72) +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1751 +r0:=7451/75/(3+2*x)^(3/2)-3/10*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^2)+_ + 1/50*(9146+10551*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2))+310*_ + atanh(sqrt(3+2*x))-45603/125*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + 6853/125/sqrt(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 4185000x + 20227500x + 38130000x + 35107500x + 15810000x +--R + +--R 2790000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R 5 4 3 2 +--R - 4925124x - 23804766x - 44873352x - 41316318x - 18606024x +--R + +--R - 3283416 +--R * +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +--R \|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 5 4 3 2 +-+ +--R (740124x + 4247856x + 9453447x + 10168583x + 5278129x + 1057511)\|5 +--R / +--R 5 4 3 2 +-+ +------+ +--R (13500x + 65250x + 123000x + 113250x + 51000x + 9000)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (2092500x + 10113750x + 19065000x + 17553750x + 7905000x + 1395000) +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R 5 4 3 2 +--R - 2092500x - 10113750x - 19065000x - 17553750x - 7905000x +--R + +--R - 1395000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R 5 4 3 2 +--R (2462562x + 11902383x + 22436676x + 20658159x + 9303012x + 1641708) +--R * +--R +-+ +------+ +-+ +--R +-+ +------+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R \|3 \|2x + 3 log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--R (740124x + 4247856x + 9453447x + 10168583x + 5278129x + 1057511)\|5 +--R / +--R 5 4 3 2 +-+ +------+ +--R (13500x + 65250x + 123000x + 113250x + 51000x + 9000)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1198 + +--S 1199 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 38750\|5 log(\|2x + 3 + 1) - 38750\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 45603\|3 log(-------------------------------) - 77500\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 91206\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 250\|5 +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +)clear all + +--S 1201 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 9 8 7 6 5 4 3 +--R 216x + 2052x + 8550x + 20503x + 31179x + 31179x + 20503x +--R + +--R 2 +--R 8550x + 2052x + 216 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1751 +r0:=56399/625/(3+2*x)^(5/2)+102697/1875/(3+2*x)^(3/2)-3/10*(37+47*x)/_ + ((3+2*x)^(5/2)*(2+5*x+3*x^2)^2)+1/50*(8852+9957*x)/((3+2*x)^(5/2)*_ + (2+5*x+3*x^2))+266*atanh(sqrt(3+2*x))-806841/3125*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(3/5)+(-24409/3125)/sqrt(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 179550000x + 1137150000x + 2937637500x + 3960075000x +--R + +--R 2 +--R 2937637500x + 1137150000x + 179550000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R 6 5 4 3 +--R - 174277656x - 1103758488x - 2851376094x - 3843790524x +--R + +--R 2 +--R - 2851376094x - 1103758488x - 174277656 +--R * +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +--R \|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 6 5 4 3 2 +--R - 5272344x - 14906052x + 18312714x + 114099329x + 160041829x +--R + +--R 94082723x + 20250051 +--R * +--R +-+ +--R \|5 +--R / +--R 6 5 4 3 2 +--R 675000x + 4275000x + 11043750x + 14887500x + 11043750x + 4275000x +--R + +--R 675000 +--R * +--R +-+ +------+ +--R \|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 89775000x + 568575000x + 1468818750x + 1980037500x + 1468818750x +--R + +--R 568575000x + 89775000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R 6 5 4 3 +--R - 89775000x - 568575000x - 1468818750x - 1980037500x +--R + +--R 2 +--R - 1468818750x - 568575000x - 89775000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R 6 5 4 3 2 +--R 87138828x + 551879244x + 1425688047x + 1921895262x + 1425688047x +--R + +--R 551879244x + 87138828 +--R * +--R +-+ +------+ +-+ +--R +-+ +------+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R \|3 \|2x + 3 log(-------------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R - 5272344x - 14906052x + 18312714x + 114099329x + 160041829x +--R + +--R 94082723x + 20250051 +--R * +--R +-+ +--R \|5 +--R / +--R 6 5 4 3 2 +--R 675000x + 4275000x + 11043750x + 14887500x + 11043750x + 4275000x +--R + +--R 675000 +--R * +--R +-+ +------+ +--R \|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1203 + +--S 1204 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 831250\|5 log(\|2x + 3 + 1) - 831250\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R 806841\|3 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R - 1662500\|5 atanh(\|2x + 3 ) + 1613682\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 6250\|5 +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1205 + +)clear all + +--S 1206 of 1751 +t0:=(5+10*x+sqrt(35))/((2+3*x+5*x^2)*sqrt(1+2*x)) +--R +--R +--R +--+ +--R \|35 + 10x + 5 +--R (1) ----------------------- +--R 2 +------+ +--R (5x + 3x + 2)\|2x + 1 +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1751 +r0:=-2*atan((-sqrt(10+20*x)+sqrt(2+sqrt(35)))/sqrt(-2+sqrt(35)))*_ + sqrt(10/(-2+sqrt(35)))+2*atan((sqrt(10+20*x)+sqrt(2+sqrt(35)))/_ + sqrt(-2+sqrt(35)))*sqrt(10/(-2+sqrt(35))),-2*atan((-10*sqrt(1+2*x)+_ + sqrt(10*(2+sqrt(35))))/sqrt(10*(-2+sqrt(35))))*sqrt(10/(-2+sqrt(35)))+_ + 2*atan((10*sqrt(1+2*x)+sqrt(10*(2+sqrt(35))))/sqrt(10*(-2+sqrt(35))))*_ + sqrt(10/(-2+sqrt(35))) +--R +--R +--R (2) +--R [ +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 + \|20x + 10 +--R 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R + +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 - \|20x + 10 +--R - 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R / +--R +--+ +--R \|31 +--R , +--R +--R +------------+ +--R +------------+ | +--+ +------+ +--R | +--+ \|10\|35 + 20 + 10\|2x + 1 +--R 2\|10\|35 + 20 atan(-----------------------------) +--R +------------+ +--R | +--+ +--R \|10\|35 - 20 +--R + +--R +------------+ +--R +------------+ | +--+ +------+ +--R | +--+ \|10\|35 + 20 - 10\|2x + 1 +--R - 2\|10\|35 + 20 atan(-----------------------------) +--R +------------+ +--R | +--+ +--R \|10\|35 - 20 +--R / +--R +--+ +--R \|31 +--R ] +--R Type: Tuple(Expression(Integer)) +--E 1207 + +--S 1208 of 1751 +a0:=integrate(t0,x) +--R +--R +--R +------------+ +--R +------------+ +--+ +------+ | +--+ +--R | +--+ (31\|35 + 62)\|2x + 1 \|10\|35 + 20 +--R 2\|10\|35 + 20 atan(---------------------------------------) +--R +--+ +--+ +--+ +--R (40x - 19)\|31 \|35 + (390x + 55)\|31 +--R (3) - ------------------------------------------------------------- +--R +--+ +--R \|31 +--R Type: Union(Expression(Integer),...) +--E 1208 + +--S 1209 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +------------+ +--+ +------+ | +--+ +--R | +--+ (31\|35 + 62)\|2x + 1 \|10\|35 + 20 +--R - 2\|10\|35 + 20 atan(---------------------------------------) +--R +--+ +--+ +--+ +--R (40x - 19)\|31 \|35 + (390x + 55)\|31 +--R + +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 + \|20x + 10 +--R - 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R + +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 - \|20x + 10 +--R 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R / +--R +--+ +--R \|31 +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +--+ +--+ +--+ +------+ +--R ((- 3120x - 3641)\|31 \|35 + (- 20810x - 21325)\|31 )\|2x + 1 +--R * +--R +---------+ +------------+ +--R +--------+ | +--+ | +--+ +--R \|20x + 10 \|\|35 - 2 \|10\|35 + 20 +--R + +--R 2 +--+ 2 +--R (1934400x + 3224620x + 1128710)\|35 + 12902200x + 19672600x + 6610750 +--R / +--R 3 2 +--+ 3 2 +--R (967200x + 1063920x + 677040x + 193440)\|35 + 6451100x + 7096210x +--R + +--R 4515770x + 1290220 +--R * +--R +------+ +--R \|2x + 1 +--R Type: Expression(Integer) +--E 1210 + +)clear all + +--S 1211 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 3 2 +------+ | 2 +--R (1) (- 4x + 8x + 51x + 45)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1751 +--r0:=730/891*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)-2/33*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(3/2)+12130/6237*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 32567/48114*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-63541/168399*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+_ +-- 1/56133*(250447+280359*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1212 + +--S 1213 of 1751 +--a0:=integrate(t0,x) +--E 1213 + +--S 1214 of 1751 +--m0:=a0-r0 +--E 1214 + +--S 1215 of 1751 +--d0:=D(m0,x) +--E 1215 + +)clear all + +--S 1216 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 2 +------+ | 2 +--R (1) (- 2x + 7x + 15)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1751 +--r0:=-2/27*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)+202/189*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+4729/1458*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-7892/5103*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+1/8505*(27914+30033*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1217 + +--S 1218 of 1751 +--a0:=integrate(t0,x) +--E 1218 + +--S 1219 of 1751 +--m0:=a0-r0 +--E 1219 + +--S 1220 of 1751 +--d0:=D(m0,x) +--E 1220 + +)clear all + +--S 1221 of 1751 +t0:=(5-x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R +------+ | 2 +--R (1) (- x + 5)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1751 +--r0:=-2/21*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+697/162*elliptic_e(asin(sqrt(3+_ +-- 2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 881/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1/945*(2327+2169*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1222 + +--S 1223 of 1751 +--a0:=integrate(t0,x) +--E 1223 + +--S 1224 of 1751 +--m0:=a0-r0 +--E 1224 + +--S 1225 of 1751 +--d0:=D(m0,x) +--E 1225 + +)clear all + +--S 1226 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1751 +--r0:=761/54*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-94/27*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/45*(88-9*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1227 + +--S 1228 of 1751 +--a0:=integrate(t0,x) +--E 1228 + +--S 1229 of 1751 +--m0:=a0-r0 +--E 1229 + +--S 1230 of 1751 +--d0:=D(m0,x) +--E 1230 + +)clear all + +--S 1231 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1751 +--r0:=61/9*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-121/18*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-1/3*(21+x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1232 + +--S 1233 of 1751 +--a0:=integrate(t0,x) +--E 1233 + +--S 1234 of 1751 +--m0:=a0-r0 +--E 1234 + +--S 1235 of 1751 +--d0:=D(m0,x) +--E 1235 + +)clear all + +--S 1236 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1751 +--r0:=67/6*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-8/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-1/3*(11+3*x)*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+67/15*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1237 + +--S 1238 of 1751 +--a0:=integrate(t0,x) +--E 1238 + +--S 1239 of 1751 +--m0:=a0-r0 +--E 1239 + +--S 1240 of 1751 +--d0:=D(m0,x) +--E 1240 + +)clear all + +--S 1241 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1751 +--r0:=49/50*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-11/25*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+9/25*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+1/5*(1+5*x)*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(5/2)+49/125*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1242 + +--S 1243 of 1751 +--a0:=integrate(t0,x) +--E 1243 + +--S 1244 of 1751 +--m0:=a0-r0 +--E 1244 + +--S 1245 of 1751 +--d0:=D(m0,x) +--E 1245 + +)clear all + +--S 1246 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R (1) +--R 6 5 4 3 2 +------+ +--R (- 24x - 28x + 382x + 1367x + 1872x + 1161x + 270)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1751 +--r0:=2086/1989*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)+42/85*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(5/2)-2/51*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2)+_ +-- 1/196911*(591064+699377*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 108934/65637*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-2200387/21266388*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1284593/10633194*elliptic_f(asin(sqrt(3+_ +-- 2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/17721990*(6668831+8076357*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1247 + +--S 1248 of 1751 +--a0:=integrate(t0,x) +--E 1248 + +--S 1249 of 1751 +--m0:=a0-r0 +--E 1249 + +--S 1250 of 1751 +--d0:=D(m0,x) +--E 1250 + +)clear all + +--S 1251 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (1) (- 12x + 4x + 185x + 406x + 327x + 90)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1751 +--r0:=202/351*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)-2/45*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(5/2)+1/243243*(534271+629153*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+13318/11583*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+_ +-- 207851/3752892*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+397651/6567561*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-1/21891870*(6006884+7817373*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1252 + +--S 1253 of 1751 +--a0:=integrate(t0,x) +--E 1253 + +--S 1254 of 1751 +--m0:=a0-r0 +--E 1254 + +--S 1255 of 1751 +--d0:=D(m0,x) +--E 1255 + +)clear all + +--S 1256 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (1) (- 6x + 11x + 76x + 89x + 30)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1751 +--r0:=-2/39*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)+1/27027*(43822+50771*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+886/1287*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+152657/416988*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 35611/1459458*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-1/2432430*(486863+783711*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1257 + +--S 1258 of 1751 +--a0:=integrate(t0,x) +--E 1258 + +--S 1259 of 1751 +--m0:=a0-r0 +--E 1259 + +--S 1260 of 1751 +--d0:=D(m0,x) +--E 1260 + +)clear all + +--S 1261 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x) +--R +--R +--R +------------+ +--R 3 2 +------+ | 2 +--R (1) (- 3x + 10x + 23x + 10)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1751 +--r0:=1/99*(119+127*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-_ +-- 2/33*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+15283/10692*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-706/2673*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/8910*(1246+3987*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1262 + +--S 1263 of 1751 +--a0:=integrate(t0,x) +--E 1263 + +--S 1264 of 1751 +--m0:=a0-r0 +--E 1264 + +--S 1265 of 1751 +--d0:=D(m0,x) +--E 1265 + +)clear all + +--S 1266 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1751 +--r0:=1/63*(52-7*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+11123/972*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-8179/3402*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/5670*(107+12429*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1267 + +--S 1268 of 1751 +--a0:=integrate(t0,x) +--E 1268 + +--S 1269 of 1751 +--m0:=a0-r0 +--E 1269 + +--S 1270 of 1751 +--d0:=D(m0,x) +--E 1270 + +)clear all + +--S 1271 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1751 +--r0:=-1/7*(47+x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x)-2411/36*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+899/63*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/210*(136-2493*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1272 + +--S 1273 of 1751 +--a0:=integrate(t0,x) +--E 1273 + +--S 1274 of 1751 +--m0:=a0-r0 +--E 1274 + +--S 1275 of 1751 +--d0:=D(m0,x) +--E 1275 + +)clear all + +--S 1276 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1751 +--r0:=-1/15*(37+3*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2)+367/4*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-39/2*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/10*(241+69*x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1277 + +--S 1278 of 1751 +--a0:=integrate(t0,x) +--E 1278 + +--S 1279 of 1751 +--m0:=a0-r0 +--E 1279 + +--S 1280 of 1751 +--d0:=D(m0,x) +--E 1280 + +)clear all + +--S 1281 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1751 +--r0:=-1/15*(27+5*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2)-2779/60*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+148/15*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/30*(707+411*x)*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-2779/150*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1282 + +--S 1283 of 1751 +--a0:=integrate(t0,x) +--E 1283 + +--S 1284 of 1751 +--m0:=a0-r0 +--E 1284 + +--S 1285 of 1751 +--d0:=D(m0,x) +--E 1285 + +)clear all + +--S 1286 of 1751 +t0:=(5-x)*(3+2*x)^(9/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 144x - 624x + 1304x + 14784x + 44295x + 70799x + 67449x +--R + +--R 2 +--R 38421x + 12096x + 1620 +--R * +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1751 +--r0:=222422/200583*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)+25418/35397*_ +-- (3+2*x)^(5/2)*(2+5*x+3*x^2)^(7/2)+1538/4347*(3+2*x)^(7/2)*_ +-- (2+5*x+3*x^2)^(7/2)-2/69*(3+2*x)^(9/2)*(2+5*x+3*x^2)^(7/2)-_ +-- 5/97580821338*(5514025312+6580844291*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+1/2323352889*(6295010279+7506271641*x)*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+8515726/5415741*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+_ +-- 12104518303/1505532672072*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-18804590219/5269364352252*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1/1756454784084*(62607985973+_ +-- 65705093631*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1287 + +--S 1288 of 1751 +--a0:=integrate(t0,x) +--E 1288 + +--S 1289 of 1751 +--m0:=a0-r0 +--E 1289 + +--S 1290 of 1751 +--d0:=D(m0,x) +--E 1290 + +)clear all + +--S 1291 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 72x - 204x + 958x + 5955x + 13215x + 15577x + 10359x + 3672x +--R + +--R 540 +--R * +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1751 +--r0:=2218/2907*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)+202/513*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(7/2)-2/63*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(7/2)-_ +-- 5/108785754*(4498331+5420233*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 1/2590137*(5130052+6113283*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+_ +-- 89294/78489*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+18269789/1678408776*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-10791761/2937215358*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1/1958143572*(51436624+44779653*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1292 + +--S 1293 of 1751 +--a0:=integrate(t0,x) +--E 1293 + +--S 1294 of 1751 +--m0:=a0-r0 +--E 1294 + +--S 1295 of 1751 +--d0:=D(m0,x) +--E 1295 + +)clear all + +--S 1296 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +------+ +--R (- 36x - 48x + 551x + 2151x + 3381x + 2717x + 1104x + 180)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1751 +--r0:=430/969*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)-2/57*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(7/2)-125/52378326*(64006+79583*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+25/1247103*(72737+86493*x)*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+2350/2907*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+_ +-- 16503475/808122744*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-15117425/2828429604*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+25/942809868*(749099+216603*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1297 + +--S 1298 of 1751 +--a0:=integrate(t0,x) +--E 1298 + +--S 1299 of 1751 +--m0:=a0-r0 +--E 1299 + +--S 1300 of 1751 +--d0:=D(m0,x) +--E 1300 + +)clear all + +--S 1301 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R +------------+ +--R 6 5 4 3 2 +------+ | 2 +--R (- 18x + 3x + 271x + 669x + 687x + 328x + 60)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1751 +--r0:=-2/51*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)-1/8270262*(949997+1332121*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/984555*(1063774+1253571*x)*_ +-- (2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+1166/2295*(2+5*x+3*x^2)^(7/2)*_ +-- sqrt(3+2*x)+34355693/127598328*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6809266/111648537*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+1/744323580*(12174838-22593339*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1302 + +--S 1303 of 1751 +--a0:=integrate(t0,x) +--E 1303 + +--S 1304 of 1751 +--m0:=a0-r0 +--E 1304 + +--S 1305 of 1751 +--d0:=D(m0,x) +--E 1305 + +)clear all + +--S 1306 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x) +--R +--R +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (1) (- 9x + 15x + 113x + 165x + 96x + 20)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1751 +--r0:=-1/162162*(15076+34643*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/19305*_ +-- (15467+17193*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-_ +-- 2/45*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+2742319/2501928*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-2066087/8756748*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 1/14594580*(287729-2667537*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1307 + +--S 1308 of 1751 +--a0:=integrate(t0,x) +--E 1308 + +--S 1309 of 1751 +--m0:=a0-r0 +--E 1309 + +--S 1310 of 1751 +--d0:=D(m0,x) +--E 1310 + +)clear all + +--S 1311 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1751 +--r0:=-5/18018*(563+4669*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 1/429*(224-33*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+651617/277992*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-242783/486486*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+_ +-- 1/324324*(34372-676791*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1312 + +--S 1313 of 1751 +--a0:=integrate(t0,x) +--E 1313 + +--S 1314 of 1751 +--m0:=a0-r0 +--E 1314 + +--S 1315 of 1751 +--d0:=D(m0,x) +--E 1315 + +)clear all + +--S 1316 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1751 +--r0:=-1/11*(73+x)*(2+5*x+3*x^2)^(5/2)/sqrt(3+2*x)+5/1386*(218+3031*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-451331/21384*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+336013/74844*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-_ +-- 1/24948*(21871-471213*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1317 + +--S 1318 of 1751 +--a0:=integrate(t0,x) +--E 1318 + +--S 1319 of 1751 +--m0:=a0-r0 +--E 1319 + +--S 1320 of 1751 +--d0:=D(m0,x) +--E 1320 + +)clear all + +--S 1321 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1751 +--r0:=-1/9*(21+x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(3/2)+5/126*(745+121*x)*_ +-- (2+5*x+3*x^2)^(3/2)/sqrt(3+2*x)+33335/648*elliptic_e(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-_ +-- 6205/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+5/756*(326-6957*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1322 + +--S 1323 of 1751 +--a0:=integrate(t0,x) +--E 1323 + +--S 1324 of 1751 +--m0:=a0-r0 +--E 1324 + +--S 1325 of 1751 +--d0:=D(m0,x) +--E 1325 + +)clear all + +--S 1326 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1751 +--r0:=1/210*(2291+879*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2)-1/35*(53+5*x)*_ +-- (2+5*x+3*x^2)^(5/2)/(3+2*x)^(5/2)-2333/8*elliptic_e(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1737/28*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-1/140*(10763+3117*x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1327 + +--S 1328 of 1751 +--a0:=integrate(t0,x) +--E 1328 + +--S 1329 of 1751 +--m0:=a0-r0 +--E 1329 + +--S 1330 of 1751 +--d0:=D(m0,x) +--E 1330 + +)clear all + +--S 1331 of 1751 +t0:=(A+B*x)*(d+e*x)^(1/2)/(a+b*x+c*x^2)^(1/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1751 +--r0:=2/3*B*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c-1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*_ +-- (b*B*d-3*A*c*d+a*B*e)+(B*c*d-2*b*B*e+3*A*c*e)*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(B*c*d-2*b*B*e+3*A*c*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (c^(5/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 1332 + +--S 1333 of 1751 +--a0:=integrate(t0,x) +--E 1333 + +--S 1334 of 1751 +--m0:=a0-r0 +--E 1334 + +--S 1335 of 1751 +--d0:=D(m0,x) +--E 1335 + +)clear all + +--S 1336 of 1751 +t0:=(A+B*x)/((d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)) +--R +--R +--R B x + A +--R (1) --------------------------- +--R +--------------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1751 +--r0:=-elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*B-2*A*c-B*sqrt(b^2-4*a*c))*sqrt(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- B*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 1337 + +--S 1338 of 1751 +--a0:=integrate(t0,x) +--E 1338 + +--S 1339 of 1751 +--m0:=a0-r0 +--E 1339 + +--S 1340 of 1751 +--d0:=D(m0,x) +--E 1340 + +)clear all + +--S 1341 of 1751 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^(1/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------ +--R +--------------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1751 +--r0:=2*(B*d-A*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))+_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c))))*(-2*(b*B*d-A*c*d-a*B*e)+(B*d-A*e)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(B*d-A*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 1342 + +--S 1343 of 1751 +--a0:=integrate(t0,x) +--E 1343 + +--S 1344 of 1751 +--m0:=a0-r0 +--E 1344 + +--S 1345 of 1751 +--d0:=D(m0,x) +--E 1345 + +)clear all + +--S 1346 of 1751 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1751 +--r0:=-2*(A*b-2*a*B-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/((b^2-4*a*c)*_ +-- sqrt(a+b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/_ +-- (c*(b^2-4*a*c))+elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(b^2*B*d-2*a*c*(3*B*d+A*e)+_ +-- b*(A*c*d+a*B*e))+(b*B*c*d-2*A*c^2*d-2*b^2*B*e+A*b*c*e+6*a*B*c*e)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(5/2)*(b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))-(2*b^2*B*e-_ +-- b*c*(B*d+A*e)+2*c*(A*c*d-3*a*B*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (c^(5/2)*(b^2-4*a*c)*e*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 1347 + +--S 1348 of 1751 +--a0:=integrate(t0,x) +--E 1348 + +--S 1349 of 1751 +--m0:=a0-r0 +--E 1349 + +--S 1350 of 1751 +--d0:=D(m0,x) +--E 1350 + +)clear all + +--S 1351 of 1751 +t0:=(A+B*x)*(d+e*x)^(1/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1751 +--r0:=-2*(A*b-2*a*B-(b*B-2*A*c)*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ +-- sqrt(a+b*x+c*x^2))+elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*A*b*c-4*a*B*c+(b*B-2*A*c)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))+(b*B-2*A*c)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*(b^2-4*a*c)*e*_ +-- sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 1352 + +--S 1353 of 1751 +--a0:=integrate(t0,x) +--E 1353 + +--S 1354 of 1751 +--m0:=a0-r0 +--E 1354 + +--S 1355 of 1751 +--d0:=D(m0,x) +--E 1355 + +)clear all + +--S 1356 of 1751 +t0:=(A+B*x)/((d+e*x)^(1/2)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +--------------+ +--R 2 +-------+ | 2 +--R (c x + b x + a)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1751 +--r0:=2*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-_ +-- 2*a*B*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(a+b*x+c*x^2))-elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*b^2*B*d-4*a*c*(B*d-A*e)-_ +-- 2*b*(A*c*d+a*B*e)-(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(b*(B*d+A*e)-2*(A*c*d+a*B*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*e*(c*d^2-e*(b*d-a*e))*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 1357 + +--S 1358 of 1751 +--a0:=integrate(t0,x) +--E 1358 + +--S 1359 of 1751 +--m0:=a0-r0 +--E 1359 + +--S 1360 of 1751 +--d0:=D(m0,x) +--E 1360 + +)clear all + +--S 1361 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1751 +--r0:=-865/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+4540/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+10/7*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)-2/21*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)+_ +-- 1010/189*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1362 + +--S 1363 of 1751 +--a0:=integrate(t0,x) +--E 1363 + +--S 1364 of 1751 +--m0:=a0-r0 +--E 1364 + +--S 1365 of 1751 +--d0:=D(m0,x) +--E 1365 + +)clear all + +--S 1366 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1751 +--r0:=-2743/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+2254/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2/15*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+326/135*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1367 + +--S 1368 of 1751 +--a0:=integrate(t0,x) +--E 1368 + +--S 1369 of 1751 +--m0:=a0-r0 +--E 1369 + +--S 1370 of 1751 +--d0:=D(m0,x) +--E 1370 + +)clear all + +--S 1371 of 1751 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ------------------ +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1371 + +--S 1372 of 1751 +--r0:=-101/27*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+104/27*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-2/9*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1372 + +--S 1373 of 1751 +--a0:=integrate(t0,x) +--E 1373 + +--S 1374 of 1751 +--m0:=a0-r0 +--E 1374 + +--S 1375 of 1751 +--d0:=D(m0,x) +--E 1375 + +)clear all + +--S 1376 of 1751 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------ +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1376 + +--S 1377 of 1751 +--r0:=34/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1/3*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2) +--E 1377 + +--S 1378 of 1751 +--a0:=integrate(t0,x) +--E 1378 + +--S 1379 of 1751 +--m0:=a0-r0 +--E 1379 + +--S 1380 of 1751 +--d0:=D(m0,x) +--E 1380 + +)clear all + +--S 1381 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------- +--R +------------+ +--R +------+ | 2 +--R (2x + 3)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1381 + +--S 1382 of 1751 +--r0:=-13*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+12*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 26/5*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1382 + +--S 1383 of 1751 +--a0:=integrate(t0,x) +--E 1383 + +--S 1384 of 1751 +--m0:=a0-r0 +--E 1384 + +--S 1385 of 1751 +--d0:=D(m0,x) +--E 1385 + +)clear all + +--S 1386 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------- +--R +------------+ +--R 2 +------+ | 2 +--R (4x + 12x + 9)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1386 + +--S 1387 of 1751 +--r0:=-193/15*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+154/15*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 26/15*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-386/75*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1387 + +--S 1388 of 1751 +--a0:=integrate(t0,x) +--E 1388 + +--S 1389 of 1751 +--m0:=a0-r0 +--E 1389 + +--S 1390 of 1751 +--d0:=D(m0,x) +--E 1390 + +)clear all + +--S 1391 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------- +--R +------------+ +--R 3 2 +------+ | 2 +--R (8x + 36x + 54x + 27)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1391 + +--S 1392 of 1751 +--r0:=-4501/375*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+3328/375*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-26/25*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-_ +-- 782/375*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-9002/1875*sqrt(2+5*x+3*x^2)/_ +-- sqrt(3+2*x) +--E 1392 + +--S 1393 of 1751 +--a0:=integrate(t0,x) +--E 1393 + +--S 1394 of 1751 +--m0:=a0-r0 +--E 1394 + +--S 1395 of 1751 +--d0:=D(m0,x) +--E 1395 + +)clear all + +--S 1396 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1396 + +--S 1397 of 1751 +--r0:=-2*(3+2*x)^(7/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-34174/81*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+16072/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+308/5*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+140/3*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)+_ +-- 12068/135*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1397 + +--S 1398 of 1751 +--a0:=integrate(t0,x) +--E 1398 + +--S 1399 of 1751 +--m0:=a0-r0 +--E 1399 + +--S 1400 of 1751 +--d0:=D(m0,x) +--E 1400 + +)clear all + +--S 1401 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1401 + +--S 1402 of 1751 +--r0:=-2*(3+2*x)^(5/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-3830/81*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1340/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+140/3*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+1660/27*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1402 + +--S 1403 of 1751 +--a0:=integrate(t0,x) +--E 1403 + +--S 1404 of 1751 +--m0:=a0-r0 +--E 1404 + +--S 1405 of 1751 +--d0:=D(m0,x) +--E 1405 + +)clear all + +--S 1406 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1406 + +--S 1407 of 1751 +--r0:=-2*(3+2*x)^(3/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-274/9*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- sqrt(2+5*x+3*x^2)+64/9*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+140/3*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1407 + +--S 1408 of 1751 +--a0:=integrate(t0,x) +--E 1408 + +--S 1409 of 1751 +--m0:=a0-r0 +--E 1409 + +--S 1410 of 1751 +--d0:=D(m0,x) +--E 1410 + +)clear all + +--S 1411 of 1751 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1411 + +--S 1412 of 1751 +--r0:=68/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-70/3*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-2*(29+35*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 1412 + +--S 1413 of 1751 +--a0:=integrate(t0,x) +--E 1413 + +--S 1414 of 1751 +--m0:=a0-r0 +--E 1414 + +--S 1415 of 1751 +--d0:=D(m0,x) +--E 1415 + +)clear all + +--S 1416 of 1751 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R +------------+ +--R 2 +------+ | 2 +--R (3x + 5x + 2)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1416 + +--S 1417 of 1751 +--r0:=-94*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+24*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6/5*(37+47*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 1417 + +--S 1418 of 1751 +--a0:=integrate(t0,x) +--E 1418 + +--S 1419 of 1751 +--m0:=a0-r0 +--E 1419 + +--S 1420 of 1751 +--d0:=D(m0,x) +--E 1420 + +)clear all + +--S 1421 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------- +--R +------------+ +--R 3 2 +------+ | 2 +--R (6x + 19x + 19x + 6)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1421 + +--S 1422 of 1751 +--r0:=-454/5*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+172/5*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6/5*(37+47*x)/_ +-- (sqrt(3+2*x)*sqrt(2+5*x+3*x^2))-908/25*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1422 + +--S 1423 of 1751 +--a0:=integrate(t0,x) +--E 1423 + +--S 1424 of 1751 +--m0:=a0-r0 +--E 1424 + +--S 1425 of 1751 +--d0:=D(m0,x) +--E 1425 + +)clear all + +--S 1426 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------- +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (12x + 56x + 95x + 69x + 18)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1426 + +--S 1427 of 1751 +--r0:=-6/5*(37+47*x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2))-7438/75*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+3664/75*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2516/75*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-14876/375*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1427 + +--S 1428 of 1751 +--a0:=integrate(t0,x) +--E 1428 + +--S 1429 of 1751 +--m0:=a0-r0 +--E 1429 + +--S 1430 of 1751 +--d0:=D(m0,x) +--E 1430 + +)clear all + +--S 1431 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------------ +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (24x + 148x + 358x + 423x + 243x + 54)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1431 + +--S 1432 of 1751 +--r0:=-6/5*(37+47*x)/((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2))-213374/1875*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+121172/1875*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-4124/125*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-61468/1875*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(3/2)-426748/9375*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1432 + +--S 1433 of 1751 +--a0:=integrate(t0,x) +--E 1433 + +--S 1434 of 1751 +--m0:=a0-r0 +--E 1434 + +--S 1435 of 1751 +--d0:=D(m0,x) +--E 1435 + +)clear all + +--S 1436 of 1751 +t0:=(5-x)*(3+2*x)^(9/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 16x - 16x + 264x + 864x + 999x + 405)\|2x + 3 +--R (1) ----------------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1436 + +--S 1437 of 1751 +--r0:=-2/3*(3+2*x)^(9/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+4/3*(3+2*x)^(7/2)*_ +-- (445+569*x)/sqrt(2+5*x+3*x^2)+110516/243*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-21248/243*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-5416/9*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)-_ +-- 4552/9*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)-59512/81*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1437 + +--S 1438 of 1751 +--a0:=integrate(t0,x) +--E 1438 + +--S 1439 of 1751 +--m0:=a0-r0 +--E 1439 + +--S 1440 of 1751 +--d0:=D(m0,x) +--E 1440 + +)clear all + +--S 1441 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1441 + +--S 1442 of 1751 +--r0:=-2/3*(3+2*x)^(7/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+28/3*(3+2*x)^(5/2)*_ +-- (65+81*x)/sqrt(2+5*x+3*x^2)+31892/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-6776/81*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-504*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)-_ +-- 16744/27*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1442 + +--S 1443 of 1751 +--a0:=integrate(t0,x) +--E 1443 + +--S 1444 of 1751 +--m0:=a0-r0 +--E 1444 + +--S 1445 of 1751 +--d0:=D(m0,x) +--E 1445 + +)clear all + +--S 1446 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1446 + +--S 1447 of 1751 +--r0:=-2/3*(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+20/3*(3+2*x)^(3/2)*_ +-- (93+113*x)/sqrt(2+5*x+3*x^2)+8620/27*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-1840/27*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- sqrt(2+5*x+3*x^2)-4520/9*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1447 + +--S 1448 of 1751 +--a0:=integrate(t0,x) +--E 1448 + +--S 1449 of 1751 +--m0:=a0-r0 +--E 1449 + +--S 1450 of 1751 +--d0:=D(m0,x) +--E 1450 + +)clear all + +--S 1451 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1451 + +--S 1452 of 1751 +--r0:=-2/3*(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)-2392/9*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+2252/9*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+4/3*(475+563*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 1452 + +--S 1453 of 1751 +--a0:=integrate(t0,x) +--E 1453 + +--S 1454 of 1751 +--m0:=a0-r0 +--E 1454 + +--S 1455 of 1751 +--d0:=D(m0,x) +--E 1455 + +)clear all + +--S 1456 of 1751 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1456 + +--S 1457 of 1751 +--r0:=-2/3*(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+2852/3*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-608/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/15*(1759+2139*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 1457 + +--S 1458 of 1751 +--a0:=integrate(t0,x) +--E 1458 + +--S 1459 of 1751 +--m0:=a0-r0 +--E 1459 + +--S 1460 of 1751 +--d0:=D(m0,x) +--E 1460 + +)clear all + +--S 1461 of 1751 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------- +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (9x + 30x + 37x + 20x + 4)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1461 + +--S 1462 of 1751 +--r0:=-2/5*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+3476/5*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-728/5*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/25*(2152+2607*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 1462 + +--S 1463 of 1751 +--a0:=integrate(t0,x) +--E 1463 + +--S 1464 of 1751 +--m0:=a0-r0 +--E 1464 + +--S 1465 of 1751 +--d0:=D(m0,x) +--E 1465 + +)clear all + +--S 1466 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (18x + 87x + 164x + 151x + 68x + 12)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1466 + +--S 1467 of 1751 +--r0:=-2/5*(37+47*x)/((2+5*x+3*x^2)^(3/2)*sqrt(3+2*x))+11732/25*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-2096/25*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/25*(2054+2409*x)/(sqrt(3+2*x)*sqrt(2+5*x+3*x^2))+_ +-- 23464/125*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1467 + +--S 1468 of 1751 +--a0:=integrate(t0,x) +--E 1468 + +--S 1469 of 1751 +--m0:=a0-r0 +--E 1469 + +--S 1470 of 1751 +--d0:=D(m0,x) +--E 1470 + +)clear all + +--S 1471 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R -------------------------------------------------------------------------- +--R +------------+ +--R 6 5 4 3 2 +------+ | 2 +--R (36x + 228x + 589x + 794x + 589x + 228x + 36)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1471 + +--S 1472 of 1751 +--r0:=-2/5*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2))+_ +-- 12/25*(652+737*x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2))+_ +-- 95396/375*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2888/375*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+61672/375*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(3/2)+190792/1875*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1472 + +--S 1473 of 1751 +--a0:=integrate(t0,x) +--E 1473 + +--S 1474 of 1751 +--m0:=a0-r0 +--E 1474 + +--S 1475 of 1751 +--d0:=D(m0,x) +--E 1475 + +)clear all + +--S 1476 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 7 6 5 4 3 2 +------+ +--R (72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1476 + +--S 1477 of 1751 +--r0:=-2/5*(37+47*x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2))+4/25*(1858+2013*x)/_ +-- ((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2))+107548/3125*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+280256/3125*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+87144/625*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(5/2)+258536/3125*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+_ +-- 215096/15625*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1477 + +--S 1478 of 1751 +--a0:=integrate(t0,x) +--E 1478 + +--S 1479 of 1751 +--m0:=a0-r0 +--E 1479 + +--S 1480 of 1751 +--d0:=D(m0,x) +--E 1480 + +)clear all + +--S 1481 of 1751 +t0:=sqrt(x)/((1+x^2)*sqrt(1+x)) +--R +--R +--R +-+ +--R \|x +--R (1) ---------------- +--R 2 +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 1481 + +--S 1482 of 1751 +r0:=-1/2*(1-%i)^(3/2)*atanh(sqrt(1-%i)*sqrt(x)/sqrt(1+x))-_ + 1/2*(1+%i)^(3/2)*atanh(sqrt(1+%i)*sqrt(x)/sqrt(1+x)) +--R +--R +--R +------+ +-+ +------+ +-+ +--R +------+ \|1 + %i \|x +------+ \|1 - %i \|x +--R - %i\|1 + %i atanh(-------------) - \|1 - %i atanh(-------------) +--R +-----+ +-----+ +--R \|x + 1 \|x + 1 +--R (2) ----------------------------------------------------------------- +--R 1 + %i +--R Type: Expression(Complex(Integer)) +--E 1482 + +--S 1483 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R +-+4+-+ %pi +-+4+-+ %pi +-+ +-----+ +--R (\|2 \|2 sin(---) + \|2 \|2 cos(---) + 2x)\|x \|x + 1 +--R 8 8 +--R + +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) + (x - 1)\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R (x + 1)\|2 \|2 cos(---) + 2x + x + 1 +--R 8 +--R + +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R +-+4+-+ %pi +-+4+-+ %pi +-+ +-----+ +--R (- \|2 \|2 sin(---) - \|2 \|2 cos(---) + 2x)\|x \|x + 1 +--R 8 8 +--R + +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) + (- x + 1)\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R (- x - 1)\|2 \|2 cos(---) + 2x + x + 1 +--R 8 +--R + +--R - +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) + \|2 +--R 8 8 +--R atan(------------------------------------------------------) +--R +-+ +-+ +-----+ 4+-+ %pi 4+-+ %pi +-+ +--R \|2 \|x \|x + 1 - \|2 sin(---) - \|2 cos(---) + x\|2 +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) - \|2 +--R 4+-+ %pi 8 8 +--R - 2\|2 sin(---)atan(------------------------------------------------------) +--R 8 +-+ +-+ +-----+ 4+-+ %pi 4+-+ %pi +-+ +--R \|2 \|x \|x + 1 + \|2 sin(---) + \|2 cos(---) + x\|2 +--R 8 8 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 1483 + +--S 1484 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R +-+4+-+ %pi +-+4+-+ %pi +-+ +-----+ +--R (\|2 \|2 sin(---) + \|2 \|2 cos(---) + 2x)\|x \|x + 1 +--R 8 8 +--R + +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) + (x - 1)\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R (x + 1)\|2 \|2 cos(---) + 2x + x + 1 +--R 8 +--R + +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R +-+4+-+ %pi +-+4+-+ %pi +-+ +-----+ +--R (- \|2 \|2 sin(---) - \|2 \|2 cos(---) + 2x)\|x \|x + 1 +--R 8 8 +--R + +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) + (- x + 1)\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R (- x - 1)\|2 \|2 cos(---) + 2x + x + 1 +--R 8 +--R + +--R +------+ +-+ +--R +------+ +-+ \|1 + %i \|x +--R (1 + %i)\|1 + %i \|2 atanh(-------------) +--R +-----+ +--R \|x + 1 +--R + +--R +------+ +-+ +--R +------+ +-+ \|1 - %i \|x +--R (1 - %i)\|1 - %i \|2 atanh(-------------) +--R +-----+ +--R \|x + 1 +--R + +--R - +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) + \|2 +--R 8 8 +--R atan(------------------------------------------------------) +--R +-+ +-+ +-----+ 4+-+ %pi 4+-+ %pi +-+ +--R \|2 \|x \|x + 1 - \|2 sin(---) - \|2 cos(---) + x\|2 +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) - \|2 +--R 4+-+ %pi 8 8 +--R - 2\|2 sin(---)atan(------------------------------------------------------) +--R 8 +-+ +-+ +-----+ 4+-+ %pi 4+-+ %pi +-+ +--R \|2 \|x \|x + 1 + \|2 sin(---) + \|2 cos(---) + x\|2 +--R 8 8 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Complex(Integer)) +--E 1484 + +--S 1485 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 2 %pi 12 3 2 %pi %pi 11 +--R (- 8x - 4x - 4)sin(---) + (- 32x - 16x - 16)cos(---)sin(---) +--R 8 8 8 +--R + +--R 3 2 %pi 2 +--R (- 80x - 40x - 40)cos(---) +--R 8 +--R + +--R 5 3 2 4+-+2 +--R (48x - 10x + 18x - 26x + 2)\|2 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 3 +--R (- 160x - 80x - 80)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (160x - 64x - 124x - 4x - 124x - 4)\|2 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 4 +--R (- 248x - 124x - 124)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 7 +--R (592x + 128x - 166x + 110x - 214x - 34)\|2 cos(---) - 64x +--R 8 +--R + +--R 6 5 4 3 2 +--R 544x + 668x + 230x + 332x + 84x - 2 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 5 +--R (- 320x - 160x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (1152x + 512x - 112x + 304x - 240x - 80)\|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi +--R (- 1024x + 512x + 1472x + 96x + 512x + 160x - 64x)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 6 +--R (- 352x - 176x - 176)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (1696x + 1024x + 52x + 540x - 172x - 132)\|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi 2 +--R (- 3584x - 768x + 2336x - 848x - 80x - 80x - 432x)cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R - 128x - 896x - 544x + 768x + 471x 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+--R + +--R 3 2 +--R 2552x + 840x - 11x - 3 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 2048x - 6912x - 12160x - 11520x - 7304x - 2962x - 192x +--R + +--R 3 2 +--R 20x + 8x - 2x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 9 +--R (- 160x - 80x - 80)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 7 +--R (1408x + 1536x + 688x + 784x + 304x - 112)\|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 9216x - 13824x - 4160x - 288x + 960x + 2336x + 640x +--R + +--R - 128 +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 17920x + 19968x - 13184x - 25728x - 18916x - 11796x +--R + +--R 3 2 +--R - 2400x + 672x + 68x - 12 +--R * +--R 4+-+2 %pi 3 +--R \|2 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R 8192x + 45056x + 78336x + 62208x + 29984x + 7792x +--R + +--R 5 4 3 2 +--R - 2712x - 1280x + 368x + 144x + 8x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 10 +--R (- 80x - 40x - 40)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 8 +--R (816x + 1024x + 534x + 530x + 262x - 62)\|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 6656x - 12544x - 8096x - 4464x - 1776x + 848x + 624x +--R + +--R - 64 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 11904x + 28032x + 18336x - 512x - 6267x - 6923x +--R + +--R 3 2 +--R - 3656x - 280x + 83x - 13 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 28672x - 38912x + 33024x + 93312x + 86160x + 53704x +--R + +--R 5 4 3 2 +--R 20012x + 2560x + 168x + 184x + 28x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 +--R - 4096x - 16384x - 32256x - 36352x - 27408x +--R + +--R 8 7 6 5 4 3 2 +--R - 15840x - 6890x - 2446x - 648x - 128x - 14x - 2x +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 11 +--R (- 32x - 16x - 16)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 9 +--R (288x + 448x + 276x + 236x + 148x - 20)\|2 cos(---) +--R 8 +--R + 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+--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 1152x + 4992x + 7968x + 7168x + 4913x + 2409x + 472x +--R + +--R 2 +--R - 24x + 7x - 1 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 4096x - 16384x - 30208x - 32512x - 23312x - 12320x +--R + +--R 5 4 3 +--R - 4218x - 480x + 68x + 6x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 4096x + 16384x + 28160x + 26112x + 14352x + 4448x +--R + +--R 7 6 5 4 3 2 +--R - 166x - 890x - 504x - 176x - 34x - 6x +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 7 +--R 8192x + 24576x + 35840x + 34816x + 24352x + 12832x + 5156x +--R + +--R 6 5 4 3 +--R 1552x + 344x + 48x + 4x +--R * +--R +-+ +-----+ +--R \|x \|x + 1 +--R + +--R 4 3 2 %pi 12 +--R (- 8x - 8x - 8x - 8x)sin(---) +--R 8 +--R + +--R 4 3 2 %pi %pi 11 +--R (- 32x - 32x - 32x - 32x)cos(---)sin(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (- 80x - 80x - 80x - 80x)cos(---) +--R 8 +--R + +--R 6 5 4 3 4+-+2 +--R (48x + 24x - 16x + 16x - 8x)\|2 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (- 160x - 160x - 160x - 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi +--R (160x + 16x - 176x - 48x - 80x - 64x)\|2 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (- 248x - 248x - 248x - 248x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 2 8 +--R (592x + 424x - 176x + 48x - 128x - 184x)\|2 cos(---) - 64x +--R 8 +--R + +--R 7 6 5 4 3 2 +--R 512x + 948x + 492x + 400x + 240x - 36x + 4x +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (- 320x - 320x - 320x - 320x)cos(---) +--R 8 +--R + +--R 6 5 3 2 4+-+2 %pi 3 +--R (1152x + 1088x + 256x - 128x - 320x)\|2 cos(---) +--R 8 +--R + +--R 8 6 5 4 3 2 %pi +--R (- 1024x + 1856x + 704x + 448x + 448x - 128x )cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (- 352x - 352x - 352x - 352x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 4 +--R (1696x + 1872x + 352x + 544x - 64x - 432x)\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (- 3584x - 2560x + 2400x + 192x - 704x + 64x - 544x - 128x) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 128x - 960x - 976x + 600x + 872x + 496x + 416x + 56x +--R + +--R 2 +--R 8x +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 7 +--R (- 320x - 320x - 320x - 320x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 5 +--R (2112x + 2720x + 992x + 992x + 160x - 448x)\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R - 5632x - 3072x + 8160x + 6880x + 3392x + 2112x - 416x +--R + +--R - 416x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R 1792x + 640x - 1824x + 3312x + 6984x + 5256x + 2976x +--R + +--R 3 2 +--R 720x - 8x - 8x +--R * +--R 4+-+2 %pi +--R \|2 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 8 +--R (- 248x - 248x - 248x - 248x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 6 +--R (1888x + 2736x + 1312x + 1120x + 320x - 336x)\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R - 11648x - 16896x - 1544x + 4136x + 3040x + 3872x + 744x +--R + +--R - 520x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R 1408x - 12992x - 36368x - 33096x - 16152x - 4336x + 2528x +--R + +--R 3 2 +--R 2008x + 136x - 32x +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 5 +--R - 2048x - 7936x - 15360x - 16864x - 11896x - 5720x - 1152x +--R + +--R 4 3 2 +--R 64x - 8x - 8x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 9 +--R (- 160x - 160x - 160x - 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 7 +--R (1408x + 2240x + 1280x + 1024x + 384x - 192x)\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R - 9216x - 18432x - 9920x - 1216x + 832x + 2880x + 1280x +--R + +--R - 256x +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R 17920x + 28928x - 5440x - 33696x - 29584x - 19152x +--R + +--R 4 3 2 +--R - 6848x + 288x + 272x - 48x +--R * +--R 4+-+2 %pi 3 +--R \|2 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 8192x + 49152x + 99840x + 96256x + 53792x + 18368x +--R + +--R 6 5 4 3 2 +--R - 672x - 2816x + 96x + 320x + 32x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 10 +--R (- 80x - 80x - 80x - 80x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 8 +--R (816x + 1432x + 944x + 720x + 320x - 72x)\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (- 6656x - 15872x - 13536x - 7360x - 3520x + 320x + 800x ) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R 11904x + 33984x + 30864x + 5896x - 7528x - 9616x - 6560x +--R + +--R 3 2 +--R - 1496x + 56x - 32x +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R - 28672x - 53248x + 17152x + 112896x + 127376x + 87920x +--R + +--R 6 5 4 3 2 +--R 40160x + 8832x + 560x + 272x + 96x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 4096x - 18432x - 39936x - 50688x - 42416x - 26488x +--R + +--R 8 7 6 5 4 +--R - 12760x - 4816x - 1472x - 312x - 56x +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 11 +--R (- 32x - 32x - 32x - 32x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 9 +--R (288x + 592x + 464x + 336x + 176x )\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R - 2560x - 7168x - 7648x - 5216x - 3136x - 832x + 160x +--R + +--R 32x +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R 6912x + 22656x + 29024x + 20272x + 9224x + 1288x - 1888x +--R + +--R 3 2 +--R - 1008x - 72x - 8x +--R * +--R 4+-+2 %pi 5 +--R \|2 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R - 16384x - 65536x - 96256x - 58880x - 3520x + 22208x +--R + +--R 6 5 4 3 2 +--R 23616x + 12288x + 2880x + 320x + 64x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R 8192x + 20480x + 2048x - 46080x - 77216x - 72144x +--R + +--R 8 7 6 5 4 3 +--R - 46848x - 22384x - 8128x - 2192x - 416x - 48x +--R * +--R 4+-+2 %pi 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64x - 16x +--R * +--R 4+-+2 %pi 5 +--R \|2 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R - 9216x - 52224x - 109824x - 138240x - 133384x - 90856x +--R + +--R 6 5 4 3 2 +--R - 33560x - 5112x - 760x - 280x + 24x - 8x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 +--R 20480x + 71680x + 124672x + 157056x + 149328x +--R + +--R 9 8 7 6 5 4 3 2 +--R 100984x + 48344x + 15976x + 3240x + 392x + 40x + 24x + 8x +--R * +--R 4+-+2 %pi +--R \|2 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 12 +--R (- 8x - 8x - 8x - 8x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 10 +--R (32x + 80x + 80x + 80x + 48x )\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 %pi 8 +--R (- 192x - 896x - 1464x - 1544x - 1360x - 656x - 88x - 8x)cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 3 +--R 512x + 2560x + 5728x + 7552x + 7328x + 5312x + 2144x + 320x +--R + +--R 2 +--R 32x +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R - 2304x - 11008x - 26432x - 40704x - 44674x - 37258x +--R + +--R 6 5 4 3 2 +--R - 22070x - 7806x - 1534x - 246x - 10x - 2x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R 2048x + 15360x + 40320x + 63936x + 76424x + 69164x +--R + +--R 8 7 6 5 4 3 2 +--R 45868x + 22564x + 8052x + 2004x + 340x + 28x + 4x +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 16 15 14 13 12 11 +--R - 8192x - 32768x - 68608x - 103424x - 119584x - 107840x +--R + +--R 10 9 8 7 6 5 4 3 +--R - 77156x - 43892x - 19884x - 7100x - 1948x - 396x - 52x - 4x +--R Type: Expression(Complex(Integer)) +--E 1485 + +)clear all + +--S 1486 of 1751 +t0:=(-1+2*x^2)/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 2 +--R 2x - 1 +--R (1) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 1486 + +--S 1487 of 1751 +r0:=x*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R (2) x\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 1487 + +--S 1488 of 1751 +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R (3) x\|x - 1 \|x + 1 +--R Type: Union(Expression(Integer),...) +--E 1488 + +--S 1489 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1489 + +--S 1490 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1490 + +)clear all + +--S 1491 of 1751 +t0:=(a+c*x^2)/(sqrt(d+e*x)*sqrt(f+g*x)) +--R +--R +--R 2 +--R c x + a +--R (1) -------------------- +--R +-------+ +-------+ +--R \|e x + d \|g x + f +--R Type: Expression(Integer) +--E 1491 + +--S 1492 of 1751 +r0:=-1/4*c*(4*d*e*f*g-3*(e*f+d*g)^2)*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*_ + sqrt(f+g*x)))/(e^(5/2)*g^(5/2))+2*a*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*_ + sqrt(f+g*x)))/(sqrt(e)*sqrt(g))-3/4*c*(e*f+d*g)*sqrt(d+e*x)*_ + sqrt(f+g*x)/(e^2*g^2)+1/2*c*x*sqrt(d+e*x)*sqrt(f+g*x)/(e*g) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 \|g \|e x + d +--R ((8a e + 3c d )g + 2c d e f g + 3c e f )atanh(--------------) +--R +-+ +-------+ +--R \|e \|g x + f +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2c e g x - 3c d g - 3c e f)\|e \|g \|e x + d \|g x + f +--R / +--R 2 2 +-+ +-+ +--R 4e g \|e \|g +--R Type: Expression(Integer) +--E 1492 + +--S 1493 of 1751 +--a0:=integrate(t0,x) +--E 1493 + +--S 1494 of 1751 +--m0:=a0-r0 +--E 1494 + +--S 1495 of 1751 +--d0:=D(m0,x) +--E 1495 + +)clear all + +--S 1496 of 1751 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - e g x + (- 3d e g - 2e f g)x + (- 3d e g - 6d e f g - e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- d g - 6d e f g - 3d e f )x + (- 2d f g - 3d e f )x - d f +--R / +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1496 + +--S 1497 of 1751 +r0:=-d^2*(7*e^2*f^2+16*d*e*f*g+8*d^2*g^2)*x/e^2-d*(2*e^2*f^2+7*d*e*f*g+_ + 4*d^2*g^2)*x^2/e-1/3*(e*f+d*g)*(e*f+7*d*g)*x^3-1/2*e*g*(e*f+2*d*g)*x^4-_ + 1/5*e^2*g^2*x^5-8*d^3*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 5 2 4 3 2 2 5 2 5 +--R (- 240d g - 480d e f g - 240d e f )log(- e x + d) - 6e g x +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (- 30d e g - 15e f g)x + (- 70d e g - 80d e f g - 10e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 120d e g - 210d e f g - 60d e f )x +--R + +--R 4 2 3 2 2 3 2 +--R (- 240d e g - 480d e f g - 210d e f )x +--R / +--R 3 +--R 30e +--R Type: Expression(Integer) +--E 1497 + +--S 1498 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 3 2 2 5 2 5 +--R (- 240d g - 480d e f g - 240d e f )log(e x - d) - 6e g x +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (- 30d e g - 15e f g)x + (- 70d e g - 80d e f g - 10e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 120d e g - 210d e f g - 60d e f )x +--R + +--R 4 2 3 2 2 3 2 +--R (- 240d e g - 480d e f g - 210d e f )x +--R / +--R 3 +--R 30e +--R Type: Union(Expression(Integer),...) +--E 1498 + +--S 1499 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 4 3 2 2 +--R (- 8d g - 16d e f g - 8d e f )log(e x - d) +--R + +--R 5 2 4 3 2 2 +--R (8d g + 16d e f g + 8d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1499 + +--S 1500 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1500 + +)clear all + +--S 1501 of 1751 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R - e g x + (- 2d e g - 2e f g)x + (- d g - 4d e f g - e f )x +--R + +--R 2 2 2 2 +--R (- 2d f g - 2d e f )x - d f +--R / +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1501 + +--S 1502 of 1751 +r0:=-d*(e*f+2*d*g)*(3*e*f+2*d*g)*x/e^2-1/2*(e^2*f^2+6*d*e*f*g+_ + 4*d^2*g^2)*x^2/e-1/3*g*(2*e*f+3*d*g)*x^3-1/4*e*g^2*x^4-_ + 4*d^2*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 3 2 2 2 4 2 4 +--R (- 48d g - 96d e f g - 48d e f )log(- e x + d) - 3e g x +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (- 12d e g - 8e f g)x + (- 24d e g - 36d e f g - 6e f )x +--R + +--R 3 2 2 2 3 2 +--R (- 48d e g - 96d e f g - 36d e f )x +--R / +--R 3 +--R 12e +--R Type: Expression(Integer) +--E 1502 + +--S 1503 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 2 2 2 4 2 4 +--R (- 48d g - 96d e f g - 48d e f )log(e x - d) - 3e g x +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (- 12d e g - 8e f g)x + (- 24d e g - 36d e f g - 6e f )x +--R + +--R 3 2 2 2 3 2 +--R (- 48d e g - 96d e f g - 36d e f )x +--R / +--R 3 +--R 12e +--R Type: Union(Expression(Integer),...) +--E 1503 + +--S 1504 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 3 2 2 2 +--R (- 4d g - 8d e f g - 4d e f )log(e x - d) +--R + +--R 4 2 3 2 2 2 +--R (4d g + 8d e f g + 4d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1504 + +--S 1505 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1505 + +)clear all + +--S 1506 of 1751 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R - e g x + (- d g - 2e f g)x + (- 2d f g - e f )x - d f +--R (1) ---------------------------------------------------------- +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1506 + +--S 1507 of 1751 +r0:=-2*d*g*(e*f+d*g)*x/e^2-d*(f+g*x)^2/e-1/3*(f+g*x)^3/g-_ + 2*d*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 +--R (- 6d g - 12d e f g - 6d e f g)log(- e x + d) - e g x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 2 2 +--R (- 3d e g - 3e f g )x + (- 6d e g - 12d e f g - 3e f g)x - 3d e f g +--R + +--R 3 3 +--R - e f +--R / +--R 3 +--R 3e g +--R Type: Expression(Integer) +--E 1507 + +--S 1508 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 2 3 +--R (- 6d g - 12d e f g - 6d e f )log(e x - d) - e g x +--R + +--R 2 2 3 2 2 2 2 3 2 +--R (- 3d e g - 3e f g)x + (- 6d e g - 12d e f g - 3e f )x +--R / +--R 3 +--R 3e +--R Type: Union(Expression(Integer),...) +--E 1508 + +--S 1509 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 +--R (- 6d g - 12d e f g - 6d e f g)log(e x - d) +--R + +--R 3 3 2 2 2 2 2 2 3 3 +--R (6d g + 12d e f g + 6d e f g)log(- e x + d) + 3d e f g + e f +--R / +--R 3 +--R 3e g +--R Type: Expression(Integer) +--E 1509 + +--S 1510 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1510 + +)clear all + +--S 1511 of 1751 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------- +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1511 + +--S 1512 of 1751 +r0:=-g*(e*f+d*g)*x/e^2-1/2*(f+g*x)^2/e-(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (- 2d g - 4d e f g - 2e f )log(- e x + d) - e g x +--R + +--R 2 2 2 2 +--R (- 2d e g - 4e f g)x - e f +--R / +--R 3 +--R 2e +--R Type: Expression(Integer) +--E 1512 + +--S 1513 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R (- 2d g - 4d e f g - 2e f )log(e x - d) - e g x + (- 2d e g - 4e f g)x +--R ------------------------------------------------------------------------- +--R 3 +--R 2e +--R Type: Union(Expression(Integer),...) +--E 1513 + +--S 1514 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- 2d g - 4d e f g - 2e f )log(e x - d) +--R + +--R 2 2 2 2 2 2 +--R (2d g + 4d e f g + 2e f )log(- e x + d) + e f +--R / +--R 3 +--R 2e +--R Type: Expression(Integer) +--E 1514 + +--S 1515 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1515 + +)clear all + +--S 1516 of 1751 +t0:=(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------- +--R 2 2 2 +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1516 + +--S 1517 of 1751 +r0:=-g^2*x/e^2-1/2*(e*f+d*g)^2*log(d-e*x)/(d*e^3)+_ + 1/2*(e*f-d*g)^2*log(d+e*x)/(d*e^3) +--R +--R +--R (2) +--R 2 2 2 2 +--R (d g - 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 2 +--R (- d g - 2d e f g - e f )log(- e x + d) - 2d e g x +--R / +--R 3 +--R 2d e +--R Type: Expression(Integer) +--E 1517 + +--S 1518 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R (d g - 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) - 2d e g x +--R / +--R 3 +--R 2d e +--R Type: Union(Expression(Integer),...) +--E 1518 + +--S 1519 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 +--R (d g + 2d e f g + e f )log(- e x + d) +--R / +--R 3 +--R 2d e +--R Type: Expression(Integer) +--E 1519 + +--S 1520 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1520 + +)clear all + +--S 1521 of 1751 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------------- +--R 3 3 2 2 2 3 +--R e x + d e x - d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1521 + +--S 1522 of 1751 +r0:=-1/2*(e*f-d*g)^2/(d*e^3*(d+e*x))-1/4*(e*f+d*g)^2*log(d-e*x)/(d^2*e^3)+_ + 1/4*(e*f-d*g)*(e*f+3*d*g)*log(d+e*x)/(d^2*e^3) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3d e g + 2d e f g + e f )x - 3d g + 2d e f g + d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- d e g - 2d e f g - e f )x - d g - 2d e f g - d e f )log(- e x + d) +--R + +--R 3 2 2 2 2 +--R - 2d g + 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x + 4d e +--R Type: Expression(Integer) +--E 1522 + +--S 1523 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3d e g + 2d e f g + e f )x - 3d g + 2d e f g + d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- d e g - 2d e f g - e f )x - d g - 2d e f g - d e f )log(e x - d) +--R + +--R 3 2 2 2 2 +--R - 2d g + 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 1523 + +--S 1524 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 +--R (d g + 2d e f g + e f )log(- e x + d) +--R / +--R 2 3 +--R 4d e +--R Type: Expression(Integer) +--E 1524 + +--S 1525 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1525 + +)clear all + +--S 1526 of 1751 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 4 4 3 3 3 4 +--R e x + 2d e x - 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1526 + +--S 1527 of 1751 +r0:=-1/4*(e*f-d*g)^2/(d*e^3*(d+e*x)^2)-1/4*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x))+1/4*(e*f+d*g)^2*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 4 2 +--R (d e g + 2d e f g + e f )x + (2d e g + 4d e f g + 2d e f )x + d g +--R + +--R 3 2 2 2 +--R 2d e f g + d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (3d e g - 2d e f g - d e f )x + 2d g - 2d e f +--R / +--R 3 5 2 4 4 5 3 +--R 4d e x + 8d e x + 4d e +--R Type: Expression(Integer) +--E 1527 + +--S 1528 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 4 2 +--R (d e g + 2d e f g + e f )x + (2d e g + 4d e f g + 2d e f )x + d g +--R + +--R 3 2 2 2 +--R 2d e f g + d e f +--R * +--R log(e x + d) +--R + +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (- d e g - 2d e f g - e f )x + (- 2d e g - 4d e f g - 2d e f )x +--R + +--R 4 2 3 2 2 2 +--R - d g - 2d e f g - d e f +--R * +--R log(e x - d) +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (6d e g - 4d e f g - 2d e f )x + 4d g - 4d e f +--R / +--R 3 5 2 4 4 5 3 +--R 8d e x + 16d e x + 8d e +--R Type: Union(Expression(Integer),...) +--E 1528 + +--S 1529 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g + 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g - 4d e f g - 2e f )atanh(---) +--R d +--R / +--R 3 3 +--R 8d e +--R Type: Expression(Integer) +--E 1529 + +--S 1530 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1530 + +)clear all + +--S 1531 of 1751 +t0:=(f+g*x)^2/((d+e*x)^3*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 3d e x + 2d e x - 2d e x - 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1531 + +--S 1532 of 1751 +r0:=-1/6*(e*f-d*g)^2/(d*e^3*(d+e*x)^3)-1/8*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x)^2)-1/8*(e*f+d*g)^2/(d^3*e^3*(d+e*x))+_ + 1/8*(e*f+d*g)^2*atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (3d e g + 6d e f g + 3e f )x + (9d e g + 18d e f g + 9d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (9d e g + 18d e f g + 9d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (- 3d e g - 6d e f g - 3d e f )x + (3d e g - 18d e f g - 9d e f )x +--R + +--R 5 2 4 3 2 2 +--R 2d g - 4d e f g - 10d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 24d e x + 72d e x + 72d e x + 24d e +--R Type: Expression(Integer) +--E 1532 + +--S 1533 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (3d e g + 6d e f g + 3e f )x + (9d e g + 18d e f g + 9d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (9d e g + 18d e f g + 9d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R log(e x + d) +--R + +--R 2 3 2 4 5 2 3 +--R (- 3d e g - 6d e f g - 3e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 9d e g - 18d e f g - 9d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 9d e g - 18d e f g - 9d e f )x - 3d g - 6d e f g - 3d e f +--R * +--R log(e x - d) +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (- 6d e g - 12d e f g - 6d e f )x + (6d e g - 36d e f g - 18d e f )x +--R + +--R 5 2 4 3 2 2 +--R 4d g - 8d e f g - 20d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 48d e x + 144d e x + 144d e x + 48d e +--R Type: Union(Expression(Integer),...) +--E 1533 + +--S 1534 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g + 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g - 4d e f g - 2e f )atanh(---) +--R d +--R / +--R 4 3 +--R 16d e +--R Type: Expression(Integer) +--E 1534 + +--S 1535 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1535 + +)clear all + +--S 1536 of 1751 +t0:=(f+g*x)^2/((d+e*x)^4*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------ +--R 6 6 5 5 2 4 4 4 2 2 5 6 +--R e x + 4d e x + 5d e x - 5d e x - 4d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1536 + +--S 1537 of 1751 +r0:=-1/8*(e*f-d*g)^2/(d*e^3*(d+e*x)^4)-1/12*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x)^3)-1/16*(e*f+d*g)^2/(d^3*e^3*(d+e*x)^2)-_ + 1/16*(e*f+d*g)^2/(d^4*e^3*(d+e*x))+1/16*(e*f+d*g)^2*atanh(e*x/d)/(d^5*e^3) +--R +--R +--R (2) +--R 2 4 2 5 6 2 4 3 3 2 2 4 5 2 3 +--R (3d e g + 6d e f g + 3e f )x + (12d e g + 24d e f g + 12d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (18d e g + 36d e f g + 18d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (12d e g + 24d e f g + 12d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 3d e g - 6d e f g - 3d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 12d e g - 24d e f g - 12d e f )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (- 3d e g - 38d e f g - 19d e f )x - 8d e f g - 16d e f +--R / +--R 5 7 4 6 6 3 7 5 2 8 4 9 3 +--R 48d e x + 192d e x + 288d e x + 192d e x + 48d e +--R Type: Expression(Integer) +--E 1537 + +--S 1538 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 5 6 2 4 3 3 2 2 4 5 2 3 +--R (3d e g + 6d e f g + 3e f )x + (12d e g + 24d e f g + 12d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (18d e g + 36d e f g + 18d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (12d e g + 24d e f g + 12d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R log(e x + d) +--R + +--R 2 4 2 5 6 2 4 +--R (- 3d e g - 6d e f g - 3e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 12d e g - 24d e f g - 12d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 18d e g - 36d e f g - 18d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 12d e g - 24d e f g - 12d e f )x - 3d g - 6d e f g - 3d e f +--R * +--R log(e x - d) +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 6d e g - 12d e f g - 6d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 24d e g - 48d e f g - 24d e f )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (- 6d e g - 76d e f g - 38d e f )x - 16d e f g - 32d e f +--R / +--R 5 7 4 6 6 3 7 5 2 8 4 9 3 +--R 96d e x + 384d e x + 576d e x + 384d e x + 96d e +--R Type: Union(Expression(Integer),...) +--E 1538 + +--S 1539 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g + 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g - 4d e f g - 2e f )atanh(---) +--R d +--R / +--R 5 3 +--R 32d e +--R Type: Expression(Integer) +--E 1539 + +--S 1540 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1540 + +)clear all + +--S 1541 of 1751 +t0:=(d+e*x)^7*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R e g x + (5d e g + 2e f g)x + (10d e g + 10d e f g + e f )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10d e g + 20d e f g + 5d e f )x + (5d e g + 20d e f g + 10d e f )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (d g + 10d e f g + 10d e f )x + (2d f g + 5d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1541 + +--S 1542 of 1751 +r0:=d^3*(49*e^2*f^2+160*d*e*f*g+112*d^2*g^2)*x/e^2+1/2*d^2*(23*e^2*f^2+_ + 98*d*e*f*g+80*d^2*g^2)*x^2/e+1/3*d*(7*e^2*f^2+46*d*e*f*g+49*d^2*g^2)*_ + x^3+1/4*e*(e^2*f^2+14*d*e*f*g+23*d^2*g^2)*x^4+1/5*e^2*g*(2*e*f+7*d*g)*_ + x^5+1/6*e^3*g^2*x^6+32*d^5*(e*f+d*g)^2/(e^3*(d-e*x))+_ + 16*d^4*(e*f+d*g)*(5*e*f+9*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 6 2 5 2 4 3 2 7 2 6 +--R (8640d e g + 13440d e f g + 4800d e f )x - 8640d g - 13440d e f g +--R + +--R 5 2 2 +--R - 4800d e f +--R * +--R log(- e x + d) +--R + +--R 7 2 7 6 2 7 6 2 5 2 6 7 2 5 +--R 10e g x + (74d e g + 24e f g)x + (261d e g + 186d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (635d e g + 710d e f g + 125d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (1420d e g + 2020d e f g + 550d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (4320d e g + 6660d e f g + 2250d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 +--R (- 6720d e g - 9600d e f g - 2940d e f )x - 1920d g - 3840d e f g +--R + +--R 5 2 2 +--R - 1920d e f +--R / +--R 4 3 +--R 60e x - 60d e +--R Type: Expression(Integer) +--E 1542 + +--S 1543 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 5 2 4 3 2 7 2 6 +--R (8640d e g + 13440d e f g + 4800d e f )x - 8640d g - 13440d e f g +--R + +--R 5 2 2 +--R - 4800d e f +--R * +--R log(e x - d) +--R + +--R 7 2 7 6 2 7 6 2 5 2 6 7 2 5 +--R 10e g x + (74d e g + 24e f g)x + (261d e g + 186d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (635d e g + 710d e f g + 125d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (1420d e g + 2020d e f g + 550d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (4320d e g + 6660d e f g + 2250d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 +--R (- 6720d e g - 9600d e f g - 2940d e f )x - 1920d g - 3840d e f g +--R + +--R 5 2 2 +--R - 1920d e f +--R / +--R 4 3 +--R 60e x - 60d e +--R Type: Union(Expression(Integer),...) +--E 1543 + +--S 1544 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 2 5 4 2 2 +--R (144d g + 224d e f g + 80d e f )log(e x - d) +--R + +--R 6 2 5 4 2 2 +--R (- 144d g - 224d e f g - 80d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1544 + +--S 1545 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1545 + +)clear all + +--S 1546 of 1751 +t0:=(d+e*x)^6*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R e g x + (4d e g + 2e f g)x + (6d e g + 8d e f g + e f )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4d e g + 12d e f g + 4d e f )x + (d g + 8d e f g + 6d e f )x +--R + +--R 4 3 2 4 2 +--R (2d f g + 4d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1546 + +--S 1547 of 1751 +r0:=d^2*(17*e^2*f^2+64*d*e*f*g+48*d^2*g^2)*x/e^2+d*(3*e^2*f^2+17*d*e*f*g+_ + 16*d^2*g^2)*x^2/e+1/3*(e^2*f^2+12*d*e*f*g+17*d^2*g^2)*x^3+_ + 1/2*e*g*(e*f+3*d*g)*x^4+1/5*e^2*g^2*x^5+16*d^4*(e*f+d*g)^2/(e^3*(d-e*x))+_ + 32*d^3*(e*f+d*g)*(e*f+2*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 5 2 4 2 3 3 2 6 2 5 +--R (1920d e g + 2880d e f g + 960d e f )x - 1920d g - 2880d e f g +--R + +--R 4 2 2 +--R - 960d e f +--R * +--R log(- e x + d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 6e g x + (39d e g + 15e f g)x + (125d e g + 105d e f g + 10e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (310d e g + 390d e f g + 80d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (960d e g + 1410d e f g + 420d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (- 1440d e g - 1920d e f g - 510d e f )x - 480d g - 960d e f g +--R + +--R 4 2 2 +--R - 480d e f +--R / +--R 4 3 +--R 30e x - 30d e +--R Type: Expression(Integer) +--E 1547 + +--S 1548 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 2 3 3 2 6 2 5 +--R (1920d e g + 2880d e f g + 960d e f )x - 1920d g - 2880d e f g +--R + +--R 4 2 2 +--R - 960d e f +--R * +--R log(e x - d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 6e g x + (39d e g + 15e f g)x + (125d e g + 105d e f g + 10e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (310d e g + 390d e f g + 80d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (960d e g + 1410d e f g + 420d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (- 1440d e g - 1920d e f g - 510d e f )x - 480d g - 960d e f g +--R + +--R 4 2 2 +--R - 480d e f +--R / +--R 4 3 +--R 30e x - 30d e +--R Type: Union(Expression(Integer),...) +--E 1548 + +--S 1549 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 4 3 2 2 +--R (64d g + 96d e f g + 32d e f )log(e x - d) +--R + +--R 5 2 4 3 2 2 +--R (- 64d g - 96d e f g - 32d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1549 + +--S 1550 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1550 + +)clear all + +--S 1551 of 1751 +t0:=(d+e*x)^5*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R e g x + (3d e g + 2e f g)x + (3d e g + 6d e f g + e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (d g + 6d e f g + 3d e f )x + (2d f g + 3d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1551 + +--S 1552 of 1751 +r0:=d*(5*e^2*f^2+24*d*e*f*g+20*d^2*g^2)*x/e^2+1/2*(e^2*f^2+_ + 10*d*e*f*g+12*d^2*g^2)*x^2/e+1/3*g*(2*e*f+5*d*g)*x^3+1/4*e*g^2*x^4+_ + 8*d^3*(e*f+d*g)^2/(e^3*(d-e*x))+4*d^2*(e*f+d*g)*(3*e*f+7*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 3 2 2 3 2 5 2 4 +--R (336d e g + 480d e f g + 144d e f )x - 336d g - 480d e f g +--R + +--R 3 2 2 +--R - 144d e f +--R * +--R log(- e x + d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 3e g x + (17d e g + 8e f g)x + (52d e g + 52d e f g + 6e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (168d e g + 228d e f g + 54d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 240d e g - 288d e f g - 60d e f )x - 96d g - 192d e f g - 96d e f +--R / +--R 4 3 +--R 12e x - 12d e +--R Type: Expression(Integer) +--E 1552 + +--S 1553 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 2 2 3 2 5 2 4 +--R (336d e g + 480d e f g + 144d e f )x - 336d g - 480d e f g +--R + +--R 3 2 2 +--R - 144d e f +--R * +--R log(e x - d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 3e g x + (17d e g + 8e f g)x + (52d e g + 52d e f g + 6e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (168d e g + 228d e f g + 54d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 240d e g - 288d e f g - 60d e f )x - 96d g - 192d e f g - 96d e f +--R / +--R 4 3 +--R 12e x - 12d e +--R Type: Union(Expression(Integer),...) +--E 1553 + +--S 1554 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 3 2 2 2 +--R (28d g + 40d e f g + 12d e f )log(e x - d) +--R + +--R 4 2 3 2 2 2 +--R (- 28d g - 40d e f g - 12d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1554 + +--S 1555 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1555 + +)clear all + +--S 1556 of 1751 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R e g x + (2d e g + 2e f g)x + (d g + 4d e f g + e f )x +--R + +--R 2 2 2 2 +--R (2d f g + 2d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1556 + +--S 1557 of 1751 +r0:=(e^2*f^2+8*d*e*f*g+8*d^2*g^2)*x/e^2+g*(e*f+2*d*g)*x^2/e+1/3*g^2*x^3+_ + 4*d^2*(e*f+d*g)^2/(e^3*(d-e*x))+4*d*(e*f+d*g)*(e*f+3*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R ((36d e g + 48d e f g + 12d e f )x - 36d g - 48d e f g - 12d e f ) +--R * +--R log(- e x + d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R e g x + (5d e g + 3e f g)x + (18d e g + 21d e f g + 3e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- 24d e g - 24d e f g - 3d e f )x - 12d g - 24d e f g - 12d e f +--R / +--R 4 3 +--R 3e x - 3d e +--R Type: Expression(Integer) +--E 1557 + +--S 1558 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R ((36d e g + 48d e f g + 12d e f )x - 36d g - 48d e f g - 12d e f ) +--R * +--R log(e x - d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R e g x + (5d e g + 3e f g)x + (18d e g + 21d e f g + 3e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- 24d e g - 24d e f g - 3d e f )x - 12d g - 24d e f g - 12d e f +--R / +--R 4 3 +--R 3e x - 3d e +--R Type: Union(Expression(Integer),...) +--E 1558 + +--S 1559 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 2 2 +--R (12d g + 16d e f g + 4d e f )log(e x - d) +--R + +--R 3 2 2 2 2 +--R (- 12d g - 16d e f g - 4d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1559 + +--S 1560 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1560 + +)clear all + +--S 1561 of 1751 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R e g x + (d g + 2e f g)x + (2d f g + e f )x + d f +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1561 + +--S 1562 of 1751 +r0:=g*(2*e*f+3*d*g)*x/e^2+1/2*g^2*x^2/e+2*d*(e*f+d*g)^2/(e^3*(d-e*x))+_ + (e*f+d*g)*(e*f+5*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((10d e g + 12d e f g + 2e f )x - 10d g - 12d e f g - 2d e f ) +--R * +--R log(- e x + d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R e g x + (5d e g + 4e f g)x + (- 6d e g - 4d e f g)x - 4d g +--R + +--R 2 2 2 +--R - 8d e f g - 4d e f +--R / +--R 4 3 +--R 2e x - 2d e +--R Type: Expression(Integer) +--E 1562 + +--S 1563 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((10d e g + 12d e f g + 2e f )x - 10d g - 12d e f g - 2d e f ) +--R * +--R log(e x - d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R e g x + (5d e g + 4e f g)x + (- 6d e g - 4d e f g)x - 4d g +--R + +--R 2 2 2 +--R - 8d e f g - 4d e f +--R / +--R 4 3 +--R 2e x - 2d e +--R Type: Union(Expression(Integer),...) +--E 1563 + +--S 1564 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (5d g + 6d e f g + e f )log(e x - d) +--R + +--R 2 2 2 2 +--R (- 5d g - 6d e f g - e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1564 + +--S 1565 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1565 + +)clear all + +--S 1566 of 1751 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------ +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1566 + +--S 1567 of 1751 +r0:=g^2*x/e^2+(e*f+d*g)^2/(e^3*(d-e*x))+2*g*(e*f+d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R ((2d e g + 2e f g)x - 2d g - 2d e f g)log(- e x + d) + e g x - d e g x +--R + +--R 2 2 2 2 +--R - d g - 2d e f g - e f +--R / +--R 4 3 +--R e x - d e +--R Type: Expression(Integer) +--E 1567 + +--S 1568 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 +--R ((2d e g + 2e f g)x - 2d g - 2d e f g)log(e x - d) + e g x - d e g x +--R + +--R 2 2 2 2 +--R - d g - 2d e f g - e f +--R / +--R 4 3 +--R e x - d e +--R Type: Union(Expression(Integer),...) +--E 1568 + +--S 1569 of 1751 +m0:=a0-r0 +--R +--R +--R 2 2 +--R (2d g + 2e f g)log(e x - d) + (- 2d g - 2e f g)log(- e x + d) +--R (4) --------------------------------------------------------------- +--R 3 +--R e +--R Type: Expression(Integer) +--E 1569 + +--S 1570 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1570 + +)clear all + +--S 1571 of 1751 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) -------------------------- +--R 3 3 2 2 2 3 +--R e x - d e x - d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1571 + +--S 1572 of 1751 +r0:=1/2*(e*f+d*g)^2/(d*e^3*(d-e*x))-1/4*(e*f-3*d*g)*(e*f+d*g)*_ + log(d-e*x)/(d^2*e^3)+1/4*(e*f-d*g)^2*log(d+e*x)/(d^2*e^3) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((d e g - 2d e f g + e f )x - d g + 2d e f g - d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((3d e g + 2d e f g - e f )x - 3d g - 2d e f g + d e f )log(- e x + d) +--R + +--R 3 2 2 2 2 +--R - 2d g - 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x - 4d e +--R Type: Expression(Integer) +--E 1572 + +--S 1573 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((d e g - 2d e f g + e f )x - d g + 2d e f g - d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((3d e g + 2d e f g - e f )x - 3d g - 2d e f g + d e f )log(e x - d) +--R + +--R 3 2 2 2 2 +--R - 2d g - 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x - 4d e +--R Type: Union(Expression(Integer),...) +--E 1573 + +--S 1574 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (3d g + 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 +--R (- 3d g - 2d e f g + e f )log(- e x + d) +--R / +--R 2 3 +--R 4d e +--R Type: Expression(Integer) +--E 1574 + +--S 1575 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1575 + +)clear all + +--S 1576 of 1751 +t0:=(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------- +--R 4 4 2 2 2 4 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1576 + +--S 1577 of 1751 +r0:=1/2*(d^2*g+e^2*f*x)*(f+g*x)/(d^2*e^2*(d^2-e^2*x^2))+1/2*(e*f-d*g)*_ + (e*f+d*g)*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 4 2 2 4 2 2 2 2 e x 3 2 +--R ((- d e g + e f )x + d g - d e f )atanh(---) - d e f g x +--R d +--R + +--R 3 2 3 2 3 +--R (- d e g - d e f )x - d e f g +--R / +--R 3 5 2 5 3 +--R 2d e x - 2d e +--R Type: Expression(Integer) +--E 1577 + +--S 1578 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 4 2 2 4 2 2 2 2 +--R ((- d e g + e f )x + d g - d e f )log(e x + d) +--R + +--R 2 2 2 4 2 2 4 2 2 2 2 3 2 3 2 +--R ((d e g - e f )x - d g + d e f )log(e x - d) + (- 2d e g - 2d e f )x +--R + +--R 3 +--R - 4d e f g +--R / +--R 3 5 2 5 3 +--R 4d e x - 4d e +--R Type: Union(Expression(Integer),...) +--E 1578 + +--S 1579 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 +--R (- d g + e f )log(e x + d) + (d g - e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g - 2e f )atanh(---) + 2d e f g +--R d +--R / +--R 3 3 +--R 4d e +--R Type: Expression(Integer) +--E 1579 + +--S 1580 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1580 + +)clear all + +--S 1581 of 1751 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ---------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + d e x - 2d e x - 2d e x + d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1581 + +--S 1582 of 1751 +r0:=1/8*(e*f+d*g)^2/(d^3*e^3*(d-e*x))-1/8*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^2)+_ + 1/4*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x))+1/8*(3*e*f-d*g)*(e*f+d*g)*_ + atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g + 2d e f g + 3e f )x + (- d e g + 2d e f g + 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g - 2d e f g - 3d e f )x + d g - 2d e f g - 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (d e g - 2d e f g - 3d e f )x + (- 3d e g - 2d e f g - 3d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 2d g - 4d e f g + 2d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 8d e x + 8d e x - 8d e x - 8d e +--R Type: Expression(Integer) +--E 1582 + +--S 1583 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g + 2d e f g + 3e f )x + (- d e g + 2d e f g + 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g - 2d e f g - 3d e f )x + d g - 2d e f g - 3d e f +--R * +--R log(e x + d) +--R + +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (d e g - 2d e f g - 3e f )x + (d e g - 2d e f g - 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- d e g + 2d e f g + 3d e f )x - d g + 2d e f g + 3d e f +--R * +--R log(e x - d) +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (2d e g - 4d e f g - 6d e f )x + (- 6d e g - 4d e f g - 6d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 4d g - 8d e f g + 4d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 16d e x + 16d e x - 16d e x - 16d e +--R Type: Union(Expression(Integer),...) +--E 1583 + +--S 1584 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g + 2d e f g + 3e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (d g - 2d e f g - 3e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g - 4d e f g - 6e f )atanh(---) +--R d +--R / +--R 4 3 +--R 16d e +--R Type: Expression(Integer) +--E 1584 + +--S 1585 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1585 + +)clear all + +--S 1586 of 1751 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) -------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 2d e x - d e x - 4d e x - d e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1586 + +--S 1587 of 1751 +r0:=1/16*(e*f+d*g)^2/(d^4*e^3*(d-e*x))-1/12*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^3)+_ + 1/8*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^2)-1/16*(3*e*f-d*g)*(e*f+d*g)/_ + (d^4*e^3*(d+e*x))+1/4*f*(e*f+d*g)*atanh(e*x/d)/(d^5*e^2) +--R +--R +--R (2) +--R 5 6 2 4 2 4 5 2 3 +--R (3d e f g + 3e f )x + (6d e f g + 6d e f )x +--R + +--R 4 2 3 3 2 5 4 2 2 +--R (- 6d e f g - 6d e f )x - 3d e f g - 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 2 4 5 2 3 3 3 2 4 2 2 +--R (- 3d e f g - 3d e f )x + (- 6d e f g - 6d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 4d e g - d e f g - d e f )x - 2d g - 2d e f g + 4d e f +--R / +--R 5 7 4 6 6 3 8 4 9 3 +--R 12d e x + 24d e x - 24d e x - 12d e +--R Type: Expression(Integer) +--E 1587 + +--S 1588 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 2 4 2 4 5 2 3 +--R (3d e f g + 3e f )x + (6d e f g + 6d e f )x +--R + +--R 4 2 3 3 2 5 4 2 2 +--R (- 6d e f g - 6d e f )x - 3d e f g - 3d e f +--R * +--R log(e x + d) +--R + +--R 5 6 2 4 2 4 5 2 3 +--R (- 3d e f g - 3e f )x + (- 6d e f g - 6d e f )x +--R + +--R 4 2 3 3 2 5 4 2 2 +--R (6d e f g + 6d e f )x + 3d e f g + 3d e f +--R * +--R log(e x - d) +--R + +--R 2 4 5 2 3 3 3 2 4 2 2 +--R (- 6d e f g - 6d e f )x + (- 12d e f g - 12d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 8d e g - 2d e f g - 2d e f )x - 4d g - 4d e f g + 8d e f +--R / +--R 5 7 4 6 6 3 8 4 9 3 +--R 24d e x + 48d e x - 48d e x - 24d e +--R Type: Union(Expression(Integer),...) +--E 1588 + +--S 1589 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 +--R (d f g + e f )log(e x + d) + (- d f g - e f )log(e x - d) +--R + +--R 2 e x +--R (- 2d f g - 2e f )atanh(---) +--R d +--R / +--R 5 2 +--R 8d e +--R Type: Expression(Integer) +--E 1589 + +--S 1590 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1590 + +)clear all + +--S 1591 of 1751 +t0:=(f+g*x)^2/((d+e*x)^3*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 3d e x + d e x - 5d e x - 5d e x + d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1591 + +--S 1592 of 1751 +r0:=1/32*(e*f+d*g)^2/(d^5*e^3*(d-e*x))-1/16*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^4)+_ + 1/12*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^3)-1/32*(3*e*f-d*g)*(e*f+d*g)/_ + (d^4*e^3*(d+e*x)^2)-1/8*f*(e*f+d*g)/(d^5*e^2*(d+e*x))+1/32*(e*f+d*g)*_ + (5*e*f+d*g)*atanh(e*x/d)/(d^6*e^3) +--R +--R +--R (2) +--R 2 5 2 6 7 2 5 3 4 2 2 5 6 2 4 +--R (3d e g + 18d e f g + 15e f )x + (9d e g + 54d e f g + 45d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g + 36d e f g + 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 6d e g - 36d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 9d e g - 54d e f g - 45d e f )x - 3d g - 18d e f g - 15d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 3d e g - 18d e f g - 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 9d e g - 54d e f g - 45d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 7d e g - 42d e f g - 35d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 5 2 2 +--R (- 21d e g + 18d e f g + 15d e f )x - 8d g + 32d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 96d e x + 288d e x + 192d e x - 192d e x - 288d e x - 96d e +--R Type: Expression(Integer) +--E 1592 + +--S 1593 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 6 7 2 5 3 4 2 2 5 6 2 4 +--R (3d e g + 18d e f g + 15e f )x + (9d e g + 54d e f g + 45d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g + 36d e f g + 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 6d e g - 36d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 9d e g - 54d e f g - 45d e f )x - 3d g - 18d e f g - 15d e f +--R * +--R log(e x + d) +--R + +--R 2 5 2 6 7 2 5 +--R (- 3d e g - 18d e f g - 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 9d e g - 54d e f g - 45d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 6d e g - 36d e f g - 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (6d e g + 36d e f g + 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (9d e g + 54d e f g + 45d e f )x + 3d g + 18d e f g + 15d e f +--R * +--R log(e x - d) +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 6d e g - 36d e f g - 30d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 18d e g - 108d e f g - 90d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 14d e g - 84d e f g - 70d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 5 2 2 +--R (- 42d e g + 36d e f g + 30d e f )x - 16d g + 64d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 192d e x + 576d e x + 384d e x - 384d e x - 576d e x - 192d e +--R Type: Union(Expression(Integer),...) +--E 1593 + +--S 1594 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g + 6d e f g + 5e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g - 6d e f g - 5e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g - 12d e f g - 10e f )atanh(---) +--R d +--R / +--R 6 3 +--R 64d e +--R Type: Expression(Integer) +--E 1594 + +--S 1595 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1595 + +)clear all + +--S 1596 of 1751 +t0:=(f+g*x)^2/((d+e*x)^4*(d^2-e^2*x^2)^2) +--R +--R +--R (1) +--R 2 2 2 +--R g x + 2f g x + f +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 4d e x + 4d e x - 4d e x - 10d e x - 4d e x + 4d e x +--R + +--R 7 8 +--R 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1596 + +--S 1597 of 1751 +r0:=1/64*(e*f+d*g)^2/(d^6*e^3*(d-e*x))-1/20*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^5)+_ + 1/16*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^4)-1/48*(3*e*f-d*g)*_ + (e*f+d*g)/(d^4*e^3*(d+e*x)^3)-1/16*f*(e*f+d*g)/(d^5*e^2*(d+e*x)^2)-_ + 1/64*(e*f+d*g)*(5*e*f+d*g)/(d^6*e^3*(d+e*x))+1/32*(e*f+d*g)*_ + (3*e*f+d*g)*atanh(e*x/d)/(d^7*e^3) +--R +--R +--R (2) +--R 2 6 2 7 8 2 6 +--R (15d e g + 60d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (60d e g + 240d e f g + 180d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (75d e g + 300d e f g + 225d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 75d e g - 300d e f g - 225d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 60d e g - 240d e f g - 180d e f )x - 15d g - 60d e f g - 45d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 15d e g - 60d e f g - 45d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 60d e g - 240d e f g - 180d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 80d e g - 320d e f g - 240d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 20d e g - 80d e f g - 60d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 49d e g + 188d e f g + 141d e f )x - 16d g + 32d e f g + 144d e f +--R / +--R 7 9 6 8 8 5 9 7 4 11 5 2 12 4 13 3 +--R 480d e x + 1920d e x + 2400d e x - 2400d e x - 1920d e x - 480d e +--R Type: Expression(Integer) +--E 1597 + +--S 1598 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 2 7 8 2 6 +--R (15d e g + 60d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (60d e g + 240d e f g + 180d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (75d e g + 300d e f g + 225d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 75d e g - 300d e f g - 225d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 60d e g - 240d e f g - 180d e f )x - 15d g - 60d e f g - 45d e f +--R * +--R log(e x + d) +--R + +--R 2 6 2 7 8 2 6 +--R (- 15d e g - 60d e f g - 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 60d e g - 240d e f g - 180d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 75d e g - 300d e f g - 225d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (75d e g + 300d e f g + 225d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (60d e g + 240d e f g + 180d e f )x + 15d g + 60d e f g + 45d e f +--R * +--R log(e x - d) +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 30d e g - 120d e f g - 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 120d e g - 480d e f g - 360d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 160d e g - 640d e f g - 480d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 40d e g - 160d e f g - 120d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 98d e g + 376d e f g + 282d e f )x - 32d g + 64d e f g + 288d e f +--R / +--R 7 9 6 8 8 5 9 7 4 11 5 2 12 4 13 3 +--R 960d e x + 3840d e x + 4800d e x - 4800d e x - 3840d e x - 960d e +--R Type: Union(Expression(Integer),...) +--E 1598 + +--S 1599 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g + 4d e f g + 3e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g - 4d e f g - 3e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g - 8d e f g - 6e f )atanh(---) +--R d +--R / +--R 7 3 +--R 64d e +--R Type: Expression(Integer) +--E 1599 + +--S 1600 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1600 + +)clear all + +--S 1601 of 1751 +t0:=(d+e*x)^7*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R - e g x + (- 4d e g - 2e f g)x + (- 6d e g - 8d e f g - e f )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (- 4d e g - 12d e f g - 4d e f )x + (- d g - 8d e f g - 6d e f )x +--R + +--R 4 3 2 4 2 +--R (- 2d f g - 4d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1601 + +--S 1602 of 1751 +r0:=-d*(7*e^2*f^2+48*d*e*f*g+56*d^2*g^2)*x/e^2-1/2*(e*f+2*d*g)*(e*f+12*d*g)*_ + x^2/e-1/3*g*(2*e*f+7*d*g)*x^3-1/4*e*g^2*x^4+8*d^4*(e*f+d*g)^2/(e^3*_ + (d-e*x)^2)-32*d^3*(e*f+d*g)*(e*f+2*d*g)/(e^3*(d-e*x))-8*d^2*(3*e^2*f^2+_ + 14*d*e*f*g+13*d^2*g^2)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 2 3 3 2 4 2 2 +--R (- 1248d e g - 1344d e f g - 288d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (2496d e g + 2688d e f g + 576d e f )x - 1248d g - 1344d e f g +--R + +--R 4 2 2 +--R - 288d e f +--R * +--R log(- e x + d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R - 3e g x + (- 22d e g - 8e f g)x + (- 91d e g - 68d e f g - 6e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 412d e g - 416d e f g - 72d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (1200d e g + 1068d e f g + 162d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (96d e g + 576d e f g + 300d e f )x - 672d g - 960d e f g - 288d e f +--R / +--R 5 2 4 2 3 +--R 12e x - 24d e x + 12d e +--R Type: Expression(Integer) +--E 1602 + +--S 1603 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 2 3 3 2 4 2 2 +--R (- 1248d e g - 1344d e f g - 288d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (2496d e g + 2688d e f g + 576d e f )x - 1248d g - 1344d e f g +--R + +--R 4 2 2 +--R - 288d e f +--R * +--R log(e x - d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R - 3e g x + (- 22d e g - 8e f g)x + (- 91d e g - 68d e f g - 6e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 412d e g - 416d e f g - 72d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (1200d e g + 1068d e f g + 162d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (96d e g + 576d e f g + 300d e f )x - 672d g - 960d e f g - 288d e f +--R / +--R 5 2 4 2 3 +--R 12e x - 24d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1603 + +--S 1604 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 3 2 2 2 +--R (- 104d g - 112d e f g - 24d e f )log(e x - d) +--R + +--R 4 2 3 2 2 2 +--R (104d g + 112d e f g + 24d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1604 + +--S 1605 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1605 + +)clear all + +--S 1606 of 1751 +t0:=(d+e*x)^6*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - e g x + (- 3d e g - 2e f g)x + (- 3d e g - 6d e f g - e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- d g - 6d e f g - 3d e f )x + (- 2d f g - 3d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1606 + +--S 1607 of 1751 +r0:=-(e^2*f^2+12*d*e*f*g+18*d^2*g^2)*x/e^2-g*(e*f+3*d*g)*x^2/e-1/3*g^2*x^3+_ + 4*d^3*(e*f+d*g)^2/(e^3*(d-e*x)^2)-4*d^2*(e*f+d*g)*(3*e*f+7*d*g)/(e^3*_ + (d-e*x))-2*d*(3*e^2*f^2+18*d*e*f*g+19*d^2*g^2)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 2 2 2 3 4 2 2 +--R (- 114d e g - 108d e f g - 18d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (228d e g + 216d e f g + 36d e f )x - 114d g - 108d e f g - 18d e f +--R * +--R log(- e x + d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R - e g x + (- 7d e g - 3e f g)x + (- 37d e g - 30d e f g - 3e f )x +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (99d e g + 69d e f g + 6d e f )x + (30d e g + 84d e f g + 33d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 72d g - 96d e f g - 24d e f +--R / +--R 5 2 4 2 3 +--R 3e x - 6d e x + 3d e +--R Type: Expression(Integer) +--E 1607 + +--S 1608 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 3 4 2 2 +--R (- 114d e g - 108d e f g - 18d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (228d e g + 216d e f g + 36d e f )x - 114d g - 108d e f g - 18d e f +--R * +--R log(e x - d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R - e g x + (- 7d e g - 3e f g)x + (- 37d e g - 30d e f g - 3e f )x +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (99d e g + 69d e f g + 6d e f )x + (30d e g + 84d e f g + 33d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 72d g - 96d e f g - 24d e f +--R / +--R 5 2 4 2 3 +--R 3e x - 6d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 1608 + +--S 1609 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 2 2 +--R (- 38d g - 36d e f g - 6d e f )log(e x - d) +--R + +--R 3 2 2 2 2 +--R (38d g + 36d e f g + 6d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1609 + +--S 1610 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1610 + +)clear all + +--S 1611 of 1751 +t0:=(d+e*x)^5*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R - e g x + (- 2d e g - 2e f g)x + (- d g - 4d e f g - e f )x +--R + +--R 2 2 2 2 +--R (- 2d f g - 2d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1611 + +--S 1612 of 1751 +r0:=-g*(2*e*f+5*d*g)*x/e^2-1/2*g^2*x^2/e+2*d^2*(e*f+d*g)^2/(e^3*(d-e*x)^2)-_ + 4*d*(e*f+d*g)*(e*f+3*d*g)/(e^3*(d-e*x))-(e^2*f^2+10*d*e*f*g+13*d^2*g^2)*_ + log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 +--R (- 26d e g - 20d e f g - 2e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (52d e g + 40d e f g + 4d e f )x - 26d g - 20d e f g - 2d e f +--R * +--R log(- e x + d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 2 +--R - e g x + (- 8d e g - 4e f g)x + (19d e g + 8d e f g)x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (14d e g + 28d e f g + 8d e f )x - 20d g - 24d e f g - 4d e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Expression(Integer) +--E 1612 + +--S 1613 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 2 +--R (- 26d e g - 20d e f g - 2e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (52d e g + 40d e f g + 4d e f )x - 26d g - 20d e f g - 2d e f +--R * +--R log(e x - d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 2 +--R - e g x + (- 8d e g - 4e f g)x + (19d e g + 8d e f g)x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (14d e g + 28d e f g + 8d e f )x - 20d g - 24d e f g - 4d e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 1613 + +--S 1614 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- 13d g - 10d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 +--R (13d g + 10d e f g + e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1614 + +--S 1615 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1615 + +)clear all + +--S 1616 of 1751 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R - e g x + (- d g - 2e f g)x + (- 2d f g - e f )x - d f +--R (1) ---------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1616 + +--S 1617 of 1751 +r0:=-g^2*x/e^2+d*(e*f+d*g)^2/(e^3*(d-e*x)^2)-(e*f+d*g)*(e*f+5*d*g)/(e^3*_ + (d-e*x))-2*g*(e*f+2*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 3 2 2 2 2 3 2 2 +--R ((- 4d e g - 2e f g)x + (8d e g + 4d e f g)x - 4d g - 2d e f g) +--R * +--R log(- e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 3 2 3 2 2 +--R - e g x + 2d e g x + (4d e g + 6d e f g + e f )x - 4d g - 4d e f g +--R / +--R 5 2 4 2 3 +--R e x - 2d e x + d e +--R Type: Expression(Integer) +--E 1617 + +--S 1618 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 2 2 2 2 3 2 2 +--R ((- 4d e g - 2e f g)x + (8d e g + 4d e f g)x - 4d g - 2d e f g) +--R * +--R log(e x - d) +--R + +--R 3 2 3 2 2 2 2 2 2 3 2 3 2 2 +--R - e g x + 2d e g x + (4d e g + 6d e f g + e f )x - 4d g - 4d e f g +--R / +--R 5 2 4 2 3 +--R e x - 2d e x + d e +--R Type: Union(Expression(Integer),...) +--E 1618 + +--S 1619 of 1751 +m0:=a0-r0 +--R +--R +--R 2 2 +--R (- 4d g - 2e f g)log(e x - d) + (4d g + 2e f g)log(- e x + d) +--R (4) --------------------------------------------------------------- +--R 3 +--R e +--R Type: Expression(Integer) +--E 1619 + +--S 1620 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1620 + +)clear all + +--S 1621 of 1751 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1621 + +--S 1622 of 1751 +r0:=1/2*(e*f+d*g)^2/(e^3*(d-e*x)^2)-2*g*(e*f+d*g)/(e^3*(d-e*x))-_ + g^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (- 2e g x + 4d e g x - 2d g )log(- e x + d) + (4d e g + 4e f g)x +--R + +--R 2 2 2 2 +--R - 3d g - 2d e f g + e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Expression(Integer) +--E 1622 + +--S 1623 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2e g x + 4d e g x - 2d g )log(e x - d) + (4d e g + 4e f g)x - 3d g +--R + +--R 2 2 +--R - 2d e f g + e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 1623 + +--S 1624 of 1751 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - g log(e x - d) + g log(- e x + d) +--R (4) ----------------------------------- +--R 3 +--R e +--R Type: Expression(Integer) +--E 1624 + +--S 1625 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1625 + +)clear all + +--S 1626 of 1751 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 4 4 3 3 3 4 +--R e x - 2d e x + 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1626 + +--S 1627 of 1751 +r0:=1/4*(e*f+d*g)^2/(d*e^3*(d-e*x)^2)+1/4*(e*f-3*d*g)*(e*f+d*g)/_ + (d^2*e^3*(d-e*x))+1/4*(e*f-d*g)^2*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (d e g - 2d e f g + e f )x + (- 2d e g + 4d e f g - 2d e f )x +--R + +--R 4 2 3 2 2 2 +--R d g - 2d e f g + d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (3d e g + 2d e f g - d e f )x - 2d g + 2d e f +--R / +--R 3 5 2 4 4 5 3 +--R 4d e x - 8d e x + 4d e +--R Type: Expression(Integer) +--E 1627 + +--S 1628 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (d e g - 2d e f g + e f )x + (- 2d e g + 4d e f g - 2d e f )x +--R + +--R 4 2 3 2 2 2 +--R d g - 2d e f g + d e f +--R * +--R log(e x + d) +--R + +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (- d e g + 2d e f g - e f )x + (2d e g - 4d e f g + 2d e f )x +--R + +--R 4 2 3 2 2 2 +--R - d g + 2d e f g - d e f +--R * +--R log(e x - d) +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (6d e g + 4d e f g - 2d e f )x - 4d g + 4d e f +--R / +--R 3 5 2 4 4 5 3 +--R 8d e x - 16d e x + 8d e +--R Type: Union(Expression(Integer),...) +--E 1628 + +--S 1629 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g - 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g + 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g + 4d e f g - 2e f )atanh(---) +--R d +--R / +--R 3 3 +--R 8d e +--R Type: Expression(Integer) +--E 1629 + +--S 1630 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1630 + +)clear all + +--S 1631 of 1751 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x - d e x - 2d e x + 2d e x + d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1631 + +--S 1632 of 1751 +r0:=1/8*(e*f+d*g)^2/(d^2*e^3*(d-e*x)^2)+1/4*(e^2*f^2-d^2*g^2)/(d^3*e^3*_ + (d-e*x))-1/8*(e*f-d*g)^2/(d^3*e^3*(d+e*x))+1/8*(e*f-d*g)*(3*e*f+d*g)*_ + atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g - 2d e f g + 3e f )x + (d e g + 2d e f g - 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g + 2d e f g - 3d e f )x - d g - 2d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 5 2 +--R (d e g + 2d e f g - 3d e f )x + (3d e g - 2d e f g + 3d e f )x - 2d g +--R + +--R 4 3 2 2 +--R 4d e f g + 2d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 8d e x - 8d e x - 8d e x + 8d e +--R Type: Expression(Integer) +--E 1632 + +--S 1633 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g - 2d e f g + 3e f )x + (d e g + 2d e f g - 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g + 2d e f g - 3d e f )x - d g - 2d e f g + 3d e f +--R * +--R log(e x + d) +--R + +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (d e g + 2d e f g - 3e f )x + (- d e g - 2d e f g + 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- d e g - 2d e f g + 3d e f )x + d g + 2d e f g - 3d e f +--R * +--R log(e x - d) +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (2d e g + 4d e f g - 6d e f )x + (6d e g - 4d e f g + 6d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 4d g + 8d e f g + 4d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 16d e x - 16d e x - 16d e x + 16d e +--R Type: Union(Expression(Integer),...) +--E 1633 + +--S 1634 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g - 2d e f g + 3e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (d g + 2d e f g - 3e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g + 4d e f g - 6e f )atanh(---) +--R d +--R / +--R 4 3 +--R 16d e +--R Type: Expression(Integer) +--E 1634 + +--S 1635 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1635 + +)clear all + +--S 1636 of 1751 +t0:=(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ----------------------------- +--R 6 6 2 4 4 4 2 2 6 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1636 + +--S 1637 of 1751 +r0:=-1/4*(d^2*g-e^2*f*x)*(f+g*x)^3/(d^2*(e^2*f^2-d^2*g^2)*(d^2-e^2*x^2)^2)+_ + 1/8*(3*e^2*f^2-d^2*g^2)*(d^2*g+e^2*f*x)*(f+g*x)/(d^4*e^2*_ + (e^2*f^2-d^2*g^2)*(d^2-e^2*x^2))+1/8*(3*e^2*f^2-d^2*g^2)*atanh(e*x/d)/_ + (d^5*e^3) +--R +--R +--R (2) +--R 2 4 2 6 2 4 4 2 2 2 4 2 2 6 2 4 2 2 e x +--R ((- d e g + 3e f )x + (2d e g - 6d e f )x - d g + 3d e f )atanh(---) +--R d +--R + +--R 5 4 3 3 2 5 2 3 3 3 2 5 2 3 3 2 +--R - 3d e f g x + (d e g - 3d e f )x + 6d e f g x + (d e g + 5d e f )x +--R + +--R 5 +--R d e f g +--R / +--R 5 7 4 7 5 2 9 3 +--R 8d e x - 16d e x + 8d e +--R Type: Expression(Integer) +--E 1637 + +--S 1638 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 6 2 4 4 2 2 2 4 2 2 6 2 4 2 2 +--R ((- d e g + 3e f )x + (2d e g - 6d e f )x - d g + 3d e f ) +--R * +--R log(e x + d) +--R + +--R 2 4 2 6 2 4 4 2 2 2 4 2 2 6 2 4 2 2 +--R ((d e g - 3e f )x + (- 2d e g + 6d e f )x + d g - 3d e f ) +--R * +--R log(e x - d) +--R + +--R 3 3 2 5 2 3 5 2 3 3 2 5 +--R (2d e g - 6d e f )x + (2d e g + 10d e f )x + 8d e f g +--R / +--R 5 7 4 7 5 2 9 3 +--R 16d e x - 32d e x + 16d e +--R Type: Union(Expression(Integer),...) +--E 1638 + +--S 1639 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 +--R (- d g + 3e f )log(e x + d) + (d g - 3e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g - 6e f )atanh(---) + 6d e f g +--R d +--R / +--R 5 3 +--R 16d e +--R Type: Expression(Integer) +--E 1639 + +--S 1640 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1640 + +)clear all + +--S 1641 of 1751 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)^3) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + d e x - 3d e x - 3d e x + 3d e x + 3d e x - d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1641 + +--S 1642 of 1751 +r0:=1/32*(e*f+d*g)^2/(d^4*e^3*(d-e*x)^2)+1/8*f*(e*f+d*g)/(d^5*e^2*(d-e*x))-_ + 1/24*(e*f-d*g)^2/(d^3*e^3*(d+e*x)^3)-1/32*(e*f-d*g)*(3*e*f+d*g)/_ + (d^4*e^3*(d+e*x)^2)+1/16*(-3*e^2*f^2+d^2*g^2)/(d^5*e^3*(d+e*x))+_ + 1/16*(5*e^2*f^2+2*d*e*f*g-d^2*g^2)*atanh(e*x/d)/(d^6*e^3) +--R +--R +--R (2) +--R 2 5 2 6 7 2 5 +--R (- 3d e g + 6d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 3d e g + 6d e f g + 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 3d e g + 6d e f g + 15d e f )x - 3d g + 6d e f g + 15d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 3 4 2 5 2 3 +--R (3d e g - 6d e f g - 15d e f )x + (3d e g - 6d e f g - 15d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (- 5d e g + 10d e f g + 25d e f )x + (7d e g + 10d e f g + 25d e f )x +--R + +--R 7 2 6 5 2 2 +--R 4d g + 16d e f g - 8d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 48d e x + 48d e x - 96d e x - 96d e x + 48d e x + 48d e +--R Type: Expression(Integer) +--E 1642 + +--S 1643 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 6 7 2 5 +--R (- 3d e g + 6d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 3d e g + 6d e f g + 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 3d e g + 6d e f g + 15d e f )x - 3d g + 6d e f g + 15d e f +--R * +--R log(e x + d) +--R + +--R 2 5 2 6 7 2 5 3 4 2 2 5 6 2 4 +--R (3d e g - 6d e f g - 15e f )x + (3d e g - 6d e f g - 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 6d e g + 12d e f g + 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 6d e g + 12d e f g + 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (3d e g - 6d e f g - 15d e f )x + 3d g - 6d e f g - 15d e f +--R * +--R log(e x - d) +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 3 4 2 5 2 3 +--R (6d e g - 12d e f g - 30d e f )x + (6d e g - 12d e f g - 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 10d e g + 20d e f g + 50d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (14d e g + 20d e f g + 50d e f )x + 8d g + 32d e f g - 16d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 96d e x + 96d e x - 192d e x - 192d e x + 96d e x + 96d e +--R Type: Union(Expression(Integer),...) +--E 1643 + +--S 1644 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g + 2d e f g + 5e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (d g - 2d e f g - 5e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g - 4d e f g - 10e f )atanh(---) +--R d +--R / +--R 6 3 +--R 32d e +--R Type: Expression(Integer) +--E 1644 + +--S 1645 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1645 + +)clear all + +--S 1646 of 1751 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)^3) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------------------------------------------------------- +--R 8 8 7 7 2 6 6 3 5 5 5 3 3 6 2 2 7 8 +--R e x + 2d e x - 2d e x - 6d e x + 6d e x + 2d e x - 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1646 + +--S 1647 of 1751 +r0:=1/64*(e*f+d*g)^2/(d^5*e^3*(d-e*x)^2)+1/64*(e*f+d*g)*(5*e*f+d*g)/_ + (d^6*e^3*(d-e*x))-1/32*(e*f-d*g)^2/(d^3*e^3*(d+e*x)^4)-1/48*(e*f-d*g)*_ + (3*e*f+d*g)/(d^4*e^3*(d+e*x)^3)+1/32*(-3*e^2*f^2+d^2*g^2)/(d^5*e^3*_ + (d+e*x)^2)+1/32*(-5*e^2*f^2-2*d*e*f*g+d^2*g^2)/(d^6*e^3*(d+e*x))+_ + 1/64*(15*e^2*f^2+10*d*e*f*g-d^2*g^2)*atanh(e*x/d)/(d^7*e^3) +--R +--R +--R (2) +--R 2 6 2 7 8 2 6 +--R (- 3d e g + 30d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 6d e g + 60d e f g + 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (12d e g - 120d e f g - 180d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 6d e g + 60d e f g + 90d e f )x - 3d g + 30d e f g + 45d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 5 2 2 6 7 2 5 4 4 2 3 5 2 6 2 4 +--R (3d e g - 30d e f g - 45d e f )x + (6d e g - 60d e f g - 90d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 2d e g + 20d e f g + 30d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 10d e g + 100d e f g + 150d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (35d e g + 34d e f g + 51d e f )x + 16d g + 32d e f g - 48d e f +--R / +--R 7 9 6 8 8 5 9 7 4 10 6 3 11 5 2 12 4 +--R 192d e x + 384d e x - 192d e x - 768d e x - 192d e x + 384d e x +--R + +--R 13 3 +--R 192d e +--R Type: Expression(Integer) +--E 1647 + +--S 1648 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 2 7 8 2 6 +--R (- 3d e g + 30d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 6d e g + 60d e f g + 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (12d e g - 120d e f g - 180d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 6d e g + 60d e f g + 90d e f )x - 3d g + 30d e f g + 45d e f +--R * +--R log(e x + d) +--R + +--R 2 6 2 7 8 2 6 3 5 2 2 6 7 2 5 +--R (3d e g - 30d e f g - 45e f )x + (6d e g - 60d e f g - 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 3d e g + 30d e f g + 45d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 12d e g + 120d e f g + 180d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 3d e g + 30d e f g + 45d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (6d e g - 60d e f g - 90d e f )x + 3d g - 30d e f g - 45d e f +--R * +--R log(e x - d) +--R + +--R 3 5 2 2 6 7 2 5 +--R (6d e g - 60d e f g - 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (12d e g - 120d e f g - 180d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 4d e g + 40d e f g + 60d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 20d e g + 200d e f g + 300d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (70d e g + 68d e f g + 102d e f )x + 32d g + 64d e f g - 96d e f +--R / +--R 7 9 6 8 8 5 9 7 4 10 6 3 11 5 2 12 4 +--R 384d e x + 768d e x - 384d e x - 1536d e x - 384d e x + 768d e x +--R + +--R 13 3 +--R 384d e +--R Type: Union(Expression(Integer),...) +--E 1648 + +--S 1649 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g + 10d e f g + 15e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (d g - 10d e f g - 15e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g - 20d e f g - 30e f )atanh(---) +--R d +--R / +--R 7 3 +--R 128d e +--R Type: Expression(Integer) +--E 1649 + +--S 1650 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1650 + +)clear all + +--S 1651 of 1751 +t0:=(a+b*x+c*x^2)/((d+e*x)*(f+g*x)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) --------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 1651 + +--S 1652 of 1751 +r0:=c*x/(e*g)+(c*d^2-b*d*e+a*e^2)*log(d+e*x)/(e^2*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))*log(f+g*x)/(g^2*(e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (a e g - b e f g + c e f )log(g x + f) +--R + +--R 2 2 2 2 2 +--R (- a e + b d e - c d )g log(e x + d) + (c d e g - c e f g)x +--R / +--R 2 3 3 2 +--R d e g - e f g +--R Type: Expression(Integer) +--E 1652 + +--S 1653 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (a e g - b e f g + c e f )log(g x + f) +--R + +--R 2 2 2 2 2 +--R (- a e + b d e - c d )g log(e x + d) + (c d e g - c e f g)x +--R / +--R 2 3 3 2 +--R d e g - e f g +--R Type: Union(Expression(Integer),...) +--E 1653 + +--S 1654 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1654 + +--S 1655 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1655 + +)clear all + +--S 1656 of 1751 +t0:=(a+b*x+c*x^2)^2/((d+e*x)*(f+g*x)) +--R +--R +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R (1) -------------------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 1656 + +--S 1657 of 1751 +r0:=(b^2*e^2*g^2-2*c*e*g*(b*e*f+b*d*g-a*e*g)+c^2*(e^2*f^2+d*e*f*g+_ + d^2*g^2))*x/(e^3*g^3)-1/2*c*(c*e*f+c*d*g-2*b*e*g)*x^2/(e^2*g^2)+_ + 1/3*c^2*x^3/(e*g)+(c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/(e^4*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))^2*log(f+g*x)/(g^4*(e*f-d*g)) +--R +--R +--R (2) +--R 2 4 4 4 3 2 4 2 2 4 3 2 4 4 +--R (6a e g - 12a b e f g + (12a c + 6b )e f g - 12b c e f g + 6c e f ) +--R * +--R log(g x + f) +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (- 6a e + 12a b d e + (- 12a c - 6b )d e + 12b c d e - 6c d )g +--R * +--R log(e x + d) +--R + +--R 2 3 4 2 4 3 3 +--R (2c d e g - 2c e f g )x +--R + +--R 3 2 2 2 4 4 3 2 4 2 2 2 +--R ((6b c d e - 3c d e )g - 6b c e f g + 3c e f g )x +--R + +--R 2 3 2 2 2 3 4 2 4 3 +--R ((12a c + 6b )d e - 12b c d e + 6c d e)g + (- 12a c - 6b )e f g +--R + +--R 4 2 2 2 4 3 +--R 12b c e f g - 6c e f g +--R * +--R x +--R / +--R 4 5 5 4 +--R 6d e g - 6e f g +--R Type: Expression(Integer) +--E 1657 + +--S 1658 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 3 2 4 2 2 4 3 2 4 4 +--R (6a e g - 12a b e f g + (12a c + 6b )e f g - 12b c e f g + 6c e f ) +--R * +--R log(g x + f) +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (- 6a e + 12a b d e + (- 12a c - 6b )d e + 12b c d e - 6c d )g +--R * +--R log(e x + d) +--R + +--R 2 3 4 2 4 3 3 +--R (2c d e g - 2c e f g )x +--R + +--R 3 2 2 2 4 4 3 2 4 2 2 2 +--R ((6b c d e - 3c d e )g - 6b c e f g + 3c e f g )x +--R + +--R 2 3 2 2 2 3 4 2 4 3 +--R ((12a c + 6b )d e - 12b c d e + 6c d e)g + (- 12a c - 6b )e f g +--R + +--R 4 2 2 2 4 3 +--R 12b c e f g - 6c e f g +--R * +--R x +--R / +--R 4 5 5 4 +--R 6d e g - 6e f g +--R Type: Union(Expression(Integer),...) +--E 1658 + +--S 1659 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1659 + +--S 1660 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1660 + +)clear all + +--S 1661 of 1751 +t0:=(a+b*x+c*x^2)^3/((d+e*x)*(f+g*x)) +--R +--R +--R (1) +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R / +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 1661 + +--S 1662 of 1751 +r0:=-(b^2*e^3*g^3*(b*e*f+b*d*g-3*a*e*g)-c^3*(e^4*f^4+d*e^3*f^3*g+_ + d^2*e^2*f^2*g^2+d^3*e*f*g^3+d^4*g^4)-3*c*e^2*g^2*(a^2*e^2*g^2-_ + 2*a*b*e*g*(e*f+d*g)+b^2*(e^2*f^2+d*e*f*g+d^2*g^2))-3*c^2*e*g*(a*e*g*_ + (e^2*f^2+d*e*f*g+d^2*g^2)-b*(e^3*f^3+d*e^2*f^2*g+d^2*e*f*g^2+d^3*g^3)))*_ + x/(e^5*g^5)+1/2*(b^3*e^3*g^3-3*b*c*e^2*g^2*(b*e*f+b*d*g-2*a*e*g)-c^3*_ + (e^3*f^3+d*e^2*f^2*g+d^2*e*f*g^2+d^3*g^3)-3*c^2*e*g*(a*e*g*(e*f+d*g)-_ + b*(e^2*f^2+d*e*f*g+d^2*g^2)))*x^2/(e^4*g^4)+1/3*c*(3*b^2*e^2*g^2-_ + 3*c*e*g*(b*e*f+b*d*g-a*e*g)+c^2*(e^2*f^2+d*e*f*g+d^2*g^2))*_ + x^3/(e^3*g^3)-1/4*c^2*(c*e*f+c*d*g-3*b*e*g)*x^4/(e^2*g^2)+_ + 1/5*c^3*x^5/(e*g)+(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/(e^6*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))^3*log(f+g*x)/(g^6*(e*f-d*g)) +--R +--R +--R (2) +--R 3 6 6 2 6 5 2 2 6 2 4 +--R 60a e g - 180a b e f g + (180a c + 180a b )e f g +--R + +--R 3 6 3 3 2 2 6 4 2 2 6 5 +--R (- 360a b c - 60b )e f g + (180a c + 180b c)e f g - 180b c e f g +--R + +--R 3 6 6 +--R 60c e f +--R * +--R log(g x + f) +--R + +--R 3 6 2 5 2 2 2 4 +--R - 60a e + 180a b d e + (- 180a c - 180a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (360a b c + 60b )d e + (- 180a c - 180b c)d e + 180b c d e - 60c d +--R * +--R 6 +--R g log(e x + d) +--R + +--R 3 5 6 3 6 5 5 +--R (12c d e g - 12c e f g )x +--R + +--R 2 5 3 2 4 6 2 6 5 3 6 2 4 4 +--R ((45b c d e - 15c d e )g - 45b c e f g + 15c e f g )x +--R + +--R 2 2 5 2 2 4 3 3 3 6 +--R ((60a c + 60b c)d e - 60b c d e + 20c d e )g +--R + +--R 2 2 6 5 2 6 2 4 3 6 3 3 +--R (- 60a c - 60b c)e f g + 60b c e f g - 20c e f g +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 2 4 2 3 3 +--R (180a b c + 30b )d e + (- 90a c - 90b c)d e + 90b c d e +--R + +--R 3 4 2 +--R - 30c d e +--R * +--R 6 +--R g +--R + +--R 3 6 5 2 2 6 2 4 2 6 3 3 +--R (- 180a b c - 30b )e f g + (90a c + 90b c)e f g - 90b c e f g +--R + +--R 3 6 4 2 +--R 30c e f g +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 2 4 +--R (180a c + 180a b )d e + (- 360a b c - 60b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (180a c + 180b c)d e - 180b c d e + 60c d e +--R * +--R 6 +--R g +--R + +--R 2 2 6 5 3 6 2 4 +--R (- 180a c - 180a b )e f g + (360a b c + 60b )e f g +--R + +--R 2 2 6 3 3 2 6 4 2 3 6 5 +--R (- 180a c - 180b c)e f g + 180b c e f g - 60c e f g +--R * +--R x +--R / +--R 6 7 7 6 +--R 60d e g - 60e f g +--R Type: Expression(Integer) +--E 1662 + +--S 1663 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 2 6 5 2 2 6 2 4 +--R 60a e g - 180a b e f g + (180a c + 180a b )e f g +--R + +--R 3 6 3 3 2 2 6 4 2 2 6 5 +--R (- 360a b c - 60b )e f g + (180a c + 180b c)e f g - 180b c e f g +--R + +--R 3 6 6 +--R 60c e f +--R * +--R log(g x + f) +--R + +--R 3 6 2 5 2 2 2 4 +--R - 60a e + 180a b d e + (- 180a c - 180a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (360a b c + 60b )d e + (- 180a c - 180b c)d e + 180b c d e - 60c d +--R * +--R 6 +--R g log(e x + d) +--R + +--R 3 5 6 3 6 5 5 +--R (12c d e g - 12c e f g )x +--R + +--R 2 5 3 2 4 6 2 6 5 3 6 2 4 4 +--R ((45b c d e - 15c d e )g - 45b c e f g + 15c e f g )x +--R + +--R 2 2 5 2 2 4 3 3 3 6 +--R ((60a c + 60b c)d e - 60b c d e + 20c d e )g +--R + +--R 2 2 6 5 2 6 2 4 3 6 3 3 +--R (- 60a c - 60b c)e f g + 60b c e f g - 20c e f g +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 2 4 2 3 3 +--R (180a b c + 30b )d e + (- 90a c - 90b c)d e + 90b c d e +--R + +--R 3 4 2 +--R - 30c d e +--R * +--R 6 +--R g +--R + +--R 3 6 5 2 2 6 2 4 2 6 3 3 +--R (- 180a b c - 30b )e f g + (90a c + 90b c)e f g - 90b c e f g +--R + +--R 3 6 4 2 +--R 30c e f g +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 2 4 +--R (180a c + 180a b )d e + (- 360a b c - 60b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (180a c + 180b c)d e - 180b c d e + 60c d e +--R * +--R 6 +--R g +--R + +--R 2 2 6 5 3 6 2 4 +--R (- 180a c - 180a b )e f g + (360a b c + 60b )e f g +--R + +--R 2 2 6 3 3 2 6 4 2 3 6 5 +--R (- 180a c - 180b c)e f g + 180b c e f g - 60c e f g +--R * +--R x +--R / +--R 6 7 7 6 +--R 60d e g - 60e f g +--R Type: Union(Expression(Integer),...) +--E 1663 + +--S 1664 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1664 + +--S 1665 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1665 + +)clear all + +--S 1666 of 1751 +t0:=1/((d+e*x)*(f+g*x)*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 3 2 +--R c e g x + ((b e + c d)g + c e f)x + ((a e + b d)g + (b e + c d)f)x +--R + +--R (a d g + (a e + b d)f)x + a d f +--R Type: Fraction(Polynomial(Integer)) +--E 1666 + +--S 1667 of 1751 +r0:=e^2*log(d+e*x)/((c*d^2-b*d*e+a*e^2)*(e*f-d*g))-g^2*log(f+g*x)/_ + ((e*f-d*g)*(c*f^2-g*(b*f-a*g)))-1/2*(c*e*f+c*d*g-b*e*g)*_ + log(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g)))-_ + (2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g))*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((4a c - 2b )d e + 2b c d )g + ((- 4a c + 2b )e - 4c d )f g +--R + +--R 2 2 2 +--R (- 2b c e + 4c d e)f +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 +--R ((b d e - c d )g - b e f g + c e f )log(c x + b x + a) +--R + +--R 2 2 2 +--R (2a e - 2b d e + 2c d )g log(g x + f) +--R + +--R 2 2 2 2 2 +--R (- 2a e g + 2b e f g - 2c e f )log(e x + d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 2 2 3 3 +--R (2a d e - 2a b d e + 2a c d )g +--R + +--R 2 3 2 2 3 2 +--R (- 2a e + (- 2a c + 2b )d e - 2b c d )f g +--R + +--R 3 2 2 2 3 2 +--R (2a b e + (2a c - 2b )d e + 2c d )f g +--R + +--R 3 2 2 2 3 +--R (- 2a c e + 2b c d e - 2c d e)f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1667 + +--S 1668 of 1751 +--a0:=integrate(t0,x) +--E 1668 + +--S 1669 of 1751 +--m0:=a0-r0 +--E 1669 + +--S 1670 of 1751 +--d0:=D(m0,x) +--E 1670 + +)clear all + +--S 1671 of 1751 +t0:=1/((d+e*x)*(f+g*x)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 6 2 2 5 +--R c e g x + ((2b c e + c d)g + c e f)x +--R + +--R 2 2 4 +--R (((2a c + b )e + 2b c d)g + (2b c e + c d)f)x +--R + +--R 2 2 3 +--R ((2a b e + (2a c + b )d)g + ((2a c + b )e + 2b c d)f)x +--R + +--R 2 2 2 +--R ((a e + 2a b d)g + (2a b e + (2a c + b )d)f)x +--R + +--R 2 2 2 +--R (a d g + (a e + 2a b d)f)x + a d f +--R Type: Fraction(Polynomial(Integer)) +--E 1671 + +--S 1672 of 1751 +r0:=(-b^3*e*g+b^2*c*(e*f+d*g)-2*a*c^2*(e*f+d*g)-b*c*(c*d*f-3*a*e*g)-_ + c*(2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g))*(a+b*x+c*x^2))+2*c*_ + (2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)*(c*f^2-_ + g*(b*f-a*g)))+e^4*log(d+e*x)/((c*d^2-b*d*e+a*e^2)^2*(e*f-d*g))-_ + g^4*log(f+g*x)/((e*f-d*g)*(c*f^2-g*(b*f-a*g))^2)-1/2*(c*e*f+c*d*g-_ + b*e*g)*(c*(e^2*f^2+d^2*g^2)+e*g*(2*a*e*g-b*(e*f+d*g)))*log(a+b*x+_ + c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(c*f^2-g*(b*f-a*g))^2)+(b^2*e^2*g^2*_ + (b*e*f+b*d*g-2*a*e*g)-2*c^3*d*f*(e^2*f^2+d*e*f*g+d^2*g^2)+2*c*e*g*_ + (a^2*e^2*g^2+a*b*e*g*(e*f+d*g)-b^2*(e*f+d*g)^2)-c^2*(4*a*d*e^2*f*g^2-_ + b*(e^3*f^3+5*d*e^2*f^2*g+5*d^2*e*f*g^2+d^3*g^3)))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*(c*f^2-g*(b*f-a*g))^2*_ + sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 3 3 2 2 2 4 3 +--R (24a c - 24a b c + 4a b c)d e +--R + +--R 2 3 3 2 5 2 2 +--R (12a b c + 8a b c - 2b c)d e +--R + +--R 2 4 2 3 4 2 3 4 3 3 4 +--R (8a c - 24a b c + 4b c )d e + (12a b c - 2b c )d +--R * +--R 4 +--R g +--R + +--R 3 3 2 2 2 4 4 2 4 2 2 4 3 +--R (- 24a c + 24a b c - 4a b c)e - 48a c d e + 32a b c d e +--R + +--R 5 4 +--R - 24a c d +--R * +--R 3 +--R f g +--R + +--R 2 3 3 2 5 4 2 4 3 +--R (- 12a b c - 8a b c + 2b c)e + 48a c d e +--R + +--R 5 2 4 3 5 4 +--R (16a c - 16b c )d e + 12b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 4 2 3 4 2 4 4 3 +--R (- 8a c + 24a b c - 4b c )e - 32a b c d e +--R + +--R 5 2 4 2 2 6 4 +--R (- 16a c + 16b c )d e - 8c d +--R * +--R 3 +--R f g +--R + +--R 4 3 3 4 5 3 5 2 2 6 3 4 +--R ((- 12a b c + 2b c )e + 24a c d e - 12b c d e + 8c d e)f +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 3 +--R (24a b c - 24a b c + 4a b )d e +--R + +--R 2 2 2 4 6 2 2 +--R (12a b c + 8a b c - 2b )d e +--R + +--R 2 3 3 2 5 3 2 3 4 2 4 +--R (8a b c - 24a b c + 4b c)d e + (12a b c - 2b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 2 3 5 4 2 3 2 2 2 3 3 +--R (- 24a b c + 24a b c - 4a b )e - 48a b c d e + 32a b c d e +--R + +--R 4 4 +--R - 24a b c d +--R * +--R 3 +--R f g +--R + +--R 2 2 2 4 6 4 2 3 3 +--R (- 12a b c - 8a b c + 2b )e + 48a b c d e +--R + +--R 4 3 3 3 2 4 4 +--R (16a b c - 16b c )d e + 12b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 3 3 2 5 4 2 3 3 +--R (- 8a b c + 24a b c - 4b c)e - 32a b c d e +--R + +--R 4 3 3 2 2 5 4 +--R (- 16a b c + 16b c )d e - 8b c d +--R * +--R 3 +--R f g +--R + +--R 2 3 4 2 4 4 3 2 4 2 2 5 3 4 +--R ((- 12a b c + 2b c )e + 24a b c d e - 12b c d e + 8b c d e)f +--R * +--R x +--R + +--R 4 2 3 2 2 4 3 3 2 2 3 5 2 2 +--R (24a c - 24a b c + 4a b )d e + (12a b c + 8a b c - 2a b )d e +--R + +--R 3 3 2 2 2 4 3 2 3 3 2 4 +--R (8a c - 24a b c + 4a b c)d e + (12a b c - 2a b c )d +--R * +--R 4 +--R g +--R + +--R 4 2 3 2 2 4 4 3 3 2 2 2 3 3 +--R (- 24a c + 24a b c - 4a b )e - 48a c d e + 32a b c d e +--R + +--R 2 4 4 +--R - 24a c d +--R * +--R 3 +--R f g +--R + +--R 3 2 2 3 5 4 3 3 3 +--R (- 12a b c - 8a b c + 2a b )e + 48a c d e +--R + +--R 2 4 2 3 3 4 4 +--R (16a c - 16a b c )d e + 12a b c d +--R * +--R 2 2 +--R f g +--R + +--R 3 3 2 2 2 4 4 2 3 3 +--R (- 8a c + 24a b c - 4a b c)e - 32a b c d e +--R + +--R 2 4 2 3 2 2 5 4 +--R (- 16a c + 16a b c )d e - 8a c d +--R * +--R 3 +--R f g +--R + +--R 2 3 3 2 4 2 4 3 4 2 2 5 3 4 +--R ((- 12a b c + 2a b c )e + 24a c d e - 12a b c d e + 8a c d e)f +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 3 2 3 2 2 4 2 2 +--R (8a b c - 2a b c)d e + (- 8a c - 2a b c + b c)d e +--R + +--R 3 3 2 3 4 2 3 4 +--R (8a b c - 2b c )d e + (- 4a c + b c )d +--R * +--R 4 +--R g +--R + +--R 2 2 3 4 3 2 3 2 2 4 4 2 2 +--R (- 8a b c + 2a b c)e f g + (8a c + 2a b c - b c)e f g +--R + +--R 3 3 2 4 3 4 2 3 4 4 +--R (- 8a b c + 2b c )e f g + (4a c - b c )e f +--R * +--R 2 +--R x +--R + +--R 2 2 4 3 2 2 3 5 2 2 +--R (8a b c - 2a b )d e + (- 8a b c - 2a b c + b )d e +--R + +--R 2 2 4 3 3 3 2 4 +--R (8a b c - 2b c)d e + (- 4a b c + b c )d +--R * +--R 4 +--R g +--R + +--R 2 2 4 4 3 2 2 3 5 4 2 2 +--R (- 8a b c + 2a b )e f g + (8a b c + 2a b c - b )e f g +--R + +--R 2 2 4 4 3 3 3 2 4 4 +--R (- 8a b c + 2b c)e f g + (4a b c - b c )e f +--R * +--R x +--R + +--R 3 2 3 3 3 2 2 2 4 2 2 +--R (8a b c - 2a b )d e + (- 8a c - 2a b c + a b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (8a b c - 2a b c)d e + (- 4a c + a b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 3 4 3 3 2 2 2 4 4 2 2 +--R (- 8a b c + 2a b )e f g + (8a c + 2a b c - a b )e f g +--R + +--R 2 2 3 4 3 2 3 2 2 4 4 +--R (- 8a b c + 2a b c)e f g + (4a c - a b c )e f +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 4 2 2 3 3 +--R (8a c - 2a b c)e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (16a c + 4a b c - 2b c)d e + (- 16a b c + 4b c )d e +--R + +--R 4 2 3 4 +--R (8a c - 2b c )d +--R * +--R 4 2 +--R g x +--R + +--R 3 2 3 4 2 2 4 3 +--R (8a b c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (16a b c + 4a b c - 2b )d e + (- 16a b c + 4b c)d e +--R + +--R 3 3 2 4 +--R (8a b c - 2b c )d +--R * +--R 4 +--R g x +--R + +--R 4 3 2 4 3 2 3 3 +--R (8a c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 +--R (8a c - 2a b c )d +--R * +--R 4 +--R g +--R * +--R log(g x + f) +--R + +--R 3 2 2 2 4 4 2 2 3 4 3 +--R (- 8a c + 2a b c)e g + (16a b c - 4a b c)e f g +--R + +--R 2 3 2 2 4 4 2 2 3 3 2 4 3 +--R (- 16a c - 4a b c + 2b c)e f g + (16a b c - 4b c )e f g +--R + +--R 4 2 3 4 4 +--R (- 8a c + 2b c )e f +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 4 2 2 4 4 3 +--R (- 8a b c + 2a b )e g + (16a b c - 4a b )e f g +--R + +--R 2 2 3 5 4 2 2 2 2 4 4 3 +--R (- 16a b c - 4a b c + 2b )e f g + (16a b c - 4b c)e f g +--R + +--R 3 3 2 4 4 +--R (- 8a b c + 2b c )e f +--R * +--R x +--R + +--R 4 3 2 4 4 3 2 3 4 3 +--R (- 8a c + 2a b )e g + (16a b c - 4a b )e f g +--R + +--R 3 2 2 2 4 4 2 2 2 2 3 4 3 +--R (- 16a c - 4a b c + 2a b )e f g + (16a b c - 4a b c)e f g +--R + +--R 2 3 2 2 4 4 +--R (- 8a c + 2a b c )e f +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 3 2 2 +--R (- 4a c + 2a b c)d e + (2a b c - 2a b c)d e +--R + +--R 2 3 2 2 3 3 4 +--R (- 4a c + 4a b c )d e - 2a b c d +--R * +--R 4 +--R g +--R + +--R 3 2 2 2 4 2 3 2 2 4 2 2 3 2 3 +--R (4a c - 2a b c)e + (8a c - 4a b c + 2b c)d e - 4b c d e +--R + +--R 4 2 3 4 +--R (4a c + 2b c )d +--R * +--R 3 +--R f g +--R + +--R 2 2 3 4 2 3 2 2 4 3 +--R (- 2a b c + 2a b c)e + (- 8a c + 4a b c - 2b c)d e +--R + +--R 4 2 3 3 4 4 +--R (- 8a c + 8b c )d e - 6b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 3 2 2 4 3 2 3 4 2 3 2 2 5 4 +--R ((4a c - 4a b c )e + 4b c d e + (8a c - 8b c )d e + 4c d ) +--R * +--R 3 +--R f g +--R + +--R 3 4 4 2 3 3 4 2 2 5 3 4 +--R (2a b c e + (- 4a c - 2b c )d e + 6b c d e - 4c d e)f +--R * +--R x +--R + +--R 3 2 3 3 3 2 2 2 4 2 2 +--R (- 6a b c + 2a b )d e + (4a c + 4a b c - 2a b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 10a b c + 4a b c)d e + (4a c - 2a b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 3 4 2 2 3 5 2 2 +--R (6a b c - 2a b )e + (4a b c - 6a b c + 2b )d e +--R + +--R 2 2 4 3 3 3 2 4 +--R (8a b c - 4b c)d e + (- 2a b c + 2b c )d +--R * +--R 3 +--R f g +--R + +--R 3 2 2 2 4 4 2 2 3 5 3 +--R (- 4a c - 4a b c + 2a b )e + (- 4a b c + 6a b c - 2b )d e +--R + +--R 3 3 2 3 4 2 3 4 +--R (- 12a b c + 6b c )d e + (4a c - 4b c )d +--R * +--R 2 2 +--R f g +--R + +--R 2 2 3 4 2 2 4 3 +--R (10a b c - 4a b c)e + (- 8a b c + 4b c)d e +--R + +--R 3 3 2 2 2 4 4 +--R (12a b c - 6b c )d e + 2b c d +--R * +--R 3 +--R f g +--R + +--R 2 3 2 2 4 3 3 2 3 +--R (- 4a c + 2a b c )e + (2a b c - 2b c )d e +--R + +--R 4 2 3 2 2 4 3 +--R (- 4a c + 4b c )d e - 2b c d e +--R * +--R 4 +--R f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 2 4 4 2 3 3 2 3 +--R (8a c - 2a b c)d e + (- 16a b c + 4a b c)d e +--R + +--R 4 3 3 2 2 2 4 3 2 3 3 2 3 2 4 +--R (16a c + 4a b c - 2a b c)d e + (- 16a b c + 4a b c )d e +--R + +--R 3 4 2 2 3 5 +--R (8a c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 5 2 4 2 5 4 3 3 2 2 2 4 2 3 +--R (- 8a c + 2a b c)e + (- 16a c + 28a b c - 6a b c)d e +--R + +--R 3 3 2 3 2 5 3 2 +--R (- 16a b c - 12a b c + 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 4 2 4 3 3 5 +--R (- 8a c + 34a b c - 8a b c )d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 2 3 3 5 4 3 3 2 2 2 4 4 +--R (16a b c - 4a b c)e + (16a c - 28a b c + 6a b c)d e +--R + +--R 3 4 2 2 3 4 2 6 3 2 +--R (32a c - 8a b c + 8a b c - 2b c)d e +--R + +--R 2 4 3 3 5 2 4 2 5 2 4 4 3 5 +--R (- 16a b c - 12a b c + 4b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 3 +--R f g +--R + +--R 4 3 3 2 2 2 4 5 +--R (- 16a c - 4a b c + 2a b c)e +--R + +--R 3 3 2 3 2 5 4 +--R (16a b c + 12a b c - 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 6 2 3 +--R (- 32a c + 8a b c - 8a b c + 2b c)d e +--R + +--R 2 5 2 4 4 3 4 5 3 4 5 +--R (- 16a c + 28a b c - 6b c )d e + (- 16a b c + 4b c )d +--R * +--R 3 2 +--R f g +--R + +--R 3 3 2 3 2 5 3 4 2 2 3 4 2 4 +--R (16a b c - 4a b c )e + (8a c - 34a b c + 8a b c )d e +--R + +--R 2 4 3 3 5 2 2 3 +--R (16a b c + 12a b c - 4b c )d e +--R + +--R 2 5 2 4 4 3 3 2 6 2 5 5 +--R (16a c - 28a b c + 6b c )d e + (8a c - 2b c )d +--R * +--R 4 +--R f g +--R + +--R 3 4 2 2 3 5 2 4 3 3 4 +--R (- 8a c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 2 5 2 4 4 3 2 3 5 3 4 3 2 +--R (- 16a c - 4a b c + 2b c )d e + (16a b c - 4b c )d e +--R + +--R 6 2 5 4 +--R (- 8a c + 2b c )d e +--R * +--R 5 +--R f +--R * +--R 2 +--R x +--R + +--R 5 4 3 4 4 2 3 4 2 3 +--R (8a b c - 2a b )d e + (- 16a b c + 4a b )d e +--R + +--R 4 2 3 3 2 5 3 2 3 2 2 2 4 4 +--R (16a b c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 3 3 2 3 2 5 +--R (8a b c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 5 4 3 5 4 2 3 3 2 5 2 3 +--R (- 8a b c + 2a b )e + (- 16a b c + 28a b c - 6a b )d e +--R + +--R 3 2 2 2 4 6 3 2 +--R (- 16a b c - 12a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 3 4 2 5 +--R (- 8a b c + 34a b c - 8a b c)d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 2 3 4 5 4 2 3 3 2 5 4 +--R (16a b c - 4a b )e + (16a b c - 28a b c + 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 2 +--R (32a b c - 8a b c + 8a b c - 2b )d e +--R + +--R 2 2 3 4 2 6 4 +--R (- 16a b c - 12a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 5 +--R (16a b c + 4a b c - 2b c )d +--R * +--R 2 3 +--R f g +--R + +--R 4 2 3 3 2 5 5 +--R (- 16a b c - 4a b c + 2a b )e +--R + +--R 3 2 2 2 4 6 4 +--R (16a b c + 12a b c - 4a b )d e +--R + +--R 3 3 2 3 2 5 7 2 3 +--R (- 32a b c + 8a b c - 8a b c + 2b )d e +--R + +--R 2 4 3 3 5 2 4 2 4 4 3 5 +--R (- 16a b c + 28a b c - 6b c )d e + (- 16a b c + 4b c )d +--R * +--R 3 2 +--R f g +--R + +--R 3 2 2 2 4 5 3 3 2 3 2 5 4 +--R (16a b c - 4a b c)e + (8a b c - 34a b c + 8a b c)d e +--R + +--R 2 2 3 4 2 6 2 3 +--R (16a b c + 12a b c - 4b c)d e +--R + +--R 2 4 3 3 5 2 3 2 5 3 4 5 +--R (16a b c - 28a b c + 6b c )d e + (8a b c - 2b c )d +--R * +--R 4 +--R f g +--R + +--R 3 3 2 3 2 5 2 2 3 4 2 4 +--R (- 8a b c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 2 4 3 3 5 2 2 3 2 4 4 3 3 2 +--R (- 16a b c - 4a b c + 2b c )d e + (16a b c - 4b c )d e +--R + +--R 5 3 4 4 +--R (- 8a b c + 2b c )d e +--R * +--R 5 +--R f +--R * +--R x +--R + +--R 6 5 2 4 5 4 3 2 3 +--R (8a c - 2a b )d e + (- 16a b c + 4a b )d e +--R + +--R 5 2 4 2 3 4 3 2 4 2 3 3 4 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 4 3 3 2 2 5 +--R (8a c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 6 5 2 5 5 2 4 2 3 4 2 3 +--R (- 8a c + 2a b )e + (- 16a c + 28a b c - 6a b )d e +--R + +--R 4 2 3 3 2 5 3 2 +--R (- 16a b c - 12a b c + 4a b )d e +--R + +--R 4 3 3 2 2 2 4 4 3 3 2 3 2 5 +--R (- 8a c + 34a b c - 8a b c)d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 5 4 3 5 5 2 4 2 3 4 4 +--R (16a b c - 4a b )e + (16a c - 28a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (32a c - 8a b c + 8a b c - 2a b )d e +--R + +--R 3 3 2 3 2 5 4 3 4 2 2 3 4 2 5 +--R (- 16a b c - 12a b c + 4a b c)d e + (16a c + 4a b c - 2a b c )d +--R * +--R 2 3 +--R f g +--R + +--R 5 2 4 2 3 4 5 4 2 3 3 2 5 4 +--R (- 16a c - 4a b c + 2a b )e + (16a b c + 12a b c - 4a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 3 +--R (- 32a c + 8a b c - 8a b c + 2a b )d e +--R + +--R 3 4 2 2 3 4 2 4 2 4 3 3 5 +--R (- 16a c + 28a b c - 6a b c )d e + (- 16a b c + 4a b c )d +--R * +--R 3 2 +--R f g +--R + +--R 4 2 3 3 5 4 3 3 2 2 2 4 4 +--R (16a b c - 4a b c)e + (8a c - 34a b c + 8a b c)d e +--R + +--R 3 3 2 3 2 5 2 3 +--R (16a b c + 12a b c - 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 3 2 2 5 2 4 5 +--R (16a c - 28a b c + 6a b c )d e + (8a c - 2a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 3 3 2 2 5 3 3 2 3 2 4 +--R (- 8a c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 3 2 4 3 3 3 2 +--R (- 16a c - 4a b c + 2a b c )d e + (16a b c - 4a b c )d e +--R + +--R 2 5 2 4 4 +--R (- 8a c + 2a b c )d e +--R * +--R 5 +--R f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1672 + +--S 1673 of 1751 +--a0:=integrate(t0,x) +--E 1673 + +--S 1674 of 1751 +--m0:=a0-r0 +--E 1674 + +--S 1675 of 1751 +--d0:=D(m0,x) +--E 1675 + +)clear all + +--S 1676 of 1751 +t0:=sqrt(a+b*x+c*x^2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R (1) --------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 1676 + +--S 1677 of 1751 +r0:=atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/(e*g)+_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/(e*(e*f-d*g))-atanh(1/2*_ + (b*f-2*a*g+(2*c*f-b*g)*x)/(sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))*_ + sqrt(c*f^2-b*f*g+a*g^2)/(g*(e*f-d*g)) +--R +--R +--R (2) +--R +-+ 2c x + b +--R (d g - e f)\|c atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 (b e - 2c d)x + 2a e - b d +--R g\|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 (b g - 2c f)x + 2a g - b f +--R - e\|a g - b f g + c f atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R / +--R 2 2 +--R d e g - e f g +--R Type: Expression(Integer) +--E 1677 + +--S 1678 of 1751 +--a0:=integrate(t0,x) +--E 1678 + +--S 1679 of 1751 +--m0:=a0-r0 +--E 1679 + +--S 1680 of 1751 +--d0:=D(m0,x) +--E 1680 + +)clear all + +--S 1681 of 1751 +t0:=(a+b*x+c*x^2)^(3/2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R (1) --------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 1681 + +--S 1682 of 1751 +r0:=(c*d^2-b*d*e+a*e^2)^(3/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^3*(e*f-d*g))-_ + (c*f^2-b*f*g+a*g^2)^(3/2)*atanh(1/2*(b*f-2*a*g+(2*c*f-b*g)*x)/_ + (sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))/(g^3*(e*f-d*g))-_ + 1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^3*(e*f-d*g)*sqrt(c))+1/8*(8*c^2*e*f^3+b*g^2*_ + (3*b*e*f+b*d*g-4*a*e*g)-4*c*g*(3*b*e*f^2-a*g*(3*e*f-d*g)))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e*g^3*(e*f-d*g)*_ + sqrt(c))+(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)/(e^2*(e*f-d*g))-_ + 1/4*(4*c*e*f^2-g*(5*b*e*f-b*d*g-4*a*e*g)-2*c*g*(e*f-d*g)*x)*_ + sqrt(a+b*x+c*x^2)/(e*g^2*(e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 2 3 3 2 3 2 +--R ((12a c + 3b )d e - 12b c d e + 8c d )g + (- 12a c - 3b )e f g +--R + +--R 3 2 2 3 3 +--R 12b c e f g - 8c e f +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R 2 2 3 +-+ | 2 2 +--R (8a e - 8b d e + 8c d )g \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 3 2 3 3 2 +-+ | 2 2 +--R (- 8a e g + 8b e f g - 8c e f )\|c \|a g - b f g + c f +--R * +--R (b g - 2c f)x + 2a g - b f +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (4c d e g - 4c e f g )x + (10b d e - 8c d e)g - 10b e f g +--R + +--R 3 2 +--R 8c e f g +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 4 4 3 +-+ +--R (8d e g - 8e f g )\|c +--R Type: Expression(Integer) +--E 1682 + +--S 1683 of 1751 +--a0:=integrate(t0,x) +--E 1683 + +--S 1684 of 1751 +--m0:=a0-r0 +--E 1684 + +--S 1685 of 1751 +--d0:=D(m0,x) +--E 1685 + +)clear all + +--S 1686 of 1751 +t0:=(a+b*x+c*x^2)^(5/2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R (1) --------------------------------------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 1686 + +--S 1687 of 1751 +r0:=1/3*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2)/(e^2*(e*f-d*g))-_ + 1/24*(8*c*e*f^2-g*(11*b*e*f-3*b*d*g-8*a*e*g)-6*c*g*(e*f-d*g)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e*g^2*(e*f-d*g))-1/16*(2*c*d-b*e)*(c*d^2-b*d*e+_ + a*e^2)*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*e^5*(e*f-d*g))+1/128*_ + (128*c^4*e*f^5-320*c^3*e*f^3*g*(b*f-a*g)-b^3*g^4*(5*b*e*f+3*b*d*g-_ + 8*a*e*g)+48*c^2*g^2*(5*b^2*e*f^3-10*a*b*e*f^2*g+a^2*g^2*(5*e*f-d*g))-_ + 8*b*c*g^3*(5*b^2*e*f^2+12*a^2*e*g^2-3*a*b*g*(5*e*f+d*g)))*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*e*g^5*(e*f-d*g))+_ + (c*d^2-b*d*e+a*e^2)^(5/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*(e*f-d*g))-_ + (c*f^2-b*f*g+a*g^2)^(5/2)*atanh(1/2*(b*f-2*a*g+(2*c*f-b*g)*x)/_ + (sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))/(g^5*(e*f-d*g))+_ + 1/8*(c*d^2-b*d*e+a*e^2)*(8*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-4*a*e)-_ + 2*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(c*e^4*(e*f-d*g))-_ + 1/64*(64*c^3*e*f^4-16*c^2*e*f^2*g*(9*b*f-8*a*g)-b^2*g^3*(5*b*e*f+_ + 3*b*d*g-8*a*e*g)+4*c*g^2*(22*b^2*e*f^2+16*a^2*e*g^2-3*a*b*g*(13*e*f-_ + d*g))-2*c*g*(16*c^2*e*f^3+b*g^2*(5*b*e*f+3*b*d*g-8*a*e*g)-_ + 4*c*g*(6*b*e*f^2-a*g*(7*e*f-3*d*g)))*x)*sqrt(a+b*x+c*x^2)/(c*e*g^4*_ + (e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 4 4 2 3 2 3 +--R (720a c + 360a b c - 15b )d e + (- 1440a b c - 120b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (960a c + 720b c )d e - 960b c d e + 384c d +--R * +--R 5 +--R g +--R + +--R 2 2 2 4 5 4 2 3 5 2 3 +--R (- 720a c - 360a b c + 15b )e f g + (1440a b c + 120b c)e f g +--R + +--R 3 2 2 5 3 2 3 5 4 4 5 5 +--R (- 960a c - 720b c )e f g + 960b c e f g - 384c e f +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 4 3 2 2 2 2 2 3 +--R 384a c e - 768a b c d e + (768a c + 384b c)d e - 768b c d e +--R + +--R 3 4 +--R 384c d +--R * +--R +-------------------+ +--R 5 +-+ | 2 2 +--R g \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 5 4 5 3 2 2 5 2 2 +--R - 384a c e g + 768a b c e f g + (- 768a c - 384b c)e f g +--R + +--R 2 5 3 3 5 4 +--R 768b c e f g - 384c e f +--R * +--R +-------------------+ +--R +-+ | 2 2 (b g - 2c f)x + 2a g - b f +--R \|c \|a g - b f g + c f atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R + +--R 3 4 5 3 5 4 3 +--R (96c d e g - 96c e f g )x +--R + +--R 2 4 3 2 3 5 2 5 4 3 5 2 3 2 +--R ((272b c d e - 128c d e )g - 272b c e f g + 128c e f g )x +--R + +--R 2 2 4 2 2 3 3 3 2 5 +--R ((432a c + 236b c)d e - 416b c d e + 192c d e )g +--R + +--R 2 2 5 4 2 5 2 3 3 5 3 2 +--R (- 432a c - 236b c)e f g + 416b c e f g - 192c e f g +--R * +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (1112a b c + 30b )d e + (- 896a c - 528b c)d e + 864b c d e +--R + +--R 3 4 +--R - 384c d e +--R * +--R 5 +--R g +--R + +--R 3 5 4 2 2 5 2 3 2 5 3 2 +--R (- 1112a b c - 30b )e f g + (896a c + 528b c)e f g - 864b c e f g +--R + +--R 3 5 4 +--R 384c e f g +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 6 6 5 +-+ +--R (384c d e g - 384c e f g )\|c +--R Type: Expression(Integer) +--E 1687 + +--S 1688 of 1751 +--a0:=integrate(t0,x) +--E 1688 + +--S 1689 of 1751 +--m0:=a0-r0 +--E 1689 + +--S 1690 of 1751 +--d0:=D(m0,x) +--E 1690 + +)clear all + +--S 1691 of 1751 +t0:=(d+e*x)^m*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 2 m +--R (c x + b x + a)(e x + d) +--R (1) -------------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1691 + +--S 1692 of 1751 +--r0:=2*a*(d+e*x)^(1+m)/((e^2-d*f)*sqrt(e+f*x))+2*c*e^2*(d+e*x)^(1+m)/_ +-- (f^2*(e^2-d*f)*sqrt(e+f*x))-2*b*e*(d+e*x)^(1+m)/(f*(e^2-d*f)*_ +-- sqrt(e+f*x))+2*c*(d+e*x)^(1+m)*sqrt(e+f*x)/(e*f^2*(3+2*m))-_ +-- 2*a*e*(1+2*m)*(d+e*x)^m*hypergeometric(1/2,-m,3/2,e*(e+f*x)/_ +-- (e^2-d*f))*sqrt(e+f*x)/(f*(e^2-d*f)*(-f*(d+e*x)/(e^2-d*f))^m)-_ +-- 2*b*(d*f-2*e^2*(1+m))*(d+e*x)^m*hypergeometric(1/2,-m,3/2,_ +-- e*(e+f*x)/(e^2-d*f))*sqrt(e+f*x)/(f^2*(e^2-d*f)*(-f*(d+e*x)/_ +-- (e^2-d*f))^m)+2*c*(d^2*f^2+4*d*e^2*f*(1+m)-4*e^4*(2+3*m+m^2))*_ +-- (d+e*x)^m*hypergeometric(1/2,-m,3/2,e*(e+f*x)/(e^2-d*f))*_ +-- sqrt(e+f*x)/(e*f^3*(e^2-d*f)*(3+2*m)*(-f*(d+e*x)/(e^2-d*f))^m) +--E 1692 + +--S 1693 of 1751 +--a0:=integrate(t0,x) +--E 1693 + +--S 1694 of 1751 +--m0:=a0-r0 +--E 1694 + +--S 1695 of 1751 +--d0:=D(m0,x) +--E 1695 + +)clear all + +--S 1696 of 1751 +t0:=(d+e*x)^3*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R (1) +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R / +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1696 + +--S 1697 of 1751 +r0:=2/3*(e^2-d*f)*(3*e*f*(2*b*e^2-b*d*f-a*e*f)-c*(10*e^4-8*d*e^2*f+_ + d^2*f^2))*(e+f*x)^(3/2)/f^6-2/5*e*(e*f*(4*b*e^2-3*b*d*f-a*e*f)-_ + c*(10*e^4-12*d*e^2*f+3*d^2*f^2))*(e+f*x)^(5/2)/f^6-2/7*e^2*(5*c*e^2-_ + 3*c*d*f-b*e*f)*(e+f*x)^(7/2)/f^6+2/9*c*e^3*(e+f*x)^(9/2)/f^6+_ + 2*(e^2-d*f)^3*(c*e^2-f*(b*e-a*f))/(f^6*sqrt(e+f*x))-2*(e^2-d*f)^2*_ + (f*(4*b*e^2-b*d*f-3*a*e*f)-c*(5*e^3-2*d*e*f))*sqrt(e+f*x)/f^6 +--R +--R +--R (2) +--R 3 5 5 3 2 5 4 4 4 +--R 70c e f x + ((90b e + 270c d e )f - 100c e f )x +--R + +--R 3 2 2 5 4 3 4 +--R (126a e + 378b d e + 378c d e)f + (- 144b e - 432c d e )f +--R + +--R 5 3 +--R 160c e f +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 +--R (630a d e + 630b d e + 210c d )f +--R + +--R 4 3 2 2 4 5 4 3 +--R (- 252a e - 756b d e - 756c d e )f + (288b e + 864c d e )f +--R + +--R 6 2 +--R - 320c e f +--R * +--R 2 +--R x +--R + +--R 2 3 5 3 2 2 3 4 +--R (1890a d e + 630b d )f + (- 2520a d e - 2520b d e - 840c d e)f +--R + +--R 5 4 2 3 3 6 5 2 +--R (1008a e + 3024b d e + 3024c d e )f + (- 1152b e - 3456c d e )f +--R + +--R 7 +--R 1280c e f +--R * +--R x +--R + +--R 3 5 2 2 3 4 +--R - 630a d f + (3780a d e + 1260b d e)f +--R + +--R 4 2 3 3 2 3 +--R (- 5040a d e - 5040b d e - 1680c d e )f +--R + +--R 6 5 2 4 2 7 6 +--R (2016a e + 6048b d e + 6048c d e )f + (- 2304b e - 6912c d e )f +--R + +--R 8 +--R 2560c e +--R / +--R 6 +-------+ +--R 315f \|f x + e +--R Type: Expression(Integer) +--E 1697 + +--S 1698 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 3 2 5 4 4 4 +--R 70c e f x + ((90b e + 270c d e )f - 100c e f )x +--R + +--R 3 2 2 5 4 3 4 +--R (126a e + 378b d e + 378c d e)f + (- 144b e - 432c d e )f +--R + +--R 5 3 +--R 160c e f +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 +--R (630a d e + 630b d e + 210c d )f +--R + +--R 4 3 2 2 4 5 4 3 +--R (- 252a e - 756b d e - 756c d e )f + (288b e + 864c d e )f +--R + +--R 6 2 +--R - 320c e f +--R * +--R 2 +--R x +--R + +--R 2 3 5 3 2 2 3 4 +--R (1890a d e + 630b d )f + (- 2520a d e - 2520b d e - 840c d e)f +--R + +--R 5 4 2 3 3 6 5 2 +--R (1008a e + 3024b d e + 3024c d e )f + (- 1152b e - 3456c d e )f +--R + +--R 7 +--R 1280c e f +--R * +--R x +--R + +--R 3 5 2 2 3 4 +--R - 630a d f + (3780a d e + 1260b d e)f +--R + +--R 4 2 3 3 2 3 +--R (- 5040a d e - 5040b d e - 1680c d e )f +--R + +--R 6 5 2 4 2 7 6 +--R (2016a e + 6048b d e + 6048c d e )f + (- 2304b e - 6912c d e )f +--R + +--R 8 +--R 2560c e +--R / +--R 6 +-------+ +--R 315f \|f x + e +--R Type: Union(Expression(Integer),...) +--E 1698 + +--S 1699 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1699 + +--S 1700 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1700 + +)clear all + +--S 1701 of 1751 +t0:=(d+e*x)^2*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R / +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1701 + +--S 1702 of 1751 +r0:=-2/3*(e*f*(3*b*e^2-2*b*d*f-a*e*f)-c*(6*e^4-6*d*e^2*f+d^2*f^2))*_ + (e+f*x)^(3/2)/f^5-2/5*e*(4*c*e^2-2*c*d*f-b*e*f)*(e+f*x)^(5/2)/f^5+_ + 2/7*c*e^2*(e+f*x)^(7/2)/f^5-2*(e^2-d*f)^2*(c*e^2-f*(b*e-a*f))/_ + (f^5*sqrt(e+f*x))+2*(e^2-d*f)*(f*(3*b*e^2-b*d*f-2*a*e*f)-_ + c*(4*e^3-2*d*e*f))*sqrt(e+f*x)/f^5 +--R +--R +--R (2) +--R 2 4 4 2 4 3 3 3 +--R 30c e f x + ((42b e + 84c d e)f - 48c e f )x +--R + +--R 2 2 4 3 2 3 4 2 2 +--R ((70a e + 140b d e + 70c d )f + (- 84b e - 168c d e )f + 96c e f )x +--R + +--R 2 4 3 2 2 3 +--R (420a d e + 210b d )f + (- 280a e - 560b d e - 280c d e)f +--R + +--R 4 3 2 5 +--R (336b e + 672c d e )f - 384c e f +--R * +--R x +--R + +--R 2 4 2 2 3 +--R - 210a d f + (840a d e + 420b d e)f +--R + +--R 4 3 2 2 2 5 4 6 +--R (- 560a e - 1120b d e - 560c d e )f + (672b e + 1344c d e )f - 768c e +--R / +--R 5 +-------+ +--R 105f \|f x + e +--R Type: Expression(Integer) +--E 1702 + +--S 1703 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 2 4 3 3 3 +--R 30c e f x + ((42b e + 84c d e)f - 48c e f )x +--R + +--R 2 2 4 3 2 3 4 2 2 +--R ((70a e + 140b d e + 70c d )f + (- 84b e - 168c d e )f + 96c e f )x +--R + +--R 2 4 3 2 2 3 +--R (420a d e + 210b d )f + (- 280a e - 560b d e - 280c d e)f +--R + +--R 4 3 2 5 +--R (336b e + 672c d e )f - 384c e f +--R * +--R x +--R + +--R 2 4 2 2 3 +--R - 210a d f + (840a d e + 420b d e)f +--R + +--R 4 3 2 2 2 5 4 6 +--R (- 560a e - 1120b d e - 560c d e )f + (672b e + 1344c d e )f - 768c e +--R / +--R 5 +-------+ +--R 105f \|f x + e +--R Type: Union(Expression(Integer),...) +--E 1703 + +--S 1704 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1704 + +--S 1705 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1705 + +)clear all + +--S 1706 of 1751 +t0:=(d+e*x)*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R (1) ------------------------------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1706 + +--S 1707 of 1751 +r0:=-2/3*(3*c*e^2-c*d*f-b*e*f)*(e+f*x)^(3/2)/f^4+2/5*c*e*(e+f*x)^(5/2)/f^4+_ + 2*(e^2-d*f)*(c*e^2-f*(b*e-a*f))/(f^4*sqrt(e+f*x))-2*(f*(2*b*e^2-_ + b*d*f-a*e*f)-c*(3*e^3-2*d*e*f))*sqrt(e+f*x)/f^4 +--R +--R +--R (2) +--R 3 3 3 2 2 2 +--R 6c e f x + ((10b e + 10c d)f - 12c e f )x +--R + +--R 3 2 2 3 3 +--R ((30a e + 30b d)f + (- 40b e - 40c d e)f + 48c e f)x - 30a d f +--R + +--R 2 2 3 2 4 +--R (60a e + 60b d e)f + (- 80b e - 80c d e )f + 96c e +--R / +--R 4 +-------+ +--R 15f \|f x + e +--R Type: Expression(Integer) +--E 1707 + +--S 1708 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 2 +--R 6c e f x + ((10b e + 10c d)f - 12c e f )x +--R + +--R 3 2 2 3 3 +--R ((30a e + 30b d)f + (- 40b e - 40c d e)f + 48c e f)x - 30a d f +--R + +--R 2 2 3 2 4 +--R (60a e + 60b d e)f + (- 80b e - 80c d e )f + 96c e +--R / +--R 4 +-------+ +--R 15f \|f x + e +--R Type: Union(Expression(Integer),...) +--E 1708 + +--S 1709 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1709 + +--S 1710 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1710 + +)clear all + +--S 1711 of 1751 +t0:=(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 2 +--R c x + b x + a +--R (1) ------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1711 + +--S 1712 of 1751 +r0:=2/3*c*(e+f*x)^(3/2)/f^3-2*(c*e^2-f*(b*e-a*f))/(f^3*sqrt(e+f*x))-_ + 2*(2*c*e-b*f)*sqrt(e+f*x)/f^3 +--R +--R +--R 2 2 2 2 2 +--R 2c f x + (6b f - 8c e f)x - 6a f + 12b e f - 16c e +--R (2) ------------------------------------------------------ +--R 3 +-------+ +--R 3f \|f x + e +--R Type: Expression(Integer) +--E 1712 + +--S 1713 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 +--R 2c f x + (6b f - 8c e f)x - 6a f + 12b e f - 16c e +--R (3) ------------------------------------------------------ +--R 3 +-------+ +--R 3f \|f x + e +--R Type: Union(Expression(Integer),...) +--E 1713 + +--S 1714 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1714 + +--S 1715 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1715 + +)clear all + +--S 1716 of 1751 +t0:=(a+b*x+c*x^2)/((d+e*x)*(e+f*x)^(3/2)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) -------------------------------------- +--R 2 2 +-------+ +--R (e f x + (d f + e )x + d e)\|f x + e +--R Type: Expression(Integer) +--E 1716 + +--S 1717 of 1751 +r0:=-2*(c*d^2-b*d*e+a*e^2)*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(3/2))+2*(c*e^2-f*(b*e-a*f))/(f^2*(e^2-d*f)*_ + sqrt(e+f*x))+2*c*sqrt(e+f*x)/(e*f^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-------+ \|e \|f x + e +--R (2a e - 2b d e + 2c d )f \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 2 2 2 2 3 +--R ((2c d f - 2c e f)x - 2a e f + (2b e + 2c d e)f - 4c e ) +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R +----------+ +--R 3 3 2 | 2 +-+ +-------+ +--R (d e f - e f )\|- d f + e \|e \|f x + e +--R Type: Expression(Integer) +--E 1717 + +--S 1718 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +-------+ +--R (a e - b d e + c d )f \|f x + e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 2 3 +--R ((2c d f - 2c e f)x - 2a e f + (2b e + 2c d e)f - 4c e ) +--R * +--R +------------+ +--R | 3 +--R \|- d e f + e +--R / +--R +------------+ +--R 3 3 2 | 3 +-------+ +--R (d e f - e f )\|- d e f + e \|f x + e +--R , +--R +--R +----------+ +--R | 3 +-------+ +--R 2 2 2 +-------+ \|d e f - e \|f x + e +--R (- 2a e + 2b d e - 2c d )f \|f x + e atan(-----------------------) +--R 2 +--R d f - e +--R + +--R +----------+ +--R 2 2 2 2 3 | 3 +--R ((2c d f - 2c e f)x - 2a e f + (2b e + 2c d e)f - 4c e )\|d e f - e +--R / +--R +----------+ +--R 3 3 2 | 3 +-------+ +--R (d e f - e f )\|d e f - e \|f x + e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1718 + +--S 1719 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 2 2 | 2 +-+ +--R (a e - b d e + c d )\|- d f + e \|e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R +------------+ +-+ +-------+ +--R 2 2 | 3 \|e \|f x + e +--R (- 2a e + 2b d e - 2c d )\|- d e f + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R / +--R +------------+ +----------+ +--R 3 | 3 | 2 +-+ +--R (d e f - e )\|- d e f + e \|- d f + e \|e +--R Type: Expression(Integer) +--E 1719 + +--S 1720 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1720 + +--S 1721 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------+ +-+ +-------+ +--R 2 2 | 3 \|e \|f x + e +--R (- 2a e + 2b d e - 2c d )\|d e f - e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R +----------+ +--R +----------+ | 3 +-------+ +--R 2 2 | 2 +-+ \|d e f - e \|f x + e +--R (- 2a e + 2b d e - 2c d )\|- d f + e \|e atan(-----------------------) +--R 2 +--R d f - e +--R / +--R +----------+ +----------+ +--R 3 | 2 +-+ | 3 +--R (d e f - e )\|- d f + e \|e \|d e f - e +--R Type: Expression(Integer) +--E 1721 + +--S 1722 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1722 + +)clear all + +--S 1723 of 1751 +t0:=(a+b*x+c*x^2)/((d+e*x)^2*(e+f*x)^(3/2)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) ----------------------------------------------------------- +--R 2 3 3 2 2 2 2 +-------+ +--R (e f x + (2d e f + e )x + (d f + 2d e )x + d e)\|f x + e +--R Type: Expression(Integer) +--E 1723 + +--S 1724 of 1751 +r0:=(c*d^2-b*d*e+a*e^2)*f*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(5/2))-2*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/(e^(3/2)*(e^2-d*f)^(5/2))-_ + 2*(c*e^2-f*(b*e-a*f))/(f*(e^2-d*f)^2*sqrt(e+f*x))+(c*d^2-b*d*e+a*e^2)*_ + f*sqrt(e+f*x)/(e*(e^2-d*f)^2*(e^2-d*f-e*(e+f*x))) +--R +--R +--R (2) +--R 3 2 2 2 4 3 +--R ((3a e - b d e - c d e)f + (- 2b e + 4c d e )f)x +--R + +--R 2 2 3 2 3 2 2 +--R (3a d e - b d e - c d )f + (- 2b d e + 4c d e )f +--R * +--R +-+ +-------+ +--R +-------+ \|e \|f x + e +--R \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 2 2 2 3 4 2 +--R ((- 3a e + b d e - c d )f + 2b e f - 2c e )x - 2a d e f +--R + +--R 3 2 2 3 +--R (- a e + 3b d e - c d e)f - 2c d e +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R +----------+ +--R 2 2 3 4 2 6 3 3 2 3 2 5 | 2 +-+ +--R ((d e f - 2d e f + e f)x + d e f - 2d e f + d e f)\|- d f + e \|e +--R * +--R +-------+ +--R \|f x + e +--R Type: Expression(Integer) +--E 1724 + +--S 1725 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 4 3 +--R ((3a e - b d e - c d e)f + (- 2b e + 4c d e )f)x +--R + +--R 2 2 3 2 3 2 2 +--R (3a d e - b d e - c d )f + (- 2b d e + 4c d e )f +--R * +--R +-------+ +--R \|f x + e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 3 4 2 +--R ((- 6a e + 2b d e - 2c d )f + 4b e f - 4c e )x - 4a d e f +--R + +--R 3 2 2 3 +--R (- 2a e + 6b d e - 2c d e)f - 4c d e +--R * +--R +------------+ +--R | 3 +--R \|- d e f + e +--R / +--R 2 2 3 4 2 6 3 3 2 3 2 5 +--R ((2d e f - 4d e f + 2e f)x + 2d e f - 4d e f + 2d e f) +--R * +--R +------------+ +--R | 3 +-------+ +--R \|- d e f + e \|f x + e +--R , +--R +--R 3 2 2 2 4 3 +--R ((- 3a e + b d e + c d e)f + (2b e - 4c d e )f)x +--R + +--R 2 2 3 2 3 2 2 +--R (- 3a d e + b d e + c d )f + (2b d e - 4c d e )f +--R * +--R +----------+ +--R | 3 +-------+ +--R +-------+ \|d e f - e \|f x + e +--R \|f x + e atan(-----------------------) +--R 2 +--R d f - e +--R + +--R 2 2 2 3 4 2 +--R ((- 3a e + b d e - c d )f + 2b e f - 2c e )x - 2a d e f +--R + +--R 3 2 2 3 +--R (- a e + 3b d e - c d e)f - 2c d e +--R * +--R +----------+ +--R | 3 +--R \|d e f - e +--R / +--R +----------+ +--R 2 2 3 4 2 6 3 3 2 3 2 5 | 3 +--R ((d e f - 2d e f + e f)x + d e f - 2d e f + d e f)\|d e f - e +--R * +--R +-------+ +--R \|f x + e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1725 + +--S 1726 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 2 2 3 2 | 2 +-+ +--R ((3a e - b d e - c d )f - 2b e + 4c d e )\|- d f + e \|e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R +------------+ +--R 2 2 3 2 | 3 +--R ((- 6a e + 2b d e + 2c d )f + 4b e - 8c d e )\|- d e f + e +--R * +--R +-+ +-------+ +--R \|e \|f x + e +--R atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R / +--R +------------+ +----------+ +--R 2 2 3 5 | 3 | 2 +-+ +--R (2d e f - 4d e f + 2e )\|- d e f + e \|- d f + e \|e +--R Type: Expression(Integer) +--E 1726 + +--S 1727 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1727 + +--S 1728 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------+ +--R 2 2 3 2 | 3 +--R ((- 3a e + b d e + c d )f + 2b e - 4c d e )\|d e f - e +--R * +--R +-+ +-------+ +--R \|e \|f x + e +--R atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R +----------+ +--R 2 2 3 2 | 2 +-+ +--R ((- 3a e + b d e + c d )f + 2b e - 4c d e )\|- d f + e \|e +--R * +--R +----------+ +--R | 3 +-------+ +--R \|d e f - e \|f x + e +--R atan(-----------------------) +--R 2 +--R d f - e +--R / +--R +----------+ +----------+ +--R 2 2 3 5 | 2 +-+ | 3 +--R (d e f - 2d e f + e )\|- d f + e \|e \|d e f - e +--R Type: Expression(Integer) +--E 1728 + +--S 1729 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1729 + +)clear all + +--S 1730 of 1751 +t0:=(a+b*x+c*x^2)/((d+e*x)^3*(e+f*x)^(3/2)) +--R +--R +--R (1) +--R 2 +--R c x + b x + a +--R / +--R 3 4 2 4 3 2 3 2 3 2 2 3 +--R (e f x + (3d e f + e )x + (3d e f + 3d e )x + (d f + 3d e )x + d e) +--R * +--R +-------+ +--R \|f x + e +--R Type: Expression(Integer) +--E 1730 + +--S 1731 of 1751 +r0:=-3/4*(c*d^2-b*d*e+a*e^2)*f^2*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(7/2))+f*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/(e^(3/2)*(e^2-d*f)^(7/2))-_ + 2*(c*e^2-f*(b*e-a*f))*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))*_ + sqrt(e)/(e^2-d*f)^(7/2)+2*(c*e^2-f*(b*e-a*f))/((e^2-d*f)^3*_ + sqrt(e+f*x))-1/2*(c*d^2-b*d*e+a*e^2)*f^2*sqrt(e+f*x)/(e*(e^2-d*f)^2*_ + (e^2-d*f-e*(e+f*x))^2)-3/4*(c*d^2-b*d*e+a*e^2)*f^2*sqrt(e+f*x)/_ + (e*(e^2-d*f)^3*(e^2-d*f-e*(e+f*x)))+f*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + sqrt(e+f*x)/(e*(e^2-d*f)^3*(e^2-d*f-e*(e+f*x))) +--R +--R +--R (2) +--R 4 3 2 2 2 5 4 6 2 +--R ((15a e - 3b d e - c d e )f + (- 12b e + 8c d e )f + 8c e )x +--R + +--R 3 2 2 3 2 4 2 3 +--R (30a d e - 6b d e - 2c d e)f + (- 24b d e + 16c d e )f +--R + +--R 5 +--R 16c d e +--R * +--R x +--R + +--R 2 2 3 4 2 2 3 3 2 2 4 +--R (15a d e - 3b d e - c d )f + (- 12b d e + 8c d e )f + 8c d e +--R * +--R +-+ +-------+ +--R +-------+ \|e \|f x + e +--R \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 3 2 2 2 4 3 5 2 +--R ((- 15a e + 3b d e + c d e)f + (12b e - 8c d e )f - 8c e )x +--R + +--R 2 2 3 2 4 3 2 2 +--R (- 25a d e + 5b d e - c d )f + (- 5a e + 21b d e - 5c d e )f +--R + +--R 5 4 +--R 4b e - 24c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 5 4 +--R - 8a d e f + (- 9a d e + 13b d e - c d e)f + 2a e + 2b d e +--R + +--R 2 3 +--R - 14c d e +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R 3 3 3 2 5 2 7 9 2 +--R (4d e f - 12d e f + 12d e f - 4e )x +--R + +--R 4 2 3 3 4 2 2 6 8 5 3 4 3 2 3 5 +--R (8d e f - 24d e f + 24d e f - 8d e )x + 4d e f - 12d e f + 12d e f +--R + +--R 2 7 +--R - 4d e +--R * +--R +----------+ +--R | 2 +-+ +-------+ +--R \|- d f + e \|e \|f x + e +--R Type: Expression(Integer) +--E 1731 + +--S 1732 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 2 2 2 5 4 6 2 +--R ((15a e - 3b d e - c d e )f + (- 12b e + 8c d e )f + 8c e )x +--R + +--R 3 2 2 3 2 4 2 3 +--R (30a d e - 6b d e - 2c d e)f + (- 24b d e + 16c d e )f +--R + +--R 5 +--R 16c d e +--R * +--R x +--R + +--R 2 2 3 4 2 2 3 3 2 2 4 +--R (15a d e - 3b d e - c d )f + (- 12b d e + 8c d e )f + 8c d e +--R * +--R +-------+ +--R \|f x + e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R 3 2 2 2 4 3 5 2 +--R ((- 30a e + 6b d e + 2c d e)f + (24b e - 16c d e )f - 16c e )x +--R + +--R 2 2 3 2 +--R (- 50a d e + 10b d e - 2c d )f +--R + +--R 4 3 2 2 5 4 +--R (- 10a e + 42b d e - 10c d e )f + 8b e - 48c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 5 4 +--R - 16a d e f + (- 18a d e + 26b d e - 2c d e)f + 4a e + 4b d e +--R + +--R 2 3 +--R - 28c d e +--R * +--R +------------+ +--R | 3 +--R \|- d e f + e +--R / +--R 3 3 3 2 5 2 7 9 2 +--R (8d e f - 24d e f + 24d e f - 8e )x +--R + +--R 4 2 3 3 4 2 2 6 8 5 3 4 3 2 +--R (16d e f - 48d e f + 48d e f - 16d e )x + 8d e f - 24d e f +--R + +--R 3 5 2 7 +--R 24d e f - 8d e +--R * +--R +------------+ +--R | 3 +-------+ +--R \|- d e f + e \|f x + e +--R , +--R +--R 4 3 2 2 2 5 4 6 2 +--R ((- 15a e + 3b d e + c d e )f + (12b e - 8c d e )f - 8c e )x +--R + +--R 3 2 2 3 2 4 2 3 +--R (- 30a d e + 6b d e + 2c d e)f + (24b d e - 16c d e )f +--R + +--R 5 +--R - 16c d e +--R * +--R x +--R + +--R 2 2 3 4 2 2 3 3 2 2 4 +--R (- 15a d e + 3b d e + c d )f + (12b d e - 8c d e )f - 8c d e +--R * +--R +----------+ +--R | 3 +-------+ +--R +-------+ \|d e f - e \|f x + e +--R \|f x + e atan(-----------------------) +--R 2 +--R d f - e +--R + +--R 3 2 2 2 4 3 5 2 +--R ((- 15a e + 3b d e + c d e)f + (12b e - 8c d e )f - 8c e )x +--R + +--R 2 2 3 2 +--R (- 25a d e + 5b d e - c d )f +--R + +--R 4 3 2 2 5 4 +--R (- 5a e + 21b d e - 5c d e )f + 4b e - 24c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 5 4 +--R - 8a d e f + (- 9a d e + 13b d e - c d e)f + 2a e + 2b d e +--R + +--R 2 3 +--R - 14c d e +--R * +--R +----------+ +--R | 3 +--R \|d e f - e +--R / +--R 3 3 3 2 5 2 7 9 2 +--R (4d e f - 12d e f + 12d e f - 4e )x +--R + +--R 4 2 3 3 4 2 2 6 8 5 3 4 3 2 +--R (8d e f - 24d e f + 24d e f - 8d e )x + 4d e f - 12d e f +--R + +--R 3 5 2 7 +--R 12d e f - 4d e +--R * +--R +----------+ +--R | 3 +-------+ +--R \|d e f - e \|f x + e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1732 + +--S 1733 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 3 2 4 +--R ((15a e - 3b d e - c d )f + (- 12b e + 8c d e )f + 8c e ) +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 3 2 4 +--R ((- 30a e + 6b d e + 2c d )f + (24b e - 16c d e )f - 16c e ) +--R * +--R +------------+ +-+ +-------+ +--R | 3 \|e \|f x + e +--R \|- d e f + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R / +--R +------------+ +----------+ +--R 3 3 2 3 2 5 7 | 3 | 2 +-+ +--R (8d e f - 24d e f + 24d e f - 8e )\|- d e f + e \|- d f + e \|e +--R Type: Expression(Integer) +--E 1733 + +--S 1734 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1734 + +--S 1735 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 3 2 4 +--R ((- 15a e + 3b d e + c d )f + (12b e - 8c d e )f - 8c e ) +--R * +--R +----------+ +-+ +-------+ +--R | 3 \|e \|f x + e +--R \|d e f - e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 2 2 2 3 2 4 +--R ((- 15a e + 3b d e + c d )f + (12b e - 8c d e )f - 8c e ) +--R * +--R +----------+ +--R +----------+ | 3 +-------+ +--R | 2 +-+ \|d e f - e \|f x + e +--R \|- d f + e \|e atan(-----------------------) +--R 2 +--R d f - e +--R / +--R +----------+ +----------+ +--R 3 3 2 3 2 5 7 | 2 +-+ | 3 +--R (4d e f - 12d e f + 12d e f - 4e )\|- d f + e \|e \|d e f - e +--R Type: Expression(Integer) +--E 1735 + +--S 1736 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1736 + +)clear all + +--S 1737 of 1751 +t0:=x^m*(1-a^2*x^2)^p/(1+a*x) +--R +--R +--R 2 2 p m +--R (- a x + 1) x +--R (1) --------------- +--R a x + 1 +--R Type: Expression(Integer) +--E 1737 + +--S 1738 of 1751 +--r0:=x^(1+m)*AppellF1(1+m,-p,1-p,2+m,a*x,-a*x)/(1+m) +--E 1738 + +--S 1739 of 1751 +--a0:=integrate(t0,x) +--E 1739 + +--S 1740 of 1751 +--m0:=a0-r0 +--E 1740 + +--S 1741 of 1751 +--d0:=D(m0,x) +--E 1741 + +)clear all + +--S 1742 of 1751 +t0:=sqrt(-1+x)*sqrt(1+x)/(1+x-x^2) +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (1) - ---------------- +--R 2 +--R x - x - 1 +--R Type: Expression(Integer) +--E 1742 + +--S 1743 of 1751 +r0:=-acosh(x)-atan(sqrt(-1+x)*sqrt(-2+sqrt(5))/sqrt(1+x))*_ + sqrt(2/5*(-1+sqrt(5)))+atanh(sqrt(-1+x)*sqrt(2+sqrt(5))/sqrt(1+x))*_ + sqrt(2/5*(1+sqrt(5))) +--R +--R +--R (2) +--R +--------+ +--R +---------+ +-----+ | +-+ +--R | +-+ \|x - 1 \|\|5 + 2 +--R \|2\|5 + 2 atanh(-------------------) +--R +-----+ +--R \|x + 1 +--R + +--R +--------+ +--R +---------+ +-----+ | +-+ +--R | +-+ \|x - 1 \|\|5 - 2 +-+ +--R - \|2\|5 - 2 atan(-------------------) - \|5 acosh(x) +--R +-----+ +--R \|x + 1 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 1743 + +--S 1744 of 1751 +--a0:=integrate(t0,x) +--E 1744 + +--S 1745 of 1751 +--m0:=a0-r0 +--E 1745 + +--S 1746 of 1751 +--d0:=D(m0,x) +--E 1746 + +)clear all + +--S 1747 of 1751 +t0:=(a+b*x+c*x^2)/(sqrt(d+e*x)*sqrt(f+g*x)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) -------------------- +--R +-------+ +-------+ +--R \|e x + d \|g x + f +--R Type: Expression(Integer) +--E 1747 + +--S 1748 of 1751 +r0:=-b*(e*f+d*g)*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/_ + (e^(3/2)*g^(3/2))-1/4*c*(4*d*e*f*g-3*(e*f+d*g)^2)*atanh(sqrt(g)*_ + sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/(e^(5/2)*g^(5/2))+2*a*atanh(sqrt(g)*_ + sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/(sqrt(e)*sqrt(g))+b*sqrt(d+e*x)*_ + sqrt(f+g*x)/(e*g)-3/4*c*(e*f+d*g)*sqrt(d+e*x)*sqrt(f+g*x)/(e^2*g^2)+_ + 1/2*c*x*sqrt(d+e*x)*sqrt(f+g*x)/(e*g) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R ((8a e - 4b d e + 3c d )g + (- 4b e + 2c d e)f g + 3c e f ) +--R * +--R +-+ +-------+ +--R \|g \|e x + d +--R atanh(--------------) +--R +-+ +-------+ +--R \|e \|g x + f +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2c e g x + (4b e - 3c d)g - 3c e f)\|e \|g \|e x + d \|g x + f +--R / +--R 2 2 +-+ +-+ +--R 4e g \|e \|g +--R Type: Expression(Integer) +--E 1748 + +--S 1749 of 1751 +--a0:=integrate(t0,x) +--E 1749 + +--S 1750 of 1751 +--m0:=a0-r0 +--E 1750 + +--S 1751 of 1751 +--d0:=D(m0,x) +--E 1751 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richder12a.input.pamphlet b/src/axiom-website/CATS/richder12a.input.pamphlet new file mode 100644 index 0000000..5476ecd --- /dev/null +++ b/src/axiom-website/CATS/richder12a.input.pamphlet @@ -0,0 +1,19660 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +All derivatives match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12a.output +)spool richder12a.output +)set message test on +)set message auto off +)clear all + +--S 1 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + A b x)(e x + d) +--R Type: Expression(Integer) +--E 1 + +--S 2 OF 765 +r0:=-d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R ((A c + B b)e - 3B c d)m + ((7A c + 7B b)e - 21B c d)m +--R + +--R ((14A c + 14B b)e - 42B c d)m + (8A c + 8B b)e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R (A b e + (- 2A c - 2B b)d e + 3B c d )m +--R + +--R 2 2 2 +--R (8A b e + (- 16A c - 16B b)d e + 24B c d )m +--R + +--R 2 2 2 +--R (19A b e + (- 38A c - 38B b)d e + 57B c d )m + 12A b e +--R + +--R 2 +--R (- 24A c - 24B b)d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 +--R (- A b d e + (A c + B b)d e - B c d )m +--R + +--R 2 2 3 2 +--R (- 9A b d e + (9A c + 9B b)d e - 9B c d )m +--R + +--R 2 2 3 2 +--R (- 26A b d e + (26A c + 26B b)d e - 26B c d )m - 24A b d e +--R + +--R 2 3 +--R (24A c + 24B b)d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 2 + +--S 3 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 3 + +)clear all + +--S 4 OF 765 +t0:=(A+B*x)*(d+e*x)^5*(b*x+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 +--R B c e x + ((A c + B b)e + 5B c d e )x +--R + +--R 5 4 2 3 6 +--R (A b e + (5A c + 5B b)d e + 10B c d e )x +--R + +--R 4 2 3 3 2 5 +--R (5A b d e + (10A c + 10B b)d e + 10B c d e )x +--R + +--R 2 3 3 2 4 4 +--R (10A b d e + (10A c + 10B b)d e + 5B c d e)x +--R + +--R 3 2 4 5 3 4 5 2 +--R (10A b d e + (5A c + 5B b)d e + B c d )x + (5A b d e + (A c + B b)d )x +--R + +--R 5 +--R A b d x +--R Type: Polynomial(Integer) +--E 4 + +--S 5 OF 765 +r0:=-1/6*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^6/e^4+1/7*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^7/e^4-1/8*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^8/e^4+_ + 1/9*B*c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 1 9 5 8 8 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 9 8 8 8 +--R + +--R 1 9 5 5 8 10 2 7 7 +--R (- A b e + (- A c + - B b)d e + -- B c d e )x +--R 7 7 7 7 +--R + +--R 5 8 5 5 2 7 5 3 6 6 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 6 3 3 3 +--R + +--R 2 7 3 6 4 5 5 +--R (2A b d e + (2A c + 2B b)d e + B c d e )x +--R + +--R 5 3 6 5 5 4 5 1 5 4 4 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 2 4 4 4 +--R + +--R 5 4 5 1 1 5 4 3 1 5 4 2 1 7 2 +--R (- A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 3 2 42 +--R + +--R 1 1 8 1 9 +--R (--- A c + --- B b)d e - --- B c d +--R 168 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 5 + +--S 6 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 6 + +)clear all + +--S 7 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 +--R B c e x + ((A c + B b)e + 4B c d e )x +--R + +--R 4 3 2 2 5 +--R (A b e + (4A c + 4B b)d e + 6B c d e )x +--R + +--R 3 2 2 3 4 +--R (4A b d e + (6A c + 6B b)d e + 4B c d e)x +--R + +--R 2 2 3 4 3 3 4 2 +--R (6A b d e + (4A c + 4B b)d e + B c d )x + (4A b d e + (A c + B b)d )x +--R + +--R 4 +--R A b d x +--R Type: Polynomial(Integer) +--E 7 + +--S 8 OF 765 +r0:=-1/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^5/e^4+1/6*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^7/e^4+_ + 1/8*B*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 1 8 4 7 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 8 2 2 7 2 6 6 +--R (- A b e + (- A c + - B b)d e + B c d e )x +--R 6 3 3 +--R + +--R 4 7 6 6 2 6 4 3 5 5 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 3 2 6 3 5 1 4 4 4 +--R (- A b d e + (A c + B b)d e + - B c d e )x +--R 2 4 +--R + +--R 4 3 5 1 1 4 4 3 1 4 4 2 1 6 2 +--R (- A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 3 2 30 +--R + +--R 1 1 7 1 8 +--R (--- A c + --- B b)d e - --- B c d +--R 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 8 + +--S 9 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 9 + +)clear all + +--S 10 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R (A b e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 2 2 3 3 2 3 2 +--R (3A b d e + (3A c + 3B b)d e + B c d )x + (3A b d e + (A c + B b)d )x +--R + +--R 3 +--R A b d x +--R Type: Polynomial(Integer) +--E 10 + +--S 11 OF 765 +r0:=-1/4*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^4/e^4+1/5*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^6/e^4+_ + 1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 1 7 1 6 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 7 3 3 6 3 2 5 5 +--R (- A b e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 3 6 3 3 2 5 1 3 4 4 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 2 5 1 1 3 4 3 1 3 4 2 1 5 2 +--R (A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 2 20 +--R + +--R 1 1 6 1 7 +--R (-- A c + -- B b)d e - --- B c d +--R 60 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 11 + +--S 12 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R Type: Polynomial(Integer) +--E 13 + +--S 14 OF 765 +r0:=1/2*A*b*d^2*x^2+1/3*d*(b*B*d+A*c*d+2*A*b*e)*x^3+1/4*(A*e*(2*c*d+b*e)+_ + B*d*(c*d+2*b*e))*x^4+1/5*e*(2*B*c*d+b*B*e+A*c*e)*x^5+1/6*B*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 1 2 2 5 +--R - B c e x + ((- A c + - B b)e + - B c d e)x +--R 6 5 5 5 +--R + +--R 1 2 1 1 1 2 4 +--R (- A b e + (- A c + - B b)d e + - B c d )x +--R 4 2 2 4 +--R + +--R 2 1 1 2 3 1 2 2 +--R (- A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 14 + +--S 15 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 OF 765 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x +--R Type: Polynomial(Integer) +--E 16 + +--S 17 OF 765 +r0:=1/2*A*b*d*x^2+1/3*(b*B*d+A*c*d+A*b*e)*x^3+1/4*(B*c*d+b*B*e+A*c*e)*x^4+_ + 1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 3 1 2 +--R (- A b e + (- A c + - B b)d)x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 18 + +)clear all + +--S 19 OF 765 +t0:=(A+B*x)*(b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + (A c + B b)x + A b x +--R Type: Polynomial(Integer) +--E 19 + +--S 20 OF 765 +r0:=1/2*A*b*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 1 3 1 2 +--R (2) - B c x + (- A c + - B b)x + - A b x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +--S 21 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 22 + +--S 23 OF 765 +r0:=(B*d-A*e)*(c*d-b*e)*x/e^3-1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+_ + 1/3*B*c*x^3/e-d*(B*d-A*e)*(c*d-b*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 2 3 3 3 +--R (- 6A b d e + (6A c + 6B b)d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 +--R ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R (6A b e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 23 + +--S 24 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 24 + +)clear all + +--S 25 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 25 + +--S 26 OF 765 +r0:=-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+d*(B*d-A*e)*_ + (c*d-b*e)/(e^4*(d+e*x))+(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 +--R (2A b e + (- 4A c - 4B b)d e + 6B c d e)x + 2A b d e +--R + +--R 2 3 +--R (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 2 2 3 +--R ((2A c + 2B b)d e - 4B c d e)x + 2A b d e + (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 26 + +--S 27 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 27 + +)clear all + +--S 28 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 28 + +--S 29 OF 765 +r0:=B*c*x/e^3+1/2*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^2)+(-B*d*(3*c*d-_ + 2*b*e)+A*e*(2*c*d-b*e))/(e^4*(d+e*x))-(3*B*c*d-b*B*e-A*c*e)*log(d+_ + e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 +--R 2B c e x + 4B c d e x + (- 2A b e + (4A c + 4B b)d e - 4B c d e)x +--R + +--R 2 2 3 +--R - A b d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 29 + +--S 30 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 OF 765 +r0:=1/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^3)+1/2*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^2)+(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+_ + B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 2 +--R (- 3A b e + (- 6A c - 6B b)d e + 27B c d e)x - A b d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 32 + +--S 33 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 34 + +--S 35 OF 765 +r0:=1/4*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^4)+1/3*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^2)-B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 1 3 3 2 2 +--R - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 2 2 +--R + +--R 1 3 1 1 2 2 1 2 +--R (- - A b e + (- - A c - - B b)d e - B c d e)x - -- A b d e +--R 3 3 3 12 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - - B c d +--R 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 35 + +--S 36 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 36 + +)clear all + +--S 37 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 37 + +--S 38 OF 765 +r0:=1/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^5)+1/4*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 3 3 2 +--R + +--R 1 3 1 1 2 1 2 1 2 +--R (- - A b e + (- - A c - - B b)d e - - B c d e)x - -- A b d e +--R 4 6 6 4 20 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - -- B c d +--R 30 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 38 + +--S 39 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 39 + +)clear all + +--S 40 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 40 + +--S 41 OF 765 +r0:=1/6*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^6)+1/5*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^5)+1/4*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 3 4 4 4 +--R + +--R 1 3 1 1 2 1 2 1 2 +--R (- - A b e + (- -- A c - -- B b)d e - -- B c d e)x - -- A b d e +--R 5 10 10 10 30 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - -- B c d +--R 60 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 41 + +--S 42 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 42 + +)clear all + +--S 43 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 m +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )(e x + d) +--R Type: Expression(Integer) +--E 43 + +--S 44 OF 765 +r0:=-d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(1+m)/(e^6*(1+m))+d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^6*(2+m))+_ + (A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(4+m)/(e^6*(4+m))-_ + c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*_ + (d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((A c + 2B b c)e - 5B c d)m + ((16A c + 32B b c)e - 80B c d)m +--R + +--R 2 2 3 +--R ((95A c + 190B b c)e - 475B c d)m +--R + +--R 2 2 2 +--R ((260A c + 520B b c)e - 1300B c d)m +--R + +--R 2 2 2 2 +--R ((324A c + 648B b c)e - 1620B c d)m + (144A c + 288B b c)e - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (- 4A c - 8B b c)d e + 10B c d )m +--R + +--R 2 2 2 2 2 4 +--R ((34A b c + 17B b )e + (- 68A c - 136B b c)d e + 170B c d )m +--R + +--R 2 2 2 2 2 3 +--R ((214A b c + 107B b )e + (- 428A c - 856B b c)d e + 1070B c d )m +--R + +--R 2 2 2 2 2 2 +--R ((614A b c + 307B b )e + (- 1228A c - 2456B b c)d e + 3070B c d )m +--R + +--R 2 2 2 2 2 +--R ((792A b c + 396B b )e + (- 1584A c - 3168B b c)d e + 3960B c d )m +--R + +--R 2 2 2 2 2 +--R (360A b c + 180B b )e + (- 720A c - 1440B b c)d e + 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (- 6A b c - 3B b )d e + (6A c + 12B b c)d e - 10B c d )m +--R + +--R 2 3 2 2 2 2 +--R 18A b e + (- 108A b c - 54B b )d e + (108A c + 216B b c)d e +--R + +--R 2 3 +--R - 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 2 2 +--R 121A b e + (- 726A b c - 363B b )d e + (726A c + 1452B b c)d e +--R + +--R 2 3 +--R - 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 +--R 372A b e + (- 2232A b c - 1116B b )d e +--R + +--R 2 2 2 3 +--R (2232A c + 4464B b c)d e - 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 +--R 508A b e + (- 3048A b c - 1524B b )d e +--R + +--R 2 2 2 3 +--R (3048A c + 6096B b c)d e - 5080B c d +--R * +--R m +--R + +--R 2 3 2 2 2 2 +--R 240A b e + (- 1440A b c - 720B b )d e + (1440A c + 2880B b c)d e +--R + +--R 2 3 +--R - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 3 +--R - 2A b d e + (6A b c + 3B b )d e + (- 4A c - 8B b c)d e +--R + +--R 2 4 +--R 5B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 2 2 2 3 +--R - 38A b d e + (114A b c + 57B b )d e + (- 76A c - 152B b c)d e +--R + +--R 2 4 +--R 95B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 2 +--R - 274A b d e + (822A b c + 411B b )d e +--R + +--R 2 3 2 4 +--R (- 548A c - 1096B b c)d e + 685B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 2 +--R - 922A b d e + (2766A b c + 1383B b )d e +--R + +--R 2 3 2 4 +--R (- 1844A c - 3688B b c)d e + 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 +--R - 1404A b d e + (4212A b c + 2106B b )d e +--R + +--R 2 3 2 4 +--R (- 2808A c - 5616B b c)d e + 3510B c d +--R * +--R m +--R + +--R 2 3 2 2 2 +--R - 720A b d e + (2160A b c + 1080B b )d e +--R + +--R 2 3 2 4 +--R (- 1440A c - 2880B b c)d e + 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 2 3 2 2 4 2 5 5 +--R (A b d e + (- 2A b c - B b )d e + (A c + 2B b c)d e - B c d )m +--R + +--R 2 2 3 2 3 2 2 4 +--R 20A b d e + (- 40A b c - 20B b )d e + (20A c + 40B b c)d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 2 3 2 3 2 +--R 155A b d e + (- 310A b c - 155B b )d e +--R + +--R 2 4 2 5 +--R (155A c + 310B b c)d e - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 2 3 2 3 2 +--R 580A b d e + (- 1160A b c - 580B b )d e +--R + +--R 2 4 2 5 +--R (580A c + 1160B b c)d e - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 2 3 2 3 2 +--R 1044A b d e + (- 2088A b c - 1044B b )d e +--R + +--R 2 4 2 5 +--R (1044A c + 2088B b c)d e - 1044B c d +--R * +--R m +--R + +--R 2 2 3 2 3 2 2 4 +--R 720A b d e + (- 1440A b c - 720B b )d e + (720A c + 1440B b c)d e +--R + +--R 2 5 +--R - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 44 + +--S 45 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 +--R B c e x + ((A c + 2B b c)e + 4B c d e )x +--R + +--R 2 4 2 3 2 2 2 7 +--R ((2A b c + B b )e + (4A c + 8B b c)d e + 6B c d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 6 +--R (A b e + (8A b c + 4B b )d e + (6A c + 12B b c)d e + 4B c d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 5 +--R (4A b d e + (12A b c + 6B b )d e + (4A c + 8B b c)d e + B c d )x +--R + +--R 2 2 2 2 3 2 4 4 +--R (6A b d e + (8A b c + 4B b )d e + (A c + 2B b c)d )x +--R + +--R 2 3 2 4 3 2 4 2 +--R (4A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 46 + +--S 47 OF 765 +r0:=-1/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^5/e^6+1/6*d*(c*d-b*e)*(B*d*_ + (5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^6/e^6+1/7*(A*e*(6*c^2*d^2-_ + 6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^7/e^6-1/8*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+_ + b^2*e^2))*(d+e*x)^8/e^6-1/9*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^9/e^6+1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 2 10 4 2 9 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 2 10 1 2 9 3 2 2 8 8 +--R ((- A b c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 8 2 4 +--R + +--R 1 2 10 8 4 2 9 6 2 12 2 8 +--R - A b e + (- A b c + - B b )d e + (- A c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 4 2 3 7 +--R - B c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 2 2 9 2 2 8 2 2 4 3 7 +--R - A b d e + (2A b c + B b )d e + (- A c + - B b c)d e +--R 3 3 3 +--R + +--R 1 2 4 6 +--R - B c d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 6 2 2 8 8 4 2 3 7 1 2 2 4 6 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d e )x +--R 5 5 5 5 5 +--R + +--R 2 3 7 1 1 2 4 6 4 1 2 4 6 3 1 2 7 3 +--R (A b d e + (- A b c + - B b )d e )x + - A b d e x + --- A b d e +--R 2 4 3 105 +--R + +--R 1 1 2 8 2 1 2 1 9 1 2 10 +--R (- --- A b c - --- B b )d e + (--- A c + --- B b c)d e - ---- B c d +--R 140 280 630 315 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 48 + +)clear all + +--S 49 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R ((2A b c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (6A b c + 3B b )d e + (3A c + 6B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 3 4 +--R (3A b d e + (6A b c + 3B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 3 2 3 2 +--R (3A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 49 + +--S 50 OF 765 +r0:=1/3*A*b^2*d^3*x^3+1/4*b*d^2*(b*B*d+2*A*c*d+3*A*b*e)*x^4+1/5*d*(A*c^2*_ + d^2+3*b^2*e*(B*d+A*e)+2*b*c*d*(B*d+3*A*e))*x^5+1/6*(A*e*(3*c^2*d^2+_ + 6*b*c*d*e+b^2*e^2)+B*d*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^6+1/7*e*_ + (A*c*e*(3*c*d+2*b*e)+B*(3*c^2*d^2+6*b*c*d*e+b^2*e^2))*x^7+_ + 1/8*c*e^2*(3*B*c*d+2*b*B*e+A*c*e)*x^8+1/9*B*c^2*e^3*x^9 +--R +--R +--R (2) +--R 1 2 3 9 1 2 1 3 3 2 2 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 3 3 2 6 2 3 2 2 7 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d e)x +--R 7 7 7 7 7 +--R + +--R 1 2 3 1 2 2 1 2 2 1 2 3 6 +--R (- A b e + (A b c + - B b )d e + (- A c + B b c)d e + - B c d )x +--R 6 2 2 6 +--R + +--R 3 2 2 6 3 2 2 1 2 2 3 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 3 2 2 1 1 2 3 4 1 2 3 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 50 + +--S 51 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 51 + +)clear all + +--S 52 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 52 + +--S 53 OF 765 +r0:=1/3*A*b^2*d^2*x^3+1/4*b*d*(b*B*d+2*A*c*d+2*A*b*e)*x^4+1/5*(A*c^2*d^2+_ + b^2*e*(2*B*d+A*e)+2*b*c*d*(B*d+2*A*e))*x^5+1/6*(2*A*c*e*(c*d+b*e)+_ + B*(c^2*d^2+4*b*c*d*e+b^2*e^2))*x^6+1/7*c*e*(A*c*e+2*B*(c*d+b*e))*_ + x^7+1/8*B*c^2*e^2*x^8 +--R +--R +--R (2) +--R 1 2 2 8 1 2 2 2 2 2 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e)x +--R 8 7 7 7 +--R + +--R 1 1 2 2 1 2 2 1 2 2 6 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d )x +--R 3 6 3 3 6 +--R + +--R 1 2 2 4 2 2 1 2 2 2 5 +--R (- A b e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 1 2 1 1 2 2 4 1 2 2 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 2 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 53 + +--S 54 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 54 + +)clear all + +--S 55 OF 765 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R Type: Polynomial(Integer) +--E 55 + +--S 56 OF 765 +r0:=1/3*A*b^2*d*x^3+1/4*b*(b*B*d+2*A*c*d+A*b*e)*x^4+1/5*(A*c^2*d+b^2*B*e+_ + 2*b*c*(B*d+A*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 1 2 1 2 2 5 +--R ((- A b c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 +--R + +--R 1 2 1 1 2 4 1 2 3 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 56 + +--S 57 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R (1) B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R Type: Polynomial(Integer) +--E 58 + +--S 59 OF 765 +r0:=1/3*A*b^2*x^3+1/4*b*(b*B+2*A*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6 +--R +--R +--R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 +--R (2) - B c x + (- A c + - B b c)x + (- A b c + - B b )x + - A b x +--R 6 5 5 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 59 + +--S 60 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 OF 765 +r0:=d*(B*d-A*e)*(c*d-b*e)^2*x/e^5-1/2*(B*d-A*e)*(c*d-b*e)^2*x^2/e^4-_ + 1/3*(A*c*e*(c*d-2*b*e)-B*(c*d-b*e)^2)*x^3/e^3-1/4*c*(B*c*d-2*b*B*e-_ + A*c*e)*x^4/e^2+1/5*B*c^2*x^5/e-d^2*(B*d-A*e)*(c*d-b*e)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 3 2 3 2 2 4 +--R 60A b d e + (- 120A b c - 60B b )d e + (60A c + 120B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((40A b c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 60A b c - 30B b )d e + (30A c + 60B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 60A b d e + (120A b c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 62 + +--S 63 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 64 + +--S 65 OF 765 +r0:=-(c*d-b*e)*(2*B*d*(2*c*d-b*e)-A*e*(3*c*d-b*e))*x/e^5+1/2*(c*d-b*e)*_ + (3*B*c*d-b*B*e-2*A*c*e)*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x))+d*_ + (c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 4 2 2 3 2 3 2 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 12A b e + (- 36A b c - 18B b )d e + (24A c + 48B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 48A b c - 24B b )d e + (36A c + 72B b c)d e +--R + +--R 2 4 +--R - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 12A b d e + (24A b c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 65 + +--S 66 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 66 + +)clear all + +--S 67 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 67 + +--S 68 OF 765 +r0:=-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2-6*b*c*d*e+b^2*e^2))*x/e^5-1/2*c*_ + (3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*(d+e*x)^2)-d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*_ + (2*c*d-b*e))/(e^6*(d+e*x))+(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-_ + B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 +--R 6A b e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e +--R + +--R 2 3 2 +--R - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 72A b c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 6A b d e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((24A b c + 12B b )d e + (- 33A c - 66B b c)d e + 63B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 24A b c - 12B b )d e + (6A c + 12B b c)d e +--R + +--R 2 4 +--R 6B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 9A b d e + (- 30A b c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 68 + +--S 69 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 69 + +)clear all + +--S 70 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 70 + +--S 71 OF 765 +r0:=-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*(d+e*x)^3)-1/2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-_ + 2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^2)+(-A*e*(6*c^2*d^2-6*b*c*d*e+_ + b^2*e^2)+B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*(d+e*x))-_ + (2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 24A c - 48B b c)d e + 60B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e )x +--R + +--R 2 2 3 2 3 2 2 4 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e)x +--R + +--R 2 3 2 2 4 2 5 +--R (12A b c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 6A b e + (36A b c + 18B b )d e + (- 18A c - 36B b c)d e +--R + +--R 2 3 2 +--R - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 6A b d e + (54A b c + 27B b )d e + (- 54A c - 108B b c)d e +--R + +--R 2 4 +--R 81B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 2A b d e + (22A b c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 71 + +--S 72 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 73 + +--S 74 OF 765 +r0:=-d^3*(B*d-A*e)*(c*d-b*e)^3*(d+e*x)^(1+m)/(e^8*(1+m))+d^2*(c*d-b*e)^2*_ + (B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^8*(2+m))+_ + 3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-_ + 8*b*c*d*e+2*b^2*e^2))*(d+e*x)^(3+m)/(e^8*(3+m))+(B*d*(35*c^3*d^3-_ + 60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-A*e*(20*c^3*d^3-30*b*c^2*_ + d^2*e+12*b^2*c*d*e^2-b^3*e^3))*(d+e*x)^(4+m)/(e^8*(4+m))+(3*A*c*e*_ + (5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*(35*c^3*d^3-45*b*c^2*d^2*e+15*b^2*_ + c*d*e^2-b^3*e^3))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2-6*b*c*d*e+b^2*e^2))*(d+e*x)^(6+m)/(e^8*(6+m))-c^2*_ + (7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*_ + (d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 2 3 7 3 2 3 6 +--R ((A c + 3B b c )e - 7B c d)m + ((29A c + 87B b c )e - 203B c d)m +--R + +--R 3 2 3 5 +--R ((343A c + 1029B b c )e - 2401B c d)m +--R + +--R 3 2 3 4 +--R ((2135A c + 6405B b c )e - 14945B c d)m +--R + +--R 3 2 3 3 +--R ((7504A c + 22512B b c )e - 52528B c d)m +--R + +--R 3 2 3 2 +--R ((14756A c + 44268B b c )e - 103292B c d)m +--R + +--R 3 2 3 +--R ((14832A c + 44496B b c )e - 103824B c d)m +--R + +--R 3 2 3 +--R (5760A c + 17280B b c )e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 7 +--R ((3A b c + 3B b c)e + (- 6A c - 18B b c )d e + 21B c d )m +--R + +--R 2 2 2 3 2 3 2 6 +--R ((90A b c + 90B b c)e + (- 180A c - 540B b c )d e + 630B c d )m +--R + +--R 2 2 2 3 2 +--R (1098A b c + 1098B b c)e + (- 2196A c - 6588B b c )d e +--R + +--R 3 2 +--R 7686B c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 3 2 +--R (7020A b c + 7020B b c)e + (- 14040A c - 42120B b c )d e +--R + +--R 3 2 +--R 49140B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 3 2 +--R (25227A b c + 25227B b c)e + (- 50454A c - 151362B b c )d e +--R + +--R 3 2 +--R 176589B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 3 2 +--R (50490A b c + 50490B b c)e + (- 100980A c - 302940B b c )d e +--R + +--R 3 2 +--R 353430B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 3 2 +--R (51432A b c + 51432B b c)e + (- 102864A c - 308592B b c )d e +--R + +--R 3 2 +--R 360024B c d +--R * +--R m +--R + +--R 2 2 2 3 2 +--R (20160A b c + 20160B b c)e + (- 40320A c - 120960B b c )d e +--R + +--R 3 2 +--R 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 3 2 2 2 +--R (3A b c + B b )e + (- 15A b c - 15B b c)d e +--R + +--R 3 2 2 3 3 +--R (15A c + 45B b c )d e - 35B c d +--R * +--R 7 +--R m +--R + +--R 2 3 3 2 2 2 +--R (93A b c + 31B b )e + (- 465A b c - 465B b c)d e +--R + +--R 3 2 2 3 3 +--R (465A c + 1395B b c )d e - 1085B c d +--R * +--R 6 +--R m +--R + +--R 2 3 3 2 2 2 +--R (1173A b c + 391B b )e + (- 5865A b c - 5865B b c)d e +--R + +--R 3 2 2 3 3 +--R (5865A c + 17595B b c )d e - 13685B c d +--R * +--R 5 +--R m +--R + +--R 2 3 3 2 2 2 +--R (7743A b c + 2581B b )e + (- 38715A b c - 38715B b c)d e +--R + +--R 3 2 2 3 3 +--R (38715A c + 116145B b c )d e - 90335B c d +--R * +--R 4 +--R m +--R + +--R 2 3 3 2 2 2 +--R (28632A b c + 9544B b )e + (- 143160A b c - 143160B b c)d e +--R + +--R 3 2 2 3 3 +--R (143160A c + 429480B b c )d e - 334040B c d +--R * +--R 3 +--R m +--R + +--R 2 3 3 2 2 2 +--R (58692A b c + 19564B b )e + (- 293460A b c - 293460B b c)d e +--R + +--R 3 2 2 3 3 +--R (293460A c + 880380B b c )d e - 684740B c d +--R * +--R 2 +--R m +--R + +--R 2 3 3 2 2 2 +--R (60912A b c + 20304B b )e + (- 304560A b c - 304560B b c)d e +--R + +--R 3 2 2 3 3 +--R (304560A c + 913680B b c )d e - 710640B c d +--R * +--R m +--R + +--R 2 3 3 2 2 2 +--R (24192A b c + 8064B b )e + (- 120960A b c - 120960B b c)d e +--R + +--R 3 2 2 3 3 +--R (120960A c + 362880B b c )d e - 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (- 12A b c - 4B b )d e + (30A b c + 30B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 20A c - 60B b c )d e + 35B c d +--R * +--R 7 +--R m +--R + +--R 3 4 2 3 3 +--R 32A b e + (- 384A b c - 128B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (960A b c + 960B b c)d e + (- 640A c - 1920B b c )d e +--R + +--R 3 4 +--R 1120B c d +--R * +--R 6 +--R m +--R + +--R 3 4 2 3 3 +--R 418A b e + (- 5016A b c - 1672B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (12540A b c + 12540B b c)d e + (- 8360A c - 25080B b c )d e +--R + +--R 3 4 +--R 14630B c d +--R * +--R 5 +--R m +--R + +--R 3 4 2 3 3 +--R 2864A b e + (- 34368A b c - 11456B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (85920A b c + 85920B b c)d e + (- 57280A c - 171840B b c )d e +--R + +--R 3 4 +--R 100240B c d +--R * +--R 4 +--R m +--R + +--R 3 4 2 3 3 +--R 10993A b e + (- 131916A b c - 43972B b )d e +--R + +--R 2 2 2 2 +--R (329790A b c + 329790B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 219860A c - 659580B b c )d e + 384755B c d +--R * +--R 3 +--R m +--R + +--R 3 4 2 3 3 +--R 23312A b e + (- 279744A b c - 93248B b )d e +--R + +--R 2 2 2 2 +--R (699360A b c + 699360B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 466240A c - 1398720B b c )d e + 815920B c d +--R * +--R 2 +--R m +--R + +--R 3 4 2 3 3 +--R 24876A b e + (- 298512A b c - 99504B b )d e +--R + +--R 2 2 2 2 +--R (746280A b c + 746280B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 497520A c - 1492560B b c )d e + 870660B c d +--R * +--R m +--R + +--R 3 4 2 3 3 +--R 10080A b e + (- 120960A b c - 40320B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (302400A b c + 302400B b c)d e + (- 201600A c - 604800B b c )d e +--R + +--R 3 4 +--R 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 4 2 3 2 3 2 2 3 2 +--R - 3A b d e + (18A b c + 6B b )d e + (- 30A b c - 30B b c)d e +--R + +--R 3 2 4 3 5 +--R (15A c + 45B b c )d e - 21B c d +--R * +--R 7 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 99A b d e + (594A b c + 198B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (- 990A b c - 990B b c)d e + (495A c + 1485B b c )d e +--R + +--R 3 5 +--R - 693B c d +--R * +--R 6 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 1341A b d e + (8046A b c + 2682B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (- 13410A b c - 13410B b c)d e + (6705A c + 20115B b c )d e +--R + +--R 3 5 +--R - 9387B c d +--R * +--R 5 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 9585A b d e + (57510A b c + 19170B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (- 95850A b c - 95850B b c)d e + (47925A c + 143775B b c )d e +--R + +--R 3 5 +--R - 67095B c d +--R * +--R 4 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 38592A b d e + (231552A b c + 77184B b )d e +--R + +--R 2 2 3 2 +--R (- 385920A b c - 385920B b c)d e +--R + +--R 3 2 4 3 5 +--R (192960A c + 578880B b c )d e - 270144B c d +--R * +--R 3 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 86076A b d e + (516456A b c + 172152B b )d e +--R + +--R 2 2 3 2 +--R (- 860760A b c - 860760B b c)d e +--R + +--R 3 2 4 3 5 +--R (430380A c + 1291140B b c )d e - 602532B c d +--R * +--R 2 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 96144A b d e + (576864A b c + 192288B b )d e +--R + +--R 2 2 3 2 +--R (- 961440A b c - 961440B b c)d e +--R + +--R 3 2 4 3 5 +--R (480720A c + 1442160B b c )d e - 673008B c d +--R * +--R m +--R + +--R 3 4 2 3 2 3 +--R - 40320A b d e + (241920A b c + 80640B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (- 403200A b c - 403200B b c)d e + (201600A c + 604800B b c )d e +--R + +--R 3 5 +--R - 282240B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 2 4 2 3 3 3 2 2 4 2 +--R 3A b d e + (- 12A b c - 4B b )d e + (15A b c + 15B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 6A c - 18B b c )d e + 7B c d +--R * +--R 7 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 102A b d e + (- 408A b c - 136B b )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (510A b c + 510B b c)d e + (- 204A c - 612B b c )d e + 238B c d +--R * +--R 6 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 1434A b d e + (- 5736A b c - 1912B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (7170A b c + 7170B b c)d e + (- 2868A c - 8604B b c )d e +--R + +--R 3 6 +--R 3346B c d +--R * +--R 5 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 10740A b d e + (- 42960A b c - 14320B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (53700A b c + 53700B b c)d e + (- 21480A c - 64440B b c )d e +--R + +--R 3 6 +--R 25060B c d +--R * +--R 4 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 45867A b d e + (- 183468A b c - 61156B b )d e +--R + +--R 2 2 4 2 +--R (229335A b c + 229335B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 91734A c - 275202B b c )d e + 107023B c d +--R * +--R 3 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 110118A b d e + (- 440472A b c - 146824B b )d e +--R + +--R 2 2 4 2 +--R (550590A b c + 550590B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 220236A c - 660708B b c )d e + 256942B c d +--R * +--R 2 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 134136A b d e + (- 536544A b c - 178848B b )d e +--R + +--R 2 2 4 2 +--R (670680A b c + 670680B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 268272A c - 804816B b c )d e + 312984B c d +--R * +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 60480A b d e + (- 241920A b c - 80640B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (302400A b c + 302400B b c)d e + (- 120960A c - 362880B b c )d e +--R + +--R 3 6 +--R 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - A b d e + (3A b c + B b )d e + (- 3A b c - 3B b c)d e +--R + +--R 3 2 6 3 7 +--R (A c + 3B b c )d e - B c d +--R * +--R 7 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 35A b d e + (105A b c + 35B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 105A b c - 105B b c)d e + (35A c + 105B b c )d e - 35B c d +--R * +--R 6 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 511A b d e + (1533A b c + 511B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (- 1533A b c - 1533B b c)d e + (511A c + 1533B b c )d e +--R + +--R 3 7 +--R - 511B c d +--R * +--R 5 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 4025A b d e + (12075A b c + 4025B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (- 12075A b c - 12075B b c)d e + (4025A c + 12075B b c )d e +--R + +--R 3 7 +--R - 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 18424A b d e + (55272A b c + 18424B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (- 55272A b c - 55272B b c)d e + (18424A c + 55272B b c )d e +--R + +--R 3 7 +--R - 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 48860A b d e + (146580A b c + 48860B b )d e +--R + +--R 2 2 5 2 +--R (- 146580A b c - 146580B b c)d e +--R + +--R 3 2 6 3 7 +--R (48860A c + 146580B b c )d e - 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 69264A b d e + (207792A b c + 69264B b )d e +--R + +--R 2 2 5 2 +--R (- 207792A b c - 207792B b c)d e +--R + +--R 3 2 6 3 7 +--R (69264A c + 207792B b c )d e - 69264B c d +--R * +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 40320A b d e + (120960A b c + 40320B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (- 120960A b c - 120960B b c)d e + (40320A c + 120960B b c )d e +--R + +--R 3 7 +--R - 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 74 + +--S 75 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 2 4 3 3 10 +--R B c e x + ((A c + 3B b c )e + 4B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 9 +--R ((3A b c + 3B b c)e + (4A c + 12B b c )d e + 6B c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 2 +--R (3A b c + B b )e + (12A b c + 12B b c)d e + (6A c + 18B b c )d e +--R + +--R 3 3 +--R 4B c d e +--R * +--R 8 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (12A b c + 4B b )d e + (18A b c + 18B b c)d e +--R + +--R 3 2 3 3 4 +--R (4A c + 12B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 3 3 2 3 2 2 2 2 3 +--R 4A b d e + (18A b c + 6B b )d e + (12A b c + 12B b c)d e +--R + +--R 3 2 4 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 2 2 2 3 3 2 2 4 5 +--R (6A b d e + (12A b c + 4B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 3 2 3 4 4 3 4 3 +--R (4A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 OF 765 +r0:=1/4*A*b^3*d^4*x^4+1/5*b^2*d^3*(b*B*d+3*A*c*d+4*A*b*e)*x^5+1/6*b*d^2*_ + (3*A*c^2*d^2+2*b^2*e*(2*B*d+3*A*e)+3*b*c*d*(B*d+4*A*e))*x^6+1/7*d*_ + (A*c^3*d^3+2*b^3*e^2*(3*B*d+2*A*e)+6*b^2*c*d*e*(2*B*d+3*A*e)+3*b*_ + c^2*d^2*(B*d+4*A*e))*x^7+1/8*(A*e*(4*c^3*d^3+18*b*c^2*d^2*e+12*_ + b^2*c*d*e^2+b^3*e^3)+B*d*(c^3*d^3+12*b*c^2*d^2*e+18*b^2*c*d*e^2+4*_ + b^3*e^3))*x^8+1/9*e*(3*A*c*e*(2*c^2*d^2+4*b*c*d*e+b^2*e^2)+B*_ + (4*c^3*d^3+18*b*c^2*d^2*e+12*b^2*c*d*e^2+b^3*e^3))*x^9+1/10*c*e^2*_ + (A*c*e*(4*c*d+3*b*e)+3*B*(2*c^2*d^2+4*b*c*d*e+b^2*e^2))*x^10+1/11*_ + c^2*e^3*(4*B*c*d+3*b*B*e+A*c*e)*x^11+1/12*B*c^3*e^4*x^12 +--R +--R +--R (2) +--R 1 3 4 12 1 3 3 2 4 4 3 3 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 2 3 2 4 2 3 6 2 3 3 3 2 2 10 +--R ((-- A b c + -- B b c)e + (- A c + - B b c )d e + - B c d e )x +--R 10 10 5 5 5 +--R + +--R 1 2 1 3 4 4 2 4 2 3 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 3 9 3 3 +--R + +--R 2 3 2 2 2 4 3 3 +--R (- A c + 2B b c )d e + - B c d e +--R 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 4 3 2 1 3 3 9 2 9 2 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 8 2 2 4 4 +--R + +--R 1 3 3 2 3 1 3 4 +--R (- A c + - B b c )d e + - B c d +--R 2 2 8 +--R * +--R 8 +--R x +--R + +--R 4 3 3 18 2 6 3 2 2 12 2 12 2 3 +--R - A b d e + (-- A b c + - B b )d e + (-- A b c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 4 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 2 2 2 3 3 1 2 1 2 4 6 +--R (A b d e + (2A b c + - B b )d e + (- A b c + - B b c)d )x +--R 3 2 2 +--R + +--R 4 3 3 3 2 1 3 4 5 1 3 4 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 77 + +--S 78 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 2 3 3 2 9 +--R B c e x + ((A c + 3B b c )e + 3B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 8 +--R ((3A b c + 3B b c)e + (3A c + 9B b c )d e + 3B c d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A b c + B b )e + (9A b c + 9B b c)d e + (3A c + 9B b c )d e +--R + +--R 3 3 +--R B c d +--R * +--R 7 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R A b e + (9A b c + 3B b )d e + (9A b c + 9B b c)d e +--R + +--R 3 2 3 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 2 2 3 2 2 2 3 5 +--R (3A b d e + (9A b c + 3B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 2 2 3 3 4 3 3 3 +--R (3A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 79 + +--S 80 OF 765 +r0:=1/4*A*b^3*d^3*x^4+1/5*b^2*d^2*(b*B*d+3*A*c*d+3*A*b*e)*x^5+1/2*b*d*_ + (A*c^2*d^2+b^2*e*(B*d+A*e)+b*c*d*(B*d+3*A*e))*x^6+1/7*(A*c^3*d^3+_ + 9*b^2*c*d*e*(B*d+A*e)+b^3*e^2*(3*B*d+A*e)+3*b*c^2*d^2*(B*d+3*A*e))*_ + x^7+1/8*(3*A*c*e*(c^2*d^2+3*b*c*d*e+b^2*e^2)+B*(c^3*d^3+9*b*c^2*d^2*e+_ + 9*b^2*c*d*e^2+b^3*e^3))*x^8+1/3*c*e*(A*c*e*(c*d+b*e)+B*(c^2*d^2+_ + 3*b*c*d*e+b^2*e^2))*x^9+1/10*c^2*e^2*(A*c*e+3*B*(c*d+b*e))*x^10+_ + 1/11*B*c^3*e^3*x^11 +--R +--R +--R (2) +--R 1 3 3 11 1 3 3 2 3 3 3 2 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 2 1 2 3 1 3 2 2 1 3 2 9 +--R ((- A b c + - B b c)e + (- A c + B b c )d e + - B c d e)x +--R 3 3 3 3 +--R + +--R 3 2 1 3 3 9 2 9 2 2 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 8 8 8 8 +--R + +--R 3 3 9 2 2 1 3 3 +--R (- A c + - B b c )d e + - B c d +--R 8 8 8 +--R * +--R 8 +--R x +--R + +--R 1 3 3 9 2 3 3 2 9 2 9 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 3 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 2 3 2 1 3 2 1 2 1 2 3 6 +--R (- A b d e + (- A b c + - B b )d e + (- A b c + - B b c)d )x +--R 2 2 2 2 2 +--R + +--R 3 3 2 3 2 1 3 3 5 1 3 3 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +--S 81 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 2 3 8 +--R B c e x + ((A c + 3B b c )e + 2B c d e)x +--R + +--R 2 2 2 3 2 3 2 7 +--R ((3A b c + 3B b c)e + (2A c + 6B b c )d e + B c d )x +--R + +--R 2 3 2 2 2 3 2 2 6 +--R ((3A b c + B b )e + (6A b c + 6B b c)d e + (A c + 3B b c )d )x +--R + +--R 3 2 2 3 2 2 2 5 +--R (A b e + (6A b c + 2B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 2 3 2 4 3 2 3 +--R (2A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 82 + +--S 83 OF 765 +r0:=1/4*A*b^3*d^2*x^4+1/5*b^2*d*(b*B*d+3*A*c*d+2*A*b*e)*x^5+1/6*b*_ + (3*A*c^2*d^2+b^2*e*(2*B*d+A*e)+3*b*c*d*(B*d+2*A*e))*x^6+1/7*_ + (A*c^3*d^2+b^3*B*e^2+3*b^2*c*e*(2*B*d+A*e)+3*b*c^2*d*(B*d+2*A*e))*x^7+_ + 1/8*c*(A*c*e*(2*c*d+3*b*e)+B*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^8+_ + 1/9*c^2*e*(2*B*c*d+3*b*B*e+A*c*e)*x^9+1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R ((- A b c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 4 4 8 +--R + +--R 3 2 1 3 2 6 2 6 2 1 3 3 2 2 7 +--R ((- A b c + - B b )e + (- A b c + - B b c)d e + (- A c + - B b c )d )x +--R 7 7 7 7 7 7 +--R + +--R 1 3 2 2 1 3 1 2 1 2 2 6 +--R (- A b e + (A b c + - B b )d e + (- A b c + - B b c)d )x +--R 6 3 2 2 +--R + +--R 2 3 3 2 1 3 2 5 1 3 2 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 OF 765 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 2 3 7 +--R B c e x + ((A c + 3B b c )e + B c d)x +--R + +--R 2 2 3 2 6 +--R ((3A b c + 3B b c)e + (A c + 3B b c )d)x +--R + +--R 2 3 2 2 5 3 2 3 4 +--R ((3A b c + B b )e + (3A b c + 3B b c)d)x + (A b e + (3A b c + B b )d)x +--R + +--R 3 3 +--R A b d x +--R Type: Polynomial(Integer) +--E 85 + +--S 86 OF 765 +r0:=1/4*A*b^3*d*x^4+1/5*b^2*(b*B*d+3*A*c*d+A*b*e)*x^5+1/6*b*(3*A*c^2*d+_ + b^2*B*e+3*b*c*(B*d+A*e))*x^6+1/7*c*(A*c^2*d+3*b^2*B*e+3*b*c*(B*d+_ + A*e))*x^7+1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 2 3 2 1 3 3 2 7 +--R ((- A b c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 +--R + +--R 1 2 1 3 1 2 1 2 6 +--R ((- A b c + - B b )e + (- A b c + - B b c)d)x +--R 2 6 2 2 +--R + +--R 1 3 3 2 1 3 5 1 3 4 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 86 + +--S 87 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R Type: Polynomial(Integer) +--E 88 + +--S 89 OF 765 +r0:=1/4*A*b^3*x^4+1/5*b^2*(b*B+3*A*c)*x^5+1/2*b*c*(b*B+A*c)*x^6+_ + 1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8 +--R +--R +--R (2) +--R 1 3 8 1 3 3 2 7 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + (- A b c + - B b c)x +--R 8 7 7 2 2 +--R + +--R 3 2 1 3 5 1 3 4 +--R (- A b c + - B b )x + - A b x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 89 + +--S 90 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 OF 765 +r0:=d^2*(B*d-A*e)*(c*d-b*e)^3*x/e^7-1/2*d*(B*d-A*e)*(c*d-b*e)^3*x^2/e^6+_ + 1/3*(B*d-A*e)*(c*d-b*e)^3*x^3/e^5-1/4*(B*(c*d-b*e)^3-A*c*e*(c^2*d^2-_ + 3*b*c*d*e+3*b^2*e^2))*x^4/e^4-1/5*c*(A*c*e*(c*d-3*b*e)-B*(c^2*d^2-_ + 3*b*c*d*e+3*b^2*e^2))*x^5/e^3-1/6*c^2*(B*c*d-3*b*B*e-A*c*e)*x^6/e^2+_ + 1/7*B*c^3*x^7/e-d^3*(B*d-A*e)*(c*d-b*e)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 3 4 2 3 4 3 +--R - 420A b d e + (1260A b c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 1260A b c - 1260B b c)d e + (420A c + 1260B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((252A b c + 252B b c)e + (- 84A c - 252B b c )d e + 84B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (315A b c + 105B b )e + (- 315A b c - 315B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (105A c + 315B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 140A b e + (- 420A b c - 140B b )d e + (420A b c + 420B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 140A c - 420B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 210A b d e + (630A b c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 630A b c - 630B b c)d e + (210A c + 630B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 420A b d e + (- 1260A b c - 420B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1260A b c + 1260B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 92 + +--S 93 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 94 + +--S 95 OF 765 +r0:=d*(c*d-b*e)^2*(A*e*(5*c*d-2*b*e)-3*B*d*(2*c*d-b*e))*x/e^7+_ + 1/2*(c*d-b*e)^2*(B*d*(5*c*d-2*b*e)-A*e*(4*c*d-b*e))*x^2/e^6-_ + 1/3*(c*d-b*e)^2*(4*B*c*d-b*B*e-3*A*c*e)*x^3/e^5-1/4*c*(A*c*e*_ + (2*c*d-3*b*e)-3*B*(c*d-b*e)^2)*x^4/e^4-1/5*c^2*(2*B*c*d-3*b*B*e-_ + A*c*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*_ + (d+e*x))+d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 5 2 3 3 4 +--R 180A b d e + (- 720A b c - 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (900A b c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 180A b d e + (- 720A b c - 240B b )d e + (900A b c + 900B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 360A c - 1080B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((45A b c + 45B b c)e + (- 18A c - 54B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (60A b c + 20B b )e + (- 75A b c - 75B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (30A c + 90B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 30A b e + (- 120A b c - 40B b )d e + (150A b c + 150B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 60A c - 180B b c )d e + 70B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 90A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 450A b c - 450B b c)d e + (180A c + 540B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (540A b c + 180B b )d e +--R + +--R 2 2 4 3 3 2 5 2 3 6 +--R (- 720A b c - 720B b c)d e + (300A c + 900B b c )d e - 360B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 60A b d e + (- 180A b c - 60B b )d e + (180A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 60A c - 180B b c )d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 95 + +--S 96 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 97 + +--S 98 OF 765 +r0:=-(c*d-b*e)*(A*e*(10*c^2*d^2-8*b*c*d*e+b^2*e^2)-3*B*d*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2))*x/e^7+1/2*(c*d-b*e)*(3*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*x^2/e^6+c*(c*d-b*e)*(2*B*c*d-b*B*e-_ + A*c*e)*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*x^4/e^4+1/5*B*c^3*_ + x^5/e^3+1/2*d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*(d+e*x)^2)-d^2*_ + (c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))/(e^8*(d+e*x))+_ + 3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-_ + 8*b*c*d*e+2*b^2*e^2))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 6 2 3 2 5 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 5 2 +--R - 420B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (720A b c + 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1200A b c - 1200B b c)d e + (600A c + 1800B b c )d e +--R + +--R 3 6 +--R - 840B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((20A b c + 20B b c)e + (- 10A c - 30B b c )d e + 14B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (30A b c + 10B b )e + (- 50A b c - 50B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (25A c + 75B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 20A b e + (- 120A b c - 40B b )d e + (200A b c + 200B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 100A c - 300B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 40A b d e + (- 330A b c - 110B b )d e + (630A b c + 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 340A c - 1020B b c )d e + 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R - 40A b d e + (60A b c + 20B b )d e + (60A b c + 60B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 80A c - 240B b c )d e + 160B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 50A b d e + (210A b c + 70B b )d e + (- 270A b c - 270B b c)d e +--R + +--R 3 2 6 3 7 +--R (110A c + 330B b c )d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 98 + +--S 99 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 100 + +--S 101 OF 765 +r0:=(A*c*e*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2)-B*(20*c^3*d^3-30*b*c^2*d^2*e+_ + 12*b^2*c*d*e^2-b^3*e^3))*x/e^7-1/2*c*(A*c*e*(4*c*d-3*b*e)-_ + B*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*x^2/e^6-1/3*c^2*(4*B*c*d-_ + 3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*d^3*(B*d-A*e)*_ + (c*d-b*e)^3/(e^8*(d+e*x)^3)-1/2*d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-_ + 3*A*e*(2*c*d-b*e))/(e^8*(d+e*x)^2)-3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-8*b*c*d*e+2*b^2*e^2))/(e^8*_ + (d+e*x))+(B*d*(35*c^3*d^3-60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-_ + A*e*(20*c^3*d^3-30*b*c^2*d^2*e+12*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 3 6 2 2 2 5 +--R 12A b e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 12A b d e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 240A c - 720B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((18A b c + 18B b c)e + (- 12A c - 36B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (36A b c + 12B b )e + (- 90A b c - 90B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (60A c + 180B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 2 5 +--R (108A b c + 36B b )d e + (- 378A b c - 378B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (292A c + 876B b c )d e - 556B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 36A b d e + (- 108A b c - 36B b )d e + (- 54A b c - 54B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (156A c + 468B b c )d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R 54A b d e + (- 324A b c - 108B b )d e + (486A b c + 486B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 204A c - 612B b c )d e + 222B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 22A b d e + (- 156A b c - 52B b )d e + (282A b c + 282B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 148A c - 444B b c )d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 101 + +--S 102 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 103 + +--S 104 OF 765 +r0:=e*(A*c*e*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)+B*(4*c^3*d^3-6*b*c^2*d^2*e+_ + 4*b^2*c*d*e^2-b^3*e^3))*x/c^4+1/2*e^2*(A*c*e*(4*c*d-b*e)+B*_ + (6*c^2*d^2-4*b*c*d*e+b^2*e^2))*x^2/c^3+1/3*e^3*(4*B*c*d-b*B*e+_ + A*c*e)*x^3/c^2+1/4*B*e^4*x^4/c+A*d^4*log(x)/b+(b*B-A*c)*_ + (c*d-b*e)^4*log(b+c*x)/(b*c^5) +--R +--R +--R (2) +--R 4 5 4 3 2 4 3 +--R (- 12A b c + 12B b )e + (48A b c - 48B b c)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A b c + 72B b c )d e + (48A b c - 48B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 12B b c )d +--R * +--R log(c x + b) +--R + +--R 5 4 4 4 4 4 2 3 4 4 3 3 +--R 12A c d log(x) + 3B b c e x + ((4A b c - 4B b c )e + 16B b c d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 6A b c + 6B b c )e + (24A b c - 24B b c )d e + 36B b c d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A b c - 12B b c)e + (- 48A b c + 48B b c )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A b c - 72B b c )d e + 48B b c d e +--R * +--R x +--R / +--R 5 +--R 12b c +--R Type: Expression(Integer) +--E 104 + +--S 105 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 OF 765 +r0:=e*(A*c*e*(3*c*d-b*e)+B*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*x/c^3+_ + 1/2*e^2*(3*B*c*d-b*B*e+A*c*e)*x^2/c^2+1/3*B*e^3*x^3/c+A*d^3*_ + log(x)/b+(b*B-A*c)*(c*d-b*e)^3*log(b+c*x)/(b*c^4) +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (6A b c - 6B b )e + (- 18A b c + 18B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A b c - 18B b c )d e + (- 6A c + 6B b c )d +--R * +--R log(c x + b) +--R + +--R 4 3 3 3 3 3 2 2 3 3 2 2 +--R 6A c d log(x) + 2B b c e x + ((3A b c - 3B b c )e + 9B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 6A b c + 6B b c)e + (18A b c - 18B b c )d e + 18B b c d e)x +--R / +--R 4 +--R 6b c +--R Type: Expression(Integer) +--E 107 + +--S 108 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 109 + +--S 110 OF 765 +r0:=e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+A*d^2*log(x)/b+_ + (b*B-A*c)*(c*d-b*e)^2*log(b+c*x)/(b*c^3) +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 2B b )e + (4A b c - 4B b c)d e + (- 2A c + 2B b c )d ) +--R * +--R log(c x + b) +--R + +--R 3 2 2 2 2 2 2 2 2 +--R 2A c d log(x) + B b c e x + ((2A b c - 2B b c)e + 4B b c d e)x +--R / +--R 3 +--R 2b c +--R Type: Expression(Integer) +--E 110 + +--S 111 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 OF 765 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 112 + +--S 113 OF 765 +r0:=B*e*x/c+A*d*log(x)/b+(b*B-A*c)*(c*d-b*e)*log(b+c*x)/(b*c^2) +--R +--R +--R (2) +--R 2 2 2 +--R ((A b c - B b )e + (- A c + B b c)d)log(c x + b) + A c d log(x) + B b c e x +--R ---------------------------------------------------------------------------- +--R 2 +--R b c +--R Type: Expression(Integer) +--E 113 + +--S 114 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 OF 765 +t0:=(A+B*x)/(b*x+c*x^2) +--R +--R +--R B x + A +--R (1) ---------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 OF 765 +r0:=A*log(x)/b+(b*B-A*c)*log(b+c*x)/(b*c) +--R +--R +--R (- A c + B b)log(c x + b) + A c log(x) +--R (2) -------------------------------------- +--R b c +--R Type: Expression(Integer) +--E 116 + +--S 117 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 OF 765 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R 3 2 +--R c e x + (b e + c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 OF 765 +r0:=A*log(x)/(b*d)+(b*B-A*c)*log(b+c*x)/(b*(c*d-b*e))-_ + (B*d-A*e)*log(d+e*x)/(d*(c*d-b*e)) +--R +--R +--R (2) +--R (- A b e + B b d)log(e x + d) + (A c - B b)d log(c x + b) +--R + +--R (A b e - A c d)log(x) +--R / +--R 2 2 +--R b d e - b c d +--R Type: Expression(Integer) +--E 119 + +--S 120 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------ +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 OF 765 +r0:=(B*d-A*e)/(d*(c*d-b*e)*(d+e*x))+A*log(x)/(b*d^2)+c*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^2)-(B*c*d^2-A*e*(2*c*d-b*e))*log(d+e*x)/_ + (d^2*(c*d-b*e)^2) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R (- A b e + 2A b c d e - B b c d e)x - A b d e + 2A b c d e +--R + +--R 3 +--R - B b c d +--R * +--R log(e x + d) +--R + +--R 2 2 2 3 +--R ((- A c + B b c)d e x + (- A c + B b c)d )log(c x + b) +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((A b e - 2A b c d e + A c d e)x + A b d e - 2A b c d e + A c d ) +--R * +--R log(x) +--R + +--R 2 2 2 2 3 +--R A b d e + (- A b c - B b )d e + B b c d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d +--R Type: Expression(Integer) +--E 122 + +--S 123 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 OF 765 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R Type: Fraction(Polynomial(Integer)) +--E 124 + +--S 125 OF 765 +r0:=1/2*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^2)+(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x))+A*log(x)/(b*d^3)+c^2*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^3)-(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+_ + b^2*e^2))*log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (- 2A b e + 6A b c d e - 6A b c d e + 2B b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 2 4 3 2 3 +--R (- 4A b d e + 12A b c d e - 12A b c d e + 4B b c d e)x - 2A b d e +--R + +--R 2 3 2 2 4 2 5 +--R 6A b c d e - 6A b c d e + 2B b c d +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 3 2 4 +--R (2A c - 2B b c )d e x + (4A c - 4B b c )d e x +--R + +--R 3 2 5 +--R (2A c - 2B b c )d +--R * +--R log(c x + b) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2A b e - 6A b c d e + 6A b c d e - 2A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (4A b d e - 12A b c d e + 12A b c d e - 4A c d e)x + 2A b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 6A b c d e + 6A b c d e - 2A c d +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 2 3 2 2 4 +--R (2A b d e - 6A b c d e + (4A b c + 2B b c)d e - 2B b c d e)x +--R + +--R 3 2 3 2 3 3 2 2 2 4 2 5 +--R 3A b d e + (- 8A b c - B b )d e + (5A b c + 4B b c)d e - 3B b c d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e)x + 2b d e - 6b c d e +--R + +--R 2 2 7 3 8 +--R 6b c d e - 2b c d +--R Type: Expression(Integer) +--E 125 + +--S 126 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 OF 765 +t0:=(A+B*x)/((d+e*x)^4*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 6 4 3 5 3 2 2 4 +--R c e x + (b e + 4c d e )x + (4b d e + 6c d e )x +--R + +--R 2 2 3 3 3 4 2 4 +--R (6b d e + 4c d e)x + (4b d e + c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 127 + +--S 128 OF 765 +r0:=1/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^3)+1/2*(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x)^2)+(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+_ + b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x))+A*log(x)/(b*d^4)+c^3*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^4)-(B*c^3*d^4-A*e*(4*c^3*d^3-_ + 6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 6A b e + 24A b c d e - 36A b c d e + 24A b c d e +--R + +--R 3 4 3 +--R - 6B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R - 18A b d e + 72A b c d e - 108A b c d e + 72A b c d e +--R + +--R 3 5 2 +--R - 18B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R - 18A b d e + 72A b c d e - 108A b c d e + 72A b c d e +--R + +--R 3 6 +--R - 18B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 3 7 +--R - 6A b d e + 24A b c d e - 36A b c d e + 24A b c d e - 6B b c d +--R * +--R log(e x + d) +--R + +--R 4 3 4 3 3 4 3 5 2 2 +--R (- 6A c + 6B b c )d e x + (- 18A c + 18B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (- 18A c + 18B b c )d e x + (- 6A c + 6B b c )d +--R * +--R log(c x + b) +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (6A b e - 24A b c d e + 36A b c d e - 24A b c d e + 6A c d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R 18A b d e - 72A b c d e + 108A b c d e - 72A b c d e +--R + +--R 4 5 2 +--R 18A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R 18A b d e - 72A b c d e + 108A b c d e - 72A b c d e +--R + +--R 4 6 +--R 18A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 6A b d e - 24A b c d e + 36A b c d e - 24A b c d e + 6A c d +--R * +--R log(x) +--R + +--R 4 6 3 2 5 2 2 3 4 3 2 2 4 3 +--R 6A b d e - 24A b c d e + 36A b c d e + (- 18A b c - 6B b c )d e +--R + +--R 3 5 2 +--R 6B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 15A b d e - 60A b c d e + (87A b c + 3B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 42A b c - 18B b c )d e + 15B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 2 2 3 5 2 +--R 11A b d e + (- 42A b c - 2B b )d e + (57A b c + 9B b c)d e +--R + +--R 3 2 2 6 3 7 +--R (- 26A b c - 18B b c )d e + 11B b c d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (6b d e - 24b c d e + 36b c d e - 24b c d e + 6b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 4 9 2 2 +--R (18b d e - 72b c d e + 108b c d e - 72b c d e + 18b c d e )x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 4 10 +--R (18b d e - 72b c d e + 108b c d e - 72b c d e + 18b c d e)x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 6b d e - 24b c d e + 36b c d e - 24b c d e + 6b c d +--R Type: Expression(Integer) +--E 128 + +--S 129 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 130 + +--S 131 OF 765 +r0:=-A*d^4/(b^2*x)+e^3*(4*B*c*d-2*b*B*e+A*c*e)*x/c^3+1/2*B*e^4*x^2/c^2+_ + (b*B-A*c)*(c*d-b*e)^4/(b^2*c^4*(b+c*x))+d^3*(b*B*d-2*A*c*d+_ + 4*A*b*e)*log(x)/b^3+(c*d-b*e)^3*(2*A*c^2*d-3*b^2*B*e-b*c*(B*d-_ + 2*A*e))*log(b+c*x)/(b^3*c^4) +--R +--R +--R (2) +--R 4 2 5 4 3 3 4 2 3 3 3 2 2 +--R (- 4A b c + 6B b c)e + (8A b c - 16B b c )d e + 12B b c d e +--R + +--R 5 3 6 5 4 +--R - 8A b c d e + (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 4 2 2 2 +--R (- 4A b c + 6B b )e + (8A b c - 16B b c)d e + 12B b c d e +--R + +--R 2 4 3 5 2 4 4 +--R - 8A b c d e + (4A b c - 2B b c )d +--R * +--R x +--R * +--R log(c x + b) +--R + +--R 5 3 6 5 4 2 +--R (8A b c d e + (- 4A c + 2B b c )d )x +--R + +--R 2 4 3 5 2 4 4 +--R (8A b c d e + (- 4A b c + 2B b c )d )x +--R * +--R log(x) +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 3 3 +--R B b c e x + ((2A b c - 3B b c )e + 8B b c d e )x +--R + +--R 4 2 5 4 4 2 3 2 +--R ((2A b c - 4B b c)e + 8B b c d e )x +--R + +--R 5 6 4 4 2 5 3 +--R (- 2A b c + 2B b )e + (8A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 12A b c + 12B b c )d e + (8A b c - 8B b c )d e +--R + +--R 5 2 4 4 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 4 4 +--R - 2A b c d +--R / +--R 3 5 2 4 4 +--R 2b c x + 2b c x +--R Type: Expression(Integer) +--E 131 + +--S 132 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 133 + +--S 134 OF 765 +r0:=-A*d^3/(b^2*x)+B*e^3*x/c^2+(b*B-A*c)*(c*d-b*e)^3/(b^2*c^3*(b+c*x))+_ + d^2*(b*B*d-2*A*c*d+3*A*b*e)*log(x)/b^3-(c*d-b*e)^2*(b*B*c*d-_ + 2*A*c^2*d+2*b^2*B*e-A*b*c*e)*log(b+c*x)/(b^3*c^3) +--R +--R +--R (2) +--R 3 2 4 3 3 2 2 4 2 +--R (A b c - 2B b c)e + 3B b c d e - 3A b c d e +--R + +--R 5 4 3 +--R (2A c - B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 2 3 2 4 2 3 3 +--R ((A b c - 2B b )e + 3B b c d e - 3A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 4 2 5 4 3 2 +--R (3A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (3A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 3 3 4 3 2 +--R B b c e x + B b c e x +--R + +--R 4 5 3 3 2 4 2 2 3 3 2 2 +--R (A b c - B b )e + (- 3A b c + 3B b c)d e + (3A b c - 3B b c )d e +--R + +--R 4 2 3 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - A b c d +--R / +--R 3 4 2 4 3 +--R b c x + b c x +--R Type: Expression(Integer) +--E 134 + +--S 135 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 OF 765 +r0:=-A*d^2/(b^2*x)+(b*B-A*c)*(c*d-b*e)^2/(b^2*c^2*(b+c*x))+d*_ + (b*B*d-2*A*c*d+2*A*b*e)*log(x)/b^3-(c*d-b*e)*(b*B*c*d-2*A*c^2*d+_ + b^2*B*e)*log(b+c*x)/(b^3*c^2) +--R +--R +--R (2) +--R 3 2 3 4 3 2 2 +--R (B b c e - 2A b c d e + (2A c - B b c )d )x +--R + +--R 4 2 2 2 3 2 2 2 +--R (B b e - 2A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 4 3 2 2 +--R (2A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (2A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((- A b c + B b )e + (2A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 2 2 2 +--R - A b c d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R Type: Expression(Integer) +--E 137 + +--S 138 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 OF 765 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 139 + +--S 140 OF 765 +r0:=-A*d/(b^2*x)+(b*B-A*c)*(c*d-b*e)/(b^2*c*(b+c*x))+(b*B*d-2*A*c*d+A*b*e)*_ + log(x)/b^3-(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^3 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((- A b c e + (2A c - B b c )d)x + (- A b c e + (2A b c - B b c)d)x) +--R * +--R log(c x + b) +--R + +--R 2 3 2 2 2 2 2 +--R ((A b c e + (- 2A c + B b c )d)x + (A b c e + (- 2A b c + B b c)d)x) +--R * +--R log(x) +--R + +--R 2 3 2 2 2 +--R ((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R Type: Expression(Integer) +--E 140 + +--S 141 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 OF 765 +t0:=(A+B*x)/(b*x+c*x^2)^2 +--R +--R +--R B x + A +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 142 + +--S 143 OF 765 +r0:=-A/(b^2*x)+(b*B-A*c)/(b^2*(b+c*x))+(b*B-2*A*c)*log(x)/b^3-(b*B-2*A*c)*_ + log(b+c*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R ((2A c - B b c)x + (2A b c - B b )x)log(c x + b) +--R + +--R 2 2 2 2 +--R ((- 2A c + B b c)x + (- 2A b c + B b )x)log(x) + (- 2A b c + B b )x +--R + +--R 2 +--R - A b +--R / +--R 3 2 4 +--R b c x + b x +--R Type: Expression(Integer) +--E 143 + +--S 144 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 OF 765 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +--R c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 145 + +--S 146 OF 765 +r0:=-A/(b^2*d*x)+c*(b*B-A*c)/(b^2*(c*d-b*e)*(b+c*x))+(b*B*d-2*A*c*d-A*b*e)*_ + log(x)/(b^3*d^2)+c*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+3*A*e))*log(b+c*x)/_ + (b^3*(c*d-b*e)^2)-e^2*(B*d-A*e)*log(d+e*x)/(d^2*(c*d-b*e)^2) +--R +--R +--R (2) +--R 3 3 3 2 2 4 3 4 2 +--R ((A b c e - B b c d e )x + (A b e - B b d e )x)log(e x + d) +--R + +--R 3 2 2 2 4 3 3 2 +--R ((- 3A b c + 2B b c )d e + (2A c - B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((- 3A b c + 2B b c)d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 3 3 2 3 2 2 2 +--R - A b c e + B b c d e + (3A b c - 2B b c )d e +--R + +--R 4 3 3 +--R (- 2A c + B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 2 2 3 2 3 2 2 3 +--R (- A b e + B b d e + (3A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 2 2 3 +--R (- A b c d e + (3A b c - B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R (b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x +--R Type: Expression(Integer) +--E 146 + +--S 147 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 148 + +--S 149 OF 765 +r0:=-A/(b^2*d^2*x)+c^2*(b*B-A*c)/(b^2*(c*d-b*e)^2*(b+c*x))+e^2*(B*d-A*e)/_ + (d^2*(c*d-b*e)^2*(d+e*x))+(b*B*d-2*A*c*d-2*A*b*e)*log(x)/(b^3*d^3)+_ + c^2*(2*A*c^2*d+3*b^2*B*e-b*c*(B*d+4*A*e))*log(b+c*x)/(b^3*_ + (c*d-b*e)^3)+e^2*(2*A*e*(2*c*d-b*e)-B*d*(3*c*d-b*e))*log(d+e*x)/_ + (d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 4 5 3 2 4 4 3 2 2 3 3 +--R (2A b c e + (- 4A b c - B b c)d e + 3B b c d e )x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 2A b e + (- 2A b c - B b )d e + (- 4A b c + 2B b c)d e +--R + +--R 3 2 3 2 +--R 3B b c d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R (2A b d e + (- 4A b c - B b )d e + 3B b c d e )x +--R * +--R log(e x + d) +--R + +--R 4 2 3 3 2 5 4 4 3 +--R ((4A b c - 3B b c )d e + (- 2A c + B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (4A b c - 3B b c )d e + (2A b c - 2B b c )d e +--R + +--R 5 4 5 +--R (- 2A c + B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((4A b c - 3B b c )d e + (- 2A b c + B b c )d )x +--R * +--R log(c x + b) +--R + +--R 4 5 3 2 4 4 3 2 2 3 +--R - 2A b c e + (4A b c + B b c)d e - 3B b c d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 4A b c + 3B b c )d e + (2A c - B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 2A b e + (2A b c + B b )d e + (4A b c - 2B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R - 4A b c d e + (- 2A b c + 2B b c )d e + (2A c - B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R - 2A b d e + (4A b c + B b )d e - 3B b c d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (- 4A b c + 3B b c )d e + (2A b c - B b c )d +--R * +--R x +--R * +--R log(x) +--R + +--R 4 4 3 2 4 2 3 2 3 3 2 +--R - 2A b c d e + (4A b c + B b c)d e - 4A b c d e +--R + +--R 4 2 3 4 +--R (2A b c - B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R - 2A b d e + (3A b c + B b )d e - B b c d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (- 3A b c + B b c )d e + (2A b c - B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - A b d e + 3A b c d e - 3A b c d e + A b c d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (b c d e - 3b c d e + 3b c d e - b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (b d e - 2b c d e + 2b c d e - b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (b d e - 3b c d e + 3b c d e - b c d )x +--R Type: Expression(Integer) +--E 149 + +--S 150 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 OF 765 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 OF 765 +r0:=-A/(b^2*d^3*x)+c^3*(b*B-A*c)/(b^2*(c*d-b*e)^3*(b+c*x))+1/2*e^2*_ + (B*d-A*e)/(d^2*(c*d-b*e)^2*(d+e*x)^2)-e^2*(2*A*e*(2*c*d-b*e)-B*d*_ + (3*c*d-b*e))/(d^3*(c*d-b*e)^3*(d+e*x))+(b*B*d-2*A*c*d-3*A*b*e)*_ + log(x)/(b^3*d^4)+c^3*(2*A*c^2*d+4*b^2*B*e-b*c*(B*d+5*A*e))*log(b+_ + c*x)/(b^3*(c*d-b*e)^4)-e^2*(B*d*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)-_ + A*e*(10*c^2*d^2-10*b*c*d*e+3*b^2*e^2))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 5 7 4 2 5 6 3 3 4 2 2 5 +--R 6A b c e + (- 20A b c - 2B b c)d e + (20A b c + 8B b c )d e +--R + +--R 3 3 3 4 +--R - 12B b c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R 6A b e + (- 8A b c - 2B b )d e + (- 20A b c + 4B b c)d e +--R + +--R 3 3 4 2 3 4 3 3 4 3 +--R (40A b c + 4B b c )d e - 24B b c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R 12A b d e + (- 34A b c - 4B b )d e + (20A b c + 14B b c)d e +--R + +--R 3 3 4 2 4 3 3 3 5 2 +--R (20A b c - 16B b c )d e - 12B b c d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R 6A b d e + (- 20A b c - 2B b )d e + (20A b c + 8B b c)d e +--R + +--R 4 2 5 2 +--R - 12B b c d e +--R * +--R x +--R * +--R log(e x + d) +--R + +--R 5 2 4 4 3 6 5 5 2 4 +--R ((- 10A b c + 8B b c )d e + (4A c - 2B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 10A b c + 8B b c )d e + (- 16A b c + 14B b c )d e +--R + +--R 6 5 6 +--R (8A c - 4B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 20A b c + 16B b c )d e + (- 2A b c + 4B b c )d e +--R + +--R 6 5 7 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((- 10A b c + 8B b c )d e + (4A b c - 2B b c )d )x +--R * +--R log(c x + b) +--R + +--R 5 7 4 2 5 6 +--R - 6A b c e + (20A b c + 2B b c)d e +--R + +--R 3 3 4 2 2 5 3 3 3 4 +--R (- 20A b c - 8B b c )d e + 12B b c d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (10A b c - 8B b c )d e + (- 4A c + 2B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 6A b e + (8A b c + 2B b )d e + (20A b c - 4B b c)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (- 40A b c - 4B b c )d e + (10A b c + 16B b c )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (16A b c - 14B b c )d e + (- 8A c + 4B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R - 12A b d e + (34A b c + 4B b )d e + (- 20A b c - 14B b c)d e +--R + +--R 3 3 4 2 4 3 2 4 3 3 5 2 +--R (- 20A b c + 16B b c )d e + (20A b c - 4B b c )d e +--R + +--R 5 2 4 6 6 5 7 +--R (2A b c - 4B b c )d e + (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R - 6A b d e + (20A b c + 2B b )d e + (- 20A b c - 8B b c)d e +--R + +--R 4 2 5 2 2 4 3 3 6 5 2 4 7 +--R 12B b c d e + (10A b c - 8B b c )d e + (- 4A b c + 2B b c )d +--R * +--R x +--R * +--R log(x) +--R + +--R 5 6 4 2 5 2 5 3 3 4 2 3 4 +--R - 6A b c d e + (20A b c + 2B b c)d e + (- 20A b c - 8B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (10A b c + 4B b c )d e + (- 4A b c + 2B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R - 6A b d e + (11A b c + 2B b )d e + (10A b c - 5B b c)d e +--R + +--R 3 3 4 2 4 3 2 4 3 3 5 2 +--R (- 25A b c - 4B b c )d e + (18A b c + 3B b c )d e +--R + +--R 5 2 4 6 +--R (- 8A b c + 4B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R - 9A b d e + (28A b c + 3B b )d e + (- 25A b c - 10B b c)d e +--R + +--R 3 3 4 2 5 2 2 4 3 3 6 +--R (4A b c + 7B b c )d e + (6A b c - 2B b c )d e +--R + +--R 5 2 4 7 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 2A b d e + 8A b c d e - 12A b c d e + 8A b c d e - 2A b c d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (2b c d e - 8b c d e + 12b c d e - 8b c d e + 2b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3 +--R (2b d e - 4b c d e - 4b c d e + 16b c d e - 14b c d e + 4b c d e)x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2 +--R (4b d e - 14b c d e + 16b c d e - 4b c d e - 4b c d e + 2b c d )x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )x +--R Type: Expression(Integer) +--E 152 + +--S 153 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 OF 765 +t0:=(A+B*x)*(d+e*x)^5/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 154 + +--S 155 OF 765 +r0:=-1/2*A*d^5/(b^3*x^2)-d^4*(b*B*d-3*A*c*d+5*A*b*e)/(b^4*x)+B*e^5*x/c^3-_ + 1/2*(b*B-A*c)*(c*d-b*e)^5/(b^3*c^4*(b+c*x)^2)-(c*d-b*e)^4*(2*b*B*c*d-_ + 3*A*c^2*d+3*b^2*B*e-2*A*b*c*e)/(b^4*c^4*(b+c*x))+d^3*(6*A*c^2*d^2+_ + 5*b^2*e*(B*d+2*A*e)-3*b*c*d*(B*d+5*A*e))*log(x)/b^5-(c*d-b*e)^3*_ + (6*A*c^3*d^2-3*b^3*B*e^2-3*b*c^2*d*(B*d-A*e)-b^2*c*e*(4*B*d-A*e))*_ + log(b+c*x)/(b^5*c^4) +--R +--R +--R (2) +--R 5 3 6 2 5 5 3 4 2 6 3 2 +--R (2A b c - 6B b c )e + 10B b c d e - 20A b c d e +--R + +--R 7 2 6 4 8 7 5 +--R (30A b c - 10B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 2 7 5 6 2 4 3 5 3 2 +--R (4A b c - 12B b c)e + 20B b c d e - 40A b c d e +--R + +--R 2 6 3 5 4 7 2 6 5 +--R (60A b c - 20B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 7 4 4 4 3 2 +--R (2A b c - 6B b )e + 10B b c d e - 20A b c d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (30A b c - 10B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 6 3 2 7 2 6 4 8 7 5 4 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 5 3 2 2 6 3 5 4 +--R 40A b c d e + (- 60A b c + 20B b c )d e +--R + +--R 7 2 6 5 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 3 2 3 5 4 4 4 2 6 3 5 5 2 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 5 5 6 2 5 4 +--R 2B b c e x + 4B b c e x +--R + +--R 6 2 7 5 5 3 6 2 4 5 3 2 3 +--R (4A b c - 4B b c)e + (- 10A b c + 20B b c )d e - 20B b c d e +--R + +--R 3 5 3 2 2 6 3 5 4 7 2 6 5 +--R 20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 6 2 7 4 +--R (3A b c - 5B b )e + (- 5A b c + 15B b c)d e +--R + +--R 5 3 6 2 2 3 4 4 5 3 3 2 +--R (- 10A b c - 10B b c )d e + (30A b c - 10B b c )d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (- 45A b c + 15B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 5 4 4 5 4 4 5 +--R (- 10A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 6 4 6 5 3 7 4 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 155 + +--S 156 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 157 + +--S 158 OF 765 +r0:=-1/2*A*d^4/(b^3*x^2)-d^3*(b*B*d-3*A*c*d+4*A*b*e)/(b^4*x)-1/2*(b*B-_ + A*c)*(c*d-b*e)^4/(b^3*c^3*(b+c*x)^2)+(c*d-b*e)^3*(3*A*c^2*d-2*b^2*_ + B*e-b*c*(2*B*d-A*e))/(b^4*c^3*(b+c*x))+d^2*(6*A*c^2*d^2+2*b^2*e*_ + (2*B*d+3*A*e)-3*b*c*d*(B*d+4*A*e))*log(x)/b^5+(c*d-b*e)^2*(3*b*B*_ + c^2*d^2-6*A*c^3*d^2+2*b^2*B*c*d*e+b^3*B*e^2)*log(b+c*x)/(b^5*c^3) +--R +--R +--R (2) +--R 5 2 4 2 5 2 2 6 2 5 3 +--R 2B b c e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 7 6 4 +--R (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 4 3 4 2 2 2 5 3 4 3 +--R 4B b c e - 24A b c d e + (48A b c - 16B b c )d e +--R + +--R 6 2 5 4 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 4 4 3 2 2 3 4 4 3 3 +--R 2B b e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 2 5 3 4 4 +--R (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 5 2 2 6 2 5 3 7 6 4 4 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 4 2 2 2 5 3 4 3 +--R 24A b c d e + (- 48A b c + 16B b c )d e +--R + +--R 6 2 5 4 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 2 3 4 4 3 3 2 5 3 4 4 2 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 2 6 4 5 2 3 3 4 2 2 +--R (- 2A b c + 4B b c)e - 8B b c d e + 12A b c d e +--R + +--R 2 5 3 4 3 6 2 5 4 +--R (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- A b c + 3B b )e + (- 4A b c - 4B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (18A b c - 6B b c )d e + (- 36A b c + 12B b c )d e +--R + +--R 2 5 3 4 4 +--R (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 3 4 4 3 4 +--R (- 8A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 5 4 6 4 3 7 3 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 158 + +--S 159 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 OF 765 +r0:=-1/2*A*d^3/(b^3*x^2)-d^2*(b*B*d-3*A*c*d+3*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)^3/(b^3*c^2*(b+c*x)^2)-(c*d-b*e)^2*(2*b*B*c*d-3*A*c^2*d+_ + b^2*B*e)/(b^4*c^2*(b+c*x))-3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*_ + log(x)/b^5+3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 12A b c d e + (36A b c - 12B b c )d e +--R + +--R 5 2 4 3 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R 12A b c d e + (- 36A b c + 12B b c )d e +--R + +--R 5 2 4 3 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 3 3 2 2 4 3 3 2 +--R - 2B b c e + 6A b c d e + (- 18A b c + 6B b c )d e +--R + +--R 5 2 4 3 +--R (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - B b )e + (9A b c - 3B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 27A b c + 9B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 6A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 161 + +--S 162 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 OF 765 +r0:=-1/2*A*d^2/(b^3*x^2)-d*(b*B*d-3*A*c*d+2*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)^2/(b^3*c*(b+c*x)^2)-(c*d-b*e)*(2*b*B*d-3*A*c*d+A*b*e)/_ + (b^4*(b+c*x))+(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*_ + log(x)/b^5-(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*_ + log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 3 2 4 2 3 5 4 2 4 +--R (- 2A b c e + (12A b c - 4B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- 4A b c e + (24A b c - 8B b c )d e + (- 24A b c + 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 2A b c e + (12A b c - 4B b c)d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (4A b c e + (- 24A b c + 8B b c )d e + (24A b c - 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (2A b c e + (- 12A b c + 4B b c)d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A b c - 6B b c )d )x +--R + +--R 4 5 2 3 2 4 2 3 3 2 2 2 +--R ((3A b c - B b )e + (- 18A b c + 6B b c)d e + (18A b c - 9B b c )d )x +--R + +--R 4 3 2 4 2 4 2 +--R (- 4A b c d e + (4A b c - 2B b c)d )x - A b c d +--R / +--R 5 3 4 6 2 3 7 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 164 + +--S 165 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 OF 765 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^3 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 OF 765 +r0:=-1/2*A*d/(b^3*x^2)+(-b*B*d+3*A*c*d-A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)/(b^3*(b+c*x)^2)+(3*A*c^2*d+b^2*B*e-2*b*c*(B*d+A*e))/_ + (b^4*(b+c*x))+(6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(x)/b^5-_ + (6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 3 2 2 4 3 4 +--R ((6A b c - 2B b c )e + (- 12A c + 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((12A b c - 4B b c)e + (- 24A b c + 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((6A b c - 2B b )e + (- 12A b c + 6B b c)d)x +--R * +--R log(c x + b) +--R + +--R 3 2 2 4 3 4 +--R ((- 6A b c + 2B b c )e + (12A c - 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 4B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 6A b c + 2B b )e + (12A b c - 6B b c)d)x +--R * +--R log(x) +--R + +--R 2 2 3 3 2 2 3 +--R ((- 6A b c + 2B b c)e + (12A b c - 6B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 9A b c + 3B b )e + (18A b c - 9B b c)d)x +--R + +--R 4 3 4 4 +--R (- 2A b e + (4A b c - 2B b )d)x - A b d +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 167 + +--S 168 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 OF 765 +t0:=(A+B*x)/(b*x+c*x^2)^3 +--R +--R +--R B x + A +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 169 + +--S 170 OF 765 +r0:=-1/2*A/(b^3*x^2)+(-b*B+3*A*c)/(b^4*x)-1/2*c*(b*B-A*c)/(b^3*(b+c*x)^2)-_ + c*(2*b*B-3*A*c)/(b^4*(b+c*x))-3*c*(b*B-2*A*c)*log(x)/b^5+3*c*(b*B-_ + 2*A*c)*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 4 3 4 3 2 2 3 +--R (- 12A c + 6B b c )x + (- 24A b c + 12B b c )x +--R + +--R 2 2 3 2 +--R (- 12A b c + 6B b c)x +--R * +--R log(c x + b) +--R + +--R 4 3 4 3 2 2 3 +--R (12A c - 6B b c )x + (24A b c - 12B b c )x +--R + +--R 2 2 3 2 +--R (12A b c - 6B b c)x +--R * +--R log(x) +--R + +--R 3 2 2 3 2 2 3 2 3 4 4 +--R (12A b c - 6B b c )x + (18A b c - 9B b c)x + (4A b c - 2B b )x - A b +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 170 + +--S 171 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 OF 765 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R --------------------------------------------------------------------------- +--R 3 7 2 3 6 2 2 5 3 2 4 3 3 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 172 + +--S 173 OF 765 +r0:=-1/2*A/(b^3*d*x^2)+(-b*B*d+3*A*c*d+A*b*e)/(b^4*d^2*x)-1/2*c^2*(b*B-_ + A*c)/(b^3*(c*d-b*e)*(b+c*x)^2)+c^2*(3*A*c^2*d+3*b^2*B*e-2*b*c*(B*d+_ + 2*A*e))/(b^4*(c*d-b*e)^2*(b+c*x))+(6*A*c^2*d^2-3*b*c*d*(B*d-A*e)-_ + b^2*e*(B*d-A*e))*log(x)/(b^5*d^3)-c^2*(6*A*c^3*d^2-6*b^3*B*e^2-_ + 3*b*c^2*d*(B*d+5*A*e)+2*b^2*c*e*(4*B*d+5*A*e))*log(b+c*x)/(b^5*(c*d-_ + b*e)^3)-e^4*(B*d-A*e)*log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 5 2 5 5 2 4 4 6 5 6 4 3 +--R (- 2A b c e + 2B b c d e )x + (- 4A b c e + 4B b c d e )x +--R + +--R 7 5 7 4 2 +--R (- 2A b e + 2B b d e )x +--R * +--R log(e x + d) +--R + +--R 2 5 3 4 3 2 6 2 5 4 +--R (20A b c - 12B b c )d e + (- 30A b c + 16B b c )d e +--R + +--R 7 6 5 +--R (12A c - 6B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 3 2 2 5 3 4 4 +--R (40A b c - 24B b c )d e + (- 60A b c + 32B b c )d e +--R + +--R 6 2 5 5 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (20A b c - 12B b c )d e + (- 30A b c + 16B b c )d e +--R + +--R 2 5 3 4 5 +--R (12A b c - 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 5 2 5 5 2 4 2 5 3 4 3 2 +--R 2A b c e - 2B b c d e + (- 20A b c + 12B b c )d e +--R + +--R 6 2 5 4 7 6 5 +--R (30A b c - 16B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 5 6 4 3 4 4 3 3 2 +--R 4A b c e - 4B b c d e + (- 40A b c + 24B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (60A b c - 32B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 7 4 4 3 5 2 3 2 +--R 2A b e - 2B b d e + (- 20A b c + 12B b c )d e +--R + +--R 3 4 4 3 4 2 5 3 4 5 +--R (30A b c - 16B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(x) +--R + +--R 5 2 4 5 2 2 3 3 4 4 3 3 2 +--R 2A b c d e - 2B b c d e + (- 20A b c + 12B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (30A b c - 16B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 2 6 2 3 4 3 5 2 3 2 +--R 4A b c d e + (- A b c - 4B b c)d e + (- 30A b c + 19B b c )d e +--R + +--R 3 4 4 3 4 2 5 3 4 5 +--R (45A b c - 24B b c )d e + (- 18A b c + 9B b c )d +--R * +--R 2 +--R x +--R + +--R 7 4 6 7 2 3 5 2 6 3 2 +--R 2A b d e + (- 2A b c - 2B b )d e + (- 6A b c + 6B b c)d e +--R + +--R 4 3 5 2 4 3 4 4 3 5 +--R (10A b c - 6B b c )d e + (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - A b d e + 3A b c d e - 3A b c d e + A b c d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (2b c d e - 6b c d e + 6b c d e - 2b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d )x +--R Type: Expression(Integer) +--E 173 + +--S 174 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 OF 765 +r0:=-1/2*A/(b^3*d^2*x^2)+(-b*B*d+3*A*c*d+2*A*b*e)/(b^4*d^3*x)-1/2*c^3*(b*B-_ + A*c)/(b^3*(c*d-b*e)^2*(b+c*x)^2)-c^3*(2*b*B*c*d-3*A*c^2*d-4*b^2*B*e+_ + 5*A*b*c*e)/(b^4*(c*d-b*e)^3*(b+c*x))+e^4*(B*d-A*e)/(d^3*(c*d-b*e)^3*_ + (d+e*x))+(6*A*c^2*d^2-b^2*e*(2*B*d-3*A*e)-3*b*c*d*(B*d-2*A*e))*_ + log(x)/(b^5*d^4)-c^3*(6*A*c^3*d^2-10*b^3*B*e^2+5*b^2*c*e*(2*B*d+_ + 3*A*e)-3*b*c^2*d*(B*d+6*A*e))*log(b+c*x)/(b^5*(c*d-b*e)^4)-e^4*_ + (B*d*(5*c*d-2*b*e)-3*A*e*(2*c*d-b*e))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 6 2 7 5 3 6 2 6 5 3 2 5 5 +--R (- 6A b c e + (12A b c + 4B b c )d e - 10B b c d e )x +--R + +--R 7 7 6 2 7 6 +--R - 12A b c e + (18A b c + 8B b c)d e +--R + +--R 5 3 6 2 2 5 5 3 3 4 +--R (12A b c - 16B b c )d e - 10B b c d e +--R * +--R 4 +--R x +--R + +--R 8 7 8 6 6 2 7 2 5 6 2 3 4 3 +--R (- 6A b e + 4B b d e + (24A b c - 2B b c)d e - 20B b c d e )x +--R + +--R 8 6 7 8 2 5 7 3 4 2 +--R (- 6A b d e + (12A b c + 4B b )d e - 10B b c d e )x +--R * +--R log(e x + d) +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 30A b c + 20B b c )d e + (36A b c - 20B b c )d e +--R + +--R 8 7 6 +--R (- 12A c + 6B b c )d e +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 60A b c + 40B b c )d e + (42A b c - 20B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (12A b c - 8B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (- 30A b c + 20B b c )d e + (- 24A b c + 20B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (60A b c - 34B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (- 30A b c + 20B b c )d e + (36A b c - 20B b c )d e +--R + +--R 2 6 3 5 7 +--R (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 6 2 7 5 3 6 2 6 5 3 2 5 +--R 6A b c e + (- 12A b c - 4B b c )d e + 10B b c d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 8 7 6 +--R (12A c - 6B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R 12A b c e + (- 18A b c - 8B b c)d e +--R + +--R 5 3 6 2 2 5 5 3 3 4 +--R (- 12A b c + 16B b c )d e + 10B b c d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (60A b c - 40B b c )d e + (- 42A b c + 20B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (- 12A b c + 8B b c )d e + (12A c - 6B b c )d +--R * +--R 4 +--R x +--R + +--R 8 7 8 6 6 2 7 2 5 6 2 3 4 +--R 6A b e - 4B b d e + (- 24A b c + 2B b c)d e + 20B b c d e +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (30A b c - 20B b c )d e + (24A b c - 20B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 60A b c + 34B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 7 3 4 +--R 6A b d e + (- 12A b c - 4B b )d e + 10B b c d e +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 2 6 3 5 7 +--R (12A b c - 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(x) +--R + +--R 6 2 6 5 3 6 2 2 5 5 3 3 4 +--R 6A b c d e + (- 12A b c - 4B b c )d e + 10B b c d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 7 2 6 6 +--R (12A b c - 6B b c )d e +--R * +--R 4 +--R x +--R + +--R 7 6 6 2 7 2 5 5 3 6 2 3 4 +--R 12A b c d e + (- 21A b c - 8B b c)d e + (- 6A b c + 18B b c )d e +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (45A b c - 25B b c )d e + (- 24A b c + 10B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 18A b c + 11B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 6 2 7 3 4 +--R 6A b d e + (- 6A b c - 4B b )d e + (- 13A b c + 6B b c)d e +--R + +--R 5 3 6 2 4 3 4 4 5 3 5 2 +--R (12A b c + 4B b c )d e + (33A b c - 25B b c )d e +--R + +--R 3 5 4 4 6 2 6 3 5 7 +--R (- 50A b c + 28B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 8 3 4 6 2 7 4 3 +--R 3A b d e + (- 8A b c - 2B b )d e + (2A b c + 8B b c)d e +--R + +--R 5 3 6 2 5 2 4 4 5 3 6 +--R (12A b c - 12B b c )d e + (- 13A b c + 8B b c )d e +--R + +--R 3 5 4 4 7 +--R (4A b c - 2B b c )d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - A b d e + 4A b c d e - 6A b c d e + 4A b c d e - A b c d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (2b c d e - 8b c d e + 12b c d e - 8b c d e + 2b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 5 6 9 4 +--R (4b c d e - 14b c d e + 16b c d e - 4b c d e - 4b c d e + 2b c d )x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 6 5 9 3 +--R (2b d e - 4b c d e - 4b c d e + 16b c d e - 14b c d e + 4b c d )x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )x +--R Type: Expression(Integer) +--E 176 + +--S 177 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 OF 765 +t0:=(A+B*x)*(d+e*x)^3*sqrt(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 178 + +--S 179 OF 765 +r0:=1/960*(4*A*c*e*(132*c^2*d^2-132*b*c*d*e+35*b^2*e^2)+B*(64*c^3*d^3-_ + 360*b*c^2*d^2*e+366*b^2*c*d*e^2-105*b^3*e^3))*(b*x+c*x^2)^(3/2)/c^4+_ + 1/20*(2*B*c*d-3*b*B*e+4*A*c*e)*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c^2+_ + 1/6*B*(d+e*x)^3*(b*x+c*x^2)^(3/2)/c-1/160*e*(d*(16*b*B*c*d-40*A*c^2*d-_ + 9*b^2*B*e+12*A*b*c*e)-(28*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-36*b*c*d*e+_ + 21*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/c^3-1/512*b^2*(128*A*c^4*d^3+_ + 21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-28*b^3*c*e^2*(3*B*d+A*e)-_ + 64*b*c^3*d^2*(B*d+3*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+_ + 1/512*b*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-_ + 28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/c^5+_ + 1/256*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-_ + 28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*x*sqrt(b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 5 6 3 4 2 5 2 +--R (420A b c - 315B b )e + (- 1800A b c + 1260B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (2880A b c - 1800B b c )d e + (- 1920A b c + 960B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 3 5 5 4 3 5 2 4 +--R 1280B c e x + ((1536A c + 128B b c )e + 4608B c d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (192A b c - 144B b c )e + (5760A c + 576B b c )d e +--R + +--R 5 2 +--R 5760B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 224A b c + 168B b c )e + (960A b c - 672B b c )d e +--R + +--R 5 4 2 5 3 +--R (7680A c + 960B b c )d e + 2560B c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (280A b c - 210B b c)e + (- 1200A b c + 840B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (1920A b c - 1200B b c )d e + (3840A c + 640B b c )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 420A b c + 315B b )e + (1800A b c - 1260B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 2880A b c + 1800B b c )d e + (1920A b c - 960B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 179 + +--S 180 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 OF 765 +t0:=(A+B*x)*(d+e*x)^2*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R 2 3 2 2 2 2 | 2 +--R (1) (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|c x + b x +--R Type: Expression(Integer) +--E 181 + +--S 182 OF 765 +r0:=1/240*(50*A*c*e*(2*c*d-b*e)+B*(32*c^2*d^2-82*b*c*d*e+35*b^2*e^2))*_ + (b*x+c*x^2)^(3/2)/c^3+1/5*B*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c-1/40*e*_ + ((3*b*B-10*A*c)*d-(4*B*c*d-7*b*B*e+10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/c^2-_ + 1/128*b^2*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-_ + 16*b*c^2*d*(B*d+2*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)+_ + 1/128*b*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*_ + d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/c^4+1/64*(32*A*c^3*d^2-7*b^3*B*e^2+_ + 10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 4 5 2 3 2 4 +--R (- 150A b c + 105B b )e + (480A b c - 300B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 480A b c + 240B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 2 4 4 3 2 4 3 +--R 384B c e x + ((480A c + 48B b c )e + 960B c d e)x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((80A b c - 56B b c )e + (1280A c + 160B b c )d e + 640B c d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 100A b c + 70B b c)e + (320A b c - 200B b c )d e +--R + +--R 4 3 2 +--R (960A c + 160B b c )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (150A b c - 105B b )e + (- 480A b c + 300B b c)d e +--R + +--R 3 2 2 2 +--R (480A b c - 240B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 1920c \|c +--R Type: Expression(Integer) +--E 182 + +--S 183 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 OF 765 +t0:=(A+B*x)*(d+e*x)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (1) (B e x + (A e + B d)x + A d)\|c x + b x +--R Type: Expression(Integer) +--E 184 + +--S 185 OF 765 +r0:=1/24*(2*B*c*d-5*b*B*e+8*A*c*e)*(b*x+c*x^2)^(3/2)/c^2+1/4*B*(d+e*x)*_ + (b*x+c*x^2)^(3/2)/c-1/64*b^2*(16*A*c^2*d+5*b^2*B*e-8*b*c*(B*d+A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/64*b*(16*A*c^2*d+5*b^2*B*e-_ + 8*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^3+1/32*(16*A*c^2*d+5*b^2*B*e-_ + 8*b*c*(B*d+A*e))*x*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 3 4 2 2 3 x\|c +--R ((24A b c - 15B b )e + (- 48A b c + 24B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 3 3 2 3 2 +--R 48B c e x + ((64A c + 8B b c )e + 64B c d)x +--R + +--R 2 2 3 2 +--R ((16A b c - 10B b c)e + (96A c + 16B b c )d)x +--R + +--R 2 3 2 2 +--R (- 24A b c + 15B b )e + (48A b c - 24B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 185 + +--S 186 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R | 2 +--R (1) (B x + A)\|c x + b x +--R Type: Expression(Integer) +--E 187 + +--S 188 OF 765 +r0:=1/3*B*(b*x+c*x^2)^(3/2)/c+1/8*b^2*(b*B-2*A*c)*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/c^(5/2)-1/8*b*(b*B-2*A*c)*sqrt(b*x+c*x^2)/c^2-_ + 1/4*(b*B-2*A*c)*x*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 2 3 x\|c +--R (- 6A b c + 3B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R 2 2 2 2 +-+ | 2 +--R (8B c x + (12A c + 2B b c)x + 6A b c - 3B b )\|c \|c x + b x +--R / +--R 2 +-+ +--R 24c \|c +--R Type: Expression(Integer) +--E 188 + +--S 189 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R e x + d +--R Type: Expression(Integer) +--E 190 + +--S 191 OF 765 +r0:=-1/4*(4*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-4*b*c*d*e-b^2*e^2))*atanh(x*_ + sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^3)-(B*d-A*e)*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*_ + sqrt(c*d-b*e)/e^3-1/4*(4*B*c*d-b*B*e-4*A*c*e-2*B*c*e*x)*sqrt(b*x+_ + c*x^2)/(c*e^2) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 2 2 x\|c +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ +--R (- 4A c e + 4B c d)\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R 2 2 +-+ | 2 +--R (2B c e x + (4A c + B b)e - 4B c d e)\|c \|c x + b x +--R / +--R 3 +-+ +--R 4c e \|c +--R Type: Expression(Integer) +--E 191 + +--S 192 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 193 + +--S 194 OF 765 +r0:=-(4*B*c*d-b*B*e-2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^3*sqrt(c))+_ + 1/2*(B*d*(4*c*d-3*b*e)-A*e*(2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^3*sqrt(d)*sqrt(c*d-b*e))+_ + (2*B*d-A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)) +--R +--R +--R (2) +--R 2 2 +--R (((4A c + 2B b)e - 8B c d e)x + (4A c + 2B b)d e - 8B c d ) +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 2 2 +--R (- A b e + (2A c + 3B b)d e - 4B c d e)x - A b d e +--R + +--R 2 3 +--R (2A c + 3B b)d e - 4B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R 2 2 +-----------+ +-+ +-+ | 2 +--R (2B e x - 2A e + 4B d e)\|- b e + c d \|c \|d \|c x + b x +--R / +--R 4 3 +-----------+ +-+ +-+ +--R (2e x + 2d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 194 + +--S 195 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 196 + +--S 197 OF 765 +r0:=1/2*(B*d-A*e)*(b*x+c*x^2)^(3/2)/(d*(c*d-b*e)*(d+e*x)^2)-1/8*(A*b^2*e^3+_ + B*d*(8*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*e^3*(c*d-b*e)^(3/2))+_ + 2*B*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^3+1/4*(A*b*e^2-B*d*_ + (4*c*d-3*b*e)-2*c*e*(B*d-A*e)*x)*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 3 +--R (16B b d e - 16B c d e )x + (32B b d e - 32B c d e)x + 16B b d e +--R + +--R 4 +--R - 16B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 4 2 3 2 3 2 2 +--R (- A b e - 3B b d e + 12B b c d e - 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (- 2A b d e - 6B b d e + 24B b c d e - 16B c d e)x - A b d e +--R + +--R 2 3 2 4 2 5 +--R - 3B b d e + 12B b c d e - 8B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 3 2 2 3 +--R (2A b e + (- 4A c - 10B b)d e + 12B c d e )x - 2A b d e +--R + +--R 2 2 3 +--R - 6B b d e + 8B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((8b d e - 8c d e )x + (16b d e - 16c d e )x + 8b d e - 8c d e ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 197 + +--S 198 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 199 + +--S 200 OF 765 +r0:=1/16*b^2*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+1/12*(B*_ + d*(4*c*d-5*b*e)+A*e*(2*c*d-b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*_ + (d+e*x)^2)+1/24*(B*d*(8*c^2*d^2-14*b*c*d*e+3*b^2*e^2)+A*e*(4*c^2*_ + d^2-4*b*c*d*e+3*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*_ + (d+e*x))-1/3*(2*B*d+A*e+3*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)^3) +--R +--R +--R (2) +--R 3 4 2 3 3 3 +--R (- 3A b e + (6A b c - 3B b )d e )x +--R + +--R 3 3 2 3 2 2 2 +--R (- 9A b d e + (18A b c - 9B b )d e )x +--R + +--R 3 2 2 2 3 3 3 3 2 3 4 +--R (- 9A b d e + (18A b c - 9B b )d e)x - 3A b d e + (6A b c - 3B b )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 2 +--R 6A b e + (- 8A b c + 6B b )d e + (8A c - 28B b c)d e +--R + +--R 2 3 +--R 16B c d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 +--R (16A b d e + (- 28A b c - 16B b )d e + (24A c + 4B b c)d )x +--R + +--R 2 2 2 3 +--R - 6A b d e + (12A b c - 6B b )d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (48b d e - 96b c d e + 48c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (144b d e - 288b c d e + 144c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (144b d e - 288b c d e + 144c d e)x + 48b d e - 96b c d e + 48c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 200 + +--S 201 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 202 + +--S 203 OF 765 +r0:=-1/128*b^2*(16*A*c^2*d^2-8*b*c*d*(B*d+2*A*e)+b^2*e*(3*B*d+5*A*e))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+1/24*(B*d*(2*c*d-3*b*e)+A*e*(2*c*d-_ + b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)^3)+1/96*(B*d*_ + (8*c^2*d^2-16*b*c*d*e+3*b^2*e^2)+A*e*(8*c^2*d^2-8*b*c*d*e+_ + 5*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*(d+e*x)^2)+_ + 1/192*(A*e*(16*c^3*d^3-24*b*c^2*d^2*e+38*b^2*c*d*e^2-15*b^3*e^3)+_ + B*d*(16*c^3*d^3-40*b*c^2*d^2*e+18*b^2*c*d*e^2-9*b^3*e^3))*_ + sqrt(b*x+c*x^2)/(d^3*e^2*(c*d-b*e)^3*(d+e*x))-1/4*(B*d+A*e+_ + 2*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)^4) +--R +--R +--R (2) +--R 4 6 3 4 5 2 2 3 2 4 4 +--R (- 15A b e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d e )x +--R + +--R 4 5 3 4 2 4 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 3 3 +--R (- 192A b c + 96B b c)d e +--R * +--R 3 +--R x +--R + +--R 4 2 4 3 4 3 3 +--R - 90A b d e + (288A b c - 54B b )d e +--R + +--R 2 2 3 4 2 +--R (- 288A b c + 144B b c)d e +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 2 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 5 +--R (- 192A b c + 96B b c)d e +--R * +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 +--R - 15A b d e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 5 2 3 4 2 2 2 3 +--R 30A b e + (- 76A b c + 18B b )d e + (48A b c - 36B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 32A c + 80B b c )d e - 32B c d e +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 3 +--R 110A b d e + (- 280A b c + 66B b )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (208A b c - 184B b c)d e + (- 128A c + 336B b c )d e - 128B c d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 3 2 +--R 146A b d e + (- 396A b c - 66B b )d e +--R + +--R 2 2 4 3 2 5 +--R (352A b c + 188B b c)d e + (- 192A c - 32B b c )d +--R * +--R x +--R + +--R 3 3 2 2 3 4 2 2 5 +--R - 30A b d e + (96A b c - 18B b )d e + (- 96A b c + 48B b c)d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (384b d e - 1152b c d e + 1152b c d e - 384c d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (2304b d e - 6912b c d e + 6912b c d e - 2304c d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e)x + 384b d e +--R + +--R 2 8 2 2 9 3 10 +--R - 1152b c d e + 1152b c d e - 384c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 203 + +--S 204 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 205 + +--S 206 OF 765 +r0:=1/192*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+_ + 2*A*e))*x*(b*x+c*x^2)^(3/2)/c^3+1/840*(98*A*c*e*(2*c*d-b*e)+B*(48*_ + c^2*d^2-146*b*c*d*e+63*b^2*e^2))*(b*x+c*x^2)^(5/2)/c^3+1/7*B*_ + (d+e*x)^2*(b*x+c*x^2)^(5/2)/c-1/84*e*((5*b*B-14*A*c)*d-(4*B*c*d-_ + 9*b*B*e+14*A*c*e)*x)*(b*x+c*x^2)^(5/2)/c^2+1/1024*b^4*(48*A*c^3*d^2-_ + 9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)-1/1024*b^3*(48*A*c^3*d^2-_ + 9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*sqrt(b*x+_ + c*x^2)/c^5+1/1536*b^2*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+_ + A*e)-24*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^4+1/384*b*_ + (48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+_ + 2*A*e))*x^2*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 6 7 2 5 2 6 +--R (1470A b c - 945B b )e + (- 5040A b c + 2940B b c)d e +--R + +--R 4 3 5 2 2 +--R (5040A b c - 2520B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 2 6 6 5 2 6 5 +--R 15360B c e x + ((17920A c + 19200B b c )e + 35840B c d e)x +--R + +--R 5 2 4 2 6 5 +--R (23296A b c + 384B b c )e + (43008A c + 46592B b c )d e +--R + +--R 6 2 +--R 21504B c d +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 2 5 2 4 +--R (672A b c - 432B b c )e + (59136A b c + 1344B b c )d e +--R + +--R 6 5 2 +--R (26880A c + 29568B b c )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 784A b c + 504B b c )e + (2688A b c - 1568B b c )d e +--R + +--R 5 2 4 2 +--R (40320A b c + 1344B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (980A b c - 630B b c)e + (- 3360A b c + 1960B b c )d e +--R + +--R 2 4 3 3 2 +--R (3360A b c - 1680B b c )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 1470A b c + 945B b )e + (5040A b c - 2940B b c)d e +--R + +--R 3 3 4 2 2 +--R (- 5040A b c + 2520B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 107520c \|c +--R Type: Expression(Integer) +--E 206 + +--S 207 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 OF 765 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 4 3 2 +--R (B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x) +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 208 + +--S 209 OF 765 +r0:=1/96*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x*(b*x+c*x^2)^(3/2)/c^2+_ + 1/60*(2*B*c*d-7*b*B*e+12*A*c*e)*(b*x+c*x^2)^(5/2)/c^2+1/6*B*(d+e*x)*_ + (b*x+c*x^2)^(5/2)/c+1/512*b^4*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+_ + A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-1/512*b^3*_ + (24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^4+_ + 1/768*b^2*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x*sqrt(b*x+_ + c*x^2)/c^3+1/192*b*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x^2*_ + sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 5 6 4 2 5 x\|c +--R ((- 180A b c + 105B b )e + (360A b c - 180B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 5 5 4 5 4 +--R 1280B c e x + ((1536A c + 1664B b c )e + 1536B c d)x +--R + +--R 4 2 3 5 4 3 +--R ((2112A b c + 48B b c )e + (1920A c + 2112B b c )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((96A b c - 56B b c )e + (2880A b c + 96B b c )d)x +--R + +--R 3 2 4 2 3 3 2 +--R ((- 120A b c + 70B b c)e + (240A b c - 120B b c )d)x +--R + +--R 4 5 3 2 4 +--R (180A b c - 105B b )e + (- 360A b c + 180B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 209 + +--S 210 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (1) (B c x + (A c + B b)x + A b x)\|c x + b x +--R Type: Expression(Integer) +--E 211 + +--S 212 OF 765 +r0:=-1/8*(b*B-2*A*c)*x*(b*x+c*x^2)^(3/2)/c+1/5*B*(b*x+c*x^2)^(5/2)/c-_ + 3/128*b^4*(b*B-2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+_ + 3/128*b^3*(b*B-2*A*c)*sqrt(b*x+c*x^2)/c^3-1/64*b^2*(b*B-2*A*c)*x*_ + sqrt(b*x+c*x^2)/c^2-1/16*b*(b*B-2*A*c)*x^2*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 4 5 x\|c +--R (30A b c - 15B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 4 4 3 3 3 2 2 2 +--R 128B c x + (160A c + 176B b c )x + (240A b c + 8B b c )x +--R + +--R 2 2 3 3 4 +--R (20A b c - 10B b c)x - 30A b c + 15B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 640c \|c +--R Type: Expression(Integer) +--E 212 + +--S 213 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 214 + +--S 215 OF 765 +r0:=-1/24*(8*B*c*d-3*b*B*e-8*A*c*e-6*B*c*e*x)*(b*x+c*x^2)^(3/2)/(c*e^2)-_ + 1/64*(8*A*c*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3)-_ + B*(128*c^4*d^4-192*b*c^3*d^3*e+48*b^2*c^2*d^2*e^2+8*b^3*c*d*e^3+_ + 3*b^4*e^4))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^5)-d^(3/2)*_ + (B*d-A*e)*(c*d-b*e)^(3/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^5+1/64*(8*A*c*e*(8*c^2*d^2-_ + 10*b*c*d*e+b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+8*b^2*c*d*e^2+_ + 3*b^3*e^3)-2*c*e*(8*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-8*b*c*d*e-_ + 3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^4) +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 +--R (- 24A b c + 9B b )e + (- 144A b c + 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (576A b c + 144B b c )d e + (- 384A c - 576B b c )d e + 384B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 2 2 3 3 +-----------+ +--R (192A b c d e + (- 192A c - 192B b c )d e + 192B c d )\|- b e + c d +--R * +--R +-+ +-+ (b e - 2c d)x - b d +--R \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 48B c e x + ((64A c + 72B b c )e - 64B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 +--R ((112A b c + 6B b c)e + (- 96A c - 112B b c )d e + 96B c d e )x +--R + +--R 2 3 4 2 2 3 +--R (24A b c - 9B b )e + (- 240A b c - 24B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (192A c + 240B b c )d e - 192B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 5 +-+ +--R 192c e \|c +--R Type: Expression(Integer) +--E 215 + +--S 216 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 217 + +--S 218 OF 765 +r0:=1/3*(4*B*d-3*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x))+1/8*(4*b*c*e*_ + (4*B*d-3*A*e)*(2*c*d-b*e)-(8*B*c*d-b*B*e-6*A*c*e)*(8*c^2*d^2-_ + 4*b*c*d*e-b^2*e^2))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^5)+_ + 1/2*(B*d*(8*c*d-5*b*e)-3*A*e*(2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-_ + b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-_ + b*e)/e^5-1/8*(6*A*c*e*(4*c*d-3*b*e)-B*(32*c^2*d^2-28*b*c*d*e+_ + b^2*e^2)+2*c*e*(8*B*c*d-b*B*e-6*A*c*e)*x)*sqrt(b*x+c*x^2)/(c*e^4) +--R +--R +--R (2) +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 2 2 2 2 +--R (- 36A b c e + (72A c + 60B b c)d e - 96B c d e)x - 36A b c d e +--R + +--R 2 2 2 3 +--R (72A c + 60B b c)d e - 96B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 4 3 2 4 2 3 2 +--R 8B c e x + ((12A c + 14B b c)e - 16B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((30A b c + 3B b )e + (- 36A c - 46B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (54A b c + 3B b )d e + (- 72A c - 84B b c)d e + 96B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 5 +-+ +--R (24c e x + 24c d e )\|c +--R Type: Expression(Integer) +--E 218 + +--S 219 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 220 + +--S 221 OF 765 +r0:=1/2*(2*B*d-A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)-3/4*(4*A*c*e*_ + (2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+b^2*e^2))*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/(e^5*sqrt(c))+3/8*(A*e*(8*c^2*d^2-8*b*c*d*e+_ + b^2*e^2)-B*d*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2))*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^5*_ + sqrt(d)*sqrt(c*d-b*e))-3/4*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+_ + e*(4*B*c*d-b*B*e-2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 +--R ((24A b c + 6B b )e + (- 48A c - 72B b c)d e + 96B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((48A b c + 12B b )d e + (- 96A c - 144B b c)d e + 192B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 2 +--R 48B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 6A b d e + (48A b c + 30B b )d e + (- 48A c - 120B b c)d e +--R + +--R 2 4 +--R 96B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 3A b d e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 5 +--R 48B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 3 4 3 2 +--R 4B c e x + ((8A c + 10B b)e - 16B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 10A b e + (36A c + 38B b)d e - 72B c d e )x - 6A b d e +--R + +--R 2 2 3 +--R (24A c + 24B b)d e - 48B c d e +--R * +--R +----------+ +--R +-----------+ +-+ +-+ | 2 +--R \|- b e + c d \|c \|d \|c x + b x +--R / +--R 7 2 6 2 5 +-----------+ +-+ +-+ +--R (8e x + 16d e x + 8d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 221 + +--S 222 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +--)clear all +--R +--S 223 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (4) --------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 223 + +--S 224 OF 765 +r0:=-1/4*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*(b*x+c*x^2)^(3/2)/(d*e^2*_ + (c*d-b*e)*(d+e*x)^2)+1/3*(4*B*d-A*e+3*B*e*x)*(b*x+c*x^2)^(3/2)/_ + (e^2*(d+e*x)^3)+1/16*(B*d*(64*c^3*d^3-120*b*c^2*d^2*e+60*b^2*c*d*e^2-_ + 5*b^3*e^3)-A*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(3/2)*e^5*(c*d-b*e)^(3/2))-(8*B*c*d-3*b*B*e-2*A*c*e)*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^5-1/8*(A*e*(8*c^2*d^2-_ + 6*b*c*d*e-b^2*e^2)-B*d*(32*c^2*d^2-36*b*c*d*e+5*b^2*e^2)-_ + 2*c*e*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*x)*sqrt(b*x+c*x^2)/_ + (d*e^4*(c*d-b*e)*(d+e*x)) +--R +--R +--R (5) +--R 2 5 2 2 4 2 3 3 3 +--R ((96A b c + 144B b )d e + (- 96A c - 528B b c)d e + 384B c d e )x +--R + +--R 2 2 4 2 3 3 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 4 2 +--R 1152B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 5 +--R 1152B c d e +--R * +--R x +--R + +--R 2 4 2 2 5 2 6 +--R (96A b c + 144B b )d e + (- 96A c - 528B b c)d e + 384B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R - 3A b e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 48A c - 360B b c )d e + 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 5 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 6 +--R 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48A c - 360B b c )d e + 192B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 2 2 4 3 +--R (48B b c d e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 6A b e + (- 88A b c - 66B b )d e + (88A c + 412B b c)d e +--R + +--R 2 3 3 +--R - 352B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 16A b d e + (- 92A b c - 80B b )d e +--R + +--R 2 3 3 2 4 2 +--R (120A c + 548B b c)d e - 480B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 6A b d e + (- 36A b c - 30B b )d e + (48A c + 216B b c)d e +--R + +--R 2 5 +--R - 192B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (48b d e - 48c d e )x + (144b d e - 144c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (144b d e - 144c d e )x + 48b d e - 48c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 224 + +--S 225 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 226 + +--S 227 OF 765 +r0:=1/32*(3*A*b^2*e^3+B*d*(16*c^2*d^2-24*b*c*d*e+5*b^2*e^2))*_ + (b*x+c*x^2)^(3/2)/(d^2*e^2*(c*d-b*e)^2*(d+e*x)^2)+1/24*(3*A*b*e^2-_ + B*d*(8*c*d-5*b*e)-6*c*e*(B*d-A*e)*x)*(b*x+c*x^2)^(3/2)/(d*e^2*_ + (c*d-b*e)*(d+e*x)^3)+1/4*(B*d-A*e)*(b*x+c*x^2)^(5/2)/(d*(c*d-b*e)*_ + (d+e*x)^4)+2*B*c^(3/2)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/e^5+_ + 1/128*(3*A*b^4*e^5-B*d*(128*c^4*d^4-320*b*c^3*d^3*e+240*b^2*c^2*_ + d^2*e^2-40*b^3*c*d*e^3-5*b^4*e^4))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*e^5*_ + (c*d-b*e)^(5/2))-1/64*(3*A*b^3*e^4+B*d*(64*c^3*d^3-112*b*c^2*_ + d^2*e+40*b^2*c*d*e^2+5*b^3*e^3)+2*c*e*(3*A*b^2*e^3+B*d*(16*c^2*_ + d^2-24*b*c*d*e+5*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d^2*e^4*_ + (c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 2 6 2 3 5 3 4 4 4 +--R (768B b c d e - 1536B b c d e + 768B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (3072B b c d e - 6144B b c d e + 3072B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (4608B b c d e - 9216B b c d e + 4608B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (3072B b c d e - 6144B b c d e + 3072B c d e)x + 768B b c d e +--R + +--R 2 7 3 8 +--R - 1536B b c d e + 768B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 9 4 8 3 2 7 2 2 3 6 +--R - 9A b e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R - 960B b c d e + 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R - 3840B b c d e + 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R - 54A b d e - 90B b d e - 720B b c d e + 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R - 5760B b c d e + 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 7 2 4 8 +--R - 3840B b c d e + 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R - 9A b d e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 8 4 9 +--R - 960B b c d e + 384B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 18A b e + (12A b c + 30B b )d e + (- 144A b c - 764B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (96A c + 1552B b c )d e - 800B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 66A b d e + (- 264A b c - 146B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (144A b c - 1096B b c)d e + 2960B b c d e - 1664B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 66A b d e + (12A b c - 110B b )d e - 860B b c d e +--R + +--R 2 5 3 3 6 2 +--R 2368B b c d e - 1344B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 3 7 +--R - 18A b d e - 30B b d e - 240B b c d e + 672B b c d e - 384B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (384b d e - 768b c d e + 384c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (1536b d e - 3072b c d e + 1536c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (2304b d e - 4608b c d e + 2304c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (1536b d e - 3072b c d e + 1536c d e )x + 384b d e - 768b c d e +--R + +--R 2 8 5 +--R 384c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 227 + +--S 228 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 229 + +--S 230 OF 765 +r0:=-1/5*(4*B*d+A*e+5*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^5)-_ + 3/256*b^4*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+_ + 1/80*(A*e*(4*c^2*d^2-4*b*c*d*e-b^2*e^2)+B*d*(16*c^2*d^2-26*b*c*d*e+_ + 11*b^2*e^2))*sqrt(b*x+c*x^2)/(d*e^4*(c*d-b*e)*(d+e*x)^3)+1/320*_ + (A*e*(16*c^3*d^3-24*b*c^2*d^2*e-2*b^2*c*d*e^2+5*b^3*e^3)+B*d*_ + (64*c^3*d^3-136*b*c^2*d^2*e+72*b^2*c*d*e^2+5*b^3*e^3))*_ + sqrt(b*x+c*x^2)/(d^2*e^4*(c*d-b*e)^2*(d+e*x)^2)+1/640*(B*d*_ + (128*c^4*d^4-336*b*c^3*d^3*e+248*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-_ + 15*b^4*e^4)+A*e*(32*c^4*d^4-64*b*c^3*d^3*e+12*b^2*c^2*d^2*e^2+_ + 20*b^3*c*d*e^3-15*b^4*e^4))*sqrt(b*x+c*x^2)/(d^3*e^4*(c*d-b*e)^3*_ + (d+e*x))-3/40*(B*d*(8*c*d-b*e)+A*e*(2*c*d+b*e)+2*e*(8*B*c*d-_ + 5*b*B*e+2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x)^4) +--R +--R +--R (2) +--R 5 6 4 5 5 5 +--R (- 15A b e + (30A b c - 15B b )d e )x +--R + +--R 5 5 4 5 2 4 4 +--R (- 75A b d e + (150A b c - 75B b )d e )x +--R + +--R 5 2 4 4 5 3 3 3 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 3 3 4 5 4 2 2 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 4 2 4 5 5 5 5 +--R (- 75A b d e + (150A b c - 75B b )d e)x - 15A b d e +--R + +--R 4 5 6 +--R (30A b c - 15B b )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 30A b e + (- 40A b c + 30B b )d e + (- 24A b c + 20B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (128A b c - 496B b c )d e + (- 64A c + 672B b c )d e - 256B c d +--R * +--R 4 +--R x +--R + +--R 4 4 3 4 2 3 +--R 140A b d e + (- 188A b c + 140B b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 184A b c - 932B b c)d e + (672A b c + 1024B b c )d e +--R + +--R 4 3 5 +--R (- 320A c - 352B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 4 3 2 +--R 256A b d e + (- 932A b c - 256B b )d e +--R + +--R 2 2 3 4 3 2 2 5 +--R (1336A b c + 92B b c)d e + (- 480A b c - 16B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 +--R (- 140A b d e + (300A b c - 140B b )d e + (- 40A b c + 20B b c)d )x +--R + +--R 4 4 3 4 5 +--R - 30A b d e + (60A b c - 30B b )d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (1280b d e - 3840b c d e + 3840b c d e - 1280c d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e)x + 1280b d e +--R + +--R 2 9 2 2 10 3 11 +--R - 3840b c d e + 3840b c d e - 1280c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 230 + +--S 231 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 232 + +--S 233 OF 765 +r0:=1/768*b*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*_ + (B*d+2*A*e))*x^2*(b*x+c*x^2)^(3/2)/c^3+1/384*(64*A*c^3*d^2-11*b^3*_ + B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*x*(b*x+_ + c*x^2)^(5/2)/c^3+1/2016*(162*A*c*e*(2*c*d-b*e)+B*(64*c^2*d^2-_ + 226*b*c*d*e+99*b^2*e^2))*(b*x+c*x^2)^(7/2)/c^3+1/9*B*(d+e*x)^2*_ + (b*x+c*x^2)^(7/2)/c-1/144*e*((7*b*B-18*A*c)*d-(4*B*c*d-11*b*B*e+_ + 18*A*c*e)*x)*(b*x+c*x^2)^(7/2)/c^2-5/32768*b^6*(64*A*c^3*d^2-_ + 11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(13/2)+5/32768*b^5*(64*A*c^3*_ + d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*_ + sqrt(b*x+c*x^2)/c^6-5/49152*b^4*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*_ + c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^5+_ + 1/12288*b^3*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-_ + 32*b*c^2*d*(B*d+2*A*e))*x^2*sqrt(b*x+c*x^2)/c^4+1/2048*b^2*_ + (64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*_ + (B*d+2*A*e))*x^3*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 8 9 2 7 2 8 +--R (- 5670A b c + 3465B b )e + (20160A b c - 11340B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 20160A b c + 10080B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 8 2 8 8 7 2 8 7 +--R 229376B c e x + ((258048A c + 530432B b c )e + 516096B c d e)x +--R + +--R 7 2 6 2 8 7 +--R (608256A b c + 316416B b c )e + (589824A c + 1216512B b c )d e +--R + +--R 8 2 +--R 294912B c d +--R * +--R 6 +--R x +--R + +--R 2 6 3 5 2 7 2 6 +--R (373248A b c + 1280B b c )e + (1425408A b c + 746496B b c )d e +--R + +--R 8 7 2 +--R (344064A c + 712704B b c )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (2304A b c - 1408B b c )e + (909312A b c + 4608B b c )d e +--R + +--R 7 2 6 2 +--R (860160A b c + 454656B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (- 2592A b c + 1584B b c )e + (9216A b c - 5184B b c )d e +--R + +--R 2 6 3 5 2 +--R (580608A b c + 4608B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (3024A b c - 1848B b c )e + (- 10752A b c + 6048B b c )d e +--R + +--R 3 5 4 4 2 +--R (10752A b c - 5376B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 3780A b c + 2310B b c)e + (13440A b c - 7560B b c )d e +--R + +--R 4 4 5 3 2 +--R (- 13440A b c + 6720B b c )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 +--R (5670A b c - 3465B b )e + (- 20160A b c + 11340B b c)d e +--R + +--R 5 3 6 2 2 +--R (20160A b c - 10080B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 +-+ +--R 2064384c \|c +--R Type: Expression(Integer) +--E 233 + +--S 234 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 OF 765 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 235 + +--S 236 OF 765 +r0:=1/384*b*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^2*_ + (b*x+c*x^2)^(3/2)/c^2+1/192*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*_ + x*(b*x+c*x^2)^(5/2)/c^2+1/112*(2*B*c*d-9*b*B*e+16*A*c*e)*_ + (b*x+c*x^2)^(7/2)/c^2+1/8*B*(d+e*x)*(b*x+c*x^2)^(7/2)/c-_ + 5/16384*b^6*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*atanh(x*_ + sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+5/16384*b^5*(32*A*c^2*d+9*b^2*B*e-_ + 16*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^5-5/24576*b^4*(32*A*c^2*d+_ + 9*b^2*B*e-16*b*c*(B*d+A*e))*x*sqrt(b*x+c*x^2)/c^4+1/6144*b^3*_ + (32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^2*sqrt(b*x+c*x^2)/c^3+_ + 1/1024*b^2*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^3*_ + sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 7 8 6 2 7 +--R ((1680A b c - 945B b )e + (- 3360A b c + 1680B b c)d) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 7 7 7 6 7 6 +--R 43008B c e x + ((49152A c + 101376B b c )e + 49152B c d)x +--R + +--R 6 2 5 7 6 5 +--R ((118784A b c + 62208B b c )e + (57344A c + 118784B b c )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((75776A b c + 384B b c )e + (143360A b c + 75776B b c )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((768A b c - 432B b c )e + (96768A b c + 768B b c )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((- 896A b c + 504B b c )e + (1792A b c - 896B b c )d)x +--R + +--R 5 2 6 4 3 5 2 +--R ((1120A b c - 630B b c)e + (- 2240A b c + 1120B b c )d)x +--R + +--R 6 7 5 2 6 +--R (- 1680A b c + 945B b )e + (3360A b c - 1680B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 344064c \|c +--R Type: Expression(Integer) +--E 236 + +--S 237 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2) +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R Type: Expression(Integer) +--E 238 + +--S 239 OF 765 +r0:=-1/24*b*(b*B-2*A*c)*x^2*(b*x+c*x^2)^(3/2)/c-1/12*(b*B-2*A*c)*x*_ + (b*x+c*x^2)^(5/2)/c+1/7*B*(b*x+c*x^2)^(7/2)/c+5/1024*b^6*(b*B-_ + 2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-5/1024*b^5*(b*B-_ + 2*A*c)*sqrt(b*x+c*x^2)/c^4+5/1536*b^4*(b*B-2*A*c)*x*sqrt(b*x+_ + c*x^2)/c^3-1/384*b^3*(b*B-2*A*c)*x^2*sqrt(b*x+c*x^2)/c^2-1/64*b^2*_ + (b*B-2*A*c)*x^3*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 6 7 x\|c +--R (- 210A b c + 105B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 6 6 5 5 5 2 4 4 +--R 3072B c x + (3584A c + 7424B b c )x + (8960A b c + 4736B b c )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 +--R (6048A b c + 48B b c )x + (112A b c - 56B b c )x +--R + +--R 4 2 5 5 6 +--R (- 140A b c + 70B b c)x + 210A b c - 105B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 21504c \|c +--R Type: Expression(Integer) +--E 239 + +--S 240 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x) +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 241 + +--S 242 OF 765 +r0:=1/192*(4*A*c*e*(16*c^2*d^2-22*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-_ + 88*b*c^2*d^2*e+12*b^2*c*d*e^2+5*b^3*e^3)-2*c*e*(12*A*c*e*(2*c*d-_ + b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/_ + (c^2*e^4)-1/60*(12*B*c*d-5*b*B*e-12*A*c*e-10*B*c*e*x)*(b*x+_ + c*x^2)^(5/2)/(c*e^2)-1/512*(4*A*c*e*(256*c^5*d^5-640*b*c^4*d^4*e+_ + 480*b^2*c^3*d^3*e^2-80*b^3*c^2*d^2*e^3-10*b^4*c*d*e^4-3*b^5*e^5)-_ + B*(1024*c^6*d^6-2560*b*c^5*d^5*e+1920*b^2*c^4*d^4*e^2-320*b^3*_ + c^3*d^3*e^3-40*b^4*c^2*d^2*e^4-12*b^5*c*d*e^5-5*b^6*e^6))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(7/2)*e^7)-d^(5/2)*(B*d-A*e)*_ + (c*d-b*e)^(5/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7+1/1536*(3*(4*A*c*e*(128*c^4*d^4-_ + 288*b*c^3*d^3*e+176*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-3*b^4*e^4)-_ + B*(512*c^5*d^5-1152*b*c^4*d^4*e+704*b^2*c^3*d^3*e^2-40*b^3*c^2*_ + d^2*e^3-12*b^4*c*d*e^4-5*b^5*e^5))-2*c*e*(8*b*c*d*e*(2*c*d-b*e)*_ + (12*B*c*d-5*b*B*e-12*A*c*e)+(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2)*_ + (12*A*c*e*(2*c*d-b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2)))*x)*_ + sqrt(b*x+c*x^2)/(c^3*e^6) +--R +--R +--R (2) +--R 5 6 6 4 2 5 5 +--R (180A b c - 75B b )e + (600A b c - 180B b c)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (4800A b c - 600B b c )d e + (- 28800A b c - 4800B b c )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (38400A b c + 28800B b c )d e + (- 15360A c - 38400B b c )d e +--R + +--R 6 6 +--R 15360B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 3 4 2 3 3 2 +--R - 7680A b c d e + (15360A b c + 7680B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 7680A c - 15360B b c )d e + 7680B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 6 5 5 4 6 5 5 4 +--R 1280B c e x + ((1536A c + 3200B b c )e - 1536B c d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (4032A b c + 2160B b c )e + (- 1920A c - 4032B b c )d e +--R + +--R 5 2 4 +--R 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2976A b c + 40B b c )e + (- 5440A b c - 2976B b c )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2560A c + 5440B b c )d e - 2560B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (120A b c - 50B b c)e + (- 4720A b c - 120B b c )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (8320A b c + 4720B b c )d e + (- 3840A c - 8320B b c )d e +--R + +--R 5 4 2 +--R 3840B c d e +--R * +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 180A b c + 75B b )e + (- 600A b c + 180B b c)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (10560A b c + 600B b c )d e + (- 17280A b c - 10560B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (7680A c + 17280B b c )d e - 7680B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 7 +-+ +--R 7680c e \|c +--R Type: Expression(Integer) +--E 242 + +--S 243 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 244 + +--S 245 OF 765 +r0:=-1/48*(10*A*c*e*(8*c*d-7*b*e)-B*(96*c^2*d^2-92*b*c*d*e+3*b^2*e^2)+_ + 6*c*e*(12*B*c*d-b*B*e-10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(c*e^4)+_ + 1/5*(6*B*d-5*A*e+B*e*x)*(b*x+c*x^2)^(5/2)/(e^2*(d+e*x))+_ + 1/128*(10*A*c*e*(128*c^4*d^4-256*b*c^3*d^3*e+144*b^2*c^2*d^2*e^2-_ + 16*b^3*c*d*e^3-b^4*e^4)-B*(1536*c^5*d^5-3200*b*c^4*d^4*e+_ + 1920*b^2*c^3*d^3*e^2-240*b^3*c^2*d^2*e^3-20*b^4*c*d*e^4-3*b^5*e^5))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^7)+1/2*d^(3/2)*_ + (c*d-b*e)^(3/2)*(B*d*(12*c*d-7*b*e)-5*A*e*(2*c*d-b*e))*atanh(1/2*_ + (b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7-_ + 1/128*(10*A*c*e*(64*c^3*d^3-112*b*c^2*d^2*e+48*b^2*c*d*e^2-b^3*e^3)-_ + B*(768*c^4*d^4-1408*b*c^3*d^3*e+656*b^2*c^2*d^2*e^2-20*b^3*c*d*e^3-_ + 3*b^4*e^4)-2*c*e*(8*b*c*e*(6*B*d-5*A*e)*(2*c*d-b*e)-(12*B*c*d-b*B*e-_ + 10*A*c*e)*(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^6) +--R +--R +--R (2) +--R 4 5 6 3 2 4 5 +--R (- 150A b c + 45B b )e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (21600A b c + 3600B b c )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 38400A b c - 28800B b c )d e + (19200A c + 48000B b c )d e +--R + +--R 5 5 +--R - 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (- 150A b c + 45B b )d e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (21600A b c + 3600B b c )d e + (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (19200A c + 48000B b c )d e - 23040B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 4 3 2 2 2 3 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (9600A c + 18240B b c )d e - 11520B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 4 4 5 +--R (9600A c + 18240B b c )d e - 11520B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 384B c e x + ((480A c + 1008B b c )e - 576B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (1360A b c + 744B b c )e + (- 800A c - 1712B b c )d e +--R + +--R 4 2 4 +--R 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (1180A b c + 30B b c)e + (- 2800A b c - 1616B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (1600A c + 3520B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (150A b c - 45B b )e + (- 4100A b c - 270B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (8800A b c + 5560B b c )d e + (- 4800A c - 11040B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (150A b c - 45B b )d e + (- 7200A b c - 300B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (16800A b c + 9840B b c )d e + (- 9600A c - 21120B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 8 2 7 +-+ +--R (1920c e x + 1920c d e )\|c +--R Type: Expression(Integer) +--E 245 + +--S 246 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 247 + +--S 248 OF 765 +r0:=-5/24*(B*d*(24*c*d-13*b*e)-2*A*e*(8*c*d-3*b*e)+e*(6*B*c*d-b*B*e-_ + 4*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/4*(3*B*d-2*A*e+B*e*x)*_ + (b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)-5/64*(8*A*c*e*(32*c^3*d^3-48*b*c^2*_ + d^2*e+18*b^2*c*d*e^2-b^3*e^3)-B*(384*c^4*d^4-640*b*c^3*d^3*e+288*b^2*_ + c^2*d^2*e^2-24*b^3*c*d*e^3-b^4*e^4))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/_ + (c^(3/2)*e^7)+5/8*(A*e*(16*c^2*d^2-16*b*c*d*e+3*b^2*e^2)-B*d*(24*c^2*_ + d^2-28*b*c*d*e+7*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-b*e)/e^7+5/64*_ + (8*A*c*e*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2)-B*(192*c^3*d^3-272*b*c^2*_ + d^2*e+88*b^2*c*d*e^2-b^3*e^3)-2*c*e*(16*A*c*e*(2*c*d-b*e)-B*(48*c^2*_ + d^2-32*b*c*d*e+b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c*e^6) +--R +--R +--R (2) +--R 3 4 6 2 2 3 5 +--R (120A b c - 15B b )e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (240A b c - 30B b )d e + (- 4320A b c - 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (11520A b c + 8640B b c )d e + (- 7680A c - 19200B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (120A b c - 15B b )d e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 6 +--R 5760B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 2 4 +--R - 360A b c e + (1920A b c + 840B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 1920A c - 3360B b c )d e + 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R - 720A b c d e + (3840A b c + 1680B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 3840A c - 6720B b c )d e + 5760B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R - 360A b c d e + (1920A b c + 840B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 1920A c - 3360B b c )d e + 2880B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 48B c e x + ((64A c + 136B b c )e - 96B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (208A b c + 118B b c)e + (- 160A c - 352B b c )d e +--R + +--R 3 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (264A b c + 15B b )e + (- 880A b c - 556B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (640A c + 1480B b c )d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (960A b c + 30B b )d e + (- 3680A b c - 2090B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 6240B b c )d e - 4320B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (600A b c + 15B b )d e + (- 2400A b c - 1320B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1920A c + 4080B b c )d e - 2880B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 9 2 8 2 7 +-+ +--R (192c e x + 384c d e x + 192c d e )\|c +--R Type: Expression(Integer) +--E 248 + +--S 249 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 250 + +--S 251 OF 765 +r0:=-5/12*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+e*(4*B*c*d-b*B*e-2*A*c*e)*x)*_ + (b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(2*B*d-A*e+B*e*x)*_ + (b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)+5/8*(2*A*c*e*(16*c^2*d^2-_ + 16*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+24*b^2*c*d*e^2-_ + b^3*e^3))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^7*sqrt(c))+5/16*(B*d*_ + (64*c^3*d^3-112*b*c^2*d^2*e+56*b^2*c*d*e^2-7*b^3*e^3)-A*e*(32*c^3*d^3-_ + 48*b*c^2*d^2*e+18*b^2*c*d*e^2-b^3*e^3))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^7*sqrt(d)*sqrt(c*d-b*e))-_ + 5/8*(A*e*(16*c^2*d^2-12*b*c*d*e+b^2*e^2)-2*B*d*(16*c^2*d^2-_ + 16*b*c*d*e+3*b^2*e^2)+e*(4*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+_ + b^2*e^2))*x)*sqrt(b*x+c*x^2)/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 3 6 2 2 5 +--R (180A b c + 30B b )e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (960A c + 2400B b c )d e - 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (180A b c + 30B b )d e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 5 3 6 +--R (960A c + 2400B b c )d e - 1920B c d +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 7 2 3 6 +--R - 15A b e + (270A b c + 105B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e +--R + +--R 3 4 3 +--R - 960B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 5 2 +--R - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 6 +--R - 2880B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 15A b d e + (270A b c + 105B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e - 960B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 6 5 2 6 2 5 4 +--R 16B c e x + ((24A c + 52B b c)e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 3 +--R ((108A b c + 66B b )e + (- 120A c - 276B b c)d e + 240B c d e )x +--R + +--R 2 6 2 5 +--R - 66A b e + (700A b c + 372B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 880A c - 1840B b c)d e + 1760B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 80A b d e + (920A b c + 470B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 1200A c - 2440B b c)d e + 2400B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 30A b d e + (360A b c + 180B b )d e + (- 480A c - 960B b c)d e +--R + +--R 2 5 +--R 960B c d e +--R * +--R +----------+ +--R +-----------+ +-+ +-+ | 2 +--R \|- b e + c d \|c \|d \|c x + b x +--R / +--R 10 3 9 2 2 8 3 7 +-----------+ +-+ +-+ +--R (48e x + 144d e x + 144d e x + 48d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 251 + +--S 252 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 253 + +--S 254 OF 765 +r0:=-5/32*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*d^2-64*b*c*d*e+_ + 17*b^2*e^2))*(b*x+c*x^2)^(3/2)/(d*e^4*(c*d-b*e)*(d+e*x)^2)-5/24*_ + (B*d*(24*c*d-11*b*e)-A*e*(8*c*d-b*e)+6*e*(3*B*c*d-b*B*e-A*c*e)*x)*_ + (b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^3)+1/4*(3*B*d-A*e+2*B*e*x)*(b*x+_ + c*x^2)^(5/2)/(e^2*(d+e*x)^4)+5/128*(A*e*(128*c^4*d^4-256*b*c^3*d^3*e+_ + 144*b^2*c^2*d^2*e^2-16*b^3*c*d*e^3-b^4*e^4)-B*d*(384*c^4*d^4-_ + 896*b*c^3*d^3*e+672*b^2*c^2*d^2*e^2-168*b^3*c*d*e^3+7*b^4*e^4))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(3/2)*e^7*(c*d-b*e)^(3/2))-5/4*(4*A*c*e*(2*c*d-b*e)-_ + B*(24*c^2*d^2-20*b*c*d*e+3*b^2*e^2))*atanh(x*sqrt(c)/sqrt(b*x+_ + c*x^2))*sqrt(c)/e^7-5/64*(B*d*(192*c^3*d^3-304*b*c^2*d^2*e+120*_ + b^2*c*d*e^2-7*b^3*e^3)-A*e*(64*c^3*d^3-80*b*c^2*d^2*e+16*b^2*c*d*_ + e^2+b^3*e^3)-2*c*e*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*_ + d^2-64*b*c*d*e+17*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d*e^6*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 3 7 2 2 2 6 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (3840A c + 21120B b c )d e - 11520B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (11520A b c + 8640B b )d e + (- 34560A b c - 66240B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (23040A c + 126720B b c )d e - 69120B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 7 3 8 +--R (3840A c + 21120B b c )d e - 11520B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 9 3 4 8 +--R - 15A b e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (1920A c + 13440B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 3 6 3 2 2 4 5 +--R (8640A b c + 10080B b c)d e + (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R - 90A b d e + (- 1440A b c - 630B b )d e +--R + +--R 2 2 3 4 5 +--R (12960A b c + 15120B b c)d e +--R + +--R 3 2 2 5 4 4 3 6 3 +--R (- 23040A b c - 60480B b c )d e + (11520A c + 80640B b c )d e +--R + +--R 4 7 2 +--R - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (8640A b c + 10080B b c)d e + (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (1920A c + 13440B b c )d e - 5760B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 7 3 2 6 5 +--R (192B b c d e - 192B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (384A b c + 864B b c)d e + (- 384A c - 2016B b c )d e +--R + +--R 3 3 5 +--R 1152B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 30A b e + (- 1292A b c - 558B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (5232A b c + 8284B b c)d e + (- 4000A c - 19696B b c )d e +--R + +--R 3 4 4 +--R 12000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 146A b d e + (- 2264A b c - 1022B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (10640A b c + 16392B b c)d e + (- 8320A c - 40240B b c )d e +--R + +--R 3 5 3 +--R 24960B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 110A b d e + (- 1740A b c - 770B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (8480A b c + 12860B b c)d e + (- 6720A c - 32160B b c )d e +--R + +--R 3 6 2 +--R 20160B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 30A b d e + (- 480A b c - 210B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (2400A b c + 3600B b c)d e + (- 1920A c - 9120B b c )d e +--R + +--R 3 7 +--R 5760B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (384b d e - 384c d e )x + (1536b d e - 1536c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (2304b d e - 2304c d e )x + (1536b d e - 1536c d e )x + 384b d e +--R + +--R 6 7 +--R - 384c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 254 + +--S 255 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 OF 765 +t0:=(A+B*x)*(d+e*x)^3/sqrt(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 256 + +--S 257 OF 765 +r0:=1/64*(128*A*c^4*d^3+35*b^4*B*e^3+144*b^2*c^2*d*e*(B*d+A*e)-40*b^3*_ + c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/c^(9/2)+1/192*(8*A*c*e*(52*c^2*d^2-52*b*c*d*e+_ + 15*b^2*e^2)+B*(96*c^3*d^3-352*b*c^2*d^2*e+346*b^2*c*d*e^2-105*_ + b^3*e^3))*sqrt(b*x+c*x^2)/c^4+1/24*(6*B*c*d-7*b*B*e+8*A*c*e)*_ + (d+e*x)^2*sqrt(b*x+c*x^2)/c^2+1/4*B*(d+e*x)^3*sqrt(b*x+c*x^2)/c-_ + 1/96*e*(d*(12*b*B*c*d-48*A*c^2*d-7*b^2*B*e+8*A*b*c*e)-(40*A*c*e*_ + (2*c*d-b*e)+B*(24*c^2*d^2-64*b*c*d*e+35*b^2*e^2))*x)*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (- 120A b c + 105B b )e + (432A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 576A b c + 432B b c )d e + (384A c - 192B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B c e x + ((64A c - 56B b c )e + 192B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 80A b c + 70B b c)e + (288A c - 240B b c )d e + 288B c d e)x +--R + +--R 2 3 3 2 2 2 +--R (120A b c - 105B b )e + (- 432A b c + 360B b c)d e +--R + +--R 3 2 2 3 3 +--R (576A c - 432B b c )d e + 192B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 257 + +--S 258 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 OF 765 +t0:=(A+B*x)*(d+e*x)^2/sqrt(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 259 + +--S 260 OF 765 +r0:=1/8*(16*A*c^3*d^2-5*b^3*B*e^2+6*b^2*c*e*(2*B*d+A*e)-8*b*c^2*d*_ + (B*d+2*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/24*(18*A*c*_ + e*(2*c*d-b*e)+B*(16*c^2*d^2-34*b*c*d*e+15*b^2*e^2))*sqrt(b*x+_ + c*x^2)/c^3+1/3*B*(d+e*x)^2*sqrt(b*x+c*x^2)/c-1/12*e*((b*B-6*A*c)*_ + d-(4*B*c*d-5*b*B*e+6*A*c*e)*x)*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R (18A b c - 15B b )e + (- 48A b c + 36B b c)d e +--R + +--R 3 2 2 +--R (48A c - 24B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 2 2 +--R 8B c e x + ((12A c - 10B b c)e + 24B c d e)x +--R + +--R 2 2 2 2 2 +--R (- 18A b c + 15B b )e + (48A c - 36B b c)d e + 24B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 24c \|c +--R Type: Expression(Integer) +--E 260 + +--S 261 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 OF 765 +t0:=(A+B*x)*(d+e*x)/sqrt(b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 262 + +--S 263 OF 765 +r0:=1/4*(8*A*c^2*d+3*b^2*B*e-4*b*c*(B*d+A*e))*atanh(x*sqrt(c)/sqrt(b*x+_ + c*x^2))/c^(5/2)+1/4*(2*B*c*d-3*b*B*e+4*A*c*e)*sqrt(b*x+c*x^2)/c^2+_ + 1/2*B*(d+e*x)*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 2 2 x\|c +--R ((- 4A b c + 3B b )e + (8A c - 4B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +-+ | 2 +--R (2B c e x + (4A c - 3B b)e + 4B c d)\|c \|c x + b x +--R / +--R 2 +-+ +--R 4c \|c +--R Type: Expression(Integer) +--E 263 + +--S 264 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 OF 765 +t0:=(A+B*x)/sqrt(b*x+c*x^2) +--R +--R +--R B x + A +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 265 + +--S 266 OF 765 +r0:=-(b*B-2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+B*sqrt(b*x+c*x^2)/c +--R +--R +--R +-+ +----------+ +--R x\|c +-+ | 2 +--R (2A c - B b)atanh(-------------) + B\|c \|c x + b x +--R +----------+ +--R | 2 +--R \|c x + b x +--R (2) ----------------------------------------------------- +--R +-+ +--R c\|c +--R Type: Expression(Integer) +--E 266 + +--S 267 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 OF 765 +t0:=(A+B*x)/((d+e*x)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ---------------------- +--R +----------+ +--R | 2 +--R (e x + d)\|c x + b x +--R Type: Expression(Integer) +--E 268 + +--S 269 OF 765 +r0:=2*B*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e*sqrt(c))-(B*d-A*e)*atanh(1/2*_ + (b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/_ + (e*sqrt(d)*sqrt(c*d-b*e)) +--R +--R +--R (2) +--R +-+ +--R +-----------+ +-+ x\|c +--R 2B\|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-+ (b e - 2c d)x - b d +--R (- A e + B d)\|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +-----------+ +-+ +-+ +--R e\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 269 + +--S 270 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 OF 765 +t0:=(A+B*x)/((d+e*x)^2*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (e x + 2d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 271 + +--S 272 OF 765 +r0:=-1/2*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))+(B*d-A*e)*_ + sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 2 +--R ((- A b e + (2A c - B b)d e)x - A b d e + (2A c - B b)d ) +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +-----------+ +-+ | 2 +--R (2A e - 2B d)\|- b e + c d \|d \|c x + b x +--R / +--R 2 2 2 3 +-----------+ +-+ +--R ((2b d e - 2c d e)x + 2b d e - 2c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 272 + +--S 273 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 OF 765 +t0:=(A+B*x)/((d+e*x)^3*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +----------+ +--R 3 3 2 2 2 3 | 2 +--R (e x + 3d e x + 3d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 274 + +--S 275 OF 765 +r0:=1/8*(8*A*c^2*d^2-4*b*c*d*(B*d+2*A*e)+b^2*e*(B*d+3*A*e))*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*_ + (c*d-b*e)^(5/2))+1/2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ + (d+e*x)^2)-1/4*(3*A*e*(2*c*d-b*e)-B*d*(2*c*d+b*e))*sqrt(b*x+c*x^2)/_ + (d^2*(c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 +--R (- 3A b e + (8A b c - B b )d e + (- 8A c + 4B b c)d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (- 6A b d e + (16A b c - 2B b )d e + (- 16A c + 8B b c)d e)x +--R + +--R 2 2 2 2 3 2 4 +--R - 3A b d e + (8A b c - B b )d e + (- 8A c + 4B b c)d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 2 2 +--R (6A b e + (- 12A c + 2B b)d e + 4B c d e)x + 10A b d e +--R + +--R 2 3 +--R (- 16A c - 2B b)d e + 8B c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (8b d e - 16b c d e + 8c d e )x + (16b d e - 32b c d e + 16c d e)x +--R + +--R 2 4 2 5 2 6 +--R 8b d e - 16b c d e + 8c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 275 + +--S 276 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 OF 765 +t0:=(A+B*x)/((d+e*x)^4*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R +----------+ +--R 4 4 3 3 2 2 2 3 4 | 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 277 + +--S 278 OF 765 +r0:=1/16*(16*A*c^3*d^3-8*b*c^2*d^2*(B*d+3*A*e)-b^3*e^2*(B*d+5*A*e)+_ + 2*b^2*c*d*e*(2*B*d+9*A*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+_ + 1/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^3)-_ + 1/12*(5*A*e*(2*c*d-b*e)-B*d*(4*c*d+b*e))*sqrt(b*x+c*x^2)/(d^2*_ + (c*d-b*e)^2*(d+e*x)^2)+1/24*(B*d*(8*c^2*d^2+10*b*c*d*e-3*b^2*e^2)-_ + A*e*(44*c^2*d^2-44*b*c*d*e+15*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*_ + (c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 3 6 2 3 5 2 2 2 4 +--R - 15A b e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 3 3 +--R (48A c - 24B b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 2 4 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 3 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R x +--R + +--R 3 3 3 2 3 4 2 2 2 5 +--R - 15A b d e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 6 +--R (48A c - 24B b c )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 88A b c + 6B b )d e + (88A c - 20B b c)d e +--R + +--R 2 3 2 +--R - 16B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 80A b d e + (- 236A b c + 16B b )d e + (216A c - 28B b c)d e +--R + +--R 2 4 +--R - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 66A b d e + (- 180A b c - 6B b )d e + (144A c + 24B b c)d e +--R + +--R 2 5 +--R - 48B c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (48b d e - 144b c d e + 144b c d e - 48c d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (144b d e - 432b c d e + 432b c d e - 144c d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (144b d e - 432b c d e + 432b c d e - 144c d e)x + 48b d e +--R + +--R 2 7 2 2 8 3 9 +--R - 144b c d e + 144b c d e - 48c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 278 + +--S 279 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 280 + +--S 281 OF 765 +r0:=3/4*e*(4*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-12*b*c*d*e+5*b^2*e^2))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-2*(A*b-(b*B-2*A*c)*x)*_ + (d+e*x)^3/(b^2*sqrt(b*x+c*x^2))+1/4*e*(32*A*c^3*d^2-15*b^3*B*e^2-_ + 16*b*c^2*d*(B*d+2*A*e)+2*b^2*c*e*(17*B*d+6*A*e))*sqrt(b*x+c*x^2)/_ + (b^2*c^3)-2*(b*B-2*A*c)*e*(d+e*x)^2*sqrt(b*x+c*x^2)/(b^2*c)+_ + 1/2*e^2*(b*(b*B+4*A*c)*d+(8*A*c^2*d+5*b^2*B*e-4*b*c*(B*d+A*e))*x)*_ + sqrt(b*x+c*x^2)/(b^2*c^2) +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 2 2 2 +--R ((- 12A b c + 15B b )e + (24A b c - 36B b c)d e + 24B b c d e) +--R * +--R +----------+ +-+ +--R | 2 x\|c +--R \|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 3 2 2 3 3 2 2 2 2 +--R 2B b c e x + ((4A b c - 5B b c)e + 12B b c d e )x +--R + +--R 3 4 3 2 2 3 2 +--R (12A b c - 15B b )e + (- 24A b c + 36B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (24A b c - 24B b c )d e + (- 16A c + 8B b c )d +--R * +--R x +--R + +--R 3 3 +--R - 8A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 3 +-+ | 2 +--R 4b c \|c \|c x + b x +--R Type: Expression(Integer) +--E 281 + +--S 282 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 283 + +--S 284 OF 765 +r0:=e*(4*B*c*d-3*b*B*e+2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-_ + 2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*sqrt(b*x+c*x^2))+e*(8*A*c^2*d+_ + 3*b^2*B*e-4*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/(b^2*c^2)+2*e^2*(A*b-_ + (b*B-2*A*c)*x)*sqrt(b*x+c*x^2)/(b^2*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 2 3 2 2 | 2 x\|c +--R ((2A b c - 3B b )e + 4B b c d e)\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 +--R B b c e x +--R + +--R 2 3 2 2 2 +--R (- 2A b c + 3B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 +--R (- 4A c + 2B b c )d +--R * +--R x +--R + +--R 2 2 +--R - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 2 +-+ | 2 +--R b c \|c \|c x + b x +--R Type: Expression(Integer) +--E 284 + +--S 285 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 OF 765 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 286 + +--S 287 OF 765 +r0:=2*B*e*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)-2*(A*b-(b*B-2*A*c)*x)*_ + (d+e*x)/(b^2*sqrt(b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(b*x+c*x^2)/(b^2*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 2 | 2 x\|c +--R 2B b e\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 +-+ +--R (((2A b c - 2B b )e + (- 4A c + 2B b c)d)x - 2A b c d)\|c +--R / +--R +----------+ +--R 2 +-+ | 2 +--R b c\|c \|c x + b x +--R Type: Expression(Integer) +--E 287 + +--S 288 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 OF 765 +t0:=(A+B*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R B x + A +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 289 + +--S 290 OF 765 +r0:=-2*(A*b-(b*B-2*A*c)*x)/(b^2*sqrt(b*x+c*x^2)) +--R +--R +--R (- 4A c + 2B b)x - 2A b +--R (2) ----------------------- +--R +----------+ +--R 2 | 2 +--R b \|c x + b x +--R Type: Expression(Integer) +--E 290 + +--S 291 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 OF 765 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------- +--R +----------+ +--R 3 2 | 2 +--R (c e x + (b e + c d)x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 292 + +--S 293 OF 765 +r0:=-e*(B*d-A*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))-2*(A*b*(c*d-b*e)+_ + c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R +----------+ +--R 2 2 2 | 2 (b e - 2c d)x - b d +--R (A b e - B b d e)\|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +--R ((- 2A b c e + (4A c - 2B b c)d)x - 2A b e + 2A b c d)\|- b e + c d \|d +--R / +--R +----------+ +--R 3 2 2 +-----------+ +-+ | 2 +--R (b d e - b c d )\|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 293 + +--S 294 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------------------------- +--R +----------+ +--R 2 4 2 3 2 2 2 | 2 +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 295 + +--S 296 OF 765 +r0:=1/2*e*(3*A*e*(2*c*d-b*e)-B*d*(4*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-_ + b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-_ + b*e)^(5/2))-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*_ + (c*d-b*e)*(d+e*x)*sqrt(b*x+c*x^2))-e*(4*A*c^2*d^2-b^2*e*(B*d-_ + 3*A*e)-2*b*c*d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 3 4 2 3 3 2 2 2 3 3 +--R (3A b e + (- 6A b c - B b )d e + 4B b c d e )x + 3A b d e +--R + +--R 2 3 2 2 2 3 +--R (- 6A b c - B b )d e + 4B b c d e +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 3 2 2 2 +--R (- 6A b c e + (8A b c + 2B b c)d e + (- 8A c + 4B b c )d e)x +--R + +--R 3 3 2 3 2 2 2 +--R - 6A b e + (4A b c + 2B b )d e + 4A b c d e +--R + +--R 3 2 3 +--R (- 8A c + 4B b c )d +--R * +--R x +--R + +--R 3 2 2 2 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((2b d e - 4b c d e + 2b c d e)x + 2b d e - 4b c d e + 2b c d ) +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 296 + +--S 297 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 OF 765 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 298 + +--S 299 OF 765 +r0:=-3/8*e*(B*d*(8*c^2*d^2-4*b*c*d*e+b^2*e^2)-A*e*(16*c^2*d^2-16*b*c*d*e+_ + 5*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))-2*(A*b*(c*d-b*e)+_ + c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)^2*sqrt(b*x+_ + c*x^2))-1/2*e*(8*A*c^2*d^2-b^2*e*(B*d-5*A*e)-4*b*c*d*(B*d+2*A*e))*_ + sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^2)-1/4*e*(16*A*c^3*d^3-_ + 2*b^2*c*d*e*(5*B*d-19*A*e)+3*b^3*e^2*(B*d-5*A*e)-8*b*c^2*d^2*_ + (B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 4 6 3 4 5 2 2 3 2 4 +--R 15A b e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 30A b d e + (- 96A b c - 6B b )d e + (96A b c + 24B b c)d e +--R + +--R 2 2 4 2 +--R - 48B b c d e +--R * +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A b d e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 5 +--R - 24B b c d e +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 5 2 2 3 4 +--R - 30A b c e + (76A b c + 6B b c)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 48A b c - 20B b c )d e + (32A c - 16B b c )d e +--R * +--R 3 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 30A b e + (26A b c + 6B b )d e + (80A b c - 10B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (- 80A b c - 24B b c )d e + (64A c - 32B b c )d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 4 2 3 +--R - 50A b d e + (112A b c + 10B b )d e +--R + +--R 2 2 3 3 2 3 4 4 3 5 +--R (- 48A b c - 24B b c)d e - 16A b c d e + (32A c - 16B b c )d +--R * +--R x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 16A b d e + 48A b c d e - 48A b c d e + 16A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (16b d e - 48b c d e + 48b c d e - 16b c d e)x + 8b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 24b c d e + 24b c d e - 8b c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 299 + +--S 300 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 301 + +--S 302 OF 765 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^4/(b^2*(b*x+c*x^2)^(3/2))+e^3*(8*B*c*d-_ + 5*b*B*e+2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-8/3*_ + (d+e*x)^3*(b*(b*B*d-2*A*c*d+2*A*b*e)-(4*A*c^2*d-b^2*B*e-2*b*c*(B*d+_ + A*e))*x)/(b^4*sqrt(b*x+c*x^2))-1/3*e*(64*A*c^4*d^3-15*b^4*B*e^3-_ + 32*b*c^3*d^2*(B*d+3*A*e)+2*b^3*c*e^2*(11*B*d+3*A*e)+4*b^2*c^2*d*_ + e*(4*B*d+5*A*e))*sqrt(b*x+c*x^2)/(b^4*c^3)-8/3*e*(4*A*c^2*d-b^2*B*e-_ + 2*b*c*(B*d+A*e))*(d+e*x)^2*sqrt(b*x+c*x^2)/(b^4*c)+2/3*e^2*(b*d*_ + (4*b*B*c*d-8*A*c^2*d-b^2*B*e+10*A*b*c*e)-(16*A*c^3*d^2+5*b^3*B*e^2-_ + 2*A*b^2*c*e^2-8*b*c^2*d*(B*d+2*A*e))*x)*sqrt(b*x+c*x^2)/(b^4*c^2) +--R +--R +--R (2) +--R 4 2 5 4 4 2 3 2 +--R ((6A b c - 15B b c)e + 24B b c d e )x +--R + +--R 5 6 4 5 3 +--R ((6A b c - 15B b )e + 24B b c d e )x +--R * +--R +----------+ +-+ +--R | 2 x\|c +--R \|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 2 4 4 +--R 3B b c e x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 8A b c + 20B b c)e + (8A b c - 32B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (24A b c + 12B b c )d e + (- 64A b c + 16B b c )d e +--R + +--R 6 5 4 +--R (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 4 5 3 3 3 2 2 +--R (- 6A b c + 15B b )e - 24B b c d e + 36A b c d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 96A b c + 24B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 4 3 3 4 3 3 4 +--R (- 24A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 4 2 5 3 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R Type: Expression(Integer) +--E 302 + +--S 303 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 304 + +--S 305 OF 765 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^3/(b^2*(b*x+c*x^2)^(3/2))+2*B*e^3*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-4/3*(d+e*x)^2*(b*(2*b*B*d-_ + 4*A*c*d+3*A*b*e)-(8*A*c^2*d-b^2*B*e-4*b*c*(B*d+A*e))*x)/(b^4*_ + sqrt(b*x+c*x^2))-2/3*e*(32*A*c^3*d^2+3*b^3*B*e^2-16*b*c^2*d*(B*d+_ + 2*A*e)+2*b^2*c*e*(2*B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^4*c^2)+4/3*e^2*_ + (b*(2*b*B*d-4*A*c*d+3*A*b*e)-(8*A*c^2*d-b^2*B*e-4*b*c*(B*d+A*e))*x)*_ + sqrt(b*x+c*x^2)/(b^4*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 4 3 2 5 3 | 2 x\|c +--R (6B b c e x + 6B b e x)\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2A b c - 8B b c)e + (12A b c + 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 12B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 3 2 2 2 3 3 2 2 +--R - 6B b e + 18A b c d e + (- 72A b c + 18B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 3 2 3 3 2 3 +--R (- 18A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 3 2 5 2 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R Type: Expression(Integer) +--E 305 + +--S 306 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 307 + +--S 308 OF 765 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*(b*x+c*x^2)^(3/2))-_ + 8/3*(b*B*d-2*A*c*d+A*b*e)*(b*d+(2*c*d-b*e)*x)/(b^4*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 3 +--R ((4A b c + 2B b )e + (- 32A b c + 8B b c)d e + (32A c - 16B b c )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (6A b e + (- 48A b c + 12B b )d e + (48A b c - 24B b c)d )x +--R + +--R 3 2 3 2 3 2 +--R (- 12A b d e + (12A b c - 6B b )d )x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 308 + +--S 309 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 OF 765 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 310 + +--S 311 OF 765 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))-_ + 4/3*(b*(2*b*B*d-4*A*c*d+A*b*e)-(8*A*c^2*d+b^2*B*e-_ + 4*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R 2 2 3 2 3 +--R ((- 16A b c + 4B b c)e + (32A c - 16B b c )d)x +--R + +--R 2 3 2 2 2 +--R ((- 24A b c + 6B b )e + (48A b c - 24B b c)d)x +--R + +--R 3 2 3 3 +--R (- 6A b e + (12A b c - 6B b )d)x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 311 + +--S 312 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 OF 765 +t0:=(A+B*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R B x + A +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 313 + +--S 314 OF 765 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)/(b^2*(b*x+c*x^2)^(3/2))+8/3*(b*B-2*A*c)/_ + (b^3*sqrt(b*x+c*x^2))-16/3*(b*B-2*A*c)*sqrt(b*x+c*x^2)/(b^4*x) +--R +--R +--R (2) +--R 3 2 3 2 2 2 2 3 3 +--R (32A c - 16B b c )x + (48A b c - 24B b c)x + (12A b c - 6B b )x - 2A b +--R --------------------------------------------------------------------------- +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 314 + +--S 315 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 OF 765 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^(5/2)) +--R +--R +--R B x + A +--R (1) -------------------------------------------------------------------- +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|c x + b x +--R Type: Expression(Integer) +--E 316 + +--S 317 OF 765 +r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ + (b*x+c*x^2)^(3/2))-e^3*(B*d-A*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+_ + 2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+3*b^2*e*(B*d-A*e)-4*b*c*d*(B*d+A*e))+_ + c*(16*A*c^3*d^3-3*b^3*e^2*(B*d-A*e)+2*b^2*c*d*e*(7*B*d+A*e)-_ + 8*b*c^2*d^2*(B*d+3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R +----------+ +--R 4 4 4 3 2 5 4 5 3 | 2 +--R ((- 3A b c e + 3B b c d e )x + (- 3A b e + 3B b d e )x)\|c x + b x +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 3 2 3 3 2 2 4 2 3 2 +--R 6A b c e + (4A b c - 6B b c )d e + (- 48A b c + 28B b c )d e +--R + +--R 5 4 3 +--R (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 4 2 2 3 3 2 2 +--R 12A b c e + (6A b c - 12B b c)d e + (- 72A b c + 42B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 5 2 3 2 4 2 +--R 6A b e - 6B b d e + (- 18A b c + 12B b c)d e +--R + +--R 2 3 3 2 3 +--R (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 4 2 3 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 317 + +--S 318 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 319 + +--S 320 OF 765 +r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ + (d+e*x)*(b*x+c*x^2)^(3/2))-1/2*e^3*(B*d*(8*c*d-3*b*e)-5*A*e*_ + (2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+2/3*(b*(c*d-b*e)*_ + (8*A*c^2*d^2+b^2*e*(3*B*d-5*A*e)-2*b*c*d*(2*B*d+A*e))+c*(16*A*c^3*d^3-_ + b^3*e^2*(3*B*d-5*A*e)+2*b^2*c*d*e*(8*B*d-A*e)-8*b*c^2*d^2*(B*d+_ + 3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*(d+e*x)*sqrt(b*x+c*x^2))+1/3*e*_ + (32*A*c^4*d^4-2*b^3*c*d*e^2*(9*B*d-10*A*e)+3*b^4*e^3*(3*B*d-5*A*e)+_ + 4*b^2*c^2*d^2*e*(10*B*d+3*A*e)-16*b*c^3*d^3*(B*d+4*A*e))*sqrt(b*x+_ + c*x^2)/(b^4*d^3*(c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 5 4 2 2 4 3 +--R (- 15A b c e + (30A b c + 9B b c)d e - 24B b c d e )x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 15A b e + (15A b c + 9B b )d e + (30A b c - 15B b c)d e +--R + +--R 4 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 6 5 5 6 2 4 5 3 3 +--R (- 15A b d e + (30A b c + 9B b )d e - 24B b c d e )x +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 2 5 3 3 4 2 4 +--R 30A b c e + (- 40A b c - 18B b c )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 24A b c + 36B b c )d e + (128A b c - 80B b c )d e +--R + +--R 6 5 4 +--R (- 64A c + 32B b c )d e +--R * +--R 4 +--R x +--R + +--R 5 5 4 2 5 4 +--R 60A b c e + (- 60A b c - 36B b c)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 76A b c + 60B b c )d e + (168A b c - 84B b c )d e +--R + +--R 5 2 4 4 6 5 5 +--R (32A b c - 32B b c )d e + (- 64A c + 32B b c )d +--R * +--R 3 +--R x +--R + +--R 6 5 6 4 4 2 5 2 3 +--R 30A b e - 18B b d e + (- 84A b c + 12B b c)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (12A b c + 36B b c )d e + (168A b c - 108B b c )d e +--R + +--R 5 2 4 5 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R + +--R 6 4 5 6 2 3 +--R 20A b d e + (- 36A b c - 12B b )d e +--R + +--R 4 2 5 3 2 3 3 4 2 4 +--R (- 12A b c + 36B b c)d e + (52A b c - 36B b c )d e +--R + +--R 2 4 3 3 5 +--R (- 24A b c + 12B b c )d +--R * +--R x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 4A b d e + 12A b c d e - 12A b c d e + 4A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 320 + +--S 321 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R (A b e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 2 2 3 3 2 3 2 +--R (3A b d e + (3A c + 3B b)d e + B c d )x + (3A b d e + (A c + B b)d )x +--R + +--R 3 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 322 + +--S 323 OF 765 +r0:=-2/9*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(9/2)/e^4+2/11*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^4-2/13*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(13/2)/e^4+2/15*B*c*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 7 7 7 6 6 +--R 858B c e x + ((990A c + 990B b)e + 3036B c d e )x +--R + +--R 7 6 2 5 5 +--R (1170A b e + (3600A c + 3600B b)d e + 3708B c d e )x +--R + +--R 6 2 5 3 4 4 +--R (4420A b d e + (4580A c + 4580B b)d e + 1600B c d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (5980A b d e + (2120A c + 2120B b)d e + 10B c d e )x +--R + +--R 3 4 4 3 5 2 2 +--R (3120A b d e + (30A c + 30B b)d e - 12B c d e )x +--R + +--R 4 3 5 2 6 5 2 +--R (130A b d e + (- 40A c - 40B b)d e + 16B c d e)x - 260A b d e +--R + +--R 6 7 +--R (80A c + 80B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 323 + +--S 324 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 325 + +--S 326 OF 765 +r0:=-2/7*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(7/2)/e^4+2/9*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^4-2/11*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(11/2)/e^4+2/13*B*c*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 1386B c e x + ((1638A c + 1638B b)e + 3402B c d e )x +--R + +--R 6 5 2 4 4 +--R (2002A b e + (4186A c + 4186B b)d e + 2226B c d e )x +--R + +--R 5 2 4 3 3 3 +--R (5434A b d e + (2938A c + 2938B b)d e + 30B c d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (4290A b d e + (78A c + 78B b)d e - 36B c d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (286A b d e + (- 104A c - 104B b)d e + 48B c d e)x - 572A b d e +--R + +--R 5 6 +--R (208A c + 208B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 326 + +--S 327 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R (B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 328 + +--S 329 OF 765 +r0:=-2/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(5/2)/e^4+2/7*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^4-2/9*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(9/2)/e^4+2/11*B*c*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 630B c e x + ((770A c + 770B b)e + 840B c d e )x +--R + +--R 5 4 2 3 3 +--R (990A b e + (1100A c + 1100B b)d e + 30B c d e )x +--R + +--R 4 2 3 3 2 2 +--R (1584A b d e + (66A c + 66B b)d e - 36B c d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (198A b d e + (- 88A c - 88B b)d e + 48B c d e)x - 396A b d e +--R + +--R 4 5 +--R (176A c + 176B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 329 + +--S 330 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)*sqrt(d+e*x) +--R +--R +--R 3 2 +-------+ +--R (1) (B c x + (A c + B b)x + A b x)\|e x + d +--R Type: Expression(Integer) +--E 331 + +--S 332 OF 765 +r0:=-2/3*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(3/2)/e^4+2/5*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^4-2/7*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B c e x + ((90A c + 90B b)e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126A b e + (18A c + 18B b)d e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (42A b d e + (- 24A c - 24B b)d e + 16B c d e)x - 84A b d e +--R + +--R 3 4 +--R (48A c + 48B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 332 + +--S 333 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 334 + +--S 335 OF 765 +r0:=2/3*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^4-2/5*(3*B*c*d-_ + b*B*e-A*c*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-2*d*_ + (B*d-A*e)*(c*d-b*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + ((42A c + 42B b)e - 36B c d e )x +--R + +--R 3 2 2 2 +--R (70A b e + (- 56A c - 56B b)d e + 48B c d e)x - 140A b d e +--R + +--R 2 3 +--R (112A c + 112B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 335 + +--S 336 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 336 + +)clear all + +--S 337 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 337 + +--S 338 OF 765 +r0:=-2/3*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+_ + 2*d*(B*d-A*e)*(c*d-b*e)/(e^4*sqrt(d+e*x))+2*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 6B c e x + ((10A c + 10B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (30A b e + (- 40A c - 40B b)d e + 48B c d e)x + 60A b d e +--R + +--R 2 3 +--R (- 80A c - 80B b)d e + 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 338 + +--S 339 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 339 + +)clear all + +--S 340 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 340 + +--S 341 OF 765 +r0:=2/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(3/2))+2/3*B*c*(d+e*x)^(3/2)/e^4-_ + 2*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))/(e^4*sqrt(d+e*x))-_ + 2*(3*B*c*d-b*B*e-A*c*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 2B c e x + ((6A c + 6B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (- 6A b e + (24A c + 24B b)d e - 48B c d e)x - 4A b d e +--R + +--R 2 3 +--R (16A c + 16B b)d e - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 341 + +--S 342 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 343 + +--S 344 OF 765 +r0:=2/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(5/2))-2/3*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^(3/2))+2*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + ((- 30A c - 30B b)e + 180B c d e )x +--R + +--R 3 2 2 2 +--R (- 10A b e + (- 40A c - 40B b)d e + 240B c d e)x - 4A b d e +--R + +--R 2 3 +--R (- 16A c - 16B b)d e + 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 344 + +--S 345 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R ((2A b c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (6A b c + 3B b )d e + (3A c + 6B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 3 4 +--R (3A b d e + (6A b c + 3B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 3 2 3 2 +--R (3A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 346 + +--S 347 OF 765 +r0:=-2/9*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(9/2)/e^6+2/11*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^6+_ + 2/13*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(15/2)/e^6-2/17*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(17/2)/e^6+2/19*B*c^2*(d+e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 2 9 9 2 9 2 8 8 +--R 218790B c e x + ((244530A c + 489060B b c)e + 746460B c d e )x +--R + +--R 2 9 2 8 +--R (554268A b c + 277134B b )e + (847704A c + 1695408B b c)d e +--R + +--R 2 2 7 +--R 866580B c d e +--R * +--R 7 +--R x +--R + +--R 2 9 2 8 +--R 319770A b e + (1961256A b c + 980628B b )d e +--R + +--R 2 2 7 2 3 6 +--R (1005708A c + 2011416B b c)d e + 345840B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 2 7 +--R 1162800A b d e + (2395368A b c + 1197684B b )d e +--R + +--R 2 3 6 2 4 5 +--R (414504A c + 829008B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 7 2 3 6 +--R 1479340A b d e + (1033600A b c + 516800B b )d e +--R + +--R 2 4 5 2 5 4 +--R (1330A c + 2660B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 4 5 +--R 684760A b d e + (6460A b c + 3230B b )d e +--R + +--R 2 5 4 2 6 3 +--R (- 1520A c - 3040B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 5 2 5 4 +--R 9690A b d e + (- 7752A b c - 3876B b )d e +--R + +--R 2 6 3 2 7 2 +--R (1824A c + 3648B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 4 2 6 3 +--R - 12920A b d e + (10336A b c + 5168B b )d e +--R + +--R 2 7 2 2 8 +--R (- 2432A c - 4864B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 6 3 2 7 2 +--R 25840A b d e + (- 20672A b c - 10336B b )d e +--R + +--R 2 8 2 9 +--R (4864A c + 9728B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Expression(Integer) +--E 347 + +--S 348 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 349 + +--S 350 OF 765 +r0:=-2/7*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(7/2)/e^6+2/9*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^6+2/11*_ + (A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(15/2)/e^6+2/17*B*c^2*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 2 8 8 2 8 2 7 7 +--R 90090B c e x + ((102102A c + 204204B b c)e + 210210B c d e )x +--R + +--R 2 8 2 7 +--R (235620A b c + 117810B b )e + (243474A c + 486948B b c)d e +--R + +--R 2 2 6 +--R 127050B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 7 +--R 139230A b e + (578340A b c + 289170B b )d e +--R + +--R 2 2 6 2 3 5 +--R (152082A c + 304164B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 2 6 +--R 355810A b d e + (378420A b c + 189210B b )d e +--R + +--R 2 3 5 2 4 4 +--R (1190A c + 2380B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 6 2 3 5 +--R 249730A b d e + (5100A b c + 2550B b )d e +--R + +--R 2 4 4 2 5 3 +--R (- 1360A c - 2720B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 4 4 +--R 6630A b d e + (- 6120A b c - 3060B b )d e +--R + +--R 2 5 3 2 6 2 +--R (1632A c + 3264B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 5 3 +--R - 8840A b d e + (8160A b c + 4080B b )d e +--R + +--R 2 6 2 2 7 +--R (- 2176A c - 4352B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 3 2 6 2 +--R 17680A b d e + (- 16320A b c - 8160B b )d e +--R + +--R 2 7 2 8 +--R (4352A c + 8704B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Expression(Integer) +--E 350 + +--S 351 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 352 + +--S 353 OF 765 +r0:=-2/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(5/2)/e^6+2/7*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^6+2/9*(A*e*_ + (6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^(9/2)/e^6-2/11*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+_ + b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(13/2)/e^6+2/15*B*c^2*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 2 7 7 2 7 2 6 6 +--R 6006B c e x + ((6930A c + 13860B b c)e + 7392B c d e )x +--R + +--R 2 7 2 6 +--R (16380A b c + 8190B b )e + (8820A c + 17640B b c)d e +--R + +--R 2 2 5 +--R 126B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 10010A b e + (21840A b c + 10920B b )d e +--R + +--R 2 2 5 2 3 4 +--R (210A c + 420B b c)d e - 140B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 14300A b d e + (780A b c + 390B b )d e +--R + +--R 2 3 4 2 4 3 +--R (- 240A c - 480B b c)d e + 160B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 858A b d e + (- 936A b c - 468B b )d e + (288A c + 576B b c)d e +--R + +--R 2 5 2 +--R - 192B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 +--R - 1144A b d e + (1248A b c + 624B b )d e +--R + +--R 2 5 2 2 6 +--R (- 384A c - 768B b c)d e + 256B c d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 2288A b d e + (- 2496A b c - 1248B b )d e + (768A c + 1536B b c)d e +--R + +--R 2 7 +--R - 512B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 353 + +--S 354 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +-------+ +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|e x + d +--R Type: Expression(Integer) +--E 355 + +--S 356 OF 765 +r0:=-2/3*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(3/2)/e^6+2/5*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^6+2/7*(A*e*_ + (6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^(7/2)/e^6-2/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(9/2)/e^6-2/11*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + ((8190A c + 16380B b c)e + 630B c d e )x +--R + +--R 2 6 2 5 +--R (20020A b c + 10010B b )e + (910A c + 1820B b c)d e +--R + +--R 2 2 4 +--R - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 12870A b e + (2860A b c + 1430B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 1040A c - 2080B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 +--R 2574A b d e + (- 3432A b c - 1716B b )d e +--R + +--R 2 3 3 2 4 2 +--R (1248A c + 2496B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R - 3432A b d e + (4576A b c + 2288B b )d e +--R + +--R 2 4 2 2 5 +--R (- 1664A c - 3328B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 6864A b d e + (- 9152A b c - 4576B b )d e + (3328A c + 6656B b c)d e +--R + +--R 2 6 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 356 + +--S 357 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 358 + +--S 359 OF 765 +r0:=2/3*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^6+_ + 2/5*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(7/2)/e^6-2/9*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(9/2)/e^6+2/11*B*c^2*(d+e*x)^(11/2)/e^6-2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + ((770A c + 1540B b c)e - 700B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A b c + 990B b )e + (- 880A c - 1760B b c)d e + 800B c d e )x +--R + +--R 2 5 2 4 +--R 1386A b e + (- 2376A b c - 1188B b )d e +--R + +--R 2 2 3 2 3 2 +--R (1056A c + 2112B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 1848A b d e + (3168A b c + 1584B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1408A c - 2816B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 3696A b d e + (- 6336A b c - 3168B b )d e + (2816A c + 5632B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 359 + +--S 360 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 361 + +--S 362 OF 765 +r0:=2/3*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*sqrt(d+e*x))+2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-_ + 2*A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + ((90A c + 180B b c)e - 100B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((252A b c + 126B b )e + (- 144A c - 288B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 504A b c - 252B b )d e + (288A c + 576B b c)d e +--R + +--R 2 3 2 +--R - 320B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 840A b d e + (2016A b c + 1008B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1152A c - 2304B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 1680A b d e + (4032A b c + 2016B b )d e + (- 2304A c - 4608B b c)d e +--R + +--R 2 5 +--R 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 362 + +--S 363 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 364 + +--S 365 OF 765 +r0:=2/3*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(3/2))-2/3*(2*A*c*e*(2*c*d-_ + b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-_ + 2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*sqrt(d+e*x))+_ + 2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + ((42A c + 84B b c)e - 60B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((140A b c + 70B b )e + (- 112A c - 224B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 840A b c - 420B b )d e + (672A c + 1344B b c)d e +--R + +--R 2 3 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R 840A b d e + (- 3360A b c - 1680B b )d e +--R + +--R 2 3 2 2 4 +--R (2688A c + 5376B b c)d e - 3840B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 560A b d e + (- 2240A b c - 1120B b )d e + (1792A c + 3584B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 365 + +--S 366 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 367 + +--S 368 OF 765 +r0:=2/5*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(5/2))-2/3*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^(3/2))-2/3*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6-_ + 2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))/(e^6*sqrt(d+e*x))-2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + ((10A c + 20B b c)e - 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((60A b c + 30B b )e + (- 80A c - 160B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 30A b e + (360A b c + 180B b )d e + (- 480A c - 960B b c)d e +--R + +--R 2 3 2 +--R 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 40A b d e + (480A b c + 240B b )d e + (- 640A c - 1280B b c)d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 16A b d e + (192A b c + 96B b )d e + (- 256A c - 512B b c)d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 368 + +--S 369 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 370 + +--S 371 OF 765 +r0:=2/3*(B*(c*d-b*e)^2+A*c*e*(2*c*d-b*e))*(d+e*x)^(3/2)/c^3+2/5*_ + (B*c*d-b*B*e+A*c*e)*(d+e*x)^(5/2)/c^2+2/7*B*(d+e*x)^(7/2)/c-_ + 2*A*d^(7/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(7/2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(9/2))+2*(B*(c*d-b*e)^3+_ + A*c*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/c^4 +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (- 210A b c + 210B b )e + (630A b c - 630B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 630A b c + 630B b c )d e + (210A c - 210B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 4 3 +-+ +-+ \|e x + d +--R - 210A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 4 +-+ +--R 105b c \|c +--R Type: Expression(Integer) +--E 371 + +--S 372 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 373 + +--S 374 OF 765 +r0:=2/3*(B*c*d-b*B*e+A*c*e)*(d+e*x)^(3/2)/c^2+2/5*B*(d+e*x)^(5/2)/c-_ + 2*A*d^(5/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(5/2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(7/2))+2*(B*(c*d-b*e)^2+_ + A*c*e*(2*c*d-b*e))*sqrt(d+e*x)/c^3 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R (30A b c - 30B b )e + (- 60A b c + 60B b c)d e +--R + +--R 3 2 2 +--R (30A c - 30B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 +-+ +-+ \|e x + d +--R - 30A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 +-+ +--R 15b c \|c +--R Type: Expression(Integer) +--E 374 + +--S 375 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 376 + +--S 377 OF 765 +r0:=2/3*B*(d+e*x)^(3/2)/c-2*A*d^(3/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-_ + 2*(b*B-A*c)*(c*d-b*e)^(3/2)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*c^(5/2))+2*(B*c*d-b*B*e+A*c*e)*sqrt(d+e*x)/c^2 +--R +--R +--R (2) +--R 2 2 +-----------+ +--R ((- 6A b c + 6B b )e + (6A c - 6B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R - 6A c d\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 +-+ +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|c \|e x + d +--R / +--R 2 +-+ +--R 3b c \|c +--R Type: Expression(Integer) +--E 377 + +--S 378 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 379 + +--S 380 OF 765 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b*c^(3/2))+2*B*sqrt(d+e*x)/c +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R (2A c - 2B b)\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-+ +-+ \|e x + d +-+ +-------+ +--R - 2A c\|c \|d atanh(----------) + 2B b\|c \|e x + d +--R +-+ +--R \|d +--R / +--R +-+ +--R b c\|c +--R Type: Expression(Integer) +--E 380 + +--S 381 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 OF 765 +t0:=(A+B*x)/((b*x+c*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ---------------------- +--R 2 +-------+ +--R (c x + b x)\|e x + d +--R Type: Expression(Integer) +--E 382 + +--S 383 OF 765 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*sqrt(d))-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b*sqrt(c)*sqrt(c*d-b*e)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R (2A c - 2B b)\|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R - 2A\|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R / +--R +-----------+ +-+ +-+ +--R b\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 383 + +--S 384 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------ +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 385 + +--S 386 OF 765 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(3/2))-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b*(c*d-b*e)^(3/2))+_ + 2*(B*d-A*e)/(d*(c*d-b*e)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R (- 2A c + 2B b)d\|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R (- 2A b e + 2A c d)\|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R +-----------+ +-+ +--R (2A b e - 2B b d)\|- b e + c d \|d +--R / +--R 2 2 +-----------+ +-+ +-------+ +--R (b d e - b c d )\|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 386 + +--S 387 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 OF 765 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------------ +--R 2 4 2 3 2 2 2 +-------+ +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 388 + +--S 389 OF 765 +r0:=2/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(3/2))-2*A*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b*d^(5/2))-2*c^(3/2)*(b*B-A*c)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*(c*d-b*e)^(5/2))+2*(B*c*d^2-A*e*(2*c*d-b*e))/(d^2*_ + (c*d-b*e)^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 3 +-+ +-+ +-------+ +--R ((6A c - 6B b c)d e x + (6A c - 6B b c)d )\|c \|d \|e x + d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 2 2 2 2 2 +--R (- 6A b e + 12A b c d e - 6A c d e)x - 6A b d e + 12A b c d e +--R + +--R 2 3 +--R - 6A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 389 + +--S 390 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 OF 765 +t0:=(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 391 + +--S 392 OF 765 +r0:=2/5*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(5/2))+2/3*(B*c*d^2-A*e*(2*c*d-_ + b*e))/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-2*A*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b*d^(7/2))-2*c^(5/2)*(b*B-A*c)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*(c*d-b*e)^(7/2))+2*(B*c^2*d^3-A*e*(3*c^2*d^2-_ + 3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 2 2 3 2 4 +--R (- 30A c + 30B b c )d e x + (- 60A c + 60B b c )d e x +--R + +--R 3 2 5 +--R (- 30A c + 30B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30A b e + 90A b c d e - 90A b c d e + 30A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (- 60A b d e + 180A b c d e - 180A b c d e + 60A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R - 30A b d e + 90A b c d e - 90A b c d e + 30A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 392 + +--S 393 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 OF 765 +t0:=(A+B*x)/((d+e*x)^(9/2)*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 6 4 3 5 3 2 2 4 +--R c e x + (b e + 4c d e )x + (4b d e + 6c d e )x +--R + +--R 2 2 3 3 3 4 2 4 +--R (6b d e + 4c d e)x + (4b d e + c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 394 + +--S 395 OF 765 +r0:=2/7*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(7/2))+2/5*(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x)^(5/2))+2/3*(B*c^2*d^3-A*e*(3*c^2*d^2-_ + 3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x)^(3/2))-_ + 2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(9/2))-2*c^(7/2)*(b*B-A*c)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*(c*d-b*e)^(9/2))+_ + 2*(B*c^3*d^4-A*e*(4*c^3*d^3-6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))/_ + (d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 3 3 4 3 5 2 2 +--R (210A c - 210B b c )d e x + (630A c - 630B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (630A c - 630B b c )d e x + (210A c - 210B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 210A b e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 4 3 +--R - 210A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R - 630A b d e + 2520A b c d e - 3780A b c d e + 2520A b c d e +--R + +--R 4 5 2 +--R - 630A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R - 630A b d e + 2520A b c d e - 3780A b c d e + 2520A b c d e +--R + +--R 4 6 +--R - 630A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R - 210A b d e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 7 +--R - 210A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 4 10 +--R (315b d e - 1260b c d e + 1890b c d e - 1260b c d e + 315b c d e)x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 395 + +--S 396 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 OF 765 +t0:=(A+B*x)*(d+e*x)^(9/2)/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 397 + +--S 398 OF 765 +r0:=1/3*e*(6*A*c^3*d^2-7*b^3*B*e^2-3*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ + (12*B*d+5*A*e))*(d+e*x)^(3/2)/(b^2*c^3)+1/5*e*(10*A*c^2*d+7*b^2*B*e-_ + 5*b*c*(B*d+A*e))*(d+e*x)^(5/2)/(b^2*c^2)+(b*B-2*A*c)*(c*d-b*e)*_ + (d+e*x)^(7/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(9/2)/(b*x*(b+c*x))-_ + d^(7/2)*(2*b*B*d-4*A*c*d+9*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/b^3-_ + (c*d-b*e)^(7/2)*(4*A*c^2*d-7*b^2*B*e-b*c*(2*B*d-5*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(9/2))+_ + e*(2*A*c^4*d^3+7*b^4*B*e^3-b*c^3*d^2*(B*d+3*A*e)-b^3*c*e^2*_ + (19*B*d+5*A*e)+b^2*c^2*d*e*(15*B*d+11*A*e))*sqrt(d+e*x)/(b^2*c^4) +--R +--R +--R (2) +--R 4 2 5 4 3 3 4 2 3 +--R (75A b c - 105B b c)e + (- 165A b c + 285B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (45A b c - 225B b c )d e + (105A b c + 15B b c )d e +--R + +--R 6 5 4 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (75A b c - 105B b )e + (- 165A b c + 285B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (45A b c - 225B b c )d e + (105A b c + 15B b c )d e +--R + +--R 5 2 4 4 +--R (- 60A b c + 30B b c )d +--R * +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 3 6 5 4 2 +--R (- 135A b c d e + (60A c - 30B b c )d )x +--R + +--R 2 4 3 5 2 4 4 +--R (- 135A b c d e + (60A b c - 30B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 3 3 +--R 6B b c e x + ((10A b c - 14B b c )e + 42B b c d e )x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 50A b c + 70B b c)e + (130A b c - 218B b c )d e +--R + +--R 3 3 2 2 +--R 216B b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 75A b c + 105B b )e + (190A b c - 320B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 90A b c + 306B b c )d e + (60A b c - 60B b c )d e +--R + +--R 5 2 4 4 +--R (- 30A b c + 15B b c )d +--R * +--R x +--R + +--R 2 4 4 +--R - 15A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 5 2 4 4 +-+ +--R (15b c x + 15b c x)\|c +--R Type: Expression(Integer) +--E 398 + +--S 399 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 400 + +--S 401 OF 765 +r0:=1/3*e*(6*A*c^2*d+5*b^2*B*e-3*b*c*(B*d+A*e))*(d+e*x)^(3/2)/(b^2*c^2)+_ + (b*B-2*A*c)*(c*d-b*e)*(d+e*x)^(5/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(7/2)/_ + (b*x*(b+c*x))-d^(5/2)*(2*b*B*d-4*A*c*d+7*A*b*e)*atanh(sqrt(d+e*x)/_ + sqrt(d))/b^3+(c*d-b*e)^(5/2)*(2*b*B*c*d-4*A*c^2*d+5*b^2*B*e-_ + 3*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(7/2))+_ + e*(2*A*c^3*d^2-5*b^3*B*e^2-b*c^2*d*(B*d+2*A*e)+b^2*c*e*(8*B*d+_ + 3*A*e))*sqrt(d+e*x)/(b^2*c^3) +--R +--R +--R (2) +--R 3 2 4 3 2 3 3 2 2 +--R (- 9A b c + 15B b c)e + (6A b c - 24B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (15A b c + 3B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 9A b c + 15B b )e + (6A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (15A b c + 3B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 2 5 4 3 2 +--R (- 21A b c d e + (12A c - 6B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (- 21A b c d e + (12A b c - 6B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 2B b c e x + ((6A b c - 10B b c)e + 20B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (9A b c - 15B b )e + (- 9A b c + 29B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (9A b c - 9B b c )d e + (- 6A b c + 3B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 3A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 4 2 4 3 +-+ +--R (3b c x + 3b c x)\|c +--R Type: Expression(Integer) +--E 401 + +--S 402 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 403 + +--S 404 OF 765 +r0:=(b*B-2*A*c)*(c*d-b*e)*(d+e*x)^(3/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(5/2)/_ + (b*x*(b+c*x))-d^(3/2)*(2*b*B*d-4*A*c*d+5*A*b*e)*atanh(sqrt(d+e*x)/_ + sqrt(d))/b^3-(c*d-b*e)^(3/2)*(4*A*c^2*d-3*b^2*B*e-b*c*(2*B*d-A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(5/2))+e*(2*A*c^2*d+_ + 3*b^2*B*e-b*c*(B*d+A*e))*sqrt(d+e*x)/(b^2*c^2) +--R +--R +--R (2) +--R 2 2 3 2 3 2 2 +--R (A b c - 3B b c)e + (3A b c + B b c )d e +--R + +--R 4 3 2 +--R (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 4 3 2 2 +--R (- 5A b c d e + (4A c - 2B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (- 5A b c d e + (4A b c - 2B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 +--R 2B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- A b c + 3B b )e + (2A b c - 2B b c)d e +--R + +--R 3 2 2 2 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 3 2 4 2 +-+ +--R (b c x + b c x)\|c +--R Type: Expression(Integer) +--E 404 + +--S 405 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 406 + +--S 407 OF 765 +r0:=-A*(d+e*x)^(3/2)/(b*x*(b+c*x))-(2*b*B*d-4*A*c*d+3*A*b*e)*_ + atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b^3-(4*A*c^2*d-b^2*B*e-_ + b*c*(2*B*d+A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*_ + sqrt(c*d-b*e)/(b^3*c^(3/2))+(b*B-2*A*c)*(c*d-b*e)*sqrt(d+e*x)/_ + (b^2*c*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 +--R ((A b c + B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((A b c + B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 2 +--R (- 3A b c e + (4A c - 2B b c )d)x +--R + +--R 2 2 2 +--R (- 3A b c e + (4A b c - 2B b c)d)x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 +-+ +-------+ +--R (((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d)\|c \|e x + d +--R / +--R 3 2 2 4 +-+ +--R (b c x + b c x)\|c +--R Type: Expression(Integer) +--E 407 + +--S 408 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 409 + +--S 410 OF 765 +r0:=-(2*b*B*d-4*A*c*d+A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*sqrt(d))+_ + (2*b*B*c*d-4*A*c^2*d-b^2*B*e+3*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b^3*sqrt(c)*sqrt(c*d-b*e))+(b*B-2*A*c)*sqrt(d+e*x)/_ + (b^2*(b+c*x))-A*sqrt(d+e*x)/(b*x*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 +--R ((3A b c - B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((3A b c - B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 +--R ((- A b c e + (4A c - 2B b c)d)x + (- A b e + (4A b c - 2B b )d)x) +--R * +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 +-----------+ +-+ +-+ +-------+ +--R ((- 2A b c + B b )x - A b )\|- b e + c d \|c \|d \|e x + d +--R / +--R 3 2 4 +-----------+ +-+ +-+ +--R (b c x + b x)\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 410 + +--S 411 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 OF 765 +t0:=(A+B*x)/((b*x+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (c x + 2b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 412 + +--S 413 OF 765 +r0:=-(2*b*B*d-4*A*c*d-A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(3/2))+_ + (2*b*B*c*d-4*A*c^2*d-3*b^2*B*e+5*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))*sqrt(c)/(b^3*(c*d-b*e)^(3/2))+c*(b*B*d-2*A*c*d+A*b*e)*_ + sqrt(d+e*x)/(b^2*d*(c*d-b*e)*(b+c*x))-A*sqrt(d+e*x)/(b*d*x*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 2 +--R ((- 5A b c + 3B b c)d e + (4A c - 2B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((- 5A b c + 3B b )d e + (4A b c - 2B b c)d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 3 2 2 2 +--R (A b c e + (3A b c - 2B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (A b e + (3A b c - 2B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 3 2 +-----------+ +-+ +--R ((- A b c e + (2A b c - B b c)d)x - A b e + A b c d)\|- b e + c d \|d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-----------+ +-+ +--R ((b c d e - b c d )x + (b d e - b c d )x)\|- b e + c d \|d +--R Type: Expression(Integer) +--E 413 + +--S 414 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R Type: Expression(Integer) +--E 415 + +--S 416 OF 765 +r0:=-(2*b*B*d-4*A*c*d-3*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(5/2))-_ + c^(3/2)*(4*A*c^2*d+5*b^2*B*e-b*c*(2*B*d+7*A*e))*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(5/2))-e*(2*A*c^2*d^2-_ + b^2*e*(2*B*d-3*A*e)-b*c*d*(B*d+2*A*e))/(b^2*d^2*(c*d-b*e)^2*_ + sqrt(d+e*x))+c*(b*B*d-2*A*c*d+A*b*e)/(b^2*d*(c*d-b*e)*(b+c*x)*_ + sqrt(d+e*x))-A/(b*d*x*(b+c*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 2 4 3 3 2 +--R ((7A b c - 5B b c )d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((7A b c - 5B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 2 3 2 3 2 2 2 +--R 3A b c e + (- 2A b c - 2B b c)d e + (- 5A b c + 4B b c )d e +--R + +--R 4 3 3 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 2 3 +--R (4A b c - 2B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 3A b c e + (2A b c + 2B b c)d e + (- 2A b c + B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 3A b e + (A b c + 2B b )d e + A b c d e +--R + +--R 3 2 2 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x) +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 416 + +--S 417 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 OF 765 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 418 + +--S 419 OF 765 +r0:=-1/3*e*(6*A*c^2*d^2-b^2*e*(2*B*d-5*A*e)-3*b*c*d*(B*d+2*A*e))/_ + (b^2*d^2*(c*d-b*e)^2*(d+e*x)^(3/2))+c*(b*B*d-2*A*c*d+A*b*e)/_ + (b^2*d*(c*d-b*e)*(b+c*x)*(d+e*x)^(3/2))-A/(b*d*x*(b+c*x)*_ + (d+e*x)^(3/2))-(2*b*B*d-4*A*c*d-5*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^3*d^(7/2))+c^(5/2)*(2*b*B*c*d-4*A*c^2*d-7*b^2*B*e+9*A*b*c*e)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(7/2))-_ + e*(2*A*c^3*d^3-b^2*c*d*e*(6*B*d-11*A*e)+b^3*e^2*(2*B*d-5*A*e)-_ + b*c^2*d^2*(B*d+3*A*e))/(b^2*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 2 3 3 2 5 4 4 3 +--R ((- 27A b c + 21B b c )d e + (12A c - 6B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 27A b c + 21B b c )d e + (- 15A b c + 15B b c )d e +--R + +--R 5 4 5 +--R (12A c - 6B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((- 27A b c + 21B b c )d e + (12A b c - 6B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 5 3 2 4 4 2 3 3 2 2 3 +--R 15A b c e + (- 33A b c - 6B b c)d e + (9A b c + 18B b c )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (21A b c - 18B b c )d e + (- 12A c + 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 15A b e + (- 18A b c - 6B b )d e + (- 24A b c + 12B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R 30A b c d e + (9A b c - 12B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 15A b d e + (- 33A b c - 6B b )d e + (9A b c + 18B b c)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (21A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 5 3 2 4 4 +--R - 15A b c e + (33A b c + 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 9A b c - 18B b c )d e + (6A b c - 3B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 15A b e + (13A b c + 6B b )d e + (35A b c - 10B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 15A b c - 20B b c )d e + (12A b c - 6B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R - 20A b d e + (41A b c + 8B b )d e + (- 9A b c - 20B b c)d e +--R + +--R 2 3 4 4 2 3 5 +--R - 3A b c d e + (6A b c - 3B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 3A b d e + 9A b c d e - 9A b c d e + 3A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 419 + +--S 420 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 OF 765 +t0:=(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 421 + +--S 422 OF 765 +r0:=-1/5*e*(10*A*c^2*d^2-b^2*e*(2*B*d-7*A*e)-5*b*c*d*(B*d+2*A*e))/_ + (b^2*d^2*(c*d-b*e)^2*(d+e*x)^(5/2))+c*(b*B*d-2*A*c*d+A*b*e)/_ + (b^2*d*(c*d-b*e)*(b+c*x)*(d+e*x)^(5/2))-A/(b*d*x*(b+c*x)*_ + (d+e*x)^(5/2))-1/3*e*(6*A*c^3*d^3-b^2*c*d*e*(6*B*d-17*A*e)+_ + b^3*e^2*(2*B*d-7*A*e)-3*b*c^2*d^2*(B*d+3*A*e))/(b^2*d^3*_ + (c*d-b*e)^3*(d+e*x)^(3/2))-(2*b*B*d-4*A*c*d-7*A*b*e)*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(9/2))-c^(7/2)*(4*A*c^2*d+9*b^2*B*e-_ + b*c*(2*B*d+11*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^3*(c*d-b*e)^(9/2))-e*(2*A*c^4*d^4-2*b^2*c^2*d^2*e*(6*B*d-13*A*e)-_ + b^4*e^3*(2*B*d-7*A*e)+8*b^3*c*d*e^2*(B*d-3*A*e)-b*c^3*d^3*_ + (B*d+4*A*e))/(b^2*d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 2 4 4 3 6 5 5 2 4 +--R ((165A b c - 135B b c )d e + (- 60A c + 30B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (165A b c - 135B b c )d e + (270A b c - 240B b c )d e +--R + +--R 6 5 6 +--R (- 120A c + 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (330A b c - 270B b c )d e + (45A b c - 75B b c )d e +--R + +--R 6 5 7 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((165A b c - 135B b c )d e + (- 60A b c + 30B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 7 4 2 5 6 +--R 105A b c e + (- 360A b c - 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (390A b c + 120B b c )d e + (- 60A b c - 180B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 135A b c + 120B b c )d e + (60A c - 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 105A b e + (- 150A b c - 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 330A b c + 60B b c)d e + (720A b c + 60B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 255A b c - 240B b c )d e + (- 210A b c + 210B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 210A b d e + (- 615A b c - 60B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (420A b c + 210B b c)d e + (270A b c - 240B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 60B b c )d e + (- 15A b c + 60B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 105A b d e + (- 360A b c - 30B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (390A b c + 120B b c)d e + (- 60A b c - 180B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 135A b c + 120B b c )d e + (60A b c - 30B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 7 4 2 5 6 +--R - 105A b c e + (360A b c + 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 390A b c - 120B b c )d e + (60A b c + 180B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 30A b c + 15B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 105A b e + (115A b c + 30B b )d e + (450A b c - 50B b c)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (- 850A b c - 100B b c )d e + (165A b c + 390B b c )d e +--R + +--R 5 2 4 5 2 +--R (- 90A b c + 45B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 245A b d e + (679A b c + 70B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 358A b c - 234B b c)d e + (- 436A b c + 218B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (135A b c + 216B b c )d e + (- 90A b c + 45B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 161A b d e + (537A b c + 46B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 556A b c - 172B b c)d e + (90A b c + 216B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 15A b c d e + (- 30A b c + 15B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 15A b d e + 60A b c d e - 90A b c d e + 60A b c d e - 15A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (15b c d e - 60b c d e + 90b c d e - 60b c d e + 15b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 15b d e - 30b c d e - 30b c d e + 120b c d e - 105b c d e +--R + +--R 3 5 9 +--R 30b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 30b d e - 105b c d e + 120b c d e - 30b c d e - 30b c d e +--R + +--R 3 5 10 +--R 15b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (15b d e - 60b c d e + 90b c d e - 60b c d e + 15b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 422 + +--S 423 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 OF 765 +t0:=(A+B*x)*(d+e*x)^(9/2)/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 424 + +--S 425 OF 765 +r0:=1/4*(c*d-b*e)*(24*A*c^3*d^2+5*b^3*B*e^2+b^2*c*e*(3*B*d-A*e)-_ + 12*b*c^2*d*(B*d+2*A*e))*(d+e*x)^(3/2)/(b^4*c^2*(b+c*x))-_ + 1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+13*A*b*c*e)*_ + (d+e*x)^(5/2)/(b^3*c*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+9*A*b*e)*_ + (d+e*x)^(7/2)/(b^2*x*(b+c*x)^2)-1/2*A*(d+e*x)^(9/2)/(b*x^2*_ + (b+c*x)^2)-3/4*d^(5/2)*(16*A*c^2*d^2+3*b^2*e*(4*B*d+7*A*e)-_ + 4*b*c*d*(2*B*d+9*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/b^5+_ + 3/4*(c*d-b*e)^(5/2)*(16*A*c^3*d^2-5*b^3*B*e^2-4*b*c^2*d*_ + (2*B*d-A*e)-b^2*c*e*(8*B*d-A*e))*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b^5*c^(7/2))-3/4*e*(8*A*c^4*d^3-5*b^4*B*e^3+_ + b^3*c*e^2*(2*B*d+A*e)+b^2*c^2*d*e*(3*B*d+2*A*e)-4*b*c^3*d^2*_ + (B*d+3*A*e))*sqrt(d+e*x)/(b^4*c^3) +--R +--R +--R (2) +--R 4 3 5 2 4 3 4 4 3 3 +--R (3A b c - 15B b c )e + (6A b c + 6B b c )d e +--R + +--R 2 5 3 4 2 2 6 2 5 3 +--R (27A b c + 9B b c )d e + (- 84A b c + 24B b c )d e +--R + +--R 7 6 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (6A b c - 30B b c)e + (12A b c + 12B b c )d e +--R + +--R 3 4 4 3 2 2 2 5 3 4 3 +--R (54A b c + 18B b c )d e + (- 168A b c + 48B b c )d e +--R + +--R 6 2 5 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (3A b c - 15B b )e + (6A b c + 6B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (27A b c + 9B b c )d e + (- 84A b c + 24B b c )d e +--R + +--R 2 5 3 4 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 5 2 2 6 2 5 3 +--R - 63A b c d e + (108A b c - 36B b c )d e +--R + +--R 7 6 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 2 5 3 4 3 +--R - 126A b c d e + (216A b c - 72B b c )d e +--R + +--R 6 2 5 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 2 3 4 4 3 3 +--R - 63A b c d e + (108A b c - 36B b c )d e +--R + +--R 2 5 3 4 4 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 2 4 4 +--R 8B b c e x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (- 5A b c + 25B b c)e + (3A b c - 19B b c )d e +--R + +--R 3 4 4 3 2 2 2 5 3 4 3 +--R (21A b c + 3B b c )d e + (- 48A b c + 15B b c )d e +--R + +--R 6 2 5 4 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- 3A b c + 15B b )e + (- 5A b c - 11B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (33A b c - 9B b c )d e + (- 73A b c + 23B b c )d e +--R + +--R 2 5 3 4 4 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 3 4 4 3 4 +--R (- 17A b c d e + (8A b c - 4B b c )d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 5 4 6 4 3 7 3 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 425 + +--S 426 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 427 + +--S 428 OF 765 +r0:=-1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+11*A*b*c*e)*_ + (d+e*x)^(3/2)/(b^3*c*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+7*A*b*e)*_ + (d+e*x)^(5/2)/(b^2*x*(b+c*x)^2)-1/2*A*(d+e*x)^(7/2)/(b*x^2*_ + (b+c*x)^2)-1/4*d^(3/2)*(48*A*c^2*d^2+7*b^2*e*(4*B*d+5*A*e)-_ + 12*b*c*d*(2*B*d+7*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/b^5+1/4*_ + (c*d-b*e)^(3/2)*(48*A*c^3*d^2-3*b^3*B*e^2-12*b*c^2*d*(2*B*d+A*e)-_ + b^2*c*e*(8*B*d+A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^5*c^(5/2))+1/4*(c*d-b*e)*(24*A*c^3*d^2+3*b^3*B*e^2+b^2*c*e*_ + (5*B*d+A*e)-12*b*c^2*d*(B*d+2*A*e))*sqrt(d+e*x)/(b^4*c^2*(b+c*x)) +--R +--R +--R (2) +--R 3 3 4 2 3 2 4 3 3 2 +--R (A b c + 3B b c )e + (11A b c + 5B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c + 6B b c)e + (22A b c + 10B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A b c + 16B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 4 2 5 2 4 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 6 5 3 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 70A b c d e + (168A b c - 56B b c )d e +--R + +--R 5 2 4 3 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 2 4 3 3 3 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (A b c - 5B b c)e + (10A b c + 2B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 36A b c + 11B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - 3B b )e + (16A b c - 4B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 55A b c + 17B b c )d e + (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 13A b c d e + (8A b c - 4B b c )d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 428 + +--S 429 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 430 + +--S 431 OF 765 +r0:=-1/4*(4*b*B*d-8*A*c*d+5*A*b*e)*(d+e*x)^(3/2)/(b^2*x*(b+c*x)^2)-_ + 1/2*A*(d+e*x)^(5/2)/(b*x^2*(b+c*x)^2)-1/4*(48*A*c^2*d^2+5*b^2*e*_ + (4*B*d+3*A*e)-12*b*c*d*(2*B*d+5*A*e))*atanh(sqrt(d+e*x)/sqrt(d))*_ + sqrt(d)/b^5+1/4*(48*A*c^3*d^2+b^3*B*e^2-12*b*c^2*d*(2*B*d+3*A*e)+_ + b^2*c*e*(8*B*d+3*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*_ + sqrt(c*d-b*e)/(b^5*c^(3/2))-1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-_ + 2*b^2*B*e+9*A*b*c*e)*sqrt(d+e*x)/(b^3*c*(b+c*x)^2)+1/4*_ + (24*A*c^3*d^2+b^3*B*e^2-12*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ + (7*B*d+3*A*e))*sqrt(d+e*x)/(b^4*c*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 +--R (3A b c + B b c )e + (- 36A b c + 8B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 72A b c + 16B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (3A b c + B b )e + (- 36A b c + 8B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (- 15A b c e + (60A b c - 20B b c )d e + (- 48A c + 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 +--R - 30A b c e + (120A b c - 40B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 15A b c e + (60A b c - 20B b c)d e + (- 48A b c + 24B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 4 2 2 3 3 2 +--R (3A b c + B b c)e + (- 24A b c + 7B b c )d e +--R + +--R 4 2 3 2 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (5A b c - B b )e + (- 37A b c + 11B b c)d e +--R + +--R 2 3 3 2 2 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 9A b c d e + (8A b c - 4B b c)d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 431 + +--S 432 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 433 + +--S 434 OF 765 +r0:=-1/2*A*(d+e*x)^(3/2)/(b*x^2*(b+c*x)^2)-3/4*(16*A*c^2*d^2+b^2*e*_ + (4*B*d+A*e)-4*b*c*d*(2*B*d+3*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^5*sqrt(d))+3/4*(16*A*c^3*d^2-b^3*B*e^2-4*b*c^2*d*(2*B*d+5*A*e)+_ + b^2*c*e*(8*B*d+5*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^5*sqrt(c)*sqrt(c*d-b*e))-1/4*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+_ + 7*A*b*c*e)*sqrt(d+e*x)/(b^3*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+3*A*b*e)*_ + sqrt(d+e*x)/(b^2*x*(b+c*x)^2)+3/4*(8*A*c^2*d+b^2*B*e-4*b*c*(B*d+A*e))*_ + sqrt(d+e*x)/(b^4*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 +--R (15A b c - 3B b c )e + (- 60A b c + 24B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (30A b c - 6B b c)e + (- 120A b c + 48B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (15A b c - 3B b )e + (- 60A b c + 24B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 2 2 4 3 2 4 +--R (- 3A b c e + (36A b c - 12B b c )d e + (- 48A c + 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 2 2 3 +--R (- 6A b c e + (72A b c - 24B b c)d e + (- 96A b c + 48B b c )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- 3A b e + (36A b c - 12B b )d e + (- 48A b c + 24B b c)d )x +--R * +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 3B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 19A b c + 5B b )e + (36A b c - 18B b c)d)x +--R + +--R 4 3 4 4 +--R (- 5A b e + (8A b c - 4B b )d)x - 2A b d +--R * +--R +-----------+ +-+ +-+ +-------+ +--R \|- b e + c d \|c \|d \|e x + d +--R / +--R 5 2 4 6 3 7 2 +-----------+ +-+ +-+ +--R (4b c x + 8b c x + 4b x )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 434 + +--S 435 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 436 + +--S 437 OF 765 +r0:=-1/4*(48*A*c^2*d^2+b^2*e*(4*B*d-A*e)-12*b*c*d*(2*B*d+A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(3/2))+1/4*(48*A*c^3*d^2-_ + 15*b^3*B*e^2-12*b*c^2*d*(2*B*d+7*A*e)+5*b^2*c*e*(8*B*d+7*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b^5*_ + (c*d-b*e)^(3/2))-1/4*c*(6*b*B*d-12*A*c*d+A*b*e)*sqrt(d+e*x)/_ + (b^3*d*(b+c*x)^2)-1/2*A*sqrt(d+e*x)/(b*x^2*(b+c*x)^2)-_ + 1/4*(4*b*B*d-8*A*c*d+A*b*e)*sqrt(d+e*x)/(b^2*d*x*(b+c*x)^2)+_ + 1/4*c*(24*A*c^2*d^2+b^2*e*(11*B*d+A*e)-12*b*c*d*(B*d+2*A*e))*_ + sqrt(d+e*x)/(b^4*d*(c*d-b*e)*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 2 +--R (- 35A b c + 15B b c )d e + (84A b c - 40B b c )d e +--R + +--R 5 4 3 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (- 70A b c + 30B b c)d e + (168A b c - 80B b c )d e +--R + +--R 4 2 3 3 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (- 35A b c + 15B b )d e + (84A b c - 40B b c)d e +--R + +--R 2 3 3 2 3 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 2 3 2 3 3 2 2 4 2 3 2 +--R A b c e + (11A b c - 4B b c )d e + (- 60A b c + 28B b c )d e +--R + +--R 5 4 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 2 3 3 2 2 +--R 2A b c e + (22A b c - 8B b c)d e + (- 120A b c + 56B b c )d e +--R + +--R 4 2 3 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- A b c e + (24A b c - 11B b c )d e + (- 24A b c + 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 2A b c e + (37A b c - 17B b c)d e + (- 36A b c + 18B b c )d )x +--R + +--R 5 2 4 5 3 2 4 2 5 +--R (- A b e + (9A b c - 4B b )d e + (- 8A b c + 4B b c)d )x - 2A b d e +--R + +--R 4 2 +--R 2A b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 8 7 2 2 +--R ((4b c d e - 4b c d )x + (8b c d e - 8b c d )x + (4b d e - 4b c d )x ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 437 + +--S 438 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 OF 765 +t0:=(A+B*x)/((b*x+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R 3 6 2 5 2 4 3 3 +-------+ +--R (c x + 3b c x + 3b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 439 + +--S 440 OF 765 +r0:=-1/4*(48*A*c^2*d^2-b^2*e*(4*B*d-3*A*e)-12*b*c*d*(2*B*d-A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(5/2))+1/4*c^(3/2)*_ + (48*A*c^3*d^2-35*b^3*B*e^2-12*b*c^2*d*(2*B*d+9*A*e)+7*b^2*c*e*_ + (8*B*d+9*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*_ + (c*d-b*e)^(5/2))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-3*A*e)-b*c*d*_ + (6*B*d+7*A*e))*sqrt(d+e*x)/(b^3*d^2*(c*d-b*e)*(b+c*x)^2)-1/2*A*_ + sqrt(d+e*x)/(b*d*x^2*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d-3*A*b*e)*_ + sqrt(d+e*x)/(b^2*d^2*x*(b+c*x)^2)+1/4*c*(24*A*c^3*d^3-b^3*e^2*_ + (4*B*d-3*A*e)-12*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(19*B*d+6*A*e))*_ + sqrt(d+e*x)/(b^4*d^2*(c*d-b*e)^2*(b+c*x)) +--R +--R +--R (2) +--R 2 4 3 3 2 2 5 2 4 3 +--R (63A b c - 35B b c )d e + (- 108A b c + 56B b c )d e +--R + +--R 6 5 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (126A b c - 70B b c )d e + (- 216A b c + 112B b c )d e +--R + +--R 5 2 4 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (63A b c - 35B b c)d e + (- 108A b c + 56B b c )d e +--R + +--R 2 4 3 3 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 2 4 3 3 4 2 3 +--R - 3A b c e + (- 6A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 27A b c + 16B b c )d e + (84A b c - 44B b c )d e +--R + +--R 6 5 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 +--R - 6A b c e + (- 12A b c + 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 54A b c + 32B b c )d e + (168A b c - 88B b c )d e +--R + +--R 5 2 4 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R - 3A b e + (- 6A b c + 4B b )d e + (- 27A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (84A b c - 44B b c )d e + (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 3 3 3 4 2 2 2 4 3 3 2 +--R 3A b c e + (6A b c - 4B b c )d e + (- 36A b c + 19B b c )d e +--R + +--R 5 2 4 3 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 3 3 4 2 2 +--R 6A b c e + (10A b c - 8B b c)d e + (- 55A b c + 29B b c )d e +--R + +--R 2 4 3 3 3 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 3A b e + (2A b c - 4B b )d e + (- 13A b c + 8B b c)d e +--R + +--R 3 3 4 2 3 +--R (8A b c - 4B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (4b c d e - 8b c d e + 4b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 9 2 2 8 3 7 2 4 2 +--R (8b c d e - 16b c d e + 8b c d )x + (4b d e - 8b c d e + 4b c d )x +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 440 + +--S 441 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 441 + +)clear all + +--S 442 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 7 2 3 6 2 2 5 3 2 4 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x +--R + +--R 3 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 442 + +--S 443 OF 765 +r0:=-3/4*(16*A*c^2*d^2-b^2*e*(4*B*d-5*A*e)-4*b*c*d*(2*B*d-3*A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(7/2))+3/4*c^(5/2)*(16*A*c^3*d^2-_ + 21*b^3*B*e^2-4*b*c^2*d*(2*B*d+11*A*e)+3*b^2*c*e*(8*B*d+11*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(7/2))+_ + 3/4*e*(8*A*c^4*d^4+b^4*e^3*(4*B*d-5*A*e)-b^3*c*d*e^2*(4*B*d-3*A*e)-_ + 4*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*e*(9*B*d+5*A*e))/(b^4*d^3*_ + (c*d-b*e)^3*sqrt(d+e*x))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-5*A*e)-_ + b*c*d*(6*B*d+5*A*e))/(b^3*d^2*(c*d-b*e)*(b+c*x)^2*sqrt(d+e*x))-_ + 1/2*A/(b*d*x^2*(b+c*x)^2*sqrt(d+e*x))+1/4*(-4*b*B*d+8*A*c*d+_ + 5*A*b*e)/(b^2*d^2*x*(b+c*x)^2*sqrt(d+e*x))+1/4*c*(24*A*c^3*d^3-_ + b^3*e^2*(4*B*d-5*A*e)+b^2*c*d*e*(21*B*d+2*A*e)-12*b*c^2*d^2*(B*d+_ + 3*A*e))/(b^4*d^2*(c*d-b*e)^2*(b+c*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 5 3 4 3 2 6 2 5 4 +--R (- 99A b c + 63B b c )d e + (132A b c - 72B b c )d e +--R + +--R 7 6 5 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 3 2 2 5 3 4 4 +--R (- 198A b c + 126B b c )d e + (264A b c - 144B b c )d e +--R + +--R 6 2 5 5 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (- 99A b c + 63B b c )d e + (132A b c - 72B b c )d e +--R + +--R 2 5 3 4 5 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 2 5 4 3 5 2 4 +--R - 15A b c e + (9A b c + 12B b c )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (15A b c - 12B b c )d e + (51A b c - 36B b c )d e +--R + +--R 6 2 5 4 7 6 5 +--R (- 108A b c + 60B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 6 4 +--R - 30A b c e + (18A b c + 24B b c)d e +--R + +--R 4 3 5 2 2 3 3 4 4 3 3 2 +--R (30A b c - 24B b c )d e + (102A b c - 72B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (- 216A b c + 120B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 6 7 4 5 2 6 2 3 +--R - 15A b e + (9A b c + 12B b )d e + (15A b c - 12B b c)d e +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (51A b c - 36B b c )d e + (- 108A b c + 60B b c )d e +--R + +--R 2 5 3 4 5 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 2 5 4 3 5 2 4 +--R 15A b c e + (- 9A b c - 12B b c )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (- 15A b c + 12B b c )d e + (48A b c - 27B b c )d e +--R + +--R 6 2 5 4 +--R (- 24A b c + 12B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 6 4 +--R 30A b c e + (- 13A b c - 24B b c)d e +--R + +--R 4 3 5 2 2 3 3 4 4 3 3 2 +--R (- 33A b c + 20B b c )d e + (58A b c - 29B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (12A b c - 9B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 6 7 4 5 2 6 2 3 +--R 15A b e + (A b c - 12B b )d e + (- 23A b c + 4B b c)d e +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (- 7A b c + 12B b c )d e + (65A b c - 37B b c )d e +--R + +--R 2 5 3 4 5 +--R (- 36A b c + 18B b c )d +--R * +--R 2 +--R x +--R + +--R 7 4 6 7 2 3 5 2 6 3 2 +--R 5A b d e + (- 7A b c - 4B b )d e + (- 9A b c + 12B b c)d e +--R + +--R 4 3 5 2 4 3 4 4 3 5 +--R (19A b c - 12B b c )d e + (- 8A b c + 4B b c )d +--R * +--R x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - 2A b d e + 6A b c d e - 6A b c d e + 2A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (8b c d e - 24b c d e + 24b c d e - 8b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 443 + +--S 444 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 OF 765 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 445 + +--S 446 OF 765 +r0:=1/12*e*(72*A*c^4*d^4+5*b^4*e^3*(4*B*d-7*A*e)-9*b^3*c*d*e^2*(4*B*d-_ + 5*A*e)-36*b*c^3*d^3*(B*d+4*A*e)+3*b^2*c^2*d^2*e*(29*B*d+9*A*e))/(b^4*_ + d^3*(c*d-b*e)^3*(d+e*x)^(3/2))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-7*A*e)-_ + 3*b*c*d*(2*B*d+A*e))/(b^3*d^2*(c*d-b*e)*(b+c*x)^2*(d+e*x)^(3/2))-_ + 1/2*A/(b*d*x^2*(b+c*x)^2*(d+e*x)^(3/2))+1/4*(-4*b*B*d+8*A*c*d+7*A*b*e)/_ + (b^2*d^2*x*(b+c*x)^2*(d+e*x)^(3/2))+1/4*c*(24*A*c^3*d^3-b^3*e^2*_ + (4*B*d-7*A*e)+b^2*c*d*e*(23*B*d-2*A*e)-12*b*c^2*d^2*(B*d+3*A*e))/_ + (b^4*d^2*(c*d-b*e)^2*(b+c*x)*(d+e*x)^(3/2))-1/4*(48*A*c^2*d^2-_ + 5*b^2*e*(4*B*d-7*A*e)-12*b*c*d*(2*B*d-5*A*e))*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b^5*d^(9/2))+1/4*c^(7/2)*(48*A*c^3*d^2-99*b^3*B*e^2-_ + 12*b*c^2*d*(2*B*d+13*A*e)+11*b^2*c*e*(8*B*d+13*A*e))*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(9/2))+1/4*e*(24*A*c^5*d^5+_ + 8*b^4*c*d*e^3*(7*B*d-10*A*e)-5*b^5*e^4*(4*B*d-7*A*e)-6*b^3*_ + c^2*d^2*e^2*(4*B*d-3*A*e)+7*b^2*c^3*d^3*e*(5*B*d+4*A*e)-12*b*c^4*d^4*_ + (B*d+5*A*e))/(b^4*d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (429A b c - 297B b c )d e + (- 468A b c + 264B b c )d e +--R + +--R 8 7 6 +--R (144A c - 72B b c )d e +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (858A b c - 594B b c )d e + (- 507A b c + 231B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (- 180A b c + 120B b c )d e + (144A c - 72B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (429A b c - 297B b c )d e + (390A b c - 330B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 792A b c + 456B b c )d e + (288A b c - 144B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (429A b c - 297B b c )d e + (- 468A b c + 264B b c )d e +--R + +--R 2 6 3 5 7 +--R (144A b c - 72B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 6 2 7 5 3 6 2 6 +--R - 105A b c e + (240A b c + 60B b c )d e +--R + +--R 4 4 5 3 2 5 3 5 4 4 3 4 +--R (- 54A b c - 168B b c )d e + (- 84A b c + 72B b c )d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 249A b c + 192B b c )d e + (396A b c - 228B b c )d e +--R + +--R 8 7 6 +--R (- 144A c + 72B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R - 210A b c e + (375A b c + 120B b c)d e +--R + +--R 5 3 6 2 2 5 4 4 5 3 3 4 +--R (132A b c - 276B b c )d e + (- 222A b c - 24B b c )d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 582A b c + 456B b c )d e + (543A b c - 264B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (108A b c - 84B b c )d e + (- 144A c + 72B b c )d +--R * +--R 4 +--R x +--R + +--R 8 7 7 8 6 6 2 7 2 5 +--R - 105A b e + (30A b c + 60B b )d e + (426A b c - 48B b c)d e +--R + +--R 5 3 6 2 3 4 4 4 5 3 4 3 +--R (- 192A b c - 264B b c )d e + (- 417A b c + 336B b c )d e +--R + +--R 3 5 4 4 5 2 2 6 3 5 6 +--R (- 102A b c + 156B b c )d e + (648A b c - 384B b c )d e +--R + +--R 7 2 6 7 +--R (- 288A b c + 144B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 +--R - 105A b d e + (240A b c + 60B b )d e +--R + +--R 6 2 7 3 4 5 3 6 2 4 3 +--R (- 54A b c - 168B b c)d e + (- 84A b c + 72B b c )d e +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (- 249A b c + 192B b c )d e + (396A b c - 228B b c )d e +--R + +--R 2 6 3 5 7 +--R (- 144A b c + 72B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 6 2 7 5 3 6 2 6 +--R 105A b c e + (- 240A b c - 60B b c )d e +--R + +--R 4 4 5 3 2 5 3 5 4 4 3 4 +--R (54A b c + 168B b c )d e + (84A b c - 72B b c )d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 180A b c + 105B b c )d e + (72A b c - 36B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R 210A b c e + (- 340A b c - 120B b c)d e +--R + +--R 5 3 6 2 2 5 4 4 5 3 3 4 +--R (- 212A b c + 256B b c )d e + (240A b c + 80B b c )d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 105A b c + 15B b c )d e + (- 252A b c + 156B b c )d e +--R + +--R 7 2 6 6 +--R (144A b c - 72B b c )d e +--R * +--R 4 +--R x +--R + +--R 8 7 7 8 6 6 2 7 2 5 +--R 105A b e + (40A b c - 60B b )d e + (- 565A b c + 8B b c)d e +--R + +--R 5 3 6 2 3 4 4 4 5 3 4 3 +--R (180A b c + 364B b c )d e + (255A b c - 192B b c )d e +--R + +--R 3 5 4 4 5 2 2 6 3 5 6 +--R (- 438A b c + 234B b c )d e + (36A b c - 3B b c )d e +--R + +--R 7 2 6 7 +--R (72A b c - 36B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 +--R 140A b d e + (- 278A b c - 80B b )d e +--R + +--R 6 2 7 3 4 5 3 6 2 4 3 +--R (- 30A b c + 200B b c)d e + (180A b c - 48B b c )d e +--R + +--R 5 3 5 2 3 5 4 4 6 +--R - 48B b c d e + (- 225A b c + 135B b c )d e +--R + +--R 2 6 3 5 7 +--R (108A b c - 54B b c )d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 8 3 4 6 2 7 4 3 +--R 21A b d e + (- 60A b c - 12B b )d e + (30A b c + 48B b c)d e +--R + +--R 5 3 6 2 5 2 4 4 5 3 6 +--R (60A b c - 72B b c )d e + (- 75A b c + 48B b c )d e +--R + +--R 3 5 4 4 7 +--R (24A b c - 12B b c )d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - 6A b d e + 24A b c d e - 36A b c d e + 24A b c d e - 6A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (12b c d e - 48b c d e + 72b c d e - 48b c d e + 12b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 +--R 24b c d e - 84b c d e + 96b c d e - 24b c d e - 24b c d e +--R + +--R 5 6 9 +--R 12b c d +--R * +--R 4 +--R x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 +--R 12b d e - 24b c d e - 24b c d e + 96b c d e - 84b c d e +--R + +--R 6 5 9 +--R 24b c d +--R * +--R 3 +--R x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (12b d e - 48b c d e + 72b c d e - 48b c d e + 12b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 446 + +--S 447 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 OF 765 +t0:=(A+B*x)*(d+e*x)^(1/2)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R +-------+ | 2 +--R (1) (B x + A)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 448 + +--S 449 OF 765 +--r0:=2/7*B*(b*x+c*x^2)^(3/2)*sqrt(d+e*x)/c-2/105*(14*A*c*e*(c^2*d^2-_ +-- b*c*d*e+b^2*e^2)-B*(8*c^3*d^3-5*b*c^2*d^2*e-5*b^2*c*d*e^2+8*_ +-- b^3*e^3))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^3*e^(5/2)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/105*(-b)^(3/2)*_ +-- (c*d-b*e)*(7*A*c*e*(c*d-2*b*e)-B*(4*c^2*d^2+b*c*d*e-8*b^2*e^2))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*e^2*sqrt(d+e*x)*sqrt(b*x+_ +-- c*x^2))+2/105*(7*A*c*e*(c*d+b*e)-B*(4*c^2*d^2-2*b*c*d*e+4*b^2*e^2)+_ +-- 3*c*e*(B*c*d-4*b*B*e+7*A*c*e)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^2) +--E 449 + +--S 450 OF 765 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 451 + +--S 452 OF 765 +--r0:=-2/15*(5*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^2*e^(5/2)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*(-b)^(3/2)*(c*d-b*e)*(4*B*c*d+_ +-- 2*b*B*e-5*A*c*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*e^2*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(4*B*c*d-b*B*e-5*A*c*e-3*B*c*e*x)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c*e^2) +--E 452 + +--S 453 OF 765 +--d0:=D(m0,x) +--E 453 + +)clear all + +--S 454 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 454 + +--S 455 OF 765 +--r0:=-2/3*(8*B*c*d-b*B*e-6*A*c*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (c*e^(5/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*(-b)^(3/2)*(4*B*c*d-b*B*e-3*A*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+_ +-- e*x)/d)/(c^(3/2)*e^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(4*B*d-_ +-- 3*A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*sqrt(d+e*x)) +--E 455 + +--S 456 OF 765 +--d0:=D(m0,x) +--E 456 + +)clear all + +--S 457 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 457 + +--S 458 OF 765 +--r0:=-2/3*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(e^(5/2)*(c*d-b*e)*sqrt(-d)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(-b)^(3/2)*(4*B*d-A*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*e^2*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*(4*B*d-A*e+3*B*e*x)*sqrt(b*x+c*x^2)/(e^2*_ +-- (d+e*x)^(3/2))-2/3*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*_ +-- sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*sqrt(d+e*x)) +--E 458 + +--S 459 OF 765 +--d0:=D(m0,x) +--E 459 + +)clear all + +--S 460 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 460 + +--S 461 OF 765 +--r0:=-2/15*(2*A*e*(c^2*d^2-b*c*d*e+b^2*e^2)+B*d*(8*c^2*d^2-13*b*c*d*e+_ +-- 3*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(3/2)*e^(5/2)*(c*d-b*e)^2*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(-b)^(3/2)*(B*d*_ +-- (4*c*d-3*b*e)+A*e*(c*d-2*b*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*_ +-- e^2*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*(B*d*(8*c*d-_ +-- 9*b*e)+A*e*(2*c*d-b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+_ +-- e*x)^(3/2))-2/5*(4*B*d+A*e+5*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+_ +-- e*x)^(5/2))+2/15*(2*A*e*(c^2*d^2-b*c*d*e+b^2*e^2)+B*d*(8*c^2*d^2-_ +-- 13*b*c*d*e+3*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 461 + +--S 462 OF 765 +--d0:=D(m0,x) +--E 462 + +)clear all + +--S 463 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(1/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 463 + +--S 464 OF 765 +--r0:=-2/63*(8*B*c*d-3*b*B*e-9*A*c*e-7*B*c*e*x)*(b*x+c*x^2)^(3/2)*_ +-- sqrt(d+e*x)/(c*e^2)-2/315*(18*A*c*e*(8*c^3*d^3-12*b*c^2*d^2*e+_ +-- 2*b^2*c*d*e^2+b^3*e^3)-B*(128*c^4*d^4-184*b*c^3*d^3*e+27*_ +-- b^2*c^2*d^2*e^2+11*b^3*c*d*e^3+8*b^4*e^4))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^3*e^(9/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/315*(-b)^(3/2)*(c*d-b*e)*(9*A*c*e*(8*c^2*d^2-_ +-- 5*b*c*d*e-2*b^2*e^2)-B*(64*c^3*d^3-36*b*c^2*d^2*e-15*b^2*c*d*e^2-_ +-- 8*b^3*e^3))*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*e^4*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/315*(9*A*c*e*(8*c^2*d^2-11*b*c*d*e+b^2*e^2)-_ +-- 2*B*(32*c^3*d^3-42*b*c^2*d^2*e+3*b^2*c*d*e^2+2*b^3*e^3)-3*c*e*_ +-- (9*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-7*b*c*d*e-4*b^2*e^2))*x)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^4) +--E 464 + +--S 465 OF 765 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 466 + +--S 467 OF 765 +--r0:=2/7*(8*B*d-7*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+2/35*_ +-- (5*b*c*e*(8*B*d-7*A*e)*(2*c*d-b*e)-(16*B*c*d-b*B*e-14*A*c*e)*_ +-- (8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (c^2*e^(9/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/35*_ +-- (-b)^(3/2)*(c*d-b*e)*(7*A*c*e*(8*c*d-b*e)-2*B*(32*c^2*d^2-6*b*c*d*e-_ +-- b^2*e^2))*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*e^4*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/35*(7*A*c*e*(8*c*d-7*b*e)-B*(64*c^2*d^2-60*b*c*_ +-- d*e+b^2*e^2)+3*c*e*(16*B*c*d-b*B*e-14*A*c*e)*x)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/(c*e^4) +--E 467 + +--S 468 OF 765 +--d0:=D(m0,x) +--E 468 + +)clear all + +--S 469 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 469 + +--S 470 OF 765 +--r0:=2/15*(8*B*d-5*A*e+3*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/15*(40*A*c*e*(2*c*d-b*e)-B*(128*c^2*d^2-88*b*c*d*e+3*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c*e^(9/2)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(-b)^(3/2)*(5*A*c*e*(8*c*d-5*b*e)-_ +-- B*(64*c^2*d^2-52*b*c*d*e+3*b^2*e^2))*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(3/2)*e^4*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/15*(4*B*d*(16*c*d-9*b*e)-5*A*e*(8*c*d-3*b*e)+e*(16*B*c*d-_ +-- 3*b*B*e-10*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*sqrt(d+e*x)) +--E 470 + +--S 471 OF 765 +--d0:=D(m0,x) +--E 471 + +)clear all + +--S 472 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 472 + +--S 473 OF 765 +--r0:=2/15*(8*B*d-3*A*e+5*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 2/15*(3*A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(128*c^2*d^2-_ +-- 168*b*c*d*e+43*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/(e^(9/2)*(c*d-b*e)*_ +-- sqrt(-d)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/15*(-b)^(3/2)*(4*B*d*(16*c*d-7*b*e)-3*A*e*(8*c*d-b*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*e^4*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/15*(4*B*d*(16*c*d-7*b*e)-3*A*e*(8*c*d-b*e)+_ +-- 3*e*(16*B*c*d-5*b*B*e-6*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*_ +-- (d+e*x)^(3/2))-2/15*(3*A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*_ +-- (128*c^2*d^2-168*b*c*d*e+43*b^2*e^2))*sqrt(b*x+c*x^2)/(d*e^4*_ +-- (c*d-b*e)*sqrt(d+e*x)) +--E 473 + +--S 474 OF 765 +--d0:=D(m0,x) +--E 474 + +)clear all + +--S 475 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/sqrt(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 475 + +--S 476 OF 765 +--r0:=2/105*(7*A*c*e*(23*c^2*d^2-23*b*c*d*e+8*b^2*e^2)+B*(15*c^3*d^3-_ +-- 103*b*c^2*d^2*e+128*b^2*c*d*e^2-48*b^3*e^3))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^4*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/105*(c*d-b*e)*(105*A*c^3*d^2-48*b^3*B*e^2+_ +-- 8*b^2*c*e*(13*B*d+7*A*e)-b*c^2*d*(60*B*d+133*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/35*(5*B*c*d-6*b*B*e+7*A*c*e)*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/c^2+2/7*B*(d+e*x)^(5/2)*sqrt(b*x+c*x^2)/c+2/105*_ +-- (28*A*c*e*(2*c*d-b*e)+B*(15*c^2*d^2-43*b*c*d*e+24*b^2*e^2))*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/c^3 +--E 476 + +--S 477 OF 765 +--d0:=D(m0,x) +--E 477 + +)clear all + +--S 478 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 478 + +--S 479 OF 765 +--r0:=2/15*(10*A*c*e*(2*c*d-b*e)+B*(3*c^2*d^2-13*b*c*d*e+8*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^3*sqrt(e)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(c*d-b*e)*(9*b*B*c*d-15*A*c^2*d-_ +-- 8*b^2*B*e+10*A*b*c*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (c^(7/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*B*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/c+2/15*(3*B*c*d-4*b*B*e+5*A*c*e)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/c^2 +--E 479 + +--S 480 OF 765 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(b*x+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 481 + +--S 482 OF 765 +--r0:=2/3*(B*c*d-2*b*B*e+3*A*c*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^2*_ +-- sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*(2*b*B-_ +-- 3*A*c)*(c*d-b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (c^(5/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*B*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/c +--E 482 + +--S 483 OF 765 +--d0:=D(m0,x) +--E 483 + +)clear all + +--S 484 OF 765 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------- +--R +----------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 484 + +--S 485 OF 765 +--r0:=2*B*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c*sqrt(e)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(b*B-A*c)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(3/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 485 + +--S 486 OF 765 +--d0:=D(m0,x) +--E 486 + +)clear all + +--S 487 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) -------------------------------- +--R +----------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 487 + +--S 488 OF 765 +--r0:=2*(B*d-A*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((c*d-b*e)*sqrt(-d)*sqrt(e)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*A*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*sqrt(d+e*x)) +--E 488 + +--S 489 OF 765 +--d0:=D(m0,x) +--E 489 + +)clear all + +--S 490 OF 765 +t0:=(A+B*x)/((d+e*x)^(5/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +----------+ +--R 2 2 2 +-------+ | 2 +--R (e x + 2d e x + d )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 490 + +--S 491 OF 765 +--r0:=2/3*(2*A*e*(2*c*d-b*e)-B*d*(c*d+b*e))*(b+c*x)*elliptic_e(asin(_ +-- sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/_ +-- ((-d)^(3/2)*(c*d-b*e)^2*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/3*(b*B*d-3*A*c*d+2*A*b*e)*elliptic_f(asin(_ +-- sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ +-- (d+e*x)^(3/2))-2/3*(2*A*e*(2*c*d-b*e)-B*d*(c*d+b*e))*sqrt(b*x+_ +-- c*x^2)/(d^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 491 + +--S 492 OF 765 +--d0:=D(m0,x) +--E 492 + +)clear all + +--S 493 OF 765 +t0:=(A+B*x)/((d+e*x)^(7/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R +----------+ +--R 3 3 2 2 2 3 +-------+ | 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 493 + +--S 494 OF 765 +--r0:=2/15*(B*d*(3*c^2*d^2+7*b*c*d*e-2*b^2*e^2)-A*e*(23*c^2*d^2-_ +-- 23*b*c*d*e+8*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(5/2)*_ +-- (c*d-b*e)^3*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+_ +-- 2/15*(15*A*c^2*d^2+2*b^2*e*(B*d+4*A*e)-b*c*d*(6*B*d+19*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^3*(c*d-b*e)^2*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*(B*d-A*e)*sqrt(b*x+c*x^2)/_ +-- (d*(c*d-b*e)*(d+e*x)^(5/2))-2/15*(4*A*e*(2*c*d-b*e)-B*d*(3*c*d+_ +-- b*e))*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))+2/15*(B*d*_ +-- (3*c^2*d^2+7*b*c*d*e-2*b^2*e^2)-A*e*(23*c^2*d^2-23*b*c*d*e+_ +-- 8*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 494 + +--S 495 OF 765 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 496 + +--S 497 OF 765 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(7/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2/15*(30*A*c^4*d^3+48*b^4*B*e^3-15*b*c^3*d^2*(B*d+3*A*e)-_ +-- 8*b^3*c*e^2*(16*B*d+5*A*e)+b^2*c^2*d*e*(103*B*d+95*A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^4*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*e*(c*d-b*e)*(15*A*c^3*d^2-_ +-- 48*b^3*B*e^2-15*b*c^2*d*(4*B*d+5*A*e)+8*b^2*c*e*(13*B*d+5*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/5*e*(10*A*c^2*d+6*b^2*B*e-5*b*c*(B*d+A*e))*_ +-- (d+e*x)^(3/2)*sqrt(b*x+c*x^2)/(b^2*c^2)-2*(b*B-2*A*c)*e*_ +-- (d+e*x)^(5/2)*sqrt(b*x+c*x^2)/(b^2*c)+2/15*e*(30*A*c^3*d^2-_ +-- 24*b^3*B*e^2-15*b*c^2*d*(B*d+2*A*e)+b^2*c*e*(43*B*d+20*A*e))*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c^3) +--E 497 + +--S 498 OF 765 +--d0:=D(m0,x) +--E 498 + +)clear all + +--S 499 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 499 + +--S 500 OF 765 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(5/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2/3*(6*A*c^3*d^2-8*b^3*B*e^2-3*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ +-- (13*B*d+6*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^3*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(c*d-b*e)*_ +-- (9*b*B*c*d-3*A*c^2*d-8*b^2*B*e+6*A*b*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(7/2)*sqrt(-b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2*(b*B-2*A*c)*e*(d+e*x)^(3/2)*sqrt(b*x+c*x^2)/(b^2*c)+2/3*e*_ +-- (6*A*c^2*d+4*b^2*B*e-3*b*c*(B*d+A*e))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/_ +-- (b^2*c^2) +--E 500 + +--S 501 OF 765 +--d0:=D(m0,x) +--E 501 + +)clear all + +--S 502 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 502 + +--S 503 OF 765 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^2*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(2*b*B-A*c)*e*(c*d-b*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c) +--E 503 + +--S 504 OF 765 +--d0:=D(m0,x) +--E 504 + +)clear all + +--S 505 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 505 + +--S 506 OF 765 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*sqrt(b*x+c*x^2))-_ +-- 2*(b*B-2*A*c)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(b*B-A*c)*e*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(3/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)) +--E 506 + +--S 507 OF 765 +--d0:=D(m0,x) +--E 507 + +)clear all + +--S 508 OF 765 +t0:=(A+B*x)/((b*x+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ----------------------------------- +--R +----------+ +--R 2 +-------+ | 2 +--R (c x + b x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 508 + +--S 509 OF 765 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*d*_ +-- (c*d-b*e)*sqrt(b*x+c*x^2))+2*(b*B*d-2*A*c*d+A*b*e)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^2*(c*d-b*e)*sqrt(-d)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*A*e*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(d*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 509 + +--S 510 OF 765 +--d0:=D(m0,x) +--E 510 + +)clear all + +--S 511 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------- +--R +----------+ +--R 3 2 +-------+ | 2 +--R (c e x + (b e + c d)x + b d x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 511 + +--S 512 OF 765 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*(2*A*c^2*d^2-b^2*e*(B*d-2*A*e)-_ +-- b*c*d*(B*d+2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (b^2*(-d)^(3/2)*(c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*e*(b*B*d+A*c*d-2*A*b*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(d^2*(c*d-b*e)*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2*e*(2*A*c^2*d^2-b^2*e*(B*d-2*A*e)-b*c*d*(B*d+_ +-- 2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 512 + +--S 513 OF 765 +--d0:=D(m0,x) +--E 513 + +)clear all + +--S 514 OF 765 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 4 2 3 2 2 2 +-------+ +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 514 + +--S 515 OF 765 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- (d+e*x)^(3/2)*sqrt(b*x+c*x^2))-2/3*(6*A*c^3*d^3-b^2*c*d*e*(7*B*d-_ +-- 19*A*e)+2*b^3*e^2*(B*d-4*A*e)-3*b*c^2*d^2*(B*d+3*A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^2*(-d)^(5/2)*(c*d-b*e)^3*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(3*A*c^2*d^2+3*b*c*d*(2*B*d-_ +-- 5*A*e)-2*b^2*e*(B*d-4*A*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (d^3*(c*d-b*e)^2*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*e*(6*A*c^2*d^2-b^2*e*(B*d-4*A*e)-3*b*c*d*(B*d+2*A*e))*_ +-- sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-_ +-- 2/3*e*(6*A*c^3*d^3-b^2*c*d*e*(7*B*d-19*A*e)+2*b^3*e^2*(B*d-4*A*e)-_ +-- 3*b*c^2*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*_ +-- sqrt(d+e*x)) +--E 515 + +--S 516 OF 765 +--d0:=D(m0,x) +--E 516 + +)clear all + +--S 517 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 517 + +--S 518 OF 765 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(7/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(d+e*x)^(5/2)*(b*(4*b*B*d-8*A*c*d+7*A*b*e)-(16*A*c^2*d-_ +-- 3*b^2*B*e-8*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^4*d^3-8*b^4*B*e^3+b^3*c*e^2*(5*B*d+2*A*e)-8*b*c^3*d^2*_ +-- (B*d+3*A*e)+b^2*c^2*d*e*(5*B*d+4*A*e))*(b+c*x)*elliptic_e(asin(_ +-- sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(b^4*c^3*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+_ +-- c*x^2))-2/3*e*(c*d-b*e)*(8*A*c^3*d^2+8*b^3*B*e^2-b^2*c*e*(B*d+_ +-- 2*A*e)-b*c^2*d*(4*B*d+5*A*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- ((-b)^(5/2)*c^(7/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*_ +-- (16*A*c^2*d-3*b^2*B*e-8*b*c*(B*d+A*e))*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/(b^4*c)-2/3*e*(16*A*c^3*d^2+4*b^3*B*e^2+b^2*c*e*_ +-- (B*d-A*e)-8*b*c^2*d*(B*d+2*A*e))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^4*c^2) +--E 518 + +--S 519 OF 765 +--d0:=D(m0,x) +--E 519 + +)clear all + +--S 520 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 520 + +--S 521 OF 765 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(5/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(d+e*x)^(3/2)*(b*(4*b*B*d-8*A*c*d+5*A*b*e)-(16*A*c^2*d-_ +-- b^2*B*e-8*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^3*d^2+2*b^3*B*e^2+b^2*c*e*(3*B*d+A*e)-8*b*c^2*d*(B*d+_ +-- 2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/_ +-- (b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*c^2*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(c*d-b*e)*_ +-- (8*A*c^2*d-2*b^2*B*e-b*c*(4*B*d+A*e))*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/((-b)^(5/2)*c^(5/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*e*(16*A*c^2*d-b^2*B*e-8*b*c*(B*d+A*e))*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/(b^4*c) +--E 521 + +--S 522 OF 765 +--d0:=D(m0,x) +--E 522 + +)clear all + +--S 523 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 523 + +--S 524 OF 765 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(b*(4*b*B*d-8*A*c*d+3*A*b*e)-(16*A*c^2*d+b^2*B*e-8*b*c*_ +-- (B*d+A*e))*x)*sqrt(d+e*x)/(b^4*sqrt(b*x+c*x^2))-2/3*(16*A*c^2*d+_ +-- b^2*B*e-8*b*c*(B*d+A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (b^4*c*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*_ +-- (4*b*B*c*d-8*A*c^2*d-b^2*B*e+5*A*b*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/((-b)^(5/2)*c^(3/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 524 + +--S 525 OF 765 +--d0:=D(m0,x) +--E 525 + +)clear all + +--S 526 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 526 + +--S 527 OF 765 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(b*(c*d-b*e)*(4*b*B*d-8*A*c*d+A*b*e)-c*(16*A*c^2*d^2+b^2*e*_ +-- (7*B*d+A*e)-8*b*c*d*(B*d+2*A*e))*x)*sqrt(d+e*x)/(b^4*d*(c*d-b*e)*_ +-- sqrt(b*x+c*x^2))+2/3*(16*A*c^2*d^2+b^2*e*(7*B*d+A*e)-8*b*c*d*_ +-- (B*d+2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*(c*d-b*e)*sqrt(-d)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(4*b*B*d-_ +-- 8*A*c*d+A*b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 527 + +--S 528 OF 765 +--d0:=D(m0,x) +--E 528 + +)clear all + +--S 529 OF 765 +t0:=(A+B*x)/((b*x+c*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ---------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 +-------+ | 2 +--R (c x + 2b c x + b x )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 529 + +--S 530 OF 765 +--r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/_ +-- (b^2*d*(c*d-b*e)*(b*x+c*x^2)^(3/2))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+_ +-- b^2*e*(3*B*d-2*A*e)-b*c*d*(4*B*d+5*A*e))+c*(16*A*c^3*d^3-b^3*e^2*_ +-- (3*B*d-2*A*e)-8*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(13*B*d+4*A*e))*x)*_ +-- sqrt(d+e*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^3*d^3-b^3*e^2*(3*B*d-2*A*e)-8*b*c^2*d^2*(B*d+3*A*e)+_ +-- b^2*c*d*e*(13*B*d+4*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*(-d)^(3/2)*_ +-- (c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*_ +-- (8*A*c^2*d^2+b^2*e*(3*B*d-2*A*e)-b*c*d*(4*B*d+5*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d^2*(c*d-b*e)*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 530 + +--S 531 OF 765 +--d0:=D(m0,x) +--E 531 + +)clear all + +--S 532 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 5 2 4 2 3 2 2 +-------+ +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 532 + +--S 533 OF 765 +--r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- (b*x+c*x^2)^(3/2)*sqrt(d+e*x))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+b^2*_ +-- e*(3*B*d-4*A*e)-b*c*d*(4*B*d+3*A*e))+c*(16*A*c^3*d^3+15*b^2*B*_ +-- c*d^2*e-b^3*e^2*(3*B*d-4*A*e)-8*b*c^2*d^2*(B*d+3*A*e))*x)/_ +-- (b^4*d^2*(c*d-b*e)^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*_ +-- (16*A*c^4*d^4-b^3*c*d*e^2*(9*B*d-7*A*e)-8*b*c^3*d^3*(B*d+4*A*e)+_ +-- b^2*c^2*d^2*e*(19*B*d+9*A*e)+b^4*(6*B*d*e^3-8*A*e^4))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^4*(-d)^(5/2)*(c*d-b*e)^3*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(8*A*c^3*d^3+3*b^2*c*d*e*_ +-- (2*B*d-A*e)-b*c^2*d^2*(4*B*d+9*A*e)-b^3*(6*B*d*e^2-8*A*e^3))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d^3*(c*d-b*e)^2*_ +-- sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(16*A*c^4*d^4-_ +-- b^3*c*d*e^2*(9*B*d-7*A*e)-8*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*_ +-- e*(19*B*d+9*A*e)+b^4*(6*B*d*e^3-8*A*e^4))*sqrt(b*x+c*x^2)/_ +-- (b^4*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 533 + +--S 534 OF 765 +--d0:=D(m0,x) +--E 534 + +)clear all + +--S 535 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + A c x + B a x + A a)(e x + d) +--R Type: Expression(Integer) +--E 535 + +--S 536 OF 765 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(3*B*c*d^2-2*A*_ + c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^4*(2+m))-c*(3*B*d-A*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R (A c e - 3B c d)m + (7A c e - 21B c d)m + (14A c e - 42B c d)m +--R + +--R 8A c e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 2 2 2 +--R (B a e - 2A c d e + 3B c d )m + (8B a e - 16A c d e + 24B c d )m +--R + +--R 2 2 2 2 +--R (19B a e - 38A c d e + 57B c d )m + 12B a e - 24A c d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (A a e - B a d e + A c d e - B c d )m +--R + +--R 3 2 2 3 2 +--R (9A a e - 9B a d e + 9A c d e - 9B c d )m +--R + +--R 3 2 2 3 3 +--R (26A a e - 26B a d e + 26A c d e - 26B c d )m + 24A a e +--R + +--R 2 2 3 +--R - 24B a d e + 24A c d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 536 + +--S 537 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 OF 765 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 5 4 2 3 6 +--R B c e x + (A c e + 5B c d e )x + (B a e + 5A c d e + 10B c d e )x +--R + +--R 5 4 2 3 3 2 5 +--R (A a e + 5B a d e + 10A c d e + 10B c d e )x +--R + +--R 4 2 3 3 2 4 4 +--R (5A a d e + 10B a d e + 10A c d e + 5B c d e)x +--R + +--R 2 3 3 2 4 5 3 +--R (10A a d e + 10B a d e + 5A c d e + B c d )x +--R + +--R 3 2 4 5 2 4 5 5 +--R (10A a d e + 5B a d e + A c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 538 + +--S 539 OF 765 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^6/e^4+1/7*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^7/e^4-1/8*c*(3*B*d-A*e)*(d+e*x)^8/e^4+1/9*B*_ + c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 1 9 5 8 10 2 7 7 +--R (- B a e + - A c d e + -- B c d e )x +--R 7 7 7 +--R + +--R 1 9 5 8 5 2 7 5 3 6 6 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 6 6 3 3 +--R + +--R 8 2 7 3 6 4 5 5 +--R (A a d e + 2B a d e + 2A c d e + B c d e )x +--R + +--R 5 2 7 5 3 6 5 4 5 1 5 4 4 +--R (- A a d e + - B a d e + - A c d e + - B c d e )x +--R 2 2 4 4 +--R + +--R 10 3 6 5 4 5 1 5 4 3 5 4 5 1 5 4 2 +--R (-- A a d e + - B a d e + - A c d e )x + (- A a d e + - B a d e )x +--R 3 3 3 2 2 +--R + +--R 5 4 1 6 3 1 7 2 1 8 1 9 +--R A a d e x + - A a d e - -- B a d e + --- A c d e - --- B c d +--R 6 42 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 539 + +--S 540 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 4 3 2 2 5 +--R B c e x + (A c e + 4B c d e )x + (B a e + 4A c d e + 6B c d e )x +--R + +--R 4 3 2 2 3 4 +--R (A a e + 4B a d e + 6A c d e + 4B c d e)x +--R + +--R 3 2 2 3 4 3 +--R (4A a d e + 6B a d e + 4A c d e + B c d )x +--R + +--R 2 2 3 4 2 3 4 4 +--R (6A a d e + 4B a d e + A c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 541 + +--S 542 OF 765 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^5/e^4+1/6*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^6/e^4-1/7*c*(3*B*d-A*e)*(d+e*x)^7/e^4+1/8*B*c*_ + (d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 8 4 7 7 +--R - B c e x + (- A c e + - B c d e )x +--R 8 7 7 +--R + +--R 1 8 2 7 2 6 6 +--R (- B a e + - A c d e + B c d e )x +--R 6 3 +--R + +--R 1 8 4 7 6 2 6 4 3 5 5 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 7 3 2 6 3 5 1 4 4 4 +--R (A a d e + - B a d e + A c d e + - B c d e )x +--R 2 4 +--R + +--R 2 6 4 3 5 1 4 4 3 3 5 1 4 4 2 +--R (2A a d e + - B a d e + - A c d e )x + (2A a d e + - B a d e )x +--R 3 3 2 +--R + +--R 4 4 1 5 3 1 6 2 1 7 1 8 +--R A a d e x + - A a d e - -- B a d e + --- A c d e - --- B c d +--R 5 30 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 542 + +--S 543 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 3 2 2 4 +--R B c e x + (A c e + 3B c d e )x + (B a e + 3A c d e + 3B c d e)x +--R + +--R 3 2 2 3 3 +--R (A a e + 3B a d e + 3A c d e + B c d )x +--R + +--R 2 2 3 2 2 3 3 +--R (3A a d e + 3B a d e + A c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 544 + +--S 545 OF 765 +r0:=-1/4*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^4/e^4+1/5*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^5/e^4-1/6*c*(3*B*d-A*e)*(d+e*x)^6/e^4+_ + 1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 7 1 6 6 +--R - B c e x + (- A c e + - B c d e )x +--R 7 6 2 +--R + +--R 1 7 3 6 3 2 5 5 +--R (- B a e + - A c d e + - B c d e )x +--R 5 5 5 +--R + +--R 1 7 3 6 3 2 5 1 3 4 4 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 6 2 5 1 3 4 3 3 2 5 1 3 4 2 +--R (A a d e + B a d e + - A c d e )x + (- A a d e + - B a d e )x +--R 3 2 2 +--R + +--R 3 4 1 4 3 1 5 2 1 6 1 7 +--R A a d e x + - A a d e - -- B a d e + -- A c d e - --- B c d +--R 4 20 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 545 + +--S 546 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 546 + +)clear all + +--S 547 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 2 2 3 +--R B c e x + (A c e + 2B c d e)x + (B a e + 2A c d e + B c d )x +--R + +--R 2 2 2 2 2 +--R (A a e + 2B a d e + A c d )x + (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 547 + +--S 548 OF 765 +r0:=a*A*d^2*x+1/2*a*d*(B*d+2*A*e)*x^2+1/3*(A*c*d^2+2*a*B*d*e+a*A*e^2)*x^3+_ + 1/4*(B*c*d^2+2*A*c*d*e+a*B*e^2)*x^4+1/5*c*e*(2*B*d+A*e)*x^5+_ + 1/6*B*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - B c e x + (- A c e + - B c d e)x + (- B a e + - A c d e + - B c d )x +--R 6 5 5 4 2 4 +--R + +--R 1 2 2 1 2 3 1 2 2 2 +--R (- A a e + - B a d e + - A c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 548 + +--S 549 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 OF 765 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + (A c e + B c d)x + (B a e + A c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 550 + +--S 551 OF 765 +r0:=a*A*d*x+1/2*a*(B*d+A*e)*x^2+1/3*(A*c*d+a*B*e)*x^3+1/4*c*(B*d+A*e)*x^4+_ + 1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 4 1 1 3 +--R - B c e x + (- A c e + - B c d)x + (- B a e + - A c d)x +--R 5 4 4 3 3 +--R + +--R 1 1 2 +--R (- A a e + - B a d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 551 + +--S 552 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 OF 765 +t0:=(A+B*x)*(a+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + A c x + B a x + A a +--R Type: Polynomial(Integer) +--E 553 + +--S 554 OF 765 +r0:=a*A*x+1/2*a*B*x^2+1/3*A*c*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 3 1 2 +--R (2) - B c x + - A c x + - B a x + A a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 554 + +--S 555 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 OF 765 +r0:=(B*c*d^2-A*c*d*e+a*B*e^2)*x/e^3-1/2*c*(B*d-A*e)*x^2/e^2+1/3*B*c*x^3/e-_ + (B*d-A*e)*(c*d^2+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 3 3 3 +--R (6A a e - 6B a d e + 6A c d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 3 2 2 +--R (3A c e - 3B c d e )x + (6B a e - 6A c d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 557 + +--S 558 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 559 + +--S 560 OF 765 +r0:=-c*(2*B*d-A*e)*x/e^3+1/2*B*c*x^2/e^2+(B*d-A*e)*(c*d^2+a*e^2)/_ + (e^4*(d+e*x))+(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((2B a e - 4A c d e + 6B c d e)x + 2B a d e - 4A c d e + 6B c d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 2 2 3 +--R B c e x + (2A c e - 3B c d e )x + (2A c d e - 4B c d e)x - 2A a e +--R + +--R 2 2 3 +--R 2B a d e - 2A c d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 560 + +--S 561 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 561 + +)clear all + +--S 562 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 562 + +--S 563 OF 765 +r0:=B*c*x/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^2)+(-3*B*c*d^2+_ + 2*A*c*d*e-a*B*e^2)/(e^4*(d+e*x))-c*(3*B*d-A*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 +--R (2A c e - 6B c d e )x + (4A c d e - 12B c d e)x + 2A c d e +--R + +--R 3 +--R - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 3 +--R 2B c e x + 4B c d e x + (- 2B a e + 4A c d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R - B a d e + 3A c d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 563 + +--S 564 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 565 + +--S 566 OF 765 +r0:=1/3*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^2)+c*(3*B*d-A*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 +--R (- 6A c e + 18B c d e )x + (- 3B a e - 6A c d e + 27B c d e)x +--R + +--R 3 2 2 3 +--R - 2A a e - B a d e - 2A c d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 566 + +--S 567 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 568 + +--S 569 OF 765 +r0:=1/4*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^3)+1/2*c*(3*B*d-A*e)/(e^4*(d+e*x)^2)-_ + B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 3 3 2 2 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 1 3 1 2 2 1 3 1 2 +--R (- - B a e - - A c d e - B c d e)x - - A a e - -- B a d e +--R 3 3 4 12 +--R + +--R 1 2 1 3 +--R - -- A c d e - - B c d +--R 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 569 + +--S 570 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 OF 765 +r0:=1/5*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^5)+1/4*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^4)+1/3*c*(3*B*d-A*e)/(e^4*(d+e*x)^3)-_ + 1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 2 +--R + +--R 1 3 1 2 1 2 1 3 1 2 +--R (- - B a e - - A c d e - - B c d e)x - - A a e - -- B a d e +--R 4 6 4 5 20 +--R + +--R 1 2 1 3 +--R - -- A c d e - -- B c d +--R 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 572 + +--S 573 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + A c x + B a x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 574 + +--S 575 OF 765 +r0:=1/6*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^6)+1/5*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^5)+1/4*c*(3*B*d-A*e)/(e^4*(d+e*x)^4)-_ + 1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 +--R - - B c e x + (- - A c e - - B c d e )x +--R 3 4 4 +--R + +--R 1 3 1 2 1 2 1 3 1 2 +--R (- - B a e - -- A c d e - -- B c d e)x - - A a e - -- B a d e +--R 5 10 10 6 30 +--R + +--R 1 2 1 3 +--R - -- A c d e - -- B c d +--R 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 575 + +--S 576 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 576 + +)clear all + +--S 577 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 m +--R (1) (B c x + A c x + 2B a c x + 2A a c x + B a x + A a )(e x + d) +--R Type: Expression(Integer) +--E 577 + +--S 578 OF 765 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))+(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^6*(2+m))-2*c*_ + (5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3+m)/(e^6*_ + (3+m))+2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(4+m)/(e^6*(4+m))-_ + c^2*(5*B*d-A*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 2 2 3 +--R (A c e - 5B c d)m + (16A c e - 80B c d)m + (95A c e - 475B c d)m +--R + +--R 2 2 2 2 2 2 +--R (260A c e - 1300B c d)m + (324A c e - 1620B c d)m + 144A c e +--R + +--R 2 +--R - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 5 +--R (2B a c e - 4A c d e + 10B c d )m +--R + +--R 2 2 2 2 4 +--R (34B a c e - 68A c d e + 170B c d )m +--R + +--R 2 2 2 2 3 +--R (214B a c e - 428A c d e + 1070B c d )m +--R + +--R 2 2 2 2 2 +--R (614B a c e - 1228A c d e + 3070B c d )m +--R + +--R 2 2 2 2 2 2 +--R (792B a c e - 1584A c d e + 3960B c d )m + 360B a c e - 720A c d e +--R + +--R 2 2 +--R 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 5 +--R (2A a c e - 6B a c d e + 6A c d e - 10B c d )m +--R + +--R 3 2 2 2 2 3 4 +--R (36A a c e - 108B a c d e + 108A c d e - 180B c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (242A a c e - 726B a c d e + 726A c d e - 1210B c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (744A a c e - 2232B a c d e + 2232A c d e - 3720B c d )m +--R + +--R 3 2 2 2 2 3 +--R (1016A a c e - 3048B a c d e + 3048A c d e - 5080B c d )m +--R + +--R 3 2 2 2 2 3 +--R 480A a c e - 1440B a c d e + 1440A c d e - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 3 2 2 2 3 2 4 5 +--R (B a e - 4A a c d e + 6B a c d e - 4A c d e + 5B c d )m +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (19B a e - 76A a c d e + 114B a c d e - 76A c d e + 95B c d )m +--R + +--R 2 4 3 2 2 2 3 +--R 137B a e - 548A a c d e + 822B a c d e - 548A c d e +--R + +--R 2 4 +--R 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R 461B a e - 1844A a c d e + 2766B a c d e - 1844A c d e +--R + +--R 2 4 +--R 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R 702B a e - 2808A a c d e + 4212B a c d e - 2808A c d e +--R + +--R 2 4 +--R 3510B c d +--R * +--R m +--R + +--R 2 4 3 2 2 2 3 2 4 +--R 360B a e - 1440A a c d e + 2160B a c d e - 1440A c d e + 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 5 +--R (A a e - B a d e + 2A a c d e - 2B a c d e + A c d e - B c d )m +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R 20A a e - 20B a d e + 40A a c d e - 40B a c d e + 20A c d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 155A a e - 155B a d e + 310A a c d e - 310B a c d e +--R + +--R 2 4 2 5 +--R 155A c d e - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 580A a e - 580B a d e + 1160A a c d e - 1160B a c d e +--R + +--R 2 4 2 5 +--R 580A c d e - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 1044A a e - 1044B a d e + 2088A a c d e - 2088B a c d e +--R + +--R 2 4 2 5 +--R 1044A c d e - 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 720A a e - 720B a d e + 1440A a c d e - 1440B a c d e +--R + +--R 2 4 2 5 +--R 720A c d e - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 578 + +--S 579 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 OF 765 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 10 2 5 2 4 9 5 2 4 2 2 3 8 +--R B c e x + (A c e + 5B c d e )x + (2B a c e + 5A c d e + 10B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 7 +--R (2A a c e + 10B a c d e + 10A c d e + 10B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 6 +--R (B a e + 10A a c d e + 20B a c d e + 10A c d e + 5B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 5 +--R (A a e + 5B a d e + 20A a c d e + 20B a c d e + 5A c d e + B c d )x +--R + +--R 2 4 2 2 3 3 2 4 2 5 4 +--R (5A a d e + 10B a d e + 20A a c d e + 10B a c d e + A c d )x +--R + +--R 2 2 3 2 3 2 4 5 3 +--R (10A a d e + 10B a d e + 10A a c d e + 2B a c d )x +--R + +--R 2 3 2 2 4 5 2 2 4 2 5 2 5 +--R (10A a d e + 5B a d e + 2A a c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 580 + +--S 581 OF 765 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^6/e^6+1/7*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^6-1/4*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^8/e^6+2/9*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^9/e^6-1/10*c^2*(5*B*d-A*e)*(d+e*x)^10/e^6+_ + 1/11*B*c^2*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 2 11 11 1 2 11 1 2 10 10 +--R -- B c e x + (-- A c e + - B c d e )x +--R 11 10 2 +--R + +--R 2 11 5 2 10 10 2 2 9 9 +--R (- B a c e + - A c d e + -- B c d e )x +--R 9 9 9 +--R + +--R 1 11 5 10 5 2 2 9 5 2 3 8 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 1 2 11 10 10 20 2 9 10 2 3 8 5 2 4 7 7 +--R (- B a e + -- A a c d e + -- B a c d e + -- A c d e + - B c d e )x +--R 7 7 7 7 7 +--R + +--R 1 2 11 5 2 10 10 2 9 10 3 8 5 2 4 7 +--R - A a e + - B a d e + -- A a c d e + -- B a c d e + - A c d e +--R 6 6 3 3 6 +--R + +--R 1 2 5 6 +--R - B c d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 2 10 2 2 9 3 8 4 7 1 2 5 6 5 +--R (A a d e + 2B a d e + 4A a c d e + 2B a c d e + - A c d e )x +--R 5 +--R + +--R 5 2 2 9 5 2 3 8 5 4 7 1 5 6 4 +--R (- A a d e + - B a d e + - A a c d e + - B a c d e )x +--R 2 2 2 2 +--R + +--R 10 2 3 8 5 2 4 7 2 5 6 3 5 2 4 7 1 2 5 6 2 +--R (-- A a d e + - B a d e + - A a c d e )x + (- A a d e + - B a d e )x +--R 3 3 3 2 2 +--R + +--R 2 5 6 1 2 6 5 1 2 7 4 1 8 3 1 9 2 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 6 42 84 252 +--R + +--R 1 2 10 1 2 11 +--R ---- A c d e - ---- B c d +--R 1260 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 581 + +--S 582 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 4 2 3 2 2 2 7 +--R B c e x + (A c e + 4B c d e )x + (2B a c e + 4A c d e + 6B c d e )x +--R + +--R 4 3 2 2 2 2 3 6 +--R (2A a c e + 8B a c d e + 6A c d e + 4B c d e)x +--R + +--R 2 4 3 2 2 2 3 2 4 5 +--R (B a e + 8A a c d e + 12B a c d e + 4A c d e + B c d )x +--R + +--R 2 4 2 3 2 2 3 2 4 4 +--R (A a e + 4B a d e + 12A a c d e + 8B a c d e + A c d )x +--R + +--R 2 3 2 2 2 3 4 3 +--R (4A a d e + 6B a d e + 8A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 3 4 2 2 3 2 4 2 4 +--R (6A a d e + 4B a d e + 2A a c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 583 + +--S 584 OF 765 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^5/e^6+1/6*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^6-2/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^7/e^6+1/4*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^8/e^6-1/9*c^2*(5*B*d-A*e)*(d+e*x)^9/e^6+_ + 1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 10 4 2 9 9 +--R -- B c e x + (- A c e + - B c d e )x +--R 10 9 9 +--R + +--R 1 10 1 2 9 3 2 2 8 8 +--R (- B a c e + - A c d e + - B c d e )x +--R 4 2 4 +--R + +--R 2 10 8 9 6 2 2 8 4 2 3 7 7 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 7 7 7 7 +--R + +--R 1 2 10 4 9 2 8 2 2 3 7 1 2 4 6 6 +--R (- B a e + - A a c d e + 2B a c d e + - A c d e + - B c d e )x +--R 6 3 3 6 +--R + +--R 1 2 10 4 2 9 12 2 8 8 3 7 1 2 4 6 5 +--R (- A a e + - B a d e + -- A a c d e + - B a c d e + - A c d e )x +--R 5 5 5 5 5 +--R + +--R 2 9 3 2 2 8 3 7 1 4 6 4 +--R (A a d e + - B a d e + 2A a c d e + - B a c d e )x +--R 2 2 +--R + +--R 2 2 8 4 2 3 7 2 4 6 3 2 3 7 1 2 4 6 2 +--R (2A a d e + - B a d e + - A a c d e )x + (2A a d e + - B a d e )x +--R 3 3 2 +--R + +--R 2 4 6 1 2 5 5 1 2 6 4 2 7 3 1 8 2 +--R A a d e x + - A a d e - -- B a d e + --- A a c d e - --- B a c d e +--R 5 30 105 140 +--R + +--R 1 2 9 1 2 10 +--R --- A c d e - ---- B c d +--R 630 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 584 + +--S 585 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 3 2 2 2 2 6 +--R B c e x + (A c e + 3B c d e )x + (2B a c e + 3A c d e + 3B c d e)x +--R + +--R 3 2 2 2 2 3 5 +--R (2A a c e + 6B a c d e + 3A c d e + B c d )x +--R + +--R 2 3 2 2 2 3 4 +--R (B a e + 6A a c d e + 6B a c d e + A c d )x +--R + +--R 2 3 2 2 2 3 3 +--R (A a e + 3B a d e + 6A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 3 2 2 2 2 3 2 3 +--R (3A a d e + 3B a d e + 2A a c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 586 + +--S 587 OF 765 +r0:=-1/4*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^4/e^6+1/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^5/e^6-1/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^6/e^6+2/7*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^6-1/8*c^2*(5*B*d-A*e)*(d+e*x)^8/e^6+_ + 1/9*B*c^2*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 1 2 9 9 1 2 9 3 2 8 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 2 9 3 2 8 3 2 2 7 7 +--R (- B a c e + - A c d e + - B c d e )x +--R 7 7 7 +--R + +--R 1 9 8 1 2 2 7 1 2 3 6 6 +--R (- A a c e + B a c d e + - A c d e + - B c d e )x +--R 3 2 6 +--R + +--R 1 2 9 6 8 6 2 7 1 2 3 6 5 +--R (- B a e + - A a c d e + - B a c d e + - A c d e )x +--R 5 5 5 5 +--R + +--R 1 2 9 3 2 8 3 2 7 1 3 6 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d e )x +--R 4 4 2 2 +--R + +--R 2 8 2 2 7 2 3 6 3 3 2 2 7 1 2 3 6 2 +--R (A a d e + B a d e + - A a c d e )x + (- A a d e + - B a d e )x +--R 3 2 2 +--R + +--R 2 3 6 1 2 4 5 1 2 5 4 1 6 3 1 7 2 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - -- B a c d e +--R 4 20 30 70 +--R + +--R 1 2 8 1 2 9 +--R --- A c d e - --- B c d +--R 280 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 587 + +--S 588 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 2 2 2 2 5 +--R B c e x + (A c e + 2B c d e)x + (2B a c e + 2A c d e + B c d )x +--R + +--R 2 2 2 4 2 2 2 3 +--R (2A a c e + 4B a c d e + A c d )x + (B a e + 4A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (A a e + 2B a d e + 2A a c d )x + (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 589 + +--S 590 OF 765 +r0:=a^2*A*d^2*x+1/2*a^2*d*(B*d+2*A*e)*x^2+1/3*a*(2*A*c*d^2+2*a*B*d*e+_ + a*A*e^2)*x^3+1/4*a*(2*B*c*d^2+4*A*c*d*e+a*B*e^2)*x^4+1/5*c*(A*c*d^2+_ + 4*a*B*d*e+2*a*A*e^2)*x^5+1/6*c*(B*c*d^2+2*A*c*d*e+2*a*B*e^2)*x^6+_ + 1/7*c^2*e*(2*B*d+A*e)*x^7+1/8*B*c^2*e^2*x^8 +--R +--R +--R (2) +--R 1 2 2 8 1 2 2 2 2 7 +--R - B c e x + (- A c e + - B c d e)x +--R 8 7 7 +--R + +--R 1 2 1 2 1 2 2 6 +--R (- B a c e + - A c d e + - B c d )x +--R 3 3 6 +--R + +--R 2 2 4 1 2 2 5 +--R (- A a c e + - B a c d e + - A c d )x +--R 5 5 5 +--R + +--R 1 2 2 1 2 4 +--R (- B a e + A a c d e + - B a c d )x +--R 4 2 +--R + +--R 1 2 2 2 2 2 2 3 2 1 2 2 2 2 2 +--R (- A a e + - B a d e + - A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 590 + +--S 591 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 591 + +)clear all + +--S 592 OF 765 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 2 4 +--R B c e x + (A c e + B c d)x + (2B a c e + A c d)x +--R + +--R 3 2 2 2 2 2 +--R (2A a c e + 2B a c d)x + (B a e + 2A a c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 592 + +--S 593 OF 765 +r0:=a^2*A*d*x+1/2*a^2*(B*d+A*e)*x^2+1/3*a*(2*A*c*d+a*B*e)*x^3+1/2*a*c*_ + (B*d+A*e)*x^4+1/5*c*(A*c*d+2*a*B*e)*x^5+1/6*c^2*(B*d+A*e)*x^6+_ + 1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 2 6 2 1 2 5 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 7 6 6 5 5 +--R + +--R 1 1 4 1 2 2 3 1 2 1 2 2 +--R (- A a c e + - B a c d)x + (- B a e + - A a c d)x + (- A a e + - B a d)x +--R 2 2 3 3 2 2 +--R + +--R 2 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 593 + +--S 594 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R (1) B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R Type: Polynomial(Integer) +--E 595 + +--S 596 OF 765 +r0:=a^2*A*x+2/3*a*A*c*x^3+1/5*A*c^2*x^5+1/6*B*(a+c*x^2)^3/c +--R +--R +--R (2) +--R 1 3 6 1 3 5 1 2 4 2 2 3 1 2 2 2 1 3 +--R - B c x + - A c x + - B a c x + - A a c x + - B a c x + A a c x + - B a +--R 6 5 2 3 2 6 +--R ----------------------------------------------------------------------------- +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 596 + +--S 597 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 598 + +--S 599 OF 765 +r0:=(B*(c*d^2+a*e^2)^2-A*c*d*e*(c*d^2+2*a*e^2))*x/e^5-1/2*c*(B*d-A*e)*_ + (c*d^2+2*a*e^2)*x^2/e^4+1/3*c*(B*c*d^2-A*c*d*e+2*a*B*e^2)*x^3/e^3-_ + 1/4*c^2*(B*d-A*e)*x^4/e^2+1/5*B*c^2*x^5/e-(B*d-A*e)*(c*d^2+a*e^2)^2*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 3 3 2 2 4 +--R 60A a e - 60B a d e + 120A a c d e - 120B a c d e + 60A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + (15A c e - 15B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (40B a c e - 20A c d e + 20B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (60A a c e - 60B a c d e + 30A c d e - 30B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (60B a e - 120A a c d e + 120B a c d e - 60A c d e + 60B c d e)x +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 599 + +--S 600 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 601 + +--S 602 OF 765 +r0:=-c*(4*B*c*d^3-3*A*c*d^2*e+4*a*B*d*e^2-2*a*A*e^3)*x/e^5+1/2*c*_ + (3*B*c*d^2-2*A*c*d*e+2*a*B*e^2)*x^2/e^4-1/3*c^2*(2*B*d-A*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x))+_ + (c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 4 2 3 2 3 2 2 4 +--R (12B a e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d e)x +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + (4A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 8A c d e + 10B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (24A a c e - 36B a c d e + 24A c d e - 30B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 5 +--R (24A a c d e - 48B a c d e + 36A c d e - 48B c d e)x - 12A a e +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 24A a c d e + 24B a c d e - 12A c d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 602 + +--S 603 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^3 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 604 + +--S 605 OF 765 +r0:=c*(6*B*c*d^2-3*A*c*d*e+2*a*B*e^2)*x/e^5-1/2*c^2*(3*B*d-A*e)*x^2/e^4+_ + 1/3*B*c^2*x^3/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^2)-_ + (c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x))-_ + 2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 4 2 2 3 2 3 2 2 +--R (12A a c e - 36B a c d e + 36A c d e - 60B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (24A a c d e - 72B a c d e + 72A c d e - 120B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R 12A a c d e - 36B a c d e + 36A c d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + (3A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 12A c d e + 20B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (24B a c d e - 33A c d e + 63B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 6B a e + 24A a c d e - 24B a c d e + 6A c d e + 6B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - 3B a d e + 18A a c d e - 30B a c d e + 21A c d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 605 + +--S 606 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 606 + +)clear all + +--S 607 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^4 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 607 + +--S 608 OF 765 +r0:=-c^2*(4*B*d-A*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*(B*d-A*e)*(c*d^2+_ + a*e^2)^2/(e^6*(d+e*x)^3)-1/2*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+_ + a*B*e^2)/(e^6*(d+e*x)^2)+2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-_ + a*A*e^3)/(e^6*(d+e*x))+2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 2 4 2 2 3 3 +--R (12B a c e - 24A c d e + 60B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (36B a c d e - 72A c d e + 180B c d e )x +--R + +--R 2 3 2 3 2 2 4 3 2 2 4 +--R (36B a c d e - 72A c d e + 180B c d e)x + 12B a c d e - 24A c d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 2 4 2 2 3 3 +--R 3B c e x + (6A c e - 15B c d e )x + (18A c d e - 63B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e + 36B a c d e - 18A c d e - 9B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 3B a e - 12A a c d e + 54B a c d e - 54A c d e + 81B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 2A a e - B a d e - 4A a c d e + 22B a c d e - 26A c d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 608 + +--S 609 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^5 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 610 + +--S 611 OF 765 +r0:=B*c^2*x/e^5+1/4*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^4)-1/3*(c*d^2+_ + a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^3)+c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^2)-2*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x))-c^2*(5*B*d-A*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 4 2 4 2 2 3 3 +--R (12A c e - 60B c d e )x + (48A c d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 2 3 2 2 4 2 4 +--R (72A c d e - 360B c d e )x + (48A c d e - 240B c d e)x + 12A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 5 2 4 2 2 3 3 +--R 12B c e x + 48B c d e x + (- 24B a c e + 48A c d e - 48B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e - 36B a c d e + 108A c d e - 252B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 4B a e - 8A a c d e - 24B a c d e + 88A c d e - 248B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - B a d e - 2A a c d e - 6B a c d e + 25A c d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 611 + +--S 612 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^6 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 613 + +--S 614 OF 765 +r0:=1/5*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^5)-1/4*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^4)+2/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^3)-c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^2)+c^2*(5*B*d-A*e)/(e^6*(d+e*x))+_ + B*c^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R (- 60A c e + 300B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 60B a c e - 120A c d e + 900B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 40A a c e - 60B a c d e - 120A c d e + 1100B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 15B a e - 20A a c d e - 30B a c d e - 60A c d e + 625B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 12A a e - 3B a d e - 4A a c d e - 6B a c d e - 12A c d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Expression(Integer) +--E 614 + +--S 615 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 616 + +--S 617 OF 765 +r0:=1/6*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^6)-1/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^5)+1/2*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^4)-2/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^3)+1/2*c^2*(5*B*d-A*e)/_ + (e^6*(d+e*x)^2)-B*c^2/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 5 5 1 2 5 5 2 4 4 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 2 5 2 2 4 10 2 2 3 3 +--R (- - B a c e - - A c d e - -- B c d e )x +--R 3 3 3 +--R + +--R 1 5 1 4 1 2 2 3 5 2 3 2 2 +--R (- - A a c e - - B a c d e - - A c d e - - B c d e )x +--R 2 2 2 2 +--R + +--R 1 2 5 1 4 1 2 3 1 2 3 2 2 4 +--R (- - B a e - - A a c d e - - B a c d e - - A c d e - B c d e)x +--R 5 5 5 5 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - -- A a c d e - -- B a c d e - -- A c d e +--R 6 30 30 30 30 +--R + +--R 1 2 5 +--R - - B c d +--R 6 +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 617 + +--S 618 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 619 + +--S 620 OF 765 +r0:=1/7*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^7)-1/6*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^6)+2/5*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^5)-1/2*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^4)+1/3*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^3)-1/2*B*c^2/(e^6*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 5 2 4 4 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 6 +--R + +--R 1 5 1 2 4 5 2 2 3 3 +--R (- - B a c e - - A c d e - - B c d e )x +--R 2 3 6 +--R + +--R 2 5 3 4 1 2 2 3 1 2 3 2 2 +--R (- - A a c e - -- B a c d e - - A c d e - - B c d e )x +--R 5 10 5 2 +--R + +--R 1 2 5 2 4 1 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - - B c d e)x +--R 6 15 10 15 6 +--R + +--R 1 2 5 1 2 4 2 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - --- A a c d e - -- B a c d e - --- A c d e +--R 7 42 105 70 105 +--R + +--R 1 2 5 +--R - -- B c d +--R 42 +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 6 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 620 + +--S 621 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 622 + +--S 623 OF 765 +r0:=1/8*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^8)-1/7*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^7)+1/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^6)-2/5*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^5)+1/4*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^4)-1/3*B*c^2/(e^6*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 5 2 4 4 +--R - - B c e x + (- - A c e - -- B c d e )x +--R 3 4 12 +--R + +--R 2 5 1 2 4 1 2 2 3 3 +--R (- - B a c e - - A c d e - - B c d e )x +--R 5 5 3 +--R + +--R 1 5 1 4 1 2 2 3 1 2 3 2 2 +--R (- - A a c e - - B a c d e - -- A c d e - - B c d e )x +--R 3 5 10 6 +--R + +--R 1 2 5 2 4 2 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - -- B c d e)x +--R 7 21 35 35 21 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e - --- A c d e +--R 8 56 84 140 280 +--R + +--R 1 2 5 +--R - --- B c d +--R 168 +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 5 9 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 8 2 7 7 8 6 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 623 + +--S 624 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^10 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 625 + +--S 626 OF 765 +r0:=1/9*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^9)-1/8*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^8)+2/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^7)-1/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^6)+1/5*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^5)-1/4*B*c^2/(e^6*(d+e*x)^4) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 1 2 4 4 +--R - - B c e x + (- - A c e - - B c d e )x +--R 4 5 4 +--R + +--R 1 5 2 2 4 1 2 2 3 3 +--R (- - B a c e - -- A c d e - - B c d e )x +--R 3 15 6 +--R + +--R 2 5 1 4 2 2 2 3 1 2 3 2 2 +--R (- - A a c e - - B a c d e - -- A c d e - -- B c d e )x +--R 7 7 35 14 +--R + +--R 1 2 5 1 4 1 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - -- B c d e)x +--R 8 14 28 70 56 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - --- A a c d e - --- B a c d e - --- A c d e +--R 9 72 126 252 630 +--R + +--R 1 2 5 +--R - --- B c d +--R 504 +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 5 10 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 9 3 7 8 2 8 7 9 6 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 626 + +--S 627 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 628 + +--S 629 OF 765 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))+(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^8*(2+m))-3*c*(c*d^2+_ + a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3+m)/_ + (e^8*(3+m))-c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*_ + c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(4+m)/(e^8*(4+m))-c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(5+m)/(e^8*(5+m))+_ + 3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(6+m)/(e^8*(6+m))-_ + c^3*(7*B*d-A*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 3 7 3 3 6 +--R (A c e - 7B c d)m + (29A c e - 203B c d)m +--R + +--R 3 3 5 3 3 4 +--R (343A c e - 2401B c d)m + (2135A c e - 14945B c d)m +--R + +--R 3 3 3 3 3 2 +--R (7504A c e - 52528B c d)m + (14756A c e - 103292B c d)m +--R + +--R 3 3 3 3 +--R (14832A c e - 103824B c d)m + 5760A c e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 3 3 2 7 +--R (3B a c e - 6A c d e + 21B c d )m +--R + +--R 2 2 3 3 2 6 +--R (90B a c e - 180A c d e + 630B c d )m +--R + +--R 2 2 3 3 2 5 +--R (1098B a c e - 2196A c d e + 7686B c d )m +--R + +--R 2 2 3 3 2 4 +--R (7020B a c e - 14040A c d e + 49140B c d )m +--R + +--R 2 2 3 3 2 3 +--R (25227B a c e - 50454A c d e + 176589B c d )m +--R + +--R 2 2 3 3 2 2 +--R (50490B a c e - 100980A c d e + 353430B c d )m +--R + +--R 2 2 3 3 2 2 2 +--R (51432B a c e - 102864A c d e + 360024B c d )m + 20160B a c e +--R + +--R 3 3 2 +--R - 40320A c d e + 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 2 2 3 2 3 3 7 +--R (3A a c e - 15B a c d e + 15A c d e - 35B c d )m +--R + +--R 2 3 2 2 3 2 3 3 6 +--R (93A a c e - 465B a c d e + 465A c d e - 1085B c d )m +--R + +--R 2 3 2 2 3 2 3 3 5 +--R (1173A a c e - 5865B a c d e + 5865A c d e - 13685B c d )m +--R + +--R 2 3 2 2 3 2 3 3 4 +--R (7743A a c e - 38715B a c d e + 38715A c d e - 90335B c d )m +--R + +--R 2 3 2 2 3 2 3 3 3 +--R (28632A a c e - 143160B a c d e + 143160A c d e - 334040B c d )m +--R + +--R 2 3 2 2 3 2 3 3 2 +--R (58692A a c e - 293460B a c d e + 293460A c d e - 684740B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R (60912A a c e - 304560B a c d e + 304560A c d e - 710640B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R 24192A a c e - 120960B a c d e + 120960A c d e - 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 4 2 3 2 2 2 3 3 3 4 7 +--R (3B a c e - 12A a c d e + 30B a c d e - 20A c d e + 35B c d )m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 96B a c e - 384A a c d e + 960B a c d e - 640A c d e +--R + +--R 3 4 +--R 1120B c d +--R * +--R 6 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 1254B a c e - 5016A a c d e + 12540B a c d e - 8360A c d e +--R + +--R 3 4 +--R 14630B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 8592B a c e - 34368A a c d e + 85920B a c d e - 57280A c d e +--R + +--R 3 4 +--R 100240B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 32979B a c e - 131916A a c d e + 329790B a c d e +--R + +--R 3 3 3 4 +--R - 219860A c d e + 384755B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 69936B a c e - 279744A a c d e + 699360B a c d e +--R + +--R 3 3 3 4 +--R - 466240A c d e + 815920B c d +--R * +--R 2 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 74628B a c e - 298512A a c d e + 746280B a c d e +--R + +--R 3 3 3 4 +--R - 497520A c d e + 870660B c d +--R * +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 30240B a c e - 120960A a c d e + 302400B a c d e - 201600A c d e +--R + +--R 3 4 +--R 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 +--R 3A a c e - 9B a c d e + 18A a c d e - 30B a c d e + 15A c d e +--R + +--R 3 5 +--R - 21B c d +--R * +--R 7 +--R m +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 99A a c e - 297B a c d e + 594A a c d e - 990B a c d e +--R + +--R 3 4 3 5 +--R 495A c d e - 693B c d +--R * +--R 6 +--R m +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 1341A a c e - 4023B a c d e + 8046A a c d e - 13410B a c d e +--R + +--R 3 4 3 5 +--R 6705A c d e - 9387B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 9585A a c e - 28755B a c d e + 57510A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 95850B a c d e + 47925A c d e - 67095B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 38592A a c e - 115776B a c d e + 231552A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 385920B a c d e + 192960A c d e - 270144B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 86076A a c e - 258228B a c d e + 516456A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 860760B a c d e + 430380A c d e - 602532B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 96144A a c e - 288432B a c d e + 576864A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 961440B a c d e + 480720A c d e - 673008B c d +--R * +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 40320A a c e - 120960B a c d e + 241920A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 403200B a c d e + 201600A c d e - 282240B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 6 2 5 2 2 4 2 3 3 2 4 2 +--R B a e - 6A a c d e + 9B a c d e - 12A a c d e + 15B a c d e +--R + +--R 3 5 3 6 +--R - 6A c d e + 7B c d +--R * +--R 7 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 34B a e - 204A a c d e + 306B a c d e - 408A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 510B a c d e - 204A c d e + 238B c d +--R * +--R 6 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 478B a e - 2868A a c d e + 4302B a c d e - 5736A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 7170B a c d e - 2868A c d e + 3346B c d +--R * +--R 5 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 3580B a e - 21480A a c d e + 32220B a c d e - 42960A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 53700B a c d e - 21480A c d e + 25060B c d +--R * +--R 4 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 15289B a e - 91734A a c d e + 137601B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R - 183468A a c d e + 229335B a c d e - 91734A c d e + 107023B c d +--R * +--R 3 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 36706B a e - 220236A a c d e + 330354B a c d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 440472A a c d e + 550590B a c d e - 220236A c d e +--R + +--R 3 6 +--R 256942B c d +--R * +--R 2 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 44712B a e - 268272A a c d e + 402408B a c d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 536544A a c d e + 670680B a c d e - 268272A c d e +--R + +--R 3 6 +--R 312984B c d +--R * +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 20160B a e - 120960A a c d e + 181440B a c d e - 241920A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 302400B a c d e - 120960A c d e + 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R A a e - B a d e + 3A a c d e - 3B a c d e + 3A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 3B a c d e + A c d e - B c d +--R * +--R 7 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 35A a e - 35B a d e + 105A a c d e - 105B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 105A a c d e - 105B a c d e + 35A c d e - 35B c d +--R * +--R 6 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 511A a e - 511B a d e + 1533A a c d e - 1533B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 1533A a c d e - 1533B a c d e + 511A c d e - 511B c d +--R * +--R 5 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 4025A a e - 4025B a d e + 12075A a c d e - 12075B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 12075A a c d e - 12075B a c d e + 4025A c d e - 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 18424A a e - 18424B a d e + 55272A a c d e - 55272B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 55272A a c d e - 55272B a c d e + 18424A c d e - 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 48860A a e - 48860B a d e + 146580A a c d e - 146580B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 146580A a c d e - 146580B a c d e + 48860A c d e - 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 69264A a e - 69264B a d e + 207792A a c d e - 207792B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 207792A a c d e - 207792B a c d e + 69264A c d e - 69264B c d +--R * +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 40320A a e - 40320B a d e + 120960A a c d e - 120960B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 120960A a c d e - 120960B a c d e + 40320A c d e - 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 629 + +--S 630 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 OF 765 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 5 12 3 5 3 4 11 +--R B c e x + (A c e + 5B c d e )x +--R + +--R 2 5 3 4 3 2 3 10 +--R (3B a c e + 5A c d e + 10B c d e )x +--R + +--R 2 5 2 4 3 2 3 3 3 2 9 +--R (3A a c e + 15B a c d e + 10A c d e + 10B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 3 2 3 4 8 +--R (3B a c e + 15A a c d e + 30B a c d e + 10A c d e + 5B c d e)x +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 +--R 3A a c e + 15B a c d e + 30A a c d e + 30B a c d e + 5A c d e +--R + +--R 3 5 +--R B c d +--R * +--R 7 +--R x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R B a e + 15A a c d e + 30B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R 6 +--R x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R A a e + 5B a d e + 30A a c d e + 30B a c d e + 15A a c d e +--R + +--R 2 5 +--R 3B a c d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 4 +--R (5A a d e + 10B a d e + 30A a c d e + 15B a c d e + 3A a c d )x +--R + +--R 3 2 3 3 3 2 2 4 2 5 3 +--R (10A a d e + 10B a d e + 15A a c d e + 3B a c d )x +--R + +--R 3 3 2 3 4 2 5 2 3 4 3 5 3 5 +--R (10A a d e + 5B a d e + 3A a c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 631 + +--S 632 OF 765 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^6/e^8+1/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^8-3/8*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^8/e^8-1/9*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))*(d+e*x)^9/e^8-1/10*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*_ + B*d*e^2-3*a*A*e^3)*(d+e*x)^10/e^8+3/11*c^2*(7*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^11/e^8-1/12*c^3*(7*B*d-A*e)*(d+e*x)^12/e^8+1/13*_ + B*c^3*(d+e*x)^13/e^8 +--R +--R +--R (2) +--R 1 3 13 13 1 3 13 5 3 12 12 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 13 12 12 +--R + +--R 3 2 13 5 3 12 10 3 2 11 11 +--R (-- B a c e + -- A c d e + -- B c d e )x +--R 11 11 11 +--R + +--R 3 2 13 3 2 12 3 2 11 3 3 10 10 +--R (-- A a c e + - B a c d e + A c d e + B c d e )x +--R 10 2 +--R + +--R 1 2 13 5 2 12 10 2 2 11 10 3 3 10 +--R - B a c e + - A a c d e + -- B a c d e + -- A c d e +--R 3 3 3 9 +--R + +--R 5 3 4 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 13 15 2 12 15 2 2 11 15 2 3 10 +--R - A a c e + -- B a c d e + -- A a c d e + -- B a c d e +--R 8 8 4 4 +--R + +--R 5 3 4 9 1 3 5 8 +--R - A c d e + - B c d e +--R 8 8 +--R * +--R 8 +--R x +--R + +--R 1 3 13 15 2 12 30 2 2 11 30 2 3 10 +--R - B a e + -- A a c d e + -- B a c d e + -- A a c d e +--R 7 7 7 7 +--R + +--R 15 2 4 9 1 3 5 8 +--R -- B a c d e + - A c d e +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 13 5 3 12 2 2 11 2 3 10 5 2 4 9 +--R - A a e + - B a d e + 5A a c d e + 5B a c d e + - A a c d e +--R 6 6 2 +--R + +--R 1 2 5 8 +--R - B a c d e +--R 2 +--R * +--R 6 +--R x +--R + +--R 3 12 3 2 11 2 3 10 2 4 9 3 2 5 8 5 +--R (A a d e + 2B a d e + 6A a c d e + 3B a c d e + - A a c d e )x +--R 5 +--R + +--R 5 3 2 11 5 3 3 10 15 2 4 9 3 2 5 8 4 +--R (- A a d e + - B a d e + -- A a c d e + - B a c d e )x +--R 2 2 4 4 +--R + +--R 10 3 3 10 5 3 4 9 2 5 8 3 5 3 4 9 1 3 5 8 2 +--R (-- A a d e + - B a d e + A a c d e )x + (- A a d e + - B a d e )x +--R 3 3 2 2 +--R + +--R 3 5 8 1 3 6 7 1 3 7 6 1 2 8 5 1 2 9 4 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 6 42 56 168 +--R + +--R 1 2 10 3 1 2 11 2 1 3 12 1 3 13 +--R --- A a c d e - --- B a c d e + ---- A c d e - ----- B c d +--R 420 924 5544 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 632 + +--S 633 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 4 3 3 10 2 4 3 3 3 2 2 9 +--R B c e x + (A c e + 4B c d e )x + (3B a c e + 4A c d e + 6B c d e )x +--R + +--R 2 4 2 3 3 2 2 3 3 8 +--R (3A a c e + 12B a c d e + 6A c d e + 4B c d e)x +--R + +--R 2 4 2 3 2 2 2 3 3 3 4 7 +--R (3B a c e + 12A a c d e + 18B a c d e + 4A c d e + B c d )x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 6 +--R (3A a c e + 12B a c d e + 18A a c d e + 12B a c d e + A c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 5 +--R (B a e + 12A a c d e + 18B a c d e + 12A a c d e + 3B a c d )x +--R + +--R 3 4 3 3 2 2 2 2 3 2 4 4 +--R (A a e + 4B a d e + 18A a c d e + 12B a c d e + 3A a c d )x +--R + +--R 3 3 3 2 2 2 3 2 4 3 +--R (4A a d e + 6B a d e + 12A a c d e + 3B a c d )x +--R + +--R 3 2 2 3 3 2 4 2 3 3 3 4 3 4 +--R (6A a d e + 4B a d e + 3A a c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 634 + +--S 635 OF 765 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^5/e^8+1/6*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^8-3/7*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^7/e^8-1/8*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))*(d+e*x)^8/e^8-1/9*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)*(d+e*x)^9/e^8+3/10*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*_ + (d+e*x)^10/e^8-1/11*c^3*(7*B*d-A*e)*(d+e*x)^11/e^8+1/12*B*c^3*_ + (d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 3 12 12 1 3 12 4 3 11 11 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 12 11 11 +--R + +--R 3 2 12 2 3 11 3 3 2 10 10 +--R (-- B a c e + - A c d e + - B c d e )x +--R 10 5 5 +--R + +--R 1 2 12 4 2 11 2 3 2 10 4 3 3 9 9 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 3 3 3 9 +--R + +--R 3 2 12 3 2 11 9 2 2 10 1 3 3 9 1 3 4 8 8 +--R (- B a c e + - A a c d e + - B a c d e + - A c d e + - B c d e )x +--R 8 2 4 2 8 +--R + +--R 3 2 12 12 2 11 18 2 2 10 12 2 3 9 +--R - A a c e + -- B a c d e + -- A a c d e + -- B a c d e +--R 7 7 7 7 +--R + +--R 1 3 4 8 +--R - A c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 1 3 12 2 11 2 2 10 2 3 9 1 2 4 8 6 +--R (- B a e + 2A a c d e + 3B a c d e + 2A a c d e + - B a c d e )x +--R 6 2 +--R + +--R 1 3 12 4 3 11 18 2 2 10 12 2 3 9 +--R - A a e + - B a d e + -- A a c d e + -- B a c d e +--R 5 5 5 5 +--R + +--R 3 2 4 8 +--R - A a c d e +--R 5 +--R * +--R 5 +--R x +--R + +--R 3 11 3 3 2 10 2 3 9 3 2 4 8 4 +--R (A a d e + - B a d e + 3A a c d e + - B a c d e )x +--R 2 4 +--R + +--R 3 2 10 4 3 3 9 2 4 8 3 3 3 9 1 3 4 8 2 +--R (2A a d e + - B a d e + A a c d e )x + (2A a d e + - B a d e )x +--R 3 2 +--R + +--R 3 4 8 1 3 5 7 1 3 6 6 1 2 7 5 3 2 8 4 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 5 30 35 280 +--R + +--R 1 2 9 3 1 2 10 2 1 3 11 1 3 12 +--R --- A a c d e - --- B a c d e + ---- A c d e - ---- B c d +--R 210 420 2310 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 635 + +--S 636 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 3 3 2 9 2 3 3 2 3 2 8 +--R B c e x + (A c e + 3B c d e )x + (3B a c e + 3A c d e + 3B c d e)x +--R + +--R 2 3 2 2 3 2 3 3 7 +--R (3A a c e + 9B a c d e + 3A c d e + B c d )x +--R + +--R 2 3 2 2 2 2 3 3 6 +--R (3B a c e + 9A a c d e + 9B a c d e + A c d )x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (3A a c e + 9B a c d e + 9A a c d e + 3B a c d )x +--R + +--R 3 3 2 2 2 2 2 3 4 +--R (B a e + 9A a c d e + 9B a c d e + 3A a c d )x +--R + +--R 3 3 3 2 2 2 2 3 3 +--R (A a e + 3B a d e + 9A a c d e + 3B a c d )x +--R + +--R 3 2 3 2 2 3 2 3 2 3 3 3 3 +--R (3A a d e + 3B a d e + 3A a c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 637 + +--S 638 OF 765 +r0:=a^3*A*d^3*x+1/2*a^3*d^2*(B*d+3*A*e)*x^2+a^2*d*(A*c*d^2+a*B*d*e+_ + a*A*e^2)*x^3+1/4*a^2*(3*B*c*d^3+9*A*c*d^2*e+3*a*B*d*e^2+a*A*e^3)*_ + x^4+1/5*a*(a*B*e*(9*c*d^2+a*e^2)+3*A*c*d*(c*d^2+3*a*e^2))*x^5+_ + 1/2*a*c*(B*c*d^3+3*A*c*d^2*e+3*a*B*d*e^2+a*A*e^3)*x^6+1/7*c*(3*a*_ + B*e*(3*c*d^2+a*e^2)+A*c*d*(c*d^2+9*a*e^2))*x^7+1/8*c^2*(B*c*d^3+3*_ + A*c*d^2*e+9*a*B*d*e^2+3*a*A*e^3)*x^8+1/3*c^2*e*(B*c*d^2+A*c*d*e+_ + a*B*e^2)*x^9+1/10*c^3*e^2*(3*B*d+A*e)*x^10+1/11*B*c^3*e^3*x^11 +--R +--R +--R (2) +--R 1 3 3 11 1 3 3 3 3 2 10 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 11 10 10 +--R + +--R 1 2 3 1 3 2 1 3 2 9 +--R (- B a c e + - A c d e + - B c d e)x +--R 3 3 3 +--R + +--R 3 2 3 9 2 2 3 3 2 1 3 3 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d )x +--R 8 8 8 8 +--R + +--R 3 2 3 9 2 2 9 2 2 1 3 3 7 +--R (- B a c e + - A a c d e + - B a c d e + - A c d )x +--R 7 7 7 7 +--R + +--R 1 2 3 3 2 2 3 2 2 1 2 3 6 +--R (- A a c e + - B a c d e + - A a c d e + - B a c d )x +--R 2 2 2 2 +--R + +--R 1 3 3 9 2 2 9 2 2 3 2 3 5 +--R (- B a e + - A a c d e + - B a c d e + - A a c d )x +--R 5 5 5 5 +--R + +--R 1 3 3 3 3 2 9 2 2 3 2 3 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d )x +--R 4 4 4 4 +--R + +--R 3 2 3 2 2 3 3 3 3 2 1 3 3 2 3 3 +--R (A a d e + B a d e + A a c d )x + (- A a d e + - B a d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 638 + +--S 639 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 3 8 2 2 3 3 2 7 +--R B c e x + (A c e + 2B c d e)x + (3B a c e + 2A c d e + B c d )x +--R + +--R 2 2 2 3 2 6 +--R (3A a c e + 6B a c d e + A c d )x +--R + +--R 2 2 2 2 2 5 +--R (3B a c e + 6A a c d e + 3B a c d )x +--R + +--R 2 2 2 2 2 4 +--R (3A a c e + 6B a c d e + 3A a c d )x +--R + +--R 3 2 2 2 2 3 3 2 3 2 2 2 +--R (B a e + 6A a c d e + 3B a c d )x + (A a e + 2B a d e + 3A a c d )x +--R + +--R 3 3 2 3 2 +--R (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 640 + +--S 641 OF 765 +r0:=a^3*A*d^2*x+1/2*a^3*d*(B*d+2*A*e)*x^2+1/3*a^2*(3*A*c*d^2+2*a*B*d*e+_ + a*A*e^2)*x^3+1/4*a^2*(3*B*c*d^2+6*A*c*d*e+a*B*e^2)*x^4+3/5*a*c*_ + (A*c*d^2+2*a*B*d*e+a*A*e^2)*x^5+1/2*a*c*(B*c*d^2+2*A*c*d*e+a*B*_ + e^2)*x^6+1/7*c^2*(A*c*d^2+6*a*B*d*e+3*a*A*e^2)*x^7+1/8*c^2*(B*c*d^2+_ + 2*A*c*d*e+3*a*B*e^2)*x^8+1/9*c^3*e*(2*B*d+A*e)*x^9+1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 2 2 3 9 +--R -- B c e x + (- A c e + - B c d e)x +--R 10 9 9 +--R + +--R 3 2 2 1 3 1 3 2 8 +--R (- B a c e + - A c d e + - B c d )x +--R 8 4 8 +--R + +--R 3 2 2 6 2 1 3 2 7 +--R (- A a c e + - B a c d e + - A c d )x +--R 7 7 7 +--R + +--R 1 2 2 2 1 2 2 6 +--R (- B a c e + A a c d e + - B a c d )x +--R 2 2 +--R + +--R 3 2 2 6 2 3 2 2 5 +--R (- A a c e + - B a c d e + - A a c d )x +--R 5 5 5 +--R + +--R 1 3 2 3 2 3 2 2 4 +--R (- B a e + - A a c d e + - B a c d )x +--R 4 2 4 +--R + +--R 1 3 2 2 3 2 2 3 3 1 3 2 2 3 2 +--R (- A a e + - B a d e + A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 641 + +--S 642 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 OF 765 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 3 7 2 3 6 +--R B c e x + (A c e + B c d)x + (3B a c e + A c d)x +--R + +--R 2 2 5 2 2 4 2 2 3 +--R (3A a c e + 3B a c d)x + (3B a c e + 3A a c d)x + (3A a c e + 3B a c d)x +--R + +--R 3 2 2 3 3 3 +--R (B a e + 3A a c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 643 + +--S 644 OF 765 +r0:=a^3*A*d*x+1/2*a^3*(B*d+A*e)*x^2+1/3*a^2*(3*A*c*d+a*B*e)*x^3+3/4*_ + a^2*c*(B*d+A*e)*x^4+3/5*a*c*(A*c*d+a*B*e)*x^5+1/2*a*c^2*(B*d+A*e)*_ + x^6+1/7*c^2*(A*c*d+3*a*B*e)*x^7+1/8*c^3*(B*d+A*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 1 3 8 3 2 1 3 7 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 9 8 8 7 7 +--R + +--R 1 2 1 2 6 3 2 3 2 5 +--R (- A a c e + - B a c d)x + (- B a c e + - A a c d)x +--R 2 2 5 5 +--R + +--R 3 2 3 2 4 1 3 2 3 1 3 1 3 2 +--R (- A a c e + - B a c d)x + (- B a e + A a c d)x + (- A a e + - B a d)x +--R 4 4 3 2 2 +--R + +--R 3 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 644 + +--S 645 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R Type: Polynomial(Integer) +--E 646 + +--S 647 OF 765 +r0:=a^3*A*x+a^2*A*c*x^3+3/5*a*A*c^2*x^5+1/7*A*c^3*x^7+1/8*B*(a+c*x^2)^4/c +--R +--R +--R (2) +--R 1 4 8 1 4 7 1 3 6 3 3 5 3 2 2 4 2 2 3 +--R - B c x + - A c x + - B a c x + - A a c x + - B a c x + A a c x +--R 8 7 2 5 4 +--R + +--R 1 3 2 3 1 4 +--R - B a c x + A a c x + - B a +--R 2 8 +--R / +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 647 + +--S 648 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 649 + +--S 650 OF 765 +r0:=(B*(c*d^2+a*e^2)^3-A*c*d*e*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4))*x/e^7-_ + 1/2*c*(B*d-A*e)*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4)*x^2/e^6-1/3*c*_ + (A*c*d*e*(c*d^2+3*a*e^2)-B*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4))*_ + x^3/e^5-1/4*c^2*(B*d-A*e)*(c*d^2+3*a*e^2)*x^4/e^4+1/5*c^2*(B*c*_ + d^2-A*c*d*e+3*a*B*e^2)*x^5/e^3-1/6*c^3*(B*d-A*e)*x^6/e^2+1/7*B*_ + c^3*x^7/e-(B*d-A*e)*(c*d^2+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 6 2 2 5 2 3 4 +--R 420A a e - 420B a d e + 1260A a c d e - 1260B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 1260A a c d e - 1260B a c d e + 420A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 60B c e x + (70A c e - 70B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (252B a c e - 84A c d e + 84B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (315A a c e - 315B a c d e + 105A c d e - 105B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 420B a c e - 420A a c d e + 420B a c d e - 140A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 630A a c e - 630B a c d e + 630A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R 210A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 420B a e - 1260A a c d e + 1260B a c d e - 1260A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 1260B a c d e - 420A c d e + 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 650 + +--S 651 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 652 + +--S 653 OF 765 +r0:=-c*(6*B*d*(c*d^2+a*e^2)^2-A*e*(5*c^2*d^4+9*a*c*d^2*e^2+3*a^2*e^4))*_ + x/e^7-1/2*c*(2*A*c*d*e*(2*c*d^2+3*a*e^2)-B*(5*c^2*d^4+9*a*c*d^2*e^2+_ + 3*a^2*e^4))*x^2/e^6+1/3*c^2*(3*A*e*(c*d^2+a*e^2)-B*(4*c*d^3+_ + 6*a*d*e^2))*x^3/e^5-1/4*c^2*(2*A*c*d*e-3*B*(c*d^2+a*e^2))*x^4/e^4-_ + 1/5*c^3*(2*B*d-A*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+(B*d-A*e)*(c*d^2+_ + a*e^2)^3/(e^8*(d+e*x))+(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+_ + a*B*e^2)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 6 2 2 5 2 3 4 +--R 60B a e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 900B a c d e - 360A c d e + 420B c d e +--R * +--R x +--R + +--R 3 6 2 2 5 2 3 4 2 4 3 +--R 60B a d e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 900B a c d e - 360A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (12A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (45B a c e - 18A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (60A a c e - 75B a c d e + 30A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 3 4 3 3 +--R (90B a c e - 120A a c d e + 150B a c d e - 60A c d e + 70B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 180A a c e - 270B a c d e + 360A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 180A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 180A a c d e - 360B a c d e + 540A a c d e - 720B a c d e +--R + +--R 3 5 2 3 6 +--R 300A c d e - 360B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e + 60B a d e - 180A a c d e + 180B a c d e - 180A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 180B a c d e - 60A c d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 653 + +--S 654 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 655 + +--S 656 OF 765 +r0:=-c*(A*c*d*e*(10*c*d^2+9*a*e^2)-3*B*(5*c^2*d^4+6*a*c*d^2*e^2+_ + a^2*e^4))*x/e^7-1/2*c^2*(10*B*c*d^3-6*A*c*d^2*e+9*a*B*d*e^2-_ + 3*a*A*e^3)*x^2/e^6+c^2*(2*B*c*d^2-A*c*d*e+a*B*e^2)*x^3/e^5-_ + 1/4*c^3*(3*B*d-A*e)*x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*(B*d-A*e)*_ + (c*d^2+a*e^2)^3/(e^8*(d+e*x)^2)-(c*d^2+a*e^2)^2*(7*B*c*d^2-_ + 6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x))-3*c*(c*d^2+a*e^2)*(7*B*c*d^3-_ + 5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 2 2 5 2 3 4 +--R 60A a c e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 4 3 3 5 2 +--R 300A c d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 120A a c d e - 360B a c d e + 720A a c d e - 1200B a c d e +--R + +--R 3 5 2 3 6 +--R 600A c d e - 840B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 2 5 2 +--R 60A a c d e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 6 3 7 +--R 300A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (5A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (20B a c e - 10A c d e + 14B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30A a c e - 50B a c d e + 25A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 60B a c e - 120A a c d e + 200B a c d e - 100A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 120B a c d e - 330A a c d e + 630B a c d e - 340A c d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 20B a e + 120A a c d e - 120B a c d e + 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 60B a c d e - 80A c d e + 160B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 10B a d e + 90A a c d e - 150B a c d e + 210A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 270B a c d e + 110A c d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 656 + +--S 657 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 658 + +--S 659 OF 765 +r0:=-c^2*(20*B*c*d^3-10*A*c*d^2*e+12*a*B*d*e^2-3*a*A*e^3)*x/e^7+1/2*_ + c^2*(10*B*c*d^2-4*A*c*d*e+3*a*B*e^2)*x^2/e^6-1/3*c^3*(4*B*d-A*e)*_ + x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+_ + e*x)^3)-1/2*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*_ + (d+e*x)^2)+3*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-_ + a*A*e^3)/(e^8*(d+e*x))-c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*_ + d^4+30*a*c*d^2*e^2+3*a^2*e^4))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 2 2 5 3 3 4 +--R 36B a c e - 144A a c d e + 360B a c d e - 240A c d e +--R + +--R 3 4 3 +--R 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 3 5 2 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 3 6 3 7 +--R 36B a c d e - 144A a c d e + 360B a c d e - 240A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 3B c e x + (4A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (18B a c e - 12A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 90B a c d e + 60A c d e - 105B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (108A a c d e - 378B a c d e + 292A c d e - 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 36A a c e + 108B a c d e - 108A a c d e - 54B a c d e +--R + +--R 3 4 3 3 5 2 +--R 156A c d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6B a e - 36A a c d e + 162B a c d e - 324A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 486B a c d e - 204A c d e + 222B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - 2B a d e - 12A a c d e + 66B a c d e - 156A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 282B a c d e - 148A c d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 659 + +--S 660 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 661 + +--S 662 OF 765 +r0:=-c^2*(5*A*c*d*e-3*B*(5*c*d^2+a*e^2))*x/e^7-1/2*c^3*(5*B*d-A*e)*_ + x^2/e^6+1/3*B*c^3*x^3/e^5+1/4*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*_ + (d+e*x)^4)-1/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^3)+3/2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*_ + d*e^2-a*A*e^3)/(e^8*(d+e*x)^2)+c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*_ + (35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x))-c^2*(35*B*c*_ + d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 180B a c d e + 180A c d e - 420B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e )x +--R + +--R 2 2 5 2 3 4 3 4 3 3 5 2 2 +--R (216A a c d e - 1080B a c d e + 1080A c d e - 2520B c d e )x +--R + +--R 2 3 4 2 4 3 3 5 2 3 6 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e)x +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 36A a c d e - 180B a c d e + 180A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (6A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (36B a c e - 36A c d e + 84B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (144B a c d e - 204A c d e + 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 36B a c e + 144A a c d e - 144B a c d e - 96A c d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 18A a c e - 54B a c d e + 324A a c d e - 756B a c d e +--R + +--R 3 4 3 3 5 2 +--R 396A c d e - 444B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 4B a e - 12A a c d e - 36B a c d e + 264A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 744B a c d e + 504A c d e - 856B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 3A a e - B a d e - 3A a c d e - 9B a c d e + 75A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 231B a c d e + 171A c d e - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 662 + +--S 663 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^6 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 664 + +--S 665 OF 765 +r0:=-c^3*(6*B*d-A*e)*x/e^7+1/2*B*c^3*x^2/e^6+1/5*(B*d-A*e)*(c*d^2+_ + a*e^2)^3/(e^8*(d+e*x)^5)-1/4*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+_ + a*B*e^2)/(e^8*(d+e*x)^4)+c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+_ + 3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^3)+1/2*c*(4*A*c*d*e*(5*c*d^2+_ + 3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^2)+_ + c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*(d+e*x))+_ + 3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 3 6 3 2 5 5 +--R (60B a c e - 120A c d e + 420B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (300B a c d e - 600A c d e + 2100B c d e )x +--R + +--R 2 2 5 3 3 4 3 4 3 3 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 3 4 3 4 3 3 5 2 2 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 4 3 3 5 2 3 6 2 5 2 +--R (300B a c d e - 600A c d e + 2100B c d e)x + 60B a c d e +--R + +--R 3 6 3 7 +--R - 120A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 3 6 3 2 5 5 +--R 10B c e x + (20A c e - 70B c d e )x + (100A c d e - 500B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 60A a c e + 300B a c d e - 100A c d e - 400B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 30B a c e - 120A a c d e + 900B a c d e - 800A c d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 20A a c e - 30B a c d e - 120A a c d e + 1100B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1200A c d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 5B a e - 10A a c d e - 15B a c d e - 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 625B a c d e - 750A c d e + 1875B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - B a d e - 2A a c d e - 3B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 137B a c d e - 174A c d e + 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Expression(Integer) +--E 665 + +--S 666 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^7 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 667 + +--S 668 OF 765 +r0:=B*c^3*x/e^7+1/6*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^6)-1/5*(c*d^2+_ + a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^5)+3/4*c*(c*d^2+_ + a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^4)+_ + 1/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))/(e^8*(d+e*x)^3)+1/2*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*_ + d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^2)-3*c^2*(7*B*c*d^2-2*A*c*d*e+a*_ + B*e^2)/(e^8*(d+e*x))-c^3*(7*B*d-A*e)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 6 6 3 6 3 2 5 5 +--R (60A c e - 420B c d e )x + (360A c d e - 2520B c d e )x +--R + +--R 3 2 5 3 3 4 4 3 3 4 3 4 3 3 +--R (900A c d e - 6300B c d e )x + (1200A c d e - 8400B c d e )x +--R + +--R 3 4 3 3 5 2 2 3 5 2 3 6 +--R (900A c d e - 6300B c d e )x + (360A c d e - 2520B c d e)x +--R + +--R 3 6 3 7 +--R 60A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 180B a c e + 360A c d e - 360B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 90A a c e - 450B a c d e + 1350A c d e - 4050B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 60B a c e - 120A a c d e - 600B a c d e + 2200A c d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 45A a c e - 45B a c d e - 90A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 1875A c d e - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 12B a e - 18A a c d e - 18B a c d e - 36A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 180B a c d e + 822A c d e - 3594B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 2B a d e - 3A a c d e - 3B a c d e - 6A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e + 147A c d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Expression(Integer) +--E 668 + +--S 669 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^8 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 670 + +--S 671 OF 765 +r0:=1/7*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^7)-1/6*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^6)+3/5*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^5)+1/4*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^4)+1/3*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^3)-3/2*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^2)+c^3*(7*B*d-A*e)/(e^8*(d+e*x))+B*c^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 3 6 6 +--R (- 420A c e + 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 630B a c e - 1260A c d e + 13230B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 420A a c e - 1050B a c d e - 2100A c d e + 26950B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 315B a c e - 420A a c d e - 1050B a c d e - 2100A c d e +--R + +--R 3 4 3 +--R 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 252A a c e - 189B a c d e - 252A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1260A c d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 70B a e - 84A a c d e - 63B a c d e - 84A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 210B a c d e - 420A c d e + 7203B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e - 10B a d e - 12A a c d e - 9B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e - 60A c d e + 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Expression(Integer) +--E 671 + +--S 672 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^9 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 673 + +--S 674 OF 765 +r0:=1/8*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^8)-1/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^7)+1/2*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^6)+1/5*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^5)+1/4*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^4)-c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^8*_ + (d+e*x)^3)+1/2*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^2)-B*c^3/(e^8*(d+e*x)) +--R +--R +--R (2) +--R 3 7 7 1 3 7 7 3 6 6 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 2 7 3 6 3 2 5 5 +--R (- B a c e - A c d e - 7B c d e )x +--R + +--R 3 2 7 5 2 6 5 3 2 5 35 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - -- B c d e )x +--R 4 4 4 4 +--R + +--R 3 2 7 3 2 6 2 2 5 3 3 4 3 4 3 3 +--R (- - B a c e - - A a c d e - B a c d e - A c d e - 7B c d e )x +--R 5 5 +--R + +--R 1 2 7 3 2 6 3 2 2 5 1 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - - B a c d e +--R 2 10 10 2 +--R + +--R 1 3 4 3 7 3 5 2 +--R - - A c d e - - B c d e +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 1 3 7 1 2 6 3 2 2 5 3 2 3 4 +--R - - B a e - - A a c d e - -- B a c d e - -- A a c d e +--R 7 7 35 35 +--R + +--R 1 2 4 3 1 3 5 2 3 6 +--R - - B a c d e - - A c d e - B c d e +--R 7 7 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 3 2 3 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e +--R 8 56 56 280 +--R + +--R 3 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - -- B a c d e - -- A c d e - - B c d +--R 280 56 56 8 +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 10 2 7 9 8 8 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 674 + +--S 675 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^10 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 676 + +--S 677 OF 765 +r0:=1/9*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^9)-1/8*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^8)+3/7*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^7)+1/6*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))/(e^8*(d+e*x)^6)+1/5*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*_ + d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^5)-3/4*c^2*(7*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)/(e^8*(d+e*x)^4)+1/3*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^3)-_ + 1/2*B*c^3/(e^8*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 7 7 1 3 7 7 3 6 6 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 6 +--R + +--R 3 2 7 1 3 6 7 3 2 5 5 +--R (- - B a c e - - A c d e - - B c d e )x +--R 4 2 4 +--R + +--R 3 2 7 3 2 6 1 3 2 5 7 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - - B c d e )x +--R 5 4 2 4 +--R + +--R 1 2 7 2 2 6 1 2 2 5 1 3 3 4 7 3 4 3 3 +--R (- - B a c e - - A a c d e - - B a c d e - - A c d e - - B c d e )x +--R 2 5 2 3 6 +--R + +--R 3 2 7 3 2 6 6 2 2 5 3 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - -- B a c d e +--R 7 14 35 14 +--R + +--R 1 3 4 3 1 3 5 2 +--R - - A c d e - - B c d e +--R 7 2 +--R * +--R 2 +--R x +--R + +--R 1 3 7 3 2 6 3 2 2 5 3 2 3 4 +--R - - B a e - -- A a c d e - -- B a c d e - -- A a c d e +--R 8 28 56 70 +--R + +--R 3 2 4 3 1 3 5 2 1 3 6 +--R - -- B a c d e - -- A c d e - - B c d e +--R 56 28 8 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 1 2 3 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e +--R 9 72 84 168 +--R + +--R 1 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - --- B a c d e - --- A c d e - -- B c d +--R 210 168 252 72 +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 5 12 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 11 3 7 10 2 8 9 9 8 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 677 + +--S 678 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 678 + +)clear all + +--S 679 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^11 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 679 + +--S 680 OF 765 +r0:=1/10*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^10)-1/9*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^9)+3/8*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^8)+1/7*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^7)+1/6*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^6)-3/5*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^5)+1/4*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^4)-1/3*B*c^3/_ + (e^8*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 7 7 1 3 7 7 3 6 6 +--R - - B c e x + (- - A c e - -- B c d e )x +--R 3 4 12 +--R + +--R 3 2 7 3 3 6 7 3 2 5 5 +--R (- - B a c e - -- A c d e - -- B c d e )x +--R 5 10 10 +--R + +--R 1 2 7 1 2 6 1 3 2 5 7 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - -- B c d e )x +--R 2 2 4 12 +--R + +--R 3 2 7 2 2 6 2 2 2 5 1 3 3 4 1 3 4 3 3 +--R (- - B a c e - - A a c d e - - B a c d e - - A c d e - - B c d e )x +--R 7 7 7 7 3 +--R + +--R 3 2 7 9 2 6 3 2 2 5 3 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - -- B a c d e +--R 8 56 28 28 +--R + +--R 3 3 4 3 1 3 5 2 +--R - -- A c d e - - B c d e +--R 56 8 +--R * +--R 2 +--R x +--R + +--R 1 3 7 1 2 6 1 2 2 5 1 2 3 4 +--R - - B a e - -- A a c d e - -- B a c d e - -- A a c d e +--R 9 12 28 42 +--R + +--R 1 2 4 3 1 3 5 2 1 3 6 +--R - -- B a c d e - -- A c d e - -- B c d e +--R 42 84 36 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 1 2 3 4 +--R - -- A a e - -- B a d e - --- A a c d e - --- B a c d e +--R 10 90 120 280 +--R + +--R 1 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - --- B a c d e - --- A c d e - --- B c d +--R 420 420 840 360 +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 5 13 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 12 4 7 11 3 8 10 2 9 9 10 8 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 680 + +--S 681 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 OF 765 +t0:=(A+B*x)*(d+e*x)^m/(a+c*x^2) +--R +--R +--R m +--R (B x + A)(e x + d) +--R (1) ------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 682 + +--S 683 OF 765 +--r0:=-1/2*(d+e*x)^(1+m)*hypergeometric(1,1+m,2+m,(d+e*x)*sqrt(c)/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(A+B*sqrt(-a)/sqrt(c))/((1+m)*sqrt(-a)*_ +-- (e*sqrt(-a)+d*sqrt(c)))-1/2*(d+e*x)^(1+m)*hypergeometric(1,1+m,2+_ +-- m,(d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*B+A*sqrt(-a)*sqrt(c))/_ +-- (a*(1+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c))) +--E 683 + +--S 684 OF 765 +--d0:=D(m0,x) +--E 684 + +)clear all + +--S 685 OF 765 +t0:=(A+B*x)*(d+e*x)^(1+m)/(a+c*x^2) +--R +--R +--R m + 1 +--R (B x + A)(e x + d) +--R (1) ----------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 685 + +--S 686 OF 765 +--r0:=-1/2*(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,(d+e*x)*sqrt(c)/(e*_ +-- sqrt(-a)+d*sqrt(c)))*(A+B*sqrt(-a)/sqrt(c))/((2+m)*sqrt(-a)*(e*_ +-- sqrt(-a)+d*sqrt(c)))-1/2*(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,_ +-- (d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*B+A*sqrt(-a)*sqrt(c))/_ +-- (a*(2+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c))) +--E 686 + +--S 687 OF 765 +--d0:=D(m0,x) +--E 687 + +)clear all + +--S 688 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 688 + +--S 689 OF 765 +r0:=e*(4*B*c*d^3+6*A*c*d^2*e-4*a*B*d*e^2-a*A*e^3)*x/c^2+1/2*e^2*(6*B*c*d^2+_ + 4*A*c*d*e-a*B*e^2)*x^2/c^2+1/3*e^3*(4*B*d+A*e)*x^3/c+1/4*B*e^4*x^4/c+_ + 1/2*(4*A*c*d*e*(c*d^2-a*e^2)+B*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*_ + log(a+c*x^2)/c^3-(4*a*B*d*e*(c*d^2-a*e^2)-A*(c^2*d^4-6*a*c*d^2*_ + e^2+a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (12A a c e + 48B a c d e - 72A a c d e - 48B a c d e + 12A c d ) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 2 4 +--R (6B a e - 24A a c d e - 36B a c d e + 24A c d e + 6B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R 3B c e x + (4A c e + 16B c d e )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 6B a c e + 24A c d e + 36B c d e )x +--R + +--R 4 3 2 2 2 2 3 +--R (- 12A a c e - 48B a c d e + 72A c d e + 48B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 +-+ +-+ +--R 12c \|a \|c +--R Type: Expression(Integer) +--E 689 + +--S 690 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 691 + +--S 692 OF 765 +r0:=e*(3*B*c*d^2+3*A*c*d*e-a*B*e^2)*x/c^2+1/2*e^2*(3*B*d+A*e)*x^2/c+_ + 1/3*B*e^3*x^3/c+1/2*(B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*_ + log(a+c*x^2)/c^2+(A*c*d*(c*d^2-3*a*e^2)-a*B*e*(3*c*d^2-a*e^2))*_ + atan(x*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R 2 3 2 2 2 3 x\|c +--R (6B a e - 18A a c d e - 18B a c d e + 6A c d )atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 3 2 3 3 +--R (- 3A a e - 9B a d e + 9A c d e + 3B c d )log(c x + a) + 2B c e x +--R + +--R 3 2 2 3 2 2 +--R (3A c e + 9B c d e )x + (- 6B a e + 18A c d e + 18B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 +-+ +-+ +--R 6c \|a \|c +--R Type: Expression(Integer) +--E 692 + +--S 693 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 694 + +--S 695 OF 765 +r0:=e*(2*B*d+A*e)*x/c+1/2*B*e^2*x^2/c+1/2*(B*c*d^2+2*A*c*d*e-a*B*e^2)*_ + log(a+c*x^2)/c^2+(A*c*d^2-2*a*B*d*e-a*A*e^2)*atan(x*sqrt(c)/_ + sqrt(a))/(c^(3/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 x\|c +--R (- 2A a c e - 4B a c d e + 2A c d )atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 +--R (- B a e + 2A c d e + B c d )log(c x + a) + B c e x +--R + +--R 2 +--R (2A c e + 4B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 +-+ +-+ +--R 2c \|a \|c +--R Type: Expression(Integer) +--E 695 + +--S 696 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 OF 765 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 697 + +--S 698 OF 765 +r0:=B*e*x/c+1/2*(B*d+A*e)*log(a+c*x^2)/c+(A*c*d-a*B*e)*atan(x*sqrt(c)/_ + sqrt(a))/(c^(3/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R x\|c 2 +-+ +-+ +--R (- 2B a e + 2A c d)atan(-----) + ((A e + B d)log(c x + a) + 2B e x)\|a \|c +--R +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +-+ +--R 2c\|a \|c +--R Type: Expression(Integer) +--E 698 + +--S 699 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 OF 765 +t0:=(A+B*x)/(a+c*x^2) +--R +--R +--R B x + A +--R (1) -------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 700 + +--S 701 OF 765 +r0:=1/2*B*log(a+c*x^2)/c+A*atan(x*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c)) +--R +--R +--R +-+ +--R x\|c 2 +-+ +-+ +--R 2A c atan(-----) + B log(c x + a)\|a \|c +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R +-+ +-+ +--R 2c\|a \|c +--R Type: Expression(Integer) +--E 701 + +--S 702 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 OF 765 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------- +--R 3 2 +--R c e x + c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 703 + +--S 704 OF 765 +r0:=-(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)+1/2*(B*d-A*e)*log(a+c*x^2)/_ + (c*d^2+a*e^2)+(A*c*d+a*B*e)*atan(x*sqrt(c)/sqrt(a))/((c*d^2+a*e^2)*_ + sqrt(a)*sqrt(c)) +--R +--R +--R (2) +--R +-+ +--R x\|c +--R (2B a e + 2A c d)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-+ +-+ +--R ((- A e + B d)log(c x + a) + (2A e - 2B d)log(e x + d))\|a \|c +--R / +--R 2 2 +-+ +-+ +--R (2a e + 2c d )\|a \|c +--R Type: Expression(Integer) +--E 704 + +--S 705 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------ +--R 2 4 3 2 2 2 2 +--R c e x + 2c d e x + (a e + c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 706 + +--S 707 OF 765 +r0:=(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x))-(B*c*d^2-2*A*c*d*e-a*B*e^2)*_ + log(d+e*x)/(c*d^2+a*e^2)^2+1/2*(B*c*d^2-2*A*c*d*e-a*B*e^2)*_ + log(a+c*x^2)/(c*d^2+a*e^2)^2+(A*c*d^2+2*a*B*d*e-a*A*e^2)*_ + atan(x*sqrt(c)/sqrt(a))*sqrt(c)/((c*d^2+a*e^2)^2*sqrt(a)) +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((- 2A a e + 4B a d e + 2A c d e)x - 2A a d e + 4B a d e + 2A c d ) +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 2 3 +--R ((- B a e - 2A c d e + B c d e)x - B a d e - 2A c d e + B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 2 2 2 +--R (2B a e + 4A c d e - 2B c d e)x + 2B a d e + 4A c d e +--R + +--R 3 +--R - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + 2B a d e - 2A c d e + 2B c d +--R * +--R +-+ +--R \|a +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +-+ +--R ((2a e + 4a c d e + 2c d e)x + 2a d e + 4a c d e + 2c d )\|a +--R Type: Expression(Integer) +--E 707 + +--S 708 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 OF 765 +t0:=(A+B*x)/((d+e*x)^3*(a+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------------- +--R 3 5 2 4 3 2 3 2 3 2 2 3 +--R c e x + 3c d e x + (a e + 3c d e)x + (3a d e + c d )x + 3a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 709 + +--S 710 OF 765 +r0:=1/2*(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x)^2)+(B*c*d^2-2*A*c*d*e-a*B*e^2)/_ + ((c*d^2+a*e^2)^2*(d+e*x))-c*(B*c*d^3-3*A*c*d^2*e-3*a*B*d*e^2+_ + a*A*e^3)*log(d+e*x)/(c*d^2+a*e^2)^3+1/2*c*(B*c*d^3-3*A*c*d^2*e-_ + 3*a*B*d*e^2+a*A*e^3)*log(a+c*x^2)/(c*d^2+a*e^2)^3+(A*c*d*(c*d^2-_ + 3*a*e^2)+a*B*e*(3*c*d^2-a*e^2))*atan(x*sqrt(c)/sqrt(a))*sqrt(c)/_ + ((c*d^2+a*e^2)^3*sqrt(a)) +--R +--R +--R (2) +--R 2 5 4 2 3 2 3 2 2 +--R (- 2B a e - 6A a c d e + 6B a c d e + 2A c d e )x +--R + +--R 2 4 2 3 3 2 2 4 2 2 3 +--R (- 4B a d e - 12A a c d e + 12B a c d e + 4A c d e)x - 2B a d e +--R + +--R 3 2 4 2 5 +--R - 6A a c d e + 6B a c d e + 2A c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (A a c e - 3B a c d e - 3A c d e + B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 3 +--R (2A a c d e - 6B a c d e - 6A c d e + 2B c d e)x + A a c d e +--R + +--R 3 2 2 4 2 5 +--R - 3B a c d e - 3A c d e + B c d +--R * +--R 2 +--R log(c x + a) +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 2A a c e + 6B a c d e + 6A c d e - 2B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (- 4A a c d e + 12B a c d e + 12A c d e - 4B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R - 2A a c d e + 6B a c d e + 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 4 2 3 2 2 4 2 5 2 4 +--R (- 2B a e - 4A a c d e - 4A c d e + 2B c d e)x - A a e - B a d e +--R + +--R 2 3 3 2 2 4 2 5 +--R - 6A a c d e + 2B a c d e - 5A c d e + 3B c d +--R * +--R +-+ +--R \|a +--R / +--R 3 8 2 2 6 2 4 4 3 6 2 2 +--R (2a e + 6a c d e + 6a c d e + 2c d e )x +--R + +--R 3 7 2 3 5 2 5 3 3 7 3 2 6 2 4 4 +--R (4a d e + 12a c d e + 12a c d e + 4c d e)x + 2a d e + 6a c d e +--R + +--R 2 6 2 3 8 +--R 6a c d e + 2c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 710 + +--S 711 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 711 + +)clear all + +--S 712 OF 765 +t0:=(A+B*x)*(d+e*x)^5/(a+c*x^2)^2 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 712 + +--S 713 OF 765 +r0:=-5/2*e^2*(A*c*d*(2*c*d^2-3*a*e^2)-a*B*e*(6*c*d^2-a*e^2))*x/(a*c^3)-_ + e^3*(5*A*c*d^2-5*a*B*d*e-a*A*e^2)*x^2/(a*c^2)-5/6*e^4*(3*A*c*d-a*B*e)*_ + x^3/(a*c^2)-1/2*A*e^5*x^4/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^5/(a*c*_ + (a+c*x^2))+1/2*(A*c*d*(c^2*d^4+10*a*c*d^2*e^2-15*a^2*e^4)+5*a*B*_ + e*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(3/2)*c^(7/2))+e^2*(5*B*c*d^3+5*A*c*d^2*e-5*a*B*d*e^2-a*A*e^3)*_ + log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 15B a c e - 45A a c d e - 90B a c d e + 30A a c d e +--R + +--R 3 4 4 5 +--R 15B a c d e + 3A c d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 15B a e - 45A a c d e - 90B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 2 3 2 3 2 2 +--R (- 6A a c e - 30B a c d e + 30A a c d e + 30B a c d e )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 +--R - 6A a e - 30B a d e + 30A a c d e + 30B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B a c e x + (3A a c e + 15B a c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (- 10B a c e + 30A a c d e + 60B a c d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 6A a c e + 30B a c d e - 30A a c d e - 30B a c d e +--R + +--R 3 4 +--R 15A c d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 4 2 2 3 2 3 2 +--R - 15B a e + 45A a c d e + 90B a c d e - 30A a c d e +--R + +--R 2 4 3 5 +--R - 15B a c d e + 3A c d +--R * +--R x +--R + +--R 2 5 +--R - 3B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 +-+ +-+ +--R (6a c x + 6a c )\|a \|c +--R Type: Expression(Integer) +--E 713 + +--S 714 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 715 + +--S 716 OF 765 +r0:=-3/2*e^2*(2*A*c*d^2-4*a*B*d*e-a*A*e^2)*x/(a*c^2)-e^3*(2*A*c*d-a*B*e)*_ + x^2/(a*c^2)-1/2*A*e^4*x^3/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^4/(a*c*_ + (a+c*x^2))+1/2*(4*a*B*d*e*(c*d^2-3*a*e^2)+A*(c^2*d^4+6*a*c*d^2*_ + e^2-3*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(5/2))+e^2*_ + (3*B*c*d^2+2*A*c*d*e-a*B*e^2)*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 2 +--R (- 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A c d )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R - 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (- 2B a c e + 4A a c d e + 6B a c d e )x - 2B a e +--R + +--R 2 3 2 2 2 +--R 4A a c d e + 6B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R B a c e x + (2A a c e + 8B a c d e )x +--R + +--R 2 4 2 3 2 2 2 3 3 2 +--R (2B a c e - 4A a c d e - 6B a c d e + 4A c d e)x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e + A c d )x +--R + +--R 2 4 +--R - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 716 + +--S 717 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 718 + +--S 719 OF 765 +r0:=-3/2*e^2*(A*c*d-a*B*e)*x/(a*c^2)-1/2*A*e^3*x^2/(a*c)-1/2*(a*B-A*c*x)*_ + (d+e*x)^3/(a*c*(a+c*x^2))+1/2*(3*a*B*e*(c*d^2-a*e^2)+A*c*d*_ + (c*d^2+3*a*e^2))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(5/2))+1/2*_ + e^2*(3*B*d+A*e)*log(a+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 3B a c e + 3A a c d e + 3B a c d e + A c d )x - 3B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e + 3B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((A a c e + 3B a c d e )x + A a e + 3B a d e )log(c x + a) +--R + +--R 3 3 3 2 2 2 2 +--R 2B a c e x + (- A a c e - 3B a c d e + 3A c d e)x +--R + +--R 2 3 2 2 2 3 3 +--R (3B a e - 3A a c d e - 3B a c d e + A c d )x - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 719 + +--S 720 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 721 + +--S 722 OF 765 +r0:=-1/2*A*e^2*x/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^2/(a*c*(a+c*x^2))+_ + 1/2*(A*c*d^2+2*a*B*d*e+a*A*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*_ + c^(3/2))+1/2*B*e^2*log(a+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 3 2 2 2 2 2 2 2 +--R ((A a c e + 2B a c d e + A c d )x + A a c e + 2B a c d e + A a c d ) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 2 2 2 +--R (B a c e x + B a e )log(c x + a) + (- B a c e + 2A c d e)x +--R + +--R 2 2 2 2 +--R (- A a c e - 2B a c d e + A c d )x - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 722 + +--S 723 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 OF 765 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 724 + +--S 725 OF 765 +r0:=-1/2*(a*B-A*c*x)*(d+e*x)/(a*c*(a+c*x^2))+1/2*(A*c*d+a*B*e)*_ + atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(3/2)) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 x\|c +--R ((B a c e + A c d)x + B a e + A a c d)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-+ +-+ +--R (A c e x + (- B a e + A c d)x - B a d)\|a \|c +--R / +--R 2 2 2 +-+ +-+ +--R (2a c x + 2a c)\|a \|c +--R Type: Expression(Integer) +--E 725 + +--S 726 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 726 + +)clear all + +--S 727 OF 765 +t0:=(A+B*x)/(a+c*x^2)^2 +--R +--R +--R B x + A +--R (1) ------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 727 + +--S 728 OF 765 +r0:=1/2*(-a*B+A*c*x)/(a*c*(a+c*x^2))+1/2*A*atan(x*sqrt(c)/sqrt(a))/_ + (a^(3/2)*sqrt(c)) +--R +--R +--R +-+ +--R 2 2 x\|c +-+ +-+ +--R (A c x + A a c)atan(-----) + (A c x - B a)\|a \|c +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 2 2 2 +-+ +-+ +--R (2a c x + 2a c)\|a \|c +--R Type: Expression(Integer) +--E 728 + +--S 729 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 OF 765 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R 2 5 2 4 3 2 2 2 +--R c e x + c d x + 2a c e x + 2a c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 730 + +--S 731 OF 765 +r0:=1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2))-_ + e^2*(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)^2+1/2*e^2*(B*d-A*e)*log(a+_ + c*x^2)/(c*d^2+a*e^2)^2-1/2*(a*B*e*(c*d^2-a*e^2)-A*c*d*(c*d^2+_ + 3*a*e^2))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*(c*d^2+a*e^2)^2*sqrt(c)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (B a c e + 3A a c d e - B a c d e + A c d )x + B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e - B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((- A a c e + B a c d e )x - A a e + B a d e )log(c x + a) +--R + +--R 3 2 2 2 3 2 2 +--R ((2A a c e - 2B a c d e )x + 2A a e - 2B a d e )log(e x + d) +--R + +--R 2 3 2 2 2 3 2 3 2 2 +--R (B a e + A a c d e + B a c d e + A c d )x + A a e - B a d e +--R + +--R 2 3 +--R A a c d e - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +-+ +-+ +--R ((2a c e + 4a c d e + 2a c d )x + 2a e + 4a c d e + 2a c d )\|a \|c +--R Type: Expression(Integer) +--E 731 + +--S 732 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 732 + +)clear all + +--S 733 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 5 2 2 2 4 3 +--R c e x + 2c d e x + (2a c e + c d )x + 4a c d e x +--R + +--R 2 2 2 2 2 2 2 +--R (a e + 2a c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 733 + +--S 734 OF 765 +r0:=1/2*e*(A*c*d^2+4*a*B*d*e-3*a*A*e^2)/(a*(c*d^2+a*e^2)^2*(d+e*x))+_ + 1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(d+e*x)*_ + (a+c*x^2))-e^2*(3*B*c*d^2-4*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+_ + a*e^2)^3+1/2*e^2*(3*B*c*d^2-4*A*c*d*e-a*B*e^2)*log(a+c*x^2)/_ + (c*d^2+a*e^2)^3-1/2*(2*a*B*d*e*(c*d^2-3*a*e^2)-A*(c^2*d^4+6*a*_ + c*d^2*e^2-3*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))*sqrt(c)/(a^(3/2)*_ + (c*d^2+a*e^2)^3) +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 2 3 2 3 4 3 +--R (- 3A a c e + 6B a c d e + 6A a c d e - 2B a c d e + A c d e)x +--R + +--R 2 4 2 2 3 2 3 2 2 4 3 5 2 +--R (- 3A a c d e + 6B a c d e + 6A a c d e - 2B a c d e + A c d )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R (- 3A a e + 6B a d e + 6A a c d e - 2B a c d e + A a c d e)x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 +--R - 3A a d e + 6B a d e + 6A a c d e - 2B a c d e + A a c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 2 3 3 +--R (- B a c e - 4A a c d e + 3B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (- B a c d e - 4A a c d e + 3B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (- B a e - 4A a c d e + 3B a c d e )x - B a d e - 4A a c d e +--R + +--R 2 3 2 +--R 3B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 2 4 2 2 3 3 +--R (2B a c e + 8A a c d e - 6B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (2B a c d e + 8A a c d e - 6B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (2B a e + 8A a c d e - 6B a c d e )x + 2B a d e + 8A a c d e +--R + +--R 2 3 2 +--R - 6B a c d e +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 2 +--R (- 3A a c e + 4B a c d e - 2A a c d e + 4B a c d e + A c d e)x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R B a e + A a c d e + 2B a c d e + 2A a c d e + B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R x +--R + +--R 3 5 3 4 2 3 2 2 4 2 5 +--R - 2A a e + 3B a d e + 2B a c d e + 2A a c d e - B a c d +--R * +--R +-+ +--R \|a +--R / +--R 4 7 3 2 2 5 2 3 4 3 4 6 3 +--R (2a c e + 6a c d e + 6a c d e + 2a c d e)x +--R + +--R 4 6 3 2 3 4 2 3 5 2 4 7 2 +--R (2a c d e + 6a c d e + 6a c d e + 2a c d )x +--R + +--R 5 7 4 2 5 3 2 4 3 2 3 6 5 6 4 3 4 +--R (2a e + 6a c d e + 6a c d e + 2a c d e)x + 2a d e + 6a c d e +--R + +--R 3 2 5 2 2 3 7 +--R 6a c d e + 2a c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 734 + +--S 735 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 OF 765 +t0:=(A+B*x)*(d+e*x)^5/(a+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 736 + +--S 737 OF 765 +r0:=-3/8*e^2*(5*a*B*e*(2*c*d^2-a*e^2)+A*c*d*(6*c*d^2+5*a*e^2))*x/(a^2*c^3)-_ + 1/2*e^3*(3*A*c*d^2+5*a*B*d*e+a*A*e^2)*x^2/(a^2*c^2)-1/8*e^4*(3*A*_ + c*d+5*a*B*e)*x^3/(a^2*c^2)-1/4*(a*B-A*c*x)*(d+e*x)^5/(a*c*(a+_ + c*x^2)^2)+1/8*(d+e*x)^4*(2*a*A*e+(3*A*c*d+5*a*B*e)*x)/(a^2*c*(a+_ + c*x^2))+1/8*(5*a*B*e*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4)+A*c*d*_ + (3*c^2*d^4+10*a*c*d^2*e^2+15*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(5/2)*c^(7/2))+1/2*e^4*(5*B*d+A*e)*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R - 15B a c e + 15A a c d e + 30B a c d e + 10A a c d e +--R + +--R 4 4 5 5 +--R 5B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R - 30B a c e + 30A a c d e + 60B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R 10B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R - 15B a e + 15A a c d e + 30B a c d e + 10A a c d e + 5B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (4A a c e + 20B a c d e )x + (8A a c e + 40B a c d e )x +--R + +--R 4 5 4 4 +--R 4A a e + 20B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 5 +--R 8B a c e x +--R + +--R 2 2 5 2 2 4 3 2 3 3 3 2 +--R - 6A a c e - 30B a c d e + 20A a c d e + 20B a c d e +--R + +--R 4 4 +--R 12A c d e +--R * +--R 4 +--R x +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 25B a c e - 25A a c d e - 50B a c d e + 10A a c d e +--R + +--R 3 4 4 5 +--R 5B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 3 4 2 +--R (- 4A a c e - 20B a c d e + 24A a c d e)x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e +--R + +--R 2 2 4 3 5 +--R - 5B a c d e + 5A a c d +--R * +--R x +--R + +--R 2 2 4 2 2 5 +--R 2A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 5 4 3 4 2 4 3 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 737 + +--S 738 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 738 + +)clear all + +--S 739 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 739 + +--S 740 OF 765 +r0:=-3/8*e^2*(3*A*c*d^2+4*a*B*d*e+a*A*e^2)*x/(a^2*c^2)-1/8*e^3*(3*A*c*d+_ + 4*a*B*e)*x^2/(a^2*c^2)-1/4*(a*B-A*c*x)*(d+e*x)^4/(a*c*(a+c*x^2)^2)+_ + 1/8*(d+e*x)^3*(a*A*e+(3*A*c*d+4*a*B*e)*x)/(a^2*c*(a+c*x^2))+_ + 1/8*(3*A*(c*d^2+a*e^2)^2+4*a*B*d*e*(c*d^2+3*a*e^2))*atan(x*_ + sqrt(c)/sqrt(a))/(a^(5/2)*c^(5/2))+1/2*B*e^4*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 3 4 2 3 3 4 2 2 4 3 5 4 4 +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 2 4 3 2 3 2 3 2 2 2 3 3 4 4 2 +--R (6A a c e + 24B a c d e + 12A a c d e + 8B a c d e + 6A a c d )x +--R + +--R 4 4 4 3 3 2 2 2 3 2 3 2 3 4 +--R 3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 4 4 3 4 2 4 4 2 +--R (4B a c e x + 8B a c e x + 4B a e )log(c x + a) +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 6B a c e + 8A a c d e + 12B a c d e + 9A c d e)x +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 3 +--R (- 5A a c e - 20B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 4 3 3 2 +--R (- 4B a c e + 18A a c d e)x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R (- 3A a c e - 12B a c d e - 6A a c d e - 4B a c d e + 5A a c d )x +--R + +--R 2 2 3 2 2 4 +--R A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 5 4 3 4 2 4 3 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 740 + +--S 741 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 741 + +)clear all + +--S 742 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 742 + +--S 743 OF 765 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^3/(a*c*(a+c*x^2)^2)-3/8*(A*c*d+a*B*e)*_ + (a*e-c*d*x)*(d+e*x)/(a^2*c^2*(a+c*x^2))+3/8*(A*c*d+a*B*e)*(c*d^2+_ + a*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(5/2)) +--R +--R +--R (2) +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 6A a c d e + 6B a c d e + 6A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 3A a c d e + 3B a c d e + 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 2 3 2 4 +--R (2A a c e + 3B a c d e + 3A c d e)x +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 5B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 +--R (- 6B a c d e + 6A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 2 +--R (- 3B a e - 3A a c d e - 3B a c d e + 5A a c d )x - 3B a d e +--R + +--R 2 2 2 3 +--R - 3A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 4 4 3 3 2 4 2 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 743 + +--S 744 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 744 + +)clear all + +--S 745 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 745 + +--S 746 OF 765 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^2/(a*c*(a+c*x^2)^2)-1/8*(a*e-c*d*x)*_ + (3*A*c*d+2*a*B*e+A*c*e*x)/(a^2*c^2*(a+c*x^2))+1/8*(3*A*c*d^2+2*a*_ + B*d*e+a*A*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(3/2)) +--R +--R +--R (2) +--R 3 2 3 4 2 4 +--R (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 3 2 2 3 2 3 +--R (2A a c e + 4B a c d e + 6A a c d )x + A a c e + 2B a c d e +--R + +--R 2 2 2 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 4 2 2 2 3 2 3 +--R A c d e x + (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 4B a c e + 2A a c d e)x + (- A a c e - 2B a c d e + 5A a c d )x +--R + +--R 3 2 2 2 2 +--R - 2B a e - 3A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 4 4 3 3 2 4 2 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 746 + +--S 747 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 747 + +)clear all + +--S 748 OF 765 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2)^3 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 748 + +--S 749 OF 765 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)/(a*c*(a+c*x^2)^2)+1/8*(-2*a*A*e+(3*A*c*d+_ + a*B*e)*x)/(a^2*c*(a+c*x^2))+1/8*(3*A*c*d+a*B*e)*atan(x*sqrt(c)/_ + sqrt(a))/(a^(5/2)*c^(3/2)) +--R +--R +--R (2) +--R 2 3 4 2 2 2 3 2 +--R ((B a c e + 3A c d)x + (2B a c e + 6A a c d)x + B a e + 3A a c d) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 2 2 +-+ +-+ +--R ((B a c e + 3A c d)x + (- B a e + 5A a c d)x - 2A a e - 2B a d)\|a \|c +--R / +--R 2 3 4 3 2 2 4 +-+ +-+ +--R (8a c x + 16a c x + 8a c)\|a \|c +--R Type: Expression(Integer) +--E 749 + +--S 750 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 OF 765 +t0:=(A+B*x)/(a+c*x^2)^3 +--R +--R +--R B x + A +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 751 + +--S 752 OF 765 +r0:=1/4*(-a*B+A*c*x)/(a*c*(a+c*x^2)^2)+3/8*A*x/(a^2*(a+c*x^2))+_ + 3/8*A*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*sqrt(c)) +--R +--R +--R (2) +--R +-+ +--R 3 4 2 2 2 x\|c +--R (3A c x + 6A a c x + 3A a c)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 +-+ +-+ +--R (3A c x + 5A a c x - 2B a )\|a \|c +--R / +--R 2 3 4 3 2 2 4 +-+ +-+ +--R (8a c x + 16a c x + 8a c)\|a \|c +--R Type: Expression(Integer) +--E 752 + +--S 753 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 OF 765 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------------- +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 3 +--R c e x + c d x + 3a c e x + 3a c d x + 3a c e x + 3a c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 754 + +--S 755 OF 765 +r0:=1/4*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2)^2)+_ + 1/8*(-4*a^2*e^2*(B*d-A*e)-(a*B*e*(c*d^2-3*a*e^2)-A*c*d*(3*c*d^2+7*_ + a*e^2))*x)/(a^2*(c*d^2+a*e^2)^2*(a+c*x^2))-e^4*(B*d-A*e)*log(d+_ + e*x)/(c*d^2+a*e^2)^3+1/2*e^4*(B*d-A*e)*log(a+c*x^2)/(c*d^2+_ + a*e^2)^3-1/8*(a*B*e*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4)-A*c*d*_ + (3*c^2*d^4+10*a*c*d^2*e^2+15*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(5/2)*(c*d^2+a*e^2)^3*sqrt(c)) +--R +--R +--R (2) +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 4 4 +--R 3B a c e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 5 5 +--R 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R 6B a c e + 30A a c d e - 12B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R - 2B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (- 4A a c e + 4B a c d e )x + (- 8A a c e + 8B a c d e )x +--R + +--R 4 5 4 4 +--R - 4A a e + 4B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (8A a c e - 8B a c d e )x + (16A a c e - 16B a c d e )x +--R + +--R 4 5 4 4 +--R 8A a e - 8B a d e +--R * +--R log(e x + d) +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 3 4 +--R 3B a c e + 7A a c d e + 2B a c d e + 10A a c d e - B a c d e +--R + +--R 4 5 +--R 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (4A a c e - 4B a c d e + 4A a c d e - 4B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 5B a e + 9A a c d e + 6B a c d e + 14A a c d e + B a c d e +--R + +--R 3 5 +--R 5A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 6A a e - 6B a d e + 8A a c d e - 8B a c d e + 2A a c d e +--R + +--R 2 2 5 +--R - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 2 6 4 3 2 4 3 4 4 2 2 5 6 4 +--R (8a c e + 24a c d e + 24a c d e + 8a c d )x +--R + +--R 6 6 5 2 2 4 4 3 4 2 3 4 6 2 7 6 6 2 4 +--R (16a c e + 48a c d e + 48a c d e + 16a c d )x + 8a e + 24a c d e +--R + +--R 5 2 4 2 4 3 6 +--R 24a c d e + 8a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R Type: Expression(Integer) +--E 755 + +--S 756 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 756 + +)clear all + +--S 757 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 3 7 2 2 3 2 6 2 5 +--R c e x + 2c d e x + (3a c e + c d )x + 6a c d e x +--R + +--R 2 2 2 2 4 2 3 3 2 2 2 2 3 3 2 +--R (3a c e + 3a c d )x + 6a c d e x + (a e + 3a c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 757 + +--S 758 OF 765 +r0:=-1/8*e*(2*a*B*d*e*(c*d^2-11*a*e^2)-3*A*(c^2*d^4+4*a*c*d^2*e^2-_ + 5*a^2*e^4))/(a^2*(c*d^2+a*e^2)^3*(d+e*x))+1/4*(-a*(B*d-A*e)+_ + (A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(d+e*x)*(a+c*x^2)^2)+1/8*(-a*_ + e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)-(2*a*B*e*(c*d^2-2*a*e^2)-3*A*c*d*_ + (c*d^2+3*a*e^2))*x)/(a^2*(c*d^2+a*e^2)^2*(d+e*x)*(a+c*x^2))-e^4*_ + (5*B*c*d^2-6*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+a*e^2)^4+1/2*e^4*_ + (5*B*c*d^2-6*A*c*d*e-a*B*e^2)*log(a+c*x^2)/(c*d^2+a*e^2)^4-1/8*_ + (2*a*B*d*e*(c^2*d^4+10*a*c*d^2*e^2-15*a^2*e^4)-3*A*(c^3*d^6+_ + 5*a*c^2*d^4*e^2+15*a^2*c*d^2*e^4-5*a^3*e^6))*atan(x*sqrt(c)/_ + sqrt(a))*sqrt(c)/(a^(5/2)*(c*d^2+a*e^2)^4) +--R +--R +--R (2) +--R 3 2 7 3 2 6 2 3 2 5 2 3 3 4 +--R - 15A a c e + 30B a c d e + 45A a c d e - 20B a c d e +--R + +--R 4 4 3 4 5 2 5 6 +--R 15A a c d e - 2B a c d e + 3A c d e +--R * +--R 5 +--R x +--R + +--R 3 2 6 3 2 2 5 2 3 3 4 2 3 4 3 +--R - 15A a c d e + 30B a c d e + 45A a c d e - 20B a c d e +--R + +--R 4 5 2 4 6 5 7 +--R 15A a c d e - 2B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 7 4 6 3 2 2 5 3 2 3 4 +--R - 30A a c e + 60B a c d e + 90A a c d e - 40B a c d e +--R + +--R 2 3 4 3 2 3 5 2 4 6 +--R 30A a c d e - 4B a c d e + 6A a c d e +--R * +--R 3 +--R x +--R + +--R 4 6 4 2 5 3 2 3 4 3 2 4 3 +--R - 30A a c d e + 60B a c d e + 90A a c d e - 40B a c d e +--R + +--R 2 3 5 2 2 3 6 4 7 +--R 30A a c d e - 4B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 7 5 6 4 2 5 4 3 4 +--R - 15A a e + 30B a d e + 45A a c d e - 20B a c d e +--R + +--R 3 2 4 3 3 2 5 2 2 3 6 +--R 15A a c d e - 2B a c d e + 3A a c d e +--R * +--R x +--R + +--R 5 6 5 2 5 4 3 4 4 4 3 +--R - 15A a d e + 30B a d e + 45A a c d e - 20B a c d e +--R + +--R 3 2 5 2 3 2 6 2 3 7 +--R 15A a c d e - 2B a c d e + 3A a c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 7 2 3 6 2 3 2 5 5 +--R (- 4B a c e - 24A a c d e + 20B a c d e )x +--R + +--R 3 2 6 2 3 2 5 2 3 3 4 4 +--R (- 4B a c d e - 24A a c d e + 20B a c d e )x +--R + +--R 4 7 3 2 6 3 2 2 5 3 +--R (- 8B a c e - 48A a c d e + 40B a c d e )x +--R + +--R 4 6 3 2 2 5 3 2 3 4 2 +--R (- 8B a c d e - 48A a c d e + 40B a c d e )x +--R + +--R 5 7 4 6 4 2 5 5 6 +--R (- 4B a e - 24A a c d e + 20B a c d e )x - 4B a d e +--R + +--R 4 2 5 4 3 4 +--R - 24A a c d e + 20B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 7 2 3 6 2 3 2 5 5 +--R (8B a c e + 48A a c d e - 40B a c d e )x +--R + +--R 3 2 6 2 3 2 5 2 3 3 4 4 +--R (8B a c d e + 48A a c d e - 40B a c d e )x +--R + +--R 4 7 3 2 6 3 2 2 5 3 +--R (16B a c e + 96A a c d e - 80B a c d e )x +--R + +--R 4 6 3 2 2 5 3 2 3 4 2 +--R (16B a c d e + 96A a c d e - 80B a c d e )x +--R + +--R 5 7 4 6 4 2 5 5 6 +--R (8B a e + 48A a c d e - 40B a c d e )x + 8B a d e +--R + +--R 4 2 5 4 3 4 +--R 48A a c d e - 40B a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 7 3 2 6 2 3 2 5 2 3 3 4 +--R - 15A a c e + 22B a c d e - 3A a c d e + 20B a c d e +--R + +--R 4 4 3 4 5 2 5 6 +--R 15A a c d e - 2B a c d e + 3A c d e +--R * +--R 4 +--R x +--R + +--R 4 7 3 2 6 3 2 2 5 2 3 3 4 +--R 4B a c e + 9A a c d e + 6B a c d e + 21A a c d e +--R + +--R 4 5 2 4 6 5 7 +--R 15A a c d e - 2B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 4 7 4 6 3 2 2 5 3 2 3 4 +--R - 25A a c e + 38B a c d e + 3A a c d e + 28B a c d e +--R + +--R 2 3 4 3 2 3 5 2 4 6 +--R 33A a c d e - 10B a c d e + 5A a c d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 6 4 2 5 3 2 3 4 +--R 6B a e + 11A a c d e + 12B a c d e + 27A a c d e +--R + +--R 3 2 4 3 2 3 5 2 4 7 +--R 6B a c d e + 21A a c d e + 5A a c d +--R * +--R x +--R + +--R 5 7 5 6 4 2 5 4 3 4 3 2 4 3 +--R - 8A a e + 14B a d e + 12A a c d e + 2B a c d e + 24A a c d e +--R + +--R 3 2 5 2 2 3 6 2 3 7 +--R - 14B a c d e + 4A a c d e - 2B a c d +--R * +--R +-+ +--R \|a +--R / +--R 6 2 9 5 3 2 7 4 4 4 5 3 5 6 3 2 6 8 5 +--R (8a c e + 32a c d e + 48a c d e + 32a c d e + 8a c d e)x +--R + +--R 6 2 8 5 3 3 6 4 4 5 4 3 5 7 2 2 6 9 4 +--R (8a c d e + 32a c d e + 48a c d e + 32a c d e + 8a c d )x +--R + +--R 7 9 6 2 2 7 5 3 4 5 4 4 6 3 3 5 8 3 +--R (16a c e + 64a c d e + 96a c d e + 64a c d e + 16a c d e)x +--R + +--R 7 8 6 2 3 6 5 3 5 4 4 4 7 2 3 5 9 2 +--R (16a c d e + 64a c d e + 96a c d e + 64a c d e + 16a c d )x +--R + +--R 8 9 7 2 7 6 2 4 5 5 3 6 3 4 4 8 8 8 +--R (8a e + 32a c d e + 48a c d e + 32a c d e + 8a c d e)x + 8a d e +--R + +--R 7 3 6 6 2 5 4 5 3 7 2 4 4 9 +--R 32a c d e + 48a c d e + 32a c d e + 8a c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 758 + +--S 759 OF 765 +--d0:=D(m0,x) +--E 759 + +)clear all + +--S 760 OF 765 +t0:=(-11+6*x)/((-1+2*x)*(-1+x^2)) +--R +--R +--R 6x - 11 +--R (1) ----------------- +--R 3 2 +--R 2x - x - 2x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 760 + +--S 761 OF 765 +r0:=16/3*log(1-2*x)-5/2*log(1-x)-17/6*log(1+x) +--R +--R +--R - 17log(x + 1) - 15log(- x + 1) + 32log(- 2x + 1) +--R (2) ------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 761 + +--S 762 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 762 + +)clear all + +--S 763 OF 765 +t0:=(5-x)*(3+2*x)^4*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (1) (- 16x - 16x + 264x + 864x + 999x + 405)\|3x + 2 +--R Type: Expression(Integer) +--E 763 + +--S 764 OF 765 +r0:=8275/162*(2+3*x^2)^(3/2)+923/315*(3+2*x)^2*(2+3*x^2)^(3/2)+29/63*_ + (3+2*x)^3*(2+3*x^2)^(3/2)-1/21*(3+2*x)^4*(2+3*x^2)^(3/2)+1/270*_ + (4583+6132*x)*(2+3*x^2)^(3/2)+2341/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 2341/18*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 12960x - 15120x + 297648x + 1222200x + 1956174x + 1558935x +--R + +--R 1167988 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1474830asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 5670\|3 +--R Type: Expression(Integer) +--E 764 + +--S 765 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 765 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richder12b.input.pamphlet b/src/axiom-website/CATS/richder12b.input.pamphlet new file mode 100644 index 0000000..5052ab0 --- /dev/null +++ b/src/axiom-website/CATS/richder12b.input.pamphlet @@ -0,0 +1,5677 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12b.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There is 1 derivative that did not match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12b.output +)spool richder12b.output +)set message test on +)set message auto off +)clear all + +--S 1 of 300 +t0:=(5-x)*(3+2*x)^3*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 4 3 2 | 2 +--R (1) (- 8x + 4x + 126x + 243x + 135)\|3x + 2 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 300 +r0:=875/54*(2+3*x^2)^(3/2)+17/30*(3+2*x)^2*(2+3*x^2)^(3/2)-1/18*(3+2*x)^3*_ + (2+3*x^2)^(3/2)+7/90*(91+89*x)*(2+3*x^2)^(3/2)+1022/9*asinh(x*_ + sqrt(3/2))/sqrt(3)+511/9*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 360x + 216x + 8445x + 21918x + 21120x + 14516)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 30660asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 270\|3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 3 + +)clear all + +--S 4 of 300 +t0:=(5-x)*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (1) (- 4x + 8x + 51x + 45)\|3x + 2 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 300 +r0:=205/54*(2+3*x^2)^(3/2)-1/15*(3+2*x)^2*(2+3*x^2)^(3/2)+1/90*(233+132*x)*_ + (2+3*x^2)^(3/2)+131/3*asinh(x*sqrt(3/2))/sqrt(3)+131/6*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +-+ +--R 4 3 2 +-+ | 2 x\|3 +--R (- 216x + 540x + 4542x + 6255x + 3124)\|3 \|3x + 2 + 11790asinh(-----) +--R +-+ +--R \|2 +--R --------------------------------------------------------------------------- +--R +-+ +--R 270\|3 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 6 + +)clear all + +--S 7 of 300 +t0:=(5-x)*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (1) (- 2x + 7x + 15)\|3x + 2 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 300 +r0:=37/36*(2+3*x^2)^(3/2)-1/12*(3+2*x)*(2+3*x^2)^(3/2)+46/3*asinh(x*_ + sqrt(3/2))/sqrt(3)+23/3*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 3 2 +-+ | 2 x\|3 +--R (- 9x + 42x + 132x + 28)\|3 \|3x + 2 + 276asinh(-----) +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------------- +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 8 + +--S 9 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 9 + +)clear all + +--S 10 of 300 +t0:=(5-x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) (- x + 5)\|3x + 2 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 300 +r0:=-1/9*(2+3*x^2)^(3/2)+5*asinh(x*sqrt(3/2))/sqrt(3)+_ + 5/2*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 2 +-+ | 2 x\|3 +--R (- 6x + 45x - 4)\|3 \|3x + 2 + 90asinh(-----) +--R +-+ +--R \|2 +--R (2) ------------------------------------------------ +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 13 + +--S 14 of 300 +r0:=-121/8*asinh(x*sqrt(3/2))/sqrt(3)-13/8*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))*sqrt(35)+1/4*(13-x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R +-+ +--+ 9x - 4 +-+ | 2 +--R 13\|3 \|35 atanh(---------------) + (- 2x + 26)\|3 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R - 121asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 8\|3 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 300 +r0:=2*asinh(x*sqrt(3/2))*sqrt(3)+19*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)-1/2*(8+x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 9x - 4 +--+ | 2 +--R (- 76x - 114)atanh(---------------) + (- x - 8)\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R +-+ +--+ x\|3 +--R (8x + 12)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R +--+ +--R (4x + 6)\|35 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 18 + +)clear all + +--S 19 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^3 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) --------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 300 +r0:=-13/70*(2+3*x^2)^(3/2)/(3+2*x)^2-1/8*asinh(x*sqrt(3/2))*sqrt(3)-_ + 471/280*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/140*(35+39*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 9x - 4 +--R (1884x + 5652x + 4239)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R +--+ | 2 2 +-+ +--+ x\|3 +--R (374x + 106)\|35 \|3x + 2 + (- 140x - 420x - 315)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 2 +--+ +--R (1120x + 3360x + 2520)\|35 +--R Type: Expression(Integer) +--E 20 + +--S 21 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^4 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------------------- +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 300 +r0:=-123/1225*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 1/6*(2-3*x)*sqrt(2+3*x^2)/(3+2*x)^3+1/70*sqrt(2+3*x^2)/(3+2*x)^2-_ + 43/2450*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 9x - 4 +--R (5904x + 26568x + 39852x + 19926)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (- 516x + 2337x - 3296)\|35 \|3x + 2 +--R / +--R 3 2 +--+ +--R (58800x + 264600x + 396900x + 198450)\|35 +--R Type: Expression(Integer) +--E 23 + +--S 24 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 24 + +)clear all + +--S 25 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^5 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 300 +r0:=-198/8575*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 1/16*(7-4*x)*sqrt(2+3*x^2)/(3+2*x)^4+47/1680*sqrt(2+3*x^2)/(3+2*x)^3-_ + 3/3920*sqrt(2+3*x^2)/(3+2*x)^2-739/137200*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 9x - 4 +--R (19008x + 114048x + 256608x + 256608x + 96228)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 2217x - 10134x + 304x - 26028)\|35 \|3x + 2 +--R / +--R 4 3 2 +--+ +--R (823200x + 4939200x + 11113200x + 11113200x + 4167450)\|35 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 27 + +)clear all + +--S 28 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^6 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 28 + +--S 29 of 300 +r0:=-1017/214375*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 1/30*(12-5*x)*sqrt(2+3*x^2)/(3+2*x)^5+11/525*sqrt(2+3*x^2)/(3+2*x)^4+_ + 1/875*sqrt(2+3*x^2)/(3+2*x)^3-12/6125*sqrt(2+3*x^2)/(3+2*x)^2-_ + 366/214375*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (65088x + 488160x + 1464480x + 2196720x + 1647540x + 494262) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 4 3 2 +--+ | 2 +--R (- 11712x - 76992x - 186392x - 108167x - 222112)\|35 \|3x + 2 +--R / +--R 5 4 3 2 +--R 13720000x + 102900000x + 308700000x + 463050000x + 347287500x +--R + +--R 104186250 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^7 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 300 +r0:=-6102/7503125*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 1/48*(17-6*x)*sqrt(2+3*x^2)/(3+2*x)^6+43/2800*sqrt(2+3*x^2)/(3+2*x)^5+_ + 127/98000*sqrt(2+3*x^2)/(3+2*x)^4-479/490000*sqrt(2+3*x^2)/(3+2*x)^3-_ + 2727/3430000*sqrt(2+3*x^2)/(3+2*x)^2-53511/120050000*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 2343168x + 21088512x + 79081920x + 158163840x + 177934320x +--R + +--R 106760592x + 26690148 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 642132x - 5388660x - 18236055x - 30753930x - 18651300x +--R + +--R - 22308548 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R / +--R 6 5 4 3 +--R 2881200000x + 25930800000x + 97240500000x + 194481000000x +--R + +--R 2 +--R 218791125000x + 131274675000x + 32818668750 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 of 300 +t0:=(5-x)*(3+2*x)^4*(2+3*x^2)^(3/2) +--R +--R +--R (1) +--R +-------+ +--R 7 6 5 4 3 2 | 2 +--R (- 48x - 48x + 760x + 2560x + 3525x + 2943x + 1998x + 810)\|3x + 2 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 300 +r0:=2777/36*x*(2+3*x^2)^(3/2)+193027/7290*(2+3*x^2)^(5/2)+_ + 4421/2268*(3+2*x)^2*(2+3*x^2)^(5/2)+13/36*(3+2*x)^3*(2+3*x^2)^(5/2)-_ + 1/27*(3+2*x)^4*(2+3*x^2)^(5/2)+1/10206*(126712+136053*x)*_ + (2+3*x^2)^(5/2)+2777/6*asinh(x*sqrt(3/2))/sqrt(3)+2777/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 181440x - 204120x + 3676320x + 14492520x + 24490404x +--R + +--R 3 2 +--R 27468315x + 27537072x + 19683405x + 8598544 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 15745590asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 34020\|3 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 36 + +)clear all + +--S 37 of 300 +t0:=(5-x)*(3+2*x)^3*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (1) (- 24x + 12x + 362x + 737x + 657x + 486x + 270)\|3x + 2 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 300 +r0:=1087/36*x*(2+3*x^2)^(3/2)+4687/540*(2+3*x^2)^(5/2)+71/168*(3+2*x)^2*_ + (2+3*x^2)^(5/2)-1/24*(3+2*x)^3*(2+3*x^2)^(5/2)+1/756*(3622+3243*x)*_ + (2+3*x^2)^(5/2)+1087/6*asinh(x*sqrt(3/2))/sqrt(3)+1087/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 3780x + 2160x + 75600x + 186012x + 219975x + 245136x +--R + +--R 226065x + 81392 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 228270asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 1260\|3 +--R Type: Expression(Integer) +--E 38 + +--S 39 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 39 + +)clear all + +--S 40 of 300 +t0:=(5-x)*(3+2*x)^2*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (1) (- 12x + 24x + 145x + 151x + 102x + 90)\|3x + 2 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 300 +r0:=397/36*x*(2+3*x^2)^(3/2)+293/135*(2+3*x^2)^(5/2)-1/21*(3+2*x)^2*_ + (2+3*x^2)^(5/2)+1/189*(323+192*x)*(2+3*x^2)^(5/2)+_ + 397/6*asinh(x*sqrt(3/2))/sqrt(3)+397/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 6 5 4 3 2 +-+ +--R (- 2160x + 5040x + 36252x + 48405x + 51216x + 71715x + 17392)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 83370asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 1260\|3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 42 + +)clear all + +--S 43 of 300 +t0:=(5-x)*(3+2*x)*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 4 3 2 | 2 +--R (1) (- 6x + 21x + 41x + 14x + 30)\|3x + 2 +--R Type: Expression(Integer) +--E 43 + +--S 44 of 300 +r0:=137/36*x*(2+3*x^2)^(3/2)+19/30*(2+3*x^2)^(5/2)-1/18*(3+2*x)*_ + (2+3*x^2)^(5/2)+137/6*asinh(x*sqrt(3/2))/sqrt(3)+137/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 60x + 252x + 605x + 336x + 1115x + 112)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1370asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 60\|3 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (1) (- 3x + 15x - 2x + 10)\|3x + 2 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 300 +r0:=5/4*x*(2+3*x^2)^(3/2)-1/15*(2+3*x^2)^(5/2)+5/2*asinh(x*sqrt(3/2))*_ + sqrt(3)+15/4*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 4 3 2 | 2 +-+ x\|3 +--R (- 36x + 225x - 48x + 375x - 16)\|3x + 2 + 150\|3 asinh(-----) +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------------- +--R 60 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 48 + +)clear all + +--S 49 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 300 +r0:=1/24*(26-3*x)*(2+3*x^2)^(3/2)-1529/32*asinh(x*sqrt(3/2))*sqrt(3)-_ + 455/32*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+_ + 1/16*(455-123*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R 1365\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R 3 2 | 2 +-+ x\|3 +--R (- 36x + 312x - 762x + 2938)\|3x + 2 - 4587\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 96 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 51 + +)clear all + +--S 52 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 300 +r0:=-1/6*(21+x)*(2+3*x^2)^(3/2)/(3+2*x)+663/16*asinh(x*sqrt(3/2))*_ + sqrt(3)+193/16*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)-_ + 1/8*(193-63*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R (- 1158x - 1737)\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R 3 2 | 2 +-+ x\|3 +--R (- 24x + 252x - 1198x - 3810)\|3x + 2 + (3978x + 5967)\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 96x + 144 +--R Type: Expression(Integer) +--E 53 + +--S 54 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 54 + +)clear all + +--S 55 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^3 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 300 +r0:=-1/4*(8+x)*(2+3*x^2)^(3/2)/(3+2*x)^2-111/8*asinh(x*sqrt(3/2))*_ + sqrt(3)-1143/8*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 3/4*(37+12*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 9x - 4 +--R (4572x + 13716x + 10287)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 6x + 96x + 656x + 634)\|35 \|3x + 2 +--R + +--R +-+ +--R 2 +-+ +--+ x\|3 +--R (- 444x - 1332x - 999)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 2 +--+ +--R (32x + 96x + 72)\|35 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^4 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 58 + +--S 59 of 300 +r0:=111/140*(2+3*x^2)^(3/2)/(3+2*x)^2-1/6*(11+3*x)*(2+3*x^2)^(3/2)/_ + (3+2*x)^3+33/16*asinh(x*sqrt(3/2))*sqrt(3)+11727/560*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-3/280*(385+111*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 9x - 4 +--R (- 281448x - 1266516x - 1899774x - 949887)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 2520x - 48948x - 97494x - 60538)\|35 \|3x + 2 +--R + +--R +-+ +--R 3 2 +-+ +--+ x\|3 +--R (27720x + 124740x + 187110x + 93555)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 3 2 +--+ +--R (13440x + 60480x + 90720x + 45360)\|35 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^5 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 300 +r0:=-549/9800*(2+3*x^2)^(3/2)/(3+2*x)^2+1/840*(70+117*x)*_ + (2+3*x^2)^(3/2)/(3+2*x)^3-13/140*(2+3*x^2)^(5/2)/(3+2*x)^4-_ + 3/32*asinh(x*sqrt(3/2))*sqrt(3)-39663/39200*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+3/19600*(1225+549*x)*_ + sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1903824x + 11422944x + 25701624x + 25701624x + 9638109) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (501204x + 1119528x + 1436882x + 491886)\|35 \|3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (- 176400x - 1058400x - 2381400x - 2381400x - 893025)\|3 \|35 +--R * +--R +-+ +--R x\|3 +--R asinh(-----) +--R +-+ +--R \|2 +--R / +--R 4 3 2 +--+ +--R (1881600x + 11289600x + 25401600x + 25401600x + 9525600)\|35 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^6 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 300 +r0:=1/10*(1+5*x)*(2+3*x^2)^(3/2)/(3+2*x)^5-1107/85750*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-3/160*(11-12*x)*sqrt(2+3*x^2)/_ + (3+2*x)^4+51/5600*sqrt(2+3*x^2)/(3+2*x)^3-117/39200*sqrt(2+3*x^2)/_ + (3+2*x)^2-5301/1372000*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (70848x + 531360x + 1594080x + 2391120x + 1793340x + 538002) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 4 3 2 +--+ | 2 +--R (- 10602x + 189543x - 26682x + 64493x - 125252)\|35 \|3x + 2 +--R / +--R 5 4 3 2 +--R 5488000x + 41160000x + 123480000x + 185220000x + 138915000x +--R + +--R 41674500 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 66 + +)clear all + +--S 67 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^7 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 300 +r0:=-1/12*(2-3*x)*(2+3*x^2)^(3/2)/(3+2*x)^6-27/8750*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+37/1400*sqrt(2+3*x^2)/(3+2*x)^4+_ + 51/7000*sqrt(2+3*x^2)/(3+2*x)^3+9/7000*sqrt(2+3*x^2)/(3+2*x)^2-_ + 9/35000*sqrt(2+3*x^2)/(3+2*x)-1/20*(6+5*x)*sqrt(2+3*x^2)/(3+2*x)^5 +--R +--R +--R (2) +--R 6 5 4 3 2 +--R (10368x + 93312x + 349920x + 699840x + 787320x + 472392x + 118098) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 +--+ | 2 +--R (- 432x - 2160x + 39195x - 33180x - 3675x - 39748)\|35 \|3x + 2 +--R / +--R 6 5 4 3 2 +--R 3360000x + 30240000x + 113400000x + 226800000x + 255150000x +--R + +--R 153090000x + 38272500 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 68 + +--S 69 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 69 + +)clear all + +--S 70 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^8 +--R +--R +--R (1) +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R / +--R 8 7 6 5 4 3 2 +--R 256x + 3072x + 16128x + 48384x + 90720x + 108864x + 81648x +--R + +--R 34992x + 6561 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 300 +r0:=-1/42*(9-7*x)*(2+3*x^2)^(3/2)/(3+2*x)^7-72603/105043750*_ + atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+627/39200*_ + sqrt(2+3*x^2)/(3+2*x)^5+6703/1372000*sqrt(2+3*x^2)/(3+2*x)^4+_ + 7569/6860000*sqrt(2+3*x^2)/(3+2*x)^3+3897/48020000*sqrt(2+3*x^2)/_ + (3+2*x)^2-212679/1680700000*sqrt(2+3*x^2)/(3+2*x)-1/672*(137+162*x)*_ + sqrt(2+3*x^2)/(3+2*x)^6 +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 55759104x + 585470592x + 2634617664x + 6586544160x + 9879816240x +--R + +--R 2 +--R 8891834616x + 4445917308x + 952696566 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 5104296x - 44301924x - 148868010x + 98810025x - 740031210x +--R + +--R - 256388969x - 471103116 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R / +--R 7 6 5 4 +--R 80673600000x + 847072800000x + 3811827600000x + 9529569000000x +--R + +--R 3 2 +--R 14294353500000x + 12864918150000x + 6432459075000x + 1378384087500 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 of 300 +t0:=(5-x)*(3+2*x)^4*(2+3*x^2)^(5/2) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 144x - 144x + 2184x + 7584x + 12095x + 13949x + 13044x + 8316x +--R + +--R 3996x + 1620 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 73 + +--S 74 of 300 +r0:=4991/36*x*(2+3*x^2)^(3/2)+4991/90*x*(2+3*x^2)^(5/2)+_ + 928171/53460*(2+3*x^2)^(7/2)+6433/4455*(3+2*x)^2*(2+3*x^2)^(7/2)+_ + 49/165*(3+2*x)^3*(2+3*x^2)^(7/2)-1/33*(3+2*x)^4*(2+3*x^2)^(7/2)+_ + 7/53460*(74539+71136*x)*(2+3*x^2)^(7/2)+4991/6*asinh(x*_ + sqrt(3/2))/sqrt(3)+4991/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 10 9 8 7 6 +--R - 699840x - 769824x + 12921120x + 50615928x + 93646260x +--R + +--R 5 4 3 2 +--R 129966606x + 150762600x + 127123425x + 92160240x + 64370295x +--R + +--R 19537120 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 44469810asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 53460\|3 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 300 +t0:=(5-x)*(3+2*x)^3*(2+3*x^2)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (- 72x + 36x + 1038x + 2235x + 2695x + 2932x + 2124x + 972x + 540) +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 300 +r0:=3731/72*x*(2+3*x^2)^(3/2)+3731/180*x*(2+3*x^2)^(5/2)+_ + 9371/1620*(2+3*x^2)^(7/2)+91/270*(3+2*x)^2*(2+3*x^2)^(7/2)-_ + 1/30*(3+2*x)^3*(2+3*x^2)^(7/2)+7/1620*(839+711*x)*(2+3*x^2)^(7/2)+_ + 3731/12*asinh(x*sqrt(3/2))/sqrt(3)+3731/24*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 9 8 7 6 5 4 +--R - 23328x + 12960x + 418446x + 1035720x + 1503522x + 2036880x +--R + +--R 3 2 +--R 1922805x + 1350240x + 1245915x + 299200 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1007370asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 3240\|3 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 300 +t0:=(5-x)*(3+2*x)^2*(2+3*x^2)^(5/2) +--R +--R +--R +-------+ +--R 7 6 5 4 3 2 | 2 +--R (1) (- 36x + 72x + 411x + 501x + 596x + 572x + 204x + 180)\|3x + 2 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 300 +r0:=665/36*x*(2+3*x^2)^(3/2)+133/18*x*(2+3*x^2)^(5/2)+491/324*_ + (2+3*x^2)^(7/2)-1/27*(3+2*x)^2*(2+3*x^2)^(7/2)+7/324*(59+36*x)*_ + (2+3*x^2)^(7/2)+665/6*asinh(x*sqrt(3/2))/sqrt(3)+665/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 8 7 6 5 4 3 2 +--R - 1296x + 2916x + 18900x + 27378x + 41256x + 50571x + 28272x +--R + +--R 40365x + 6368 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 35910asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 324\|3 +--R Type: Expression(Integer) +--E 80 + +--S 81 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 of 300 +t0:=(5-x)*(3+2*x)*(2+3*x^2)^(5/2) +--R +--R +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (1) (- 18x + 63x + 111x + 84x + 172x + 28x + 60)\|3x + 2 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 300 +r0:=455/72*x*(2+3*x^2)^(3/2)+91/36*x*(2+3*x^2)^(5/2)+11/24*_ + (2+3*x^2)^(7/2)-1/24*(3+2*x)*(2+3*x^2)^(7/2)+455/12*_ + asinh(x*sqrt(3/2))/sqrt(3)+455/24*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +-+ +--R (- 54x + 216x + 438x + 432x + 1111x + 288x + 985x + 64)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 910asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 24\|3 +--R Type: Expression(Integer) +--E 83 + +--S 84 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (1) (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R Type: Expression(Integer) +--E 85 + +--S 86 of 300 +r0:=25/12*x*(2+3*x^2)^(3/2)+5/6*x*(2+3*x^2)^(5/2)-1/21*(2+3*x^2)^(7/2)+_ + 25/2*asinh(x*sqrt(3/2))/sqrt(3)+25/4*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 6 5 4 3 2 +-+ | 2 +--R (- 108x + 630x - 216x + 1365x - 144x + 1155x - 32)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1050asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 84\|3 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 2x + 3 +--R Type: Expression(Integer) +--E 88 + +--S 89 of 300 +r0:=7/96*(130-53*x)*(2+3*x^2)^(3/2)+1/60*(39-5*x)*(2+3*x^2)^(5/2)-_ + 162673/128*asinh(x*sqrt(3/2))/sqrt(3)-15925/128*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+7/64*(2275-691*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +--+ 9x - 4 +--R 238875\|3 \|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 1440x + 11232x - 24180x + 69576x - 160590x + 519142)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R - 2440095asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 1920\|3 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 300 +r0:=-1/24*(310-153*x)*(2+3*x^2)^(3/2)-1/10*(34+x)*(2+3*x^2)^(5/2)/(3+2*x)+_ + 18543/32*asinh(x*sqrt(3/2))*sqrt(3)+5425/32*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))*sqrt(35)-7/16*(775-243*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R (- 162750x - 244125)\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 432x + 3672x - 10236x + 38916x - 179042x - 531978)\|3x + 2 +--R + +--R +-+ +--R +-+ x\|3 +--R (556290x + 834435)\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 960x + 1440 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^3 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 300 +r0:=5/32*(178+29*x)*(2+3*x^2)^(3/2)/(3+2*x)-1/16*(29+2*x)*_ + (2+3*x^2)^(5/2)/(3+2*x)^2-43995/128*asinh(x*sqrt(3/2))*sqrt(3)-_ + 12885/128*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+15/64*_ + (859-267*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 2 +--+ 9x - 4 +--R (51540x + 154620x + 115965)\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 144x + 1392x - 5652x + 38536x + 254806x + 252362)\|3x + 2 +--R + +--R +-+ +--R 2 +-+ x\|3 +--R (- 175980x - 527940x - 395955)\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 2 +--R 512x + 1536x + 1152 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^4 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 300 +r0:=5/12*(37+12*x)*(2+3*x^2)^(3/2)/(3+2*x)^2-1/6*(8+x)*(2+3*x^2)^(5/2)/_ + (3+2*x)^3+3657/16*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(5/7)+_ + 1785/16*asinh(x*sqrt(3/2))*sqrt(3)-15/8*(119+37*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 +-+ 9x - 4 +--R (- 87768x - 394956x - 592434x - 296217)\|5 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 72x + 864x - 6816x - 75948x - 154122x - 92206)\|7 \|3x + 2 +--R + +--R +-+ +--R 3 2 +-+ +-+ x\|3 +--R (42840x + 192780x + 289170x + 144585)\|3 \|7 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 3 2 +-+ +--R (384x + 1728x + 2592x + 1296)\|7 +--R Type: Expression(Integer) +--E 98 + +--S 99 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R +-+ +-+ +--+ +--R 3657\|5 \|7 \|35 - 127995 +--R (3) -------------------------- +--R +-------+ +--R | 2 +--R (224x + 336)\|3x + 2 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^5 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 100 + +--S 101 of 300 +r0:=-1917/224*(2+3*x^2)^(3/2)/(3+2*x)^2+5/96*(350+171*x)*(2+3*x^2)^(3/2)/_ + (3+2*x)^3-1/16*(19+4*x)*(2+3*x^2)^(5/2)/(3+2*x)^4-2625/128*asinh(x*_ + sqrt(3/2))*sqrt(3)-188379/896*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)+3/448*(6125+1917*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (9042192x + 54253152x + 122069592x + 122069592x + 45776097) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--+ +--R (- 6048x + 114912x + 1797468x + 5525640x + 6670018x + 2843910)\|35 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (- 882000x - 5292000x - 11907000x - 11907000x - 4465125)\|3 \|35 +--R * +--R +-+ +--R x\|3 +--R asinh(-----) +--R +-+ +--R \|2 +--R / +--R 4 3 2 +--+ +--R (43008x + 258048x + 580608x + 580608x + 217728)\|35 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^6 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 103 + +--S 104 of 300 +r0:=7929/9800*(2+3*x^2)^(3/2)/(3+2*x)^2-1/280*(490+219*x)*(2+3*x^2)^(3/2)/_ + (3+2*x)^3+73/140*(2+3*x^2)^(5/2)/(3+2*x)^4-1/10*(14+5*x)*_ + (2+3*x^2)^(5/2)/(3+2*x)^5+63/32*asinh(x*sqrt(3/2))*sqrt(3)+_ + 789723/39200*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 9/19600*(8575+2643*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 25271136x - 189533520x - 568600560x - 852900840x - 639675630x +--R + +--R - 191902689 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 176400x - 5480376x - 22735476x - 41822596x - 35880926x +--R + +--R - 11998726 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R 2469600x + 18522000x + 55566000x + 83349000x + 62511750x +--R + +--R 18753525 +--R * +--R +-+ +--R +-+ +--+ x\|3 +--R \|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 5 4 3 2 +--R (1254400x + 9408000x + 28224000x + 42336000x + 31752000x + 9525600) +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^7 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 300 +r0:=-1737/54880*(2+3*x^2)^(3/2)/(3+2*x)^2+1/1568*(98+69*x)*_ + (2+3*x^2)^(3/2)/(3+2*x)^3-23/784*(2+3*x^2)^(5/2)/(3+2*x)^4+_ + 1/140*(7+13*x)*(2+3*x^2)^(5/2)/(3+2*x)^5-13/210*(2+3*x^2)^(7/2)/_ + (3+2*x)^6-9/128*asinh(x*sqrt(3/2))*sqrt(3)-159759/219520*_ + atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+9/109760*_ + (1715+579*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 30673728x + 276063552x + 1035238320x + 2070476640x + 2329286220x +--R + +--R 1397571732x + 349392933 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R 8739216x + 37830672x + 94907604x + 118513176x + 79687218x +--R + +--R 20723614 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 2963520x - 26671680x - 100018800x - 200037600x - 225042300x +--R + +--R - 135025380x - 33756345 +--R * +--R +-+ +--R +-+ +--+ x\|3 +--R \|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 6 5 4 3 2 +--R 42147840x + 379330560x + 1422489600x + 2844979200x + 3200601600x +--R + +--R 1920360960x + 480090240 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^8 +--R +--R +--R (1) +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R / +--R 8 7 6 5 4 3 2 +--R 256x + 3072x + 16128x + 48384x + 90720x + 108864x + 81648x +--R + +--R 34992x + 6561 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 300 +r0:=5/84*(11+18*x)*(2+3*x^2)^(3/2)/(3+2*x)^6+1/14*(4+7*x)*_ + (2+3*x^2)^(5/2)/(3+2*x)^7-1107/600250*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)-1/56*(3-55*x)*sqrt(2+3*x^2)/(3+2*x)^5-_ + 193/7840*sqrt(2+3*x^2)/(3+2*x)^4-639/39200*sqrt(2+3*x^2)/(3+2*x)^3-_ + 2007/274400*sqrt(2+3*x^2)/(3+2*x)^2-27351/9604000*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 850176x + 8926848x + 40170816x + 100427040x + 150640560x +--R + +--R 2 +--R 135576504x + 67788252x + 14526054 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 656424x + 9455994x + 2997810x + 15015225x - 3488490x + 593639x +--R + +--R - 4499004 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R / +--R 7 6 5 4 +--R 460992000x + 4840416000x + 21781872000x + 54454680000x +--R + +--R 3 2 +--R 81682020000x + 73513818000x + 36756909000x + 7876480500 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 300 +t0:=(5-x)*(3+2*x)^4/sqrt(2+3*x^2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 300 +r0:=343/3*asinh(x*sqrt(3/2))/sqrt(3)+16660/81*sqrt(2+3*x^2)+_ + 1477/270*(3+2*x)^2*sqrt(2+3*x^2)+19/30*(3+2*x)^3*sqrt(2+3*x^2)-_ + 1/15*(3+2*x)^4*sqrt(2+3*x^2)+49/81*(43+99*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 4 3 2 +-+ | 2 +--R (- 432x - 540x + 12264x + 58860x + 118513)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 46305asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 405\|3 +--R Type: Expression(Integer) +--E 113 + +--S 114 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 300 +t0:=(5-x)*(3+2*x)^3/sqrt(2+3*x^2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 115 + +--S 116 of 300 +r0:=275/3*asinh(x*sqrt(3/2))/sqrt(3)+3305/54*sqrt(2+3*x^2)+_ + 31/36*(3+2*x)^2*sqrt(2+3*x^2)-1/12*(3+2*x)^3*sqrt(2+3*x^2)+_ + 5/54*(148+171*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 3 2 +-+ | 2 x\|3 +--R (- 18x + 12x + 585x + 2171)\|3 \|3x + 2 + 2475asinh(-----) +--R +-+ +--R \|2 +--R (2) -------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 300 +t0:=(5-x)*(3+2*x)^2/sqrt(2+3*x^2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 118 + +--S 119 of 300 +r0:=127/3*asinh(x*sqrt(3/2))/sqrt(3)+359/27*sqrt(2+3*x^2)-_ + 1/9*(3+2*x)^2*sqrt(2+3*x^2)+1/27*(143+72*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 2 +-+ | 2 x\|3 +--R (- 12x + 36x + 475)\|3 \|3x + 2 + 1143asinh(-----) +--R +-+ +--R \|2 +--R (2) ----------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 300 +t0:=(5-x)*(3+2*x)/sqrt(2+3*x^2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 300 +r0:=47/3*asinh(x*sqrt(3/2))/sqrt(3)+17/6*sqrt(2+3*x^2)-_ + 1/6*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R +-+ | 2 x\|3 +--R (- x + 7)\|3 \|3x + 2 + 47asinh(-----) +--R +-+ +--R \|2 +--R (2) ---------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 300 +t0:=(5-x)/sqrt(2+3*x^2) +--R +--R +--R - x + 5 +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 300 +r0:=5*asinh(x*sqrt(3/2))/sqrt(3)-1/3*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R +-+ | 2 x\|3 +--R - \|3 \|3x + 2 + 15asinh(-----) +--R +-+ +--R \|2 +--R (2) --------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 125 + +--S 126 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 of 300 +t0:=(5-x)/((3+2*x)*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------ +--R +-------+ +--R | 2 +--R (2x + 3)\|3x + 2 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 300 +r0:=-1/2*asinh(x*sqrt(3/2))/sqrt(3)-13/2*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35) +--R +--R +--R +-+ +--R +-+ 9x - 4 +--+ x\|3 +--R 13\|3 atanh(---------------) - \|35 asinh(-----) +--R +-------+ +-+ +--R +--+ | 2 \|2 +--R \|35 \|3x + 2 +--R (2) ------------------------------------------------ +--R +-+ +--+ +--R 2\|3 \|35 +--R Type: Expression(Integer) +--E 128 + +--S 129 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 300 +t0:=(5-x)/((3+2*x)^2*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------- +--R +-------+ +--R 2 | 2 +--R (4x + 12x + 9)\|3x + 2 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 300 +r0:=-41/35*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/35*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R +-------+ +--R 9x - 4 +--+ | 2 +--R (82x + 123)atanh(---------------) - 13\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R (2) ----------------------------------------------------- +--R +--+ +--R (70x + 105)\|35 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 300 +t0:=(5-x)/((3+2*x)^3*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------- +--R +-------+ +--R 3 2 | 2 +--R (8x + 36x + 54x + 27)\|3x + 2 +--R Type: Expression(Integer) +--E 133 + +--S 134 of 300 +r0:=-291/1225*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/70*sqrt(2+3*x^2)/(3+2*x)^2-281/2450*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 2 9x - 4 +--+ | 2 +--R (1164x + 3492x + 2619)atanh(---------------) + (- 281x - 649)\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R ----------------------------------------------------------------------------- +--R 2 +--+ +--R (4900x + 14700x + 11025)\|35 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 300 +t0:=(5-x)/((3+2*x)^4*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------- +--R +-------+ +--R 4 3 2 | 2 +--R (16x + 96x + 216x + 216x + 81)\|3x + 2 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 300 +r0:=-57/1715*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/105*sqrt(2+3*x^2)/(3+2*x)^3-16/245*sqrt(2+3*x^2)/(3+2*x)^2-_ + 10/343*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 9x - 4 +--R (1368x + 6156x + 9234x + 4617)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (- 600x - 2472x - 2995)\|35 \|3x + 2 +--R / +--R 3 2 +--+ +--R (41160x + 185220x + 277830x + 138915)\|35 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 300 +t0:=(5-x)/((3+2*x)^5*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------ +--R +-------+ +--R 5 4 3 2 | 2 +--R (32x + 240x + 720x + 1080x + 810x + 243)\|3x + 2 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 300 +r0:=27/42875*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/140*sqrt(2+3*x^2)/(3+2*x)^4-97/2100*sqrt(2+3*x^2)/(3+2*x)^3-_ + 87/4900*sqrt(2+3*x^2)/(3+2*x)^2-991/171500*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 9x - 4 +--R (- 1296x - 7776x - 17496x - 17496x - 6561)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 5946x - 35892x - 79423x - 70389)\|35 \|3x + 2 +--R / +--R 4 3 2 +--+ +--R (2058000x + 12348000x + 27783000x + 27783000x + 10418625)\|35 +--R Type: Expression(Integer) +--E 140 + +--S 141 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 of 300 +t0:=(5-x)/((3+2*x)^6*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------------- +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (64x + 576x + 2160x + 4320x + 4860x + 2916x + 729)\|3x + 2 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 300 +r0:=19737/7503125*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/175*sqrt(2+3*x^2)/(3+2*x)^5-439/12250*sqrt(2+3*x^2)/(3+2*x)^4-_ + 797/61250*sqrt(2+3*x^2)/(3+2*x)^3-1611/428750*sqrt(2+3*x^2)/(3+2*x)^2-_ + 10023/15006250*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 631584x - 4736880x - 14210640x - 21315960x - 15986970x +--R + +--R - 4796091 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 4 3 2 +--+ | 2 +--R (- 80184x - 706644x - 2487944x - 4314244x - 3409859)\|35 \|3x + 2 +--R / +--R 5 4 3 2 +--R 240100000x + 1800750000x + 5402250000x + 8103375000x + 6077531250x +--R + +--R 1823259375 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 143 + +--S 144 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 300 +t0:=(5-x)*(3+2*x)^4/(2+3*x^2)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 145 + +--S 146 of 300 +r0:=880/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^4*(2+15*x)/sqrt(2+3*x^2)+_ + 1255/81*sqrt(2+3*x^2)-115/9*(3+2*x)*sqrt(2+3*x^2)-_ + 151/27*(3+2*x)^2*sqrt(2+3*x^2)-5/3*(3+2*x)^3*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R x\|3 | 2 +--R 47520asinh(-----)\|3x + 2 +--R +-+ +--R \|2 +--R + +--R 4 3 2 +-+ +--R (- 288x - 432x + 15024x - 14715x - 33914)\|3 +--R / +--R +-------+ +--R +-+ | 2 +--R 162\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 300 +t0:=(5-x)*(3+2*x)^3/(2+3*x^2)^(3/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 148 + +--S 149 of 300 +r0:=134/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^3*(2+15*x)/sqrt(2+3*x^2)-_ + 109/9*sqrt(2+3*x^2)-17/3*(3+2*x)*sqrt(2+3*x^2)-5/3*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 3 2 +-+ +--R 804asinh(-----)\|3x + 2 + (- 24x + 24x + 411x - 1426)\|3 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------- +--R +-------+ +--R +-+ | 2 +--R 18\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 300 +t0:=(5-x)*(3+2*x)^2/(2+3*x^2)^(3/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 300 +r0:=8/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^2*(2+15*x)/sqrt(2+3*x^2)-_ + 53/9*sqrt(2+3*x^2)-5/3*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 2 +-+ +--R 48asinh(-----)\|3x + 2 + (- 24x + 357x - 338)\|3 +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------- +--R +-------+ +--R +-+ | 2 +--R 18\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 300 +t0:=(5-x)*(3+2*x)/(2+3*x^2)^(3/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 300 +r0:=-2/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)*(2+15*x)/sqrt(2+3*x^2)-_ + 5/3*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 +-+ +--R - 4asinh(-----)\|3x + 2 + (49x - 14)\|3 +--R +-+ +--R \|2 +--R (2) ------------------------------------------ +--R +-------+ +--R +-+ | 2 +--R 6\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 300 +t0:=(5-x)/(2+3*x^2)^(3/2) +--R +--R +--R - x + 5 +--R (1) ------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 300 +r0:=1/6*(2+15*x)/sqrt(2+3*x^2) +--R +--R +--R 15x + 2 +--R (2) ----------- +--R +-------+ +--R | 2 +--R 6\|3x + 2 +--R Type: Expression(Integer) +--E 158 + +--S 159 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 300 +t0:=(5-x)/((3+2*x)*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------ +--R +-------+ +--R 3 2 | 2 +--R (6x + 9x + 4x + 6)\|3x + 2 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 300 +r0:=-26/35*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R | 2 9x - 4 +--+ +--R 52\|3x + 2 atanh(---------------) + (41x + 26)\|35 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R (2) ---------------------------------------------------- +--R +-------+ +--R +--+ | 2 +--R 70\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 300 +t0:=(5-x)/((3+2*x)^2*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------- +--R +-------+ +--R 4 3 2 | 2 +--R (12x + 36x + 35x + 24x + 18)\|3x + 2 +--R Type: Expression(Integer) +--E 163 + +--S 164 of 300 +r0:=-632/1225*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)*sqrt(2+3*x^2))+19/1225*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R | 2 9x - 4 2 +--+ +--R (2528x + 3792)\|3x + 2 atanh(---------------) + (114x + 1435x + 986)\|35 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R --------------------------------------------------------------------------- +--R +-------+ +--R +--+ | 2 +--R (4900x + 7350)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 300 +t0:=(5-x)/((3+2*x)^3*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------- +--R +-------+ +--R 5 4 3 2 | 2 +--R (24x + 108x + 178x + 153x + 108x + 54)\|3x + 2 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 300 +r0:=-1962/8575*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^2*sqrt(2+3*x^2))+9/245*sqrt(2+3*x^2)/(3+2*x)^2-_ + 331/8575*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 2 | 2 9x - 4 +--R (15696x + 47088x + 35316)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 3 2 +--+ +--R (- 3972x - 4068x + 7397x + 3658)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 +--R (68600x + 205800x + 154350)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 300 +t0:=(5-x)/((3+2*x)^4*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------- +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (48x + 288x + 680x + 840x + 675x + 432x + 162)\|3x + 2 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 300 +r0:=-3312/42875*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^3*sqrt(2+3*x^2))+23/525*sqrt(2+3*x^2)/_ + (3+2*x)^3-27/1225*sqrt(2+3*x^2)/(3+2*x)^2-1051/42875*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 3 2 | 2 9x - 4 +--R (158976x + 715392x + 1073088x + 536544)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 4 3 2 +--+ +--R (- 75672x - 261036x - 237930x - 23349x - 29438)\|35 +--R / +--R +-------+ +--R 3 2 +--+ | 2 +--R (2058000x + 9261000x + 13891500x + 6945750)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 300 +t0:=(5-x)/((3+2*x)^5*(2+3*x^2)^(3/2)) +--R +--R +--R (1) +--R - x + 5 +--R -------------------------------------------------------------------------- +--R +-------+ +--R 7 6 5 4 3 2 | 2 +--R (96x + 720x + 2224x + 3720x + 3870x + 2889x + 1620x + 486)\|3x + 2 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 300 +r0:=-30078/1500625*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^4*sqrt(2+3*x^2))+58/1225*sqrt(2+3*x^2)/_ + (3+2*x)^4-298/18375*sqrt(2+3*x^2)/(3+2*x)^3-708/42875*_ + sqrt(2+3*x^2)/(3+2*x)^2-14944/1500625*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 4 3 2 | 2 +--R (2887488x + 17324928x + 38981088x + 38981088x + 14617908)\|3x + 2 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 2151936x - 11467872x - 22188792x - 18957672x - 8562487x +--R + +--R - 4197366 +--R * +--R +--+ +--R \|35 +--R / +--R 4 3 2 +--+ +--R (144060000x + 864360000x + 1944810000x + 1944810000x + 729303750)\|35 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 173 + +--S 174 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 300 +t0:=(5-x)*(3+2*x)^4/(2+3*x^2)^(5/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 175 + +--S 176 of 300 +r0:=1/18*(3+2*x)^4*(2+15*x)/(2+3*x^2)^(3/2)-16/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 1/18*(3+2*x)^3*(20+37*x)/sqrt(2+3*x^2)-2027/81*sqrt(2+3*x^2)-_ + 19/3*(3+2*x)*sqrt(2+3*x^2)-37/27*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 x\|3 | 2 +--R (- 864x - 576)asinh(-----)\|3x + 2 +--R +-+ +--R \|2 +--R + +--R 4 3 2 +-+ +--R (- 864x + 57285x - 16560x + 33381x - 25342)\|3 +--R / +--R +-------+ +--R 2 +-+ | 2 +--R (486x + 324)\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 300 +t0:=(5-x)*(3+2*x)^3/(2+3*x^2)^(5/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 178 + +--S 179 of 300 +r0:=1/18*(3+2*x)^3*(2+15*x)/(2+3*x^2)^(3/2)-8/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 1/18*(3+2*x)^2*(10+39*x)/sqrt(2+3*x^2)-157/27*sqrt(2+3*x^2)-_ + 13/9*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 x\|3 | 2 3 2 +-+ +--R (- 144x - 96)asinh(-----)\|3x + 2 + (4971x - 72x + 3741x - 1490)\|3 +--R +-+ +--R \|2 +--R ------------------------------------------------------------------------- +--R +-------+ +--R 2 +-+ | 2 +--R (162x + 108)\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 300 +t0:=(5-x)*(3+2*x)^2/(2+3*x^2)^(5/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 300 +r0:=1/18*(3+2*x)^2*(2+15*x)/(2+3*x^2)^(3/2)-41/54*(4-9*x)/sqrt(2+3*x^2) +--R +--R +--R 3 2 +--R 1287x + 72x + 1215x - 274 +--R (2) --------------------------- +--R +-------+ +--R 2 | 2 +--R (162x + 108)\|3x + 2 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 of 300 +t0:=(5-x)*(3+2*x)/(2+3*x^2)^(5/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 300 +r0:=1/18*(3+2*x)*(2+15*x)/(2+3*x^2)^(3/2)+1/18*(-10+43*x)/sqrt(2+3*x^2) +--R +--R +--R 3 +--R 129x + 135x - 14 +--R (2) --------------------- +--R +-------+ +--R 2 | 2 +--R (54x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 185 + +--S 186 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 300 +t0:=(5-x)/(2+3*x^2)^(5/2) +--R +--R +--R - x + 5 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 300 +r0:=1/18*(2+15*x)/(2+3*x^2)^(3/2)+5/6*x/sqrt(2+3*x^2) +--R +--R +--R 3 +--R 45x + 45x + 2 +--R (2) --------------------- +--R +-------+ +--R 2 | 2 +--R (54x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 188 + +--S 189 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 300 +t0:=(5-x)/((3+2*x)*(2+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------- +--R +-------+ +--R 5 4 3 2 | 2 +--R (18x + 27x + 24x + 36x + 8x + 12)\|3x + 2 +--R Type: Expression(Integer) +--E 190 + +--S 191 of 300 +r0:=1/210*(26+41*x)/(2+3*x^2)^(3/2)-104/1225*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)+1/7350*(312+2137*x)/sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 2 | 2 9x - 4 +--R (1872x + 1248)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 3 2 +--+ +--R (6411x + 936x + 5709x + 1534)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 +--R (22050x + 14700)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 300 +t0:=(5-x)/((3+2*x)^2*(2+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------- +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (36x + 108x + 129x + 144x + 124x + 48x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 193 + +--S 194 of 300 +r0:=1/210*(26+41*x)/((3+2*x)*(2+3*x^2)^(3/2))-176/1715*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/1470*(34+507*x)/((3+2*x)*_ + sqrt(2+3*x^2))+277/5145*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 3 2 | 2 9x - 4 +--R (6336x + 9504x + 4224x + 6336)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 4 3 2 +--+ +--R (4986x + 10647x + 7362x + 9107x + 3966)\|35 +--R / +--R +-------+ +--R 3 2 +--+ | 2 +--R (61740x + 92610x + 41160x + 61740)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 300 +t0:=(5-x)/((3+2*x)^3*(2+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------------------- +--R +-------+ +--R 7 6 5 4 3 2 | 2 +--R (72x + 324x + 582x + 675x + 680x + 468x + 216x + 108)\|3x + 2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 300 +r0:=1/210*(26+41*x)/((3+2*x)^2*(2+3*x^2)^(3/2))-3072/42875*_ + atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/1050*(4+419*x)/_ + ((3+2*x)^2*sqrt(2+3*x^2))+83/1225*sqrt(2+3*x^2)/(3+2*x)^2+_ + 857/128625*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 4 3 2 | 2 +--R (73728x + 221184x + 215040x + 147456x + 110592)\|3x + 2 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--+ +--R (10284x + 67716x + 116367x + 91268x + 89749x + 41366)\|35 +--R / +--R +-------+ +--R 4 3 2 +--+ | 2 +--R (1029000x + 3087000x + 3001250x + 2058000x + 1543500)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 300 +t0:=(5-x)/((3+2*x)^4*(2+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 8 7 6 5 4 3 2 +--R (144x + 864x + 2136x + 3096x + 3385x + 2976x + 1836x + 864x + 324) +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 300 +r0:=1/210*(26+41*x)/((3+2*x)^3*(2+3*x^2)^(3/2))-55344/1500625*_ + atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/7350*(-114+_ + 3331*x)/((3+2*x)^3*sqrt(2+3*x^2))+1471/18375*sqrt(2+3*x^2)/_ + (3+2*x)^3+541/42875*sqrt(2+3*x^2)/(3+2*x)^2-5987/1500625*_ + sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 7969536x + 35862912x + 59107392x + 50805792x + 35862912x +--R + +--R 17931456 +--R * +--R +-------+ +--R | 2 9x - 4 +--R \|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 1293192x - 1834596x + 4920642x + 9795297x + 7866162x +--R + +--R 9103449x + 3788738 +--R * +--R +--+ +--R \|35 +--R / +--R 5 4 3 2 +--R 216090000x + 972405000x + 1602667500x + 1377573750x + 972405000x +--R + +--R 486202500 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 300 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + (A c e + B c d)x + (B a e + A c d)x + (A a e + B a d)x +--R + +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 202 + +--S 203 of 300 +r0:=-2/5*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(5/2)/e^4+2/7*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(7/2)/e^4-2/9*c*(3*B*d-A*e)*_ + (d+e*x)^(9/2)/e^4+2/11*B*c*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 630B c e x + (770A c e + 840B c d e )x +--R + +--R 5 4 2 3 3 +--R (990B a e + 1100A c d e + 30B c d e )x +--R + +--R 5 4 2 3 3 2 2 +--R (1386A a e + 1584B a d e + 66A c d e - 36B c d e )x +--R + +--R 4 2 3 3 2 4 2 3 +--R (2772A a d e + 198B a d e - 88A c d e + 48B c d e)x + 1386A a d e +--R + +--R 3 2 4 5 +--R - 396B a d e + 176A c d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 203 + +--S 204 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 300 +t0:=(A+B*x)*(a+c*x^2)*sqrt(d+e*x) +--R +--R +--R 3 2 +-------+ +--R (1) (B c x + A c x + B a x + A a)\|e x + d +--R Type: Expression(Integer) +--E 205 + +--S 206 of 300 +r0:=-2/3*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(3/2)/e^4+2/5*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^4-2/7*c*(3*B*d-A*e)*_ + (d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B c e x + (90A c e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126B a e + 18A c d e - 12B c d e )x +--R + +--R 4 3 2 2 3 3 +--R (210A a e + 42B a d e - 24A c d e + 16B c d e)x + 210A a d e +--R + +--R 2 2 3 4 +--R - 84B a d e + 48A c d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 206 + +--S 207 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 300 +t0:=(A+B*x)*(a+c*x^2)/sqrt(d+e*x) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 208 + +--S 209 of 300 +r0:=2/3*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^4-_ + 2/5*c*(3*B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-_ + 2*(B*d-A*e)*(c*d^2+a*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + (42A c e - 36B c d e )x +--R + +--R 3 2 2 3 2 +--R (70B a e - 56A c d e + 48B c d e)x + 210A a e - 140B a d e +--R + +--R 2 3 +--R 112A c d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 209 + +--S 210 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 300 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 211 + +--S 212 of 300 +r0:=-2/3*c*(3*B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*sqrt(d+e*x))+2*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 6B c e x + (10A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (30B a e - 40A c d e + 48B c d e)x - 30A a e + 60B a d e - 80A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 212 + +--S 213 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 300 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 214 + +--S 215 of 300 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^(3/2))+2/3*B*c*_ + (d+e*x)^(3/2)/e^4-2*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^4*sqrt(d+e*x))-_ + 2*c*(3*B*d-A*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 2B c e x + (6A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 6B a e + 24A c d e - 48B c d e)x - 2A a e - 4B a d e + 16A c d e +--R + +--R 3 +--R - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 215 + +--S 216 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 300 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 217 + +--S 218 of 300 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^(5/2))-2/3*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^4*(d+e*x)^(3/2))+2*c*(3*B*d-A*e)/_ + (e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + (- 30A c e + 180B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 10B a e - 40A c d e + 240B c d e)x - 6A a e - 4B a d e - 16A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 218 + +--S 219 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 300 +t0:=(A+B*x)*(a+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +-------+ +--R (1) (B c x + A c x + 2B a c x + 2A a c x + B a x + A a )\|e x + d +--R Type: Expression(Integer) +--E 220 + +--S 221 of 300 +r0:=-2/3*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^(3/2)/e^6+2/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^6-4/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(7/2)/e^6+4/9*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(9/2)/e^6-2/11*c^2*(5*B*d-A*e)*_ + (d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + (8190A c e + 630B c d e )x +--R + +--R 6 2 5 2 2 4 4 +--R (20020B a c e + 910A c d e - 700B c d e )x +--R + +--R 6 5 2 2 4 2 3 3 3 +--R (25740A a c e + 2860B a c d e - 1040A c d e + 800B c d e )x +--R + +--R 2 6 5 2 4 2 3 3 +--R 18018B a e + 5148A a c d e - 3432B a c d e + 1248A c d e +--R + +--R 2 4 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 2 4 3 3 +--R 30030A a e + 6006B a d e - 6864A a c d e + 4576B a c d e +--R + +--R 2 4 2 2 5 +--R - 1664A c d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 30030A a d e - 12012B a d e + 13728A a c d e - 9152B a c d e +--R + +--R 2 5 2 6 +--R 3328A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 221 + +--S 222 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 300 +t0:=(A+B*x)*(a+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 223 + +--S 224 of 300 +r0:=2/3*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^6-_ + 4/5*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(5/2)/e^6+_ + 4/7*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(7/2)/e^6-_ + 2/9*c^2*(5*B*d-A*e)*(d+e*x)^(9/2)/e^6+2/11*B*c^2*_ + (d+e*x)^(11/2)/e^6-2*(B*d-A*e)*(c*d^2+a*e^2)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + (770A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (1980B a c e - 880A c d e + 800B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (2772A a c e - 2376B a c d e + 1056A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 2310B a e - 3696A a c d e + 3168B a c d e - 1408A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R 6930A a e - 4620B a d e + 7392A a c d e - 6336B a c d e +--R + +--R 2 4 2 5 +--R 2816A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 224 + +--S 225 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 300 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 226 + +--S 227 of 300 +r0:=-4/3*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3/2)/e^6+_ + 4/5*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^6-_ + 2/7*c^2*(5*B*d-A*e)*(d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*sqrt(d+e*x))+2*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (90A c e - 100B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (252B a c e - 144A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 504B a c d e + 288A c d e - 320B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 630B a e - 1680A a c d e + 2016B a c d e - 1152A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R - 630A a e + 1260B a d e - 3360A a c d e + 4032B a c d e +--R + +--R 2 4 2 5 +--R - 2304A c d e + 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 227 + +--S 228 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 300 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 229 + +--S 230 of 300 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(3/2))+4/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^6-2/5*c^2*(5*B*d-A*e)*_ + (d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-2*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*sqrt(d+e*x))-4*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + (42A c e - 60B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (140B a c e - 112A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 840B a c d e + 672A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 210B a e + 1680A a c d e - 3360B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 3840B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 70A a e - 140B a d e + 1120A a c d e - 2240B a c d e + 1792A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 230 + +--S 231 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 of 300 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 232 + +--S 233 of 300 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(5/2))-2/3*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^(3/2))-2/3*c^2*_ + (5*B*d-A*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6+4*c*_ + (5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*sqrt(d+e*x))+4*c*_ + (5*B*c*d^2-2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + (10A c e - 20B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (60B a c e - 80A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 60A a c e + 360B a c d e - 480A c d e + 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 10B a e - 80A a c d e + 480B a c d e - 640A c d e + 1280B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 6A a e - 4B a d e - 32A a c d e + 192B a c d e - 256A c d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 233 + +--S 234 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 300 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(9/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 235 + +--S 236 of 300 +r0:=2/7*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(7/2))-2/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^(5/2))+4/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^(3/2))+2/3*B*c^2*_ + (d+e*x)^(3/2)/e^6-4*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*_ + sqrt(d+e*x))-2*c^2*(5*B*d-A*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (210A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 420B a c e + 1680A c d e - 5600B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 140A a c e - 840B a c d e + 3360A c d e - 11200B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 42B a e - 112A a c d e - 672B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 8960B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 30A a e - 12B a d e - 32A a c d e - 192B a c d e + 768A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 9 3 8 2 2 7 3 6 +-------+ +--R (105e x + 315d e x + 315d e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 236 + +--S 237 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 238 + +--S 239 of 300 +r0:=2/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^8-_ + 6/5*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*_ + (d+e*x)^(5/2)/e^8-2/7*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+_ + 30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(7/2)/e^8-2/9*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(9/2)/e^8+6/11*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(11/2)/e^8-2/13*c^3*_ + (7*B*d-A*e)*(d+e*x)^(13/2)/e^8+2/15*B*c^3*(d+e*x)^(15/2)/e^8-_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^3*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 6006B c e x + (6930A c e - 6468B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (24570B a c e - 7560A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30030A a c e - 27300B a c d e + 8400A c d e - 7840B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 38610B a c e - 34320A a c d e + 31200B a c d e - 9600A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 54054A a c e - 46332B a c d e + 41184A a c d e - 37440B a c d e +--R + +--R 3 4 3 3 5 2 +--R 11520A c d e - 10752B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 72072A a c d e + 61776B a c d e - 54912A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 49920B a c d e - 15360A c d e + 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 90090A a e - 60060B a d e + 144144A a c d e - 123552B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 109824A a c d e - 99840B a c d e + 30720A c d e - 28672B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 239 + +--S 240 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 241 + +--S 242 of 300 +r0:=-2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*_ + (d+e*x)^(3/2)/e^8-2/5*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+_ + 30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(5/2)/e^8-2/7*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(7/2)/e^8+2/3*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(9/2)/e^8-2/11*c^3*_ + (7*B*d-A*e)*(d+e*x)^(11/2)/e^8+2/13*B*c^3*(d+e*x)^(13/2)/e^8+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*sqrt(d+e*x))+2*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 2310B c e x + (2730A c e - 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (10010B a c e - 3640A c d e + 3920B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (12870A a c e - 14300B a c d e + 5200A c d e - 5600B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 18018B a c e - 20592A a c d e + 22880B a c d e - 8320A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 30030A a c e - 36036B a c d e + 41184A a c d e - 45760B a c d e +--R + +--R 3 4 3 3 5 2 +--R 16640A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 120120A a c d e + 144144B a c d e - 164736A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 183040B a c d e - 66560A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 30030A a e + 60060B a d e - 240240A a c d e + 288288B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 329472A a c d e + 366080B a c d e - 133120A c d e + 143360B c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Expression(Integer) +--E 242 + +--S 243 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 244 + +--S 245 of 300 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(3/2))-2/3*c*(4*A*c*d*e*_ + (5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*_ + (d+e*x)^(3/2)/e^8-2/5*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)*(d+e*x)^(5/2)/e^8+6/7*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*_ + (d+e*x)^(7/2)/e^8-2/9*c^3*(7*B*d-A*e)*(d+e*x)^(9/2)/e^8+_ + 2/11*B*c^3*(d+e*x)^(11/2)/e^8-2*(c*d^2+a*e^2)^2*(7*B*c*d^2-_ + 6*A*c*d*e+a*B*e^2)/(e^8*sqrt(d+e*x))-6*c*(c*d^2+a*e^2)*(7*B*c*d^3-_ + 5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 630B c e x + (770A c e - 980B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (2970B a c e - 1320A c d e + 1680B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (4158A a c e - 5940B a c d e + 2640A c d e - 3360B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 6930B a c e - 11088A a c d e + 15840B a c d e - 7040A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 20790A a c e - 41580B a c d e + 66528A a c d e - 95040B a c d e +--R + +--R 3 4 3 3 5 2 +--R 42240A c d e - 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6930B a e + 83160A a c d e - 166320B a c d e + 266112A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 380160B a c d e + 168960A c d e - 215040B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 2310A a e - 4620B a d e + 55440A a c d e - 110880B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 177408A a c d e - 253440B a c d e + 112640A c d e - 143360B c d +--R / +--R 9 8 +-------+ +--R (3465e x + 3465d e )\|e x + d +--R Type: Expression(Integer) +--E 245 + +--S 246 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 247 + +--S 248 of 300 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(5/2))-2/3*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(3/2))-2/3*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(3/2)/e^8+6/5*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^8-2/7*c^3*(7*B*d-A*e)*_ + (d+e*x)^(7/2)/e^8+2/9*B*c^3*(d+e*x)^(9/2)/e^8+6*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*sqrt(d+e*x))-_ + 2*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 70B c e x + (90A c e - 140B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (378B a c e - 216A c d e + 336B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (630A a c e - 1260B a c d e + 720A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 1890B a c e - 5040A a c d e + 10080B a c d e - 5760A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 1890A a c e + 11340B a c d e - 30240A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 34560A c d e + 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 210B a e - 2520A a c d e + 15120B a c d e - 40320A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 80640B a c d e - 46080A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 126A a e - 84B a d e - 1008A a c d e + 6048B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 16128A a c d e + 32256B a c d e - 18432A c d e + 28672B c d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 248 + +--S 249 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(9/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 250 + +--S 251 of 300 +r0:=2/7*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(7/2))-2/5*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(5/2))+2*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^(3/2))+_ + 2*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^8-2/5*c^3*_ + (7*B*d-A*e)*(d+e*x)^(5/2)/e^8+2/7*B*c^3*(d+e*x)^(7/2)/e^8+2*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))/(e^8*sqrt(d+e*x))-2*c^2*(35*B*c*d^3-15*A*c*d^2*e+_ + 15*a*B*d*e^2-3*a*A*e^3)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (14A c e - 28B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (70B a c e - 56A c d e + 112B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (210A a c e - 700B a c d e + 560A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 210B a c e + 1680A a c d e - 5600B a c d e + 4480A c d e +--R + +--R 3 4 3 +--R - 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 70A a c e - 420B a c d e + 3360A a c d e - 11200B a c d e +--R + +--R 3 4 3 3 5 2 +--R 8960A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 14B a e - 56A a c d e - 336B a c d e + 2688A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 8960B a c d e + 7168A c d e - 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 4B a d e - 16A a c d e - 96B a c d e + 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 2560B a c d e + 2048A c d e - 4096B c d +--R / +--R 11 3 10 2 2 9 3 8 +-------+ +--R (35e x + 105d e x + 105d e x + 35d e )\|e x + d +--R Type: Expression(Integer) +--E 251 + +--S 252 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(11/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 253 + +--S 254 of 300 +r0:=2/9*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(9/2))-2/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(7/2))+6/5*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^(5/2))+_ + 2/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))/(e^8*(d+e*x)^(3/2))-2/3*c^3*(7*B*d-A*e)*(d+e*x)^(3/2)/_ + e^8+2/5*B*c^3*(d+e*x)^(5/2)/e^8+2*c^2*(35*B*c*d^3-15*A*c*d^2*e+_ + 15*a*B*d*e^2-3*a*A*e^3)/(e^8*sqrt(d+e*x))+6*c^2*(7*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 126B c e x + (210A c e - 588B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (1890B a c e - 2520A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 1890A a c e + 18900B a c d e - 25200A c d e + 70560B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 630B a c e - 5040A a c d e + 50400B a c d e - 67200A c d e +--R + +--R 3 4 3 +--R 188160B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 378A a c e - 756B a c d e - 6048A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 80640A c d e + 225792B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 90B a e - 216A a c d e - 432B a c d e - 3456A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 34560B a c d e - 46080A c d e + 129024B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 70A a e - 20B a d e - 48A a c d e - 96B a c d e - 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 7680B a c d e - 10240A c d e + 28672B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +-------+ +--R (315e x + 1260d e x + 1890d e x + 1260d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 254 + +--S 255 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 300 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 300 +r0:=2/3*(B*d+A*e)*(d+e*x)^(3/2)/c+2/5*B*(d+e*x)^(5/2)/c+2*(B*c*d^2+_ + 2*A*c*d*e-a*B*e^2)*sqrt(d+e*x)/c^2-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ + sqrt(-a)+d*sqrt(c)))*((-A*c*d*(c*d^2-3*a*e^2)+a*B*e*(3*c*d^2-a*e^2))/_ + sqrt(-a)+(B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*sqrt(c))/(c^(9/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+_ + d*sqrt(c)))*((A*c*d*(c*d^2-3*a*e^2)-a*B*e*(3*c*d^2-a*e^2))/sqrt(-a)+_ + (B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*sqrt(c))/(c^(9/4)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 3 +---+ +-+ 2 3 +--R (15A a e + 45B a d e - 45A c d e - 15B c d )\|- a \|c + 15B a e +--R + +--R 2 2 2 3 +--R - 45A a c d e - 45B a c d e + 15A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 3 +---+ +-+ 2 3 +--R (15A a e + 45B a d e - 45A c d e - 15B c d )\|- a \|c - 15B a e +--R + +--R 2 2 2 3 +--R 45A a c d e + 45B a c d e - 15A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 2 2 +--R (6B c e x + (10A c e + 22B c d e)x - 30B a e + 70A c d e + 46B c d ) +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 15c \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 257 + +--S 258 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 300 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 300 +r0:=2/3*B*(d+e*x)^(3/2)/c+2*(B*d+A*e)*sqrt(d+e*x)/c-atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2+2*A*c*d*e-_ + a*B*e^2-(A*c*d^2-2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/(c^(7/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*_ + sqrt(-a)+d*sqrt(c)))*(B*c*d^2+2*A*c*d*e-a*B*e^2+(A*c*d^2-2*a*B*d*e-_ + a*A*e^2)*sqrt(c)/sqrt(-a))/(c^(7/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 +-+ +--R (- 3A a e - 6B a d e + 3A c d )\|c +--R + +--R 2 2 +---+ +--R (3B a e - 6A c d e - 3B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 +-+ +--R (3A a e + 6B a d e - 3A c d )\|c +--R + +--R 2 2 +---+ +--R (3B a e - 6A c d e - 3B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ +--R (2B e x + 6A e + 8B d)\|- a \|c \|e x + d \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R 3c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 260 + +--S 261 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 300 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 262 + +--S 263 of 300 +r0:=2*B*sqrt(d+e*x)/c-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((-A*c*d+a*B*e)/sqrt(-a)+(B*d+A*e)*sqrt(c))/(c^(5/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*_ + sqrt(-a)+d*sqrt(c)))*((A*c*d-a*B*e)/sqrt(-a)+(B*d+A*e)*sqrt(c))/_ + (c^(5/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- A e - B d)\|- a \|c - B a e + A c d)\|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- A e - B d)\|- a \|c + B a e - A c d)\|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R 2B\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 263 + +--S 264 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 300 +t0:=(A+B*x)/((a+c*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) -------------------- +--R 2 +-------+ +--R (c x + a)\|e x + d +--R Type: Expression(Integer) +--E 265 + +--S 266 of 300 +r0:=-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (B+a*A*sqrt(c)/(-a)^(3/2))/(c^(3/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(B+A*sqrt(c)/_ + sqrt(-a))/(c^(3/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (A\|c - B\|- a )\|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (- A\|c - B\|- a )\|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 266 + +--S 267 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 300 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R 3 2 +-------+ +--R (c e x + c d x + a e x + a d)\|e x + d +--R Type: Expression(Integer) +--E 268 + +--S 269 of 300 +r0:=2*(B*d-A*e)/((c*d^2+a*e^2)*sqrt(d+e*x))-atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))*((-A*c*d-a*B*e)/sqrt(-a)+(B*d-A*e)*_ + sqrt(c))/(c^(1/4)*(c*d^2+a*e^2)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*_ + ((A*c*d+a*B*e)/sqrt(-a)+(B*d-A*e)*sqrt(c))/(c^(1/4)*(c*d^2+a*e^2)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ +--R +---+ +-+ +-------+ | +-+ +---+ +--R ((A e - B d)\|- a \|c + B a e + A c d)\|e x + d \|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ +-------+ | +-+ +---+ +--R ((A e - B d)\|- a \|c - B a e - A c d)\|e x + d \|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (- 2A e + 2B d)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R (a e + c d )\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 300 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------------ +--R 2 4 3 2 2 2 2 +-------+ +--R (c e x + 2c d e x + (a e + c d )x + 2a d e x + a d )\|e x + d +--R Type: Expression(Integer) +--E 271 + +--S 272 of 300 +r0:=2/3*(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x)^(3/2))+2*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2)/((c*d^2+a*e^2)^2*sqrt(d+e*x))-c^(1/4)*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2-(A*c*d^2+2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/((c*d^2+_ + a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))-c^(1/4)*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2+(A*c*d^2+2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/((c*d^2+_ + a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 +--R (- 3A a e + 6B a d e + 3A c d e)x - 3A a d e + 6B a d e +--R + +--R 3 +--R 3A c d +--R * +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 +--R (3B a e + 6A c d e - 3B c d e)x + 3B a d e + 6A c d e +--R + +--R 3 +--R - 3B c d +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ +-------+ | +-+ +---+ \|c \|e x + d +--R \|c \|e x + d \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 +--R (3A a e - 6B a d e - 3A c d e)x + 3A a d e - 6B a d e +--R + +--R 3 +--R - 3A c d +--R * +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 +--R (3B a e + 6A c d e - 3B c d e)x + 3B a d e + 6A c d e +--R + +--R 3 +--R - 3B c d +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ +-------+ | +-+ +---+ \|c \|e x + d +--R \|c \|e x + d \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 3 2 2 3 2 +--R (- 6B a e - 12A c d e + 6B c d e)x - 2A a e - 4B a d e +--R + +--R 2 3 +--R - 14A c d e + 8B c d +--R * +--R +---------------+ +---------------+ +--R +---+ | +-+ +---+ | +-+ +---+ +--R \|- a \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +---+ +--R ((3a e + 6a c d e + 3c d e)x + 3a d e + 6a c d e + 3c d )\|- a +--R * +--R +---------------+ +---------------+ +--R +-------+ | +-+ +---+ | +-+ +---+ +--R \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 272 + +--S 273 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 300 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 274 + +--S 275 of 300 +r0:=-1/2*A*e*(d+e*x)^(3/2)/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^(5/2)/(a*c*_ + (a+c*x^2))-1/2*e*(A*c*d-5*a*B*e)*sqrt(d+e*x)/(a*c^2)-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + ((-5*a*B*e*(c*d^2-a*e^2)-2*A*c*d*(c*d^2+2*a*e^2))/sqrt(-a)+_ + e*(A*c*d^2+10*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a*c^(9/4)*sqrt(-e*_ + sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+_ + d*sqrt(c)))*((5*a*B*e*(c*d^2-a*e^2)+2*A*c*d*(c*d^2+2*a*e^2))/_ + sqrt(-a)+e*(A*c*d^2+10*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a*c^(9/4)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 2 2 +--R (- 3A a c e - 10B a c d e - A c d e)x - 3A a e - 10B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 5B a c e + 4A a c d e + 5B a c d e + 2A c d )x - 5B a e +--R + +--R 2 2 2 2 2 3 +--R 4A a c d e + 5B a c d e + 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 3A a c e - 10B a c d e - A c d e)x - 3A a e - 10B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (5B a c e - 4A a c d e - 5B a c d e - 2A c d )x + 5B a e +--R + +--R 2 2 2 2 2 3 +--R - 4A a c d e - 5B a c d e - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R 8B a c e x + (- 2A a c e - 4B a c d e + 2A c d )x + 10B a e +--R + +--R 2 +--R - 4A a c d e - 2B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 3 2 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c )\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 300 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 300 +r0:=-1/2*(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*(a+c*x^2))-1/2*A*e*sqrt(d+e*x)/(a*c)-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(e*(A*c*d+_ + 3*a*B*e)+a*(2*A*c*d^2+3*a*B*d*e+a*A*e^2)*sqrt(c)/(-a)^(3/2))/(a*_ + c^(7/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(A*c*d+3*a*B*e)+(2*A*c*d^2+_ + 3*a*B*d*e+a*A*e^2)*sqrt(c)/sqrt(-a))/(a*c^(7/4)*sqrt(e*sqrt(-a)+_ + d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (A a c e + 3B a c d e + 2A c d )x + A a e + 3B a d e +--R + +--R 2 +--R 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- 3B a c e - A c d e)x - 3B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R (- A a c e - 3B a c d e - 2A c d )x - A a e - 3B a d e +--R + +--R 2 +--R - 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- 3B a c e - A c d e)x - 3B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---+4+-+3 +-------+ +--R ((- 2B a e + 2A c d)x - 2A a e - 2B a d)\|- a \|c \|e x + d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 2 +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 278 + +--S 279 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 300 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 300 +r0:=-1/2*(a*B-A*c*x)*sqrt(d+e*x)/(a*c*(a+c*x^2))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*((-2*A*c*d-a*B*e)/sqrt(-a)+_ + A*e*sqrt(c))/(a*c^(5/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*((2*A*c*d+a*B*e)/sqrt(-a)+_ + A*e*sqrt(c))/(a*c^(5/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 +---+ +-+ 2 2 2 +--R (- A c e x - A a e)\|- a \|c + (B a c e + 2A c d)x + B a e +--R + +--R 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 +---+ +-+ 2 2 2 +--R (- A c e x - A a e)\|- a \|c + (- B a c e - 2A c d)x - B a e +--R + +--R - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R (2A c x - 2B a)\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 281 + +--S 282 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 300 +t0:=(A+B*x)/((a+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R 2 4 2 2 +-------+ +--R (c x + 2a c x + a )\|e x + d +--R Type: Expression(Integer) +--E 283 + +--S 284 of 300 +r0:=-1/2*(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ + (a+c*x^2))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (e*(A*c*d+a*B*e)-(2*A*c*d^2-a*B*d*e+3*a*A*e^2)*sqrt(c)/sqrt(-a))/_ + (a*c^(3/4)*(c*d^2+a*e^2)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*_ + (e*(A*c*d+a*B*e)+(2*A*c*d^2-a*B*d*e+3*a*A*e^2)*sqrt(c)/sqrt(-a))/_ + (a*c^(3/4)*(c*d^2+a*e^2)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (3A a c e - B a c d e + 2A c d )x + 3A a e - B a d e +--R + +--R 2 +--R 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- B a c e - A c d e)x - B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R (- 3A a c e + B a c d e - 2A c d )x - 3A a e + B a d e +--R + +--R 2 +--R - 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- B a c e - A c d e)x - B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---+4+-+3 +-------+ +--R ((2B a e + 2A c d)x + 2A a e - 2B a d)\|- a \|c \|e x + d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 2 2 2 2 3 2 2 2 +---+4+-+3 | +-+ +---+ +--R ((4a c e + 4a c d )x + 4a e + 4a c d )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 300 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 3 2 2 2 +-------+ +--R (c e x + c d x + 2a c e x + 2a c d x + a e x + a d)\|e x + d +--R Type: Expression(Integer) +--E 286 + +--S 287 of 300 +r0:=1/2*e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)/(a*(c*d^2+a*e^2)^2*sqrt(d+e*x))+_ + 1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2)*_ + sqrt(d+e*x))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((3*a*B*e*(c*d^2-a*e^2)-2*A*c*d*(c*d^2+4*a*e^2))/_ + sqrt(-a)+e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)*sqrt(c))/(a*c^(1/4)*_ + (c*d^2+a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*((-3*a*B*e*(c*d^2-a*e^2)+_ + 2*A*c*d*(c*d^2+4*a*e^2))/sqrt(-a)+e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)*_ + sqrt(c))/(a*c^(1/4)*(c*d^2+a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 2 2 +--R (5A a c e - 6B a c d e - A c d e)x + 5A a e - 6B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (3B a c e + 8A a c d e - 3B a c d e + 2A c d )x + 3B a e +--R + +--R 2 2 2 2 2 3 +--R 8A a c d e - 3B a c d e + 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R +-------+ | +-+ +---+ \|c \|e x + d +--R \|e x + d \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (5A a c e - 6B a c d e - A c d e)x + 5A a e - 6B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 3B a c e - 8A a c d e + 3B a c d e - 2A c d )x - 3B a e +--R + +--R 2 2 2 2 2 3 +--R - 8A a c d e + 3B a c d e - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R +-------+ | +-+ +---+ \|c \|e x + d +--R \|e x + d \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 3 2 2 2 2 +--R (- 10A a c e + 12B a c d e + 2A c d e)x +--R + +--R 2 3 2 2 2 3 2 3 +--R (2B a e + 2A a c d e + 2B a c d e + 2A c d )x - 8A a e +--R + +--R 2 2 2 3 +--R 10B a d e + 4A a c d e - 2B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +---+ +--R ((4a c e + 8a c d e + 4a c d )x + 4a e + 8a c d e + 4a c d )\|- a +--R * +--R +---------------+ +---------------+ +--R 4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 300 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 300 +r0:=-1/16*e*(6*A*c*d+7*a*B*e)*(d+e*x)^(3/2)/(a^2*c^2)-1/4*(a*B-A*c*x)*_ + (d+e*x)^(7/2)/(a*c*(a+c*x^2)^2)+1/16*(d+e*x)^(5/2)*(a*A*e+(6*A*c*d+_ + 7*a*B*e)*x)/(a^2*c*(a+c*x^2))-1/16*e*(6*A*c*d^2+7*a*B*d*e+5*a*A*e^2)*_ + sqrt(d+e*x)/(a^2*c^2)-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*(e*(7*a*B*e*(c*d^2+3*a*e^2)+2*A*c*d*(3*c*d^2+4*a*e^2))+_ + a*(14*a*B*d*e*(c*d^2+2*a*e^2)+A*(12*c^2*d^4+19*a*c*d^2*e^2+5*a^2*e^4))*_ + sqrt(c)/(-a)^(3/2))/(a^2*c^(11/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + 1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(7*a*B*_ + e*(c*d^2+3*a*e^2)+2*A*c*d*(3*c*d^2+4*a*e^2))+(14*a*B*d*e*(c*d^2+_ + 2*a*e^2)+A*(12*c^2*d^4+19*a*c*d^2*e^2+5*a^2*e^4))*sqrt(c)/sqrt(-a))/_ + (a^2*c^(11/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 +--R 5A a c e + 28B a c d e + 19A a c d e + 14B a c d e +--R + +--R 4 4 +--R 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R 10A a c e + 56B a c d e + 38A a c d e + 28B a c d e +--R + +--R 3 4 +--R 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R 5A a e + 28B a d e + 19A a c d e + 14B a c d e + 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 21B a c e - 8A a c d e - 7B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 42B a c e - 16A a c d e - 14B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 21B a e - 8A a c d e - 7B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 +--R - 5A a c e - 28B a c d e - 19A a c d e - 14B a c d e +--R + +--R 4 4 +--R - 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 10A a c e - 56B a c d e - 38A a c d e - 28B a c d e +--R + +--R 3 4 +--R - 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R - 5A a e - 28B a d e - 19A a c d e - 14B a c d e - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 21B a c e - 8A a c d e - 7B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 42B a c e - 16A a c d e - 14B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 21B a e - 8A a c d e - 7B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 22B a c e + 16A a c d e + 14B a c d e + 12A c d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 18A a c e - 52B a c d e + 2A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (- 14B a e - 8A a c d e - 10B a c d e + 20A a c d )x - 10A a e +--R + +--R 3 2 2 2 2 3 +--R - 28B a d e - 22A a c d e - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 4 4 3 3 2 4 2 +---+4+-+3 | +-+ +---+ +--R (32a c x + 64a c x + 32a c )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 290 + +--S 291 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 300 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 300 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^(5/2)/(a*c*(a+c*x^2)^2)-1/16*(d+e*x)^(3/2)*_ + (a*A*e-(6*A*c*d+5*a*B*e)*x)/(a^2*c*(a+c*x^2))-1/16*e*(6*A*c*d+5*a*B*e)*_ + sqrt(d+e*x)/(a^2*c^2)-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((-5*a*B*e*(2*c*d^2+a*e^2)-3*A*c*d*(4*c*d^2+3*a*e^2))/_ + sqrt(-a)+e*(6*A*c*d^2+5*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a^2*c^(9/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*((5*a*B*e*(2*c*d^2+a*e^2)+3*A*c*d*(4*c*d^2+_ + 3*a*e^2))/sqrt(-a)+e*(6*A*c*d^2+5*a*B*d*e+3*a*A*e^2)*sqrt(c))/_ + (a^2*c^(9/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 3A a c e - 5B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 6A a c e - 10B a c d e - 12A a c d e)x - 3A a e +--R + +--R 3 2 2 2 +--R - 5B a d e - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (5B a c e + 9A a c d e + 10B a c d e + 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (10B a c e + 18A a c d e + 20B a c d e + 24A a c d )x + 5B a e +--R + +--R 3 2 3 2 2 2 3 +--R 9A a c d e + 10B a c d e + 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 3 2 2 3 2 4 +--R (- 3A a c e - 5B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 6A a c e - 10B a c d e - 12A a c d e)x - 3A a e +--R + +--R 3 2 2 2 +--R - 5B a d e - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (- 5B a c e - 9A a c d e - 10B a c d e - 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (- 10B a c e - 18A a c d e - 20B a c d e - 24A a c d )x - 5B a e +--R + +--R 3 2 3 2 2 2 3 +--R - 9A a c d e - 10B a c d e - 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 3 2 3 +--R (6A a c e + 10B a c d e + 12A c d )x +--R + +--R 2 2 2 2 +--R (- 18B a c e + 2A a c d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 2A a c e - 6B a c d e + 20A a c d )x - 10B a e - 14A a c d e +--R + +--R 2 2 +--R - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 4 4 3 3 2 4 2 +---+4+-+ | +-+ +---+ +--R (32a c x + 64a c x + 32a c )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 293 + +--S 294 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 300 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 295 + +--S 296 of 300 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*(a+c*x^2)^2)-3/16*(a*A*e-_ + (2*A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a^2*c*(a+c*x^2))-3/32*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(e*(2*A*c*d+a*B*e)+a*_ + (4*A*c*d^2+2*a*B*d*e+a*A*e^2)*sqrt(c)/(-a)^(3/2))/(a^2*c^(7/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-3/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(2*A*c*d+a*B*e)+(4*A*c*d^2+_ + 2*a*B*d*e+a*A*e^2)*sqrt(c)/sqrt(-a))/(a^2*c^(7/4)*sqrt(e*sqrt(-a)+_ + d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 3 2 4 +--R (3A a c e + 6B a c d e + 12A c d )x +--R + +--R 2 2 2 2 2 2 3 2 3 +--R (6A a c e + 12B a c d e + 24A a c d )x + 3A a e + 6B a d e +--R + +--R 2 2 +--R 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 3 4 2 2 2 2 +--R (- 3B a c e - 6A c d e)x + (- 6B a c e - 12A a c d e)x +--R + +--R 3 2 2 +--R - 3B a e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 3 2 4 +--R (- 3A a c e - 6B a c d e - 12A c d )x +--R + +--R 2 2 2 2 2 2 3 2 3 +--R (- 6A a c e - 12B a c d e - 24A a c d )x - 3A a e - 6B a d e +--R + +--R 2 2 +--R - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 3 4 2 2 2 2 +--R (- 3B a c e - 6A c d e)x + (- 6B a c e - 12A a c d e)x +--R + +--R 3 2 2 +--R - 3B a e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 +--R (6B a c e + 12A c d)x + 2A a c e x + (- 2B a e + 20A a c d)x +--R + +--R 2 2 +--R - 6A a e - 8B a d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 3 4 3 2 2 4 +---+4+-+3 | +-+ +---+ +--R (32a c x + 64a c x + 32a c)\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 300 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 300 +r0:=-1/4*(a*B-A*c*x)*sqrt(d+e*x)/(a*c*(a+c*x^2)^2)+1/16*(a*e*(A*c*d+a*B*e)+_ + c*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*x)*sqrt(d+e*x)/(a^2*c*(c*d^2+a*e^2)*_ + (a+c*x^2))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + ((-a*B*e*(2*c*d^2+3*a*e^2)-A*c*d*(12*c*d^2+13*a*e^2))/sqrt(-a)+_ + e*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*sqrt(c))/(a^2*c^(5/4)*(c*d^2+a*e^2)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*((a*B*e*(2*c*d^2+3*a*e^2)+A*c*d*(12*c*d^2+_ + 13*a*e^2))/sqrt(-a)+e*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*sqrt(c))/_ + (a^2*c^(5/4)*(c*d^2+a*e^2)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 5A a c e - B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 +--R (- 10A a c e - 2B a c d e - 12A a c d e)x - 5A a e - B a d e +--R + +--R 2 2 +--R - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 13A a c d e + 2B a c d e + 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 26A a c d e + 4B a c d e + 24A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 13A a c d e + 2B a c d e + 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 3 2 2 3 2 4 +--R (- 5A a c e - B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 +--R (- 10A a c e - 2B a c d e - 12A a c d e)x - 5A a e - B a d e +--R + +--R 2 2 +--R - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (- 3B a c e - 13A a c d e - 2B a c d e - 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (- 6B a c e - 26A a c d e - 4B a c d e - 24A a c d )x - 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R - 13A a c d e - 2B a c d e - 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (10A a c e + 2B a c d e + 12A c d )x + (2B a c e + 2A a c d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R (18A a c e + 2B a c d e + 20A a c d )x - 6B a e + 2A a c d e +--R + +--R 2 2 +--R - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 4 2 2 +--R ((32a c e + 32a c d )x + (64a c e + 64a c d )x + 32a c e + 32a c d ) +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 299 + +--S 300 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richder12c.input.pamphlet b/src/axiom-website/CATS/richder12c.input.pamphlet new file mode 100644 index 0000000..0ae9ec1 --- /dev/null +++ b/src/axiom-website/CATS/richder12c.input.pamphlet @@ -0,0 +1,13664 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12c.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +All derivatives match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12c.output +)spool richder12c.output +)set message test on +)set message auto off +)clear all + +--S 1 of 465 +t0:=(A+B*x)/((a+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R 3 6 2 4 2 2 3 +-------+ +--R (c x + 3a c x + 3a c x + a )\|e x + d +--R Type: Expression(Integer) +--E 1 + +--S 2 of 465 +r0:=-1/4*(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ + (a+c*x^2)^2)+1/16*(a*e*(A*c*d^2-6*a*B*d*e+7*a*A*e^2)-(a*B*e*(c*d^2-_ + 5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))*x)*sqrt(d+e*x)/(a^2*(c*d^2+a*e^2)^2*_ + (a+c*x^2))+1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (e*(a*B*e*(c*d^2-5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))-(2*a*B*d*e*(c*d^2+_ + 4*a*e^2)-3*A*(4*c^2*d^4+9*a*c*d^2*e^2+7*a^2*e^4))*sqrt(c)/sqrt(-a))/_ + (a^2*c^(3/4)*(c*d^2+a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))+_ + 1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(a*B*e*_ + (c*d^2-5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))+(2*a*B*d*e*(c*d^2+4*a*e^2)-_ + 3*A*(4*c^2*d^4+9*a*c*d^2*e^2+7*a^2*e^4))*sqrt(c)/sqrt(-a))/(a^2*c^(3/4)*_ + (c*d^2+a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 +--R 21A a c e - 8B a c d e + 27A a c d e - 2B a c d e +--R + +--R 4 4 +--R 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R 42A a c e - 16B a c d e + 54A a c d e - 4B a c d e +--R + +--R 3 4 +--R 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R 21A a e - 8B a d e + 27A a c d e - 2B a c d e + 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 5B a c e - 12A a c d e + B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 10B a c e - 24A a c d e + 2B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 5B a e - 12A a c d e + B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 +--R - 21A a c e + 8B a c d e - 27A a c d e + 2B a c d e +--R + +--R 4 4 +--R - 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 42A a c e + 16B a c d e - 54A a c d e + 4B a c d e +--R + +--R 3 4 +--R - 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R - 21A a e + 8B a d e - 27A a c d e + 2B a c d e - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 5B a c e - 12A a c d e + B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 10B a c e - 24A a c d e + 2B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 5B a e - 12A a c d e + B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (10B a c e + 24A a c d e - 2B a c d e + 12A c d )x +--R + +--R 2 3 2 2 2 2 2 +--R (14A a c e - 12B a c d e + 2A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (18B a e + 32A a c d e + 6B a c d e + 20A a c d )x + 22A a e +--R + +--R 3 2 2 2 2 3 +--R - 20B a d e + 10A a c d e - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 4 2 4 3 3 2 2 2 4 4 4 +--R (32a c e + 64a c d e + 32a c d )x +--R + +--R 5 4 4 2 2 2 3 3 4 2 6 4 5 2 2 4 2 4 +--R (64a c e + 128a c d e + 64a c d )x + 32a e + 64a c d e + 32a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 3 + +)clear all + +--S 4 of 465 +t0:=x*sqrt(1+x)/(1+x^2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (1) --------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 465 +r0:=-atanh(sqrt(1+x)/sqrt(1-%i))*sqrt(1-%i)-atanh(sqrt(1+x)/sqrt(1+%i))*_ + sqrt(1+%i)+2*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R +------+ \|x + 1 +------+ \|x + 1 +-----+ +--R (2) - \|1 - %i atanh(---------) - \|1 + %i atanh(---------) + 2\|x + 1 +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 5 + +--S 6 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Complex(Integer)) +--E 6 + +)clear all + +--S 7 of 465 +t0:=(1-x)*sqrt(1+x)/(1+x^2) +--R +--R +--R +-----+ +--R (- x + 1)\|x + 1 +--R (1) ----------------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 465 +r0:=(1-%i)^(3/2)*atanh(sqrt(1+x)/sqrt(1-%i))+(1+%i)^(3/2)*_ + atanh(sqrt(1+x)/sqrt(1+%i))-2*sqrt(1+x) +--R +--R +--R (2) +--R +-----+ +-----+ +--R +------+ \|x + 1 +------+ \|x + 1 +--R (1 - %i)\|1 - %i atanh(---------) + (1 + %i)\|1 + %i atanh(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R + +--R +-----+ +--R - 2\|x + 1 +--R Type: Expression(Complex(Integer)) +--E 8 + +--S 9 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Complex(Integer)) +--E 9 + +)clear all + +--S 10 of 465 +t0:=(A+B*x)*sqrt(d+e*x)*sqrt(a+c*x^2) +--R +--R +--R +--------+ +--R +-------+ | 2 +--R (1) (B x + A)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 10 + +--S 11 of 465 +--r0:=2/7*B*(a+c*x^2)^(3/2)*sqrt(d+e*x)/c-2/105*(4*B*c*d^2-7*A*c*d*e+_ +-- 5*a*B*e^2-3*c*e*(B*d+7*A*e)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/(c*e^2)+_ +-- 4/105*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*_ +-- (4*c^(3/2)*d^3-c*d^2*e*sqrt(-a)-5*a*e^3*sqrt(-a)+8*a*d*e^2*sqrt(c))+_ +-- 7*A*e*sqrt(c)*(c*d^2-3*a*e^2-4*d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*e^3*_ +-- sqrt(a+c*x^2))-4/105*(4*B*c*d^3-7*A*c*d^2*e+8*a*B*d*e^2+21*a*A*e^3)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^4*sqrt(a+c*x^2)) +--E 11 + +--S 12 of 465 +--d0:=D(m0,x) +--E 12 + +)clear all + +--S 13 of 465 +t0:=(A+B*x)*sqrt(a+c*x^2)/sqrt(d+e*x) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) -------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 13 + +--S 14 of 465 +--r0:=-2/15*(4*B*d-5*A*e-3*B*e*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^2-_ +-- 4/15*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(4*B*c*d^2-_ +-- 5*A*c*d*e+3*a*B*e^2-B*d*e*sqrt(-a)*sqrt(c)+5*A*e^2*sqrt(-a)*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(3/4)*e^3*sqrt(a+c*x^2))-4/15*(4*B*c*d^2-5*A*c*d*e+3*a*B*e^2)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^4*sqrt(a+c*x^2)) +--E 14 + +--S 15 of 465 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 465 +t0:=(A+B*x)*sqrt(a+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) -------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 16 + +--S 17 of 465 +--r0:=2/3*(4*B*d-3*A*e+B*e*x)*sqrt(a+c*x^2)/(e^2*sqrt(d+e*x))+_ +-- 4/3*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*e*_ +-- sqrt(-a)+4*B*d*sqrt(c)-3*A*e*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e^3*sqrt(a+c*x^2))+_ +-- 4/3*c^(1/4)*(4*B*d-3*A*e)*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^4*sqrt(a+c*x^2)) +--E 17 + +--S 18 of 465 +--d0:=D(m0,x) +--E 18 + +)clear all + +--S 19 of 465 +t0:=(A+B*x)*sqrt(a+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 19 + +--S 20 of 465 +--r0:=2/3*(4*B*d-A*e+3*B*e*x)*sqrt(a+c*x^2)/(e^2*(d+e*x)^(3/2))-_ +-- 4/3*(4*B*c*d^2-A*c*d*e+3*a*B*e^2)*sqrt(a+c*x^2)/(e^2*(c*d^2+a*e^2)*_ +-- sqrt(d+e*x))-4/3*c^(1/4)*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-a)*(4*B*c*d^2-A*c*d*e+3*a*B*e^2-B*d*e*sqrt(-a)*sqrt(c)+A*e^2*_ +-- sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-_ +-- x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*_ +-- sqrt(-a)+d*sqrt(c)))/(e^3*(c*d^2+a*e^2)*sqrt(a+c*x^2))-4/3*c^(1/4)*_ +-- (4*B*c*d^2-A*c*d*e+3*a*B*e^2)*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^4*(c*d^2+a*e^2)*sqrt(a+c*x^2)) +--E 20 + +--S 21 of 465 +--d0:=D(m0,x) +--E 21 + +)clear all + +--S 22 of 465 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 22 + +--S 23 of 465 +--r0:=-2/63*(8*B*d-9*A*e-7*B*e*x)*(a+c*x^2)^(3/2)*sqrt(d+e*x)/e^2-_ +-- 4/315*(32*B*c*d^3-36*A*c*d^2*e+33*a*B*d*e^2-45*a*A*e^3-3*e*(8*B*c*d^2-_ +-- 9*A*c*d*e+7*a*B*e^2)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^4+8/315*_ +-- elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(9*A*e*_ +-- sqrt(c)*(4*c^(3/2)*d^3+5*(-a)^(3/2)*e^3-c*d^2*e*sqrt(-a)+_ +-- 8*a*d*e^2*sqrt(c))-B*(32*c^2*d^4+57*a*c*d^2*e^2+21*a^2*e^4-8*c^(3/2)*_ +-- d^3*e*sqrt(-a)-12*a*d*e^3*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^5*_ +-- sqrt(a+c*x^2))+8/315*(36*A*c*d*e*(c*d^2+2*a*e^2)-B*(32*c^2*d^4+_ +-- 57*a*c*d^2*e^2+21*a^2*e^4))*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^6*sqrt(a+c*x^2)) +--E 23 + +--S 24 of 465 +--d0:=D(m0,x) +--E 24 + +)clear all + +--S 25 of 465 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 25 + +--S 26 of 465 +--r0:=2/7*(8*B*d-7*A*e+B*e*x)*(a+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+_ +-- 4/35*(5*a*B*e^2+4*c*d*(8*B*d-7*A*e)-3*c*e*(8*B*d-7*A*e)*x)*_ +-- sqrt(d+e*x)*sqrt(a+c*x^2)/e^4-8/35*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*(32*c^(3/2)*d^3-8*c*d^2*e*_ +-- sqrt(-a)-5*a*e^3*sqrt(-a)+29*a*d*e^2*sqrt(c))+7*A*e*sqrt(c)*(4*c*d^2+_ +-- 3*a*e^2-d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e^5*sqrt(a+c*x^2))+_ +-- 8/35*c^(1/4)*(32*B*c*d^3-28*A*c*d^2*e+29*a*B*d*e^2-21*a*A*e^3)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(e^6*sqrt(a+c*x^2)) +--E 26 + +--S 27 of 465 +--d0:=D(m0,x) +--E 27 + +)clear all + +--S 28 of 465 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 28 + +--S 29 of 465 +--r0:=2/15*(8*B*d-5*A*e+3*B*e*x)*(a+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 4/15*(9*a*B*e^2+4*c*d*(8*B*d-5*A*e)+c*e*(8*B*d-5*A*e)*x)*_ +-- sqrt(a+c*x^2)/(e^4*sqrt(d+e*x))-8/15*c^(1/4)*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(32*B*c*d^2-20*A*c*d*e+9*a*B*e^2-_ +-- 8*B*d*e*sqrt(-a)*sqrt(c)+5*A*e^2*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^5*_ +-- sqrt(a+c*x^2))-8/15*c^(1/4)*(9*a*B*e^2+4*c*d*(8*B*d-5*A*e))*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(e^6*sqrt(a+c*x^2)) +--E 29 + +--S 30 of 465 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 465 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 31 + +--S 32 of 465 +--r0:=2/15*(8*B*d-3*A*e+5*B*e*x)*(a+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 4/15*(5*a*B*e^2+4*c*d*(8*B*d-3*A*e)+3*c*e*(8*B*d-3*A*e)*x)*_ +-- sqrt(a+c*x^2)/(e^4*(d+e*x)^(3/2))+8/15*c*(32*B*c*d^3-12*A*c*d^2*e+_ +-- 29*a*B*d*e^2-9*a*A*e^3)*sqrt(a+c*x^2)/(e^4*(c*d^2+a*e^2)*sqrt(d+e*x))-_ +-- 8/15*c^(3/4)*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*_ +-- (-B*(32*c^(3/2)*d^3-8*c*d^2*e*sqrt(-a)-5*a*e^3*sqrt(-a)+29*a*d*e^2*_ +-- sqrt(c))+3*A*e*sqrt(c)*(4*c*d^2+3*a*e^2-d*e*sqrt(-a)*sqrt(c)))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (e^5*(c*d^2+a*e^2)*sqrt(a+c*x^2))+8/15*c^(5/4)*(32*B*c*d^3-_ +-- 12*A*c*d^2*e+29*a*B*d*e^2-9*a*A*e^3)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^6*(c*d^2+_ +-- a*e^2)*sqrt(a+c*x^2)) +--E 32 + +--S 33 of 465 +--d0:=D(m0,x) +--E 33 + +)clear all + +--S 34 of 465 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(a+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------+ +--R | 2 +--R \|c x + a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 465 +--r0:=2/5*B*(d+e*x)^(3/2)*sqrt(a+c*x^2)/c+2/15*(3*B*d+5*A*e)*sqrt(d+e*x)*_ +-- sqrt(a+c*x^2)/c-2/15*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- (3*B*(3*(-a)^(3/2)*e^2+c*d^2*sqrt(-a)+4*a*d*e*sqrt(c))-5*A*sqrt(c)*_ +-- (3*c*d^2-a*e^2-4*d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(7/4)*e*sqrt(a+c*x^2))-_ +-- 2/15*(3*B*c*d^2+20*A*c*d*e-9*a*B*e^2)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(7/4)*e^2*_ +-- sqrt(a+c*x^2)) +--E 35 + +--S 36 of 465 +--d0:=D(m0,x) +--E 36 + +)clear all + +--S 37 of 465 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(a+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +--------+ +--R | 2 +--R \|c x + a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 465 +--r0:=2/3*B*sqrt(d+e*x)*sqrt(a+c*x^2)/c-2/3*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(-3*A*c*d+a*B*e+B*d*sqrt(-a)*sqrt(c)+3*A*e*_ +-- sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-_ +-- x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*e*sqrt(a+c*x^2))-2/3*(B*d+3*A*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^2*sqrt(a+c*x^2)) +--E 38 + +--S 39 of 465 +--d0:=D(m0,x) +--E 39 + +)clear all + +--S 40 of 465 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(a+c*x^2)) +--R +--R +--R B x + A +--R (1) --------------------- +--R +--------+ +--R +-------+ | 2 +--R \|e x + d \|c x + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 465 +--r0:=-2*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(B*sqrt(-a)-A*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(3/4)*e*sqrt(a+c*x^2))-2*B*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^2*sqrt(a+c*x^2)) +--E 41 + +--S 42 of 465 +--d0:=D(m0,x) +--E 42 + +)clear all + +--S 43 of 465 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R +--------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 43 + +--S 44 of 465 +--r0:=2*(B*d-A*e)*sqrt(a+c*x^2)/((c*d^2+a*e^2)*sqrt(d+e*x))+_ +-- 2*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(A*c*d+a*B*e+B*d*_ +-- sqrt(-a)*sqrt(c)-A*e*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e*(c*d^2+a*e^2)*_ +-- sqrt(a+c*x^2))+2*c^(1/4)*(B*d-A*e)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^2*(c*d^2+_ +-- a*e^2)*sqrt(a+c*x^2)) +--E 44 + +--S 45 of 465 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 465 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------+ +--R 2 | 2 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 465 +--r0:=-(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*sqrt(a+c*x^2))-A*e*sqrt(d+e*x)*_ +-- sqrt(a+c*x^2)/(a*c)+elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- (-A*c*d+3*a*B*e+3*B*d*sqrt(-a)*sqrt(c)+A*e*sqrt(-a)*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(7/4)*sqrt(-a)*sqrt(a+c*x^2))+(A*c*d-3*a*B*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(a*c^(7/4)*e*sqrt(a+c*x^2)) +--E 47 + +--S 48 of 465 +--d0:=D(m0,x) +--E 48 + +)clear all + +--S 49 of 465 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 465 +--r0:=-(a*B-A*c*x)*sqrt(d+e*x)/(a*c*sqrt(a+c*x^2))+elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(B*sqrt(-a)-A*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*_ +-- sqrt(-a)*sqrt(a+c*x^2))+A*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(a*c^(3/4)*e*sqrt(a+c*x^2)) +--E 50 + +--S 51 of 465 +--d0:=D(m0,x) +--E 51 + +)clear all + +--S 52 of 465 +t0:=(A+B*x)/((a+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R +--------+ +--R 2 +-------+ | 2 +--R (c x + a)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 465 +--r0:=-(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ +-- sqrt(a+c*x^2))-elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(A*c*d+_ +-- a*B*e+B*d*sqrt(-a)*sqrt(c)-A*e*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*_ +-- (c*d^2+a*e^2)*sqrt(-a)*sqrt(a+c*x^2))+(A*c*d+a*B*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(a*c^(3/4)*e*(c*d^2+a*e^2)*sqrt(a+c*x^2)) +--E 53 + +--S 54 of 465 +--d0:=D(m0,x) +--E 54 + +)clear all + +--S 55 of 465 +t0:=(-a*e+c*d*x)*(d+e*x)^(-3-2*p)*(a+c*x^2)^p +--R +--R +--R - 2p - 3 2 p +--R (1) (c d x - a e)(e x + d) (c x + a) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 465 +r0:=1/2*(a+c*x^2)^(1+p)/((1+p)*(d+e*x)^(2*(1+p))) +--R +--R +--R 2 p + 1 +--R (c x + a) +--R (2) ----------------------- +--R 2p + 2 +--R (2p + 2)(e x + d) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 465 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 m +--R (1) (2c x + 3b c x + (2a c + b )x + a b)(e x + d) +--R Type: Expression(Integer) +--E 58 + +--S 59 of 465 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(2+m)/(e^4*(2+m))-3*c*(2*c*d-b*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+2*c^2*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 m + 4 +--R (2c m + 12c m + 22c m + 12c )(e x + d) +--R + +--R 2 3 2 2 2 +--R (3b c e - 6c d)m + (21b c e - 42c d)m + (42b c e - 84c d)m +--R + +--R 2 +--R 24b c e - 48c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 3 +--R ((2a c + b )e - 6b c d e + 6c d )m +--R + +--R 2 2 2 2 2 +--R ((16a c + 8b )e - 48b c d e + 48c d )m +--R + +--R 2 2 2 2 2 2 +--R ((38a c + 19b )e - 114b c d e + 114c d )m + (24a c + 12b )e +--R + +--R 2 2 +--R - 72b c d e + 72c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (- 2a c - b )d e + 3b c d e - 2c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (9a b e + (- 18a c - 9b )d e + 27b c d e - 18c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (26a b e + (- 52a c - 26b )d e + 78b c d e - 52c d )m + 24a b e +--R + +--R 2 2 2 2 3 +--R (- 48a c - 24b )d e + 72b c d e - 48c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 59 + +--S 60 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 465 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 7 4 2 3 6 2 4 3 2 2 2 5 +--R 2c e x + (3b c e + 8c d e )x + ((2a c + b )e + 12b c d e + 12c d e )x +--R + +--R 4 2 3 2 2 2 3 4 +--R (a b e + (8a c + 4b )d e + 18b c d e + 8c d e)x +--R + +--R 3 2 2 2 3 2 4 3 +--R (4a b d e + (12a c + 6b )d e + 12b c d e + 2c d )x +--R + +--R 2 2 2 3 4 2 3 2 4 +--R (6a b d e + (8a c + 4b )d e + 3b c d )x + (4a b d e + (2a c + b )d )x +--R + +--R 4 +--R a b d +--R Type: Polynomial(Integer) +--E 61 + +--S 62 of 465 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4+1/6*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^6/e^4-3/7*c*(2*c*d-b*e)*(d+e*x)^7/e^4+_ + 1/4*c^2*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 2 8 8 3 8 8 2 7 7 +--R - c e x + (- b c e + - c d e )x +--R 4 7 7 +--R + +--R 1 1 2 8 7 2 2 6 6 +--R ((- a c + - b )e + 2b c d e + 2c d e )x +--R 3 6 +--R + +--R 1 8 8 4 2 7 18 2 6 8 2 3 5 5 +--R (- a b e + (- a c + - b )d e + -- b c d e + - c d e )x +--R 5 5 5 5 5 +--R + +--R 7 3 2 2 6 3 5 1 2 4 4 4 +--R (a b d e + (3a c + - b )d e + 3b c d e + - c d e )x +--R 2 2 +--R + +--R 2 6 8 4 2 3 5 4 4 3 +--R (2a b d e + (- a c + - b )d e + b c d e )x +--R 3 3 +--R + +--R 3 5 1 2 4 4 2 4 4 1 5 3 +--R (2a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 5 +--R + +--R 1 1 2 6 2 1 7 1 2 8 +--R (- -- a c - -- b )d e + -- b c d e - --- c d +--R 15 30 35 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R 2c e x + (3b c e + 6c d e )x + ((2a c + b )e + 9b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (6a c + 3b )d e + 9b c d e + 2c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R (3a b d e + (6a c + 3b )d e + 3b c d )x + (3a b d e + (2a c + b )d )x +--R + +--R 3 +--R a b d +--R Type: Polynomial(Integer) +--E 64 + +--S 65 of 465 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4+1/5*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^5/e^4-1/2*c*(2*c*d-b*e)*(d+e*x)^6/e^4+_ + 2/7*c^2*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 2 2 7 7 1 7 2 6 6 +--R - c e x + (- b c e + c d e )x +--R 7 2 +--R + +--R 2 1 2 7 9 6 6 2 2 5 5 +--R ((- a c + - b )e + - b c d e + - c d e )x +--R 5 5 5 5 +--R + +--R 1 7 3 3 2 6 9 2 5 1 2 3 4 4 +--R (- a b e + (- a c + - b )d e + - b c d e + - c d e )x +--R 4 2 4 4 2 +--R + +--R 6 2 2 5 3 4 3 +--R (a b d e + (2a c + b )d e + b c d e )x +--R + +--R 3 2 5 1 2 3 4 2 3 4 1 4 3 +--R (- a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 2 4 +--R + +--R 1 1 2 5 2 1 6 1 2 7 +--R (- -- a c - -- b )d e + -- b c d e - -- c d +--R 10 20 20 70 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 65 + +--S 66 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 66 + +)clear all + +--S 67 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x + a b d +--R Type: Polynomial(Integer) +--E 67 + +--S 68 of 465 +r0:=-1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3/e^4+1/4*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^4/e^4-3/5*c*(2*c*d-b*e)*_ + (d+e*x)^5/e^4+1/3*c^2*(d+e*x)^6/e^4 +--R +--R +--R (2) +--R 1 2 6 6 3 6 4 2 5 5 +--R - c e x + (- b c e + - c d e )x +--R 3 5 5 +--R + +--R 1 1 2 6 3 5 1 2 2 4 4 +--R ((- a c + - b )e + - b c d e + - c d e )x +--R 2 4 2 2 +--R + +--R 1 6 4 2 2 5 2 4 3 +--R (- a b e + (- a c + - b )d e + b c d e )x +--R 3 3 3 +--R + +--R 5 1 2 2 4 2 2 4 1 3 3 +--R (a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 3 +--R + +--R 1 1 2 4 2 1 5 1 2 6 +--R (- - a c - -- b )d e + -- b c d e - -- c d +--R 6 12 10 30 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 68 + +--S 69 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 69 + +)clear all + +--S 70 of 465 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R Type: Polynomial(Integer) +--E 70 + +--S 71 of 465 +r0:=a*b*d*x+1/2*(b^2*d+2*a*c*d+a*b*e)*x^2+1/3*(3*b*c*d+b^2*e+2*a*c*e)*x^3+_ + 1/4*c*(2*c*d+3*b*e)*x^4+2/5*c^2*e*x^5 +--R +--R +--R (2) +--R 2 2 5 3 1 2 4 2 1 2 3 +--R - c e x + (- b c e + - c d)x + ((- a c + - b )e + b c d)x +--R 5 4 2 3 3 +--R + +--R 1 1 2 2 +--R (- a b e + (a c + - b )d)x + a b d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 71 + +--S 72 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 +--R (1) 2c x + 3b c x + (2a c + b )x + a b +--R Type: Polynomial(Integer) +--E 73 + +--S 74 of 465 +r0:=1/2*(a+b*x+c*x^2)^2 +--R +--R +--R 1 2 4 3 1 2 2 1 2 +--R (2) - c x + b c x + (a c + - b )x + a b x + - a +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 465 +r0:=(2*c^2*d^2+b^2*e^2-c*e*(3*b*d-2*a*e))*x/e^3-1/2*c*(2*c*d-3*b*e)*x^2/e^2+_ + 2/3*c^2*x^3/e-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R (6a b e + (- 12a c - 6b )d e + 18b c d e - 12c d )log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 4c e x + (9b c e - 6c d e )x + ((12a c + 6b )e - 18b c d e + 12c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 77 + +--S 78 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 79 + +--S 80 of 465 +r0:=-c*(4*c*d-3*b*e)*x/e^3+c^2*x^2/e^2+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/_ + (e^4*(d+e*x))+(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 2 +--R ((2a c + b )e - 6b c d e + 6c d e)x + (2a c + b )d e - 6b c d e +--R + +--R 2 3 +--R 6c d +--R * +--R log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 2 2 3 +--R c e x + (3b c e - 3c d e )x + (3b c d e - 4c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (2a c + b )d e - 3b c d e + 2c d +--R / +--R 5 4 +--R e x + d e +--R Type: Expression(Integer) +--E 80 + +--S 81 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 82 + +--S 83 of 465 +r0:=2*c^2*x/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x))-3*c*(2*c*d-b*e)*_ + log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 2 2 2 3 +--R ((6b c e - 12c d e )x + (12b c d e - 24c d e)x + 6b c d e - 12c d ) +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 2 3 2 2 2 3 +--R 4c e x + 8c d e x + ((- 4a c - 2b )e + 12b c d e - 8c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (- 2a c - b )d e + 9b c d e - 10c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 83 + +--S 84 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 85 + +--S 86 of 465 +r0:=1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+_ + 1/2*(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x)^2)+_ + 3*c*(2*c*d-b*e)/(e^4*(d+e*x))+2*c^2*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 2 2 2 3 +--R (12c e x + 36c d e x + 36c d e x + 12c d )log(e x + d) +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 18b c e + 36c d e )x + ((- 6a c - 3b )e - 18b c d e + 54c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (- 2a c - b )d e - 6b c d e + 22c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 86 + +--S 87 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 88 + +--S 89 of 465 +r0:=1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+_ + 1/3*(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x)^3)+_ + 3/2*c*(2*c*d-b*e)/(e^4*(d+e*x)^2)-2*c^2/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 3 3 3 3 2 2 2 +--R - 2c e x + (- - b c e - 3c d e )x +--R 2 +--R + +--R 2 1 2 3 2 2 2 1 3 +--R ((- - a c - - b )e - b c d e - 2c d e)x - - a b e +--R 3 3 4 +--R + +--R 1 1 2 2 1 2 1 2 3 +--R (- - a c - -- b )d e - - b c d e - - c d +--R 6 12 4 2 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 465 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 465 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))+_ + 2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(2+m)/(e^6*(2+m))-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(3+m)/(e^6*(3+m))+4*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(4+m)/(e^6*(4+m))-5*c^2*(2*c*d-b*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+2*c^3*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 3 5 3 4 3 3 3 2 3 3 m + 6 +--R (2c m + 30c m + 170c m + 450c m + 548c m + 240c )(e x + d) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R (5b c e - 10c d)m + (80b c e - 160c d)m + (475b c e - 950c d)m +--R + +--R 2 3 2 2 3 2 3 +--R (1300b c e - 2600c d)m + (1620b c e - 3240c d)m + 720b c e - 1440c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 3 2 5 +--R ((4a c + 4b c)e - 20b c d e + 20c d )m +--R + +--R 2 2 2 2 3 2 4 +--R ((68a c + 68b c)e - 340b c d e + 340c d )m +--R + +--R 2 2 2 2 3 2 3 +--R ((428a c + 428b c)e - 2140b c d e + 2140c d )m +--R + +--R 2 2 2 2 3 2 2 +--R ((1228a c + 1228b c)e - 6140b c d e + 6140c d )m +--R + +--R 2 2 2 2 3 2 +--R ((1584a c + 1584b c)e - 7920b c d e + 7920c d )m +--R + +--R 2 2 2 2 3 2 +--R (720a c + 720b c)e - 3600b c d e + 3600c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (- 12a c - 12b c)d e + 30b c d e - 20c d )m +--R + +--R 3 3 2 2 2 2 2 +--R (108a b c + 18b )e + (- 216a c - 216b c)d e + 540b c d e +--R + +--R 3 3 +--R - 360c d +--R * +--R 4 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (726a b c + 121b )e + (- 1452a c - 1452b c)d e + 3630b c d e +--R + +--R 3 3 +--R - 2420c d +--R * +--R 3 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (2232a b c + 372b )e + (- 4464a c - 4464b c)d e + 11160b c d e +--R + +--R 3 3 +--R - 7440c d +--R * +--R 2 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (3048a b c + 508b )e + (- 6096a c - 6096b c)d e + 15240b c d e +--R + +--R 3 3 +--R - 10160c d +--R * +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (1440a b c + 240b )e + (- 2880a c - 2880b c)d e + 7200b c d e +--R + +--R 3 3 +--R - 4800c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (2a c + 2a b )e + (- 12a b c - 2b )d e + (12a c + 12b c)d e +--R + +--R 2 3 3 4 +--R - 20b c d e + 10c d +--R * +--R 5 +--R m +--R + +--R 2 2 4 3 3 +--R (38a c + 38a b )e + (- 228a b c - 38b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (228a c + 228b c)d e - 380b c d e + 190c d +--R * +--R 4 +--R m +--R + +--R 2 2 4 3 3 +--R (274a c + 274a b )e + (- 1644a b c - 274b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (1644a c + 1644b c)d e - 2740b c d e + 1370c d +--R * +--R 3 +--R m +--R + +--R 2 2 4 3 3 +--R (922a c + 922a b )e + (- 5532a b c - 922b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (5532a c + 5532b c)d e - 9220b c d e + 4610c d +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 3 +--R (1404a c + 1404a b )e + (- 8424a b c - 1404b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (8424a c + 8424b c)d e - 14040b c d e + 7020c d +--R * +--R m +--R + +--R 2 2 4 3 3 +--R (720a c + 720a b )e + (- 4320a b c - 720b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (4320a c + 4320b c)d e - 7200b c d e + 3600c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 2 4 3 2 3 +--R a b e + (- 2a c - 2a b )d e + (6a b c + b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 4a c - 4b c)d e + 5b c d e - 2c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 20a b e + (- 40a c - 40a b )d e + (120a b c + 20b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 80a c - 80b c)d e + 100b c d e - 40c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 155a b e + (- 310a c - 310a b )d e + (930a b c + 155b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 620a c - 620b c)d e + 775b c d e - 310c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 580a b e + (- 1160a c - 1160a b )d e + (3480a b c + 580b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 2320a c - 2320b c)d e + 2900b c d e - 1160c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 1044a b e + (- 2088a c - 2088a b )d e +--R + +--R 3 2 3 2 2 3 2 +--R (6264a b c + 1044b )d e + (- 4176a c - 4176b c)d e +--R + +--R 2 4 3 5 +--R 5220b c d e - 2088c d +--R * +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 720a b e + (- 1440a c - 1440a b )d e + (4320a b c + 720b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 2880a c - 2880b c)d e + 3600b c d e - 1440c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 92 + +--S 93 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 465 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 9 2 4 3 3 8 +--R 2c e x + (5b c e + 8c d e )x +--R + +--R 2 2 4 2 3 3 2 2 7 +--R ((4a c + 4b c)e + 20b c d e + 12c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 6 +--R ((6a b c + b )e + (16a c + 16b c)d e + 30b c d e + 8c d e)x +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (2a c + 2a b )e + (24a b c + 4b )d e + (24a c + 24b c)d e +--R + +--R 2 3 3 4 +--R 20b c d e + 2c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 2 3 3 2 2 2 2 3 +--R a b e + (8a c + 8a b )d e + (36a b c + 6b )d e + (16a c + 16b c)d e +--R + +--R 2 4 +--R 5b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 3 +--R 4a b d e + (12a c + 12a b )d e + (24a b c + 4b )d e +--R + +--R 2 2 4 +--R (4a c + 4b c)d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 3 3 4 2 +--R (6a b d e + (8a c + 8a b )d e + (6a b c + b )d )x +--R + +--R 2 3 2 2 4 2 4 +--R (4a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 94 + +--S 95 of 465 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^5/e^6+1/3*(c*d^2-b*d*e+_ + a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^6/e^6-1/7*(2*c*d-_ + b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^7/e^6+1/2*c*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^8/e^6-5/9*c^2*(2*c*d-b*e)*_ + (d+e*x)^9/e^6+1/5*c^3*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 3 10 10 5 2 10 8 3 9 9 +--R - c e x + (- b c e + - c d e )x +--R 5 9 9 +--R + +--R 1 2 1 2 10 5 2 9 3 3 2 8 8 +--R ((- a c + - b c)e + - b c d e + - c d e )x +--R 2 2 2 2 +--R + +--R 6 1 3 10 16 2 16 2 9 30 2 2 8 8 3 3 7 7 +--R ((- a b c + - b )e + (-- a c + -- b c)d e + -- b c d e + - c d e )x +--R 7 7 7 7 7 7 +--R + +--R 1 2 1 2 10 2 3 9 2 2 2 8 +--R (- a c + - a b )e + (4a b c + - b )d e + (4a c + 4b c)d e +--R 3 3 3 +--R + +--R 10 2 3 7 1 3 4 6 +--R -- b c d e + - c d e +--R 3 3 +--R * +--R 6 +--R x +--R + +--R 1 2 10 8 2 8 2 9 36 6 3 2 8 +--R - a b e + (- a c + - a b )d e + (-- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 16 2 16 2 3 7 2 4 6 +--R (-- a c + -- b c)d e + b c d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 2 9 2 2 2 8 3 3 7 2 2 4 6 4 +--R (a b d e + (3a c + 3a b )d e + (6a b c + b )d e + (a c + b c)d e )x +--R + +--R 2 2 8 8 2 8 2 3 7 1 3 4 6 3 +--R (2a b d e + (- a c + - a b )d e + (2a b c + - b )d e )x +--R 3 3 3 +--R + +--R 2 3 7 2 2 4 6 2 2 4 6 1 2 5 5 +--R (2a b d e + (a c + a b )d e )x + a b d e x + - a b d e +--R 5 +--R + +--R 1 2 1 2 6 4 2 1 3 7 3 +--R (- -- a c - -- a b )d e + (-- a b c + --- b )d e +--R 15 15 35 105 +--R + +--R 1 2 1 2 8 2 1 2 9 1 3 10 +--R (- -- a c - -- b c)d e + --- b c d e - --- c d +--R 70 70 126 630 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 95 + +--S 96 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 3 8 2 3 3 2 7 +--R 2c e x + (5b c e + 6c d e )x +--R + +--R 2 2 3 2 2 3 2 6 +--R ((4a c + 4b c)e + 15b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (12a c + 12b c)d e + 15b c d e + 2c d )x +--R + +--R 2 2 3 3 2 2 2 2 2 3 4 +--R ((2a c + 2a b )e + (18a b c + 3b )d e + (12a c + 12b c)d e + 5b c d )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 3 +--R (a b e + (6a c + 6a b )d e + (18a b c + 3b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 6a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 3 2 3 +--R (3a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 97 + +--S 98 of 465 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4/e^6+2/5*(c*d^2-_ + b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^5/e^6-_ + 1/6*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^6/e^6+4/7*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^7/e^6-5/8*c^2*(2*c*d-b*e)*(d+e*x)^8/e^6+2/9*c^3*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 2 3 9 9 5 2 9 3 3 8 8 +--R - c e x + (- b c e + - c d e )x +--R 9 8 4 +--R + +--R 4 2 4 2 9 15 2 8 6 3 2 7 7 +--R ((- a c + - b c)e + -- b c d e + - c d e )x +--R 7 7 7 7 +--R + +--R 1 3 9 2 2 8 5 2 2 7 1 3 3 6 6 +--R ((a b c + - b )e + (2a c + 2b c)d e + - b c d e + - c d e )x +--R 6 2 3 +--R + +--R 2 2 2 2 9 18 3 3 8 12 2 12 2 2 7 +--R (- a c + - a b )e + (-- a b c + - b )d e + (-- a c + -- b c)d e +--R 5 5 5 5 5 5 +--R + +--R 2 3 6 +--R b c d e +--R * +--R 5 +--R x +--R + +--R 1 2 9 3 2 3 2 8 9 3 3 2 7 +--R - a b e + (- a c + - a b )d e + (- a b c + - b )d e +--R 4 2 2 2 4 +--R + +--R 2 2 3 6 +--R (a c + b c)d e +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 2 7 1 3 3 6 3 +--R (a b d e + (2a c + 2a b )d e + (2a b c + - b )d e )x +--R 3 +--R + +--R 3 2 2 7 2 2 3 6 2 2 3 6 1 2 4 5 +--R (- a b d e + (a c + a b )d e )x + a b d e x + - a b d e +--R 2 4 +--R + +--R 1 2 1 2 5 4 1 1 3 6 3 +--R (- -- a c - -- a b )d e + (-- a b c + -- b )d e +--R 10 10 10 60 +--R + +--R 1 2 1 2 7 2 1 2 8 1 3 9 +--R (- -- a c - -- b c)d e + -- b c d e - --- c d +--R 35 35 56 252 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 98 + +--S 99 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 100 + +--S 101 of 465 +r0:=a^2*b*d^2*x+a*d*(b^2*d+a*c*d+a*b*e)*x^2+1/3*(b^3*d^2+4*a*b^2*d*e+_ + 4*a^2*c*d*e+a*b*(6*c*d^2+a*e^2))*x^3+1/2*(b^3*d*e+6*a*b*c*d*e+b^2*_ + (2*c*d^2+a*e^2)+a*c*(2*c*d^2+a*e^2))*x^4+1/5*(8*b^2*c*d*e+_ + 8*a*c^2*d*e+b^3*e^2+b*c*(5*c*d^2+6*a*e^2))*x^5+1/3*c*(c^2*d^2+_ + 2*b^2*e^2+c*e*(5*b*d+2*a*e))*x^6+1/7*c^2*e*(4*c*d+5*b*e)*x^7+_ + 1/4*c^3*e^2*x^8 +--R +--R +--R (2) +--R 1 3 2 8 5 2 2 4 3 7 +--R - c e x + (- b c e + - c d e)x +--R 4 7 7 +--R + +--R 2 2 2 2 2 5 2 1 3 2 6 +--R ((- a c + - b c)e + - b c d e + - c d )x +--R 3 3 3 3 +--R + +--R 6 1 3 2 8 2 8 2 2 2 5 +--R ((- a b c + - b )e + (- a c + - b c)d e + b c d )x +--R 5 5 5 5 +--R + +--R 1 2 1 2 2 1 3 2 2 2 4 +--R ((- a c + - a b )e + (3a b c + - b )d e + (a c + b c)d )x +--R 2 2 2 +--R + +--R 1 2 2 4 2 4 2 1 3 2 3 +--R (- a b e + (- a c + - a b )d e + (2a b c + - b )d )x +--R 3 3 3 3 +--R + +--R 2 2 2 2 2 2 2 +--R (a b d e + (a c + a b )d )x + a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 101 + +--S 102 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 465 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 2 2 3 2 +--R ((6a b c + b )e + (4a c + 4b c)d)x + ((2a c + 2a b )e + (6a b c + b )d)x +--R + +--R 2 2 2 2 +--R (a b e + (2a c + 2a b )d)x + a b d +--R Type: Polynomial(Integer) +--E 103 + +--S 104 of 465 +r0:=a^2*b*d*x+1/2*a*(2*b^2*d+2*a*c*d+a*b*e)*x^2+1/3*(b^3*d+6*a*b*c*d+_ + 2*a*b^2*e+2*a^2*c*e)*x^3+1/4*(4*b^2*c*d+4*a*c^2*d+b^3*e+6*a*b*c*e)*x^4+_ + 1/5*c*(5*b*c*d+4*b^2*e+4*a*c*e)*x^5+1/6*c^2*(2*c*d+5*b*e)*x^6+2/7*c^3*e*x^7 +--R +--R +--R (2) +--R 2 3 7 5 2 1 3 6 4 2 4 2 2 5 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c)e + b c d)x +--R 7 6 3 5 5 +--R + +--R 3 1 3 2 2 4 +--R ((- a b c + - b )e + (a c + b c)d)x +--R 2 4 +--R + +--R 2 2 2 2 1 3 3 1 2 2 2 2 +--R ((- a c + - a b )e + (2a b c + - b )d)x + (- a b e + (a c + a b )d)x +--R 3 3 3 2 +--R + +--R 2 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 104 + +--S 105 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 465 +r0:=1/3*(a+b*x+c*x^2)^3 +--R +--R +--R (2) +--R 1 3 6 2 5 2 2 4 1 3 3 2 2 2 +--R - c x + b c x + (a c + b c)x + (2a b c + - b )x + (a c + a b )x +--R 3 3 +--R + +--R 2 1 3 +--R a b x + - a +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 107 + +--S 108 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 109 + +--S 110 of 465 +r0:=2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*x/e^5-_ + 1/2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^2/e^6+4/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^3/e^6-_ + 5/4*c^2*(2*c*d-b*e)*(d+e*x)^4/e^6+2/5*c^3*(d+e*x)^5/e^6-(2*c*d-b*e)*_ + (c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 2 4 3 2 3 +--R 60a b e + (- 120a c - 120a b )d e + (360a b c + 60b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 240a c - 240b c)d e + 300b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 24c e x + (75b c e - 30c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((80a c + 80b c)e - 100b c d e + 40c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (180a b c + 30b )e + (- 120a c - 120b c)d e + 150b c d e +--R + +--R 3 3 2 +--R - 60c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (120a c + 120a b )e + (- 360a b c - 60b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (240a c + 240b c)d e - 300b c d e + 120c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (180a b c + 30b )d e + (- 280a c - 280b c)d e + 575b c d e - 326c d +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 110 + +--S 111 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 112 + +--S 113 of 465 +r0:=-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*x/e^5+_ + (2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x))+2*c*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^2/e^6-5/3*c^2*(2*c*d-b*e)*_ + (d+e*x)^3/e^6+1/2*c^3*(d+e*x)^4/e^6+2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 5 3 4 +--R (12a c + 12a b )e + (- 72a b c - 12b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (72a c + 72b c)d e - 120b c d e + 60c d e +--R * +--R x +--R + +--R 2 2 4 3 2 3 2 2 3 2 +--R (12a c + 12a b )d e + (- 72a b c - 12b )d e + (72a c + 72b c)d e +--R + +--R 2 4 3 5 +--R - 120b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 3c e x + (10b c e - 5c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 20b c d e + 10c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((36a b c + 6b )e + (- 36a c - 36b c)d e + 60b c d e - 30c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((36a b c + 6b )d e + (- 36a c - 36b c)d e + 40b c d e - 5c d e)x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 6a b e + (12a c + 12a b )d e + (- 36a b c - 6b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (36a c + 36b c)d e - 80b c d e + 55c d +--R / +--R 7 6 +--R 6e x + 6d e +--R Type: Expression(Integer) +--E 113 + +--S 114 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 of 465 +r0:=c*(12*c^2*d^2+4*b^2*e^2-c*e*(15*b*d-4*a*e))*x/e^5-1/2*c^2*(6*c*d-_ + 5*b*e)*x^2/e^4+2/3*c^3*x^3/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+_ + a*e^2)^2/(e^6*(d+e*x)^2)-2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))/(e^6*(d+e*x))-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 2 2 4 2 2 3 +--R (36a b c + 6b )e + (- 72a c - 72b c)d e + 180b c d e +--R + +--R 3 3 2 +--R - 120c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (72a b c + 12b )d e + (- 144a c - 144b c)d e + 360b c d e +--R + +--R 3 4 +--R - 240c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (36a b c + 6b )d e + (- 72a c - 72b c)d e + 180b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 4c e x + (15b c e - 10c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((24a c + 24b c)e - 60b c d e + 40c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((48a c + 48b c)d e - 165b c d e + 126c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 12a c - 12a b )e + (72a b c + 12b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 30b c d e + 12c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 6a c - 6a b )d e + (54a b c + 9b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 60a c - 60b c)d e + 105b c d e - 54c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 116 + +--S 117 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 of 465 +r0:=-c^2*(8*c*d-5*b*e)*x/e^5+c^3*x^2/e^4+1/3*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^2/(e^6*(d+e*x)^3)-(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))/(e^6*(d+e*x)^2)+(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))/(e^6*(d+e*x))+4*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 60b c d e + 60c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e )x +--R + +--R 2 2 2 3 2 3 2 3 4 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e)x +--R + +--R 2 2 3 2 2 4 3 5 +--R (12a c + 12b c)d e - 60b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 2 4 3 2 3 3 +--R 3c e x + (15b c e - 15c d e )x + (45b c d e - 63c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 18a b c - 3b )e + (36a c + 36b c)d e - 45b c d e - 9c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 3a c - 3a b )e + (- 18a b c - 3b )d e + (54a c + 54b c)d e +--R + +--R 2 3 2 3 4 +--R - 135b c d e + 81c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (- a c - a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (22a c + 22b c)d e - 65b c d e + 47c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Expression(Integer) +--E 119 + +--S 120 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 465 +r0:=2*c^3*x/e^5+1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^4)-_ + 2/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/_ + (e^6*(d+e*x)^3)+1/2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-_ + 3*a*e))/(e^6*(d+e*x)^2)-4*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/_ + (e^6*(d+e*x))-5*c^2*(2*c*d-b*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 3 4 4 2 4 3 2 3 3 +--R (60b c e - 120c d e )x + (240b c d e - 480c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 3 4 2 4 +--R (360b c d e - 720c d e )x + (240b c d e - 480c d e)x + 60b c d e +--R + +--R 3 5 +--R - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 3 4 4 2 2 5 2 4 3 2 3 3 +--R 24c e x + 96c d e x + ((- 48a c - 48b c)e + 240b c d e - 96c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 36a b c - 6b )e + (- 72a c - 72b c)d e + 540b c d e +--R + +--R 3 3 2 +--R - 504c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 8a c - 8a b )e + (- 24a b c - 4b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 440b c d e - 496c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 2a c - 2a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12a c - 12b c)d e + 125b c d e - 154c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 122 + +--S 123 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 465 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 124 + +--S 125 of 465 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))+_ + (c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(2+m)/(e^8*(2+m))-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(3+m)/(e^8*(3+m))+_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*_ + (7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*_ + (d+e*x)^(4+m)/(e^8*(4+m))-5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^(5+m)/(e^8*(5+m))+3*c^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(6+m)/(e^8*(6+m))-_ + 7*c^3*(2*c*d-b*e)*(d+e*x)^(7+m)/(e^8*(7+m))+2*c^4*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 4 7 4 6 4 5 4 4 4 3 4 2 +--R 2c m + 56c m + 644c m + 3920c m + 13538c m + 26264c m +--R + +--R 4 4 +--R 26136c m + 10080c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 4 7 3 4 6 3 4 5 +--R (7b c e - 14c d)m + (203b c e - 406c d)m + (2401b c e - 4802c d)m +--R + +--R 3 4 4 3 4 3 +--R (14945b c e - 29890c d)m + (52528b c e - 105056c d)m +--R + +--R 3 4 2 3 4 3 +--R (103292b c e - 206584c d)m + (103824b c e - 207648c d)m + 40320b c e +--R + +--R 4 +--R - 80640c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 3 2 2 2 3 4 2 7 +--R ((6a c + 9b c )e - 42b c d e + 42c d )m +--R + +--R 3 2 2 2 3 4 2 6 +--R ((180a c + 270b c )e - 1260b c d e + 1260c d )m +--R + +--R 3 2 2 2 3 4 2 5 +--R ((2196a c + 3294b c )e - 15372b c d e + 15372c d )m +--R + +--R 3 2 2 2 3 4 2 4 +--R ((14040a c + 21060b c )e - 98280b c d e + 98280c d )m +--R + +--R 3 2 2 2 3 4 2 3 +--R ((50454a c + 75681b c )e - 353178b c d e + 353178c d )m +--R + +--R 3 2 2 2 3 4 2 2 +--R ((100980a c + 151470b c )e - 706860b c d e + 706860c d )m +--R + +--R 3 2 2 2 3 4 2 +--R ((102864a c + 154296b c )e - 720048b c d e + 720048c d )m +--R + +--R 3 2 2 2 3 4 2 +--R (40320a c + 60480b c )e - 282240b c d e + 282240c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 3 3 2 2 2 3 2 +--R (15a b c + 5b c)e + (- 30a c - 45b c )d e + 105b c d e +--R + +--R 4 3 +--R - 70c d +--R * +--R 7 +--R m +--R + +--R 2 3 3 3 2 2 2 3 2 +--R (465a b c + 155b c)e + (- 930a c - 1395b c )d e + 3255b c d e 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c)d e + (107400a c + 161100b c )d e +--R + +--R 3 5 4 6 +--R - 150360b c d e + 50120c d +--R * +--R 4 +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (30578a c + 45867a b )e + (- 275202a b c - 91734a b )d e +--R + +--R 2 2 2 4 2 4 +--R (275202a c + 550404a b c + 45867b )d e +--R + +--R 2 3 3 3 3 2 2 4 2 +--R (- 917340a b c - 305780b c)d e + (458670a c + 688005b c )d e +--R + +--R 3 5 4 6 +--R - 642138b c d e + 214046c d +--R * +--R 3 +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (73412a c + 110118a b )e + (- 660708a b c - 220236a b )d e +--R + +--R 2 2 2 4 2 4 +--R (660708a c + 1321416a b c + 110118b )d e +--R + +--R 2 3 3 3 +--R (- 2202360a b c - 734120b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (1101180a c + 1651770b c )d e - 1541652b c d e + 513884c d +--R * +--R 2 +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (89424a c + 134136a b )e + (- 804816a b c - 268272a b )d e +--R + +--R 2 2 2 4 2 4 +--R (804816a c + 1609632a b c + 134136b )d e +--R + +--R 2 3 3 3 +--R (- 2682720a b c - 894240b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (1341360a c + 2012040b c )d e - 1877904b c d e + 625968c d +--R * +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (40320a c + 60480a b )e + (- 362880a b c - 120960a b )d e +--R + +--R 2 2 2 4 2 4 +--R (362880a c + 725760a b c + 60480b )d e +--R + +--R 2 3 3 3 3 2 2 4 2 +--R (- 1209600a b c - 403200b c)d e + (604800a c + 907200b c )d e +--R + +--R 3 5 4 6 +--R - 846720b c d e + 282240c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R a b e + (- 2a c - 3a b )d e + (9a b c + 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 6a c - 12a b c - b )d e + (15a b c + 5b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 6a c - 9b c )d e + 7b c d e - 2c d +--R * +--R 7 +--R m +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R 35a b e + (- 70a c - 105a b )d e + (315a b c + 105a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 210a c - 420a b c - 35b )d e + (525a b c + 175b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 210a c - 315b c )d e + 245b c d e - 70c d +--R * +--R 6 +--R m +--R + +--R 3 7 3 2 2 6 +--R 511a b e + (- 1022a c - 1533a b )d e +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (4599a b c + 1533a b )d e + (- 3066a c - 6132a b c - 511b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (7665a b c + 2555b c)d e + (- 3066a c - 4599b c )d e +--R + +--R 3 6 4 7 +--R 3577b c d e - 1022c d +--R * +--R 5 +--R m +--R + +--R 3 7 3 2 2 6 +--R 4025a b e + (- 8050a c - 12075a b )d e +--R + +--R 2 3 2 5 +--R (36225a b c + 12075a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 24150a c - 48300a b c - 4025b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (60375a b c + 20125b c)d e + (- 24150a c - 36225b c )d e +--R + +--R 3 6 4 7 +--R 28175b c d e - 8050c d +--R * +--R 4 +--R m +--R + +--R 3 7 3 2 2 6 +--R 18424a b e + (- 36848a c - 55272a b )d e +--R + +--R 2 3 2 5 +--R (165816a b c + 55272a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 110544a c - 221088a b c - 18424b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (276360a b c + 92120b c)d e + (- 110544a c - 165816b c )d e +--R + +--R 3 6 4 7 +--R 128968b c d e - 36848c d +--R * +--R 3 +--R m +--R + +--R 3 7 3 2 2 6 +--R 48860a b e + (- 97720a c - 146580a b )d e +--R + +--R 2 3 2 5 +--R (439740a b c + 146580a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 293160a c - 586320a b c - 48860b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (732900a b c + 244300b c)d e + (- 293160a c - 439740b c )d e +--R + +--R 3 6 4 7 +--R 342020b c d e - 97720c d +--R * +--R 2 +--R m +--R + +--R 3 7 3 2 2 6 +--R 69264a b e + (- 138528a c - 207792a b )d e +--R + +--R 2 3 2 5 +--R (623376a b c + 207792a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 415584a c - 831168a b c - 69264b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (1038960a b c + 346320b c)d e + (- 415584a c - 623376b c )d e +--R + +--R 3 6 4 7 +--R 484848b c d e - 138528c d +--R * +--R m +--R + +--R 3 7 3 2 2 6 +--R 40320a b e + (- 80640a c - 120960a b )d e +--R + +--R 2 3 2 5 +--R (362880a b c + 120960a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 241920a c - 483840a b c - 40320b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (604800a b c + 201600b c)d e + (- 241920a c - 362880b c )d e +--R + +--R 3 6 4 7 +--R 282240b c d e - 80640c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 125 + +--S 126 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 of 465 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 4 11 3 4 4 3 10 +--R 2c e x + (7b c e + 8c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 9 +--R ((6a c + 9b c )e + 28b c d e + 12c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 8 +--R ((15a b c + 5b c)e + (24a c + 36b c )d e + 42b c d e + 8c d e)x +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c + 12a b c + b )e + (60a b c + 20b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (36a c + 54b c )d e + 28b c d e + 2c d +--R * +--R 7 +--R x +--R + +--R 2 3 4 2 2 2 4 3 +--R (9a b c + 3a b )e + (24a c + 48a b c + 4b )d e +--R + +--R 2 3 2 2 3 2 2 3 3 4 +--R (90a b c + 30b c)d e + (24a c + 36b c )d e + 7b c d +--R * +--R 6 +--R x +--R + +--R 3 2 2 4 2 3 3 +--R (2a c + 3a b )e + (36a b c + 12a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 3 2 2 4 +--R (36a c + 72a b c + 6b )d e + (60a b c + 20b c)d e + (6a c + 9b c )d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 +--R a b e + (8a c + 12a b )d e + (54a b c + 18a b )d e +--R + +--R 2 2 2 4 3 2 3 4 +--R (24a c + 48a b c + 4b )d e + (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 3 3 2 2 2 2 2 3 3 +--R 4a b d e + (12a c + 18a b )d e + (36a b c + 12a b )d e +--R + +--R 2 2 2 4 4 +--R (6a c + 12a b c + b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 3 2 3 4 2 +--R (6a b d e + (8a c + 12a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 3 2 2 4 3 4 +--R (4a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 127 + +--S 128 of 465 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^5/e^8+1/6*(c*d^2-b*d*e+_ + a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^6/e^8-_ + 3/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^7/e^8+1/8*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+_ + a^2*e^2))*(d+e*x)^8/e^8-5/9*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^9/e^8+3/10*c^2*(14*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(7*b*d-a*e))*(d+e*x)^10/e^8-7/11*c^3*(2*c*d-b*e)*_ + (d+e*x)^11/e^8+1/6*c^4*(d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 4 12 12 7 3 12 8 4 11 11 +--R - c e x + (-- b c e + -- c d e )x +--R 6 11 11 +--R + +--R 3 3 9 2 2 12 14 3 11 6 4 2 10 10 +--R ((- a c + -- b c )e + -- b c d e + - c d e )x +--R 5 10 5 5 +--R + +--R 5 2 5 3 12 8 3 2 2 11 14 3 2 10 +--R (- a b c + - b c)e + (- a c + 4b c )d e + -- b c d e +--R 3 9 3 3 +--R + +--R 8 4 3 9 +--R - c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 2 3 2 1 4 12 15 2 5 3 11 +--R (- a c + - a b c + - b )e + (-- a b c + - b c)d e +--R 4 2 8 2 2 +--R + +--R 9 3 27 2 2 2 10 7 3 3 9 1 4 4 8 +--R (- a c + -- b c )d e + - b c d e + - c d e +--R 2 4 2 4 +--R * +--R 8 +--R x +--R + +--R 9 2 3 3 12 24 2 2 48 2 4 4 11 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 7 7 7 7 7 +--R + +--R 90 2 30 3 2 10 24 3 36 2 2 3 9 3 4 8 +--R (-- a b c + -- b c)d e + (-- a c + -- b c )d e + b c d e +--R 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 1 2 2 12 2 3 11 +--R (- a c + - a b )e + (6a b c + 2a b )d e +--R 3 2 +--R + +--R 2 2 2 4 2 10 2 10 3 3 9 +--R (6a c + 12a b c + b )d e + (10a b c + -- b c)d e +--R 3 +--R + +--R 3 3 2 2 4 8 +--R (a c + - b c )d e +--R 2 +--R * +--R 6 +--R x +--R + +--R 1 3 12 8 3 12 2 2 11 54 2 18 3 2 10 +--R - a b e + (- a c + -- a b )d e + (-- a b c + -- a b )d e +--R 5 5 5 5 5 +--R + +--R 24 2 2 48 2 4 4 3 9 2 3 4 8 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d e +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 11 3 9 2 2 2 10 2 3 3 9 +--R a b d e + (3a c + - a b )d e + (9a b c + 3a b )d e +--R 2 +--R + +--R 3 2 2 2 1 4 4 8 +--R (- a c + 3a b c + - b )d e +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 2 10 8 3 2 2 3 9 2 3 4 8 3 +--R (2a b d e + (- a c + 4a b )d e + (3a b c + a b )d e )x +--R 3 +--R + +--R 3 3 9 3 3 2 2 4 8 2 3 4 8 1 3 5 7 +--R (2a b d e + (a c + - a b )d e )x + a b d e x + - a b d e +--R 2 5 +--R + +--R 1 3 1 2 2 6 6 3 2 1 3 7 5 +--R (- -- a c - -- a b )d e + (-- a b c + -- a b )d e +--R 15 10 35 35 +--R + +--R 3 2 2 3 2 1 4 8 4 1 2 1 3 9 3 +--R (- --- a c - -- a b c - --- b )d e + (-- a b c + --- b c)d e +--R 140 70 280 42 126 +--R + +--R 1 3 1 2 2 10 2 1 3 11 1 4 12 +--R (- --- a c - --- b c )d e + --- b c d e - ---- c d +--R 210 140 330 1980 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 128 + +--S 129 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 3 10 3 3 4 2 9 +--R 2c e x + (7b c e + 6c d e )x +--R + +--R 3 2 2 3 3 2 4 2 8 +--R ((6a c + 9b c )e + 21b c d e + 6c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 4 3 7 +--R ((15a b c + 5b c)e + (18a c + 27b c )d e + 21b c d e + 2c d )x +--R + +--R 2 2 2 4 3 2 3 2 +--R (6a c + 12a b c + b )e + (45a b c + 15b c)d e +--R + +--R 3 2 2 2 3 3 +--R (18a c + 27b c )d e + 7b c d +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 2 2 4 2 +--R (9a b c + 3a b )e + (18a c + 36a b c + 3b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (45a b c + 15b c)d e + (6a c + 9b c )d +--R * +--R 5 +--R x +--R + +--R 3 2 2 3 2 3 2 2 2 2 4 2 +--R (2a c + 3a b )e + (27a b c + 9a b )d e + (18a c + 36a b c + 3b )d e +--R + +--R 2 3 3 +--R (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 3 3 2 2 2 2 3 2 +--R a b e + (6a c + 9a b )d e + (27a b c + 9a b )d e +--R + +--R 2 2 2 4 3 +--R (6a c + 12a b c + b )d +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 9a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 2 3 2 2 3 3 3 +--R (3a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 130 + +--S 131 of 465 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^4/e^8+1/5*(c*d^2-b*d*e+_ + a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^5/e^8-_ + 1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^6/e^8+1/7*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-_ + 10*a*b*d*e+a^2*e^2))*(d+e*x)^7/e^8-5/8*c*(2*c*d-b*e)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^8/e^8+1/3*c^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^9/e^8-7/10*c^3*(2*c*d-b*e)*_ + (d+e*x)^10/e^8+2/11*c^4*(d+e*x)^11/e^8 +--R +--R +--R (2) +--R 2 4 11 11 7 3 11 3 4 10 10 +--R -- c e x + (-- b c e + - c d e )x +--R 11 10 5 +--R + +--R 2 3 2 2 11 7 3 10 2 4 2 9 9 +--R ((- a c + b c )e + - b c d e + - c d e )x +--R 3 3 3 +--R + +--R 15 2 5 3 11 9 3 27 2 2 10 21 3 2 9 +--R (-- a b c + - b c)e + (- a c + -- b c )d e + -- b c d e +--R 8 8 4 8 8 +--R + +--R 1 4 3 8 +--R - c d e +--R 4 +--R * +--R 8 +--R x +--R + +--R 6 2 2 12 2 1 4 11 45 2 15 3 10 +--R (- a c + -- a b c + - b )e + (-- a b c + -- b c)d e +--R 7 7 7 7 7 +--R + +--R 18 3 27 2 2 2 9 3 3 8 +--R (-- a c + -- b c )d e + b c d e +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 1 3 11 2 2 2 1 4 10 +--R (- a b c + - a b )e + (3a c + 6a b c + - b )d e +--R 2 2 2 +--R + +--R 15 2 5 3 2 9 3 3 2 2 3 8 +--R (-- a b c + - b c)d e + (a c + - b c )d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 2 11 27 2 9 3 10 +--R (- a c + - a b )e + (-- a b c + - a b )d e +--R 5 5 5 5 +--R + +--R 18 2 2 36 2 3 4 2 9 2 3 3 8 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d e +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 11 3 3 9 2 2 10 27 2 9 3 2 9 +--R - a b e + (- a c + - a b )d e + (-- a b c + - a b )d e +--R 4 2 4 4 4 +--R + +--R 3 2 2 2 1 4 3 8 +--R (- a c + 3a b c + - b )d e +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 10 3 2 2 2 9 2 3 3 8 3 +--R (a b d e + (2a c + 3a b )d e + (3a b c + a b )d e )x +--R + +--R 3 3 2 9 3 3 2 2 3 8 2 3 3 8 1 3 4 7 +--R (- a b d e + (a c + - a b )d e )x + a b d e x + - a b d e +--R 2 2 4 +--R + +--R 1 3 3 2 2 5 6 3 2 1 3 6 5 +--R (- -- a c - -- a b )d e + (-- a b c + -- a b )d e +--R 10 20 20 20 +--R + +--R 3 2 2 3 2 1 4 7 4 3 2 1 3 8 3 +--R (- -- a c - -- a b c - --- b )d e + (-- a b c + -- b c)d e +--R 70 35 140 56 56 +--R + +--R 1 3 1 2 2 9 2 1 3 10 1 4 11 +--R (- -- a c - -- b c )d e + --- b c d e - --- c d +--R 84 56 120 660 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 131 + +--S 132 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 2 9 3 2 4 8 3 2 2 2 3 4 2 7 +--R 2c e x + (7b c e + 4c d e)x + ((6a c + 9b c )e + 14b c d e + 2c d )x +--R + +--R 2 3 2 3 2 2 3 2 6 +--R ((15a b c + 5b c)e + (12a c + 18b c )d e + 7b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 2 2 5 +--R ((6a c + 12a b c + b )e + (30a b c + 10b c)d e + (6a c + 9b c )d )x +--R + +--R 2 3 2 2 2 2 4 2 3 2 4 +--R ((9a b c + 3a b )e + (12a c + 24a b c + 2b )d e + (15a b c + 5b c)d )x +--R + +--R 3 2 2 2 2 3 2 2 2 4 2 3 +--R ((2a c + 3a b )e + (18a b c + 6a b )d e + (6a c + 12a b c + b )d )x +--R + +--R 3 2 3 2 2 2 3 2 2 +--R (a b e + (4a c + 6a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 2 2 2 3 2 +--R (2a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 133 + +--S 134 of 465 +r0:=a^3*b*d^2*x+1/2*a^2*d*(3*b^2*d+2*a*c*d+2*a*b*e)*x^2+1/3*a*(3*b^3*d^2+_ + 6*a*b^2*d*e+4*a^2*c*d*e+a*b*(9*c*d^2+a*e^2))*x^3+1/4*(b^4*d^2+_ + 6*a*b^3*d*e+18*a^2*b*c*d*e+2*a^2*c*(3*c*d^2+a*e^2)+3*a*b^2*(4*c*d^2+_ + a*e^2))*x^4+1/5*(2*b^4*d*e+24*a*b^2*c*d*e+12*a^2*c^2*d*e+b^3*_ + (5*c*d^2+3*a*e^2)+3*a*b*c*(5*c*d^2+3*a*e^2))*x^5+1/6*(10*b^3*c*d*e+_ + 30*a*b*c^2*d*e+b^4*e^2+6*a*c^2*(c*d^2+a*e^2)+3*b^2*c*(3*c*d^2+_ + 4*a*e^2))*x^6+1/7*c*(18*b^2*c*d*e+12*a*c^2*d*e+5*b^3*e^2+b*c*_ + (7*c*d^2+15*a*e^2))*x^7+1/8*c^2*(2*c^2*d^2+9*b^2*e^2+2*c*e*_ + (7*b*d+3*a*e))*x^8+1/9*c^3*e*(4*c*d+7*b*e)*x^9+1/5*c^4*e^2*x^10 +--R +--R +--R (2) +--R 1 4 2 10 7 3 2 4 4 9 +--R - c e x + (- b c e + - c d e)x +--R 5 9 9 +--R + +--R 3 3 9 2 2 2 7 3 1 4 2 8 +--R ((- a c + - b c )e + - b c d e + - c d )x +--R 4 8 4 4 +--R + +--R 15 2 5 3 2 12 3 18 2 2 3 2 7 +--R ((-- a b c + - b c)e + (-- a c + -- b c )d e + b c d )x +--R 7 7 7 7 +--R + +--R 2 2 2 1 4 2 2 5 3 3 3 2 2 2 6 +--R ((a c + 2a b c + - b )e + (5a b c + - b c)d e + (a c + - b c )d )x +--R 6 3 2 +--R + +--R 9 2 3 3 2 12 2 2 24 2 2 4 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 2 3 2 +--R (3a b c + b c)d +--R * +--R 5 +--R x +--R + +--R 1 3 3 2 2 2 9 2 3 3 3 2 2 2 1 4 2 4 +--R ((- a c + - a b )e + (- a b c + - a b )d e + (- a c + 3a b c + - b )d )x +--R 2 4 2 2 2 4 +--R + +--R 1 3 2 4 3 2 2 2 3 2 3 +--R (- a b e + (- a c + 2a b )d e + (3a b c + a b )d )x +--R 3 3 +--R + +--R 3 3 3 2 2 2 2 3 2 +--R (a b d e + (a c + - a b )d )x + a b d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 465 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 8 3 4 7 3 2 2 3 6 +--R 2c e x + (7b c e + 2c d)x + ((6a c + 9b c )e + 7b c d)x +--R + +--R 2 3 3 2 2 5 +--R ((15a b c + 5b c)e + (6a c + 9b c )d)x +--R + +--R 2 2 2 4 2 3 4 +--R ((6a c + 12a b c + b )e + (15a b c + 5b c)d)x +--R + +--R 2 3 2 2 2 4 3 +--R ((9a b c + 3a b )e + (6a c + 12a b c + b )d)x +--R + +--R 3 2 2 2 3 2 3 3 2 2 3 +--R ((2a c + 3a b )e + (9a b c + 3a b )d)x + (a b e + (2a c + 3a b )d)x + a b d +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 465 +r0:=a^3*b*d*x+1/2*a^2*(3*b^2*d+2*a*c*d+a*b*e)*x^2+1/3*a*(3*b^3*d+_ + 9*a*b*c*d+3*a*b^2*e+2*a^2*c*e)*x^3+1/4*(b^4*d+12*a*b^2*c*d+_ + 6*a^2*c^2*d+3*a*b^3*e+9*a^2*b*c*e)*x^4+1/5*(5*b^3*c*d+15*a*b*c^2*d+_ + b^4*e+12*a*b^2*c*e+6*a^2*c^2*e)*x^5+1/6*c*(9*b^2*c*d+6*a*c^2*d+_ + 5*b^3*e+15*a*b*c*e)*x^6+1/7*c^2*(7*b*c*d+9*b^2*e+6*a*c*e)*x^7+_ + 1/8*c^3*(2*c*d+7*b*e)*x^8+2/9*c^4*e*x^9 +--R +--R +--R (2) +--R 2 4 9 7 3 1 4 8 6 3 9 2 2 3 7 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c )e + b c d)x +--R 9 8 4 7 7 +--R + +--R 5 2 5 3 3 3 2 2 6 +--R ((- a b c + - b c)e + (a c + - b c )d)x +--R 2 6 2 +--R + +--R 6 2 2 12 2 1 4 2 3 5 +--R ((- a c + -- a b c + - b )e + (3a b c + b c)d)x +--R 5 5 5 +--R + +--R 9 2 3 3 3 2 2 2 1 4 4 +--R ((- a b c + - a b )e + (- a c + 3a b c + - b )d)x +--R 4 4 2 4 +--R + +--R 2 3 2 2 2 3 3 1 3 3 3 2 2 2 +--R ((- a c + a b )e + (3a b c + a b )d)x + (- a b e + (a c + - a b )d)x +--R 3 2 2 +--R + +--R 3 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R Type: Polynomial(Integer) +--E 139 + +--S 140 of 465 +r0:=1/4*(a+b*x+c*x^2)^4 +--R +--R +--R (2) +--R 1 4 8 3 7 3 3 2 2 6 2 3 5 +--R - c x + b c x + (a c + - b c )x + (3a b c + b c)x +--R 4 2 +--R + +--R 3 2 2 2 1 4 4 2 3 3 3 3 2 2 2 3 +--R (- a c + 3a b c + - b )x + (3a b c + a b )x + (a c + - a b )x + a b x +--R 2 4 2 +--R + +--R 1 4 +--R - a +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +--S 141 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 142 + +--S 143 of 465 +r0:=(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*x/e^7-_ + 3/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^2/e^8+1/3*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+_ + a^2*e^2))*(d+e*x)^3/e^8-5/4*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^4/e^8+3/5*c^2*(14*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(7*b*d-a*e))*(d+e*x)^5/e^8-7/6*c^3*(2*c*d-b*e)*(d+e*x)^6/e^8+_ + 2/7*c^4*(d+e*x)^7/e^8-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 2 2 6 2 3 2 5 +--R 420a b e + (- 840a c - 1260a b )d e + (3780a b c + 1260a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 2520a c - 5040a b c - 420b )d e + (6300a b c + 2100b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 2520a c - 3780b c )d e + 2940b c d e - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 120c e x + (490b c e - 140c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((504a c + 756b c )e - 588b c d e + 168c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (1575a b c + 525b c)e + (- 630a c - 945b c )d e + 735b c d e +--R + +--R 4 3 4 +--R - 210c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (840a c + 1680a b c + 140b )e + (- 2100a b c - 700b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (840a c + 1260b c )d e - 980b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (1890a b c + 630a b )e + (- 1260a c - 2520a b c - 210b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (3150a b c + 1050b c)d e + (- 1260a c - 1890b c )d e +--R + +--R 3 4 3 4 5 2 +--R 1470b c d e - 420c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (840a c + 1260a b )e + (- 3780a b c - 1260a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (2520a c + 5040a b c + 420b )d e + (- 6300a b c - 2100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (2520a c + 3780b c )d e - 2940b c d e + 840c d e +--R * +--R x +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (1890a b c + 630a b )d e + (- 2940a c - 5880a b c - 490b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (12075a b c + 4025b c)d e + (- 6846a c - 10269b c )d e + 10437b c d e +--R + +--R 4 7 +--R - 3702c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 143 + +--S 144 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 145 + +--S 146 of 465 +r0:=-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*x/e^7+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x))+1/2*_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^2/e^8-_ + 5/3*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^3/e^8+3/4*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^4/e^8-7/5*c^3*(2*c*d-b*e)*(d+e*x)^5/e^8+1/3*c^4*_ + (d+e*x)^6/e^8+(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*_ + (7*b*d-a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 2 7 2 3 6 +--R (120a c + 180a b )e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d e +--R * +--R x +--R + +--R 3 2 2 6 2 3 2 5 +--R (120a c + 180a b )d e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 20c e x + (84b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((90a c + 135b c )e - 126b c d e + 42c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (300a b c + 100b c)e + (- 150a c - 225b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (180a c + 360a b c + 30b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (300a c + 450b c )d e - 420b c d e + 140c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (540a b c + 180a b )e + (- 540a c - 1080a b c - 90b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 3 4 3 +--R (1800a b c + 600b c)d e + (- 900a c - 1350b c )d e + 1260b c d e +--R + +--R 4 5 2 +--R - 420c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (540a b c + 180a b )d e + (- 540a c - 1080a b c - 90b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 3 5 2 +--R (1200a b c + 400b c)d e + (- 150a c - 225b c )d e - 546b c d e +--R + +--R 4 6 +--R 462c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 60a b e + (120a c + 180a b )d e + (- 540a b c - 180a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (540a c + 1080a b c + 90b )d e + (- 2400a b c - 800b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (1650a c + 2475b c )d e - 3066b c d e + 1302c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 146 + +--S 147 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 148 + +--S 149 of 465 +r0:=(30*c^4*d^4+b^4*e^4-2*c^3*d^2*e*(35*b*d-18*a*e)-3*b^2*c*e^3*_ + (5*b*d-4*a*e)+3*c^2*e^2*(18*b^2*d^2-15*a*b*d*e+2*a^2*e^2))*x/e^7-_ + 1/2*c*(20*c^3*d^3-5*b^3*e^3+3*b*c*e^2*(9*b*d-5*a*e)-6*c^2*d*e*(7*b*d-_ + 3*a*e))*x^2/e^6+c^2*(4*c^2*d^2+3*b^2*e^2-c*e*(7*b*d-2*a*e))*x^3/e^5-_ + 1/4*c^3*(6*c*d-7*b*e)*x^4/e^4+2/5*c^4*x^5/e^3+1/2*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^3/(e^8*(d+e*x)^2)-(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x))-3*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 2 2 2 4 6 +--R (180a b c + 60a b )e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2100b c d e - 840c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (360a b c + 120a b )d e + (- 720a c - 1440a b c - 120b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (3600a b c + 1200b c)d e + (- 2400a c - 3600b c )d e +--R + +--R 3 5 2 4 6 +--R 4200b c d e - 1680c d e +--R * +--R x +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (180a b c + 60a b )d e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e + 2100b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (35b c e - 14c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((40a c + 60b c )e - 70b c d e + 28c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (150a b c + 50b c)e + (- 100a c - 150b c )d e + 175b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (120a c + 240a b c + 20b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (400a c + 600b c )d e - 700b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (240a c + 480a b c + 40b )d e + (- 1650a b c - 550b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1260a c + 1890b c )d e - 2380b c d e + 1000c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 40a c - 60a b )e + (360a b c + 120a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 240a c - 480a b c - 40b )d e + (300a b c + 100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (120a c + 180b c )d e - 560b c d e + 320c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 10a b e + (- 20a c - 30a b )d e + (270a b c + 90a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 300a c - 600a b c - 50b )d e + (1050a b c + 350b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 540a c - 810b c )d e + 770b c d e - 260c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 149 + +--S 150 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 465 +r0:=-5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*x/e^7+_ + 1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^3)-1/2*(c*d^2-_ + b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x)^2)+_ + 3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))/(e^8*(d+e*x))+3/2*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^2/e^8-7/3*c^3*(2*c*d-b*e)*(d+e*x)^3/e^8+1/2*c^4*(d+e*x)^4/e^8+_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 2 4 7 2 3 6 +--R (36a c + 72a b c + 6b )e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (360a c + 540b c )d e - 840b c d e + 420c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (36a c + 72a b c + 6b )d e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (360a c + 540b c )d e - 840b c d e + 420c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 3c e x + (14b c e - 7c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((18a c + 27b c )e - 42b c d e + 21c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (90a b c + 30b c)e + (- 90a c - 135b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 105c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 3 3 4 +--R (270a b c + 90b c)d e + (- 360a c - 540b c )d e + 910b c d e +--R + +--R 4 4 3 +--R - 455c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (108a c + 216a b c + 18b )d e +--R + +--R 2 3 2 5 3 4 3 4 5 2 +--R (- 270a b c - 90b c)d e + 210b c d e - 105c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 6a c - 9a b )e + (- 54a b c - 18a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (162a c + 324a b c + 27b )d e + (- 810a b c - 270b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (540a c + 810b c )d e - 1050b c d e + 525c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 2a b e + (- 2a c - 3a b )d e + (- 18a b c - 6a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (66a c + 132a b c + 11b )d e + (- 390a b c - 130b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (300a c + 450b c )d e - 630b c d e + 315c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 152 + +--S 153 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 154 + +--S 155 of 465 +r0:=c^2*(30*c^2*d^2+9*b^2*e^2-c*e*(35*b*d-6*a*e))*x/e^7-1/2*c^3*_ + (10*c*d-7*b*e)*x^2/e^6+2/3*c^4*x^3/e^5+1/4*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^3/(e^8*(d+e*x)^4)-1/3*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x)^3)+3/2*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))/(e^8*(d+e*x)^2)+_ + (-70*c^4*d^4-b^4*e^4+4*b^2*c*e^3*(5*b*d-3*a*e)+20*c^3*d^2*e*(7*b*d-_ + 3*a*e)-6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))/(e^8*(d+e*x))-_ + 5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 3 2 2 6 3 2 5 +--R (180a b c + 60b c)e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 3 4 +--R - 840c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 3 4 4 4 3 +--R 5040b c d e - 3360c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1080a b c + 360b c)d e + (- 2160a c - 3240b c )d e +--R + +--R 3 4 3 4 5 2 +--R 7560b c d e - 5040c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 5 2 4 6 +--R 5040b c d e - 3360c d e +--R * +--R x +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (180a b c + 60b c)d e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (42b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((72a c + 108b c )e - 252b c d e + 168c d e )x +--R + +--R 3 2 2 6 3 2 5 4 3 4 4 +--R ((288a c + 432b c )d e - 1428b c d e + 1112c d e )x +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 72a c - 144a b c - 12b )e + (720a b c + 240b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 288a c - 432b c )d e - 672b c d e + 1088c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (- 108a c - 216a b c - 18b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1620a b c + 540b c)d e + (- 1512a c - 2268b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2772b c d e - 888c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 8a c - 12a b )e + (- 36a b c - 12a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 72a c - 144a b c - 12b )d e + (1320a b c + 440b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 1488a c - 2232b c )d e + 3528b c d e - 1712c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 3a b e + (- 2a c - 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 18a c - 36a b c - 3b )d e + (375a b c + 125b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 462a c - 693b c )d e + 1197b c d e - 638c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 155 + +--S 156 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 465 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 157 + +--S 158 of 465 +r0:=e*(8*c^3*d^3-b^3*e^3+b*c*e^2*(4*b*d+3*a*e)-2*c^2*d*e*(3*b*d+4*a*e))*_ + x/c^3+1/2*e^2*(12*c^2*d^2+b^2*e^2-2*c*e*(2*b*d+a*e))*x^2/c^2+1/3*e^3*_ + (8*c*d-b*e)*x^3/c+1/2*e^4*x^4+1/2*(2*c^4*d^4+b^4*e^4-4*b^2*c*e^3*_ + (b*d+a*e)-4*c^3*d^2*e*(b*d+3*a*e)+2*c^2*e^2*(3*b^2*d^2+6*a*b*d*e+_ + a^2*e^2))*log(a+b*x+c*x^2)/c^4-e*(2*c*d-b*e)*(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^4 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 12a b c + 6b )e + (24a c - 24b c)d e + 36b c d e - 24c d e) +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c - 12a b c + 3b )e + (36a b c - 12b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 36a c + 18b c )d e - 12b c d e + 6c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3c e x + (- 2b c e + 16c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 2 +--R ((- 6a c + 3b c )e - 12b c d e + 36c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 +--R ((18a b c - 6b c)e + (- 48a c + 24b c )d e - 36b c d e + 48c d e)x +--R / +--R 4 +--R 6c +--R Type: Expression(Integer) +--E 158 + +--S 159 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 of 465 +r0:=e*(6*c^2*d^2+b^2*e^2-c*e*(3*b*d+2*a*e))*x/c^2+1/2*e^2*(6*c*d-b*e)*x^2/c+_ + 2/3*e^3*x^3+1/2*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(a+b*x+_ + c*x^2)/c^3-e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^3 +--R +--R +--R (2) +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((6a c - 6b )e + 18b c d e - 18c d e)\|- 4a c + b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((9a b c - 3b )e + (- 18a c + 9b c)d e - 9b c d e + 6c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 3 2 3 3 2 2 +--R 4c e x + (- 3b c e + 18c d e )x +--R + +--R 2 2 3 2 2 3 2 +--R ((- 12a c + 6b c)e - 18b c d e + 36c d e)x +--R / +--R 3 +--R 6c +--R Type: Expression(Integer) +--E 161 + +--S 162 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 of 465 +r0:=e*(4*d-b*e/c)*x+e^2*x^2+1/2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + log(a+b*x+c*x^2)/c^2-e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*_ + sqrt(b^2-4*a*c)/c^2 +--R +--R +--R (2) +--R +-----------+ +--R 2 | 2 2c x + b +--R (2b e - 4c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d )log(c x + b x + a) + 2c e x +--R + +--R 2 2 +--R (- 2b c e + 8c d e)x +--R / +--R 2 +--R 2c +--R Type: Expression(Integer) +--E 164 + +--S 165 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 465 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) ----------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 465 +r0:=2*e*x+1/2*(2*c*d-b*e)*log(a+b*x+c*x^2)/c-e*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c +--R +--R +--R (2) +--R +-----------+ +--R | 2 2c x + b +--R - 2e\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R (- b e + 2c d)log(c x + b x + a) + 4c e x +--R / +--R 2c +--R Type: Expression(Integer) +--E 167 + +--S 168 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 465 +t0:=(b+2*c*x)/(a+b*x+c*x^2) +--R +--R +--R 2c x + b +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 169 + +--S 170 of 465 +r0:=log(a+b*x+c*x^2) +--R +--R +--R 2 +--R (2) log(c x + b x + a) +--R Type: Expression(Integer) +--E 170 + +--S 171 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 465 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------- +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 172 + +--S 173 of 465 +r0:=-(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)+1/2*(2*c*d-b*e)*log(a+b*x+_ + c*x^2)/(c*d^2-b*d*e+a*e^2)+e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-_ + 4*a*c)/(c*d^2-b*d*e+a*e^2) +--R +--R +--R (2) +--R +-----------+ +--R | 2 2c x + b 2 +--R 2e\|- 4a c + b atanh(--------------) + (- b e + 2c d)log(c x + b x + a) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R (2b e - 4c d)log(e x + d) +--R / +--R 2 2 +--R 2a e - 2b d e + 2c d +--R Type: Expression(Integer) +--E 173 + +--S 174 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 465 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 of 465 +r0:=(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x))-(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2+1/2*(2*c^2*d^2+_ + b^2*e^2-2*c*e*(b*d+a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2+_ + e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/_ + (c*d^2-b*d*e+a*e^2)^2 +--R +--R +--R (2) +--R +-----------+ +--R 3 2 2 2 | 2 +--R ((- 2b e + 4c d e )x - 2b d e + 4c d e)\|- 4a c + b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d e)x + (- 2a c + b )d e +--R + +--R 2 2 3 +--R - 2b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 2 2 2 2 +--R ((4a c - 2b )e + 4b c d e - 4c d e)x + (4a c - 2b )d e + 4b c d e +--R + +--R 2 3 +--R - 4c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (4a c + 2b )d e - 6b c d e + 4c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R Type: Expression(Integer) +--E 176 + +--S 177 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 465 +t0:=(b+2*c*x)/((d+e*x)^3*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 178 + +--S 179 of 465 +r0:=1/2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))-(2*c*d-b*e)*(c^2*d^2+_ + b^2*e^2-c*e*(b*d+3*a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*(2*c*d-_ + b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+_ + a*e^2)^3+e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/(c*d^2-b*d*e+a*e^2)^3 +--R +--R +--R (2) +--R 2 5 4 2 2 3 2 +--R ((- 2a c + 2b )e - 6b c d e + 6c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 +--R ((- 4a c + 4b )d e - 12b c d e + 12c d e )x + (- 2a c + 2b )d e +--R + +--R 3 2 2 4 +--R - 6b c d e + 6c d e +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((6a b c - 2b )d e + (- 12a c + 6b c)d e - 6b c d e + 4c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (3a b c - b )d e + (- 6a c + 3b c)d e - 3b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((- 12a b c + 4b )d e + (24a c - 12b c)d e + 12b c d e - 8c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 6a b c + 2b )d e + (12a c - 6b c)d e + 6b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 2 2 5 3 4 2 2 3 2 3 2 3 4 2 5 +--R ((- 4a c + 2a b )e - 2b d e + 6b c d e - 8b c d e + 4c d e)x - a b e +--R + +--R 2 2 4 3 2 3 2 2 3 2 +--R (- 2a c + 4a b )d e + (- 6a b c - 3b )d e + (4a c + 10b c)d e +--R + +--R 2 4 3 5 +--R - 13b c d e + 6c d +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R Type: Expression(Integer) +--E 179 + +--S 180 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 465 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 465 +r0:=4*e^3*(3*c*d-b*e)*x/c^2+2*e^4*x^2/c-(d+e*x)^4/(a+b*x+c*x^2)+_ + 2*e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(a+b*x+c*x^2)/c^3-_ + 4*e*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 3 2 2 +--R (- 12a b c + 4b c)e + (24a c - 12b c )d e + 12b c d e +--R + +--R 4 3 +--R - 8c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 3 3 2 2 2 2 +--R (- 12a b c + 4b )e + (24a b c - 12b c)d e + 12b c d e +--R + +--R 3 3 +--R - 8b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (- 12a b c + 4a b )e + (24a c - 12a b c)d e + 12a b c d e +--R + +--R 3 3 +--R - 8a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 2a c + 2b c)e - 6b c d e + 6c d e )x +--R + +--R 3 4 2 3 2 2 2 +--R ((- 2a b c + 2b )e - 6b c d e + 6b c d e )x +--R + +--R 2 2 4 3 2 2 2 +--R (- 2a c + 2a b )e - 6a b c d e + 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 4 4 2 4 3 3 3 +--R c e x + (- 2b c e + 8c d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((2a c - 4b c)e + 12b c d e - 6c d e )x +--R + +--R 4 2 3 3 3 3 4 +--R (- 4a b c e + 12a c d e - 4c d e)x - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 3 | 2 +--R (c x + b c x + a c )\|- 4a c + b +--R Type: Expression(Integer) +--E 182 + +--S 183 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 184 + +--S 185 of 465 +r0:=3*e^3*x/c-(d+e*x)^3/(a+b*x+c*x^2)+3/2*e^2*(2*c*d-b*e)*_ + log(a+b*x+c*x^2)/c^2-3*e*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 2 3 2 2 +--R ((12a c - 6b c)e + 12b c d e - 12c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((12a b c - 6b )e + 12b c d e - 12b c d e)x + (12a c - 6a b )e +--R + +--R 2 2 2 +--R 12a b c d e - 12a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- 3b c e + 6c d e )x + (- 3b e + 6b c d e )x - 3a b e +--R + +--R 2 +--R 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 3 2 2 2 3 2 2 2 3 +--R 4c e x + (6b c e - 6c d e )x + (6a c e - 6c d e)x - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 | 2 +--R (2c x + 2b c x + 2a c )\|- 4a c + b +--R Type: Expression(Integer) +--E 185 + +--S 186 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 187 + +--S 188 of 465 +r0:=-(d+e*x)^2/(a+b*x+c*x^2)+e^2*log(a+b*x+c*x^2)/c-2*e*(2*c*d-b*e)*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R ((2b c e - 4c d e)x + (2b e - 4b c d e)x + 2a b e - 4a c d e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 2 2 +--R ((c e x + b e x + a e )log(c x + b x + a) - c e x - 2c d e x - c d ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (c x + b c x + a c)\|- 4a c + b +--R Type: Expression(Integer) +--E 188 + +--S 189 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 465 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 190 + +--S 191 of 465 +r0:=(-d-e*x)/(a+b*x+c*x^2)-2*e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c) +--R +--R +--R (2) +--R +-----------+ +--R 2 2c x + b | 2 +--R (- 2c e x - 2b e x - 2a e)atanh(--------------) + (- e x - d)\|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R ---------------------------------------------------------------------------- +--R +-----------+ +--R 2 | 2 +--R (c x + b x + a)\|- 4a c + b +--R Type: Expression(Integer) +--E 191 + +--S 192 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 465 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^2 +--R +--R +--R 2c x + b +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 193 + +--S 194 of 465 +r0:=(-1)/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (2) - -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 194 + +--S 195 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 465 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 465 +r0:=(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))-e^2*(2*c*d-b*e)*log(d+e*x)/_ + (c*d^2-b*d*e+a*e^2)^2+1/2*e^2*(2*c*d-b*e)*log(a+b*x+c*x^2)/_ + (c*d^2-b*d*e+a*e^2)^2+e*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 2 3 2 2 +--R ((- 4a c + 2b c)e - 4b c d e + 4c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 4a b c + 2b )e - 4b c d e + 4b c d e)x + (- 4a c + 2a b )e +--R + +--R 2 2 2 +--R - 4a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- b c e + 2c d e )x + (- b e + 2b c d e )x - a b e +--R + +--R 2 +--R 2a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 2 3 2 3 +--R (2b c e - 4c d e )x + (2b e - 4b c d e )x + 2a b e +--R + +--R 2 +--R - 4a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 +--R (2a c e - 2b c d e + 2c d e)x + 2a b e + (- 2a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (2a c e - 4a b c d e + (4a c + 2b c)d e - 4b c d e + 2c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 +--R (2a b e - 4a b d e + (4a b c + 2b )d e - 4b c d e + 2b c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R 2a e - 4a b d e + (4a c + 2a b )d e - 4a b c d e + 2a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 197 + +--S 198 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 465 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + ((2a c + b )e + 4b c d e + c d )x +--R + +--R 2 2 2 3 +--R (2a b e + (4a c + 2b )d e + 2b c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (a e + 4a b d e + (2a c + b )d )x + (2a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 199 + +--S 200 of 465 +r0:=2*e^2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))+(-(b^2-4*a*c)*_ + (c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*_ + (a+b*x+c*x^2))-2*e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(d+e*x)/_ + (c*d^2-b*d*e+a*e^2)^3+e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*_ + log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3+2*e*(2*c*d-b*e)*(c^2*d^2+_ + b^2*e^2-c*e*(b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + ((c*d^2-b*d*e+a*e^2)^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 5 3 2 2 4 3 2 3 4 3 2 3 +--R ((6a b c - 2b c)e + (- 12a c + 6b c )d e - 6b c d e + 4c d e )x +--R + +--R 2 4 5 2 3 4 3 2 3 +--R (6a b c - 2b )e + (- 6a b c + 4b c)d e - 12a c d e +--R + +--R 3 3 2 4 4 +--R - 2b c d e + 4c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (6a b c - 2a b )e + (- 12a c + 12a b c - 2b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 +--R (- 18a b c + 6b c)d e + (4a c - 6b c )d e + 4b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 2 3 2 3 2 3 4 +--R (6a b c - 2a b )d e + (- 12a c + 6a b c)d e - 6a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((- a c + b c)e - 3b c d e + 3c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((- a b c + b )e + (- a c - 2b c)d e + 3c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- a c + a b )e + (- 4a b c + b )d e + (3a c - 3b c)d e +--R + +--R 2 3 2 +--R 3b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (- a c + a b )d e - 3a b c d e + 3a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((2a c - 2b c)e + 6b c d e - 6c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((2a b c - 2b )e + (2a c + 4b c)d e - 6c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (2a c - 2a b )e + (8a b c - 2b )d e + (- 6a c + 6b c)d e +--R + +--R 2 3 2 +--R - 6b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (2a c - 2a b )d e + 6a b c d e - 6a c d e +--R * +--R log(e x + d) +--R + +--R 5 2 2 4 2 2 3 3 3 2 2 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (a c - 2a b )e + (2a b c + 2b )d e + (2a c - 5b c)d e +--R + +--R 2 3 2 3 4 +--R 2b c d e + c d e +--R * +--R x +--R + +--R 2 5 2 4 3 2 3 2 2 3 2 +--R - a b e + 3a c d e + (- 2a b c + b )d e + (2a c - 3b c)d e +--R + +--R 2 4 3 5 +--R 3b c d e - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 7 2 6 2 2 2 2 5 2 3 3 4 +--R a c e - 3a b c d e + (3a c + 3a b c)d e + (- 6a b c - b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (3a c + 3b c )d e - 3b c d e + c d e +--R * +--R 3 +--R x +--R + +--R 3 7 3 2 2 6 3 2 5 2 2 2 4 3 4 +--R a b e + (a c - 3a b )d e + 3a b d e + (3a c - 3a b c - b )d e +--R + +--R 2 3 4 3 3 5 2 3 6 4 7 +--R (- 3a b c + 2b c)d e + 3a c d e - 2b c d e + c d +--R * +--R 2 +--R x +--R + +--R 4 7 3 6 3 2 5 2 3 3 4 +--R a e - 2a b d e + 3a c d e + (- 3a b c + 2a b )d e +--R + +--R 2 2 2 4 4 3 3 5 2 3 2 2 6 3 7 +--R (3a c - 3a b c - b )d e + 3b c d e + (a c - 3b c )d e + b c d +--R * +--R x +--R + +--R 4 6 3 2 5 3 2 2 3 4 2 3 4 3 +--R a d e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - a b )d e +--R + +--R 2 2 2 5 2 2 6 3 7 +--R (3a c + 3a b c)d e - 3a b c d e + a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 200 + +--S 201 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 465 +t0:=(b+2*c*x)*(d+e*x)^5/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R 2c e x + (b e + 10c d e )x + (5b d e + 20c d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10b d e + 20c d e )x + (10b d e + 10c d e)x + (5b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 202 + +--S 203 of 465 +r0:=5*e^3*(3*c^2*d^2+b^2*e^2-c*e*(2*b*d+3*a*e))*x/(c^2*(b^2-4*a*c))+_ + 5/2*e^4*(2*c*d-b*e)*x^2/(c*(b^2-4*a*c))-1/2*(d+e*x)^5/(a+b*x+c*x^2)^2-_ + 5/2*e*(d+e*x)^3*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+_ + 5*e*(2*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(b*d-3*a*e)-6*a*c^2*e^3*(2*b*d+a*e)+_ + 2*b^2*c*e^3*(b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*(b^2-_ + 4*a*c)^(3/2))+5/2*e^4*(2*c*d-b*e)*log(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (60a c - 60a b c + 10b c )e + (120a b c - 20b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R - 120a c d e + 40b c d e - 20c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (120a b c - 120a b c + 20b c)e + (240a b c - 40b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R - 240a b c d e + 80b c d e - 40b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (120a c - 60a b c - 40a b c + 10b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (240a b c + 80a b c - 20b c)d e + (- 240a c - 120a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (80a b c + 40b c )d e + (- 40a c - 20b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (120a b c - 120a b c + 20a b )e + (240a b c - 40a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R - 240a b c d e + 80a b c d e - 40a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (60a c - 60a b c + 10a b )e + (120a b c - 20a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R - 120a c d e + 40a b c d e - 20a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 20a b c + 5b c )e + (40a c - 10b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 40a b c + 10b c)e + (80a b c - 20b c )d e )x +--R + +--R 2 2 3 5 5 +--R (- 40a b c - 10a b c + 5b )e +--R + +--R 2 3 2 2 4 4 +--R (80a c + 20a b c - 10b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 40a b c + 10a b )e + (80a b c - 20a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 20a b c + 5a b )e + (40a c - 10a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 2 3 5 5 +--R (16a c - 4b c )e x +--R + +--R 3 3 2 5 4 2 3 4 4 2 3 +--R (55a b c - 15b c )e + (- 60a c + 25b c )d e - 30b c d e +--R + +--R 5 3 2 +--R 30c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (50a c + 20a b c - 10b c)e + (- 20a b c + 20b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (- 100a c - 20b c )d e + 40b c d e + 10c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 3 2 3 +--R (65a b c - 20a b c)e + (- 40a c + 40a b c )d e - 90a b c d e +--R + +--R 4 2 3 3 2 4 4 +--R (- 20a c + 20b c )d e + 15b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 5 2 2 4 2 3 2 3 +--R (30a c - 10a b c)e + 20a b c d e - 60a c d e +--R + +--R 4 2 3 4 +--R (- 10a c + 10b c )d e +--R * +--R x +--R + +--R 2 3 3 2 3 4 4 2 3 5 +--R - 10a c d e + 5a b c d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 6 2 5 4 5 3 4 3 2 5 2 4 4 3 2 +--R (8a c - 2b c )x + (16a b c - 4b c )x + (16a c + 4a b c - 2b c )x +--R + +--R 2 4 3 3 3 4 2 2 3 +--R (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 203 + +--S 204 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 465 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 205 + +--S 206 of 465 +r0:=2*e^3*(2*c*d-b*e)*x/(c*(b^2-4*a*c))-1/2*(d+e*x)^4/(a+b*x+c*x^2)^2-_ + 2*e*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+_ + 2*e*(2*c*d-b*e)*(2*c^2*d^2-b^2*e^2-2*c*e*(b*d-3*a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(c^2*(b^2-4*a*c)^(3/2))+e^4*log(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 3 3 2 4 4 3 4 2 2 5 3 4 +--R ((24a b c - 4b c )e - 48a c d e + 24b c d e - 16c d e)x +--R + +--R 2 2 4 4 3 3 2 3 2 2 4 3 3 +--R ((48a b c - 8b c)e - 96a b c d e + 48b c d e - 32b c d e)x +--R + +--R 2 2 3 5 4 2 3 2 2 3 +--R (48a b c + 16a b c - 4b )e + (- 96a c - 48a b c )d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (48a b c + 24b c )d e + (- 32a c - 16b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 2 2 2 2 3 3 +--R ((48a b c - 8a b )e - 96a b c d e + 48a b c d e - 32a b c d e)x +--R + +--R 3 2 3 4 3 2 3 2 2 2 2 2 3 3 +--R (24a b c - 4a b )e - 48a c d e + 24a b c d e - 16a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 4 4 2 3 4 3 +--R (8a c - 2b c )e x + (16a b c - 4b c)e x +--R + +--R 2 2 2 4 4 2 2 3 4 +--R (16a c + 4a b c - 2b )e x + (16a b c - 4a b )e x +--R + +--R 3 2 2 4 +--R (8a c - 2a b )e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 12a c + 5b c )e - 12b c d e + 16c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (- 4a b c + 4b c)e + (- 40a c - 8b c )d e + 20b c d e +--R + +--R 4 3 +--R 8c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 2 3 3 2 2 2 2 +--R (- 8a c + 8a b c)e - 36a b c d e + (- 16a c + 10b c )d e +--R + +--R 3 3 +--R 12b c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 2 2 3 2 2 3 +--R (4a b c e - 24a c d e - 4a b c d e + (- 8a c + 8b c )d e)x +--R + +--R 2 2 2 2 2 3 3 2 2 4 +--R - 8a c d e + 4a b c d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 4 4 3 3 3 2 4 2 3 4 2 2 +--R (8a c - 2b c )x + (16a b c - 4b c )x + (16a c + 4a b c - 2b c )x +--R + +--R 2 3 3 2 3 3 2 2 2 +--R (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 206 + +--S 207 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 208 + +--S 209 of 465 +r0:=-1/2*(d+e*x)^3/(a+b*x+c*x^2)^2-3/2*e*(d+e*x)*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + ((b^2-4*a*c)*(a+b*x+c*x^2))+6*e*(c*d^2-b*d*e+a*e^2)*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 12a c e + 12b c d e - 12c d e)x +--R + +--R 3 2 2 2 2 3 +--R (- 24a b c e + 24b c d e - 24b c d e)x +--R + +--R 2 2 3 3 2 +--R (- 24a c - 12a b )e + (24a b c + 12b )d e +--R + +--R 2 2 2 +--R (- 24a c - 12b c)d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 3 3 2 2 +--R (- 24a b e + 24a b d e - 24a b c d e)x - 12a e + 12a b d e +--R + +--R 2 2 +--R - 12a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 4 2 3 2 2 2 3 +--R (- 3b c e + 6c d e )x + ((- 10a c - 2b )e + 6b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 +--R (- 9a b e + (- 12a c + 3b )d e + 9b c d e)x +--R + +--R 2 3 2 2 2 2 2 2 +--R (- 6a e - 6a b d e + (- 6a c + 6b )d e)x - 6a d e + 3a b d e +--R + +--R 2 3 +--R (- 4a c + b )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 209 + +--S 210 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 465 +r0:=-1/2*(d+e*x)^2/(a+b*x+c*x^2)^2-e*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*_ + (a+b*x+c*x^2))+2*e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 2 2 3 4 2 2 2 3 +--R (4b c e - 8c d e)x + (8b c e - 16b c d e)x +--R + +--R 3 2 2 2 2 +--R ((8a b c + 4b )e + (- 16a c - 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (8a b e - 16a b c d e)x + 4a b e - 8a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 2 +--R (- 2b c e + 4c d e)x + ((- 8a c - b )e + 6b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 6a b e + (- 4a c + 4b )d e)x - 4a e + 2a b d e + (- 4a c + b )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 212 + +--S 213 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 465 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 214 + +--S 215 of 465 +r0:=1/2*(-d-e*x)/(a+b*x+c*x^2)^2-1/2*e*(b+2*c*x)/((b^2-4*a*c)*_ + (a+b*x+c*x^2))+2*c*e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 2 +--R (- 4c e x - 8b c e x + (- 8a c - 4b c)e x - 8a b c e x - 4a c e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 2 +--R (2c e x + 3b c e x + (- 2a c + 2b )e x + a b e + (- 4a c + b )d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 215 + +--S 216 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 465 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 217 + +--S 218 of 465 +r0:=(-1/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 1 +--R - +--R 2 +--R (2) - -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 218 + +--S 219 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 465 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^3) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 7 2 3 6 2 2 2 5 +--R c e x + (3b c e + c d)x + ((3a c + 3b c)e + 3b c d)x +--R + +--R 3 2 2 4 +--R ((6a b c + b )e + (3a c + 3b c)d)x +--R + +--R 2 2 3 3 2 2 2 2 +--R ((3a c + 3a b )e + (6a b c + b )d)x + (3a b e + (3a c + 3a b )d)x +--R + +--R 3 2 3 +--R (a e + 3a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 220 + +--S 221 of 465 +r0:=1/2*(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)-1/2*e*(3*b^2*c*d*e-8*a*c^2*d*e-_ + 2*b^3*e^2-b*c*(c*d^2-7*a*e^2)-2*c*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*(a+b*x+c*x^2))-e*(2*c^4*d^4-b^4*e^4-_ + 4*c^3*d^2*e*(b*d-3*a*e)-6*a*c^2*e^3*(2*b*d+a*e)+2*b^2*c*e^3*_ + (b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((b^2-4*a*c)^(3/2)*_ + (c*d^2-b*d*e+a*e^2)^3)-e^4*(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+_ + 1/2*e^4*(2*c*d-b*e)*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3 +--R +--R +--R (2) +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (- 12a c + 12a b c - 2b c )e + (- 24a b c + 4b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R 24a c d e - 8b c d e + 4c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (- 24a b c + 24a b c - 4b c)e + (- 48a b c + 8b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R 48a b c d e - 16b c d e + 8b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 24a c + 12a b c + 8a b c - 2b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (- 48a b c - 16a b c + 4b c)d e + (48a c + 24a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (- 16a b c - 8b c )d e + (8a c + 4b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (- 24a b c + 24a b c - 4a b )e + (- 48a b c + 8a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R 48a b c d e - 16a b c d e + 8a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (- 12a c + 12a b c - 2a b )e + (- 24a b c + 4a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R 24a c d e - 8a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 4a b c + b c )e + (8a c - 2b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 8a b c + 2b c)e + (16a b c - 4b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((- 8a b c - 2a b c + b )e + (16a c + 4a b c - 2b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 8a b c + 2a b )e + (16a b c - 4a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 4a b c + a b )e + (8a c - 2a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((8a b c - 2b c )e + (- 16a c + 4b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((16a b c - 4b c)e + (- 32a b c + 8b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((16a b c + 4a b c - 2b )e + (- 32a c - 8a b c + 4b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((16a b c - 4a b )e + (- 32a b c + 8a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (8a b c - 2a b )e + (- 16a c + 4a b c)d e +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 5 3 3 2 4 +--R (6a c - 2a b c )e + (- 4a b c + 2b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (4a c - 4b c )d e + 4b c d e - 2c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 4 +--R (13a b c - 4a b c)e + (- 8a c - 8a b c + 4b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (18a b c - 9b c )d e + (- 8a c + 8b c )d e - 3b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 5 4 +--R (10a c + 4a b c - 2a b )e + (- 20a b c + 2b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (12a c + 12a b c - 6b c)d e + (- 12a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (2a c - 2b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (11a b c - 3a b )e + (- 12a c - 11a b c + 4a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (30a b c - 5a b c - b )d e + (- 16a c - 6a b c + 3b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (11a b c - 3b c )d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 3 3 2 2 6 3 3 2 3 2 5 +--R (8a c - 2a b c )e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 4 +--R (24a c + 18a b c - 6a b c )d e +--R + +--R 2 4 3 3 5 2 3 3 +--R (- 48a b c + 4a b c + 2b c )d e +--R + +--R 2 5 2 4 4 3 4 2 5 3 4 5 +--R (24a c + 18a b c - 6b c )d e + (- 24a b c + 6b c )d e +--R + +--R 6 2 5 6 +--R (8a c - 2b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 6 3 2 2 2 4 5 +--R (16a b c - 4a b c)e + (- 48a b c + 12a b c)d e +--R + +--R 3 3 2 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b c)d e +--R + +--R 2 2 3 4 2 6 3 3 +--R (- 96a b c + 8a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 4 2 2 4 4 3 5 +--R (48a b c + 36a b c - 12b c )d e + (- 48a b c + 12b c )d e +--R + +--R 5 3 4 6 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 6 4 2 3 3 2 5 5 +--R (16a c + 4a b c - 2a b )e + (- 48a b c - 12a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 4 +--R (48a c + 60a b c + 6a b c - 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 96a b c - 40a b c + 8a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 4 2 +--R (48a c + 60a b c + 6a b c - 6b c)d e +--R + +--R 2 4 3 3 5 2 5 2 5 2 4 4 3 6 +--R (- 48a b c - 12a b c + 6b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 3 6 4 2 3 4 5 +--R (16a b c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b )d e +--R + +--R 3 2 2 2 4 6 3 3 +--R (- 96a b c + 8a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 2 3 4 2 5 +--R (48a b c + 36a b c - 12a b c)d e + (- 48a b c + 12a b c )d e +--R + +--R 2 4 3 3 6 +--R (16a b c - 4a b c )d +--R * +--R x +--R + +--R 6 5 2 6 5 4 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 5 2 4 2 3 4 2 4 4 2 3 3 2 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2a b )d e +--R + +--R 4 3 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (24a c + 18a b c - 6a b c)d e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 6 +--R (8a c - 2a b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 221 + +--S 222 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 465 +t0:=(b+2*c*x)*(d+e*x)^4*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 223 + +--S 224 of 465 +r0:=1/1680*(128*c^4*d^4+105*b^4*e^4-16*c^3*d^2*e*(16*b*d+93*a*e)-_ + 4*b^2*c*e^3*(109*b*d+101*a*e)+4*c^2*e^2*(141*b^2*d^2+372*a*b*d*e+_ + 16*a^2*e^2))*(a+b*x+c*x^2)^(3/2)/c^4+1/35*(4*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(b*d+2*a*e))*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)/c^2+2/21*(2*c*d-b*e)*_ + (d+e*x)^3*(a+b*x+c*x^2)^(3/2)/c+2/7*(d+e*x)^4*(a+b*x+c*x^2)^(3/2)-_ + 1/280*e*(9*b^3*d*e^2+8*a*c*e*(17*c*d^2-4*a*e^2)-4*b*c*d*(2*c*d^2+_ + 15*a*e^2)-b^2*(22*c*d^2*e-12*a*e^3)-(2*c*d-b*e)*(8*c^2*d^2+_ + 21*b^2*e^2-4*c*e*(2*b*d+19*a*e))*x)*(a+b*x+c*x^2)^(3/2)/c^3-_ + 1/256*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(8*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(2*b*d+a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/_ + c^(11/2)+1/128*(b^2-4*a*c)*e*(2*c*d-b*e)*(8*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(2*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 3 3 2 3 2 5 7 4 +--R (- 6720a b c + 8400a b c - 2940a b c + 315b )e +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (13440a c - 30240a b c + 12600a b c - 1470b c)d e +--R + +--R 2 4 3 3 5 2 2 2 +--R (40320a b c - 20160a b c + 2520b c )d e +--R + +--R 2 5 2 4 4 3 3 +--R (- 26880a c + 13440a b c - 1680b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 6 4 6 5 4 6 3 5 +--R 7680c e x + (5120b c e + 35840c d e )x +--R + +--R 5 2 4 4 5 3 6 2 2 4 +--R ((1536a c - 256b c )e + 25088b c d e + 64512c d e )x +--R + +--R 4 3 3 4 5 2 4 3 +--R (- 1408a b c + 288b c )e + (8960a c - 1344b c )d e +--R + +--R 5 2 2 6 3 +--R 48384b c d e + 53760c d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 4 2 4 +--R (- 2048a c + 1984a b c - 336b c )e +--R + +--R 4 3 3 3 5 2 4 2 2 +--R (- 8064a b c + 1568b c )d e + (21504a c - 2688b c )d e +--R + +--R 5 3 6 4 +--R 44800b c d e + 17920c d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 5 4 +--R (4672a b c - 2912a b c + 420b c)e +--R + +--R 2 4 2 3 4 2 3 +--R (- 13440a c + 12096a b c - 1960b c )d e +--R + +--R 4 3 3 2 2 5 2 4 3 +--R (- 18816a b c + 3360b c )d e + (26880a c - 2240b c )d e +--R + +--R 5 4 +--R 17920b c d +--R * +--R x +--R + +--R 3 3 2 2 2 4 6 4 +--R (4096a c - 10976a b c + 5040a b c - 630b )e +--R + +--R 2 3 3 2 5 3 +--R (36288a b c - 21280a b c + 2940b c)d e +--R + +--R 2 4 2 3 4 2 2 2 +--R (- 43008a c + 33600a b c - 5040b c )d e +--R + +--R 4 3 3 3 5 4 +--R (- 22400a b c + 3360b c )d e + 17920a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 26880c \|c +--R Type: Expression(Integer) +--E 224 + +--S 225 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 465 +r0:=1/480*(2*c*d-b*e)*(32*c^2*d^2+35*b^2*e^2-4*c*e*(8*b*d+27*a*e))*_ + (a+b*x+c*x^2)^(3/2)/c^3+1/10*(2*c*d-b*e)*(d+e*x)^2*_ + (a+b*x+c*x^2)^(3/2)/c+1/3*(d+e*x)^3*(a+b*x+c*x^2)^(3/2)+1/80*e*_ + (3*b^2*d*e-28*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+7*b^2*e^2-4*c*e*_ + (2*b*d+5*a*e))*x)*(a+b*x+c*x^2)^(3/2)/c^2-1/512*(b^2-4*a*c)^2*e*_ + (24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)+1/256*(b^2-4*a*c)*e*(24*c^2*d^2+_ + 7*b^2*e^2-4*c*e*(6*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 3 +--R (960a c - 2160a b c + 900a b c - 105b )e +--R + +--R 2 3 3 2 5 2 +--R (5760a b c - 2880a b c + 360b c)d e +--R + +--R 2 4 2 3 4 2 2 +--R (- 5760a c + 2880a b c - 360b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 5 3 5 4 3 5 2 4 +--R 2560c e x + (1792b c e + 9216c d e )x +--R + +--R 4 2 3 3 4 2 5 2 3 +--R ((640a c - 96b c )e + 6912b c d e + 11520c d e)x +--R + +--R 3 3 2 3 4 2 3 2 +--R (- 576a b c + 112b c )e + (3072a c - 384b c )d e +--R + +--R 4 2 5 3 +--R 9600b c d e + 5120c d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 4 3 3 3 2 2 +--R (- 960a c + 864a b c - 140b c)e + (- 2688a b c + 480b c )d e +--R + +--R 4 2 3 2 4 3 +--R (5760a c - 480b c )d e + 5120b c d +--R * +--R x +--R + +--R 2 2 3 5 3 +--R (2592a b c - 1520a b c + 210b )e +--R + +--R 2 3 2 2 4 2 3 3 2 2 +--R (- 6144a c + 4800a b c - 720b c)d e + (- 4800a b c + 720b c )d e +--R + +--R 4 3 +--R 5120a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 227 + +--S 228 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R +--------------+ +--R 2 3 2 2 2 2 | 2 +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|c x + b x + a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 465 +r0:=1/60*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*(a+b*x+c*x^2)^(3/2)/c^2+_ + 2/5*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)+1/10*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/c-1/64*(b^2-4*a*c)^2*e*(2*c*d-b*e)*atanh(1/2*(b+_ + 2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+1/32*(b^2-4*a*c)*e*(2*c*d-_ + b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 2 3 5 2 2 3 2 2 4 +--R ((240a b c - 120a b c + 15b )e + (- 480a c + 240a b c - 30b c)d e) +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 4 2 4 3 2 4 3 +--R 384c e x + (288b c e + 960c d e)x +--R + +--R 3 2 2 2 3 4 2 2 +--R ((128a c - 16b c )e + 800b c d e + 640c d )x +--R + +--R 2 3 2 3 2 2 3 2 +--R ((- 112a b c + 20b c)e + (480a c - 40b c )d e + 640b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 +--R (- 256a c + 200a b c - 30b )e + (- 400a b c + 60b c)d e + 640a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 960c \|c +--R Type: Expression(Integer) +--E 230 + +--S 231 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 of 465 +t0:=(b+2*c*x)*(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (1) (2c e x + (b e + 2c d)x + b d)\|c x + b x + a +--R Type: Expression(Integer) +--E 232 + +--S 233 of 465 +r0:=1/12*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/c+1/2*(d+e*x)*(a+b*x+c*x^2)^(3/2)-_ + 1/64*(b^2-4*a*c)^2*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(5/2)+1/32*(b^2-4*a*c)*e*(b+2*c*x)*_ + sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 4 2c x + b +--R (- 48a c + 24a b c - 3b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 3 2 3 2 2 2 2 +--R 96c e x + (80b c e + 128c d)x + ((48a c - 4b c)e + 128b c d)x +--R + +--R 3 2 +--R (- 40a b c + 6b )e + 128a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 233 + +--S 234 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R (1) (2c x + b)\|c x + b x + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 465 +r0:=2/3*(a+b*x+c*x^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (2c x + 2b x + 2a)\|c x + b x + a +--R (2) ------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 238 + +--S 239 of 465 +r0:=1/4*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^3*sqrt(c))-(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-_ + b*d*e+a*e^2)/e^3-1/2*(4*c*d-3*b*e-2*c*e*x)*sqrt(a+b*x+c*x^2)/e^2 +--R +--R +--R (2) +--R 2 2 2 2 2c x + b +--R ((4a c + b )e - 8b c d e + 8c d )atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R +-+ | 2 2 +--R (- 4b e + 8c d)\|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +--------------+ +--R 2 2 +-+ | 2 +--R (4c e x + 6b e - 8c d e)\|c \|c x + b x + a +--R / +--R 3 +-+ +--R 4e \|c +--R Type: Expression(Integer) +--E 239 + +--S 240 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 241 + +--S 242 of 465 +r0:=-2*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*_ + sqrt(c)/e^3+1/2*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*atanh(1/2*_ + (b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (e^3*sqrt(c*d^2-b*d*e+a*e^2))+(4*c*d-b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/_ + (e^2*(d+e*x)) +--R +--R +--R (2) +--R +-------------------+ +--R 2 2 +-+ | 2 2 +--R ((4b e - 8c d e)x + 4b d e - 8c d )\|c \|a e - b d e + c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 +--R ((- 4a c - b )e + 8b c d e - 8c d e)x + (- 4a c - b )d e +--R + +--R 2 2 3 +--R 8b c d e - 8c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R 2 2 | 2 2 | 2 +--R (4c e x - 2b e + 8c d e)\|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 4 3 | 2 2 +--R (2e x + 2d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 242 + +--S 243 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 244 + +--S 245 of 465 +r0:=1/2*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+_ + 2*c^(3/2)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/e^3-_ + 1/8*(2*c*d-b*e)*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*atanh(1/2*_ + (b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (e^3*(c*d^2-b*d*e+a*e^2)^(3/2))-1/4*(8*c^2*d^2-6*b*c*d*e-b^2*e^2+_ + 8*a*c*e^2+2*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-_ + b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 4 3 2 2 2 2 +--R (16a c e - 16b c d e + 16c d e )x +--R + +--R 3 2 2 2 3 2 2 3 2 4 +--R (32a c d e - 32b c d e + 32c d e)x + 16a c d e - 16b c d e + 16c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 12a b c + b )e + (24a c + 6b c)d e - 24b c d e + 16c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 24a b c + 2b )d e + (48a c + 12b c)d e - 48b c d e +--R + +--R 3 4 +--R 32c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 12a b c + b )d e + (24a c + 6b c)d e - 24b c d e + 16c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 2 2 2 4 +--R ((- 16a c - 2b )e + 24b c d e - 24c d e )x - 4a b e +--R + +--R 2 3 2 2 2 3 +--R (- 8a c + 2b )d e + 12b c d e - 16c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 7 6 2 5 2 6 2 5 3 4 +--R (8a e - 8b d e + 8c d e )x + (16a d e - 16b d e + 16c d e )x +--R + +--R 2 5 3 4 4 3 +--R 8a d e - 8b d e + 8c d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 245 + +--S 246 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 247 + +--S 248 of 465 +r0:=1/16*(b^2-4*a*c)^2*e*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+_ + 1/12*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*sqrt(a+b*x+c*x^2)/_ + (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+1/24*(2*c*d-b*e)*(8*c^2*d^2-_ + 3*b^2*e^2-4*c*e*(2*b*d-5*a*e))*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-_ + b*d*e+a*e^2)^2*(d+e*x))-1/3*(4*c*d+b*e+6*c*e*x)*sqrt(a+b*x+c*x^2)/_ + (e^2*(d+e*x)^3) +--R +--R +--R (2) +--R 2 2 2 4 4 3 2 2 2 4 3 2 +--R (- 48a c + 24a b c - 3b )e x + (- 144a c + 72a b c - 9b )d e x +--R + +--R 2 2 2 4 2 2 2 2 2 4 3 +--R (- 144a c + 72a b c - 9b )d e x + (- 48a c + 24a b c - 3b )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 2 2 2 2 3 3 2 +--R ((- 40a b c + 6b )e + (80a c + 4b c)d e - 48b c d e + 32c d )x +--R + +--R 2 2 3 3 2 2 2 2 +--R (- 48a c - 4a b )e + (32a b c + 16b )d e + (48a c - 60b c)d e +--R + +--R 2 3 +--R 32b c d +--R * +--R x +--R + +--R 2 3 2 2 2 3 2 2 3 +--R - 16a b e + (- 16a c + 28a b )d e + (- 24a b c - 6b )d e + 32a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 2 7 6 2 2 5 3 4 2 4 3 3 +--R (48a e - 96a b d e + (96a c + 48b )d e - 96b c d e + 48c d e )x +--R + +--R 2 6 2 5 2 3 4 4 3 +--R 144a d e - 288a b d e + (288a c + 144b )d e - 288b c d e +--R + +--R 2 5 2 +--R 144c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 2 4 3 5 2 +--R 144a d e - 288a b d e + (288a c + 144b )d e - 288b c d e +--R + +--R 2 6 +--R 144c d e +--R * +--R x +--R + +--R 2 3 4 4 3 2 5 2 6 2 7 +--R 48a d e - 96a b d e + (96a c + 48b )d e - 96b c d e + 48c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 248 + +--S 249 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 250 + +--S 251 of 465 +r0:=5/128*(b^2-4*a*c)^2*e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (c*d^2-b*d*e+a*e^2)^(7/2)+1/24*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3)+_ + 1/96*(2*c*d-b*e)*(8*c^2*d^2-5*b^2*e^2-4*c*e*(2*b*d-7*a*e))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^2)+_ + 1/192*(32*c^4*d^4-15*b^4*e^4-16*c^3*d^2*e*(4*b*d-9*a*e)+_ + 20*b^2*c*e^3*(b*d+5*a*e)+4*c^2*e^2*(3*b^2*d^2-36*a*b*d*e-32*a^2*e^2))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)^3*(d+e*x))-1/4*(2*c*d+b*e+_ + 4*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^4) +--R +--R +--R (2) +--R 2 2 3 5 6 +--R (240a b c - 120a b c + 15b )e +--R + +--R 2 3 2 2 4 5 +--R (- 480a c + 240a b c - 30b c)d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 5 +--R (960a b c - 480a b c + 60b )d e +--R + +--R 2 3 2 2 4 2 4 +--R (- 1920a c + 960a b c - 120b c)d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 4 +--R (1440a b c - 720a b c + 90b )d e +--R + +--R 2 3 2 2 4 3 3 +--R (- 2880a c + 1440a b c - 180b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 5 3 3 +--R (960a b c - 480a b c + 60b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (- 1920a c + 960a b c - 120b c)d e +--R * +--R x +--R + +--R 2 2 3 5 4 2 2 3 2 2 4 5 +--R (240a b c - 120a b c + 15b )d e + (- 480a c + 240a b c - 30b c)d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 4 5 2 3 4 +--R (- 256a c + 200a b c - 30b )e + (- 288a b c + 40b c)d e +--R + +--R 3 2 2 2 3 3 3 2 4 4 +--R (288a c + 24b c )d e - 128b c d e + 64c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (- 112a b c + 20a b )e + (- 544a c + 704a b c - 110b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 +--R (- 1296a b c + 148b c)d e + (1152a c + 160b c )d e +--R + +--R 3 4 4 5 +--R - 544b c d e + 256c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 5 2 3 4 +--R (- 256a c - 16a b )e + (608a b c + 72a b )d e +--R + +--R 2 2 2 4 2 3 2 3 3 2 +--R (- 1152a c - 120a b c - 146b )d e + (64a b c + 528b c)d e +--R + +--R 3 2 2 4 3 5 +--R (544a c - 728b c )d e + 256b c d +--R * +--R x +--R + +--R 3 5 3 2 2 4 2 3 2 3 +--R - 96a b e + (- 64a c + 272a b )d e + (- 144a b c - 236a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (- 288a c + 528a b c + 30b )d e + (- 368a b c - 60b c)d e +--R + +--R 3 5 +--R 256a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 3 10 2 9 2 2 2 8 +--R 384a e - 1152a b d e + (1152a c + 1152a b )d e +--R + +--R 3 3 7 2 2 4 6 2 5 5 +--R (- 2304a b c - 384b )d e + (1152a c + 1152b c)d e - 1152b c d e +--R + +--R 3 6 4 +--R 384c d e +--R * +--R 4 +--R x +--R + +--R 3 9 2 2 8 2 2 3 7 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 4 6 2 2 5 5 +--R (- 9216a b c - 1536b )d e + (4608a c + 4608b c)d e +--R + +--R 2 6 4 3 7 3 +--R - 4608b c d e + 1536c d e +--R * +--R 3 +--R x +--R + +--R 3 2 8 2 3 7 2 2 4 6 +--R 2304a d e - 6912a b d e + (6912a c + 6912a b )d e +--R + +--R 3 5 5 2 2 6 4 +--R (- 13824a b c - 2304b )d e + (6912a c + 6912b c)d e +--R + +--R 2 7 3 3 8 2 +--R - 6912b c d e + 2304c d e +--R * +--R 2 +--R x +--R + +--R 3 3 7 2 4 6 2 2 5 5 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 6 4 2 2 7 3 +--R (- 9216a b c - 1536b )d e + (4608a c + 4608b c)d e +--R + +--R 2 8 2 3 9 +--R - 4608b c d e + 1536c d e +--R * +--R x +--R + +--R 3 4 6 2 5 5 2 2 6 4 +--R 384a d e - 1152a b d e + (1152a c + 1152a b )d e +--R + +--R 3 7 3 2 2 8 2 2 9 +--R (- 2304a b c - 384b )d e + (1152a c + 1152b c)d e - 1152b c d e +--R + +--R 3 10 +--R 384c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 251 + +--S 252 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R 2c e x + (3b c e + 6c d e )x + ((2a c + b )e + 9b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (6a c + 3b )d e + 9b c d e + 2c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R (3a b d e + (6a c + 3b )d e + 3b c d )x + (3a b d e + (2a c + b )d )x +--R + +--R 3 +--R a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 465 +r0:=1/1024*(b^2-4*a*c)*e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*_ + (b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+3/2240*(2*c*d-b*e)*(16*c^2*d^2+_ + 21*b^2*e^2-4*c*e*(4*b*d+17*a*e))*(a+b*x+c*x^2)^(5/2)/c^3+3/56*(2*c*d-_ + b*e)*(d+e*x)^2*(a+b*x+c*x^2)^(5/2)/c+1/4*(d+e*x)^3*(a+b*x+c*x^2)^(5/2)+_ + 1/224*e*(5*b^2*d*e-36*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+9*b^2*e^2-_ + 4*c*e*(2*b*d+7*a*e))*x)*(a+b*x+c*x^2)^(5/2)/c^2+3/16384*(b^2-4*a*c)^3*_ + e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)-3/8192*(b^2-4*a*c)^2*e*(32*c^2*_ + d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 4 4 3 2 3 2 4 2 6 8 3 +--R (26880a c - 80640a b c + 50400a b c - 11760a b c + 945b )e +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (215040a b c - 161280a b c + 40320a b c - 3360b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (- 215040a c + 161280a b c - 40320a b c + 3360b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 7 3 7 6 3 7 2 6 +--R 143360c e x + (256000b c e + 491520c d e )x +--R + +--R 6 2 5 3 6 2 7 2 5 +--R ((215040a c + 104960b c )e + 901120b c d e + 573440c d e)x +--R + +--R 5 3 4 3 6 2 5 2 +--R (144384a b c - 768b c )e + (786432a c + 385024b c )d e +--R + +--R 6 2 7 3 +--R 1089536b c d e + 229376c d +--R * +--R 4 +--R x +--R + +--R 2 5 2 4 4 3 3 +--R (17920a c - 6912a b c + 864b c )e +--R + +--R 5 3 4 2 6 2 5 2 +--R (569344a b c - 3072b c )d e + (1003520a c + 494592b c )d e +--R + +--R 6 3 +--R 458752b c d +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 3 +--R (- 22272a b c + 9088a b c - 1008b c )e +--R + +--R 2 5 2 4 4 3 2 +--R (98304a c - 30720a b c + 3584b c )d e +--R + +--R 5 3 4 2 6 2 5 3 +--R (817152a b c - 3584b c )d e + (458752a c + 229376b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (- 26880a c + 38208a b c - 12656a b c + 1260b c)e +--R + +--R 2 4 3 3 5 2 2 +--R (- 116736a b c + 43008a b c - 4480b c )d e +--R + +--R 2 5 2 4 4 3 2 5 3 +--R (215040a c - 43008a b c + 4480b c )d e + 458752a b c d +--R * +--R x +--R + +--R 3 3 2 3 2 5 7 3 +--R (84864a b c - 75488a b c + 21000a b c - 1890b )e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 196608a c + 236544a b c - 71680a b c + 6720b c)d e +--R + +--R 2 4 3 3 5 2 2 2 5 3 +--R (- 236544a b c + 71680a b c - 6720b c )d e + 229376a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 573440c \|c +--R Type: Expression(Integer) +--E 254 + +--S 255 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x +--R + +--R 2 +--R a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 465 +r0:=1/96*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3+_ + 1/210*(24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*(a+b*x+c*x^2)^(5/2)/c^2+_ + 2/7*(d+e*x)^2*(a+b*x+c*x^2)^(5/2)+1/21*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(5/2)/c+1/512*(b^2-4*a*c)^3*e*(2*c*d-b*e)*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)-1/256*(b^2-4*a*c)^2*e*_ + (2*c*d-b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 3 3 2 3 2 5 7 2 +--R (6720a b c - 5040a b c + 1260a b c - 105b )e +--R + +--R 3 4 2 2 3 4 2 6 +--R (- 13440a c + 10080a b c - 2520a b c + 210b c)d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 6 2 6 5 2 6 5 +--R 15360c e x + (28160b c e + 35840c d e)x +--R + +--R 5 2 4 2 5 6 2 4 +--R ((24576a c + 12032b c )e + 68096b c d e + 21504c d )x +--R + +--R 4 3 3 2 5 2 4 +--R (17792a b c - 96b c )e + (62720a c + 30912b c )d e +--R + +--R 5 2 +--R 43008b c d +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 4 2 2 4 3 3 +--R (3072a c - 960a b c + 112b c )e + (51072a b c - 224b c )d e +--R + +--R 5 2 4 2 +--R (43008a c + 21504b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 5 2 +--R (- 3648a b c + 1344a b c - 140b c)e +--R + +--R 2 4 2 3 4 2 4 2 +--R (13440a c - 2688a b c + 280b c )d e + 43008a b c d +--R * +--R x +--R + +--R 3 3 2 2 2 4 6 2 +--R (- 6144a c + 7392a b c - 2240a b c + 210b )e +--R + +--R 2 3 3 2 5 2 4 2 +--R (- 14784a b c + 4480a b c - 420b c)d e + 21504a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 53760c \|c +--R Type: Expression(Integer) +--E 257 + +--S 258 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 465 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 465 +r0:=1/96*(b^2-4*a*c)*e*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^2+1/30*(2*c*d-b*e)*_ + (a+b*x+c*x^2)^(5/2)/c+1/3*(d+e*x)*(a+b*x+c*x^2)^(5/2)+1/512*(b^2-4*a*c)^3*_ + e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-1/256*(b^2-_ + 4*a*c)^2*e*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 2c x + b +--R (- 960a c + 720a b c - 180a b c + 15b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 5 5 4 5 4 +--R 2560c e x + (4864b c e + 3072c d)x +--R + +--R 4 2 3 4 3 +--R ((4480a c + 2208b c )e + 6144b c d)x +--R + +--R 3 3 2 4 2 3 2 +--R ((3648a b c - 16b c )e + (6144a c + 3072b c )d)x +--R + +--R 2 3 2 2 4 3 +--R ((960a c - 192a b c + 20b c)e + 6144a b c d)x +--R + +--R 2 2 3 5 2 3 +--R (- 1056a b c + 320a b c - 30b )e + 3072a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 260 + +--S 261 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (1) (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R Type: Expression(Integer) +--E 262 + +--S 263 of 465 +r0:=2/5*(a+b*x+c*x^2)^(5/2) +--R +--R +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (2c x + 4b c x + (4a c + 2b )x + 4a b x + 2a )\|c x + b x + a +--R (2) ------------------------------------------------------------------ +--R 5 +--R Type: Expression(Integer) +--E 263 + +--S 264 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 265 + +--S 266 of 465 +r0:=-1/12*(8*c*d-7*b*e-6*c*e*x)*(a+b*x+c*x^2)^(3/2)/e^2+1/64*(128*c^4*d^4-_ + b^4*e^4-8*b^2*c*e^3*(2*b*d-3*a*e)-64*c^3*d^2*e*(4*b*d-3*a*e)+48*c^2*_ + e^2*(3*b^2*d^2-4*a*b*d*e+a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(c^(3/2)*e^5)-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^(3/2)*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/e^5-1/32*(64*c^3*d^3-b^3*e^3+4*b*c*e^2*(12*b*d-_ + 11*a*e)-16*c^2*d*e*(7*b*d-4*a*e)-2*c*e*(16*c^2*d^2+b^2*e^2-_ + 4*c*e*(4*b*d-3*a*e))*x)*sqrt(a+b*x+c*x^2)/(c*e^4) +--R +--R +--R (2) +--R 2 2 2 4 4 2 3 3 +--R (144a c + 72a b c - 3b )e + (- 576a b c - 48b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (576a c + 432b c )d e - 768b c d e + 384c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 2 3 3 +-+ +--R (- 192a b c e + (384a c + 192b c)d e - 576b c d e + 384c d )\|c +--R * +--R +-------------------+ +--R | 2 2 (b e - 2c d)x + 2a e - b d +--R \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 4 3 2 4 3 3 2 +--R 96c e x + (208b c e - 128c d e )x +--R + +--R 2 2 4 2 3 3 2 2 +--R ((240a c + 124b c)e - 320b c d e + 192c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (376a b c + 6b )e + (- 512a c - 288b c)d e + 672b c d e - 384c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 192c e \|c +--R Type: Expression(Integer) +--E 266 + +--S 267 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 268 + +--S 269 of 465 +r0:=1/3*(8*c*d-3*b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x))-_ + 1/4*(2*c*d-b*e)*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e^5*sqrt(c))+1/2*(16*c^2*d^2+_ + 3*b^2*e^2-4*c*e*(4*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^5+_ + 1/2*(16*c^2*d^2+5*b^2*e^2-4*c*e*(5*b*d-a*e)-4*c*e*(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/e^4 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((36a b c + 3b )e + (- 72a c - 54b c)d e + 144b c d e - 96c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 4 +--R (36a b c + 3b )d e + (- 72a c - 54b c)d e + 144b c d e - 96c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 +--R ((- 24a c - 18b )e + 96b c d e - 96c d e)x + (- 24a c - 18b )d e +--R + +--R 2 2 3 +--R 96b c d e - 96c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 3 2 +--R 8c e x + (20b c e - 16c d e )x +--R + +--R 2 4 3 2 2 2 4 +--R ((32a c + 18b )e - 64b c d e + 48c d e )x - 12a b e +--R + +--R 2 3 2 2 2 3 +--R (56a c + 30b )d e - 120b c d e + 96c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 6 5 +-+ +--R (12e x + 12d e )\|c +--R Type: Expression(Integer) +--E 269 + +--S 270 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 271 + +--S 272 of 465 +r0:=1/2*(4*c*d-b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)+_ + 3/4*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e^5-3/8*(2*c*d-b*e)*(16*c^2*d^2+_ + b^2*e^2-4*c*e*(4*b*d-3*a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*sqrt(c*d^2-b*d*e+_ + a*e^2))-3/4*(16*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-a*e)+4*c*e*(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 4 3 2 2 2 2 +--R ((24a c + 18b )e - 96b c d e + 96c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 +--R ((48a c + 36b )d e - 192b c d e + 192c d e)x + (24a c + 18b )d e +--R + +--R 3 2 4 +--R - 96b c d e + 96c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 36a b c - 3b )e + (72a c + 54b c)d e - 144b c d e +--R + +--R 3 3 2 +--R 96c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 72a b c - 6b )d e + (144a c + 108b c)d e - 288b c d e +--R + +--R 3 4 +--R 192c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 36a b c - 3b )d e + (72a c + 54b c)d e - 144b c d e + 96c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 3 2 +--R 8c e x + (28b c e - 32c d e )x +--R + +--R 2 4 3 2 2 2 4 +--R ((- 16a c - 10b )e + 112b c d e - 144c d e )x - 4a b e +--R + +--R 2 3 2 2 2 3 +--R (- 8a c - 6b )d e + 72b c d e - 96c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 7 2 6 2 5 | 2 2 +--R (8e x + 16d e x + 8d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 272 + +--S 273 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 274 + +--S 275 of 465 +r0:=-1/4*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*(a+b*x+c*x^2)^(3/2)/_ + (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+1/3*(8*c*d-b*e+6*c*e*x)*(a+b*x+_ + c*x^2)^(3/2)/(e^2*(d+e*x)^3)-4*c^(3/2)*(2*c*d-b*e)*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/e^5+1/16*(128*c^4*d^4-b^4*e^4-_ + 8*b^2*c*e^3*(2*b*d-3*a*e)-64*c^3*d^2*e*(4*b*d-3*a*e)+48*c^2*e^2*_ + (3*b^2*d^2-4*a*b*d*e+a^2*e^2))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*(c*d^2-b*d*e+_ + a*e^2)^(3/2))+1/8*(64*c^3*d^3+b^3*e^3+4*b*c*e^2*(4*b*d-5*a*e)-_ + 16*c^2*d*e*(5*b*d-4*a*e)+2*c*e*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-_ + 3*a*e))*x)*sqrt(a+b*x+c*x^2)/(e^4*(c*d^2-b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 6 2 2 5 2 2 4 3 3 3 3 +--R (192a b c e + (- 384a c - 192b c)d e + 576b c d e - 384c d e )x +--R + +--R 5 2 2 2 4 2 3 3 +--R 576a b c d e + (- 1152a c - 576b c)d e + 1728b c d e +--R + +--R 3 4 2 +--R - 1152c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 3 2 4 2 +--R 576a b c d e + (- 1152a c - 576b c)d e + 1728b c d e +--R + +--R 3 5 +--R - 1152c d e +--R * +--R x +--R + +--R 3 3 2 2 4 2 2 5 3 6 +--R 192a b c d e + (- 384a c - 192b c)d e + 576b c d e - 384c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 144a c - 72a b c + 3b )e + (576a b c + 48b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 576a c - 432b c )d e + 768b c d e - 384c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (- 432a c - 216a b c + 9b )d e + (1728a b c + 144b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (- 1728a c - 1296b c )d e + 2304b c d e - 1152c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 432a c - 216a b c + 9b )d e + (1728a b c + 144b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 1728a c - 1296b c )d e + 2304b c d e - 1152c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 144a c - 72a b c + 3b )d e + (576a b c + 48b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 576a c - 432b c )d e + 768b c d e - 384c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 6 2 5 3 2 4 3 +--R (96a c e - 96b c d e + 96c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (- 184a b c - 6b )e + (656a c + 220b c)d e - 912b c d e +--R + +--R 3 3 3 +--R 704c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 48a c - 28a b )e + (- 160a b c + 16b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (816a c + 252b c)d e - 1216b c d e + 960c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 16a b e + (- 16a c + 4a b )d e + (- 72a b c + 6b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (320a c + 96b c)d e - 480b c d e + 384c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 10 9 2 8 3 +--R (48a e - 48b d e + 48c d e )x +--R + +--R 9 2 8 3 7 2 +--R (144a d e - 144b d e + 144c d e )x +--R + +--R 2 8 3 7 4 6 3 7 4 6 5 5 +--R (144a d e - 144b d e + 144c d e )x + 48a d e - 48b d e + 48c d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 275 + +--S 276 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 3 8 2 3 3 2 7 +--R 2c e x + (5b c e + 6c d e )x +--R + +--R 2 2 3 2 2 3 2 6 +--R ((4a c + 4b c)e + 15b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (12a c + 12b c)d e + 15b c d e + 2c d )x +--R + +--R 2 2 3 3 2 2 2 2 +--R (2a c + 2a b )e + (18a b c + 3b )d e + (12a c + 12b c)d e +--R + +--R 2 3 +--R 5b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 3 2 2 2 3 3 +--R (a b e + (6a c + 6a b )d e + (18a b c + 3b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 6a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 3 2 3 +--R (3a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 465 +r0:=-1/8192*(b^2-4*a*c)^2*e*(40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*_ + (b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^5+1/2560*(b^2-4*a*c)*e*(40*c^2*d^2+_ + 11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^4+_ + 1/6720*(2*c*d-b*e)*(64*c^2*d^2+99*b^2*e^2-4*c*e*(16*b*d+83*a*e))*_ + (a+b*x+c*x^2)^(7/2)/c^3+1/30*(2*c*d-b*e)*(d+e*x)^2*(a+b*x+_ + c*x^2)^(7/2)/c+1/5*(d+e*x)^3*(a+b*x+c*x^2)^(7/2)+1/480*e*(7*b^2*d*e-_ + 44*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+11*b^2*e^2-4*c*e*(2*b*d+_ + 9*a*e))*x)*(a+b*x+c*x^2)^(7/2)/c^2-3/131072*(b^2-4*a*c)^4*e*_ + (40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(13/2)+3/65536*(b^2-4*a*c)^3*e*_ + (40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^6 +--R +--R +--R (2) +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 322560a c - 1209600a b c + 1008000a b c - 352800a b c +--R + +--R 8 10 +--R 56700a b c - 3465b +--R * +--R 3 +--R e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R 3225600a b c - 3225600a b c + 1209600a b c - 201600a b c +--R + +--R 9 +--R 12600b c +--R * +--R 2 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R - 3225600a c + 3225600a b c - 1209600a b c + 201600a b c +--R + +--R 8 2 +--R - 12600b c +--R * +--R 2 +--R d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 9 3 9 8 3 9 2 8 +--R 2752512c e x + (7798784b c e + 9175040c d e )x +--R + +--R 8 2 7 3 8 2 9 2 7 +--R ((7225344a c + 7196672b c )e + 26378240b c d e + 10321920c d e)x +--R + +--R 7 3 6 3 +--R (12836864a b c + 2119680b c )e +--R + +--R 8 2 7 2 8 2 9 3 +--R (24903680a c + 24821760b c )d e + 30228480b c d e + 3932160c d +--R * +--R 6 +--R x +--R + +--R 2 7 2 6 4 5 3 +--R (5332992a c + 5222400a b c - 2560b c )e +--R + +--R 7 3 6 2 +--R (45465600a b c + 7516160b c )d e +--R + +--R 8 2 7 2 8 3 +--R (29245440a c + 29184000b c )d e + 11796480b c d +--R * +--R 5 +--R x +--R + +--R 2 6 3 5 5 4 3 +--R (3502080a b c - 30720a b c + 2816b c )e +--R + +--R 2 7 2 6 4 5 2 +--R (19660800a c + 19292160a b c - 10240b c )d e +--R + +--R 7 3 6 2 8 2 7 3 +--R (55418880a b c + 9185280b c )d e + (11796480a c + 11796480b c )d +--R * +--R 4 +--R x +--R + +--R 3 6 2 2 5 4 4 6 3 3 +--R (215040a c - 145920a b c + 37760a b c - 3168b c )e +--R + +--R 2 6 3 5 5 4 2 +--R (13946880a b c - 133120a b c + 11520b c )d e +--R + +--R 2 7 2 6 4 5 2 +--R (25374720a c + 25036800a b c - 11520b c )d e +--R + +--R 7 3 6 3 +--R (23592960a b c + 3932160b c )d +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (- 332800a b c + 211200a b c - 47808a b c + 3696b c )e +--R + +--R 3 6 2 2 5 4 4 6 3 2 +--R (1310720a c - 706560a b c + 168960a b c - 13440b c )d e +--R + +--R 2 6 3 5 5 4 2 +--R (20367360a b c - 168960a b c + 13440b c )d e +--R + +--R 2 7 2 6 3 +--R (11796480a c + 11796480a b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R - 322560a c + 634880a b c - 320640a b c + 64512a b c +--R + +--R 8 +--R - 4620b c +--R * +--R 3 +--R e +--R + +--R 3 5 2 3 4 5 3 7 2 2 +--R (- 1914880a b c + 1082880a b c - 228480a b c + 16800b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 2 +--R (3225600a c - 1082880a b c + 228480a b c - 16800b c )d e +--R + +--R 2 6 3 +--R 11796480a b c d +--R * +--R x +--R + +--R 4 4 3 3 3 2 5 2 7 +--R 1149440a b c - 1374720a b c + 576576a b c - 104160a b c +--R + +--R 9 +--R 6930b +--R * +--R 3 +--R e +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R - 2621440a c + 4285440a b c - 1962240a b c + 369600a b c +--R + +--R 8 +--R - 25200b c +--R * +--R 2 +--R d e +--R + +--R 3 5 2 3 4 5 3 7 2 2 +--R (- 4285440a b c + 1962240a b c - 369600a b c + 25200b c )d e +--R + +--R 3 6 3 +--R 3932160a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 6 +-+ +--R 13762560c \|c +--R Type: Expression(Integer) +--E 278 + +--S 279 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 465 +r0:=-5/3072*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+_ + 1/192*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^3+_ + 1/504*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*_ + (a+b*x+c*x^2)^(7/2)/c^2+2/9*(d+e*x)^2*(a+b*x+c*x^2)^(7/2)+_ + 1/36*e*(b*d-2*a*e+(2*c*d-b*e)*x)*(a+b*x+c*x^2)^(7/2)/c-_ + 5/16384*(b^2-4*a*c)^4*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(11/2)+5/8192*(b^2-4*a*c)^3*e*(2*c*d-b*e)*_ + (b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 4 4 3 3 3 2 5 2 7 9 2 +--R (80640a b c - 80640a b c + 30240a b c - 5040a b c + 315b )e +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 +--R (- 161280a c + 161280a b c - 60480a b c + 10080a b c - 630b c)d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 8 2 8 7 2 8 7 +--R 229376c e x + (659456b c e + 516096c d e)x +--R + +--R 7 2 6 2 7 8 2 6 +--R ((622592a c + 620544b c )e + 1511424b c d e + 294912c d )x +--R + +--R 6 3 5 2 7 2 6 +--R (1136640a b c + 187904b c )e + (1462272a c + 1459200b c )d e +--R + +--R 7 2 +--R 884736b c d +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 4 4 2 +--R (491520a c + 482304a b c - 256b c )e +--R + +--R 6 3 5 7 2 6 2 +--R (2770944a b c + 459264b c )d e + (884736a c + 884736b c )d +--R * +--R 4 +--R x +--R + +--R 2 5 3 4 5 3 2 +--R (348672a b c - 3328a b c + 288b c )e +--R + +--R 2 6 2 5 4 4 +--R (1268736a c + 1251840a b c - 576b c )d e +--R + +--R 6 3 5 2 +--R (1769472a b c + 294912b c )d +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (32768a c - 17664a b c + 4224a b c - 336b c )e +--R + +--R 2 5 3 4 5 3 +--R (1018368a b c - 8448a b c + 672b c )d e +--R + +--R 2 6 2 5 2 +--R (884736a c + 884736a b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (- 47872a b c + 27072a b c - 5712a b c + 420b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (161280a c - 54144a b c + 11424a b c - 840b c )d e +--R + +--R 2 5 2 +--R 884736a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 2 4 2 6 8 2 +--R (- 65536a c + 107136a b c - 49056a b c + 9240a b c - 630b )e +--R + +--R 3 4 2 3 3 5 2 7 +--R (- 214272a b c + 98112a b c - 18480a b c + 1260b c)d e +--R + +--R 3 5 2 +--R 294912a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 1032192c \|c +--R Type: Expression(Integer) +--E 281 + +--S 282 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 465 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 +--R ((6a b c + b )e + (4a c + 4b c)d)x +--R + +--R 2 2 3 2 2 2 2 2 +--R ((2a c + 2a b )e + (6a b c + b )d)x + (a b e + (2a c + 2a b )d)x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 465 +r0:=-5/3072*(b^2-4*a*c)^2*e*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3+_ + 1/192*(b^2-4*a*c)*e*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^2+1/56*(2*c*d-b*e)*_ + (a+b*x+c*x^2)^(7/2)/c+1/4*(d+e*x)*(a+b*x+c*x^2)^(7/2)-_ + 5/16384*(b^2-4*a*c)^4*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(9/2)+5/8192*(b^2-4*a*c)^3*e*(b+2*c*x)*_ + sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 4 4 3 2 3 2 4 2 6 8 +--R (- 26880a c + 26880a b c - 10080a b c + 1680a b c - 105b )e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 7 7 6 7 6 +--R 86016c e x + (251904b c e + 98304c d)x +--R + +--R 6 2 5 6 5 +--R ((243712a c + 243200b c )e + 294912b c d)x +--R + +--R 5 3 4 6 2 5 4 +--R ((461824a b c + 76544b c )e + (294912a c + 294912b c )d)x +--R + +--R 2 5 2 4 4 3 +--R (211456a c + 208640a b c - 96b c )e +--R + +--R 5 3 4 +--R (589824a b c + 98304b c )d +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 +--R (169728a b c - 1408a b c + 112b c )e +--R + +--R 2 5 2 4 +--R (294912a c + 294912a b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 3 4 2 6 2 4 +--R ((26880a c - 9024a b c + 1904a b c - 140b c)e + 294912a b c d)x +--R + +--R 3 3 2 3 2 5 7 3 4 +--R (- 35712a b c + 16352a b c - 3080a b c + 210b )e + 98304a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 344064c \|c +--R Type: Expression(Integer) +--E 284 + +--S 285 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 465 +r0:=2/7*(a+b*x+c*x^2)^(7/2) +--R +--R +--R (2) +--R 3 6 2 5 2 2 4 3 3 +--R 2c x + 6b c x + (6a c + 6b c)x + (12a b c + 2b )x +--R + +--R 2 2 2 2 3 +--R (6a c + 6a b )x + 6a b x + 2a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 7 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R e x + d +--R Type: Expression(Integer) +--E 289 + +--S 290 of 465 +r0:=-1/96*(64*c^3*d^3-b^3*e^3+4*b*c*e^2*(14*b*d-13*a*e)-8*c^2*d*e*_ + (15*b*d-8*a*e)-2*c*e*(24*c^2*d^2+b^2*e^2-4*c*e*(6*b*d-5*a*e))*x)*_ + (a+b*x+c*x^2)^(3/2)/(c*e^4)-1/30*(12*c*d-11*b*e-10*c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/e^2+1/512*(1024*c^6*d^6+b^6*e^6+4*b^4*c*e^5*_ + (2*b*d-5*a*e)-512*c^5*d^4*e*(6*b*d-5*a*e)-320*c^3*e^3*(b*d-a*e)^2*_ + (4*b*d-a*e)+640*c^4*d^2*e^2*(5*b^2*d^2-8*a*b*d*e+3*a^2*e^2)+_ + 40*b^2*c^2*e^4*(3*b^2*d^2-8*a*b*d*e+6*a^2*e^2))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(5/2)*e^7)-(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^(5/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/e^7-1/256*(512*c^5*d^5+b^5*e^5-_ + 128*c^4*d^3*e*(11*b*d-8*a*e)+8*b^3*c*e^4*(b*d-2*a*e)+32*c^3*d*e^2*_ + (40*b^2*d^2-55*a*b*d*e+16*a^2*e^2)-8*b*c^2*e^3*(49*b^2*d^2-_ + 92*a*b*d*e+42*a^2*e^2)-2*c*e*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*_ + (8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/(c^2*e^6) +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 6 +--R (4800a c + 3600a b c - 300a b c + 15b )e +--R + +--R 2 3 3 2 5 5 +--R (- 28800a b c - 4800a b c + 120b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (28800a c + 43200a b c + 1800b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (- 76800a b c - 19200b c )d e + (38400a c + 48000b c )d e +--R + +--R 5 5 6 6 +--R - 46080b c d e + 15360c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 5 2 3 2 2 4 +--R - 7680a b c e + (15360a c + 15360a b c )d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (- 46080a b c - 7680b c )d e + (30720a c + 30720b c )d e +--R + +--R 4 4 5 5 +--R - 38400b c d e + 15360c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 5 6 5 4 6 5 5 4 +--R 2560c e x + (7936b c e - 3072c d e )x +--R + +--R 4 2 3 6 4 5 5 2 4 3 +--R ((8320a c + 8352b c )e - 9984b c d e + 3840c d e )x +--R + +--R 3 3 2 6 4 2 3 5 +--R (18112a b c + 3056b c )e + (- 11264a c - 11392b c )d e +--R + +--R 4 2 4 5 3 3 +--R 13440b c d e - 5120c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 4 6 +--R (10560a c + 10912a b c + 20b c)e +--R + +--R 3 3 2 5 4 2 3 2 4 +--R (- 28544a b c - 4960b c )d e + (17280a c + 17760b c )d e +--R + +--R 4 3 3 5 4 2 +--R - 20480b c d e + 7680c d e +--R * +--R x +--R + +--R 2 2 3 5 6 +--R (17056a b c + 560a b c - 30b )e +--R + +--R 2 3 2 2 4 5 +--R (- 23552a c - 26560a b c - 240b c)d e +--R + +--R 3 3 2 2 4 4 2 3 3 3 +--R (62400a b c + 11760b c )d e + (- 35840a c - 38400b c )d e +--R + +--R 4 4 2 5 5 +--R 42240b c d e - 15360c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 7 +-+ +--R 7680c e \|c +--R Type: Expression(Integer) +--E 290 + +--S 291 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 292 + +--S 293 of 465 +r0:=1/12*(48*c^2*d^2-66*b*c*d*e+19*b^2*e^2+8*a*c*e^2-18*c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/e^4+1/5*(12*c*d-5*b*e+2*c*e*x)*(a+b*x+c*x^2)^(5/2)/_ + (e^2*(d+e*x))-1/64*(2*c*d-b*e)*(384*c^4*d^4-b^4*e^4-8*b^2*c*e^3*(4*b*d-_ + 5*a*e)-128*c^3*d^2*e*(6*b*d-5*a*e)+16*c^2*e^2*(26*b^2*d^2-40*a*b*d*e+_ + 15*a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*_ + e^7)+1/2*(c*d^2-b*d*e+a*e^2)^(3/2)*(24*c^2*d^2+5*b^2*e^2-4*c*e*_ + (6*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+_ + a*e^2)*sqrt(a+b*x+c*x^2)))/e^7+1/32*(384*c^4*d^4+b^4*e^4-2*b^2*c*e^3*_ + (65*b*d-62*a*e)-32*c^3*d^2*e*(27*b*d-14*a*e)+8*c^2*e^2*(76*b^2*d^2-_ + 67*a*b*d*e+8*a^2*e^2)-2*c*e*(2*c*d-b*e)*(48*c^2*d^2-48*b*c*d*e+_ + b^2*e^2+44*a*c*e^2)*x)*sqrt(a+b*x+c*x^2)/(c*e^6) +--R +--R +--R (2) +--R 2 2 3 5 6 +--R (3600a b c + 600a b c - 15b )e +--R + +--R 2 3 2 2 4 5 +--R (- 7200a c - 10800a b c - 450b c)d e +--R + +--R 3 3 2 2 4 4 2 3 3 3 +--R (28800a b c + 7200b c )d e + (- 19200a c - 24000b c )d e +--R + +--R 4 4 2 5 5 +--R 28800b c d e - 11520c d e +--R * +--R x +--R + +--R 2 2 3 5 5 +--R (3600a b c + 600a b c - 15b )d e +--R + +--R 2 3 2 2 4 2 4 +--R (- 7200a c - 10800a b c - 450b c)d e +--R + +--R 3 3 2 3 3 4 2 3 4 2 +--R (28800a b c + 7200b c )d e + (- 19200a c - 24000b c )d e +--R + +--R 4 5 5 6 +--R 28800b c d e - 11520c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 5 2 3 4 +--R (- 1920a c - 2400a b c)e + (13440a b c + 2400b c)d e +--R + +--R 3 2 2 2 3 3 3 2 4 4 +--R (- 13440a c - 13920b c )d e + 23040b c d e - 11520c d e +--R * +--R x +--R + +--R 2 2 2 4 2 3 2 3 +--R (- 1920a c - 2400a b c)d e + (13440a b c + 2400b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (- 13440a c - 13920b c )d e + 23040b c d e - 11520c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 4 6 5 3 6 4 5 4 +--R 384c e x + (1248b c e - 576c d e )x +--R + +--R 3 2 2 6 3 5 4 2 4 3 +--R ((1408a c + 1424b c )e - 2112b c d e + 960c d e )x +--R + +--R 2 3 6 3 2 2 5 +--R (3568a b c + 620b c)e + (- 2912a c - 3016b c )d e +--R + +--R 3 2 4 4 3 3 +--R 4320b c d e - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 6 2 3 5 +--R (2944a c + 3320a b c + 30b )e + (- 12032a b c - 2320b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (9120a c + 9960b c )d e - 13440b c d e + 5760c d e +--R * +--R x +--R + +--R 2 6 2 2 2 4 5 +--R - 960a b c e + (4864a c + 5240a b c + 30b )d e +--R + +--R 2 3 2 4 3 2 2 3 3 +--R (- 21360a b c - 3900b c)d e + (17280a c + 18240b c )d e +--R + +--R 3 4 2 4 5 +--R - 25920b c d e + 11520c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 8 7 +-+ +--R (960c e x + 960c d e )\|c +--R Type: Expression(Integer) +--E 293 + +--S 294 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 295 + +--S 296 of 465 +r0:=-5/4*(8*c^2*d^2+b^2*e^2-c*e*(7*b*d-2*a*e)+c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/2*(3*c*d-b*e+c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)+15/64*(128*c^4*d^4+b^4*e^4-_ + 8*b^2*c*e^3*(4*b*d-3*a*e)-128*c^3*d^2*e*(2*b*d-a*e)+16*c^2*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^7*sqrt(c))-15/8*(2*c*d-b*e)*(8*c^2*d^2+b^2*e^2-_ + 4*c*e*(2*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^7-_ + 15/32*(64*c^3*d^3-7*b^3*e^3+4*b*c*e^2*(14*b*d-5*a*e)-16*c^2*d*e*_ + (7*b*d-2*a*e)-2*c*e*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*x)*_ + sqrt(a+b*x+c*x^2)/e^6 +--R +--R +--R (2) +--R 2 2 2 4 6 2 3 5 +--R (240a c + 360a b c + 15b )e + (- 1920a b c - 480b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (1920a c + 2400b c )d e - 3840b c d e + 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 5 2 3 2 4 +--R (480a c + 720a b c + 30b )d e + (- 3840a b c - 960b c)d e +--R + +--R 3 2 2 3 3 3 4 2 4 5 +--R (3840a c + 4800b c )d e - 7680b c d e + 3840c d e +--R * +--R x +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (240a c + 360a b c + 15b )d e + (- 1920a b c - 480b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (1920a c + 2400b c )d e - 3840b c d e + 1920c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 480a b c - 120b )e + (960a c + 1200b c)d e - 2880b c d e +--R + +--R 3 3 2 +--R 1920c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 960a b c - 240b )d e + (1920a c + 2400b c)d e +--R + +--R 2 3 2 3 4 +--R - 5760b c d e + 3840c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 +--R (- 480a b c - 120b )d e + (960a c + 1200b c)d e - 2880b c d e +--R + +--R 3 5 +--R 1920c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 6 5 2 6 3 5 4 +--R 32c e x + (112b c e - 64c d e )x +--R + +--R 2 2 6 2 5 3 2 4 3 +--R ((144a c + 148b c)e - 288b c d e + 160c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (520a b c + 98b )e + (- 608a c - 664b c)d e + 1200b c d e +--R + +--R 3 3 3 +--R - 640c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 128a c - 144a b )e + (1872a b c + 340b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 2480a c - 2620b c)d e + 5120b c d e - 2880c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 32a b e + (- 64a c - 80a b )d e + (1160a b c + 210b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (- 1600a c - 1680b c)d e + 3360b c d e - 1920c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 9 2 8 2 7 +-+ +--R (64e x + 128d e x + 64d e )\|c +--R Type: Expression(Integer) +--E 296 + +--S 297 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 298 + +--S 299 of 465 +r0:=-5/12*(16*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-a*e)+4*c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(4*c*d-b*e+2*c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)-5/2*(2*c*d-b*e)*(8*c^2*d^2+b^2*e^2-_ + 4*c*e*(2*b*d-a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*_ + sqrt(c)/e^7+5/16*(128*c^4*d^4+b^4*e^4-8*b^2*c*e^3*(4*b*d-3*a*e)-_ + 128*c^3*d^2*e*(2*b*d-a*e)+16*c^2*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2))*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(e^7*sqrt(c*d^2-b*d*e+a*e^2))+5/8*(64*c^3*d^3-_ + b^3*e^3-16*c^2*d*e*(5*b*d-2*a*e)+12*b*c*e^2*(2*b*d-a*e)+2*c*e*_ + (16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 3 6 2 2 5 2 2 4 +--R (480a b c + 120b )e + (- 960a c - 1200b c)d e + 2880b c d e +--R + +--R 3 3 3 +--R - 1920c d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 2 4 +--R (1440a b c + 360b )d e + (- 2880a c - 3600b c)d e +--R + +--R 2 3 3 3 4 2 +--R 8640b c d e - 5760c d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 2 3 3 +--R (1440a b c + 360b )d e + (- 2880a c - 3600b c)d e +--R + +--R 2 4 2 3 5 +--R 8640b c d e - 5760c d e +--R * +--R x +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (480a b c + 120b )d e + (- 960a c - 1200b c)d e + 2880b c d e +--R + +--R 3 6 +--R - 1920c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 240a c - 360a b c - 15b )e + (1920a b c + 480b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 1920a c - 2400b c )d e + 3840b c d e - 1920c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (- 720a c - 1080a b c - 45b )d e + (5760a b c + 1440b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (- 5760a c - 7200b c )d e + 11520b c d e - 5760c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 720a c - 1080a b c - 45b )d e + (5760a b c + 1440b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 5760a c - 7200b c )d e + 11520b c d e - 5760c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 240a c - 360a b c - 15b )d e + (1920a b c + 480b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 1920a c - 2400b c )d e + 3840b c d e - 1920c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 6 5 2 6 3 5 4 +--R 32c e x + (128b c e - 96c d e )x +--R + +--R 2 2 6 2 5 3 2 4 3 +--R ((224a c + 240b c)e - 672b c d e + 480c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (- 328a b c - 66b )e + (1328a c + 1444b c)d e - 4560b c d e +--R + +--R 3 3 3 +--R 3520c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 48a c - 52a b )e + (- 352a b c - 80b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (1680a c + 1860b c)d e - 6080b c d e + 4800c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 16a b e + (- 16a c - 20a b )d e + (- 120a b c - 30b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (640a c + 720b c)d e - 2400b c d e + 1920c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 10 3 9 2 2 8 3 7 | 2 2 +--R (48e x + 144d e x + 144d e x + 48d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 299 + +--S 300 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 465 +r0:=3/64*(b^2-4*a*c)*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+_ + 1/32*(2*c*d-b*e)*(16*c^2*d^2+15*b^2*e^2-4*c*e*(4*b*d+11*a*e))*_ + sqrt(a+b*x+c*x^2)/c^3+1/4*(2*c*d-b*e)*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+_ + 1/2*(d+e*x)^3*sqrt(a+b*x+c*x^2)+1/16*e*(b^2*d*e-20*a*c*d*e+4*b*_ + (c*d^2+a*e^2)+(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*x)*_ + sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 4 3 2 3 2 +--R (48a c - 72a b c + 15b )e + (192a b c - 48b c)d e +--R + +--R 3 2 2 2 +--R (- 192a c + 48b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 32c e x + (- 16b c e + 128c d e )x +--R + +--R 2 2 3 2 2 3 2 3 3 +--R ((- 48a c + 20b c)e - 64b c d e + 192c d e)x + (104a b c - 30b )e +--R + +--R 2 2 2 2 2 3 3 +--R (- 256a c + 96b c)d e - 96b c d e + 128c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 64c \|c +--R Type: Expression(Integer) +--E 302 + +--S 303 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 304 + +--S 305 of 465 +r0:=1/4*(b^2-4*a*c)*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(5/2)+1/6*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+_ + a*e))*sqrt(a+b*x+c*x^2)/c^2+2/3*(d+e*x)^2*sqrt(a+b*x+c*x^2)+1/3*e*_ + (b*d-2*a*e+(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R 3 2 2 2 2c x + b +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e)atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 2 2 2 2 +--R 8c e x + (- 4b c e + 24c d e)x + (- 16a c + 6b )e - 12b c d e +--R + +--R 2 2 +--R 24c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 +-+ +--R 12c \|c +--R Type: Expression(Integer) +--E 305 + +--S 306 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 465 +t0:=(b+2*c*x)*(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) ----------------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 465 +r0:=1/4*(b^2-4*a*c)*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/_ + c^(3/2)+1/2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/c+(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R (2) +--R 2 2c x + b +--R (- 4a c + b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R +-+ | 2 +--R (4c e x - 2b e + 8c d)\|c \|c x + b x + a +--R / +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 308 + +--S 309 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 465 +t0:=(b+2*c*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2c x + b +--R (1) ----------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 465 +r0:=2*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R (2) 2\|c x + b x + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 465 +t0:=(b+2*c*x)/((d+e*x)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) -------------------------- +--R +--------------+ +--R | 2 +--R (e x + d)\|c x + b x + a +--R Type: Expression(Integer) +--E 313 + +--S 314 of 465 +r0:=2*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e-_ + (2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(e*sqrt(c*d^2-b*d*e+a*e^2)) +--R +--R +--R (2) +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R 2\|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R (b e - 2c d)x + 2a e - b d +--R (- b e + 2c d)atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R | 2 2 +--R e\|a e - b d e + c d +--R Type: Expression(Integer) +--E 314 + +--S 315 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 465 +t0:=(b+2*c*x)/((d+e*x)^2*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------- +--R +--------------+ +--R 2 2 2 | 2 +--R (e x + 2d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 465 +r0:=-1/2*(b^2-4*a*c)*e*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)+(2*c*d-b*e)*_ + sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 +--R ((- 4a c + b )e x + (- 4a c + b )d e) +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R (- 2b e + 4c d)\|a e - b d e + c d \|c x + b x + a +--R / +--R 3 2 2 2 2 3 +--R ((2a e - 2b d e + 2c d e)x + 2a d e - 2b d e + 2c d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 317 + +--S 318 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 of 465 +t0:=(b+2*c*x)/((d+e*x)^3*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ----------------------------------------------- +--R +--------------+ +--R 3 3 2 2 2 3 | 2 +--R (e x + 3d e x + 3d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 465 +r0:=-3/8*(b^2-4*a*c)*e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+_ + 1/2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+_ + 1/4*(4*c^2*d^2+3*b^2*e^2-4*c*e*(b*d+2*a*e))*sqrt(a+b*x+c*x^2)/_ + ((c*d^2-b*d*e+a*e^2)^2*(d+e*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 2 +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e )x +--R + +--R 3 3 2 2 2 2 3 2 2 +--R ((24a b c - 6b )d e + (- 48a c + 12b c)d e )x + (12a b c - 3b )d e +--R + +--R 2 2 3 +--R (- 24a c + 6b c)d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 2 2 2 3 +--R ((- 16a c + 6b )e - 8b c d e + 8c d e)x - 4a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c + 10b )d e - 20b c d e + 16c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 2 6 5 2 2 4 3 3 2 4 2 2 +--R (8a e - 16a b d e + (16a c + 8b )d e - 16b c d e + 8c d e )x +--R + +--R 2 5 2 4 2 3 3 4 2 2 5 +--R (16a d e - 32a b d e + (32a c + 16b )d e - 32b c d e + 16c d e)x +--R + +--R 2 2 4 3 3 2 4 2 5 2 6 +--R 8a d e - 16a b d e + (16a c + 8b )d e - 16b c d e + 8c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 320 + +--S 321 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 465 +t0:=(b+2*c*x)/((d+e*x)^4*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) --------------------------------------------------------- +--R +--------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 465 +r0:=-1/16*(b^2-4*a*c)*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)+1/3*(2*c*d-b*e)*_ + sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^3)+1/12*(8*c^2*d^2+_ + 5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+_ + a*e^2)^2*(d+e*x)^2)+1/24*(2*c*d-b*e)*(8*c^2*d^2+15*b^2*e^2-4*c*e*_ + (2*b*d+13*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^3*(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 4 6 2 3 5 +--R (48a c - 72a b c + 15b )e + (192a b c - 48b c)d e +--R + +--R 3 2 2 2 4 +--R (- 192a c + 48b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 5 2 3 2 4 +--R (144a c - 216a b c + 45b )d e + (576a b c - 144b c)d e +--R + +--R 3 2 2 3 3 +--R (- 576a c + 144b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (144a c - 216a b c + 45b )d e + (576a b c - 144b c)d e +--R + +--R 3 2 2 4 2 +--R (- 576a c + 144b c )d e +--R * +--R x +--R + +--R 2 2 2 4 3 3 2 3 4 2 +--R (48a c - 72a b c + 15b )d e + (192a b c - 48b c)d e +--R + +--R 3 2 2 5 +--R (- 192a c + 48b c )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (104a b c - 30b )e + (- 208a c + 76b c)d e - 48b c d e +--R + +--R 3 3 2 +--R 32c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (- 48a c + 20a b )e + (224a b c - 80b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (- 432a c + 204b c)d e - 160b c d e + 96c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 16a b e + (- 16a c + 52a b )d e + (24a b c - 66b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 160a c + 192b c)d e - 192b c d e + 96c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 3 9 2 8 2 2 2 7 +--R 48a e - 144a b d e + (144a c + 144a b )d e +--R + +--R 3 3 6 2 2 4 5 2 5 4 +--R (- 288a b c - 48b )d e + (144a c + 144b c)d e - 144b c d e +--R + +--R 3 6 3 +--R 48c d e +--R * +--R 3 +--R x +--R + +--R 3 8 2 2 7 2 2 3 6 +--R 144a d e - 432a b d e + (432a c + 432a b )d e +--R + +--R 3 4 5 2 2 5 4 2 6 3 +--R (- 864a b c - 144b )d e + (432a c + 432b c)d e - 432b c d e +--R + +--R 3 7 2 +--R 144c d e +--R * +--R 2 +--R x +--R + +--R 3 2 7 2 3 6 2 2 4 5 +--R 144a d e - 432a b d e + (432a c + 432a b )d e +--R + +--R 3 5 4 2 2 6 3 2 7 2 +--R (- 864a b c - 144b )d e + (432a c + 432b c)d e - 432b c d e +--R + +--R 3 8 +--R 144c d e +--R * +--R x +--R + +--R 3 3 6 2 4 5 2 2 5 4 +--R 48a d e - 144a b d e + (144a c + 144a b )d e +--R + +--R 3 6 3 2 2 7 2 2 8 3 9 +--R (- 288a b c - 48b )d e + (144a c + 144b c)d e - 144b c d e + 48c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 323 + +--S 324 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 of 465 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 465 +r0:=1/2*e*(2*c*d-b*e)*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-2*(d+e*x)^4/_ + sqrt(a+b*x+c*x^2)+1/3*e^2*(52*c^2*d^2+15*b^2*e^2-4*c*e*(13*b*d+2*a*e))*_ + sqrt(a+b*x+c*x^2)/c^3+8/3*e^2*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+2/3*e^2*_ + (6*c*d^2-e*(b*d+4*a*e)+5*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((36a b c - 15b )e + (- 72a c + 54b c)d e - 72b c d e + 48c d e) +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 4 4 2 4 3 3 3 +--R 4c e x + (- 4b c e + 24c d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 16a c + 10b c)e - 36b c d e + 72c d e )x +--R + +--R 3 4 2 2 3 2 2 2 +--R (- 52a b c + 30b )e + (72a c - 108b c)d e + 144b c d e +--R + +--R 3 3 +--R - 48c d e +--R * +--R x +--R + +--R 2 2 4 3 2 2 2 3 4 +--R (- 32a c + 30a b )e - 108a b c d e + 144a c d e - 12c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 3 +-+ | 2 +--R 6c \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 465 +r0:=3/4*e*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-2*(d+e*x)^3/sqrt(a+b*x+c*x^2)+_ + 9/2*e^2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/c^2+3*e^2*(d+e*x)*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R +--------------+ +--R 2 3 2 2 2 | 2 +--R ((- 12a c + 9b )e - 24b c d e + 24c d e)\|c x + b x + a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 3 3 2 2 2 +--R 4c e x + (- 6b c e + 24c d e )x +--R + +--R 2 3 2 2 2 3 2 +--R ((12a c - 18b )e + 48b c d e - 24c d e)x - 18a b e + 48a c d e +--R + +--R 2 3 +--R - 8c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 2 +-+ | 2 +--R 4c \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 329 + +--S 330 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 465 +r0:=2*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-_ + 2*(d+e*x)^2/sqrt(a+b*x+c*x^2)+4*e^2*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R +--------------+ +--R 2 | 2 2c x + b +--R (- 2b e + 4c d e)\|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 2 2 +-+ +--R (2c e x + (4b e - 4c d e)x + 4a e - 2c d )\|c +--R / +--R +--------------+ +--R +-+ | 2 +--R c\|c \|c x + b x + a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 465 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 465 +r0:=2*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/sqrt(c)-_ + 2*(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 2c x + b +-+ +--R 2e\|c x + b x + a atanh(----------------------) + (- 2e x - 2d)\|c +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R (2) -------------------------------------------------------------------- +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 336 + +)clear all + +--S 337 of 465 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2c x + b +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 465 +r0:=(-2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +--R (2) - ----------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 339 + +)clear all + +--S 340 of 465 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R 2c x + b +--R (1) -------------------------------------------------------------- +--R +--------------+ +--R 3 2 | 2 +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|c x + b x + a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 465 +r0:=-e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)-_ + 2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R +--------------+ +--R 2 | 2 +--R (- b e + 2c d e)\|c x + b x + a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 +--R (2c e x + 2b e - 2c d)\|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 2 2 | 2 2 | 2 +--R (a e - b d e + c d )\|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 465 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x +--R + +--R 2 2 +--R (2a d e + b d )x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 465 +r0:=-1/2*e*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (c*d^2-b*d*e+a*e^2)^(5/2)-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*sqrt(a+b*x+c*x^2))+3*e^2*_ + (2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 4 3 2 2 2 2 3 +--R ((- 4a c + 3b )e - 8b c d e + 8c d e )x + (- 4a c + 3b )d e +--R + +--R 2 2 2 3 +--R - 8b c d e + 8c d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 6b c e + 12c d e )x + ((4a c - 6b )e + 8b c d e + 4c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (8a c - 4b )d e + 8b c d e - 4c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 465 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 465 +r0:=-2/3*(d+e*x)^4/(a+b*x+c*x^2)^(3/2)+4*e^3*(2*c*d-b*e)*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-_ + 16/3*e*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*_ + sqrt(a+b*x+c*x^2))+8/3*e^2*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*_ + sqrt(a+b*x+c*x^2)/(c^2*(b^2-4*a*c))+16/3*e^3*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/(c*(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 2 +--R ((- 48a b c + 12b c)e + (96a c - 24b c )d e )x +--R + +--R 2 4 4 2 3 3 +--R ((- 48a b c + 12b )e + (96a b c - 24b c)d e )x +--R + +--R 2 3 4 2 2 2 3 +--R (- 48a b c + 12a b )e + (96a c - 24a b c)d e +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 4 4 +--R (24a c - 6b c )e x +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (112a b c - 32b c)e + (- 128a c + 56b c )d e - 48b c d e +--R + +--R 4 3 +--R 32c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 4 2 3 3 +--R (96a c + 48a b c - 24b )e + (- 48a b c + 48b c)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 144a c - 36b c )d e + 48b c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (144a b c - 48a b )e + (- 96a c + 96a b c)d e - 144a b c d e +--R + +--R 2 2 3 +--R 24b c d e +--R * +--R x +--R + +--R 3 2 2 4 2 3 2 2 2 2 2 3 +--R (64a c - 24a b )e + 48a b c d e - 96a c d e + 16a b c d e +--R + +--R 3 2 2 4 +--R (- 8a c + 2b c )d +--R * +--R +-+ +--R \|c +--R / +--R 4 2 3 2 3 3 2 2 3 2 2 +-+ +--R ((12a c - 3b c )x + (12a b c - 3b c )x + 12a c - 3a b c )\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 465 +r0:=-2/3*(d+e*x)^3/(a+b*x+c*x^2)^(3/2)+2*e^3*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-4*e*(d+e*x)*(b*d-2*a*e+(2*c*d-_ + b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+4*e^2*(2*c*d-b*e)*sqrt(a+b*x+_ + c*x^2)/(c*(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 3 3 2 2 3 +--R ((24a c - 6b c)e x + (24a b c - 6b )e x + (24a c - 6a b )e ) +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 32a c + 14b c)e - 24b c d e + 24c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 12a b c + 12b )e + (- 72a c - 18b c)d e + 36b c d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R ((- 24a c + 24a b )e - 72a b c d e + 18b c d e)x + 12a b e +--R + +--R 2 2 2 2 2 3 +--R - 48a c d e + 12a b c d e + (- 8a c + 2b c)d +--R * +--R +-+ +--R \|c +--R / +--R 3 2 2 2 2 3 2 2 2 +-+ +--R ((12a c - 3b c )x + (12a b c - 3b c)x + 12a c - 3a b c)\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 465 +r0:=-2/3*(d+e*x)^2/(a+b*x+c*x^2)^(3/2)-8/3*e*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + ((b^2-4*a*c)*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 2 3 2 2 2 +--R (- 8b c e + 16c d e)x + ((- 24a c - 6b )e + 24b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 24a b e + 12b d e)x - 16a e + 8a b d e + (- 8a c + 2b )d +--R / +--R +--------------+ +--R 2 2 2 3 2 2 | 2 +--R ((12a c - 3b c)x + (12a b c - 3b )x + 12a c - 3a b )\|c x + b x + a +--R Type: Expression(Integer) +--E 353 + +--S 354 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 465 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 355 + +--S 356 of 465 +r0:=-2/3*(d+e*x)/(a+b*x+c*x^2)^(3/2)-4/3*e*(b+2*c*x)/((b^2-4*a*c)*_ + sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 2 +--R 8c e x + 12b c e x + 6b e x + 4a b e + (- 8a c + 2b )d +--R ----------------------------------------------------------------------- +--R +--------------+ +--R 2 2 2 3 2 2 | 2 +--R ((12a c - 3b c)x + (12a b c - 3b )x + 12a c - 3a b )\|c x + b x + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 465 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2c x + b +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 358 + +--S 359 of 465 +r0:=(-2/3)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R (2) - ------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (3c x + 3b x + 3a)\|c x + b x + a +--R Type: Expression(Integer) +--E 359 + +--S 360 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 465 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 465 +r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-e^3*(2*c*d-b*e)*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)-2/3*e*(5*b^2*c*d*e-_ + 12*a*c^2*d*e-3*b^3*e^2-2*b*c*(c*d^2-5*a*e^2)-c*(4*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(b*d+2*a*e))*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 2 +--R ((- 12a b c + 3b c)e + (24a c - 6b c )d e )x +--R + +--R 2 4 4 2 3 3 +--R ((- 12a b c + 3b )e + (24a b c - 6b c)d e )x +--R + +--R 2 3 4 2 2 2 3 +--R (- 12a b c + 3a b )e + (24a c - 6a b c)d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 3 3 2 4 2 3 +--R ((16a c - 6b c )e + 8b c d e - 8c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 2 +--R ((36a b c - 12b c)e + (- 24a c + 18b c )d e - 12b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 2 2 2 +--R ((24a c + 12a b c - 6b )e + (- 24a b c + 12b c)d e - 6b c d e)x +--R + +--R 2 3 3 2 2 2 4 2 +--R (28a b c - 8a b )e + (- 32a c + 4a b c + 2b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (12a b c - 4b c)d e + (- 8a c + 2b c )d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 3 2 2 2 4 2 2 3 3 +--R (12a c - 3a b c)e + (- 24a b c + 6a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (24a c + 6a b c - 3b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (12a c - 3b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 2 2 4 3 +--R (12a b c - 3a b )e + (- 24a b c + 6a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (24a b c + 6a b c - 3b )d e + (- 24a b c + 6b c)d e +--R + +--R 3 3 2 4 +--R (12a b c - 3b c )d +--R * +--R x +--R + +--R 4 3 2 4 3 2 3 3 +--R (12a c - 3a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (24a c + 6a b c - 3a b )d e + (- 24a b c + 6a b c)d e +--R + +--R 2 3 2 2 4 +--R (12a c - 3a b c )d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 362 + +--S 363 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 465 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + ((2a c + b )e + 4b c d e + c d )x +--R + +--R 2 2 2 3 +--R (2a b e + (4a c + 2b )d e + 2b c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (a e + 4a b d e + (2a c + b )d )x + (2a d e + 2a b d )x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 364 + +--S 365 of 465 +r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(d+e*x)*(a+b*x+c*x^2)^(3/2))-1/2*e^3*(16*c^2*d^2+_ + 5*b^2*e^2-4*c*e*(4*b*d+a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)-_ + 2/3*e*(9*b^2*c*d*e-20*a*c^2*d*e-5*b^3*e^2-4*b*c*(c*d^2-4*a*e^2)-_ + c*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*x)/((b^2-4*a*c)*(c*d^2-_ + b*d*e+a*e^2)^2*(d+e*x)*sqrt(a+b*x+c*x^2))+1/3*e^2*(2*c*d-b*e)*_ + (8*c^2*d^2+15*b^2*e^2-4*c*e*(2*b*d+13*a*e))*sqrt(a+b*x+c*x^2)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)) +--R +--R +--R (2) +--R 2 3 2 2 4 6 3 3 2 5 +--R (- 48a c + 72a b c - 15b c)e + (- 192a b c + 48b c )d e +--R + +--R 4 2 3 2 4 +--R (192a c - 48b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 6 +--R (- 48a b c + 72a b c - 15b )e +--R + +--R 2 3 2 2 4 5 4 2 3 3 3 +--R (- 48a c - 120a b c + 33b c)d e + (192a c - 48b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 6 +--R (- 48a c + 72a b c - 15a b )e +--R + +--R 2 2 3 5 5 +--R (- 240a b c + 120a b c - 15b )d e +--R + +--R 2 3 2 2 4 2 4 3 3 2 3 3 +--R (192a c - 240a b c + 48b c)d e + (192a b c - 48b c )d e +--R * +--R x +--R + +--R 3 2 2 2 4 5 2 2 3 2 4 +--R (- 48a c + 72a b c - 15a b )d e + (- 192a b c + 48a b c)d e +--R + +--R 2 3 2 2 3 3 +--R (192a c - 48a b c )d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 5 4 2 3 4 4 2 3 +--R (- 104a b c + 30b c )e + (208a c - 76b c )d e + 48b c d e +--R + +--R 5 3 2 +--R - 32c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (48a c - 228a b c + 60b c)e + (400a b c - 132b c )d e +--R + +--R 4 2 3 2 3 5 4 +--R (16a c + 44b c )d e - 32c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 5 +--R (- 96a b c - 84a b c + 30b )e +--R + +--R 2 3 2 2 4 4 3 3 2 2 3 +--R (336a c + 12a b c - 36b c)d e + (240a b c - 60b c )d e +--R + +--R 4 2 3 3 2 4 4 +--R (- 144a c + 84b c )d e - 48b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 +--R (64a c - 168a b c + 40a b )e +--R + +--R 2 2 3 5 4 +--R (288a b c - 152a b c + 20b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (48a c + 180a b c - 60b c)d e + (- 112a b c + 60b c )d e +--R + +--R 4 2 3 4 +--R (- 16a c - 20b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (- 24a b c + 6a b )e + (112a c - 132a b c + 28a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (240a b c - 56a b c - 4b )d e + (- 144a c + 12a b c + 12b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (32a b c - 12b c )d e + (- 16a c + 4b c )d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 4 2 3 2 7 3 2 2 3 6 +--R (24a c - 6a b c)e + (- 72a b c + 18a b c)d e +--R + +--R 3 3 2 2 2 4 2 5 +--R (72a c + 54a b c - 18a b c)d e +--R + +--R 2 3 3 2 5 3 4 +--R (- 144a b c + 12a b c + 6b c)d e +--R + +--R 2 4 2 3 4 2 4 3 4 3 3 5 2 +--R (72a c + 54a b c - 18b c )d e + (- 72a b c + 18b c )d e +--R + +--R 5 2 4 6 +--R (24a c - 6b c )d e +--R * +--R 3 +--R x +--R + +--R 4 3 3 7 4 2 3 2 2 4 6 +--R (24a b c - 6a b )e + (24a c - 78a b c + 18a b )d e +--R + +--R 2 3 5 2 5 3 3 2 2 2 4 6 3 4 +--R (72a b c - 18a b )d e + (72a c - 90a b c - 6a b c + 6b )d e +--R + +--R 2 3 3 2 5 4 3 2 4 2 3 5 2 +--R (- 72a b c + 66a b c - 12b c)d e + (72a c - 18a b c )d e +--R + +--R 4 3 3 6 5 2 4 7 +--R (- 48a b c + 12b c )d e + (24a c - 6b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 2 7 4 3 3 6 +--R (24a c - 6a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 2 2 5 3 2 2 3 5 3 4 +--R (72a c - 18a b c)d e + (- 72a b c + 66a b c - 12a b )d e +--R + +--R 3 3 2 2 2 4 6 4 3 3 2 5 5 2 +--R (72a c - 90a b c - 6a b c + 6b )d e + (72a b c - 18b c)d e +--R + +--R 2 4 2 3 4 2 6 4 3 3 7 +--R (24a c - 78a b c + 18b c )d e + (24a b c - 6b c )d +--R * +--R x +--R + +--R 5 4 2 6 4 3 3 2 5 +--R (24a c - 6a b )d e + (- 72a b c + 18a b )d e +--R + +--R 4 2 3 2 2 4 3 4 3 2 2 3 5 4 3 +--R (72a c + 54a b c - 18a b )d e + (- 144a b c + 12a b c + 6a b )d e +--R + +--R 3 3 2 2 2 4 5 2 2 3 3 2 6 +--R (72a c + 54a b c - 18a b c)d e + (- 72a b c + 18a b c )d e +--R + +--R 2 4 2 3 7 +--R (24a c - 6a b c )d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 365 + +--S 366 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 of 465 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x +--R + +--R 2 +--R a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 367 + +--S 368 of 465 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(7/2)/e^4+2/9*_ + (6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(9/2)/e^4-6/11*c*_ + (2*c*d-b*e)*(d+e*x)^(11/2)/e^4+4/13*c^2*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 +--R 2772c e x + (4914b c e + 6804c d e )x +--R + +--R 2 6 5 2 2 4 4 +--R ((4004a c + 2002b )e + 12558b c d e + 4452c d e )x +--R + +--R 6 2 5 2 4 2 3 3 3 +--R (2574a b e + (10868a c + 5434b )d e + 8814b c d e + 60c d e )x +--R + +--R 5 2 2 4 3 3 2 4 2 2 +--R (7722a b d e + (8580a c + 4290b )d e + 234b c d e - 72c d e )x +--R + +--R 2 4 2 3 3 4 2 2 5 +--R (7722a b d e + (572a c + 286b )d e - 312b c d e + 96c d e)x +--R + +--R 3 3 2 4 2 5 2 6 +--R 2574a b d e + (- 1144a c - 572b )d e + 624b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 368 + +--S 369 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 370 + +--S 371 of 465 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(5/2)/e^4+_ + 2/7*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(7/2)/e^4-_ + 2/3*c*(2*c*d-b*e)*(d+e*x)^(9/2)/e^4+4/11*c^2*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 +--R 420c e x + (770b c e + 560c d e )x +--R + +--R 2 5 4 2 2 3 3 +--R ((660a c + 330b )e + 1100b c d e + 20c d e )x +--R + +--R 5 2 4 2 3 2 3 2 2 +--R (462a b e + (1056a c + 528b )d e + 66b c d e - 24c d e )x +--R + +--R 4 2 2 3 3 2 2 4 +--R (924a b d e + (132a c + 66b )d e - 88b c d e + 32c d e)x +--R + +--R 2 3 2 3 2 4 2 5 +--R 462a b d e + (- 264a c - 132b )d e + 176b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Expression(Integer) +--E 371 + +--S 372 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)*sqrt(d+e*x) +--R +--R +--R 2 3 2 2 +-------+ +--R (1) (2c x + 3b c x + (2a c + b )x + a b)\|e x + d +--R Type: Expression(Integer) +--E 373 + +--S 374 of 465 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2)/e^4+_ + 2/5*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(5/2)/e^4-_ + 6/7*c*(2*c*d-b*e)*(d+e*x)^(7/2)/e^4+4/9*c^2*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 140c e x + (270b c e + 20c d e )x +--R + +--R 2 4 3 2 2 2 2 +--R ((252a c + 126b )e + 54b c d e - 24c d e )x +--R + +--R 4 2 3 2 2 2 3 3 +--R (210a b e + (84a c + 42b )d e - 72b c d e + 32c d e)x + 210a b d e +--R + +--R 2 2 2 3 2 4 +--R (- 168a c - 84b )d e + 144b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 374 + +--S 375 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 376 + +--S 377 of 465 +r0:=2/3*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(3/2)/e^4-_ + 6/5*c*(2*c*d-b*e)*(d+e*x)^(5/2)/e^4+4/7*c^2*(d+e*x)^(7/2)/e^4-_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 60c e x + (126b c e - 72c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((140a c + 70b )e - 168b c d e + 96c d e)x + 210a b e +--R + +--R 2 2 2 2 3 +--R (- 280a c - 140b )d e + 336b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 377 + +--S 378 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 379 + +--S 380 of 465 +r0:=-2*c*(2*c*d-b*e)*(d+e*x)^(3/2)/e^4+4/5*c^2*(d+e*x)^(5/2)/e^4+_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*sqrt(d+e*x))+2*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 4c e x + (10b c e - 8c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((20a c + 10b )e - 40b c d e + 32c d e)x - 10a b e +--R + +--R 2 2 2 2 3 +--R (40a c + 20b )d e - 80b c d e + 64c d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Expression(Integer) +--E 380 + +--S 381 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 382 + +--S 383 of 465 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^(3/2))+_ + 4/3*c^2*(d+e*x)^(3/2)/e^4-2*(6*c^2*d^2+b^2*e^2-2*c*e*_ + (3*b*d-a*e))/(e^4*sqrt(d+e*x))-6*c*(2*c*d-b*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 4c e x + (18b c e - 24c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((- 12a c - 6b )e + 72b c d e - 96c d e)x - 2a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c - 4b )d e + 48b c d e - 64c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 383 + +--S 384 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 of 465 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 385 + +--S 386 of 465 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(7/2)/e^6+_ + 4/9*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(9/2)/e^6-2/11*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(11/2)/e^6+8/13*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(13/2)/e^6-2/3*c^2*(2*c*d-b*e)*_ + (d+e*x)^(15/2)/e^6+4/17*c^3*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 3 8 8 2 8 3 7 7 +--R 36036c e x + (102102b c e + 84084c d e )x +--R + +--R 2 2 8 2 7 3 2 6 6 +--R ((94248a c + 94248b c)e + 243474b c d e + 50820c d e )x +--R + +--R 3 8 2 2 7 +--R (167076a b c + 27846b )e + (231336a c + 231336b c)d e +--R + +--R 2 2 6 3 3 5 +--R 152082b c d e + 252c d e +--R * +--R 5 +--R x +--R + +--R 2 2 8 3 7 +--R (68068a c + 68068a b )e + (426972a b c + 71162b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (151368a c + 151368b c)d e + 1190b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 7 +--R 43758a b e + (184756a c + 184756a b )d e +--R + +--R 3 2 6 2 2 3 5 +--R (299676a b c + 49946b )d e + (2040a c + 2040b c)d e +--R + +--R 2 4 4 3 5 3 +--R - 1360b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 2 6 +--R 131274a b d e + (145860a c + 145860a b )d e +--R + +--R 3 3 5 2 2 4 4 +--R (7956a b c + 1326b )d e + (- 2448a c - 2448b c)d e +--R + +--R 2 5 3 3 6 2 +--R 1632b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 2 2 3 5 +--R 131274a b d e + (9724a c + 9724a b )d e +--R + +--R 3 4 4 2 2 5 3 +--R (- 10608a b c - 1768b )d e + (3264a c + 3264b c)d e +--R + +--R 2 6 2 3 7 +--R - 2176b c d e + 512c d e +--R * +--R x +--R + +--R 2 3 5 2 2 4 4 +--R 43758a b d e + (- 19448a c - 19448a b )d e +--R + +--R 3 5 3 2 2 6 2 2 7 +--R (21216a b c + 3536b )d e + (- 6528a c - 6528b c)d e + 4352b c d e +--R + +--R 3 8 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Expression(Integer) +--E 386 + +--S 387 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 +--R ((6a b c + b )e + (4a c + 4b c)d)x +--R + +--R 2 2 3 2 2 2 2 2 +--R ((2a c + 2a b )e + (6a b c + b )d)x + (a b e + (2a c + 2a b )d)x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 388 + +--S 389 of 465 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(5/2)/e^6+_ + 4/7*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(7/2)/e^6-2/9*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(9/2)/e^6+8/11*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(11/2)/e^6-10/13*c^2*(2*c*d-b*e)*_ + (d+e*x)^(13/2)/e^6+4/15*c^3*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 3 7 7 2 7 3 6 6 +--R 12012c e x + (34650b c e + 14784c d e )x +--R + +--R 2 2 7 2 6 3 2 5 5 +--R ((32760a c + 32760b c)e + 44100b c d e + 252c d e )x +--R + +--R 3 7 2 2 6 +--R (60060a b c + 10010b )e + (43680a c + 43680b c)d e +--R + +--R 2 2 5 3 3 4 +--R 1050b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 2 7 3 6 +--R (25740a c + 25740a b )e + (85800a b c + 14300b )d e +--R + +--R 2 2 2 5 2 3 4 3 4 3 +--R (1560a c + 1560b c)d e - 1200b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 6 3 2 5 +--R 18018a b e + (41184a c + 41184a b )d e + (5148a b c + 858b )d e +--R + +--R 2 2 3 4 2 4 3 3 5 2 +--R (- 1872a c - 1872b c)d e + 1440b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 2 5 +--R 36036a b d e + (5148a c + 5148a b )d e +--R + +--R 3 3 4 2 2 4 3 +--R (- 6864a b c - 1144b )d e + (2496a c + 2496b c)d e +--R + +--R 2 5 2 3 6 +--R - 1920b c d e + 512c d e +--R * +--R x +--R + +--R 2 2 5 2 2 3 4 +--R 18018a b d e + (- 10296a c - 10296a b )d e +--R + +--R 3 4 3 2 2 5 2 2 6 +--R (13728a b c + 2288b )d e + (- 4992a c - 4992b c)d e + 3840b c d e +--R + +--R 3 7 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 389 + +--S 390 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 391 + +--S 392 of 465 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(3/2)/e^6+_ + 4/5*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(5/2)/e^6-2/7*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))*(d+e*x)^(7/2)/e^6+8/9*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(9/2)/e^6-10/11*c^2*(2*c*d-b*e)*_ + (d+e*x)^(11/2)/e^6+4/13*c^3*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 13860c e x + (40950b c e + 1260c d e )x +--R + +--R 2 2 6 2 5 3 2 4 4 +--R ((40040a c + 40040b c)e + 4550b c d e - 1400c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (77220a b c + 12870b )e + (5720a c + 5720b c)d e - 5200b c d e +--R + +--R 3 3 3 +--R 1600c d e +--R * +--R 3 +--R x +--R + +--R 2 2 6 3 5 +--R (36036a c + 36036a b )e + (15444a b c + 2574b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 6864a c - 6864b c)d e + 6240b c d e - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 +--R 30030a b e + (12012a c + 12012a b )d e +--R + +--R 3 2 4 2 2 3 3 +--R (- 20592a b c - 3432b )d e + (9152a c + 9152b c)d e +--R + +--R 2 4 2 3 5 +--R - 8320b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 2 4 +--R 30030a b d e + (- 24024a c - 24024a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (41184a b c + 6864b )d e + (- 18304a c - 18304b c)d e + 16640b c d e +--R + +--R 3 6 +--R - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 392 + +--S 393 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 394 + +--S 395 of 465 +r0:=4/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(3/2)/e^6-2/5*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(5/2)/e^6+8/7*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(7/2)/e^6-10/9*c^2*(2*c*d-b*e)*_ + (d+e*x)^(9/2)/e^6+4/11*c^3*(d+e*x)^(11/2)/e^6-2*(2*c*d-b*e)*_ + (c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 1260c e x + (3850b c e - 1400c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((3960a c + 3960b c)e - 4400b c d e + 1600c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (8316a b c + 1386b )e + (- 4752a c - 4752b c)d e + 5280b c d e +--R + +--R 3 3 2 +--R - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (4620a c + 4620a b )e + (- 11088a b c - 1848b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (6336a c + 6336b c)d e - 7040b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R 6930a b e + (- 9240a c - 9240a b )d e + (22176a b c + 3696b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12672a c - 12672b c)d e + 14080b c d e - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 395 + +--S 396 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 397 + +--S 398 of 465 +r0:=-2/3*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^(3/2)/e^6+8/5*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(5/2)/e^6-10/7*c^2*(2*c*d-b*e)*(d+e*x)^(7/2)/e^6+4/9*c^3*_ + (d+e*x)^(9/2)/e^6+2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*_ + sqrt(d+e*x))+4*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 140c e x + (450b c e - 200c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((504a c + 504b c)e - 720b c d e + 320c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (1260a b c + 210b )e + (- 1008a c - 1008b c)d e + 1440b c d e +--R + +--R 3 3 2 +--R - 640c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (1260a c + 1260a b )e + (- 5040a b c - 840b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (4032a c + 4032b c)d e - 5760b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 630a b e + (2520a c + 2520a b )d e + (- 10080a b c - 1680b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (8064a c + 8064b c)d e - 11520b c d e + 5120c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 398 + +--S 399 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 400 + +--S 401 of 465 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^(3/2))+_ + 8/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(3/2)/e^6-_ + 2*c^2*(2*c*d-b*e)*(d+e*x)^(5/2)/e^6+4/7*c^3*(d+e*x)^(7/2)/e^6-_ + 4*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/(e^6*_ + sqrt(d+e*x))-2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 12c e x + (42b c e - 24c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((56a c + 56b c)e - 112b c d e + 64c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (252a b c + 42b )e + (- 336a c - 336b c)d e + 672b c d e +--R + +--R 3 3 2 +--R - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (- 84a c - 84a b )e + (1008a b c + 168b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (- 1344a c - 1344b c)d e + 2688b c d e - 1536c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 14a b e + (- 56a c - 56a b )d e + (672a b c + 112b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 896a c - 896b c)d e + 1792b c d e - 1024c d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Expression(Integer) +--E 401 + +--S 402 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 465 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 2 9 3 2 4 8 +--R 2c e x + (7b c e + 4c d e)x +--R + +--R 3 2 2 2 3 4 2 7 +--R ((6a c + 9b c )e + 14b c d e + 2c d )x +--R + +--R 2 3 2 3 2 2 3 2 6 +--R ((15a b c + 5b c)e + (12a c + 18b c )d e + 7b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 2 2 5 +--R ((6a c + 12a b c + b )e + (30a b c + 10b c)d e + (6a c + 9b c )d )x +--R + +--R 2 3 2 2 2 2 4 +--R (9a b c + 3a b )e + (12a c + 24a b c + 2b )d e +--R + +--R 2 3 2 +--R (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 2 3 2 2 2 4 2 3 +--R ((2a c + 3a b )e + (18a b c + 6a b )d e + (6a c + 12a b c + b )d )x +--R + +--R 3 2 3 2 2 2 3 2 2 +--R (a b e + (4a c + 6a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 2 2 2 3 2 +--R (2a b d e + (2a c + 3a b )d )x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 403 + +--S 404 of 465 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(7/2)/e^8+_ + 2/9*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(9/2)/e^8-6/11*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(11/2)/e^8+2/13*(70*c^4*d^4+_ + b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+_ + 6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(13/2)/e^8-_ + 2/3*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^(15/2)/e^8+6/17*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(17/2)/e^8-14/19*c^3*(2*c*d-b*e)*(d+e*x)^(19/2)/e^8+_ + 4/21*c^4*(d+e*x)^(21/2)/e^8 +--R +--R +--R (2) +--R 4 10 10 3 10 4 9 9 +--R 554268c e x + (2144142b c e + 1254396c d e )x +--R + +--R 3 2 2 10 3 9 4 2 8 8 +--R ((2054052a c + 3081078b c )e + 4918914b c d e + 725868c d e )x +--R + +--R 2 3 10 3 2 2 9 +--R (5819814a b c + 1939938b c)e + (4792788a c + 7189182b c )d e +--R + +--R 3 2 8 4 3 7 +--R 2900898b c d e + 1716c d e +--R * +--R 7 +--R x +--R + +--R 2 2 2 4 10 +--R (2686068a c + 5372136a b c + 447678b )e +--R + +--R 2 3 9 3 2 2 2 8 +--R (13878018a b c + 4626006b c)d e + (2896740a c + 4345110b c )d e +--R + +--R 3 3 7 4 4 6 +--R 9702b c d e - 1848c d e +--R * +--R 6 +--R x +--R + +--R 2 3 10 +--R (4761666a b c + 1587222a b )e +--R + +--R 2 2 2 4 9 +--R (6593076a c + 13186152a b c + 1098846b )d e +--R + +--R 2 3 2 8 3 2 2 3 7 +--R (8668674a b c + 2889558b c)d e + (14364a c + 21546b c )d e +--R + +--R 3 4 6 4 5 5 +--R - 10584b c d e + 2016c d e +--R * +--R 5 +--R x +--R + +--R 3 2 2 10 2 3 9 +--R (1293292a c + 1939938a b )e + (12168702a b c + 4056234a b )d e +--R + +--R 2 2 2 4 2 8 +--R (4313988a c + 8627976a b c + 718998b )d e +--R + +--R 2 3 3 7 3 2 2 4 6 +--R (67830a b c + 22610b c)d e + (- 15960a c - 23940b c )d e +--R + +--R 3 5 5 4 6 4 +--R 11760b c d e - 2240c d e +--R * +--R 4 +--R x +--R + +--R 3 10 3 2 2 9 +--R 831402a b e + (3510364a c + 5265546a b )d e +--R + +--R 2 3 2 8 +--R (8540766a b c + 2846922a b )d e +--R + +--R 2 2 2 4 3 7 +--R (58140a c + 116280a b c + 9690b )d e +--R + +--R 2 3 4 6 3 2 2 5 5 +--R (- 77520a b c - 25840b c)d e + (18240a c + 27360b c )d e +--R + +--R 3 6 4 4 7 3 +--R - 13440b c d e + 2560c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 2 8 +--R 2494206a b d e + (2771340a c + 4157010a b )d e +--R + +--R 2 3 3 7 +--R (226746a b c + 75582a b )d e +--R + +--R 2 2 2 4 4 6 +--R (- 69768a c - 139536a b c - 11628b )d e +--R + +--R 2 3 5 5 3 2 2 6 4 +--R (93024a b c + 31008b c)d e + (- 21888a c - 32832b c )d e +--R + +--R 3 7 3 4 8 2 +--R 16128b c d e - 3072c d e +--R * +--R 2 +--R x +--R + +--R 3 2 8 3 2 2 3 7 +--R 2494206a b d e + (184756a c + 277134a b )d e +--R + +--R 2 3 4 6 +--R (- 302328a b c - 100776a b )d e +--R + +--R 2 2 2 4 5 5 +--R (93024a c + 186048a b c + 15504b )d e +--R + +--R 2 3 6 4 3 2 2 7 3 +--R (- 124032a b c - 41344b c)d e + (29184a c + 43776b c )d e +--R + +--R 3 8 2 4 9 +--R - 21504b c d e + 4096c d e +--R * +--R x +--R + +--R 3 3 7 3 2 2 4 6 +--R 831402a b d e + (- 369512a c - 554268a b )d e +--R + +--R 2 3 5 5 +--R (604656a b c + 201552a b )d e +--R + +--R 2 2 2 4 6 4 +--R (- 186048a c - 372096a b c - 31008b )d e +--R + +--R 2 3 7 3 3 2 2 8 2 +--R (248064a b c + 82688b c)d e + (- 58368a c - 87552b c )d e +--R + +--R 3 9 4 10 +--R 43008b c d e - 8192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Expression(Integer) +--E 404 + +--S 405 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 8 3 4 7 3 2 2 3 6 +--R 2c e x + (7b c e + 2c d)x + ((6a c + 9b c )e + 7b c d)x +--R + +--R 2 3 3 2 2 5 +--R ((15a b c + 5b c)e + (6a c + 9b c )d)x +--R + +--R 2 2 2 4 2 3 4 +--R ((6a c + 12a b c + b )e + (15a b c + 5b c)d)x +--R + +--R 2 3 2 2 2 4 3 +--R ((9a b c + 3a b )e + (6a c + 12a b c + b )d)x +--R + +--R 3 2 2 2 3 2 3 3 2 2 +--R ((2a c + 3a b )e + (9a b c + 3a b )d)x + (a b e + (2a c + 3a b )d)x +--R + +--R 3 +--R a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 406 + +--S 407 of 465 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(5/2)/e^8+_ + 2/7*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(7/2)/e^8-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(9/2)/e^8+2/11*(70*c^4*d^4+_ + b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+_ + 6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(11/2)/e^8-_ + 10/13*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^(13/2)/e^8+2/5*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(15/2)/e^8-14/17*c^3*(2*c*d-b*e)*(d+e*x)^(17/2)/e^8+_ + 4/19*c^4*(d+e*x)^(19/2)/e^8 +--R +--R +--R (2) +--R 4 9 9 3 9 4 8 8 +--R 1021020c e x + (3993990b c e + 1201200c d e )x +--R + +--R 3 2 2 9 3 8 4 2 7 7 +--R ((3879876a c + 5819814b c )e + 4792788b c d e + 12012c d e )x +--R + +--R 2 3 9 3 2 2 8 +--R (11191950a b c + 3730650b c)e + (4775232a c + 7162848b c )d e +--R + +--R 3 2 7 4 3 6 +--R 61446b c d e - 12936c d e +--R * +--R 6 +--R x +--R + +--R 2 2 2 4 9 +--R (5290740a c + 10581480a b c + 881790b )e +--R + +--R 2 3 8 3 2 2 2 7 +--R (14244300a b c + 4748100b c)d e + (81396a c + 122094b c )d e +--R + +--R 3 3 6 4 4 5 +--R - 67032b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 3 9 +--R (9699690a b c + 3233230a b )e +--R + +--R 2 2 2 4 8 +--R (7054320a c + 14108640a b c + 1175720b )d e +--R + +--R 2 3 2 7 3 2 2 3 6 +--R (339150a b c + 113050b c)d e + (- 90440a c - 135660b c )d e +--R + +--R 3 4 5 4 5 4 +--R 74480b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 3 2 2 9 2 3 8 +--R (2771340a c + 4157010a b )e + (13856700a b c + 4618900a b )d e +--R + +--R 2 2 2 4 2 7 +--R (251940a c + 503880a b c + 41990b )d e +--R + +--R 2 3 3 6 3 2 2 4 5 +--R (- 387600a b c - 129200b c)d e + (103360a c + 155040b c )d e +--R + +--R 3 5 4 4 6 3 +--R - 85120b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 8 +--R 1939938a b e + (4434144a c + 6651216a b )d e +--R + +--R 2 3 2 7 +--R (831402a b c + 277134a b )d e +--R + +--R 2 2 2 4 3 6 +--R (- 302328a c - 604656a b c - 50388b )d e +--R + +--R 2 3 4 5 3 2 2 5 4 +--R (465120a b c + 155040b c)d e + (- 124032a c - 186048b c )d e +--R + +--R 3 6 3 4 7 2 +--R 102144b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 2 7 +--R 3879876a b d e + (554268a c + 831402a b )d e +--R + +--R 2 3 3 6 +--R (- 1108536a b c - 369512a b )d e +--R + +--R 2 2 2 4 4 5 +--R (403104a c + 806208a b c + 67184b )d e +--R + +--R 2 3 5 4 3 2 2 6 3 +--R (- 620160a b c - 206720b c)d e + (165376a c + 248064b c )d e +--R + +--R 3 7 2 4 8 +--R - 136192b c d e + 28672c d e +--R * +--R x +--R + +--R 3 2 7 3 2 2 3 6 +--R 1939938a b d e + (- 1108536a c - 1662804a b )d e +--R + +--R 2 3 4 5 +--R (2217072a b c + 739024a b )d e +--R + +--R 2 2 2 4 5 4 +--R (- 806208a c - 1612416a b c - 134368b )d e +--R + +--R 2 3 6 3 3 2 2 7 2 +--R (1240320a b c + 413440b c)d e + (- 330752a c - 496128b c )d e +--R + +--R 3 8 4 9 +--R 272384b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 4849845e +--R Type: Expression(Integer) +--E 407 + +--S 408 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 409 + +--S 410 of 465 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(3/2)/e^8+_ + 2/5*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(5/2)/e^8-6/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(7/2)/e^8+2/9*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(9/2)/e^8-10/11*c*_ + (2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(11/2)/e^8+_ + 6/13*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(13/2)/e^8-_ + 14/15*c^3*(2*c*d-b*e)*(d+e*x)^(15/2)/e^8+4/17*c^4*(d+e*x)^(17/2)/e^8 +--R +--R +--R (2) +--R 4 8 8 3 8 4 7 7 +--R 180180c e x + (714714b c e + 12012c d e )x +--R + +--R 3 2 2 8 3 7 4 2 6 6 +--R ((706860a c + 1060290b c )e + 54978b c d e - 12936c d e )x +--R + +--R 2 3 8 3 2 2 7 +--R (2088450a b c + 696150b c)e + (64260a c + 96390b c )d e +--R + +--R 3 2 6 4 3 5 +--R - 59976b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 2 2 4 8 +--R (1021020a c + 2042040a b c + 170170b )e +--R + +--R 2 3 7 3 2 2 2 6 +--R (232050a b c + 77350b c)d e + (- 71400a c - 107100b c )d e +--R + +--R 3 3 5 4 4 4 +--R 66640b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 3 8 +--R (1969110a b c + 656370a b )e +--R + +--R 2 2 2 4 7 +--R (145860a c + 291720a b c + 24310b )d e +--R + +--R 2 3 2 6 3 2 2 3 5 +--R (- 265200a b c - 88400b c)d e + (81600a c + 122400b c )d e +--R + +--R 3 4 4 4 5 3 +--R - 76160b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 8 2 3 7 +--R (612612a c + 918918a b )e + (393822a b c + 131274a b )d e +--R + +--R 2 2 2 4 2 6 +--R (- 175032a c - 350064a b c - 29172b )d e +--R + +--R 2 3 3 5 3 2 2 4 4 +--R (318240a b c + 106080b c)d e + (- 97920a c - 146880b c )d e +--R + +--R 3 5 3 4 6 2 +--R 91392b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 7 +--R 510510a b e + (204204a c + 306306a b )d e +--R + +--R 2 3 2 6 +--R (- 525096a b c - 175032a b )d e +--R + +--R 2 2 2 4 3 5 +--R (233376a c + 466752a b c + 38896b )d e +--R + +--R 2 3 4 4 3 2 2 5 3 +--R (- 424320a b c - 141440b c)d e + (130560a c + 195840b c )d e +--R + +--R 3 6 2 4 7 +--R - 121856b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 2 6 +--R 510510a b d e + (- 408408a c - 612612a b )d e +--R + +--R 2 3 3 5 +--R (1050192a b c + 350064a b )d e +--R + +--R 2 2 2 4 4 4 +--R (- 466752a c - 933504a b c - 77792b )d e +--R + +--R 2 3 5 3 3 2 2 6 2 +--R (848640a b c + 282880b c)d e + (- 261120a c - 391680b c )d e +--R + +--R 3 7 4 8 +--R 243712b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Expression(Integer) +--E 410 + +--S 411 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 412 + +--S 413 of 465 +r0:=2/3*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(3/2)/e^8-6/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5/2)/e^8+2/7*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(7/2)/e^8-10/9*c*(2*c*d-b*e)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(9/2)/e^8+6/11*c^2*_ + (14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(11/2)/e^8-14/13*c^3*_ + (2*c*d-b*e)*(d+e*x)^(13/2)/e^8+4/15*c^4*(d+e*x)^(15/2)/e^8-_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 12012c e x + (48510b c e - 12936c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((49140a c + 73710b c )e - 52920b c d e + 14112c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (150150a b c + 50050b c)e + (- 54600a c - 81900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 58800b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 +--R (77220a c + 154440a b c + 12870b )e +--R + +--R 2 3 6 3 2 2 2 5 +--R (- 171600a b c - 57200b c)d e + (62400a c + 93600b c )d e +--R + +--R 3 3 4 4 4 3 +--R - 67200b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (162162a b c + 54054a b )e +--R + +--R 2 2 2 4 6 +--R (- 92664a c - 185328a b c - 15444b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 74880a c - 112320b c )d e +--R + +--R 3 4 3 4 5 2 +--R 80640b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 216216a b c - 72072a b )d e +--R + +--R 2 2 2 4 2 5 +--R (123552a c + 247104a b c + 20592b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 274560a b c - 91520b c)d e + (99840a c + 149760b c )d e +--R + +--R 3 5 2 4 6 +--R - 107520b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R 90090a b e + (- 120120a c - 180180a b )d e +--R + +--R 2 3 2 5 +--R (432432a b c + 144144a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 247104a c - 494208a b c - 41184b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (549120a b c + 183040b c)d e + (- 199680a c - 299520b c )d e +--R + +--R 3 6 4 7 +--R 215040b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 413 + +--S 414 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 415 + +--S 416 of 465 +r0:=-2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^(3/2)/e^8+2/5*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(5/2)/e^8-10/7*c*(2*c*d-b*e)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(7/2)/e^8+2/3*c^2*_ + (14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(9/2)/e^8-14/11*c^3*_ + (2*c*d-b*e)*(d+e*x)^(11/2)/e^8+4/13*c^4*(d+e*x)^(13/2)/e^8+_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*sqrt(d+e*x))+2*(c*d^2-_ + b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 4620c e x + (19110b c e - 5880c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((20020a c + 30030b c )e - 25480b c d e + 7840c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (64350a b c + 21450b c)e + (- 28600a c - 42900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 36400b c d e - 11200c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (36036a c + 72072a b c + 6006b )e + (- 102960a b c - 34320b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (45760a c + 68640b c )d e - 58240b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (90090a b c + 30030a b )e +--R + +--R 2 2 2 4 6 +--R (- 72072a c - 144144a b c - 12012b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 91520a c - 137280b c )d e +--R + +--R 3 4 3 4 5 2 +--R 116480b c d e - 35840c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 360360a b c - 120120a b )d e +--R + +--R 2 2 2 4 2 5 +--R (288288a c + 576576a b c + 48048b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 823680a b c - 274560b c)d e + (366080a c + 549120b c )d e +--R + +--R 3 5 2 4 6 +--R - 465920b c d e + 143360c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R - 30030a b e + (120120a c + 180180a b )d e +--R + +--R 2 3 2 5 +--R (- 720720a b c - 240240a b )d e +--R + +--R 2 2 2 4 3 4 +--R (576576a c + 1153152a b c + 96096b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 1647360a b c - 549120b c)d e + (732160a c + 1098240b c )d e +--R + +--R 3 6 4 7 +--R - 931840b c d e + 286720c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Expression(Integer) +--E 416 + +--S 417 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 418 + +--S 419 of 465 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^(3/2))+2/3*_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(3/2)/e^8-_ + 2*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5/2)/_ + e^8+6/7*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(7/2)/_ + e^8-14/9*c^3*(2*c*d-b*e)*(d+e*x)^(9/2)/e^8+4/11*c^4*(d+e*x)^(11/2)/_ + e^8-2*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/_ + (e^8*sqrt(d+e*x))-6*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 252c e x + (1078b c e - 392c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((1188a c + 1782b c )e - 1848b c d e + 672c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (4158a b c + 1386b c)e + (- 2376a c - 3564b c )d e + 3696b c d e +--R + +--R 4 3 4 +--R - 1344c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (2772a c + 5544a b c + 462b )e + (- 11088a b c - 3696b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (6336a c + 9504b c )d e - 9856b c d e + 3584c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (12474a b c + 4158a b )e + (- 16632a c - 33264a b c - 2772b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (66528a b c + 22176b c)d e + (- 38016a c - 57024b c )d e +--R + +--R 3 4 3 4 5 2 +--R 59136b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 2772a c - 4158a b )e + (49896a b c + 16632a b )d e +--R + +--R 2 2 2 4 2 5 +--R (- 66528a c - 133056a b c - 11088b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (266112a b c + 88704b c)d e + (- 152064a c - 228096b c )d e +--R + +--R 3 5 2 4 6 +--R 236544b c d e - 86016c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 462a b e + (- 1848a c - 2772a b )d e + (33264a b c + 11088a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 44352a c - 88704a b c - 7392b )d e + (177408a b c + 59136b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 101376a c - 152064b c )d e + 157696b c d e - 57344c d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Expression(Integer) +--E 419 + +--S 420 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 465 +r0:=4/3*(d+e*x)^(3/2)+2*(2*c*d-b*e)*sqrt(d+e*x)/c-atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c^2*d^2+b^2*_ + e^2-2*c*e*(b*d+a*e)+e*(2*c*d-b*e)*sqrt(b^2-4*a*c))/(c^(3/2)*sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e)-_ + e*(2*c*d-b*e)*sqrt(b^2-4*a*c))/(c^(3/2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R 2 +-+ | 2 +--R (- 3b e + 6c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((6a c - 3b )e + 6b c d e - 6c d )\|2 +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 +-+ | 2 +--R (3b e - 6c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((6a c - 3b )e + 6b c d e - 6c d )\|2 +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R (4c e x - 6b e + 16c d)\|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R +-+ | | 2 | | 2 +--R 3c\|c \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 422 + +--S 423 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 465 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 465 +r0:=4*sqrt(d+e*x)-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ + sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))/sqrt(c)-_ + atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ + sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/sqrt(c) +--R +--R +--R (2) +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|2 \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|2 \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-+ +-------+ +--R 4\|c \|e x + d +--R / +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 425 + +--S 426 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 of 465 +t0:=(b+2*c*x)/((a+b*x+c*x^2)*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) -------------------------- +--R 2 +-------+ +--R (c x + b x + a)\|e x + d +--R Type: Expression(Integer) +--E 427 + +--S 428 of 465 +r0:=-2*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ + sqrt(2)*sqrt(c)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))-2*atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*_ + sqrt(c)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))) +--R +--R +--R (2) +--R - +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 428 + +--S 429 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 of 465 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------------------- +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 430 + +--S 431 of 465 +r0:=2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))+atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b*e*_ + (b+sqrt(b^2-4*a*c))-2*c*(2*a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*_ + (b*e*(b-sqrt(b^2-4*a*c))+2*c*(-2*a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-_ + b*d*e+a*e^2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +-------+ +--R ((b e - 2c d)\|2 \|- 4a c + b + (4a c - b )e\|2 )\|c \|e x + d +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +-------+ +--R ((b e - 2c d)\|2 \|- 4a c + b + (- 4a c + b )e\|2 )\|c \|e x + d +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R (- 2b e + 4c d)\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 2 | 2 +-------+ +--R (a e - b d e + c d )\|- 4a c + b \|e x + d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 431 + +--S 432 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 465 +t0:=(b+2*c*x)/((d+e*x)^(5/2)*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x +--R + +--R 2 2 +--R (2a d e + b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 433 + +--S 434 of 465 +r0:=2/3*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+_ + 2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))/((c*d^2-b*d*e+a*e^2)^2*_ + sqrt(d+e*x))-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b^2*e^2*(b+sqrt(b^2-4*a*c))+_ + 2*c^2*d*(4*a*e+d*sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e+b*d*_ + sqrt(b^2-4*a*c)+a*e*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*_ + sqrt(c)*(b^2*e^2*(b-sqrt(b^2-4*a*c))-2*c^2*d*(-4*a*e+d*_ + sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e-b*d*sqrt(b^2-4*a*c)-_ + a*e*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((6a c - 3b )e + 6b c d e - 6c d e)x + (6a c - 3b )d e +--R + +--R 2 2 3 +--R 6b c d e - 6c d +--R * +--R +-----------+ +--R +-+ | 2 +--R \|2 \|- 4a c + b +--R + +--R 3 3 2 2 2 +--R ((- 12a b c + 3b )e + (24a c - 6b c)d e )x +--R + +--R 3 2 2 2 2 +--R (- 12a b c + 3b )d e + (24a c - 6b c)d e +--R * +--R +-+ +--R \|2 +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 2 2 +--R ((6a c - 3b )e + 6b c d e - 6c d e)x + (6a c - 3b )d e +--R + +--R 2 2 3 +--R 6b c d e - 6c d +--R * +--R +-----------+ +--R +-+ | 2 +--R \|2 \|- 4a c + b +--R + +--R 3 3 2 2 2 +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e )x +--R + +--R 3 2 2 2 2 +--R (12a b c - 3b )d e + (- 24a c + 6b c)d e +--R * +--R +-+ +--R \|2 +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 3 +--R ((- 12a c + 6b )e - 12b c d e + 12c d e)x - 2a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c + 8b )d e - 18b c d e + 16c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (3a e - 6a b d e + (6a c + 3b )d e - 6b c d e + 3c d e)x + 3a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 6a b d e + (6a c + 3b )d e - 6b c d e + 3c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-------+ | | 2 +--R \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 434 + +--S 435 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 465 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 465 +r0:=-(d+e*x)^(5/2)/(a+b*x+c*x^2)+5*e^2*sqrt(d+e*x)/c-5*e*atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))/sqrt(b^2-4*a*c))/(c^(3/2)*_ + sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-5*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (-2*c^2*d^2-b^2*e^2+2*c*e*(b*d+a*e))/sqrt(b^2-4*a*c))/(c^(3/2)*_ + sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 2 2 3 2 3 +--R (5b c e - 10c d e )x + (5b e - 10b c d e )x + 5a b e +--R + +--R 2 +--R - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((- 10a c + 5b c)e - 10b c d e + 10c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 10a b c + 5b )e - 10b c d e + 10b c d e)x + (- 10a c + 5a b )e +--R + +--R 2 2 2 +--R - 10a b c d e + 10a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 3 +--R (5b c e - 10c d e )x + (5b e - 10b c d e )x + 5a b e +--R + +--R 2 +--R - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((10a c - 5b c)e + 10b c d e - 10c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((10a b c - 5b )e + 10b c d e - 10b c d e)x + (10a c - 5a b )e +--R + +--R 2 2 2 +--R 10a b c d e - 10a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 2 2 2 2 +-+ | 2 +-+ +--R (4c e x + (5b e - 2c d e)x + 5a e - c d )\|2 \|- 4a c + b \|c +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-------+ | | 2 +--R \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 2 +-+ | 2 +-+ +--R (c x + b c x + a c)\|2 \|- 4a c + b \|c +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 437 + +--S 438 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 465 +r0:=-(d+e*x)^(3/2)/(a+b*x+c*x^2)-3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ + (sqrt(2)*sqrt(c)*sqrt(b^2-4*a*c))+3*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c)))/(sqrt(2)*sqrt(c)*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R +------------------------------+ +--R | +-----------+ +--R 2 | | 2 +--R (3c e x + 3b e x + 3a e)\|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R | +-----------+ +--R 2 | | 2 +--R (- 3c e x - 3b e x - 3a e)\|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-------+ +--R (- e x - d)\|2 \|- 4a c + b \|c \|e x + d +--R / +--R +-----------+ +--R 2 +-+ | 2 +-+ +--R (c x + b x + a)\|2 \|- 4a c + b \|c +--R Type: Expression(Integer) +--E 440 + +--S 441 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 441 + +)clear all + +--S 442 of 465 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^2 +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 465 +r0:=-sqrt(d+e*x)/(a+b*x+c*x^2)-e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/(sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/_ + (sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +----------------------------+ +--R | +-----------+ +--R 2 +-+ +-+ | | 2 +--R (c e x + b e x + a e)\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R 2 +-+ +-+ | | 2 +--R (- c e x - b e x - a e)\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-------+ | | 2 +--R \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 +--R (c x + b x + a)\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 443 + +--S 444 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 465 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) -------------------------------------------------------- +--R 2 4 3 2 2 2 +-------+ +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 445 + +--S 446 of 465 +r0:=-((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))+e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(2*c*d-e*(b+_ + sqrt(b^2-4*a*c)))/((c*d^2-e*(b*d-a*e))*sqrt(2)*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(2*c*d-_ + e*(b-sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R 2 2 2 2 | 2 2 2 2 +--R (- c e x - b e x - a e )\|- 4a c + b + (b c e - 2c d e)x +--R + +--R 2 2 2 +--R (b e - 2b c d e)x + a b e - 2a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 2 2 2 | 2 2 2 2 +--R (- c e x - b e x - a e )\|- 4a c + b + (- b c e + 2c d e)x +--R + +--R 2 2 2 +--R (- b e + 2b c d e)x - a b e + 2a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-------+ +--R (c e x + b e - c d)\|2 \|- 4a c + b \|e x + d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (a c e - b c d e + c d )x + (a b e - b d e + b c d )x + a e +--R + +--R 2 +--R - a b d e + a c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 446 + +--S 447 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 465 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 448 + +--S 449 of 465 +r0:=3*e^2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))+(-(b^2-4*a*c)*_ + (c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ + (a+b*x+c*x^2)*sqrt(d+e*x))+3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(2*c^2*d^2+b*e^2*(b+_ + sqrt(b^2-4*a*c))-2*c*e*(b*d+a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+_ + a*e^2)^2*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-_ + 3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c))))*sqrt(c)*(2*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-_ + 2*c*e*(b*d+a*e-d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(2)*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 2 2 3 2 3 +--R (3b c e - 6c d e )x + (3b e - 6b c d e )x + 3a b e +--R + +--R 2 +--R - 6a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((6a c - 3b c)e + 6b c d e - 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((6a b c - 3b )e + 6b c d e - 6b c d e)x + (6a c - 3a b )e +--R + +--R 2 2 2 +--R 6a b c d e - 6a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 3 +--R (3b c e - 6c d e )x + (3b e - 6b c d e )x + 3a b e +--R + +--R 2 +--R - 6a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((- 6a c + 3b c)e - 6b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 6a b c + 3b )e - 6b c d e + 6b c d e)x + (- 6a c + 3a b )e +--R + +--R 2 2 2 +--R - 6a b c d e + 6a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 3b c e + 6c d e )x + ((a c - 3b )e + 5b c d e + c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (5a c - b )d e + 2b c d e - c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (a c e - 2a b c d e + (2a c + b c)d e - 2b c d e + c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 3 4 +--R (a b e - 2a b d e + (2a b c + b )d e - 2b c d e + b c d )x + a e +--R + +--R 2 3 2 2 2 2 3 2 4 +--R - 2a b d e + (2a c + a b )d e - 2a b c d e + a c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 449 + +--S 450 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 465 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 465 +r0:=-1/2*(d+e*x)^(7/2)/(a+b*x+c*x^2)^2-7/4*e*(d+e*x)^(3/2)*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+7/4*e^2*(2*c*d-b*e)*_ + sqrt(d+e*x)/(c*(b^2-4*a*c))+7/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c^2*d^2-b^2*e^2-2*c*e*_ + (b*d-3*a*e))+(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))/_ + sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))+7/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(e*(2*c^2*d^2-b^2*e^2-2*c*e*_ + (b*d-3*a*e))-(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))/_ + sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(2*c*d-e*_ + (b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 42a c + 7b c )e + 14b c d e - 14c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 84a b c + 14b c)e + 28b c d e - 28b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 84a c - 28a b c + 7b )e + (28a b c + 14b c)d e +--R + +--R 3 2 2 2 2 +--R (- 28a c - 14b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 84a b c + 14a b )e + 28a b c d e - 28a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 42a c + 7a b )e + 14a b c d e - 14a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (- 56a b c + 7b c )e + (112a c + 14b c )d e - 84b c d e +--R + +--R 5 3 +--R 56c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (- 112a b c + 14b c)e + (224a b c + 28b c )d e - 168b c d e +--R + +--R 4 3 +--R 112b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 +--R (- 112a b c - 42a b c + 7b )e +--R + +--R 2 3 2 2 4 3 3 3 2 2 2 +--R (224a c + 140a b c + 14b c)d e + (- 168a b c - 84b c )d e +--R + +--R 4 2 3 3 +--R (112a c + 56b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 +--R (- 112a b c + 14a b )e + (224a b c + 28a b c)d e +--R + +--R 2 2 2 2 3 3 +--R - 168a b c d e + 112a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 +--R (- 56a b c + 7a b )e + (112a c + 14a b c)d e - 84a b c d e +--R + +--R 2 3 3 +--R 56a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 42a c + 7b c )e + 14b c d e - 14c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 84a b c + 14b c)e + 28b c d e - 28b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 84a c - 28a b c + 7b )e + (28a b c + 14b c)d e +--R + +--R 3 2 2 2 2 +--R (- 28a c - 14b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 84a b c + 14a b )e + 28a b c d e - 28a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 42a c + 7a b )e + 14a b c d e - 14a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (56a b c - 7b c )e + (- 112a c - 14b c )d e + 84b c d e +--R + +--R 5 3 +--R - 56c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (112a b c - 14b c)e + (- 224a b c - 28b c )d e + 168b c d e +--R + +--R 4 3 +--R - 112b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 +--R (112a b c + 42a b c - 7b )e +--R + +--R 2 3 2 2 4 3 3 3 2 2 2 +--R (- 224a c - 140a b c - 14b c)d e + (168a b c + 84b c )d e +--R + +--R 4 2 3 3 +--R (- 112a c - 56b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 +--R (112a b c - 14a b )e + (- 224a b c - 28a b c)d e +--R + +--R 2 2 2 2 3 3 +--R 168a b c d e - 112a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 +--R (56a b c - 7a b )e + (- 112a c - 14a b c)d e + 84a b c d e +--R + +--R 2 3 3 +--R - 56a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 22a c + 9b c)e - 14b c d e + 14c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 7a b c + 7b )e + (- 52a c - 8b c)d e + 21b c d e)x +--R + +--R 2 2 3 2 2 2 2 +--R ((- 14a c + 14a b )e - 42a b c d e + (- 10a c + 13b c)d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R 7a b e - 28a c d e + 7a b c d e + (- 8a c + 2b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-------+ | | 2 +--R \|2 \|- 4a c + b \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 4 2 3 4 3 3 2 3 2 3 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c )x + (32a c + 8a b c - 4b c)x +--R + +--R 2 2 3 3 2 2 2 +--R (32a b c - 8a b c)x + 16a c - 4a b c +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R \|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 452 + +--S 453 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 465 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 465 +r0:=-1/2*(d+e*x)^(5/2)/(a+b*x+c*x^2)^2-5/4*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + sqrt(d+e*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+5/4*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))/sqrt(b^2-4*a*c))/((b^2-4*a*c)*_ + sqrt(2)*sqrt(c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-5/4*e*_ + atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ + (8*c^2*d^2+b*e^2*(b+sqrt(b^2-4*a*c))-2*c*e*(4*b*d-2*a*e+d*_ + sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(c)*sqrt(2*c*d-e*_ + (b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 3 2 4 2 3 2 2 3 +--R (5b c e - 10c d e )x + (10b c e - 20b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((10a b c + 5b )e + (- 20a c - 10b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (10a b e - 20a b c d e )x + 5a b e - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((20a c + 5b c )e - 40b c d e + 40c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((40a b c + 10b c)e - 80b c d e + 80b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (40a c + 30a b c + 5b )e + (- 80a b c - 40b c)d e +--R + +--R 3 2 2 2 +--R (80a c + 40b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((40a b c + 10a b )e - 80a b c d e + 80a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (20a c + 5a b )e - 40a b c d e + 40a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 3 2 4 2 3 2 2 3 +--R (5b c e - 10c d e )x + (10b c e - 20b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((10a b c + 5b )e + (- 20a c - 10b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (10a b e - 20a b c d e )x + 5a b e - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((- 20a c - 5b c )e + 40b c d e - 40c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((- 40a b c - 10b c)e + 80b c d e - 80b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (- 40a c - 30a b c - 5b )e + (80a b c + 40b c)d e +--R + +--R 3 2 2 2 +--R (- 80a c - 40b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((- 40a b c - 10a b )e + 80a b c d e - 80a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (- 20a c - 5a b )e + 40a b c d e - 40a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 2 2 2 +--R (- 5b c e + 10c d e)x + ((- 18a c - 3b )e + 15b c d e)x +--R + +--R 2 2 2 2 +--R (- 15a b e + (- 6a c + 9b )d e)x - 10a e + 5a b d e +--R + +--R 2 2 +--R (- 8a c + 2b )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-------+ | | 2 +--R \|2 \|- 4a c + b \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c)x + (32a c + 8a b c - 4b )x +--R + +--R 2 3 3 2 2 +--R (32a b c - 8a b )x + 16a c - 4a b +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R \|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 455 + +--S 456 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 456 + +)clear all + +--S 457 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 465 +r0:=-1/2*(d+e*x)^(3/2)/(a+b*x+c*x^2)^2-3/4*e*(b+2*c*x)*sqrt(d+e*x)/_ + ((b^2-4*a*c)*(a+b*x+c*x^2))+3/2*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(4*c*d-e*(2*b-_ + sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b-_ + sqrt(b^2-4*a*c))))-3/2*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(4*c*d-e*(2*b+sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 2 4 2 3 2 2 2 2 2 2 +--R (- 6c e x - 12b c e x + (- 12a c - 6b )e x - 12a b e x - 6a e ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 4 2 2 2 3 +--R (- 12b c e + 24c d e)x + (- 24b c e + 48b c d e)x +--R + +--R 3 2 2 2 2 +--R ((- 24a b c - 12b )e + (48a c + 24b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 24a b e + 48a b c d e)x - 12a b e + 24a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 4 2 3 2 2 2 2 2 2 +--R (- 6c e x - 12b c e x + (- 12a c - 6b )e x - 12a b e x - 6a e ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 4 2 2 2 3 +--R (12b c e - 24c d e)x + (24b c e - 48b c d e)x +--R + +--R 3 2 2 2 2 +--R ((24a b c + 12b )e + (- 48a c - 24b c)d e)x +--R + +--R 2 2 2 2 2 +--R (24a b e - 48a b c d e)x + 12a b e - 24a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 +--R (6c e x + 9b c e x + (- 2a c + 5b )e x + 3a b e + (- 8a c + 2b )d) +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c)x + (32a c + 8a b c - 4b )x +--R + +--R 2 3 3 2 2 +--R (32a b c - 8a b )x + 16a c - 4a b +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 458 + +--S 459 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 465 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R +-------+ +--R (2c x + b)\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 460 + +--S 461 of 465 +r0:=-1/2*sqrt(d+e*x)/(a+b*x+c*x^2)^2-1/4*e*(b*c*d-b^2*e+2*a*c*e+_ + c*(2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ + (a+b*x+c*x^2))+1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^2*d^2-b*e^2*(b+sqrt(b^2-4*a*c))-_ + 2*c*e*(4*b*d-6*a*e-d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-_ + e*(b*d-a*e))*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-_ + 1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^2*d^2-b*e^2*(b-sqrt(b^2-4*a*c))-_ + 2*c*e*(4*b*d-6*a*e+d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-_ + b*d*e+a*e^2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 3 2 4 2 3 2 2 3 +--R (b c e - 2c d e )x + (2b c e - 4b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((2a b c + b )e + (- 4a c - 2b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (2a b e - 4a b c d e )x + a b e - 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((12a c - b c )e - 8b c d e + 8c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((24a b c - 2b c)e - 16b c d e + 16b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (24a c + 10a b c - b )e + (- 16a b c - 8b c)d e +--R + +--R 3 2 2 2 +--R (16a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((24a b c - 2a b )e - 16a b c d e + 16a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (12a c - a b )e - 8a b c d e + 8a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 3 2 4 2 3 2 2 3 +--R (b c e - 2c d e )x + (2b c e - 4b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((2a b c + b )e + (- 4a c - 2b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (2a b e - 4a b c d e )x + a b e - 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((- 12a c + b c )e + 8b c d e - 8c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((- 24a b c + 2b c)e + 16b c d e - 16b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (- 24a c - 10a b c + b )e + (16a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 16a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((- 24a b c + 2a b )e + 16a b c d e - 16a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (- 12a c + a b )e + 8a b c d e - 8a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 3 2 2 2 2 2 +--R (- b c e + 2c d e)x + ((2a c - 2b c)e + 3b c d e)x +--R + +--R 3 2 2 2 2 2 2 +--R ((a b c - b )e + (2a c + b c)d e)x + (- 6a c + a b )e +--R + +--R 3 2 2 2 +--R (9a b c - 2b )d e + (- 8a c + 2b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 3 2 2 2 3 3 2 4 2 3 2 4 +--R ((16a c - 4a b c )e + (- 16a b c + 4b c )d e + (16a c - 4b c )d )x +--R + +--R 2 2 3 2 2 2 4 +--R (32a b c - 8a b c)e + (- 32a b c + 8b c)d e +--R + +--R 3 3 2 2 +--R (32a b c - 8b c )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 4 2 2 2 3 5 +--R (32a c + 8a b c - 4a b )e + (- 32a b c - 8a b c + 4b )d e +--R + +--R 2 3 2 2 4 2 +--R (32a c + 8a b c - 4b c)d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 4 2 2 3 2 +--R ((32a b c - 8a b )e + (- 32a b c + 8a b )d e + (32a b c - 8a b c)d )x +--R + +--R 4 3 2 2 3 2 3 3 2 2 2 2 +--R (16a c - 4a b )e + (- 16a b c + 4a b )d e + (16a c - 4a b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 461 + +--S 462 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 465 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 463 + +--S 464 of 465 +r0:=-1/2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)+1/4*e*(5*a*c*e*_ + (2*c*d-b*e)+(c*d-3*b*e)*(b*c*d-b^2*e+2*a*c*e)+c*(2*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(b*d+5*a*e))*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ + (a+b*x+c*x^2))-1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^3*d^3+3*b^2*e^3*(b+_ + sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-16*a*e-d*sqrt(b^2-4*a*c))-2*c*e^2*_ + (b^2*d+8*a*b*e+b*d*sqrt(b^2-4*a*c)+5*a*e*sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))+1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^3*d^3+3*b^2*e^3*_ + (b-sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-16*a*e+d*sqrt(b^2-4*a*c))-_ + 2*c*e^2*(b^2*d+8*a*b*e-b*d*sqrt(b^2-4*a*c)-5*a*e*sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 10a c + 3b c )e - 2b c d e + 2c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 20a b c + 6b c)e - 4b c d e + 4b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 20a c - 4a b c + 3b )e + (- 4a b c - 2b c)d e +--R + +--R 3 2 2 2 2 +--R (4a c + 2b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 20a b c + 6a b )e - 4a b c d e + 4a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 10a c + 3a b )e - 2a b c d e + 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (16a b c - 3b c )e + (- 32a c + 2b c )d e + 12b c d e +--R + +--R 5 3 +--R - 8c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (32a b c - 6b c)e + (- 64a b c + 4b c )d e + 24b c d e +--R + +--R 4 3 +--R - 16b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 2 3 2 2 4 3 +--R (32a b c + 10a b c - 3b )e + (- 64a c - 28a b c + 2b c)d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (24a b c + 12b c )d e + (- 16a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 2 2 2 2 +--R (32a b c - 6a b )e + (- 64a b c + 4a b c)d e + 24a b c d e +--R + +--R 3 3 +--R - 16a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 2 3 3 +--R (16a b c - 3a b )e + (- 32a c + 2a b c)d e + 12a b c d e - 8a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 10a c + 3b c )e - 2b c d e + 2c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 20a b c + 6b c)e - 4b c d e + 4b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 20a c - 4a b c + 3b )e + (- 4a b c - 2b c)d e +--R + +--R 3 2 2 2 2 +--R (4a c + 2b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 20a b c + 6a b )e - 4a b c d e + 4a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 10a c + 3a b )e - 2a b c d e + 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (- 16a b c + 3b c )e + (32a c - 2b c )d e - 12b c d e +--R + +--R 5 3 +--R 8c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (- 32a b c + 6b c)e + (64a b c - 4b c )d e - 24b c d e +--R + +--R 4 3 +--R 16b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 2 3 2 2 4 3 +--R (- 32a b c - 10a b c + 3b )e + (64a c + 28a b c - 2b c)d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (- 24a b c - 12b c )d e + (16a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 2 2 2 2 +--R (- 32a b c + 6a b )e + (64a b c - 4a b c)d e - 24a b c d e +--R + +--R 3 3 +--R 16a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 2 3 3 +--R (- 16a b c + 3a b )e + (32a c - 2a b c)d e - 12a b c d e + 8a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 3 3 2 4 2 3 +--R ((10a c - 3b c )e + 2b c d e - 2c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 2 +--R ((21a b c - 6b c)e + (- 12a c + 6b c )d e - 3b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (18a c + 6a b c - 3b )e + (- 18a b c + 6b c)d e +--R + +--R 3 2 2 2 +--R (6a c - 3b c )d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 4 2 +--R (19a b c - 5a b )e + (- 20a c - 2a b c + 2b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (15a b c - 4b c)d e + (- 8a c + 2b c )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 3 2 2 2 4 2 3 3 2 3 +--R (16a c - 4a b c )e + (- 32a b c + 8a b c )d e +--R + +--R 2 4 2 3 4 2 2 2 4 3 3 3 +--R (32a c + 8a b c - 4b c )d e + (- 32a b c + 8b c )d e +--R + +--R 5 2 4 4 +--R (16a c - 4b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 4 2 2 2 4 3 +--R (32a b c - 8a b c)e + (- 64a b c + 16a b c)d e +--R + +--R 2 3 3 2 5 2 2 2 3 4 2 3 +--R (64a b c + 16a b c - 8b c)d e + (- 64a b c + 16b c )d e +--R + +--R 4 3 3 4 +--R (32a b c - 8b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 3 2 2 3 5 3 +--R (32a c + 8a b c - 4a b )e + (- 64a b c - 16a b c + 8a b )d e +--R + +--R 3 3 2 2 2 6 2 2 2 3 3 2 5 3 +--R (64a c + 48a b c - 4b )d e + (- 64a b c - 16a b c + 8b c)d e +--R + +--R 2 4 2 3 4 2 4 +--R (32a c + 8a b c - 4b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 3 2 2 4 3 +--R (32a b c - 8a b )e + (- 64a b c + 16a b )d e +--R + +--R 3 2 2 3 5 2 2 2 2 2 4 3 +--R (64a b c + 16a b c - 8a b )d e + (- 64a b c + 16a b c)d e +--R + +--R 2 3 3 2 4 +--R (32a b c - 8a b c )d +--R * +--R x +--R + +--R 5 4 2 4 4 3 3 3 +--R (16a c - 4a b )e + (- 32a b c + 8a b )d e +--R + +--R 4 2 3 2 2 4 2 2 3 2 2 3 3 +--R (32a c + 8a b c - 4a b )d e + (- 32a b c + 8a b c)d e +--R + +--R 3 3 2 2 2 4 +--R (16a c - 4a b c )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 464 + +--S 465 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 465 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richder12d.input.pamphlet b/src/axiom-website/CATS/richder12d.input.pamphlet new file mode 100644 index 0000000..c4c5460 --- /dev/null +++ b/src/axiom-website/CATS/richder12d.input.pamphlet @@ -0,0 +1,23660 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12d.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +All derivatives match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12d.output +)spool richder12d.output +)set message test on +)set message auto off +)clear all + +--S 1 of 764 +t0:=(b+2*c*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R +-------+ | 2 +--R (1) (2c x + b)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 764 +--r0:=4/7*(a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)-2/105*(8*c^2*d^2+b^2*e^2-_ +-- c*e*(11*b*d-10*a*e)-3*c*e*(2*c*d-b*e)*x)*sqrt(d+e*x)*sqrt(a+b*x+_ +-- c*x^2)/(c*e^2)-1/105*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(5*c*e*(b*d-2*a*e)^2-_ +-- (2*c*d-b*e)*(4*b*c*d^2-b^2*d*e-2*a*c*d*e-a*b*e^2))+(2*c*d-b*e)*_ +-- (4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e^3*sqrt(a+b*x+_ +-- c*x^2))-1/105*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*e^4*sqrt(a+b*x+c*x^2)) +--E 2 + +--S 3 of 764 +--d0:=D(m0,x) +--E 3 + +)clear all + +--S 4 of 764 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 4 + +--S 5 of 764 +--r0:=-2/15*(8*c*d-7*b*e-6*c*e*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/e^2-_ +-- 1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*(2*c*(7*b^2*d*e+4*a*c*d*e-8*b*(c*d^2+a*e^2))+_ +-- (16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e^3*sqrt(2)*sqrt(a+b*x+_ +-- c*x^2))-1/15*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*e^4*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 5 + +--S 6 of 764 +--d0:=D(m0,x) +--E 6 + +)clear all + +--S 7 of 764 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 7 + +--S 8 of 764 +--r0:=2/3*(8*c*d-3*b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*sqrt(d+e*x))-_ +-- 1/3*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(b*e*(b-4*sqrt(b^2-4*a*c))+c*(-4*a*e+_ +-- 8*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^3*sqrt(c)*sqrt(a+b*x+c*x^2))+4/3*(2*c*d-b*e)*elliptic_e(asin(_ +-- sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^4*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 8 + +--S 9 of 764 +--d0:=D(m0,x) +--E 9 + +)clear all + +--S 10 of 764 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 10 + +--S 11 of 764 +--r0:=2/3*(8*c*d-b*e+6*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/3*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*sqrt(a+b*x+c*x^2)/_ +-- (e^2*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(7*b^2*d*e+_ +-- 4*a*c*d*e-8*b*(c*d^2+a*e^2))+(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-_ +-- 3*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^3*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-_ +-- 4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-_ +-- 4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-_ +-- 4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^4*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 11 + +--S 12 of 764 +--d0:=D(m0,x) +--E 12 + +)clear all + +--S 13 of 764 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 13 + +--S 14 of 764 +--r0:=2/15*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*sqrt(a+b*x+c*x^2)/_ +-- (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))-2/5*(8*c*d+b*e+10*c*e*x)*_ +-- sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^(5/2))+4/15*(2*c*d-b*e)*(4*c^2*d^2-_ +-- b^2*e^2-4*c*e*(b*d-2*a*e))*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*_ +-- e^2)^2*sqrt(d+e*x))+1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+_ +-- e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*_ +-- a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*(b^3*d*e^2-4*a*_ +-- c*e*(c*d^2+5*a*e^2)+4*b*c*d*(2*c*d^2+5*a*e^2)-b^2*(11*c*d^2*e-a*e^3))+_ +-- (2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e^3*(c*d^2-b*d*e+a*e^2)^2*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2))+1/15*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-_ +-- 2*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^4*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 14 + +--S 15 of 764 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 764 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 16 + +--S 17 of 764 +--r0:=-2/63*(16*c*d-15*b*e-14*c*e*x)*(a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)/e^2-_ +-- 2/315*(128*c^3*d^3-b^3*e^3+3*b*c*e^2*(37*b*d-36*a*e)-12*c^2*d*_ +-- e*(20*b*d-11*a*e)-3*c*e*(32*c^2*d^2+b^2*e^2-4*c*e*(8*b*d-7*a*e))*x)*_ +-- sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*e^4)-1/315*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*((4*b*c*_ +-- d^2-b^2*d*e-2*a*c*d*e-a*b*e^2)*(32*c^2*d^2+b^2*e^2-4*c*e*(8*b*d-_ +-- 7*a*e))+5*c*e*(b*d-2*a*e)*(15*b^2*d*e+4*a*c*d*e-16*b*(c*d^2+a*e^2)))+_ +-- (128*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(64*b*d-57*a*e)-b^2*c*e^3*(7*b*d-_ +-- 15*a*e)+3*c^2*e^2*(45*b^2*d^2-76*a*b*d*e+28*a^2*e^2))*(b-sqrt(b^2-_ +-- 4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e^5*sqrt(a+b*x+_ +-- c*x^2))-1/315*(128*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(64*b*d-57*a*e)-_ +-- b^2*c*e^3*(7*b*d-15*a*e)+3*c^2*e^2*(45*b^2*d^2-76*a*b*d*e+28*a^2*_ +-- e^2))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*e^6*sqrt(a+b*x+c*x^2)) +--E 17 + +--S 18 of 764 +--d0:=D(m0,x) +--E 18 + +)clear all + +--S 19 of 764 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 19 + +--S 20 of 764 +--r0:=2/7*(16*c*d-7*b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+_ +-- 2/35*(128*c^2*d^2+51*b^2*e^2-4*c*e*(44*b*d-5*a*e)-48*c*e*(2*c*d-_ +-- b*e)*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/e^4+1/35*elliptic_f(asin(_ +-- sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- (-2*c*(51*b^3*d*e^2-8*a*c*e*(8*c*d^2+5*a*e^2)+4*b*c*d*(32*c*d^2+_ +-- 45*a*e^2)-2*b^2*(88*c*d^2*e+27*a*e^3))+(2*c*d-b*e)*(128*c^2*d^2+_ +-- 3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e^5*sqrt(2)*sqrt(a+b*x+c*x^2))+_ +-- 1/35*(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*e^6*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 20 + +--S 21 of 764 +--d0:=D(m0,x) +--E 21 + +)clear all + +--S 22 of 764 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 22 + +--S 23 of 764 +--r0:=2/15*(16*c*d-5*b*e+6*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/15*(128*c^2*d^2+15*b^2*e^2-4*c*e*(28*b*d-9*a*e)+16*c*e*(2*c*d-_ +-- b*e)*x)*sqrt(a+b*x+c*x^2)/(e^4*sqrt(d+e*x))-1/15*elliptic_f(_ +-- asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(b^2*e^2*(8*b-23*sqrt(b^2-4*a*c))-64*c^2*d*(-a*e+2*d*_ +-- sqrt(b^2-4*a*c))-4*c*e*(4*b^2*d+8*a*b*e-32*b*d*sqrt(b^2-4*a*c)+_ +-- 9*a*e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^5*sqrt(c)*sqrt(a+b*x+c*x^2))-1/15*(128*c^2*d^2+23*b^2*e^2-_ +-- 4*c*e*(32*b*d-9*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^6*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 23 + +--S 24 of 764 +--d0:=D(m0,x) +--E 24 + +)clear all + +--S 25 of 764 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 25 + +--S 26 of 764 +--r0:=2/15*(16*c*d-3*b*e+10*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 2/15*(128*c^2*d^2+3*b^2*e^2-20*c*e*(4*b*d-a*e)+48*c*e*(2*c*d-b*e)*x)*_ +-- sqrt(a+b*x+c*x^2)/(e^4*(d+e*x)^(3/2))+2/15*(2*c*d-b*e)*(128*c^2*d^2+_ +-- 3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*sqrt(a+b*x+c*x^2)/(e^4*(c*d^2-_ +-- b*d*e+a*e^2)*sqrt(d+e*x))+1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(-2*c*(51*b^3*d*e^2-_ +-- 8*a*c*e*(8*c*d^2+5*a*e^2)+4*b*c*d*(32*c*d^2+45*a*e^2)-2*b^2*(88*c*_ +-- d^2*e+27*a*e^3))+(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-_ +-- 29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^5*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+_ +-- 1/15*(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^6*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 26 + +--S 27 of 764 +--d0:=D(m0,x) +--E 27 + +)clear all + +--S 28 of 764 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 28 + +--S 29 of 764 +--r0:=2/7*(2*c*d-b*e)*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)/c+4/7*(d+e*x)^(5/2)*_ +-- sqrt(a+b*x+c*x^2)+4/21*(3*c^2*d^2+2*b^2*e^2-c*e*(3*b*d+5*a*e))*_ +-- sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c^2-1/21*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(4*b^3*_ +-- d*e^2+2*a*c*e*(27*c*d^2-5*a*e^2)-b*c*d*(3*c*d^2+25*a*e^2)-b^2*_ +-- (9*c*d^2*e-4*a*e^3))+(2*c*d-b*e)*(3*c^2*d^2+8*b^2*e^2-c*e*(3*b*d+_ +-- 29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(7/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-1/21*(2*c*d-b*e)*(3*c^2*d^2+_ +-- 8*b^2*e^2-c*e*(3*b*d+29*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(7/2)*_ +-- e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 29 + +--S 30 of 764 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 764 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 31 + +--S 32 of 764 +--r0:=4/5*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)+2/5*(2*c*d-b*e)*sqrt(d+e*x)*_ +-- sqrt(a+b*x+c*x^2)/c+1/5*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*_ +-- d*e+a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e*sqrt(a+b*x+c*x^2))-_ +-- 1/5*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- e^2*sqrt(a+b*x+c*x^2)) +--E 32 + +--S 33 of 764 +--d0:=D(m0,x) +--E 33 + +)clear all + +--S 34 of 764 +t0:=(b+2*c*x)*sqrt(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 764 +--r0:=4/3*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)+1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(b*e*(b-_ +-- sqrt(b^2-4*a*c))+2*c*(-2*a*e+d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 35 + +--S 36 of 764 +--d0:=D(m0,x) +--E 36 + +)clear all + +--S 37 of 764 +t0:=(b+2*c*x)/(sqrt(d+e*x)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) --------------------------- +--R +--------------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 764 +--r0:=elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/(e*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 38 + +--S 39 of 764 +--d0:=D(m0,x) +--E 39 + +)clear all + +--S 40 of 764 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------ +--R +--------------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 764 +--r0:=2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+2*d*sqrt(b^2-_ +-- 4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(2*c*d-b*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 41 + +--S 42 of 764 +--d0:=D(m0,x) +--E 42 + +)clear all + +--S 43 of 764 +t0:=(b+2*c*x)/((d+e*x)^(5/2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ----------------------------------------------- +--R +--------------+ +--R 2 2 2 +-------+ | 2 +--R (e x + 2d e x + d )\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 43 + +--S 44 of 764 +--r0:=2/3*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+_ +-- 4/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-_ +-- b*d*e+a*e^2)^2*sqrt(d+e*x))-1/3*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+_ +-- b^2*d*e-8*a*c*d*e+a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*_ +-- sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+_ +-- 2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*(c*d^2-_ +-- b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2))+1/3*(c^2*d^2+b^2*e^2-_ +-- c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 44 + +--S 45 of 764 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 764 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 764 +--r0:=-2*(d+e*x)^(7/2)/sqrt(a+b*x+c*x^2)+14/5*e^2*(d+e*x)^(3/2)*_ +-- sqrt(a+b*x+c*x^2)/c+56/15*e^2*(2*c*d-b*e)*sqrt(d+e*x)*sqrt(a+_ +-- b*x+c*x^2)/c^2-7/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(-2*c*(15*c^2*d^3+4*b*e^2*(b*d+a*e)-_ +-- c*d*e*(11*b*d+17*a*e))+e*(23*c^2*d^2+8*b^2*e^2-c*e*(23*b*d+9*a*e))*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(7/2)*sqrt(2)*sqrt(a+b*x+c*x^2))-7/15*(23*c^2*d^2+8*b^2*e^2-_ +-- c*e*(23*b*d+9*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(7/2)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 47 + +--S 48 of 764 +--d0:=D(m0,x) +--E 48 + +)clear all + +--S 49 of 764 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 764 +--r0:=-2*(d+e*x)^(5/2)/sqrt(a+b*x+c*x^2)+10/3*e^2*sqrt(d+e*x)*_ +-- sqrt(a+b*x+c*x^2)/c-5/3*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*(3*c*d^2-e*(b*d+a*e))+_ +-- e*(2*c*d-b*e)*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(5/2)*sqrt(a+b*x+c*x^2))-5/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- sqrt(a+b*x+c*x^2)) +--E 50 + +--S 51 of 764 +--d0:=D(m0,x) +--E 51 + +)clear all + +--S 52 of 764 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 764 +--r0:=-2*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2)+3*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))^(3/2)*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*sqrt(2)*sqrt(a+b*x+c*x^2))-3*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 53 + +--S 54 of 764 +--d0:=D(m0,x) +--E 54 + +)clear all + +--S 55 of 764 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 55 + +--S 56 of 764 +--r0:=-2*sqrt(d+e*x)/sqrt(a+b*x+c*x^2)+elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/(sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 56 + +--S 57 of 764 +--d0:=D(m0,x) +--E 57 + +)clear all + +--S 58 of 764 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------- +--R +--------------+ +--R 2 +-------+ | 2 +--R (c x + b x + a)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 58 + +--S 59 of 764 +--r0:=-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ +-- (c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2))-elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))^(3/2)*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+_ +-- c*x^2))+elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 59 + +--S 60 of 764 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 764 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R 2c x + b +--R ------------------------------------------------------------------------ +--R +--------------+ +--R 3 2 +-------+ | 2 +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 764 +--r0:=-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-_ +-- b*d*e+a*e^2)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))+4*e^2*(2*c*d-b*e)*_ +-- sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))-_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(3*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-_ +-- c*e*(3*b*d+a*e-2*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- ((c*d^2-b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2))+(2*c*d-b*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 62 + +--S 63 of 764 +--d0:=D(m0,x) +--E 63 + +)clear all + +--S 64 of 764 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 764 +--r0:=-2/3*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(3/2)-14/3*e*(d+e*x)^(3/2)*(b*d-_ +-- 2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+14/3*e^2*(2*c*d-_ +-- b*e)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*(b^2-4*a*c))+7/3*e*_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*d*e+a*b*e^2)-_ +-- (c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))-_ +-- 7/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- (b^2-4*a*c)*sqrt(a+b*x+c*x^2)) +--E 65 + +--S 66 of 764 +--d0:=D(m0,x) +--E 66 + +)clear all + +--S 67 of 764 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 764 +--r0:=-2/3*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2)-10/3*e*(b*d-2*a*e+(2*c*d-_ +-- b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+5/3*e*_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+2*d*_ +-- sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*(b^2-_ +-- 4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))-5/3*(2*c*d-b*e)*elliptic_e(_ +-- asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*_ +-- (b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 68 + +--S 69 of 764 +--d0:=D(m0,x) +--E 69 + +)clear all + +--S 70 of 764 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 70 + +--S 71 of 764 +--r0:=-2/3*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2)-2*e*(b+2*c*x)*sqrt(d+e*x)/_ +-- ((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+e*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(sqrt(c)*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2))-_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 71 + +--S 72 of 764 +--d0:=D(m0,x) +--E 72 + +)clear all + +--S 73 of 764 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 73 + +--S 74 of 764 +--r0:=-2/3*sqrt(d+e*x)/(a+b*x+c*x^2)^(3/2)-2/3*e*(b*c*d-b^2*e+2*a*c*e+c*_ +-- (2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(a+b*x+c*x^2))+1/3*e*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+_ +-- 2*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- ((b^2-4*a*c)*(c*d^2-e*(b*d-a*e))*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*(c*d^2-e*(b*d-a*e))*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 74 + +--S 75 of 764 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 764 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R (1) +--R 2c x + b +--R ------------------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 +-------+ | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 764 +--r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-_ +-- 4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-2/3*e*(3*b^2*c*d*e-_ +-- 8*a*c^2*d*e-2*b^3*e^2-b*c*(c*d^2-7*a*e^2)-2*c*(c^2*d^2+b^2*e^2-_ +-- c*e*(b*d+3*a*e))*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(a+b*x+c*x^2))-1/3*e*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*d*e+_ +-- a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2))+1/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-_ +-- 4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 77 + +--S 78 of 764 +--d0:=D(m0,x) +--E 78 + +)clear all + +--S 79 of 764 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 m +--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(e x + d) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 764 +r0:=-(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(b*d-a*e)*(3*b*B*d-_ + 2*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^4*(2+m))-b*(3*b*B*d-A*b*e-2*a*B*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+b^2*B*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 m + 4 +--R (B b m + 6B b m + 11B b m + 6B b )(e x + d) +--R + +--R 2 2 3 2 2 2 +--R ((A b + 2B a b)e - 3B b d)m + ((7A b + 14B a b)e - 21B b d)m +--R + +--R 2 2 2 2 +--R ((14A b + 28B a b)e - 42B b d)m + (8A b + 16B a b)e - 24B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (- 2A b - 4B a b)d e + 3B b d )m +--R + +--R 2 2 2 2 2 2 +--R ((16A a b + 8B a )e + (- 16A b - 32B a b)d e + 24B b d )m +--R + +--R 2 2 2 2 2 +--R ((38A a b + 19B a )e + (- 38A b - 76B a b)d e + 57B b d )m +--R + +--R 2 2 2 2 2 +--R (24A a b + 12B a )e + (- 24A b - 48B a b)d e + 36B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (- 2A a b - B a )d e + (A b + 2B a b)d e - B b d )m +--R + +--R 2 3 2 2 2 2 +--R 9A a e + (- 18A a b - 9B a )d e + (9A b + 18B a b)d e +--R + +--R 2 3 +--R - 9B b d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 2 +--R 26A a e + (- 52A a b - 26B a )d e + (26A b + 52B a b)d e +--R + +--R 2 3 +--R - 26B b d +--R * +--R m +--R + +--R 2 3 2 2 2 2 2 3 +--R 24A a e + (- 48A a b - 24B a )d e + (24A b + 48B a b)d e - 24B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 80 + +--S 81 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 of 764 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 5 8 2 5 2 4 7 +--R B b e x + ((A b + 2B a b)e + 5B b d e )x +--R + +--R 2 5 2 4 2 2 3 6 +--R ((2A a b + B a )e + (5A b + 10B a b)d e + 10B b d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 5 +--R (A a e + (10A a b + 5B a )d e + (10A b + 20B a b)d e + 10B b d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 4 4 +--R (5A a d e + (20A a b + 10B a )d e + (10A b + 20B a b)d e + 5B b d e)x +--R + +--R 2 2 3 2 3 2 2 4 2 5 3 +--R (10A a d e + (20A a b + 10B a )d e + (5A b + 10B a b)d e + B b d )x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 82 + +--S 83 of 764 +r0:=-1/6*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^6/e^4+1/7*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^7/e^4-1/8*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^8/e^4+_ + 1/9*b^2*B*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 2 9 9 1 2 1 9 5 2 8 8 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 9 5 2 10 8 10 2 2 7 7 +--R ((- A a b + - B a )e + (- A b + -- B a b)d e + -- B b d e )x +--R 7 7 7 7 7 +--R + +--R 1 2 9 5 5 2 8 5 2 10 2 7 +--R - A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e +--R 6 3 6 3 3 +--R + +--R 5 2 3 6 +--R - B b d e +--R 3 +--R * +--R 6 +--R x +--R + +--R 2 8 2 2 7 2 3 6 2 4 5 5 +--R (A a d e + (4A a b + 2B a )d e + (2A b + 4B a b)d e + B b d e )x +--R + +--R 5 2 2 7 5 2 3 6 5 2 5 4 5 +--R - A a d e + (5A a b + - B a )d e + (- A b + - B a b)d e +--R 2 2 4 2 +--R + +--R 1 2 5 4 +--R - B b d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 10 2 3 6 10 5 2 4 5 1 2 2 5 4 3 +--R (-- A a d e + (-- A a b + - B a )d e + (- A b + - B a b)d e )x +--R 3 3 3 3 3 +--R + +--R 5 2 4 5 1 2 5 4 2 2 5 4 1 2 6 3 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 1 1 2 7 2 1 2 1 8 1 2 9 +--R (- -- A a b - -- B a )d e + (--- A b + -- B a b)d e - --- B b d +--R 21 42 168 84 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 83 + +--S 84 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 764 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 7 2 4 2 3 6 +--R B b e x + ((A b + 2B a b)e + 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((2A a b + B a )e + (4A b + 8B a b)d e + 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (A a e + (8A a b + 4B a )d e + (6A b + 12B a b)d e + 4B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 3 +--R (4A a d e + (12A a b + 6B a )d e + (4A b + 8B a b)d e + B b d )x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 85 + +--S 86 of 764 +r0:=-1/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^5/e^4+1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^6/e^4-1/7*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^7/e^4+_ + 1/8*b^2*B*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 2 8 8 1 2 2 8 4 2 7 7 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 8 7 7 7 +--R + +--R 1 1 2 8 2 2 4 7 2 2 6 6 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + B b d e )x +--R 3 6 3 3 +--R + +--R 1 2 8 8 4 2 7 6 2 12 2 6 +--R - A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e +--R 5 5 5 5 5 +--R + +--R 4 2 3 5 +--R - B b d e +--R 5 +--R * +--R 5 +--R x +--R + +--R 2 7 3 2 2 6 2 3 5 1 2 4 4 4 +--R (A a d e + (3A a b + - B a )d e + (A b + 2B a b)d e + - B b d e )x +--R 2 4 +--R + +--R 2 2 6 8 4 2 3 5 1 2 2 4 4 3 +--R (2A a d e + (- A a b + - B a )d e + (- A b + - B a b)d e )x +--R 3 3 3 3 +--R + +--R 2 3 5 1 2 4 4 2 2 4 4 1 2 5 3 +--R (2A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 5 +--R + +--R 1 1 2 6 2 1 2 2 7 1 2 8 +--R (- -- A a b - -- B a )d e + (--- A b + --- B a b)d e - --- B b d +--R 15 30 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 86 + +--S 87 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 764 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 88 + +--S 89 of 764 +r0:=-1/4*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^4/e^4+1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^5/e^4-1/6*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^6/e^4+_ + 1/7*b^2*B*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 2 7 7 1 2 1 7 1 2 6 6 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 7 6 3 2 +--R + +--R 2 1 2 7 3 2 6 6 3 2 2 5 5 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + - B b d e )x +--R 5 5 5 5 5 +--R + +--R 1 2 7 3 3 2 6 3 2 3 2 5 +--R - A a e + (- A a b + - B a )d e + (- A b + - B a b)d e +--R 4 2 4 4 2 +--R + +--R 1 2 3 4 +--R - B b d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 1 2 2 3 4 3 +--R (A a d e + (2A a b + B a )d e + (- A b + - B a b)d e )x +--R 3 3 +--R + +--R 3 2 2 5 1 2 3 4 2 2 3 4 1 2 4 3 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 4 +--R + +--R 1 1 2 5 2 1 2 1 6 1 2 7 +--R (- -- A a b - -- B a )d e + (-- A b + -- B a b)d e - --- B b d +--R 10 20 60 30 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 764 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 764 +r0:=1/3*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^3/b^4+1/4*(b*d-a*e)*(b*B*d+2*A*b*e-_ + 3*a*B*e)*(a+b*x)^4/b^4+1/5*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^5/b^4+_ + 1/6*B*e^2*(a+b*x)^6/b^4 +--R +--R +--R (2) +--R 1 6 2 6 1 6 2 5 2 2 6 5 +--R - B b e x + ((- A b + - B a b )e + - B b d e)x +--R 6 5 5 5 +--R + +--R 1 5 1 2 4 2 1 6 5 1 6 2 4 +--R ((- A a b + - B a b )e + (- A b + B a b )d e + - B b d )x +--R 2 4 2 4 +--R + +--R 1 2 4 2 4 5 2 2 4 1 6 2 5 2 3 +--R (- A a b e + (- A a b + - B a b )d e + (- A b + - B a b )d )x +--R 3 3 3 3 3 +--R + +--R 2 4 5 1 2 4 2 2 2 4 2 +--R (A a b d e + (A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 5 1 6 2 1 4 2 1 5 +--R (-- A a b - -- B a )e + (- - A a b + -- B a b)d e +--R 30 60 6 15 +--R + +--R 1 3 3 1 4 2 2 +--R (- A a b - -- B a b )d +--R 3 12 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 764 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 94 + +--S 95 of 764 +r0:=1/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)^3/b^3+1/4*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^4/b^3+1/5*B*e*(a+b*x)^5/b^3 +--R +--R +--R (2) +--R 1 5 5 1 5 1 4 1 5 4 +--R - B b e x + ((- A b + - B a b )e + - B b d)x +--R 5 4 2 4 +--R + +--R 2 4 1 2 3 1 5 2 4 3 +--R ((- A a b + - B a b )e + (- A b + - B a b )d)x +--R 3 3 3 3 +--R + +--R 1 2 3 4 1 2 3 2 2 3 +--R (- A a b e + (A a b + - B a b )d)x + A a b d x +--R 2 2 +--R + +--R 1 4 1 5 1 3 2 1 4 +--R (- -- A a b + -- B a )e + (- A a b - -- B a b)d +--R 12 30 3 12 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 95 + +--S 96 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 97 + +--S 98 of 764 +r0:=1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2 +--R +--R +--R (2) +--R 1 4 4 1 4 2 3 3 3 1 2 2 2 2 2 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x + A a b x +--R 4 3 3 2 +--R + +--R 1 3 1 4 +--R - A a b - -- B a +--R 3 12 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 98 + +--S 99 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 100 + +--S 101 of 764 +r0:=b*(b*d-a*e)*(B*d-A*e)*x/e^3-1/2*(B*d-A*e)*(a+b*x)^2/e^2+_ + 1/3*B*(a+b*x)^3/(b*e)-(b*d-a*e)^2*(B*d-A*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 +--R 6A a b e + (- 12A a b - 6B a b)d e + (6A b + 12B a b )d e +--R + +--R 3 3 +--R - 6B b d +--R * +--R log(e x + d) +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 2B b e x + ((3A b + 6B a b )e - 3B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((12A a b + 6B a b)e + (- 6A b - 12B a b )d e + 6B b d e)x +--R + +--R 2 3 3 2 2 +--R (3A a b + 2B a )e - 3B a b d e +--R / +--R 4 +--R 6b e +--R Type: Expression(Integer) +--E 101 + +--S 102 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 103 + +--S 104 of 764 +r0:=-b*(2*b*B*d-A*b*e-2*a*B*e)*x/e^3+1/2*b^2*B*x^2/e^2+(b*d-a*e)^2*_ + (B*d-A*e)/(e^4*(d+e*x))+(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 2 +--R ((4A a b + 2B a )e + (- 4A b - 8B a b)d e + 6B b d e)x +--R + +--R 2 2 2 2 2 3 +--R (4A a b + 2B a )d e + (- 4A b - 8B a b)d e + 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 3 2 2 2 +--R B b e x + ((2A b + 4B a b)e - 3B b d e )x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A b + 4B a b)d e - 4B b d e)x - 2A a e + (4A a b + 2B a )d e +--R + +--R 2 2 2 3 +--R (- 2A b - 4B a b)d e + 2B b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 104 + +--S 105 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 764 +r0:=b^2*B*x/e^3+1/2*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^2)-(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x))-b*(3*b*B*d-A*b*e-2*a*B*e)*_ + log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R ((2A b + 4B a b)e - 6B b d e )x +--R + +--R 2 2 2 2 2 2 2 3 +--R ((4A b + 8B a b)d e - 12B b d e)x + (2A b + 4B a b)d e - 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 +--R 2B b e x + 4B b d e x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 4A a b - 2B a )e + (4A b + 8B a b)d e - 4B b d e)x - A a e +--R + +--R 2 2 2 2 2 3 +--R (- 2A a b - B a )d e + (3A b + 6B a b)d e - 5B b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 107 + +--S 108 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 109 + +--S 110 of 764 +r0:=-1/3*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^3)-1/2*B*(b*d-a*e)^2/_ + (e^4*(d+e*x)^2)+2*b*B*(b*d-a*e)/(e^4*(d+e*x))+b^2*B*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 4 3 3 3 2 3 3 2 2 2 +--R (6B a b e - 6B b d e )x + (18B a b d e - 18B b d e )x +--R + +--R 2 2 2 3 3 2 3 3 4 +--R (18B a b d e - 18B b d e)x + 6B a b d e - 6B b d +--R * +--R log(e x + d) +--R + +--R 3 4 3 3 3 +--R (- 2A b e + 2B b d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 6A a b - 12B a b)e + 30B a b d e - 12B b d e )x +--R + +--R 2 3 4 2 3 2 2 2 3 3 +--R ((- 6A a b - 3B a )e - 9B a b d e + 39B a b d e - 21B b d e)x +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 +--R - 2A a e - B a d e - 3B a b d e + 15B a b d e - 9B b d +--R / +--R 8 7 3 7 2 6 2 2 6 3 5 +--R (6a e - 6b d e )x + (18a d e - 18b d e )x + (18a d e - 18b d e )x +--R + +--R 3 5 4 4 +--R 6a d e - 6b d e +--R Type: Expression(Integer) +--E 110 + +--S 111 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 112 + +--S 113 of 764 +r0:=-1/4*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^4)+1/12*(3*b*B*d+A*b*e-_ + 4*a*B*e)*(a+b*x)^3/(e*(b*d-a*e)^2*(d+e*x)^3) +--R +--R +--R (2) +--R 1 4 1 3 1 4 4 +--R ((-- A b - - B a b )e + - B b d)x +--R 12 3 4 +--R + +--R 2 2 1 4 2 3 3 +--R (- B a b e + (- A b + - B a b )d)x +--R 3 3 +--R + +--R 1 2 2 3 3 1 2 2 2 +--R ((- - A a b - B a b)e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 2 3 1 4 2 2 1 4 1 3 1 4 +--R ((- - A a b - - B a )e + A a b d)x - - A a e + (- A a b - -- B a )d +--R 3 3 4 3 12 +--R / +--R 2 6 5 2 2 4 4 2 5 2 4 2 3 3 3 +--R (a e - 2a b d e + b d e )x + (4a d e - 8a b d e + 4b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (6a d e - 12a b d e + 6b d e )x + (4a d e - 8a b d e + 4b d e)x +--R + +--R 2 4 2 5 2 6 +--R a d e - 2a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 113 + +--S 114 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 of 764 +r0:=1/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^5)-1/4*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^4)+1/3*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^3)-_ + 1/2*b^2*B/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 3 3 1 2 2 3 1 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - - B b d e )x +--R 2 3 3 2 +--R + +--R 1 1 2 3 1 2 1 2 1 2 2 +--R ((- - A a b - - B a )e + (- - A b - - B a b)d e - - B b d e)x +--R 2 4 6 3 4 +--R + +--R 1 2 3 1 1 2 2 1 2 1 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A b - -- B a b)d e +--R 5 10 20 30 15 +--R + +--R 1 2 3 +--R - -- B b d +--R 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 116 + +--S 117 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 of 764 +r0:=1/6*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^6)-1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^5)+1/4*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^4)-_ + 1/3*b^2*B/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 3 3 1 2 1 3 1 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - - B b d e )x +--R 3 4 2 4 +--R + +--R 2 1 2 3 1 2 1 2 1 2 2 +--R ((- - A a b - - B a )e + (- -- A b - - B a b)d e - -- B b d e)x +--R 5 5 10 5 10 +--R + +--R 1 2 3 1 1 2 2 1 2 1 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A b - -- B a b)d e +--R 6 15 30 60 30 +--R + +--R 1 2 3 +--R - -- B b d +--R 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 119 + +--S 120 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^8 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 764 +r0:=1/7*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^7)-1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^6)+1/5*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^5)-_ + 1/4*b^2*B/(e^4*(d+e*x)^4) +--R +--R +--R (2) +--R 1 2 3 3 1 2 2 3 3 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - -- B b d e )x +--R 4 5 5 20 +--R + +--R 1 1 2 3 1 2 2 2 1 2 2 +--R ((- - A a b - - B a )e + (- -- A b - -- B a b)d e - -- B b d e)x +--R 3 6 15 15 20 +--R + +--R 1 2 3 1 1 2 2 1 2 2 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- --- A b - --- B a b)d e +--R 7 21 42 105 105 +--R + +--R 1 2 3 +--R - --- B b d +--R 140 +--R / +--R 11 7 10 6 2 9 5 3 8 4 4 7 3 5 6 2 6 5 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 4 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 122 + +--S 123 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 764 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 124 + +--S 125 of 764 +r0:=-(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(1+m)/(e^6*(1+m))+(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^6*(2+m))-2*b*(b*d-a*e)^2*(5*b*B*d-_ + 3*A*b*e-2*a*B*e)*(d+e*x)^(3+m)/(e^6*(3+m))+2*b^2*(b*d-a*e)*(5*b*B*d-_ + 2*A*b*e-3*a*B*e)*(d+e*x)^(4+m)/(e^6*(4+m))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+b^4*B*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 4 5 4 4 4 3 4 2 4 4 +--R (B b m + 15B b m + 85B b m + 225B b m + 274B b m + 120B b ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 4 3 4 5 4 3 4 4 +--R ((A b + 4B a b )e - 5B b d)m + ((16A b + 64B a b )e - 80B b d)m +--R + +--R 4 3 4 3 +--R ((95A b + 380B a b )e - 475B b d)m +--R + +--R 4 3 4 2 +--R ((260A b + 1040B a b )e - 1300B b d)m +--R + +--R 4 3 4 4 3 +--R ((324A b + 1296B a b )e - 1620B b d)m + (144A b + 576B a b )e +--R + +--R 4 +--R - 720B b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (- 4A b - 16B a b )d e + 10B b d )m +--R + +--R 3 2 2 2 4 3 4 2 4 +--R ((68A a b + 102B a b )e + (- 68A b - 272B a b )d e + 170B b d )m +--R + +--R 3 2 2 2 4 3 +--R (428A a b + 642B a b )e + (- 428A b - 1712B a b )d e +--R + +--R 4 2 +--R 1070B b d +--R * +--R 3 +--R m +--R + +--R 3 2 2 2 4 3 +--R (1228A a b + 1842B a b )e + (- 1228A b - 4912B a b )d e +--R + +--R 4 2 +--R 3070B b d +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 4 3 +--R (1584A a b + 2376B a b )e + (- 1584A b - 6336B a b )d e +--R + +--R 4 2 +--R 3960B b d +--R * +--R m +--R + +--R 3 2 2 2 4 3 4 2 +--R (720A a b + 1080B a b )e + (- 720A b - 2880B a b )d e + 1800B b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (- 12A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (6A b + 24B a b )d e - 10B b d +--R * +--R 5 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (108A a b + 72B a b)e + (- 216A a b - 324B a b )d e +--R + +--R 4 3 2 4 3 +--R (108A b + 432B a b )d e - 180B b d +--R * +--R 4 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (726A a b + 484B a b)e + (- 1452A a b - 2178B a b )d e +--R + +--R 4 3 2 4 3 +--R (726A b + 2904B a b )d e - 1210B b d +--R * +--R 3 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (2232A a b + 1488B a b)e + (- 4464A a b - 6696B a b )d e +--R + +--R 4 3 2 4 3 +--R (2232A b + 8928B a b )d e - 3720B b d +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (3048A a b + 2032B a b)e + (- 6096A a b - 9144B a b )d e +--R + +--R 4 3 2 4 3 +--R (3048A b + 12192B a b )d e - 5080B b d +--R * +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (1440A a b + 960B a b)e + (- 2880A a b - 4320B a b )d e +--R + +--R 4 3 2 4 3 +--R (1440A b + 5760B a b )d e - 2400B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (12A a b + 18B a b )d e + (- 4A b - 16B a b )d e + 5B b d +--R * +--R 5 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (76A a b + 19B a )e + (- 228A a b - 152B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (228A a b + 342B a b )d e + (- 76A b - 304B a b )d e + 95B b d +--R * +--R 4 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (548A a b + 137B a )e + (- 1644A a b - 1096B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1644A a b + 2466B a b )d e + (- 548A b - 2192B a b )d e +--R + +--R 4 4 +--R 685B b d +--R * +--R 3 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (1844A a b + 461B a )e + (- 5532A a b - 3688B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (5532A a b + 8298B a b )d e + (- 1844A b - 7376B a b )d e +--R + +--R 4 4 +--R 2305B b d +--R * +--R 2 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (2808A a b + 702B a )e + (- 8424A a b - 5616B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (8424A a b + 12636B a b )d e + (- 2808A b - 11232B a b )d e +--R + +--R 4 4 +--R 3510B b d +--R * +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (1440A a b + 360B a )e + (- 4320A a b - 2880B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (4320A a b + 6480B a b )d e + (- 1440A b - 5760B a b )d e +--R + +--R 4 4 +--R 1800B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (- 4A a b - B a )d e + (6A a b + 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 4A a b - 6B a b )d e + (A b + 4B a b )d e - B b d +--R * +--R 5 +--R m +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 20A a e + (- 80A a b - 20B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 80A a b - 120B a b )d e + (20A b + 80B a b )d e - 20B b d +--R * +--R 4 +--R m +--R + +--R 4 5 3 4 4 +--R 155A a e + (- 620A a b - 155B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (930A a b + 620B a b)d e + (- 620A a b - 930B a b )d e +--R + +--R 4 3 4 4 5 +--R (155A b + 620B a b )d e - 155B b d +--R * +--R 3 +--R m +--R + +--R 4 5 3 4 4 +--R 580A a e + (- 2320A a b - 580B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (3480A a b + 2320B a b)d e + (- 2320A a b - 3480B a b )d e +--R + +--R 4 3 4 4 5 +--R (580A b + 2320B a b )d e - 580B b d +--R * +--R 2 +--R m +--R + +--R 4 5 3 4 4 +--R 1044A a e + (- 4176A a b - 1044B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (6264A a b + 4176B a b)d e + (- 4176A a b - 6264B a b )d e +--R + +--R 4 3 4 4 5 +--R (1044A b + 4176B a b )d e - 1044B b d +--R * +--R m +--R + +--R 4 5 3 4 4 +--R 720A a e + (- 2880A a b - 720B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (4320A a b + 2880B a b)d e + (- 2880A a b - 4320B a b )d e +--R + +--R 4 3 4 4 5 +--R (720A b + 2880B a b )d e - 720B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 125 + +--S 126 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 of 764 +t0:=(A+B*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 7 12 4 3 7 4 6 11 +--R B b e x + ((A b + 4B a b )e + 7B b d e )x +--R + +--R 3 2 2 7 4 3 6 4 2 5 10 +--R ((4A a b + 6B a b )e + (7A b + 28B a b )d e + 21B b d e )x +--R + +--R 2 2 3 7 3 2 2 6 +--R (6A a b + 4B a b)e + (28A a b + 42B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (21A b + 84B a b )d e + 35B b d e +--R * +--R 9 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (4A a b + B a )e + (42A a b + 28B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 4 4 3 +--R (84A a b + 126B a b )d e + (35A b + 140B a b )d e + 35B b d e +--R * +--R 8 +--R x +--R + +--R 4 7 3 4 6 2 2 3 2 5 +--R A a e + (28A a b + 7B a )d e + (126A a b + 84B a b)d e +--R + +--R 3 2 2 3 4 4 3 4 3 4 5 2 +--R (140A a b + 210B a b )d e + (35A b + 140B a b )d e + 21B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 2 5 2 2 3 3 4 +--R 7A a d e + (84A a b + 21B a )d e + (210A a b + 140B a b)d e +--R + +--R 3 2 2 4 3 4 3 5 2 4 6 +--R (140A a b + 210B a b )d e + (21A b + 84B a b )d e + 7B b d e +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 4 3 4 2 2 3 4 3 +--R 21A a d e + (140A a b + 35B a )d e + (210A a b + 140B a b)d e +--R + +--R 3 2 2 5 2 4 3 6 4 7 +--R (84A a b + 126B a b )d e + (7A b + 28B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 3 4 3 4 4 3 2 2 3 5 2 +--R 35A a d e + (140A a b + 35B a )d e + (126A a b + 84B a b)d e +--R + +--R 3 2 2 6 4 3 7 +--R (28A a b + 42B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 4 3 3 4 5 2 2 2 3 6 +--R 35A a d e + (84A a b + 21B a )d e + (42A a b + 28B a b)d e +--R + +--R 3 2 2 7 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 4 6 2 2 3 7 2 +--R (21A a d e + (28A a b + 7B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 6 3 4 7 4 7 +--R (7A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 127 + +--S 128 of 764 +r0:=-1/8*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^8/e^6+1/9*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^9/e^6-1/5*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^10/e^6+2/11*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^11/e^6-1/12*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^12/e^6+_ + 1/13*b^4*B*(d+e*x)^13/e^6 +--R +--R +--R (2) +--R 1 4 13 13 1 4 1 3 13 7 4 12 12 +--R -- B b e x + ((-- A b + - B a b )e + -- B b d e )x +--R 13 12 3 12 +--R + +--R 4 3 6 2 2 13 7 4 28 3 12 +--R (-- A a b + -- B a b )e + (-- A b + -- B a b )d e +--R 11 11 11 11 +--R + +--R 21 4 2 11 +--R -- B b d e +--R 11 +--R * +--R 11 +--R x +--R + +--R 3 2 2 2 3 13 14 3 21 2 2 12 +--R (- A a b + - B a b)e + (-- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 21 4 42 3 2 11 7 4 3 10 +--R (-- A b + -- B a b )d e + - B b d e +--R 10 5 2 +--R * +--R 10 +--R x +--R + +--R 4 3 1 4 13 14 2 2 28 3 12 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 9 9 3 9 +--R + +--R 28 3 2 2 2 11 35 4 140 3 3 10 35 4 4 9 +--R (-- A a b + 14B a b )d e + (-- A b + --- B a b )d e + -- B b d e +--R 3 9 9 9 +--R * +--R 9 +--R x +--R + +--R 1 4 13 7 3 7 4 12 63 2 2 21 3 2 11 +--R - A a e + (- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 8 2 8 4 2 +--R + +--R 35 3 105 2 2 3 10 35 4 35 3 4 9 21 4 5 8 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + -- B b d e +--R 2 4 8 2 8 +--R * +--R 8 +--R x +--R + +--R 4 12 3 4 2 11 2 2 3 3 10 +--R A a d e + (12A a b + 3B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 4 9 4 3 5 8 4 6 7 +--R (20A a b + 30B a b )d e + (3A b + 12B a b )d e + B b d e +--R * +--R 7 +--R x +--R + +--R 7 4 2 11 70 3 35 4 3 10 2 2 70 3 4 9 +--R - A a d e + (-- A a b + -- B a )d e + (35A a b + -- B a b)d e +--R 2 3 6 3 +--R + +--R 3 2 2 5 8 7 4 14 3 6 7 1 4 7 6 +--R (14A a b + 21B a b )d e + (- A b + -- B a b )d e + - B b d e +--R 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 3 10 3 4 4 9 126 2 2 84 3 5 8 +--R 7A a d e + (28A a b + 7B a )d e + (--- A a b + -- B a b)d e +--R 5 5 +--R + +--R 28 3 42 2 2 6 7 1 4 4 3 7 6 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 35 4 4 9 3 21 4 5 8 21 2 2 3 6 7 +--R -- A a d e + (21A a b + -- B a )d e + (-- A a b + 7B a b)d e +--R 4 4 2 +--R + +--R 3 3 2 2 7 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 5 8 28 3 7 4 6 7 2 2 4 3 7 6 3 +--R (7A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d e )x +--R 3 3 3 +--R + +--R 7 4 6 7 3 1 4 7 6 2 4 7 6 1 4 8 5 +--R (- A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 8 +--R + +--R 1 3 1 4 9 4 1 2 2 1 3 10 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 18 72 60 90 +--R + +--R 1 3 1 2 2 11 2 1 4 1 3 12 +--R (- --- A a b - --- B a b )d e + (---- A b + --- B a b )d e +--R 330 220 3960 990 +--R + +--R 1 4 13 +--R - ----- B b d +--R 10296 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 128 + +--S 129 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 764 +t0:=(A+B*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 11 4 3 6 4 5 10 +--R B b e x + ((A b + 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 6 4 3 5 4 2 4 9 +--R ((4A a b + 6B a b )e + (6A b + 24B a b )d e + 15B b d e )x +--R + +--R 2 2 3 6 3 2 2 5 +--R (6A a b + 4B a b)e + (24A a b + 36B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (15A b + 60B a b )d e + 20B b d e +--R * +--R 8 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (4A a b + B a )e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 4 4 2 +--R (60A a b + 90B a b )d e + (20A b + 80B a b )d e + 15B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 5 2 2 3 2 4 +--R A a e + (24A a b + 6B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 3 3 4 3 4 2 4 5 +--R (80A a b + 120B a b )d e + (15A b + 60B a b )d e + 6B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 6A a d e + (60A a b + 15B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (60A a b + 90B a b )d e + (6A b + 24B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A a d e + (80A a b + 20B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 5 4 3 6 +--R (24A a b + 36B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 4 4 2 2 2 3 5 +--R 20A a d e + (60A a b + 15B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 6 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 2 +--R (15A a d e + (24A a b + 6B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 5 3 4 6 4 6 +--R (6A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 130 + +--S 131 of 764 +r0:=-1/7*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^7/e^6+1/8*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^8/e^6-2/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^9/e^6+1/5*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^10/e^6-1/11*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^11/e^6+_ + 1/12*b^4*B*(d+e*x)^12/e^6 +--R +--R +--R (2) +--R 1 4 12 12 1 4 4 3 12 6 4 11 11 +--R -- B b e x + ((-- A b + -- B a b )e + -- B b d e )x +--R 12 11 11 11 +--R + +--R 2 3 3 2 2 12 3 4 12 3 11 3 4 2 10 10 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e )x +--R 5 5 5 5 2 +--R + +--R 2 2 2 4 3 12 8 3 2 2 11 +--R (- A a b + - B a b)e + (- A a b + 4B a b )d e +--R 3 9 3 +--R + +--R 5 4 20 3 2 10 20 4 3 9 +--R (- A b + -- B a b )d e + -- B b d e +--R 3 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 1 4 12 9 2 2 3 11 +--R (- A a b + - B a )e + (- A a b + 3B a b)d e +--R 2 8 2 +--R + +--R 15 3 45 2 2 2 10 5 4 3 3 9 15 4 4 8 +--R (-- A a b + -- B a b )d e + (- A b + 10B a b )d e + -- B b d e +--R 2 4 2 8 +--R * +--R 8 +--R x +--R + +--R 1 4 12 24 3 6 4 11 90 2 2 60 3 2 10 +--R - A a e + (-- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 80 3 120 2 2 3 9 15 4 60 3 4 8 6 4 5 7 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 4 11 3 5 4 2 10 2 2 40 3 3 9 +--R A a d e + (10A a b + - B a )d e + (20A a b + -- B a b)d e +--R 2 3 +--R + +--R 3 2 2 4 8 4 3 5 7 1 4 6 6 +--R (10A a b + 15B a b )d e + (A b + 4B a b )d e + - B b d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 4 2 10 3 4 3 9 2 2 3 4 8 +--R 3A a d e + (16A a b + 4B a )d e + (18A a b + 12B a b)d e +--R + +--R 24 3 36 2 2 5 7 1 4 4 3 6 6 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 3 9 3 15 4 4 8 2 2 3 5 7 +--R 5A a d e + (15A a b + -- B a )d e + (9A a b + 6B a b)d e +--R 4 +--R + +--R 3 3 2 2 6 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 4 8 3 4 5 7 2 2 4 3 6 6 3 +--R (5A a d e + (8A a b + 2B a )d e + (2A a b + - B a b)d e )x +--R 3 +--R + +--R 4 5 7 3 1 4 6 6 2 4 6 6 1 4 7 5 +--R (3A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 7 +--R + +--R 1 3 1 4 8 4 1 2 2 1 3 9 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 14 56 42 63 +--R + +--R 1 3 1 2 2 10 2 1 4 2 3 11 +--R (- --- A a b - --- B a b )d e + (---- A b + ---- B a b )d e +--R 210 140 2310 1155 +--R + +--R 1 4 12 +--R - ---- B b d +--R 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 131 + +--S 132 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 764 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 10 4 3 5 4 4 9 +--R B b e x + ((A b + 4B a b )e + 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 8 +--R ((4A a b + 6B a b )e + (5A b + 20B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (6A a b + 4B a b)e + (20A a b + 30B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (10A b + 40B a b )d e + 10B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b + B a )e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (40A a b + 60B a b )d e + (10A b + 40B a b )d e + 5B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (20A a b + 5B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (40A a b + 60B a b )d e + (5A b + 20B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R 5A a d e + (40A a b + 10B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 4 4 3 5 +--R (20A a b + 30B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 3 2 2 2 3 4 +--R 10A a d e + (40A a b + 10B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 5 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 2 +--R (10A a d e + (20A a b + 5B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 4 3 4 5 4 5 +--R (5A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 133 + +--S 134 of 764 +r0:=-1/6*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^6/e^6+1/7*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^7/e^6-1/4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^8/e^6+2/9*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^9/e^6-1/10*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^10/e^6+_ + 1/11*b^4*B*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 4 11 11 1 4 2 3 11 1 4 10 10 +--R -- B b e x + ((-- A b + - B a b )e + - B b d e )x +--R 11 10 5 2 +--R + +--R 4 3 2 2 2 11 5 4 20 3 10 10 4 2 9 9 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + -- B b d e )x +--R 9 3 9 9 9 +--R + +--R 3 2 2 1 3 11 5 3 15 2 2 10 +--R (- A a b + - B a b)e + (- A a b + -- B a b )d e +--R 4 2 2 4 +--R + +--R 5 4 3 2 9 5 4 3 8 +--R (- A b + 5B a b )d e + - B b d e +--R 4 4 +--R * +--R 8 +--R x +--R + +--R 4 3 1 4 11 30 2 2 20 3 10 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 7 7 7 7 +--R + +--R 40 3 60 2 2 2 9 10 4 40 3 3 8 5 4 4 7 +--R (-- A a b + -- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 4 11 10 3 5 4 10 2 2 20 3 2 9 +--R - A a e + (-- A a b + - B a )d e + (10A a b + -- B a b)d e +--R 6 3 6 3 +--R + +--R 20 3 2 2 3 8 5 4 10 3 4 7 1 4 5 6 +--R (-- A a b + 10B a b )d e + (- A b + -- B a b )d e + - B b d e +--R 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 10 3 4 2 9 2 2 3 3 8 +--R A a d e + (8A a b + 2B a )d e + (12A a b + 8B a b)d e +--R + +--R 3 2 2 4 7 1 4 4 3 5 6 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 4 2 9 3 5 4 3 8 15 2 2 3 4 7 +--R - A a d e + (10A a b + - B a )d e + (-- A a b + 5B a b)d e +--R 2 2 2 +--R + +--R 3 3 2 2 5 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 10 4 3 8 20 3 5 4 4 7 2 2 4 3 5 6 3 +--R (-- A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d e )x +--R 3 3 3 3 +--R + +--R 5 4 4 7 3 1 4 5 6 2 4 5 6 1 4 6 5 +--R (- A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 2 3 1 4 7 4 1 2 2 1 3 8 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 21 42 28 42 +--R + +--R 1 3 1 2 2 9 2 1 4 1 3 10 +--R (- --- A a b - -- B a b )d e + (---- A b + --- B a b )d e +--R 126 84 1260 315 +--R + +--R 1 4 11 +--R - ---- B b d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 134 + +--S 135 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 764 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 4 9 4 3 4 4 3 8 +--R B b e x + ((A b + 4B a b )e + 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((4A a b + 6B a b )e + (4A b + 16B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (6A a b + 4B a b)e + (16A a b + 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (6A b + 24B a b )d e + 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (24A a b + 36B a b )d e + (4A b + 16B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R A a e + (16A a b + 4B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (16A a b + 24B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 4A a d e + (24A a b + 6B a )d e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 4 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (6A a d e + (16A a b + 4B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (4A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 764 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^4*(a+b*x)^5/b^6+1/6*(b*d-a*e)^3*(b*B*d+4*A*b*e-_ + 5*a*B*e)*(a+b*x)^6/b^6+2/7*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*_ + (a+b*x)^7/b^6+1/4*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^8/_ + b^6+1/9*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^9/b^6+1/10*B*e^4*_ + (a+b*x)^10/b^6 +--R +--R +--R (2) +--R 1 10 4 10 1 10 4 9 4 4 10 3 9 +--R -- B b e x + ((- A b + - B a b )e + - B b d e )x +--R 10 9 9 9 +--R + +--R 1 9 3 2 8 4 1 10 9 3 3 10 2 2 8 +--R ((- A a b + - B a b )e + (- A b + 2B a b )d e + - B b d e )x +--R 2 4 2 4 +--R + +--R 6 2 8 4 3 7 4 16 9 24 2 8 3 +--R (- A a b + - B a b )e + (-- A a b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 6 10 24 9 2 2 4 10 3 +--R (- A b + -- B a b )d e + - B b d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 2 3 7 1 4 6 4 2 8 8 3 7 3 +--R (- A a b + - B a b )e + (4A a b + - B a b )d e +--R 3 6 3 +--R + +--R 9 2 8 2 2 2 10 8 9 3 1 10 4 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d e + - B b d +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 4 6 4 16 3 7 4 4 6 3 36 2 8 24 3 7 2 2 +--R - A a b e + (-- A a b + - B a b )d e + (-- A a b + -- B a b )d e +--R 5 5 5 5 5 +--R + +--R 16 9 24 2 8 3 1 10 4 9 4 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 6 3 3 7 3 4 6 2 2 2 8 3 7 3 +--R A a b d e + (6A a b + - B a b )d e + (6A a b + 4B a b )d e +--R 2 +--R + +--R 9 3 2 8 4 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 6 2 2 16 3 7 4 4 6 3 2 8 4 3 7 4 3 +--R (2A a b d e + (-- A a b + - B a b )d e + (2A a b + - B a b )d )x +--R 3 3 3 +--R + +--R 4 6 3 3 7 1 4 6 4 2 4 6 4 +--R (2A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 9 1 10 4 1 8 2 2 9 3 +--R (--- A a b - ---- B a )e + (- -- A a b + --- B a b)d e +--R 630 1260 70 315 +--R + +--R 2 7 3 3 8 2 2 2 2 6 4 4 7 3 3 +--R (-- A a b - --- B a b )d e + (- -- A a b + --- B a b )d e +--R 35 140 15 105 +--R + +--R 1 5 5 1 6 4 4 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 137 + +--S 138 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 764 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e + (12A a b + 18B a b )d e +--R + +--R 4 3 3 +--R (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 139 + +--S 140 of 764 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^3*(a+b*x)^5/b^5+1/6*(b*d-a*e)^2*(b*B*d+3*A*b*e-_ + 4*a*B*e)*(a+b*x)^6/b^5+3/7*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^7/b^5+1/8*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^8/b^5+_ + 1/9*B*e^3*(a+b*x)^9/b^5 +--R +--R +--R (2) +--R 1 9 3 9 1 9 1 8 3 3 9 2 8 +--R - B b e x + ((- A b + - B a b )e + - B b d e )x +--R 9 8 2 8 +--R + +--R 4 8 6 2 7 3 3 9 12 8 2 3 9 2 7 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e)x +--R 7 7 7 7 7 +--R + +--R 2 7 2 3 6 3 8 2 7 2 +--R (A a b + - B a b )e + (2A a b + 3B a b )d e +--R 3 +--R + +--R 1 9 8 2 1 9 3 +--R (- A b + 2B a b )d e + - B b d +--R 2 6 +--R * +--R 6 +--R x +--R + +--R 4 3 6 1 4 5 3 18 2 7 12 3 6 2 +--R (- A a b + - B a b )e + (-- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 12 8 18 2 7 2 1 9 4 8 3 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 4 5 3 3 6 3 4 5 2 9 2 7 3 6 2 +--R - A a b e + (3A a b + - B a b )d e + (- A a b + 3B a b )d e +--R 4 4 2 +--R + +--R 8 3 2 7 3 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 5 2 3 6 4 5 2 2 7 4 3 6 3 3 +--R (A a b d e + (4A a b + B a b )d e + (2A a b + - B a b )d )x +--R 3 +--R + +--R 3 4 5 2 3 6 1 4 5 3 2 4 5 3 +--R (- A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 2 +--R + +--R 1 8 1 9 3 1 7 2 3 8 2 +--R (- --- A a b + --- B a )e + (-- A a b - --- B a b)d e +--R 280 630 35 280 +--R + +--R 1 6 3 1 7 2 2 1 5 4 1 6 3 3 +--R (- -- A a b + -- B a b )d e + (- A a b - -- B a b )d +--R 10 35 5 30 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 140 + +--S 141 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 of 764 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 142 + +--S 143 of 764 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^5/b^4+1/6*(b*d-a*e)*(b*B*d+2*A*b*e-_ + 3*a*B*e)*(a+b*x)^6/b^4+1/7*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^7/b^4+_ + 1/8*B*e^2*(a+b*x)^8/b^4 +--R +--R +--R (2) +--R 1 8 2 8 1 8 4 7 2 2 8 7 +--R - B b e x + ((- A b + - B a b )e + - B b d e)x +--R 8 7 7 7 +--R + +--R 2 7 2 6 2 1 8 4 7 1 8 2 6 +--R ((- A a b + B a b )e + (- A b + - B a b )d e + - B b d )x +--R 3 3 3 6 +--R + +--R 6 2 6 4 3 5 2 8 7 12 2 6 +--R (- A a b + - B a b )e + (- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 1 8 4 7 2 +--R (- A b + - B a b )d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 3 5 1 4 4 2 2 6 3 5 +--R (A a b + - B a b )e + (3A a b + 2B a b )d e +--R 4 +--R + +--R 7 3 2 6 2 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 1 4 4 2 8 3 5 2 4 4 2 6 4 3 5 2 3 +--R (- A a b e + (- A a b + - B a b )d e + (2A a b + - B a b )d )x +--R 3 3 3 3 +--R + +--R 4 4 3 5 1 4 4 2 2 4 4 2 +--R (A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 7 1 8 2 1 6 2 2 7 +--R (--- A a b - --- B a )e + (- -- A a b + --- B a b)d e +--R 105 280 15 105 +--R + +--R 1 5 3 1 6 2 2 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 143 + +--S 144 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 764 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R Type: Polynomial(Integer) +--E 145 + +--S 146 of 764 +r0:=1/5*(A*b-a*B)*(b*d-a*e)*(a+b*x)^5/b^3+1/6*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^6/b^3+1/7*B*e*(a+b*x)^7/b^3 +--R +--R +--R (2) +--R 1 7 7 1 7 2 6 1 7 6 +--R - B b e x + ((- A b + - B a b )e + - B b d)x +--R 7 6 3 6 +--R + +--R 4 6 6 2 5 1 7 4 6 5 +--R ((- A a b + - B a b )e + (- A b + - B a b )d)x +--R 5 5 5 5 +--R + +--R 3 2 5 3 4 6 3 2 5 4 +--R ((- A a b + B a b )e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 3 4 1 4 3 2 5 4 3 4 3 +--R ((- A a b + - B a b )e + (2A a b + - B a b )d)x +--R 3 3 3 +--R + +--R 1 4 3 3 4 1 4 3 2 4 3 +--R (- A a b e + (2A a b + - B a b )d)x + A a b d x +--R 2 2 +--R + +--R 1 6 1 7 1 5 2 1 6 +--R (- -- A a b + --- B a )e + (- A a b - -- B a b)d +--R 30 105 5 30 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 146 + +--S 147 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 2 2 3 2 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x + (6A a b + 4B a b)x +--R + +--R 3 4 4 +--R (4A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 148 + +--S 149 of 764 +r0:=1/5*(A*b-a*B)*(a+b*x)^5/b^2+1/6*B*(a+b*x)^6/b^2 +--R +--R +--R (2) +--R 1 6 6 1 6 4 5 5 5 3 2 4 4 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x +--R 6 5 5 2 +--R + +--R 2 4 4 3 3 3 3 3 1 4 2 2 4 2 1 5 +--R (2A a b + - B a b )x + (2A a b + - B a b )x + A a b x + - A a b +--R 3 2 5 +--R + +--R 1 6 +--R - -- B a +--R 30 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 764 +r0:=b*(b*d-a*e)^3*(B*d-A*e)*x/e^5-1/2*(b*d-a*e)^2*(B*d-A*e)*(a+b*x)^2/e^4+_ + 1/3*(b*d-a*e)*(B*d-A*e)*(a+b*x)^3/e^3-1/4*(B*d-A*e)*(a+b*x)^4/e^2+_ + 1/5*B*(a+b*x)^5/(b*e)-(b*d-a*e)^4*(B*d-A*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 3 2 4 4 +--R 60A a b e + (- 240A a b - 60B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (360A a b + 240B a b )d e + (- 240A a b - 360B a b )d e +--R + +--R 5 4 4 5 5 +--R (60A b + 240B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 5 4 5 5 4 4 +--R 12B b e x + ((15A b + 60B a b )e - 15B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 3 +--R ((80A a b + 120B a b )e + (- 20A b - 80B a b )d e + 20B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (180A a b + 120B a b )e + (- 120A a b - 180B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b + 120B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b + 60B a b)e + (- 360A a b - 240B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (240A a b + 360B a b )d e + (- 60A b - 240B a b )d e + 60B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (65A a b + 12B a )e + (- 80A a b - 65B a b)d e +--R + +--R 2 3 3 2 2 3 2 3 3 2 +--R (30A a b + 80B a b )d e - 30B a b d e +--R / +--R 6 +--R 60b e +--R Type: Expression(Integer) +--E 152 + +--S 153 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 154 + +--S 155 of 764 +r0:=-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*x/e^5+(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x))+b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^2/e^6-1/3*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^3/e^6+1/4*b^4*_ + B*(d+e*x)^4/e^6+(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 4 5 2 2 3 4 +--R (48A a b + 12B a )e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e +--R + +--R 4 4 +--R 60B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 2 3 +--R (48A a b + 12B a )d e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((4A b + 16B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 8A b - 32B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (72A a b + 48B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (24A b + 96B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (16A b + 64B a b )d e - 5B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 12A a e + (48A a b + 12B a )d e + (- 72A a b - 48B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (72A a b + 108B a b )d e + (- 32A b - 128B a b )d e + 55B b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 155 + +--S 156 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 157 + +--S 158 of 764 +r0:=2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*x/e^5+1/2*(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x)^2)-(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*_ + (d+e*x))-1/2*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^2/e^6+1/3*b^4*B*_ + (d+e*x)^3/e^6-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 3 5 3 2 2 4 +--R (36A a b + 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (36A b + 144B a b )d e - 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 144A a b - 216B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (72A b + 288B a b )d e - 120B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (36A a b + 24B a b)d e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 4 4 5 +--R (36A b + 144B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 2B b e x + ((3A b + 12B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 12A b - 48B a b )d e + 20B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 4 3 2 2 +--R ((48A a b + 72B a b )d e + (- 30A b - 120B a b )d e + 50B b d e )x +--R + +--R 3 4 5 2 2 3 4 +--R (- 24A a b - 6B a )e + (72A a b + 48B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (12A b + 48B a b )d e - 20B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 12A a b - 3B a )d e + (54A a b + 36B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 60A a b - 90B a b )d e + (24A b + 96B a b )d e - 40B b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 158 + +--S 159 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 of 764 +r0:=-b^3*(4*b*B*d-A*b*e-4*a*B*e)*x/e^5+1/2*b^4*B*x^2/e^4+1/3*(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x)^3)-1/2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/_ + (e^6*(d+e*x)^2)+2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*(d+_ + e*x))+2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 24A b - 96B a b )d e + 60B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 3 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 4 +--R 180B b d e +--R * +--R x +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (24A a b + 36B a b )d e + (- 24A b - 96B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((6A b + 24B a b )e - 15B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((18A b + 72B a b )d e - 63B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (72A a b + 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 18A b - 72B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 12A a b - 3B a )e + (- 36A a b - 24B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (108A a b + 162B a b )d e + (- 54A b - 216B a b )d e + 81B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 2A a e + (- 4A a b - B a )d e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (44A a b + 66B a b )d e + (- 26A b - 104B a b )d e + 47B b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 161 + +--S 162 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 of 764 +r0:=b^4*B*x/e^5+1/4*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^4)-1/3*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^3)+b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^2)-2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 3 5 4 4 4 +--R ((12A b + 48B a b )e - 60B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((48A b + 192B a b )d e - 240B b d e )x +--R + +--R 4 3 2 3 4 3 2 2 +--R ((72A b + 288B a b )d e - 360B b d e )x +--R + +--R 4 3 3 2 4 4 4 3 4 +--R ((48A b + 192B a b )d e - 240B b d e)x + (12A b + 48B a b )d e +--R + +--R 4 5 +--R - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 4 4 +--R 12B b e x + 48B b d e x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((- 48A a b - 72B a b )e + (48A b + 192B a b )d e - 48B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (108A b + 432B a b )d e - 252B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 16A a b - 4B a )e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (88A b + 352B a b )d e - 248B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 4A a b - B a )d e + (- 6A a b - 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 12A a b - 18B a b )d e + (25A b + 100B a b )d e - 77B b d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 164 + +--S 165 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^6 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 764 +r0:=-1/5*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^5)-1/4*B*(b*d-a*e)^4/_ + (e^6*(d+e*x)^4)+4/3*b*B*(b*d-a*e)^3/(e^6*(d+e*x)^3)-3*b^2*B*(b*d-_ + a*e)^2/(e^6*(d+e*x)^2)+4*b^3*B*(b*d-a*e)/(e^6*(d+e*x))+b^4*B*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 6 5 5 5 4 5 5 2 4 4 +--R (60B a b e - 60B b d e )x + (300B a b d e - 300B b d e )x +--R + +--R 4 2 4 5 3 3 3 4 3 3 5 4 2 2 +--R (600B a b d e - 600B b d e )x + (600B a b d e - 600B b d e )x +--R + +--R 4 4 2 5 5 4 5 5 6 +--R (300B a b d e - 300B b d e)x + 60B a b d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 5 6 5 5 5 +--R (- 12A b e + 12B b d e )x +--R + +--R 4 2 3 6 4 5 5 2 4 4 +--R ((- 60A a b - 240B a b )e + 540B a b d e - 240B b d e )x +--R + +--R 2 3 3 2 6 2 3 5 4 2 4 +--R (- 120A a b - 180B a b )e - 300B a b d e + 1380B a b d e +--R + +--R 5 3 3 +--R - 780B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 3 2 5 2 3 2 4 +--R (- 120A a b - 80B a b)e - 100B a b d e - 300B a b d e +--R + +--R 4 3 3 5 4 2 +--R 1580B a b d e - 980B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 4 5 3 2 2 4 2 3 3 3 +--R (- 60A a b - 15B a )e - 25B a b d e - 50B a b d e - 150B a b d e +--R + +--R 4 4 2 5 5 +--R 865B a b d e - 565B b d e +--R * +--R x +--R + +--R 5 6 5 5 4 2 4 3 2 3 3 2 3 4 2 +--R - 12A a e - 3B a d e - 5B a b d e - 10B a b d e - 30B a b d e +--R + +--R 4 5 5 6 +--R 185B a b d e - 125B b d +--R / +--R 12 11 5 11 2 10 4 +--R (60a e - 60b d e )x + (300a d e - 300b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (600a d e - 600b d e )x + (600a d e - 600b d e )x +--R + +--R 4 8 5 7 5 7 6 6 +--R (300a d e - 300b d e )x + 60a d e - 60b d e +--R Type: Expression(Integer) +--E 167 + +--S 168 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 169 + +--S 170 of 764 +r0:=-1/6*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^6)+1/30*(5*b*B*d+A*b*e-_ + 6*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^5) +--R +--R +--R (2) +--R 1 6 1 5 1 6 6 +--R ((-- A b - - B a b )e + - B b d)x +--R 30 5 6 +--R + +--R 2 4 1 6 4 5 5 +--R (- B a b e + (- A b + - B a b )d)x +--R 5 5 +--R + +--R 1 2 4 3 3 5 3 2 4 4 +--R ((- - A a b - 2B a b )e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 3 3 4 2 2 4 4 3 3 3 +--R ((- - A a b - 2B a b )e + (2A a b + - B a b )d)x +--R 3 3 +--R + +--R 3 4 2 5 3 3 1 4 2 2 +--R ((- - A a b - B a b)e + (2A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 5 1 6 4 2 1 6 1 5 1 6 +--R ((- - A a b - - B a )e + A a b d)x - - A a e + (- A a b - -- B a )d +--R 5 5 6 5 30 +--R / +--R 2 8 7 2 2 6 6 2 7 2 6 2 3 5 5 +--R (a e - 2a b d e + b d e )x + (6a d e - 12a b d e + 6b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (15a d e - 30a b d e + 15b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (20a d e - 40a b d e + 20b d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 2 5 3 6 2 2 7 +--R (15a d e - 30a b d e + 15b d e )x + (6a d e - 12a b d e + 6b d e)x +--R + +--R 2 6 2 7 2 8 +--R a d e - 2a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 170 + +--S 171 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 172 + +--S 173 of 764 +r0:=-1/7*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^7)+1/42*(5*b*B*d+2*A*b*e-_ + 7*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^6)+1/210*b*(5*b*B*d+2*A*b*e-_ + 7*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 1 7 1 6 2 1 7 7 +--R ((- --- A b + -- B a b )e - -- B b d e)x +--R 105 30 42 +--R + +--R 1 7 7 6 1 7 2 6 +--R ((- -- A b + -- B a b )d e - - B b d )x +--R 15 30 6 +--R + +--R 1 3 4 2 3 2 5 1 7 4 6 2 5 +--R (- - B a b e + - B a b d e + (- - A b - - B a b )d )x +--R 2 2 5 5 +--R + +--R 1 3 4 4 4 3 2 2 5 19 3 4 +--R (- - A a b - - B a b )e + (A a b + -- B a b )d e +--R 3 3 6 +--R + +--R 6 3 2 5 2 +--R (- A a b - - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 3 3 5 2 2 8 3 4 19 4 3 +--R (- A a b - - B a b )e + (- A a b + -- B a b )d e +--R 2 3 6 +--R + +--R 2 5 4 3 4 2 +--R (- 2A a b - - B a b )d +--R 3 +--R * +--R 3 +--R x +--R + +--R 6 5 2 4 6 2 4 3 3 5 2 +--R (- - A a b - - B a b)e + (3A a b + - B a b )d e +--R 5 5 2 +--R + +--R 3 4 1 4 3 2 +--R (- 2A a b - - B a b )d +--R 2 +--R * +--R 2 +--R x +--R + +--R 2 6 1 7 2 8 5 2 7 6 4 3 2 +--R ((- - A a b - - B a )e + (- A a b + -- B a b)d e - A a b d )x +--R 3 6 5 30 +--R + +--R 1 7 2 1 6 1 7 1 5 2 1 6 2 +--R - - A a e + (- A a b - -- B a )d e + (- - A a b + -- B a b)d +--R 7 3 42 5 30 +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (a e - 3a b d e + 3a b d e - b d e )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (7a d e - 21a b d e + 21a b d e - 7b d e )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (21a d e - 63a b d e + 63a b d e - 21b d e )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (35a d e - 105a b d e + 105a b d e - 35b d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (35a d e - 105a b d e + 105a b d e - 35b d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (21a d e - 63a b d e + 63a b d e - 21b d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 2 8 2 +--R (7a d e - 21a b d e + 21a b d e - 7b d e)x + a d e - 3a b d e +--R + +--R 2 9 3 10 +--R 3a b d e - b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 173 + +--S 174 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 of 764 +r0:=-1/8*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^8)+1/56*(5*b*B*d+3*A*b*e-_ + 8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^7)+1/168*b*(5*b*B*d+3*A*b*e-_ + 8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^3*(d+e*x)^6)+1/840*b^2*(5*b*B*d+_ + 3*A*b*e-8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 1 8 1 7 3 1 8 2 8 +--R ((--- A b - --- B a b )e + --- B b d e )x +--R 280 105 168 +--R + +--R 1 8 8 7 2 1 8 2 7 +--R ((-- A b - --- B a b )d e + -- B b d e)x +--R 35 105 21 +--R + +--R 1 8 4 7 2 1 8 3 6 +--R ((-- A b - -- B a b )d e + - B b d )x +--R 10 15 6 +--R + +--R 1 4 4 3 4 3 5 2 2 6 2 1 8 4 7 3 5 +--R (- - B a b e + - B a b d e - 2B a b d e + (- A b + - B a b )d )x +--R 3 3 5 5 +--R + +--R 1 4 4 5 3 3 3 5 43 4 4 2 +--R (- - A a b - B a b )e + (A a b + -- B a b )d e +--R 4 12 +--R + +--R 3 2 6 13 3 5 2 7 3 2 6 3 +--R (- - A a b - -- B a b )d e + (A a b + - B a b )d +--R 2 3 2 +--R * +--R 4 +--R x +--R + +--R 4 5 3 6 6 2 3 4 4 5 3 2 +--R (- - A a b - - B a b )e + (3A a b + 4B a b )d e +--R 5 5 +--R + +--R 3 5 13 4 4 2 2 6 4 3 5 3 +--R (- 4A a b - -- B a b )d e + (2A a b + - B a b )d +--R 3 3 +--R * +--R 3 +--R x +--R + +--R 6 2 2 7 3 18 5 3 31 6 2 2 +--R (- A a b - - B a b)e + (-- A a b + -- B a b )d e +--R 3 5 15 +--R + +--R 9 4 4 5 3 2 3 5 1 4 4 3 +--R (- - A a b - 2B a b )d e + (2A a b + - B a b )d +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 4 7 1 8 3 6 2 8 7 2 +--R (- - A a b - - B a )e + (2A a b + -- B a b)d e +--R 7 7 21 +--R + +--R 12 5 3 4 6 2 2 4 4 3 +--R (- -- A a b - -- B a b )d e + A a b d +--R 5 15 +--R * +--R x +--R + +--R 1 8 3 3 7 1 8 2 1 6 2 1 7 2 +--R - - A a e + (- A a b - -- B a )d e + (- - A a b + -- B a b)d e +--R 8 7 56 2 21 +--R + +--R 1 5 3 1 6 2 3 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 4 12 3 11 2 2 2 10 3 3 9 4 4 8 8 +--R (a e - 4a b d e + 6a b d e - 4a b d e + b d e )x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 4 5 7 7 +--R (8a d e - 32a b d e + 48a b d e - 32a b d e + 8b d e )x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 4 6 6 6 +--R (28a d e - 112a b d e + 168a b d e - 112a b d e + 28b d e )x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 4 7 5 5 +--R (56a d e - 224a b d e + 336a b d e - 224a b d e + 56b d e )x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 8 4 4 +--R (70a d e - 280a b d e + 420a b d e - 280a b d e + 70b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 8 4 4 9 3 3 +--R (56a d e - 224a b d e + 336a b d e - 224a b d e + 56b d e )x +--R + +--R 4 6 6 3 7 5 2 2 8 4 3 9 3 4 10 2 2 +--R (28a d e - 112a b d e + 168a b d e - 112a b d e + 28b d e )x +--R + +--R 4 7 5 3 8 4 2 2 9 3 3 10 2 4 11 4 8 4 +--R (8a d e - 32a b d e + 48a b d e - 32a b d e + 8b d e)x + a d e +--R + +--R 3 9 3 2 2 10 2 3 11 4 12 +--R - 4a b d e + 6a b d e - 4a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 176 + +--S 177 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^10 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 178 + +--S 179 of 764 +r0:=1/9*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^9)-1/8*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^8)+2/7*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^7)-1/3*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^6)+1/5*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^5)-_ + 1/4*b^4*B/(e^6*(d+e*x)^4) +--R +--R +--R (2) +--R 1 4 5 5 1 4 4 3 5 1 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - - B b d e )x +--R 4 5 5 4 +--R + +--R 2 3 2 2 5 2 4 8 3 4 1 4 2 3 3 +--R ((- - A a b - B a b )e + (- -- A b - -- B a b )d e - - B b d e )x +--R 3 15 15 6 +--R + +--R 6 2 2 4 3 5 2 3 3 2 2 4 +--R (- - A a b - - B a b)e + (- - A a b - - B a b )d e +--R 7 7 7 7 +--R + +--R 2 4 8 3 2 3 1 4 3 2 +--R (- -- A b - -- B a b )d e - -- B b d e +--R 35 35 14 +--R * +--R 2 +--R x +--R + +--R 1 3 1 4 5 3 2 2 1 3 4 +--R (- - A a b - - B a )e + (- -- A a b - - B a b)d e +--R 2 8 14 7 +--R + +--R 1 3 3 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- -- A b - -- B a b )d e +--R 14 28 70 35 +--R + +--R 1 4 4 +--R - -- B b d e +--R 56 +--R * +--R x +--R + +--R 1 4 5 1 3 1 4 4 1 2 2 1 3 2 3 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A a b - -- B a b)d e +--R 9 18 72 42 63 +--R + +--R 1 3 1 2 2 3 2 1 4 2 3 4 1 4 5 +--R (- --- A a b - -- B a b )d e + (- --- A b - --- B a b )d e - --- B b d +--R 126 84 630 315 504 +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 5 10 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 9 3 7 8 2 8 7 9 6 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 179 + +--S 180 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^11 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 764 +r0:=1/10*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^10)-1/9*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^9)+1/4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^8)-2/7*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^7)+1/6*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^6)-_ + 1/5*b^4*B/(e^6*(d+e*x)^5) +--R +--R +--R (2) +--R 1 4 5 5 1 4 2 3 5 1 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - - B b d e )x +--R 5 6 3 6 +--R + +--R 4 3 6 2 2 5 2 4 8 3 4 2 4 2 3 3 +--R ((- - A a b - - B a b )e + (- -- A b - -- B a b )d e - -- B b d e )x +--R 7 7 21 21 21 +--R + +--R 3 2 2 1 3 5 3 3 9 2 2 4 +--R (- - A a b - - B a b)e + (- -- A a b - -- B a b )d e +--R 4 2 14 28 +--R + +--R 1 4 1 3 2 3 1 4 3 2 +--R (- -- A b - - B a b )d e - -- B b d e +--R 28 7 28 +--R * +--R 2 +--R x +--R + +--R 4 3 1 4 5 1 2 2 1 3 4 +--R (- - A a b - - B a )e + (- - A a b - - B a b)d e +--R 9 9 6 9 +--R + +--R 1 3 1 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- --- A b - -- B a b )d e +--R 21 14 126 63 +--R + +--R 1 4 4 +--R - --- B b d e +--R 126 +--R * +--R x +--R + +--R 1 4 5 2 3 1 4 4 1 2 2 1 3 2 3 +--R - -- A a e + (- -- A a b - -- B a )d e + (- -- A a b - -- B a b)d e +--R 10 45 90 60 90 +--R + +--R 1 3 1 2 2 3 2 1 4 1 3 4 +--R (- --- A a b - --- B a b )d e + (- ---- A b - --- B a b )d e +--R 210 140 1260 315 +--R + +--R 1 4 5 +--R - ---- B b d +--R 1260 +--R / +--R 16 10 15 9 2 14 8 3 13 7 4 12 6 5 11 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 10 4 7 9 3 8 8 2 9 7 10 6 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 182 + +--S 183 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^12 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 184 + +--S 185 of 764 +r0:=1/11*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^11)-1/10*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^10)+2/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^9)-1/4*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^8)+1/7*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^7)-_ + 1/6*b^4*B/(e^6*(d+e*x)^6) +--R +--R +--R (2) +--R 1 4 5 5 1 4 4 3 5 5 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - -- B b d e )x +--R 6 7 7 42 +--R + +--R 1 3 3 2 2 5 1 4 2 3 4 5 4 2 3 3 +--R ((- - A a b - - B a b )e + (- -- A b - - B a b )d e - -- B b d e )x +--R 2 4 14 7 84 +--R + +--R 2 2 2 4 3 5 1 3 1 2 2 4 +--R (- - A a b - - B a b)e + (- - A a b - - B a b )d e +--R 3 9 6 4 +--R + +--R 1 4 2 3 2 3 5 4 3 2 +--R (- -- A b - -- B a b )d e - --- B b d e +--R 42 21 252 +--R * +--R 2 +--R x +--R + +--R 2 3 1 4 5 2 2 2 4 3 4 +--R (- - A a b - -- B a )e + (- -- A a b - -- B a b)d e +--R 5 10 15 45 +--R + +--R 1 3 1 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- --- A b - --- B a b )d e +--R 30 20 210 105 +--R + +--R 1 4 4 +--R - --- B b d e +--R 252 +--R * +--R x +--R + +--R 1 4 5 2 3 1 4 4 +--R - -- A a e + (- -- A a b - --- B a )d e +--R 11 55 110 +--R + +--R 2 2 2 4 3 2 3 1 3 1 2 2 3 2 +--R (- --- A a b - --- B a b)d e + (- --- A a b - --- B a b )d e +--R 165 495 330 220 +--R + +--R 1 4 2 3 4 1 4 5 +--R (- ---- A b - ---- B a b )d e - ---- B b d +--R 2310 1155 2772 +--R / +--R 17 11 16 10 2 15 9 3 14 8 4 13 7 5 12 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 11 5 7 10 4 8 9 3 9 8 2 10 7 11 6 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 185 + +--S 186 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 764 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 187 + +--S 188 of 764 +r0:=2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*x/b^5-(A*b-a*B)*(b*d-a*e)^4/_ + (b^6*(a+b*x))+e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^2/b^6+_ + 1/3*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^3/b^6+1/4*B*e^4*(a+b*x)^4/b^6+_ + (b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 3 2 4 4 2 3 3 2 3 +--R (- 48A a b + 60B a b)e + (144A a b - 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 144A a b + 216B a b )d e + (48A b - 96B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 60B a )e + (144A a b - 192B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 144A a b + 216B a b )d e + (48A a b - 96B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - 5B a b )e + 16B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 8A a b + 10B a b )e + (24A b - 32B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (24A a b - 30B a b )e + (- 72A a b + 96B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (72A b - 108B a b )d e + 48B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (16A a b - 5B a b)e + (- 72A a b + 64B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 108B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 32A a b + 55B a )e + (72A a b - 128B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A a b + 108B a b )d e + (48A a b - 48B a b )d e +--R + +--R 5 4 4 +--R (- 12A b + 12B a b )d +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 188 + +--S 189 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 764 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 190 + +--S 191 of 764 +r0:=3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*x/b^4-(A*b-a*B)*(b*d-a*e)^3/(b^5*_ + (a+b*x))+1/2*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^2/b^5+1/3*B*e^3*_ + (a+b*x)^3/b^5+(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 24B a b)e + (- 36A a b + 54B a b )d e +--R + +--R 4 3 2 4 3 +--R (18A b - 36B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (18A a b - 24B a )e + (- 36A a b + 54B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A a b - 36B a b )d e + 6B a b d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - 4B a b )e + 9B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 9A a b + 12B a b )e + (18A b - 27B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 9A a b + 8B a b)e + (18A a b - 27B a b )d e + 18B a b d e)x +--R + +--R 3 4 3 2 2 3 2 +--R (9A a b - 16B a )e + (- 18A a b + 27B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A a b - 18B a b )d e + (- 6A b + 6B a b )d +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Expression(Integer) +--E 191 + +--S 192 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 764 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 193 + +--S 194 of 764 +r0:=e*(2*b*B*d+A*b*e-2*a*B*e)*x/b^3+1/2*B*e^2*x^2/b^2-(A*b-a*B)*_ + (b*d-a*e)^2/(b^4*(a+b*x))+(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((- 4A a b + 6B a b)e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 4A a b + 6B a )e + (4A a b - 8B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((2A a b - 4B a b)e + 4B a b d e)x + (- 2A a b + 2B a )e +--R + +--R 2 2 3 2 2 +--R (4A a b - 4B a b)d e + (- 2A b + 2B a b )d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 194 + +--S 195 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 764 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 764 +r0:=B*e*x/b^2-(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x))+(b*B*d+A*b*e-2*a*B*e)*_ + log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (((A b - 2B a b)e + B b d)x + (A a b - 2B a )e + B a b d)log(b x + a) +--R + +--R 2 2 2 2 +--R B b e x + B a b e x + (A a b - B a )e + (- A b + B a b)d +--R / +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 197 + +--S 198 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 764 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R B x + A +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 199 + +--S 200 of 764 +r0:=(-A*b+a*B)/(b^2*(a+b*x))+B*log(a+b*x)/b^2 +--R +--R +--R (B b x + B a)log(b x + a) - A b + B a +--R (2) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 200 + +--S 201 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 764 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (2a b e + b d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 202 + +--S 203 of 764 +r0:=(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x))+(B*d-A*e)*log(a+b*x)/(b*d-a*e)^2-_ + (B*d-A*e)*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (2) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(b x + a) + (A a b - B a )e +--R + +--R 2 +--R (- A b + B a b)d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R (a b e - 2a b d e + b d )x + a b e - 2a b d e + a b d +--R Type: Expression(Integer) +--E 203 + +--S 204 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 764 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 205 + +--S 206 of 764 +r0:=(-A*b+a*B)/((b*d-a*e)^2*(a+b*x))+(B*d-A*e)/((b*d-a*e)^2*(d+e*x))+_ + (b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^3-(b*B*d-2*A*b*e+a*B*e)*_ + log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 2A b + B a b)e + B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 2A a b + B a )e + (- 2A b + 2B a b)d e + B b d )x +--R + +--R 2 2 +--R (- 2A a b + B a )d e + B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R ((2A b - B a b)e - B b d e)x +--R + +--R 2 2 2 2 2 +--R ((2A a b - B a )e + (2A b - 2B a b)d e - B b d )x +--R + +--R 2 2 +--R (2A a b - B a )d e - B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2A a b + B a )e + 2A b d e - B b d )x - A a e + 2B a d e +--R + +--R 2 2 +--R (A b - 2B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Expression(Integer) +--E 206 + +--S 207 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 764 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 208 + +--S 209 of 764 +r0:=-b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x))+1/2*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^2)+_ + (b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x))+b*(b*B*d-3*A*b*e+2*a*B*e)*_ + log(a+b*x)/(b*d-a*e)^4-b*(b*B*d-3*A*b*e+2*a*B*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((6A b - 4B a b )e - 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (12A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((12A a b - 8B a b)d e + (6A b - 8B a b )d e - 2B b d )x +--R + +--R 2 2 2 2 3 +--R (6A a b - 4B a b)d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((- 6A b + 4B a b )e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 4B a b)e + (- 12A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((- 12A a b + 8B a b)d e + (- 6A b + 8B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 3 +--R (- 6A a b + 4B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (- 6A b + 2B a b )d e + 2B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b - 2B a )e + (6A a b - 5B a b)d e + (- 9A b + 4B a b )d e +--R + +--R 3 3 +--R 3B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - A a e + (6A a b - B a )d e + (- 3A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- 2A b + 5B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 209 + +--S 210 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 764 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 764 +r0:=e^3*(4*b*B*d+A*b*e-4*a*B*e)*x/b^5+1/2*B*e^4*x^2/b^4-1/3*(A*b-a*B)*_ + (b*d-a*e)^4/(b^6*(a+b*x)^3)-1/2*(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)/_ + (b^6*(a+b*x)^2)-2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)/(b^6*(a+b*x))+_ + 2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 24A a b + 60B a b )e + (24A b - 96B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 72A a b + 180B a b )e + (72A a b - 288B a b )d e +--R + +--R 4 2 2 +--R 108B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 72A a b + 180B a b)e + (72A a b - 288B a b )d e +--R + +--R 2 3 2 2 +--R 108B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 3 2 2 2 +--R (- 24A a b + 60B a )e + (24A a b - 96B a b)d e + 36B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((6A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((18A a b - 63B a b )e + 72B a b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 18A a b - 9B a b )e + (72A a b - 72B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 54A a b + 81B a b)e + (108A a b - 216B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 36A a b + 162B a b )d e + (- 12A b - 24B a b )d e - 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 26A a b + 47B a )e + (44A a b - 104B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 12A a b + 66B a b )d e + (- 4A a b - 8B a b )d e +--R + +--R 5 4 4 +--R (- 2A b - B a b )d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 212 + +--S 213 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 764 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 214 + +--S 215 of 764 +r0:=B*e^3*x/b^4-1/3*(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x)^3)-1/2*(b*d-a*e)^2*_ + (b*B*d+3*A*b*e-4*a*B*e)/(b^5*(a+b*x)^2)-3*e*(b*d-a*e)*(b*B*d+A*b*e-_ + 2*a*B*e)/(b^5*(a+b*x))+e^2*(3*b*B*d+A*b*e-4*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((6A b - 24B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((18A a b - 72B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((18A a b - 72B a b)e + 54B a b d e )x + (6A a b - 24B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 3 +--R 6B b e x + 18B a b e x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((18A a b - 18B a b )e + (- 18A b + 54B a b )d e - 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (27A a b - 54B a b)e + (- 18A a b + 81B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 9A b - 18B a b )d e - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (11A a b - 26B a )e + (- 6A a b + 33B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b - 6B a b )d e + (- 2A b - B a b )d +--R / +--R 8 3 7 2 2 6 3 5 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 215 + +--S 216 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 764 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 217 + +--S 218 of 764 +r0:=-1/2*B*(b*d-a*e)^2/(b^4*(a+b*x)^2)-2*B*e*(b*d-a*e)/(b^4*(a+b*x))-_ + 1/3*(A*b-a*B)*(d+e*x)^3/(b*(b*d-a*e)*(a+b*x)^3)+B*e^2*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 4 2 3 2 2 3 3 2 2 +--R (6B a b e - 6B b d e )x + (18B a b e - 18B a b d e )x +--R + +--R 3 3 2 2 2 4 3 3 2 +--R (18B a b e - 18B a b d e )x + 6B a e - 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 3 3 +--R (2A b - 2B a b )e x +--R + +--R 2 2 3 4 3 2 4 2 2 +--R (12B a b e + (6A b - 30B a b )d e + 12B b d e)x +--R + +--R 3 3 2 2 2 4 3 2 4 3 4 3 +--R (21B a b e - 39B a b d e + (6A b + 9B a b )d e + 3B b d )x + 9B a e +--R + +--R 3 2 2 2 2 4 3 3 +--R - 15B a b d e + 3B a b d e + (2A b + B a b )d +--R / +--R 7 8 3 2 6 7 2 3 5 2 6 4 4 +--R (6a b e - 6b d)x + (18a b e - 18a b d)x + (18a b e - 18a b d)x + 6a b e +--R + +--R 3 5 +--R - 6a b d +--R Type: Expression(Integer) +--E 218 + +--S 219 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 764 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 220 + +--S 221 of 764 +r0:=-1/3*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)^3)+1/2*(-b*B*d-A*b*e+2*a*B*e)/_ + (b^3*(a+b*x)^2)-B*e/(b^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 1 2 1 2 1 1 2 +--R - B b e x + ((- - A b - B a b)e - - B b d)x + (- - A a b - - B a )e +--R 2 2 6 3 +--R + +--R 1 2 1 +--R (- - A b - - B a b)d +--R 3 6 +--R / +--R 6 3 5 2 2 4 3 3 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 221 + +--S 222 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 764 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R B x + A +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 223 + +--S 224 of 764 +r0:=1/3*(-A*b+a*B)/(b^2*(a+b*x)^3)-1/2*B/(b^2*(a+b*x)^2) +--R +--R +--R 1 1 1 +--R - - B b x - - A b - - B a +--R 2 3 6 +--R (2) ------------------------------ +--R 5 3 4 2 2 3 3 2 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 224 + +--S 225 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 764 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 764 +r0:=1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3)+1/2*(-B*d+A*e)/((b*d-a*e)^2*_ + (a+b*x)^2)+e*(B*d-A*e)/((b*d-a*e)^3*(a+b*x))+e^2*(B*d-A*e)*log(a+b*x)/_ + (b*d-a*e)^4-e^2*(B*d-A*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 4 3 4 2 3 3 3 3 2 2 +--R (6A b e - 6B b d e )x + (18A a b e - 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (18A a b e - 18B a b d e )x + 6A a b e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 2 3 3 3 3 2 2 +--R (- 6A b e + 6B b d e )x + (- 18A a b e + 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (- 18A a b e + 18B a b d e )x - 6A a b e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 4 3 2 4 2 2 +--R (6A a b e + (- 6A b - 6B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 2 2 2 4 3 2 +--R 15A a b e + (- 18A a b - 15B a b )d e + (3A b + 18B a b )d e +--R + +--R 4 3 +--R - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (11A a b - 2B a )e + (- 18A a b - 3B a b)d e + (9A a b + 6B a b )d e +--R + +--R 4 3 3 +--R (- 2A b - B a b )d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 3 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 2 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 7 4 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x + 6a b e +--R + +--R 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R Type: Expression(Integer) +--E 227 + +--S 228 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 764 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 229 + +--S 230 of 764 +r0:=1/3*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^3)+1/2*(-b*B*d+2*A*b*e-a*B*e)/_ + ((b*d-a*e)^3*(a+b*x)^2)+e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(a+b*x))+_ + e^2*(B*d-A*e)/((b*d-a*e)^4*(d+e*x))+e^2*(3*b*B*d-4*A*b*e+a*B*e)*_ + log(a+b*x)/(b*d-a*e)^5-e^2*(3*b*B*d-4*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 24A b + 6B a b )e + 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 72A a b + 18B a b )e + (- 24A b + 60B a b )d e +--R + +--R 4 2 2 +--R 18B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 72A a b + 18B a b)e + (- 72A a b + 72B a b )d e +--R + +--R 3 2 2 +--R 54B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((- 24A a b + 6B a )e + (- 72A a b + 36B a b)d e + 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (- 24A a b + 6B a )d e + 18B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((24A b - 6B a b )e - 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((72A a b - 18B a b )e + (24A b - 60B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 3 2 2 2 +--R ((72A a b - 18B a b)e + (72A a b - 72B a b )d e - 54B a b d e )x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((24A a b - 6B a )e + (72A a b - 36B a b)d e - 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (24A a b - 6B a )d e - 18B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 24A a b + 6B a b )e + (24A b + 12B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 60A a b + 15B a b)e + (48A a b + 33B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 39B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 44A a b + 11B a )e + (12A a b + 30B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (36A a b - 18B a b )d e + (- 4A b - 26B a b )d e + 3B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (- 20A a b + 17B a )d e + (36A a b - 9B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 12A a b - 9B a b )d e + (2A b + B a b )d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 8 5 4 +--R (6a b e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6b d e)x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 18a b e - 84a b d e + 150a b d e - 120a b d e + 30a b d e +--R + +--R 7 5 8 6 +--R 12a b d e - 6b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 18a b e - 72a b d e + 90a b d e - 90a b d e + 72a b d e +--R + +--R 7 6 +--R - 18a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 6a e - 12a b d e - 30a b d e + 120a b d e - 150a b d e +--R + +--R 3 5 5 2 6 6 +--R 84a b d e - 18a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 3 5 6 +--R 6a d e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6a b d +--R Type: Expression(Integer) +--E 230 + +--S 231 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 of 764 +t0:=(A+B*x)*(d+e*x)^m*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R m | 2 2 2 +--R (1) (B x + A)(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 232 + +--S 233 of 764 +r0:=(A*b*e*(3+m)-B*(2*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2*(2+m)*(3+m))-(b*d-a*e)*(A*b*e*(3+m)-B*(2*b*d+_ + a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(1+m)*_ + (2+m)*(3+m)*(a+b*x))+B*(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e*(3+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (B b e m + 3B b e m + 2B b e )x +--R + +--R 2 2 2 2 +--R (A b + B a)e m + ((4A b + 4B a)e - 2B b d e)m + (3A b + 3B a)e +--R + +--R - 2B b d e +--R * +--R x +--R + +--R 2 2 2 2 +--R A a e m + (5A a e + (- A b - B a)d e)m + 6A a e + (- 3A b - 3B a)d e +--R + +--R 2 +--R 2B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 233 + +--S 234 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 764 +t0:=(A+B*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 764 +r0:=-1/42*(2*b*B*d-7*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/210*(b*d-a*e)*(2*b*B*d-7*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/7*B*(a+b*x)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 7 7 7 6 6 +--R 30B b e x + ((35A b + 35B a)e + 140B b d e )x +--R + +--R 7 6 2 5 5 +--R (42A a e + (168A b + 168B a)d e + 252B b d e )x +--R + +--R 6 2 5 3 4 4 +--R (210A a d e + (315A b + 315B a)d e + 210B b d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (420A a d e + (280A b + 280B a)d e + 70B b d e )x +--R + +--R 3 4 4 3 2 4 3 5 2 +--R (420A a d e + (105A b + 105B a)d e )x + 210A a d e x + 42A a d e +--R + +--R 6 7 +--R (- 7A b - 7B a)d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 210b e x + 210a e +--R Type: Expression(Integer) +--E 236 + +--S 237 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 764 +t0:=(A+B*x)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 764 +r0:=-1/15*(b*B*d-3*A*b*e+2*a*B*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/60*(b*d-a*e)*(b*B*d-3*A*b*e+2*a*B*e)*(d+e*x)^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/6*B*(a+b*x)*(d+e*x)^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 10B b e x + ((12A b + 12B a)e + 36B b d e )x +--R + +--R 6 5 2 4 4 +--R (15A a e + (45A b + 45B a)d e + 45B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (60A a d e + (60A b + 60B a)d e + 20B b d e )x +--R + +--R 2 4 3 3 2 3 3 4 2 +--R (90A a d e + (30A b + 30B a)d e )x + 60A a d e x + 15A a d e +--R + +--R 5 6 +--R (- 3A b - 3B a)d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 239 + +--S 240 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 764 +t0:=(A+B*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 764 +r0:=-1/20*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/60*(b*d-a*e)*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/5*B*(a+b*x)*(d+e*x)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 12B b e x + ((15A b + 15B a)e + 30B b d e )x +--R + +--R 5 4 2 3 3 +--R (20A a e + (40A b + 40B a)d e + 20B b d e )x +--R + +--R 4 2 3 2 2 3 3 2 +--R (60A a d e + (30A b + 30B a)d e )x + 60A a d e x + 20A a d e +--R + +--R 4 5 +--R (- 5A b - 5B a)d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 242 + +--S 243 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 764 +t0:=(A+B*x)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 | 2 2 2 +--R (1) (B e x + (A e + B d)x + A d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 764 +r0:=1/6*(2*A*b*e-B*(b*d+a*e))*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^3+1/4*(b*d-_ + a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b^3*e)+_ + 1/4*B*(a+b*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 3 3 3 2 3 2 +--R 3B b e x + ((4A b + B a b )e + 4B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((2A a b - B a b)e + (6A b + 2B a b )d)x + (- 2A a b + B a )e +--R + +--R 2 2 +--R (6A a b - 2B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 12b +--R Type: Expression(Integer) +--E 245 + +--S 246 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (1) (B x + A)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 764 +r0:=1/3*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/b^2 +--R +--R +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R (2B b x + (3A b + B a b)x + 3A a b - B a )\|b x + 2a b x + a +--R (2) ----------------------------------------------------------------- +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 248 + +--S 249 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 250 + +--S 251 of 764 +r0:=-(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/2*B*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e)+(b*d-a*e)*(B*d-A*e)*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (2A a b e + (- 2A b - 2B a b)d e + 2B b d )log(e x + d) + B b e x +--R + +--R 2 2 2 2 2 +--R ((2A b + 2B a b)e - 2B b d e)x + (2A a b + B a )e - 2B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 3 3 +--R 2b e x + 2a b e +--R Type: Expression(Integer) +--E 251 + +--S 252 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 253 + +--S 254 of 764 +r0:=(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*(d+e*x))-_ + (2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 +--R (((A b + B a)e - 2B b d e)x + (A b + B a)d e - 2B b d )log(e x + d) +--R + +--R 2 2 2 2 +--R B b e x + ((- A b + B a)e + 2B b d e)x - A a e + 2B a d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 254 + +--S 255 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 256 + +--S 257 of 764 +r0:=-1/2*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^2)+B*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*_ + (d+e*x))+b*B*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 3 2 2 2 2 2 2 2 +--R (2B a b e - 2B b d e )x + (4B a b d e - 4B b d e)x + 2B a b d e +--R + +--R 2 3 +--R - 2B b d +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- A b e + B b d e )x +--R + +--R 2 3 2 2 2 2 3 2 2 +--R ((- 2A a b - 2B a )e + 6B a b d e - 2B b d e)x - A a e - B a d e +--R + +--R 2 2 3 +--R 4B a b d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 5 3 2 6 5 2 2 4 2 +--R (2a b e - 2b d e )x + (2a e + 2a b d e - 4b d e )x +--R + +--R 2 5 2 4 2 3 3 2 2 4 3 3 +--R (4a d e - 2a b d e - 2b d e )x + 2a d e - 2a b d e +--R Type: Expression(Integer) +--E 257 + +--S 258 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 259 + +--S 260 of 764 +r0:=1/3*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^3)+_ + 1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^2) +--R +--R +--R (2) +--R 2 2 2 +--R ((A b - 3B a b)e + 2B b d)x +--R + +--R 2 2 2 2 +--R ((- A a b - 3B a )e + (3A b + B a b)d)x - 2A a e + (3A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 5 4 2 2 3 3 2 4 2 3 2 3 2 2 +--R (6a e - 12a b d e + 6b d e )x + (18a d e - 36a b d e + 18b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (18a d e - 36a b d e + 18b d e)x + 6a d e - 12a b d e + 6b d +--R Type: Expression(Integer) +--E 260 + +--S 261 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 262 + +--S 263 of 764 +r0:=-1/4*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/4*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^3)-1/12*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^3) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a)e - 4B b d e)x - 3A a e +--R + +--R 2 +--R (- A b - B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 5 7 6 4 6 2 5 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 5 3 4 2 3 4 4 3 4 3 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 263 + +--S 264 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 265 + +--S 266 of 764 +r0:=-1/5*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^5)-1/15*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^4)-1/60*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^4) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 20B b e x + ((- 15A b - 15B a)e - 10B b d e)x - 12A a e +--R + +--R 2 +--R (- 3A b - 3B a)d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 6 8 7 5 7 2 6 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 6 3 5 3 3 5 4 4 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 4 5 3 5 3 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 266 + +--S 267 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 268 + +--S 269 of 764 +r0:=-1/6*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^6)-1/12*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^5)-1/60*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 15B b e x + ((- 12A b - 12B a)e - 6B b d e)x - 10A a e +--R + +--R 2 +--R (- 2A b - 2B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 269 + +--S 270 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 764 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 m +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(e x + d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 764 +r0:=(A*b*e*(5+m)-B*(4*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2*(4+m)*(5+m))+B*(a+b*x)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(b*e*(5+m))+6*(b*d-a*e)^2*(A*b*e*(5+m)-_ + B*(4*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4*_ + (2+m)*(3+m)*(4+m)*(5+m))-6*(b*d-a*e)^3*(A*b*e*(5+m)-B*(4*b*d+a*e*_ + (1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(1+m)*(2+m)*_ + (3+m)*(4+m)*(5+m)*(a+b*x))-3*(b*d-a*e)*(A*b*e*(5+m)-B*(4*b*d+a*e*_ + (1+m)))*(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*_ + (3+m)*(4+m)*(5+m)) +--R +--R +--R (2) +--R 3 4 4 3 4 3 3 4 2 3 4 3 4 4 +--R (B b e m + 10B b e m + 35B b e m + 50B b e m + 24B b e )x +--R + +--R 3 2 4 4 3 2 4 3 3 3 +--R (A b + 3B a b )e m + ((11A b + 33B a b )e - 4B b d e )m +--R + +--R 3 2 4 3 3 2 +--R ((41A b + 123B a b )e - 24B b d e )m +--R + +--R 3 2 4 3 3 3 2 4 +--R ((61A b + 183B a b )e - 44B b d e )m + (30A b + 90B a b )e +--R + +--R 3 3 +--R - 24B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 +--R (3A a b + 3B a b)e m +--R + +--R 2 2 4 3 2 3 3 +--R ((36A a b + 36B a b)e + (- 3A b - 9B a b )d e )m +--R + +--R 2 2 4 3 2 3 +--R (147A a b + 147B a b)e + (- 24A b - 72B a b )d e +--R + +--R 3 2 2 +--R 12B b d e +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 2 3 +--R (234A a b + 234B a b)e + (- 51A b - 153B a b )d e +--R + +--R 3 2 2 +--R 36B b d e +--R * +--R m +--R + +--R 2 2 4 3 2 3 3 2 2 +--R (120A a b + 120B a b)e + (- 30A b - 90B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 +--R (3A a b + B a )e m +--R + +--R 2 3 4 2 2 3 3 +--R ((39A a b + 13B a )e + (- 6A a b - 6B a b)d e )m +--R + +--R 2 3 4 2 2 3 +--R (177A a b + 59B a )e + (- 60A a b - 60B a b)d e +--R + +--R 3 2 2 2 +--R (6A b + 18B a b )d e +--R * +--R 2 +--R m +--R + +--R 2 3 4 2 2 3 +--R (321A a b + 107B a )e + (- 174A a b - 174B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (36A b + 108B a b )d e - 24B b d e +--R * +--R m +--R + +--R 2 3 4 2 2 3 +--R (180A a b + 60B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (30A b + 90B a b )d e - 24B b d e +--R * +--R x +--R + +--R 3 4 4 3 4 2 3 3 3 +--R A a e m + (14A a e + (- 3A a b - B a )d e )m +--R + +--R 3 4 2 3 3 2 2 2 2 2 +--R (71A a e + (- 36A a b - 12B a )d e + (6A a b + 6B a b)d e )m +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 154A a e + (- 141A a b - 47B a )d e + (54A a b + 54B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 18B a b )d e +--R * +--R m +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 120A a e + (- 180A a b - 60B a )d e + (120A a b + 120B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 30A b - 90B a b )d e + 24B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 272 + +--S 273 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 764 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 5 8 2 5 2 4 7 +--R B b e x + ((A b + 2B a b)e + 5B b d e )x +--R + +--R 2 5 2 4 2 2 3 6 +--R ((2A a b + B a )e + (5A b + 10B a b)d e + 10B b d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 5 +--R (A a e + (10A a b + 5B a )d e + (10A b + 20B a b)d e + 10B b d e )x +--R + +--R 2 4 2 2 3 2 3 2 +--R 5A a d e + (20A a b + 10B a )d e + (10A b + 20B a b)d e +--R + +--R 2 4 +--R 5B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 3 +--R (10A a d e + (20A a b + 10B a )d e + (5A b + 10B a b)d e + B b d )x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 274 + +--S 275 of 764 +r0:=-1/45*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/10*B*(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-_ + 1/420*(b*d-a*e)^2*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^6*sqrt(a^2+2*a*b*_ + x+b^2*x^2)/(b*e^4)+1/2520*(b*d-a*e)^3*(2*b*B*d-5*A*b*e+3*a*B*e)*_ + (d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))+1/120*(b*d-a*e)*_ + (2*b*B*d-5*A*b*e+3*a*B*e)*(a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 10 10 3 2 10 3 9 9 +--R 252B b e x + ((280A b + 840B a b )e + 1400B b d e )x +--R + +--R 2 2 10 3 2 9 +--R (945A a b + 945B a b)e + (1575A b + 4725B a b )d e +--R + +--R 3 2 8 +--R 3150B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 10 2 2 9 +--R (1080A a b + 360B a )e + (5400A a b + 5400B a b)d e +--R + +--R 3 2 2 8 3 3 7 +--R (3600A b + 10800B a b )d e + 3600B b d e +--R * +--R 7 +--R x +--R + +--R 3 10 2 3 9 +--R 420A a e + (6300A a b + 2100B a )d e +--R + +--R 2 2 2 8 3 2 3 7 +--R (12600A a b + 12600B a b)d e + (4200A b + 12600B a b )d e +--R + +--R 3 4 6 +--R 2100B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 2 8 +--R 2520A a d e + (15120A a b + 5040B a )d e +--R + +--R 2 2 3 7 3 2 4 6 +--R (15120A a b + 15120B a b)d e + (2520A b + 7560B a b )d e +--R + +--R 3 5 5 +--R 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 8 2 3 3 7 +--R 6300A a d e + (18900A a b + 6300B a )d e +--R + +--R 2 2 4 6 3 2 5 5 +--R (9450A a b + 9450B a b)d e + (630A b + 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 3 7 2 3 4 6 +--R 8400A a d e + (12600A a b + 4200B a )d e +--R + +--R 2 2 5 5 +--R (2520A a b + 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 3 5 5 2 3 5 5 +--R (6300A a d e + (3780A a b + 1260B a )d e )x + 2520A a d e x +--R + +--R 3 6 4 2 3 7 3 2 2 8 2 +--R 420A a d e + (- 180A a b - 60B a )d e + (45A a b + 45B a b)d e +--R + +--R 3 2 9 3 10 +--R (- 5A b - 15B a b )d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 275 + +--S 276 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 764 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 7 2 4 2 3 6 +--R B b e x + ((A b + 2B a b)e + 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((2A a b + B a )e + (4A b + 8B a b)d e + 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (A a e + (8A a b + 4B a )d e + (6A b + 12B a b)d e + 4B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 3 +--R (4A a d e + (12A a b + 6B a )d e + (4A b + 8B a b)d e + B b d )x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 764 +r0:=-1/72*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/9*B*(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-_ + 1/504*(b*d-a*e)^2*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^4)+1/2520*(b*d-a*e)^3*(4*b*B*d-9*A*b*e+5*a*B*e)*_ + (d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))+1/168*(b*d-a*e)*_ + (4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 9 9 3 2 9 3 8 8 +--R 280B b e x + ((315A b + 945B a b )e + 1260B b d e )x +--R + +--R 2 2 9 3 2 8 +--R (1080A a b + 1080B a b)e + (1440A b + 4320B a b )d e +--R + +--R 3 2 7 +--R 2160B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 9 2 2 8 +--R (1260A a b + 420B a )e + (5040A a b + 5040B a b)d e +--R + +--R 3 2 2 7 3 3 6 +--R (2520A b + 7560B a b )d e + 1680B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 8 +--R 504A a e + (6048A a b + 2016B a )d e +--R + +--R 2 2 2 7 3 2 3 6 +--R (9072A a b + 9072B a b)d e + (2016A b + 6048B a b )d e +--R + +--R 3 4 5 +--R 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 2 7 +--R 2520A a d e + (11340A a b + 3780B a )d e +--R + +--R 2 2 3 6 3 2 4 5 +--R (7560A a b + 7560B a b)d e + (630A b + 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 2 7 2 3 3 6 +--R 5040A a d e + (10080A a b + 3360B a )d e +--R + +--R 2 2 4 5 +--R (2520A a b + 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 3 6 2 3 4 5 2 3 4 5 +--R (5040A a d e + (3780A a b + 1260B a )d e )x + 2520A a d e x +--R + +--R 3 5 4 2 3 6 3 2 2 7 2 +--R 504A a d e + (- 252A a b - 84B a )d e + (72A a b + 72B a b)d e +--R + +--R 3 2 8 3 9 +--R (- 9A b - 27B a b )d e + 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 278 + +--S 279 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 764 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 764 +r0:=1/14*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/8*B*(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)+_ + 1/70*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^4)-1/280*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))-1/28*(b*d-a*e)*(2*A*b*e-_ + B*(b*d+a*e))*(a+b*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 8 8 3 2 8 3 7 7 +--R 35B b e x + ((40A b + 120B a b )e + 120B b d e )x +--R + +--R 2 2 8 3 2 7 3 2 6 6 +--R ((140A a b + 140B a b)e + (140A b + 420B a b )d e + 140B b d e )x +--R + +--R 2 3 8 2 2 7 +--R (168A a b + 56B a )e + (504A a b + 504B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (168A b + 504B a b )d e + 56B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 70A a e + (630A a b + 210B a )d e + (630A a b + 630B a b)d e +--R + +--R 3 2 3 5 +--R (70A b + 210B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 2 2 3 5 3 +--R (280A a d e + (840A a b + 280B a )d e + (280A a b + 280B a b)d e )x +--R + +--R 3 2 6 2 3 3 5 2 3 3 5 3 4 4 +--R (420A a d e + (420A a b + 140B a )d e )x + 280A a d e x + 70A a d e +--R + +--R 2 3 5 3 2 2 6 2 +--R (- 42A a b - 14B a )d e + (14A a b + 14B a b)d e +--R + +--R 3 2 7 3 8 +--R (- 2A b - 6B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 280b e x + 280a e +--R Type: Expression(Integer) +--E 281 + +--S 282 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 764 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 764 +r0:=-1/84*(b*d-a*e)^2*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b^4*e)-1/42*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(d+_ + e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*e)+1/7*B*(a+b*x)*(d+e*x)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-1/105*(b*d-a*e)*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4 +--R +--R +--R (2) +--R 6 2 6 6 5 2 6 5 +--R 60B b e x + ((70A b + 150B a b )e + 140B b d e)x +--R + +--R 5 2 4 2 6 5 6 2 4 +--R ((182A a b + 102B a b )e + (168A b + 364B a b )d e + 84B b d )x +--R + +--R 2 4 3 3 2 5 2 4 +--R (133A a b + 3B a b )e + (462A a b + 266B a b )d e +--R + +--R 6 5 2 +--R (105A b + 231B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (7A a b - 3B a b )e + (378A a b + 14B a b )d e +--R + +--R 5 2 4 2 +--R (315A a b + 189B a b )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (- 7A a b + 3B a b)e + (42A a b - 14B a b )d e +--R + +--R 2 4 3 3 2 +--R (315A a b + 21B a b )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 3 3 4 2 2 +--R (7A a b - 3B a )e + (- 42A a b + 14B a b)d e + (105A a b - 21B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 420b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 764 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 764 +r0:=-1/12*(b*d-a*e)*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b^3*e)+1/6*B*(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-1/15*(2*b*B*d-3*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b^3 +--R +--R +--R (2) +--R 5 5 5 4 5 4 +--R 10B b e x + ((12A b + 26B a b )e + 12B b d)x +--R + +--R 4 2 3 5 4 3 +--R ((33A a b + 19B a b )e + (15A b + 33B a b )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((27A a b + B a b )e + (45A a b + 27B a b )d)x +--R + +--R 3 2 4 2 3 3 2 4 5 +--R ((3A a b - B a b)e + (45A a b + 3B a b )d)x + (- 3A a b + B a )e +--R + +--R 3 2 4 +--R (15A a b - 3B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 60b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 764 +r0:=1/4*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+_ + 1/5*B*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2 +--R +--R +--R (2) +--R 4 4 4 3 3 3 2 2 2 +--R 4B b x + (5A b + 11B a b )x + (15A a b + 9B a b )x +--R + +--R 2 2 3 3 4 +--R (15A a b + B a b)x + 5A a b - B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 20b +--R Type: Expression(Integer) +--E 290 + +--S 291 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 292 + +--S 293 of 764 +r0:=-1/3*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/4*B*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-(b*d-a*e)^2*(B*d-A*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^4+1/2*(b*d-a*e)*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^3+(b*d-a*e)^3*(B*d-A*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 3 3 2 2 2 2 +--R 12A a b e + (- 36A a b - 12B a b)d e + (36A a b + 36B a b )d e +--R + +--R 4 3 3 4 4 +--R (- 12A b - 36B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 3B b e x + ((4A b + 12B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((18A a b + 18B a b )e + (- 6A b - 18B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (36A a b + 12B a b)e + (- 36A a b - 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b + 36B a b )d e - 12B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (22A a b + 3B a )e + (- 30A a b - 22B a b)d e +--R + +--R 3 2 2 2 2 3 3 +--R (12A a b + 30B a b )d e - 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 5 5 +--R 12b e x + 12a b e +--R Type: Expression(Integer) +--E 293 + +--S 294 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 295 + +--S 296 of 764 +r0:=1/3*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*(d+e*x))+_ + (b*d-a*e)*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-_ + 1/2*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-_ + (b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 3 4 2 2 3 +--R (18A a b + 6B a )e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A b + 54B a b )d e - 24B b d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A a b + 6B a )d e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 3 3 4 +--R (18A b + 54B a b )d e - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 2B b e x + ((3A b + 9B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((18A a b + 18B a b)e + (- 9A b - 27B a b )d e + 12B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (9A a b + 11B a )e + (18A a b - 6B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 18A b - 30B a b )d e + 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (27A a b + 17B a )d e + (- 18A a b - 42B a b)d e +--R + +--R 2 3 +--R 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +--R 6b e x + (6a e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 296 + +--S 297 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 298 + +--S 299 of 764 +r0:=-1/2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^2)-(2*b*B*d-A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*_ + (b*d-a*e)*(d+e*x))-3*b*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*_ + x^2)/e^4+3/2*b*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*_ + x^2)/(e^3*(b*d-a*e))+3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 2 4 3 2 3 3 2 2 2 +--R ((6A a b + 6B a b)e + (- 6A b - 18B a b )d e + 12B b d e )x +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((12A a b + 12B a b)d e + (- 12A b - 36B a b )d e + 24B b d e)x +--R + +--R 2 2 2 2 3 2 3 3 4 +--R (6A a b + 6B a b)d e + (- 6A b - 18B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R B b e x + ((2A b + 6B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 3A a b + 3B a b)e + (9A b + 15B a b )d e - 18B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 6A a b - 2B a )e + (6A a b + 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (6A b - 6B a b )d e - 12B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 3 +--R - A a e + (- 3A a b - B a )d e + (6A a b + 12B a b)d e - 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 299 + +--S 300 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 301 + +--S 302 of 764 +r0:=-1/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^3)-1/6*(4*b*B*d-A*b*e-3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^2)+b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(b*d-a*e))-1/2*b*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x))-b^2*(4*b*B*d-A*b*e-_ + 3*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 2 4 3 3 3 +--R ((6A b + 18B a b )e - 24B b d e )x +--R + +--R 3 2 3 3 2 2 2 +--R ((18A b + 54B a b )d e - 72B b d e )x +--R + +--R 3 2 2 2 3 3 3 2 3 +--R ((18A b + 54B a b )d e - 72B b d e)x + (6A b + 18B a b )d e +--R + +--R 3 4 +--R - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((- 11A b - 9B a b )e + 44B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 18A a b - 18B a b)e + (- 15A b + 27B a b )d e + 60B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 9A a b - 3B a )e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 6A b + 54B a b )d e + 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (- 3A a b - B a )d e + (- 6A a b - 6B a b)d e +--R + +--R 2 3 +--R 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 6 3 5 3 5 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 302 + +--S 303 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 304 + +--S 305 of 764 +r0:=-1/4*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/3*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^3)-_ + 1/2*b*B*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^2)+b^2*B*_ + (b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))+b^3*B*_ + log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 5 4 4 4 3 4 4 2 3 3 +--R (12B a b e - 12B b d e )x + (48B a b d e - 48B b d e )x +--R + +--R 3 2 3 4 3 2 2 3 3 2 4 4 +--R (72B a b d e - 72B b d e )x + (48B a b d e - 48B b d e)x +--R + +--R 3 4 4 5 +--R 12B a b d e - 12B b d +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 4 +--R ((- 3A b - 10B a b )e + 13B b d e )x +--R + +--R 3 2 2 5 3 4 4 2 3 3 +--R ((- 12A a b - 36B a b )e + 44B a b d e + 4B b d e )x +--R + +--R 2 2 3 5 2 2 4 3 2 3 +--R (- 18A a b - 18B a b)e - 36B a b d e + 102B a b d e +--R + +--R 4 3 2 +--R - 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 3 4 2 2 2 3 3 3 2 +--R (- 12A a b - 4B a )e - 8B a b d e - 24B a b d e + 84B a b d e +--R + +--R 4 4 +--R - 36B b d e +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R - 3A a e - B a d e - 2B a b d e - 6B a b d e + 24B a b d e - 12B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 2 9 5 2 10 9 2 2 8 4 +--R (12a b e - 12b d e )x + (12a e + 36a b d e - 48b d e )x +--R + +--R 2 9 2 8 2 3 7 3 +--R (48a d e + 24a b d e - 72b d e )x +--R + +--R 2 2 8 3 7 2 4 6 2 +--R (72a d e - 24a b d e - 48b d e )x +--R + +--R 2 3 7 4 6 2 5 5 2 4 6 5 5 +--R (48a d e - 36a b d e - 12b d e )x + 12a d e - 12a b d e +--R Type: Expression(Integer) +--E 305 + +--S 306 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 307 + +--S 308 of 764 +r0:=1/4*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*_ + (d+e*x)^4)+1/5*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*_ + (d+e*x)^5) +--R +--R +--R (2) +--R 4 3 4 4 +--R ((A b - 5B a b )e + 4B b d)x +--R + +--R 3 2 2 4 3 3 +--R ((- A a b - 15B a b )e + (5A b + 11B a b )d)x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 9A a b - 15B a b)e + (15A a b + 9B a b )d)x +--R + +--R 3 4 2 2 3 4 3 4 +--R ((- 11A a b - 5B a )e + (15A a b + B a b)d)x - 4A a e + (5A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 7 6 2 2 5 5 +--R (20a e - 40a b d e + 20b d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (100a d e - 200a b d e + 100b d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (100a d e - 200a b d e + 100b d e)x + 20a d e - 40a b d e + 20b d +--R Type: Expression(Integer) +--E 308 + +--S 309 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 310 + +--S 311 of 764 +r0:=-1/6*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^6)+1/12*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^5)+1/60*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 5 4 2 5 5 +--R ((- A b + 3B a b )e - 2B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 4 +--R ((A a b - 3B a b )e + (- 6A b + 20B a b )d e - 12B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (- A a b - 27B a b )e + (6A a b + 70B a b )d e +--R + +--R 5 4 2 +--R (- 15A b - 33B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 19A a b - 33B a b)e + (54A a b + 70B a b )d e +--R + +--R 4 2 3 2 +--R (- 45A a b - 27B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 26A a b - 12B a )e + (66A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 +--R (- 45A a b - 3B a b )d +--R * +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R - 10A a e + (24A a b - 2B a )d e + (- 15A a b + 3B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 9 2 8 2 2 7 3 3 6 6 +--R (60a e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 8 2 2 7 2 3 6 3 4 5 5 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e )x +--R + +--R 3 2 7 2 3 6 2 4 5 3 5 4 4 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (1200a d e - 3600a b d e + 3600a b d e - 1200b d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e)x + 60a d e +--R + +--R 2 7 2 2 8 3 9 +--R - 180a b d e + 180a b d e - 60b d +--R Type: Expression(Integer) +--E 311 + +--S 312 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 313 + +--S 314 of 764 +r0:=-1/7*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^7)+1/42*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^6)+1/84*b*(4*b*B*d+3*A*b*e-_ + 7*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)^3*_ + (d+e*x)^5)+1/420*b*(4*b*B*d+3*A*b*e-7*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 6 5 3 6 2 6 +--R ((3A b - 7B a b )e + 4B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 5 +--R ((- 3A a b + 7B a b )e + (21A b - 53B a b )d e + 28B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (3A a b - 7B a b )e + (- 21A a b + 53B a b )d e +--R + +--R 6 5 2 6 3 +--R (63A b - 175B a b )d e + 84B b d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (- 3A a b - 133B a b )e + (21A a b + 507B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 63A a b - 665B a b )d e + (105A b + 231B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 102A a b - 182B a b)e + (399A a b + 613B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 567A a b - 665B a b )d e + (315A a b + 189B a b )d +--R * +--R 2 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 150A a b - 70B a )e + (546A a b + 206B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 693A a b - 175B a b )d e + (315A a b + 21B a b )d +--R * +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R - 60A a e + (210A a b - 10B a )d e + (- 252A a b + 28B a b)d e +--R + +--R 3 3 4 2 3 +--R (105A a b - 21B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 11 3 10 2 2 2 9 3 3 8 4 4 7 7 +--R (420a e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e )x +--R + +--R 4 10 3 2 9 2 2 3 8 3 4 7 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 5 6 +--R 2940b d e +--R * +--R 6 +--R x +--R + +--R 4 2 9 3 3 8 2 2 4 7 3 5 6 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 6 5 +--R 8820b d e +--R * +--R 5 +--R x +--R + +--R 4 3 8 3 4 7 2 2 5 6 3 6 5 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 7 4 +--R 14700b d e +--R * +--R 4 +--R x +--R + +--R 4 4 7 3 5 6 2 2 6 5 3 7 4 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 8 3 +--R 14700b d e +--R * +--R 3 +--R x +--R + +--R 4 5 6 3 6 5 2 2 7 4 3 8 3 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 9 2 +--R 8820b d e +--R * +--R 2 +--R x +--R + +--R 4 6 5 3 7 4 2 2 8 3 3 9 2 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 10 +--R 2940b d e +--R * +--R x +--R + +--R 4 7 4 3 8 3 2 2 9 2 3 10 4 11 +--R 420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R Type: Expression(Integer) +--E 314 + +--S 315 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 316 + +--S 317 of 764 +r0:=-1/8*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^8)-1/14*(b*B*d+A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^7)-1/28*b*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^6)-1/56*b^2*_ + (b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(b*d-a*e)*_ + (d+e*x)^5)-1/280*b^2*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 70B b e x + ((- 56A b - 168B a b )e - 56B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 140A a b - 140B a b)e + (- 28A b - 84B a b )d e - 28B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 120A a b - 40B a )e + (- 40A a b - 40B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 8A b - 24B a b )d e - 8B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 35A a e + (- 15A a b - 5B a )d e + (- 5A a b - 5B a b)d e +--R + +--R 3 2 3 3 4 +--R (- A b - 3B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 9 13 12 8 12 2 11 7 +--R 280b e x + (280a e + 2240b d e )x + (2240a d e + 7840b d e )x +--R + +--R 2 11 3 10 6 3 10 4 9 5 +--R (7840a d e + 15680b d e )x + (15680a d e + 19600b d e )x +--R + +--R 4 9 5 8 4 5 8 6 7 3 +--R (19600a d e + 15680b d e )x + (15680a d e + 7840b d e )x +--R + +--R 6 7 7 6 2 7 6 8 5 8 5 +--R (7840a d e + 2240b d e )x + (2240a d e + 280b d e )x + 280a d e +--R Type: Expression(Integer) +--E 317 + +--S 318 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 319 + +--S 320 of 764 +r0:=-1/9*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^9)-1/72*(4*b*B*d+5*A*b*e-9*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^8)-1/168*b*(4*b*B*d+5*A*b*e-_ + 9*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^7)-_ + 1/420*b^2*(4*b*B*d+5*A*b*e-9*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^6)-1/2520*b^2*(4*b*B*d+5*A*b*e-9*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 504B b e x + ((- 420A b - 1260B a b )e - 336B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 1080A a b - 1080B a b)e + (- 180A b - 540B a b )d e +--R + +--R 3 2 2 +--R - 144B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 945A a b - 315B a )e + (- 270A a b - 270B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 45A b - 135B a b )d e - 36B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 280A a e + (- 105A a b - 35B a )d e + (- 30A a b - 30B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 5A b - 15B a b )d e - 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 10 14 13 9 +--R 2520b e x + (2520a e + 22680b d e )x +--R + +--R 13 2 12 8 2 12 3 11 7 +--R (22680a d e + 90720b d e )x + (90720a d e + 211680b d e )x +--R + +--R 3 11 4 10 6 4 10 5 9 5 +--R (211680a d e + 317520b d e )x + (317520a d e + 317520b d e )x +--R + +--R 5 9 6 8 4 6 8 7 7 3 +--R (317520a d e + 211680b d e )x + (211680a d e + 90720b d e )x +--R + +--R 7 7 8 6 2 8 6 9 5 9 5 +--R (90720a d e + 22680b d e )x + (22680a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 320 + +--S 321 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 322 + +--S 323 of 764 +r0:=-1/10*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^10)-1/45*(2*b*B*d+3*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^9)-1/120*b*(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^8)-_ + 1/360*b^2*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^7)-1/2520*b^2*(2*b*B*d+3*A*b*e-5*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 420B b e x + ((- 360A b - 1080B a b )e - 240B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 945A a b - 945B a b)e + (- 135A b - 405B a b )d e +--R + +--R 3 2 2 +--R - 90B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 840A a b - 280B a )e + (- 210A a b - 210B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 30A b - 90B a b )d e - 20B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 252A a e + (- 84A a b - 28B a )d e + (- 21A a b - 21B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 3A b - 9B a b )d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 15 11 15 14 10 +--R 2520b e x + (2520a e + 25200b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (25200a d e + 113400b d e )x + (113400a d e + 302400b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (302400a d e + 529200b d e )x + (529200a d e + 635040b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (635040a d e + 529200b d e )x + (529200a d e + 302400b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (302400a d e + 113400b d e )x + (113400a d e + 25200b d e )x +--R + +--R 9 6 10 5 10 5 +--R (25200a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 323 + +--S 324 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 325 + +--S 326 of 764 +r0:=-1/11*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^11)-1/110*(4*b*B*d+7*A*b*e-11*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^10)-1/330*b*(4*b*B*d+7*A*b*e-_ + 11*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^9)-_ + 1/1155*b^2*(4*b*B*d+7*A*b*e-11*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^8)-1/9240*b^2*(4*b*B*d+7*A*b*e-11*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 1320B b e x + ((- 1155A b - 3465B a b )e - 660B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 3080A a b - 3080B a b)e + (- 385A b - 1155B a b )d e +--R + +--R 3 2 2 +--R - 220B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 2772A a b - 924B a )e + (- 616A a b - 616B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 77A b - 231B a b )d e - 44B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 840A a e + (- 252A a b - 84B a )d e + (- 56A a b - 56B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 7A b - 21B a b )d e - 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 16 12 16 15 11 +--R 9240b e x + (9240a e + 101640b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (101640a d e + 508200b d e )x + (508200a d e + 1524600b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (1524600a d e + 3049200b d e )x + (3049200a d e + 4268880b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (4268880a d e + 4268880b d e )x + (4268880a d e + 3049200b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (3049200a d e + 1524600b d e )x + (1524600a d e + 508200b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (508200a d e + 101640b d e )x + (101640a d e + 9240b d e )x +--R + +--R 11 5 +--R 9240a d e +--R Type: Expression(Integer) +--E 326 + +--S 327 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 764 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R m | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 764 +r0:=20*(b*d-a*e)^2*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4*(4+m)*(5+m)*(6+m)*(7+m))-_ + 5*(b*d-a*e)*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(a+b*x)*(d+e*x)^(1+m)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3*(5+m)*(6+m)*(7+m))+(A*b*e*(7+m)-_ + B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (b*e^2*(6+m)*(7+m))+B*(a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e*(7+m))+120*(b*d-a*e)^4*(A*b*e*(7+m)-B*(6*b*d+_ + a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6*_ + (2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m))-120*(b*d-a*e)^5*(A*b*e*(7+m)-_ + B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^7*(1+m)*(2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)*(a+b*x))-60*(b*d-_ + a*e)^3*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(a+b*x)*(d+e*x)^(1+m)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)) +--R +--R +--R (2) +--R 5 6 6 5 6 5 5 6 4 5 6 3 5 6 2 +--R B b e m + 21B b e m + 175B b e m + 735B b e m + 1624B b e m +--R + +--R 5 6 5 6 +--R 1764B b e m + 720B b e +--R * +--R 6 +--R x +--R + +--R 5 4 6 6 5 4 6 5 5 5 +--R (A b + 5B a b )e m + ((22A b + 110B a b )e - 6B b d e )m +--R + +--R 5 4 6 5 5 4 +--R ((190A b + 950B a b )e - 90B b d e )m +--R + +--R 5 4 6 5 5 3 +--R ((820A b + 4100B a b )e - 510B b d e )m +--R + +--R 5 4 6 5 5 2 +--R ((1849A b + 9245B a b )e - 1350B b d e )m +--R + +--R 5 4 6 5 5 +--R ((2038A b + 10190B a b )e - 1644B b d e )m +--R + +--R 5 4 6 5 5 +--R (840A b + 4200B a b )e - 720B b d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 6 6 +--R (5A a b + 10B a b )e m +--R + +--R 4 2 3 6 5 4 5 5 +--R ((115A a b + 230B a b )e + (- 5A b - 25B a b )d e )m +--R + +--R 4 2 3 6 5 4 5 +--R (1035A a b + 2070B a b )e + (- 85A b - 425B a b )d e +--R + +--R 5 2 4 +--R 30B b d e +--R * +--R 4 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (4625A a b + 9250B a b )e + (- 525A b - 2625B a b )d e +--R + +--R 5 2 4 +--R 300B b d e +--R * +--R 3 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (10720A a b + 21440B a b )e + (- 1475A b - 7375B a b )d e +--R + +--R 5 2 4 +--R 1050B b d e +--R * +--R 2 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (12060A a b + 24120B a b )e + (- 1870A b - 9350B a b )d e +--R + +--R 5 2 4 +--R 1500B b d e +--R * +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (5040A a b + 10080B a b )e + (- 840A b - 4200B a b )d e +--R + +--R 5 2 4 +--R 720B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 6 +--R (10A a b + 10B a b )e m +--R + +--R 2 3 3 2 6 4 2 3 5 5 +--R ((240A a b + 240B a b )e + (- 20A a b - 40B a b )d e )m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2260A a b + 2260B a b )e + (- 380A a b - 760B a b )d e +--R + +--R 5 4 2 4 +--R (20A b + 100B a b )d e +--R * +--R 4 +--R m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (10560A a b + 10560B a b )e + (- 2620A a b - 5240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (260A b + 1300B a b )d e - 120B b d e +--R * +--R 3 +--R m +--R + +--R 2 3 3 2 6 +--R (25450A a b + 25450B a b )e +--R + +--R 4 2 3 5 5 4 2 4 +--R (- 8020A a b - 16040B a b )d e + (1060A b + 5300B a b )d e +--R + +--R 5 3 3 +--R - 720B b d e +--R * +--R 2 +--R m +--R + +--R 2 3 3 2 6 +--R (29520A a b + 29520B a b )e +--R + +--R 4 2 3 5 5 4 2 4 +--R (- 10800A a b - 21600B a b )d e + (1660A b + 8300B a b )d e +--R + +--R 5 3 3 +--R - 1320B b d e +--R * +--R m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (12600A a b + 12600B a b )e + (- 5040A a b - 10080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (840A b + 4200B a b )d e - 720B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 6 +--R (10A a b + 5B a b)e m +--R + +--R 3 2 4 6 2 3 3 2 5 5 +--R ((250A a b + 125B a b)e + (- 30A a b - 30B a b )d e )m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (2470A a b + 1235B a b)e + (- 630A a b - 630B a b )d e +--R + +--R 4 2 3 2 4 +--R (60A a b + 120B a b )d e +--R * +--R 4 +--R m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (12190A a b + 6095B a b)e + (- 4890A a b - 4890B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (960A a b + 1920B a b )d e + (- 60A b - 300B a b )d e +--R * +--R 3 +--R m +--R + +--R 3 2 4 6 +--R (31120A a b + 15560B a b)e +--R + +--R 2 3 3 2 5 +--R (- 17010A a b - 17010B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (4980A a b + 9960B a b )d e + (- 600A b - 3000B a b )d e +--R + +--R 5 4 2 +--R 360B b d e +--R * +--R 2 +--R m +--R + +--R 3 2 4 6 +--R (37960A a b + 18980B a b)e +--R + +--R 2 3 3 2 5 +--R (- 25320A a b - 25320B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (9120A a b + 18240B a b )d e + (- 1380A b - 6900B a b )d e +--R + +--R 5 4 2 +--R 1080B b d e +--R * +--R m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (16800A a b + 8400B a b)e + (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (5040A a b + 10080B a b )d e + (- 840A b - 4200B a b )d e +--R + +--R 5 4 2 +--R 720B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 6 +--R (5A a b + B a )e m +--R + +--R 4 5 6 3 2 4 5 5 +--R ((130A a b + 26B a )e + (- 20A a b - 10B a b)d e )m +--R + +--R 4 5 6 3 2 4 5 +--R (1350A a b + 270B a )e + (- 460A a b - 230B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (60A a b + 60B a b )d e +--R * +--R 4 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (7100A a b + 1420B a )e + (- 4020A a b - 2010B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1140A a b + 1140B a b )d e + (- 120A a b - 240B a b )d e +--R * +--R 3 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (19645A a b + 3929B a )e + (- 16340A a b - 8170B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (7500A a b + 7500B a b )d e + (- 1680A a b - 3360B a b )d e +--R + +--R 5 4 4 2 +--R (120A b + 600B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (26370A a b + 5274B a )e + (- 29560A a b - 14780B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (19020A a b + 19020B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 6600A a b - 13200B a b )d e + (960A b + 4800B a b )d e +--R + +--R 5 5 +--R - 720B b d e +--R * +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (12600A a b + 2520B a )e + (- 16800A a b - 8400B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (12600A a b + 12600B a b )d e + (- 5040A a b - 10080B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (840A b + 4200B a b )d e - 720B b d e +--R * +--R x +--R + +--R 5 6 6 5 6 4 5 5 5 +--R A a e m + (27A a e + (- 5A a b - B a )d e )m +--R + +--R 5 6 4 5 5 3 2 4 2 4 4 +--R (295A a e + (- 125A a b - 25B a )d e + (20A a b + 10B a b)d e )m +--R + +--R 5 6 4 5 5 +--R 1665A a e + (- 1225A a b - 245B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (440A a b + 220B a b)d e + (- 60A a b - 60B a b )d e +--R * +--R 3 +--R m +--R + +--R 5 6 4 5 5 +--R 5104A a e + (- 5875A a b - 1175B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (3580A a b + 1790B a b)d e + (- 1080A a b - 1080B a b )d e +--R + +--R 4 2 3 4 2 +--R (120A a b + 240B a b )d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 5 5 +--R 8028A a e + (- 13770A a b - 2754B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (12760A a b + 6380B a b)d e + (- 6420A a b - 6420B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (1560A a b + 3120B a b )d e + (- 120A b - 600B a b )d e +--R * +--R m +--R + +--R 5 6 4 5 5 +--R 5040A a e + (- 12600A a b - 2520B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (16800A a b + 8400B a b)d e + (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (5040A a b + 10080B a b )d e + (- 840A b - 4200B a b )d e + 720B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m + 13132b e m +--R + +--R 7 7 +--R 13068b e m + 5040b e +--R * +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a e m + 28a e m + 322a e m + 1960a e m + 6769a e m + 13132a e m +--R + +--R 7 7 +--R 13068a e m + 5040a e +--R Type: Expression(Integer) +--E 329 + +--S 330 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 764 +t0:=(A+B*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 11 4 3 6 4 5 10 +--R B b e x + ((A b + 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 6 4 3 5 4 2 4 9 +--R ((4A a b + 6B a b )e + (6A b + 24B a b )d e + 15B b d e )x +--R + +--R 2 2 3 6 3 2 2 5 +--R (6A a b + 4B a b)e + (24A a b + 36B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (15A b + 60B a b )d e + 20B b d e +--R * +--R 8 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (4A a b + B a )e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 4 4 2 +--R (60A a b + 90B a b )d e + (20A b + 80B a b )d e + 15B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 5 2 2 3 2 4 +--R A a e + (24A a b + 6B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 3 3 4 3 4 2 4 5 +--R (80A a b + 120B a b )d e + (15A b + 60B a b )d e + 6B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 6A a d e + (60A a b + 15B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (60A a b + 90B a b )d e + (6A b + 24B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A a d e + (80A a b + 20B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 5 4 3 6 +--R (24A a b + 36B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 4 4 2 2 2 3 5 +--R 20A a d e + (60A a b + 15B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 6 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 2 +--R (15A a d e + (24A a b + 6B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 5 3 4 6 4 6 +--R (6A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 764 +r0:=-1/858*(b*d-a*e)^2*(6*b*B*d-13*A*b*e+7*a*B*e)*(d+e*x)^7*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)+5/1716*(b*d-a*e)*(6*b*B*d-13*A*b*e+7*a*B*e)*_ + (a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-1/156*(6*b*B*d-_ + 13*A*b*e+7*a*B*e)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+_ + 1/13*B*(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 1/10296*(b*d-a*e)^4*(6*b*B*d-13*A*b*e+7*a*B*e)*(d+e*x)^7*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^6)+1/72072*(b*d-a*e)^5*(6*b*B*d-13*A*b*e+_ + 7*a*B*e)*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+_ + 1/2574*(b*d-a*e)^3*(6*b*B*d-13*A*b*e+7*a*B*e)*(a+b*x)*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 13 13 5 4 13 5 12 12 +--R 5544B b e x + ((6006A b + 30030B a b )e + 36036B b d e )x +--R + +--R 4 2 3 13 5 4 12 +--R (32760A a b + 65520B a b )e + (39312A b + 196560B a b )d e +--R + +--R 5 2 11 +--R 98280B b d e +--R * +--R 11 +--R x +--R + +--R 2 3 3 2 13 4 2 3 12 +--R (72072A a b + 72072B a b )e + (216216A a b + 432432B a b )d e +--R + +--R 5 4 2 11 5 3 10 +--R (108108A b + 540540B a b )d e + 144144B b d e +--R * +--R 10 +--R x +--R + +--R 3 2 4 13 2 3 3 2 12 +--R (80080A a b + 40040B a b)e + (480480A a b + 480480B a b )d e +--R + +--R 4 2 3 2 11 +--R (600600A a b + 1201200B a b )d e +--R + +--R 5 4 3 10 5 4 9 +--R (160160A b + 800800B a b )d e + 120120B b d e +--R * +--R 9 +--R x +--R + +--R 4 5 13 3 2 4 12 +--R (45045A a b + 9009B a )e + (540540A a b + 270270B a b)d e +--R + +--R 2 3 3 2 2 11 +--R (1351350A a b + 1351350B a b )d e +--R + +--R 4 2 3 3 10 +--R (900900A a b + 1801800B a b )d e +--R + +--R 5 4 4 9 5 5 8 +--R (135135A b + 675675B a b )d e + 54054B b d e +--R * +--R 8 +--R x +--R + +--R 5 13 4 5 12 +--R 10296A a e + (308880A a b + 61776B a )d e +--R + +--R 3 2 4 2 11 +--R (1544400A a b + 772200B a b)d e +--R + +--R 2 3 3 2 3 10 +--R (2059200A a b + 2059200B a b )d e +--R + +--R 4 2 3 4 9 5 4 5 8 +--R (772200A a b + 1544400B a b )d e + (61776A b + 308880B a b )d e +--R + +--R 5 6 7 +--R 10296B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 2 11 +--R 72072A a d e + (900900A a b + 180180B a )d e +--R + +--R 3 2 4 3 10 +--R (2402400A a b + 1201200B a b)d e +--R + +--R 2 3 3 2 4 9 +--R (1801800A a b + 1801800B a b )d e +--R + +--R 4 2 3 5 8 5 4 6 7 +--R (360360A a b + 720720B a b )d e + (12012A b + 60060B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 2 11 4 5 3 10 +--R 216216A a d e + (1441440A a b + 288288B a )d e +--R + +--R 3 2 4 4 9 +--R (2162160A a b + 1081080B a b)d e +--R + +--R 2 3 3 2 5 8 4 2 3 6 7 +--R (864864A a b + 864864B a b )d e + (72072A a b + 144144B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 3 10 4 5 4 9 +--R 360360A a d e + (1351350A a b + 270270B a )d e +--R + +--R 3 2 4 5 8 2 3 3 2 6 7 +--R (1081080A a b + 540540B a b)d e + (180180A a b + 180180B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 4 9 4 5 5 8 +--R 360360A a d e + (720720A a b + 144144B a )d e +--R + +--R 3 2 4 6 7 +--R (240240A a b + 120120B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 5 8 4 5 6 7 2 5 6 7 +--R (216216A a d e + (180180A a b + 36036B a )d e )x + 72072A a d e x +--R + +--R 5 7 6 4 5 8 5 +--R 10296A a d e + (- 6435A a b - 1287B a )d e +--R + +--R 3 2 4 9 4 2 3 3 2 10 3 +--R (2860A a b + 1430B a b)d e + (- 858A a b - 858B a b )d e +--R + +--R 4 2 3 11 2 5 4 12 5 13 +--R (156A a b + 312B a b )d e + (- 13A b - 65B a b )d e + 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 72072b e x + 72072a e +--R Type: Expression(Integer) +--E 332 + +--S 333 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 764 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 10 4 3 5 4 4 9 +--R B b e x + ((A b + 4B a b )e + 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 8 +--R ((4A a b + 6B a b )e + (5A b + 20B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (6A a b + 4B a b)e + (20A a b + 30B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (10A b + 40B a b )d e + 10B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b + B a )e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (40A a b + 60B a b )d e + (10A b + 40B a b )d e + 5B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (20A a b + 5B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (40A a b + 60B a b )d e + (5A b + 20B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R 5A a d e + (40A a b + 10B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 4 4 3 5 +--R (20A a b + 30B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 3 2 2 2 3 4 +--R 10A a d e + (40A a b + 10B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 5 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 2 +--R (10A a d e + (20A a b + 5B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 4 3 4 5 4 5 +--R (5A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 764 +r0:=1/99*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^6*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)-1/44*(b*d-a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)+1/22*(2*A*b*e-B*(b*d+_ + a*e))*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+1/12*B*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)+1/924*(b*d-a*e)^4*(2*A*b*e-_ + B*(b*d+a*e))*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)-_ + 1/5544*(b*d-a*e)^5*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^7*(a+b*x))-1/264*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*_ + (a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 12 12 5 4 12 5 11 11 +--R 462B b e x + ((504A b + 2520B a b )e + 2520B b d e )x +--R + +--R 4 2 3 12 5 4 11 +--R (2772A a b + 5544B a b )e + (2772A b + 13860B a b )d e +--R + +--R 5 2 10 +--R 5544B b d e +--R * +--R 10 +--R x +--R + +--R 2 3 3 2 12 4 2 3 11 +--R (6160A a b + 6160B a b )e + (15400A a b + 30800B a b )d e +--R + +--R 5 4 2 10 5 3 9 +--R (6160A b + 30800B a b )d e + 6160B b d e +--R * +--R 9 +--R x +--R + +--R 3 2 4 12 2 3 3 2 11 +--R (6930A a b + 3465B a b)e + (34650A a b + 34650B a b )d e +--R + +--R 4 2 3 2 10 5 4 3 9 +--R (34650A a b + 69300B a b )d e + (6930A b + 34650B a b )d e +--R + +--R 5 4 8 +--R 3465B b d e +--R * +--R 8 +--R x +--R + +--R 4 5 12 3 2 4 11 +--R (3960A a b + 792B a )e + (39600A a b + 19800B a b)d e +--R + +--R 2 3 3 2 2 10 4 2 3 3 9 +--R (79200A a b + 79200B a b )d e + (39600A a b + 79200B a b )d e +--R + +--R 5 4 4 8 5 5 7 +--R (3960A b + 19800B a b )d e + 792B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 11 +--R 924A a e + (23100A a b + 4620B a )d e +--R + +--R 3 2 4 2 10 2 3 3 2 3 9 +--R (92400A a b + 46200B a b)d e + (92400A a b + 92400B a b )d e +--R + +--R 4 2 3 4 8 5 4 5 7 +--R (23100A a b + 46200B a b )d e + (924A b + 4620B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 11 4 5 2 10 +--R 5544A a d e + (55440A a b + 11088B a )d e +--R + +--R 3 2 4 3 9 2 3 3 2 4 8 +--R (110880A a b + 55440B a b)d e + (55440A a b + 55440B a b )d e +--R + +--R 4 2 3 5 7 +--R (5544A a b + 11088B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 2 10 4 5 3 9 +--R 13860A a d e + (69300A a b + 13860B a )d e +--R + +--R 3 2 4 4 8 2 3 3 2 5 7 +--R (69300A a b + 34650B a b)d e + (13860A a b + 13860B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 3 9 4 5 4 8 +--R 18480A a d e + (46200A a b + 9240B a )d e +--R + +--R 3 2 4 5 7 +--R (18480A a b + 9240B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 4 8 4 5 5 7 2 5 5 7 +--R (13860A a d e + (13860A a b + 2772B a )d e )x + 5544A a d e x +--R + +--R 5 6 6 4 5 7 5 3 2 4 8 4 +--R 924A a d e + (- 660A a b - 132B a )d e + (330A a b + 165B a b)d e +--R + +--R 2 3 3 2 9 3 4 2 3 10 2 +--R (- 110A a b - 110B a b )d e + (22A a b + 44B a b )d e +--R + +--R 5 4 11 5 12 +--R (- 2A b - 10B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 5544b e x + 5544a e +--R Type: Expression(Integer) +--E 335 + +--S 336 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 336 + +)clear all + +--S 337 of 764 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 4 9 4 3 4 4 3 8 +--R B b e x + ((A b + 4B a b )e + 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((4A a b + 6B a b )e + (4A b + 16B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (6A a b + 4B a b)e + (16A a b + 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (6A b + 24B a b )d e + 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (24A a b + 36B a b )d e + (4A b + 16B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R A a e + (16A a b + 4B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (16A a b + 24B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 4A a d e + (24A a b + 6B a )d e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 4 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (6A a d e + (16A a b + 4B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (4A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 764 +r0:=-1/1980*(b*d-a*e)^4*(6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^6*e)-1/660*(b*d-a*e)^2*(6*b*B*d-11*A*b*e+5*a*B*e)*_ + (a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^4*e)-2/495*(b*d-a*e)*_ + (6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^3*e)-1/110*(6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*_ + (d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+1/11*B*(a+b*x)*(d+_ + e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-1/2310*(b*d-a*e)^3*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6 +--R +--R +--R (2) +--R 10 4 10 10 9 4 10 3 9 +--R 1260B b e x + ((1386A b + 5670B a b )e + 5544B b d e )x +--R + +--R 9 2 8 4 10 9 3 +--R (6314A a b + 9730B a b )e + (6160A b + 25256B a b )d e +--R + +--R 10 2 2 +--R 9240B b d e +--R * +--R 8 +--R x +--R + +--R 2 8 3 7 4 9 2 8 3 +--R (11011A a b + 7595B a b )e + (28490A a b + 44044B a b )d e +--R + +--R 10 9 2 2 10 3 +--R (10395A b + 42735B a b )d e + 6930B b d e +--R * +--R 7 +--R x +--R + +--R 3 7 4 6 4 2 8 3 7 3 +--R (8789A a b + 2305B a b )e + (50710A a b + 35156B a b )d e +--R + +--R 9 2 8 2 2 10 9 3 +--R (49005A a b + 76065B a b )d e + (7920A b + 32670B a b )d e +--R + +--R 10 4 +--R 1980B b d +--R * +--R 6 +--R x +--R + +--R 4 6 5 5 4 3 7 4 6 3 +--R (2761A a b + 5B a b )e + (41690A a b + 11044B a b )d e +--R + +--R 2 8 3 7 2 2 9 2 8 3 +--R (89595A a b + 62535B a b )d e + (38280A a b + 59730B a b )d e +--R + +--R 10 9 4 +--R (2310A b + 9570B a b )d +--R * +--R 5 +--R x +--R + +--R 5 5 6 4 4 4 6 5 5 3 +--R (11A a b - 5B a b )e + (13750A a b + 44B a b )d e +--R + +--R 3 7 4 6 2 2 2 8 3 7 3 +--R (76725A a b + 20625B a b )d e + (72600A a b + 51150B a b )d e +--R + +--R 9 2 8 4 +--R (11550A a b + 18150B a b )d +--R * +--R 4 +--R x +--R + +--R 6 4 7 3 4 5 5 6 4 3 +--R (- 11A a b + 5B a b )e + (110A a b - 44B a b )d e +--R + +--R 4 6 5 5 2 2 3 7 4 6 3 +--R (27225A a b + 165B a b )d e + (66000A a b + 18150B a b )d e +--R + +--R 2 8 3 7 4 +--R (23100A a b + 16500B a b )d +--R * +--R 3 +--R x +--R + +--R 7 3 8 2 4 6 4 7 3 3 +--R (11A a b - 5B a b )e + (- 110A a b + 44B a b )d e +--R + +--R 5 5 6 4 2 2 4 6 5 5 3 +--R (495A a b - 165B a b )d e + (26400A a b + 330B a b )d e +--R + +--R 3 7 4 6 4 +--R (23100A a b + 6600B a b )d +--R * +--R 2 +--R x +--R + +--R 8 2 9 4 7 3 8 2 3 +--R (- 11A a b + 5B a b)e + (110A a b - 44B a b )d e +--R + +--R 6 4 7 3 2 2 5 5 6 4 3 +--R (- 495A a b + 165B a b )d e + (1320A a b - 330B a b )d e +--R + +--R 4 6 5 5 4 +--R (11550A a b + 330B a b )d +--R * +--R x +--R + +--R 9 10 4 8 2 9 3 +--R (11A a b - 5B a )e + (- 110A a b + 44B a b)d e +--R + +--R 7 3 8 2 2 2 6 4 7 3 3 +--R (495A a b - 165B a b )d e + (- 1320A a b + 330B a b )d e +--R + +--R 5 5 6 4 4 +--R (2310A a b - 330B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 +--R 13860b +--R Type: Expression(Integer) +--E 338 + +--S 339 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 339 + +)clear all + +--S 340 of 764 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 764 +r0:=-1/360*(b*d-a*e)^3*(3*b*B*d-5*A*b*e+2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^5*e)-1/120*(b*d-a*e)*(3*b*B*d-5*A*b*e+2*a*B*e)*_ + (a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^3*e)-1/45*(3*b*B*d-_ + 5*A*b*e+2*a*B*e)*(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+_ + 1/10*B*(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 1/420*(b*d-a*e)^2*(3*b*B*d-5*A*b*e+2*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^5 +--R +--R +--R (2) +--R 9 3 9 9 8 3 9 2 8 +--R 252B b e x + ((280A b + 1148B a b )e + 840B b d e )x +--R + +--R 8 2 7 3 9 8 2 +--R (1295A a b + 2002B a b )e + (945A b + 3885B a b )d e +--R + +--R 9 2 +--R 945B b d e +--R * +--R 7 +--R x +--R + +--R 2 7 3 6 3 8 2 7 2 +--R (2305A a b + 1598B a b )e + (4455A a b + 6915B a b )d e +--R + +--R 9 8 2 9 3 +--R (1080A b + 4455B a b )d e + 360B b d +--R * +--R 6 +--R x +--R + +--R 3 6 4 5 3 2 7 3 6 2 +--R (1895A a b + 502B a b )e + (8145A a b + 5685B a b )d e +--R + +--R 8 2 7 2 9 8 3 +--R (5220A a b + 8145B a b )d e + (420A b + 1740B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 5 4 3 3 6 4 5 2 +--R (625A a b + 2B a b )e + (6975A a b + 1875B a b )d e +--R + +--R 2 7 3 6 2 8 2 7 3 +--R (9900A a b + 6975B a b )d e + (2100A a b + 3300B a b )d +--R * +--R 4 +--R x +--R + +--R 5 4 6 3 3 4 5 5 4 2 +--R (5A a b - 2B a b )e + (2475A a b + 15B a b )d e +--R + +--R 3 6 4 5 2 2 7 3 6 3 +--R (9000A a b + 2475B a b )d e + (4200A a b + 3000B a b )d +--R * +--R 3 +--R x +--R + +--R 6 3 7 2 3 5 4 6 3 2 +--R (- 5A a b + 2B a b )e + (45A a b - 15B a b )d e +--R + +--R 4 5 5 4 2 3 6 4 5 3 +--R (3600A a b + 45B a b )d e + (4200A a b + 1200B a b )d +--R * +--R 2 +--R x +--R + +--R 7 2 8 3 6 3 7 2 2 +--R (5A a b - 2B a b)e + (- 45A a b + 15B a b )d e +--R + +--R 5 4 6 3 2 4 5 5 4 3 +--R (180A a b - 45B a b )d e + (2100A a b + 60B a b )d +--R * +--R x +--R + +--R 8 9 3 7 2 8 2 +--R (- 5A a b + 2B a )e + (45A a b - 15B a b)d e +--R + +--R 6 3 7 2 2 5 4 6 3 3 +--R (- 180A a b + 45B a b )d e + (420A a b - 60B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 2520b +--R Type: Expression(Integer) +--E 341 + +--S 342 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 764 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 764 +r0:=-1/72*(b*d-a*e)^2*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^4*e)-1/24*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(d+_ + e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+1/9*B*(a+b*x)*(d+e*x)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-1/84*(b*d-a*e)*(2*b*B*d-3*A*b*e+_ + a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4 +--R +--R +--R (2) +--R 8 2 8 8 7 2 8 7 +--R 56B b e x + ((63A b + 259B a b )e + 126B b d e)x +--R + +--R 7 2 6 2 8 7 8 2 6 +--R ((297A a b + 461B a b )e + (144A b + 594B a b )d e + 72B b d )x +--R + +--R 2 6 3 5 2 7 2 6 +--R (543A a b + 379B a b )e + (696A a b + 1086B a b )d e +--R + +--R 8 7 2 +--R (84A b + 348B a b )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (465A a b + 125B a b )e + (1320A a b + 930B a b )d e +--R + +--R 7 2 6 2 +--R (420A a b + 660B a b )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (165A a b + B a b )e + (1200A a b + 330B a b )d e +--R + +--R 2 6 3 5 2 +--R (840A a b + 600B a b )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (3A a b - B a b )e + (480A a b + 6B a b )d e +--R + +--R 3 5 4 4 2 +--R (840A a b + 240B a b )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 3A a b + B a b)e + (24A a b - 6B a b )d e +--R + +--R 4 4 5 3 2 +--R (420A a b + 12B a b )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 5 3 6 2 2 +--R (3A a b - B a )e + (- 24A a b + 6B a b)d e + (84A a b - 12B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 504b +--R Type: Expression(Integer) +--E 344 + +--S 345 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 764 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 764 +r0:=-1/24*(b*d-a*e)*(3*b*B*d-4*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^3*e)+1/8*B*(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-1/28*(3*b*B*d-4*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^3 +--R +--R +--R (2) +--R 7 7 7 6 7 6 +--R 21B b e x + ((24A b + 99B a b )e + 24B b d)x +--R + +--R 6 2 5 7 6 5 +--R ((116A a b + 181B a b )e + (28A b + 116B a b )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((220A a b + 155B a b )e + (140A a b + 220B a b )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((200A a b + 55B a b )e + (280A a b + 200B a b )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((80A a b + B a b )e + (280A a b + 80B a b )d)x +--R + +--R 5 2 6 4 3 5 2 6 7 +--R ((4A a b - B a b)e + (140A a b + 4B a b )d)x + (- 4A a b + B a )e +--R + +--R 5 2 6 +--R (28A a b - 4B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 168b +--R Type: Expression(Integer) +--E 347 + +--S 348 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 764 +r0:=1/6*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+_ + 1/7*B*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2 +--R +--R +--R (2) +--R 6 6 6 5 5 5 2 4 4 +--R 6B b x + (7A b + 29B a b )x + (35A a b + 55B a b )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 4 2 5 +--R (70A a b + 50B a b )x + (70A a b + 20B a b )x + (35A a b + B a b)x +--R + +--R 5 6 +--R 7A a b - B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 42b +--R Type: Expression(Integer) +--E 350 + +--S 351 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R e x + d +--R Type: Expression(Integer) +--E 352 + +--S 353 of 764 +r0:=-1/3*(b*d-a*e)^2*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/4*(b*d-a*e)*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/5*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/6*B*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-(b*d-a*e)^4*(B*d-A*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/2*(b*d-a*e)^3*(B*d-A*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+(b*d-a*e)^5*(B*d-A*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 5 +--R 60A a b e + (- 300A a b - 60B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (600A a b + 300B a b )d e + (- 600A a b - 600B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (300A a b + 600B a b )d e + (- 60A b - 300B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 6 5 6 6 5 5 +--R 10B b e x + ((12A b + 60B a b )e - 12B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 4 +--R ((75A a b + 150B a b )e + (- 15A b - 75B a b )d e + 15B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (200A a b + 200B a b )e + (- 100A a b - 200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (20A b + 100B a b )d e - 20B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (300A a b + 150B a b )e + (- 300A a b - 300B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (150A a b + 300B a b )d e + (- 30A b - 150B a b )d e + 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (300A a b + 60B a b)e + (- 600A a b - 300B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (60A b + 300B a b )d e - 60B b d e +--R * +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (137A a b + 10B a )e + (- 385A a b - 137B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (470A a b + 385B a b )d e + (- 270A a b - 470B a b )d e +--R + +--R 5 2 4 4 2 5 5 +--R (60A a b + 270B a b )d e - 60B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 7 7 +--R 60b e x + 60a b e +--R Type: Expression(Integer) +--E 353 + +--S 354 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 355 + +--S 356 of 764 +r0:=1/3*(b*d-a*e)*(6*b*B*d-5*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-_ + 1/4*(6*b*B*d-5*A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3+_ + 1/5*(6*b*B*d-5*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x))+_ + (b*d-a*e)^3*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 1/2*(b*d-a*e)^2*(6*b*B*d-5*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^5-(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 5 6 3 2 4 5 +--R (300A a b + 60B a )e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (300A b + 1500B a b )d e - 360B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (300A a b + 60B a )d e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 5 5 6 +--R (300A b + 1500B a b )d e - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 12B b e x + ((15A b + 75B a b )e - 18B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((100A a b + 200B a b )e + (- 25A b - 125B a b )d e + 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (300A a b + 300B a b )e + (- 200A a b - 400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (50A b + 250B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (600A a b + 300B a b)e + (- 900A a b - 900B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (600A a b + 1200B a b )d e + (- 150A b - 750B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (325A a b + 137B a )e + (- 100A a b - 410B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 750A a b - 30B a b )d e + (900A a b + 1080B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 300A b - 1140B a b )d e + 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 60A a e + (625A a b + 197B a )d e + (- 1300A a b - 1010B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (1050A a b + 1770B a b )d e + (- 300A a b - 1320B a b )d e +--R + +--R 4 5 +--R 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +--R 60b e x + (60a e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 356 + +--S 357 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 358 + +--S 359 of 764 +r0:=-5/3*b*(3*b*B*d-2*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 5/4*b*(3*b*B*d-2*A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e))-1/2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e*(b*d-a*e)*(d+e*x)^2)-(3*b*B*d-2*A*b*e-a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x))-5*b*(b*d-a*e)^2*(3*b*B*d-_ + 2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+5/2*b*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+5*b*_ + (b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 3 2 4 6 2 3 3 2 5 +--R (120A a b + 60B a b)e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 2 4 +--R (240A a b + 120B a b)d e + (- 720A a b - 720B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (720A a b + 1440B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 360B b d e +--R * +--R x +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (120A a b + 60B a b)d e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 3B b e x + ((4A b + 20B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 10A b - 50B a b )d e + 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (120A a b + 120B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (40A b + 200B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (40A a b + 65B a b)e + (240A a b + 60B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 420A a b - 570B a b )d e + (180A b + 720B a b )d e +--R + +--R 5 4 2 +--R - 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 60A a b - 12B a )e + (320A a b + 250B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 240A a b - 600B a b )d e + (- 120A a b + 300B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (120A b + 240B a b )d e - 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 6A a e + (- 30A a b - 6B a )d e + (220A a b + 155B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 300A a b - 480B a b )d e + (120A a b + 510B a b )d e +--R + +--R 4 5 +--R - 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 12b e x + (12a e + 24b d e )x + (24a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 359 + +--S 360 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 361 + +--S 362 of 764 +r0:=10/3*b^2*(2*b*B*d-A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-_ + a*e))-5/2*b*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x))-1/3*(B*d-A*e)*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^3)-1/2*(2*b*B*d-A*b*e-_ + a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^2)+_ + 10*b^2*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 5*b^2*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-_ + 10*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 2 3 3 2 6 4 2 3 5 +--R (60A a b + 60B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (60A b + 300B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 2 4 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R x +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (60A a b + 60B a b )d e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 120B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 2B b e x + ((3A b + 15B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 15A b - 75B a b )d e + 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 20A a b + 20B a b )e + (160A a b + 200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 110A b - 430B a b )d e + 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (120A a b + 240B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (120A a b - 120B a b )d e + (- 150A b - 390B a b )d e +--R + +--R 5 4 2 +--R 300B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 15A a b - 3B a )e + (- 60A a b - 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (210A a b + 330B a b )d e + (- 60A a b - 480B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b + 60B a b )d e + 120B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 2A a e + (- 5A a b - B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (90A a b + 130B a b )d e + (- 60A a b - 240B a b )d e + 120B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 8 3 7 3 7 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 362 + +--S 363 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 364 + +--S 365 of 764 +r0:=-5/12*b*(3*b*B*d-A*b*e-2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^2)-5/3*b^2*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x))-_ + 1/4*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/6*(3*b*B*d-A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^3)-5*b^3*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^6+5/2*b^3*(3*b*B*d-A*b*e-2*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e))+5*b^3*(b*d-a*e)*(3*b*B*d-_ + A*b*e-2*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 2 3 6 5 4 5 +--R (60A a b + 120B a b )e + (- 60A b - 300B a b )d e +--R + +--R 5 2 4 +--R 180B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 5 5 4 2 4 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 3 3 +--R 720B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 360A b - 1800B a b )d e +--R + +--R 5 4 2 +--R 1080B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 720B b d e +--R * +--R x +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (60A a b + 120B a b )d e + (- 60A b - 300B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 6B b e x + ((12A b + 60B a b )e - 36B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((- 65A a b - 40B a b )e + (125A b + 445B a b )d e - 375B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 120A a b - 120B a b )e + (- 20A a b + 320B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (260A b + 580B a b )d e - 780B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (- 180A a b - 180B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (150A a b + 840B a b )d e + (210A b - 30B a b )d e - 630B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 20A a b - 4B a )e + (- 40A a b - 20B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 120A a b - 120B a b )d e + (180A a b + 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (60A b - 420B a b )d e - 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 3A a e + (- 5A a b - B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (- 30A a b - 30B a b )d e + (60A a b + 210B a b )d e - 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 365 + +--S 366 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^6 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 367 + +--S 368 of 764 +r0:=-1/12*b*(6*b*B*d-A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e)*(d+e*x)^3)-1/6*b^2*(6*b*B*d-A*b*e-5*a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^2)-1/5*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^5)-_ + 1/20*(6*b*B*d-A*b*e-5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*_ + (b*d-a*e)*(d+e*x)^4)+b^4*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^6*(b*d-a*e))-1/2*b^3*(6*b*B*d-A*b*e-5*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*(d+e*x))-b^4*(6*b*B*d-A*b*e-_ + 5*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 4 6 5 5 5 +--R ((60A b + 300B a b )e - 360B b d e )x +--R + +--R 5 4 5 5 2 4 4 +--R ((300A b + 1500B a b )d e - 1800B b d e )x +--R + +--R 5 4 2 4 5 3 3 3 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 3 3 5 4 2 2 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 4 2 5 5 +--R ((300A b + 1500B a b )d e - 1800B b d e)x +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 60B b e x + ((- 137A b - 325B a b )e + 822B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 300A a b - 600B a b )e + (- 385A b - 125B a b )d e +--R + +--R 5 2 4 +--R 2310B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 300A a b - 300B a b )e + (- 600A a b - 1200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 470A b + 1250B a b )d e + 2820B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 200A a b - 100B a b)e + (- 300A a b - 300B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 600A a b - 1200B a b )d e + (- 270A b + 2250B a b )d e +--R + +--R 5 4 2 +--R 1620B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 75A a b - 15B a )e + (- 100A a b - 50B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 150A a b - 150B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b + 1500B a b )d e + 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 12A a e + (- 15A a b - 3B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (- 30A a b - 30B a b )d e + (- 60A a b - 120B a b )d e + 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 8 5 7 5 7 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 368 + +--S 369 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^7 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 370 + +--S 371 of 764 +r0:=-1/4*b*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^4)-_ + 1/3*b^2*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^3)-1/6*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^6)-_ + 1/5*B*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^5)-1/2*b^3*B*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^2)+b^4*B*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))+b^5*B*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 7 6 6 6 5 6 6 2 5 5 +--R (60B a b e - 60B b d e )x + (360B a b d e - 360B b d e )x +--R + +--R 5 2 5 6 3 4 4 5 3 4 6 4 3 3 +--R (900B a b d e - 900B b d e )x + (1200B a b d e - 1200B b d e )x +--R + +--R 5 4 3 6 5 2 2 5 5 2 6 6 +--R (900B a b d e - 900B b d e )x + (360B a b d e - 360B b d e)x +--R + +--R 5 6 6 7 +--R 60B a b d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 6 5 7 6 6 6 +--R ((- 10A b - 77B a b )e + 87B b d e )x +--R + +--R 5 2 4 7 5 6 6 2 5 5 +--R ((- 60A a b - 300B a b )e + 198B a b d e + 162B b d e )x +--R + +--R 2 4 3 3 7 2 4 6 5 2 5 +--R (- 150A a b - 300B a b )e - 450B a b d e + 945B a b d e +--R + +--R 6 3 4 +--R - 45B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 3 3 6 2 4 2 5 +--R (- 200A a b - 200B a b )e - 200B a b d e - 600B a b d e +--R + +--R 5 3 4 6 4 3 +--R 1660B a b d e - 460B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 4 2 6 3 3 2 5 +--R (- 150A a b - 75B a b)e - 75B a b d e - 150B a b d e +--R + +--R 2 4 3 4 5 4 3 6 5 2 +--R - 450B a b d e + 1470B a b d e - 570B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 5 6 4 2 2 5 3 3 3 4 +--R (- 60A a b - 12B a )e - 18B a b d e - 30B a b d e - 60B a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 180B a b d e + 660B a b d e - 300B b d e +--R * +--R x +--R + +--R 6 7 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 10A a e - 2B a d e - 3B a b d e - 5B a b d e - 10B a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R - 30B a b d e + 120B a b d e - 60B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 2 13 7 2 14 13 2 2 12 6 +--R (60a b e - 60b d e )x + (60a e + 300a b d e - 360b d e )x +--R + +--R 2 13 2 12 2 3 11 5 +--R (360a d e + 540a b d e - 900b d e )x +--R + +--R 2 2 12 3 11 2 4 10 4 +--R (900a d e + 300a b d e - 1200b d e )x +--R + +--R 2 3 11 4 10 2 5 9 3 +--R (1200a d e - 300a b d e - 900b d e )x +--R + +--R 2 4 10 5 9 2 6 8 2 +--R (900a d e - 540a b d e - 360b d e )x +--R + +--R 2 5 9 6 8 2 7 7 2 6 8 7 7 +--R (360a d e - 300a b d e - 60b d e )x + 60a d e - 60a b d e +--R Type: Expression(Integer) +--E 371 + +--S 372 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^8 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 373 + +--S 374 of 764 +r0:=1/6*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*_ + (d+e*x)^6)+1/7*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*_ + (d+e*x)^7) +--R +--R +--R (2) +--R 6 5 6 6 +--R ((A b - 7B a b )e + 6B b d)x +--R + +--R 5 2 4 6 5 5 +--R ((- A a b - 35B a b )e + (7A b + 29B a b )d)x +--R + +--R 2 4 3 3 5 2 4 4 +--R ((- 20A a b - 70B a b )e + (35A a b + 55B a b )d)x +--R + +--R 3 3 4 2 2 4 3 3 3 +--R ((- 50A a b - 70B a b )e + (70A a b + 50B a b )d)x +--R + +--R 4 2 5 3 3 4 2 2 +--R ((- 55A a b - 35B a b)e + (70A a b + 20B a b )d)x +--R + +--R 5 6 4 2 5 6 5 6 +--R ((- 29A a b - 7B a )e + (35A a b + B a b)d)x - 6A a e + (7A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 9 8 2 2 7 7 +--R (42a e - 84a b d e + 42b d e )x +--R + +--R 2 8 2 7 2 3 6 6 +--R (294a d e - 588a b d e + 294b d e )x +--R + +--R 2 2 7 3 6 2 4 5 5 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 3 6 4 5 2 5 4 4 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 4 5 5 4 2 6 3 3 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 5 4 6 3 2 7 2 2 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 6 3 7 2 2 8 2 7 2 8 2 9 +--R (294a d e - 588a b d e + 294b d e)x + 42a d e - 84a b d e + 42b d +--R Type: Expression(Integer) +--E 374 + +--S 375 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^9 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 376 + +--S 377 of 764 +r0:=-1/8*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^8)+1/24*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^7)+1/168*(3*b*B*d+A*b*e-_ + 4*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^7) +--R +--R +--R (2) +--R 7 6 2 7 7 +--R ((- A b + 4B a b )e - 3B b d e)x +--R + +--R 6 2 5 2 7 6 7 2 6 +--R ((A a b - 4B a b )e + (- 8A b + 35B a b )d e - 24B b d )x +--R + +--R 2 5 3 4 2 6 2 5 +--R (- A a b - 80B a b )e + (8A a b + 217B a b )d e +--R + +--R 7 6 2 +--R (- 28A b - 116B a b )d +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 2 2 5 3 4 +--R (- 55A a b - 200B a b )e + (160A a b + 455B a b )d e +--R + +--R 6 2 5 2 +--R (- 140A a b - 220B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 2 3 4 4 3 +--R (- 155A a b - 220B a b )e + (400A a b + 455B a b )d e +--R + +--R 2 5 3 4 2 +--R (- 280A a b - 200B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 6 2 4 3 5 2 +--R (- 181A a b - 116B a b)e + (440A a b + 217B a b )d e +--R + +--R 3 4 4 3 2 +--R (- 280A a b - 80B a b )d +--R * +--R 2 +--R x +--R + +--R 6 7 2 5 2 6 +--R (- 99A a b - 24B a )e + (232A a b + 35B a b)d e +--R + +--R 4 3 5 2 2 +--R (- 140A a b - 4B a b )d +--R * +--R x +--R + +--R 7 2 6 7 5 2 6 2 +--R - 21A a e + (48A a b - 3B a )d e + (- 28A a b + 4B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 11 2 10 2 2 9 3 3 8 8 +--R (168a e - 504a b d e + 504a b d e - 168b d e )x +--R + +--R 3 10 2 2 9 2 3 8 3 4 7 7 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e )x +--R + +--R 3 2 9 2 3 8 2 4 7 3 5 6 6 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (11760a d e - 35280a b d e + 35280a b d e - 11760b d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e)x + 168a d e +--R + +--R 2 9 2 2 10 3 11 +--R - 504a b d e + 504a b d e - 168b d +--R Type: Expression(Integer) +--E 377 + +--S 378 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^10 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 379 + +--S 380 of 764 +r0:=-1/9*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^9)+1/24*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^8)+1/72*b*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)^3*_ + (d+e*x)^7)+1/504*b*(2*b*B*d+A*b*e-3*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^7) +--R +--R +--R (2) +--R 8 7 3 8 2 8 +--R ((A b - 3B a b )e + 2B b d e )x +--R + +--R 7 2 6 3 8 7 2 8 2 7 +--R ((- A a b + 3B a b )e + (9A b - 29B a b )d e + 18B b d e)x +--R + +--R 2 6 3 5 3 7 2 6 2 +--R (A a b - 3B a b )e + (- 9A a b + 29B a b )d e +--R + +--R 8 7 2 8 3 +--R (36A b - 126B a b )d e + 72B b d +--R * +--R 6 +--R x +--R + +--R 3 5 4 4 3 2 6 3 5 2 +--R (- A a b - 165B a b )e + (9A a b + 643B a b )d e +--R + +--R 7 2 6 2 8 7 3 +--R (- 36A a b - 882B a b )d e + (84A b + 348B a b )d +--R * +--R 5 +--R x +--R + +--R 4 4 5 3 3 3 5 4 4 2 +--R (- 125A a b - 465B a b )e + (495A a b + 1625B a b )d e +--R + +--R 2 6 3 5 2 7 2 6 3 +--R (- 720A a b - 1890B a b )d e + (420A a b + 660B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 6 2 3 4 4 5 3 2 +--R (- 379A a b - 543B a b )e + (1395A a b + 1777B a b )d e +--R + +--R 3 5 4 4 2 2 6 3 5 3 +--R (- 1800A a b - 1890B a b )d e + (840A a b + 600B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 7 3 5 3 6 2 2 +--R (- 461A a b - 297B a b)e + (1629A a b + 911B a b )d e +--R + +--R 4 4 5 3 2 3 5 4 4 3 +--R (- 1980A a b - 882B a b )d e + (840A a b + 240B a b )d +--R * +--R 2 +--R x +--R + +--R 7 8 3 6 2 7 2 +--R (- 259A a b - 63B a )e + (891A a b + 169B a b)d e +--R + +--R 5 3 6 2 2 4 4 5 3 3 +--R (- 1044A a b - 126B a b )d e + (420A a b + 12B a b )d +--R * +--R x +--R + +--R 8 3 7 8 2 6 2 7 2 +--R - 56A a e + (189A a b - 7B a )d e + (- 216A a b + 18B a b)d e +--R + +--R 5 3 6 2 3 +--R (84A a b - 12B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 13 3 12 2 2 2 11 3 3 10 4 4 9 9 +--R (504a e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d e )x +--R + +--R 4 12 3 2 11 2 2 3 10 3 4 9 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 5 8 +--R 4536b d e +--R * +--R 8 +--R x +--R + +--R 4 2 11 3 3 10 2 2 4 9 3 5 8 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 6 7 +--R 18144b d e +--R * +--R 7 +--R x +--R + +--R 4 3 10 3 4 9 2 2 5 8 3 6 7 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 7 6 +--R 42336b d e +--R * +--R 6 +--R x +--R + +--R 4 4 9 3 5 8 2 2 6 7 3 7 6 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 8 5 +--R 63504b d e +--R * +--R 5 +--R x +--R + +--R 4 5 8 3 6 7 2 2 7 6 3 8 5 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 9 4 +--R 63504b d e +--R * +--R 4 +--R x +--R + +--R 4 6 7 3 7 6 2 2 8 5 3 9 4 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 10 3 +--R 42336b d e +--R * +--R 3 +--R x +--R + +--R 4 7 6 3 8 5 2 2 9 4 3 10 3 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 11 2 +--R 18144b d e +--R * +--R 2 +--R x +--R + +--R 4 8 5 3 9 4 2 2 10 3 3 11 2 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 12 +--R 4536b d e +--R * +--R x +--R + +--R 4 9 4 3 10 3 2 2 11 2 3 12 4 13 +--R 504a d e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d +--R Type: Expression(Integer) +--E 380 + +--S 381 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^11 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 382 + +--S 383 of 764 +r0:=-1/10*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^10)+1/45*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^9)+1/120*b*(3*b*B*d+2*A*b*e-_ + 5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)^3*(d+_ + e*x)^8)+1/360*b^2*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^4*(d+e*x)^7)+1/2520*b^2*(3*b*B*d+2*A*b*e-_ + 5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^7) +--R +--R +--R (2) +--R 9 8 4 9 3 9 +--R ((- 2A b + 5B a b )e - 3B b d e )x +--R + +--R 8 2 7 4 9 8 3 9 2 2 8 +--R ((2A a b - 5B a b )e + (- 20A b + 53B a b )d e - 30B b d e )x +--R + +--R 2 7 3 6 4 8 2 7 3 +--R (- 2A a b + 5B a b )e + (20A a b - 53B a b )d e +--R + +--R 9 8 2 2 9 3 +--R (- 90A b + 255B a b )d e - 135B b d e +--R * +--R 7 +--R x +--R + +--R 3 6 4 5 4 2 7 3 6 3 +--R (2A a b - 5B a b )e + (- 20A a b + 53B a b )d e +--R + +--R 8 2 7 2 2 9 8 3 9 4 +--R (90A a b - 255B a b )d e + (- 240A b + 735B a b )d e - 360B b d +--R * +--R 6 +--R x +--R + +--R 4 5 5 4 4 3 6 4 5 3 +--R (- 2A a b - 625B a b )e + (20A a b + 3097B a b )d e +--R + +--R 2 7 3 6 2 2 8 2 7 3 +--R (- 90A a b - 6045B a b )d e + (240A a b + 5565B a b )d e +--R + +--R 9 8 4 +--R (- 420A b - 1740B a b )d +--R * +--R 5 +--R x +--R + +--R 5 4 6 3 4 4 5 5 4 3 +--R (- 502A a b - 1895B a b )e + (2500A a b + 8747B a b )d e +--R + +--R 3 6 4 5 2 2 2 7 3 6 3 +--R (- 4950A a b - 15375B a b )d e + (4800A a b + 12075B a b )d e +--R + +--R 8 2 7 4 +--R (- 2100A a b - 3300B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 7 2 4 5 4 6 3 3 +--R (- 1598A a b - 2305B a b )e + (7580A a b + 10153B a b )d e +--R + +--R 4 5 5 4 2 2 3 6 4 5 3 +--R (- 13950A a b - 16755B a b )d e + (12000A a b + 12075B a b )d e +--R + +--R 2 7 3 6 4 +--R (- 4200A a b - 3000B a b )d +--R * +--R 3 +--R x +--R + +--R 7 2 8 4 6 3 7 2 3 +--R (- 2002A a b - 1295B a b)e + (9220A a b + 5447B a b )d e +--R + +--R 5 4 6 3 2 2 4 5 5 4 3 +--R (- 16290A a b - 8445B a b )d e + (13200A a b + 5565B a b )d e +--R + +--R 3 6 4 5 4 +--R (- 4200A a b - 1200B a b )d +--R * +--R 2 +--R x +--R + +--R 8 9 4 7 2 8 3 +--R (- 1148A a b - 280B a )e + (5180A a b + 1078B a b)d e +--R + +--R 6 3 7 2 2 2 5 4 6 3 3 +--R (- 8910A a b - 1455B a b )d e + (6960A a b + 735B a b )d e +--R + +--R 4 5 5 4 4 +--R (- 2100A a b - 60B a b )d +--R * +--R x +--R + +--R 9 4 8 9 3 7 2 8 2 2 +--R - 252A a e + (1120A a b - 28B a )d e + (- 1890A a b + 105B a b)d e +--R + +--R 6 3 7 2 3 5 4 6 3 4 +--R (1440A a b - 135B a b )d e + (- 420A a b + 60B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 15 4 14 3 2 2 13 2 3 3 12 +--R 2520a e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 4 11 5 5 10 +--R 12600a b d e - 2520b d e +--R * +--R 10 +--R x +--R + +--R 5 14 4 2 13 3 2 3 12 2 3 4 11 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 5 10 5 6 9 +--R 126000a b d e - 25200b d e +--R * +--R 9 +--R x +--R + +--R 5 2 13 4 3 12 3 2 4 11 2 3 5 10 +--R 113400a d e - 567000a b d e + 1134000a b d e - 1134000a b d e +--R + +--R 4 6 9 5 7 8 +--R 567000a b d e - 113400b d e +--R * +--R 8 +--R x +--R + +--R 5 3 12 4 4 11 3 2 5 10 2 3 6 9 +--R 302400a d e - 1512000a b d e + 3024000a b d e - 3024000a b d e +--R + +--R 4 7 8 5 8 7 +--R 1512000a b d e - 302400b d e +--R * +--R 7 +--R x +--R + +--R 5 4 11 4 5 10 3 2 6 9 2 3 7 8 +--R 529200a d e - 2646000a b d e + 5292000a b d e - 5292000a b d e +--R + +--R 4 8 7 5 9 6 +--R 2646000a b d e - 529200b d e +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 2 7 8 2 3 8 7 +--R 635040a d e - 3175200a b d e + 6350400a b d e - 6350400a b d e +--R + +--R 4 9 6 5 10 5 +--R 3175200a b d e - 635040b d e +--R * +--R 5 +--R x +--R + +--R 5 6 9 4 7 8 3 2 8 7 2 3 9 6 +--R 529200a d e - 2646000a b d e + 5292000a b d e - 5292000a b d e +--R + +--R 4 10 5 5 11 4 +--R 2646000a b d e - 529200b d e +--R * +--R 4 +--R x +--R + +--R 5 7 8 4 8 7 3 2 9 6 2 3 10 5 +--R 302400a d e - 1512000a b d e + 3024000a b d e - 3024000a b d e +--R + +--R 4 11 4 5 12 3 +--R 1512000a b d e - 302400b d e +--R * +--R 3 +--R x +--R + +--R 5 8 7 4 9 6 3 2 10 5 2 3 11 4 +--R 113400a d e - 567000a b d e + 1134000a b d e - 1134000a b d e +--R + +--R 4 12 3 5 13 2 +--R 567000a b d e - 113400b d e +--R * +--R 2 +--R x +--R + +--R 5 9 6 4 10 5 3 2 11 4 2 3 12 3 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 13 2 5 14 +--R 126000a b d e - 25200b d e +--R * +--R x +--R + +--R 5 10 5 4 11 4 3 2 12 3 2 3 13 2 +--R 2520a d e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 14 5 15 +--R 12600a b d e - 2520b d +--R Type: Expression(Integer) +--E 383 + +--S 384 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^12 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 385 + +--S 386 of 764 +r0:=-1/198*b*(6*b*B*d+5*A*b*e-11*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^9)-1/396*b^2*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^8)-_ + 1/11*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^11)-1/110*(6*b*B*d+5*A*b*e-11*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^10)-1/924*b^3*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*_ + (d+e*x)^7)-1/2310*b^4*(6*b*B*d+5*A*b*e-11*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^6)-1/13860*b^4*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 2772B b e x + ((- 2310A b - 11550B a b )e - 2772B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 9900A a b - 19800B a b )e + (- 1650A b - 8250B a b )d e +--R + +--R 5 2 4 +--R - 1980B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 17325A a b - 17325B a b )e + (- 4950A a b - 9900B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 825A b - 4125B a b )d e - 990B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 15400A a b - 7700B a b)e + (- 5775A a b - 5775B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 1650A a b - 3300B a b )d e + (- 275A b - 1375B a b )d e +--R + +--R 5 4 2 +--R - 330B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 6930A a b - 1386B a )e + (- 3080A a b - 1540B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 1155A a b - 1155B a b )d e + (- 330A a b - 660B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 55A b - 275B a b )d e - 66B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 1260A a e + (- 630A a b - 126B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 280A a b - 140B a b)d e + (- 105A a b - 105B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (- 30A a b - 60B a b )d e + (- 5A b - 25B a b )d e - 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 18 12 18 17 11 +--R 13860b e x + (13860a e + 152460b d e )x +--R + +--R 17 2 16 10 2 16 3 15 9 +--R (152460a d e + 762300b d e )x + (762300a d e + 2286900b d e )x +--R + +--R 3 15 4 14 8 4 14 5 13 7 +--R (2286900a d e + 4573800b d e )x + (4573800a d e + 6403320b d e )x +--R + +--R 5 13 6 12 6 6 12 7 11 5 +--R (6403320a d e + 6403320b d e )x + (6403320a d e + 4573800b d e )x +--R + +--R 7 11 8 10 4 8 10 9 9 3 +--R (4573800a d e + 2286900b d e )x + (2286900a d e + 762300b d e )x +--R + +--R 9 9 10 8 2 10 8 11 7 +--R (762300a d e + 152460b d e )x + (152460a d e + 13860b d e )x +--R + +--R 11 7 +--R 13860a d e +--R Type: Expression(Integer) +--E 386 + +--S 387 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^13 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R e x + 13d e x + 78d e x + 286d e x + 715d e x + 1287d e x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 +--R 1716d e x + 1716d e x + 1287d e x + 715d e x + 286d e x + 78d e x +--R + +--R 12 13 +--R 13d e x + d +--R Type: Expression(Integer) +--E 388 + +--S 389 of 764 +r0:=-1/44*b*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e)*(d+e*x)^10)-1/99*b^2*(b*B*d+A*b*e-2*a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^9)-1/12*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^12)-_ + 1/22*(b*B*d+A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-_ + a*e)*(d+e*x)^11)-1/264*b^3*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*(d+e*x)^8)-1/792*b^4*(b*B*d+A*b*e-_ + 2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^7)-_ + 1/5544*b^4*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*_ + (a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 924B b e x + ((- 792A b - 3960B a b )e - 792B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 3465A a b - 6930B a b )e + (- 495A b - 2475B a b )d e +--R + +--R 5 2 4 +--R - 495B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 6160A a b - 6160B a b )e + (- 1540A a b - 3080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 220A b - 1100B a b )d e - 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 5544A a b - 2772B a b)e + (- 1848A a b - 1848B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 462A a b - 924B a b )d e + (- 66A b - 330B a b )d e +--R + +--R 5 4 2 +--R - 66B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 2520A a b - 504B a )e + (- 1008A a b - 504B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 336A a b - 336B a b )d e + (- 84A a b - 168B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 12A b - 60B a b )d e - 12B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 462A a e + (- 210A a b - 42B a )d e + (- 84A a b - 42B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 28A a b - 28B a b )d e + (- 7A a b - 14B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 19 13 19 18 12 +--R 5544b e x + (5544a e + 66528b d e )x +--R + +--R 18 2 17 11 2 17 3 16 10 +--R (66528a d e + 365904b d e )x + (365904a d e + 1219680b d e )x +--R + +--R 3 16 4 15 9 4 15 5 14 8 +--R (1219680a d e + 2744280b d e )x + (2744280a d e + 4390848b d e )x +--R + +--R 5 14 6 13 7 6 13 7 12 6 +--R (4390848a d e + 5122656b d e )x + (5122656a d e + 4390848b d e )x +--R + +--R 7 12 8 11 5 8 11 9 10 4 +--R (4390848a d e + 2744280b d e )x + (2744280a d e + 1219680b d e )x +--R + +--R 9 10 10 9 3 10 9 11 8 2 +--R (1219680a d e + 365904b d e )x + (365904a d e + 66528b d e )x +--R + +--R 11 8 12 7 12 7 +--R (66528a d e + 5544b d e )x + 5544a d e +--R Type: Expression(Integer) +--E 389 + +--S 390 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^14 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R e x + 14d e x + 91d e x + 364d e x + 1001d e x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002d e x + 3003d e x + 3432d e x + 3003d e x + 2002d e x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001d e x + 364d e x + 91d e x + 14d e x + d +--R Type: Expression(Integer) +--E 391 + +--S 392 of 764 +r0:=-5/1716*b*(6*b*B*d+7*A*b*e-13*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^11)-1/858*b^2*(6*b*B*d+7*A*b*e-_ + 13*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^10)-_ + 1/13*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^13)-1/156*(6*b*B*d+7*A*b*e-13*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^12)-1/2574*b^3*(6*b*B*d+_ + 7*A*b*e-13*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-_ + a*e)*(d+e*x)^9)-1/9009*b^4*(6*b*B*d+7*A*b*e-13*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^8)-1/72072*b^4*(6*b*B*d+_ + 7*A*b*e-13*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 10296B b e x + ((- 9009A b - 45045B a b )e - 7722B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 40040A a b - 80080B a b )e + (- 5005A b - 25025B a b )d e +--R + +--R 5 2 4 +--R - 4290B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 72072A a b - 72072B a b )e + (- 16016A a b - 32032B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 2002A b - 10010B a b )d e - 1716B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 65520A a b - 32760B a b)e + (- 19656A a b - 19656B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 4368A a b - 8736B a b )d e + (- 546A b - 2730B a b )d e +--R + +--R 5 4 2 +--R - 468B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 30030A a b - 6006B a )e + (- 10920A a b - 5460B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 3276A a b - 3276B a b )d e + (- 728A a b - 1456B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 91A b - 455B a b )d e - 78B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 5544A a e + (- 2310A a b - 462B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 840A a b - 420B a b)d e + (- 252A a b - 252B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (- 56A a b - 112B a b )d e + (- 7A b - 35B a b )d e - 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 20 14 20 19 13 +--R 72072b e x + (72072a e + 936936b d e )x +--R + +--R 19 2 18 12 +--R (936936a d e + 5621616b d e )x +--R + +--R 2 18 3 17 11 +--R (5621616a d e + 20612592b d e )x +--R + +--R 3 17 4 16 10 +--R (20612592a d e + 51531480b d e )x +--R + +--R 4 16 5 15 9 +--R (51531480a d e + 92756664b d e )x +--R + +--R 5 15 6 14 8 +--R (92756664a d e + 123675552b d e )x +--R + +--R 6 14 7 13 7 +--R (123675552a d e + 123675552b d e )x +--R + +--R 7 13 8 12 6 +--R (123675552a d e + 92756664b d e )x +--R + +--R 8 12 9 11 5 +--R (92756664a d e + 51531480b d e )x +--R + +--R 9 11 10 10 4 +--R (51531480a d e + 20612592b d e )x +--R + +--R 10 10 11 9 3 +--R (20612592a d e + 5621616b d e )x +--R + +--R 11 9 12 8 2 12 8 13 7 +--R (5621616a d e + 936936b d e )x + (936936a d e + 72072b d e )x +--R + +--R 13 7 +--R 72072a d e +--R Type: Expression(Integer) +--E 392 + +--S 393 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 764 +t0:=(A+B*x)*(d+e*x)^3/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 764 +r0:=1/2*(A*b-a*B)*(b*d-a*e)*(a+b*x)*(d+e*x)^2/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+1/3*(A*b-a*B)*(a+b*x)*(d+e*x)^3/(b^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+1/4*B*(a+b*x)*(d+e*x)^4/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*(b*d-a*e)^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+(A*b-a*B)*e*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 2 4 4 2 3 3 2 3 +--R (- 12A a b + 12B a b)e + (36A a b - 36B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 36A a b + 36B a b )d e + (12A a b - 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 2A a b + 2B a b )e + (18A b - 6B a b )d e + 18B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (6A a b - 6B a b )e + (- 18A a b + 18B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 18B a b )d e + 12B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (24A a b - 24B a b)e + (- 60A a b + 60B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (42A a b - 42B a b )d e + (10A b + 2B a b )d e + 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (12A a b - 12B a )e + (- 24A a b + 24B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (6A a b - 6B a b )d e + (10A a b - 10B a b )d e + 3B a b d +--R / +--R +------------------+ +--R 5 | 2 2 2 +--R 12b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 395 + +--S 396 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 of 764 +t0:=(A+B*x)*(d+e*x)^2/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 764 +r0:=1/2*(A*b-a*B)*(a+b*x)*(d+e*x)^2/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 1/3*B*(a+b*x)*(d+e*x)^3/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*_ + (b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*e*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (6A a b - 6B a b)e + (- 12A a b + 12B a b )d e +--R + +--R 4 3 2 +--R (6A b - 6B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (6A a b - 6B a )e + (- 12A a b + 12B a b)d e +--R + +--R 3 2 2 2 +--R (6A a b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 3A a b + 3B a b )e + (12A b - 6B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 12A a b + 12B a b)e + (18A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 3B a b )d e + 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (- 6A a b + 6B a )e + (6A a b - 6B a b)d e + (3A a b - 3B a b )d e +--R + +--R 3 3 +--R 2B a b d +--R / +--R +------------------+ +--R 4 | 2 2 2 +--R 6b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 398 + +--S 399 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 of 764 +t0:=(A+B*x)*(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 400 + +--S 401 of 764 +r0:=1/2*B*(a+b*x)*(d+e*x)^2/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*_ + (b*d-a*e)*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-_ + a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3 +--R +--R +--R (2) +--R 2 2 2 3 2 +--R ((- 2A a b + 2B a b)e + (2A b - 2B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (- 2A a b + 2B a )e + (2A a b - 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - B a b )e + 2B b d e)x +--R + +--R 2 2 2 2 3 2 2 3 2 +--R ((4A a b - 4B a b)e + 2B a b d e + B b d )x + (2A a b - 2B a )e +--R + +--R 2 2 +--R B a b d +--R / +--R +------------------+ +--R 3 | 2 2 2 +--R 2b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 764 +t0:=(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R B x + A +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 764 +r0:=(A*b-a*B)*(a+b*x)*log(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + B*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2 +--R +--R +--R (2) +--R 2 2 2 2 2 +--R ((A b - B a b)x + A a b - B a )log(b x + a) + B b x + 2B a b x + B a +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 404 + +--S 405 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 764 +t0:=(A+B*x)/((d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 764 +r0:=(A*b-a*B)*(a+b*x)*log(a+b*x)/(b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (B*d-A*e)*(a+b*x)*log(d+e*x)/(e*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 +--R ((- A b + B a b)e x + (- A a b + B a )e)log(b x + a) +--R / +--R +------------------+ +--R 2 2 | 2 2 2 +--R (a b e - b d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 407 + +--S 408 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 764 +t0:=(A+B*x)/((d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 764 +r0:=-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (- A b + B a b)e x + ((- A a b + B a )e + (- A b + B a b)d e)x +--R + +--R 2 +--R (- A a b + B a )d e +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 2 2 +--R (A b - B a b)e x + ((A a b - B a )e + (A b - B a b)d e)x +--R + +--R 2 +--R (A a b - B a )d e +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R (- A a b e + (A b + B a b)d e - B b d )x - A a e + (A a b + B a )d e +--R + +--R 2 +--R - B a b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 of 764 +t0:=(A+B*x)/((d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 412 + +--S 413 of 764 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + b*(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b*(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (A*b-a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 +--R (2A b - 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((2A a b - 2B a b)e + (4A b - 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((4A a b - 4B a b)d e + (2A b - 2B a b )d e)x +--R + +--R 2 2 2 +--R (2A a b - 2B a b)d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 +--R (- 2A b + 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 2A a b + 2B a b)e + (- 4A b + 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 4A a b + 4B a b)d e + (- 2A b + 2B a b )d e)x +--R + +--R 2 2 2 +--R (- 2A a b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 3 2 2 2 +--R (2A b - 2B a b )e x + ((4A a b - 4B a b)e + (2A b - 2B a b )d e )x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (A a b - 2B a )e + (6A a b - 3B a b)d e + (- A b - 2B a b )d e +--R + +--R 3 3 +--R B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R - A a e + (4A a b - B a )d e + (- A a b - 2B a b)d e + B a b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 764 +t0:=(A+B*x)/((d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 415 + +--S 416 of 764 +r0:=-1/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 1/2*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + b^2*(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b^2*(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b*(A*b-a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^4*(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 +--R (- 6A b + 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((- 6A a b + 6B a b )e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((- 18A a b + 18B a b )d e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((- 18A a b + 18B a b )d e + (- 6A b + 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (- 6A a b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 +--R (6A b - 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((6A a b - 6B a b )e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((18A a b - 18B a b )d e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((18A a b - 18B a b )d e + (6A b - 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (6A a b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 +--R (- 6A b + 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((- 12A a b + 12B a b )e + (- 12A b + 12B a b )d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 3A a b + 3B a b)e + (- 30A a b + 30B a b )d e +--R + +--R 4 3 2 2 +--R (- 3A b + 3B a b )d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (A a b - 3B a )e + (- 9A a b + 17B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 21A a b + 9B a b )d e + (5A b + 3B a b )d e - 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (5A a b + 3B a b )d e - 2B a b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4 7 +--R 6a d e - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 416 + +--S 417 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 764 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 418 + +--S 419 of 764 +r0:=-1/6*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^4/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/3*B*(a+b*x)*(d+e*x)^5/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+e*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^2/(b^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-2/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^3/_ + (b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*(a+b*x)*log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2*e^2*(b*d-a*e)*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6 +--R +--R +--R (2) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 90A a b + 150B a b )e + (144A a b - 300B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 156B a b )d e - 4B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 108A a b + 180B a b)e + (144A a b - 312B a b )d e +--R + +--R 2 3 2 2 5 4 3 5 4 +--R 96B a b d e + (- 24A b + 40B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 36A a b + 60B a )e + (36A a b - 84B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (18A a b - 6B a b )d e + (- 12A a b + 32B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R / +--R +------------------+ +--R 7 6 | 2 2 2 +--R (6b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 764 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 764 +r0:=-1/2*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*(d+e*x)^3/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/2*B*(a+b*x)*(d+e*x)^4/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-3/2*(b*B*d+A*b*e-2*a*B*e)*(d+e*x)^2/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*B*d+A*b*e-_ + 2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 24B a b)e + (12A a b - 36B a b )d e + 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((15A a b - 30B a b )e + (- 9A b + 33B a b )d e - 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 36B a b)e + (- 6A a b + 30B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 6B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 3 2 3 2 2 2 +--R (6A a b - 12B a )e + 6B a b d e + (- 3A a b + 6B a b )d e +--R + +--R 4 3 3 +--R (- A b - B a b )d +--R / +--R +------------------+ +--R 6 5 | 2 2 2 +--R (2b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 764 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 764 +r0:=-1/2*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^2/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+B*(a+b*x)*(d+e*x)^3/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + (2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 2 +--R 2B b e x + (- 3A b + 9B a b )e x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 2A a b + 6B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 2 3 2 2 +--R (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R / +--R +------------------+ +--R 5 4 | 2 2 2 +--R (2b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 425 + +--S 426 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 of 764 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 764 +r0:=-1/2*(A*b-a*B)*(a+b*x)*(d+e*x)^2/(b*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-B*(b*d-a*e)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + B*e*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2)),-1/2*B*(a+_ + b*x)*(d+e*x)^2/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*(B*d-A*e)*(a+_ + b*x)*(d+e*x)^2/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-B*(d+e*x)/_ + (b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e*(a+b*x)*log(a+b*x)/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R [ +--R 2 2 3 2 2 2 2 3 2 +--R (2B a b e - 2B b d e)x + (4B a b e - 4B a b d e)x + 2B a e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 2 2 2 3 2 3 2 +--R (A b - B a b )e x + (2B a b e + (2A b - 6B a b )d e + 2B b d )x +--R + +--R 3 2 2 3 2 2 +--R 2B a e - 4B a b d e + (A b + B a b )d +--R / +--R +------------------+ +--R 4 5 2 3 4 | 2 2 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|b x + 2a b x + a +--R , +--R +--R 2 2 3 2 2 2 2 3 2 +--R (2B a b e - 2B b d e)x + (4B a b e - 4B a b d e)x + 2B a e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 3 2 +--R ((A b - 3B a b )e + 2B b d e)x +--R + +--R 2 2 3 2 3 2 2 +--R (- 2B a b e + (2A b - 2B a b )d e + 2B b d )x - 2B a b d e +--R + +--R 3 2 2 +--R (A b + B a b )d +--R / +--R +------------------+ +--R 4 5 2 3 4 | 2 2 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|b x + 2a b x + a +--R ] +--R Type: Tuple(Expression(Integer)) +--E 428 + +--S 429 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 of 764 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 430 + +--S 431 of 764 +r0:=-1/2*(a+b*x)*(A+B*x)^2/((A*b-a*B)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 2 2 2 +--R - B x - 2A B x - A +--R (2) --------------------------------------------------------- +--R +------------------+ +--R 2 2 | 2 2 2 +--R ((2A b - 2B a b)x + 2A a b - 2B a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 764 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 433 + +--S 434 of 764 +r0:=-1/2*(A*b-a*B)*(a+b*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + (-B*d+A*e)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(B*d-A*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + e*(B*d-A*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x - 2A a b e +--R + +--R 2 +--R 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R / +--R 3 2 3 2 3 2 4 2 5 3 4 3 3 2 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x + 2a b e - 6a b d e +--R + +--R 2 3 2 4 3 +--R 6a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 764 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 764 +r0:=1/2*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+(-2*b*B*d+3*A*b*e-a*B*e)/((b*d-a*e)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-e*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/_ + ((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(2*b*B*d-3*A*b*e+a*B*e)*_ + (a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e + (3A b - 5B a b )d e +--R + +--R 3 3 +--R - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (2a e - 6a b d e + 4a b d e + 4a b d e - 6a b d e + 2b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 764 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 764 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/2*(b*B*d-2*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-3/2*(b*B*d-2*A*b*e+a*B*e)/_ + ((b*d-a*e)^3*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3*b*e*(b*B*d-_ + 2*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*b*e*(b*B*d-2*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*B*d-2*A*b*e+a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/((b*d-a*e)^5*(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 12B a b )e + (24A b - 24B a b )d e - 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (24A a b - 24B a b )d e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((36A a b - 18B a b )e + (12A b - 24B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (30A a b - 15B a b)e + (48A a b - 39B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 6A b - 21B a b )d e + 3B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R (4A a b - 2B a )e + (48A a b - 26B a b)d e - 24B a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 2B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - A a e + (8A a b - B a )d e + (12A a b - 15B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 8A a b + 3B a b )d e + (A b + B a b )d +--R / +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e +--R + +--R 6 5 2 +--R - 2b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 6 3 3 3 4 2 4 4 3 5 5 2 6 6 2 +--R (2a e - 6a b d e + 20a b d e - 30a b d e + 18a b d e - 4b d e)x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5 6 6 7 +--R (4a d e - 18a b d e + 30a b d e - 20a b d e + 6a b d e - 2b d )x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 440 + +--S 441 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 441 + +)clear all + +--S 442 of 764 +t0:=(A+B*x)*(d+e*x)^5/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 764 +r0:=-1/4*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^5/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/2*B*(a+b*x)*(d+e*x)^6/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-5/6*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^3/_ + (b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/12*(2*b*B*d+A*b*e-3*a*B*e)*_ + (d+e*x)^4/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/2*e^2*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(d+e*x)^2/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+5*e^3*(b*d-a*e)*_ + (2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*log(a+b*x)/(b^7*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+5*e^4*(2*b*B*d+A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7 +--R +--R +--R (2) +--R 5 2 4 5 6 5 4 +--R (- 60A a b + 180B a b )e + (60A b - 300B a b )d e +--R + +--R 6 2 3 +--R 120B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 240A a b + 720B a b )e + (240A a b - 1200B a b )d e +--R + +--R 5 2 3 +--R 480B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 360A a b + 1080B a b )e + (360A a b - 1800B a b )d e +--R + +--R 2 4 2 3 +--R 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 720B a b)e + (240A a b - 1200B a b )d e +--R + +--R 3 3 2 3 +--R 480B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 4 2 2 3 +--R (- 60A a b + 180B a )e + (60A a b - 300B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 6B b e x + ((12A b - 36B a b )e + 60B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((185A a b - 555B a b )e + (- 125A b + 745B a b )d e - 160B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (500A a b - 1500B a b )e + (- 260A a b + 1780B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 120A b - 160B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (570A a b - 1710B a b )e + (- 210A a b + 1770B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 180A a b + 120B a b )d e + (- 60A b - 180B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (300A a b - 900B a b)e + (- 60A a b + 780B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 120A a b + 240B a b )d e + (- 40A a b - 120B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 20A b - 20B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 6 5 5 4 3 3 4 2 2 3 +--R (60A a b - 180B a )e + 120B a b d e + (- 30A a b + 90B a b )d e +--R + +--R 2 4 3 3 3 2 5 2 4 4 +--R (- 10A a b - 30B a b )d e + (- 5A a b - 5B a b )d e +--R + +--R 6 5 5 +--R (- 3A b - B a b )d +--R / +--R +------------------+ +--R 10 3 9 2 2 8 3 7 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 443 + +--S 444 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 764 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 764 +r0:=-1/4*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^4/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+B*(a+b*x)*(d+e*x)^5/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))-_ + 1/2*e*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^2/(b^4*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-1/3*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)^3/(b^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))-e^2*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)/(b^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*_ + log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((12A b - 60B a b )e + 48B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((48A a b - 240B a b )e + 192B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((72A a b - 360B a b )e + 288B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((48A a b - 240B a b)e + 192B a b d e )x + (12A a b - 60B a )e +--R + +--R 4 3 +--R 48B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 12B b e x + ((- 25A b + 125B a b )e - 40B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 52A a b + 260B a b )e + (- 48A b + 32B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 42A a b + 210B a b )e + (- 72A a b + 192B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b - 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 12A a b + 60B a b)e + (- 48A a b + 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 24A a b - 72B a b )d e + (- 16A b - 16B a b )d e - 4B b d +--R * +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (- 12A a b + 60B a b)d e + (- 6A a b - 18B a b )d e +--R + +--R 4 2 3 3 5 4 4 +--R (- 4A a b - 4B a b )d e + (- 3A b - B a b )d +--R / +--R +------------------+ +--R 9 3 8 2 2 7 3 6 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 446 + +--S 447 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 764 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 448 + +--S 449 of 764 +r0:=-1/4*(A*b-a*B)*(a+b*x)*(d+e*x)^4/(b*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/2*B*e*(a+b*x)*(d+e*x)^2/(b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-1/3*B*(d+e*x)^3/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + B*e^2*(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e^3*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)),-1/4*B*(a+b*x)*_ + (d+e*x)^4/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+1/4*(B*d-A*e)*(a+b*x)*_ + (d+e*x)^4/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-1/2*B*e*(a+b*x)*_ + (d+e*x)^2/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/3*B*(d+e*x)^3/(b^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-B*e^2*(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+B*e^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R [ +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12B a b e - 12B b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 +--R (72B a b e - 72B a b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 5 4 4 3 +--R 12B a e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 4 5 3 4 +--R ((3A b - 25B a b )e + 22B b d e )x +--R + +--R 2 3 4 5 4 3 5 2 2 3 +--R (- 52B a b e + (12A b + 4B a b )d e + 36B b d e )x +--R + +--R 3 2 4 2 3 3 5 4 2 2 5 3 2 +--R (- 42B a b e - 30B a b d e + (18A b + 36B a b )d e + 18B b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 5 4 3 +--R - 12B a b e - 36B a b d e + 24B a b d e + (12A b + 8B a b )d e +--R + +--R 5 4 +--R 4B b d +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 5 4 4 +--R - 12B a b d e + 6B a b d e + 2B a b d e + (3A b + B a b )d +--R / +--R 8 9 3 2 7 8 2 3 6 2 7 +--R (12a b e - 12b d)x + (36a b e - 36a b d)x + (36a b e - 36a b d)x +--R + +--R 4 5 3 6 +--R 12a b e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R , +--R +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12B a b e - 12B b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 +--R (72B a b e - 72B a b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 5 4 4 3 +--R 12B a e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 4 5 3 4 +--R ((3A b - 25B a b )e + 22B b d e )x +--R + +--R 2 3 4 5 4 3 5 2 2 3 +--R (- 52B a b e + (12A b + 4B a b )d e + 36B b d e )x +--R + +--R 3 2 4 2 3 3 5 4 2 2 5 3 2 +--R (- 42B a b e - 30B a b d e + (18A b + 36B a b )d e + 18B b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 5 4 3 +--R - 12B a b e - 36B a b d e + 24B a b d e + (12A b + 8B a b )d e +--R + +--R 5 4 +--R 4B b d +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 5 4 4 +--R - 12B a b d e + 6B a b d e + 2B a b d e + (3A b + B a b )d +--R / +--R 8 9 3 2 7 8 2 3 6 2 7 +--R (12a b e - 12b d)x + (36a b e - 36a b d)x + (36a b e - 36a b d)x +--R + +--R 4 5 3 6 +--R 12a b e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R ] +--R Type: Tuple(Expression(Integer)) +--E 449 + +--S 450 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 764 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 764 +r0:=-1/4*(A*b-a*B)*(a+b*x)*(d+e*x)^4/((b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/3*(B*d-A*e)*(d+e*x)^3/((b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 4 3 4 4 3 2 2 3 +--R ((A b + 3B a)e - 4B b d e )x + (4A a e + 8B a d e - 12B b d e )x +--R + +--R 3 2 2 3 2 +--R (12A a d e + (- 6A b + 6B a)d e - 12B b d e)x +--R + +--R 2 2 3 4 3 4 +--R (12A a d e - 8A b d e - 4B b d )x + 4A a d e + (- 3A b - B a)d +--R / +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (12a b e - 24a b d e + 12b d )x + (36a b e - 72a b d e + 36a b d )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (36a b e - 72a b d e + 36a b d )x + 12a e - 24a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 764 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 764 +r0:=1/4*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)/(b^3*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/2*B*(a+b*x)*(d+e*x)^2/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/3*(2*b*B*d-A*b*e-a*B*e)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a b)e - 4B b d)x + (- A a b - B a )e +--R + +--R 2 +--R (- 3A b - B a b)d +--R / +--R +------------------+ +--R 6 3 5 2 2 4 3 3 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 455 + +--S 456 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 456 + +)clear all + +--S 457 of 764 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 764 +r0:=-1/4*(A*b-a*B)*(a+b*x)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2))-_ + 1/3*B/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R - 4B b x - 3A b - B a +--R (2) ----------------------------------------------------------- +--R +------------------+ +--R 5 3 4 2 2 3 3 2 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 458 + +--S 459 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 764 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 460 + +--S 461 of 764 +r0:=-1/4*(A*b-a*B)*(a+b*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/3*(-B*d+A*e)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/2*e*(B*d-A*e)*(a+b*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + e^2*(B*d-A*e)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(B*d-A*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*_ + (B*d-A*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 3 4 4 4 4 3 3 +--R (12A b e - 12B b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (72A a b e - 72B a b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 4 4 4 3 +--R 12A a b e - 12B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 3 4 4 4 4 3 3 +--R (- 12A b e + 12B b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (- 72A a b e + 72B a b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 4 4 4 3 +--R - 12A a b e + 12B a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 5 4 3 5 2 2 3 +--R (12A a b e + (- 12A b - 12B a b )d e + 12B b d e )x +--R + +--R 2 3 4 4 2 3 3 5 4 2 2 +--R 42A a b e + (- 48A a b - 42B a b )d e + (6A b + 48B a b )d e +--R + +--R 5 3 +--R - 6B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 2 3 4 2 3 2 2 +--R 52A a b e + (- 72A a b - 52B a b )d e + (24A a b + 72B a b )d e +--R + +--R 5 4 3 5 4 +--R (- 4A b - 24B a b )d e + 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 3B a )e + (- 48A a b - 10B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 5 4 4 +--R (36A a b + 18B a b )d e + (- 16A a b - 6B a b )d e + (3A b + B a b )d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 9 5 +--R - 12b d +--R * +--R 3 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 2 7 4 +--R 36a b e - 180a b d e + 360a b d e - 360a b d e + 180a b d e +--R + +--R 8 5 +--R - 36a b d +--R * +--R 2 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 3 6 4 +--R 36a b e - 180a b d e + 360a b d e - 360a b d e + 180a b d e +--R + +--R 2 7 5 +--R - 36a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 4 5 4 3 6 5 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 764 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 463 + +--S 464 of 764 +r0:=1/4*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2))+1/3*(-4*b*B*d+5*A*b*e-a*B*e)/((b*d-a*e)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*e*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)/_ + ((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2*(4*b*B*d-5*A*b*e+_ + a*B*e)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+e^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/_ + ((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((- 60A b + 12B a b )e + 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 240A a b + 48B a b )e + (- 60A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 360A a b + 72B a b )e + (- 240A a b + 336B a b )d e +--R + +--R 4 2 3 +--R 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 240A a b + 48B a b)e + (- 360A a b + 264B a b )d e +--R + +--R 2 3 2 3 +--R 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 60A a b + 12B a )e + (- 240A a b + 96B a b)d e +--R + +--R 3 2 2 3 +--R 192B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 60A a b + 12B a )d e + 48B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 12B a b )e - 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((240A a b - 48B a b )e + (60A b - 204B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (360A a b - 72B a b )e + (240A a b - 336B a b )d e +--R + +--R 4 2 3 +--R - 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b - 48B a b)e + (360A a b - 264B a b )d e +--R + +--R 2 3 2 3 +--R - 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 3 2 2 3 +--R ((60A a b - 12B a )e + (240A a b - 96B a b)d e - 192B a b d e )x +--R + +--R 4 5 4 4 2 3 +--R (60A a b - 12B a )d e - 48B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 12B a b )e + (60A b + 36B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 210A a b + 42B a b )e + (180A a b + 132B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b - 150B a b )d e - 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 260A a b + 52B a b)e + (150A a b + 178B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b - 144B a b )d e + (- 10A b - 94B a b )d e + 8B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 125A a b + 25B a )e + (- 20A a b + 104B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 20B a b )d e + (- 40A a b - 136B a b )d e +--R + +--R 5 4 4 5 5 +--R (5A b + 31B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 12A a e + (- 65A a b + 37B a )d e + (120A a b - 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 60A a b - 36B a b )d e + (20A a b + 8B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - B a b )d +--R / +--R 6 3 7 5 4 6 4 5 2 5 3 6 3 4 2 7 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 8 5 2 9 6 +--R - 72a b d e + 12b d e +--R * +--R 4 +--R x +--R + +--R 7 2 7 6 3 6 5 4 2 5 4 5 3 4 3 6 4 3 +--R 36a b e - 204a b d e + 468a b d e - 540a b d e + 300a b d e +--R + +--R 2 7 5 2 8 6 9 7 +--R - 36a b d e - 36a b d e + 12b d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 4 5 4 3 +--R 36a b e - 180a b d e + 324a b d e - 180a b d e - 180a b d e +--R + +--R 3 6 5 2 2 7 6 8 7 +--R 324a b d e - 180a b d e + 36a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 6 7 2 2 5 6 3 3 4 5 4 4 3 +--R 12a e - 36a b d e - 36a b d e + 300a b d e - 540a b d e +--R + +--R 4 5 5 2 3 6 6 2 7 7 +--R 468a b d e - 204a b d e + 36a b d +--R * +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 4 5 6 3 6 7 +--R - 72a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 464 + +--S 465 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 764 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 764 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/4*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-5/12*(2*b*B*d-3*A*b*e+a*B*e)/_ + ((b*d-a*e)^3*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5/6*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)*(a+b*x)/((b*d-a*e)^4*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-5/2*e^2*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^5*(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-5*b*e^3*(2*b*B*d-3*A*b*e+a*B*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^7*sqrt(a^2+2*a*b*x+b^2*x^2))+5*b*e^3*_ + (2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^7*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+5*e^4*(2*b*B*d-3*A*b*e+a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/((b*d-a*e)^7*(d+e*x)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (720A a b - 240B a b )e + (360A b - 600B a b )d e +--R + +--R 6 2 4 +--R - 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (1080A a b - 360B a b )e + (1440A a b - 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (180A b - 1020B a b )d e - 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (720A a b - 240B a b )e + (2160A a b - 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (720A a b - 1680B a b )d e - 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (180A a b - 60B a b)e + (1440A a b - 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (1080A a b - 1320B a b )d e - 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (360A a b - 120B a b)d e + (720A a b - 480B a b )d e +--R + +--R 3 3 3 3 +--R - 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (180A a b - 60B a b)d e - 120B a b d e +--R * +--R log(e x + d) +--R + +--R 6 5 6 6 5 6 +--R ((- 180A b + 60B a b )e + 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 720A a b + 240B a b )e + (- 360A b + 600B a b )d e +--R + +--R 6 2 4 +--R 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 1080A a b + 360B a b )e + (- 1440A a b + 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 180A b + 1020B a b )d e + 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 720A a b + 240B a b )e + (- 2160A a b + 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (- 720A a b + 1680B a b )d e + 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 180A a b + 60B a b)e + (- 1440A a b + 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (- 1080A a b + 1320B a b )d e + 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (- 360A a b + 120B a b)d e + (- 720A a b + 480B a b )d e +--R + +--R 3 3 3 3 +--R 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (- 180A a b + 60B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 6 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((900A a b - 300B a b )e + (180A b - 660B a b )d e - 120B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (1710A a b - 570B a b )e + (1080A a b - 1500B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 90A b - 690B a b )d e + 60B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (1500A a b - 500B a b )e + (2340A a b - 1780B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 180A a b - 1500B a b )d e + (- 60A b + 140B a b )d e +--R + +--R 6 4 2 +--R 40B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (555A a b - 185B a b)e + (2280A a b - 1130B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (90A a b - 1550B a b )d e + (- 240A a b + 20B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (15A b + 155B a b )d e - 10B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (36A a b - 12B a )e + (930A a b - 334B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (420A a b - 760B a b )d e + (- 360A a b - 160B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (60A a b + 220B a b )d e + (- 6A b - 38B a b )d e + 4B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 6A a e + (72A a b - 6B a )d e + (285A a b - 185B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 240A a b - 40B a b )d e + (90A a b + 60B a b )d e +--R + +--R 5 2 4 5 6 5 6 +--R (- 24A a b - 10B a b )d e + (3A b + B a b )d +--R / +--R 7 3 9 6 4 8 5 5 2 7 4 6 3 6 3 7 4 5 +--R 12a b e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 2 8 5 4 9 6 3 10 7 2 +--R - 252a b d e + 84a b d e - 12b d e +--R * +--R 5 +--R x +--R + +--R 8 2 9 7 3 8 6 4 2 7 5 5 3 6 4 6 4 5 +--R 36a b e - 228a b d e + 588a b d e - 756a b d e + 420a b d e +--R + +--R 3 7 5 4 2 8 6 3 9 7 2 10 8 +--R 84a b d e - 252a b d e + 132a b d e - 24b d e +--R * +--R 4 +--R x +--R + +--R 9 9 8 2 8 7 3 2 7 6 4 3 6 5 5 4 5 +--R 36a b e - 180a b d e + 264a b d e + 168a b d e - 1008a b d e +--R + +--R 4 6 5 4 3 7 6 3 2 8 7 2 9 8 10 9 +--R 1344a b d e - 840a b d e + 216a b d e + 12a b d e - 12b d +--R * +--R 3 +--R x +--R + +--R 10 9 9 8 8 2 2 7 7 3 3 6 6 4 4 5 +--R 12a e - 12a b d e - 216a b d e + 840a b d e - 1344a b d e +--R + +--R 5 5 5 4 4 6 6 3 3 7 7 2 2 8 8 9 9 +--R 1008a b d e - 168a b d e - 264a b d e + 180a b d e - 36a b d +--R * +--R 2 +--R x +--R + +--R 10 8 9 2 7 8 2 3 6 7 3 4 5 6 4 5 4 +--R 24a d e - 132a b d e + 252a b d e - 84a b d e - 420a b d e +--R + +--R 5 5 6 3 4 6 7 2 3 7 8 2 8 9 +--R 756a b d e - 588a b d e + 228a b d e - 36a b d +--R * +--R x +--R + +--R 10 2 7 9 3 6 8 2 4 5 7 3 5 4 6 4 6 3 +--R 12a d e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 5 5 7 2 4 6 8 3 7 9 +--R - 252a b d e + 84a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 469 + +--S 470 of 764 +r0:=-2/9*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(9/2)/e^4+2/11*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^4-2/13*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(13/2)/e^4+2/15*b^2*B*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 2 7 7 2 7 2 6 6 +--R 858B b e x + ((990A b + 1980B a b)e + 3036B b d e )x +--R + +--R 2 7 2 6 +--R (2340A a b + 1170B a )e + (3600A b + 7200B a b)d e +--R + +--R 2 2 5 +--R 3708B b d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 1430A a e + (8840A a b + 4420B a )d e +--R + +--R 2 2 5 2 3 4 +--R (4580A b + 9160B a b)d e + 1600B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 5720A a d e + (11960A a b + 5980B a )d e +--R + +--R 2 3 4 2 4 3 +--R (2120A b + 4240B a b)d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 8580A a d e + (6240A a b + 3120B a )d e + (30A b + 60B a b)d e +--R + +--R 2 5 2 +--R - 12B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 5720A a d e + (260A a b + 130B a )d e + (- 40A b - 80B a b)d e +--R + +--R 2 6 +--R 16B b d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 1430A a d e + (- 520A a b - 260B a )d e + (80A b + 160B a b)d e +--R + +--R 2 7 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 470 + +--S 471 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 471 + +)clear all + +--S 472 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 472 + +--S 473 of 764 +r0:=-2/7*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(7/2)/e^4+2/9*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^4-2/11*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(11/2)/e^4+2/13*b^2*B*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 1386B b e x + ((1638A b + 3276B a b)e + 3402B b d e )x +--R + +--R 2 6 2 5 +--R (4004A a b + 2002B a )e + (4186A b + 8372B a b)d e +--R + +--R 2 2 4 +--R 2226B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 2574A a e + (10868A a b + 5434B a )d e +--R + +--R 2 2 4 2 3 3 +--R (2938A b + 5876B a b)d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 7722A a d e + (8580A a b + 4290B a )d e + (78A b + 156B a b)d e +--R + +--R 2 4 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R 7722A a d e + (572A a b + 286B a )d e +--R + +--R 2 4 2 2 5 +--R (- 104A b - 208B a b)d e + 48B b d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 2574A a d e + (- 1144A a b - 572B a )d e + (208A b + 416B a b)d e +--R + +--R 2 6 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 473 + +--S 474 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 474 + +)clear all + +--S 475 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 475 + +--S 476 of 764 +r0:=-2/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^4-2/9*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(9/2)/e^4+2/11*b^2*B*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B b e x + ((770A b + 1540B a b)e + 840B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A a b + 990B a )e + (1100A b + 2200B a b)d e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 1386A a e + (3168A a b + 1584B a )d e + (66A b + 132B a b)d e +--R + +--R 2 3 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 2772A a d e + (396A a b + 198B a )d e + (- 88A b - 176B a b)d e +--R + +--R 2 4 +--R 48B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 1386A a d e + (- 792A a b - 396B a )d e + (176A b + 352B a b)d e +--R + +--R 2 5 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 476 + +--S 477 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--R Type: Expression(Integer) +--E 478 + +--S 479 of 764 +r0:=-2/3*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^4-2/7*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(7/2)/e^4+2/9*b^2*B*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 2 4 4 2 4 2 3 3 +--R 70B b e x + ((90A b + 180B a b)e + 10B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((252A a b + 126B a )e + (18A b + 36B a b)d e - 12B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 210A a e + (84A a b + 42B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 16B b d e +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 210A a d e + (- 168A a b - 84B a )d e + (48A b + 96B a b)d e +--R + +--R 2 4 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 479 + +--S 480 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 481 + +--S 482 of 764 +r0:=2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^4-2/5*b*_ + (3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^4+2/7*b^2*B*(d+e*x)^(7/2)/e^4-_ + 2*(b*d-a*e)^2*(B*d-A*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((42A b + 84B a b)e - 36B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((140A a b + 70B a )e + (- 56A b - 112B a b)d e + 48B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 210A a e + (- 280A a b - 140B a )d e + (112A b + 224B a b)d e +--R + +--R 2 3 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 482 + +--S 483 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 484 + +--S 485 of 764 +r0:=-2/3*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^4+2/5*b^2*B*_ + (d+e*x)^(5/2)/e^4+2*(b*d-a*e)^2*(B*d-A*e)/(e^4*sqrt(d+e*x))+_ + 2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((10A b + 20B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((60A a b + 30B a )e + (- 40A b - 80B a b)d e + 48B b d e)x - 30A a e +--R + +--R 2 2 2 2 2 3 +--R (120A a b + 60B a )d e + (- 80A b - 160B a b)d e + 96B b d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 485 + +--S 486 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 486 + +)clear all + +--S 487 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 487 + +--S 488 of 764 +r0:=2/3*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(3/2))+2/3*b^2*B*_ + (d+e*x)^(3/2)/e^4-2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*_ + sqrt(d+e*x))-2*b*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((6A b + 12B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12A a b - 6B a )e + (24A b + 48B a b)d e - 48B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 8A a b - 4B a )d e + (16A b + 32B a b)d e - 32B b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 488 + +--S 489 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 489 + +)clear all + +--S 490 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 490 + +--S 491 of 764 +r0:=2/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(5/2))-2/3*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^(3/2))+2*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)/(e^4*sqrt(d+e*x))+2*b^2*B*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((- 30A b - 60B a b)e + 180B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 20A a b - 10B a )e + (- 40A b - 80B a b)d e + 240B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 6A a e + (- 8A a b - 4B a )d e + (- 16A b - 32B a b)d e + 96B b d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 491 + +--S 492 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 493 + +--S 494 of 764 +r0:=-2/9*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(9/2)/e^6+2/11*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^6-4/13*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^6+4/15*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^6-2/17*b^3*(5*b*B*d-_ + A*b*e-4*a*B*e)*(d+e*x)^(17/2)/e^6+2/19*b^4*B*(d+e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 4 9 9 4 3 9 4 8 8 +--R 218790B b e x + ((244530A b + 978120B a b )e + 746460B b d e )x +--R + +--R 3 2 2 9 +--R (1108536A a b + 1662804B a b )e +--R + +--R 4 3 8 4 2 7 +--R (847704A b + 3390816B a b )d e + 866580B b d e +--R * +--R 7 +--R x +--R + +--R 2 2 3 9 +--R (1918620A a b + 1279080B a b)e +--R + +--R 3 2 2 8 +--R (3922512A a b + 5883768B a b )d e +--R + +--R 4 3 2 7 4 3 6 +--R (1005708A b + 4022832B a b )d e + 345840B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 9 2 2 3 8 +--R (1511640A a b + 377910B a )e + (6976800A a b + 4651200B a b)d e +--R + +--R 3 2 2 2 7 +--R (4790736A a b + 7186104B a b )d e +--R + +--R 4 3 3 6 4 4 5 +--R (414504A b + 1658016B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 4 9 3 4 8 +--R 461890A a e + (5710640A a b + 1427660B a )d e +--R + +--R 2 2 3 2 7 +--R (8876040A a b + 5917360B a b)d e +--R + +--R 3 2 2 3 6 4 3 4 5 +--R (2067200A a b + 3100800B a b )d e + (1330A b + 5320B a b )d e +--R + +--R 4 5 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R 1847560A a d e + (7726160A a b + 1931540B a )d e +--R + +--R 2 2 3 3 6 +--R (4108560A a b + 2739040B a b)d e +--R + +--R 3 2 2 4 5 4 3 5 4 +--R (12920A a b + 19380B a b )d e + (- 1520A b - 6080B a b )d e +--R + +--R 4 6 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 2771340A a d e + (4031040A a b + 1007760B a )d e +--R + +--R 2 2 3 4 5 3 2 2 5 4 +--R (58140A a b + 38760B a b)d e + (- 15504A a b - 23256B a b )d e +--R + +--R 4 3 6 3 4 7 2 +--R (1824A b + 7296B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R 1847560A a d e + (167960A a b + 41990B a )d e +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (- 77520A a b - 51680B a b)d e + (20672A a b + 31008B a b )d e +--R + +--R 4 3 7 2 4 8 +--R (- 2432A b - 9728B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R 461890A a d e + (- 335920A a b - 83980B a )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (155040A a b + 103360B a b)d e + (- 41344A a b - 62016B a b )d e +--R + +--R 4 3 8 4 9 +--R (4864A b + 19456B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 496 + +--S 497 of 764 +r0:=-2/7*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(7/2)/e^6+2/9*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^6-4/11*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(11/2)/e^6+4/13*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(13/2)/e^6-2/15*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(15/2)/e^6+2/17*b^4*B*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 4 8 8 4 3 8 4 7 7 +--R 90090B b e x + ((102102A b + 408408B a b )e + 210210B b d e )x +--R + +--R 3 2 2 8 4 3 7 +--R (471240A a b + 706860B a b )e + (243474A b + 973896B a b )d e +--R + +--R 4 2 6 +--R 127050B b d e +--R * +--R 6 +--R x +--R + +--R 2 2 3 8 +--R (835380A a b + 556920B a b)e +--R + +--R 3 2 2 7 +--R (1156680A a b + 1735020B a b )d e +--R + +--R 4 3 2 6 4 3 5 +--R (152082A b + 608328B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 8 2 2 3 7 +--R (680680A a b + 170170B a )e + (2134860A a b + 1423240B a b)d e +--R + +--R 3 2 2 2 6 4 3 3 5 +--R (756840A a b + 1135260B a b )d e + (1190A b + 4760B a b )d e +--R + +--R 4 4 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 7 +--R 218790A a e + (1847560A a b + 461890B a )d e +--R + +--R 2 2 3 2 6 3 2 2 3 5 +--R (1498380A a b + 998920B a b)d e + (10200A a b + 15300B a b )d e +--R + +--R 4 3 4 4 4 5 3 +--R (- 1360A b - 5440B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 2 6 +--R 656370A a d e + (1458600A a b + 364650B a )d e +--R + +--R 2 2 3 3 5 3 2 2 4 4 +--R (39780A a b + 26520B a b)d e + (- 12240A a b - 18360B a b )d e +--R + +--R 4 3 5 3 4 6 2 +--R (1632A b + 6528B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 6 3 4 3 5 +--R 656370A a d e + (97240A a b + 24310B a )d e +--R + +--R 2 2 3 4 4 3 2 2 5 3 +--R (- 53040A a b - 35360B a b)d e + (16320A a b + 24480B a b )d e +--R + +--R 4 3 6 2 4 7 +--R (- 2176A b - 8704B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 3 5 3 4 4 4 +--R 218790A a d e + (- 194480A a b - 48620B a )d e +--R + +--R 2 2 3 5 3 3 2 2 6 2 +--R (106080A a b + 70720B a b)d e + (- 32640A a b - 48960B a b )d e +--R + +--R 4 3 7 4 8 +--R (4352A b + 17408B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Expression(Integer) +--E 497 + +--S 498 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 499 + +--S 500 of 764 +r0:=-2/5*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(5/2)/e^6+2/7*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^6-4/9*b*(b*d-a*e)^2*(5*b*B*d-_ + 3*A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^6+4/11*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-_ + 3*a*B*e)*(d+e*x)^(11/2)/e^6-2/13*b^3*(5*b*B*d-A*b*e-4*a*B*e)*_ + (d+e*x)^(13/2)/e^6+2/15*b^4*B*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 4 7 7 4 3 7 4 6 6 +--R 6006B b e x + ((6930A b + 27720B a b )e + 7392B b d e )x +--R + +--R 3 2 2 7 4 3 6 +--R (32760A a b + 49140B a b )e + (8820A b + 35280B a b )d e +--R + +--R 4 2 5 +--R 126B b d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 3 2 2 6 +--R (60060A a b + 40040B a b)e + (43680A a b + 65520B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (210A b + 840B a b )d e - 140B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (51480A a b + 12870B a )e + (85800A a b + 57200B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 +--R (1560A a b + 2340B a b )d e + (- 240A b - 960B a b )d e +--R + +--R 4 4 3 +--R 160B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 6 +--R 18018A a e + (82368A a b + 20592B a )d e +--R + +--R 2 2 3 2 5 3 2 2 3 4 +--R (5148A a b + 3432B a b)d e + (- 1872A a b - 2808B a b )d e +--R + +--R 4 3 4 3 4 5 2 +--R (288A b + 1152B a b )d e - 192B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 2 5 +--R 36036A a d e + (10296A a b + 2574B a )d e +--R + +--R 2 2 3 3 4 3 2 2 4 3 +--R (- 6864A a b - 4576B a b)d e + (2496A a b + 3744B a b )d e +--R + +--R 4 3 5 2 4 6 +--R (- 384A b - 1536B a b )d e + 256B b d e +--R * +--R x +--R + +--R 4 2 5 3 4 3 4 +--R 18018A a d e + (- 20592A a b - 5148B a )d e +--R + +--R 2 2 3 4 3 3 2 2 5 2 +--R (13728A a b + 9152B a b)d e + (- 4992A a b - 7488B a b )d e +--R + +--R 4 3 6 4 7 +--R (768A b + 3072B a b )d e - 512B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 500 + +--S 501 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 501 + +)clear all + +--S 502 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 502 + +--S 503 of 764 +r0:=-2/3*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(3/2)/e^6+2/5*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^6-4/7*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^6+4/9*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^6-2/11*b^3*_ + (5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(11/2)/e^6+2/13*b^4*B*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 4 6 6 4 3 6 4 5 5 +--R 6930B b e x + ((8190A b + 32760B a b )e + 630B b d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (40040A a b + 60060B a b )e + (910A b + 3640B a b )d e +--R + +--R 4 2 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (77220A a b + 51480B a b)e + (5720A a b + 8580B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (- 1040A b - 4160B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (72072A a b + 18018B a )e + (15444A a b + 10296B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 6864A a b - 10296B a b )d e + (1248A b + 4992B a b )d e +--R + +--R 4 4 2 +--R - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 5 +--R 30030A a e + (24024A a b + 6006B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 20592A a b - 13728B a b)d e + (9152A a b + 13728B a b )d e +--R + +--R 4 3 4 2 4 5 +--R (- 1664A b - 6656B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 2 4 +--R 30030A a d e + (- 48048A a b - 12012B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (41184A a b + 27456B a b)d e + (- 18304A a b - 27456B a b )d e +--R + +--R 4 3 5 4 6 +--R (3328A b + 13312B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 503 + +--S 504 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 504 + +)clear all + +--S 505 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 505 + +--S 506 of 764 +r0:=2/3*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^6-4/5*b*_ + (b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^6+4/7*b^2*_ + (b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^6-2/9*b^3*_ + (5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(9/2)/e^6+2/11*b^4*B*(d+e*x)^(11/2)/e^6-_ + 2*(b*d-a*e)^4*(B*d-A*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 630B b e x + ((770A b + 3080B a b )e - 700B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (3960A a b + 5940B a b )e + (- 880A b - 3520B a b )d e +--R + +--R 4 2 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (8316A a b + 5544B a b)e + (- 4752A a b - 7128B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (1056A b + 4224B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (9240A a b + 2310B a )e + (- 11088A a b - 7392B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (6336A a b + 9504B a b )d e + (- 1408A b - 5632B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R 6930A a e + (- 18480A a b - 4620B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (22176A a b + 14784B a b)d e + (- 12672A a b - 19008B a b )d e +--R + +--R 4 3 4 4 5 +--R (2816A b + 11264B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 506 + +--S 507 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 508 + +--S 509 of 764 +r0:=-4/3*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^6+_ + 4/5*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^6-_ + 2/7*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(7/2)/e^6+2/9*b^4*B*_ + (d+e*x)^(9/2)/e^6+2*(b*d-a*e)^4*(B*d-A*e)/(e^6*sqrt(d+e*x))+_ + 2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 70B b e x + ((90A b + 360B a b )e - 100B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((504A a b + 756B a b )e + (- 144A b - 576B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1008A a b - 1512B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (288A b + 1152B a b )d e - 320B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (2520A a b + 630B a )e + (- 5040A a b - 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (4032A a b + 6048B a b )d e + (- 1152A b - 4608B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R - 630A a e + (5040A a b + 1260B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 10080A a b - 6720B a b)d e + (8064A a b + 12096B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 2304A b - 9216B a b )d e + 2560B b d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 509 + +--S 510 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 511 + +--S 512 of 764 +r0:=2/3*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^(3/2))+4/3*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^6-2/5*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(5/2)/e^6+2/7*b^4*B*(d+e*x)^(7/2)/e^6-2*(b*d-_ + a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*sqrt(d+e*x))-4*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 30B b e x + ((42A b + 168B a b )e - 60B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((280A a b + 420B a b )e + (- 112A b - 448B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1680A a b - 2520B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (672A b + 2688B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 840A a b - 210B a )e + (5040A a b + 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 6720A a b - 10080B a b )d e + (2688A b + 10752B a b )d e +--R + +--R 4 4 +--R - 3840B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 70A a e + (- 560A a b - 140B a )d e + (3360A a b + 2240B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 4480A a b - 6720B a b )d e + (1792A b + 7168B a b )d e - 2560B b d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 512 + +--S 513 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 514 + +--S 515 of 764 +r0:=2/5*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^(5/2))-2/3*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^(3/2))-2/3*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(3/2)/e^6+2/5*b^4*B*(d+e*x)^(5/2)/e^6+4*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*sqrt(d+e*x))+4*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 6B b e x + ((10A b + 40B a b )e - 20B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((120A a b + 180B a b )e + (- 80A b - 320B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 180A a b - 120B a b)e + (720A a b + 1080B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 480A b - 1920B a b )d e + 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 40A a b - 10B a )e + (- 240A a b - 160B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (960A a b + 1440B a b )d e + (- 640A b - 2560B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 6A a e + (- 16A a b - 4B a )d e + (- 96A a b - 64B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (384A a b + 576B a b )d e + (- 256A b - 1024B a b )d e + 512B b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 515 + +--S 516 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 516 + +)clear all + +--S 517 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 6 3 10 6 5 3 6 2 9 +--R B b e x + ((A b + 6B a b )e + 3B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 8 +--R ((6A a b + 15B a b )e + (3A b + 18B a b )d e + 3B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (15A a b + 20B a b )e + (18A a b + 45B a b )d e +--R + +--R 6 5 2 6 3 +--R (3A b + 18B a b )d e + B b d +--R * +--R 7 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (20A a b + 15B a b )e + (45A a b + 60B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (18A a b + 45B a b )d e + (A b + 6B a b )d +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (15A a b + 6B a b)e + (60A a b + 45B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (45A a b + 60B a b )d e + (6A a b + 15B a b )d +--R * +--R 5 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (6A a b + B a )e + (45A a b + 18B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (60A a b + 45B a b )d e + (15A a b + 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R A a e + (18A a b + 3B a )d e + (45A a b + 18B a b)d e +--R + +--R 3 3 4 2 3 +--R (20A a b + 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 2 4 2 5 3 2 +--R (3A a d e + (18A a b + 3B a )d e + (15A a b + 6B a b)d )x +--R + +--R 6 2 5 6 3 6 3 +--R (3A a d e + (6A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 517 + +--S 518 of 764 +r0:=-2/9*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(9/2)/e^8+2/11*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^8-6/13*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^8+2/3*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^8-10/17*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(17/2)/e^8+6/19*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(19/2)/e^8-2/21*b^5*(7*b*B*d-A*b*e-_ + 6*a*B*e)*(d+e*x)^(21/2)/e^8+2/23*b^6*B*(d+e*x)^(23/2)/e^8 +--R +--R +--R (2) +--R 6 11 11 +--R 5819814B b e x +--R + +--R 6 5 11 6 10 10 +--R ((6374082A b + 38244492B a b )e + 19399380B b d e )x +--R + +--R 5 2 4 11 +--R (42270228A a b + 105675570B a b )e +--R + +--R 6 5 10 6 2 9 +--R (21470592A b + 128823552B a b )d e + 21849828B b d e +--R * +--R 9 +--R x +--R + +--R 2 4 3 3 11 +--R (118107990A a b + 157477320B a b )e +--R + +--R 5 2 4 10 +--R (144216072A a b + 360540180B a b )d e +--R + +--R 6 5 2 9 6 3 8 +--R (24509628A b + 147057768B a b )d e + 8360352B b d e +--R * +--R 8 +--R x +--R + +--R 3 3 4 2 11 +--R (178474296A a b + 133855722B a b )e +--R + +--R 2 4 3 3 10 +--R (409441032A a b + 545921376B a b )d e +--R + +--R 5 2 4 2 9 +--R (167423256A a b + 418558140B a b )d e +--R + +--R 6 5 3 8 6 4 7 +--R (9551256A b + 57307536B a b )d e + 6006B b d e +--R * +--R 7 +--R x +--R + +--R 4 2 5 11 +--R (154448910A a b + 61779564B a b)e +--R + +--R 3 3 4 2 10 +--R (631524432A a b + 473643324B a b )d e +--R + +--R 2 4 3 3 2 9 +--R (485756964A a b + 647675952B a b )d e +--R + +--R 5 2 4 3 8 +--R (66816288A a b + 167040720B a b )d e +--R + +--R 6 5 4 7 6 5 6 +--R (10626A b + 63756B a b )d e - 6468B b d e +--R * +--R 6 +--R x +--R + +--R 5 6 11 +--R (73012212A a b + 12168702B a )e +--R + +--R 4 2 5 10 +--R (561632400A a b + 224652960B a b)d e +--R + +--R 3 3 4 2 2 9 +--R (771308496A a b + 578481372B a b )d e +--R + +--R 2 4 3 3 3 8 +--R (200205432A a b + 266940576B a b )d e +--R + +--R 5 2 4 4 7 6 5 5 6 +--R (121716A a b + 304290B a b )d e + (- 11592A b - 69552B a b )d e +--R + +--R 6 6 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 6 11 5 6 10 +--R 14872858A a e + (275823912A a b + 45970652B a )d e +--R + +--R 4 2 5 2 9 +--R (714521220A a b + 285808488B a b)d e +--R + +--R 3 3 4 2 3 8 +--R (332819200A a b + 249614400B a b )d e +--R + +--R 2 4 3 3 4 7 +--R (642390A a b + 856520B a b )d e +--R + +--R 5 2 4 5 6 6 5 6 5 +--R (- 135240A a b - 338100B a b )d e + (12880A b + 77280B a b )d e +--R + +--R 6 7 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 6 10 5 6 2 9 +--R 59491432A a d e + (373173528A a b + 62195588B a )d e +--R + +--R 4 2 5 3 8 +--R (330739080A a b + 132295632B a b)d e +--R + +--R 3 3 4 2 4 7 +--R (2080120A a b + 1560090B a b )d e +--R + +--R 2 4 3 3 5 6 +--R (- 734160A a b - 978880B a b )d e +--R + +--R 5 2 4 6 5 6 5 7 4 +--R (154560A a b + 386400B a b )d e + (- 14720A b - 88320B a b )d e +--R + +--R 6 8 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 6 2 9 5 6 3 8 +--R 89237148A a d e + (194699232A a b + 32449872B a )d e +--R + +--R 4 2 5 4 7 +--R (4680270A a b + 1872108B a b)d e +--R + +--R 3 3 4 2 5 6 +--R (- 2496144A a b - 1872108B a b )d e +--R + +--R 2 4 3 3 6 5 +--R (880992A a b + 1174656B a b )d e +--R + +--R 5 2 4 7 4 +--R (- 185472A a b - 463680B a b )d e +--R + +--R 6 5 8 3 6 9 2 +--R (17664A b + 105984B a b )d e - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 6 3 8 5 6 4 7 +--R 59491432A a d e + (8112468A a b + 1352078B a )d e +--R + +--R 4 2 5 5 6 +--R (- 6240360A a b - 2496144B a b)d e +--R + +--R 3 3 4 2 6 5 +--R (3328192A a b + 2496144B a b )d e +--R + +--R 2 4 3 3 7 4 +--R (- 1174656A a b - 1566208B a b )d e +--R + +--R 5 2 4 8 3 +--R (247296A a b + 618240B a b )d e +--R + +--R 6 5 9 2 6 10 +--R (- 23552A b - 141312B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 4 7 5 6 5 6 +--R 14872858A a d e + (- 16224936A a b - 2704156B a )d e +--R + +--R 4 2 5 6 5 +--R (12480720A a b + 4992288B a b)d e +--R + +--R 3 3 4 2 7 4 +--R (- 6656384A a b - 4992288B a b )d e +--R + +--R 2 4 3 3 8 3 +--R (2349312A a b + 3132416B a b )d e +--R + +--R 5 2 4 9 2 6 5 10 +--R (- 494592A a b - 1236480B a b )d e + (47104A b + 282624B a b )d e +--R + +--R 6 11 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 66927861e +--R Type: Expression(Integer) +--E 518 + +--S 519 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 519 + +)clear all + 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15B a b )e + (A b + 6B a b )d)x +--R + +--R 2 4 3 3 5 2 4 5 +--R ((15A a b + 20B a b )e + (6A a b + 15B a b )d)x +--R + +--R 3 3 4 2 2 4 3 3 4 +--R ((20A a b + 15B a b )e + (15A a b + 20B a b )d)x +--R + +--R 4 2 5 3 3 4 2 3 +--R ((15A a b + 6B a b)e + (20A a b + 15B a b )d)x +--R + +--R 5 6 4 2 5 2 6 5 6 +--R ((6A a b + B a )e + (15A a b + 6B a b)d)x + (A a e + (6A a b + B a )d)x +--R + +--R 6 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 523 + +--S 524 of 764 +r0:=-2/5*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(5/2)/e^8+2/7*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^8-2/3*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^8+10/11*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(11/2)/e^8-10/13*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(13/2)/e^8+2/5*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(15/2)/e^8-2/17*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(17/2)/e^8+2/19*b^6*B*(d+e*x)^(19/2)/e^8 +--R +--R +--R (2) +--R 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63840B a b )d e +--R + +--R 6 5 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 5 6 9 +--R (8314020A a b + 1385670B a )e +--R + +--R 4 2 5 8 +--R (23094500A a b + 9237800B a b)d e +--R + +--R 3 3 4 2 2 7 +--R (839800A a b + 629850B a b )d e +--R + +--R 2 4 3 3 3 6 +--R (- 387600A a b - 516800B a b )d e +--R + +--R 5 2 4 4 5 6 5 5 4 +--R (103360A a b + 258400B a b )d e + (- 12160A b - 72960B a b )d e +--R + +--R 6 6 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 6 9 5 6 8 +--R 1939938A a e + (13302432A a b + 2217072B a )d e +--R + +--R 4 2 5 2 7 +--R (1385670A a b + 554268B a b)d e +--R + +--R 3 3 4 2 3 6 +--R (- 1007760A a b - 755820B a b )d e +--R + +--R 2 4 3 3 4 5 +--R (465120A a b + 620160B a b )d e +--R + +--R 5 2 4 5 4 6 5 6 3 +--R (- 124032A a b - 310080B a b )d e + (14592A b + 87552B a b )d e +--R + +--R 6 7 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 6 8 5 6 2 7 +--R 3879876A a d e + (1662804A a b + 277134B a )d e +--R + +--R 4 2 5 3 6 +--R (- 1847560A a b - 739024B a b)d e +--R + +--R 3 3 4 2 4 5 +--R (1343680A a b + 1007760B a b )d e +--R + +--R 2 4 3 3 5 4 +--R (- 620160A a b - 826880B a b )d e +--R + +--R 5 2 4 6 3 +--R (165376A a b + 413440B a b )d e +--R + +--R 6 5 7 2 6 8 +--R (- 19456A b - 116736B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 2 7 5 6 3 6 +--R 1939938A a d e + (- 3325608A a b - 554268B a )d e +--R + +--R 4 2 5 4 5 +--R (3695120A a b + 1478048B a b)d e +--R + +--R 3 3 4 2 5 4 +--R (- 2687360A a b - 2015520B a b )d e +--R + +--R 2 4 3 3 6 3 +--R (1240320A a b + 1653760B a b )d e +--R + +--R 5 2 4 7 2 6 5 8 +--R (- 330752A a b - 826880B a b )d e + (38912A b + 233472B a b )d e +--R + +--R 6 9 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 4849845e +--R Type: Expression(Integer) +--E 524 + +--S 525 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 526 + +--S 527 of 764 +r0:=-2/3*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(3/2)/e^8+2/5*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^8-6/7*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^8+10/9*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^8-10/11*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(11/2)/e^8+6/13*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(13/2)/e^8-2/15*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(15/2)/e^8+2/17*b^6*B*(d+e*x)^(17/2)/e^8 +--R +--R +--R (2) +--R 6 8 8 6 5 8 6 7 7 +--R 90090B b e x + ((102102A b + 612612B a b )e + 6006B b d e )x +--R + +--R 5 2 4 8 6 5 7 +--R (706860A a b + 1767150B a b )e + (7854A b + 47124B a b )d e +--R + +--R 6 2 6 +--R - 6468B b d e +--R * +--R 6 +--R x +--R + +--R 2 4 3 3 8 +--R (2088450A a b + 2784600B a b )e +--R + +--R 5 2 4 7 6 5 2 6 +--R (64260A a b + 160650B a b )d e + (- 8568A b - 51408B a b )d e +--R + +--R 6 3 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 3 3 4 2 8 +--R (3403400A a b + 2552550B a b )e +--R + +--R 2 4 3 3 7 +--R (232050A a b + 309400B a b )d e +--R + +--R 5 2 4 2 6 6 5 3 5 +--R (- 71400A a b - 178500B a b )d e + (9520A b + 57120B a b )d e +--R + +--R 6 4 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 5 8 +--R (3281850A a b + 1312740B a b)e +--R + +--R 3 3 4 2 7 +--R (486200A a b + 364650B a b )d e +--R + +--R 2 4 3 3 2 6 +--R (- 265200A a b - 353600B a b )d e +--R + +--R 5 2 4 3 5 6 5 4 4 +--R (81600A a b + 204000B a b )d e + (- 10880A b - 65280B a b )d e +--R + +--R 6 5 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 5 6 8 4 2 5 7 +--R (1837836A a b + 306306B a )e + (656370A a b + 262548B a b)d e +--R + +--R 3 3 4 2 2 6 +--R (- 583440A a b - 437580B a b )d e +--R + +--R 2 4 3 3 3 5 +--R (318240A a b + 424320B a b )d e +--R + +--R 5 2 4 4 4 6 5 5 3 +--R (- 97920A a b - 244800B a b )d e + (13056A b + 78336B a b )d e +--R + +--R 6 6 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 6 8 5 6 7 +--R 510510A a e + (612612A a b + 102102B a )d e +--R + +--R 4 2 5 2 6 +--R (- 875160A a b - 350064B a b)d e +--R + +--R 3 3 4 2 3 5 +--R (777920A a b + 583440B a b )d e +--R + +--R 2 4 3 3 4 4 +--R (- 424320A a b - 565760B a b )d e +--R + +--R 5 2 4 5 3 +--R (130560A a b + 326400B a b )d e +--R + +--R 6 5 6 2 6 7 +--R (- 17408A b - 104448B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 2 6 +--R 510510A a d e + (- 1225224A a b - 204204B a )d e +--R + +--R 4 2 5 3 5 +--R (1750320A a b + 700128B a b)d e +--R + +--R 3 3 4 2 4 4 +--R (- 1555840A a b - 1166880B a b )d e +--R + +--R 2 4 3 3 5 3 +--R (848640A a b + 1131520B a b )d e +--R + +--R 5 2 4 6 2 6 5 7 +--R (- 261120A a b - 652800B a b )d e + (34816A b + 208896B a b )d e +--R + +--R 6 8 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Expression(Integer) +--E 527 + +--S 528 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 528 + +)clear all + +--S 529 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 529 + +--S 530 of 764 +r0:=2/3*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^8-6/5*b*_ + (b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^8+10/7*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^8-10/9*b^3*_ + (b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(9/2)/e^8+6/11*b^4*_ + (b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(11/2)/e^8-2/13*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(13/2)/e^8+2/15*b^6*B*_ + (d+e*x)^(15/2)/e^8-2*(b*d-a*e)^6*(B*d-A*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 6006B b e x + ((6930A b + 41580B a b )e - 6468B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (49140A a b + 122850B a b )e + (- 7560A b - 45360B a b )d e +--R + +--R 6 2 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 +--R (150150A a b + 200200B a b )e +--R + +--R 5 2 4 6 6 5 2 5 +--R (- 54600A a b - 136500B a b )d e + (8400A b + 50400B a b )d e +--R + +--R 6 3 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 +--R (257400A a b + 193050B a b )e +--R + +--R 2 4 3 3 6 +--R (- 171600A a b - 228800B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (62400A a b + 156000B a b )d e + (- 9600A b - 57600B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 +--R (270270A a b + 108108B a b)e +--R + +--R 3 3 4 2 6 +--R (- 308880A a b - 231660B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (205920A a b + 274560B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (- 74880A a b - 187200B a b )d e + (11520A b + 69120B a b )d e +--R + +--R 6 5 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (180180A a b + 30030B a )e + (- 360360A a b - 144144B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (411840A a b + 308880B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 274560A a b - 366080B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (99840A a b + 249600B a b )d e + (- 15360A b - 92160B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R 90090A a e + (- 360360A a b - 60060B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (720720A a b + 288288B a b)d e + (- 823680A a b - 617760B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (549120A a b + 732160B a b )d e + (- 199680A a b - 499200B a b )d e +--R + +--R 6 5 6 6 7 +--R (30720A b + 184320B a b )d e - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 530 + +--S 531 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 531 + +)clear all + +--S 532 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 532 + +--S 533 of 764 +r0:=-2*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^8+2*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^8-10/7*b^3*_ + (b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(7/2)/e^8+2/3*b^4*_ + (b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(9/2)/e^8-2/11*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(11/2)/e^8+2/13*b^6*B*_ + (d+e*x)^(13/2)/e^8+2*(b*d-a*e)^6*(B*d-A*e)/(e^8*sqrt(d+e*x))+_ + 2*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 462B b e x + ((546A b + 3276B a b )e - 588B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (4004A a b + 10010B a b )e + (- 728A b - 4368B a b )d e +--R + +--R 6 2 5 +--R 784B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (12870A a b + 17160B a b )e + (- 5720A a b - 14300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (1040A b + 6240B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (24024A a b + 18018B a b )e + (- 20592A a b - 27456B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (9152A a b + 22880B a b )d e + (- 1664A b - 9984B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (30030A a b + 12012B a b)e + (- 48048A a b - 36036B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (41184A a b + 54912B a b )d e + (- 18304A a b - 45760B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (3328A b + 19968B a b )d e - 3584B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (36036A a b + 6006B a )e + (- 120120A a b - 48048B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (192192A a b + 144144B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 164736A a b - 219648B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (73216A a b + 183040B a b )d e + (- 13312A b - 79872B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 6006A a e + (72072A a b + 12012B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 240240A a b - 96096B a b)d e + (384384A a b + 288288B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 329472A a b - 439296B a b )d e + (146432A a b + 366080B a b )d e +--R + +--R 6 5 6 6 7 +--R (- 26624A b - 159744B a b )d e + 28672B b d +--R / +--R 8 +-------+ +--R 3003e \|e x + d +--R Type: Expression(Integer) +--E 533 + +--S 534 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 534 + +)clear all + +--S 535 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 535 + +--S 536 of 764 +r0:=2/3*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^(3/2))+10/3*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^8-2*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(5/2)/e^8+6/7*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(7/2)/e^8-2/9*b^5*(7*b*B*d-A*b*e-_ + 6*a*B*e)*(d+e*x)^(9/2)/e^8+2/11*b^6*B*(d+e*x)^(11/2)/e^8-2*_ + (b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*sqrt(d+e*x))-6*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 126B b e x + ((154A b + 924B a b )e - 196B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (1188A a b + 2970B a b )e + (- 264A b - 1584B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (4158A a b + 5544B a b )e + (- 2376A a b - 5940B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (528A b + 3168B a b )d e - 672B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (9240A a b + 6930B a b )e + (- 11088A a b - 14784B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (6336A a b + 15840B a b )d e + (- 1408A b - 8448B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (20790A a b + 8316B a b)e + (- 55440A a b - 41580B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (66528A a b + 88704B a b )d e + (- 38016A a b - 95040B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (8448A b + 50688B a b )d e - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 8316A a b - 1386B a )e + (83160A a b + 33264B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (- 221760A a b - 166320B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (266112A a b + 354816B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 152064A a b - 380160B a b )d e + (33792A b + 202752B a b )d e +--R + +--R 6 6 +--R - 43008B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 462A a e + (- 5544A a b - 924B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (55440A a b + 22176B a b)d e + (- 147840A a b - 110880B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (177408A a b + 236544B a b )d e + (- 101376A a b - 253440B a b )d e +--R + +--R 6 5 6 6 7 +--R (22528A b + 135168B a b )d e - 28672B b d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Expression(Integer) +--E 536 + +--S 537 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 538 + +--S 539 of 764 +r0:=2/5*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^(5/2))-2/3*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^(3/2))-10/3*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(3/2)/e^8+6/5*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(5/2)/e^8-2/7*b^5*(7*b*B*d-_ + A*b*e-6*a*B*e)*(d+e*x)^(7/2)/e^8+2/9*b^6*B*(d+e*x)^(9/2)/e^8+6*b*_ + (b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*sqrt(d+e*x))+10*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 70B b e x + ((90A b + 540B a b )e - 140B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (756A a b + 1890B a b )e + (- 216A b - 1296B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (3150A a b + 4200B a b )e + (- 2520A a b - 6300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (720A b + 4320B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (12600A a b + 9450B a b )e + (- 25200A a b - 33600B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (20160A a b + 50400B a b )d e + (- 5760A b - 34560B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (- 9450A a b - 3780B a b)e + (75600A a b + 56700B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (- 151200A a b - 201600B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (120960A a b + 302400B a b )d e + (- 34560A b - 207360B a b )d e +--R + +--R 6 5 2 +--R 53760B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 1260A a b - 210B a )e + (- 12600A a b - 5040B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (100800A a b + 75600B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 201600A a b - 268800B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (161280A a b + 403200B a b )d e + (- 46080A b - 276480B a b )d e +--R + +--R 6 6 +--R 71680B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 126A a e + (- 504A a b - 84B a )d e + (- 5040A a b - 2016B a b)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (40320A a b + 30240B a b )d e + (- 80640A a b - 107520B a b )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (64512A a b + 161280B a b )d e + (- 18432A b - 110592B a b )d e +--R + +--R 6 7 +--R 28672B b d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 539 + +--S 540 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 541 + +--S 542 of 764 +r0:=1/3*(b*d-a*e)*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+_ + 1/5*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/b^3+1/7*(2*b*B*d+7*A*b*e-_ + 9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(9/2)/(b*_ + (b*d-a*e)*(a+b*x))-(b*d-a*e)^(5/2)*(2*b*B*d+7*A*b*e-9*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+(b*d-a*e)^2*_ + (2*b*B*d+7*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (- 735A a b + 945B a b)e + (1470A a b - 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 735A b + 1365B a b )d e - 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 735A a b + 945B a )e + (1470A a b - 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 735A a b + 1365B a b )d e - 210B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 54B a b )e + 132B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 98A a b + 126B a b )e + (224A b - 316B a b )d e +--R + +--R 4 2 +--R 244B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (490A a b - 630B a b)e + (- 1176A a b + 1652B a b )d e +--R + +--R 4 3 2 4 3 +--R (812A b - 1380B a b )d e + 352B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1715A a b + 2415B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (1127A a b - 1939B a b )d e + (- 105A b + 457B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 5 +-+ +--R (105b x + 105a b )\|b +--R Type: Expression(Integer) +--E 542 + +--S 543 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 544 + +--S 545 of 764 +r0:=1/3*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/b^3+1/5*(2*b*B*d+5*A*b*e-_ + 7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(7/2)/(b*_ + (b*d-a*e)*(a+b*x))-(b*d-a*e)^(3/2)*(2*b*B*d+5*A*b*e-7*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+(b*d-a*e)*(2*b*B*d+_ + 5*A*b*e-7*a*B*e)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 14B a b )e + 22B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 50A a b + 70B a b)e + (70A b - 118B a b )d e + 46B b d )x +--R + +--R 2 3 2 2 2 +--R (- 75A a b + 105B a )e + (100A a b - 170B a b)d e +--R + +--R 3 2 2 +--R (- 15A b + 61B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 5 4 +-+ +--R (15b x + 15a b )\|b +--R Type: Expression(Integer) +--E 545 + +--S 546 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 546 + +)clear all + +--S 547 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 547 + +--S 548 of 764 +r0:=1/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e))-_ + (A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+_ + (2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (((- 9A b + 15B a b)e - 6B b d)x + (- 9A a b + 15B a )e - 6B a b d) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 10B a b)e + 8B b d)x + (9A a b - 15B a )e +--R + +--R 2 +--R (- 3A b + 11B a b)d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 548 + +--S 549 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 550 + +--S 551 of 764 +r0:=-(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+A*b*e-3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))+_ + (2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)) +--R +--R +--R (2) +--R 2 2 2 +--R (((- A b + 3B a b)e - 2B b d)x + (- A a b + 3B a )e - 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (2B b x - A b + 3B a)\|- a e + b d \|b \|e x + d +--R / +--R 3 2 +-----------+ +-+ +--R (b x + a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 551 + +--S 552 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 764 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 553 + +--S 554 of 764 +r0:=-(2*b*B*d-A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(3/2)*(b*d-a*e)^(3/2))-(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 +--R (((- A b - B a b)e + 2B b d)x + (- A a b - B a )e + 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (A b - B a)\|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 2 +-----------+ +-+ +--R ((a b e - b d)x + a b e - a b d)\|- a e + b d \|b +--R Type: Expression(Integer) +--E 554 + +--S 555 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 556 + +--S 557 of 764 +r0:=-(2*b*B*d-3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(5/2)*sqrt(b))+(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^2*_ + sqrt(d+e*x))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 +-------+ +--R (((3A b - B a b)e - 2B b d)x + (3A a b - B a )e - 2B a b d)\|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R (((- 3A b + B a)e + 2B b d)x - 2A a e + (- A b + 3B a)d)\|- a e + b d \|b +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-----------+ +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R Type: Expression(Integer) +--E 557 + +--S 558 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 559 + +--S 560 of 764 +r0:=1/3*(2*b*B*d-5*A*b*e+3*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+(-A*b+a*B)/_ + (b*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2))-(2*b*B*d-5*A*b*e+3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(7/2)+_ + (2*b*B*d-5*A*b*e+3*a*B*e)/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 15A b + 9B a b)e + 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 15A a b + 9B a )e + (- 15A b + 15B a b)d e + 6B b d )x +--R + +--R 2 2 +--R (- 15A a b + 9B a )d e + 6B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((10A a b - 6B a )e + (20A b - 16B a b)d e - 8B b d )x - 2A a e +--R + +--R 2 2 2 +--R (14A a b - 4B a )d e + (3A b - 11B a b)d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 560 + +--S 561 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 561 + +)clear all + +--S 562 of 764 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 562 + +--S 563 of 764 +r0:=1/5*(2*b*B*d-7*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+_ + (-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(5/2))+1/3*(2*b*B*d-7*A*b*e+_ + 5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2))-b^(3/2)*(2*b*B*d-7*A*b*e+_ + 5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+_ + b*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((105A b - 75B a b )e - 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((105A a b - 75B a b)e + (210A b - 180B a b )d e - 60B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((210A a b - 150B a b)d e + (105A b - 135B a b )d e - 30B b d )x +--R + +--R 2 2 2 2 3 +--R (105A a b - 75B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 70A a b + 50B a b)e + (- 245A b + 195B a b )d e +--R + +--R 3 2 +--R 70B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 10B a )e + (- 168A a b + 116B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 161A b + 163B a b )d e + 46B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (32A a b - 4B a )d e + (- 116A a b + 48B a b)d e +--R + +--R 3 2 3 +--R (- 15A b + 61B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 563 + +--S 564 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 of 764 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 565 + +--S 566 of 764 +r0:=7/8*e^2*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(3/2)/b^5+21/40*e^2*_ + (6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*(b*d-a*e))-3/8*e*_ + (6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(7/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/12*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(9/2)/(b^2*(b*d-a*e)*_ + (a+b*x)^2)-1/3*(A*b-a*B)*(d+e*x)^(11/2)/(b*(b*d-a*e)*(a+b*x)^3)-_ + 21/8*e^2*(b*d-a*e)^(3/2)*(6*b*B*d+5*A*b*e-11*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(13/2)+21/8*e^2*(b*d-a*e)*(6*b*B*d+_ + 5*A*b*e-11*a*B*e)*sqrt(d+e*x)/b^6 +--R +--R +--R (2) +--R 4 2 3 4 5 4 3 +--R (1575A a b - 3465B a b )e + (- 1575A b + 5355B a b )d e +--R + +--R 5 2 2 +--R - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4725A a b - 10395B a b )e + (- 4725A a b + 16065B a b )d e +--R + +--R 4 2 2 +--R - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (4725A a b - 10395B a b)e + (- 4725A a b + 16065B a b )d e +--R + +--R 2 3 2 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (1575A a b - 3465B a )e + (- 1575A a b + 5355B a b)d e +--R + +--R 3 2 2 2 +--R - 1890B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 48B b e x + ((80A b - 176B a b )e + 336B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 720A a b + 1584B a b )e + (1040A b - 3152B a b )d e +--R + +--R 5 2 2 +--R 1728B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 3465A a b + 7623B a b )e + (4770A a b - 14652B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 825A b + 7539B a b )d e - 510B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 4200A a b + 9240B a b)e + (5670A a b - 17514B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 900A a b + 8784B a b )d e + (- 250A b - 530B a b )d e +--R + +--R 5 4 +--R - 60B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 1575A a b + 3465B a )e + (2100A a b - 6510B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 315A a b + 3213B a b )d e + (- 90A a b - 180B a b )d e +--R + +--R 5 4 4 +--R (- 40A b - 20B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 9 3 8 2 2 7 3 6 +-+ +--R (120b x + 360a b x + 360a b x + 120a b )\|b +--R Type: Expression(Integer) +--E 566 + +--S 567 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 568 + +--S 569 of 764 +r0:=35/24*e^2*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e))-_ + 7/8*e*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(5/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/4*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^3)-35/8*e^2*(2*b*B*d+_ + A*b*e-3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-_ + a*e)/b^(11/2)+35/8*e^2*(2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 105A b + 315B a b )e - 210B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 315A a b + 945B a b )e - 630B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 315A a b + 945B a b)e - 630B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 105A a b + 315B a )e - 210B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 16B b e x + ((48A b - 144B a b )e + 160B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (231A a b - 693B a b )e + (- 87A b + 723B a b )d e +--R + +--R 4 2 +--R - 78B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (280A a b - 840B a b)e + (- 98A a b + 854B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 38A b - 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (105A a b - 315B a )e + (- 35A a b + 315B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 14A a b - 28B a b )d e + (- 8A b - 4B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +-+ +--R (24b x + 72a b x + 72a b x + 24a b )\|b +--R Type: Expression(Integer) +--E 569 + +--S 570 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 764 +r0:=-5/24*e*(6*b*B*d+A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/12*(6*b*B*d+A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^3)-5/8*e^2*_ + (6*b*B*d+A*b*e-7*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(9/2)*sqrt(b*d-a*e))+5/8*e^2*(6*b*B*d+A*b*e-7*a*B*e)*sqrt(d+e*x)/_ + (b^4*(b*d-a*e)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 15A b + 105B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 45A a b + 315B a b )e - 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 45A a b + 315B a b)e - 270B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 15A a b + 105B a )e - 90B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 48B b e x + ((- 33A b + 231B a b )e - 54B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 40A a b + 280B a b)e + (- 26A b - 58B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (- 15A a b + 105B a )e + (- 10A a b - 20B a b)d e +--R + +--R 3 2 2 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 3 6 2 2 5 3 4 +-----------+ +-+ +--R (24b x + 72a b x + 72a b x + 24a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 572 + +--S 573 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 574 + +--S 575 of 764 +r0:=-1/12*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^3)-1/8*e^2*(6*b*B*d-_ + A*b*e-5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*_ + (b*d-a*e)^(3/2))-1/8*e*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*_ + (b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 3A b - 15B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 9A a b - 45B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 9A a b - 45B a b)e + 54B a b d e )x + (- 3A a b - 15B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b - 33B a b )e + 30B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 8A a b - 40B a b)e + (14A b + 22B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 15B a )e + (- 2A a b + 8B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 6 7 3 2 5 6 2 3 4 2 5 +--R (24a b e - 24b d)x + (72a b e - 72a b d)x + (72a b e - 72a b d)x +--R + +--R 4 3 3 4 +--R 24a b e - 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 575 + +--S 576 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 576 + +)clear all + +--S 577 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 577 + +--S 578 of 764 +r0:=-1/3*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^3)+1/8*e^2*(2*b*B*d-_ + A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*_ + (b*d-a*e)^(5/2))-1/4*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^2*_ + (b*d-a*e)*(a+b*x)^2)-1/8*e*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 3A b - 3B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 9A a b - 9B a b )e + 18B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 9A a b - 9B a b)e + 18B a b d e )x + (- 3A a b - 3B a )e +--R + +--R 3 2 +--R 6B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b + 3B a b )e - 6B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((8A a b - 8B a b)e + (- 2A b + 14B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 3B a )e + (14A a b + 4B a b)d e + (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 5 2 6 7 2 3 +--R (24a b e - 48a b d e + 24b d )x +--R + +--R 3 4 2 2 5 6 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 2 2 4 3 3 4 2 +--R (72a b e - 144a b d e + 72a b d )x + 24a b e - 48a b d e + 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 578 + +--S 579 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 of 764 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 580 + +--S 581 of 764 +r0:=-1/8*e^2*(6*b*B*d-5*A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(7/2))-1/3*(A*b-a*B)*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^3)-1/12*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*(a+b*x)^2)+1/8*e*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 15A b - 3B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 45A a b - 9B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 45A a b - 9B a b)e + 54B a b d e )x + (- 15A a b - 3B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((15A b + 3B a b )e - 18B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((40A a b + 8B a b)e + (- 10A b - 50B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (33A a b - 3B a )e + (- 26A a b - 16B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 6 3 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x + 24a b e +--R + +--R 5 2 2 4 3 2 3 4 3 +--R - 72a b d e + 72a b d e - 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 581 + +--S 582 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 583 + +--S 584 of 764 +r0:=-5/8*e^2*(6*b*B*d-7*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(b))+5/8*e^2*(6*b*B*d-7*A*b*e+_ + a*B*e)/(b*(b*d-a*e)^4*sqrt(d+e*x))+1/3*(-A*b+a*B)/(b*(b*d-a*e)*_ + (a+b*x)^3*sqrt(d+e*x))+1/12*(-6*b*B*d+7*A*b*e-a*B*e)/(b*(b*d-a*e)^2*_ + (a+b*x)^2*sqrt(d+e*x))+5/24*e*(6*b*B*d-7*A*b*e+a*B*e)/(b*(b*d-a*e)^3*_ + (a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((105A b - 15B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((315A a b - 45B a b )e - 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((315A a b - 45B a b)e - 270B a b d e )x + (105A a b - 15B a )e +--R + +--R 3 2 +--R - 90B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 15B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 280A a b + 40B a b)e + (- 35A b + 245B a b )d e +--R + +--R 3 2 +--R 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 231A a b + 33B a )e + (- 98A a b + 212B a b)d e +--R + +--R 3 2 2 3 3 +--R (14A b + 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 48A a e + (- 87A a b + 81B a )d e + (38A a b + 28B a b)d e +--R + +--R 3 2 3 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 584 + +--S 585 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 586 + +--S 587 of 764 +r0:=35/24*e^2*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(3/2))+_ + 1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(3/2))+1/4*(-2*b*B*d+_ + 3*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(3/2))+7/8*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(3/2))-35/8*e^2*(2*b*B*d-_ + 3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-_ + a*e)^(11/2)+35/8*e^2*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 315A b + 105B a b )e + 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 945A a b + 315B a b )e + (- 315A b + 735B a b )d e +--R + +--R 4 2 2 +--R 210B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 945A a b + 315B a b)e + (- 945A a b + 945B a b )d e +--R + +--R 3 2 2 +--R 630B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 315A a b + 105B a )e + (- 945A a b + 525B a b)d e +--R + +--R 2 2 2 2 +--R 630B a b d e +--R * +--R x +--R + +--R 3 4 3 3 2 2 +--R (- 315A a b + 105B a )d e + 210B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((315A b - 105B a b )e - 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (840A a b - 280B a b )e + (420A b - 700B a b )d e +--R + +--R 4 2 2 +--R - 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (693A a b - 231B a b)e + (1134A a b - 840B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (63A b - 777B a b )d e - 42B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 48B a )e + (954A a b - 414B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (180A a b - 696B a b )d e + (- 18A b - 114B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 16A a e + (208A a b - 32B a )d e + (165A a b - 247B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 50A a b - 40B a b )d e + (8A b + 4B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 8 5 +--R - 24b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b e - 336a b d e + 600a b d e - 480a b d e + 120a b d e +--R + +--R 7 5 8 6 +--R 48a b d e - 24b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b e - 288a b d e + 360a b d e - 360a b d e + 288a b d e +--R + +--R 7 6 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a e - 48a b d e - 120a b d e + 480a b d e - 600a b d e +--R + +--R 3 5 5 2 6 6 +--R 336a b d e - 72a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 3 5 6 +--R - 24a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 587 + +--S 588 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 of 764 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 589 + +--S 590 of 764 +r0:=21/40*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(5/2))+_ + 1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(5/2))+1/12*(-6*b*B*d+_ + 11*A*b*e-5*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(5/2))+3/8*e*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(5/2))+7/8*e^2*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)/((b*d-a*e)^5*(d+e*x)^(3/2))-21/8*b^(3/2)*e^2*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b*d-a*e)^(13/2)+21/8*b*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/((b*d-a*e)^6*_ + sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((3465A b - 1575B a b )e - 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (10395A a b - 4725B a b )e + (6930A b - 8820B a b )d e +--R + +--R 5 2 3 +--R - 3780B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (10395A a b - 4725B a b )e + (20790A a b - 15120B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (3465A b - 12915B a b )d e - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (3465A a b - 1575B a b)e + (20790A a b - 11340B a b )d e +--R + +--R 4 2 3 2 3 4 3 2 +--R (10395A a b - 16065B a b )d e - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 2 3 +--R (6930A a b - 3150B a b)d e + (10395A a b - 8505B a b )d e +--R + +--R 2 3 3 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 2 3 2 +--R (3465A a b - 1575B a b)d e - 1890B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 1575B a b )e + 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 9240A a b + 4200B a b )e + (- 8085A b + 8715B a b )d e +--R + +--R 5 2 3 +--R 4410B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 7623A a b + 3465B a b )e + (- 21714A a b + 14028B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 5313A b + 14259B a b )d e + 2898B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 1584A a b + 720B a b)e + (- 18117A a b + 9099B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 14454A a b + 16452B a b )d e + (- 495A b + 8109B a b )d e +--R + +--R 5 4 +--R 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (176A a b - 80B a )e + (- 3872A a b + 1664B a b)d e +--R + +--R 2 3 3 2 2 3 +--R (- 12309A a b + 7707B a b )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 1430A a b + 7364B a b )d e + (110A b + 730B a b )d e +--R + +--R 5 5 +--R - 60B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 48A a e + (416A a b - 32B a )d e + (- 2768A a b + 704B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 1335A a b + 2553B a b )d e + (310A a b + 260B a b )d e +--R + +--R 5 4 5 +--R (- 40A b - 20B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 120a b e - 720a b d e + 1800a b d e - 2400a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 1800a b d e - 720a b d e + 120b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 360a b e - 1920a b d e + 3960a b d e - 3600a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 600a b d e + 1440a b d e - 1080a b d e + 240b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 360a b e - 1440a b d e + 1200a b d e + 2880a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 7200a b d e + 6240a b d e - 2160a b d e + 120b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 4 5 5 3 +--R 120a e - 2160a b d e + 6240a b d e - 7200a b d e + 2880a b d e +--R + +--R 3 6 6 2 2 7 7 8 8 +--R 1200a b d e - 1440a b d e + 360a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 +--R 240a d e - 1080a b d e + 1440a b d e + 600a b d e +--R + +--R 5 4 5 3 4 5 6 2 3 6 7 2 7 8 +--R - 3600a b d e + 3960a b d e - 1920a b d e + 360a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 120a d e - 720a b d e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 5 7 3 6 8 +--R - 720a b d e + 120a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 590 + +--S 591 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 591 + +)clear all + +--S 592 of 764 +t0:=(A+B*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 592 + +--S 593 of 764 +r0:=77/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(3/2)/(b^6*(b*d-a*e))-_ + 231/640*e^3*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(5/2)/(b^5*(b*d-a*e)*_ + (a+b*x))-33/320*e^2*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(7/2)/(b^4*_ + (b*d-a*e)*(a+b*x)^2)-11/240*e*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(9/2)/_ + (b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d+3*A*b*e-13*a*B*e)*_ + (d+e*x)^(11/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(13/2)/_ + (b*(b*d-a*e)*(a+b*x)^5)-231/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(15/2)+_ + 231/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*sqrt(d+e*x)/b^7 +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 10395A b + 45045B a b )e - 34650B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 51975A a b + 225225B a b )e - 173250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 51975A a b + 225225B a b)e - 173250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 10395A a b + 45045B a )e - 34650B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 1280B b e x + ((3840A b - 16640B a b )e + 20480B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (31845A a b - 137995B a b )e + (- 12645A b + 160945B a b )d e +--R + +--R 6 2 3 +--R - 22950B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (78210A a b - 338910B a b )e +--R + +--R 5 2 4 4 +--R (- 29040A a b + 386540B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 10770A b - 50130B a b )d e - 10300B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (88704A a b - 384384B a b )e +--R + +--R 2 4 3 3 4 +--R (- 31482A a b + 432102B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 12078A a b - 52602B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 6744A b - 11036B a b )d e - 3280B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (48510A a b - 210210B a b)e +--R + +--R 3 3 4 2 4 +--R (- 16632A a b + 233772B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 6534A a b - 27126B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3696A a b - 5764B a b )d e + (- 2448A b - 1712B a b )d e +--R + +--R 6 5 +--R - 480B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (10395A a b - 45045B a )e + (- 3465A a b + 49665B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 1386A a b - 5544B a b )d e + (- 792A a b - 1188B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 528A a b - 352B a b )d e + (- 384A b - 96B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 +--R 1920b x + 9600a b x + 19200a b x + 19200a b x + 9600a b x +--R + +--R 5 7 +--R 1920a b +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 593 + +--S 594 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 of 764 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 595 + +--S 596 of 764 +r0:=-21/128*e^3*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(3/2)/(b^5*(b*d-a*e)*_ + (a+b*x))-21/320*e^2*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*_ + (b*d-a*e)*(a+b*x)^2)-3/80*e*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(7/2)/_ + (b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d+A*b*e-11*a*B*e)*_ + (d+e*x)^(9/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(11/2)/_ + (b*(b*d-a*e)*(a+b*x)^5)-63/128*e^4*(10*b*B*d+A*b*e-11*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(13/2)*sqrt(b*d-a*e))+_ + 63/128*e^4*(10*b*B*d+A*b*e-11*a*B*e)*sqrt(d+e*x)/(b^6*(b*d-a*e)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 315A b + 3465B a b )e - 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 1575A a b + 17325B a b )e - 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 3150A a b + 34650B a b )e - 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 3150A a b + 34650B a b )e - 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 1575A a b + 17325B a b)e - 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 315A a b + 3465B a )e - 3150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 1280B b e x + ((- 965A b + 10615B a b )e - 3250B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 2370A a b + 26070B a b )e + (- 1490A b - 7310B a b )d e +--R + +--R 5 2 2 +--R - 2100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 2688A a b + 29568B a b )e + (- 1734A a b - 7806B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1368A b - 2292B a b )d e - 880B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 1470A a b + 16170B a b)e + (- 966A a b - 4074B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 768A a b - 1212B a b )d e + (- 656A b - 464B a b )d e +--R + +--R 5 4 +--R - 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 315A a b + 3465B a )e + (- 210A a b - 840B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 168A a b - 252B a b )d e + (- 144A a b - 96B a b )d e +--R + +--R 5 4 4 +--R (- 128A b - 32B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R (640b x + 3200a b x + 6400a b x + 6400a b x + 3200a b x + 640a b ) +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 596 + +--S 597 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 598 + +--S 599 of 764 +r0:=-7/192*e^2*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e)*_ + (a+b*x)^2)-7/240*e*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(5/2)/(b^3*_ + (b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(7/2)/_ + (b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*_ + (a+b*x)^5)-7/128*e^4*(10*b*B*d-A*b*e-9*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(11/2)*(b*d-a*e)^(3/2))-_ + 7/128*e^3*(10*b*B*d-A*b*e-9*a*B*e)*sqrt(d+e*x)/(b^5*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 105A b - 945B a b )e + 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 525A a b - 4725B a b )e + 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 1050A a b - 9450B a b )e + 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 1050A a b - 9450B a b )e + 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 525A a b - 4725B a b)e + 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 105A a b - 945B a )e + 1050B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b - 2895B a b )e + 2790B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 790A a b - 7110B a b )e + (1210A b + 3430B a b )d e +--R + +--R 5 2 2 +--R 3260B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 896A a b - 8064B a b )e + (- 578A a b + 3758B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (2104A b + 1676B a b )d e + 2000B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 490A a b - 4410B a b)e + (- 322A a b + 2002B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 256A a b + 916B a b )d e + (1488A b + 592B a b )d e +--R + +--R 5 4 +--R 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 945B a )e + (- 70A a b + 420B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 56A a b + 196B a b )d e + (- 48A a b + 128B a b )d e +--R + +--R 5 4 4 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 10 11 5 2 9 10 4 +--R (1920a b e - 1920b d)x + (9600a b e - 9600a b d)x +--R + +--R 3 8 2 9 3 4 7 3 8 2 +--R (19200a b e - 19200a b d)x + (19200a b e - 19200a b d)x +--R + +--R 5 6 4 7 6 5 5 6 +--R (9600a b e - 9600a b d)x + 1920a b e - 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 599 + +--S 600 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 601 + +--S 602 of 764 +r0:=-1/48*e*(10*b*B*d-3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*_ + (a+b*x)^3)-1/40*(10*b*B*d-3*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-_ + a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^5)+_ + 1/128*e^4*(10*b*B*d-3*A*b*e-7*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(9/2)*(b*d-a*e)^(5/2))-1/64*e^2*(10*b*B*d-_ + 3*A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)*(a+b*x)^2)-_ + 1/128*e^3*(10*b*B*d-3*A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 45A b - 105B a b )e + 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 225A a b - 525B a b )e + 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 450A a b - 1050B a b )e + 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 450A a b - 1050B a b )e + 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 225A a b - 525B a b)e + 750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 45A a b - 105B a )e + 150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((45A b + 105B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (210A a b - 790B a b )e + (- 30A b + 1790B a b )d e +--R + +--R 5 2 2 +--R - 1180B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 384A a b - 896B a b )e + (1398A a b + 702B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 744A b + 1284B a b )d e - 1360B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 210A a b - 490B a b)e + (- 138A a b + 378B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (1536A a b + 204B a b )d e + (- 1008A b + 208B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 45A a b - 105B a )e + (- 30A a b + 80B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 24A a b + 44B a b )d e + (528A a b + 32B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 9 2 10 11 2 5 +--R (1920a b e - 3840a b d e + 1920b d )x +--R + +--R 3 8 2 2 9 10 2 4 +--R (9600a b e - 19200a b d e + 9600a b d )x +--R + +--R 4 7 2 3 8 2 9 2 3 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 5 6 2 4 7 3 8 2 2 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 6 5 2 5 6 4 7 2 7 4 2 6 5 +--R (9600a b e - 19200a b d e + 9600a b d )x + 1920a b e - 3840a b d e +--R + +--R 5 6 2 +--R 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 602 + +--S 603 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 604 + +--S 605 of 764 +r0:=-1/8*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-_ + 1/5*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^5)-3/128*e^4*(2*b*B*d-_ + A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-_ + a*e)^(7/2))-1/16*e*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)*_ + (a+b*x)^3)-1/64*e^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)^2*_ + (a+b*x)^2)+3/128*e^3*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*_ + (b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 15A b - 15B a b )e + 30B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 75A a b - 75B a b )e + 150B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 150A a b - 150B a b )e + 300B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 150A a b - 150B a b )e + 300B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((- 75A a b - 75B a b)e + 150B a b d e )x + (- 15A a b - 15B a )e +--R + +--R 5 4 +--R 30B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((15A b + 15B a b )e - 30B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((70A a b + 70B a b )e + (- 10A b - 150B a b )d e + 20B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (128A a b - 128B a b )e + (- 46A a b + 466B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (8A b - 668B a b )d e + 240B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 70A a b - 70B a b)e + (466A a b + 94B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 512A a b + 92B a b )d e + (176A b - 336B a b )d e + 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 15A a b - 15B a )e + (- 10A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (248A a b + 12B a b )d e + (- 336A a b - 64B a b )d e +--R + +--R 5 4 4 +--R (128A b + 32B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 8 3 2 9 2 10 2 11 3 5 +--R (640a b e - 1920a b d e + 1920a b d e - 640b d )x +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 4 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x +--R + +--R 5 6 3 4 7 2 3 8 2 2 9 3 3 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 6 5 3 5 6 2 4 7 2 3 8 3 2 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 7 4 3 6 5 2 5 6 2 4 7 3 8 3 3 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x + 640a b e +--R + +--R 7 4 2 6 5 2 5 6 3 +--R - 1920a b d e + 1920a b d e - 640a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 605 + +--S 606 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 606 + +)clear all + +--S 607 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 607 + +--S 608 of 764 +r0:=-1/5*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^5)+1/128*e^4*_ + (10*b*B*d-7*A*b*e-3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(5/2)*(b*d-a*e)^(9/2))-1/40*(10*b*B*d-7*A*b*e-3*a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)*(a+b*x)^4)-1/240*e*(10*b*B*d-7*A*b*e-3*a*B*e)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x)^3)+1/192*e^2*(10*b*B*d-7*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^3*(a+b*x)^2)-1/128*e^3*(10*b*B*d-_ + 7*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^4*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 105A b - 45B a b )e + 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 525A a b - 225B a b )e + 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 1050A a b - 450B a b )e + 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 1050A a b - 450B a b )e + 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 525A a b - 225B a b)e + 750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 105A a b - 45B a )e + 150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b + 45B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (490A a b + 210B a b )e + (- 70A b - 730B a b )d e +--R + +--R 5 2 2 +--R 100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (896A a b + 384B a b )e + (- 322A a b - 1418B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (56A b + 484B a b )d e - 80B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (790A a b - 210B a b)e + (- 578A a b + 818B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (256A a b - 2356B a b )d e + (- 48A b + 1808B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 45B a )e + (1210A a b + 120B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 2104A a b - 436B a b )d e + (1488A a b + 352B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 7 4 3 8 3 2 9 2 2 10 3 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e +--R + +--R 11 4 +--R 1920b d +--R * +--R 5 +--R x +--R + +--R 5 6 4 4 7 3 3 8 2 2 2 9 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 10 4 +--R 9600a b d +--R * +--R 4 +--R x +--R + +--R 6 5 4 5 6 3 4 7 2 2 3 8 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 2 9 4 +--R 19200a b d +--R * +--R 3 +--R x +--R + +--R 7 4 4 6 5 3 5 6 2 2 4 7 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 3 8 4 +--R 19200a b d +--R * +--R 2 +--R x +--R + +--R 8 3 4 7 4 3 6 5 2 2 5 6 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 4 7 4 +--R 9600a b d +--R * +--R x +--R + +--R 9 2 4 8 3 3 7 4 2 2 6 5 3 5 6 4 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e + 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 608 + +--S 609 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 764 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x)) +--R +--R +--R (1) +--R B x + A +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 610 + +--S 611 of 764 +r0:=-7/128*e^4*(10*b*B*d-9*A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(11/2))-1/5*(A*b-a*B)*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^5)-1/40*(10*b*B*d-9*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*(a+b*x)^4)+7/240*e*(10*b*B*d-9*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x)^3)-7/192*e^2*(10*b*B*d-9*A*b*e-_ + a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^4*(a+b*x)^2)+7/128*e^3*(10*b*B*d-_ + 9*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^5*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 945A b - 105B a b )e + 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 4725A a b - 525B a b )e + 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 9450A a b - 1050B a b )e + 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 9450A a b - 1050B a b )e + 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 4725A a b - 525B a b)e + 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 945A a b - 105B a )e + 1050B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((945A b + 105B a b )e - 1050B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (4410A a b + 490B a b )e + (- 630A b - 4970B a b )d e +--R + +--R 5 2 2 +--R 700B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (8064A a b + 896B a b )e + (- 2898A a b - 9282B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (504A b + 3276B a b )d e - 560B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (7110A a b + 790B a b)e + (- 5202A a b - 8478B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (2304A a b + 6036B a b )d e + (- 432A b - 2608B a b )d e +--R + +--R 5 4 +--R 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (2895A a b - 105B a )e + (- 4470A a b - 1580B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (4104A a b + 1156B a b )d e + (- 1968A a b - 512B a b )d e +--R + +--R 5 4 4 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 +--R 1920a b e - 9600a b d e + 19200a b d e - 19200a b d e +--R + +--R 10 4 11 5 +--R 9600a b d e - 1920b d +--R * +--R 5 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R 9600a b e - 48000a b d e + 96000a b d e - 96000a b d e +--R + +--R 2 9 4 10 5 +--R 48000a b d e - 9600a b d +--R * +--R 4 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R 19200a b e - 96000a b d e + 192000a b d e - 192000a b d e +--R + +--R 3 8 4 2 9 5 +--R 96000a b d e - 19200a b d +--R * +--R 3 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 +--R 19200a b e - 96000a b d e + 192000a b d e - 192000a b d e +--R + +--R 4 7 4 3 8 5 +--R 96000a b d e - 19200a b d +--R * +--R 2 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 +--R 9600a b e - 48000a b d e + 96000a b d e - 96000a b d e +--R + +--R 5 6 4 4 7 5 +--R 48000a b d e - 9600a b d +--R * +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 +--R 1920a b e - 9600a b d e + 19200a b d e - 19200a b d e +--R + +--R 6 5 4 5 6 5 +--R 9600a b d e - 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 611 + +--S 612 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 7 5 6 6 2 4 5 5 +--R b e x + (6a b e + b d)x + (15a b e + 6a b d)x +--R + +--R 3 3 2 4 4 4 2 3 3 3 5 4 2 2 +--R (20a b e + 15a b d)x + (15a b e + 20a b d)x + (6a b e + 15a b d)x +--R + +--R 6 5 6 +--R (a e + 6a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 613 + +--S 614 of 764 +r0:=-63/128*e^4*(10*b*B*d-11*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/((b*d-a*e)^(13/2)*sqrt(b))+63/128*e^4*(10*b*B*d-_ + 11*A*b*e+a*B*e)/(b*(b*d-a*e)^6*sqrt(d+e*x))+1/5*(-A*b+a*B)/(b*(b*d-_ + a*e)*(a+b*x)^5*sqrt(d+e*x))+1/40*(-10*b*B*d+11*A*b*e-a*B*e)/(b*(b*d-_ + a*e)^2*(a+b*x)^4*sqrt(d+e*x))+3/80*e*(10*b*B*d-11*A*b*e+a*B*e)/(b*_ + (b*d-a*e)^3*(a+b*x)^3*sqrt(d+e*x))-21/320*e^2*(10*b*B*d-11*A*b*e+_ + a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*sqrt(d+e*x))+21/128*e^3*(10*b*B*d-_ + 11*A*b*e+a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((3465A b - 315B a b )e - 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((17325A a b - 1575B a b )e - 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((34650A a b - 3150B a b )e - 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((34650A a b - 3150B a b )e - 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((17325A a b - 1575B a b)e - 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (3465A a b - 315B a )e - 3150B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 315B a b )e + 3150B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 16170A a b + 1470B a b )e + (- 1155A b + 14805B a b )d e +--R + +--R 5 2 3 +--R 1050B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 29568A a b + 2688B a b )e + (- 5544A a b + 27384B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (462A b + 4998B a b )d e - 420B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 26070A a b + 2370B a b)e + (- 10494A a b + 24654B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2178A a b + 9342B a b )d e + (- 264A b - 1956B a b )d e +--R + +--R 5 4 +--R 240B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 10615A a b + 965B a )e + (- 9680A a b + 10530B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (4026A a b + 8434B a b )d e + (- 1232A a b - 3548B a b )d e +--R + +--R 5 4 4 5 5 +--R (176A b + 1104B a b )d e - 160B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 1280A a e + (- 4215A a b + 2245B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (3590A a b + 1760B a b)d e + (- 2248A a b - 732B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (816A a b + 224B a b )d e + (- 128A b - 32B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 6 5 6 5 6 5 4 7 2 4 3 8 3 3 +--R 640a b e - 3840a b d e + 9600a b d e - 12800a b d e +--R + +--R 2 9 4 2 10 5 11 6 +--R 9600a b d e - 3840a b d e + 640b d +--R * +--R 5 +--R x +--R + +--R 7 4 6 6 5 5 5 6 2 4 4 7 3 3 +--R 3200a b e - 19200a b d e + 48000a b d e - 64000a b d e +--R + +--R 3 8 4 2 2 9 5 10 6 +--R 48000a b d e - 19200a b d e + 3200a b d +--R * +--R 4 +--R x +--R + +--R 8 3 6 7 4 5 6 5 2 4 5 6 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 4 7 4 2 3 8 5 2 9 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 3 +--R x +--R + +--R 9 2 6 8 3 5 7 4 2 4 6 5 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 5 6 4 2 4 7 5 3 8 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 2 +--R x +--R + +--R 10 6 9 2 5 8 3 2 4 7 4 3 3 +--R 3200a b e - 19200a b d e + 48000a b d e - 64000a b d e +--R + +--R 6 5 4 2 5 6 5 4 7 6 +--R 48000a b d e - 19200a b d e + 3200a b d +--R * +--R x +--R + +--R 11 6 10 5 9 2 2 4 8 3 3 3 7 4 4 2 +--R 640a e - 3840a b d e + 9600a b d e - 12800a b d e + 9600a b d e +--R + +--R 6 5 5 5 6 6 +--R - 3840a b d e + 640a b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 614 + +--S 615 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 2 8 5 2 6 7 2 4 2 5 6 2 6 +--R b e x + (6a b e + 2b d e)x + (15a b e + 12a b d e + b d )x +--R + +--R 3 3 2 2 4 5 2 5 +--R (20a b e + 30a b d e + 6a b d )x +--R + +--R 4 2 2 3 3 2 4 2 4 +--R (15a b e + 40a b d e + 15a b d )x +--R + +--R 5 2 4 2 3 3 2 3 6 2 5 4 2 2 2 +--R (6a b e + 30a b d e + 20a b d )x + (a e + 12a b d e + 15a b d )x +--R + +--R 6 5 2 6 2 +--R (2a d e + 6a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 616 + +--S 617 of 764 +r0:=77/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^6*(d+e*x)^(3/2))+_ + 1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*(d+e*x)^(3/2))+1/40*(-10*b*B*d+_ + 13*A*b*e-3*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*(d+e*x)^(3/2))+11/240*e*_ + (10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*(d+e*x)^(3/2))-_ + 33/320*e^2*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*_ + (d+e*x)^(3/2))+231/640*e^3*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^5*_ + (a+b*x)*(d+e*x)^(3/2))-231/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(15/2)+_ + 231/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)/((b*d-a*e)^7*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((- 45045A b + 10395B a b )e + 34650B b d e )x +--R + +--R 5 2 4 6 +--R (- 225225A a b + 51975B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 45045A b + 183645B a b )d e + 34650B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 450450A a b + 103950B a b )e +--R + +--R 5 2 4 5 5 2 4 +--R (- 225225A a b + 398475B a b )d e + 173250B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 450450A a b + 103950B a b )e +--R + +--R 2 4 3 3 5 2 4 2 4 +--R (- 450450A a b + 450450B a b )d e + 346500B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 225225A a b + 51975B a b)e +--R + +--R 3 3 4 2 5 3 3 2 4 +--R (- 450450A a b + 277200B a b )d e + 346500B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 45045A a b + 10395B a )e + (- 225225A a b + 86625B a b)d e +--R + +--R 4 2 2 4 +--R 173250B a b d e +--R * +--R x +--R + +--R 5 6 5 5 2 4 +--R (- 45045A a b + 10395B a )d e + 34650B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 6 +--R ((45045A b - 10395B a b )e - 34650B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (210210A a b - 48510B a b )e + (60060A b - 175560B a b )d e +--R + +--R 6 2 4 +--R - 46200B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (384384A a b - 88704B a b )e +--R + +--R 5 2 4 5 6 5 2 4 +--R (282282A a b - 360822B a b )d e + (9009A b - 219219B a b )d e +--R + +--R 6 3 3 +--R - 6930B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (338910A a b - 78210B a b )e +--R + +--R 2 4 3 3 5 +--R (520806A a b - 380886B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (43758A a b - 410718B a b )d e + (- 2574A b - 33066B a b )d e +--R + +--R 6 4 2 +--R 1980B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (137995A a b - 31845B a b)e + (464750A a b - 213400B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (84084A a b - 376904B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 12298A a b - 61842B a b )d e + (1144A b + 9196B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (16640A a b - 3840B a )e + (192790A a b - 57290B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (79170A a b - 166570B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 23114A a b - 55566B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (5408A a b + 16532B a b )d e + (- 624A b - 4016B a b )d e +--R + +--R 6 6 +--R 480B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 1280A a e + (24320A a b - 2560B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (35595A a b - 33125B a b)d e + (- 21070A a b - 12180B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (10024A a b + 3556B a b )d e + (- 2928A a b - 832B a b )d e +--R + +--R 6 5 6 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 5 8 6 6 7 5 7 2 6 4 8 3 5 +--R 1920a b e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 3 9 4 4 2 10 5 3 11 6 2 12 7 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920b d e +--R * +--R 6 +--R x +--R + +--R 8 4 8 7 5 7 6 6 2 6 5 7 3 5 +--R 9600a b e - 65280a b d e + 188160a b d e - 295680a b d e +--R + +--R 4 8 4 4 3 9 5 3 2 10 6 2 11 7 +--R 268800a b d e - 134400a b d e + 26880a b d e + 3840a b d e +--R + +--R 12 8 +--R - 1920b d +--R * +--R 5 +--R x +--R + +--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5 +--R 19200a b e - 124800a b d e + 336000a b d e - 470400a b d e +--R + +--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7 +--R 336000a b d e - 67200a b d e - 67200a b d e + 48000a b d e +--R + +--R 11 8 +--R - 9600a b d +--R * +--R 4 +--R x +--R + +--R 10 2 8 9 3 7 8 4 2 6 7 5 3 5 +--R 19200a b e - 115200a b d e + 268800a b d e - 268800a b d e +--R + +--R 5 7 5 3 4 8 6 2 3 9 7 2 10 8 +--R 268800a b d e - 268800a b d e + 115200a b d e - 19200a b d +--R * +--R 3 +--R x +--R + +--R 11 8 10 2 7 9 3 2 6 8 4 3 5 +--R 9600a b e - 48000a b d e + 67200a b d e + 67200a b d e +--R + +--R 7 5 4 4 6 6 5 3 5 7 6 2 4 8 7 +--R - 336000a b d e + 470400a b d e - 336000a b d e + 124800a b d e +--R + +--R 3 9 8 +--R - 19200a b d +--R * +--R 2 +--R x +--R + +--R 12 8 11 7 10 2 2 6 9 3 3 5 +--R 1920a e - 3840a b d e - 26880a b d e + 134400a b d e +--R + +--R 8 4 4 4 7 5 5 3 6 6 6 2 5 7 7 +--R - 268800a b d e + 295680a b d e - 188160a b d e + 65280a b d e +--R + +--R 4 8 8 +--R - 9600a b d +--R * +--R x +--R + +--R 12 7 11 2 6 10 2 3 5 9 3 4 4 +--R 1920a d e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 8 4 5 3 7 5 6 2 6 6 7 5 7 8 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 617 + +--S 618 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 764 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 3 9 5 3 6 2 8 2 4 3 5 2 6 2 7 +--R b e x + (6a b e + 3b d e )x + (15a b e + 18a b d e + 3b d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (20a b e + 45a b d e + 18a b d e + b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (15a b e + 60a b d e + 45a b d e + 6a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (6a b e + 45a b d e + 60a b d e + 15a b d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (a e + 18a b d e + 45a b d e + 20a b d )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (3a d e + 18a b d e + 15a b d )x + (3a d e + 6a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 619 + +--S 620 of 764 +r0:=3003/640*e^4*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^6*(d+e*x)^(5/2))+_ + 1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*(d+e*x)^(5/2))+1/8*(-2*b*B*d+_ + 3*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*(d+e*x)^(5/2))+13/48*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*(d+e*x)^(5/2))-143/192*e^2*_ + (2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*(d+e*x)^(5/2))+_ + 429/128*e^3*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*_ + (d+e*x)^(5/2))+1001/128*e^4*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^7*_ + (d+e*x)^(3/2))-3003/128*b^(3/2)*e^4*(2*b*B*d-3*A*b*e+a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(17/2)+_ + 3003/128*b*e^4*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^8*sqrt(d+e*x)) +--R +--R +--R (2) +--R 7 6 7 7 6 7 +--R ((135135A b - 45045B a b )e - 90090B b d e )x +--R + +--R 6 2 5 7 7 6 6 +--R (675675A a b - 225225B a b )e + (270270A b - 540540B a b )d e +--R + +--R 7 2 5 +--R - 180180B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 7 +--R (1351350A a b - 450450B a b )e +--R + +--R 6 2 5 6 +--R (1351350A a b - 1351350B a b )d e +--R + +--R 7 6 2 5 7 3 4 +--R (135135A b - 945945B a b )d e - 90090B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 7 +--R (1351350A a b - 450450B a b )e +--R + +--R 2 5 3 4 6 +--R (2702700A a b - 1801800B a b )d e +--R + +--R 6 2 5 2 5 6 3 4 +--R (675675A a b - 2027025B a b )d e - 450450B a b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 +--R (675675A a b - 225225B a b )e +--R + +--R 3 4 4 3 6 +--R (2702700A a b - 1351350B a b )d e +--R + +--R 2 5 3 4 2 5 2 5 3 4 +--R (1351350A a b - 2252250B a b )d e - 900900B a b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 7 +--R (135135A a b - 45045B a b)e +--R + +--R 4 3 5 2 6 +--R (1351350A a b - 540540B a b )d e +--R + +--R 3 4 4 3 2 5 3 4 3 4 +--R (1351350A a b - 1351350B a b )d e - 900900B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 6 +--R (270270A a b - 90090B a b)d e +--R + +--R 4 3 5 2 2 5 4 3 3 4 +--R (675675A a b - 405405B a b )d e - 450450B a b d e +--R * +--R x +--R + +--R 5 2 6 2 5 5 2 3 4 +--R (135135A a b - 45045B a b)d e - 90090B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 7 6 7 7 6 7 +--R ((- 135135A b + 45045B a b )e + 90090B b d e )x +--R + +--R 6 2 5 7 +--R (- 630630A a b + 210210B a b )e +--R + +--R 7 6 6 7 2 5 +--R (- 315315A b + 525525B a b )d e + 210210B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 7 +--R (- 1153152A a b + 384384B a b )e +--R + +--R 6 2 5 6 +--R (- 1477476A a b + 1261260B a b )d e +--R + +--R 7 6 2 5 7 3 4 +--R (- 207207A b + 1054053B a b )d e + 138138B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 7 +--R (- 1016730A a b + 338910B a b )e +--R + +--R 2 5 3 4 6 +--R (- 2715570A a b + 1583010B a b )d e +--R + +--R 6 2 5 2 5 +--R (- 978120A a b + 2136420B a b )d e +--R + +--R 7 6 3 4 7 4 3 +--R (- 19305A b + 658515B a b )d e + 12870B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 +--R (- 413985A a b + 137995B a b )e +--R + +--R 3 4 4 3 6 +--R (- 2410980A a b + 1079650B a b )d e +--R + +--R 2 5 3 4 2 5 +--R (- 1814670A a b + 2212210B a b )d e +--R + +--R 6 2 5 3 4 +--R (- 94380A a b + 1241240B a b )d e +--R + +--R 7 6 4 3 7 5 2 +--R (4290A b + 61490B a b )d e - 2860B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 7 +--R (- 49920A a b + 16640B a b)e +--R + +--R 4 3 5 2 6 +--R (- 992355A a b + 364065B a b )d e +--R + +--R 3 4 4 3 2 5 +--R (- 1631760A a b + 1205490B a b )d e +--R + +--R 2 5 3 4 3 4 +--R (- 182910A a b + 1148810B a b )d e +--R + +--R 6 2 5 4 3 7 6 5 2 +--R (20670A a b + 115050B a b )d e + (- 1560A b - 13260B a b )d e +--R + +--R 7 6 +--R 1040B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 7 5 2 6 6 +--R (3840A a b - 1280B a )e + (- 122880A a b + 38400B a b)d e +--R + +--R 4 3 5 2 2 5 +--R (- 685155A a b + 310305B a b )d e +--R + +--R 3 4 4 3 3 4 +--R (- 174300A a b + 514870B a b )d e +--R + +--R 2 5 3 4 4 3 +--R (39270A a b + 103110B a b )d e +--R + +--R 6 2 5 5 2 7 6 6 +--R (- 7440A a b - 23700B a b )d e + (720A b + 4720B a b )d e +--R + +--R 7 7 +--R - 480B b d +--R * +--R x +--R + +--R 7 7 6 7 6 +--R - 768A a e + (9216A a b - 512B a )d e +--R + +--R 5 2 6 2 5 4 3 5 2 3 4 +--R (- 89088A a b + 16384B a b)d e + (- 79905A a b + 100363B a b )d e +--R + +--R 3 4 4 3 4 3 2 5 3 4 5 2 +--R (36330A a b + 23240B a b )d e + (- 13944A a b - 5236B a b )d e +--R + +--R 6 2 5 6 7 6 7 +--R (3408A a b + 992B a b )d e + (- 384A b - 96B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 8 5 10 7 6 9 6 7 2 8 5 8 3 7 +--R 1920a b e - 15360a b d e + 53760a b d e - 107520a b d e +--R + +--R 4 9 4 6 3 10 5 5 2 11 6 4 12 7 3 +--R 134400a b d e - 107520a b d e + 53760a b d e - 15360a b d e +--R + +--R 13 8 2 +--R 1920b d e +--R * +--R 7 +--R x +--R + +--R 9 4 10 8 5 9 7 6 2 8 6 7 3 7 +--R 9600a b e - 72960a b d e + 238080a b d e - 430080a b d e +--R + +--R 5 8 4 6 4 9 5 5 3 10 6 4 2 11 7 3 +--R 456960a b d e - 268800a b d e + 53760a b d e + 30720a b d e +--R + +--R 12 8 2 13 9 +--R - 21120a b d e + 3840b d e +--R * +--R 6 +--R x +--R + +--R 10 3 10 9 4 9 8 5 2 8 7 6 3 7 +--R 19200a b e - 134400a b d e + 385920a b d e - 552960a b d e +--R + +--R 6 7 4 6 5 8 5 5 4 9 6 4 3 10 7 3 +--R 322560a b d e + 161280a b d e - 403200a b d e + 276480a b d e +--R + +--R 2 11 8 2 12 9 13 10 +--R - 80640a b d e + 3840a b d e + 1920b d +--R * +--R 5 +--R x +--R + +--R 11 2 10 10 3 9 9 4 2 8 8 5 3 7 +--R 19200a b e - 115200a b d e + 240000a b d e - 76800a b d e +--R + +--R 7 6 4 6 6 7 5 5 5 8 6 4 +--R - 537600a b d e + 1075200a b d e - 940800a b d e +--R + +--R 4 9 7 3 3 10 8 2 2 11 9 12 10 +--R 384000a b d e - 19200a b d e - 38400a b d e + 9600a b d +--R * +--R 4 +--R x +--R + +--R 12 10 11 2 9 10 3 2 8 9 4 3 7 +--R 9600a b e - 38400a b d e - 19200a b d e + 384000a b d e +--R + +--R 8 5 4 6 7 6 5 5 6 7 6 4 5 8 7 3 +--R - 940800a b d e + 1075200a b d e - 537600a b d e - 76800a b d e +--R + +--R 4 9 8 2 3 10 9 2 11 10 +--R 240000a b d e - 115200a b d e + 19200a b d +--R * +--R 3 +--R x +--R + +--R 13 10 12 9 11 2 2 8 10 3 3 7 +--R 1920a e + 3840a b d e - 80640a b d e + 276480a b d e +--R + +--R 9 4 4 6 8 5 5 5 7 6 6 4 6 7 7 3 +--R - 403200a b d e + 161280a b d e + 322560a b d e - 552960a b d e +--R + +--R 5 8 8 2 4 9 9 3 10 10 +--R 385920a b d e - 134400a b d e + 19200a b d +--R * +--R 2 +--R x +--R + +--R 13 9 12 2 8 11 2 3 7 10 3 4 6 +--R 3840a d e - 21120a b d e + 30720a b d e + 53760a b d e +--R + +--R 9 4 5 5 8 5 6 4 7 6 7 3 6 7 8 2 +--R - 268800a b d e + 456960a b d e - 430080a b d e + 238080a b d e +--R + +--R 5 8 9 4 9 10 +--R - 72960a b d e + 9600a b d +--R * +--R x +--R + +--R 13 2 8 12 3 7 11 2 4 6 10 3 5 5 +--R 1920a d e - 15360a b d e + 53760a b d e - 107520a b d e +--R + +--R 9 4 6 4 8 5 7 3 7 6 8 2 6 7 9 +--R 134400a b d e - 107520a b d e + 53760a b d e - 15360a b d e +--R + +--R 5 8 10 +--R 1920a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 620 + +--S 621 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 622 + +--S 623 of 764 +r0:=-2/143*(4*b*B*d-13*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/1287*(b*d-a*e)*(4*b*B*d-13*A*b*e+9*a*B*e)*_ + (d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+_ + 2/13*B*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 198B b e x + ((234A b + 234B a)e + 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (286A a e + (884A b + 884B a)d e + 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (1144A a d e + (1196A b + 1196B a)d e + 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (1716A a d e + (624A b + 624B a)d e + 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (1144A a d e + (26A b + 26B a)d e - 8B b d e)x + 286A a d e +--R + +--R 5 6 +--R (- 52A b - 52B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 623 + +--S 624 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 625 + +--S 626 of 764 +r0:=-2/99*(4*b*B*d-11*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/693*(b*d-a*e)*(4*b*B*d-11*A*b*e+7*a*B*e)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/11*B*_ + (a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 126B b e x + ((154A b + 154B a)e + 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (198A a e + (418A b + 418B a)d e + 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (594A a d e + (330A b + 330B a)d e + 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (594A a d e + (22A b + 22B a)d e - 8B b d e)x + 198A a d e +--R + +--R 4 5 +--R (- 44A b - 44B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 626 + +--S 627 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (1) (B e x + (A e + B d)x + A d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 628 + +--S 629 of 764 +r0:=-2/63*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/315*(b*d-a*e)*(4*b*B*d-9*A*b*e+5*a*B*e)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/9*B*_ + (a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B b e x + ((90A b + 90B a)e + 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (126A a e + (144A b + 144B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (252A a d e + (18A b + 18B a)d e - 8B b d e)x + 126A a d e +--R + +--R 3 4 +--R (- 36A b - 36B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 629 + +--S 630 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 764 +t0:=(A+B*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R +-------+ | 2 2 2 +--R (1) (B x + A)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 631 + +--S 632 of 764 +r0:=-2/35*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/105*(b*d-a*e)*(4*b*B*d-7*A*b*e+3*a*B*e)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/7*B*_ + (a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B b e x + ((42A b + 42B a)e + 6B b d e )x +--R + +--R 3 2 2 2 +--R (70A a e + (14A b + 14B a)d e - 8B b d e)x + 70A a d e +--R + +--R 2 3 +--R (- 28A b - 28B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 632 + +--S 633 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 634 + +--S 635 of 764 +r0:=-2/15*(4*b*B*d-5*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/15*(b*d-a*e)*(4*b*B*d-5*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/5*B*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 2 2 2 2 +--R 6B b e x + ((10A b + 10B a)e - 8B b d e)x + 30A a e +--R + +--R 2 +--R (- 20A b - 20B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 635 + +--S 636 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 637 + +--S 638 of 764 +r0:=-2*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+2/3*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^2*(b*d-a*e))-4/3*(4*b*B*d-3*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R 2B b e x + ((6A b + 6B a)e - 8B b d e)x - 6A a e +--R + +--R 2 +--R (12A b + 12B a)d e - 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 638 + +--S 639 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 640 + +--S 641 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))+2/3*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^2*(b*d-a*e)*sqrt(d+e*x))+4/3*(4*b*B*d-A*b*e-3*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R 6B b e x + ((- 6A b - 6B a)e + 24B b d e)x - 2A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e + 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 641 + +--S 642 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 643 + +--S 644 of 764 +r0:=-2/5*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/5*(4*b*B*d+A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/15*(4*b*B*d+A*b*e-5*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 30B b e x + ((- 10A b - 10B a)e - 40B b d e)x - 6A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e - 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 644 + +--S 645 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 764 +r0:=-2/255*(8*b*B*d-17*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/17*B*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/12155*(b*d-a*e)^2*(8*b*B*d-17*A*b*e+_ + 9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/109395*_ + (b*d-a*e)^3*(8*b*B*d-17*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5*(a+b*x))+4/1105*(b*d-a*e)*(8*b*B*d-17*A*b*e+_ + 9*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 8 8 3 2 8 3 7 7 +--R 12870B b e x + ((14586A b + 43758B a b )e + 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (50490A a b + 50490B a b)e + (51612A b + 154836B a b )d e +--R + +--R 3 2 6 +--R 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (59670A a b + 19890B a )e + (183600A a b + 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (63036A b + 189108B a b )d e + 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R 24310A a e + (225420A a b + 75140B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (233580A a b + 233580B a b)d e + (27200A b + 81600B a b )d e +--R + +--R 3 4 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R 97240A a d e + (304980A a b + 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (108120A a b + 108120B a b)d e + (170A b + 510B a b )d e +--R + +--R 3 5 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R 145860A a d e + (159120A a b + 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (1530A a b + 1530B a b)d e + (- 204A b - 612B a b )d e +--R + +--R 3 6 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R 97240A a d e + (6630A a b + 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (- 2040A a b - 2040B a b)d e + (272A b + 816B a b )d e +--R + +--R 3 7 +--R - 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (4080A a b + 4080B a b)d e + (- 544A b - 1632B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 109395b e x + 109395a e +--R Type: Expression(Integer) +--E 647 + +--S 648 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 649 + +--S 650 of 764 +r0:=-2/195*(8*b*B*d-15*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/15*B*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/6435*(b*d-a*e)^2*(8*b*B*d-15*A*b*e+7*a*B*e)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/45045*(b*d-a*e)^3*_ + (8*b*B*d-15*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/715*(b*d-a*e)*(8*b*B*d-15*A*b*e+7*a*B*e)*(a+b*x)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 7 7 3 2 7 3 6 6 +--R 6006B b e x + ((6930A b + 20790B a b )e + 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (24570A a b + 24570B a b)e + (17010A b + 51030B a b )d e +--R + +--R 3 2 5 +--R 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (30030A a b + 10010B a )e + (62790A a b + 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (11130A b + 33390B a b )d e + 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R 12870A a e + (81510A a b + 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (44070A a b + 44070B a b)d e + (150A b + 450B a b )d e +--R + +--R 3 4 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 38610A a d e + (64350A a b + 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1170A a b + 1170B a b)d e + (- 180A b - 540B a b )d e +--R + +--R 3 5 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 38610A a d e + (4290A a b + 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1560A a b - 1560B a b)d e + (240A b + 720B a b )d e +--R + +--R 3 6 +--R - 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (3120A a b + 3120B a b)d e + (- 480A b - 1440B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 650 + +--S 651 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 652 + +--S 653 of 764 +r0:=-2/143*(8*b*B*d-13*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/13*B*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/3003*(b*d-a*e)^2*(8*b*B*d-13*A*b*e+5*a*B*e)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/15015*(b*d-a*e)^3*_ + (8*b*B*d-13*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/429*(b*d-a*e)*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 6 6 3 2 6 3 5 5 +--R 2310B b e x + ((2730A b + 8190B a b )e + 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (10010A a b + 10010B a b)e + (3640A b + 10920B a b )d e +--R + +--R 3 2 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (12870A a b + 4290B a )e + (14300A a b + 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (130A b + 390B a b )d e - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R 6006A a e + (20592A a b + 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 3 4 2 +--R (858A a b + 858B a b)d e + (- 156A b - 468B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R 12012A a d e + (2574A a b + 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 1144A a b - 1144B a b)d e + (208A b + 624B a b )d e +--R + +--R 3 5 +--R - 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (2288A a b + 2288B a b)d e + (- 416A b - 1248B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 653 + +--S 654 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 655 + +--S 656 of 764 +r0:=-2/99*(8*b*B*d-11*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/11*B*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/1155*(b*d-a*e)^2*(8*b*B*d-11*A*b*e+3*a*B*e)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/3465*(b*d-a*e)^3*_ + (8*b*B*d-11*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/231*(b*d-a*e)*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 5 5 3 2 5 3 4 4 +--R 630B b e x + ((770A b + 2310B a b )e + 70B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((2970A a b + 2970B a b)e + (110A b + 330B a b )d e - 80B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (4158A a b + 1386B a )e + (594A a b + 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 132A b - 396B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R 2310A a e + (1386A a b + 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R (- 792A a b - 792B a b)d e + (176A b + 528B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (1584A a b + 1584B a b)d e + (- 352A b - 1056B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 656 + +--S 657 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 658 + +--S 659 of 764 +r0:=-2/63*(8*b*B*d-9*A*b*e+a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(b*e^2)+2/9*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(b*e)-16/315*(b*d-a*e)^2*(8*b*B*d-9*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/315*(b*d-a*e)^3*_ + (8*b*B*d-9*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/105*(b*d-a*e)*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((90A b + 270B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((378A a b + 378B a b)e + (- 108A b - 324B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (630A a b + 210B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (144A b + 432B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 630A a e + (- 1260A a b - 420B a )d e + (1008A a b + 1008B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 288A b - 864B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 659 + +--S 660 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 661 + +--S 662 of 764 +r0:=-2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+2/7*(8*b*B*d-7*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(e^2*(b*d-a*e))+16/35*(b*d-a*e)*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-32/35*(b*d-a*e)^2*(8*b*B*d-_ + 7*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-_ + 12/35*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^3 +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((14A b + 42B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((70A a b + 70B a b)e + (- 28A b - 84B a b )d e + 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (210A a b + 70B a )e + (- 280A a b - 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (112A b + 336B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (224A b + 672B a b )d e - 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 662 + +--S 663 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 664 + +--S 665 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))-2/3*(8*b*B*d-5*A*b*e-3*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*sqrt(d+e*x))-16/15*b*(8*b*B*d-5*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+32/15*b*(b*d-a*e)*_ + (8*b*B*d-5*A*b*e-3*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x))+4/5*b*(8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((10A b + 30B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((90A a b + 90B a b)e + (- 60A b - 180B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 90A a b - 30B a )e + (360A a b + 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 160A b - 480B a b )d e + 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 665 + +--S 666 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 667 + +--S 668 of 764 +r0:=-2/5*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/15*(8*b*B*d-3*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/5*b*(8*b*B*d-_ + 3*A*b*e-5*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*_ + sqrt(d+e*x))+16/15*b^2*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(b*d-a*e))-32/15*b^2*(8*b*B*d-3*A*b*e-_ + 5*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((30A b + 90B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (180A b + 540B a b )d e - 480B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 30A a b - 10B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (96A b + 288B a b )d e - 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 668 + +--S 669 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 670 + +--S 671 of 764 +r0:=-32/6783*(b*d-a*e)^2*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+20/2261*(b*d-a*e)*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-_ + 2/133*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/21*B*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/323323*(b*d-a*e)^4*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/2909907*(b*d-a*e)^5*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/29393*(b*d-a*e)^3*_ + (4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 10 10 5 4 10 5 9 9 +--R 277134B b e x + ((306306A b + 1531530B a b )e + 933504B b d e )x +--R + +--R 4 2 3 10 +--R (1711710A a b + 3423420B a b )e +--R + +--R 5 4 9 5 2 8 +--R (1045044A b + 5225220B a b )d e + 1065636B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 3 2 10 +--R (3879876A a b + 3879876B a b )e +--R + +--R 4 2 3 9 +--R (5933928A a b + 11867856B a b )d e +--R + +--R 5 4 2 8 5 3 7 +--R (1213212A b + 6066060B a b )d e + 415272B b d e +--R * +--R 7 +--R x +--R + +--R 3 2 4 10 +--R (4476780A a b + 2238390B a b)e +--R + +--R 2 3 3 2 9 +--R (13728792A a b + 13728792B a b )d e +--R + +--R 4 2 3 2 8 +--R (7039956A a b + 14079912B a b )d e +--R + +--R 5 4 3 7 5 4 6 +--R (484176A b + 2420880B a b )d e + 462B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 10 +--R (2645370A a b + 529074B a )e +--R + +--R 3 2 4 9 +--R (16279200A a b + 8139600B a b)d e +--R + +--R 2 3 3 2 2 8 +--R (16767576A a b + 16767576B a b )d e +--R + +--R 4 2 3 3 7 5 4 4 6 +--R (2901528A a b + 5803056B a b )d e + (882A b + 4410B a b )d e +--R + +--R 5 5 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 5 10 4 5 9 +--R 646646A a e + (9993620A a b + 1998724B a )d e +--R + +--R 3 2 4 2 8 +--R (20710760A a b + 10355380B a b)d e +--R + +--R 2 3 3 2 3 7 +--R (7235200A a b + 7235200B a b )d e +--R + +--R 4 2 3 4 6 5 4 5 5 +--R (9310A a b + 18620B a b )d e + (- 980A b - 4900B a b )d e +--R + +--R 5 6 4 +--R 560B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 2 8 +--R 2586584A a d e + (13520780A a b + 2704156B a )d e +--R + +--R 3 2 4 3 7 +--R (9586640A a b + 4793320B a b)d e +--R + +--R 2 3 3 2 4 6 4 2 3 5 5 +--R (45220A a b + 45220B a b )d e + (- 10640A a b - 21280B a b )d e +--R + +--R 5 4 6 4 5 7 3 +--R (1120A b + 5600B a b )d e - 640B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 8 4 5 3 7 +--R 3879876A a d e + (7054320A a b + 1410864B a )d e +--R + +--R 3 2 4 4 6 2 3 3 2 5 5 +--R (135660A a b + 67830B a b)d e + (- 54264A a b - 54264B a b )d e +--R + +--R 4 2 3 6 4 5 4 7 3 +--R (12768A a b + 25536B a b )d e + (- 1344A b - 6720B a b )d e +--R + +--R 5 8 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 3 7 4 5 4 6 +--R 2586584A a d e + (293930A a b + 58786B a )d e +--R + +--R 3 2 4 5 5 2 3 3 2 6 4 +--R (- 180880A a b - 90440B a b)d e + (72352A a b + 72352B a b )d e +--R + +--R 4 2 3 7 3 5 4 8 2 +--R (- 17024A a b - 34048B a b )d e + (1792A b + 8960B a b )d e +--R + +--R 5 9 +--R - 1024B b d e +--R * +--R x +--R + +--R 5 4 6 4 5 5 5 +--R 646646A a d e + (- 587860A a b - 117572B a )d e +--R + +--R 3 2 4 6 4 2 3 3 2 7 3 +--R (361760A a b + 180880B a b)d e + (- 144704A a b - 144704B a b )d e +--R + +--R 4 2 3 8 2 5 4 9 +--R (34048A a b + 68096B a b )d e + (- 3584A b - 17920B a b )d e +--R + +--R 5 10 +--R 2048B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 2909907b e x + 2909907a e +--R Type: Expression(Integer) +--E 671 + +--S 672 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 673 + +--S 674 of 764 +r0:=-32/12597*(b*d-a*e)^2*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+4/969*(b*d-a*e)*(12*b*B*d-19*A*b*e+_ + 7*a*B*e)*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-_ + 2/323*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/19*B*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/415701*(b*d-a*e)^4*(12*b*B*d-19*A*b*e+_ + 7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/2909907*(b*d-a*e)^5*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/46189*(b*d-a*e)^3*_ + (12*b*B*d-19*A*b*e+7*a*B*e)*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 9 9 5 4 9 5 8 8 +--R 306306B b e x + ((342342A b + 1711710B a b )e + 702702B b d e )x +--R + +--R 4 2 3 9 +--R (1939938A a b + 3879876B a b )e +--R + +--R 5 4 8 5 2 7 +--R (798798A b + 3993990B a b )d e + 414414B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 3 2 9 +--R (4476780A a b + 4476780B a b )e +--R + +--R 4 2 3 8 +--R (4626006A a b + 9252012B a b )d e +--R + +--R 5 4 2 7 5 3 6 +--R (482790A b + 2413950B a b )d e + 1386B b d e +--R * +--R 6 +--R x +--R + +--R 3 2 4 9 +--R (5290740A a b + 2645370B a b)e +--R + +--R 2 3 3 2 8 +--R (10988460A a b + 10988460B a b )d e +--R + +--R 4 2 3 2 7 5 4 3 6 +--R (2889558A a b + 5779116B a b )d e + (2394A b + 11970B a b )d e +--R + +--R 5 4 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 4 5 9 3 2 4 8 +--R (3233230A a b + 646646B a )e + (13520780A a b + 6760390B a b)d e +--R + +--R 2 3 3 2 2 7 +--R (7189980A a b + 7189980B a b )d e +--R + +--R 4 2 3 3 6 5 4 4 5 +--R (22610A a b + 45220B a b )d e + (- 2660A b - 13300B a b )d e +--R + +--R 5 5 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 8 +--R 831402A a e + (8775910A a b + 1755182B a )d e +--R + +--R 3 2 4 2 7 +--R (9489740A a b + 4744870B a b)d e +--R + +--R 2 3 3 2 3 6 4 2 3 4 5 +--R (96900A a b + 96900B a b )d e + (- 25840A a b - 51680B a b )d e +--R + +--R 5 4 5 4 5 6 3 +--R (3040A b + 15200B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 2 7 +--R 2494206A a d e + (6928350A a b + 1385670B a )d e +--R + +--R 3 2 4 3 6 +--R (251940A a b + 125970B a b)d e +--R + +--R 2 3 3 2 4 5 +--R (- 116280A a b - 116280B a b )d e +--R + +--R 4 2 3 5 4 5 4 6 3 +--R (31008A a b + 62016B a b )d e + (- 3648A b - 18240B a b )d e +--R + +--R 5 7 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 7 4 5 3 6 +--R 2494206A a d e + (461890A a b + 92378B a )d e +--R + +--R 3 2 4 4 5 +--R (- 335920A a b - 167960B a b)d e +--R + +--R 2 3 3 2 5 4 +--R (155040A a b + 155040B a b )d e +--R + +--R 4 2 3 6 3 5 4 7 2 +--R (- 41344A a b - 82688B a b )d e + (4864A b + 24320B a b )d e +--R + +--R 5 8 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 3 6 4 5 4 5 +--R 831402A a d e + (- 923780A a b - 184756B a )d e +--R + +--R 3 2 4 5 4 2 3 3 2 6 3 +--R (671840A a b + 335920B a b)d e + (- 310080A a b - 310080B a b )d e +--R + +--R 4 2 3 7 2 5 4 8 +--R (82688A a b + 165376B a b )d e + (- 9728A b - 48640B a b )d e +--R + +--R 5 9 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 2909907b e x + 2909907a e +--R Type: Expression(Integer) +--E 674 + +--S 675 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 764 +r0:=-32/7293*(b*d-a*e)^2*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+4/663*(b*d-a*e)*(12*b*B*d-_ + 17*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^3)-2/255*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/17*B*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/153153*(b*d-a*e)^4*(12*b*B*d-17*A*b*e+_ + 5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/765765*(b*d-a*e)^5*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/21879*(b*d-a*e)^3*_ + (12*b*B*d-17*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 8 8 5 4 8 5 7 7 +--R 90090B b e x + ((102102A b + 510510B a b )e + 108108B b d e )x +--R + +--R 4 2 3 8 5 4 7 +--R (589050A a b + 1178100B a b )e + (125664A b + 628320B a b )d e +--R + +--R 5 2 6 +--R 1386B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 8 +--R (1392300A a b + 1392300B a b )e +--R + +--R 4 2 3 7 5 4 2 6 +--R (749700A a b + 1499400B a b )d e + (2142A b + 10710B a b )d e +--R + +--R 5 3 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 4 8 +--R (1701700A a b + 850850B a b)e +--R + +--R 2 3 3 2 7 +--R (1856400A a b + 1856400B a b )d e +--R + +--R 4 2 3 2 6 5 4 3 5 +--R (17850A a b + 35700B a b )d e + (- 2380A b - 11900B a b )d e +--R + +--R 5 4 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 4 5 8 3 2 4 7 +--R (1093950A a b + 218790B a )e + (2431000A a b + 1215500B a b)d e +--R + +--R 2 3 3 2 2 6 4 2 3 3 5 +--R (66300A a b + 66300B a b )d e + (- 20400A a b - 40800B a b )d e +--R + +--R 5 4 4 4 5 5 3 +--R (2720A b + 13600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 7 +--R 306306A a e + (1750320A a b + 350064B a )d e +--R + +--R 3 2 4 2 6 2 3 3 2 3 5 +--R (145860A a b + 72930B a b)d e + (- 79560A a b - 79560B a b )d e +--R + +--R 4 2 3 4 4 5 4 5 3 +--R (24480A a b + 48960B a b )d e + (- 3264A b - 16320B a b )d e +--R + +--R 5 6 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 2 6 +--R 612612A a d e + (218790A a b + 43758B a )d e +--R + +--R 3 2 4 3 5 +--R (- 194480A a b - 97240B a b)d e +--R + +--R 2 3 3 2 4 4 +--R (106080A a b + 106080B a b )d e +--R + +--R 4 2 3 5 3 5 4 6 2 +--R (- 32640A a b - 65280B a b )d e + (4352A b + 21760B a b )d e +--R + +--R 5 7 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 2 6 4 5 3 5 +--R 306306A a d e + (- 437580A a b - 87516B a )d e +--R + +--R 3 2 4 4 4 2 3 3 2 5 3 +--R (388960A a b + 194480B a b)d e + (- 212160A a b - 212160B a b )d e +--R + +--R 4 2 3 6 2 5 4 7 +--R (65280A a b + 130560B a b )d e + (- 8704A b - 43520B a b )d e +--R + +--R 5 8 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 765765b e x + 765765a e +--R Type: Expression(Integer) +--E 677 + +--S 678 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 678 + +)clear all + +--S 679 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 679 + +--S 680 of 764 +r0:=-32/1287*(b*d-a*e)^2*(4*b*B*d-5*A*b*e+a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)+4/143*(b*d-a*e)*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-2/65*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+_ + 2/15*B*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 256/15015*(b*d-a*e)^4*(4*b*B*d-5*A*b*e+a*B*e)*(d+e*x)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+512/45045*(b*d-a*e)^5*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*_ + (a+b*x))+64/3003*(b*d-a*e)^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 7 7 5 4 7 5 6 6 +--R 6006B b e x + ((6930A b + 34650B a b )e + 462B b d e )x +--R + +--R 4 2 3 7 5 4 6 +--R (40950A a b + 81900B a b )e + (630A b + 3150B a b )d e +--R + +--R 5 2 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (100100A a b + 100100B a b )e + (4550A a b + 9100B a b )d e +--R + +--R 5 4 2 5 5 3 4 +--R (- 700A b - 3500B a b )d e + 560B b d e +--R * +--R 4 +--R x +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (128700A a b + 64350B a b)e + (14300A a b + 14300B a b )d e +--R + +--R 4 2 3 2 5 5 4 3 4 +--R (- 5200A a b - 10400B a b )d e + (800A b + 4000B a b )d e +--R + +--R 5 4 3 +--R - 640B b d e +--R * +--R 3 +--R x +--R + +--R 4 5 7 3 2 4 6 +--R (90090A a b + 18018B a )e + (25740A a b + 12870B a b)d e +--R + +--R 2 3 3 2 2 5 4 2 3 3 4 +--R (- 17160A a b - 17160B a b )d e + (6240A a b + 12480B a b )d e +--R + +--R 5 4 4 3 5 5 2 +--R (- 960A b - 4800B a b )d e + 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 6 +--R 30030A a e + (30030A a b + 6006B a )d e +--R + +--R 3 2 4 2 5 2 3 3 2 3 4 +--R (- 34320A a b - 17160B a b)d e + (22880A a b + 22880B a b )d e +--R + +--R 4 2 3 4 3 5 4 5 2 +--R (- 8320A a b - 16640B a b )d e + (1280A b + 6400B a b )d e +--R + +--R 5 6 +--R - 1024B b d e +--R * +--R x +--R + +--R 5 6 4 5 2 5 +--R 30030A a d e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 3 4 2 3 3 2 4 3 +--R (68640A a b + 34320B a b)d e + (- 45760A a b - 45760B a b )d e +--R + +--R 4 2 3 5 2 5 4 6 +--R (16640A a b + 33280B a b )d e + (- 2560A b - 12800B a b )d e +--R + +--R 5 7 +--R 2048B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 680 + +--S 681 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 682 + +--S 683 of 764 +r0:=-160/9009*(b*d-a*e)^2*(12*b*B*d-13*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x)/(b*e^4)+20/1287*(b*d-a*e)*(12*b*B*d-_ + 13*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/_ + (b*e^3)-2/143*(12*b*B*d-13*A*b*e+a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x)/(b*e^2)+2/13*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x)/(b*e)-256/9009*(b*d-a*e)^4*(12*b*B*d-13*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+512/9009*(b*d-a*e)^5*_ + (12*b*B*d-13*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^7*(a+b*x))+64/3003*(b*d-a*e)^3*(12*b*B*d-13*A*b*e+a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 1386B b e x + ((1638A b + 8190B a b )e - 1512B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (10010A a b + 20020B a b )e + (- 1820A b - 9100B a b )d e +--R + +--R 5 2 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (25740A a b + 25740B a b )e + (- 11440A a b - 22880B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2080A b + 10400B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (36036A a b + 18018B a b)e + (- 30888A a b - 30888B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (13728A a b + 27456B a b )d e + (- 2496A b - 12480B a b )d e +--R + +--R 5 4 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (30030A a b + 6006B a )e + (- 48048A a b - 24024B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (41184A a b + 41184B a b )d e + (- 18304A a b - 36608B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (3328A b + 16640B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R 18018A a e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (96096A a b + 48048B a b)d e + (- 82368A a b - 82368B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (36608A a b + 73216B a b )d e + (- 6656A b - 33280B a b )d e +--R + +--R 5 6 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 9009b e x + 9009a e +--R Type: Expression(Integer) +--E 683 + +--S 684 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 685 + +--S 686 of 764 +r0:=-2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+160/693*(b*d-a*e)*(12*b*B*d-11*A*b*e-a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4-20/99*(12*b*B*d-11*A*b*e-_ + a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3+2/11*_ + (12*b*B*d-11*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/_ + (e^2*(b*d-a*e))+256/693*(b*d-a*e)^3*(12*b*B*d-11*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-512/693*(b*d-a*e)^4*_ + (12*b*B*d-11*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x))-64/231*(b*d-a*e)^2*(12*b*B*d-11*A*b*e-a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 126B b e x + ((154A b + 770B a b )e - 168B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (990A a b + 1980B a b )e + (- 220A b - 1100B a b )d e +--R + +--R 5 2 4 +--R 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2772A a b + 2772B a b )e + (- 1584A a b - 3168B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (352A b + 1760B a b )d e - 384B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (4620A a b + 2310B a b)e + (- 5544A a b - 5544B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (3168A a b + 6336B a b )d e + (- 704A b - 3520B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (6930A a b + 1386B a )e + (- 18480A a b - 9240B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (22176A a b + 22176B a b )d e + (- 12672A a b - 25344B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (2816A b + 14080B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 1386A a e + (13860A a b + 2772B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 36960A a b - 18480B a b)d e + (44352A a b + 44352B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 25344A a b - 50688B a b )d e + (5632A b + 28160B a b )d e +--R + +--R 5 6 +--R - 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +-------+ +--R (693b e x + 693a e )\|e x + d +--R Type: Expression(Integer) +--E 686 + +--S 687 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 688 + +--S 689 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))-2*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(b*d-a*e)*sqrt(d+e*x))-160/63*b*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+20/9*b*(4*b*B*d-3*A*b*e-a*B*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/(e^3*(b*d-a*e))-_ + 256/63*b*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^6+512/63*b*(b*d-a*e)^3*(4*b*B*d-3*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+64/21*b*(b*d-_ + a*e)*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 14B b e x + ((18A b + 90B a b )e - 24B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((126A a b + 252B a b )e + (- 36A b - 180B a b )d e + 48B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (420A a b + 420B a b )e + (- 336A a b - 672B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (96A b + 480B a b )d e - 128B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (1260A a b + 630B a b)e + (- 2520A a b - 2520B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (2016A a b + 4032B a b )d e + (- 576A b - 2880B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 630A a b - 126B a )e + (5040A a b + 2520B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 10080A a b - 10080B a b )d e + (8064A a b + 16128B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 2304A b - 11520B a b )d e + 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 420A a b - 84B a )d e + (3360A a b + 1680B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 6720A a b - 6720B a b )d e + (5376A a b + 10752B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 1536A b - 7680B a b )d e + 2048B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 689 + +--S 690 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 691 + +--S 692 of 764 +r0:=-2/5*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/15*(12*b*B*d-7*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/3*b*(12*b*B*d-_ + 7*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*_ + sqrt(d+e*x))+32/21*b^2*(12*b*B*d-7*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x)/(e^4*(b*d-a*e))+256/105*b^2*(b*d-a*e)*_ + (12*b*B*d-7*A*b*e-5*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 512/105*b^2*(b*d-a*e)^2*(12*b*B*d-7*A*b*e-5*a*B*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-64/35*b^2*(12*b*B*d-7*A*b*_ + e-5*a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 30B b e x + ((42A b + 210B a b )e - 72B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (350A a b + 700B a b )e + (- 140A b - 700B a b )d e +--R + +--R 5 2 4 +--R 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2100A a b + 2100B a b )e + (- 2800A a b - 5600B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (1120A b + 5600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 2100A a b - 1050B a b)e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 16800A a b - 33600B a b )d e + (6720A b + 33600B a b )d e +--R + +--R 5 4 2 +--R - 11520B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 350A a b - 70B a )e + (- 2800A a b - 1400B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (16800A a b + 16800B a b )d e + (- 22400A a b - 44800B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (8960A b + 44800B a b )d e - 15360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 140A a b - 28B a )d e + (- 1120A a b - 560B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (6720A a b + 6720B a b )d e + (- 8960A a b - 17920B a b )d e +--R + +--R 5 4 5 5 6 +--R (3584A b + 17920B a b )d e - 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 +--R 105b e x + (105a e + 210b d e )x + (210a d e + 105b d e )x +--R + +--R 2 7 +--R 105a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 692 + +--S 693 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 694 + +--S 695 of 764 +r0:=2/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/5*(A*b-a*B)*(a+b*x)*(d+e*x)^(5/2)/(b^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/7*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(b*d-a*e)^(5/2)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (- 210A a b + 210B a b)e + (420A a b - 420B a b )d e +--R + +--R 4 3 2 +--R (- 210A b + 210B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 2 +--R (- 210A a b + 210B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 12B a b )e + 90B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 28A a b + 28B a b )e + (154A b - 64B a b )d e + 90B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (140A a b - 140B a b)e + (- 336A a b + 336B a b )d e +--R + +--R 4 3 2 4 3 +--R (322A b - 232B a b )d e + 30B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (322A a b - 322B a b )d e + 30B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 105b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 695 + +--S 696 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 697 + +--S 698 of 764 +r0:=2/3*(A*b-a*B)*(a+b*x)*(d+e*x)^(3/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2/5*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(b*d-a*e)^(3/2)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (b*d-a*e)*(a+b*x)*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 3 2 +--R ((30A a b - 30B a b)e + (- 30A b + 30B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (30A a b - 30B a )e + (- 30A a b + 30B a b)d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 4B a b )e + 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 20A a b + 20B a b)e + (40A b - 28B a b )d e + 6B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A a b - 40B a b)d e + 6B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 15b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 698 + +--S 699 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 700 + +--S 701 of 764 +r0:=2/3*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b*d-a*e)/(b^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (a+b*x)*sqrt(d+e*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 +-----------+ +--R ((- 6A b + 6B a b)e x + (- 6A a b + 6B a )e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 4B a b)e + 2B b d)x + (6A a b - 6B a )e +--R + +--R 2B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R 3b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 701 + +--S 702 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 764 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 703 + +--S 704 of 764 +r0:=-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(3/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*B*(a+b*x)*_ + sqrt(d+e*x)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 \|b \|e x + d +--R ((- 2A b + 2B a b)e x + (- 2A a b + 2B a )e)atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (2B b x + 2B a)\|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R b e\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 704 + +--S 705 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 764 +r0:=-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(3/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*(B*d-A*e)*_ + (a+b*x)/(e*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 +-------+ \|b \|e x + d +--R ((2A b - 2B a b)e x + (2A a b - 2B a )e)\|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R ((- 2A b e + 2B b d)x - 2A a e + 2B a d)\|- a e + b d \|b +--R / +--R +------------------+ +--R 2 +-----------+ +-+ +-------+ | 2 2 2 +--R (a e - b d e)\|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 707 + +--S 708 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 709 + +--S 710 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))*sqrt(b)/((b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-_ + a*B)*(a+b*x)/((b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 +--R (- 6A b + 6B a b)e x +--R + +--R 2 2 2 2 +--R ((- 6A a b + 6B a )e + (- 6A b + 6B a b)d e)x + (- 6A a b + 6B a )d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +--R (6A b - 6B a b)e x +--R + +--R 2 2 2 2 2 2 2 +--R ((4A a b - 6B a )e + (8A b - 4B a b)d e - 2B b d )x - 2A a e +--R + +--R 2 2 +--R (8A a b - 4B a )d e - 2B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e) +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 710 + +--S 711 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 711 + +)clear all + +--S 712 of 764 +t0:=(A+B*x)/((d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 712 + +--S 713 of 764 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/3*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-2*b^(3/2)*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2*b*(A*b-a*B)*(a+b*x)/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 +--R (30A b - 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((30A a b - 30B a b)e + (60A b - 60B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((60A a b - 60B a b)d e + (30A b - 30B a b )d e)x +--R + +--R 2 2 2 +--R (30A a b - 30B a b)d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 +--R (- 30A b + 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 20A a b + 20B a b)e + (- 70A b + 70B a b )d e )x +--R + +--R 2 3 3 2 2 2 +--R (4A a b - 10B a )e + (- 48A a b + 66B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 46A b + 28B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (22A a b - 4B a )d e + (- 46A a b + 28B a b)d e +--R + +--R 2 3 +--R 6B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 713 + +--S 714 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 715 + +--S 716 of 764 +r0:=-1/10*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*(d+e*x)^(7/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+2/5*B*(a+b*x)*(d+e*x)^(9/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+7/12*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-7/20*(4*b*B*d+5*A*b*e-_ + 9*a*B*e)*(d+e*x)^(5/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*e*(b*d-_ + a*e)^(3/2)*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/(b^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*e*(b*d-_ + a*e)*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 5 +-+ | 2 2 2 +--R (60b x + 60a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 718 + +--S 719 of 764 +r0:=-1/6*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*(d+e*x)^(5/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+2/3*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))-5/12*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/_ + (b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/_ + (b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*_ + (a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x + (- 45A a b + 105B a )e +--R + +--R 2 +--R - 60B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 5 4 +-+ | 2 2 2 +--R (12b x + 12a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 719 + +--S 720 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 721 + +--S 722 of 764 +r0:=-1/2*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+2*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-3/4*(4*b*B*d+A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 3A b + 15B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b + 30B a b)e - 24B a b d e)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 4 3 +-----------+ +-+ | 2 2 2 +--R (4b x + 4a b )\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 722 + +--S 723 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 764 +r0:=-2*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/2*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-1/4*e*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 2A a b - 6B a b)e + 8B a b d e)x + (- A a b - 3B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e + (2A b + 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 3 4 2 2 3 +-----------+ +-+ | 2 2 2 +--R ((4a b e - 4b d)x + 4a b e - 4a b d)\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 725 + +--S 726 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 726 + +)clear all + +--S 727 of 764 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 727 + +--S 728 of 764 +r0:=-2/3*B*(a+b*x)*sqrt(d+e*x)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/6*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/4*e*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 3A b - B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b - 2B a b)e + 8B a b d e)x + (- 3A a b - B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((3A b + B a b)e - 4B b d)x + (5A a b - B a )e + (- 2A b - 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R ((4a b e - 8a b d e + 4b d )x + 4a b e - 8a b d e + 4a b d ) +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 728 + +)clear all + +--S 729 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 729 + +--S 730 of 764 +r0:=-2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x))+1/2*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/(e*_ + (b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+3/4*e*(4*b*B*d-5*A*b*e+_ + a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-_ + a*e)^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-3/4*(4*b*B*d-5*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x - 8A a e +--R + +--R 2 2 2 +--R (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x + 4a e - 12a b d e +--R + +--R 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 730 + +--S 731 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 731 + +)clear all + +--S 732 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 732 + +--S 733 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/6*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))+5/4*e*(4*b*B*d-_ + 7*A*b*e+3*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b)/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/12*(4*b*B*d-_ + 7*A*b*e+3*a*B*e)/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 105A b + 45B a b )e + 60B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 210A a b + 90B a b)e + (- 105A b + 165B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 105A a b + 45B a )e + (- 210A a b + 150B a b)d e +--R + +--R 2 2 +--R 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (- 105A a b + 45B a )d e + 60B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (12a e - 36a b d e + 24a b d e + 24a b d e - 36a b d e + 12b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 734 + +)clear all + +--S 735 of 764 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 735 + +--S 736 of 764 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/10*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-7/20*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-7/12*e*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^4*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*b^(3/2)*e*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*b*e*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 5 2 +--R - 60b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 6 3 3 3 4 2 4 4 3 5 5 2 +--R 60a e - 180a b d e + 600a b d e - 900a b d e + 540a b d e +--R + +--R 6 6 +--R - 120b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5 6 +--R 120a d e - 540a b d e + 900a b d e - 600a b d e + 180a b d e +--R + +--R 6 7 +--R - 60b d +--R * +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 5 7 +--R - 60a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 736 + +--S 737 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 737 + +)clear all + +--S 738 of 764 +t0:=(A+B*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 738 + +--S 739 of 764 +r0:=-1/20*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*(d+e*x)^(11/2)/(b^2*e*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))+2/5*B*(a+b*x)*(d+e*x)^(13/2)/(b*e*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-33/160*e*(8*b*B*d+5*A*b*e-13*a*B*e)*_ + (a+b*x)*(d+e*x)^(7/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-11/120*_ + (8*b*B*d+5*A*b*e-13*a*B*e)*(d+e*x)^(9/2)/(b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+77/64*e^3*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*(d+_ + e*x)^(3/2)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))-231/320*e^2*(8*b*B*d+_ + 5*A*b*e-13*a*B*e)*(d+e*x)^(5/2)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 231/64*e^3*(b*d-a*e)^(3/2)*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(15/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+231/64*e^3*(b*d-a*e)*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*_ + sqrt(d+e*x)/(b^7*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 2 4 5 6 5 4 +--R (17325A a b - 45045B a b )e + (- 17325A b + 72765B a b )d e +--R + +--R 6 2 3 +--R - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (69300A a b - 180180B a b )e +--R + +--R 5 2 4 4 5 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (103950A a b - 270270B a b )e +--R + +--R 2 4 3 3 4 2 4 2 3 +--R (- 103950A a b + 436590B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (69300A a b - 180180B a b)e +--R + +--R 3 3 4 2 4 3 3 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (17325A a b - 45045B a )e + (- 17325A a b + 72765B a b)d e +--R + +--R 4 2 2 3 +--R - 27720B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 384B b e x + ((640A b - 1664B a b )e + 3328B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 7040A a b + 18304B a b )e + (10240A b - 37888B a b )d e +--R + +--R 6 2 3 +--R 22144B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (- 46035A a b + 119691B a b )e +--R + +--R 5 2 4 4 +--R (63910A a b - 239822B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 11475A b + 132091B a b )d e - 10680B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (- 84315A a b + 219219B a b )e +--R + +--R 2 4 3 3 4 +--R (114840A a b - 433488B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 18975A a b + 233079B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 5150A b - 16970B a b )d e - 2480B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 63525A a b + 165165B a b)e +--R + +--R 3 3 4 2 4 +--R (85470A a b - 323862B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 13365A a b + 171501B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3740A a b - 11660B a b )d e + (- 1640A b - 1720B a b )d e +--R + +--R 6 5 +--R - 320B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 17325A a b + 45045B a )e + (23100A a b - 87780B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 3465A a b + 45969B a b )d e + (- 990A a b - 2970B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 440A a b - 440B a b )d e + (- 240A b - 80B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 10 3 9 2 2 8 3 7 +-+ | 2 2 2 +--R (960b x + 2880a b x + 2880a b x + 960a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 739 + +--S 740 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 740 + +)clear all + +--S 741 of 764 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 741 + +--S 742 of 764 +r0:=-1/12*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*(d+e*x)^(9/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2))+2/3*B*(a+b*x)*(d+e*x)^(11/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-7/32*e*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*(d+_ + e*x)^(5/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/8*(8*b*B*d+3*A*b*e-_ + 11*a*B*e)*(d+e*x)^(7/2)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 35/64*e^2*(8*b*B*d+3*A*b*e-11*a*B*e)*(d+e*x)^(3/2)/(b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-105/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(13/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+105/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*_ + (a+b*x)*sqrt(d+e*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 128B b e x + ((384A b - 1408B a b )e + 1664B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (2511A a b - 9207B a b )e + (- 975A b + 10271B a b )d e +--R + +--R 5 2 2 +--R - 1320B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4599A a b - 16863B a b )e + (- 1665A a b + 18369B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 630A b - 2130B a b )d e - 400B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (3465A a b - 12705B a b)e + (- 1197A a b + 13629B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 468A a b - 1476B a b )d e + (- 264A b - 280B a b )d e +--R + +--R 5 4 +--R - 64B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (945A a b - 3465B a )e + (- 315A a b + 3675B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 126A a b - 378B a b )d e + (- 72A a b - 72B a b )d e +--R + +--R 5 4 4 +--R (- 48A b - 16B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 9 3 8 2 2 7 3 6 +-+ | 2 2 2 +--R (192b x + 576a b x + 576a b x + 192a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 742 + +--S 743 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 744 + +--S 745 of 764 +r0:=-1/4*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*(d+e*x)^(7/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+2*B*(a+b*x)*(d+e*x)^(9/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-35/96*e*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*(d+_ + e*x)^(3/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-7/24*(8*b*B*d+A*b*e-_ + 9*a*B*e)*(d+e*x)^(5/2)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-35/64*e^3*_ + (8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))/(b^(11/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*_ + (8*b*B*d+A*b*e-9*a*B*e)*sqrt(d+e*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 105A b + 945B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 420A a b + 3780B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 630A a b + 5670B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 420A a b + 3780B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 105A a b + 945B a )e - 840B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 384B b e x + ((- 279A b + 2511B a b )e - 696B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 511A a b + 4599B a b )e + (- 326A b - 1154B a b )d e +--R + +--R 4 2 +--R - 304B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 385A a b + 3465B a b)e + (- 252A a b - 812B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 200A b - 216B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 105A a b + 945B a )e + (- 70A a b - 210B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 56A a b - 56B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +-----------+ +-+ +--R (192b x + 576a b x + 576a b x + 192a b )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 745 + +--S 746 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 746 + +)clear all + +--S 747 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 747 + +--S 748 of 764 +r0:=1/4*(8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*(d+e*x)^(5/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-2*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+5/24*(8*b*B*d-A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+5/32*e*(8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/64*e^3*_ + (8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))/(b^(9/2)*(b*d-a*e)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^2*_ + (8*b*B*d-A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 15A b - 105B a b )e + 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 60A a b - 420B a b )e + 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 90A a b - 630B a b )e + 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 60A a b - 420B a b)e + 480B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 15A a b - 105B a )e + 120B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b - 279B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 73A a b - 511B a b )e + (118A b + 258B a b )d e +--R + +--R 4 2 +--R 208B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 55A a b - 385B a b)e + (- 36A a b + 188B a b )d e +--R + +--R 4 3 2 4 3 +--R (136A b + 88B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 105B a )e + (- 10A a b + 50B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 8A a b + 24B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 8 3 2 6 7 2 +--R (192a b e - 192b d)x + (576a b e - 576a b d)x +--R + +--R 3 5 2 6 4 4 3 5 +--R (576a b e - 576a b d)x + 192a b e - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 748 + +--S 749 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 749 + +)clear all + +--S 750 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 750 + +--S 751 of 764 +r0:=1/12*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-2/3*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/24*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/96*e*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+_ + b*x)*sqrt(d+e*x)/(b^3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/64*e^3*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-1/64*e^2*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*(b*d-_ + a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 9A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 36A a b - 60B a b )e + 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 54A a b - 90B a b )e + 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((- 36A a b - 60B a b)e + 96B a b d e )x + (- 9A a b - 15B a )e +--R + +--R 4 3 +--R 24B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((33A a b - 73B a b )e + (- 6A b + 158B a b )d e - 112B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 33A a b - 55B a b)e + (132A a b + 52B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 72A b + 40B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 9A a b - 15B a )e + (- 6A a b + 14B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (72A a b + 8B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 6 2 7 8 2 3 +--R (192a b e - 384a b d e + 192b d )x +--R + +--R 3 5 2 2 6 7 2 2 +--R (576a b e - 1152a b d e + 576a b d )x +--R + +--R 4 4 2 3 5 2 6 2 5 3 2 4 4 +--R (576a b e - 1152a b d e + 576a b d )x + 192a b e - 384a b d e +--R + +--R 3 5 2 +--R 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 751 + +--S 752 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 752 + +)clear all + +--S 753 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 753 + +--S 754 of 764 +r0:=-2/5*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/20*(8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-1/24*(8*b*B*d-5*A*b*e-3*a*B*e)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/96*e*_ + (8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-1/64*e^3*(8*b*B*d-5*A*b*e-3*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-_ + a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/64*e^2*(8*b*B*d-5*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 15A b - 9B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 60A a b - 36B a b )e + 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 90A a b - 54B a b )e + 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((- 60A a b - 36B a b)e + 96B a b d e )x + (- 15A a b - 9B a )e +--R + +--R 4 3 +--R 24B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((55A a b + 33B a b )e + (- 10A b - 94B a b )d e + 16B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (73A a b - 33B a b)e + (- 36A a b + 92B a b )d e +--R + +--R 4 3 2 4 3 +--R (8A b - 168B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 9B a )e + (118A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 136A a b - 40B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 3 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 2 +--R (576a b e - 1728a b d e + 1728a b d e - 576a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 6 2 3 +--R (576a b e - 1728a b d e + 1728a b d e - 576a b d )x + 192a b e +--R + +--R 5 3 2 4 4 2 3 5 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 754 + +--S 755 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 764 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 756 + +--S 757 of 764 +r0:=-2/7*B*(a+b*x)*sqrt(d+e*x)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/28*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-1/24*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5/96*e*_ + (8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+5/64*e^3*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^2*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 105A b - 15B a b )e + 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 420A a b - 60B a b )e + 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 630A a b - 90B a b )e + 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 420A a b - 60B a b)e + 480B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 105A a b - 15B a )e + 120B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((385A a b + 55B a b )e + (- 70A b - 450B a b )d e + 80B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (511A a b + 73B a b)e + (- 252A a b - 620B a b )d e +--R + +--R 4 3 2 4 3 +--R (56A b + 296B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (279A a b - 15B a )e + (- 326A a b - 146B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (200A a b + 72B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 3 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 2 +--R (576a b e - 2304a b d e + 3456a b d e - 2304a b d e + 576a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 +--R (576a b e - 2304a b d e + 3456a b d e - 2304a b d e + 576a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R 192a b e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 757 + +--S 758 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 758 + +)clear all + +--S 759 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 759 + +--S 760 of 764 +r0:=-2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x))+1/4*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/(e*_ + (b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2))-7/24*(8*b*B*d-9*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/96*e*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^4*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+35/64*e^3*(8*b*B*d-9*A*b*e+a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(11/2)*_ + sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*(8*b*B*d-9*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((945A b - 105B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((3780A a b - 420B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((5670A a b - 630B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((3780A a b - 420B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (945A a b - 105B a )e - 840B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3465A a b + 385B a b )e + (- 315A b + 3115B a b )d e +--R + +--R 4 2 2 +--R 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 4599A a b + 511B a b)e + (- 1197A a b + 4221B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (126A b + 1050B a b )d e - 112B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 2511A a b + 279B a )e + (- 1665A a b + 2417B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (468A a b + 1428B a b )d e + (- 72A b - 408B a b )d e + 64B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 384A a e + (- 975A a b + 663B a )d e + (630A a b + 370B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 264A a b - 104B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 5 3 5 4 4 4 3 5 2 3 2 6 3 2 7 4 +--R 192a b e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 8 5 +--R - 192b d +--R * +--R 3 +--R x +--R + +--R 6 2 5 5 3 4 4 4 2 3 3 5 3 2 +--R 576a b e - 2880a b d e + 5760a b d e - 5760a b d e +--R + +--R 2 6 4 7 5 +--R 2880a b d e - 576a b d +--R * +--R 2 +--R x +--R + +--R 7 5 6 2 4 5 3 2 3 4 4 3 2 +--R 576a b e - 2880a b d e + 5760a b d e - 5760a b d e +--R + +--R 3 5 4 2 6 5 +--R 2880a b d e - 576a b d +--R * +--R x +--R + +--R 8 5 7 4 6 2 2 3 5 3 3 2 4 4 4 +--R 192a e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 3 5 5 +--R - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 760 + +--S 761 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 761 + +)clear all + +--S 762 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 762 + +--S 763 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/12*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x))+1/8*(-8*b*B*d+11*A*b*e-_ + 3*a*B*e)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))+_ + 7/32*e*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x))+105/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-_ + a*e)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*(8*b*B*d-11*A*b*e+_ + 3*a*B*e)/((b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 105/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^6*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((- 3465A b + 945B a b )e + 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 13860A a b + 3780B a b )e + (- 3465A b + 11025B a b )d e +--R + +--R 5 2 3 +--R 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 +--R (- 20790A a b + 5670B a b )e +--R + +--R 4 2 3 4 4 2 3 +--R (- 13860A a b + 18900B a b )d e + 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 13860A a b + 3780B a b)e + (- 20790A a b + 15750B a b )d e +--R + +--R 2 3 2 3 +--R 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 3465A a b + 945B a )e + (- 13860A a b + 6300B a b)d e +--R + +--R 3 2 2 3 +--R 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 3465A a b + 945B a )d e + 2520B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (12705A a b - 3465B a b )e + (4620A b - 10500B a b )d e +--R + +--R 5 2 3 +--R - 3360B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (16863A a b - 4599B a b )e + (17094A a b - 16926B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (693A b - 12621B a b )d e - 504B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (9207A a b - 2511B a b)e + (22968A a b - 12960B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2673A a b - 17433B a b )d e + (- 198A b - 1890B a b )d e +--R + +--R 5 4 +--R 144B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (1408A a b - 384B a )e + (12782A a b - 4510B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (3795A a b - 10331B a b )d e + (- 748A a b - 2556B a b )d e +--R + +--R 5 4 4 5 5 +--R (88A b + 520B a b )d e - 64B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 128A a e + (2048A a b - 256B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (2295A a b - 2639B a b)d e + (- 1030A a b - 690B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (328A a b + 136B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 7 5 4 6 4 5 2 5 3 6 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 7 4 3 8 5 2 9 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 4 +--R x +--R + +--R 7 2 7 6 3 6 5 4 2 5 4 5 3 4 +--R 576a b e - 3264a b d e + 7488a b d e - 8640a b d e +--R + +--R 3 6 4 3 2 7 5 2 8 6 9 7 +--R 4800a b d e - 576a b d e - 576a b d e + 192b d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 +--R 576a b e - 2880a b d e + 5184a b d e - 2880a b d e +--R + +--R 4 5 4 3 3 6 5 2 2 7 6 8 7 +--R - 2880a b d e + 5184a b d e - 2880a b d e + 576a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 6 7 2 2 5 6 3 3 4 5 4 4 3 +--R 192a e - 576a b d e - 576a b d e + 4800a b d e - 8640a b d e +--R + +--R 4 5 5 2 3 6 6 2 7 7 +--R 7488a b d e - 3264a b d e + 576a b d +--R * +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e + 2880a b d e +--R + +--R 4 5 6 3 6 7 +--R - 1152a b d e + 192a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 763 + +--S 764 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 764 + + + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richder12e.input.pamphlet b/src/axiom-website/CATS/richder12e.input.pamphlet new file mode 100644 index 0000000..4663f7a --- /dev/null +++ b/src/axiom-website/CATS/richder12e.input.pamphlet @@ -0,0 +1,17949 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12e.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +All derivatives match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12e.output +)spool richder12e.output +)set message test on +)set message auto off +)clear all + +--S 1 of 765 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 765 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/20*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-11/120*(8*b*B*d-13*A*b*e+_ + 5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 33/160*e*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-231/320*e^2*(8*b*B*d-13*A*b*e+5*a*B*e)/_ + ((b*d-a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-77/64*e^3*(8*b*B*d-_ + 13*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+231/64*b^(3/2)*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(15/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-231/64*b*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/_ + ((b*d-a*e)^7*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((45045A b - 17325B a b )e - 27720B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (180180A a b - 69300B a b )e + (90090A b - 145530B a b )d e +--R + +--R 6 2 4 +--R - 55440B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (270270A a b - 103950B a b )e +--R + +--R 5 2 4 5 +--R (360360A a b - 304920B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (45045A b - 239085B a b )d e - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (180180A a b - 69300B a b )e +--R + +--R 2 4 3 3 5 +--R (540540A a b - 318780B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (180180A a b - 401940B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (45045A a b - 17325B a b)e + (360360A a b - 166320B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (270270A a b - 325710B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (90090A a b - 34650B a b)d e +--R + +--R 3 3 4 2 2 4 3 3 3 3 +--R (180180A a b - 124740B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (45045A a b - 17325B a b)d e - 27720B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 165165A a b + 63525B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 105105A b + 142065B a b )d e + 64680B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 219219A a b + 84315B a b )e +--R + +--R 5 2 4 5 +--R (- 387387A a b + 283899B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 69069A b + 264957B a b )d e + 42504B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 119691A a b + 46035B a b )e +--R + +--R 2 4 3 3 5 +--R (- 517803A a b + 272811B a b )d e +--R + +--R 5 2 4 2 4 +--R (- 256971A a b + 417483B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 6435A b + 160611B a b )d e + 3960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 18304A a b + 7040B a b)e +--R + +--R 3 3 4 2 5 +--R (- 285857A a b + 121209B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (- 347919A a b + 309727B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 25025A a b + 223729B a b )d e + (1430A b + 14850B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (1664A a b - 640B a )e + (- 44928A a b + 16256B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (- 196001A a b + 103033B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 35945A a b + 134441B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (5460A a b + 20020B a b )d e + (- 520A b - 3160B a b )d e +--R + +--R 6 6 +--R 320B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 384A a e + (3968A a b - 256B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 32384A a b + 6912B a b)d e + (- 22155A a b + 33619B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (7630A a b + 5530B a b )d e + (- 1960A a b - 840B a b )d e +--R + +--R 6 5 6 +--R (240A b + 80B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 3 9 6 4 8 5 5 2 7 4 6 3 6 +--R 960a b e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 3 7 4 5 2 8 5 4 9 6 3 10 7 2 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960b d e +--R * +--R 5 +--R x +--R + +--R 8 2 9 7 3 8 6 4 2 7 5 5 3 6 +--R 2880a b e - 18240a b d e + 47040a b d e - 60480a b d e +--R + +--R 4 6 4 5 3 7 5 4 2 8 6 3 9 7 2 +--R 33600a b d e + 6720a b d e - 20160a b d e + 10560a b d e +--R + +--R 10 8 +--R - 1920b d e +--R * +--R 4 +--R x +--R + +--R 9 9 8 2 8 7 3 2 7 6 4 3 6 +--R 2880a b e - 14400a b d e + 21120a b d e + 13440a b d e +--R + +--R 5 5 4 5 4 6 5 4 3 7 6 3 2 8 7 2 +--R - 80640a b d e + 107520a b d e - 67200a b d e + 17280a b d e +--R + +--R 9 8 10 9 +--R 960a b d e - 960b d +--R * +--R 3 +--R x +--R + +--R 10 9 9 8 8 2 2 7 7 3 3 6 +--R 960a e - 960a b d e - 17280a b d e + 67200a b d e +--R + +--R 6 4 4 5 5 5 5 4 4 6 6 3 3 7 7 2 +--R - 107520a b d e + 80640a b d e - 13440a b d e - 21120a b d e +--R + +--R 2 8 8 9 9 +--R 14400a b d e - 2880a b d +--R * +--R 2 +--R x +--R + +--R 10 8 9 2 7 8 2 3 6 7 3 4 5 +--R 1920a d e - 10560a b d e + 20160a b d e - 6720a b d e +--R + +--R 6 4 5 4 5 5 6 3 4 6 7 2 3 7 8 +--R - 33600a b d e + 60480a b d e - 47040a b d e + 18240a b d e +--R + +--R 2 8 9 +--R - 2880a b d +--R * +--R x +--R + +--R 10 2 7 9 3 6 8 2 4 5 7 3 5 4 +--R 960a d e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 6 4 6 3 5 5 7 2 4 6 8 3 7 9 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 3 + +)clear all + +--S 4 of 765 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 m +--R (1) (b x + 3a b x + 3a b x + a )(e x + d) +--R Type: Expression(Integer) +--E 4 + +--S 5 of 765 +r0:=-(b*d-a*e)^3*(d+e*x)^(1+m)/(e^4*(1+m))+3*b*(b*d-a*e)^2*_ + (d+e*x)^(2+m)/(e^4*(2+m))-3*b^2*(b*d-a*e)*(d+e*x)^(3+m)/(e^4*(3+m))+_ + b^3*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 4 +--R (b m + 6b m + 11b m + 6b )(e x + d) +--R + +--R 2 3 3 2 3 2 2 3 +--R (3a b e - 3b d)m + (21a b e - 21b d)m + (42a b e - 42b d)m +--R + +--R 2 3 +--R 24a b e - 24b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 3 2 2 +--R (3a b e - 6a b d e + 3b d )m + (24a b e - 48a b d e + 24b d )m +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (57a b e - 114a b d e + 57b d )m + 36a b e - 72a b d e + 36b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e - 3a b d e + 3a b d e - b d )m +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (9a e - 27a b d e + 27a b d e - 9b d )m +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (26a e - 78a b d e + 78a b d e - 26b d )m + 24a e - 72a b d e +--R + +--R 2 2 3 3 +--R 72a b d e - 24b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 5 + +--S 6 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 6 + +)clear all + +--S 7 of 765 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 5 8 2 5 3 4 7 2 5 2 4 3 2 3 6 +--R b e x + (3a b e + 5b d e )x + (3a b e + 15a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 5 +--R (a e + 15a b d e + 30a b d e + 10b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 4 +--R (5a d e + 30a b d e + 30a b d e + 5b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (10a d e + 30a b d e + 15a b d e + b d )x +--R + +--R 3 3 2 2 4 2 5 2 3 4 2 5 3 5 +--R (10a d e + 15a b d e + 3a b d )x + (5a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 7 + +--S 8 of 765 +r0:=-1/6*(b*d-a*e)^3*(d+e*x)^6/e^4+3/7*b*(b*d-a*e)^2*(d+e*x)^7/e^4-_ + 3/8*b^2*(b*d-a*e)*(d+e*x)^8/e^4+1/9*b^3*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 3 9 9 3 2 9 5 3 8 8 +--R - b e x + (- a b e + - b d e )x +--R 9 8 8 +--R + +--R 3 2 9 15 2 8 10 3 2 7 7 +--R (- a b e + -- a b d e + -- b d e )x +--R 7 7 7 +--R + +--R 1 3 9 5 2 8 2 2 7 5 3 3 6 6 +--R (- a e + - a b d e + 5a b d e + - b d e )x +--R 6 2 3 +--R + +--R 3 8 2 2 7 2 3 6 3 4 5 5 +--R (a d e + 6a b d e + 6a b d e + b d e )x +--R + +--R 5 3 2 7 15 2 3 6 15 2 4 5 1 3 5 4 4 +--R (- a d e + -- a b d e + -- a b d e + - b d e )x +--R 2 2 4 4 +--R + +--R 10 3 3 6 2 4 5 2 5 4 3 5 3 4 5 3 2 5 4 2 +--R (-- a d e + 5a b d e + a b d e )x + (- a d e + - a b d e )x +--R 3 2 2 +--R + +--R 3 5 4 1 3 6 3 1 2 7 2 1 2 8 1 3 9 +--R a d e x + - a d e - -- a b d e + -- a b d e - --- b d +--R 6 14 56 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 8 + +--S 9 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 9 + +)clear all + +--S 10 of 765 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 10 + +--S 11 of 765 +r0:=-1/5*(b*d-a*e)^3*(d+e*x)^5/e^4+1/2*b*(b*d-a*e)^2*(d+e*x)^6/e^4-_ + 3/7*b^2*(b*d-a*e)*(d+e*x)^7/e^4+1/8*b^3*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 3 8 8 3 2 8 4 3 7 7 1 2 8 2 7 3 2 6 6 +--R - b e x + (- a b e + - b d e )x + (- a b e + 2a b d e + b d e )x +--R 8 7 7 2 +--R + +--R 1 3 8 12 2 7 18 2 2 6 4 3 3 5 5 +--R (- a e + -- a b d e + -- a b d e + - b d e )x +--R 5 5 5 5 +--R + +--R 3 7 9 2 2 6 2 3 5 1 3 4 4 4 +--R (a d e + - a b d e + 3a b d e + - b d e )x +--R 2 4 +--R + +--R 3 2 6 2 3 5 2 4 4 3 3 3 5 3 2 4 4 2 3 4 4 +--R (2a d e + 4a b d e + a b d e )x + (2a d e + - a b d e )x + a d e x +--R 2 +--R + +--R 1 3 5 3 1 2 6 2 1 2 7 1 3 8 +--R - a d e - -- a b d e + -- a b d e - --- b d +--R 5 10 35 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 11 + +--S 12 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 765 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 13 + +--S 14 of 765 +r0:=1/4*(b*d-a*e)^3*(a+b*x)^4/b^4+3/5*e*(b*d-a*e)^2*(a+b*x)^5/b^4+_ + 1/2*e^2*(b*d-a*e)*(a+b*x)^6/b^4+1/7*e^3*(a+b*x)^7/b^4 +--R +--R +--R (2) +--R 1 7 3 7 1 6 3 1 7 2 6 3 2 5 3 9 6 2 3 7 2 5 +--R - b e x + (- a b e + - b d e )x + (- a b e + - a b d e + - b d e)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 4 3 9 2 5 2 9 6 2 1 7 3 4 +--R (- a b e + - a b d e + - a b d e + - b d )x +--R 4 4 4 4 +--R + +--R 3 4 2 2 5 2 6 3 3 3 3 4 2 3 2 5 3 2 3 4 3 +--R (a b d e + 3a b d e + a b d )x + (- a b d e + - a b d )x + a b d x +--R 2 2 +--R + +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R - --- a e + -- a b d e - -- a b d e + - a b d +--R 140 20 20 4 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 14 + +--S 15 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 765 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 765 +r0:=1/4*(b*d-a*e)^2*(a+b*x)^4/b^3+2/5*e*(b*d-a*e)*(a+b*x)^5/b^3+_ + 1/6*e^2*(a+b*x)^6/b^3 +--R +--R +--R (2) +--R 1 6 2 6 3 5 2 2 6 5 3 2 4 2 3 5 1 6 2 4 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 3 2 2 4 5 2 3 3 3 3 2 4 2 2 3 3 2 +--R (- a b e + 2a b d e + a b d )x + (a b d e + - a b d )x + a b d x +--R 3 2 +--R + +--R 1 6 2 1 5 1 4 2 2 +--R -- a e - -- a b d e + - a b d +--R 60 10 4 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 17 + +--S 18 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 18 + +)clear all + +--S 19 of 765 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d +--R Type: Polynomial(Integer) +--E 19 + +--S 20 of 765 +r0:=1/4*(b*d-a*e)*(a+b*x)^4/b^2+1/5*e*(a+b*x)^5/b^2 +--R +--R +--R (2) +--R 1 5 5 3 4 1 5 4 2 3 4 3 +--R - b e x + (- a b e + - b d)x + (a b e + a b d)x +--R 5 4 4 +--R + +--R 1 3 2 3 2 3 2 3 2 1 5 1 4 +--R (- a b e + - a b d)x + a b d x - -- a e + - a b d +--R 2 2 20 4 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 20 + +--S 21 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 22 + +--S 23 of 765 +r0:=1/4*(a+b*x)^4/b +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - b x + a b x + - a b x + a b x + - a +--R 4 2 4 +--R (2) ----------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 23 + +--S 24 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 24 + +)clear all + +--S 25 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 25 + +--S 26 of 765 +r0:=b*(b*d-a*e)^2*x/e^3-1/2*(b*d-a*e)*(a+b*x)^2/e^2+1/3*(a+b*x)^3/e-_ + (b*d-a*e)^3*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a e - 18a b d e + 18a b d e - 6b d )log(e x + d) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (9a b e - 3b d e )x + (18a b e - 18a b d e + 6b d e)x + 5a e +--R + +--R 2 2 +--R - 3a b d e +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 26 + +--S 27 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 27 + +)clear all + +--S 28 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 28 + +--S 29 of 765 +r0:=-b^2*(2*b*d-3*a*e)*x/e^3+1/2*b^3*x^2/e^2+(b*d-a*e)^3/(e^4*(d+e*x))+_ + 3*b*(b*d-a*e)^2*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b e - 12a b d e + 6b d e)x + 6a b d e - 12a b d e + 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 3 3 +--R b e x + (6a b e - 3b d e )x + (6a b d e - 4b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 6a b d e + 2b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 29 + +--S 30 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 765 +r0:=b^3*x/e^3+1/2*(b*d-a*e)^3/(e^4*(d+e*x)^2)-3*b*(b*d-a*e)^2/(e^4*(d+e*x))-_ + 3*b^2*(b*d-a*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 2 3 2 2 2 3 3 +--R ((6a b e - 6b d e )x + (12a b d e - 12b d e)x + 6a b d e - 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 3 2 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4b d e x + (- 6a b e + 12a b d e - 4b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 9a b d e - 5b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 32 + +--S 33 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 34 + +--S 35 of 765 +r0:=1/3*(b*d-a*e)^3/(e^4*(d+e*x)^3)-3/2*b*(b*d-a*e)^2/(e^4*(d+e*x)^2)+_ + 3*b^2*(b*d-a*e)/(e^4*(d+e*x))+b^3*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(e x + d) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 18a b e + 18b d e )x + (- 9a b e - 18a b d e + 27b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e - 6a b d e + 11b d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 35 + +--S 36 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 36 + +)clear all + +--S 37 of 765 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 m +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )(e x + d) +--R Type: Expression(Integer) +--E 37 + +--S 38 of 765 +r0:=-(b*d-a*e)^5*(d+e*x)^(1+m)/(e^6*(1+m))+5*b*(b*d-a*e)^4*(d+e*x)^(2+m)/_ + (e^6*(2+m))-10*b^2*(b*d-a*e)^3*(d+e*x)^(3+m)/(e^6*(3+m))+10*b^3*_ + (b*d-a*e)^2*(d+e*x)^(4+m)/(e^6*(4+m))-5*b^4*(b*d-a*e)*(d+e*x)^(5+m)/_ + (e^6*(5+m))+b^5*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 5 5 5 4 5 3 5 2 5 5 m + 6 +--R (b m + 15b m + 85b m + 225b m + 274b m + 120b )(e x + d) +--R + +--R 4 5 5 4 5 4 4 5 3 +--R (5a b e - 5b d)m + (80a b e - 80b d)m + (475a b e - 475b d)m +--R + +--R 4 5 2 4 5 4 5 +--R (1300a b e - 1300b d)m + (1620a b e - 1620b d)m + 720a b e - 720b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 3 2 4 5 2 5 +--R (10a b e - 20a b d e + 10b d )m +--R + +--R 2 3 2 4 5 2 4 +--R (170a b e - 340a b d e + 170b d )m +--R + +--R 2 3 2 4 5 2 3 +--R (1070a b e - 2140a b d e + 1070b d )m +--R + +--R 2 3 2 4 5 2 2 +--R (3070a b e - 6140a b d e + 3070b d )m +--R + +--R 2 3 2 4 5 2 2 3 2 4 +--R (3960a b e - 7920a b d e + 3960b d )m + 1800a b e - 3600a b d e +--R + +--R 5 2 +--R 1800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e - 30a b d e + 30a b d e - 10b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (180a b e - 540a b d e + 540a b d e - 180b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (1210a b e - 3630a b d e + 3630a b d e - 1210b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (3720a b e - 11160a b d e + 11160a b d e - 3720b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 2 3 +--R (5080a b e - 15240a b d e + 15240a b d e - 5080b d )m + 2400a b e +--R + +--R 2 3 2 4 2 5 3 +--R - 7200a b d e + 7200a b d e - 2400b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e - 20a b d e + 30a b d e - 20a b d e + 5b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 4 +--R (95a b e - 380a b d e + 570a b d e - 380a b d e + 95b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (685a b e - 2740a b d e + 4110a b d e - 2740a b d e + 685b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 2305a b e - 9220a b d e + 13830a b d e - 9220a b d e +--R + +--R 5 4 +--R 2305b d +--R * +--R 2 +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 3510a b e - 14040a b d e + 21060a b d e - 14040a b d e +--R + +--R 5 4 +--R 3510b d +--R * +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R 1800a b e - 7200a b d e + 10800a b d e - 7200a b d e + 1800b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e - 5a b d e + 10a b d e - 10a b d e + 5a b d e - b d )m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 20a e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 5 5 +--R - 20b d +--R * +--R 4 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 155a e - 775a b d e + 1550a b d e - 1550a b d e + 775a b d e +--R + +--R 5 5 +--R - 155b d +--R * +--R 3 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R 580a e - 2900a b d e + 5800a b d e - 5800a b d e +--R + +--R 4 4 5 5 +--R 2900a b d e - 580b d +--R * +--R 2 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R 1044a e - 5220a b d e + 10440a b d e - 10440a b d e +--R + +--R 4 4 5 5 +--R 5220a b d e - 1044b d +--R * +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 720a e - 3600a b d e + 7200a b d e - 7200a b d e + 3600a b d e +--R + +--R 5 5 +--R - 720b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 38 + +--S 39 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 39 + +)clear all + +--S 40 of 765 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 11 4 6 5 5 10 2 3 6 4 5 5 2 4 9 +--R b e x + (5a b e + 6b d e )x + (10a b e + 30a b d e + 15b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 8 +--R (10a b e + 60a b d e + 75a b d e + 20b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 7 +--R (5a b e + 60a b d e + 150a b d e + 100a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 6 +--R (a e + 30a b d e + 150a b d e + 200a b d e + 75a b d e + 6b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 5 +--R (6a d e + 75a b d e + 200a b d e + 150a b d e + 30a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 4 +--R (15a d e + 100a b d e + 150a b d e + 60a b d e + 5a b d )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 3 +--R (20a d e + 75a b d e + 60a b d e + 10a b d )x +--R + +--R 5 4 2 4 5 3 2 6 2 5 5 4 6 5 6 +--R (15a d e + 30a b d e + 10a b d )x + (6a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 40 + +--S 41 of 765 +r0:=-1/7*(b*d-a*e)^5*(d+e*x)^7/e^6+5/8*b*(b*d-a*e)^4*(d+e*x)^8/e^6-_ + 10/9*b^2*(b*d-a*e)^3*(d+e*x)^9/e^6+b^3*(b*d-a*e)^2*(d+e*x)^10/e^6-_ + 5/11*b^4*(b*d-a*e)*(d+e*x)^11/e^6+1/12*b^5*(d+e*x)^12/e^6 +--R +--R +--R (2) +--R 1 5 12 12 5 4 12 6 5 11 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 2 3 12 4 11 3 5 2 10 10 +--R (a b e + 3a b d e + - b d e )x +--R 2 +--R + +--R 10 3 2 12 20 2 3 11 25 4 2 10 20 5 3 9 9 +--R (-- a b e + -- a b d e + -- a b d e + -- b d e )x +--R 9 3 3 9 +--R + +--R 5 4 12 15 3 2 11 75 2 3 2 10 25 4 3 9 15 5 4 8 8 +--R (- a b e + -- a b d e + -- a b d e + -- a b d e + -- b d e )x +--R 8 2 4 2 8 +--R + +--R 1 5 12 30 4 11 150 3 2 2 10 200 2 3 3 9 75 4 4 8 +--R - a e + -- a b d e + --- a b d e + --- a b d e + -- a b d e +--R 7 7 7 7 7 +--R + +--R 6 5 5 7 +--R - b d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 5 11 25 4 2 10 100 3 2 3 9 2 3 4 8 4 5 7 +--R a d e + -- a b d e + --- a b d e + 25a b d e + 5a b d e +--R 2 3 +--R + +--R 1 5 6 6 +--R - b d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 2 4 8 2 3 5 7 4 6 6 5 +--R (3a d e + 20a b d e + 30a b d e + 12a b d e + a b d e )x +--R + +--R 5 3 9 75 4 4 8 3 2 5 7 5 2 3 6 6 4 +--R (5a d e + -- a b d e + 15a b d e + - a b d e )x +--R 4 2 +--R + +--R 5 4 8 4 5 7 10 3 2 6 6 3 5 5 7 5 4 6 6 2 +--R (5a d e + 10a b d e + -- a b d e )x + (3a d e + - a b d e )x +--R 3 2 +--R + +--R 5 6 6 1 5 7 5 5 4 8 4 5 3 2 9 3 1 2 3 10 2 +--R a d e x + - a d e - -- a b d e + --- a b d e - -- a b d e +--R 7 56 126 84 +--R + +--R 1 4 11 1 5 12 +--R --- a b d e - ---- b d +--R 462 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 41 + +--S 42 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 42 + +)clear all + +--S 43 of 765 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 5 10 4 5 5 4 9 2 3 5 4 4 5 2 3 8 +--R b e x + (5a b e + 5b d e )x + (10a b e + 25a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 7 +--R (10a b e + 50a b d e + 50a b d e + 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 6 +--R (5a b e + 50a b d e + 100a b d e + 50a b d e + 5b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e + 25a b d e + 100a b d e + 100a b d e + 25a b d e + b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4 +--R (5a d e + 50a b d e + 100a b d e + 50a b d e + 5a b d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 3 +--R (10a d e + 50a b d e + 50a b d e + 10a b d )x +--R + +--R 5 3 2 4 4 3 2 5 2 5 4 4 5 5 5 +--R (10a d e + 25a b d e + 10a b d )x + (5a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 43 + +--S 44 of 765 +r0:=1/6*(b*d-a*e)^5*(a+b*x)^6/b^6+5/7*e*(b*d-a*e)^4*(a+b*x)^7/b^6+_ + 5/4*e^2*(b*d-a*e)^3*(a+b*x)^8/b^6+10/9*e^3*(b*d-a*e)^2*(a+b*x)^9/b^6+_ + 1/2*e^4*(b*d-a*e)*(a+b*x)^10/b^6+1/11*e^5*(a+b*x)^11/b^6 +--R +--R +--R (2) +--R 1 11 5 11 1 10 5 1 11 4 10 +--R -- b e x + (- a b e + - b d e )x +--R 11 2 2 +--R + +--R 10 2 9 5 25 10 4 10 11 2 3 9 +--R (-- a b e + -- a b d e + -- b d e )x +--R 9 9 9 +--R + +--R 5 3 8 5 25 2 9 4 25 10 2 3 5 11 3 2 8 +--R (- a b e + -- a b d e + -- a b d e + - b d e )x +--R 4 4 4 4 +--R + +--R 5 4 7 5 50 3 8 4 100 2 9 2 3 50 10 3 2 5 11 4 7 +--R (- a b e + -- a b d e + --- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 7 +--R + +--R 1 5 6 5 25 4 7 4 50 3 8 2 3 50 2 9 3 2 25 10 4 +--R - a b e + -- a b d e + -- a b d e + -- a b d e + -- a b d e +--R 6 6 3 3 6 +--R + +--R 1 11 5 +--R - b d +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 6 4 4 7 2 3 3 8 3 2 2 9 4 10 5 5 +--R (a b d e + 10a b d e + 20a b d e + 10a b d e + a b d )x +--R + +--R 5 5 6 2 3 25 4 7 3 2 25 3 8 4 5 2 9 5 4 +--R (- a b d e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 10 5 6 3 2 25 4 7 4 10 3 8 5 3 5 5 6 4 5 4 7 5 2 +--R (-- a b d e + -- a b d e + -- a b d )x + (- a b d e + - a b d )x +--R 3 3 3 2 2 +--R + +--R 5 6 5 1 11 5 1 10 4 5 9 2 2 3 5 8 3 3 2 +--R a b d x - ---- a e + --- a b d e - --- a b d e + -- a b d e +--R 2772 252 252 84 +--R + +--R 5 7 4 4 1 6 5 5 +--R - -- a b d e + - a b d +--R 42 6 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 44 + +--S 45 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 765 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 46 + +--S 47 of 765 +r0:=1/6*(b*d-a*e)^4*(a+b*x)^6/b^5+4/7*e*(b*d-a*e)^3*(a+b*x)^7/b^5+3/4*e^2*_ + (b*d-a*e)^2*(a+b*x)^8/b^5+4/9*e^3*(b*d-a*e)*(a+b*x)^9/b^5+1/10*e^4*_ + (a+b*x)^10/b^5 +--R +--R +--R (2) +--R 1 10 4 10 5 9 4 4 10 3 9 +--R -- b e x + (- a b e + - b d e )x +--R 10 9 9 +--R + +--R 5 2 8 4 5 9 3 3 10 2 2 8 +--R (- a b e + - a b d e + - b d e )x +--R 4 2 4 +--R + +--R 10 3 7 4 40 2 8 3 30 9 2 2 4 10 3 7 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 +--R + +--R 5 4 6 4 20 3 7 3 2 8 2 2 10 9 3 1 10 4 6 +--R (- a b e + -- a b d e + 10a b d e + -- a b d e + - b d )x +--R 6 3 3 6 +--R + +--R 1 5 5 4 4 6 3 3 7 2 2 2 8 3 9 4 5 +--R (- a b e + 4a b d e + 12a b d e + 8a b d e + a b d )x +--R 5 +--R + +--R 5 5 3 15 4 6 2 2 3 7 3 5 2 8 4 4 +--R (a b d e + -- a b d e + 10a b d e + - a b d )x +--R 2 2 +--R + +--R 5 5 2 2 20 4 6 3 10 3 7 4 3 5 5 3 5 4 6 4 2 +--R (2a b d e + -- a b d e + -- a b d )x + (2a b d e + - a b d )x +--R 3 3 2 +--R + +--R 5 5 4 1 10 4 1 9 3 1 8 2 2 2 2 7 3 3 1 6 4 4 +--R a b d x + ---- a e - --- a b d e + -- a b d e - -- a b d e + - a b d +--R 1260 126 28 21 6 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 48 + +)clear all + +--S 49 of 765 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 49 + +--S 50 of 765 +r0:=1/6*(b*d-a*e)^3*(a+b*x)^6/b^4+3/7*e*(b*d-a*e)^2*(a+b*x)^7/b^4+_ + 3/8*e^2*(b*d-a*e)*(a+b*x)^8/b^4+1/9*e^3*(a+b*x)^9/b^4 +--R +--R +--R (2) +--R 1 9 3 9 5 8 3 3 9 2 8 +--R - b e x + (- a b e + - b d e )x +--R 9 8 8 +--R + +--R 10 2 7 3 15 8 2 3 9 2 7 +--R (-- a b e + -- a b d e + - b d e)x +--R 7 7 7 +--R + +--R 5 3 6 3 2 7 2 5 8 2 1 9 3 6 +--R (- a b e + 5a b d e + - a b d e + - b d )x +--R 3 2 6 +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (a b e + 6a b d e + 6a b d e + a b d )x +--R + +--R 1 5 4 3 15 4 5 2 15 3 6 2 5 2 7 3 4 +--R (- a b e + -- a b d e + -- a b d e + - a b d )x +--R 4 4 2 2 +--R + +--R 5 4 2 4 5 2 10 3 6 3 3 3 5 4 2 5 4 5 3 2 5 4 3 +--R (a b d e + 5a b d e + -- a b d )x + (- a b d e + - a b d )x + a b d x +--R 3 2 2 +--R + +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R - --- a e + -- a b d e - -- a b d e + - a b d +--R 504 56 14 6 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 50 + +--S 51 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 51 + +)clear all + +--S 52 of 765 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 52 + +--S 53 of 765 +r0:=1/6*(b*d-a*e)^2*(a+b*x)^6/b^3+2/7*e*(b*d-a*e)*(a+b*x)^7/b^3+_ + 1/8*e^2*(a+b*x)^8/b^3 +--R +--R +--R (2) +--R 1 8 2 8 5 7 2 2 8 7 5 2 6 2 5 7 1 8 2 6 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 8 7 7 3 3 6 +--R + +--R 3 5 2 2 6 7 2 5 5 4 4 2 3 5 5 2 6 2 4 +--R (2a b e + 4a b d e + a b d )x + (- a b e + 5a b d e + - a b d )x +--R 4 2 +--R + +--R 1 5 3 2 10 4 4 10 3 5 2 3 5 3 5 4 4 2 2 5 3 2 +--R (- a b e + -- a b d e + -- a b d )x + (a b d e + - a b d )x + a b d x +--R 3 3 3 2 +--R + +--R 1 8 2 1 7 1 6 2 2 +--R --- a e - -- a b d e + - a b d +--R 168 21 6 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 53 + +--S 54 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 54 + +)clear all + +--S 55 of 765 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R Type: Polynomial(Integer) +--E 55 + +--S 56 of 765 +r0:=1/6*(b*d-a*e)*(a+b*x)^6/b^2+1/7*e*(a+b*x)^7/b^2 +--R +--R +--R (2) +--R 1 7 7 5 6 1 7 6 2 5 6 5 +--R - b e x + (- a b e + - b d)x + (2a b e + a b d)x +--R 7 6 6 +--R + +--R 5 3 4 5 2 5 4 5 4 3 10 3 4 3 1 5 2 5 4 3 2 +--R (- a b e + - a b d)x + (- a b e + -- a b d)x + (- a b e + - a b d)x +--R 2 2 3 3 2 2 +--R + +--R 5 2 1 7 1 6 +--R a b d x - -- a e + - a b d +--R 42 6 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 56 + +--S 57 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Polynomial(Integer) +--E 58 + +--S 59 of 765 +r0:=1/6*(a+b*x)^6/b +--R +--R +--R 1 6 6 5 5 5 2 4 4 10 3 3 3 5 4 2 2 5 1 6 +--R - b x + a b x + - a b x + -- a b x + - a b x + a b x + - a +--R 6 2 3 2 6 +--R (2) ---------------------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 59 + +--S 60 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 765 +r0:=b*(b*d-a*e)^4*x/e^5-1/2*(b*d-a*e)^3*(a+b*x)^2/e^4+1/3*(b*d-a*e)^2*_ + (a+b*x)^3/e^3-1/4*(b*d-a*e)*(a+b*x)^4/e^2+1/5*(a+b*x)^5/e-(b*d-a*e)^5*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 5 5 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b e x + (75a b e - 15b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b e - 100a b d e + 20b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b e - 300a b d e + 150a b d e - 30b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (300a b e - 600a b d e + 600a b d e - 300a b d e + 60b d e)x + 77a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 +--R - 145a b d e + 110a b d e - 30a b d e +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 62 + +--S 63 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 64 + +--S 65 of 765 +r0:=-10*b^2*(b*d-a*e)^3*x/e^5+(b*d-a*e)^5/(e^6*(d+e*x))+5*b^3*(b*d-a*e)^2*_ + (d+e*x)^2/e^6-5/3*b^4*(b*d-a*e)*(d+e*x)^3/e^6+1/4*b^5*(d+e*x)^4/e^6+_ + 5*b*(b*d-a*e)^4*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b e x + (20a b e - 5b d e )x + (60a b e - 40a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b e - 180a b d e + 120a b d e - 30b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 5 5 4 4 +--R (120a b d e - 180a b d e + 80a b d e - 5b d e)x - 12a e + 60a b d e +--R + +--R 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 120a b d e + 180a b d e - 160a b d e + 55b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 65 + +--S 66 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 66 + +)clear all + +--S 67 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 67 + +--S 68 of 765 +r0:=10*b^3*(b*d-a*e)^2*x/e^5+1/2*(b*d-a*e)^5/(e^6*(d+e*x)^2)-_ + 5*b*(b*d-a*e)^4/(e^6*(d+e*x))-5/2*b^4*(b*d-a*e)*(d+e*x)^2/e^6+_ + 1/3*b^5*(d+e*x)^3/e^6-10*b^2*(b*d-a*e)^3*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b d e - 360a b d e + 360a b d e - 120b d e)x + 60a b d e +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b e x + (15a b e - 5b d e )x + (60a b e - 60a b d e + 20b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (120a b d e - 150a b d e + 50b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b e + 120a b d e - 120a b d e + 60a b d e - 20b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b d e + 90a b d e - 150a b d e + 120a b d e - 40b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 68 + +--S 69 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 69 + +)clear all + +--S 70 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^4 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 70 + +--S 71 of 765 +r0:=-b^4*(4*b*d-5*a*e)*x/e^5+1/2*b^5*x^2/e^4+1/3*(b*d-a*e)^5/(e^6*(d+e*x)^3)-_ + 5/2*b*(b*d-a*e)^4/(e^6*(d+e*x)^2)+10*b^2*(b*d-a*e)^3/(e^6*(d+e*x))+_ + 10*b^3*(b*d-a*e)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e - 360a b d e + 180b d e )x +--R + +--R 2 3 2 3 4 3 2 5 4 2 3 3 2 4 4 +--R (180a b d e - 360a b d e + 180b d e)x + 60a b d e - 120a b d e +--R + +--R 5 5 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 4 4 5 2 3 3 +--R 3b e x + (30a b e - 15b d e )x + (90a b d e - 63b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 60a b e + 180a b d e - 90a b d e - 9b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 15a b e - 60a b d e + 270a b d e - 270a b d e + 81b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 5a b d e - 20a b d e + 110a b d e - 130a b d e + 47b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 71 + +--S 72 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 of 765 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 73 + +--S 74 of 765 +r0:=-(b*d-a*e)^7*(d+e*x)^(1+m)/(e^8*(1+m))+7*b*(b*d-a*e)^6*(d+e*x)^(2+m)/_ + (e^8*(2+m))-21*b^2*(b*d-a*e)^5*(d+e*x)^(3+m)/(e^8*(3+m))+35*b^3*_ + (b*d-a*e)^4*(d+e*x)^(4+m)/(e^8*(4+m))-35*b^4*(b*d-a*e)^3*(d+e*x)^(5+m)/_ + (e^8*(5+m))+21*b^5*(b*d-a*e)^2*(d+e*x)^(6+m)/(e^8*(6+m))-7*b^6*(b*d-_ + a*e)*(d+e*x)^(7+m)/(e^8*(7+m))+b^7*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R b m + 28b m + 322b m + 1960b m + 6769b m + 13132b m + 13068b m +--R + +--R 7 +--R 5040b +--R * +--R m + 8 +--R (e x + d) +--R + +--R 6 7 7 6 7 6 6 7 5 +--R (7a b e - 7b d)m + (203a b e - 203b d)m + (2401a b e - 2401b d)m +--R + +--R 6 7 4 6 7 3 +--R (14945a b e - 14945b d)m + (52528a b e - 52528b d)m +--R + +--R 6 7 2 6 7 6 +--R (103292a b e - 103292b d)m + (103824a b e - 103824b d)m + 40320a b e +--R + +--R 7 +--R - 40320b d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 5 2 6 7 2 7 +--R (21a b e - 42a b d e + 21b d )m +--R + +--R 2 5 2 6 7 2 6 +--R (630a b e - 1260a b d e + 630b d )m +--R + +--R 2 5 2 6 7 2 5 +--R (7686a b e - 15372a b d e + 7686b d )m +--R + +--R 2 5 2 6 7 2 4 +--R (49140a b e - 98280a b d e + 49140b d )m +--R + +--R 2 5 2 6 7 2 3 +--R (176589a b e - 353178a b d e + 176589b d )m +--R + +--R 2 5 2 6 7 2 2 +--R (353430a b e - 706860a b d e + 353430b d )m +--R + +--R 2 5 2 6 7 2 2 5 2 +--R (360024a b e - 720048a b d e + 360024b d )m + 141120a b e +--R + +--R 6 7 2 +--R - 282240a b d e + 141120b d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e - 105a b d e + 105a b d e - 35b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 6 +--R (1085a b e - 3255a b d e + 3255a b d e - 1085b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 5 +--R (13685a b e - 41055a b d e + 41055a b d e - 13685b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (90335a b e - 271005a b d e + 271005a b d e - 90335b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (334040a b e - 1002120a b d e + 1002120a b d e - 334040b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 2 +--R (684740a b e - 2054220a b d e + 2054220a b d e - 684740b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R (710640a b e - 2131920a b d e + 2131920a b d e - 710640b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R 282240a b e - 846720a b d e + 846720a b d e - 282240b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (35a b e - 140a b d e + 210a b d e - 140a b d e + 35b d )m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 6 +--R (1120a b e - 4480a b d e + 6720a b d e - 4480a b d e + 1120b d )m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 14630a b e - 58520a b d e + 87780a b d e - 58520a b d e +--R + +--R 7 4 +--R 14630b d +--R * +--R 5 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 100240a b e - 400960a b d e + 601440a b d e - 400960a b d e +--R + +--R 7 4 +--R 100240b d +--R * +--R 4 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 384755a b e - 1539020a b d e + 2308530a b d e - 1539020a b d e +--R + +--R 7 4 +--R 384755b d +--R * +--R 3 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 815920a b e - 3263680a b d e + 4895520a b d e - 3263680a b d e +--R + +--R 7 4 +--R 815920b d +--R * +--R 2 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 870660a b e - 3482640a b d e + 5223960a b d e - 3482640a b d e +--R + +--R 7 4 +--R 870660b d +--R * +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 352800a b e - 1411200a b d e + 2116800a b d e - 1411200a b d e +--R + +--R 7 4 +--R 352800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R 21a b e - 105a b d e + 210a b d e - 210a b d e + 105a b d e +--R + +--R 7 5 +--R - 21b d +--R * +--R 7 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 693a b e - 3465a b d e + 6930a b d e - 6930a b d e +--R + +--R 6 4 7 5 +--R 3465a b d e - 693b d +--R * +--R 6 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 9387a b e - 46935a b d e + 93870a b d e - 93870a b d e +--R + +--R 6 4 7 5 +--R 46935a b d e - 9387b d +--R * +--R 5 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 67095a b e - 335475a b d e + 670950a b d e - 670950a b d e +--R + +--R 6 4 7 5 +--R 335475a b d e - 67095b d +--R * +--R 4 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 270144a b e - 1350720a b d e + 2701440a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 2701440a b d e + 1350720a b d e - 270144b d +--R * +--R 3 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 602532a b e - 3012660a b d e + 6025320a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 6025320a b d e + 3012660a b d e - 602532b d +--R * +--R 2 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 673008a b e - 3365040a b d e + 6730080a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 6730080a b d e + 3365040a b d e - 673008b d +--R * +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 282240a b e - 1411200a b d e + 2822400a b d e - 2822400a b d e +--R + +--R 6 4 7 5 +--R 1411200a b d e - 282240b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 7a b e - 42a b d e + 105a b d e - 140a b d e + 105a b d e +--R + +--R 6 5 7 6 +--R - 42a b d e + 7b d +--R * +--R 7 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 238a b e - 1428a b d e + 3570a b d e - 4760a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 3570a b d e - 1428a b d e + 238b d +--R * +--R 6 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 3346a b e - 20076a b d e + 50190a b d e - 66920a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 50190a b d e - 20076a b d e + 3346b d +--R * +--R 5 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 25060a b e - 150360a b d e + 375900a b d e - 501200a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 375900a b d e - 150360a b d e + 25060b d +--R * +--R 4 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 107023a b e - 642138a b d e + 1605345a b d e - 2140460a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 1605345a b d e - 642138a b d e + 107023b d +--R * +--R 3 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R 256942a b e - 1541652a b d e + 3854130a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R - 5138840a b d e + 3854130a b d e - 1541652a b d e + 256942b d +--R * +--R 2 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R 312984a b e - 1877904a b d e + 4694760a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R - 6259680a b d e + 4694760a b d e - 1877904a b d e + 312984b d +--R * +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 141120a b e - 846720a b d e + 2116800a b d e - 2822400a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 2116800a b d e - 846720a b d e + 141120b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R a e - 7a b d e + 21a b d e - 35a b d e + 35a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 21a b d e + 7a b d e - b d +--R * +--R 7 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 35a e - 245a b d e + 735a b d e - 1225a b d e + 1225a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 735a b d e + 245a b d e - 35b d +--R * +--R 6 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 511a e - 3577a b d e + 10731a b d e - 17885a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 17885a b d e - 10731a b d e + 3577a b d e - 511b d +--R * +--R 5 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 4025a e - 28175a b d e + 84525a b d e - 140875a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 140875a b d e - 84525a b d e + 28175a b d e - 4025b d +--R * +--R 4 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 18424a e - 128968a b d e + 386904a b d e - 644840a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 644840a b d e - 386904a b d e + 128968a b d e - 18424b d +--R * +--R 3 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 48860a e - 342020a b d e + 1026060a b d e - 1710100a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 1710100a b d e - 1026060a b d e + 342020a b d e - 48860b d +--R * +--R 2 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 69264a e - 484848a b d e + 1454544a b d e - 2424240a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 2424240a b d e - 1454544a b d e + 484848a b d e - 69264b d +--R * +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 40320a e - 282240a b d e + 846720a b d e - 1411200a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 1411200a b d e - 846720a b d e + 282240a b d e - 40320b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 74 + +--S 75 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 765 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 6 13 6 6 7 5 12 2 5 6 6 5 7 2 4 11 +--R b e x + (7a b e + 6b d e )x + (21a b e + 42a b d e + 15b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 10 +--R (35a b e + 126a b d e + 105a b d e + 20b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 9 +--R (35a b e + 210a b d e + 315a b d e + 140a b d e + 15b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 21a b e + 210a b d e + 525a b d e + 420a b d e + 105a b d e +--R + +--R 7 5 +--R 6b d e +--R * +--R 8 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 7a b e + 126a b d e + 525a b d e + 700a b d e + 315a b d e +--R + +--R 6 5 7 6 +--R 42a b d e + b d +--R * +--R 7 +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R a e + 42a b d e + 315a b d e + 700a b d e + 525a b d e +--R + +--R 2 5 5 6 6 +--R 126a b d e + 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 +--R 6a d e + 105a b d e + 420a b d e + 525a b d e + 210a b d e +--R + +--R 2 5 6 +--R 21a b d +--R * +--R 5 +--R x +--R + +--R 7 2 4 6 3 3 5 2 4 2 4 3 5 3 4 6 4 +--R (15a d e + 140a b d e + 315a b d e + 210a b d e + 35a b d )x +--R + +--R 7 3 3 6 4 2 5 2 5 4 3 6 3 +--R (20a d e + 105a b d e + 126a b d e + 35a b d )x +--R + +--R 7 4 2 6 5 5 2 6 2 7 5 6 6 7 6 +--R (15a d e + 42a b d e + 21a b d )x + (6a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 765 +r0:=1/8*(b*d-a*e)^6*(a+b*x)^8/b^7+2/3*e*(b*d-a*e)^5*(a+b*x)^9/b^7+_ + 3/2*e^2*(b*d-a*e)^4*(a+b*x)^10/b^7+20/11*e^3*(b*d-a*e)^3*(a+b*x)^11/b^7+_ + 5/4*e^4*(b*d-a*e)^2*(a+b*x)^12/b^7+6/13*e^5*(b*d-a*e)*(a+b*x)^13/b^7+_ + 1/14*e^6*(a+b*x)^14/b^7 +--R +--R +--R (2) +--R 1 14 6 14 7 13 6 6 14 5 13 +--R -- b e x + (-- a b e + -- b d e )x +--R 14 13 13 +--R + +--R 7 2 12 6 7 13 5 5 14 2 4 12 +--R (- a b e + - a b d e + - b d e )x +--R 4 2 4 +--R + +--R 35 3 11 6 126 2 12 5 105 13 2 4 20 14 3 3 11 +--R (-- a b e + --- a b d e + --- a b d e + -- b d e )x +--R 11 11 11 11 +--R + +--R 7 4 10 6 3 11 5 63 2 12 2 4 13 3 3 3 14 4 2 10 +--R (- a b e + 21a b d e + -- a b d e + 14a b d e + - b d e )x +--R 2 2 2 +--R + +--R 7 5 9 6 70 4 10 5 175 3 11 2 4 140 2 12 3 3 +--R - a b e + -- a b d e + --- a b d e + --- a b d e +--R 3 3 3 3 +--R + +--R 35 13 4 2 2 14 5 +--R -- a b d e + - b d e +--R 3 3 +--R * +--R 9 +--R x +--R + +--R 7 6 8 6 63 5 9 5 525 4 10 2 4 175 3 11 3 3 +--R - a b e + -- a b d e + --- a b d e + --- a b d e +--R 8 4 8 2 +--R + +--R 315 2 12 4 2 21 13 5 1 14 6 +--R --- a b d e + -- a b d e + - b d +--R 8 4 8 +--R * +--R 8 +--R x +--R + +--R 1 7 7 6 6 8 5 5 9 2 4 4 10 3 3 3 11 4 2 +--R - a b e + 6a b d e + 45a b d e + 100a b d e + 75a b d e +--R 7 +--R + +--R 2 12 5 13 6 +--R 18a b d e + a b d +--R * +--R 7 +--R x +--R + +--R 7 7 5 35 6 8 2 4 5 9 3 3 175 4 10 4 2 3 11 5 +--R a b d e + -- a b d e + 70a b d e + --- a b d e + 35a b d e +--R 2 2 +--R + +--R 7 2 12 6 +--R - a b d +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 7 2 4 6 8 3 3 5 9 4 2 4 10 5 3 11 6 5 +--R (3a b d e + 28a b d e + 63a b d e + 42a b d e + 7a b d )x +--R + +--R 7 7 3 3 105 6 8 4 2 63 5 9 5 35 4 10 6 4 +--R (5a b d e + --- a b d e + -- a b d e + -- a b d )x +--R 4 2 4 +--R + +--R 7 7 4 2 6 8 5 5 9 6 3 7 7 5 7 6 8 6 2 7 7 6 +--R (5a b d e + 14a b d e + 7a b d )x + (3a b d e + - a b d )x + a b d x +--R 2 +--R + +--R 1 14 6 1 13 5 1 12 2 2 4 1 11 3 3 3 +--R ----- a e - ---- a b d e + --- a b d e - -- a b d e +--R 24024 1716 264 66 +--R + +--R 1 10 4 4 2 1 9 5 5 1 8 6 6 +--R -- a b d e - -- a b d e + - a b d +--R 24 12 8 +--R / +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 765 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 5 12 6 5 7 4 11 2 5 5 6 4 7 2 3 10 +--R b e x + (7a b e + 5b d e )x + (21a b e + 35a b d e + 10b d e )x +--R + +--R 3 4 5 2 5 4 6 2 3 7 3 2 9 +--R (35a b e + 105a b d e + 70a b d e + 10b d e )x +--R + +--R 4 3 5 3 4 4 2 5 2 3 6 3 2 7 4 8 +--R (35a b e + 175a b d e + 210a b d e + 70a b d e + 5b d e)x +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 7 5 7 +--R (21a b e + 175a b d e + 350a b d e + 210a b d e + 35a b d e + b d )x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 7a b e + 105a b d e + 350a b d e + 350a b d e + 105a b d e +--R + +--R 6 5 +--R 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 5 +--R (a e + 35a b d e + 210a b d e + 350a b d e + 175a b d e + 21a b d )x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 4 +--R (5a d e + 70a b d e + 210a b d e + 175a b d e + 35a b d )x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 3 +--R (10a d e + 70a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 2 6 4 5 2 5 2 7 4 6 5 7 5 +--R (10a d e + 35a b d e + 21a b d )x + (5a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 79 + +--S 80 of 765 +r0:=1/8*(b*d-a*e)^5*(a+b*x)^8/b^6+5/9*e*(b*d-a*e)^4*(a+b*x)^9/b^6+e^2*_ + (b*d-a*e)^3*(a+b*x)^10/b^6+10/11*e^3*(b*d-a*e)^2*(a+b*x)^11/b^6+_ + 5/12*e^4*(b*d-a*e)*(a+b*x)^12/b^6+1/13*e^5*(a+b*x)^13/b^6 +--R +--R +--R (2) +--R 1 13 5 13 7 12 5 5 13 4 12 +--R -- b e x + (-- a b e + -- b d e )x +--R 13 12 12 +--R + +--R 21 2 11 5 35 12 4 10 13 2 3 11 +--R (-- a b e + -- a b d e + -- b d e )x +--R 11 11 11 +--R + +--R 7 3 10 5 21 2 11 4 12 2 3 13 3 2 10 +--R (- a b e + -- a b d e + 7a b d e + b d e )x +--R 2 2 +--R + +--R 35 4 9 5 175 3 10 4 70 2 11 2 3 70 12 3 2 5 13 4 9 +--R (-- a b e + --- a b d e + -- a b d e + -- a b d e + - b d e)x +--R 9 9 3 9 9 +--R + +--R 21 5 8 5 175 4 9 4 175 3 10 2 3 105 2 11 3 2 +--R -- a b e + --- a b d e + --- a b d e + --- a b d e +--R 8 8 4 4 +--R + +--R 35 12 4 1 13 5 +--R -- a b d e + - b d +--R 8 8 +--R * +--R 8 +--R x +--R + +--R 6 7 5 5 8 4 4 9 2 3 3 10 3 2 2 11 4 12 5 7 +--R (a b e + 15a b d e + 50a b d e + 50a b d e + 15a b d e + a b d )x +--R + +--R 1 7 6 5 35 6 7 4 5 8 2 3 175 4 9 3 2 175 3 10 4 +--R - a b e + -- a b d e + 35a b d e + --- a b d e + --- a b d e +--R 6 6 3 6 +--R + +--R 7 2 11 5 +--R - a b d +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 6 4 6 7 2 3 5 8 3 2 4 9 4 3 10 5 5 +--R (a b d e + 14a b d e + 42a b d e + 35a b d e + 7a b d )x +--R + +--R 5 7 6 2 3 35 6 7 3 2 105 5 8 4 35 4 9 5 4 +--R (- a b d e + -- a b d e + --- a b d e + -- a b d )x +--R 2 2 4 4 +--R + +--R 10 7 6 3 2 35 6 7 4 5 8 5 3 5 7 6 4 7 6 7 5 2 +--R (-- a b d e + -- a b d e + 7a b d )x + (- a b d e + - a b d )x +--R 3 3 2 2 +--R + +--R 7 6 5 1 13 5 1 12 4 1 11 2 2 3 1 10 3 3 2 +--R a b d x - ----- a e + --- a b d e - --- a b d e + -- a b d e +--R 10296 792 132 36 +--R + +--R 5 9 4 4 1 8 5 5 +--R - -- a b d e + - a b d +--R 72 8 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 80 + +--S 81 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 of 765 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 4 11 6 4 7 3 10 2 5 4 6 3 7 2 2 9 +--R b e x + (7a b e + 4b d e )x + (21a b e + 28a b d e + 6b d e )x +--R + +--R 3 4 4 2 5 3 6 2 2 7 3 8 +--R (35a b e + 84a b d e + 42a b d e + 4b d e)x +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (35a b e + 140a b d e + 126a b d e + 28a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 6 +--R (21a b e + 140a b d e + 210a b d e + 84a b d e + 7a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 5 +--R (7a b e + 84a b d e + 210a b d e + 140a b d e + 21a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 4 +--R (a e + 28a b d e + 126a b d e + 140a b d e + 35a b d )x +--R + +--R 7 3 6 2 2 5 2 3 4 3 4 3 +--R (4a d e + 42a b d e + 84a b d e + 35a b d )x +--R + +--R 7 2 2 6 3 5 2 4 2 7 3 6 4 7 4 +--R (6a d e + 28a b d e + 21a b d )x + (4a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 82 + +--S 83 of 765 +r0:=1/8*(b*d-a*e)^4*(a+b*x)^8/b^5+4/9*e*(b*d-a*e)^3*(a+b*x)^9/b^5+3/5*e^2*_ + (b*d-a*e)^2*(a+b*x)^10/b^5+4/11*e^3*(b*d-a*e)*(a+b*x)^11/b^5+1/12*e^4*_ + (a+b*x)^12/b^5 +--R +--R +--R (2) +--R 1 12 4 12 7 11 4 4 12 3 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 21 2 10 4 14 11 3 3 12 2 2 10 +--R (-- a b e + -- a b d e + - b d e )x +--R 10 5 5 +--R + +--R 35 3 9 4 28 2 10 3 14 11 2 2 4 12 3 9 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 9 3 3 9 +--R + +--R 35 4 8 4 35 3 9 3 63 2 10 2 2 7 11 3 1 12 4 8 +--R (-- a b e + -- a b d e + -- a b d e + - a b d e + - b d )x +--R 8 2 4 2 8 +--R + +--R 5 7 4 4 8 3 3 9 2 2 2 10 3 11 4 7 +--R (3a b e + 20a b d e + 30a b d e + 12a b d e + a b d )x +--R + +--R 7 6 6 4 5 7 3 4 8 2 2 70 3 9 3 7 2 10 4 6 +--R (- a b e + 14a b d e + 35a b d e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 1 7 5 4 28 6 6 3 126 5 7 2 2 4 8 3 3 9 4 5 +--R (- a b e + -- a b d e + --- a b d e + 28a b d e + 7a b d )x +--R 5 5 5 +--R + +--R 7 5 3 21 6 6 2 2 5 7 3 35 4 8 4 4 +--R (a b d e + -- a b d e + 21a b d e + -- a b d )x +--R 2 4 +--R + +--R 7 5 2 2 28 6 6 3 5 7 4 3 7 5 3 7 6 6 4 2 7 5 4 +--R (2a b d e + -- a b d e + 7a b d )x + (2a b d e + - a b d )x + a b d x +--R 3 2 +--R + +--R 1 12 4 1 11 3 1 10 2 2 2 1 9 3 3 1 8 4 4 +--R ---- a e - --- a b d e + -- a b d e - -- a b d e + - a b d +--R 3960 330 60 18 8 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 83 + +--S 84 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 765 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 3 10 6 3 7 2 9 2 5 3 6 2 7 2 8 +--R b e x + (7a b e + 3b d e )x + (21a b e + 21a b d e + 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e + 63a b d e + 21a b d e + b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (35a b e + 105a b d e + 63a b d e + 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (21a b e + 105a b d e + 105a b d e + 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (7a b e + 63a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (a e + 21a b d e + 63a b d e + 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (3a d e + 21a b d e + 21a b d )x + (3a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 85 + +--S 86 of 765 +r0:=1/8*(b*d-a*e)^3*(a+b*x)^8/b^4+1/3*e*(b*d-a*e)^2*(a+b*x)^9/b^4+3/10*e^2*_ + (b*d-a*e)*(a+b*x)^10/b^4+1/11*e^3*(a+b*x)^11/b^4 +--R +--R +--R (2) +--R 1 11 3 11 7 10 3 3 11 2 10 +--R -- b e x + (-- a b e + -- b d e )x +--R 11 10 10 +--R + +--R 7 2 9 3 7 10 2 1 11 2 9 +--R (- a b e + - a b d e + - b d e)x +--R 3 3 3 +--R + +--R 35 3 8 3 63 2 9 2 21 10 2 1 11 3 8 +--R (-- a b e + -- a b d e + -- a b d e + - b d )x +--R 8 8 8 8 +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 7 +--R (5a b e + 15a b d e + 9a b d e + a b d )x +--R + +--R 7 5 6 3 35 4 7 2 35 3 8 2 7 2 9 3 6 +--R (- a b e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 7 6 5 3 63 5 6 2 4 7 2 3 8 3 5 +--R (- a b e + -- a b d e + 21a b d e + 7a b d )x +--R 5 5 +--R + +--R 1 7 4 3 21 6 5 2 63 5 6 2 35 4 7 3 4 +--R (- a b e + -- a b d e + -- a b d e + -- a b d )x +--R 4 4 4 4 +--R + +--R 7 4 2 6 5 2 5 6 3 3 3 7 4 2 7 6 5 3 2 7 4 3 +--R (a b d e + 7a b d e + 7a b d )x + (- a b d e + - a b d )x + a b d x +--R 2 2 +--R + +--R 1 11 3 1 10 2 1 9 2 2 1 8 3 3 +--R - ---- a e + --- a b d e - -- a b d e + - a b d +--R 1320 120 24 8 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 86 + +--S 87 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 765 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R b e x + (7a b e + 2b d e)x + (21a b e + 14a b d e + b d )x +--R + +--R 3 4 2 2 5 6 2 6 4 3 2 3 4 2 5 2 5 +--R (35a b e + 42a b d e + 7a b d )x + (35a b e + 70a b d e + 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 6 2 5 2 4 3 2 3 +--R (21a b e + 70a b d e + 35a b d )x + (7a b e + 42a b d e + 35a b d )x +--R + +--R 7 2 6 5 2 2 2 7 6 2 7 2 +--R (a e + 14a b d e + 21a b d )x + (2a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 88 + +--S 89 of 765 +r0:=1/8*(b*d-a*e)^2*(a+b*x)^8/b^3+2/9*e*(b*d-a*e)*(a+b*x)^9/b^3+1/10*e^2*_ + (a+b*x)^10/b^3 +--R +--R +--R (2) +--R 1 10 2 10 7 9 2 2 10 9 +--R -- b e x + (- a b e + - b d e)x +--R 10 9 9 +--R + +--R 21 2 8 2 7 9 1 10 2 8 3 7 2 2 8 9 2 7 +--R (-- a b e + - a b d e + - b d )x + (5a b e + 6a b d e + a b d )x +--R 8 4 8 +--R + +--R 35 4 6 2 35 3 7 7 2 8 2 6 +--R (-- a b e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 21 5 5 2 4 6 3 7 2 5 +--R (-- a b e + 14a b d e + 7a b d )x +--R 5 +--R + +--R 7 6 4 2 21 5 5 35 4 6 2 4 +--R (- a b e + -- a b d e + -- a b d )x +--R 4 2 4 +--R + +--R 1 7 3 2 14 6 4 5 5 2 3 7 3 7 6 4 2 2 7 3 2 +--R (- a b e + -- a b d e + 7a b d )x + (a b d e + - a b d )x + a b d x +--R 3 3 2 +--R + +--R 1 10 2 1 9 1 8 2 2 +--R --- a e - -- a b d e + - a b d +--R 360 36 8 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 765 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 8 6 7 7 2 5 6 6 3 4 2 5 5 +--R b e x + (7a b e + b d)x + (21a b e + 7a b d)x + (35a b e + 21a b d)x +--R + +--R 4 3 3 4 4 5 2 4 3 3 6 5 2 2 +--R (35a b e + 35a b d)x + (21a b e + 35a b d)x + (7a b e + 21a b d)x +--R + +--R 7 6 7 +--R (a e + 7a b d)x + a d +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 765 +r0:=1/8*(b*d-a*e)*(a+b*x)^8/b^2+1/9*e*(a+b*x)^9/b^2 +--R +--R +--R (2) +--R 1 9 9 7 8 1 9 8 2 7 8 7 +--R - b e x + (- a b e + - b d)x + (3a b e + a b d)x +--R 9 8 8 +--R + +--R 35 3 6 7 2 7 6 4 5 3 6 5 21 5 4 35 4 5 4 +--R (-- a b e + - a b d)x + (7a b e + 7a b d)x + (-- a b e + -- a b d)x +--R 6 2 4 4 +--R + +--R 7 6 3 5 4 3 1 7 2 7 6 3 2 7 2 1 9 1 8 +--R (- a b e + 7a b d)x + (- a b e + - a b d)x + a b d x - -- a e + - a b d +--R 3 2 2 72 8 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Polynomial(Integer) +--E 94 + +--S 95 of 765 +r0:=1/8*(a+b*x)^8/b +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - b x + a b x + - a b x + 7a b x + -- a b x + 7a b x + - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R a b x + - a +--R 8 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 95 + +--S 96 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 97 + +--S 98 of 765 +r0:=b*(b*d-a*e)^6*x/e^7-1/2*(b*d-a*e)^5*(a+b*x)^2/e^6+1/3*(b*d-a*e)^4*_ + (a+b*x)^3/e^5-1/4*(b*d-a*e)^3*(a+b*x)^4/e^4+1/5*(b*d-a*e)^2*(a+b*x)^5/e^3-_ + 1/6*(b*d-a*e)*(a+b*x)^6/e^2+1/7*(a+b*x)^7/e-(b*d-a*e)^7*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a e - 2940a b d e + 8820a b d e - 14700a b d e + 14700a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 8820a b d e + 2940a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b e x + (490a b e - 70b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (1764a b e - 588a b d e + 84b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (3675a b e - 2205a b d e + 735a b d e - 105b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (4900a b e - 4900a b d e + 2940a b d e - 980a b d e + 140b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4410a b e - 7350a b d e + 7350a b d e - 4410a b d e +--R + +--R 6 4 3 7 5 2 +--R 1470a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 2940a b e - 8820a b d e + 14700a b d e - 14700a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 8820a b d e - 2940a b d e + 420b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 669a e - 2163a b d e + 3339a b d e - 2765a b d e + 1190a b d e +--R + +--R 2 5 5 2 +--R - 210a b d e +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 98 + +--S 99 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 100 + +--S 101 of 765 +r0:=-21*b^2*(b*d-a*e)^5*x/e^7+(b*d-a*e)^7/(e^8*(d+e*x))+35/2*b^3*_ + (b*d-a*e)^4*(d+e*x)^2/e^8-35/3*b^4*(b*d-a*e)^3*(d+e*x)^3/e^8+_ + 21/4*b^5*(b*d-a*e)^2*(d+e*x)^4/e^8-7/5*b^6*(b*d-a*e)*(d+e*x)^5/e^8+_ + 1/6*b^7*(d+e*x)^6/e^8+7*b*(b*d-a*e)^6*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b d e - 2520a b d e + 420b d e +--R * +--R x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a b d e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 6300a b d e - 2520a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (84a b e - 14b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (315a b e - 126a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (700a b e - 525a b d e + 210a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1050a b e - 1400a b d e + 1050a b d e - 420a b d e + 70b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b e - 3150a b d e + 4200a b d e - 3150a b d e +--R + +--R 6 4 3 7 5 2 +--R 1260a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 1260a b d e - 3150a b d e + 2800a b d e - 525a b d e +--R + +--R 6 5 2 7 6 +--R - 546a b d e + 231b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a e + 420a b d e - 1260a b d e + 3150a b d e - 5600a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 5775a b d e - 3066a b d e + 651b d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 101 + +--S 102 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 103 + +--S 104 of 765 +r0:=35*b^3*(b*d-a*e)^4*x/e^7+1/2*(b*d-a*e)^7/(e^8*(d+e*x)^2)-_ + 7*b*(b*d-a*e)^6/(e^8*(d+e*x))-35/2*b^4*(b*d-a*e)^3*(d+e*x)^2/e^8+_ + 7*b^5*(b*d-a*e)^2*(d+e*x)^3/e^8-7/4*b^6*(b*d-a*e)*(d+e*x)^4/e^8+_ + 1/5*b^7*(d+e*x)^5/e^8-21*b^2*(b*d-a*e)^5*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 420a b e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 4 3 7 5 2 +--R 2100a b d e - 420b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 840a b d e - 4200a b d e + 8400a b d e - 8400a b d e +--R + +--R 6 5 2 7 6 +--R 4200a b d e - 840b d e +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 420a b d e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 6 7 7 +--R 2100a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 4b e x + (35a b e - 7b d e )x + (140a b e - 70a b d e + 14b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (350a b e - 350a b d e + 175a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (700a b e - 1400a b d e + 1400a b d e - 700a b d e + 140b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (1400a b d e - 3500a b d e + 3500a b d e - 1575a b d e + 259b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 140a b e + 840a b d e - 1400a b d e + 1400a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 1400a b d e + 1050a b d e - 322b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a e - 70a b d e + 630a b d e - 1750a b d e + 2800a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 2800a b d e + 1575a b d e - 371b d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 104 + +--S 105 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 765 +r0:=-35*b^4*(b*d-a*e)^3*x/e^7+1/3*(b*d-a*e)^7/(e^8*(d+e*x)^3)-_ + 7/2*b*(b*d-a*e)^6/(e^8*(d+e*x)^2)+21*b^2*(b*d-a*e)^5/(e^8*(d+e*x))+_ + 21/2*b^5*(b*d-a*e)^2*(d+e*x)^2/e^8-7/3*b^6*(b*d-a*e)*(d+e*x)^3/e^8+_ + 1/4*b^7*(d+e*x)^4/e^8+35*b^3*(b*d-a*e)^4*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b e - 1680a b d e + 2520a b d e - 1680a b d e +--R + +--R 7 4 3 +--R 420b d e +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 5 2 +--R 1260b d e +--R * +--R 2 +--R x +--R + +--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 6 +--R 1260b d e +--R * +--R x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 3b e x + (28a b e - 7b d e )x + (126a b e - 84a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b e - 630a b d e + 420a b d e - 105b d e )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1260a b d e - 2520a b d e + 1820a b d e - 455b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 6 4 3 7 5 2 2 +--R (- 252a b e + 1260a b d e - 1260a b d e + 420a b d e - 105b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 42a b e - 252a b d e + 1890a b d e - 3780a b d e + 3780a b d e +--R + +--R 6 5 2 7 6 +--R - 2100a b d e + 525b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e - 14a b d e - 84a b d e + 770a b d e - 1820a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 2100a b d e - 1260a b d e + 315b d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 107 + +--S 108 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 765 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 109 + +--S 110 of 765 +r0:=e*(b*d-a*e)^3*x/b^4+1/2*(b*d-a*e)^2*(d+e*x)^2/b^3+1/3*(b*d-a*e)*_ + (d+e*x)^3/b^2+1/4*(d+e*x)^4/b+(b*d-a*e)^4*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (- 4a b e + 16b d e )x + (6a b e - 24a b d e + 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 2 2 2 3 3 +--R (- 12a b e + 48a b d e - 72a b d e + 48b d e)x + 6a b d e - 16a b d e +--R + +--R 4 4 +--R 13b d +--R / +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 110 + +--S 111 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 765 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 112 + +--S 113 of 765 +r0:=e*(b*d-a*e)^2*x/b^3+1/2*(b*d-a*e)*(d+e*x)^2/b^2+1/3*(d+e*x)^3/b+_ + (b*d-a*e)^3*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (- 6a e + 18a b d e - 18a b d e + 6b d )log(b x + a) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 2 2 +--R (- 3a b e + 9b d e )x + (6a b e - 18a b d e + 18b d e)x - 3a b d e +--R + +--R 3 3 +--R 5b d +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 113 + +--S 114 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 765 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------ +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 of 765 +r0:=e*(b*d-a*e)*x/b^2+1/2*(d+e*x)^2/b+(b*d-a*e)^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(b x + a) + b e x + (- 2a b e + 4b d e)x +--R + +--R 2 2 +--R b d +--R / +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 116 + +--S 117 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 765 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R e x + d +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 of 765 +r0:=e*x/b+(b*d-a*e)*log(a+b*x)/b^2 +--R +--R +--R (- a e + b d)log(b x + a) + b e x +--R (2) --------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 119 + +--S 120 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 765 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 1 +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 765 +r0:=log(a+b*x)/b +--R +--R +--R log(b x + a) +--R (2) ------------ +--R b +--R Type: Expression(Integer) +--E 122 + +--S 123 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 765 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--R b e x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 124 + +--S 125 of 765 +r0:=log(a+b*x)/(b*d-a*e)-log(d+e*x)/(b*d-a*e) +--R +--R +--R log(e x + d) - log(b x + a) +--R (2) --------------------------- +--R a e - b d +--R Type: Expression(Integer) +--E 125 + +--S 126 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 of 765 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (a e + 2b d e)x + (2a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 127 + +--S 128 of 765 +r0:=1/((b*d-a*e)*(d+e*x))+b*log(a+b*x)/(b*d-a*e)^2-b*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (- b e x - b d)log(e x + d) + (b e x + b d)log(b x + a) - a e + b d +--R (2) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a e - 2a b d e + b d e)x + a d e - 2a b d e + b d +--R Type: Expression(Integer) +--E 128 + +--S 129 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 765 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 130 + +--S 131 of 765 +r0:=1/2/((b*d-a*e)*(d+e*x)^2)+b/((b*d-a*e)^2*(d+e*x))+b^2*log(a+b*x)/_ + (b*d-a*e)^3-b^2*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4b d e x - 2b d )log(b x + a) + (2a b e - 2b d e)x - a e +--R + +--R 2 2 +--R 4a b d e - 3b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a d e - 12a b d e + 12a b d e - 4b d e)x + 2a d e - 6a b d e +--R + +--R 2 4 3 5 +--R 6a b d e - 2b d +--R Type: Expression(Integer) +--E 131 + +--S 132 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 765 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 133 + +--S 134 of 765 +r0:=1/3/((b*d-a*e)*(d+e*x)^3)+1/2*b/((b*d-a*e)^2*(d+e*x)^2)+_ + b^2/((b*d-a*e)^3*(d+e*x))+b^3*log(a+b*x)/(b*d-a*e)^4-_ + b^3*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 3 3 3 2 2 3 2 3 3 +--R (- 6b e x - 18b d e x - 18b d e x - 6b d )log(e x + d) +--R + +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (3a b e - 18a b d e + 15b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 18a b d e + 11b d +--R / +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4 3 4 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e)x + 6a d e +--R + +--R 3 4 3 2 2 5 2 3 6 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d +--R Type: Expression(Integer) +--E 134 + +--S 135 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 765 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 765 +r0:=e^3*(4*b*d-3*a*e)*x/b^4+1/2*e^4*x^2/b^3-1/2*(b*d-a*e)^4/(b^5*(a+b*x)^2)-_ + 4*e*(b*d-a*e)^3/(b^5*(a+b*x))+6*e^2*(b*d-a*e)^2*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (24a b e - 48a b d e + 24a b d e )x + 12a e - 24a b d e +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R b e x + (- 4a b e + 8b d e )x + (- 11a b e + 16a b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (2a b e - 16a b d e + 24a b d e - 8b d e)x + 7a e - 20a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 4a b d e - b d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 137 + +--S 138 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 765 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 139 + +--S 140 of 765 +r0:=e^3*x/b^3-1/2*(b*d-a*e)^3/(b^4*(a+b*x)^2)-3*e*(b*d-a*e)^2/(b^4*(a+b*x))+_ + 3*e^2*(b*d-a*e)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b e + 6b d e )x + (- 12a b e + 12a b d e )x - 6a e +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4a b e x + (- 4a b e + 12a b d e - 6b d e)x - 5a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 3a b d e - b d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 140 + +--S 141 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 of 765 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 142 + +--S 143 of 765 +r0:=-1/2*(b*d-a*e)^2/(b^3*(a+b*x)^2)-2*e*(b*d-a*e)/(b^3*(a+b*x))+_ + e^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(b x + a) + (4a b e - 4b d e)x + 3a e +--R + +--R 2 2 +--R - 2a b d e - b d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 143 + +--S 144 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 765 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 145 + +--S 146 of 765 +r0:=-1/2*(d+e*x)^2/((b*d-a*e)*(a+b*x)^2) +--R +--R +--R 1 2 2 1 2 +--R - e x + d e x + - d +--R 2 2 +--R (2) -------------------------------------------------- +--R 2 3 2 2 2 3 2 +--R (a b e - b d)x + (2a b e - 2a b d)x + a e - a b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 146 + +--S 147 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 765 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 1 +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 148 + +--S 149 of 765 +r0:=(-1/2)/(b*(a+b*x)^2) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ------------------- +--R 3 2 2 2 +--R b x + 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 765 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 765 +r0:=(-1/2)/((b*d-a*e)*(a+b*x)^2)+e/((b*d-a*e)^2*(a+b*x))+_ + e^2*log(a+b*x)/(b*d-a*e)^3-e^2*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4a b e x - 2a e )log(b x + a) + (2a b e - 2b d e)x + 3a e +--R + +--R 2 2 +--R - 4a b d e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a e - 6a b d e +--R + +--R 3 2 2 2 3 3 +--R 6a b d e - 2a b d +--R Type: Expression(Integer) +--E 152 + +--S 153 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 765 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 154 + +--S 155 of 765 +r0:=-1/2*b/((b*d-a*e)^2*(a+b*x)^2)+2*b*e/((b*d-a*e)^3*(a+b*x))+_ + e^2/((b*d-a*e)^3*(d+e*x))+3*b*e^2*log(a+b*x)/(b*d-a*e)^4-_ + 3*b*e^2*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R - 6b e x + (- 12a b e - 6b d e )x + (- 6a b e - 12a b d e )x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 6b e x + (12a b e + 6b d e )x + (6a b e + 12a b d e )x +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (- 9a b e + 6a b d e + 3b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 6a b d e - b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 155 + +--S 156 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 765 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 157 + +--S 158 of 765 +r0:=-1/2*b^2/((b*d-a*e)^3*(a+b*x)^2)+3*b^2*e/((b*d-a*e)^4*(a+b*x))+_ + 1/2*e^2/((b*d-a*e)^3*(d+e*x)^2)+3*b*e^2/((b*d-a*e)^4*(d+e*x))+_ + 6*b^2*e^2*log(a+b*x)/(b*d-a*e)^5-6*b^2*e^2*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 12b e x + (24a b e + 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b e + 48a b d e + 12b d e )x + (24a b d e + 24a b d e )x +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b e x + (- 24a b e - 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b e - 48a b d e - 12b d e )x + (- 24a b d e - 24a b d e )x +--R + +--R 2 2 2 2 +--R - 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b e - 12b d e )x + (18a b e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b e + 24a b d e - 24a b d e - 4b d e)x - a e + 8a b d e +--R + +--R 3 3 4 4 +--R - 8a b d e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Expression(Integer) +--E 158 + +--S 159 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 765 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 of 765 +r0:=-1/2*b^3/((b*d-a*e)^4*(a+b*x)^2)+4*b^3*e/((b*d-a*e)^5*(a+b*x))+_ + 1/3*e^2/((b*d-a*e)^3*(d+e*x)^3)+3/2*b*e^2/((b*d-a*e)^4*(d+e*x)^2)+_ + 6*b^2*e^2/((b*d-a*e)^5*(d+e*x))+10*b^3*e^2*log(a+b*x)/(b*d-a*e)^6-_ + 10*b^3*e^2*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 120a b e - 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 60a b e - 360a b d e - 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (- 180a b d e - 360a b d e - 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (- 180a b d e - 120a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (120a b e + 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e + 360a b d e + 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e + 360a b d e + 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (180a b d e + 120a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 90a b e - 60a b d e + 150b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 20a b e - 210a b d e + 120a b d e + 110b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (5a b e - 60a b d e - 120a b d e + 160a b d e + 15b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 15a b d e - 60a b d e + 20a b d e + 30a b d e - 3b d +--R / +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 4 8 6 3 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 12a b e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 198a b d e - 96a b d e + 18b d e +--R * +--R 4 +--R x +--R + +--R 8 9 6 2 2 7 5 3 3 6 4 4 4 5 3 5 5 4 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 2 6 6 3 7 7 2 8 8 +--R 60a b d e - 72a b d e + 18b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4 +--R 18a d e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 5 6 3 2 6 7 2 8 9 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 2 7 7 3 6 6 2 4 5 5 3 5 4 4 4 6 3 +--R 18a d e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 3 5 7 2 2 6 8 7 9 +--R 72a b d e - 54a b d e + 12a b d +--R * +--R x +--R + +--R 8 3 6 7 4 5 6 2 5 4 5 3 6 3 4 4 7 2 3 5 8 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 2 6 9 +--R 6a b d +--R Type: Expression(Integer) +--E 161 + +--S 162 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 765 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 of 765 +r0:=-1/4*(b*d-a*e)^4/(b^5*(a+b*x)^4)-4/3*e*(b*d-a*e)^3/(b^5*(a+b*x)^3)-_ + 3*e^2*(b*d-a*e)^2/(b^5*(a+b*x)^2)-4*e^3*(b*d-a*e)/(b^5*(a+b*x))+_ + e^4*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (48a b e - 48b d e )x + (108a b e - 72a b d e - 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (88a b e - 48a b d e - 24a b d e - 16b d e)x + 25a e - 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 4a b d e - 3b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Expression(Integer) +--E 164 + +--S 165 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 765 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 765 +r0:=-1/4*(d+e*x)^4/((b*d-a*e)*(a+b*x)^4) +--R +--R +--R (2) +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - e x + d e x + - d e x + d e x + - d +--R 4 2 4 +--R / +--R 4 5 4 2 3 4 3 3 2 2 3 2 +--R (a b e - b d)x + (4a b e - 4a b d)x + (6a b e - 6a b d)x +--R + +--R 4 3 2 5 4 +--R (4a b e - 4a b d)x + a e - a b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 167 + +--S 168 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 765 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 169 + +--S 170 of 765 +r0:=-1/4*(b*d-a*e)^2/(b^3*(a+b*x)^4)-2/3*e*(b*d-a*e)/(b^3*(a+b*x)^3)-_ + 1/2*e^2/(b^3*(a+b*x)^2) +--R +--R +--R 1 2 2 2 1 2 2 2 1 2 2 1 1 2 2 +--R - - b e x + (- - a b e - - b d e)x - -- a e - - a b d e - - b d +--R 2 3 3 12 6 4 +--R (2) ------------------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 170 + +--S 171 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 765 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 172 + +--S 173 of 765 +r0:=1/4*(-b*d+a*e)/(b^2*(a+b*x)^4)-1/3*e/(b^2*(a+b*x)^3) +--R +--R +--R 1 1 1 +--R - - b e x - -- a e - - b d +--R 3 12 4 +--R (2) ---------------------------------------- +--R 6 4 5 3 2 4 2 3 3 4 2 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 173 + +--S 174 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 765 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 of 765 +r0:=(-1/4)/(b*(a+b*x)^4) +--R +--R +--R 1 +--R - +--R 4 +--R (2) - --------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 176 + +--S 177 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 765 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 178 + +--S 179 of 765 +r0:=(-1/4)/((b*d-a*e)*(a+b*x)^4)+1/3*e/((b*d-a*e)^2*(a+b*x)^3)-_ + 1/2*e^2/((b*d-a*e)^3*(a+b*x)^2)+e^3/((b*d-a*e)^4*(a+b*x))+_ + e^4*log(a+b*x)/(b*d-a*e)^5-e^4*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(e x + d) +--R + +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 12b e x - 48a b e x - 72a b e x - 48a b e x - 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (42a b e - 48a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (52a b e - 72a b d e + 24a b d e - 4b d e)x + 25a e - 48a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 36a b d e - 16a b d e + 3b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 9 5 +--R - 12b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 2 7 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 3 6 4 +--R 72a b e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 2 7 5 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 4 5 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 6 5 +--R - 48a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 4 5 5 +--R 12a e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R Type: Expression(Integer) +--E 179 + +--S 180 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 765 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 765 +r0:=-1/4*b/((b*d-a*e)^2*(a+b*x)^4)+2/3*b*e/((b*d-a*e)^3*(a+b*x)^3)-_ + 3/2*b*e^2/((b*d-a*e)^4*(a+b*x)^2)+4*b*e^3/((b*d-a*e)^5*(a+b*x))+_ + e^4/((b*d-a*e)^5*(d+e*x))+5*b*e^4*log(a+b*x)/(b*d-a*e)^6-_ + 5*b*e^4*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 240a b e - 60b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (- 360a b e - 240a b d e )x + (- 240a b e - 360a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (- 60a b e - 240a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 3 +--R 60b e x + (240a b e + 60b d e )x + (360a b e + 240a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 4 4 +--R (240a b e + 360a b d e )x + (60a b e + 240a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 210a b e + 180a b d e + 30b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 260a b e + 150a b d e + 120a b d e - 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 125a b e - 20a b d e + 180a b d e - 40a b d e + 5b d e)x - 12a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 65a b d e + 120a b d e - 60a b d e + 20a b d e - 3b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 2 8 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 9 5 2 10 6 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 3 7 4 3 +--R 48a b e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 8 5 2 9 6 10 7 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 4 6 4 3 +--R 72a b e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 3 7 5 2 2 8 6 9 7 +--R 288a b d e - 216a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 5 5 4 3 +--R 48a b e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 4 6 5 2 3 7 6 2 8 7 +--R 792a b d e - 384a b d e + 72a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 6 4 4 3 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 5 5 5 2 4 6 6 3 7 7 +--R 648a b d e - 276a b d e + 48a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 5 5 6 4 6 7 +--R - 72a b d e + 12a b d +--R Type: Expression(Integer) +--E 182 + +--S 183 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 of 765 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 184 + +--S 185 of 765 +r0:=-1/4*b^2/((b*d-a*e)^3*(a+b*x)^4)+b^2*e/((b*d-a*e)^4*(a+b*x)^3)-_ + 3*b^2*e^2/((b*d-a*e)^5*(a+b*x)^2)+10*b^2*e^3/((b*d-a*e)^6*(a+b*x))+_ + 1/2*e^4/((b*d-a*e)^5*(d+e*x)^2)+5*b*e^4/((b*d-a*e)^6*(d+e*x))+_ + 15*b^2*e^4*log(a+b*x)/(b*d-a*e)^7-15*b^2*e^4*log(d+e*x)/(b*d-a*e)^7 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 60b e x + (240a b e + 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (360a b e + 480a b d e + 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (240a b e + 720a b d e + 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (60a b e + 480a b d e + 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (120a b d e + 240a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 60b e x + (- 240a b e - 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 360a b e - 480a b d e - 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (- 240a b e - 720a b d e - 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (- 60a b e - 480a b d e - 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (- 120a b d e - 240a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (210a b e - 120a b d e - 90b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (260a b e + 60a b d e - 300a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (125a b e + 280a b d e - 330a b d e - 80a b d e + 5b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 12a b e + 190a b d e - 100a b d e - 120a b d e + 20a b d e +--R + +--R 6 5 +--R - 2b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e + 24a b d e + 35a b d e - 80a b d e + 30a b d e - 8a b d e +--R + +--R 6 6 +--R b d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 3 8 4 5 +--R 4a b e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 2 9 5 4 10 6 3 11 7 2 +--R - 84a b d e + 28a b d e - 4b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 4 7 4 5 +--R 16a b e - 104a b d e + 280a b d e - 392a b d e + 280a b d e +--R + +--R 3 8 5 4 2 9 6 3 10 7 2 11 8 +--R - 56a b d e - 56a b d e + 40a b d e - 8b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 5 6 4 5 +--R 24a b e - 136a b d e + 284a b d e - 196a b d e - 196a b d e +--R + +--R 4 7 5 4 3 8 6 3 2 9 7 2 10 8 11 9 +--R 476a b d e - 364a b d e + 116a b d e - 4a b d e - 4b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 6 5 4 5 +--R 16a b e - 64a b d e + 16a b d e + 336a b d e - 784a b d e +--R + +--R 5 6 5 4 4 7 6 3 3 8 7 2 2 9 8 10 9 +--R 784a b d e - 336a b d e - 16a b d e + 64a b d e - 16a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5 +--R 4a e + 4a b d e - 116a b d e + 364a b d e - 476a b d e +--R + +--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9 +--R 196a b d e + 196a b d e - 284a b d e + 136a b d e - 24a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 7 4 5 4 +--R 8a d e - 40a b d e + 56a b d e + 56a b d e - 280a b d e +--R + +--R 6 5 6 3 5 6 7 2 4 7 8 3 8 9 +--R 392a b d e - 280a b d e + 104a b d e - 16a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 7 4 6 3 +--R 4a d e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 6 5 7 2 5 6 8 4 7 9 +--R - 84a b d e + 28a b d e - 4a b d +--R Type: Expression(Integer) +--E 185 + +--S 186 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 765 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 187 + +--S 188 of 765 +r0:=-1/4*b^3/((b*d-a*e)^4*(a+b*x)^4)+4/3*b^3*e/((b*d-a*e)^5*(a+b*x)^3)-_ + 5*b^3*e^2/((b*d-a*e)^6*(a+b*x)^2)+20*b^3*e^3/((b*d-a*e)^7*(a+b*x))+_ + 1/3*e^4/((b*d-a*e)^5*(d+e*x)^3)+5/2*b*e^4/((b*d-a*e)^6*(d+e*x)^2)+_ + 15*b^2*e^4/((b*d-a*e)^7*(d+e*x))+35*b^3*e^4*log(a+b*x)/(b*d-a*e)^8-_ + 35*b^3*e^4*log(d+e*x)/(b*d-a*e)^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R - 420b e x + (- 1680a b e - 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 2520a b e - 5040a b d e - 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1680a b e - 7560a b d e - 5040a b d e - 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (- 420a b e - 5040a b d e - 7560a b d e - 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (- 1260a b d e - 5040a b d e - 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (- 1260a b d e - 1680a b d e )x - 420a b d e +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 420b e x + (1680a b e + 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2520a b e + 5040a b d e + 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1680a b e + 7560a b d e + 5040a b d e + 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (420a b e + 5040a b d e + 7560a b d e + 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (1260a b d e + 5040a b d e + 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (1260a b d e + 1680a b d e )x + 420a b d e +--R * +--R log(b x + a) +--R + +--R 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R (- 420a b e + 420b d e )x + (- 1470a b e + 420a b d e + 1050b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1820a b e - 1890a b d e + 2940a b d e + 770b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 875a b e - 3780a b d e + 1890a b d e + 2660a b d e + 105b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 84a b e - 2205a b d e - 1260a b d e + 3150a b d e + 420a b d e +--R + +--R 7 5 2 +--R - 21b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 14a b e - 252a b d e - 1575a b d e + 1260a b d e + 630a b d e +--R + +--R 6 5 2 7 6 +--R - 84a b d e + 7b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e + 42a b d e - 252a b d e - 105a b d e + 420a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 126a b d e + 28a b d e - 3b d +--R / +--R 8 4 11 7 5 10 6 6 2 9 5 7 3 8 4 8 4 7 +--R 12a b e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 3 9 5 6 2 10 6 5 11 7 4 12 8 3 +--R - 672a b d e + 336a b d e - 96a b d e + 12b d e +--R * +--R 7 +--R x +--R + +--R 9 3 11 8 4 10 7 5 2 9 6 6 3 8 5 7 4 7 +--R 48a b e - 348a b d e + 1056a b d e - 1680a b d e + 1344a b d e +--R + +--R 4 8 5 6 3 9 6 5 2 10 7 4 11 8 3 12 9 2 +--R - 168a b d e - 672a b d e + 624a b d e - 240a b d e + 36b d e +--R * +--R 6 +--R x +--R + +--R 10 2 11 9 3 10 8 4 2 9 7 5 3 8 6 6 4 7 +--R 72a b e - 432a b d e + 900a b d e - 288a b d e - 2016a b d e +--R + +--R 5 7 5 6 4 8 6 5 3 9 7 4 2 10 8 3 +--R 4032a b d e - 3528a b d e + 1440a b d e - 72a b d e +--R + +--R 11 9 2 12 10 +--R - 144a b d e + 36b d e +--R * +--R 5 +--R x +--R + +--R 11 11 10 2 10 9 3 2 9 8 4 3 8 +--R 48a b e - 168a b d e - 240a b d e + 2220a b d e +--R + +--R 7 5 4 7 6 6 5 6 5 7 6 5 4 8 7 4 +--R - 4800a b d e + 4704a b d e - 1344a b d e - 1560a b d e +--R + +--R 3 9 8 3 2 10 9 2 11 10 12 11 +--R 1680a b d e - 600a b d e + 48a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 12 11 11 10 10 2 2 9 9 3 3 8 8 4 4 7 +--R 12a e + 48a b d e - 600a b d e + 1680a b d e - 1560a b d e +--R + +--R 7 5 5 6 6 6 6 5 5 7 7 4 4 8 8 3 +--R - 1344a b d e + 4704a b d e - 4800a b d e + 2220a b d e +--R + +--R 3 9 9 2 2 10 10 11 11 +--R - 240a b d e - 168a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 12 10 11 2 9 10 2 3 8 9 3 4 7 8 4 5 6 +--R 36a d e - 144a b d e - 72a b d e + 1440a b d e - 3528a b d e +--R + +--R 7 5 6 5 6 6 7 4 5 7 8 3 4 8 9 2 3 9 10 +--R 4032a b d e - 2016a b d e - 288a b d e + 900a b d e - 432a b d e +--R + +--R 2 10 11 +--R 72a b d +--R * +--R 2 +--R x +--R + +--R 12 2 9 11 3 8 10 2 4 7 9 3 5 6 8 4 6 5 +--R 36a d e - 240a b d e + 624a b d e - 672a b d e - 168a b d e +--R + +--R 7 5 7 4 6 6 8 3 5 7 9 2 4 8 10 3 9 11 +--R 1344a b d e - 1680a b d e + 1056a b d e - 348a b d e + 48a b d +--R * +--R x +--R + +--R 12 3 8 11 4 7 10 2 5 6 9 3 6 5 8 4 7 4 +--R 12a d e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 7 5 8 3 6 6 9 2 5 7 10 4 8 11 +--R - 672a b d e + 336a b d e - 96a b d e + 12a b d +--R Type: Expression(Integer) +--E 188 + +--S 189 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 765 +t0:=(a+b*x)*(d+e*x)^m*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R m | 2 2 2 +--R (1) (b x + a)(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 765 +r0:=-2*(b*d-a*e)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(2+m)*(3+m))+_ + 2*(b*d-a*e)^2*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(1+m)*_ + (2+m)*(3+m)*(a+b*x))+(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e*(3+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (b e m + 3b e m + 2b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a b e m + (8a b e - 2b d e)m + 6a b e - 2b d e)x + a e m +--R + +--R 2 2 2 2 2 2 +--R (5a e - 2a b d e)m + 6a e - 6a b d e + 2b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 191 + +--S 192 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 765 +t0:=(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b e x + (a e + 5b d e )x + (5a d e + 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a d e + 10b d e )x + (10a d e + 5b d e)x + (5a d e + b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 193 + +--S 194 of 765 +r0:=-1/28*(b*d-a*e)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 1/168*(b*d-a*e)^2*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 1/8*(a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 8 8 8 2 7 7 +--R 21b e x + (48a b e + 120b d e )x +--R + +--R 2 8 7 2 2 6 6 +--R (28a e + 280a b d e + 280b d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (168a d e + 672a b d e + 336b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (420a d e + 840a b d e + 210b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 2 4 4 5 3 2 +--R (560a d e + 560a b d e + 56b d e )x + (420a d e + 168a b d e )x +--R + +--R 2 5 3 2 6 2 7 2 8 +--R 168a d e x + 28a d e - 8a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 168b e x + 168a e +--R Type: Expression(Integer) +--E 194 + +--S 195 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 765 +t0:=(a+b*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 196 + +--S 197 of 765 +r0:=-1/21*(b*d-a*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 1/105*(b*d-a*e)^2*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 1/7*(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 7 7 7 2 6 6 +--R 15b e x + (35a b e + 70b d e )x +--R + +--R 2 7 6 2 2 5 5 +--R (21a e + 168a b d e + 126b d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (105a d e + 315a b d e + 105b d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 2 3 4 4 3 2 +--R (210a d e + 280a b d e + 35b d e )x + (210a d e + 105a b d e )x +--R + +--R 2 4 3 2 5 2 6 2 7 +--R 105a d e x + 21a d e - 7a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 197 + +--S 198 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 765 +t0:=(a+b*x)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 765 +r0:=-1/15*(b*d-a*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/60*(b*d-_ + a*e)^2*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+1/6*(a+b*x)*_ + (d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 2 6 5 2 2 4 4 +--R 10b e x + (24a b e + 36b d e )x + (15a e + 90a b d e + 45b d e )x +--R + +--R 2 5 2 4 2 3 3 3 2 2 4 3 3 2 +--R (60a d e + 120a b d e + 20b d e )x + (90a d e + 60a b d e )x +--R + +--R 2 3 3 2 4 2 5 2 6 +--R 60a d e x + 15a d e - 6a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 200 + +--S 201 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 765 +t0:=(a+b*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 202 + +--S 203 of 765 +r0:=1/30*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^3+1/10*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/5*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/b +--R +--R +--R (2) +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R 6b e x + (9a b e + 15b d e)x + (a b e + 25a b d e + 10b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- a b e + 5a b d e + 20a b d )x + a e - 5a b d e + 10a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 30b +--R Type: Expression(Integer) +--E 203 + +--S 204 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 765 +t0:=(a+b*x)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 | 2 2 2 +--R (1) (b e x + (a e + b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 205 + +--S 206 of 765 +r0:=1/12*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/4*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/b +--R +--R +--R (2) +--R 3 3 2 3 2 2 2 3 2 +--R (3b e x + (5a b e + 4b d)x + (a b e + 8a b d)x - a e + 4a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 12b +--R Type: Expression(Integer) +--E 206 + +--S 207 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (1) (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 208 + +--S 209 of 765 +r0:=1/3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b +--R +--R +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R (2) ----------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 209 + +--S 210 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 211 + +--S 212 of 765 +r0:=-(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e+(b*d-a*e)^2*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(e x + d) + b e x + (4a b e - 2b d e)x +--R + +--R 2 2 +--R 3a e - 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 2b e x + 2a e +--R Type: Expression(Integer) +--E 212 + +--S 213 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 214 + +--S 215 of 765 +r0:=2*b*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2-(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e*(d+e*x))-2*b*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((2a b e - 2b d e)x + 2a b d e - 2b d )log(e x + d) + b e x +--R + +--R 2 2 2 +--R 2b d e x - a e + 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 215 + +--S 216 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 217 + +--S 218 of 765 +r0:=-1/2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^2)+b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x))+b^2*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) - b e x +--R + +--R 2 2 2 2 2 2 +--R (- 4a b e + 2b d e)x - a e - 2a b d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 218 + +--S 219 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 220 + +--S 221 of 765 +r0:=1/3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^3) +--R +--R +--R (2) +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (- b x - 2a b x - a )\|b x + 2a b x + a +--R / +--R 4 3 3 3 2 2 2 2 2 3 +--R (3a e - 3b d e )x + (9a d e - 9b d e )x + (9a d e - 9b d e)x +--R + +--R 3 4 +--R 3a d e - 3b d +--R Type: Expression(Integer) +--E 221 + +--S 222 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 223 + +--S 224 of 765 +r0:=1/4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^4)+_ + 1/12*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^3) +--R +--R +--R (2) +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (- a b e + 4b d)x + (- 5a b e + 8a b d)x - 3a e + 4a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 6 5 2 2 4 4 2 5 2 4 2 3 3 3 +--R (12a e - 24a b d e + 12b d e )x + (48a d e - 96a b d e + 48b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (72a d e - 144a b d e + 72b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (48a d e - 96a b d e + 48b d e)x + 12a d e - 24a b d e + 12b d +--R Type: Expression(Integer) +--E 224 + +--S 225 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 226 + +--S 227 of 765 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^5)+_ + 1/10*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^4)+_ + 1/30*b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^3*(d+e*x)^3) +--R +--R +--R (2) +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R - b e x + (a b e - 5b d e)x + (- a b e + 5a b d e - 10b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- 9a b e + 25a b d e - 20a b d )x - 6a e + 15a b d e - 10a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 8 2 7 2 2 6 3 3 5 5 +--R (30a e - 90a b d e + 90a b d e - 30b d e )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 4 +--R (150a d e - 450a b d e + 450a b d e - 150b d e )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 3 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 6 2 2 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 4 4 2 5 3 2 6 2 3 7 3 5 3 +--R (150a d e - 450a b d e + 450a b d e - 150b d e)x + 30a d e +--R + +--R 2 6 2 2 7 3 8 +--R - 90a b d e + 90a b d e - 30b d +--R Type: Expression(Integer) +--E 227 + +--S 228 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 229 + +--S 230 of 765 +r0:=-1/6*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^6)-_ + 1/12*b*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^5)-1/60*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 15b e x + (- 24a b e - 6b d e)x - 10a e - 4a b d e - b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 230 + +--S 231 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 232 + +--S 233 of 765 +r0:=-1/7*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^7)-_ + 2/35*b*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^6)-1/105*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 21b e x + (- 35a b e - 7b d e)x - 15a e - 5a b d e - b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 8 10 9 7 9 2 8 6 +--R 105b e x + (105a e + 735b d e )x + (735a d e + 2205b d e )x +--R + +--R 2 8 3 7 5 3 7 4 6 4 +--R (2205a d e + 3675b d e )x + (3675a d e + 3675b d e )x +--R + +--R 4 6 5 5 3 5 5 6 4 2 +--R (3675a d e + 2205b d e )x + (2205a d e + 735b d e )x +--R + +--R 6 4 7 3 7 3 +--R (735a d e + 105b d e )x + 105a d e +--R Type: Expression(Integer) +--E 233 + +--S 234 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 765 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 m | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 765 +r0:=-4*(b*d-a*e)*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(4+m)*(5+m))+_ + (a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(5+m))-_ + 24*(b*d-a*e)^3*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(2+m)*_ + (3+m)*(4+m)*(5+m))+24*(b*d-a*e)^4*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(1+m)*(2+m)*(3+m)*(4+m)*(5+m)*(a+b*x))+12*(b*d-a*e)^2*_ + (a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(3+m)*(4+m)*(5+m)) +--R +--R +--R (2) +--R 4 4 4 4 4 3 4 4 2 4 4 4 4 4 +--R (b e m + 10b e m + 35b e m + 50b e m + 24b e )x +--R + +--R 3 4 4 3 4 4 3 3 3 4 4 3 2 +--R 4a b e m + (44a b e - 4b d e )m + (164a b e - 24b d e )m +--R + +--R 3 4 4 3 3 4 4 3 +--R (244a b e - 44b d e )m + 120a b e - 24b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 2 2 4 3 3 3 +--R 6a b e m + (72a b e - 12a b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (294a b e - 96a b d e + 12b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 2 4 3 3 +--R (468a b e - 204a b d e + 36b d e )m + 240a b e - 120a b d e +--R + +--R 4 2 2 +--R 24b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 4 2 2 3 3 +--R 4a b e m + (52a b e - 12a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 2 +--R (236a b e - 120a b d e + 24a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 4 +--R (428a b e - 348a b d e + 144a b d e - 24b d e)m + 240a b e +--R + +--R 2 2 3 3 2 2 4 3 +--R - 240a b d e + 120a b d e - 24b d e +--R * +--R x +--R + +--R 4 4 4 4 4 3 3 3 4 4 3 3 2 2 2 2 2 +--R a e m + (14a e - 4a b d e )m + (71a e - 48a b d e + 12a b d e )m +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (154a e - 188a b d e + 108a b d e - 24a b d e)m + 120a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 240a b d e + 240a b d e - 120a b d e + 24b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 236 + +--S 237 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 765 +t0:=(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 7 10 2 7 3 6 9 2 7 2 6 3 2 5 8 +--R b e x + (3a b e + 7b d e )x + (3a b e + 21a b d e + 21b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 7 +--R (a e + 21a b d e + 63a b d e + 35b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 6 +--R (7a d e + 63a b d e + 105a b d e + 35b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 5 +--R (21a d e + 105a b d e + 105a b d e + 21b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 4 +--R (35a d e + 105a b d e + 63a b d e + 7b d e)x +--R + +--R 3 4 3 2 5 2 2 6 3 7 3 +--R (35a d e + 63a b d e + 21a b d e + b d )x +--R + +--R 3 5 2 2 6 2 7 2 3 6 2 7 3 7 +--R (21a d e + 21a b d e + 3a b d )x + (7a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 765 +r0:=-1/33*(b*d-a*e)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/12*(a+b*x)*_ + (d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/495*(b*d-a*e)^3*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/3960*(b*d-a*e)^4*(d+e*x)^8*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/110*(b*d-a*e)^2*(a+b*x)*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 12 12 3 12 4 11 11 +--R 330b e x + (1440a b e + 2520b d e )x +--R + +--R 2 2 12 3 11 4 2 10 10 +--R (2376a b e + 11088a b d e + 8316b d e )x +--R + +--R 3 12 2 2 11 3 2 10 4 3 9 9 +--R (1760a b e + 18480a b d e + 36960a b d e + 15400b d e )x +--R + +--R 4 12 3 11 2 2 2 10 3 3 9 +--R 495a e + 13860a b d e + 62370a b d e + 69300a b d e +--R + +--R 4 4 8 +--R 17325b d e +--R * +--R 8 +--R x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 +--R 3960a d e + 47520a b d e + 118800a b d e + 79200a b d e +--R + +--R 4 5 7 +--R 11880b d e +--R * +--R 7 +--R x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 +--R 13860a d e + 92400a b d e + 138600a b d e + 55440a b d e +--R + +--R 4 6 6 +--R 4620b d e +--R * +--R 6 +--R x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 +--R 27720a d e + 110880a b d e + 99792a b d e + 22176a b d e +--R + +--R 4 7 5 +--R 792b d e +--R * +--R 5 +--R x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 +--R (34650a d e + 83160a b d e + 41580a b d e + 3960a b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 +--R (27720a d e + 36960a b d e + 7920a b d e )x +--R + +--R 4 6 6 3 7 5 2 4 7 5 4 8 4 3 9 3 +--R (13860a d e + 7920a b d e )x + 3960a d e x + 495a d e - 220a b d e +--R + +--R 2 2 10 2 3 11 4 12 +--R 66a b d e - 12a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 3960b e x + 3960a e +--R Type: Expression(Integer) +--E 239 + +--S 240 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 765 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 6 9 2 6 3 5 8 2 6 2 5 3 2 4 7 +--R b e x + (3a b e + 6b d e )x + (3a b e + 18a b d e + 15b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 6 +--R (a e + 18a b d e + 45a b d e + 20b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 5 +--R (6a d e + 45a b d e + 60a b d e + 15b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 4 +--R (15a d e + 60a b d e + 45a b d e + 6b d e)x +--R + +--R 3 3 3 2 4 2 2 5 3 6 3 +--R (20a d e + 45a b d e + 18a b d e + b d )x +--R + +--R 3 4 2 2 5 2 6 2 3 5 2 6 3 6 +--R (15a d e + 18a b d e + 3a b d )x + (6a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 765 +r0:=-2/55*(b*d-a*e)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/11*(a+b*x)*_ + (d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/330*(b*d-a*e)^3*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/2310*(b*d-a*e)^4*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/165*(b*d-a*e)^2*(a+b*x)*_ + (d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 11 11 3 11 4 10 10 +--R 210b e x + (924a b e + 1386b d e )x +--R + +--R 2 2 11 3 10 4 2 9 9 +--R (1540a b e + 6160a b d e + 3850b d e )x +--R + +--R 3 11 2 2 10 3 2 9 4 3 8 8 +--R (1155a b e + 10395a b d e + 17325a b d e + 5775b d e )x +--R + +--R 4 11 3 10 2 2 2 9 3 3 8 +--R 330a e + 7920a b d e + 29700a b d e + 26400a b d e +--R + +--R 4 4 7 +--R 4950b d e +--R * +--R 7 +--R x +--R + +--R 4 10 3 2 9 2 2 3 8 3 4 7 +--R 2310a d e + 23100a b d e + 46200a b d e + 23100a b d e +--R + +--R 4 5 6 +--R 2310b d e +--R * +--R 6 +--R x +--R + +--R 4 2 9 3 3 8 2 2 4 7 3 5 6 +--R 6930a d e + 36960a b d e + 41580a b d e + 11088a b d e +--R + +--R 4 6 5 +--R 462b d e +--R * +--R 5 +--R x +--R + +--R 4 3 8 3 4 7 2 2 5 6 3 6 5 4 +--R (11550a d e + 34650a b d e + 20790a b d e + 2310a b d e )x +--R + +--R 4 4 7 3 5 6 2 2 6 5 3 +--R (11550a d e + 18480a b d e + 4620a b d e )x +--R + +--R 4 5 6 3 6 5 2 4 6 5 4 7 4 3 8 3 +--R (6930a d e + 4620a b d e )x + 2310a d e x + 330a d e - 165a b d e +--R + +--R 2 2 9 2 3 10 4 11 +--R 55a b d e - 11a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2310b e x + 2310a e +--R Type: Expression(Integer) +--E 242 + +--S 243 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 765 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 5 8 2 5 3 4 7 2 5 2 4 3 2 3 6 +--R b e x + (3a b e + 5b d e )x + (3a b e + 15a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 5 +--R (a e + 15a b d e + 30a b d e + 10b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 4 +--R (5a d e + 30a b d e + 30a b d e + 5b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (10a d e + 30a b d e + 15a b d e + b d )x +--R + +--R 3 3 2 2 4 2 5 2 3 4 2 5 3 5 +--R (10a d e + 15a b d e + 3a b d )x + (5a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 765 +r0:=-2/45*(b*d-a*e)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/10*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/210*(b*d-a*e)^3*(d+e*x)^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/1260*(b*d-a*e)^4*(d+e*x)^6*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/60*(b*d-a*e)^2*(a+b*x)*(d+e*x)^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 10 10 3 10 4 9 9 +--R 126b e x + (560a b e + 700b d e )x +--R + +--R 2 2 10 3 9 4 2 8 8 +--R (945a b e + 3150a b d e + 1575b d e )x +--R + +--R 3 10 2 2 9 3 2 8 4 3 7 7 +--R (720a b e + 5400a b d e + 7200a b d e + 1800b d e )x +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 4 4 6 6 +--R (210a e + 4200a b d e + 12600a b d e + 8400a b d e + 1050b d e )x +--R + +--R 4 9 3 2 8 2 2 3 7 3 4 6 +--R 1260a d e + 10080a b d e + 15120a b d e + 5040a b d e +--R + +--R 4 5 5 +--R 252b d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 3 3 7 2 2 4 6 3 5 5 4 +--R (3150a d e + 12600a b d e + 9450a b d e + 1260a b d e )x +--R + +--R 4 3 7 3 4 6 2 2 5 5 3 +--R (4200a d e + 8400a b d e + 2520a b d e )x +--R + +--R 4 4 6 3 5 5 2 4 5 5 4 6 4 3 7 3 +--R (3150a d e + 2520a b d e )x + 1260a d e x + 210a d e - 120a b d e +--R + +--R 2 2 8 2 3 9 4 10 +--R 45a b d e - 10a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 1260b e x + 1260a e +--R Type: Expression(Integer) +--E 245 + +--S 246 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 of 765 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 765 +r0:=1/630*(b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^5+1/126*(b*d-a*e)^3*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4+1/42*(b*d-a*e)^2*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+1/18*(b*d-a*e)*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/b^2+1/9*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 8 4 8 7 4 8 3 7 +--R 70b e x + (245a b e + 315b d e )x +--R + +--R 2 6 4 7 3 8 2 2 6 +--R (295a b e + 1125a b d e + 540b d e )x +--R + +--R 3 5 4 2 6 3 7 2 2 8 3 5 +--R (125a b e + 1395a b d e + 1980a b d e + 420b d e)x +--R + +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (a b e + 621a b d e + 2556a b d e + 1596a b d e + 126b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (- a b e + 9a b d e + 1224a b d e + 2184a b d e + 504a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (a b e - 9a b d e + 36a b d e + 1176a b d e + 756a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 8 4 +--R (- a b e + 9a b d e - 36a b d e + 84a b d e + 504a b d )x + a e +--R + +--R 7 3 6 2 2 2 5 3 3 4 4 4 +--R - 9a b d e + 36a b d e - 84a b d e + 126a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 630b +--R Type: Expression(Integer) +--E 248 + +--S 249 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 765 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 765 +r0:=1/280*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4+1/56*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+3/56*(b*d-a*e)*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/8*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 7 3 7 6 3 7 2 6 +--R 35b e x + (125a b e + 120b d e )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (155a b e + 440a b d e + 140b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (69a b e + 568a b d e + 532a b d e + 56b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (a b e + 272a b d e + 728a b d e + 224a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- a b e + 8a b d e + 392a b d e + 336a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 6 2 +--R (a b e - 8a b d e + 28a b d e + 224a b d )x - a e + 8a b d e +--R + +--R 5 2 2 4 3 3 +--R - 28a b d e + 56a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 280b +--R Type: Expression(Integer) +--E 251 + +--S 252 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 765 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 765 +r0:=1/105*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+1/21*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/7*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 15b e x + (55a b e + 35b d e)x + (71a b e + 133a b d e + 21b d )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (34a b e + 182a b d e + 84a b d )x +--R + +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (a b e + 98a b d e + 126a b d )x + (- a b e + 7a b d e + 84a b d )x +--R + +--R 6 2 5 4 2 2 +--R a e - 7a b d e + 21a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 105b +--R Type: Expression(Integer) +--E 254 + +--S 255 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 765 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 765 +r0:=1/30*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/6*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 5 5 4 5 4 2 3 4 3 +--R 5b e x + (19a b e + 6b d)x + (26a b e + 24a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (14a b e + 36a b d)x + (a b e + 24a b d)x - a e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 30b +--R Type: Expression(Integer) +--E 257 + +--S 258 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 765 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R (2) ------------------------------------------------------------- +--R 5b +--R Type: Expression(Integer) +--E 260 + +--S 261 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 262 + +--S 263 of 765 +r0:=-1/3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/4*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/e-(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/2*(b*d-_ + a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3+(b*d-a*e)^4*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (16a b e - 4b d e )x + (36a b e - 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (48a b e - 72a b d e + 48a b d e - 12b d e)x + 25a e - 52a b d e +--R + +--R 2 2 2 2 3 3 +--R 42a b d e - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 12b e x + 12a e +--R Type: Expression(Integer) +--E 263 + +--S 264 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 265 + +--S 266 of 765 +r0:=4/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2-(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(d+e*x))+4*b*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^4-2*b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-_ + 4*b*(b*d-a*e)^3*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b e - 36a b d e + 36a b d e - 12b d e)x + 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b d e + 36a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (6a b e - 2b d e )x + (18a b e - 18a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (10a b e + 6a b d e - 24a b d e + 12b d e)x - 3a e + 22a b d e +--R + +--R 2 2 2 2 3 3 +--R - 30a b d e + 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +--R 3b e x + (3a e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 266 + +--S 267 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 268 + +--S 269 of 765 +r0:=-1/2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^2)-_ + 2*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x))-6*b^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+3*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + e^3+6*b^2*(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 +--R (24a b d e - 48a b d e + 24b d e)x + 12a b d e - 24a b d e +--R + +--R 4 4 +--R 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R b e x + (8a b e - 4b d e )x + (24a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 4 3 4 4 3 3 2 2 2 2 +--R (- 8a b e + 24a b d e - 12b d e)x - a e - 4a b d e + 18a b d e +--R + +--R 3 3 +--R - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 269 + +--S 270 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 271 + +--S 272 of 765 +r0:=-1/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^3)-_ + 2/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^2)+4*b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^4-2*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+_ + e*x))-4*b^3*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 4 3 3 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (36a b d e - 36b d e )x +--R + +--R 3 2 2 4 3 3 3 4 4 +--R (36a b d e - 36b d e)x + 12a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3b e x + (- 10a b e + 22b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 18a b e + 6a b d e + 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 6a b e - 18a b d e + 24a b d e + 12b d e)x - a e - 2a b d e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e + 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 6 3 5 3 5 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 272 + +--S 273 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 274 + +--S 275 of 765 +r0:=-1/4*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^4)-1/3*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^3)-1/2*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^3*(d+e*x)^2)+b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x)*(d+e*x))+b^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 4 3 3 4 2 2 2 4 3 4 4 +--R (12b e x + 48b d e x + 72b d e x + 48b d e x + 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 13b e x + (- 48a b e - 4b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 36a b e - 72a b d e + 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 16a b e - 24a b d e - 48a b d e + 36b d e)x - 3a e - 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 12a b d e + 12b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 275 + +--S 276 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 277 + +--S 278 of 765 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^5) +--R +--R +--R (2) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (- b x - 4a b x - 6a b x - 4a b x - a )\|b x + 2a b x + a +--R / +--R 6 5 5 5 2 4 4 2 4 3 3 3 +--R (5a e - 5b d e )x + (25a d e - 25b d e )x + (50a d e - 50b d e )x +--R + +--R 3 3 4 2 2 4 2 5 5 6 +--R (50a d e - 50b d e )x + (25a d e - 25b d e)x + 5a d e - 5b d +--R Type: Expression(Integer) +--E 278 + +--S 279 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 280 + +--S 281 of 765 +r0:=1/6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^6)+_ + 1/30*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^5) +--R +--R +--R (2) +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (- a b e + 6b d)x + (- 14a b e + 24a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 26a b e + 36a b d)x + (- 19a b e + 24a b d)x - 5a e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 8 7 2 2 6 6 +--R (30a e - 60a b d e + 30b d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (180a d e - 360a b d e + 180b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (600a d e - 1200a b d e + 600b d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 5 3 6 2 2 7 2 6 2 7 2 8 +--R (180a d e - 360a b d e + 180b d e)x + 30a d e - 60a b d e + 30b d +--R Type: Expression(Integer) +--E 281 + +--S 282 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 283 + +--S 284 of 765 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^7)+_ + 1/21*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^6)+_ + 1/105*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R - b e x + (a b e - 7b d e)x + (- a b e + 7a b d e - 21b d )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 34a b e + 98a b d e - 84a b d )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 71a b e + 182a b d e - 126a b d )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 55a b e + 133a b d e - 84a b d )x - 15a e + 35a b d e - 21a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (105a e - 315a b d e + 315a b d e - 105b d e )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e)x + 105a d e +--R + +--R 2 8 2 2 9 3 10 +--R - 315a b d e + 315a b d e - 105b d +--R Type: Expression(Integer) +--E 284 + +--S 285 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 286 + +--S 287 of 765 +r0:=1/8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^8)+_ + 3/56*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^7)+_ + 1/56*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^6)+_ + 1/280*b^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 7 3 7 6 3 7 2 6 2 5 3 6 2 7 2 5 +--R b e x + (- a b e + 8b d e )x + (a b e - 8a b d e + 28b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- a b e + 8a b d e - 28a b d e + 56b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (- 69a b e + 272a b d e - 392a b d e + 224a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 155a b e + 568a b d e - 728a b d e + 336a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (- 125a b e + 440a b d e - 532a b d e + 224a b d )x - 35a e +--R + +--R 6 2 5 2 2 4 3 3 +--R 120a b d e - 140a b d e + 56a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 12 3 11 2 2 2 10 3 3 9 4 4 8 8 +--R (280a e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d e )x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 +--R 2240a d e - 8960a b d e + 13440a b d e - 8960a b d e +--R + +--R 4 5 7 +--R 2240b d e +--R * +--R 7 +--R x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 6 6 +--R 7840b d e +--R * +--R 6 +--R x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 7 5 +--R 15680b d e +--R * +--R 5 +--R x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 +--R 19600a d e - 78400a b d e + 117600a b d e - 78400a b d e +--R + +--R 4 8 4 +--R 19600b d e +--R * +--R 4 +--R x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 8 4 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 9 3 +--R 15680b d e +--R * +--R 3 +--R x +--R + +--R 4 6 6 3 7 5 2 2 8 4 3 9 3 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 10 2 +--R 7840b d e +--R * +--R 2 +--R x +--R + +--R 4 7 5 3 8 4 2 2 9 3 3 10 2 4 11 +--R (2240a d e - 8960a b d e + 13440a b d e - 8960a b d e + 2240b d e)x +--R + +--R 4 8 4 3 9 3 2 2 10 2 3 11 4 12 +--R 280a d e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d +--R Type: Expression(Integer) +--E 287 + +--S 288 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 289 + +--S 290 of 765 +r0:=1/9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^9)+_ + 1/18*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^8)+_ + 1/42*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^7)+_ + 1/126*b^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^6)+_ + 1/630*b^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^5*(d+e*x)^5) +--R +--R +--R (2) +--R 8 4 8 7 4 8 3 7 2 6 4 7 3 8 2 2 6 +--R - b e x + (a b e - 9b d e )x + (- a b e + 9a b d e - 36b d e )x +--R + +--R 3 5 4 2 6 3 7 2 2 8 3 5 +--R (a b e - 9a b d e + 36a b d e - 84b d e)x +--R + +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (- a b e + 9a b d e - 36a b d e + 84a b d e - 126b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (- 125a b e + 621a b d e - 1224a b d e + 1176a b d e - 504a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (- 295a b e + 1395a b d e - 2556a b d e + 2184a b d e - 756a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (- 245a b e + 1125a b d e - 1980a b d e + 1596a b d e - 504a b d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R - 70a e + 315a b d e - 540a b d e + 420a b d e - 126a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 14 4 13 3 2 2 12 2 3 3 11 +--R 630a e - 3150a b d e + 6300a b d e - 6300a b d e +--R + +--R 4 4 10 5 5 9 +--R 3150a b d e - 630b d e +--R * +--R 9 +--R x +--R + +--R 5 13 4 2 12 3 2 3 11 2 3 4 10 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 5 9 5 6 8 +--R 28350a b d e - 5670b d e +--R * +--R 8 +--R x +--R + +--R 5 2 12 4 3 11 3 2 4 10 2 3 5 9 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 6 8 5 7 7 +--R 113400a b d e - 22680b d e +--R * +--R 7 +--R x +--R + +--R 5 3 11 4 4 10 3 2 5 9 2 3 6 8 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 7 7 5 8 6 +--R 264600a b d e - 52920b d e +--R * +--R 6 +--R x +--R + +--R 5 4 10 4 5 9 3 2 6 8 2 3 7 7 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 8 6 5 9 5 +--R 396900a b d e - 79380b d e +--R * +--R 5 +--R x +--R + +--R 5 5 9 4 6 8 3 2 7 7 2 3 8 6 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 9 5 5 10 4 +--R 396900a b d e - 79380b d e +--R * +--R 4 +--R x +--R + +--R 5 6 8 4 7 7 3 2 8 6 2 3 9 5 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 10 4 5 11 3 +--R 264600a b d e - 52920b d e +--R * +--R 3 +--R x +--R + +--R 5 7 7 4 8 6 3 2 9 5 2 3 10 4 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 11 3 5 12 2 +--R 113400a b d e - 22680b d e +--R * +--R 2 +--R x +--R + +--R 5 8 6 4 9 5 3 2 10 4 2 3 11 3 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 12 2 5 13 +--R 28350a b d e - 5670b d e +--R * +--R x +--R + +--R 5 9 5 4 10 4 3 2 11 3 2 3 12 2 4 13 +--R 630a d e - 3150a b d e + 6300a b d e - 6300a b d e + 3150a b d e +--R + +--R 5 14 +--R - 630b d +--R Type: Expression(Integer) +--E 290 + +--S 291 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 292 + +--S 293 of 765 +r0:=-1/10*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^10)-_ + 2/45*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^9)-1/60*b^2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^8)-1/180*b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(d+e*x)^7)-1/1260*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 210b e x + (- 720a b e - 120b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 945a b e - 270a b d e - 45b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 560a b e - 210a b d e - 60a b d e - 10b d e)x - 126a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 56a b d e - 21a b d e - 6a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 15 11 15 14 10 +--R 1260b e x + (1260a e + 12600b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (12600a d e + 56700b d e )x + (56700a d e + 151200b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (151200a d e + 264600b d e )x + (264600a d e + 317520b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (317520a d e + 264600b d e )x + (264600a d e + 151200b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (151200a d e + 56700b d e )x + (56700a d e + 12600b d e )x +--R + +--R 9 6 10 5 10 5 +--R (12600a d e + 1260b d e )x + 1260a d e +--R Type: Expression(Integer) +--E 293 + +--S 294 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 295 + +--S 296 of 765 +r0:=-1/11*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^11)-_ + 2/55*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^10)-2/165*b^2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^9)-4/1155*b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(d+e*x)^8)-1/2310*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 330b e x + (- 1155a b e - 165b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1540a b e - 385a b d e - 55b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 924a b e - 308a b d e - 77a b d e - 11b d e)x - 210a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 84a b d e - 28a b d e - 7a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 16 12 16 15 11 +--R 2310b e x + (2310a e + 25410b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (25410a d e + 127050b d e )x + (127050a d e + 381150b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (381150a d e + 762300b d e )x + (762300a d e + 1067220b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (1067220a d e + 1067220b d e )x + (1067220a d e + 762300b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (762300a d e + 381150b d e )x + (381150a d e + 127050b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (127050a d e + 25410b d e )x + (25410a d e + 2310b d e )x +--R + +--R 11 5 +--R 2310a d e +--R Type: Expression(Integer) +--E 296 + +--S 297 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 765 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 m +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )(e x + d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 765 +r0:=-120*(b*d-a*e)^3*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(4+m)*_ + (5+m)*(6+m)*(7+m))+30*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(5+m)*(6+m)*(7+m))-6*(b*d-a*e)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(6+m)*(7+m))+(a+b*x)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(7+m))-720*(b*d-a*e)^5*(d+e*x)^(1+m)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m))+_ + 720*(b*d-a*e)^6*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(1+m)*_ + (2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)*(a+b*x))+360*(b*d-a*e)^4*(a+b*x)*_ + (d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)) +--R +--R +--R (2) +--R 6 6 6 6 6 5 6 6 4 6 6 3 6 6 2 6 6 +--R b e m + 21b e m + 175b e m + 735b e m + 1624b e m + 1764b e m +--R + +--R 6 6 +--R 720b e +--R * +--R 6 +--R x +--R + +--R 5 6 6 5 6 6 5 5 5 6 6 5 4 +--R 6a b e m + (132a b e - 6b d e )m + (1140a b e - 90b d e )m +--R + +--R 5 6 6 5 3 5 6 6 5 2 +--R (4920a b e - 510b d e )m + (11094a b e - 1350b d e )m +--R + +--R 5 6 6 5 5 6 6 5 +--R (12228a b e - 1644b d e )m + 5040a b e - 720b d e +--R * +--R 5 +--R x +--R + +--R 2 4 6 6 2 4 6 5 5 5 +--R 15a b e m + (345a b e - 30a b d e )m +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (3105a b e - 510a b d e + 30b d e )m +--R + +--R 2 4 6 5 5 6 2 4 3 +--R (13875a b e - 3150a b d e + 300b d e )m +--R + +--R 2 4 6 5 5 6 2 4 2 +--R (32160a b e - 8850a b d e + 1050b d e )m +--R + +--R 2 4 6 5 5 6 2 4 2 4 6 +--R (36180a b e - 11220a b d e + 1500b d e )m + 15120a b e +--R + +--R 5 5 6 2 4 +--R - 5040a b d e + 720b d e +--R * +--R 4 +--R x +--R + +--R 3 3 6 6 3 3 6 2 4 5 5 +--R 20a b e m + (480a b e - 60a b d e )m +--R + +--R 3 3 6 2 4 5 5 2 4 4 +--R (4520a b e - 1140a b d e + 120a b d e )m +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (21120a b e - 7860a b d e + 1560a b d e - 120b d e )m +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 2 +--R (50900a b e - 24060a b d e + 6360a b d e - 720b d e )m +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 +--R (59040a b e - 32400a b d e + 9960a b d e - 1320b d e )m +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 +--R 25200a b e - 15120a b d e + 5040a b d e - 720b d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 6 4 2 6 3 3 5 5 +--R 15a b e m + (375a b e - 60a b d e )m +--R + +--R 4 2 6 3 3 5 2 4 2 4 4 +--R (3705a b e - 1260a b d e + 180a b d e )m +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 3 +--R (18285a b e - 9780a b d e + 2880a b d e - 360a b d e )m +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 46680a b e - 34020a b d e + 14940a b d e - 3600a b d e +--R + +--R 6 4 2 +--R 360b d e +--R * +--R 2 +--R m +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 56940a b e - 50640a b d e + 27360a b d e - 8280a b d e +--R + +--R 6 4 2 +--R 1080b d e +--R * +--R m +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 25200a b e - 25200a b d e + 15120a b d e - 5040a b d e +--R + +--R 6 4 2 +--R 720b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 5 6 4 2 5 5 +--R 6a b e m + (156a b e - 30a b d e )m +--R + +--R 5 6 4 2 5 3 3 2 4 4 +--R (1620a b e - 690a b d e + 120a b d e )m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 3 +--R (8520a b e - 6030a b d e + 2280a b d e - 360a b d e )m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 23574a b e - 24510a b d e + 15000a b d e - 5040a b d e +--R + +--R 5 4 2 +--R 720a b d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 31644a b e - 44340a b d e + 38040a b d e - 19800a b d e +--R + +--R 5 4 2 6 5 +--R 5760a b d e - 720b d e +--R * +--R m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 15120a b e - 25200a b d e + 25200a b d e - 15120a b d e +--R + +--R 5 4 2 6 5 +--R 5040a b d e - 720b d e +--R * +--R x +--R + +--R 6 6 6 6 6 5 5 5 +--R a e m + (27a e - 6a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 4 +--R (295a e - 150a b d e + 30a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 3 +--R (1665a e - 1470a b d e + 660a b d e - 120a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 2 +--R (5104a e - 7050a b d e + 5370a b d e - 2160a b d e + 360a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 8028a e - 16524a b d e + 19140a b d e - 12840a b d e +--R + +--R 2 4 4 2 5 5 +--R 4680a b d e - 720a b d e +--R * +--R m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 5040a e - 15120a b d e + 25200a b d e - 25200a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 15120a b d e - 5040a b d e + 720b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m + 13132b e m +--R + +--R 7 7 +--R 13068b e m + 5040b e +--R * +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a e m + 28a e m + 322a e m + 1960a e m + 6769a e m + 13132a e m +--R + +--R 7 7 +--R 13068a e m + 5040a e +--R Type: Expression(Integer) +--E 299 + +--S 300 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 765 +t0:=(a+b*x)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 9 14 4 9 5 8 13 2 3 9 4 8 5 2 7 12 +--R b e x + (5a b e + 9b d e )x + (10a b e + 45a b d e + 36b d e )x +--R + +--R 3 2 9 2 3 8 4 2 7 5 3 6 11 +--R (10a b e + 90a b d e + 180a b d e + 84b d e )x +--R + +--R 4 9 3 2 8 2 3 2 7 4 3 6 5 4 5 10 +--R (5a b e + 90a b d e + 360a b d e + 420a b d e + 126b d e )x +--R + +--R 5 9 4 8 3 2 2 7 2 3 3 6 4 4 5 +--R a e + 45a b d e + 360a b d e + 840a b d e + 630a b d e +--R + +--R 5 5 4 +--R 126b d e +--R * +--R 9 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 4 5 4 +--R 9a d e + 180a b d e + 840a b d e + 1260a b d e + 630a b d e +--R + +--R 5 6 3 +--R 84b d e +--R * +--R 8 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 4 6 3 +--R 36a d e + 420a b d e + 1260a b d e + 1260a b d e + 420a b d e +--R + +--R 5 7 2 +--R 36b d e +--R * +--R 7 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 4 7 2 +--R 84a d e + 630a b d e + 1260a b d e + 840a b d e + 180a b d e +--R + +--R 5 8 +--R 9b d e +--R * +--R 6 +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 4 8 +--R 126a d e + 630a b d e + 840a b d e + 360a b d e + 45a b d e +--R + +--R 5 9 +--R b d +--R * +--R 5 +--R x +--R + +--R 5 5 4 4 6 3 3 2 7 2 2 3 8 4 9 4 +--R (126a d e + 420a b d e + 360a b d e + 90a b d e + 5a b d )x +--R + +--R 5 6 3 4 7 2 3 2 8 2 3 9 3 +--R (84a d e + 180a b d e + 90a b d e + 10a b d )x +--R + +--R 5 7 2 4 8 3 2 9 2 5 8 4 9 5 9 +--R (36a d e + 45a b d e + 10a b d )x + (9a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 765 +r0:=-1/364*(b*d-a*e)^3*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/112*(b*d-a*e)^2*(a+b*x)*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/40*(b*d-a*e)*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/16*(a+b*x)*_ + (d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/8008*(b*d-a*e)^5*(d+e*x)^10*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/80080*(b*d-a*e)^6*(d+e*x)^10*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/1456*(b*d-a*e)^4*(a+b*x)*(d+e*x)^10*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 16 16 5 16 6 15 15 +--R 5005b e x + (32032a b e + 48048b d e )x +--R + +--R 2 4 16 5 15 6 2 14 14 +--R (85800a b e + 308880a b d e + 205920b d e )x +--R + +--R 3 3 16 2 4 15 5 2 14 6 3 13 13 +--R (123200a b e + 831600a b d e + 1330560a b d e + 517440b d e )x +--R + +--R 4 2 16 3 3 15 2 4 2 14 +--R 100100a b e + 1201200a b d e + 3603600a b d e +--R + +--R 5 3 13 6 4 12 +--R 3363360a b d e + 840840b d e +--R * +--R 12 +--R x +--R + +--R 5 16 4 2 15 3 3 2 14 +--R 43680a b e + 982800a b d e + 5241600a b d e +--R + +--R 2 4 3 13 5 4 12 6 5 11 +--R 9172800a b d e + 5503680a b d e + 917280b d e +--R * +--R 11 +--R x +--R + +--R 6 16 5 15 4 2 2 14 3 3 3 13 +--R 8008a e + 432432a b d e + 4324320a b d e + 13453440a b d e +--R + +--R 2 4 4 12 5 5 11 6 6 10 +--R 15135120a b d e + 6054048a b d e + 672672b d e +--R * +--R 10 +--R x +--R + +--R 6 15 5 2 14 4 2 3 13 +--R 80080a d e + 1921920a b d e + 11211200a b d e +--R + +--R 3 3 4 12 2 4 5 11 5 6 10 +--R 22422400a b d e + 16816800a b d e + 4484480a b d e +--R + +--R 6 7 9 +--R 320320b d e +--R * +--R 9 +--R x +--R + +--R 6 2 14 5 3 13 4 2 4 12 +--R 360360a d e + 5045040a b d e + 18918900a b d e +--R + +--R 3 3 5 11 2 4 6 10 5 7 9 6 8 8 +--R 25225200a b d e + 12612600a b d e + 2162160a b d e + 90090b d e +--R * +--R 8 +--R x +--R + +--R 6 3 13 5 4 12 4 2 5 11 +--R 960960a d e + 8648640a b d e + 21621600a b d e +--R + +--R 3 3 6 10 2 4 7 9 5 8 8 6 9 7 +--R 19219200a b d e + 6177600a b d e + 617760a b d e + 11440b d e +--R * +--R 7 +--R x +--R + +--R 6 4 12 5 5 11 4 2 6 10 +--R 1681680a d e + 10090080a b d e + 16816800a b d e +--R + +--R 3 3 7 9 2 4 8 8 5 9 7 +--R 9609600a b d e + 1801800a b d e + 80080a b d e +--R * +--R 6 +--R x +--R + +--R 6 5 11 5 6 10 4 2 7 9 +--R 2018016a d e + 8072064a b d e + 8648640a b d e +--R + +--R 3 3 8 8 2 4 9 7 +--R 2882880a b d e + 240240a b d e +--R * +--R 5 +--R x +--R + +--R 6 6 10 5 7 9 4 2 8 8 3 3 9 7 4 +--R (1681680a d e + 4324320a b d e + 2702700a b d e + 400400a b d e )x +--R + +--R 6 7 9 5 8 8 4 2 9 7 3 +--R (960960a d e + 1441440a b d e + 400400a b d e )x +--R + +--R 6 8 8 5 9 7 2 6 9 7 6 10 6 +--R (360360a d e + 240240a b d e )x + 80080a d e x + 8008a d e +--R + +--R 5 11 5 4 2 12 4 3 3 13 3 2 4 14 2 +--R - 4368a b d e + 1820a b d e - 560a b d e + 120a b d e +--R + +--R 5 15 6 16 +--R - 16a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 80080b e x + 80080a e +--R Type: Expression(Integer) +--E 302 + +--S 303 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 765 +t0:=(a+b*x)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 8 13 4 8 5 7 12 2 3 8 4 7 5 2 6 11 +--R b e x + (5a b e + 8b d e )x + (10a b e + 40a b d e + 28b d e )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 10 +--R (10a b e + 80a b d e + 140a b d e + 56b d e )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 5 4 4 9 +--R (5a b e + 80a b d e + 280a b d e + 280a b d e + 70b d e )x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 4 4 4 +--R a e + 40a b d e + 280a b d e + 560a b d e + 350a b d e +--R + +--R 5 5 3 +--R 56b d e +--R * +--R 8 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 4 5 3 +--R 8a d e + 140a b d e + 560a b d e + 700a b d e + 280a b d e +--R + +--R 5 6 2 +--R 28b d e +--R * +--R 7 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 4 6 2 +--R 28a d e + 280a b d e + 700a b d e + 560a b d e + 140a b d e +--R + +--R 5 7 +--R 8b d e +--R * +--R 6 +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 4 7 5 8 5 +--R (56a d e + 350a b d e + 560a b d e + 280a b d e + 40a b d e + b d )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 4 +--R (70a d e + 280a b d e + 280a b d e + 80a b d e + 5a b d )x +--R + +--R 5 5 3 4 6 2 3 2 7 2 3 8 3 +--R (56a d e + 140a b d e + 80a b d e + 10a b d )x +--R + +--R 5 6 2 4 7 3 2 8 2 5 7 4 8 5 8 +--R (28a d e + 40a b d e + 10a b d )x + (8a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 304 + +--S 305 of 765 +r0:=-1/273*(b*d-a*e)^3*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/91*(b*d-a*e)^2*(a+b*x)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/35*(b*d-a*e)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/15*(a+b*x)*_ + (d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/5005*(b*d-a*e)^5*(d+e*x)^9*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/45045*(b*d-a*e)^6*(d+e*x)^9*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/1001*(b*d-a*e)^4*(a+b*x)*(d+e*x)^9*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 15 15 5 15 6 14 14 +--R 3003b e x + (19305a b e + 25740b d e )x +--R + +--R 2 4 15 5 14 6 2 13 13 +--R (51975a b e + 166320a b d e + 97020b d e )x +--R + +--R 3 3 15 2 4 14 5 2 13 6 3 12 12 +--R (75075a b e + 450450a b d e + 630630a b d e + 210210b d e )x +--R + +--R 4 2 15 3 3 14 2 4 2 13 +--R 61425a b e + 655200a b d e + 1719900a b d e +--R + +--R 5 3 12 6 4 11 +--R 1375920a b d e + 286650b d e +--R * +--R 11 +--R x +--R + +--R 5 15 4 2 14 3 3 2 13 +--R 27027a b e + 540540a b d e + 2522520a b d e +--R + +--R 2 4 3 12 5 4 11 6 5 10 +--R 3783780a b d e + 1891890a b d e + 252252b d e +--R * +--R 10 +--R x +--R + +--R 6 15 5 14 4 2 2 13 3 3 3 12 +--R 5005a e + 240240a b d e + 2102100a b d e + 5605600a b d e +--R + +--R 2 4 4 11 5 5 10 6 6 9 +--R 5255250a b d e + 1681680a b d e + 140140b d e +--R * +--R 9 +--R x +--R + +--R 6 14 5 2 13 4 2 3 12 +--R 45045a d e + 945945a b d e + 4729725a b d e +--R + +--R 3 3 4 11 2 4 5 10 5 6 9 6 7 8 +--R 7882875a b d e + 4729725a b d e + 945945a b d e + 45045b d e +--R * +--R 8 +--R x +--R + +--R 6 2 13 5 3 12 4 2 4 11 +--R 180180a d e + 2162160a b d e + 6756750a b d e +--R + +--R 3 3 5 10 2 4 6 9 5 7 8 6 8 7 +--R 7207200a b d e + 2702700a b d e + 308880a b d e + 6435b d e +--R * +--R 7 +--R x +--R + +--R 6 3 12 5 4 11 4 2 5 10 +--R 420420a d e + 3153150a b d e + 6306300a b d e +--R + +--R 3 3 6 9 2 4 7 8 5 8 7 +--R 4204200a b d e + 900900a b d e + 45045a b d e +--R * +--R 6 +--R x +--R + +--R 6 4 11 5 5 10 4 2 6 9 +--R 630630a d e + 3027024a b d e + 3783780a b d e +--R + +--R 3 3 7 8 2 4 8 7 +--R 1441440a b d e + 135135a b d e +--R * +--R 5 +--R x +--R + +--R 6 5 10 5 6 9 4 2 7 8 3 3 8 7 4 +--R (630630a d e + 1891890a b d e + 1351350a b d e + 225225a b d e )x +--R + +--R 6 6 9 5 7 8 4 2 8 7 3 +--R (420420a d e + 720720a b d e + 225225a b d e )x +--R + +--R 6 7 8 5 8 7 2 6 8 7 6 9 6 +--R (180180a d e + 135135a b d e )x + 45045a d e x + 5005a d e +--R + +--R 5 10 5 4 2 11 4 3 3 12 3 2 4 13 2 +--R - 3003a b d e + 1365a b d e - 455a b d e + 105a b d e +--R + +--R 5 14 6 15 +--R - 15a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 305 + +--S 306 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 765 +t0:=(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 7 12 4 7 5 6 11 2 3 7 4 6 5 2 5 10 +--R b e x + (5a b e + 7b d e )x + (10a b e + 35a b d e + 21b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 9 +--R (10a b e + 70a b d e + 105a b d e + 35b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 8 +--R (5a b e + 70a b d e + 210a b d e + 175a b d e + 35b d e )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 +--R a e + 35a b d e + 210a b d e + 350a b d e + 175a b d e +--R + +--R 5 5 2 +--R 21b d e +--R * +--R 7 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 +--R 7a d e + 105a b d e + 350a b d e + 350a b d e + 105a b d e +--R + +--R 5 6 +--R 7b d e +--R * +--R 6 +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 5 7 5 +--R (21a d e + 175a b d e + 350a b d e + 210a b d e + 35a b d e + b d )x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 4 +--R (35a d e + 175a b d e + 210a b d e + 70a b d e + 5a b d )x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 3 +--R (35a d e + 105a b d e + 70a b d e + 10a b d )x +--R + +--R 5 5 2 4 6 3 2 7 2 5 6 4 7 5 7 +--R (21a d e + 35a b d e + 10a b d )x + (7a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 765 +r0:=-5/1001*(b*d-a*e)^3*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 5/364*(b*d-a*e)^2*(a+b*x)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 3/91*(b*d-a*e)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/14*(a+b*x)*_ + (d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/3003*(b*d-a*e)^5*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/24024*(b*d-a*e)^6*(d+e*x)^8*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+3/2002*(b*d-a*e)^4*(a+b*x)*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 14 14 5 14 6 13 13 +--R 1716b e x + (11088a b e + 12936b d e )x +--R + +--R 2 4 14 5 13 6 2 12 12 +--R (30030a b e + 84084a b d e + 42042b d e )x +--R + +--R 3 3 14 2 4 13 5 2 12 6 3 11 11 +--R (43680a b e + 229320a b d e + 275184a b d e + 76440b d e )x +--R + +--R 4 2 14 3 3 13 2 4 2 12 5 3 11 +--R 36036a b e + 336336a b d e + 756756a b d e + 504504a b d e +--R + +--R 6 4 10 +--R 84084b d e +--R * +--R 10 +--R x +--R + +--R 5 14 4 2 13 3 3 2 12 +--R 16016a b e + 280280a b d e + 1121120a b d e +--R + +--R 2 4 3 11 5 4 10 6 5 9 +--R 1401400a b d e + 560560a b d e + 56056b d e +--R * +--R 9 +--R x +--R + +--R 6 14 5 13 4 2 2 12 3 3 3 11 +--R 3003a e + 126126a b d e + 945945a b d e + 2102100a b d e +--R + +--R 2 4 4 10 5 5 9 6 6 8 +--R 1576575a b d e + 378378a b d e + 21021b d e +--R * +--R 8 +--R x +--R + +--R 6 13 5 2 12 4 2 3 11 +--R 24024a d e + 432432a b d e + 1801800a b d e +--R + +--R 3 3 4 10 2 4 5 9 5 6 8 6 7 7 +--R 2402400a b d e + 1081080a b d e + 144144a b d e + 3432b d e +--R * +--R 7 +--R x +--R + +--R 6 2 12 5 3 11 4 2 4 10 3 3 5 9 +--R 84084a d e + 840840a b d e + 2102100a b d e + 1681680a b d e +--R + +--R 2 4 6 8 5 7 7 +--R 420420a b d e + 24024a b d e +--R * +--R 6 +--R x +--R + +--R 6 3 11 5 4 10 4 2 5 9 3 3 6 8 +--R 168168a d e + 1009008a b d e + 1513512a b d e + 672672a b d e +--R + +--R 2 4 7 7 +--R 72072a b d e +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 2 6 8 3 3 7 7 4 +--R (210210a d e + 756756a b d e + 630630a b d e + 120120a b d e )x +--R + +--R 6 5 9 5 6 8 4 2 7 7 3 +--R (168168a d e + 336336a b d e + 120120a b d e )x +--R + +--R 6 6 8 5 7 7 2 6 7 7 6 8 6 +--R (84084a d e + 72072a b d e )x + 24024a d e x + 3003a d e +--R + +--R 5 9 5 4 2 10 4 3 3 11 3 2 4 12 2 +--R - 2002a b d e + 1001a b d e - 364a b d e + 91a b d e +--R + +--R 5 13 6 14 +--R - 14a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 24024b e x + 24024a e +--R Type: Expression(Integer) +--E 308 + +--S 309 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 765 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 11 4 6 5 5 10 2 3 6 4 5 5 2 4 9 +--R b e x + (5a b e + 6b d e )x + (10a b e + 30a b d e + 15b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 8 +--R (10a b e + 60a b d e + 75a b d e + 20b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 7 +--R (5a b e + 60a b d e + 150a b d e + 100a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 6 +--R (a e + 30a b d e + 150a b d e + 200a b d e + 75a b d e + 6b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 5 +--R (6a d e + 75a b d e + 200a b d e + 150a b d e + 30a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 4 +--R (15a d e + 100a b d e + 150a b d e + 60a b d e + 5a b d )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 3 +--R (20a d e + 75a b d e + 60a b d e + 10a b d )x +--R + +--R 5 4 2 4 5 3 2 6 2 5 5 4 6 5 6 +--R (15a d e + 30a b d e + 10a b d )x + (6a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 765 +r0:=1/12012*(b*d-a*e)^6*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^7+1/1716*(b*d-a*e)^5*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6+1/429*(b*d-a*e)^4*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/143*(b*d-a*e)^3*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^4+5/286*(b*d-a*e)^2*(d+e*x)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^3+1/26*(b*d-a*e)*(d+e*x)^5*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/13*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 12 6 12 11 6 12 5 11 +--R 924b e x + (5082a b e + 6006b d e )x +--R + +--R 2 10 6 11 5 12 2 4 10 +--R (11298a b e + 33306a b d e + 16380b d e )x +--R + +--R 3 9 6 2 10 5 11 2 4 12 3 3 9 +--R (12726a b e + 74802a b d e + 91728a b d e + 24024b d e )x +--R + +--R 4 8 6 3 9 5 2 10 2 4 11 3 3 +--R 7294a b e + 85358a b d e + 208572a b d e + 136136a b d e +--R + +--R 12 4 2 +--R 20020b d e +--R * +--R 8 +--R x +--R + +--R 5 7 6 4 8 5 3 9 2 4 2 10 3 3 +--R 1715a b e + 49777a b d e + 241878a b d e + 314314a b d e +--R + +--R 11 4 2 12 5 +--R 115115a b d e + 9009b d e +--R * +--R 7 +--R x +--R + +--R 6 6 6 5 7 5 4 8 2 4 3 9 3 3 +--R a b e + 11999a b d e + 144222a b d e + 372086a b d e +--R + +--R 2 10 4 2 11 5 12 6 +--R 270985a b d e + 52767a b d e + 1716b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 6 6 5 5 7 2 4 4 8 3 3 +--R - a b e + 13a b d e + 35958a b d e + 228514a b d e +--R + +--R 3 9 4 2 2 10 5 11 6 +--R 329615a b d e + 127413a b d e + 10296a b d +--R * +--R 5 +--R x +--R + +--R 8 4 6 7 5 5 6 6 2 4 5 7 3 3 4 8 4 2 +--R a b e - 13a b d e + 78a b d e + 59774a b d e + 210925a b d e +--R + +--R 3 9 5 2 10 6 +--R 160875a b d e + 25740a b d +--R * +--R 4 +--R x +--R + +--R 9 3 6 8 4 5 7 5 2 4 6 6 3 3 5 7 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e + 59345a b d e +--R + +--R 4 8 5 3 9 6 +--R 109395a b d e + 34320a b d +--R * +--R 3 +--R x +--R + +--R 10 2 6 9 3 5 8 4 2 4 7 5 3 3 6 6 4 2 +--R a b e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 5 7 5 4 8 6 +--R 34749a b d e + 25740a b d +--R * +--R 2 +--R x +--R + +--R 11 6 10 2 5 9 3 2 4 8 4 3 3 7 5 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e - 715a b d e +--R + +--R 6 6 5 5 7 6 +--R 1287a b d e + 10296a b d +--R * +--R x +--R + +--R 12 6 11 5 10 2 2 4 9 3 3 3 8 4 4 2 +--R a e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 7 5 5 6 6 6 +--R - 1287a b d e + 1716a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 +--R 12012b +--R Type: Expression(Integer) +--E 311 + +--S 312 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 765 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 5 10 4 5 5 4 9 2 3 5 4 4 5 2 3 8 +--R b e x + (5a b e + 5b d e )x + (10a b e + 25a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 7 +--R (10a b e + 50a b d e + 50a b d e + 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 6 +--R (5a b e + 50a b d e + 100a b d e + 50a b d e + 5b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e + 25a b d e + 100a b d e + 100a b d e + 25a b d e + b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4 +--R (5a d e + 50a b d e + 100a b d e + 50a b d e + 5a b d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 3 +--R (10a d e + 50a b d e + 50a b d e + 10a b d )x +--R + +--R 5 3 2 4 4 3 2 5 2 5 4 4 5 5 5 +--R (10a d e + 25a b d e + 10a b d )x + (5a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 313 + +--S 314 of 765 +r0:=1/5544*(b*d-a*e)^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6+1/792*(b*d-a*e)^4*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/198*(b*d-a*e)^3*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+1/66*(b*d-a*e)^2*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^3+5/132*(b*d-a*e)*(d+e*x)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/12*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 11 5 11 10 5 11 4 10 +--R 462b e x + (2562a b e + 2520b d e )x +--R + +--R 2 9 5 10 4 11 2 3 9 +--R (5754a b e + 14112a b d e + 5544b d e )x +--R + +--R 3 8 5 2 9 4 10 2 3 11 3 2 8 +--R (6566a b e + 32088a b d e + 31416a b d e + 6160b d e )x +--R + +--R 4 7 5 3 8 4 2 9 2 3 10 3 2 +--R 3829a b e + 37212a b d e + 72534a b d e + 35420a b d e +--R + +--R 11 4 +--R 3465b d e +--R * +--R 7 +--R x +--R + +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 +--R 923a b e + 22188a b d e + 85866a b d e + 83380a b d e +--R + +--R 10 4 11 5 +--R 20295a b d e + 792b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R a b e + 5532a b d e + 52734a b d e + 101420a b d e +--R + +--R 2 9 4 10 5 +--R 49005a b d e + 4752a b d +--R * +--R 5 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R - a b e + 12a b d e + 13794a b d e + 64900a b d e +--R + +--R 3 8 4 2 9 5 +--R 61875a b d e + 11880a b d +--R * +--R 4 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 4 7 4 +--R a b e - 12a b d e + 66a b d e + 18260a b d e + 42075a b d e +--R + +--R 3 8 5 +--R 15840a b d +--R * +--R 3 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 5 6 4 +--R - a b e + 12a b d e - 66a b d e + 220a b d e + 13365a b d e +--R + +--R 4 7 5 +--R 11880a b d +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 6 5 4 +--R a b e - 12a b d e + 66a b d e - 220a b d e + 495a b d e +--R + +--R 5 6 5 +--R 4752a b d +--R * +--R x +--R + +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 6 5 5 +--R - a e + 12a b d e - 66a b d e + 220a b d e - 495a b d e + 792a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 +--R 5544b +--R Type: Expression(Integer) +--E 314 + +--S 315 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 765 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 765 +r0:=1/2310*(b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/330*(b*d-a*e)^3*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+2/165*(b*d-a*e)^2*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+2/55*(b*d-a*e)*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/11*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 10 4 10 9 4 10 3 9 +--R 210b e x + (1176a b e + 924b d e )x +--R + +--R 2 8 4 9 3 10 2 2 8 +--R (2674a b e + 5236a b d e + 1540b d e )x +--R + +--R 3 7 4 2 8 3 9 2 2 10 3 7 +--R (3101a b e + 12089a b d e + 8855a b d e + 1155b d e)x +--R + +--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 6 +--R (1849a b e + 14311a b d e + 20845a b d e + 6765a b d e + 330b d )x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R 461a b e + 8789a b d e + 25355a b d e + 16335a b d e +--R + +--R 9 4 +--R 1980a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 2 8 4 4 +--R (a b e + 2299a b d e + 16225a b d e + 20625a b d e + 4950a b d )x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 3 7 4 3 +--R (- a b e + 11a b d e + 4565a b d e + 14025a b d e + 6600a b d )x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 4 6 4 2 +--R (a b e - 11a b d e + 55a b d e + 4455a b d e + 4950a b d )x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 5 5 4 10 4 +--R (- a b e + 11a b d e - 55a b d e + 165a b d e + 1980a b d )x + a e +--R + +--R 9 3 8 2 2 2 7 3 3 6 4 4 +--R - 11a b d e + 55a b d e - 165a b d e + 330a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 2310b +--R Type: Expression(Integer) +--E 317 + +--S 318 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 of 765 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 765 +r0:=1/840*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+1/120*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+1/30*(b*d-a*e)*(d+e*x)^2*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^2+1/10*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 9 3 9 8 3 9 2 8 +--R 84b e x + (476a b e + 280b d e )x +--R + +--R 2 7 3 8 2 9 2 7 +--R (1099a b e + 1610a b d e + 315b d e)x +--R + +--R 3 6 3 2 7 2 8 2 9 3 6 +--R (1301a b e + 3790a b d e + 1845a b d e + 120b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (799a b e + 4610a b d e + 4455a b d e + 720a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 4 +--R (209a b e + 2950a b d e + 5625a b d e + 1800a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (a b e + 830a b d e + 3825a b d e + 2400a b d )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (- a b e + 10a b d e + 1215a b d e + 1800a b d )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 8 2 +--R (a b e - 10a b d e + 45a b d e + 720a b d )x - a e + 10a b d e +--R + +--R 7 2 2 6 3 3 +--R - 45a b d e + 120a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 840b +--R Type: Expression(Integer) +--E 320 + +--S 321 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 765 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 765 +r0:=1/252*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+1/36*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2+1/9*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 8 2 8 7 2 8 7 +--R 28b e x + (161a b e + 63b d e)x +--R + +--R 2 6 2 7 8 2 6 +--R (379a b e + 369a b d e + 36b d )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (461a b e + 891a b d e + 216a b d )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (295a b e + 1125a b d e + 540a b d )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (83a b e + 765a b d e + 720a b d )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (a b e + 243a b d e + 540a b d )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- a b e + 9a b d e + 216a b d )x + a e - 9a b d e + 36a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 252b +--R Type: Expression(Integer) +--E 323 + +--S 324 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 of 765 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 765 +r0:=1/56*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2+1/8*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 7 7 6 7 6 2 5 6 5 +--R 7b e x + (41a b e + 8b d)x + (99a b e + 48a b d)x +--R + +--R 3 4 2 5 4 4 3 3 4 3 +--R (125a b e + 120a b d)x + (85a b e + 160a b d)x +--R + +--R 5 2 4 3 2 6 5 2 7 6 +--R (27a b e + 120a b d)x + (a b e + 48a b d)x - a e + 8a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 56b +--R Type: Expression(Integer) +--E 326 + +--S 327 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 765 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7b +--R Type: Expression(Integer) +--E 329 + +--S 330 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 331 + +--S 332 of 765 +r0:=-1/3*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+1/4*(b*d-a*e)^2*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-1/5*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/e^2+1/6*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-(b*d-_ + a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/2*(b*d-a*e)^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+(b*d-a*e)^6*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 60a e - 360a b d e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 5 5 6 6 +--R - 360a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (72a b e - 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (225a b e - 90a b d e + 15b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b e - 300a b d e + 120a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (450a b e - 600a b d e + 450a b d e - 180a b d e + 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 360a b e - 900a b d e + 1200a b d e - 900a b d e + 360a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 147a e - 522a b d e + 855a b d e - 740a b d e + 330a b d e +--R + +--R 5 5 +--R - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 332 + +--S 333 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 334 + +--S 335 of 765 +r0:=2*b*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-3/2*b*(b*d-a*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3+6/5*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/e^2-(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x))+_ + 6*b*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-3*b*(b*d-a*e)^3*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-6*b*(b*d-a*e)^5*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e +--R + +--R 5 4 2 6 5 +--R 300a b d e - 60b d e +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 60a b d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 6 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 2b e x + (15a b e - 3b d e )x + (50a b e - 25a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b e - 100a b d e + 50a b d e - 10b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (150a b e - 300a b d e + 300a b d e - 150a b d e + 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 77a b e - 85a b d e - 130a b d e + 330a b d e - 240a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e + 137a b d e - 385a b d e + 470a b d e - 270a b d e +--R + +--R 5 5 +--R 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +--R 10b e x + (10a e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 335 + +--S 336 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 336 + +)clear all + +--S 337 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 337 + +--S 338 of 765 +r0:=-5*b^2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+15/4*b^2*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-1/2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(d+e*x)^2)-3*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(d+e*x))-15*b^2*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+_ + 15/2*b^2*(b*d-a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+_ + 15*b^2*(b*d-a*e)^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b d e - 480a b d e + 720a b d e - 480a b d e + 120b d e)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (8a b e - 2b d e )x + (30a b e - 20a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b e - 120a b d e + 80a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (35a b e + 100a b d e - 330a b d e + 300a b d e - 90b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b e + 190a b d e - 280a b d e + 60a b d e + 120a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a e - 12a b d e + 125a b d e - 260a b d e + 210a b d e +--R + +--R 5 5 +--R - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 4b e x + (4a e + 8b d e )x + (8a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 338 + +--S 339 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 339 + +)clear all + +--S 340 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 340 + +--S 341 of 765 +r0:=20/3*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-5*b^2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(d+e*x))-1/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e*(d+e*x)^3)-b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^2)+20*b^3*_ + (b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-10*b^3*(b*d-a*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-20*b^3*(b*d-a*e)^3*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e )x +--R + +--R 3 3 2 4 2 4 3 3 5 4 2 6 5 3 3 3 3 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e)x + 60a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (9a b e - 3b d e )x + (45a b e - 45a b d e + 15b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (180a b d e - 270a b d e + 110b d e )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 2 +--R (- 45a b e + 180a b d e - 270a b d e + 150b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 6 5 6 6 +--R (- 9a b e - 45a b d e + 270a b d e - 270a b d e + 60b d e)x - a e +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 3a b d e - 15a b d e + 110a b d e - 150a b d e + 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 8 3 7 3 7 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 341 + +--S 342 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 343 + +--S 344 of 765 +r0:=-5/4*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^2)-_ + 5*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x))-1/4*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^4)-1/2*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^3)-15*b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6+15/2*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+_ + 15*b^4*(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 2 4 6 5 5 6 2 4 4 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (240a b d e - 480a b d e + 240b d e )x +--R + +--R 2 4 2 4 5 3 3 6 4 2 2 +--R (360a b d e - 720a b d e + 360b d e )x +--R + +--R 2 4 3 3 5 4 2 6 5 2 4 4 2 5 5 +--R (240a b d e - 480a b d e + 240b d e)x + 60a b d e - 120a b d e +--R + +--R 6 6 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 2b e x + (24a b e - 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 35a b e + 190a b d e - 125b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 80a b e + 100a b d e + 280a b d e - 260b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 30a b e - 120a b d e + 330a b d e + 60a b d e - 210b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 8a b e - 20a b d e - 80a b d e + 300a b d e - 120a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - a e - 2a b d e - 5a b d e - 20a b d e + 90a b d e - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 4b e x + (4a e + 16b d e )x + (16a d e + 24b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (24a d e + 16b d e )x + (16a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 344 + +--S 345 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^6 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 346 + +--S 347 of 765 +r0:=-1/2*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^3)-_ + b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^2)-1/5*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^5)-3/10*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^4)+6*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 3*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x))-_ + 6*b^5*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 6 5 5 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (300a b d e - 300b d e )x +--R + +--R 5 2 4 6 3 3 3 5 3 3 6 4 2 2 +--R (600a b d e - 600b d e )x + (600a b d e - 600b d e )x +--R + +--R 5 4 2 6 5 5 5 6 6 +--R (300a b d e - 300b d e)x + 60a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (- 77a b e + 137b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 150a b e - 85a b d e + 385b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 100a b e - 300a b d e + 130a b d e + 470b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 50a b e - 100a b d e - 300a b d e + 330a b d e + 270b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 15a b e - 25a b d e - 50a b d e - 150a b d e + 240a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e - 3a b d e - 5a b d e - 10a b d e - 30a b d e + 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 10b e x + (10a e + 50b d e )x + (50a d e + 100b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (100a d e + 100b d e )x + (100a d e + 50b d e )x +--R + +--R 4 8 5 7 5 7 +--R (50a d e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 347 + +--S 348 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 349 + +--S 350 of 765 +r0:=-1/4*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^4)-_ + 1/3*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^3)-1/6*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^6)-1/5*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^5)-1/2*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^2)+b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x))+b^6*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 6 6 5 5 6 2 4 4 6 3 3 3 6 4 2 2 +--R 60b e x + 360b d e x + 900b d e x + 1200b d e x + 900b d e x +--R + +--R 6 5 6 6 +--R 360b d e x + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 87b e x + (- 360a b e - 162b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 450a b e - 900a b d e + 45b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 400a b e - 600a b d e - 1200a b d e + 460b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 225a b e - 300a b d e - 450a b d e - 900a b d e + 570b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 72a b e - 90a b d e - 120a b d e - 180a b d e - 360a b d e +--R + +--R 6 5 +--R 300b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e - 12a b d e - 15a b d e - 20a b d e - 30a b d e +--R + +--R 5 5 6 6 +--R - 60a b d e + 60b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 7 13 12 6 12 2 11 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 11 3 10 4 3 10 4 9 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 9 5 8 2 5 8 6 7 6 7 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 350 + +--S 351 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 352 + +--S 353 of 765 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^7) +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- b x - 6a b x - 15a b x - 20a b x - 15a b x - 6a b x - a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 7 7 7 2 6 6 2 6 3 5 5 +--R (7a e - 7b d e )x + (49a d e - 49b d e )x + (147a d e - 147b d e )x +--R + +--R 3 5 4 4 4 4 4 5 3 3 +--R (245a d e - 245b d e )x + (245a d e - 245b d e )x +--R + +--R 5 3 6 2 2 6 2 7 7 8 +--R (147a d e - 147b d e )x + (49a d e - 49b d e)x + 7a d e - 7b d +--R Type: Expression(Integer) +--E 353 + +--S 354 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 355 + +--S 356 of 765 +r0:=1/8*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^8)+_ + 1/56*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^7) +--R +--R +--R (2) +--R 7 7 6 7 6 2 5 6 5 +--R b e x + (- a b e + 8b d)x + (- 27a b e + 48a b d)x +--R + +--R 3 4 2 5 4 4 3 3 4 3 +--R (- 85a b e + 120a b d)x + (- 125a b e + 160a b d)x +--R + +--R 5 2 4 3 2 6 5 2 7 6 +--R (- 99a b e + 120a b d)x + (- 41a b e + 48a b d)x - 7a e + 8a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 10 9 2 2 8 8 +--R (56a e - 112a b d e + 56b d e )x +--R + +--R 2 9 2 8 2 3 7 7 +--R (448a d e - 896a b d e + 448b d e )x +--R + +--R 2 2 8 3 7 2 4 6 6 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 3 7 4 6 2 5 5 5 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 4 6 5 5 2 6 4 4 +--R (3920a d e - 7840a b d e + 3920b d e )x +--R + +--R 2 5 5 6 4 2 7 3 3 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 6 4 7 3 2 8 2 2 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 7 3 8 2 2 9 2 8 2 9 2 10 +--R (448a d e - 896a b d e + 448b d e)x + 56a d e - 112a b d e + 56b d +--R Type: Expression(Integer) +--E 356 + +--S 357 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 358 + +--S 359 of 765 +r0:=1/9*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^9)+_ + 1/36*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^8)+_ + 1/252*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^7) +--R +--R +--R (2) +--R 8 2 8 7 2 8 7 2 6 2 7 8 2 6 +--R - b e x + (a b e - 9b d e)x + (- a b e + 9a b d e - 36b d )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 83a b e + 243a b d e - 216a b d )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 295a b e + 765a b d e - 540a b d )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 461a b e + 1125a b d e - 720a b d )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 379a b e + 891a b d e - 540a b d )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 161a b e + 369a b d e - 216a b d )x - 28a e + 63a b d e - 36a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 12 2 11 2 2 10 3 3 9 9 +--R (252a e - 756a b d e + 756a b d e - 252b d e )x +--R + +--R 3 11 2 2 10 2 3 9 3 4 8 8 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e )x +--R + +--R 3 2 10 2 3 9 2 4 8 3 5 7 7 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 3 9 2 4 8 2 5 7 3 6 6 6 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 4 8 2 5 7 2 6 6 3 7 5 5 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 5 7 2 6 6 2 7 5 3 8 4 4 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 6 6 2 7 5 2 8 4 3 9 3 3 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 7 5 2 8 4 2 9 3 3 10 2 2 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 8 4 2 9 3 2 10 2 3 11 3 9 3 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e)x + 252a d e +--R + +--R 2 10 2 2 11 3 12 +--R - 756a b d e + 756a b d e - 252b d +--R Type: Expression(Integer) +--E 359 + +--S 360 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 361 + +--S 362 of 765 +r0:=1/10*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^10)+_ + 1/30*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^9)+_ + 1/120*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^8)+_ + 1/840*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^7) +--R +--R +--R (2) +--R 9 3 9 8 3 9 2 8 2 7 3 8 2 9 2 7 +--R b e x + (- a b e + 10b d e )x + (a b e - 10a b d e + 45b d e)x +--R + +--R 3 6 3 2 7 2 8 2 9 3 6 +--R (- a b e + 10a b d e - 45a b d e + 120b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (- 209a b e + 830a b d e - 1215a b d e + 720a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 4 +--R (- 799a b e + 2950a b d e - 3825a b d e + 1800a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (- 1301a b e + 4610a b d e - 5625a b d e + 2400a b d )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (- 1099a b e + 3790a b d e - 4455a b d e + 1800a b d )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 +--R (- 476a b e + 1610a b d e - 1845a b d e + 720a b d )x - 84a e +--R + +--R 8 2 7 2 2 6 3 3 +--R 280a b d e - 315a b d e + 120a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 14 3 13 2 2 2 12 3 3 11 4 4 10 +--R (840a e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d e ) +--R * +--R 10 +--R x +--R + +--R 4 13 3 2 12 2 2 3 11 3 4 10 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 5 9 +--R 8400b d e +--R * +--R 9 +--R x +--R + +--R 4 2 12 3 3 11 2 2 4 10 3 5 9 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 6 8 +--R 37800b d e +--R * +--R 8 +--R x +--R + +--R 4 3 11 3 4 10 2 2 5 9 3 6 8 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 7 7 +--R 100800b d e +--R * +--R 7 +--R x +--R + +--R 4 4 10 3 5 9 2 2 6 8 3 7 7 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 8 6 +--R 176400b d e +--R * +--R 6 +--R x +--R + +--R 4 5 9 3 6 8 2 2 7 7 3 8 6 +--R 211680a d e - 846720a b d e + 1270080a b d e - 846720a b d e +--R + +--R 4 9 5 +--R 211680b d e +--R * +--R 5 +--R x +--R + +--R 4 6 8 3 7 7 2 2 8 6 3 9 5 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 10 4 +--R 176400b d e +--R * +--R 4 +--R x +--R + +--R 4 7 7 3 8 6 2 2 9 5 3 10 4 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 11 3 +--R 100800b d e +--R * +--R 3 +--R x +--R + +--R 4 8 6 3 9 5 2 2 10 4 3 11 3 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 12 2 +--R 37800b d e +--R * +--R 2 +--R x +--R + +--R 4 9 5 3 10 4 2 2 11 3 3 12 2 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 13 +--R 8400b d e +--R * +--R x +--R + +--R 4 10 4 3 11 3 2 2 12 2 3 13 4 14 +--R 840a d e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d +--R Type: Expression(Integer) +--E 362 + +--S 363 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 364 + +--S 365 of 765 +r0:=1/11*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^11)+_ + 2/55*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^10)+_ + 2/165*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^9)+_ + 1/330*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^8)+_ + 1/2310*b^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^7) +--R +--R +--R (2) +--R 10 4 10 9 4 10 3 9 +--R - b e x + (a b e - 11b d e )x +--R + +--R 2 8 4 9 3 10 2 2 8 +--R (- a b e + 11a b d e - 55b d e )x +--R + +--R 3 7 4 2 8 3 9 2 2 10 3 7 +--R (a b e - 11a b d e + 55a b d e - 165b d e)x +--R + +--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 6 +--R (- a b e + 11a b d e - 55a b d e + 165a b d e - 330b d )x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R - 461a b e + 2299a b d e - 4565a b d e + 4455a b d e +--R + +--R 9 4 +--R - 1980a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 +--R - 1849a b e + 8789a b d e - 16225a b d e + 14025a b d e +--R + +--R 2 8 4 +--R - 4950a b d +--R * +--R 4 +--R x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 +--R - 3101a b e + 14311a b d e - 25355a b d e + 20625a b d e +--R + +--R 3 7 4 +--R - 6600a b d +--R * +--R 3 +--R x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 +--R - 2674a b e + 12089a b d e - 20845a b d e + 16335a b d e +--R + +--R 4 6 4 +--R - 4950a b d +--R * +--R 2 +--R x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 +--R - 1176a b e + 5236a b d e - 8855a b d e + 6765a b d e +--R + +--R 5 5 4 +--R - 1980a b d +--R * +--R x +--R + +--R 10 4 9 3 8 2 2 2 7 3 3 6 4 4 +--R - 210a e + 924a b d e - 1540a b d e + 1155a b d e - 330a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 16 4 15 3 2 2 14 2 3 3 13 +--R 2310a e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 4 12 5 5 11 +--R 11550a b d e - 2310b d e +--R * +--R 11 +--R x +--R + +--R 5 15 4 2 14 3 2 3 13 2 3 4 12 +--R 25410a d e - 127050a b d e + 254100a b d e - 254100a b d e +--R + +--R 4 5 11 5 6 10 +--R 127050a b d e - 25410b d e +--R * +--R 10 +--R x +--R + +--R 5 2 14 4 3 13 3 2 4 12 2 3 5 11 +--R 127050a d e - 635250a b d e + 1270500a b d e - 1270500a b d e +--R + +--R 4 6 10 5 7 9 +--R 635250a b d e - 127050b d e +--R * +--R 9 +--R x +--R + +--R 5 3 13 4 4 12 3 2 5 11 +--R 381150a d e - 1905750a b d e + 3811500a b d e +--R + +--R 2 3 6 10 4 7 9 5 8 8 +--R - 3811500a b d e + 1905750a b d e - 381150b d e +--R * +--R 8 +--R x +--R + +--R 5 4 12 4 5 11 3 2 6 10 2 3 7 9 +--R 762300a d e - 3811500a b d e + 7623000a b d e - 7623000a b d e +--R + +--R 4 8 8 5 9 7 +--R 3811500a b d e - 762300b d e +--R * +--R 7 +--R x +--R + +--R 5 5 11 4 6 10 3 2 7 9 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 8 8 4 9 7 5 10 6 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 6 +--R x +--R + +--R 5 6 10 4 7 9 3 2 8 8 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 9 7 4 10 6 5 11 5 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 5 +--R x +--R + +--R 5 7 9 4 8 8 3 2 9 7 2 3 10 6 +--R 762300a d e - 3811500a b d e + 7623000a b d e - 7623000a b d e +--R + +--R 4 11 5 5 12 4 +--R 3811500a b d e - 762300b d e +--R * +--R 4 +--R x +--R + +--R 5 8 8 4 9 7 3 2 10 6 2 3 11 5 +--R 381150a d e - 1905750a b d e + 3811500a b d e - 3811500a b d e +--R + +--R 4 12 4 5 13 3 +--R 1905750a b d e - 381150b d e +--R * +--R 3 +--R x +--R + +--R 5 9 7 4 10 6 3 2 11 5 2 3 12 4 +--R 127050a d e - 635250a b d e + 1270500a b d e - 1270500a b d e +--R + +--R 4 13 3 5 14 2 +--R 635250a b d e - 127050b d e +--R * +--R 2 +--R x +--R + +--R 5 10 6 4 11 5 3 2 12 4 2 3 13 3 +--R 25410a d e - 127050a b d e + 254100a b d e - 254100a b d e +--R + +--R 4 14 2 5 15 +--R 127050a b d e - 25410b d e +--R * +--R x +--R + +--R 5 11 5 4 12 4 3 2 13 3 2 3 14 2 +--R 2310a d e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 15 5 16 +--R 11550a b d e - 2310b d +--R Type: Expression(Integer) +--E 365 + +--S 366 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^13 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R e x + 13d e x + 78d e x + 286d e x + 715d e x + 1287d e x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 +--R 1716d e x + 1716d e x + 1287d e x + 715d e x + 286d e x + 78d e x +--R + +--R 12 13 +--R 13d e x + d +--R Type: Expression(Integer) +--E 367 + +--S 368 of 765 +r0:=1/12*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^12)+_ + 5/132*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^11)+_ + 1/66*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^10)+_ + 1/198*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^9)+_ + 1/792*b^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^8)+_ + 1/5544*b^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^6*(d+e*x)^7) +--R +--R +--R (2) +--R 11 5 11 10 5 11 4 10 +--R b e x + (- a b e + 12b d e )x +--R + +--R 2 9 5 10 4 11 2 3 9 +--R (a b e - 12a b d e + 66b d e )x +--R + +--R 3 8 5 2 9 4 10 2 3 11 3 2 8 +--R (- a b e + 12a b d e - 66a b d e + 220b d e )x +--R + +--R 4 7 5 3 8 4 2 9 2 3 10 3 2 11 4 7 +--R (a b e - 12a b d e + 66a b d e - 220a b d e + 495b d e)x +--R + +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 10 4 +--R - a b e + 12a b d e - 66a b d e + 220a b d e - 495a b d e +--R + +--R 11 5 +--R 792b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R - 923a b e + 5532a b d e - 13794a b d e + 18260a b d e +--R + +--R 2 9 4 10 5 +--R - 13365a b d e + 4752a b d +--R * +--R 5 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R - 3829a b e + 22188a b d e - 52734a b d e + 64900a b d e +--R + +--R 3 8 4 2 9 5 +--R - 42075a b d e + 11880a b d +--R * +--R 4 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 +--R - 6566a b e + 37212a b d e - 85866a b d e + 101420a b d e +--R + +--R 4 7 4 3 8 5 +--R - 61875a b d e + 15840a b d +--R * +--R 3 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 +--R - 5754a b e + 32088a b d e - 72534a b d e + 83380a b d e +--R + +--R 5 6 4 4 7 5 +--R - 49005a b d e + 11880a b d +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 +--R - 2562a b e + 14112a b d e - 31416a b d e + 35420a b d e +--R + +--R 6 5 4 5 6 5 +--R - 20295a b d e + 4752a b d +--R * +--R x +--R + +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 +--R - 462a e + 2520a b d e - 5544a b d e + 6160a b d e - 3465a b d e +--R + +--R 6 5 5 +--R 792a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 18 5 17 4 2 2 16 3 3 3 15 +--R 5544a e - 33264a b d e + 83160a b d e - 110880a b d e +--R + +--R 2 4 4 14 5 5 13 6 6 12 +--R 83160a b d e - 33264a b d e + 5544b d e +--R * +--R 12 +--R x +--R + +--R 6 17 5 2 16 4 2 3 15 3 3 4 14 +--R 66528a d e - 399168a b d e + 997920a b d e - 1330560a b d e +--R + +--R 2 4 5 13 5 6 12 6 7 11 +--R 997920a b d e - 399168a b d e + 66528b d e +--R * +--R 11 +--R x +--R + +--R 6 2 16 5 3 15 4 2 4 14 +--R 365904a d e - 2195424a b d e + 5488560a b d e +--R + +--R 3 3 5 13 2 4 6 12 5 7 11 +--R - 7318080a b d e + 5488560a b d e - 2195424a b d e +--R + +--R 6 8 10 +--R 365904b d e +--R * +--R 10 +--R x +--R + +--R 6 3 15 5 4 14 4 2 5 13 +--R 1219680a d e - 7318080a b d e + 18295200a b d e +--R + +--R 3 3 6 12 2 4 7 11 5 8 10 +--R - 24393600a b d e + 18295200a b d e - 7318080a b d e +--R + +--R 6 9 9 +--R 1219680b d e +--R * +--R 9 +--R x +--R + +--R 6 4 14 5 5 13 4 2 6 12 +--R 2744280a d e - 16465680a b d e + 41164200a b d e +--R + +--R 3 3 7 11 2 4 8 10 5 9 9 +--R - 54885600a b d e + 41164200a b d e - 16465680a b d e +--R + +--R 6 10 8 +--R 2744280b d e +--R * +--R 8 +--R x +--R + +--R 6 5 13 5 6 12 4 2 7 11 +--R 4390848a d e - 26345088a b d e + 65862720a b d e +--R + +--R 3 3 8 10 2 4 9 9 5 10 8 +--R - 87816960a b d e + 65862720a b d e - 26345088a b d e +--R + +--R 6 11 7 +--R 4390848b d e +--R * +--R 7 +--R x +--R + +--R 6 6 12 5 7 11 4 2 8 10 +--R 5122656a d e - 30735936a b d e + 76839840a b d e +--R + +--R 3 3 9 9 2 4 10 8 5 11 7 +--R - 102453120a b d e + 76839840a b d e - 30735936a b d e +--R + +--R 6 12 6 +--R 5122656b d e +--R * +--R 6 +--R x +--R + +--R 6 7 11 5 8 10 4 2 9 9 +--R 4390848a d e - 26345088a b d e + 65862720a b d e +--R + +--R 3 3 10 8 2 4 11 7 5 12 6 +--R - 87816960a b d e + 65862720a b d e - 26345088a b d e +--R + +--R 6 13 5 +--R 4390848b d e +--R * +--R 5 +--R x +--R + +--R 6 8 10 5 9 9 4 2 10 8 +--R 2744280a d e - 16465680a b d e + 41164200a b d e +--R + +--R 3 3 11 7 2 4 12 6 5 13 5 +--R - 54885600a b d e + 41164200a b d e - 16465680a b d e +--R + +--R 6 14 4 +--R 2744280b d e +--R * +--R 4 +--R x +--R + +--R 6 9 9 5 10 8 4 2 11 7 +--R 1219680a d e - 7318080a b d e + 18295200a b d e +--R + +--R 3 3 12 6 2 4 13 5 5 14 4 +--R - 24393600a b d e + 18295200a b d e - 7318080a b d e +--R + +--R 6 15 3 +--R 1219680b d e +--R * +--R 3 +--R x +--R + +--R 6 10 8 5 11 7 4 2 12 6 +--R 365904a d e - 2195424a b d e + 5488560a b d e +--R + +--R 3 3 13 5 2 4 14 4 5 15 3 +--R - 7318080a b d e + 5488560a b d e - 2195424a b d e +--R + +--R 6 16 2 +--R 365904b d e +--R * +--R 2 +--R x +--R + +--R 6 11 7 5 12 6 4 2 13 5 3 3 14 4 +--R 66528a d e - 399168a b d e + 997920a b d e - 1330560a b d e +--R + +--R 2 4 15 3 5 16 2 6 17 +--R 997920a b d e - 399168a b d e + 66528b d e +--R * +--R x +--R + +--R 6 12 6 5 13 5 4 2 14 4 3 3 15 3 +--R 5544a d e - 33264a b d e + 83160a b d e - 110880a b d e +--R + +--R 2 4 16 2 5 17 6 18 +--R 83160a b d e - 33264a b d e + 5544b d +--R Type: Expression(Integer) +--E 368 + +--S 369 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^14 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R e x + 14d e x + 91d e x + 364d e x + 1001d e x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002d e x + 3003d e x + 3432d e x + 3003d e x + 2002d e x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001d e x + 364d e x + 91d e x + 14d e x + d +--R Type: Expression(Integer) +--E 370 + +--S 371 of 765 +r0:=1/13*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^13)+_ + 1/26*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^12)+_ + 5/286*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^11)+_ + 1/143*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^10)+_ + 1/429*b^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^9)+_ + 1/1716*b^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^6*(d+e*x)^8)+_ + 1/12012*b^6*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^7*(d+e*x)^7) +--R +--R +--R (2) +--R 12 6 12 11 6 12 5 11 +--R - b e x + (a b e - 13b d e )x +--R + +--R 2 10 6 11 5 12 2 4 10 +--R (- a b e + 13a b d e - 78b d e )x +--R + +--R 3 9 6 2 10 5 11 2 4 12 3 3 9 +--R (a b e - 13a b d e + 78a b d e - 286b d e )x +--R + +--R 4 8 6 3 9 5 2 10 2 4 11 3 3 12 4 2 8 +--R (- a b e + 13a b d e - 78a b d e + 286a b d e - 715b d e )x +--R + +--R 5 7 6 4 8 5 3 9 2 4 2 10 3 3 11 4 2 +--R a b e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 12 5 +--R - 1287b d e +--R * +--R 7 +--R x +--R + +--R 6 6 6 5 7 5 4 8 2 4 3 9 3 3 2 10 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e - 715a b d e +--R + +--R 11 5 12 6 +--R 1287a b d e - 1716b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 6 6 5 5 7 2 4 4 8 3 3 +--R - 1715a b e + 11999a b d e - 35958a b d e + 59774a b d e +--R + +--R 3 9 4 2 2 10 5 11 6 +--R - 59345a b d e + 34749a b d e - 10296a b d +--R * +--R 5 +--R x +--R + +--R 8 4 6 7 5 5 6 6 2 4 5 7 3 3 +--R - 7294a b e + 49777a b d e - 144222a b d e + 228514a b d e +--R + +--R 4 8 4 2 3 9 5 2 10 6 +--R - 210925a b d e + 109395a b d e - 25740a b d +--R * +--R 4 +--R x +--R + +--R 9 3 6 8 4 5 7 5 2 4 6 6 3 3 +--R - 12726a b e + 85358a b d e - 241878a b d e + 372086a b d e +--R + +--R 5 7 4 2 4 8 5 3 9 6 +--R - 329615a b d e + 160875a b d e - 34320a b d +--R * +--R 3 +--R x +--R + +--R 10 2 6 9 3 5 8 4 2 4 7 5 3 3 +--R - 11298a b e + 74802a b d e - 208572a b d e + 314314a b d e +--R + +--R 6 6 4 2 5 7 5 4 8 6 +--R - 270985a b d e + 127413a b d e - 25740a b d +--R * +--R 2 +--R x +--R + +--R 11 6 10 2 5 9 3 2 4 8 4 3 3 +--R - 5082a b e + 33306a b d e - 91728a b d e + 136136a b d e +--R + +--R 7 5 4 2 6 6 5 5 7 6 +--R - 115115a b d e + 52767a b d e - 10296a b d +--R * +--R x +--R + +--R 12 6 11 5 10 2 2 4 9 3 3 3 +--R - 924a e + 6006a b d e - 16380a b d e + 24024a b d e +--R + +--R 8 4 4 2 7 5 5 6 6 6 +--R - 20020a b d e + 9009a b d e - 1716a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 20 6 19 5 2 2 18 4 3 3 17 +--R 12012a e - 84084a b d e + 252252a b d e - 420420a b d e +--R + +--R 3 4 4 16 2 5 5 15 6 6 14 7 7 13 +--R 420420a b d e - 252252a b d e + 84084a b d e - 12012b d e +--R * +--R 13 +--R x +--R + +--R 7 19 6 2 18 5 2 3 17 +--R 156156a d e - 1093092a b d e + 3279276a b d e +--R + +--R 4 3 4 16 3 4 5 15 2 5 6 14 +--R - 5465460a b d e + 5465460a b d e - 3279276a b d e +--R + +--R 6 7 13 7 8 12 +--R 1093092a b d e - 156156b d e +--R * +--R 12 +--R x +--R + +--R 7 2 18 6 3 17 5 2 4 16 +--R 936936a d e - 6558552a b d e + 19675656a b d e +--R + +--R 4 3 5 15 3 4 6 14 2 5 7 13 +--R - 32792760a b d e + 32792760a b d e - 19675656a b d e +--R + +--R 6 8 12 7 9 11 +--R 6558552a b d e - 936936b d e +--R * +--R 11 +--R x +--R + +--R 7 3 17 6 4 16 5 2 5 15 +--R 3435432a d e - 24048024a b d e + 72144072a b d e +--R + +--R 4 3 6 14 3 4 7 13 2 5 8 12 +--R - 120240120a b d e + 120240120a b d e - 72144072a b d e +--R + +--R 6 9 11 7 10 10 +--R 24048024a b d e - 3435432b d e +--R * +--R 10 +--R x +--R + +--R 7 4 16 6 5 15 5 2 6 14 +--R 8588580a d e - 60120060a b d e + 180360180a b d e +--R + +--R 4 3 7 13 3 4 8 12 2 5 9 11 +--R - 300600300a b d e + 300600300a b d e - 180360180a b d e +--R + +--R 6 10 10 7 11 9 +--R 60120060a b d e - 8588580b d e +--R * +--R 9 +--R x +--R + +--R 7 5 15 6 6 14 5 2 7 13 +--R 15459444a d e - 108216108a b d e + 324648324a b d e +--R + +--R 4 3 8 12 3 4 9 11 2 5 10 10 +--R - 541080540a b d e + 541080540a b d e - 324648324a b d e +--R + +--R 6 11 9 7 12 8 +--R 108216108a b d e - 15459444b d e +--R * +--R 8 +--R x +--R + +--R 7 6 14 6 7 13 5 2 8 12 +--R 20612592a d e - 144288144a b d e + 432864432a b d e +--R + +--R 4 3 9 11 3 4 10 10 2 5 11 9 +--R - 721440720a b d e + 721440720a b d e - 432864432a b d e +--R + +--R 6 12 8 7 13 7 +--R 144288144a b d e - 20612592b d e +--R * +--R 7 +--R x +--R + +--R 7 7 13 6 8 12 5 2 9 11 +--R 20612592a d e - 144288144a b d e + 432864432a b d e +--R + +--R 4 3 10 10 3 4 11 9 2 5 12 8 +--R - 721440720a b d e + 721440720a b d e - 432864432a b d e +--R + +--R 6 13 7 7 14 6 +--R 144288144a b d e - 20612592b d e +--R * +--R 6 +--R x +--R + +--R 7 8 12 6 9 11 5 2 10 10 +--R 15459444a d e - 108216108a b d e + 324648324a b d e +--R + +--R 4 3 11 9 3 4 12 8 2 5 13 7 +--R - 541080540a b d e + 541080540a b d e - 324648324a b d e +--R + +--R 6 14 6 7 15 5 +--R 108216108a b d e - 15459444b d e +--R * +--R 5 +--R x +--R + +--R 7 9 11 6 10 10 5 2 11 9 +--R 8588580a d e - 60120060a b d e + 180360180a b d e +--R + +--R 4 3 12 8 3 4 13 7 2 5 14 6 +--R - 300600300a b d e + 300600300a b d e - 180360180a b d e +--R + +--R 6 15 5 7 16 4 +--R 60120060a b d e - 8588580b d e +--R * +--R 4 +--R x +--R + +--R 7 10 10 6 11 9 5 2 12 8 +--R 3435432a d e - 24048024a b d e + 72144072a b d e +--R + +--R 4 3 13 7 3 4 14 6 2 5 15 5 +--R - 120240120a b d e + 120240120a b d e - 72144072a b d e +--R + +--R 6 16 4 7 17 3 +--R 24048024a b d e - 3435432b d e +--R * +--R 3 +--R x +--R + +--R 7 11 9 6 12 8 5 2 13 7 +--R 936936a d e - 6558552a b d e + 19675656a b d e +--R + +--R 4 3 14 6 3 4 15 5 2 5 16 4 +--R - 32792760a b d e + 32792760a b d e - 19675656a b d e +--R + +--R 6 17 3 7 18 2 +--R 6558552a b d e - 936936b d e +--R * +--R 2 +--R x +--R + +--R 7 12 8 6 13 7 5 2 14 6 +--R 156156a d e - 1093092a b d e + 3279276a b d e +--R + +--R 4 3 15 5 3 4 16 4 2 5 17 3 +--R - 5465460a b d e + 5465460a b d e - 3279276a b d e +--R + +--R 6 18 2 7 19 +--R 1093092a b d e - 156156b d e +--R * +--R x +--R + +--R 7 13 7 6 14 6 5 2 15 5 4 3 16 4 +--R 12012a d e - 84084a b d e + 252252a b d e - 420420a b d e +--R + +--R 3 4 17 3 2 5 18 2 6 19 7 20 +--R 420420a b d e - 252252a b d e + 84084a b d e - 12012b d +--R Type: Expression(Integer) +--E 371 + +--S 372 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^15 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 15 15 14 14 2 13 13 3 12 12 4 11 11 +--R e x + 15d e x + 105d e x + 455d e x + 1365d e x +--R + +--R 5 10 10 6 9 9 7 8 8 8 7 7 9 6 6 +--R 3003d e x + 5005d e x + 6435d e x + 6435d e x + 5005d e x +--R + +--R 10 5 5 11 4 4 12 3 3 13 2 2 14 15 +--R 3003d e x + 1365d e x + 455d e x + 105d e x + 15d e x + d +--R Type: Expression(Integer) +--E 373 + +--S 374 of 765 +r0:=-5/364*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^12)-_ + 5/1001*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^11)-1/14*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^14)-3/91*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^13)-3/2002*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^10)-3/8008*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^6*(d+e*x)^9)-1/24024*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x)^9) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 3003b e x + (- 16016a b e - 2002b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 36036a b e - 8008a b d e - 1001b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 43680a b e - 13104a b d e - 2912a b d e - 364b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 30030a b e - 10920a b d e - 3276a b d e - 728a b d e +--R + +--R 6 4 2 +--R - 91b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 11088a b e - 4620a b d e - 1680a b d e - 504a b d e +--R + +--R 5 4 2 6 5 +--R - 112a b d e - 14b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 1716a e - 792a b d e - 330a b d e - 120a b d e - 36a b d e +--R + +--R 5 5 6 6 +--R - 8a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 21 15 21 20 14 +--R 24024b e x + (24024a e + 336336b d e )x +--R + +--R 20 2 19 13 +--R (336336a d e + 2186184b d e )x +--R + +--R 2 19 3 18 12 +--R (2186184a d e + 8744736b d e )x +--R + +--R 3 18 4 17 11 +--R (8744736a d e + 24048024b d e )x +--R + +--R 4 17 5 16 10 +--R (24048024a d e + 48096048b d e )x +--R + +--R 5 16 6 15 9 +--R (48096048a d e + 72144072b d e )x +--R + +--R 6 15 7 14 8 +--R (72144072a d e + 82450368b d e )x +--R + +--R 7 14 8 13 7 +--R (82450368a d e + 72144072b d e )x +--R + +--R 8 13 9 12 6 +--R (72144072a d e + 48096048b d e )x +--R + +--R 9 12 10 11 5 +--R (48096048a d e + 24048024b d e )x +--R + +--R 10 11 11 10 4 +--R (24048024a d e + 8744736b d e )x +--R + +--R 11 10 12 9 3 12 9 13 8 2 +--R (8744736a d e + 2186184b d e )x + (2186184a d e + 336336b d e )x +--R + +--R 13 8 14 7 14 7 +--R (336336a d e + 24024b d e )x + 24024a d e +--R Type: Expression(Integer) +--E 374 + +--S 375 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^16 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 16 16 15 15 2 14 14 3 13 13 4 12 12 +--R e x + 16d e x + 120d e x + 560d e x + 1820d e x +--R + +--R 5 11 11 6 10 10 7 9 9 8 8 8 9 7 7 +--R 4368d e x + 8008d e x + 11440d e x + 12870d e x + 11440d e x +--R + +--R 10 6 6 11 5 5 12 4 4 13 3 3 14 2 2 +--R 8008d e x + 4368d e x + 1820d e x + 560d e x + 120d e x +--R + +--R 15 16 +--R 16d e x + d +--R Type: Expression(Integer) +--E 376 + +--S 377 of 765 +r0:=-1/91*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^13)-_ + 1/273*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^12)-1/15*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^15)-1/35*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^14)-1/1001*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^11)-2/9009*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^6*(d+e*x)^10)-1/45045*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x)^10) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 5005b e x + (- 27027a b e - 3003b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 61425a b e - 12285a b d e - 1365b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 75075a b e - 20475a b d e - 4095a b d e - 455b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 51975a b e - 17325a b d e - 4725a b d e - 945a b d e +--R + +--R 6 4 2 +--R - 105b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 19305a b e - 7425a b d e - 2475a b d e - 675a b d e +--R + +--R 5 4 2 6 5 +--R - 135a b d e - 15b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 3003a e - 1287a b d e - 495a b d e - 165a b d e - 45a b d e +--R + +--R 5 5 6 6 +--R - 9a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 22 16 22 21 15 +--R 45045b e x + (45045a e + 675675b d e )x +--R + +--R 21 2 20 14 +--R (675675a d e + 4729725b d e )x +--R + +--R 2 20 3 19 13 +--R (4729725a d e + 20495475b d e )x +--R + +--R 3 19 4 18 12 +--R (20495475a d e + 61486425b d e )x +--R + +--R 4 18 5 17 11 +--R (61486425a d e + 135270135b d e )x +--R + +--R 5 17 6 16 10 +--R (135270135a d e + 225450225b d e )x +--R + +--R 6 16 7 15 9 +--R (225450225a d e + 289864575b d e )x +--R + +--R 7 15 8 14 8 +--R (289864575a d e + 289864575b d e )x +--R + +--R 8 14 9 13 7 +--R (289864575a d e + 225450225b d e )x +--R + +--R 9 13 10 12 6 +--R (225450225a d e + 135270135b d e )x +--R + +--R 10 12 11 11 5 +--R (135270135a d e + 61486425b d e )x +--R + +--R 11 11 12 10 4 +--R (61486425a d e + 20495475b d e )x +--R + +--R 12 10 13 9 3 +--R (20495475a d e + 4729725b d e )x +--R + +--R 13 9 14 8 2 14 8 15 7 +--R (4729725a d e + 675675b d e )x + (675675a d e + 45045b d e )x +--R + +--R 15 7 +--R 45045a d e +--R Type: Expression(Integer) +--E 377 + +--S 378 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^17 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 17 17 16 16 2 15 15 3 14 14 4 13 13 +--R e x + 17d e x + 136d e x + 680d e x + 2380d e x +--R + +--R 5 12 12 6 11 11 7 10 10 8 9 9 9 8 8 +--R 6188d e x + 12376d e x + 19448d e x + 24310d e x + 24310d e x +--R + +--R 10 7 7 11 6 6 12 5 5 13 4 4 14 3 3 +--R 19448d e x + 12376d e x + 6188d e x + 2380d e x + 680d e x +--R + +--R 15 2 2 16 17 +--R 136d e x + 17d e x + d +--R Type: Expression(Integer) +--E 379 + +--S 380 of 765 +r0:=-1/112*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^14)-_ + 1/364*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^13)-1/16*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^16)-1/40*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^15)-1/1456*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^12)-1/7280*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^6*(d+e*x)^11)-1/80080*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x)^11) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 8008b e x + (- 43680a b e - 4368b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 100100a b e - 18200a b d e - 1820b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 123200a b e - 30800a b d e - 5600a b d e - 560b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 85800a b e - 26400a b d e - 6600a b d e - 1200a b d e +--R + +--R 6 4 2 +--R - 120b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 32032a b e - 11440a b d e - 3520a b d e - 880a b d e +--R + +--R 5 4 2 6 5 +--R - 160a b d e - 16b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 5005a e - 2002a b d e - 715a b d e - 220a b d e - 55a b d e +--R + +--R 5 5 6 6 +--R - 10a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 23 17 23 22 16 +--R 80080b e x + (80080a e + 1281280b d e )x +--R + +--R 22 2 21 15 +--R (1281280a d e + 9609600b d e )x +--R + +--R 2 21 3 20 14 +--R (9609600a d e + 44844800b d e )x +--R + +--R 3 20 4 19 13 +--R (44844800a d e + 145745600b d e )x +--R + +--R 4 19 5 18 12 +--R (145745600a d e + 349789440b d e )x +--R + +--R 5 18 6 17 11 +--R (349789440a d e + 641280640b d e )x +--R + +--R 6 17 7 16 10 +--R (641280640a d e + 916115200b d e )x +--R + +--R 7 16 8 15 9 +--R (916115200a d e + 1030629600b d e )x +--R + +--R 8 15 9 14 8 +--R (1030629600a d e + 916115200b d e )x +--R + +--R 9 14 10 13 7 +--R (916115200a d e + 641280640b d e )x +--R + +--R 10 13 11 12 6 +--R (641280640a d e + 349789440b d e )x +--R + +--R 11 12 12 11 5 +--R (349789440a d e + 145745600b d e )x +--R + +--R 12 11 13 10 4 +--R (145745600a d e + 44844800b d e )x +--R + +--R 13 10 14 9 3 +--R (44844800a d e + 9609600b d e )x +--R + +--R 14 9 15 8 2 15 8 16 7 +--R (9609600a d e + 1281280b d e )x + (1281280a d e + 80080b d e )x +--R + +--R 16 7 +--R 80080a d e +--R Type: Expression(Integer) +--E 380 + +--S 381 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 of 765 +t0:=(a+b*x)*(d+e*x)^m/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R m +--R (b x + a)(e x + d) +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 382 + +--S 383 of 765 +r0:=(a+b*x)*(d+e*x)^(1+m)/(e*(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R m + 1 +--R (b x + a)(e x + d) +--R (2) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e m + e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 383 + +--S 384 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 of 765 +t0:=(a+b*x)*(d+e*x)^4/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 385 + +--S 386 of 765 +r0:=1/5*(a+b*x)*(d+e*x)^5/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 6 5 4 5 4 2 3 4 +--R b e x + (a e + 5b d e )x + (5a d e + 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a d e + 10b d e )x + (10a d e + 5b d e)x + (5a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 386 + +--S 387 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 765 +t0:=(a+b*x)*(d+e*x)^3/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 388 + +--S 389 of 765 +r0:=1/4*(a+b*x)*(d+e*x)^4/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 4e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 389 + +--S 390 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 765 +t0:=(a+b*x)*(d+e*x)^2/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R b e x + (a e + 2b d e)x + (2a d e + b d )x + a d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 391 + +--S 392 of 765 +r0:=1/3*(a+b*x)*(d+e*x)^3/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 392 + +--S 393 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 765 +t0:=(a+b*x)*(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R b e x + (a e + b d)x + a d +--R (1) --------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 765 +r0:=d*x*(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2)+1/2*e*x^2*(a+b*x)/_ + sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 2 +--R b e x + (a e + 2b d)x + 2a d x +--R (2) -------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 2\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 395 + +--S 396 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 of 765 +t0:=(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R b x + a +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 765 +r0:=sqrt(a^2+2*a*b*x+b^2*x^2)/b +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (2) --------------------- +--R b +--R Type: Expression(Integer) +--E 398 + +--S 399 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 of 765 +t0:=(a+b*x)/((d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 400 + +--S 401 of 765 +r0:=(a+b*x)*log(d+e*x)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b x + a)log(e x + d) +--R (2) ---------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 765 +t0:=(a+b*x)/((d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 765 +r0:=(-a-b*x)/(e*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) -------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (e x + d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 404 + +--S 405 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 765 +t0:=(a+b*x)/((d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 765 +r0:=1/2*(-a-b*x)/(e*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) -------------------------------------------- +--R +------------------+ +--R 3 2 2 2 | 2 2 2 +--R (2e x + 4d e x + 2d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 407 + +--S 408 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 765 +t0:=(a+b*x)/((d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 765 +r0:=1/3*(-a-b*x)/(e*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) ------------------------------------------------------ +--R +------------------+ +--R 4 3 3 2 2 2 3 | 2 2 2 +--R (3e x + 9d e x + 9d e x + 3d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 of 765 +t0:=(a+b*x)/((d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R b x + a +--R ------------------------------------------------------------------------- +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 412 + +--S 413 of 765 +r0:=1/4*(-a-b*x)/(e*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R 5 4 4 3 2 3 2 3 2 4 | 2 2 2 +--R (4e x + 16d e x + 24d e x + 16d e x + 4d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 765 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 415 + +--S 416 of 765 +r0:=2*e*(b*d-a*e)*(a+b*x)*(d+e*x)^2/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 4/3*e*(a+b*x)*(d+e*x)^3/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^4/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+4*e*(b*d-a*e)^3*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^2*(b*d-a*e)^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 12a b e + 36a b d e - 36a b d e + 12b d e)x - 12a e +--R + +--R 3 3 2 2 2 2 3 3 +--R 36a b d e - 36a b d e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (- 2a b e + 6b d e )x + (6a b e - 18a b d e + 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (24a b e - 60a b d e + 42a b d e - 2b d e)x + 12a e - 24a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 6a b d e + 10a b d e - 3b d +--R / +--R +------------------+ +--R 5 | 2 2 2 +--R 3b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 416 + +--S 417 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 765 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 418 + +--S 419 of 765 +r0:=3/2*e*(a+b*x)*(d+e*x)^2/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-(d+e*x)^3/_ + (b*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/_ + (b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b e - 12a b d e + 6b d e)x + 6a e - 12a b d e + 6a b d e) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R b e x + (- 3a b e + 6b d e )x + (- 12a b e + 18a b d e - 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 6a e + 6a b d e + 3a b d e - 2b d +--R / +--R +------------------+ +--R 4 | 2 2 2 +--R 2b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 765 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 765 +r0:=-(d+e*x)^2/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)*(a+b*x)*_ + log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((- 2a b e + 2b d e)x - 2a e + 2a b d e)log(b x + a) + b e x +--R + +--R 2 2 2 2 2 2 +--R (4a b e - 2b d e)x + 2a e - b d +--R / +--R +------------------+ +--R 3 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 765 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 765 +r0:=(-d-e*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(a+b*x)*log(a+b*x)/_ + (b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b e x + a e)log(b x + a) - b e x - b d +--R (2) --------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 425 + +--S 426 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 of 765 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 765 +r0:=(-1)/(b*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (2) - ---------------------- +--R +------------------+ +--R | 2 2 2 +--R b\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 428 + +--S 429 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 of 765 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 430 + +--S 431 of 765 +r0:=(-1)/((b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(a+b*x)*log(a+b*x)/_ + ((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(a+b*x)*log(d+e*x)/_ + ((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b e x + a e)log(e x + d) + (- b e x - a e)log(b x + a) + a e - b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R (a e - 2a b d e + b d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 765 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 433 + +--S 434 of 765 +r0:=-2*b/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/((b*d-a*e)*(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-2*b*e*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+2*b*e*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (- 2b e x + (- 2a b e - 2b d e)x - 2a b d e)log(e x + d) +--R + +--R 2 2 2 2 2 +--R (2b e x + (2a b e + 2b d e)x + 2a b d e)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b e + 2b d e)x - a e + b d +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 2 3 +--R (a e - 3a b d e + 3a b d e - b d e)x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 765 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 765 +r0:=-3*b^2/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2/((b*d-a*e)*(d+e*x)^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+3/2*b/((b*d-a*e)^2*(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-3*b^2*e*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*b^2*e*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 2 2 2 +--R (6b e x + (6a b e + 12b d e )x + (12a b d e + 6b d e)x + 6a b d e) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b e x + (- 6a b e - 12b d e )x + (- 12a b d e - 6b d e)x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (3a b e + 6a b d e - 9b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 3a b d e - 2b d +--R / +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (2a e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4 2 4 +--R (4a d e - 16a b d e + 24a b d e - 16a b d e + 4b d e)x + 2a d e +--R + +--R 3 3 3 2 2 4 2 3 5 4 6 +--R - 8a b d e + 12a b d e - 8a b d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 765 +t0:=(a+b*x)*(d+e*x)^5/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 765 +r0:=-5/6*e*(a+b*x)*(d+e*x)^4/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^5/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5*e^3*(a+b*x)*_ + (d+e*x)^2/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-10/3*e^2*(d+e*x)^3/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10*e^3*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10*e^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6 +--R +--R +--R (2) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (180a b e - 360a b d e + 180a b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 5 5 4 4 +--R (180a b e - 360a b d e + 180a b d e )x + 60a e - 120a b d e +--R + +--R 3 2 2 3 +--R 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 5 5 4 5 5 4 4 +--R 3b e x + (- 15a b e + 30b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 170a b e + 280a b d e - 80b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 330a b e + 480a b d e - 60a b d e - 60b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 240a b e + 300a b d e + 30a b d e - 60a b d e - 15b d e)x - 60a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e + 30a b d e - 20a b d e - 5a b d e - 2b d +--R / +--R +------------------+ +--R 8 2 7 2 6 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 440 + +--S 441 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 441 + +)clear all + +--S 442 of 765 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 765 +r0:=-2/3*e*(a+b*x)*(d+e*x)^3/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^4/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-2*e^2*(d+e*x)^2/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^3*(b*d-a*e)*(a+b*x)*log(a+b*x)/(b^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 4 4 3 3 2 2 4 3 3 2 +--R (- 12a b e + 12b d e )x + (- 36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 4 4 3 3 +--R (- 36a b e + 36a b d e )x - 12a e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (34a b e - 22b d e )x + (66a b e - 30a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 2 2 2 2 +--R (48a b e - 12a b d e - 18a b d e - 6b d e)x + 12a e - 6a b d e +--R + +--R 3 3 4 4 +--R - 2a b d e - b d +--R / +--R +------------------+ +--R 7 2 6 2 5 | 2 2 2 +--R (3b x + 6a b x + 3a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 443 + +--S 444 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 765 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 765 +r0:=-1/2*e*(a+b*x)*(d+e*x)^2/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^3/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2*(d+e*x)/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(b x + a) - 11b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (- 15a b e - 18b d e )x + (- 6a b e - 18a b d e - 9b d e)x +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e - 3a b d e - 2b d +--R / +--R +------------------+ +--R 6 2 5 2 4 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 446 + +--S 447 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 765 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 448 + +--S 449 of 765 +r0:=-1/3*(d+e*x)^3/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R ----------------------------------------------------------------------------- +--R +------------------+ +--R 2 3 2 2 2 3 2 | 2 2 2 +--R ((3a b e - 3b d)x + (6a b e - 6a b d)x + 3a e - 3a b d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 765 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 765 +r0:=-1/6*e*(a+b*x)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/3*(-d-e*x)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R - 3b e x - a e - 2b d +--R (2) ---------------------------------------------- +--R +------------------+ +--R 4 2 3 2 2 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 765 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 1 +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 765 +r0:=(-1/3)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (2) - -------------------------------------------- +--R +------------------+ +--R 3 2 2 2 | 2 2 2 +--R (3b x + 6a b x + 3a b)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 455 + +--S 456 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 456 + +)clear all + +--S 457 of 765 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 765 +r0:=(-1/3)/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*e*(a+b*x)/_ + ((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(e x + d) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (- 6b e x - 18a b e x - 18a b e x - 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (15a b e - 18a b d e + 3b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 18a b d e + 9a b d e - 2b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 6 4 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12a b d )x + 6a e +--R + +--R 5 3 4 2 2 2 3 3 3 2 4 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 458 + +--S 459 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 765 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 460 + +--S 461 of 765 +r0:=-4/3*b/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+2*b*e*(a+b*x)/_ + ((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/((b*d-a*e)*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-4*b*e^2/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-4*b*e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+4*b*e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R - 12b e x + (- 36a b e - 12b d e )x + (- 36a b e - 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (- 12a b e - 36a b d e )x - 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 12b e x + (36a b e + 12b d e )x + (36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (12a b e + 36a b d e )x + 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (- 12a b e + 12b d e )x + (- 30a b e + 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 22a b e + 6a b d e + 18a b d e - 2b d e)x - 3a e - 10a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 6a b d e + b d +--R / +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 3a b e - 15a b d e + 30a b d e - 30a b d e + 15a b d e +--R + +--R 7 5 +--R - 3b d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 6 5 7 6 2 +--R (6a b e - 27a b d e + 45a b d e - 30a b d e + 9a b d e - 3b d )x +--R + +--R 7 6 6 5 4 3 3 3 3 4 4 2 2 5 5 6 6 +--R (3a e - 9a b d e + 30a b d e - 45a b d e + 27a b d e - 6a b d )x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 2 5 6 +--R 3a d e - 15a b d e + 30a b d e - 30a b d e + 15a b d e - 3a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 765 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 463 + +--S 464 of 765 +r0:=-10/3*b^2/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5*b^2*e*(a+b*x)/_ + ((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2/((b*d-a*e)*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+5/2*b/((b*d-a*e)^2*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-10*b^2*e^2/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 10*b^2*e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 10*b^2*e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (180a b e + 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (180a b e + 360a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (60a b e + 360a b d e + 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (120a b d e + 180a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 180a b e - 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 180a b e - 360a b d e - 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (- 60a b e - 360a b d e - 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (- 120a b d e - 180a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (60a b e - 60b d e )x + (150a b e - 60a b d e - 90b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (110a b e + 120a b d e - 210a b d e - 20b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (15a b e + 160a b d e - 120a b d e - 60a b d e + 5b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 30a b d e + 20a b d e - 60a b d e + 15a b d e - 2b d +--R / +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 2 6 4 4 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 3 8 6 2 +--R - 36a b d e + 6b d e +--R * +--R 4 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R 12a b e - 60a b d e + 108a b d e - 60a b d e - 60a b d e +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 108a b d e - 60a b d e + 12b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R 6a e - 12a b d e - 48a b d e + 204a b d e - 300a b d e +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R 204a b d e - 48a b d e - 12a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R 12a d e - 60a b d e + 108a b d e - 60a b d e - 60a b d e +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 108a b d e - 60a b d e + 12a b d +--R * +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 3 5 7 2 6 8 +--R - 36a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 464 + +--S 465 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 466 + +--S 467 of 765 +r0:=-2/9*(b*d-a*e)^3*(d+e*x)^(9/2)/e^4+6/11*b*(b*d-a*e)^2*(d+e*x)^(11/2)/e^4-_ + 6/13*b^2*(b*d-a*e)*(d+e*x)^(13/2)/e^4+2/15*b^3*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 3 7 7 2 7 3 6 6 +--R 858b e x + (2970a b e + 3036b d e )x +--R + +--R 2 7 2 6 3 2 5 5 +--R (3510a b e + 10800a b d e + 3708b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (1430a e + 13260a b d e + 13740a b d e + 1600b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (5720a d e + 17940a b d e + 6360a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (8580a d e + 9360a b d e + 90a b d e - 12b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 3 4 3 +--R (5720a d e + 390a b d e - 120a b d e + 16b d e)x + 1430a d e +--R + +--R 2 5 2 2 6 3 7 +--R - 780a b d e + 240a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 467 + +--S 468 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 469 + +--S 470 of 765 +r0:=-2/7*(b*d-a*e)^3*(d+e*x)^(7/2)/e^4+2/3*b*(b*d-a*e)^2*(d+e*x)^(9/2)/e^4-_ + 6/11*b^2*(b*d-a*e)*(d+e*x)^(11/2)/e^4+2/13*b^3*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 462b e x + (1638a b e + 1134b d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (2002a b e + 4186a b d e + 742b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (858a e + 5434a b d e + 2938a b d e + 10b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (2574a d e + 4290a b d e + 78a b d e - 12b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (2574a d e + 286a b d e - 104a b d e + 16b d e)x + 858a d e +--R + +--R 2 4 2 2 5 3 6 +--R - 572a b d e + 208a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3003e +--R Type: Expression(Integer) +--E 470 + +--S 471 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 471 + +)clear all + +--S 472 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 472 + +--S 473 of 765 +r0:=-2/5*(b*d-a*e)^3*(d+e*x)^(5/2)/e^4+6/7*b*(b*d-a*e)^2*(d+e*x)^(7/2)/e^4-_ + 2/3*b^2*(b*d-a*e)*(d+e*x)^(9/2)/e^4+2/11*b^3*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 210b e x + (770a b e + 280b d e )x +--R + +--R 2 5 2 4 3 2 3 3 +--R (990a b e + 1100a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (462a e + 1584a b d e + 66a b d e - 12b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (924a d e + 198a b d e - 88a b d e + 16b d e)x + 462a d e +--R + +--R 2 3 2 2 4 3 5 +--R - 396a b d e + 176a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Expression(Integer) +--E 473 + +--S 474 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 474 + +)clear all + +--S 475 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (1) (b x + 3a b x + 3a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 475 + +--S 476 of 765 +r0:=-2/3*(b*d-a*e)^3*(d+e*x)^(3/2)/e^4+6/5*b*(b*d-a*e)^2*(d+e*x)^(5/2)/e^4-_ + 6/7*b^2*(b*d-a*e)*(d+e*x)^(7/2)/e^4+2/9*b^3*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 3 4 4 2 4 3 3 3 +--R 70b e x + (270a b e + 10b d e )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (378a b e + 54a b d e - 12b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 +--R (210a e + 126a b d e - 72a b d e + 16b d e)x + 210a d e +--R + +--R 2 2 2 2 3 3 4 +--R - 252a b d e + 144a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 476 + +--S 477 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 478 + +--S 479 of 765 +r0:=2*b*(b*d-a*e)^2*(d+e*x)^(3/2)/e^4-6/5*b^2*(b*d-a*e)*(d+e*x)^(5/2)/e^4+_ + 2/7*b^3*(d+e*x)^(7/2)/e^4-2*(b*d-a*e)^3*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 10b e x + (42a b e - 12b d e )x + (70a b e - 56a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R 70a e - 140a b d e + 112a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 35e +--R Type: Expression(Integer) +--E 479 + +--S 480 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 481 + +--S 482 of 765 +r0:=-2*b^2*(b*d-a*e)*(d+e*x)^(3/2)/e^4+2/5*b^3*(d+e*x)^(5/2)/e^4+_ + 2*(b*d-a*e)^3/(e^4*sqrt(d+e*x))+6*b*(b*d-a*e)^2*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (10a b e - 4b d e )x + (30a b e - 40a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 10a e + 60a b d e - 80a b d e + 32b d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Expression(Integer) +--E 482 + +--S 483 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 484 + +--S 485 of 765 +r0:=2/3*(b*d-a*e)^3/(e^4*(d+e*x)^(3/2))+2/3*b^3*(d+e*x)^(3/2)/e^4-_ + 6*b*(b*d-a*e)^2/(e^4*sqrt(d+e*x))-6*b^2*(b*d-a*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (18a b e - 12b d e )x + (- 18a b e + 72a b d e - 48b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a e - 12a b d e + 48a b d e - 32b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 485 + +--S 486 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 486 + +)clear all + +--S 487 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 487 + +--S 488 of 765 +r0:=2/5*(b*d-a*e)^3/(e^4*(d+e*x)^(5/2))-2*b*(b*d-a*e)^2/(e^4*(d+e*x)^(3/2))+_ + 6*b^2*(b*d-a*e)/(e^4*sqrt(d+e*x))+2*b^3*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R 10b e x + (- 30a b e + 60b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 10a b e - 40a b d e + 80b d e)x - 2a e - 4a b d e - 16a b d e +--R + +--R 3 3 +--R 32b d +--R / +--R 6 2 5 2 4 +-------+ +--R (5e x + 10d e x + 5d e )\|e x + d +--R Type: Expression(Integer) +--E 488 + +--S 489 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 489 + +)clear all + +--S 490 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 490 + +--S 491 of 765 +r0:=-2/9*(b*d-a*e)^5*(d+e*x)^(9/2)/e^6+10/11*b*(b*d-a*e)^4*(d+e*x)^(11/2)/_ + e^6-20/13*b^2*(b*d-a*e)^3*(d+e*x)^(13/2)/e^6+4/3*b^3*(b*d-a*e)^2*(d+_ + e*x)^(15/2)/e^6-10/17*b^4*(b*d-a*e)*(d+e*x)^(17/2)/e^6+2/19*b^5*(d+_ + e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 5 9 9 4 9 5 8 8 +--R 43758b e x + (244530a b e + 149292b d e )x +--R + +--R 2 3 9 4 8 5 2 7 7 +--R (554268a b e + 847704a b d e + 173316b d e )x +--R + +--R 3 2 9 2 3 8 4 2 7 5 3 6 6 +--R (639540a b e + 1961256a b d e + 1005708a b d e + 69168b d e )x +--R + +--R 4 9 3 2 8 2 3 2 7 4 3 6 +--R 377910a b e + 2325600a b d e + 2395368a b d e + 414504a b d e +--R + +--R 5 4 5 +--R 126b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 8 3 2 2 7 2 3 3 6 +--R 92378a e + 1427660a b d e + 2958680a b d e + 1033600a b d e +--R + +--R 4 4 5 5 5 4 +--R 1330a b d e - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 +--R 369512a d e + 1931540a b d e + 1369520a b d e + 6460a b d e +--R + +--R 4 5 4 5 6 3 +--R - 1520a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 +--R 554268a d e + 1007760a b d e + 19380a b d e - 7752a b d e +--R + +--R 4 6 3 5 7 2 +--R 1824a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 +--R 369512a d e + 41990a b d e - 25840a b d e + 10336a b d e +--R + +--R 4 7 2 5 8 +--R - 2432a b d e + 256b d e +--R * +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 +--R 92378a d e - 83980a b d e + 51680a b d e - 20672a b d e +--R + +--R 4 8 5 9 +--R 4864a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 415701e +--R Type: Expression(Integer) +--E 491 + +--S 492 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 493 + +--S 494 of 765 +r0:=-2/7*(b*d-a*e)^5*(d+e*x)^(7/2)/e^6+10/9*b*(b*d-a*e)^4*(d+e*x)^(9/2)/e^6-_ + 20/11*b^2*(b*d-a*e)^3*(d+e*x)^(11/2)/e^6+20/13*b^3*(b*d-a*e)^2*(d+_ + e*x)^(13/2)/e^6-2/3*b^4*(b*d-a*e)*(d+e*x)^(15/2)/e^6+2/17*b^5*(d+_ + e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 5 8 8 4 8 5 7 7 +--R 18018b e x + (102102a b e + 42042b d e )x +--R + +--R 2 3 8 4 7 5 2 6 6 +--R (235620a b e + 243474a b d e + 25410b d e )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 5 +--R (278460a b e + 578340a b d e + 152082a b d e + 126b d e )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 +--R 170170a b e + 711620a b d e + 378420a b d e + 1190a b d e +--R + +--R 5 4 4 +--R - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 +--R 43758a e + 461890a b d e + 499460a b d e + 5100a b d e +--R + +--R 4 4 4 5 5 3 +--R - 1360a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 +--R 131274a d e + 364650a b d e + 13260a b d e - 6120a b d e +--R + +--R 4 5 3 5 6 2 +--R 1632a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 +--R 131274a d e + 24310a b d e - 17680a b d e + 8160a b d e +--R + +--R 4 6 2 5 7 +--R - 2176a b d e + 256b d e +--R * +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 +--R 43758a d e - 48620a b d e + 35360a b d e - 16320a b d e +--R + +--R 4 7 5 8 +--R 4352a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 496 + +--S 497 of 765 +r0:=-2/5*(b*d-a*e)^5*(d+e*x)^(5/2)/e^6+10/7*b*(b*d-a*e)^4*(d+e*x)^(7/2)/e^6-_ + 20/9*b^2*(b*d-a*e)^3*(d+e*x)^(9/2)/e^6+20/11*b^3*(b*d-a*e)^2*(d+_ + e*x)^(11/2)/e^6-10/13*b^4*(b*d-a*e)*(d+e*x)^(13/2)/e^6+2/15*b^5*(d+_ + e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 5 7 7 4 7 5 6 6 +--R 6006b e x + (34650a b e + 7392b d e )x +--R + +--R 2 3 7 4 6 5 2 5 5 +--R (81900a b e + 44100a b d e + 126b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (100100a b e + 109200a b d e + 1050a b d e - 140b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 +--R 64350a b e + 143000a b d e + 3900a b d e - 1200a b d e +--R + +--R 5 4 3 +--R 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 18018a e + 102960a b d e + 8580a b d e - 4680a b d e +--R + +--R 4 4 3 5 5 2 +--R 1440a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 +--R 36036a d e + 12870a b d e - 11440a b d e + 6240a b d e +--R + +--R 4 5 2 5 6 +--R - 1920a b d e + 256b d e +--R * +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 +--R 18018a d e - 25740a b d e + 22880a b d e - 12480a b d e +--R + +--R 4 6 5 7 +--R 3840a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 497 + +--S 498 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 499 + +--S 500 of 765 +r0:=-2/3*(b*d-a*e)^5*(d+e*x)^(3/2)/e^6+2*b*(b*d-a*e)^4*(d+e*x)^(5/2)/e^6-_ + 20/7*b^2*(b*d-a*e)^3*(d+e*x)^(7/2)/e^6+20/9*b^3*(b*d-a*e)^2*(d+_ + e*x)^(9/2)/e^6-10/11*b^4*(b*d-a*e)*(d+e*x)^(11/2)/e^6+2/13*b^5*(d+_ + e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 5 6 6 4 6 5 5 5 +--R 1386b e x + (8190a b e + 126b d e )x +--R + +--R 2 3 6 4 5 5 2 4 4 +--R (20020a b e + 910a b d e - 140b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (25740a b e + 2860a b d e - 1040a b d e + 160b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 18018a b e + 5148a b d e - 3432a b d e + 1248a b d e +--R + +--R 5 4 2 +--R - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 6006a e + 6006a b d e - 6864a b d e + 4576a b d e +--R + +--R 4 4 2 5 5 +--R - 1664a b d e + 256b d e +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 6006a d e - 12012a b d e + 13728a b d e - 9152a b d e + 3328a b d e +--R + +--R 5 6 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 9009e +--R Type: Expression(Integer) +--E 500 + +--S 501 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 501 + +)clear all + +--S 502 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 502 + +--S 503 of 765 +r0:=10/3*b*(b*d-a*e)^4*(d+e*x)^(3/2)/e^6-4*b^2*(b*d-a*e)^3*(d+e*x)^(5/2)/e^6+_ + 20/7*b^3*(b*d-a*e)^2*(d+e*x)^(7/2)/e^6-10/9*b^4*(b*d-a*e)*_ + (d+e*x)^(9/2)/e^6+2/11*b^5*(d+e*x)^(11/2)/e^6-2*(b*d-a*e)^5*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 126b e x + (770a b e - 140b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (1980a b e - 880a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (2772a b e - 2376a b d e + 1056a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 1386a e - 4620a b d e + 7392a b d e - 6336a b d e + 2816a b d e +--R + +--R 5 5 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 693e +--R Type: Expression(Integer) +--E 503 + +--S 504 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 504 + +)clear all + +--S 505 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 505 + +--S 506 of 765 +r0:=-20/3*b^2*(b*d-a*e)^3*(d+e*x)^(3/2)/e^6+4*b^3*(b*d-a*e)^2*_ + (d+e*x)^(5/2)/e^6-10/7*b^4*(b*d-a*e)*(d+e*x)^(7/2)/e^6+2/9*b^5*_ + (d+e*x)^(9/2)/e^6+2*(b*d-a*e)^5/(e^6*sqrt(d+e*x))+10*b*(b*d-a*e)^4*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 14b e x + (90a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (252a b e - 144a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 504a b d e + 288a b d e - 64b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (630a b e - 1680a b d e + 2016a b d e - 1152a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 126a e + 1260a b d e - 3360a b d e + 4032a b d e - 2304a b d e +--R + +--R 5 5 +--R 512b d +--R / +--R 6 +-------+ +--R 63e \|e x + d +--R Type: Expression(Integer) +--E 506 + +--S 507 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 508 + +--S 509 of 765 +r0:=2/3*(b*d-a*e)^5/(e^6*(d+e*x)^(3/2))+20/3*b^3*(b*d-a*e)^2*_ + (d+e*x)^(3/2)/e^6-2*b^4*(b*d-a*e)*(d+e*x)^(5/2)/e^6+2/7*b^5*_ + (d+e*x)^(7/2)/e^6-10*b*(b*d-a*e)^4/(e^6*sqrt(d+e*x))-20*b^2*_ + (b*d-a*e)^3*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (42a b e - 12b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 840a b d e + 672a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b e + 1680a b d e - 3360a b d e + 2688a b d e - 768b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 14a e - 140a b d e + 1120a b d e - 2240a b d e + 1792a b d e +--R + +--R 5 5 +--R - 512b d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Expression(Integer) +--E 509 + +--S 510 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 511 + +--S 512 of 765 +r0:=2/5*(b*d-a*e)^5/(e^6*(d+e*x)^(5/2))-10/3*b*(b*d-a*e)^4/(e^6*_ + (d+e*x)^(3/2))-10/3*b^4*(b*d-a*e)*(d+e*x)^(3/2)/e^6+2/5*b^5*_ + (d+e*x)^(5/2)/e^6+20*b^2*(b*d-a*e)^3/(e^6*sqrt(d+e*x))+20*b^3*_ + (b*d-a*e)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (50a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (300a b e - 400a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 300a b e + 1800a b d e - 2400a b d e + 960b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 50a b e - 400a b d e + 2400a b d e - 3200a b d e + 1280b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 6a e - 20a b d e - 160a b d e + 960a b d e - 1280a b d e + 512b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 512 + +--S 513 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 3 10 6 3 7 2 9 2 5 3 6 2 7 2 8 +--R b e x + (7a b e + 3b d e )x + (21a b e + 21a b d e + 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e + 63a b d e + 21a b d e + b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (35a b e + 105a b d e + 63a b d e + 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (21a b e + 105a b d e + 105a b d e + 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (7a b e + 63a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (a e + 21a b d e + 63a b d e + 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (3a d e + 21a b d e + 21a b d )x + (3a d e + 7a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 514 + +--S 515 of 765 +r0:=-2/9*(b*d-a*e)^7*(d+e*x)^(9/2)/e^8+14/11*b*(b*d-a*e)^6*_ + (d+e*x)^(11/2)/e^8-42/13*b^2*(b*d-a*e)^5*(d+e*x)^(13/2)/e^8+_ + 14/3*b^3*(b*d-a*e)^4*(d+e*x)^(15/2)/e^8-70/17*b^4*(b*d-a*e)^3*_ + (d+e*x)^(17/2)/e^8+42/19*b^5*(b*d-a*e)^2*(d+e*x)^(19/2)/e^8-_ + 2/3*b^6*(b*d-a*e)*(d+e*x)^(21/2)/e^8+2/23*b^7*(d+e*x)^(23/2)/e^8 +--R +--R +--R (2) +--R 7 11 11 6 11 7 10 10 +--R 831402b e x + (6374082a b e + 2771340b d e )x +--R + +--R 2 5 11 6 10 7 2 9 9 +--R (21135114a b e + 21470592a b d e + 3121404b d e )x +--R + +--R 3 4 11 2 5 10 6 2 9 +--R 39369330a b e + 72108036a b d e + 24509628a b d e +--R + +--R 7 3 8 +--R 1194336b d e +--R * +--R 8 +--R x +--R + +--R 4 3 11 3 4 10 2 5 2 9 +--R 44618574a b e + 136480344a b d e + 83711628a b d e +--R + +--R 6 3 8 7 4 7 +--R 9551256a b d e + 858b d e +--R * +--R 7 +--R x +--R + +--R 5 2 11 4 3 10 3 4 2 9 +--R 30889782a b e + 157881108a b d e + 161918988a b d e +--R + +--R 2 5 3 8 6 4 7 7 5 6 +--R 33408144a b d e + 10626a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 6 11 5 2 10 4 3 2 9 +--R 12168702a b e + 112326480a b d e + 192827124a b d e +--R + +--R 3 4 3 8 2 5 4 7 6 5 6 7 6 5 +--R 66735144a b d e + 60858a b d e - 11592a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 7 11 6 10 5 2 2 9 +--R 2124694a e + 45970652a b d e + 142904244a b d e +--R + +--R 4 3 3 8 3 4 4 7 2 5 5 6 6 6 5 +--R 83204800a b d e + 214130a b d e - 67620a b d e + 12880a b d e +--R + +--R 7 7 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 2 9 5 2 3 8 +--R 8498776a d e + 62195588a b d e + 66147816a b d e +--R + +--R 4 3 4 7 3 4 5 6 2 5 6 5 6 7 4 +--R 520030a b d e - 244720a b d e + 77280a b d e - 14720a b d e +--R + +--R 7 8 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 2 4 7 4 3 5 6 +--R 12748164a d e + 32449872a b d e + 936054a b d e - 624036a b d e +--R + +--R 3 4 6 5 2 5 7 4 6 8 3 7 9 2 +--R 293664a b d e - 92736a b d e + 17664a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 3 8 6 4 7 5 2 5 6 4 3 6 5 +--R 8498776a d e + 1352078a b d e - 1248072a b d e + 832048a b d e +--R + +--R 3 4 7 4 2 5 8 3 6 9 2 7 10 +--R - 391552a b d e + 123648a b d e - 23552a b d e + 2048b d e +--R * +--R x +--R + +--R 7 4 7 6 5 6 5 2 6 5 4 3 7 4 +--R 2124694a d e - 2704156a b d e + 2496144a b d e - 1664096a b d e +--R + +--R 3 4 8 3 2 5 9 2 6 10 7 11 +--R 783104a b d e - 247296a b d e + 47104a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 9561123e +--R Type: Expression(Integer) +--E 515 + +--S 516 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 516 + +)clear all + +--S 517 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R b e x + (7a b e + 2b d e)x + (21a b e + 14a b d e + b d )x +--R + +--R 3 4 2 2 5 6 2 6 4 3 2 3 4 2 5 2 5 +--R (35a b e + 42a b d e + 7a b d )x + (35a b e + 70a b d e + 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 6 2 5 2 4 3 2 3 +--R (21a b e + 70a b d e + 35a b d )x + (7a b e + 42a b d e + 35a b d )x +--R + +--R 7 2 6 5 2 2 2 7 6 2 7 2 +--R (a e + 14a b d e + 21a b d )x + (2a d e + 7a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 517 + +--S 518 of 765 +r0:=-2/7*(b*d-a*e)^7*(d+e*x)^(7/2)/e^8+14/9*b*(b*d-a*e)^6*_ + (d+e*x)^(9/2)/e^8-42/11*b^2*(b*d-a*e)^5*(d+e*x)^(11/2)/e^8+_ + 70/13*b^3*(b*d-a*e)^4*(d+e*x)^(13/2)/e^8-14/3*b^4*(b*d-a*e)^3*_ + (d+e*x)^(15/2)/e^8+42/17*b^5*(b*d-a*e)^2*(d+e*x)^(17/2)/e^8-_ + 14/19*b^6*(b*d-a*e)*(d+e*x)^(19/2)/e^8+2/21*b^7*(d+e*x)^(21/2)/e^8 +--R +--R +--R (2) +--R 7 10 10 6 10 7 9 9 +--R 277134b e x + (2144142a b e + 627198b d e )x +--R + +--R 2 5 10 6 9 7 2 8 8 +--R (7189182a b e + 4918914a b d e + 362934b d e )x +--R + +--R 3 4 10 2 5 9 6 2 8 7 3 7 7 +--R (13579566a b e + 16774758a b d e + 2900898a b d e + 858b d e )x +--R + +--R 4 3 10 3 4 9 2 5 2 8 +--R 15668730a b e + 32382042a b d e + 10138590a b d e +--R + +--R 6 3 7 7 4 6 +--R 9702a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 4 2 8 +--R 11110554a b e + 38459610a b d e + 20226906a b d e +--R + +--R 2 5 3 7 6 4 6 7 5 5 +--R 50274a b d e - 10584a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 6 10 5 2 9 4 3 2 8 +--R 4526522a b e + 28393638a b d e + 25164930a b d e +--R + +--R 3 4 3 7 2 5 4 6 6 5 5 7 6 4 +--R 158270a b d e - 55860a b d e + 11760a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 +--R 831402a e + 12286274a b d e + 19928454a b d e + 339150a b d e +--R + +--R 3 4 4 6 2 5 5 5 6 6 4 7 7 3 +--R - 180880a b d e + 63840a b d e - 13440a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 +--R 2494206a d e + 9699690a b d e + 529074a b d e - 406980a b d e +--R + +--R 3 4 5 5 2 5 6 4 6 7 3 7 8 2 +--R 217056a b d e - 76608a b d e + 16128a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 +--R 2494206a d e + 646646a b d e - 705432a b d e + 542640a b d e +--R + +--R 3 4 6 4 2 5 7 3 6 8 2 7 9 +--R - 289408a b d e + 102144a b d e - 21504a b d e + 2048b d e +--R * +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 +--R 831402a d e - 1293292a b d e + 1410864a b d e - 1085280a b d e +--R + +--R 3 4 7 3 2 5 8 2 6 9 7 10 +--R 578816a b d e - 204288a b d e + 43008a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Expression(Integer) +--E 518 + +--S 519 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 519 + +)clear all + +--S 520 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 8 6 7 7 2 5 6 6 3 4 2 5 5 +--R b e x + (7a b e + b d)x + (21a b e + 7a b d)x + (35a b e + 21a b d)x +--R + +--R 4 3 3 4 4 5 2 4 3 3 6 5 2 2 +--R (35a b e + 35a b d)x + (21a b e + 35a b d)x + (7a b e + 21a b d)x +--R + +--R 7 6 7 +--R (a e + 7a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 520 + +--S 521 of 765 +r0:=-2/5*(b*d-a*e)^7*(d+e*x)^(5/2)/e^8+2*b*(b*d-a*e)^6*(d+e*x)^(7/2)/e^8-_ + 14/3*b^2*(b*d-a*e)^5*(d+e*x)^(9/2)/e^8+70/11*b^3*(b*d-a*e)^4*_ + (d+e*x)^(11/2)/e^8-70/13*b^4*(b*d-a*e)^3*(d+e*x)^(13/2)/e^8+_ + 14/5*b^5*(b*d-a*e)^2*(d+e*x)^(15/2)/e^8-14/17*b^6*(b*d-a*e)*_ + (d+e*x)^(17/2)/e^8+2/19*b^7*(d+e*x)^(19/2)/e^8 +--R +--R +--R (2) +--R 7 9 9 6 9 7 8 8 +--R 72930b e x + (570570a b e + 85800b d e )x +--R + +--R 2 5 9 6 8 7 2 7 7 +--R (1939938a b e + 684684a b d e + 858b d e )x +--R + +--R 3 4 9 2 5 8 6 2 7 7 3 6 6 +--R (3730650a b e + 2387616a b d e + 8778a b d e - 924b d e )x +--R + +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 +--R 4408950a b e + 4748100a b d e + 40698a b d e - 9576a b d e +--R + +--R 7 4 5 +--R 1008b d e +--R * +--R 5 +--R x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 +--R 3233230a b e + 5878600a b d e + 113050a b d e - 45220a b d e +--R + +--R 6 4 5 7 5 4 +--R 10640a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 2 8 4 3 2 7 3 4 3 6 +--R 1385670a b e + 4618900a b d e + 209950a b d e - 129200a b d e +--R + +--R 2 5 4 5 6 5 4 7 6 3 +--R 51680a b d e - 12160a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 +--R 277134a e + 2217072a b d e + 277134a b d e - 251940a b d e +--R + +--R 3 4 4 5 2 5 5 4 6 6 3 7 7 2 +--R 155040a b d e - 62016a b d e + 14592a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 +--R 554268a d e + 277134a b d e - 369512a b d e + 335920a b d e +--R + +--R 3 4 5 4 2 5 6 3 6 7 2 7 8 +--R - 206720a b d e + 82688a b d e - 19456a b d e + 2048b d e +--R * +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 +--R 277134a d e - 554268a b d e + 739024a b d e - 671840a b d e +--R + +--R 3 4 6 3 2 5 7 2 6 8 7 9 +--R 413440a b d e - 165376a b d e + 38912a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 692835e +--R Type: Expression(Integer) +--E 521 + +--S 522 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 522 + +)clear all + +--S 523 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 523 + +--S 524 of 765 +r0:=-2/3*(b*d-a*e)^7*(d+e*x)^(3/2)/e^8+14/5*b*(b*d-a*e)^6*(d+e*x)^(5/2)/e^8-_ + 6*b^2*(b*d-a*e)^5*(d+e*x)^(7/2)/e^8+70/9*b^3*(b*d-a*e)^4*_ + (d+e*x)^(9/2)/e^8-70/11*b^4*(b*d-a*e)^3*(d+e*x)^(11/2)/e^8+42/13*b^5*_ + (b*d-a*e)^2*(d+e*x)^(13/2)/e^8-14/15*b^6*(b*d-a*e)*(d+e*x)^(15/2)/e^8+_ + 2/17*b^7*(d+e*x)^(17/2)/e^8 +--R +--R +--R (2) +--R 7 8 8 6 8 7 7 7 +--R 12870b e x + (102102a b e + 858b d e )x +--R + +--R 2 5 8 6 7 7 2 6 6 +--R (353430a b e + 7854a b d e - 924b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 5 +--R (696150a b e + 32130a b d e - 8568a b d e + 1008b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 +--R 850850a b e + 77350a b d e - 35700a b d e + 9520a b d e +--R + +--R 7 4 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 +--R 656370a b e + 121550a b d e - 88400a b d e + 40800a b d e +--R + +--R 6 4 4 7 5 3 +--R - 10880a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 +--R 306306a b e + 131274a b d e - 145860a b d e + 106080a b d e +--R + +--R 2 5 4 4 6 5 3 7 6 2 +--R - 48960a b d e + 13056a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 +--R 72930a e + 102102a b d e - 175032a b d e + 194480a b d e +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 +--R - 141440a b d e + 65280a b d e - 17408a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 72930a d e - 204204a b d e + 350064a b d e - 388960a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 +--R 282880a b d e - 130560a b d e + 34816a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 109395e +--R Type: Expression(Integer) +--E 524 + +--S 525 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 526 + +--S 527 of 765 +r0:=14/3*b*(b*d-a*e)^6*(d+e*x)^(3/2)/e^8-42/5*b^2*(b*d-a*e)^5*_ + (d+e*x)^(5/2)/e^8+10*b^3*(b*d-a*e)^4*(d+e*x)^(7/2)/e^8-70/9*b^4*_ + (b*d-a*e)^3*(d+e*x)^(9/2)/e^8+42/11*b^5*(b*d-a*e)^2*(d+e*x)^(11/2)/e^8-_ + 14/13*b^6*(b*d-a*e)*(d+e*x)^(13/2)/e^8+2/15*b^7*(d+e*x)^(15/2)/e^8-_ + 2*(b*d-a*e)^7*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 858b e x + (6930a b e - 924b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (24570a b e - 7560a b d e + 1008b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (50050a b e - 27300a b d e + 8400a b d e - 1120b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 64350a b e - 57200a b d e + 31200a b d e - 9600a b d e +--R + +--R 7 4 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 54054a b e - 77220a b d e + 68640a b d e - 37440a b d e +--R + +--R 6 4 3 7 5 2 +--R 11520a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 30030a b e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 49920a b d e - 15360a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 12870a e - 60060a b d e + 144144a b d e - 205920a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 183040a b d e - 99840a b d e + 30720a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 6435e +--R Type: Expression(Integer) +--E 527 + +--S 528 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 528 + +)clear all + +--S 529 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 529 + +--S 530 of 765 +r0:=-14*b^2*(b*d-a*e)^5*(d+e*x)^(3/2)/e^8+14*b^3*(b*d-a*e)^4*_ + (d+e*x)^(5/2)/e^8-10*b^4*(b*d-a*e)^3*(d+e*x)^(7/2)/e^8+14/3*b^5*_ + (b*d-a*e)^2*(d+e*x)^(9/2)/e^8-14/11*b^6*(b*d-a*e)*(d+e*x)^(11/2)/e^8+_ + 2/13*b^7*(d+e*x)^(13/2)/e^8+2*(b*d-a*e)^7/(e^8*sqrt(d+e*x))+_ + 14*b*(b*d-a*e)^6*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 66b e x + (546a b e - 84b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2002a b e - 728a b d e + 112b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (4290a b e - 2860a b d e + 1040a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (6006a b e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 6006a b e - 12012a b d e + 13728a b d e - 9152a b d e +--R + +--R 6 4 3 7 5 2 +--R 3328a b d e - 512b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 6006a b e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 36608a b d e - 13312a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 858a e + 12012a b d e - 48048a b d e + 96096a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 109824a b d e + 73216a b d e - 26624a b d e + 4096b d +--R / +--R 8 +-------+ +--R 429e \|e x + d +--R Type: Expression(Integer) +--E 530 + +--S 531 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 531 + +)clear all + +--S 532 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 532 + +--S 533 of 765 +r0:=2/3*(b*d-a*e)^7/(e^8*(d+e*x)^(3/2))+70/3*b^3*(b*d-a*e)^4*_ + (d+e*x)^(3/2)/e^8-14*b^4*(b*d-a*e)^3*(d+e*x)^(5/2)/e^8+6*b^5*_ + (b*d-a*e)^2*(d+e*x)^(7/2)/e^8-14/9*b^6*(b*d-a*e)*(d+e*x)^(9/2)/e^8+_ + 2/11*b^7*(d+e*x)^(11/2)/e^8-14*b*(b*d-a*e)^6/(e^8*sqrt(d+e*x))-_ + 42*b^2*(b*d-a*e)^5*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 18b e x + (154a b e - 28b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (594a b e - 264a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1386a b e - 1188a b d e + 528a b d e - 96b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4158a b e - 13860a b d e + 22176a b d e - 19008a b d e +--R + +--R 6 4 3 7 5 2 +--R 8448a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 1386a b e + 16632a b d e - 55440a b d e + 88704a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 76032a b d e + 33792a b d e - 6144b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 66a e - 924a b d e + 11088a b d e - 36960a b d e + 59136a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 50688a b d e + 22528a b d e - 4096b d +--R / +--R 9 8 +-------+ +--R (99e x + 99d e )\|e x + d +--R Type: Expression(Integer) +--E 533 + +--S 534 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 534 + +)clear all + +--S 535 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 535 + +--S 536 of 765 +r0:=2/5*(b*d-a*e)^7/(e^8*(d+e*x)^(5/2))-14/3*b*(b*d-a*e)^6/(e^8*_ + (d+e*x)^(3/2))-70/3*b^4*(b*d-a*e)^3*(d+e*x)^(3/2)/e^8+42/5*b^5*_ + (b*d-a*e)^2*(d+e*x)^(5/2)/e^8-2*b^6*(b*d-a*e)*(d+e*x)^(7/2)/e^8+_ + 2/9*b^7*(d+e*x)^(9/2)/e^8+42*b^2*(b*d-a*e)^5/(e^8*sqrt(d+e*x))+_ + 70*b^3*(b*d-a*e)^4*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (90a b e - 20b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1050a b e - 1260a b d e + 720a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (3150a b e - 8400a b d e + 10080a b d e - 5760a b d e + 1280b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1890a b e + 18900a b d e - 50400a b d e + 60480a b d e +--R + +--R 6 4 3 7 5 2 +--R - 34560a b d e + 7680b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 210a b e - 2520a b d e + 25200a b d e - 67200a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 80640a b d e - 46080a b d e + 10240b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 18a e - 84a b d e - 1008a b d e + 10080a b d e - 26880a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 32256a b d e - 18432a b d e + 4096b d +--R / +--R 10 2 9 2 8 +-------+ +--R (45e x + 90d e x + 45d e )\|e x + d +--R Type: Expression(Integer) +--E 536 + +--S 537 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 538 + +--S 539 of 765 +r0:=2/3*(b*d-a*e)^2*(d+e*x)^(3/2)/b^3+2/5*(b*d-a*e)*(d+e*x)^(5/2)/b^2+_ + 2/7*(d+e*x)^(7/2)/b-2*(b*d-a*e)^(7/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/b^(9/2)+2*(b*d-a*e)^3*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (210a e - 630a b d e + 630a b d e - 210b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (- 42a b e + 132b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 224a b d e + 244b d e)x - 210a e + 700a b d e +--R + +--R 2 2 3 3 +--R - 812a b d e + 352b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 +-+ +--R 105b \|b +--R Type: Expression(Integer) +--E 539 + +--S 540 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R b x + a +--R Type: Expression(Integer) +--E 541 + +--S 542 of 765 +r0:=2/3*(b*d-a*e)*(d+e*x)^(3/2)/b^2+2/5*(d+e*x)^(5/2)/b-2*(b*d-a*e)^(5/2)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(7/2)+2*(b*d-a*e)^2*_ + sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|e x + d +--R (- 30a e + 60a b d e - 30b d )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (6b e x + (- 10a b e + 22b d e)x + 30a e - 70a b d e + 46b d )\|b +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 542 + +--S 543 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------- +--R b x + a +--R Type: Expression(Integer) +--E 544 + +--S 545 of 765 +r0:=2/3*(d+e*x)^(3/2)/b-2*(b*d-a*e)^(3/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/b^(5/2)+2*(b*d-a*e)*sqrt(d+e*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (6a e - 6b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-+ +-------+ +--R (2b e x - 6a e + 8b d)\|b \|e x + d +--R / +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 545 + +--S 546 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 546 + +)clear all + +--S 547 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ---------- +--R b x + a +--R Type: Expression(Integer) +--E 547 + +--S 548 of 765 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(3/2)+_ + 2*sqrt(d+e*x)/b +--R +--R +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +-+ +-------+ +--R - 2\|- a e + b d atanh(--------------) + 2\|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) -------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 548 + +--S 549 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 765 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|e x + d +--R Type: Expression(Integer) +--E 550 + +--S 551 of 765 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(sqrt(b)*sqrt(b*d-a*e)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +--R 2atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R (2) - ---------------------- +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 551 + +--S 552 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 765 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) --------------------------------------- +--R 2 +-------+ +--R (b e x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 553 + +--S 554 of 765 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(3/2)+_ + 2/((b*d-a*e)*sqrt(d+e*x)) +--R +--R +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +-----------+ +--R 2\|b \|e x + d atanh(--------------) - 2\|- a e + b d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------ +--R +-----------+ +-------+ +--R (a e - b d)\|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 554 + +--S 555 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 765 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R Type: Expression(Integer) +--E 556 + +--S 557 of 765 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2))-2*b^(3/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b*d-a*e)^(5/2)+2*b/((b*d-a*e)^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R (- 6b e x - 6b d)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R (6b e x - 2a e + 8b d)\|- a e + b d +--R / +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e)x + 3a d e - 6a b d e + 3b d ) +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 557 + +--S 558 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 of 765 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 559 + +--S 560 of 765 +r0:=2/5/((b*d-a*e)*(d+e*x)^(5/2))+2/3*b/((b*d-a*e)^2*(d+e*x)^(3/2))-_ + 2*b^(5/2)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(7/2)+_ + 2*b^2/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-+ +-------+ \|b \|e x + d +--R (30b e x + 60b d e x + 30b d )\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 30b e x + (10a b e - 70b d e)x - 6a e + 22a b d e - 46b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (30a d e - 90a b d e + 90a b d e - 30b d e)x + 15a d e - 45a b d e +--R + +--R 2 4 3 5 +--R 45a b d e - 15b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 560 + +--S 561 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 561 + +)clear all + +--S 562 of 765 +t0:=(a+b*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 562 + +--S 563 of 765 +r0:=21/4*e^2*(b*d-a*e)*(d+e*x)^(3/2)/b^4+63/20*e^2*(d+e*x)^(5/2)/b^3-_ + 9/4*e*(d+e*x)^(7/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(9/2)/(b*(a+b*x)^2)-_ + 63/4*e^2*(b*d-a*e)^(5/2)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + b^(11/2)+63/4*e^2*(b*d-a*e)^2*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (- 315a b e + 630a b d e - 315b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (- 630a b e + 1260a b d e - 630a b d e )x - 315a e + 630a b d e +--R + +--R 2 2 2 2 +--R - 315a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 8b e x + (- 24a b e + 56b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (168a b e - 408a b d e + 288b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (525a b e - 1239a b d e + 831a b d e - 85b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 735a b d e + 483a b d e - 45a b d e - 10b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 7 2 6 2 5 +-+ +--R (20b x + 40a b x + 20a b )\|b +--R Type: Expression(Integer) +--E 563 + +--S 564 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 565 + +--S 566 of 765 +r0:=35/12*e^2*(d+e*x)^(3/2)/b^3-7/4*e*(d+e*x)^(5/2)/(b^2*(a+b*x))-_ + 1/2*(d+e*x)^(7/2)/(b*(a+b*x)^2)-35/4*e^2*(b*d-a*e)^(3/2)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+35/4*e^2*(b*d-a*e)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (105a b e - 105b d e )x + (210a b e - 210a b d e )x + 105a e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 8b e x + (- 56a b e + 80b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 175a b e + 238a b d e - 39b d e)x - 105a e + 140a b d e +--R + +--R 2 2 3 3 +--R - 21a b d e - 6b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 2 5 2 4 +-+ +--R (12b x + 24a b x + 12a b )\|b +--R Type: Expression(Integer) +--E 566 + +--S 567 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 568 + +--S 569 of 765 +r0:=-5/4*e*(d+e*x)^(3/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(5/2)/(b*(a+b*x)^2)-_ + 15/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+_ + 15/4*e^2*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-----------+ \|b \|e x + d +--R (- 15b e x - 30a b e x - 15a e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-------+ +--R (8b e x + (25a b e - 9b d e)x + 15a e - 5a b d e - 2b d )\|b \|e x + d +--R / +--R 5 2 4 2 3 +-+ +--R (4b x + 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 569 + +--S 570 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 765 +r0:=-1/2*(d+e*x)^(3/2)/(b*(a+b*x)^2)-3/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))-3/4*e*sqrt(d+e*x)/(b^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- 3b e x - 6a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (- 5b e x - 3a e - 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 4 2 3 2 2 +-----------+ +-+ +--R (4b x + 8a b x + 4a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 572 + +--S 573 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 574 + +--S 575 of 765 +r0:=1/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + (b*d-a*e)^(3/2))-1/2*sqrt(d+e*x)/(b*(a+b*x)^2)-1/4*e*_ + sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- b e x - 2a b e x - a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (b e x - a e + 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 3 4 2 2 2 3 3 2 2 +-----------+ +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|- a e + b d +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 575 + +--S 576 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 576 + +)clear all + +--S 577 of 765 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 577 + +--S 578 of 765 +r0:=-3/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(5/2)*_ + sqrt(b))-1/2*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^2)+3/4*e*sqrt(d+e*x)/_ + ((b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- 3b e x - 6a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (3b e x + 5a e - 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 2 +--R 4a e - 8a b d e + 4a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 578 + +--S 579 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 of 765 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 580 + +--S 581 of 765 +r0:=-15/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/_ + (b*d-a*e)^(7/2)+15/4*e^2/((b*d-a*e)^3*sqrt(d+e*x))+(-1/2)/((b*d-a*e)*_ + (a+b*x)^2*sqrt(d+e*x))+5/4*e/((b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-+ +-------+ \|b \|e x + d +--R (15b e x + 30a b e x + 15a e )\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 15b e x + (- 25a b e - 5b d e)x - 8a e - 9a b d e + 2b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 581 + +--S 582 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 of 765 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 583 + +--S 584 of 765 +r0:=35/12*e^2/((b*d-a*e)^3*(d+e*x)^(3/2))+(-1/2)/((b*d-a*e)*(a+b*x)^2*_ + (d+e*x)^(3/2))+7/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2))-35/4*b^(3/2)*_ + e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+35/4*b*_ + e^2/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 210a b e - 105b d e )x +--R + +--R 2 3 2 2 2 2 +--R (- 105a b e - 210a b d e )x - 105a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (175a b e + 140b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (56a b e + 238a b d e + 21b d e)x - 8a e + 80a b d e + 39a b d e +--R + +--R 3 3 +--R - 6b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e + 24a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 584 + +--S 585 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 765 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 586 + +--S 587 of 765 +r0:=63/20*e^2/((b*d-a*e)^3*(d+e*x)^(5/2))+(-1/2)/((b*d-a*e)*(a+b*x)^2*_ + (d+e*x)^(5/2))+9/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2))+21/4*b*_ + e^2/((b*d-a*e)^4*(d+e*x)^(3/2))-63/4*b^(5/2)*e^2*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(11/2)+63/4*b^2*e^2/((b*d-a*e)^5*_ + sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (630a b e + 630b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (315a b e + 1260a b d e + 315b d e )x +--R + +--R 2 2 3 3 2 2 2 2 2 2 +--R (630a b d e + 630a b d e )x + 315a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 525a b e - 735b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 168a b e - 1239a b d e - 483b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (24a b e - 408a b d e - 831a b d e - 45b d e)x - 8a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 56a b d e - 288a b d e - 85a b d e + 10b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 20a b e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 7 5 2 +--R - 20b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 40a b e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 7 6 +--R - 40b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 20a e - 20a b d e - 180a b d e + 500a b d e - 500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 180a b d e + 20a b d e - 20b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 40a d e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 6 7 +--R - 40a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 20a d e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 2 5 7 +--R - 20a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 587 + +--S 588 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 of 765 +t0:=(a+b*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 589 + +--S 590 of 765 +r0:=385/64*e^4*(d+e*x)^(3/2)/b^5-231/64*e^3*(d+e*x)^(5/2)/(b^4*(a+b*x))-_ + 33/32*e^2*(d+e*x)^(7/2)/(b^3*(a+b*x)^2)-11/24*e*(d+e*x)^(9/2)/(b^2*_ + (a+b*x)^3)-1/4*(d+e*x)^(11/2)/(b*(a+b*x)^4)-1155/64*e^4*(b*d-a*e)^(3/2)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(13/2)+1155/64*e^4*(b*d-_ + a*e)*sqrt(d+e*x)/b^6 +--R +--R +--R (2) +--R 4 5 5 4 4 2 3 5 4 4 3 +--R (3465a b e - 3465b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 +--R (20790a b e - 20790a b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 5 5 4 4 +--R 3465a e - 3465a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R 128b e x + (- 1408a b e + 2048b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 9207a b e + 12782a b d e - 2295b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 16863a b e + 22968a b d e - 3795a b d e - 1030b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 +--R - 12705a b e + 17094a b d e - 2673a b d e - 748a b d e +--R + +--R 5 4 +--R - 328b d e +--R * +--R x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 3465a e + 4620a b d e - 693a b d e - 198a b d e - 88a b d e +--R + +--R 5 5 +--R - 48b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|b +--R Type: Expression(Integer) +--E 590 + +--S 591 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 591 + +)clear all + +--S 592 of 765 +t0:=(a+b*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 592 + +--S 593 of 765 +r0:=-105/64*e^3*(d+e*x)^(3/2)/(b^4*(a+b*x))-21/32*e^2*(d+e*x)^(5/2)/_ + (b^3*(a+b*x)^2)-3/8*e*(d+e*x)^(7/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(9/2)/_ + (b*(a+b*x)^4)-315/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b*d-a*e)/b^(11/2)+315/64*e^4*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 315b e x - 1260a b e x - 1890a b e x - 1260a b e x - 315a e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 128b e x + (837a b e - 325b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1533a b e - 555a b d e - 210b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1155a b e - 399a b d e - 156a b d e - 88b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 105a b d e - 42a b d e - 24a b d e - 16b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +-+ +--R (64b x + 256a b x + 384a b x + 256a b x + 64a b )\|b +--R Type: Expression(Integer) +--E 593 + +--S 594 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 595 + +--S 596 of 765 +r0:=-35/96*e^2*(d+e*x)^(3/2)/(b^3*(a+b*x)^2)-7/24*e*(d+e*x)^(5/2)/_ + (b^2*(a+b*x)^3)-1/4*(d+e*x)^(7/2)/(b*(a+b*x)^4)-35/64*e^4*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(b*d-a*e))-_ + 35/64*e^3*sqrt(d+e*x)/(b^4*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 105b e x - 420a b e x - 630a b e x - 420a b e x - 105a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 279b e x + (- 511a b e - 326b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 385a b e - 252a b d e - 200b d e)x - 105a e - 70a b d e +--R + +--R 2 2 3 3 +--R - 56a b d e - 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +-----------+ +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 596 + +--S 597 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 598 + +--S 599 of 765 +r0:=-5/24*e*(d+e*x)^(3/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(5/2)/(b*(a+b*x)^4)+_ + 5/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*_ + (b*d-a*e)^(3/2))-5/32*e^2*sqrt(d+e*x)/(b^3*(a+b*x)^2)-5/64*e^3*_ + sqrt(d+e*x)/(b^3*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 15b e x - 60a b e x - 90a b e x - 60a b e x - 15a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (- 73a b e + 118b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 55a b e - 36a b d e + 136b d e)x - 15a e - 10a b d e +--R + +--R 2 2 3 3 +--R - 8a b d e + 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 8 4 2 6 7 3 +--R (192a b e - 192b d)x + (768a b e - 768a b d)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 4 4 +--R (1152a b e - 1152a b d)x + (768a b e - 768a b d)x + 192a b e - 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 599 + +--S 600 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 601 + +--S 602 of 765 +r0:=-1/4*(d+e*x)^(3/2)/(b*(a+b*x)^4)-3/64*e^4*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(5/2))-1/8*e*_ + sqrt(d+e*x)/(b^2*(a+b*x)^3)-1/32*e^2*sqrt(d+e*x)/(b^2*(b*d-a*e)*_ + (a+b*x)^2)+3/64*e^3*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 3b e x - 12a b e x - 18a b e x - 12a b e x - 3a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 3b e x + (11a b e - 2b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 11a b e + 44a b d e - 24b d e)x - 3a e - 2a b d e + 24a b d e +--R + +--R 3 3 +--R - 16b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 6 2 7 8 2 4 +--R (64a b e - 128a b d e + 64b d )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (256a b e - 512a b d e + 256a b d )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (384a b e - 768a b d e + 384a b d )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 4 4 2 +--R (256a b e - 512a b d e + 256a b d )x + 64a b e - 128a b d e + 64a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 602 + +--S 603 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R \|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 604 + +--S 605 of 765 +r0:=5/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + (b*d-a*e)^(7/2))-1/4*sqrt(d+e*x)/(b*(a+b*x)^4)-1/24*e*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^3)+5/96*e^2*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x)^2)-_ + 5/64*e^3*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 15b e x - 60a b e x - 90a b e x - 60a b e x - 15a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (55a b e - 10b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (73a b e - 36a b d e + 8b d e)x - 15a e + 118a b d e - 136a b d e +--R + +--R 3 3 +--R 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (1152a b e - 3456a b d e + 3456a b d e - 1152a b d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x + 192a b e +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 605 + +--S 606 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 606 + +)clear all + +--S 607 of 765 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 607 + +--S 608 of 765 +r0:=-35/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*_ + sqrt(b))-1/4*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^4)+7/24*e*sqrt(d+e*x)/_ + ((b*d-a*e)^2*(a+b*x)^3)-35/96*e^2*sqrt(d+e*x)/((b*d-a*e)^3*(a+b*x)^2)+_ + 35/64*e^3*sqrt(d+e*x)/((b*d-a*e)^4*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 105b e x - 420a b e x - 630a b e x - 420a b e x - 105a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (385a b e - 70b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (511a b e - 252a b d e + 56b d e)x + 279a e - 326a b d e +--R + +--R 2 2 3 3 +--R 200a b d e - 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (1152a b e - 4608a b d e + 6912a b d e - 4608a b d e + 1152a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 192a e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 608 + +--S 609 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 765 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 6 4 5 5 2 3 4 4 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (10a b e + 10a b d)x + (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 610 + +--S 611 of 765 +r0:=-315/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-_ + a*e)^(11/2)+315/64*e^4/((b*d-a*e)^5*sqrt(d+e*x))+(-1/4)/((b*d-a*e)*_ + (a+b*x)^4*sqrt(d+e*x))+3/8*e/((b*d-a*e)^2*(a+b*x)^3*sqrt(d+e*x))-_ + 21/32*e^2/((b*d-a*e)^3*(a+b*x)^2*sqrt(d+e*x))+105/64*e^3/((b*d-a*e)^4*_ + (a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +-+ +--R (315b e x + 1260a b e x + 1890a b e x + 1260a b e x + 315a e )\|b +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 1155a b e - 105b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1533a b e - 399a b d e + 42b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 837a b e - 555a b d e + 156a b d e - 24b d e)x - 128a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 325a b d e + 210a b d e - 88a b d e + 16b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 64a b e - 320a b d e + 640a b d e - 640a b d e + 320a b d e +--R + +--R 9 5 +--R - 64b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 2 7 4 8 5 +--R 1280a b d e - 256a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 384a b e - 1920a b d e + 3840a b d e - 3840a b d e +--R + +--R 3 6 4 2 7 5 +--R 1920a b d e - 384a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 4 5 4 3 6 5 +--R 1280a b d e - 256a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 4 5 5 +--R 64a e - 320a b d e + 640a b d e - 640a b d e + 320a b d e - 64a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 611 + +--S 612 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 765 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 613 + +--S 614 of 765 +r0:=385/64*e^4/((b*d-a*e)^5*(d+e*x)^(3/2))+(-1/4)/((b*d-a*e)*(a+b*x)^4*_ + (d+e*x)^(3/2))+11/24*e/((b*d-a*e)^2*(a+b*x)^3*(d+e*x)^(3/2))-_ + 33/32*e^2/((b*d-a*e)^3*(a+b*x)^2*(d+e*x)^(3/2))+231/64*e^3/((b*d-a*e)^4*_ + (a+b*x)*(d+e*x)^(3/2))-1155/64*b^(3/2)*e^4*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b*d-a*e)^(13/2)+1155/64*b*e^4/((b*d-a*e)^6*sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 3465b e x + (- 13860a b e - 3465b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (- 20790a b e - 13860a b d e )x + (- 13860a b e - 20790a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (- 3465a b e - 13860a b d e )x - 3465a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (12705a b e + 4620b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (16863a b e + 17094a b d e + 693b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (9207a b e + 22968a b d e + 2673a b d e - 198b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (1408a b e + 12782a b d e + 3795a b d e - 748a b d e + 88b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 128a e + 2048a b d e + 2295a b d e - 1030a b d e + 328a b d e +--R + +--R 5 5 +--R - 48b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 768a b e - 4416a b d e + 10368a b d e - 12480a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 7680a b d e - 1728a b d e - 384a b d e + 192b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 1152a b e - 6144a b d e + 12672a b d e - 11520a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 1920a b d e + 4608a b d e - 3456a b d e + 768a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 768a b e - 3456a b d e + 4608a b d e + 1920a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 11520a b d e + 12672a b d e - 6144a b d e + 1152a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 192a e - 384a b d e - 1728a b d e + 7680a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 12480a b d e + 10368a b d e - 4416a b d e + 768a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e + 2880a b d e +--R + +--R 5 5 6 4 6 7 +--R - 1152a b d e + 192a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 614 + +--S 615 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 616 + +--S 617 of 765 +r0:=-8/143*(b*d-a*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/1287*(b*d-a*e)^2*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+_ + b*x))+2/13*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 +--R 198b e x + (468a b e + 720b d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (286a e + 1768a b d e + 916b d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (1144a d e + 2392a b d e + 424b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (1716a d e + 1248a b d e + 6b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (1144a d e + 52a b d e - 8b d e)x + 286a d e - 104a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 617 + +--S 618 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 619 + +--S 620 of 765 +r0:=-8/99*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/693*(b*d-a*e)^2*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+_ + b*x))+2/11*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 +--R 126b e x + (308a b e + 322b d e )x +--R + +--R 2 5 4 2 2 3 3 +--R (198a e + 836a b d e + 226b d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (594a d e + 660a b d e + 6b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (594a d e + 44a b d e - 8b d e)x + 198a d e - 88a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 620 + +--S 621 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (1) (b e x + (a e + b d)x + a d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 622 + +--S 623 of 765 +r0:=-8/63*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/315*(b*d-a*e)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 2/9*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 70b e x + (180a b e + 100b d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (126a e + 288a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (252a d e + 36a b d e - 8b d e)x + 126a d e - 72a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 623 + +--S 624 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 of 765 +t0:=(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R +-------+ | 2 2 2 +--R (1) (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 625 + +--S 626 of 765 +r0:=-8/35*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/105*(b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 2/7*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 30b e x + (84a b e + 6b d e )x + (70a e + 28a b d e - 8b d e)x +--R + +--R 2 2 2 2 3 +--R 70a d e - 56a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 626 + +--S 627 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 628 + +--S 629 of 765 +r0:=-8/15*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+16/15*(b*d-_ + a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/5*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (6b e x + (20a b e - 8b d e)x + 30a e - 40a b d e + 16b d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 629 + +--S 630 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 631 + +--S 632 of 765 +r0:=-2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*sqrt(d+e*x))+8/3*b*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^2-16/3*b*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2b e x + (12a b e - 8b d e)x - 6a e + 24a b d e - 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 632 + +--S 633 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 634 + +--S 635 of 765 +r0:=-2/3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^(3/2))+8/3*b*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*sqrt(d+e*x))+16/3*b*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 12a b e + 24b d e)x - 2a e - 8a b d e + 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 635 + +--S 636 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 637 + +--S 638 of 765 +r0:=-2/5*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^(5/2))-8/5*b*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^(3/2))-16/15*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 30b e x + (- 20a b e - 40b d e)x - 6a e - 8a b d e - 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 638 + +--S 639 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 640 + +--S 641 of 765 +r0:=-16/195*(b*d-a*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/15*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/6435*(b*d-_ + a*e)^3*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/45045*(b*d-_ + a*e)^4*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/715*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 6006b e x + (27720a b e + 14322b d e )x +--R + +--R 2 2 7 3 6 4 2 5 5 +--R (49140a b e + 68040a b d e + 8946b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 4 +--R (40040a b e + 125580a b d e + 44520a b d e + 70b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (12870a e + 108680a b d e + 88140a b d e + 600a b d e - 80b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (38610a d e + 85800a b d e + 2340a b d e - 720a b d e + 96b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 +--R (38610a d e + 5720a b d e - 3120a b d e + 960a b d e - 128b d e)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 12870a d e - 11440a b d e + 6240a b d e - 1920a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 641 + +--S 642 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 643 + +--S 644 of 765 +r0:=-16/143*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/13*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/3003*_ + (b*d-a*e)^3*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/15015*_ + (b*d-a*e)^4*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/429*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 6 6 3 6 4 5 5 +--R 2310b e x + (10920a b e + 2940b d e )x +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (20020a b e + 14560a b d e + 70b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (17160a b e + 28600a b d e + 520a b d e - 80b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (6006a e + 27456a b d e + 1716a b d e - 624a b d e + 96b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (12012a d e + 3432a b d e - 2288a b d e + 832a b d e - 128b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 6006a d e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 644 + +--S 645 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 765 +r0:=-16/99*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/11*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/1155*_ + (b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/3465*_ + (b*d-a*e)^4*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/231*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 5 5 3 5 4 4 4 +--R 630b e x + (3080a b e + 70b d e )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (5940a b e + 440a b d e - 80b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (5544a b e + 1188a b d e - 528a b d e + 96b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (2310a e + 1848a b d e - 1584a b d e + 704a b d e - 128b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 2310a d e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 647 + +--S 648 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 649 + +--S 650 of 765 +r0:=-16/63*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^2+_ + 2/9*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e-_ + 128/315*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+_ + 256/315*(b*d-a*e)^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/105*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (360a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (756a b e - 432a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1680a b d e + 2016a b d e - 1152a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 650 + +--S 651 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 652 + +--S 653 of 765 +r0:=-2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*sqrt(d+e*x))+16/7*b*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^2+128/35*b*(b*d-a*e)^2*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-256/35*b*(b*d-a*e)^3*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-96/35*b*(b*d-a*e)*_ + (a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (56a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (280a b e - 560a b d e + 448a b d e - 128b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 560a b d e - 1120a b d e + 896a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 653 + +--S 654 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 655 + +--S 656 of 765 +r0:=-2/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(3/2))-_ + 16/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*sqrt(d+e*x))-_ + 128/15*b^2*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+_ + 256/15*b^2*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*_ + (a+b*x))+32/5*b^2*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 6b e x + (40a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (180a b e - 240a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 120a b e + 720a b d e - 960a b d e + 384b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e + 480a b d e - 640a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 656 + +--S 657 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 658 + +--S 659 of 765 +r0:=-2/5*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(5/2))-_ + 16/15*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-32/5*b^2*_ + (a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*sqrt(d+e*x))+128/15*b^3*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-256/15*b^3*(b*d-a*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (120a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 180a b e + 720a b d e - 480b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 40a b e - 240a b d e + 960a b d e - 640b d e)x - 6a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 96a b d e + 384a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 659 + +--S 660 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(9/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 661 + +--S 662 of 765 +r0:=-2/7*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(7/2))-_ + 16/35*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ + 32/35*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(3/2))+_ + 128/35*b^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*sqrt(d+e*x))+_ + 256/35*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (- 280a b e + 560b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 140a b e - 560a b d e + 1120b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 56a b e - 112a b d e - 448a b d e + 896b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 32a b d e - 128a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 6 3 5 3 5 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 662 + +--S 663 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(11/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 664 + +--S 665 of 765 +r0:=-2/9*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(9/2))-_ + 16/63*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(7/2))-_ + 32/105*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(5/2))-_ + 128/105*b^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(d+e*x)^(3/2))-_ + 256/315*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 630b e x + (- 840a b e - 1680b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 756a b e - 1008a b d e - 2016b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 360a b e - 432a b d e - 576a b d e - 1152b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e - 96a b d e - 128a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 315b e x + (315a e + 1260b d e )x + (1260a d e + 1890b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (1890a d e + 1260b d e )x + (1260a d e + 315b d e )x + 315a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 665 + +--S 666 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 667 + +--S 668 of 765 +r0:=-2/11*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(11/2))-_ + 16/99*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(9/2))-32/231*b^2*_ + (a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(7/2))-128/693*b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(d+e*x)^(5/2))-256/3465*b^3*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 2310b e x + (- 5544a b e - 3696b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 5940a b e - 4752a b d e - 3168b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 3080a b e - 2640a b d e - 2112a b d e - 1408b d e)x - 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 560a b d e - 480a b d e - 384a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 6 10 9 5 +--R 3465b e x + (3465a e + 17325b d e )x +--R + +--R 9 2 8 4 2 8 3 7 3 +--R (17325a d e + 34650b d e )x + (34650a d e + 34650b d e )x +--R + +--R 3 7 4 6 2 4 6 5 5 5 5 +--R (34650a d e + 17325b d e )x + (17325a d e + 3465b d e )x + 3465a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 668 + +--S 669 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 670 + +--S 671 of 765 +r0:=-128/4199*(b*d-a*e)^3*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/323*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 24/323*(b*d-a*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/19*_ + (a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/138567*(b*d-_ + a*e)^5*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/969969*(b*d-_ + a*e)^6*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+768/46189*_ + (b*d-a*e)^4*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 9 9 5 9 6 8 8 +--R 102102b e x + (684684a b e + 234234b d e )x +--R + +--R 2 4 9 5 8 6 2 7 7 +--R (1939938a b e + 1597596a b d e + 138138b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 6 +--R (2984520a b e + 4626006a b d e + 965580a b d e + 462b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 5 3 6 +--R 2645370a b e + 7325640a b d e + 2889558a b d e + 4788a b d e +--R + +--R 6 4 5 +--R - 504b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 2 8 3 3 2 7 2 4 3 6 +--R 1293292a b e + 6760390a b d e + 4793320a b d e + 22610a b d e +--R + +--R 5 4 5 6 5 4 +--R - 5320a b d e + 560b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 +--R 277134a e + 3510364a b d e + 4744870a b d e + 64600a b d e +--R + +--R 2 4 4 5 5 5 4 6 6 3 +--R - 25840a b d e + 6080a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R 831402a d e + 2771340a b d e + 125970a b d e - 77520a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R 31008a b d e - 7296a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 2 7 5 3 6 4 2 4 5 3 3 5 4 +--R 831402a d e + 184756a b d e - 167960a b d e + 103360a b d e +--R + +--R 2 4 6 3 5 7 2 6 8 +--R - 41344a b d e + 9728a b d e - 1024b d e +--R * +--R x +--R + +--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 +--R 277134a d e - 369512a b d e + 335920a b d e - 206720a b d e +--R + +--R 2 4 7 2 5 8 6 9 +--R 82688a b d e - 19456a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 969969b e x + 969969a e +--R Type: Expression(Integer) +--E 671 + +--S 672 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 673 + +--S 674 of 765 +r0:=-128/2431*(b*d-a*e)^3*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/221*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 8/85*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/17*(a+_ + b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/51051*(b*d-a*e)^5*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/255255*(b*d-a*e)^6*(d+_ + e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/7293*(b*d-a*e)^4*_ + (a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 8 8 5 8 6 7 7 +--R 30030b e x + (204204a b e + 36036b d e )x +--R + +--R 2 4 8 5 7 6 2 6 6 +--R (589050a b e + 251328a b d e + 462b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (928200a b e + 749700a b d e + 4284a b d e - 504b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 +--R 850850a b e + 1237600a b d e + 17850a b d e - 4760a b d e +--R + +--R 6 4 4 +--R 560b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 +--R 437580a b e + 1215500a b d e + 44200a b d e - 20400a b d e +--R + +--R 5 4 4 6 5 3 +--R 5440a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 +--R 102102a e + 700128a b d e + 72930a b d e - 53040a b d e +--R + +--R 2 4 4 4 5 5 3 6 6 2 +--R 24480a b d e - 6528a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 +--R 204204a d e + 87516a b d e - 97240a b d e + 70720a b d e +--R + +--R 2 4 5 3 5 6 2 6 7 +--R - 32640a b d e + 8704a b d e - 1024b d e +--R * +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R 102102a d e - 175032a b d e + 194480a b d e - 141440a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R 65280a b d e - 17408a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 255255b e x + 255255a e +--R Type: Expression(Integer) +--E 674 + +--S 675 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 765 +r0:=-128/1287*(b*d-a*e)^3*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/143*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 8/65*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/15*(a+_ + b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/15015*(b*d-_ + a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/45045*(b*d-_ + a*e)^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+_ + 256/3003*(b*d-a*e)^4*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 7 7 5 7 6 6 6 +--R 6006b e x + (41580a b e + 462b d e )x +--R + +--R 2 4 7 5 6 6 2 5 5 +--R (122850a b e + 3780a b d e - 504b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 4 +--R (200200a b e + 13650a b d e - 4200a b d e + 560b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 +--R 193050a b e + 28600a b d e - 15600a b d e + 4800a b d e +--R + +--R 6 4 3 +--R - 640b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 108108a b e + 38610a b d e - 34320a b d e + 18720a b d e +--R + +--R 5 4 3 6 5 2 +--R - 5760a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 30030a e + 36036a b d e - 51480a b d e + 45760a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 24960a b d e + 7680a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 30030a d e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R 49920a b d e - 15360a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 677 + +--S 678 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 678 + +)clear all + +--S 679 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 679 + +--S 680 of 765 +r0:=-640/3003*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+_ + 80/429*(b*d-a*e)^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3-_ + 24/143*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e^2+2/13*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e-1024/3003*(b*d-a*e)^5*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/3003*(b*d-a*e)^6*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/1001*(b*d-_ + a*e)^4*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (3276a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (10010a b e - 3640a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (17160a b e - 11440a b d e + 4160a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 18018a b e - 20592a b d e + 13728a b d e - 4992a b d e +--R + +--R 6 4 2 +--R 768b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 12012a b e - 24024a b d e + 27456a b d e - 18304a b d e +--R + +--R 5 4 2 6 5 +--R 6656a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 6006a e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 36608a b d e - 13312a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 3003b e x + 3003a e +--R Type: Expression(Integer) +--E 680 + +--S 681 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 682 + +--S 683 of 765 +r0:=-2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*sqrt(d+e*x))+640/231*b*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4-80/33*b*(b*d-a*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3+24/11*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e^2+1024/231*b*(b*d-a*e)^4*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-2048/231*b*(b*d-a*e)^5*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-256/77*b*(b*d-a*e)^3*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (308a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (990a b e - 440a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1848a b e - 1584a b d e + 704a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 2772a b e - 9240a b d e + 14784a b d e - 12672a b d e +--R + +--R 5 4 2 6 5 +--R 5632a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 462a e + 5544a b d e - 18480a b d e + 29568a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 25344a b d e + 11264a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +-------+ +--R (231b e x + 231a e )\|e x + d +--R Type: Expression(Integer) +--E 683 + +--S 684 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 685 + +--S 686 of 765 +r0:=-2/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(3/2))-8*b*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*sqrt(d+e*x))-640/63*b^2*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+80/9*b^2*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3-1024/63*b^2*(b*d-a*e)^3*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/63*b^2*(b*d-a*e)^4*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/21*b^2*(b*d-a*e)^2*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (108a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (1890a b e - 5040a b d e + 6048a b d e - 3456a b d e + 768b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 756a b e + 7560a b d e - 20160a b d e + 24192a b d e +--R + +--R 5 4 2 6 5 +--R - 13824a b d e + 3072b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 504a b d e + 5040a b d e - 13440a b d e + 16128a b d e +--R + +--R 5 5 6 6 +--R - 9216a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 686 + +--S 687 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 688 + +--S 689 of 765 +r0:=-2/5*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(5/2))-8/5*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(3/2))-16*b^2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*sqrt(d+e*x))+128/7*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/e^4+1024/35*b^3*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6-2048/35*b^3*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x))-768/35*b^3*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (84a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (350a b e - 280a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1400a b e - 2800a b d e + 2240a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1050a b e + 8400a b d e - 16800a b d e + 13440a b d e +--R + +--R 6 4 2 +--R - 3840b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 140a b e - 1400a b d e + 11200a b d e - 22400a b d e +--R + +--R 5 4 2 6 5 +--R 17920a b d e - 5120b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 56a b d e - 560a b d e + 4480a b d e - 8960a b d e +--R + +--R 5 5 6 6 +--R 7168a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R (35b e x + (35a e + 70b d e )x + (70a d e + 35b d e )x + 35a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 689 + +--S 690 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(9/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 691 + +--S 692 of 765 +r0:=-16/7*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(3/2))-_ + 2/7*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(7/2))-24/35*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(5/2))-128/7*b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^4*sqrt(d+e*x))-1024/35*b^4*(b*d-a*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/35*b^4*(b*d-a*e)^2*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+768/35*b^4*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (140a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (1050a b e - 1400a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1400a b e + 8400a b d e - 11200a b d e + 4480b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 350a b e - 2800a b d e + 16800a b d e - 22400a b d e +--R + +--R 6 4 2 +--R 8960b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 84a b e - 280a b d e - 2240a b d e + 13440a b d e +--R + +--R 5 4 2 6 5 +--R - 17920a b d e + 7168b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e - 24a b d e - 80a b d e - 640a b d e + 3840a b d e +--R + +--R 5 5 6 6 +--R - 5120a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 8 3 7 3 7 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 692 + +--S 693 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(11/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 694 + +--S 695 of 765 +r0:=-16/21*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(5/2))-_ + 128/63*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(3/2))-2/9*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(9/2))-8/21*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^(7/2))-256/21*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*sqrt(d+e*x))+1024/63*b^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6-2048/63*b^5*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (756a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1890a b e + 7560a b d e - 5040b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 840a b e - 5040a b d e + 20160a b d e - 13440b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 378a b e - 1008a b d e - 6048a b d e + 24192a b d e +--R + +--R 6 4 2 +--R - 16128b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 108a b e - 216a b d e - 576a b d e - 3456a b d e +--R + +--R 5 4 2 6 5 +--R 13824a b d e - 9216b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 24a b d e - 48a b d e - 128a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R 3072a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 63b e x + (63a e + 252b d e )x + (252a d e + 378b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (378a d e + 252b d e )x + (252a d e + 63b d e )x + 63a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 695 + +--S 696 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 697 + +--S 698 of 765 +r0:=-80/231*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(7/2))-_ + 128/231*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(5/2))-2/11*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(11/2))-8/33*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(9/2))-256/231*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(3/2))+1024/231*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*sqrt(d+e*x))+2048/231*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (- 2772a b e + 5544b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 2310a b e - 9240a b d e + 18480b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1848a b e - 3696a b d e - 14784a b d e + 29568b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 990a b e - 1584a b d e - 3168a b d e - 12672a b d e +--R + +--R 6 4 2 +--R 25344b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 308a b e - 440a b d e - 704a b d e - 1408a b d e +--R + +--R 5 4 2 6 5 +--R - 5632a b d e + 11264b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 56a b d e - 80a b d e - 128a b d e - 256a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 231b e x + (231a e + 1155b d e )x + (1155a d e + 2310b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (2310a d e + 2310b d e )x + (2310a d e + 1155b d e )x +--R + +--R 4 8 5 7 5 7 +--R (1155a d e + 231b d e )x + 231a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 698 + +--S 699 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(15/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 700 + +--S 701 of 765 +r0:=-80/429*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(9/2))-_ + 640/3003*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(7/2))-2/13*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(13/2))-24/143*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(11/2))-256/1001*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(5/2))-1024/1001*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(d+e*x)^(3/2))-2048/3003*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 6006b e x + (- 12012a b e - 24024b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 18018a b e - 24024a b d e - 48048b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 17160a b e - 20592a b d e - 27456a b d e - 54912b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 10010a b e - 11440a b d e - 13728a b d e - 18304a b d e +--R + +--R 6 4 2 +--R - 36608b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 3276a b e - 3640a b d e - 4160a b d e - 4992a b d e +--R + +--R 5 4 2 6 5 +--R - 6656a b d e - 13312b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 462a e - 504a b d e - 560a b d e - 640a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 7 13 12 6 +--R 3003b e x + (3003a e + 18018b d e )x +--R + +--R 12 2 11 5 2 11 3 10 4 +--R (18018a d e + 45045b d e )x + (45045a d e + 60060b d e )x +--R + +--R 3 10 4 9 3 4 9 5 8 2 +--R (60060a d e + 45045b d e )x + (45045a d e + 18018b d e )x +--R + +--R 5 8 6 7 6 7 +--R (18018a d e + 3003b d e )x + 3003a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 701 + +--S 702 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(17/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 703 + +--S 704 of 765 +r0:=-16/143*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(11/2))-_ + 128/1287*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(9/2))-2/15*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(15/2))-8/65*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(13/2))-256/3003*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(7/2))-1024/9009*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(d+e*x)^(5/2))-2048/45045*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 30030b e x + (- 108108a b e - 72072b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 193050a b e - 154440a b d e - 102960b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 200200a b e - 171600a b d e - 137280a b d e - 91520b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 122850a b e - 109200a b d e - 93600a b d e - 74880a b d e +--R + +--R 6 4 2 +--R - 49920b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 41580a b e - 37800a b d e - 33600a b d e - 28800a b d e +--R + +--R 5 4 2 6 5 +--R - 23040a b d e - 15360b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 6006a e - 5544a b d e - 5040a b d e - 4480a b d e - 3840a b d e +--R + +--R 5 5 6 6 +--R - 3072a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 8 14 13 7 +--R 45045b e x + (45045a e + 315315b d e )x +--R + +--R 13 2 12 6 2 12 3 11 5 +--R (315315a d e + 945945b d e )x + (945945a d e + 1576575b d e )x +--R + +--R 3 11 4 10 4 4 10 5 9 3 +--R (1576575a d e + 1576575b d e )x + (1576575a d e + 945945b d e )x +--R + +--R 5 9 6 8 2 6 8 7 7 +--R (945945a d e + 315315b d e )x + (315315a d e + 45045b d e )x +--R + +--R 7 7 +--R 45045a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 704 + +--S 705 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 765 +r0:=2/9*(a+b*x)*(d+e*x)^(9/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 5 4 3 4 3 2 2 3 +--R 2b e x + (2a e + 8b d e )x + (8a d e + 12b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (12a d e + 8b d e)x + (8a d e + 2b d )x + 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 9e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 707 + +--S 708 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 709 + +--S 710 of 765 +r0:=2/7*(a+b*x)*(d+e*x)^(7/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 4 3 2 3 2 2 2 +--R 2b e x + (2a e + 6b d e )x + (6a d e + 6b d e)x +--R + +--R 2 3 3 +--R (6a d e + 2b d )x + 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 7e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 710 + +--S 711 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 711 + +)clear all + +--S 712 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (b e x + (a e + b d)x + a d)\|e x + d +--R (1) --------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 712 + +--S 713 of 765 +r0:=2/5*(a+b*x)*(d+e*x)^(5/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2b e x + (2a e + 4b d e)x + (4a d e + 2b d )x + 2a d )\|e x + d +--R (2) -------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 713 + +--S 714 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (b x + a)\|e x + d +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 715 + +--S 716 of 765 +r0:=2/3*(a+b*x)*(d+e*x)^(3/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 2 +-------+ +--R (2b e x + (2a e + 2b d)x + 2a d)\|e x + d +--R (2) ------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 765 +t0:=(a+b*x)/(sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 718 + +--S 719 of 765 +r0:=2*(a+b*x)*sqrt(d+e*x)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R +-------+ +--R (2b x + 2a)\|e x + d +--R (2) ---------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 719 + +--S 720 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 765 +t0:=(a+b*x)/((d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 721 + +--S 722 of 765 +r0:=-2*(a+b*x)/(e*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) -------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R e\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 722 + +--S 723 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 of 765 +t0:=(a+b*x)/((d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 765 +r0:=-2/3*(a+b*x)/(e*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) -------------------------------------------- +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (3e x + 3d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 725 + +--S 726 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 726 + +)clear all + +--S 727 of 765 +t0:=(a+b*x)/((d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 727 + +--S 728 of 765 +r0:=-2/5*(a+b*x)/(e*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) ------------------------------------------------------- +--R +------------------+ +--R 3 2 2 2 +-------+ | 2 2 2 +--R (5e x + 10d e x + 5d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 728 + +--S 729 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 730 + +--S 731 of 765 +r0:=7/3*e*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 7/5*e*(a+b*x)*(d+e*x)^(5/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^(7/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-7*e*(b*d-a*e)^(5/2)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+7*e*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 105a b e + 210a b d e - 105b d e)x - 105a e + 210a b d e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b e x + (- 14a b e + 32b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 168a b d e + 116b d e)x + 105a e - 245a b d e +--R + +--R 2 2 3 3 +--R 161a b d e - 15b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 15b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 731 + +--S 732 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 732 + +)clear all + +--S 733 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 765 +r0:=5/3*e*(a+b*x)*(d+e*x)^(3/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^(5/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-5*e*(b*d-a*e)^(3/2)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+5*e*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 +-----------+ +--R ((15a b e - 15b d e)x + 15a e - 15a b d e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (2b e x + (- 10a b e + 14b d e)x - 15a e + 20a b d e - 3b d )\|b +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 3b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 734 + +--S 735 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 736 + +--S 737 of 765 +r0:=-(d+e*x)^(3/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-3*e*(a+b*x)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*e*(a+b*x)*sqrt(d+e*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (- 3b e x - 3a e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-+ +-------+ +--R (2b e x + 3a e - b d)\|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 737 + +--S 738 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 738 + +)clear all + +--S 739 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 739 + +--S 740 of 765 +r0:=-e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-sqrt(d+e*x)/(b*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +-----------+ +-+ +-------+ +--R (- b e x - a e)atanh(--------------) - \|- a e + b d \|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R b\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 740 + +--S 741 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 741 + +)clear all + +--S 742 of 765 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 742 + +--S 743 of 765 +r0:=e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(3/2)*_ + sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-sqrt(d+e*x)/((b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +-----------+ +-+ +-------+ +--R (- b e x - a e)atanh(--------------) + \|- a e + b d \|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (a e - b d)\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 743 + +--S 744 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 744 + +)clear all + +--S 745 of 765 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------ +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 745 + +--S 746 of 765 +r0:=3*e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-_ + a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2/((b*d-a*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-3*b*sqrt(d+e*x)/((b*d-a*e)^2*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R (3b e x + 3a e)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R (- 3b e x - 2a e - b d)\|- a e + b d +--R / +--R +------------------+ +--R 2 2 2 2 +-----------+ +-------+ | 2 2 2 +--R (a e - 2a b d e + b d )\|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 746 + +--S 747 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 747 + +)clear all + +--S 748 of 765 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 748 + +--S 749 of 765 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5*b^(3/2)*e*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10/3*b/((b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-5*b^2*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +-+ +-------+ +--R (- 15b e x + (- 15a b e - 15b d e)x - 15a b d e)\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (10a b e + 20b d e)x - 2a e + 14a b d e + 3b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a e - 9a b d e + 9a b d e - 3b d e)x + 3a d e - 9a b d e +--R + +--R 2 3 3 4 +--R 9a b d e - 3b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 749 + +--S 750 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 765 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 751 + +--S 752 of 765 +r0:=2/5/((b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+14/15*b/((b*d-_ + a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7*b^(5/2)*e*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+14/3*b^2/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-7*b^3*sqrt(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R 105b e x + (105a b e + 210b d e )x + (210a b d e + 105b d e)x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 70a b e - 245b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (14a b e - 168a b d e - 161b d e)x - 6a e + 32a b d e +--R + +--R 2 2 3 3 +--R - 116a b d e - 15b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (15a e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (30a d e - 120a b d e + 180a b d e - 120a b d e + 30b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 752 + +--S 753 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 754 + +--S 755 of 765 +r0:=-7/12*e*(a+b*x)*(d+e*x)^(5/2)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^(7/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-35/24*e^2*_ + (d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-35/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+35/8*e^3*(a+b*x)*sqrt(d+e*x)/(b^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +--R (- 105b e x - 315a b e x - 315a b e x - 105a e )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b e x + (231a b e - 87b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (280a b e - 98a b d e - 38b d e)x + 105a e - 35a b d e +--R + +--R 2 2 3 3 +--R - 14a b d e - 8b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 2 5 2 4 +-+ | 2 2 2 +--R (24b x + 48a b x + 24a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 755 + +--S 756 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 756 + +)clear all + +--S 757 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 757 + +--S 758 of 765 +r0:=-5/12*e*(a+b*x)*(d+e*x)^(3/2)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^(5/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-5/8*e^2*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 15b e x - 45a b e x - 45a b e x - 15a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 33b e x + (- 40a b e - 26b d e)x - 15a e - 10a b d e - 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 5 2 4 2 3 +-----------+ +-+ | 2 2 2 +--R (24b x + 48a b x + 24a b )\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 758 + +--S 759 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 759 + +)clear all + +--S 760 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 760 + +--S 761 of 765 +r0:=-1/3*(d+e*x)^(3/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/4*e*(a+b*x)*_ + (d+e*x)^(3/2)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/8*e^3*(a+_ + b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+1/8*e^2*sqrt(d+e*x)/(b^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 3b e x - 9a b e x - 9a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (- 8a b e + 14b d e)x - 3a e - 2a b d e + 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +--R ((24a b e - 24b d)x + (48a b e - 48a b d)x + 24a b e - 24a b d) +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 761 + +--S 762 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 762 + +)clear all + +--S 763 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 763 + +--S 764 of 765 +r0:=-1/3*sqrt(d+e*x)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/12*e*(a+b*x)*_ + sqrt(d+e*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+1/8*e^2*sqrt(d+e*x)/(b*(b*d-a*e)^2*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 3b e x - 9a b e x - 9a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (8a b e - 2b d e)x - 3a e + 14a b d e - 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (24a b e - 48a b d e + 24b d )x + (48a b e - 96a b d e + 48a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 24a b e - 48a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 764 + +--S 765 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 765 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richder12f.input.pamphlet b/src/axiom-website/CATS/richder12f.input.pamphlet new file mode 100644 index 0000000..05cc5d5 --- /dev/null +++ b/src/axiom-website/CATS/richder12f.input.pamphlet @@ -0,0 +1,20523 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12f.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are 3 derivatives that did not match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12f.output +)spool richder12f.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1035 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1035 +r0:=-1/3*sqrt(d+e*x)/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 5/12*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 5/8*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 5/8*e^2*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 15b e x - 45a b e x - 45a b e x - 15a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (40a b e - 10b d e)x + 33a e - 26a b d e + 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (48a b e - 144a b d e + 144a b d e - 48a b d )x + 24a e - 72a b d e +--R + +--R 3 2 2 2 3 3 +--R 72a b d e - 24a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 3 + +)clear all + +--S 4 of 1035 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1035 +r0:=2/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))-_ + 7/3*b*sqrt(d+e*x)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/12*b*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/8*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b)/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 35/8*b*e^2*sqrt(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-+ +-------+ +--R (105b e x + 315a b e x + 315a b e x + 105a e )\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 280a b e - 35b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 231a b e - 98a b d e + 14b d e)x - 48a e - 87a b d e +--R + +--R 2 2 3 3 +--R 38a b d e - 8b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 +--R (48a b e - 192a b d e + 288a b d e - 192a b d e + 48a b d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 5 + +--S 6 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 6 + +)clear all + +--S 7 of 1035 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1035 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 6*b/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))-_ + 7*b^2*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/4*b^2*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 105/8*b^(3/2)*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 105/8*b^2*e^2*sqrt(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 945a b e - 315b d e )x +--R + +--R 2 2 4 3 3 2 3 4 2 2 3 +--R (- 945a b e - 945a b d e )x + (- 315a b e - 945a b d e )x +--R + +--R 3 3 +--R - 315a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (840a b e + 420b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (693a b e + 1134a b d e + 63b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (144a b e + 954a b d e + 180a b d e - 18b d e)x - 16a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 208a b d e + 165a b d e - 50a b d e + 8b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 7 5 +--R - 24b d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 6 5 +--R 48a b e - 216a b d e + 360a b d e - 240a b d e + 72a b d e +--R + +--R 7 6 +--R - 24b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 5 4 3 3 3 3 4 4 2 2 5 5 +--R 24a e - 72a b d e + 240a b d e - 360a b d e + 216a b d e +--R + +--R 6 6 +--R - 48a b d +--R * +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 2 5 6 +--R - 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 8 + +--S 9 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 9 + +)clear all + +--S 10 of 1035 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 10 + +--S 11 of 1035 +r0:=2/5/((b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 22/15*b/((b*d-a*e)^2*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 66/5*b^2/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))-_ + 77/5*b^3*sqrt(d+e*x)/((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 77/4*b^3*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 231/8*b^(5/2)*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 231/8*b^3*e^2*sqrt(d+e*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (10395a b e + 6930b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (10395a b e + 20790a b d e + 3465b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (3465a b e + 20790a b d e + 10395a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (6930a b d e + 10395a b d e )x + 3465a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R - 3465b e x + (- 9240a b e - 8085b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 7623a b e - 21714a b d e - 5313b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 1584a b e - 18117a b d e - 14454a b d e - 495b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (176a b e - 3872a b d e - 12309a b d e - 1430a b d e + 110b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 48a e + 416a b d e - 2768a b d e - 1335a b d e + 310a b d e +--R + +--R 5 5 +--R - 40b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 +--R 120a b e - 720a b d e + 1800a b d e - 2400a b d e +--R + +--R 2 6 4 4 7 5 3 8 6 2 +--R 1800a b d e - 720a b d e + 120b d e +--R * +--R 4 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 +--R 240a b e - 1200a b d e + 2160a b d e - 1200a b d e +--R + +--R 3 5 4 4 2 6 5 3 7 6 2 8 7 +--R - 1200a b d e + 2160a b d e - 1200a b d e + 240b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R 120a e - 240a b d e - 960a b d e + 4080a b d e - 6000a b d e +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R 4080a b d e - 960a b d e - 240a b d e + 120b d +--R * +--R 2 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 +--R 240a d e - 1200a b d e + 2160a b d e - 1200a b d e +--R + +--R 4 4 5 3 3 5 6 2 2 6 7 7 8 +--R - 1200a b d e + 2160a b d e - 1200a b d e + 240a b d +--R * +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 +--R 120a d e - 720a b d e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 3 5 7 2 6 8 +--R - 720a b d e + 120a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 1035 +t0:=(a+b*x)*(d+e*x)^(-3-2*p)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R - 2p - 3 2 2 2 p +--R (1) (b x + a)(e x + d) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 13 + +--S 14 of 1035 +r0:=1/2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/((b*d-a*e)*(1+p)*(d+e*x)^(2*(1+p))) +--R +--R +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R (2) - --------------------------------------------- +--R 2p + 2 +--R ((2a e - 2b d)p + 2a e - 2b d)(e x + d) +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1035 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R 2 2 2 p +--R (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1035 +r0:=3/2*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^4*(1+p)*(2+p)*(3+2*p)*_ + (5+2*p))+3*(b*d-a*e)^2*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^3*(2+p)*_ + (3+2*p)*(5+2*p))+3/2*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/_ + (b^2*(2+p)*(5+2*p))+(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(5+2*p)) +--R +--R +--R (2) +--R 3 3 3 3 3 2 3 3 3 3 3 +--R (4b e p + 18b e p + 26b e p + 12b e )x +--R + +--R 3 2 3 2 3 3 2 2 2 3 3 2 +--R 12b d e p + (- 6a b e + 60b d e )p + (- 15a b e + 93b d e )p +--R + +--R 2 3 3 2 +--R - 9a b e + 45b d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 3 2 2 +--R 12b d e p + (- 12a b d e + 66b d e)p +--R + +--R 2 3 2 2 3 2 2 3 2 2 3 2 +--R (6a b e - 42a b d e + 114b d e)p + 6a b e - 30a b d e + 60b d e +--R * +--R x +--R + +--R 3 3 3 2 2 3 3 2 2 2 2 2 3 3 +--R 4b d p + (- 6a b d e + 24b d )p + (6a b d e - 27a b d e + 47b d )p +--R + +--R 3 3 2 2 2 2 3 3 +--R - 3a e + 15a b d e - 30a b d e + 30b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 4 4 4 3 4 2 4 4 +--R 8b p + 56b p + 142b p + 154b p + 60b +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 18 + +)clear all + +--S 19 of 1035 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R (1) +--R 2 3 2 2 2 2 2 2 2 p +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1035 +r0:=1/2*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^3*(1+p)*(2+p)*(3+2*p))+_ + (b*d-a*e)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^2*(2+p)*(3+2*p))+_ + 1/2*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(2+p)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (2b e p + 5b e p + 3b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4b d e p + (- 2a b e + 12b d e)p - 2a b e + 8b d e)x + 2b d p +--R + +--R 2 2 2 2 2 2 +--R (- 2a b d e + 7b d )p + a e - 4a b d e + 6b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 3 3 3 2 3 3 +--R 4b p + 18b p + 26b p + 12b +--R Type: Expression(Integer) +--E 20 + +--S 21 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 of 1035 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R 2 2 2 2 p +--R (1) (b e x + (a e + b d)x + a d)(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1035 +r0:=1/2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^2*(1+p)*(3+2*p))+(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(3+2*p)) +--R +--R +--R 2 2 2 p + 1 +--R ((2b e p + 2b e)x + 2b d p - a e + 3b d)(b x + 2a b x + a ) +--R (2) ----------------------------------------------------------------- +--R 2 2 2 2 +--R 4b p + 10b p + 6b +--R Type: Expression(Integer) +--E 23 + +--S 24 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 24 + +)clear all + +--S 25 of 1035 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R 2 2 2 p +--R (1) (b x + a)(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 25 + +--S 26 of 1035 +r0:=1/2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(1+p)) +--R +--R +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R (2) ------------------------- +--R 2b p + 2b +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 27 + +)clear all + +--S 28 of 1035 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p/(d+e*x) +--R +--R +--R 2 2 2 p +--R (b x + a)(b x + 2a b x + a ) +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 28 + +--S 29 of 1035 +--r0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p/(e*(1+2*p))-(a+b*x)*_ +-- (a^2+2*a*b*x+b^2*x^2)^p*hypergeometric(1,1+2*p,2*(1+p),_ +-- -e*(a+b*x)/(b*d-a*e))/(e*(1+2*p)) +--E 29 + +--S 30 of 1035 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 1035 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R * +--R m +--R (b c x + a c) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1035 +r0:=(A*b-a*B)*(a*c+b*c*x)^(7+m)/(b^2*c^7*(7+m))+B*(a*c+b*c*x)^(8+m)/_ + (b^2*c^8*(8+m)) +--R +--R +--R (2) +--R m + 8 +--R (B m + 7B)(b c x + a c) +--R + +--R m + 7 +--R ((A b - B a)c m + (8A b - 8B a)c)(b c x + a c) +--R / +--R 2 8 2 2 8 2 8 +--R b c m + 15b c m + 56b c +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 of 1035 +t0:=(A+B*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R m +--R (B x + A)(b c x + a c) +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1035 +r0:=-(A*b-a*B)*c^5*(a*c+b*c*x)^(-5+m)/(b^2*(5-m))-B*c^4*(a*c+b*c*x)^(-4+m)/_ + (b^2*(4-m)) +--R +--R +--R (2) +--R 4 4 m - 4 +--R (B c m - 5B c )(b c x + a c) +--R + +--R 5 5 m - 5 +--R ((A b - B a)c m + (- 4A b + 4B a)c )(b c x + a c) +--R / +--R 2 2 2 2 +--R b m - 9b m + 20b +--R Type: Expression(Integer) +--E 35 + +--S 36 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 36 + +)clear all + +--S 37 of 1035 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 m +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(b c x + a c) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1035 +r0:=(A*b-a*B)*(a*c+b*c*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*c*(4+m))+_ + B*(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*c^2*(5+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R ((B b m + 4B b )x + (2B a b m + 8B a b)x + B a m + 4B a ) +--R * +--R m + 2 +--R (b c x + a c) +--R + +--R 3 2 3 2 2 +--R ((A b - B a b )c m + (5A b - 5B a b )c)x +--R + +--R 2 2 2 2 +--R ((2A a b - 2B a b)c m + (10A a b - 10B a b)c)x +--R + +--R 2 3 2 3 +--R (A a b - B a )c m + (5A a b - 5B a )c +--R * +--R m + 1 +--R (b c x + a c) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 2 2 2 2 +--R b c m + 9b c m + 20b c +--R Type: Expression(Integer) +--E 38 + +--S 39 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 39 + +)clear all + +--S 40 of 1035 +t0:=(A+B*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R m +--R (B x + A)(b c x + a c) +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1035 +r0:=-(A*b-a*B)*(a*c+b*c*x)^(1+m)/(b^2*c*(2-m)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + B*(a*c+b*c*x)^(2+m)/(b^2*c^2*(1-m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R m + 2 +--R (B m - 2B)(b c x + a c) +--R + +--R m + 1 +--R ((A b - B a)c m + (- A b + B a)c)(b c x + a c) +--R / +--R 4 2 2 4 2 4 2 2 3 2 2 3 2 3 2 +--R (b c m - 3b c m + 2b c )x + (2a b c m - 6a b c m + 4a b c )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R a b c m - 3a b c m + 2a b c +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 42 + +)clear all + +--S 43 of 1035 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R m 2 2 2 p +--R (1) (B x + A)(b c x + a c) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 43 + +--S 44 of 1035 +r0:=(A*b-a*B)*(a*c+b*c*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*c*(1+m+2*p))+_ + B*(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*c^2*(2+m+2*p)) +--R +--R +--R (2) +--R m + 2 +--R (2B p + B m + B)(b c x + a c) +--R + +--R m + 1 +--R ((2A b - 2B a)c p + (A b - B a)c m + (2A b - 2B a)c)(b c x + a c) +--R * +--R 2 2 2 p +--R (b x + 2a b x + a ) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +--R 4b c p + (4b c m + 6b c )p + b c m + 3b c m + 2b c +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1035 +t0:=(a+b*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R m 2 2 2 p +--R (1) (b x + a)(b c x + a c) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1035 +r0:=(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b*c^2*(2+m+2*p)) +--R +--R +--R m + 2 2 2 2 p +--R (b c x + a c) (b x + 2a b x + a ) +--R (2) --------------------------------------- +--R 2 2 2 +--R 2b c p + b c m + 2b c +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 48 + +)clear all + +--S 49 of 1035 +t0:=(a+b*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R m +--R (b c x + a c) +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1035 +r0:=(a*c+b*c*x)^(8+m)/(b*c^8*(8+m)) +--R +--R +--R m + 8 +--R (b c x + a c) +--R (2) ------------------ +--R 8 8 +--R b c m + 8b c +--R Type: Expression(Integer) +--E 50 + +--S 51 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 51 + +)clear all + +--S 52 of 1035 +t0:=(a+b*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R m +--R (b c x + a c) +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1035 +r0:=-c^4*(a*c+b*c*x)^(-4+m)/(b*(4-m)) +--R +--R +--R 4 m - 4 +--R c (b c x + a c) +--R (2) -------------------- +--R b m - 4b +--R Type: Expression(Integer) +--E 53 + +--S 54 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 54 + +)clear all + +--S 55 of 1035 +t0:=x*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (c x + b x + a x)(e x + d) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1035 +r0:=-d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(3*c*d^2-_ + e*(2*b*d-a*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*c*d-b*e)*(d+e*x)^(3+m)/_ + (e^4*(3+m))+c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (c m + 6c m + 11c m + 6c)(e x + d) +--R + +--R 3 2 +--R ((b e - 3c d)m + (7b e - 21c d)m + (14b e - 42c d)m + 8b e - 24c d) +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 2 2 2 +--R (a e - 2b d e + 3c d )m + (8a e - 16b d e + 24c d )m +--R + +--R 2 2 2 2 +--R (19a e - 38b d e + 57c d )m + 12a e - 24b d e + 36c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 2 2 3 2 +--R (- a d e + b d e - c d )m + (- 9a d e + 9b d e - 9c d )m +--R + +--R 2 2 3 2 2 3 +--R (- 26a d e + 26b d e - 26c d )m - 24a d e + 24b d e - 24c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 1035 +t0:=x*(d+e*x)^5*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 5 4 2 3 6 +--R c e x + (b e + 5c d e )x + (a e + 5b d e + 10c d e )x +--R + +--R 4 2 3 3 2 5 2 3 3 2 4 4 +--R (5a d e + 10b d e + 10c d e )x + (10a d e + 10b d e + 5c d e)x +--R + +--R 3 2 4 5 3 4 5 2 5 +--R (10a d e + 5b d e + c d )x + (5a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 58 + +--S 59 of 1035 +r0:=-1/6*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^6/e^4+1/7*(3*c*d^2-e*(2*b*d-a*e))*_ + (d+e*x)^7/e^4-1/8*(3*c*d-b*e)*(d+e*x)^8/e^4+1/9*c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 1 9 5 8 10 2 7 7 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + -- c d e )x +--R 9 8 8 7 7 7 +--R + +--R 5 8 5 2 7 5 3 6 6 2 7 3 6 4 5 5 +--R (- a d e + - b d e + - c d e )x + (2a d e + 2b d e + c d e )x +--R 6 3 3 +--R + +--R 5 3 6 5 4 5 1 5 4 4 5 4 5 1 5 4 3 1 5 4 2 +--R (- a d e + - b d e + - c d e )x + (- a d e + - b d e )x + - a d e x +--R 2 4 4 3 3 2 +--R + +--R 1 7 2 1 8 1 9 +--R - -- a d e + --- b d e - --- c d +--R 42 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 59 + +--S 60 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1035 +t0:=x*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 4 3 2 2 5 +--R c e x + (b e + 4c d e )x + (a e + 4b d e + 6c d e )x +--R + +--R 3 2 2 3 4 2 2 3 4 3 +--R (4a d e + 6b d e + 4c d e)x + (6a d e + 4b d e + c d )x +--R + +--R 3 4 2 4 +--R (4a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 61 + +--S 62 of 1035 +r0:=-1/5*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4+1/6*(3*c*d^2-e*(2*b*d-a*e))*_ + (d+e*x)^6/e^4-1/7*(3*c*d-b*e)*(d+e*x)^7/e^4+1/8*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 8 4 7 7 1 8 2 7 2 6 6 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + c d e )x +--R 8 7 7 6 3 +--R + +--R 4 7 6 2 6 4 3 5 5 3 2 6 3 5 1 4 4 4 +--R (- a d e + - b d e + - c d e )x + (- a d e + b d e + - c d e )x +--R 5 5 5 2 4 +--R + +--R 4 3 5 1 4 4 3 1 4 4 2 1 6 2 1 7 1 8 +--R (- a d e + - b d e )x + - a d e x - -- a d e + --- b d e - --- c d +--R 3 3 2 30 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 1035 +t0:=x*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 3 2 2 4 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 3 2 3 2 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 64 + +--S 65 of 1035 +r0:=1/2*a*d^3*x^2+1/3*d^2*(b*d+3*a*e)*x^3+1/4*d*(c*d^2+3*e*(b*d+a*e))*x^4+_ + 1/5*e*(3*c*d^2+e*(3*b*d+a*e))*x^5+1/6*e^2*(3*c*d+b*e)*x^6+1/7*c*e^3*x^7 +--R +--R +--R (2) +--R 1 3 7 1 3 1 2 6 1 3 3 2 3 2 5 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + - c d e)x +--R 7 6 2 5 5 5 +--R + +--R 3 2 3 2 1 3 4 2 1 3 3 1 3 2 +--R (- a d e + - b d e + - c d )x + (a d e + - b d )x + - a d x +--R 4 4 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 65 + +--S 66 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 66 + +)clear all + +--S 67 of 1035 +t0:=x*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 2 2 3 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d x +--R Type: Polynomial(Integer) +--E 67 + +--S 68 of 1035 +r0:=1/2*a*d^2*x^2+1/3*d*(b*d+2*a*e)*x^3+1/4*(c*d^2+e*(2*b*d+a*e))*x^4+_ + 1/5*e*(2*c*d+b*e)*x^5+1/6*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - c e x + (- b e + - c d e)x + (- a e + - b d e + - c d )x +--R 6 5 5 4 2 4 +--R + +--R 2 1 2 3 1 2 2 +--R (- a d e + - b d )x + - a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 68 + +--S 69 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 69 + +)clear all + +--S 70 of 1035 +t0:=x*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R 4 3 2 +--R (1) c e x + (b e + c d)x + (a e + b d)x + a d x +--R Type: Polynomial(Integer) +--E 70 + +--S 71 of 1035 +r0:=1/2*a*d*x^2+1/3*(b*d+a*e)*x^3+1/4*(c*d+b*e)*x^4+1/5*c*e*x^5 +--R +--R +--R 1 5 1 1 4 1 1 3 1 2 +--R (2) - c e x + (- b e + - c d)x + (- a e + - b d)x + - a d x +--R 5 4 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 71 + +--S 72 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 of 1035 +t0:=x*(a+b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) c x + b x + a x +--R Type: Polynomial(Integer) +--E 73 + +--S 74 of 1035 +r0:=1/2*a*x^2+1/3*b*x^3+1/4*c*x^4 +--R +--R +--R 1 4 1 3 1 2 +--R (2) - c x + - b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ----------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 1035 +r0:=(c*d^2-b*d*e+a*e^2)*x/e^3-1/2*(c*d-b*e)*x^2/e^2+1/3*c*x^3/e-_ + d*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 2 3 3 3 3 2 2 +--R (- 6a d e + 6b d e - 6c d )log(e x + d) + 2c e x + (3b e - 3c d e )x +--R + +--R 3 2 2 +--R (6a e - 6b d e + 6c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 79 + +--S 80 of 1035 +r0:=-(2*c*d-b*e)*x/e^3+1/2*c*x^2/e^2+d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))+_ + (3*c*d^2-e*(2*b*d-a*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((2a e - 4b d e + 6c d e)x + 2a d e - 4b d e + 6c d )log(e x + d) +--R + +--R 3 3 3 2 2 2 2 2 2 +--R c e x + (2b e - 3c d e )x + (2b d e - 4c d e)x + 2a d e - 2b d e +--R + +--R 3 +--R 2c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 80 + +--S 81 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 82 + +--S 83 of 1035 +r0:=c*x/e^3+1/2*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (-3*c*d^2+e*(2*b*d-a*e))/(e^4*(d+e*x))-(3*c*d-b*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 +--R ((2b e - 6c d e )x + (4b d e - 12c d e)x + 2b d e - 6c d )log(e x + d) +--R + +--R 3 3 2 2 3 2 2 2 2 +--R 2c e x + 4c d e x + (- 2a e + 4b d e - 4c d e)x - a d e + 3b d e +--R + +--R 3 +--R - 5c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 83 + +--S 84 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 85 + +--S 86 of 1035 +r0:=1/3*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-3*c*d^2+_ + e*(2*b*d-a*e))/(e^4*(d+e*x)^2)+(3*c*d-b*e)/(e^4*(d+e*x))+c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6c e x + 18c d e x + 18c d e x + 6c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 2 2 +--R (- 6b e + 18c d e )x + (- 3a e - 6b d e + 27c d e)x - a d e - 2b d e +--R + +--R 3 +--R 11c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 88 + +--S 89 of 1035 +r0:=1/4*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^3)+1/2*(3*c*d-b*e)/(e^4*(d+e*x)^2)-c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 3 3 2 2 1 3 1 2 2 +--R - c e x + (- - b e - - c d e )x + (- - a e - - b d e - c d e)x +--R 2 2 3 3 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - - c d +--R 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 1035 +r0:=1/5*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^5)+1/4*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^4)+1/3*(3*c*d-b*e)/(e^4*(d+e*x)^3)-1/2*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 1 3 1 2 1 2 +--R - - c e x + (- - b e - - c d e )x + (- - a e - - b d e - - c d e)x +--R 2 3 2 4 6 4 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - -- c d +--R 20 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R c x + b x + a x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 94 + +--S 95 of 1035 +r0:=1/6*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^6)+1/5*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^5)+1/4*(3*c*d-b*e)/(e^4*(d+e*x)^4)-1/3*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 1 3 1 2 1 2 +--R - - c e x + (- - b e - - c d e )x + (- - a e - -- b d e - -- c d e)x +--R 3 4 4 5 10 10 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - -- c d +--R 30 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 95 + +--S 96 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 of 1035 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + (A b + B a)x + A a)(e x + d) +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1035 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))-_ + (A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^(2+m)/(e^4*(2+m))-_ + (3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3+m)/(e^4*(3+m))+_ + B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R ((A c + B b)e - 3B c d)m + ((7A c + 7B b)e - 21B c d)m +--R + +--R ((14A c + 14B b)e - 42B c d)m + (8A c + 8B b)e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R ((A b + B a)e + (- 2A c - 2B b)d e + 3B c d )m +--R + +--R 2 2 2 +--R ((8A b + 8B a)e + (- 16A c - 16B b)d e + 24B c d )m +--R + +--R 2 2 +--R ((19A b + 19B a)e + (- 38A c - 38B b)d e + 57B c d )m +--R + +--R 2 2 +--R (12A b + 12B a)e + (- 24A c - 24B b)d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (A a e + (- A b - B a)d e + (A c + B b)d e - B c d )m +--R + +--R 3 2 2 3 2 +--R (9A a e + (- 9A b - 9B a)d e + (9A c + 9B b)d e - 9B c d )m +--R + +--R 3 2 2 3 +--R (26A a e + (- 26A b - 26B a)d e + (26A c + 26B b)d e - 26B c d )m +--R + +--R 3 2 2 3 +--R 24A a e + (- 24A b - 24B a)d e + (24A c + 24B b)d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 98 + +--S 99 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 1035 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 +--R B c e x + ((A c + B b)e + 4B c d e )x +--R + +--R 4 3 2 2 5 +--R ((A b + B a)e + (4A c + 4B b)d e + 6B c d e )x +--R + +--R 4 3 2 2 3 4 +--R (A a e + (4A b + 4B a)d e + (6A c + 6B b)d e + 4B c d e)x +--R + +--R 3 2 2 3 4 3 +--R (4A a d e + (6A b + 6B a)d e + (4A c + 4B b)d e + B c d )x +--R + +--R 2 2 3 4 2 +--R (6A a d e + (4A b + 4B a)d e + (A c + B b)d )x +--R + +--R 3 4 4 +--R (4A a d e + (A b + B a)d )x + A a d +--R Type: Polynomial(Integer) +--E 100 + +--S 101 of 1035 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4-1/6*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^7/e^4+1/8*B*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 1 8 4 7 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 1 8 2 2 7 2 6 6 +--R ((- A b + - B a)e + (- A c + - B b)d e + B c d e )x +--R 6 6 3 3 +--R + +--R 1 8 4 4 7 6 6 2 6 4 3 5 5 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 5 5 +--R + +--R 7 3 3 2 6 3 5 1 4 4 4 +--R (A a d e + (- A b + - B a)d e + (A c + B b)d e + - B c d e )x +--R 2 2 4 +--R + +--R 2 6 4 4 3 5 1 1 4 4 3 +--R (2A a d e + (- A b + - B a)d e + (- A c + - B b)d e )x +--R 3 3 3 3 +--R + +--R 3 5 1 1 4 4 2 4 4 1 5 3 +--R (2A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 5 +--R + +--R 1 1 6 2 1 1 7 1 8 +--R (- -- A b - -- B a)d e + (--- A c + --- B b)d e - --- B c d +--R 30 30 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 101 + +--S 102 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 1035 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R ((A b + B a)e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 3 2 2 3 3 +--R (A a e + (3A b + 3B a)d e + (3A c + 3B b)d e + B c d )x +--R + +--R 2 2 3 2 +--R (3A a d e + (3A b + 3B a)d e + (A c + B b)d )x +--R + +--R 2 3 3 +--R (3A a d e + (A b + B a)d )x + A a d +--R Type: Polynomial(Integer) +--E 103 + +--S 104 of 1035 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4-1/5*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^6/e^4+1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 1 7 1 6 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 1 7 3 3 6 3 2 5 5 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 5 +--R + +--R 1 7 3 3 6 3 3 2 5 1 3 4 4 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d e )x +--R 4 4 4 4 4 4 +--R + +--R 6 2 5 1 1 3 4 3 +--R (A a d e + (A b + B a)d e + (- A c + - B b)d e )x +--R 3 3 +--R + +--R 3 2 5 1 1 3 4 2 3 4 1 4 3 +--R (- A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 2 4 +--R + +--R 1 1 5 2 1 1 6 1 7 +--R (- -- A b - -- B a)d e + (-- A c + -- B b)d e - --- B c d +--R 20 20 60 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 104 + +--S 105 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1035 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 +--R ((A b + B a)e + (2A c + 2B b)d e + B c d )x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + (A c + B b)d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 1035 +r0:=-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3/e^4-1/4*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^4/e^4-1/5*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^5/e^4+1/6*B*c*(d+e*x)^6/e^4 +--R +--R +--R (2) +--R 1 6 6 1 1 6 2 5 5 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 6 5 5 5 +--R + +--R 1 1 6 1 1 5 1 2 4 4 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d e )x +--R 4 4 2 2 4 +--R + +--R 1 6 2 2 5 1 1 2 4 3 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e )x +--R 3 3 3 3 3 +--R + +--R 5 1 1 2 4 2 2 4 1 3 3 +--R (A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 3 +--R + +--R 1 1 4 2 1 1 5 1 6 +--R (- -- A b - -- B a)d e + (-- A c + -- B b)d e - -- B c d +--R 12 12 30 30 60 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 107 + +--S 108 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 1035 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + ((A c + B b)e + B c d)x + ((A b + B a)e + (A c + B b)d)x +--R + +--R (A a e + (A b + B a)d)x + A a d +--R Type: Polynomial(Integer) +--E 109 + +--S 110 of 1035 +r0:=a*A*d*x+1/2*(A*b*d+a*B*d+a*A*e)*x^2+1/3*(b*B*d+A*c*d+A*b*e+a*B*e)*x^3+_ + 1/4*(B*c*d+b*B*e+A*c*e)*x^4+1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 1 3 1 1 1 2 +--R ((- A b + - B a)e + (- A c + - B b)d)x + (- A a e + (- A b + - B a)d)x +--R 3 3 3 3 2 2 2 +--R + +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 110 + +--S 111 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + (A c + B b)x + (A b + B a)x + A a +--R Type: Polynomial(Integer) +--E 112 + +--S 113 of 1035 +r0:=a*A*x+1/2*(A*b+a*B)*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 1 3 1 1 2 +--R (2) - B c x + (- A c + - B b)x + (- A b + - B a)x + A a x +--R 4 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 of 1035 +r0:=-(A*e*(c*d-b*e)-B*(c*d^2-e*(b*d-a*e)))*x/e^3-_ + 1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+1/3*B*c*x^3/e-_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 3 +--R (6A a e + (- 6A b - 6B a)d e + (6A c + 6B b)d e - 6B c d )log(e x + d) +--R + +--R 3 3 3 2 2 +--R 2B c e x + ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R ((6A b + 6B a)e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 of 1035 +r0:=-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))-(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 +--R ((2A b + 2B a)e + (- 4A c - 4B b)d e + 6B c d e)x +--R + +--R 2 2 3 +--R (2A b + 2B a)d e + (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 3 2 +--R ((2A c + 2B b)d e - 4B c d e)x - 2A a e + (2A b + 2B a)d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 1035 +r0:=B*c*x/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x))-_ + (3*B*c*d-b*B*e-A*c*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 +--R 2B c e x + 4B c d e x +--R + +--R 3 2 2 3 +--R ((- 2A b - 2B a)e + (4A c + 4B b)d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 124 + +--S 125 of 1035 +r0:=1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+_ + 1/2*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^2)+_ + (3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 3 +--R ((- 3A b - 3B a)e + (- 6A c - 6B b)d e + 27B c d e)x - 2A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 125 + +--S 126 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 127 + +--S 128 of 1035 +r0:=1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^2)-B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 1 3 3 2 2 +--R - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 2 2 +--R + +--R 1 1 3 1 1 2 2 1 3 +--R ((- - A b - - B a)e + (- - A c - - B b)d e - B c d e)x - - A a e +--R 3 3 3 3 4 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - - B c d +--R 12 12 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 128 + +--S 129 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 130 + +--S 131 of 1035 +r0:=1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^5)+1/4*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 3 3 2 +--R + +--R 1 1 3 1 1 2 1 2 1 3 +--R ((- - A b - - B a)e + (- - A c - - B b)d e - - B c d e)x - - A a e +--R 4 4 6 6 4 5 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - -- B c d +--R 20 20 30 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 131 + +--S 132 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 133 + +--S 134 of 1035 +r0:=1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^6)+1/5*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^5)+1/4*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 3 4 4 4 +--R + +--R 1 1 3 1 1 2 1 2 1 3 +--R ((- - A b - - B a)e + (- -- A c - -- B b)d e - -- B c d e)x - - A a e +--R 5 5 10 10 10 6 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - -- B c d +--R 30 30 60 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 134 + +--S 135 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1035 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1035 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))-_ + (c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^(2+m)/(e^6*(2+m))-(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^(4+m)/(e^6*(4+m))-c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((A c + 2B b c)e - 5B c d)m + ((16A c + 32B b c)e - 80B c d)m +--R + +--R 2 2 3 +--R ((95A c + 190B b c)e - 475B c d)m +--R + +--R 2 2 2 +--R ((260A c + 520B b c)e - 1300B c d)m +--R + +--R 2 2 2 2 +--R ((324A c + 648B b c)e - 1620B c d)m + (144A c + 288B b c)e - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R (((2A b + 2B a)c + B b )e + (- 4A c - 8B b c)d e + 10B c d )m +--R + +--R 2 2 2 +--R ((34A b + 34B a)c + 17B b )e + (- 68A c - 136B b c)d e +--R + +--R 2 2 +--R 170B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 +--R ((214A b + 214B a)c + 107B b )e + (- 428A c - 856B b c)d e +--R + +--R 2 2 +--R 1070B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 +--R ((614A b + 614B a)c + 307B b )e + (- 1228A c - 2456B b c)d e +--R + +--R 2 2 +--R 3070B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 +--R ((792A b + 792B a)c + 396B b )e + (- 1584A c - 3168B b c)d e +--R + +--R 2 2 +--R 3960B c d +--R * +--R m +--R + +--R 2 2 2 +--R ((360A b + 360B a)c + 180B b )e + (- 720A c - 1440B b c)d e +--R + +--R 2 2 +--R 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 +--R (2A a c + A b + 2B a b)e + ((- 6A b - 6B a)c - 3B b )d e +--R + +--R 2 2 2 3 +--R (6A c + 12B b c)d e - 10B c d +--R * +--R 5 +--R m +--R + +--R 2 3 +--R (36A a c + 18A b + 36B a b)e +--R + +--R 2 2 2 2 +--R ((- 108A b - 108B a)c - 54B b )d e + (108A c + 216B b c)d e +--R + +--R 2 3 +--R - 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 +--R (242A a c + 121A b + 242B a b)e +--R + +--R 2 2 2 2 +--R ((- 726A b - 726B a)c - 363B b )d e + (726A c + 1452B b c)d e +--R + +--R 2 3 +--R - 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 +--R (744A a c + 372A b + 744B a b)e +--R + +--R 2 2 +--R ((- 2232A b - 2232B a)c - 1116B b )d e +--R + +--R 2 2 2 3 +--R (2232A c + 4464B b c)d e - 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 +--R (1016A a c + 508A b + 1016B a b)e +--R + +--R 2 2 +--R ((- 3048A b - 3048B a)c - 1524B b )d e +--R + +--R 2 2 2 3 +--R (3048A c + 6096B b c)d e - 5080B c d +--R * +--R m +--R + +--R 2 3 +--R (480A a c + 240A b + 480B a b)e +--R + +--R 2 2 2 2 +--R ((- 1440A b - 1440B a)c - 720B b )d e + (1440A c + 2880B b c)d e +--R + +--R 2 3 +--R - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 2 3 +--R (2A a b + B a )e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 2 2 2 3 2 4 +--R ((6A b + 6B a)c + 3B b )d e + (- 4A c - 8B b c)d e + 5B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 +--R (38A a b + 19B a )e + (- 76A a c - 38A b - 76B a b)d e +--R + +--R 2 2 2 2 3 +--R ((114A b + 114B a)c + 57B b )d e + (- 76A c - 152B b c)d e +--R + +--R 2 4 +--R 95B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 +--R (274A a b + 137B a )e + (- 548A a c - 274A b - 548B a b)d e +--R + +--R 2 2 2 2 3 +--R ((822A b + 822B a)c + 411B b )d e + (- 548A c - 1096B b c)d e +--R + +--R 2 4 +--R 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 +--R (922A a b + 461B a )e + (- 1844A a c - 922A b - 1844B a b)d e +--R + +--R 2 2 2 +--R ((2766A b + 2766B a)c + 1383B b )d e +--R + +--R 2 3 2 4 +--R (- 1844A c - 3688B b c)d e + 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 +--R (1404A a b + 702B a )e +--R + +--R 2 3 +--R (- 2808A a c - 1404A b - 2808B a b)d e +--R + +--R 2 2 2 +--R ((4212A b + 4212B a)c + 2106B b )d e +--R + +--R 2 3 2 4 +--R (- 2808A c - 5616B b c)d e + 3510B c d +--R * +--R m +--R + +--R 2 4 2 3 +--R (720A a b + 360B a )e + (- 1440A a c - 720A b - 1440B a b)d e +--R + +--R 2 2 2 2 3 +--R ((2160A b + 2160B a)c + 1080B b )d e + (- 1440A c - 2880B b c)d e +--R + +--R 2 4 +--R 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (- 2A a b - B a )d e + (2A a c + A b + 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 2A b - 2B a)c - B b )d e + (A c + 2B b c)d e - B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 +--R 20A a e + (- 40A a b - 20B a )d e +--R + +--R 2 2 3 +--R (40A a c + 20A b + 40B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 40A b - 40B a)c - 20B b )d e + (20A c + 40B b c)d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 +--R 155A a e + (- 310A a b - 155B a )d e +--R + +--R 2 2 3 +--R (310A a c + 155A b + 310B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 310A b - 310B a)c - 155B b )d e + (155A c + 310B b c)d e +--R + +--R 2 5 +--R - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 +--R 580A a e + (- 1160A a b - 580B a )d e +--R + +--R 2 2 3 +--R (1160A a c + 580A b + 1160B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 1160A b - 1160B a)c - 580B b )d e + (580A c + 1160B b c)d e +--R + +--R 2 5 +--R - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 +--R 1044A a e + (- 2088A a b - 1044B a )d e +--R + +--R 2 2 3 +--R (2088A a c + 1044A b + 2088B a b)d e +--R + +--R 2 3 2 +--R ((- 2088A b - 2088B a)c - 1044B b )d e +--R + +--R 2 4 2 5 +--R (1044A c + 2088B b c)d e - 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 +--R 720A a e + (- 1440A a b - 720B a )d e +--R + +--R 2 2 3 +--R (1440A a c + 720A b + 1440B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 1440A b - 1440B a)c - 720B b )d e + (720A c + 1440B b c)d e +--R + +--R 2 5 +--R - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 1035 +t0:=(A+B*x)*(d+e*x)^5*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 10 2 5 2 4 9 +--R B c e x + ((A c + 2B b c)e + 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 8 +--R (((2A b + 2B a)c + B b )e + (5A c + 10B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 +--R (2A a c + A b + 2B a b)e + ((10A b + 10B a)c + 5B b )d e +--R + +--R 2 2 3 2 3 2 +--R (10A c + 20B b c)d e + 10B c d e +--R * +--R 7 +--R x +--R + +--R 2 5 2 4 +--R (2A a b + B a )e + (10A a c + 5A b + 10B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((20A b + 20B a)c + 10B b )d e + (10A c + 20B b c)d e + 5B c d e +--R * +--R 6 +--R x +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (10A a b + 5B a )d e + (20A a c + 10A b + 20B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((20A b + 20B a)c + 10B b )d e + (5A c + 10B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 5A a d e + (20A a b + 10B a )d e + (20A a c + 10A b + 20B a b)d e +--R + +--R 2 4 2 5 +--R ((10A b + 10B a)c + 5B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 10A a d e + (20A a b + 10B a )d e + (10A a c + 5A b + 10B a b)d e +--R + +--R 2 5 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 139 + +--S 140 of 1035 +r0:=-1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^6/e^6-_ + 1/7*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-_ + e*(3*b*d-a*e)))*(d+e*x)^7/e^6-1/8*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^8/e^6-1/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^9/e^6-1/10*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^10/e^6+1/11*B*c^2*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 2 11 11 1 2 1 11 1 2 10 10 +--R -- B c e x + ((-- A c + - B b c)e + - B c d e )x +--R 11 10 5 2 +--R + +--R 2 2 1 2 11 5 2 10 10 +--R ((- A b + - B a)c + - B b )e + (- A c + -- B b c)d e +--R 9 9 9 9 9 +--R + +--R 10 2 2 9 +--R -- B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 1 1 2 1 11 5 5 5 2 10 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 4 8 4 4 4 8 +--R + +--R 5 2 5 2 9 5 2 3 8 +--R (- A c + - B b c)d e + - B c d e +--R 4 2 4 +--R * +--R 8 +--R x +--R + +--R 2 1 2 11 10 5 2 10 10 +--R (- A a b + - B a )e + (-- A a c + - A b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 20 20 10 2 2 9 10 2 20 3 8 +--R ((-- A b + -- B a)c + -- B b )d e + (-- A c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 5 2 4 7 +--R - B c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 1 2 11 5 5 2 10 +--R - A a e + (- A a b + - B a )d e +--R 6 3 6 +--R + +--R 10 5 2 10 2 9 +--R (-- A a c + - A b + -- B a b)d e +--R 3 3 3 +--R + +--R 10 10 5 2 3 8 5 2 5 4 7 1 2 5 6 +--R ((-- A b + -- B a)c + - B b )d e + (- A c + - B b c)d e + - B c d e +--R 3 3 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 2 10 2 2 9 2 3 8 +--R A a d e + (4A a b + 2B a )d e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 4 7 1 2 2 5 6 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 2 2 9 5 2 3 8 5 5 2 5 4 7 +--R - A a d e + (5A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 2 2 2 4 2 +--R + +--R 1 1 1 2 5 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 10 2 3 8 10 5 2 4 7 +--R -- A a d e + (-- A a b + - B a )d e +--R 3 3 3 +--R + +--R 2 1 2 2 5 6 +--R (- A a c + - A b + - B a b)d e +--R 3 3 3 +--R * +--R 3 +--R x +--R + +--R 5 2 4 7 1 2 5 6 2 2 5 6 1 2 6 5 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 1 1 2 7 4 1 1 2 1 8 3 +--R (- -- A a b - -- B a )d e + (-- A a c + --- A b + -- B a b)d e +--R 21 42 84 168 84 +--R + +--R 1 1 1 2 9 2 1 2 1 10 +--R ((- --- A b - --- B a)c - --- B b )d e + (---- A c + --- B b c)d e +--R 252 252 504 1260 630 +--R + +--R 1 2 11 +--R - ---- B c d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 140 + +--S 141 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 of 1035 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 +--R B c e x + ((A c + 2B b c)e + 4B c d e )x +--R + +--R 2 4 2 3 2 2 2 7 +--R (((2A b + 2B a)c + B b )e + (4A c + 8B b c)d e + 6B c d e )x +--R + +--R 2 4 2 3 +--R (2A a c + A b + 2B a b)e + ((8A b + 8B a)c + 4B b )d e +--R + +--R 2 2 2 2 3 +--R (6A c + 12B b c)d e + 4B c d e +--R * +--R 6 +--R x +--R + +--R 2 4 2 3 +--R (2A a b + B a )e + (8A a c + 4A b + 8B a b)d e +--R + +--R 2 2 2 2 3 2 4 +--R ((12A b + 12B a)c + 6B b )d e + (4A c + 8B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 3 2 2 2 +--R A a e + (8A a b + 4B a )d e + (12A a c + 6A b + 12B a b)d e +--R + +--R 2 3 2 4 +--R ((8A b + 8B a)c + 4B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 4A a d e + (12A a b + 6B a )d e + (8A a c + 4A b + 8B a b)d e +--R + +--R 2 4 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 142 + +--S 143 of 1035 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^5/e^6-_ + 1/6*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^7/e^6-_ + 1/8*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*_ + (d+e*x)^8/e^6-1/9*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^9/e^6+_ + 1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 2 10 4 2 9 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 1 2 10 1 2 9 3 2 2 8 8 +--R (((- A b + - B a)c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 4 8 2 4 +--R + +--R 2 1 2 2 10 8 8 4 2 9 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 7 7 7 7 7 7 +--R + +--R 6 2 12 2 8 4 2 3 7 +--R (- A c + -- B b c)d e + - B c d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 1 2 10 4 2 2 4 9 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 3 6 3 3 3 +--R + +--R 2 2 8 2 2 4 3 7 1 2 4 6 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d e + - B c d e +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 2 10 8 4 2 9 +--R - A a e + (- A a b + - B a )d e +--R 5 5 5 +--R + +--R 12 6 2 12 2 8 8 8 4 2 3 7 +--R (-- A a c + - A b + -- B a b)d e + ((- A b + - B a)c + - B b )d e +--R 5 5 5 5 5 5 +--R + +--R 1 2 2 4 6 +--R (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 2 9 3 2 2 8 2 3 7 +--R A a d e + (3A a b + - B a )d e + (2A a c + A b + 2B a b)d e +--R 2 +--R + +--R 1 1 1 2 4 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 2 8 8 4 2 3 7 2 1 2 2 4 6 3 +--R (2A a d e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 3 3 +--R + +--R 2 3 7 1 2 4 6 2 2 4 6 1 2 5 5 +--R (2A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 5 +--R + +--R 1 1 2 6 4 2 1 2 2 7 3 +--R (- -- A a b - -- B a )d e + (--- A a c + --- A b + --- B a b)d e +--R 15 30 105 105 105 +--R + +--R 1 1 1 2 8 2 1 2 1 9 +--R ((- --- A b - --- B a)c - --- B b )d e + (--- A c + --- B b c)d e +--R 140 140 280 630 315 +--R + +--R 1 2 10 +--R - ---- B c d +--R 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 143 + +--S 144 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 1035 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R (((2A b + 2B a)c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 +--R (2A a c + A b + 2B a b)e + ((6A b + 6B a)c + 3B b )d e +--R + +--R 2 2 2 3 +--R (3A c + 6B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 3 2 2 +--R (2A a b + B a )e + (6A a c + 3A b + 6B a b)d e +--R + +--R 2 2 2 3 +--R ((6A b + 6B a)c + 3B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 +--R A a e + (6A a b + 3B a )d e + (6A a c + 3A b + 6B a b)d e +--R + +--R 2 3 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 145 + +--S 146 of 1035 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4/e^6-_ + 1/5*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^5/e^6-1/6*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^7/e^6-1/8*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^8/e^6+1/9*B*c^2*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 1 2 9 9 1 2 1 9 3 2 8 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 2 1 2 9 3 2 6 8 3 2 2 7 7 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d e )x +--R 7 7 7 7 7 7 +--R + +--R 1 1 2 1 9 1 2 8 +--R (- A a c + - A b + - B a b)e + ((A b + B a)c + - B b )d e +--R 3 6 3 2 +--R + +--R 1 2 2 7 1 2 3 6 +--R (- A c + B b c)d e + - B c d e +--R 2 6 +--R * +--R 6 +--R x +--R + +--R 2 1 2 9 6 3 2 6 8 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 6 6 3 2 2 7 1 2 2 3 6 +--R ((- A b + - B a)c + - B b )d e + (- A c + - B b c)d e +--R 5 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 2 9 3 3 2 8 3 3 2 3 2 7 +--R - A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 4 2 4 2 4 2 +--R + +--R 1 1 1 2 3 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 7 2 1 2 2 3 6 3 +--R (A a d e + (2A a b + B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 +--R + +--R 3 2 2 7 1 2 3 6 2 2 3 6 1 2 4 5 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 4 +--R + +--R 1 1 2 5 4 1 1 2 1 6 3 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A b + -- B a b)d e +--R 10 20 30 60 30 +--R + +--R 1 1 1 2 7 2 1 2 1 8 +--R ((- -- A b - -- B a)c - --- B b )d e + (--- A c + --- B b c)d e +--R 70 70 140 280 140 +--R + +--R 1 2 9 +--R - --- B c d +--R 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 146 + +--S 147 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 1035 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R (((2A b + 2B a)c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 +--R (2A a c + A b + 2B a b)e + ((4A b + 4B a)c + 2B b )d e +--R + +--R 2 2 +--R (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 2 2 +--R (2A a b + B a )e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 2 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 148 + +--S 149 of 1035 +r0:=-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^3/e^6-1/4*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*(d+e*x)^4/e^6-_ + 1/5*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^5/e^6-_ + 1/6*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^7/e^6+_ + 1/8*B*c^2*(d+e*x)^8/e^6 +--R +--R +--R (2) +--R 1 2 8 8 1 2 2 8 2 2 7 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 1 1 2 8 1 2 2 7 1 2 2 6 6 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d e )x +--R 3 3 6 3 3 6 +--R + +--R 2 1 2 2 8 4 4 2 2 7 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 5 5 5 5 5 5 +--R + +--R 1 2 2 2 6 +--R (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 1 1 2 8 1 2 7 +--R (- A a b + - B a )e + (A a c + - A b + B a b)d e +--R 2 4 2 +--R + +--R 1 1 1 2 2 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 1 2 8 4 2 2 7 2 1 2 2 2 6 3 +--R (- A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 3 3 3 +--R + +--R 2 7 1 2 2 6 2 2 2 6 1 2 3 5 +--R (A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 3 +--R + +--R 1 1 2 4 4 1 1 2 1 5 3 +--R (- - A a b - -- B a )d e + (-- A a c + -- A b + -- B a b)d e +--R 6 12 15 30 15 +--R + +--R 1 1 1 2 6 2 1 2 2 7 +--R ((- -- A b - -- B a)c - -- B b )d e + (--- A c + --- B b c)d e +--R 30 30 60 105 105 +--R + +--R 1 2 8 +--R - --- B c d +--R 168 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1035 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 +--R (((2A b + 2B a)c + B b )e + (A c + 2B b c)d)x +--R + +--R 2 2 3 +--R ((2A a c + A b + 2B a b)e + ((2A b + 2B a)c + B b )d)x +--R + +--R 2 2 2 +--R ((2A a b + B a )e + (2A a c + A b + 2B a b)d)x +--R + +--R 2 2 2 +--R (A a e + (2A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 151 + +--S 152 of 1035 +r0:=a^2*A*d*x+1/2*a*(2*A*b*d+a*B*d+a*A*e)*x^2+1/3*(a*B*(2*b*d+a*e)+_ + A*(b^2*d+2*a*c*d+2*a*b*e))*x^3+1/4*(b^2*(B*d+A*e)+2*a*c*(B*d+A*e)+_ + 2*b*(A*c*d+a*B*e))*x^4+1/5*(b^2*B*e+2*b*c*(B*d+A*e)+_ + c*(A*c*d+2*a*B*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 2 1 2 1 2 2 5 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 5 +--R + +--R 1 1 2 1 1 1 1 2 4 +--R ((- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d)x +--R 2 4 2 2 2 4 +--R + +--R 2 1 2 2 1 2 2 3 +--R ((- A a b + - B a )e + (- A a c + - A b + - B a b)d)x +--R 3 3 3 3 3 +--R + +--R 1 2 1 2 2 2 +--R (- A a e + (A a b + - B a )d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 152 + +--S 153 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 154 + +--S 155 of 1035 +r0:=a^2*A*x+1/2*a*(2*A*b+a*B)*x^2+1/3*(2*a*b*B+A*(b^2+2*a*c))*x^3+_ + 1/4*(b^2*B+2*A*b*c+2*a*B*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 1 1 2 4 +--R - B c x + (- A c + - B b c)x + ((- A b + - B a)c + - B b )x +--R 6 5 5 2 2 4 +--R + +--R 2 1 2 2 3 1 2 2 2 +--R (- A a c + - A b + - B a b)x + (A a b + - B a )x + A a x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 155 + +--S 156 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 157 + +--S 158 of 1035 +r0:=-(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + x/e^5-1/2*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^2/e^6-1/3*(2*A*c*e*_ + (2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*(d+e*x)^3/e^6-_ + 1/4*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^4/e^6+1/5*B*c^2*(d+e*x)^5/e^6-_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R 60A a e + (- 120A a b - 60B a )d e +--R + +--R 2 2 3 +--R (120A a c + 60A b + 120B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 120A b - 120B a)c - 60B b )d e + (60A c + 120B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((40A b + 40B a)c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 +--R (60A a c + 30A b + 60B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (30A c + 60B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (120A a b + 60B a )e + (- 120A a c - 60A b - 120B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((120A b + 120B a)c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 +--R (60A a c + 30A b + 60B a b)d e + ((- 140A b - 140B a)c - 70B b )d e +--R + +--R 2 4 2 5 +--R (115A c + 230B b c)d e - 163B c d +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 158 + +--S 159 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 of 1035 +r0:=-(2*B*(2*c*d-b*e)*(c*d^2-e*(b*d-a*e))-A*e*(3*c^2*d^2+b^2*e^2-_ + 2*c*e*(2*b*d-a*e)))*x/e^5-1/2*(2*A*c*e*(c*d-b*e)-B*(3*c^2*d^2+b^2*e^2-_ + 2*c*e*(2*b*d-a*e)))*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x))-_ + (c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R (24A a b + 12B a )e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 4 2 2 3 +--R (24A a b + 12B a )d e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 +--R (24A a c + 12A b + 24B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (24A c + 48B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R (24A a c + 12A b + 24B a b)d e + ((- 48A b - 48B a)c - 24B b )d e +--R + +--R 2 3 2 2 4 +--R (36A c + 72B b c)d e - 48B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (24A a b + 12B a )d e + (- 24A a c - 12A b - 24B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((24A b + 24B a)c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 161 + +--S 162 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 of 1035 +r0:=-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*x/e^5-_ + 1/2*c*(3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^2)+(c*d^2-b*d*e+a*e^2)*(2*A*e*_ + (2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x))-(B*(10*c^2*d^3+_ + b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-_ + 2*c*e*(3*b*d-a*e)))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R (12A a c + 6A b + 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (36A c + 72B b c)d e - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 +--R (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 72A b - 72B a)c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 +--R (12A a c + 6A b + 12B a b)d e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 4 2 5 +--R (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 +--R ((24A b + 24B a)c + 12B b )d e + (- 33A c - 66B b c)d e +--R + +--R 2 3 2 +--R 63B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 12A a b - 6B a )e + (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((- 24A b - 24B a)c - 12B b )d e + (6A c + 12B b c)d e + 6B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 6A a b - 3B a )d e + (18A a c + 9A b + 18B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 30A b - 30B a)c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1035 +r0:=-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^3)+1/2*(c*d^2-b*d*e+a*e^2)*(2*A*e*_ + (2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^2)+(B*(10*c^2*d^3+_ + b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-_ + 2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(4*b*d-a*e)))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R ((12A b + 12B a)c + 6B b )e + (- 24A c - 48B b c)d e +--R + +--R 2 2 3 +--R 60B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 2 3 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 3 2 +--R 180B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 4 +--R 180B c d e +--R * +--R x +--R + +--R 2 3 2 2 4 2 5 +--R ((12A b + 12B a)c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((36A b + 36B a)c + 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 18A c - 36B b c)d e - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 6A a b - 3B a )e + (- 12A a c - 6A b - 12B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((54A b + 54B a)c + 27B b )d e + (- 54A c - 108B b c)d e + 81B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 2A a e + (- 2A a b - B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((22A b + 22B a)c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 169 + +--S 170 of 1035 +r0:=B*c^2*x/e^5+1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^4)+_ + 1/3*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/_ + (e^6*(d+e*x)^3)+1/2*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-_ + a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^2)+_ + (2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*_ + (d+e*x))-c*(5*B*c*d-2*b*B*e-A*c*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 4 +--R ((12A c + 24B b c)e - 60B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((48A c + 96B b c)d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 +--R ((72A c + 144B b c)d e - 360B c d e )x +--R + +--R 2 3 2 2 4 2 4 +--R ((48A c + 96B b c)d e - 240B c d e)x + (12A c + 24B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 +--R 12B c e x + 48B c d e x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((- 24A b - 24B a)c - 12B b )e + (48A c + 96B b c)d e - 48B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (108A c + 216B b c)d e - 252B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 8A a b - 4B a )e + (- 8A a c - 4A b - 8B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 24A b - 24B a)c - 12B b )d e + (88A c + 176B b c)d e +--R + +--R 2 4 +--R - 248B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 2A a b - B a )d e + (- 2A a c - A b - 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (25A c + 50B b c)d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^6 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 172 + +--S 173 of 1035 +r0:=1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^5)+1/4*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^4)+_ + 1/3*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^3)+_ + 1/2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^2)+c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x))+B*c^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R ((- 60A c - 120B b c)e + 300B c d e )x +--R + +--R 2 5 2 4 +--R ((- 60A b - 60B a)c - 30B b )e + (- 120A c - 240B b c)d e +--R + +--R 2 2 3 +--R 900B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 4 +--R (- 40A a c - 20A b - 40B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 120A c - 240B b c)d e + 1100B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 30A a b - 15B a )e + (- 20A a c - 10A b - 20B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 30A b - 30B a)c - 15B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 625B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (- 6A a b - 3B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (- 12A c - 24B b c)d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Expression(Integer) +--E 173 + +--S 174 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 of 1035 +r0:=1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^6)+1/5*(c*d^2-_ + b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+_ + e*x)^5)+1/4*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^4)+_ + 1/3*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^3)+1/2*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^2)-_ + B*c^2/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 5 5 1 2 5 5 2 4 4 +--R - B c e x + ((- - A c - B b c)e - - B c d e )x +--R 2 2 +--R + +--R 2 2 1 2 5 2 2 4 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 3 3 3 3 3 +--R + +--R 10 2 2 3 +--R - -- B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 1 1 2 1 5 1 1 1 2 4 +--R (- - A a c - - A b - - B a b)e + ((- - A b - - B a)c - - B b )d e +--R 2 4 2 2 2 4 +--R + +--R 1 2 2 3 5 2 3 2 +--R (- - A c - B b c)d e - - B c d e +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 2 1 2 5 1 1 2 1 4 +--R (- - A a b - - B a )e + (- - A a c - -- A b - - B a b)d e +--R 5 5 5 10 5 +--R + +--R 1 1 1 2 2 3 1 2 2 3 2 2 4 +--R ((- - A b - - B a)c - -- B b )d e + (- - A c - - B b c)d e - B c d e +--R 5 5 10 5 5 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 6 15 30 +--R + +--R 1 1 2 1 2 3 +--R (- -- A a c - -- A b - -- B a b)d e +--R 30 60 30 +--R + +--R 1 1 1 2 3 2 1 2 1 4 1 2 5 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e - - B c d +--R 30 30 60 30 15 6 +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 176 + +--S 177 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 178 + +--S 179 of 1035 +r0:=1/7*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^7)+1/6*(c*d^2-_ + b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*_ + (d+e*x)^6)+1/5*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^5)+_ + 1/4*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^4)+1/3*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^3)-_ + 1/2*B*c^2/(e^6*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 5 5 1 2 2 5 5 2 4 4 +--R - - B c e x + ((- - A c - - B b c)e - - B c d e )x +--R 2 3 3 6 +--R + +--R 1 1 1 2 5 1 2 2 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 2 2 4 3 3 +--R + +--R 5 2 2 3 +--R - - B c d e +--R 6 +--R * +--R 3 +--R x +--R + +--R 2 1 2 2 5 +--R (- - A a c - - A b - - B a b)e +--R 5 5 5 +--R + +--R 3 3 3 2 4 1 2 2 2 3 +--R ((- -- A b - -- B a)c - -- B b )d e + (- - A c - - B b c)d e +--R 10 10 20 5 5 +--R + +--R 1 2 3 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 1 1 2 5 2 1 2 2 4 +--R (- - A a b - - B a )e + (- -- A a c - -- A b - -- B a b)d e +--R 3 6 15 15 15 +--R + +--R 1 1 1 2 2 3 1 2 2 3 2 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e +--R 10 10 20 15 15 +--R + +--R 1 2 4 +--R - - B c d e +--R 6 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 7 21 42 +--R + +--R 2 1 2 2 2 3 +--R (- --- A a c - --- A b - --- B a b)d e +--R 105 105 105 +--R + +--R 1 1 1 2 3 2 1 2 2 4 +--R ((- -- A b - -- B a)c - --- B b )d e + (- --- A c - --- B b c)d e +--R 70 70 140 105 105 +--R + +--R 1 2 5 +--R - -- B c d +--R 42 +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 6 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 179 + +--S 180 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1035 +r0:=1/8*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^8)+1/7*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^7)+_ + 1/6*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*_ + d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^6)+1/5*(2*A*c*e*(2*c*d-_ + b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*(d+e*x)^5)+_ + 1/4*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^4)-1/3*B*c^2/(e^6*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 5 5 1 2 1 5 5 2 4 4 +--R - - B c e x + ((- - A c - - B b c)e - -- B c d e )x +--R 3 4 2 12 +--R + +--R 2 2 1 2 5 1 2 2 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 5 5 5 5 5 +--R + +--R 1 2 2 3 +--R - - B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 1 1 2 1 5 1 1 1 2 4 +--R (- - A a c - - A b - - B a b)e + ((- - A b - - B a)c - -- B b )d e +--R 3 6 3 5 5 10 +--R + +--R 1 2 1 2 3 1 2 3 2 +--R (- -- A c - - B b c)d e - - B c d e +--R 10 5 6 +--R * +--R 2 +--R x +--R + +--R 2 1 2 5 2 1 2 2 4 +--R (- - A a b - - B a )e + (- -- A a c - -- A b - -- B a b)d e +--R 7 7 21 21 21 +--R + +--R 2 2 1 2 2 3 1 2 2 3 2 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e +--R 35 35 35 35 35 +--R + +--R 1 2 4 +--R - -- B c d e +--R 21 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 8 28 56 +--R + +--R 1 1 2 1 2 3 +--R (- -- A a c - --- A b - -- B a b)d e +--R 84 168 84 +--R + +--R 1 1 1 2 3 2 1 2 1 4 +--R ((- --- A b - --- B a)c - --- B b )d e + (- --- A c - --- B b c)d e +--R 140 140 280 280 140 +--R + +--R 1 2 5 +--R - --- B c d +--R 168 +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 5 9 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 8 2 7 7 8 6 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 182 + +--S 183 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 of 1035 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1035 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))-_ + (c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*_ + (d+e*x)^(2+m)/(e^8*(2+m))-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*(d+e*x)^(3+m)/(e^8*(3+m))-(A*e*(2*c*d-b*e)*_ + (10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*_ + (4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+_ + a^2*e^2)))*(d+e*x)^(4+m)/(e^8*(4+m))-(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*_ + (5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^(6+m)/(e^8*(6+m))-_ + c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*_ + (d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 2 3 7 3 2 3 6 +--R ((A c + 3B b c )e - 7B c d)m + ((29A c + 87B b c )e - 203B c d)m +--R + +--R 3 2 3 5 +--R ((343A c + 1029B b c )e - 2401B c d)m +--R + +--R 3 2 3 4 +--R ((2135A c + 6405B b c )e - 14945B c d)m +--R + +--R 3 2 3 3 +--R ((7504A c + 22512B b c )e - 52528B c d)m +--R + +--R 3 2 3 2 +--R ((14756A c + 44268B b c )e - 103292B c d)m +--R + +--R 3 2 3 +--R ((14832A c + 44496B b c )e - 103824B c d)m +--R + +--R 3 2 3 +--R (5760A c + 17280B b c )e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 7 +--R (((3A b + 3B a)c + 3B b c)e + (- 6A c - 18B b c )d e + 21B c d )m +--R + +--R 2 2 2 3 2 +--R ((90A b + 90B a)c + 90B b c)e + (- 180A c - 540B b c )d e +--R + +--R 3 2 +--R 630B c d +--R * +--R 6 +--R m +--R + +--R 2 2 2 +--R ((1098A b + 1098B a)c + 1098B b c)e +--R + +--R 3 2 3 2 +--R (- 2196A c - 6588B b c )d e + 7686B c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 +--R ((7020A b + 7020B a)c + 7020B b c)e +--R + +--R 3 2 3 2 +--R (- 14040A c - 42120B b c )d e + 49140B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 +--R ((25227A b + 25227B a)c + 25227B b c)e +--R + +--R 3 2 3 2 +--R (- 50454A c - 151362B b c )d e + 176589B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 +--R ((50490A b + 50490B a)c + 50490B b c)e +--R + +--R 3 2 3 2 +--R (- 100980A c - 302940B b c )d e + 353430B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 +--R ((51432A b + 51432B a)c + 51432B b c)e +--R + +--R 3 2 3 2 +--R (- 102864A c - 308592B b c )d e + 360024B c d +--R * +--R m +--R + +--R 2 2 2 +--R ((20160A b + 20160B a)c + 20160B b c)e +--R + +--R 3 2 3 2 +--R (- 40320A c - 120960B b c )d e + 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 3 3 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 2 3 2 2 +--R ((- 15A b - 15B a)c - 15B b c)d e + (15A c + 45B b c )d e +--R + +--R 3 3 +--R - 35B c d +--R * +--R 7 +--R m +--R + +--R 2 2 3 3 +--R (93A a c + (93A b + 186B a b)c + 31B b )e +--R + +--R 2 2 2 +--R ((- 465A b - 465B a)c - 465B b c)d e +--R + +--R 3 2 2 3 3 +--R (465A c + 1395B b c )d e - 1085B c d +--R * +--R 6 +--R m +--R + +--R 2 2 3 3 +--R (1173A a c + (1173A b + 2346B a b)c + 391B b )e +--R + +--R 2 2 2 +--R ((- 5865A b - 5865B a)c - 5865B b c)d e +--R + +--R 3 2 2 3 3 +--R (5865A c + 17595B b c )d e - 13685B c d +--R * +--R 5 +--R m +--R + +--R 2 2 3 3 +--R (7743A a c + (7743A b + 15486B a b)c + 2581B b )e +--R + +--R 2 2 2 +--R ((- 38715A b - 38715B a)c - 38715B b c)d e +--R + +--R 3 2 2 3 3 +--R (38715A c + 116145B b c )d e - 90335B c d +--R * +--R 4 +--R m +--R + +--R 2 2 3 3 +--R (28632A a c + (28632A b + 57264B a b)c + 9544B b )e +--R + +--R 2 2 2 +--R ((- 143160A b - 143160B a)c - 143160B b c)d e +--R + +--R 3 2 2 3 3 +--R (143160A c + 429480B b c )d e - 334040B c d +--R * +--R 3 +--R m +--R + +--R 2 2 3 3 +--R (58692A a c + (58692A b + 117384B a b)c + 19564B b )e +--R + +--R 2 2 2 +--R ((- 293460A b - 293460B a)c - 293460B b c)d e +--R + +--R 3 2 2 3 3 +--R (293460A c + 880380B b c )d e - 684740B c d +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 +--R (60912A a c + (60912A b + 121824B a b)c + 20304B b )e +--R + +--R 2 2 2 +--R ((- 304560A b - 304560B a)c - 304560B b c)d e +--R + +--R 3 2 2 3 3 +--R (304560A c + 913680B b c )d e - 710640B c d +--R * +--R m +--R + +--R 2 2 3 3 +--R (24192A a c + (24192A b + 48384B a b)c + 8064B b )e +--R + +--R 2 2 2 +--R ((- 120960A b - 120960B a)c - 120960B b c)d e +--R + +--R 3 2 2 3 3 +--R (120960A c + 362880B b c )d e - 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R ((30A b + 30B a)c + 30B b c)d e + (- 20A c - 60B b c )d e +--R + +--R 3 4 +--R 35B c d +--R * +--R 7 +--R m +--R + +--R 2 3 2 4 +--R ((192A a b + 96B a )c + 32A b + 96B a b )e +--R + +--R 2 2 3 3 +--R (- 384A a c + (- 384A b - 768B a b)c - 128B b )d e +--R + +--R 2 2 2 2 +--R ((960A b + 960B a)c + 960B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 640A c - 1920B b c )d e + 1120B c d +--R * +--R 6 +--R m +--R + +--R 2 3 2 4 +--R ((2508A a b + 1254B a )c + 418A b + 1254B a b )e +--R + +--R 2 2 3 3 +--R (- 5016A a c + (- 5016A b - 10032B a b)c - 1672B b )d e +--R + +--R 2 2 2 2 +--R ((12540A b + 12540B a)c + 12540B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 8360A c - 25080B b c )d e + 14630B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 4 +--R ((17184A a b + 8592B a )c + 2864A b + 8592B a b )e +--R + +--R 2 2 3 3 +--R (- 34368A a c + (- 34368A b - 68736B a b)c - 11456B b )d e +--R + +--R 2 2 2 2 +--R ((85920A b + 85920B a)c + 85920B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 57280A c - 171840B b c )d e + 100240B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 4 +--R ((65958A a b + 32979B a )c + 10993A b + 32979B a b )e +--R + +--R 2 2 3 3 +--R (- 131916A a c + (- 131916A b - 263832B a b)c - 43972B b )d e +--R + +--R 2 2 2 2 +--R ((329790A b + 329790B a)c + 329790B b c)d e +--R + +--R 3 2 3 3 4 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366936B a b)c - 61156B b )d e +--R + +--R 2 2 4 2 +--R ((229335A b + 229335B a)c + 229335B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 91734A c - 275202B b c )d e + 107023B c d +--R * +--R 3 +--R m +--R + +--R 2 3 6 +--R (110118A a b + 36706B a )e +--R + +--R 2 2 2 5 +--R (- 220236A a c - 220236A a b - 220236B a b)d e +--R + +--R 2 3 2 2 4 +--R ((660708A a b + 330354B a )c + 110118A b + 330354B a b )d e +--R + +--R 2 2 3 3 3 +--R (- 440472A a c + (- 440472A b - 880944B a b)c - 146824B b )d e +--R + +--R 2 2 4 2 +--R ((550590A b + 550590B a)c + 550590B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 220236A c - 660708B b c )d e + 256942B c d +--R * +--R 2 +--R m +--R + +--R 2 3 6 +--R (134136A a b + 44712B a )e +--R + +--R 2 2 2 5 +--R (- 268272A a c - 268272A a b - 268272B a b)d e +--R + +--R 2 3 2 2 4 +--R ((804816A a b + 402408B a )c + 134136A b + 402408B a b )d e +--R + +--R 2 2 3 +--R (- 536544A a c + (- 536544A b - 1073088B a b)c - 178848B b ) +--R * +--R 3 3 +--R d e +--R + +--R 2 2 4 2 +--R ((670680A b + 670680B a)c + 670680B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 268272A c - 804816B b c )d e + 312984B c d +--R * +--R m +--R + +--R 2 3 6 +--R (60480A a b + 20160B a )e +--R + +--R 2 2 2 5 +--R (- 120960A a c - 120960A a b - 120960B a b)d e +--R + +--R 2 3 2 2 4 +--R ((362880A a b + 181440B a )c + 60480A b + 181440B a b )d e +--R + +--R 2 2 3 3 3 +--R (- 241920A a c + (- 241920A b - 483840B a b)c - 80640B b )d e +--R + +--R 2 2 4 2 +--R ((302400A b + 302400B a)c + 302400B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 120960A c - 362880B b c )d e + 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R A a e + (- 3A a b - B a )d e + (3A a c + 3A a b + 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (3A a c + (3A b + 6B a b)c + B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 3A b - 3B a)c - 3B b c)d e + (A c + 3B b c )d e - B c d +--R * +--R 7 +--R m +--R + +--R 3 7 2 3 6 +--R 35A a e + (- 105A a b - 35B a )d e +--R + +--R 2 2 2 2 5 +--R (105A a c + 105A a b + 105B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 210A a b - 105B a )c - 35A b - 105B a b )d e +--R + +--R 2 2 3 4 3 +--R (105A a c + (105A b + 210B a b)c + 35B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 105A b - 105B a)c - 105B b c)d e + (35A c + 105B b c )d e +--R + +--R 3 7 +--R - 35B c d +--R * +--R 6 +--R m +--R + +--R 3 7 2 3 6 +--R 511A a e + (- 1533A a b - 511B a )d e +--R + +--R 2 2 2 2 5 +--R (1533A a c + 1533A a b + 1533B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 3066A a b - 1533B a )c - 511A b - 1533B a b )d e +--R + +--R 2 2 3 4 3 +--R (1533A a c + (1533A b + 3066B a b)c + 511B b )d e +--R + +--R 2 2 5 2 +--R ((- 1533A b - 1533B a)c - 1533B b c)d e +--R + +--R 3 2 6 3 7 +--R (511A c + 1533B b c )d e - 511B c d +--R * +--R 5 +--R m +--R + +--R 3 7 2 3 6 +--R 4025A a e + (- 12075A a b - 4025B a )d e +--R + +--R 2 2 2 2 5 +--R (12075A a c + 12075A a b + 12075B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 24150A a b - 12075B a )c - 4025A b - 12075B a b )d e +--R + +--R 2 2 3 4 3 +--R (12075A a c + (12075A b + 24150B a b)c + 4025B b )d e +--R + +--R 2 2 5 2 +--R ((- 12075A b - 12075B a)c - 12075B b c)d e +--R + +--R 3 2 6 3 7 +--R (4025A c + 12075B b c )d e - 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 7 2 3 6 +--R 18424A a e + (- 55272A a b - 18424B a )d e +--R + +--R 2 2 2 2 5 +--R (55272A a c + 55272A a b + 55272B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 110544A a b - 55272B a )c - 18424A b - 55272B a b )d e +--R + +--R 2 2 3 4 3 +--R (55272A a c + (55272A b + 110544B a b)c + 18424B b )d e +--R + +--R 2 2 5 2 +--R ((- 55272A b - 55272B a)c - 55272B b c)d e +--R + +--R 3 2 6 3 7 +--R (18424A c + 55272B b c )d e - 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 7 2 3 6 +--R 48860A a e + (- 146580A a b - 48860B a )d e +--R + +--R 2 2 2 2 5 +--R (146580A a c + 146580A a b + 146580B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 293160A a b - 146580B a )c - 48860A b - 146580B a b )d e +--R + +--R 2 2 3 4 3 +--R (146580A a c + (146580A b + 293160B a b)c + 48860B b )d e +--R + +--R 2 2 5 2 +--R ((- 146580A b - 146580B a)c - 146580B b c)d e +--R + +--R 3 2 6 3 7 +--R (48860A c + 146580B b c )d e - 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 7 2 3 6 +--R 69264A a e + (- 207792A a b - 69264B a )d e +--R + +--R 2 2 2 2 5 +--R (207792A a c + 207792A a b + 207792B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 415584A a b - 207792B a )c - 69264A b - 207792B a b )d e +--R + +--R 2 2 3 4 3 +--R (207792A a c + (207792A b + 415584B a b)c + 69264B b )d e +--R + +--R 2 2 5 2 +--R ((- 207792A b - 207792B a)c - 207792B b c)d e +--R + +--R 3 2 6 3 7 +--R (69264A c + 207792B b c )d e - 69264B c d +--R * +--R m +--R + +--R 3 7 2 3 6 +--R 40320A a e + (- 120960A a b - 40320B a )d e +--R + +--R 2 2 2 2 5 +--R (120960A a c + 120960A a b + 120960B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 241920A a b - 120960B a )c - 40320A b - 120960B a b )d e +--R + +--R 2 2 3 4 3 +--R (120960A a c + (120960A b + 241920B a b)c + 40320B b )d e +--R + +--R 2 2 5 2 +--R ((- 120960A b - 120960B a)c - 120960B b c)d e +--R + +--R 3 2 6 3 7 +--R (40320A c + 120960B b c )d e - 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 185 + +--S 186 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 1035 +t0:=(A+B*x)*(d+e*x)^5*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 5 12 3 2 5 3 4 11 +--R B c e x + ((A c + 3B b c )e + 5B c d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 10 +--R (((3A b + 3B a)c + 3B b c)e + (5A c + 15B b c )d e + 10B c d e )x +--R + +--R 2 2 3 5 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 4 3 2 2 3 3 3 2 +--R ((15A b + 15B a)c + 15B b c)d e + (10A c + 30B b c )d e + 10B c d e +--R * +--R 9 +--R x +--R + +--R 2 3 2 5 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 4 +--R (15A a c + (15A b + 30B a b)c + 5B b )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R ((30A b + 30B a)c + 30B b c)d e + (10A c + 30B b c )d e + 5B c d e +--R * +--R 8 +--R x +--R + +--R 2 2 2 5 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 4 +--R ((30A a b + 15B a )c + 5A b + 15B a b )d e +--R + +--R 2 2 3 2 3 +--R (30A a c + (30A b + 60B a b)c + 10B b )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R ((30A b + 30B a)c + 30B b c)d e + (5A c + 15B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (3A a b + B a )e + (15A a c + 15A a b + 15B a b)d e +--R + +--R 2 3 2 2 3 +--R ((60A a b + 30B a )c + 10A b + 30B a b )d e +--R + +--R 2 2 3 3 2 +--R (30A a c + (30A b + 60B a b)c + 10B b )d e +--R + +--R 2 2 4 3 2 5 +--R ((15A b + 15B a)c + 15B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 5 2 3 4 2 2 2 2 3 +--R A a e + (15A a b + 5B a )d e + (30A a c + 30A a b + 30B a b)d e +--R + +--R 2 3 2 3 2 +--R ((60A a b + 30B a )c + 10A b + 30B a b )d e +--R + +--R 2 2 3 4 +--R (15A a c + (15A b + 30B a b)c + 5B b )d e +--R + +--R 2 2 5 +--R ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 2 3 2 2 2 3 2 +--R 5A a d e + (30A a b + 10B a )d e + (30A a c + 30A a b + 30B a b)d e +--R + +--R 2 3 2 4 +--R ((30A a b + 15B a )c + 5A b + 15B a b )d e +--R + +--R 2 2 3 5 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 2 4 +--R 10A a d e + (30A a b + 10B a )d e + (15A a c + 15A a b + 15B a b)d e +--R + +--R 2 3 2 5 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 4 2 2 2 5 2 +--R (10A a d e + (15A a b + 5B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 4 2 3 5 3 5 +--R (5A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 187 + +--S 188 of 1035 +r0:=-1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^6/e^8-_ + 1/7*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-_ + e*(4*b*d-a*e)))*(d+e*x)^7/e^8-3/8*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*(d+e*x)^8/e^8-1/9*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*_ + (d+e*x)^9/e^8-1/10*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + (d+e*x)^10/e^8-3/11*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-_ + c*e*(6*b*d-a*e)))*(d+e*x)^11/e^8-1/12*c^2*(7*B*c*d-3*b*B*e-A*c*e)*_ + (d+e*x)^12/e^8+1/13*B*c^3*(d+e*x)^13/e^8 +--R +--R +--R (2) +--R 1 3 13 13 1 3 1 2 13 5 3 12 12 +--R -- B c e x + ((-- A c + - B b c )e + -- B c d e )x +--R 13 12 4 12 +--R + +--R 3 3 2 3 2 13 5 3 15 2 12 +--R ((-- A b + -- B a)c + -- B b c)e + (-- A c + -- B b c )d e +--R 11 11 11 11 11 +--R + +--R 10 3 2 11 +--R -- B c d e +--R 11 +--R * +--R 11 +--R x +--R + +--R 3 2 3 2 3 1 3 13 +--R (-- A a c + (-- A b + - B a b)c + -- B b )e +--R 10 10 5 10 +--R + +--R 3 3 2 3 2 12 3 2 2 11 3 3 10 +--R ((- A b + - B a)c + - B b c)d e + (A c + 3B b c )d e + B c d e +--R 2 2 2 +--R * +--R 10 +--R x +--R + +--R 2 1 2 1 3 1 2 13 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 3 3 9 3 +--R + +--R 5 2 5 2 10 5 3 12 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 3 3 3 9 +--R + +--R 10 10 2 10 2 2 11 10 3 10 2 3 10 +--R ((-- A b + -- B a)c + -- B b c)d e + (-- A c + -- B b c )d e +--R 3 3 3 9 3 +--R + +--R 5 3 4 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 3 2 3 2 13 +--R (- A a c + - A a b + - B a b)e +--R 8 8 8 +--R + +--R 15 15 2 5 3 15 2 12 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 4 8 8 8 +--R + +--R 15 2 15 2 15 5 3 2 11 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 4 4 2 4 +--R + +--R 15 15 2 15 2 3 10 5 3 15 2 4 9 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + -- B b c )d e +--R 4 4 4 8 8 +--R + +--R 1 3 5 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 3 2 1 3 13 15 2 15 2 15 2 12 +--R (- A a b + - B a )e + (-- A a c + -- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 60 30 2 10 3 30 2 2 11 +--R ((-- A a b + -- B a )c + -- A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 30 2 30 2 60 10 3 3 10 +--R (-- A a c + (-- A b + -- B a b)c + -- B b )d e +--R 7 7 7 7 +--R + +--R 15 15 2 15 2 4 9 1 3 3 2 5 8 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 13 5 2 5 3 12 +--R - A a e + (- A a b + - B a )d e +--R 6 2 6 +--R + +--R 2 2 2 2 11 +--R (5A a c + 5A a b + 5B a b)d e +--R + +--R 2 5 3 2 3 10 +--R ((10A a b + 5B a )c + - A b + 5B a b )d e +--R 3 +--R + +--R 5 2 5 2 5 3 4 9 +--R (- A a c + (- A b + 5B a b)c + - B b )d e +--R 2 2 6 +--R + +--R 1 1 2 1 2 5 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 12 2 3 2 11 2 2 2 3 10 +--R A a d e + (6A a b + 2B a )d e + (6A a c + 6A a b + 6B a b)d e +--R + +--R 2 3 2 4 9 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 3 2 3 2 6 1 3 5 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 5 3 2 11 15 2 5 3 3 10 +--R - A a d e + (-- A a b + - B a )d e +--R 2 2 2 +--R + +--R 15 2 15 2 15 2 4 9 +--R (-- A a c + -- A a b + -- B a b)d e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 5 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 10 3 3 10 2 5 3 4 9 2 2 2 5 8 3 +--R (-- A a d e + (5A a b + - B a )d e + (A a c + A a b + B a b)d e )x +--R 3 3 +--R + +--R 5 3 4 9 3 2 1 3 5 8 2 3 5 8 1 3 6 7 +--R (- A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 2 6 +--R + +--R 1 2 1 3 7 6 1 2 1 2 1 2 8 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 14 42 56 56 56 +--R + +--R 1 1 2 1 3 1 2 9 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 84 168 504 168 +--R + +--R 1 2 1 2 1 1 3 10 3 +--R (--- A a c + (--- A b + --- B a b)c + ---- B b )d e +--R 420 420 210 1260 +--R + +--R 1 1 2 1 2 11 2 +--R ((- --- A b - --- B a)c - --- B b c)d e +--R 924 924 924 +--R + +--R 1 3 1 2 12 1 3 13 +--R (---- A c + ---- B b c )d e - ----- B c d +--R 5544 1848 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 188 + +--S 189 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 1035 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 2 4 3 3 10 +--R B c e x + ((A c + 3B b c )e + 4B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 9 +--R (((3A b + 3B a)c + 3B b c)e + (4A c + 12B b c )d e + 6B c d e )x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((12A b + 12B a)c + 12B b c)d e + (6A c + 18B b c )d e + 4B c d e +--R * +--R 8 +--R x +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 3 +--R (12A a c + (12A b + 24B a b)c + 4B b )d e +--R + +--R 2 2 2 2 3 2 3 3 4 +--R ((18A b + 18B a)c + 18B b c)d e + (4A c + 12B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 2 2 4 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 3 +--R ((24A a b + 12B a )c + 4A b + 12B a b )d e +--R + +--R 2 2 3 2 2 +--R (18A a c + (18A b + 36B a b)c + 6B b )d e +--R + +--R 2 2 3 3 2 4 +--R ((12A b + 12B a)c + 12B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 3 4 2 2 2 3 +--R (3A a b + B a )e + (12A a c + 12A a b + 12B a b)d e +--R + +--R 2 3 2 2 2 +--R ((36A a b + 18B a )c + 6A b + 18B a b )d e +--R + +--R 2 2 3 3 +--R (12A a c + (12A b + 24B a b)c + 4B b )d e +--R + +--R 2 2 4 +--R ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 +--R A a e + (12A a b + 4B a )d e + (18A a c + 18A a b + 18B a b)d e +--R + +--R 2 3 2 3 +--R ((24A a b + 12B a )c + 4A b + 12B a b )d e +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R 4A a d e + (18A a b + 6B a )d e + (12A a c + 12A a b + 12B a b)d e +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 3 3 2 2 2 4 2 +--R (6A a d e + (12A a b + 4B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 3 2 3 4 3 4 +--R (4A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 190 + +--S 191 of 1035 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^5/e^8-1/6*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^6/e^8-_ + 3/7*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^7/e^8-_ + 1/8*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^8/e^8-1/9*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*_ + d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^9/e^8-3/10*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^10/e^8-1/11*c^2*(7*B*c*d-_ + 3*b*B*e-A*c*e)*(d+e*x)^11/e^8+1/12*B*c^3*(d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 3 12 12 1 3 3 2 12 4 3 11 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 3 2 3 2 12 2 3 6 2 11 +--R ((-- A b + -- B a)c + -- B b c)e + (- A c + - B b c )d e +--R 10 10 10 5 5 +--R + +--R 3 3 2 10 +--R - B c d e +--R 5 +--R * +--R 10 +--R x +--R + +--R 1 2 1 2 2 1 3 12 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 3 3 3 9 +--R + +--R 4 4 2 4 2 11 2 3 2 2 10 +--R ((- A b + - B a)c + - B b c)d e + (- A c + 2B b c )d e +--R 3 3 3 3 +--R + +--R 4 3 3 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 3 2 1 3 3 2 12 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 4 8 8 8 +--R + +--R 3 2 3 2 1 3 11 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 9 9 2 9 2 2 10 1 3 3 2 3 9 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 4 4 4 2 2 +--R + +--R 1 3 4 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 3 2 3 2 3 2 12 +--R (- A a c + - A a b + - B a b)e +--R 7 7 7 +--R + +--R 24 12 2 4 3 12 2 11 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 18 2 18 2 36 6 3 2 10 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 12 12 2 12 2 3 9 1 3 3 2 4 8 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 12 2 2 2 11 +--R (- A a b + - B a )e + (2A a c + 2A a b + 2B a b)d e +--R 2 6 +--R + +--R 2 3 2 2 10 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 2 2 2 3 3 9 +--R (2A a c + (2A b + 4B a b)c + - B b )d e +--R 3 +--R + +--R 1 1 2 1 2 4 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 1 3 12 12 2 4 3 11 +--R - A a e + (-- A a b + - B a )d e +--R 5 5 5 +--R + +--R 18 2 18 2 18 2 2 10 +--R (-- A a c + -- A a b + -- B a b)d e +--R 5 5 5 +--R + +--R 24 12 2 4 3 12 2 3 9 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 4 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 11 9 2 3 3 2 10 2 2 2 3 9 +--R A a d e + (- A a b + - B a )d e + (3A a c + 3A a b + 3B a b)d e +--R 2 2 +--R + +--R 3 3 2 1 3 3 2 4 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 2 10 2 4 3 3 9 2 2 2 4 8 3 +--R (2A a d e + (4A a b + - B a )d e + (A a c + A a b + B a b)d e )x +--R 3 +--R + +--R 3 3 9 3 2 1 3 4 8 2 3 4 8 1 3 5 7 +--R (2A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 5 +--R + +--R 1 2 1 3 6 6 1 2 1 2 1 2 7 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 10 30 35 35 35 +--R + +--R 3 3 2 1 3 3 2 8 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 280 280 +--R + +--R 1 2 1 2 1 1 3 9 3 +--R (--- A a c + (--- A b + --- B a b)c + --- B b )d e +--R 210 210 105 630 +--R + +--R 1 1 2 1 2 10 2 1 3 1 2 11 +--R ((- --- A b - --- B a)c - --- B b c)d e + (---- A c + --- B b c )d e +--R 420 420 420 2310 770 +--R + +--R 1 3 12 +--R - ---- B c d +--R 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 191 + +--S 192 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 1035 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 2 3 3 2 9 +--R B c e x + ((A c + 3B b c )e + 3B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 8 +--R (((3A b + 3B a)c + 3B b c)e + (3A c + 9B b c )d e + 3B c d e)x +--R + +--R 2 2 3 3 2 2 2 +--R (3A a c + (3A b + 6B a b)c + B b )e + ((9A b + 9B a)c + 9B b c)d e +--R + +--R 3 2 2 3 3 +--R (3A c + 9B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 3 2 3 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 2 +--R (9A a c + (9A b + 18B a b)c + 3B b )d e +--R + +--R 2 2 2 3 2 3 +--R ((9A b + 9B a)c + 9B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 2 2 3 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 2 +--R ((18A a b + 9B a )c + 3A b + 9B a b )d e +--R + +--R 2 2 3 2 2 2 3 +--R (9A a c + (9A b + 18B a b)c + 3B b )d e + ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (3A a b + B a )e + (9A a c + 9A a b + 9B a b)d e +--R + +--R 2 3 2 2 +--R ((18A a b + 9B a )c + 3A b + 9B a b )d e +--R + +--R 2 2 3 3 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 +--R A a e + (9A a b + 3B a )d e + (9A a c + 9A a b + 9B a b)d e +--R + +--R 2 3 2 3 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 2 3 2 +--R (3A a d e + (9A a b + 3B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 2 2 3 3 3 3 +--R (3A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 193 + +--S 194 of 1035 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^4/e^8-1/5*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^5/e^8-_ + 1/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^6/e^8-_ + 1/7*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^7/e^8-1/8*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^8/e^8-1/3*c*(A*c*e*(2*c*d-_ + b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^9/e^8-1/10*c^2*_ + (7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^10/e^8+1/11*B*c^3*(d+e*x)^11/e^8 +--R +--R +--R (2) +--R 1 3 11 11 1 3 3 2 11 3 3 10 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 1 2 1 2 11 1 3 2 10 +--R ((- A b + - B a)c + - B b c)e + (- A c + B b c )d e +--R 3 3 3 3 +--R + +--R 1 3 2 9 +--R - B c d e +--R 3 +--R * +--R 9 +--R x +--R + +--R 3 2 3 2 3 1 3 11 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 8 8 4 8 +--R + +--R 9 9 2 9 2 10 3 3 9 2 2 9 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 8 8 8 8 8 +--R + +--R 1 3 3 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 6 3 2 1 3 3 2 11 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 7 7 7 7 +--R + +--R 9 2 9 2 18 3 3 10 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 9 9 2 9 2 2 9 1 3 3 2 3 8 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 2 1 2 11 +--R (- A a c + - A a b + - B a b)e +--R 2 2 2 +--R + +--R 3 2 1 3 3 2 10 +--R ((3A a b + - B a )c + - A b + - B a b )d e +--R 2 2 2 +--R + +--R 3 2 3 2 1 3 2 9 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 1 1 2 1 2 3 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 1 3 11 9 2 9 2 9 2 10 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 18 9 2 3 3 9 2 2 9 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 3 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 11 9 2 3 3 10 +--R - A a e + (- A a b + - B a )d e +--R 4 4 4 +--R + +--R 9 2 9 2 9 2 2 9 +--R (- A a c + - A a b + - B a b)d e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 3 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 10 2 3 2 9 2 2 2 3 8 3 +--R (A a d e + (3A a b + B a )d e + (A a c + A a b + B a b)d e )x +--R + +--R 3 3 2 9 3 2 1 3 3 8 2 3 3 8 1 3 4 7 +--R (- A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 2 4 +--R + +--R 3 2 1 3 5 6 1 2 1 2 1 2 6 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 20 20 20 20 20 +--R + +--R 3 3 2 1 3 3 2 7 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 70 140 140 140 +--R + +--R 3 2 3 2 3 1 3 8 3 +--R (--- A a c + (--- A b + --- B a b)c + --- B b )d e +--R 280 280 140 280 +--R + +--R 1 1 2 1 2 9 2 1 3 1 2 10 +--R ((- --- A b - --- B a)c - --- B b c)d e + (--- A c + --- B b c )d e +--R 168 168 168 840 280 +--R + +--R 1 3 11 +--R - ---- B c d +--R 1320 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 194 + +--S 195 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1035 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 2 3 8 +--R B c e x + ((A c + 3B b c )e + 2B c d e)x +--R + +--R 2 2 2 3 2 3 2 7 +--R (((3A b + 3B a)c + 3B b c)e + (2A c + 6B b c )d e + B c d )x +--R + +--R 2 2 3 2 2 2 +--R (3A a c + (3A b + 6B a b)c + B b )e + ((6A b + 6B a)c + 6B b c)d e +--R + +--R 3 2 2 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 3 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 2 2 2 +--R (6A a c + (6A b + 12B a b)c + 2B b )d e + ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 2 2 2 2 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 +--R ((12A a b + 6B a )c + 2A b + 6B a b )d e +--R + +--R 2 2 3 2 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 +--R (3A a b + B a )e + (6A a c + 6A a b + 6B a b)d e +--R + +--R 2 3 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (A a e + (6A a b + 2B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 2 3 2 3 2 +--R (2A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 1035 +r0:=a^3*A*d^2*x+1/2*a^2*d*(3*A*b*d+a*B*d+2*a*A*e)*x^2+1/3*a*(a*B*d*_ + (3*b*d+2*a*e)+A*(3*b^2*d^2+6*a*b*d*e+a*(3*c*d^2+a*e^2)))*x^3+1/4*(A*_ + (b^3*d^2+6*a*b^2*d*e+6*a^2*c*d*e+3*a*b*(2*c*d^2+a*e^2))+a*B*_ + (3*b^2*d^2+6*a*b*d*e+a*(3*c*d^2+a*e^2)))*x^4+1/5*(b^3*d*(B*d+2*A*e)+_ + 3*b^2*(A*c*d^2+2*a*B*d*e+a*A*e^2)+3*a*c*(A*c*d^2+2*a*B*d*e+a*A*e^2)+_ + 3*a*b*(2*B*c*d^2+4*A*c*d*e+a*B*e^2))*x^5+1/6*(b^3*e*(2*B*d+A*e)+_ + 3*b*c*(A*c*d^2+4*a*B*d*e+2*a*A*e^2)+3*b^2*(B*c*d^2+2*A*c*d*e+a*B*e^2)+_ + 3*a*c*(B*c*d^2+2*A*c*d*e+a*B*e^2))*x^6+1/7*(b^3*B*e^2+3*b^2*c*e*_ + (2*B*d+A*e)+c^2*(A*c*d^2+6*a*B*d*e+3*a*A*e^2)+3*b*c*(B*c*d^2+2*A*c*d*e+_ + 2*a*B*e^2))*x^7+1/8*c*(A*c*e*(2*c*d+3*b*e)+B*(c^2*d^2+3*b^2*e^2+_ + 3*c*e*(2*b*d+a*e)))*x^8+1/9*c^2*e*(2*B*c*d+3*b*B*e+A*c*e)*x^9+_ + 1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 8 4 4 8 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 7 7 7 7 +--R + +--R 6 6 2 6 2 1 3 3 2 2 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 1 2 2 +--R ((A a b + - B a )c + - A b + - B a b )e +--R 2 6 2 +--R + +--R 2 2 1 3 1 1 2 1 2 2 +--R (A a c + (A b + 2B a b)c + - B b )d e + ((- A b + - B a)c + - B b c)d +--R 3 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 3 2 3 2 2 +--R (- A a c + - A a b + - B a b)e +--R 5 5 5 +--R + +--R 12 6 2 2 3 6 2 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 1 3 2 3 2 3 2 3 2 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 4 4 2 2 2 +--R + +--R 3 3 2 1 3 3 2 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 1 3 2 2 2 3 2 2 2 2 3 +--R (- A a e + (2A a b + - B a )d e + (A a c + A a b + B a b)d )x +--R 3 3 +--R + +--R 3 3 2 1 3 2 2 3 2 +--R (A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 1035 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 2 3 7 +--R B c e x + ((A c + 3B b c )e + B c d)x +--R + +--R 2 2 3 2 6 +--R (((3A b + 3B a)c + 3B b c)e + (A c + 3B b c )d)x +--R + +--R 2 2 3 2 2 5 +--R ((3A a c + (3A b + 6B a b)c + B b )e + ((3A b + 3B a)c + 3B b c)d)x +--R + +--R 2 3 2 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 2 2 2 2 3 2 3 +--R ((3A a c + 3A a b + 3B a b)e + ((6A a b + 3B a )c + A b + 3B a b )d)x +--R + +--R 2 3 2 2 2 2 +--R ((3A a b + B a )e + (3A a c + 3A a b + 3B a b)d)x +--R + +--R 3 2 3 3 +--R (A a e + (3A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 199 + +--S 200 of 1035 +r0:=a^3*A*d*x+1/2*a^2*(3*A*b*d+a*B*d+a*A*e)*x^2+1/3*a*(a*B*(3*b*d+a*e)+_ + 3*A*(b^2*d+a*c*d+a*b*e))*x^3+1/4*(3*a*B*(b^2*d+a*c*d+a*b*e)+A*(b^3*d+_ + 6*a*b*c*d+3*a*b^2*e+3*a^2*c*e))*x^4+1/5*(b^3*(B*d+A*e)+6*a*b*c*(B*d+_ + A*e)+3*b^2*(A*c*d+a*B*e)+3*a*c*(A*c*d+a*B*e))*x^5+1/6*(b^3*B*e+_ + 3*b^2*c*(B*d+A*e)+3*a*c^2*(B*d+A*e)+3*b*c*(A*c*d+2*a*B*e))*x^6+_ + 1/7*c*(3*b^2*B*e+3*b*c*(B*d+A*e)+c*(A*c*d+3*a*B*e))*x^7+_ + 1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 3 2 3 2 1 3 3 2 7 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 7 +--R + +--R 1 2 1 2 1 3 +--R (- A a c + (- A b + B a b)c + - B b )e +--R 2 2 6 +--R + +--R 1 1 2 1 2 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 6 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 3 2 +--R (- A a c + - A a b + - B a b)e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 2 1 3 2 2 2 3 +--R ((A a b + - B a )e + (A a c + A a b + B a b)d)x +--R 3 +--R + +--R 1 3 3 2 1 3 2 3 +--R (- A a e + (- A a b + - B a )d)x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 200 + +--S 201 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 202 + +--S 203 of 1035 +r0:=a^3*A*x+1/2*a^2*(3*A*b+a*B)*x^2+a*(a*b*B+A*(b^2+a*c))*x^3+_ + 1/4*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^4+1/5*(b^3*B+3*A*b^2*c+_ + 6*a*b*B*c+3*a*A*c^2)*x^5+1/2*c*(b^2*B+A*b*c+a*B*c)*x^6+_ + 1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8 +--R +--R +--R (2) +--R 1 3 8 1 3 3 2 7 1 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + ((- A b + - B a)c + - B b c)x +--R 8 7 7 2 2 2 +--R + +--R 3 2 3 2 6 1 3 5 +--R (- A a c + (- A b + - B a b)c + - B b )x +--R 5 5 5 5 +--R + +--R 3 3 2 1 3 3 2 4 2 2 2 3 +--R ((- A a b + - B a )c + - A b + - B a b )x + (A a c + A a b + B a b)x +--R 2 4 4 4 +--R + +--R 3 2 1 3 2 3 +--R (- A a b + - B a )x + A a x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 203 + +--S 204 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 205 + +--S 206 of 1035 +r0:=-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*_ + (4*b*d-a*e)))*x/e^7-3/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*_ + (8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))*(d+e*x)^2/e^8-1/3*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^3/e^8-_ + 1/4*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^4/e^8-_ + 3/5*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*_ + (d+e*x)^5/e^8-1/6*c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^6/e^8+1/7*B*c^3*_ + (d+e*x)^7/e^8-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 3 6 +--R 420A a e + (- 1260A a b - 420B a )d e +--R + +--R 2 2 2 2 5 +--R (1260A a c + 1260A a b + 1260B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 2520A a b - 1260B a )c - 420A b - 1260B a b )d e +--R + +--R 2 2 3 4 3 +--R (1260A a c + (1260A b + 2520B a b)c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 1260A b - 1260B a)c - 1260B b c)d e + (420A c + 1260B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((252A b + 252B a)c + 252B b c)e + (- 84A c - 252B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (315A a c + (315A b + 630B a b)c + 105B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 315A b - 315B a)c - 315B b c)d e + (105A c + 315B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((840A a b + 420B a )c + 140A b + 420B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((420A b + 420B a)c + 420B b c)d e + (- 140A c - 420B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (630A a c + 630A a b + 630B a b)e +--R + +--R 2 3 2 6 +--R ((- 1260A a b - 630B a )c - 210A b - 630B a b )d e +--R + +--R 2 2 3 2 5 +--R (630A a c + (630A b + 1260B a b)c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 630A b - 630B a)c - 630B b c)d e + (210A c + 630B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (1260A a b + 420B a )e + (- 1260A a c - 1260A a b - 1260B a b)d e +--R + +--R 2 3 2 2 5 +--R ((2520A a b + 1260B a )c + 420A b + 1260B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 1260A a c + (- 1260A b - 2520B a b)c - 420B b )d e +--R + +--R 2 2 4 3 +--R ((1260A b + 1260B a)c + 1260B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 420A c - 1260B b c )d e + 420B c d e +--R * +--R x +--R + +--R 2 2 2 2 5 +--R (630A a c + 630A a b + 630B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 2940A a b - 1470B a )c - 490A b - 1470B a b )d e +--R + +--R 2 2 3 4 3 +--R (2415A a c + (2415A b + 4830B a b)c + 805B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 3423A b - 3423B a)c - 3423B b c)d e + (1491A c + 4473B b c )d e +--R + +--R 3 7 +--R - 1851B c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 208 + +--S 209 of 1035 +r0:=-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*_ + (2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*x/e^7+(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x))-1/2*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*_ + (d+e*x)^2/e^8-1/3*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + (d+e*x)^3/e^8-3/4*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))*(d+e*x)^4/e^8-1/5*c^2*(7*B*c*d-3*b*B*e-A*c*e)*_ + (d+e*x)^5/e^8+1/6*B*c^3*(d+e*x)^6/e^8-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*_ + (2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 2 2 2 6 +--R (180A a b + 60B a )e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 2 5 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 4 3 +--R ((900A b + 900B a)c + 900B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 360A c - 1080B b c )d e + 420B c d e +--R * +--R x +--R + +--R 2 3 6 2 2 2 2 5 +--R (180A a b + 60B a )d e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 3 4 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((900A b + 900B a)c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((45A b + 45B a)c + 45B b c)e + (- 18A c - 54B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (60A a c + (60A b + 120B a b)c + 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 75A b - 75B a)c - 75B b c)d e + (30A c + 90B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((180A a b + 90B a )c + 30A b + 90B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((150A b + 150B a)c + 150B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 4 3 +--R 70B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (180A a c + 180A a b + 180B a b)e +--R + +--R 2 3 2 6 +--R ((- 540A a b - 270B a )c - 90A b - 270B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (180A a c + 180A a b + 180B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 540A a b - 270B a )c - 90A b - 270B a b )d e +--R + +--R 2 2 3 3 4 +--R (240A a c + (240A b + 480B a b)c + 80B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 75A b - 75B a)c - 75B b c)d e + (- 78A c - 234B b c )d e +--R + +--R 3 6 +--R 231B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (180A a b + 60B a )d e +--R + +--R 2 2 2 2 5 +--R (- 180A a c - 180A a b - 180B a b)d e +--R + +--R 2 3 2 3 4 +--R ((540A a b + 270B a )c + 90A b + 270B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 480A a c + (- 480A b - 960B a b)c - 160B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((825A b + 825B a)c + 825B b c)d e + (- 438A c - 1314B b c )d e +--R + +--R 3 7 +--R 651B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1035 +r0:=-(A*e*(10*c^3*d^3-b^3*e^3+3*b*c*e^2*(3*b*d-2*a*e)-9*c^2*d*e*(2*b*d-a*e))-_ + 3*B*(5*c^3*d^4-2*c^2*d^2*e*(5*b*d-3*a*e)-b^2*e^3*(b*d-a*e)+c*e^2*_ + (6*b^2*d^2-6*a*b*d*e+a^2*e^2)))*x/e^7-1/2*(B*(10*c^3*d^3-b^3*e^3+_ + 3*b*c*e^2*(3*b*d-2*a*e)-9*c^2*d*e*(2*b*d-a*e))-3*A*c*e*(2*c^2*d^2+_ + b^2*e^2-c*e*(3*b*d-a*e)))*x^2/e^6-c*(A*c*e*(c*d-b*e)-B*(2*c^2*d^2+_ + b^2*e^2-c*e*(3*b*d-a*e)))*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*_ + x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*_ + (d+e*x)^2)+(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-_ + e*(4*b*d-a*e)))/(e^8*(d+e*x))-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 2 7 +--R (60A a c + 60A a b + 60B a b)e +--R + +--R 2 3 2 6 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (300A c + 900B b c )d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 720A a b - 360B a )c - 120A b - 360B a b )d e +--R + +--R 2 2 3 3 4 +--R (720A a c + (720A b + 1440B a b)c + 240B b )d e +--R + +--R 2 2 4 3 +--R ((- 1200A b - 1200B a)c - 1200B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (600A c + 1800B b c )d e - 840B c d e +--R * +--R x +--R + +--R 2 2 2 2 5 +--R (60A a c + 60A a b + 60B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 4 3 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 600A b - 600B a)c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((20A b + 20B a)c + 20B b c)e + (- 10A c - 30B b c )d e +--R + +--R 3 2 5 +--R 14B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (30A a c + (30A b + 60B a b)c + 10B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 50A b - 50B a)c - 50B b c)d e + (25A c + 75B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((120A a b + 60B a )c + 20A b + 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((200A b + 200B a)c + 200B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((240A a b + 120B a )c + 40A b + 120B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 330A a c + (- 330A b - 660B a b)c - 110B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((630A b + 630B a)c + 630B b c)d e + (- 340A c - 1020B b c )d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 60A a b - 20B a )e + (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 240A a b - 120B a )c - 40A b - 120B a b )d e +--R + +--R 2 2 3 3 4 +--R (60A a c + (60A b + 120B a b)c + 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((60A b + 60B a)c + 60B b c)d e + (- 80A c - 240B b c )d e +--R + +--R 3 6 +--R 160B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 10A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (90A a c + 90A a b + 90B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 300A a b - 150B a )c - 50A b - 150B a b )d e +--R + +--R 2 2 3 4 3 +--R (210A a c + (210A b + 420B a b)c + 70B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 270A b - 270B a)c - 270B b c)d e + (110A c + 330B b c )d e +--R + +--R 3 7 +--R - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 214 + +--S 215 of 1035 +r0:=-(B*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + A*c*e*(10*c^2*d^2+3*b^2*e^2-3*c*e*(4*b*d-a*e)))*x/e^7-1/2*c*(A*c*e*_ + (4*c*d-3*b*e)-B*(10*c^2*d^2+3*b^2*e^2-3*c*e*(4*b*d-a*e)))*x^2/e^6-_ + 1/3*c^2*(4*B*c*d-3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+_ + 1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^3)+1/2*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^2)+3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x))-(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+_ + 3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 2 7 +--R ((72A a b + 36B a )c + 12A b + 36B a b )e +--R + +--R 2 2 3 6 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 2 5 +--R ((360A b + 360B a)c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 3 4 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 5 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 4 3 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R x +--R + +--R 2 3 2 3 4 +--R ((72A a b + 36B a )c + 12A b + 36B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((360A b + 360B a)c + 360B b c)d e + (- 240A c - 720B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((18A b + 18B a)c + 18B b c)e + (- 12A c - 36B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 90A b - 90B a)c - 90B b c)d e + (60A c + 180B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (108A a c + (108A b + 216B a b)c + 36B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 378A b - 378B a)c - 378B b c)d e + (292A c + 876B b c )d e +--R + +--R 3 4 3 +--R - 556B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 36A a c - 36A a b - 36B a b)e +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 108A a c + (- 108A b - 216B a b)c - 36B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 54A b - 54B a)c - 54B b c)d e + (156A c + 468B b c )d e +--R + +--R 3 5 2 +--R - 408B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 18A a b - 6B a )e + (- 36A a c - 36A a b - 36B a b)d e +--R + +--R 2 3 2 2 5 +--R ((324A a b + 162B a )c + 54A b + 162B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 324A a c + (- 324A b - 648B a b)c - 108B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((486A b + 486B a)c + 486B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 6 +--R 222B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 6A a b - 2B a )d e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((132A a b + 66B a )c + 22A b + 66B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 156A a c + (- 156A b - 312B a b)c - 52B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((282A b + 282B a)c + 282B b c)d e + (- 148A c - 444B b c )d e +--R + +--R 3 7 +--R 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 217 + +--S 218 of 1035 +r0:=-c*(A*c*e*(5*c*d-3*b*e)-3*B*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*x/e^7-_ + 1/2*c^2*(5*B*c*d-3*b*B*e-A*c*e)*x^2/e^6+1/3*B*c^3*x^3/e^5+1/4*_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^4)+1/3*_ + (c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/_ + (e^8*(d+e*x)^3)+3/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*_ + (8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))/(e^8*(d+e*x)^2)+(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/_ + (e^8*(d+e*x))-(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (180A c + 540B b c )d e - 420B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 5 +--R (216A a c + (216A b + 432B a b)c + 72B b )d e +--R + +--R 2 2 3 4 +--R ((- 1080A b - 1080B a)c - 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (1080A c + 3240B b c )d e - 2520B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 4 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 4 3 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R x +--R + +--R 2 2 3 4 3 +--R (36A a c + (36A b + 72B a b)c + 12B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((6A c + 18B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((36A b + 36B a)c + 36B b c)e + (- 36A c - 108B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 3 2 2 5 +--R ((144A b + 144B a)c + 144B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 3 4 +--R 556B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )e +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 144A b - 144B a)c - 144B b c)d e + (- 96A c - 288B b c )d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 18A a c - 18A a b - 18B a b)e +--R + +--R 2 3 2 6 +--R ((- 108A a b - 54B a )c - 18A b - 54B a b )d e +--R + +--R 2 2 3 2 5 +--R (324A a c + (324A b + 648B a b)c + 108B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 756A b - 756B a)c - 756B b c)d e + (396A c + 1188B b c )d e +--R + +--R 3 5 2 +--R - 444B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 12A a b - 4B a )e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )d e +--R + +--R 2 2 3 3 4 +--R (264A a c + (264A b + 528B a b)c + 88B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 744A b - 744B a)c - 744B b c)d e + (504A c + 1512B b c )d e +--R + +--R 3 6 +--R - 856B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 3A a e + (- 3A a b - B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (75A a c + (75A b + 150B a b)c + 25B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 231A b - 231B a)c - 231B b c)d e + (171A c + 513B b c )d e +--R + +--R 3 7 +--R - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^6 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 220 + +--S 221 of 1035 +r0:=-c^2*(6*B*c*d-3*b*B*e-A*c*e)*x/e^7+1/2*B*c^3*x^2/e^6+1/5*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^5)+1/4*(c*d^2-b*d*e+a*e^2)^2*_ + (3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^4)+_ + (c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*_ + (2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^3)+_ + 1/2*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+_ + 3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^2)+_ + (B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-_ + 3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x))-_ + 3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 7 3 2 6 +--R ((60A b + 60B a)c + 60B b c)e + (- 120A c - 360B b c )d e +--R + +--R 3 2 5 +--R 420B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 5 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 3 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 2 6 +--R ((60A b + 60B a)c + 60B b c)d e + (- 120A c - 360B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((20A c + 60B b c )e - 70B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((100A c + 300B b c )d e - 500B c d e )x +--R + +--R 2 2 3 7 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((300A b + 300B a)c + 300B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 3 4 +--R - 400B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((900A b + 900B a)c + 900B b c)d e + (- 800A c - 2400B b c )d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 20A a c - 20A a b - 20B a b)e +--R + +--R 2 3 2 6 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 3 4 +--R ((1100A b + 1100B a)c + 1100B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 15A a b - 5B a )e + (- 10A a c - 10A a b - 10B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 30A a b - 15B a )c - 5A b - 15B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((625A b + 625B a)c + 625B b c)d e + (- 750A c - 2250B b c )d e +--R + +--R 3 6 +--R 1875B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 3A a b - B a )d e + (- 2A a c - 2A a b - 2B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((137A b + 137B a)c + 137B b c)d e + (- 174A c - 522B b c )d e +--R + +--R 3 7 +--R 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^7 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 223 + +--S 224 of 1035 +r0:=B*c^3*x/e^7+1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^6)+_ + 1/5*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-_ + a*e)))/(e^8*(d+e*x)^5)+3/4*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^4)+1/3*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/_ + (e^8*(d+e*x)^3)+1/2*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/_ + (e^8*(d+e*x)^2)+3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x))-c^2*(7*B*c*d-3*b*B*e-A*c*e)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 7 3 6 6 +--R ((60A c + 180B b c )e - 420B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((360A c + 1080B b c )d e - 2520B c d e )x +--R + +--R 3 2 2 5 3 3 4 4 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 3 4 3 4 3 3 +--R ((1200A c + 3600B b c )d e - 8400B c d e )x +--R + +--R 3 2 4 3 3 5 2 2 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 5 2 3 6 3 2 6 +--R ((360A c + 1080B b c )d e - 2520B c d e)x + (60A c + 180B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 2 7 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)e + (360A c + 1080B b c )d e +--R + +--R 3 2 5 +--R - 360B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1350A c + 4050B b c )d e +--R + +--R 3 3 4 +--R - 4050B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 120A a b - 60B a )c - 20A b - 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e + (2200A c + 6600B b c )d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 45A a c - 45A a b - 45B a b)e +--R + +--R 2 3 2 6 +--R ((- 90A a b - 45B a )c - 15A b - 45B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1875A c + 5625B b c )d e +--R + +--R 3 5 2 +--R - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 36A a b - 12B a )e + (- 18A a c - 18A a b - 18B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 36A a b - 18B a )c - 6A b - 18B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 36A a c + (- 36A b - 72B a b)c - 12B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 180A b - 180B a)c - 180B b c)d e + (822A c + 2466B b c )d e +--R + +--R 3 6 +--R - 3594B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 10A a e + (- 6A a b - 2B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 6A a c + (- 6A b - 12B a b)c - 2B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 30A b - 30B a)c - 30B b c)d e + (147A c + 441B b c )d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^8 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 1035 +r0:=1/7*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^7)+1/6*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+3/5*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^5)+1/4*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^4)+_ + 1/3*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^3)+3/2*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x)^2)+c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*_ + (d+e*x))+B*c^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 2 7 3 6 6 +--R ((- 420A c - 1260B b c )e + 2940B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((- 630A b - 630B a)c - 630B b c)e + (- 1260A c - 3780B b c )d e +--R + +--R 3 2 5 +--R 13230B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )e +--R + +--R 2 2 6 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 2100A c - 6300B b c )d e + 26950B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 630A a b - 315B a )c - 105A b - 315B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 2100A c - 6300B b c )d e + 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 252A a c - 252A a b - 252B a b)e +--R + +--R 2 3 2 6 +--R ((- 378A a b - 189B a )c - 63A b - 189B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 252A a c + (- 252A b - 504B a b)c - 84B b )d e +--R + +--R 2 2 3 4 +--R ((- 630A b - 630B a)c - 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1260A c - 3780B b c )d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 210A a b - 70B a )e + (- 84A a c - 84A a b - 84B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 126A a b - 63B a )c - 21A b - 63B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 84A a c + (- 84A b - 168B a b)c - 28B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 210A b - 210B a)c - 210B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 7203B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 30A b - 30B a)c - 30B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 7 +--R 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^9 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 229 + +--S 230 of 1035 +r0:=1/8*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^8)+1/7*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^7)+1/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+1/5*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^5)+_ + 1/4*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-_ + a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^4)+c*_ + (A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*_ + (d+e*x)^3)+1/2*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^2)-B*c^3/_ + (e^8*(d+e*x)) +--R +--R +--R (2) +--R 3 7 7 1 3 3 2 7 7 3 6 6 +--R - B c e x + ((- - A c - - B b c )e - - B c d e )x +--R 2 2 2 +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R (((- A b - B a)c - B b c)e + (- A c - 3B b c )d e - 7B c d e )x +--R + +--R 3 2 3 2 3 1 3 7 +--R (- - A a c + (- - A b - - B a b)c - - B b )e +--R 4 4 2 4 +--R + +--R 5 5 2 5 2 6 5 3 15 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - -- B b c )d e +--R 4 4 4 4 4 +--R + +--R 35 3 3 4 +--R - -- B c d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 6 3 2 1 3 3 2 7 +--R ((- - A a b - - B a )c - - A b - - B a b )e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 6 +--R (- - A a c + (- - A b - - B a b)c - - B b )d e +--R 5 5 5 5 +--R + +--R 2 2 2 5 3 2 3 4 3 4 3 +--R ((- A b - B a)c - B b c)d e + (- A c - 3B b c )d e - 7B c d e +--R * +--R 3 +--R x +--R + +--R 1 2 1 2 1 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 2 2 2 +--R + +--R 3 3 2 1 3 3 2 6 +--R ((- - A a b - -- B a )c - -- A b - -- B a b )d e +--R 5 10 10 10 +--R + +--R 3 2 3 2 3 1 3 2 5 +--R (- -- A a c + (- -- A b - - B a b)c - -- B b )d e +--R 10 10 5 10 +--R + +--R 1 1 2 1 2 3 4 1 3 3 2 4 3 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 2 2 2 2 2 +--R + +--R 7 3 5 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 3 2 1 3 7 1 2 1 2 1 2 6 +--R (- - A a b - - B a )e + (- - A a c - - A a b - - B a b)d e +--R 7 7 7 7 7 +--R + +--R 6 3 2 1 3 3 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 35 35 35 35 +--R + +--R 3 2 3 2 6 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 35 35 35 35 +--R + +--R 1 1 2 1 2 4 3 1 3 3 2 5 2 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 7 7 7 7 7 +--R + +--R 3 6 +--R - B c d e +--R * +--R x +--R + +--R 1 3 7 3 2 1 3 6 +--R - - A a e + (- -- A a b - -- B a )d e +--R 8 56 56 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 56 56 56 +--R + +--R 3 3 2 1 3 3 2 3 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 280 280 +--R + +--R 3 2 3 2 3 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 280 280 140 280 +--R + +--R 1 1 2 1 2 5 2 1 3 3 2 6 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 56 56 56 56 56 +--R + +--R 1 3 7 +--R - - B c d +--R 8 +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 10 2 7 9 8 8 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 230 + +--S 231 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^10 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 232 + +--S 233 of 1035 +r0:=1/9*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^9)+1/8*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^8)+_ + 3/7*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^7)+_ + 1/6*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^6)+1/5*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^5)+3/4*c*(A*c*e*_ + (2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*(d+e*x)^4)+_ + 1/3*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^3)-1/2*B*c^3/(e^8*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 7 7 1 3 2 7 7 3 6 6 +--R - - B c e x + ((- - A c - B b c )e - - B c d e )x +--R 2 3 6 +--R + +--R 3 3 2 3 2 7 1 3 3 2 6 +--R ((- - A b - - B a)c - - B b c)e + (- - A c - - B b c )d e +--R 4 4 4 2 2 +--R + +--R 7 3 2 5 +--R - - B c d e +--R 4 +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 6 1 3 7 +--R (- - A a c + (- - A b - - B a b)c - - B b )e +--R 5 5 5 5 +--R + +--R 3 3 2 3 2 6 1 3 3 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 4 4 4 2 2 +--R + +--R 7 3 3 4 +--R - - B c d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 1 2 1 3 1 2 7 +--R ((- A a b - - B a )c - - A b - - B a b )e +--R 2 6 2 +--R + +--R 2 2 2 2 4 2 3 6 +--R (- - A a c + (- - A b - - B a b)c - -- B b )d e +--R 5 5 5 15 +--R + +--R 1 1 2 1 2 2 5 1 3 2 3 4 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - B b c )d e +--R 2 2 2 3 +--R + +--R 7 3 4 3 +--R - - B c d e +--R 6 +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 3 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 7 7 7 +--R + +--R 3 3 2 1 3 3 2 6 +--R ((- - A a b - -- B a )c - -- A b - -- B a b )d e +--R 7 14 14 14 +--R + +--R 6 2 6 2 12 2 3 2 5 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 35 35 35 35 +--R + +--R 3 3 2 3 2 3 4 1 3 3 2 4 3 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- - A c - - B b c )d e +--R 14 14 14 7 7 +--R + +--R 1 3 5 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 3 2 1 3 7 3 2 3 2 3 2 6 +--R (- - A a b - - B a )e + (- -- A a c - -- A a b - -- B a b)d e +--R 8 8 28 28 28 +--R + +--R 3 3 2 1 3 3 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 28 56 56 56 +--R + +--R 3 2 3 2 3 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 70 70 35 70 +--R + +--R 3 3 2 3 2 4 3 1 3 3 2 5 2 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 56 56 56 28 28 +--R + +--R 1 3 6 +--R - - B c d e +--R 8 +--R * +--R x +--R + +--R 1 3 7 1 2 1 3 6 +--R - - A a e + (- -- A a b - -- B a )d e +--R 9 24 72 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 84 84 84 +--R + +--R 1 1 2 1 3 1 2 3 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 84 168 504 168 +--R + +--R 1 2 1 2 1 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 210 210 105 630 +--R + +--R 1 1 2 1 2 5 2 1 3 1 2 6 +--R ((- --- A b - --- B a)c - --- B b c)d e + (- --- A c - -- B b c )d e +--R 168 168 168 252 84 +--R + +--R 1 3 7 +--R - -- B c d +--R 72 +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 5 12 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 11 3 7 10 2 8 9 9 8 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 233 + +--S 234 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^11 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 235 + +--S 236 of 1035 +r0:=1/10*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^10)+1/9*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^9)+3/8*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^8)+1/7*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^7)+_ + 1/6*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+3/5*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x)^5)+1/4*c^2*(7*B*c*d-3*b*B*e-A*c*e)/_ + (e^8*(d+e*x)^4)-1/3*B*c^3/(e^8*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 7 7 1 3 3 2 7 7 3 6 6 +--R - - B c e x + ((- - A c - - B b c )e - -- B c d e )x +--R 3 4 4 12 +--R + +--R 3 3 2 3 2 7 3 3 9 2 6 +--R ((- - A b - - B a)c - - B b c)e + (- -- A c - -- B b c )d e +--R 5 5 5 10 10 +--R + +--R 7 3 2 5 +--R - -- B c d e +--R 10 +--R * +--R 5 +--R x +--R + +--R 1 2 1 2 1 3 7 +--R (- - A a c + (- - A b - B a b)c - - B b )e +--R 2 2 6 +--R + +--R 1 1 2 1 2 6 1 3 3 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 2 2 2 4 4 +--R + +--R 7 3 3 4 +--R - -- B c d e +--R 12 +--R * +--R 4 +--R x +--R + +--R 6 3 2 1 3 3 2 7 +--R ((- - A a b - - B a )c - - A b - - B a b )e +--R 7 7 7 7 +--R + +--R 2 2 2 2 4 2 3 6 +--R (- - A a c + (- - A b - - B a b)c - -- B b )d e +--R 7 7 7 21 +--R + +--R 2 2 2 2 2 2 5 1 3 3 2 3 4 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 7 7 7 7 7 +--R + +--R 1 3 4 3 +--R - - B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 3 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 8 8 8 +--R + +--R 9 9 2 3 3 9 2 6 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 28 56 56 56 +--R + +--R 3 2 3 2 3 1 3 2 5 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 28 28 14 28 +--R + +--R 3 3 2 3 2 3 4 3 3 9 2 4 3 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 28 28 28 56 56 +--R + +--R 1 3 5 2 +--R - - B c d e +--R 8 +--R * +--R 2 +--R x +--R + +--R 1 2 1 3 7 1 2 1 2 1 2 6 +--R (- - A a b - - B a )e + (- -- A a c - -- A a b - -- B a b)d e +--R 3 9 12 12 12 +--R + +--R 1 1 2 1 3 1 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 14 28 84 28 +--R + +--R 1 2 1 2 1 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - --- B b )d e +--R 42 42 21 126 +--R + +--R 1 1 2 1 2 4 3 1 3 1 2 5 2 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 42 42 42 84 28 +--R + +--R 1 3 6 +--R - -- B c d e +--R 36 +--R * +--R x +--R + +--R 1 3 7 1 2 1 3 6 +--R - -- A a e + (- -- A a b - -- B a )d e +--R 10 30 90 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- --- A a c - --- A a b - --- B a b)d e +--R 120 120 120 +--R + +--R 1 1 2 1 3 1 2 3 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 840 280 +--R + +--R 1 2 1 2 1 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - ---- B b )d e +--R 420 420 210 1260 +--R + +--R 1 1 2 1 2 5 2 1 3 1 2 6 +--R ((- --- A b - --- B a)c - --- B b c)d e + (- --- A c - --- B b c )d e +--R 420 420 420 840 280 +--R + +--R 1 3 7 +--R - --- B c d +--R 360 +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 5 13 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 12 4 7 11 3 8 10 2 9 9 10 8 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 236 + +--S 237 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 1035 +t0:=(e*x)^m*(A+B*x) +--R +--R +--R m +--R (1) (B x + A)(e x) +--R Type: Expression(Integer) +--E 238 + +--S 239 of 1035 +r0:=A*(e*x)^(1+m)/(e*(1+m))+B*(e*x)^(2+m)/(e^2*(2+m)) +--R +--R +--R m + 2 m + 1 +--R (B m + B)(e x) + (A e m + 2A e)(e x) +--R (2) ---------------------------------------------- +--R 2 2 2 2 +--R e m + 3e m + 2e +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1035 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + (A b + B a)x + A a)(e x) +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1035 +r0:=a*A*(e*x)^(1+m)/(e*(1+m))+(A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+(b*B+A*c)*_ + (e*x)^(3+m)/(e^3*(3+m))+B*c*(e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x) +--R + +--R 3 2 +--R (A c + B b)e m + (7A c + 7B b)e m + (14A c + 14B b)e m +--R + +--R (8A c + 8B b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 2 2 2 +--R (A b + B a)e m + (8A b + 8B a)e m + (19A b + 19B a)e m +--R + +--R 2 +--R (12A b + 12B a)e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 3 3 2 3 3 m + 1 +--R (A a e m + 9A a e m + 26A a e m + 24A a e )(e x) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 1035 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R * +--R m +--R (e x) +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1035 +r0:=a^2*A*(e*x)^(1+m)/(e*(1+m))+a*(2*A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+_ + (2*a*b*B+A*(b^2+2*a*c))*(e*x)^(3+m)/(e^3*(3+m))+(b^2*B+2*A*b*c+2*a*B*c)*_ + (e*x)^(4+m)/(e^4*(4+m))+c*(2*b*B+A*c)*(e*x)^(5+m)/(e^5*(5+m))+_ + B*c^2*(e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 m + 6 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c )(e x) +--R + +--R 2 5 2 4 +--R (A c + 2B b c)e m + (16A c + 32B b c)e m +--R + +--R 2 3 2 2 +--R (95A c + 190B b c)e m + (260A c + 520B b c)e m +--R + +--R 2 2 +--R (324A c + 648B b c)e m + (144A c + 288B b c)e +--R * +--R m + 5 +--R (e x) +--R + +--R 2 2 5 2 2 4 +--R ((2A b + 2B a)c + B b )e m + ((34A b + 34B a)c + 17B b )e m +--R + +--R 2 2 3 +--R ((214A b + 214B a)c + 107B b )e m +--R + +--R 2 2 2 +--R ((614A b + 614B a)c + 307B b )e m +--R + +--R 2 2 2 2 +--R ((792A b + 792B a)c + 396B b )e m + ((360A b + 360B a)c + 180B b )e +--R * +--R m + 4 +--R (e x) +--R + +--R 2 3 5 2 3 4 +--R (2A a c + A b + 2B a b)e m + (36A a c + 18A b + 36B a b)e m +--R + +--R 2 3 3 +--R (242A a c + 121A b + 242B a b)e m +--R + +--R 2 3 2 +--R (744A a c + 372A b + 744B a b)e m +--R + +--R 2 3 +--R (1016A a c + 508A b + 1016B a b)e m +--R + +--R 2 3 +--R (480A a c + 240A b + 480B a b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 4 5 2 4 4 +--R (2A a b + B a )e m + (38A a b + 19B a )e m +--R + +--R 2 4 3 2 4 2 +--R (274A a b + 137B a )e m + (922A a b + 461B a )e m +--R + +--R 2 4 2 4 +--R (1404A a b + 702B a )e m + (720A a b + 360B a )e +--R * +--R m + 2 +--R (e x) +--R + +--R 2 5 5 2 5 4 2 5 3 2 5 2 2 5 +--R A a e m + 20A a e m + 155A a e m + 580A a e m + 1044A a e m +--R + +--R 2 5 +--R 720A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 245 + +--S 246 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 of 1035 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R m +--R (e x) +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1035 +r0:=a^3*A*(e*x)^(1+m)/(e*(1+m))+a^2*(3*A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+_ + 3*a*(a*b*B+A*(b^2+a*c))*(e*x)^(3+m)/(e^3*(3+m))+(3*a*B*(b^2+a*c)+A*_ + (b^3+6*a*b*c))*(e*x)^(4+m)/(e^4*(4+m))+(b^3*B+3*A*b^2*c+6*a*b*B*c+_ + 3*a*A*c^2)*(e*x)^(5+m)/(e^5*(5+m))+3*c*(b^2*B+A*b*c+a*B*c)*_ + (e*x)^(6+m)/(e^6*(6+m))+c^2*(3*b*B+A*c)*(e*x)^(7+m)/(e^7*(7+m))+_ + B*c^3*(e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x) +--R + +--R 3 2 7 3 2 6 +--R (A c + 3B b c )e m + (29A c + 87B b c )e m +--R + +--R 3 2 5 3 2 4 +--R (343A c + 1029B b c )e m + (2135A c + 6405B b c )e m +--R + +--R 3 2 3 3 2 2 +--R (7504A c + 22512B b c )e m + (14756A c + 44268B b c )e m +--R + +--R 3 2 3 2 +--R (14832A c + 44496B b c )e m + (5760A c + 17280B b c )e +--R * +--R m + 7 +--R (e x) +--R + +--R 2 2 2 7 2 2 2 6 +--R ((3A b + 3B a)c + 3B b c)e m + ((90A b + 90B a)c + 90B b c)e m +--R + +--R 2 2 2 5 +--R ((1098A b + 1098B a)c + 1098B b c)e m +--R + +--R 2 2 2 4 +--R ((7020A b + 7020B a)c + 7020B b c)e m +--R + +--R 2 2 2 3 +--R ((25227A b + 25227B a)c + 25227B b c)e m +--R + +--R 2 2 2 2 +--R ((50490A b + 50490B a)c + 50490B b c)e m +--R + +--R 2 2 2 +--R ((51432A b + 51432B a)c + 51432B b c)e m +--R + +--R 2 2 2 +--R ((20160A b + 20160B a)c + 20160B b c)e +--R * +--R m + 6 +--R (e x) +--R + +--R 2 2 3 3 7 +--R (3A a c + (3A b + 6B a b)c + B b )e m +--R + +--R 2 2 3 3 6 +--R (93A a c + (93A b + 186B a b)c + 31B b )e m +--R + +--R 2 2 3 3 5 +--R (1173A a c + (1173A b + 2346B a b)c + 391B b )e m +--R + +--R 2 2 3 3 4 +--R (7743A a c + (7743A b + 15486B a b)c + 2581B b )e m +--R + +--R 2 2 3 3 3 +--R (28632A a c + (28632A b + 57264B a b)c + 9544B b )e m +--R + +--R 2 2 3 3 2 +--R (58692A a c + (58692A b + 117384B a b)c + 19564B b )e m +--R + +--R 2 2 3 3 +--R (60912A a c + (60912A b + 121824B a b)c + 20304B b )e m +--R + +--R 2 2 3 3 +--R (24192A a c + (24192A b + 48384B a b)c + 8064B b )e +--R * +--R m + 5 +--R (e x) +--R + +--R 2 3 2 4 7 +--R ((6A a b + 3B a )c + A b + 3B a b )e m +--R + +--R 2 3 2 4 6 +--R ((192A a b + 96B a )c + 32A b + 96B a b )e m +--R + +--R 2 3 2 4 5 +--R ((2508A a b + 1254B a )c + 418A b + 1254B a b )e m +--R + +--R 2 3 2 4 4 +--R ((17184A a b + 8592B a )c + 2864A b + 8592B a b )e m +--R + +--R 2 3 2 4 3 +--R ((65958A a b + 32979B a )c + 10993A b + 32979B a b )e m +--R + +--R 2 3 2 4 2 +--R ((139872A a b + 69936B a )c + 23312A b + 69936B a b )e m +--R + +--R 2 3 2 4 +--R ((149256A a b + 74628B a )c + 24876A b + 74628B a b )e m +--R + +--R 2 3 2 4 +--R ((60480A a b + 30240B a )c + 10080A b + 30240B a b )e +--R * +--R m + 4 +--R (e x) +--R + +--R 2 2 2 5 7 2 2 2 5 6 +--R (3A a c + 3A a b + 3B a b)e m + (99A a c + 99A a b + 99B a b)e m +--R + +--R 2 2 2 5 5 +--R (1341A a c + 1341A a b + 1341B a b)e m +--R + +--R 2 2 2 5 4 +--R (9585A a c + 9585A a b + 9585B a b)e m +--R + +--R 2 2 2 5 3 +--R (38592A a c + 38592A a b + 38592B a b)e m +--R + +--R 2 2 2 5 2 +--R (86076A a c + 86076A a b + 86076B a b)e m +--R + +--R 2 2 2 5 +--R (96144A a c + 96144A a b + 96144B a b)e m +--R + +--R 2 2 2 5 +--R (40320A a c + 40320A a b + 40320B a b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 6 7 2 3 6 6 +--R (3A a b + B a )e m + (102A a b + 34B a )e m +--R + +--R 2 3 6 5 2 3 6 4 +--R (1434A a b + 478B a )e m + (10740A a b + 3580B a )e m +--R + +--R 2 3 6 3 2 3 6 2 +--R (45867A a b + 15289B a )e m + (110118A a b + 36706B a )e m +--R + +--R 2 3 6 2 3 6 +--R (134136A a b + 44712B a )e m + (60480A a b + 20160B a )e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 7 7 3 7 6 3 7 5 3 7 4 3 7 3 +--R A a e m + 35A a e m + 511A a e m + 4025A a e m + 18424A a e m +--R + +--R 3 7 2 3 7 3 7 +--R 48860A a e m + 69264A a e m + 40320A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 248 + +--S 249 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 1035 +t0:=(A+B*x)*(d+e*x)^m/(a+b*x+c*x^2) +--R +--R +--R m +--R (B x + A)(e x + d) +--R (1) ------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1035 +--r0:=-(d+e*x)^(1+m)*hypergeometric(1,1+m,2+m,2*c*(d+e*x)/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/((1+m)*_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))-(d+e*x)^(1+m)*hypergeometric(1,1+m,_ +-- 2+m,2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(B+(b*B-2*A*c)/_ +-- sqrt(b^2-4*a*c))/((1+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--E 251 + +--S 252 of 1035 +--d0:=D(m0,x) +--E 252 + +)clear all + +--S 253 of 1035 +t0:=(A+B*x)*(d+e*x)^(1+m)/(a+b*x+c*x^2) +--R +--R +--R m + 1 +--R (B x + A)(e x + d) +--R (1) ----------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 1035 +--r0:=-(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,2*c*(d+e*x)/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/((2+m)*_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))-(d+e*x)^(2+m)*_ +-- hypergeometric(1,2+m,3+m,2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- (B+(b*B-2*A*c)/sqrt(b^2-4*a*c))/((2+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--E 254 + +--S 255 of 1035 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 1035 +t0:=(A+B*x)*(d+e*x)^2/(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1035 +r0:=e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+1/2*(A*c*e*(2*c*d-b*e)+_ + B*(c^2*d^2+b^2*e^2-c*e*(2*b*d+a*e)))*log(a+b*x+c*x^2)/c^3+(b^3*B*e^2-_ + b^2*c*e*(2*B*d+A*e)-2*c^2*(A*c*d^2-2*a*B*d*e-a*A*e^2)+b*c*(B*c*d^2+_ + 2*A*c*d*e-3*a*B*e^2))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-_ + 4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 +--R (4A a c + (- 2A b - 6B a b)c + 2B b )e +--R + +--R 2 2 3 2 2 +--R ((4A b + 8B a)c - 4B b c)d e + (- 4A c + 2B b c )d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 +--R (((- A b - B a)c + B b )e + (2A c - 2B b c)d e + B c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 2 2 2 2 +--R B c e x + ((2A c - 2B b c)e + 4B c d e)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 1035 +t0:=(A+B*x)*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 259 + +--S 260 of 1035 +r0:=B*e*x/c+1/2*(B*c*d-b*B*e+A*c*e)*log(a+b*x+c*x^2)/c^2-(b^2*B*e-b*c*_ + (B*d+A*e)+2*c*(A*c*d-a*B*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (c^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2c x + b +--R (((2A b + 4B a)c - 2B b )e + (- 4A c + 2B b c)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R (((A c - B b)e + B c d)log(c x + b x + a) + 2B c e x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 1035 +t0:=(A+B*x)/(a+b*x+c*x^2) +--R +--R +--R B x + A +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 262 + +--S 263 of 1035 +r0:=1/2*B*log(a+b*x+c*x^2)/c+(b*B-2*A*c)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (c*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R +-----------+ +--R 2c x + b 2 | 2 +--R (- 4A c + 2B b)atanh(--------------) + B log(c x + b x + a)\|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R -------------------------------------------------------------------------- +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 1035 +t0:=(A+B*x)/((d+e*x)*(a+b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 265 + +--S 266 of 1035 +r0:=-(B*d-A*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)+1/2*(B*d-A*e)*_ + log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)+(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2c x + b +--R ((2A b - 4B a)e + (- 4A c + 2B b)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R ((- A e + B d)log(c x + b x + a) + (2A e - 2B d)log(e x + d)) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 1035 +t0:=(A+B*x)/((d+e*x)^2*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R Type: Fraction(Polynomial(Integer)) +--E 268 + +--S 269 of 1035 +r0:=(B*d-A*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x))+(A*e*(2*c*d-b*e)-_ + B*(c*d^2-a*e^2))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2-1/2*(A*e*(2*c*d-b*e)-_ + B*(c*d^2-a*e^2))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2-(A*b^2*e^2+_ + 2*c*(A*c*d^2+2*a*B*d*e-a*A*e^2)-b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 2 +--R (4A a c - 2A b + 2B a b)e + (4A b - 8B a)c d e +--R + +--R 2 2 +--R (- 4A c + 2B b c)d e +--R * +--R x +--R + +--R 2 2 2 +--R (4A a c - 2A b + 2B a b)d e + (4A b - 8B a)c d e +--R + +--R 2 3 +--R (- 4A c + 2B b c)d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 +--R ((A b - B a)e - 2A c d e + B c d e)x + (A b - B a)d e +--R + +--R 2 3 +--R - 2A c d e + B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 +--R ((- 2A b + 2B a)e + 4A c d e - 2B c d e)x + (- 2A b + 2B a)d e +--R + +--R 2 3 +--R 4A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + (2A b + 2B a)d e + (- 2A c - 2B b)d e + 2B c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1035 +t0:=(A+B*x)/((d+e*x)^3*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1035 +r0:=1/2*(B*d-A*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+(-A*e*(2*c*d-b*e)+_ + B*(c*d^2-a*e^2))/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))-(B*(c^2*d^3-_ + 3*a*c*d*e^2+a*b*e^3)-A*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*_ + log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*(B*(c^2*d^3-3*a*c*d*e^2+a*b*e^3)-_ + A*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*log(a+b*x+c*x^2)/(c*d^2-_ + b*d*e+a*e^2)^3+(A*b^3*e^3-b^2*e^2*(3*A*c*d+a*B*e)+b*c*(B*c*d^3+_ + 3*A*c*d^2*e+3*a*B*d*e^2-3*a*A*e^3)-2*c*(A*c*d*(c*d^2-3*a*e^2)+_ + a*B*e*(3*c*d^2-a*e^2)))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + ((c*d^2-b*d*e+a*e^2)^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 2 5 +--R ((- 6A a b + 4B a )c + 2A b - 2B a b )e +--R + +--R 2 2 4 2 2 3 +--R (12A a c + (- 6A b + 6B a b)c)d e + (6A b - 12B a)c d e +--R + +--R 3 2 3 2 +--R (- 4A c + 2B b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 +--R ((- 12A a b + 8B a )c + 4A b - 4B a b )d e +--R + +--R 2 2 2 3 2 3 2 +--R (24A a c + (- 12A b + 12B a b)c)d e + (12A b - 24B a)c d e +--R + +--R 3 2 4 +--R (- 8A c + 4B b c )d e +--R * +--R x +--R + +--R 2 3 2 2 3 +--R ((- 6A a b + 4B a )c + 2A b - 2B a b )d e +--R + +--R 2 2 3 2 2 4 +--R (12A a c + (- 6A b + 6B a b)c)d e + (6A b - 12B a)c d e +--R + +--R 3 2 5 +--R (- 4A c + 2B b c )d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 5 4 2 2 3 +--R (A a c - A b + B a b)e + (3A b - 3B a)c d e - 3A c d e +--R + +--R 2 3 2 +--R B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 +--R (2A a c - 2A b + 2B a b)d e + (6A b - 6B a)c d e +--R + +--R 2 3 2 2 4 +--R - 6A c d e + 2B c d e +--R * +--R x +--R + +--R 2 2 3 3 2 2 4 +--R (A a c - A b + B a b)d e + (3A b - 3B a)c d e - 3A c d e +--R + +--R 2 5 +--R B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 5 4 +--R (- 2A a c + 2A b - 2B a b)e + (- 6A b + 6B a)c d e +--R + +--R 2 2 3 2 3 2 +--R 6A c d e - 2B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 +--R (- 4A a c + 4A b - 4B a b)d e + (- 12A b + 12B a)c d e +--R + +--R 2 3 2 2 4 +--R 12A c d e - 4B c d e +--R * +--R x +--R + +--R 2 2 3 3 2 +--R (- 2A a c + 2A b - 2B a b)d e + (- 6A b + 6B a)c d e +--R + +--R 2 4 2 5 +--R 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 +--R (2A a b - 2B a )e + (- 4A a c - 2A b + 2B a b)d e +--R + +--R 2 3 2 3 2 2 4 +--R 6A b c d e + (- 4A c - 2B b c)d e + 2B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - A a e + (4A a b - B a )d e + (- 6A a c - 3A b )d e +--R + +--R 2 3 2 2 4 2 5 +--R ((8A b + 2B a)c + B b )d e + (- 5A c - 4B b c)d e + 3B c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 1035 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 274 + +--S 275 of 1035 +r0:=11576/81*x+1156/27*x^2+32/27*x^3-4/3*x^4-6*log(1+x)+10625/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R 10625log(3x + 2) - 1458log(x + 1) - 324x + 288x + 10404x + 34728x +--R (2) -------------------------------------------------------------------- +--R 243 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 1035 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 277 + +--S 278 of 1035 +r0:=922/27*x+26/9*x^2-8/9*x^3-6*log(1+x)+2125/81*log(2+3*x) +--R +--R +--R 3 2 +--R 2125log(3x + 2) - 486log(x + 1) - 72x + 234x + 2766x +--R (2) ------------------------------------------------------ +--R 81 +--R Type: Expression(Integer) +--E 278 + +--S 279 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 1035 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 280 + +--S 281 of 1035 +r0:=44/9*x-2/3*x^2-6*log(1+x)+425/27*log(2+3*x) +--R +--R +--R 2 +--R 425log(3x + 2) - 162log(x + 1) - 18x + 132x +--R (2) -------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 1035 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 283 + +--S 284 of 1035 +r0:=-2/3*x-6*log(1+x)+85/9*log(2+3*x) +--R +--R +--R 85log(3x + 2) - 54log(x + 1) - 6x +--R (2) --------------------------------- +--R 9 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1035 +t0:=(5-x)/(2+5*x+3*x^2) +--R +--R +--R - x + 5 +--R (1) ------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1035 +r0:=-6*log(1+x)+17/3*log(2+3*x) +--R +--R +--R 17log(3x + 2) - 18log(x + 1) +--R (2) ---------------------------- +--R 3 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 1035 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) -------------------- +--R 3 2 +--R 6x + 19x + 19x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 289 + +--S 290 of 1035 +r0:=-6*log(1+x)+13/5*log(3+2*x)+17/5*log(2+3*x) +--R +--R +--R 17log(3x + 2) + 13log(2x + 3) - 30log(x + 1) +--R (2) -------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 1035 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------- +--R 4 3 2 +--R 12x + 56x + 95x + 69x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 292 + +--S 293 of 1035 +r0:=(-13/5)/(3+2*x)-6*log(1+x)+99/25*log(3+2*x)+51/25*log(2+3*x) +--R +--R +--R (2) +--R (102x + 153)log(3x + 2) + (198x + 297)log(2x + 3) +--R + +--R (- 300x - 450)log(x + 1) - 65 +--R / +--R 50x + 75 +--R Type: Expression(Integer) +--E 293 + +--S 294 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 1035 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 24x + 148x + 358x + 423x + 243x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 295 + +--S 296 of 1035 +r0:=(-13/10)/(3+2*x)^2+(-99/25)/(3+2*x)-6*log(1+x)+597/125*log(3+2*x)+_ + 153/125*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (1224x + 3672x + 2754)log(3x + 2) + (4776x + 14328x + 10746)log(2x + 3) +--R + +--R 2 +--R (- 6000x - 18000x - 13500)log(x + 1) - 1980x - 3295 +--R / +--R 2 +--R 1000x + 3000x + 2250 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 1035 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------- +--R 6 5 4 3 2 +--R 48x + 368x + 1160x + 1920x + 1755x + 837x + 162 +--R Type: Fraction(Polynomial(Integer)) +--E 298 + +--S 299 of 1035 +r0:=(-13/15)/(3+2*x)^3+(-99/50)/(3+2*x)^2+(-597/125)/(3+2*x)-6*log(1+x)+_ + 3291/625*log(3+2*x)+459/625*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (22032x + 99144x + 148716x + 74358)log(3x + 2) +--R + +--R 3 2 +--R (157968x + 710856x + 1066284x + 533142)log(2x + 3) +--R + +--R 3 2 2 +--R (- 180000x - 810000x - 1215000x - 607500)log(x + 1) - 71640x - 229770x +--R + +--R - 186715 +--R / +--R 3 2 +--R 30000x + 135000x + 202500x + 101250 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1035 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^2 +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1035 +r0:=15496/9*x+2888/3*x^2+560/3*x^3-(3+2*x)^4*(29+35*x)/(2+5*x+3*x^2)+_ + 83*log(1+x)-1625/27*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 4875x - 8125x - 3250)log(3x + 2) + (6723x + 11205x + 4482)log(x + 1) +--R + +--R 4 3 2 +--R - 72x + 216x - 88824x - 152697x - 63423 +--R / +--R 2 +--R 81x + 135x + 54 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 1035 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^2 +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 304 + +--S 305 of 1035 +r0:=3068/9*x+280/3*x^2-(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)+71*log(1+x)-_ + 1825/27*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 5475x - 9125x - 3650)log(3x + 2) + (5751x + 9585x + 3834)log(x + 1) +--R + +--R 3 2 +--R - 72x - 28158x - 49389x - 21141 +--R / +--R 2 +--R 81x + 135x + 54 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 1035 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^2 +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 307 + +--S 308 of 1035 +r0:=140/3*x-(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)+59*log(1+x)-535/9*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 1605x - 2675x - 1070)log(3x + 2) + (1593x + 2655x + 1062)log(x + 1) +--R + +--R 2 +--R - 2724x - 5127x - 2349 +--R / +--R 2 +--R 27x + 45x + 18 +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 1035 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^2 +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 310 + +--S 311 of 1035 +r0:=-(3+2*x)*(29+35*x)/(2+5*x+3*x^2)+94*atanh(5+6*x) +--R +--R +--R 2 2 +--R (282x + 470x + 188)atanh(6x + 5) - 70x - 163x - 87 +--R (2) ---------------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 1035 +t0:=(5-x)/(2+5*x+3*x^2)^2 +--R +--R +--R - x + 5 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 313 + +--S 314 of 1035 +r0:=(-29-35*x)/(2+5*x+3*x^2)+70*atanh(5+6*x) +--R +--R +--R 2 +--R (210x + 350x + 140)atanh(6x + 5) - 35x - 29 +--R (2) -------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1035 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R 5 4 3 2 +--R 18x + 87x + 164x + 151x + 68x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1035 +r0:=-3/5*(37+47*x)/(2+5*x+3*x^2)+23*log(1+x)+52/25*log(3+2*x)-627/25*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 1881x - 3135x - 1254)log(3x + 2) + (156x + 260x + 104)log(2x + 3) +--R + +--R 2 +--R (1725x + 2875x + 1150)log(x + 1) - 705x - 555 +--R / +--R 2 +--R 75x + 125x + 50 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 of 1035 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------ +--R 6 5 4 3 2 +--R 36x + 228x + 589x + 794x + 589x + 228x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 319 + +--S 320 of 1035 +r0:=(-454/25)/(3+2*x)-3/5*(37+47*x)/((3+2*x)*(2+5*x+3*x^2))+11*log(1+x)+_ + 812/125*log(3+2*x)-2187/125*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (- 13122x - 41553x - 41553x - 13122)log(3x + 2) +--R + +--R 3 2 +--R (4872x + 15428x + 15428x + 4872)log(2x + 3) +--R + +--R 3 2 2 +--R (8250x + 26125x + 26125x + 8250)log(x + 1) - 6810x - 14875x - 7315 +--R / +--R 3 2 +--R 750x + 2375x + 2375x + 750 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 1035 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 322 + +--S 323 of 1035 +r0:=(-428/25)/(3+2*x)^2+(-2618/125)/(3+2*x)-3/5*(37+47*x)/((3+2*x)^2*_ + (2+5*x+3*x^2))-log(1+x)+8104/625*log(3+2*x)-7479/625*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 89748x - 418824x - 710505x - 516051x - 134622)log(3x + 2) +--R + +--R 4 3 2 +--R (97248x + 453824x + 769880x + 559176x + 145872)log(2x + 3) +--R + +--R 4 3 2 3 +--R (- 7500x - 35000x - 59375x - 43125x - 11250)log(x + 1) - 78540x +--R + +--R 2 +--R - 280810x - 319835x - 113815 +--R / +--R 4 3 2 +--R 7500x + 35000x + 59375x + 43125x + 11250 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 of 1035 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^2) +--R +--R +--R (1) +--R - x + 5 +--R ---------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 144x + 1344x + 5416x + 12296x + 17185x + 15126x + 8181x + 2484x + 324 +--R Type: Fraction(Polynomial(Integer)) +--E 325 + +--S 326 of 1035 +r0:=(-1258/75)/(3+2*x)^3+(-2212/125)/(3+2*x)^2+(-16522/625)/(3+2*x)-_ + 3/5*(37+47*x)/((3+2*x)^3*(2+5*x+3*x^2))-13*log(1+x)+65816/3125*_ + log(3+2*x)-25191/3125*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 1813752x - 11184804x - 27055134x - 31967379x - 18364239x +--R + +--R - 4080942 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 4738752x + 29222304x + 70686384x + 83520504x + 47979864x +--R + +--R 10662192 +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 2925000x - 18037500x - 43631250x - 51553125x - 29615625x +--R + +--R - 6581250 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R - 2973960x - 14873880x - 27167700x - 21302995x - 5978965 +--R / +--R 5 4 3 2 +--R 225000x + 1387500x + 3356250x + 3965625x + 2278125x + 506250 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 1035 +t0:=(5-x)*(3+2*x)^5/(2+5*x+3*x^2)^3 +--R +--R +--R 6 5 4 3 2 +--R - 32x - 80x + 480x + 2520x + 4590x + 3807x + 1215 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 328 + +--S 329 of 1035 +r0:=-182920/9*x-34760/3*x^2-6800/3*x^3-1/2*(3+2*x)^5*(29+35*x)/_ + (2+5*x+3*x^2)^2+5/2*(3+2*x)^4*(137+170*x)/(2+5*x+3*x^2)-_ + 1085*log(1+x)+29375/27*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (528750x + 1762500x + 2173750x + 1175000x + 235000)log(3x + 2) +--R + +--R 4 3 2 +--R (- 527310x - 1757700x - 2167830x - 1171800x - 234360)log(x + 1) +--R + +--R 5 4 3 2 +--R - 576x + 6126120x + 20591850x + 25603665x + 13944270x + 2805921 +--R / +--R 4 3 2 +--R 486x + 1620x + 1998x + 1080x + 216 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1035 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^3 +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1035 +r0:=-36892/9*x-3392/3*x^2-1/2*(3+2*x)^4*(29+35*x)/(2+5*x+3*x^2)^2+_ + 1/2*(3+2*x)^3*(695+848*x)/(2+5*x+3*x^2)-883*log(1+x)+23825/27*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (428850x + 1429500x + 1763050x + 953000x + 190600)log(3x + 2) +--R + +--R 4 3 2 +--R (- 429138x - 1430460x - 1764234x - 953640x - 190728)log(x + 1) +--R + +--R 4 3 2 +--R 1971108x + 6712446x + 8456811x + 4665198x + 949887 +--R / +--R 4 3 2 +--R 486x + 1620x + 1998x + 1080x + 216 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 1035 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^3 +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 334 + +--S 335 of 1035 +r0:=-1/2*(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)^2+141/2*(3+2*x)*(7+8*x)/_ + (2+5*x+3*x^2)-1410*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 4 +--R (- 25380x - 84600x - 104340x - 56400x - 11280)atanh(6x + 5) + 6488x +--R + +--R 3 2 +--R 25862x + 37251x + 23010x + 5139 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 336 + +)clear all + +--S 337 of 1035 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^3 +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 337 + +--S 338 of 1035 +r0:=-1/2*(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)^2+1/2*(7+8*x)*(199+70*x)/_ + (2+5*x+3*x^2)-1102*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 4 +--R (- 19836x - 66120x - 81548x - 44080x - 8816)atanh(6x + 5) + 1680x +--R + +--R 3 2 +--R 8906x + 15173x + 10466x + 2525 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 338 + +--S 339 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 339 + +)clear all + +--S 340 of 1035 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^3 +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 340 + +--S 341 of 1035 +r0:=-1/2*(3+2*x)*(29+35*x)/(2+5*x+3*x^2)^2+1/2*(725+842*x)/(2+5*x+3*x^2)-_ + 842*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (- 15156x - 50520x - 62308x - 33680x - 6736)atanh(6x + 5) + 2526x +--R + +--R 2 +--R 6315x + 5146x + 1363 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 1035 +t0:=(5-x)/(2+5*x+3*x^2)^3 +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 343 + +--S 344 of 1035 +r0:=1/2*(-29-35*x)/(2+5*x+3*x^2)^2+105/2*(5+6*x)/(2+5*x+3*x^2)-630*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (- 11340x - 37800x - 46620x - 25200x - 5040)atanh(6x + 5) + 1890x +--R + +--R 2 +--R 4725x + 3850x + 1021 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1035 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 54x + 351x + 963x + 1447x + 1287x + 678x + 196x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 1035 +r0:=-3/10*(37+47*x)/(2+5*x+3*x^2)^2+1/50*(9587+11442*x)/(2+5*x+3*x^2)-_ + 233*log(1+x)+208/125*log(3+2*x)+28917/125*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (520506x + 1735020x + 2139858x + 1156680x + 231336)log(3x + 2) +--R + +--R 4 3 2 +--R (3744x + 12480x + 15392x + 8320x + 1664)log(2x + 3) +--R + +--R 4 3 2 +--R (- 524250x - 1747500x - 2155250x - 1165000x - 233000)log(x + 1) +--R + +--R 3 2 +--R 171630x + 429855x + 350570x + 93095 +--R / +--R 4 3 2 +--R 2250x + 7500x + 9250x + 5000x + 1000 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 1035 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 108x + 864x + 2979x + 5783x + 6915x + 5217x + 2426x + 636x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 349 + +--S 350 of 1035 +r0:=12946/125/(3+2*x)-3/10*(37+47*x)/((3+2*x)*(2+5*x+3*x^2)^2)+_ + 1/50*(9293+10848*x)/((3+2*x)*(2+5*x+3*x^2))-175*log(1+x)+_ + 4912/625*log(3+2*x)+104463/625*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3760668x + 18176562x + 34263864x + 31547826x + 14206968x +--R + +--R 2507112 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (176832x + 854688x + 1611136x + 1483424x + 668032x + 117888) +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 3937500x - 19031250x - 35875000x - 33031250x - 14875000x +--R + +--R - 2625000 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R 1165140x + 4697400x + 6842995x + 4275600x + 968615 +--R / +--R 5 4 3 2 +--R 22500x + 108750x + 205000x + 188750x + 85000x + 15000 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 of 1035 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 9 8 7 6 5 4 3 2 +--R 216x + 2052x + 8550x + 20503x + 31179x + 31179x + 20503x + 8550x +--R + +--R 2052x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 352 + +--S 353 of 1035 +r0:=11856/125/(3+2*x)^2+35886/625/(3+2*x)-3/10*(37+47*x)/((3+2*x)^2*_ + (2+5*x+3*x^2)^2)+1/50*(8999+10254*x)/((3+2*x)^2*(2+5*x+3*x^2))-_ + 141*log(1+x)+68592/3125*log(3+2*x)+372033/3125*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 26786376x + 169647048x + 438254874x + 590788404x + 438254874x +--R + +--R 169647048x + 26786376 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R 4938624x + 31277952x + 80801376x + 108924096x + 80801376x +--R + +--R 31277952x + 4938624 +--R * +--R log(2x + 3) +--R + +--R 6 5 4 3 2 +--R - 31725000x - 200925000x - 519056250x - 699712500x - 519056250x +--R + +--R - 200925000x - 31725000 +--R * +--R log(x + 1) +--R + +--R 5 4 3 2 +--R 6459480x + 36556020x + 80482290x + 85904835x + 44358230x + 8857895 +--R / +--R 6 5 4 3 2 +--R 225000x + 1425000x + 3681250x + 4962500x + 3681250x + 1425000x +--R + +--R 225000 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 1035 +t0:=x/((-1+x)^3*(3+5*x+4*x^2)^2) +--R +--R +--R x +--R (1) ----------------------------------------------- +--R 7 6 5 4 3 2 +--R 16x - 8x - 23x - 13x + 26x + 14x - 3x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 355 + +--S 356 of 1035 +r0:=(-21/736)/(1-x)^2+(-97/4416)/(1-x)+1/276*(39+44*x)/((1-x)^2*_ + (3+5*x+4*x^2))+11/2304*log(1-x)-11/4608*log(3+5*x+4*x^2)+_ + 6023/52992*atan((5+8*x)/sqrt(23))/sqrt(23) +--R +--R +--R (2) +--R 4 3 2 +--+ 2 +--R (- 1012x + 759x + 759x + 253x - 759)\|23 log(4x + 5x + 3) +--R + +--R 4 3 2 +--+ +--R (2024x - 1518x - 1518x - 506x + 1518)\|23 log(- x + 1) +--R + +--R +--+ +--R 4 3 2 (8x + 5)\|23 +--R (48184x - 36138x - 36138x - 12046x + 36138)atan(-------------) +--R 23 +--R + +--R 3 2 +--+ +--R (9312x - 9768x - 2880x - 1080)\|23 +--R / +--R 4 3 2 +--+ +--R (423936x - 317952x - 317952x - 105984x + 317952)\|23 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 1035 +t0:=(x^2+x^3)/(-2+x+x^2) +--R +--R +--R 3 2 +--R x + x +--R (1) ---------- +--R 2 +--R x + x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 358 + +--S 359 of 1035 +r0:=1/2*x^2+2/3*log(1-x)+4/3*log(2+x) +--R +--R +--R 2 +--R 8log(x + 2) + 4log(- x + 1) + 3x +--R (2) --------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1035 +t0:=(5-x)*(3+2*x)^4*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (1) (- 16x - 16x + 264x + 864x + 999x + 405)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1035 +r0:=19609/3402*(2+5*x+3*x^2)^(3/2)+478/315*(3+2*x)^2*(2+5*x+3*x^2)^(3/2)+_ + 229/378*(3+2*x)^3*(2+5*x+3*x^2)^(3/2)-1/21*(3+2*x)^4*(2+5*x+3*x^2)^(3/2)+_ + 1/7560*(53569+42086*x)*(2+5*x+3*x^2)^(3/2)-25969/31104*atanh(1/2*_ + (5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+25969/15552*(5+6*x)*_ + sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 908915atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R - 2488320x - 3248640x + 57298176x + 247266720x + 417203088x +--R + +--R 323830900x + 94018206 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 1088640\|3 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 1035 +t0:=(5-x)*(3+2*x)^3*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 4 3 2 | 2 +--R (1) (- 8x + 4x + 126x + 243x + 135)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1035 +r0:=304/81*(2+5*x+3*x^2)^(3/2)+11/15*(3+2*x)^2*(2+5*x+3*x^2)^(3/2)-_ + 1/18*(3+2*x)^3*(2+5*x+3*x^2)^(3/2)+1/360*(1703+1282*x)*_ + (2+5*x+3*x^2)^(3/2)-6221/10368*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)+6221/5184*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 31105atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 69120x + 29952x + 1651680x + 4635696x + 4864700x + 1719402)\|3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R +-+ +--R 51840\|3 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 of 1035 +t0:=(5-x)*(3+2*x)^2*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (1) (- 4x + 8x + 51x + 45)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1035 +r0:=337/162*(2+5*x+3*x^2)^(3/2)-1/15*(3+2*x)^2*(2+5*x+3*x^2)^(3/2)+_ + 1/180*(511+334*x)*(2+5*x+3*x^2)^(3/2)-2267/5184*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+2267/2592*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 11335atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (- 20736x + 47520x + 458832x + 750500x + 337254)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 25920\|3 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 1035 +t0:=(5-x)*(3+2*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (1) (- 2x + 7x + 15)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1035 +r0:=34/27*(2+5*x+3*x^2)^(3/2)-1/12*(3+2*x)*(2+5*x+3*x^2)^(3/2)-_ + 559/1728*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 559/864*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 559atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 864x + 3792x + 14852x + 9078)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 1728\|3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 +--R (1) (- x + 5)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1035 +r0:=-1/9*(2+5*x+3*x^2)^(3/2)-35/144*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)+35/72*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 6x + 5 2 +-+ | 2 +--R - 35atanh(--------------------) + (- 48x + 340x + 318)\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R -------------------------------------------------------------------------- +--R +-+ +--R 144\|3 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1035 +r0:=-311/48*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 13/8*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+_ + 1/24*(73-6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +-+ +-+ 8x + 7 +--R - 311atanh(--------------------) + 78\|3 \|5 atanh(--------------------) +--R +------------+ +------------+ +--R +-+ | 2 +-+ | 2 +--R 2\|3 \|3x + 5x + 2 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (- 12x + 146)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 48\|3 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1035 +r0:=43/8*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 57/8*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/2*(8+x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-+ 6x + 5 +--R (86x + 129)\|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ 8x + 7 +--R (- 114x - 171)\|3 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (- 4x - 32)\|3 \|5 \|3x + 5x + 2 +--R / +--R +-+ +-+ +--R (16x + 24)\|3 \|5 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^3 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1035 +r0:=-13/10*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/8*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+27/80*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3/40*(25+26*x)*sqrt(2+5*x+3*x^2)/_ + (3+2*x) +--R +--R +--R (2) +--R 2 +-+ +-+ 6x + 5 +--R (- 40x - 120x - 90)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 2 8x + 7 +--R (108x + 324x + 243)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (248x + 242)\|5 \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (320x + 960x + 720)\|5 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^4 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------------- +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1035 +r0:=-47/400*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/6*(2-3*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^3+37/120*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2+29/100*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 8x + 7 +--R (- 1128x - 5076x - 7614x - 3807)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 2 +-+ | 2 +--R (1392x + 5516x + 3842)\|5 \|3x + 5x + 2 +--R / +--R 3 2 +-+ +--R (9600x + 43200x + 64800x + 32400)\|5 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^5 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1035 +r0:=-153/1600*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/16*(7-4*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^4+7/40*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^3+5/32*sqrt(2+5*x+3*x^2)/(3+2*x)^2+33/200*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 2448x - 14688x - 33048x - 33048x - 12393) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (2112x + 10504x + 18216x + 9518)\|5 \|3x + 5x + 2 +--R / +--R 4 3 2 +-+ +--R (25600x + 153600x + 345600x + 345600x + 129600)\|5 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^6 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1035 +r0:=-3159/40000*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/30*(12-5*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^5+131/1200*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^4+12/125*sqrt(2+5*x+3*x^2)/(3+2*x)^3+3/32*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2+549/5000*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (- 101088x - 758160x - 2274480x - 3411720x - 2558790x - 767637) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (70272x + 451632x + 1099032x + 1212652x + 488662)\|5 \|3x + 5x + 2 +--R / +--R 5 4 3 2 +-+ +--R (1280000x + 9600000x + 28800000x + 43200000x + 32400000x + 9720000)\|5 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^7 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1035 +r0:=-26453/400000*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/48*(17-6*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^6+89/1200*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^5+259/4000*sqrt(2+5*x+3*x^2)/(3+2*x)^4+923/15000*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^3+311/4800*sqrt(2+5*x+3*x^2)/(3+2*x)^2+_ + 4083/50000*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 5078976x - 45710784x - 171415440x - 342830880x - 385684740x +--R + +--R - 231410844x - 57852711 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R 3135744x + 24762080x + 78608960x + 125594400x + 101415280x +--R + +--R 32644786 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R / +--R 6 5 4 3 2 +--R 76800000x + 691200000x + 2592000000x + 5184000000x + 5832000000x +--R + +--R 3499200000x + 874800000 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 of 1035 +t0:=(5-x)*(3+2*x)^4*(2+5*x+3*x^2)^(3/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (- 48x - 128x + 680x + 3880x + 7845x + 7938x + 4023x + 810) +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1035 +r0:=454969/559872*(5+6*x)*(2+5*x+3*x^2)^(3/2)+127367/43740*_ + (2+5*x+3*x^2)^(5/2)+487/486*(3+2*x)^2*(2+5*x+3*x^2)^(5/2)+299/648*_ + (3+2*x)^3*(2+5*x+3*x^2)^(5/2)-1/27*(3+2*x)^4*(2+5*x+3*x^2)^(5/2)+_ + 1/34992*(150539+113346*x)*(2+5*x+3*x^2)^(5/2)+454969/8957952*_ + atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 454969/4478976*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 2274845atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 8 7 6 5 +--R - 238878720x - 741519360x + 4287375360x + 29622965760x +--R + +--R 4 3 2 +--R 74525490432x + 99834752160x + 75301381776x + 30098597300x +--R + +--R 4943976702 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 44789760\|3 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 of 1035 +t0:=(5-x)*(3+2*x)^3*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 6 5 4 3 2 | 2 +--R (1) (- 24x - 28x + 382x + 1367x + 1872x + 1161x + 270)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1035 +r0:=12277/20736*(5+6*x)*(2+5*x+3*x^2)^(3/2)+22577/11340*(2+5*x+_ + 3*x^2)^(5/2)+67/126*(3+2*x)^2*(2+5*x+3*x^2)^(5/2)-1/24*(3+2*x)^3*_ + (2+5*x+3*x^2)^(5/2)+1/9072*(27209+19926*x)*(2+5*x+3*x^2)^(5/2)+_ + 12277/331776*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 12277/165888*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 429695atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 7 6 5 4 3 +--R - 34836480x - 50595840x + 736473600x + 3300302592x + 5986095840x +--R + +--R 2 +--R 5524835376x + 2552224700x + 466274922 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 11612160\|3 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 1035 +t0:=(5-x)*(3+2*x)^2*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (1) (- 12x + 4x + 185x + 406x + 327x + 90)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1035 +r0:=1129/2592*(5+6*x)*(2+5*x+3*x^2)^(3/2)+1111/945*(2+5*x+3*x^2)^(5/2)-_ + 1/21*(3+2*x)^2*(2+5*x+3*x^2)^(5/2)+1/378*(721+474*x)*(2+5*x+_ + 3*x^2)^(5/2)+1129/41472*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+_ + 3*x^2)))/sqrt(3)-1129/20736*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 39515atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R - 2488320x + 622080x + 54169344x + 158099040x + 189722352x +--R + +--R 103942700x + 21339474 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 1451520\|3 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1035 +t0:=(5-x)*(3+2*x)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 4 3 2 | 2 +--R (1) (- 6x + 11x + 76x + 89x + 30)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1035 +r0:=839/2592*(5+6*x)*(2+5*x+3*x^2)^(3/2)+103/135*(2+5*x+3*x^2)^(5/2)-_ + 1/18*(3+2*x)*(2+5*x+3*x^2)^(5/2)+839/41472*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-839/20736*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 4195atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R (- 207360x + 421632x + 4065120x + 7134576x + 4813900x + 1123842) +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 207360\|3 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (1) (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1035 +r0:=35/144*(5+6*x)*(2+5*x+3*x^2)^(3/2)-1/15*(2+5*x+3*x^2)^(5/2)+_ + 35/2304*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 35/1152*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 175atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (- 6912x + 27360x + 97584x + 86140x + 23178)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 11520\|3 +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1035 +r0:=1/48*(47-6*x)*(2+5*x+3*x^2)^(3/2)-2011/256*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+65/32*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+1/128*(175-414*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 6033atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R 1560\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 288x + 1776x + 1084x + 2554)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 768\|3 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1035 +r0:=-1/6*(21+x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)+3743/192*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-161/32*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)-1/96*(361-726*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R (7486x + 11229)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R (- 1932x - 2898)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 96x + 728x - 512x - 3510)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R (384x + 576)\|3 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1035 +r0:=-1/4*(8+x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-343/64*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+1329/64*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3/16*(93+43*x)*sqrt(2+5*x+3*x^2)/_ + (3+2*x) +--R +--R +--R (2) +--R 2 +-+ +-+ 6x + 5 +--R (- 1372x - 4116x - 3087)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 2 8x + 7 +--R (5316x + 15948x + 11961)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 48x + 568x + 3108x + 3092)\|5 \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (256x + 768x + 576)\|5 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1035 +r0:=67/40*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/6*(11+3*x)*(2+5*x+3*x^2)^(3/2)/_ + (3+2*x)^3+51/32*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*_ + sqrt(3)-1973/320*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/_ + sqrt(5)-1/160*(845+402*x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 +-+ +-+ 6x + 5 +--R (12240x + 55080x + 82620x + 41310)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 3 2 8x + 7 +--R (- 47352x - 213084x - 319626x - 159813)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 1440x - 26352x - 61756x - 39502)\|5 \|3x + 5x + 2 +--R / +--R 3 2 +-+ +--R (7680x + 34560x + 51840x + 25920)\|5 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^5 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1035 +r0:=-41/800*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2+1/240*(215+234*x)*_ + (2+5*x+3*x^2)^(3/2)/(3+2*x)^3-13/20*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4-_ + 3/32*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+_ + 2359/6400*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+_ + 1/3200*(805+246*x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +-+ +--R (- 28800x - 172800x - 388800x - 388800x - 145800)\|3 \|5 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R (113232x + 679392x + 1528632x + 1528632x + 573237) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (121152x + 380824x + 422296x + 165978)\|5 \|3x + 5x + 2 +--R / +--R 4 3 2 +-+ +--R (307200x + 1843200x + 4147200x + 4147200x + 1555200)\|5 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^6 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1035 +r0:=1/10*(1+5*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^5+141/32000*atanh(1/2*_ + (7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+41/800*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^3+23/640*sqrt(2+5*x+3*x^2)/(3+2*x)^2+99/4000*sqrt(2+5*x+3*x^2)/_ + (3+2*x)-3/320*(87+76*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^4 +--R +--R +--R (2) +--R 5 4 3 2 +--R (4512x + 33840x + 101520x + 152280x + 114210x + 34263) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (12672x + 133232x + 263032x + 180252x + 38062)\|5 \|3x + 5x + 2 +--R / +--R 5 4 3 2 +-+ +--R (1024000x + 7680000x + 23040000x + 34560000x + 25920000x + 7776000)\|5 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^7 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1035 +r0:=-1/12*(2-3*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^6+1141/320000*atanh(1/2*_ + (7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+77/3200*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^4+97/6000*sqrt(2+5*x+3*x^2)/(3+2*x)^3+41/3840*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2+249/40000*sqrt(2+5*x+3*x^2)/(3+2*x)-1/80*(49+45*x)*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^5 +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 219072x + 1971648x + 7393680x + 14787360x + 16635780x + 9981468x +--R + +--R 2495367 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (191232x + 1598240x + 6130880x + 8959200x + 5053840x + 825358)\|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R 6 5 4 3 2 +--R 61440000x + 552960000x + 2073600000x + 4147200000x + 4665600000x +--R + +--R 2799360000x + 699840000 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^8 +--R +--R +--R (1) +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R / +--R 8 7 6 5 4 3 2 +--R 256x + 3072x + 16128x + 48384x + 90720x + 108864x + 81648x +--R + +--R 34992x + 6561 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1035 +r0:=-1/42*(9-7*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^7+4663/1600000*atanh(1/2*_ + (7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+367/33600*sqrt(2+5*x+_ + 3*x^2)/(3+2*x)^5+111/16000*sqrt(2+5*x+3*x^2)/(3+2*x)^4+1769/420000*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^3+293/134400*sqrt(2+5*x+3*x^2)/(3+2*x)^2+_ + 249/1400000*sqrt(2+5*x+3*x^2)/(3+2*x)-1/1344*(559+534*x)*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^6 +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 12534144x + 131608512x + 592238304x + 1480595760x + 2220893640x +--R + +--R 2 +--R 1998804276x + 999402138x + 214157601 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R 382464x + 5786176x + 32752480x + 110807040x + 128281280x +--R + +--R 31518236x - 13108926 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R / +--R 7 6 5 4 +--R 4300800000x + 45158400000x + 203212800000x + 508032000000x +--R + +--R 3 2 +--R 762048000000x + 685843200000x + 342921600000x + 73483200000 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1035 +t0:=(5-x)*(3+2*x)^4*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 144x - 624x + 1304x + 14784x + 44295x + 70799x + 67449x +--R + +--R 2 +--R 38421x + 12096x + 1620 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1035 +r0:=-249299/4478976*(5+6*x)*(2+5*x+3*x^2)^(3/2)+249299/466560*(5+6*x)*_ + (2+5*x+3*x^2)^(5/2)+64067/34020*(2+5*x+3*x^2)^(7/2)+_ + 3298/4455*(3+2*x)^2*(2+5*x+3*x^2)^(7/2)+41/110*(3+2*x)^3*(2+5*x+_ + 3*x^2)^(7/2)-1/33*(3+2*x)^4*(2+5*x+3*x^2)^(7/2)+1/213840*(655267+_ + 480818*x)*(2+5*x+3*x^2)^(7/2)-249299/71663616*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+249299/35831808*(5+6*x)*_ + sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 95980115atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 10 9 8 +--R - 361184624640x - 1751745429504x + 3864341053440x +--R + +--R 7 6 5 +--R 51518646079488x + 180191859517440x + 344946733733376x +--R + +--R 4 3 2 +--R 409710253190400x + 310310741757600x + 146139720113040x +--R + +--R 39043400722420x + 4522595653470 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 27590492160\|3 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 1035 +t0:=(5-x)*(3+2*x)^3*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 72x - 204x + 958x + 5955x + 13215x + 15577x + 10359x + 3672x +--R + +--R 540 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1035 +r0:=-182917/4478976*(5+6*x)*(2+5*x+3*x^2)^(3/2)+182917/466560*(5+6*x)*_ + (2+5*x+3*x^2)^(5/2)+22493/17010*(2+5*x+3*x^2)^(7/2)+169/405*(3+2*x)^2*_ + (2+5*x+3*x^2)^(7/2)-1/30*(3+2*x)^3*(2+5*x+3*x^2)^(7/2)+1/19440*_ + (42451+30554*x)*(2+5*x+3*x^2)^(7/2)-182917/71663616*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+182917/35831808*(5+6*x)*_ + sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 6402095atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 9 8 7 6 +--R - 18059231232x - 58525286400x + 295894093824x + 2173375825920x +--R + +--R 5 4 3 2 +--R 5786089901568x + 8507866763520x + 7525492434720x + 3991828554960x +--R + +--R 1171498832260x + 146357368950 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 2508226560\|3 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 441 + +)clear all + +--S 442 of 1035 +t0:=(5-x)*(3+2*x)^2*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (- 36x - 48x + 551x + 2151x + 3381x + 2717x + 1104x + 180) +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1035 +r0:=-22535/746496*(5+6*x)*(2+5*x+3*x^2)^(3/2)+4507/15552*(5+6*x)*_ + (2+5*x+3*x^2)^(5/2)+1847/2268*(2+5*x+3*x^2)^(7/2)-1/27*(3+2*x)^2*_ + (2+5*x+3*x^2)^(7/2)+1/648*(931+614*x)*(2+5*x+3*x^2)^(7/2)-_ + 22535/11943936*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 22535/5971968*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 157745atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 8 7 6 5 +--R - 334430208x - 536481792x + 6551746560x + 30911721984x +--R + +--R 4 3 2 +--R 60711522048x + 64952003808x + 39524314416x + 12869874940x +--R + +--R 1743650634 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 83607552\|3 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 1035 +t0:=(5-x)*(3+2*x)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R +------------+ +--R 6 5 4 3 2 | 2 +--R (1) (- 18x + 3x + 271x + 669x + 687x + 328x + 60)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1035 +r0:=-1865/82944*(5+6*x)*(2+5*x+3*x^2)^(3/2)+373/1728*(5+6*x)*_ + (2+5*x+3*x^2)^(5/2)+23/42*(2+5*x+3*x^2)^(7/2)-1/24*(3+2*x)*_ + (2+5*x+3*x^2)^(7/2)-1865/1327104*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)+1865/663552*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 13055atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 7 6 5 4 3 +--R - 20901888x + 1492992x + 422309376x + 1310425344x + 1795636512x +--R + +--R 2 +--R 1285991376x + 470446660x + 69554838 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 9289728\|3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (1) (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1035 +r0:=-175/10368*(5+6*x)*(2+5*x+3*x^2)^(3/2)+35/216*(5+6*x)*_ + (2+5*x+3*x^2)^(5/2)-1/21*(2+5*x+3*x^2)^(7/2)-175/165888*_ + atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 175/82944*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 1225atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R - 1492992x + 2695680x + 26908416x + 52777440x + 46221744x +--R + +--R 19303580x + 3137082 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 1161216\|3 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1035 +r0:=1/3456*(25-5586*x)*(2+5*x+3*x^2)^(3/2)+1/360*(209-30*x)*_ + (2+5*x+3*x^2)^(5/2)-543811/55296*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)+325/128*atanh(1/2*(7+8*x)/(sqrt(5)*_ + sqrt(2+5*x+3*x^2)))*sqrt(5)+1/27648*(51455-106734*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 2719055atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R 702000\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R (- 207360x + 753408x + 2622240x + 3249744x + 1166980x + 1160598) +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 276480\|3 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^2 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1035 +r0:=-1/192*(65-1194*x)*(2+5*x+3*x^2)^(3/2)-1/10*(34+x)*_ + (2+5*x+3*x^2)^(5/2)/(3+2*x)+41053/1024*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)-1325/128*atanh(1/2*(7+8*x)/(sqrt(5)*_ + sqrt(2+5*x+3*x^2)))*sqrt(5)-1/512*(3865-8082*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R (1231590x + 1847385)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R (- 318000x - 477000)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 13824x + 57024x + 160128x + 237992x - 80824x - 587946)\|3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R +-+ +--R (30720x + 46080)\|3 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 456 + +)clear all + +--S 457 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^3 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1035 +r0:=5/192*(573+164*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)-1/16*(29+2*x)*_ + (2+5*x+3*x^2)^(5/2)/(3+2*x)^2-199615/3072*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+4295/256*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+5/1536*(3763-7854*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 2 6x + 5 +--R (- 798460x - 2395380x - 1796535)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 2 +-+ +-+ 8x + 7 +--R (206160x + 618480x + 463860)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 3456x + 17088x + 28912x + 114584x + 581484x + 591438)\|3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (12288x + 36864x + 27648)\|3 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1035 +r0:=5/48*(93+43*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/6*(8+x)*_ + (2+5*x+3*x^2)^(5/2)/(3+2*x)^3+13505/256*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)-3487/256*atanh(1/2*(7+8*x)/(sqrt(5)*_ + sqrt(2+5*x+3*x^2)))*sqrt(5)-5/64*(736+343*x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 6x + 5 +--R (324120x + 1458540x + 2187810x + 1093905)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ +--R (- 83688x - 376596x - 564894x - 282447)\|3 \|5 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 1152x + 7584x - 7776x - 257328x - 574132x - 356896)\|3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R 3 2 +-+ +--R (6144x + 27648x + 41472x + 20736)\|3 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1035 +r0:=-953/128*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2+5/192*(485+282*x)*_ + (2+5*x+3*x^2)^(3/2)/(3+2*x)^3-1/16*(19+4*x)*(2+5*x+3*x^2)^(5/2)/_ + (3+2*x)^4-1875/256*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*_ + sqrt(3)+29047/1024*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/_ + sqrt(5)+1/512*(12265+5718*x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +-+ +--R (- 360000x - 2160000x - 4860000x - 4860000x - 1822500)\|3 \|5 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R (1394256x + 8365536x + 18822456x + 18822456x + 7058421) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 6912x + 79488x + 1066560x + 3344536x + 4118536x + 1793442)\|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R 4 3 2 +-+ +--R (49152x + 294912x + 663552x + 663552x + 248832)\|5 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1035 +r0:=4489/3200*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/960*(2335+1386*x)*_ + (2+5*x+3*x^2)^(3/2)/(3+2*x)^3+77/80*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4-_ + 1/10*(14+5*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5+177/128*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-137111/25600*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-1/12800*(57845+26934*x)*_ + sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3398400x + 25488000x + 76464000x + 114696000x + 86022000x +--R + +--R 25806600 +--R * +--R +-+ +-+ 6x + 5 +--R \|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 13162656x - 98719920x - 296159760x - 444239640x - 333179730x +--R + +--R - 99953919 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 345600x - 9261696x - 43173616x - 83282296x - 74039676x +--R + +--R - 25200366 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R / +--R 5 4 3 2 +--R (2457600x + 18432000x + 55296000x + 82944000x + 62208000x + 18662400) +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^7 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1035 +r0:=-469/6400*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2+1/1920*(175+66*x)*_ + (2+5*x+3*x^2)^(3/2)/(3+2*x)^3-11/480*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4+_ + 1/120*(71+78*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5-13/30*(2+5*x+_ + 3*x^2)^(7/2)/(3+2*x)^6-9/128*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))*sqrt(3)+13931/51200*atanh(1/2*(7+8*x)/(sqrt(5)*_ + sqrt(2+5*x+3*x^2)))/sqrt(5)+1/25600*(5945+2814*x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 691200x - 6220800x - 23328000x - 46656000x - 52488000x +--R + +--R - 31492800x - 7873200 +--R * +--R +-+ +-+ 6x + 5 +--R \|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R 2674752x + 24072768x + 90272880x + 180545760x + 203113980x +--R + +--R 121868388x + 30467097 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R 2702592x + 15259360x + 36435520x + 45708960x + 29843120x +--R + +--R 8031698 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R / +--R 6 5 4 3 2 +--R 9830400x + 88473600x + 331776000x + 663552000x + 746496000x +--R + +--R 447897600x + 111974400 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 471 + +)clear all + +--S 472 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^8 +--R +--R +--R (1) +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R / +--R 8 7 6 5 4 3 2 +--R 256x + 3072x + 16128x + 48384x + 90720x + 108864x + 81648x +--R + +--R 34992x + 6561 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1035 +r0:=-5/336*(41+33*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^6+1/14*(4+7*x)*_ + (2+5*x+3*x^2)^(5/2)/(3+2*x)^7-47/256000*atanh(1/2*(7+8*x)/(sqrt(5)*_ + sqrt(2+5*x+3*x^2)))/sqrt(5)+41/2560*sqrt(2+5*x+3*x^2)/(3+2*x)^4+_ + 191/16800*sqrt(2+5*x+3*x^2)/(3+2*x)^3+179/21504*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2+1419/224000*sqrt(2+5*x+3*x^2)/(3+2*x)-1/448*(154+135*x)*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^5 +--R +--R +--R (2) +--R 7 6 5 4 3 +--R - 126336x - 1326528x - 5969376x - 14923440x - 22385160x +--R + +--R 2 +--R - 20146644x - 10073322x - 2158569 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R 2179584x + 45240256x + 163902880x + 255114240x + 201423680x +--R + +--R 79962116x + 12808494 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R / +--R 7 6 5 4 +--R 688128000x + 7225344000x + 32514048000x + 81285120000x +--R + +--R 3 2 +--R 121927680000x + 109734912000x + 54867456000x + 11757312000 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 474 + +)clear all + +--S 475 of 1035 +t0:=(5-x)*(3+2*x)^4/sqrt(2+5*x+3*x^2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1035 +r0:=28051/1296*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 4043/162*sqrt(2+5*x+3*x^2)+391/135*(3+2*x)^2*sqrt(2+5*x+3*x^2)+_ + 53/60*(3+2*x)^3*sqrt(2+5*x+3*x^2)-1/15*(3+2*x)^4*sqrt(2+5*x+3*x^2)+_ + 1/648*(11347+9650*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 140255atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (- 6912x + 4320x + 187824x + 537500x + 563658)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 6480\|3 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 1035 +t0:=(5-x)*(3+2*x)^3/sqrt(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1035 +r0:=19405/1296*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 2375/162*sqrt(2+5*x+3*x^2)+32/27*(3+2*x)^2*sqrt(2+5*x+3*x^2)-_ + 1/12*(3+2*x)^3*sqrt(2+5*x+3*x^2)+5/648*(1361+1078*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 19405atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 864x + 2256x + 23380x + 43518)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 1296\|3 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1035 +t0:=(5-x)*(3+2*x)^2/sqrt(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1035 +r0:=1147/108*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 199/27*sqrt(2+5*x+3*x^2)-1/9*(3+2*x)^2*sqrt(2+5*x+3*x^2)+1/54*_ + (301+194*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 6x + 5 2 +-+ | 2 +--R 1147atanh(--------------------) + (- 48x + 244x + 1290)\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R --------------------------------------------------------------------------- +--R +-+ +--R 108\|3 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1035 +t0:=(5-x)*(3+2*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1035 +r0:=31/4*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 11/3*sqrt(2+5*x+3*x^2)-1/6*(3+2*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 6x + 5 +-+ | 2 +--R 93atanh(--------------------) + (- 4x + 38)\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 486 + +)clear all + +--S 487 of 1035 +t0:=(5-x)/sqrt(2+5*x+3*x^2) +--R +--R +--R - x + 5 +--R (1) --------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1035 +r0:=35/6*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 1/3*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 6x + 5 +-+ | 2 +--R 35atanh(--------------------) - 2\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ---------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 489 + +)clear all + +--S 490 of 1035 +t0:=(5-x)/((3+2*x)*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ----------------------- +--R +------------+ +--R | 2 +--R (2x + 3)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1035 +r0:=-1/2*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 13/2*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5) +--R +--R +--R +-+ 6x + 5 +-+ 8x + 7 +--R - \|5 atanh(--------------------) + 13\|3 atanh(--------------------) +--R +------------+ +------------+ +--R +-+ | 2 +-+ | 2 +--R 2\|3 \|3x + 5x + 2 2\|5 \|3x + 5x + 2 +--R (2) --------------------------------------------------------------------- +--R +-+ +-+ +--R 2\|3 \|5 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 1035 +t0:=(5-x)/((3+2*x)^2*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------ +--R +------------+ +--R 2 | 2 +--R (4x + 12x + 9)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1035 +r0:=47/10*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/5*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R +------------+ +--R 8x + 7 +-+ | 2 +--R (94x + 141)atanh(--------------------) - 26\|5 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R (2) -------------------------------------------------------------- +--R +-+ +--R (20x + 30)\|5 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1035 +t0:=(5-x)/((3+2*x)^3*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R +------------+ +--R 3 2 | 2 +--R (8x + 36x + 54x + 27)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1035 +r0:=389/100*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/10*sqrt(2+5*x+3*x^2)/(3+2*x)^2-73/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 8x + 7 +--R (1556x + 4668x + 3501)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (- 584x - 1006)\|5 \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (400x + 1200x + 900)\|5 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 1035 +t0:=(5-x)/((3+2*x)^4*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------ +--R +------------+ +--R 4 3 2 | 2 +--R (16x + 96x + 216x + 216x + 81)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1035 +r0:=331/100*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/15*sqrt(2+5*x+3*x^2)/(3+2*x)^3-49/30*sqrt(2+5*x+3*x^2)/(3+2*x)^2-_ + 72/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 8x + 7 +--R (7944x + 35748x + 53622x + 26811)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 2 +-+ | 2 +--R (- 3456x - 11348x - 9506)\|5 \|3x + 5x + 2 +--R / +--R 3 2 +-+ +--R (2400x + 10800x + 16200x + 8100)\|5 +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 501 + +)clear all + +--S 502 of 1035 +t0:=(5-x)/((3+2*x)^5*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 | 2 +--R (32x + 240x + 720x + 1080x + 810x + 243)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1035 +r0:=5771/2000*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/20*sqrt(2+5*x+3*x^2)/(3+2*x)^4-86/75*sqrt(2+5*x+3*x^2)/(3+2*x)^3-_ + 41/24*sqrt(2+5*x+3*x^2)/(3+2*x)^2-681/250*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (277008x + 1662048x + 3739608x + 3739608x + 1402353) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 130752x - 629384x - 1019336x - 558078)\|5 \|3x + 5x + 2 +--R / +--R 4 3 2 +-+ +--R (96000x + 576000x + 1296000x + 1296000x + 486000)\|5 +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 504 + +)clear all + +--S 505 of 1035 +t0:=(5-x)/((3+2*x)^6*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------------------- +--R +------------+ +--R 6 5 4 3 2 | 2 +--R (64x + 576x + 2160x + 4320x + 4860x + 2916x + 729)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 1035 +r0:=128381/50000*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/25*sqrt(2+5*x+3*x^2)/(3+2*x)^5-443/500*sqrt(2+5*x+3*x^2)/(3+2*x)^4-_ + 2321/1875*sqrt(2+5*x+3*x^2)/(3+2*x)^3-1007/600*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2-15891/6250*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 12324576x + 92434320x + 277302960x + 415954440x + 311965830x +--R + +--R 93589749 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 6102144x - 38626864x - 92184664x - 98467404x - 39837174)\|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R 5 4 3 2 +--R 4800000x + 36000000x + 108000000x + 162000000x + 121500000x +--R + +--R 36450000 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 1035 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1035 +r0:=6265/81*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 2*(3+2*x)^4*(29+35*x)/sqrt(2+5*x+3*x^2)+4040/27*sqrt(2+5*x+3*x^2)+_ + 7190/81*(3+2*x)*sqrt(2+5*x+3*x^2)+1664/27*(3+2*x)^2*sqrt(2+5*x+3*x^2)+_ + 140/3*(3+2*x)^3*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R | 2 6x + 5 +--R 6265\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 144x + 204x + 6662x - 13840x - 19182)\|3 +--R / +--R +------------+ +--R +-+ | 2 +--R 81\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1035 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1035 +r0:=247/9*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 2*(3+2*x)^3*(29+35*x)/sqrt(2+5*x+3*x^2)+272/3*sqrt(2+5*x+3*x^2)+_ + 554/9*(3+2*x)*sqrt(2+5*x+3*x^2)+140/3*(3+2*x)^2*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R | 2 6x + 5 +--R 247\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 12x + 62x - 1612x - 1578)\|3 +--R / +--R +------------+ +--R +-+ | 2 +--R 9\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 1035 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1035 +r0:=2*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-2*(3+2*x)^2*_ + (29+35*x)/sqrt(2+5*x+3*x^2)+184/3*sqrt(2+5*x+3*x^2)+140/3*(3+2*x)*_ + sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R +-+ | 2 6x + 5 2 +--R 6\|3 \|3x + 5x + 2 atanh(--------------------) - 4x - 398x - 358 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ------------------------------------------------------------------ +--R +------------+ +--R | 2 +--R 3\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 516 + +)clear all + +--S 517 of 1035 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1035 +r0:=-2/3*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 2*(3+2*x)*(29+35*x)/sqrt(2+5*x+3*x^2)+140/3*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 6x + 5 +-+ +--R - 2\|3x + 5x + 2 atanh(--------------------) + (- 278x - 242)\|3 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ------------------------------------------------------------------ +--R +------------+ +--R +-+ | 2 +--R 3\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 519 + +)clear all + +--S 520 of 1035 +t0:=(5-x)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R - x + 5 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1035 +r0:=-2*(29+35*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R - 70x - 58 +--R (2) --------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 522 + +)clear all + +--S 523 of 1035 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------- +--R +------------+ +--R 3 2 | 2 +--R (6x + 19x + 19x + 6)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1035 +r0:=26/5*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 8x + 7 +-+ +--R 26\|3x + 5x + 2 atanh(--------------------) + (- 282x - 222)\|5 +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R (2) ----------------------------------------------------------------- +--R +------------+ +--R +-+ | 2 +--R 5\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1035 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (12x + 56x + 95x + 69x + 18)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1035 +r0:=302/25*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/((3+2*x)*sqrt(2+5*x+3*x^2))-856/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R | 2 8x + 7 +--R (604x + 906)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (- 2568x - 5690x - 2822)\|5 +--R / +--R +------------+ +--R +-+ | 2 +--R (50x + 75)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 528 + +)clear all + +--S 529 of 1035 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 | 2 +--R (24x + 148x + 358x + 423x + 243x + 54)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1035 +r0:=483/25*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/((3+2*x)^2*sqrt(2+5*x+3*x^2))-166/5*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2-864/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R 2 | 2 8x + 7 +--R (1932x + 5796x + 4347)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 5184x - 18906x - 21976x - 7954)\|5 +--R / +--R +------------+ +--R 2 +-+ | 2 +--R (100x + 300x + 225)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 531 + +)clear all + +--S 532 of 1035 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------------------- +--R +------------+ +--R 6 5 4 3 2 | 2 +--R (48x + 368x + 1160x + 1920x + 1755x + 837x + 162)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1035 +r0:=3289/125*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/((3+2*x)^3*sqrt(2+5*x+3*x^2))-2464/75*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^3-478/15*sqrt(2+5*x+3*x^2)/(3+2*x)^2-_ + 4632/125*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R 3 2 | 2 +--R (78936x + 355212x + 532818x + 266409)\|3x + 5x + 2 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 166752x - 849876x - 1584130x - 1268624x - 363118)\|5 +--R / +--R +------------+ +--R 3 2 +-+ | 2 +--R (3000x + 13500x + 20250x + 10125)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 534 + +)clear all + +--S 535 of 1035 +t0:=(5-x)/((3+2*x)^5*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 7 6 5 4 3 2 +--R (96x + 880x + 3424x + 7320x + 9270x + 6939x + 2835x + 486) +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1035 +r0:=82039/2500*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/((3+2*x)^4*sqrt(2+5*x+3*x^2))-817/25*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^4-11596/375*sqrt(2+5*x+3*x^2)/(3+2*x)^3-973/30*sqrt(2+5*x+_ + 3*x^2)/(3+2*x)^2-25458/625*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (3937872x + 23627232x + 53161272x + 53161272x + 19935477) +--R * +--R +------------+ +--R | 2 8x + 7 +--R \|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 7331904x - 48132408x - 124381088x - 157475338x - 97074758x +--R + +--R - 23090004 +--R * +--R +-+ +--R \|5 +--R / +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (120000x + 720000x + 1620000x + 1620000x + 607500)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1035 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1035 +r0:=-2/3*(3+2*x)^4*(29+35*x)/(2+5*x+3*x^2)^(3/2)+152/27*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+8/3*(3+2*x)^3*(225+284*x)/_ + sqrt(2+5*x+3*x^2)-6848/9*sqrt(2+5*x+3*x^2)-16496/27*(3+2*x)*_ + sqrt(2+5*x+3*x^2)-4544/9*(3+2*x)^2*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 2 | 2 6x + 5 +--R (456x + 760x + 304)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 144x + 117440x + 292360x + 236306x + 61638)\|3 +--R / +--R +------------+ +--R 2 +-+ | 2 +--R (81x + 135x + 54)\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1035 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1035 +r0:=-2/3*(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)^(3/2)-8/9*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+8/3*(3+2*x)^2*(230+283*x)/_ + sqrt(2+5*x+3*x^2)-1888/3*sqrt(2+5*x+3*x^2)-4528/9*(3+2*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 2 | 2 6x + 5 +--R (- 24x - 40x - 16)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (32896x + 82148x + 66886x + 17670)\|3 +--R / +--R +------------+ +--R 2 +-+ | 2 +--R (27x + 45x + 18)\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 of 1035 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1035 +r0:=-2/3*(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)^(3/2)+376/3*(7+8*x)/_ + sqrt(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R 8744x + 21864x + 17850x + 4742 +--R (2) -------------------------------- +--R +------------+ +--R 2 | 2 +--R (9x + 15x + 6)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 546 + +)clear all + +--S 547 of 1035 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1035 +r0:=-2/3*(3+2*x)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+8/3*(240+281*x)/_ + sqrt(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R 2248x + 5620x + 4590x + 1222 +--R (2) ------------------------------ +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 1035 +t0:=(5-x)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R - x + 5 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1035 +r0:=-2/3*(29+35*x)/(2+5*x+3*x^2)^(3/2)+280/3*(5+6*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R 1680x + 4200x + 3430x + 914 +--R (2) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 1035 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 | 2 +--R (18x + 87x + 164x + 151x + 68x + 12)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1035 +r0:=-2/5*(37+47*x)/(2+5*x+3*x^2)^(3/2)+104/25*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+12/25*(701+836*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 2 | 2 8x + 7 +--R (312x + 520x + 208)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (30096x + 75396x + 61654x + 16454)\|5 +--R / +--R +------------+ +--R 2 +-+ | 2 +--R (75x + 125x + 50)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1035 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------------- +--R +------------+ +--R 6 5 4 3 2 | 2 +--R (36x + 228x + 589x + 794x + 589x + 228x + 36)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1035 +r0:=-2/5*(37+47*x)/((3+2*x)*(2+5*x+3*x^2)^(3/2))+408/25*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+4/5*(401+462*x)/((3+2*x)*_ + sqrt(2+5*x+3*x^2))+4416/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R 3 2 | 2 +--R (2448x + 7752x + 7752x + 2448)\|3x + 5x + 2 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (39744x + 160200x + 233652x + 146430x + 33334)\|5 +--R / +--R +------------+ +--R 3 2 +-+ | 2 +--R (150x + 475x + 475x + 150)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 of 1035 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 7 6 5 4 3 2 +--R (72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108) +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1035 +r0:=-2/5*(37+47*x)/((3+2*x)^2*(2+5*x+3*x^2)^(3/2))+4884/125*_ + atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+4/25*(1907+_ + 2112*x)/((3+2*x)^2*sqrt(2+5*x+3*x^2))+152*sqrt(2+5*x+3*x^2)/(3+2*x)^2+_ + 11808/125*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R 4 3 2 | 2 +--R (58608x + 273504x + 463980x + 336996x + 87912)\|3x + 5x + 2 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (212544x + 1198296x + 2633232x + 2811628x + 1455774x + 292126)\|5 +--R / +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (1500x + 7000x + 11875x + 8625x + 2250)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 561 + +)clear all + +--S 562 of 1035 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 8 7 6 5 4 3 2 +--R 144x + 1344x + 5416x + 12296x + 17185x + 15126x + 8181x + 2484x +--R + +--R 324 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1035 +r0:=-2/5*(37+47*x)/((3+2*x)^3*(2+5*x+3*x^2)^(3/2))+46108/625*_ + atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+12/25*_ + (603+638*x)/((3+2*x)^3*sqrt(2+5*x+3*x^2))+47552/375*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^3+1048/15*sqrt(2+5*x+3*x^2)/(3+2*x)^2+_ + 9696/625*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3319776x + 20471952x + 49519992x + 58511052x + 33612732x +--R + +--R 7469496 +--R * +--R +------------+ +--R | 2 8x + 7 +--R \|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R 1047168x + 8990064x + 30669672x + 53435272x + 50210052x +--R + +--R 24121914x + 4627858 +--R * +--R +-+ +--R \|5 +--R / +--R 5 4 3 2 +-+ +--R (45000x + 277500x + 671250x + 793125x + 455625x + 101250)\|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2) +--R +--R +--R 6 5 4 3 2 +------+ +--R (1) (- 24x - 28x + 382x + 1367x + 1872x + 1161x + 270)\|2x + 3 +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1035 +r0:=65/72*(3+2*x)^(9/2)-109/88*(3+2*x)^(11/2)+47/104*(3+2*x)^(13/2)-_ + 1/40*(3+2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 20592x - 30096x + 447048x + 2029120x + 3733305x + 3496257x +--R + +--R 1636821x + 301887 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 6435 +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2) +--R +--R +--R 5 4 3 2 +------+ +--R (1) (- 12x + 4x + 185x + 406x + 327x + 90)\|2x + 3 +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1035 +r0:=65/56*(3+2*x)^(7/2)-109/72*(3+2*x)^(9/2)+47/88*(3+2*x)^(11/2)-_ + 3/104*(3+2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 16632x + 4284x + 375242x + 1116057x + 1364067x + 758349x +--R + +--R 157383 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 9009 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +------+ +--R (1) (- 6x + 11x + 76x + 89x + 30)\|2x + 3 +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1035 +r0:=13/8*(3+2*x)^(5/2)-109/56*(3+2*x)^(7/2)+47/72*(3+2*x)^(9/2)-_ + 3/88*(3+2*x)^(11/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 756x + 1568x + 15627x + 28143x + 19251x + 4617)\|2x + 3 +--R (2) --------------------------------------------------------------- +--R 693 +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)*sqrt(3+2*x) +--R +--R +--R 3 2 +------+ +--R (1) (- 3x + 10x + 23x + 10)\|2x + 3 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1035 +r0:=65/24*(3+2*x)^(3/2)-109/40*(3+2*x)^(5/2)+47/56*(3+2*x)^(7/2)-_ + 1/24*(3+2*x)^(9/2) +--R +--R +--R 4 3 2 +------+ +--R (- 70x + 285x + 1083x + 949x + 303)\|2x + 3 +--R (2) ----------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 576 + +)clear all + +--S 577 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)/sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ----------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1035 +r0:=-109/24*(3+2*x)^(3/2)+47/40*(3+2*x)^(5/2)-3/56*(3+2*x)^(7/2)+_ + 65/8*sqrt(3+2*x) +--R +--R +--R 3 2 +------+ +--R (- 45x + 291x + 223x + 381)\|2x + 3 +--R (2) -------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(3/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ----------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1035 +r0:=47/24*(3+2*x)^(3/2)-3/40*(3+2*x)^(5/2)+(-65/8)/sqrt(3+2*x)-_ + 109/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 9x + 77x - 117x - 501 +--R (2) ------------------------- +--R +------+ +--R 15\|2x + 3 +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(5/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ------------------------ +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1035 +r0:=(-65/24)/(3+2*x)^(3/2)-1/8*(3+2*x)^(3/2)+109/8/sqrt(3+2*x)+_ + 47/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 3x + 57x + 273x + 263 +--R (2) ------------------------- +--R +------+ +--R (6x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(7/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1035 +r0:=(-13/8)/(3+2*x)^(5/2)+109/24/(3+2*x)^(3/2)+(-47/8)/sqrt(3+2*x)-_ + 3/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 9x - 111x - 245x - 153 +--R (2) -------------------------- +--R 2 +------+ +--R (12x + 36x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 72x - 204x + 958x + 5955x + 13215x + 15577x + 10359x + 3672x +--R + +--R 540 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1035 +r0:=325/288*(3+2*x)^(9/2)-1065/352*(3+2*x)^(11/2)+651/208*(3+2*x)^(13/2)-_ + 359/240*(3+2*x)^(15/2)+165/544*(3+2*x)^(17/2)-9/608*(3+2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R - 15752880x - 51274080x + 262729896x + 1939330008x + 5196312621x +--R + +--R 4 3 2 +--R 7690154020x + 6844462215x + 3651616134x + 1077299892x + 135278424 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 2078505 +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 591 + +)clear all + +--S 592 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^2 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +------+ +--R (- 36x - 48x + 551x + 2151x + 3381x + 2717x + 1104x + 180)\|2x + 3 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1035 +r0:=325/224*(3+2*x)^(7/2)-355/96*(3+2*x)^(9/2)+651/176*(3+2*x)^(11/2)-_ + 359/208*(3+2*x)^(13/2)+11/32*(3+2*x)^(15/2)-9/544*(3+2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 216216x - 348348x + 4324782x + 20560239x + 40692820x +--R + +--R 3 2 +--R 43843941x + 26848368x + 8789688x + 1198476 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 51051 +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^2 +--R +--R +--R 6 5 4 3 2 +------+ +--R (1) (- 18x + 3x + 271x + 669x + 687x + 328x + 60)\|2x + 3 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1035 +r0:=65/32*(3+2*x)^(5/2)-1065/224*(3+2*x)^(7/2)+217/48*(3+2*x)^(9/2)-_ + 359/176*(3+2*x)^(11/2)+165/416*(3+2*x)^(13/2)-3/160*(3+2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 36036x + 2772x + 747579x + 2342620x + 3236325x + 2333766x +--R + +--R 857988x + 128736 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15015 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^2*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +------+ +--R (1) (- 9x + 15x + 113x + 165x + 96x + 20)\|2x + 3 +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1035 +r0:=325/96*(3+2*x)^(3/2)-213/32*(3+2*x)^(5/2)+93/16*(3+2*x)^(7/2)-_ + 359/144*(3+2*x)^(9/2)+15/32*(3+2*x)^(11/2)-9/416*(3+2*x)^(13/2) +--R +--R +--R 6 5 4 3 2 +------+ +--R (- 162x + 297x + 3028x + 5991x + 5292x + 2208x + 396)\|2x + 3 +--R (2) ------------------------------------------------------------------- +--R 117 +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^2/sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1035 +r0:=-355/32*(3+2*x)^(3/2)+651/80*(3+2*x)^(5/2)-359/112*(3+2*x)^(7/2)+_ + 55/96*(3+2*x)^(9/2)-9/352*(3+2*x)^(11/2)+325/32*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +------+ +--R (- 945x + 3500x + 12645x + 15354x + 6252x + 4344)\|2x + 3 +--R (2) -------------------------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1035 +r0:=217/16*(3+2*x)^(3/2)-359/80*(3+2*x)^(5/2)+165/224*(3+2*x)^(7/2)-_ + 1/32*(3+2*x)^(9/2)+(-325/32)/sqrt(3+2*x)-1065/32*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 35x + 150x + 431x + 632x - 432x - 1996 +--R (2) -------------------------------------------- +--R +------+ +--R 35\|2x + 3 +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 606 + +)clear all + +--S 607 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(5/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1035 +r0:=(-325/96)/(3+2*x)^(3/2)-359/48*(3+2*x)^(3/2)+33/32*(3+2*x)^(5/2)-_ + 9/224*(3+2*x)^(7/2)+1065/32/sqrt(3+2*x)+651/16*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 27x + 144x + 215x + 1530x + 7164x + 7024 +--R (2) ---------------------------------------------- +--R +------+ +--R (42x + 63)\|2x + 3 +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(7/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1035 +r0:=(-65/32)/(3+2*x)^(5/2)+355/32/(3+2*x)^(3/2)+55/32*(3+2*x)^(3/2)-_ + 9/160*(3+2*x)^(5/2)+(-651/16)/sqrt(3+2*x)-359/16*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 9x + 70x - 275x - 3300x - 6760x - 4076 +--R (2) -------------------------------------------- +--R 2 +------+ +--R (20x + 60x + 45)\|2x + 3 +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 216x - 972x + 1710x + 22247x + 71336x + 124716x + 135392x +--R + +--R 3 2 +--R 93965x + 40698x + 10044x + 1080 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1035 +r0:=1625/1152*(3+2*x)^(9/2)-7925/1408*(3+2*x)^(11/2)+_ + 16005/1664*(3+2*x)^(13/2)-17201/1920*(3+2*x)^(15/2)+_ + 10475/2176*(3+2*x)^(17/2)-3519/2432*(3+2*x)^(19/2)+_ + 27/128*(3+2*x)^(21/2)-27/2944*(3+2*x)^(23/2) +--R +--R +--R (2) +--R 11 10 9 8 +--R - 897914160x - 4489570800x + 8356902840x + 126274674240x +--R + +--R 7 6 5 4 +--R 465368338149x + 952484547267x + 1244240822034x + 1081998930520x +--R + +--R 3 2 +--R 626194644675x + 232269229971x + 50041179918x + 4766652846 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 47805615 +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 108x - 324x + 1341x + 9112x + 22000x + 29358x + 23659x + 11494x +--R + +--R 3108x + 360 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1035 +r0:=1625/896*(3+2*x)^(7/2)-7925/1152*(3+2*x)^(9/2)+_ + 1455/128*(3+2*x)^(11/2)-17201/1664*(3+2*x)^(13/2)+_ + 2095/384*(3+2*x)^(15/2)-207/128*(3+2*x)^(17/2)+_ + 567/2432*(3+2*x)^(19/2)-9/896*(3+2*x)^(21/2) +--R +--R +--R (2) +--R 10 9 8 7 6 +--R - 160056x - 543348x + 2428218x + 19193889x + 54383679x +--R + +--R 5 4 3 2 +--R 87436314x + 88365578x + 57400347x + 23339691x + 5418846x + 549342 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15561 +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (- 54x - 81x + 792x + 3368x + 5948x + 5757x + 3194x + 956x + 120) +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1035 +r0:=325/128*(3+2*x)^(5/2)-7925/896*(3+2*x)^(7/2)+_ + 5335/384*(3+2*x)^(9/2)-17201/1408*(3+2*x)^(11/2)+_ + 10475/1664*(3+2*x)^(13/2)-1173/640*(3+2*x)^(15/2)+_ + 567/2176*(3+2*x)^(17/2)-27/2432*(3+2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R - 27567540x - 48648600x + 511413903x + 2573238129x + 5488936698x +--R + +--R 4 3 2 +--R 6671966560x + 4954126305x + 2231396337x + 561646746x + 61003962 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 4849845 +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^3*sqrt(3+2*x) +--R +--R +--R 7 5 4 3 2 +------+ +--R (1) (- 27x + 396x + 1090x + 1339x + 870x + 292x + 40)\|2x + 3 +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1035 +r0:=1625/384*(3+2*x)^(3/2)-1585/128*(3+2*x)^(5/2)+_ + 16005/896*(3+2*x)^(7/2)-17201/1152*(3+2*x)^(9/2)+_ + 10475/1408*(3+2*x)^(11/2)-3519/1664*(3+2*x)^(13/2)+_ + 189/640*(3+2*x)^(15/2)-27/2176*(3+2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 2432430x - 243243x + 47045691x + 157479462x + 243619810x +--R + +--R 3 2 +--R 212153055x + 107295183x + 29433414x + 3591558 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 765765 +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^3/sqrt(3+2*x) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1035 +r0:=-7925/384*(3+2*x)^(3/2)+3201/128*(3+2*x)^(5/2)-17201/896*(3+2*x)^(7/2)+_ + 10475/1152*(3+2*x)^(9/2)-3519/1408*(3+2*x)^(11/2)+567/1664*(3+2*x)^(13/2)-_ + 9/640*(3+2*x)^(15/2)+1625/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 81081x + 130977x + 1407294x + 3109960x + 3285105x + 1924641x +--R + +--R 535098x + 196506 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 45045 +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(3/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1035 +r0:=5335/128*(3+2*x)^(3/2)-17201/640*(3+2*x)^(5/2)+10475/896*(3+2*x)^(7/2)-_ + 391/128*(3+2*x)^(9/2)+567/1408*(3+2*x)^(11/2)-27/1664*(3+2*x)^(13/2)+_ + (-1625/128)/sqrt(3+2*x)-7925/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 10395x + 19845x + 180530x + 392500x + 398339x + 256433x - 77138x +--R + +--R - 431614 +--R / +--R +------+ +--R 5005\|2x + 3 +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(5/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1035 +r0:=(-1625/384)/(3+2*x)^(3/2)-17201/384*(3+2*x)^(3/2)+2095/128*(3+2*x)^(5/2)-_ + 3519/896*(3+2*x)^(7/2)+63/128*(3+2*x)^(9/2)-27/1408*(3+2*x)^(11/2)+_ + 7925/128/sqrt(3+2*x)+16005/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 567x + 1323x + 9666x + 21360x + 17663x + 42003x + 184566x + 181486 +--R -------------------------------------------------------------------------- +--R +------+ +--R (462x + 693)\|2x + 3 +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(7/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1035 +r0:=(-325/128)/(3+2*x)^(5/2)+7925/384/(3+2*x)^(3/2)+10475/384*(3+2*x)^(3/2)-_ + 3519/640*(3+2*x)^(5/2)+81/128*(3+2*x)^(7/2)-3/128*(3+2*x)^(9/2)+_ + (-16005/128)/sqrt(3+2*x)-17201/128*sqrt(3+2*x) +--R +--R +--R 7 6 5 4 3 2 +--R - 45x + 135x + 702x + 1940x - 3195x - 41805x - 85070x - 51162 +--R (2) ------------------------------------------------------------------- +--R 2 +------+ +--R (60x + 180x + 135)\|2x + 3 +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1035 +r0:=526/81*(3+2*x)^(3/2)+62/45*(3+2*x)^(5/2)-2/21*(3+2*x)^(7/2)+_ + 12*atanh(sqrt(3+2*x))-4250/81*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+_ + 3278/81*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 34020\|3 atanh(\|2x + 3 ) - 148750\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (- 2160x + 5904x + 69112x + 197824)\|3 \|2x + 3 +--R / +--R +-+ +--R 2835\|3 +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1035 +r0:=62/27*(3+2*x)^(3/2)-2/15*(3+2*x)^(5/2)+12*atanh(sqrt(3+2*x))-_ + 850/27*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+526/27*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 1620\|3 atanh(\|2x + 3 ) - 4250\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +------+ +--R (- 72x + 404x + 3398)\|3 \|2x + 3 +--R / +--R +-+ +--R 135\|3 +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1035 +r0:=-2/9*(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-170/9*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(5/3)+62/9*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 108\|3 atanh(\|2x + 3 ) - 170\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +------+ +--R (- 4x + 56)\|3 \|2x + 3 +--R / +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1035 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ------------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1035 +r0:=12*atanh(sqrt(3+2*x))-34/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-_ + 2/3*sqrt(3+2*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +-+ +------+ +--R 36\|3 atanh(\|2x + 3 ) - 34\|5 atanh(-------------) - 2\|3 \|2x + 3 +--R +-+ +--R \|5 +--R (2) -------------------------------------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 1035 +t0:=(5-x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) ----------------------- +--R 2 +------+ +--R (3x + 5x + 2)\|2x + 3 +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1035 +r0:=12*atanh(sqrt(3+2*x))-34*atanh(sqrt(3/5)*sqrt(3+2*x))/sqrt(15) +--R +--R +--R +-+ +------+ +--R +--+ +------+ \|3 \|2x + 3 +--R 12\|15 atanh(\|2x + 3 ) - 34atanh(-------------) +--R +-+ +--R \|5 +--R (2) ------------------------------------------------ +--R +--+ +--R \|15 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R +-+ +-+ +--+ +--R - 17\|3 \|5 \|15 + 255 +--R (3) ----------------------- +--R +------+ +--R (45x + 30)\|2x + 3 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------- +--R 3 2 +------+ +--R (6x + 19x + 19x + 6)\|2x + 3 +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1035 +r0:=12*atanh(sqrt(3+2*x))-34/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-26/5)/sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +------+ +-+ +------+ \|3 \|2x + 3 +--R 60\|5 \|2x + 3 atanh(\|2x + 3 ) - 34\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +--R - 26\|5 +--R / +--R +-+ +------+ +--R 5\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------- +--R 4 3 2 +------+ +--R (12x + 56x + 95x + 69x + 18)\|2x + 3 +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1035 +r0:=(-26/15)/(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-102/25*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(3/5)+(-198/25)/sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +------+ +--R (1800x + 2700)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +-+ +--R (- 612x - 918)\|3 \|2x + 3 atanh(-------------) + (- 1188x - 1912)\|5 +--R +-+ +--R \|5 +--R / +--R +-+ +------+ +--R (150x + 225)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------- +--R 5 4 3 2 +------+ +--R (24x + 148x + 358x + 423x + 243x + 54)\|2x + 3 +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1035 +r0:=(-26/25)/(3+2*x)^(5/2)+(-66/25)/(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-_ + 306/125*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-1194/125)/sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +------+ +--R (6000x + 18000x + 13500)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ +------+ \|3 \|2x + 3 +--R (- 1224x - 3672x - 2754)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +--R (- 4776x - 14988x - 11866)\|5 +--R / +--R 2 +-+ +------+ +--R (500x + 1500x + 1125)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1035 +r0:=826/27*(3+2*x)^(3/2)+70/3*(3+2*x)^(5/2)-(3+2*x)^(7/2)*(29+35*x)/_ + (2+5*x+3*x^2)-154*atanh(sqrt(3+2*x))+2800/27*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(5/3)+1358/27*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 12474x - 20790x - 8316)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (8400x + 14000x + 5600)\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (- 48x + 400x - 1843x - 2129)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (81x + 135x + 54)\|3 +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1035 +r0:=70/3*(3+2*x)^(3/2)-(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)-_ + 130*atanh(sqrt(3+2*x))+100*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+_ + 30*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 1170x - 1950x - 780)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (900x + 1500x + 600)\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +------+ +--R (- 8x - 209x - 183)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1035 +r0:=-(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)-106*atanh(sqrt(3+2*x))+_ + 248/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+70/3*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 954x - 1590x - 636)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +-+ +------+ +--R (744x + 1240x + 496)\|5 atanh(-------------) + (- 139x - 121)\|3 \|2x + 3 +--R +-+ +--R \|5 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1035 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2 +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1035 +r0:=-82*atanh(sqrt(3+2*x))+316*atanh(sqrt(3/5)*sqrt(3+2*x))/sqrt(15)-_ + (29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 2 +--+ +------+ +--R (- 246x - 410x - 164)\|15 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 \|3 \|2x + 3 +--+ +------+ +--R (948x + 1580x + 632)atanh(-------------) + (- 35x - 29)\|15 \|2x + 3 +--R +-+ +--R \|5 +--R / +--R 2 +--+ +--R (3x + 5x + 2)\|15 +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R +-+ +-+ +--+ +--R 158\|3 \|5 \|15 - 2370 +--R (3) ----------------------- +--R +------+ +--R (45x + 30)\|2x + 3 +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 1035 +t0:=(5-x)/((2+5*x+3*x^2)^2*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R 4 3 2 +------+ +--R (9x + 30x + 37x + 20x + 4)\|2x + 3 +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1035 +r0:=-58*atanh(sqrt(3+2*x))+384/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 3/5*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 870x - 1450x - 580)\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (1152x + 1920x + 768)\|3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +------+ +--R (- 141x - 111)\|5 \|2x + 3 +--R / +--R 2 +-+ +--R (15x + 25x + 10)\|5 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +------+ +--R (18x + 87x + 164x + 151x + 68x + 12)\|2x + 3 +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1035 +r0:=-34*atanh(sqrt(3+2*x))+1356/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-506/25)/sqrt(3+2*x)-3/5*(37+47*x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R (2) +--R 2 +-+ +------+ +------+ +--R (- 2550x - 4250x - 1700)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ +------+ \|3 \|2x + 3 +--R (4068x + 6780x + 2712)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +--R (- 1518x - 3235x - 1567)\|5 +--R / +--R 2 +-+ +------+ +--R (75x + 125x + 50)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 678 + +)clear all + +--S 679 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (36x + 228x + 589x + 794x + 589x + 228x + 36)\|2x + 3 +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1035 +r0:=(-262/15)/(3+2*x)^(3/2)-3/5*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2))-_ + 10*atanh(sqrt(3+2*x))+936/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-686/25)/sqrt(3+2*x) +--R +--R +--R (2) +--R 3 2 +-+ +------+ +------+ +--R (- 4500x - 14250x - 14250x - 4500)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 3 2 +-+ +------+ \|3 \|2x + 3 +--R (16848x + 53352x + 53352x + 16848)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +--R (- 12348x - 43032x - 47767x - 16633)\|5 +--R / +--R 3 2 +-+ +------+ +--R (450x + 1425x + 1425x + 450)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^2) +--R +--R +--R (1) +--R - x + 5 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +------+ +--R (72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108)\|2x + 3 +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1035 +r0:=(-2114/125)/(3+2*x)^(5/2)+(-7042/375)/(3+2*x)^(3/2)-3/5*(37+47*x)/_ + ((3+2*x)^(5/2)*(2+5*x+3*x^2))+14*atanh(sqrt(3+2*x))+_ + 15876/625*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-24626/625)/sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (315000x + 1470000x + 2493750x + 1811250x + 472500)\|5 \|2x + 3 +--R * +--R +------+ +--R atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +------+ +--R (571536x + 2667168x + 4524660x + 3286332x + 857304)\|3 \|2x + 3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +--R (- 886536x - 4348428x - 7782530x - 5977997x - 1646109)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (22500x + 105000x + 178125x + 129375x + 33750)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 1035 +t0:=(5-x)*(3+2*x)^(9/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 5 4 3 2 +------+ +--R (- 16x - 16x + 264x + 864x + 999x + 405)\|2x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1035 +r0:=-3151/9*(3+2*x)^(3/2)-283*(3+2*x)^(5/2)-1/2*(3+2*x)^(9/2)*(29+35*x)/_ + (2+5*x+3*x^2)^2+3/2*(3+2*x)^(7/2)*(230+283*x)/(2+5*x+3*x^2)+_ + 1962*atanh(sqrt(3+2*x))-13675/9*atanh(sqrt(3/5)*sqrt(3+2*x))*_ + sqrt(5/3)-3983/9*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (317844x + 1059480x + 1306692x + 706320x + 141264)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 246150x - 820500x - 1011950x - 547000x - 109400)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +------+ +--R (- 192x + 45083x + 112467x + 90465x + 23327)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (162x + 540x + 666x + 360x + 72)\|3 +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1035 +r0:=-847/3*(3+2*x)^(3/2)-1/2*(3+2*x)^(7/2)*(29+35*x)/(2+5*x+3*x^2)^2+_ + 7/2*(3+2*x)^(5/2)*(100+121*x)/(2+5*x+3*x^2)+1582*atanh(sqrt(3+2*x))-_ + 1225*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-357*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (85428x + 284760x + 351204x + 189840x + 37968)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 66150x - 220500x - 271950x - 147000x - 29400)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (12443x + 30979x + 25073x + 6555)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1035 +r0:=-1/2*(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)^2+5/2*(3+2*x)^(3/2)*_ + (142+169*x)/(2+5*x+3*x^2)+1250*atanh(sqrt(3+2*x))-_ + 2905/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-845/3*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (67500x + 225000x + 277500x + 150000x + 30000)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 52290x - 174300x - 214970x - 116200x - 23240)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (9825x + 24497x + 19891x + 5237)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1035 +r0:=-1/2*(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)^2+966*atanh(sqrt(3+2*x))-_ + 1247*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+3/2*(240+281*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (17388x + 57960x + 71484x + 38640x + 7728)\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 4 3 2 +-+ \|3 \|2x + 3 +--R (- 22446x - 74820x - 92278x - 49880x - 9976)\|3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (2529x + 6305x + 5123x + 1353)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (18x + 60x + 74x + 40x + 8)\|5 +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 of 1035 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^3 +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1035 +r0:=730*atanh(sqrt(3+2*x))-4713/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 1/2*(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+3/10*(878+1063*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (65700x + 219000x + 270100x + 146000x + 29200)\|5 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 84834x - 282780x - 348762x - 188520x - 37704)\|3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (9567x + 23847x + 19373x + 5123)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (90x + 300x + 370x + 200x + 40)\|5 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 1035 +t0:=(5-x)/((2+5*x+3*x^2)^3*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (27x + 135x + 279x + 305x + 186x + 60x + 8)\|2x + 3 +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1035 +r0:=542*atanh(sqrt(3+2*x))-17463/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 3/10*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+1/50*(9734+11739*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (243900x + 813000x + 1002700x + 542000x + 108400)\|5 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 314334x - 1047780x - 1292262x - 698520x - 139704)\|3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (35217x + 87897x + 71443x + 18913)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +------+ +--R (54x + 351x + 963x + 1447x + 1287x + 678x + 196x + 24)\|2x + 3 +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1035 +r0:=402*atanh(sqrt(3+2*x))-12717/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + 2667/25/sqrt(3+2*x)-3/10*(37+47*x)/((2+5*x+3*x^2)^2*sqrt(3+2*x))+_ + 1/10*(1888+2229*x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (180900x + 603000x + 743700x + 402000x + 80400)\|5 \|2x + 3 +--R * +--R +------+ +--R atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +------+ +--R (- 228906x - 763020x - 941058x - 508680x - 101736)\|3 \|2x + 3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +--R (48006x + 193455x + 281403x + 175465x + 39661)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 8 7 6 5 4 3 2 +--R (108x + 864x + 2979x + 5783x + 6915x + 5217x + 2426x + 636x + 72) +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1035 +r0:=7451/75/(3+2*x)^(3/2)-3/10*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^2)+_ + 1/50*(9146+10551*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2))+310*_ + atanh(sqrt(3+2*x))-45603/125*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + 6853/125/sqrt(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 4185000x + 20227500x + 38130000x + 35107500x + 15810000x +--R + +--R 2790000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R 5 4 3 2 +--R - 4925124x - 23804766x - 44873352x - 41316318x - 18606024x +--R + +--R - 3283416 +--R * +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +--R \|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 5 4 3 2 +-+ +--R (740124x + 4247856x + 9453447x + 10168583x + 5278129x + 1057511)\|5 +--R / +--R 5 4 3 2 +-+ +------+ +--R (13500x + 65250x + 123000x + 113250x + 51000x + 9000)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 9 8 7 6 5 4 3 +--R 216x + 2052x + 8550x + 20503x + 31179x + 31179x + 20503x +--R + +--R 2 +--R 8550x + 2052x + 216 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1035 +r0:=56399/625/(3+2*x)^(5/2)+102697/1875/(3+2*x)^(3/2)-3/10*(37+47*x)/_ + ((3+2*x)^(5/2)*(2+5*x+3*x^2)^2)+1/50*(8852+9957*x)/((3+2*x)^(5/2)*_ + (2+5*x+3*x^2))+266*atanh(sqrt(3+2*x))-806841/3125*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(3/5)+(-24409/3125)/sqrt(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 179550000x + 1137150000x + 2937637500x + 3960075000x +--R + +--R 2 +--R 2937637500x + 1137150000x + 179550000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R 6 5 4 3 +--R - 174277656x - 1103758488x - 2851376094x - 3843790524x +--R + +--R 2 +--R - 2851376094x - 1103758488x - 174277656 +--R * +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +--R \|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 6 5 4 3 2 +--R - 5272344x - 14906052x + 18312714x + 114099329x + 160041829x +--R + +--R 94082723x + 20250051 +--R * +--R +-+ +--R \|5 +--R / +--R 6 5 4 3 2 +--R 675000x + 4275000x + 11043750x + 14887500x + 11043750x + 4275000x +--R + +--R 675000 +--R * +--R +-+ +------+ +--R \|5 \|2x + 3 +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 711 + +)clear all + +--S 712 of 1035 +t0:=(5+10*x+sqrt(35))/((2+3*x+5*x^2)*sqrt(1+2*x)) +--R +--R +--R +--+ +--R \|35 + 10x + 5 +--R (1) ----------------------- +--R 2 +------+ +--R (5x + 3x + 2)\|2x + 1 +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1035 +r0:=-2*atan((-sqrt(10+20*x)+sqrt(2+sqrt(35)))/sqrt(-2+sqrt(35)))*_ + sqrt(10/(-2+sqrt(35)))+2*atan((sqrt(10+20*x)+sqrt(2+sqrt(35)))/_ + sqrt(-2+sqrt(35)))*sqrt(10/(-2+sqrt(35))),-2*atan((-10*sqrt(1+2*x)+_ + sqrt(10*(2+sqrt(35))))/sqrt(10*(-2+sqrt(35))))*sqrt(10/(-2+sqrt(35)))+_ + 2*atan((10*sqrt(1+2*x)+sqrt(10*(2+sqrt(35))))/sqrt(10*(-2+sqrt(35))))*_ + sqrt(10/(-2+sqrt(35))) +--R +--R +--R (2) +--R [ +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 + \|20x + 10 +--R 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R + +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 - \|20x + 10 +--R - 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R / +--R +--+ +--R \|31 +--R , +--R +--R +------------+ +--R +------------+ | +--+ +------+ +--R | +--+ \|10\|35 + 20 + 10\|2x + 1 +--R 2\|10\|35 + 20 atan(-----------------------------) +--R +------------+ +--R | +--+ +--R \|10\|35 - 20 +--R + +--R +------------+ +--R +------------+ | +--+ +------+ +--R | +--+ \|10\|35 + 20 - 10\|2x + 1 +--R - 2\|10\|35 + 20 atan(-----------------------------) +--R +------------+ +--R | +--+ +--R \|10\|35 - 20 +--R / +--R +--+ +--R \|31 +--R ] +--R Type: Tuple(Expression(Integer)) +--E 713 + +--S 714 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) +--R +---------+ +--R +--+ +--+ +--+ +------+ +--------+ | +--+ +--R (- \|31 \|35 + (- 10x - 5)\|31 )\|2x + 1 \|20x + 10 \|\|35 - 2 +--R * +--R +------------+ +--R | +--+ +--R \|10\|35 + 20 +--R + +--R +--+ 2 +--R (620x + 310)\|35 + 6200x + 6200x + 1550 +--R / +--R 3 2 +------+ +--R (3100x + 3410x + 2170x + 620)\|2x + 1 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 3 2 +------+ | 2 +--R (1) (- 4x + 8x + 51x + 45)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1035 +--r0:=730/891*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)-2/33*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(3/2)+12130/6237*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 32567/48114*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-63541/168399*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+_ +-- 1/56133*(250447+280359*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 716 + +--S 717 of 1035 +--d0:=D(m0,x) +--E 717 + +)clear all + +--S 718 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 2 +------+ | 2 +--R (1) (- 2x + 7x + 15)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1035 +--r0:=-2/27*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)+202/189*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+4729/1458*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-7892/5103*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+1/8505*(27914+30033*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 719 + +--S 720 of 1035 +--d0:=D(m0,x) +--E 720 + +)clear all + +--S 721 of 1035 +t0:=(5-x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R +------+ | 2 +--R (1) (- x + 5)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1035 +--r0:=-2/21*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+697/162*elliptic_e(asin(sqrt(3+_ +-- 2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 881/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1/945*(2327+2169*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 722 + +--S 723 of 1035 +--d0:=D(m0,x) +--E 723 + +)clear all + +--S 724 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1035 +--r0:=761/54*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-94/27*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/45*(88-9*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 725 + +--S 726 of 1035 +--d0:=D(m0,x) +--E 726 + +)clear all + +--S 727 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1035 +--r0:=61/9*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-121/18*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-1/3*(21+x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 728 + +--S 729 of 1035 +--d0:=D(m0,x) +--E 729 + +)clear all + +--S 730 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1035 +--r0:=67/6*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-8/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-1/3*(11+3*x)*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+67/15*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 731 + +--S 732 of 1035 +--d0:=D(m0,x) +--E 732 + +)clear all + +--S 733 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1035 +--r0:=49/50*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-11/25*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+9/25*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+1/5*(1+5*x)*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(5/2)+49/125*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 734 + +--S 735 of 1035 +--d0:=D(m0,x) +--E 735 + +)clear all + +--S 736 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R (1) +--R 6 5 4 3 2 +------+ +--R (- 24x - 28x + 382x + 1367x + 1872x + 1161x + 270)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1035 +--r0:=2086/1989*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)+42/85*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(5/2)-2/51*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2)+_ +-- 1/196911*(591064+699377*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 108934/65637*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-2200387/21266388*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1284593/10633194*elliptic_f(asin(sqrt(3+_ +-- 2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/17721990*(6668831+8076357*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 737 + +--S 738 of 1035 +--d0:=D(m0,x) +--E 738 + +)clear all + +--S 739 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (1) (- 12x + 4x + 185x + 406x + 327x + 90)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1035 +--r0:=202/351*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)-2/45*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(5/2)+1/243243*(534271+629153*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+13318/11583*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+_ +-- 207851/3752892*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+397651/6567561*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-1/21891870*(6006884+7817373*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 740 + +--S 741 of 1035 +--d0:=D(m0,x) +--E 741 + +)clear all + +--S 742 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (1) (- 6x + 11x + 76x + 89x + 30)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1035 +--r0:=-2/39*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)+1/27027*(43822+50771*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+886/1287*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+152657/416988*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 35611/1459458*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-1/2432430*(486863+783711*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 743 + +--S 744 of 1035 +--d0:=D(m0,x) +--E 744 + +)clear all + +--S 745 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x) +--R +--R +--R +------------+ +--R 3 2 +------+ | 2 +--R (1) (- 3x + 10x + 23x + 10)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1035 +--r0:=1/99*(119+127*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-_ +-- 2/33*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+15283/10692*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-706/2673*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/8910*(1246+3987*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 746 + +--S 747 of 1035 +--d0:=D(m0,x) +--E 747 + +)clear all + +--S 748 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1035 +--r0:=1/63*(52-7*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+11123/972*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-8179/3402*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/5670*(107+12429*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 749 + +--S 750 of 1035 +--d0:=D(m0,x) +--E 750 + +)clear all + +--S 751 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1035 +--r0:=-1/7*(47+x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x)-2411/36*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+899/63*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/210*(136-2493*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 752 + +--S 753 of 1035 +--d0:=D(m0,x) +--E 753 + +)clear all + +--S 754 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1035 +--r0:=-1/15*(37+3*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2)+367/4*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-39/2*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/10*(241+69*x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 755 + +--S 756 of 1035 +--d0:=D(m0,x) +--E 756 + +)clear all + +--S 757 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1035 +--r0:=-1/15*(27+5*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2)-2779/60*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+148/15*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/30*(707+411*x)*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-2779/150*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 758 + +--S 759 of 1035 +--d0:=D(m0,x) +--E 759 + +)clear all + +--S 760 of 1035 +t0:=(5-x)*(3+2*x)^(9/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 144x - 624x + 1304x + 14784x + 44295x + 70799x + 67449x +--R + +--R 2 +--R 38421x + 12096x + 1620 +--R * +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1035 +--r0:=222422/200583*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)+25418/35397*_ +-- (3+2*x)^(5/2)*(2+5*x+3*x^2)^(7/2)+1538/4347*(3+2*x)^(7/2)*_ +-- (2+5*x+3*x^2)^(7/2)-2/69*(3+2*x)^(9/2)*(2+5*x+3*x^2)^(7/2)-_ +-- 5/97580821338*(5514025312+6580844291*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+1/2323352889*(6295010279+7506271641*x)*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+8515726/5415741*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+_ +-- 12104518303/1505532672072*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-18804590219/5269364352252*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1/1756454784084*(62607985973+_ +-- 65705093631*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 761 + +--S 762 of 1035 +--d0:=D(m0,x) +--E 762 + +)clear all + +--S 763 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 72x - 204x + 958x + 5955x + 13215x + 15577x + 10359x + 3672x +--R + +--R 540 +--R * +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1035 +--r0:=2218/2907*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)+202/513*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(7/2)-2/63*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(7/2)-_ +-- 5/108785754*(4498331+5420233*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 1/2590137*(5130052+6113283*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+_ +-- 89294/78489*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+18269789/1678408776*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-10791761/2937215358*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1/1958143572*(51436624+44779653*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 764 + +--S 765 of 1035 +--d0:=D(m0,x) +--E 765 + +)clear all + +--S 766 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +------+ +--R (- 36x - 48x + 551x + 2151x + 3381x + 2717x + 1104x + 180)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1035 +--r0:=430/969*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)-2/57*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(7/2)-125/52378326*(64006+79583*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+25/1247103*(72737+86493*x)*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+2350/2907*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+_ +-- 16503475/808122744*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-15117425/2828429604*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+25/942809868*(749099+216603*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 767 + +--S 768 of 1035 +--d0:=D(m0,x) +--E 768 + +)clear all + +--S 769 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R +------------+ +--R 6 5 4 3 2 +------+ | 2 +--R (- 18x + 3x + 271x + 669x + 687x + 328x + 60)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1035 +--r0:=-2/51*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)-1/8270262*(949997+1332121*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/984555*(1063774+1253571*x)*_ +-- (2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+1166/2295*(2+5*x+3*x^2)^(7/2)*_ +-- sqrt(3+2*x)+34355693/127598328*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6809266/111648537*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+1/744323580*(12174838-22593339*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 770 + +--S 771 of 1035 +--d0:=D(m0,x) +--E 771 + +)clear all + +--S 772 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x) +--R +--R +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (1) (- 9x + 15x + 113x + 165x + 96x + 20)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1035 +--r0:=-1/162162*(15076+34643*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/19305*_ +-- (15467+17193*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-_ +-- 2/45*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+2742319/2501928*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-2066087/8756748*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 1/14594580*(287729-2667537*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 773 + +--S 774 of 1035 +--d0:=D(m0,x) +--E 774 + +)clear all + +--S 775 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1035 +--r0:=-5/18018*(563+4669*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 1/429*(224-33*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+651617/277992*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-242783/486486*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+_ +-- 1/324324*(34372-676791*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 776 + +--S 777 of 1035 +--d0:=D(m0,x) +--E 777 + +)clear all + +--S 778 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1035 +--r0:=-1/11*(73+x)*(2+5*x+3*x^2)^(5/2)/sqrt(3+2*x)+5/1386*(218+3031*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-451331/21384*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+336013/74844*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-_ +-- 1/24948*(21871-471213*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 779 + +--S 780 of 1035 +--d0:=D(m0,x) +--E 780 + +)clear all + +--S 781 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1035 +--r0:=-1/9*(21+x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(3/2)+5/126*(745+121*x)*_ +-- (2+5*x+3*x^2)^(3/2)/sqrt(3+2*x)+33335/648*elliptic_e(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-_ +-- 6205/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+5/756*(326-6957*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 782 + +--S 783 of 1035 +--d0:=D(m0,x) +--E 783 + +)clear all + +--S 784 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1035 +--r0:=1/210*(2291+879*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2)-1/35*(53+5*x)*_ +-- (2+5*x+3*x^2)^(5/2)/(3+2*x)^(5/2)-2333/8*elliptic_e(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1737/28*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-1/140*(10763+3117*x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 785 + +--S 786 of 1035 +--d0:=D(m0,x) +--E 786 + +)clear all + +--S 787 of 1035 +t0:=(A+B*x)*(d+e*x)^(1/2)/(a+b*x+c*x^2)^(1/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1035 +--r0:=2/3*B*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c-1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*_ +-- (b*B*d-3*A*c*d+a*B*e)+(B*c*d-2*b*B*e+3*A*c*e)*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(B*c*d-2*b*B*e+3*A*c*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (c^(5/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 788 + +--S 789 of 1035 +--d0:=D(m0,x) +--E 789 + +)clear all + +--S 790 of 1035 +t0:=(A+B*x)/((d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)) +--R +--R +--R B x + A +--R (1) --------------------------- +--R +--------------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1035 +--r0:=-elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*B-2*A*c-B*sqrt(b^2-4*a*c))*sqrt(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- B*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 791 + +--S 792 of 1035 +--d0:=D(m0,x) +--E 792 + +)clear all + +--S 793 of 1035 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^(1/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------ +--R +--------------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1035 +--r0:=2*(B*d-A*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))+_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c))))*(-2*(b*B*d-A*c*d-a*B*e)+(B*d-A*e)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(B*d-A*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 794 + +--S 795 of 1035 +--d0:=D(m0,x) +--E 795 + +)clear all + +--S 796 of 1035 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1035 +--r0:=-2*(A*b-2*a*B-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/((b^2-4*a*c)*_ +-- sqrt(a+b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/_ +-- (c*(b^2-4*a*c))+elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(b^2*B*d-2*a*c*(3*B*d+A*e)+_ +-- b*(A*c*d+a*B*e))+(b*B*c*d-2*A*c^2*d-2*b^2*B*e+A*b*c*e+6*a*B*c*e)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(5/2)*(b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))-(2*b^2*B*e-_ +-- b*c*(B*d+A*e)+2*c*(A*c*d-3*a*B*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (c^(5/2)*(b^2-4*a*c)*e*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 797 + +--S 798 of 1035 +--d0:=D(m0,x) +--E 798 + +)clear all + +--S 799 of 1035 +t0:=(A+B*x)*(d+e*x)^(1/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1035 +--r0:=-2*(A*b-2*a*B-(b*B-2*A*c)*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ +-- sqrt(a+b*x+c*x^2))+elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*A*b*c-4*a*B*c+(b*B-2*A*c)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))+(b*B-2*A*c)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*(b^2-4*a*c)*e*_ +-- sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 800 + +--S 801 of 1035 +--d0:=D(m0,x) +--E 801 + +)clear all + +--S 802 of 1035 +t0:=(A+B*x)/((d+e*x)^(1/2)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +--------------+ +--R 2 +-------+ | 2 +--R (c x + b x + a)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1035 +--r0:=2*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-_ +-- 2*a*B*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(a+b*x+c*x^2))-elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*b^2*B*d-4*a*c*(B*d-A*e)-_ +-- 2*b*(A*c*d+a*B*e)-(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(b*(B*d+A*e)-2*(A*c*d+a*B*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*e*(c*d^2-e*(b*d-a*e))*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 803 + +--S 804 of 1035 +--d0:=D(m0,x) +--E 804 + +)clear all + +--S 805 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1035 +--r0:=-865/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+4540/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+10/7*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)-2/21*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)+_ +-- 1010/189*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 806 + +--S 807 of 1035 +--d0:=D(m0,x) +--E 807 + +)clear all + +--S 808 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1035 +--r0:=-2743/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+2254/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2/15*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+326/135*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 809 + +--S 810 of 1035 +--d0:=D(m0,x) +--E 810 + +)clear all + +--S 811 of 1035 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ------------------ +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1035 +--r0:=-101/27*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+104/27*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-2/9*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 812 + +--S 813 of 1035 +--d0:=D(m0,x) +--E 813 + +)clear all + +--S 814 of 1035 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------ +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1035 +--r0:=34/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1/3*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2) +--E 815 + +--S 816 of 1035 +--d0:=D(m0,x) +--E 816 + +)clear all + +--S 817 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------- +--R +------------+ +--R +------+ | 2 +--R (2x + 3)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1035 +--r0:=-13*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+12*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 26/5*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 818 + +--S 819 of 1035 +--d0:=D(m0,x) +--E 819 + +)clear all + +--S 820 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------- +--R +------------+ +--R 2 +------+ | 2 +--R (4x + 12x + 9)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1035 +--r0:=-193/15*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+154/15*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 26/15*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-386/75*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 821 + +--S 822 of 1035 +--d0:=D(m0,x) +--E 822 + +)clear all + +--S 823 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------- +--R +------------+ +--R 3 2 +------+ | 2 +--R (8x + 36x + 54x + 27)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1035 +--r0:=-4501/375*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+3328/375*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-26/25*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-_ +-- 782/375*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-9002/1875*sqrt(2+5*x+3*x^2)/_ +-- sqrt(3+2*x) +--E 824 + +--S 825 of 1035 +--d0:=D(m0,x) +--E 825 + +)clear all + +--S 826 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1035 +--r0:=-2*(3+2*x)^(7/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-34174/81*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+16072/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+308/5*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+140/3*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)+_ +-- 12068/135*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 827 + +--S 828 of 1035 +--d0:=D(m0,x) +--E 828 + +)clear all + +--S 829 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1035 +--r0:=-2*(3+2*x)^(5/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-3830/81*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1340/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+140/3*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+1660/27*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 830 + +--S 831 of 1035 +--d0:=D(m0,x) +--E 831 + +)clear all + +--S 832 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1035 +--r0:=-2*(3+2*x)^(3/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-274/9*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- sqrt(2+5*x+3*x^2)+64/9*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+140/3*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 833 + +--S 834 of 1035 +--d0:=D(m0,x) +--E 834 + +)clear all + +--S 835 of 1035 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1035 +--r0:=68/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-70/3*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-2*(29+35*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 836 + +--S 837 of 1035 +--d0:=D(m0,x) +--E 837 + +)clear all + +--S 838 of 1035 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R +------------+ +--R 2 +------+ | 2 +--R (3x + 5x + 2)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1035 +--r0:=-94*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+24*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6/5*(37+47*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 839 + +--S 840 of 1035 +--d0:=D(m0,x) +--E 840 + +)clear all + +--S 841 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------- +--R +------------+ +--R 3 2 +------+ | 2 +--R (6x + 19x + 19x + 6)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1035 +--r0:=-454/5*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+172/5*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6/5*(37+47*x)/_ +-- (sqrt(3+2*x)*sqrt(2+5*x+3*x^2))-908/25*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 842 + +--S 843 of 1035 +--d0:=D(m0,x) +--E 843 + +)clear all + +--S 844 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------- +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (12x + 56x + 95x + 69x + 18)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1035 +--r0:=-6/5*(37+47*x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2))-7438/75*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+3664/75*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2516/75*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-14876/375*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 845 + +--S 846 of 1035 +--d0:=D(m0,x) +--E 846 + +)clear all + +--S 847 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------------ +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (24x + 148x + 358x + 423x + 243x + 54)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1035 +--r0:=-6/5*(37+47*x)/((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2))-213374/1875*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+121172/1875*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-4124/125*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-61468/1875*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(3/2)-426748/9375*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 848 + +--S 849 of 1035 +--d0:=D(m0,x) +--E 849 + +)clear all + +--S 850 of 1035 +t0:=(5-x)*(3+2*x)^(9/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 16x - 16x + 264x + 864x + 999x + 405)\|2x + 3 +--R (1) ----------------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1035 +--r0:=-2/3*(3+2*x)^(9/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+4/3*(3+2*x)^(7/2)*_ +-- (445+569*x)/sqrt(2+5*x+3*x^2)+110516/243*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-21248/243*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-5416/9*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)-_ +-- 4552/9*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)-59512/81*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 851 + +--S 852 of 1035 +--d0:=D(m0,x) +--E 852 + +)clear all + +--S 853 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1035 +--r0:=-2/3*(3+2*x)^(7/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+28/3*(3+2*x)^(5/2)*_ +-- (65+81*x)/sqrt(2+5*x+3*x^2)+31892/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-6776/81*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-504*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)-_ +-- 16744/27*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 854 + +--S 855 of 1035 +--d0:=D(m0,x) +--E 855 + +)clear all + +--S 856 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1035 +--r0:=-2/3*(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+20/3*(3+2*x)^(3/2)*_ +-- (93+113*x)/sqrt(2+5*x+3*x^2)+8620/27*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-1840/27*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- sqrt(2+5*x+3*x^2)-4520/9*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 857 + +--S 858 of 1035 +--d0:=D(m0,x) +--E 858 + +)clear all + +--S 859 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1035 +--r0:=-2/3*(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)-2392/9*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+2252/9*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+4/3*(475+563*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 860 + +--S 861 of 1035 +--d0:=D(m0,x) +--E 861 + +)clear all + +--S 862 of 1035 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1035 +--r0:=-2/3*(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+2852/3*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-608/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/15*(1759+2139*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 863 + +--S 864 of 1035 +--d0:=D(m0,x) +--E 864 + +)clear all + +--S 865 of 1035 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------- +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (9x + 30x + 37x + 20x + 4)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1035 +--r0:=-2/5*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+3476/5*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-728/5*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/25*(2152+2607*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 866 + +--S 867 of 1035 +--d0:=D(m0,x) +--E 867 + +)clear all + +--S 868 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (18x + 87x + 164x + 151x + 68x + 12)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1035 +--r0:=-2/5*(37+47*x)/((2+5*x+3*x^2)^(3/2)*sqrt(3+2*x))+11732/25*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-2096/25*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/25*(2054+2409*x)/(sqrt(3+2*x)*sqrt(2+5*x+3*x^2))+_ +-- 23464/125*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 869 + +--S 870 of 1035 +--d0:=D(m0,x) +--E 870 + +)clear all + +--S 871 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R -------------------------------------------------------------------------- +--R +------------+ +--R 6 5 4 3 2 +------+ | 2 +--R (36x + 228x + 589x + 794x + 589x + 228x + 36)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1035 +--r0:=-2/5*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2))+_ +-- 12/25*(652+737*x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2))+_ +-- 95396/375*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2888/375*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+61672/375*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(3/2)+190792/1875*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 872 + +--S 873 of 1035 +--d0:=D(m0,x) +--E 873 + +)clear all + +--S 874 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 7 6 5 4 3 2 +------+ +--R (72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1035 +--r0:=-2/5*(37+47*x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2))+4/25*(1858+2013*x)/_ +-- ((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2))+107548/3125*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+280256/3125*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+87144/625*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(5/2)+258536/3125*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+_ +-- 215096/15625*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 875 + +--S 876 of 1035 +--d0:=D(m0,x) +--E 876 + +)clear all + +--S 877 of 1035 +t0:=sqrt(x)/((1+x^2)*sqrt(1+x)) +--R +--R +--R +-+ +--R \|x +--R (1) ---------------- +--R 2 +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1035 +r0:=-1/2*(1-%i)^(3/2)*atanh(sqrt(1-%i)*sqrt(x)/sqrt(1+x))-_ + 1/2*(1+%i)^(3/2)*atanh(sqrt(1+%i)*sqrt(x)/sqrt(1+x)) +--R +--R +--R +------+ +-+ +------+ +-+ +--R +------+ \|1 + %i \|x +------+ \|1 - %i \|x +--R - %i\|1 + %i atanh(-------------) - \|1 - %i atanh(-------------) +--R +-----+ +-----+ +--R \|x + 1 \|x + 1 +--R (2) ----------------------------------------------------------------- +--R 1 + %i +--R Type: Expression(Complex(Integer)) +--E 878 + +--S 879 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Complex(Integer)) +--E 879 + +)clear all + +--S 880 of 1035 +t0:=(-1+2*x^2)/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 2 +--R 2x - 1 +--R (1) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1035 +r0:=x*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R (2) x\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 882 + +)clear all + +--S 883 of 1035 +t0:=(a+c*x^2)/(sqrt(d+e*x)*sqrt(f+g*x)) +--R +--R +--R 2 +--R c x + a +--R (1) -------------------- +--R +-------+ +-------+ +--R \|e x + d \|g x + f +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1035 +r0:=-1/4*c*(4*d*e*f*g-3*(e*f+d*g)^2)*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*_ + sqrt(f+g*x)))/(e^(5/2)*g^(5/2))+2*a*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*_ + sqrt(f+g*x)))/(sqrt(e)*sqrt(g))-3/4*c*(e*f+d*g)*sqrt(d+e*x)*_ + sqrt(f+g*x)/(e^2*g^2)+1/2*c*x*sqrt(d+e*x)*sqrt(f+g*x)/(e*g) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 \|g \|e x + d +--R ((8a e + 3c d )g + 2c d e f g + 3c e f )atanh(--------------) +--R +-+ +-------+ +--R \|e \|g x + f +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2c e g x - 3c d g - 3c e f)\|e \|g \|e x + d \|g x + f +--R / +--R 2 2 +-+ +-+ +--R 4e g \|e \|g +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1035 +--d0:=D(m0,x) +--E 885 + +)clear all + +--S 886 of 1035 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - e g x + (- 3d e g - 2e f g)x + (- 3d e g - 6d e f g - e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- d g - 6d e f g - 3d e f )x + (- 2d f g - 3d e f )x - d f +--R / +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 886 + +--S 887 of 1035 +r0:=-d^2*(7*e^2*f^2+16*d*e*f*g+8*d^2*g^2)*x/e^2-d*(2*e^2*f^2+7*d*e*f*g+_ + 4*d^2*g^2)*x^2/e-1/3*(e*f+d*g)*(e*f+7*d*g)*x^3-1/2*e*g*(e*f+2*d*g)*x^4-_ + 1/5*e^2*g^2*x^5-8*d^3*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 5 2 4 3 2 2 5 2 5 +--R (- 240d g - 480d e f g - 240d e f )log(- e x + d) - 6e g x +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (- 30d e g - 15e f g)x + (- 70d e g - 80d e f g - 10e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 120d e g - 210d e f g - 60d e f )x +--R + +--R 4 2 3 2 2 3 2 +--R (- 240d e g - 480d e f g - 210d e f )x +--R / +--R 3 +--R 30e +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 888 + +)clear all + +--S 889 of 1035 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R - e g x + (- 2d e g - 2e f g)x + (- d g - 4d e f g - e f )x +--R + +--R 2 2 2 2 +--R (- 2d f g - 2d e f )x - d f +--R / +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 889 + +--S 890 of 1035 +r0:=-d*(e*f+2*d*g)*(3*e*f+2*d*g)*x/e^2-1/2*(e^2*f^2+6*d*e*f*g+_ + 4*d^2*g^2)*x^2/e-1/3*g*(2*e*f+3*d*g)*x^3-1/4*e*g^2*x^4-_ + 4*d^2*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 3 2 2 2 4 2 4 +--R (- 48d g - 96d e f g - 48d e f )log(- e x + d) - 3e g x +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (- 12d e g - 8e f g)x + (- 24d e g - 36d e f g - 6e f )x +--R + +--R 3 2 2 2 3 2 +--R (- 48d e g - 96d e f g - 36d e f )x +--R / +--R 3 +--R 12e +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 891 + +)clear all + +--S 892 of 1035 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R - e g x + (- d g - 2e f g)x + (- 2d f g - e f )x - d f +--R (1) ---------------------------------------------------------- +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 892 + +--S 893 of 1035 +r0:=-2*d*g*(e*f+d*g)*x/e^2-d*(f+g*x)^2/e-1/3*(f+g*x)^3/g-_ + 2*d*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 +--R (- 6d g - 12d e f g - 6d e f g)log(- e x + d) - e g x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 2 2 +--R (- 3d e g - 3e f g )x + (- 6d e g - 12d e f g - 3e f g)x - 3d e f g +--R + +--R 3 3 +--R - e f +--R / +--R 3 +--R 3e g +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 894 + +)clear all + +--S 895 of 1035 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------- +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 895 + +--S 896 of 1035 +r0:=-g*(e*f+d*g)*x/e^2-1/2*(f+g*x)^2/e-(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (- 2d g - 4d e f g - 2e f )log(- e x + d) - e g x +--R + +--R 2 2 2 2 +--R (- 2d e g - 4e f g)x - e f +--R / +--R 3 +--R 2e +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 897 + +)clear all + +--S 898 of 1035 +t0:=(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------- +--R 2 2 2 +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 898 + +--S 899 of 1035 +r0:=-g^2*x/e^2-1/2*(e*f+d*g)^2*log(d-e*x)/(d*e^3)+_ + 1/2*(e*f-d*g)^2*log(d+e*x)/(d*e^3) +--R +--R +--R (2) +--R 2 2 2 2 +--R (d g - 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 2 +--R (- d g - 2d e f g - e f )log(- e x + d) - 2d e g x +--R / +--R 3 +--R 2d e +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 900 + +)clear all + +--S 901 of 1035 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------------- +--R 3 3 2 2 2 3 +--R e x + d e x - d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 901 + +--S 902 of 1035 +r0:=-1/2*(e*f-d*g)^2/(d*e^3*(d+e*x))-1/4*(e*f+d*g)^2*log(d-e*x)/(d^2*e^3)+_ + 1/4*(e*f-d*g)*(e*f+3*d*g)*log(d+e*x)/(d^2*e^3) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3d e g + 2d e f g + e f )x - 3d g + 2d e f g + d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- d e g - 2d e f g - e f )x - d g - 2d e f g - d e f )log(- e x + d) +--R + +--R 3 2 2 2 2 +--R - 2d g + 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x + 4d e +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 903 + +)clear all + +--S 904 of 1035 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 4 4 3 3 3 4 +--R e x + 2d e x - 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 904 + +--S 905 of 1035 +r0:=-1/4*(e*f-d*g)^2/(d*e^3*(d+e*x)^2)-1/4*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x))+1/4*(e*f+d*g)^2*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 4 2 +--R (d e g + 2d e f g + e f )x + (2d e g + 4d e f g + 2d e f )x + d g +--R + +--R 3 2 2 2 +--R 2d e f g + d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (3d e g - 2d e f g - d e f )x + 2d g - 2d e f +--R / +--R 3 5 2 4 4 5 3 +--R 4d e x + 8d e x + 4d e +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 906 + +)clear all + +--S 907 of 1035 +t0:=(f+g*x)^2/((d+e*x)^3*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 3d e x + 2d e x - 2d e x - 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 907 + +--S 908 of 1035 +r0:=-1/6*(e*f-d*g)^2/(d*e^3*(d+e*x)^3)-1/8*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x)^2)-1/8*(e*f+d*g)^2/(d^3*e^3*(d+e*x))+_ + 1/8*(e*f+d*g)^2*atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (3d e g + 6d e f g + 3e f )x + (9d e g + 18d e f g + 9d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (9d e g + 18d e f g + 9d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (- 3d e g - 6d e f g - 3d e f )x + (3d e g - 18d e f g - 9d e f )x +--R + +--R 5 2 4 3 2 2 +--R 2d g - 4d e f g - 10d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 24d e x + 72d e x + 72d e x + 24d e +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 909 + +)clear all + +--S 910 of 1035 +t0:=(f+g*x)^2/((d+e*x)^4*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------ +--R 6 6 5 5 2 4 4 4 2 2 5 6 +--R e x + 4d e x + 5d e x - 5d e x - 4d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 910 + +--S 911 of 1035 +r0:=-1/8*(e*f-d*g)^2/(d*e^3*(d+e*x)^4)-1/12*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x)^3)-1/16*(e*f+d*g)^2/(d^3*e^3*(d+e*x)^2)-_ + 1/16*(e*f+d*g)^2/(d^4*e^3*(d+e*x))+1/16*(e*f+d*g)^2*atanh(e*x/d)/(d^5*e^3) +--R +--R +--R (2) +--R 2 4 2 5 6 2 4 3 3 2 2 4 5 2 3 +--R (3d e g + 6d e f g + 3e f )x + (12d e g + 24d e f g + 12d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (18d e g + 36d e f g + 18d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (12d e g + 24d e f g + 12d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 3d e g - 6d e f g - 3d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 12d e g - 24d e f g - 12d e f )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (- 3d e g - 38d e f g - 19d e f )x - 8d e f g - 16d e f +--R / +--R 5 7 4 6 6 3 7 5 2 8 4 9 3 +--R 48d e x + 192d e x + 288d e x + 192d e x + 48d e +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 912 + +)clear all + +--S 913 of 1035 +t0:=(d+e*x)^7*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R e g x + (5d e g + 2e f g)x + (10d e g + 10d e f g + e f )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10d e g + 20d e f g + 5d e f )x + (5d e g + 20d e f g + 10d e f )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (d g + 10d e f g + 10d e f )x + (2d f g + 5d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 913 + +--S 914 of 1035 +r0:=d^3*(49*e^2*f^2+160*d*e*f*g+112*d^2*g^2)*x/e^2+1/2*d^2*(23*e^2*f^2+_ + 98*d*e*f*g+80*d^2*g^2)*x^2/e+1/3*d*(7*e^2*f^2+46*d*e*f*g+49*d^2*g^2)*_ + x^3+1/4*e*(e^2*f^2+14*d*e*f*g+23*d^2*g^2)*x^4+1/5*e^2*g*(2*e*f+7*d*g)*_ + x^5+1/6*e^3*g^2*x^6+32*d^5*(e*f+d*g)^2/(e^3*(d-e*x))+_ + 16*d^4*(e*f+d*g)*(5*e*f+9*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 6 2 5 2 4 3 2 7 2 6 +--R (8640d e g + 13440d e f g + 4800d e f )x - 8640d g - 13440d e f g +--R + +--R 5 2 2 +--R - 4800d e f +--R * +--R log(- e x + d) +--R + +--R 7 2 7 6 2 7 6 2 5 2 6 7 2 5 +--R 10e g x + (74d e g + 24e f g)x + (261d e g + 186d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (635d e g + 710d e f g + 125d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (1420d e g + 2020d e f g + 550d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (4320d e g + 6660d e f g + 2250d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 +--R (- 6720d e g - 9600d e f g - 2940d e f )x - 1920d g - 3840d e f g +--R + +--R 5 2 2 +--R - 1920d e f +--R / +--R 4 3 +--R 60e x - 60d e +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 915 + +)clear all + +--S 916 of 1035 +t0:=(d+e*x)^6*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R e g x + (4d e g + 2e f g)x + (6d e g + 8d e f g + e f )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4d e g + 12d e f g + 4d e f )x + (d g + 8d e f g + 6d e f )x +--R + +--R 4 3 2 4 2 +--R (2d f g + 4d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 916 + +--S 917 of 1035 +r0:=d^2*(17*e^2*f^2+64*d*e*f*g+48*d^2*g^2)*x/e^2+d*(3*e^2*f^2+17*d*e*f*g+_ + 16*d^2*g^2)*x^2/e+1/3*(e^2*f^2+12*d*e*f*g+17*d^2*g^2)*x^3+_ + 1/2*e*g*(e*f+3*d*g)*x^4+1/5*e^2*g^2*x^5+16*d^4*(e*f+d*g)^2/(e^3*(d-e*x))+_ + 32*d^3*(e*f+d*g)*(e*f+2*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 5 2 4 2 3 3 2 6 2 5 +--R (1920d e g + 2880d e f g + 960d e f )x - 1920d g - 2880d e f g +--R + +--R 4 2 2 +--R - 960d e f +--R * +--R log(- e x + d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 6e g x + (39d e g + 15e f g)x + (125d e g + 105d e f g + 10e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (310d e g + 390d e f g + 80d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (960d e g + 1410d e f g + 420d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (- 1440d e g - 1920d e f g - 510d e f )x - 480d g - 960d e f g +--R + +--R 4 2 2 +--R - 480d e f +--R / +--R 4 3 +--R 30e x - 30d e +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 918 + +)clear all + +--S 919 of 1035 +t0:=(d+e*x)^5*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R e g x + (3d e g + 2e f g)x + (3d e g + 6d e f g + e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (d g + 6d e f g + 3d e f )x + (2d f g + 3d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 919 + +--S 920 of 1035 +r0:=d*(5*e^2*f^2+24*d*e*f*g+20*d^2*g^2)*x/e^2+1/2*(e^2*f^2+_ + 10*d*e*f*g+12*d^2*g^2)*x^2/e+1/3*g*(2*e*f+5*d*g)*x^3+1/4*e*g^2*x^4+_ + 8*d^3*(e*f+d*g)^2/(e^3*(d-e*x))+4*d^2*(e*f+d*g)*(3*e*f+7*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 3 2 2 3 2 5 2 4 +--R (336d e g + 480d e f g + 144d e f )x - 336d g - 480d e f g +--R + +--R 3 2 2 +--R - 144d e f +--R * +--R log(- e x + d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 3e g x + (17d e g + 8e f g)x + (52d e g + 52d e f g + 6e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (168d e g + 228d e f g + 54d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 240d e g - 288d e f g - 60d e f )x - 96d g - 192d e f g - 96d e f +--R / +--R 4 3 +--R 12e x - 12d e +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 921 + +)clear all + +--S 922 of 1035 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R e g x + (2d e g + 2e f g)x + (d g + 4d e f g + e f )x +--R + +--R 2 2 2 2 +--R (2d f g + 2d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 922 + +--S 923 of 1035 +r0:=(e^2*f^2+8*d*e*f*g+8*d^2*g^2)*x/e^2+g*(e*f+2*d*g)*x^2/e+1/3*g^2*x^3+_ + 4*d^2*(e*f+d*g)^2/(e^3*(d-e*x))+4*d*(e*f+d*g)*(e*f+3*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R ((36d e g + 48d e f g + 12d e f )x - 36d g - 48d e f g - 12d e f ) +--R * +--R log(- e x + d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R e g x + (5d e g + 3e f g)x + (18d e g + 21d e f g + 3e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- 24d e g - 24d e f g - 3d e f )x - 12d g - 24d e f g - 12d e f +--R / +--R 4 3 +--R 3e x - 3d e +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 924 + +)clear all + +--S 925 of 1035 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R e g x + (d g + 2e f g)x + (2d f g + e f )x + d f +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 925 + +--S 926 of 1035 +r0:=g*(2*e*f+3*d*g)*x/e^2+1/2*g^2*x^2/e+2*d*(e*f+d*g)^2/(e^3*(d-e*x))+_ + (e*f+d*g)*(e*f+5*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((10d e g + 12d e f g + 2e f )x - 10d g - 12d e f g - 2d e f ) +--R * +--R log(- e x + d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R e g x + (5d e g + 4e f g)x + (- 6d e g - 4d e f g)x - 4d g +--R + +--R 2 2 2 +--R - 8d e f g - 4d e f +--R / +--R 4 3 +--R 2e x - 2d e +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 927 + +)clear all + +--S 928 of 1035 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------ +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 928 + +--S 929 of 1035 +r0:=g^2*x/e^2+(e*f+d*g)^2/(e^3*(d-e*x))+2*g*(e*f+d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R ((2d e g + 2e f g)x - 2d g - 2d e f g)log(- e x + d) + e g x - d e g x +--R + +--R 2 2 2 2 +--R - d g - 2d e f g - e f +--R / +--R 4 3 +--R e x - d e +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 930 + +)clear all + +--S 931 of 1035 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) -------------------------- +--R 3 3 2 2 2 3 +--R e x - d e x - d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 931 + +--S 932 of 1035 +r0:=1/2*(e*f+d*g)^2/(d*e^3*(d-e*x))-1/4*(e*f-3*d*g)*(e*f+d*g)*_ + log(d-e*x)/(d^2*e^3)+1/4*(e*f-d*g)^2*log(d+e*x)/(d^2*e^3) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((d e g - 2d e f g + e f )x - d g + 2d e f g - d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((3d e g + 2d e f g - e f )x - 3d g - 2d e f g + d e f )log(- e x + d) +--R + +--R 3 2 2 2 2 +--R - 2d g - 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x - 4d e +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 933 + +)clear all + +--S 934 of 1035 +t0:=(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------- +--R 4 4 2 2 2 4 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 934 + +--S 935 of 1035 +r0:=1/2*(d^2*g+e^2*f*x)*(f+g*x)/(d^2*e^2*(d^2-e^2*x^2))+1/2*(e*f-d*g)*_ + (e*f+d*g)*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 4 2 2 4 2 2 2 2 e x 3 2 +--R ((- d e g + e f )x + d g - d e f )atanh(---) - d e f g x +--R d +--R + +--R 3 2 3 2 3 +--R (- d e g - d e f )x - d e f g +--R / +--R 3 5 2 5 3 +--R 2d e x - 2d e +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 936 + +)clear all + +--S 937 of 1035 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ---------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + d e x - 2d e x - 2d e x + d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 937 + +--S 938 of 1035 +r0:=1/8*(e*f+d*g)^2/(d^3*e^3*(d-e*x))-1/8*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^2)+_ + 1/4*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x))+1/8*(3*e*f-d*g)*(e*f+d*g)*_ + atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g + 2d e f g + 3e f )x + (- d e g + 2d e f g + 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g - 2d e f g - 3d e f )x + d g - 2d e f g - 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (d e g - 2d e f g - 3d e f )x + (- 3d e g - 2d e f g - 3d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 2d g - 4d e f g + 2d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 8d e x + 8d e x - 8d e x - 8d e +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 939 + +)clear all + +--S 940 of 1035 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) -------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 2d e x - d e x - 4d e x - d e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 940 + +--S 941 of 1035 +r0:=1/16*(e*f+d*g)^2/(d^4*e^3*(d-e*x))-1/12*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^3)+_ + 1/8*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^2)-1/16*(3*e*f-d*g)*(e*f+d*g)/_ + (d^4*e^3*(d+e*x))+1/4*f*(e*f+d*g)*atanh(e*x/d)/(d^5*e^2) +--R +--R +--R (2) +--R 5 6 2 4 2 4 5 2 3 +--R (3d e f g + 3e f )x + (6d e f g + 6d e f )x +--R + +--R 4 2 3 3 2 5 4 2 2 +--R (- 6d e f g - 6d e f )x - 3d e f g - 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 2 4 5 2 3 3 3 2 4 2 2 +--R (- 3d e f g - 3d e f )x + (- 6d e f g - 6d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 4d e g - d e f g - d e f )x - 2d g - 2d e f g + 4d e f +--R / +--R 5 7 4 6 6 3 8 4 9 3 +--R 12d e x + 24d e x - 24d e x - 12d e +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 942 + +)clear all + +--S 943 of 1035 +t0:=(f+g*x)^2/((d+e*x)^3*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 3d e x + d e x - 5d e x - 5d e x + d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 943 + +--S 944 of 1035 +r0:=1/32*(e*f+d*g)^2/(d^5*e^3*(d-e*x))-1/16*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^4)+_ + 1/12*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^3)-1/32*(3*e*f-d*g)*(e*f+d*g)/_ + (d^4*e^3*(d+e*x)^2)-1/8*f*(e*f+d*g)/(d^5*e^2*(d+e*x))+1/32*(e*f+d*g)*_ + (5*e*f+d*g)*atanh(e*x/d)/(d^6*e^3) +--R +--R +--R (2) +--R 2 5 2 6 7 2 5 3 4 2 2 5 6 2 4 +--R (3d e g + 18d e f g + 15e f )x + (9d e g + 54d e f g + 45d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g + 36d e f g + 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 6d e g - 36d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 9d e g - 54d e f g - 45d e f )x - 3d g - 18d e f g - 15d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 3d e g - 18d e f g - 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 9d e g - 54d e f g - 45d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 7d e g - 42d e f g - 35d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 5 2 2 +--R (- 21d e g + 18d e f g + 15d e f )x - 8d g + 32d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 96d e x + 288d e x + 192d e x - 192d e x - 288d e x - 96d e +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 945 + +)clear all + +--S 946 of 1035 +t0:=(f+g*x)^2/((d+e*x)^4*(d^2-e^2*x^2)^2) +--R +--R +--R (1) +--R 2 2 2 +--R g x + 2f g x + f +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 4d e x + 4d e x - 4d e x - 10d e x - 4d e x + 4d e x +--R + +--R 7 8 +--R 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 946 + +--S 947 of 1035 +r0:=1/64*(e*f+d*g)^2/(d^6*e^3*(d-e*x))-1/20*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^5)+_ + 1/16*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^4)-1/48*(3*e*f-d*g)*_ + (e*f+d*g)/(d^4*e^3*(d+e*x)^3)-1/16*f*(e*f+d*g)/(d^5*e^2*(d+e*x)^2)-_ + 1/64*(e*f+d*g)*(5*e*f+d*g)/(d^6*e^3*(d+e*x))+1/32*(e*f+d*g)*_ + (3*e*f+d*g)*atanh(e*x/d)/(d^7*e^3) +--R +--R +--R (2) +--R 2 6 2 7 8 2 6 +--R (15d e g + 60d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (60d e g + 240d e f g + 180d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (75d e g + 300d e f g + 225d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 75d e g - 300d e f g - 225d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 60d e g - 240d e f g - 180d e f )x - 15d g - 60d e f g - 45d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 15d e g - 60d e f g - 45d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 60d e g - 240d e f g - 180d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 80d e g - 320d e f g - 240d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 20d e g - 80d e f g - 60d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 49d e g + 188d e f g + 141d e f )x - 16d g + 32d e f g + 144d e f +--R / +--R 7 9 6 8 8 5 9 7 4 11 5 2 12 4 13 3 +--R 480d e x + 1920d e x + 2400d e x - 2400d e x - 1920d e x - 480d e +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 948 + +)clear all + +--S 949 of 1035 +t0:=(d+e*x)^7*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R - e g x + (- 4d e g - 2e f g)x + (- 6d e g - 8d e f g - e f )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (- 4d e g - 12d e f g - 4d e f )x + (- d g - 8d e f g - 6d e f )x +--R + +--R 4 3 2 4 2 +--R (- 2d f g - 4d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 949 + +--S 950 of 1035 +r0:=-d*(7*e^2*f^2+48*d*e*f*g+56*d^2*g^2)*x/e^2-1/2*(e*f+2*d*g)*(e*f+12*d*g)*_ + x^2/e-1/3*g*(2*e*f+7*d*g)*x^3-1/4*e*g^2*x^4+8*d^4*(e*f+d*g)^2/(e^3*_ + (d-e*x)^2)-32*d^3*(e*f+d*g)*(e*f+2*d*g)/(e^3*(d-e*x))-8*d^2*(3*e^2*f^2+_ + 14*d*e*f*g+13*d^2*g^2)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 2 3 3 2 4 2 2 +--R (- 1248d e g - 1344d e f g - 288d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (2496d e g + 2688d e f g + 576d e f )x - 1248d g - 1344d e f g +--R + +--R 4 2 2 +--R - 288d e f +--R * +--R log(- e x + d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R - 3e g x + (- 22d e g - 8e f g)x + (- 91d e g - 68d e f g - 6e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 412d e g - 416d e f g - 72d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (1200d e g + 1068d e f g + 162d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (96d e g + 576d e f g + 300d e f )x - 672d g - 960d e f g - 288d e f +--R / +--R 5 2 4 2 3 +--R 12e x - 24d e x + 12d e +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 951 + +)clear all + +--S 952 of 1035 +t0:=(d+e*x)^6*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - e g x + (- 3d e g - 2e f g)x + (- 3d e g - 6d e f g - e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- d g - 6d e f g - 3d e f )x + (- 2d f g - 3d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 952 + +--S 953 of 1035 +r0:=-(e^2*f^2+12*d*e*f*g+18*d^2*g^2)*x/e^2-g*(e*f+3*d*g)*x^2/e-1/3*g^2*x^3+_ + 4*d^3*(e*f+d*g)^2/(e^3*(d-e*x)^2)-4*d^2*(e*f+d*g)*(3*e*f+7*d*g)/(e^3*_ + (d-e*x))-2*d*(3*e^2*f^2+18*d*e*f*g+19*d^2*g^2)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 2 2 2 3 4 2 2 +--R (- 114d e g - 108d e f g - 18d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (228d e g + 216d e f g + 36d e f )x - 114d g - 108d e f g - 18d e f +--R * +--R log(- e x + d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R - e g x + (- 7d e g - 3e f g)x + (- 37d e g - 30d e f g - 3e f )x +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (99d e g + 69d e f g + 6d e f )x + (30d e g + 84d e f g + 33d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 72d g - 96d e f g - 24d e f +--R / +--R 5 2 4 2 3 +--R 3e x - 6d e x + 3d e +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 954 + +)clear all + +--S 955 of 1035 +t0:=(d+e*x)^5*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R - e g x + (- 2d e g - 2e f g)x + (- d g - 4d e f g - e f )x +--R + +--R 2 2 2 2 +--R (- 2d f g - 2d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 955 + +--S 956 of 1035 +r0:=-g*(2*e*f+5*d*g)*x/e^2-1/2*g^2*x^2/e+2*d^2*(e*f+d*g)^2/(e^3*(d-e*x)^2)-_ + 4*d*(e*f+d*g)*(e*f+3*d*g)/(e^3*(d-e*x))-(e^2*f^2+10*d*e*f*g+13*d^2*g^2)*_ + log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 +--R (- 26d e g - 20d e f g - 2e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (52d e g + 40d e f g + 4d e f )x - 26d g - 20d e f g - 2d e f +--R * +--R log(- e x + d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 2 +--R - e g x + (- 8d e g - 4e f g)x + (19d e g + 8d e f g)x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (14d e g + 28d e f g + 8d e f )x - 20d g - 24d e f g - 4d e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 957 + +)clear all + +--S 958 of 1035 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R - e g x + (- d g - 2e f g)x + (- 2d f g - e f )x - d f +--R (1) ---------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 958 + +--S 959 of 1035 +r0:=-g^2*x/e^2+d*(e*f+d*g)^2/(e^3*(d-e*x)^2)-(e*f+d*g)*(e*f+5*d*g)/(e^3*_ + (d-e*x))-2*g*(e*f+2*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 3 2 2 2 2 3 2 2 +--R ((- 4d e g - 2e f g)x + (8d e g + 4d e f g)x - 4d g - 2d e f g) +--R * +--R log(- e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 3 2 3 2 2 +--R - e g x + 2d e g x + (4d e g + 6d e f g + e f )x - 4d g - 4d e f g +--R / +--R 5 2 4 2 3 +--R e x - 2d e x + d e +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1035 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 961 + +--S 962 of 1035 +r0:=1/2*(e*f+d*g)^2/(e^3*(d-e*x)^2)-2*g*(e*f+d*g)/(e^3*(d-e*x))-_ + g^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (- 2e g x + 4d e g x - 2d g )log(- e x + d) + (4d e g + 4e f g)x +--R + +--R 2 2 2 2 +--R - 3d g - 2d e f g + e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 963 + +)clear all + +--S 964 of 1035 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 4 4 3 3 3 4 +--R e x - 2d e x + 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 964 + +--S 965 of 1035 +r0:=1/4*(e*f+d*g)^2/(d*e^3*(d-e*x)^2)+1/4*(e*f-3*d*g)*(e*f+d*g)/_ + (d^2*e^3*(d-e*x))+1/4*(e*f-d*g)^2*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (d e g - 2d e f g + e f )x + (- 2d e g + 4d e f g - 2d e f )x +--R + +--R 4 2 3 2 2 2 +--R d g - 2d e f g + d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (3d e g + 2d e f g - d e f )x - 2d g + 2d e f +--R / +--R 3 5 2 4 4 5 3 +--R 4d e x - 8d e x + 4d e +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 966 + +)clear all + +--S 967 of 1035 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x - d e x - 2d e x + 2d e x + d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 967 + +--S 968 of 1035 +r0:=1/8*(e*f+d*g)^2/(d^2*e^3*(d-e*x)^2)+1/4*(e^2*f^2-d^2*g^2)/(d^3*e^3*_ + (d-e*x))-1/8*(e*f-d*g)^2/(d^3*e^3*(d+e*x))+1/8*(e*f-d*g)*(3*e*f+d*g)*_ + atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g - 2d e f g + 3e f )x + (d e g + 2d e f g - 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g + 2d e f g - 3d e f )x - d g - 2d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 5 2 +--R (d e g + 2d e f g - 3d e f )x + (3d e g - 2d e f g + 3d e f )x - 2d g +--R + +--R 4 3 2 2 +--R 4d e f g + 2d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 8d e x - 8d e x - 8d e x + 8d e +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 969 + +)clear all + +--S 970 of 1035 +t0:=(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ----------------------------- +--R 6 6 2 4 4 4 2 2 6 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 970 + +--S 971 of 1035 +r0:=-1/4*(d^2*g-e^2*f*x)*(f+g*x)^3/(d^2*(e^2*f^2-d^2*g^2)*(d^2-e^2*x^2)^2)+_ + 1/8*(3*e^2*f^2-d^2*g^2)*(d^2*g+e^2*f*x)*(f+g*x)/(d^4*e^2*_ + (e^2*f^2-d^2*g^2)*(d^2-e^2*x^2))+1/8*(3*e^2*f^2-d^2*g^2)*atanh(e*x/d)/_ + (d^5*e^3) +--R +--R +--R (2) +--R 2 4 2 6 2 4 4 2 2 2 4 2 2 6 2 4 2 2 e x +--R ((- d e g + 3e f )x + (2d e g - 6d e f )x - d g + 3d e f )atanh(---) +--R d +--R + +--R 5 4 3 3 2 5 2 3 3 3 2 5 2 3 3 2 +--R - 3d e f g x + (d e g - 3d e f )x + 6d e f g x + (d e g + 5d e f )x +--R + +--R 5 +--R d e f g +--R / +--R 5 7 4 7 5 2 9 3 +--R 8d e x - 16d e x + 8d e +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 972 + +)clear all + +--S 973 of 1035 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)^3) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + d e x - 3d e x - 3d e x + 3d e x + 3d e x - d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 973 + +--S 974 of 1035 +r0:=1/32*(e*f+d*g)^2/(d^4*e^3*(d-e*x)^2)+1/8*f*(e*f+d*g)/(d^5*e^2*(d-e*x))-_ + 1/24*(e*f-d*g)^2/(d^3*e^3*(d+e*x)^3)-1/32*(e*f-d*g)*(3*e*f+d*g)/_ + (d^4*e^3*(d+e*x)^2)+1/16*(-3*e^2*f^2+d^2*g^2)/(d^5*e^3*(d+e*x))+_ + 1/16*(5*e^2*f^2+2*d*e*f*g-d^2*g^2)*atanh(e*x/d)/(d^6*e^3) +--R +--R +--R (2) +--R 2 5 2 6 7 2 5 +--R (- 3d e g + 6d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 3d e g + 6d e f g + 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 3d e g + 6d e f g + 15d e f )x - 3d g + 6d e f g + 15d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 3 4 2 5 2 3 +--R (3d e g - 6d e f g - 15d e f )x + (3d e g - 6d e f g - 15d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (- 5d e g + 10d e f g + 25d e f )x + (7d e g + 10d e f g + 25d e f )x +--R + +--R 7 2 6 5 2 2 +--R 4d g + 16d e f g - 8d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 48d e x + 48d e x - 96d e x - 96d e x + 48d e x + 48d e +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1035 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)^3) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------------------------------------------------------- +--R 8 8 7 7 2 6 6 3 5 5 5 3 3 6 2 2 7 8 +--R e x + 2d e x - 2d e x - 6d e x + 6d e x + 2d e x - 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 976 + +--S 977 of 1035 +r0:=1/64*(e*f+d*g)^2/(d^5*e^3*(d-e*x)^2)+1/64*(e*f+d*g)*(5*e*f+d*g)/_ + (d^6*e^3*(d-e*x))-1/32*(e*f-d*g)^2/(d^3*e^3*(d+e*x)^4)-1/48*(e*f-d*g)*_ + (3*e*f+d*g)/(d^4*e^3*(d+e*x)^3)+1/32*(-3*e^2*f^2+d^2*g^2)/(d^5*e^3*_ + (d+e*x)^2)+1/32*(-5*e^2*f^2-2*d*e*f*g+d^2*g^2)/(d^6*e^3*(d+e*x))+_ + 1/64*(15*e^2*f^2+10*d*e*f*g-d^2*g^2)*atanh(e*x/d)/(d^7*e^3) +--R +--R +--R (2) +--R 2 6 2 7 8 2 6 +--R (- 3d e g + 30d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 6d e g + 60d e f g + 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (12d e g - 120d e f g - 180d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 6d e g + 60d e f g + 90d e f )x - 3d g + 30d e f g + 45d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 5 2 2 6 7 2 5 4 4 2 3 5 2 6 2 4 +--R (3d e g - 30d e f g - 45d e f )x + (6d e g - 60d e f g - 90d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 2d e g + 20d e f g + 30d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 10d e g + 100d e f g + 150d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (35d e g + 34d e f g + 51d e f )x + 16d g + 32d e f g - 48d e f +--R / +--R 7 9 6 8 8 5 9 7 4 10 6 3 11 5 2 12 4 +--R 192d e x + 384d e x - 192d e x - 768d e x - 192d e x + 384d e x +--R + +--R 13 3 +--R 192d e +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 978 + +)clear all + +--S 979 of 1035 +t0:=(a+b*x+c*x^2)/((d+e*x)*(f+g*x)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) --------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 979 + +--S 980 of 1035 +r0:=c*x/(e*g)+(c*d^2-b*d*e+a*e^2)*log(d+e*x)/(e^2*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))*log(f+g*x)/(g^2*(e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (a e g - b e f g + c e f )log(g x + f) +--R + +--R 2 2 2 2 2 +--R (- a e + b d e - c d )g log(e x + d) + (c d e g - c e f g)x +--R / +--R 2 3 3 2 +--R d e g - e f g +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 981 + +)clear all + +--S 982 of 1035 +t0:=(a+b*x+c*x^2)^2/((d+e*x)*(f+g*x)) +--R +--R +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R (1) -------------------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 982 + +--S 983 of 1035 +r0:=(b^2*e^2*g^2-2*c*e*g*(b*e*f+b*d*g-a*e*g)+c^2*(e^2*f^2+d*e*f*g+_ + d^2*g^2))*x/(e^3*g^3)-1/2*c*(c*e*f+c*d*g-2*b*e*g)*x^2/(e^2*g^2)+_ + 1/3*c^2*x^3/(e*g)+(c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/(e^4*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))^2*log(f+g*x)/(g^4*(e*f-d*g)) +--R +--R +--R (2) +--R 2 4 4 4 3 2 4 2 2 4 3 2 4 4 +--R (6a e g - 12a b e f g + (12a c + 6b )e f g - 12b c e f g + 6c e f ) +--R * +--R log(g x + f) +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (- 6a e + 12a b d e + (- 12a c - 6b )d e + 12b c d e - 6c d )g +--R * +--R log(e x + d) +--R + +--R 2 3 4 2 4 3 3 +--R (2c d e g - 2c e f g )x +--R + +--R 3 2 2 2 4 4 3 2 4 2 2 2 +--R ((6b c d e - 3c d e )g - 6b c e f g + 3c e f g )x +--R + +--R 2 3 2 2 2 3 4 2 4 3 +--R ((12a c + 6b )d e - 12b c d e + 6c d e)g + (- 12a c - 6b )e f g +--R + +--R 4 2 2 2 4 3 +--R 12b c e f g - 6c e f g +--R * +--R x +--R / +--R 4 5 5 4 +--R 6d e g - 6e f g +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 984 + +)clear all + +--S 985 of 1035 +t0:=(a+b*x+c*x^2)^3/((d+e*x)*(f+g*x)) +--R +--R +--R (1) +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R / +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 985 + +--S 986 of 1035 +r0:=-(b^2*e^3*g^3*(b*e*f+b*d*g-3*a*e*g)-c^3*(e^4*f^4+d*e^3*f^3*g+_ + d^2*e^2*f^2*g^2+d^3*e*f*g^3+d^4*g^4)-3*c*e^2*g^2*(a^2*e^2*g^2-_ + 2*a*b*e*g*(e*f+d*g)+b^2*(e^2*f^2+d*e*f*g+d^2*g^2))-3*c^2*e*g*(a*e*g*_ + (e^2*f^2+d*e*f*g+d^2*g^2)-b*(e^3*f^3+d*e^2*f^2*g+d^2*e*f*g^2+d^3*g^3)))*_ + x/(e^5*g^5)+1/2*(b^3*e^3*g^3-3*b*c*e^2*g^2*(b*e*f+b*d*g-2*a*e*g)-c^3*_ + (e^3*f^3+d*e^2*f^2*g+d^2*e*f*g^2+d^3*g^3)-3*c^2*e*g*(a*e*g*(e*f+d*g)-_ + b*(e^2*f^2+d*e*f*g+d^2*g^2)))*x^2/(e^4*g^4)+1/3*c*(3*b^2*e^2*g^2-_ + 3*c*e*g*(b*e*f+b*d*g-a*e*g)+c^2*(e^2*f^2+d*e*f*g+d^2*g^2))*_ + x^3/(e^3*g^3)-1/4*c^2*(c*e*f+c*d*g-3*b*e*g)*x^4/(e^2*g^2)+_ + 1/5*c^3*x^5/(e*g)+(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/(e^6*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))^3*log(f+g*x)/(g^6*(e*f-d*g)) +--R +--R +--R (2) +--R 3 6 6 2 6 5 2 2 6 2 4 +--R 60a e g - 180a b e f g + (180a c + 180a b )e f g +--R + +--R 3 6 3 3 2 2 6 4 2 2 6 5 +--R (- 360a b c - 60b )e f g + (180a c + 180b c)e f g - 180b c e f g +--R + +--R 3 6 6 +--R 60c e f +--R * +--R log(g x + f) +--R + +--R 3 6 2 5 2 2 2 4 +--R - 60a e + 180a b d e + (- 180a c - 180a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (360a b c + 60b )d e + (- 180a c - 180b c)d e + 180b c d e - 60c d +--R * +--R 6 +--R g log(e x + d) +--R + +--R 3 5 6 3 6 5 5 +--R (12c d e g - 12c e f g )x +--R + +--R 2 5 3 2 4 6 2 6 5 3 6 2 4 4 +--R ((45b c d e - 15c d e )g - 45b c e f g + 15c e f g )x +--R + +--R 2 2 5 2 2 4 3 3 3 6 +--R ((60a c + 60b c)d e - 60b c d e + 20c d e )g +--R + +--R 2 2 6 5 2 6 2 4 3 6 3 3 +--R (- 60a c - 60b c)e f g + 60b c e f g - 20c e f g +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 2 4 2 3 3 +--R (180a b c + 30b )d e + (- 90a c - 90b c)d e + 90b c d e +--R + +--R 3 4 2 +--R - 30c d e +--R * +--R 6 +--R g +--R + +--R 3 6 5 2 2 6 2 4 2 6 3 3 +--R (- 180a b c - 30b )e f g + (90a c + 90b c)e f g - 90b c e f g +--R + +--R 3 6 4 2 +--R 30c e f g +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 2 4 +--R (180a c + 180a b )d e + (- 360a b c - 60b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (180a c + 180b c)d e - 180b c d e + 60c d e +--R * +--R 6 +--R g +--R + +--R 2 2 6 5 3 6 2 4 +--R (- 180a c - 180a b )e f g + (360a b c + 60b )e f g +--R + +--R 2 2 6 3 3 2 6 4 2 3 6 5 +--R (- 180a c - 180b c)e f g + 180b c e f g - 60c e f g +--R * +--R x +--R / +--R 6 7 7 6 +--R 60d e g - 60e f g +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 987 + +)clear all + +--S 988 of 1035 +t0:=1/((d+e*x)*(f+g*x)*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 3 2 +--R c e g x + ((b e + c d)g + c e f)x + ((a e + b d)g + (b e + c d)f)x +--R + +--R (a d g + (a e + b d)f)x + a d f +--R Type: Fraction(Polynomial(Integer)) +--E 988 + +--S 989 of 1035 +r0:=e^2*log(d+e*x)/((c*d^2-b*d*e+a*e^2)*(e*f-d*g))-g^2*log(f+g*x)/_ + ((e*f-d*g)*(c*f^2-g*(b*f-a*g)))-1/2*(c*e*f+c*d*g-b*e*g)*_ + log(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g)))-_ + (2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g))*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((4a c - 2b )d e + 2b c d )g + ((- 4a c + 2b )e - 4c d )f g +--R + +--R 2 2 2 +--R (- 2b c e + 4c d e)f +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 +--R ((b d e - c d )g - b e f g + c e f )log(c x + b x + a) +--R + +--R 2 2 2 +--R (2a e - 2b d e + 2c d )g log(g x + f) +--R + +--R 2 2 2 2 2 +--R (- 2a e g + 2b e f g - 2c e f )log(e x + d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 2 2 3 3 +--R (2a d e - 2a b d e + 2a c d )g +--R + +--R 2 3 2 2 3 2 +--R (- 2a e + (- 2a c + 2b )d e - 2b c d )f g +--R + +--R 3 2 2 2 3 2 +--R (2a b e + (2a c - 2b )d e + 2c d )f g +--R + +--R 3 2 2 2 3 +--R (- 2a c e + 2b c d e - 2c d e)f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1035 +--d0:=D(m0,x) +--E 990 + +)clear all + +--S 991 of 1035 +t0:=1/((d+e*x)*(f+g*x)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 6 2 2 5 +--R c e g x + ((2b c e + c d)g + c e f)x +--R + +--R 2 2 4 +--R (((2a c + b )e + 2b c d)g + (2b c e + c d)f)x +--R + +--R 2 2 3 +--R ((2a b e + (2a c + b )d)g + ((2a c + b )e + 2b c d)f)x +--R + +--R 2 2 2 +--R ((a e + 2a b d)g + (2a b e + (2a c + b )d)f)x +--R + +--R 2 2 2 +--R (a d g + (a e + 2a b d)f)x + a d f +--R Type: Fraction(Polynomial(Integer)) +--E 991 + +--S 992 of 1035 +r0:=(-b^3*e*g+b^2*c*(e*f+d*g)-2*a*c^2*(e*f+d*g)-b*c*(c*d*f-3*a*e*g)-_ + c*(2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g))*(a+b*x+c*x^2))+2*c*_ + (2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)*(c*f^2-_ + g*(b*f-a*g)))+e^4*log(d+e*x)/((c*d^2-b*d*e+a*e^2)^2*(e*f-d*g))-_ + g^4*log(f+g*x)/((e*f-d*g)*(c*f^2-g*(b*f-a*g))^2)-1/2*(c*e*f+c*d*g-_ + b*e*g)*(c*(e^2*f^2+d^2*g^2)+e*g*(2*a*e*g-b*(e*f+d*g)))*log(a+b*x+_ + c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(c*f^2-g*(b*f-a*g))^2)+(b^2*e^2*g^2*_ + (b*e*f+b*d*g-2*a*e*g)-2*c^3*d*f*(e^2*f^2+d*e*f*g+d^2*g^2)+2*c*e*g*_ + (a^2*e^2*g^2+a*b*e*g*(e*f+d*g)-b^2*(e*f+d*g)^2)-c^2*(4*a*d*e^2*f*g^2-_ + b*(e^3*f^3+5*d*e^2*f^2*g+5*d^2*e*f*g^2+d^3*g^3)))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*(c*f^2-g*(b*f-a*g))^2*_ + sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 3 3 2 2 2 4 3 +--R (24a c - 24a b c + 4a b c)d e +--R + +--R 2 3 3 2 5 2 2 +--R (12a b c + 8a b c - 2b c)d e +--R + +--R 2 4 2 3 4 2 3 4 3 3 4 +--R (8a c - 24a b c + 4b c )d e + (12a b c - 2b c )d +--R * +--R 4 +--R g +--R + +--R 3 3 2 2 2 4 4 2 4 2 2 4 3 +--R (- 24a c + 24a b c - 4a b c)e - 48a c d e + 32a b c d e +--R + +--R 5 4 +--R - 24a c d +--R * +--R 3 +--R f g +--R + +--R 2 3 3 2 5 4 2 4 3 +--R (- 12a b c - 8a b c + 2b c)e + 48a c d e +--R + +--R 5 2 4 3 5 4 +--R (16a c - 16b c )d e + 12b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 4 2 3 4 2 4 4 3 +--R (- 8a c + 24a b c - 4b c )e - 32a b c d e +--R + +--R 5 2 4 2 2 6 4 +--R (- 16a c + 16b c )d e - 8c d +--R * +--R 3 +--R f g +--R + +--R 4 3 3 4 5 3 5 2 2 6 3 4 +--R ((- 12a b c + 2b c )e + 24a c d e - 12b c d e + 8c d e)f +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 3 +--R (24a b c - 24a b c + 4a b )d e +--R + +--R 2 2 2 4 6 2 2 +--R (12a b c + 8a b c - 2b )d e +--R + +--R 2 3 3 2 5 3 2 3 4 2 4 +--R (8a b c - 24a b c + 4b c)d e + (12a b c - 2b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 2 3 5 4 2 3 2 2 2 3 3 +--R (- 24a b c + 24a b c - 4a b )e - 48a b c d e + 32a b c d e +--R + +--R 4 4 +--R - 24a b c d +--R * +--R 3 +--R f g +--R + +--R 2 2 2 4 6 4 2 3 3 +--R (- 12a b c - 8a b c + 2b )e + 48a b c d e +--R + +--R 4 3 3 3 2 4 4 +--R (16a b c - 16b c )d e + 12b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 3 3 2 5 4 2 3 3 +--R (- 8a b c + 24a b c - 4b c)e - 32a b c d e +--R + +--R 4 3 3 2 2 5 4 +--R (- 16a b c + 16b c )d e - 8b c d +--R * +--R 3 +--R f g +--R + +--R 2 3 4 2 4 4 3 2 4 2 2 5 3 4 +--R ((- 12a b c + 2b c )e + 24a b c d e - 12b c d e + 8b c d e)f +--R * +--R x +--R + +--R 4 2 3 2 2 4 3 3 2 2 3 5 2 2 +--R (24a c - 24a b c + 4a b )d e + (12a b c + 8a b c - 2a b )d e +--R + +--R 3 3 2 2 2 4 3 2 3 3 2 4 +--R (8a c - 24a b c + 4a b c)d e + (12a b c - 2a b c )d +--R * +--R 4 +--R g +--R + +--R 4 2 3 2 2 4 4 3 3 2 2 2 3 3 +--R (- 24a c + 24a b c - 4a b )e - 48a c d e + 32a b c d e +--R + +--R 2 4 4 +--R - 24a c d +--R * +--R 3 +--R f g +--R + +--R 3 2 2 3 5 4 3 3 3 +--R (- 12a b c - 8a b c + 2a b )e + 48a c d e +--R + +--R 2 4 2 3 3 4 4 +--R (16a c - 16a b c )d e + 12a b c d +--R * +--R 2 2 +--R f g +--R + +--R 3 3 2 2 2 4 4 2 3 3 +--R (- 8a c + 24a b c - 4a b c)e - 32a b c d e +--R + +--R 2 4 2 3 2 2 5 4 +--R (- 16a c + 16a b c )d e - 8a c d +--R * +--R 3 +--R f g +--R + +--R 2 3 3 2 4 2 4 3 4 2 2 5 3 4 +--R ((- 12a b c + 2a b c )e + 24a c d e - 12a b c d e + 8a c d e)f +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 3 2 3 2 2 4 2 2 +--R (8a b c - 2a b c)d e + (- 8a c - 2a b c + b c)d e +--R + +--R 3 3 2 3 4 2 3 4 +--R (8a b c - 2b c )d e + (- 4a c + b c )d +--R * +--R 4 +--R g +--R + +--R 2 2 3 4 3 2 3 2 2 4 4 2 2 +--R (- 8a b c + 2a b c)e f g + (8a c + 2a b c - b c)e f g +--R + +--R 3 3 2 4 3 4 2 3 4 4 +--R (- 8a b c + 2b c )e f g + (4a c - b c )e f +--R * +--R 2 +--R x +--R + +--R 2 2 4 3 2 2 3 5 2 2 +--R (8a b c - 2a b )d e + (- 8a b c - 2a b c + b )d e +--R + +--R 2 2 4 3 3 3 2 4 +--R (8a b c - 2b c)d e + (- 4a b c + b c )d +--R * +--R 4 +--R g +--R + +--R 2 2 4 4 3 2 2 3 5 4 2 2 +--R (- 8a b c + 2a b )e f g + (8a b c + 2a b c - b )e f g +--R + +--R 2 2 4 4 3 3 3 2 4 4 +--R (- 8a b c + 2b c)e f g + (4a b c - b c )e f +--R * +--R x +--R + +--R 3 2 3 3 3 2 2 2 4 2 2 +--R (8a b c - 2a b )d e + (- 8a c - 2a b c + a b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (8a b c - 2a b c)d e + (- 4a c + a b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 3 4 3 3 2 2 2 4 4 2 2 +--R (- 8a b c + 2a b )e f g + (8a c + 2a b c - a b )e f g +--R + +--R 2 2 3 4 3 2 3 2 2 4 4 +--R (- 8a b c + 2a b c)e f g + (4a c - a b c )e f +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 4 2 2 3 3 +--R (8a c - 2a b c)e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (16a c + 4a b c - 2b c)d e + (- 16a b c + 4b c )d e +--R + +--R 4 2 3 4 +--R (8a c - 2b c )d +--R * +--R 4 2 +--R g x +--R + +--R 3 2 3 4 2 2 4 3 +--R (8a b c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (16a b c + 4a b c - 2b )d e + (- 16a b c + 4b c)d e +--R + +--R 3 3 2 4 +--R (8a b c - 2b c )d +--R * +--R 4 +--R g x +--R + +--R 4 3 2 4 3 2 3 3 +--R (8a c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 +--R (8a c - 2a b c )d +--R * +--R 4 +--R g +--R * +--R log(g x + f) +--R + +--R 3 2 2 2 4 4 2 2 3 4 3 +--R (- 8a c + 2a b c)e g + (16a b c - 4a b c)e f g +--R + +--R 2 3 2 2 4 4 2 2 3 3 2 4 3 +--R (- 16a c - 4a b c + 2b c)e f g + (16a b c - 4b c )e f g +--R + +--R 4 2 3 4 4 +--R (- 8a c + 2b c )e f +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 4 2 2 4 4 3 +--R (- 8a b c + 2a b )e g + (16a b c - 4a b )e f g +--R + +--R 2 2 3 5 4 2 2 2 2 4 4 3 +--R (- 16a b c - 4a b c + 2b )e f g + (16a b c - 4b c)e f g +--R + +--R 3 3 2 4 4 +--R (- 8a b c + 2b c )e f +--R * +--R x +--R + +--R 4 3 2 4 4 3 2 3 4 3 +--R (- 8a c + 2a b )e g + (16a b c - 4a b )e f g +--R + +--R 3 2 2 2 4 4 2 2 2 2 3 4 3 +--R (- 16a c - 4a b c + 2a b )e f g + (16a b c - 4a b c)e f g +--R + +--R 2 3 2 2 4 4 +--R (- 8a c + 2a b c )e f +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 3 2 2 +--R (- 4a c + 2a b c)d e + (2a b c - 2a b c)d e +--R + +--R 2 3 2 2 3 3 4 +--R (- 4a c + 4a b c )d e - 2a b c d +--R * +--R 4 +--R g +--R + +--R 3 2 2 2 4 2 3 2 2 4 2 2 3 2 3 +--R (4a c - 2a b c)e + (8a c - 4a b c + 2b c)d e - 4b c d e +--R + +--R 4 2 3 4 +--R (4a c + 2b c )d +--R * +--R 3 +--R f g +--R + +--R 2 2 3 4 2 3 2 2 4 3 +--R (- 2a b c + 2a b c)e + (- 8a c + 4a b c - 2b c)d e +--R + +--R 4 2 3 3 4 4 +--R (- 8a c + 8b c )d e - 6b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 3 2 2 4 3 2 3 4 2 3 2 2 5 4 +--R ((4a c - 4a b c )e + 4b c d e + (8a c - 8b c )d e + 4c d ) +--R * +--R 3 +--R f g +--R + +--R 3 4 4 2 3 3 4 2 2 5 3 4 +--R (2a b c e + (- 4a c - 2b c )d e + 6b c d e - 4c d e)f +--R * +--R x +--R + +--R 3 2 3 3 3 2 2 2 4 2 2 +--R (- 6a b c + 2a b )d e + (4a c + 4a b c - 2a b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 10a b c + 4a b c)d e + (4a c - 2a b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 3 4 2 2 3 5 2 2 +--R (6a b c - 2a b )e + (4a b c - 6a b c + 2b )d e +--R + +--R 2 2 4 3 3 3 2 4 +--R (8a b c - 4b c)d e + (- 2a b c + 2b c )d +--R * +--R 3 +--R f g +--R + +--R 3 2 2 2 4 4 2 2 3 5 3 +--R (- 4a c - 4a b c + 2a b )e + (- 4a b c + 6a b c - 2b )d e +--R + +--R 3 3 2 3 4 2 3 4 +--R (- 12a b c + 6b c )d e + (4a c - 4b c )d +--R * +--R 2 2 +--R f g +--R + +--R 2 2 3 4 2 2 4 3 +--R (10a b c - 4a b c)e + (- 8a b c + 4b c)d e +--R + +--R 3 3 2 2 2 4 4 +--R (12a b c - 6b c )d e + 2b c d +--R * +--R 3 +--R f g +--R + +--R 2 3 2 2 4 3 3 2 3 +--R (- 4a c + 2a b c )e + (2a b c - 2b c )d e +--R + +--R 4 2 3 2 2 4 3 +--R (- 4a c + 4b c )d e - 2b c d e +--R * +--R 4 +--R f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 2 4 4 2 3 3 2 3 +--R (8a c - 2a b c)d e + (- 16a b c + 4a b c)d e +--R + +--R 4 3 3 2 2 2 4 3 2 3 3 2 3 2 4 +--R (16a c + 4a b c - 2a b c)d e + (- 16a b c + 4a b c )d e +--R + +--R 3 4 2 2 3 5 +--R (8a c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 5 2 4 2 5 4 3 3 2 2 2 4 2 3 +--R (- 8a c + 2a b c)e + (- 16a c + 28a b c - 6a b c)d e +--R + +--R 3 3 2 3 2 5 3 2 +--R (- 16a b c - 12a b c + 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 4 2 4 3 3 5 +--R (- 8a c + 34a b c - 8a b c )d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 2 3 3 5 4 3 3 2 2 2 4 4 +--R (16a b c - 4a b c)e + (16a c - 28a b c + 6a b c)d e +--R + +--R 3 4 2 2 3 4 2 6 3 2 +--R (32a c - 8a b c + 8a b c - 2b c)d e +--R + +--R 2 4 3 3 5 2 4 2 5 2 4 4 3 5 +--R (- 16a b c - 12a b c + 4b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 3 +--R f g +--R + +--R 4 3 3 2 2 2 4 5 +--R (- 16a c - 4a b c + 2a b c)e +--R + +--R 3 3 2 3 2 5 4 +--R (16a b c + 12a b c - 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 6 2 3 +--R (- 32a c + 8a b c - 8a b c + 2b c)d e +--R + +--R 2 5 2 4 4 3 4 5 3 4 5 +--R (- 16a c + 28a b c - 6b c )d e + (- 16a b c + 4b c )d +--R * +--R 3 2 +--R f g +--R + +--R 3 3 2 3 2 5 3 4 2 2 3 4 2 4 +--R (16a b c - 4a b c )e + (8a c - 34a b c + 8a b c )d e +--R + +--R 2 4 3 3 5 2 2 3 +--R (16a b c + 12a b c - 4b c )d e +--R + +--R 2 5 2 4 4 3 3 2 6 2 5 5 +--R (16a c - 28a b c + 6b c )d e + (8a c - 2b c )d +--R * +--R 4 +--R f g +--R + +--R 3 4 2 2 3 5 2 4 3 3 4 +--R (- 8a c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 2 5 2 4 4 3 2 3 5 3 4 3 2 +--R (- 16a c - 4a b c + 2b c )d e + (16a b c - 4b c )d e +--R + +--R 6 2 5 4 +--R (- 8a c + 2b c )d e +--R * +--R 5 +--R f +--R * +--R 2 +--R x +--R + +--R 5 4 3 4 4 2 3 4 2 3 +--R (8a b c - 2a b )d e + (- 16a b c + 4a b )d e +--R + +--R 4 2 3 3 2 5 3 2 3 2 2 2 4 4 +--R (16a b c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 3 3 2 3 2 5 +--R (8a b c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 5 4 3 5 4 2 3 3 2 5 2 3 +--R (- 8a b c + 2a b )e + (- 16a b c + 28a b c - 6a b )d e +--R + +--R 3 2 2 2 4 6 3 2 +--R (- 16a b c - 12a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 3 4 2 5 +--R (- 8a b c + 34a b c - 8a b c)d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 2 3 4 5 4 2 3 3 2 5 4 +--R (16a b c - 4a b )e + (16a b c - 28a b c + 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 2 +--R (32a b c - 8a b c + 8a b c - 2b )d e +--R + +--R 2 2 3 4 2 6 4 +--R (- 16a b c - 12a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 5 +--R (16a b c + 4a b c - 2b c )d +--R * +--R 2 3 +--R f g +--R + +--R 4 2 3 3 2 5 5 +--R (- 16a b c - 4a b c + 2a b )e +--R + +--R 3 2 2 2 4 6 4 +--R (16a b c + 12a b c - 4a b )d e +--R + +--R 3 3 2 3 2 5 7 2 3 +--R (- 32a b c + 8a b c - 8a b c + 2b )d e +--R + +--R 2 4 3 3 5 2 4 2 4 4 3 5 +--R (- 16a b c + 28a b c - 6b c )d e + (- 16a b c + 4b c )d +--R * +--R 3 2 +--R f g +--R + +--R 3 2 2 2 4 5 3 3 2 3 2 5 4 +--R (16a b c - 4a b c)e + (8a b c - 34a b c + 8a b c)d e +--R + +--R 2 2 3 4 2 6 2 3 +--R (16a b c + 12a b c - 4b c)d e +--R + +--R 2 4 3 3 5 2 3 2 5 3 4 5 +--R (16a b c - 28a b c + 6b c )d e + (8a b c - 2b c )d +--R * +--R 4 +--R f g +--R + +--R 3 3 2 3 2 5 2 2 3 4 2 4 +--R (- 8a b c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 2 4 3 3 5 2 2 3 2 4 4 3 3 2 +--R (- 16a b c - 4a b c + 2b c )d e + (16a b c - 4b c )d e +--R + +--R 5 3 4 4 +--R (- 8a b c + 2b c )d e +--R * +--R 5 +--R f +--R * +--R x +--R + +--R 6 5 2 4 5 4 3 2 3 +--R (8a c - 2a b )d e + (- 16a b c + 4a b )d e +--R + +--R 5 2 4 2 3 4 3 2 4 2 3 3 4 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 4 3 3 2 2 5 +--R (8a c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 6 5 2 5 5 2 4 2 3 4 2 3 +--R (- 8a c + 2a b )e + (- 16a c + 28a b c - 6a b )d e +--R + +--R 4 2 3 3 2 5 3 2 +--R (- 16a b c - 12a b c + 4a b )d e +--R + +--R 4 3 3 2 2 2 4 4 3 3 2 3 2 5 +--R (- 8a c + 34a b c - 8a b c)d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 5 4 3 5 5 2 4 2 3 4 4 +--R (16a b c - 4a b )e + (16a c - 28a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (32a c - 8a b c + 8a b c - 2a b )d e +--R + +--R 3 3 2 3 2 5 4 3 4 2 2 3 4 2 5 +--R (- 16a b c - 12a b c + 4a b c)d e + (16a c + 4a b c - 2a b c )d +--R * +--R 2 3 +--R f g +--R + +--R 5 2 4 2 3 4 5 4 2 3 3 2 5 4 +--R (- 16a c - 4a b c + 2a b )e + (16a b c + 12a b c - 4a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 3 +--R (- 32a c + 8a b c - 8a b c + 2a b )d e +--R + +--R 3 4 2 2 3 4 2 4 2 4 3 3 5 +--R (- 16a c + 28a b c - 6a b c )d e + (- 16a b c + 4a b c )d +--R * +--R 3 2 +--R f g +--R + +--R 4 2 3 3 5 4 3 3 2 2 2 4 4 +--R (16a b c - 4a b c)e + (8a c - 34a b c + 8a b c)d e +--R + +--R 3 3 2 3 2 5 2 3 +--R (16a b c + 12a b c - 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 3 2 2 5 2 4 5 +--R (16a c - 28a b c + 6a b c )d e + (8a c - 2a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 3 3 2 2 5 3 3 2 3 2 4 +--R (- 8a c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 3 2 4 3 3 3 2 +--R (- 16a c - 4a b c + 2a b c )d e + (16a b c - 4a b c )d e +--R + +--R 2 5 2 4 4 +--R (- 8a c + 2a b c )d e +--R * +--R 5 +--R f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1035 +--d0:=D(m0,x) +--E 993 + +)clear all + +--S 994 of 1035 +t0:=sqrt(a+b*x+c*x^2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R (1) --------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1035 +r0:=atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/(e*g)+_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/(e*(e*f-d*g))-atanh(1/2*_ + (b*f-2*a*g+(2*c*f-b*g)*x)/(sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))*_ + sqrt(c*f^2-b*f*g+a*g^2)/(g*(e*f-d*g)) +--R +--R +--R (2) +--R +-+ 2c x + b +--R (d g - e f)\|c atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 (b e - 2c d)x + 2a e - b d +--R g\|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 (b g - 2c f)x + 2a g - b f +--R - e\|a g - b f g + c f atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R / +--R 2 2 +--R d e g - e f g +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1035 +--d0:=D(m0,x) +--E 996 + +)clear all + +--S 997 of 1035 +t0:=(a+b*x+c*x^2)^(3/2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R (1) --------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1035 +r0:=(c*d^2-b*d*e+a*e^2)^(3/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^3*(e*f-d*g))-_ + (c*f^2-b*f*g+a*g^2)^(3/2)*atanh(1/2*(b*f-2*a*g+(2*c*f-b*g)*x)/_ + (sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))/(g^3*(e*f-d*g))-_ + 1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^3*(e*f-d*g)*sqrt(c))+1/8*(8*c^2*e*f^3+b*g^2*_ + (3*b*e*f+b*d*g-4*a*e*g)-4*c*g*(3*b*e*f^2-a*g*(3*e*f-d*g)))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e*g^3*(e*f-d*g)*_ + sqrt(c))+(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)/(e^2*(e*f-d*g))-_ + 1/4*(4*c*e*f^2-g*(5*b*e*f-b*d*g-4*a*e*g)-2*c*g*(e*f-d*g)*x)*_ + sqrt(a+b*x+c*x^2)/(e*g^2*(e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 2 3 3 2 3 2 +--R ((12a c + 3b )d e - 12b c d e + 8c d )g + (- 12a c - 3b )e f g +--R + +--R 3 2 2 3 3 +--R 12b c e f g - 8c e f +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R 2 2 3 +-+ | 2 2 +--R (8a e - 8b d e + 8c d )g \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 3 2 3 3 2 +-+ | 2 2 +--R (- 8a e g + 8b e f g - 8c e f )\|c \|a g - b f g + c f +--R * +--R (b g - 2c f)x + 2a g - b f +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (4c d e g - 4c e f g )x + (10b d e - 8c d e)g - 10b e f g +--R + +--R 3 2 +--R 8c e f g +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 4 4 3 +-+ +--R (8d e g - 8e f g )\|c +--R Type: Expression(Integer) +--E 998 + +--S 999 of 1035 +--d0:=D(m0,x) +--E 999 + +)clear all + +--S 1000 of 1035 +t0:=(a+b*x+c*x^2)^(5/2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R (1) --------------------------------------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1035 +r0:=1/3*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2)/(e^2*(e*f-d*g))-_ + 1/24*(8*c*e*f^2-g*(11*b*e*f-3*b*d*g-8*a*e*g)-6*c*g*(e*f-d*g)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e*g^2*(e*f-d*g))-1/16*(2*c*d-b*e)*(c*d^2-b*d*e+_ + a*e^2)*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*e^5*(e*f-d*g))+1/128*_ + (128*c^4*e*f^5-320*c^3*e*f^3*g*(b*f-a*g)-b^3*g^4*(5*b*e*f+3*b*d*g-_ + 8*a*e*g)+48*c^2*g^2*(5*b^2*e*f^3-10*a*b*e*f^2*g+a^2*g^2*(5*e*f-d*g))-_ + 8*b*c*g^3*(5*b^2*e*f^2+12*a^2*e*g^2-3*a*b*g*(5*e*f+d*g)))*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*e*g^5*(e*f-d*g))+_ + (c*d^2-b*d*e+a*e^2)^(5/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*(e*f-d*g))-_ + (c*f^2-b*f*g+a*g^2)^(5/2)*atanh(1/2*(b*f-2*a*g+(2*c*f-b*g)*x)/_ + (sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))/(g^5*(e*f-d*g))+_ + 1/8*(c*d^2-b*d*e+a*e^2)*(8*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-4*a*e)-_ + 2*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(c*e^4*(e*f-d*g))-_ + 1/64*(64*c^3*e*f^4-16*c^2*e*f^2*g*(9*b*f-8*a*g)-b^2*g^3*(5*b*e*f+_ + 3*b*d*g-8*a*e*g)+4*c*g^2*(22*b^2*e*f^2+16*a^2*e*g^2-3*a*b*g*(13*e*f-_ + d*g))-2*c*g*(16*c^2*e*f^3+b*g^2*(5*b*e*f+3*b*d*g-8*a*e*g)-_ + 4*c*g*(6*b*e*f^2-a*g*(7*e*f-3*d*g)))*x)*sqrt(a+b*x+c*x^2)/(c*e*g^4*_ + (e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 4 4 2 3 2 3 +--R (720a c + 360a b c - 15b )d e + (- 1440a b c - 120b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (960a c + 720b c )d e - 960b c d e + 384c d +--R * +--R 5 +--R g +--R + +--R 2 2 2 4 5 4 2 3 5 2 3 +--R (- 720a c - 360a b c + 15b )e f g + (1440a b c + 120b c)e f g +--R + +--R 3 2 2 5 3 2 3 5 4 4 5 5 +--R (- 960a c - 720b c )e f g + 960b c e f g - 384c e f +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 4 3 2 2 2 2 2 3 +--R 384a c e - 768a b c d e + (768a c + 384b c)d e - 768b c d e +--R + +--R 3 4 +--R 384c d +--R * +--R +-------------------+ +--R 5 +-+ | 2 2 +--R g \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 5 4 5 3 2 2 5 2 2 +--R - 384a c e g + 768a b c e f g + (- 768a c - 384b c)e f g +--R + +--R 2 5 3 3 5 4 +--R 768b c e f g - 384c e f +--R * +--R +-------------------+ +--R +-+ | 2 2 (b g - 2c f)x + 2a g - b f +--R \|c \|a g - b f g + c f atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R + +--R 3 4 5 3 5 4 3 +--R (96c d e g - 96c e f g )x +--R + +--R 2 4 3 2 3 5 2 5 4 3 5 2 3 2 +--R ((272b c d e - 128c d e )g - 272b c e f g + 128c e f g )x +--R + +--R 2 2 4 2 2 3 3 3 2 5 +--R ((432a c + 236b c)d e - 416b c d e + 192c d e )g +--R + +--R 2 2 5 4 2 5 2 3 3 5 3 2 +--R (- 432a c - 236b c)e f g + 416b c e f g - 192c e f g +--R * +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (1112a b c + 30b )d e + (- 896a c - 528b c)d e + 864b c d e +--R + +--R 3 4 +--R - 384c d e +--R * +--R 5 +--R g +--R + +--R 3 5 4 2 2 5 2 3 2 5 3 2 +--R (- 1112a b c - 30b )e f g + (896a c + 528b c)e f g - 864b c e f g +--R + +--R 3 5 4 +--R 384c e f g +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 6 6 5 +-+ +--R (384c d e g - 384c e f g )\|c +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1035 +--d0:=D(m0,x) +--E 1002 + +)clear all + +--S 1003 of 1035 +t0:=(d+e*x)^m*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 2 m +--R (c x + b x + a)(e x + d) +--R (1) -------------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1035 +--r0:=2*a*(d+e*x)^(1+m)/((e^2-d*f)*sqrt(e+f*x))+2*c*e^2*(d+e*x)^(1+m)/_ +-- (f^2*(e^2-d*f)*sqrt(e+f*x))-2*b*e*(d+e*x)^(1+m)/(f*(e^2-d*f)*_ +-- sqrt(e+f*x))+2*c*(d+e*x)^(1+m)*sqrt(e+f*x)/(e*f^2*(3+2*m))-_ +-- 2*a*e*(1+2*m)*(d+e*x)^m*hypergeometric(1/2,-m,3/2,e*(e+f*x)/_ +-- (e^2-d*f))*sqrt(e+f*x)/(f*(e^2-d*f)*(-f*(d+e*x)/(e^2-d*f))^m)-_ +-- 2*b*(d*f-2*e^2*(1+m))*(d+e*x)^m*hypergeometric(1/2,-m,3/2,_ +-- e*(e+f*x)/(e^2-d*f))*sqrt(e+f*x)/(f^2*(e^2-d*f)*(-f*(d+e*x)/_ +-- (e^2-d*f))^m)+2*c*(d^2*f^2+4*d*e^2*f*(1+m)-4*e^4*(2+3*m+m^2))*_ +-- (d+e*x)^m*hypergeometric(1/2,-m,3/2,e*(e+f*x)/(e^2-d*f))*_ +-- sqrt(e+f*x)/(e*f^3*(e^2-d*f)*(3+2*m)*(-f*(d+e*x)/(e^2-d*f))^m) +--E 1004 + +--S 1005 of 1035 +--d0:=D(m0,x) +--E 1005 + +)clear all + +--S 1006 of 1035 +t0:=(d+e*x)^3*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R (1) +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R / +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1035 +r0:=2/3*(e^2-d*f)*(3*e*f*(2*b*e^2-b*d*f-a*e*f)-c*(10*e^4-8*d*e^2*f+_ + d^2*f^2))*(e+f*x)^(3/2)/f^6-2/5*e*(e*f*(4*b*e^2-3*b*d*f-a*e*f)-_ + c*(10*e^4-12*d*e^2*f+3*d^2*f^2))*(e+f*x)^(5/2)/f^6-2/7*e^2*(5*c*e^2-_ + 3*c*d*f-b*e*f)*(e+f*x)^(7/2)/f^6+2/9*c*e^3*(e+f*x)^(9/2)/f^6+_ + 2*(e^2-d*f)^3*(c*e^2-f*(b*e-a*f))/(f^6*sqrt(e+f*x))-2*(e^2-d*f)^2*_ + (f*(4*b*e^2-b*d*f-3*a*e*f)-c*(5*e^3-2*d*e*f))*sqrt(e+f*x)/f^6 +--R +--R +--R (2) +--R 3 5 5 3 2 5 4 4 4 +--R 70c e f x + ((90b e + 270c d e )f - 100c e f )x +--R + +--R 3 2 2 5 4 3 4 +--R (126a e + 378b d e + 378c d e)f + (- 144b e - 432c d e )f +--R + +--R 5 3 +--R 160c e f +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 +--R (630a d e + 630b d e + 210c d )f +--R + +--R 4 3 2 2 4 5 4 3 +--R (- 252a e - 756b d e - 756c d e )f + (288b e + 864c d e )f +--R + +--R 6 2 +--R - 320c e f +--R * +--R 2 +--R x +--R + +--R 2 3 5 3 2 2 3 4 +--R (1890a d e + 630b d )f + (- 2520a d e - 2520b d e - 840c d e)f +--R + +--R 5 4 2 3 3 6 5 2 +--R (1008a e + 3024b d e + 3024c d e )f + (- 1152b e - 3456c d e )f +--R + +--R 7 +--R 1280c e f +--R * +--R x +--R + +--R 3 5 2 2 3 4 +--R - 630a d f + (3780a d e + 1260b d e)f +--R + +--R 4 2 3 3 2 3 +--R (- 5040a d e - 5040b d e - 1680c d e )f +--R + +--R 6 5 2 4 2 7 6 +--R (2016a e + 6048b d e + 6048c d e )f + (- 2304b e - 6912c d e )f +--R + +--R 8 +--R 2560c e +--R / +--R 6 +-------+ +--R 315f \|f x + e +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1008 + +)clear all + +--S 1009 of 1035 +t0:=(d+e*x)^2*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R / +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1035 +r0:=-2/3*(e*f*(3*b*e^2-2*b*d*f-a*e*f)-c*(6*e^4-6*d*e^2*f+d^2*f^2))*_ + (e+f*x)^(3/2)/f^5-2/5*e*(4*c*e^2-2*c*d*f-b*e*f)*(e+f*x)^(5/2)/f^5+_ + 2/7*c*e^2*(e+f*x)^(7/2)/f^5-2*(e^2-d*f)^2*(c*e^2-f*(b*e-a*f))/_ + (f^5*sqrt(e+f*x))+2*(e^2-d*f)*(f*(3*b*e^2-b*d*f-2*a*e*f)-_ + c*(4*e^3-2*d*e*f))*sqrt(e+f*x)/f^5 +--R +--R +--R (2) +--R 2 4 4 2 4 3 3 3 +--R 30c e f x + ((42b e + 84c d e)f - 48c e f )x +--R + +--R 2 2 4 3 2 3 4 2 2 +--R ((70a e + 140b d e + 70c d )f + (- 84b e - 168c d e )f + 96c e f )x +--R + +--R 2 4 3 2 2 3 +--R (420a d e + 210b d )f + (- 280a e - 560b d e - 280c d e)f +--R + +--R 4 3 2 5 +--R (336b e + 672c d e )f - 384c e f +--R * +--R x +--R + +--R 2 4 2 2 3 +--R - 210a d f + (840a d e + 420b d e)f +--R + +--R 4 3 2 2 2 5 4 6 +--R (- 560a e - 1120b d e - 560c d e )f + (672b e + 1344c d e )f - 768c e +--R / +--R 5 +-------+ +--R 105f \|f x + e +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1011 + +)clear all + +--S 1012 of 1035 +t0:=(d+e*x)*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R (1) ------------------------------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1035 +r0:=-2/3*(3*c*e^2-c*d*f-b*e*f)*(e+f*x)^(3/2)/f^4+2/5*c*e*(e+f*x)^(5/2)/f^4+_ + 2*(e^2-d*f)*(c*e^2-f*(b*e-a*f))/(f^4*sqrt(e+f*x))-2*(f*(2*b*e^2-_ + b*d*f-a*e*f)-c*(3*e^3-2*d*e*f))*sqrt(e+f*x)/f^4 +--R +--R +--R (2) +--R 3 3 3 2 2 2 +--R 6c e f x + ((10b e + 10c d)f - 12c e f )x +--R + +--R 3 2 2 3 3 +--R ((30a e + 30b d)f + (- 40b e - 40c d e)f + 48c e f)x - 30a d f +--R + +--R 2 2 3 2 4 +--R (60a e + 60b d e)f + (- 80b e - 80c d e )f + 96c e +--R / +--R 4 +-------+ +--R 15f \|f x + e +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1014 + +)clear all + +--S 1015 of 1035 +t0:=(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 2 +--R c x + b x + a +--R (1) ------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1035 +r0:=2/3*c*(e+f*x)^(3/2)/f^3-2*(c*e^2-f*(b*e-a*f))/(f^3*sqrt(e+f*x))-_ + 2*(2*c*e-b*f)*sqrt(e+f*x)/f^3 +--R +--R +--R 2 2 2 2 2 +--R 2c f x + (6b f - 8c e f)x - 6a f + 12b e f - 16c e +--R (2) ------------------------------------------------------ +--R 3 +-------+ +--R 3f \|f x + e +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1017 + +)clear all + +--S 1018 of 1035 +t0:=(a+b*x+c*x^2)/((d+e*x)*(e+f*x)^(3/2)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) -------------------------------------- +--R 2 2 +-------+ +--R (e f x + (d f + e )x + d e)\|f x + e +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1035 +r0:=-2*(c*d^2-b*d*e+a*e^2)*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(3/2))+2*(c*e^2-f*(b*e-a*f))/(f^2*(e^2-d*f)*_ + sqrt(e+f*x))+2*c*sqrt(e+f*x)/(e*f^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-------+ \|e \|f x + e +--R (2a e - 2b d e + 2c d )f \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 2 2 2 2 3 +--R ((2c d f - 2c e f)x - 2a e f + (2b e + 2c d e)f - 4c e ) +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R +----------+ +--R 3 3 2 | 2 +-+ +-------+ +--R (d e f - e f )\|- d f + e \|e \|f x + e +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 1035 +t0:=(a+b*x+c*x^2)/((d+e*x)^2*(e+f*x)^(3/2)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) ----------------------------------------------------------- +--R 2 3 3 2 2 2 2 +-------+ +--R (e f x + (2d e f + e )x + (d f + 2d e )x + d e)\|f x + e +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1035 +r0:=(c*d^2-b*d*e+a*e^2)*f*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(5/2))-2*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/(e^(3/2)*(e^2-d*f)^(5/2))-_ + 2*(c*e^2-f*(b*e-a*f))/(f*(e^2-d*f)^2*sqrt(e+f*x))+(c*d^2-b*d*e+a*e^2)*_ + f*sqrt(e+f*x)/(e*(e^2-d*f)^2*(e^2-d*f-e*(e+f*x))) +--R +--R +--R (2) +--R 3 2 2 2 4 3 +--R ((3a e - b d e - c d e)f + (- 2b e + 4c d e )f)x +--R + +--R 2 2 3 2 3 2 2 +--R (3a d e - b d e - c d )f + (- 2b d e + 4c d e )f +--R * +--R +-+ +-------+ +--R +-------+ \|e \|f x + e +--R \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 2 2 2 3 4 2 +--R ((- 3a e + b d e - c d )f + 2b e f - 2c e )x - 2a d e f +--R + +--R 3 2 2 3 +--R (- a e + 3b d e - c d e)f - 2c d e +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R +----------+ +--R 2 2 3 4 2 6 3 3 2 3 2 5 | 2 +-+ +--R ((d e f - 2d e f + e f)x + d e f - 2d e f + d e f)\|- d f + e \|e +--R * +--R +-------+ +--R \|f x + e +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1023 + +)clear all + +--S 1024 of 1035 +t0:=(a+b*x+c*x^2)/((d+e*x)^3*(e+f*x)^(3/2)) +--R +--R +--R (1) +--R 2 +--R c x + b x + a +--R / +--R 3 4 2 4 3 2 3 2 3 2 2 3 +--R (e f x + (3d e f + e )x + (3d e f + 3d e )x + (d f + 3d e )x + d e) +--R * +--R +-------+ +--R \|f x + e +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1035 +r0:=-3/4*(c*d^2-b*d*e+a*e^2)*f^2*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(7/2))+f*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/(e^(3/2)*(e^2-d*f)^(7/2))-_ + 2*(c*e^2-f*(b*e-a*f))*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))*_ + sqrt(e)/(e^2-d*f)^(7/2)+2*(c*e^2-f*(b*e-a*f))/((e^2-d*f)^3*_ + sqrt(e+f*x))-1/2*(c*d^2-b*d*e+a*e^2)*f^2*sqrt(e+f*x)/(e*(e^2-d*f)^2*_ + (e^2-d*f-e*(e+f*x))^2)-3/4*(c*d^2-b*d*e+a*e^2)*f^2*sqrt(e+f*x)/_ + (e*(e^2-d*f)^3*(e^2-d*f-e*(e+f*x)))+f*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + sqrt(e+f*x)/(e*(e^2-d*f)^3*(e^2-d*f-e*(e+f*x))) +--R +--R +--R (2) +--R 4 3 2 2 2 5 4 6 2 +--R ((15a e - 3b d e - c d e )f + (- 12b e + 8c d e )f + 8c e )x +--R + +--R 3 2 2 3 2 4 2 3 +--R (30a d e - 6b d e - 2c d e)f + (- 24b d e + 16c d e )f +--R + +--R 5 +--R 16c d e +--R * +--R x +--R + +--R 2 2 3 4 2 2 3 3 2 2 4 +--R (15a d e - 3b d e - c d )f + (- 12b d e + 8c d e )f + 8c d e +--R * +--R +-+ +-------+ +--R +-------+ \|e \|f x + e +--R \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 3 2 2 2 4 3 5 2 +--R ((- 15a e + 3b d e + c d e)f + (12b e - 8c d e )f - 8c e )x +--R + +--R 2 2 3 2 4 3 2 2 +--R (- 25a d e + 5b d e - c d )f + (- 5a e + 21b d e - 5c d e )f +--R + +--R 5 4 +--R 4b e - 24c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 5 4 +--R - 8a d e f + (- 9a d e + 13b d e - c d e)f + 2a e + 2b d e +--R + +--R 2 3 +--R - 14c d e +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R 3 3 3 2 5 2 7 9 2 +--R (4d e f - 12d e f + 12d e f - 4e )x +--R + +--R 4 2 3 3 4 2 2 6 8 5 3 4 3 2 3 5 +--R (8d e f - 24d e f + 24d e f - 8d e )x + 4d e f - 12d e f + 12d e f +--R + +--R 2 7 +--R - 4d e +--R * +--R +----------+ +--R | 2 +-+ +-------+ +--R \|- d f + e \|e \|f x + e +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1026 + +)clear all + +--S 1027 of 1035 +t0:=x^m*(1-a^2*x^2)^p/(1+a*x) +--R +--R +--R 2 2 p m +--R (- a x + 1) x +--R (1) --------------- +--R a x + 1 +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1035 +--r0:=x^(1+m)*AppellF1(1+m,-p,1-p,2+m,a*x,-a*x)/(1+m) +--E 1028 + +--S 1029 of 1035 +--d0:=D(m0,x) +--E 1029 + +)clear all + +--S 1030 of 1035 +t0:=sqrt(-1+x)*sqrt(1+x)/(1+x-x^2) +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (1) - ---------------- +--R 2 +--R x - x - 1 +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1035 +r0:=-acosh(x)-atan(sqrt(-1+x)*sqrt(-2+sqrt(5))/sqrt(1+x))*_ + sqrt(2/5*(-1+sqrt(5)))+atanh(sqrt(-1+x)*sqrt(2+sqrt(5))/sqrt(1+x))*_ + sqrt(2/5*(1+sqrt(5))) +--R +--R +--R (2) +--R +--------+ +--R +---------+ +-----+ | +-+ +--R | +-+ \|x - 1 \|\|5 + 2 +--R \|2\|5 + 2 atanh(-------------------) +--R +-----+ +--R \|x + 1 +--R + +--R +--------+ +--R +---------+ +-----+ | +-+ +--R | +-+ \|x - 1 \|\|5 - 2 +-+ +--R - \|2\|5 - 2 atan(-------------------) - \|5 acosh(x) +--R +-----+ +--R \|x + 1 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1035 +--d0:=D(m0,x) +--E 1032 + +)clear all + +--S 1033 of 1035 +t0:=(a+b*x+c*x^2)/(sqrt(d+e*x)*sqrt(f+g*x)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) -------------------- +--R +-------+ +-------+ +--R \|e x + d \|g x + f +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1035 +r0:=-b*(e*f+d*g)*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/_ + (e^(3/2)*g^(3/2))-1/4*c*(4*d*e*f*g-3*(e*f+d*g)^2)*atanh(sqrt(g)*_ + sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/(e^(5/2)*g^(5/2))+2*a*atanh(sqrt(g)*_ + sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/(sqrt(e)*sqrt(g))+b*sqrt(d+e*x)*_ + sqrt(f+g*x)/(e*g)-3/4*c*(e*f+d*g)*sqrt(d+e*x)*sqrt(f+g*x)/(e^2*g^2)+_ + 1/2*c*x*sqrt(d+e*x)*sqrt(f+g*x)/(e*g) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R ((8a e - 4b d e + 3c d )g + (- 4b e + 2c d e)f g + 3c e f ) +--R * +--R +-+ +-------+ +--R \|g \|e x + d +--R atanh(--------------) +--R +-+ +-------+ +--R \|e \|g x + f +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2c e g x + (4b e - 3c d)g - 3c e f)\|e \|g \|e x + d \|g x + f +--R / +--R 2 2 +-+ +-+ +--R 4e g \|e \|g +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1035 +--d0:=D(m0,x) +--E 1035 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 789ea1d..8aa4d5a 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4256,6 +4256,10 @@ src/axiom-website/CATS/rich3c src/axiom-website/CATS/rich4*, src/input/rich4* 20130811.01.tpd.patch src/axiom-website/CATS/rich5,6*, src/input/rich5,6* +20130827.01.tpd.patch +src/axiom-website/CATS/rich*, richder*, src/input/rich* +20131112.01.tpd.patch +src/axiom-website/CATS/rich*, richder*, src/input/rich* diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 77a2b77..17ba9e2 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -465,11 +465,10 @@ NEWRICHTESTSa= rich1a.regress rich1b.regress rich2.regress \ richder6d.regress richder6e.regress -NEWRICHTESTS = rich11a.regress rich11b.regress \ - rich11c.regress rich11d.regress rich11e.regress \ - richder5.regress \ - richder6a.regress richder6b.regress richder6c.regress \ - richder6d.regress richder6e.regress +NEWRICHTESTS = rich12a.regress rich12b.regress rich12c.regress \ + rich12d.regress rich12e.regress rich12f.regress \ + richder12a.regress richder12b.regress richder12c.regress \ + richder12d.regress richder12e.regress richder12f.regress RICHTESTS= \ richalgebraic000-099.regress \ @@ -846,6 +845,9 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/rich11a.input ${OUT}/rich11b.input \ ${OUT}/rich11c.input ${OUT}/rich11d.input \ ${OUT}/rich11e.input \ + ${OUT}/rich12a.input ${OUT}/rich12b.input \ + ${OUT}/rich12c.input ${OUT}/rich12d.input \ + ${OUT}/rich12e.input ${OUT}/rich12f.input \ ${OUT}/richder1a.input ${OUT}/richder1b.input \ ${OUT}/richder2.input ${OUT}/richder3a.input \ ${OUT}/richder3b.input ${OUT}/richder3c.input \ @@ -865,6 +867,9 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richder6a.input ${OUT}/richder6b.input \ ${OUT}/richder6c.input ${OUT}/richder6d.input \ ${OUT}/richder6e.input \ + ${OUT}/richder12a.input ${OUT}/richder12b.input \ + ${OUT}/richder12c.input ${OUT}/richder12d.input \ + ${OUT}/richder12e.input ${OUT}/richder12f.input \ ${OUT}/rk4draw.input \ ${OUT}/r20abugs.input \ ${OUT}/r20bugs.input ${OUT}/r21bugsbig.input \ @@ -1296,6 +1301,9 @@ DOCFILES= \ ${DOC}/rich11a.input.dvi ${DOC}/rich11b.input.dvi \ ${DOC}/rich11c.input.dvi ${DOC}/rich11d.input.dvi \ ${DOC}/rich11e.input.dvi \ + ${DOC}/rich12a.input.dvi ${DOC}/rich12b.input.dvi \ + ${DOC}/rich12c.input.dvi ${DOC}/rich12d.input.dvi \ + ${DOC}/rich12e.input.dvi ${DOC}/rich12f.input.dvi \ ${DOC}/richder1a.input.dvi ${DOC}/richder1b.input.dvi \ ${DOC}/richder2.input.dvi ${DOC}/richder3a.input.dvi \ ${DOC}/richder3b.input.dvi ${DOC}/richder3c.input.dvi \ @@ -1314,6 +1322,9 @@ DOCFILES= \ ${DOC}/richder6a.input.dvi ${DOC}/richder6b.input.dvi \ ${DOC}/richder6c.input.dvi ${DOC}/richder6d.input.dvi \ ${DOC}/richder6e.input.dvi \ + ${DOC}/richder12a.input.dvi ${DOC}/richder12b.input.dvi \ + ${DOC}/richder12c.input.dvi ${DOC}/richder12d.input.dvi \ + ${DOC}/richder12e.input.dvi ${DOC}/richder12f.input.dvi \ ${DOC}/richalgebraic000-099.input.dvi \ ${DOC}/richalgebraic100-199.input.dvi \ ${DOC}/richalgebraic200-299.input.dvi \ diff --git a/src/input/rich12a.input.pamphlet b/src/input/rich12a.input.pamphlet new file mode 100644 index 0000000..2f89471 --- /dev/null +++ b/src/input/rich12a.input.pamphlet @@ -0,0 +1,50704 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 307 matching answers. +\item 0 cases where Axiom answer differs from Rubi +\item 91 cases where Axiom supplied 2 results. +\item 12 cases that Axiom failed to integrate. +\item 31 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12a.output +)spool rich12a.output +)set message test on +)set message auto off +)clear all + + +--S 1 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + A b x)(e x + d) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1457 +r0:=-d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R ((A c + B b)e - 3B c d)m + ((7A c + 7B b)e - 21B c d)m +--R + +--R ((14A c + 14B b)e - 42B c d)m + (8A c + 8B b)e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R (A b e + (- 2A c - 2B b)d e + 3B c d )m +--R + +--R 2 2 2 +--R (8A b e + (- 16A c - 16B b)d e + 24B c d )m +--R + +--R 2 2 2 +--R (19A b e + (- 38A c - 38B b)d e + 57B c d )m + 12A b e +--R + +--R 2 +--R (- 24A c - 24B b)d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 +--R (- A b d e + (A c + B b)d e - B c d )m +--R + +--R 2 2 3 2 +--R (- 9A b d e + (9A c + 9B b)d e - 9B c d )m +--R + +--R 2 2 3 2 +--R (- 26A b d e + (26A c + 26B b)d e - 26B c d )m - 24A b d e +--R + +--R 2 3 +--R (24A c + 24B b)d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R ((A c + B b)e + B c d e )m + ((7A c + 7B b)e + 3B c d e )m +--R + +--R 4 3 4 +--R ((14A c + 14B b)e + 2B c d e )m + (8A c + 8B b)e +--R * +--R 3 +--R x +--R + +--R 4 3 3 +--R (A b e + (A c + B b)d e )m +--R + +--R 4 3 2 2 2 +--R (8A b e + (5A c + 5B b)d e - 3B c d e )m +--R + +--R 4 3 2 2 4 +--R (19A b e + (4A c + 4B b)d e - 3B c d e )m + 12A b e +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 2 2 +--R A b d e m + (7A b d e + (- 2A c - 2B b)d e )m +--R + +--R 3 2 2 3 +--R (12A b d e + (- 8A c - 8B b)d e + 6B c d e)m +--R * +--R x +--R + +--R 2 2 2 2 2 3 2 2 +--R - A b d e m + (- 7A b d e + (2A c + 2B b)d e)m - 12A b d e +--R + +--R 3 4 +--R (8A c + 8B b)d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R ((A c + B b)e + B c d e )m + ((7A c + 7B b)e + 3B c d e )m +--R + +--R 4 3 4 +--R ((14A c + 14B b)e + 2B c d e )m + (8A c + 8B b)e +--R * +--R 3 +--R x +--R + +--R 4 3 3 +--R (A b e + (A c + B b)d e )m +--R + +--R 4 3 2 2 2 +--R (8A b e + (5A c + 5B b)d e - 3B c d e )m +--R + +--R 4 3 2 2 4 +--R (19A b e + (4A c + 4B b)d e - 3B c d e )m + 12A b e +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 2 2 +--R A b d e m + (7A b d e + (- 2A c - 2B b)d e )m +--R + +--R 3 2 2 3 +--R (12A b d e + (- 8A c - 8B b)d e + 6B c d e)m +--R * +--R x +--R + +--R 2 2 2 2 2 3 2 2 +--R - A b d e m + (- 7A b d e + (2A c + 2B b)d e)m - 12A b d e +--R + +--R 3 4 +--R (8A c + 8B b)d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 2 m + 4 +--R (- B c m - 6B c m - 11B c m - 6B c)(e x + d) +--R + +--R 3 2 +--R ((- A c - B b)e + 3B c d)m + ((- 7A c - 7B b)e + 21B c d)m +--R + +--R ((- 14A c - 14B b)e + 42B c d)m + (- 8A c - 8B b)e + 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R (- A b e + (2A c + 2B b)d e - 3B c d )m +--R + +--R 2 2 2 +--R (- 8A b e + (16A c + 16B b)d e - 24B c d )m +--R + +--R 2 2 2 +--R (- 19A b e + (38A c + 38B b)d e - 57B c d )m - 12A b e +--R + +--R 2 +--R (24A c + 24B b)d e - 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 +--R (A b d e + (- A c - B b)d e + B c d )m +--R + +--R 2 2 3 2 +--R (9A b d e + (- 9A c - 9B b)d e + 9B c d )m +--R + +--R 2 2 3 2 +--R (26A b d e + (- 26A c - 26B b)d e + 26B c d )m + 24A b d e +--R + +--R 2 3 +--R (- 24A c - 24B b)d e + 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1457 +t0:=(A+B*x)*(d+e*x)^5*(b*x+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 +--R B c e x + ((A c + B b)e + 5B c d e )x +--R + +--R 5 4 2 3 6 +--R (A b e + (5A c + 5B b)d e + 10B c d e )x +--R + +--R 4 2 3 3 2 5 +--R (5A b d e + (10A c + 10B b)d e + 10B c d e )x +--R + +--R 2 3 3 2 4 4 +--R (10A b d e + (10A c + 10B b)d e + 5B c d e)x +--R + +--R 3 2 4 5 3 4 5 2 +--R (10A b d e + (5A c + 5B b)d e + B c d )x + (5A b d e + (A c + B b)d )x +--R + +--R 5 +--R A b d x +--R Type: Polynomial(Integer) +--E 6 + +--S 7 of 1457 +r0:=-1/6*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^6/e^4+1/7*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^7/e^4-1/8*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^8/e^4+_ + 1/9*B*c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 1 9 5 8 8 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 9 8 8 8 +--R + +--R 1 9 5 5 8 10 2 7 7 +--R (- A b e + (- A c + - B b)d e + -- B c d e )x +--R 7 7 7 7 +--R + +--R 5 8 5 5 2 7 5 3 6 6 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 6 3 3 3 +--R + +--R 2 7 3 6 4 5 5 +--R (2A b d e + (2A c + 2B b)d e + B c d e )x +--R + +--R 5 3 6 5 5 4 5 1 5 4 4 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 2 4 4 4 +--R + +--R 5 4 5 1 1 5 4 3 1 5 4 2 1 7 2 +--R (- A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 3 2 42 +--R + +--R 1 1 8 1 9 +--R (--- A c + --- B b)d e - --- B c d +--R 168 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 7 + +--S 8 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 9 1 1 5 5 4 8 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 9 8 8 8 +--R + +--R 1 5 5 5 4 10 2 3 7 +--R (- A b e + (- A c + - B b)d e + -- B c d e )x +--R 7 7 7 7 +--R + +--R 5 4 5 5 2 3 5 3 2 6 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 6 3 3 3 +--R + +--R 2 3 3 2 4 5 +--R (2A b d e + (2A c + 2B b)d e + B c d e)x +--R + +--R 5 3 2 5 5 4 1 5 4 +--R (- A b d e + (- A c + - B b)d e + - B c d )x +--R 2 4 4 4 +--R + +--R 5 4 1 1 5 3 1 5 2 +--R (- A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 1457 +m0:=a0-r0 +--R +--R +--R 1 7 2 1 1 8 1 9 +--R -- A b d e + (- --- A c - --- B b)d e + --- B c d +--R 42 168 168 504 +--R (4) --------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 9 + +--S 10 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 10 + +)clear all + +--S 11 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 +--R B c e x + ((A c + B b)e + 4B c d e )x +--R + +--R 4 3 2 2 5 +--R (A b e + (4A c + 4B b)d e + 6B c d e )x +--R + +--R 3 2 2 3 4 +--R (4A b d e + (6A c + 6B b)d e + 4B c d e)x +--R + +--R 2 2 3 4 3 3 4 2 +--R (6A b d e + (4A c + 4B b)d e + B c d )x + (4A b d e + (A c + B b)d )x +--R + +--R 4 +--R A b d x +--R Type: Polynomial(Integer) +--E 11 + +--S 12 of 1457 +r0:=-1/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^5/e^4+1/6*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^7/e^4+_ + 1/8*B*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 1 8 4 7 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 8 2 2 7 2 6 6 +--R (- A b e + (- A c + - B b)d e + B c d e )x +--R 6 3 3 +--R + +--R 4 7 6 6 2 6 4 3 5 5 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 3 2 6 3 5 1 4 4 4 +--R (- A b d e + (A c + B b)d e + - B c d e )x +--R 2 4 +--R + +--R 4 3 5 1 1 4 4 3 1 4 4 2 1 6 2 +--R (- A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 3 2 30 +--R + +--R 1 1 7 1 8 +--R (--- A c + --- B b)d e - --- B c d +--R 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 12 + +--S 13 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 8 1 1 4 4 3 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 4 2 2 3 2 2 6 +--R (- A b e + (- A c + - B b)d e + B c d e )x +--R 6 3 3 +--R + +--R 4 3 6 6 2 2 4 3 5 +--R (- A b d e + (- A c + - B b)d e + - B c d e)x +--R 5 5 5 5 +--R + +--R 3 2 2 3 1 4 4 +--R (- A b d e + (A c + B b)d e + - B c d )x +--R 2 4 +--R + +--R 4 3 1 1 4 3 1 4 2 +--R (- A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 1457 +m0:=a0-r0 +--R +--R +--R 1 6 2 1 1 7 1 8 +--R -- A b d e + (- --- A c - --- B b)d e + --- B c d +--R 30 105 105 280 +--R (4) --------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 14 + +--S 15 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 15 + +)clear all + +--S 16 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R (A b e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 2 2 3 3 2 3 2 +--R (3A b d e + (3A c + 3B b)d e + B c d )x + (3A b d e + (A c + B b)d )x +--R + +--R 3 +--R A b d x +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 1457 +r0:=-1/4*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^4/e^4+1/5*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^6/e^4+_ + 1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 1 7 1 6 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 7 3 3 6 3 2 5 5 +--R (- A b e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 3 6 3 3 2 5 1 3 4 4 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 2 5 1 1 3 4 3 1 3 4 2 1 5 2 +--R (A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 2 20 +--R + +--R 1 1 6 1 7 +--R (-- A c + -- B b)d e - --- B c d +--R 60 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 17 + +--S 18 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 7 1 1 3 1 2 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 3 3 3 2 3 2 5 +--R (- A b e + (- A c + - B b)d e + - B c d e)x +--R 5 5 5 5 +--R + +--R 3 2 3 3 2 1 3 4 +--R (- A b d e + (- A c + - B b)d e + - B c d )x +--R 4 4 4 4 +--R + +--R 2 1 1 3 3 1 3 2 +--R (A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 1457 +m0:=a0-r0 +--R +--R +--R 1 5 2 1 1 6 1 7 +--R -- A b d e + (- -- A c - -- B b)d e + --- B c d +--R 20 60 60 140 +--R (4) ------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 19 + +--S 20 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 20 + +)clear all + +--S 21 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 1457 +r0:=1/2*A*b*d^2*x^2+1/3*d*(b*B*d+A*c*d+2*A*b*e)*x^3+1/4*(A*e*(2*c*d+b*e)+_ + B*d*(c*d+2*b*e))*x^4+1/5*e*(2*B*c*d+b*B*e+A*c*e)*x^5+1/6*B*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 1 2 2 5 +--R - B c e x + ((- A c + - B b)e + - B c d e)x +--R 6 5 5 5 +--R + +--R 1 2 1 1 1 2 4 +--R (- A b e + (- A c + - B b)d e + - B c d )x +--R 4 2 2 4 +--R + +--R 2 1 1 2 3 1 2 2 +--R (- A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 6 1 1 2 2 5 +--R - B c e x + ((- A c + - B b)e + - B c d e)x +--R 6 5 5 5 +--R + +--R 1 2 1 1 1 2 4 +--R (- A b e + (- A c + - B b)d e + - B c d )x +--R 4 2 2 4 +--R + +--R 2 1 1 2 3 1 2 2 +--R (- A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 1457 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 1457 +r0:=1/2*A*b*d*x^2+1/3*(b*B*d+A*c*d+A*b*e)*x^3+1/4*(B*c*d+b*B*e+A*c*e)*x^4+_ + 1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 3 1 2 +--R (- A b e + (- A c + - B b)d)x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 3 1 2 +--R (- A b e + (- A c + - B b)d)x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 1457 +t0:=(A+B*x)*(b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + (A c + B b)x + A b x +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 1457 +r0:=1/2*A*b*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 1 3 1 2 +--R (2) - B c x + (- A c + - B b)x + - A b x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 1457 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 1 3 1 2 +--R (3) - B c x + (- A c + - B b)x + - A b x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1457 +r0:=(B*d-A*e)*(c*d-b*e)*x/e^3-1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+_ + 1/3*B*c*x^3/e-d*(B*d-A*e)*(c*d-b*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 2 3 3 3 +--R (- 6A b d e + (6A c + 6B b)d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 +--R ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R (6A b e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 3 +--R (- 6A b d e + (6A c + 6B b)d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 +--R ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R (6A b e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1457 +r0:=-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+d*(B*d-A*e)*_ + (c*d-b*e)/(e^4*(d+e*x))+(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 +--R (2A b e + (- 4A c - 4B b)d e + 6B c d e)x + 2A b d e +--R + +--R 2 3 +--R (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 2 2 3 +--R ((2A c + 2B b)d e - 4B c d e)x + 2A b d e + (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 +--R (2A b e + (- 4A c - 4B b)d e + 6B c d e)x + 2A b d e +--R + +--R 2 3 +--R (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 2 2 3 +--R ((2A c + 2B b)d e - 4B c d e)x + 2A b d e + (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1457 +r0:=B*c*x/e^3+1/2*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^2)+(-B*d*(3*c*d-_ + 2*b*e)+A*e*(2*c*d-b*e))/(e^4*(d+e*x))-(3*B*c*d-b*B*e-A*c*e)*log(d+_ + e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 +--R 2B c e x + 4B c d e x + (- 2A b e + (4A c + 4B b)d e - 4B c d e)x +--R + +--R 2 2 3 +--R - A b d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 +--R 2B c e x + 4B c d e x + (- 2A b e + (4A c + 4B b)d e - 4B c d e)x +--R + +--R 2 2 3 +--R - A b d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1457 +r0:=1/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^3)+1/2*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^2)+(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+_ + B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 2 +--R (- 3A b e + (- 6A c - 6B b)d e + 27B c d e)x - A b d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 2 +--R (- 3A b e + (- 6A c - 6B b)d e + 27B c d e)x - A b d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 1457 +r0:=1/4*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^4)+1/3*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^2)-B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 1 3 3 2 2 +--R - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 2 2 +--R + +--R 1 3 1 1 2 2 1 2 +--R (- - A b e + (- - A c - - B b)d e - B c d e)x - -- A b d e +--R 3 3 3 12 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - - B c d +--R 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 57 + +--S 58 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 12B c e x + ((- 6A c - 6B b)e - 18B c d e )x +--R + +--R 3 2 2 2 +--R (- 4A b e + (- 4A c - 4B b)d e - 12B c d e)x - A b d e +--R + +--R 2 3 +--R (- A c - B b)d e - 3B c d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 1457 +r0:=1/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^5)+1/4*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 3 3 2 +--R + +--R 1 3 1 1 2 1 2 1 2 +--R (- - A b e + (- - A c - - B b)d e - - B c d e)x - -- A b d e +--R 4 6 6 4 20 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - -- B c d +--R 30 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 30B c e x + ((- 20A c - 20B b)e - 30B c d e )x +--R + +--R 3 2 2 2 +--R (- 15A b e + (- 10A c - 10B b)d e - 15B c d e)x - 3A b d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e - 3B c d +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 1457 +r0:=1/6*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^6)+1/5*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^5)+1/4*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 3 4 4 4 +--R + +--R 1 3 1 1 2 1 2 1 2 +--R (- - A b e + (- -- A c - -- B b)d e - -- B c d e)x - -- A b d e +--R 5 10 10 10 30 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - -- B c d +--R 60 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 67 + +--S 68 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 20B c e x + ((- 15A c - 15B b)e - 15B c d e )x +--R + +--R 3 2 2 2 +--R (- 12A b e + (- 6A c - 6B b)d e - 6B c d e)x - 2A b d e +--R + +--R 2 3 +--R (- A c - B b)d e - B c d +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 4 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 m +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )(e x + d) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1457 +r0:=-d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(1+m)/(e^6*(1+m))+d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^6*(2+m))+_ + (A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(4+m)/(e^6*(4+m))-_ + c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*_ + (d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((A c + 2B b c)e - 5B c d)m + ((16A c + 32B b c)e - 80B c d)m +--R + +--R 2 2 3 +--R ((95A c + 190B b c)e - 475B c d)m +--R + +--R 2 2 2 +--R ((260A c + 520B b c)e - 1300B c d)m +--R + +--R 2 2 2 2 +--R ((324A c + 648B b c)e - 1620B c d)m + (144A c + 288B b c)e - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (- 4A c - 8B b c)d e + 10B c d )m +--R + +--R 2 2 2 2 2 4 +--R ((34A b c + 17B b )e + (- 68A c - 136B b c)d e + 170B c d )m +--R + +--R 2 2 2 2 2 3 +--R ((214A b c + 107B b )e + (- 428A c - 856B b c)d e + 1070B c d )m +--R + +--R 2 2 2 2 2 2 +--R ((614A b c + 307B b )e + (- 1228A c - 2456B b c)d e + 3070B c d )m +--R + +--R 2 2 2 2 2 +--R ((792A b c + 396B b )e + (- 1584A c - 3168B b c)d e + 3960B c d )m +--R + +--R 2 2 2 2 2 +--R (360A b c + 180B b )e + (- 720A c - 1440B b c)d e + 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (- 6A b c - 3B b )d e + (6A c + 12B b c)d e - 10B c d )m +--R + +--R 2 3 2 2 2 2 +--R 18A b e + (- 108A b c - 54B b )d e + (108A c + 216B b c)d e +--R + +--R 2 3 +--R - 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 2 2 +--R 121A b e + (- 726A b c - 363B b )d e + (726A c + 1452B b c)d e +--R + +--R 2 3 +--R - 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 +--R 372A b e + (- 2232A b c - 1116B b )d e +--R + +--R 2 2 2 3 +--R (2232A c + 4464B b c)d e - 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 +--R 508A b e + (- 3048A b c - 1524B b )d e +--R + +--R 2 2 2 3 +--R (3048A c + 6096B b c)d e - 5080B c d +--R * +--R m +--R + +--R 2 3 2 2 2 2 +--R 240A b e + (- 1440A b c - 720B b )d e + (1440A c + 2880B b c)d e +--R + +--R 2 3 +--R - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 3 +--R - 2A b d e + (6A b c + 3B b )d e + (- 4A c - 8B b c)d e +--R + +--R 2 4 +--R 5B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 2 2 2 3 +--R - 38A b d e + (114A b c + 57B b )d e + (- 76A c - 152B b c)d e +--R + +--R 2 4 +--R 95B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 2 +--R - 274A b d e + (822A b c + 411B b )d e +--R + +--R 2 3 2 4 +--R (- 548A c - 1096B b c)d e + 685B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 2 +--R - 922A b d e + (2766A b c + 1383B b )d e +--R + +--R 2 3 2 4 +--R (- 1844A c - 3688B b c)d e + 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 +--R - 1404A b d e + (4212A b c + 2106B b )d e +--R + +--R 2 3 2 4 +--R (- 2808A c - 5616B b c)d e + 3510B c d +--R * +--R m +--R + +--R 2 3 2 2 2 +--R - 720A b d e + (2160A b c + 1080B b )d e +--R + +--R 2 3 2 4 +--R (- 1440A c - 2880B b c)d e + 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 2 3 2 2 4 2 5 5 +--R (A b d e + (- 2A b c - B b )d e + (A c + 2B b c)d e - B c d )m +--R + +--R 2 2 3 2 3 2 2 4 +--R 20A b d e + (- 40A b c - 20B b )d e + (20A c + 40B b c)d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 2 3 2 3 2 +--R 155A b d e + (- 310A b c - 155B b )d e +--R + +--R 2 4 2 5 +--R (155A c + 310B b c)d e - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 2 3 2 3 2 +--R 580A b d e + (- 1160A b c - 580B b )d e +--R + +--R 2 4 2 5 +--R (580A c + 1160B b c)d e - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 2 3 2 3 2 +--R 1044A b d e + (- 2088A b c - 1044B b )d e +--R + +--R 2 4 2 5 +--R (1044A c + 2088B b c)d e - 1044B c d +--R * +--R m +--R + +--R 2 2 3 2 3 2 2 4 +--R 720A b d e + (- 1440A b c - 720B b )d e + (720A c + 1440B b c)d e +--R + +--R 2 5 +--R - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 +--R ((A c + 2B b c)e + B c d e )m +--R + +--R 2 6 2 5 4 +--R ((16A c + 32B b c)e + 10B c d e )m +--R + +--R 2 6 2 5 3 +--R ((95A c + 190B b c)e + 35B c d e )m +--R + +--R 2 6 2 5 2 +--R ((260A c + 520B b c)e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R ((324A c + 648B b c)e + 24B c d e )m + (144A c + 288B b c)e +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A b c + B b )e + (A c + 2B b c)d e )m +--R + +--R 2 6 2 5 2 2 4 4 +--R ((34A b c + 17B b )e + (12A c + 24B b c)d e - 5B c d e )m +--R + +--R 2 6 2 5 2 2 4 3 +--R ((214A b c + 107B b )e + (47A c + 94B b c)d e - 30B c d e )m +--R + +--R 2 6 2 5 2 2 4 2 +--R ((614A b c + 307B b )e + (72A c + 144B b c)d e - 55B c d e )m +--R + +--R 2 6 2 5 2 2 4 +--R ((792A b c + 396B b )e + (36A c + 72B b c)d e - 30B c d e )m +--R + +--R 2 6 +--R (360A b c + 180B b )e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 5 +--R (A b e + (2A b c + B b )d e )m +--R + +--R 2 6 2 5 2 2 4 4 +--R (18A b e + (28A b c + 14B b )d e + (- 4A c - 8B b c)d e )m +--R + +--R 2 6 2 5 2 2 4 +--R 121A b e + (130A b c + 65B b )d e + (- 36A c - 72B b c)d e +--R + +--R 2 3 3 +--R 20B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R 372A b e + (224A b c + 112B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 80A c - 160B b c)d e + 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 2 2 4 +--R 508A b e + (120A b c + 60B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 3 3 +--R 40B c d e +--R * +--R m +--R + +--R 2 6 +--R 240A b e +--R * +--R 3 +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A b d e m + (16A b d e + (- 6A b c - 3B b )d e )m +--R + +--R 2 5 2 2 4 2 3 3 3 +--R (89A b d e + (- 72A b c - 36B b )d e + (12A c + 24B b c)d e )m +--R + +--R 2 5 2 2 4 +--R 194A b d e + (- 246A b c - 123B b )d e +--R + +--R 2 3 3 2 4 2 +--R (84A c + 168B b c)d e - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 120A b d e + (- 180A b c - 90B b )d e +--R + +--R 2 3 3 2 4 2 +--R (72A c + 144B b c)d e - 60B c d e +--R * +--R m +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 4 2 3 3 3 +--R - 2A b d e m + (- 30A b d e + (12A b c + 6B b )d e )m +--R + +--R 2 2 4 2 3 3 +--R - 148A b d e + (132A b c + 66B b )d e +--R + +--R 2 4 2 +--R (- 24A c - 48B b c)d e +--R * +--R 2 +--R m +--R + +--R 2 2 4 2 3 3 +--R - 240A b d e + (360A b c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 144A c - 288B b c)d e + 120B c d e +--R * +--R m +--R * +--R x +--R + +--R 2 3 3 3 2 3 3 2 4 2 2 +--R 2A b d e m + (30A b d e + (- 12A b c - 6B b )d e )m +--R + +--R 2 3 3 2 4 2 2 5 +--R (148A b d e + (- 132A b c - 66B b )d e + (24A c + 48B b c)d e)m +--R + +--R 2 3 3 2 4 2 2 5 +--R 240A b d e + (- 360A b c - 180B b )d e + (144A c + 288B b c)d e +--R + +--R 2 6 +--R - 120B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 +--R ((A c + 2B b c)e + B c d e )m +--R + +--R 2 6 2 5 4 +--R ((16A c + 32B b c)e + 10B c d e )m +--R + +--R 2 6 2 5 3 +--R ((95A c + 190B b c)e + 35B c d e )m +--R + +--R 2 6 2 5 2 +--R ((260A c + 520B b c)e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R ((324A c + 648B b c)e + 24B c d e )m + (144A c + 288B b c)e +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A b c + B b )e + (A c + 2B b c)d e )m +--R + +--R 2 6 2 5 2 2 4 4 +--R ((34A b c + 17B b )e + (12A c + 24B b c)d e - 5B c d e )m +--R + +--R 2 6 2 5 2 2 4 3 +--R ((214A b c + 107B b )e + (47A c + 94B b c)d e - 30B c d e )m +--R + +--R 2 6 2 5 2 2 4 2 +--R ((614A b c + 307B b )e + (72A c + 144B b c)d e - 55B c d e )m +--R + +--R 2 6 2 5 2 2 4 +--R ((792A b c + 396B b )e + (36A c + 72B b c)d e - 30B c d e )m +--R + +--R 2 6 +--R (360A b c + 180B b )e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 5 +--R (A b e + (2A b c + B b )d e )m +--R + +--R 2 6 2 5 2 2 4 4 +--R (18A b e + (28A b c + 14B b )d e + (- 4A c - 8B b c)d e )m +--R + +--R 2 6 2 5 +--R 121A b e + (130A b c + 65B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 36A c - 72B b c)d e + 20B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R 372A b e + (224A b c + 112B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 80A c - 160B b c)d e + 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R 508A b e + (120A b c + 60B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 48A c - 96B b c)d e + 40B c d e +--R * +--R m +--R + +--R 2 6 +--R 240A b e +--R * +--R 3 +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A b d e m + (16A b d e + (- 6A b c - 3B b )d e )m +--R + +--R 2 5 2 2 4 +--R 89A b d e + (- 72A b c - 36B b )d e +--R + +--R 2 3 3 +--R (12A c + 24B b c)d e +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 +--R 194A b d e + (- 246A b c - 123B b )d e +--R + +--R 2 3 3 2 4 2 +--R (84A c + 168B b c)d e - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 120A b d e + (- 180A b c - 90B b )d e +--R + +--R 2 3 3 2 4 2 +--R (72A c + 144B b c)d e - 60B c d e +--R * +--R m +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 4 2 3 3 3 +--R - 2A b d e m + (- 30A b d e + (12A b c + 6B b )d e )m +--R + +--R 2 2 4 2 3 3 +--R - 148A b d e + (132A b c + 66B b )d e +--R + +--R 2 4 2 +--R (- 24A c - 48B b c)d e +--R * +--R 2 +--R m +--R + +--R 2 2 4 2 3 3 +--R - 240A b d e + (360A b c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 144A c - 288B b c)d e + 120B c d e +--R * +--R m +--R * +--R x +--R + +--R 2 3 3 3 2 3 3 2 4 2 2 +--R 2A b d e m + (30A b d e + (- 12A b c - 6B b )d e )m +--R + +--R 2 3 3 2 4 2 2 5 +--R (148A b d e + (- 132A b c - 66B b )d e + (24A c + 48B b c)d e)m +--R + +--R 2 3 3 2 4 2 2 5 +--R 240A b d e + (- 360A b c - 180B b )d e + (144A c + 288B b c)d e +--R + +--R 2 6 +--R - 120B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (- B c m - 15B c m - 85B c m - 225B c m - 274B c m - 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((- A c - 2B b c)e + 5B c d)m + ((- 16A c - 32B b c)e + 80B c d)m +--R + +--R 2 2 3 +--R ((- 95A c - 190B b c)e + 475B c d)m +--R + +--R 2 2 2 +--R ((- 260A c - 520B b c)e + 1300B c d)m +--R + +--R 2 2 2 +--R ((- 324A c - 648B b c)e + 1620B c d)m + (- 144A c - 288B b c)e +--R + +--R 2 +--R 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R ((- 2A b c - B b )e + (4A c + 8B b c)d e - 10B c d )m +--R + +--R 2 2 2 2 2 4 +--R ((- 34A b c - 17B b )e + (68A c + 136B b c)d e - 170B c d )m +--R + +--R 2 2 2 2 2 3 +--R ((- 214A b c - 107B b )e + (428A c + 856B b c)d e - 1070B c d )m +--R + +--R 2 2 2 2 2 2 +--R ((- 614A b c - 307B b )e + (1228A c + 2456B b c)d e - 3070B c d )m +--R + +--R 2 2 2 2 2 +--R ((- 792A b c - 396B b )e + (1584A c + 3168B b c)d e - 3960B c d )m +--R + +--R 2 2 2 2 2 +--R (- 360A b c - 180B b )e + (720A c + 1440B b c)d e - 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 +--R - A b e + (6A b c + 3B b )d e + (- 6A c - 12B b c)d e +--R + +--R 2 3 +--R 10B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 2 2 2 +--R - 18A b e + (108A b c + 54B b )d e + (- 108A c - 216B b c)d e +--R + +--R 2 3 +--R 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 +--R - 121A b e + (726A b c + 363B b )d e +--R + +--R 2 2 2 3 +--R (- 726A c - 1452B b c)d e + 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 +--R - 372A b e + (2232A b c + 1116B b )d e +--R + +--R 2 2 2 3 +--R (- 2232A c - 4464B b c)d e + 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 +--R - 508A b e + (3048A b c + 1524B b )d e +--R + +--R 2 2 2 3 +--R (- 3048A c - 6096B b c)d e + 5080B c d +--R * +--R m +--R + +--R 2 3 2 2 2 2 +--R - 240A b e + (1440A b c + 720B b )d e + (- 1440A c - 2880B b c)d e +--R + +--R 2 3 +--R 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 3 +--R 2A b d e + (- 6A b c - 3B b )d e + (4A c + 8B b c)d e +--R + +--R 2 4 +--R - 5B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 2 2 2 3 +--R 38A b d e + (- 114A b c - 57B b )d e + (76A c + 152B b c)d e +--R + +--R 2 4 +--R - 95B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 2 +--R 274A b d e + (- 822A b c - 411B b )d e +--R + +--R 2 3 2 4 +--R (548A c + 1096B b c)d e - 685B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 2 +--R 922A b d e + (- 2766A b c - 1383B b )d e +--R + +--R 2 3 2 4 +--R (1844A c + 3688B b c)d e - 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 +--R 1404A b d e + (- 4212A b c - 2106B b )d e +--R + +--R 2 3 2 4 +--R (2808A c + 5616B b c)d e - 3510B c d +--R * +--R m +--R + +--R 2 3 2 2 2 +--R 720A b d e + (- 2160A b c - 1080B b )d e +--R + +--R 2 3 2 4 +--R (1440A c + 2880B b c)d e - 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 2 3 2 2 4 2 5 5 +--R (- A b d e + (2A b c + B b )d e + (- A c - 2B b c)d e + B c d )m +--R + +--R 2 2 3 2 3 2 2 4 +--R - 20A b d e + (40A b c + 20B b )d e + (- 20A c - 40B b c)d e +--R + +--R 2 5 +--R 20B c d +--R * +--R 4 +--R m +--R + +--R 2 2 3 2 3 2 +--R - 155A b d e + (310A b c + 155B b )d e +--R + +--R 2 4 2 5 +--R (- 155A c - 310B b c)d e + 155B c d +--R * +--R 3 +--R m +--R + +--R 2 2 3 2 3 2 +--R - 580A b d e + (1160A b c + 580B b )d e +--R + +--R 2 4 2 5 +--R (- 580A c - 1160B b c)d e + 580B c d +--R * +--R 2 +--R m +--R + +--R 2 2 3 2 3 2 +--R - 1044A b d e + (2088A b c + 1044B b )d e +--R + +--R 2 4 2 5 +--R (- 1044A c - 2088B b c)d e + 1044B c d +--R * +--R m +--R + +--R 2 2 3 2 3 2 +--R - 720A b d e + (1440A b c + 720B b )d e +--R + +--R 2 4 2 5 +--R (- 720A c - 1440B b c)d e + 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 +--R B c e x + ((A c + 2B b c)e + 4B c d e )x +--R + +--R 2 4 2 3 2 2 2 7 +--R ((2A b c + B b )e + (4A c + 8B b c)d e + 6B c d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 6 +--R (A b e + (8A b c + 4B b )d e + (6A c + 12B b c)d e + 4B c d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 5 +--R (4A b d e + (12A b c + 6B b )d e + (4A c + 8B b c)d e + B c d )x +--R + +--R 2 2 2 2 3 2 4 4 +--R (6A b d e + (8A b c + 4B b )d e + (A c + 2B b c)d )x +--R + +--R 2 3 2 4 3 2 4 2 +--R (4A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 1457 +r0:=-1/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^5/e^6+1/6*d*(c*d-b*e)*(B*d*_ + (5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^6/e^6+1/7*(A*e*(6*c^2*d^2-_ + 6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^7/e^6-1/8*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+_ + b^2*e^2))*(d+e*x)^8/e^6-1/9*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^9/e^6+1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 2 10 4 2 9 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 2 10 1 2 9 3 2 2 8 8 +--R ((- A b c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 8 2 4 +--R + +--R 1 2 10 8 4 2 9 6 2 12 2 8 +--R - A b e + (- A b c + - B b )d e + (- A c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 4 2 3 7 +--R - B c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 2 2 9 2 2 8 2 2 4 3 7 +--R - A b d e + (2A b c + B b )d e + (- A c + - B b c)d e +--R 3 3 3 +--R + +--R 1 2 4 6 +--R - B c d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 6 2 2 8 8 4 2 3 7 1 2 2 4 6 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d e )x +--R 5 5 5 5 5 +--R + +--R 2 3 7 1 1 2 4 6 4 1 2 4 6 3 1 2 7 3 +--R (A b d e + (- A b c + - B b )d e )x + - A b d e x + --- A b d e +--R 2 4 3 105 +--R + +--R 1 1 2 8 2 1 2 1 9 1 2 10 +--R (- --- A b c - --- B b )d e + (--- A c + --- B b c)d e - ---- B c d +--R 140 280 630 315 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 10 1 2 2 4 4 2 3 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 2 4 1 2 3 3 2 2 2 8 +--R ((- A b c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 8 2 4 +--R + +--R 1 2 4 8 4 2 3 6 2 12 2 2 4 2 3 7 +--R (- A b e + (- A b c + - B b )d e + (- A c + -- B b c)d e + - B c d e)x +--R 7 7 7 7 7 7 +--R + +--R 2 2 3 2 2 2 2 2 4 3 1 2 4 6 +--R (- A b d e + (2A b c + B b )d e + (- A c + - B b c)d e + - B c d )x +--R 3 3 3 6 +--R + +--R 6 2 2 2 8 4 2 3 1 2 2 4 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 2 3 1 1 2 4 4 1 2 4 3 +--R (A b d e + (- A b c + - B b )d )x + - A b d x +--R 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 78 + +--S 79 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 7 3 1 1 2 8 2 1 2 1 9 +--R - --- A b d e + (--- A b c + --- B b )d e + (- --- A c - --- B b c)d e +--R 105 140 280 630 315 +--R + +--R 1 2 10 +--R ---- B c d +--R 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 79 + +--S 80 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 80 + +)clear all + +--S 81 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R ((2A b c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (6A b c + 3B b )d e + (3A c + 6B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 3 4 +--R (3A b d e + (6A b c + 3B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 3 2 3 2 +--R (3A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 81 + +--S 82 of 1457 +r0:=1/3*A*b^2*d^3*x^3+1/4*b*d^2*(b*B*d+2*A*c*d+3*A*b*e)*x^4+1/5*d*(A*c^2*_ + d^2+3*b^2*e*(B*d+A*e)+2*b*c*d*(B*d+3*A*e))*x^5+1/6*(A*e*(3*c^2*d^2+_ + 6*b*c*d*e+b^2*e^2)+B*d*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^6+1/7*e*_ + (A*c*e*(3*c*d+2*b*e)+B*(3*c^2*d^2+6*b*c*d*e+b^2*e^2))*x^7+_ + 1/8*c*e^2*(3*B*c*d+2*b*B*e+A*c*e)*x^8+1/9*B*c^2*e^3*x^9 +--R +--R +--R (2) +--R 1 2 3 9 1 2 1 3 3 2 2 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 3 3 2 6 2 3 2 2 7 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d e)x +--R 7 7 7 7 7 +--R + +--R 1 2 3 1 2 2 1 2 2 1 2 3 6 +--R (- A b e + (A b c + - B b )d e + (- A c + B b c)d e + - B c d )x +--R 6 2 2 6 +--R + +--R 3 2 2 6 3 2 2 1 2 2 3 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 3 2 2 1 1 2 3 4 1 2 3 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 82 + +--S 83 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 3 9 1 2 1 3 3 2 2 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 3 3 2 6 2 3 2 2 7 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d e)x +--R 7 7 7 7 7 +--R + +--R 1 2 3 1 2 2 1 2 2 1 2 3 6 +--R (- A b e + (A b c + - B b )d e + (- A c + B b c)d e + - B c d )x +--R 6 2 2 6 +--R + +--R 3 2 2 6 3 2 2 1 2 2 3 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 3 2 2 1 1 2 3 4 1 2 3 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 84 + +--S 85 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +)clear all + +--S 86 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 86 + +--S 87 of 1457 +r0:=1/3*A*b^2*d^2*x^3+1/4*b*d*(b*B*d+2*A*c*d+2*A*b*e)*x^4+1/5*(A*c^2*d^2+_ + b^2*e*(2*B*d+A*e)+2*b*c*d*(B*d+2*A*e))*x^5+1/6*(2*A*c*e*(c*d+b*e)+_ + B*(c^2*d^2+4*b*c*d*e+b^2*e^2))*x^6+1/7*c*e*(A*c*e+2*B*(c*d+b*e))*_ + x^7+1/8*B*c^2*e^2*x^8 +--R +--R +--R (2) +--R 1 2 2 8 1 2 2 2 2 2 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e)x +--R 8 7 7 7 +--R + +--R 1 1 2 2 1 2 2 1 2 2 6 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d )x +--R 3 6 3 3 6 +--R + +--R 1 2 2 4 2 2 1 2 2 2 5 +--R (- A b e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 1 2 1 1 2 2 4 1 2 2 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 2 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 87 + +--S 88 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 8 1 2 2 2 2 2 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e)x +--R 8 7 7 7 +--R + +--R 1 1 2 2 1 2 2 1 2 2 6 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d )x +--R 3 6 3 3 6 +--R + +--R 1 2 2 4 2 2 1 2 2 2 5 +--R (- A b e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 1 2 1 1 2 2 4 1 2 2 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 2 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 88 + +--S 89 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 89 + +--S 90 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 90 + +)clear all + +--S 91 of 1457 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 1457 +r0:=1/3*A*b^2*d*x^3+1/4*b*(b*B*d+2*A*c*d+A*b*e)*x^4+1/5*(A*c^2*d+b^2*B*e+_ + 2*b*c*(B*d+A*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 1 2 1 2 2 5 +--R ((- A b c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 +--R + +--R 1 2 1 1 2 4 1 2 3 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 92 + +--S 93 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 1 2 1 2 2 5 +--R ((- A b c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 +--R + +--R 1 2 1 1 2 4 1 2 3 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 93 + +--S 94 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 94 + +--S 95 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 95 + +)clear all + +--S 96 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R (1) B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R Type: Polynomial(Integer) +--E 96 + +--S 97 of 1457 +r0:=1/3*A*b^2*x^3+1/4*b*(b*B+2*A*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6 +--R +--R +--R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 +--R (2) - B c x + (- A c + - B b c)x + (- A b c + - B b )x + - A b x +--R 6 5 5 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 1457 +a0:=integrate(t0,x) +--R +--R +--R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 +--R (3) - B c x + (- A c + - B b c)x + (- A b c + - B b )x + - A b x +--R 6 5 5 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +)clear all + +--S 101 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 1457 +r0:=d*(B*d-A*e)*(c*d-b*e)^2*x/e^5-1/2*(B*d-A*e)*(c*d-b*e)^2*x^2/e^4-_ + 1/3*(A*c*e*(c*d-2*b*e)-B*(c*d-b*e)^2)*x^3/e^3-1/4*c*(B*c*d-2*b*B*e-_ + A*c*e)*x^4/e^2+1/5*B*c^2*x^5/e-d^2*(B*d-A*e)*(c*d-b*e)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 3 2 3 2 2 4 +--R 60A b d e + (- 120A b c - 60B b )d e + (60A c + 120B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((40A b c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 60A b c - 30B b )d e + (30A c + 60B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 60A b d e + (120A b c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 2 3 2 2 4 +--R 60A b d e + (- 120A b c - 60B b )d e + (60A c + 120B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((40A b c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 60A b c - 30B b )d e + (30A c + 60B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 60A b d e + (120A b c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 1457 +r0:=-(c*d-b*e)*(2*B*d*(2*c*d-b*e)-A*e*(3*c*d-b*e))*x/e^5+1/2*(c*d-b*e)*_ + (3*B*c*d-b*B*e-2*A*c*e)*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x))+d*_ + (c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 4 2 2 3 2 3 2 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 12A b e + (- 36A b c - 18B b )d e + (24A c + 48B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 48A b c - 24B b )d e + (36A c + 72B b c)d e +--R + +--R 2 4 +--R - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 12A b d e + (24A b c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 3 2 3 2 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 12A b e + (- 36A b c - 18B b )d e + (24A c + 48B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 48A b c - 24B b )d e + (36A c + 72B b c)d e +--R + +--R 2 4 +--R - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 12A b d e + (24A b c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 1457 +r0:=-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2-6*b*c*d*e+b^2*e^2))*x/e^5-1/2*c*_ + (3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*(d+e*x)^2)-d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*_ + (2*c*d-b*e))/(e^6*(d+e*x))+(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-_ + B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 +--R 6A b e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e +--R + +--R 2 3 2 +--R - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 72A b c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 6A b d e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((24A b c + 12B b )d e + (- 33A c - 66B b c)d e + 63B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 24A b c - 12B b )d e + (6A c + 12B b c)d e +--R + +--R 2 4 +--R 6B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 9A b d e + (- 30A b c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 2 2 3 +--R 6A b e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e +--R + +--R 2 3 2 +--R - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 72A b c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 6A b d e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((24A b c + 12B b )d e + (- 33A c - 66B b c)d e + 63B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 24A b c - 12B b )d e + (6A c + 12B b c)d e +--R + +--R 2 4 +--R 6B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 9A b d e + (- 30A b c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 1457 +r0:=-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*(d+e*x)^3)-1/2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-_ + 2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^2)+(-A*e*(6*c^2*d^2-6*b*c*d*e+_ + b^2*e^2)+B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*(d+e*x))-_ + (2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 24A c - 48B b c)d e + 60B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e )x +--R + +--R 2 2 3 2 3 2 2 4 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e)x +--R + +--R 2 3 2 2 4 2 5 +--R (12A b c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 6A b e + (36A b c + 18B b )d e + (- 18A c - 36B b c)d e +--R + +--R 2 3 2 +--R - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 6A b d e + (54A b c + 27B b )d e + (- 54A c - 108B b c)d e +--R + +--R 2 4 +--R 81B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 2A b d e + (22A b c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 24A c - 48B b c)d e + 60B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e )x +--R + +--R 2 2 3 2 3 2 2 4 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e)x +--R + +--R 2 3 2 2 4 2 5 +--R (12A b c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 6A b e + (36A b c + 18B b )d e + (- 18A c - 36B b c)d e +--R + +--R 2 3 2 +--R - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 6A b d e + (54A b c + 27B b )d e + (- 54A c - 108B b c)d e +--R + +--R 2 4 +--R 81B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 2A b d e + (22A b c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1457 +r0:=-d^3*(B*d-A*e)*(c*d-b*e)^3*(d+e*x)^(1+m)/(e^8*(1+m))+d^2*(c*d-b*e)^2*_ + (B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^8*(2+m))+_ + 3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-_ + 8*b*c*d*e+2*b^2*e^2))*(d+e*x)^(3+m)/(e^8*(3+m))+(B*d*(35*c^3*d^3-_ + 60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-A*e*(20*c^3*d^3-30*b*c^2*_ + d^2*e+12*b^2*c*d*e^2-b^3*e^3))*(d+e*x)^(4+m)/(e^8*(4+m))+(3*A*c*e*_ + (5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*(35*c^3*d^3-45*b*c^2*d^2*e+15*b^2*_ + c*d*e^2-b^3*e^3))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2-6*b*c*d*e+b^2*e^2))*(d+e*x)^(6+m)/(e^8*(6+m))-c^2*_ + (7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*_ + (d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 2 3 7 3 2 3 6 +--R ((A c + 3B b c )e - 7B c d)m + ((29A c + 87B b c )e - 203B c d)m +--R + +--R 3 2 3 5 +--R ((343A c + 1029B b c )e - 2401B c d)m +--R + +--R 3 2 3 4 +--R ((2135A c + 6405B b c )e - 14945B c d)m +--R + +--R 3 2 3 3 +--R ((7504A c + 22512B b c )e - 52528B c d)m +--R + +--R 3 2 3 2 +--R ((14756A c + 44268B b c )e - 103292B c d)m +--R + +--R 3 2 3 +--R ((14832A c + 44496B b c )e - 103824B c d)m +--R + +--R 3 2 3 +--R (5760A c + 17280B b c )e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 7 +--R ((3A b c + 3B b c)e + (- 6A c - 18B b c )d e + 21B c d )m +--R + +--R 2 2 2 3 2 3 2 6 +--R ((90A b c + 90B b c)e + (- 180A c - 540B b c )d e + 630B c d )m +--R + +--R 2 2 2 3 2 +--R (1098A b c + 1098B b c)e + (- 2196A c - 6588B b c )d e +--R + +--R 3 2 +--R 7686B c d 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5 3 +--R - 1506A b d e + (1512A b c + 504B b )d e +--R + +--R 2 2 6 2 +--R (- 360A b c - 360B b c)d e +--R * +--R 2 +--R m +--R + +--R 3 4 4 2 3 5 3 +--R - 6396A b d e + (10512A b c + 3504B b )d e +--R + +--R 2 2 6 2 3 2 7 +--R (- 5400A b c - 5400B b c)d e + (720A c + 2160B b c )d e +--R * +--R m +--R + +--R 3 4 4 2 3 5 3 +--R - 10080A b d e + (24192A b c + 8064B b )d e +--R + +--R 2 2 6 2 3 2 7 +--R (- 20160A b c - 20160B b c)d e + (5760A c + 17280B b c )d e +--R + +--R 3 8 +--R - 5040B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 8 7 3 8 6 3 8 5 3 8 4 3 8 3 +--R B c e m + 28B c e m + 322B c e m + 1960B c e m + 6769B c e m +--R + +--R 3 8 2 3 8 3 8 +--R 13132B c e m + 13068B c e m + 5040B c e +--R * +--R 8 +--R x +--R + +--R 3 2 8 3 7 7 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+--R (- 15A c - 45B b c )d e + 35B c d +--R * +--R 7 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 93A b c - 31B b )e + (465A b c + 465B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 465A c - 1395B b c )d e + 1085B c d +--R * +--R 6 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 1173A b c - 391B b )e + (5865A b c + 5865B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 5865A c - 17595B b c )d e + 13685B c d +--R * +--R 5 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 7743A b c - 2581B b )e + (38715A b c + 38715B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 38715A c - 116145B b c )d e + 90335B c d +--R * +--R 4 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 28632A b c - 9544B b )e + (143160A b c + 143160B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 143160A c - 429480B b c )d e + 334040B c d +--R * +--R 3 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 58692A b c - 19564B b )e + (293460A b c + 293460B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 293460A c - 880380B b c )d e + 684740B c d +--R * +--R 2 +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 60912A b c - 20304B b )e + (304560A b c + 304560B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 304560A c - 913680B b c )d e + 710640B c d +--R * +--R m +--R + +--R 2 3 3 2 2 2 +--R (- 24192A b c - 8064B b )e + (120960A b c + 120960B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 120960A c - 362880B b c )d e + 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - A b e + (12A b c + 4B b )d e + (- 30A b c - 30B b c)d e +--R + +--R 3 2 3 3 4 +--R (20A c + 60B b c )d e - 35B c d +--R * +--R 7 +--R m +--R + +--R 3 4 2 3 3 +--R - 32A b e + (384A b c + 128B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (- 960A b c - 960B b c)d e + (640A c + 1920B b c )d e +--R + +--R 3 4 +--R - 1120B c d +--R * +--R 6 +--R m +--R + +--R 3 4 2 3 3 +--R - 418A b e + (5016A b c + 1672B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (- 12540A b c - 12540B b c)d e + (8360A c + 25080B b c )d e +--R + +--R 3 4 +--R - 14630B c d +--R * +--R 5 +--R m +--R + +--R 3 4 2 3 3 +--R - 2864A b e + (34368A b c + 11456B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (- 85920A b c - 85920B b c)d e + (57280A c + 171840B b c )d e +--R + +--R 3 4 +--R - 100240B c d +--R * +--R 4 +--R m +--R + +--R 3 4 2 3 3 +--R - 10993A b e + (131916A b c + 43972B b )d e +--R + +--R 2 2 2 2 +--R (- 329790A b c - 329790B b c)d e +--R + +--R 3 2 3 3 4 +--R (219860A c + 659580B b c )d e - 384755B c d +--R * +--R 3 +--R m +--R + +--R 3 4 2 3 3 +--R - 23312A b e + (279744A b c + 93248B b )d e +--R + +--R 2 2 2 2 +--R (- 699360A b c - 699360B b c)d e +--R + +--R 3 2 3 3 4 +--R (466240A c + 1398720B b c )d e - 815920B c d +--R * +--R 2 +--R m +--R + +--R 3 4 2 3 3 +--R - 24876A b e + (298512A b c + 99504B b )d e +--R + +--R 2 2 2 2 +--R (- 746280A b c - 746280B b c)d e +--R + +--R 3 2 3 3 4 +--R (497520A c + 1492560B b c )d e - 870660B c d +--R * +--R m +--R + +--R 3 4 2 3 3 +--R - 10080A b e + (120960A b c + 40320B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (- 302400A b c - 302400B b c)d e + (201600A c + 604800B b c )d e +--R + +--R 3 4 +--R - 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 4 2 3 2 3 2 2 3 2 +--R 3A b d e + (- 18A b c - 6B b )d e + (30A b c + 30B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 15A c - 45B b c )d e + 21B c d +--R * +--R 7 +--R m +--R + +--R 3 4 2 3 2 3 +--R 99A b d e + (- 594A b c - 198B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (990A b c + 990B b c)d e + (- 495A c - 1485B b c )d e +--R + +--R 3 5 +--R 693B c d +--R * +--R 6 +--R m +--R + +--R 3 4 2 3 2 3 +--R 1341A b d e + (- 8046A b c - 2682B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (13410A b c + 13410B b c)d e + (- 6705A c - 20115B b c )d e +--R + +--R 3 5 +--R 9387B c d +--R * +--R 5 +--R m +--R + +--R 3 4 2 3 2 3 +--R 9585A b d e + (- 57510A b c - 19170B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (95850A b c + 95850B b c)d e + (- 47925A c - 143775B b c )d e +--R + +--R 3 5 +--R 67095B c d +--R * +--R 4 +--R m +--R + +--R 3 4 2 3 2 3 +--R 38592A b d e + (- 231552A b c - 77184B b )d e +--R + +--R 2 2 3 2 +--R (385920A b c + 385920B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 192960A c - 578880B b c )d e + 270144B c d +--R * +--R 3 +--R m +--R + +--R 3 4 2 3 2 3 +--R 86076A b d e + (- 516456A b c - 172152B b )d e +--R + +--R 2 2 3 2 +--R (860760A b c + 860760B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 430380A c - 1291140B b c )d e + 602532B c d +--R * +--R 2 +--R m +--R + +--R 3 4 2 3 2 3 +--R 96144A b d e + (- 576864A b c - 192288B b )d e +--R + +--R 2 2 3 2 +--R (961440A b c + 961440B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 480720A c - 1442160B b c )d e + 673008B c d +--R * +--R m +--R + +--R 3 4 2 3 2 3 +--R 40320A b d e + (- 241920A b c - 80640B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (403200A b c + 403200B b c)d e + (- 201600A c - 604800B b c )d e +--R + +--R 3 5 +--R 282240B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 2 4 2 3 3 3 2 2 4 2 +--R - 3A b d e + (12A b c + 4B b )d e + (- 15A b c - 15B b c)d e +--R + +--R 3 2 5 3 6 +--R (6A c + 18B b c )d e - 7B c d +--R * +--R 7 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 102A b d e + (408A b c + 136B b )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (- 510A b c - 510B b c)d e + (204A c + 612B b c )d e - 238B c d +--R * +--R 6 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 1434A b d e + (5736A b c + 1912B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 7170A b c - 7170B b c)d e + (2868A c + 8604B b c )d e +--R + +--R 3 6 +--R - 3346B c d +--R * +--R 5 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 10740A b d e + (42960A b c + 14320B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 53700A b c - 53700B b c)d e + (21480A c + 64440B b c )d e +--R + +--R 3 6 +--R - 25060B c d +--R * +--R 4 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 45867A b d e + (183468A b c + 61156B b )d e +--R + +--R 2 2 4 2 +--R (- 229335A b c - 229335B b c)d e +--R + +--R 3 2 5 3 6 +--R (91734A c + 275202B b c )d e - 107023B c d +--R * +--R 3 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 110118A b d e + (440472A b c + 146824B b )d e +--R + +--R 2 2 4 2 +--R (- 550590A b c - 550590B b c)d e +--R + +--R 3 2 5 3 6 +--R (220236A c + 660708B b c )d e - 256942B c d +--R * +--R 2 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 134136A b d e + (536544A b c + 178848B b )d e +--R + +--R 2 2 4 2 +--R (- 670680A b c - 670680B b c)d e +--R + +--R 3 2 5 3 6 +--R (268272A c + 804816B b c )d e - 312984B c d +--R * +--R m +--R + +--R 3 2 4 2 3 3 3 +--R - 60480A b d e + (241920A b c + 80640B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 302400A b c - 302400B b c)d e + (120960A c + 362880B b c )d e +--R + +--R 3 6 +--R - 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R A b d e + (- 3A b c - B b )d e + (3A b c + 3B b c)d e +--R + +--R 3 2 6 3 7 +--R (- A c - 3B b c )d e + B c d +--R * +--R 7 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 35A b d e + (- 105A b c - 35B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (105A b c + 105B b c)d e + (- 35A c - 105B b c )d e + 35B c d +--R * +--R 6 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 511A b d e + (- 1533A b c - 511B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (1533A b c + 1533B b c)d e + (- 511A c - 1533B b c )d e +--R + +--R 3 7 +--R 511B c d +--R * +--R 5 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 4025A b d e + (- 12075A b c - 4025B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (12075A b c + 12075B b c)d e + (- 4025A c - 12075B b c )d e +--R + +--R 3 7 +--R 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 18424A b d e + (- 55272A b c - 18424B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (55272A b c + 55272B b c)d e + (- 18424A c - 55272B b c )d e +--R + +--R 3 7 +--R 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 48860A b d e + (- 146580A b c - 48860B b )d e +--R + +--R 2 2 5 2 +--R (146580A b c + 146580B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48860A c - 146580B b c )d e + 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 69264A b d e + (- 207792A b c - 69264B b )d e +--R + +--R 2 2 5 2 +--R (207792A b c + 207792B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 69264A c - 207792B b c )d e + 69264B c d +--R * +--R m +--R + +--R 3 3 4 2 3 4 3 +--R 40320A b d e + (- 120960A b c - 40320B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (120960A b c + 120960B b c)d e + (- 40320A c - 120960B b c )d e +--R + +--R 3 7 +--R 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 2 4 3 3 10 +--R B c e x + ((A c + 3B b c )e + 4B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 9 +--R ((3A b c + 3B b c)e + (4A c + 12B b c )d e + 6B c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 2 +--R (3A b c + B b )e + (12A b c + 12B b c)d e + (6A c + 18B b c )d e +--R + +--R 3 3 +--R 4B c d e +--R * +--R 8 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (12A b c + 4B b )d e + (18A b c + 18B b c)d e +--R + +--R 3 2 3 3 4 +--R (4A c + 12B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 3 3 2 3 2 2 2 2 3 +--R 4A b d e + (18A b c + 6B b )d e + (12A b c + 12B b c)d e +--R + +--R 3 2 4 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 2 2 2 3 3 2 2 4 5 +--R (6A b d e + (12A b c + 4B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 3 2 3 4 4 3 4 3 +--R (4A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 126 + +--S 127 of 1457 +r0:=1/4*A*b^3*d^4*x^4+1/5*b^2*d^3*(b*B*d+3*A*c*d+4*A*b*e)*x^5+1/6*b*d^2*_ + (3*A*c^2*d^2+2*b^2*e*(2*B*d+3*A*e)+3*b*c*d*(B*d+4*A*e))*x^6+1/7*d*_ + (A*c^3*d^3+2*b^3*e^2*(3*B*d+2*A*e)+6*b^2*c*d*e*(2*B*d+3*A*e)+3*b*_ + c^2*d^2*(B*d+4*A*e))*x^7+1/8*(A*e*(4*c^3*d^3+18*b*c^2*d^2*e+12*_ + b^2*c*d*e^2+b^3*e^3)+B*d*(c^3*d^3+12*b*c^2*d^2*e+18*b^2*c*d*e^2+4*_ + b^3*e^3))*x^8+1/9*e*(3*A*c*e*(2*c^2*d^2+4*b*c*d*e+b^2*e^2)+B*_ + (4*c^3*d^3+18*b*c^2*d^2*e+12*b^2*c*d*e^2+b^3*e^3))*x^9+1/10*c*e^2*_ + (A*c*e*(4*c*d+3*b*e)+3*B*(2*c^2*d^2+4*b*c*d*e+b^2*e^2))*x^10+1/11*_ + c^2*e^3*(4*B*c*d+3*b*B*e+A*c*e)*x^11+1/12*B*c^3*e^4*x^12 +--R +--R +--R (2) +--R 1 3 4 12 1 3 3 2 4 4 3 3 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 2 3 2 4 2 3 6 2 3 3 3 2 2 10 +--R ((-- A b c + -- B b c)e + (- A c + - B b c )d e + - B c d e )x +--R 10 10 5 5 5 +--R + +--R 1 2 1 3 4 4 2 4 2 3 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 3 9 3 3 +--R + +--R 2 3 2 2 2 4 3 3 +--R (- A c + 2B b c )d e + - B c d e +--R 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 4 3 2 1 3 3 9 2 9 2 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 8 2 2 4 4 +--R + +--R 1 3 3 2 3 1 3 4 +--R (- A c + - B b c )d e + - B c d +--R 2 2 8 +--R * +--R 8 +--R x +--R + +--R 4 3 3 18 2 6 3 2 2 12 2 12 2 3 +--R - A b d e + (-- A b c + - B b )d e + (-- A b c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 4 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 2 2 2 3 3 1 2 1 2 4 6 +--R (A b d e + (2A b c + - B b )d e + (- A b c + - B b c)d )x +--R 3 2 2 +--R + +--R 4 3 3 3 2 1 3 4 5 1 3 4 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 12 1 3 3 2 4 4 3 3 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 2 3 2 4 2 3 6 2 3 3 3 2 2 10 +--R ((-- A b c + -- B b c)e + (- A c + - B b c )d e + - B c d e )x +--R 10 10 5 5 5 +--R + +--R 1 2 1 3 4 4 2 4 2 3 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 3 9 3 3 +--R + +--R 2 3 2 2 2 4 3 3 +--R (- A c + 2B b c )d e + - B c d e +--R 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 4 3 2 1 3 3 9 2 9 2 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 8 2 2 4 4 +--R + +--R 1 3 3 2 3 1 3 4 +--R (- A c + - B b c )d e + - B c d +--R 2 2 8 +--R * +--R 8 +--R x +--R + +--R 4 3 3 18 2 6 3 2 2 12 2 12 2 3 +--R - A b d e + (-- A b c + - B b )d e + (-- A b c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 4 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 2 2 2 3 3 1 2 1 2 4 6 +--R (A b d e + (2A b c + - B b )d e + (- A b c + - B b c)d )x +--R 3 2 2 +--R + +--R 4 3 3 3 2 1 3 4 5 1 3 4 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +--S 129 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 129 + +--S 130 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +)clear all + +--S 131 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 2 3 3 2 9 +--R B c e x + ((A c + 3B b c )e + 3B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 8 +--R ((3A b c + 3B b c)e + (3A c + 9B b c )d e + 3B c d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A b c + B b )e + (9A b c + 9B b c)d e + (3A c + 9B b c )d e +--R + +--R 3 3 +--R B c d +--R * +--R 7 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R A b e + (9A b c + 3B b )d e + (9A b c + 9B b c)d e +--R + +--R 3 2 3 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 2 2 3 2 2 2 3 5 +--R (3A b d e + (9A b c + 3B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 2 2 3 3 4 3 3 3 +--R (3A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 131 + +--S 132 of 1457 +r0:=1/4*A*b^3*d^3*x^4+1/5*b^2*d^2*(b*B*d+3*A*c*d+3*A*b*e)*x^5+1/2*b*d*_ + (A*c^2*d^2+b^2*e*(B*d+A*e)+b*c*d*(B*d+3*A*e))*x^6+1/7*(A*c^3*d^3+_ + 9*b^2*c*d*e*(B*d+A*e)+b^3*e^2*(3*B*d+A*e)+3*b*c^2*d^2*(B*d+3*A*e))*_ + x^7+1/8*(3*A*c*e*(c^2*d^2+3*b*c*d*e+b^2*e^2)+B*(c^3*d^3+9*b*c^2*d^2*e+_ + 9*b^2*c*d*e^2+b^3*e^3))*x^8+1/3*c*e*(A*c*e*(c*d+b*e)+B*(c^2*d^2+_ + 3*b*c*d*e+b^2*e^2))*x^9+1/10*c^2*e^2*(A*c*e+3*B*(c*d+b*e))*x^10+_ + 1/11*B*c^3*e^3*x^11 +--R +--R +--R (2) +--R 1 3 3 11 1 3 3 2 3 3 3 2 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 2 1 2 3 1 3 2 2 1 3 2 9 +--R ((- A b c + - B b c)e + (- A c + B b c )d e + - B c d e)x +--R 3 3 3 3 +--R + +--R 3 2 1 3 3 9 2 9 2 2 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 8 8 8 8 +--R + +--R 3 3 9 2 2 1 3 3 +--R (- A c + - B b c )d e + - B c d +--R 8 8 8 +--R * +--R 8 +--R x +--R + +--R 1 3 3 9 2 3 3 2 9 2 9 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 3 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 2 3 2 1 3 2 1 2 1 2 3 6 +--R (- A b d e + (- A b c + - B b )d e + (- A b c + - B b c)d )x +--R 2 2 2 2 2 +--R + +--R 3 3 2 3 2 1 3 3 5 1 3 3 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 3 11 1 3 3 2 3 3 3 2 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 2 1 2 3 1 3 2 2 1 3 2 9 +--R ((- A b c + - B b c)e + (- A c + B b c )d e + - B c d e)x +--R 3 3 3 3 +--R + +--R 3 2 1 3 3 9 2 9 2 2 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 8 8 8 8 +--R + +--R 3 3 9 2 2 1 3 3 +--R (- A c + - B b c )d e + - B c d +--R 8 8 8 +--R * +--R 8 +--R x +--R + +--R 1 3 3 9 2 3 3 2 9 2 9 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 3 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 2 3 2 1 3 2 1 2 1 2 3 6 +--R (- A b d e + (- A b c + - B b )d e + (- A b c + - B b c)d )x +--R 2 2 2 2 2 +--R + +--R 3 3 2 3 2 1 3 3 5 1 3 3 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +--S 134 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +)clear all + +--S 136 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 2 3 8 +--R B c e x + ((A c + 3B b c )e + 2B c d e)x +--R + +--R 2 2 2 3 2 3 2 7 +--R ((3A b c + 3B b c)e + (2A c + 6B b c )d e + B c d )x +--R + +--R 2 3 2 2 2 3 2 2 6 +--R ((3A b c + B b )e + (6A b c + 6B b c)d e + (A c + 3B b c )d )x +--R + +--R 3 2 2 3 2 2 2 5 +--R (A b e + (6A b c + 2B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 2 3 2 4 3 2 3 +--R (2A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 1457 +r0:=1/4*A*b^3*d^2*x^4+1/5*b^2*d*(b*B*d+3*A*c*d+2*A*b*e)*x^5+1/6*b*_ + (3*A*c^2*d^2+b^2*e*(2*B*d+A*e)+3*b*c*d*(B*d+2*A*e))*x^6+1/7*_ + (A*c^3*d^2+b^3*B*e^2+3*b^2*c*e*(2*B*d+A*e)+3*b*c^2*d*(B*d+2*A*e))*x^7+_ + 1/8*c*(A*c*e*(2*c*d+3*b*e)+B*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^8+_ + 1/9*c^2*e*(2*B*c*d+3*b*B*e+A*c*e)*x^9+1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R ((- A b c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 4 4 8 +--R + +--R 3 2 1 3 2 6 2 6 2 1 3 3 2 2 7 +--R ((- A b c + - B b )e + (- A b c + - B b c)d e + (- A c + - B b c )d )x +--R 7 7 7 7 7 7 +--R + +--R 1 3 2 2 1 3 1 2 1 2 2 6 +--R (- A b e + (A b c + - B b )d e + (- A b c + - B b c)d )x +--R 6 3 2 2 +--R + +--R 2 3 3 2 1 3 2 5 1 3 2 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R ((- A b c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 4 4 8 +--R + +--R 3 2 1 3 2 6 2 6 2 1 3 3 2 2 7 +--R ((- A b c + - B b )e + (- A b c + - B b c)d e + (- A c + - B b c )d )x +--R 7 7 7 7 7 7 +--R + +--R 1 3 2 2 1 3 1 2 1 2 2 6 +--R (- A b e + (A b c + - B b )d e + (- A b c + - B b c)d )x +--R 6 3 2 2 +--R + +--R 2 3 3 2 1 3 2 5 1 3 2 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 139 + +--S 140 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +)clear all + +--S 141 of 1457 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 2 3 7 +--R B c e x + ((A c + 3B b c )e + B c d)x +--R + +--R 2 2 3 2 6 +--R ((3A b c + 3B b c)e + (A c + 3B b c )d)x +--R + +--R 2 3 2 2 5 3 2 3 4 +--R ((3A b c + B b )e + (3A b c + 3B b c)d)x + (A b e + (3A b c + B b )d)x +--R + +--R 3 3 +--R A b d x +--R Type: Polynomial(Integer) +--E 141 + +--S 142 of 1457 +r0:=1/4*A*b^3*d*x^4+1/5*b^2*(b*B*d+3*A*c*d+A*b*e)*x^5+1/6*b*(3*A*c^2*d+_ + b^2*B*e+3*b*c*(B*d+A*e))*x^6+1/7*c*(A*c^2*d+3*b^2*B*e+3*b*c*(B*d+_ + A*e))*x^7+1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 2 3 2 1 3 3 2 7 +--R ((- A b c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 +--R + +--R 1 2 1 3 1 2 1 2 6 +--R ((- A b c + - B b )e + (- A b c + - B b c)d)x +--R 2 6 2 2 +--R + +--R 1 3 3 2 1 3 5 1 3 4 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 142 + +--S 143 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 2 3 2 1 3 3 2 7 +--R ((- A b c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 +--R + +--R 1 2 1 3 1 2 1 2 6 +--R ((- A b c + - B b )e + (- A b c + - B b c)d)x +--R 2 6 2 2 +--R + +--R 1 3 3 2 1 3 5 1 3 4 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 143 + +--S 144 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 144 + +--S 145 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 145 + +)clear all + +--S 146 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R Type: Polynomial(Integer) +--E 146 + +--S 147 of 1457 +r0:=1/4*A*b^3*x^4+1/5*b^2*(b*B+3*A*c)*x^5+1/2*b*c*(b*B+A*c)*x^6+_ + 1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8 +--R +--R +--R (2) +--R 1 3 8 1 3 3 2 7 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + (- A b c + - B b c)x +--R 8 7 7 2 2 +--R + +--R 3 2 1 3 5 1 3 4 +--R (- A b c + - B b )x + - A b x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 147 + +--S 148 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 8 1 3 3 2 7 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + (- A b c + - B b c)x +--R 8 7 7 2 2 +--R + +--R 3 2 1 3 5 1 3 4 +--R (- A b c + - B b )x + - A b x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 148 + +--S 149 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 149 + +--S 150 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 150 + +)clear all + +--S 151 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 1457 +r0:=d^2*(B*d-A*e)*(c*d-b*e)^3*x/e^7-1/2*d*(B*d-A*e)*(c*d-b*e)^3*x^2/e^6+_ + 1/3*(B*d-A*e)*(c*d-b*e)^3*x^3/e^5-1/4*(B*(c*d-b*e)^3-A*c*e*(c^2*d^2-_ + 3*b*c*d*e+3*b^2*e^2))*x^4/e^4-1/5*c*(A*c*e*(c*d-3*b*e)-B*(c^2*d^2-_ + 3*b*c*d*e+3*b^2*e^2))*x^5/e^3-1/6*c^2*(B*c*d-3*b*B*e-A*c*e)*x^6/e^2+_ + 1/7*B*c^3*x^7/e-d^3*(B*d-A*e)*(c*d-b*e)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 3 4 2 3 4 3 +--R - 420A b d e + (1260A b c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 1260A b c - 1260B b c)d e + (420A c + 1260B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((252A b c + 252B b c)e + (- 84A c - 252B b c )d e + 84B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (315A b c + 105B b )e + (- 315A b c - 315B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (105A c + 315B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 140A b e + (- 420A b c - 140B b )d e + (420A b c + 420B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 140A c - 420B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 210A b d e + (630A b c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 630A b c - 630B b c)d e + (210A c + 630B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 420A b d e + (- 1260A b c - 420B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1260A b c + 1260B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 4 2 3 4 3 +--R - 420A b d e + (1260A b c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 1260A b c - 1260B b c)d e + (420A c + 1260B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((252A b c + 252B b c)e + (- 84A c - 252B b c )d e + 84B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (315A b c + 105B b )e + (- 315A b c - 315B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (105A c + 315B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 140A b e + (- 420A b c - 140B b )d e + (420A b c + 420B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 140A c - 420B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 210A b d e + (630A b c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 630A b c - 630B b c)d e + (210A c + 630B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 420A b d e + (- 1260A b c - 420B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1260A b c + 1260B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 1457 +r0:=d*(c*d-b*e)^2*(A*e*(5*c*d-2*b*e)-3*B*d*(2*c*d-b*e))*x/e^7+_ + 1/2*(c*d-b*e)^2*(B*d*(5*c*d-2*b*e)-A*e*(4*c*d-b*e))*x^2/e^6-_ + 1/3*(c*d-b*e)^2*(4*B*c*d-b*B*e-3*A*c*e)*x^3/e^5-1/4*c*(A*c*e*_ + (2*c*d-3*b*e)-3*B*(c*d-b*e)^2)*x^4/e^4-1/5*c^2*(2*B*c*d-3*b*B*e-_ + A*c*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*_ + (d+e*x))+d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 5 2 3 3 4 +--R 180A b d e + (- 720A b c - 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (900A b c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 180A b d e + (- 720A b c - 240B b )d e + (900A b c + 900B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 360A c - 1080B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((45A b c + 45B b c)e + (- 18A c - 54B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (60A b c + 20B b )e + (- 75A b c - 75B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (30A c + 90B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 30A b e + (- 120A b c - 40B b )d e + (150A b c + 150B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 60A c - 180B b c )d e + 70B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 90A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 450A b c - 450B b c)d e + (180A c + 540B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (540A b c + 180B b )d e +--R + +--R 2 2 4 3 3 2 5 2 3 6 +--R (- 720A b c - 720B b c)d e + (300A c + 900B b c )d e - 360B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 60A b d e + (- 180A b c - 60B b )d e + (180A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 60A c - 180B b c )d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 5 2 3 3 4 +--R 180A b d e + (- 720A b c - 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (900A b c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 180A b d e + (- 720A b c - 240B b )d e + (900A b c + 900B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 360A c - 1080B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((45A b c + 45B b c)e + (- 18A c - 54B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (60A b c + 20B b )e + (- 75A b c - 75B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (30A c + 90B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 30A b e + (- 120A b c - 40B b )d e + (150A b c + 150B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 60A c - 180B b c )d e + 70B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 90A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 450A b c - 450B b c)d e + (180A c + 540B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (540A b c + 180B b )d e +--R + +--R 2 2 4 3 3 2 5 2 3 6 +--R (- 720A b c - 720B b c)d e + (300A c + 900B b c )d e - 360B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 60A b d e + (- 180A b c - 60B b )d e + (180A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 60A c - 180B b c )d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 1457 +r0:=-(c*d-b*e)*(A*e*(10*c^2*d^2-8*b*c*d*e+b^2*e^2)-3*B*d*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2))*x/e^7+1/2*(c*d-b*e)*(3*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*x^2/e^6+c*(c*d-b*e)*(2*B*c*d-b*B*e-_ + A*c*e)*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*x^4/e^4+1/5*B*c^3*_ + x^5/e^3+1/2*d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*(d+e*x)^2)-d^2*_ + (c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))/(e^8*(d+e*x))+_ + 3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-_ + 8*b*c*d*e+2*b^2*e^2))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 6 2 3 2 5 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 5 2 +--R - 420B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (720A b c + 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1200A b c - 1200B b c)d e + (600A c + 1800B b c )d e +--R + +--R 3 6 +--R - 840B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((20A b c + 20B b c)e + (- 10A c - 30B b c )d e + 14B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (30A b c + 10B b )e + (- 50A b c - 50B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (25A c + 75B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 20A b e + (- 120A b c - 40B b )d e + (200A b c + 200B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 100A c - 300B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 40A b d e + (- 330A b c - 110B b )d e + (630A b c + 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 340A c - 1020B b c )d e + 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R - 40A b d e + (60A b c + 20B b )d e + (60A b c + 60B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 80A c - 240B b c )d e + 160B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 50A b d e + (210A b c + 70B b )d e + (- 270A b c - 270B b c)d e +--R + +--R 3 2 6 3 7 +--R (110A c + 330B b c )d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 3 2 5 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 5 2 +--R - 420B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (720A b c + 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1200A b c - 1200B b c)d e + (600A c + 1800B b c )d e +--R + +--R 3 6 +--R - 840B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((20A b c + 20B b c)e + (- 10A c - 30B b c )d e + 14B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (30A b c + 10B b )e + (- 50A b c - 50B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (25A c + 75B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 20A b e + (- 120A b c - 40B b )d e + (200A b c + 200B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 100A c - 300B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 40A b d e + (- 330A b c - 110B b )d e + (630A b c + 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 340A c - 1020B b c )d e + 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R - 40A b d e + (60A b c + 20B b )d e + (60A b c + 60B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 80A c - 240B b c )d e + 160B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 50A b d e + (210A b c + 70B b )d e + (- 270A b c - 270B b c)d e +--R + +--R 3 2 6 3 7 +--R (110A c + 330B b c )d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1457 +r0:=(A*c*e*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2)-B*(20*c^3*d^3-30*b*c^2*d^2*e+_ + 12*b^2*c*d*e^2-b^3*e^3))*x/e^7-1/2*c*(A*c*e*(4*c*d-3*b*e)-_ + B*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*x^2/e^6-1/3*c^2*(4*B*c*d-_ + 3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*d^3*(B*d-A*e)*_ + (c*d-b*e)^3/(e^8*(d+e*x)^3)-1/2*d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-_ + 3*A*e*(2*c*d-b*e))/(e^8*(d+e*x)^2)-3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-8*b*c*d*e+2*b^2*e^2))/(e^8*_ + (d+e*x))+(B*d*(35*c^3*d^3-60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-_ + A*e*(20*c^3*d^3-30*b*c^2*d^2*e+12*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 3 6 2 2 2 5 +--R 12A b e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 12A b d e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 240A c - 720B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((18A b c + 18B b c)e + (- 12A c - 36B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (36A b c + 12B b )e + (- 90A b c - 90B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (60A c + 180B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 2 5 +--R (108A b c + 36B b )d e + (- 378A b c - 378B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (292A c + 876B b c )d e - 556B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 36A b d e + (- 108A b c - 36B b )d e + (- 54A b c - 54B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (156A c + 468B b c )d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R 54A b d e + (- 324A b c - 108B b )d e + (486A b c + 486B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 204A c - 612B b c )d e + 222B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 22A b d e + (- 156A b c - 52B b )d e + (282A b c + 282B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 148A c - 444B b c )d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 2 3 6 2 2 2 5 +--R 12A b e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 12A b d e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 240A c - 720B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((18A b c + 18B b c)e + (- 12A c - 36B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (36A b c + 12B b )e + (- 90A b c - 90B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (60A c + 180B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 2 5 +--R (108A b c + 36B b )d e + (- 378A b c - 378B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (292A c + 876B b c )d e - 556B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 36A b d e + (- 108A b c - 36B b )d e + (- 54A b c - 54B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (156A c + 468B b c )d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R 54A b d e + (- 324A b c - 108B b )d e + (486A b c + 486B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 204A c - 612B b c )d e + 222B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 22A b d e + (- 156A b c - 52B b )d e + (282A b c + 282B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 148A c - 444B b c )d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1457 +r0:=e*(A*c*e*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)+B*(4*c^3*d^3-6*b*c^2*d^2*e+_ + 4*b^2*c*d*e^2-b^3*e^3))*x/c^4+1/2*e^2*(A*c*e*(4*c*d-b*e)+B*_ + (6*c^2*d^2-4*b*c*d*e+b^2*e^2))*x^2/c^3+1/3*e^3*(4*B*c*d-b*B*e+_ + A*c*e)*x^3/c^2+1/4*B*e^4*x^4/c+A*d^4*log(x)/b+(b*B-A*c)*_ + (c*d-b*e)^4*log(b+c*x)/(b*c^5) +--R +--R +--R (2) +--R 4 5 4 3 2 4 3 +--R (- 12A b c + 12B b )e + (48A b c - 48B b c)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A b c + 72B b c )d e + (48A b c - 48B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 12B b c )d +--R * +--R log(c x + b) +--R + +--R 5 4 4 4 4 4 2 3 4 4 3 3 +--R 12A c d log(x) + 3B b c e x + ((4A b c - 4B b c )e + 16B b c d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 6A b c + 6B b c )e + (24A b c - 24B b c )d e + 36B b c d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A b c - 12B b c)e + (- 48A b c + 48B b c )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A b c - 72B b c )d e + 48B b c d e +--R * +--R x +--R / +--R 5 +--R 12b c +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 4 3 2 4 3 +--R (- 12A b c + 12B b )e + (48A b c - 48B b c)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A b c + 72B b c )d e + (48A b c - 48B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 12B b c )d +--R * +--R log(c x + b) +--R + +--R 5 4 4 4 4 4 2 3 4 4 3 3 +--R 12A c d log(x) + 3B b c e x + ((4A b c - 4B b c )e + 16B b c d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 6A b c + 6B b c )e + (24A b c - 24B b c )d e + 36B b c d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A b c - 12B b c)e + (- 48A b c + 48B b c )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A b c - 72B b c )d e + 48B b c d e +--R * +--R x +--R / +--R 5 +--R 12b c +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1457 +r0:=e*(A*c*e*(3*c*d-b*e)+B*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*x/c^3+_ + 1/2*e^2*(3*B*c*d-b*B*e+A*c*e)*x^2/c^2+1/3*B*e^3*x^3/c+A*d^3*_ + log(x)/b+(b*B-A*c)*(c*d-b*e)^3*log(b+c*x)/(b*c^4) +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (6A b c - 6B b )e + (- 18A b c + 18B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A b c - 18B b c )d e + (- 6A c + 6B b c )d +--R * +--R log(c x + b) +--R + +--R 4 3 3 3 3 3 2 2 3 3 2 2 +--R 6A c d log(x) + 2B b c e x + ((3A b c - 3B b c )e + 9B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 6A b c + 6B b c)e + (18A b c - 18B b c )d e + 18B b c d e)x +--R / +--R 4 +--R 6b c +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 2 3 2 +--R (6A b c - 6B b )e + (- 18A b c + 18B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A b c - 18B b c )d e + (- 6A c + 6B b c )d +--R * +--R log(c x + b) +--R + +--R 4 3 3 3 3 3 2 2 3 3 2 2 +--R 6A c d log(x) + 2B b c e x + ((3A b c - 3B b c )e + 9B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 6A b c + 6B b c)e + (18A b c - 18B b c )d e + 18B b c d e)x +--R / +--R 4 +--R 6b c +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1457 +r0:=e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+A*d^2*log(x)/b+_ + (b*B-A*c)*(c*d-b*e)^2*log(b+c*x)/(b*c^3) +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 2B b )e + (4A b c - 4B b c)d e + (- 2A c + 2B b c )d ) +--R * +--R log(c x + b) +--R + +--R 3 2 2 2 2 2 2 2 2 +--R 2A c d log(x) + B b c e x + ((2A b c - 2B b c)e + 4B b c d e)x +--R / +--R 3 +--R 2b c +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 2B b )e + (4A b c - 4B b c)d e + (- 2A c + 2B b c )d ) +--R * +--R log(c x + b) +--R + +--R 3 2 2 2 2 2 2 2 2 +--R 2A c d log(x) + B b c e x + ((2A b c - 2B b c)e + 4B b c d e)x +--R / +--R 3 +--R 2b c +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1457 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1457 +r0:=B*e*x/c+A*d*log(x)/b+(b*B-A*c)*(c*d-b*e)*log(b+c*x)/(b*c^2) +--R +--R +--R (2) +--R 2 2 2 +--R ((A b c - B b )e + (- A c + B b c)d)log(c x + b) + A c d log(x) + B b c e x +--R ---------------------------------------------------------------------------- +--R 2 +--R b c +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R ((A b c - B b )e + (- A c + B b c)d)log(c x + b) + A c d log(x) + B b c e x +--R ---------------------------------------------------------------------------- +--R 2 +--R b c +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1457 +t0:=(A+B*x)/(b*x+c*x^2) +--R +--R +--R B x + A +--R (1) ---------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1457 +r0:=A*log(x)/b+(b*B-A*c)*log(b+c*x)/(b*c) +--R +--R +--R (- A c + B b)log(c x + b) + A c log(x) +--R (2) -------------------------------------- +--R b c +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (- A c + B b)log(c x + b) + A c log(x) +--R (3) -------------------------------------- +--R b c +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1457 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R 3 2 +--R c e x + (b e + c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1457 +r0:=A*log(x)/(b*d)+(b*B-A*c)*log(b+c*x)/(b*(c*d-b*e))-_ + (B*d-A*e)*log(d+e*x)/(d*(c*d-b*e)) +--R +--R +--R (2) +--R (- A b e + B b d)log(e x + d) + (A c - B b)d log(c x + b) +--R + +--R (A b e - A c d)log(x) +--R / +--R 2 2 +--R b d e - b c d +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (- A b e + B b d)log(e x + d) + (A c - B b)d log(c x + b) +--R + +--R (A b e - A c d)log(x) +--R / +--R 2 2 +--R b d e - b c d +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------ +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1457 +r0:=(B*d-A*e)/(d*(c*d-b*e)*(d+e*x))+A*log(x)/(b*d^2)+c*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^2)-(B*c*d^2-A*e*(2*c*d-b*e))*log(d+e*x)/_ + (d^2*(c*d-b*e)^2) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R (- A b e + 2A b c d e - B b c d e)x - A b d e + 2A b c d e +--R + +--R 3 +--R - B b c d +--R * +--R log(e x + d) +--R + +--R 2 2 2 3 +--R ((- A c + B b c)d e x + (- A c + B b c)d )log(c x + b) +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((A b e - 2A b c d e + A c d e)x + A b d e - 2A b c d e + A c d ) +--R * +--R log(x) +--R + +--R 2 2 2 2 3 +--R A b d e + (- A b c - B b )d e + B b c d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 +--R (- A b e + 2A b c d e - B b c d e)x - A b d e + 2A b c d e +--R + +--R 3 +--R - B b c d +--R * +--R log(e x + d) +--R + +--R 2 2 2 3 +--R ((- A c + B b c)d e x + (- A c + B b c)d )log(c x + b) +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((A b e - 2A b c d e + A c d e)x + A b d e - 2A b c d e + A c d ) +--R * +--R log(x) +--R + +--R 2 2 2 2 3 +--R A b d e + (- A b c - B b )d e + B b c d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1457 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1457 +r0:=1/2*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^2)+(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x))+A*log(x)/(b*d^3)+c^2*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^3)-(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+_ + b^2*e^2))*log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (- 2A b e + 6A b c d e - 6A b c d e + 2B b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 2 4 3 2 3 +--R (- 4A b d e + 12A b c d e - 12A b c d e + 4B b c d e)x - 2A b d e +--R + +--R 2 3 2 2 4 2 5 +--R 6A b c d e - 6A b c d e + 2B b c d +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 3 2 4 +--R (2A c - 2B b c )d e x + (4A c - 4B b c )d e x +--R + +--R 3 2 5 +--R (2A c - 2B b c )d +--R * +--R log(c x + b) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2A b e - 6A b c d e + 6A b c d e - 2A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (4A b d e - 12A b c d e + 12A b c d e - 4A c d e)x + 2A b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 6A b c d e + 6A b c d e - 2A c d +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 2 3 2 2 4 +--R (2A b d e - 6A b c d e + (4A b c + 2B b c)d e - 2B b c d e)x +--R + +--R 3 2 3 2 3 3 2 2 2 4 2 5 +--R 3A b d e + (- 8A b c - B b )d e + (5A b c + 4B b c)d e - 3B b c d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e)x + 2b d e - 6b c d e +--R + +--R 2 2 7 3 8 +--R 6b c d e - 2b c d +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (- 2A b e + 6A b c d e - 6A b c d e + 2B b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 2 4 3 2 3 +--R (- 4A b d e + 12A b c d e - 12A b c d e + 4B b c d e)x - 2A b d e +--R + +--R 2 3 2 2 4 2 5 +--R 6A b c d e - 6A b c d e + 2B b c d +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 3 2 4 +--R (2A c - 2B b c )d e x + (4A c - 4B b c )d e x +--R + +--R 3 2 5 +--R (2A c - 2B b c )d +--R * +--R log(c x + b) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2A b e - 6A b c d e + 6A b c d e - 2A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (4A b d e - 12A b c d e + 12A b c d e - 4A c d e)x + 2A b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 6A b c d e + 6A b c d e - 2A c d +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 2 3 2 2 4 +--R (2A b d e - 6A b c d e + (4A b c + 2B b c)d e - 2B b c d e)x +--R + +--R 3 2 3 2 3 3 2 2 2 4 2 5 +--R 3A b d e + (- 8A b c - B b )d e + (5A b c + 4B b c)d e - 3B b c d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e)x + 2b d e - 6b c d e +--R + +--R 2 2 7 3 8 +--R 6b c d e - 2b c d +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1457 +t0:=(A+B*x)/((d+e*x)^4*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 6 4 3 5 3 2 2 4 +--R c e x + (b e + 4c d e )x + (4b d e + 6c d e )x +--R + +--R 2 2 3 3 3 4 2 4 +--R (6b d e + 4c d e)x + (4b d e + c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1457 +r0:=1/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^3)+1/2*(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x)^2)+(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+_ + b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x))+A*log(x)/(b*d^4)+c^3*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^4)-(B*c^3*d^4-A*e*(4*c^3*d^3-_ + 6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 6A b e + 24A b c d e - 36A b c d e + 24A b c d e +--R + +--R 3 4 3 +--R - 6B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R - 18A b d e + 72A b c d e - 108A b c d e + 72A b c d e +--R + +--R 3 5 2 +--R - 18B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R - 18A b d e + 72A b c d e - 108A b c d e + 72A b c d e +--R + +--R 3 6 +--R - 18B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 3 7 +--R - 6A b d e + 24A b c d e - 36A b c d e + 24A b c d e - 6B b c d +--R * +--R log(e x + d) +--R + +--R 4 3 4 3 3 4 3 5 2 2 +--R (- 6A c + 6B b c )d e x + (- 18A c + 18B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (- 18A c + 18B b c )d e x + (- 6A c + 6B b c )d +--R * +--R log(c x + b) +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (6A b e - 24A b c d e + 36A b c d e - 24A b c d e + 6A c d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R 18A b d e - 72A b c d e + 108A b c d e - 72A b c d e +--R + +--R 4 5 2 +--R 18A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R 18A b d e - 72A b c d e + 108A b c d e - 72A b c d e +--R + +--R 4 6 +--R 18A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 6A b d e - 24A b c d e + 36A b c d e - 24A b c d e + 6A c d +--R * +--R log(x) +--R + +--R 4 6 3 2 5 2 2 3 4 3 2 2 4 3 +--R 6A b d e - 24A b c d e + 36A b c d e + (- 18A b c - 6B b c )d e +--R + +--R 3 5 2 +--R 6B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 15A b d e - 60A b c d e + (87A b c + 3B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 42A b c - 18B b c )d e + 15B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 2 2 3 5 2 +--R 11A b d e + (- 42A b c - 2B b )d e + (57A b c + 9B b c)d e +--R + +--R 3 2 2 6 3 7 +--R (- 26A b c - 18B b c )d e + 11B b c d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (6b d e - 24b c d e + 36b c d e - 24b c d e + 6b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 4 9 2 2 +--R (18b d e - 72b c d e + 108b c d e - 72b c d e + 18b c d e )x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 4 10 +--R (18b d e - 72b c d e + 108b c d e - 72b c d e + 18b c d e)x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 6b d e - 24b c d e + 36b c d e - 24b c d e + 6b c d +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1457 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 1457 +--m0:=a0-r0 +--E 214 + +--S 215 of 1457 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 1457 +r0:=-A*d^4/(b^2*x)+e^3*(4*B*c*d-2*b*B*e+A*c*e)*x/c^3+1/2*B*e^4*x^2/c^2+_ + (b*B-A*c)*(c*d-b*e)^4/(b^2*c^4*(b+c*x))+d^3*(b*B*d-2*A*c*d+_ + 4*A*b*e)*log(x)/b^3+(c*d-b*e)^3*(2*A*c^2*d-3*b^2*B*e-b*c*(B*d-_ + 2*A*e))*log(b+c*x)/(b^3*c^4) +--R +--R +--R (2) +--R 4 2 5 4 3 3 4 2 3 3 3 2 2 +--R (- 4A b c + 6B b c)e + (8A b c - 16B b c )d e + 12B b c d e +--R + +--R 5 3 6 5 4 +--R - 8A b c d e + (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 4 2 2 2 +--R (- 4A b c + 6B b )e + (8A b c - 16B b c)d e + 12B b c d e +--R + +--R 2 4 3 5 2 4 4 +--R - 8A b c d e + (4A b c - 2B b c )d +--R * +--R x +--R * +--R log(c x + b) +--R + +--R 5 3 6 5 4 2 +--R (8A b c d e + (- 4A c + 2B b c )d )x +--R + +--R 2 4 3 5 2 4 4 +--R (8A b c d e + (- 4A b c + 2B b c )d )x +--R * +--R log(x) +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 3 3 +--R B b c e x + ((2A b c - 3B b c )e + 8B b c d e )x +--R + +--R 4 2 5 4 4 2 3 2 +--R ((2A b c - 4B b c)e + 8B b c d e )x +--R + +--R 5 6 4 4 2 5 3 +--R (- 2A b c + 2B b )e + (8A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 12A b c + 12B b c )d e + (8A b c - 8B b c )d e +--R + +--R 5 2 4 4 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 4 4 +--R - 2A b c d +--R / +--R 3 5 2 4 4 +--R 2b c x + 2b c x +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 5 4 3 3 4 2 3 3 3 2 2 +--R (- 4A b c + 6B b c)e + (8A b c - 16B b c )d e + 12B b c d e +--R + +--R 5 3 6 5 4 +--R - 8A b c d e + (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 4 2 2 2 +--R (- 4A b c + 6B b )e + (8A b c - 16B b c)d e + 12B b c d e +--R + +--R 2 4 3 5 2 4 4 +--R - 8A b c d e + (4A b c - 2B b c )d +--R * +--R x +--R * +--R log(c x + b) +--R + +--R 5 3 6 5 4 2 +--R (8A b c d e + (- 4A c + 2B b c )d )x +--R + +--R 2 4 3 5 2 4 4 +--R (8A b c d e + (- 4A b c + 2B b c )d )x +--R * +--R log(x) +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 3 3 +--R B b c e x + ((2A b c - 3B b c )e + 8B b c d e )x +--R + +--R 4 2 5 4 4 2 3 2 +--R ((2A b c - 4B b c)e + 8B b c d e )x +--R + +--R 5 6 4 4 2 5 3 +--R (- 2A b c + 2B b )e + (8A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 12A b c + 12B b c )d e + (8A b c - 8B b c )d e +--R + +--R 5 2 4 4 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 4 4 +--R - 2A b c d +--R / +--R 3 5 2 4 4 +--R 2b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 1457 +r0:=-A*d^3/(b^2*x)+B*e^3*x/c^2+(b*B-A*c)*(c*d-b*e)^3/(b^2*c^3*(b+c*x))+_ + d^2*(b*B*d-2*A*c*d+3*A*b*e)*log(x)/b^3-(c*d-b*e)^2*(b*B*c*d-_ + 2*A*c^2*d+2*b^2*B*e-A*b*c*e)*log(b+c*x)/(b^3*c^3) +--R +--R +--R (2) +--R 3 2 4 3 3 2 2 4 2 +--R (A b c - 2B b c)e + 3B b c d e - 3A b c d e +--R + +--R 5 4 3 +--R (2A c - B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 2 3 2 4 2 3 3 +--R ((A b c - 2B b )e + 3B b c d e - 3A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 4 2 5 4 3 2 +--R (3A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (3A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 3 3 4 3 2 +--R B b c e x + B b c e x +--R + +--R 4 5 3 3 2 4 2 2 3 3 2 2 +--R (A b c - B b )e + (- 3A b c + 3B b c)d e + (3A b c - 3B b c )d e +--R + +--R 4 2 3 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - A b c d +--R / +--R 3 4 2 4 3 +--R b c x + b c x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 3 2 2 4 2 +--R (A b c - 2B b c)e + 3B b c d e - 3A b c d e +--R + +--R 5 4 3 +--R (2A c - B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 2 3 2 4 2 3 3 +--R ((A b c - 2B b )e + 3B b c d e - 3A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 4 2 5 4 3 2 +--R (3A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (3A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 3 3 4 3 2 +--R B b c e x + B b c e x +--R + +--R 4 5 3 3 2 4 2 2 3 3 2 2 +--R (A b c - B b )e + (- 3A b c + 3B b c)d e + (3A b c - 3B b c )d e +--R + +--R 4 2 3 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - A b c d +--R / +--R 3 4 2 4 3 +--R b c x + b c x +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 1457 +r0:=-A*d^2/(b^2*x)+(b*B-A*c)*(c*d-b*e)^2/(b^2*c^2*(b+c*x))+d*_ + (b*B*d-2*A*c*d+2*A*b*e)*log(x)/b^3-(c*d-b*e)*(b*B*c*d-2*A*c^2*d+_ + b^2*B*e)*log(b+c*x)/(b^3*c^2) +--R +--R +--R (2) +--R 3 2 3 4 3 2 2 +--R (B b c e - 2A b c d e + (2A c - B b c )d )x +--R + +--R 4 2 2 2 3 2 2 2 +--R (B b e - 2A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 4 3 2 2 +--R (2A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (2A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((- A b c + B b )e + (2A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 2 2 2 +--R - A b c d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 4 3 2 2 +--R (B b c e - 2A b c d e + (2A c - B b c )d )x +--R + +--R 4 2 2 2 3 2 2 2 +--R (B b e - 2A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 4 3 2 2 +--R (2A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (2A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((- A b c + B b )e + (2A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 2 2 2 +--R - A b c d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1457 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 1457 +r0:=-A*d/(b^2*x)+(b*B-A*c)*(c*d-b*e)/(b^2*c*(b+c*x))+(b*B*d-2*A*c*d+A*b*e)*_ + log(x)/b^3-(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^3 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((- A b c e + (2A c - B b c )d)x + (- A b c e + (2A b c - B b c)d)x) +--R * +--R log(c x + b) +--R + +--R 2 3 2 2 2 2 2 +--R ((A b c e + (- 2A c + B b c )d)x + (A b c e + (- 2A b c + B b c)d)x) +--R * +--R log(x) +--R + +--R 2 3 2 2 2 +--R ((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 +--R ((- A b c e + (2A c - B b c )d)x + (- A b c e + (2A b c - B b c)d)x) +--R * +--R log(c x + b) +--R + +--R 2 3 2 2 2 2 2 +--R ((A b c e + (- 2A c + B b c )d)x + (A b c e + (- 2A b c + B b c)d)x) +--R * +--R log(x) +--R + +--R 2 3 2 2 2 +--R ((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1457 +t0:=(A+B*x)/(b*x+c*x^2)^2 +--R +--R +--R B x + A +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 1457 +r0:=-A/(b^2*x)+(b*B-A*c)/(b^2*(b+c*x))+(b*B-2*A*c)*log(x)/b^3-(b*B-2*A*c)*_ + log(b+c*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R ((2A c - B b c)x + (2A b c - B b )x)log(c x + b) +--R + +--R 2 2 2 2 +--R ((- 2A c + B b c)x + (- 2A b c + B b )x)log(x) + (- 2A b c + B b )x +--R + +--R 2 +--R - A b +--R / +--R 3 2 4 +--R b c x + b x +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R ((2A c - B b c)x + (2A b c - B b )x)log(c x + b) +--R + +--R 2 2 2 2 +--R ((- 2A c + B b c)x + (- 2A b c + B b )x)log(x) + (- 2A b c + B b )x +--R + +--R 2 +--R - A b +--R / +--R 3 2 4 +--R b c x + b x +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1457 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +--R c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 1457 +r0:=-A/(b^2*d*x)+c*(b*B-A*c)/(b^2*(c*d-b*e)*(b+c*x))+(b*B*d-2*A*c*d-A*b*e)*_ + log(x)/(b^3*d^2)+c*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+3*A*e))*log(b+c*x)/_ + (b^3*(c*d-b*e)^2)-e^2*(B*d-A*e)*log(d+e*x)/(d^2*(c*d-b*e)^2) +--R +--R +--R (2) +--R 3 3 3 2 2 4 3 4 2 +--R ((A b c e - B b c d e )x + (A b e - B b d e )x)log(e x + d) +--R + +--R 3 2 2 2 4 3 3 2 +--R ((- 3A b c + 2B b c )d e + (2A c - B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((- 3A b c + 2B b c)d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 3 3 2 3 2 2 2 +--R - A b c e + B b c d e + (3A b c - 2B b c )d e +--R + +--R 4 3 3 +--R (- 2A c + B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 2 2 3 2 3 2 2 3 +--R (- A b e + B b d e + (3A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 2 2 3 +--R (- A b c d e + (3A b c - B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R (b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 4 3 4 2 +--R ((A b c e - B b c d e )x + (A b e - B b d e )x)log(e x + d) +--R + +--R 3 2 2 2 4 3 3 2 +--R ((- 3A b c + 2B b c )d e + (2A c - B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((- 3A b c + 2B b c)d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 3 3 2 3 2 2 2 +--R - A b c e + B b c d e + (3A b c - 2B b c )d e +--R + +--R 4 3 3 +--R (- 2A c + B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 2 2 3 2 3 2 2 3 +--R (- A b e + B b d e + (3A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 2 2 3 +--R (- A b c d e + (3A b c - B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R (b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1457 +r0:=-A/(b^2*d^2*x)+c^2*(b*B-A*c)/(b^2*(c*d-b*e)^2*(b+c*x))+e^2*(B*d-A*e)/_ + (d^2*(c*d-b*e)^2*(d+e*x))+(b*B*d-2*A*c*d-2*A*b*e)*log(x)/(b^3*d^3)+_ + c^2*(2*A*c^2*d+3*b^2*B*e-b*c*(B*d+4*A*e))*log(b+c*x)/(b^3*_ + (c*d-b*e)^3)+e^2*(2*A*e*(2*c*d-b*e)-B*d*(3*c*d-b*e))*log(d+e*x)/_ + (d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 4 5 3 2 4 4 3 2 2 3 3 +--R (2A b c e + (- 4A b c - B b c)d e + 3B b c d e )x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 2A b e + (- 2A b c - B b )d e + (- 4A b c + 2B b c)d e +--R + +--R 3 2 3 2 +--R 3B b c d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R (2A b d e + (- 4A b c - B b )d e + 3B b c d e )x +--R * +--R log(e x + d) +--R + +--R 4 2 3 3 2 5 4 4 3 +--R ((4A b c - 3B b c )d e + (- 2A c + B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (4A b c - 3B b c )d e + (2A b c - 2B b c )d e +--R + +--R 5 4 5 +--R (- 2A c + B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((4A b c - 3B b c )d e + (- 2A b c + B b c )d )x +--R * +--R log(c x + b) +--R + +--R 4 5 3 2 4 4 3 2 2 3 +--R - 2A b c e + (4A b c + B b c)d e - 3B b c d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 4A b c + 3B b c )d e + (2A c - B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 2A b e + (2A b c + B b )d e + (4A b c - 2B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R - 4A b c d e + (- 2A b c + 2B b c )d e + (2A c - B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R - 2A b d e + (4A b c + B b )d e - 3B b c d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (- 4A b c + 3B b c )d e + (2A b c - B b c )d +--R * +--R x +--R * +--R log(x) +--R + +--R 4 4 3 2 4 2 3 2 3 3 2 +--R - 2A b c d e + (4A b c + B b c)d e - 4A b c d e +--R + +--R 4 2 3 4 +--R (2A b c - B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R - 2A b d e + (3A b c + B b )d e - B b c d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (- 3A b c + B b c )d e + (2A b c - B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - A b d e + 3A b c d e - 3A b c d e + A b c d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (b c d e - 3b c d e + 3b c d e - b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (b d e - 2b c d e + 2b c d e - b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (b d e - 3b c d e + 3b c d e - b c d )x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1457 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 1457 +--m0:=a0-r0 +--E 249 + +--S 250 of 1457 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 1457 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1457 +r0:=-A/(b^2*d^3*x)+c^3*(b*B-A*c)/(b^2*(c*d-b*e)^3*(b+c*x))+1/2*e^2*_ + (B*d-A*e)/(d^2*(c*d-b*e)^2*(d+e*x)^2)-e^2*(2*A*e*(2*c*d-b*e)-B*d*_ + (3*c*d-b*e))/(d^3*(c*d-b*e)^3*(d+e*x))+(b*B*d-2*A*c*d-3*A*b*e)*_ + log(x)/(b^3*d^4)+c^3*(2*A*c^2*d+4*b^2*B*e-b*c*(B*d+5*A*e))*log(b+_ + c*x)/(b^3*(c*d-b*e)^4)-e^2*(B*d*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)-_ + A*e*(10*c^2*d^2-10*b*c*d*e+3*b^2*e^2))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 5 7 4 2 5 6 3 3 4 2 2 5 +--R 6A b c e + (- 20A b c - 2B b c)d e + (20A b c + 8B b c )d e +--R + +--R 3 3 3 4 +--R - 12B b c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R 6A b e + (- 8A b c - 2B b )d e + (- 20A b c + 4B b c)d e +--R + +--R 3 3 4 2 3 4 3 3 4 3 +--R (40A b c + 4B b c )d e - 24B b c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R 12A b d e + (- 34A b c - 4B b )d e + (20A b c + 14B b c)d e +--R + +--R 3 3 4 2 4 3 3 3 5 2 +--R (20A b c - 16B b c )d e - 12B b c d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R 6A b d e + (- 20A b c - 2B b )d e + (20A b c + 8B b c)d e +--R + +--R 4 2 5 2 +--R - 12B b c d e +--R * +--R x +--R * +--R log(e x + d) +--R + +--R 5 2 4 4 3 6 5 5 2 4 +--R ((- 10A b c + 8B b c )d e + (4A c - 2B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 10A b c + 8B b c )d e + (- 16A b c + 14B b c )d e +--R + +--R 6 5 6 +--R (8A c - 4B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 20A b c + 16B b c )d e + (- 2A b c + 4B b c )d e +--R + +--R 6 5 7 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((- 10A b c + 8B b c )d e + (4A b c - 2B b c )d )x +--R * +--R log(c x + b) +--R + +--R 5 7 4 2 5 6 +--R - 6A b c e + (20A b c + 2B b c)d e +--R + +--R 3 3 4 2 2 5 3 3 3 4 +--R (- 20A b c - 8B b c )d e + 12B b c d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (10A b c - 8B b c )d e + (- 4A c + 2B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 6A b e + (8A b c + 2B b )d e + (20A b c - 4B b c)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (- 40A b c - 4B b c )d e + (10A b c + 16B b c )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (16A b c - 14B b c )d e + (- 8A c + 4B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R - 12A b d e + (34A b c + 4B b )d e + (- 20A b c - 14B b c)d e +--R + +--R 3 3 4 2 4 3 2 4 3 3 5 2 +--R (- 20A b c + 16B b c )d e + (20A b c - 4B b c )d e +--R + +--R 5 2 4 6 6 5 7 +--R (2A b c - 4B b c )d e + (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R - 6A b d e + (20A b c + 2B b )d e + (- 20A b c - 8B b c)d e +--R + +--R 4 2 5 2 2 4 3 3 6 5 2 4 7 +--R 12B b c d e + (10A b c - 8B b c )d e + (- 4A b c + 2B b c )d +--R * +--R x +--R * +--R log(x) +--R + +--R 5 6 4 2 5 2 5 3 3 4 2 3 4 +--R - 6A b c d e + (20A b c + 2B b c)d e + (- 20A b c - 8B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (10A b c + 4B b c )d e + (- 4A b c + 2B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R - 6A b d e + (11A b c + 2B b )d e + (10A b c - 5B b c)d e +--R + +--R 3 3 4 2 4 3 2 4 3 3 5 2 +--R (- 25A b c - 4B b c )d e + (18A b c + 3B b c )d e +--R + +--R 5 2 4 6 +--R (- 8A b c + 4B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R - 9A b d e + (28A b c + 3B b )d e + (- 25A b c - 10B b c)d e +--R + +--R 3 3 4 2 5 2 2 4 3 3 6 +--R (4A b c + 7B b c )d e + (6A b c - 2B b c )d e +--R + +--R 5 2 4 7 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 2A b d e + 8A b c d e - 12A b c d e + 8A b c d e - 2A b c d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (2b c d e - 8b c d e + 12b c d e - 8b c d e + 2b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3 +--R (2b d e - 4b c d e - 4b c d e + 16b c d e - 14b c d e + 4b c d e)x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2 +--R (4b d e - 14b c d e + 16b c d e - 4b c d e - 4b c d e + 2b c d )x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1457 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 1457 +--m0:=a0-r0 +--E 254 + +--S 255 of 1457 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 1457 +t0:=(A+B*x)*(d+e*x)^5/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1457 +r0:=-1/2*A*d^5/(b^3*x^2)-d^4*(b*B*d-3*A*c*d+5*A*b*e)/(b^4*x)+B*e^5*x/c^3-_ + 1/2*(b*B-A*c)*(c*d-b*e)^5/(b^3*c^4*(b+c*x)^2)-(c*d-b*e)^4*(2*b*B*c*d-_ + 3*A*c^2*d+3*b^2*B*e-2*A*b*c*e)/(b^4*c^4*(b+c*x))+d^3*(6*A*c^2*d^2+_ + 5*b^2*e*(B*d+2*A*e)-3*b*c*d*(B*d+5*A*e))*log(x)/b^5-(c*d-b*e)^3*_ + (6*A*c^3*d^2-3*b^3*B*e^2-3*b*c^2*d*(B*d-A*e)-b^2*c*e*(4*B*d-A*e))*_ + log(b+c*x)/(b^5*c^4) +--R +--R +--R (2) +--R 5 3 6 2 5 5 3 4 2 6 3 2 +--R (2A b c - 6B b c )e + 10B b c d e - 20A b c d e +--R + +--R 7 2 6 4 8 7 5 +--R (30A b c - 10B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 2 7 5 6 2 4 3 5 3 2 +--R (4A b c - 12B b c)e + 20B b c d e - 40A b c d e +--R + +--R 2 6 3 5 4 7 2 6 5 +--R (60A b c - 20B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 7 4 4 4 3 2 +--R (2A b c - 6B b )e + 10B b c d e - 20A b c d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (30A b c - 10B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 6 3 2 7 2 6 4 8 7 5 4 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 5 3 2 2 6 3 5 4 +--R 40A b c d e + (- 60A b c + 20B b c )d e +--R + +--R 7 2 6 5 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 3 2 3 5 4 4 4 2 6 3 5 5 2 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 5 5 6 2 5 4 +--R 2B b c e x + 4B b c e x +--R + +--R 6 2 7 5 5 3 6 2 4 5 3 2 3 +--R (4A b c - 4B b c)e + (- 10A b c + 20B b c )d e - 20B b c d e +--R + +--R 3 5 3 2 2 6 3 5 4 7 2 6 5 +--R 20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 6 2 7 4 +--R (3A b c - 5B b )e + (- 5A b c + 15B b c)d e +--R + +--R 5 3 6 2 2 3 4 4 5 3 3 2 +--R (- 10A b c - 10B b c )d e + (30A b c - 10B b c )d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (- 45A b c + 15B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 5 4 4 5 4 4 5 +--R (- 10A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 6 4 6 5 3 7 4 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 6 2 5 5 3 4 2 6 3 2 +--R (2A b c - 6B b c )e + 10B b c d e - 20A b c d e +--R + +--R 7 2 6 4 8 7 5 +--R (30A b c - 10B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 2 7 5 6 2 4 3 5 3 2 +--R (4A b c - 12B b c)e + 20B b c d e - 40A b c d e +--R + +--R 2 6 3 5 4 7 2 6 5 +--R (60A b c - 20B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 7 4 4 4 3 2 +--R (2A b c - 6B b )e + 10B b c d e - 20A b c d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (30A b c - 10B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 6 3 2 7 2 6 4 8 7 5 4 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 5 3 2 2 6 3 5 4 +--R 40A b c d e + (- 60A b c + 20B b c )d e +--R + +--R 7 2 6 5 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 3 2 3 5 4 4 4 2 6 3 5 5 2 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 5 5 6 2 5 4 +--R 2B b c e x + 4B b c e x +--R + +--R 6 2 7 5 5 3 6 2 4 5 3 2 3 +--R (4A b c - 4B b c)e + (- 10A b c + 20B b c )d e - 20B b c d e +--R + +--R 3 5 3 2 2 6 3 5 4 7 2 6 5 +--R 20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 6 2 7 4 +--R (3A b c - 5B b )e + (- 5A b c + 15B b c)d e +--R + +--R 5 3 6 2 2 3 4 4 5 3 3 2 +--R (- 10A b c - 10B b c )d e + (30A b c - 10B b c )d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (- 45A b c + 15B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 5 4 4 5 4 4 5 +--R (- 10A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 6 4 6 5 3 7 4 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1457 +r0:=-1/2*A*d^4/(b^3*x^2)-d^3*(b*B*d-3*A*c*d+4*A*b*e)/(b^4*x)-1/2*(b*B-_ + A*c)*(c*d-b*e)^4/(b^3*c^3*(b+c*x)^2)+(c*d-b*e)^3*(3*A*c^2*d-2*b^2*_ + B*e-b*c*(2*B*d-A*e))/(b^4*c^3*(b+c*x))+d^2*(6*A*c^2*d^2+2*b^2*e*_ + (2*B*d+3*A*e)-3*b*c*d*(B*d+4*A*e))*log(x)/b^5+(c*d-b*e)^2*(3*b*B*_ + c^2*d^2-6*A*c^3*d^2+2*b^2*B*c*d*e+b^3*B*e^2)*log(b+c*x)/(b^5*c^3) +--R +--R +--R (2) +--R 5 2 4 2 5 2 2 6 2 5 3 +--R 2B b c e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 7 6 4 +--R (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 4 3 4 2 2 2 5 3 4 3 +--R 4B b c e - 24A b c d e + (48A b c - 16B b c )d e +--R + +--R 6 2 5 4 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 4 4 3 2 2 3 4 4 3 3 +--R 2B b e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 2 5 3 4 4 +--R (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 5 2 2 6 2 5 3 7 6 4 4 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 4 2 2 2 5 3 4 3 +--R 24A b c d e + (- 48A b c + 16B b c )d e +--R + +--R 6 2 5 4 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 2 3 4 4 3 3 2 5 3 4 4 2 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 2 6 4 5 2 3 3 4 2 2 +--R (- 2A b c + 4B b c)e - 8B b c d e + 12A b c d e +--R + +--R 2 5 3 4 3 6 2 5 4 +--R (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- A b c + 3B b )e + (- 4A b c - 4B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (18A b c - 6B b c )d e + (- 36A b c + 12B b c )d e +--R + +--R 2 5 3 4 4 +--R (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 3 4 4 3 4 +--R (- 8A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 5 4 6 4 3 7 3 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 2 5 2 2 6 2 5 3 +--R 2B b c e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 7 6 4 +--R (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 4 3 4 2 2 2 5 3 4 3 +--R 4B b c e - 24A b c d e + (48A b c - 16B b c )d e +--R + +--R 6 2 5 4 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 4 4 3 2 2 3 4 4 3 3 +--R 2B b e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 2 5 3 4 4 +--R (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 5 2 2 6 2 5 3 7 6 4 4 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 4 2 2 2 5 3 4 3 +--R 24A b c d e + (- 48A b c + 16B b c )d e +--R + +--R 6 2 5 4 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 2 3 4 4 3 3 2 5 3 4 4 2 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 2 6 4 5 2 3 3 4 2 2 +--R (- 2A b c + 4B b c)e - 8B b c d e + 12A b c d e +--R + +--R 2 5 3 4 3 6 2 5 4 +--R (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- A b c + 3B b )e + (- 4A b c - 4B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (18A b c - 6B b c )d e + (- 36A b c + 12B b c )d e +--R + +--R 2 5 3 4 4 +--R (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 3 4 4 3 4 +--R (- 8A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 5 4 6 4 3 7 3 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1457 +r0:=-1/2*A*d^3/(b^3*x^2)-d^2*(b*B*d-3*A*c*d+3*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)^3/(b^3*c^2*(b+c*x)^2)-(c*d-b*e)^2*(2*b*B*c*d-3*A*c^2*d+_ + b^2*B*e)/(b^4*c^2*(b+c*x))-3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*_ + log(x)/b^5+3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 12A b c d e + (36A b c - 12B b c )d e +--R + +--R 5 2 4 3 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R 12A b c d e + (- 36A b c + 12B b c )d e +--R + +--R 5 2 4 3 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 3 3 2 2 4 3 3 2 +--R - 2B b c e + 6A b c d e + (- 18A b c + 6B b c )d e +--R + +--R 5 2 4 3 +--R (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - B b )e + (9A b c - 3B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 27A b c + 9B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 6A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 12A b c d e + (36A b c - 12B b c )d e +--R + +--R 5 2 4 3 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R 12A b c d e + (- 36A b c + 12B b c )d e +--R + +--R 5 2 4 3 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 3 3 2 2 4 3 3 2 +--R - 2B b c e + 6A b c d e + (- 18A b c + 6B b c )d e +--R + +--R 5 2 4 3 +--R (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - B b )e + (9A b c - 3B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 27A b c + 9B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 6A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1457 +r0:=-1/2*A*d^2/(b^3*x^2)-d*(b*B*d-3*A*c*d+2*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)^2/(b^3*c*(b+c*x)^2)-(c*d-b*e)*(2*b*B*d-3*A*c*d+A*b*e)/_ + (b^4*(b+c*x))+(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*_ + log(x)/b^5-(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*_ + log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 3 2 4 2 3 5 4 2 4 +--R (- 2A b c e + (12A b c - 4B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- 4A b c e + (24A b c - 8B b c )d e + (- 24A b c + 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 2A b c e + (12A b c - 4B b c)d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (4A b c e + (- 24A b c + 8B b c )d e + (24A b c - 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (2A b c e + (- 12A b c + 4B b c)d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A b c - 6B b c )d )x +--R + +--R 4 5 2 3 2 4 2 3 3 2 2 2 +--R ((3A b c - B b )e + (- 18A b c + 6B b c)d e + (18A b c - 9B b c )d )x +--R + +--R 4 3 2 4 2 4 2 +--R (- 4A b c d e + (4A b c - 2B b c)d )x - A b c d +--R / +--R 5 3 4 6 2 3 7 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 2 3 5 4 2 4 +--R (- 2A b c e + (12A b c - 4B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- 4A b c e + (24A b c - 8B b c )d e + (- 24A b c + 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 2A b c e + (12A b c - 4B b c)d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (4A b c e + (- 24A b c + 8B b c )d e + (24A b c - 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (2A b c e + (- 12A b c + 4B b c)d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A b c - 6B b c )d )x +--R + +--R 4 5 2 3 2 4 2 3 3 2 2 2 +--R ((3A b c - B b )e + (- 18A b c + 6B b c)d e + (18A b c - 9B b c )d )x +--R + +--R 4 3 2 4 2 4 2 +--R (- 4A b c d e + (4A b c - 2B b c)d )x - A b c d +--R / +--R 5 3 4 6 2 3 7 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1457 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^3 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1457 +r0:=-1/2*A*d/(b^3*x^2)+(-b*B*d+3*A*c*d-A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)/(b^3*(b+c*x)^2)+(3*A*c^2*d+b^2*B*e-2*b*c*(B*d+A*e))/_ + (b^4*(b+c*x))+(6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(x)/b^5-_ + (6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 3 2 2 4 3 4 +--R ((6A b c - 2B b c )e + (- 12A c + 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((12A b c - 4B b c)e + (- 24A b c + 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((6A b c - 2B b )e + (- 12A b c + 6B b c)d)x +--R * +--R log(c x + b) +--R + +--R 3 2 2 4 3 4 +--R ((- 6A b c + 2B b c )e + (12A c - 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 4B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 6A b c + 2B b )e + (12A b c - 6B b c)d)x +--R * +--R log(x) +--R + +--R 2 2 3 3 2 2 3 +--R ((- 6A b c + 2B b c)e + (12A b c - 6B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 9A b c + 3B b )e + (18A b c - 9B b c)d)x +--R + +--R 4 3 4 4 +--R (- 2A b e + (4A b c - 2B b )d)x - A b d +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 4 3 4 +--R ((6A b c - 2B b c )e + (- 12A c + 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((12A b c - 4B b c)e + (- 24A b c + 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((6A b c - 2B b )e + (- 12A b c + 6B b c)d)x +--R * +--R log(c x + b) +--R + +--R 3 2 2 4 3 4 +--R ((- 6A b c + 2B b c )e + (12A c - 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 4B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 6A b c + 2B b )e + (12A b c - 6B b c)d)x +--R * +--R log(x) +--R + +--R 2 2 3 3 2 2 3 +--R ((- 6A b c + 2B b c)e + (12A b c - 6B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 9A b c + 3B b )e + (18A b c - 9B b c)d)x +--R + +--R 4 3 4 4 +--R (- 2A b e + (4A b c - 2B b )d)x - A b d +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1457 +t0:=(A+B*x)/(b*x+c*x^2)^3 +--R +--R +--R B x + A +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1457 +r0:=-1/2*A/(b^3*x^2)+(-b*B+3*A*c)/(b^4*x)-1/2*c*(b*B-A*c)/(b^3*(b+c*x)^2)-_ + c*(2*b*B-3*A*c)/(b^4*(b+c*x))-3*c*(b*B-2*A*c)*log(x)/b^5+3*c*(b*B-_ + 2*A*c)*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 4 3 4 3 2 2 3 +--R (- 12A c + 6B b c )x + (- 24A b c + 12B b c )x +--R + +--R 2 2 3 2 +--R (- 12A b c + 6B b c)x +--R * +--R log(c x + b) +--R + +--R 4 3 4 3 2 2 3 +--R (12A c - 6B b c )x + (24A b c - 12B b c )x +--R + +--R 2 2 3 2 +--R (12A b c - 6B b c)x +--R * +--R log(x) +--R + +--R 3 2 2 3 2 2 3 2 3 4 4 +--R (12A b c - 6B b c )x + (18A b c - 9B b c)x + (4A b c - 2B b )x - A b +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 3 2 2 3 +--R (- 12A c + 6B b c )x + (- 24A b c + 12B b c )x +--R + +--R 2 2 3 2 +--R (- 12A b c + 6B b c)x +--R * +--R log(c x + b) +--R + +--R 4 3 4 3 2 2 3 +--R (12A c - 6B b c )x + (24A b c - 12B b c )x +--R + +--R 2 2 3 2 +--R (12A b c - 6B b c)x +--R * +--R log(x) +--R + +--R 3 2 2 3 2 2 3 2 3 4 4 +--R (12A b c - 6B b c )x + (18A b c - 9B b c)x + (4A b c - 2B b )x - A b +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1457 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R --------------------------------------------------------------------------- +--R 3 7 2 3 6 2 2 5 3 2 4 3 3 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1457 +r0:=-1/2*A/(b^3*d*x^2)+(-b*B*d+3*A*c*d+A*b*e)/(b^4*d^2*x)-1/2*c^2*(b*B-_ + A*c)/(b^3*(c*d-b*e)*(b+c*x)^2)+c^2*(3*A*c^2*d+3*b^2*B*e-2*b*c*(B*d+_ + 2*A*e))/(b^4*(c*d-b*e)^2*(b+c*x))+(6*A*c^2*d^2-3*b*c*d*(B*d-A*e)-_ + b^2*e*(B*d-A*e))*log(x)/(b^5*d^3)-c^2*(6*A*c^3*d^2-6*b^3*B*e^2-_ + 3*b*c^2*d*(B*d+5*A*e)+2*b^2*c*e*(4*B*d+5*A*e))*log(b+c*x)/(b^5*(c*d-_ + b*e)^3)-e^4*(B*d-A*e)*log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 5 2 5 5 2 4 4 6 5 6 4 3 +--R (- 2A b c e + 2B b c d e )x + (- 4A b c e + 4B b c d e )x +--R + +--R 7 5 7 4 2 +--R (- 2A b e + 2B b d e )x +--R * +--R log(e x + d) +--R + +--R 2 5 3 4 3 2 6 2 5 4 +--R (20A b c - 12B b c )d e + (- 30A b c + 16B b c )d e +--R + +--R 7 6 5 +--R (12A c - 6B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 3 2 2 5 3 4 4 +--R (40A b c - 24B b c )d e + (- 60A b c + 32B b c )d e +--R + +--R 6 2 5 5 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (20A b c - 12B b c )d e + (- 30A b c + 16B b c )d e +--R + +--R 2 5 3 4 5 +--R (12A b c - 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 5 2 5 5 2 4 2 5 3 4 3 2 +--R 2A b c e - 2B b c d e + (- 20A b c + 12B b c )d e +--R + +--R 6 2 5 4 7 6 5 +--R (30A b c - 16B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 5 6 4 3 4 4 3 3 2 +--R 4A b c e - 4B b c d e + (- 40A b c + 24B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (60A b c - 32B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 7 4 4 3 5 2 3 2 +--R 2A b e - 2B b d e + (- 20A b c + 12B b c )d e +--R + +--R 3 4 4 3 4 2 5 3 4 5 +--R (30A b c - 16B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(x) +--R + +--R 5 2 4 5 2 2 3 3 4 4 3 3 2 +--R 2A b c d e - 2B b c d e + (- 20A b c + 12B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (30A b c - 16B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 2 6 2 3 4 3 5 2 3 2 +--R 4A b c d e + (- A b c - 4B b c)d e + (- 30A b c + 19B b c )d e +--R + +--R 3 4 4 3 4 2 5 3 4 5 +--R (45A b c - 24B b c )d e + (- 18A b c + 9B b c )d +--R * +--R 2 +--R x +--R + +--R 7 4 6 7 2 3 5 2 6 3 2 +--R 2A b d e + (- 2A b c - 2B b )d e + (- 6A b c + 6B b c)d e +--R + +--R 4 3 5 2 4 3 4 4 3 5 +--R (10A b c - 6B b c )d e + (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - A b d e + 3A b c d e - 3A b c d e + A b c d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (2b c d e - 6b c d e + 6b c d e - 2b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d )x +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1457 +--a0:=integrate(t0,x) +--E 288 + +--S 289 of 1457 +--m0:=a0-r0 +--E 289 + +--S 290 of 1457 +--d0:=D(m0,x) +--E 290 + +)clear all + +--S 291 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1457 +r0:=-1/2*A/(b^3*d^2*x^2)+(-b*B*d+3*A*c*d+2*A*b*e)/(b^4*d^3*x)-1/2*c^3*(b*B-_ + A*c)/(b^3*(c*d-b*e)^2*(b+c*x)^2)-c^3*(2*b*B*c*d-3*A*c^2*d-4*b^2*B*e+_ + 5*A*b*c*e)/(b^4*(c*d-b*e)^3*(b+c*x))+e^4*(B*d-A*e)/(d^3*(c*d-b*e)^3*_ + (d+e*x))+(6*A*c^2*d^2-b^2*e*(2*B*d-3*A*e)-3*b*c*d*(B*d-2*A*e))*_ + log(x)/(b^5*d^4)-c^3*(6*A*c^3*d^2-10*b^3*B*e^2+5*b^2*c*e*(2*B*d+_ + 3*A*e)-3*b*c^2*d*(B*d+6*A*e))*log(b+c*x)/(b^5*(c*d-b*e)^4)-e^4*_ + (B*d*(5*c*d-2*b*e)-3*A*e*(2*c*d-b*e))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 6 2 7 5 3 6 2 6 5 3 2 5 5 +--R (- 6A b c e + (12A b c + 4B b c )d e - 10B b c d e )x +--R + +--R 7 7 6 2 7 6 +--R - 12A b c e + (18A b c + 8B b c)d e +--R + +--R 5 3 6 2 2 5 5 3 3 4 +--R (12A b c - 16B b c )d e - 10B b c d e +--R * +--R 4 +--R x +--R + +--R 8 7 8 6 6 2 7 2 5 6 2 3 4 3 +--R (- 6A b e + 4B b d e + (24A b c - 2B b c)d e - 20B b c d e )x +--R + +--R 8 6 7 8 2 5 7 3 4 2 +--R (- 6A b d e + (12A b c + 4B b )d e - 10B b c d e )x +--R * +--R log(e x + d) +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 30A b c + 20B b c )d e + (36A b c - 20B b c )d e +--R + +--R 8 7 6 +--R (- 12A c + 6B b c )d e +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 60A b c + 40B b c )d e + (42A b c - 20B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (12A b c - 8B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (- 30A b c + 20B b c )d e + (- 24A b c + 20B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (60A b c - 34B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (- 30A b c + 20B b c )d e + (36A b c - 20B b c )d e +--R + +--R 2 6 3 5 7 +--R (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 6 2 7 5 3 6 2 6 5 3 2 5 +--R 6A b c e + (- 12A b c - 4B b c )d e + 10B b c d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 8 7 6 +--R (12A c - 6B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R 12A b c e + (- 18A b c - 8B b c)d e +--R + +--R 5 3 6 2 2 5 5 3 3 4 +--R (- 12A b c + 16B b c )d e + 10B b c d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (60A b c - 40B b c )d e + (- 42A b c + 20B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (- 12A b c + 8B b c )d e + (12A c - 6B b c )d +--R * +--R 4 +--R x +--R + +--R 8 7 8 6 6 2 7 2 5 6 2 3 4 +--R 6A b e - 4B b d e + (- 24A b c + 2B b c)d e + 20B b c d e +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (30A b c - 20B b c )d e + (24A b c - 20B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 60A b c + 34B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 7 3 4 +--R 6A b d e + (- 12A b c - 4B b )d e + 10B b c d e +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 2 6 3 5 7 +--R (12A b c - 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(x) +--R + +--R 6 2 6 5 3 6 2 2 5 5 3 3 4 +--R 6A b c d e + (- 12A b c - 4B b c )d e + 10B b c d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 7 2 6 6 +--R (12A b c - 6B b c )d e +--R * +--R 4 +--R x +--R + +--R 7 6 6 2 7 2 5 5 3 6 2 3 4 +--R 12A b c d e + (- 21A b c - 8B b c)d e + (- 6A b c + 18B b c )d e +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (45A b c - 25B b c )d e + (- 24A b c + 10B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 18A b c + 11B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 6 2 7 3 4 +--R 6A b d e + (- 6A b c - 4B b )d e + (- 13A b c + 6B b c)d e +--R + +--R 5 3 6 2 4 3 4 4 5 3 5 2 +--R (12A b c + 4B b c )d e + (33A b c - 25B b c )d e +--R + +--R 3 5 4 4 6 2 6 3 5 7 +--R (- 50A b c + 28B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 8 3 4 6 2 7 4 3 +--R 3A b d e + (- 8A b c - 2B b )d e + (2A b c + 8B b c)d e +--R + +--R 5 3 6 2 5 2 4 4 5 3 6 +--R (12A b c - 12B b c )d e + (- 13A b c + 8B b c )d e +--R + +--R 3 5 4 4 7 +--R (4A b c - 2B b c )d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - A b d e + 4A b c d e - 6A b c d e + 4A b c d e - A b c d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (2b c d e - 8b c d e + 12b c d e - 8b c d e + 2b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 5 6 9 4 +--R (4b c d e - 14b c d e + 16b c d e - 4b c d e - 4b c d e + 2b c d )x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 6 5 9 3 +--R (2b d e - 4b c d e - 4b c d e + 16b c d e - 14b c d e + 4b c d )x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )x +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1457 +--a0:=integrate(t0,x) +--E 293 + +--S 294 of 1457 +--m0:=a0-r0 +--E 294 + +--S 295 of 1457 +--d0:=D(m0,x) +--E 295 + +)clear all + +--S 296 of 1457 +t0:=(A+B*x)*(d+e*x)^3*sqrt(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1457 +r0:=1/960*(4*A*c*e*(132*c^2*d^2-132*b*c*d*e+35*b^2*e^2)+B*(64*c^3*d^3-_ + 360*b*c^2*d^2*e+366*b^2*c*d*e^2-105*b^3*e^3))*(b*x+c*x^2)^(3/2)/c^4+_ + 1/20*(2*B*c*d-3*b*B*e+4*A*c*e)*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c^2+_ + 1/6*B*(d+e*x)^3*(b*x+c*x^2)^(3/2)/c-1/160*e*(d*(16*b*B*c*d-40*A*c^2*d-_ + 9*b^2*B*e+12*A*b*c*e)-(28*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-36*b*c*d*e+_ + 21*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/c^3-1/512*b^2*(128*A*c^4*d^3+_ + 21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-28*b^3*c*e^2*(3*B*d+A*e)-_ + 64*b*c^3*d^2*(B*d+3*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+_ + 1/512*b*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-_ + 28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/c^5+_ + 1/256*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-_ + 28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*x*sqrt(b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 5 6 3 4 2 5 2 +--R (420A b c - 315B b )e + (- 1800A b c + 1260B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (2880A b c - 1800B b c )d e + (- 1920A b c + 960B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 3 5 5 4 3 5 2 4 +--R 1280B c e x + ((1536A c + 128B b c )e + 4608B c d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (192A b c - 144B b c )e + (5760A c + 576B b c )d e +--R + +--R 5 2 +--R 5760B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 224A b c + 168B b c )e + (960A b c - 672B b c )d e +--R + +--R 5 4 2 5 3 +--R (7680A c + 960B b c )d e + 2560B c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (280A b c - 210B b c)e + (- 1200A b c + 840B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (1920A b c - 1200B b c )d e + (3840A c + 640B b c )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 420A b c + 315B b )e + (1800A b c - 1260B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 2880A b c + 1800B b c )d e + (1920A b c - 960B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 6 3 4 2 5 2 +--R (420A b c - 315B b )e + (- 1800A b c + 1260B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (2880A b c - 1800B b c )d e + (- 1920A b c + 960B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 5 3 5 5 4 3 5 2 4 +--R 2560B c e x + ((3072A c + 256B b c )e + 9216B c d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (384A b c - 288B b c )e + (11520A c + 1152B b c )d e +--R + +--R 5 2 +--R 11520B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 448A b c + 336B b c )e + (1920A b c - 1344B b c )d e +--R + +--R 5 4 2 5 3 +--R (15360A c + 1920B b c )d e + 5120B c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (560A b c - 420B b c)e + (- 2400A b c + 1680B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (3840A b c - 2400B b c )d e + (7680A c + 1280B b c )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 840A b c + 630B b )e + (3600A b c - 2520B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 5760A b c + 3600B b c )d e + (3840A b c - 1920B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 15360c \|c +--R , +--R +--R 5 6 3 4 2 5 2 +--R (420A b c - 315B b )e + (- 1800A b c + 1260B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (2880A b c - 1800B b c )d e + (- 1920A b c + 960B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 5 3 5 5 4 3 5 2 4 +--R 1280B c e x + ((1536A c + 128B b c )e + 4608B c d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (192A b c - 144B b c )e + (5760A c + 576B b c )d e +--R + +--R 5 2 +--R 5760B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 224A b c + 168B b c )e + (960A b c - 672B b c )d e +--R + +--R 5 4 2 5 3 +--R (7680A c + 960B b c )d e + 2560B c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (280A b c - 210B b c)e + (- 1200A b c + 840B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (1920A b c - 1200B b c )d e + (3840A c + 640B b c )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 420A b c + 315B b )e + (1800A b c - 1260B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 2880A b c + 1800B b c )d e + (1920A b c - 960B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 5 +---+ +--R 7680c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 298 + +--S 299 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 6 3 4 2 5 2 +--R (28A b c - 21B b )e + (- 120A b c + 84B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (192A b c - 120B b c )d e + (- 128A b c + 64B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 5 6 3 4 2 5 2 +--R (- 56A b c + 42B b )e + (240A b c - 168B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 384A b c + 240B b c )d e + (256A b c - 128B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 5 +-+ +--R 1024c \|c +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 6 3 4 2 5 2 +--R (- 28A b c + 21B b )e + (120A b c - 84B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 192A b c + 120B b c )d e + (128A b c - 64B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 6 3 4 2 5 2 +--R (28A b c - 21B b )e + (- 120A b c + 84B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (192A b c - 120B b c )d e + (- 128A b c + 64B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 5 +---+ +-+ +--R 512c \|- c \|c +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 302 + +)clear all + +--S 303 of 1457 +t0:=(A+B*x)*(d+e*x)^2*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R 2 3 2 2 2 2 | 2 +--R (1) (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|c x + b x +--R Type: Expression(Integer) +--E 303 + +--S 304 of 1457 +r0:=1/240*(50*A*c*e*(2*c*d-b*e)+B*(32*c^2*d^2-82*b*c*d*e+35*b^2*e^2))*_ + (b*x+c*x^2)^(3/2)/c^3+1/5*B*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c-1/40*e*_ + ((3*b*B-10*A*c)*d-(4*B*c*d-7*b*B*e+10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/c^2-_ + 1/128*b^2*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-_ + 16*b*c^2*d*(B*d+2*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)+_ + 1/128*b*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*_ + d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/c^4+1/64*(32*A*c^3*d^2-7*b^3*B*e^2+_ + 10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 4 5 2 3 2 4 +--R (- 150A b c + 105B b )e + (480A b c - 300B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 480A b c + 240B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 2 4 4 3 2 4 3 +--R 384B c e x + ((480A c + 48B b c )e + 960B c d e)x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((80A b c - 56B b c )e + (1280A c + 160B b c )d e + 640B c d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 100A b c + 70B b c)e + (320A b c - 200B b c )d e +--R + +--R 4 3 2 +--R (960A c + 160B b c )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (150A b c - 105B b )e + (- 480A b c + 300B b c)d e +--R + +--R 3 2 2 2 +--R (480A b c - 240B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 1920c \|c +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 5 2 3 2 4 +--R (150A b c - 105B b )e + (- 480A b c + 300B b c)d e +--R + +--R 2 3 3 2 2 +--R (480A b c - 240B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 2 4 4 3 2 4 3 +--R 768B c e x + ((960A c + 96B b c )e + 1920B c d e)x +--R + +--R 3 2 2 2 4 3 +--R (160A b c - 112B b c )e + (2560A c + 320B b c )d e +--R + +--R 4 2 +--R 1280B c d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 2 +--R (- 200A b c + 140B b c)e + (640A b c - 400B b c )d e +--R + +--R 4 3 2 +--R (1920A c + 320B b c )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (300A b c - 210B b )e + (- 960A b c + 600B b c)d e +--R + +--R 3 2 2 2 +--R (960A b c - 480B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 3840c \|c +--R , +--R +--R 4 5 2 3 2 4 +--R (- 150A b c + 105B b )e + (480A b c - 300B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 480A b c + 240B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 4 2 4 4 3 2 4 3 +--R 384B c e x + ((480A c + 48B b c )e + 960B c d e)x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((80A b c - 56B b c )e + (1280A c + 160B b c )d e + 640B c d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 100A b c + 70B b c)e + (320A b c - 200B b c )d e +--R + +--R 4 3 2 +--R (960A c + 160B b c )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (150A b c - 105B b )e + (- 480A b c + 300B b c)d e +--R + +--R 3 2 2 2 +--R (480A b c - 240B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 1920c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 305 + +--S 306 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 5 2 3 2 4 +--R (10A b c - 7B b )e + (- 32A b c + 20B b c)d e +--R + +--R 2 3 3 2 2 +--R (32A b c - 16B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 5 2 3 2 4 +--R (20A b c - 14B b )e + (- 64A b c + 40B b c)d e +--R + +--R 2 3 3 2 2 +--R (64A b c - 32B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 256c \|c +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 5 2 3 2 4 +--R (10A b c - 7B b )e + (- 32A b c + 20B b c)d e +--R + +--R 2 3 3 2 2 +--R (32A b c - 16B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 5 2 3 2 4 +--R (- 10A b c + 7B b )e + (32A b c - 20B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 32A b c + 16B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 128c \|- c \|c +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 1457 +t0:=(A+B*x)*(d+e*x)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (1) (B e x + (A e + B d)x + A d)\|c x + b x +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1457 +r0:=1/24*(2*B*c*d-5*b*B*e+8*A*c*e)*(b*x+c*x^2)^(3/2)/c^2+1/4*B*(d+e*x)*_ + (b*x+c*x^2)^(3/2)/c-1/64*b^2*(16*A*c^2*d+5*b^2*B*e-8*b*c*(B*d+A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/64*b*(16*A*c^2*d+5*b^2*B*e-_ + 8*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^3+1/32*(16*A*c^2*d+5*b^2*B*e-_ + 8*b*c*(B*d+A*e))*x*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 3 4 2 2 3 x\|c +--R ((24A b c - 15B b )e + (- 48A b c + 24B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 3 3 2 3 2 +--R 48B c e x + ((64A c + 8B b c )e + 64B c d)x +--R + +--R 2 2 3 2 +--R ((16A b c - 10B b c)e + (96A c + 16B b c )d)x +--R + +--R 2 3 2 2 +--R (- 24A b c + 15B b )e + (48A b c - 24B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 2 3 +--R ((24A b c - 15B b )e + (- 48A b c + 24B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 3 3 2 3 2 +--R 96B c e x + ((128A c + 16B b c )e + 128B c d)x +--R + +--R 2 2 3 2 +--R ((32A b c - 20B b c)e + (192A c + 32B b c )d)x +--R + +--R 2 3 2 2 +--R (- 48A b c + 30B b )e + (96A b c - 48B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 384c \|c +--R , +--R +--R 3 4 2 2 3 +--R ((24A b c - 15B b )e + (- 48A b c + 24B b c)d) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 3 3 2 3 2 +--R 48B c e x + ((64A c + 8B b c )e + 64B c d)x +--R + +--R 2 2 3 2 +--R ((16A b c - 10B b c)e + (96A c + 16B b c )d)x +--R + +--R 2 3 2 2 +--R (- 24A b c + 15B b )e + (48A b c - 24B b c)d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 3 +---+ +--R 192c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 312 + +--S 313 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 +--R ((8A b c - 5B b )e + (- 16A b c + 8B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 3 4 2 2 3 x\|c +--R ((- 16A b c + 10B b )e + (32A b c - 16B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 128c \|c +--R Type: Expression(Integer) +--E 313 + +--S 314 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 3 4 2 2 3 +---+ x\|c +--R ((- 8A b c + 5B b )e + (16A b c - 8B b c)d)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 3 4 2 2 3 +-+ \|- c \|c x + b x +--R ((8A b c - 5B b )e + (- 16A b c + 8B b c)d)\|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 64c \|- c \|c +--R Type: Expression(Integer) +--E 315 + +--S 316 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 316 + +)clear all + +--S 317 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R | 2 +--R (1) (B x + A)\|c x + b x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1457 +r0:=1/3*B*(b*x+c*x^2)^(3/2)/c+1/8*b^2*(b*B-2*A*c)*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/c^(5/2)-1/8*b*(b*B-2*A*c)*sqrt(b*x+c*x^2)/c^2-_ + 1/4*(b*B-2*A*c)*x*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 2 3 x\|c +--R (- 6A b c + 3B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R 2 2 2 2 +-+ | 2 +--R (8B c x + (12A c + 2B b c)x + 6A b c - 3B b )\|c \|c x + b x +--R / +--R 2 +-+ +--R 24c \|c +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 2 3 | 2 +-+ +--R (6A b c - 3B b )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R 2 2 2 2 +-+ | 2 +--R (16B c x + (24A c + 4B b c)x + 12A b c - 6B b )\|c \|c x + b x +--R / +--R 2 +-+ +--R 48c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 2 3 \|- c \|c x + b x +--R (- 6A b c + 3B b )atan(-------------------) +--R c x +--R + +--R +----------+ +--R 2 2 2 2 +---+ | 2 +--R (8B c x + (12A c + 2B b c)x + 6A b c - 3B b )\|- c \|c x + b x +--R / +--R 2 +---+ +--R 24c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 319 + +--S 320 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 2 3 | 2 +-+ +--R (2A b c - B b )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 2 3 x\|c +--R (4A b c - 2B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 2 +-+ +--R 16c \|c +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 3 +---+ x\|c +--R (2A b c - B b )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 2 3 +-+ \|- c \|c x + b x +--R (- 2A b c + B b )\|c atan(-------------------) +--R c x +--R / +--R 2 +---+ +-+ +--R 8c \|- c \|c +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 323 + +)clear all + +--S 324 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R e x + d +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1457 +r0:=-1/4*(4*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-4*b*c*d*e-b^2*e^2))*atanh(x*_ + sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^3)-(B*d-A*e)*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*_ + sqrt(c*d-b*e)/e^3-1/4*(4*B*c*d-b*B*e-4*A*c*e-2*B*c*e*x)*sqrt(b*x+_ + c*x^2)/(c*e^2) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 2 2 x\|c +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ +--R (- 4A c e + 4B c d)\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R 2 2 +-+ | 2 +--R (2B c e x + (4A c + B b)e - 4B c d e)\|c \|c x + b x +--R / +--R 3 +-+ +--R 4c e \|c +--R Type: Expression(Integer) +--E 325 + +--S 326 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R | 2 +-+ +--R (8A c e - 8B c d)\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R 2 2 +-+ | 2 +--R (4B c e x + (8A c + 2B b)e - 8B c d e)\|c \|c x + b x +--R / +--R 3 +-+ +--R 8c e \|c +--R , +--R +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R (16A c e - 16B c d)\|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R +----------+ +--R 2 2 +-+ | 2 +--R (4B c e x + (8A c + 2B b)e - 8B c d e)\|c \|c x + b x +--R / +--R 3 +-+ +--R 8c e \|c +--R , +--R +--R +--------------+ +--R | 2 +---+ +--R (4A c e - 4B c d)\|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R +----------+ +--R 2 2 +---+ | 2 +--R (2B c e x + (4A c + B b)e - 4B c d e)\|- c \|c x + b x +--R / +--R 3 +---+ +--R 4c e \|- c +--R , +--R +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 d\|c x + b x +--R (8A c e - 8B c d)\|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R +----------+ +--R 2 2 +---+ | 2 +--R (2B c e x + (4A c + B b)e - 4B c d e)\|- c \|c x + b x +--R / +--R 3 +---+ +--R 4c e \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 326 + +--S 327 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R | 2 +-+ +--R (8A c e - 8B c d)\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 2 2 +--R ((- 8A b c + 2B b )e + (16A c + 8B b c)d e - 16B c d ) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ +--R (8A c e - 8B c d)\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 3 +-+ +--R 8c e \|c +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 2 2 +--R ((- 8A b c + 2B b )e + (16A c + 8B b c)d e - 16B c d ) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ +--R (8A c e - 8B c d)\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R (16A c e - 16B c d)\|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 3 +-+ +--R 8c e \|c +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1457 +r0:=-(4*B*c*d-b*B*e-2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^3*sqrt(c))+_ + 1/2*(B*d*(4*c*d-3*b*e)-A*e*(2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^3*sqrt(d)*sqrt(c*d-b*e))+_ + (2*B*d-A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)) +--R +--R +--R (2) +--R 2 2 +--R (((4A c + 2B b)e - 8B c d e)x + (4A c + 2B b)d e - 8B c d ) +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 2 2 +--R (- A b e + (2A c + 3B b)d e - 4B c d e)x - A b d e +--R + +--R 2 3 +--R (2A c + 3B b)d e - 4B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R 2 2 +-----------+ +-+ +-+ | 2 +--R (2B e x - 2A e + 4B d e)\|- b e + c d \|c \|d \|c x + b x +--R / +--R 4 3 +-----------+ +-+ +-+ +--R (2e x + 2d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (((2A c + B b)e - 4B c d e)x + (2A c + B b)d e - 4B c d ) +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +-+ +--R \|- b d e + c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 2 2 2 +--R (A b e + (- 2A c - 3B b)d e + 4B c d e)x + A b d e +--R + +--R 2 3 +--R (- 2A c - 3B b)d e + 4B c d +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +----------+ +--R 2 2 | 2 +-+ | 2 +--R (2B e x - 2A e + 4B d e)\|- b d e + c d \|c \|c x + b x +--R / +--R +--------------+ +--R 4 3 | 2 +-+ +--R (2e x + 2d e )\|- b d e + c d \|c +--R , +--R +--R 2 2 +--R (((2A c + B b)e - 4B c d e)x + (2A c + B b)d e - 4B c d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +-+ +--R \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 2 2 2 +--R (- 2A b e + (4A c + 6B b)d e - 8B c d e)x - 2A b d e +--R + +--R 2 3 +--R (4A c + 6B b)d e - 8B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-+ \|b d e - c d \|c x + b x +--R \|c atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +----------+ +--R 2 2 +-+ | 2 | 2 +--R (2B e x - 2A e + 4B d e)\|c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 4 3 +-+ | 2 +--R (2e x + 2d e )\|c \|b d e - c d +--R , +--R +--R 3 2 2 2 +--R (A b e + (- 2A c - 3B b)d e + 4B c d e)x + A b d e +--R + +--R 2 3 +--R (- 2A c - 3B b)d e + 4B c d +--R * +--R +---+ +--R \|- c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 2 +--R (((4A c + 2B b)e - 8B c d e)x + (4A c + 2B b)d e - 8B c d ) +--R * +--R +----------+ +--R +--------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|- b d e + c d atan(-------------------) +--R c x +--R + +--R +--------------+ +----------+ +--R 2 2 | 2 +---+ | 2 +--R (2B e x - 2A e + 4B d e)\|- b d e + c d \|- c \|c x + b x +--R / +--R +--------------+ +--R 4 3 | 2 +---+ +--R (2e x + 2d e )\|- b d e + c d \|- c +--R , +--R +--R 3 2 2 2 +--R (- A b e + (2A c + 3B b)d e - 4B c d e)x - A b d e +--R + +--R 2 3 +--R (2A c + 3B b)d e - 4B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +---+ \|b d e - c d \|c x + b x +--R \|- c atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 2 +--R (((2A c + B b)e - 4B c d e)x + (2A c + B b)d e - 4B c d ) +--R * +--R +----------+ +--R +------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|b d e - c d atan(-------------------) +--R c x +--R + +--R +------------+ +----------+ +--R 2 2 +---+ | 2 | 2 +--R (B e x - A e + 2B d e)\|- c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 4 3 +---+ | 2 +--R (e x + d e )\|- c \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 333 + +--S 334 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R | 2 +-----------+ +-+ +--R ((2A c + B b)e - 4B c d)\|- b d e + c d \|- b e + c d \|d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 +-----------+ +-+ +-+ +--R (A b e + (- 2A c - 3B b)d e + 4B c d )\|- b e + c d \|c \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R | 2 +-----------+ +-+ +--R ((- 4A c - 2B b)e + 8B c d)\|- b d e + c d \|- b e + c d \|d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +--------------+ +--R 2 2 | 2 +-+ +--R (A b e + (- 2A c - 3B b)d e + 4B c d )\|- b d e + c d \|c +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 | 2 +-----------+ +-+ +-+ +--R 2e \|- b d e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R +-----------+ +-+ | 2 +--R ((2A c + B b)e - 4B c d)\|- b e + c d \|d \|b d e - c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +------------+ +--R +-----------+ +-+ | 2 +--R ((- 4A c - 2B b)e + 8B c d)\|- b e + c d \|d \|b d e - c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +------------+ +--R 2 2 +-+ | 2 +--R (A b e + (- 2A c - 3B b)d e + 4B c d )\|c \|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +-+ +--R (- 2A b e + (4A c + 6B b)d e - 8B c d )\|- b e + c d \|c \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 3 +-----------+ +-+ +-+ | 2 +--R 2e \|- b e + c d \|c \|d \|b d e - c d +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 337 + +)clear all + +--S 338 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 338 + +--S 339 of 1457 +r0:=1/2*(B*d-A*e)*(b*x+c*x^2)^(3/2)/(d*(c*d-b*e)*(d+e*x)^2)-1/8*(A*b^2*e^3+_ + B*d*(8*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*e^3*(c*d-b*e)^(3/2))+_ + 2*B*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^3+1/4*(A*b*e^2-B*d*_ + (4*c*d-3*b*e)-2*c*e*(B*d-A*e)*x)*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 3 +--R (16B b d e - 16B c d e )x + (32B b d e - 32B c d e)x + 16B b d e +--R + +--R 4 +--R - 16B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 4 2 3 2 3 2 2 +--R (- A b e - 3B b d e + 12B b c d e - 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (- 2A b d e - 6B b d e + 24B b c d e - 16B c d e)x - A b d e +--R + +--R 2 3 2 4 2 5 +--R - 3B b d e + 12B b c d e - 8B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 3 2 2 3 +--R (2A b e + (- 4A c - 10B b)d e + 12B c d e )x - 2A b d e +--R + +--R 2 2 3 +--R - 6B b d e + 8B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((8b d e - 8c d e )x + (16b d e - 16c d e )x + 8b d e - 8c d e ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 2 3 3 +--R (8B b d e - 8B c d e )x + (16B b d e - 16B c d e)x + 8B b d e +--R + +--R 4 +--R - 8B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R \|- b d e + c d \|c log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 5 2 4 2 3 2 3 2 2 +--R (A b e + 3B b d e - 12B b c d e + 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (2A b d e + 6B b d e - 24B b c d e + 16B c d e)x + A b d e +--R + +--R 2 3 2 4 2 5 +--R 3B b d e - 12B b c d e + 8B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 3 2 2 3 +--R (2A b e + (- 4A c - 10B b)d e + 12B c d e )x - 2A b d e +--R + +--R 2 2 3 +--R - 6B b d e + 8B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((8b d e - 8c d e )x + (16b d e - 16c d e )x + 8b d e - 8c d e ) +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 3 2 2 2 2 2 3 3 +--R (4B b d e - 4B c d e )x + (8B b d e - 8B c d e)x + 4B b d e +--R + +--R 4 +--R - 4B c d +--R * +--R +------------+ +----------+ +--R +-+ | 2 +-+ | 2 +--R \|c \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 5 2 4 2 3 2 3 2 2 +--R (- A b e - 3B b d e + 12B b c d e - 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (- 2A b d e - 6B b d e + 24B b c d e - 16B c d e)x - A b d e +--R + +--R 2 3 2 4 2 5 +--R - 3B b d e + 12B b c d e - 8B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 4 3 2 2 3 2 2 +--R (A b e + (- 2A c - 5B b)d e + 6B c d e )x - A b d e - 3B b d e +--R + +--R 3 +--R 4B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((4b d e - 4c d e )x + (8b d e - 8c d e )x + 4b d e - 4c d e ) +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R , +--R +--R 2 5 2 4 2 3 2 3 2 2 +--R (A b e + 3B b d e - 12B b c d e + 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (2A b d e + 6B b d e - 24B b c d e + 16B c d e)x + A b d e +--R + +--R 2 3 2 4 2 5 +--R 3B b d e - 12B b c d e + 8B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 2 2 2 2 2 3 3 +--R (16B b d e - 16B c d e )x + (32B b d e - 32B c d e)x + 16B b d e +--R + +--R 4 +--R - 16B c d +--R * +--R +----------+ +--R +--------------+ | 2 +--R | 2 +---+ \|c x + b x +--R \|- b d e + c d \|- c atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 4 3 2 2 3 +--R (2A b e + (- 4A c - 10B b)d e + 12B c d e )x - 2A b d e +--R + +--R 2 2 3 +--R - 6B b d e + 8B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((8b d e - 8c d e )x + (16b d e - 16c d e )x + 8b d e - 8c d e ) +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 5 2 4 2 3 2 3 2 2 +--R (- A b e - 3B b d e + 12B b c d e - 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (- 2A b d e - 6B b d e + 24B b c d e - 16B c d e)x - A b d e +--R + +--R 2 3 2 4 2 5 +--R - 3B b d e + 12B b c d e - 8B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 2 2 2 2 2 3 3 +--R (8B b d e - 8B c d e )x + (16B b d e - 16B c d e)x + 8B b d e +--R + +--R 4 +--R - 8B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 \|c x + b x +--R \|- c \|b d e - c d atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 4 3 2 2 3 2 2 +--R (A b e + (- 2A c - 5B b)d e + 6B c d e )x - A b d e - 3B b d e +--R + +--R 3 +--R 4B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((4b d e - 4c d e )x + (8b d e - 8c d e )x + 4b d e - 4c d e ) +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 340 + +--S 341 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +-+ +--R (8B b d e - 8B c d )\|- b d e + c d \|- b e + c d \|c \|d +--R * +--R +----------+ +--R +-+ | 2 +--R log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 3 2 2 2 2 3 +-----------+ +-+ +--R (A b e + 3B b d e - 12B b c d e + 8B c d )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +-+ +--R (- 16B b d e + 16B c d )\|- b d e + c d \|- b e + c d \|c \|d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +--------------+ +--R 2 3 2 2 2 2 3 | 2 +--R (A b e + 3B b d e - 12B b c d e + 8B c d )\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 4 2 3 | 2 +-----------+ +-+ +--R (8b d e - 8c d e )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 2 +-----------+ +-+ +-+ | 2 +--R (8B b d e - 8B c d )\|- b e + c d \|c \|d \|b d e - c d +--R * +--R +----------+ +--R +-+ | 2 +--R log(2\|c \|c x + b x + 2c x + b) +--R + +--R +------------+ +--R 2 +-----------+ +-+ +-+ | 2 +--R (- 16B b d e + 16B c d )\|- b e + c d \|c \|d \|b d e - c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +------------+ +--R 2 3 2 2 2 2 3 | 2 +--R (A b e + 3B b d e - 12B b c d e + 8B c d )\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 2 3 +-----------+ +-+ +--R (- 2A b e - 6B b d e + 24B b c d e - 16B c d )\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 4 2 3 +-----------+ +-+ | 2 +--R (8b d e - 8c d e )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 344 + +)clear all + +--S 345 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 345 + +--S 346 of 1457 +r0:=1/16*b^2*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+1/12*(B*_ + d*(4*c*d-5*b*e)+A*e*(2*c*d-b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*_ + (d+e*x)^2)+1/24*(B*d*(8*c^2*d^2-14*b*c*d*e+3*b^2*e^2)+A*e*(4*c^2*_ + d^2-4*b*c*d*e+3*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*_ + (d+e*x))-1/3*(2*B*d+A*e+3*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)^3) +--R +--R +--R (2) +--R 3 4 2 3 3 3 +--R (- 3A b e + (6A b c - 3B b )d e )x +--R + +--R 3 3 2 3 2 2 2 +--R (- 9A b d e + (18A b c - 9B b )d e )x +--R + +--R 3 2 2 2 3 3 3 3 2 3 4 +--R (- 9A b d e + (18A b c - 9B b )d e)x - 3A b d e + (6A b c - 3B b )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 2 +--R 6A b e + (- 8A b c + 6B b )d e + (8A c - 28B b c)d e +--R + +--R 2 3 +--R 16B c d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 +--R (16A b d e + (- 28A b c - 16B b )d e + (24A c + 4B b c)d )x +--R + +--R 2 2 2 3 +--R - 6A b d e + (12A b c - 6B b )d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (48b d e - 96b c d e + 48c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (144b d e - 288b c d e + 144c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (144b d e - 288b c d e + 144c d e)x + 48b d e - 96b c d e + 48c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 3 3 3 +--R (3A b e + (- 6A b c + 3B b )d e )x +--R + +--R 3 3 2 3 2 2 2 +--R (9A b d e + (- 18A b c + 9B b )d e )x +--R + +--R 3 2 2 2 3 3 3 3 +--R (9A b d e + (- 18A b c + 9B b )d e)x + 3A b d e +--R + +--R 2 3 4 +--R (- 6A b c + 3B b )d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 2 2 2 2 +--R 6A b e + (- 8A b c + 6B b )d e + (8A c - 28B b c)d e +--R + +--R 2 3 +--R 16B c d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 +--R (16A b d e + (- 28A b c - 16B b )d e + (24A c + 4B b c)d )x +--R + +--R 2 2 2 3 +--R - 6A b d e + (12A b c - 6B b )d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (48b d e - 96b c d e + 48c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (144b d e - 288b c d e + 144c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (144b d e - 288b c d e + 144c d e)x + 48b d e - 96b c d e + 48c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 3 4 2 3 3 3 +--R (- 3A b e + (6A b c - 3B b )d e )x +--R + +--R 3 3 2 3 2 2 2 +--R (- 9A b d e + (18A b c - 9B b )d e )x +--R + +--R 3 2 2 2 3 3 3 3 2 3 4 +--R (- 9A b d e + (18A b c - 9B b )d e)x - 3A b d e + (6A b c - 3B b )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 3 2 2 2 2 +--R 3A b e + (- 4A b c + 3B b )d e + (4A c - 14B b c)d e +--R + +--R 2 3 +--R 8B c d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 +--R (8A b d e + (- 14A b c - 8B b )d e + (12A c + 2B b c)d )x +--R + +--R 2 2 2 3 +--R - 3A b d e + (6A b c - 3B b )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (24b d e - 48b c d e + 24c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (72b d e - 144b c d e + 72c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (72b d e - 144b c d e + 72c d e)x + 24b d e - 48b c d e + 24c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 347 + +--S 348 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 3 +-----------+ +-+ +--R (A b e + (- 2A b c + B b )d)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 3 2 3 | 2 +--R (A b e + (- 2A b c + B b )d)\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (16b d e - 32b c d e + 16c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 348 + +--S 349 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 3 2 3 | 2 +--R (A b e + (- 2A b c + B b )d)\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 3 +-----------+ +-+ +--R (- 2A b e + (4A b c - 2B b )d)\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (16b d e - 32b c d e + 16c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1457 +r0:=-1/128*b^2*(16*A*c^2*d^2-8*b*c*d*(B*d+2*A*e)+b^2*e*(3*B*d+5*A*e))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+1/24*(B*d*(2*c*d-3*b*e)+A*e*(2*c*d-_ + b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)^3)+1/96*(B*d*_ + (8*c^2*d^2-16*b*c*d*e+3*b^2*e^2)+A*e*(8*c^2*d^2-8*b*c*d*e+_ + 5*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*(d+e*x)^2)+_ + 1/192*(A*e*(16*c^3*d^3-24*b*c^2*d^2*e+38*b^2*c*d*e^2-15*b^3*e^3)+_ + B*d*(16*c^3*d^3-40*b*c^2*d^2*e+18*b^2*c*d*e^2-9*b^3*e^3))*_ + sqrt(b*x+c*x^2)/(d^3*e^2*(c*d-b*e)^3*(d+e*x))-1/4*(B*d+A*e+_ + 2*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)^4) +--R +--R +--R (2) +--R 4 6 3 4 5 2 2 3 2 4 4 +--R (- 15A b e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d e )x +--R + +--R 4 5 3 4 2 4 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 3 3 +--R (- 192A b c + 96B b c)d e +--R * +--R 3 +--R x +--R + +--R 4 2 4 3 4 3 3 +--R - 90A b d e + (288A b c - 54B b )d e +--R + +--R 2 2 3 4 2 +--R (- 288A b c + 144B b c)d e +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 2 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 5 +--R (- 192A b c + 96B b c)d e +--R * +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 +--R - 15A b d e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 5 2 3 4 2 2 2 3 +--R 30A b e + (- 76A b c + 18B b )d e + (48A b c - 36B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 32A c + 80B b c )d e - 32B c d e +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 3 +--R 110A b d e + (- 280A b c + 66B b )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (208A b c - 184B b c)d e + (- 128A c + 336B b c )d e - 128B c d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 3 2 +--R 146A b d e + (- 396A b c - 66B b )d e +--R + +--R 2 2 4 3 2 5 +--R (352A b c + 188B b c)d e + (- 192A c - 32B b c )d +--R * +--R x +--R + +--R 3 3 2 2 3 4 2 2 5 +--R - 30A b d e + (96A b c - 18B b )d e + (- 96A b c + 48B b c)d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (384b d e - 1152b c d e + 1152b c d e - 384c d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (2304b d e - 6912b c d e + 6912b c d e - 2304c d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e)x + 384b d e +--R + +--R 2 8 2 2 9 3 10 +--R - 1152b c d e + 1152b c d e - 384c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 6 3 4 5 2 2 3 2 4 4 +--R (15A b e + (- 48A b c + 9B b )d e + (48A b c - 24B b c)d e )x +--R + +--R 4 5 3 4 2 4 +--R 60A b d e + (- 192A b c + 36B b )d e +--R + +--R 2 2 3 3 3 +--R (192A b c - 96B b c)d e +--R * +--R 3 +--R x +--R + +--R 4 2 4 3 4 3 3 +--R 90A b d e + (- 288A b c + 54B b )d e +--R + +--R 2 2 3 4 2 +--R (288A b c - 144B b c)d e +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 2 +--R 60A b d e + (- 192A b c + 36B b )d e +--R + +--R 2 2 3 5 +--R (192A b c - 96B b c)d e +--R * +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 +--R 15A b d e + (- 48A b c + 9B b )d e + (48A b c - 24B b c)d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 5 2 3 4 2 2 2 3 +--R 30A b e + (- 76A b c + 18B b )d e + (48A b c - 36B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 32A c + 80B b c )d e - 32B c d e +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 3 +--R 110A b d e + (- 280A b c + 66B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (208A b c - 184B b c)d e + (- 128A c + 336B b c )d e +--R + +--R 3 5 +--R - 128B c d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 3 2 +--R 146A b d e + (- 396A b c - 66B b )d e +--R + +--R 2 2 4 3 2 5 +--R (352A b c + 188B b c)d e + (- 192A c - 32B b c )d +--R * +--R x +--R + +--R 3 3 2 2 3 4 2 2 5 +--R - 30A b d e + (96A b c - 18B b )d e + (- 96A b c + 48B b c)d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (384b d e - 1152b c d e + 1152b c d e - 384c d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (2304b d e - 6912b c d e + 6912b c d e - 2304c d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e)x + 384b d e +--R + +--R 2 8 2 2 9 3 10 +--R - 1152b c d e + 1152b c d e - 384c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 4 6 3 4 5 2 2 3 2 4 4 +--R (- 15A b e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d e )x +--R + +--R 4 5 3 4 2 4 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 3 3 +--R (- 192A b c + 96B b c)d e +--R * +--R 3 +--R x +--R + +--R 4 2 4 3 4 3 3 +--R - 90A b d e + (288A b c - 54B b )d e +--R + +--R 2 2 3 4 2 +--R (- 288A b c + 144B b c)d e +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 2 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 5 +--R (- 192A b c + 96B b c)d e +--R * +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 +--R - 15A b d e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 5 2 3 4 2 2 2 3 +--R 15A b e + (- 38A b c + 9B b )d e + (24A b c - 18B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 16A c + 40B b c )d e - 16B c d e +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 3 +--R 55A b d e + (- 140A b c + 33B b )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (104A b c - 92B b c)d e + (- 64A c + 168B b c )d e - 64B c d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 3 2 +--R 73A b d e + (- 198A b c - 33B b )d e +--R + +--R 2 2 4 3 2 5 +--R (176A b c + 94B b c)d e + (- 96A c - 16B b c )d +--R * +--R x +--R + +--R 3 3 2 2 3 4 2 2 5 +--R - 15A b d e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (192b d e - 576b c d e + 576b c d e - 192c d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (768b d e - 2304b c d e + 2304b c d e - 768c d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (1152b d e - 3456b c d e + 3456b c d e - 1152c d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (768b d e - 2304b c d e + 2304b c d e - 768c d e)x + 192b d e +--R + +--R 2 8 2 2 9 3 10 +--R - 576b c d e + 576b c d e - 192c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 354 + +--S 355 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 2 3 4 2 2 3 2 +--R (5A b e + (- 16A b c + 3B b )d e + (16A b c - 8B b c)d ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 2 3 4 2 2 3 2 +--R (5A b e + (- 16A b c + 3B b )d e + (16A b c - 8B b c)d ) +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +--R (128b d e - 384b c d e + 384b c d e - 128c d )\|- b d e + c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 355 + +--S 356 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 2 3 4 2 2 3 2 +--R (5A b e + (- 16A b c + 3B b )d e + (16A b c - 8B b c)d ) +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 2 3 4 2 2 3 2 +--R (- 10A b e + (32A b c - 6B b )d e + (- 32A b c + 16B b c)d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ +--R (128b d e - 384b c d e + 384b c d e - 128c d )\|- b e + c d \|d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 358 + +)clear all + +--S 359 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1457 +r0:=1/192*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+_ + 2*A*e))*x*(b*x+c*x^2)^(3/2)/c^3+1/840*(98*A*c*e*(2*c*d-b*e)+B*(48*_ + c^2*d^2-146*b*c*d*e+63*b^2*e^2))*(b*x+c*x^2)^(5/2)/c^3+1/7*B*_ + (d+e*x)^2*(b*x+c*x^2)^(5/2)/c-1/84*e*((5*b*B-14*A*c)*d-(4*B*c*d-_ + 9*b*B*e+14*A*c*e)*x)*(b*x+c*x^2)^(5/2)/c^2+1/1024*b^4*(48*A*c^3*d^2-_ + 9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)-1/1024*b^3*(48*A*c^3*d^2-_ + 9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*sqrt(b*x+_ + c*x^2)/c^5+1/1536*b^2*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+_ + A*e)-24*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^4+1/384*b*_ + (48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+_ + 2*A*e))*x^2*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 6 7 2 5 2 6 +--R (1470A b c - 945B b )e + (- 5040A b c + 2940B b c)d e +--R + +--R 4 3 5 2 2 +--R (5040A b c - 2520B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 2 6 6 5 2 6 5 +--R 15360B c e x + ((17920A c + 19200B b c )e + 35840B c d e)x +--R + +--R 5 2 4 2 6 5 +--R (23296A b c + 384B b c )e + (43008A c + 46592B b c )d e +--R + +--R 6 2 +--R 21504B c d +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 2 5 2 4 +--R (672A b c - 432B b c )e + (59136A b c + 1344B b c )d e +--R + +--R 6 5 2 +--R (26880A c + 29568B b c )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 784A b c + 504B b c )e + (2688A b c - 1568B b c )d e +--R + +--R 5 2 4 2 +--R (40320A b c + 1344B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (980A b c - 630B b c)e + (- 3360A b c + 1960B b c )d e +--R + +--R 2 4 3 3 2 +--R (3360A b c - 1680B b c )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 1470A b c + 945B b )e + (5040A b c - 2940B b c)d e +--R + +--R 3 3 4 2 2 +--R (- 5040A b c + 2520B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 107520c \|c +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 7 2 5 2 6 +--R (1470A b c - 945B b )e + (- 5040A b c + 2940B b c)d e +--R + +--R 4 3 5 2 2 +--R (5040A b c - 2520B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 6 2 6 6 5 2 6 5 +--R 30720B c e x + ((35840A c + 38400B b c )e + 71680B c d e)x +--R + +--R 5 2 4 2 6 5 +--R (46592A b c + 768B b c )e + (86016A c + 93184B b c )d e +--R + +--R 6 2 +--R 43008B c d +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 2 5 2 4 +--R (1344A b c - 864B b c )e + (118272A b c + 2688B b c )d e +--R + +--R 6 5 2 +--R (53760A c + 59136B b c )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 1568A b c + 1008B b c )e + (5376A b c - 3136B b c )d e +--R + +--R 5 2 4 2 +--R (80640A b c + 2688B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (1960A b c - 1260B b c)e + (- 6720A b c + 3920B b c )d e +--R + +--R 2 4 3 3 2 +--R (6720A b c - 3360B b c )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 2940A b c + 1890B b )e + (10080A b c - 5880B b c)d e +--R + +--R 3 3 4 2 2 +--R (- 10080A b c + 5040B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 215040c \|c +--R , +--R +--R 6 7 2 5 2 6 +--R (1470A b c - 945B b )e + (- 5040A b c + 2940B b c)d e +--R + +--R 4 3 5 2 2 +--R (5040A b c - 2520B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 6 2 6 6 5 2 6 5 +--R 15360B c e x + ((17920A c + 19200B b c )e + 35840B c d e)x +--R + +--R 5 2 4 2 6 5 +--R (23296A b c + 384B b c )e + (43008A c + 46592B b c )d e +--R + +--R 6 2 +--R 21504B c d +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 2 5 2 4 +--R (672A b c - 432B b c )e + (59136A b c + 1344B b c )d e +--R + +--R 6 5 2 +--R (26880A c + 29568B b c )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 784A b c + 504B b c )e + (2688A b c - 1568B b c )d e +--R + +--R 5 2 4 2 +--R (40320A b c + 1344B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (980A b c - 630B b c)e + (- 3360A b c + 1960B b c )d e +--R + +--R 2 4 3 3 2 +--R (3360A b c - 1680B b c )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 1470A b c + 945B b )e + (5040A b c - 2940B b c)d e +--R + +--R 3 3 4 2 2 +--R (- 5040A b c + 2520B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 5 +---+ +--R 107520c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 361 + +--S 362 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 6 7 2 5 2 6 +--R (14A b c - 9B b )e + (- 48A b c + 28B b c)d e +--R + +--R 4 3 5 2 2 +--R (48A b c - 24B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 6 7 2 5 2 6 +--R (- 28A b c + 18B b )e + (96A b c - 56B b c)d e +--R + +--R 4 3 5 2 2 +--R (- 96A b c + 48B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 5 +-+ +--R 2048c \|c +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 7 2 5 2 6 +--R (- 14A b c + 9B b )e + (48A b c - 28B b c)d e +--R + +--R 4 3 5 2 2 +--R (- 48A b c + 24B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 7 2 5 2 6 +--R (14A b c - 9B b )e + (- 48A b c + 28B b c)d e +--R + +--R 4 3 5 2 2 +--R (48A b c - 24B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 5 +---+ +-+ +--R 1024c \|- c \|c +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 1457 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 4 3 2 +--R (B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x) +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1457 +r0:=1/96*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x*(b*x+c*x^2)^(3/2)/c^2+_ + 1/60*(2*B*c*d-7*b*B*e+12*A*c*e)*(b*x+c*x^2)^(5/2)/c^2+1/6*B*(d+e*x)*_ + (b*x+c*x^2)^(5/2)/c+1/512*b^4*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+_ + A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-1/512*b^3*_ + (24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^4+_ + 1/768*b^2*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x*sqrt(b*x+_ + c*x^2)/c^3+1/192*b*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x^2*_ + sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 5 6 4 2 5 x\|c +--R ((- 180A b c + 105B b )e + (360A b c - 180B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 5 5 4 5 4 +--R 1280B c e x + ((1536A c + 1664B b c )e + 1536B c d)x +--R + +--R 4 2 3 5 4 3 +--R ((2112A b c + 48B b c )e + (1920A c + 2112B b c )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((96A b c - 56B b c )e + (2880A b c + 96B b c )d)x +--R + +--R 3 2 4 2 3 3 2 +--R ((- 120A b c + 70B b c)e + (240A b c - 120B b c )d)x +--R + +--R 4 5 3 2 4 +--R (180A b c - 105B b )e + (- 360A b c + 180B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 6 4 2 5 +--R ((180A b c - 105B b )e + (- 360A b c + 180B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 5 5 5 4 5 4 +--R 2560B c e x + ((3072A c + 3328B b c )e + 3072B c d)x +--R + +--R 4 2 3 5 4 3 +--R ((4224A b c + 96B b c )e + (3840A c + 4224B b c )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((192A b c - 112B b c )e + (5760A b c + 192B b c )d)x +--R + +--R 3 2 4 2 3 3 2 +--R ((- 240A b c + 140B b c)e + (480A b c - 240B b c )d)x +--R + +--R 4 5 3 2 4 +--R (360A b c - 210B b )e + (- 720A b c + 360B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 15360c \|c +--R , +--R +--R 5 6 4 2 5 +--R ((- 180A b c + 105B b )e + (360A b c - 180B b c)d) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 5 5 5 4 5 4 +--R 1280B c e x + ((1536A c + 1664B b c )e + 1536B c d)x +--R + +--R 4 2 3 5 4 3 +--R ((2112A b c + 48B b c )e + (1920A c + 2112B b c )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((96A b c - 56B b c )e + (2880A b c + 96B b c )d)x +--R + +--R 3 2 4 2 3 3 2 +--R ((- 120A b c + 70B b c)e + (240A b c - 120B b c )d)x +--R + +--R 4 5 3 2 4 +--R (180A b c - 105B b )e + (- 360A b c + 180B b c)d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 7680c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 368 + +--S 369 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 6 4 2 5 +--R ((12A b c - 7B b )e + (- 24A b c + 12B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 5 6 4 2 5 x\|c +--R ((24A b c - 14B b )e + (- 48A b c + 24B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 1024c \|c +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 5 6 4 2 5 +---+ x\|c +--R ((12A b c - 7B b )e + (- 24A b c + 12B b c)d)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 5 6 4 2 5 +-+ \|- c \|c x + b x +--R ((- 12A b c + 7B b )e + (24A b c - 12B b c)d)\|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 512c \|- c \|c +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (1) (B c x + (A c + B b)x + A b x)\|c x + b x +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1457 +r0:=-1/8*(b*B-2*A*c)*x*(b*x+c*x^2)^(3/2)/c+1/5*B*(b*x+c*x^2)^(5/2)/c-_ + 3/128*b^4*(b*B-2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+_ + 3/128*b^3*(b*B-2*A*c)*sqrt(b*x+c*x^2)/c^3-1/64*b^2*(b*B-2*A*c)*x*_ + sqrt(b*x+c*x^2)/c^2-1/16*b*(b*B-2*A*c)*x^2*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 4 5 x\|c +--R (30A b c - 15B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 4 4 3 3 3 2 2 2 +--R 128B c x + (160A c + 176B b c )x + (240A b c + 8B b c )x +--R + +--R 2 2 3 3 4 +--R (20A b c - 10B b c)x - 30A b c + 15B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 640c \|c +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 4 5 | 2 +-+ +--R (30A b c - 15B b )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 4 4 3 3 3 2 2 2 +--R 256B c x + (320A c + 352B b c )x + (480A b c + 16B b c )x +--R + +--R 2 2 3 3 4 +--R (40A b c - 20B b c)x - 60A b c + 30B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 1280c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 4 5 \|- c \|c x + b x +--R (30A b c - 15B b )atan(-------------------) +--R c x +--R + +--R 4 4 4 3 3 3 2 2 2 +--R 128B c x + (160A c + 176B b c )x + (240A b c + 8B b c )x +--R + +--R 2 2 3 3 4 +--R (20A b c - 10B b c)x - 30A b c + 15B b +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 3 +---+ +--R 640c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 375 + +--S 376 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 4 5 | 2 +-+ +--R (6A b c - 3B b )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 4 5 x\|c +--R (- 12A b c + 6B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 256c \|c +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 4 5 +---+ x\|c +--R (- 6A b c + 3B b )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 4 5 +-+ \|- c \|c x + b x +--R (6A b c - 3B b )\|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 128c \|- c \|c +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 379 + +)clear all + +--S 380 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1457 +r0:=-1/24*(8*B*c*d-3*b*B*e-8*A*c*e-6*B*c*e*x)*(b*x+c*x^2)^(3/2)/(c*e^2)-_ + 1/64*(8*A*c*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3)-_ + B*(128*c^4*d^4-192*b*c^3*d^3*e+48*b^2*c^2*d^2*e^2+8*b^3*c*d*e^3+_ + 3*b^4*e^4))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^5)-d^(3/2)*_ + (B*d-A*e)*(c*d-b*e)^(3/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^5+1/64*(8*A*c*e*(8*c^2*d^2-_ + 10*b*c*d*e+b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+8*b^2*c*d*e^2+_ + 3*b^3*e^3)-2*c*e*(8*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-8*b*c*d*e-_ + 3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^4) +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 +--R (- 24A b c + 9B b )e + (- 144A b c + 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (576A b c + 144B b c )d e + (- 384A c - 576B b c )d e + 384B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 2 2 3 3 +-----------+ +--R (192A b c d e + (- 192A c - 192B b c )d e + 192B c d )\|- b e + c d +--R * +--R +-+ +-+ (b e - 2c d)x - b d +--R \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 48B c e x + ((64A c + 72B b c )e - 64B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 +--R ((112A b c + 6B b c)e + (- 96A c - 112B b c )d e + 96B c d e )x +--R + +--R 2 3 4 2 2 3 +--R (24A b c - 9B b )e + (- 240A b c - 24B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (192A c + 240B b c )d e - 192B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 5 +-+ +--R 192c e \|c +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 3 3 +--R (- 384A b c d e + (384A c + 384B b c )d e - 384B c d ) +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 3 4 4 2 2 3 3 +--R (24A b c - 9B b )e + (144A b c - 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 576A b c - 144B b c )d e + (384A c + 576B b c )d e - 384B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 96B c e x + ((128A c + 144B b c )e - 128B c d e )x +--R + +--R 2 2 4 3 2 3 +--R (224A b c + 12B b c)e + (- 192A c - 224B b c )d e +--R + +--R 3 2 2 +--R 192B c d e +--R * +--R x +--R + +--R 2 3 4 2 2 3 +--R (48A b c - 18B b )e + (- 480A b c - 48B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (384A c + 480B b c )d e - 384B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 5 +-+ +--R 384c e \|c +--R , +--R +--R 3 4 4 2 2 3 3 +--R (24A b c - 9B b )e + (144A b c - 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 576A b c - 144B b c )d e + (384A c + 576B b c )d e - 384B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 3 2 2 3 3 +-+ +--R (- 768A b c d e + (768A c + 768B b c )d e - 768B c d )\|c +--R * +--R +----------+ +--R +------------+ | 2 +--R | 2 d\|c x + b x +--R \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 96B c e x + ((128A c + 144B b c )e - 128B c d e )x +--R + +--R 2 2 4 3 2 3 +--R (224A b c + 12B b c)e + (- 192A c - 224B b c )d e +--R + +--R 3 2 2 +--R 192B c d e +--R * +--R x +--R + +--R 2 3 4 2 2 3 +--R (48A b c - 18B b )e + (- 480A b c - 48B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (384A c + 480B b c )d e - 384B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 5 +-+ +--R 384c e \|c +--R , +--R +--R 2 2 3 2 2 3 3 +--R (- 192A b c d e + (192A c + 192B b c )d e - 192B c d ) +--R * +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 3 4 4 2 2 3 3 +--R (- 24A b c + 9B b )e + (- 144A b c + 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (576A b c + 144B b c )d e + (- 384A c - 576B b c )d e + 384B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 48B c e x + ((64A c + 72B b c )e - 64B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 +--R ((112A b c + 6B b c)e + (- 96A c - 112B b c )d e + 96B c d e )x +--R + +--R 2 3 4 2 2 3 +--R (24A b c - 9B b )e + (- 240A b c - 24B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (192A c + 240B b c )d e - 192B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 2 5 +---+ +--R 192c e \|- c +--R , +--R +--R 3 4 4 2 2 3 3 +--R (- 24A b c + 9B b )e + (- 144A b c + 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (576A b c + 144B b c )d e + (- 384A c - 576B b c )d e + 384B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 2 3 2 2 3 3 +---+ +--R (- 384A b c d e + (384A c + 384B b c )d e - 384B c d )\|- c +--R * +--R +----------+ +--R +------------+ | 2 +--R | 2 d\|c x + b x +--R \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 48B c e x + ((64A c + 72B b c )e - 64B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 +--R ((112A b c + 6B b c)e + (- 96A c - 112B b c )d e + 96B c d e )x +--R + +--R 2 3 4 2 2 3 +--R (24A b c - 9B b )e + (- 240A b c - 24B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (192A c + 240B b c )d e - 192B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 2 5 +---+ +--R 192c e \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 382 + +--S 383 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 3 2 2 3 3 +--R (- 128A b c d e + (128A c + 128B b c )d e - 128B c d ) +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 3 4 4 2 2 3 3 +--R (8A b c - 3B b )e + (48A b c - 8B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 192A b c - 48B b c )d e + (128A c + 192B b c )d e - 128B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 4 2 2 3 3 +--R (16A b c - 6B b )e + (96A b c - 16B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 384A b c - 96B b c )d e + (256A c + 384B b c )d e - 256B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 2 2 3 3 +-----------+ +--R (- 128A b c d e + (128A c + 128B b c )d e - 128B c d )\|- b e + c d +--R * +--R +-+ +-+ (b e - 2c d)x - b d +--R \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 2 5 +-+ +--R 128c e \|c +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 4 2 2 3 3 +--R (8A b c - 3B b )e + (48A b c - 8B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 192A b c - 48B b c )d e + (128A c + 192B b c )d e - 128B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 4 2 2 3 3 +--R (16A b c - 6B b )e + (96A b c - 16B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 384A b c - 96B b c )d e + (256A c + 384B b c )d e - 256B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 2 2 3 3 +-----------+ +--R (- 128A b c d e + (128A c + 128B b c )d e - 128B c d )\|- b e + c d +--R * +--R +-+ +-+ (b e - 2c d)x - b d +--R \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 3 2 2 3 3 +-+ +--R (- 256A b c d e + (256A c + 256B b c )d e - 256B c d )\|c +--R * +--R +----------+ +--R +------------+ | 2 +--R | 2 d\|c x + b x +--R \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 2 5 +-+ +--R 128c e \|c +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 386 + +)clear all + +--S 387 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1457 +r0:=1/3*(4*B*d-3*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x))+1/8*(4*b*c*e*_ + (4*B*d-3*A*e)*(2*c*d-b*e)-(8*B*c*d-b*B*e-6*A*c*e)*(8*c^2*d^2-_ + 4*b*c*d*e-b^2*e^2))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^5)+_ + 1/2*(B*d*(8*c*d-5*b*e)-3*A*e*(2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-_ + b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-_ + b*e)/e^5-1/8*(6*A*c*e*(4*c*d-3*b*e)-B*(32*c^2*d^2-28*b*c*d*e+_ + b^2*e^2)+2*c*e*(8*B*c*d-b*B*e-6*A*c*e)*x)*sqrt(b*x+c*x^2)/(c*e^4) +--R +--R +--R (2) +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 2 2 2 2 +--R (- 36A b c e + (72A c + 60B b c)d e - 96B c d e)x - 36A b c d e +--R + +--R 2 2 2 3 +--R (72A c + 60B b c)d e - 96B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 4 3 2 4 2 3 2 +--R 8B c e x + ((12A c + 14B b c)e - 16B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((30A b c + 3B b )e + (- 36A c - 46B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (54A b c + 3B b )d e + (- 72A c - 84B b c)d e + 96B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 5 +-+ +--R (24c e x + 24c d e )\|c +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 +--R (72A b c e + (- 144A c - 120B b c)d e + 192B c d e)x +--R + +--R 2 2 2 2 3 +--R 72A b c d e + (- 144A c - 120B b c)d e + 192B c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 4 3 2 4 2 3 2 +--R 16B c e x + ((24A c + 28B b c)e - 32B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((60A b c + 6B b )e + (- 72A c - 92B b c)d e + 96B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (108A b c + 6B b )d e + (- 144A c - 168B b c)d e + 192B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 5 +-+ +--R (48c e x + 48c d e )\|c +--R , +--R +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 2 2 2 2 +--R (144A b c e + (- 288A c - 240B b c)d e + 384B c d e)x +--R + +--R 2 2 2 2 3 +--R 144A b c d e + (- 288A c - 240B b c)d e + 384B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 2 4 3 2 4 2 3 2 +--R 16B c e x + ((24A c + 28B b c)e - 32B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((60A b c + 6B b )e + (- 72A c - 92B b c)d e + 96B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (108A b c + 6B b )d e + (- 144A c - 168B b c)d e + 192B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 5 +-+ +--R (48c e x + 48c d e )\|c +--R , +--R +--R 3 2 2 2 2 2 +--R (36A b c e + (- 72A c - 60B b c)d e + 96B c d e)x + 36A b c d e +--R + +--R 2 2 2 3 +--R (- 72A c - 60B b c)d e + 96B c d +--R * +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 4 3 2 4 2 3 2 +--R 8B c e x + ((12A c + 14B b c)e - 16B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((30A b c + 3B b )e + (- 36A c - 46B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (54A b c + 3B b )d e + (- 72A c - 84B b c)d e + 96B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 6 5 +---+ +--R (24c e x + 24c d e )\|- c +--R , +--R +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 2 2 2 2 +--R (72A b c e + (- 144A c - 120B b c)d e + 192B c d e)x +--R + +--R 2 2 2 2 3 +--R 72A b c d e + (- 144A c - 120B b c)d e + 192B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 d\|c x + b x +--R \|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 2 4 3 2 4 2 3 2 +--R 8B c e x + ((12A c + 14B b c)e - 16B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((30A b c + 3B b )e + (- 36A c - 46B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (54A b c + 3B b )d e + (- 72A c - 84B b c)d e + 96B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 6 5 +---+ +--R (24c e x + 24c d e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 389 + +--S 390 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 2 2 | 2 +-+ +--R (24A b c e + (- 48A c - 40B b c)d e + 64B c d )\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 3 3 2 2 2 +--R (6A b c - B b )e + (- 48A b c - 12B b c)d e +--R + +--R 3 2 2 3 3 +--R (48A c + 72B b c )d e - 64B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 3 2 2 2 +--R (- 12A b c + 2B b )e + (96A b c + 24B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 96A c - 144B b c )d e + 128B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 +-----------+ +-+ +-+ +--R (24A b c e + (- 48A c - 40B b c)d e + 64B c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 5 +-+ +--R 16c e \|c +--R Type: Expression(Integer) +--E 390 + +--S 391 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 +--R (6A b c - B b )e + (- 48A b c - 12B b c)d e +--R + +--R 3 2 2 3 3 +--R (48A c + 72B b c )d e - 64B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 3 2 2 2 +--R (- 12A b c + 2B b )e + (96A b c + 24B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 96A c - 144B b c )d e + 128B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 +-----------+ +-+ +-+ +--R (24A b c e + (- 48A c - 40B b c)d e + 64B c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +--R 2 2 2 2 +-+ | 2 +--R (48A b c e + (- 96A c - 80B b c)d e + 128B c d )\|c \|b d e - c d +--R * +--R +----------+ +--R | 2 +--R d\|c x + b x +--R atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 5 +-+ +--R 16c e \|c +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1457 +r0:=1/2*(2*B*d-A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)-3/4*(4*A*c*e*_ + (2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+b^2*e^2))*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/(e^5*sqrt(c))+3/8*(A*e*(8*c^2*d^2-8*b*c*d*e+_ + b^2*e^2)-B*d*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2))*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^5*_ + sqrt(d)*sqrt(c*d-b*e))-3/4*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+_ + e*(4*B*c*d-b*B*e-2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 +--R ((24A b c + 6B b )e + (- 48A c - 72B b c)d e + 96B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((48A b c + 12B b )d e + (- 96A c - 144B b c)d e + 192B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 2 +--R 48B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 6A b d e + (48A b c + 30B b )d e + (- 48A c - 120B b c)d e +--R + +--R 2 4 +--R 96B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 3A b d e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 5 +--R 48B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 3 4 3 2 +--R 4B c e x + ((8A c + 10B b)e - 16B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 10A b e + (36A c + 38B b)d e - 72B c d e )x - 6A b d e +--R + +--R 2 2 3 +--R (24A c + 24B b)d e - 48B c d e +--R * +--R +----------+ +--R +-----------+ +-+ +-+ | 2 +--R \|- b e + c d \|c \|d \|c x + b x +--R / +--R 7 2 6 2 5 +-----------+ +-+ +-+ +--R (8e x + 16d e x + 8d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 395 + +--S 396 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 2 3 2 2 2 2 +--R ((12A b c + 3B b )e + (- 24A c - 36B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (12A b c + 3B b )d e + (- 24A c - 36B b c)d e + 48B c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +-+ +--R \|- b d e + c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 5 2 4 2 2 3 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 2 +--R 48B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 6A b d e + (48A b c + 30B b )d e +--R + +--R 2 3 2 2 4 +--R (- 48A c - 120B b c)d e + 96B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 3A b d e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 5 +--R 48B c d +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 3 4 3 2 +--R 4B c e x + ((8A c + 10B b)e - 16B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 10A b e + (36A c + 38B b)d e - 72B c d e )x - 6A b d e +--R + +--R 2 2 3 +--R (24A c + 24B b)d e - 48B c d e +--R * +--R +--------------+ +----------+ +--R | 2 +-+ | 2 +--R \|- b d e + c d \|c \|c x + b x +--R / +--R +--------------+ +--R 7 2 6 2 5 | 2 +-+ +--R (8e x + 16d e x + 8d e )\|- b d e + c d \|c +--R , +--R +--R 2 4 2 3 2 2 2 2 +--R ((12A b c + 3B b )e + (- 24A c - 36B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (12A b c + 3B b )d e + (- 24A c - 36B b c)d e + 48B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +-+ +--R \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 5 2 4 2 2 3 +--R - 6A b e + (48A b c + 30B b )d e + (- 48A c - 120B b c)d e +--R + +--R 2 3 2 +--R 96B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 12A b d e + (96A b c + 60B b )d e +--R + +--R 2 3 2 2 4 +--R (- 96A c - 240B b c)d e + 192B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 6A b d e + (48A b c + 30B b )d e + (- 48A c - 120B b c)d e +--R + +--R 2 5 +--R 96B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-+ \|b d e - c d \|c x + b x +--R \|c atan(----------------------------) +--R (b e - c d)x +--R + +--R 4 3 4 3 2 +--R 4B c e x + ((8A c + 10B b)e - 16B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 10A b e + (36A c + 38B b)d e - 72B c d e )x - 6A b d e +--R + +--R 2 2 3 +--R (24A c + 24B b)d e - 48B c d e +--R * +--R +------------+ +----------+ +--R +-+ | 2 | 2 +--R \|c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 7 2 6 2 5 +-+ | 2 +--R (8e x + 16d e x + 8d e )\|c \|b d e - c d +--R , +--R +--R 2 5 2 4 2 2 3 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 2 +--R 48B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 6A b d e + (48A b c + 30B b )d e +--R + +--R 2 3 2 2 4 +--R (- 48A c - 120B b c)d e + 96B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 3A b d e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 5 +--R 48B c d +--R * +--R +---+ +--R \|- c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 4 2 3 2 2 2 2 +--R ((24A b c + 6B b )e + (- 48A c - 72B b c)d e + 96B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((48A b c + 12B b )d e + (- 96A c - 144B b c)d e + 192B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d +--R * +--R +----------+ +--R +--------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|- b d e + c d atan(-------------------) +--R c x +--R + +--R 4 3 4 3 2 +--R 4B c e x + ((8A c + 10B b)e - 16B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 10A b e + (36A c + 38B b)d e - 72B c d e )x - 6A b d e +--R + +--R 2 2 3 +--R (24A c + 24B b)d e - 48B c d e +--R * +--R +--------------+ +----------+ +--R | 2 +---+ | 2 +--R \|- b d e + c d \|- c \|c x + b x +--R / +--R +--------------+ +--R 7 2 6 2 5 | 2 +---+ +--R (8e x + 16d e x + 8d e )\|- b d e + c d \|- c +--R , +--R +--R 2 5 2 4 2 2 3 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 2 +--R 48B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 6A b d e + (48A b c + 30B b )d e +--R + +--R 2 3 2 2 4 +--R (- 48A c - 120B b c)d e + 96B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 3A b d e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 5 +--R 48B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +---+ \|b d e - c d \|c x + b x +--R \|- c atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((12A b c + 3B b )e + (- 24A c - 36B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (12A b c + 3B b )d e + (- 24A c - 36B b c)d e + 48B c d +--R * +--R +----------+ +--R +------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|b d e - c d atan(-------------------) +--R c x +--R + +--R 4 3 4 3 2 +--R 2B c e x + ((4A c + 5B b)e - 8B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 5A b e + (18A c + 19B b)d e - 36B c d e )x - 3A b d e +--R + +--R 2 2 3 +--R (12A c + 12B b)d e - 24B c d e +--R * +--R +------------+ +----------+ +--R +---+ | 2 | 2 +--R \|- c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 7 2 6 2 5 +---+ | 2 +--R (4e x + 8d e x + 4d e )\|- c \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 396 + +--S 397 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 +--R ((12A b c + 3B b )e + (- 24A c - 36B b c)d e + 48B c d ) +--R * +--R +--------------+ +----------+ +--R | 2 +-----------+ +-+ | 2 +-+ +--R \|- b d e + c d \|- b e + c d \|d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 2 2 2 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 +--R 48B c d +--R * +--R +-----------+ +-+ +-+ +--R \|- b e + c d \|c \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 2 2 2 2 +--R ((- 24A b c - 6B b )e + (48A c + 72B b c)d e - 96B c d ) +--R * +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ x\|c +--R \|- b d e + c d \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 2 2 3 +--R (3A b e + (- 24A b c - 15B b )d e + (24A c + 60B b c)d e - 48B c d ) +--R * +--R +--------------+ +--R | 2 +-+ (b e - 2c d)x - b d +--R \|- b d e + c d \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 5 | 2 +-----------+ +-+ +-+ +--R 8e \|- b d e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +--R ((12A b c + 3B b )e + (- 24A c - 36B b c)d e + 48B c d ) +--R * +--R +------------+ +----------+ +--R +-----------+ +-+ | 2 | 2 +-+ +--R \|- b e + c d \|d \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 2 2 +--R ((- 24A b c - 6B b )e + (48A c + 72B b c)d e - 96B c d ) +--R * +--R +------------+ +-+ +--R +-----------+ +-+ | 2 x\|c +--R \|- b e + c d \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 2 2 3 +--R (3A b e + (- 24A b c - 15B b )d e + (24A c + 60B b c)d e - 48B c d ) +--R * +--R +------------+ +--R +-+ | 2 (b e - 2c d)x - b d +--R \|c \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 2 +--R - 6A b e + (48A b c + 30B b )d e + (- 48A c - 120B b c)d e +--R + +--R 2 3 +--R 96B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|c \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 5 +-----------+ +-+ +-+ | 2 +--R 8e \|- b e + c d \|c \|d \|b d e - c d +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1457 +r0:=-1/4*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*(b*x+c*x^2)^(3/2)/(d*e^2*_ + (c*d-b*e)*(d+e*x)^2)+1/3*(4*B*d-A*e+3*B*e*x)*(b*x+c*x^2)^(3/2)/_ + (e^2*(d+e*x)^3)+1/16*(B*d*(64*c^3*d^3-120*b*c^2*d^2*e+60*b^2*c*d*e^2-_ + 5*b^3*e^3)-A*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(3/2)*e^5*(c*d-b*e)^(3/2))-(8*B*c*d-3*b*B*e-2*A*c*e)*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^5-1/8*(A*e*(8*c^2*d^2-_ + 6*b*c*d*e-b^2*e^2)-B*d*(32*c^2*d^2-36*b*c*d*e+5*b^2*e^2)-_ + 2*c*e*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*x)*sqrt(b*x+c*x^2)/_ + (d*e^4*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 5 2 2 4 2 3 3 3 +--R ((96A b c + 144B b )d e + (- 96A c - 528B b c)d e + 384B c d e )x +--R + +--R 2 2 4 2 3 3 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 4 2 +--R 1152B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 5 +--R 1152B c d e +--R * +--R x +--R + +--R 2 4 2 2 5 2 6 +--R (96A b c + 144B b )d e + (- 96A c - 528B b c)d e + 384B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R - 3A b e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 48A c - 360B b c )d e + 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 5 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 6 +--R 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48A c - 360B b c )d e + 192B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 2 2 4 3 +--R (48B b c d e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 6A b e + (- 88A b c - 66B b )d e + (88A c + 412B b c)d e +--R + +--R 2 3 3 +--R - 352B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 16A b d e + (- 92A b c - 80B b )d e +--R + +--R 2 3 3 2 4 2 +--R (120A c + 548B b c)d e - 480B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 6A b d e + (- 36A b c - 30B b )d e + (48A c + 216B b c)d e +--R + +--R 2 5 +--R - 192B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (48b d e - 48c d e )x + (144b d e - 144c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (144b d e - 144c d e )x + 48b d e - 48c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 5 2 2 4 +--R (48A b c + 72B b )d e + (- 48A c - 264B b c)d e +--R + +--R 2 3 3 +--R 192B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R (144A b c + 216B b )d e + (- 144A c - 792B b c)d e +--R + +--R 2 4 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 +--R (144A b c + 216B b )d e + (- 144A c - 792B b c)d e +--R + +--R 2 5 +--R 576B c d e +--R * +--R x +--R + +--R 2 4 2 2 5 2 6 +--R (48A b c + 72B b )d e + (- 48A c - 264B b c)d e + 192B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R \|- b d e + c d \|c log(2\|c \|c x + b x + 2c x + b) +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 3A b e + (18A b c + 15B b )d e + (- 72A b c - 180B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (48A c + 360B b c )d e - 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 9A b d e + (54A b c + 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 216A b c - 540B b c)d e + (144A c + 1080B b c )d e +--R + +--R 3 5 2 +--R - 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 9A b d e + (54A b c + 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 216A b c - 540B b c)d e + (144A c + 1080B b c )d e +--R + +--R 3 6 +--R - 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 3A b d e + (18A b c + 15B b )d e + (- 72A b c - 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (48A c + 360B b c )d e - 192B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 5 2 2 4 3 +--R (48B b c d e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 6A b e + (- 88A b c - 66B b )d e + (88A c + 412B b c)d e +--R + +--R 2 3 3 +--R - 352B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 16A b d e + (- 92A b c - 80B b )d e +--R + +--R 2 3 3 2 4 2 +--R (120A c + 548B b c)d e - 480B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 6A b d e + (- 36A b c - 30B b )d e + (48A c + 216B b c)d e +--R + +--R 2 5 +--R - 192B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (48b d e - 48c d e )x + (144b d e - 144c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (144b d e - 144c d e )x + 48b d e - 48c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 5 2 2 4 2 3 3 3 +--R ((24A b c + 36B b )d e + (- 24A c - 132B b c)d e + 96B c d e )x +--R + +--R 2 2 4 2 3 3 +--R (72A b c + 108B b )d e + (- 72A c - 396B b c)d e +--R + +--R 2 4 2 +--R 288B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R ((72A b c + 108B b )d e + (- 72A c - 396B b c)d e + 288B c d e)x +--R + +--R 2 4 2 2 5 2 6 +--R (24A b c + 36B b )d e + (- 24A c - 132B b c)d e + 96B c d +--R * +--R +------------+ +----------+ +--R +-+ | 2 +-+ | 2 +--R \|c \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 3 7 2 3 6 +--R - 3A b e + (- 18A b c - 15B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (72A b c + 180B b c)d e + (- 48A c - 360B b c )d e +--R + +--R 3 4 3 +--R 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 5 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 6 +--R 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48A c - 360B b c )d e + 192B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 5 2 2 4 3 +--R (24B b c d e - 24B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 3A b e + (- 44A b c - 33B b )d e + (44A c + 206B b c)d e +--R + +--R 2 3 3 +--R - 176B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 8A b d e + (- 46A b c - 40B b )d e +--R + +--R 2 3 3 2 4 2 +--R (60A c + 274B b c)d e - 240B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (24A c + 108B b c)d e +--R + +--R 2 5 +--R - 96B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (24b d e - 24c d e )x + (72b d e - 72c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (72b d e - 72c d e )x + 24b d e - 24c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R , +--R +--R 3 7 2 3 6 2 2 2 5 +--R 3A b e + (18A b c + 15B b )d e + (- 72A b c - 180B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (48A c + 360B b c )d e - 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 9A b d e + (54A b c + 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 216A b c - 540B b c)d e + (144A c + 1080B b c )d e +--R + +--R 3 5 2 +--R - 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 9A b d e + (54A b c + 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 216A b c - 540B b c)d e + (144A c + 1080B b c )d e +--R + +--R 3 6 +--R - 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 3A b d e + (18A b c + 15B b )d e + (- 72A b c - 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (48A c + 360B b c )d e - 192B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 5 2 2 4 +--R (96A b c + 144B b )d e + (- 96A c - 528B b c)d e +--R + +--R 2 3 3 +--R 384B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 4 2 +--R 1152B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 5 +--R 1152B c d e +--R * +--R x +--R + +--R 2 4 2 2 5 2 6 +--R (96A b c + 144B b )d e + (- 96A c - 528B b c)d e + 384B c d +--R * +--R +----------+ +--R +--------------+ | 2 +--R | 2 +---+ \|c x + b x +--R \|- b d e + c d \|- c atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 5 2 2 4 3 +--R (48B b c d e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 6A b e + (- 88A b c - 66B b )d e + (88A c + 412B b c)d e +--R + +--R 2 3 3 +--R - 352B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 16A b d e + (- 92A b c - 80B b )d e +--R + +--R 2 3 3 2 4 2 +--R (120A c + 548B b c)d e - 480B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 6A b d e + (- 36A b c - 30B b )d e + (48A c + 216B b c)d e +--R + +--R 2 5 +--R - 192B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (48b d e - 48c d e )x + (144b d e - 144c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (144b d e - 144c d e )x + 48b d e - 48c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 3 7 2 3 6 +--R - 3A b e + (- 18A b c - 15B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (72A b c + 180B b c)d e + (- 48A c - 360B b c )d e +--R + +--R 3 4 3 +--R 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 5 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 6 +--R 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48A c - 360B b c )d e + 192B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 5 2 2 4 +--R (48A b c + 72B b )d e + (- 48A c - 264B b c)d e +--R + +--R 2 3 3 +--R 192B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R (144A b c + 216B b )d e + (- 144A c - 792B b c)d e +--R + +--R 2 4 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 +--R (144A b c + 216B b )d e + (- 144A c - 792B b c)d e +--R + +--R 2 5 +--R 576B c d e +--R * +--R x +--R + +--R 2 4 2 2 5 2 6 +--R (48A b c + 72B b )d e + (- 48A c - 264B b c)d e + 192B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 \|c x + b x +--R \|- c \|b d e - c d atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 5 2 2 4 3 +--R (24B b c d e - 24B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 3A b e + (- 44A b c - 33B b )d e + (44A c + 206B b c)d e +--R + +--R 2 3 3 +--R - 176B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 8A b d e + (- 46A b c - 40B b )d e +--R + +--R 2 3 3 2 4 2 +--R (60A c + 274B b c)d e - 240B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (24A c + 108B b c)d e +--R + +--R 2 5 +--R - 96B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (24b d e - 24c d e )x + (72b d e - 72c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (72b d e - 72c d e )x + 24b d e - 24c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 403 + +--S 404 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 3 +--R ((16A b c + 24B b )d e + (- 16A c - 88B b c)d e + 64B c d ) +--R * +--R +--------------+ +----------+ +--R | 2 +-----------+ +-+ +-+ +-+ | 2 +--R \|- b d e + c d \|- b e + c d \|c \|d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (6A b c + 5B b )d e + (- 24A b c - 60B b c)d e +--R + +--R 3 2 3 3 4 +--R (16A c + 120B b c )d e - 64B c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 2 2 2 2 3 +--R ((- 32A b c - 48B b )d e + (32A c + 176B b c)d e - 128B c d ) +--R * +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ +-+ x\|c +--R \|- b d e + c d \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (6A b c + 5B b )d e + (- 24A b c - 60B b c)d e +--R + +--R 3 2 3 3 4 +--R (16A c + 120B b c )d e - 64B c d +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 6 2 5 | 2 +-----------+ +-+ +--R (16b d e - 16c d e )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 3 +--R ((16A b c + 24B b )d e + (- 16A c - 88B b c)d e + 64B c d ) +--R * +--R +------------+ +----------+ +--R +-----------+ +-+ +-+ | 2 +-+ | 2 +--R \|- b e + c d \|c \|d \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 2 2 2 2 3 +--R ((- 32A b c - 48B b )d e + (32A c + 176B b c)d e - 128B c d ) +--R * +--R +------------+ +-+ +--R +-----------+ +-+ +-+ | 2 x\|c +--R \|- b e + c d \|c \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (6A b c + 5B b )d e + (- 24A b c - 60B b c)d e +--R + +--R 3 2 3 3 4 +--R (16A c + 120B b c )d e - 64B c d +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A b e + (- 12A b c - 10B b )d e + (48A b c + 120B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 32A c - 240B b c )d e + 128B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 6 2 5 +-----------+ +-+ | 2 +--R (16b d e - 16c d e )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 407 + +)clear all + +--S 408 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1457 +r0:=1/32*(3*A*b^2*e^3+B*d*(16*c^2*d^2-24*b*c*d*e+5*b^2*e^2))*_ + (b*x+c*x^2)^(3/2)/(d^2*e^2*(c*d-b*e)^2*(d+e*x)^2)+1/24*(3*A*b*e^2-_ + B*d*(8*c*d-5*b*e)-6*c*e*(B*d-A*e)*x)*(b*x+c*x^2)^(3/2)/(d*e^2*_ + (c*d-b*e)*(d+e*x)^3)+1/4*(B*d-A*e)*(b*x+c*x^2)^(5/2)/(d*(c*d-b*e)*_ + (d+e*x)^4)+2*B*c^(3/2)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/e^5+_ + 1/128*(3*A*b^4*e^5-B*d*(128*c^4*d^4-320*b*c^3*d^3*e+240*b^2*c^2*_ + d^2*e^2-40*b^3*c*d*e^3-5*b^4*e^4))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*e^5*_ + (c*d-b*e)^(5/2))-1/64*(3*A*b^3*e^4+B*d*(64*c^3*d^3-112*b*c^2*_ + d^2*e+40*b^2*c*d*e^2+5*b^3*e^3)+2*c*e*(3*A*b^2*e^3+B*d*(16*c^2*_ + d^2-24*b*c*d*e+5*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d^2*e^4*_ + (c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 2 6 2 3 5 3 4 4 4 +--R (768B b c d e - 1536B b c d e + 768B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (3072B b c d e - 6144B b c d e + 3072B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (4608B b c d e - 9216B b c d e + 4608B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (3072B b c d e - 6144B b c d e + 3072B c d e)x + 768B b c d e +--R + +--R 2 7 3 8 +--R - 1536B b c d e + 768B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 9 4 8 3 2 7 2 2 3 6 +--R - 9A b e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R - 960B b c d e + 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R - 3840B b c d e + 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R - 54A b d e - 90B b d e - 720B b c d e + 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R - 5760B b c d e + 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 7 2 4 8 +--R - 3840B b c d e + 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R - 9A b d e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 8 4 9 +--R - 960B b c d e + 384B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 18A b e + (12A b c + 30B b )d e + (- 144A b c - 764B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (96A c + 1552B b c )d e - 800B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 66A b d e + (- 264A b c - 146B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (144A b c - 1096B b c)d e + 2960B b c d e - 1664B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 66A b d e + (12A b c - 110B b )d e - 860B b c d e +--R + +--R 2 5 3 3 6 2 +--R 2368B b c d e - 1344B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 3 7 +--R - 18A b d e - 30B b d e - 240B b c d e + 672B b c d e - 384B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (384b d e - 768b c d e + 384c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (1536b d e - 3072b c d e + 1536c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (2304b d e - 4608b c d e + 2304c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (1536b d e - 3072b c d e + 1536c d e )x + 384b d e - 768b c d e +--R + +--R 2 8 5 +--R 384c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 6 2 3 5 3 4 4 4 +--R (384B b c d e - 768B b c d e + 384B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (1536B b c d e - 3072B b c d e + 1536B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (2304B b c d e - 4608B b c d e + 2304B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (1536B b c d e - 3072B b c d e + 1536B c d e)x + 384B b c d e +--R + +--R 2 7 3 8 +--R - 768B b c d e + 384B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R \|- b d e + c d \|c log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 9 4 8 3 2 7 2 2 3 6 +--R 9A b e + 15B b d e + 120B b c d e - 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R 960B b c d e - 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R 36A b d e + 60B b d e + 480B b c d e - 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R 3840B b c d e - 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R 54A b d e + 90B b d e + 720B b c d e - 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R 5760B b c d e - 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R 36A b d e + 60B b d e + 480B b c d e - 2880B b c d e +--R + +--R 3 7 2 4 8 +--R 3840B b c d e - 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R 9A b d e + 15B b d e + 120B b c d e - 720B b c d e +--R + +--R 3 8 4 9 +--R 960B b c d e - 384B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 8 2 3 7 +--R 18A b e + (12A b c + 30B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (- 144A b c - 764B b c)d e + (96A c + 1552B b c )d e +--R + +--R 3 4 4 +--R - 800B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 66A b d e + (- 264A b c - 146B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (144A b c - 1096B b c)d e + 2960B b c d e - 1664B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 66A b d e + (12A b c - 110B b )d e - 860B b c d e +--R + +--R 2 5 3 3 6 2 +--R 2368B b c d e - 1344B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 +--R - 18A b d e - 30B b d e - 240B b c d e + 672B b c d e +--R + +--R 3 7 +--R - 384B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (384b d e - 768b c d e + 384c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (1536b d e - 3072b c d e + 1536c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (2304b d e - 4608b c d e + 2304c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (1536b d e - 3072b c d e + 1536c d e )x + 384b d e - 768b c d e +--R + +--R 2 8 5 +--R 384c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 2 6 2 3 5 3 4 4 4 +--R (192B b c d e - 384B b c d e + 192B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (768B b c d e - 1536B b c d e + 768B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (1152B b c d e - 2304B b c d e + 1152B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (768B b c d e - 1536B b c d e + 768B c d e)x + 192B b c d e +--R + +--R 2 7 3 8 +--R - 384B b c d e + 192B c d +--R * +--R +------------+ +----------+ +--R +-+ | 2 +-+ | 2 +--R \|c \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 9 4 8 3 2 7 2 2 3 6 +--R - 9A b e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R - 960B b c d e + 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R - 3840B b c d e + 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R - 54A b d e - 90B b d e - 720B b c d e + 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R - 5760B b c d e + 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 7 2 4 8 +--R - 3840B b c d e + 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R - 9A b d e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 8 4 9 +--R - 960B b c d e + 384B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 9A b e + (6A b c + 15B b )d e + (- 72A b c - 382B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (48A c + 776B b c )d e - 400B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 33A b d e + (- 132A b c - 73B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (72A b c - 548B b c)d e + 1480B b c d e - 832B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 33A b d e + (6A b c - 55B b )d e - 430B b c d e +--R + +--R 2 5 3 3 6 2 +--R 1184B b c d e - 672B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 3 7 +--R - 9A b d e - 15B b d e - 120B b c d e + 336B b c d e - 192B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (192b d e - 384b c d e + 192c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (768b d e - 1536b c d e + 768c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (1152b d e - 2304b c d e + 1152c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (768b d e - 1536b c d e + 768c d e )x + 192b d e - 384b c d e +--R + +--R 2 8 5 +--R 192c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R , +--R +--R 4 9 4 8 3 2 7 2 2 3 6 +--R 9A b e + 15B b d e + 120B b c d e - 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R 960B b c d e - 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R 36A b d e + 60B b d e + 480B b c d e - 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R 3840B b c d e - 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R 54A b d e + 90B b d e + 720B b c d e - 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R 5760B b c d e - 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R 36A b d e + 60B b d e + 480B b c d e - 2880B b c d e +--R + +--R 3 7 2 4 8 +--R 3840B b c d e - 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R 9A b d e + 15B b d e + 120B b c d e - 720B b c d e +--R + +--R 3 8 4 9 +--R 960B b c d e - 384B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 2 6 2 3 5 3 4 4 4 +--R (768B b c d e - 1536B b c d e + 768B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (3072B b c d e - 6144B b c d e + 3072B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (4608B b c d e - 9216B b c d e + 4608B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (3072B b c d e - 6144B b c d e + 3072B c d e)x + 768B b c d e +--R + +--R 2 7 3 8 +--R - 1536B b c d e + 768B c d +--R * +--R +----------+ +--R +--------------+ | 2 +--R | 2 +---+ \|c x + b x +--R \|- b d e + c d \|- c atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 3 8 2 3 7 +--R 18A b e + (12A b c + 30B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (- 144A b c - 764B b c)d e + (96A c + 1552B b c )d e +--R + +--R 3 4 4 +--R - 800B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 66A b d e + (- 264A b c - 146B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (144A b c - 1096B b c)d e + 2960B b c d e - 1664B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 66A b d e + (12A b c - 110B b )d e - 860B b c d e +--R + +--R 2 5 3 3 6 2 +--R 2368B b c d e - 1344B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 +--R - 18A b d e - 30B b d e - 240B b c d e + 672B b c d e +--R + +--R 3 7 +--R - 384B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (384b d e - 768b c d e + 384c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (1536b d e - 3072b c d e + 1536c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (2304b d e - 4608b c d e + 2304c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (1536b d e - 3072b c d e + 1536c d e )x + 384b d e - 768b c d e +--R + +--R 2 8 5 +--R 384c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 4 9 4 8 3 2 7 2 2 3 6 +--R - 9A b e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R - 960B b c d e + 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R - 3840B b c d e + 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R - 54A b d e - 90B b d e - 720B b c d e + 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R - 5760B b c d e + 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 7 2 4 8 +--R - 3840B b c d e + 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R - 9A b d e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 8 4 9 +--R - 960B b c d e + 384B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 2 6 2 3 5 3 4 4 4 +--R (384B b c d e - 768B b c d e + 384B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (1536B b c d e - 3072B b c d e + 1536B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (2304B b c d e - 4608B b c d e + 2304B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (1536B b c d e - 3072B b c d e + 1536B c d e)x + 384B b c d e +--R + +--R 2 7 3 8 +--R - 768B b c d e + 384B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 \|c x + b x +--R \|- c \|b d e - c d atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 9A b e + (6A b c + 15B b )d e + (- 72A b c - 382B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (48A c + 776B b c )d e - 400B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 33A b d e + (- 132A b c - 73B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (72A b c - 548B b c)d e + 1480B b c d e - 832B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 33A b d e + (6A b c - 55B b )d e - 430B b c d e +--R + +--R 2 5 3 3 6 2 +--R 1184B b c d e - 672B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 3 7 +--R - 9A b d e - 15B b d e - 120B b c d e + 336B b c d e - 192B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (192b d e - 384b c d e + 192c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (768b d e - 1536b c d e + 768c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (1152b d e - 2304b c d e + 1152c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (768b d e - 1536b c d e + 768c d e )x + 192b d e - 384b c d e +--R + +--R 2 8 5 +--R 192c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 410 + +--S 411 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 2 2 3 3 4 | 2 +--R (128B b c d e - 256B b c d e + 128B c d )\|- b d e + c d +--R * +--R +----------+ +--R +-----------+ +-+ +-+ +-+ | 2 +--R \|- b e + c d \|c \|d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 +--R 3A b e + 5B b d e + 40B b c d e - 240B b c d e + 320B b c d e +--R + +--R 4 5 +--R - 128B c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 2 2 2 3 3 4 | 2 +--R (- 256B b c d e + 512B b c d e - 256B c d )\|- b d e + c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 +--R 3A b e + 5B b d e + 40B b c d e - 240B b c d e + 320B b c d e +--R + +--R 4 5 +--R - 128B c d +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 7 3 6 2 4 5 | 2 +-----------+ +-+ +--R (128b d e - 256b c d e + 128c d e )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 3 3 4 +-----------+ +-+ +-+ +--R (128B b c d e - 256B b c d e + 128B c d )\|- b e + c d \|c \|d +--R * +--R +------------+ +----------+ +--R | 2 +-+ | 2 +--R \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 2 2 2 3 3 4 +-----------+ +-+ +-+ +--R (- 256B b c d e + 512B b c d e - 256B c d )\|- b e + c d \|c \|d +--R * +--R +------------+ +-+ +--R | 2 x\|c +--R \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 +--R 3A b e + 5B b d e + 40B b c d e - 240B b c d e + 320B b c d e +--R + +--R 4 5 +--R - 128B c d +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 +--R - 6A b e - 10B b d e - 80B b c d e + 480B b c d e - 640B b c d e +--R + +--R 4 5 +--R 256B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 7 3 6 2 4 5 +-----------+ +-+ | 2 +--R (128b d e - 256b c d e + 128c d e )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1457 +r0:=-1/5*(4*B*d+A*e+5*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^5)-_ + 3/256*b^4*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+_ + 1/80*(A*e*(4*c^2*d^2-4*b*c*d*e-b^2*e^2)+B*d*(16*c^2*d^2-26*b*c*d*e+_ + 11*b^2*e^2))*sqrt(b*x+c*x^2)/(d*e^4*(c*d-b*e)*(d+e*x)^3)+1/320*_ + (A*e*(16*c^3*d^3-24*b*c^2*d^2*e-2*b^2*c*d*e^2+5*b^3*e^3)+B*d*_ + (64*c^3*d^3-136*b*c^2*d^2*e+72*b^2*c*d*e^2+5*b^3*e^3))*_ + sqrt(b*x+c*x^2)/(d^2*e^4*(c*d-b*e)^2*(d+e*x)^2)+1/640*(B*d*_ + (128*c^4*d^4-336*b*c^3*d^3*e+248*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-_ + 15*b^4*e^4)+A*e*(32*c^4*d^4-64*b*c^3*d^3*e+12*b^2*c^2*d^2*e^2+_ + 20*b^3*c*d*e^3-15*b^4*e^4))*sqrt(b*x+c*x^2)/(d^3*e^4*(c*d-b*e)^3*_ + (d+e*x))-3/40*(B*d*(8*c*d-b*e)+A*e*(2*c*d+b*e)+2*e*(8*B*c*d-_ + 5*b*B*e+2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x)^4) +--R +--R +--R (2) +--R 5 6 4 5 5 5 +--R (- 15A b e + (30A b c - 15B b )d e )x +--R + +--R 5 5 4 5 2 4 4 +--R (- 75A b d e + (150A b c - 75B b )d e )x +--R + +--R 5 2 4 4 5 3 3 3 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 3 3 4 5 4 2 2 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 4 2 4 5 5 5 5 +--R (- 75A b d e + (150A b c - 75B b )d e)x - 15A b d e +--R + +--R 4 5 6 +--R (30A b c - 15B b )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 30A b e + (- 40A b c + 30B b )d e + (- 24A b c + 20B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (128A b c - 496B b c )d e + (- 64A c + 672B b c )d e - 256B c d +--R * +--R 4 +--R x +--R + +--R 4 4 3 4 2 3 +--R 140A b d e + (- 188A b c + 140B b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 184A b c - 932B b c)d e + (672A b c + 1024B b c )d e +--R + +--R 4 3 5 +--R (- 320A c - 352B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 4 3 2 +--R 256A b d e + (- 932A b c - 256B b )d e +--R + +--R 2 2 3 4 3 2 2 5 +--R (1336A b c + 92B b c)d e + (- 480A b c - 16B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 +--R (- 140A b d e + (300A b c - 140B b )d e + (- 40A b c + 20B b c)d )x +--R + +--R 4 4 3 4 5 +--R - 30A b d e + (60A b c - 30B b )d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (1280b d e - 3840b c d e + 3840b c d e - 1280c d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e)x + 1280b d e +--R + +--R 2 9 2 2 10 3 11 +--R - 3840b c d e + 3840b c d e - 1280c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 6 4 5 5 5 +--R (15A b e + (- 30A b c + 15B b )d e )x +--R + +--R 5 5 4 5 2 4 4 +--R (75A b d e + (- 150A b c + 75B b )d e )x +--R + +--R 5 2 4 4 5 3 3 3 +--R (150A b d e + (- 300A b c + 150B b )d e )x +--R + +--R 5 3 3 4 5 4 2 2 +--R (150A b d e + (- 300A b c + 150B b )d e )x +--R + +--R 5 4 2 4 5 5 5 5 +--R (75A b d e + (- 150A b c + 75B b )d e)x + 15A b d e +--R + +--R 4 5 6 +--R (- 30A b c + 15B b )d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 5 3 4 4 +--R 30A b e + (- 40A b c + 30B b )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 24A b c + 20B b c)d e + (128A b c - 496B b c )d e +--R + +--R 4 3 4 4 5 +--R (- 64A c + 672B b c )d e - 256B c d +--R * +--R 4 +--R x +--R + +--R 4 4 3 4 2 3 +--R 140A b d e + (- 188A b c + 140B b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 184A b c - 932B b c)d e + (672A b c + 1024B b c )d e +--R + +--R 4 3 5 +--R (- 320A c - 352B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 4 3 2 +--R 256A b d e + (- 932A b c - 256B b )d e +--R + +--R 2 2 3 4 3 2 2 5 +--R (1336A b c + 92B b c)d e + (- 480A b c - 16B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 3 4 4 +--R - 140A b d e + (300A b c - 140B b )d e +--R + +--R 2 2 3 5 +--R (- 40A b c + 20B b c)d +--R * +--R x +--R + +--R 4 4 3 4 5 +--R - 30A b d e + (60A b c - 30B b )d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (1280b d e - 3840b c d e + 3840b c d e - 1280c d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e)x +--R + +--R 3 8 3 2 9 2 2 10 3 11 +--R 1280b d e - 3840b c d e + 3840b c d e - 1280c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 5 6 4 5 5 5 +--R (- 15A b e + (30A b c - 15B b )d e )x +--R + +--R 5 5 4 5 2 4 4 +--R (- 75A b d e + (150A b c - 75B b )d e )x +--R + +--R 5 2 4 4 5 3 3 3 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 3 3 4 5 4 2 2 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 4 2 4 5 5 5 5 +--R (- 75A b d e + (150A b c - 75B b )d e)x - 15A b d e +--R + +--R 4 5 6 +--R (30A b c - 15B b )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 4 5 3 4 4 +--R 15A b e + (- 20A b c + 15B b )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 12A b c + 10B b c)d e + (64A b c - 248B b c )d e +--R + +--R 4 3 4 4 5 +--R (- 32A c + 336B b c )d e - 128B c d +--R * +--R 4 +--R x +--R + +--R 4 4 3 4 2 3 +--R 70A b d e + (- 94A b c + 70B b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 92A b c - 466B b c)d e + (336A b c + 512B b c )d e +--R + +--R 4 3 5 +--R (- 160A c - 176B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 4 3 2 +--R 128A b d e + (- 466A b c - 128B b )d e +--R + +--R 2 2 3 4 3 2 2 5 +--R (668A b c + 46B b c)d e + (- 240A b c - 8B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 +--R (- 70A b d e + (150A b c - 70B b )d e + (- 20A b c + 10B b c)d )x +--R + +--R 4 4 3 4 5 +--R - 15A b d e + (30A b c - 15B b )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (640b d e - 1920b c d e + 1920b c d e - 640c d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (3200b d e - 9600b c d e + 9600b c d e - 3200c d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (3200b d e - 9600b c d e + 9600b c d e - 3200c d e)x + 640b d e +--R + +--R 2 9 2 2 10 3 11 +--R - 1920b c d e + 1920b c d e - 640c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 417 + +--S 418 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 5 +-----------+ +-+ +--R (3A b e + (- 6A b c + 3B b )d)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 5 4 5 | 2 +--R (3A b e + (- 6A b c + 3B b )d)\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +--R (256b d e - 768b c d e + 768b c d e - 256c d )\|- b d e + c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 5 4 5 | 2 +--R (3A b e + (- 6A b c + 3B b )d)\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 4 5 +-----------+ +-+ +--R (- 6A b e + (12A b c - 6B b )d)\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ +--R (256b d e - 768b c d e + 768b c d e - 256c d )\|- b e + c d \|d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 421 + +)clear all + +--S 422 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1457 +r0:=1/768*b*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*_ + (B*d+2*A*e))*x^2*(b*x+c*x^2)^(3/2)/c^3+1/384*(64*A*c^3*d^2-11*b^3*_ + B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*x*(b*x+_ + c*x^2)^(5/2)/c^3+1/2016*(162*A*c*e*(2*c*d-b*e)+B*(64*c^2*d^2-_ + 226*b*c*d*e+99*b^2*e^2))*(b*x+c*x^2)^(7/2)/c^3+1/9*B*(d+e*x)^2*_ + (b*x+c*x^2)^(7/2)/c-1/144*e*((7*b*B-18*A*c)*d-(4*B*c*d-11*b*B*e+_ + 18*A*c*e)*x)*(b*x+c*x^2)^(7/2)/c^2-5/32768*b^6*(64*A*c^3*d^2-_ + 11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(13/2)+5/32768*b^5*(64*A*c^3*_ + d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*_ + sqrt(b*x+c*x^2)/c^6-5/49152*b^4*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*_ + c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^5+_ + 1/12288*b^3*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-_ + 32*b*c^2*d*(B*d+2*A*e))*x^2*sqrt(b*x+c*x^2)/c^4+1/2048*b^2*_ + (64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*_ + (B*d+2*A*e))*x^3*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 8 9 2 7 2 8 +--R (- 5670A b c + 3465B b )e + (20160A b c - 11340B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 20160A b c + 10080B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 8 2 8 8 7 2 8 7 +--R 229376B c e x + ((258048A c + 530432B b c )e + 516096B c d e)x +--R + +--R 7 2 6 2 8 7 +--R (608256A b c + 316416B b c )e + (589824A c + 1216512B b c )d e +--R + +--R 8 2 +--R 294912B c d +--R * +--R 6 +--R x +--R + +--R 2 6 3 5 2 7 2 6 +--R (373248A b c + 1280B b c )e + (1425408A b c + 746496B b c )d e +--R + +--R 8 7 2 +--R (344064A c + 712704B b c )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (2304A b c - 1408B b c )e + (909312A b c + 4608B b c )d e +--R + +--R 7 2 6 2 +--R (860160A b c + 454656B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (- 2592A b c + 1584B b c )e + (9216A b c - 5184B b c )d e +--R + +--R 2 6 3 5 2 +--R (580608A b c + 4608B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (3024A b c - 1848B b c )e + (- 10752A b c + 6048B b c )d e +--R + +--R 3 5 4 4 2 +--R (10752A b c - 5376B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 3780A b c + 2310B b c)e + (13440A b c - 7560B b c )d e +--R + +--R 4 4 5 3 2 +--R (- 13440A b c + 6720B b c )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 +--R (5670A b c - 3465B b )e + (- 20160A b c + 11340B b c)d e +--R + +--R 5 3 6 2 2 +--R (20160A b c - 10080B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 +-+ +--R 2064384c \|c +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 8 9 2 7 2 8 +--R (- 5670A b c + 3465B b )e + (20160A b c - 11340B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 20160A b c + 10080B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 8 2 8 +--R 458752B c e x +--R + +--R 8 7 2 8 7 +--R ((516096A c + 1060864B b c )e + 1032192B c d e)x +--R + +--R 7 2 6 2 +--R (1216512A b c + 632832B b c )e +--R + +--R 8 7 8 2 +--R (1179648A c + 2433024B b c )d e + 589824B c d +--R * +--R 6 +--R x +--R + +--R 2 6 3 5 2 +--R (746496A b c + 2560B b c )e +--R + +--R 7 2 6 +--R (2850816A b c + 1492992B b c )d e +--R + +--R 8 7 2 +--R (688128A c + 1425408B b c )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (4608A b c - 2816B b c )e + (1818624A b c + 9216B b c )d e +--R + +--R 7 2 6 2 +--R (1720320A b c + 909312B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (- 5184A b c + 3168B b c )e + (18432A b c - 10368B b c )d e +--R + +--R 2 6 3 5 2 +--R (1161216A b c + 9216B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (6048A b c - 3696B b c )e + (- 21504A b c + 12096B b c )d e +--R + +--R 3 5 4 4 2 +--R (21504A b c - 10752B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 7560A b c + 4620B b c)e + (26880A b c - 15120B b c )d e +--R + +--R 4 4 5 3 2 +--R (- 26880A b c + 13440B b c )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 +--R (11340A b c - 6930B b )e + (- 40320A b c + 22680B b c)d e +--R + +--R 5 3 6 2 2 +--R (40320A b c - 20160B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 +-+ +--R 4128768c \|c +--R , +--R +--R 8 9 2 7 2 8 +--R (- 5670A b c + 3465B b )e + (20160A b c - 11340B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 20160A b c + 10080B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 8 2 8 8 7 2 8 7 +--R 229376B c e x + ((258048A c + 530432B b c )e + 516096B c d e)x +--R + +--R 7 2 6 2 +--R (608256A b c + 316416B b c )e +--R + +--R 8 7 8 2 +--R (589824A c + 1216512B b c )d e + 294912B c d +--R * +--R 6 +--R x +--R + +--R 2 6 3 5 2 +--R (373248A b c + 1280B b c )e +--R + +--R 7 2 6 8 7 2 +--R (1425408A b c + 746496B b c )d e + (344064A c + 712704B b c )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (2304A b c - 1408B b c )e + (909312A b c + 4608B b c )d e +--R + +--R 7 2 6 2 +--R (860160A b c + 454656B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (- 2592A b c + 1584B b c )e + (9216A b c - 5184B b c )d e +--R + +--R 2 6 3 5 2 +--R (580608A b c + 4608B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (3024A b c - 1848B b c )e + (- 10752A b c + 6048B b c )d e +--R + +--R 3 5 4 4 2 +--R (10752A b c - 5376B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 3780A b c + 2310B b c)e + (13440A b c - 7560B b c )d e +--R + +--R 4 4 5 3 2 +--R (- 13440A b c + 6720B b c )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 +--R (5670A b c - 3465B b )e + (- 20160A b c + 11340B b c)d e +--R + +--R 5 3 6 2 2 +--R (20160A b c - 10080B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 6 +---+ +--R 2064384c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 424 + +--S 425 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 8 9 2 7 2 8 +--R (- 90A b c + 55B b )e + (320A b c - 180B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 320A b c + 160B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 8 9 2 7 2 8 +--R (180A b c - 110B b )e + (- 640A b c + 360B b c)d e +--R + +--R 6 3 7 2 2 +--R (640A b c - 320B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 6 +-+ +--R 65536c \|c +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 8 9 2 7 2 8 +--R (90A b c - 55B b )e + (- 320A b c + 180B b c)d e +--R + +--R 6 3 7 2 2 +--R (320A b c - 160B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 8 9 2 7 2 8 +--R (- 90A b c + 55B b )e + (320A b c - 180B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 320A b c + 160B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 6 +---+ +-+ +--R 32768c \|- c \|c +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 428 + +)clear all + +--S 429 of 1457 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1457 +r0:=1/384*b*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^2*_ + (b*x+c*x^2)^(3/2)/c^2+1/192*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*_ + x*(b*x+c*x^2)^(5/2)/c^2+1/112*(2*B*c*d-9*b*B*e+16*A*c*e)*_ + (b*x+c*x^2)^(7/2)/c^2+1/8*B*(d+e*x)*(b*x+c*x^2)^(7/2)/c-_ + 5/16384*b^6*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*atanh(x*_ + sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+5/16384*b^5*(32*A*c^2*d+9*b^2*B*e-_ + 16*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^5-5/24576*b^4*(32*A*c^2*d+_ + 9*b^2*B*e-16*b*c*(B*d+A*e))*x*sqrt(b*x+c*x^2)/c^4+1/6144*b^3*_ + (32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^2*sqrt(b*x+c*x^2)/c^3+_ + 1/1024*b^2*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^3*_ + sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 7 8 6 2 7 +--R ((1680A b c - 945B b )e + (- 3360A b c + 1680B b c)d) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 7 7 7 6 7 6 +--R 43008B c e x + ((49152A c + 101376B b c )e + 49152B c d)x +--R + +--R 6 2 5 7 6 5 +--R ((118784A b c + 62208B b c )e + (57344A c + 118784B b c )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((75776A b c + 384B b c )e + (143360A b c + 75776B b c )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((768A b c - 432B b c )e + (96768A b c + 768B b c )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((- 896A b c + 504B b c )e + (1792A b c - 896B b c )d)x +--R + +--R 5 2 6 4 3 5 2 +--R ((1120A b c - 630B b c)e + (- 2240A b c + 1120B b c )d)x +--R + +--R 6 7 5 2 6 +--R (- 1680A b c + 945B b )e + (3360A b c - 1680B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 344064c \|c +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 7 8 6 2 7 +--R ((1680A b c - 945B b )e + (- 3360A b c + 1680B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 7 7 7 6 7 6 +--R 86016B c e x + ((98304A c + 202752B b c )e + 98304B c d)x +--R + +--R 6 2 5 7 6 5 +--R ((237568A b c + 124416B b c )e + (114688A c + 237568B b c )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((151552A b c + 768B b c )e + (286720A b c + 151552B b c )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((1536A b c - 864B b c )e + (193536A b c + 1536B b c )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((- 1792A b c + 1008B b c )e + (3584A b c - 1792B b c )d)x +--R + +--R 5 2 6 4 3 5 2 +--R ((2240A b c - 1260B b c)e + (- 4480A b c + 2240B b c )d)x +--R + +--R 6 7 5 2 6 +--R (- 3360A b c + 1890B b )e + (6720A b c - 3360B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 688128c \|c +--R , +--R +--R 7 8 6 2 7 +--R ((1680A b c - 945B b )e + (- 3360A b c + 1680B b c)d) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 7 7 7 6 7 6 +--R 43008B c e x + ((49152A c + 101376B b c )e + 49152B c d)x +--R + +--R 6 2 5 7 6 5 +--R ((118784A b c + 62208B b c )e + (57344A c + 118784B b c )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((75776A b c + 384B b c )e + (143360A b c + 75776B b c )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((768A b c - 432B b c )e + (96768A b c + 768B b c )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((- 896A b c + 504B b c )e + (1792A b c - 896B b c )d)x +--R + +--R 5 2 6 4 3 5 2 +--R ((1120A b c - 630B b c)e + (- 2240A b c + 1120B b c )d)x +--R + +--R 6 7 5 2 6 +--R (- 1680A b c + 945B b )e + (3360A b c - 1680B b c)d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 5 +---+ +--R 344064c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 431 + +--S 432 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 7 8 6 2 7 +--R ((80A b c - 45B b )e + (- 160A b c + 80B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 7 8 6 2 7 x\|c +--R ((- 160A b c + 90B b )e + (320A b c - 160B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 5 +-+ +--R 32768c \|c +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 7 8 6 2 7 +---+ +--R ((- 80A b c + 45B b )e + (160A b c - 80B b c)d)\|- c +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 7 8 6 2 7 +-+ +--R ((80A b c - 45B b )e + (- 160A b c + 80B b c)d)\|c +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R / +--R 5 +---+ +-+ +--R 16384c \|- c \|c +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2) +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1457 +r0:=-1/24*b*(b*B-2*A*c)*x^2*(b*x+c*x^2)^(3/2)/c-1/12*(b*B-2*A*c)*x*_ + (b*x+c*x^2)^(5/2)/c+1/7*B*(b*x+c*x^2)^(7/2)/c+5/1024*b^6*(b*B-_ + 2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-5/1024*b^5*(b*B-_ + 2*A*c)*sqrt(b*x+c*x^2)/c^4+5/1536*b^4*(b*B-2*A*c)*x*sqrt(b*x+_ + c*x^2)/c^3-1/384*b^3*(b*B-2*A*c)*x^2*sqrt(b*x+c*x^2)/c^2-1/64*b^2*_ + (b*B-2*A*c)*x^3*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 6 7 x\|c +--R (- 210A b c + 105B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 6 6 5 5 5 2 4 4 +--R 3072B c x + (3584A c + 7424B b c )x + (8960A b c + 4736B b c )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 +--R (6048A b c + 48B b c )x + (112A b c - 56B b c )x +--R + +--R 4 2 5 5 6 +--R (- 140A b c + 70B b c)x + 210A b c - 105B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 21504c \|c +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 6 7 | 2 +-+ +--R (210A b c - 105B b )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 6 6 6 5 5 +--R 6144B c x + (7168A c + 14848B b c )x +--R + +--R 5 2 4 4 2 4 3 3 3 +--R (17920A b c + 9472B b c )x + (12096A b c + 96B b c )x +--R + +--R 3 3 4 2 2 4 2 5 5 +--R (224A b c - 112B b c )x + (- 280A b c + 140B b c)x + 420A b c +--R + +--R 6 +--R - 210B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 43008c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 6 7 \|- c \|c x + b x +--R (- 210A b c + 105B b )atan(-------------------) +--R c x +--R + +--R 6 6 6 5 5 +--R 3072B c x + (3584A c + 7424B b c )x +--R + +--R 5 2 4 4 2 4 3 3 3 +--R (8960A b c + 4736B b c )x + (6048A b c + 48B b c )x +--R + +--R 3 3 4 2 2 4 2 5 5 +--R (112A b c - 56B b c )x + (- 140A b c + 70B b c)x + 210A b c +--R + +--R 6 +--R - 105B b +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 21504c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 438 + +--S 439 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 6 7 | 2 +-+ +--R (10A b c - 5B b )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 6 7 x\|c +--R (20A b c - 10B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 2048c \|c +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 6 7 +---+ x\|c +--R (10A b c - 5B b )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 6 7 +-+ \|- c \|c x + b x +--R (- 10A b c + 5B b )\|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 1024c \|- c \|c +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x) +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1457 +r0:=1/192*(4*A*c*e*(16*c^2*d^2-22*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-_ + 88*b*c^2*d^2*e+12*b^2*c*d*e^2+5*b^3*e^3)-2*c*e*(12*A*c*e*(2*c*d-_ + b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/_ + (c^2*e^4)-1/60*(12*B*c*d-5*b*B*e-12*A*c*e-10*B*c*e*x)*(b*x+_ + c*x^2)^(5/2)/(c*e^2)-1/512*(4*A*c*e*(256*c^5*d^5-640*b*c^4*d^4*e+_ + 480*b^2*c^3*d^3*e^2-80*b^3*c^2*d^2*e^3-10*b^4*c*d*e^4-3*b^5*e^5)-_ + B*(1024*c^6*d^6-2560*b*c^5*d^5*e+1920*b^2*c^4*d^4*e^2-320*b^3*_ + c^3*d^3*e^3-40*b^4*c^2*d^2*e^4-12*b^5*c*d*e^5-5*b^6*e^6))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(7/2)*e^7)-d^(5/2)*(B*d-A*e)*_ + (c*d-b*e)^(5/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7+1/1536*(3*(4*A*c*e*(128*c^4*d^4-_ + 288*b*c^3*d^3*e+176*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-3*b^4*e^4)-_ + B*(512*c^5*d^5-1152*b*c^4*d^4*e+704*b^2*c^3*d^3*e^2-40*b^3*c^2*_ + d^2*e^3-12*b^4*c*d*e^4-5*b^5*e^5))-2*c*e*(8*b*c*d*e*(2*c*d-b*e)*_ + (12*B*c*d-5*b*B*e-12*A*c*e)+(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2)*_ + (12*A*c*e*(2*c*d-b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2)))*x)*_ + sqrt(b*x+c*x^2)/(c^3*e^6) +--R +--R +--R (2) +--R 5 6 6 4 2 5 5 +--R (180A b c - 75B b )e + (600A b c - 180B b c)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (4800A b c - 600B b c )d e + (- 28800A b c - 4800B b c )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (38400A b c + 28800B b c )d e + (- 15360A c - 38400B b c )d e +--R + +--R 6 6 +--R 15360B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 3 4 2 3 3 2 +--R - 7680A b c d e + (15360A b c + 7680B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 7680A c - 15360B b c )d e + 7680B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 6 5 5 4 6 5 5 4 +--R 1280B c e x + ((1536A c + 3200B b c )e - 1536B c d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (4032A b c + 2160B b c )e + (- 1920A c - 4032B b c )d e +--R + +--R 5 2 4 +--R 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2976A b c + 40B b c )e + (- 5440A b c - 2976B b c )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2560A c + 5440B b c )d e - 2560B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (120A b c - 50B b c)e + (- 4720A b c - 120B b c )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (8320A b c + 4720B b c )d e + (- 3840A c - 8320B b c )d e +--R + +--R 5 4 2 +--R 3840B c d e +--R * +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 180A b c + 75B b )e + (- 600A b c + 180B b c)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (10560A b c + 600B b c )d e + (- 17280A b c - 10560B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (7680A c + 17280B b c )d e - 7680B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 7 +-+ +--R 7680c e \|c +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1457 +--a0:=integrate(t0,x) +--E 445 + +--S 446 of 1457 +--m0:=a0-r0 +--E 446 + +--S 447 of 1457 +--d0:=D(m0,x) +--E 447 + +)clear all + +--S 448 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1457 +r0:=-1/48*(10*A*c*e*(8*c*d-7*b*e)-B*(96*c^2*d^2-92*b*c*d*e+3*b^2*e^2)+_ + 6*c*e*(12*B*c*d-b*B*e-10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(c*e^4)+_ + 1/5*(6*B*d-5*A*e+B*e*x)*(b*x+c*x^2)^(5/2)/(e^2*(d+e*x))+_ + 1/128*(10*A*c*e*(128*c^4*d^4-256*b*c^3*d^3*e+144*b^2*c^2*d^2*e^2-_ + 16*b^3*c*d*e^3-b^4*e^4)-B*(1536*c^5*d^5-3200*b*c^4*d^4*e+_ + 1920*b^2*c^3*d^3*e^2-240*b^3*c^2*d^2*e^3-20*b^4*c*d*e^4-3*b^5*e^5))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^7)+1/2*d^(3/2)*_ + (c*d-b*e)^(3/2)*(B*d*(12*c*d-7*b*e)-5*A*e*(2*c*d-b*e))*atanh(1/2*_ + (b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7-_ + 1/128*(10*A*c*e*(64*c^3*d^3-112*b*c^2*d^2*e+48*b^2*c*d*e^2-b^3*e^3)-_ + B*(768*c^4*d^4-1408*b*c^3*d^3*e+656*b^2*c^2*d^2*e^2-20*b^3*c*d*e^3-_ + 3*b^4*e^4)-2*c*e*(8*b*c*e*(6*B*d-5*A*e)*(2*c*d-b*e)-(12*B*c*d-b*B*e-_ + 10*A*c*e)*(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^6) +--R +--R +--R (2) +--R 4 5 6 3 2 4 5 +--R (- 150A b c + 45B b )e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (21600A b c + 3600B b c )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 38400A b c - 28800B b c )d e + (19200A c + 48000B b c )d e +--R + +--R 5 5 +--R - 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (- 150A b c + 45B b )d e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (21600A b c + 3600B b c )d e + (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (19200A c + 48000B b c )d e - 23040B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 4 3 2 2 2 3 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (9600A c + 18240B b c )d e - 11520B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 4 4 5 +--R (9600A c + 18240B b c )d e - 11520B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 384B c e x + ((480A c + 1008B b c )e - 576B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (1360A b c + 744B b c )e + (- 800A c - 1712B b c )d e +--R + +--R 4 2 4 +--R 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (1180A b c + 30B b c)e + (- 2800A b c - 1616B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (1600A c + 3520B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (150A b c - 45B b )e + (- 4100A b c - 270B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (8800A b c + 5560B b c )d e + (- 4800A c - 11040B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (150A b c - 45B b )d e + (- 7200A b c - 300B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (16800A b c + 9840B b c )d e + (- 9600A c - 21120B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 8 2 7 +-+ +--R (1920c e x + 1920c d e )\|c +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 5 6 3 2 4 5 +--R (150A b c - 45B b )e + (2400A b c - 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (- 21600A b c - 3600B b c )d e +--R + +--R 4 2 3 3 3 +--R (38400A b c + 28800B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (- 19200A c - 48000B b c )d e + 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (150A b c - 45B b )d e + (2400A b c - 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 21600A b c - 3600B b c )d e + (38400A b c + 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (- 19200A c - 48000B b c )d e + 23040B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 4 3 2 2 2 3 +--R 9600A b c d e + (- 28800A b c - 13440B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (19200A c + 36480B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R 9600A b c d e + (- 28800A b c - 13440B b c )d e +--R + +--R 4 3 4 4 5 +--R (19200A c + 36480B b c )d e - 23040B c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 768B c e x + ((960A c + 2016B b c )e - 1152B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (2720A b c + 1488B b c )e + (- 1600A c - 3424B b c )d e +--R + +--R 4 2 4 +--R 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (2360A b c + 60B b c)e + (- 5600A b c - 3232B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (3200A c + 7040B b c )d e - 3840B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (300A b c - 90B b )e + (- 8200A b c - 540B b c)d e +--R + +--R 3 2 2 2 4 +--R (17600A b c + 11120B b c )d e +--R + +--R 4 3 3 3 4 4 2 +--R (- 9600A c - 22080B b c )d e + 11520B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (300A b c - 90B b )d e + (- 14400A b c - 600B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (33600A b c + 19680B b c )d e + (- 19200A c - 42240B b c )d e +--R + +--R 4 5 +--R 23040B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 8 2 7 +-+ +--R (3840c e x + 3840c d e )\|c +--R , +--R +--R 4 5 6 3 2 4 5 +--R (150A b c - 45B b )e + (2400A b c - 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (- 21600A b c - 3600B b c )d e +--R + +--R 4 2 3 3 3 +--R (38400A b c + 28800B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (- 19200A c - 48000B b c )d e + 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (150A b c - 45B b )d e + (2400A b c - 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 21600A b c - 3600B b c )d e + (38400A b c + 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (- 19200A c - 48000B b c )d e + 23040B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 4 3 2 2 2 3 +--R - 19200A b c d e + (57600A b c + 26880B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (- 38400A c - 72960B b c )d e + 46080B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R - 19200A b c d e + (57600A b c + 26880B b c )d e +--R + +--R 4 3 4 4 5 +--R (- 38400A c - 72960B b c )d e + 46080B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 768B c e x + ((960A c + 2016B b c )e - 1152B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (2720A b c + 1488B b c )e + (- 1600A c - 3424B b c )d e +--R + +--R 4 2 4 +--R 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (2360A b c + 60B b c)e + (- 5600A b c - 3232B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (3200A c + 7040B b c )d e - 3840B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (300A b c - 90B b )e + (- 8200A b c - 540B b c)d e +--R + +--R 3 2 2 2 4 +--R (17600A b c + 11120B b c )d e +--R + +--R 4 3 3 3 4 4 2 +--R (- 9600A c - 22080B b c )d e + 11520B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (300A b c - 90B b )d e + (- 14400A b c - 600B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (33600A b c + 19680B b c )d e + (- 19200A c - 42240B b c )d e +--R + +--R 4 5 +--R 23040B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 8 2 7 +-+ +--R (3840c e x + 3840c d e )\|c +--R , +--R +--R 2 2 4 3 2 2 2 3 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (9600A c + 18240B b c )d e - 11520B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 4 4 5 +--R (9600A c + 18240B b c )d e - 11520B c d +--R * +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 4 5 6 3 2 4 5 +--R (- 150A b c + 45B b )e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (21600A b c + 3600B b c )d e +--R + +--R 4 2 3 3 3 +--R (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (19200A c + 48000B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (- 150A b c + 45B b )d e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (21600A b c + 3600B b c )d e + (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (19200A c + 48000B b c )d e - 23040B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 384B c e x + ((480A c + 1008B b c )e - 576B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (1360A b c + 744B b c )e + (- 800A c - 1712B b c )d e +--R + +--R 4 2 4 +--R 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (1180A b c + 30B b c)e + (- 2800A b c - 1616B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (1600A c + 3520B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (150A b c - 45B b )e + (- 4100A b c - 270B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (8800A b c + 5560B b c )d e + (- 4800A c - 11040B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (150A b c - 45B b )d e + (- 7200A b c - 300B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (16800A b c + 9840B b c )d e + (- 9600A c - 21120B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 2 8 2 7 +---+ +--R (1920c e x + 1920c d e )\|- c +--R , +--R +--R 4 5 6 3 2 4 5 +--R (- 150A b c + 45B b )e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (21600A b c + 3600B b c )d e +--R + +--R 4 2 3 3 3 +--R (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (19200A c + 48000B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (- 150A b c + 45B b )d e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (21600A b c + 3600B b c )d e + (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (19200A c + 48000B b c )d e - 23040B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 2 4 3 2 2 2 3 +--R - 9600A b c d e + (28800A b c + 13440B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (- 19200A c - 36480B b c )d e + 23040B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R - 9600A b c d e + (28800A b c + 13440B b c )d e +--R + +--R 4 3 4 4 5 +--R (- 19200A c - 36480B b c )d e + 23040B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 d\|c x + b x +--R \|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 384B c e x + ((480A c + 1008B b c )e - 576B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (1360A b c + 744B b c )e + (- 800A c - 1712B b c )d e +--R + +--R 4 2 4 +--R 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (1180A b c + 30B b c)e + (- 2800A b c - 1616B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (1600A c + 3520B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (150A b c - 45B b )e + (- 4100A b c - 270B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (8800A b c + 5560B b c )d e + (- 4800A c - 11040B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (150A b c - 45B b )d e + (- 7200A b c - 300B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (16800A b c + 9840B b c )d e + (- 9600A c - 21120B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 2 8 2 7 +---+ +--R (1920c e x + 1920c d e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 450 + +--S 451 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 5 5 3 2 4 4 +--R (10A b c - 3B b )e + (160A b c - 20B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 1440A b c - 240B b c )d e + (2560A b c + 1920B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 1280A c - 3200B b c )d e + 1536B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 3 3 2 2 2 2 +--R 640A b c d e + (- 1920A b c - 896B b c )d e +--R + +--R 4 3 3 4 4 +--R (1280A c + 2432B b c )d e - 1536B c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 4 5 5 3 2 4 4 +--R (20A b c - 6B b )e + (320A b c - 40B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 2880A b c - 480B b c )d e + (5120A b c + 3840B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 2560A c - 6400B b c )d e + 3072B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 3 2 2 2 2 +--R - 640A b c d e + (1920A b c + 896B b c )d e +--R + +--R 4 3 3 4 4 +--R (- 1280A c - 2432B b c )d e + 1536B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 2 7 +-+ +--R 256c e \|c +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 5 5 3 2 4 4 +--R (10A b c - 3B b )e + (160A b c - 20B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 1440A b c - 240B b c )d e + (2560A b c + 1920B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 1280A c - 3200B b c )d e + 1536B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 5 5 3 2 4 4 +--R (20A b c - 6B b )e + (320A b c - 40B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 2880A b c - 480B b c )d e + (5120A b c + 3840B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 2560A c - 6400B b c )d e + 3072B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 3 2 2 2 2 +--R - 640A b c d e + (1920A b c + 896B b c )d e +--R + +--R 4 3 3 4 4 +--R (- 1280A c - 2432B b c )d e + 1536B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 3 3 2 2 2 2 +--R - 1280A b c d e + (3840A b c + 1792B b c )d e +--R + +--R 4 3 3 4 4 +--R (- 2560A c - 4864B b c )d e + 3072B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 2 7 +-+ +--R 256c e \|c +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 454 + +)clear all + +--S 455 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1457 +r0:=-5/24*(B*d*(24*c*d-13*b*e)-2*A*e*(8*c*d-3*b*e)+e*(6*B*c*d-b*B*e-_ + 4*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/4*(3*B*d-2*A*e+B*e*x)*_ + (b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)-5/64*(8*A*c*e*(32*c^3*d^3-48*b*c^2*_ + d^2*e+18*b^2*c*d*e^2-b^3*e^3)-B*(384*c^4*d^4-640*b*c^3*d^3*e+288*b^2*_ + c^2*d^2*e^2-24*b^3*c*d*e^3-b^4*e^4))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/_ + (c^(3/2)*e^7)+5/8*(A*e*(16*c^2*d^2-16*b*c*d*e+3*b^2*e^2)-B*d*(24*c^2*_ + d^2-28*b*c*d*e+7*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-b*e)/e^7+5/64*_ + (8*A*c*e*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2)-B*(192*c^3*d^3-272*b*c^2*_ + d^2*e+88*b^2*c*d*e^2-b^3*e^3)-2*c*e*(16*A*c*e*(2*c*d-b*e)-B*(48*c^2*_ + d^2-32*b*c*d*e+b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c*e^6) +--R +--R +--R (2) +--R 3 4 6 2 2 3 5 +--R (120A b c - 15B b )e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (240A b c - 30B b )d e + (- 4320A b c - 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (11520A b c + 8640B b c )d e + (- 7680A c - 19200B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (120A b c - 15B b )d e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 6 +--R 5760B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 2 4 +--R - 360A b c e + (1920A b c + 840B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 1920A c - 3360B b c )d e + 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R - 720A b c d e + (3840A b c + 1680B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 3840A c - 6720B b c )d e + 5760B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R - 360A b c d e + (1920A b c + 840B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 1920A c - 3360B b c )d e + 2880B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 48B c e x + ((64A c + 136B b c )e - 96B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (208A b c + 118B b c)e + (- 160A c - 352B b c )d e +--R + +--R 3 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (264A b c + 15B b )e + (- 880A b c - 556B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (640A c + 1480B b c )d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (960A b c + 30B b )d e + (- 3680A b c - 2090B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 6240B b c )d e - 4320B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (600A b c + 15B b )d e + (- 2400A b c - 1320B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1920A c + 4080B b c )d e - 2880B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 9 2 8 2 7 +-+ +--R (192c e x + 384c d e x + 192c d e )\|c +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 6 2 2 3 5 +--R (- 120A b c + 15B b )e + (2160A b c + 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 5760A b c - 4320B b c )d e + (3840A c + 9600B b c )d e +--R + +--R 4 4 2 +--R - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (- 240A b c + 30B b )d e + (4320A b c + 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (- 11520A b c - 8640B b c )d e + (7680A c + 19200B b c )d e +--R + +--R 4 5 +--R - 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (- 120A b c + 15B b )d e + (2160A b c + 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (- 5760A b c - 4320B b c )d e + (3840A c + 9600B b c )d e +--R + +--R 4 6 +--R - 5760B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 5 2 2 4 +--R - 720A b c e + (3840A b c + 1680B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 3840A c - 6720B b c )d e + 5760B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R - 1440A b c d e + (7680A b c + 3360B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 7680A c - 13440B b c )d e + 11520B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R - 720A b c d e + (3840A b c + 1680B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 3840A c - 6720B b c )d e + 5760B c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 96B c e x + ((128A c + 272B b c )e - 192B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (416A b c + 236B b c)e + (- 320A c - 704B b c )d e +--R + +--R 3 2 4 +--R 480B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (528A b c + 30B b )e + (- 1760A b c - 1112B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (1280A c + 2960B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (1920A b c + 60B b )d e + (- 7360A b c - 4180B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (5760A c + 12480B b c )d e - 8640B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (1200A b c + 30B b )d e + (- 4800A b c - 2640B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (3840A c + 8160B b c )d e - 5760B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 9 2 8 2 7 +-+ +--R (384c e x + 768c d e x + 384c d e )\|c +--R , +--R +--R 3 4 6 2 2 3 5 +--R (- 120A b c + 15B b )e + (2160A b c + 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 5760A b c - 4320B b c )d e + (3840A c + 9600B b c )d e +--R + +--R 4 4 2 +--R - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (- 240A b c + 30B b )d e + (4320A b c + 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (- 11520A b c - 8640B b c )d e + (7680A c + 19200B b c )d e +--R + +--R 4 5 +--R - 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (- 120A b c + 15B b )d e + (2160A b c + 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (- 5760A b c - 4320B b c )d e + (3840A c + 9600B b c )d e +--R + +--R 4 6 +--R - 5760B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 5 2 2 4 +--R 1440A b c e + (- 7680A b c - 3360B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (7680A c + 13440B b c )d e - 11520B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R 2880A b c d e + (- 15360A b c - 6720B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (15360A c + 26880B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R 1440A b c d e + (- 7680A b c - 3360B b c)d e +--R + +--R 3 2 4 3 5 +--R (7680A c + 13440B b c )d e - 11520B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 96B c e x + ((128A c + 272B b c )e - 192B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (416A b c + 236B b c)e + (- 320A c - 704B b c )d e +--R + +--R 3 2 4 +--R 480B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (528A b c + 30B b )e + (- 1760A b c - 1112B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (1280A c + 2960B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (1920A b c + 60B b )d e + (- 7360A b c - 4180B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (5760A c + 12480B b c )d e - 8640B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (1200A b c + 30B b )d e + (- 4800A b c - 2640B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (3840A c + 8160B b c )d e - 5760B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 9 2 8 2 7 +-+ +--R (384c e x + 768c d e x + 384c d e )\|c +--R , +--R +--R 2 5 2 2 4 +--R - 360A b c e + (1920A b c + 840B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 1920A c - 3360B b c )d e + 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R - 720A b c d e + (3840A b c + 1680B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 3840A c - 6720B b c )d e + 5760B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R - 360A b c d e + (1920A b c + 840B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 1920A c - 3360B b c )d e + 2880B c d +--R * +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 3 4 6 2 2 3 5 +--R (120A b c - 15B b )e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (240A b c - 30B b )d e + (- 4320A b c - 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (11520A b c + 8640B b c )d e + (- 7680A c - 19200B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (120A b c - 15B b )d e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 6 +--R 5760B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 48B c e x + ((64A c + 136B b c )e - 96B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (208A b c + 118B b c)e + (- 160A c - 352B b c )d e +--R + +--R 3 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (264A b c + 15B b )e + (- 880A b c - 556B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (640A c + 1480B b c )d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (960A b c + 30B b )d e + (- 3680A b c - 2090B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 6240B b c )d e - 4320B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (600A b c + 15B b )d e + (- 2400A b c - 1320B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1920A c + 4080B b c )d e - 2880B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 9 2 8 2 7 +---+ +--R (192c e x + 384c d e x + 192c d e )\|- c +--R , +--R +--R 3 4 6 2 2 3 5 +--R (120A b c - 15B b )e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (240A b c - 30B b )d e + (- 4320A b c - 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (11520A b c + 8640B b c )d e + (- 7680A c - 19200B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (120A b c - 15B b )d e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 6 +--R 5760B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 5 2 2 4 +--R 720A b c e + (- 3840A b c - 1680B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (3840A c + 6720B b c )d e - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R 1440A b c d e + (- 7680A b c - 3360B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (7680A c + 13440B b c )d e - 11520B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R 720A b c d e + (- 3840A b c - 1680B b c)d e +--R + +--R 3 2 4 3 5 +--R (3840A c + 6720B b c )d e - 5760B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 d\|c x + b x +--R \|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 48B c e x + ((64A c + 136B b c )e - 96B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (208A b c + 118B b c)e + (- 160A c - 352B b c )d e +--R + +--R 3 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (264A b c + 15B b )e + (- 880A b c - 556B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (640A c + 1480B b c )d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (960A b c + 30B b )d e + (- 3680A b c - 2090B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 6240B b c )d e - 4320B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (600A b c + 15B b )d e + (- 2400A b c - 1320B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1920A c + 4080B b c )d e - 2880B c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 9 2 8 2 7 +---+ +--R (192c e x + 384c d e x + 192c d e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 457 + +--S 458 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 4 2 2 3 3 +--R (- 40A b c + 5B b )e + (720A b c + 120B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 1920A b c - 1440B b c )d e + (1280A c + 3200B b c )d e +--R + +--R 4 4 +--R - 1920B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 2 2 +--R - 240A b c e + (1280A b c + 560B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 1280A c - 2240B b c )d e + 1920B c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 3 4 4 2 2 3 3 +--R (- 80A b c + 10B b )e + (1440A b c + 240B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 3840A b c - 2880B b c )d e + (2560A c + 6400B b c )d e +--R + +--R 4 4 +--R - 3840B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 +--R 240A b c e + (- 1280A b c - 560B b c)d e +--R + +--R 3 2 2 3 3 +--R (1280A c + 2240B b c )d e - 1920B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 7 +-+ +--R 128c e \|c +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 4 2 2 3 3 +--R (- 40A b c + 5B b )e + (720A b c + 120B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 1920A b c - 1440B b c )d e + (1280A c + 3200B b c )d e +--R + +--R 4 4 +--R - 1920B c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 4 2 2 3 3 +--R (- 80A b c + 10B b )e + (1440A b c + 240B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 3840A b c - 2880B b c )d e + (2560A c + 6400B b c )d e +--R + +--R 4 4 +--R - 3840B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 +--R 240A b c e + (- 1280A b c - 560B b c)d e +--R + +--R 3 2 2 3 3 +--R (1280A c + 2240B b c )d e - 1920B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 +--R 480A b c e + (- 2560A b c - 1120B b c)d e +--R + +--R 3 2 2 3 3 +--R (2560A c + 4480B b c )d e - 3840B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 7 +-+ +--R 128c e \|c +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 461 + +)clear all + +--S 462 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1457 +r0:=-5/12*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+e*(4*B*c*d-b*B*e-2*A*c*e)*x)*_ + (b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(2*B*d-A*e+B*e*x)*_ + (b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)+5/8*(2*A*c*e*(16*c^2*d^2-_ + 16*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+24*b^2*c*d*e^2-_ + b^3*e^3))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^7*sqrt(c))+5/16*(B*d*_ + (64*c^3*d^3-112*b*c^2*d^2*e+56*b^2*c*d*e^2-7*b^3*e^3)-A*e*(32*c^3*d^3-_ + 48*b*c^2*d^2*e+18*b^2*c*d*e^2-b^3*e^3))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^7*sqrt(d)*sqrt(c*d-b*e))-_ + 5/8*(A*e*(16*c^2*d^2-12*b*c*d*e+b^2*e^2)-2*B*d*(16*c^2*d^2-_ + 16*b*c*d*e+3*b^2*e^2)+e*(4*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+_ + b^2*e^2))*x)*sqrt(b*x+c*x^2)/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 3 6 2 2 5 +--R (180A b c + 30B b )e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (960A c + 2400B b c )d e - 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (180A b c + 30B b )d e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 5 3 6 +--R (960A c + 2400B b c )d e - 1920B c d +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 7 2 3 6 +--R - 15A b e + (270A b c + 105B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e +--R + +--R 3 4 3 +--R - 960B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 5 2 +--R - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 6 +--R - 2880B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 15A b d e + (270A b c + 105B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e - 960B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 6 5 2 6 2 5 4 +--R 16B c e x + ((24A c + 52B b c)e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 3 +--R ((108A b c + 66B b )e + (- 120A c - 276B b c)d e + 240B c d e )x +--R + +--R 2 6 2 5 +--R - 66A b e + (700A b c + 372B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 880A c - 1840B b c)d e + 1760B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 80A b d e + (920A b c + 470B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 1200A c - 2440B b c)d e + 2400B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 30A b d e + (360A b c + 180B b )d e + (- 480A c - 960B b c)d e +--R + +--R 2 5 +--R 960B c d e +--R * +--R +----------+ +--R +-----------+ +-+ +-+ | 2 +--R \|- b e + c d \|c \|d \|c x + b x +--R / +--R 10 3 9 2 2 8 3 7 +-----------+ +-+ +-+ +--R (48e x + 144d e x + 144d e x + 48d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 6 2 2 5 +--R (90A b c + 15B b )e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (480A c + 1200B b c )d e - 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (90A b c + 15B b )d e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 5 3 6 +--R (480A c + 1200B b c )d e - 960B c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +-+ +--R \|- b d e + c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 7 2 3 6 +--R - 15A b e + (270A b c + 105B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e +--R + +--R 3 4 3 +--R - 960B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 2160A b c - 2520B b c)d e + 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d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 80A b d e + (920A b c + 470B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 1200A c - 2440B b c)d e + 2400B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 +--R - 30A b d e + (360A b c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 480A c - 960B b c)d e + 960B c d e +--R * +--R +--------------+ +----------+ +--R | 2 +-+ | 2 +--R \|- b d e + c d \|c \|c x + b x +--R / +--R +--------------+ +--R 10 3 9 2 2 8 3 7 | 2 +-+ +--R (48e x + 144d e x + 144d e x + 48d e )\|- b d e + c d \|c +--R , +--R +--R 2 3 6 2 2 5 +--R (90A b c + 15B b )e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (480A c + 1200B b c )d e - 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (90A b c + 15B b )d e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 5 3 6 +--R (480A c + 1200B b c )d e - 960B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +-+ +--R \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 7 2 3 6 +--R - 30A b e + (540A b c + 210B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 1440A b c - 1680B b c)d e + (960A c + 3360B b c )d e +--R + +--R 3 4 3 +--R - 1920B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 90A b d e + (1620A b c + 630B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 4320A b c - 5040B b c)d e + (2880A c + 10080B b c )d e +--R + +--R 3 5 2 +--R - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 90A b d e + (1620A b c + 630B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 4320A b c - 5040B b c)d e + (2880A c + 10080B b c )d e +--R + +--R 3 6 +--R - 5760B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 30A b d e + (540A b c + 210B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (- 1440A b c - 1680B b c)d e + (960A c + 3360B b c )d e +--R + +--R 3 7 +--R - 1920B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-+ \|b d e - c d \|c x + b x +--R \|c atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 6 5 2 6 2 5 4 +--R 16B c e x + ((24A c + 52B b c)e - 48B c d e )x +--R + +--R 2 6 2 5 +--R (108A b c + 66B b )e + (- 120A c - 276B b c)d e +--R + +--R 2 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 5 +--R - 66A b e + (700A b c + 372B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 880A c - 1840B b c)d e + 1760B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 80A b d e + (920A b c + 470B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 1200A c - 2440B b c)d e + 2400B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 +--R - 30A b d e + (360A b c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 480A c - 960B b c)d e + 960B c d e +--R * +--R +------------+ +----------+ +--R +-+ | 2 | 2 +--R \|c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 10 3 9 2 2 8 3 7 +-+ | 2 +--R (48e x + 144d e x + 144d e x + 48d e )\|c \|b d e - c d +--R , +--R +--R 3 7 2 3 6 +--R - 15A b e + (270A b c + 105B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e +--R + +--R 3 4 3 +--R - 960B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 5 2 +--R - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 6 +--R - 2880B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 15A b d e + (270A b c + 105B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e - 960B c d +--R * +--R +---+ +--R \|- c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 6 2 2 5 +--R (180A b c + 30B b )e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (960A c + 2400B b c )d e - 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (180A b c + 30B b )d e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 5 3 6 +--R (960A c + 2400B b c )d e - 1920B c d +--R * +--R +----------+ +--R +--------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|- b d e + c d atan(-------------------) +--R c x +--R + +--R 2 6 5 2 6 2 5 4 +--R 16B c e x + ((24A c + 52B b c)e - 48B c d e )x +--R + +--R 2 6 2 5 +--R (108A b c + 66B b )e + (- 120A c - 276B b c)d e +--R + +--R 2 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 5 +--R - 66A b e + (700A b c + 372B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 880A c - 1840B b c)d e + 1760B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 80A b d e + (920A b c + 470B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 1200A c - 2440B b c)d e + 2400B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 +--R - 30A b d e + (360A b c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 480A c - 960B b c)d e + 960B c d e +--R * +--R +--------------+ +----------+ +--R | 2 +---+ | 2 +--R \|- b d e + c d \|- c \|c x + b x +--R / +--R +--------------+ +--R 10 3 9 2 2 8 3 7 | 2 +---+ +--R (48e x + 144d e x + 144d e x + 48d e )\|- b d e + c d \|- c +--R , +--R +--R 3 7 2 3 6 +--R - 15A b e + (270A b c + 105B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e +--R + +--R 3 4 3 +--R - 960B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 5 2 +--R - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 6 +--R - 2880B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 15A b d e + (270A b c + 105B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e - 960B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +---+ \|b d e - c d \|c x + b x +--R \|- c atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 3 6 2 2 5 +--R (90A b c + 15B b )e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (480A c + 1200B b c )d e - 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (270A b c + 45B b )d e + (- 1440A b c - 1080B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1440A c + 3600B b c )d e - 2880B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (90A b c + 15B b )d e + (- 480A b c - 360B b c)d e +--R + +--R 3 2 5 3 6 +--R (480A c + 1200B b c )d e - 960B c d +--R * +--R +----------+ +--R +------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|b d e - c d atan(-------------------) +--R c x +--R + +--R 2 6 5 2 6 2 5 4 +--R 8B c e x + ((12A c + 26B b c)e - 24B c d e )x +--R + +--R 2 6 2 5 2 2 4 3 +--R ((54A b c + 33B b )e + (- 60A c - 138B b c)d e + 120B c d e )x +--R + +--R 2 6 2 5 +--R - 33A b e + (350A b c + 186B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 440A c - 920B b c)d e + 880B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 40A b d e + (460A b c + 235B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 600A c - 1220B b c)d e + 1200B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 15A b d e + (180A b c + 90B b )d e + (- 240A c - 480B b c)d e +--R + +--R 2 5 +--R 480B c d e +--R * +--R +------------+ +----------+ +--R +---+ | 2 | 2 +--R \|- c \|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 10 3 9 2 2 8 3 7 +---+ | 2 +--R (24e x + 72d e x + 72d e x + 24d e )\|- c \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 464 + +--S 465 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 +--R (30A b c + 5B b )e + (- 160A b c - 120B b c)d e +--R + +--R 3 2 2 3 3 +--R (160A c + 400B b c )d e - 320B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-----------+ +-+ | 2 +-+ +--R \|- b d e + c d \|- b e + c d \|d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 5A b e + (90A b c + 35B b )d e + (- 240A b c - 280B b c)d e +--R + +--R 3 2 3 3 4 +--R (160A c + 560B b c )d e - 320B c d +--R * +--R +-----------+ +-+ +-+ +--R \|- b e + c d \|c \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 3 2 2 2 +--R (- 60A b c - 10B b )e + (320A b c + 240B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 320A c - 800B b c )d e + 640B c d +--R * +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ x\|c +--R \|- b d e + c d \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 5A b e + (- 90A b c - 35B b )d e + (240A b c + 280B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 160A c - 560B b c )d e + 320B c d +--R * +--R +--------------+ +--R | 2 +-+ (b e - 2c d)x - b d +--R \|- b d e + c d \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 7 | 2 +-----------+ +-+ +-+ +--R 16e \|- b d e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 +--R (30A b c + 5B b )e + (- 160A b c - 120B b c)d e +--R + +--R 3 2 2 3 3 +--R (160A c + 400B b c )d e - 320B c d +--R * +--R +------------+ +----------+ +--R +-----------+ +-+ | 2 | 2 +-+ +--R \|- b e + c d \|d \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 3 2 2 2 +--R (- 60A b c - 10B b )e + (320A b c + 240B b c)d e +--R + +--R 3 2 2 3 3 +--R (- 320A c - 800B b c )d e + 640B c d +--R * +--R +------------+ +-+ +--R +-----------+ +-+ | 2 x\|c +--R \|- b e + c d \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 5A b e + (- 90A b c - 35B b )d e + (240A b c + 280B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 160A c - 560B b c )d e + 320B c d +--R * +--R +------------+ +--R +-+ | 2 (b e - 2c d)x - b d +--R \|c \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A b e + (180A b c + 70B b )d e + (- 480A b c - 560B b c)d e +--R + +--R 3 2 3 3 4 +--R (320A c + 1120B b c )d e - 640B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|c \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 7 +-----------+ +-+ +-+ | 2 +--R 16e \|- b e + c d \|c \|d \|b d e - c d +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1457 +r0:=-5/32*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*d^2-64*b*c*d*e+_ + 17*b^2*e^2))*(b*x+c*x^2)^(3/2)/(d*e^4*(c*d-b*e)*(d+e*x)^2)-5/24*_ + (B*d*(24*c*d-11*b*e)-A*e*(8*c*d-b*e)+6*e*(3*B*c*d-b*B*e-A*c*e)*x)*_ + (b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^3)+1/4*(3*B*d-A*e+2*B*e*x)*(b*x+_ + c*x^2)^(5/2)/(e^2*(d+e*x)^4)+5/128*(A*e*(128*c^4*d^4-256*b*c^3*d^3*e+_ + 144*b^2*c^2*d^2*e^2-16*b^3*c*d*e^3-b^4*e^4)-B*d*(384*c^4*d^4-_ + 896*b*c^3*d^3*e+672*b^2*c^2*d^2*e^2-168*b^3*c*d*e^3+7*b^4*e^4))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(3/2)*e^7*(c*d-b*e)^(3/2))-5/4*(4*A*c*e*(2*c*d-b*e)-_ + B*(24*c^2*d^2-20*b*c*d*e+3*b^2*e^2))*atanh(x*sqrt(c)/sqrt(b*x+_ + c*x^2))*sqrt(c)/e^7-5/64*(B*d*(192*c^3*d^3-304*b*c^2*d^2*e+120*_ + b^2*c*d*e^2-7*b^3*e^3)-A*e*(64*c^3*d^3-80*b*c^2*d^2*e+16*b^2*c*d*_ + e^2+b^3*e^3)-2*c*e*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*_ + d^2-64*b*c*d*e+17*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d*e^6*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 3 7 2 2 2 6 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (3840A c + 21120B b c )d e - 11520B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (11520A b c + 8640B b )d e + (- 34560A b c - 66240B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (23040A c + 126720B b c )d e - 69120B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 7 3 8 +--R (3840A c + 21120B b c )d e - 11520B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 9 3 4 8 +--R - 15A b e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (1920A c + 13440B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 3 6 3 2 2 4 5 +--R (8640A b c + 10080B b c)d e + (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R - 90A b d e + (- 1440A b c - 630B b )d e +--R + +--R 2 2 3 4 5 +--R (12960A b c + 15120B b c)d e +--R + +--R 3 2 2 5 4 4 3 6 3 +--R (- 23040A b c - 60480B b c )d e + (11520A c + 80640B b c )d e +--R + +--R 4 7 2 +--R - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (8640A b c + 10080B b c)d e + (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (1920A c + 13440B b c )d e - 5760B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 7 3 2 6 5 +--R (192B b c d e - 192B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (384A b c + 864B b c)d e + (- 384A c - 2016B b c )d e +--R + +--R 3 3 5 +--R 1152B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 30A b e + (- 1292A b c - 558B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (5232A b c + 8284B b c)d e + (- 4000A c - 19696B b c )d e +--R + +--R 3 4 4 +--R 12000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 146A b d e + (- 2264A b c - 1022B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (10640A b c + 16392B b c)d e + (- 8320A c - 40240B b c )d e +--R + +--R 3 5 3 +--R 24960B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 110A b d e + (- 1740A b c - 770B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (8480A b c + 12860B b c)d e + (- 6720A c - 32160B b c )d e +--R + +--R 3 6 2 +--R 20160B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 30A b d e + (- 480A b c - 210B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (2400A b c + 3600B b c)d e + (- 1920A c - 9120B b c )d e +--R + +--R 3 7 +--R 5760B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (384b d e - 384c d e )x + (1536b d e - 1536c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (2304b d e - 2304c d e )x + (1536b d e - 1536c d e )x + 384b d e +--R + +--R 6 7 +--R - 384c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 7 2 2 2 6 +--R (960A b c + 720B b )d e + (- 2880A b c - 5520B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (1920A c + 10560B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (3840A b c + 2880B b )d e + (- 11520A b c - 22080B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (7680A c + 42240B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (5760A b c + 4320B b )d e + (- 17280A b c - 33120B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (11520A c + 63360B b c )d e - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (3840A b c + 2880B b )d e + (- 11520A b c - 22080B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (7680A c + 42240B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (960A b c + 720B b )d e + (- 2880A b c - 5520B b c)d e +--R + +--R 3 2 7 3 8 +--R (1920A c + 10560B b c )d e - 5760B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R \|- b d e + c d \|c log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 9 3 4 8 +--R 15A b e + (240A b c + 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (- 2160A b c - 2520B b c)d e + (3840A b c + 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (- 1920A c - 13440B b c )d e + 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R 60A b d e + (960A b c + 420B b )d e +--R + +--R 2 2 3 3 6 +--R (- 8640A b c - 10080B b c)d e +--R + +--R 3 2 2 4 5 +--R (15360A b c + 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (- 7680A c - 53760B b c )d e + 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 90A b d e + (1440A b c + 630B b )d e +--R + +--R 2 2 3 4 5 +--R (- 12960A b c - 15120B b c)d e +--R + +--R 3 2 2 5 4 +--R (23040A b c + 60480B b c )d e +--R + +--R 4 3 6 3 4 7 2 +--R (- 11520A c - 80640B b c )d e + 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R 60A b d e + (960A b c + 420B b )d e +--R + +--R 2 2 3 5 4 +--R (- 8640A b c - 10080B b c)d e +--R + +--R 3 2 2 6 3 +--R (15360A b c + 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (- 7680A c - 53760B b c )d e + 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R 15A b d e + (240A b c + 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (- 2160A b c - 2520B b c)d e + (3840A b c + 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (- 1920A c - 13440B b c )d e + 5760B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 7 3 2 6 5 +--R (192B b c d e - 192B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (384A b c + 864B b c)d e + (- 384A c - 2016B b c )d e +--R + +--R 3 3 5 +--R 1152B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 30A b e + (- 1292A b c - 558B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (5232A b c + 8284B b c)d e + (- 4000A c - 19696B b c )d e +--R + +--R 3 4 4 +--R 12000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 146A b d e + (- 2264A b c - 1022B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (10640A b c + 16392B b c)d e + (- 8320A c - 40240B b c )d e +--R + +--R 3 5 3 +--R 24960B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 110A b d e + (- 1740A b c - 770B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (8480A b c + 12860B b c)d e + (- 6720A c - 32160B b c )d e +--R + +--R 3 6 2 +--R 20160B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 30A b d e + (- 480A b c - 210B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (2400A b c + 3600B b c)d e + (- 1920A c - 9120B b c )d e +--R + +--R 3 7 +--R 5760B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (384b d e - 384c d e )x + (1536b d e - 1536c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (2304b d e - 2304c d e )x + (1536b d e - 1536c d e )x + 384b d e +--R + +--R 6 7 +--R - 384c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 3 7 2 2 2 6 +--R (480A b c + 360B b )d e + (- 1440A b c - 2760B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (960A c + 5280B b c )d e - 2880B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (3840A c + 21120B b c )d e - 11520B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (2880A b c + 2160B b )d e + (- 8640A b c - 16560B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (5760A c + 31680B b c )d e - 17280B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (3840A c + 21120B b c )d e - 11520B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (480A b c + 360B b )d e + (- 1440A b c - 2760B b c)d e +--R + +--R 3 2 7 3 8 +--R (960A c + 5280B b c )d e - 2880B c d +--R * +--R +------------+ +----------+ +--R +-+ | 2 +-+ | 2 +--R \|c \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 9 3 4 8 +--R - 15A b e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (1920A c + 13440B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 3 6 +--R (8640A b c + 10080B b c)d e +--R + +--R 3 2 2 4 5 +--R (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R - 90A b d e + (- 1440A b c - 630B b )d e +--R + +--R 2 2 3 4 5 +--R (12960A b c + 15120B b c)d e +--R + +--R 3 2 2 5 4 +--R (- 23040A b c - 60480B b c )d e +--R + +--R 4 3 6 3 4 7 2 +--R (11520A c + 80640B b c )d e - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 5 4 +--R (8640A b c + 10080B b c)d e +--R + +--R 3 2 2 6 3 +--R (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (1920A c + 13440B b c )d e - 5760B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 7 3 2 6 5 +--R (96B b c d e - 96B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (192A b c + 432B b c)d e + (- 192A c - 1008B b c )d e +--R + +--R 3 3 5 +--R 576B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 15A b e + (- 646A b c - 279B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (2616A b c + 4142B b c)d e + (- 2000A c - 9848B b c )d e +--R + +--R 3 4 4 +--R 6000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 73A b d e + (- 1132A b c - 511B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (5320A b c + 8196B b c)d e + (- 4160A c - 20120B b c )d e +--R + +--R 3 5 3 +--R 12480B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 55A b d e + (- 870A b c - 385B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (4240A b c + 6430B b c)d e + (- 3360A c - 16080B b c )d e +--R + +--R 3 6 2 +--R 10080B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (1200A b c + 1800B b c)d e + (- 960A c - 4560B b c )d e +--R + +--R 3 7 +--R 2880B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (192b d e - 192c d e )x + (768b d e - 768c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (1152b d e - 1152c d e )x + (768b d e - 768c d e )x + 192b d e +--R + +--R 6 7 +--R - 192c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R , +--R +--R 4 9 3 4 8 +--R 15A b e + (240A b c + 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (- 2160A b c - 2520B b c)d e + (3840A b c + 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (- 1920A c - 13440B b c )d e + 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R 60A b d e + (960A b c + 420B b )d e +--R + +--R 2 2 3 3 6 +--R (- 8640A b c - 10080B b c)d e +--R + +--R 3 2 2 4 5 +--R (15360A b c + 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (- 7680A c - 53760B b c )d e + 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 90A b d e + (1440A b c + 630B b )d e +--R + +--R 2 2 3 4 5 +--R (- 12960A b c - 15120B b c)d e +--R + +--R 3 2 2 5 4 +--R (23040A b c + 60480B b c )d e +--R + +--R 4 3 6 3 4 7 2 +--R (- 11520A c - 80640B b c )d e + 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R 60A b d e + (960A b c + 420B b )d e +--R + +--R 2 2 3 5 4 +--R (- 8640A b c - 10080B b c)d e +--R + +--R 3 2 2 6 3 +--R (15360A b c + 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (- 7680A c - 53760B b c )d e + 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R 15A b d e + (240A b c + 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (- 2160A b c - 2520B b c)d e + (3840A b c + 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (- 1920A c - 13440B b c )d e + 5760B c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 7 2 2 2 6 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (3840A c + 21120B b c )d e - 11520B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (11520A b c + 8640B b )d e + (- 34560A b c - 66240B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (23040A c + 126720B b c )d e - 69120B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 7 3 8 +--R (3840A c + 21120B b c )d e - 11520B c d +--R * +--R +----------+ +--R +--------------+ | 2 +--R | 2 +---+ \|c x + b x +--R \|- b d e + c d \|- c atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 2 7 3 2 6 5 +--R (192B b c d e - 192B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (384A b c + 864B b c)d e + (- 384A c - 2016B b c )d e +--R + +--R 3 3 5 +--R 1152B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 30A b e + (- 1292A b c - 558B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (5232A b c + 8284B b c)d e + (- 4000A c - 19696B b c )d e +--R + +--R 3 4 4 +--R 12000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 146A b d e + (- 2264A b c - 1022B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (10640A b c + 16392B b c)d e + (- 8320A c - 40240B b c )d e +--R + +--R 3 5 3 +--R 24960B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 110A b d e + (- 1740A b c - 770B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (8480A b c + 12860B b c)d e + (- 6720A c - 32160B b c )d e +--R + +--R 3 6 2 +--R 20160B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 30A b d e + (- 480A b c - 210B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (2400A b c + 3600B b c)d e + (- 1920A c - 9120B b c )d e +--R + +--R 3 7 +--R 5760B c d e +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (384b d e - 384c d e )x + (1536b d e - 1536c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (2304b d e - 2304c d e )x + (1536b d e - 1536c d e )x + 384b d e +--R + +--R 6 7 +--R - 384c d e +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 4 9 3 4 8 +--R - 15A b e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (1920A c + 13440B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 3 6 +--R (8640A b c + 10080B b c)d e +--R + +--R 3 2 2 4 5 +--R (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R - 90A b d e + (- 1440A b c - 630B b )d e +--R + +--R 2 2 3 4 5 +--R (12960A b c + 15120B b c)d e +--R + +--R 3 2 2 5 4 +--R (- 23040A b c - 60480B b c )d e +--R + +--R 4 3 6 3 4 7 2 +--R (11520A c + 80640B b c )d e - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 5 4 +--R (8640A b c + 10080B b c)d e +--R + +--R 3 2 2 6 3 +--R (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (1920A c + 13440B b c )d e - 5760B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 3 7 2 2 2 6 +--R (960A b c + 720B b )d e + (- 2880A b c - 5520B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (1920A c + 10560B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (3840A b c + 2880B b )d e + (- 11520A b c - 22080B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (7680A c + 42240B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (5760A b c + 4320B b )d e + (- 17280A b c - 33120B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (11520A c + 63360B b c )d e - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (3840A b c + 2880B b )d e + (- 11520A b c - 22080B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (7680A c + 42240B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (960A b c + 720B b )d e + (- 2880A b c - 5520B b c)d e +--R + +--R 3 2 7 3 8 +--R (1920A c + 10560B b c )d e - 5760B c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 \|c x + b x +--R \|- c \|b d e - c d atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 2 7 3 2 6 5 +--R (96B b c d e - 96B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (192A b c + 432B b c)d e + (- 192A c - 1008B b c )d e +--R + +--R 3 3 5 +--R 576B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 15A b e + (- 646A b c - 279B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (2616A b c + 4142B b c)d e + (- 2000A c - 9848B b c )d e +--R + +--R 3 4 4 +--R 6000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 73A b d e + (- 1132A b c - 511B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (5320A b c + 8196B b c)d e + (- 4160A c - 20120B b c )d e +--R + +--R 3 5 3 +--R 12480B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 55A b d e + (- 870A b c - 385B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (4240A b c + 6430B b c)d e + (- 3360A c - 16080B b c )d e +--R + +--R 3 6 2 +--R 10080B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (1200A b c + 1800B b c)d e + (- 960A c - 4560B b c )d e +--R + +--R 3 7 +--R 2880B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (192b d e - 192c d e )x + (768b d e - 768c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (1152b d e - 1152c d e )x + (768b d e - 768c d e )x + 192b d e +--R + +--R 6 7 +--R - 192c d e +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 471 + +--S 472 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 2 +--R (320A b c + 240B b )d e + (- 960A b c - 1840B b c)d e +--R + +--R 3 2 3 3 4 +--R (640A c + 3520B b c )d e - 1920B c d +--R * +--R +--------------+ +----------+ +--R | 2 +-----------+ +-+ +-+ +-+ | 2 +--R \|- b d e + c d \|- b e + c d \|c \|d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 5A b e + (80A b c + 35B b )d e + (- 720A b c - 840B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (1280A b c + 3360B b c )d e + (- 640A c - 4480B b c )d e +--R + +--R 4 5 +--R 1920B c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 3 2 2 2 2 +--R (- 640A b c - 480B b )d e + (1920A b c + 3680B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 1280A c - 7040B b c )d e + 3840B c d +--R * +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ +-+ x\|c +--R \|- b d e + c d \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 5A b e + (80A b c + 35B b )d e + (- 720A b c - 840B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (1280A b c + 3360B b c )d e + (- 640A c - 4480B b c )d e +--R + +--R 4 5 +--R 1920B c d +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 8 2 7 | 2 +-----------+ +-+ +--R (128b d e - 128c d e )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 2 +--R (320A b c + 240B b )d e + (- 960A b c - 1840B b c)d e +--R + +--R 3 2 3 3 4 +--R (640A c + 3520B b c )d e - 1920B c d +--R * +--R +------------+ +----------+ +--R +-----------+ +-+ +-+ | 2 +-+ | 2 +--R \|- b e + c d \|c \|d \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 3 3 2 2 2 2 +--R (- 640A b c - 480B b )d e + (1920A b c + 3680B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 1280A c - 7040B b c )d e + 3840B c d +--R * +--R +------------+ +-+ +--R +-----------+ +-+ +-+ | 2 x\|c +--R \|- b e + c d \|c \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 5A b e + (80A b c + 35B b )d e + (- 720A b c - 840B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (1280A b c + 3360B b c )d e + (- 640A c - 4480B b c )d e +--R + +--R 4 5 +--R 1920B c d +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 10A b e + (- 160A b c - 70B b )d e + (1440A b c + 1680B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (- 2560A b c - 6720B b c )d e + (1280A c + 8960B b c )d e +--R + +--R 4 5 +--R - 3840B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 8 2 7 +-----------+ +-+ | 2 +--R (128b d e - 128c d e )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 1457 +t0:=(A+B*x)*(d+e*x)^3/sqrt(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1457 +r0:=1/64*(128*A*c^4*d^3+35*b^4*B*e^3+144*b^2*c^2*d*e*(B*d+A*e)-40*b^3*_ + c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/c^(9/2)+1/192*(8*A*c*e*(52*c^2*d^2-52*b*c*d*e+_ + 15*b^2*e^2)+B*(96*c^3*d^3-352*b*c^2*d^2*e+346*b^2*c*d*e^2-105*_ + b^3*e^3))*sqrt(b*x+c*x^2)/c^4+1/24*(6*B*c*d-7*b*B*e+8*A*c*e)*_ + (d+e*x)^2*sqrt(b*x+c*x^2)/c^2+1/4*B*(d+e*x)^3*sqrt(b*x+c*x^2)/c-_ + 1/96*e*(d*(12*b*B*c*d-48*A*c^2*d-7*b^2*B*e+8*A*b*c*e)-(40*A*c*e*_ + (2*c*d-b*e)+B*(24*c^2*d^2-64*b*c*d*e+35*b^2*e^2))*x)*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (- 120A b c + 105B b )e + (432A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 576A b c + 432B b c )d e + (384A c - 192B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B c e x + ((64A c - 56B b c )e + 192B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 80A b c + 70B b c)e + (288A c - 240B b c )d e + 288B c d e)x +--R + +--R 2 3 3 2 2 2 +--R (120A b c - 105B b )e + (- 432A b c + 360B b c)d e +--R + +--R 3 2 2 3 3 +--R (576A c - 432B b c )d e + 192B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 3 2 2 3 2 +--R (120A b c - 105B b )e + (- 432A b c + 360B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (576A b c - 432B b c )d e + (- 384A c + 192B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 96B c e x + ((128A c - 112B b c )e + 384B c d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 160A b c + 140B b c)e + (576A c - 480B b c )d e +--R + +--R 3 2 +--R 576B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 +--R (240A b c - 210B b )e + (- 864A b c + 720B b c)d e +--R + +--R 3 2 2 3 3 +--R (1152A c - 864B b c )d e + 384B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 384c \|c +--R , +--R +--R 3 4 3 2 2 3 2 +--R (- 120A b c + 105B b )e + (432A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 576A b c + 432B b c )d e + (384A c - 192B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B c e x + ((64A c - 56B b c )e + 192B c d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 80A b c + 70B b c)e + (288A c - 240B b c )d e +--R + +--R 3 2 +--R 288B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 +--R (120A b c - 105B b )e + (- 432A b c + 360B b c)d e +--R + +--R 3 2 2 3 3 +--R (576A c - 432B b c )d e + 192B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 192c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 478 + +--S 479 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 +--R (40A b c - 35B b )e + (- 144A b c + 120B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (192A b c - 144B b c )d e + (- 128A c + 64B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 4 3 2 2 3 2 +--R (80A b c - 70B b )e + (- 288A b c + 240B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (384A b c - 288B b c )d e + (- 256A c + 128B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 128c \|c +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 3 2 2 3 2 +--R (40A b c - 35B b )e + (- 144A b c + 120B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (192A b c - 144B b c )d e + (- 128A c + 64B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 4 3 2 2 3 2 +--R (- 40A b c + 35B b )e + (144A b c - 120B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 192A b c + 144B b c )d e + (128A c - 64B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 64c \|- c \|c +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 482 + +)clear all + +--S 483 of 1457 +t0:=(A+B*x)*(d+e*x)^2/sqrt(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1457 +r0:=1/8*(16*A*c^3*d^2-5*b^3*B*e^2+6*b^2*c*e*(2*B*d+A*e)-8*b*c^2*d*_ + (B*d+2*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/24*(18*A*c*_ + e*(2*c*d-b*e)+B*(16*c^2*d^2-34*b*c*d*e+15*b^2*e^2))*sqrt(b*x+_ + c*x^2)/c^3+1/3*B*(d+e*x)^2*sqrt(b*x+c*x^2)/c-1/12*e*((b*B-6*A*c)*_ + d-(4*B*c*d-5*b*B*e+6*A*c*e)*x)*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R (18A b c - 15B b )e + (- 48A b c + 36B b c)d e +--R + +--R 3 2 2 +--R (48A c - 24B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 2 2 +--R 8B c e x + ((12A c - 10B b c)e + 24B c d e)x +--R + +--R 2 2 2 2 2 +--R (- 18A b c + 15B b )e + (48A c - 36B b c)d e + 24B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 24c \|c +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 +--R (18A b c - 15B b )e + (- 48A b c + 36B b c)d e +--R + +--R 3 2 2 +--R (48A c - 24B b c )d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 2 2 2 +--R 16B c e x + ((24A c - 20B b c)e + 48B c d e)x +--R + +--R 2 2 2 2 2 +--R (- 36A b c + 30B b )e + (96A c - 72B b c)d e + 48B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 48c \|c +--R , +--R +--R 2 3 2 2 2 +--R (18A b c - 15B b )e + (- 48A b c + 36B b c)d e +--R + +--R 3 2 2 +--R (48A c - 24B b c )d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 2 2 2 2 2 +--R 8B c e x + ((12A c - 10B b c)e + 24B c d e)x +--R + +--R 2 2 2 2 2 +--R (- 18A b c + 15B b )e + (48A c - 36B b c)d e + 24B c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 3 +---+ +--R 24c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 485 + +--S 486 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 2 2 +--R ((6A b c - 5B b )e + (- 16A b c + 12B b c)d e + (16A c - 8B b c )d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 2 2 +--R (- 12A b c + 10B b )e + (32A b c - 24B b c)d e +--R + +--R 3 2 2 +--R (- 32A c + 16B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 16c \|c +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 2 2 2 +--R (- 6A b c + 5B b )e + (16A b c - 12B b c)d e +--R + +--R 3 2 2 +--R (- 16A c + 8B b c )d +--R * +--R +-+ +--R +---+ x\|c +--R \|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((6A b c - 5B b )e + (- 16A b c + 12B b c)d e + (16A c - 8B b c )d ) +--R * +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R \|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 8c \|- c \|c +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 489 + +)clear all + +--S 490 of 1457 +t0:=(A+B*x)*(d+e*x)/sqrt(b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1457 +r0:=1/4*(8*A*c^2*d+3*b^2*B*e-4*b*c*(B*d+A*e))*atanh(x*sqrt(c)/sqrt(b*x+_ + c*x^2))/c^(5/2)+1/4*(2*B*c*d-3*b*B*e+4*A*c*e)*sqrt(b*x+c*x^2)/c^2+_ + 1/2*B*(d+e*x)*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 2 2 x\|c +--R ((- 4A b c + 3B b )e + (8A c - 4B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +-+ | 2 +--R (2B c e x + (4A c - 3B b)e + 4B c d)\|c \|c x + b x +--R / +--R 2 +-+ +--R 4c \|c +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R ((4A b c - 3B b )e + (- 8A c + 4B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R +-+ | 2 +--R (4B c e x + (8A c - 6B b)e + 8B c d)\|c \|c x + b x +--R / +--R 2 +-+ +--R 8c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 2 2 \|- c \|c x + b x +--R ((- 4A b c + 3B b )e + (8A c - 4B b c)d)atan(-------------------) +--R c x +--R + +--R +----------+ +--R +---+ | 2 +--R (2B c e x + (4A c - 3B b)e + 4B c d)\|- c \|c x + b x +--R / +--R 2 +---+ +--R 4c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 492 + +--S 493 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 +--R ((4A b c - 3B b )e + (- 8A c + 4B b c)d) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 2 2 x\|c +--R ((8A b c - 6B b )e + (- 16A c + 8B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 2 +-+ +--R 8c \|c +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 2 +---+ x\|c +--R ((4A b c - 3B b )e + (- 8A c + 4B b c)d)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 2 2 +-+ \|- c \|c x + b x +--R ((- 4A b c + 3B b )e + (8A c - 4B b c)d)\|c atan(-------------------) +--R c x +--R / +--R 2 +---+ +-+ +--R 4c \|- c \|c +--R Type: Expression(Integer) +--E 495 + +--S 496 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 496 + +)clear all + +--S 497 of 1457 +t0:=(A+B*x)/sqrt(b*x+c*x^2) +--R +--R +--R B x + A +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1457 +r0:=-(b*B-2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+B*sqrt(b*x+c*x^2)/c +--R +--R +--R +-+ +----------+ +--R x\|c +-+ | 2 +--R (2A c - B b)atanh(-------------) + B\|c \|c x + b x +--R +----------+ +--R | 2 +--R \|c x + b x +--R (2) ----------------------------------------------------- +--R +-+ +--R c\|c +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R (2A c - B b)log(2c\|c x + b x + (2c x + b)\|c ) + 2B\|c \|c x + b x +--R [-----------------------------------------------------------------------, +--R +-+ +--R 2c\|c +--R +----------+ +--R +---+ | 2 +----------+ +--R \|- c \|c x + b x +---+ | 2 +--R (2A c - B b)atan(-------------------) + B\|- c \|c x + b x +--R c x +--R ------------------------------------------------------------] +--R +---+ +--R c\|- c +--R Type: Union(List(Expression(Integer)),...) +--E 499 + +--S 500 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R | 2 +-+ +--R (2A c - B b)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R x\|c +--R (- 4A c + 2B b)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R +---+ x\|c +--R (- 2A c + B b)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R (2A c - B b)\|c atan(-------------------) +--R c x +--R / +--R +---+ +-+ +--R c\|- c \|c +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 503 + +)clear all + +--S 504 of 1457 +t0:=(A+B*x)/((d+e*x)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ---------------------- +--R +----------+ +--R | 2 +--R (e x + d)\|c x + b x +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1457 +r0:=2*B*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e*sqrt(c))-(B*d-A*e)*atanh(1/2*_ + (b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/_ + (e*sqrt(d)*sqrt(c*d-b*e)) +--R +--R +--R (2) +--R +-+ +--R +-----------+ +-+ x\|c +--R 2B\|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-+ (b e - 2c d)x - b d +--R (- A e + B d)\|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +-----------+ +-+ +-+ +--R e\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 505 + +--S 506 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +----------+ +--R | 2 | 2 +-+ +--R B\|- b d e + c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R (A e - B d)\|c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R / +--R +--------------+ +--R | 2 +-+ +--R e\|- b d e + c d \|c +--R , +--R +--R +------------+ +----------+ +--R | 2 | 2 +-+ +--R B\|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R +-+ \|b d e - c d \|c x + b x +--R (- 2A e + 2B d)\|c atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R +-+ | 2 +--R e\|c \|b d e - c d +--R , +--R +--R +---+ +--R (A e - B d)\|- c +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +----------+ +--R +--------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R 2B\|- b d e + c d atan(-------------------) +--R c x +--R / +--R +--------------+ +--R | 2 +---+ +--R e\|- b d e + c d \|- c +--R , +--R +--R +------------+ +----------+ +--R | 2 | 2 +--R +---+ \|b d e - c d \|c x + b x +--R (- 2A e + 2B d)\|- c atan(----------------------------) +--R (b e - c d)x +--R + +--R +----------+ +--R +------------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R 2B\|b d e - c d atan(-------------------) +--R c x +--R / +--R +------------+ +--R +---+ | 2 +--R e\|- c \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 506 + +--S 507 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +----------+ +--R | 2 +-----------+ +-+ | 2 +-+ +--R B\|- b d e + c d \|- b e + c d \|d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-----------+ +-+ +-+ +--R (A e - B d)\|- b e + c d \|c \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ x\|c +--R - 2B\|- b d e + c d \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +--------------+ +--R | 2 +-+ (b e - 2c d)x - b d +--R (A e - B d)\|- b d e + c d \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R | 2 +-----------+ +-+ +-+ +--R e\|- b d e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +----------+ +--R +-----------+ +-+ | 2 | 2 +-+ +--R B\|- b e + c d \|d \|b d e - c d log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +------------+ +-+ +--R +-----------+ +-+ | 2 x\|c +--R - 2B\|- b e + c d \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +------------+ +--R +-+ | 2 (b e - 2c d)x - b d +--R (A e - B d)\|c \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ +-+ \|b d e - c d \|c x + b x +--R (- 2A e + 2B d)\|- b e + c d \|c \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R +-----------+ +-+ +-+ | 2 +--R e\|- b e + c d \|c \|d \|b d e - c d +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1457 +t0:=(A+B*x)/((d+e*x)^2*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (e x + 2d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1457 +r0:=-1/2*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))+(B*d-A*e)*_ + sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 2 +--R ((- A b e + (2A c - B b)d e)x - A b d e + (2A c - B b)d ) +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +-----------+ +-+ | 2 +--R (2A e - 2B d)\|- b e + c d \|d \|c x + b x +--R / +--R 2 2 2 3 +-----------+ +-+ +--R ((2b d e - 2c d e)x + 2b d e - 2c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R ((A b e + (- 2A c + B b)d e)x + A b d e + (- 2A c + B b)d ) +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +----------+ +--R | 2 | 2 +--R (2A e - 2B d)\|- b d e + c d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 | 2 +--R ((2b d e - 2c d e)x + 2b d e - 2c d )\|- b d e + c d +--R , +--R +--R 2 2 +--R ((- A b e + (2A c - B b)d e)x - A b d e + (2A c - B b)d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R (A e - B d)\|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 2 2 2 3 | 2 +--R ((b d e - c d e)x + b d e - c d )\|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 513 + +--S 514 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R (A b e + (- 2A c + B b)d)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R | 2 +--R (A b e + (- 2A c + B b)d)\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +--R (2b d e - 2c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R | 2 +--R (A b e + (- 2A c + B b)d)\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +-----------+ +-+ +--R (- 2A b e + (4A c - 2B b)d)\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 +-----------+ +-+ | 2 +--R (2b d e - 2c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 517 + +)clear all + +--S 518 of 1457 +t0:=(A+B*x)/((d+e*x)^3*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +----------+ +--R 3 3 2 2 2 3 | 2 +--R (e x + 3d e x + 3d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1457 +r0:=1/8*(8*A*c^2*d^2-4*b*c*d*(B*d+2*A*e)+b^2*e*(B*d+3*A*e))*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*_ + (c*d-b*e)^(5/2))+1/2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ + (d+e*x)^2)-1/4*(3*A*e*(2*c*d-b*e)-B*d*(2*c*d+b*e))*sqrt(b*x+c*x^2)/_ + (d^2*(c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 +--R (- 3A b e + (8A b c - B b )d e + (- 8A c + 4B b c)d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (- 6A b d e + (16A b c - 2B b )d e + (- 16A c + 8B b c)d e)x +--R + +--R 2 2 2 2 3 2 4 +--R - 3A b d e + (8A b c - B b )d e + (- 8A c + 4B b c)d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 2 2 +--R (6A b e + (- 12A c + 2B b)d e + 4B c d e)x + 10A b d e +--R + +--R 2 3 +--R (- 16A c - 2B b)d e + 8B c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (8b d e - 16b c d e + 8c d e )x + (16b d e - 32b c d e + 16c d e)x +--R + +--R 2 4 2 5 2 6 +--R 8b d e - 16b c d e + 8c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 2 3 2 2 2 2 +--R (3A b e + (- 8A b c + B b )d e + (8A c - 4B b c)d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (6A b d e + (- 16A b c + 2B b )d e + (16A c - 8B b c)d e)x +--R + +--R 2 2 2 2 3 2 4 +--R 3A b d e + (- 8A b c + B b )d e + (8A c - 4B b c)d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 2 2 2 +--R (6A b e + (- 12A c + 2B b)d e + 4B c d e)x + 10A b d e +--R + +--R 2 3 +--R (- 16A c - 2B b)d e + 8B c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 +--R (8b d e - 16b c d e + 8c d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (16b d e - 32b c d e + 16c d e)x + 8b d e - 16b c d e + 8c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 4 2 3 2 2 2 2 +--R (- 3A b e + (8A b c - B b )d e + (- 8A c + 4B b c)d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (- 6A b d e + (16A b c - 2B b )d e + (- 16A c + 8B b c)d e)x +--R + +--R 2 2 2 2 3 2 4 +--R - 3A b d e + (8A b c - B b )d e + (- 8A c + 4B b c)d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 2 2 2 +--R (3A b e + (- 6A c + B b)d e + 2B c d e)x + 5A b d e +--R + +--R 2 3 +--R (- 8A c - B b)d e + 4B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (4b d e - 8b c d e + 4c d e )x + (8b d e - 16b c d e + 8c d e)x +--R + +--R 2 4 2 5 2 6 +--R 4b d e - 8b c d e + 4c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 520 + +--S 521 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 +-----------+ +-+ +--R (3A b e + (- 8A b c + B b )d e + (8A c - 4B b c)d )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 2 2 2 2 | 2 +--R (3A b e + (- 8A b c + B b )d e + (8A c - 4B b c)d )\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (8b d e - 16b c d e + 8c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 2 2 2 2 2 | 2 +--R (3A b e + (- 8A b c + B b )d e + (8A c - 4B b c)d )\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 2 2 2 +--R (- 6A b e + (16A b c - 2B b )d e + (- 16A c + 8B b c)d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (8b d e - 16b c d e + 8c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 524 + +)clear all + +--S 525 of 1457 +t0:=(A+B*x)/((d+e*x)^4*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R +----------+ +--R 4 4 3 3 2 2 2 3 4 | 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1457 +r0:=1/16*(16*A*c^3*d^3-8*b*c^2*d^2*(B*d+3*A*e)-b^3*e^2*(B*d+5*A*e)+_ + 2*b^2*c*d*e*(2*B*d+9*A*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+_ + 1/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^3)-_ + 1/12*(5*A*e*(2*c*d-b*e)-B*d*(4*c*d+b*e))*sqrt(b*x+c*x^2)/(d^2*_ + (c*d-b*e)^2*(d+e*x)^2)+1/24*(B*d*(8*c^2*d^2+10*b*c*d*e-3*b^2*e^2)-_ + A*e*(44*c^2*d^2-44*b*c*d*e+15*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*_ + (c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 3 6 2 3 5 2 2 2 4 +--R - 15A b e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 3 3 +--R (48A c - 24B b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 2 4 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 3 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R x +--R + +--R 3 3 3 2 3 4 2 2 2 5 +--R - 15A b d e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 6 +--R (48A c - 24B b c )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 88A b c + 6B b )d e + (88A c - 20B b c)d e +--R + +--R 2 3 2 +--R - 16B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 80A b d e + (- 236A b c + 16B b )d e + (216A c - 28B b c)d e +--R + +--R 2 4 +--R - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 66A b d e + (- 180A b c - 6B b )d e + (144A c + 24B b c)d e +--R + +--R 2 5 +--R - 48B c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (48b d e - 144b c d e + 144b c d e - 48c d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (144b d e - 432b c d e + 432b c d e - 144c d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (144b d e - 432b c d e + 432b c d e - 144c d e)x + 48b d e +--R + +--R 2 7 2 2 8 3 9 +--R - 144b c d e + 144b c d e - 48c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 6 2 3 5 2 2 2 4 +--R 15A b e + (- 54A b c + 3B b )d e + (72A b c - 12B b c)d e +--R + +--R 3 2 3 3 +--R (- 48A c + 24B b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 2 4 +--R 45A b d e + (- 162A b c + 9B b )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (216A b c - 36B b c)d e + (- 144A c + 72B b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 45A b d e + (- 162A b c + 9B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (216A b c - 36B b c)d e + (- 144A c + 72B b c )d e +--R * +--R x +--R + +--R 3 3 3 2 3 4 2 2 2 5 +--R 15A b d e + (- 54A b c + 3B b )d e + (72A b c - 12B b c)d e +--R + +--R 3 2 6 +--R (- 48A c + 24B b c )d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 88A b c + 6B b )d e + (88A c - 20B b c)d e +--R + +--R 2 3 2 +--R - 16B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R 80A b d e + (- 236A b c + 16B b )d e +--R + +--R 2 3 2 2 4 +--R (216A c - 28B b c)d e - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 66A b d e + (- 180A b c - 6B b )d e + (144A c + 24B b c)d e +--R + +--R 2 5 +--R - 48B c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (48b d e - 144b c d e + 144b c d e - 48c d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (144b d e - 432b c d e + 432b c d e - 144c d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (144b d e - 432b c d e + 432b c d e - 144c d e)x + 48b d e +--R + +--R 2 7 2 2 8 3 9 +--R - 144b c d e + 144b c d e - 48c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 3 6 2 3 5 2 2 2 4 +--R - 15A b e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 3 3 +--R (48A c - 24B b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 2 4 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 3 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R x +--R + +--R 3 3 3 2 3 4 2 2 2 5 +--R - 15A b d e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 6 +--R (48A c - 24B b c )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 5 2 4 2 2 3 +--R 15A b e + (- 44A b c + 3B b )d e + (44A c - 10B b c)d e +--R + +--R 2 3 2 +--R - 8B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 40A b d e + (- 118A b c + 8B b )d e + (108A c - 14B b c)d e +--R + +--R 2 4 +--R - 24B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 33A b d e + (- 90A b c - 3B b )d e + (72A c + 12B b c)d e +--R + +--R 2 5 +--R - 24B c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (24b d e - 72b c d e + 72b c d e - 24c d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (72b d e - 216b c d e + 216b c d e - 72c d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (72b d e - 216b c d e + 216b c d e - 72c d e)x + 24b d e +--R + +--R 2 7 2 2 8 3 9 +--R - 72b c d e + 72b c d e - 24c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 527 + +--S 528 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 3 2 2 2 2 +--R 5A b e + (- 18A b c + B b )d e + (24A b c - 4B b c)d e +--R + +--R 3 2 3 +--R (- 16A c + 8B b c )d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 3 2 3 2 2 2 2 +--R 5A b e + (- 18A b c + B b )d e + (24A b c - 4B b c)d e +--R + +--R 3 2 3 +--R (- 16A c + 8B b c )d +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +--R (16b d e - 48b c d e + 48b c d e - 16c d )\|- b d e + c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 3 2 2 2 2 +--R 5A b e + (- 18A b c + B b )d e + (24A b c - 4B b c)d e +--R + +--R 3 2 3 +--R (- 16A c + 8B b c )d +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 10A b e + (36A b c - 2B b )d e + (- 48A b c + 8B b c)d e +--R + +--R 3 2 3 +--R (32A c - 16B b c )d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ +--R (16b d e - 48b c d e + 48b c d e - 16c d )\|- b e + c d \|d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 531 + +)clear all + +--S 532 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1457 +r0:=3/4*e*(4*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-12*b*c*d*e+5*b^2*e^2))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-2*(A*b-(b*B-2*A*c)*x)*_ + (d+e*x)^3/(b^2*sqrt(b*x+c*x^2))+1/4*e*(32*A*c^3*d^2-15*b^3*B*e^2-_ + 16*b*c^2*d*(B*d+2*A*e)+2*b^2*c*e*(17*B*d+6*A*e))*sqrt(b*x+c*x^2)/_ + (b^2*c^3)-2*(b*B-2*A*c)*e*(d+e*x)^2*sqrt(b*x+c*x^2)/(b^2*c)+_ + 1/2*e^2*(b*(b*B+4*A*c)*d+(8*A*c^2*d+5*b^2*B*e-4*b*c*(B*d+A*e))*x)*_ + sqrt(b*x+c*x^2)/(b^2*c^2) +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 2 2 2 +--R ((- 12A b c + 15B b )e + (24A b c - 36B b c)d e + 24B b c d e) +--R * +--R +----------+ +-+ +--R | 2 x\|c +--R \|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 3 2 2 3 3 2 2 2 2 +--R 2B b c e x + ((4A b c - 5B b c)e + 12B b c d e )x +--R + +--R 3 4 3 2 2 3 2 +--R (12A b c - 15B b )e + (- 24A b c + 36B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (24A b c - 24B b c )d e + (- 16A c + 8B b c )d +--R * +--R x +--R + +--R 3 3 +--R - 8A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 3 +-+ | 2 +--R 4b c \|c \|c x + b x +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 3 2 2 3 2 2 2 2 +--R ((- 12A b c + 15B b )e + (24A b c - 36B b c)d e + 24B b c d e) +--R * +--R +----------+ +----------+ +--R | 2 | 2 +-+ +--R \|c x + b x log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 3 3 2 2 3 3 2 2 2 2 +--R 4B b c e x + ((8A b c - 10B b c)e + 24B b c d e )x +--R + +--R 3 4 3 2 2 3 2 +--R (24A b c - 30B b )e + (- 48A b c + 72B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (48A b c - 48B b c )d e + (- 32A c + 16B b c )d +--R * +--R x +--R + +--R 3 3 +--R - 16A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 3 +-+ | 2 +--R 8b c \|c \|c x + b x +--R , +--R +--R 3 4 3 2 2 3 2 2 2 2 +--R ((- 12A b c + 15B b )e + (24A b c - 36B b c)d e + 24B b c d e) +--R * +--R +----------+ +--R +----------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|c x + b x atan(-------------------) +--R c x +--R + +--R 2 2 3 3 2 2 3 3 2 2 2 2 +--R 2B b c e x + ((4A b c - 5B b c)e + 12B b c d e )x +--R + +--R 3 4 3 2 2 3 2 +--R (12A b c - 15B b )e + (- 24A b c + 36B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (24A b c - 24B b c )d e + (- 16A c + 8B b c )d +--R * +--R x +--R + +--R 3 3 +--R - 8A b c d +--R * +--R +---+ +--R \|- c +--R / +--R +----------+ +--R 2 3 +---+ | 2 +--R 4b c \|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 534 + +--S 535 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 +--R ((- 12A b c + 15B b )e + (24A c - 36B b c)d e + 24B c d e) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 2 2 2 +--R ((24A b c - 30B b )e + (- 48A c + 72B b c)d e - 48B c d e) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 8c \|c +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 2 2 2 2 +---+ +--R ((12A b c - 15B b )e + (- 24A c + 36B b c)d e - 24B c d e)\|- c +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 2 +-+ +--R ((- 12A b c + 15B b )e + (24A c - 36B b c)d e + 24B c d e)\|c +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 4c \|- c \|c +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 538 + +)clear all + +--S 539 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1457 +r0:=e*(4*B*c*d-3*b*B*e+2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-_ + 2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*sqrt(b*x+c*x^2))+e*(8*A*c^2*d+_ + 3*b^2*B*e-4*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/(b^2*c^2)+2*e^2*(A*b-_ + (b*B-2*A*c)*x)*sqrt(b*x+c*x^2)/(b^2*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 2 3 2 2 | 2 x\|c +--R ((2A b c - 3B b )e + 4B b c d e)\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 +--R B b c e x +--R + +--R 2 3 2 2 2 +--R (- 2A b c + 3B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 +--R (- 4A c + 2B b c )d +--R * +--R x +--R + +--R 2 2 +--R - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 2 +-+ | 2 +--R b c \|c \|c x + b x +--R Type: Expression(Integer) +--E 540 + +--S 541 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 2 3 2 2 | 2 +--R ((2A b c - 3B b )e + 4B b c d e)\|c x + b x +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 +--R 2B b c e x +--R + +--R 2 3 2 2 2 +--R (- 4A b c + 6B b )e + (8A b c - 8B b c)d e +--R + +--R 3 2 2 +--R (- 8A c + 4B b c )d +--R * +--R x +--R + +--R 2 2 +--R - 4A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 2 +-+ | 2 +--R 2b c \|c \|c x + b x +--R , +--R +--R +----------+ +--R +----------+ +---+ | 2 +--R 2 3 2 2 | 2 \|- c \|c x + b x +--R ((2A b c - 3B b )e + 4B b c d e)\|c x + b x atan(-------------------) +--R c x +--R + +--R 2 2 2 +--R B b c e x +--R + +--R 2 3 2 2 2 +--R (- 2A b c + 3B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 +--R (- 4A c + 2B b c )d +--R * +--R x +--R + +--R 2 2 +--R - 2A b c d +--R * +--R +---+ +--R \|- c +--R / +--R +----------+ +--R 2 2 +---+ | 2 +--R b c \|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 541 + +--S 542 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 2 | 2 +-+ +--R ((2A c - 3B b)e + 4B c d e)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 2 x\|c +--R ((- 4A c + 6B b)e - 8B c d e)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 2 +-+ +--R 2c \|c +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 +---+ x\|c +--R ((- 2A c + 3B b)e - 4B c d e)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 2 +-+ \|- c \|c x + b x +--R ((2A c - 3B b)e + 4B c d e)\|c atan(-------------------) +--R c x +--R / +--R 2 +---+ +-+ +--R c \|- c \|c +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1457 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1457 +r0:=2*B*e*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)-2*(A*b-(b*B-2*A*c)*x)*_ + (d+e*x)/(b^2*sqrt(b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(b*x+c*x^2)/(b^2*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 2 | 2 x\|c +--R 2B b e\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 +-+ +--R (((2A b c - 2B b )e + (- 4A c + 2B b c)d)x - 2A b c d)\|c +--R / +--R +----------+ +--R 2 +-+ | 2 +--R b c\|c \|c x + b x +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +----------+ +--R 2 | 2 | 2 +-+ +--R B b e\|c x + b x log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 +-+ +--R (((2A b c - 2B b )e + (- 4A c + 2B b c)d)x - 2A b c d)\|c +--R / +--R +----------+ +--R 2 +-+ | 2 +--R b c\|c \|c x + b x +--R , +--R +--R +----------+ +--R +----------+ +---+ | 2 +--R 2 | 2 \|- c \|c x + b x +--R 2B b e\|c x + b x atan(-------------------) +--R c x +--R + +--R 2 2 +---+ +--R (((2A b c - 2B b )e + (- 4A c + 2B b c)d)x - 2A b c d)\|- c +--R / +--R +----------+ +--R 2 +---+ | 2 +--R b c\|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 548 + +--S 549 of 1457 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R | 2 +-+ x\|c +--R B e log(2c\|c x + b x + (2c x + b)\|c ) - 2B e atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (4) --------------------------------------------------------------------- +--R +-+ +--R c\|c +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1457 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R +---+ x\|c +-+ \|- c \|c x + b x +--R - 2B e\|- c atanh(-------------) + 2B e\|c atan(-------------------) +--R +----------+ c x +--R | 2 +--R \|c x + b x +--R (6) -------------------------------------------------------------------- +--R +---+ +-+ +--R c\|- c \|c +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 1457 +t0:=(A+B*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R B x + A +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1457 +r0:=-2*(A*b-(b*B-2*A*c)*x)/(b^2*sqrt(b*x+c*x^2)) +--R +--R +--R (- 4A c + 2B b)x - 2A b +--R (2) ----------------------- +--R +----------+ +--R 2 | 2 +--R b \|c x + b x +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (- 4A c + 2B b)x - 2A b +--R (3) ----------------------- +--R +----------+ +--R 2 | 2 +--R b \|c x + b x +--R Type: Union(Expression(Integer),...) +--E 555 + +--S 556 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 557 + +)clear all + +--S 558 of 1457 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------- +--R +----------+ +--R 3 2 | 2 +--R (c e x + (b e + c d)x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1457 +r0:=-e*(B*d-A*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))-2*(A*b*(c*d-b*e)+_ + c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R +----------+ +--R 2 2 2 | 2 (b e - 2c d)x - b d +--R (A b e - B b d e)\|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +--R ((- 2A b c e + (4A c - 2B b c)d)x - 2A b e + 2A b c d)\|- b e + c d \|d +--R / +--R +----------+ +--R 3 2 2 +-----------+ +-+ | 2 +--R (b d e - b c d )\|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 2 2 2 | 2 +--R (A b e - B b d e)\|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 2 | 2 +--R ((- 2A b c e + (4A c - 2B b c)d)x - 2A b e + 2A b c d)\|- b d e + c d +--R / +--R +--------------+ +----------+ +--R 3 2 2 | 2 | 2 +--R (b d e - b c d )\|- b d e + c d \|c x + b x +--R , +--R +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R 2 2 2 | 2 \|b d e - c d \|c x + b x +--R (2A b e - 2B b d e)\|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +--R 2 2 | 2 +--R ((- 2A b c e + (4A c - 2B b c)d)x - 2A b e + 2A b c d)\|b d e - c d +--R / +--R +------------+ +----------+ +--R 3 2 2 | 2 | 2 +--R (b d e - b c d )\|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 560 + +--S 561 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R (A e - B d e)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 | 2 (b e - 2c d)x - b d +--R (- A e + B d e)\|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +--R (b d e - c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 2 | 2 (b e - 2c d)x - b d +--R (- A e + B d e)\|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 2 +-----------+ +-+ \|b d e - c d \|c x + b x +--R (2A e - 2B d e)\|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 +-----------+ +-+ | 2 +--R (b d e - c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------------------------- +--R +----------+ +--R 2 4 2 3 2 2 2 | 2 +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1457 +r0:=1/2*e*(3*A*e*(2*c*d-b*e)-B*d*(4*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-_ + b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-_ + b*e)^(5/2))-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*_ + (c*d-b*e)*(d+e*x)*sqrt(b*x+c*x^2))-e*(4*A*c^2*d^2-b^2*e*(B*d-_ + 3*A*e)-2*b*c*d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 3 4 2 3 3 2 2 2 3 3 +--R (3A b e + (- 6A b c - B b )d e + 4B b c d e )x + 3A b d e +--R + +--R 2 3 2 2 2 3 +--R (- 6A b c - B b )d e + 4B b c d e +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 3 2 2 2 +--R (- 6A b c e + (8A b c + 2B b c)d e + (- 8A c + 4B b c )d e)x +--R + +--R 3 3 2 3 2 2 2 +--R - 6A b e + (4A b c + 2B b )d e + 4A b c d e +--R + +--R 3 2 3 +--R (- 8A c + 4B b c )d +--R * +--R x +--R + +--R 3 2 2 2 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((2b d e - 4b c d e + 2b c d e)x + 2b d e - 4b c d e + 2b c d ) +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 3 3 2 2 2 3 3 +--R (3A b e + (- 6A b c - B b )d e + 4B b c d e )x + 3A b d e +--R + +--R 2 3 2 2 2 3 +--R (- 6A b c - B b )d e + 4B b c d e +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 2 2 2 3 2 2 2 +--R (- 6A b c e + (8A b c + 2B b c)d e + (- 8A c + 4B b c )d e)x +--R + +--R 3 3 2 3 2 2 2 +--R - 6A b e + (4A b c + 2B b )d e + 4A b c d e +--R + +--R 3 2 3 +--R (- 8A c + 4B b c )d +--R * +--R x +--R + +--R 3 2 2 2 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((2b d e - 4b c d e + 2b c d e)x + 2b d e - 4b c d e + 2b c d ) +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R 3 4 2 3 3 2 2 2 3 3 +--R (3A b e + (- 6A b c - B b )d e + 4B b c d e )x + 3A b d e +--R + +--R 2 3 2 2 2 3 +--R (- 6A b c - B b )d e + 4B b c d e +--R * +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R | 2 \|b d e - c d \|c x + b x +--R \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 3 2 2 2 3 2 2 2 +--R (- 3A b c e + (4A b c + B b c)d e + (- 4A c + 2B b c )d e)x +--R + +--R 3 3 2 3 2 2 2 +--R - 3A b e + (2A b c + B b )d e + 2A b c d e +--R + +--R 3 2 3 +--R (- 4A c + 2B b c )d +--R * +--R x +--R + +--R 3 2 2 2 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 567 + +--S 568 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 +-----------+ +-+ +--R (3A b e + (- 6A c - B b)d e + 4B c d e)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 3 2 2 | 2 +--R (- 3A b e + (6A c + B b)d e - 4B c d e)\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (2b d e - 4b c d e + 2c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 3 2 2 | 2 +--R (- 3A b e + (6A c + B b)d e - 4B c d e)\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 2 +-----------+ +-+ +--R (6A b e + (- 12A c - 2B b)d e + 8B c d e)\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (2b d e - 4b c d e + 2c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 571 + +)clear all + +--S 572 of 1457 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1457 +r0:=-3/8*e*(B*d*(8*c^2*d^2-4*b*c*d*e+b^2*e^2)-A*e*(16*c^2*d^2-16*b*c*d*e+_ + 5*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))-2*(A*b*(c*d-b*e)+_ + c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)^2*sqrt(b*x+_ + c*x^2))-1/2*e*(8*A*c^2*d^2-b^2*e*(B*d-5*A*e)-4*b*c*d*(B*d+2*A*e))*_ + sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^2)-1/4*e*(16*A*c^3*d^3-_ + 2*b^2*c*d*e*(5*B*d-19*A*e)+3*b^3*e^2*(B*d-5*A*e)-8*b*c^2*d^2*_ + (B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 4 6 3 4 5 2 2 3 2 4 +--R 15A b e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 30A b d e + (- 96A b c - 6B b )d e + (96A b c + 24B b c)d e +--R + +--R 2 2 4 2 +--R - 48B b c d e +--R * +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A b d e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 5 +--R - 24B b c d e +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 5 2 2 3 4 +--R - 30A b c e + (76A b c + 6B b c)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 48A b c - 20B b c )d e + (32A c - 16B b c )d e +--R * +--R 3 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 30A b e + (26A b c + 6B b )d e + (80A b c - 10B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (- 80A b c - 24B b c )d e + (64A c - 32B b c )d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 4 2 3 +--R - 50A b d e + (112A b c + 10B b )d e +--R + +--R 2 2 3 3 2 3 4 4 3 5 +--R (- 48A b c - 24B b c)d e - 16A b c d e + (32A c - 16B b c )d +--R * +--R x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 16A b d e + 48A b c d e - 48A b c d e + 16A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (16b d e - 48b c d e + 48b c d e - 16b c d e)x + 8b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 24b c d e + 24b c d e - 8b c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 6 3 4 5 2 2 3 2 4 +--R - 15A b e + (48A b c + 3B b )d e + (- 48A b c - 12B b c)d e +--R + +--R 2 2 3 3 +--R 24B b c d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 4 +--R - 30A b d e + (96A b c + 6B b )d e +--R + +--R 2 2 3 3 3 2 2 4 2 +--R (- 96A b c - 24B b c)d e + 48B b c d e +--R * +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R - 15A b d e + (48A b c + 3B b )d e + (- 48A b c - 12B b c)d e +--R + +--R 2 2 5 +--R 24B b c d e +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 5 2 2 3 4 +--R - 30A b c e + (76A b c + 6B b c)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 48A b c - 20B b c )d e + (32A c - 16B b c )d e +--R * +--R 3 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 30A b e + (26A b c + 6B b )d e + (80A b c - 10B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (- 80A b c - 24B b c )d e + (64A c - 32B b c )d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 4 2 3 +--R - 50A b d e + (112A b c + 10B b )d e +--R + +--R 2 2 3 3 2 3 4 4 3 5 +--R (- 48A b c - 24B b c)d e - 16A b c d e + (32A c - 16B b c )d +--R * +--R x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 16A b d e + 48A b c d e - 48A b c d e + 16A b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (16b d e - 48b c d e + 48b c d e - 16b c d e)x + 8b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 24b c d e + 24b c d e - 8b c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R 4 6 3 4 5 2 2 3 2 4 +--R 15A b e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 30A b d e + (- 96A b c - 6B b )d e + (96A b c + 24B b c)d e +--R + +--R 2 2 4 2 +--R - 48B b c d e +--R * +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A b d e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 5 +--R - 24B b c d e +--R * +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R | 2 \|b d e - c d \|c x + b x +--R \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 5 2 2 3 4 +--R - 15A b c e + (38A b c + 3B b c)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 24A b c - 10B b c )d e + (16A c - 8B b c )d e +--R * +--R 3 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 15A b e + (13A b c + 3B b )d e + (40A b c - 5B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (- 40A b c - 12B b c )d e + (32A c - 16B b c )d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 4 2 3 +--R - 25A b d e + (56A b c + 5B b )d e +--R + +--R 2 2 3 3 2 3 4 4 3 5 +--R (- 24A b c - 12B b c)d e - 8A b c d e + (16A c - 8B b c )d +--R * +--R x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 8A b d e + 24A b c d e - 24A b c d e + 8A b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e)x + 4b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 12b c d e + 12b c d e - 4b c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 574 + +--S 575 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 2 2 +--R - 15A b e + (48A b c + 3B b )d e + (- 48A c - 12B b c)d e +--R + +--R 2 3 +--R 24B c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 4 2 3 2 2 2 +--R - 15A b e + (48A b c + 3B b )d e + (- 48A c - 12B b c)d e +--R + +--R 2 3 +--R 24B c d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +-----------+ +--R (8b d e - 24b c d e + 24b c d e - 8c d )\|- b d e + c d \|- b e + c d +--R * +--R +-+ +--R \|d +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 4 2 3 2 2 2 +--R - 15A b e + (48A b c + 3B b )d e + (- 48A c - 12B b c)d e +--R + +--R 2 3 +--R 24B c d e +--R * +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 4 2 3 2 2 2 +--R 30A b e + (- 96A b c - 6B b )d e + (96A c + 24B b c)d e +--R + +--R 2 3 +--R - 48B c d e +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ | 2 +--R (8b d e - 24b c d e + 24b c d e - 8c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 578 + +)clear all + +--S 579 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1457 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^4/(b^2*(b*x+c*x^2)^(3/2))+e^3*(8*B*c*d-_ + 5*b*B*e+2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-8/3*_ + (d+e*x)^3*(b*(b*B*d-2*A*c*d+2*A*b*e)-(4*A*c^2*d-b^2*B*e-2*b*c*(B*d+_ + A*e))*x)/(b^4*sqrt(b*x+c*x^2))-1/3*e*(64*A*c^4*d^3-15*b^4*B*e^3-_ + 32*b*c^3*d^2*(B*d+3*A*e)+2*b^3*c*e^2*(11*B*d+3*A*e)+4*b^2*c^2*d*_ + e*(4*B*d+5*A*e))*sqrt(b*x+c*x^2)/(b^4*c^3)-8/3*e*(4*A*c^2*d-b^2*B*e-_ + 2*b*c*(B*d+A*e))*(d+e*x)^2*sqrt(b*x+c*x^2)/(b^4*c)+2/3*e^2*(b*d*_ + (4*b*B*c*d-8*A*c^2*d-b^2*B*e+10*A*b*c*e)-(16*A*c^3*d^2+5*b^3*B*e^2-_ + 2*A*b^2*c*e^2-8*b*c^2*d*(B*d+2*A*e))*x)*sqrt(b*x+c*x^2)/(b^4*c^2) +--R +--R +--R (2) +--R 4 2 5 4 4 2 3 2 +--R ((6A b c - 15B b c)e + 24B b c d e )x +--R + +--R 5 6 4 5 3 +--R ((6A b c - 15B b )e + 24B b c d e )x +--R * +--R +----------+ +-+ +--R | 2 x\|c +--R \|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 2 4 4 +--R 3B b c e x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 8A b c + 20B b c)e + (8A b c - 32B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (24A b c + 12B b c )d e + (- 64A b c + 16B b c )d e +--R + +--R 6 5 4 +--R (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 4 5 3 3 3 2 2 +--R (- 6A b c + 15B b )e - 24B b c d e + 36A b c d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 96A b c + 24B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 4 3 3 4 3 3 4 +--R (- 24A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 4 2 5 3 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 5 4 4 2 3 2 +--R ((6A b c - 15B b c)e + 24B b c d e )x +--R + +--R 5 6 4 5 3 +--R ((6A b c - 15B b )e + 24B b c d e )x +--R * +--R +----------+ +----------+ +--R | 2 | 2 +-+ +--R \|c x + b x log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 2 4 4 +--R 6B b c e x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 16A b c + 40B b c)e + (16A b c - 64B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (48A b c + 24B b c )d e + (- 128A b c + 32B b c )d e +--R + +--R 6 5 4 +--R (64A c - 32B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 4 5 3 3 3 2 2 +--R (- 12A b c + 30B b )e - 48B b c d e + 72A b c d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 192A b c + 48B b c )d e + (96A b c - 48B b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 4 3 3 4 3 3 4 +--R (- 48A b c d e + (24A b c - 12B b c )d )x - 4A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 4 2 5 3 +-+ | 2 +--R (6b c x + 6b c x)\|c \|c x + b x +--R , +--R +--R 4 2 5 4 4 2 3 2 +--R ((6A b c - 15B b c)e + 24B b c d e )x +--R + +--R 5 6 4 5 3 +--R ((6A b c - 15B b )e + 24B b c d e )x +--R * +--R +----------+ +--R +----------+ +---+ | 2 +--R | 2 \|- c \|c x + b x +--R \|c x + b x atan(-------------------) +--R c x +--R + +--R 4 2 4 4 +--R 3B b c e x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 8A b c + 20B b c)e + (8A b c - 32B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (24A b c + 12B b c )d e + (- 64A b c + 16B b c )d e +--R + +--R 6 5 4 +--R (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 4 5 3 3 3 2 2 +--R (- 6A b c + 15B b )e - 24B b c d e + 36A b c d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 96A b c + 24B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 4 3 3 4 3 3 4 +--R (- 24A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +---+ +--R \|- c +--R / +--R +----------+ +--R 4 4 2 5 3 +---+ | 2 +--R (3b c x + 3b c x)\|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 581 + +--S 582 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 4 3 | 2 +-+ +--R ((2A c - 5B b)e + 8B c d e )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 4 3 x\|c +--R ((- 4A c + 10B b)e - 16B c d e )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 2c \|c +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 4 3 +---+ x\|c +--R ((- 2A c + 5B b)e - 8B c d e )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 4 3 +-+ \|- c \|c x + b x +--R ((2A c - 5B b)e + 8B c d e )\|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R c \|- c \|c +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1457 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^3/(b^2*(b*x+c*x^2)^(3/2))+2*B*e^3*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-4/3*(d+e*x)^2*(b*(2*b*B*d-_ + 4*A*c*d+3*A*b*e)-(8*A*c^2*d-b^2*B*e-4*b*c*(B*d+A*e))*x)/(b^4*_ + sqrt(b*x+c*x^2))-2/3*e*(32*A*c^3*d^2+3*b^3*B*e^2-16*b*c^2*d*(B*d+_ + 2*A*e)+2*b^2*c*e*(2*B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^4*c^2)+4/3*e^2*_ + (b*(2*b*B*d-4*A*c*d+3*A*b*e)-(8*A*c^2*d-b^2*B*e-4*b*c*(B*d+A*e))*x)*_ + sqrt(b*x+c*x^2)/(b^4*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 4 3 2 5 3 | 2 x\|c +--R (6B b c e x + 6B b e x)\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2A b c - 8B b c)e + (12A b c + 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 12B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 3 2 2 2 3 3 2 2 +--R - 6B b e + 18A b c d e + (- 72A b c + 18B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 3 2 3 3 2 3 +--R (- 18A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 3 2 5 2 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 4 3 2 5 3 | 2 +--R (3B b c e x + 3B b e x)\|c x + b x +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2A b c - 8B b c)e + (12A b c + 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 12B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 3 2 2 2 3 3 2 2 +--R - 6B b e + 18A b c d e + (- 72A b c + 18B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 3 2 3 3 2 3 +--R (- 18A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 3 2 5 2 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R , +--R +--R +----------+ +--R +----------+ +---+ | 2 +--R 4 3 2 5 3 | 2 \|- c \|c x + b x +--R (6B b c e x + 6B b e x)\|c x + b x atan(-------------------) +--R c x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2A b c - 8B b c)e + (12A b c + 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 12B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 3 2 2 2 3 3 2 2 +--R - 6B b e + 18A b c d e + (- 72A b c + 18B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 3 2 3 3 2 3 +--R (- 18A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +---+ +--R \|- c +--R / +--R +----------+ +--R 4 3 2 5 2 +---+ | 2 +--R (3b c x + 3b c x)\|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 588 + +--S 589 of 1457 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R 3 | 2 +-+ 3 x\|c +--R B e log(2c\|c x + b x + (2c x + b)\|c ) - 2B e atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (4) --------------------------------------------------------------------- +--R 2 +-+ +--R c \|c +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1457 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R 3 +---+ x\|c 3 +-+ \|- c \|c x + b x +--R - 2B e \|- c atanh(-------------) + 2B e \|c atan(-------------------) +--R +----------+ c x +--R | 2 +--R \|c x + b x +--R (6) ---------------------------------------------------------------------- +--R 2 +---+ +-+ +--R c \|- c \|c +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 592 + +)clear all + +--S 593 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1457 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*(b*x+c*x^2)^(3/2))-_ + 8/3*(b*B*d-2*A*c*d+A*b*e)*(b*d+(2*c*d-b*e)*x)/(b^4*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 3 +--R ((4A b c + 2B b )e + (- 32A b c + 8B b c)d e + (32A c - 16B b c )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (6A b e + (- 48A b c + 12B b )d e + (48A b c - 24B b c)d )x +--R + +--R 3 2 3 2 3 2 +--R (- 12A b d e + (12A b c - 6B b )d )x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 3 2 2 3 +--R ((4A b c + 2B b )e + (- 32A b c + 8B b c)d e + (32A c - 16B b c )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (6A b e + (- 48A b c + 12B b )d e + (48A b c - 24B b c)d )x +--R + +--R 3 2 3 2 3 2 +--R (- 12A b d e + (12A b c - 6B b )d )x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Union(Expression(Integer),...) +--E 595 + +--S 596 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1457 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1457 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))-_ + 4/3*(b*(2*b*B*d-4*A*c*d+A*b*e)-(8*A*c^2*d+b^2*B*e-_ + 4*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R 2 2 3 2 3 +--R ((- 16A b c + 4B b c)e + (32A c - 16B b c )d)x +--R + +--R 2 3 2 2 2 +--R ((- 24A b c + 6B b )e + (48A b c - 24B b c)d)x +--R + +--R 3 2 3 3 +--R (- 6A b e + (12A b c - 6B b )d)x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 2 3 +--R ((- 16A b c + 4B b c)e + (32A c - 16B b c )d)x +--R + +--R 2 3 2 2 2 +--R ((- 24A b c + 6B b )e + (48A b c - 24B b c)d)x +--R + +--R 3 2 3 3 +--R (- 6A b e + (12A b c - 6B b )d)x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Union(Expression(Integer),...) +--E 600 + +--S 601 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 602 + +)clear all + +--S 603 of 1457 +t0:=(A+B*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R B x + A +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1457 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)/(b^2*(b*x+c*x^2)^(3/2))+8/3*(b*B-2*A*c)/_ + (b^3*sqrt(b*x+c*x^2))-16/3*(b*B-2*A*c)*sqrt(b*x+c*x^2)/(b^4*x) +--R +--R +--R (2) +--R 3 2 3 2 2 2 2 3 3 +--R (32A c - 16B b c )x + (48A b c - 24B b c)x + (12A b c - 6B b )x - 2A b +--R --------------------------------------------------------------------------- +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 2 2 2 3 3 +--R (32A c - 16B b c )x + (48A b c - 24B b c)x + (12A b c - 6B b )x - 2A b +--R --------------------------------------------------------------------------- +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Union(Expression(Integer),...) +--E 605 + +--S 606 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 607 + +)clear all + +--S 608 of 1457 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^(5/2)) +--R +--R +--R B x + A +--R (1) -------------------------------------------------------------------- +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|c x + b x +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1457 +r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ + (b*x+c*x^2)^(3/2))-e^3*(B*d-A*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+_ + 2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+3*b^2*e*(B*d-A*e)-4*b*c*d*(B*d+A*e))+_ + c*(16*A*c^3*d^3-3*b^3*e^2*(B*d-A*e)+2*b^2*c*d*e*(7*B*d+A*e)-_ + 8*b*c^2*d^2*(B*d+3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R +----------+ +--R 4 4 4 3 2 5 4 5 3 | 2 +--R ((- 3A b c e + 3B b c d e )x + (- 3A b e + 3B b d e )x)\|c x + b x +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 3 2 3 3 2 2 4 2 3 2 +--R 6A b c e + (4A b c - 6B b c )d e + (- 48A b c + 28B b c )d e +--R + +--R 5 4 3 +--R (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 4 2 2 3 3 2 2 +--R 12A b c e + (6A b c - 12B b c)d e + (- 72A b c + 42B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 5 2 3 2 4 2 +--R 6A b e - 6B b d e + (- 18A b c + 12B b c)d e +--R + +--R 2 3 3 2 3 +--R (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 4 2 3 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 4 4 4 3 2 5 4 5 3 | 2 +--R ((3A b c e - 3B b c d e )x + (3A b e - 3B b d e )x)\|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 2 3 2 3 3 2 2 +--R 6A b c e + (4A b c - 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 28B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 4 2 +--R 12A b c e + (6A b c - 12B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 72A b c + 42B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 5 2 3 2 4 2 +--R 6A b e - 6B b d e + (- 18A b c + 12B b c)d e +--R + +--R 2 3 3 2 3 +--R (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 4 2 3 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R 4 4 4 3 2 5 4 5 3 +--R ((- 6A b c e + 6B b c d e )x + (- 6A b e + 6B b d e )x) +--R * +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R | 2 \|b d e - c d \|c x + b x +--R \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 2 3 2 3 3 2 2 +--R 6A b c e + (4A b c - 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 28B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 4 2 +--R 12A b c e + (6A b c - 12B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 72A b c + 42B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 5 2 3 2 4 2 +--R 6A b e - 6B b d e + (- 18A b c + 12B b c)d e +--R + +--R 2 3 3 2 3 +--R (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 4 2 3 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 610 + +--S 611 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 3 +-----------+ +-+ +--R (A e - B d e )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 4 3 | 2 (b e - 2c d)x - b d +--R (A e - B d e )\|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (b d e - 2b c d e + c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 4 3 | 2 (b e - 2c d)x - b d +--R (A e - B d e )\|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 4 3 +-----------+ +-+ \|b d e - c d \|c x + b x +--R (- 2A e + 2B d e )\|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (b d e - 2b c d e + c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 614 + +)clear all + +--S 615 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1457 +r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ + (d+e*x)*(b*x+c*x^2)^(3/2))-1/2*e^3*(B*d*(8*c*d-3*b*e)-5*A*e*_ + (2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+2/3*(b*(c*d-b*e)*_ + (8*A*c^2*d^2+b^2*e*(3*B*d-5*A*e)-2*b*c*d*(2*B*d+A*e))+c*(16*A*c^3*d^3-_ + b^3*e^2*(3*B*d-5*A*e)+2*b^2*c*d*e*(8*B*d-A*e)-8*b*c^2*d^2*(B*d+_ + 3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*(d+e*x)*sqrt(b*x+c*x^2))+1/3*e*_ + (32*A*c^4*d^4-2*b^3*c*d*e^2*(9*B*d-10*A*e)+3*b^4*e^3*(3*B*d-5*A*e)+_ + 4*b^2*c^2*d^2*e*(10*B*d+3*A*e)-16*b*c^3*d^3*(B*d+4*A*e))*sqrt(b*x+_ + c*x^2)/(b^4*d^3*(c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 5 4 2 2 4 3 +--R (- 15A b c e + (30A b c + 9B b c)d e - 24B b c d e )x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 15A b e + (15A b c + 9B b )d e + (30A b c - 15B b c)d e +--R + +--R 4 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 6 5 5 6 2 4 5 3 3 +--R (- 15A b d e + (30A b c + 9B b )d e - 24B b c d e )x +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 2 5 3 3 4 2 4 +--R 30A b c e + (- 40A b c - 18B b c )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 24A b c + 36B b c )d e + (128A b c - 80B b c )d e +--R + +--R 6 5 4 +--R (- 64A c + 32B b c )d e +--R * +--R 4 +--R x +--R + +--R 5 5 4 2 5 4 +--R 60A b c e + (- 60A b c - 36B b c)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 76A b c + 60B b c )d e + (168A b c - 84B b c )d e +--R + +--R 5 2 4 4 6 5 5 +--R (32A b c - 32B b c )d e + (- 64A c + 32B b c )d +--R * +--R 3 +--R x +--R + +--R 6 5 6 4 4 2 5 2 3 +--R 30A b e - 18B b d e + (- 84A b c + 12B b c)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (12A b c + 36B b c )d e + (168A b c - 108B b c )d e +--R + +--R 5 2 4 5 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R + +--R 6 4 5 6 2 3 +--R 20A b d e + (- 36A b c - 12B b )d e +--R + +--R 4 2 5 3 2 3 3 4 2 4 +--R (- 12A b c + 36B b c)d e + (52A b c - 36B b c )d e +--R + +--R 2 4 3 3 5 +--R (- 24A b c + 12B b c )d +--R * +--R x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 4A b d e + 12A b c d e - 12A b c d e + 4A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 6 4 2 5 5 4 2 2 4 3 +--R (15A b c e + (- 30A b c - 9B b c)d e + 24B b c d e )x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R 15A b e + (- 15A b c - 9B b )d e + (- 30A b c + 15B b c)d e +--R + +--R 4 2 3 3 +--R 24B b c d e +--R * +--R 2 +--R x +--R + +--R 6 5 5 6 2 4 5 3 3 +--R (15A b d e + (- 30A b c - 9B b )d e + 24B b c d e )x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 2 5 3 3 4 2 4 +--R 30A b c e + (- 40A b c - 18B b c )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 24A b c + 36B b c )d e + (128A b c - 80B b c )d e +--R + +--R 6 5 4 +--R (- 64A c + 32B b c )d e +--R * +--R 4 +--R x +--R + +--R 5 5 4 2 5 4 +--R 60A b c e + (- 60A b c - 36B b c)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 76A b c + 60B b c )d e + (168A b c - 84B b c )d e +--R + +--R 5 2 4 4 6 5 5 +--R (32A b c - 32B b c )d e + (- 64A c + 32B b c )d +--R * +--R 3 +--R x +--R + +--R 6 5 6 4 4 2 5 2 3 +--R 30A b e - 18B b d e + (- 84A b c + 12B b c)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (12A b c + 36B b c )d e + (168A b c - 108B b c )d e +--R + +--R 5 2 4 5 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R + +--R 6 4 5 6 2 3 +--R 20A b d e + (- 36A b c - 12B b )d e +--R + +--R 4 2 5 3 2 3 3 4 2 4 +--R (- 12A b c + 36B b c)d e + (52A b c - 36B b c )d e +--R + +--R 2 4 3 3 5 +--R (- 24A b c + 12B b c )d +--R * +--R x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 4A b d e + 12A b c d e - 12A b c d e + 4A b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R 5 6 4 2 5 5 4 2 2 4 3 +--R (- 15A b c e + (30A b c + 9B b c)d e - 24B b c d e )x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 15A b e + (15A b c + 9B b )d e + (30A b c - 15B b c)d e +--R + +--R 4 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 6 5 5 6 2 4 5 3 3 +--R (- 15A b d e + (30A b c + 9B b )d e - 24B b c d e )x +--R * +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R | 2 \|b d e - c d \|c x + b x +--R \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 4 2 5 3 3 4 2 4 +--R 15A b c e + (- 20A b c - 9B b c )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 12A b c + 18B b c )d e + (64A b c - 40B b c )d e +--R + +--R 6 5 4 +--R (- 32A c + 16B b c )d e +--R * +--R 4 +--R x +--R + +--R 5 5 4 2 5 4 +--R 30A b c e + (- 30A b c - 18B b c)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 38A b c + 30B b c )d e + (84A b c - 42B b c )d e +--R + +--R 5 2 4 4 6 5 5 +--R (16A b c - 16B b c )d e + (- 32A c + 16B b c )d +--R * +--R 3 +--R x +--R + +--R 6 5 6 4 4 2 5 2 3 +--R 15A b e - 9B b d e + (- 42A b c + 6B b c)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (6A b c + 18B b c )d e + (84A b c - 54B b c )d e +--R + +--R 5 2 4 5 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R + +--R 6 4 5 6 2 3 +--R 10A b d e + (- 18A b c - 6B b )d e +--R + +--R 4 2 5 3 2 3 3 4 2 4 +--R (- 6A b c + 18B b c)d e + (26A b c - 18B b c )d e +--R + +--R 2 4 3 3 5 +--R (- 12A b c + 6B b c )d +--R * +--R x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 2A b d e + 6A b c d e - 6A b c d e + 2A b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 617 + +--S 618 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 2 3 +-----------+ +-+ +--R (5A b e + (- 10A c - 3B b)d e + 8B c d e )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 5 4 2 3 | 2 +--R (5A b e + (- 10A c - 3B b)d e + 8B c d e )\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +-----------+ +-+ +--R (2b d e - 6b c d e + 6b c d e - 2c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 5 4 2 3 | 2 +--R (5A b e + (- 10A c - 3B b)d e + 8B c d e )\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 4 2 3 +-----------+ +-+ +--R (- 10A b e + (20A c + 6B b)d e - 16B c d e )\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ | 2 +--R (2b d e - 6b c d e + 6b c d e - 2c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R (A b e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 2 2 3 3 2 3 2 +--R (3A b d e + (3A c + 3B b)d e + B c d )x + (3A b d e + (A c + B b)d )x +--R + +--R 3 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1457 +r0:=-2/9*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(9/2)/e^4+2/11*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^4-2/13*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(13/2)/e^4+2/15*B*c*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 7 7 7 6 6 +--R 858B c e x + ((990A c + 990B b)e + 3036B c d e )x +--R + +--R 7 6 2 5 5 +--R (1170A b e + (3600A c + 3600B b)d e + 3708B c d e )x +--R + +--R 6 2 5 3 4 4 +--R (4420A b d e + (4580A c + 4580B b)d e + 1600B c d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (5980A b d e + (2120A c + 2120B b)d e + 10B c d e )x +--R + +--R 3 4 4 3 5 2 2 +--R (3120A b d e + (30A c + 30B b)d e - 12B c d e )x +--R + +--R 4 3 5 2 6 5 2 +--R (130A b d e + (- 40A c - 40B b)d e + 16B c d e)x - 260A b d e +--R + +--R 6 7 +--R (80A c + 80B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 6 +--R 858B c e x + ((990A c + 990B b)e + 3036B c d e )x +--R + +--R 7 6 2 5 5 +--R (1170A b e + (3600A c + 3600B b)d e + 3708B c d e )x +--R + +--R 6 2 5 3 4 4 +--R (4420A b d e + (4580A c + 4580B b)d e + 1600B c d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (5980A b d e + (2120A c + 2120B b)d e + 10B c d e )x +--R + +--R 3 4 4 3 5 2 2 +--R (3120A b d e + (30A c + 30B b)d e - 12B c d e )x +--R + +--R 4 3 5 2 6 5 2 +--R (130A b d e + (- 40A c - 40B b)d e + 16B c d e)x - 260A b d e +--R + +--R 6 7 +--R (80A c + 80B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Union(Expression(Integer),...) +--E 624 + +--S 625 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 626 + +)clear all + +--S 627 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1457 +r0:=-2/7*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(7/2)/e^4+2/9*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^4-2/11*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(11/2)/e^4+2/13*B*c*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 1386B c e x + ((1638A c + 1638B b)e + 3402B c d e )x +--R + +--R 6 5 2 4 4 +--R (2002A b e + (4186A c + 4186B b)d e + 2226B c d e )x +--R + +--R 5 2 4 3 3 3 +--R (5434A b d e + (2938A c + 2938B b)d e + 30B c d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (4290A b d e + (78A c + 78B b)d e - 36B c d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (286A b d e + (- 104A c - 104B b)d e + 48B c d e)x - 572A b d e +--R + +--R 5 6 +--R (208A c + 208B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 5 +--R 1386B c e x + ((1638A c + 1638B b)e + 3402B c d e )x +--R + +--R 6 5 2 4 4 +--R (2002A b e + (4186A c + 4186B b)d e + 2226B c d e )x +--R + +--R 5 2 4 3 3 3 +--R (5434A b d e + (2938A c + 2938B b)d e + 30B c d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (4290A b d e + (78A c + 78B b)d e - 36B c d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (286A b d e + (- 104A c - 104B b)d e + 48B c d e)x - 572A b d e +--R + +--R 5 6 +--R (208A c + 208B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 629 + +--S 630 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 631 + +)clear all + +--S 632 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R (B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1457 +r0:=-2/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(5/2)/e^4+2/7*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^4-2/9*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(9/2)/e^4+2/11*B*c*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 630B c e x + ((770A c + 770B b)e + 840B c d e )x +--R + +--R 5 4 2 3 3 +--R (990A b e + (1100A c + 1100B b)d e + 30B c d e )x +--R + +--R 4 2 3 3 2 2 +--R (1584A b d e + (66A c + 66B b)d e - 36B c d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (198A b d e + (- 88A c - 88B b)d e + 48B c d e)x - 396A b d e +--R + +--R 4 5 +--R (176A c + 176B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 4 +--R 630B c e x + ((770A c + 770B b)e + 840B c d e )x +--R + +--R 5 4 2 3 3 +--R (990A b e + (1100A c + 1100B b)d e + 30B c d e )x +--R + +--R 4 2 3 3 2 2 +--R (1584A b d e + (66A c + 66B b)d e - 36B c d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (198A b d e + (- 88A c - 88B b)d e + 48B c d e)x - 396A b d e +--R + +--R 4 5 +--R (176A c + 176B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 634 + +--S 635 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)*sqrt(d+e*x) +--R +--R +--R 3 2 +-------+ +--R (1) (B c x + (A c + B b)x + A b x)\|e x + d +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1457 +r0:=-2/3*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(3/2)/e^4+2/5*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^4-2/7*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B c e x + ((90A c + 90B b)e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126A b e + (18A c + 18B b)d e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (42A b d e + (- 24A c - 24B b)d e + 16B c d e)x - 84A b d e +--R + +--R 3 4 +--R (48A c + 48B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 3 +--R 70B c e x + ((90A c + 90B b)e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126A b e + (18A c + 18B b)d e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (42A b d e + (- 24A c - 24B b)d e + 16B c d e)x - 84A b d e +--R + +--R 3 4 +--R (48A c + 48B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 639 + +--S 640 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 641 + +)clear all + +--S 642 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1457 +r0:=2/3*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^4-2/5*(3*B*c*d-_ + b*B*e-A*c*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-2*d*_ + (B*d-A*e)*(c*d-b*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + ((42A c + 42B b)e - 36B c d e )x +--R + +--R 3 2 2 2 +--R (70A b e + (- 56A c - 56B b)d e + 48B c d e)x - 140A b d e +--R + +--R 2 3 +--R (112A c + 112B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B c e x + ((42A c + 42B b)e - 36B c d e )x +--R + +--R 3 2 2 2 +--R (70A b e + (- 56A c - 56B b)d e + 48B c d e)x - 140A b d e +--R + +--R 2 3 +--R (112A c + 112B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 644 + +--S 645 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 646 + +)clear all + +--S 647 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1457 +r0:=-2/3*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+_ + 2*d*(B*d-A*e)*(c*d-b*e)/(e^4*sqrt(d+e*x))+2*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 6B c e x + ((10A c + 10B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (30A b e + (- 40A c - 40B b)d e + 48B c d e)x + 60A b d e +--R + +--R 2 3 +--R (- 80A c - 80B b)d e + 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 6B c e x + ((10A c + 10B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (30A b e + (- 40A c - 40B b)d e + 48B c d e)x + 60A b d e +--R + +--R 2 3 +--R (- 80A c - 80B b)d e + 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 649 + +--S 650 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1457 +r0:=2/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(3/2))+2/3*B*c*(d+e*x)^(3/2)/e^4-_ + 2*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))/(e^4*sqrt(d+e*x))-_ + 2*(3*B*c*d-b*B*e-A*c*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 2B c e x + ((6A c + 6B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (- 6A b e + (24A c + 24B b)d e - 48B c d e)x - 4A b d e +--R + +--R 2 3 +--R (16A c + 16B b)d e - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 2B c e x + ((6A c + 6B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (- 6A b e + (24A c + 24B b)d e - 48B c d e)x - 4A b d e +--R + +--R 2 3 +--R (16A c + 16B b)d e - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 654 + +--S 655 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 656 + +)clear all + +--S 657 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1457 +r0:=2/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(5/2))-2/3*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^(3/2))+2*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + ((- 30A c - 30B b)e + 180B c d e )x +--R + +--R 3 2 2 2 +--R (- 10A b e + (- 40A c - 40B b)d e + 240B c d e)x - 4A b d e +--R + +--R 2 3 +--R (- 16A c - 16B b)d e + 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B c e x + ((- 30A c - 30B b)e + 180B c d e )x +--R + +--R 3 2 2 2 +--R (- 10A b e + (- 40A c - 40B b)d e + 240B c d e)x - 4A b d e +--R + +--R 2 3 +--R (- 16A c - 16B b)d e + 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 659 + +--S 660 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 661 + +)clear all + +--S 662 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R ((2A b c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (6A b c + 3B b )d e + (3A c + 6B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 3 4 +--R (3A b d e + (6A b c + 3B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 3 2 3 2 +--R (3A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1457 +r0:=-2/9*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(9/2)/e^6+2/11*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^6+_ + 2/13*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(15/2)/e^6-2/17*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(17/2)/e^6+2/19*B*c^2*(d+e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 2 9 9 2 9 2 8 8 +--R 218790B c e x + ((244530A c + 489060B b c)e + 746460B c d e )x +--R + +--R 2 9 2 8 +--R (554268A b c + 277134B b )e + (847704A c + 1695408B b c)d e +--R + +--R 2 2 7 +--R 866580B c d e +--R * +--R 7 +--R x +--R + +--R 2 9 2 8 +--R 319770A b e + (1961256A b c + 980628B b )d e +--R + +--R 2 2 7 2 3 6 +--R (1005708A c + 2011416B b c)d e + 345840B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 2 7 +--R 1162800A b d e + (2395368A b c + 1197684B b )d e +--R + +--R 2 3 6 2 4 5 +--R (414504A c + 829008B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 7 2 3 6 +--R 1479340A b d e + (1033600A b c + 516800B b )d e +--R + +--R 2 4 5 2 5 4 +--R (1330A c + 2660B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 4 5 +--R 684760A b d e + (6460A b c + 3230B b )d e +--R + +--R 2 5 4 2 6 3 +--R (- 1520A c - 3040B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 5 2 5 4 +--R 9690A b d e + (- 7752A b c - 3876B b )d e +--R + +--R 2 6 3 2 7 2 +--R (1824A c + 3648B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 4 2 6 3 +--R - 12920A b d e + (10336A b c + 5168B b )d e +--R + +--R 2 7 2 2 8 +--R (- 2432A c - 4864B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 6 3 2 7 2 +--R 25840A b d e + (- 20672A b c - 10336B b )d e +--R + +--R 2 8 2 9 +--R (4864A c + 9728B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 9 2 9 2 8 8 +--R 218790B c e x + ((244530A c + 489060B b c)e + 746460B c d e )x +--R + +--R 2 9 2 8 +--R (554268A b c + 277134B b )e + (847704A c + 1695408B b c)d e +--R + +--R 2 2 7 +--R 866580B c d e +--R * +--R 7 +--R x +--R + +--R 2 9 2 8 +--R 319770A b e + (1961256A b c + 980628B b )d e +--R + +--R 2 2 7 2 3 6 +--R (1005708A c + 2011416B b c)d e + 345840B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 2 7 +--R 1162800A b d e + (2395368A b c + 1197684B b )d e +--R + +--R 2 3 6 2 4 5 +--R (414504A c + 829008B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 7 2 3 6 +--R 1479340A b d e + (1033600A b c + 516800B b )d e +--R + +--R 2 4 5 2 5 4 +--R (1330A c + 2660B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 4 5 +--R 684760A b d e + (6460A b c + 3230B b )d e +--R + +--R 2 5 4 2 6 3 +--R (- 1520A c - 3040B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 5 2 5 4 +--R 9690A b d e + (- 7752A b c - 3876B b )d e +--R + +--R 2 6 3 2 7 2 +--R (1824A c + 3648B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 4 2 6 3 +--R - 12920A b d e + (10336A b c + 5168B b )d e +--R + +--R 2 7 2 2 8 +--R (- 2432A c - 4864B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 6 3 2 7 2 +--R 25840A b d e + (- 20672A b c - 10336B b )d e +--R + +--R 2 8 2 9 +--R (4864A c + 9728B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Union(Expression(Integer),...) +--E 664 + +--S 665 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1457 +r0:=-2/7*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(7/2)/e^6+2/9*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^6+2/11*_ + (A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(15/2)/e^6+2/17*B*c^2*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 2 8 8 2 8 2 7 7 +--R 90090B c e x + ((102102A c + 204204B b c)e + 210210B c d e )x +--R + +--R 2 8 2 7 +--R (235620A b c + 117810B b )e + (243474A c + 486948B b c)d e +--R + +--R 2 2 6 +--R 127050B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 7 +--R 139230A b e + (578340A b c + 289170B b )d e +--R + +--R 2 2 6 2 3 5 +--R (152082A c + 304164B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 2 6 +--R 355810A b d e + (378420A b c + 189210B b )d e +--R + +--R 2 3 5 2 4 4 +--R (1190A c + 2380B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 6 2 3 5 +--R 249730A b d e + (5100A b c + 2550B b )d e +--R + +--R 2 4 4 2 5 3 +--R (- 1360A c - 2720B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 4 4 +--R 6630A b d e + (- 6120A b c - 3060B b )d e +--R + +--R 2 5 3 2 6 2 +--R (1632A c + 3264B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 5 3 +--R - 8840A b d e + (8160A b c + 4080B b )d e +--R + +--R 2 6 2 2 7 +--R (- 2176A c - 4352B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 3 2 6 2 +--R 17680A b d e + (- 16320A b c - 8160B b )d e +--R + +--R 2 7 2 8 +--R (4352A c + 8704B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 8 2 8 2 7 7 +--R 90090B c e x + ((102102A c + 204204B b c)e + 210210B c d e )x +--R + +--R 2 8 2 7 +--R (235620A b c + 117810B b )e + (243474A c + 486948B b c)d e +--R + +--R 2 2 6 +--R 127050B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 7 +--R 139230A b e + (578340A b c + 289170B b )d e +--R + +--R 2 2 6 2 3 5 +--R (152082A c + 304164B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 2 6 +--R 355810A b d e + (378420A b c + 189210B b )d e +--R + +--R 2 3 5 2 4 4 +--R (1190A c + 2380B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 6 2 3 5 +--R 249730A b d e + (5100A b c + 2550B b )d e +--R + +--R 2 4 4 2 5 3 +--R (- 1360A c - 2720B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 4 4 +--R 6630A b d e + (- 6120A b c - 3060B b )d e +--R + +--R 2 5 3 2 6 2 +--R (1632A c + 3264B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 5 3 +--R - 8840A b d e + (8160A b c + 4080B b )d e +--R + +--R 2 6 2 2 7 +--R (- 2176A c - 4352B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 3 2 6 2 +--R 17680A b d e + (- 16320A b c - 8160B b )d e +--R + +--R 2 7 2 8 +--R (4352A c + 8704B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Union(Expression(Integer),...) +--E 669 + +--S 670 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 671 + +)clear all + +--S 672 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1457 +r0:=-2/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(5/2)/e^6+2/7*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^6+2/9*(A*e*_ + (6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^(9/2)/e^6-2/11*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+_ + b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(13/2)/e^6+2/15*B*c^2*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 2 7 7 2 7 2 6 6 +--R 6006B c e x + ((6930A c + 13860B b c)e + 7392B c d e )x +--R + +--R 2 7 2 6 +--R (16380A b c + 8190B b )e + (8820A c + 17640B b c)d e +--R + +--R 2 2 5 +--R 126B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 10010A b e + (21840A b c + 10920B b )d e +--R + +--R 2 2 5 2 3 4 +--R (210A c + 420B b c)d e - 140B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 14300A b d e + (780A b c + 390B b )d e +--R + +--R 2 3 4 2 4 3 +--R (- 240A c - 480B b c)d e + 160B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 858A b d e + (- 936A b c - 468B b )d e + (288A c + 576B b c)d e +--R + +--R 2 5 2 +--R - 192B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 +--R - 1144A b d e + (1248A b c + 624B b )d e +--R + +--R 2 5 2 2 6 +--R (- 384A c - 768B b c)d e + 256B c d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 2288A b d e + (- 2496A b c - 1248B b )d e + (768A c + 1536B b c)d e +--R + +--R 2 7 +--R - 512B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 7 2 7 2 6 6 +--R 6006B c e x + ((6930A c + 13860B b c)e + 7392B c d e )x +--R + +--R 2 7 2 6 +--R (16380A b c + 8190B b )e + (8820A c + 17640B b c)d e +--R + +--R 2 2 5 +--R 126B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 10010A b e + (21840A b c + 10920B b )d e +--R + +--R 2 2 5 2 3 4 +--R (210A c + 420B b c)d e - 140B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 14300A b d e + (780A b c + 390B b )d e +--R + +--R 2 3 4 2 4 3 +--R (- 240A c - 480B b c)d e + 160B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 858A b d e + (- 936A b c - 468B b )d e + (288A c + 576B b c)d e +--R + +--R 2 5 2 +--R - 192B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 +--R - 1144A b d e + (1248A b c + 624B b )d e +--R + +--R 2 5 2 2 6 +--R (- 384A c - 768B b c)d e + 256B c d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 2288A b d e + (- 2496A b c - 1248B b )d e + (768A c + 1536B b c)d e +--R + +--R 2 7 +--R - 512B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 674 + +--S 675 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 676 + +)clear all + +--S 677 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +-------+ +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|e x + d +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1457 +r0:=-2/3*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(3/2)/e^6+2/5*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^6+2/7*(A*e*_ + (6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^(7/2)/e^6-2/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(9/2)/e^6-2/11*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + ((8190A c + 16380B b c)e + 630B c d e )x +--R + +--R 2 6 2 5 +--R (20020A b c + 10010B b )e + (910A c + 1820B b c)d e +--R + +--R 2 2 4 +--R - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 12870A b e + (2860A b c + 1430B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 1040A c - 2080B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 +--R 2574A b d e + (- 3432A b c - 1716B b )d e +--R + +--R 2 3 3 2 4 2 +--R (1248A c + 2496B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R - 3432A b d e + (4576A b c + 2288B b )d e +--R + +--R 2 4 2 2 5 +--R (- 1664A c - 3328B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 6864A b d e + (- 9152A b c - 4576B b )d e + (3328A c + 6656B b c)d e +--R + +--R 2 6 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + ((8190A c + 16380B b c)e + 630B c d e )x +--R + +--R 2 6 2 5 +--R (20020A b c + 10010B b )e + (910A c + 1820B b c)d e +--R + +--R 2 2 4 +--R - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 12870A b e + (2860A b c + 1430B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 1040A c - 2080B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 +--R 2574A b d e + (- 3432A b c - 1716B b )d e +--R + +--R 2 3 3 2 4 2 +--R (1248A c + 2496B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R - 3432A b d e + (4576A b c + 2288B b )d e +--R + +--R 2 4 2 2 5 +--R (- 1664A c - 3328B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 6864A b d e + (- 9152A b c - 4576B b )d e + (3328A c + 6656B b c)d e +--R + +--R 2 6 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 679 + +--S 680 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1457 +r0:=2/3*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^6+_ + 2/5*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(7/2)/e^6-2/9*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(9/2)/e^6+2/11*B*c^2*(d+e*x)^(11/2)/e^6-2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + ((770A c + 1540B b c)e - 700B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A b c + 990B b )e + (- 880A c - 1760B b c)d e + 800B c d e )x +--R + +--R 2 5 2 4 +--R 1386A b e + (- 2376A b c - 1188B b )d e +--R + +--R 2 2 3 2 3 2 +--R (1056A c + 2112B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 1848A b d e + (3168A b c + 1584B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1408A c - 2816B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 3696A b d e + (- 6336A b c - 3168B b )d e + (2816A c + 5632B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + ((770A c + 1540B b c)e - 700B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A b c + 990B b )e + (- 880A c - 1760B b c)d e + 800B c d e )x +--R + +--R 2 5 2 4 +--R 1386A b e + (- 2376A b c - 1188B b )d e +--R + +--R 2 2 3 2 3 2 +--R (1056A c + 2112B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 1848A b d e + (3168A b c + 1584B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1408A c - 2816B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 3696A b d e + (- 6336A b c - 3168B b )d e + (2816A c + 5632B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 684 + +--S 685 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 686 + +)clear all + +--S 687 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1457 +r0:=2/3*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*sqrt(d+e*x))+2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-_ + 2*A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + ((90A c + 180B b c)e - 100B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((252A b c + 126B b )e + (- 144A c - 288B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 504A b c - 252B b )d e + (288A c + 576B b c)d e +--R + +--R 2 3 2 +--R - 320B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 840A b d e + (2016A b c + 1008B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1152A c - 2304B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 1680A b d e + (4032A b c + 2016B b )d e + (- 2304A c - 4608B b c)d e +--R + +--R 2 5 +--R 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + ((90A c + 180B b c)e - 100B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((252A b c + 126B b )e + (- 144A c - 288B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 504A b c - 252B b )d e + (288A c + 576B b c)d e +--R + +--R 2 3 2 +--R - 320B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 840A b d e + (2016A b c + 1008B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1152A c - 2304B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 1680A b d e + (4032A b c + 2016B b )d e + (- 2304A c - 4608B b c)d e +--R + +--R 2 5 +--R 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 689 + +--S 690 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 691 + +)clear all + +--S 692 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1457 +r0:=2/3*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(3/2))-2/3*(2*A*c*e*(2*c*d-_ + b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-_ + 2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*sqrt(d+e*x))+_ + 2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + ((42A c + 84B b c)e - 60B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((140A b c + 70B b )e + (- 112A c - 224B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 840A b c - 420B b )d e + (672A c + 1344B b c)d e +--R + +--R 2 3 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R 840A b d e + (- 3360A b c - 1680B b )d e +--R + +--R 2 3 2 2 4 +--R (2688A c + 5376B b c)d e - 3840B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 560A b d e + (- 2240A b c - 1120B b )d e + (1792A c + 3584B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + ((42A c + 84B b c)e - 60B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((140A b c + 70B b )e + (- 112A c - 224B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 840A b c - 420B b )d e + (672A c + 1344B b c)d e +--R + +--R 2 3 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R 840A b d e + (- 3360A b c - 1680B b )d e +--R + +--R 2 3 2 2 4 +--R (2688A c + 5376B b c)d e - 3840B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 560A b d e + (- 2240A b c - 1120B b )d e + (1792A c + 3584B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 694 + +--S 695 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1457 +r0:=2/5*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(5/2))-2/3*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^(3/2))-2/3*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6-_ + 2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))/(e^6*sqrt(d+e*x))-2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + ((10A c + 20B b c)e - 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((60A b c + 30B b )e + (- 80A c - 160B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 30A b e + (360A b c + 180B b )d e + (- 480A c - 960B b c)d e +--R + +--R 2 3 2 +--R 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 40A b d e + (480A b c + 240B b )d e + (- 640A c - 1280B b c)d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 16A b d e + (192A b c + 96B b )d e + (- 256A c - 512B b c)d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + ((10A c + 20B b c)e - 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((60A b c + 30B b )e + (- 80A c - 160B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 30A b e + (360A b c + 180B b )d e + (- 480A c - 960B b c)d e +--R + +--R 2 3 2 +--R 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 40A b d e + (480A b c + 240B b )d e + (- 640A c - 1280B b c)d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 16A b d e + (192A b c + 96B b )d e + (- 256A c - 512B b c)d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 699 + +--S 700 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 701 + +)clear all + +--S 702 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1457 +r0:=2/3*(B*(c*d-b*e)^2+A*c*e*(2*c*d-b*e))*(d+e*x)^(3/2)/c^3+2/5*_ + (B*c*d-b*B*e+A*c*e)*(d+e*x)^(5/2)/c^2+2/7*B*(d+e*x)^(7/2)/c-_ + 2*A*d^(7/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(7/2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(9/2))+2*(B*(c*d-b*e)^3+_ + A*c*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/c^4 +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (- 210A b c + 210B b )e + (630A b c - 630B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 630A b c + 630B b c )d e + (210A c - 210B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 4 3 +-+ +-+ \|e x + d +--R - 210A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 4 +-+ +--R 105b c \|c +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 3 2 2 3 2 +--R (- 105A b c + 105B b )e + (315A b c - 315B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 315A b c + 315B b c )d e + (105A c - 105B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R +-+ +-------+ +--R 4 3 +-+ - 2\|d \|e x + d + e x + 2d +--R 105A c d \|d log(----------------------------) +--R x +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b c +--R , +--R +--R +-+ +-------+ +--R 4 3 +-+ - 2\|d \|e x + d + e x + 2d +--R 105A c d \|d log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A b c + 210B b )e + (630A b c - 630B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 630A b c + 630B b c )d e + (210A c - 210B b c )d +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b c +--R , +--R +--R 3 4 3 2 2 3 2 +--R (- 105A b c + 105B b )e + (315A b c - 315B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 315A b c + 315B b c )d e + (105A c - 105B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R +-------+ +--R 4 3 +---+ \|e x + d +--R - 210A c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b c +--R , +--R +--R +-------+ +--R 4 3 +---+ \|e x + d +--R - 210A c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A b c + 210B b )e + (630A b c - 630B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 630A b c + 630B b c )d e + (210A c - 210B b c )d +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 704 + +--S 705 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 +--R (- A b c + B b )e + (3A b c - 3B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A b c + 3B b c )d e + (A c - B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-----------------------------------------------) +--R \| c c x + b +--R + +--R +-+ +-------+ +--R 4 3 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d \|c \|d log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (2A b c - 2B b )e + (- 6A b c + 6B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (6A b c - 6B b c )d e + (- 2A c + 2B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 4 3 +-+ +-+ \|e x + d +--R 2A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 4 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 3 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d \|c \|d log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (2A b c - 2B b )e + (- 6A b c + 6B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (6A b c - 6B b c )d e + (- 2A c + 2B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 4 3 +-+ +-+ \|e x + d +--R 2A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 4 3 2 2 3 2 +--R (- 2A b c + 2B b )e + (6A b c - 6B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 6A b c + 6B b c )d e + (2A c - 2B b c )d +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 4 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1457 +r0:=2/3*(B*c*d-b*B*e+A*c*e)*(d+e*x)^(3/2)/c^2+2/5*B*(d+e*x)^(5/2)/c-_ + 2*A*d^(5/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(5/2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(7/2))+2*(B*(c*d-b*e)^2+_ + A*c*e*(2*c*d-b*e))*sqrt(d+e*x)/c^3 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R (30A b c - 30B b )e + (- 60A b c + 60B b c)d e +--R + +--R 3 2 2 +--R (30A c - 30B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 +-+ +-+ \|e x + d +--R - 30A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 +-+ +--R 15b c \|c +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 +--R (- 15A b c + 15B b )e + (30A b c - 30B b c)d e +--R + +--R 3 2 2 +--R (- 15A c + 15B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-------------------------------------------------) +--R \| c c x + b +--R + +--R +-+ +-------+ +--R 3 2 +-+ - 2\|d \|e x + d + e x + 2d +--R 15A c d \|d log(----------------------------) +--R x +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R , +--R +--R +-+ +-------+ +--R 3 2 +-+ - 2\|d \|e x + d + e x + 2d +--R 15A c d \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 +--R (30A b c - 30B b )e + (- 60A b c + 60B b c)d e +--R + +--R 3 2 2 +--R (30A c - 30B b c )d +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R , +--R +--R 2 3 2 2 2 +--R (- 15A b c + 15B b )e + (30A b c - 30B b c)d e +--R + +--R 3 2 2 +--R (- 15A c + 15B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-------------------------------------------------) +--R \| c c x + b +--R + +--R +-------+ +--R 3 2 +---+ \|e x + d +--R - 30A c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R , +--R +--R +-------+ +--R 3 2 +---+ \|e x + d +--R - 30A c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 3 2 2 2 +--R (30A b c - 30B b )e + (- 60A b c + 60B b c)d e +--R + +--R 3 2 2 +--R (30A c - 30B b c )d +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 711 + +--S 712 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 2 2 +--R ((- A b c + B b )e + (2A b c - 2B b c)d e + (- A c + B b c )d ) +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-------------------------------------------------) +--R \| c c x + b +--R + +--R +-+ +-------+ +--R 3 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d \|c \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 2B b )e + (4A b c - 4B b c)d e + (- 2A c + 2B b c )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 +-+ +-+ \|e x + d +--R 2A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d \|c \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 2B b )e + (4A b c - 4B b c)d e + (- 2A c + 2B b c )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 +-+ +-+ \|e x + d +--R 2A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 3 2 2 +--R ((2A b c - 2B b )e + (- 4A b c + 4B b c)d e + (2A c - 2B b c )d ) +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1457 +r0:=2/3*B*(d+e*x)^(3/2)/c-2*A*d^(3/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-_ + 2*(b*B-A*c)*(c*d-b*e)^(3/2)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*c^(5/2))+2*(B*c*d-b*B*e+A*c*e)*sqrt(d+e*x)/c^2 +--R +--R +--R (2) +--R 2 2 +-----------+ +--R ((- 6A b c + 6B b )e + (6A c - 6B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R - 6A c d\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 +-+ +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|c \|e x + d +--R / +--R 2 +-+ +--R 3b c \|c +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 |- b e + c d +--R ((- 3A b c + 3B b )e + (3A c - 3B b c)d) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 +-+ - 2\|d \|e x + d + e x + 2d +--R 3A c d\|d log(----------------------------) +--R x +--R + +--R 2 +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d +--R / +--R 2 +--R 3b c +--R , +--R +--R +-+ +-------+ +--R 2 +-+ - 2\|d \|e x + d + e x + 2d +--R 3A c d\|d log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 |b e - c d \|e x + d +--R ((- 6A b c + 6B b )e + (6A c - 6B b c)d) |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d +--R / +--R 2 +--R 3b c +--R , +--R +--R +-----------+ +--R 2 2 |- b e + c d +--R ((- 3A b c + 3B b )e + (3A c - 3B b c)d) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-------+ +--R 2 +---+ \|e x + d +--R - 6A c d\|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d +--R / +--R 2 +--R 3b c +--R , +--R +--R +-------+ +--R 2 +---+ \|e x + d +--R - 6A c d\|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R +---------+ +-------+ +--R 2 2 |b e - c d \|e x + d +--R ((- 6A b c + 6B b )e + (6A c - 6B b c)d) |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d +--R / +--R 2 +--R 3b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 718 + +--S 719 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 |- b e + c d +-+ +--R ((- A b c + B b )e + (A c - B b c)d) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d\|c \|d log(----------------------------) +--R x +--R + +--R 2 2 +-----------+ +--R ((2A b c - 2B b )e + (- 2A c + 2B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R 2A c d\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 2 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R A c d\|c \|d log(----------------------------) +--R x +--R + +--R 2 2 +-----------+ +--R ((2A b c - 2B b )e + (- 2A c + 2B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R 2A c d\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 2 2 +-+ |b e - c d \|e x + d +--R ((- 2A b c + 2B b )e + (2A c - 2B b c)d)\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 2 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 722 + +)clear all + +--S 723 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1457 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b*c^(3/2))+2*B*sqrt(d+e*x)/c +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R (2A c - 2B b)\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-+ +-+ \|e x + d +-+ +-------+ +--R - 2A c\|c \|d atanh(----------) + 2B b\|c \|e x + d +--R +-+ +--R \|d +--R / +--R +-+ +--R b c\|c +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1457 +--a0:=integrate(t0,x) +--E 725 + +--S 726 of 1457 +--m0a:=a0.1-r0 +--E 726 + +--S 727 of 1457 +--d0a:=D(m0a,x) +--E 727 + +--S 728 of 1457 +--m0b:=a0.2-r0 +--E 728 + +--S 729 of 1457 +--d0b:=D(m0b,x) +--E 729 + +)clear all + +--S 730 of 1457 +t0:=(A+B*x)/((b*x+c*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ---------------------- +--R 2 +-------+ +--R (c x + b x)\|e x + d +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1457 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*sqrt(d))-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b*sqrt(c)*sqrt(c*d-b*e)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R (2A c - 2B b)\|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R - 2A\|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R / +--R +-----------+ +-+ +-+ +--R b\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R A\|- b c e + c d log(-------------------------------) +--R x +--R + +--R +-+ +--R (A c - B b)\|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R / +--R +-------------+ +--R | 2 +-+ +--R b\|- b c e + c d \|d +--R , +--R +--R +-----------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R A\|b c e - c d log(-------------------------------) +--R x +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-+ \|b c e - c d \|e x + d +--R (- 2A c + 2B b)\|d atan(------------------------) +--R b e - c d +--R / +--R +-----------+ +--R +-+ | 2 +--R b\|d \|b c e - c d +--R , +--R +--R +---+ +--R (A c - B b)\|- d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R + +--R +-------------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R - 2A\|- b c e + c d atan(----------------) +--R d +--R / +--R +-------------+ +--R | 2 +---+ +--R b\|- b c e + c d \|- d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R +---+ \|b c e - c d \|e x + d +--R (- 2A c + 2B b)\|- d atan(------------------------) +--R b e - c d +--R + +--R +-----------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R - 2A\|b c e - c d atan(----------------) +--R d +--R / +--R +-----------+ +--R +---+ | 2 +--R b\|- d \|b c e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 732 + +--S 733 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-------------+ +-------+ +-+ +--R | 2 +-----------+ +-+ - 2d\|e x + d + (e x + 2d)\|d +--R A\|- b c e + c d \|- b e + c d \|c log(-------------------------------) +--R x +--R + +--R +-----------+ +-+ +-+ +--R (A c - B b)\|- b e + c d \|c \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R + +--R +-------------+ +-+ +-------+ +--R | 2 +-+ \|c \|e x + d +--R (- 2A c + 2B b)\|- b c e + c d \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------------+ +-------+ +--R | 2 +-----------+ +-+ \|e x + d +--R 2A\|- b c e + c d \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R / +--R +-------------+ +--R | 2 +-----------+ +-+ +-+ +--R b\|- b c e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-------+ +-+ +--R +-----------+ +-+ | 2 - 2d\|e x + d + (e x + 2d)\|d +--R A\|- b e + c d \|c \|b c e - c d log(-------------------------------) +--R x +--R + +--R +-----------+ +-+ +-------+ +--R +-+ | 2 \|c \|e x + d +--R (- 2A c + 2B b)\|d \|b c e - c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-----------+ +-------+ +--R +-----------+ +-+ | 2 \|e x + d +--R 2A\|- b e + c d \|c \|b c e - c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ +-+ \|b c e - c d \|e x + d +--R (- 2A c + 2B b)\|- b e + c d \|c \|d atan(------------------------) +--R b e - c d +--R / +--R +-----------+ +--R +-----------+ +-+ +-+ | 2 +--R b\|- b e + c d \|c \|d \|b c e - c d +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 736 + +)clear all + +--S 737 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------ +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1457 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(3/2))-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b*(c*d-b*e)^(3/2))+_ + 2*(B*d-A*e)/(d*(c*d-b*e)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R (- 2A c + 2B b)d\|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R (- 2A b e + 2A c d)\|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R +-----------+ +-+ +--R (2A b e - 2B b d)\|- b e + c d \|d +--R / +--R 2 2 +-----------+ +-+ +-------+ +--R (b d e - b c d )\|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | c +-+ +-------+ +--R (A c - B b)d |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R (A b e - A c d)\|e x + d log(-------------------------------) +--R x +--R + +--R +-+ +--R (2A b e - 2B b d)\|d +--R / +--R 2 2 +-+ +-------+ +--R (b d e - b c d )\|d \|e x + d +--R , +--R +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R (A b e - A c d)\|e x + d log(-------------------------------) +--R x +--R + +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R (2A c - 2B b)d |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R +-+ +--R (2A b e - 2B b d)\|d +--R / +--R 2 2 +-+ +-------+ +--R (b d e - b c d )\|d \|e x + d +--R , +--R +--R +-----------+ +--R +---+ | c +-------+ +--R (A c - B b)d\|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R (- 2A b e + 2A c d)\|e x + d atan(----------------) +--R d +--R + +--R +---+ +--R (2A b e - 2B b d)\|- d +--R / +--R 2 2 +---+ +-------+ +--R (b d e - b c d )\|- d \|e x + d +--R , +--R +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R (- 2A b e + 2A c d)\|e x + d atan(----------------) +--R d +--R + +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R (2A c - 2B b)d\|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R +---+ +--R (2A b e - 2B b d)\|- d +--R / +--R 2 2 +---+ +-------+ +--R (b d e - b c d )\|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 739 + +--S 740 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | c +-+ +--R (A c - B b)d\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R (A b e - A c d)\|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R (2A c - 2B b)d\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ \|e x + d +--R (2A b e - 2A c d)\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 2 2 +-----------+ +-+ +--R (b d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R (A b e - A c d)\|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R (2A c - 2B b)d\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ \|e x + d +--R (2A b e - 2A c d)\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R +-----------+ | c +-+ c\|e x + d +--R (2A c - 2B b)d\|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 2 2 +-----------+ +-+ +--R (b d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 1457 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------------ +--R 2 4 2 3 2 2 2 +-------+ +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1457 +r0:=2/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(3/2))-2*A*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b*d^(5/2))-2*c^(3/2)*(b*B-A*c)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*(c*d-b*e)^(5/2))+2*(B*c*d^2-A*e*(2*c*d-b*e))/(d^2*_ + (c*d-b*e)^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 3 +-+ +-+ +-------+ +--R ((6A c - 6B b c)d e x + (6A c - 6B b c)d )\|c \|d \|e x + d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 2 2 2 2 2 +--R (- 6A b e + 12A b c d e - 6A c d e)x - 6A b d e + 12A b c d e +--R + +--R 2 3 +--R - 6A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 2 2 2 +--R (3A b e - 6A b c d e + 3A c d e)x + 3A b d e - 6A b c d e +--R + +--R 2 3 +--R 3A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 2 3 | c +-+ +--R ((3A c - 3B b c)d e x + (3A c - 3B b c)d ) |- --------- \|d +--R \| b e - c d +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +-+ +--R \|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +-+ +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d )\|d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 3 2 2 2 2 2 2 +--R (3A b e - 6A b c d e + 3A c d e)x + 3A b d e - 6A b c d e +--R + +--R 2 3 +--R 3A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R +---------+ +--R 2 2 2 3 | c +-+ +--R ((- 6A c + 6B b c)d e x + (- 6A c + 6B b c)d ) |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R +-------+ c\|e x + d +--R \|e x + d atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +-+ +--R \|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +-+ +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d )\|d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +-----------+ +--R 2 2 2 3 +---+ | c +--R ((3A c - 3B b c)d e x + (3A c - 3B b c)d )\|- d |- --------- +--R \| b e - c d +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 3 2 2 2 2 2 2 +--R (- 6A b e + 12A b c d e - 6A c d e)x - 6A b d e + 12A b c d e +--R + +--R 2 3 +--R - 6A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 2 3 2 2 2 2 2 2 +--R (- 6A b e + 12A b c d e - 6A c d e)x - 6A b d e + 12A b c d e +--R + +--R 2 3 +--R - 6A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R +---------+ +--R 2 2 2 3 +---+ | c +--R ((- 6A c + 6B b c)d e x + (- 6A c + 6B b c)d )\|- d |--------- +--R \|b e - c d +--R * +--R +-------+ +--R +-------+ c\|e x + d +--R \|e x + d atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 746 + +--S 747 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 +-----------+ +--R (A b e - 2A b c d e + A c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 +-----------+ | c +-+ +--R (A c - B b c)d \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|c \|e x + d +--R (- 2A c + 2B b c)d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|e x + d +--R (2A b e - 4A b c d e + 2A c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 2 2 2 3 2 4 +-----------+ +-+ +--R (b d e - 2b c d e + b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 +-----------+ +--R (A b e - 2A b c d e + A c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|c \|e x + d +--R (- 2A c + 2B b c)d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|e x + d +--R (2A b e - 4A b c d e + 2A c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 2 +-----------+ | c +-+ +--R (- 2A c + 2B b c)d \|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 3 2 2 2 3 2 4 +-----------+ +-+ +--R (b d e - 2b c d e + b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 1457 +t0:=(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1457 +r0:=2/5*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(5/2))+2/3*(B*c*d^2-A*e*(2*c*d-_ + b*e))/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-2*A*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b*d^(7/2))-2*c^(5/2)*(b*B-A*c)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*(c*d-b*e)^(7/2))+2*(B*c^2*d^3-A*e*(3*c^2*d^2-_ + 3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 2 2 3 2 4 +--R (- 30A c + 30B b c )d e x + (- 60A c + 60B b c )d e x +--R + +--R 3 2 5 +--R (- 30A c + 30B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30A b e + 90A b c d e - 90A b c d e + 30A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (- 60A b d e + 180A b c d e - 180A b c d e + 60A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R - 30A b d e + 90A b c d e - 90A b c d e + 30A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 2 2 3 2 4 +--R (15A c - 15B b c )d e x + (30A c - 30B b c )d e x +--R + +--R 3 2 5 +--R (15A c - 15B b c )d +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15A b e - 45A b c d e + 45A b c d e - 15A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (30A b d e - 90A b c d e + 90A b c d e - 30A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R 15A b d e - 45A b c d e + 45A b c d e - 15A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +-+ +--R \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15A b e - 45A b c d e + 45A b c d e - 15A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (30A b d e - 90A b c d e + 90A b c d e - 30A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R 15A b d e - 45A b c d e + 45A b c d e - 15A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 3 2 3 2 2 3 2 4 +--R (30A c - 30B b c )d e x + (60A c - 60B b c )d e x +--R + +--R 3 2 5 +--R (30A c - 30B b c )d +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +-+ +--R \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 3 2 3 2 2 3 2 4 +--R (15A c - 15B b c )d e x + (30A c - 30B b c )d e x +--R + +--R 3 2 5 +--R (15A c - 15B b c )d +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30A b e + 90A b c d e - 90A b c d e + 30A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (- 60A b d e + 180A b c d e - 180A b c d e + 60A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R - 30A b d e + 90A b c d e - 90A b c d e + 30A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30A b e + 90A b c d e - 90A b c d e + 30A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (- 60A b d e + 180A b c d e - 180A b c d e + 60A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R - 30A b d e + 90A b c d e - 90A b c d e + 30A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 3 2 3 2 2 3 2 4 +--R (30A c - 30B b c )d e x + (60A c - 60B b c )d e x +--R + +--R 3 2 5 +--R (30A c - 30B b c )d +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 753 + +--S 754 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 3 +-----------+ | c +-+ +--R (A c - B b c )d \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (A b e - 3A b c d e + 3A b c d e - A c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 2 3 +-+ +-+ \|c \|e x + d +--R (2A c - 2B b c )d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (2A b e - 6A b c d e + 6A b c d e - 2A c d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R / +--R 4 3 3 3 4 2 2 2 5 3 6 +-----------+ +-+ +--R (b d e - 3b c d e + 3b c d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (A b e - 3A b c d e + 3A b c d e - A c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 2 3 +-+ +-+ \|c \|e x + d +--R (2A c - 2B b c )d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (2A b e - 6A b c d e + 6A b c d e - 2A c d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 3 2 3 +-----------+ | c +-+ +--R (2A c - 2B b c )d \|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 4 3 3 3 4 2 2 2 5 3 6 +-----------+ +-+ +--R (b d e - 3b c d e + 3b c d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 757 + +)clear all + +--S 758 of 1457 +t0:=(A+B*x)/((d+e*x)^(9/2)*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 6 4 3 5 3 2 2 4 +--R c e x + (b e + 4c d e )x + (4b d e + 6c d e )x +--R + +--R 2 2 3 3 3 4 2 4 +--R (6b d e + 4c d e)x + (4b d e + c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1457 +r0:=2/7*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(7/2))+2/5*(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x)^(5/2))+2/3*(B*c^2*d^3-A*e*(3*c^2*d^2-_ + 3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x)^(3/2))-_ + 2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(9/2))-2*c^(7/2)*(b*B-A*c)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*(c*d-b*e)^(9/2))+_ + 2*(B*c^3*d^4-A*e*(4*c^3*d^3-6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))/_ + (d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 3 3 4 3 5 2 2 +--R (210A c - 210B b c )d e x + (630A c - 630B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (630A c - 630B b c )d e x + (210A c - 210B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 210A b e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 4 3 +--R - 210A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R - 630A b d e + 2520A b c d e - 3780A b c d e + 2520A b c d e +--R + +--R 4 5 2 +--R - 630A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R - 630A b d e + 2520A b c d e - 3780A b c d e + 2520A b c d e +--R + +--R 4 6 +--R - 630A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R - 210A b d e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 7 +--R - 210A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 4 10 +--R (315b d e - 1260b c d e + 1890b c d e - 1260b c d e + 315b c d e)x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 105A b e - 420A b c d e + 630A b c d e - 420A b c d e +--R + +--R 4 4 3 +--R 105A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R 315A b d e - 1260A b c d e + 1890A b c d e - 1260A b c d e +--R + +--R 4 5 2 +--R 315A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R 315A b d e - 1260A b c d e + 1890A b c d e - 1260A b c d e +--R + +--R 4 6 +--R 315A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R 105A b d e - 420A b c d e + 630A b c d e - 420A b c d e +--R + +--R 4 7 +--R 105A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 4 3 4 3 3 4 3 5 2 2 +--R (105A c - 105B b c )d e x + (315A c - 315B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (315A c - 315B b c )d e x + (105A c - 105B b c )d +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +-+ +--R \|d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 10 +--R 315b c d e +--R * +--R x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 105A b e - 420A b c d e + 630A b c d e - 420A b c d e +--R + +--R 4 4 3 +--R 105A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R 315A b d e - 1260A b c d e + 1890A b c d e - 1260A b c d e +--R + +--R 4 5 2 +--R 315A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R 315A b d e - 1260A b c d e + 1890A b c d e - 1260A b c d e +--R + +--R 4 6 +--R 315A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R 105A b d e - 420A b c d e + 630A b c d e - 420A b c d e +--R + +--R 4 7 +--R 105A c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 4 3 4 3 3 4 3 5 2 2 +--R (- 210A c + 210B b c )d e x + (- 630A c + 630B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (- 630A c + 630B b c )d e x + (- 210A c + 210B b c )d +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +-+ +--R \|d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 10 +--R 315b c d e +--R * +--R x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 4 3 4 3 3 4 3 5 2 2 +--R (105A c - 105B b c )d e x + (315A c - 315B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (315A c - 315B b c )d e x + (105A c - 105B b c )d +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 210A b e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 4 3 +--R - 210A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R - 630A b d e + 2520A b c d e - 3780A b c d e +--R + +--R 3 4 3 4 5 2 +--R 2520A b c d e - 630A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 +--R - 630A b d e + 2520A b c d e - 3780A b c d e +--R + +--R 3 5 2 4 6 +--R 2520A b c d e - 630A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R - 210A b d e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 7 +--R - 210A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 10 +--R 315b c d e +--R * +--R x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 210A b e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 4 3 +--R - 210A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R - 630A b d e + 2520A b c d e - 3780A b c d e +--R + +--R 3 4 3 4 5 2 +--R 2520A b c d e - 630A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 +--R - 630A b d e + 2520A b c d e - 3780A b c d e +--R + +--R 3 5 2 4 6 +--R 2520A b c d e - 630A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R - 210A b d e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 7 +--R - 210A c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 4 3 4 3 3 4 3 5 2 2 +--R (- 210A c + 210B b c )d e x + (- 630A c + 630B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (- 630A c + 630B b c )d e x + (- 210A c + 210B b c )d +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +---+ +--R \|- d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 10 +--R 315b c d e +--R * +--R x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 760 + +--S 761 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (A b e - 4A b c d e + 6A b c d e - 4A b c d e + A c d ) +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 4 3 4 +-----------+ | c +-+ +--R (A c - B b c )d \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 4 3 4 +-+ +-+ \|c \|e x + d +--R (- 2A c + 2B b c )d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (2A b e - 8A b c d e + 12A b c d e - 8A b c d e + 2A c d ) +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 +-----------+ +-+ +--R (b d e - 4b c d e + 6b c d e - 4b c d e + b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (A b e - 4A b c d e + 6A b c d e - 4A b c d e + A c d ) +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 4 3 4 +-+ +-+ \|c \|e x + d +--R (- 2A c + 2B b c )d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (2A b e - 8A b c d e + 12A b c d e - 8A b c d e + 2A c d ) +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 4 3 4 +-----------+ | c +-+ +--R (- 2A c + 2B b c )d \|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 +-----------+ +-+ +--R (b d e - 4b c d e + 6b c d e - 4b c d e + b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 764 + +)clear all + +--S 765 of 1457 +t0:=(A+B*x)*(d+e*x)^(9/2)/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 765 + +--S 766 of 1457 +r0:=1/3*e*(6*A*c^3*d^2-7*b^3*B*e^2-3*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ + (12*B*d+5*A*e))*(d+e*x)^(3/2)/(b^2*c^3)+1/5*e*(10*A*c^2*d+7*b^2*B*e-_ + 5*b*c*(B*d+A*e))*(d+e*x)^(5/2)/(b^2*c^2)+(b*B-2*A*c)*(c*d-b*e)*_ + (d+e*x)^(7/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(9/2)/(b*x*(b+c*x))-_ + d^(7/2)*(2*b*B*d-4*A*c*d+9*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/b^3-_ + (c*d-b*e)^(7/2)*(4*A*c^2*d-7*b^2*B*e-b*c*(2*B*d-5*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(9/2))+_ + e*(2*A*c^4*d^3+7*b^4*B*e^3-b*c^3*d^2*(B*d+3*A*e)-b^3*c*e^2*_ + (19*B*d+5*A*e)+b^2*c^2*d*e*(15*B*d+11*A*e))*sqrt(d+e*x)/(b^2*c^4) +--R +--R +--R (2) +--R 4 2 5 4 3 3 4 2 3 +--R (75A b c - 105B b c)e + (- 165A b c + 285B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (45A b c - 225B b c )d e + (105A b c + 15B b c )d e +--R + +--R 6 5 4 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (75A b c - 105B b )e + (- 165A b c + 285B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (45A b c - 225B b c )d e + (105A b c + 15B b c )d e +--R + +--R 5 2 4 4 +--R (- 60A b c + 30B b c )d +--R * +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 3 6 5 4 2 +--R (- 135A b c d e + (60A c - 30B b c )d )x +--R + +--R 2 4 3 5 2 4 4 +--R (- 135A b c d e + (60A b c - 30B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 3 3 +--R 6B b c e x + ((10A b c - 14B b c )e + 42B b c d e )x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 50A b c + 70B b c)e + (130A b c - 218B b c )d e +--R + +--R 3 3 2 2 +--R 216B b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 75A b c + 105B b )e + (190A b c - 320B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 90A b c + 306B b c )d e + (60A b c - 60B b c )d e +--R + +--R 5 2 4 4 +--R (- 30A b c + 15B b c )d +--R * +--R x +--R + +--R 2 4 4 +--R - 15A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 5 2 4 4 +-+ +--R (15b c x + 15b c x)\|c +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1457 +--a0:=integrate(t0,x) +--E 767 + +--S 768 of 1457 +--m0a:=a0.1-r0 +--E 768 + +--S 769 of 1457 +--d0a:=D(m0a,x) +--E 769 + +--S 770 of 1457 +--m0b:=a0.2-r0 +--E 770 + +--S 771 of 1457 +--d0b:=D(m0b,x) +--E 771 + +)clear all + +--S 772 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1457 +r0:=1/3*e*(6*A*c^2*d+5*b^2*B*e-3*b*c*(B*d+A*e))*(d+e*x)^(3/2)/(b^2*c^2)+_ + (b*B-2*A*c)*(c*d-b*e)*(d+e*x)^(5/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(7/2)/_ + (b*x*(b+c*x))-d^(5/2)*(2*b*B*d-4*A*c*d+7*A*b*e)*atanh(sqrt(d+e*x)/_ + sqrt(d))/b^3+(c*d-b*e)^(5/2)*(2*b*B*c*d-4*A*c^2*d+5*b^2*B*e-_ + 3*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(7/2))+_ + e*(2*A*c^3*d^2-5*b^3*B*e^2-b*c^2*d*(B*d+2*A*e)+b^2*c*e*(8*B*d+_ + 3*A*e))*sqrt(d+e*x)/(b^2*c^3) +--R +--R +--R (2) +--R 3 2 4 3 2 3 3 2 2 +--R (- 9A b c + 15B b c)e + (6A b c - 24B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (15A b c + 3B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 9A b c + 15B b )e + (6A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (15A b c + 3B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 2 5 4 3 2 +--R (- 21A b c d e + (12A c - 6B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (- 21A b c d e + (12A b c - 6B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 2B b c e x + ((6A b c - 10B b c)e + 20B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (9A b c - 15B b )e + (- 9A b c + 29B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (9A b c - 9B b c )d e + (- 6A b c + 3B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 3A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 4 2 4 3 +-+ +--R (3b c x + 3b c x)\|c +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 4 3 2 3 3 2 2 +--R (9A b c - 15B b c)e + (- 6A b c + 24B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 15A b c - 3B b c )d e + (12A c - 6B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (9A b c - 15B b )e + (- 6A b c + 24B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 15A b c - 3B b c )d e + (12A b c - 6B b c )d +--R * +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-------------------------------------------------) +--R \| c c x + b +--R + +--R 4 2 5 4 3 2 +--R (21A b c d e + (- 12A c + 6B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (21A b c d e + (- 12A b c + 6B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 4B b c e x + ((12A b c - 20B b c)e + 40B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (18A b c - 30B b )e + (- 18A b c + 58B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (18A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 6A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 6b c x + 6b c x +--R , +--R +--R 4 2 5 4 3 2 +--R (21A b c d e + (- 12A c + 6B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (21A b c d e + (- 12A b c + 6B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 18A b c + 30B b c)e + (12A b c - 48B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (30A b c + 6B b c )d e + (- 24A c + 12B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 18A b c + 30B b )e + (12A b c - 48B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (30A b c + 6B b c )d e + (- 24A b c + 12B b c )d +--R * +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 4B b c e x + ((12A b c - 20B b c)e + 40B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (18A b c - 30B b )e + (- 18A b c + 58B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (18A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 6A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 6b c x + 6b c x +--R , +--R +--R 3 2 4 3 2 3 3 2 2 +--R (9A b c - 15B b c)e + (- 6A b c + 24B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 15A b c - 3B b c )d e + (12A c - 6B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (9A b c - 15B b )e + (- 6A b c + 24B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 15A b c - 3B b c )d e + (12A b c - 6B b c )d +--R * +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-------------------------------------------------) +--R \| c c x + b +--R + +--R 4 2 5 4 3 2 +--R (- 42A b c d e + (24A c - 12B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (- 42A b c d e + (24A b c - 12B b c )d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 4B b c e x + ((12A b c - 20B b c)e + 40B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (18A b c - 30B b )e + (- 18A b c + 58B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (18A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 6A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 6b c x + 6b c x +--R , +--R +--R 4 2 5 4 3 2 +--R (- 21A b c d e + (12A c - 6B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (- 21A b c d e + (12A b c - 6B b c )d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 9A b c + 15B b c)e + (6A b c - 24B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (15A b c + 3B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 9A b c + 15B b )e + (6A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (15A b c + 3B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 2B b c e x + ((6A b c - 10B b c)e + 20B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (9A b c - 15B b )e + (- 9A b c + 29B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (9A b c - 9B b c )d e + (- 6A b c + 3B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 3A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 3b c x + 3b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 774 + +--S 775 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 +--R (3A b c - 5B b )e + (- 2A b c + 8B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 5A b c - B b c )d e + (4A c - 2B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-------------------------------------------------) +--R \| c c x + b +--R + +--R 3 2 4 3 3 +-+ +-+ +--R (7A b c d e + (- 4A c + 2B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (6A b c - 10B b )e + (- 4A b c + 16B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 10A b c - 2B b c )d e + (8A c - 4B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 4 3 3 +-+ +-+ \|e x + d +--R (14A b c d e + (- 8A c + 4B b c )d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 3 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 2 4 3 3 +-+ +-+ +--R (7A b c d e + (- 4A c + 2B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (6A b c - 10B b )e + (- 4A b c + 16B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 10A b c - 2B b c )d e + (8A c - 4B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 4 3 3 +-+ +-+ \|e x + d +--R (14A b c d e + (- 8A c + 4B b c )d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 4 3 2 2 3 2 +--R (- 6A b c + 10B b )e + (4A b c - 16B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (10A b c + 2B b c )d e + (- 8A c + 4B b c )d +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 3 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 778 + +)clear all + +--S 779 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1457 +r0:=(b*B-2*A*c)*(c*d-b*e)*(d+e*x)^(3/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(5/2)/_ + (b*x*(b+c*x))-d^(3/2)*(2*b*B*d-4*A*c*d+5*A*b*e)*atanh(sqrt(d+e*x)/_ + sqrt(d))/b^3-(c*d-b*e)^(3/2)*(4*A*c^2*d-3*b^2*B*e-b*c*(2*B*d-A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(5/2))+e*(2*A*c^2*d+_ + 3*b^2*B*e-b*c*(B*d+A*e))*sqrt(d+e*x)/(b^2*c^2) +--R +--R +--R (2) +--R 2 2 3 2 3 2 2 +--R (A b c - 3B b c)e + (3A b c + B b c )d e +--R + +--R 4 3 2 +--R (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 4 3 2 2 +--R (- 5A b c d e + (4A c - 2B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (- 5A b c d e + (4A b c - 2B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 +--R 2B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- A b c + 3B b )e + (2A b c - 2B b c)d e +--R + +--R 3 2 2 2 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 3 2 4 2 +-+ +--R (b c x + b c x)\|c +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 3 2 2 +--R (A b c - 3B b c)e + (3A b c + B b c )d e +--R + +--R 4 3 2 +--R (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 3 4 3 2 2 +--R (5A b c d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (5A b c d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 2 2 +--R 4B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- 2A b c + 6B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 2 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - 2A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R 2b c x + 2b c x +--R , +--R +--R 3 4 3 2 2 +--R (5A b c d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (5A b c d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 2 3 2 3 2 2 +--R (2A b c - 6B b c)e + (6A b c + 2B b c )d e +--R + +--R 4 3 2 +--R (- 8A c + 4B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 +--R (2A b c - 6B b )e + (6A b c + 2B b c)d e +--R + +--R 3 2 2 2 +--R (- 8A b c + 4B b c )d +--R * +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 2 +--R 4B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- 2A b c + 6B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 2 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - 2A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R 2b c x + 2b c x +--R , +--R +--R 2 2 3 2 3 2 2 +--R (A b c - 3B b c)e + (3A b c + B b c )d e +--R + +--R 4 3 2 +--R (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 3 4 3 2 2 +--R (- 10A b c d e + (8A c - 4B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (- 10A b c d e + (8A b c - 4B b c )d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 2 +--R 4B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- 2A b c + 6B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 2 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - 2A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R 2b c x + 2b c x +--R , +--R +--R 3 4 3 2 2 +--R (- 5A b c d e + (4A c - 2B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (- 5A b c d e + (4A b c - 2B b c )d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 2 3 2 3 2 2 +--R (A b c - 3B b c)e + (3A b c + B b c )d e +--R + +--R 4 3 2 +--R (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 2 +--R 2B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- A b c + 3B b )e + (2A b c - 2B b c)d e +--R + +--R 3 2 2 2 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 781 + +--S 782 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A c + 2B b c )d ) +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 2 +-+ +-+ +--R (5A b c d e + (- 4A c + 2B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 6B b )e + (- 6A b c - 2B b c)d e + (8A c - 4B b c )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 3 2 2 +-+ +-+ \|e x + d +--R (10A b c d e + (- 8A c + 4B b c )d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 2 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 2 2 +-+ +-+ +--R (5A b c d e + (- 4A c + 2B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 6B b )e + (- 6A b c - 2B b c)d e + (8A c - 4B b c )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 3 2 2 +-+ +-+ \|e x + d +--R (10A b c d e + (- 8A c + 4B b c )d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 3 2 2 +--R ((2A b c - 6B b )e + (6A b c + 2B b c)d e + (- 8A c + 4B b c )d ) +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 2 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1457 +r0:=-A*(d+e*x)^(3/2)/(b*x*(b+c*x))-(2*b*B*d-4*A*c*d+3*A*b*e)*_ + atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b^3-(4*A*c^2*d-b^2*B*e-_ + b*c*(2*B*d+A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*_ + sqrt(c*d-b*e)/(b^3*c^(3/2))+(b*B-2*A*c)*(c*d-b*e)*sqrt(d+e*x)/_ + (b^2*c*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 +--R ((A b c + B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((A b c + B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 2 +--R (- 3A b c e + (4A c - 2B b c )d)x +--R + +--R 2 2 2 +--R (- 3A b c e + (4A b c - 2B b c)d)x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 +-+ +-------+ +--R (((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d)\|c \|e x + d +--R / +--R 3 2 2 4 +-+ +--R (b c x + b c x)\|c +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 +--R ((A b c + B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((A b c + B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 2 +--R (3A b c e + (- 4A c + 2B b c )d)x +--R + +--R 2 2 2 +--R (3A b c e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 +-------+ +--R (((2A b c - 2B b )e + (- 4A b c + 2B b c)d)x - 2A b c d)\|e x + d +--R / +--R 3 2 2 4 +--R 2b c x + 2b c x +--R , +--R +--R 2 3 2 2 +--R (3A b c e + (- 4A c + 2B b c )d)x +--R + +--R 2 2 2 +--R (3A b c e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 2 3 2 2 +--R ((2A b c + 2B b c)e + (- 8A c + 4B b c )d)x +--R + +--R 2 3 2 2 +--R ((2A b c + 2B b )e + (- 8A b c + 4B b c)d)x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 3 2 2 2 +-------+ +--R (((2A b c - 2B b )e + (- 4A b c + 2B b c)d)x - 2A b c d)\|e x + d +--R / +--R 3 2 2 4 +--R 2b c x + 2b c x +--R , +--R +--R 2 2 3 2 2 +--R ((A b c + B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((A b c + B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 2 +--R (- 6A b c e + (8A c - 4B b c )d)x +--R + +--R 2 2 2 +--R (- 6A b c e + (8A b c - 4B b c)d)x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 3 2 2 2 +-------+ +--R (((2A b c - 2B b )e + (- 4A b c + 2B b c)d)x - 2A b c d)\|e x + d +--R / +--R 3 2 2 4 +--R 2b c x + 2b c x +--R , +--R +--R 2 3 2 2 +--R (- 3A b c e + (4A c - 2B b c )d)x +--R + +--R 2 2 2 +--R (- 3A b c e + (4A b c - 2B b c)d)x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 2 3 2 2 +--R ((A b c + B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((A b c + B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 3 2 2 2 +-------+ +--R (((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d)\|e x + d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 788 + +--S 789 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 |- b e + c d +-+ +--R ((A b c + B b )e + (- 4A c + 2B b c)d) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (3A b c e + (- 4A c + 2B b c)d)\|c \|d log(----------------------------) +--R x +--R + +--R 2 2 +-----------+ +--R ((- 2A b c - 2B b )e + (8A c - 4B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R (6A b c e + (- 8A c + 4B b c)d)\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 +-+ +--R 2b c\|c +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (3A b c e + (- 4A c + 2B b c)d)\|c \|d log(----------------------------) +--R x +--R + +--R 2 2 +-----------+ +--R ((- 2A b c - 2B b )e + (8A c - 4B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R (6A b c e + (- 8A c + 4B b c)d)\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 2 2 +-+ |b e - c d \|e x + d +--R ((2A b c + 2B b )e + (- 8A c + 4B b c)d)\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 +-+ +--R 2b c\|c +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 792 + +)clear all + +--S 793 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1457 +r0:=-(2*b*B*d-4*A*c*d+A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*sqrt(d))+_ + (2*b*B*c*d-4*A*c^2*d-b^2*B*e+3*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b^3*sqrt(c)*sqrt(c*d-b*e))+(b*B-2*A*c)*sqrt(d+e*x)/_ + (b^2*(b+c*x))-A*sqrt(d+e*x)/(b*x*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 +--R ((3A b c - B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((3A b c - B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 +--R ((- A b c e + (4A c - 2B b c)d)x + (- A b e + (4A b c - 2B b )d)x) +--R * +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 +-----------+ +-+ +-+ +-------+ +--R ((- 2A b c + B b )x - A b )\|- b e + c d \|c \|d \|e x + d +--R / +--R 3 2 4 +-----------+ +-+ +-+ +--R (b c x + b x)\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 +--R ((A b c e + (- 4A c + 2B b c)d)x + (A b e + (- 4A b c + 2B b )d)x) +--R * +--R +-------------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R \|- b c e + c d log(-------------------------------) +--R x +--R + +--R 2 2 3 2 2 +--R ((3A b c - B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((3A b c - B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +--R \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R + +--R +-------------+ +--R 2 2 | 2 +-+ +-------+ +--R ((- 4A b c + 2B b )x - 2A b )\|- b c e + c d \|d \|e x + d +--R / +--R +-------------+ +--R 3 2 4 | 2 +-+ +--R (2b c x + 2b x)\|- b c e + c d \|d +--R , +--R +--R 2 2 2 2 +--R ((A b c e + (- 4A c + 2B b c)d)x + (A b e + (- 4A b c + 2B b )d)x) +--R * +--R +-----------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R \|b c e - c d log(-------------------------------) +--R x +--R + +--R 2 2 3 2 2 +--R ((- 6A b c + 2B b c)e + (8A c - 4B b c )d)x +--R + +--R 2 3 2 2 +--R ((- 6A b c + 2B b )e + (8A b c - 4B b c)d)x +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-+ \|b c e - c d \|e x + d +--R \|d atan(------------------------) +--R b e - c d +--R + +--R +-----------+ +--R 2 2 +-+ | 2 +-------+ +--R ((- 4A b c + 2B b )x - 2A b )\|d \|b c e - c d \|e x + d +--R / +--R +-----------+ +--R 3 2 4 +-+ | 2 +--R (2b c x + 2b x)\|d \|b c e - c d +--R , +--R +--R 2 2 3 2 2 +--R ((3A b c - B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((3A b c - B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +---+ +--R \|- d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 +--R (- 2A b c e + (8A c - 4B b c)d)x +--R + +--R 2 2 +--R (- 2A b e + (8A b c - 4B b )d)x +--R * +--R +-------------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R \|- b c e + c d atan(----------------) +--R d +--R + +--R +-------------+ +--R 2 2 | 2 +---+ +-------+ +--R ((- 4A b c + 2B b )x - 2A b )\|- b c e + c d \|- d \|e x + d +--R / +--R +-------------+ +--R 3 2 4 | 2 +---+ +--R (2b c x + 2b x)\|- b c e + c d \|- d +--R , +--R +--R 2 2 3 2 2 +--R ((- 3A b c + B b c)e + (4A c - 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((- 3A b c + B b )e + (4A b c - 2B b c)d)x +--R * +--R +-----------+ +--R | 2 +-------+ +--R +---+ \|b c e - c d \|e x + d +--R \|- d atan(------------------------) +--R b e - c d +--R + +--R 2 2 2 2 +--R ((- A b c e + (4A c - 2B b c)d)x + (- A b e + (4A b c - 2B b )d)x) +--R * +--R +-----------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R \|b c e - c d atan(----------------) +--R d +--R + +--R +-----------+ +--R 2 2 +---+ | 2 +-------+ +--R ((- 2A b c + B b )x - A b )\|- d \|b c e - c d \|e x + d +--R / +--R +-----------+ +--R 3 2 4 +---+ | 2 +--R (b c x + b x)\|- d \|b c e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 795 + +--S 796 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-------------+ +--R | 2 +-----------+ +-+ +--R (A b e + (- 4A c + 2B b)d)\|- b c e + c d \|- b e + c d \|c +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R 2 2 +-----------+ +-+ +-+ +--R ((3A b c - B b )e + (- 4A c + 2B b c)d)\|- b e + c d \|c \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2b c e + 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(------------------------------------------------------------------) +--R c x + b +--R + +--R +-------------+ +--R 2 2 | 2 +-+ +--R ((- 6A b c + 2B b )e + (8A c - 4B b c)d)\|- b c e + c d \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------------+ +--R | 2 +-----------+ +-+ +--R (2A b e + (- 8A c + 4B b)d)\|- b c e + c d \|- b e + c d \|c +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R / +--R +-------------+ +--R 3 | 2 +-----------+ +-+ +-+ +--R 2b \|- b c e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R +-----------+ +-+ | 2 +--R (A b e + (- 4A c + 2B b)d)\|- b e + c d \|c \|b c e - c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 +-+ | 2 +--R ((- 6A b c + 2B b )e + (8A c - 4B b c)d)\|d \|b c e - c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-----------+ +--R +-----------+ +-+ | 2 +--R (2A b e + (- 8A c + 4B b)d)\|- b e + c d \|c \|b c e - c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 +-----------+ +-+ +-+ +--R ((- 6A b c + 2B b )e + (8A c - 4B b c)d)\|- b e + c d \|c \|d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|b c e - c d \|e x + d +--R atan(------------------------) +--R b e - c d +--R / +--R +-----------+ +--R 3 +-----------+ +-+ +-+ | 2 +--R 2b \|- b e + c d \|c \|d \|b c e - c d +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 799 + +)clear all + +--S 800 of 1457 +t0:=(A+B*x)/((b*x+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (c x + 2b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1457 +r0:=-(2*b*B*d-4*A*c*d-A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(3/2))+_ + (2*b*B*c*d-4*A*c^2*d-3*b^2*B*e+5*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))*sqrt(c)/(b^3*(c*d-b*e)^(3/2))+c*(b*B*d-2*A*c*d+A*b*e)*_ + sqrt(d+e*x)/(b^2*d*(c*d-b*e)*(b+c*x))-A*sqrt(d+e*x)/(b*d*x*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 2 +--R ((- 5A b c + 3B b c)d e + (4A c - 2B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((- 5A b c + 3B b )d e + (4A b c - 2B b c)d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 3 2 2 2 +--R (A b c e + (3A b c - 2B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (A b e + (3A b c - 2B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 3 2 +-----------+ +-+ +--R ((- A b c e + (2A b c - B b c)d)x - A b e + A b c d)\|- b e + c d \|d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-----------+ +-+ +--R ((b c d e - b c d )x + (b d e - b c d )x)\|- b e + c d \|d +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 2 +--R ((5A b c - 3B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((5A b c - 3B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 2 3 2 2 2 +--R (A b c e + (3A b c - 2B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (A b e + (3A b c - 2B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 2 2 3 2 +-+ +-------+ +--R ((- 2A b c e + (4A b c - 2B b c)d)x - 2A b e + 2A b c d)\|d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-+ +--R ((2b c d e - 2b c d )x + (2b d e - 2b c d )x)\|d +--R , +--R +--R 2 2 2 2 3 2 2 2 +--R (A b c e + (3A b c - 2B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (A b e + (3A b c - 2B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 2 3 2 2 2 +--R ((10A b c - 6B b c)d e + (- 8A c + 4B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((10A b c - 6B b )d e + (- 8A b c + 4B b c)d )x +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 2 2 3 2 +-+ +-------+ +--R ((- 2A b c e + (4A b c - 2B b c)d)x - 2A b e + 2A b c d)\|d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-+ +--R ((2b c d e - 2b c d )x + (2b d e - 2b c d )x)\|d +--R , +--R +--R 2 2 3 2 2 2 +--R ((5A b c - 3B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((5A b c - 3B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-----------+ +--R +---+ | c +--R \|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 2 3 2 2 2 +--R (2A b c e + (6A b c - 4B b c)d e + (- 8A c + 4B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (2A b e + (6A b c - 4B b )d e + (- 8A b c + 4B b c)d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 2 2 3 2 +---+ +-------+ +--R ((- 2A b c e + (4A b c - 2B b c)d)x - 2A b e + 2A b c d)\|- d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +---+ +--R ((2b c d e - 2b c d )x + (2b d e - 2b c d )x)\|- d +--R , +--R +--R 2 2 2 2 3 2 2 2 +--R (A b c e + (3A b c - 2B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (A b e + (3A b c - 2B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 2 3 2 2 2 +--R ((5A b c - 3B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((5A b c - 3B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +---------+ +-------+ +--R +---+ | c c\|e x + d +--R \|- d |--------- atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 2 2 3 2 +---+ +-------+ +--R ((- A b c e + (2A b c - B b c)d)x - A b e + A b c d)\|- d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +---+ +--R ((b c d e - b c d )x + (b d e - b c d )x)\|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 802 + +--S 803 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 +-----------+ +--R ((5A b c - 3B b )d e + (- 4A c + 2B b c)d )\|- b e + c d +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 2 2 +-----------+ +--R (A b e + (3A b c - 2B b )d e + (- 4A c + 2B b c)d )\|- b e + c d +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 2 2 +-+ +-+ +--R ((10A b c - 6B b )d e + (- 8A c + 4B b c)d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 2 +-----------+ +--R (- 2A b e + (- 6A b c + 4B b )d e + (8A c - 4B b c)d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R / +--R 4 3 2 +-----------+ +-+ +--R (2b d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +-----------+ +--R (A b e + (3A b c - 2B b )d e + (- 4A c + 2B b c)d )\|- b e + c d +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 2 2 +-+ +-+ +--R ((10A b c - 6B b )d e + (- 8A c + 4B b c)d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 2 +-----------+ +--R (- 2A b e + (- 6A b c + 4B b )d e + (8A c - 4B b c)d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 2 2 +-----------+ | c +--R ((10A b c - 6B b )d e + (- 8A c + 4B b c)d )\|- b e + c d |--------- +--R \|b e - c d +--R * +--R +-------+ +--R +-+ c\|e x + d +--R \|d atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 4 3 2 +-----------+ +-+ +--R (2b d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1457 +r0:=-(2*b*B*d-4*A*c*d-3*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(5/2))-_ + c^(3/2)*(4*A*c^2*d+5*b^2*B*e-b*c*(2*B*d+7*A*e))*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(5/2))-e*(2*A*c^2*d^2-_ + b^2*e*(2*B*d-3*A*e)-b*c*d*(B*d+2*A*e))/(b^2*d^2*(c*d-b*e)^2*_ + sqrt(d+e*x))+c*(b*B*d-2*A*c*d+A*b*e)/(b^2*d*(c*d-b*e)*(b+c*x)*_ + sqrt(d+e*x))-A/(b*d*x*(b+c*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 2 4 3 3 2 +--R ((7A b c - 5B b c )d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((7A b c - 5B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 2 3 2 3 2 2 2 +--R 3A b c e + (- 2A b c - 2B b c)d e + (- 5A b c + 4B b c )d e +--R + +--R 4 3 3 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 2 3 +--R (4A b c - 2B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 3A b c e + (2A b c + 2B b c)d e + (- 2A b c + B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 3A b e + (A b c + 2B b )d e + A b c d e +--R + +--R 3 2 2 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x) +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 3 2 3 2 2 2 +--R 3A b c e + (- 2A b c - 2B b c)d e + (- 5A b c + 4B b c )d e +--R + +--R 4 3 3 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 2 3 +--R (4A b c - 2B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 3 2 2 2 4 3 3 2 +--R ((7A b c - 5B b c )d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((7A b c - 5B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 6A b c e + (4A b c + 4B b c)d e + (- 4A b c + 2B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 6A b e + (2A b c + 4B b )d e + 2A b c d e +--R + +--R 3 2 2 3 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-+ +--R \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2b c d e - 4b c d e + 2b c d )x + (2b d e - 4b c d e + 2b c d )x) +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 3 3 2 2 3 2 3 2 2 2 +--R 3A b c e + (- 2A b c - 2B b c)d e + (- 5A b c + 4B b c )d e +--R + +--R 4 3 3 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 2 3 +--R (4A b c - 2B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 3 2 2 2 4 3 3 2 +--R ((- 14A b c + 10B b c )d e + (8A c - 4B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((- 14A b c + 10B b c)d e + (8A b c - 4B b c )d )x +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 6A b c e + (4A b c + 4B b c)d e + (- 4A b c + 2B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 6A b e + (2A b c + 4B b )d e + 2A b c d e +--R + +--R 3 2 2 3 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-+ +--R \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2b c d e - 4b c d e + 2b c d )x + (2b d e - 4b c d e + 2b c d )x) +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 3 2 2 2 4 3 3 2 +--R ((7A b c - 5B b c )d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((7A b c - 5B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 2 3 2 +--R 6A b c e + (- 4A b c - 4B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 10A b c + 8B b c )d e + (8A c - 4B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 6A b e + (- 4A b c - 4B b )d e + (- 10A b c + 8B b c)d e +--R + +--R 3 2 2 3 +--R (8A b c - 4B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 6A b c e + (4A b c + 4B b c)d e + (- 4A b c + 2B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 6A b e + (2A b c + 4B b )d e + 2A b c d e +--R + +--R 3 2 2 3 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2b c d e - 4b c d e + 2b c d )x + (2b d e - 4b c d e + 2b c d )x) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 3 3 2 2 3 2 3 2 2 2 +--R 3A b c e + (- 2A b c - 2B b c)d e + (- 5A b c + 4B b c )d e +--R + +--R 4 3 3 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 2 3 +--R (4A b c - 2B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 3 2 2 2 4 3 3 2 +--R ((- 7A b c + 5B b c )d e + (4A c - 2B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((- 7A b c + 5B b c)d e + (4A b c - 2B b c )d )x +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 3A b c e + (2A b c + 2B b c)d e + (- 2A b c + B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 3A b e + (A b c + 2B b )d e + A b c d e +--R + +--R 3 2 2 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 809 + +--S 810 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 3 2 2 2 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 3 +--R (4A c - 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 2 2 2 3 2 3 +-----------+ +--R ((7A b c - 5B b c)d e + (- 4A c + 2B b c )d )\|- b e + c d +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 3 2 3 +-+ +-+ +--R ((- 14A b c + 10B b c)d e + (8A c - 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A b e + (4A b c + 4B b )d e + (10A b c - 8B b c)d e +--R + +--R 3 2 3 +--R (- 8A c + 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 2 2 4 3 3 2 4 +-----------+ +-+ +--R (2b d e - 4b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 3 2 2 2 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 3 +--R (4A c - 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 2 2 2 3 2 3 +-+ +-+ +--R ((- 14A b c + 10B b c)d e + (8A c - 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A b e + (4A b c + 4B b )d e + (10A b c - 8B b c)d e +--R + +--R 3 2 3 +--R (- 8A c + 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 3 2 3 +-----------+ +--R ((- 14A b c + 10B b c)d e + (8A c - 4B b c )d )\|- b e + c d +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 5 2 2 4 3 3 2 4 +-----------+ +-+ +--R (2b d e - 4b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1457 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1457 +r0:=-1/3*e*(6*A*c^2*d^2-b^2*e*(2*B*d-5*A*e)-3*b*c*d*(B*d+2*A*e))/_ + (b^2*d^2*(c*d-b*e)^2*(d+e*x)^(3/2))+c*(b*B*d-2*A*c*d+A*b*e)/_ + (b^2*d*(c*d-b*e)*(b+c*x)*(d+e*x)^(3/2))-A/(b*d*x*(b+c*x)*_ + (d+e*x)^(3/2))-(2*b*B*d-4*A*c*d-5*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^3*d^(7/2))+c^(5/2)*(2*b*B*c*d-4*A*c^2*d-7*b^2*B*e+9*A*b*c*e)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(7/2))-_ + e*(2*A*c^3*d^3-b^2*c*d*e*(6*B*d-11*A*e)+b^3*e^2*(2*B*d-5*A*e)-_ + b*c^2*d^2*(B*d+3*A*e))/(b^2*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 2 3 3 2 5 4 4 3 +--R ((- 27A b c + 21B b c )d e + (12A c - 6B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 27A b c + 21B b c )d e + (- 15A b c + 15B b c )d e +--R + +--R 5 4 5 +--R (12A c - 6B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((- 27A b c + 21B b c )d e + (12A b c - 6B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 5 3 2 4 4 2 3 3 2 2 3 +--R 15A b c e + (- 33A b c - 6B b c)d e + (9A b c + 18B b c )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (21A b c - 18B b c )d e + (- 12A c + 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 15A b e + (- 18A b c - 6B b )d e + (- 24A b c + 12B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R 30A b c d e + (9A b c - 12B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 15A b d e + (- 33A b c - 6B b )d e + (9A b c + 18B b c)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (21A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 5 3 2 4 4 +--R - 15A b c e + (33A b c + 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 9A b c - 18B b c )d e + (6A b c - 3B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 15A b e + (13A b c + 6B b )d e + (35A b c - 10B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 15A b c - 20B b c )d e + (12A b c - 6B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R - 20A b d e + (41A b c + 8B b )d e + (- 9A b c - 20B b c)d e +--R + +--R 2 3 4 4 2 3 5 +--R - 3A b c d e + (6A b c - 3B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 3A b d e + 9A b c d e - 9A b c d e + 3A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 3 3 2 5 4 4 3 +--R ((27A b c - 21B b c )d e + (- 12A c + 6B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (27A b c - 21B b c )d e + (15A b c - 15B b c )d e +--R + +--R 5 4 5 +--R (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((27A b c - 21B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 4 5 3 2 4 4 +--R 15A b c e + (- 33A b c - 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (9A b c + 18B b c )d e + (21A b c - 18B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 15A b e + (- 18A b c - 6B b )d e + (- 24A b c + 12B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R 30A b c d e + (9A b c - 12B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 15A b d e + (- 33A b c - 6B b )d e + (9A b c + 18B b c)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (21A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 4 5 3 2 4 4 +--R - 30A b c e + (66A b c + 12B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 18A b c - 36B b c )d e + (12A b c - 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 30A b e + (26A b c + 12B b )d e + (70A b c - 20B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 30A b c - 40B b c )d e + (24A b c - 12B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 +--R - 40A b d e + (82A b c + 16B b )d e +--R + +--R 3 2 4 3 2 2 3 4 4 2 3 5 +--R (- 18A b c - 40B b c)d e - 6A b c d e + (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6A b d e + 18A b c d e - 18A b c d e + 6A b c d +--R * +--R +-+ +--R \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 4 5 3 2 4 4 +--R 15A b c e + (- 33A b c - 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (9A b c + 18B b c )d e + (21A b c - 18B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 15A b e + (- 18A b c - 6B b )d e + (- 24A b c + 12B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R 30A b c d e + (9A b c - 12B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 15A b d e + (- 33A b c - 6B b )d e + (9A b c + 18B b c)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (21A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 4 2 3 3 2 5 4 4 3 +--R ((54A b c - 42B b c )d e + (- 24A c + 12B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (54A b c - 42B b c )d e + (30A b c - 30B b c )d e +--R + +--R 5 4 5 +--R (- 24A c + 12B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((54A b c - 42B b c )d e + (- 24A b c + 12B b c )d )x +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 5 3 2 4 4 +--R - 30A b c e + (66A b c + 12B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 18A b c - 36B b c )d e + (12A b c - 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 30A b e + (26A b c + 12B b )d e + (70A b c - 20B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 30A b c - 40B b c )d e + (24A b c - 12B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 +--R - 40A b d e + (82A b c + 16B b )d e +--R + +--R 3 2 4 3 2 2 3 4 4 2 3 5 +--R (- 18A b c - 40B b c)d e - 6A b c d e + (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6A b d e + 18A b c d e - 18A b c d e + 6A b c d +--R * +--R +-+ +--R \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 4 2 3 3 2 5 4 4 3 +--R ((27A b c - 21B b c )d e + (- 12A c + 6B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (27A b c - 21B b c )d e + (15A b c - 15B b c )d e +--R + +--R 5 4 5 +--R (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((27A b c - 21B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 4 5 3 2 4 4 +--R 30A b c e + (- 66A b c - 12B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (18A b c + 36B b c )d e + (42A b c - 36B b c )d e +--R + +--R 5 4 4 +--R (- 24A c + 12B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 +--R 30A b e + (- 36A b c - 12B b )d e +--R + +--R 3 2 4 2 3 2 3 3 2 +--R (- 48A b c + 24B b c)d e + 60A b c d e +--R + +--R 4 2 3 4 5 4 5 +--R (18A b c - 24B b c )d e + (- 24A c + 12B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 +--R 30A b d e + (- 66A b c - 12B b )d e +--R + +--R 3 2 4 3 2 2 3 3 2 4 +--R (18A b c + 36B b c)d e + (42A b c - 36B b c )d e +--R + +--R 4 2 3 5 +--R (- 24A b c + 12B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 4 5 3 2 4 4 +--R - 30A b c e + (66A b c + 12B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 18A b c - 36B b c )d e + (12A b c - 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 30A b e + (26A b c + 12B b )d e + (70A b c - 20B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 30A b c - 40B b c )d e + (24A b c - 12B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 +--R - 40A b d e + (82A b c + 16B b )d e +--R + +--R 3 2 4 3 2 2 3 4 4 2 3 5 +--R (- 18A b c - 40B b c)d e - 6A b c d e + (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6A b d e + 18A b c d e - 18A b c d e + 6A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 4 5 3 2 4 4 +--R 15A b c e + (- 33A b c - 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (9A b c + 18B b c )d e + (21A b c - 18B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 15A b e + (- 18A b c - 6B b )d e + (- 24A b c + 12B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R 30A b c d e + (9A b c - 12B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 15A b d e + (- 33A b c - 6B b )d e + (9A b c + 18B b c)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (21A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 4 2 3 3 2 5 4 4 3 +--R ((27A b c - 21B b c )d e + (- 12A c + 6B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (27A b c - 21B b c )d e + (15A b c - 15B b c )d e +--R + +--R 5 4 5 +--R (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((27A b c - 21B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 5 3 2 4 4 +--R - 15A b c e + (33A b c + 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 9A b c - 18B b c )d e + (6A b c - 3B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 15A b e + (13A b c + 6B b )d e + (35A b c - 10B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 15A b c - 20B b c )d e + (12A b c - 6B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 +--R - 20A b d e + (41A b c + 8B b )d e +--R + +--R 3 2 4 3 2 2 3 4 4 2 3 5 +--R (- 9A b c - 20B b c)d e - 3A b c d e + (6A b c - 3B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 3A b d e + 9A b c d e - 9A b c d e + 3A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 816 + +--S 817 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 4 3 4 +-----------+ +--R ((9A b c - 7B b c )d e + (- 4A c + 2B b c )d )\|- b e + c d +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R 5A b e + (- 11A b c - 2B b )d e + (3A b c + 6B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (7A b c - 6B b c )d e + (- 4A c + 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 3 2 2 3 4 3 4 +-+ +-+ +--R ((18A b c - 14B b c )d e + (- 8A c + 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 10A b e + (22A b c + 4B b )d e + (- 6A b c - 12B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 14A b c + 12B b c )d e + (8A c - 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ +--R (2b d e - 6b c d e + 6b c d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 4 3 2 2 3 2 2 +--R 5A b e + (- 11A b c - 2B b )d e + (3A b c + 6B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (7A b c - 6B b c )d e + (- 4A c + 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 3 2 2 3 4 3 4 +-+ +-+ +--R ((18A b c - 14B b c )d e + (- 8A c + 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 10A b e + (22A b c + 4B b )d e + (- 6A b c - 12B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 14A b c + 12B b c )d e + (8A c - 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 3 4 3 4 +-----------+ +--R ((18A b c - 14B b c )d e + (- 8A c + 4B b c )d )\|- b e + c d +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ +--R (2b d e - 6b c d e + 6b c d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 1457 +t0:=(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1457 +r0:=-1/5*e*(10*A*c^2*d^2-b^2*e*(2*B*d-7*A*e)-5*b*c*d*(B*d+2*A*e))/_ + (b^2*d^2*(c*d-b*e)^2*(d+e*x)^(5/2))+c*(b*B*d-2*A*c*d+A*b*e)/_ + (b^2*d*(c*d-b*e)*(b+c*x)*(d+e*x)^(5/2))-A/(b*d*x*(b+c*x)*_ + (d+e*x)^(5/2))-1/3*e*(6*A*c^3*d^3-b^2*c*d*e*(6*B*d-17*A*e)+_ + b^3*e^2*(2*B*d-7*A*e)-3*b*c^2*d^2*(B*d+3*A*e))/(b^2*d^3*_ + (c*d-b*e)^3*(d+e*x)^(3/2))-(2*b*B*d-4*A*c*d-7*A*b*e)*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(9/2))-c^(7/2)*(4*A*c^2*d+9*b^2*B*e-_ + b*c*(2*B*d+11*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^3*(c*d-b*e)^(9/2))-e*(2*A*c^4*d^4-2*b^2*c^2*d^2*e*(6*B*d-13*A*e)-_ + b^4*e^3*(2*B*d-7*A*e)+8*b^3*c*d*e^2*(B*d-3*A*e)-b*c^3*d^3*_ + (B*d+4*A*e))/(b^2*d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 2 4 4 3 6 5 5 2 4 +--R ((165A b c - 135B b c )d e + (- 60A c + 30B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (165A b c - 135B b c )d e + (270A b c - 240B b c )d e +--R + +--R 6 5 6 +--R (- 120A c + 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (330A b c - 270B b c )d e + (45A b c - 75B b c )d e +--R + +--R 6 5 7 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((165A b c - 135B b c )d e + (- 60A b c + 30B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 7 4 2 5 6 +--R 105A b c e + (- 360A b c - 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (390A b c + 120B b c )d e + (- 60A b c - 180B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 135A b c + 120B b c )d e + (60A c - 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 105A b e + (- 150A b c - 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 330A b c + 60B b c)d e + (720A b c + 60B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 255A b c - 240B b c )d e + (- 210A b c + 210B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 210A b d e + (- 615A b c - 60B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (420A b c + 210B b c)d e + (270A b c - 240B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 60B b c )d e + (- 15A b c + 60B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 105A b d e + (- 360A b c - 30B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (390A b c + 120B b c)d e + (- 60A b c - 180B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 135A b c + 120B b c )d e + (60A b c - 30B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 7 4 2 5 6 +--R - 105A b c e + (360A b c + 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 390A b c - 120B b c )d e + (60A b c + 180B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 30A b c + 15B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 105A b e + (115A b c + 30B b )d e + (450A b c - 50B b c)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (- 850A b c - 100B b c )d e + (165A b c + 390B b c )d e +--R + +--R 5 2 4 5 2 +--R (- 90A b c + 45B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 245A b d e + (679A b c + 70B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 358A b c - 234B b c)d e + (- 436A b c + 218B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (135A b c + 216B b c )d e + (- 90A b c + 45B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 161A b d e + (537A b c + 46B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 556A b c - 172B b c)d e + (90A b c + 216B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 15A b c d e + (- 30A b c + 15B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 15A b d e + 60A b c d e - 90A b c d e + 60A b c d e - 15A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (15b c d e - 60b c d e + 90b c d e - 60b c d e + 15b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 15b d e - 30b c d e - 30b c d e + 120b c d e - 105b c d e +--R + +--R 3 5 9 +--R 30b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 30b d e - 105b c d e + 120b c d e - 30b c d e - 30b c d e +--R + +--R 3 5 10 +--R 15b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (15b d e - 60b c d e + 90b c d e - 60b c d e + 15b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 7 4 2 5 6 +--R 105A b c e + (- 360A b c - 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (390A b c + 120B b c )d e + (- 60A b c - 180B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 135A b c + 120B b c )d e + (60A c - 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 105A b e + (- 150A b c - 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 330A b c + 60B b c)d e + (720A b c + 60B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 255A b c - 240B b c )d e + (- 210A b c + 210B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 210A b d e + (- 615A b c - 60B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (420A b c + 210B b c)d e + (270A b c - 240B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 60B b c )d e + (- 15A b c + 60B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 105A b d e + (- 360A b c - 30B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (390A b c + 120B b c)d e + (- 60A b c - 180B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 135A b c + 120B b c )d e + (60A b c - 30B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 5 2 4 4 3 6 5 5 2 4 +--R ((165A b c - 135B b c )d e + (- 60A c + 30B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (165A b c - 135B b c )d e + (270A b c - 240B b c )d e +--R + +--R 6 5 6 +--R (- 120A c + 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (330A b c - 270B b c )d e + (45A b c - 75B b c )d e +--R + +--R 6 5 7 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((165A b c - 135B b c )d e + (- 60A b c + 30B b c )d )x +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 5 7 4 2 5 6 +--R - 210A b c e + (720A b c + 60B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 780A b c - 240B b c )d e + (120A b c + 360B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 60A b c + 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R - 210A b e + (230A b c + 60B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (900A b c - 100B b c)d e + (- 1700A b c - 200B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (330A b c + 780B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 490A b d e + (1358A b c + 140B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 716A b c - 468B b c)d e + (- 872A b c + 436B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (270A b c + 432B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 322A b d e + (1074A b c + 92B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 1112A b c - 344B b c)d e + (180A b c + 432B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 30A b c d e + (- 60A b c + 30B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 +--R - 30A b d e + 120A b c d e - 180A b c d e + 120A b c d e +--R + +--R 2 4 7 +--R - 30A b c d +--R * +--R +-+ +--R \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (30b c d e - 120b c d e + 180b c d e - 120b c d e + 30b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 30b d e - 60b c d e - 60b c d e + 240b c d e - 210b c d e +--R + +--R 3 5 9 +--R 60b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 60b d e - 210b c d e + 240b c d e - 60b c d e - 60b c d e +--R + +--R 3 5 10 +--R 30b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (30b d e - 120b c d e + 180b c d e - 120b c d e + 30b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 5 7 4 2 5 6 +--R 105A b c e + (- 360A b c - 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (390A b c + 120B b c )d e + (- 60A b c - 180B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 135A b c + 120B b c )d e + (60A c - 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 105A b e + (- 150A b c - 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 330A b c + 60B b c)d e + (720A b c + 60B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 255A b c - 240B b c )d e + (- 210A b c + 210B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 210A b d e + (- 615A b c - 60B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (420A b c + 210B b c)d e + (270A b c - 240B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 60B b c )d e + (- 15A b c + 60B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 105A b d e + (- 360A b c - 30B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (390A b c + 120B b c)d e + (- 60A b c - 180B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 135A b c + 120B b c )d e + (60A b c - 30B b c )d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 5 2 4 4 3 6 5 5 2 4 +--R ((- 330A b c + 270B b c )d e + (120A c - 60B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 330A b c + 270B b c )d e + (- 540A b c + 480B b c )d e +--R + +--R 6 5 6 +--R (240A c - 120B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 660A b c + 540B b c )d e + (- 90A b c + 150B b c )d e +--R + +--R 6 5 7 +--R (120A c - 60B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((- 330A b c + 270B b c )d e + (120A b c - 60B b c )d )x +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 5 7 4 2 5 6 +--R - 210A b c e + (720A b c + 60B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 780A b c - 240B b c )d e + (120A b c + 360B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 60A b c + 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R - 210A b e + (230A b c + 60B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (900A b c - 100B b c)d e + (- 1700A b c - 200B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (330A b c + 780B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 490A b d e + (1358A b c + 140B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 716A b c - 468B b c)d e + (- 872A b c + 436B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (270A b c + 432B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 322A b d e + (1074A b c + 92B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 1112A b c - 344B b c)d e + (180A b c + 432B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 30A b c d e + (- 60A b c + 30B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 +--R - 30A b d e + 120A b c d e - 180A b c d e + 120A b c d e +--R + +--R 2 4 7 +--R - 30A b c d +--R * +--R +-+ +--R \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (30b c d e - 120b c d e + 180b c d e - 120b c d e + 30b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 30b d e - 60b c d e - 60b c d e + 240b c d e - 210b c d e +--R + +--R 3 5 9 +--R 60b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 60b d e - 210b c d e + 240b c d e - 60b c d e - 60b c d e +--R + +--R 3 5 10 +--R 30b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (30b d e - 120b c d e + 180b c d e - 120b c d e + 30b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 5 2 4 4 3 6 5 5 2 4 +--R ((165A b c - 135B b c )d e + (- 60A c + 30B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (165A b c - 135B b c )d e + (270A b c - 240B b c )d e +--R + +--R 6 5 6 +--R (- 120A c + 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (330A b c - 270B b c )d e + (45A b c - 75B b c )d e +--R + +--R 6 5 7 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((165A b c - 135B b c )d e + (- 60A b c + 30B b c )d )x +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 5 7 4 2 5 6 +--R 210A b c e + (- 720A b c - 60B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (780A b c + 240B b c )d e + (- 120A b c - 360B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 270A b c + 240B b c )d e + (120A c - 60B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 210A b e + (- 300A b c - 60B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 660A b c + 120B b c)d e + (1440A b c + 120B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 510A b c - 480B b c )d e + (- 420A b c + 420B b c )d e +--R + +--R 6 5 6 +--R (240A c - 120B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 420A b d e + (- 1230A b c - 120B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (840A b c + 420B b c)d e + (540A b c - 480B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 660A b c + 120B b c )d e + (- 30A b c + 120B b c )d e +--R + +--R 6 5 7 +--R (120A c - 60B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 210A b d e + (- 720A b c - 60B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (780A b c + 240B b c)d e + (- 120A b c - 360B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 270A b c + 240B b c )d e + (120A b c - 60B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 5 7 4 2 5 6 +--R - 210A b c e + (720A b c + 60B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 780A b c - 240B b c )d e + (120A b c + 360B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 60A b c + 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R - 210A b e + (230A b c + 60B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (900A b c - 100B b c)d e + (- 1700A b c - 200B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (330A b c + 780B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 490A b d e + (1358A b c + 140B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 716A b c - 468B b c)d e + (- 872A b c + 436B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (270A b c + 432B b c )d e + (- 180A b c + 90B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 322A b d e + (1074A b c + 92B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 1112A b c - 344B b c)d e + (180A b c + 432B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 30A b c d e + (- 60A b c + 30B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 +--R - 30A b d e + 120A b c d e - 180A b c d e + 120A b c d e +--R + +--R 2 4 7 +--R - 30A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (30b c d e - 120b c d e + 180b c d e - 120b c d e + 30b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 30b d e - 60b c d e - 60b c d e + 240b c d e - 210b c d e +--R + +--R 3 5 9 +--R 60b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 60b d e - 210b c d e + 240b c d e - 60b c d e - 60b c d e +--R + +--R 3 5 10 +--R 30b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (30b d e - 120b c d e + 180b c d e - 120b c d e + 30b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 5 7 4 2 5 6 +--R 105A b c e + (- 360A b c - 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (390A b c + 120B b c )d e + (- 60A b c - 180B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 135A b c + 120B b c )d e + (60A c - 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 105A b e + (- 150A b c - 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 330A b c + 60B b c)d e + (720A b c + 60B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 255A b c - 240B b c )d e + (- 210A b c + 210B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 210A b d e + (- 615A b c - 60B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (420A b c + 210B b c)d e + (270A b c - 240B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 60B b c )d e + (- 15A b c + 60B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 105A b d e + (- 360A b c - 30B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (390A b c + 120B b c)d e + (- 60A b c - 180B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 135A b c + 120B b c )d e + (60A b c - 30B b c )d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 5 2 4 4 3 6 5 5 2 4 +--R ((- 165A b c + 135B b c )d e + (60A c - 30B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 165A b c + 135B b c )d e + (- 270A b c + 240B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 270B b c )d e + (- 45A b c + 75B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((- 165A b c + 135B b c )d e + (60A b c - 30B b c )d )x +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 5 7 4 2 5 6 +--R - 105A b c e + (360A b c + 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 390A b c - 120B b c )d e + (60A b c + 180B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 30A b c + 15B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R - 105A b e + (115A b c + 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (450A b c - 50B b c)d e + (- 850A b c - 100B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (165A b c + 390B b c )d e + (- 90A b c + 45B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 245A b d e + (679A b c + 70B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 358A b c - 234B b c)d e + (- 436A b c + 218B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (135A b c + 216B b c )d e + (- 90A b c + 45B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 161A b d e + (537A b c + 46B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 556A b c - 172B b c)d e + (90A b c + 216B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 15A b c d e + (- 30A b c + 15B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 15A b d e + 60A b c d e - 90A b c d e + 60A b c d e - 15A b c d +--R * +--R +---+ +--R \|- d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (15b c d e - 60b c d e + 90b c d e - 60b c d e + 15b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 15b d e - 30b c d e - 30b c d e + 120b c d e - 105b c d e +--R + +--R 3 5 9 +--R 30b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 30b d e - 105b c d e + 120b c d e - 30b c d e - 30b c d e +--R + +--R 3 5 10 +--R 15b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (15b d e - 60b c d e + 90b c d e - 60b c d e + 15b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 823 + +--S 824 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 5 4 5 4 3 2 4 2 3 +--R 7A b e + (- 24A b c - 2B b )d e + (26A b c + 8B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 4A b c - 12B b c )d e + (- 9A b c + 8B b c )d e +--R + +--R 5 4 5 +--R (4A c - 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 4 2 3 4 5 4 5 +-----------+ +--R ((11A b c - 9B b c )d e + (- 4A c + 2B b c )d )\|- b e + c d +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 2 3 4 5 4 5 +-+ +-+ +--R ((- 22A b c + 18B b c )d e + (8A c - 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 14A b e + (48A b c + 4B b )d e + (- 52A b c - 16B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (8A b c + 24B b c )d e + (18A b c - 16B b c )d e +--R + +--R 5 4 5 +--R (- 8A c + 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 +-----------+ +-+ +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 5 4 5 4 3 2 4 2 3 +--R 7A b e + (- 24A b c - 2B b )d e + (26A b c + 8B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 4A b c - 12B b c )d e + (- 9A b c + 8B b c )d e +--R + +--R 5 4 5 +--R (4A c - 2B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 4 2 3 4 5 4 5 +-+ +-+ +--R ((- 22A b c + 18B b c )d e + (8A c - 4B b c )d )\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 14A b e + (48A b c + 4B b )d e + (- 52A b c - 16B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (8A b c + 24B b c )d e + (18A b c - 16B b c )d e +--R + +--R 5 4 5 +--R (- 8A c + 4B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 3 4 5 4 5 +-----------+ +--R ((- 22A b c + 18B b c )d e + (8A c - 4B b c )d )\|- b e + c d +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 +-----------+ +-+ +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 827 + +)clear all + +--S 828 of 1457 +t0:=(A+B*x)*(d+e*x)^(9/2)/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1457 +r0:=1/4*(c*d-b*e)*(24*A*c^3*d^2+5*b^3*B*e^2+b^2*c*e*(3*B*d-A*e)-_ + 12*b*c^2*d*(B*d+2*A*e))*(d+e*x)^(3/2)/(b^4*c^2*(b+c*x))-_ + 1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+13*A*b*c*e)*_ + (d+e*x)^(5/2)/(b^3*c*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+9*A*b*e)*_ + (d+e*x)^(7/2)/(b^2*x*(b+c*x)^2)-1/2*A*(d+e*x)^(9/2)/(b*x^2*_ + (b+c*x)^2)-3/4*d^(5/2)*(16*A*c^2*d^2+3*b^2*e*(4*B*d+7*A*e)-_ + 4*b*c*d*(2*B*d+9*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/b^5+_ + 3/4*(c*d-b*e)^(5/2)*(16*A*c^3*d^2-5*b^3*B*e^2-4*b*c^2*d*_ + (2*B*d-A*e)-b^2*c*e*(8*B*d-A*e))*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b^5*c^(7/2))-3/4*e*(8*A*c^4*d^3-5*b^4*B*e^3+_ + b^3*c*e^2*(2*B*d+A*e)+b^2*c^2*d*e*(3*B*d+2*A*e)-4*b*c^3*d^2*_ + (B*d+3*A*e))*sqrt(d+e*x)/(b^4*c^3) +--R +--R +--R (2) +--R 4 3 5 2 4 3 4 4 3 3 +--R (3A b c - 15B b c )e + (6A b c + 6B b c )d e +--R + +--R 2 5 3 4 2 2 6 2 5 3 +--R (27A b c + 9B b c )d e + (- 84A b c + 24B b c )d e +--R + +--R 7 6 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (6A b c - 30B b c)e + (12A b c + 12B b c )d e +--R + +--R 3 4 4 3 2 2 2 5 3 4 3 +--R (54A b c + 18B b c )d e + (- 168A b c + 48B b c )d e +--R + +--R 6 2 5 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (3A b c - 15B b )e + (6A b c + 6B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (27A b c + 9B b c )d e + (- 84A b c + 24B b c )d e +--R + +--R 2 5 3 4 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 5 2 2 6 2 5 3 +--R - 63A b c d e + (108A b c - 36B b c )d e +--R + +--R 7 6 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 2 5 3 4 3 +--R - 126A b c d e + (216A b c - 72B b c )d e +--R + +--R 6 2 5 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 2 3 4 4 3 3 +--R - 63A b c d e + (108A b c - 36B b c )d e +--R + +--R 2 5 3 4 4 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 2 4 4 +--R 8B b c e x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (- 5A b c + 25B b c)e + (3A b c - 19B b c )d e +--R + +--R 3 4 4 3 2 2 2 5 3 4 3 +--R (21A b c + 3B b c )d e + (- 48A b c + 15B b c )d e +--R + +--R 6 2 5 4 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- 3A b c + 15B b )e + (- 5A b c - 11B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (33A b c - 9B b c )d e + (- 73A b c + 23B b c )d e +--R + +--R 2 5 3 4 4 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 3 4 4 3 4 +--R (- 17A b c d e + (8A b c - 4B b c )d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 5 4 6 4 3 7 3 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1457 +--a0:=integrate(t0,x) +--E 830 + +--S 831 of 1457 +--m0:=a0-r0 +--E 831 + +--S 832 of 1457 +--d0:=D(m0,x) +--E 832 + +)clear all + +--S 833 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1457 +r0:=-1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+11*A*b*c*e)*_ + (d+e*x)^(3/2)/(b^3*c*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+7*A*b*e)*_ + (d+e*x)^(5/2)/(b^2*x*(b+c*x)^2)-1/2*A*(d+e*x)^(7/2)/(b*x^2*_ + (b+c*x)^2)-1/4*d^(3/2)*(48*A*c^2*d^2+7*b^2*e*(4*B*d+5*A*e)-_ + 12*b*c*d*(2*B*d+7*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/b^5+1/4*_ + (c*d-b*e)^(3/2)*(48*A*c^3*d^2-3*b^3*B*e^2-12*b*c^2*d*(2*B*d+A*e)-_ + b^2*c*e*(8*B*d+A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^5*c^(5/2))+1/4*(c*d-b*e)*(24*A*c^3*d^2+3*b^3*B*e^2+b^2*c*e*_ + (5*B*d+A*e)-12*b*c^2*d*(B*d+2*A*e))*sqrt(d+e*x)/(b^4*c^2*(b+c*x)) +--R +--R +--R (2) +--R 3 3 4 2 3 2 4 3 3 2 +--R (A b c + 3B b c )e + (11A b c + 5B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c + 6B b c)e + (22A b c + 10B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A b c + 16B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 4 2 5 2 4 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 6 5 3 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 70A b c d e + (168A b c - 56B b c )d e +--R + +--R 5 2 4 3 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 2 4 3 3 3 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (A b c - 5B b c)e + (10A b c + 2B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 36A b c + 11B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - 3B b )e + (16A b c - 4B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 55A b c + 17B b c )d e + (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 13A b c d e + (8A b c - 4B b c )d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 4 2 3 2 4 3 3 2 +--R (A b c + 3B b c )e + (11A b c + 5B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c + 6B b c)e + (22A b c + 10B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A b c + 16B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 4 2 5 2 4 2 +--R 35A b c d e + (- 84A b c + 28B b c )d e +--R + +--R 6 5 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R 70A b c d e + (- 168A b c + 56B b c )d e +--R + +--R 5 2 4 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R 35A b c d e + (- 84A b c + 28B b c )d e +--R + +--R 2 4 3 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c - 10B b c)e + (20A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 22B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 2A b c - 6B b )e + (32A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 34B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 26A b c d e + (16A b c - 8B b c )d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 4 2 5 2 4 2 +--R 35A b c d e + (- 84A b c + 28B b c )d e +--R + +--R 6 5 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R 70A b c d e + (- 168A b c + 56B b c )d e +--R + +--R 5 2 4 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R 35A b c d e + (- 84A b c + 28B b c )d e +--R + +--R 2 4 3 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (2A b c + 6B b c )e + (22A b c + 10B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 120A b c + 32B b c )d e + (96A c - 48B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (4A b c + 12B b c)e + (44A b c + 20B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 240A b c + 64B b c )d e + (192A b c - 96B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (2A b c + 6B b )e + (22A b c + 10B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c - 10B b c)e + (20A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 22B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 2A b c - 6B b )e + (32A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 34B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 26A b c d e + (16A b c - 8B b c )d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 3 3 4 2 3 2 4 3 3 2 +--R (A b c + 3B b c )e + (11A b c + 5B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c + 6B b c)e + (22A b c + 10B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A b c + 16B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 4 2 5 2 4 2 +--R - 70A b c d e + (168A b c - 56B b c )d e +--R + +--R 6 5 3 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 140A b c d e + (336A b c - 112B b c )d e +--R + +--R 5 2 4 3 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R - 70A b c d e + (168A b c - 56B b c )d e +--R + +--R 2 4 3 3 3 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c - 10B b c)e + (20A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 22B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 2A b c - 6B b )e + (32A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 34B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 26A b c d e + (16A b c - 8B b c )d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 4 2 5 2 4 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 6 5 3 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 70A b c d e + (168A b c - 56B b c )d e +--R + +--R 5 2 4 3 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 2 4 3 3 3 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (A b c + 3B b c )e + (11A b c + 5B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c + 6B b c)e + (22A b c + 10B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A b c + 16B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (A b c - 5B b c)e + (10A b c + 2B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 36A b c + 11B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - 3B b )e + (16A b c - 4B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 55A b c + 17B b c )d e + (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 13A b c d e + (8A b c - 4B b c )d )x - 2A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 4b c x + 8b c x + 4b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 835 + +--S 836 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 2 2 3 2 2 2 4 3 3 +-+ +--R (35A b c d e + (- 84A b c + 28B b c )d e + (48A c - 24B b c )d )\|c +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 2A b c - 6B b )e + (- 22A b c - 10B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (120A b c - 32B b c )d e + (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 2 2 2 4 3 3 +--R (70A b c d e + (- 168A b c + 56B b c )d e + (96A c - 48B b c )d ) +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 2 +-+ +--R 8b c \|c +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 3 2 2 2 4 3 3 +-+ +--R (35A b c d e + (- 84A b c + 28B b c )d e + (48A c - 24B b c )d )\|c +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 2A b c - 6B b )e + (- 22A b c - 10B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (120A b c - 32B b c )d e + (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 2 2 2 4 3 3 +--R (70A b c d e + (- 168A b c + 56B b c )d e + (96A c - 48B b c )d ) +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 4 3 2 2 3 2 +--R (2A b c + 6B b )e + (22A b c + 10B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 120A b c + 32B b c )d e + (96A c - 48B b c )d +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 5 2 +-+ +--R 8b c \|c +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 839 + +)clear all + +--S 840 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1457 +r0:=-1/4*(4*b*B*d-8*A*c*d+5*A*b*e)*(d+e*x)^(3/2)/(b^2*x*(b+c*x)^2)-_ + 1/2*A*(d+e*x)^(5/2)/(b*x^2*(b+c*x)^2)-1/4*(48*A*c^2*d^2+5*b^2*e*_ + (4*B*d+3*A*e)-12*b*c*d*(2*B*d+5*A*e))*atanh(sqrt(d+e*x)/sqrt(d))*_ + sqrt(d)/b^5+1/4*(48*A*c^3*d^2+b^3*B*e^2-12*b*c^2*d*(2*B*d+3*A*e)+_ + b^2*c*e*(8*B*d+3*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*_ + sqrt(c*d-b*e)/(b^5*c^(3/2))-1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-_ + 2*b^2*B*e+9*A*b*c*e)*sqrt(d+e*x)/(b^3*c*(b+c*x)^2)+1/4*_ + (24*A*c^3*d^2+b^3*B*e^2-12*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ + (7*B*d+3*A*e))*sqrt(d+e*x)/(b^4*c*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 +--R (3A b c + B b c )e + (- 36A b c + 8B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 72A b c + 16B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (3A b c + B b )e + (- 36A b c + 8B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (- 15A b c e + (60A b c - 20B b c )d e + (- 48A c + 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 +--R - 30A b c e + (120A b c - 40B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 15A b c e + (60A b c - 20B b c)d e + (- 48A b c + 24B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 4 2 2 3 3 2 +--R (3A b c + B b c)e + (- 24A b c + 7B b c )d e +--R + +--R 4 2 3 2 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (5A b c - B b )e + (- 37A b c + 11B b c)d e +--R + +--R 2 3 3 2 2 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 9A b c d e + (8A b c - 4B b c)d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 4 2 3 +--R (3A b c + B b c )e + (- 36A b c + 8B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 72A b c + 16B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (3A b c + B b )e + (- 36A b c + 8B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (15A b c e + (- 60A b c + 20B b c )d e + (48A c - 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 +--R 30A b c e + (- 120A b c + 40B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (15A b c e + (- 60A b c + 20B b c)d e + (48A b c - 24B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 48A b c + 14B b c )d e +--R + +--R 4 2 3 2 +--R (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (10A b c - 2B b )e + (- 74A b c + 22B b c)d e +--R + +--R 2 3 3 2 2 +--R (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 18A b c d e + (16A b c - 8B b c)d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 3 2 4 2 3 5 4 2 4 +--R (15A b c e + (- 60A b c + 20B b c )d e + (48A c - 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 +--R 30A b c e + (- 120A b c + 40B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (15A b c e + (- 60A b c + 20B b c)d e + (48A b c - 24B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 3 3 2 2 4 2 3 +--R (6A b c + 2B b c )e + (- 72A b c + 16B b c )d e +--R + +--R 5 4 2 +--R (96A c - 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (12A b c + 4B b c)e + (- 144A b c + 32B b c )d e +--R + +--R 4 2 3 2 +--R (192A b c - 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (6A b c + 2B b )e + (- 72A b c + 16B b c)d e +--R + +--R 2 3 3 2 2 +--R (96A b c - 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 48A b c + 14B b c )d e +--R + +--R 4 2 3 2 +--R (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (10A b c - 2B b )e + (- 74A b c + 22B b c)d e +--R + +--R 2 3 3 2 2 +--R (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 18A b c d e + (16A b c - 8B b c)d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 3 3 2 2 4 2 3 +--R (3A b c + B b c )e + (- 36A b c + 8B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 72A b c + 16B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (3A b c + B b )e + (- 36A b c + 8B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 4 2 3 +--R - 30A b c e + (120A b c - 40B b c )d e +--R + +--R 5 4 2 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 3 3 2 +--R - 60A b c e + (240A b c - 80B b c )d e +--R + +--R 4 2 3 2 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 30A b c e + (120A b c - 40B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 48A b c + 14B b c )d e +--R + +--R 4 2 3 2 +--R (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (10A b c - 2B b )e + (- 74A b c + 22B b c)d e +--R + +--R 2 3 3 2 2 +--R (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 18A b c d e + (16A b c - 8B b c)d )x - 4A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 3 2 4 2 3 +--R - 15A b c e + (60A b c - 20B b c )d e +--R + +--R 5 4 2 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 3 3 2 +--R - 30A b c e + (120A b c - 40B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 15A b c e + (60A b c - 20B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 3 3 2 2 4 2 3 +--R (3A b c + B b c )e + (- 36A b c + 8B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 72A b c + 16B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (3A b c + B b )e + (- 36A b c + 8B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 4 2 2 3 3 2 +--R (3A b c + B b c)e + (- 24A b c + 7B b c )d e +--R + +--R 4 2 3 2 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (5A b c - B b )e + (- 37A b c + 11B b c)d e +--R + +--R 2 3 3 2 2 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 9A b c d e + (8A b c - 4B b c)d )x - 2A b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 4b c x + 8b c x + 4b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 842 + +--S 843 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 2 2 +--R ((3A b c + B b )e + (- 36A b c + 8B b c)d e + (48A c - 24B b c )d ) +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 2 2 2 3 2 2 +-+ +--R (15A b c e + (- 60A b c + 20B b c)d e + (48A c - 24B b c )d )\|c +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 +--R (- 6A b c - 2B b )e + (72A b c - 16B b c)d e +--R + +--R 3 2 2 +--R (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 3 2 2 +-+ +--R (30A b c e + (- 120A b c + 40B b c)d e + (96A c - 48B b c )d )\|c +--R * +--R +-------+ +--R +-+ \|e x + d +--R \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 +-+ +--R 8b c\|c +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 3 2 2 +-+ +--R (15A b c e + (- 60A b c + 20B b c)d e + (48A c - 24B b c )d )\|c +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 2 +--R (- 6A b c - 2B b )e + (72A b c - 16B b c)d e +--R + +--R 3 2 2 +--R (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 3 2 2 +-+ +--R (30A b c e + (- 120A b c + 40B b c)d e + (96A c - 48B b c )d )\|c +--R * +--R +-------+ +--R +-+ \|e x + d +--R \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 +--R (6A b c + 2B b )e + (- 72A b c + 16B b c)d e +--R + +--R 3 2 2 +--R (96A c - 48B b c )d +--R * +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R \|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 5 +-+ +--R 8b c\|c +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 846 + +)clear all + +--S 847 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1457 +r0:=-1/2*A*(d+e*x)^(3/2)/(b*x^2*(b+c*x)^2)-3/4*(16*A*c^2*d^2+b^2*e*_ + (4*B*d+A*e)-4*b*c*d*(2*B*d+3*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^5*sqrt(d))+3/4*(16*A*c^3*d^2-b^3*B*e^2-4*b*c^2*d*(2*B*d+5*A*e)+_ + b^2*c*e*(8*B*d+5*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^5*sqrt(c)*sqrt(c*d-b*e))-1/4*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+_ + 7*A*b*c*e)*sqrt(d+e*x)/(b^3*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+3*A*b*e)*_ + sqrt(d+e*x)/(b^2*x*(b+c*x)^2)+3/4*(8*A*c^2*d+b^2*B*e-4*b*c*(B*d+A*e))*_ + sqrt(d+e*x)/(b^4*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 +--R (15A b c - 3B b c )e + (- 60A b c + 24B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (30A b c - 6B b c)e + (- 120A b c + 48B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (15A b c - 3B b )e + (- 60A b c + 24B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 2 2 4 3 2 4 +--R (- 3A b c e + (36A b c - 12B b c )d e + (- 48A c + 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 2 2 3 +--R (- 6A b c e + (72A b c - 24B b c)d e + (- 96A b c + 48B b c )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- 3A b e + (36A b c - 12B b )d e + (- 48A b c + 24B b c)d )x +--R * +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 3B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 19A b c + 5B b )e + (36A b c - 18B b c)d)x +--R + +--R 4 3 4 4 +--R (- 5A b e + (8A b c - 4B b )d)x - 2A b d +--R * +--R +-----------+ +-+ +-+ +-------+ +--R \|- b e + c d \|c \|d \|e x + d +--R / +--R 5 2 4 6 3 7 2 +-----------+ +-+ +-+ +--R (4b c x + 8b c x + 4b x )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 4 2 3 +--R (- 15A b c + 3B b c )e + (60A b c - 24B b c )d e +--R + +--R 5 4 2 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 30A b c + 6B b c)e + (120A b c - 48B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 15A b c + 3B b )e + (60A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +--R \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2b c e - 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(----------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 3 2 2 4 3 2 4 +--R (3A b c e + (- 36A b c + 12B b c )d e + (48A c - 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 2 2 3 +--R (6A b c e + (- 72A b c + 24B b c)d e + (96A b c - 48B b c )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (3A b e + (- 36A b c + 12B b )d e + (48A b c - 24B b c)d )x +--R * +--R +-------------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R \|- b c e + c d log(-------------------------------) +--R x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 24A b c + 6B b c)e + (48A b c - 24B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 38A b c + 10B b )e + (72A b c - 36B b c)d)x +--R + +--R 4 3 4 4 +--R (- 10A b e + (16A b c - 8B b )d)x - 4A b d +--R * +--R +-------------+ +--R | 2 +-+ +-------+ +--R \|- b c e + c d \|d \|e x + d +--R / +--R +-------------+ +--R 5 2 4 6 3 7 2 | 2 +-+ +--R (8b c x + 16b c x + 8b x )\|- b c e + c d \|d +--R , +--R +--R 2 2 2 3 2 2 4 3 2 4 +--R (3A b c e + (- 36A b c + 12B b c )d e + (48A c - 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 2 2 3 +--R (6A b c e + (- 72A b c + 24B b c)d e + (96A b c - 48B b c )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (3A b e + (- 36A b c + 12B b )d e + (48A b c - 24B b c)d )x +--R * +--R +-----------+ +-------+ +-+ +--R | 2 - 2d\|e x + d + (e x + 2d)\|d +--R \|b c e - c d log(-------------------------------) +--R x +--R + +--R 2 3 3 2 2 4 2 3 +--R (- 30A b c + 6B b c )e + (120A b c - 48B b c )d e +--R + +--R 5 4 2 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 60A b c + 12B b c)e + (240A b c - 96B b c )d e +--R + +--R 4 2 3 2 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 30A b c + 6B b )e + (120A b c - 48B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-+ \|b c e - c d \|e x + d +--R \|d atan(------------------------) +--R b e - c d +--R + +--R 2 2 3 3 2 2 3 +--R ((- 24A b c + 6B b c)e + (48A b c - 24B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 38A b c + 10B b )e + (72A b c - 36B b c)d)x +--R + +--R 4 3 4 4 +--R (- 10A b e + (16A b c - 8B b )d)x - 4A b d +--R * +--R +-----------+ +--R +-+ | 2 +-------+ +--R \|d \|b c e - c d \|e x + d +--R / +--R +-----------+ +--R 5 2 4 6 3 7 2 +-+ | 2 +--R (8b c x + 16b c x + 8b x )\|d \|b c e - c d +--R , +--R +--R 2 3 3 2 2 4 2 3 +--R (- 15A b c + 3B b c )e + (60A b c - 24B b c )d e +--R + +--R 5 4 2 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 30A b c + 6B b c)e + (120A b c - 48B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 15A b c + 3B b )e + (60A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---+ +--R \|- d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2b c e - 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(----------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 3 2 2 +--R - 6A b c e + (72A b c - 24B b c )d e +--R + +--R 4 3 2 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 3 +--R - 12A b c e + (144A b c - 48B b c)d e +--R + +--R 3 2 2 2 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- 6A b e + (72A b c - 24B b )d e + (- 96A b c + 48B b c)d )x +--R * +--R +-------------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R \|- b c e + c d atan(----------------) +--R d +--R + +--R 2 2 3 3 2 2 3 +--R ((- 24A b c + 6B b c)e + (48A b c - 24B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 38A b c + 10B b )e + (72A b c - 36B b c)d)x +--R + +--R 4 3 4 4 +--R (- 10A b e + (16A b c - 8B b )d)x - 4A b d +--R * +--R +-------------+ +--R | 2 +---+ +-------+ +--R \|- b c e + c d \|- d \|e x + d +--R / +--R +-------------+ +--R 5 2 4 6 3 7 2 | 2 +---+ +--R (8b c x + 16b c x + 8b x )\|- b c e + c d \|- d +--R , +--R +--R 2 3 3 2 2 4 2 3 +--R (- 15A b c + 3B b c )e + (60A b c - 24B b c )d e +--R + +--R 5 4 2 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 30A b c + 6B b c)e + (120A b c - 48B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 15A b c + 3B b )e + (60A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R | 2 +-------+ +--R +---+ \|b c e - c d \|e x + d +--R \|- d atan(------------------------) +--R b e - c d +--R + +--R 2 2 2 3 2 2 +--R - 3A b c e + (36A b c - 12B b c )d e +--R + +--R 4 3 2 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 3 +--R - 6A b c e + (72A b c - 24B b c)d e +--R + +--R 3 2 2 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- 3A b e + (36A b c - 12B b )d e + (- 48A b c + 24B b c)d )x +--R * +--R +-----------+ +---+ +-------+ +--R | 2 \|- d \|e x + d +--R \|b c e - c d atan(----------------) +--R d +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 3B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 19A b c + 5B b )e + (36A b c - 18B b c)d)x +--R + +--R 4 3 4 4 +--R (- 5A b e + (8A b c - 4B b )d)x - 2A b d +--R * +--R +-----------+ +--R +---+ | 2 +-------+ +--R \|- d \|b c e - c d \|e x + d +--R / +--R +-----------+ +--R 5 2 4 6 3 7 2 +---+ | 2 +--R (4b c x + 8b c x + 4b x )\|- d \|b c e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 849 + +--S 850 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 +--R (- 15A b c + 3B b )e + (60A b c - 24B b c)d e +--R + +--R 3 2 2 +--R (- 48A c + 24B b c )d +--R * +--R +-----------+ +-+ +-+ +--R \|- b e + c d \|c \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2b c e - 2c d)\|e x + d + (c e x - b e + 2c d)\|- b c e + c d +--R log(----------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 2 2 +--R (3A b e + (- 36A b c + 12B b )d e + (48A c - 24B b c)d ) +--R * +--R +-------------+ +-------+ +-+ +--R | 2 +-----------+ +-+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b c e + c d \|- b e + c d \|c log(-------------------------------) +--R x +--R + +--R 2 3 2 2 2 +--R (- 30A b c + 6B b )e + (120A b c - 48B b c)d e +--R + +--R 3 2 2 +--R (- 96A c + 48B b c )d +--R * +--R +-------------+ +-+ +-------+ +--R | 2 +-+ \|c \|e x + d +--R \|- b c e + c d \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 2 +--R (6A b e + (- 72A b c + 24B b )d e + (96A c - 48B b c)d ) +--R * +--R +-------------+ +-------+ +--R | 2 +-----------+ +-+ \|e x + d +--R \|- b c e + c d \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R / +--R +-------------+ +--R 5 | 2 +-----------+ +-+ +-+ +--R 8b \|- b c e + c d \|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +--R (3A b e + (- 36A b c + 12B b )d e + (48A c - 24B b c)d ) +--R * +--R +-----------+ +-------+ +-+ +--R +-----------+ +-+ | 2 - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d \|c \|b c e - c d log(-------------------------------) +--R x +--R + +--R 2 3 2 2 2 +--R (- 30A b c + 6B b )e + (120A b c - 48B b c)d e +--R + +--R 3 2 2 +--R (- 96A c + 48B b c )d +--R * +--R +-----------+ +-+ +-------+ +--R +-+ | 2 \|c \|e x + d +--R \|d \|b c e - c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 2 +--R (6A b e + (- 72A b c + 24B b )d e + (96A c - 48B b c)d ) +--R * +--R +-----------+ +-------+ +--R +-----------+ +-+ | 2 \|e x + d +--R \|- b e + c d \|c \|b c e - c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 +--R (- 30A b c + 6B b )e + (120A b c - 48B b c)d e +--R + +--R 3 2 2 +--R (- 96A c + 48B b c )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ +-+ \|b c e - c d \|e x + d +--R \|- b e + c d \|c \|d atan(------------------------) +--R b e - c d +--R / +--R +-----------+ +--R 5 +-----------+ +-+ +-+ | 2 +--R 8b \|- b e + c d \|c \|d \|b c e - c d +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 853 + +)clear all + +--S 854 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1457 +r0:=-1/4*(48*A*c^2*d^2+b^2*e*(4*B*d-A*e)-12*b*c*d*(2*B*d+A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(3/2))+1/4*(48*A*c^3*d^2-_ + 15*b^3*B*e^2-12*b*c^2*d*(2*B*d+7*A*e)+5*b^2*c*e*(8*B*d+7*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b^5*_ + (c*d-b*e)^(3/2))-1/4*c*(6*b*B*d-12*A*c*d+A*b*e)*sqrt(d+e*x)/_ + (b^3*d*(b+c*x)^2)-1/2*A*sqrt(d+e*x)/(b*x^2*(b+c*x)^2)-_ + 1/4*(4*b*B*d-8*A*c*d+A*b*e)*sqrt(d+e*x)/(b^2*d*x*(b+c*x)^2)+_ + 1/4*c*(24*A*c^2*d^2+b^2*e*(11*B*d+A*e)-12*b*c*d*(B*d+2*A*e))*_ + sqrt(d+e*x)/(b^4*d*(c*d-b*e)*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 2 +--R (- 35A b c + 15B b c )d e + (84A b c - 40B b c )d e +--R + +--R 5 4 3 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (- 70A b c + 30B b c)d e + (168A b c - 80B b c )d e +--R + +--R 4 2 3 3 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (- 35A b c + 15B b )d e + (84A b c - 40B b c)d e +--R + +--R 2 3 3 2 3 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 2 3 2 3 3 2 2 4 2 3 2 +--R A b c e + (11A b c - 4B b c )d e + (- 60A b c + 28B b c )d e +--R + +--R 5 4 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 2 3 3 2 2 +--R 2A b c e + (22A b c - 8B b c)d e + (- 120A b c + 56B b c )d e +--R + +--R 4 2 3 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- A b c e + (24A b c - 11B b c )d e + (- 24A b c + 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 2A b c e + (37A b c - 17B b c)d e + (- 36A b c + 18B b c )d )x +--R + +--R 5 2 4 5 3 2 4 2 5 +--R (- A b e + (9A b c - 4B b )d e + (- 8A b c + 4B b c)d )x - 2A b d e +--R + +--R 4 2 +--R 2A b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 8 7 2 2 +--R ((4b c d e - 4b c d )x + (8b c d e - 8b c d )x + (4b d e - 4b c d )x ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 4 2 3 2 +--R (35A b c - 15B b c )d e + (- 84A b c + 40B b c )d e +--R + +--R 5 4 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (70A b c - 30B b c)d e + (- 168A b c + 80B b c )d e +--R + +--R 4 2 3 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (35A b c - 15B b )d e + (- 84A b c + 40B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 2 3 2 3 3 2 2 +--R A b c e + (11A b c - 4B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 60A b c + 28B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 +--R 2A b c e + (22A b c - 8B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 120A b c + 56B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 3 2 2 2 3 3 2 +--R - 2A b c e + (48A b c - 22B b c )d e +--R + +--R 4 2 3 2 +--R (- 48A b c + 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 4A b c e + (74A b c - 34B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 72A b c + 36B b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R (- 2A b e + (18A b c - 8B b )d e + (- 16A b c + 8B b c)d )x +--R + +--R 5 4 2 +--R - 4A b d e + 4A b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (8b c d e - 8b c d )x + (16b c d e - 16b c d )x +--R + +--R 8 7 2 2 +--R (8b d e - 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 3 2 3 2 3 3 2 2 +--R A b c e + (11A b c - 4B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 60A b c + 28B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 +--R 2A b c e + (22A b c - 8B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 120A b c + 56B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 3 3 2 2 4 2 3 2 +--R (70A b c - 30B b c )d e + (- 168A b c + 80B b c )d e +--R + +--R 5 4 3 +--R (96A c - 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (140A b c - 60B b c)d e + (- 336A b c + 160B b c )d e +--R + +--R 4 2 3 3 +--R (192A b c - 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (70A b c - 30B b )d e + (- 168A b c + 80B b c)d e +--R + +--R 2 3 3 2 3 +--R (96A b c - 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 2 2 2 3 3 2 +--R - 2A b c e + (48A b c - 22B b c )d e +--R + +--R 4 2 3 2 +--R (- 48A b c + 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 4A b c e + (74A b c - 34B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 72A b c + 36B b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R (- 2A b e + (18A b c - 8B b )d e + (- 16A b c + 8B b c)d )x +--R + +--R 5 4 2 +--R - 4A b d e + 4A b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (8b c d e - 8b c d )x + (16b c d e - 16b c d )x +--R + +--R 8 7 2 2 +--R (8b d e - 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 2 3 3 2 2 4 2 3 2 +--R (35A b c - 15B b c )d e + (- 84A b c + 40B b c )d e +--R + +--R 5 4 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (70A b c - 30B b c)d e + (- 168A b c + 80B b c )d e +--R + +--R 4 2 3 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (35A b c - 15B b )d e + (- 84A b c + 40B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R +---+ | c +--R \|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 2 3 2 3 3 2 2 +--R 2A b c e + (22A b c - 8B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 120A b c + 56B b c )d e + (96A c - 48B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 +--R 4A b c e + (44A b c - 16B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 240A b c + 112B b c )d e + (192A b c - 96B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R 2A b e + (22A b c - 8B b )d e + (- 120A b c + 56B b c)d e +--R + +--R 2 3 3 2 3 +--R (96A b c - 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 3 2 2 2 3 3 2 +--R - 2A b c e + (48A b c - 22B b c )d e +--R + +--R 4 2 3 2 +--R (- 48A b c + 24B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 4A b c e + (74A b c - 34B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 72A b c + 36B b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R (- 2A b e + (18A b c - 8B b )d e + (- 16A b c + 8B b c)d )x +--R + +--R 5 4 2 +--R - 4A b d e + 4A b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (8b c d e - 8b c d )x + (16b c d e - 16b c d )x +--R + +--R 8 7 2 2 +--R (8b d e - 8b c d )x +--R * +--R +---+ +--R \|- d +--R , +--R +--R 3 2 3 2 3 3 2 2 +--R A b c e + (11A b c - 4B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 60A b c + 28B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 +--R 2A b c e + (22A b c - 8B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 120A b c + 56B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 3 3 2 2 4 2 3 2 +--R (35A b c - 15B b c )d e + (- 84A b c + 40B b c )d e +--R + +--R 5 4 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (70A b c - 30B b c)d e + (- 168A b c + 80B b c )d e +--R + +--R 4 2 3 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (35A b c - 15B b )d e + (- 84A b c + 40B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R +---+ | c c\|e x + d +--R \|- d |--------- atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 2 2 2 3 3 2 +--R - A b c e + (24A b c - 11B b c )d e +--R + +--R 4 2 3 2 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 +--R - 2A b c e + (37A b c - 17B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 36A b c + 18B b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R (- A b e + (9A b c - 4B b )d e + (- 8A b c + 4B b c)d )x +--R + +--R 5 4 2 +--R - 2A b d e + 2A b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (4b c d e - 4b c d )x + (8b c d e - 8b c d )x +--R + +--R 8 7 2 2 +--R (4b d e - 4b c d )x +--R * +--R +---+ +--R \|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 856 + +--S 857 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 +--R (35A b c - 15B b )d e + (- 84A b c + 40B b c)d e +--R + +--R 3 2 3 +--R (48A c - 24B b c )d +--R * +--R +-----------+ +--R +-----------+ | c +-+ +--R \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 3 2 2 2 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 3 2 3 +--R (48A c - 24B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 2 3 2 2 2 2 +--R (70A b c - 30B b )d e + (- 168A b c + 80B b c)d e +--R + +--R 3 2 3 +--R (96A c - 48B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A b e + (- 22A b c + 8B b )d e + (120A b c - 56B b c)d e +--R + +--R 3 2 3 +--R (- 96A c + 48B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 6 5 2 +-----------+ +-+ +--R (8b d e - 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 857 + +--S 858 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 3 2 2 2 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 3 2 3 +--R (48A c - 24B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R 2 3 2 2 2 2 +--R (70A b c - 30B b )d e + (- 168A b c + 80B b c)d e +--R + +--R 3 2 3 +--R (96A c - 48B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A b e + (- 22A b c + 8B b )d e + (120A b c - 56B b c)d e +--R + +--R 3 2 3 +--R (- 96A c + 48B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 2 +--R (70A b c - 30B b )d e + (- 168A b c + 80B b c)d e +--R + +--R 3 2 3 +--R (96A c - 48B b c )d +--R * +--R +---------+ +-------+ +--R +-----------+ | c +-+ c\|e x + d +--R \|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 6 5 2 +-----------+ +-+ +--R (8b d e - 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 1457 +t0:=(A+B*x)/((b*x+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R 3 6 2 5 2 4 3 3 +-------+ +--R (c x + 3b c x + 3b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1457 +r0:=-1/4*(48*A*c^2*d^2-b^2*e*(4*B*d-3*A*e)-12*b*c*d*(2*B*d-A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(5/2))+1/4*c^(3/2)*_ + (48*A*c^3*d^2-35*b^3*B*e^2-12*b*c^2*d*(2*B*d+9*A*e)+7*b^2*c*e*_ + (8*B*d+9*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*_ + (c*d-b*e)^(5/2))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-3*A*e)-b*c*d*_ + (6*B*d+7*A*e))*sqrt(d+e*x)/(b^3*d^2*(c*d-b*e)*(b+c*x)^2)-1/2*A*_ + sqrt(d+e*x)/(b*d*x^2*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d-3*A*b*e)*_ + sqrt(d+e*x)/(b^2*d^2*x*(b+c*x)^2)+1/4*c*(24*A*c^3*d^3-b^3*e^2*_ + (4*B*d-3*A*e)-12*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(19*B*d+6*A*e))*_ + sqrt(d+e*x)/(b^4*d^2*(c*d-b*e)^2*(b+c*x)) +--R +--R +--R (2) +--R 2 4 3 3 2 2 5 2 4 3 +--R (63A b c - 35B b c )d e + (- 108A b c + 56B b c )d e +--R + +--R 6 5 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (126A b c - 70B b c )d e + (- 216A b c + 112B b c )d e +--R + +--R 5 2 4 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (63A b c - 35B b c)d e + (- 108A b c + 56B b c )d e +--R + +--R 2 4 3 3 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 2 4 3 3 4 2 3 +--R - 3A b c e + (- 6A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 27A b c + 16B b c )d e + (84A b c - 44B b c )d e +--R + +--R 6 5 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 +--R - 6A b c e + (- 12A b c + 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 54A b c + 32B b c )d e + (168A b c - 88B b c )d e +--R + +--R 5 2 4 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R - 3A b e + (- 6A b c + 4B b )d e + (- 27A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (84A b c - 44B b c )d e + (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 3 3 3 4 2 2 2 4 3 3 2 +--R 3A b c e + (6A b c - 4B b c )d e + (- 36A b c + 19B b c )d e +--R + +--R 5 2 4 3 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 3 3 4 2 2 +--R 6A b c e + (10A b c - 8B b c)d e + (- 55A b c + 29B b c )d e +--R + +--R 2 4 3 3 3 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 3A b e + (2A b c - 4B b )d e + (- 13A b c + 8B b c)d e +--R + +--R 3 3 4 2 3 +--R (8A b c - 4B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (4b c d e - 8b c d e + 4b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 9 2 2 8 3 7 2 4 2 +--R (8b c d e - 16b c d e + 8b c d )x + (4b d e - 8b c d e + 4b c d )x +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 4 3 3 4 2 3 2 4 3 3 2 2 +--R 3A b c e + (6A b c - 4B b c )d e + (27A b c - 16B b c )d e +--R + +--R 5 2 4 3 6 5 4 +--R (- 84A b c + 44B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 3 3 4 2 2 2 +--R 6A b c e + (12A b c - 8B b c)d e + (54A b c - 32B b c )d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 168A b c + 88B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R 3A b e + (6A b c - 4B b )d e + (27A b c - 16B b c)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (- 84A b c + 44B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (63A b c - 35B b c )d e + (- 108A b c + 56B b c )d e +--R + +--R 6 5 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (126A b c - 70B b c )d e + (- 216A b c + 112B b c )d e +--R + +--R 5 2 4 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (63A b c - 35B b c)d e + (- 108A b c + 56B b c )d e +--R + +--R 2 4 3 3 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 2 3 3 3 4 2 2 +--R 6A b c e + (12A b c - 8B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 38B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 +--R 12A b c e + (20A b c - 16B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 58B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 6A b e + (4A b c - 8B b )d e + (- 26A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 +--R (16A b c - 8B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (8b c d e - 16b c d e + 8b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 +--R (16b c d e - 32b c d e + 16b c d )x +--R + +--R 9 2 2 8 3 7 2 4 2 +--R (8b d e - 16b c d e + 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 4 2 4 3 3 4 2 3 2 4 3 3 2 2 +--R 3A b c e + (6A b c - 4B b c )d e + (27A b c - 16B b c )d e +--R + +--R 5 2 4 3 6 5 4 +--R (- 84A b c + 44B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 3 3 4 2 2 2 +--R 6A b c e + (12A b c - 8B b c)d e + (54A b c - 32B b c )d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 168A b c + 88B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R 3A b e + (6A b c - 4B b )d e + (27A b c - 16B b c)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (- 84A b c + 44B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 126A b c + 70B b c )d e + (216A b c - 112B b c )d e +--R + +--R 6 5 4 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 252A b c + 140B b c )d e + (432A b c - 224B b c )d e +--R + +--R 5 2 4 4 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (- 126A b c + 70B b c)d e + (216A b c - 112B b c )d e +--R + +--R 2 4 3 3 4 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 2 3 3 3 4 2 2 +--R 6A b c e + (12A b c - 8B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 38B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 +--R 12A b c e + (20A b c - 16B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 58B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 6A b e + (4A b c - 8B b )d e + (- 26A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 +--R (16A b c - 8B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (8b c d e - 16b c d e + 8b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 +--R (16b c d e - 32b c d e + 16b c d )x +--R + +--R 9 2 2 8 3 7 2 4 2 +--R (8b d e - 16b c d e + 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 2 4 3 3 2 2 5 2 4 3 +--R (63A b c - 35B b c )d e + (- 108A b c + 56B b c )d e +--R + +--R 6 5 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (126A b c - 70B b c )d e + (- 216A b c + 112B b c )d e +--R + +--R 5 2 4 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (63A b c - 35B b c)d e + (- 108A b c + 56B b c )d e +--R + +--R 2 4 3 3 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-----------+ +--R +---+ | c +--R \|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 2 4 3 3 4 2 3 +--R - 6A b c e + (- 12A b c + 8B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 54A b c + 32B b c )d e + (168A b c - 88B b c )d e +--R + +--R 6 5 4 +--R (- 96A c + 48B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 +--R - 12A b c e + (- 24A b c + 16B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 108A b c + 64B b c )d e + (336A b c - 176B b c )d e +--R + +--R 5 2 4 4 +--R (- 192A b c + 96B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 +--R - 6A b e + (- 12A b c + 8B b )d e +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (- 54A b c + 32B b c)d e + (168A b c - 88B b c )d e +--R + +--R 2 4 3 3 4 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 4 2 3 3 3 4 2 2 +--R 6A b c e + (12A b c - 8B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 72A b c + 38B b c )d e + (48A b c - 24B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 +--R 12A b c e + (20A b c - 16B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 110A b c + 58B b c )d e + (72A b c - 36B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 6A b e + (4A b c - 8B b )d e + (- 26A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 +--R (16A b c - 8B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (8b c d e - 16b c d e + 8b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 +--R (16b c d e - 32b c d e + 16b c d )x +--R + +--R 9 2 2 8 3 7 2 4 2 +--R (8b d e - 16b c d e + 8b c d )x +--R * +--R +---+ +--R \|- d +--R , +--R +--R 4 2 4 3 3 4 2 3 +--R - 3A b c e + (- 6A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 27A b c + 16B b c )d e + (84A b c - 44B b c )d e +--R + +--R 6 5 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 +--R - 6A b c e + (- 12A b c + 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 54A b c + 32B b c )d e + (168A b c - 88B b c )d e +--R + +--R 5 2 4 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R - 3A b e + (- 6A b c + 4B b )d e + (- 27A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (84A b c - 44B b c )d e + (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 63A b c + 35B b c )d e + (108A b c - 56B b c )d e +--R + +--R 6 5 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 126A b c + 70B b c )d e + (216A b c - 112B b c )d e +--R + +--R 5 2 4 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (- 63A b c + 35B b c)d e + (108A b c - 56B b c )d e +--R + +--R 2 4 3 3 4 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +---------+ +-------+ +--R +---+ | c c\|e x + d +--R \|- d |--------- atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 2 3 3 3 4 2 2 +--R 3A b c e + (6A b c - 4B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 36A b c + 19B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 +--R 6A b c e + (10A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 55A b c + 29B b c )d e + (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 3A b e + (2A b c - 4B b )d e + (- 13A b c + 8B b c)d e +--R + +--R 3 3 4 2 3 +--R (8A b c - 4B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (4b c d e - 8b c d e + 4b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 9 2 2 8 3 7 2 4 2 +--R (8b c d e - 16b c d e + 8b c d )x + (4b d e - 8b c d e + 4b c d )x +--R * +--R +---+ +--R \|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 863 + +--S 864 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 4 3 4 3 2 2 3 2 2 +--R 3A b e + (6A b c - 4B b )d e + (27A b c - 16B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 84A b c + 44B b c )d e + (48A c - 24B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (63A b c - 35B b c)d e + (- 108A b c + 56B b c )d e +--R + +--R 4 3 4 +--R (48A c - 24B b c )d +--R * +--R +-----------+ +--R +-----------+ | c +-+ +--R \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (- 126A b c + 70B b c)d e + (216A b c - 112B b c )d e +--R + +--R 4 3 4 +--R (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R 6A b e + (12A b c - 8B b )d e + (54A b c - 32B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 168A b c + 88B b c )d e + (96A c - 48B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 7 2 2 6 3 5 2 4 +-----------+ +-+ +--R (8b d e - 16b c d e + 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 4 3 2 2 3 2 2 +--R 3A b e + (6A b c - 4B b )d e + (27A b c - 16B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 84A b c + 44B b c )d e + (48A c - 24B b c )d +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (- 126A b c + 70B b c)d e + (216A b c - 112B b c )d e +--R + +--R 4 3 4 +--R (- 96A c + 48B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R 6A b e + (12A b c - 8B b )d e + (54A b c - 32B b c)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 168A b c + 88B b c )d e + (96A c - 48B b c )d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (- 126A b c + 70B b c)d e + (216A b c - 112B b c )d e +--R + +--R 4 3 4 +--R (- 96A c + 48B b c )d +--R * +--R +---------+ +-------+ +--R +-----------+ | c +-+ c\|e x + d +--R \|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 7 2 2 6 3 5 2 4 +-----------+ +-+ +--R (8b d e - 16b c d e + 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 7 2 3 6 2 2 5 3 2 4 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x +--R + +--R 3 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1457 +r0:=-3/4*(16*A*c^2*d^2-b^2*e*(4*B*d-5*A*e)-4*b*c*d*(2*B*d-3*A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(7/2))+3/4*c^(5/2)*(16*A*c^3*d^2-_ + 21*b^3*B*e^2-4*b*c^2*d*(2*B*d+11*A*e)+3*b^2*c*e*(8*B*d+11*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(7/2))+_ + 3/4*e*(8*A*c^4*d^4+b^4*e^3*(4*B*d-5*A*e)-b^3*c*d*e^2*(4*B*d-3*A*e)-_ + 4*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*e*(9*B*d+5*A*e))/(b^4*d^3*_ + (c*d-b*e)^3*sqrt(d+e*x))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-5*A*e)-_ + b*c*d*(6*B*d+5*A*e))/(b^3*d^2*(c*d-b*e)*(b+c*x)^2*sqrt(d+e*x))-_ + 1/2*A/(b*d*x^2*(b+c*x)^2*sqrt(d+e*x))+1/4*(-4*b*B*d+8*A*c*d+_ + 5*A*b*e)/(b^2*d^2*x*(b+c*x)^2*sqrt(d+e*x))+1/4*c*(24*A*c^3*d^3-_ + b^3*e^2*(4*B*d-5*A*e)+b^2*c*d*e*(21*B*d+2*A*e)-12*b*c^2*d^2*(B*d+_ + 3*A*e))/(b^4*d^2*(c*d-b*e)^2*(b+c*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 5 3 4 3 2 6 2 5 4 +--R (- 99A b c + 63B b c )d e + (132A b c - 72B b c )d e +--R + +--R 7 6 5 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 3 2 2 5 3 4 4 +--R (- 198A b c + 126B b c )d e + (264A b c - 144B b c )d e +--R + +--R 6 2 5 5 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (- 99A b c + 63B b c )d e + (132A b c - 72B b c )d e +--R + +--R 2 5 3 4 5 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 2 5 4 3 5 2 4 +--R - 15A b c e + (9A b c + 12B b c )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (15A b c - 12B b c )d e + (51A b c - 36B b c )d e +--R + +--R 6 2 5 4 7 6 5 +--R (- 108A b c + 60B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 6 4 +--R - 30A b c e + (18A b c + 24B b c)d e +--R + +--R 4 3 5 2 2 3 3 4 4 3 3 2 +--R (30A b c - 24B b c )d e + (102A b c - 72B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (- 216A b c + 120B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 6 7 4 5 2 6 2 3 +--R - 15A b e + (9A b c + 12B b )d e + (15A b c - 12B b c)d e +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (51A b c - 36B b c )d e + (- 108A b c + 60B b c )d e +--R + +--R 2 5 3 4 5 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 2 5 4 3 5 2 4 +--R 15A b c e + (- 9A b c - 12B b c )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (- 15A b c + 12B b c )d e + (48A b c - 27B b c )d e +--R + +--R 6 2 5 4 +--R (- 24A b c + 12B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 6 4 +--R 30A b c e + (- 13A b c - 24B b c)d e +--R + +--R 4 3 5 2 2 3 3 4 4 3 3 2 +--R (- 33A b c + 20B b c )d e + (58A b c - 29B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (12A b c - 9B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 6 7 4 5 2 6 2 3 +--R 15A b e + (A b c - 12B b )d e + (- 23A b c + 4B b c)d e +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (- 7A b c + 12B b c )d e + (65A b c - 37B b c )d e +--R + +--R 2 5 3 4 5 +--R (- 36A b c + 18B b c )d +--R * +--R 2 +--R x +--R + +--R 7 4 6 7 2 3 5 2 6 3 2 +--R 5A b d e + (- 7A b c - 4B b )d e + (- 9A b c + 12B b c)d e +--R + +--R 4 3 5 2 4 3 4 4 3 5 +--R (19A b c - 12B b c )d e + (- 8A b c + 4B b c )d +--R * +--R x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - 2A b d e + 6A b c d e - 6A b c d e + 2A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (8b c d e - 24b c d e + 24b c d e - 8b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1457 +--a0:=integrate(t0,x) +--E 870 + +--S 871 of 1457 +--m0a:=a0.1-r0 +--E 871 + +--S 872 of 1457 +--d0a:=D(m0a,x) +--E 872 + +--S 873 of 1457 +--m0b:=a0.2-r0 +--E 873 + +--S 874 of 1457 +--d0b:=D(m0b,x) +--E 874 + +)clear all + +--S 875 of 1457 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1457 +r0:=1/12*e*(72*A*c^4*d^4+5*b^4*e^3*(4*B*d-7*A*e)-9*b^3*c*d*e^2*(4*B*d-_ + 5*A*e)-36*b*c^3*d^3*(B*d+4*A*e)+3*b^2*c^2*d^2*e*(29*B*d+9*A*e))/(b^4*_ + d^3*(c*d-b*e)^3*(d+e*x)^(3/2))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-7*A*e)-_ + 3*b*c*d*(2*B*d+A*e))/(b^3*d^2*(c*d-b*e)*(b+c*x)^2*(d+e*x)^(3/2))-_ + 1/2*A/(b*d*x^2*(b+c*x)^2*(d+e*x)^(3/2))+1/4*(-4*b*B*d+8*A*c*d+7*A*b*e)/_ + (b^2*d^2*x*(b+c*x)^2*(d+e*x)^(3/2))+1/4*c*(24*A*c^3*d^3-b^3*e^2*_ + (4*B*d-7*A*e)+b^2*c*d*e*(23*B*d-2*A*e)-12*b*c^2*d^2*(B*d+3*A*e))/_ + (b^4*d^2*(c*d-b*e)^2*(b+c*x)*(d+e*x)^(3/2))-1/4*(48*A*c^2*d^2-_ + 5*b^2*e*(4*B*d-7*A*e)-12*b*c*d*(2*B*d-5*A*e))*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b^5*d^(9/2))+1/4*c^(7/2)*(48*A*c^3*d^2-99*b^3*B*e^2-_ + 12*b*c^2*d*(2*B*d+13*A*e)+11*b^2*c*e*(8*B*d+13*A*e))*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(9/2))+1/4*e*(24*A*c^5*d^5+_ + 8*b^4*c*d*e^3*(7*B*d-10*A*e)-5*b^5*e^4*(4*B*d-7*A*e)-6*b^3*_ + c^2*d^2*e^2*(4*B*d-3*A*e)+7*b^2*c^3*d^3*e*(5*B*d+4*A*e)-12*b*c^4*d^4*_ + (B*d+5*A*e))/(b^4*d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (429A b c - 297B b c )d e + (- 468A b c + 264B b c )d e +--R + +--R 8 7 6 +--R (144A c - 72B b c )d e +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (858A b c - 594B b c )d e + (- 507A b c + 231B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (- 180A b c + 120B b c )d e + (144A c - 72B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (429A b c - 297B b c )d e + (390A b c - 330B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 792A b c + 456B b c )d e + (288A b c - 144B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (429A b c - 297B b c )d e + (- 468A b c + 264B b c )d e +--R + +--R 2 6 3 5 7 +--R (144A b c - 72B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 6 2 7 5 3 6 2 6 +--R - 105A b c e + (240A b c + 60B b c )d e +--R + +--R 4 4 5 3 2 5 3 5 4 4 3 4 +--R (- 54A b c - 168B b c )d e + (- 84A b c + 72B b c )d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 249A b c + 192B b c )d e + (396A b c - 228B b c )d e +--R + +--R 8 7 6 +--R (- 144A c + 72B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R - 210A b c e + (375A b c + 120B b c)d e +--R + +--R 5 3 6 2 2 5 4 4 5 3 3 4 +--R (132A b c - 276B b c )d e + (- 222A b c - 24B b c )d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 582A b c + 456B b c )d e + (543A b c - 264B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (108A b c - 84B b c )d e + (- 144A c + 72B b c )d +--R * +--R 4 +--R x +--R + +--R 8 7 7 8 6 6 2 7 2 5 +--R - 105A b e + (30A b c + 60B b )d e + (426A b c - 48B b c)d e +--R + +--R 5 3 6 2 3 4 4 4 5 3 4 3 +--R (- 192A b c - 264B b c )d e + (- 417A b c + 336B b c )d e +--R + +--R 3 5 4 4 5 2 2 6 3 5 6 +--R (- 102A b c + 156B b c )d e + (648A b c - 384B b c )d e +--R + +--R 7 2 6 7 +--R (- 288A b c + 144B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 +--R - 105A b d e + (240A b c + 60B b )d e +--R + +--R 6 2 7 3 4 5 3 6 2 4 3 +--R (- 54A b c - 168B b c)d e + (- 84A b c + 72B b c )d e +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (- 249A b c + 192B b c )d e + (396A b c - 228B b c )d e +--R + +--R 2 6 3 5 7 +--R (- 144A b c + 72B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 6 2 7 5 3 6 2 6 +--R 105A b c e + (- 240A b c - 60B b c )d e +--R + +--R 4 4 5 3 2 5 3 5 4 4 3 4 +--R (54A b c + 168B b c )d e + (84A b c - 72B b c )d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 180A b c + 105B b c )d e + (72A b c - 36B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R 210A b c e + (- 340A b c - 120B b c)d e +--R + +--R 5 3 6 2 2 5 4 4 5 3 3 4 +--R (- 212A b c + 256B b c )d e + (240A b c + 80B b c )d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 105A b c + 15B b c )d e + (- 252A b c + 156B b c )d e +--R + +--R 7 2 6 6 +--R (144A b c - 72B b c )d e +--R * +--R 4 +--R x +--R + +--R 8 7 7 8 6 6 2 7 2 5 +--R 105A b e + (40A b c - 60B b )d e + (- 565A b c + 8B b c)d e +--R + +--R 5 3 6 2 3 4 4 4 5 3 4 3 +--R (180A b c + 364B b c )d e + (255A b c - 192B b c )d e +--R + +--R 3 5 4 4 5 2 2 6 3 5 6 +--R (- 438A b c + 234B b c )d e + (36A b c - 3B b c )d e +--R + +--R 7 2 6 7 +--R (72A b c - 36B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 +--R 140A b d e + (- 278A b c - 80B b )d e +--R + +--R 6 2 7 3 4 5 3 6 2 4 3 +--R (- 30A b c + 200B b c)d e + (180A b c - 48B b c )d e +--R + +--R 5 3 5 2 3 5 4 4 6 +--R - 48B b c d e + (- 225A b c + 135B b c )d e +--R + +--R 2 6 3 5 7 +--R (108A b c - 54B b c )d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 8 3 4 6 2 7 4 3 +--R 21A b d e + (- 60A b c - 12B b )d e + (30A b c + 48B b c)d e +--R + +--R 5 3 6 2 5 2 4 4 5 3 6 +--R (60A b c - 72B b c )d e + (- 75A b c + 48B b c )d e +--R + +--R 3 5 4 4 7 +--R (24A b c - 12B b c )d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - 6A b d e + 24A b c d e - 36A b c d e + 24A b c d e - 6A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (12b c d e - 48b c d e + 72b c d e - 48b c d e + 12b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 +--R 24b c d e - 84b c d e + 96b c d e - 24b c d e - 24b c d e +--R + +--R 5 6 9 +--R 12b c d +--R * +--R 4 +--R x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 +--R 12b d e - 24b c d e - 24b c d e + 96b c d e - 84b c d e +--R + +--R 6 5 9 +--R 24b c d +--R * +--R 3 +--R x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (12b d e - 48b c d e + 72b c d e - 48b c d e + 12b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1457 +--a0:=integrate(t0,x) +--E 877 + +--S 878 of 1457 +--m0a:=a0.1-r0 +--E 878 + +--S 879 of 1457 +--d0a:=D(m0a,x) +--E 879 + +--S 880 of 1457 +--m0b:=a0.2-r0 +--E 880 + +--S 881 of 1457 +--d0b:=D(m0b,x) +--E 881 + +)clear all + +--S 882 of 1457 +t0:=(A+B*x)*(d+e*x)^(1/2)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R +-------+ | 2 +--R (1) (B x + A)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1457 +--r0:=2/7*B*(b*x+c*x^2)^(3/2)*sqrt(d+e*x)/c-2/105*(14*A*c*e*(c^2*d^2-_ +-- b*c*d*e+b^2*e^2)-B*(8*c^3*d^3-5*b*c^2*d^2*e-5*b^2*c*d*e^2+8*_ +-- b^3*e^3))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^3*e^(5/2)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/105*(-b)^(3/2)*_ +-- (c*d-b*e)*(7*A*c*e*(c*d-2*b*e)-B*(4*c^2*d^2+b*c*d*e-8*b^2*e^2))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*e^2*sqrt(d+e*x)*sqrt(b*x+_ +-- c*x^2))+2/105*(7*A*c*e*(c*d+b*e)-B*(4*c^2*d^2-2*b*c*d*e+4*b^2*e^2)+_ +-- 3*c*e*(B*c*d-4*b*B*e+7*A*c*e)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^2) +--E 883 + +--S 884 of 1457 +--a0:=integrate(t0,x) +--E 884 + +--S 885 of 1457 +--m0:=a0-r0 +--E 885 + +--S 886 of 1457 +--d0:=D(m0,x) +--E 886 + +)clear all + +--S 887 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1457 +--r0:=-2/15*(5*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^2*e^(5/2)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*(-b)^(3/2)*(c*d-b*e)*(4*B*c*d+_ +-- 2*b*B*e-5*A*c*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*e^2*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(4*B*c*d-b*B*e-5*A*c*e-3*B*c*e*x)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c*e^2) +--E 888 + +--S 889 of 1457 +--a0:=integrate(t0,x) +--E 889 + +--S 890 of 1457 +--m0:=a0-r0 +--E 890 + +--S 891 of 1457 +--d0:=D(m0,x) +--E 891 + +)clear all + +--S 892 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1457 +--r0:=-2/3*(8*B*c*d-b*B*e-6*A*c*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (c*e^(5/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*(-b)^(3/2)*(4*B*c*d-b*B*e-3*A*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+_ +-- e*x)/d)/(c^(3/2)*e^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(4*B*d-_ +-- 3*A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*sqrt(d+e*x)) +--E 893 + +--S 894 of 1457 +--a0:=integrate(t0,x) +--E 894 + +--S 895 of 1457 +--m0:=a0-r0 +--E 895 + +--S 896 of 1457 +--d0:=D(m0,x) +--E 896 + +)clear all + +--S 897 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1457 +--r0:=-2/3*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(e^(5/2)*(c*d-b*e)*sqrt(-d)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(-b)^(3/2)*(4*B*d-A*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*e^2*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*(4*B*d-A*e+3*B*e*x)*sqrt(b*x+c*x^2)/(e^2*_ +-- (d+e*x)^(3/2))-2/3*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*_ +-- sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*sqrt(d+e*x)) +--E 898 + +--S 899 of 1457 +--a0:=integrate(t0,x) +--E 899 + +--S 900 of 1457 +--m0:=a0-r0 +--E 900 + +--S 901 of 1457 +--d0:=D(m0,x) +--E 901 + +)clear all + +--S 902 of 1457 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1457 +--r0:=-2/15*(2*A*e*(c^2*d^2-b*c*d*e+b^2*e^2)+B*d*(8*c^2*d^2-13*b*c*d*e+_ +-- 3*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(3/2)*e^(5/2)*(c*d-b*e)^2*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(-b)^(3/2)*(B*d*_ +-- (4*c*d-3*b*e)+A*e*(c*d-2*b*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*_ +-- e^2*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*(B*d*(8*c*d-_ +-- 9*b*e)+A*e*(2*c*d-b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+_ +-- e*x)^(3/2))-2/5*(4*B*d+A*e+5*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+_ +-- e*x)^(5/2))+2/15*(2*A*e*(c^2*d^2-b*c*d*e+b^2*e^2)+B*d*(8*c^2*d^2-_ +-- 13*b*c*d*e+3*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 903 + +--S 904 of 1457 +--a0:=integrate(t0,x) +--E 904 + +--S 905 of 1457 +--m0:=a0-r0 +--E 905 + +--S 906 of 1457 +--d0:=D(m0,x) +--E 906 + +)clear all + +--S 907 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(1/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1457 +--r0:=-2/63*(8*B*c*d-3*b*B*e-9*A*c*e-7*B*c*e*x)*(b*x+c*x^2)^(3/2)*_ +-- sqrt(d+e*x)/(c*e^2)-2/315*(18*A*c*e*(8*c^3*d^3-12*b*c^2*d^2*e+_ +-- 2*b^2*c*d*e^2+b^3*e^3)-B*(128*c^4*d^4-184*b*c^3*d^3*e+27*_ +-- b^2*c^2*d^2*e^2+11*b^3*c*d*e^3+8*b^4*e^4))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^3*e^(9/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/315*(-b)^(3/2)*(c*d-b*e)*(9*A*c*e*(8*c^2*d^2-_ +-- 5*b*c*d*e-2*b^2*e^2)-B*(64*c^3*d^3-36*b*c^2*d^2*e-15*b^2*c*d*e^2-_ +-- 8*b^3*e^3))*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*e^4*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/315*(9*A*c*e*(8*c^2*d^2-11*b*c*d*e+b^2*e^2)-_ +-- 2*B*(32*c^3*d^3-42*b*c^2*d^2*e+3*b^2*c*d*e^2+2*b^3*e^3)-3*c*e*_ +-- (9*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-7*b*c*d*e-4*b^2*e^2))*x)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^4) +--E 908 + +--S 909 of 1457 +--a0:=integrate(t0,x) +--E 909 + +--S 910 of 1457 +--m0:=a0-r0 +--E 910 + +--S 911 of 1457 +--d0:=D(m0,x) +--E 911 + +)clear all + +--S 912 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1457 +--r0:=2/7*(8*B*d-7*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+2/35*_ +-- (5*b*c*e*(8*B*d-7*A*e)*(2*c*d-b*e)-(16*B*c*d-b*B*e-14*A*c*e)*_ +-- (8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (c^2*e^(9/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/35*_ +-- (-b)^(3/2)*(c*d-b*e)*(7*A*c*e*(8*c*d-b*e)-2*B*(32*c^2*d^2-6*b*c*d*e-_ +-- b^2*e^2))*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*e^4*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/35*(7*A*c*e*(8*c*d-7*b*e)-B*(64*c^2*d^2-60*b*c*_ +-- d*e+b^2*e^2)+3*c*e*(16*B*c*d-b*B*e-14*A*c*e)*x)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/(c*e^4) +--E 913 + +--S 914 of 1457 +--a0:=integrate(t0,x) +--E 914 + +--S 915 of 1457 +--m0:=a0-r0 +--E 915 + +--S 916 of 1457 +--d0:=D(m0,x) +--E 916 + +)clear all + +--S 917 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1457 +--r0:=2/15*(8*B*d-5*A*e+3*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/15*(40*A*c*e*(2*c*d-b*e)-B*(128*c^2*d^2-88*b*c*d*e+3*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c*e^(9/2)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(-b)^(3/2)*(5*A*c*e*(8*c*d-5*b*e)-_ +-- B*(64*c^2*d^2-52*b*c*d*e+3*b^2*e^2))*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(3/2)*e^4*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/15*(4*B*d*(16*c*d-9*b*e)-5*A*e*(8*c*d-3*b*e)+e*(16*B*c*d-_ +-- 3*b*B*e-10*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*sqrt(d+e*x)) +--E 918 + +--S 919 of 1457 +--a0:=integrate(t0,x) +--E 919 + +--S 920 of 1457 +--m0:=a0-r0 +--E 920 + +--S 921 of 1457 +--d0:=D(m0,x) +--E 921 + +)clear all + +--S 922 of 1457 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1457 +--r0:=2/15*(8*B*d-3*A*e+5*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 2/15*(3*A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(128*c^2*d^2-_ +-- 168*b*c*d*e+43*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/(e^(9/2)*(c*d-b*e)*_ +-- sqrt(-d)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/15*(-b)^(3/2)*(4*B*d*(16*c*d-7*b*e)-3*A*e*(8*c*d-b*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*e^4*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/15*(4*B*d*(16*c*d-7*b*e)-3*A*e*(8*c*d-b*e)+_ +-- 3*e*(16*B*c*d-5*b*B*e-6*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*_ +-- (d+e*x)^(3/2))-2/15*(3*A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*_ +-- (128*c^2*d^2-168*b*c*d*e+43*b^2*e^2))*sqrt(b*x+c*x^2)/(d*e^4*_ +-- (c*d-b*e)*sqrt(d+e*x)) +--E 923 + +--S 924 of 1457 +--a0:=integrate(t0,x) +--E 924 + +--S 925 of 1457 +--m0:=a0-r0 +--E 925 + +--S 926 of 1457 +--d0:=D(m0,x) +--E 926 + +)clear all + +--S 927 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/sqrt(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1457 +--r0:=2/105*(7*A*c*e*(23*c^2*d^2-23*b*c*d*e+8*b^2*e^2)+B*(15*c^3*d^3-_ +-- 103*b*c^2*d^2*e+128*b^2*c*d*e^2-48*b^3*e^3))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^4*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/105*(c*d-b*e)*(105*A*c^3*d^2-48*b^3*B*e^2+_ +-- 8*b^2*c*e*(13*B*d+7*A*e)-b*c^2*d*(60*B*d+133*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/35*(5*B*c*d-6*b*B*e+7*A*c*e)*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/c^2+2/7*B*(d+e*x)^(5/2)*sqrt(b*x+c*x^2)/c+2/105*_ +-- (28*A*c*e*(2*c*d-b*e)+B*(15*c^2*d^2-43*b*c*d*e+24*b^2*e^2))*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/c^3 +--E 928 + +--S 929 of 1457 +--a0:=integrate(t0,x) +--E 929 + +--S 930 of 1457 +--m0:=a0-r0 +--E 930 + +--S 931 of 1457 +--d0:=D(m0,x) +--E 931 + +)clear all + +--S 932 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1457 +--r0:=2/15*(10*A*c*e*(2*c*d-b*e)+B*(3*c^2*d^2-13*b*c*d*e+8*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^3*sqrt(e)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(c*d-b*e)*(9*b*B*c*d-15*A*c^2*d-_ +-- 8*b^2*B*e+10*A*b*c*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (c^(7/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*B*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/c+2/15*(3*B*c*d-4*b*B*e+5*A*c*e)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/c^2 +--E 933 + +--S 934 of 1457 +--a0:=integrate(t0,x) +--E 934 + +--S 935 of 1457 +--m0:=a0-r0 +--E 935 + +--S 936 of 1457 +--d0:=D(m0,x) +--E 936 + +)clear all + +--S 937 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(b*x+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1457 +--r0:=2/3*(B*c*d-2*b*B*e+3*A*c*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^2*_ +-- sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*(2*b*B-_ +-- 3*A*c)*(c*d-b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (c^(5/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*B*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/c +--E 938 + +--S 939 of 1457 +--a0:=integrate(t0,x) +--E 939 + +--S 940 of 1457 +--m0:=a0-r0 +--E 940 + +--S 941 of 1457 +--d0:=D(m0,x) +--E 941 + +)clear all + +--S 942 of 1457 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------- +--R +----------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1457 +--r0:=2*B*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c*sqrt(e)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(b*B-A*c)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(3/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 943 + +--S 944 of 1457 +--a0:=integrate(t0,x) +--E 944 + +--S 945 of 1457 +--m0:=a0-r0 +--E 945 + +--S 946 of 1457 +--d0:=D(m0,x) +--E 946 + +)clear all + +--S 947 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) -------------------------------- +--R +----------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1457 +--r0:=2*(B*d-A*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((c*d-b*e)*sqrt(-d)*sqrt(e)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*A*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*sqrt(d+e*x)) +--E 948 + +--S 949 of 1457 +--a0:=integrate(t0,x) +--E 949 + +--S 950 of 1457 +--m0:=a0-r0 +--E 950 + +--S 951 of 1457 +--d0:=D(m0,x) +--E 951 + +)clear all + +--S 952 of 1457 +t0:=(A+B*x)/((d+e*x)^(5/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +----------+ +--R 2 2 2 +-------+ | 2 +--R (e x + 2d e x + d )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1457 +--r0:=2/3*(2*A*e*(2*c*d-b*e)-B*d*(c*d+b*e))*(b+c*x)*elliptic_e(asin(_ +-- sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/_ +-- ((-d)^(3/2)*(c*d-b*e)^2*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/3*(b*B*d-3*A*c*d+2*A*b*e)*elliptic_f(asin(_ +-- sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ +-- (d+e*x)^(3/2))-2/3*(2*A*e*(2*c*d-b*e)-B*d*(c*d+b*e))*sqrt(b*x+_ +-- c*x^2)/(d^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 953 + +--S 954 of 1457 +--a0:=integrate(t0,x) +--E 954 + +--S 955 of 1457 +--m0:=a0-r0 +--E 955 + +--S 956 of 1457 +--d0:=D(m0,x) +--E 956 + +)clear all + +--S 957 of 1457 +t0:=(A+B*x)/((d+e*x)^(7/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R +----------+ +--R 3 3 2 2 2 3 +-------+ | 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1457 +--r0:=2/15*(B*d*(3*c^2*d^2+7*b*c*d*e-2*b^2*e^2)-A*e*(23*c^2*d^2-_ +-- 23*b*c*d*e+8*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(5/2)*_ +-- (c*d-b*e)^3*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+_ +-- 2/15*(15*A*c^2*d^2+2*b^2*e*(B*d+4*A*e)-b*c*d*(6*B*d+19*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^3*(c*d-b*e)^2*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*(B*d-A*e)*sqrt(b*x+c*x^2)/_ +-- (d*(c*d-b*e)*(d+e*x)^(5/2))-2/15*(4*A*e*(2*c*d-b*e)-B*d*(3*c*d+_ +-- b*e))*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))+2/15*(B*d*_ +-- (3*c^2*d^2+7*b*c*d*e-2*b^2*e^2)-A*e*(23*c^2*d^2-23*b*c*d*e+_ +-- 8*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 958 + +--S 959 of 1457 +--a0:=integrate(t0,x) +--E 959 + +--S 960 of 1457 +--m0:=a0-r0 +--E 960 + +--S 961 of 1457 +--d0:=D(m0,x) +--E 961 + +)clear all + +--S 962 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1457 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(7/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2/15*(30*A*c^4*d^3+48*b^4*B*e^3-15*b*c^3*d^2*(B*d+3*A*e)-_ +-- 8*b^3*c*e^2*(16*B*d+5*A*e)+b^2*c^2*d*e*(103*B*d+95*A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^4*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*e*(c*d-b*e)*(15*A*c^3*d^2-_ +-- 48*b^3*B*e^2-15*b*c^2*d*(4*B*d+5*A*e)+8*b^2*c*e*(13*B*d+5*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/5*e*(10*A*c^2*d+6*b^2*B*e-5*b*c*(B*d+A*e))*_ +-- (d+e*x)^(3/2)*sqrt(b*x+c*x^2)/(b^2*c^2)-2*(b*B-2*A*c)*e*_ +-- (d+e*x)^(5/2)*sqrt(b*x+c*x^2)/(b^2*c)+2/15*e*(30*A*c^3*d^2-_ +-- 24*b^3*B*e^2-15*b*c^2*d*(B*d+2*A*e)+b^2*c*e*(43*B*d+20*A*e))*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c^3) +--E 963 + +--S 964 of 1457 +--a0:=integrate(t0,x) +--E 964 + +--S 965 of 1457 +--m0:=a0-r0 +--E 965 + +--S 966 of 1457 +--d0:=D(m0,x) +--E 966 + +)clear all + +--S 967 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1457 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(5/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2/3*(6*A*c^3*d^2-8*b^3*B*e^2-3*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ +-- (13*B*d+6*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^3*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(c*d-b*e)*_ +-- (9*b*B*c*d-3*A*c^2*d-8*b^2*B*e+6*A*b*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(7/2)*sqrt(-b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2*(b*B-2*A*c)*e*(d+e*x)^(3/2)*sqrt(b*x+c*x^2)/(b^2*c)+2/3*e*_ +-- (6*A*c^2*d+4*b^2*B*e-3*b*c*(B*d+A*e))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/_ +-- (b^2*c^2) +--E 968 + +--S 969 of 1457 +--a0:=integrate(t0,x) +--E 969 + +--S 970 of 1457 +--m0:=a0-r0 +--E 970 + +--S 971 of 1457 +--d0:=D(m0,x) +--E 971 + +)clear all + +--S 972 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1457 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^2*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(2*b*B-A*c)*e*(c*d-b*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c) +--E 973 + +--S 974 of 1457 +--a0:=integrate(t0,x) +--E 974 + +--S 975 of 1457 +--m0:=a0-r0 +--E 975 + +--S 976 of 1457 +--d0:=D(m0,x) +--E 976 + +)clear all + +--S 977 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1457 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*sqrt(b*x+c*x^2))-_ +-- 2*(b*B-2*A*c)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(b*B-A*c)*e*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(3/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)) +--E 978 + +--S 979 of 1457 +--a0:=integrate(t0,x) +--E 979 + +--S 980 of 1457 +--m0:=a0-r0 +--E 980 + +--S 981 of 1457 +--d0:=D(m0,x) +--E 981 + +)clear all + +--S 982 of 1457 +t0:=(A+B*x)/((b*x+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ----------------------------------- +--R +----------+ +--R 2 +-------+ | 2 +--R (c x + b x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1457 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*d*_ +-- (c*d-b*e)*sqrt(b*x+c*x^2))+2*(b*B*d-2*A*c*d+A*b*e)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^2*(c*d-b*e)*sqrt(-d)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*A*e*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(d*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 983 + +--S 984 of 1457 +--a0:=integrate(t0,x) +--E 984 + +--S 985 of 1457 +--m0:=a0-r0 +--E 985 + +--S 986 of 1457 +--d0:=D(m0,x) +--E 986 + +)clear all + +--S 987 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------- +--R +----------+ +--R 3 2 +-------+ | 2 +--R (c e x + (b e + c d)x + b d x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1457 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*(2*A*c^2*d^2-b^2*e*(B*d-2*A*e)-_ +-- b*c*d*(B*d+2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (b^2*(-d)^(3/2)*(c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*e*(b*B*d+A*c*d-2*A*b*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(d^2*(c*d-b*e)*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2*e*(2*A*c^2*d^2-b^2*e*(B*d-2*A*e)-b*c*d*(B*d+_ +-- 2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 988 + +--S 989 of 1457 +--a0:=integrate(t0,x) +--E 989 + +--S 990 of 1457 +--m0:=a0-r0 +--E 990 + +--S 991 of 1457 +--d0:=D(m0,x) +--E 991 + +)clear all + +--S 992 of 1457 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 4 2 3 2 2 2 +-------+ +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1457 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- (d+e*x)^(3/2)*sqrt(b*x+c*x^2))-2/3*(6*A*c^3*d^3-b^2*c*d*e*(7*B*d-_ +-- 19*A*e)+2*b^3*e^2*(B*d-4*A*e)-3*b*c^2*d^2*(B*d+3*A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^2*(-d)^(5/2)*(c*d-b*e)^3*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(3*A*c^2*d^2+3*b*c*d*(2*B*d-_ +-- 5*A*e)-2*b^2*e*(B*d-4*A*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (d^3*(c*d-b*e)^2*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*e*(6*A*c^2*d^2-b^2*e*(B*d-4*A*e)-3*b*c*d*(B*d+2*A*e))*_ +-- sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-_ +-- 2/3*e*(6*A*c^3*d^3-b^2*c*d*e*(7*B*d-19*A*e)+2*b^3*e^2*(B*d-4*A*e)-_ +-- 3*b*c^2*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*_ +-- sqrt(d+e*x)) +--E 993 + +--S 994 of 1457 +--a0:=integrate(t0,x) +--E 994 + +--S 995 of 1457 +--m0:=a0-r0 +--E 995 + +--S 996 of 1457 +--d0:=D(m0,x) +--E 996 + +)clear all + +--S 997 of 1457 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1457 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(7/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(d+e*x)^(5/2)*(b*(4*b*B*d-8*A*c*d+7*A*b*e)-(16*A*c^2*d-_ +-- 3*b^2*B*e-8*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^4*d^3-8*b^4*B*e^3+b^3*c*e^2*(5*B*d+2*A*e)-8*b*c^3*d^2*_ +-- (B*d+3*A*e)+b^2*c^2*d*e*(5*B*d+4*A*e))*(b+c*x)*elliptic_e(asin(_ +-- sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(b^4*c^3*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+_ +-- c*x^2))-2/3*e*(c*d-b*e)*(8*A*c^3*d^2+8*b^3*B*e^2-b^2*c*e*(B*d+_ +-- 2*A*e)-b*c^2*d*(4*B*d+5*A*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- ((-b)^(5/2)*c^(7/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*_ +-- (16*A*c^2*d-3*b^2*B*e-8*b*c*(B*d+A*e))*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/(b^4*c)-2/3*e*(16*A*c^3*d^2+4*b^3*B*e^2+b^2*c*e*_ +-- (B*d-A*e)-8*b*c^2*d*(B*d+2*A*e))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^4*c^2) +--E 998 + +--S 999 of 1457 +--a0:=integrate(t0,x) +--E 999 + +--S 1000 of 1457 +--m0:=a0-r0 +--E 1000 + +--S 1001 of 1457 +--d0:=D(m0,x) +--E 1001 + +)clear all + +--S 1002 of 1457 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1457 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(5/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(d+e*x)^(3/2)*(b*(4*b*B*d-8*A*c*d+5*A*b*e)-(16*A*c^2*d-_ +-- b^2*B*e-8*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^3*d^2+2*b^3*B*e^2+b^2*c*e*(3*B*d+A*e)-8*b*c^2*d*(B*d+_ +-- 2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/_ +-- (b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*c^2*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(c*d-b*e)*_ +-- (8*A*c^2*d-2*b^2*B*e-b*c*(4*B*d+A*e))*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/((-b)^(5/2)*c^(5/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*e*(16*A*c^2*d-b^2*B*e-8*b*c*(B*d+A*e))*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/(b^4*c) +--E 1003 + +--S 1004 of 1457 +--a0:=integrate(t0,x) +--E 1004 + +--S 1005 of 1457 +--m0:=a0-r0 +--E 1005 + +--S 1006 of 1457 +--d0:=D(m0,x) +--E 1006 + +)clear all + +--S 1007 of 1457 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1457 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(b*(4*b*B*d-8*A*c*d+3*A*b*e)-(16*A*c^2*d+b^2*B*e-8*b*c*_ +-- (B*d+A*e))*x)*sqrt(d+e*x)/(b^4*sqrt(b*x+c*x^2))-2/3*(16*A*c^2*d+_ +-- b^2*B*e-8*b*c*(B*d+A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (b^4*c*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*_ +-- (4*b*B*c*d-8*A*c^2*d-b^2*B*e+5*A*b*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/((-b)^(5/2)*c^(3/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 1008 + +--S 1009 of 1457 +--a0:=integrate(t0,x) +--E 1009 + +--S 1010 of 1457 +--m0:=a0-r0 +--E 1010 + +--S 1011 of 1457 +--d0:=D(m0,x) +--E 1011 + +)clear all + +--S 1012 of 1457 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1457 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(b*(c*d-b*e)*(4*b*B*d-8*A*c*d+A*b*e)-c*(16*A*c^2*d^2+b^2*e*_ +-- (7*B*d+A*e)-8*b*c*d*(B*d+2*A*e))*x)*sqrt(d+e*x)/(b^4*d*(c*d-b*e)*_ +-- sqrt(b*x+c*x^2))+2/3*(16*A*c^2*d^2+b^2*e*(7*B*d+A*e)-8*b*c*d*_ +-- (B*d+2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*(c*d-b*e)*sqrt(-d)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(4*b*B*d-_ +-- 8*A*c*d+A*b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 1013 + +--S 1014 of 1457 +--a0:=integrate(t0,x) +--E 1014 + +--S 1015 of 1457 +--m0:=a0-r0 +--E 1015 + +--S 1016 of 1457 +--d0:=D(m0,x) +--E 1016 + +)clear all + +--S 1017 of 1457 +t0:=(A+B*x)/((b*x+c*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ---------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 +-------+ | 2 +--R (c x + 2b c x + b x )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1457 +--r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/_ +-- (b^2*d*(c*d-b*e)*(b*x+c*x^2)^(3/2))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+_ +-- b^2*e*(3*B*d-2*A*e)-b*c*d*(4*B*d+5*A*e))+c*(16*A*c^3*d^3-b^3*e^2*_ +-- (3*B*d-2*A*e)-8*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(13*B*d+4*A*e))*x)*_ +-- sqrt(d+e*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^3*d^3-b^3*e^2*(3*B*d-2*A*e)-8*b*c^2*d^2*(B*d+3*A*e)+_ +-- b^2*c*d*e*(13*B*d+4*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*(-d)^(3/2)*_ +-- (c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*_ +-- (8*A*c^2*d^2+b^2*e*(3*B*d-2*A*e)-b*c*d*(4*B*d+5*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d^2*(c*d-b*e)*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 1018 + +--S 1019 of 1457 +--a0:=integrate(t0,x) +--E 1019 + +--S 1020 of 1457 +--m0:=a0-r0 +--E 1020 + +--S 1021 of 1457 +--d0:=D(m0,x) +--E 1021 + +)clear all + +--S 1022 of 1457 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 5 2 4 2 3 2 2 +-------+ +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1457 +--r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- (b*x+c*x^2)^(3/2)*sqrt(d+e*x))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+b^2*_ +-- e*(3*B*d-4*A*e)-b*c*d*(4*B*d+3*A*e))+c*(16*A*c^3*d^3+15*b^2*B*_ +-- c*d^2*e-b^3*e^2*(3*B*d-4*A*e)-8*b*c^2*d^2*(B*d+3*A*e))*x)/_ +-- (b^4*d^2*(c*d-b*e)^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*_ +-- (16*A*c^4*d^4-b^3*c*d*e^2*(9*B*d-7*A*e)-8*b*c^3*d^3*(B*d+4*A*e)+_ +-- b^2*c^2*d^2*e*(19*B*d+9*A*e)+b^4*(6*B*d*e^3-8*A*e^4))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^4*(-d)^(5/2)*(c*d-b*e)^3*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(8*A*c^3*d^3+3*b^2*c*d*e*_ +-- (2*B*d-A*e)-b*c^2*d^2*(4*B*d+9*A*e)-b^3*(6*B*d*e^2-8*A*e^3))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d^3*(c*d-b*e)^2*_ +-- sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(16*A*c^4*d^4-_ +-- b^3*c*d*e^2*(9*B*d-7*A*e)-8*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*_ +-- e*(19*B*d+9*A*e)+b^4*(6*B*d*e^3-8*A*e^4))*sqrt(b*x+c*x^2)/_ +-- (b^4*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 1023 + +--S 1024 of 1457 +--a0:=integrate(t0,x) +--E 1024 + +--S 1025 of 1457 +--m0:=a0-r0 +--E 1025 + +--S 1026 of 1457 +--d0:=D(m0,x) +--E 1026 + +)clear all + +--S 1027 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + A c x + B a x + A a)(e x + d) +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1457 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(3*B*c*d^2-2*A*_ + c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^4*(2+m))-c*(3*B*d-A*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R (A c e - 3B c d)m + (7A c e - 21B c d)m + (14A c e - 42B c d)m +--R + +--R 8A c e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 2 2 2 +--R (B a e - 2A c d e + 3B c d )m + (8B a e - 16A c d e + 24B c d )m +--R + +--R 2 2 2 2 +--R (19B a e - 38A c d e + 57B c d )m + 12B a e - 24A c d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (A a e - B a d e + A c d e - B c d )m +--R + +--R 3 2 2 3 2 +--R (9A a e - 9B a d e + 9A c d e - 9B c d )m +--R + +--R 3 2 2 3 3 +--R (26A a e - 26B a d e + 26A c d e - 26B c d )m + 24A a e +--R + +--R 2 2 3 +--R - 24B a d e + 24A c d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R (A c e + B c d e )m + (7A c e + 3B c d e )m +--R + +--R 4 3 4 +--R (14A c e + 2B c d e )m + 8A c e +--R * +--R 3 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (B a e + A c d e )m + (8B a e + 5A c d e - 3B c d e )m +--R + +--R 4 3 2 2 4 +--R (19B a e + 4A c d e - 3B c d e )m + 12B a e +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (A a e + B a d e )m + (9A a e + 7B a d e - 2A c d e )m +--R + +--R 4 3 2 2 3 4 +--R (26A a e + 12B a d e - 8A c d e + 6B c d e)m + 24A a e +--R * +--R x +--R + +--R 3 3 3 2 2 2 +--R A a d e m + (9A a d e - B a d e )m +--R + +--R 3 2 2 3 3 2 2 +--R (26A a d e - 7B a d e + 2A c d e)m + 24A a d e - 12B a d e +--R + +--R 3 4 +--R 8A c d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 1029 + +--S 1030 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R (A c e + B c d e )m + (7A c e + 3B c d e )m +--R + +--R 4 3 4 +--R (14A c e + 2B c d e )m + 8A c e +--R * +--R 3 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (B a e + A c d e )m + (8B a e + 5A c d e - 3B c d e )m +--R + +--R 4 3 2 2 4 +--R (19B a e + 4A c d e - 3B c d e )m + 12B a e +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (A a e + B a d e )m + (9A a e + 7B a d e - 2A c d e )m +--R + +--R 4 3 2 2 3 4 +--R (26A a e + 12B a d e - 8A c d e + 6B c d e)m + 24A a e +--R * +--R x +--R + +--R 3 3 3 2 2 2 +--R A a d e m + (9A a d e - B a d e )m +--R + +--R 3 2 2 3 3 2 2 +--R (26A a d e - 7B a d e + 2A c d e)m + 24A a d e - 12B a d e +--R + +--R 3 4 +--R 8A c d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 2 m + 4 +--R (- B c m - 6B c m - 11B c m - 6B c)(e x + d) +--R + +--R 3 2 +--R (- A c e + 3B c d)m + (- 7A c e + 21B c d)m +--R + +--R (- 14A c e + 42B c d)m - 8A c e + 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R (- B a e + 2A c d e - 3B c d )m +--R + +--R 2 2 2 +--R (- 8B a e + 16A c d e - 24B c d )m +--R + +--R 2 2 2 2 +--R (- 19B a e + 38A c d e - 57B c d )m - 12B a e + 24A c d e - 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (- A a e + B a d e - A c d e + B c d )m +--R + +--R 3 2 2 3 2 +--R (- 9A a e + 9B a d e - 9A c d e + 9B c d )m +--R + +--R 3 2 2 3 3 +--R (- 26A a e + 26B a d e - 26A c d e + 26B c d )m - 24A a e +--R + +--R 2 2 3 +--R 24B a d e - 24A c d e + 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1031 + +)clear all + +--S 1032 of 1457 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 5 4 2 3 6 +--R B c e x + (A c e + 5B c d e )x + (B a e + 5A c d e + 10B c d e )x +--R + +--R 5 4 2 3 3 2 5 +--R (A a e + 5B a d e + 10A c d e + 10B c d e )x +--R + +--R 4 2 3 3 2 4 4 +--R (5A a d e + 10B a d e + 10A c d e + 5B c d e)x +--R + +--R 2 3 3 2 4 5 3 +--R (10A a d e + 10B a d e + 5A c d e + B c d )x +--R + +--R 3 2 4 5 2 4 5 5 +--R (10A a d e + 5B a d e + A c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1032 + +--S 1033 of 1457 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^6/e^4+1/7*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^7/e^4-1/8*c*(3*B*d-A*e)*(d+e*x)^8/e^4+1/9*B*_ + c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 1 9 5 8 10 2 7 7 +--R (- B a e + - A c d e + -- B c d e )x +--R 7 7 7 +--R + +--R 1 9 5 8 5 2 7 5 3 6 6 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 6 6 3 3 +--R + +--R 8 2 7 3 6 4 5 5 +--R (A a d e + 2B a d e + 2A c d e + B c d e )x +--R + +--R 5 2 7 5 3 6 5 4 5 1 5 4 4 +--R (- A a d e + - B a d e + - A c d e + - B c d e )x +--R 2 2 4 4 +--R + +--R 10 3 6 5 4 5 1 5 4 3 5 4 5 1 5 4 2 +--R (-- A a d e + - B a d e + - A c d e )x + (- A a d e + - B a d e )x +--R 3 3 3 2 2 +--R + +--R 5 4 1 6 3 1 7 2 1 8 1 9 +--R A a d e x + - A a d e - -- B a d e + --- A c d e - --- B c d +--R 6 42 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1033 + +--S 1034 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 9 1 5 5 4 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 1 5 5 4 10 2 3 7 +--R (- B a e + - A c d e + -- B c d e )x +--R 7 7 7 +--R + +--R 1 5 5 4 5 2 3 5 3 2 6 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 6 6 3 3 +--R + +--R 4 2 3 3 2 4 5 +--R (A a d e + 2B a d e + 2A c d e + B c d e)x +--R + +--R 5 2 3 5 3 2 5 4 1 5 4 +--R (- A a d e + - B a d e + - A c d e + - B c d )x +--R 2 2 4 4 +--R + +--R 10 3 2 5 4 1 5 3 5 4 1 5 2 5 +--R (-- A a d e + - B a d e + - A c d )x + (- A a d e + - B a d )x + A a d x +--R 3 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1034 + +--S 1035 of 1457 +m0:=a0-r0 +--R +--R +--R 1 6 3 1 7 2 1 8 1 9 +--R - - A a d e + -- B a d e - --- A c d e + --- B c d +--R 6 42 168 504 +--R (4) ----------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1035 + +--S 1036 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1036 + +)clear all + +--S 1037 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 4 3 2 2 5 +--R B c e x + (A c e + 4B c d e )x + (B a e + 4A c d e + 6B c d e )x +--R + +--R 4 3 2 2 3 4 +--R (A a e + 4B a d e + 6A c d e + 4B c d e)x +--R + +--R 3 2 2 3 4 3 +--R (4A a d e + 6B a d e + 4A c d e + B c d )x +--R + +--R 2 2 3 4 2 3 4 4 +--R (6A a d e + 4B a d e + A c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1037 + +--S 1038 of 1457 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^5/e^4+1/6*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^6/e^4-1/7*c*(3*B*d-A*e)*(d+e*x)^7/e^4+1/8*B*c*_ + (d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 8 4 7 7 +--R - B c e x + (- A c e + - B c d e )x +--R 8 7 7 +--R + +--R 1 8 2 7 2 6 6 +--R (- B a e + - A c d e + B c d e )x +--R 6 3 +--R + +--R 1 8 4 7 6 2 6 4 3 5 5 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 7 3 2 6 3 5 1 4 4 4 +--R (A a d e + - B a d e + A c d e + - B c d e )x +--R 2 4 +--R + +--R 2 6 4 3 5 1 4 4 3 3 5 1 4 4 2 +--R (2A a d e + - B a d e + - A c d e )x + (2A a d e + - B a d e )x +--R 3 3 2 +--R + +--R 4 4 1 5 3 1 6 2 1 7 1 8 +--R A a d e x + - A a d e - -- B a d e + --- A c d e - --- B c d +--R 5 30 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1038 + +--S 1039 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 8 1 4 4 3 7 +--R - B c e x + (- A c e + - B c d e )x +--R 8 7 7 +--R + +--R 1 4 2 3 2 2 6 +--R (- B a e + - A c d e + B c d e )x +--R 6 3 +--R + +--R 1 4 4 3 6 2 2 4 3 5 +--R (- A a e + - B a d e + - A c d e + - B c d e)x +--R 5 5 5 5 +--R + +--R 3 3 2 2 3 1 4 4 +--R (A a d e + - B a d e + A c d e + - B c d )x +--R 2 4 +--R + +--R 2 2 4 3 1 4 3 3 1 4 2 4 +--R (2A a d e + - B a d e + - A c d )x + (2A a d e + - B a d )x + A a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1039 + +--S 1040 of 1457 +m0:=a0-r0 +--R +--R +--R 1 5 3 1 6 2 1 7 1 8 +--R - - A a d e + -- B a d e - --- A c d e + --- B c d +--R 5 30 105 280 +--R (4) ----------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1040 + +--S 1041 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1041 + +)clear all + +--S 1042 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 3 2 2 4 +--R B c e x + (A c e + 3B c d e )x + (B a e + 3A c d e + 3B c d e)x +--R + +--R 3 2 2 3 3 +--R (A a e + 3B a d e + 3A c d e + B c d )x +--R + +--R 2 2 3 2 2 3 3 +--R (3A a d e + 3B a d e + A c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1042 + +--S 1043 of 1457 +r0:=-1/4*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^4/e^4+1/5*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^5/e^4-1/6*c*(3*B*d-A*e)*(d+e*x)^6/e^4+_ + 1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 7 1 6 6 +--R - B c e x + (- A c e + - B c d e )x +--R 7 6 2 +--R + +--R 1 7 3 6 3 2 5 5 +--R (- B a e + - A c d e + - B c d e )x +--R 5 5 5 +--R + +--R 1 7 3 6 3 2 5 1 3 4 4 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 6 2 5 1 3 4 3 3 2 5 1 3 4 2 +--R (A a d e + B a d e + - A c d e )x + (- A a d e + - B a d e )x +--R 3 2 2 +--R + +--R 3 4 1 4 3 1 5 2 1 6 1 7 +--R A a d e x + - A a d e - -- B a d e + -- A c d e - --- B c d +--R 4 20 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1043 + +--S 1044 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 7 1 3 1 2 6 +--R - B c e x + (- A c e + - B c d e )x +--R 7 6 2 +--R + +--R 1 3 3 2 3 2 5 +--R (- B a e + - A c d e + - B c d e)x +--R 5 5 5 +--R + +--R 1 3 3 2 3 2 1 3 4 +--R (- A a e + - B a d e + - A c d e + - B c d )x +--R 4 4 4 4 +--R + +--R 2 2 1 3 3 3 2 1 3 2 3 +--R (A a d e + B a d e + - A c d )x + (- A a d e + - B a d )x + A a d x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1044 + +--S 1045 of 1457 +m0:=a0-r0 +--R +--R +--R 1 4 3 1 5 2 1 6 1 7 +--R - - A a d e + -- B a d e - -- A c d e + --- B c d +--R 4 20 60 140 +--R (4) ---------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1045 + +--S 1046 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1046 + +)clear all + +--S 1047 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 2 2 3 +--R B c e x + (A c e + 2B c d e)x + (B a e + 2A c d e + B c d )x +--R + +--R 2 2 2 2 2 +--R (A a e + 2B a d e + A c d )x + (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1047 + +--S 1048 of 1457 +r0:=a*A*d^2*x+1/2*a*d*(B*d+2*A*e)*x^2+1/3*(A*c*d^2+2*a*B*d*e+a*A*e^2)*x^3+_ + 1/4*(B*c*d^2+2*A*c*d*e+a*B*e^2)*x^4+1/5*c*e*(2*B*d+A*e)*x^5+_ + 1/6*B*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - B c e x + (- A c e + - B c d e)x + (- B a e + - A c d e + - B c d )x +--R 6 5 5 4 2 4 +--R + +--R 1 2 2 1 2 3 1 2 2 2 +--R (- A a e + - B a d e + - A c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1048 + +--S 1049 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - B c e x + (- A c e + - B c d e)x + (- B a e + - A c d e + - B c d )x +--R 6 5 5 4 2 4 +--R + +--R 1 2 2 1 2 3 1 2 2 2 +--R (- A a e + - B a d e + - A c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1049 + +--S 1050 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1050 + +--S 1051 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1051 + +)clear all + +--S 1052 of 1457 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + (A c e + B c d)x + (B a e + A c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 1052 + +--S 1053 of 1457 +r0:=a*A*d*x+1/2*a*(B*d+A*e)*x^2+1/3*(A*c*d+a*B*e)*x^3+1/4*c*(B*d+A*e)*x^4+_ + 1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 4 1 1 3 +--R - B c e x + (- A c e + - B c d)x + (- B a e + - A c d)x +--R 5 4 4 3 3 +--R + +--R 1 1 2 +--R (- A a e + - B a d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1053 + +--S 1054 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 1 1 4 1 1 3 +--R - B c e x + (- A c e + - B c d)x + (- B a e + - A c d)x +--R 5 4 4 3 3 +--R + +--R 1 1 2 +--R (- A a e + - B a d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1054 + +--S 1055 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1055 + +--S 1056 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1056 + +)clear all + +--S 1057 of 1457 +t0:=(A+B*x)*(a+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + A c x + B a x + A a +--R Type: Polynomial(Integer) +--E 1057 + +--S 1058 of 1457 +r0:=a*A*x+1/2*a*B*x^2+1/3*A*c*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 3 1 2 +--R (2) - B c x + - A c x + - B a x + A a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1058 + +--S 1059 of 1457 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 3 1 2 +--R (3) - B c x + - A c x + - B a x + A a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1059 + +--S 1060 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1060 + +--S 1061 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1061 + +)clear all + +--S 1062 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1062 + +--S 1063 of 1457 +r0:=(B*c*d^2-A*c*d*e+a*B*e^2)*x/e^3-1/2*c*(B*d-A*e)*x^2/e^2+1/3*B*c*x^3/e-_ + (B*d-A*e)*(c*d^2+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 3 3 3 +--R (6A a e - 6B a d e + 6A c d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 3 2 2 +--R (3A c e - 3B c d e )x + (6B a e - 6A c d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 3 3 +--R (6A a e - 6B a d e + 6A c d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 3 2 2 +--R (3A c e - 3B c d e )x + (6B a e - 6A c d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 1064 + +--S 1065 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1066 + +)clear all + +--S 1067 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1067 + +--S 1068 of 1457 +r0:=-c*(2*B*d-A*e)*x/e^3+1/2*B*c*x^2/e^2+(B*d-A*e)*(c*d^2+a*e^2)/_ + (e^4*(d+e*x))+(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((2B a e - 4A c d e + 6B c d e)x + 2B a d e - 4A c d e + 6B c d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 2 2 3 +--R B c e x + (2A c e - 3B c d e )x + (2A c d e - 4B c d e)x - 2A a e +--R + +--R 2 2 3 +--R 2B a d e - 2A c d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 +--R ((2B a e - 4A c d e + 6B c d e)x + 2B a d e - 4A c d e + 6B c d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 2 2 3 +--R B c e x + (2A c e - 3B c d e )x + (2A c d e - 4B c d e)x - 2A a e +--R + +--R 2 2 3 +--R 2B a d e - 2A c d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 1069 + +--S 1070 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1071 + +)clear all + +--S 1072 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1072 + +--S 1073 of 1457 +r0:=B*c*x/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^2)+(-3*B*c*d^2+_ + 2*A*c*d*e-a*B*e^2)/(e^4*(d+e*x))-c*(3*B*d-A*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 +--R (2A c e - 6B c d e )x + (4A c d e - 12B c d e)x + 2A c d e +--R + +--R 3 +--R - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 3 +--R 2B c e x + 4B c d e x + (- 2B a e + 4A c d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R - B a d e + 3A c d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 2 +--R (2A c e - 6B c d e )x + (4A c d e - 12B c d e)x + 2A c d e +--R + +--R 3 +--R - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 3 +--R 2B c e x + 4B c d e x + (- 2B a e + 4A c d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R - B a d e + 3A c d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 1074 + +--S 1075 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1076 + +)clear all + +--S 1077 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1077 + +--S 1078 of 1457 +r0:=1/3*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^2)+c*(3*B*d-A*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 +--R (- 6A c e + 18B c d e )x + (- 3B a e - 6A c d e + 27B c d e)x +--R + +--R 3 2 2 3 +--R - 2A a e - B a d e - 2A c d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 +--R (- 6A c e + 18B c d e )x + (- 3B a e - 6A c d e + 27B c d e)x +--R + +--R 3 2 2 3 +--R - 2A a e - B a d e - 2A c d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 1079 + +--S 1080 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1081 + +)clear all + +--S 1082 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1082 + +--S 1083 of 1457 +r0:=1/4*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^3)+1/2*c*(3*B*d-A*e)/(e^4*(d+e*x)^2)-_ + B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 3 3 2 2 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 1 3 1 2 2 1 3 1 2 +--R (- - B a e - - A c d e - B c d e)x - - A a e - -- B a d e +--R 3 3 4 12 +--R + +--R 1 2 1 3 +--R - -- A c d e - - B c d +--R 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1083 + +--S 1084 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 12B c e x + (- 6A c e - 18B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 4B a e - 4A c d e - 12B c d e)x - 3A a e - B a d e - A c d e +--R + +--R 3 +--R - 3B c d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1084 + +--S 1085 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1086 + +)clear all + +--S 1087 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1087 + +--S 1088 of 1457 +r0:=1/5*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^5)+1/4*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^4)+1/3*c*(3*B*d-A*e)/(e^4*(d+e*x)^3)-_ + 1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 2 +--R + +--R 1 3 1 2 1 2 1 3 1 2 +--R (- - B a e - - A c d e - - B c d e)x - - A a e - -- B a d e +--R 4 6 4 5 20 +--R + +--R 1 2 1 3 +--R - -- A c d e - -- B c d +--R 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1088 + +--S 1089 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 30B c e x + (- 20A c e - 30B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 15B a e - 10A c d e - 15B c d e)x - 12A a e - 3B a d e - 2A c d e +--R + +--R 3 +--R - 3B c d +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 1089 + +--S 1090 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1091 + +)clear all + +--S 1092 of 1457 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + A c x + B a x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1092 + +--S 1093 of 1457 +r0:=1/6*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^6)+1/5*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^5)+1/4*c*(3*B*d-A*e)/(e^4*(d+e*x)^4)-_ + 1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 +--R - - B c e x + (- - A c e - - B c d e )x +--R 3 4 4 +--R + +--R 1 3 1 2 1 2 1 3 1 2 +--R (- - B a e - -- A c d e - -- B c d e)x - - A a e - -- B a d e +--R 5 10 10 6 30 +--R + +--R 1 2 1 3 +--R - -- A c d e - -- B c d +--R 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1093 + +--S 1094 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 20B c e x + (- 15A c e - 15B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 12B a e - 6A c d e - 6B c d e)x - 10A a e - 2B a d e - A c d e +--R + +--R 3 +--R - B c d +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 4 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 1094 + +--S 1095 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1096 + +)clear all + +--S 1097 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 m +--R (1) (B c x + A c x + 2B a c x + 2A a c x + B a x + A a )(e x + d) +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1457 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))+(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^6*(2+m))-2*c*_ + (5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3+m)/(e^6*_ + (3+m))+2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(4+m)/(e^6*(4+m))-_ + c^2*(5*B*d-A*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 2 2 3 +--R (A c e - 5B c d)m + (16A c e - 80B c d)m + (95A c e - 475B c d)m +--R + +--R 2 2 2 2 2 2 +--R (260A c e - 1300B c d)m + (324A c e - 1620B c d)m + 144A c e +--R + +--R 2 +--R - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 5 +--R (2B a c e - 4A c d e + 10B c d )m +--R + +--R 2 2 2 2 4 +--R (34B a c e - 68A c d e + 170B c d )m +--R + +--R 2 2 2 2 3 +--R (214B a c e - 428A c d e + 1070B c d )m +--R + +--R 2 2 2 2 2 +--R (614B a c e - 1228A c d e + 3070B c d )m +--R + +--R 2 2 2 2 2 2 +--R (792B a c e - 1584A c d e + 3960B c d )m + 360B a c e - 720A c d e +--R + +--R 2 2 +--R 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 5 +--R (2A a c e - 6B a c d e + 6A c d e - 10B c d )m +--R + +--R 3 2 2 2 2 3 4 +--R (36A a c e - 108B a c d e + 108A c d e - 180B c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (242A a c e - 726B a c d e + 726A c d e - 1210B c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (744A a c e - 2232B a c d e + 2232A c d e - 3720B c d )m +--R + +--R 3 2 2 2 2 3 +--R (1016A a c e - 3048B a c d e + 3048A c d e - 5080B c d )m +--R + +--R 3 2 2 2 2 3 +--R 480A a c e - 1440B a c d e + 1440A c d e - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 3 2 2 2 3 2 4 5 +--R (B a e - 4A a c d e + 6B a c d e - 4A c d e + 5B c d )m +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (19B a e - 76A a c d e + 114B a c d e - 76A c d e + 95B c d )m +--R + +--R 2 4 3 2 2 2 3 +--R 137B a e - 548A a c d e + 822B a c d e - 548A c d e +--R + +--R 2 4 +--R 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R 461B a e - 1844A a c d e + 2766B a c d e - 1844A c d e +--R + +--R 2 4 +--R 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R 702B a e - 2808A a c d e + 4212B a c d e - 2808A c d e +--R + +--R 2 4 +--R 3510B c d +--R * +--R m +--R + +--R 2 4 3 2 2 2 3 2 4 +--R 360B a e - 1440A a c d e + 2160B a c d e - 1440A c d e + 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 5 +--R (A a e - B a d e + 2A a c d e - 2B a c d e + A c d e - B c d )m +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R 20A a e - 20B a d e + 40A a c d e - 40B a c d e + 20A c d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 155A a e - 155B a d e + 310A a c d e - 310B a c d e +--R + +--R 2 4 2 5 +--R 155A c d e - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 580A a e - 580B a d e + 1160A a c d e - 1160B a c d e +--R + +--R 2 4 2 5 +--R 580A c d e - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 1044A a e - 1044B a d e + 2088A a c d e - 2088B a c d e +--R + +--R 2 4 2 5 +--R 1044A c d e - 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 720A a e - 720B a d e + 1440A a c d e - 1440B a c d e +--R + +--R 2 4 2 5 +--R 720A c d e - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 2 6 2 5 4 +--R (A c e + B c d e )m + (16A c e + 10B c d e )m +--R + +--R 2 6 2 5 3 2 6 2 5 2 +--R (95A c e + 35B c d e )m + (260A c e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R (324A c e + 24B c d e )m + 144A c e +--R * +--R 5 +--R x +--R + +--R 6 2 5 5 6 2 5 2 2 4 4 +--R (2B a c e + A c d e )m + (34B a c e + 12A c d e - 5B c d e )m +--R + +--R 6 2 5 2 2 4 3 +--R (214B a c e + 47A c d e - 30B c d e )m +--R + +--R 6 2 5 2 2 4 2 +--R (614B a c e + 72A c d e - 55B c d e )m +--R + +--R 6 2 5 2 2 4 6 +--R (792B a c e + 36A c d e - 30B c d e )m + 360B a c e +--R * +--R 4 +--R x +--R + +--R 6 5 5 +--R (2A a c e + 2B a c d e )m +--R + +--R 6 5 2 2 4 4 +--R (36A a c e + 28B a c d e - 4A c d e )m +--R + +--R 6 5 2 2 4 2 3 3 3 +--R (242A a c e + 130B a c d e - 36A c d e + 20B c d e )m +--R + +--R 6 5 2 2 4 2 3 3 2 +--R (744A a c e + 224B a c d e - 80A c d e + 60B c d e )m +--R + +--R 6 5 2 2 4 2 3 3 +--R (1016A a c e + 120B a c d e - 48A c d e + 40B c d e )m +--R + +--R 6 +--R 480A a c e +--R * +--R 3 +--R x +--R + +--R 2 6 5 5 +--R (B a e + 2A a c d e )m +--R + +--R 2 6 5 2 4 4 +--R (19B a e + 32A a c d e - 6B a c d e )m +--R + +--R 2 6 5 2 4 2 3 3 3 +--R (137B a e + 178A a c d e - 72B a c d e + 12A c d e )m +--R + +--R 2 6 5 2 4 2 3 3 +--R 461B a e + 388A a c d e - 246B a c d e + 84A c d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 5 2 4 2 3 3 +--R 702B a e + 240A a c d e - 180B a c d e + 72A c d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R m +--R + +--R 2 6 +--R 360B a e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 5 2 6 2 5 2 4 4 +--R (A a e + B a d e )m + (20A a e + 18B a d e - 4A a c d e )m +--R + +--R 2 6 2 5 2 4 3 3 3 +--R (155A a e + 119B a d e - 60A a c d e + 12B a c d e )m +--R + +--R 2 6 2 5 2 4 3 3 +--R 580A a e + 342B a d e - 296A a c d e + 132B a c d e +--R + +--R 2 4 2 +--R - 24A c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 2 4 3 3 +--R 1044A a e + 360B a d e - 480A a c d e + 360B a c d e +--R + +--R 2 4 2 2 5 +--R - 144A c d e + 120B c d e +--R * +--R m +--R + +--R 2 6 +--R 720A a e +--R * +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A a d e m + (20A a d e - B a d e )m +--R + +--R 2 5 2 2 4 3 3 3 +--R (155A a d e - 18B a d e + 4A a c d e )m +--R + +--R 2 5 2 2 4 3 3 4 2 2 +--R (580A a d e - 119B a d e + 60A a c d e - 12B a c d e )m +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 1044A a d e - 342B a d e + 296A a c d e - 132B a c d e +--R + +--R 2 5 +--R 24A c d e +--R * +--R m +--R + +--R 2 5 2 2 4 3 3 4 2 2 5 +--R 720A a d e - 360B a d e + 480A a c d e - 360B a c d e + 144A c d e +--R + +--R 2 6 +--R - 120B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Union(Expression(Integer),...) +--E 1099 + +--S 1100 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 2 6 2 5 4 +--R (A c e + B c d e )m + (16A c e + 10B c d e )m +--R + +--R 2 6 2 5 3 2 6 2 5 2 +--R (95A c e + 35B c d e )m + (260A c e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R (324A c e + 24B c d e )m + 144A c e +--R * +--R 5 +--R x +--R + +--R 6 2 5 5 +--R (2B a c e + A c d e )m +--R + +--R 6 2 5 2 2 4 4 +--R (34B a c e + 12A c d e - 5B c d e )m +--R + +--R 6 2 5 2 2 4 3 +--R (214B a c e + 47A c d e - 30B c d e )m +--R + +--R 6 2 5 2 2 4 2 +--R (614B a c e + 72A c d e - 55B c d e )m +--R + +--R 6 2 5 2 2 4 6 +--R (792B a c e + 36A c d e - 30B c d e )m + 360B a c e +--R * +--R 4 +--R x +--R + +--R 6 5 5 +--R (2A a c e + 2B a c d e )m +--R + +--R 6 5 2 2 4 4 +--R (36A a c e + 28B a c d e - 4A c d e )m +--R + +--R 6 5 2 2 4 2 3 3 3 +--R (242A a c e + 130B a c d e - 36A c d e + 20B c d e )m +--R + +--R 6 5 2 2 4 2 3 3 2 +--R (744A a c e + 224B a c d e - 80A c d e + 60B c d e )m +--R + +--R 6 5 2 2 4 2 3 3 +--R (1016A a c e + 120B a c d e - 48A c d e + 40B c d e )m +--R + +--R 6 +--R 480A a c e +--R * +--R 3 +--R x +--R + +--R 2 6 5 5 +--R (B a e + 2A a c d e )m +--R + +--R 2 6 5 2 4 4 +--R (19B a e + 32A a c d e - 6B a c d e )m +--R + +--R 2 6 5 2 4 2 3 3 3 +--R (137B a e + 178A a c d e - 72B a c d e + 12A c d e )m +--R + +--R 2 6 5 2 4 2 3 3 +--R 461B a e + 388A a c d e - 246B a c d e + 84A c d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 5 2 4 2 3 3 +--R 702B a e + 240A a c d e - 180B a c d e + 72A c d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R m +--R + +--R 2 6 +--R 360B a e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 5 2 6 2 5 2 4 4 +--R (A a e + B a d e )m + (20A a e + 18B a d e - 4A a c d e )m +--R + +--R 2 6 2 5 2 4 3 3 3 +--R (155A a e + 119B a d e - 60A a c d e + 12B a c d e )m +--R + +--R 2 6 2 5 2 4 3 3 +--R 580A a e + 342B a d e - 296A a c d e + 132B a c d e +--R + +--R 2 4 2 +--R - 24A c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 2 4 3 3 +--R 1044A a e + 360B a d e - 480A a c d e + 360B a c d e +--R + +--R 2 4 2 2 5 +--R - 144A c d e + 120B c d e +--R * +--R m +--R + +--R 2 6 +--R 720A a e +--R * +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A a d e m + (20A a d e - B a d e )m +--R + +--R 2 5 2 2 4 3 3 3 +--R (155A a d e - 18B a d e + 4A a c d e )m +--R + +--R 2 5 2 2 4 3 3 4 2 2 +--R (580A a d e - 119B a d e + 60A a c d e - 12B a c d e )m +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 1044A a d e - 342B a d e + 296A a c d e - 132B a c d e +--R + +--R 2 5 +--R 24A c d e +--R * +--R m +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 720A a d e - 360B a d e + 480A a c d e - 360B a c d e +--R + +--R 2 5 2 6 +--R 144A c d e - 120B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (- B c m - 15B c m - 85B c m - 225B c m - 274B c m - 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R (- A c e + 5B c d)m + (- 16A c e + 80B c d)m +--R + +--R 2 2 3 2 2 2 +--R (- 95A c e + 475B c d)m + (- 260A c e + 1300B c d)m +--R + +--R 2 2 2 2 +--R (- 324A c e + 1620B c d)m - 144A c e + 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 5 +--R (- 2B a c e + 4A c d e - 10B c d )m +--R + +--R 2 2 2 2 4 +--R (- 34B a c e + 68A c d e - 170B c d )m +--R + +--R 2 2 2 2 3 +--R (- 214B a c e + 428A c d e - 1070B c d )m +--R + +--R 2 2 2 2 2 +--R (- 614B a c e + 1228A c d e - 3070B c d )m +--R + +--R 2 2 2 2 2 +--R (- 792B a c e + 1584A c d e - 3960B c d )m - 360B a c e +--R + +--R 2 2 2 +--R 720A c d e - 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 5 +--R (- 2A a c e + 6B a c d e - 6A c d e + 10B c d )m +--R + +--R 3 2 2 2 2 3 4 +--R (- 36A a c e + 108B a c d e - 108A c d e + 180B c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (- 242A a c e + 726B a c d e - 726A c d e + 1210B c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (- 744A a c e + 2232B a c d e - 2232A c d e + 3720B c d )m +--R + +--R 3 2 2 2 2 3 +--R (- 1016A a c e + 3048B a c d e - 3048A c d e + 5080B c d )m +--R + +--R 3 2 2 2 2 3 +--R - 480A a c e + 1440B a c d e - 1440A c d e + 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 3 2 2 2 3 2 4 5 +--R (- B a e + 4A a c d e - 6B a c d e + 4A c d e - 5B c d )m +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (- 19B a e + 76A a c d e - 114B a c d e + 76A c d e - 95B c d )m +--R + +--R 2 4 3 2 2 2 3 +--R - 137B a e + 548A a c d e - 822B a c d e + 548A c d e +--R + +--R 2 4 +--R - 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R - 461B a e + 1844A a c d e - 2766B a c d e + 1844A c d e +--R + +--R 2 4 +--R - 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R - 702B a e + 2808A a c d e - 4212B a c d e + 2808A c d e +--R + +--R 2 4 +--R - 3510B c d +--R * +--R m +--R + +--R 2 4 3 2 2 2 3 +--R - 360B a e + 1440A a c d e - 2160B a c d e + 1440A c d e +--R + +--R 2 4 +--R - 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - A a e + B a d e - 2A a c d e + 2B a c d e - A c d e +--R + +--R 2 5 +--R B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 20A a e + 20B a d e - 40A a c d e + 40B a c d e - 20A c d e +--R + +--R 2 5 +--R 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R - 155A a e + 155B a d e - 310A a c d e + 310B a c d e +--R + +--R 2 4 2 5 +--R - 155A c d e + 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R - 580A a e + 580B a d e - 1160A a c d e + 1160B a c d e +--R + +--R 2 4 2 5 +--R - 580A c d e + 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R - 1044A a e + 1044B a d e - 2088A a c d e + 2088B a c d e +--R + +--R 2 4 2 5 +--R - 1044A c d e + 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R - 720A a e + 720B a d e - 1440A a c d e + 1440B a c d e +--R + +--R 2 4 2 5 +--R - 720A c d e + 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1101 + +)clear all + +--S 1102 of 1457 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 10 2 5 2 4 9 5 2 4 2 2 3 8 +--R B c e x + (A c e + 5B c d e )x + (2B a c e + 5A c d e + 10B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 7 +--R (2A a c e + 10B a c d e + 10A c d e + 10B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 6 +--R (B a e + 10A a c d e + 20B a c d e + 10A c d e + 5B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 5 +--R (A a e + 5B a d e + 20A a c d e + 20B a c d e + 5A c d e + B c d )x +--R + +--R 2 4 2 2 3 3 2 4 2 5 4 +--R (5A a d e + 10B a d e + 20A a c d e + 10B a c d e + A c d )x +--R + +--R 2 2 3 2 3 2 4 5 3 +--R (10A a d e + 10B a d e + 10A a c d e + 2B a c d )x +--R + +--R 2 3 2 2 4 5 2 2 4 2 5 2 5 +--R (10A a d e + 5B a d e + 2A a c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1102 + +--S 1103 of 1457 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^6/e^6+1/7*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^6-1/4*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^8/e^6+2/9*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^9/e^6-1/10*c^2*(5*B*d-A*e)*(d+e*x)^10/e^6+_ + 1/11*B*c^2*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 2 11 11 1 2 11 1 2 10 10 +--R -- B c e x + (-- A c e + - B c d e )x +--R 11 10 2 +--R + +--R 2 11 5 2 10 10 2 2 9 9 +--R (- B a c e + - A c d e + -- B c d e )x +--R 9 9 9 +--R + +--R 1 11 5 10 5 2 2 9 5 2 3 8 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 1 2 11 10 10 20 2 9 10 2 3 8 5 2 4 7 7 +--R (- B a e + -- A a c d e + -- B a c d e + -- A c d e + - B c d e )x +--R 7 7 7 7 7 +--R + +--R 1 2 11 5 2 10 10 2 9 10 3 8 5 2 4 7 +--R - A a e + - B a d e + -- A a c d e + -- B a c d e + - A c d e +--R 6 6 3 3 6 +--R + +--R 1 2 5 6 +--R - B c d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 2 10 2 2 9 3 8 4 7 1 2 5 6 5 +--R (A a d e + 2B a d e + 4A a c d e + 2B a c d e + - A c d e )x +--R 5 +--R + +--R 5 2 2 9 5 2 3 8 5 4 7 1 5 6 4 +--R (- A a d e + - B a d e + - A a c d e + - B a c d e )x +--R 2 2 2 2 +--R + +--R 10 2 3 8 5 2 4 7 2 5 6 3 5 2 4 7 1 2 5 6 2 +--R (-- A a d e + - B a d e + - A a c d e )x + (- A a d e + - B a d e )x +--R 3 3 3 2 2 +--R + +--R 2 5 6 1 2 6 5 1 2 7 4 1 8 3 1 9 2 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 6 42 84 252 +--R + +--R 1 2 10 1 2 11 +--R ---- A c d e - ---- B c d +--R 1260 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1103 + +--S 1104 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 5 11 1 2 5 1 2 4 10 +--R -- B c e x + (-- A c e + - B c d e )x +--R 11 10 2 +--R + +--R 2 5 5 2 4 10 2 2 3 9 +--R (- B a c e + - A c d e + -- B c d e )x +--R 9 9 9 +--R + +--R 1 5 5 4 5 2 2 3 5 2 3 2 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 1 2 5 10 4 20 2 3 10 2 3 2 5 2 4 7 +--R (- B a e + -- A a c d e + -- B a c d e + -- A c d e + - B c d e)x +--R 7 7 7 7 7 +--R + +--R 1 2 5 5 2 4 10 2 3 10 3 2 5 2 4 +--R - A a e + - B a d e + -- A a c d e + -- B a c d e + - A c d e +--R 6 6 3 3 6 +--R + +--R 1 2 5 +--R - B c d +--R 6 +--R * +--R 6 +--R x +--R + +--R 2 4 2 2 3 3 2 4 1 2 5 5 +--R (A a d e + 2B a d e + 4A a c d e + 2B a c d e + - A c d )x +--R 5 +--R + +--R 5 2 2 3 5 2 3 2 5 4 1 5 4 +--R (- A a d e + - B a d e + - A a c d e + - B a c d )x +--R 2 2 2 2 +--R + +--R 10 2 3 2 5 2 4 2 5 3 5 2 4 1 2 5 2 2 5 +--R (-- A a d e + - B a d e + - A a c d )x + (- A a d e + - B a d )x + A a d x +--R 3 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1104 + +--S 1105 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 6 5 1 2 7 4 1 8 3 1 9 2 +--R - - A a d e + -- B a d e - -- A a c d e + --- B a c d e +--R 6 42 84 252 +--R + +--R 1 2 10 1 2 11 +--R - ---- A c d e + ---- B c d +--R 1260 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1105 + +--S 1106 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1106 + +)clear all + +--S 1107 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 4 2 3 2 2 2 7 +--R B c e x + (A c e + 4B c d e )x + (2B a c e + 4A c d e + 6B c d e )x +--R + +--R 4 3 2 2 2 2 3 6 +--R (2A a c e + 8B a c d e + 6A c d e + 4B c d e)x +--R + +--R 2 4 3 2 2 2 3 2 4 5 +--R (B a e + 8A a c d e + 12B a c d e + 4A c d e + B c d )x +--R + +--R 2 4 2 3 2 2 3 2 4 4 +--R (A a e + 4B a d e + 12A a c d e + 8B a c d e + A c d )x +--R + +--R 2 3 2 2 2 3 4 3 +--R (4A a d e + 6B a d e + 8A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 3 4 2 2 3 2 4 2 4 +--R (6A a d e + 4B a d e + 2A a c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1107 + +--S 1108 of 1457 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^5/e^6+1/6*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^6-2/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^7/e^6+1/4*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^8/e^6-1/9*c^2*(5*B*d-A*e)*(d+e*x)^9/e^6+_ + 1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 10 4 2 9 9 +--R -- B c e x + (- A c e + - B c d e )x +--R 10 9 9 +--R + +--R 1 10 1 2 9 3 2 2 8 8 +--R (- B a c e + - A c d e + - B c d e )x +--R 4 2 4 +--R + +--R 2 10 8 9 6 2 2 8 4 2 3 7 7 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 7 7 7 7 +--R + +--R 1 2 10 4 9 2 8 2 2 3 7 1 2 4 6 6 +--R (- B a e + - A a c d e + 2B a c d e + - A c d e + - B c d e )x +--R 6 3 3 6 +--R + +--R 1 2 10 4 2 9 12 2 8 8 3 7 1 2 4 6 5 +--R (- A a e + - B a d e + -- A a c d e + - B a c d e + - A c d e )x +--R 5 5 5 5 5 +--R + +--R 2 9 3 2 2 8 3 7 1 4 6 4 +--R (A a d e + - B a d e + 2A a c d e + - B a c d e )x +--R 2 2 +--R + +--R 2 2 8 4 2 3 7 2 4 6 3 2 3 7 1 2 4 6 2 +--R (2A a d e + - B a d e + - A a c d e )x + (2A a d e + - B a d e )x +--R 3 3 2 +--R + +--R 2 4 6 1 2 5 5 1 2 6 4 2 7 3 1 8 2 +--R A a d e x + - A a d e - -- B a d e + --- A a c d e - --- B a c d e +--R 5 30 105 140 +--R + +--R 1 2 9 1 2 10 +--R --- A c d e - ---- B c d +--R 630 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1108 + +--S 1109 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 10 1 2 4 4 2 3 9 +--R -- B c e x + (- A c e + - B c d e )x +--R 10 9 9 +--R + +--R 1 4 1 2 3 3 2 2 2 8 +--R (- B a c e + - A c d e + - B c d e )x +--R 4 2 4 +--R + +--R 2 4 8 3 6 2 2 2 4 2 3 7 +--R (- A a c e + - B a c d e + - A c d e + - B c d e)x +--R 7 7 7 7 +--R + +--R 1 2 4 4 3 2 2 2 2 3 1 2 4 6 +--R (- B a e + - A a c d e + 2B a c d e + - A c d e + - B c d )x +--R 6 3 3 6 +--R + +--R 1 2 4 4 2 3 12 2 2 8 3 1 2 4 5 +--R (- A a e + - B a d e + -- A a c d e + - B a c d e + - A c d )x +--R 5 5 5 5 5 +--R + +--R 2 3 3 2 2 2 3 1 4 4 +--R (A a d e + - B a d e + 2A a c d e + - B a c d )x +--R 2 2 +--R + +--R 2 2 2 4 2 3 2 4 3 2 3 1 2 4 2 2 4 +--R (2A a d e + - B a d e + - A a c d )x + (2A a d e + - B a d )x + A a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1109 + +--S 1110 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 5 5 1 2 6 4 2 7 3 1 8 2 +--R - - A a d e + -- B a d e - --- A a c d e + --- B a c d e +--R 5 30 105 140 +--R + +--R 1 2 9 1 2 10 +--R - --- A c d e + ---- B c d +--R 630 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1110 + +--S 1111 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1111 + +)clear all + +--S 1112 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 3 2 2 2 2 6 +--R B c e x + (A c e + 3B c d e )x + (2B a c e + 3A c d e + 3B c d e)x +--R + +--R 3 2 2 2 2 3 5 +--R (2A a c e + 6B a c d e + 3A c d e + B c d )x +--R + +--R 2 3 2 2 2 3 4 +--R (B a e + 6A a c d e + 6B a c d e + A c d )x +--R + +--R 2 3 2 2 2 3 3 +--R (A a e + 3B a d e + 6A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 3 2 2 2 2 3 2 3 +--R (3A a d e + 3B a d e + 2A a c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1112 + +--S 1113 of 1457 +r0:=-1/4*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^4/e^6+1/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^5/e^6-1/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^6/e^6+2/7*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^6-1/8*c^2*(5*B*d-A*e)*(d+e*x)^8/e^6+_ + 1/9*B*c^2*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 1 2 9 9 1 2 9 3 2 8 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 2 9 3 2 8 3 2 2 7 7 +--R (- B a c e + - A c d e + - B c d e )x +--R 7 7 7 +--R + +--R 1 9 8 1 2 2 7 1 2 3 6 6 +--R (- A a c e + B a c d e + - A c d e + - B c d e )x +--R 3 2 6 +--R + +--R 1 2 9 6 8 6 2 7 1 2 3 6 5 +--R (- B a e + - A a c d e + - B a c d e + - A c d e )x +--R 5 5 5 5 +--R + +--R 1 2 9 3 2 8 3 2 7 1 3 6 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d e )x +--R 4 4 2 2 +--R + +--R 2 8 2 2 7 2 3 6 3 3 2 2 7 1 2 3 6 2 +--R (A a d e + B a d e + - A a c d e )x + (- A a d e + - B a d e )x +--R 3 2 2 +--R + +--R 2 3 6 1 2 4 5 1 2 5 4 1 6 3 1 7 2 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - -- B a c d e +--R 4 20 30 70 +--R + +--R 1 2 8 1 2 9 +--R --- A c d e - --- B c d +--R 280 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1113 + +--S 1114 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 3 9 1 2 3 3 2 2 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 2 3 3 2 2 3 2 2 7 +--R (- B a c e + - A c d e + - B c d e)x +--R 7 7 7 +--R + +--R 1 3 2 1 2 2 1 2 3 6 +--R (- A a c e + B a c d e + - A c d e + - B c d )x +--R 3 2 6 +--R + +--R 1 2 3 6 2 6 2 1 2 3 5 +--R (- B a e + - A a c d e + - B a c d e + - A c d )x +--R 5 5 5 5 +--R + +--R 1 2 3 3 2 2 3 2 1 3 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d )x +--R 4 4 2 2 +--R + +--R 2 2 2 2 2 3 3 3 2 2 1 2 3 2 2 3 +--R (A a d e + B a d e + - A a c d )x + (- A a d e + - B a d )x + A a d x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1114 + +--S 1115 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 4 5 1 2 5 4 1 6 3 1 7 2 1 2 8 +--R - - A a d e + -- B a d e - -- A a c d e + -- B a c d e - --- A c d e +--R 4 20 30 70 280 +--R + +--R 1 2 9 +--R --- B c d +--R 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1115 + +--S 1116 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1116 + +)clear all + +--S 1117 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 2 2 2 2 5 +--R B c e x + (A c e + 2B c d e)x + (2B a c e + 2A c d e + B c d )x +--R + +--R 2 2 2 4 2 2 2 3 +--R (2A a c e + 4B a c d e + A c d )x + (B a e + 4A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (A a e + 2B a d e + 2A a c d )x + (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1117 + +--S 1118 of 1457 +r0:=a^2*A*d^2*x+1/2*a^2*d*(B*d+2*A*e)*x^2+1/3*a*(2*A*c*d^2+2*a*B*d*e+_ + a*A*e^2)*x^3+1/4*a*(2*B*c*d^2+4*A*c*d*e+a*B*e^2)*x^4+1/5*c*(A*c*d^2+_ + 4*a*B*d*e+2*a*A*e^2)*x^5+1/6*c*(B*c*d^2+2*A*c*d*e+2*a*B*e^2)*x^6+_ + 1/7*c^2*e*(2*B*d+A*e)*x^7+1/8*B*c^2*e^2*x^8 +--R +--R +--R (2) +--R 1 2 2 8 1 2 2 2 2 7 +--R - B c e x + (- A c e + - B c d e)x +--R 8 7 7 +--R + +--R 1 2 1 2 1 2 2 6 +--R (- B a c e + - A c d e + - B c d )x +--R 3 3 6 +--R + +--R 2 2 4 1 2 2 5 +--R (- A a c e + - B a c d e + - A c d )x +--R 5 5 5 +--R + +--R 1 2 2 1 2 4 +--R (- B a e + A a c d e + - B a c d )x +--R 4 2 +--R + +--R 1 2 2 2 2 2 2 3 2 1 2 2 2 2 2 +--R (- A a e + - B a d e + - A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1118 + +--S 1119 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 8 1 2 2 2 2 7 +--R - B c e x + (- A c e + - B c d e)x +--R 8 7 7 +--R + +--R 1 2 1 2 1 2 2 6 +--R (- B a c e + - A c d e + - B c d )x +--R 3 3 6 +--R + +--R 2 2 4 1 2 2 5 +--R (- A a c e + - B a c d e + - A c d )x +--R 5 5 5 +--R + +--R 1 2 2 1 2 4 +--R (- B a e + A a c d e + - B a c d )x +--R 4 2 +--R + +--R 1 2 2 2 2 2 2 3 2 1 2 2 2 2 2 +--R (- A a e + - B a d e + - A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1119 + +--S 1120 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1120 + +--S 1121 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1121 + +)clear all + +--S 1122 of 1457 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 2 4 +--R B c e x + (A c e + B c d)x + (2B a c e + A c d)x +--R + +--R 3 2 2 2 2 2 +--R (2A a c e + 2B a c d)x + (B a e + 2A a c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 1122 + +--S 1123 of 1457 +r0:=a^2*A*d*x+1/2*a^2*(B*d+A*e)*x^2+1/3*a*(2*A*c*d+a*B*e)*x^3+1/2*a*c*_ + (B*d+A*e)*x^4+1/5*c*(A*c*d+2*a*B*e)*x^5+1/6*c^2*(B*d+A*e)*x^6+_ + 1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 2 6 2 1 2 5 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 7 6 6 5 5 +--R + +--R 1 1 4 1 2 2 3 1 2 1 2 2 +--R (- A a c e + - B a c d)x + (- B a e + - A a c d)x + (- A a e + - B a d)x +--R 2 2 3 3 2 2 +--R + +--R 2 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1123 + +--S 1124 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 7 1 2 1 2 6 2 1 2 5 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 7 6 6 5 5 +--R + +--R 1 1 4 1 2 2 3 1 2 1 2 2 +--R (- A a c e + - B a c d)x + (- B a e + - A a c d)x + (- A a e + - B a d)x +--R 2 2 3 3 2 2 +--R + +--R 2 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1124 + +--S 1125 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1125 + +--S 1126 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1126 + +)clear all + +--S 1127 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R (1) B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R Type: Polynomial(Integer) +--E 1127 + +--S 1128 of 1457 +r0:=a^2*A*x+2/3*a*A*c*x^3+1/5*A*c^2*x^5+1/6*B*(a+c*x^2)^3/c +--R +--R +--R (2) +--R 1 3 6 1 3 5 1 2 4 2 2 3 1 2 2 2 1 3 +--R - B c x + - A c x + - B a c x + - A a c x + - B a c x + A a c x + - B a +--R 6 5 2 3 2 6 +--R ----------------------------------------------------------------------------- +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1128 + +--S 1129 of 1457 +a0:=integrate(t0,x) +--R +--R +--R 1 2 6 1 2 5 1 4 2 3 1 2 2 2 +--R (3) - B c x + - A c x + - B a c x + - A a c x + - B a x + A a x +--R 6 5 2 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1129 + +--S 1130 of 1457 +m0:=a0-r0 +--R +--R +--R 1 3 +--R - B a +--R 6 +--R (4) - ------ +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1130 + +--S 1131 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1131 + +)clear all + +--S 1132 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1132 + +--S 1133 of 1457 +r0:=(B*(c*d^2+a*e^2)^2-A*c*d*e*(c*d^2+2*a*e^2))*x/e^5-1/2*c*(B*d-A*e)*_ + (c*d^2+2*a*e^2)*x^2/e^4+1/3*c*(B*c*d^2-A*c*d*e+2*a*B*e^2)*x^3/e^3-_ + 1/4*c^2*(B*d-A*e)*x^4/e^2+1/5*B*c^2*x^5/e-(B*d-A*e)*(c*d^2+a*e^2)^2*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 3 3 2 2 4 +--R 60A a e - 60B a d e + 120A a c d e - 120B a c d e + 60A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + (15A c e - 15B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (40B a c e - 20A c d e + 20B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (60A a c e - 60B a c d e + 30A c d e - 30B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (60B a e - 120A a c d e + 120B a c d e - 60A c d e + 60B c d e)x +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 2 3 3 2 2 4 +--R 60A a e - 60B a d e + 120A a c d e - 120B a c d e + 60A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + (15A c e - 15B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (40B a c e - 20A c d e + 20B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (60A a c e - 60B a c d e + 30A c d e - 30B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (60B a e - 120A a c d e + 120B a c d e - 60A c d e + 60B c d e)x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 1134 + +--S 1135 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1136 + +)clear all + +--S 1137 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1137 + +--S 1138 of 1457 +r0:=-c*(4*B*c*d^3-3*A*c*d^2*e+4*a*B*d*e^2-2*a*A*e^3)*x/e^5+1/2*c*_ + (3*B*c*d^2-2*A*c*d*e+2*a*B*e^2)*x^2/e^4-1/3*c^2*(2*B*d-A*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x))+_ + (c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 4 2 3 2 3 2 2 4 +--R (12B a e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d e)x +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + (4A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 8A c d e + 10B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (24A a c e - 36B a c d e + 24A c d e - 30B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 5 +--R (24A a c d e - 48B a c d e + 36A c d e - 48B c d e)x - 12A a e +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 24A a c d e + 24B a c d e - 12A c d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 2 3 2 3 2 2 4 +--R (12B a e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d e)x +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + (4A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 8A c d e + 10B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (24A a c e - 36B a c d e + 24A c d e - 30B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 5 +--R (24A a c d e - 48B a c d e + 36A c d e - 48B c d e)x - 12A a e +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 24A a c d e + 24B a c d e - 12A c d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1139 + +--S 1140 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1141 + +)clear all + +--S 1142 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^3 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1142 + +--S 1143 of 1457 +r0:=c*(6*B*c*d^2-3*A*c*d*e+2*a*B*e^2)*x/e^5-1/2*c^2*(3*B*d-A*e)*x^2/e^4+_ + 1/3*B*c^2*x^3/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^2)-_ + (c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x))-_ + 2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 4 2 2 3 2 3 2 2 +--R (12A a c e - 36B a c d e + 36A c d e - 60B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (24A a c d e - 72B a c d e + 72A c d e - 120B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R 12A a c d e - 36B a c d e + 36A c d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + (3A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 12A c d e + 20B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (24B a c d e - 33A c d e + 63B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 6B a e + 24A a c d e - 24B a c d e + 6A c d e + 6B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - 3B a d e + 18A a c d e - 30B a c d e + 21A c d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 2 2 3 2 3 2 2 +--R (12A a c e - 36B a c d e + 36A c d e - 60B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (24A a c d e - 72B a c d e + 72A c d e - 120B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R 12A a c d e - 36B a c d e + 36A c d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + (3A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 12A c d e + 20B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (24B a c d e - 33A c d e + 63B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 6B a e + 24A a c d e - 24B a c d e + 6A c d e + 6B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - 3B a d e + 18A a c d e - 30B a c d e + 21A c d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 1144 + +--S 1145 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1146 + +)clear all + +--S 1147 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^4 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1147 + +--S 1148 of 1457 +r0:=-c^2*(4*B*d-A*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*(B*d-A*e)*(c*d^2+_ + a*e^2)^2/(e^6*(d+e*x)^3)-1/2*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+_ + a*B*e^2)/(e^6*(d+e*x)^2)+2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-_ + a*A*e^3)/(e^6*(d+e*x))+2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 2 4 2 2 3 3 +--R (12B a c e - 24A c d e + 60B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (36B a c d e - 72A c d e + 180B c d e )x +--R + +--R 2 3 2 3 2 2 4 3 2 2 4 +--R (36B a c d e - 72A c d e + 180B c d e)x + 12B a c d e - 24A c d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 2 4 2 2 3 3 +--R 3B c e x + (6A c e - 15B c d e )x + (18A c d e - 63B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e + 36B a c d e - 18A c d e - 9B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 3B a e - 12A a c d e + 54B a c d e - 54A c d e + 81B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 2A a e - B a d e - 4A a c d e + 22B a c d e - 26A c d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 2 2 3 3 +--R (12B a c e - 24A c d e + 60B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (36B a c d e - 72A c d e + 180B c d e )x +--R + +--R 2 3 2 3 2 2 4 3 2 2 4 +--R (36B a c d e - 72A c d e + 180B c d e)x + 12B a c d e - 24A c d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 2 4 2 2 3 3 +--R 3B c e x + (6A c e - 15B c d e )x + (18A c d e - 63B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e + 36B a c d e - 18A c d e - 9B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 3B a e - 12A a c d e + 54B a c d e - 54A c d e + 81B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 2A a e - B a d e - 4A a c d e + 22B a c d e - 26A c d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 1149 + +--S 1150 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1151 + +)clear all + +--S 1152 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^5 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1152 + +--S 1153 of 1457 +r0:=B*c^2*x/e^5+1/4*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^4)-1/3*(c*d^2+_ + a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^3)+c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^2)-2*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x))-c^2*(5*B*d-A*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 4 2 4 2 2 3 3 +--R (12A c e - 60B c d e )x + (48A c d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 2 3 2 2 4 2 4 +--R (72A c d e - 360B c d e )x + (48A c d e - 240B c d e)x + 12A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 5 2 4 2 2 3 3 +--R 12B c e x + 48B c d e x + (- 24B a c e + 48A c d e - 48B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e - 36B a c d e + 108A c d e - 252B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 4B a e - 8A a c d e - 24B a c d e + 88A c d e - 248B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - B a d e - 2A a c d e - 6B a c d e + 25A c d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 4 2 4 2 2 3 3 +--R (12A c e - 60B c d e )x + (48A c d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 2 3 2 2 4 2 4 +--R (72A c d e - 360B c d e )x + (48A c d e - 240B c d e)x + 12A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 5 2 4 2 2 3 3 +--R 12B c e x + 48B c d e x + (- 24B a c e + 48A c d e - 48B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e - 36B a c d e + 108A c d e - 252B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 4B a e - 8A a c d e - 24B a c d e + 88A c d e - 248B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - B a d e - 2A a c d e - 6B a c d e + 25A c d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1154 + +--S 1155 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1156 + +)clear all + +--S 1157 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^6 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1157 + +--S 1158 of 1457 +r0:=1/5*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^5)-1/4*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^4)+2/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^3)-c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^2)+c^2*(5*B*d-A*e)/(e^6*(d+e*x))+_ + B*c^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R (- 60A c e + 300B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 60B a c e - 120A c d e + 900B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 40A a c e - 60B a c d e - 120A c d e + 1100B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 15B a e - 20A a c d e - 30B a c d e - 60A c d e + 625B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 12A a e - 3B a d e - 4A a c d e - 6B a c d e - 12A c d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R (- 60A c e + 300B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 60B a c e - 120A c d e + 900B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 40A a c e - 60B a c d e - 120A c d e + 1100B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 15B a e - 20A a c d e - 30B a c d e - 60A c d e + 625B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 12A a e - 3B a d e - 4A a c d e - 6B a c d e - 12A c d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 1159 + +--S 1160 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1161 + +)clear all + +--S 1162 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1162 + +--S 1163 of 1457 +r0:=1/6*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^6)-1/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^5)+1/2*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^4)-2/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^3)+1/2*c^2*(5*B*d-A*e)/_ + (e^6*(d+e*x)^2)-B*c^2/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 5 5 1 2 5 5 2 4 4 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 2 5 2 2 4 10 2 2 3 3 +--R (- - B a c e - - A c d e - -- B c d e )x +--R 3 3 3 +--R + +--R 1 5 1 4 1 2 2 3 5 2 3 2 2 +--R (- - A a c e - - B a c d e - - A c d e - - B c d e )x +--R 2 2 2 2 +--R + +--R 1 2 5 1 4 1 2 3 1 2 3 2 2 4 +--R (- - B a e - - A a c d e - - B a c d e - - A c d e - B c d e)x +--R 5 5 5 5 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - -- A a c d e - -- B a c d e - -- A c d e +--R 6 30 30 30 30 +--R + +--R 1 2 5 +--R - - B c d +--R 6 +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1163 + +--S 1164 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 30B c e x + (- 15A c e - 75B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 20B a c e - 20A c d e - 100B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 15A a c e - 15B a c d e - 15A c d e - 75B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 6B a e - 6A a c d e - 6B a c d e - 6A c d e - 30B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 5A a e - B a d e - A a c d e - B a c d e - A c d e - 5B c d +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 +--R 30e x + 180d e x + 450d e x + 600d e x + 450d e x + 180d e x +--R + +--R 6 6 +--R 30d e +--R Type: Union(Expression(Integer),...) +--E 1164 + +--S 1165 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1166 + +)clear all + +--S 1167 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1167 + +--S 1168 of 1457 +r0:=1/7*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^7)-1/6*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^6)+2/5*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^5)-1/2*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^4)+1/3*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^3)-1/2*B*c^2/(e^6*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 5 2 4 4 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 6 +--R + +--R 1 5 1 2 4 5 2 2 3 3 +--R (- - B a c e - - A c d e - - B c d e )x +--R 2 3 6 +--R + +--R 2 5 3 4 1 2 2 3 1 2 3 2 2 +--R (- - A a c e - -- B a c d e - - A c d e - - B c d e )x +--R 5 10 5 2 +--R + +--R 1 2 5 2 4 1 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - - B c d e)x +--R 6 15 10 15 6 +--R + +--R 1 2 5 1 2 4 2 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - --- A a c d e - -- B a c d e - --- A c d e +--R 7 42 105 70 105 +--R + +--R 1 2 5 +--R - -- B c d +--R 42 +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 6 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1168 + +--S 1169 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 105B c e x + (- 70A c e - 175B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 105B a c e - 70A c d e - 175B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 84A a c e - 63B a c d e - 42A c d e - 105B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 35B a e - 28A a c d e - 21B a c d e - 14A c d e - 35B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 30A a e - 5B a d e - 4A a c d e - 3B a c d e - 2A c d e - 5B c d +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 +--R 210e x + 1470d e x + 4410d e x + 7350d e x + 7350d e x +--R + +--R 5 8 2 6 7 7 6 +--R 4410d e x + 1470d e x + 210d e +--R Type: Union(Expression(Integer),...) +--E 1169 + +--S 1170 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1171 + +)clear all + +--S 1172 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1172 + +--S 1173 of 1457 +r0:=1/8*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^8)-1/7*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^7)+1/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^6)-2/5*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^5)+1/4*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^4)-1/3*B*c^2/(e^6*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 5 2 4 4 +--R - - B c e x + (- - A c e - -- B c d e )x +--R 3 4 12 +--R + +--R 2 5 1 2 4 1 2 2 3 3 +--R (- - B a c e - - A c d e - - B c d e )x +--R 5 5 3 +--R + +--R 1 5 1 4 1 2 2 3 1 2 3 2 2 +--R (- - A a c e - - B a c d e - -- A c d e - - B c d e )x +--R 3 5 10 6 +--R + +--R 1 2 5 2 4 2 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - -- B c d e)x +--R 7 21 35 35 21 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e - --- A c d e +--R 8 56 84 140 280 +--R + +--R 1 2 5 +--R - --- B c d +--R 168 +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 5 9 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 8 2 7 7 8 6 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1173 + +--S 1174 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 280B c e x + (- 210A c e - 350B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 336B a c e - 168A c d e - 280B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 280A a c e - 168B a c d e - 84A c d e - 140B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 120B a e - 80A a c d e - 48B a c d e - 24A c d e - 40B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 105A a e - 15B a d e - 10A a c d e - 6B a c d e - 3A c d e - 5B c d +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 +--R 840e x + 6720d e x + 23520d e x + 47040d e x + 58800d e x +--R + +--R 5 9 3 6 8 2 7 7 8 6 +--R 47040d e x + 23520d e x + 6720d e x + 840d e +--R Type: Union(Expression(Integer),...) +--E 1174 + +--S 1175 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1176 + +)clear all + +--S 1177 of 1457 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^10 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1177 + +--S 1178 of 1457 +r0:=1/9*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^9)-1/8*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^8)+2/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^7)-1/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^6)+1/5*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^5)-1/4*B*c^2/(e^6*(d+e*x)^4) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 1 2 4 4 +--R - - B c e x + (- - A c e - - B c d e )x +--R 4 5 4 +--R + +--R 1 5 2 2 4 1 2 2 3 3 +--R (- - B a c e - -- A c d e - - B c d e )x +--R 3 15 6 +--R + +--R 2 5 1 4 2 2 2 3 1 2 3 2 2 +--R (- - A a c e - - B a c d e - -- A c d e - -- B c d e )x +--R 7 7 35 14 +--R + +--R 1 2 5 1 4 1 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - -- B c d e)x +--R 8 14 28 70 56 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - --- A a c d e - --- B a c d e - --- A c d e +--R 9 72 126 252 630 +--R + +--R 1 2 5 +--R - --- B c d +--R 504 +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 5 10 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 9 3 7 8 2 8 7 9 6 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1178 + +--S 1179 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 630B c e x + (- 504A c e - 630B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 840B a c e - 336A c d e - 420B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 720A a c e - 360B a c d e - 144A c d e - 180B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 315B a e - 180A a c d e - 90B a c d e - 36A c d e - 45B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 280A a e - 35B a d e - 20A a c d e - 10B a c d e - 4A c d e - 5B c d +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 +--R 2520e x + 22680d e x + 90720d e x + 211680d e x + 317520d e x +--R + +--R 5 10 4 6 9 3 7 8 2 8 7 9 6 +--R 317520d e x + 211680d e x + 90720d e x + 22680d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 1179 + +--S 1180 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1181 + +)clear all + +--S 1182 of 1457 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1457 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))+(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^8*(2+m))-3*c*(c*d^2+_ + a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3+m)/_ + (e^8*(3+m))-c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*_ + c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(4+m)/(e^8*(4+m))-c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(5+m)/(e^8*(5+m))+_ + 3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(6+m)/(e^8*(6+m))-_ + c^3*(7*B*d-A*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 3 7 3 3 6 +--R (A c e - 7B c d)m + (29A c e - 203B c d)m +--R + +--R 3 3 5 3 3 4 +--R (343A c e - 2401B c d)m + (2135A c e - 14945B c d)m +--R + +--R 3 3 3 3 3 2 +--R (7504A c e - 52528B c d)m + (14756A c e - 103292B c d)m +--R + +--R 3 3 3 3 +--R (14832A c e - 103824B c d)m + 5760A c e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 3 3 2 7 +--R (3B a c e - 6A c d e + 21B c d )m +--R + +--R 2 2 3 3 2 6 +--R (90B a c e - 180A c d e + 630B c d )m +--R + +--R 2 2 3 3 2 5 +--R (1098B a c e - 2196A c d e + 7686B c d )m +--R + +--R 2 2 3 3 2 4 +--R (7020B a c e - 14040A c d e + 49140B c d )m +--R + +--R 2 2 3 3 2 3 +--R (25227B a c e - 50454A c d e + 176589B c d )m +--R + +--R 2 2 3 3 2 2 +--R (50490B a c e - 100980A c d e + 353430B c d )m +--R + +--R 2 2 3 3 2 2 2 +--R (51432B a c e - 102864A c d e + 360024B c d )m + 20160B a c e +--R + +--R 3 3 2 +--R - 40320A c d e + 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 2 2 3 2 3 3 7 +--R (3A a c e - 15B a c d e + 15A c d e - 35B c d )m +--R + +--R 2 3 2 2 3 2 3 3 6 +--R (93A a c e - 465B a c d e + 465A c d e - 1085B c d )m +--R + +--R 2 3 2 2 3 2 3 3 5 +--R (1173A a c e - 5865B a c d e + 5865A c d e - 13685B c d )m +--R + +--R 2 3 2 2 3 2 3 3 4 +--R (7743A a c e - 38715B a c d e + 38715A c d e - 90335B c d )m +--R + +--R 2 3 2 2 3 2 3 3 3 +--R (28632A a c e - 143160B a c d e + 143160A c d e - 334040B c d )m +--R + +--R 2 3 2 2 3 2 3 3 2 +--R (58692A a c e - 293460B a c d e + 293460A c d e - 684740B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R (60912A a c e - 304560B a c d e + 304560A c d e - 710640B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R 24192A a c e - 120960B a c d e + 120960A c d e - 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 4 2 3 2 2 2 3 3 3 4 7 +--R (3B a c e - 12A a c d e + 30B a c d e - 20A c d e + 35B c d )m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 96B a c e - 384A a c d e + 960B a c d e - 640A c d e +--R + +--R 3 4 +--R 1120B c d +--R * +--R 6 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 1254B a c e - 5016A a c d e + 12540B a c d e - 8360A c d e +--R + +--R 3 4 +--R 14630B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 8592B a c e - 34368A a c d e + 85920B a c d e - 57280A c d e +--R + +--R 3 4 +--R 100240B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 32979B a c e - 131916A a c d e + 329790B a c d e +--R + +--R 3 3 3 4 +--R - 219860A c d e + 384755B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 69936B a c e - 279744A a c d e + 699360B a c d e +--R + +--R 3 3 3 4 +--R - 466240A c d e + 815920B c d +--R * +--R 2 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 74628B a c e - 298512A a c d e + 746280B a c d e +--R + +--R 3 3 3 4 +--R - 497520A c d e + 870660B c d +--R * +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 30240B a c e - 120960A a c d e + 302400B a c d e - 201600A c d e +--R + +--R 3 4 +--R 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 +--R 3A a c e - 9B a c d e + 18A a c d e - 30B a c d e + 15A c d e +--R + +--R 3 5 +--R - 21B c d +--R * +--R 7 +--R m +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 99A a c e - 297B a c d e + 594A a c d e - 990B a c d e +--R + +--R 3 4 3 5 +--R 495A c d e - 693B c d +--R * +--R 6 +--R m +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 1341A a c e - 4023B a c d e + 8046A a c d e - 13410B a c d e +--R + +--R 3 4 3 5 +--R 6705A c d e - 9387B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 9585A a c e - 28755B a c d e + 57510A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 95850B a c d e + 47925A c d e - 67095B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 38592A a c e - 115776B a c d e + 231552A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 385920B a c d e + 192960A c d e - 270144B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 86076A a c e - 258228B a c d e + 516456A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 860760B a c d e + 430380A c d e - 602532B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 96144A a c e - 288432B a c d e + 576864A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 961440B a c d e + 480720A c d e - 673008B c d +--R * +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 40320A a c e - 120960B a c d e + 241920A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 403200B a c d e + 201600A c d e - 282240B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 6 2 5 2 2 4 2 3 3 2 4 2 +--R B a e - 6A a c d e + 9B a c d e - 12A a c d e + 15B a c d e +--R + +--R 3 5 3 6 +--R - 6A c d e + 7B c d +--R * +--R 7 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 34B a e - 204A a c d e + 306B a c d e - 408A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 510B a c d e - 204A c d e + 238B c d +--R * +--R 6 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 478B a e - 2868A a c d e + 4302B a c d e - 5736A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 7170B a c d e - 2868A c d e + 3346B c d +--R * +--R 5 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 3580B a e - 21480A a c d e + 32220B a c d e - 42960A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 53700B a c d e - 21480A c d e + 25060B c d +--R * +--R 4 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 15289B a e - 91734A a c d e + 137601B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R - 183468A a c d e + 229335B a c d e - 91734A c d e + 107023B c d +--R * +--R 3 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 36706B a e - 220236A a c d e + 330354B a c d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 440472A a c d e + 550590B a c d e - 220236A c d e +--R + +--R 3 6 +--R 256942B c d +--R * +--R 2 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 44712B a e - 268272A a c d e + 402408B a c d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 536544A a c d e + 670680B a c d e - 268272A c d e +--R + +--R 3 6 +--R 312984B c d +--R * +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 20160B a e - 120960A a c d e + 181440B a c d e - 241920A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 302400B a c d e - 120960A c d e + 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R A a e - B a d e + 3A a c d e - 3B a c d e + 3A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 3B a c d e + A c d e - B c d +--R * +--R 7 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 35A a e - 35B a d e + 105A a c d e - 105B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 105A a c d e - 105B a c d e + 35A c d e - 35B c d +--R * +--R 6 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 511A a e - 511B a d e + 1533A a c d e - 1533B a c d e +--R 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+--R (99A a c e + 87B a c d e - 12A a c d e )m +--R + +--R 2 8 2 7 2 2 6 2 3 5 5 +--R (1341A a c e + 993B a c d e - 288A a c d e + 60B a c d e )m +--R + +--R 2 8 2 7 2 2 6 +--R 9585A a c e + 5613B a c d e - 2532A a c d e +--R + +--R 2 3 5 3 4 4 +--R 1080B a c d e - 120A c d e +--R * +--R 4 +--R m +--R + +--R 2 8 2 7 2 2 6 +--R 38592A a c e + 16140B a c d e - 9792A a c d e +--R + +--R 2 3 5 3 4 4 3 5 3 +--R 6180B a c d e - 1320A c d e + 840B c d e +--R * +--R 3 +--R m +--R + +--R 2 8 2 7 2 2 6 +--R 86076A a c e + 21516B a c d e - 15600A a c d e +--R + +--R 2 3 5 3 4 4 3 5 3 +--R 11880B a c d e - 3120A c d e + 2520B c d e +--R * +--R 2 +--R m +--R + +--R 2 8 2 7 2 2 6 +--R 96144A a c e + 10080B a c d e - 8064A a c d e +--R + +--R 2 3 5 3 4 4 3 5 3 +--R 6720B a c d e - 1920A c d e + 1680B c d e +--R * +--R m +--R + +--R 2 8 +--R 40320A a c e +--R * +--R 3 +--R x +--R + +--R 3 8 2 7 7 +--R (B a e + 3A a c d e )m +--R + +--R 3 8 2 7 2 2 6 6 +--R (34B a e + 93A a c d e - 9B a c d e )m +--R + +--R 3 8 2 7 2 2 6 2 3 5 5 +--R (478B a e + 1155A a c d e - 243B a c d e + 36A a c d e )m +--R + +--R 3 8 2 7 2 2 6 2 3 5 +--R 3580B a e + 7275A a c d e - 2493B a c d e + 792A a c d e +--R + +--R 2 4 4 +--R - 180B a c d e +--R * +--R 4 +--R m +--R + +--R 3 8 2 7 2 2 6 +--R 15289B a e + 24042A a c d e - 11853B a c d e +--R + +--R 2 3 5 2 4 4 3 5 3 +--R 6012A a c d e - 2880B a c d e + 360A c d e +--R * +--R 3 +--R m +--R + +--R 3 8 2 7 2 2 6 +--R 36706B a e + 37992A a c d e - 24714B a c d e +--R + +--R 2 3 5 2 4 4 3 5 3 3 6 2 +--R 17352A a c d e - 12780B a c d e + 3240A c d e - 2520B c d e +--R * +--R 2 +--R m +--R + +--R 3 8 2 7 2 2 6 +--R 44712B a e + 20160A a c d e - 15120B a c d e +--R + +--R 2 3 5 2 4 4 3 5 3 3 6 2 +--R 12096A a c d e - 10080B a c d e + 2880A c d e - 2520B c d e +--R * +--R m +--R + +--R 3 8 +--R 20160B a e +--R * +--R 2 +--R x +--R + +--R 3 8 3 7 7 3 8 3 7 2 2 6 6 +--R (A a e + B a d e )m + (35A a e + 33B a d e - 6A a c d e )m +--R + +--R 3 8 3 7 2 2 6 2 3 5 5 +--R (511A a e + 445B a d e - 180A a c d e + 18B a c d e )m +--R + +--R 3 8 3 7 2 2 6 2 3 5 +--R 4025A a e + 3135B a d e - 2130A a c d e + 468B a c d e +--R + +--R 2 4 4 +--R - 72A a c d e +--R * +--R 4 +--R m +--R + +--R 3 8 3 7 2 2 6 +--R 18424A a e + 12154B a d e - 12420A a c d e +--R + +--R 2 3 5 2 4 4 2 5 3 +--R 4518B a c d e - 1512A a c d e + 360B a c d e +--R * +--R 3 +--R m +--R + +--R 3 8 3 7 2 2 6 +--R 48860A a e + 24552B a d e - 35664A a c d e +--R + +--R 2 3 5 2 4 4 2 5 3 +--R 19188B a c d e - 10512A a c d e + 5400B a c d e +--R + +--R 3 6 2 +--R - 720A c d e +--R * +--R 2 +--R m +--R + +--R 3 8 3 7 2 2 6 +--R 69264A a e + 20160B a d e - 40320A a c d e +--R + +--R 2 3 5 2 4 4 2 5 3 +--R 30240B a c d e - 24192A a c d e + 20160B a c d e +--R + +--R 3 6 2 3 7 +--R - 5760A c d e + 5040B c d e +--R * +--R m +--R + +--R 3 8 +--R 40320A a e +--R * +--R x +--R + +--R 3 7 7 3 7 3 2 6 6 +--R A a d e m + (35A a d e - B a d e )m +--R + +--R 3 7 3 2 6 2 3 5 5 +--R (511A a d e - 33B a d e + 6A a c d e )m +--R + +--R 3 7 3 2 6 2 3 5 2 4 4 4 +--R (4025A a d e - 445B a d e + 180A a c d e - 18B a c d e )m +--R + +--R 3 7 3 2 6 2 3 5 2 4 4 +--R 18424A a d e - 3135B a d e + 2130A a c d e - 468B a c d e +--R + +--R 2 5 3 +--R 72A a c d e +--R * +--R 3 +--R m +--R + +--R 3 7 3 2 6 2 3 5 2 4 4 +--R 48860A a d e - 12154B a d e + 12420A a c d e - 4518B a c d e +--R + +--R 2 5 3 2 6 2 +--R 1512A a c d e - 360B a c d e +--R * +--R 2 +--R m +--R + +--R 3 7 3 2 6 2 3 5 2 4 4 +--R 69264A a d e - 24552B a d e + 35664A a c d e - 19188B a c d e +--R + +--R 2 5 3 2 6 2 3 7 +--R 10512A a c d e - 5400B a c d e + 720A c d e +--R * +--R m +--R + +--R 3 7 3 2 6 2 3 5 2 4 4 +--R 40320A a d e - 20160B a d e + 40320A a c d e - 30240B a c d e +--R + +--R 2 5 3 2 6 2 3 7 3 8 +--R 24192A a c d e - 20160B a c d e + 5760A c d e - 5040B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 7 3 6 3 5 3 4 3 3 +--R - B c m - 28B c m - 322B c m - 1960B c m - 6769B c m +--R + +--R 3 2 3 3 +--R - 13132B c m - 13068B c m - 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 3 7 3 3 6 +--R (- A c e + 7B c d)m + (- 29A c e + 203B c d)m +--R + +--R 3 3 5 3 3 4 +--R (- 343A c e + 2401B c d)m + (- 2135A c e + 14945B c d)m +--R + +--R 3 3 3 3 3 2 +--R (- 7504A c e + 52528B c d)m + (- 14756A c e + 103292B c d)m +--R + +--R 3 3 3 3 +--R (- 14832A c e + 103824B c d)m - 5760A c e + 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 3 3 2 7 +--R (- 3B a c e + 6A c d e - 21B c d )m +--R + +--R 2 2 3 3 2 6 +--R (- 90B a c e + 180A c d e - 630B c d )m +--R + +--R 2 2 3 3 2 5 +--R (- 1098B a c e + 2196A c d e - 7686B c d )m +--R + +--R 2 2 3 3 2 4 +--R (- 7020B a c e + 14040A c d e - 49140B c d )m +--R + +--R 2 2 3 3 2 3 +--R (- 25227B a c e + 50454A c d e - 176589B c d )m +--R + +--R 2 2 3 3 2 2 +--R (- 50490B a c e + 100980A c d e - 353430B c d )m +--R + +--R 2 2 3 3 2 2 2 +--R (- 51432B a c e + 102864A c d e - 360024B c d )m - 20160B a c e +--R + +--R 3 3 2 +--R 40320A c d e - 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 2 2 3 2 3 3 7 +--R (- 3A a c e + 15B a c d e - 15A c d e + 35B c d )m +--R + +--R 2 3 2 2 3 2 3 3 6 +--R (- 93A a c e + 465B a c d e - 465A c d e + 1085B c d )m +--R + +--R 2 3 2 2 3 2 3 3 5 +--R (- 1173A a c e + 5865B a c d e - 5865A c d e + 13685B c d )m +--R + +--R 2 3 2 2 3 2 3 3 4 +--R (- 7743A a c e + 38715B a c d e - 38715A c d e + 90335B c d )m +--R + +--R 2 3 2 2 3 2 3 3 3 +--R (- 28632A a c e + 143160B a c d e - 143160A c d e + 334040B c d )m +--R + +--R 2 3 2 2 3 2 3 3 2 +--R (- 58692A a c e + 293460B a c d e - 293460A c d e + 684740B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R (- 60912A a c e + 304560B a c d e - 304560A c d e + 710640B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R - 24192A a c e + 120960B a c d e - 120960A c d e + 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 4 2 3 2 2 2 3 3 3 4 7 +--R (- 3B a c e + 12A a c d e - 30B a c d e + 20A c d e - 35B c d )m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R - 96B a c e + 384A a c d e - 960B a c d e + 640A c d e +--R + +--R 3 4 +--R - 1120B c d +--R * +--R 6 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R - 1254B a c e + 5016A a c d e - 12540B a c d e + 8360A c d e +--R + +--R 3 4 +--R - 14630B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R - 8592B a c e + 34368A a c d e - 85920B a c d e + 57280A c d e +--R + +--R 3 4 +--R - 100240B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R - 32979B a c e + 131916A a c d e - 329790B a c d e +--R + +--R 3 3 3 4 +--R 219860A c d e - 384755B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R - 69936B a c e + 279744A a c d e - 699360B a c d e +--R + +--R 3 3 3 4 +--R 466240A c d e - 815920B c d +--R * +--R 2 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R - 74628B a c e + 298512A a c d e - 746280B a c d e +--R + +--R 3 3 3 4 +--R 497520A c d e - 870660B c d +--R * +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R - 30240B a c e + 120960A a c d e - 302400B a c d e + 201600A c d e +--R + +--R 3 4 +--R - 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R - 3A a c e + 9B a c d e - 18A a c d e + 30B a c d e +--R + +--R 3 4 3 5 +--R - 15A c d e + 21B c d +--R * +--R 7 +--R m +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R - 99A a c e + 297B a c d e - 594A a c d e + 990B a c d e +--R + +--R 3 4 3 5 +--R - 495A c d e + 693B c d +--R * +--R 6 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 1341A a c e + 4023B a c d e - 8046A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 13410B a c d e - 6705A c d e + 9387B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 9585A a c e + 28755B a c d e - 57510A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 95850B a c d e - 47925A c d e + 67095B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 38592A a c e + 115776B a c d e - 231552A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 385920B a c d e - 192960A c d e + 270144B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 86076A a c e + 258228B a c d e - 516456A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 860760B a c d e - 430380A c d e + 602532B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 96144A a c e + 288432B a c d e - 576864A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 961440B a c d e - 480720A c d e + 673008B c d +--R * +--R m +--R + +--R 2 5 2 4 2 2 3 +--R - 40320A a c e + 120960B a c d e - 241920A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R 403200B a c d e - 201600A c d e + 282240B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R - B a e + 6A a c d e - 9B a c d e + 12A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R - 15B a c d e + 6A c d e - 7B c d +--R * +--R 7 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R - 34B a e + 204A a c d e - 306B a c d e + 408A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R - 510B a c d e + 204A c d e - 238B c d +--R * +--R 6 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R - 478B a e + 2868A a c d e - 4302B a c d e + 5736A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R - 7170B a c d e + 2868A c d e - 3346B c d +--R * +--R 5 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R - 3580B a e + 21480A a c d e - 32220B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R 42960A a c d e - 53700B a c d e + 21480A c d e - 25060B c d +--R * +--R 4 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R - 15289B a e + 91734A a c d e - 137601B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R 183468A a c d e - 229335B a c d e + 91734A c d e - 107023B c d +--R * +--R 3 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R - 36706B a e + 220236A a c d e - 330354B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R 440472A a c d e - 550590B a c d e + 220236A c d e - 256942B c d +--R * +--R 2 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R - 44712B a e + 268272A a c d e - 402408B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R 536544A a c d e - 670680B a c d e + 268272A c d e - 312984B c d +--R * +--R m +--R + +--R 3 6 2 5 2 2 4 +--R - 20160B a e + 120960A a c d e - 181440B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R 241920A a c d e - 302400B a c d e + 120960A c d e - 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - A a e + B a d e - 3A a c d e + 3B a c d e - 3A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 3B a c d e - A c d e + B c d +--R * +--R 7 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 35A a e + 35B a d e - 105A a c d e + 105B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 105A a c d e + 105B a c d e - 35A c d e + 35B c d +--R * +--R 6 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 511A a e + 511B a d e - 1533A a c d e + 1533B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 1533A a c d e + 1533B a c d e - 511A c d e + 511B c d +--R * +--R 5 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 4025A a e + 4025B a d e - 12075A a c d e + 12075B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 12075A a c d e + 12075B a c d e - 4025A c d e + 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 18424A a e + 18424B a d e - 55272A a c d e + 55272B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 55272A a c d e + 55272B a c d e - 18424A c d e + 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 7 3 6 2 2 5 +--R - 48860A a e + 48860B a d e - 146580A a c d e +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 146580B a c d e - 146580A a c d e + 146580B a c d e +--R + +--R 3 6 3 7 +--R - 48860A c d e + 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 7 3 6 2 2 5 +--R - 69264A a e + 69264B a d e - 207792A a c d e +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 207792B a c d e - 207792A a c d e + 207792B a c d e +--R + +--R 3 6 3 7 +--R - 69264A c d e + 69264B c d +--R * +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 40320A a e + 40320B a d e - 120960A a c d e + 120960B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 120960A a c d e + 120960B a c d e - 40320A c d e + 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1457 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1186 + +)clear all + +--S 1187 of 1457 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 5 12 3 5 3 4 11 +--R B c e x + (A c e + 5B c d e )x +--R + +--R 2 5 3 4 3 2 3 10 +--R (3B a c e + 5A c d e + 10B c d e )x +--R + +--R 2 5 2 4 3 2 3 3 3 2 9 +--R (3A a c e + 15B a c d e + 10A c d e + 10B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 3 2 3 4 8 +--R (3B a c e + 15A a c d e + 30B a c d e + 10A c d e + 5B c d e)x +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 +--R 3A a c e + 15B a c d e + 30A a c d e + 30B a c d e + 5A c d e +--R + +--R 3 5 +--R B c d +--R * +--R 7 +--R x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R B a e + 15A a c d e + 30B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R 6 +--R x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R A a e + 5B a d e + 30A a c d e + 30B a c d e + 15A a c d e +--R + +--R 2 5 +--R 3B a c d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 4 +--R (5A a d e + 10B a d e + 30A a c d e + 15B a c d e + 3A a c d )x +--R + +--R 3 2 3 3 3 2 2 4 2 5 3 +--R (10A a d e + 10B a d e + 15A a c d e + 3B a c d )x +--R + +--R 3 3 2 3 4 2 5 2 3 4 3 5 3 5 +--R (10A a d e + 5B a d e + 3A a c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1187 + +--S 1188 of 1457 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^6/e^8+1/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^8-3/8*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^8/e^8-1/9*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))*(d+e*x)^9/e^8-1/10*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*_ + B*d*e^2-3*a*A*e^3)*(d+e*x)^10/e^8+3/11*c^2*(7*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^11/e^8-1/12*c^3*(7*B*d-A*e)*(d+e*x)^12/e^8+1/13*_ + B*c^3*(d+e*x)^13/e^8 +--R +--R +--R (2) +--R 1 3 13 13 1 3 13 5 3 12 12 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 13 12 12 +--R + +--R 3 2 13 5 3 12 10 3 2 11 11 +--R (-- B a c e + -- A c d e + -- B c d e )x +--R 11 11 11 +--R + +--R 3 2 13 3 2 12 3 2 11 3 3 10 10 +--R (-- A a c e + - B a c d e + A c d e + B c d e )x +--R 10 2 +--R + +--R 1 2 13 5 2 12 10 2 2 11 10 3 3 10 +--R - B a c e + - A a c d e + -- B a c d e + -- A c d e +--R 3 3 3 9 +--R + +--R 5 3 4 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 13 15 2 12 15 2 2 11 15 2 3 10 +--R - A a c e + -- B a c d e + -- A a c d e + -- B a c d e +--R 8 8 4 4 +--R + +--R 5 3 4 9 1 3 5 8 +--R - A c d e + - B c d e +--R 8 8 +--R * +--R 8 +--R x +--R + +--R 1 3 13 15 2 12 30 2 2 11 30 2 3 10 +--R - B a e + -- A a c d e + -- B a c d e + -- A a c d e +--R 7 7 7 7 +--R + +--R 15 2 4 9 1 3 5 8 +--R -- B a c d e + - A c d e +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 13 5 3 12 2 2 11 2 3 10 5 2 4 9 +--R - A a e + - B a d e + 5A a c d e + 5B a c d e + - A a c d e +--R 6 6 2 +--R + +--R 1 2 5 8 +--R - B a c d e +--R 2 +--R * +--R 6 +--R x +--R + +--R 3 12 3 2 11 2 3 10 2 4 9 3 2 5 8 5 +--R (A a d e + 2B a d e + 6A a c d e + 3B a c d e + - A a c d e )x +--R 5 +--R + +--R 5 3 2 11 5 3 3 10 15 2 4 9 3 2 5 8 4 +--R (- A a d e + - B a d e + -- A a c d e + - B a c d e )x +--R 2 2 4 4 +--R + +--R 10 3 3 10 5 3 4 9 2 5 8 3 5 3 4 9 1 3 5 8 2 +--R (-- A a d e + - B a d e + A a c d e )x + (- A a d e + - B a d e )x +--R 3 3 2 2 +--R + +--R 3 5 8 1 3 6 7 1 3 7 6 1 2 8 5 1 2 9 4 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 6 42 56 168 +--R + +--R 1 2 10 3 1 2 11 2 1 3 12 1 3 13 +--R --- A a c d e - --- B a c d e + ---- A c d e - ----- B c d +--R 420 924 5544 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1188 + +--S 1189 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 5 13 1 3 5 5 3 4 12 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 13 12 12 +--R + +--R 3 2 5 5 3 4 10 3 2 3 11 +--R (-- B a c e + -- A c d e + -- B c d e )x +--R 11 11 11 +--R + +--R 3 2 5 3 2 4 3 2 3 3 3 2 10 +--R (-- A a c e + - B a c d e + A c d e + B c d e )x +--R 10 2 +--R + +--R 1 2 5 5 2 4 10 2 2 3 10 3 3 2 5 3 4 9 +--R (- B a c e + - A a c d e + -- B a c d e + -- A c d e + - B c d e)x +--R 3 3 3 9 9 +--R + +--R 3 2 5 15 2 4 15 2 2 3 15 2 3 2 5 3 4 +--R - A a c e + -- B a c d e + -- A a c d e + -- B a c d e + - A c d e +--R 8 8 4 4 8 +--R + +--R 1 3 5 +--R - B c d +--R 8 +--R * +--R 8 +--R x +--R + +--R 1 3 5 15 2 4 30 2 2 3 30 2 3 2 15 2 4 +--R - B a e + -- A a c d e + -- B a c d e + -- A a c d e + -- B a c d e +--R 7 7 7 7 7 +--R + +--R 1 3 5 +--R - A c d +--R 7 +--R * +--R 7 +--R x +--R + +--R 1 3 5 5 3 4 2 2 3 2 3 2 5 2 4 +--R - A a e + - B a d e + 5A a c d e + 5B a c d e + - A a c d e +--R 6 6 2 +--R + +--R 1 2 5 +--R - B a c d +--R 2 +--R * +--R 6 +--R x +--R + +--R 3 4 3 2 3 2 3 2 2 4 3 2 5 5 +--R (A a d e + 2B a d e + 6A a c d e + 3B a c d e + - A a c d )x +--R 5 +--R + +--R 5 3 2 3 5 3 3 2 15 2 4 3 2 5 4 +--R (- A a d e + - B a d e + -- A a c d e + - B a c d )x +--R 2 2 4 4 +--R + +--R 10 3 3 2 5 3 4 2 5 3 5 3 4 1 3 5 2 3 5 +--R (-- A a d e + - B a d e + A a c d )x + (- A a d e + - B a d )x + A a d x +--R 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1189 + +--S 1190 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 6 7 1 3 7 6 1 2 8 5 1 2 9 4 +--R - - A a d e + -- B a d e - -- A a c d e + --- B a c d e +--R 6 42 56 168 +--R + +--R 1 2 10 3 1 2 11 2 1 3 12 1 3 13 +--R - --- A a c d e + --- B a c d e - ---- A c d e + ----- B c d +--R 420 924 5544 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1190 + +--S 1191 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1191 + +)clear all + +--S 1192 of 1457 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 4 3 3 10 2 4 3 3 3 2 2 9 +--R B c e x + (A c e + 4B c d e )x + (3B a c e + 4A c d e + 6B c d e )x +--R + +--R 2 4 2 3 3 2 2 3 3 8 +--R (3A a c e + 12B a c d e + 6A c d e + 4B c d e)x +--R + +--R 2 4 2 3 2 2 2 3 3 3 4 7 +--R (3B a c e + 12A a c d e + 18B a c d e + 4A c d e + B c d )x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 6 +--R (3A a c e + 12B a c d e + 18A a c d e + 12B a c d e + A c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 5 +--R (B a e + 12A a c d e + 18B a c d e + 12A a c d e + 3B a c d )x +--R + +--R 3 4 3 3 2 2 2 2 3 2 4 4 +--R (A a e + 4B a d e + 18A a c d e + 12B a c d e + 3A a c d )x +--R + +--R 3 3 3 2 2 2 3 2 4 3 +--R (4A a d e + 6B a d e + 12A a c d e + 3B a c d )x +--R + +--R 3 2 2 3 3 2 4 2 3 3 3 4 3 4 +--R (6A a d e + 4B a d e + 3A a c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1192 + +--S 1193 of 1457 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^5/e^8+1/6*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^8-3/7*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^7/e^8-1/8*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))*(d+e*x)^8/e^8-1/9*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)*(d+e*x)^9/e^8+3/10*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*_ + (d+e*x)^10/e^8-1/11*c^3*(7*B*d-A*e)*(d+e*x)^11/e^8+1/12*B*c^3*_ + (d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 3 12 12 1 3 12 4 3 11 11 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 12 11 11 +--R + +--R 3 2 12 2 3 11 3 3 2 10 10 +--R (-- B a c e + - A c d e + - B c d e )x +--R 10 5 5 +--R + +--R 1 2 12 4 2 11 2 3 2 10 4 3 3 9 9 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 3 3 3 9 +--R + +--R 3 2 12 3 2 11 9 2 2 10 1 3 3 9 1 3 4 8 8 +--R (- B a c e + - A a c d e + - B a c d e + - A c d e + - B c d e )x +--R 8 2 4 2 8 +--R + +--R 3 2 12 12 2 11 18 2 2 10 12 2 3 9 +--R - A a c e + -- B a c d e + -- A a c d e + -- B a c d e +--R 7 7 7 7 +--R + +--R 1 3 4 8 +--R - A c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 1 3 12 2 11 2 2 10 2 3 9 1 2 4 8 6 +--R (- B a e + 2A a c d e + 3B a c d e + 2A a c d e + - B a c d e )x +--R 6 2 +--R + +--R 1 3 12 4 3 11 18 2 2 10 12 2 3 9 +--R - A a e + - B a d e + -- A a c d e + -- B a c d e +--R 5 5 5 5 +--R + +--R 3 2 4 8 +--R - A a c d e +--R 5 +--R * +--R 5 +--R x +--R + +--R 3 11 3 3 2 10 2 3 9 3 2 4 8 4 +--R (A a d e + - B a d e + 3A a c d e + - B a c d e )x +--R 2 4 +--R + +--R 3 2 10 4 3 3 9 2 4 8 3 3 3 9 1 3 4 8 2 +--R (2A a d e + - B a d e + A a c d e )x + (2A a d e + - B a d e )x +--R 3 2 +--R + +--R 3 4 8 1 3 5 7 1 3 6 6 1 2 7 5 3 2 8 4 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 5 30 35 280 +--R + +--R 1 2 9 3 1 2 10 2 1 3 11 1 3 12 +--R --- A a c d e - --- B a c d e + ---- A c d e - ---- B c d +--R 210 420 2310 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1193 + +--S 1194 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 12 1 3 4 4 3 3 11 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 12 11 11 +--R + +--R 3 2 4 2 3 3 3 3 2 2 10 +--R (-- B a c e + - A c d e + - B c d e )x +--R 10 5 5 +--R + +--R 1 2 4 4 2 3 2 3 2 2 4 3 3 9 +--R (- A a c e + - B a c d e + - A c d e + - B c d e)x +--R 3 3 3 9 +--R + +--R 3 2 4 3 2 3 9 2 2 2 1 3 3 1 3 4 8 +--R (- B a c e + - A a c d e + - B a c d e + - A c d e + - B c d )x +--R 8 2 4 2 8 +--R + +--R 3 2 4 12 2 3 18 2 2 2 12 2 3 1 3 4 7 +--R (- A a c e + -- B a c d e + -- A a c d e + -- B a c d e + - A c d )x +--R 7 7 7 7 7 +--R + +--R 1 3 4 2 3 2 2 2 2 3 1 2 4 6 +--R (- B a e + 2A a c d e + 3B a c d e + 2A a c d e + - B a c d )x +--R 6 2 +--R + +--R 1 3 4 4 3 3 18 2 2 2 12 2 3 3 2 4 5 +--R (- A a e + - B a d e + -- A a c d e + -- B a c d e + - A a c d )x +--R 5 5 5 5 5 +--R + +--R 3 3 3 3 2 2 2 3 3 2 4 4 +--R (A a d e + - B a d e + 3A a c d e + - B a c d )x +--R 2 4 +--R + +--R 3 2 2 4 3 3 2 4 3 3 3 1 3 4 2 3 4 +--R (2A a d e + - B a d e + A a c d )x + (2A a d e + - B a d )x + A a d x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1194 + +--S 1195 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 5 7 1 3 6 6 1 2 7 5 3 2 8 4 +--R - - A a d e + -- B a d e - -- A a c d e + --- B a c d e +--R 5 30 35 280 +--R + +--R 1 2 9 3 1 2 10 2 1 3 11 1 3 12 +--R - --- A a c d e + --- B a c d e - ---- A c d e + ---- B c d +--R 210 420 2310 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1195 + +--S 1196 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1196 + +)clear all + +--S 1197 of 1457 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 3 3 2 9 2 3 3 2 3 2 8 +--R B c e x + (A c e + 3B c d e )x + (3B a c e + 3A c d e + 3B c d e)x +--R + +--R 2 3 2 2 3 2 3 3 7 +--R (3A a c e + 9B a c d e + 3A c d e + B c d )x +--R + +--R 2 3 2 2 2 2 3 3 6 +--R (3B a c e + 9A a c d e + 9B a c d e + A c d )x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (3A a c e + 9B a c d e + 9A a c d e + 3B a c d )x +--R + +--R 3 3 2 2 2 2 2 3 4 +--R (B a e + 9A a c d e + 9B a c d e + 3A a c d )x +--R + +--R 3 3 3 2 2 2 2 3 3 +--R (A a e + 3B a d e + 9A a c d e + 3B a c d )x +--R + +--R 3 2 3 2 2 3 2 3 2 3 3 3 3 +--R (3A a d e + 3B a d e + 3A a c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1197 + +--S 1198 of 1457 +r0:=a^3*A*d^3*x+1/2*a^3*d^2*(B*d+3*A*e)*x^2+a^2*d*(A*c*d^2+a*B*d*e+_ + a*A*e^2)*x^3+1/4*a^2*(3*B*c*d^3+9*A*c*d^2*e+3*a*B*d*e^2+a*A*e^3)*_ + x^4+1/5*a*(a*B*e*(9*c*d^2+a*e^2)+3*A*c*d*(c*d^2+3*a*e^2))*x^5+_ + 1/2*a*c*(B*c*d^3+3*A*c*d^2*e+3*a*B*d*e^2+a*A*e^3)*x^6+1/7*c*(3*a*_ + B*e*(3*c*d^2+a*e^2)+A*c*d*(c*d^2+9*a*e^2))*x^7+1/8*c^2*(B*c*d^3+3*_ + A*c*d^2*e+9*a*B*d*e^2+3*a*A*e^3)*x^8+1/3*c^2*e*(B*c*d^2+A*c*d*e+_ + a*B*e^2)*x^9+1/10*c^3*e^2*(3*B*d+A*e)*x^10+1/11*B*c^3*e^3*x^11 +--R +--R +--R (2) +--R 1 3 3 11 1 3 3 3 3 2 10 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 11 10 10 +--R + +--R 1 2 3 1 3 2 1 3 2 9 +--R (- B a c e + - A c d e + - B c d e)x +--R 3 3 3 +--R + +--R 3 2 3 9 2 2 3 3 2 1 3 3 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d )x +--R 8 8 8 8 +--R + +--R 3 2 3 9 2 2 9 2 2 1 3 3 7 +--R (- B a c e + - A a c d e + - B a c d e + - A c d )x +--R 7 7 7 7 +--R + +--R 1 2 3 3 2 2 3 2 2 1 2 3 6 +--R (- A a c e + - B a c d e + - A a c d e + - B a c d )x +--R 2 2 2 2 +--R + +--R 1 3 3 9 2 2 9 2 2 3 2 3 5 +--R (- B a e + - A a c d e + - B a c d e + - A a c d )x +--R 5 5 5 5 +--R + +--R 1 3 3 3 3 2 9 2 2 3 2 3 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d )x +--R 4 4 4 4 +--R + +--R 3 2 3 2 2 3 3 3 3 2 1 3 3 2 3 3 +--R (A a d e + B a d e + A a c d )x + (- A a d e + - B a d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1198 + +--S 1199 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 3 11 1 3 3 3 3 2 10 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 11 10 10 +--R + +--R 1 2 3 1 3 2 1 3 2 9 +--R (- B a c e + - A c d e + - B c d e)x +--R 3 3 3 +--R + +--R 3 2 3 9 2 2 3 3 2 1 3 3 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d )x +--R 8 8 8 8 +--R + +--R 3 2 3 9 2 2 9 2 2 1 3 3 7 +--R (- B a c e + - A a c d e + - B a c d e + - A c d )x +--R 7 7 7 7 +--R + +--R 1 2 3 3 2 2 3 2 2 1 2 3 6 +--R (- A a c e + - B a c d e + - A a c d e + - B a c d )x +--R 2 2 2 2 +--R + +--R 1 3 3 9 2 2 9 2 2 3 2 3 5 +--R (- B a e + - A a c d e + - B a c d e + - A a c d )x +--R 5 5 5 5 +--R + +--R 1 3 3 3 3 2 9 2 2 3 2 3 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d )x +--R 4 4 4 4 +--R + +--R 3 2 3 2 2 3 3 3 3 2 1 3 3 2 3 3 +--R (A a d e + B a d e + A a c d )x + (- A a d e + - B a d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1199 + +--S 1200 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1200 + +--S 1201 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1201 + +)clear all + +--S 1202 of 1457 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 3 8 2 2 3 3 2 7 +--R B c e x + (A c e + 2B c d e)x + (3B a c e + 2A c d e + B c d )x +--R + +--R 2 2 2 3 2 6 +--R (3A a c e + 6B a c d e + A c d )x +--R + +--R 2 2 2 2 2 5 +--R (3B a c e + 6A a c d e + 3B a c d )x +--R + +--R 2 2 2 2 2 4 +--R (3A a c e + 6B a c d e + 3A a c d )x +--R + +--R 3 2 2 2 2 3 3 2 3 2 2 2 +--R (B a e + 6A a c d e + 3B a c d )x + (A a e + 2B a d e + 3A a c d )x +--R + +--R 3 3 2 3 2 +--R (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 1202 + +--S 1203 of 1457 +r0:=a^3*A*d^2*x+1/2*a^3*d*(B*d+2*A*e)*x^2+1/3*a^2*(3*A*c*d^2+2*a*B*d*e+_ + a*A*e^2)*x^3+1/4*a^2*(3*B*c*d^2+6*A*c*d*e+a*B*e^2)*x^4+3/5*a*c*_ + (A*c*d^2+2*a*B*d*e+a*A*e^2)*x^5+1/2*a*c*(B*c*d^2+2*A*c*d*e+a*B*_ + e^2)*x^6+1/7*c^2*(A*c*d^2+6*a*B*d*e+3*a*A*e^2)*x^7+1/8*c^2*(B*c*d^2+_ + 2*A*c*d*e+3*a*B*e^2)*x^8+1/9*c^3*e*(2*B*d+A*e)*x^9+1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 2 2 3 9 +--R -- B c e x + (- A c e + - B c d e)x +--R 10 9 9 +--R + +--R 3 2 2 1 3 1 3 2 8 +--R (- B a c e + - A c d e + - B c d )x +--R 8 4 8 +--R + +--R 3 2 2 6 2 1 3 2 7 +--R (- A a c e + - B a c d e + - A c d )x +--R 7 7 7 +--R + +--R 1 2 2 2 1 2 2 6 +--R (- B a c e + A a c d e + - B a c d )x +--R 2 2 +--R + +--R 3 2 2 6 2 3 2 2 5 +--R (- A a c e + - B a c d e + - A a c d )x +--R 5 5 5 +--R + +--R 1 3 2 3 2 3 2 2 4 +--R (- B a e + - A a c d e + - B a c d )x +--R 4 2 4 +--R + +--R 1 3 2 2 3 2 2 3 3 1 3 2 2 3 2 +--R (- A a e + - B a d e + A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1203 + +--S 1204 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 10 1 3 2 2 3 9 +--R -- B c e x + (- A c e + - B c d e)x +--R 10 9 9 +--R + +--R 3 2 2 1 3 1 3 2 8 +--R (- B a c e + - A c d e + - B c d )x +--R 8 4 8 +--R + +--R 3 2 2 6 2 1 3 2 7 +--R (- A a c e + - B a c d e + - A c d )x +--R 7 7 7 +--R + +--R 1 2 2 2 1 2 2 6 +--R (- B a c e + A a c d e + - B a c d )x +--R 2 2 +--R + +--R 3 2 2 6 2 3 2 2 5 +--R (- A a c e + - B a c d e + - A a c d )x +--R 5 5 5 +--R + +--R 1 3 2 3 2 3 2 2 4 +--R (- B a e + - A a c d e + - B a c d )x +--R 4 2 4 +--R + +--R 1 3 2 2 3 2 2 3 3 1 3 2 2 3 2 +--R (- A a e + - B a d e + A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1204 + +--S 1205 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1205 + +--S 1206 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1206 + +)clear all + +--S 1207 of 1457 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 3 7 2 3 6 +--R B c e x + (A c e + B c d)x + (3B a c e + A c d)x +--R + +--R 2 2 5 2 2 4 2 2 3 +--R (3A a c e + 3B a c d)x + (3B a c e + 3A a c d)x + (3A a c e + 3B a c d)x +--R + +--R 3 2 2 3 3 3 +--R (B a e + 3A a c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 1207 + +--S 1208 of 1457 +r0:=a^3*A*d*x+1/2*a^3*(B*d+A*e)*x^2+1/3*a^2*(3*A*c*d+a*B*e)*x^3+3/4*_ + a^2*c*(B*d+A*e)*x^4+3/5*a*c*(A*c*d+a*B*e)*x^5+1/2*a*c^2*(B*d+A*e)*_ + x^6+1/7*c^2*(A*c*d+3*a*B*e)*x^7+1/8*c^3*(B*d+A*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 1 3 8 3 2 1 3 7 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 9 8 8 7 7 +--R + +--R 1 2 1 2 6 3 2 3 2 5 +--R (- A a c e + - B a c d)x + (- B a c e + - A a c d)x +--R 2 2 5 5 +--R + +--R 3 2 3 2 4 1 3 2 3 1 3 1 3 2 +--R (- A a c e + - B a c d)x + (- B a e + A a c d)x + (- A a e + - B a d)x +--R 4 4 3 2 2 +--R + +--R 3 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1208 + +--S 1209 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 9 1 3 1 3 8 3 2 1 3 7 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 9 8 8 7 7 +--R + +--R 1 2 1 2 6 3 2 3 2 5 +--R (- A a c e + - B a c d)x + (- B a c e + - A a c d)x +--R 2 2 5 5 +--R + +--R 3 2 3 2 4 1 3 2 3 1 3 1 3 2 +--R (- A a c e + - B a c d)x + (- B a e + A a c d)x + (- A a e + - B a d)x +--R 4 4 3 2 2 +--R + +--R 3 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1209 + +--S 1210 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1210 + +--S 1211 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1211 + +)clear all + +--S 1212 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R Type: Polynomial(Integer) +--E 1212 + +--S 1213 of 1457 +r0:=a^3*A*x+a^2*A*c*x^3+3/5*a*A*c^2*x^5+1/7*A*c^3*x^7+1/8*B*(a+c*x^2)^4/c +--R +--R +--R (2) +--R 1 4 8 1 4 7 1 3 6 3 3 5 3 2 2 4 2 2 3 +--R - B c x + - A c x + - B a c x + - A a c x + - B a c x + A a c x +--R 8 7 2 5 4 +--R + +--R 1 3 2 3 1 4 +--R - B a c x + A a c x + - B a +--R 2 8 +--R / +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1213 + +--S 1214 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 8 1 3 7 1 2 6 3 2 5 3 2 4 2 3 +--R - B c x + - A c x + - B a c x + - A a c x + - B a c x + A a c x +--R 8 7 2 5 4 +--R + +--R 1 3 2 3 +--R - B a x + A a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1214 + +--S 1215 of 1457 +m0:=a0-r0 +--R +--R +--R 1 4 +--R - B a +--R 8 +--R (4) - ------ +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1215 + +--S 1216 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1216 + +)clear all + +--S 1217 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1217 + +--S 1218 of 1457 +r0:=(B*(c*d^2+a*e^2)^3-A*c*d*e*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4))*x/e^7-_ + 1/2*c*(B*d-A*e)*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4)*x^2/e^6-1/3*c*_ + (A*c*d*e*(c*d^2+3*a*e^2)-B*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4))*_ + x^3/e^5-1/4*c^2*(B*d-A*e)*(c*d^2+3*a*e^2)*x^4/e^4+1/5*c^2*(B*c*_ + d^2-A*c*d*e+3*a*B*e^2)*x^5/e^3-1/6*c^3*(B*d-A*e)*x^6/e^2+1/7*B*_ + c^3*x^7/e-(B*d-A*e)*(c*d^2+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 6 2 2 5 2 3 4 +--R 420A a e - 420B a d e + 1260A a c d e - 1260B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 1260A a c d e - 1260B a c d e + 420A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 60B c e x + (70A c e - 70B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (252B a c e - 84A c d e + 84B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (315A a c e - 315B a c d e + 105A c d e - 105B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 420B a c e - 420A a c d e + 420B a c d e - 140A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 630A a c e - 630B a c d e + 630A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R 210A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 420B a e - 1260A a c d e + 1260B a c d e - 1260A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 1260B a c d e - 420A c d e + 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 3 6 2 2 5 2 3 4 +--R 420A a e - 420B a d e + 1260A a c d e - 1260B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 1260A a c d e - 1260B a c d e + 420A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 60B c e x + (70A c e - 70B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (252B a c e - 84A c d e + 84B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (315A a c e - 315B a c d e + 105A c d e - 105B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 420B a c e - 420A a c d e + 420B a c d e - 140A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 630A a c e - 630B a c d e + 630A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R 210A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 420B a e - 1260A a c d e + 1260B a c d e - 1260A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 1260B a c d e - 420A c d e + 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Union(Expression(Integer),...) +--E 1219 + +--S 1220 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1221 + +)clear all + +--S 1222 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1222 + +--S 1223 of 1457 +r0:=-c*(6*B*d*(c*d^2+a*e^2)^2-A*e*(5*c^2*d^4+9*a*c*d^2*e^2+3*a^2*e^4))*_ + x/e^7-1/2*c*(2*A*c*d*e*(2*c*d^2+3*a*e^2)-B*(5*c^2*d^4+9*a*c*d^2*e^2+_ + 3*a^2*e^4))*x^2/e^6+1/3*c^2*(3*A*e*(c*d^2+a*e^2)-B*(4*c*d^3+_ + 6*a*d*e^2))*x^3/e^5-1/4*c^2*(2*A*c*d*e-3*B*(c*d^2+a*e^2))*x^4/e^4-_ + 1/5*c^3*(2*B*d-A*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+(B*d-A*e)*(c*d^2+_ + a*e^2)^3/(e^8*(d+e*x))+(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+_ + a*B*e^2)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 6 2 2 5 2 3 4 +--R 60B a e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 900B a c d e - 360A c d e + 420B c d e +--R * +--R x +--R + +--R 3 6 2 2 5 2 3 4 2 4 3 +--R 60B a d e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 900B a c d e - 360A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (12A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (45B a c e - 18A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (60A a c e - 75B a c d e + 30A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 3 4 3 3 +--R (90B a c e - 120A a c d e + 150B a c d e - 60A c d e + 70B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 180A a c e - 270B a c d e + 360A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 180A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 180A a c d e - 360B a c d e + 540A a c d e - 720B a c d e +--R + +--R 3 5 2 3 6 +--R 300A c d e - 360B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e + 60B a d e - 180A a c d e + 180B a c d e - 180A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 180B a c d e - 60A c d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 2 6 2 2 5 2 3 4 +--R 60B a e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 900B a c d e - 360A c d e + 420B c d e +--R * +--R x +--R + +--R 3 6 2 2 5 2 3 4 2 4 3 +--R 60B a d e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 900B a c d e - 360A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (12A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (45B a c e - 18A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (60A a c e - 75B a c d e + 30A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 3 4 3 3 +--R (90B a c e - 120A a c d e + 150B a c d e - 60A c d e + 70B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 180A a c e - 270B a c d e + 360A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 180A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 180A a c d e - 360B a c d e + 540A a c d e - 720B a c d e +--R + +--R 3 5 2 3 6 +--R 300A c d e - 360B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e + 60B a d e - 180A a c d e + 180B a c d e - 180A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 180B a c d e - 60A c d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 1224 + +--S 1225 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1226 + +)clear all + +--S 1227 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1227 + +--S 1228 of 1457 +r0:=-c*(A*c*d*e*(10*c*d^2+9*a*e^2)-3*B*(5*c^2*d^4+6*a*c*d^2*e^2+_ + a^2*e^4))*x/e^7-1/2*c^2*(10*B*c*d^3-6*A*c*d^2*e+9*a*B*d*e^2-_ + 3*a*A*e^3)*x^2/e^6+c^2*(2*B*c*d^2-A*c*d*e+a*B*e^2)*x^3/e^5-_ + 1/4*c^3*(3*B*d-A*e)*x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*(B*d-A*e)*_ + (c*d^2+a*e^2)^3/(e^8*(d+e*x)^2)-(c*d^2+a*e^2)^2*(7*B*c*d^2-_ + 6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x))-3*c*(c*d^2+a*e^2)*(7*B*c*d^3-_ + 5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 2 2 5 2 3 4 +--R 60A a c e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 4 3 3 5 2 +--R 300A c d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 120A a c d e - 360B a c d e + 720A a c d e - 1200B a c d e +--R + +--R 3 5 2 3 6 +--R 600A c d e - 840B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 2 5 2 +--R 60A a c d e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 6 3 7 +--R 300A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (5A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (20B a c e - 10A c d e + 14B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30A a c e - 50B a c d e + 25A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 60B a c e - 120A a c d e + 200B a c d e - 100A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 120B a c d e - 330A a c d e + 630B a c d e - 340A c d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 20B a e + 120A a c d e - 120B a c d e + 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 60B a c d e - 80A c d e + 160B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 10B a d e + 90A a c d e - 150B a c d e + 210A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 270B a c d e + 110A c d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 2 6 2 2 5 2 3 4 +--R 60A a c e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 4 3 3 5 2 +--R 300A c d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 120A a c d e - 360B a c d e + 720A a c d e - 1200B a c d e +--R + +--R 3 5 2 3 6 +--R 600A c d e - 840B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 2 5 2 +--R 60A a c d e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 6 3 7 +--R 300A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (5A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (20B a c e - 10A c d e + 14B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30A a c e - 50B a c d e + 25A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 60B a c e - 120A a c d e + 200B a c d e - 100A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 120B a c d e - 330A a c d e + 630B a c d e - 340A c d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 20B a e + 120A a c d e - 120B a c d e + 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 60B a c d e - 80A c d e + 160B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 10B a d e + 90A a c d e - 150B a c d e + 210A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 270B a c d e + 110A c d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 1229 + +--S 1230 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1231 + +)clear all + +--S 1232 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1232 + +--S 1233 of 1457 +r0:=-c^2*(20*B*c*d^3-10*A*c*d^2*e+12*a*B*d*e^2-3*a*A*e^3)*x/e^7+1/2*_ + c^2*(10*B*c*d^2-4*A*c*d*e+3*a*B*e^2)*x^2/e^6-1/3*c^3*(4*B*d-A*e)*_ + x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+_ + e*x)^3)-1/2*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*_ + (d+e*x)^2)+3*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-_ + a*A*e^3)/(e^8*(d+e*x))-c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*_ + d^4+30*a*c*d^2*e^2+3*a^2*e^4))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 2 2 5 3 3 4 +--R 36B a c e - 144A a c d e + 360B a c d e - 240A c d e +--R + +--R 3 4 3 +--R 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 3 5 2 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 3 6 3 7 +--R 36B a c d e - 144A a c d e + 360B a c d e - 240A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 3B c e x + (4A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (18B a c e - 12A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 90B a c d e + 60A c d e - 105B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (108A a c d e - 378B a c d e + 292A c d e - 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 36A a c e + 108B a c d e - 108A a c d e - 54B a c d e +--R + +--R 3 4 3 3 5 2 +--R 156A c d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6B a e - 36A a c d e + 162B a c d e - 324A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 486B a c d e - 204A c d e + 222B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - 2B a d e - 12A a c d e + 66B a c d e - 156A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 282B a c d e - 148A c d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 2 6 2 2 5 3 3 4 +--R 36B a c e - 144A a c d e + 360B a c d e - 240A c d e +--R + +--R 3 4 3 +--R 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 3 5 2 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 3 6 3 7 +--R 36B a c d e - 144A a c d e + 360B a c d e - 240A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 3B c e x + (4A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (18B a c e - 12A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 90B a c d e + 60A c d e - 105B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (108A a c d e - 378B a c d e + 292A c d e - 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 36A a c e + 108B a c d e - 108A a c d e - 54B a c d e +--R + +--R 3 4 3 3 5 2 +--R 156A c d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6B a e - 36A a c d e + 162B a c d e - 324A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 486B a c d e - 204A c d e + 222B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - 2B a d e - 12A a c d e + 66B a c d e - 156A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 282B a c d e - 148A c d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1234 + +--S 1235 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1236 + +)clear all + +--S 1237 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1237 + +--S 1238 of 1457 +r0:=-c^2*(5*A*c*d*e-3*B*(5*c*d^2+a*e^2))*x/e^7-1/2*c^3*(5*B*d-A*e)*_ + x^2/e^6+1/3*B*c^3*x^3/e^5+1/4*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*_ + (d+e*x)^4)-1/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^3)+3/2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*_ + d*e^2-a*A*e^3)/(e^8*(d+e*x)^2)+c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*_ + (35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x))-c^2*(35*B*c*_ + d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 180B a c d e + 180A c d e - 420B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e )x +--R + +--R 2 2 5 2 3 4 3 4 3 3 5 2 2 +--R (216A a c d e - 1080B a c d e + 1080A c d e - 2520B c d e )x +--R + +--R 2 3 4 2 4 3 3 5 2 3 6 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e)x +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 36A a c d e - 180B a c d e + 180A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (6A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (36B a c e - 36A c d e + 84B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (144B a c d e - 204A c d e + 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 36B a c e + 144A a c d e - 144B a c d e - 96A c d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 18A a c e - 54B a c d e + 324A a c d e - 756B a c d e +--R + +--R 3 4 3 3 5 2 +--R 396A c d e - 444B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 4B a e - 12A a c d e - 36B a c d e + 264A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 744B a c d e + 504A c d e - 856B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 3A a e - B a d e - 3A a c d e - 9B a c d e + 75A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 231B a c d e + 171A c d e - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 180B a c d e + 180A c d e - 420B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e )x +--R + +--R 2 2 5 2 3 4 3 4 3 3 5 2 2 +--R (216A a c d e - 1080B a c d e + 1080A c d e - 2520B c d e )x +--R + +--R 2 3 4 2 4 3 3 5 2 3 6 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e)x +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 36A a c d e - 180B a c d e + 180A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (6A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (36B a c e - 36A c d e + 84B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (144B a c d e - 204A c d e + 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 36B a c e + 144A a c d e - 144B a c d e - 96A c d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 18A a c e - 54B a c d e + 324A a c d e - 756B a c d e +--R + +--R 3 4 3 3 5 2 +--R 396A c d e - 444B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 4B a e - 12A a c d e - 36B a c d e + 264A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 744B a c d e + 504A c d e - 856B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 3A a e - B a d e - 3A a c d e - 9B a c d e + 75A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 231B a c d e + 171A c d e - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1239 + +--S 1240 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1240 + +--S 1241 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1241 + +)clear all + +--S 1242 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^6 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1242 + +--S 1243 of 1457 +r0:=-c^3*(6*B*d-A*e)*x/e^7+1/2*B*c^3*x^2/e^6+1/5*(B*d-A*e)*(c*d^2+_ + a*e^2)^3/(e^8*(d+e*x)^5)-1/4*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+_ + a*B*e^2)/(e^8*(d+e*x)^4)+c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+_ + 3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^3)+1/2*c*(4*A*c*d*e*(5*c*d^2+_ + 3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^2)+_ + c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*(d+e*x))+_ + 3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 3 6 3 2 5 5 +--R (60B a c e - 120A c d e + 420B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (300B a c d e - 600A c d e + 2100B c d e )x +--R + +--R 2 2 5 3 3 4 3 4 3 3 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 3 4 3 4 3 3 5 2 2 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 4 3 3 5 2 3 6 2 5 2 +--R (300B a c d e - 600A c d e + 2100B c d e)x + 60B a c d e +--R + +--R 3 6 3 7 +--R - 120A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 3 6 3 2 5 5 +--R 10B c e x + (20A c e - 70B c d e )x + (100A c d e - 500B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 60A a c e + 300B a c d e - 100A c d e - 400B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 30B a c e - 120A a c d e + 900B a c d e - 800A c d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 20A a c e - 30B a c d e - 120A a c d e + 1100B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1200A c d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 5B a e - 10A a c d e - 15B a c d e - 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 625B a c d e - 750A c d e + 1875B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - B a d e - 2A a c d e - 3B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 137B a c d e - 174A c d e + 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 3 6 3 2 5 5 +--R (60B a c e - 120A c d e + 420B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (300B a c d e - 600A c d e + 2100B c d e )x +--R + +--R 2 2 5 3 3 4 3 4 3 3 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 3 4 3 4 3 3 5 2 2 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 4 3 3 5 2 3 6 2 5 2 +--R (300B a c d e - 600A c d e + 2100B c d e)x + 60B a c d e +--R + +--R 3 6 3 7 +--R - 120A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 3 6 3 2 5 5 +--R 10B c e x + (20A c e - 70B c d e )x + (100A c d e - 500B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 60A a c e + 300B a c d e - 100A c d e - 400B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 30B a c e - 120A a c d e + 900B a c d e - 800A c d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 20A a c e - 30B a c d e - 120A a c d e + 1100B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1200A c d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 5B a e - 10A a c d e - 15B a c d e - 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 625B a c d e - 750A c d e + 1875B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - B a d e - 2A a c d e - 3B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 137B a c d e - 174A c d e + 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 1244 + +--S 1245 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1246 + +)clear all + +--S 1247 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^7 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1247 + +--S 1248 of 1457 +r0:=B*c^3*x/e^7+1/6*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^6)-1/5*(c*d^2+_ + a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^5)+3/4*c*(c*d^2+_ + a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^4)+_ + 1/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))/(e^8*(d+e*x)^3)+1/2*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*_ + d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^2)-3*c^2*(7*B*c*d^2-2*A*c*d*e+a*_ + B*e^2)/(e^8*(d+e*x))-c^3*(7*B*d-A*e)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 6 6 3 6 3 2 5 5 +--R (60A c e - 420B c d e )x + (360A c d e - 2520B c d e )x +--R + +--R 3 2 5 3 3 4 4 3 3 4 3 4 3 3 +--R (900A c d e - 6300B c d e )x + (1200A c d e - 8400B c d e )x +--R + +--R 3 4 3 3 5 2 2 3 5 2 3 6 +--R (900A c d e - 6300B c d e )x + (360A c d e - 2520B c d e)x +--R + +--R 3 6 3 7 +--R 60A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 180B a c e + 360A c d e - 360B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 90A a c e - 450B a c d e + 1350A c d e - 4050B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 60B a c e - 120A a c d e - 600B a c d e + 2200A c d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 45A a c e - 45B a c d e - 90A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 1875A c d e - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 12B a e - 18A a c d e - 18B a c d e - 36A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 180B a c d e + 822A c d e - 3594B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 2B a d e - 3A a c d e - 3B a c d e - 6A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e + 147A c d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 3 6 6 3 6 3 2 5 5 +--R (60A c e - 420B c d e )x + (360A c d e - 2520B c d e )x +--R + +--R 3 2 5 3 3 4 4 3 3 4 3 4 3 3 +--R (900A c d e - 6300B c d e )x + (1200A c d e - 8400B c d e )x +--R + +--R 3 4 3 3 5 2 2 3 5 2 3 6 +--R (900A c d e - 6300B c d e )x + (360A c d e - 2520B c d e)x +--R + +--R 3 6 3 7 +--R 60A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 180B a c e + 360A c d e - 360B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 90A a c e - 450B a c d e + 1350A c d e - 4050B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 60B a c e - 120A a c d e - 600B a c d e + 2200A c d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 45A a c e - 45B a c d e - 90A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 1875A c d e - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 12B a e - 18A a c d e - 18B a c d e - 36A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 180B a c d e + 822A c d e - 3594B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 2B a d e - 3A a c d e - 3B a c d e - 6A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e + 147A c d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 1249 + +--S 1250 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1251 + +)clear all + +--S 1252 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^8 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1252 + +--S 1253 of 1457 +r0:=1/7*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^7)-1/6*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^6)+3/5*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^5)+1/4*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^4)+1/3*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^3)-3/2*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^2)+c^3*(7*B*d-A*e)/(e^8*(d+e*x))+B*c^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 3 6 6 +--R (- 420A c e + 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 630B a c e - 1260A c d e + 13230B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 420A a c e - 1050B a c d e - 2100A c d e + 26950B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 315B a c e - 420A a c d e - 1050B a c d e - 2100A c d e +--R + +--R 3 4 3 +--R 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 252A a c e - 189B a c d e - 252A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1260A c d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 70B a e - 84A a c d e - 63B a c d e - 84A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 210B a c d e - 420A c d e + 7203B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e - 10B a d e - 12A a c d e - 9B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e - 60A c d e + 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 3 6 6 +--R (- 420A c e + 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 630B a c e - 1260A c d e + 13230B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 420A a c e - 1050B a c d e - 2100A c d e + 26950B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 315B a c e - 420A a c d e - 1050B a c d e - 2100A c d e +--R + +--R 3 4 3 +--R 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 252A a c e - 189B a c d e - 252A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1260A c d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 70B a e - 84A a c d e - 63B a c d e - 84A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 210B a c d e - 420A c d e + 7203B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e - 10B a d e - 12A a c d e - 9B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e - 60A c d e + 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Union(Expression(Integer),...) +--E 1254 + +--S 1255 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1256 + +)clear all + +--S 1257 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^9 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1257 + +--S 1258 of 1457 +r0:=1/8*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^8)-1/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^7)+1/2*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^6)+1/5*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^5)+1/4*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^4)-c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^8*_ + (d+e*x)^3)+1/2*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^2)-B*c^3/(e^8*(d+e*x)) +--R +--R +--R (2) +--R 3 7 7 1 3 7 7 3 6 6 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 2 7 3 6 3 2 5 5 +--R (- B a c e - A c d e - 7B c d e )x +--R + +--R 3 2 7 5 2 6 5 3 2 5 35 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - -- B c d e )x +--R 4 4 4 4 +--R + +--R 3 2 7 3 2 6 2 2 5 3 3 4 3 4 3 3 +--R (- - B a c e - - A a c d e - B a c d e - A c d e - 7B c d e )x +--R 5 5 +--R + +--R 1 2 7 3 2 6 3 2 2 5 1 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - - B a c d e +--R 2 10 10 2 +--R + +--R 1 3 4 3 7 3 5 2 +--R - - A c d e - - B c d e +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 1 3 7 1 2 6 3 2 2 5 3 2 3 4 +--R - - B a e - - A a c d e - -- B a c d e - -- A a c d e +--R 7 7 35 35 +--R + +--R 1 2 4 3 1 3 5 2 3 6 +--R - - B a c d e - - A c d e - B c d e +--R 7 7 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 3 2 3 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e +--R 8 56 56 280 +--R + +--R 3 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - -- B a c d e - -- A c d e - - B c d +--R 280 56 56 8 +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 10 2 7 9 8 8 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1258 + +--S 1259 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R - 280B c e x + (- 140A c e - 980B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 280B a c e - 280A c d e - 1960B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 210A a c e - 350B a c d e - 350A c d e - 2450B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 168B a c e - 168A a c d e - 280B a c d e - 280A c d e +--R + +--R 3 4 3 +--R - 1960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 140A a c e - 84B a c d e - 84A a c d e - 140B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 140A c d e - 980B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 40B a e - 40A a c d e - 24B a c d e - 24A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 40B a c d e - 40A c d e - 280B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 35A a e - 5B a d e - 5A a c d e - 3B a c d e - 3A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 5B a c d e - 5A c d e - 35B c d +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 +--R 280e x + 2240d e x + 7840d e x + 15680d e x + 19600d e x +--R + +--R 5 11 3 6 10 2 7 9 8 8 +--R 15680d e x + 7840d e x + 2240d e x + 280d e +--R Type: Union(Expression(Integer),...) +--E 1259 + +--S 1260 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1261 + +)clear all + +--S 1262 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^10 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1262 + +--S 1263 of 1457 +r0:=1/9*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^9)-1/8*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^8)+3/7*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^7)+1/6*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))/(e^8*(d+e*x)^6)+1/5*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*_ + d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^5)-3/4*c^2*(7*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)/(e^8*(d+e*x)^4)+1/3*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^3)-_ + 1/2*B*c^3/(e^8*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 7 7 1 3 7 7 3 6 6 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 6 +--R + +--R 3 2 7 1 3 6 7 3 2 5 5 +--R (- - B a c e - - A c d e - - B c d e )x +--R 4 2 4 +--R + +--R 3 2 7 3 2 6 1 3 2 5 7 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - - B c d e )x +--R 5 4 2 4 +--R + +--R 1 2 7 2 2 6 1 2 2 5 1 3 3 4 7 3 4 3 3 +--R (- - B a c e - - A a c d e - - B a c d e - - A c d e - - B c d e )x +--R 2 5 2 3 6 +--R + +--R 3 2 7 3 2 6 6 2 2 5 3 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - -- B a c d e +--R 7 14 35 14 +--R + +--R 1 3 4 3 1 3 5 2 +--R - - A c d e - - B c d e +--R 7 2 +--R * +--R 2 +--R x +--R + +--R 1 3 7 3 2 6 3 2 2 5 3 2 3 4 +--R - - B a e - -- A a c d e - -- B a c d e - -- A a c d e +--R 8 28 56 70 +--R + +--R 3 2 4 3 1 3 5 2 1 3 6 +--R - -- B a c d e - -- A c d e - - B c d e +--R 56 28 8 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 1 2 3 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e +--R 9 72 84 168 +--R + +--R 1 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - --- B a c d e - --- A c d e - -- B c d +--R 210 168 252 72 +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 5 12 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 11 3 7 10 2 8 9 9 8 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1263 + +--S 1264 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R - 1260B c e x + (- 840A c e - 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 1890B a c e - 1260A c d e - 4410B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 1512A a c e - 1890B a c d e - 1260A c d e - 4410B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 1260B a c e - 1008A a c d e - 1260B a c d e - 840A c d e +--R + +--R 3 4 3 +--R - 2940B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 1080A a c e - 540B a c d e - 432A a c d e - 540B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 360A c d e - 1260B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 315B a e - 270A a c d e - 135B a c d e - 108A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 135B a c d e - 90A c d e - 315B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 280A a e - 35B a d e - 30A a c d e - 15B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 15B a c d e - 10A c d e - 35B c d +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 +--R 2520e x + 22680d e x + 90720d e x + 211680d e x + 317520d e x +--R + +--R 5 12 4 6 11 3 7 10 2 8 9 9 8 +--R 317520d e x + 211680d e x + 90720d e x + 22680d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 1264 + +--S 1265 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1266 + +)clear all + +--S 1267 of 1457 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^11 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1267 + +--S 1268 of 1457 +r0:=1/10*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^10)-1/9*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^9)+3/8*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^8)+1/7*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^7)+1/6*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^6)-3/5*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^5)+1/4*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^4)-1/3*B*c^3/_ + (e^8*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 7 7 1 3 7 7 3 6 6 +--R - - B c e x + (- - A c e - -- B c d e )x +--R 3 4 12 +--R + +--R 3 2 7 3 3 6 7 3 2 5 5 +--R (- - B a c e - -- A c d e - -- B c d e )x +--R 5 10 10 +--R + +--R 1 2 7 1 2 6 1 3 2 5 7 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - -- B c d e )x +--R 2 2 4 12 +--R + +--R 3 2 7 2 2 6 2 2 2 5 1 3 3 4 1 3 4 3 3 +--R (- - B a c e - - A a c d e - - B a c d e - - A c d e - - B c d e )x +--R 7 7 7 7 3 +--R + +--R 3 2 7 9 2 6 3 2 2 5 3 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - -- B a c d e +--R 8 56 28 28 +--R + +--R 3 3 4 3 1 3 5 2 +--R - -- A c d e - - B c d e +--R 56 8 +--R * +--R 2 +--R x +--R + +--R 1 3 7 1 2 6 1 2 2 5 1 2 3 4 +--R - - B a e - -- A a c d e - -- B a c d e - -- A a c d e +--R 9 12 28 42 +--R + +--R 1 2 4 3 1 3 5 2 1 3 6 +--R - -- B a c d e - -- A c d e - -- B c d e +--R 42 84 36 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 1 2 3 4 +--R - -- A a e - -- B a d e - --- A a c d e - --- B a c d e +--R 10 90 120 280 +--R + +--R 1 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - --- B a c d e - --- A c d e - --- B c d +--R 420 420 840 360 +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 5 13 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 12 4 7 11 3 8 10 2 9 9 10 8 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1268 + +--S 1269 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R - 840B c e x + (- 630A c e - 1470B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 1512B a c e - 756A c d e - 1764B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 1260A a c e - 1260B a c d e - 630A c d e - 1470B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 1080B a c e - 720A a c d e - 720B a c d e - 360A c d e +--R + +--R 3 4 3 +--R - 840B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 945A a c e - 405B a c d e - 270A a c d e - 270B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 135A c d e - 315B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 280B a e - 210A a c d e - 90B a c d e - 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 60B a c d e - 30A c d e - 70B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 252A a e - 28B a d e - 21A a c d e - 9B a c d e - 6A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 6B a c d e - 3A c d e - 7B c d +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 +--R 2520e x + 25200d e x + 113400d e x + 302400d e x + 529200d e x +--R + +--R 5 13 5 6 12 4 7 11 3 8 10 2 +--R 635040d e x + 529200d e x + 302400d e x + 113400d e x +--R + +--R 9 9 10 8 +--R 25200d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 1269 + +--S 1270 of 1457 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1271 + +)clear all + +--S 1272 of 1457 +t0:=(A+B*x)*(d+e*x)^m/(a+c*x^2) +--R +--R +--R m +--R (B x + A)(e x + d) +--R (1) ------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 1272 + +--S 1273 of 1457 +--r0:=-1/2*(d+e*x)^(1+m)*hypergeometric(1,1+m,2+m,(d+e*x)*sqrt(c)/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(A+B*sqrt(-a)/sqrt(c))/((1+m)*sqrt(-a)*_ +-- (e*sqrt(-a)+d*sqrt(c)))-1/2*(d+e*x)^(1+m)*hypergeometric(1,1+m,2+_ +-- m,(d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*B+A*sqrt(-a)*sqrt(c))/_ +-- (a*(1+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c))) +--E 1273 + +--S 1274 of 1457 +--a0:=integrate(t0,x) +--E 1274 + +--S 1275 of 1457 +--m0:=a0-r0 +--E 1275 + +--S 1276 of 1457 +--d0:=D(m0,x) +--E 1276 + +)clear all + +--S 1277 of 1457 +t0:=(A+B*x)*(d+e*x)^(1+m)/(a+c*x^2) +--R +--R +--R m + 1 +--R (B x + A)(e x + d) +--R (1) ----------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1457 +--r0:=-1/2*(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,(d+e*x)*sqrt(c)/(e*_ +-- sqrt(-a)+d*sqrt(c)))*(A+B*sqrt(-a)/sqrt(c))/((2+m)*sqrt(-a)*(e*_ +-- sqrt(-a)+d*sqrt(c)))-1/2*(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,_ +-- (d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*B+A*sqrt(-a)*sqrt(c))/_ +-- (a*(2+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c))) +--E 1278 + +--S 1279 of 1457 +--a0:=integrate(t0,x) +--E 1279 + +--S 1280 of 1457 +--m0:=a0-r0 +--E 1280 + +--S 1281 of 1457 +--d0:=D(m0,x) +--E 1281 + +)clear all + +--S 1282 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1282 + +--S 1283 of 1457 +r0:=e*(4*B*c*d^3+6*A*c*d^2*e-4*a*B*d*e^2-a*A*e^3)*x/c^2+1/2*e^2*(6*B*c*d^2+_ + 4*A*c*d*e-a*B*e^2)*x^2/c^2+1/3*e^3*(4*B*d+A*e)*x^3/c+1/4*B*e^4*x^4/c+_ + 1/2*(4*A*c*d*e*(c*d^2-a*e^2)+B*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*_ + log(a+c*x^2)/c^3-(4*a*B*d*e*(c*d^2-a*e^2)-A*(c^2*d^4-6*a*c*d^2*_ + e^2+a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (12A a c e + 48B a c d e - 72A a c d e - 48B a c d e + 12A c d ) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 2 4 +--R (6B a e - 24A a c d e - 36B a c d e + 24A c d e + 6B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R 3B c e x + (4A c e + 16B c d e )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 6B a c e + 24A c d e + 36B c d e )x +--R + +--R 4 3 2 2 2 2 3 +--R (- 12A a c e - 48B a c d e + 72A c d e + 48B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 +-+ +-+ +--R 12c \|a \|c +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (6A a c e + 24B a c d e - 36A a c d e - 24B a c d e + 6A c d ) +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 4 3 2 2 2 3 2 4 +--R (6B a e - 24A a c d e - 36B a c d e + 24A c d e + 6B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R 3B c e x + (4A c e + 16B c d e )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 6B a c e + 24A c d e + 36B c d e )x +--R + +--R 4 3 2 2 2 2 3 +--R (- 12A a c e - 48B a c d e + 72A c d e + 48B c d e)x +--R * +--R +-----+ +--R \|- a c +--R / +--R 3 +-----+ +--R 12c \|- a c +--R , +--R +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (12A a c e + 48B a c d e - 72A a c d e - 48B a c d e + 12A c d ) +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 4 3 2 2 2 3 2 4 +--R (6B a e - 24A a c d e - 36B a c d e + 24A c d e + 6B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R 3B c e x + (4A c e + 16B c d e )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 6B a c e + 24A c d e + 36B c d e )x +--R + +--R 4 3 2 2 2 2 3 +--R (- 12A a c e - 48B a c d e + 72A c d e + 48B c d e)x +--R * +--R +---+ +--R \|a c +--R / +--R 3 +---+ +--R 12c \|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1284 + +--S 1285 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 2 3 2 4 +-+ +-+ +--R (A a e + 4B a d e - 6A a c d e - 4B a c d e + A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 4 2 3 2 2 3 2 4 +-----+ +--R (- 2A a e - 8B a d e + 12A a c d e + 8B a c d e - 2A c d )\|- a c +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R / +--R 2 +-----+ +-+ +-+ +--R 2c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 4 2 3 2 2 3 2 4 +-+ +-+ +--R (A a e + 4B a d e - 6A a c d e - 4B a c d e + A c d )\|a \|c +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R +-+ +--R 2 4 2 3 2 2 3 2 4 +---+ x\|c +--R (- A a e - 4B a d e + 6A a c d e + 4B a c d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 +-+ +-+ +---+ +--R c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1288 + +)clear all + +--S 1289 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1289 + +--S 1290 of 1457 +r0:=e*(3*B*c*d^2+3*A*c*d*e-a*B*e^2)*x/c^2+1/2*e^2*(3*B*d+A*e)*x^2/c+_ + 1/3*B*e^3*x^3/c+1/2*(B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*_ + log(a+c*x^2)/c^2+(A*c*d*(c*d^2-3*a*e^2)-a*B*e*(3*c*d^2-a*e^2))*_ + atan(x*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R 2 3 2 2 2 3 x\|c +--R (6B a e - 18A a c d e - 18B a c d e + 6A c d )atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 3 2 3 3 +--R (- 3A a e - 9B a d e + 9A c d e + 3B c d )log(c x + a) + 2B c e x +--R + +--R 3 2 2 3 2 2 +--R (3A c e + 9B c d e )x + (- 6B a e + 18A c d e + 18B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 +-+ +-+ +--R 6c \|a \|c +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 3 +--R (3B a e - 9A a c d e - 9B a c d e + 3A c d ) +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 2 2 3 2 +--R (- 3A a e - 9B a d e + 9A c d e + 3B c d )log(c x + a) +--R + +--R 3 3 3 2 2 +--R 2B c e x + (3A c e + 9B c d e )x +--R + +--R 3 2 2 +--R (- 6B a e + 18A c d e + 18B c d e)x +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 +-----+ +--R 6c \|- a c +--R , +--R +--R +---+ +--R 2 3 2 2 2 3 x\|a c +--R (6B a e - 18A a c d e - 18B a c d e + 6A c d )atan(-------) +--R a +--R + +--R 3 2 2 3 2 +--R (- 3A a e - 9B a d e + 9A c d e + 3B c d )log(c x + a) +--R + +--R 3 3 3 2 2 +--R 2B c e x + (3A c e + 9B c d e )x +--R + +--R 3 2 2 +--R (- 6B a e + 18A c d e + 18B c d e)x +--R * +--R +---+ +--R \|a c +--R / +--R 2 +---+ +--R 6c \|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1291 + +--S 1292 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 +-+ +-+ +--R (B a e - 3A a c d e - 3B a c d e + A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 3 2 2 2 3 +-----+ x\|c +--R (- 2B a e + 6A a c d e + 6B a c d e - 2A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 +-----+ +-+ +-+ +--R 2c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 3 2 2 2 3 +-+ +-+ x\|a c +--R (B a e - 3A a c d e - 3B a c d e + A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 3 2 2 2 3 +---+ x\|c +--R (- B a e + 3A a c d e + 3B a c d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 +-+ +-+ +---+ +--R c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1295 + +)clear all + +--S 1296 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1296 + +--S 1297 of 1457 +r0:=e*(2*B*d+A*e)*x/c+1/2*B*e^2*x^2/c+1/2*(B*c*d^2+2*A*c*d*e-a*B*e^2)*_ + log(a+c*x^2)/c^2+(A*c*d^2-2*a*B*d*e-a*A*e^2)*atan(x*sqrt(c)/_ + sqrt(a))/(c^(3/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 x\|c +--R (- 2A a c e - 4B a c d e + 2A c d )atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 +--R (- B a e + 2A c d e + B c d )log(c x + a) + B c e x +--R + +--R 2 +--R (2A c e + 4B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 +-+ +-+ +--R 2c \|a \|c +--R Type: Expression(Integer) +--E 1297 + +--S 1298 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 2 2 (c x - a)\|- a c - 2a c x +--R (A a c e + 2B a c d e - A c d )log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 2 2 2 +--R (- B a e + 2A c d e + B c d )log(c x + a) + B c e x +--R + +--R 2 +--R (2A c e + 4B c d e)x +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 +-----+ +--R 2c \|- a c +--R , +--R +--R +---+ +--R 2 2 2 x\|a c +--R (- 2A a c e - 4B a c d e + 2A c d )atan(-------) +--R a +--R + +--R 2 2 2 2 2 +--R (- B a e + 2A c d e + B c d )log(c x + a) + B c e x +--R + +--R 2 +--R (2A c e + 4B c d e)x +--R * +--R +---+ +--R \|a c +--R / +--R 2 +---+ +--R 2c \|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1298 + +--S 1299 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R 2 2 +-+ +-+ (c x - a)\|- a c - 2a c x +--R (A a e + 2B a d e - A c d )\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 2 +-----+ x\|c +--R (2A a e + 4B a d e - 2A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 2c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1300 + +--S 1301 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 2 +-+ +-+ x\|a c +--R (- A a e - 2B a d e + A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 2 +---+ x\|c +--R (A a e + 2B a d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R / +--R +-+ +-+ +---+ +--R c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1302 + +)clear all + +--S 1303 of 1457 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1303 + +--S 1304 of 1457 +r0:=B*e*x/c+1/2*(B*d+A*e)*log(a+c*x^2)/c+(A*c*d-a*B*e)*atan(x*sqrt(c)/_ + sqrt(a))/(c^(3/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R x\|c 2 +-+ +-+ +--R (- 2B a e + 2A c d)atan(-----) + ((A e + B d)log(c x + a) + 2B e x)\|a \|c +--R +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +-+ +--R 2c\|a \|c +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R (B a e - A c d)log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 +-----+ +--R ((A e + B d)log(c x + a) + 2B e x)\|- a c +--R / +--R +-----+ +--R 2c\|- a c +--R , +--R +---+ +--R x\|a c 2 +---+ +--R (- 2B a e + 2A c d)atan(-------) + ((A e + B d)log(c x + a) + 2B e x)\|a c +--R a +--R ---------------------------------------------------------------------------- +--R +---+ +--R 2c\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1305 + +--S 1306 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c - 2a c x +--R (B a e - A c d)\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R +-----+ x\|c +--R (2B a e - 2A c d)\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 2c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R (- B a e + A c d)\|a \|c atan(-------) + (B a e - A c d)\|a c atan(-----) +--R a +-+ +--R \|a +--R ------------------------------------------------------------------------- +--R +-+ +-+ +---+ +--R c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1309 + +)clear all + +--S 1310 of 1457 +t0:=(A+B*x)/(a+c*x^2) +--R +--R +--R B x + A +--R (1) -------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1310 + +--S 1311 of 1457 +r0:=1/2*B*log(a+c*x^2)/c+A*atan(x*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c)) +--R +--R +--R +-+ +--R x\|c 2 +-+ +-+ +--R 2A c atan(-----) + B log(c x + a)\|a \|c +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R +-+ +-+ +--R 2c\|a \|c +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x 2 +-----+ +--R A c log(---------------------------) + B log(c x + a)\|- a c +--R 2 +--R c x + a +--R [--------------------------------------------------------------, +--R +-----+ +--R 2c\|- a c +--R +---+ +--R x\|a c 2 +---+ +--R 2A c atan(-------) + B log(c x + a)\|a c +--R a +--R ------------------------------------------] +--R +---+ +--R 2c\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1312 + +--S 1313 of 1457 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x\|c +--R A\|a \|c log(---------------------------) - 2A\|- a c atan(-----) +--R 2 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1457 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R A\|a \|c atan(-------) - A\|a c atan(-----) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R \|a \|c \|a c +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1316 + +)clear all + +--S 1317 of 1457 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------- +--R 3 2 +--R c e x + c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1317 + +--S 1318 of 1457 +r0:=-(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)+1/2*(B*d-A*e)*log(a+c*x^2)/_ + (c*d^2+a*e^2)+(A*c*d+a*B*e)*atan(x*sqrt(c)/sqrt(a))/((c*d^2+a*e^2)*_ + sqrt(a)*sqrt(c)) +--R +--R +--R (2) +--R +-+ +--R x\|c +--R (2B a e + 2A c d)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-+ +-+ +--R ((- A e + B d)log(c x + a) + (2A e - 2B d)log(e x + d))\|a \|c +--R / +--R 2 2 +-+ +-+ +--R (2a e + 2c d )\|a \|c +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R (B a e + A c d)log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 +-----+ +--R ((- A e + B d)log(c x + a) + (2A e - 2B d)log(e x + d))\|- a c +--R / +--R 2 2 +-----+ +--R (2a e + 2c d )\|- a c +--R , +--R +--R +---+ +--R x\|a c +--R (2B a e + 2A c d)atan(-------) +--R a +--R + +--R 2 +---+ +--R ((- A e + B d)log(c x + a) + (2A e - 2B d)log(e x + d))\|a c +--R / +--R 2 2 +---+ +--R (2a e + 2c d )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1319 + +--S 1320 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +--R (B a e + A c d)\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R +-----+ x\|c +--R (- 2B a e - 2A c d)\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 2 +-----+ +-+ +-+ +--R (2a e + 2c d )\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1320 + +--S 1321 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R (B a e + A c d)\|a \|c atan(-------) + (- B a e - A c d)\|a c atan(-----) +--R a +-+ +--R \|a +--R ------------------------------------------------------------------------- +--R 2 2 +-+ +-+ +---+ +--R (a e + c d )\|a \|c \|a c +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1323 + +)clear all + +--S 1324 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------ +--R 2 4 3 2 2 2 2 +--R c e x + 2c d e x + (a e + c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1324 + +--S 1325 of 1457 +r0:=(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x))-(B*c*d^2-2*A*c*d*e-a*B*e^2)*_ + log(d+e*x)/(c*d^2+a*e^2)^2+1/2*(B*c*d^2-2*A*c*d*e-a*B*e^2)*_ + log(a+c*x^2)/(c*d^2+a*e^2)^2+(A*c*d^2+2*a*B*d*e-a*A*e^2)*_ + atan(x*sqrt(c)/sqrt(a))*sqrt(c)/((c*d^2+a*e^2)^2*sqrt(a)) +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((- 2A a e + 4B a d e + 2A c d e)x - 2A a d e + 4B a d e + 2A c d ) +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 2 3 +--R ((- B a e - 2A c d e + B c d e)x - B a d e - 2A c d e + B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 2 2 2 +--R (2B a e + 4A c d e - 2B c d e)x + 2B a d e + 4A c d e +--R + +--R 3 +--R - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + 2B a d e - 2A c d e + 2B c d +--R * +--R +-+ +--R \|a +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +-+ +--R ((2a e + 4a c d e + 2c d e)x + 2a d e + 4a c d e + 2c d )\|a +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 3 +--R ((A a e - 2B a d e - A c d e)x + A a d e - 2B a d e - A c d ) +--R * +--R +---+ +--R | c 2 +--R +---+ - 2a x |- - + c x - a +--R | c \| a +--R |- - log(-----------------------) +--R \| a 2 +--R c x + a +--R + +--R 3 2 2 2 2 3 +--R ((- B a e - 2A c d e + B c d e)x - B a d e - 2A c d e + B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 2 2 2 3 +--R ((2B a e + 4A c d e - 2B c d e)x + 2B a d e + 4A c d e - 2B c d ) +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + 2B a d e - 2A c d e + 2B c d +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +--R (2a e + 4a c d e + 2c d e)x + 2a d e + 4a c d e + 2c d +--R , +--R +--R 3 2 2 2 2 3 +--R ((2A a e - 4B a d e - 2A c d e)x + 2A a d e - 4B a d e - 2A c d ) +--R * +--R +-+ +--R |c +--R +-+ a |- +--R |c \|a +--R |- atan(-----) +--R \|a c x +--R + +--R 3 2 2 2 2 3 +--R ((- B a e - 2A c d e + B c d e)x - B a d e - 2A c d e + B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 2 2 2 3 +--R ((2B a e + 4A c d e - 2B c d e)x + 2B a d e + 4A c d e - 2B c d ) +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + 2B a d e - 2A c d e + 2B c d +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +--R (2a e + 4a c d e + 2c d e)x + 2a d e + 4a c d e + 2c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1326 + +--S 1327 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---+ +--R | c 2 +--R +---+ - 2a x |- - + c x - a +--R 2 2 | c +-+ \| a +--R (A a e - 2B a d e - A c d ) |- - \|a log(-----------------------) +--R \| a 2 +--R c x + a +--R + +--R +-+ +--R 2 2 +-+ x\|c +--R (2A a e - 4B a d e - 2A c d )\|c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 4 2 2 2 4 +-+ +--R (2a e + 4a c d e + 2c d )\|a +--R Type: Expression(Integer) +--E 1327 + +--S 1328 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 2 +-+ x\|c +--R (A a e - 2B a d e - A c d )\|c atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R |c +--R +-+ a |- +--R 2 2 +-+ |c \|a +--R (A a e - 2B a d e - A c d )\|a |- atan(-----) +--R \|a c x +--R / +--R 2 4 2 2 2 4 +-+ +--R (a e + 2a c d e + c d )\|a +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1330 + +)clear all + +--S 1331 of 1457 +t0:=(A+B*x)/((d+e*x)^3*(a+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------------- +--R 3 5 2 4 3 2 3 2 3 2 2 3 +--R c e x + 3c d e x + (a e + 3c d e)x + (3a d e + c d )x + 3a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1331 + +--S 1332 of 1457 +r0:=1/2*(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x)^2)+(B*c*d^2-2*A*c*d*e-a*B*e^2)/_ + ((c*d^2+a*e^2)^2*(d+e*x))-c*(B*c*d^3-3*A*c*d^2*e-3*a*B*d*e^2+_ + a*A*e^3)*log(d+e*x)/(c*d^2+a*e^2)^3+1/2*c*(B*c*d^3-3*A*c*d^2*e-_ + 3*a*B*d*e^2+a*A*e^3)*log(a+c*x^2)/(c*d^2+a*e^2)^3+(A*c*d*(c*d^2-_ + 3*a*e^2)+a*B*e*(3*c*d^2-a*e^2))*atan(x*sqrt(c)/sqrt(a))*sqrt(c)/_ + ((c*d^2+a*e^2)^3*sqrt(a)) +--R +--R +--R (2) +--R 2 5 4 2 3 2 3 2 2 +--R (- 2B a e - 6A a c d e + 6B a c d e + 2A c d e )x +--R + +--R 2 4 2 3 3 2 2 4 2 2 3 +--R (- 4B a d e - 12A a c d e + 12B a c d e + 4A c d e)x - 2B a d e +--R + +--R 3 2 4 2 5 +--R - 6A a c d e + 6B a c d e + 2A c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (A a c e - 3B a c d e - 3A c d e + B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 3 +--R (2A a c d e - 6B a c d e - 6A c d e + 2B c d e)x + A a c d e +--R + +--R 3 2 2 4 2 5 +--R - 3B a c d e - 3A c d e + B c d +--R * +--R 2 +--R log(c x + a) +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 2A a c e + 6B a c d e + 6A c d e - 2B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (- 4A a c d e + 12B a c d e + 12A c d e - 4B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R - 2A a c d e + 6B a c d e + 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 4 2 3 2 2 4 2 5 2 4 +--R (- 2B a e - 4A a c d e - 4A c d e + 2B c d e)x - A a e - B a d e +--R + +--R 2 3 3 2 2 4 2 5 +--R - 6A a c d e + 2B a c d e - 5A c d e + 3B c d +--R * +--R +-+ +--R \|a +--R / +--R 3 8 2 2 6 2 4 4 3 6 2 2 +--R (2a e + 6a c d e + 6a c d e + 2c d e )x +--R + +--R 3 7 2 3 5 2 5 3 3 7 3 2 6 2 4 4 +--R (4a d e + 12a c d e + 12a c d e + 4c d e)x + 2a d e + 6a c d e +--R + +--R 2 6 2 3 8 +--R 6a c d e + 2c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 5 4 2 3 2 3 2 2 +--R (B a e + 3A a c d e - 3B a c d e - A c d e )x +--R + +--R 2 4 2 3 3 2 2 4 2 2 3 +--R (2B a d e + 6A a c d e - 6B a c d e - 2A c d e)x + B a d e +--R + +--R 3 2 4 2 5 +--R 3A a c d e - 3B a c d e - A c d +--R * +--R +---+ +--R | c 2 +--R +---+ - 2a x |- - + c x - a +--R | c \| a +--R |- - log(-----------------------) +--R \| a 2 +--R c x + a +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (A a c e - 3B a c d e - 3A c d e + B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 3 +--R (2A a c d e - 6B a c d e - 6A c d e + 2B c d e)x + A a c d e +--R + +--R 3 2 2 4 2 5 +--R - 3B a c d e - 3A c d e + B c d +--R * +--R 2 +--R log(c x + a) +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 2A a c e + 6B a c d e + 6A c d e - 2B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (- 4A a c d e + 12B a c d e + 12A c d e - 4B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R - 2A a c d e + 6B a c d e + 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 4 2 3 2 2 4 2 5 2 4 +--R (- 2B a e - 4A a c d e - 4A c d e + 2B c d e)x - A a e - B a d e +--R + +--R 2 3 3 2 2 4 2 5 +--R - 6A a c d e + 2B a c d e - 5A c d e + 3B c d +--R / +--R 3 8 2 2 6 2 4 4 3 6 2 2 +--R (2a e + 6a c d e + 6a c d e + 2c d e )x +--R + +--R 3 7 2 3 5 2 5 3 3 7 3 2 6 2 4 4 +--R (4a d e + 12a c d e + 12a c d e + 4c d e)x + 2a d e + 6a c d e +--R + +--R 2 6 2 3 8 +--R 6a c d e + 2c d +--R , +--R +--R 2 5 4 2 3 2 3 2 2 +--R (2B a e + 6A a c d e - 6B a c d e - 2A c d e )x +--R + +--R 2 4 2 3 3 2 2 4 2 2 3 +--R (4B a d e + 12A a c d e - 12B a c d e - 4A c d e)x + 2B a d e +--R + +--R 3 2 4 2 5 +--R 6A a c d e - 6B a c d e - 2A c d +--R * +--R +-+ +--R |c +--R +-+ a |- +--R |c \|a +--R |- atan(-----) +--R \|a c x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (A a c e - 3B a c d e - 3A c d e + B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 3 +--R (2A a c d e - 6B a c d e - 6A c d e + 2B c d e)x + A a c d e +--R + +--R 3 2 2 4 2 5 +--R - 3B a c d e - 3A c d e + B c d +--R * +--R 2 +--R log(c x + a) +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 2A a c e + 6B a c d e + 6A c d e - 2B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (- 4A a c d e + 12B a c d e + 12A c d e - 4B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R - 2A a c d e + 6B a c d e + 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 4 2 3 2 2 4 2 5 2 4 +--R (- 2B a e - 4A a c d e - 4A c d e + 2B c d e)x - A a e - B a d e +--R + +--R 2 3 3 2 2 4 2 5 +--R - 6A a c d e + 2B a c d e - 5A c d e + 3B c d +--R / +--R 3 8 2 2 6 2 4 4 3 6 2 2 +--R (2a e + 6a c d e + 6a c d e + 2c d e )x +--R + +--R 3 7 2 3 5 2 5 3 3 7 3 2 6 2 4 4 +--R (4a d e + 12a c d e + 12a c d e + 4c d e)x + 2a d e + 6a c d e +--R + +--R 2 6 2 3 8 +--R 6a c d e + 2c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1333 + +--S 1334 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---+ +--R 2 3 2 2 2 3 | c +-+ +--R (B a e + 3A a c d e - 3B a c d e - A c d ) |- - \|a +--R \| a +--R * +--R +---+ +--R | c 2 +--R - 2a x |- - + c x - a +--R \| a +--R log(-----------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 3 2 2 2 3 +-+ x\|c +--R (2B a e + 6A a c d e - 6B a c d e - 2A c d )\|c atan(-----) +--R +-+ +--R \|a +--R / +--R 3 6 2 2 4 2 4 2 3 6 +-+ +--R (2a e + 6a c d e + 6a c d e + 2c d )\|a +--R Type: Expression(Integer) +--E 1334 + +--S 1335 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 3 2 2 2 3 +-+ x\|c +--R (B a e + 3A a c d e - 3B a c d e - A c d )\|c atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R |c +--R +-+ a |- +--R 2 3 2 2 2 3 +-+ |c \|a +--R (B a e + 3A a c d e - 3B a c d e - A c d )\|a |- atan(-----) +--R \|a c x +--R / +--R 3 6 2 2 4 2 4 2 3 6 +-+ +--R (a e + 3a c d e + 3a c d e + c d )\|a +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1337 + +)clear all + +--S 1338 of 1457 +t0:=(A+B*x)*(d+e*x)^5/(a+c*x^2)^2 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1338 + +--S 1339 of 1457 +r0:=-5/2*e^2*(A*c*d*(2*c*d^2-3*a*e^2)-a*B*e*(6*c*d^2-a*e^2))*x/(a*c^3)-_ + e^3*(5*A*c*d^2-5*a*B*d*e-a*A*e^2)*x^2/(a*c^2)-5/6*e^4*(3*A*c*d-a*B*e)*_ + x^3/(a*c^2)-1/2*A*e^5*x^4/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^5/(a*c*_ + (a+c*x^2))+1/2*(A*c*d*(c^2*d^4+10*a*c*d^2*e^2-15*a^2*e^4)+5*a*B*_ + e*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(3/2)*c^(7/2))+e^2*(5*B*c*d^3+5*A*c*d^2*e-5*a*B*d*e^2-a*A*e^3)*_ + log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 15B a c e - 45A a c d e - 90B a c d e + 30A a c d e +--R + +--R 3 4 4 5 +--R 15B a c d e + 3A c d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 15B a e - 45A a c d e - 90B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 2 3 2 3 2 2 +--R (- 6A a c e - 30B a c d e + 30A a c d e + 30B a c d e )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 +--R - 6A a e - 30B a d e + 30A a c d e + 30B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B a c e x + (3A a c e + 15B a c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (- 10B a c e + 30A a c d e + 60B a c d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 6A a c e + 30B a c d e - 30A a c d e - 30B a c d e +--R + +--R 3 4 +--R 15A c d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 4 2 2 3 2 3 2 +--R - 15B a e + 45A a c d e + 90B a c d e - 30A a c d e +--R + +--R 2 4 3 5 +--R - 15B a c d e + 3A c d +--R * +--R x +--R + +--R 2 5 +--R - 3B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 +-+ +-+ +--R (6a c x + 6a c )\|a \|c +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 15B a c e - 45A a c d e - 90B a c d e + 30A a c d e +--R + +--R 3 4 4 5 +--R 15B a c d e + 3A c d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 15B a e - 45A a c d e - 90B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 5 2 4 2 2 3 2 3 2 2 +--R (- 12A a c e - 60B a c d e + 60A a c d e + 60B a c d e )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 +--R - 12A a e - 60B a d e + 60A a c d e + 60B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 5 2 5 2 4 4 +--R 4B a c e x + (6A a c e + 30B a c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (- 20B a c e + 60A a c d e + 120B a c d e )x +--R + +--R 2 5 2 4 2 +--R (6A a c e + 30B a c d e )x +--R + +--R 3 5 2 4 2 2 3 2 3 2 +--R - 30B a e + 90A a c d e + 180B a c d e - 60A a c d e +--R + +--R 2 4 3 5 +--R - 30B a c d e + 6A c d +--R * +--R x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R - 6A a e - 30B a d e + 60A a c d e + 60B a c d e - 30A a c d e +--R + +--R 2 5 +--R - 6B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 4 2 2 3 +-----+ +--R (12a c x + 12a c )\|- a c +--R , +--R +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 15B a c e - 45A a c d e - 90B a c d e + 30A a c d e +--R + +--R 3 4 4 5 +--R 15B a c d e + 3A c d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 15B a e - 45A a c d e - 90B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 5 2 4 2 2 3 2 3 2 2 +--R (- 6A a c e - 30B a c d e + 30A a c d e + 30B a c d e )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 +--R - 6A a e - 30B a d e + 30A a c d e + 30B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B a c e x + (3A a c e + 15B a c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (- 10B a c e + 30A a c d e + 60B a c d e )x +--R + +--R 2 5 2 4 2 +--R (3A a c e + 15B a c d e )x +--R + +--R 3 5 2 4 2 2 3 2 3 2 +--R - 15B a e + 45A a c d e + 90B a c d e - 30A a c d e +--R + +--R 2 4 3 5 +--R - 15B a c d e + 3A c d +--R * +--R x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R - 3A a e - 15B a d e + 30A a c d e + 30B a c d e - 15A a c d e +--R + +--R 2 5 +--R - 3B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 4 2 2 3 +---+ +--R (6a c x + 6a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1340 + +--S 1341 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 5B a e - 15A a c d e - 30B a c d e + 10A a c d e + 5B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +--R \|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R - 10B a e + 30A a c d e + 60B a c d e - 20A a c d e - 10B a c d e +--R + +--R 3 5 +--R - 2A c d +--R * +--R +-+ +--R +-----+ x\|c +--R \|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R (- 2A a e - 10B a d e + 20A a c d e + 20B a c d e - 10A c d e) +--R * +--R +-----+ +-+ +-+ +--R \|- a c \|a \|c +--R / +--R 3 +-----+ +-+ +-+ +--R 4a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 5B a e - 15A a c d e - 30B a c d e + 10A a c d e + 5B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R +---+ +--R +-+ +-+ x\|a c +--R \|a \|c atan(-------) +--R a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R - 5B a e + 15A a c d e + 30B a c d e - 10A a c d e - 5B a c d e +--R + +--R 3 5 +--R - A c d +--R * +--R +-+ +--R +---+ x\|c +--R \|a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 3 3 2 2 4 +-+ +-+ +--R (- A a e - 5B a d e + 10A a c d e + 10B a c d e - 5A c d e)\|a \|c +--R * +--R +---+ +--R \|a c +--R / +--R 3 +-+ +-+ +---+ +--R 2a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1344 + +)clear all + +--S 1345 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1345 + +--S 1346 of 1457 +r0:=-3/2*e^2*(2*A*c*d^2-4*a*B*d*e-a*A*e^2)*x/(a*c^2)-e^3*(2*A*c*d-a*B*e)*_ + x^2/(a*c^2)-1/2*A*e^4*x^3/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^4/(a*c*_ + (a+c*x^2))+1/2*(4*a*B*d*e*(c*d^2-3*a*e^2)+A*(c^2*d^4+6*a*c*d^2*_ + e^2-3*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(5/2))+e^2*_ + (3*B*c*d^2+2*A*c*d*e-a*B*e^2)*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 2 +--R (- 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A c d )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R - 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (- 2B a c e + 4A a c d e + 6B a c d e )x - 2B a e +--R + +--R 2 3 2 2 2 +--R 4A a c d e + 6B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R B a c e x + (2A a c e + 8B a c d e )x +--R + +--R 2 4 2 3 2 2 2 3 3 2 +--R (2B a c e - 4A a c d e - 6B a c d e + 4A c d e)x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e + A c d )x +--R + +--R 2 4 +--R - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 2 +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e - A c d )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R 3A a c e + 12B a c d e - 6A a c d e - 4B a c d e - A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (- 4B a c e + 8A a c d e + 12B a c d e )x - 4B a e +--R + +--R 2 3 2 2 2 +--R 8A a c d e + 12B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 2 4 2 +--R 2B a c e x + (4A a c e + 16B a c d e )x + 2B a c e x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (6A a c e + 24B a c d e - 12A a c d e - 8B a c d e + 2A c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R - 2B a e + 8A a c d e + 12B a c d e - 8A a c d e - 2B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 4 2 2 3 +-----+ +--R (4a c x + 4a c )\|- a c +--R , +--R +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 2 +--R (- 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A c d )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R - 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (- 2B a c e + 4A a c d e + 6B a c d e )x - 2B a e +--R + +--R 2 3 2 2 2 +--R 4A a c d e + 6B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 2 4 2 +--R B a c e x + (2A a c e + 8B a c d e )x + B a c e x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e + A c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R - B a e + 4A a c d e + 6B a c d e - 4A a c d e - B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 4 2 2 3 +---+ +--R (2a c x + 2a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1347 + +--S 1348 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 2 2 2 3 3 4 +-+ +-+ +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e - A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (6A a c e + 24B a c d e - 12A a c d e - 8B a c d e - 2A c d ) +--R * +--R +-+ +--R +-----+ x\|c +--R \|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 +-----+ +-+ +-+ +--R (- 2B a e + 8A a c d e + 12B a c d e - 8A c d e)\|- a c \|a \|c +--R / +--R 3 +-----+ +-+ +-+ +--R 4a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 4 2 3 2 2 2 2 3 3 4 +-+ +--R (- 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A c d )\|a +--R * +--R +---+ +--R +-+ x\|a c +--R \|c atan(-------) +--R a +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +---+ +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e - A c d )\|a c +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 +-+ +-+ +---+ +--R (- B a e + 4A a c d e + 6B a c d e - 4A c d e)\|a \|c \|a c +--R / +--R 3 +-+ +-+ +---+ +--R 2a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1351 + +)clear all + +--S 1352 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1352 + +--S 1353 of 1457 +r0:=-3/2*e^2*(A*c*d-a*B*e)*x/(a*c^2)-1/2*A*e^3*x^2/(a*c)-1/2*(a*B-A*c*x)*_ + (d+e*x)^3/(a*c*(a+c*x^2))+1/2*(3*a*B*e*(c*d^2-a*e^2)+A*c*d*_ + (c*d^2+3*a*e^2))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(5/2))+1/2*_ + e^2*(3*B*d+A*e)*log(a+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 3B a c e + 3A a c d e + 3B a c d e + A c d )x - 3B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e + 3B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((A a c e + 3B a c d e )x + A a e + 3B a d e )log(c x + a) +--R + +--R 3 3 3 2 2 2 2 +--R 2B a c e x + (- A a c e - 3B a c d e + 3A c d e)x +--R + +--R 2 3 2 2 2 3 3 +--R (3B a e - 3A a c d e - 3B a c d e + A c d )x - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (3B a c e - 3A a c d e - 3B a c d e - A c d )x + 3B a e +--R + +--R 2 2 2 2 2 3 +--R - 3A a c d e - 3B a c d e - A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((2A a c e + 6B a c d e )x + 2A a e + 6B a d e )log(c x + a) +--R + +--R 3 3 2 3 2 2 2 3 +--R 4B a c e x + (6B a e - 6A a c d e - 6B a c d e + 2A c d )x +--R + +--R 2 3 2 2 2 3 +--R 2A a e + 6B a d e - 6A a c d e - 2B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 3 2 2 2 +-----+ +--R (4a c x + 4a c )\|- a c +--R , +--R +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 3B a c e + 3A a c d e + 3B a c d e + A c d )x - 3B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e + 3B a c d e + A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((A a c e + 3B a c d e )x + A a e + 3B a d e )log(c x + a) +--R + +--R 3 3 2 3 2 2 2 3 +--R 2B a c e x + (3B a e - 3A a c d e - 3B a c d e + A c d )x +--R + +--R 2 3 2 2 2 3 +--R A a e + 3B a d e - 3A a c d e - B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 3 2 2 2 +---+ +--R (2a c x + 2a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1354 + +--S 1355 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 +-+ +-+ +--R (3B a e - 3A a c d e - 3B a c d e - A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 3 2 2 2 3 +-----+ x\|c +--R (6B a e - 6A a c d e - 6B a c d e - 2A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 +-----+ +-+ +-+ +--R (2A a e + 6B a d e - 6A c d e)\|- a c \|a \|c +--R / +--R 2 +-----+ +-+ +-+ +--R 4a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1355 + +--S 1356 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 3 2 2 2 3 +-+ +-+ x\|a c +--R (- 3B a e + 3A a c d e + 3B a c d e + A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 3 2 2 2 3 +---+ x\|c +--R (3B a e - 3A a c d e - 3B a c d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 +-+ +-+ +---+ +--R (A a e + 3B a d e - 3A c d e)\|a \|c \|a c +--R / +--R 2 +-+ +-+ +---+ +--R 2a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1357 + +--S 1358 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1358 + +)clear all + +--S 1359 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1359 + +--S 1360 of 1457 +r0:=-1/2*A*e^2*x/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^2/(a*c*(a+c*x^2))+_ + 1/2*(A*c*d^2+2*a*B*d*e+a*A*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*_ + c^(3/2))+1/2*B*e^2*log(a+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 3 2 2 2 2 2 2 2 +--R ((A a c e + 2B a c d e + A c d )x + A a c e + 2B a c d e + A a c d ) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 2 2 2 +--R (B a c e x + B a e )log(c x + a) + (- B a c e + 2A c d e)x +--R + +--R 2 2 2 2 +--R (- A a c e - 2B a c d e + A c d )x - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 2 2 2 2 +--R (A a c e + 2B a c d e + A c d )x + A a c e + 2B a c d e +--R + +--R 2 2 +--R A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 2 2 2 +--R (2B a c e x + 2B a e )log(c x + a) +--R + +--R 2 2 2 2 2 +--R (- 2A a c e - 4B a c d e + 2A c d )x + 2B a e - 4A a c d e +--R + +--R 2 +--R - 2B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 3 2 2 2 +-----+ +--R (4a c x + 4a c )\|- a c +--R , +--R +--R 2 2 2 3 2 2 2 2 2 +--R (A a c e + 2B a c d e + A c d )x + A a c e + 2B a c d e +--R + +--R 2 2 +--R A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 2 2 2 2 +--R (B a c e x + B a e )log(c x + a) +--R + +--R 2 2 2 2 2 2 +--R (- A a c e - 2B a c d e + A c d )x + B a e - 2A a c d e - B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 3 2 2 2 +---+ +--R (2a c x + 2a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1361 + +--S 1362 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R 2 2 2 +-+ +-+ (c x - a)\|- a c + 2a c x +--R (A a c e + 2B a c d e + A c d )\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 2 2 +-----+ x\|c +--R (- 2A a c e - 4B a c d e - 2A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-----+ +-+ +-+ +--R (2B a e - 4A c d e)\|- a c \|a \|c +--R / +--R 2 +-----+ +-+ +-+ +--R 4a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1362 + +--S 1363 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 2 2 +-+ +-+ x\|a c +--R (A a c e + 2B a c d e + A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 2 2 +---+ x\|c +--R (- A a c e - 2B a c d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-+ +-+ +---+ +--R (B a e - 2A c d e)\|a \|c \|a c +--R / +--R 2 +-+ +-+ +---+ +--R 2a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1364 + +--S 1365 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1365 + +)clear all + +--S 1366 of 1457 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1366 + +--S 1367 of 1457 +r0:=-1/2*(a*B-A*c*x)*(d+e*x)/(a*c*(a+c*x^2))+1/2*(A*c*d+a*B*e)*_ + atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(3/2)) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 x\|c +--R ((B a c e + A c d)x + B a e + A a c d)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-+ +-+ +--R (A c e x + (- B a e + A c d)x - B a d)\|a \|c +--R / +--R 2 2 2 +-+ +-+ +--R (2a c x + 2a c)\|a \|c +--R Type: Expression(Integer) +--E 1367 + +--S 1368 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 2 2 (c x - a)\|- a c + 2a c x +--R ((B a c e + A c d)x + B a e + A a c d)log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-----+ +--R ((- 2B a e + 2A c d)x - 2A a e - 2B a d)\|- a c +--R / +--R 2 2 2 +-----+ +--R (4a c x + 4a c)\|- a c +--R , +--R +--R +---+ +--R 2 2 2 x\|a c +--R ((B a c e + A c d)x + B a e + A a c d)atan(-------) +--R a +--R + +--R +---+ +--R ((- B a e + A c d)x - A a e - B a d)\|a c +--R / +--R 2 2 2 +---+ +--R (2a c x + 2a c)\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1368 + +--S 1369 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +--R (B a e + A c d)\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R +-----+ x\|c +-----+ +-+ +-+ +--R (- 2B a e - 2A c d)\|- a c atan(-----) - 2A e\|- a c \|a \|c +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 4a c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1369 + +--S 1370 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1370 + +--S 1371 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R (B a e + A c d)\|a \|c atan(-------) + (- B a e - A c d)\|a c atan(-----) +--R a +-+ +--R \|a +--R + +--R +-+ +-+ +---+ +--R - A e\|a \|c \|a c +--R / +--R +-+ +-+ +---+ +--R 2a c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1371 + +--S 1372 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1372 + +)clear all + +--S 1373 of 1457 +t0:=(A+B*x)/(a+c*x^2)^2 +--R +--R +--R B x + A +--R (1) ------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1373 + +--S 1374 of 1457 +r0:=1/2*(-a*B+A*c*x)/(a*c*(a+c*x^2))+1/2*A*atan(x*sqrt(c)/sqrt(a))/_ + (a^(3/2)*sqrt(c)) +--R +--R +--R +-+ +--R 2 2 x\|c +-+ +-+ +--R (A c x + A a c)atan(-----) + (A c x - B a)\|a \|c +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 2 2 2 +-+ +-+ +--R (2a c x + 2a c)\|a \|c +--R Type: Expression(Integer) +--E 1374 + +--S 1375 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R 2 2 (c x - a)\|- a c + 2a c x +-----+ +--R (A c x + A a c)log(---------------------------) + (2A c x - 2B a)\|- a c +--R 2 +--R c x + a +--R [--------------------------------------------------------------------------, +--R 2 2 2 +-----+ +--R (4a c x + 4a c)\|- a c +--R +---+ +--R 2 2 x\|a c +---+ +--R (A c x + A a c)atan(-------) + (A c x - B a)\|a c +--R a +--R ---------------------------------------------------] +--R 2 2 2 +---+ +--R (2a c x + 2a c)\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1375 + +--S 1376 of 1457 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x\|c +--R A\|a \|c log(---------------------------) - 2A\|- a c atan(-----) +--R 2 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4a\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1376 + +--S 1377 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1377 + +--S 1378 of 1457 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R A\|a \|c atan(-------) - A\|a c atan(-----) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 2a\|a \|c \|a c +--R Type: Expression(Integer) +--E 1378 + +--S 1379 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1379 + +)clear all + +--S 1380 of 1457 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R 2 5 2 4 3 2 2 2 +--R c e x + c d x + 2a c e x + 2a c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1380 + +--S 1381 of 1457 +r0:=1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2))-_ + e^2*(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)^2+1/2*e^2*(B*d-A*e)*log(a+_ + c*x^2)/(c*d^2+a*e^2)^2-1/2*(a*B*e*(c*d^2-a*e^2)-A*c*d*(c*d^2+_ + 3*a*e^2))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*(c*d^2+a*e^2)^2*sqrt(c)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (B a c e + 3A a c d e - B a c d e + A c d )x + B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e - B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((- A a c e + B a c d e )x - A a e + B a d e )log(c x + a) +--R + +--R 3 2 2 2 3 2 2 +--R ((2A a c e - 2B a c d e )x + 2A a e - 2B a d e )log(e x + d) +--R + +--R 2 3 2 2 2 3 2 3 2 2 +--R (B a e + A a c d e + B a c d e + A c d )x + A a e - B a d e +--R + +--R 2 3 +--R A a c d e - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +-+ +-+ +--R ((2a c e + 4a c d e + 2a c d )x + 2a e + 4a c d e + 2a c d )\|a \|c +--R Type: Expression(Integer) +--E 1381 + +--S 1382 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (B a c e + 3A a c d e - B a c d e + A c d )x + B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e - B a c d e + A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((- 2A a c e + 2B a c d e )x - 2A a e + 2B a d e )log(c x + a) +--R + +--R 3 2 2 2 3 2 2 +--R ((4A a c e - 4B a c d e )x + 4A a e - 4B a d e )log(e x + d) +--R + +--R 2 3 2 2 2 3 2 3 +--R (2B a e + 2A a c d e + 2B a c d e + 2A c d )x + 2A a e +--R + +--R 2 2 2 3 +--R - 2B a d e + 2A a c d e - 2B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +-----+ +--R ((4a c e + 8a c d e + 4a c d )x + 4a e + 8a c d e + 4a c d )\|- a c +--R , +--R +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (B a c e + 3A a c d e - B a c d e + A c d )x + B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e - B a c d e + A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((- A a c e + B a c d e )x - A a e + B a d e )log(c x + a) +--R + +--R 3 2 2 2 3 2 2 +--R ((2A a c e - 2B a c d e )x + 2A a e - 2B a d e )log(e x + d) +--R + +--R 2 3 2 2 2 3 2 3 2 2 +--R (B a e + A a c d e + B a c d e + A c d )x + A a e - B a d e +--R + +--R 2 3 +--R A a c d e - B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +---+ +--R ((2a c e + 4a c d e + 2a c d )x + 2a e + 4a c d e + 2a c d )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1382 + +--S 1383 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 +-+ +-+ +--R (B a e + 3A a c d e - B a c d e + A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 3 2 2 2 3 +-----+ x\|c +--R (- 2B a e - 6A a c d e + 2B a c d e - 2A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R 3 4 2 2 2 2 4 +-----+ +-+ +-+ +--R (4a e + 8a c d e + 4a c d )\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1383 + +--S 1384 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1384 + +--S 1385 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 3 2 2 2 3 +-+ +-+ x\|a c +--R (B a e + 3A a c d e - B a c d e + A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 3 2 2 2 3 +---+ x\|c +--R (- B a e - 3A a c d e + B a c d e - A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R / +--R 3 4 2 2 2 2 4 +-+ +-+ +---+ +--R (2a e + 4a c d e + 2a c d )\|a \|c \|a c +--R Type: Expression(Integer) +--E 1385 + +--S 1386 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1386 + +)clear all + +--S 1387 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 5 2 2 2 4 3 +--R c e x + 2c d e x + (2a c e + c d )x + 4a c d e x +--R + +--R 2 2 2 2 2 2 2 +--R (a e + 2a c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1387 + +--S 1388 of 1457 +r0:=1/2*e*(A*c*d^2+4*a*B*d*e-3*a*A*e^2)/(a*(c*d^2+a*e^2)^2*(d+e*x))+_ + 1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(d+e*x)*_ + (a+c*x^2))-e^2*(3*B*c*d^2-4*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+_ + a*e^2)^3+1/2*e^2*(3*B*c*d^2-4*A*c*d*e-a*B*e^2)*log(a+c*x^2)/_ + (c*d^2+a*e^2)^3-1/2*(2*a*B*d*e*(c*d^2-3*a*e^2)-A*(c^2*d^4+6*a*_ + c*d^2*e^2-3*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))*sqrt(c)/(a^(3/2)*_ + (c*d^2+a*e^2)^3) +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 2 3 2 3 4 3 +--R (- 3A a c e + 6B a c d e + 6A a c d e - 2B a c d e + A c d e)x +--R + +--R 2 4 2 2 3 2 3 2 2 4 3 5 2 +--R (- 3A a c d e + 6B a c d e + 6A a c d e - 2B a c d e + A c d )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R (- 3A a e + 6B a d e + 6A a c d e - 2B a c d e + A a c d e)x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 +--R - 3A a d e + 6B a d e + 6A a c d e - 2B a c d e + A a c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 2 3 3 +--R (- B a c e - 4A a c d e + 3B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (- B a c d e - 4A a c d e + 3B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (- B a e - 4A a c d e + 3B a c d e )x - B a d e - 4A a c d e +--R + +--R 2 3 2 +--R 3B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 2 4 2 2 3 3 +--R (2B a c e + 8A a c d e - 6B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (2B a c d e + 8A a c d e - 6B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (2B a e + 8A a c d e - 6B a c d e )x + 2B a d e + 8A a c d e +--R + +--R 2 3 2 +--R - 6B a c d e +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 2 +--R (- 3A a c e + 4B a c d e - 2A a c d e + 4B a c d e + A c d e)x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R B a e + A a c d e + 2B a c d e + 2A a c d e + B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R x +--R + +--R 3 5 3 4 2 3 2 2 4 2 5 +--R - 2A a e + 3B a d e + 2B a c d e + 2A a c d e - B a c d +--R * +--R +-+ +--R \|a +--R / +--R 4 7 3 2 2 5 2 3 4 3 4 6 3 +--R (2a c e + 6a c d e + 6a c d e + 2a c d e)x +--R + +--R 4 6 3 2 3 4 2 3 5 2 4 7 2 +--R (2a c d e + 6a c d e + 6a c d e + 2a c d )x +--R + +--R 5 7 4 2 5 3 2 4 3 2 3 6 5 6 4 3 4 +--R (2a e + 6a c d e + 6a c d e + 2a c d e)x + 2a d e + 6a c d e +--R + +--R 3 2 5 2 2 3 7 +--R 6a c d e + 2a c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1388 + +--S 1389 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 5 2 4 2 2 3 2 3 2 3 4 3 +--R (3A a c e - 6B a c d e - 6A a c d e + 2B a c d e - A c d e)x +--R + +--R 2 4 2 2 3 2 3 2 2 4 3 5 2 +--R (3A a c d e - 6B a c d e - 6A a c d e + 2B a c d e - A c d )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R (3A a e - 6B a d e - 6A a c d e + 2B a c d e - A a c d e)x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 +--R 3A a d e - 6B a d e - 6A a c d e + 2B a c d e - A a c d +--R * +--R +---+ +--R | c 2 +--R +---+ - 2a x |- - + c x - a +--R | c \| a +--R |- - log(-----------------------) +--R \| a 2 +--R c x + a +--R + +--R 2 5 2 4 2 2 3 3 +--R (- 2B a c e - 8A a c d e + 6B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (- 2B a c d e - 8A a c d e + 6B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (- 2B a e - 8A a c d e + 6B a c d e )x - 2B a d e - 8A a c d e +--R + +--R 2 3 2 +--R 6B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 2 4 2 2 3 3 +--R (4B a c e + 16A a c d e - 12B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (4B a c d e + 16A a c d e - 12B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (4B a e + 16A a c d e - 12B a c d e )x + 4B a d e + 16A a c d e +--R + +--R 2 3 2 +--R - 12B a c d e +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 2 +--R (- 6A a c e + 8B a c d e - 4A a c d e + 8B a c d e + 2A c d e)x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 2B a e + 2A a c d e + 4B a c d e + 4A a c d e + 2B a c d e +--R + +--R 3 5 +--R 2A c d +--R * +--R x +--R + +--R 3 5 3 4 2 3 2 2 4 2 5 +--R - 4A a e + 6B a d e + 4B a c d e + 4A a c d e - 2B a c d +--R / +--R 4 7 3 2 2 5 2 3 4 3 4 6 3 +--R (4a c e + 12a c d e + 12a c d e + 4a c d e)x +--R + +--R 4 6 3 2 3 4 2 3 5 2 4 7 2 +--R (4a c d e + 12a c d e + 12a c d e + 4a c d )x +--R + +--R 5 7 4 2 5 3 2 4 3 2 3 6 5 6 4 3 4 +--R (4a e + 12a c d e + 12a c d e + 4a c d e)x + 4a d e + 12a c d e +--R + +--R 3 2 5 2 2 3 7 +--R 12a c d e + 4a c d +--R , +--R +--R 2 5 2 4 2 2 3 2 3 2 3 4 3 +--R (3A a c e - 6B a c d e - 6A a c d e + 2B a c d e - A c d e)x +--R + +--R 2 4 2 2 3 2 3 2 2 4 3 5 2 +--R (3A a c d e - 6B a c d e - 6A a c d e + 2B a c d e - A c d )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R (3A a e - 6B a d e - 6A a c d e + 2B a c d e - A a c d e)x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 +--R 3A a d e - 6B a d e - 6A a c d e + 2B a c d e - A a c d +--R * +--R +-+ +--R |c +--R +-+ a |- +--R |c \|a +--R |- atan(-----) +--R \|a c x +--R + +--R 2 5 2 4 2 2 3 3 +--R (- B a c e - 4A a c d e + 3B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (- B a c d e - 4A a c d e + 3B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (- B a e - 4A a c d e + 3B a c d e )x - B a d e - 4A a c d e +--R + +--R 2 3 2 +--R 3B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 2 4 2 2 3 3 +--R (2B a c e + 8A a c d e - 6B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (2B a c d e + 8A a c d e - 6B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (2B a e + 8A a c d e - 6B a c d e )x + 2B a d e + 8A a c d e +--R + +--R 2 3 2 +--R - 6B a c d e +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 2 +--R (- 3A a c e + 4B a c d e - 2A a c d e + 4B a c d e + A c d e)x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 3 5 +--R (B a e + A a c d e + 2B a c d e + 2A a c d e + B a c d e + A c d )x +--R + +--R 3 5 3 4 2 3 2 2 4 2 5 +--R - 2A a e + 3B a d e + 2B a c d e + 2A a c d e - B a c d +--R / +--R 4 7 3 2 2 5 2 3 4 3 4 6 3 +--R (2a c e + 6a c d e + 6a c d e + 2a c d e)x +--R + +--R 4 6 3 2 3 4 2 3 5 2 4 7 2 +--R (2a c d e + 6a c d e + 6a c d e + 2a c d )x +--R + +--R 5 7 4 2 5 3 2 4 3 2 3 6 5 6 4 3 4 +--R (2a e + 6a c d e + 6a c d e + 2a c d e)x + 2a d e + 6a c d e +--R + +--R 3 2 5 2 2 3 7 +--R 6a c d e + 2a c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1389 + +--S 1390 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---+ +--R 2 4 2 3 2 2 3 2 4 | c +-+ +--R (3A a e - 6B a d e - 6A a c d e + 2B a c d e - A c d ) |- - \|a +--R \| a +--R * +--R +---+ +--R | c 2 +--R - 2a x |- - + c x - a +--R \| a +--R log(-----------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 4 2 3 2 2 3 2 4 +-+ x\|c +--R (6A a e - 12B a d e - 12A a c d e + 4B a c d e - 2A c d )\|c atan(-----) +--R +-+ +--R \|a +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +-+ +--R (4a e + 12a c d e + 12a c d e + 4a c d )\|a +--R Type: Expression(Integer) +--E 1390 + +--S 1391 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1391 + +--S 1392 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 4 2 3 2 2 3 2 4 +-+ x\|c +--R (3A a e - 6B a d e - 6A a c d e + 2B a c d e - A c d )\|c atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R 2 4 2 3 2 2 3 2 4 +-+ |c +--R (3A a e - 6B a d e - 6A a c d e + 2B a c d e - A c d )\|a |- +--R \|a +--R * +--R +-+ +--R |c +--R a |- +--R \|a +--R atan(-----) +--R c x +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +-+ +--R (2a e + 6a c d e + 6a c d e + 2a c d )\|a +--R Type: Expression(Integer) +--E 1392 + +--S 1393 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1393 + +)clear all + +--S 1394 of 1457 +t0:=(A+B*x)*(d+e*x)^5/(a+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1394 + +--S 1395 of 1457 +r0:=-3/8*e^2*(5*a*B*e*(2*c*d^2-a*e^2)+A*c*d*(6*c*d^2+5*a*e^2))*x/(a^2*c^3)-_ + 1/2*e^3*(3*A*c*d^2+5*a*B*d*e+a*A*e^2)*x^2/(a^2*c^2)-1/8*e^4*(3*A*_ + c*d+5*a*B*e)*x^3/(a^2*c^2)-1/4*(a*B-A*c*x)*(d+e*x)^5/(a*c*(a+_ + c*x^2)^2)+1/8*(d+e*x)^4*(2*a*A*e+(3*A*c*d+5*a*B*e)*x)/(a^2*c*(a+_ + c*x^2))+1/8*(5*a*B*e*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4)+A*c*d*_ + (3*c^2*d^4+10*a*c*d^2*e^2+15*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(5/2)*c^(7/2))+1/2*e^4*(5*B*d+A*e)*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R - 15B a c e + 15A a c d e + 30B a c d e + 10A a c d e +--R + +--R 4 4 5 5 +--R 5B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R - 30B a c e + 30A a c d e + 60B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R 10B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R - 15B a e + 15A a c d e + 30B a c d e + 10A a c d e + 5B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (4A a c e + 20B a c d e )x + (8A a c e + 40B a c d e )x +--R + +--R 4 5 4 4 +--R 4A a e + 20B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 5 +--R 8B a c e x +--R + +--R 2 2 5 2 2 4 3 2 3 3 3 2 +--R - 6A a c e - 30B a c d e + 20A a c d e + 20B a c d e +--R + +--R 4 4 +--R 12A c d e +--R * +--R 4 +--R x +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 25B a c e - 25A a c d e - 50B a c d e + 10A a c d e +--R + +--R 3 4 4 5 +--R 5B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 3 4 2 +--R (- 4A a c e - 20B a c d e + 24A a c d e)x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e +--R + +--R 2 2 4 3 5 +--R - 5B a c d e + 5A a c d +--R * +--R x +--R + +--R 2 2 4 2 2 5 +--R 2A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 5 4 3 4 2 4 3 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 1395 + +--S 1396 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R 15B a c e - 15A a c d e - 30B a c d e - 10A a c d e +--R + +--R 4 4 5 5 +--R - 5B a c d e - 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R 30B a c e - 30A a c d e - 60B a c d e - 20A a c d e +--R + +--R 2 3 4 4 5 +--R - 10B a c d e - 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e - 5B a c d e +--R + +--R 2 3 5 +--R - 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c - 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (8A a c e + 40B a c d e )x + (16A a c e + 80B a c d e )x +--R + +--R 4 5 4 4 +--R 8A a e + 40B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 5 +--R 16B a c e x +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 50B a c e - 50A a c d e - 100B a c d e + 20A a c d e +--R + +--R 3 4 4 5 +--R 10B a c d e + 6A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (16A a c e + 80B a c d e - 80A a c d e - 80B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 +--R 30B a e - 30A a c d e - 60B a c d e - 20A a c d e +--R + +--R 2 2 4 3 5 +--R - 10B a c d e + 10A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 12A a e + 60B a d e - 40A a c d e - 40B a c d e - 20A a c d e +--R + +--R 2 2 5 +--R - 4B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 5 4 3 4 2 4 3 +-----+ +--R (16a c x + 32a c x + 16a c )\|- a c +--R , +--R +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R - 15B a c e + 15A a c d e + 30B a c d e + 10A a c d e +--R + +--R 4 4 5 5 +--R 5B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R - 30B a c e + 30A a c d e + 60B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R 10B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 +--R - 15B a e + 15A a c d e + 30B a c d e + 10A a c d e +--R + +--R 3 2 4 2 3 5 +--R 5B a c d e + 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (4A a c e + 20B a c d e )x + (8A a c e + 40B a c d e )x +--R + +--R 4 5 4 4 +--R 4A a e + 20B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 5 +--R 8B a c e x +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 25B a c e - 25A a c d e - 50B a c d e + 10A a c d e +--R + +--R 3 4 4 5 +--R 5B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (8A a c e + 40B a c d e - 40A a c d e - 40B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e +--R + +--R 2 2 4 3 5 +--R - 5B a c d e + 5A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 6A a e + 30B a d e - 20A a c d e - 20B a c d e - 10A a c d e +--R + +--R 2 2 5 +--R - 2B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 2 5 4 3 4 2 4 3 +---+ +--R (8a c x + 16a c x + 8a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1396 + +--S 1397 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e - 5B a c d e +--R + +--R 3 5 +--R - 3A c d +--R * +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c - 2a c x +--R \|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 30B a e - 30A a c d e - 60B a c d e - 20A a c d e - 10B a c d e +--R + +--R 3 5 +--R - 6A c d +--R * +--R +-+ +--R +-----+ x\|c +--R \|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R (12A a e + 60B a d e - 40A a c d e - 40B a c d e - 24A c d e) +--R * +--R +-----+ +-+ +-+ +--R \|- a c \|a \|c +--R / +--R 2 3 +-----+ +-+ +-+ +--R 16a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1397 + +--S 1398 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1398 + +--S 1399 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R - 15B a e + 15A a c d e + 30B a c d e + 10A a c d e + 5B a c d e +--R + +--R 3 5 +--R 3A c d +--R * +--R +---+ +--R +-+ +-+ x\|a c +--R \|a \|c atan(-------) +--R a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e - 5B a c d e +--R + +--R 3 5 +--R - 3A c d +--R * +--R +-+ +--R +---+ x\|c +--R \|a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 3 3 2 2 4 +-+ +--R (6A a e + 30B a d e - 20A a c d e - 20B a c d e - 12A c d e)\|a +--R * +--R +-+ +---+ +--R \|c \|a c +--R / +--R 2 3 +-+ +-+ +---+ +--R 8a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1399 + +--S 1400 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1400 + +)clear all + +--S 1401 of 1457 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1401 + +--S 1402 of 1457 +r0:=-3/8*e^2*(3*A*c*d^2+4*a*B*d*e+a*A*e^2)*x/(a^2*c^2)-1/8*e^3*(3*A*c*d+_ + 4*a*B*e)*x^2/(a^2*c^2)-1/4*(a*B-A*c*x)*(d+e*x)^4/(a*c*(a+c*x^2)^2)+_ + 1/8*(d+e*x)^3*(a*A*e+(3*A*c*d+4*a*B*e)*x)/(a^2*c*(a+c*x^2))+_ + 1/8*(3*A*(c*d^2+a*e^2)^2+4*a*B*d*e*(c*d^2+3*a*e^2))*atan(x*_ + sqrt(c)/sqrt(a))/(a^(5/2)*c^(5/2))+1/2*B*e^4*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 3 4 2 3 3 4 2 2 4 3 5 4 4 +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 2 4 3 2 3 2 3 2 2 2 3 3 4 4 2 +--R (6A a c e + 24B a c d e + 12A a c d e + 8B a c d e + 6A a c d )x +--R + +--R 4 4 4 3 3 2 2 2 3 2 3 2 3 4 +--R 3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 4 4 3 4 2 4 4 2 +--R (4B a c e x + 8B a c e x + 4B a e )log(c x + a) +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 6B a c e + 8A a c d e + 12B a c d e + 9A c d e)x +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 3 +--R (- 5A a c e - 20B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 4 3 3 2 +--R (- 4B a c e + 18A a c d e)x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R (- 3A a c e - 12B a c d e - 6A a c d e - 4B a c d e + 5A a c d )x +--R + +--R 2 2 3 2 2 4 +--R A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 5 4 3 4 2 4 3 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 1402 + +--S 1403 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 4 2 3 3 4 2 2 4 3 5 4 4 +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 2 4 3 2 3 2 3 2 2 2 3 3 +--R 6A a c e + 24B a c d e + 12A a c d e + 8B a c d e +--R + +--R 4 4 +--R 6A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 2 3 2 3 2 3 4 +--R 3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 4 4 3 4 2 4 4 2 +--R (8B a c e x + 16B a c e x + 8B a e )log(c x + a) +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 +--R - 10A a c e - 40B a c d e + 12A a c d e + 8B a c d e +--R + +--R 4 4 +--R 6A c d +--R * +--R 3 +--R x +--R + +--R 3 4 2 2 3 2 2 2 2 2 +--R (16B a c e - 32A a c d e - 48B a c d e )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 6A a c e - 24B a c d e - 12A a c d e - 8B a c d e +--R + +--R 3 4 +--R 10A a c d +--R * +--R x +--R + +--R 4 4 3 3 3 2 2 2 2 3 2 2 4 +--R 12B a e - 16A a c d e - 24B a c d e - 16A a c d e - 4B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 5 4 3 4 2 4 3 +-----+ +--R (16a c x + 32a c x + 16a c )\|- a c +--R , +--R +--R 2 3 4 2 3 3 4 2 2 4 3 5 4 4 +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 2 4 3 2 3 2 3 2 2 2 3 3 +--R 6A a c e + 24B a c d e + 12A a c d e + 8B a c d e +--R + +--R 4 4 +--R 6A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 2 3 2 3 2 3 4 +--R 3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 2 4 4 3 4 2 4 4 2 +--R (4B a c e x + 8B a c e x + 4B a e )log(c x + a) +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 3 +--R (- 5A a c e - 20B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 4 2 2 3 2 2 2 2 2 +--R (8B a c e - 16A a c d e - 24B a c d e )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 3A a c e - 12B a c d e - 6A a c d e - 4B a c d e +--R + +--R 3 4 +--R 5A a c d +--R * +--R x +--R + +--R 4 4 3 3 3 2 2 2 2 3 2 2 4 +--R 6B a e - 8A a c d e - 12B a c d e - 8A a c d e - 2B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 2 5 4 3 4 2 4 3 +---+ +--R (8a c x + 16a c x + 8a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1403 + +--S 1404 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 2 2 2 3 3 4 +-+ +-+ +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (- 6A a c e - 24B a c d e - 12A a c d e - 8B a c d e - 6A c d ) +--R * +--R +-+ +--R +-----+ x\|c +--R \|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 +-----+ +-+ +-+ +--R (12B a e - 16A a c d e - 24B a c d e - 18A c d e)\|- a c \|a \|c +--R / +--R 2 3 +-----+ +-+ +-+ +--R 16a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1404 + +--S 1405 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1405 + +--S 1406 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 4 2 3 2 2 2 2 3 3 4 +-+ +-+ +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )\|a \|c +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +---+ +--R (- 3A a c e - 12B a c d e - 6A a c d e - 4B a c d e - 3A c d )\|a c +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 +-+ +-+ +---+ +--R (6B a e - 8A a c d e - 12B a c d e - 9A c d e)\|a \|c \|a c +--R / +--R 2 3 +-+ +-+ +---+ +--R 8a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1406 + +--S 1407 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1407 + +)clear all + +--S 1408 of 1457 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1408 + +--S 1409 of 1457 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^3/(a*c*(a+c*x^2)^2)-3/8*(A*c*d+a*B*e)*_ + (a*e-c*d*x)*(d+e*x)/(a^2*c^2*(a+c*x^2))+3/8*(A*c*d+a*B*e)*(c*d^2+_ + a*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(5/2)) +--R +--R +--R (2) +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 6A a c d e + 6B a c d e + 6A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 3A a c d e + 3B a c d e + 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 2 3 2 4 +--R (2A a c e + 3B a c d e + 3A c d e)x +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 5B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 +--R (- 6B a c d e + 6A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 2 +--R (- 3B a e - 3A a c d e - 3B a c d e + 5A a c d )x - 3B a d e +--R + +--R 2 2 2 3 +--R - 3A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 4 4 3 3 2 4 2 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 1409 + +--S 1410 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 6A a c d e + 6B a c d e + 6A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 3A a c d e + 3B a c d e + 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 10B a c e + 6A a c d e + 6B a c d e + 6A c d )x +--R + +--R 2 3 2 2 2 +--R (- 8A a c e - 24B a c d e )x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (- 6B a e - 6A a c d e - 6B a c d e + 10A a c d )x - 4A a e +--R + +--R 3 2 2 2 2 3 +--R - 12B a d e - 12A a c d e - 4B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 4 4 3 3 2 4 2 +-----+ +--R (16a c x + 32a c x + 16a c )\|- a c +--R , +--R +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 6A a c d e + 6B a c d e + 6A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 3A a c d e + 3B a c d e + 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 5B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 2 3 2 2 2 +--R (- 4A a c e - 12B a c d e )x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (- 3B a e - 3A a c d e - 3B a c d e + 5A a c d )x - 2A a e +--R + +--R 3 2 2 2 2 3 +--R - 6B a d e - 6A a c d e - 2B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 2 4 4 3 3 2 4 2 +---+ +--R (8a c x + 16a c x + 8a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1410 + +--S 1411 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 +-+ +-+ +--R (3B a e + 3A a c d e + 3B a c d e + 3A c d )\|a \|c +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 3 2 2 2 3 +-----+ x\|c +--R (- 6B a e - 6A a c d e - 6B a c d e - 6A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 +-----+ +-+ +-+ +--R (- 4A a e - 6B a d e - 6A c d e)\|- a c \|a \|c +--R / +--R 2 2 +-----+ +-+ +-+ +--R 16a c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1411 + +--S 1412 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1412 + +--S 1413 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 3 2 2 2 3 +-+ +-+ x\|a c +--R (3B a e + 3A a c d e + 3B a c d e + 3A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 3 2 2 2 3 +---+ x\|c +--R (- 3B a e - 3A a c d e - 3B a c d e - 3A c d )\|a c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 +-+ +-+ +---+ +--R (- 2A a e - 3B a d e - 3A c d e)\|a \|c \|a c +--R / +--R 2 2 +-+ +-+ +---+ +--R 8a c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1413 + +--S 1414 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1414 + +)clear all + +--S 1415 of 1457 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1415 + +--S 1416 of 1457 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^2/(a*c*(a+c*x^2)^2)-1/8*(a*e-c*d*x)*_ + (3*A*c*d+2*a*B*e+A*c*e*x)/(a^2*c^2*(a+c*x^2))+1/8*(3*A*c*d^2+2*a*_ + B*d*e+a*A*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(3/2)) +--R +--R +--R (2) +--R 3 2 3 4 2 4 +--R (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 3 2 2 3 2 3 +--R (2A a c e + 4B a c d e + 6A a c d )x + A a c e + 2B a c d e +--R + +--R 2 2 2 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 4 2 2 2 3 2 3 +--R A c d e x + (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 4B a c e + 2A a c d e)x + (- A a c e - 2B a c d e + 5A a c d )x +--R + +--R 3 2 2 2 2 +--R - 2B a e - 3A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 4 4 3 3 2 4 2 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 1416 + +--S 1417 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 4 2 4 +--R (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 3 2 2 3 2 3 +--R (2A a c e + 4B a c d e + 6A a c d )x + A a c e + 2B a c d e +--R + +--R 2 2 2 +--R 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 2 3 2 3 2 2 2 +--R (2A a c e + 4B a c d e + 6A c d )x - 8B a c e x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 2A a c e - 4B a c d e + 10A a c d )x - 4B a e - 8A a c d e +--R + +--R 2 2 +--R - 4B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 4 4 3 3 2 4 2 +-----+ +--R (16a c x + 32a c x + 16a c )\|- a c +--R , +--R +--R 3 2 3 4 2 4 +--R (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 3 2 2 3 2 3 +--R (2A a c e + 4B a c d e + 6A a c d )x + A a c e + 2B a c d e +--R + +--R 2 2 2 +--R 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 2 2 3 2 3 2 2 2 +--R (A a c e + 2B a c d e + 3A c d )x - 4B a c e x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- A a c e - 2B a c d e + 5A a c d )x - 2B a e - 4A a c d e +--R + +--R 2 2 +--R - 2B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 2 4 4 3 3 2 4 2 +---+ +--R (8a c x + 16a c x + 8a c )\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1417 + +--S 1418 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R 2 2 +-+ +-+ (c x - a)\|- a c + 2a c x +--R (A a e + 2B a d e + 3A c d )\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R 2 2 +-----+ x\|c +--R (- 2A a e - 4B a d e - 6A c d )\|- a c atan(-----) +--R +-+ +--R \|a +--R + +--R +-----+ +-+ +-+ +--R - 2A d e\|- a c \|a \|c +--R / +--R 2 +-----+ +-+ +-+ +--R 16a c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1418 + +--S 1419 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1419 + +--S 1420 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +--R 2 2 +-+ +-+ x\|a c +--R (A a e + 2B a d e + 3A c d )\|a \|c atan(-------) +--R a +--R + +--R +-+ +--R 2 2 +---+ x\|c +-+ +-+ +---+ +--R (- A a e - 2B a d e - 3A c d )\|a c atan(-----) - A d e\|a \|c \|a c +--R +-+ +--R \|a +--R / +--R 2 +-+ +-+ +---+ +--R 8a c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1420 + +--S 1421 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1421 + +)clear all + +--S 1422 of 1457 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2)^3 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1422 + +--S 1423 of 1457 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)/(a*c*(a+c*x^2)^2)+1/8*(-2*a*A*e+(3*A*c*d+_ + a*B*e)*x)/(a^2*c*(a+c*x^2))+1/8*(3*A*c*d+a*B*e)*atan(x*sqrt(c)/_ + sqrt(a))/(a^(5/2)*c^(3/2)) +--R +--R +--R (2) +--R 2 3 4 2 2 2 3 2 +--R ((B a c e + 3A c d)x + (2B a c e + 6A a c d)x + B a e + 3A a c d) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 2 2 +-+ +-+ +--R ((B a c e + 3A c d)x + (- B a e + 5A a c d)x - 2A a e - 2B a d)\|a \|c +--R / +--R 2 3 4 3 2 2 4 +-+ +-+ +--R (8a c x + 16a c x + 8a c)\|a \|c +--R Type: Expression(Integer) +--E 1423 + +--S 1424 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 4 2 2 2 3 2 +--R ((B a c e + 3A c d)x + (2B a c e + 6A a c d)x + B a e + 3A a c d) +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 3 2 2 2 +--R ((2B a c e + 6A c d)x + (- 2B a e + 10A a c d)x - 4A a e - 4B a d) +--R * +--R +-----+ +--R \|- a c +--R / +--R 2 3 4 3 2 2 4 +-----+ +--R (16a c x + 32a c x + 16a c)\|- a c +--R , +--R +--R 2 3 4 2 2 2 3 2 +--R ((B a c e + 3A c d)x + (2B a c e + 6A a c d)x + B a e + 3A a c d) +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 3 2 2 2 +---+ +--R ((B a c e + 3A c d)x + (- B a e + 5A a c d)x - 2A a e - 2B a d)\|a c +--R / +--R 2 3 4 3 2 2 4 +---+ +--R (8a c x + 16a c x + 8a c)\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1424 + +--S 1425 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +--R (B a e + 3A c d)\|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R +-+ +--R +-----+ x\|c +--R (- 2B a e - 6A c d)\|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R 2 +-----+ +-+ +-+ +--R 16a c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1425 + +--S 1426 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1426 + +--S 1427 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R (B a e + 3A c d)\|a \|c atan(-------) + (- B a e - 3A c d)\|a c atan(-----) +--R a +-+ +--R \|a +--R --------------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1427 + +--S 1428 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1428 + +)clear all + +--S 1429 of 1457 +t0:=(A+B*x)/(a+c*x^2)^3 +--R +--R +--R B x + A +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1429 + +--S 1430 of 1457 +r0:=1/4*(-a*B+A*c*x)/(a*c*(a+c*x^2)^2)+3/8*A*x/(a^2*(a+c*x^2))+_ + 3/8*A*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*sqrt(c)) +--R +--R +--R (2) +--R +-+ +--R 3 4 2 2 2 x\|c +--R (3A c x + 6A a c x + 3A a c)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 +-+ +-+ +--R (3A c x + 5A a c x - 2B a )\|a \|c +--R / +--R 2 3 4 3 2 2 4 +-+ +-+ +--R (8a c x + 16a c x + 8a c)\|a \|c +--R Type: Expression(Integer) +--E 1430 + +--S 1431 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 3 4 2 2 2 (c x - a)\|- a c + 2a c x +--R (3A c x + 6A a c x + 3A a c)log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 3 2 +-----+ +--R (6A c x + 10A a c x - 4B a )\|- a c +--R / +--R 2 3 4 3 2 2 4 +-----+ +--R (16a c x + 32a c x + 16a c)\|- a c +--R , +--R +--R +---+ +--R 3 4 2 2 2 x\|a c +--R (3A c x + 6A a c x + 3A a c)atan(-------) +--R a +--R + +--R 2 3 2 +---+ +--R (3A c x + 5A a c x - 2B a )\|a c +--R / +--R 2 3 4 3 2 2 4 +---+ +--R (8a c x + 16a c x + 8a c)\|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1431 + +--S 1432 of 1457 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x\|c +--R 3A\|a \|c log(---------------------------) - 6A\|- a c atan(-----) +--R 2 +-+ +--R c x + a \|a +--R (4) ------------------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 16a \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1432 + +--S 1433 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1433 + +--S 1434 of 1457 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a c +---+ x\|c +--R 3A\|a \|c atan(-------) - 3A\|a c atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a \|a \|c \|a c +--R Type: Expression(Integer) +--E 1434 + +--S 1435 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1435 + +)clear all + +--S 1436 of 1457 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------------- +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 3 +--R c e x + c d x + 3a c e x + 3a c d x + 3a c e x + 3a c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1436 + +--S 1437 of 1457 +r0:=1/4*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2)^2)+_ + 1/8*(-4*a^2*e^2*(B*d-A*e)-(a*B*e*(c*d^2-3*a*e^2)-A*c*d*(3*c*d^2+7*_ + a*e^2))*x)/(a^2*(c*d^2+a*e^2)^2*(a+c*x^2))-e^4*(B*d-A*e)*log(d+_ + e*x)/(c*d^2+a*e^2)^3+1/2*e^4*(B*d-A*e)*log(a+c*x^2)/(c*d^2+_ + a*e^2)^3-1/8*(a*B*e*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4)-A*c*d*_ + (3*c^2*d^4+10*a*c*d^2*e^2+15*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(5/2)*(c*d^2+a*e^2)^3*sqrt(c)) +--R +--R +--R (2) +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 4 4 +--R 3B a c e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 5 5 +--R 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R 6B a c e + 30A a c d e - 12B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R - 2B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (- 4A a c e + 4B a c d e )x + (- 8A a c e + 8B a c d e )x +--R + +--R 4 5 4 4 +--R - 4A a e + 4B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (8A a c e - 8B a c d e )x + (16A a c e - 16B a c d e )x +--R + +--R 4 5 4 4 +--R 8A a e - 8B a d e +--R * +--R log(e x + d) +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 3 4 +--R 3B a c e + 7A a c d e + 2B a c d e + 10A a c d e - B a c d e +--R + +--R 4 5 +--R 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (4A a c e - 4B a c d e + 4A a c d e - 4B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 5B a e + 9A a c d e + 6B a c d e + 14A a c d e + B a c d e +--R + +--R 3 5 +--R 5A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 6A a e - 6B a d e + 8A a c d e - 8B a c d e + 2A a c d e +--R + +--R 2 2 5 +--R - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 2 6 4 3 2 4 3 4 4 2 2 5 6 4 +--R (8a c e + 24a c d e + 24a c d e + 8a c d )x +--R + +--R 6 6 5 2 2 4 4 3 4 2 3 4 6 2 7 6 6 2 4 +--R (16a c e + 48a c d e + 48a c d e + 16a c d )x + 8a e + 24a c d e +--R + +--R 5 2 4 2 4 3 6 +--R 24a c d e + 8a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R Type: Expression(Integer) +--E 1437 + +--S 1438 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R 3B a c e + 15A a c d e - 6B a c d e + 10A a c d e +--R + +--R 4 4 5 5 +--R - B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R 6B a c e + 30A a c d e - 12B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R - 2B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R 2 +-----+ +--R (c x - a)\|- a c + 2a c x +--R log(---------------------------) +--R 2 +--R c x + a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (- 8A a c e + 8B a c d e )x + (- 16A a c e + 16B a c d e )x +--R + +--R 4 5 4 4 +--R - 8A a e + 8B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (16A a c e - 16B a c d e )x + (32A a c e - 32B a c d e )x +--R + +--R 4 5 4 4 +--R 16A a e - 16B a d e +--R * +--R log(e x + d) +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 6B a c e + 14A a c d e + 4B a c d e + 20A a c d e +--R + +--R 3 4 4 5 +--R - 2B a c d e + 6A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (8A a c e - 8B a c d e + 8A a c d e - 8B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 +--R 10B a e + 18A a c d e + 12B a c d e + 28A a c d e +--R + +--R 2 2 4 3 5 +--R 2B a c d e + 10A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 12A a e - 12B a d e + 16A a c d e - 16B a c d e + 4A a c d e +--R + +--R 2 2 5 +--R - 4B a c d +--R * +--R +-----+ +--R \|- a c +--R / +--R 5 2 6 4 3 2 4 3 4 4 2 2 5 6 4 +--R (16a c e + 48a c d e + 48a c d e + 16a c d )x +--R + +--R 6 6 5 2 2 4 4 3 4 2 3 4 6 2 7 6 +--R (32a c e + 96a c d e + 96a c d e + 32a c d )x + 16a e +--R + +--R 6 2 4 5 2 4 2 4 3 6 +--R 48a c d e + 48a c d e + 16a c d +--R * +--R +-----+ +--R \|- a c +--R , +--R +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R 3B a c e + 15A a c d e - 6B a c d e + 10A a c d e +--R + +--R 4 4 5 5 +--R - B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R 6B a c e + 30A a c d e - 12B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R - 2B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R +---+ +--R x\|a c +--R atan(-------) +--R a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (- 4A a c e + 4B a c d e )x + (- 8A a c e + 8B a c d e )x +--R + +--R 4 5 4 4 +--R - 4A a e + 4B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (8A a c e - 8B a c d e )x + (16A a c e - 16B a c d e )x +--R + +--R 4 5 4 4 +--R 8A a e - 8B a d e +--R * +--R log(e x + d) +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 3B a c e + 7A a c d e + 2B a c d e + 10A a c d e +--R + +--R 3 4 4 5 +--R - B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (4A a c e - 4B a c d e + 4A a c d e - 4B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 5B a e + 9A a c d e + 6B a c d e + 14A a c d e + B a c d e +--R + +--R 3 5 +--R 5A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 6A a e - 6B a d e + 8A a c d e - 8B a c d e + 2A a c d e +--R + +--R 2 2 5 +--R - 2B a c d +--R * +--R +---+ +--R \|a c +--R / +--R 5 2 6 4 3 2 4 3 4 4 2 2 5 6 4 +--R (8a c e + 24a c d e + 24a c d e + 8a c d )x +--R + +--R 6 6 5 2 2 4 4 3 4 2 3 4 6 2 7 6 +--R (16a c e + 48a c d e + 48a c d e + 16a c d )x + 8a e +--R + +--R 6 2 4 5 2 4 2 4 3 6 +--R 24a c d e + 24a c d e + 8a c d +--R * +--R +---+ +--R \|a c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1438 + +--S 1439 of 1457 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 3 5 +--R 3A c d +--R * +--R 2 +-----+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +--R \|a \|c log(---------------------------) +--R 2 +--R c x + a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R - 6B a e - 30A a c d e + 12B a c d e - 20A a c d e + 2B a c d e +--R + +--R 3 5 +--R - 6A c d +--R * +--R +-+ +--R +-----+ x\|c +--R \|- a c atan(-----) +--R +-+ +--R \|a +--R / +--R 5 6 4 2 4 3 2 4 2 2 3 6 +-----+ +-+ +-+ +--R (16a e + 48a c d e + 48a c d e + 16a c d )\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1439 + +--S 1440 of 1457 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1440 + +--S 1441 of 1457 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 3 5 +--R 3A c d +--R * +--R +---+ +--R +-+ +-+ x\|a c +--R \|a \|c atan(-------) +--R a +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R - 3B a e - 15A a c d e + 6B a c d e - 10A a c d e + B a c d e +--R + +--R 3 5 +--R - 3A c d +--R * +--R +-+ +--R +---+ x\|c +--R \|a c atan(-----) +--R +-+ +--R \|a +--R / +--R 5 6 4 2 4 3 2 4 2 2 3 6 +-+ +-+ +---+ +--R (8a e + 24a c d e + 24a c d e + 8a c d )\|a \|c \|a c +--R Type: Expression(Integer) +--E 1441 + +--S 1442 of 1457 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1442 + +)clear all + +--S 1443 of 1457 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 3 7 2 2 3 2 6 2 5 +--R c e x + 2c d e x + (3a c e + c d )x + 6a c d e x +--R + +--R 2 2 2 2 4 2 3 3 2 2 2 2 3 3 2 +--R (3a c e + 3a c d )x + 6a c d e x + (a e + 3a c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1443 + +--S 1444 of 1457 +r0:=-1/8*e*(2*a*B*d*e*(c*d^2-11*a*e^2)-3*A*(c^2*d^4+4*a*c*d^2*e^2-_ + 5*a^2*e^4))/(a^2*(c*d^2+a*e^2)^3*(d+e*x))+1/4*(-a*(B*d-A*e)+_ + (A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(d+e*x)*(a+c*x^2)^2)+1/8*(-a*_ + e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)-(2*a*B*e*(c*d^2-2*a*e^2)-3*A*c*d*_ + (c*d^2+3*a*e^2))*x)/(a^2*(c*d^2+a*e^2)^2*(d+e*x)*(a+c*x^2))-e^4*_ + (5*B*c*d^2-6*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+a*e^2)^4+1/2*e^4*_ + (5*B*c*d^2-6*A*c*d*e-a*B*e^2)*log(a+c*x^2)/(c*d^2+a*e^2)^4-1/8*_ + (2*a*B*d*e*(c^2*d^4+10*a*c*d^2*e^2-15*a^2*e^4)-3*A*(c^3*d^6+_ + 5*a*c^2*d^4*e^2+15*a^2*c*d^2*e^4-5*a^3*e^6))*atan(x*sqrt(c)/_ + sqrt(a))*sqrt(c)/(a^(5/2)*(c*d^2+a*e^2)^4) +--R +--R +--R (2) +--R 3 2 7 3 2 6 2 3 2 5 2 3 3 4 +--R - 15A a c e + 30B a c d e + 45A a c d e - 20B a c d e +--R + +--R 4 4 3 4 5 2 5 6 +--R 15A a c d e - 2B a c d e + 3A c d e +--R * +--R 5 +--R x +--R + +--R 3 2 6 3 2 2 5 2 3 3 4 2 3 4 3 +--R - 15A a c d e + 30B a c d e + 45A a c d e - 20B a c d e +--R + +--R 4 5 2 4 6 5 7 +--R 15A a c d e - 2B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 7 4 6 3 2 2 5 3 2 3 4 +--R - 30A a c e + 60B a c d e + 90A a c d e - 40B a c d e +--R + +--R 2 3 4 3 2 3 5 2 4 6 +--R 30A a c d e - 4B a c d e + 6A a c d e +--R * +--R 3 +--R x +--R + +--R 4 6 4 2 5 3 2 3 4 3 2 4 3 +--R - 30A a c d e + 60B a c d e + 90A a c d e - 40B a c d e +--R + +--R 2 3 5 2 2 3 6 4 7 +--R 30A a c d e - 4B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 7 5 6 4 2 5 4 3 4 +--R - 15A a e + 30B a d e + 45A a c d e - 20B a c d e +--R + +--R 3 2 4 3 3 2 5 2 2 3 6 +--R 15A a c d e - 2B a c d e + 3A a c d e +--R * +--R x +--R + +--R 5 6 5 2 5 4 3 4 4 4 3 +--R - 15A a d e + 30B a d e + 45A a c d e - 20B a c d e +--R + +--R 3 2 5 2 3 2 6 2 3 7 +--R 15A a c d e - 2B a c d e + 3A a c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 7 2 3 6 2 3 2 5 5 +--R (- 4B a c e - 24A a c d e + 20B a c d e )x +--R + +--R 3 2 6 2 3 2 5 2 3 3 4 4 +--R (- 4B a c d e - 24A a c d e + 20B a c d e )x +--R + +--R 4 7 3 2 6 3 2 2 5 3 +--R (- 8B a c e - 48A a c d e + 40B a c d e )x +--R + +--R 4 6 3 2 2 5 3 2 3 4 2 +--R (- 8B a c d e - 48A a c d e + 40B a c d e )x +--R + +--R 5 7 4 6 4 2 5 5 6 +--R (- 4B a e - 24A a c d e + 20B a c d e )x - 4B a d e +--R + +--R 4 2 5 4 3 4 +--R - 24A a c d e + 20B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 7 2 3 6 2 3 2 5 5 +--R (8B a c e + 48A a c d e - 40B a c d e )x +--R + +--R 3 2 6 2 3 2 5 2 3 3 4 4 +--R (8B a c d e + 48A a c d e - 40B a c d e )x +--R + +--R 4 7 3 2 6 3 2 2 5 3 +--R (16B a c e + 96A a c d e - 80B a c d e )x +--R + +--R 4 6 3 2 2 5 3 2 3 4 2 +--R (16B a c d e + 96A a c d e - 80B a c d e )x +--R + +--R 5 7 4 6 4 2 5 5 6 +--R (8B a e + 48A a c d e - 40B a c d e )x + 8B a d e +--R + +--R 4 2 5 4 3 4 +--R 48A a c d e - 40B a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 7 3 2 6 2 3 2 5 2 3 3 4 +--R - 15A a c e + 22B a c d e - 3A a c d e + 20B a c d e +--R + +--R 4 4 3 4 5 2 5 6 +--R 15A a c d e - 2B a c d e + 3A c d e +--R * +--R 4 +--R x +--R + +--R 4 7 3 2 6 3 2 2 5 2 3 3 4 +--R 4B a c e + 9A a c d e + 6B a c d e + 21A a c d e +--R + +--R 4 5 2 4 6 5 7 +--R 15A a c d e - 2B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 4 7 4 6 3 2 2 5 3 2 3 4 +--R - 25A a c e + 38B a c d e + 3A a c d e + 28B a c d e +--R + +--R 2 3 4 3 2 3 5 2 4 6 +--R 33A a c d e - 10B a c d e + 5A a c d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 6 4 2 5 3 2 3 4 +--R 6B a e + 11A a c d e + 12B a c d e + 27A a c d e +--R + +--R 3 2 4 3 2 3 5 2 4 7 +--R 6B a c d e + 21A a c d e + 5A a c d +--R * +--R x +--R + +--R 5 7 5 6 4 2 5 4 3 4 3 2 4 3 +--R - 8A a e + 14B a d e + 12A a c d e + 2B a c d e + 24A a c d e +--R + +--R 3 2 5 2 2 3 6 2 3 7 +--R - 14B a c d e + 4A a c d e - 2B a c d +--R * +--R +-+ +--R \|a +--R / +--R 6 2 9 5 3 2 7 4 4 4 5 3 5 6 3 2 6 8 5 +--R (8a c e + 32a c d e + 48a c d e + 32a c d e + 8a c d e)x +--R + +--R 6 2 8 5 3 3 6 4 4 5 4 3 5 7 2 2 6 9 4 +--R (8a c d e + 32a c d e + 48a c d e + 32a c d e + 8a c d )x +--R + +--R 7 9 6 2 2 7 5 3 4 5 4 4 6 3 3 5 8 3 +--R (16a c e + 64a c d e + 96a c d e + 64a c d e + 16a c d e)x +--R + +--R 7 8 6 2 3 6 5 3 5 4 4 4 7 2 3 5 9 2 +--R (16a c d e + 64a c d e + 96a c d e + 64a c d e + 16a c d )x +--R + +--R 8 9 7 2 7 6 2 4 5 5 3 6 3 4 4 8 8 8 +--R (8a e + 32a c d e + 48a c d e + 32a c d e + 8a c d e)x + 8a d e +--R + +--R 7 3 6 6 2 5 4 5 3 7 2 4 4 9 +--R 32a c d e + 48a c d e + 32a c d e + 8a c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1444 + +--S 1445 of 1457 +--a0:=integrate(t0,x) +--E 1445 + +--S 1446 of 1457 +--m0:=a0-r0 +--E 1446 + +--S 1447 of 1457 +--d0:=D(m0,x) +--E 1447 + +)clear all + +--S 1448 of 1457 +t0:=(-11+6*x)/((-1+2*x)*(-1+x^2)) +--R +--R +--R 6x - 11 +--R (1) ----------------- +--R 3 2 +--R 2x - x - 2x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1448 + +--S 1449 of 1457 +r0:=16/3*log(1-2*x)-5/2*log(1-x)-17/6*log(1+x) +--R +--R +--R - 17log(x + 1) - 15log(- x + 1) + 32log(- 2x + 1) +--R (2) ------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1449 + +--S 1450 of 1457 +a0:=integrate(t0,x) +--R +--R +--R 32log(2x - 1) - 17log(x + 1) - 15log(x - 1) +--R (3) ------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1450 + +--S 1451 of 1457 +m0:=a0-r0 +--R +--R +--R 32log(2x - 1) - 15log(x - 1) + 15log(- x + 1) - 32log(- 2x + 1) +--R (4) --------------------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1451 + +--S 1452 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1452 + +)clear all + +--S 1453 of 1457 +t0:=(5-x)*(3+2*x)^4*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (1) (- 16x - 16x + 264x + 864x + 999x + 405)\|3x + 2 +--R Type: Expression(Integer) +--E 1453 + +--S 1454 of 1457 +r0:=8275/162*(2+3*x^2)^(3/2)+923/315*(3+2*x)^2*(2+3*x^2)^(3/2)+29/63*_ + (3+2*x)^3*(2+3*x^2)^(3/2)-1/21*(3+2*x)^4*(2+3*x^2)^(3/2)+1/270*_ + (4583+6132*x)*(2+3*x^2)^(3/2)+2341/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 2341/18*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 12960x - 15120x + 297648x + 1222200x + 1956174x + 1558935x +--R + +--R 1167988 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1474830asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 5670\|3 +--R Type: Expression(Integer) +--E 1454 + +--S 1455 of 1457 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 6 4 2 +-+ | 2 +--R (4424490x + 70791840x + 157315200x + 83901440)\|2 \|3x + 2 +--R + +--R 6 4 2 +--R - 61942860x - 330361920x - 440482560x - 167802880 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 12 11 10 9 8 +--R 544320x + 635040x - 9598176x - 47945520x - 144961740x +--R + +--R 7 6 5 4 3 +--R - 334732230x - 567653520x - 712511520x - 767612160x - 604661120x +--R + +--R 2 +--R - 322237440x - 177372160x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 14 13 12 11 10 +--R - 116640x - 136080x + 734832x + 8731800x + 56861406x +--R + +--R 9 8 7 6 5 +--R 191070495x + 422782920x + 736469370x + 1052733360x + 1116121440x +--R + +--R 4 3 2 +--R 1009290240x + 737690240x + 322237440x + 177372160x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (17010x + 272160x + 604800x + 322560)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 238140x - 1270080x - 1693440x - 645120)\|3 +--R Type: Union(Expression(Integer),...) +--E 1455 + +--S 1456 of 1457 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 6 4 2 +-+ | 2 +--R (19910205x + 318563280x + 707918400x + 377556480)\|2 \|3x + 2 +--R + +--R 6 4 2 +--R - 278742870x - 1486628640x - 1982171520x - 755112960 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 6 4 2 +-+ +--R (- 19910205x - 318563280x - 707918400x - 377556480)\|2 +--R * +--R +-+ +--R x\|3 +--R asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +--R (31535676x + 504570816x + 1121268480x + 598009856)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 x\|3 +--R (278742870x + 1486628640x + 1982171520x + 755112960)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 220749732x - 1177331904x - 1569775872x - 598009856)\|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (76545x + 1224720x + 2721600x + 1451520)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 1071630x - 5715360x - 7620480x - 2903040)\|3 +--R Type: Expression(Integer) +--E 1456 + +--S 1457 of 1457 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1457 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich12b.input.pamphlet b/src/input/rich12b.input.pamphlet new file mode 100644 index 0000000..de09257 --- /dev/null +++ b/src/input/rich12b.input.pamphlet @@ -0,0 +1,24836 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12b.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 91 matching answers. +\item 0 cases where Axiom answer differs from Rubi +\item 0 cases where Axiom supplied 2 results. +\item 4 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12b.output +)spool rich12b.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(5-x)*(3+2*x)^3*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 4 3 2 | 2 +--R (1) (- 8x + 4x + 126x + 243x + 135)\|3x + 2 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=875/54*(2+3*x^2)^(3/2)+17/30*(3+2*x)^2*(2+3*x^2)^(3/2)-1/18*(3+2*x)^3*_ + (2+3*x^2)^(3/2)+7/90*(91+89*x)*(2+3*x^2)^(3/2)+1022/9*asinh(x*_ + sqrt(3/2))/sqrt(3)+511/9*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 360x + 216x + 8445x + 21918x + 21120x + 14516)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 30660asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 270\|3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 6 4 +--R (551880x + 1962240x + 1308160)\|2 \|3x + 2 - 275940x - 3311280x +--R + +--R 2 +--R - 5886720x - 2616320 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 11 10 9 8 7 6 +--R 3240x - 1944x - 37125x - 220590x - 1033020x - 2539260x +--R + +--R 5 4 3 2 +--R - 3871680x - 5271840x - 4775680x - 2799360x - 1802240x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 11 10 9 8 7 6 +--R - 19440x + 11664x + 373950x + 1232820x + 2973780x + 5705820x +--R + +--R 5 4 3 2 +--R 6946560x + 7371360x + 6127360x + 2799360x + 1802240x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (4860x + 17280x + 11520)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 2430x - 29160x - 51840x - 23040)\|3 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ | 2 6 4 +--R (827820x + 2943360x + 1962240)\|2 \|3x + 2 - 413910x - 4966920x +--R + +--R 2 +--R - 8830080x - 3924480 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (- 827820x - 2943360x - 1962240)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (783864x + 2787072x + 1858048)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 x\|3 +--R (413910x + 4966920x + 8830080x + 3924480)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 195966x - 2351592x - 4180608x - 1858048)\|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (7290x + 25920x + 17280)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 3645x - 43740x - 77760x - 34560)\|3 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(5-x)*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (1) (- 4x + 8x + 51x + 45)\|3x + 2 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=205/54*(2+3*x^2)^(3/2)-1/15*(3+2*x)^2*(2+3*x^2)^(3/2)+1/90*(233+132*x)*_ + (2+3*x^2)^(3/2)+131/3*asinh(x*sqrt(3/2))/sqrt(3)+131/6*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +-+ +--R 4 3 2 +-+ | 2 x\|3 +--R (- 216x + 540x + 4542x + 6255x + 3124)\|3 \|3x + 2 + 11790asinh(-----) +--R +-+ +--R \|2 +--R --------------------------------------------------------------------------- +--R +-+ +--R 270\|3 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (11790x + 94320x + 83840)\|2 \|3x + 2 - 117900x - 314400x +--R + +--R - 167680 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 8 7 6 5 4 3 2 +--R 2160x - 5400x - 39660x - 76950x - 143040x - 174480x - 97920x +--R + +--R - 88960x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 10 9 8 7 6 5 4 +--R - 648x + 1620x + 8010x + 32805x + 119400x + 182790x + 216480x +--R + +--R 3 2 +--R 241200x + 97920x + 88960x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 4 2 +-+ +--R (270x + 2160x + 1920)\|2 \|3 \|3x + 2 + (- 2700x - 7200x - 3840)\|3 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (53055x + 424440x + 377280)\|2 \|3x + 2 - 530550x - 1414800x +--R + +--R - 754560 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (- 53055x - 424440x - 377280)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (28116x + 224928x + 199936)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 4 2 x\|3 +--R (530550x + 1414800x + 754560)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +-+ +--R (- 140580x - 374880x - 199936)\|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (1215x + 9720x + 8640)\|2 \|3 \|3x + 2 +--R + +--R 4 2 +-+ +--R (- 12150x - 32400x - 17280)\|3 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(5-x)*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (1) (- 2x + 7x + 15)\|3x + 2 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=37/36*(2+3*x^2)^(3/2)-1/12*(3+2*x)*(2+3*x^2)^(3/2)+46/3*asinh(x*_ + sqrt(3/2))/sqrt(3)+23/3*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 3 2 +-+ | 2 x\|3 +--R (- 9x + 42x + 132x + 28)\|3 \|3x + 2 + 276asinh(-----) +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------------- +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((1104x + 1472)\|2 \|3x + 2 - 828x - 4416x - 2944) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 7 6 5 4 3 2 +-+ | 2 +--R (27x - 126x - 252x - 756x - 2016x - 672x - 1408x)\|3 \|3x + 2 +--R + +--R 7 6 5 4 3 2 +-+ +-+ +--R (- 108x + 504x + 1368x + 1260x + 3072x + 672x + 1408x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 4 2 +-+ +--R (72x + 96)\|2 \|3 \|3x + 2 + (- 54x - 288x - 192)\|3 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((1656x + 2208)\|2 \|3x + 2 - 1242x - 6624x - 4416) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((- 1656x - 2208)\|2 asinh(-----) + (336x + 448)\|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 4 2 x\|3 4 2 +-+ +-+ +--R (1242x + 6624x + 4416)asinh(-----) + (- 126x - 672x - 448)\|2 \|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 4 2 +-+ +--R (108x + 144)\|2 \|3 \|3x + 2 + (- 81x - 432x - 288)\|3 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(5-x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) (- x + 5)\|3x + 2 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-1/9*(2+3*x^2)^(3/2)+5*asinh(x*sqrt(3/2))/sqrt(3)+_ + 5/2*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 2 +-+ | 2 x\|3 +--R (- 6x + 45x - 4)\|3 \|3x + 2 + 90asinh(-----) +--R +-+ +--R \|2 +--R (2) ------------------------------------------------ +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((30x + 80)\|2 \|3x + 2 - 180x - 160) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 4 3 2 +-+ | 2 +--R (12x - 90x + 16x - 80x)\|3 \|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +-+ +--R (- 6x + 45x - 24x + 150x - 16x + 80x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 2 +-+ +--R (6x + 16)\|2 \|3 \|3x + 2 + (- 36x - 32)\|3 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((135x + 360)\|2 \|3x + 2 - 810x - 720) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((- 135x - 360)\|2 asinh(-----) + (- 12x - 32)\|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 2 x\|3 2 +-+ +-+ +--R (810x + 720)asinh(-----) + (36x + 32)\|2 \|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 2 +-+ +--R (27x + 72)\|2 \|3 \|3x + 2 + (- 162x - 144)\|3 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=-121/8*asinh(x*sqrt(3/2))/sqrt(3)-13/8*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))*sqrt(35)+1/4*(13-x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R +-+ +--+ 9x - 4 +-+ | 2 +--R 13\|3 \|35 atanh(---------------) + (- 2x + 26)\|3 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R - 121asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 8\|3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R | 2 2 +-+ +--R (484\|3x + 2 + (- 363x - 484)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|3 + 3x\|2 )\|3x + 2 + (- 3x - 2)\|2 \|3 - 6x +--R log(-----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R +-+ +--+ | 2 2 +-+ +-+ +--+ +--R (52\|3 \|35 \|3x + 2 + (- 39x - 52)\|2 \|3 \|35 ) +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((- 2x - 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (9x + 4x + 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R 3 2 +-+ +-+ | 2 3 2 +-+ +--R (6x - 78x + 8x)\|2 \|3 \|3x + 2 + (- 24x + 156x - 16x)\|3 +--R / +--R +-------+ +--R +-+ | 2 2 +-+ +-+ +--R 32\|3 \|3x + 2 + (- 24x - 32)\|2 \|3 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | 2 2 +-+ +--R (484\|3x + 2 + (- 363x - 484)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|3 + 3x\|2 )\|3x + 2 + (- 3x - 2)\|2 \|3 - 6x +--R log(-----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R +-+ +--+ | 2 2 +-+ +-+ +--+ +--R (52\|3 \|35 \|3x + 2 + (- 39x - 52)\|2 \|3 \|35 ) +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((- 2x - 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (9x + 4x + 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R +-+ +--+ | 2 2 +-+ +-+ +--+ +--R (- 52\|3 \|35 \|3x + 2 + (39x + 52)\|2 \|3 \|35 ) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +-------+ +--R x\|3 +-+ +-+ | 2 +--R (484asinh(-----) + 104\|2 \|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 2 +-+ x\|3 2 +-+ +--R (- 363x - 484)\|2 asinh(-----) + (- 156x - 208)\|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R +-+ | 2 2 +-+ +-+ +--R 32\|3 \|3x + 2 + (- 24x - 32)\|2 \|3 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=2*asinh(x*sqrt(3/2))*sqrt(3)+19*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)-1/2*(8+x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 9x - 4 +--+ | 2 +--R (- 76x - 114)atanh(---------------) + (- x - 8)\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R +-+ +--+ x\|3 +--R (8x + 12)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R +--+ +--R (4x + 6)\|35 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 3 2 +--R ((456x + 684)\|2 \|3x + 2 - 684x - 1026x - 912x - 1368) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 + 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (- 70x - 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +-+ +-+ +--+ | 2 +--R (48x + 72)\|2 \|3 \|35 \|3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (- 72x - 108x - 96x - 144)\|3 \|35 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|3 + \|2 )\|3x + 2 + x\|2 \|3 - 3x - 2 +--R log(------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R 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26678400x + 14228480)\|2 \|3x + 2 +--R + +--R 6 4 2 +--R - 10504620x - 56024640x - 74699520x - 28456960 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 12 11 10 9 8 +--R 272160x - 635040x - 3116232x - 9485910x - 28879200x +--R + +--R 7 6 5 4 3 +--R - 46080090x - 68040000x - 93283680x - 64942080x - 80778880x +--R + +--R 2 +--R - 21934080x - 24478720x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 14 13 12 11 10 +--R - 58320x + 136080x + 6804x + 3574935x + 15000552x +--R + +--R 9 8 7 6 5 +--R 30008475x + 66270960x + 98487270x + 110577600x + 146983200x +--R + +--R 4 3 2 +--R 81392640x + 99137920x + 21934080x + 24478720x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (11340x + 181440x + 403200x + 215040)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 158760x - 846720x - 1128960x - 430080)\|3 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 6 4 2 +-+ | 2 +--R (1125495x + 18007920x + 40017600x + 21342720)\|2 \|3x + 2 +--R + +--R 6 4 2 +--R - 15756930x - 84036960x - 112049280x - 42685440 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 6 4 2 +-+ x\|3 +--R (- 1125495x - 18007920x - 40017600x - 21342720)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +--R (469584x + 7513344x + 16696320x + 8904704)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 x\|3 +--R (15756930x + 84036960x + 112049280x + 42685440)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 3287088x - 17531136x - 23374848x - 8904704)\|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (17010x + 272160x + 604800x + 322560)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 238140x - 1270080x - 1693440x - 645120)\|3 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(5-x)*(3+2*x)*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 4 3 2 | 2 +--R (1) (- 6x + 21x + 41x + 14x + 30)\|3x + 2 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=137/36*x*(2+3*x^2)^(3/2)+19/30*(2+3*x^2)^(5/2)-1/18*(3+2*x)*_ + (2+3*x^2)^(5/2)+137/6*asinh(x*sqrt(3/2))/sqrt(3)+137/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 60x + 252x + 605x + 336x + 1115x + 112)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1370asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 60\|3 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 6 4 +--R (73980x + 263040x + 175360)\|2 \|3x + 2 - 36990x - 443880x +--R + +--R 2 +--R - 789120x - 350720 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 11 10 9 8 7 6 5 +--R 1620x - 6804x + 3105x - 90720x - 191565x - 257040x - 694380x +--R + +--R 4 3 2 +--R - 282240x - 797120x - 107520x - 285440x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 11 10 9 8 7 6 +--R - 9720x + 40824x + 56970x + 226800x + 548370x + 438480x +--R + +--R 5 4 3 2 +--R 1211940x + 362880x + 1011200x + 107520x + 285440x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (3240x + 11520x + 7680)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 1620x - 19440x - 34560x - 15360)\|3 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ | 2 6 4 +--R (36990x + 131520x + 87680)\|2 \|3x + 2 - 18495x - 221940x +--R + +--R 2 +--R - 394560x - 175360 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (- 36990x - 131520x - 87680)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (6048x + 21504x + 14336)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 x\|3 +--R (18495x + 221940x + 394560x + 175360)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 1512x - 18144x - 32256x - 14336)\|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (1620x + 5760x + 3840)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 810x - 9720x - 17280x - 7680)\|3 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(5-x)*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (1) (- 3x + 15x - 2x + 10)\|3x + 2 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=5/4*x*(2+3*x^2)^(3/2)-1/15*(2+3*x^2)^(5/2)+5/2*asinh(x*sqrt(3/2))*_ + sqrt(3)+15/4*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 4 3 2 | 2 +-+ x\|3 +--R (- 36x + 225x - 48x + 375x - 16)\|3x + 2 + 150\|3 asinh(-----) +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------------- +--R 60 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (450x + 3600x + 3200)\|2 \|3 \|3x + 2 +--R + +--R 4 2 +-+ +--R (- 4500x - 12000x - 6400)\|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|3 + \|2 )\|3x + 2 + x\|2 \|3 - 3x - 2 +--R log(------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 8 7 6 5 4 3 2 +--R 1080x - 6750x + 4320x - 29250x + 5760x - 39600x + 2560x +--R + +--R - 16000x +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 10 9 8 7 6 5 4 +--R - 324x + 2025x - 3240x + 20925x - 7920x + 54450x - 7680x +--R + +--R 3 2 +--R 51600x - 2560x + 16000x +--R * +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (180x + 1440x + 1280)\|2 \|3x + 2 - 1800x - 4800x - 2560 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (675x + 5400x + 4800)\|2 \|3 \|3x + 2 +--R + +--R 4 2 +-+ +--R (- 6750x - 18000x - 9600)\|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|3 + \|2 )\|3x + 2 + x\|2 \|3 - 3x - 2 +--R log(------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 4 2 +-+ +-+ x\|3 4 2 +--R ((- 675x - 5400x - 4800)\|2 \|3 asinh(-----) - 144x - 1152x - 1024) +--R +-+ +--R \|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 4 2 +-+ +--R (6750x + 18000x + 9600)\|3 asinh(-----) + (720x + 1920x + 1024)\|2 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (270x + 2160x + 1920)\|2 \|3x + 2 - 2700x - 7200x - 3840 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=1/24*(26-3*x)*(2+3*x^2)^(3/2)-1529/32*asinh(x*sqrt(3/2))*sqrt(3)-_ + 455/32*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+_ + 1/16*(455-123*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R 1365\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R 3 2 | 2 +-+ x\|3 +--R (- 36x + 312x - 762x + 2938)\|3x + 2 - 4587\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 96 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 +--R (36696x + 48928)\|3 \|3x + 2 +--R + +--R 4 2 +-+ +-+ +--R (- 13761x - 73392x - 48928)\|2 \|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (x\|2 \|3 + 2)\|3x + 2 - 2x\|3 + (- 3x - 2)\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (10920x + 14560)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 4095x - 21840x - 14560)\|2 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((- 2x - 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (9x + 4x + 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R 7 6 5 4 3 2 +-+ +--R (108x - 936x + 2862x - 13806x + 12576x - 26832x + 8128x)\|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 7 6 5 4 3 2 +--R - 864x + 7488x - 20016x + 67860x - 37344x + 53664x - 16256x +--R / +--R +-------+ +--R 2 | 2 4 2 +-+ +--R (768x + 1024)\|3x + 2 + (- 288x - 1536x - 1024)\|2 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 +--R (110088x + 146784)\|3 \|3x + 2 +--R + +--R 4 2 +-+ +-+ +--R (- 41283x - 220176x - 146784)\|2 \|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (x\|2 \|3 + 2)\|3x + 2 - 2x\|3 + (- 3x - 2)\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (32760x + 43680)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 12285x - 65520x - 43680)\|2 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((- 2x - 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (9x + 4x + 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (- 32760x - 43680)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (12285x + 65520x + 43680)\|2 \|35 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((110088x + 146784)\|3 asinh(-----) + (70512x + 94016)\|2 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 4 2 +-+ +-+ x\|3 4 2 +--R (- 41283x - 220176x - 146784)\|2 \|3 asinh(-----) - 52884x - 282048x +--R +-+ +--R \|2 +--R + +--R - 188032 +--R / +--R +-------+ +--R 2 | 2 4 2 +-+ +--R (2304x + 3072)\|3x + 2 + (- 864x - 4608x - 3072)\|2 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=-1/6*(21+x)*(2+3*x^2)^(3/2)/(3+2*x)+663/16*asinh(x*sqrt(3/2))*_ + sqrt(3)+193/16*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)-_ + 1/8*(193-63*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R (- 1158x - 1737)\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R 3 2 | 2 +-+ x\|3 +--R (- 24x + 252x - 1198x - 3810)\|3x + 2 + (3978x + 5967)\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 96x + 144 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 2 +--+ | 2 +--R (27792x + 41688x + 37056x + 55584)\|35 \|3x + 2 +--R + +--R 5 4 3 2 +-+ +--+ +--R (- 10422x - 15633x - 55584x - 83376x - 37056x - 55584)\|2 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((2x + 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (- 9x - 4x - 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R 3 2 +-+ | 2 +--R (95472x + 143208x + 127296x + 190944)\|3 \|3x + 2 +--R + +--R 5 4 3 2 +-+ +-+ +--R (- 35802x - 53703x - 190944x - 286416x - 127296x - 190944)\|2 \|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (- x\|2 \|3 + 2)\|3x + 2 + 2x\|3 + (- 3x - 2)\|2 +--R log(------------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R 7 6 5 4 3 2 +-+ +--R (216x - 2268x + 11934x + 22194x - 2688x + 83376x - 42944x)\|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 7 6 5 4 3 2 +--R - 1728x + 18144x - 43992x - 169452x + 69792x - 166752x + 85888x +--R / +--R +-------+ +--R 3 2 | 2 +--R (2304x + 3456x + 3072x + 4608)\|3x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 864x - 1296x - 4608x - 6912x - 3072x - 4608)\|2 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +--+ | 2 +--R (13896x + 18528)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 5211x - 27792x - 18528)\|2 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((2x + 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (- 9x - 4x - 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R 2 +-+ | 2 +--R (47736x + 63648)\|3 \|3x + 2 +--R + +--R 4 2 +-+ +-+ +--R (- 17901x - 95472x - 63648)\|2 \|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (- x\|2 \|3 + 2)\|3x + 2 + 2x\|3 + (- 3x - 2)\|2 +--R log(------------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (13896x + 18528)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 5211x - 27792x - 18528)\|2 \|35 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((- 47736x - 63648)\|3 asinh(-----) + (- 30480x - 40640)\|2 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 4 2 +-+ +-+ x\|3 4 2 +--R (17901x + 95472x + 63648)\|2 \|3 asinh(-----) + 22860x + 121920x +--R +-+ +--R \|2 +--R + +--R 81280 +--R / +--R +-------+ +--R 2 | 2 4 2 +-+ +--R (1152x + 1536)\|3x + 2 + (- 432x - 2304x - 1536)\|2 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^3 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=-1/4*(8+x)*(2+3*x^2)^(3/2)/(3+2*x)^2-111/8*asinh(x*sqrt(3/2))*_ + sqrt(3)-1143/8*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 3/4*(37+12*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 9x - 4 +--R (4572x + 13716x + 10287)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 6x + 96x + 656x + 634)\|35 \|3x + 2 +--R + +--R +-+ +--R 2 +-+ +--+ x\|3 +--R (- 444x - 1332x - 999)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 2 +--+ +--R (32x + 96x + 72)\|35 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 3 2 +-+ | 2 +--R (493776x + 1481328x + 1769364x + 1975104x + 1481328)\|2 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 370332x - 1110996x - 2808351x - 5925312x - 5760720x - 3950208x +--R + +--R - 2962656 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R 4 3 2 +-+ +-+ +--+ +--R (47952x + 143856x + 171828x + 191808x + 143856)\|2 \|3 \|35 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + 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949887)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 2520x - 48948x - 97494x - 60538)\|35 \|3x + 2 +--R + +--R +-+ +--R 3 2 +-+ +--+ x\|3 +--R (27720x + 124740x + 187110x + 93555)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 3 2 +--+ +--R (13440x + 60480x + 90720x + 45360)\|35 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 91189152x + 410351184x + 737112312x + 854898300x + 820702368x +--R + +--R 410351184 +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 7 6 5 4 +--R - 68391864x - 307763388x - 826401690x - 1872227277x +--R + +--R 3 2 +--R - 2705278176x - 2325323376x - 1641404736x - 820702368 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 + 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (- 70x - 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + 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4 3 2 +--+ +--R (1881600x + 11289600x + 25401600x + 25401600x + 9525600)\|35 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 68537664x + 411225984x + 1016642016x + 1473559776x +--R + +--R 2 +--R 1580649876x + 1233677952x + 462629232 +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 8 7 6 5 +--R - 51403248x - 308419488x - 968094504x - 2338847784x +--R + +--R 4 3 2 +--R - 4144029903x - 4797636480x - 3855243600x - 2467355904x - 925258464 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R 6 5 4 3 2 +--R 6350400x + 38102400x + 94197600x + 136533600x + 146456100x +--R + +--R 114307200x + 42865200 +--R * +--R +-------+ +--R +-+ +-+ +--+ | 2 +--R \|2 \|3 \|35 \|3x + 2 +--R + +--R 8 7 6 5 4 +--R - 4762800x - 28576800x - 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Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(5-x)*(3+2*x)^3*(2+3*x^2)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (- 72x + 36x + 1038x + 2235x + 2695x + 2932x + 2124x + 972x + 540) +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=3731/72*x*(2+3*x^2)^(3/2)+3731/180*x*(2+3*x^2)^(5/2)+_ + 9371/1620*(2+3*x^2)^(7/2)+91/270*(3+2*x)^2*(2+3*x^2)^(7/2)-_ + 1/30*(3+2*x)^3*(2+3*x^2)^(7/2)+7/1620*(839+711*x)*(2+3*x^2)^(7/2)+_ + 3731/12*asinh(x*sqrt(3/2))/sqrt(3)+3731/24*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 9 8 7 6 5 4 +--R - 23328x + 12960x + 418446x + 1035720x + 1503522x + 2036880x +--R + +--R 3 2 +--R 1922805x + 1350240x + 1245915x + 299200 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1007370asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 3240\|3 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 6 4 2 +--R (30221100x + 322358400x + 902603520x + 916930560x + 305643520) +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 10 8 6 4 +--R - 9066330x - 302211000x - 1611792000x - 3008678400x +--R + +--R 2 +--R - 2292326400x - 611287040 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 19 18 17 16 15 +--R 209952x - 116640x + 3232386x - 13209480x - 101740698x +--R + +--R 14 13 12 11 +--R - 349783920x - 1068202485x - 2319075360x - 4190364495x +--R + +--R 10 9 8 7 +--R - 6789614400x - 8878822884x - 10680376320x - 11411508672x +--R + +--R 6 5 4 3 +--R - 9583472640x - 9008941824x - 4665999360x - 4001935360x +--R + +--R 2 +--R - 955514880x - 756039680x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 19 18 17 16 15 +--R - 2099520x + 1166400x + 13865580x + 106434000x + 484496316x +--R + +--R 14 13 12 11 +--R 1282884480x + 2993728410x + 5704629120x + 8905905450x +--R + +--R 10 9 8 7 +--R 12899822400x + 15598337940x + 16757222400x + 17202147840x +--R + +--R 6 5 4 3 +--R 12814233600x + 11797757184x + 5382635520x + 4568965120x +--R + +--R 2 +--R 955514880x + 756039680x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 8 6 4 2 +-+ +-+ | 2 +--R (97200x + 1036800x + 2903040x + 2949120x + 983040)\|2 \|3 \|3x + 2 +--R + +--R 10 8 6 4 2 +-+ +--R (- 29160x - 972000x - 5184000x - 9676800x - 7372800x - 1966080)\|3 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 6 4 2 +--R 81596970x + 870367680x + 2437029504x + 2475712512x +--R + +--R 825237504 +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 10 8 6 4 +--R - 24479091x - 815969700x - 4351838400x - 8123431680x +--R + +--R 2 +--R - 6189281280x - 1650475008 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 8 6 4 2 +--R - 81596970x - 870367680x - 2437029504x - 2475712512x +--R + +--R - 825237504 +--R * +--R +-+ +--R +-+ x\|3 +--R \|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 8 6 4 2 +--R 48470400x + 517017600x + 1447649280x + 1470627840x +--R + +--R 490209280 +--R * +--R +-+ +--R \|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 10 8 6 4 +--R 24479091x + 815969700x + 4351838400x + 8123431680x +--R + +--R 2 +--R 6189281280x + 1650475008 +--R * +--R +-+ +--R x\|3 +--R asinh(-----) +--R +-+ +--R \|2 +--R + +--R 10 8 6 4 +--R - 7270560x - 242352000x - 1292544000x - 2412748800x +--R + +--R 2 +--R - 1838284800x - 490209280 +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R 8 6 4 2 +-+ +-+ +--R (262440x + 2799360x + 7838208x + 7962624x + 2654208)\|2 \|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 10 8 6 4 2 +--R - 78732x - 2624400x - 13996800x - 26127360x - 19906560x +--R + +--R - 5308416 +--R * +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(5-x)*(3+2*x)^2*(2+3*x^2)^(5/2) +--R +--R +--R +-------+ +--R 7 6 5 4 3 2 | 2 +--R (1) (- 36x + 72x + 411x + 501x + 596x + 572x + 204x + 180)\|3x + 2 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=665/36*x*(2+3*x^2)^(3/2)+133/18*x*(2+3*x^2)^(5/2)+491/324*_ + (2+3*x^2)^(7/2)-1/27*(3+2*x)^2*(2+3*x^2)^(7/2)+7/324*(59+36*x)*_ + (2+3*x^2)^(7/2)+665/6*asinh(x*sqrt(3/2))/sqrt(3)+665/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 8 7 6 5 4 3 2 +--R - 1296x + 2916x + 18900x + 27378x + 41256x + 50571x + 28272x +--R + +--R 40365x + 6368 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 35910asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 324\|3 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 6 4 2 +-+ +--R (107730x + 2872800x + 11491200x + 14300160x + 5447680)\|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 8 6 4 2 +--R - 1939140x - 17236800x - 41368320x - 36771840x - 10895360 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 16 15 14 13 12 +--R 69984x - 157464x - 398520x - 2878092x - 9806832x +--R + +--R 11 10 9 8 7 +--R - 19231506x - 41775264x - 60979230x - 80363520x - 106552800x +--R + +--R 6 5 4 3 2 +--R - 82587648x - 106591872x - 44728320x - 56677376x - 10027008x +--R + +--R - 12247040x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 18 17 16 15 14 +--R - 11664x + 26244x - 148716x + 963738x + 3569184x +--R + +--R 13 12 11 10 9 +--R 10456047x + 29193696x + 48816999x + 86272128x + 120448350x +--R + +--R 8 7 6 5 4 +--R 131839488x + 173139552x + 113313792x + 145655424x + 52248576x +--R + +--R 3 2 +--R 65862656x + 10027008x + 12247040x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 8 6 4 2 +-+ +-+ | 2 +--R (972x + 25920x + 103680x + 129024x + 49152)\|2 \|3 \|3x + 2 +--R + +--R 8 6 4 2 +-+ +--R (- 17496x - 155520x - 373248x - 331776x - 98304)\|3 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 6 4 2 +-+ +--R (1454355x + 38782800x + 155131200x + 193052160x + 73543680)\|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 8 6 4 2 +--R - 26178390x - 232696800x - 558472320x - 496419840x - 147087360 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 8 6 4 2 +--R (- 1454355x - 38782800x - 155131200x - 193052160x - 73543680) +--R * +--R +-+ +--R +-+ x\|3 +--R \|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 8 6 4 2 +-+ +--R (515808x + 13754880x + 55019520x + 68468736x + 26083328)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 8 6 4 2 +--R (26178390x + 232696800x + 558472320x + 496419840x + 147087360) +--R * +--R +-+ +--R x\|3 +--R asinh(-----) +--R +-+ +--R \|2 +--R + +--R 8 6 4 2 +-+ +-+ +--R (- 4642272x - 41264640x - 99035136x - 88031232x - 26083328)\|2 \|3 +--R / +--R +-------+ +--R 8 6 4 2 +-+ +-+ | 2 +--R (13122x + 349920x + 1399680x + 1741824x + 663552)\|2 \|3 \|3x + 2 +--R + +--R 8 6 4 2 +-+ +--R (- 236196x - 2099520x - 5038848x - 4478976x - 1327104)\|3 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(5-x)*(3+2*x)*(2+3*x^2)^(5/2) +--R +--R +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (1) (- 18x + 63x + 111x + 84x + 172x + 28x + 60)\|3x + 2 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=455/72*x*(2+3*x^2)^(3/2)+91/36*x*(2+3*x^2)^(5/2)+11/24*_ + (2+3*x^2)^(7/2)-1/24*(3+2*x)*(2+3*x^2)^(7/2)+455/12*_ + asinh(x*sqrt(3/2))/sqrt(3)+455/24*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +-+ +--R (- 54x + 216x + 438x + 432x + 1111x + 288x + 985x + 64)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 910asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 24\|3 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 6 4 2 +-+ | 2 8 +--R (196560x + 1310400x + 2096640x + 931840)\|2 \|3x + 2 - 73710x +--R + +--R 6 4 2 +--R - 1572480x - 5241600x - 5591040x - 1863680 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 15 14 13 12 11 10 +--R 4374x - 17496x + 57834x - 408240x - 535815x - 2013984x +--R + +--R 9 8 7 6 5 +--R - 4190697x - 4318272x - 10681920x - 4838400x - 13396608x +--R + +--R 4 3 2 +--R - 2838528x - 8327168x - 688128x - 2017280x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 15 14 13 12 11 +--R - 34992x + 139968x + 27216x + 1306368x + 2272536x +--R + +--R 10 9 8 7 6 +--R 4354560x + 9791928x + 7293888x + 18812880x + 6773760x +--R + +--R 5 4 3 2 +--R 19074624x + 3354624x + 9840128x + 688128x + 2017280x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (5184x + 34560x + 55296x + 24576)\|2 \|3 \|3x + 2 +--R + +--R 8 6 4 2 +-+ +--R (- 1944x - 41472x - 138240x - 147456x - 49152)\|3 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 6 4 2 +-+ | 2 8 +--R (98280x + 655200x + 1048320x + 465920)\|2 \|3x + 2 - 36855x +--R + +--R 6 4 2 +--R - 786240x - 2620800x - 2795520x - 931840 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 6 4 2 +-+ x\|3 +--R (- 98280x - 655200x - 1048320x - 465920)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +--R (13824x + 92160x + 147456x + 65536)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 8 6 4 2 x\|3 +--R (36855x + 786240x + 2620800x + 2795520x + 931840)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 8 6 4 2 +-+ +-+ +--R (- 2592x - 55296x - 184320x - 196608x - 65536)\|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (2592x + 17280x + 27648x + 12288)\|2 \|3 \|3x + 2 +--R + +--R 8 6 4 2 +-+ +--R (- 972x - 20736x - 69120x - 73728x - 24576)\|3 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(5-x)*(2+3*x^2)^(5/2) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (1) (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=25/12*x*(2+3*x^2)^(3/2)+5/6*x*(2+3*x^2)^(5/2)-1/21*(2+3*x^2)^(7/2)+_ + 25/2*asinh(x*sqrt(3/2))/sqrt(3)+25/4*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 6 5 4 3 2 +-+ | 2 +--R (- 108x + 630x - 216x + 1365x - 144x + 1155x - 32)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1050asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 84\|3 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 6 4 2 +-+ | 2 6 +--R (9450x + 151200x + 336000x + 179200)\|2 \|3x + 2 - 132300x +--R + +--R 4 2 +--R - 705600x - 940800x - 358400 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 12 11 10 9 8 7 +--R 13608x - 79380x + 99792x - 595350x + 260064x - 1627290x +--R + +--R 6 5 4 3 2 +--R 330624x - 2214240x + 215040x - 1500800x + 57344x - 394240x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 14 13 12 11 10 9 +--R - 2916x + 17010x - 54432x + 320355x - 235872x + 1431675x +--R + +--R 8 7 6 5 4 3 +--R - 459648x + 2949030x - 475776x + 3228960x - 258048x + 1796480x +--R + +--R 2 +--R - 57344x + 394240x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (756x + 12096x + 26880x + 14336)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 10584x - 56448x - 75264x - 28672)\|3 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 6 4 2 +-+ | 2 6 +--R (14175x + 226800x + 504000x + 268800)\|2 \|3x + 2 - 198450x +--R + +--R 4 2 +--R - 1058400x - 1411200x - 537600 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 6 4 2 +-+ x\|3 +--R (- 14175x - 226800x - 504000x - 268800)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +--R (- 864x - 13824x - 30720x - 16384)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 x\|3 +--R (198450x + 1058400x + 1411200x + 537600)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +-+ +--R (6048x + 32256x + 43008x + 16384)\|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (1134x + 18144x + 40320x + 21504)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 15876x - 84672x - 112896x - 43008)\|3 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 2x + 3 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=7/96*(130-53*x)*(2+3*x^2)^(3/2)+1/60*(39-5*x)*(2+3*x^2)^(5/2)-_ + 162673/128*asinh(x*sqrt(3/2))/sqrt(3)-15925/128*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+7/64*(2275-691*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +--+ 9x - 4 +--R 238875\|3 \|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 1440x + 11232x - 24180x + 69576x - 160590x + 519142)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R - 2440095asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 1920\|3 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 | 2 +--R (87843420x + 312332160x + 208221440)\|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 21960855x - 263530260x - 468498240x - 208221440)\|2 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|3 + 3x\|2 )\|3x + 2 + (- 3x - 2)\|2 \|3 - 6x +--R log(-----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R 4 2 +-+ +--+ | 2 +--R (8599500x + 30576000x + 20384000)\|3 \|35 \|3x + 2 +--R + +--R 6 4 2 +-+ +-+ +--+ +--R (- 2149875x - 25798500x - 45864000x - 20384000)\|2 \|3 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((- 2x - 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (9x + 4x + 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R 11 10 9 8 7 6 +--R 12960x - 101088x + 373140x - 1839240x + 4333230x - 14343030x +--R + +--R 5 4 3 2 +--R 22109160x - 51695280x + 32896640x - 39162240x + 13703680x +--R * +--R +-------+ +--R +-+ +-+ | 2 +--R \|2 \|3 \|3x + 2 +--R + +--R 11 10 9 8 7 +--R - 155520x + 1213056x - 3268080x + 12636000x - 29107080x +--R + +--R 6 5 4 3 2 +--R 84200220x - 85854960x + 162133920x - 86348800x + 78324480x +--R + +--R - 27407360x +--R * +--R +-+ +--R \|3 +--R / +--R +-------+ +--R 4 2 +-+ | 2 +--R (69120x + 245760x + 163840)\|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 17280x - 207360x - 368640x - 163840)\|2 \|3 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 | 2 +--R (263530260x + 936996480x + 624664320)\|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 65882565x - 790590780x - 1405494720x - 624664320)\|2 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|3 + 3x\|2 )\|3x + 2 + (- 3x - 2)\|2 \|3 - 6x +--R log(-----------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R +-------+ +--R 4 2 +-+ +--+ | 2 +--R (25798500x + 91728000x + 61152000)\|3 \|35 \|3x + 2 +--R + +--R 6 4 2 +-+ +-+ +--+ +--R (- 6449625x - 77395500x - 137592000x - 61152000)\|2 \|3 \|35 +--R * +--R log +--R +-------+ +--R 2 +-+ +--+ 2 | 2 +--R ((- 2x - 6x)\|2 \|35 + 35x + 24x + 36)\|3x + 2 +--R + +--R 3 2 +--+ 3 2 +-+ +--R (9x + 4x + 12x)\|35 + (- 18x - 62x - 24x - 36)\|2 +--R / +--R +-------+ +--R | 2 3 2 +-+ +--R (8x + 12)\|3x + 2 + (- 6x - 9x - 8x - 12)\|2 +--R + +--R +-------+ +--R 4 2 +-+ +--+ | 2 +--R (- 25798500x - 91728000x - 61152000)\|3 \|35 \|3x + 2 +--R + +--R 6 4 2 +-+ +-+ +--+ +--R (6449625x + 77395500x + 137592000x + 61152000)\|2 \|3 \|35 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R 4 2 x\|3 +--R (263530260x + 936996480x + 624664320)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +-+ +--R (56067336x + 199350528x + 132900352)\|2 \|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 6 4 2 +-+ x\|3 +--R (- 65882565x - 790590780x - 1405494720x - 624664320)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +--R (- 28033668x - 336404016x - 598051584x - 265800704)\|3 +--R / +--R +-------+ +--R 4 2 +-+ | 2 +--R (207360x + 737280x + 491520)\|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +-+ +--R (- 51840x - 622080x - 1105920x - 491520)\|2 \|3 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=-1/24*(310-153*x)*(2+3*x^2)^(3/2)-1/10*(34+x)*(2+3*x^2)^(5/2)/(3+2*x)+_ + 18543/32*asinh(x*sqrt(3/2))*sqrt(3)+5425/32*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))*sqrt(35)-7/16*(775-243*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R (- 162750x - 244125)\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 432x + 3672x - 10236x + 38916x - 179042x - 531978)\|3x + 2 +--R + +--R +-+ +--R +-+ x\|3 +--R (556290x + 834435)\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 960x + 1440 +--R Type: Expression(Integer) +--E 152 + 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\|3 +--R * +--R +-------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (- x\|2 \|3 + 2)\|3x + 2 + 2x\|3 + (- 3x - 2)\|2 +--R log(------------------------------------------------------) +--R +-------+ +--R | 2 +-+ +--R \|3x + 2 - \|2 +--R + +--R 11 10 9 8 7 6 +--R 11664x - 99144x + 416340x - 2240460x + 8399430x - 360450x +--R + +--R 5 4 3 2 +--R 25713720x + 91551600x - 30437760x + 92177280x - 44956160x +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 11 10 9 8 7 +--R - 139968x + 1189728x - 3907440x + 17632080x - 53524800x +--R + +--R 6 5 4 3 2 +--R - 84756780x - 31058640x - 321369120x + 128309760x - 184354560x +--R + +--R 89912320x +--R / +--R +-------+ +--R 5 4 3 2 | 2 +--R (103680x + 155520x + 368640x + 552960x + 245760x + 368640)\|3x + 2 +--R + +--R 7 6 5 4 3 2 +--R - 25920x - 38880x - 311040x - 466560x - 552960x - 829440x +--R + +--R - 245760x - 368640 +--R * +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 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8641624320)\|3 \|35 +--R * +--R +-+ +--R x\|3 +--R asinh(-----) +--R +-+ +--R \|2 +--R + +--R 6 4 2 +-+ +--+ +--R (- 559537578x - 6714450936x - 11936801664x - 5305245184)\|2 \|35 +--R / +--R +-------+ +--R 4 2 +-+ +--+ | 2 +--R (25924872960x + 92177326080x + 61451550720)\|2 \|35 \|3x + 2 +--R + +--R 6 4 2 +--+ +--R (- 12962436480x - 155549237760x - 276531978240x - 122903101440)\|35 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^8 +--R +--R +--R (1) +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R / +--R 8 7 6 5 4 3 2 +--R 256x + 3072x + 16128x + 48384x + 90720x + 108864x + 81648x +--R + +--R 34992x + 6561 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=5/84*(11+18*x)*(2+3*x^2)^(3/2)/(3+2*x)^6+1/14*(4+7*x)*_ + (2+3*x^2)^(5/2)/(3+2*x)^7-1107/600250*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)-1/56*(3-55*x)*sqrt(2+3*x^2)/(3+2*x)^5-_ + 193/7840*sqrt(2+3*x^2)/(3+2*x)^4-639/39200*sqrt(2+3*x^2)/(3+2*x)^3-_ + 2007/274400*sqrt(2+3*x^2)/(3+2*x)^2-27351/9604000*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 850176x + 8926848x + 40170816x + 100427040x + 150640560x +--R + +--R 2 +--R 135576504x + 67788252x + 14526054 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 656424x + 9455994x + 2997810x + 15015225x - 3488490x + 593639x +--R + +--R - 4499004 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R / +--R 7 6 5 4 +--R 460992000x + 4840416000x + 21781872000x + 54454680000x +--R + +--R 3 2 +--R 81682020000x + 73513818000x + 36756909000x + 7876480500 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 13 12 11 +--R 16734014208x + 175707149184x + 1058426398656x +--R + +--R 10 9 8 +--R 4788019815264x + 16210960055568x + 40543204485672x +--R + +--R 7 6 5 +--R 77205676804884x + 116597541408498x + 141766384866624x +--R + +--R 4 3 2 +--R 136940713519392x + 103667218018560x + 60769572596352x +--R + +--R 25301829482496x + 5421820603392 +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 13 12 11 +--R - 234276198912x - 2459900088576x - 12319023459456x +--R + +--R 10 9 8 +--R - 40793343135552x - 102214380201696x - 202446360761904x +--R + +--R 7 6 5 +--R - 319422330087192x - 406710599077692x - 424801317677184x +--R + +--R 4 3 2 +--R - 361986011843904x - 245287180260864x - 129671876097792x +--R + +--R - 50603658964992x - 10843641206784 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R 13 12 11 +--R - 10365705216x + 72045605520x - 3261343473540x +--R + +--R 10 9 8 +--R - 2827247202612x - 28076464341402x - 27272233384956x +--R + +--R 7 6 5 +--R - 88584658500374x - 71242777623504x - 125170088907168x +--R + +--R 4 3 2 +--R - 73616404324608x - 76587615704448x - 26222882374656x +--R + +--R - 16116095425536x +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 14 13 12 +--R - 38761180776x + 630926926218x + 292877336466x +--R + +--R 11 10 9 +--R 14008193844381x + 13587173899218x + 72279050075301x +--R + +--R 8 7 6 +--R 65531092137192x + 164321447142698x + 119079895199088x +--R + +--R 5 4 3 +--R 178078148847072x + 93283566105600x + 88674687273600x +--R + +--R 2 +--R 26222882374656x + 16116095425536x +--R * +--R +-+ +--+ +--R \|2 \|35 +--R / +--R 13 12 11 +--R 9073705536000x + 95273908128000x + 573911875152000x +--R + +--R 10 9 8 +--R 2596213996488000x + 8790089226156000x + 21983792676174000x +--R + +--R 7 6 5 +--R 41863331076903000x + 63222831283153500x + 76870164874608000x +--R + +--R 4 3 2 +--R 74253535040664000x + 56211605795520000x + 32951161653984000x +--R + +--R 13719442770432000x + 2939880593664000 +--R * +--R +-------+ +--R +-+ +--+ | 2 +--R \|2 \|35 \|3x + 2 +--R + +--R 13 12 11 +--R - 127031877504000x - 1333834713792000x - 6679759558752000x +--R + +--R 10 9 8 +--R - 22119425670384000x - 55423831721832000x - 109772744396868000x +--R + +--R 7 6 5 +--R - 173200771124514000x - 220531198822389000x - 230340551884128000x +--R + +--R 4 3 2 +--R - 196280129728368000x - 133002375746688000x - 70312144198464000x +--R + +--R - 27438885540864000x - 5879761187328000 +--R * +--R +--+ +--R \|35 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 6 4 2 +-+ | 2 +--R (65367243x + 1045875888x + 2324168640x + 1239556608)\|2 \|3x + 2 +--R + +--R 6 4 2 +--R - 915141402x - 4880754144x - 6507672192x - 2479113216 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R 6 4 2 +-+ +--R (- 65367243x - 1045875888x - 2324168640x - 1239556608)\|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 6 4 2 +--R 915141402x + 4880754144x + 6507672192x + 2479113216 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 6 4 2 +--+ | 2 +--R (- 40491036x - 647856576x - 1439681280x - 767830016)\|35 \|3x + 2 +--R + +--R 6 4 2 +-+ +--+ +--R (283437252x + 1511665344x + 2015553792x + 767830016)\|2 \|35 +--R / +--R 6 4 2 +-+ +--R (35444162250x + 567106596000x + 1260236880000x + 672126336000)\|2 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 4 2 +--+ +--R (- 496218271500x - 2646497448000x - 3528663264000x - 1344252672000)\|35 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(5-x)*(3+2*x)^4/sqrt(2+3*x^2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=343/3*asinh(x*sqrt(3/2))/sqrt(3)+16660/81*sqrt(2+3*x^2)+_ + 1477/270*(3+2*x)^2*sqrt(2+3*x^2)+19/30*(3+2*x)^3*sqrt(2+3*x^2)-_ + 1/15*(3+2*x)^4*sqrt(2+3*x^2)+49/81*(43+99*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 4 3 2 +-+ | 2 +--R (- 432x - 540x + 12264x + 58860x + 118513)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 46305asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 405\|3 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (15435x + 123480x + 109760)\|2 \|3x + 2 - 154350x - 411600x +--R + +--R - 219520 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 8 7 6 5 4 3 2 +--R 1440x + 1800x - 37040x - 191400x - 423000x - 520640x - 479520x +--R + +--R - 279040x +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R 10 9 8 7 6 5 4 +--R - 432x - 540x + 8520x + 54180x + 219425x + 503400x + 782640x +--R + +--R 3 2 +--R 729920x + 479520x + 279040x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 4 2 +-+ +--R (135x + 1080x + 960)\|2 \|3 \|3x + 2 + (- 1350x - 3600x - 1920)\|3 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ | 2 4 +--R (416745x + 3333960x + 2963520)\|2 \|3x + 2 - 4167450x +--R + +--R 2 +--R - 11113200x - 5927040 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (- 416745x - 3333960x - 2963520)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (2133234x + 17065872x + 15169664)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 4 2 x\|3 +--R (4167450x + 11113200x + 5927040)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +-+ +--R (- 10666170x - 28443120x - 15169664)\|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (3645x + 29160x + 25920)\|2 \|3 \|3x + 2 +--R + +--R 4 2 +-+ +--R (- 36450x - 97200x - 51840)\|3 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(5-x)*(3+2*x)^3/sqrt(2+3*x^2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=275/3*asinh(x*sqrt(3/2))/sqrt(3)+3305/54*sqrt(2+3*x^2)+_ + 31/36*(3+2*x)^2*sqrt(2+3*x^2)-1/12*(3+2*x)^3*sqrt(2+3*x^2)+_ + 5/54*(148+171*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 3 2 +-+ | 2 x\|3 +--R (- 18x + 12x + 585x + 2171)\|3 \|3x + 2 + 2475asinh(-----) +--R +-+ +--R \|2 +--R (2) -------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((3300x + 4400)\|2 \|3x + 2 - 2475x - 13200x - 8800) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 7 6 5 4 3 2 +-+ | 2 +--R (18x - 12x - 489x - 2235x - 3056x - 5832x - 2080x)\|3 \|3x + 2 +--R + +--R 7 6 5 4 3 2 +-+ +-+ +--R (- 72x + 48x + 2196x + 6609x + 4616x + 5832x + 2080x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 4 2 +-+ +--R (36x + 48)\|2 \|3 \|3x + 2 + (- 27x - 144x - 96)\|3 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((29700x + 39600)\|2 \|3x + 2 - 22275x - 118800x - 79200) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((- 29700x - 39600)\|2 asinh(-----) + (52104x + 69472)\|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 4 2 x\|3 +--R (22275x + 118800x + 79200)asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +-+ +--R (- 19539x - 104208x - 69472)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 4 2 +-+ +--R (324x + 432)\|2 \|3 \|3x + 2 + (- 243x - 1296x - 864)\|3 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(5-x)*(3+2*x)^2/sqrt(2+3*x^2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=127/3*asinh(x*sqrt(3/2))/sqrt(3)+359/27*sqrt(2+3*x^2)-_ + 1/9*(3+2*x)^2*sqrt(2+3*x^2)+1/27*(143+72*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 2 +-+ | 2 x\|3 +--R (- 12x + 36x + 475)\|3 \|3x + 2 + 1143asinh(-----) +--R +-+ +--R \|2 +--R (2) ----------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((381x + 1016)\|2 \|3x + 2 - 2286x - 2032) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 4 3 2 +-+ | 2 +--R (24x - 72x - 612x - 64x)\|3 \|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +-+ +--R (- 12x + 36x + 435x + 120x + 612x + 64x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 2 +-+ +--R (9x + 24)\|2 \|3 \|3x + 2 + (- 54x - 48)\|3 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((3429x + 9144)\|2 \|3x + 2 - 20574x - 18288) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 +-+ x\|3 2 +-+ | 2 +--R ((- 3429x - 9144)\|2 asinh(-----) + (2850x + 7600)\|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 2 x\|3 2 +-+ +-+ +--R (20574x + 18288)asinh(-----) + (- 8550x - 7600)\|2 \|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 2 +-+ +--R (81x + 216)\|2 \|3 \|3x + 2 + (- 486x - 432)\|3 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(5-x)*(3+2*x)/sqrt(2+3*x^2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=47/3*asinh(x*sqrt(3/2))/sqrt(3)+17/6*sqrt(2+3*x^2)-_ + 1/6*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R +-+ | 2 x\|3 +--R (- x + 7)\|3 \|3x + 2 + 47asinh(-----) +--R +-+ +--R \|2 +--R (2) ---------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 2 +--R (94\|2 \|3x + 2 - 141x - 188) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R (3x - 21x + 4x)\|3 \|3x + 2 + (- 6x + 21x - 4x)\|2 \|3 +--R / +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +--R 6\|2 \|3 \|3x + 2 + (- 9x - 12)\|3 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-+ | 2 2 +--R (94\|2 \|3x + 2 - 141x - 188) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +-+ +--R +-+ x\|3 +-+ | 2 2 x\|3 +--R (- 94\|2 asinh(-----) + 28\|3 )\|3x + 2 + (141x + 188)asinh(-----) +--R +-+ +-+ +--R \|2 \|2 +--R + +--R 2 +-+ +-+ +--R (- 21x - 28)\|2 \|3 +--R / +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +--R 6\|2 \|3 \|3x + 2 + (- 9x - 12)\|3 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(5-x)/sqrt(2+3*x^2) +--R +--R +--R - x + 5 +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=5*asinh(x*sqrt(3/2))/sqrt(3)-1/3*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R +-+ | 2 x\|3 +--R - \|3 \|3x + 2 + 15asinh(-----) +--R +-+ +--R \|2 +--R (2) --------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 +--R (5\|2 \|3x + 2 - 10) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 2 +-+ +-+ +--R - x \|2 \|3 +--R / +--R +-------+ +--R +-+ +-+ | 2 +-+ +--R \|2 \|3 \|3x + 2 - 2\|3 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-+ | 2 +--R (15\|2 \|3x + 2 - 30) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +-+ +--R +-+ x\|3 +-+ | 2 x\|3 +-+ +-+ +--R (- 15\|2 asinh(-----) - 2\|3 )\|3x + 2 + 30asinh(-----) + 2\|2 \|3 +--R +-+ +-+ +--R \|2 \|2 +--R / +--R +-------+ +--R +-+ +-+ | 2 +-+ +--R 3\|2 \|3 \|3x + 2 - 6\|3 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(5-x)/((3+2*x)*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------ +--R +-------+ +--R | 2 +--R (2x + 3)\|3x + 2 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=-1/2*asinh(x*sqrt(3/2))/sqrt(3)-13/2*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35) +--R +--R +--R +-+ +--R +-+ 9x - 4 +--+ x\|3 +--R 13\|3 atanh(---------------) - \|35 asinh(-----) +--R +-------+ +-+ +--R +--+ | 2 \|2 +--R \|35 \|3x + 2 +--R (2) ------------------------------------------------ +--R +-+ +--+ +--R 2\|3 \|35 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--R 13\|3 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R +--+ (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R \|35 log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R / +--R +-+ +--+ +--R 2\|3 \|35 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--R 13\|3 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R +--+ (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R \|35 log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R +-+ 9x - 4 +--+ x\|3 +--R - 13\|3 atanh(---------------) + \|35 asinh(-----) +--R +-------+ +-+ +--R +--+ | 2 \|2 +--R \|35 \|3x + 2 +--R / +--R +-+ +--+ +--R 2\|3 \|35 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(5-x)/((3+2*x)^2*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------- +--R +-------+ +--R 2 | 2 +--R (4x + 12x + 9)\|3x + 2 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=-41/35*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/35*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R +-------+ +--R 9x - 4 +--+ | 2 +--R (82x + 123)atanh(---------------) - 13\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R (2) ----------------------------------------------------- +--R +--+ +--R (70x + 105)\|35 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 +--R ((246x + 369)\|2 \|3x + 2 - 492x - 738) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +--+ | 2 2 +-+ +--+ +--R - 52x\|35 \|3x + 2 + (- 117x + 52x)\|2 \|35 +--R / +--R +-------+ +--R +-+ +--+ | 2 +--+ +--R (210x + 315)\|2 \|35 \|3x + 2 + (- 420x - 630)\|35 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-+ | 2 +--R (123\|2 \|3x + 2 - 246) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +-------+ +--R +-+ | 2 9x - 4 +--+ | 2 +--R (- 123\|2 \|3x + 2 + 246)atanh(---------------) - 26\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--+ +--R 26\|2 \|35 +--R / +--R +-------+ +--R +-+ +--+ | 2 +--+ +--R 105\|2 \|35 \|3x + 2 - 210\|35 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(5-x)/((3+2*x)^3*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------- +--R +-------+ +--R 3 2 | 2 +--R (8x + 36x + 54x + 27)\|3x + 2 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=-291/1225*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/70*sqrt(2+3*x^2)/(3+2*x)^2-281/2450*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 2 9x - 4 +--+ | 2 +--R (1164x + 3492x + 2619)atanh(---------------) + (- 281x - 649)\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R ----------------------------------------------------------------------------- +--R 2 +--+ +--R (4900x + 14700x + 11025)\|35 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 4 3 +--R (20952x + 62856x + 47142)\|2 \|3x + 2 - 31428x - 94284x +--R + +--R 2 +--R - 112617x - 125712x - 94284 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (7587x + 7139x - 21036x)\|35 \|3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (7788x + 8190x - 7139x + 21036x)\|2 \|35 +--R / +--R +-------+ +--R 2 +-+ +--+ | 2 +--R (88200x + 264600x + 198450)\|2 \|35 \|3x + 2 +--R + +--R 4 3 2 +--+ +--R (- 132300x - 396900x - 474075x - 529200x - 396900)\|35 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-+ | 2 2 +--R (5238\|2 \|3x + 2 - 7857x - 10476) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +-+ | 2 2 9x - 4 +--R (- 5238\|2 \|3x + 2 + 7857x + 10476)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R +--+ | 2 2 +-+ +--+ +--R - 2596\|35 \|3x + 2 + (1947x + 2596)\|2 \|35 +--R / +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R 22050\|2 \|35 \|3x + 2 + (- 33075x - 44100)\|35 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(5-x)/((3+2*x)^4*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------- +--R +-------+ +--R 4 3 2 | 2 +--R (16x + 96x + 216x + 216x + 81)\|3x + 2 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-57/1715*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/105*sqrt(2+3*x^2)/(3+2*x)^3-16/245*sqrt(2+3*x^2)/(3+2*x)^2-_ + 10/343*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 9x - 4 +--R (1368x + 6156x + 9234x + 4617)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (- 600x - 2472x - 2995)\|35 \|3x + 2 +--R / +--R 3 2 +--+ +--R (41160x + 185220x + 277830x + 138915)\|35 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (110808x + 498636x + 1043442x + 1703673x + 1994544x + 997272) +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 664848x - 2991816x - 5078700x - 4903254x - 3989088x - 1994544 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 5 4 3 2 +--+ | 2 +--R (- 143760x - 355320x - 152348x - 495540x - 1519776x)\|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R (- 145800x - 169416x + 726975x + 1292180x + 495540x + 1519776x) +--R * +--R +-+ +--+ +--R \|2 \|35 +--R / +--R 5 4 3 2 +--R 3333960x + 15002820x + 31394790x + 51259635x + 60011280x +--R + +--R 30005640 +--R * +--R +-------+ +--R +-+ +--+ | 2 +--R \|2 \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 20003760x - 90016920x - 152806500x - 147527730x - 120022560x +--R + +--R - 60011280 +--R * +--R +--+ +--R \|35 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((13851x + 36936)\|2 \|3x + 2 - 83106x - 73872) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 2 +-+ | 2 2 +--R ((- 13851x - 36936)\|2 \|3x + 2 + 83106x + 73872) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +--+ | 2 2 +-+ +--+ +--R (- 17970x - 47920)\|35 \|3x + 2 + (53910x + 47920)\|2 \|35 +--R / +--R +-------+ +--R 2 +-+ +--+ | 2 2 +--+ +--R (416745x + 1111320)\|2 \|35 \|3x + 2 + (- 2500470x - 2222640)\|35 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(5-x)/((3+2*x)^5*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------ +--R +-------+ +--R 5 4 3 2 | 2 +--R (32x + 240x + 720x + 1080x + 810x + 243)\|3x + 2 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=27/42875*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/140*sqrt(2+3*x^2)/(3+2*x)^4-97/2100*sqrt(2+3*x^2)/(3+2*x)^3-_ + 87/4900*sqrt(2+3*x^2)/(3+2*x)^2-991/171500*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 9x - 4 +--R (- 1296x - 7776x - 17496x - 17496x - 6561)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 5946x - 35892x - 79423x - 70389)\|35 \|3x + 2 +--R / +--R 4 3 2 +--+ +--R (2058000x + 12348000x + 27783000x + 27783000x + 10418625)\|35 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 15552x + 93312x + 230688x + 334368x + 358668x + 279936x +--R + +--R 104976 +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 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- 189035532000000x +--R + +--R - 56710659600000 +--R * +--R +--+ +--R \|35 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 +-+ | 2 4 +--R (43164819x + 345318552x + 306949824)\|2 \|3x + 2 - 431648190x +--R + +--R 2 +--R - 1151061840x - 613899648 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 + 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (- 70x - 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 4 2 +-+ | 2 4 +--R (43164819x + 345318552x + 306949824)\|2 \|3x + 2 - 431648190x +--R + +--R 2 +--R - 1151061840x - 613899648 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 4 2 +--+ | 2 +--R (- 61377462x - 491019696x - 436461952)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (306887310x + 818366160x + 436461952)\|2 \|35 +--R / +--R +-------+ +--R 4 2 +-+ +--+ | 2 +--R (16409334375x + 131274675000x + 116688600000)\|2 \|35 \|3x + 2 +--R + +--R 4 2 +--+ +--R (- 164093343750x - 437582250000x - 233377200000)\|35 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(5-x)*(3+2*x)^4/(2+3*x^2)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=880/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^4*(2+15*x)/sqrt(2+3*x^2)+_ + 1255/81*sqrt(2+3*x^2)-115/9*(3+2*x)*sqrt(2+3*x^2)-_ + 151/27*(3+2*x)^2*sqrt(2+3*x^2)-5/3*(3+2*x)^3*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R x\|3 | 2 +--R 47520asinh(-----)\|3x + 2 +--R +-+ +--R \|2 +--R + +--R 4 3 2 +-+ +--R (- 288x - 432x + 15024x - 14715x - 33914)\|3 +--R / +--R +-------+ +--R +-+ | 2 +--R 162\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 4 2 +--R (15840x + 84480x + 56320)\|2 \|3x + 2 - 126720x - 253440x +--R + +--R - 112640 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 6 5 4 3 2 +-+ | 2 +--R (256x + 384x - 24318x + 13592x - 47952x + 17440x)\|3 \|3x + 2 +--R + +--R 8 7 6 5 4 3 2 +--R - 96x - 144x + 4496x - 5673x + 60282x - 26672x + 47952x +--R + +--R - 17440x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 4 2 +-+ +--R (54x + 288x + 192)\|2 \|3 \|3x + 2 + (- 432x - 864x - 384)\|3 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 4 2 +-+ +--R ((570240x + 760320)\|3x + 2 + (- 213840x - 1140480x - 760320)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +--R 2 x\|3 2 +-+ +-+ +--R ((- 570240x - 760320)asinh(-----) + (- 203484x - 271312)\|2 \|3 ) +--R +-+ +--R \|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (213840x + 1140480x + 760320)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (152613x + 813936x + 542624)\|3 +--R / +--R +-------+ +--R 2 +-+ | 2 4 2 +-+ +-+ +--R (1944x + 2592)\|3 \|3x + 2 + (- 729x - 3888x - 2592)\|2 \|3 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(5-x)*(3+2*x)^3/(2+3*x^2)^(3/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=134/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^3*(2+15*x)/sqrt(2+3*x^2)-_ + 109/9*sqrt(2+3*x^2)-17/3*(3+2*x)*sqrt(2+3*x^2)-5/3*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 3 2 +-+ +--R 804asinh(-----)\|3x + 2 + (- 24x + 24x + 411x - 1426)\|3 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------- +--R +-------+ +--R +-+ | 2 +--R 18\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 4 2 +--R ((2412x + 2144)\|2 \|3x + 2 - 2412x - 8040x - 4288) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (24x - 24x - 347x - 2916x - 1096x)\|3 \|3x + 2 +--R + +--R 5 4 3 2 +-+ +-+ +--R (- 72x + 2211x + 1169x + 2916x + 1096x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 4 2 +-+ +--R (54x + 48)\|2 \|3 \|3x + 2 + (- 54x - 180x - 96)\|3 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 2 +-+ +--R ((2412x + 6432)\|3x + 2 + (- 7236x - 6432)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 x\|3 2 +-+ +-+ | 2 +--R ((- 2412x - 6432)asinh(-----) + (- 2139x - 5704)\|2 \|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 2 +-+ x\|3 2 +-+ +--R (7236x + 6432)\|2 asinh(-----) + (12834x + 11408)\|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 2 +-+ | 2 2 +-+ +-+ +--R (54x + 144)\|3 \|3x + 2 + (- 162x - 144)\|2 \|3 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(5-x)*(3+2*x)^2/(2+3*x^2)^(3/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=8/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^2*(2+15*x)/sqrt(2+3*x^2)-_ + 53/9*sqrt(2+3*x^2)-5/3*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 2 +-+ +--R 48asinh(-----)\|3x + 2 + (- 24x + 357x - 338)\|3 +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------- +--R +-------+ +--R +-+ | 2 +--R 18\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 +-+ | 2 2 +--R ((48x + 64)\|2 \|3x + 2 - 192x - 128) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 2 +-+ | 2 4 3 2 +-+ +-+ +--R (- 306x - 476x)\|3 \|3x + 2 + (- 24x + 357x + 306x + 476x)\|2 \|3 +--R / +--R +-------+ +--R 2 +-+ +-+ | 2 2 +-+ +--R (18x + 24)\|2 \|3 \|3x + 2 + (- 72x - 48)\|3 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | 2 2 +-+ +--R (96\|3x + 2 + (- 72x - 96)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 - 3x)\|3x + 2 + (- 3x - 2)\|3 + 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +-+ +--R x\|3 +-+ +-+ | 2 2 +-+ x\|3 +--R (- 96asinh(-----) - 338\|2 \|3 )\|3x + 2 + (72x + 96)\|2 asinh(-----) +--R +-+ +-+ +--R \|2 \|2 +--R + +--R 2 +-+ +--R (507x + 676)\|3 +--R / +--R +-------+ +--R +-+ | 2 2 +-+ +-+ +--R 36\|3 \|3x + 2 + (- 27x - 36)\|2 \|3 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(5-x)*(3+2*x)/(2+3*x^2)^(3/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-2/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)*(2+15*x)/sqrt(2+3*x^2)-_ + 5/3*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 +-+ +--R - 4asinh(-----)\|3x + 2 + (49x - 14)\|3 +--R +-+ +--R \|2 +--R (2) ------------------------------------------ +--R +-------+ +--R +-+ | 2 +--R 6\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 2 +--R (4\|2 \|3x + 2 - 12x - 8) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R +-+ | 2 2 +-+ +-+ +--R - 49x\|3 \|3x + 2 + (21x + 49x)\|2 \|3 +--R / +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +--R 6\|2 \|3 \|3x + 2 + (- 18x - 12)\|3 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | 2 +-+ +--R (4\|3x + 2 - 4\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +-+ +--R x\|3 +-+ +-+ | 2 +-+ x\|3 +-+ +--R (4asinh(-----) - 7\|2 \|3 )\|3x + 2 - 4\|2 asinh(-----) + 14\|3 +--R +-+ +-+ +--R \|2 \|2 +--R / +--R +-------+ +--R +-+ | 2 +-+ +-+ +--R 6\|3 \|3x + 2 - 6\|2 \|3 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(5-x)/(2+3*x^2)^(3/2) +--R +--R +--R - x + 5 +--R (1) ------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=1/6*(2+15*x)/sqrt(2+3*x^2) +--R +--R +--R 15x + 2 +--R (2) ----------- +--R +-------+ +--R | 2 +--R 6\|3x + 2 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 2 +-+ +--R - 5x\|3x + 2 + (- x + 5x)\|2 +--R (3) -------------------------------- +--R +-------+ +--R +-+ | 2 2 +--R 2\|2 \|3x + 2 - 6x - 4 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R (4) ------------------- +--R +-------+ +--R | 2 +-+ +--R 6\|3x + 2 - 6\|2 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(5-x)/((3+2*x)*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------ +--R +-------+ +--R 3 2 | 2 +--R (6x + 9x + 4x + 6)\|3x + 2 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=-26/35*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R | 2 9x - 4 +--+ +--R 52\|3x + 2 atanh(---------------) + (41x + 26)\|35 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R (2) ---------------------------------------------------- +--R +-------+ +--R +--+ | 2 +--R 70\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 2 2 +--R (52\|2 \|3x + 2 - 156x - 104) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R +--+ | 2 2 +-+ +--+ +--R - 41x\|35 \|3x + 2 + (- 39x + 41x)\|2 \|35 +--R / +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R 70\|2 \|35 \|3x + 2 + (- 210x - 140)\|35 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | 2 +-+ +--R (52\|3x + 2 - 52\|2 ) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +-------+ +--R | 2 +-+ 9x - 4 +-+ +--+ | 2 +--R (- 52\|3x + 2 + 52\|2 )atanh(---------------) + 13\|2 \|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +--+ +--R - 26\|35 +--R / +--R +-------+ +--R +--+ | 2 +-+ +--+ +--R 70\|35 \|3x + 2 - 70\|2 \|35 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(5-x)/((3+2*x)^2*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------- +--R +-------+ +--R 4 3 2 | 2 +--R (12x + 36x + 35x + 24x + 18)\|3x + 2 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=-632/1225*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)*sqrt(2+3*x^2))+19/1225*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R | 2 9x - 4 2 +--+ +--R (2528x + 3792)\|3x + 2 atanh(---------------) + (114x + 1435x + 986)\|35 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R --------------------------------------------------------------------------- +--R +-------+ +--R +--+ | 2 +--R (4900x + 7350)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 2 +-+ | 2 3 +--R (22752x + 34128x + 30336x + 45504)\|2 \|3x + 2 - 91008x +--R + +--R 2 +--R - 136512x - 60672x - 91008 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (5916x + 7506x - 9332x)\|35 \|3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (1026x + 1083x - 7506x + 9332x)\|2 \|35 +--R / +--R +-------+ +--R 3 2 +-+ +--+ | 2 +--R (44100x + 66150x + 58800x + 88200)\|2 \|35 \|3x + 2 +--R + +--R 3 2 +--+ +--R (- 176400x - 264600x - 117600x - 176400)\|35 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | 2 2 +-+ +--R (7584\|3x + 2 + (- 5688x - 7584)\|2 ) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R | 2 2 +-+ 9x - 4 +--R (- 7584\|3x + 2 + (5688x + 7584)\|2 )atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R 986\|2 \|35 \|3x + 2 + (- 1479x - 1972)\|35 +--R / +--R +-------+ +--R +--+ | 2 2 +-+ +--+ +--R 14700\|35 \|3x + 2 + (- 11025x - 14700)\|2 \|35 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(5-x)/((3+2*x)^3*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------- +--R +-------+ +--R 5 4 3 2 | 2 +--R (24x + 108x + 178x + 153x + 108x + 54)\|3x + 2 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=-1962/8575*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^2*sqrt(2+3*x^2))+9/245*sqrt(2+3*x^2)/(3+2*x)^2-_ + 331/8575*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 2 | 2 9x - 4 +--R (15696x + 47088x + 35316)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 3 2 +--+ +--R (- 3972x - 4068x + 7397x + 3658)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 +--R (68600x + 205800x + 154350)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (1271376x + 3814128x + 3990708x + 3390336x + 2542752)\|2 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 1271376x - 3814128x - 7098516x - 12713760x - 11795544x +--R + +--R - 6780672x - 5085504 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 5 4 3 2 +--+ | 2 +--R (107244x + 241524x + 481329x + 607484x - 181416x)\|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +--+ +--R (- 65844x - 519264x - 697137x - 345267x - 607484x + 181416x)\|2 \|35 +--R / +--R 4 3 2 +-+ +--+ +--R (5556600x + 16669800x + 17441550x + 14817600x + 11113200)\|2 \|35 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 5556600x - 16669800x - 31024350x - 55566000x - 51552900x +--R + +--R - 29635200x - 22226400 +--R * +--R +--+ +--R \|35 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 2 +-+ +--R ((105948x + 282528)\|3x + 2 + (- 317844x - 282528)\|2 ) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 2 | 2 2 +-+ +--R ((- 105948x - 282528)\|3x + 2 + (317844x + 282528)\|2 ) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +-+ +--+ | 2 2 +--+ +--R (5487x + 14632)\|2 \|35 \|3x + 2 + (- 32922x - 29264)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 2 +-+ +--+ +--R (463050x + 1234800)\|35 \|3x + 2 + (- 1389150x - 1234800)\|2 \|35 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(5-x)/((3+2*x)^4*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------- +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (48x + 288x + 680x + 840x + 675x + 432x + 162)\|3x + 2 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=-3312/42875*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^3*sqrt(2+3*x^2))+23/525*sqrt(2+3*x^2)/_ + (3+2*x)^3-27/1225*sqrt(2+3*x^2)/(3+2*x)^2-1051/42875*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 3 2 | 2 9x - 4 +--R (158976x + 715392x + 1073088x + 536544)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 4 3 2 +--+ +--R (- 75672x - 261036x - 237930x - 23349x - 29438)\|35 +--R / +--R +-------+ +--R 3 2 +--+ | 2 +--R (2058000x + 9261000x + 13891500x + 6945750)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 38631168x + 173840256x + 466793280x + 1057528224x +--R + +--R 3 2 +--R 1528077312x + 1313459712x + 927148032x + 463574016 +--R * +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 +--R + +--R 7 6 5 4 +--R - 309049344x - 1390722048x - 2704181760x - 3824485632x +--R + +--R 3 2 +--R - 4446876672x - 3322280448x - 1854296064x - 927148032 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R 7 6 5 4 3 +--R - 2119536x + 39497544x + 143540268x + 161536950x + 156825832x +--R + +--R 2 +--R 152583120x - 30695328x +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 8 7 6 5 4 +--R - 18388296x - 54953604x - 117736254x - 269792703x - 275974290x 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6438528x - 8584704)\|3x + 2 +--R + +--R 4 2 +-+ +--R (2414448x + 12877056x + 8584704)\|2 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +-+ +--+ | 2 +--R (- 176628x - 235504)\|2 \|35 \|3x + 2 +--R + +--R 4 2 +--+ +--R (132471x + 706512x + 471008)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 +--R (83349000x + 111132000)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 31255875x - 166698000x - 111132000)\|2 \|35 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(5-x)/((3+2*x)^5*(2+3*x^2)^(3/2)) +--R +--R +--R (1) +--R - x + 5 +--R -------------------------------------------------------------------------- +--R +-------+ +--R 7 6 5 4 3 2 | 2 +--R (96x + 720x + 2224x + 3720x + 3870x + 2889x + 1620x + 486)\|3x + 2 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=-30078/1500625*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^4*sqrt(2+3*x^2))+58/1225*sqrt(2+3*x^2)/_ + (3+2*x)^4-298/18375*sqrt(2+3*x^2)/(3+2*x)^3-708/42875*_ + sqrt(2+3*x^2)/(3+2*x)^2-14944/1500625*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 4 3 2 | 2 +--R (2887488x + 17324928x + 38981088x + 38981088x + 14617908)\|3x + 2 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 2151936x - 11467872x - 22188792x - 18957672x - 8562487x +--R + +--R - 4197366 +--R * +--R +--+ +--R \|35 +--R / +--R 4 3 2 +--+ +--R (144060000x + 864360000x + 1944810000x + 1944810000x + 729303750)\|35 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 +--R 389810880x + 2338865280x + 6301942560x + 11499420960x +--R + +--R 4 3 2 +--R 16561006956x + 17359577856x + 12746815776x + 7484368896x 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19448100000x + 116688600000x + 314410950000x + 573718950000x +--R + +--R 4 3 2 +--R 826247126250x + 866088720000x + 635952870000x + 373403520000x +--R + +--R 140026320000 +--R * +--R +-------+ +--R +-+ +--+ | 2 +--R \|2 \|35 \|3x + 2 +--R + +--R 10 9 8 7 +--R - 11668860000x - 70013160000x - 258659730000x - 764310330000x +--R + +--R 6 5 4 +--R - 1569542703750x - 2236531500000x - 2527658752500x +--R + +--R 3 2 +--R - 2292282720000x - 1481945220000x - 746807040000x - 280052640000 +--R * +--R +--+ +--R \|35 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 2 | 2 +--R (4872636x + 38981088x + 34649856)\|3x + 2 +--R + +--R 4 2 +-+ +--R (- 24363180x - 64968480x - 34649856)\|2 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 4 2 | 2 +--R (- 4872636x - 38981088x - 34649856)\|3x + 2 +--R + +--R 4 2 +-+ +--R (24363180x + 64968480x + 34649856)\|2 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 4 2 +-+ +--+ | 2 +--R (- 699561x - 5596488x - 4974656)\|2 \|35 \|3x + 2 +--R + +--R 4 2 +--+ +--R (6995610x + 18654960x + 9949312)\|35 +--R / +--R +-------+ +--R 4 2 +--+ | 2 +--R (243101250x + 1944810000x + 1728720000)\|35 \|3x + 2 +--R + +--R 4 2 +-+ +--+ +--R (- 1215506250x - 3241350000x - 1728720000)\|2 \|35 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(5-x)*(3+2*x)^4/(2+3*x^2)^(5/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=1/18*(3+2*x)^4*(2+15*x)/(2+3*x^2)^(3/2)-16/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 1/18*(3+2*x)^3*(20+37*x)/sqrt(2+3*x^2)-2027/81*sqrt(2+3*x^2)-_ + 19/3*(3+2*x)*sqrt(2+3*x^2)-37/27*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 x\|3 | 2 +--R (- 864x - 576)asinh(-----)\|3x + 2 +--R +-+ +--R \|2 +--R + +--R 4 3 2 +-+ +--R (- 864x + 57285x - 16560x + 33381x - 25342)\|3 +--R / +--R +-------+ +--R 2 +-+ | 2 +--R (486x + 324)\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 6 4 2 +-+ | 2 6 4 +--R (864x + 5184x + 6144x + 2048)\|2 \|3x + 2 - 6912x - 18432x +--R + +--R 2 +--R - 15360x - 4096 +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R 6 5 4 3 2 +-+ +--R (- 35709x - 152760x - 180846x - 292696x - 143856x - 118688x)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 8 7 6 5 4 3 +--R - 864x + 57285x + 130884x + 338901x + 288738x + 381712x +--R + +--R 2 +--R 143856x + 118688x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +-------+ +--R 6 4 2 +-+ +-+ | 2 +--R (486x + 2916x + 3456x + 1152)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 3888x - 10368x - 8640x - 2304)\|3 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 4 2 +-+ +--R ((6912x + 9216)\|3x + 2 + (- 2592x - 13824x - 9216)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 x\|3 2 +-+ +-+ | 2 +--R ((6912x + 9216)asinh(-----) + (- 152052x - 202736)\|2 \|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 4 2 +-+ x\|3 +--R (- 2592x - 13824x - 9216)\|2 asinh(-----) +--R +-+ +--R \|2 +--R + +--R 4 2 +-+ +--R (114039x + 608208x + 405472)\|3 +--R / +--R +-------+ +--R 2 +-+ | 2 4 2 +-+ +-+ +--R (3888x + 5184)\|3 \|3x + 2 + (- 1458x - 7776x - 5184)\|2 \|3 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(5-x)*(3+2*x)^3/(2+3*x^2)^(5/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=1/18*(3+2*x)^3*(2+15*x)/(2+3*x^2)^(3/2)-8/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 1/18*(3+2*x)^2*(10+39*x)/sqrt(2+3*x^2)-157/27*sqrt(2+3*x^2)-_ + 13/9*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 x\|3 | 2 3 2 +-+ +--R (- 144x - 96)asinh(-----)\|3x + 2 + (4971x - 72x + 3741x - 1490)\|3 +--R +-+ +--R \|2 +--R ------------------------------------------------------------------------- +--R +-------+ +--R 2 +-+ | 2 +--R (162x + 108)\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 6 4 2 +--R ((864x + 1344x + 512)\|2 \|3x + 2 - 864x - 3456x - 3456x - 1024) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 9942x - 13266x - 33994x - 17496x - 19952x)\|3 \|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +-+ +--R (6705x + 29826x + 26388x + 48958x + 17496x + 19952x)\|2 \|3 +--R / +--R +-------+ +--R 4 2 +-+ +-+ | 2 +--R (972x + 1512x + 576)\|2 \|3 \|3x + 2 +--R + +--R 6 4 2 +-+ +--R (- 972x - 3888x - 3888x - 1152)\|3 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 2 +-+ +--R ((288x + 768)\|3x + 2 + (- 864x - 768)\|2 ) +--R * +--R +-------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|2 \|3 + 3x)\|3x + 2 + (- 3x - 2)\|3 - 3x\|2 +--R log(----------------------------------------------------) +--R +-------+ +--R +-+ | 2 +--R \|2 \|3x + 2 - 2 +--R + +--R +-+ +-------+ +--R 2 x\|3 2 +-+ +-+ | 2 +--R ((288x + 768)asinh(-----) + (- 2235x - 5960)\|2 \|3 )\|3x + 2 +--R +-+ +--R \|2 +--R + +--R +-+ +--R 2 +-+ x\|3 2 +-+ +--R (- 864x - 768)\|2 asinh(-----) + (13410x + 11920)\|3 +--R +-+ +--R \|2 +--R / +--R +-------+ +--R 2 +-+ | 2 2 +-+ +-+ +--R (324x + 864)\|3 \|3x + 2 + (- 972x - 864)\|2 \|3 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(5-x)*(3+2*x)^2/(2+3*x^2)^(5/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=1/18*(3+2*x)^2*(2+15*x)/(2+3*x^2)^(3/2)-41/54*(4-9*x)/sqrt(2+3*x^2) +--R +--R +--R 3 2 +--R 1287x + 72x + 1215x - 274 +--R (2) --------------------------- +--R +-------+ +--R 2 | 2 +--R (162x + 108)\|3x + 2 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 858x - 870x - 3098x - 1224x - 2160x)\|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +--R (411x + 2574x + 1788x + 4718x + 1224x + 2160x)\|2 +--R / +--R +-------+ +--R 4 2 +-+ | 2 6 4 2 +--R (324x + 504x + 192)\|2 \|3x + 2 - 324x - 1296x - 1296x - 384 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R +-------+ +--R 2 +-+ | 2 2 +--R (- 411x - 1096)\|2 \|3x + 2 + 2466x + 2192 +--R (4) ---------------------------------------------- +--R +-------+ +--R 2 | 2 2 +-+ +--R (324x + 864)\|3x + 2 + (- 972x - 864)\|2 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(5-x)*(3+2*x)/(2+3*x^2)^(5/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=1/18*(3+2*x)*(2+15*x)/(2+3*x^2)^(3/2)+1/18*(-10+43*x)/sqrt(2+3*x^2) +--R +--R +--R 3 +--R 129x + 135x - 14 +--R (2) --------------------- +--R +-------+ +--R 2 | 2 +--R (54x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 258x - 126x - 958x - 168x - 720x)\|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +--R (63x + 774x + 252x + 1498x + 168x + 720x)\|2 +--R / +--R +-------+ +--R 4 2 +-+ | 2 6 4 2 +--R (324x + 504x + 192)\|2 \|3x + 2 - 324x - 1296x - 1296x - 384 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R +-------+ +--R 2 +-+ | 2 2 +--R (- 21x - 56)\|2 \|3x + 2 + 126x + 112 +--R (4) --------------------------------------------- +--R +-------+ +--R 2 | 2 2 +-+ +--R (108x + 288)\|3x + 2 + (- 324x - 288)\|2 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(5-x)/(2+3*x^2)^(5/2) +--R +--R +--R - x + 5 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=1/18*(2+15*x)/(2+3*x^2)^(3/2)+5/6*x/sqrt(2+3*x^2) +--R +--R +--R 3 +--R 45x + 45x + 2 +--R (2) --------------------- +--R +-------+ +--R 2 | 2 +--R (54x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 30x + 6x - 110x + 8x - 80x)\|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +--R (- 3x + 90x - 12x + 170x - 8x + 80x)\|2 +--R / +--R +-------+ +--R 4 2 +-+ | 2 6 4 2 +--R (108x + 168x + 64)\|2 \|3x + 2 - 108x - 432x - 432x - 128 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R +-------+ +--R 2 +-+ | 2 2 +--R (3x + 8)\|2 \|3x + 2 - 18x - 16 +--R (4) --------------------------------------------- +--R +-------+ +--R 2 | 2 2 +-+ +--R (108x + 288)\|3x + 2 + (- 324x - 288)\|2 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(5-x)/((3+2*x)*(2+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------- +--R +-------+ +--R 5 4 3 2 | 2 +--R (18x + 27x + 24x + 36x + 8x + 12)\|3x + 2 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=1/210*(26+41*x)/(2+3*x^2)^(3/2)-104/1225*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)+1/7350*(312+2137*x)/sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 2 | 2 9x - 4 +--R (1872x + 1248)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 3 2 +--+ +--R (6411x + 936x + 5709x + 1534)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 +--R (22050x + 14700)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 4 2 +-+ | 2 6 4 +--R (11232x + 17472x + 6656)\|2 \|3x + 2 - 11232x - 44928x +--R + +--R 2 +--R - 44928x - 13312 +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 5 4 3 2 +--+ | 2 +--R (- 12822x + 11934x - 45610x + 13416x - 30448x)\|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +-+ +--+ +--R (- 6903x + 38466x - 21996x + 68446x - 13416x + 30448x)\|2 \|35 +--R / +--R +-------+ +--R 4 2 +-+ +--+ | 2 +--R (132300x + 205800x + 78400)\|2 \|35 \|3x + 2 +--R + +--R 6 4 2 +--+ +--R (- 132300x - 529200x - 529200x - 156800)\|35 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 2 | 2 2 +-+ +--R ((3744x + 9984)\|3x + 2 + (- 11232x - 9984)\|2 ) +--R * +--R log +--R +-------+ +--R +-+ +--+ | 2 2 +--+ +--R ((6x + 9)\|2 \|35 - 105x)\|3x + 2 + (- 35x - 12x - 18)\|35 +--R + +--R 2 +-+ +--R (70x + 105x)\|2 +--R / +--R +-------+ +--R +-+ | 2 +--R (2x + 3)\|2 \|3x + 2 - 4x - 6 +--R + +--R +-------+ +--R 2 | 2 2 +-+ +--R ((- 3744x - 9984)\|3x + 2 + (11232x + 9984)\|2 ) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +-+ +--+ | 2 2 +--+ +--R (2301x + 6136)\|2 \|35 \|3x + 2 + (- 13806x - 12272)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 2 +-+ +--+ +--R (44100x + 117600)\|35 \|3x + 2 + (- 132300x - 117600)\|2 \|35 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(5-x)/((3+2*x)^2*(2+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------- +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (36x + 108x + 129x + 144x + 124x + 48x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=1/210*(26+41*x)/((3+2*x)*(2+3*x^2)^(3/2))-176/1715*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/1470*(34+507*x)/((3+2*x)*_ + sqrt(2+3*x^2))+277/5145*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 3 2 | 2 9x - 4 +--R (6336x + 9504x + 4224x + 6336)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 4 3 2 +--+ +--R (4986x + 10647x + 7362x + 9107x + 3966)\|35 +--R / +--R +-------+ +--R 3 2 +--+ | 2 +--R (61740x + 92610x + 41160x + 61740)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R 57024x + 85536x + 342144x + 513216x + 405504x + 608256x +--R + +--R 135168x + 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+--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(A+B*x)*(a+c*x^2)*sqrt(d+e*x) +--R +--R +--R 3 2 +-------+ +--R (1) (B c x + A c x + B a x + A a)\|e x + d +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-2/3*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(3/2)/e^4+2/5*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^4-2/7*c*(3*B*d-A*e)*_ + (d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B c e x + (90A c e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126B a e + 18A c d e - 12B c d e )x +--R + +--R 4 3 2 2 3 3 +--R (210A a e + 42B a d e - 24A c d e + 16B c d e)x + 210A a d e +--R + +--R 2 2 3 4 +--R - 84B a d e + 48A c d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 3 +--R 70B c e x + (90A c e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126B a e + 18A c d e - 12B c d e )x +--R + +--R 4 3 2 2 3 3 +--R (210A a e + 42B a d e - 24A c d e + 16B c d e)x + 210A a d e +--R + +--R 2 2 3 4 +--R - 84B a d e + 48A c d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(A+B*x)*(a+c*x^2)/sqrt(d+e*x) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=2/3*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^4-_ + 2/5*c*(3*B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-_ + 2*(B*d-A*e)*(c*d^2+a*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + (42A c e - 36B c d e )x +--R + +--R 3 2 2 3 2 +--R (70B a e - 56A c d e + 48B c d e)x + 210A a e - 140B a d e +--R + +--R 2 3 +--R 112A c d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B c e x + (42A c e - 36B c d e )x +--R + +--R 3 2 2 3 2 +--R (70B a e - 56A c d e + 48B c d e)x + 210A a e - 140B a d e +--R + +--R 2 3 +--R 112A c d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=-2/3*c*(3*B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*sqrt(d+e*x))+2*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 6B c e x + (10A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (30B a e - 40A c d e + 48B c d e)x - 30A a e + 60B a d e - 80A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 6B c e x + (10A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (30B a e - 40A c d e + 48B c d e)x - 30A a e + 60B a d e - 80A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^(3/2))+2/3*B*c*_ + (d+e*x)^(3/2)/e^4-2*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^4*sqrt(d+e*x))-_ + 2*c*(3*B*d-A*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 2B c e x + (6A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 6B a e + 24A c d e - 48B c d e)x - 2A a e - 4B a d e + 16A c d e +--R + +--R 3 +--R - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 2B c e x + (6A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 6B a e + 24A c d e - 48B c d e)x - 2A a e - 4B a d e + 16A c d e +--R + +--R 3 +--R - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^(5/2))-2/3*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^4*(d+e*x)^(3/2))+2*c*(3*B*d-A*e)/_ + (e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + (- 30A c e + 180B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 10B a e - 40A c d e + 240B c d e)x - 6A a e - 4B a d e - 16A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B c e x + (- 30A c e + 180B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 10B a e - 40A c d e + 240B c d e)x - 6A a e - 4B a d e - 16A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(A+B*x)*(a+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +-------+ +--R (1) (B c x + A c x + 2B a c x + 2A a c x + B a x + A a )\|e x + d +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-2/3*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^(3/2)/e^6+2/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^6-4/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(7/2)/e^6+4/9*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(9/2)/e^6-2/11*c^2*(5*B*d-A*e)*_ + (d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + (8190A c e + 630B c d e )x +--R + +--R 6 2 5 2 2 4 4 +--R (20020B a c e + 910A c d e - 700B c d e )x +--R + +--R 6 5 2 2 4 2 3 3 3 +--R (25740A a c e + 2860B a c d e - 1040A c d e + 800B c d e )x +--R + +--R 2 6 5 2 4 2 3 3 +--R 18018B a e + 5148A a c d e - 3432B a c d e + 1248A c d e +--R + +--R 2 4 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 2 4 3 3 +--R 30030A a e + 6006B a d e - 6864A a c d e + 4576B a c d e +--R + +--R 2 4 2 2 5 +--R - 1664A c d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 30030A a d e - 12012B a d e + 13728A a c d e - 9152B a c d e +--R + +--R 2 5 2 6 +--R 3328A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + (8190A c e + 630B c d e )x +--R + +--R 6 2 5 2 2 4 4 +--R (20020B a c e + 910A c d e - 700B c d e )x +--R + +--R 6 5 2 2 4 2 3 3 3 +--R (25740A a c e + 2860B a c d e - 1040A c d e + 800B c d e )x +--R + +--R 2 6 5 2 4 2 3 3 +--R 18018B a e + 5148A a c d e - 3432B a c d e + 1248A c d e +--R + +--R 2 4 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 2 4 3 3 +--R 30030A a e + 6006B a d e - 6864A a c d e + 4576B a c d e +--R + +--R 2 4 2 2 5 +--R - 1664A c d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 30030A a d e - 12012B a d e + 13728A a c d e - 9152B a c d e +--R + +--R 2 5 2 6 +--R 3328A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(A+B*x)*(a+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=2/3*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^6-_ + 4/5*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(5/2)/e^6+_ + 4/7*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(7/2)/e^6-_ + 2/9*c^2*(5*B*d-A*e)*(d+e*x)^(9/2)/e^6+2/11*B*c^2*_ + (d+e*x)^(11/2)/e^6-2*(B*d-A*e)*(c*d^2+a*e^2)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + (770A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (1980B a c e - 880A c d e + 800B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (2772A a c e - 2376B a c d e + 1056A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 2310B a e - 3696A a c d e + 3168B a c d e - 1408A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R 6930A a e - 4620B a d e + 7392A a c d e - 6336B a c d e +--R + +--R 2 4 2 5 +--R 2816A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + (770A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (1980B a c e - 880A c d e + 800B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (2772A a c e - 2376B a c d e + 1056A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 2310B a e - 3696A a c d e + 3168B a c d e - 1408A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R 6930A a e - 4620B a d e + 7392A a c d e - 6336B a c d e +--R + +--R 2 4 2 5 +--R 2816A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-4/3*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3/2)/e^6+_ + 4/5*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^6-_ + 2/7*c^2*(5*B*d-A*e)*(d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*sqrt(d+e*x))+2*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (90A c e - 100B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (252B a c e - 144A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 504B a c d e + 288A c d e - 320B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 630B a e - 1680A a c d e + 2016B a c d e - 1152A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R - 630A a e + 1260B a d e - 3360A a c d e + 4032B a c d e +--R + +--R 2 4 2 5 +--R - 2304A c d e + 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (90A c e - 100B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (252B a c e - 144A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 504B a c d e + 288A c d e - 320B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 630B a e - 1680A a c d e + 2016B a c d e - 1152A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R - 630A a e + 1260B a d e - 3360A a c d e + 4032B a c d e +--R + +--R 2 4 2 5 +--R - 2304A c d e + 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(3/2))+4/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^6-2/5*c^2*(5*B*d-A*e)*_ + (d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-2*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*sqrt(d+e*x))-4*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + (42A c e - 60B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (140B a c e - 112A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 840B a c d e + 672A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 210B a e + 1680A a c d e - 3360B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 3840B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 70A a e - 140B a d e + 1120A a c d e - 2240B a c d e + 1792A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + (42A c e - 60B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (140B a c e - 112A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 840B a c d e + 672A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 210B a e + 1680A a c d e - 3360B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 3840B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 70A a e - 140B a d e + 1120A a c d e - 2240B a c d e + 1792A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(5/2))-2/3*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^(3/2))-2/3*c^2*_ + (5*B*d-A*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6+4*c*_ + (5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*sqrt(d+e*x))+4*c*_ + (5*B*c*d^2-2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + (10A c e - 20B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (60B a c e - 80A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 60A a c e + 360B a c d e - 480A c d e + 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 10B a e - 80A a c d e + 480B a c d e - 640A c d e + 1280B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 6A a e - 4B a d e - 32A a c d e + 192B a c d e - 256A c d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + (10A c e - 20B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (60B a c e - 80A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 60A a c e + 360B a c d e - 480A c d e + 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 10B a e - 80A a c d e + 480B a c d e - 640A c d e + 1280B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 6A a e - 4B a d e - 32A a c d e + 192B a c d e - 256A c d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(9/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=2/7*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(7/2))-2/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^(5/2))+4/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^(3/2))+2/3*B*c^2*_ + (d+e*x)^(3/2)/e^6-4*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*_ + sqrt(d+e*x))-2*c^2*(5*B*d-A*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (210A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 420B a c e + 1680A c d e - 5600B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 140A a c e - 840B a c d e + 3360A c d e - 11200B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 42B a e - 112A a c d e - 672B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 8960B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 30A a e - 12B a d e - 32A a c d e - 192B a c d e + 768A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 9 3 8 2 2 7 3 6 +-------+ +--R (105e x + 315d e x + 315d e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (210A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 420B a c e + 1680A c d e - 5600B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 140A a c e - 840B a c d e + 3360A c d e - 11200B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 42B a e - 112A a c d e - 672B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 8960B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 30A a e - 12B a d e - 32A a c d e - 192B a c d e + 768A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 9 3 8 2 2 7 3 6 +-------+ +--R (105e x + 315d e x + 315d e x + 105d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=2/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^8-_ + 6/5*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*_ + (d+e*x)^(5/2)/e^8-2/7*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+_ + 30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(7/2)/e^8-2/9*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(9/2)/e^8+6/11*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(11/2)/e^8-2/13*c^3*_ + (7*B*d-A*e)*(d+e*x)^(13/2)/e^8+2/15*B*c^3*(d+e*x)^(15/2)/e^8-_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^3*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 6006B c e x + (6930A c e - 6468B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (24570B a c e - 7560A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30030A a c e - 27300B a c d e + 8400A c d e - 7840B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 38610B a c e - 34320A a c d e + 31200B a c d e - 9600A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 54054A a c e - 46332B a c d e + 41184A a c d e - 37440B a c d e +--R + +--R 3 4 3 3 5 2 +--R 11520A c d e - 10752B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 72072A a c d e + 61776B a c d e - 54912A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 49920B a c d e - 15360A c d e + 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 90090A a e - 60060B a d e + 144144A a c d e - 123552B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 109824A a c d e - 99840B a c d e + 30720A c d e - 28672B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 6006B c e x + (6930A c e - 6468B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (24570B a c e - 7560A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30030A a c e - 27300B a c d e + 8400A c d e - 7840B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 38610B a c e - 34320A a c d e + 31200B a c d e - 9600A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 54054A a c e - 46332B a c d e + 41184A a c d e - 37440B a c d e +--R + +--R 3 4 3 3 5 2 +--R 11520A c d e - 10752B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 72072A a c d e + 61776B a c d e - 54912A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 49920B a c d e - 15360A c d e + 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 90090A a e - 60060B a d e + 144144A a c d e - 123552B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 109824A a c d e - 99840B a c d e + 30720A c d e - 28672B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=-2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*_ + (d+e*x)^(3/2)/e^8-2/5*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+_ + 30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(5/2)/e^8-2/7*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(7/2)/e^8+2/3*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(9/2)/e^8-2/11*c^3*_ + (7*B*d-A*e)*(d+e*x)^(11/2)/e^8+2/13*B*c^3*(d+e*x)^(13/2)/e^8+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*sqrt(d+e*x))+2*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 2310B c e x + (2730A c e - 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (10010B a c e - 3640A c d e + 3920B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (12870A a c e - 14300B a c d e + 5200A c d e - 5600B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 18018B a c e - 20592A a c d e + 22880B a c d e - 8320A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 30030A a c e - 36036B a c d e + 41184A a c d e - 45760B a c d e +--R + +--R 3 4 3 3 5 2 +--R 16640A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 120120A a c d e + 144144B a c d e - 164736A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 183040B a c d e - 66560A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 30030A a e + 60060B a d e - 240240A a c d e + 288288B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 329472A a c d e + 366080B a c d e - 133120A c d e + 143360B c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 2310B c e x + (2730A c e - 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (10010B a c e - 3640A c d e + 3920B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (12870A a c e - 14300B a c d e + 5200A c d e - 5600B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 18018B a c e - 20592A a c d e + 22880B a c d e - 8320A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 30030A a c e - 36036B a c d e + 41184A a c d e - 45760B a c d e +--R + +--R 3 4 3 3 5 2 +--R 16640A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 120120A a c d e + 144144B a c d e - 164736A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 183040B a c d e - 66560A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 30030A a e + 60060B a d e - 240240A a c d e + 288288B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 329472A a c d e + 366080B a c d e - 133120A c d e + 143360B c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(3/2))-2/3*c*(4*A*c*d*e*_ + (5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*_ + (d+e*x)^(3/2)/e^8-2/5*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)*(d+e*x)^(5/2)/e^8+6/7*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*_ + (d+e*x)^(7/2)/e^8-2/9*c^3*(7*B*d-A*e)*(d+e*x)^(9/2)/e^8+_ + 2/11*B*c^3*(d+e*x)^(11/2)/e^8-2*(c*d^2+a*e^2)^2*(7*B*c*d^2-_ + 6*A*c*d*e+a*B*e^2)/(e^8*sqrt(d+e*x))-6*c*(c*d^2+a*e^2)*(7*B*c*d^3-_ + 5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 630B c e x + (770A c e - 980B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (2970B a c e - 1320A c d e + 1680B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (4158A a c e - 5940B a c d e + 2640A c d e - 3360B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 6930B a c e - 11088A a c d e + 15840B a c d e - 7040A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 20790A a c e - 41580B a c d e + 66528A a c d e - 95040B a c d e +--R + +--R 3 4 3 3 5 2 +--R 42240A c d e - 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6930B a e + 83160A a c d e - 166320B a c d e + 266112A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 380160B a c d e + 168960A c d e - 215040B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 2310A a e - 4620B a d e + 55440A a c d e - 110880B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 177408A a c d e - 253440B a c d e + 112640A c d e - 143360B c d +--R / +--R 9 8 +-------+ +--R (3465e x + 3465d e )\|e x + d +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 630B c e x + (770A c e - 980B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (2970B a c e - 1320A c d e + 1680B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (4158A a c e - 5940B a c d e + 2640A c d e - 3360B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 6930B a c e - 11088A a c d e + 15840B a c d e - 7040A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 20790A a c e - 41580B a c d e + 66528A a c d e - 95040B a c d e +--R + +--R 3 4 3 3 5 2 +--R 42240A c d e - 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6930B a e + 83160A a c d e - 166320B a c d e + 266112A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 380160B a c d e + 168960A c d e - 215040B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 2310A a e - 4620B a d e + 55440A a c d e - 110880B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 177408A a c d e - 253440B a c d e + 112640A c d e - 143360B c d +--R / +--R 9 8 +-------+ +--R (3465e x + 3465d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(5/2))-2/3*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(3/2))-2/3*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(3/2)/e^8+6/5*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^8-2/7*c^3*(7*B*d-A*e)*_ + (d+e*x)^(7/2)/e^8+2/9*B*c^3*(d+e*x)^(9/2)/e^8+6*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*sqrt(d+e*x))-_ + 2*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 70B c e x + (90A c e - 140B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (378B a c e - 216A c d e + 336B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (630A a c e - 1260B a c d e + 720A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 1890B a c e - 5040A a c d e + 10080B a c d e - 5760A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 1890A a c e + 11340B a c d e - 30240A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 34560A c d e + 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 210B a e - 2520A a c d e + 15120B a c d e - 40320A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 80640B a c d e - 46080A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 126A a e - 84B a d e - 1008A a c d e + 6048B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 16128A a c d e + 32256B a c d e - 18432A c d e + 28672B c d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 70B c e x + (90A c e - 140B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (378B a c e - 216A c d e + 336B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (630A a c e - 1260B a c d e + 720A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 1890B a c e - 5040A a c d e + 10080B a c d e - 5760A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 1890A a c e + 11340B a c d e - 30240A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 34560A c d e + 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 210B a e - 2520A a c d e + 15120B a c d e - 40320A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 80640B a c d e - 46080A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 126A a e - 84B a d e - 1008A a c d e + 6048B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 16128A a c d e + 32256B a c d e - 18432A c d e + 28672B c d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(9/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=2/7*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(7/2))-2/5*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(5/2))+2*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^(3/2))+_ + 2*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^8-2/5*c^3*_ + (7*B*d-A*e)*(d+e*x)^(5/2)/e^8+2/7*B*c^3*(d+e*x)^(7/2)/e^8+2*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))/(e^8*sqrt(d+e*x))-2*c^2*(35*B*c*d^3-15*A*c*d^2*e+_ + 15*a*B*d*e^2-3*a*A*e^3)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (14A c e - 28B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (70B a c e - 56A c d e + 112B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (210A a c e - 700B a c d e + 560A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 210B a c e + 1680A a c d e - 5600B a c d e + 4480A c d e +--R + +--R 3 4 3 +--R - 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 70A a c e - 420B a c d e + 3360A a c d e - 11200B a c d e +--R + +--R 3 4 3 3 5 2 +--R 8960A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 14B a e - 56A a c d e - 336B a c d e + 2688A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 8960B a c d e + 7168A c d e - 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 4B a d e - 16A a c d e - 96B a c d e + 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 2560B a c d e + 2048A c d e - 4096B c d +--R / +--R 11 3 10 2 2 9 3 8 +-------+ +--R (35e x + 105d e x + 105d e x + 35d e )\|e x + d +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (14A c e - 28B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (70B a c e - 56A c d e + 112B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (210A a c e - 700B a c d e + 560A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 210B a c e + 1680A a c d e - 5600B a c d e + 4480A c d e +--R + +--R 3 4 3 +--R - 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 70A a c e - 420B a c d e + 3360A a c d e - 11200B a c d e +--R + +--R 3 4 3 3 5 2 +--R 8960A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 14B a e - 56A a c d e - 336B a c d e + 2688A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 8960B a c d e + 7168A c d e - 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 4B a d e - 16A a c d e - 96B a c d e + 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 2560B a c d e + 2048A c d e - 4096B c d +--R / +--R 11 3 10 2 2 9 3 8 +-------+ +--R (35e x + 105d e x + 105d e x + 35d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(11/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=2/9*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(9/2))-2/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(7/2))+6/5*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^(5/2))+_ + 2/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))/(e^8*(d+e*x)^(3/2))-2/3*c^3*(7*B*d-A*e)*(d+e*x)^(3/2)/_ + e^8+2/5*B*c^3*(d+e*x)^(5/2)/e^8+2*c^2*(35*B*c*d^3-15*A*c*d^2*e+_ + 15*a*B*d*e^2-3*a*A*e^3)/(e^8*sqrt(d+e*x))+6*c^2*(7*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 126B c e x + (210A c e - 588B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (1890B a c e - 2520A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 1890A a c e + 18900B a c d e - 25200A c d e + 70560B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 630B a c e - 5040A a c d e + 50400B a c d e - 67200A c d e +--R + +--R 3 4 3 +--R 188160B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 378A a c e - 756B a c d e - 6048A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 80640A c d e + 225792B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 90B a e - 216A a c d e - 432B a c d e - 3456A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 34560B a c d e - 46080A c d e + 129024B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 70A a e - 20B a d e - 48A a c d e - 96B a c d e - 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 7680B a c d e - 10240A c d e + 28672B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +-------+ +--R (315e x + 1260d e x + 1890d e x + 1260d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 7 3 6 6 +--R 126B c e x + (210A c e - 588B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (1890B a c e - 2520A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 1890A a c e + 18900B a c d e - 25200A c d e + 70560B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 630B a c e - 5040A a c d e + 50400B a c d e - 67200A c d e +--R + +--R 3 4 3 +--R 188160B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 378A a c e - 756B a c d e - 6048A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 80640A c d e + 225792B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 90B a e - 216A a c d e - 432B a c d e - 3456A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 34560B a c d e - 46080A c d e + 129024B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 70A a e - 20B a d e - 48A a c d e - 96B a c d e - 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 7680B a c d e - 10240A c d e + 28672B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +-------+ +--R (315e x + 1260d e x + 1890d e x + 1260d e x + 315d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=2/3*(B*d+A*e)*(d+e*x)^(3/2)/c+2/5*B*(d+e*x)^(5/2)/c+2*(B*c*d^2+_ + 2*A*c*d*e-a*B*e^2)*sqrt(d+e*x)/c^2-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ + sqrt(-a)+d*sqrt(c)))*((-A*c*d*(c*d^2-3*a*e^2)+a*B*e*(3*c*d^2-a*e^2))/_ + sqrt(-a)+(B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*sqrt(c))/(c^(9/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+_ + d*sqrt(c)))*((A*c*d*(c*d^2-3*a*e^2)-a*B*e*(3*c*d^2-a*e^2))/sqrt(-a)+_ + (B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*sqrt(c))/(c^(9/4)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 3 +---+ +-+ 2 3 +--R (15A a e + 45B a d e - 45A c d e - 15B c d )\|- a \|c + 15B a e +--R + +--R 2 2 2 3 +--R - 45A a c d e - 45B a c d e + 15A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 3 +---+ +-+ 2 3 +--R (15A a e + 45B a d e - 45A c d e - 15B c d )\|- a \|c - 15B a e +--R + +--R 2 2 2 3 +--R 45A a c d e + 45B a c d e - 15A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 2 2 +--R (6B c e x + (10A c e + 22B c d e)x - 30B a e + 70A c d e + 46B c d ) +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 15c \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 2 +--R 15c +--R * +--R ROOT +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 2 2 5 +--R (10A a c - 10B a c)d e + 10A B a c d e + (- A c + B a c )d +--R / +--R 4 +--R a c +--R * +--R log +--R 2 7 2 2 7 8 2 +--R (2A a c e + 4B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 2 4 3 3 5 2 7 3 3 4 2 4 3 6 +--R (- A B a c + B a c )e + (2A a c - 12A B a c )d e +--R + +--R 2 3 4 3 4 3 2 5 3 2 5 2 3 4 3 4 +--R (31A B a c - 11B a c )d e + (- 20A a c + 50A B a c )d e +--R + +--R 2 2 5 3 3 4 4 3 3 6 2 2 5 5 2 +--R (- 55A B a c + 15B a c )d e + (10A a c - 32A B a c )d e +--R + +--R 2 6 3 2 5 6 2 6 7 +--R (9A B a c - 5B a c )d e + 2A B a c d +--R * +--R ROOT +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 +--R (10A a c - 10B a c)d e + 10A B a c d e +--R + +--R 2 3 2 2 5 +--R (- A c + B a c )d +--R / +--R 4 +--R a c +--R + +--R 4 4 2 4 6 9 3 4 2 3 5 8 +--R (A a c - B a )e + (10A B a c + 10A B a c)d e +--R + +--R 4 3 3 4 5 2 7 4 2 4 4 4 2 4 5 +--R (- 8A a c + 8B a c)d e + (- 14A a c + 14B a c )d e +--R + +--R 3 2 4 3 3 3 5 4 +--R (- 28A B a c - 28A B a c )d e +--R + +--R 3 5 3 2 4 7 2 4 6 4 2 4 8 +--R (- 16A B a c - 16A B a c )d e + (5A c - 5B a c )d e +--R + +--R 3 6 3 5 9 +--R (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 +--R 15c +--R * +--R ROOT +--R - +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 2 2 5 +--R (10A a c - 10B a c)d e + 10A B a c d e + (- A c + B a c )d +--R / +--R 4 +--R a c +--R * +--R log +--R 2 7 2 2 7 8 2 +--R (2A a c e + 4B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 2 4 3 3 5 2 7 3 3 4 2 4 3 6 +--R (A B a c - B a c )e + (- 2A a c + 12A B a c )d e +--R + +--R 2 3 4 3 4 3 2 5 3 2 5 2 3 4 3 4 +--R (- 31A B a c + 11B a c )d e + (20A a c - 50A B a c )d e +--R + +--R 2 2 5 3 3 4 4 3 3 6 2 2 5 5 2 +--R (55A B a c - 15B a c )d e + (- 10A a c + 32A B a c )d e +--R + +--R 2 6 3 2 5 6 2 6 7 +--R (- 9A B a c + 5B a c )d e - 2A B a c d +--R * +--R ROOT +--R - +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 +--R (10A a c - 10B a c)d e + 10A B a c d e +--R + +--R 2 3 2 2 5 +--R (- A c + B a c )d +--R / +--R 4 +--R a c +--R + +--R 4 4 2 4 6 9 3 4 2 3 5 8 +--R (A a c - B a )e + (10A B a c + 10A B a c)d e +--R + +--R 4 3 3 4 5 2 7 4 2 4 4 4 2 4 5 +--R (- 8A a c + 8B a c)d e + (- 14A a c + 14B a c )d e +--R + +--R 3 2 4 3 3 3 5 4 +--R (- 28A B a c - 28A B a c )d e +--R + +--R 3 5 3 2 4 7 2 4 6 4 2 4 8 +--R (- 16A B a c - 16A B a c )d e + (5A c - 5B a c )d e +--R + +--R 3 6 3 5 9 +--R (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 2 +--R 15c +--R * +--R ROOT +--R - +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 2 2 5 +--R (10A a c - 10B a c)d e + 10A B a c d e + (- A c + B a c )d +--R / +--R 4 +--R a c +--R * +--R log +--R 2 7 2 2 7 8 2 +--R (- 2A a c e - 4B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 2 4 3 3 5 2 7 3 3 4 2 4 3 6 +--R (- A B a c + B a c )e + (2A a c - 12A B a c )d e +--R + +--R 2 3 4 3 4 3 2 5 3 2 5 2 3 4 3 4 +--R (31A B a c - 11B a c )d e + (- 20A a c + 50A B a c )d e +--R + +--R 2 2 5 3 3 4 4 3 3 6 2 2 5 5 2 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c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 +--R (10A a c - 10B a c)d e + 10A B a c d e +--R + +--R 2 3 2 2 5 +--R (- A c + B a c )d +--R / +--R 4 +--R a c +--R + +--R 4 4 2 4 6 9 3 4 2 3 5 8 +--R (A a c - B a )e + (10A B a c + 10A B a c)d e +--R + +--R 4 3 3 4 5 2 7 4 2 4 4 4 2 4 5 +--R (- 8A a c + 8B a c)d e + (- 14A a c + 14B a c )d e +--R + +--R 3 2 4 3 3 3 5 4 +--R (- 28A B a c - 28A B a c )d e +--R + +--R 3 5 3 2 4 7 2 4 6 4 2 4 8 +--R (- 16A B a c - 16A B a c )d e + (5A c - 5B a c )d e +--R + +--R 3 6 3 5 9 +--R (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 2 +---+4+-+ +--R c \|- a \|c +--R * +--R ROOT +--R - +--R 4 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+--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 2 7 2 2 7 8 2 +--R (- 2A a c e - 4B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 2 4 3 3 5 2 7 3 3 4 2 4 3 6 +--R (- A B a c + B a c )e + (2A a c - 12A B a c )d e +--R + +--R 2 3 4 3 4 3 2 5 3 2 5 2 3 4 3 4 +--R (31A B a c - 11B a c )d e + (- 20A a c + 50A B a c )d e +--R + +--R 2 2 5 3 3 4 4 3 3 6 2 2 5 5 2 +--R (- 55A B a c + 15B a c )d e + (10A a c - 32A B a c )d e +--R + +--R 2 6 3 2 5 6 2 6 7 +--R (9A B a c - 5B a c )d e + 2A B a c d +--R * +--R ROOT +--R - +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 +--R (- 110A a c + 620A B a c - 110B a c ) +--R * +--R 4 6 +--R d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 +--R (10A a c - 10B a c)d e + 10A B a c d e +--R + +--R 2 3 2 2 5 +--R (- A c + B a c )d +--R / +--R 4 +--R a c +--R + +--R 4 4 2 4 6 9 3 4 2 3 5 8 +--R (A a c - B a )e + (10A B a c + 10A B a c)d e +--R + +--R 4 3 3 4 5 2 7 4 2 4 4 4 2 4 5 +--R (- 8A a c + 8B a c)d e + (- 14A a c + 14B a c )d e +--R + +--R 3 2 4 3 3 3 5 4 +--R (- 28A B a c - 28A B a c )d e +--R + +--R 3 5 3 2 4 7 2 4 6 4 2 4 8 +--R (- 16A B a c - 16A B a c )d e + (5A c - 5B a c )d e +--R + +--R 3 6 3 5 9 +--R (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 +---+4+-+ +--R c \|- a \|c +--R * +--R ROOT +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 2 2 5 +--R (10A a c - 10B a c)d e + 10A B a c d e + (- A c + B a c )d +--R / +--R 4 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 2 7 2 2 7 8 2 +--R (- 2A a c e - 4B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 2 4 3 3 5 2 7 3 3 4 2 4 3 6 +--R (A B a c - B a c )e + (- 2A a c + 12A B a c )d e +--R + +--R 2 3 4 3 4 3 2 5 3 2 5 2 3 4 3 4 +--R (- 31A B a c + 11B a c )d e + (20A a c - 50A B a c )d e +--R + +--R 2 2 5 3 3 4 4 3 3 6 2 2 5 5 2 +--R (55A B a c - 15B a c )d e + (- 10A a c + 32A B a c )d e +--R + +--R 2 6 3 2 5 6 2 6 7 +--R (- 9A B a c + 5B a c )d e - 2A B a c d +--R * +--R ROOT +--R 4 +--R 2a c +--R * +--R ROOT +--R 4 4 2 2 2 5 4 6 10 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 4 2 3 5 9 +--R (- 20A B a c + 20A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 8 +--R (20A a c - 140A B a c + 20B a c)d e +--R + +--R 3 3 3 3 4 2 3 7 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 4 3 3 3 5 5 +--R (- 504A B a c + 504A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 5 3 2 4 7 3 +--R (240A B a c - 240A B a c )d e +--R + +--R 4 6 2 2 5 4 2 4 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 6 3 5 9 2 2 6 10 +--R (- 20A B c + 20A B a c )d e - 4A B c d +--R / +--R 9 +--R 4a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R 2A B a e + (- 5A a c + 5B a )d e - 20A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 +--R (10A a c - 10B a c)d e + 10A B a c d e +--R + +--R 2 3 2 2 5 +--R (- A c + B a c )d +--R / +--R 4 +--R a c +--R + +--R 4 4 2 4 6 9 3 4 2 3 5 8 +--R (A a c - B a )e + (10A B a c + 10A B a c)d e +--R + +--R 4 3 3 4 5 2 7 4 2 4 4 4 2 4 5 +--R (- 8A a c + 8B a c)d e + (- 14A a c + 14B a c )d e +--R + +--R 3 2 4 3 3 3 5 4 +--R (- 28A B a c - 28A B a c )d e +--R + +--R 3 5 3 2 4 7 2 4 6 4 2 4 8 +--R (- 16A B a c - 16A B a c )d e + (5A c - 5B a c )d e +--R + +--R 3 6 3 5 9 +--R (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 3 +---+ +-+ 2 3 +--R (- 2A a e - 6B a d e + 6A c d e + 2B c d )\|- a \|c - 2B a e +--R + +--R 2 2 2 3 +--R 6A a c d e + 6B a c d e - 2A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 3 +---+ +-+ 2 3 +--R (- 2A a e - 6B a d e + 6A c d e + 2B c d )\|- a \|c + 2B a e +--R + +--R 2 2 2 3 +--R - 6A a c d e - 6B a c d e + 2A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 2c \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=2/3*B*(d+e*x)^(3/2)/c+2*(B*d+A*e)*sqrt(d+e*x)/c-atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2+2*A*c*d*e-_ + a*B*e^2-(A*c*d^2-2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/(c^(7/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*_ + sqrt(-a)+d*sqrt(c)))*(B*c*d^2+2*A*c*d*e-a*B*e^2+(A*c*d^2-2*a*B*d*e-_ + a*A*e^2)*sqrt(c)/sqrt(-a))/(c^(7/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 +-+ +--R (- 3A a e - 6B a d e + 3A c d )\|c +--R + +--R 2 2 +---+ +--R (3B a e - 6A c d e - 3B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 +-+ +--R (3A a e + 6B a d e - 3A c d )\|c +--R + +--R 2 2 +---+ +--R (3B a e - 6A c d e - 3B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ +--R (2B e x + 6A e + 8B d)\|- a \|c \|e x + d \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R 3c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3c +--R * +--R ROOT +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (3A a c - 3B a )d e + 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 3 +--R a c +--R * +--R log +--R 2 5 6 +--R (2B a c e - 2A a c d) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 3 2 3 2 3 2 4 2 2 3 3 3 2 3 +--R (- A a c + A B a c )e + (- 7A B a c + B a c )d e +--R + +--R 3 4 2 2 3 2 2 2 4 3 2 3 3 +--R (3A a c - 9A B a c )d e + (5A B a c - 3B a c )d e +--R + +--R 2 4 4 +--R 2A B a c d +--R * +--R ROOT +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (3A a c - 3B a )d e + 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 3 +--R a c +--R + +--R 4 2 2 4 4 5 3 2 2 3 3 4 +--R (A a c - B a )e + (6A B a c + 6A B a c)d e +--R + +--R 4 3 4 3 2 3 3 3 3 2 2 3 2 +--R (- 2A a c + 2B a c)d e + (4A B a c + 4A B a c )d e +--R + +--R 4 4 4 2 2 4 3 4 3 3 5 +--R (- 3A c + 3B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 3c +--R * +--R ROOT +--R - +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (3A a c - 3B a )d e + 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 3 +--R a c +--R * +--R log +--R 2 5 6 +--R (2B a c e - 2A a c d) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 3 2 3 2 3 2 4 2 2 3 3 3 2 3 +--R (A a c - A B a c )e + (7A B a c - B a c )d e +--R + +--R 3 4 2 2 3 2 2 2 4 3 2 3 3 +--R (- 3A a c + 9A B a c )d e + (- 5A B a c + 3B a c )d e +--R + +--R 2 4 4 +--R - 2A B a c d +--R * +--R ROOT +--R - +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e 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2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +---+4+-+3 +--R c\|- a \|c +--R * +--R ROOT +--R - +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (3A a c - 3B a )d e + 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 3 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 2 5 6 +--R (- 2B a c e + 2A a c d) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 3 2 3 2 3 2 4 2 2 3 3 3 2 3 +--R (- A a c + A B a c )e + (- 7A B a c + B a c )d e +--R + +--R 3 4 2 2 3 2 2 2 4 3 2 3 3 +--R (3A a c - 9A B a c )d e + (5A B a c - 3B a c )d e +--R + +--R 2 4 4 +--R 2A B a c d +--R * +--R ROOT +--R - +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (3A a c - 3B a )d e + 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 3 +--R a c +--R + +--R 4 2 2 4 4 5 3 2 2 3 3 4 +--R (A a c - B a )e + (6A B a c + 6A B a c)d e +--R + +--R 4 3 4 3 2 3 3 3 3 2 2 3 2 +--R (- 2A a c + 2B a c)d e + (4A B a c + 4A B a c )d e +--R + +--R 4 4 4 2 2 4 3 4 3 3 5 +--R (- 3A c + 3B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +---+4+-+3 +--R c\|- a \|c +--R * +--R ROOT +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (3A a c - 3B a )d e + 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 3 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 2 5 6 +--R (- 2B a c e + 2A a c d) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 3 2 3 2 3 2 4 2 2 3 3 3 2 3 +--R (A a c - A B a c )e + (7A B a c - B a c )d e +--R + +--R 3 4 2 2 3 2 2 2 4 3 2 3 3 +--R (- 3A a c + 9A B a c )d e + (- 5A B a c + 3B a c )d e +--R + +--R 2 4 4 +--R - 2A B a c d +--R * +--R ROOT +--R 3 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (- 12A B a c + 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (40A B a c - 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (- 12A B c + 12A B a c )d e - 4A B c d +--R / +--R 7 +--R 4a c +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (3A a c - 3B a )d e + 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 3 +--R a c +--R + +--R 4 2 2 4 4 5 3 2 2 3 3 4 +--R (A a c - B a )e + (6A B a c + 6A B a c)d e +--R + +--R 4 3 4 3 2 3 3 3 3 2 2 3 2 +--R (- 2A a c + 2B a c)d e + (4A B a c + 4A B a c )d e +--R + +--R 4 4 4 2 2 4 3 4 3 3 5 +--R (- 3A c + 3B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-+ +--R (2A a e + 4B a d e - 2A c d )\|c +--R + +--R 2 2 +---+ +--R (- 2B a e + 4A c d e + 2B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 +-+ +--R (- 2A a e - 4B a d e + 2A c d )\|c +--R + +--R 2 2 +---+ +--R (- 2B a e + 4A c d e + 2B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R 2c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=2*B*sqrt(d+e*x)/c-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((-A*c*d+a*B*e)/sqrt(-a)+(B*d+A*e)*sqrt(c))/(c^(5/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*_ + sqrt(-a)+d*sqrt(c)))*((A*c*d-a*B*e)/sqrt(-a)+(B*d+A*e)*sqrt(c))/_ + (c^(5/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- A e - B d)\|- a \|c - B a e + A c d)\|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- A e - B d)\|- a \|c + B a e - A c d)\|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R 2B\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R c +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R log +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (- A B a c + B a c)e - 2A B a c d +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R - +--R c +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R log +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (A B a c - B a c)e + 2A B a c d +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R c +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R log +--R - +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (- A B a c + B a c)e - 2A B a c d +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R - +--R c +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R log +--R - +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (A B a c - B a c)e + 2A B a c d +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R +-------+ +--R 4B\|e x + d +--R / +--R 2c +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+4+-+ +--R c\|- a \|c +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (- A B a c + B a c)e - 2A B a c d +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R - +--R +---+4+-+ +--R c\|- a \|c +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (A B a c - B a c)e + 2A B a c d +--R * +--R ROOT +--R - +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a 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+--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R - +--R +---+4+-+ +--R c\|- a \|c +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R - +--R 4 +--R 2A a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 3 2 2 2 +--R (A B a c - B a c)e + 2A B a c d +--R * +--R ROOT +--R 2 +--R 2a c +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (- 4A B c + 4A B a c)d e - 4A B c d +--R / +--R 5 +--R 4a c +--R + +--R 2 2 +--R 2A B a e + (- A c + B a)d +--R / +--R 2 +--R a c +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (2A B c + 2A B a c)d)\|e x + d +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((2A e + 2B d)\|- a \|c + 2B a e - 2A c d)\|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((2A e + 2B d)\|- a \|c - 2B a e + 2A c d)\|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 2c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(A+B*x)/((a+c*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) -------------------- +--R 2 +-------+ +--R (c x + a)\|e x + d +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (B+a*A*sqrt(c)/(-a)^(3/2))/(c^(3/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(B+A*sqrt(c)/_ + sqrt(-a))/(c^(3/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (A\|c - B\|- a )\|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (- A\|c - B\|- a )\|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (2B a c e + 2A a c d e + 2B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (- A a c + A B a c)e + (3A B a c - B a c)d e - 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 3 2 3 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 +--R - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (2B a c e + 2A a c d e + 2B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (A a c - A B a c)e + (- 3A B a c + B a c)d e + 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R - +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (- 2B a c e - 2A a c d e - 2B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (- A a c + A B a c)e + (3A B a c - B a c)d e - 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 3 2 3 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 +--R - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (- 2B a c e - 2A a c d e - 2B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (A a c - A B a c)e + (- 3A B a c + B a c)d e + 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +---+4+-+3 +--R \|- a \|c +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (2B a c e + 2A a c d e + 2B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (- A a c + A B a c)e + (3A B a c - B a c)d e - 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R +---+4+-+3 +--R \|- a \|c +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 3 2 3 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 +--R - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (2B a c e + 2A a c d e + 2B a c d e + 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (A a c - A B a c)e + (- 3A B a c + B a c)d e + 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R - +--R +---+4+-+3 +--R \|- a \|c +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (- 2B a c e - 2A a c d e - 2B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (- A a c + A B a c)e + (3A B a c - B a c)d e - 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (- 2a c e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R +---+4+-+3 +--R \|- a \|c +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 3 2 3 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 +--R - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 3 2 3 2 3 2 2 3 2 4 3 +--R (- 2B a c e - 2A a c d e - 2B a c d e - 2A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 3 2 2 2 2 2 2 3 2 2 2 2 +--R (A a c - A B a c)e + (- 3A B a c + B a c)d e + 2A B a c d +--R * +--R ROOT +--R 2 2 2 2 +--R (2a c e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 2 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 2 2 2 2 +--R (4A B c - 4A B a c)d e - 4A B c d +--R / +--R 3 3 4 2 4 2 2 5 4 +--R 4a c e + 8a c d e + 4a c d +--R + +--R 2 2 +--R - 2A B a e + (- A c + B a)d +--R / +--R 2 2 2 2 +--R a c e + a c d +--R + +--R 4 2 4 2 3 2 3 +-------+ +--R ((A c - B a )e + (- 2A B c - 2A B a c)d)\|e x + d +--R + +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (- 2A\|c + 2B\|- a )\|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (2A\|c + 2B\|- a )\|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R 3 2 +-------+ +--R (c e x + c d x + a e x + a d)\|e x + d +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=2*(B*d-A*e)/((c*d^2+a*e^2)*sqrt(d+e*x))-atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))*((-A*c*d-a*B*e)/sqrt(-a)+(B*d-A*e)*_ + sqrt(c))/(c^(1/4)*(c*d^2+a*e^2)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*_ + ((A*c*d+a*B*e)/sqrt(-a)+(B*d-A*e)*sqrt(c))/(c^(1/4)*(c*d^2+a*e^2)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ +--R +---+ +-+ +-------+ | +-+ +---+ +--R ((A e - B d)\|- a \|c + B a e + A c d)\|e x + d \|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ +-------+ | +-+ +---+ +--R ((A e - B d)\|- a \|c - B a e - A c d)\|e x + d \|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (- 2A e + 2B d)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R (a e + c d )\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +-------+ +--R (- a e - c d )\|e x + d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R 2A a c e - 4B a c d e + 4A a c d e - 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R - 12B a c d e - 4A a c d e - 4B a c d e - 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (- A B a c + B a )e + (- 2A a c + 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (16A B a c - 4B a c)d e + (6A a c - 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (- 7A B a c + 3B a c )d e + 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-------+ +--R (a e + c d )\|e x + d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R 2A a c e - 4B a c d e + 4A a c d e - 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R - 12B a c d e - 4A a c d e - 4B a c d e - 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (A B a c - B a )e + (2A a c - 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (- 16A B a c + 4B a c)d e + (- 6A a c + 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (7A B a c - 3B a c )d e - 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-------+ +--R (- a e - c d )\|e x + d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R - 2A a c e + 4B a c d e - 4A a c d e + 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R 12B a c d e + 4A a c d e + 4B a c d e + 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (- A B a c + B a )e + (- 2A a c + 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (16A B a c - 4B a c)d e + (6A a c - 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (- 7A B a c + 3B a c )d e + 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-------+ +--R (a e + c d )\|e x + d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R - 2A a c e + 4B a c d e - 4A a c d e + 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R 12B a c d e + 4A a c d e + 4B a c d e + 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (A B a c - B a )e + (2A a c - 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (- 16A B a c + 4B a c)d e + (- 6A a c + 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (7A B a c - 3B a c )d e - 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - 4A e + 4B d +--R / +--R 2 2 +-------+ +--R (2a e + 2c d )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 +---+4+-+ +--R (- a e - c d )\|- a \|c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R 2A a c e - 4B a c d e + 4A a c d e - 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R - 12B a c d e - 4A a c d e - 4B a c d e - 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (- A B a c + B a )e + (- 2A a c + 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (16A B a c - 4B a c)d e + (6A a c - 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (- 7A B a c + 3B a c )d e + 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +---+4+-+ +--R (a e + c d )\|- a \|c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R 2A a c e - 4B a c d e + 4A a c d e - 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R - 12B a c d e - 4A a c d e - 4B a c d e - 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (A B a c - B a )e + (2A a c - 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (- 16A B a c + 4B a c)d e + (- 6A a c + 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (7A B a c - 3B a c )d e - 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +---+4+-+ +--R (- a e - c d )\|- a \|c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R - 2A a c e + 4B a c d e - 4A a c d e + 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R 12B a c d e + 4A a c d e + 4B a c d e + 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (- A B a c + B a )e + (- 2A a c + 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (16A B a c - 4B a c)d e + (6A a c - 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (- 7A B a c + 3B a c )d e + 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a e - 6a c d e - 6a c d e - 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +---+4+-+ +--R (a e + c d )\|- a \|c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 8 5 7 4 2 2 6 4 2 3 5 +--R - 2A a c e + 4B a c d e - 4A a c d e + 12B a c d e +--R + +--R 3 3 5 3 2 4 6 2 2 4 7 5 8 +--R 12B a c d e + 4A a c d e + 4B a c d e + 2A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 3 4 5 3 2 2 2 3 4 +--R (A B a c - B a )e + (2A a c - 8A B a c)d e +--R + +--R 2 2 2 3 3 2 3 3 3 2 2 2 3 2 +--R (- 16A B a c + 4B a c)d e + (- 6A a c + 14A B a c )d e +--R + +--R 2 3 3 2 2 4 2 3 5 +--R (7A B a c - 3B a c )d e - 2A B a c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a e + 6a c d e + 6a c d e + 2a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 6 +--R (- A a c + 2A B a c - B a )e +--R + +--R 3 2 2 3 3 5 +--R (12A B a c - 12A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 4 +--R (6A a c - 48A B a c + 6B a c)d e +--R + +--R 3 3 3 2 2 3 3 +--R (- 40A B a c + 40A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 2 +--R (- 9A c + 42A B a c - 9B a c )d e +--R + +--R 3 4 3 3 5 2 2 4 6 +--R (12A B c - 12A B a c )d e - 4A B c d +--R / +--R 7 12 6 2 2 10 5 3 4 8 4 4 6 6 +--R 4a c e + 24a c d e + 60a c d e + 80a c d e +--R + +--R 3 5 8 4 2 6 10 2 7 12 +--R 60a c d e + 24a c d e + 4a c d +--R + +--R 2 3 2 2 2 2 2 +--R 2A B a e + (3A a c - 3B a )d e - 6A B a c d e +--R + +--R 2 2 2 3 +--R (- A c + B a c)d +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a e + 3a c d e + 3a c d e + a c d +--R + +--R 4 2 4 3 3 3 2 3 2 2 +--R (A a c - B a )e + (- 6A B a c - 6A B a c)d e +--R + +--R 4 3 4 2 2 3 3 3 2 3 +--R (- 3A c + 3B a c)d e + (2A B c + 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- 2A e + 2B d)\|- a \|c - 2B a e - 2A c d)\|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- 2A e + 2B d)\|- a \|c + 2B a e + 2A c d)\|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (2a e + 2c d )\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------------ +--R 2 4 3 2 2 2 2 +-------+ +--R (c e x + 2c d e x + (a e + c d )x + 2a d e x + a d )\|e x + d +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=2/3*(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x)^(3/2))+2*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2)/((c*d^2+a*e^2)^2*sqrt(d+e*x))-c^(1/4)*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2-(A*c*d^2+2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/((c*d^2+_ + a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))-c^(1/4)*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2+(A*c*d^2+2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/((c*d^2+_ + a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 +--R (- 3A a e + 6B a d e + 3A c d e)x - 3A a d e + 6B a d e +--R + +--R 3 +--R 3A c d +--R * +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 +--R (3B a e + 6A c d e - 3B c d e)x + 3B a d e + 6A c d e +--R + +--R 3 +--R - 3B c d +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ +-------+ | +-+ +---+ \|c \|e x + d +--R \|c \|e x + d \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 +--R (3A a e - 6B a d e - 3A c d e)x + 3A a d e - 6B a d e +--R + +--R 3 +--R - 3A c d +--R * +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 +--R (3B a e + 6A c d e - 3B c d e)x + 3B a d e + 6A c d e +--R + +--R 3 +--R - 3B c d +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ +-------+ | +-+ +---+ \|c \|e x + d +--R \|c \|e x + d \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 3 2 2 3 2 +--R (- 6B a e - 12A c d e + 6B c d e)x - 2A a e - 4B a d e +--R + +--R 2 3 +--R - 14A c d e + 8B c d +--R * +--R +---------------+ +---------------+ +--R +---+ | +-+ +---+ | +-+ +---+ +--R \|- a \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +---+ +--R ((3a e + 6a c d e + 3c d e)x + 3a d e + 6a c d e + 3c d )\|- a +--R * +--R +---------------+ +---------------+ +--R +-------+ | +-+ +---+ | +-+ +---+ +--R \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 3 2 4 2 4 3 2 2 5 +-------+ +--R ((3a e + 6a c d e + 3c d e)x + 3a d e + 6a c d e + 3c d )\|e x + d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R 2a e + 10a c d e + 20a c d e + 20a c d e + 10a c d e +--R + +--R 5 10 +--R 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R 2B a e + 6A a c d e + 4B a c d e + 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 +--R - 10B a c d e + 50A a c d e - 40B a c d e +--R + +--R 4 4 7 6 4 4 8 5 3 5 9 4 3 5 10 3 +--R 40A a c d e - 50B a c d e + 10A a c d e - 28B a c d e +--R + +--R 2 6 11 2 2 6 12 7 13 +--R - 4A a c d e - 6B a c d e - 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (- A a c + A B a c)e + (13A B a c - 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (13A a c - 43A B a c )d e + (- 81A B a c + 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (- 35A a c + 105A B a c )d e + (87A B a c - 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (15A a c - 41A B a c )d e + (- 11A B a c + 5B a c )d e +--R + +--R 2 5 8 +--R 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R 2a e + 10a c d e + 20a c d e + 20a c d e +--R + +--R 2 4 8 2 5 10 +--R 10a c d e + 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 5 2 3 2 4 2 4 3 2 2 5 +--R ((- 3a e - 6a c d e - 3c d e)x - 3a d e - 6a c d e - 3c d ) +--R * +--R +-------+ +--R \|e x + d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e - 10a c d e +--R + +--R 5 10 +--R - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R 2B a e + 6A a c d e + 4B a c d e + 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 +--R - 10B a c d e + 50A a c d e - 40B a c d e +--R + +--R 4 4 7 6 4 4 8 5 3 5 9 4 3 5 10 3 +--R 40A a c d e - 50B a c d e + 10A a c d e - 28B a c d e +--R + +--R 2 6 11 2 2 6 12 7 13 +--R - 4A a c d e - 6B a c d e - 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (A a c - A B a c)e + (- 13A B a c + 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (- 13A a c + 43A B a c )d e + (81A B a c - 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (35A a c - 105A B a c )d e + (- 87A B a c + 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (- 15A a c + 41A B a c )d e + (11A B a c - 5B a c )d e +--R + +--R 2 5 8 +--R - 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e +--R + +--R 2 4 8 2 5 10 +--R - 10a c d e - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 5 2 3 2 4 2 4 3 2 2 5 +-------+ +--R ((3a e + 6a c d e + 3c d e)x + 3a d e + 6a c d e + 3c d )\|e x + d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e - 10a c d e +--R + +--R 5 10 +--R - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e 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10A a c d e + 28B a c d e + 4A a c d e +--R + +--R 2 6 12 7 13 +--R 6B a c d e + 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (- A a c + A B a c)e + (13A B a c - 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (13A a c - 43A B a c )d e + (- 81A B a c + 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (- 35A a c + 105A B a c )d e + (87A B a c - 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (15A a c - 41A B a c )d e + (- 11A B a c + 5B a c )d e +--R + +--R 2 5 8 +--R 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e +--R + +--R 2 4 8 2 5 10 +--R - 10a c d e - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 5 2 3 2 4 2 4 3 2 2 5 +--R ((- 3a e - 6a c d e - 3c d e)x - 3a d e - 6a c d e - 3c d ) +--R * +--R +-------+ +--R \|e x + d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R 2a e + 10a c d e + 20a c d e + 20a c d e + 10a c d e +--R + +--R 5 10 +--R 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R - 2B a e - 6A a c d e - 4B a c d e - 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 4 4 7 6 +--R 10B a c d e - 50A a c d e + 40B a c d e - 40A a c d e +--R + +--R 4 4 8 5 3 5 9 4 3 5 10 3 2 6 11 2 +--R 50B a c d e - 10A a c d e + 28B a c d e + 4A a c d e +--R + +--R 2 6 12 7 13 +--R 6B a c d e + 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (A a c - A B a c)e + (- 13A B a c + 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (- 13A a c + 43A B a c )d e + (81A B a c - 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (35A a c - 105A B a c )d e + (- 87A B a c + 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (- 15A a c + 41A B a c )d e + (11A B a c - 5B a c )d e +--R + +--R 2 5 8 +--R - 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R 2a e + 10a c d e + 20a c d e + 20a c d e +--R + +--R 2 4 8 2 5 10 +--R 10a c d e + 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 3 2 2 +--R (- 12B a e - 24A c d e + 12B c d e)x - 4A a e - 8B a d e - 28A c d e +--R + +--R 3 +--R 16B c d +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +-------+ +--R ((6a e + 12a c d e + 6c d e)x + 6a d e + 12a c d e + 6c d )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 2 2 2 4 +---+ +--R (a e + 2a c d e + c d )\|- a +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R 2a e + 10a c d e + 20a c d e + 20a c d e + 10a c d e +--R + +--R 5 10 +--R 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R 2B a e + 6A a c d e + 4B a c d e + 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 +--R - 10B a c d e + 50A a c d e - 40B a c d e +--R + +--R 4 4 7 6 4 4 8 5 3 5 9 4 3 5 10 3 +--R 40A a c d e - 50B a c d e + 10A a c d e - 28B a c d e +--R + +--R 2 6 11 2 2 6 12 7 13 +--R - 4A a c d e - 6B a c d e - 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (- A a c + A B a c)e + (13A B a c - 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (13A a c - 43A B a c )d e + (- 81A B a c + 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (- 35A a c + 105A B a c )d e + (87A B a c - 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (15A a c - 41A B a c )d e + (- 11A B a c + 5B a c )d e +--R + +--R 2 5 8 +--R 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R 2a e + 10a c d e + 20a c d e + 20a c d e +--R + +--R 2 4 8 2 5 10 +--R 10a c d e + 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 2 2 2 4 +---+ +--R (- a e - 2a c d e - c d )\|- a +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e - 10a c d e +--R + +--R 5 10 +--R - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R 2B a e + 6A a c d e + 4B a c d e + 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 +--R - 10B a c d e + 50A a c d e - 40B a c d e +--R + +--R 4 4 7 6 4 4 8 5 3 5 9 4 3 5 10 3 +--R 40A a c d e - 50B a c d e + 10A a c d e - 28B a c d e +--R + +--R 2 6 11 2 2 6 12 7 13 +--R - 4A a c d e - 6B a c d e - 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (A a c - A B a c)e + (- 13A B a c + 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (- 13A a c + 43A B a c )d e + (81A B a c - 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (35A a c - 105A B a c )d e + (- 87A B a c + 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (- 15A a c + 41A B a c )d e + (11A B a c - 5B a c )d e +--R + +--R 2 5 8 +--R - 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e +--R + +--R 2 4 8 2 5 10 +--R - 10a c d e - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 2 2 2 4 +---+ +--R (a e + 2a c d e + c d )\|- a +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e - 10a c d e +--R + +--R 5 10 +--R - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R - 2B a e - 6A a c d e - 4B a c d e - 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 4 4 7 6 +--R 10B a c d e - 50A a c d e + 40B a c d e - 40A a c d e +--R + +--R 4 4 8 5 3 5 9 4 3 5 10 3 2 6 11 2 +--R 50B a c d e - 10A a c d e + 28B a c d e + 4A a c d e +--R + +--R 2 6 12 7 13 +--R 6B a c d e + 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (- A a c + A B a c)e + (13A B a c - 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (13A a c - 43A B a c )d e + (- 81A B a c + 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (- 35A a c + 105A B a c )d e + (87A B a c - 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (15A a c - 41A B a c )d e + (- 11A B a c + 5B a c )d e +--R + +--R 2 5 8 +--R 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R - 2a e - 10a c d e - 20a c d e - 20a c d e +--R + +--R 2 4 8 2 5 10 +--R - 10a c d e - 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 2 2 2 4 +---+ +--R (- a e - 2a c d e - c d )\|- a +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R 2a e + 10a c d e + 20a c d e + 20a c d e + 10a c d e +--R + +--R 5 10 +--R 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 2 4 2 3 5 +--R (10A a c - 10B a c )d e - 10A B a c d e + (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 5 10 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e + a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 13 7 12 7 2 11 6 2 3 10 +--R - 2B a e - 6A a c d e - 4B a c d e - 28A a c d e +--R + +--R 6 2 4 9 5 3 5 8 5 3 6 7 4 4 7 6 +--R 10B a c d e - 50A a c d e + 40B a c d e - 40A a c d e +--R + +--R 4 4 8 5 3 5 9 4 3 5 10 3 2 6 11 2 +--R 50B a c d e - 10A a c d e + 28B a c d e + 4A a c d e +--R + +--R 2 6 12 7 13 +--R 6B a c d e + 2A a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 8 3 6 14 +--R 4a e + 40a c d e + 180a c d e + 480a c d e +--R + +--R 7 4 8 12 6 5 10 10 5 6 12 8 +--R 840a c d e + 1008a c d e + 840a c d e +--R + +--R 4 7 14 6 3 8 16 4 2 9 18 2 10 20 +--R 480a c d e + 180a c d e + 40a c d e + 4a c d +--R + +--R 3 4 2 2 5 8 2 4 2 3 5 7 +--R (A a c - A B a c)e + (- 13A B a c + 3B a c)d e +--R + +--R 3 3 3 2 4 2 2 6 2 3 3 3 4 2 3 5 +--R (- 13A a c + 43A B a c )d e + (81A B a c - 31B a c )d e +--R + +--R 3 2 4 2 3 3 4 4 2 2 4 3 3 3 5 3 +--R (35A a c - 105A B a c )d e + (- 87A B a c + 25B a c )d e +--R + +--R 3 5 2 2 4 6 2 2 5 3 2 4 7 +--R (- 15A a c + 41A B a c )d e + (11A B a c - 5B a c )d e +--R + +--R 2 5 8 +--R - 2A B a c d +--R * +--R ROOT +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 +--R 2a e + 10a c d e + 20a c d e + 20a c d e +--R + +--R 2 4 8 2 5 10 +--R 10a c d e + 2a c d +--R * +--R ROOT +--R 4 4 3 2 2 5 2 4 6 10 +--R (- A a c + 2A B a c - B a c)e +--R + +--R 3 4 3 3 5 2 9 +--R (20A B a c - 20A B a c )d e +--R + +--R 4 3 4 2 2 4 3 4 5 2 2 8 +--R (20A a c - 140A B a c + 20B a c )d e +--R + +--R 3 3 4 3 4 3 3 7 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 2 5 2 2 3 4 4 4 3 4 6 +--R (- 110A a c + 620A B a c - 110B a c )d e +--R + +--R 3 2 5 3 3 4 5 5 +--R (504A B a c - 504A B a c )d e +--R + +--R 4 6 2 2 2 5 4 3 4 6 4 +--R (100A a c - 640A B a c + 100B a c )d e +--R + +--R 3 6 3 2 5 7 3 +--R (- 240A B a c + 240A B a c )d e +--R + +--R 4 7 2 2 6 4 2 5 8 2 +--R (- 25A c + 130A B a c - 25B a c )d e +--R + +--R 3 7 3 6 9 2 2 7 10 +--R (20A B c - 20A B a c )d e - 4A B c d +--R / +--R 11 20 10 2 18 9 2 4 16 +--R 4a e + 40a c d e + 180a c d e +--R + +--R 8 3 6 14 7 4 8 12 6 5 10 10 +--R 480a c d e + 840a c d e + 1008a c d e +--R + +--R 5 6 12 8 4 7 14 6 3 8 16 4 +--R 840a c d e + 480a c d e + 180a c d e +--R + +--R 2 9 18 2 10 20 +--R 40a c d e + 4a c d +--R + +--R 3 5 2 2 2 2 3 4 2 2 2 3 +--R - 2A B a c e + (- 5A a c + 5B a c)d e + 20A B a c d e +--R + +--R 2 3 2 2 2 3 2 3 4 +--R (10A a c - 10B a c )d e - 10A B a c d e +--R + +--R 2 4 2 3 5 +--R (- A c + B a c )d +--R / +--R 6 10 5 2 8 4 2 4 6 3 3 6 4 2 4 8 2 +--R a e + 5a c d e + 10a c d e + 10a c d e + 5a c d e +--R + +--R 5 10 +--R a c d +--R + +--R 4 2 3 4 4 5 3 2 3 3 3 2 4 +--R (A a c - B a c)e + (- 10A B a c - 10A B a c )d e +--R + +--R 4 4 4 3 2 2 3 3 4 3 2 3 3 2 +--R (- 10A a c + 10B a c )d e + (20A B a c + 20A B a c )d e +--R + +--R 4 5 4 2 3 4 3 5 3 4 5 +--R (5A c - 5B a c )d e + (- 2A B c - 2A B a c )d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-+ +--R (2A a e - 4B a d e - 2A c d )\|c +--R + +--R 2 2 +---+ +--R (- 2B a e - 4A c d e + 2B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ | +-+ +---+ \|c \|e x + d +--R \|c \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 +-+ +--R (- 2A a e + 4B a d e + 2A c d )\|c +--R + +--R 2 2 +---+ +--R (- 2B a e - 4A c d e + 2B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ | +-+ +---+ \|c \|e x + d +--R \|c \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 4 2 2 2 4 +---+ | +-+ +---+ | +-+ +---+ +--R (2a e + 4a c d e + 2c d )\|- a \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +--d0:=normalize(D(m0,x)) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=-1/2*A*e*(d+e*x)^(3/2)/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^(5/2)/(a*c*_ + (a+c*x^2))-1/2*e*(A*c*d-5*a*B*e)*sqrt(d+e*x)/(a*c^2)-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + ((-5*a*B*e*(c*d^2-a*e^2)-2*A*c*d*(c*d^2+2*a*e^2))/sqrt(-a)+_ + e*(A*c*d^2+10*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a*c^(9/4)*sqrt(-e*_ + sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+_ + d*sqrt(c)))*((5*a*B*e*(c*d^2-a*e^2)+2*A*c*d*(c*d^2+2*a*e^2))/_ + sqrt(-a)+e*(A*c*d^2+10*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a*c^(9/4)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 2 2 +--R (- 3A a c e - 10B a c d e - A c d e)x - 3A a e - 10B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 5B a c e + 4A a c d e + 5B a c d e + 2A c d )x - 5B a e +--R + +--R 2 2 2 2 2 3 +--R 4A a c d e + 5B a c d e + 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 3A a c e - 10B a c d e - A c d e)x - 3A a e - 10B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (5B a c e - 4A a c d e - 5B a c d e - 2A c d )x + 5B a e +--R + +--R 2 2 2 2 2 3 +--R - 4A a c d e - 5B a c d e - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R 8B a c e x + (- 2A a c e - 4B a c d e + 2A c d )x + 10B a e +--R + +--R 2 +--R - 4A a c d e - 2B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 3 2 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c )\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=normalize(D(m0,x)) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=-1/2*(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*(a+c*x^2))-1/2*A*e*sqrt(d+e*x)/(a*c)-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(e*(A*c*d+_ + 3*a*B*e)+a*(2*A*c*d^2+3*a*B*d*e+a*A*e^2)*sqrt(c)/(-a)^(3/2))/(a*_ + c^(7/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(A*c*d+3*a*B*e)+(2*A*c*d^2+_ + 3*a*B*d*e+a*A*e^2)*sqrt(c)/sqrt(-a))/(a*c^(7/4)*sqrt(e*sqrt(-a)+_ + d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (A a c e + 3B a c d e + 2A c d )x + A a e + 3B a d e +--R + +--R 2 +--R 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- 3B a c e - A c d e)x - 3B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R (- A a c e - 3B a c d e - 2A c d )x - A a e - 3B a d e +--R + +--R 2 +--R - 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- 3B a c e - A c d e)x - 3B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---+4+-+3 +-------+ +--R ((- 2B a e + 2A c d)x - 2A a e - 2B a d)\|- a \|c \|e x + d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 2 +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=normalize(D(m0,x)) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=-1/2*(a*B-A*c*x)*sqrt(d+e*x)/(a*c*(a+c*x^2))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*((-2*A*c*d-a*B*e)/sqrt(-a)+_ + A*e*sqrt(c))/(a*c^(5/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*((2*A*c*d+a*B*e)/sqrt(-a)+_ + A*e*sqrt(c))/(a*c^(5/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 +---+ +-+ 2 2 2 +--R (- A c e x - A a e)\|- a \|c + (B a c e + 2A c d)x + B a e +--R + +--R 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 +---+ +-+ 2 2 2 +--R (- A c e x - A a e)\|- a \|c + (- B a c e - 2A c d)x - B a e +--R + +--R - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R (2A c x - 2B a)\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (a c x + a c) +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 4 5 3 +--R 128A a c e + 128B a c d e + 384A a c d e + 128B a c d e +--R + +--R 3 6 4 +--R 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (4A B a c - 4B a c)e + (4A a c - 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R - 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 2 +--R (- a c x - a c) +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 4 5 3 +--R 128A a c e + 128B a c d e + 384A a c d e + 128B a c d e +--R + +--R 3 6 4 +--R 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (- 4A B a c + 4B a c)e + (- 4A a c + 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 2 +--R (a c x + a c) +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 +--R - 128A a c e - 128B a c d e - 384A a c d e +--R + +--R 4 5 3 3 6 4 +--R - 128B a c d e - 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (4A B a c - 4B a c)e + (4A a c - 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R - 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 2 +--R (- a c x - a c) +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 +--R - 128A a c e - 128B a c d e - 384A a c d e +--R + +--R 4 5 3 3 6 4 +--R - 128B a c d e - 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (- 4A B a c + 4B a c)e + (- 4A a c + 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-------+ +--R (A c x - B a)\|e x + d +--R / +--R 2 2 2 +--R 2a c x + 2a c +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+4+-+ +--R 2a c\|- a \|c +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 4 5 3 +--R 128A a c e + 128B a c d e + 384A a c d e + 128B a c d e +--R + +--R 3 6 4 +--R 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (4A B a c - 4B a c)e + (4A a c - 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R - 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +---+4+-+ +--R 2a c\|- a \|c +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 +--R 128A a c e + 128B a c d e + 384A a c d e +--R + +--R 4 5 3 3 6 4 +--R 128B a c d e + 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (- 4A B a c + 4B a c)e + (- 4A a c + 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +---+4+-+ +--R 2a c\|- a \|c +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 3 2 3 5 +--R (- A c + 2A B a c - B a )e + (4A B c - 4A B a c)d e +--R + +--R 2 2 2 2 4 +--R - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 +--R - 128A a c e - 128B a c d e - 384A a c d e +--R + +--R 4 5 3 3 6 4 +--R - 128B a c d e - 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (4A B a c - 4B a c)e + (4A a c - 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R - 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (- 32a c e - 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +---+4+-+ +--R 2a c\|- a \|c +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 5 4 4 5 4 3 4 5 2 2 +--R - 128A a c e - 128B a c d e - 384A a c d e +--R + +--R 4 5 3 3 6 4 +--R - 128B a c d e - 256A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 3 4 5 3 2 3 2 3 2 4 +--R (- 4A B a c + 4B a c)e + (- 4A a c + 12A B a c )d e +--R + +--R 2 2 3 2 3 +--R 8A B a c d e +--R * +--R ROOT +--R 4 2 2 3 3 2 +--R (32a c e + 32a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 6 +--R (- A c + 2A B a c - B a )e +--R + +--R 3 2 3 5 2 2 2 2 4 +--R (4A B c - 4A B a c)d e - 4A B c d e +--R / +--R 5 5 4 4 6 2 2 3 7 4 +--R 1024a c e + 2048a c d e + 1024a c d +--R + +--R 2 3 2 2 2 2 2 +--R - 2A B a e + (- 3A a c - B a )d e - 4A B a c d e +--R + +--R 2 2 3 +--R - 4A c d +--R / +--R 4 2 2 3 3 2 +--R 16a c e + 16a c d +--R + +--R 4 2 4 3 5 3 2 3 2 4 +--R (A a c - B a )e + (2A B a c - 6A B a c)d e +--R + +--R 4 3 2 2 2 2 3 3 3 3 2 +--R (4A c - 12A B a c )d e - 8A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R (A e\|- a \|c - B a e - 2A c d)\|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ 4+-+ +-------+ +--R +---+ +-+ | +-+ +---+ \|c \|e x + d +--R (A e\|- a \|c + B a e + 2A c d)\|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 4a c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +--d0:=normalize(D(m0,x)) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(A+B*x)/((a+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R 2 4 2 2 +-------+ +--R (c x + 2a c x + a )\|e x + d +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=-1/2*(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ + (a+c*x^2))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (e*(A*c*d+a*B*e)-(2*A*c*d^2-a*B*d*e+3*a*A*e^2)*sqrt(c)/sqrt(-a))/_ + (a*c^(3/4)*(c*d^2+a*e^2)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*_ + (e*(A*c*d+a*B*e)+(2*A*c*d^2-a*B*d*e+3*a*A*e^2)*sqrt(c)/sqrt(-a))/_ + (a*c^(3/4)*(c*d^2+a*e^2)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (3A a c e - B a c d e + 2A c d )x + 3A a e - B a d e +--R + +--R 2 +--R 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- B a c e - A c d e)x - B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R (- 3A a c e + B a c d e - 2A c d )x - 3A a e + B a d e +--R + +--R 2 +--R - 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- B a c e - A c d e)x - B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---+4+-+3 +-------+ +--R ((2B a e + 2A c d)x + 2A a e - 2B a d)\|- a \|c \|e x + d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 2 2 2 2 3 2 2 2 +---+4+-+3 | +-+ +---+ +--R ((4a c e + 4a c d )x + 4a e + 4a c d )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=normalize(D(m0,x)) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 3 2 2 2 +-------+ +--R (c e x + c d x + 2a c e x + 2a c d x + a e x + a d)\|e x + d +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=1/2*e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)/(a*(c*d^2+a*e^2)^2*sqrt(d+e*x))+_ + 1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2)*_ + sqrt(d+e*x))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((3*a*B*e*(c*d^2-a*e^2)-2*A*c*d*(c*d^2+4*a*e^2))/_ + sqrt(-a)+e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)*sqrt(c))/(a*c^(1/4)*_ + (c*d^2+a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*((-3*a*B*e*(c*d^2-a*e^2)+_ + 2*A*c*d*(c*d^2+4*a*e^2))/sqrt(-a)+e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)*_ + sqrt(c))/(a*c^(1/4)*(c*d^2+a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 2 2 +--R (5A a c e - 6B a c d e - A c d e)x + 5A a e - 6B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (3B a c e + 8A a c d e - 3B a c d e + 2A c d )x + 3B a e +--R + +--R 2 2 2 2 2 3 +--R 8A a c d e - 3B a c d e + 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R +-------+ | +-+ +---+ \|c \|e x + d +--R \|e x + d \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (5A a c e - 6B a c d e - A c d e)x + 5A a e - 6B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 3B a c e - 8A a c d e + 3B a c d e - 2A c d )x - 3B a e +--R + +--R 2 2 2 2 2 3 +--R - 8A a c d e + 3B a c d e - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R +-------+ | +-+ +---+ \|c \|e x + d +--R \|e x + d \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 3 2 2 2 2 +--R (- 10A a c e + 12B a c d e + 2A c d e)x +--R + +--R 2 3 2 2 2 3 2 3 +--R (2B a e + 2A a c d e + 2B a c d e + 2A c d )x - 8A a e +--R + +--R 2 2 2 3 +--R 10B a d e + 4A a c d e - 2B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +---+ +--R ((4a c e + 8a c d e + 4a c d )x + 4a e + 8a c d e + 4a c d )\|- a +--R * +--R +---------------+ +---------------+ +--R 4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=-1/16*e*(6*A*c*d+7*a*B*e)*(d+e*x)^(3/2)/(a^2*c^2)-1/4*(a*B-A*c*x)*_ + (d+e*x)^(7/2)/(a*c*(a+c*x^2)^2)+1/16*(d+e*x)^(5/2)*(a*A*e+(6*A*c*d+_ + 7*a*B*e)*x)/(a^2*c*(a+c*x^2))-1/16*e*(6*A*c*d^2+7*a*B*d*e+5*a*A*e^2)*_ + sqrt(d+e*x)/(a^2*c^2)-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*(e*(7*a*B*e*(c*d^2+3*a*e^2)+2*A*c*d*(3*c*d^2+4*a*e^2))+_ + a*(14*a*B*d*e*(c*d^2+2*a*e^2)+A*(12*c^2*d^4+19*a*c*d^2*e^2+5*a^2*e^4))*_ + sqrt(c)/(-a)^(3/2))/(a^2*c^(11/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + 1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(7*a*B*_ + e*(c*d^2+3*a*e^2)+2*A*c*d*(3*c*d^2+4*a*e^2))+(14*a*B*d*e*(c*d^2+_ + 2*a*e^2)+A*(12*c^2*d^4+19*a*c*d^2*e^2+5*a^2*e^4))*sqrt(c)/sqrt(-a))/_ + (a^2*c^(11/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 +--R 5A a c e + 28B a c d e + 19A a c d e + 14B a c d e +--R + +--R 4 4 +--R 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R 10A a c e + 56B a c d e + 38A a c d e + 28B a c d e +--R + +--R 3 4 +--R 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R 5A a e + 28B a d e + 19A a c d e + 14B a c d e + 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 21B a c e - 8A a c d e - 7B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 42B a c e - 16A a c d e - 14B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 21B a e - 8A a c d e - 7B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 +--R - 5A a c e - 28B a c d e - 19A a c d e - 14B a c d e +--R + +--R 4 4 +--R - 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 10A a c e - 56B a c d e - 38A a c d e - 28B a c d e +--R + +--R 3 4 +--R - 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R - 5A a e - 28B a d e - 19A a c d e - 14B a c d e - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 21B a c e - 8A a c d e - 7B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 42B a c e - 16A a c d e - 14B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 21B a e - 8A a c d e - 7B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 22B a c e + 16A a c d e + 14B a c d e + 12A c d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 18A a c e - 52B a c d e + 2A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (- 14B a e - 8A a c d e - 10B a c d e + 20A a c d )x - 10A a e +--R + +--R 3 2 2 2 2 3 +--R - 28B a d e - 22A a c d e - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 4 4 3 3 2 4 2 +---+4+-+3 | +-+ +---+ +--R (32a c x + 64a c x + 32a c )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^(5/2)/(a*c*(a+c*x^2)^2)-1/16*(d+e*x)^(3/2)*_ + (a*A*e-(6*A*c*d+5*a*B*e)*x)/(a^2*c*(a+c*x^2))-1/16*e*(6*A*c*d+5*a*B*e)*_ + sqrt(d+e*x)/(a^2*c^2)-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((-5*a*B*e*(2*c*d^2+a*e^2)-3*A*c*d*(4*c*d^2+3*a*e^2))/_ + sqrt(-a)+e*(6*A*c*d^2+5*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a^2*c^(9/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*((5*a*B*e*(2*c*d^2+a*e^2)+3*A*c*d*(4*c*d^2+_ + 3*a*e^2))/sqrt(-a)+e*(6*A*c*d^2+5*a*B*d*e+3*a*A*e^2)*sqrt(c))/_ + (a^2*c^(9/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 3A a c e - 5B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 6A a c e - 10B a c d e - 12A a c d e)x - 3A a e +--R + +--R 3 2 2 2 +--R - 5B a d e - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (5B a c e + 9A a c d e + 10B a c d e + 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (10B a c e + 18A a c d e + 20B a c d e + 24A a c d )x + 5B a e +--R + +--R 3 2 3 2 2 2 3 +--R 9A a c d e + 10B a c d e + 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 3 2 2 3 2 4 +--R (- 3A a c e - 5B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 6A a c e - 10B a c d e - 12A a c d e)x - 3A a e +--R + +--R 3 2 2 2 +--R - 5B a d e - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (- 5B a c e - 9A a c d e - 10B a c d e - 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (- 10B a c e - 18A a c d e - 20B a c d e - 24A a c d )x - 5B a e +--R + +--R 3 2 3 2 2 2 3 +--R - 9A a c d e - 10B a c d e - 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 3 2 3 +--R (6A a c e + 10B a c d e + 12A c d )x +--R + +--R 2 2 2 2 +--R (- 18B a c e + 2A a c d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 2A a c e - 6B a c d e + 20A a c d )x - 10B a e - 14A a c d e +--R + +--R 2 2 +--R - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 4 4 3 3 2 4 2 +---+4+-+ | +-+ +---+ +--R (32a c x + 64a c x + 32a c )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 3 3 2 4 2 +--R (8a c x + 16a c x + 8a c ) +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (196608A a c e + 655360B a c d e + 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (1440A B a c - 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (1728A a c - 9600A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 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c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (- 1440A B a c + 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (- 1728A a c + 9600A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R - +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R 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2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 4 3 3 2 4 2 +--R (- 8a c x - 16a c x - 8a c ) +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (- 196608A a c e - 655360B a c d e - 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (- 1440A B a c + 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (- 1728A a c + 9600A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (3A a c e + 5B a c d e + 6A c d )x + (- 9B a c e + A a c d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- A a c e - 3B a c d e + 10A a c d )x - 5B a e - 7A a c d e +--R + +--R 2 2 +--R - 4B a c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 4 4 3 3 2 4 2 +--R 16a c x + 32a c x + 16a c +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 +---+4+-+ +--R 16a c \|- a \|c +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (196608A a c e + 655360B a c d e + 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (1440A B a c - 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (1728A a c - 9600A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 2 2 +---+4+-+ +--R 16a c \|- a \|c +--R * +--R ROOT +--R - +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (196608A a c e + 655360B a c d e + 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (- 1440A B a c + 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (- 1728A a c + 9600A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R - +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 +--R (540A B c - 1500A B a c)d e +--R + +--R 2 2 2 2 8 +--R - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 +--R - 30A B a e + (- 45A a c - 75B a )d e +--R + +--R 2 2 3 2 2 2 2 3 2 +--R - 240A B a c d e + (- 180A a c - 100B a c)d e +--R + +--R 2 4 2 3 5 +--R - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +---+4+-+ +--R 16a c \|- a \|c +--R * +--R ROOT +--R - +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e 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+--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 2 2 +---+4+-+ +--R 16a c \|- a \|c +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 30A B a e + (- 45A a c - 75B a )d e - 240A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 100B a c)d e - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 6 7 2 6 7 5 8 2 +--R (- 196608A a c e - 655360B a c d e - 786432A a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 2 4 3 3 5 2 7 +--R (- 1440A B a c + 4000B a c )e +--R + +--R 3 3 4 2 4 3 6 2 3 4 2 5 +--R (- 1728A a c + 9600A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R 5 4 +--R 2048a c +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 450A B a c - 625B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (540A B c - 1500A B a c)d e - 900A B c d e +--R / +--R 5 9 +--R 4194304a c +--R + +--R 3 5 2 2 2 3 4 +--R - 30A B a e + (- 45A a c - 75B a )d e +--R + +--R 2 2 3 2 2 2 2 3 2 +--R - 240A B a c d e + (- 180A a c - 100B a c)d e +--R + +--R 2 4 2 3 5 +--R - 240A B a c d e - 144A c d +--R / +--R 5 4 +--R 1024a c +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (81A a c - 625B a )e + (810A B a c - 3750A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (972A a c - 5400A B a c - 2500B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 1080A B a c - 9000A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (1296A c - 10800A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 +---+ +-+ 2 3 2 +--R (3A a e + 5B a d e + 6A c d e)\|- a \|c - 5B a e - 9A a c d e +--R + +--R 2 2 3 +--R - 10B a c d e - 12A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 +---+ +-+ 2 3 2 +--R (3A a e + 5B a d e + 6A c d e)\|- a \|c + 5B a e + 9A a c d e +--R + +--R 2 2 3 +--R 10B a c d e + 12A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 32a c \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*(a+c*x^2)^2)-3/16*(a*A*e-_ + (2*A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a^2*c*(a+c*x^2))-3/32*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(e*(2*A*c*d+a*B*e)+a*_ + (4*A*c*d^2+2*a*B*d*e+a*A*e^2)*sqrt(c)/(-a)^(3/2))/(a^2*c^(7/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-3/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(2*A*c*d+a*B*e)+(4*A*c*d^2+_ + 2*a*B*d*e+a*A*e^2)*sqrt(c)/sqrt(-a))/(a^2*c^(7/4)*sqrt(e*sqrt(-a)+_ + d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 3 2 4 +--R (3A a c e + 6B a c d e + 12A c d )x +--R + +--R 2 2 2 2 2 2 3 2 3 +--R (6A a c e + 12B a c d e + 24A a c d )x + 3A a e + 6B a d e +--R + +--R 2 2 +--R 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 3 4 2 2 2 2 +--R (- 3B a c e - 6A c d e)x + (- 6B a c e - 12A a c d e)x +--R + +--R 3 2 2 +--R - 3B a e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 3 2 4 +--R (- 3A a c e - 6B a c d e - 12A c d )x +--R + +--R 2 2 2 2 2 2 3 2 3 +--R (- 6A a c e - 12B a c d e - 24A a c d )x - 3A a e - 6B a d e +--R + +--R 2 2 +--R - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 3 4 2 2 2 2 +--R (- 3B a c e - 6A c d e)x + (- 6B a c e - 12A a c d e)x +--R + +--R 3 2 2 +--R - 3B a e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 +--R (6B a c e + 12A c d)x + 2A a c e x + (- 2B a e + 20A a c d)x +--R + +--R 2 2 +--R - 6A a e - 8B a d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 3 4 3 2 2 4 +---+4+-+3 | +-+ +---+ +--R (32a c x + 64a c x + 32a c)\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 4 3 2 2 4 +--R (- 8a c x - 16a c x - 8a c) +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R 65536B a c e + 196608A a c d e + 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R 458752A a c d e + 131072B a c d e + 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (- 288A a c + 288A B a c )e + (288A B a c + 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (- 576A a c + 1152A B a c )d e + 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 4 3 2 2 4 +--R (8a c x + 16a c x + 8a c) +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R 65536B a c e + 196608A a c d e + 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R 458752A a c d e + 131072B a c d e + 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (288A a c - 288A B a c )e + (- 288A B a c - 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (576A a c - 1152A B a c )d e - 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 4 3 2 2 4 +--R (- 8a c x - 16a c x - 8a c) +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R - 65536B a c e - 196608A a c d e - 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R - 458752A a c d e - 131072B a c d e - 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (- 288A a c + 288A B a c )e + (288A B a c + 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (- 576A a c + 1152A B a c )d e + 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 4 3 2 2 4 +--R (8a c x + 16a c x + 8a c) +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R - 65536B a c e - 196608A a c d e - 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R - 458752A a c d e - 131072B a c d e - 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (288A a c - 288A B a c )e + (- 288A B a c - 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (576A a c - 1152A B a c )d e - 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 +--R (3B a c e + 6A c d)x + A a c e x + (- B a e + 10A a c d)x - 3A a e +--R + +--R 2 +--R - 4B a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 3 4 3 2 2 4 +--R 16a c x + 32a c x + 16a c +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 2 +---+4+-+3 +--R 16a c\|- a \|c +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R 65536B a c e + 196608A a c d e + 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R 458752A a c d e + 131072B a c d e + 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 +--R (- 288A a c + 288A B a c )e +--R + +--R 2 4 3 3 5 2 7 +--R (288A B a c + 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (- 576A a c + 1152A B a c )d e + 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 +--R - 18A B a e + (- 45A a c - 27B a )d e +--R + +--R 2 2 3 2 2 2 2 3 2 +--R - 144A B a c d e + (- 180A a c - 36B a c)d e +--R + +--R 2 4 2 3 5 +--R - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 +---+4+-+3 +--R 16a c\|- a \|c +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R 65536B a c e + 196608A a c d e + 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R 458752A a c d e + 131072B a c d e + 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (288A a c - 288A B a c )e + (- 288A B a c - 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (576A a c - 1152A B a c )d e - 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 2 +---+4+-+3 +--R 16a c\|- a \|c +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R - 65536B a c e - 196608A a c d e - 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R - 458752A a c d e - 131072B a c d e - 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 +--R (- 288A a c + 288A B a c )e +--R + +--R 2 4 3 3 5 2 7 +--R (288A B a c + 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (- 576A a c + 1152A B a c )d e + 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (- 2048a c e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 +--R - 18A B a e + (- 45A a c - 27B a )d e +--R + +--R 2 2 3 2 2 2 2 3 2 +--R - 144A B a c d e + (- 180A a c - 36B a c)d e +--R + +--R 2 4 2 3 5 +--R - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 +---+4+-+3 +--R 16a c\|- a \|c +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 8 5 5 7 6 4 7 6 2 3 +--R - 65536B a c e - 196608A a c d e - 196608B a c d e +--R + +--R 6 7 3 2 6 7 4 5 8 5 +--R - 458752A a c d e - 131072B a c d e - 262144A a c d +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 4 3 2 5 2 8 2 4 3 3 5 2 7 +--R (288A a c - 288A B a c )e + (- 288A B a c - 288B a c )d e +--R + +--R 3 3 4 2 4 3 2 6 2 3 4 3 5 +--R (576A a c - 1152A B a c )d e - 1152A B a c d e +--R * +--R ROOT +--R 6 3 2 5 4 2 +--R (2048a c e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 4 2 10 +--R (- 81A c + 162A B a c - 81B a )e +--R + +--R 3 2 3 9 2 2 2 2 8 +--R (324A B c - 324A B a c)d e - 324A B c d e +--R / +--R 7 7 4 6 8 2 2 5 9 4 +--R 4194304a c e + 8388608a c d e + 4194304a c d +--R + +--R 3 5 2 2 2 3 4 2 2 3 +--R - 18A B a e + (- 45A a c - 27B a )d e - 144A B a c d e +--R + +--R 2 2 2 2 3 2 2 4 2 3 5 +--R (- 180A a c - 36B a c)d e - 144A B a c d e - 144A c d +--R / +--R 6 3 2 5 4 2 +--R 1024a c e + 1024a c d +--R + +--R 4 2 2 4 4 9 3 2 2 3 3 8 +--R (27A a c - 27B a )e + (162A B a c - 270A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 7 +--R (324A a c - 648A B a c - 108B a c)d e +--R + +--R 3 3 3 2 2 3 6 +--R (- 216A B a c - 648A B a c )d e +--R + +--R 4 4 2 2 3 4 5 3 4 5 4 +--R (432A c - 1296A B a c )d e - 864A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +-+ 2 +---+ +--R ((- 3A a e - 6B a d e - 12A c d )\|c + (3B a e + 6A c d e)\|- a ) +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 +-+ 2 +---+ +--R ((3A a e + 6B a d e + 12A c d )\|c + (3B a e + 6A c d e)\|- a ) +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R 32a c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=-1/4*(a*B-A*c*x)*sqrt(d+e*x)/(a*c*(a+c*x^2)^2)+1/16*(a*e*(A*c*d+a*B*e)+_ + c*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*x)*sqrt(d+e*x)/(a^2*c*(c*d^2+a*e^2)*_ + (a+c*x^2))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + ((-a*B*e*(2*c*d^2+3*a*e^2)-A*c*d*(12*c*d^2+13*a*e^2))/sqrt(-a)+_ + e*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*sqrt(c))/(a^2*c^(5/4)*(c*d^2+a*e^2)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*((a*B*e*(2*c*d^2+3*a*e^2)+A*c*d*(12*c*d^2+_ + 13*a*e^2))/sqrt(-a)+e*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*sqrt(c))/_ + (a^2*c^(5/4)*(c*d^2+a*e^2)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 5A a c e - B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 +--R (- 10A a c e - 2B a c d e - 12A a c d e)x - 5A a e - B a d e +--R + +--R 2 2 +--R - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 13A a c d e + 2B a c d e + 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 26A a c d e + 4B a c d e + 24A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 13A a c d e + 2B a c d e + 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 3 2 2 3 2 4 +--R (- 5A a c e - B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 +--R (- 10A a c e - 2B a c d e - 12A a c d e)x - 5A a e - B a d e +--R + +--R 2 2 +--R - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (- 3B a c e - 13A a c d e - 2B a c d e - 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (- 6B a c e - 26A a c d e - 4B a c d e - 24A a c d )x - 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R - 13A a c d e - 2B a c d e - 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (10A a c e + 2B a c d e + 12A c d )x + (2B a c e + 2A a c d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R (18A a c e + 2B a c d e + 20A a c d )x - 6B a e + 2A a c d e +--R + +--R 2 2 +--R - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 4 2 2 +--R ((32a c e + 32a c d )x + (64a c e + 64a c d )x + 32a c e + 32a c d ) +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 4 2 2 +--R ((8a c e + 8a c d )x + (16a c e + 16a c d )x + 8a c e + 8a c d ) +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (2048a c e + 6144a c d e + 6144a c d e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R 327680A a c e + 262144B a c d e + 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R 917504B a c d e + 5505024A a c d e + 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R 6422528A a c d e + 655360B a c d e + 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R 131072B a c d e + 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 5 11 12 +--R 62914560a c d e + 25165824a c d e + 4194304a c d +--R + +--R 2 6 2 3 7 11 +--R (2400A B a c - 864B a c)e +--R + +--R 3 5 3 2 6 2 10 +--R (6400A a c - 5952A B a c )d e +--R + +--R 2 5 3 3 6 2 2 9 +--R (- 6912A B a c - 768B a c )d e +--R + +--R 3 4 4 2 5 3 3 8 +--R (10176A a c - 7104A B a c )d e +--R + +--R 2 4 4 3 5 3 4 7 +--R (- 14304A B a c - 160B a c )d e +--R + +--R 3 3 5 2 4 4 5 6 2 3 5 6 5 +--R (4032A a c - 1920A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (2048a c e + 6144a c d e + 6144a c d e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 +--R (- 8a c e - 8a c d )x + (- 16a c e - 16a c d )x - 8a c e +--R + +--R 4 2 2 +--R - 8a c d +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (- 2048a c e - 6144a c d e - 6144a c d e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R 327680A a c e + 262144B a c d e + 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R 917504B a c d e + 5505024A a c d e + 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R 6422528A a c d e + 655360B a c d e + 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R 131072B a c d e + 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 5 11 12 +--R 62914560a c d e + 25165824a c d e + 4194304a c d +--R + +--R 2 6 2 3 7 11 +--R (- 2400A B a c + 864B a c)e +--R + +--R 3 5 3 2 6 2 10 +--R (- 6400A a c + 5952A B a c )d e +--R + +--R 2 5 3 3 6 2 2 9 +--R (6912A B a c + 768B a c )d e +--R + +--R 3 4 4 2 5 3 3 8 +--R (- 10176A a c + 7104A B a c )d e +--R + +--R 2 4 4 3 5 3 4 7 +--R (14304A B a c + 160B a c )d e +--R + +--R 3 3 5 2 4 4 5 6 2 3 5 6 5 +--R (- 4032A a c + 1920A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 +--R - 2048a c e - 6144a c d e - 6144a c d e +--R + +--R 5 5 6 +--R - 2048a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 4 2 2 +--R ((8a c e + 8a c d )x + (16a c e + 16a c d )x + 8a c e + 8a c d ) +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (- 2048a c e - 6144a c d e - 6144a c d e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R - 327680A a c e - 262144B a c d e - 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R - 917504B a c d e - 5505024A a c d e - 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R - 6422528A a c d e - 655360B a c d e - 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R - 131072B a c d e - 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 5 11 12 +--R 62914560a c d e + 25165824a c d e + 4194304a c d +--R + +--R 2 6 2 3 7 11 +--R (2400A B a c - 864B a c)e +--R + +--R 3 5 3 2 6 2 10 +--R (6400A a c - 5952A B a c )d e +--R + +--R 2 5 3 3 6 2 2 9 +--R (- 6912A B a c - 768B a c )d e +--R + +--R 3 4 4 2 5 3 3 8 +--R (10176A a c - 7104A B a c )d e +--R + +--R 2 4 4 3 5 3 4 7 +--R (- 14304A B a c - 160B a c )d e +--R + +--R 3 3 5 2 4 4 5 6 2 3 5 6 5 +--R (4032A a c - 1920A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 +--R - 2048a c e - 6144a c d e - 6144a c d e +--R + +--R 5 5 6 +--R - 2048a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 +--R (- 8a c e - 8a c d )x + (- 16a c e - 16a c d )x - 8a c e +--R + +--R 4 2 2 +--R - 8a c d +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (2048a c e + 6144a c d e + 6144a c d e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R - 327680A a c e - 262144B a c d e - 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R - 917504B a c d e - 5505024A a c d e - 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R - 6422528A a c d e - 655360B a c d e - 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R - 131072B a c d e - 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 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8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 2 2 +---+4+-+ +--R (16a c e + 16a c d )\|- a \|c +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (- 2048a c e - 6144a c d e - 6144a c d e - 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R - 327680A a c e - 262144B a c d e - 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R - 917504B a c d e - 5505024A a c d e - 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R - 6422528A a c d e - 655360B a c d e - 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R - 131072B a c d e - 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 5 11 12 +--R 62914560a c d e + 25165824a c d e + 4194304a c d +--R + +--R 2 6 2 3 7 11 +--R (2400A B a c - 864B a c)e +--R + +--R 3 5 3 2 6 2 10 +--R (6400A a c - 5952A B a c )d e +--R + +--R 2 5 3 3 6 2 2 9 +--R (- 6912A B a c - 768B a c )d e +--R + +--R 3 4 4 2 5 3 3 8 +--R (10176A a c - 7104A B a c )d e +--R + +--R 2 4 4 3 5 3 4 7 +--R (- 14304A B a c - 160B a c )d e +--R + +--R 3 3 5 2 4 4 5 6 2 3 5 6 5 +--R (4032A a c - 1920A B a c )d e - 5760A B a c d e +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 +--R - 2048a c e - 6144a c d e - 6144a c d e +--R + +--R 5 5 6 +--R - 2048a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 2 2 +---+4+-+ +--R (- 16a c e - 16a c d )\|- a \|c +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (2048a c e + 6144a c d e + 6144a c d e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 9 7 4 8 +--R 4194304a c e + 25165824a c d e + 62914560a c d e +--R + +--R 8 8 6 6 7 9 8 4 +--R 83886080a c d e + 62914560a c d e +--R + +--R 6 10 10 2 5 11 12 +--R 25165824a c d e + 4194304a c d +--R + +--R 4 7 2 3 2 4 6 3 2 5 +--R - 30A B a e + (- 105A a c - 15B a )d e - 150A B a c d e +--R + +--R 2 2 2 2 3 3 4 2 2 4 3 +--R (- 385A a c - 15B a c)d e - 160A B a c d e +--R + +--R 2 3 2 2 2 5 2 3 6 2 4 7 +--R (- 420A a c - 4B a c )d e - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R * +--R log +--R 10 4 10 10 4 9 9 5 2 8 +--R - 327680A a c e - 262144B a c d e - 2228224A a c d e +--R + +--R 9 5 3 7 8 6 4 6 8 6 5 5 +--R - 917504B a c d e - 5505024A a c d e - 1179648B a c d e +--R + +--R 7 7 6 4 7 7 7 3 6 8 8 2 +--R - 6422528A a c d e - 655360B a c d e - 3604480A a c d e +--R + +--R 6 8 9 5 9 10 +--R - 131072B a c d e - 786432A a c d +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 5 11 12 +--R 62914560a c d e + 25165824a c d e + 4194304a c d +--R + +--R 2 6 2 3 7 11 +--R (- 2400A B a c + 864B a c)e +--R + +--R 3 5 3 2 6 2 10 +--R (- 6400A a c + 5952A B a c )d e +--R + +--R 2 5 3 3 6 2 2 9 +--R (6912A B a c + 768B a c )d e +--R + +--R 3 4 4 2 5 3 3 8 +--R (- 10176A a c + 7104A B a c )d e +--R + +--R 2 4 4 3 5 3 4 7 +--R (14304A B a c + 160B a c )d e +--R + +--R 3 3 5 2 4 4 5 6 2 3 5 6 5 +--R (- 4032A a c + 1920A B a c )d e + 5760A B a c d e +--R * +--R ROOT +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R (2048a c e + 6144a c d e + 6144a c d e + 2048a c d ) +--R * +--R ROOT +--R 4 2 2 2 2 3 4 4 14 +--R (- 625A a c + 450A B a c - 81B a )e +--R + +--R 3 2 2 3 3 13 +--R (1900A B a c - 684A B a c)d e +--R + +--R 4 3 2 2 2 2 4 3 2 12 +--R (- 1050A a c - 816A B a c - 90B a c)d e +--R + +--R 3 3 3 2 2 3 11 +--R (3096A B a c - 920A B a c )d e +--R + +--R 4 4 2 2 3 4 2 2 4 10 +--R (- 441A c - 2070A B a c - 25B a c )d e +--R + +--R 3 4 3 3 5 9 2 2 4 6 8 +--R (1260A B c - 300A B a c )d e - 900A B c d e +--R / +--R 11 5 12 10 6 2 10 +--R 4194304a c e + 25165824a c d e +--R + +--R 9 7 4 8 8 8 6 6 +--R 62914560a c d e + 83886080a c d e +--R + +--R 7 9 8 4 6 10 10 2 +--R 62914560a c d e + 25165824a c d e +--R + +--R 5 11 12 +--R 4194304a c d +--R + +--R 4 7 2 3 2 4 6 +--R - 30A B a e + (- 105A a c - 15B a )d e +--R + +--R 3 2 5 2 2 2 2 3 3 4 +--R - 150A B a c d e + (- 385A a c - 15B a c)d e +--R + +--R 2 2 4 3 2 3 2 2 2 5 2 +--R - 160A B a c d e + (- 420A a c - 4B a c )d e +--R + +--R 3 6 2 4 7 +--R - 48A B a c d e - 144A c d +--R / +--R 8 2 6 7 3 2 4 6 4 4 2 5 5 6 +--R 1024a c e + 3072a c d e + 3072a c d e + 1024a c d +--R + +--R 4 3 2 4 5 11 3 3 2 3 4 10 +--R (625A a c - 81B a )e + (1250A B a c - 1134A B a c)d e +--R + +--R 4 2 3 2 2 3 2 4 4 2 9 +--R (5625A a c - 5016A B a c - 81B a c)d e +--R + +--R 3 2 3 3 3 2 3 8 +--R (- 5454A B a c - 1294A B a c )d e +--R + +--R 4 4 2 2 2 3 4 3 2 4 7 +--R (7884A a c - 6696A B a c - 20B a c )d e +--R + +--R 3 4 3 2 3 5 6 +--R (- 10584A B a c - 360A B a c )d e +--R + +--R 4 5 2 2 4 6 5 3 5 7 4 +--R (3024A c - 2160A B a c )d e - 4320A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 2 2 +---+ +-+ 2 3 2 +--R (5A a e + B a d e + 6A c d e)\|- a \|c - 3B a e - 13A a c d e +--R + +--R 2 2 3 +--R - 2B a c d e - 12A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 +---+ +-+ 2 3 2 +--R (5A a e + B a d e + 6A c d e)\|- a \|c + 3B a e + 13A a c d e +--R + +--R 2 2 3 +--R 2B a c d e + 12A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 3 2 2 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (32a c e + 32a c d )\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich12c.input.pamphlet b/src/input/rich12c.input.pamphlet new file mode 100644 index 0000000..6f9fc9f --- /dev/null +++ b/src/input/rich12c.input.pamphlet @@ -0,0 +1,75902 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12c.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 155 integrals in this file. +\item 155 supplied "optimal results". +\item 211 matching answers. +\item 4 cases where Axiom answer differs from Rubi +\item 35 cases where Axiom supplied 2 results. +\item 26 cases that Axiom failed to integrate. +\item 15 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12c.output +)spool rich12c.output +)set message test on +)set message auto off +)clear all + +--S 1 of 845 +t0:=(A+B*x)/((a+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R 3 6 2 4 2 2 3 +-------+ +--R (c x + 3a c x + 3a c x + a )\|e x + d +--R Type: Expression(Integer) +--E 1 + +--S 2 of 845 +r0:=-1/4*(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ + (a+c*x^2)^2)+1/16*(a*e*(A*c*d^2-6*a*B*d*e+7*a*A*e^2)-(a*B*e*(c*d^2-_ + 5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))*x)*sqrt(d+e*x)/(a^2*(c*d^2+a*e^2)^2*_ + (a+c*x^2))+1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (e*(a*B*e*(c*d^2-5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))-(2*a*B*d*e*(c*d^2+_ + 4*a*e^2)-3*A*(4*c^2*d^4+9*a*c*d^2*e^2+7*a^2*e^4))*sqrt(c)/sqrt(-a))/_ + (a^2*c^(3/4)*(c*d^2+a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))+_ + 1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(a*B*e*_ + (c*d^2-5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))+(2*a*B*d*e*(c*d^2+4*a*e^2)-_ + 3*A*(4*c^2*d^4+9*a*c*d^2*e^2+7*a^2*e^4))*sqrt(c)/sqrt(-a))/(a^2*c^(3/4)*_ + (c*d^2+a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 +--R 21A a c e - 8B a c d e + 27A a c d e - 2B a c d e +--R + +--R 4 4 +--R 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R 42A a c e - 16B a c d e + 54A a c d e - 4B a c d e +--R + +--R 3 4 +--R 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R 21A a e - 8B a d e + 27A a c d e - 2B a c d e + 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 5B a c e - 12A a c d e + B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 10B a c e - 24A a c d e + 2B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 5B a e - 12A a c d e + B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 +--R - 21A a c e + 8B a c d e - 27A a c d e + 2B a c d e +--R + +--R 4 4 +--R - 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 42A a c e + 16B a c d e - 54A a c d e + 4B a c d e +--R + +--R 3 4 +--R - 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R - 21A a e + 8B a d e - 27A a c d e + 2B a c d e - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 5B a c e - 12A a c d e + B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 10B a c e - 24A a c d e + 2B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 5B a e - 12A a c d e + B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (10B a c e + 24A a c d e - 2B a c d e + 12A c d )x +--R + +--R 2 3 2 2 2 2 2 +--R (14A a c e - 12B a c d e + 2A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (18B a e + 32A a c d e + 6B a c d e + 20A a c d )x + 22A a e +--R + +--R 3 2 2 2 2 3 +--R - 20B a d e + 10A a c d e - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 4 2 4 3 3 2 2 2 4 4 4 +--R (32a c e + 64a c d e + 32a c d )x +--R + +--R 5 4 4 2 2 2 3 3 4 2 6 4 5 2 2 4 2 4 +--R (64a c e + 128a c d e + 64a c d )x + 32a e + 64a c d e + 32a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 4 3 3 2 2 2 4 4 4 +--R (- 8a c e - 16a c d e - 8a c d )x +--R + +--R 5 4 4 2 2 2 3 3 4 2 6 4 5 2 2 4 2 4 +--R (- 16a c e - 32a c d e - 16a c d )x - 8a e - 16a c d e - 8a c d +--R * +--R ROOT +--R 10 10 9 2 2 8 8 3 4 6 7 4 6 4 +--R 2048a c e + 10240a c d e + 20480a c d e + 20480a c d e +--R + +--R 6 5 8 2 5 6 10 +--R 10240a c d e + 2048a c d +--R * +--R ROOT 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- 260190A B a c - 1225B a c )d e +--R + +--R 3 6 3 5 9 9 +--R (79380A B c + 14700A B a c )d e +--R + +--R 2 2 6 10 8 +--R - 44100A B c d e +--R / +--R 15 3 20 14 4 2 18 +--R 4194304a c e + 41943040a c d e +--R + +--R 13 5 4 16 12 6 6 14 +--R 188743680a c d e + 503316480a c d e +--R + +--R 11 7 8 12 10 8 10 10 +--R 880803840a c d e + 1056964608a c d e +--R + +--R 9 9 12 8 8 10 14 6 +--R 880803840a c d e + 503316480a c d e +--R + +--R 7 11 16 4 6 12 18 2 +--R 188743680a c d e + 41943040a c d e +--R + +--R 5 13 20 +--R 4194304a c d +--R + +--R 5 9 2 4 2 5 8 +--R - 210A B a e + (- 945A a c + 105B a )d e +--R + +--R 4 2 7 2 3 2 2 4 3 6 +--R 420A B a c d e + (- 1890A a c - 70B a c)d e +--R + +--R 3 2 4 5 2 2 3 2 3 2 5 4 +--R 630A B a c d e + (- 1701A a c - 35B a c )d e +--R + +--R 2 3 6 3 2 4 2 2 3 7 2 +--R 336A B a c d e + (- 756A a c - 4B a c )d e +--R + +--R 4 8 2 5 9 +--R 48A B a c d e - 144A c d +--R / +--R 10 10 9 2 2 8 8 3 4 6 +--R 1024a c e + 5120a c d e + 10240a c d e +--R + +--R 7 4 6 4 6 5 8 2 5 6 10 +--R 10240a c d e + 5120a c d e + 1024a c d +--R + +--R 4 4 2 4 6 13 +--R (194481A a c - 625B a )e +--R + +--R 3 4 2 3 5 12 +--R (- 388962A B a c - 11250A B a c)d e +--R + +--R 4 3 3 2 2 4 2 4 5 2 11 +--R (388962A a c + 215784A B a c + 3750B a c)d e +--R + +--R 3 3 3 3 4 2 3 10 +--R (- 649188A B a c - 49428A B a c )d e +--R + +--R 4 2 4 2 2 3 3 4 4 2 4 9 +--R (339309A a c + 238464A B a c + 1491B a c )d e +--R + +--R 3 2 4 3 3 3 5 8 +--R (- 485514A B a c - 22554A B a c )d e +--R + +--R 4 5 2 2 2 4 4 3 3 6 7 +--R (144828A a c + 110376A B a c + 140B a c )d e +--R + +--R 3 5 3 2 4 7 6 +--R (- 176904A B a c - 2520A B a c )d e +--R + +--R 4 6 2 2 5 8 5 3 6 9 4 +--R (27216A c + 15120A B a c )d e - 30240A B c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 2 3 2 2 3 2 4 +-+ +--R (- 21A a e + 8B a d e - 27A a c d e + 2B a c d e - 12A c d )\|c +--R + +--R 2 4 3 2 2 2 3 +---+ +--R (5B a e + 12A a c d e - B a c d e + 6A c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 4 2 3 2 2 3 2 4 +-+ +--R (21A a e - 8B a d e + 27A a c d e - 2B a c d e + 12A c d )\|c +--R + +--R 2 4 3 2 2 2 3 +---+ +--R (5B a e + 12A a c d e - B a c d e + 6A c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +--R 4 4 3 2 2 2 2 4 +---+4+-+3 | +-+ +---+ +--R (32a e + 64a c d e + 32a c d )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 4 + +--S 5 of 845 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 845 +t0:=x*sqrt(1+x)/(1+x^2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (1) --------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 845 +r0:=-atanh(sqrt(1+x)/sqrt(1-%i))*sqrt(1-%i)-atanh(sqrt(1+x)/sqrt(1+%i))*_ + sqrt(1+%i)+2*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R +------+ \|x + 1 +------+ \|x + 1 +-----+ +--R (2) - \|1 - %i atanh(---------) - \|1 + %i atanh(---------) + 2\|x + 1 +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 7 + +--S 8 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(- 2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +--R 2\|2 sin(---)atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 - \|2 cos(---) +--R 8 +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +-----+ +--R 2\|2 sin(---)atan(-----------------------) + 4\|x + 1 +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 + \|2 cos(---) +--R 8 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(- 2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R +-----+ +-----+ +--R +------+ \|x + 1 +------+ \|x + 1 +--R 2\|1 - %i atanh(---------) + 2\|1 + %i atanh(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +--R 2\|2 sin(---)atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 - \|2 cos(---) +--R 8 +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +--R 2\|2 sin(---)atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 + \|2 cos(---) +--R 8 +--R / +--R 2 +--R Type: Expression(Complex(Integer)) +--E 9 + +--S 10 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 %pi 4 3 2 4+-+2 %pi 2 4 3 +--R (- 8x - 8x)cos(---) + (8x + 16x + 8x)\|2 cos(---) - 4x - 12x +--R 8 8 +--R + +--R 2 +--R - 12x - 4x +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 3 2 4+-+2 %pi 4 +--R (- 32x - 32x)cos(---) + (20x + 36x + 20x + 4)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (8x + 32x + 32x - 8)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (- 6x - 26x - 40x - 24x - 2x + 2)\|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 3 2 4+-+2 %pi 6 +--R (- 48x - 48x)cos(---) + (36x + 68x + 36x + 4)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 4 +--R (- 12x - 40x - 40x - 8x + 4)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 6 5 +--R (6x + 34x + 56x + 24x - 14x - 10)\|2 cos(---) - 6x - 36x +--R 8 +--R + +--R 4 3 2 +--R - 78x - 72x - 18x + 12x + 6 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 3 2 4+-+2 %pi 8 +--R (- 32x - 32x)cos(---) + (44x + 92x + 44x - 4)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 6 +--R (- 32x - 96x - 96x - 32x)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (- 4x - 28x - 48x - 16x + 20x + 12)\|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (8x + 56x + 128x + 112x + 8x - 40x - 16)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (- x - 9x - 27x - 35x - 15x + 9x + 11x + 3)\|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (- 8x - 8x)cos(---) + (20x + 44x + 20x - 4)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (- 40x - 140x - 140x - 20x + 20)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (20x + 100x + 160x + 80x - 20x - 20)\|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (- 10x - 70x - 160x - 140x - 10x + 50x + 20)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 7 +--R (x + 11x + 35x + 45x + 15x - 19x - 19x - 5)\|2 cos(---) - x +--R 8 +--R + +--R 6 5 4 3 2 +--R - 5x - 9x - 5x + 5x + 9x + 5x + 1 +--R / +--R 2 %pi 4 3 2 4+-+2 %pi 2 4 +--R (8x + 8)cos(---) + (- 8x - 8x - 8x - 8)\|2 cos(---) + 4x +--R 8 8 +--R + +--R 3 2 +--R 8x + 8x + 8x + 4 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 3 2 4+-+2 %pi 4 +--R (32x + 32)cos(---) + (- 16x - 16x - 16x - 16)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (- 16x - 32x - 32x - 32x - 16)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (8x + 24x + 32x + 32x + 24x + 8)\|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 3 2 4+-+2 %pi 6 +--R (48x + 48)cos(---) + (- 32x - 32x - 32x - 32)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 4 +--R (16x + 32x + 32x + 32x + 16)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 6 +--R (- 16x - 48x - 64x - 64x - 48x - 16)\|2 cos(---) + 12x +--R 8 +--R + +--R 5 4 3 2 +--R 48x + 84x + 96x + 84x + 48x + 12 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 3 2 4+-+2 %pi 8 +--R (32x + 32)cos(---) + (- 48x - 48x - 48x - 48)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 6 +--R (32x + 64x + 64x + 64x + 32)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (16x + 48x + 64x + 64x + 48x + 16)\|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (- 24x - 96x - 168x - 192x - 168x - 96x - 24)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (4x + 20x + 44x + 60x + 60x + 44x + 20x + 4)\|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (8x + 8)cos(---) + (- 24x - 24x - 24x - 24)\|2 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (60x + 120x + 120x + 120x + 60)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (- 40x - 120x - 160x - 160x - 120x - 40)\|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (30x + 120x + 210x + 240x + 210x + 120x + 30)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 8 +--R (- 6x - 30x - 66x - 90x - 90x - 66x - 30x - 6)\|2 cos(---) + x +--R 8 +--R + +--R 7 6 5 4 3 2 +--R 6x + 16x + 26x + 30x + 26x + 16x + 6x + 1 +--R * +--R +-----+ +--R \|x + 1 +--R Type: Expression(Complex(Integer)) +--E 10 + +)clear all + +--S 11 of 845 +t0:=(1-x)*sqrt(1+x)/(1+x^2) +--R +--R +--R +-----+ +--R (- x + 1)\|x + 1 +--R (1) ----------------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 845 +r0:=(1-%i)^(3/2)*atanh(sqrt(1+x)/sqrt(1-%i))+(1+%i)^(3/2)*_ + atanh(sqrt(1+x)/sqrt(1+%i))-2*sqrt(1+x) +--R +--R +--R (2) +--R +-----+ +-----+ +--R +------+ \|x + 1 +------+ \|x + 1 +--R (1 - %i)\|1 - %i atanh(---------) + (1 + %i)\|1 + %i atanh(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R + +--R +-----+ +--R - 2\|x + 1 +--R Type: Expression(Complex(Integer)) +--E 12 + +--S 13 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 4+-+ %pi +--R \|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (2\|8 sin(---) - 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi +--R \|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (- 2\|8 sin(---) + 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 2\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 - \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +-----+ +--R - 2\|8 sin(---)atan(---------------------------------------) - 4\|x + 1 +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 + \|8 sin(---) - \|8 cos(---) +--R 8 8 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 4+-+ %pi +--R \|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (2\|8 sin(---) - 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi +--R \|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (- 2\|8 sin(---) + 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R +-----+ +--R +------+ \|x + 1 +--R (- 2 + 2%i)\|1 - %i atanh(---------) +--R +------+ +--R \|1 - %i +--R + +--R +-----+ +--R +------+ \|x + 1 +--R (- 2 - 2%i)\|1 + %i atanh(---------) +--R +------+ +--R \|1 + %i +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 2\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 - \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 2\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 + \|8 sin(---) - \|8 cos(---) +--R 8 8 +--R / +--R 2 +--R Type: Expression(Complex(Integer)) +--E 14 + +--S 15 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 %pi 12 2 %pi %pi 11 +--R (8x - 8)sin(---) + (- 32x + 32)cos(---)sin(---) +--R 8 8 8 +--R + +--R 2 %pi 2 3 2 4+-+2 %pi 10 +--R ((80x - 80)cos(---) + (- 6x - 6x + 10x + 10)\|8 )sin(---) +--R 8 8 +--R + +--R 2 %pi 3 3 2 4+-+2 %pi +--R ((- 160x + 160)cos(---) + (20x + 20x - 44x - 44)\|8 cos(---)) +--R 8 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 2 %pi 4 3 2 4+-+2 %pi 2 +--R (248x - 248)cos(---) + (- 74x - 74x + 134x + 134)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 +--R 4x + 8x - 40x - 88x - 44 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 5 3 2 4+-+2 %pi 3 +--R (- 320x + 320)cos(---) + (144x + 144x - 240x - 240)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi +--R (- 64x - 128x + 192x + 512x + 256)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 3 2 4+-+2 %pi 4 +--R (352x - 352)cos(---) + (- 212x - 212x + 332x + 332)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (224x + 448x - 448x - 1344x - 672)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (x + 3x + 20x + 52x + 51x + 17)\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 7 3 2 4+-+2 %pi 5 +--R (- 320x + 320)cos(---) + (264x + 264x - 376x - 376)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 3 +--R (- 352x - 704x + 768x + 2240x + 1120)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (14x + 42x - 56x - 280x - 294x - 98)\|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 3 2 4+-+2 %pi 6 +--R (248x - 248)cos(---) + (- 236x - 236x + 308x + 308)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 4 +--R (728x + 1456x - 752x - 2960x - 1480)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 4 +--R (- 11x - 33x + 196x + 676x + 687x + 229)\|8 cos(---) - 36x +--R 8 +--R + +--R 3 2 +--R - 144x - 216x - 144x - 36 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 9 3 2 4+-+2 %pi 7 +--R (- 160x + 160)cos(---) + (176x + 176x - 208x - 208)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 5 +--R (- 576x - 1152x + 320x + 1792x + 896)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (140x + 420x + 16x - 1072x - 1212x - 404)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi +--R (32x + 128x + 368x + 832x + 1088x + 704x + 176)cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 3 2 4+-+2 %pi 8 +--R (80x - 80)cos(---) + (- 102x - 102x + 106x + 106)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 6 +--R (416x + 832x - 64x - 960x - 480)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (- 93x - 279x - 132x + 348x + 441x + 147)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (112x + 448x + 184x - 1504x - 2816x - 1952x - 488)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (2x + 10x + 26x + 50x + 70x + 62x + 30x + 6)\|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 11 3 2 4+-+2 %pi 9 +--R (- 32x + 32)cos(---) + (36x + 36x - 28x - 28)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 %pi 7 +--R (- 160x - 320x + 320x + 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (54x + 162x + 104x - 120x - 174x - 58)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 3 +--R (- 64x - 256x - 304x + 64x + 416x + 320x + 80)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi +--R (4x + 20x + 4x - 140x - 340x - 356x - 180x - 36)\|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (8x - 8)cos(---) + (- 10x - 10x + 6x + 6)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (36x + 72x + 24x - 24x - 12)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (- 9x - 27x - 20x + 12x + 21x + 7)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (16x + 64x + 76x - 16x - 104x - 80x - 20)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 6 +--R (- 2x - 10x - 18x - 10x + 10x + 18x + 10x + 2)\|8 cos(---) - 8x +--R 8 +--R + +--R 5 4 3 2 +--R - 48x - 120x - 160x - 120x - 48x - 8 +--R / +--R 2 %pi 12 2 %pi %pi 11 +--R (8x + 8)sin(---) + (- 32x - 32)cos(---)sin(---) +--R 8 8 8 +--R + +--R 2 %pi 2 3 2 4+-+2 %pi 10 +--R ((80x + 80)cos(---) + (- 8x - 8x - 8x - 8)\|8 )sin(---) +--R 8 8 +--R + +--R 2 %pi 3 3 2 4+-+2 %pi +--R ((- 160x - 160)cos(---) + (32x + 32x + 32x + 32)\|8 cos(---)) +--R 8 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 2 %pi 4 +--R (248x + 248)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 2 4 3 2 +--R (- 104x - 104x - 104x - 104)\|8 cos(---) + 24x + 48x + 48x +--R 8 +--R + +--R 48x + 24 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 5 +--R (- 320x - 320)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 3 +--R (192x + 192x + 192x + 192)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi +--R (- 160x - 320x - 320x - 320x - 160)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 +--R (352x + 352)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 4 +--R (- 272x - 272x - 272x - 272)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 2 +--R (448x + 896x + 896x + 896x + 448)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (- 8x - 24x - 32x - 32x - 24x - 8)\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 7 +--R (- 320x - 320)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 5 +--R (320x + 320x + 320x + 320)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (- 736x - 1472x - 1472x - 1472x - 736)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (56x + 168x + 224x + 224x + 168x + 56)\|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 +--R (248x + 248)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 6 +--R (- 272x - 272x - 272x - 272)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (1104x + 2208x + 2208x + 2208x + 1104)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 6 +--R (- 120x - 360x - 480x - 480x - 360x - 120)\|8 cos(---) + 18x +--R 8 +--R + +--R 5 4 3 2 +--R 72x + 126x + 144x + 126x + 72x + 18 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 9 +--R (- 160x - 160)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 7 +--R (192x + 192x + 192x + 192)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (- 736x - 1472x - 1472x - 1472x - 736)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (272x + 816x + 1088x + 1088x + 816x + 272)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi +--R (- 72x - 288x - 504x - 576x - 504x - 288x - 72)cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 +--R (80x + 80)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 8 +--R (- 104x - 104x - 104x - 104)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (448x + 896x + 896x + 896x + 448)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (- 120x - 360x - 480x - 480x - 360x - 120)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (300x + 1200x + 2100x + 2400x + 2100x + 1200x + 300)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (- 2x - 10x - 22x - 30x - 30x - 22x - 10x - 2)\|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 11 3 2 4+-+2 %pi 9 +--R (- 32x - 32)cos(---) + (32x + 32x + 32x + 32)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 7 +--R (- 160x - 320x - 320x - 320x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (56x + 168x + 224x + 224x + 168x + 56)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 3 +--R (- 72x - 288x - 504x - 576x - 504x - 288x - 72)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (20x + 100x + 220x + 300x + 300x + 220x + 100x + 20)\|8 +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (8x + 8)cos(---) + (- 8x - 8x - 8x - 8)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (24x + 48x + 48x + 48x + 24)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (- 8x - 24x - 32x - 32x - 24x - 8)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (18x + 72x + 126x + 144x + 126x + 72x + 18)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 +--R (- 2x - 10x - 22x - 30x - 30x - 22x - 10x - 2)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 4x + 24x + 64x + 104x + 120x + 104x + 64x + 24x + 4 +--R * +--R +-----+ +--R \|x + 1 +--R Type: Expression(Complex(Integer)) +--E 15 + +)clear all + +--S 16 of 845 +t0:=(A+B*x)*sqrt(d+e*x)*sqrt(a+c*x^2) +--R +--R +--R +--------+ +--R +-------+ | 2 +--R (1) (B x + A)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 845 +--r0:=2/7*B*(a+c*x^2)^(3/2)*sqrt(d+e*x)/c-2/105*(4*B*c*d^2-7*A*c*d*e+_ +-- 5*a*B*e^2-3*c*e*(B*d+7*A*e)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/(c*e^2)+_ +-- 4/105*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*_ +-- (4*c^(3/2)*d^3-c*d^2*e*sqrt(-a)-5*a*e^3*sqrt(-a)+8*a*d*e^2*sqrt(c))+_ +-- 7*A*e*sqrt(c)*(c*d^2-3*a*e^2-4*d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*e^3*_ +-- sqrt(a+c*x^2))-4/105*(4*B*c*d^3-7*A*c*d^2*e+8*a*B*d*e^2+21*a*A*e^3)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^4*sqrt(a+c*x^2)) +--E 17 + +--S 18 of 845 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 845 +--m0:=a0-r0 +--E 19 + +--S 20 of 845 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 845 +t0:=(A+B*x)*sqrt(a+c*x^2)/sqrt(d+e*x) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) -------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 21 + +--S 22 of 845 +--r0:=-2/15*(4*B*d-5*A*e-3*B*e*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^2-_ +-- 4/15*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(4*B*c*d^2-_ +-- 5*A*c*d*e+3*a*B*e^2-B*d*e*sqrt(-a)*sqrt(c)+5*A*e^2*sqrt(-a)*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(3/4)*e^3*sqrt(a+c*x^2))-4/15*(4*B*c*d^2-5*A*c*d*e+3*a*B*e^2)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^4*sqrt(a+c*x^2)) +--E 22 + +--S 23 of 845 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 845 +--m0:=a0-r0 +--E 24 + +--S 25 of 845 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 845 +t0:=(A+B*x)*sqrt(a+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) -------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 26 + +--S 27 of 845 +--r0:=2/3*(4*B*d-3*A*e+B*e*x)*sqrt(a+c*x^2)/(e^2*sqrt(d+e*x))+_ +-- 4/3*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*e*_ +-- sqrt(-a)+4*B*d*sqrt(c)-3*A*e*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e^3*sqrt(a+c*x^2))+_ +-- 4/3*c^(1/4)*(4*B*d-3*A*e)*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^4*sqrt(a+c*x^2)) +--E 27 + +--S 28 of 845 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 845 +--m0:=a0-r0 +--E 29 + +--S 30 of 845 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 845 +t0:=(A+B*x)*sqrt(a+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 31 + +--S 32 of 845 +--r0:=2/3*(4*B*d-A*e+3*B*e*x)*sqrt(a+c*x^2)/(e^2*(d+e*x)^(3/2))-_ +-- 4/3*(4*B*c*d^2-A*c*d*e+3*a*B*e^2)*sqrt(a+c*x^2)/(e^2*(c*d^2+a*e^2)*_ +-- sqrt(d+e*x))-4/3*c^(1/4)*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-a)*(4*B*c*d^2-A*c*d*e+3*a*B*e^2-B*d*e*sqrt(-a)*sqrt(c)+A*e^2*_ +-- sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-_ +-- x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*_ +-- sqrt(-a)+d*sqrt(c)))/(e^3*(c*d^2+a*e^2)*sqrt(a+c*x^2))-4/3*c^(1/4)*_ +-- (4*B*c*d^2-A*c*d*e+3*a*B*e^2)*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^4*(c*d^2+a*e^2)*sqrt(a+c*x^2)) +--E 32 + +--S 33 of 845 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 845 +--m0:=a0-r0 +--E 34 + +--S 35 of 845 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 845 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 36 + +--S 37 of 845 +--r0:=-2/63*(8*B*d-9*A*e-7*B*e*x)*(a+c*x^2)^(3/2)*sqrt(d+e*x)/e^2-_ +-- 4/315*(32*B*c*d^3-36*A*c*d^2*e+33*a*B*d*e^2-45*a*A*e^3-3*e*(8*B*c*d^2-_ +-- 9*A*c*d*e+7*a*B*e^2)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^4+8/315*_ +-- elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(9*A*e*_ +-- sqrt(c)*(4*c^(3/2)*d^3+5*(-a)^(3/2)*e^3-c*d^2*e*sqrt(-a)+_ +-- 8*a*d*e^2*sqrt(c))-B*(32*c^2*d^4+57*a*c*d^2*e^2+21*a^2*e^4-8*c^(3/2)*_ +-- d^3*e*sqrt(-a)-12*a*d*e^3*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^5*_ +-- sqrt(a+c*x^2))+8/315*(36*A*c*d*e*(c*d^2+2*a*e^2)-B*(32*c^2*d^4+_ +-- 57*a*c*d^2*e^2+21*a^2*e^4))*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^6*sqrt(a+c*x^2)) +--E 37 + +--S 38 of 845 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 845 +--m0:=a0-r0 +--E 39 + +--S 40 of 845 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 845 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 41 + +--S 42 of 845 +--r0:=2/7*(8*B*d-7*A*e+B*e*x)*(a+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+_ +-- 4/35*(5*a*B*e^2+4*c*d*(8*B*d-7*A*e)-3*c*e*(8*B*d-7*A*e)*x)*_ +-- sqrt(d+e*x)*sqrt(a+c*x^2)/e^4-8/35*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*(32*c^(3/2)*d^3-8*c*d^2*e*_ +-- sqrt(-a)-5*a*e^3*sqrt(-a)+29*a*d*e^2*sqrt(c))+7*A*e*sqrt(c)*(4*c*d^2+_ +-- 3*a*e^2-d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e^5*sqrt(a+c*x^2))+_ +-- 8/35*c^(1/4)*(32*B*c*d^3-28*A*c*d^2*e+29*a*B*d*e^2-21*a*A*e^3)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(e^6*sqrt(a+c*x^2)) +--E 42 + +--S 43 of 845 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 845 +--m0:=a0-r0 +--E 44 + +--S 45 of 845 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 845 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 46 + +--S 47 of 845 +--r0:=2/15*(8*B*d-5*A*e+3*B*e*x)*(a+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 4/15*(9*a*B*e^2+4*c*d*(8*B*d-5*A*e)+c*e*(8*B*d-5*A*e)*x)*_ +-- sqrt(a+c*x^2)/(e^4*sqrt(d+e*x))-8/15*c^(1/4)*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(32*B*c*d^2-20*A*c*d*e+9*a*B*e^2-_ +-- 8*B*d*e*sqrt(-a)*sqrt(c)+5*A*e^2*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^5*_ +-- sqrt(a+c*x^2))-8/15*c^(1/4)*(9*a*B*e^2+4*c*d*(8*B*d-5*A*e))*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(e^6*sqrt(a+c*x^2)) +--E 47 + +--S 48 of 845 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 845 +--m0:=a0-r0 +--E 49 + +--S 50 of 845 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 845 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 51 + +--S 52 of 845 +--r0:=2/15*(8*B*d-3*A*e+5*B*e*x)*(a+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 4/15*(5*a*B*e^2+4*c*d*(8*B*d-3*A*e)+3*c*e*(8*B*d-3*A*e)*x)*_ +-- sqrt(a+c*x^2)/(e^4*(d+e*x)^(3/2))+8/15*c*(32*B*c*d^3-12*A*c*d^2*e+_ +-- 29*a*B*d*e^2-9*a*A*e^3)*sqrt(a+c*x^2)/(e^4*(c*d^2+a*e^2)*sqrt(d+e*x))-_ +-- 8/15*c^(3/4)*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*_ +-- (-B*(32*c^(3/2)*d^3-8*c*d^2*e*sqrt(-a)-5*a*e^3*sqrt(-a)+29*a*d*e^2*_ +-- sqrt(c))+3*A*e*sqrt(c)*(4*c*d^2+3*a*e^2-d*e*sqrt(-a)*sqrt(c)))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (e^5*(c*d^2+a*e^2)*sqrt(a+c*x^2))+8/15*c^(5/4)*(32*B*c*d^3-_ +-- 12*A*c*d^2*e+29*a*B*d*e^2-9*a*A*e^3)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^6*(c*d^2+_ +-- a*e^2)*sqrt(a+c*x^2)) +--E 52 + +--S 53 of 845 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 845 +--m0:=a0-r0 +--E 54 + +--S 55 of 845 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 845 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(a+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------+ +--R | 2 +--R \|c x + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 845 +--r0:=2/5*B*(d+e*x)^(3/2)*sqrt(a+c*x^2)/c+2/15*(3*B*d+5*A*e)*sqrt(d+e*x)*_ +-- sqrt(a+c*x^2)/c-2/15*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- (3*B*(3*(-a)^(3/2)*e^2+c*d^2*sqrt(-a)+4*a*d*e*sqrt(c))-5*A*sqrt(c)*_ +-- (3*c*d^2-a*e^2-4*d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(7/4)*e*sqrt(a+c*x^2))-_ +-- 2/15*(3*B*c*d^2+20*A*c*d*e-9*a*B*e^2)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(7/4)*e^2*_ +-- sqrt(a+c*x^2)) +--E 57 + +--S 58 of 845 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 845 +--m0:=a0-r0 +--E 59 + +--S 60 of 845 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 845 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(a+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +--------+ +--R | 2 +--R \|c x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 845 +--r0:=2/3*B*sqrt(d+e*x)*sqrt(a+c*x^2)/c-2/3*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(-3*A*c*d+a*B*e+B*d*sqrt(-a)*sqrt(c)+3*A*e*_ +-- sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-_ +-- x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*e*sqrt(a+c*x^2))-2/3*(B*d+3*A*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^2*sqrt(a+c*x^2)) +--E 62 + +--S 63 of 845 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 845 +--m0:=a0-r0 +--E 64 + +--S 65 of 845 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 845 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(a+c*x^2)) +--R +--R +--R B x + A +--R (1) --------------------- +--R +--------+ +--R +-------+ | 2 +--R \|e x + d \|c x + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 845 +--r0:=-2*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(B*sqrt(-a)-A*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(3/4)*e*sqrt(a+c*x^2))-2*B*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^2*sqrt(a+c*x^2)) +--E 67 + +--S 68 of 845 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 845 +--m0:=a0-r0 +--E 69 + +--S 70 of 845 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 845 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R +--------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 845 +--r0:=2*(B*d-A*e)*sqrt(a+c*x^2)/((c*d^2+a*e^2)*sqrt(d+e*x))+_ +-- 2*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(A*c*d+a*B*e+B*d*_ +-- sqrt(-a)*sqrt(c)-A*e*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e*(c*d^2+a*e^2)*_ +-- sqrt(a+c*x^2))+2*c^(1/4)*(B*d-A*e)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^2*(c*d^2+_ +-- a*e^2)*sqrt(a+c*x^2)) +--E 72 + +--S 73 of 845 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 845 +--m0:=a0-r0 +--E 74 + +--S 75 of 845 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 845 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------+ +--R 2 | 2 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 845 +--r0:=-(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*sqrt(a+c*x^2))-A*e*sqrt(d+e*x)*_ +-- sqrt(a+c*x^2)/(a*c)+elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- (-A*c*d+3*a*B*e+3*B*d*sqrt(-a)*sqrt(c)+A*e*sqrt(-a)*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(7/4)*sqrt(-a)*sqrt(a+c*x^2))+(A*c*d-3*a*B*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(a*c^(7/4)*e*sqrt(a+c*x^2)) +--E 77 + +--S 78 of 845 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 845 +--m0:=a0-r0 +--E 79 + +--S 80 of 845 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 845 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 845 +--r0:=-(a*B-A*c*x)*sqrt(d+e*x)/(a*c*sqrt(a+c*x^2))+elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(B*sqrt(-a)-A*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*_ +-- sqrt(-a)*sqrt(a+c*x^2))+A*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(a*c^(3/4)*e*sqrt(a+c*x^2)) +--E 82 + +--S 83 of 845 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 845 +--m0:=a0-r0 +--E 84 + +--S 85 of 845 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 845 +t0:=(A+B*x)/((a+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R +--------+ +--R 2 +-------+ | 2 +--R (c x + a)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 845 +--r0:=-(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ +-- sqrt(a+c*x^2))-elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(A*c*d+_ +-- a*B*e+B*d*sqrt(-a)*sqrt(c)-A*e*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*_ +-- (c*d^2+a*e^2)*sqrt(-a)*sqrt(a+c*x^2))+(A*c*d+a*B*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(a*c^(3/4)*e*(c*d^2+a*e^2)*sqrt(a+c*x^2)) +--E 87 + +--S 88 of 845 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 845 +--m0:=a0-r0 +--E 89 + +--S 90 of 845 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 845 +t0:=(-a*e+c*d*x)*(d+e*x)^(-3-2*p)*(a+c*x^2)^p +--R +--R +--R - 2p - 3 2 p +--R (1) (c d x - a e)(e x + d) (c x + a) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 845 +r0:=1/2*(a+c*x^2)^(1+p)/((1+p)*(d+e*x)^(2*(1+p))) +--R +--R +--R 2 p + 1 +--R (c x + a) +--R (2) ----------------------- +--R 2p + 2 +--R (2p + 2)(e x + d) +--R Type: Expression(Integer) +--E 92 + +--S 93 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R 3 2 (- 2p - 3)log(e x + d) p log(c x + a) +--R (c e x + c d x + a e x + a d)%e %e +--R ------------------------------------------------------------------------ +--R 2p + 2 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2p + 2 (- 2p - 3)log(e x + d) +--R (c e x + c d x + a e x + a d)(e x + d) %e +--R * +--R 2 +--R p log(c x + a) +--R %e +--R + +--R 2 p + 1 +--R - (c x + a) +--R / +--R 2p + 2 +--R (2p + 2)(e x + d) +--R Type: Expression(Integer) +--E 94 + +--S 95 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 +--R 2p + 2 2 (- 2p - 3)log(e x + d) p log(c x + a) +--R (c d x - a e)((e x + d) ) %e %e +--R + +--R 2p + 1 2 p + 1 2p + 2 2 p +--R e (e x + d) (c x + a) - c x (e x + d) (c x + a) +--R / +--R 2p + 2 2 +--R ((e x + d) ) +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 845 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 m +--R (1) (2c x + 3b c x + (2a c + b )x + a b)(e x + d) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 845 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(2+m)/(e^4*(2+m))-3*c*(2*c*d-b*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+2*c^2*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 m + 4 +--R (2c m + 12c m + 22c m + 12c )(e x + d) +--R + +--R 2 3 2 2 2 +--R (3b c e - 6c d)m + (21b c e - 42c d)m + (42b c e - 84c d)m +--R + +--R 2 +--R 24b c e - 48c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 3 +--R ((2a c + b )e - 6b c d e + 6c d )m +--R + +--R 2 2 2 2 2 +--R ((16a c + 8b )e - 48b c d e + 48c d )m +--R + +--R 2 2 2 2 2 2 +--R ((38a c + 19b )e - 114b c d e + 114c d )m + (24a c + 12b )e +--R + +--R 2 2 +--R - 72b c d e + 72c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (- 2a c - b )d e + 3b c d e - 2c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (9a b e + (- 18a c - 9b )d e + 27b c d e - 18c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (26a b e + (- 52a c - 26b )d e + 78b c d e - 52c d )m + 24a b e +--R + +--R 2 2 2 2 3 +--R (- 48a c - 24b )d e + 72b c d e - 48c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 97 + +--S 98 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 4 2 2 4 2 4 4 +--R (2c e m + 12c e m + 22c e m + 12c e )x +--R + +--R 4 2 3 3 4 2 3 2 +--R (3b c e + 2c d e )m + (21b c e + 6c d e )m +--R + +--R 4 2 3 4 +--R (42b c e + 4c d e )m + 24b c e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 +--R ((2a c + b )e + 3b c d e )m +--R + +--R 2 4 3 2 2 2 2 +--R ((16a c + 8b )e + 15b c d e - 6c d e )m +--R + +--R 2 4 3 2 2 2 2 4 +--R ((38a c + 19b )e + 12b c d e - 6c d e )m + (24a c + 12b )e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 +--R (a b e + (2a c + b )d e )m +--R + +--R 4 2 3 2 2 2 +--R (9a b e + (14a c + 7b )d e - 6b c d e )m +--R + +--R 4 2 3 2 2 2 3 4 +--R (26a b e + (24a c + 12b )d e - 24b c d e + 12c d e)m + 24a b e +--R * +--R x +--R + +--R 3 3 3 2 2 2 2 +--R a b d e m + (9a b d e + (- 2a c - b )d e )m +--R + +--R 3 2 2 2 3 3 +--R (26a b d e + (- 14a c - 7b )d e + 6b c d e)m + 24a b d e +--R + +--R 2 2 2 3 2 4 +--R (- 24a c - 12b )d e + 24b c d e - 12c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 3 2 4 2 2 4 2 4 4 +--R (2c e m + 12c e m + 22c e m + 12c e )x +--R + +--R 4 2 3 3 4 2 3 2 +--R (3b c e + 2c d e )m + (21b c e + 6c d e )m +--R + +--R 4 2 3 4 +--R (42b c e + 4c d e )m + 24b c e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 +--R ((2a c + b )e + 3b c d e )m +--R + +--R 2 4 3 2 2 2 2 +--R ((16a c + 8b )e + 15b c d e - 6c d e )m +--R + +--R 2 4 3 2 2 2 2 4 +--R ((38a c + 19b )e + 12b c d e - 6c d e )m + (24a c + 12b )e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 +--R (a b e + (2a c + b )d e )m +--R + +--R 4 2 3 2 2 2 +--R (9a b e + (14a c + 7b )d e - 6b c d e )m +--R + +--R 4 2 3 2 2 2 3 4 +--R (26a b e + (24a c + 12b )d e - 24b c d e + 12c d e)m + 24a b e +--R * +--R x +--R + +--R 3 3 3 2 2 2 2 +--R a b d e m + (9a b d e + (- 2a c - b )d e )m +--R + +--R 3 2 2 2 3 3 +--R (26a b d e + (- 14a c - 7b )d e + 6b c d e)m + 24a b d e +--R + +--R 2 2 2 3 2 4 +--R (- 24a c - 12b )d e + 24b c d e - 12c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 3 2 2 2 2 m + 4 +--R (- 2c m - 12c m - 22c m - 12c )(e x + d) +--R + +--R 2 3 2 2 2 +--R (- 3b c e + 6c d)m + (- 21b c e + 42c d)m + (- 42b c e + 84c d)m +--R + +--R 2 +--R - 24b c e + 48c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 3 +--R ((- 2a c - b )e + 6b c d e - 6c d )m +--R + +--R 2 2 2 2 2 +--R ((- 16a c - 8b )e + 48b c d e - 48c d )m +--R + +--R 2 2 2 2 2 2 +--R ((- 38a c - 19b )e + 114b c d e - 114c d )m + (- 24a c - 12b )e +--R + +--R 2 2 +--R 72b c d e - 72c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 3 +--R (- a b e + (2a c + b )d e - 3b c d e + 2c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (- 9a b e + (18a c + 9b )d e - 27b c d e + 18c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (- 26a b e + (52a c + 26b )d e - 78b c d e + 52c d )m - 24a b e +--R + +--R 2 2 2 2 3 +--R (48a c + 24b )d e - 72b c d e + 48c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 99 + +--S 100 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 3 3 2 2 3 3 m log(e x + d) +--R (2c e x + 3b c e x + (2a c + b )e x + a b e )%e +--R + +--R 2 m + 3 2 m + 2 +--R - 2c (e x + d) + (- 3b c e + 6c d)(e x + d) +--R + +--R 2 2 2 2 m + 1 +--R ((- 2a c - b )e + 6b c d e - 6c d )(e x + d) +--R + +--R 3 2 2 2 2 3 m +--R (- a b e + (2a c + b )d e - 3b c d e + 2c d )(e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 845 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 7 4 2 3 6 2 4 3 2 2 2 5 +--R 2c e x + (3b c e + 8c d e )x + ((2a c + b )e + 12b c d e + 12c d e )x +--R + +--R 4 2 3 2 2 2 3 4 +--R (a b e + (8a c + 4b )d e + 18b c d e + 8c d e)x +--R + +--R 3 2 2 2 3 2 4 3 +--R (4a b d e + (12a c + 6b )d e + 12b c d e + 2c d )x +--R + +--R 2 2 2 3 4 2 3 2 4 +--R (6a b d e + (8a c + 4b )d e + 3b c d )x + (4a b d e + (2a c + b )d )x +--R + +--R 4 +--R a b d +--R Type: Polynomial(Integer) +--E 101 + +--S 102 of 845 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4+1/6*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^6/e^4-3/7*c*(2*c*d-b*e)*(d+e*x)^7/e^4+_ + 1/4*c^2*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 2 8 8 3 8 8 2 7 7 +--R - c e x + (- b c e + - c d e )x +--R 4 7 7 +--R + +--R 1 1 2 8 7 2 2 6 6 +--R ((- a c + - b )e + 2b c d e + 2c d e )x +--R 3 6 +--R + +--R 1 8 8 4 2 7 18 2 6 8 2 3 5 5 +--R (- a b e + (- a c + - b )d e + -- b c d e + - c d e )x +--R 5 5 5 5 5 +--R + +--R 7 3 2 2 6 3 5 1 2 4 4 4 +--R (a b d e + (3a c + - b )d e + 3b c d e + - c d e )x +--R 2 2 +--R + +--R 2 6 8 4 2 3 5 4 4 3 +--R (2a b d e + (- a c + - b )d e + b c d e )x +--R 3 3 +--R + +--R 3 5 1 2 4 4 2 4 4 1 5 3 +--R (2a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 5 +--R + +--R 1 1 2 6 2 1 7 1 2 8 +--R (- -- a c - -- b )d e + -- b c d e - --- c d +--R 15 30 35 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 102 + +--S 103 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 8 3 4 8 2 3 7 +--R - c e x + (- b c e + - c d e )x +--R 4 7 7 +--R + +--R 1 1 2 4 3 2 2 2 6 +--R ((- a c + - b )e + 2b c d e + 2c d e )x +--R 3 6 +--R + +--R 1 4 8 4 2 3 18 2 2 8 2 3 5 +--R (- a b e + (- a c + - b )d e + -- b c d e + - c d e)x +--R 5 5 5 5 5 +--R + +--R 3 3 2 2 2 3 1 2 4 4 +--R (a b d e + (3a c + - b )d e + 3b c d e + - c d )x +--R 2 2 +--R + +--R 2 2 8 4 2 3 4 3 3 1 2 4 2 +--R (2a b d e + (- a c + - b )d e + b c d )x + (2a b d e + (a c + - b )d )x +--R 3 3 2 +--R + +--R 4 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 103 + +--S 104 of 845 +m0:=a0-r0 +--R +--R +--R 1 5 3 1 1 2 6 2 1 7 1 2 8 +--R - - a b d e + (-- a c + -- b )d e - -- b c d e + --- c d +--R 5 15 30 35 140 +--R (4) ----------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 104 + +--S 105 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 105 + +)clear all + +--S 106 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R 2c e x + (3b c e + 6c d e )x + ((2a c + b )e + 9b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (6a c + 3b )d e + 9b c d e + 2c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R (3a b d e + (6a c + 3b )d e + 3b c d )x + (3a b d e + (2a c + b )d )x +--R + +--R 3 +--R a b d +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 845 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4+1/5*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^5/e^4-1/2*c*(2*c*d-b*e)*(d+e*x)^6/e^4+_ + 2/7*c^2*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 2 2 7 7 1 7 2 6 6 +--R - c e x + (- b c e + c d e )x +--R 7 2 +--R + +--R 2 1 2 7 9 6 6 2 2 5 5 +--R ((- a c + - b )e + - b c d e + - c d e )x +--R 5 5 5 5 +--R + +--R 1 7 3 3 2 6 9 2 5 1 2 3 4 4 +--R (- a b e + (- a c + - b )d e + - b c d e + - c d e )x +--R 4 2 4 4 2 +--R + +--R 6 2 2 5 3 4 3 +--R (a b d e + (2a c + b )d e + b c d e )x +--R + +--R 3 2 5 1 2 3 4 2 3 4 1 4 3 +--R (- a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 2 4 +--R + +--R 1 1 2 5 2 1 6 1 2 7 +--R (- -- a c - -- b )d e + -- b c d e - -- c d +--R 10 20 20 70 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 107 + +--S 108 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 7 1 3 2 2 6 +--R - c e x + (- b c e + c d e )x +--R 7 2 +--R + +--R 2 1 2 3 9 2 6 2 2 5 +--R ((- a c + - b )e + - b c d e + - c d e)x +--R 5 5 5 5 +--R + +--R 1 3 3 3 2 2 9 2 1 2 3 4 +--R (- a b e + (- a c + - b )d e + - b c d e + - c d )x +--R 4 2 4 4 2 +--R + +--R 2 2 2 3 3 3 2 1 2 3 2 +--R (a b d e + (2a c + b )d e + b c d )x + (- a b d e + (a c + - b )d )x +--R 2 2 +--R + +--R 3 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 845 +m0:=a0-r0 +--R +--R +--R 1 4 3 1 1 2 5 2 1 6 1 2 7 +--R - - a b d e + (-- a c + -- b )d e - -- b c d e + -- c d +--R 4 10 20 20 70 +--R (4) ---------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 109 + +--S 110 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 110 + +)clear all + +--S 111 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x + a b d +--R Type: Polynomial(Integer) +--E 111 + +--S 112 of 845 +r0:=-1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3/e^4+1/4*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^4/e^4-3/5*c*(2*c*d-b*e)*_ + (d+e*x)^5/e^4+1/3*c^2*(d+e*x)^6/e^4 +--R +--R +--R (2) +--R 1 2 6 6 3 6 4 2 5 5 +--R - c e x + (- b c e + - c d e )x +--R 3 5 5 +--R + +--R 1 1 2 6 3 5 1 2 2 4 4 +--R ((- a c + - b )e + - b c d e + - c d e )x +--R 2 4 2 2 +--R + +--R 1 6 4 2 2 5 2 4 3 +--R (- a b e + (- a c + - b )d e + b c d e )x +--R 3 3 3 +--R + +--R 5 1 2 2 4 2 2 4 1 3 3 +--R (a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 3 +--R + +--R 1 1 2 4 2 1 5 1 2 6 +--R (- - a c - -- b )d e + -- b c d e - -- c d +--R 6 12 10 30 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 112 + +--S 113 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 6 3 2 4 2 5 +--R - c e x + (- b c e + - c d e)x +--R 3 5 5 +--R + +--R 1 1 2 2 3 1 2 2 4 +--R ((- a c + - b )e + - b c d e + - c d )x +--R 2 4 2 2 +--R + +--R 1 2 4 2 2 2 3 1 2 2 2 +--R (- a b e + (- a c + - b )d e + b c d )x + (a b d e + (a c + - b )d )x +--R 3 3 3 2 +--R + +--R 2 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 845 +m0:=a0-r0 +--R +--R +--R 1 3 3 1 1 2 4 2 1 5 1 2 6 +--R - - a b d e + (- a c + -- b )d e - -- b c d e + -- c d +--R 3 6 12 10 30 +--R (4) --------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 114 + +--S 115 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 115 + +)clear all + +--S 116 of 845 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R Type: Polynomial(Integer) +--E 116 + +--S 117 of 845 +r0:=a*b*d*x+1/2*(b^2*d+2*a*c*d+a*b*e)*x^2+1/3*(3*b*c*d+b^2*e+2*a*c*e)*x^3+_ + 1/4*c*(2*c*d+3*b*e)*x^4+2/5*c^2*e*x^5 +--R +--R +--R (2) +--R 2 2 5 3 1 2 4 2 1 2 3 +--R - c e x + (- b c e + - c d)x + ((- a c + - b )e + b c d)x +--R 5 4 2 3 3 +--R + +--R 1 1 2 2 +--R (- a b e + (a c + - b )d)x + a b d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 5 3 1 2 4 2 1 2 3 +--R - c e x + (- b c e + - c d)x + ((- a c + - b )e + b c d)x +--R 5 4 2 3 3 +--R + +--R 1 1 2 2 +--R (- a b e + (a c + - b )d)x + a b d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +--S 119 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 119 + +--S 120 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +)clear all + +--S 121 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 +--R (1) 2c x + 3b c x + (2a c + b )x + a b +--R Type: Polynomial(Integer) +--E 121 + +--S 122 of 845 +r0:=1/2*(a+b*x+c*x^2)^2 +--R +--R +--R 1 2 4 3 1 2 2 1 2 +--R (2) - c x + b c x + (a c + - b )x + a b x + - a +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 845 +a0:=integrate(t0,x) +--R +--R +--R 1 2 4 3 1 2 2 +--R (3) - c x + b c x + (a c + - b )x + a b x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +--S 124 of 845 +m0:=a0-r0 +--R +--R +--R 1 2 +--R (4) - - a +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 124 + +--S 125 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +)clear all + +--S 126 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 845 +r0:=(2*c^2*d^2+b^2*e^2-c*e*(3*b*d-2*a*e))*x/e^3-1/2*c*(2*c*d-3*b*e)*x^2/e^2+_ + 2/3*c^2*x^3/e-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R (6a b e + (- 12a c - 6b )d e + 18b c d e - 12c d )log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 4c e x + (9b c e - 6c d e )x + ((12a c + 6b )e - 18b c d e + 12c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 127 + +--S 128 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 +--R (6a b e + (- 12a c - 6b )d e + 18b c d e - 12c d )log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 4c e x + (9b c e - 6c d e )x + ((12a c + 6b )e - 18b c d e + 12c d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 845 +r0:=-c*(4*c*d-3*b*e)*x/e^3+c^2*x^2/e^2+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/_ + (e^4*(d+e*x))+(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 2 +--R ((2a c + b )e - 6b c d e + 6c d e)x + (2a c + b )d e - 6b c d e +--R + +--R 2 3 +--R 6c d +--R * +--R log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 2 2 3 +--R c e x + (3b c e - 3c d e )x + (3b c d e - 4c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (2a c + b )d e - 3b c d e + 2c d +--R / +--R 5 4 +--R e x + d e +--R Type: Expression(Integer) +--E 132 + +--S 133 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 2 +--R ((2a c + b )e - 6b c d e + 6c d e)x + (2a c + b )d e - 6b c d e +--R + +--R 2 3 +--R 6c d +--R * +--R log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 2 2 3 +--R c e x + (3b c e - 3c d e )x + (3b c d e - 4c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (2a c + b )d e - 3b c d e + 2c d +--R / +--R 5 4 +--R e x + d e +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 845 +r0:=2*c^2*x/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x))-3*c*(2*c*d-b*e)*_ + log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 2 2 2 3 +--R ((6b c e - 12c d e )x + (12b c d e - 24c d e)x + 6b c d e - 12c d ) +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 2 3 2 2 2 3 +--R 4c e x + 8c d e x + ((- 4a c - 2b )e + 12b c d e - 8c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (- 2a c - b )d e + 9b c d e - 10c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 137 + +--S 138 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 2 2 2 2 3 +--R ((6b c e - 12c d e )x + (12b c d e - 24c d e)x + 6b c d e - 12c d ) +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 2 3 2 2 2 3 +--R 4c e x + 8c d e x + ((- 4a c - 2b )e + 12b c d e - 8c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (- 2a c - b )d e + 9b c d e - 10c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 845 +r0:=1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+_ + 1/2*(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x)^2)+_ + 3*c*(2*c*d-b*e)/(e^4*(d+e*x))+2*c^2*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 2 2 2 3 +--R (12c e x + 36c d e x + 36c d e x + 12c d )log(e x + d) +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 18b c e + 36c d e )x + ((- 6a c - 3b )e - 18b c d e + 54c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (- 2a c - b )d e - 6b c d e + 22c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 142 + +--S 143 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 2 2 2 3 +--R (12c e x + 36c d e x + 36c d e x + 12c d )log(e x + d) +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 18b c e + 36c d e )x + ((- 6a c - 3b )e - 18b c d e + 54c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (- 2a c - b )d e - 6b c d e + 22c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 845 +r0:=1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+_ + 1/3*(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x)^3)+_ + 3/2*c*(2*c*d-b*e)/(e^4*(d+e*x)^2)-2*c^2/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 3 3 3 3 2 2 2 +--R - 2c e x + (- - b c e - 3c d e )x +--R 2 +--R + +--R 2 1 2 3 2 2 2 1 3 +--R ((- - a c - - b )e - b c d e - 2c d e)x - - a b e +--R 3 3 4 +--R + +--R 1 1 2 2 1 2 1 2 3 +--R (- - a c - -- b )d e - - b c d e - - c d +--R 6 12 4 2 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 147 + +--S 148 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 +--R - 24c e x + (- 18b c e - 36c d e )x +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 8a c - 4b )e - 12b c d e - 24c d e)x - 3a b e + (- 2a c - b )d e +--R + +--R 2 2 3 +--R - 3b c d e - 6c d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 845 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 845 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))+_ + 2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(2+m)/(e^6*(2+m))-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(3+m)/(e^6*(3+m))+4*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(4+m)/(e^6*(4+m))-5*c^2*(2*c*d-b*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+2*c^3*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 3 5 3 4 3 3 3 2 3 3 m + 6 +--R (2c m + 30c m + 170c m + 450c m + 548c m + 240c )(e x + d) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R (5b c e - 10c d)m + (80b c e - 160c d)m + (475b c e - 950c d)m +--R + +--R 2 3 2 2 3 2 3 +--R (1300b c e - 2600c d)m + (1620b c e - 3240c d)m + 720b c e - 1440c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 3 2 5 +--R ((4a c + 4b c)e - 20b c d e + 20c d )m +--R + +--R 2 2 2 2 3 2 4 +--R ((68a c + 68b c)e - 340b c d e + 340c d )m +--R + +--R 2 2 2 2 3 2 3 +--R ((428a c + 428b c)e - 2140b c d e + 2140c d )m +--R + +--R 2 2 2 2 3 2 2 +--R ((1228a c + 1228b c)e - 6140b c d e + 6140c d )m +--R + +--R 2 2 2 2 3 2 +--R ((1584a c + 1584b c)e - 7920b c d e + 7920c d )m +--R + +--R 2 2 2 2 3 2 +--R (720a c + 720b c)e - 3600b c d e + 3600c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (- 12a c - 12b c)d e + 30b c d e - 20c d )m +--R + +--R 3 3 2 2 2 2 2 +--R (108a b c + 18b )e + (- 216a c - 216b c)d e + 540b c d e +--R + +--R 3 3 +--R - 360c d +--R * +--R 4 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (726a b c + 121b )e + (- 1452a c - 1452b c)d e + 3630b c d e +--R + +--R 3 3 +--R - 2420c d +--R * +--R 3 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (2232a b c + 372b )e + (- 4464a c - 4464b c)d e + 11160b c d e +--R + +--R 3 3 +--R - 7440c d +--R * +--R 2 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (3048a b c + 508b )e + (- 6096a c - 6096b c)d e + 15240b c d e +--R + +--R 3 3 +--R - 10160c d +--R * +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (1440a b c + 240b )e + (- 2880a c - 2880b c)d e + 7200b c d e +--R + +--R 3 3 +--R - 4800c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (2a c + 2a b )e + (- 12a b c - 2b )d e + (12a c + 12b c)d e +--R + +--R 2 3 3 4 +--R - 20b c d e + 10c d +--R * +--R 5 +--R m +--R + +--R 2 2 4 3 3 +--R (38a c + 38a b )e + (- 228a b c - 38b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (228a c + 228b c)d e - 380b c d e + 190c d +--R * +--R 4 +--R m +--R + +--R 2 2 4 3 3 +--R (274a c + 274a b )e + (- 1644a b c - 274b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (1644a c + 1644b c)d e - 2740b c d e + 1370c d +--R * +--R 3 +--R m +--R + +--R 2 2 4 3 3 +--R (922a c + 922a b )e + (- 5532a b c - 922b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (5532a c + 5532b c)d e - 9220b c d e + 4610c d +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 3 +--R (1404a c + 1404a b )e + (- 8424a b c - 1404b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (8424a c + 8424b c)d e - 14040b c d e + 7020c d +--R * +--R m +--R + +--R 2 2 4 3 3 +--R (720a c + 720a b )e + (- 4320a b c - 720b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (4320a c + 4320b c)d e - 7200b c d e + 3600c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 2 4 3 2 3 +--R a b e + (- 2a c - 2a b )d e + (6a b c + b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 4a c - 4b c)d e + 5b c d e - 2c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 20a b e + (- 40a c - 40a b )d e + (120a b c + 20b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 80a c - 80b c)d e + 100b c d e - 40c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 155a b e + (- 310a c - 310a b )d e + (930a b c + 155b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 620a c - 620b c)d e + 775b c d e - 310c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 580a b e + (- 1160a c - 1160a b )d e + (3480a b c + 580b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 2320a c - 2320b c)d e + 2900b c d e - 1160c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 1044a b e + (- 2088a c - 2088a b )d e +--R + +--R 3 2 3 2 2 3 2 +--R (6264a b c + 1044b )d e + (- 4176a c - 4176b c)d e +--R + +--R 2 4 3 5 +--R 5220b c d e - 2088c d +--R * +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 720a b e + (- 1440a c - 1440a b )d e + (4320a b c + 720b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 2880a c - 2880b c)d e + 3600b c d e - 1440c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 152 + +--S 153 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 5 3 6 4 3 6 3 3 6 2 3 6 3 6 6 +--R (2c e m + 30c e m + 170c e m + 450c e m + 548c e m + 240c e )x +--R + +--R 2 6 3 5 5 2 6 3 5 4 +--R (5b c e + 2c d e )m + (80b c e + 20c d e )m +--R + +--R 2 6 3 5 3 2 6 3 5 2 +--R (475b c e + 70c d e )m + (1300b c e + 100c d e )m +--R + +--R 2 6 3 5 2 6 +--R (1620b c e + 48c d e )m + 720b c e +--R * +--R 5 +--R x +--R + +--R 2 2 6 2 5 5 +--R ((4a c + 4b c)e + 5b c d e )m +--R + +--R 2 2 6 2 5 3 2 4 4 +--R ((68a c + 68b c)e + 60b c d e - 10c d e )m +--R + +--R 2 2 6 2 5 3 2 4 3 +--R ((428a c + 428b c)e + 235b c d e - 60c d e )m +--R + +--R 2 2 6 2 5 3 2 4 2 +--R ((1228a c + 1228b c)e + 360b c d e - 110c d e )m +--R + +--R 2 2 6 2 5 3 2 4 +--R ((1584a c + 1584b c)e + 180b c d e - 60c d e )m +--R + +--R 2 2 6 +--R (720a c + 720b c)e +--R * +--R 4 +--R x +--R + +--R 3 6 2 2 5 5 +--R ((6a b c + b )e + (4a c + 4b c)d e )m +--R + +--R 3 6 2 2 5 2 2 4 4 +--R ((108a b c + 18b )e + (56a c + 56b c)d e - 20b c d e )m +--R + +--R 3 6 2 2 5 2 2 4 +--R (726a b c + 121b )e + (260a c + 260b c)d e - 180b c d e +--R + +--R 3 3 3 +--R 40c d e +--R * +--R 3 +--R m +--R + +--R 3 6 2 2 5 2 2 4 +--R (2232a b c + 372b )e + (448a c + 448b c)d e - 400b c d e +--R + +--R 3 3 3 +--R 120c d e +--R * +--R 2 +--R m +--R + +--R 3 6 2 2 5 2 2 4 +--R (3048a b c + 508b )e + (240a c + 240b c)d e - 240b c d e +--R + +--R 3 3 3 +--R 80c d e +--R * +--R m +--R + +--R 3 6 +--R (1440a b c + 240b )e +--R * +--R 3 +--R x +--R + +--R 2 2 6 3 5 5 +--R ((2a c + 2a b )e + (6a b c + b )d e )m +--R + +--R 2 2 6 3 5 +--R (38a c + 38a b )e + (96a b c + 16b )d e +--R + +--R 2 2 2 4 +--R (- 12a c - 12b c)d e +--R * +--R 4 +--R m +--R + +--R 2 2 6 3 5 +--R (274a c + 274a b )e + (534a b c + 89b )d e +--R + +--R 2 2 2 4 2 3 3 +--R (- 144a c - 144b c)d e + 60b c d e +--R * +--R 3 +--R m +--R + +--R 2 2 6 3 5 +--R (922a c + 922a b )e + (1164a b c + 194b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 492a c - 492b c)d e + 420b c d e - 120c d e +--R * +--R 2 +--R m +--R + +--R 2 2 6 3 5 +--R (1404a c + 1404a b )e + (720a b c + 120b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 360a c - 360b c)d e + 360b c d e - 120c d e +--R * +--R m +--R + +--R 2 2 6 +--R (720a c + 720a b )e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 5 +--R (a b e + (2a c + 2a b )d e )m +--R + +--R 2 6 2 2 5 3 2 4 4 +--R (20a b e + (36a c + 36a b )d e + (- 12a b c - 2b )d e )m +--R + +--R 2 6 2 2 5 3 2 4 +--R 155a b e + (238a c + 238a b )d e + (- 180a b c - 30b )d e +--R + +--R 2 2 3 3 +--R (24a c + 24b c)d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 2 5 3 2 4 +--R 580a b e + (684a c + 684a b )d e + (- 888a b c - 148b )d e +--R + +--R 2 2 3 3 2 4 2 +--R (264a c + 264b c)d e - 120b c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 2 5 3 2 4 +--R 1044a b e + (720a c + 720a b )d e + (- 1440a b c - 240b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (720a c + 720b c)d e - 720b c d e + 240c d e +--R * +--R m +--R + +--R 2 6 +--R 720a b e +--R * +--R x +--R + +--R 2 5 5 2 5 2 2 2 4 4 +--R a b d e m + (20a b d e + (- 2a c - 2a b )d e )m +--R + +--R 2 5 2 2 2 4 3 3 3 3 +--R (155a b d e + (- 36a c - 36a b )d e + (12a b c + 2b )d e )m +--R + +--R 2 5 2 2 2 4 3 3 3 +--R 580a b d e + (- 238a c - 238a b )d e + (180a b c + 30b )d e +--R + +--R 2 2 4 2 +--R (- 24a c - 24b c)d e +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 2 4 3 3 3 +--R 1044a b d e + (- 684a c - 684a b )d e + (888a b c + 148b )d e +--R + +--R 2 2 4 2 2 5 +--R (- 264a c - 264b c)d e + 120b c d e +--R * +--R m +--R + +--R 2 5 2 2 2 4 3 3 3 +--R 720a b d e + (- 720a c - 720a b )d e + (1440a b c + 240b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (- 720a c - 720b c)d e + 720b c d e - 240c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 6 5 3 6 4 3 6 3 3 6 2 3 6 3 6 6 +--R (2c e m + 30c e m + 170c e m + 450c e m + 548c e m + 240c e )x +--R + +--R 2 6 3 5 5 2 6 3 5 4 +--R (5b c e + 2c d e )m + (80b c e + 20c d e )m +--R + +--R 2 6 3 5 3 2 6 3 5 2 +--R (475b c e + 70c d e )m + (1300b c e + 100c d e )m +--R + +--R 2 6 3 5 2 6 +--R (1620b c e + 48c d e )m + 720b c e +--R * +--R 5 +--R x +--R + +--R 2 2 6 2 5 5 +--R ((4a c + 4b c)e + 5b c d e )m +--R + +--R 2 2 6 2 5 3 2 4 4 +--R ((68a c + 68b c)e + 60b c d e - 10c d e )m +--R + +--R 2 2 6 2 5 3 2 4 3 +--R ((428a c + 428b c)e + 235b c d e - 60c d e )m +--R + +--R 2 2 6 2 5 3 2 4 2 +--R ((1228a c + 1228b c)e + 360b c d e - 110c d e )m +--R + +--R 2 2 6 2 5 3 2 4 +--R ((1584a c + 1584b c)e + 180b c d e - 60c d e )m +--R + +--R 2 2 6 +--R (720a c + 720b c)e +--R * +--R 4 +--R x +--R + +--R 3 6 2 2 5 5 +--R ((6a b c + b )e + (4a c + 4b c)d e )m +--R + +--R 3 6 2 2 5 2 2 4 4 +--R ((108a b c + 18b )e + (56a c + 56b c)d e - 20b c d e )m +--R + +--R 3 6 2 2 5 2 2 4 +--R (726a b c + 121b )e + (260a c + 260b c)d e - 180b c d e +--R + +--R 3 3 3 +--R 40c d e +--R * +--R 3 +--R m +--R + +--R 3 6 2 2 5 2 2 4 +--R (2232a b c + 372b )e + (448a c + 448b c)d e - 400b c d e +--R + +--R 3 3 3 +--R 120c d e +--R * +--R 2 +--R m +--R + +--R 3 6 2 2 5 2 2 4 +--R (3048a b c + 508b )e + (240a c + 240b c)d e - 240b c d e +--R + +--R 3 3 3 +--R 80c d e +--R * +--R m +--R + +--R 3 6 +--R (1440a b c + 240b )e +--R * +--R 3 +--R x +--R + +--R 2 2 6 3 5 5 +--R ((2a c + 2a b )e + (6a b c + b )d e )m +--R + +--R 2 2 6 3 5 +--R (38a c + 38a b )e + (96a b c + 16b )d e +--R + +--R 2 2 2 4 +--R (- 12a c - 12b c)d e +--R * +--R 4 +--R m +--R + +--R 2 2 6 3 5 +--R (274a c + 274a b )e + (534a b c + 89b )d e +--R + +--R 2 2 2 4 2 3 3 +--R (- 144a c - 144b c)d e + 60b c d e +--R * +--R 3 +--R m +--R + +--R 2 2 6 3 5 +--R (922a c + 922a b )e + (1164a b c + 194b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 492a c - 492b c)d e + 420b c d e - 120c d e +--R * +--R 2 +--R m +--R + +--R 2 2 6 3 5 +--R (1404a c + 1404a b )e + (720a b c + 120b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 360a c - 360b c)d e + 360b c d e - 120c d e +--R * +--R m +--R + +--R 2 2 6 +--R (720a c + 720a b )e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 5 +--R (a b e + (2a c + 2a b )d e )m +--R + +--R 2 6 2 2 5 3 2 4 4 +--R (20a b e + (36a c + 36a b )d e + (- 12a b c - 2b )d e )m +--R + +--R 2 6 2 2 5 3 2 4 +--R 155a b e + (238a c + 238a b )d e + (- 180a b c - 30b )d e +--R + +--R 2 2 3 3 +--R (24a c + 24b c)d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 2 5 3 2 4 +--R 580a b e + (684a c + 684a b )d e + (- 888a b c - 148b )d e +--R + +--R 2 2 3 3 2 4 2 +--R (264a c + 264b c)d e - 120b c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 2 5 +--R 1044a b e + (720a c + 720a b )d e +--R + +--R 3 2 4 2 2 3 3 +--R (- 1440a b c - 240b )d e + (720a c + 720b c)d e +--R + +--R 2 4 2 3 5 +--R - 720b c d e + 240c d e +--R * +--R m +--R + +--R 2 6 +--R 720a b e +--R * +--R x +--R + +--R 2 5 5 2 5 2 2 2 4 4 +--R a b d e m + (20a b d e + (- 2a c - 2a b )d e )m +--R + +--R 2 5 2 2 2 4 3 3 3 3 +--R (155a b d e + (- 36a c - 36a b )d e + (12a b c + 2b )d e )m +--R + +--R 2 5 2 2 2 4 3 3 3 +--R 580a b d e + (- 238a c - 238a b )d e + (180a b c + 30b )d e +--R + +--R 2 2 4 2 +--R (- 24a c - 24b c)d e +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 2 4 3 3 3 +--R 1044a b d e + (- 684a c - 684a b )d e + (888a b c + 148b )d e +--R + +--R 2 2 4 2 2 5 +--R (- 264a c - 264b c)d e + 120b c d e +--R * +--R m +--R + +--R 2 5 2 2 2 4 3 3 3 +--R 720a b d e + (- 720a c - 720a b )d e + (1440a b c + 240b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (- 720a c - 720b c)d e + 720b c d e - 240c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 5 3 4 3 3 3 2 3 3 m + 6 +--R (- 2c m - 30c m - 170c m - 450c m - 548c m - 240c )(e x + d) +--R + +--R 2 3 5 2 3 4 +--R (- 5b c e + 10c d)m + (- 80b c e + 160c d)m +--R + +--R 2 3 3 2 3 2 +--R (- 475b c e + 950c d)m + (- 1300b c e + 2600c d)m +--R + +--R 2 3 2 3 +--R (- 1620b c e + 3240c d)m - 720b c e + 1440c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 3 2 5 +--R ((- 4a c - 4b c)e + 20b c d e - 20c d )m +--R + +--R 2 2 2 2 3 2 4 +--R ((- 68a c - 68b c)e + 340b c d e - 340c d )m +--R + +--R 2 2 2 2 3 2 3 +--R ((- 428a c - 428b c)e + 2140b c d e - 2140c d )m +--R + +--R 2 2 2 2 3 2 2 +--R ((- 1228a c - 1228b c)e + 6140b c d e - 6140c d )m +--R + +--R 2 2 2 2 3 2 +--R ((- 1584a c - 1584b c)e + 7920b c d e - 7920c d )m +--R + +--R 2 2 2 2 3 2 +--R (- 720a c - 720b c)e + 3600b c d e - 3600c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((- 6a b c - b )e + (12a c + 12b c)d e - 30b c d e + 20c d )m +--R + +--R 3 3 2 2 2 2 2 +--R (- 108a b c - 18b )e + (216a c + 216b c)d e - 540b c d e +--R + +--R 3 3 +--R 360c d +--R * +--R 4 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (- 726a b c - 121b )e + (1452a c + 1452b c)d e - 3630b c d e +--R + +--R 3 3 +--R 2420c d +--R * +--R 3 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (- 2232a b c - 372b )e + (4464a c + 4464b c)d e - 11160b c d e +--R + +--R 3 3 +--R 7440c d +--R * +--R 2 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (- 3048a b c - 508b )e + (6096a c + 6096b c)d e - 15240b c d e +--R + +--R 3 3 +--R 10160c d +--R * +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (- 1440a b c - 240b )e + (2880a c + 2880b c)d e - 7200b c d e +--R + +--R 3 3 +--R 4800c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (- 2a c - 2a b )e + (12a b c + 2b )d e + (- 12a c - 12b c)d e +--R + +--R 2 3 3 4 +--R 20b c d e - 10c d +--R * +--R 5 +--R m +--R + +--R 2 2 4 3 3 +--R (- 38a c - 38a b )e + (228a b c + 38b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 228a c - 228b c)d e + 380b c d e - 190c d +--R * +--R 4 +--R m +--R + +--R 2 2 4 3 3 +--R (- 274a c - 274a b )e + (1644a b c + 274b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 1644a c - 1644b c)d e + 2740b c d e - 1370c d +--R * +--R 3 +--R m +--R + +--R 2 2 4 3 3 +--R (- 922a c - 922a b )e + (5532a b c + 922b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 5532a c - 5532b c)d e + 9220b c d e - 4610c d +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 3 +--R (- 1404a c - 1404a b )e + (8424a b c + 1404b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 8424a c - 8424b c)d e + 14040b c d e - 7020c d +--R * +--R m +--R + +--R 2 2 4 3 3 +--R (- 720a c - 720a b )e + (4320a b c + 720b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 4320a c - 4320b c)d e + 7200b c d e - 3600c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (2a c + 2a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (4a c + 4b c)d e - 5b c d e + 2c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R - 20a b e + (40a c + 40a b )d e + (- 120a b c - 20b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (80a c + 80b c)d e - 100b c d e + 40c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R - 155a b e + (310a c + 310a b )d e + (- 930a b c - 155b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (620a c + 620b c)d e - 775b c d e + 310c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 +--R - 580a b e + (1160a c + 1160a b )d e +--R + +--R 3 2 3 2 2 3 2 +--R (- 3480a b c - 580b )d e + (2320a c + 2320b c)d e +--R + +--R 2 4 3 5 +--R - 2900b c d e + 1160c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R - 1044a b e + (2088a c + 2088a b )d e +--R + +--R 3 2 3 2 2 3 2 +--R (- 6264a b c - 1044b )d e + (4176a c + 4176b c)d e +--R + +--R 2 4 3 5 +--R - 5220b c d e + 2088c d +--R * +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R - 720a b e + (1440a c + 1440a b )d e + (- 4320a b c - 720b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (2880a c + 2880b c)d e - 3600b c d e + 1440c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 154 + +--S 155 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 5 2 5 4 2 2 5 3 3 5 2 +--R 2c e x + 5b c e x + (4a c + 4b c)e x + (6a b c + b )e x +--R + +--R 2 2 5 2 5 +--R (2a c + 2a b )e x + a b e +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 m + 5 2 3 m + 4 +--R - 2c (e x + d) + (- 5b c e + 10c d)(e x + d) +--R + +--R 2 2 2 2 3 2 m + 3 +--R ((- 4a c - 4b c)e + 20b c d e - 20c d )(e x + d) +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((- 6a b c - b )e + (12a c + 12b c)d e - 30b c d e + 20c d ) +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (- 2a c - 2a b )e + (12a b c + 2b )d e + (- 12a c - 12b c)d e +--R + +--R 2 3 3 4 +--R 20b c d e - 10c d +--R * +--R m + 1 +--R (e x + d) +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (2a c + 2a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (4a c + 4b c)d e - 5b c d e + 2c d +--R * +--R m +--R (e x + d) +--R / +--R 5 +--R e +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 845 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 9 2 4 3 3 8 +--R 2c e x + (5b c e + 8c d e )x +--R + +--R 2 2 4 2 3 3 2 2 7 +--R ((4a c + 4b c)e + 20b c d e + 12c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 6 +--R ((6a b c + b )e + (16a c + 16b c)d e + 30b c d e + 8c d e)x +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (2a c + 2a b )e + (24a b c + 4b )d e + (24a c + 24b c)d e +--R + +--R 2 3 3 4 +--R 20b c d e + 2c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 2 3 3 2 2 2 2 3 +--R a b e + (8a c + 8a b )d e + (36a b c + 6b )d e + (16a c + 16b c)d e +--R + +--R 2 4 +--R 5b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 3 +--R 4a b d e + (12a c + 12a b )d e + (24a b c + 4b )d e +--R + +--R 2 2 4 +--R (4a c + 4b c)d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 3 3 4 2 +--R (6a b d e + (8a c + 8a b )d e + (6a b c + b )d )x +--R + +--R 2 3 2 2 4 2 4 +--R (4a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 156 + +--S 157 of 845 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^5/e^6+1/3*(c*d^2-b*d*e+_ + a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^6/e^6-1/7*(2*c*d-_ + b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^7/e^6+1/2*c*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^8/e^6-5/9*c^2*(2*c*d-b*e)*_ + (d+e*x)^9/e^6+1/5*c^3*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 3 10 10 5 2 10 8 3 9 9 +--R - c e x + (- b c e + - c d e )x +--R 5 9 9 +--R + +--R 1 2 1 2 10 5 2 9 3 3 2 8 8 +--R ((- a c + - b c)e + - b c d e + - c d e )x +--R 2 2 2 2 +--R + +--R 6 1 3 10 16 2 16 2 9 30 2 2 8 8 3 3 7 7 +--R ((- a b c + - b )e + (-- a c + -- b c)d e + -- b c d e + - c d e )x +--R 7 7 7 7 7 7 +--R + +--R 1 2 1 2 10 2 3 9 2 2 2 8 +--R (- a c + - a b )e + (4a b c + - b )d e + (4a c + 4b c)d e +--R 3 3 3 +--R + +--R 10 2 3 7 1 3 4 6 +--R -- b c d e + - c d e +--R 3 3 +--R * +--R 6 +--R x +--R + +--R 1 2 10 8 2 8 2 9 36 6 3 2 8 +--R - a b e + (- a c + - a b )d e + (-- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 16 2 16 2 3 7 2 4 6 +--R (-- a c + -- b c)d e + b c d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 2 9 2 2 2 8 3 3 7 2 2 4 6 4 +--R (a b d e + (3a c + 3a b )d e + (6a b c + b )d e + (a c + b c)d e )x +--R + +--R 2 2 8 8 2 8 2 3 7 1 3 4 6 3 +--R (2a b d e + (- a c + - a b )d e + (2a b c + - b )d e )x +--R 3 3 3 +--R + +--R 2 3 7 2 2 4 6 2 2 4 6 1 2 5 5 +--R (2a b d e + (a c + a b )d e )x + a b d e x + - a b d e +--R 5 +--R + +--R 1 2 1 2 6 4 2 1 3 7 3 +--R (- -- a c - -- a b )d e + (-- a b c + --- b )d e +--R 15 15 35 105 +--R + +--R 1 2 1 2 8 2 1 2 9 1 3 10 +--R (- -- a c - -- b c)d e + --- b c d e - --- c d +--R 70 70 126 630 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 157 + +--S 158 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 10 5 2 4 8 3 3 9 +--R - c e x + (- b c e + - c d e )x +--R 5 9 9 +--R + +--R 1 2 1 2 4 5 2 3 3 3 2 2 8 +--R ((- a c + - b c)e + - b c d e + - c d e )x +--R 2 2 2 2 +--R + +--R 6 1 3 4 16 2 16 2 3 30 2 2 2 8 3 3 7 +--R ((- a b c + - b )e + (-- a c + -- b c)d e + -- b c d e + - c d e)x +--R 7 7 7 7 7 7 +--R + +--R 1 2 1 2 4 2 3 3 2 2 2 2 +--R (- a c + - a b )e + (4a b c + - b )d e + (4a c + 4b c)d e +--R 3 3 3 +--R + +--R 10 2 3 1 3 4 +--R -- b c d e + - c d +--R 3 3 +--R * +--R 6 +--R x +--R + +--R 1 2 4 8 2 8 2 3 36 6 3 2 2 +--R - a b e + (- a c + - a b )d e + (-- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 16 2 16 2 3 2 4 +--R (-- a c + -- b c)d e + b c d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 2 3 2 2 2 2 3 3 2 2 4 4 +--R (a b d e + (3a c + 3a b )d e + (6a b c + b )d e + (a c + b c)d )x +--R + +--R 2 2 2 8 2 8 2 3 1 3 4 3 +--R (2a b d e + (- a c + - a b )d e + (2a b c + - b )d )x +--R 3 3 3 +--R + +--R 2 3 2 2 4 2 2 4 +--R (2a b d e + (a c + a b )d )x + a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 158 + +--S 159 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 5 5 1 2 1 2 6 4 2 1 3 7 3 +--R - - a b d e + (-- a c + -- a b )d e + (- -- a b c - --- b )d e +--R 5 15 15 35 105 +--R + +--R 1 2 1 2 8 2 1 2 9 1 3 10 +--R (-- a c + -- b c)d e - --- b c d e + --- c d +--R 70 70 126 630 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 159 + +--S 160 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 3 8 2 3 3 2 7 +--R 2c e x + (5b c e + 6c d e )x +--R + +--R 2 2 3 2 2 3 2 6 +--R ((4a c + 4b c)e + 15b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (12a c + 12b c)d e + 15b c d e + 2c d )x +--R + +--R 2 2 3 3 2 2 2 2 2 3 4 +--R ((2a c + 2a b )e + (18a b c + 3b )d e + (12a c + 12b c)d e + 5b c d )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 3 +--R (a b e + (6a c + 6a b )d e + (18a b c + 3b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 6a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 3 2 3 +--R (3a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 161 + +--S 162 of 845 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4/e^6+2/5*(c*d^2-_ + b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^5/e^6-_ + 1/6*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^6/e^6+4/7*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^7/e^6-5/8*c^2*(2*c*d-b*e)*(d+e*x)^8/e^6+2/9*c^3*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 2 3 9 9 5 2 9 3 3 8 8 +--R - c e x + (- b c e + - c d e )x +--R 9 8 4 +--R + +--R 4 2 4 2 9 15 2 8 6 3 2 7 7 +--R ((- a c + - b c)e + -- b c d e + - c d e )x +--R 7 7 7 7 +--R + +--R 1 3 9 2 2 8 5 2 2 7 1 3 3 6 6 +--R ((a b c + - b )e + (2a c + 2b c)d e + - b c d e + - c d e )x +--R 6 2 3 +--R + +--R 2 2 2 2 9 18 3 3 8 12 2 12 2 2 7 +--R (- a c + - a b )e + (-- a b c + - b )d e + (-- a c + -- b c)d e +--R 5 5 5 5 5 5 +--R + +--R 2 3 6 +--R b c d e +--R * +--R 5 +--R x +--R + +--R 1 2 9 3 2 3 2 8 9 3 3 2 7 +--R - a b e + (- a c + - a b )d e + (- a b c + - b )d e +--R 4 2 2 2 4 +--R + +--R 2 2 3 6 +--R (a c + b c)d e +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 2 7 1 3 3 6 3 +--R (a b d e + (2a c + 2a b )d e + (2a b c + - b )d e )x +--R 3 +--R + +--R 3 2 2 7 2 2 3 6 2 2 3 6 1 2 4 5 +--R (- a b d e + (a c + a b )d e )x + a b d e x + - a b d e +--R 2 4 +--R + +--R 1 2 1 2 5 4 1 1 3 6 3 +--R (- -- a c - -- a b )d e + (-- a b c + -- b )d e +--R 10 10 10 60 +--R + +--R 1 2 1 2 7 2 1 2 8 1 3 9 +--R (- -- a c - -- b c)d e + -- b c d e - --- c d +--R 35 35 56 252 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +--S 163 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 9 5 2 3 3 3 2 8 +--R - c e x + (- b c e + - c d e )x +--R 9 8 4 +--R + +--R 4 2 4 2 3 15 2 2 6 3 2 7 +--R ((- a c + - b c)e + -- b c d e + - c d e)x +--R 7 7 7 7 +--R + +--R 1 3 3 2 2 2 5 2 2 1 3 3 6 +--R ((a b c + - b )e + (2a c + 2b c)d e + - b c d e + - c d )x +--R 6 2 3 +--R + +--R 2 2 2 2 3 18 3 3 2 12 2 12 2 2 +--R (- a c + - a b )e + (-- a b c + - b )d e + (-- a c + -- b c)d e +--R 5 5 5 5 5 5 +--R + +--R 2 3 +--R b c d +--R * +--R 5 +--R x +--R + +--R 1 2 3 3 2 3 2 2 9 3 3 2 2 2 3 4 +--R (- a b e + (- a c + - a b )d e + (- a b c + - b )d e + (a c + b c)d )x +--R 4 2 2 2 4 +--R + +--R 2 2 2 2 2 1 3 3 3 +--R (a b d e + (2a c + 2a b )d e + (2a b c + - b )d )x +--R 3 +--R + +--R 3 2 2 2 2 3 2 2 3 +--R (- a b d e + (a c + a b )d )x + a b d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 163 + +--S 164 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 4 5 1 2 1 2 5 4 1 1 3 6 3 +--R - - a b d e + (-- a c + -- a b )d e + (- -- a b c - -- b )d e +--R 4 10 10 10 60 +--R + +--R 1 2 1 2 7 2 1 2 8 1 3 9 +--R (-- a c + -- b c)d e - -- b c d e + --- c d +--R 35 35 56 252 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 164 + +--S 165 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 166 + +--S 167 of 845 +r0:=a^2*b*d^2*x+a*d*(b^2*d+a*c*d+a*b*e)*x^2+1/3*(b^3*d^2+4*a*b^2*d*e+_ + 4*a^2*c*d*e+a*b*(6*c*d^2+a*e^2))*x^3+1/2*(b^3*d*e+6*a*b*c*d*e+b^2*_ + (2*c*d^2+a*e^2)+a*c*(2*c*d^2+a*e^2))*x^4+1/5*(8*b^2*c*d*e+_ + 8*a*c^2*d*e+b^3*e^2+b*c*(5*c*d^2+6*a*e^2))*x^5+1/3*c*(c^2*d^2+_ + 2*b^2*e^2+c*e*(5*b*d+2*a*e))*x^6+1/7*c^2*e*(4*c*d+5*b*e)*x^7+_ + 1/4*c^3*e^2*x^8 +--R +--R +--R (2) +--R 1 3 2 8 5 2 2 4 3 7 +--R - c e x + (- b c e + - c d e)x +--R 4 7 7 +--R + +--R 2 2 2 2 2 5 2 1 3 2 6 +--R ((- a c + - b c)e + - b c d e + - c d )x +--R 3 3 3 3 +--R + +--R 6 1 3 2 8 2 8 2 2 2 5 +--R ((- a b c + - b )e + (- a c + - b c)d e + b c d )x +--R 5 5 5 5 +--R + +--R 1 2 1 2 2 1 3 2 2 2 4 +--R ((- a c + - a b )e + (3a b c + - b )d e + (a c + b c)d )x +--R 2 2 2 +--R + +--R 1 2 2 4 2 4 2 1 3 2 3 +--R (- a b e + (- a c + - a b )d e + (2a b c + - b )d )x +--R 3 3 3 3 +--R + +--R 2 2 2 2 2 2 2 +--R (a b d e + (a c + a b )d )x + a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 167 + +--S 168 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 8 5 2 2 4 3 7 +--R - c e x + (- b c e + - c d e)x +--R 4 7 7 +--R + +--R 2 2 2 2 2 5 2 1 3 2 6 +--R ((- a c + - b c)e + - b c d e + - c d )x +--R 3 3 3 3 +--R + +--R 6 1 3 2 8 2 8 2 2 2 5 +--R ((- a b c + - b )e + (- a c + - b c)d e + b c d )x +--R 5 5 5 5 +--R + +--R 1 2 1 2 2 1 3 2 2 2 4 +--R ((- a c + - a b )e + (3a b c + - b )d e + (a c + b c)d )x +--R 2 2 2 +--R + +--R 1 2 2 4 2 4 2 1 3 2 3 +--R (- a b e + (- a c + - a b )d e + (2a b c + - b )d )x +--R 3 3 3 3 +--R + +--R 2 2 2 2 2 2 2 +--R (a b d e + (a c + a b )d )x + a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 168 + +--S 169 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 169 + +--S 170 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 170 + +)clear all + +--S 171 of 845 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 2 2 3 2 +--R ((6a b c + b )e + (4a c + 4b c)d)x + ((2a c + 2a b )e + (6a b c + b )d)x +--R + +--R 2 2 2 2 +--R (a b e + (2a c + 2a b )d)x + a b d +--R Type: Polynomial(Integer) +--E 171 + +--S 172 of 845 +r0:=a^2*b*d*x+1/2*a*(2*b^2*d+2*a*c*d+a*b*e)*x^2+1/3*(b^3*d+6*a*b*c*d+_ + 2*a*b^2*e+2*a^2*c*e)*x^3+1/4*(4*b^2*c*d+4*a*c^2*d+b^3*e+6*a*b*c*e)*x^4+_ + 1/5*c*(5*b*c*d+4*b^2*e+4*a*c*e)*x^5+1/6*c^2*(2*c*d+5*b*e)*x^6+2/7*c^3*e*x^7 +--R +--R +--R (2) +--R 2 3 7 5 2 1 3 6 4 2 4 2 2 5 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c)e + b c d)x +--R 7 6 3 5 5 +--R + +--R 3 1 3 2 2 4 +--R ((- a b c + - b )e + (a c + b c)d)x +--R 2 4 +--R + +--R 2 2 2 2 1 3 3 1 2 2 2 2 +--R ((- a c + - a b )e + (2a b c + - b )d)x + (- a b e + (a c + a b )d)x +--R 3 3 3 2 +--R + +--R 2 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 172 + +--S 173 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 7 5 2 1 3 6 4 2 4 2 2 5 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c)e + b c d)x +--R 7 6 3 5 5 +--R + +--R 3 1 3 2 2 4 +--R ((- a b c + - b )e + (a c + b c)d)x +--R 2 4 +--R + +--R 2 2 2 2 1 3 3 1 2 2 2 2 +--R ((- a c + - a b )e + (2a b c + - b )d)x + (- a b e + (a c + a b )d)x +--R 3 3 3 2 +--R + +--R 2 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 173 + +--S 174 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 174 + +--S 175 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 175 + +)clear all + +--S 176 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R Type: Polynomial(Integer) +--E 176 + +--S 177 of 845 +r0:=1/3*(a+b*x+c*x^2)^3 +--R +--R +--R (2) +--R 1 3 6 2 5 2 2 4 1 3 3 2 2 2 +--R - c x + b c x + (a c + b c)x + (2a b c + - b )x + (a c + a b )x +--R 3 3 +--R + +--R 2 1 3 +--R a b x + - a +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 177 + +--S 178 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 6 2 5 2 2 4 1 3 3 2 2 2 2 +--R - c x + b c x + (a c + b c)x + (2a b c + - b )x + (a c + a b )x + a b x +--R 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 178 + +--S 179 of 845 +m0:=a0-r0 +--R +--R +--R 1 3 +--R (4) - - a +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 179 + +--S 180 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 180 + +)clear all + +--S 181 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 845 +r0:=2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*x/e^5-_ + 1/2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^2/e^6+4/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^3/e^6-_ + 5/4*c^2*(2*c*d-b*e)*(d+e*x)^4/e^6+2/5*c^3*(d+e*x)^5/e^6-(2*c*d-b*e)*_ + (c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 2 4 3 2 3 +--R 60a b e + (- 120a c - 120a b )d e + (360a b c + 60b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 240a c - 240b c)d e + 300b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 24c e x + (75b c e - 30c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((80a c + 80b c)e - 100b c d e + 40c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (180a b c + 30b )e + (- 120a c - 120b c)d e + 150b c d e +--R + +--R 3 3 2 +--R - 60c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (120a c + 120a b )e + (- 360a b c - 60b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (240a c + 240b c)d e - 300b c d e + 120c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (180a b c + 30b )d e + (- 280a c - 280b c)d e + 575b c d e - 326c d +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 182 + +--S 183 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 2 4 3 2 3 +--R 60a b e + (- 120a c - 120a b )d e + (360a b c + 60b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 240a c - 240b c)d e + 300b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 24c e x + (75b c e - 30c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((80a c + 80b c)e - 100b c d e + 40c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (180a b c + 30b )e + (- 120a c - 120b c)d e + 150b c d e +--R + +--R 3 3 2 +--R - 60c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (120a c + 120a b )e + (- 360a b c - 60b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (240a c + 240b c)d e - 300b c d e + 120c d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 180a b c - 30b )d e + (280a c + 280b c)d e - 575b c d e + 326c d +--R ----------------------------------------------------------------------- +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 184 + +--S 185 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 845 +r0:=-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*x/e^5+_ + (2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x))+2*c*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^2/e^6-5/3*c^2*(2*c*d-b*e)*_ + (d+e*x)^3/e^6+1/2*c^3*(d+e*x)^4/e^6+2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 5 3 4 +--R (12a c + 12a b )e + (- 72a b c - 12b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (72a c + 72b c)d e - 120b c d e + 60c d e +--R * +--R x +--R + +--R 2 2 4 3 2 3 2 2 3 2 +--R (12a c + 12a b )d e + (- 72a b c - 12b )d e + (72a c + 72b c)d e +--R + +--R 2 4 3 5 +--R - 120b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 3c e x + (10b c e - 5c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 20b c d e + 10c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((36a b c + 6b )e + (- 36a c - 36b c)d e + 60b c d e - 30c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((36a b c + 6b )d e + (- 36a c - 36b c)d e + 40b c d e - 5c d e)x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 6a b e + (12a c + 12a b )d e + (- 36a b c - 6b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (36a c + 36b c)d e - 80b c d e + 55c d +--R / +--R 7 6 +--R 6e x + 6d e +--R Type: Expression(Integer) +--E 187 + +--S 188 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 5 3 4 +--R (12a c + 12a b )e + (- 72a b c - 12b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (72a c + 72b c)d e - 120b c d e + 60c d e +--R * +--R x +--R + +--R 2 2 4 3 2 3 2 2 3 2 +--R (12a c + 12a b )d e + (- 72a b c - 12b )d e + (72a c + 72b c)d e +--R + +--R 2 4 3 5 +--R - 120b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 3c e x + (10b c e - 5c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 20b c d e + 10c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((36a b c + 6b )e + (- 36a c - 36b c)d e + 60b c d e - 30c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((36a b c + 6b )d e + (- 48a c - 48b c)d e + 90b c d e - 48c d e)x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 6a b e + (12a c + 12a b )d e + (- 36a b c - 6b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (24a c + 24b c)d e - 30b c d e + 12c d +--R / +--R 7 6 +--R 6e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 845 +m0:=a0-r0 +--R +--R +--R 2 2 2 2 2 3 3 4 +--R (- 12a c - 12b c)d e + 50b c d e - 43c d +--R (4) ------------------------------------------- +--R 6 +--R 6e +--R Type: Expression(Integer) +--E 189 + +--S 190 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 845 +r0:=c*(12*c^2*d^2+4*b^2*e^2-c*e*(15*b*d-4*a*e))*x/e^5-1/2*c^2*(6*c*d-_ + 5*b*e)*x^2/e^4+2/3*c^3*x^3/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+_ + a*e^2)^2/(e^6*(d+e*x)^2)-2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))/(e^6*(d+e*x))-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 2 2 4 2 2 3 +--R (36a b c + 6b )e + (- 72a c - 72b c)d e + 180b c d e +--R + +--R 3 3 2 +--R - 120c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (72a b c + 12b )d e + (- 144a c - 144b c)d e + 360b c d e +--R + +--R 3 4 +--R - 240c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (36a b c + 6b )d e + (- 72a c - 72b c)d e + 180b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 4c e x + (15b c e - 10c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((24a c + 24b c)e - 60b c d e + 40c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((48a c + 48b c)d e - 165b c d e + 126c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 12a c - 12a b )e + (72a b c + 12b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 30b c d e + 12c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 6a c - 6a b )d e + (54a b c + 9b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 60a c - 60b c)d e + 105b c d e - 54c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 192 + +--S 193 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 2 2 4 2 2 3 +--R (36a b c + 6b )e + (- 72a c - 72b c)d e + 180b c d e +--R + +--R 3 3 2 +--R - 120c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (72a b c + 12b )d e + (- 144a c - 144b c)d e + 360b c d e +--R + +--R 3 4 +--R - 240c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (36a b c + 6b )d e + (- 72a c - 72b c)d e + 180b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 4c e x + (15b c e - 10c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((24a c + 24b c)e - 60b c d e + 40c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((48a c + 48b c)d e - 165b c d e + 126c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 12a c - 12a b )e + (72a b c + 12b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 30b c d e + 12c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 6a c - 6a b )d e + (54a b c + 9b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 60a c - 60b c)d e + 105b c d e - 54c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 845 +r0:=-c^2*(8*c*d-5*b*e)*x/e^5+c^3*x^2/e^4+1/3*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^2/(e^6*(d+e*x)^3)-(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))/(e^6*(d+e*x)^2)+(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))/(e^6*(d+e*x))+4*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 60b c d e + 60c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e )x +--R + +--R 2 2 2 3 2 3 2 3 4 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e)x +--R + +--R 2 2 3 2 2 4 3 5 +--R (12a c + 12b c)d e - 60b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 2 4 3 2 3 3 +--R 3c e x + (15b c e - 15c d e )x + (45b c d e - 63c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 18a b c - 3b )e + (36a c + 36b c)d e - 45b c d e - 9c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 3a c - 3a b )e + (- 18a b c - 3b )d e + (54a c + 54b c)d e +--R + +--R 2 3 2 3 4 +--R - 135b c d e + 81c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (- a c - a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (22a c + 22b c)d e - 65b c d e + 47c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Expression(Integer) +--E 197 + +--S 198 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 60b c d e + 60c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e )x +--R + +--R 2 2 2 3 2 3 2 3 4 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e)x +--R + +--R 2 2 3 2 2 4 3 5 +--R (12a c + 12b c)d e - 60b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 2 4 3 2 3 3 +--R 3c e x + (15b c e - 15c d e )x + (45b c d e - 63c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 18a b c - 3b )e + (36a c + 36b c)d e - 45b c d e - 9c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 3a c - 3a b )e + (- 18a b c - 3b )d e + (54a c + 54b c)d e +--R + +--R 2 3 2 3 4 +--R - 135b c d e + 81c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (- a c - a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (22a c + 22b c)d e - 65b c d e + 47c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 845 +r0:=2*c^3*x/e^5+1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^4)-_ + 2/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/_ + (e^6*(d+e*x)^3)+1/2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-_ + 3*a*e))/(e^6*(d+e*x)^2)-4*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/_ + (e^6*(d+e*x))-5*c^2*(2*c*d-b*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 3 4 4 2 4 3 2 3 3 +--R (60b c e - 120c d e )x + (240b c d e - 480c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 3 4 2 4 +--R (360b c d e - 720c d e )x + (240b c d e - 480c d e)x + 60b c d e +--R + +--R 3 5 +--R - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 3 4 4 2 2 5 2 4 3 2 3 3 +--R 24c e x + 96c d e x + ((- 48a c - 48b c)e + 240b c d e - 96c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 36a b c - 6b )e + (- 72a c - 72b c)d e + 540b c d e +--R + +--R 3 3 2 +--R - 504c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 8a c - 8a b )e + (- 24a b c - 4b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 440b c d e - 496c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 2a c - 2a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12a c - 12b c)d e + 125b c d e - 154c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 202 + +--S 203 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 3 4 4 2 4 3 2 3 3 +--R (60b c e - 120c d e )x + (240b c d e - 480c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 3 4 2 4 +--R (360b c d e - 720c d e )x + (240b c d e - 480c d e)x + 60b c d e +--R + +--R 3 5 +--R - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 3 4 4 2 2 5 2 4 3 2 3 3 +--R 24c e x + 96c d e x + ((- 48a c - 48b c)e + 240b c d e - 96c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 36a b c - 6b )e + (- 72a c - 72b c)d e + 540b c d e +--R + +--R 3 3 2 +--R - 504c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 8a c - 8a b )e + (- 24a b c - 4b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 440b c d e - 496c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 2a c - 2a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12a c - 12b c)d e + 125b c d e - 154c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 845 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 845 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))+_ + (c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(2+m)/(e^8*(2+m))-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(3+m)/(e^8*(3+m))+_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*_ + (7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*_ + (d+e*x)^(4+m)/(e^8*(4+m))-5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^(5+m)/(e^8*(5+m))+3*c^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(6+m)/(e^8*(6+m))-_ + 7*c^3*(2*c*d-b*e)*(d+e*x)^(7+m)/(e^8*(7+m))+2*c^4*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 4 7 4 6 4 5 4 4 4 3 4 2 +--R 2c m + 56c m + 644c m + 3920c m + 13538c m + 26264c m +--R + +--R 4 4 +--R 26136c m + 10080c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 4 7 3 4 6 3 4 5 +--R (7b c e - 14c d)m + (203b c e - 406c d)m + (2401b c e - 4802c d)m +--R + +--R 3 4 4 3 4 3 +--R (14945b c e - 29890c d)m + (52528b c e - 105056c d)m +--R + +--R 3 4 2 3 4 3 +--R (103292b c e - 206584c d)m + (103824b c e - 207648c d)m + 40320b c e +--R + +--R 4 +--R - 80640c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 3 2 2 2 3 4 2 7 +--R ((6a c + 9b c )e - 42b c d e + 42c d )m +--R + +--R 3 2 2 2 3 4 2 6 +--R ((180a c + 270b c )e - 1260b c d e + 1260c d )m +--R + +--R 3 2 2 2 3 4 2 5 +--R ((2196a c + 3294b c )e - 15372b c d e + 15372c d )m +--R + +--R 3 2 2 2 3 4 2 4 +--R ((14040a c + 21060b c )e - 98280b c d e + 98280c d )m +--R + +--R 3 2 2 2 3 4 2 3 +--R ((50454a c + 75681b c )e - 353178b c d e + 353178c d )m +--R + +--R 3 2 2 2 3 4 2 2 +--R ((100980a c + 151470b c )e - 706860b c d e + 706860c d )m +--R + +--R 3 2 2 2 3 4 2 +--R ((102864a c + 154296b c )e - 720048b c d e + 720048c d )m +--R + +--R 3 2 2 2 3 4 2 +--R (40320a c + 60480b c )e - 282240b c d e + 282240c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 3 3 2 2 2 3 2 +--R (15a b c + 5b c)e + (- 30a c - 45b c )d e + 105b c d e +--R + +--R 4 3 +--R - 70c d +--R * +--R 7 +--R m +--R + +--R 2 3 3 3 2 2 2 3 2 +--R (465a b c + 155b c)e + (- 930a c - 1395b c )d e + 3255b c d e +--R + +--R 4 3 +--R - 2170c d +--R * +--R 6 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (5865a b c + 1955b c)e + (- 11730a c - 17595b c )d e +--R + +--R 3 2 4 3 +--R 41055b c d e - 27370c d +--R * +--R 5 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (38715a b c + 12905b c)e + (- 77430a c - 116145b c )d e +--R + +--R 3 2 4 3 +--R 271005b c d e - 180670c d +--R * +--R 4 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (143160a b c + 47720b c)e + (- 286320a c - 429480b c )d e +--R + +--R 3 2 4 3 +--R 1002120b c d e - 668080c d +--R * +--R 3 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (293460a b c + 97820b c)e + (- 586920a c - 880380b c )d e +--R + +--R 3 2 4 3 +--R 2054220b c d e - 1369480c d +--R * +--R 2 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (304560a b c + 101520b c)e + (- 609120a c - 913680b c )d e +--R + +--R 3 2 4 3 +--R 2131920b c d e - 1421280c d +--R * +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (120960a b c + 40320b c)e + (- 241920a c - 362880b c )d e +--R + +--R 3 2 4 3 +--R 846720b c d e - 564480c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c + 12a b c + b )e + (- 60a b c - 20b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (60a c + 90b c )d e - 140b c d e + 70c d +--R * +--R 7 +--R m +--R + +--R 2 2 2 4 4 2 3 3 +--R (192a c + 384a b c + 32b )e + (- 1920a b c - 640b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (1920a c + 2880b c )d e - 4480b c d e + 2240c d +--R * +--R 6 +--R m +--R + +--R 2 2 2 4 4 2 3 3 +--R (2508a c + 5016a b c + 418b )e + (- 25080a b c - 8360b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (25080a c + 37620b c )d e - 58520b c d e + 29260c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 4 4 +--R (17184a c + 34368a b c + 2864b )e +--R + +--R 2 3 3 3 2 2 2 2 +--R (- 171840a b c - 57280b c)d e + (171840a c + 257760b c )d e +--R + +--R 3 3 4 4 +--R - 400960b c d e + 200480c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 4 4 +--R (65958a c + 131916a b c + 10993b )e +--R + +--R 2 3 3 3 2 2 2 2 +--R (- 659580a b c - 219860b c)d e + (659580a c + 989370b c )d e +--R + +--R 3 3 4 4 +--R - 1539020b c d e + 769510c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 4 4 +--R (139872a c + 279744a b c + 23312b )e +--R + +--R 2 3 3 +--R (- 1398720a b c - 466240b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (1398720a c + 2098080b c )d e - 3263680b c d e + 1631840c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 4 4 +--R (149256a c + 298512a b c + 24876b )e +--R + +--R 2 3 3 +--R (- 1492560a b c - 497520b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (1492560a c + 2238840b c )d e - 3482640b c d e + 1741320c d +--R * +--R m +--R + +--R 2 2 2 4 4 +--R (60480a c + 120960a b c + 10080b )e +--R + +--R 2 3 3 3 2 2 2 2 +--R (- 604800a b c - 201600b c)d e + (604800a c + 907200b c )d e +--R + +--R 3 3 4 4 +--R - 1411200b c d e + 705600c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 5 2 2 2 4 4 +--R (9a b c + 3a b )e + (- 18a c - 36a b c - 3b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 +--R (90a b c + 30b c)d e + (- 60a c - 90b c )d e + 105b c 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+--R (- 623376a b c - 207792a b )d e +--R + +--R 2 2 2 4 3 4 +--R (415584a c + 831168a b c + 69264b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 1038960a b c - 346320b c)d e + (415584a c + 623376b c )d e +--R + +--R 3 6 4 7 +--R - 484848b c d e + 138528c d +--R * +--R m +--R + +--R 3 7 3 2 2 6 +--R - 40320a b e + (80640a c + 120960a b )d e +--R + +--R 2 3 2 5 +--R (- 362880a b c - 120960a b )d e +--R + +--R 2 2 2 4 3 4 +--R (241920a c + 483840a b c + 40320b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 604800a b c - 201600b c)d e + (241920a c + 362880b c )d e +--R + +--R 3 6 4 7 +--R - 282240b c d e + 80640c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 209 + +--S 210 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 7 7 3 7 6 3 2 2 7 5 2 3 7 4 +--R 2c e x + 7b c e x + (6a c + 9b c )e x + (15a b c + 5b c)e x +--R + +--R 2 2 2 4 7 3 2 3 7 2 3 2 2 7 +--R (6a c + 12a b c + b )e x + (9a b c + 3a b )e x + (2a c + 3a b )e x +--R + +--R 3 7 +--R a b e +--R * +--R m log(e x + d) +--R %e +--R + +--R 4 m + 7 3 4 m + 6 +--R - 2c (e x + d) + (- 7b c e + 14c d)(e x + d) +--R + +--R 3 2 2 2 3 4 2 m + 5 +--R ((- 6a c - 9b c )e + 42b c d e - 42c d )(e x + d) +--R + +--R 2 3 3 3 2 2 2 3 2 4 3 +--R ((- 15a b c - 5b c)e + (30a c + 45b c )d e - 105b c d e + 70c d ) +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 6a c - 12a b c - b )e + (60a b c + 20b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 60a c - 90b c )d e + 140b c d e - 70c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 3 5 2 2 2 4 4 +--R (- 9a b c - 3a b )e + (18a c + 36a b c + 3b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 4 5 +--R (- 90a b c - 30b c)d e + (60a c + 90b c )d e - 105b c d e + 42c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 6 2 3 5 +--R (- 2a c - 3a b )e + (18a b c + 6a b )d e +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (- 18a c - 36a b c - 3b )d e + (60a b c + 20b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (- 30a c - 45b c )d e + 42b c d e - 14c d +--R * +--R m + 1 +--R (e x + d) +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - a b e + (2a c + 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (6a c + 12a b c + b )d e + (- 15a b c - 5b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (6a c + 9b c )d e - 7b c d e + 2c d +--R * +--R m +--R (e x + d) +--R / +--R 7 +--R e +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 845 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 4 11 3 4 4 3 10 +--R 2c e x + (7b c e + 8c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 9 +--R ((6a c + 9b c )e + 28b c d e + 12c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 8 +--R ((15a b c + 5b c)e + (24a c + 36b c )d e + 42b c d e + 8c d e)x +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c + 12a b c + b )e + (60a b c + 20b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (36a c + 54b c )d e + 28b c d e + 2c d +--R * +--R 7 +--R x +--R + +--R 2 3 4 2 2 2 4 3 +--R (9a b c + 3a b )e + (24a c + 48a b c + 4b )d e +--R + +--R 2 3 2 2 3 2 2 3 3 4 +--R (90a b c + 30b c)d e + (24a c + 36b c )d e + 7b c d +--R * +--R 6 +--R x +--R + +--R 3 2 2 4 2 3 3 +--R (2a c + 3a b )e + (36a b c + 12a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 3 2 2 4 +--R (36a c + 72a b c + 6b )d e + (60a b c + 20b c)d e + (6a c + 9b c )d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 +--R a b e + (8a c + 12a b )d e + (54a b c + 18a b )d e +--R + +--R 2 2 2 4 3 2 3 4 +--R (24a c + 48a b c + 4b )d e + (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 3 3 2 2 2 2 2 3 3 +--R 4a b d e + (12a c + 18a b )d e + (36a b c + 12a b )d e +--R + +--R 2 2 2 4 4 +--R (6a c + 12a b c + b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 3 2 3 4 2 +--R (6a b d e + (8a c + 12a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 3 2 2 4 3 4 +--R (4a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 845 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^5/e^8+1/6*(c*d^2-b*d*e+_ + a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^6/e^8-_ + 3/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^7/e^8+1/8*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+_ + a^2*e^2))*(d+e*x)^8/e^8-5/9*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^9/e^8+3/10*c^2*(14*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(7*b*d-a*e))*(d+e*x)^10/e^8-7/11*c^3*(2*c*d-b*e)*_ + (d+e*x)^11/e^8+1/6*c^4*(d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 4 12 12 7 3 12 8 4 11 11 +--R - c e x + (-- b c e + -- c d e )x +--R 6 11 11 +--R + +--R 3 3 9 2 2 12 14 3 11 6 4 2 10 10 +--R ((- a c + -- b c )e + -- b c d e + - c d e )x +--R 5 10 5 5 +--R + +--R 5 2 5 3 12 8 3 2 2 11 14 3 2 10 +--R (- a b c + - b c)e + (- a c + 4b c )d e + -- b c d e +--R 3 9 3 3 +--R + +--R 8 4 3 9 +--R - c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 2 3 2 1 4 12 15 2 5 3 11 +--R (- a c + - a b c + - b )e + (-- a b c + - b c)d e +--R 4 2 8 2 2 +--R + +--R 9 3 27 2 2 2 10 7 3 3 9 1 4 4 8 +--R (- a c + -- b c )d e + - b c d e + - c d e +--R 2 4 2 4 +--R * +--R 8 +--R x +--R + +--R 9 2 3 3 12 24 2 2 48 2 4 4 11 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 7 7 7 7 7 +--R + +--R 90 2 30 3 2 10 24 3 36 2 2 3 9 3 4 8 +--R (-- a b c + -- b c)d e + (-- a c + -- b c )d e + b c d e +--R 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 1 2 2 12 2 3 11 +--R (- a c + - a b )e + (6a b c + 2a b )d e +--R 3 2 +--R + +--R 2 2 2 4 2 10 2 10 3 3 9 +--R (6a c + 12a b c + b )d e + (10a b c + -- b c)d e +--R 3 +--R + +--R 3 3 2 2 4 8 +--R (a c + - b c )d e +--R 2 +--R * +--R 6 +--R x +--R + +--R 1 3 12 8 3 12 2 2 11 54 2 18 3 2 10 +--R - a b e + (- a c + -- a b )d e + (-- a b c + -- a b )d e +--R 5 5 5 5 5 +--R + +--R 24 2 2 48 2 4 4 3 9 2 3 4 8 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d e +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 11 3 9 2 2 2 10 2 3 3 9 +--R a b d e + (3a c + - a b )d e + (9a b c + 3a b )d e +--R 2 +--R + +--R 3 2 2 2 1 4 4 8 +--R (- a c + 3a b c + - b )d e +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 2 10 8 3 2 2 3 9 2 3 4 8 3 +--R (2a b d e + (- a c + 4a b )d e + (3a b c + a b )d e )x +--R 3 +--R + +--R 3 3 9 3 3 2 2 4 8 2 3 4 8 1 3 5 7 +--R (2a b d e + (a c + - a b )d e )x + a b d e x + - a b d e +--R 2 5 +--R + +--R 1 3 1 2 2 6 6 3 2 1 3 7 5 +--R (- -- a c - -- a b )d e + (-- a b c + -- a b )d e +--R 15 10 35 35 +--R + +--R 3 2 2 3 2 1 4 8 4 1 2 1 3 9 3 +--R (- --- a c - -- a b c - --- b )d e + (-- a b c + --- b c)d e +--R 140 70 280 42 126 +--R + +--R 1 3 1 2 2 10 2 1 3 11 1 4 12 +--R (- --- a c - --- b c )d e + --- b c d e - ---- c d +--R 210 140 330 1980 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 212 + +--S 213 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 4 12 7 3 4 8 4 3 11 +--R - c e x + (-- b c e + -- c d e )x +--R 6 11 11 +--R + +--R 3 3 9 2 2 4 14 3 3 6 4 2 2 10 +--R ((- a c + -- b c )e + -- b c d e + - c d e )x +--R 5 10 5 5 +--R + +--R 5 2 5 3 4 8 3 2 2 3 14 3 2 2 8 4 3 9 +--R ((- a b c + - b c)e + (- a c + 4b c )d e + -- b c d e + - c d e)x +--R 3 9 3 3 9 +--R + +--R 3 2 2 3 2 1 4 4 15 2 5 3 3 +--R (- a c + - a b c + - b )e + (-- a b c + - b c)d e +--R 4 2 8 2 2 +--R + +--R 9 3 27 2 2 2 2 7 3 3 1 4 4 +--R (- a c + -- b c )d e + - b c d e + - c d +--R 2 4 2 4 +--R * +--R 8 +--R x +--R + +--R 9 2 3 3 4 24 2 2 48 2 4 4 3 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 7 7 7 7 7 +--R + +--R 90 2 30 3 2 2 24 3 36 2 2 3 3 4 +--R (-- a b c + -- b c)d e + (-- a c + -- b c )d e + b c d +--R 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 1 2 2 4 2 3 3 2 2 2 4 2 2 +--R (- a c + - a b )e + (6a b c + 2a b )d e + (6a c + 12a b c + b )d e +--R 3 2 +--R + +--R 2 10 3 3 3 3 2 2 4 +--R (10a b c + -- b c)d e + (a c + - b c )d +--R 3 2 +--R * +--R 6 +--R x +--R + +--R 1 3 4 8 3 12 2 2 3 54 2 18 3 2 2 +--R - a b e + (- a c + -- a b )d e + (-- a b c + -- a b )d e +--R 5 5 5 5 5 +--R + +--R 24 2 2 48 2 4 4 3 2 3 4 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 3 3 9 2 2 2 2 2 3 3 +--R a b d e + (3a c + - a b )d e + (9a b c + 3a b )d e +--R 2 +--R + +--R 3 2 2 2 1 4 4 +--R (- a c + 3a b c + - b )d +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 2 2 8 3 2 2 3 2 3 4 3 +--R (2a b d e + (- a c + 4a b )d e + (3a b c + a b )d )x +--R 3 +--R + +--R 3 3 3 3 2 2 4 2 3 4 +--R (2a b d e + (a c + - a b )d )x + a b d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 5 7 1 3 1 2 2 6 6 3 2 1 3 7 5 +--R - - a b d e + (-- a c + -- a b )d e + (- -- a b c - -- a b )d e +--R 5 15 10 35 35 +--R + +--R 3 2 2 3 2 1 4 8 4 1 2 1 3 9 3 +--R (--- a c + -- a b c + --- b )d e + (- -- a b c - --- b c)d e +--R 140 70 280 42 126 +--R + +--R 1 3 1 2 2 10 2 1 3 11 1 4 12 +--R (--- a c + --- b c )d e - --- b c d e + ---- c d +--R 210 140 330 1980 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 214 + +--S 215 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 3 10 3 3 4 2 9 +--R 2c e x + (7b c e + 6c d e )x +--R + +--R 3 2 2 3 3 2 4 2 8 +--R ((6a c + 9b c )e + 21b c d e + 6c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 4 3 7 +--R ((15a b c + 5b c)e + (18a c + 27b c )d e + 21b c d e + 2c d )x +--R + +--R 2 2 2 4 3 2 3 2 +--R (6a c + 12a b c + b )e + (45a b c + 15b c)d e +--R + +--R 3 2 2 2 3 3 +--R (18a c + 27b c )d e + 7b c d +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 2 2 4 2 +--R (9a b c + 3a b )e + (18a c + 36a b c + 3b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (45a b c + 15b c)d e + (6a c + 9b c )d +--R * +--R 5 +--R x +--R + +--R 3 2 2 3 2 3 2 2 2 2 4 2 +--R (2a c + 3a b )e + (27a b c + 9a b )d e + (18a c + 36a b c + 3b )d e +--R + +--R 2 3 3 +--R (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 3 3 2 2 2 2 3 2 +--R a b e + (6a c + 9a b )d e + (27a b c + 9a b )d e +--R + +--R 2 2 2 4 3 +--R (6a c + 12a b c + b )d +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 9a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 2 3 2 2 3 3 3 +--R (3a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 845 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^4/e^8+1/5*(c*d^2-b*d*e+_ + a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^5/e^8-_ + 1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^6/e^8+1/7*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-_ + 10*a*b*d*e+a^2*e^2))*(d+e*x)^7/e^8-5/8*c*(2*c*d-b*e)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^8/e^8+1/3*c^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^9/e^8-7/10*c^3*(2*c*d-b*e)*_ + (d+e*x)^10/e^8+2/11*c^4*(d+e*x)^11/e^8 +--R +--R +--R (2) +--R 2 4 11 11 7 3 11 3 4 10 10 +--R -- c e x + (-- b c e + - c d e )x +--R 11 10 5 +--R + +--R 2 3 2 2 11 7 3 10 2 4 2 9 9 +--R ((- a c + b c )e + - b c d e + - c d e )x +--R 3 3 3 +--R + +--R 15 2 5 3 11 9 3 27 2 2 10 21 3 2 9 +--R (-- a b c + - b c)e + (- a c + -- b c )d e + -- b c d e +--R 8 8 4 8 8 +--R + +--R 1 4 3 8 +--R - c d e +--R 4 +--R * +--R 8 +--R x +--R + +--R 6 2 2 12 2 1 4 11 45 2 15 3 10 +--R (- a c + -- a b c + - b )e + (-- a b c + -- b c)d e +--R 7 7 7 7 7 +--R + +--R 18 3 27 2 2 2 9 3 3 8 +--R (-- a c + -- b c )d e + b c d e +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 1 3 11 2 2 2 1 4 10 +--R (- a b c + - a b )e + (3a c + 6a b c + - b )d e +--R 2 2 2 +--R + +--R 15 2 5 3 2 9 3 3 2 2 3 8 +--R (-- a b c + - b c)d e + (a c + - b c )d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 2 11 27 2 9 3 10 +--R (- a c + - a b )e + (-- a b c + - a b )d e +--R 5 5 5 5 +--R + +--R 18 2 2 36 2 3 4 2 9 2 3 3 8 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d e +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 11 3 3 9 2 2 10 27 2 9 3 2 9 +--R - a b e + (- a c + - a b )d e + (-- a b c + - a b )d e +--R 4 2 4 4 4 +--R + +--R 3 2 2 2 1 4 3 8 +--R (- a c + 3a b c + - b )d e +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 10 3 2 2 2 9 2 3 3 8 3 +--R (a b d e + (2a c + 3a b )d e + (3a b c + a b )d e )x +--R + +--R 3 3 2 9 3 3 2 2 3 8 2 3 3 8 1 3 4 7 +--R (- a b d e + (a c + - a b )d e )x + a b d e x + - a b d e +--R 2 2 4 +--R + +--R 1 3 3 2 2 5 6 3 2 1 3 6 5 +--R (- -- a c - -- a b )d e + (-- a b c + -- a b )d e +--R 10 20 20 20 +--R + +--R 3 2 2 3 2 1 4 7 4 3 2 1 3 8 3 +--R (- -- a c - -- a b c - --- b )d e + (-- a b c + -- b c)d e +--R 70 35 140 56 56 +--R + +--R 1 3 1 2 2 9 2 1 3 10 1 4 11 +--R (- -- a c - -- b c )d e + --- b c d e - --- c d +--R 84 56 120 660 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 217 + +--S 218 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 11 7 3 3 3 4 2 10 +--R -- c e x + (-- b c e + - c d e )x +--R 11 10 5 +--R + +--R 2 3 2 2 3 7 3 2 2 4 2 9 +--R ((- a c + b c )e + - b c d e + - c d e)x +--R 3 3 3 +--R + +--R 15 2 5 3 3 9 3 27 2 2 2 21 3 2 1 4 3 8 +--R ((-- a b c + - b c)e + (- a c + -- b c )d e + -- b c d e + - c d )x +--R 8 8 4 8 8 4 +--R + +--R 6 2 2 12 2 1 4 3 45 2 15 3 2 +--R (- a c + -- a b c + - b )e + (-- a b c + -- b c)d e +--R 7 7 7 7 7 +--R + +--R 18 3 27 2 2 2 3 3 +--R (-- a c + -- b c )d e + b c d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 1 3 3 2 2 2 1 4 2 +--R (- a b c + - a b )e + (3a c + 6a b c + - b )d e +--R 2 2 2 +--R + +--R 15 2 5 3 2 3 3 2 2 3 +--R (-- a b c + - b c)d e + (a c + - b c )d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 2 3 27 2 9 3 2 +--R (- a c + - a b )e + (-- a b c + - a b )d e +--R 5 5 5 5 +--R + +--R 18 2 2 36 2 3 4 2 2 3 3 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 3 3 3 9 2 2 2 27 2 9 3 2 +--R - a b e + (- a c + - a b )d e + (-- a b c + - a b )d e +--R 4 2 4 4 4 +--R + +--R 3 2 2 2 1 4 3 +--R (- a c + 3a b c + - b )d +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 2 3 2 2 2 2 3 3 3 +--R (a b d e + (2a c + 3a b )d e + (3a b c + a b )d )x +--R + +--R 3 3 2 3 3 2 2 3 2 3 3 +--R (- a b d e + (a c + - a b )d )x + a b d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 4 7 1 3 3 2 2 5 6 3 2 1 3 6 5 +--R - - a b d e + (-- a c + -- a b )d e + (- -- a b c - -- a b )d e +--R 4 10 20 20 20 +--R + +--R 3 2 2 3 2 1 4 7 4 3 2 1 3 8 3 +--R (-- a c + -- a b c + --- b )d e + (- -- a b c - -- b c)d e +--R 70 35 140 56 56 +--R + +--R 1 3 1 2 2 9 2 1 3 10 1 4 11 +--R (-- a c + -- b c )d e - --- b c d e + --- c d +--R 84 56 120 660 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 219 + +--S 220 of 845 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 2 9 3 2 4 8 3 2 2 2 3 4 2 7 +--R 2c e x + (7b c e + 4c d e)x + ((6a c + 9b c )e + 14b c d e + 2c d )x +--R + +--R 2 3 2 3 2 2 3 2 6 +--R ((15a b c + 5b c)e + (12a c + 18b c )d e + 7b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 2 2 5 +--R ((6a c + 12a b c + b )e + (30a b c + 10b c)d e + (6a c + 9b c )d )x +--R + +--R 2 3 2 2 2 2 4 2 3 2 4 +--R ((9a b c + 3a b )e + (12a c + 24a b c + 2b )d e + (15a b c + 5b c)d )x +--R + +--R 3 2 2 2 2 3 2 2 2 4 2 3 +--R ((2a c + 3a b )e + (18a b c + 6a b )d e + (6a c + 12a b c + b )d )x +--R + +--R 3 2 3 2 2 2 3 2 2 +--R (a b e + (4a c + 6a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 2 2 2 3 2 +--R (2a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 845 +r0:=a^3*b*d^2*x+1/2*a^2*d*(3*b^2*d+2*a*c*d+2*a*b*e)*x^2+1/3*a*(3*b^3*d^2+_ + 6*a*b^2*d*e+4*a^2*c*d*e+a*b*(9*c*d^2+a*e^2))*x^3+1/4*(b^4*d^2+_ + 6*a*b^3*d*e+18*a^2*b*c*d*e+2*a^2*c*(3*c*d^2+a*e^2)+3*a*b^2*(4*c*d^2+_ + a*e^2))*x^4+1/5*(2*b^4*d*e+24*a*b^2*c*d*e+12*a^2*c^2*d*e+b^3*_ + (5*c*d^2+3*a*e^2)+3*a*b*c*(5*c*d^2+3*a*e^2))*x^5+1/6*(10*b^3*c*d*e+_ + 30*a*b*c^2*d*e+b^4*e^2+6*a*c^2*(c*d^2+a*e^2)+3*b^2*c*(3*c*d^2+_ + 4*a*e^2))*x^6+1/7*c*(18*b^2*c*d*e+12*a*c^2*d*e+5*b^3*e^2+b*c*_ + (7*c*d^2+15*a*e^2))*x^7+1/8*c^2*(2*c^2*d^2+9*b^2*e^2+2*c*e*_ + (7*b*d+3*a*e))*x^8+1/9*c^3*e*(4*c*d+7*b*e)*x^9+1/5*c^4*e^2*x^10 +--R +--R +--R (2) +--R 1 4 2 10 7 3 2 4 4 9 +--R - c e x + (- b c e + - c d e)x +--R 5 9 9 +--R + +--R 3 3 9 2 2 2 7 3 1 4 2 8 +--R ((- a c + - b c )e + - b c d e + - c d )x +--R 4 8 4 4 +--R + +--R 15 2 5 3 2 12 3 18 2 2 3 2 7 +--R ((-- a b c + - b c)e + (-- a c + -- b c )d e + b c d )x +--R 7 7 7 7 +--R + +--R 2 2 2 1 4 2 2 5 3 3 3 2 2 2 6 +--R ((a c + 2a b c + - b )e + (5a b c + - b c)d e + (a c + - b c )d )x +--R 6 3 2 +--R + +--R 9 2 3 3 2 12 2 2 24 2 2 4 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 2 3 2 +--R (3a b c + b c)d +--R * +--R 5 +--R x +--R + +--R 1 3 3 2 2 2 9 2 3 3 3 2 2 2 1 4 2 4 +--R ((- a c + - a b )e + (- a b c + - a b )d e + (- a c + 3a b c + - b )d )x +--R 2 4 2 2 2 4 +--R + +--R 1 3 2 4 3 2 2 2 3 2 3 +--R (- a b e + (- a c + 2a b )d e + (3a b c + a b )d )x +--R 3 3 +--R + +--R 3 3 3 2 2 2 2 3 2 +--R (a b d e + (a c + - a b )d )x + a b d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 2 10 7 3 2 4 4 9 +--R - c e x + (- b c e + - c d e)x +--R 5 9 9 +--R + +--R 3 3 9 2 2 2 7 3 1 4 2 8 +--R ((- a c + - b c )e + - b c d e + - c d )x +--R 4 8 4 4 +--R + +--R 15 2 5 3 2 12 3 18 2 2 3 2 7 +--R ((-- a b c + - b c)e + (-- a c + -- b c )d e + b c d )x +--R 7 7 7 7 +--R + +--R 2 2 2 1 4 2 2 5 3 3 3 2 2 2 6 +--R ((a c + 2a b c + - b )e + (5a b c + - b c)d e + (a c + - b c )d )x +--R 6 3 2 +--R + +--R 9 2 3 3 2 12 2 2 24 2 2 4 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 2 3 2 +--R (3a b c + b c)d +--R * +--R 5 +--R x +--R + +--R 1 3 3 2 2 2 9 2 3 3 3 2 2 2 1 4 2 4 +--R ((- a c + - a b )e + (- a b c + - a b )d e + (- a c + 3a b c + - b )d )x +--R 2 4 2 2 2 4 +--R + +--R 1 3 2 4 3 2 2 2 3 2 3 +--R (- a b e + (- a c + 2a b )d e + (3a b c + a b )d )x +--R 3 3 +--R + +--R 3 3 3 2 2 2 2 3 2 +--R (a b d e + (a c + - a b )d )x + a b d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 845 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 8 3 4 7 3 2 2 3 6 +--R 2c e x + (7b c e + 2c d)x + ((6a c + 9b c )e + 7b c d)x +--R + +--R 2 3 3 2 2 5 +--R ((15a b c + 5b c)e + (6a c + 9b c )d)x +--R + +--R 2 2 2 4 2 3 4 +--R ((6a c + 12a b c + b )e + (15a b c + 5b c)d)x +--R + +--R 2 3 2 2 2 4 3 +--R ((9a b c + 3a b )e + (6a c + 12a b c + b )d)x +--R + +--R 3 2 2 2 3 2 3 3 2 2 3 +--R ((2a c + 3a b )e + (9a b c + 3a b )d)x + (a b e + (2a c + 3a b )d)x + a b d +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 845 +r0:=a^3*b*d*x+1/2*a^2*(3*b^2*d+2*a*c*d+a*b*e)*x^2+1/3*a*(3*b^3*d+_ + 9*a*b*c*d+3*a*b^2*e+2*a^2*c*e)*x^3+1/4*(b^4*d+12*a*b^2*c*d+_ + 6*a^2*c^2*d+3*a*b^3*e+9*a^2*b*c*e)*x^4+1/5*(5*b^3*c*d+15*a*b*c^2*d+_ + b^4*e+12*a*b^2*c*e+6*a^2*c^2*e)*x^5+1/6*c*(9*b^2*c*d+6*a*c^2*d+_ + 5*b^3*e+15*a*b*c*e)*x^6+1/7*c^2*(7*b*c*d+9*b^2*e+6*a*c*e)*x^7+_ + 1/8*c^3*(2*c*d+7*b*e)*x^8+2/9*c^4*e*x^9 +--R +--R +--R (2) +--R 2 4 9 7 3 1 4 8 6 3 9 2 2 3 7 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c )e + b c d)x +--R 9 8 4 7 7 +--R + +--R 5 2 5 3 3 3 2 2 6 +--R ((- a b c + - b c)e + (a c + - b c )d)x +--R 2 6 2 +--R + +--R 6 2 2 12 2 1 4 2 3 5 +--R ((- a c + -- a b c + - b )e + (3a b c + b c)d)x +--R 5 5 5 +--R + +--R 9 2 3 3 3 2 2 2 1 4 4 +--R ((- a b c + - a b )e + (- a c + 3a b c + - b )d)x +--R 4 4 2 4 +--R + +--R 2 3 2 2 2 3 3 1 3 3 3 2 2 2 +--R ((- a c + a b )e + (3a b c + a b )d)x + (- a b e + (a c + - a b )d)x +--R 3 2 2 +--R + +--R 3 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 227 + +--S 228 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 9 7 3 1 4 8 6 3 9 2 2 3 7 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c )e + b c d)x +--R 9 8 4 7 7 +--R + +--R 5 2 5 3 3 3 2 2 6 +--R ((- a b c + - b c)e + (a c + - b c )d)x +--R 2 6 2 +--R + +--R 6 2 2 12 2 1 4 2 3 5 +--R ((- a c + -- a b c + - b )e + (3a b c + b c)d)x +--R 5 5 5 +--R + +--R 9 2 3 3 3 2 2 2 1 4 4 +--R ((- a b c + - a b )e + (- a c + 3a b c + - b )d)x +--R 4 4 2 4 +--R + +--R 2 3 2 2 2 3 3 1 3 3 3 2 2 2 +--R ((- a c + a b )e + (3a b c + a b )d)x + (- a b e + (a c + - a b )d)x +--R 3 2 2 +--R + +--R 3 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 229 + +--S 230 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 230 + +)clear all + +--S 231 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 845 +r0:=1/4*(a+b*x+c*x^2)^4 +--R +--R +--R (2) +--R 1 4 8 3 7 3 3 2 2 6 2 3 5 +--R - c x + b c x + (a c + - b c )x + (3a b c + b c)x +--R 4 2 +--R + +--R 3 2 2 2 1 4 4 2 3 3 3 3 2 2 2 3 +--R (- a c + 3a b c + - b )x + (3a b c + a b )x + (a c + - a b )x + a b x +--R 2 4 2 +--R + +--R 1 4 +--R - a +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 232 + +--S 233 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 8 3 7 3 3 2 2 6 2 3 5 +--R - c x + b c x + (a c + - b c )x + (3a b c + b c)x +--R 4 2 +--R + +--R 3 2 2 2 1 4 4 2 3 3 3 3 2 2 2 3 +--R (- a c + 3a b c + - b )x + (3a b c + a b )x + (a c + - a b )x + a b x +--R 2 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 845 +m0:=a0-r0 +--R +--R +--R 1 4 +--R (4) - - a +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 234 + +--S 235 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 235 + +)clear all + +--S 236 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 845 +r0:=(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*x/e^7-_ + 3/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^2/e^8+1/3*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+_ + a^2*e^2))*(d+e*x)^3/e^8-5/4*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^4/e^8+3/5*c^2*(14*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(7*b*d-a*e))*(d+e*x)^5/e^8-7/6*c^3*(2*c*d-b*e)*(d+e*x)^6/e^8+_ + 2/7*c^4*(d+e*x)^7/e^8-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 2 2 6 2 3 2 5 +--R 420a b e + (- 840a c - 1260a b )d e + (3780a b c + 1260a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 2520a c - 5040a b c - 420b )d e + (6300a b c + 2100b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 2520a c - 3780b c )d e + 2940b c d e - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 120c e x + (490b c e - 140c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((504a c + 756b c )e - 588b c d e + 168c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (1575a b c + 525b c)e + (- 630a c - 945b c )d e + 735b c d e +--R + +--R 4 3 4 +--R - 210c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (840a c + 1680a b c + 140b )e + (- 2100a b c - 700b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (840a c + 1260b c )d e - 980b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (1890a b c + 630a b )e + (- 1260a c - 2520a b c - 210b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (3150a b c + 1050b c)d e + (- 1260a c - 1890b c )d e +--R + +--R 3 4 3 4 5 2 +--R 1470b c d e - 420c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (840a c + 1260a b )e + (- 3780a b c - 1260a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (2520a c + 5040a b c + 420b )d e + (- 6300a b c - 2100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (2520a c + 3780b c )d e - 2940b c d e + 840c d e +--R * +--R x +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (1890a b c + 630a b )d e + (- 2940a c - 5880a b c - 490b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (12075a b c + 4025b c)d e + (- 6846a c - 10269b c )d e + 10437b c d e +--R + +--R 4 7 +--R - 3702c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 237 + +--S 238 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 3 2 2 6 2 3 2 5 +--R 420a b e + (- 840a c - 1260a b )d e + (3780a b c + 1260a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 2520a c - 5040a b c - 420b )d e + (6300a b c + 2100b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 2520a c - 3780b c )d e + 2940b c d e - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 120c e x + (490b c e - 140c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((504a c + 756b c )e - 588b c d e + 168c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (1575a b c + 525b c)e + (- 630a c - 945b c )d e + 735b c d e +--R + +--R 4 3 4 +--R - 210c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (840a c + 1680a b c + 140b )e + (- 2100a b c - 700b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (840a c + 1260b c )d e - 980b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (1890a b c + 630a b )e + (- 1260a c - 2520a b c - 210b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (3150a b c + 1050b c)d e + (- 1260a c - 1890b c )d e +--R + +--R 3 4 3 4 5 2 +--R 1470b c d e - 420c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (840a c + 1260a b )e + (- 3780a b c - 1260a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (2520a c + 5040a b c + 420b )d e + (- 6300a b c - 2100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (2520a c + 3780b c )d e - 2940b c d e + 840c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 5 2 2 2 4 3 4 +--R (- 1890a b c - 630a b )d e + (2940a c + 5880a b c + 490b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (- 12075a b c - 4025b c)d e + (6846a c + 10269b c )d e - 10437b c d e +--R + +--R 4 7 +--R 3702c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 239 + +--S 240 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 845 +r0:=-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*x/e^7+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x))+1/2*_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^2/e^8-_ + 5/3*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^3/e^8+3/4*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^4/e^8-7/5*c^3*(2*c*d-b*e)*(d+e*x)^5/e^8+1/3*c^4*_ + (d+e*x)^6/e^8+(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*_ + (7*b*d-a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 2 7 2 3 6 +--R (120a c + 180a b )e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d e +--R * +--R x +--R + +--R 3 2 2 6 2 3 2 5 +--R (120a c + 180a b )d e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 20c e x + (84b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((90a c + 135b c )e - 126b c d e + 42c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (300a b c + 100b c)e + (- 150a c - 225b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (180a c + 360a b c + 30b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (300a c + 450b c )d e - 420b c d e + 140c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (540a b c + 180a b )e + (- 540a c - 1080a b c - 90b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 3 4 3 +--R (1800a b c + 600b c)d e + (- 900a c - 1350b c )d e + 1260b c d e +--R + +--R 4 5 2 +--R - 420c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (540a b c + 180a b )d e + (- 540a c - 1080a b c - 90b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 3 5 2 +--R (1200a b c + 400b c)d e + (- 150a c - 225b c )d e - 546b c d e +--R + +--R 4 6 +--R 462c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 60a b e + (120a c + 180a b )d e + (- 540a b c - 180a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (540a c + 1080a b c + 90b )d e + (- 2400a b c - 800b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (1650a c + 2475b c )d e - 3066b c d e + 1302c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 242 + +--S 243 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 7 2 3 6 +--R (120a c + 180a b )e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d e +--R * +--R x +--R + +--R 3 2 2 6 2 3 2 5 +--R (120a c + 180a b )d e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 20c e x + (84b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((90a c + 135b c )e - 126b c d e + 42c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (300a b c + 100b c)e + (- 150a c - 225b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (180a c + 360a b c + 30b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (300a c + 450b c )d e - 420b c d e + 140c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (540a b c + 180a b )e + (- 540a c - 1080a b c - 90b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 3 4 3 +--R (1800a b c + 600b c)d e + (- 900a c - 1350b c )d e + 1260b c d e +--R + +--R 4 5 2 +--R - 420c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (540a b c + 180a b )d e + (- 720a c - 1440a b c - 120b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (2700a b c + 900b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 5 2 4 6 +--R 2100b c d e - 720c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 60a b e + (120a c + 180a b )d e + (- 540a b c - 180a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (360a c + 720a b c + 60b )d e + (- 900a b c - 300b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (360a c + 540b c )d e - 420b c d e + 120c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 4 2 4 2 3 3 3 +--R (- 180a c - 360a b c - 30b )d e + (1500a b c + 500b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (- 1290a c - 1935b c )d e + 2646b c d e - 1182c d +--R / +--R 8 +--R 60e +--R Type: Expression(Integer) +--E 244 + +--S 245 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 845 +r0:=(30*c^4*d^4+b^4*e^4-2*c^3*d^2*e*(35*b*d-18*a*e)-3*b^2*c*e^3*_ + (5*b*d-4*a*e)+3*c^2*e^2*(18*b^2*d^2-15*a*b*d*e+2*a^2*e^2))*x/e^7-_ + 1/2*c*(20*c^3*d^3-5*b^3*e^3+3*b*c*e^2*(9*b*d-5*a*e)-6*c^2*d*e*(7*b*d-_ + 3*a*e))*x^2/e^6+c^2*(4*c^2*d^2+3*b^2*e^2-c*e*(7*b*d-2*a*e))*x^3/e^5-_ + 1/4*c^3*(6*c*d-7*b*e)*x^4/e^4+2/5*c^4*x^5/e^3+1/2*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^3/(e^8*(d+e*x)^2)-(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x))-3*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 2 2 2 4 6 +--R (180a b c + 60a b )e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2100b c d e - 840c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (360a b c + 120a b )d e + (- 720a c - 1440a b c - 120b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (3600a b c + 1200b c)d e + (- 2400a c - 3600b c )d e +--R + +--R 3 5 2 4 6 +--R 4200b c d e - 1680c d e +--R * +--R x +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (180a b c + 60a b )d e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e + 2100b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (35b c e - 14c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((40a c + 60b c )e - 70b c d e + 28c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (150a b c + 50b c)e + (- 100a c - 150b c )d e + 175b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (120a c + 240a b c + 20b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (400a c + 600b c )d e - 700b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (240a c + 480a b c + 40b )d e + (- 1650a b c - 550b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1260a c + 1890b c )d e - 2380b c d e + 1000c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 40a c - 60a b )e + (360a b c + 120a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 240a c - 480a b c - 40b )d e + (300a b c + 100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (120a c + 180b c )d e - 560b c d e + 320c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 10a b e + (- 20a c - 30a b )d e + (270a b c + 90a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 300a c - 600a b c - 50b )d e + (1050a b c + 350b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 540a c - 810b c )d e + 770b c d e - 260c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 247 + +--S 248 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 7 2 2 2 4 6 +--R (180a b c + 60a b )e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2100b c d e - 840c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (360a b c + 120a b )d e + (- 720a c - 1440a b c - 120b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (3600a b c + 1200b c)d e + (- 2400a c - 3600b c )d e +--R + +--R 3 5 2 4 6 +--R 4200b c d e - 1680c d e +--R * +--R x +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (180a b c + 60a b )d e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e + 2100b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (35b c e - 14c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((40a c + 60b c )e - 70b c d e + 28c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (150a b c + 50b c)e + (- 100a c - 150b c )d e + 175b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (120a c + 240a b c + 20b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (400a c + 600b c )d e - 700b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (240a c + 480a b c + 40b )d e + (- 1650a b c - 550b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1260a c + 1890b c )d e - 2380b c d e + 1000c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 40a c - 60a b )e + (360a b c + 120a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 240a c - 480a b c - 40b )d e + (300a b c + 100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (120a c + 180b c )d e - 560b c d e + 320c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 10a b e + (- 20a c - 30a b )d e + (270a b c + 90a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 300a c - 600a b c - 50b )d e + (1050a b c + 350b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 540a c - 810b c )d e + 770b c d e - 260c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 845 +r0:=-5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*x/e^7+_ + 1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^3)-1/2*(c*d^2-_ + b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x)^2)+_ + 3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))/(e^8*(d+e*x))+3/2*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^2/e^8-7/3*c^3*(2*c*d-b*e)*(d+e*x)^3/e^8+1/2*c^4*(d+e*x)^4/e^8+_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 2 4 7 2 3 6 +--R (36a c + 72a b c + 6b )e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (360a c + 540b c )d e - 840b c d e + 420c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (36a c + 72a b c + 6b )d e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (360a c + 540b c )d e - 840b c d e + 420c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 3c e x + (14b c e - 7c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((18a c + 27b c )e - 42b c d e + 21c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (90a b c + 30b c)e + (- 90a c - 135b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 105c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 3 3 4 +--R (270a b c + 90b c)d e + (- 360a c - 540b c )d e + 910b c d e +--R + +--R 4 4 3 +--R - 455c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (108a c + 216a b c + 18b )d e +--R + +--R 2 3 2 5 3 4 3 4 5 2 +--R (- 270a b c - 90b c)d e + 210b c d e - 105c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 6a c - 9a b )e + (- 54a b c - 18a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (162a c + 324a b c + 27b )d e + (- 810a b c - 270b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (540a c + 810b c )d e - 1050b c d e + 525c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 2a b e + (- 2a c - 3a b )d e + (- 18a b c - 6a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (66a c + 132a b c + 11b )d e + (- 390a b c - 130b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (300a c + 450b c )d e - 630b c d e + 315c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 252 + +--S 253 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 4 7 2 3 6 +--R (36a c + 72a b c + 6b )e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (360a c + 540b c )d e - 840b c d e + 420c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (36a c + 72a b c + 6b )d e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (360a c + 540b c )d e - 840b c d e + 420c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 3c e x + (14b c e - 7c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((18a c + 27b c )e - 42b c d e + 21c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (90a b c + 30b c)e + (- 90a c - 135b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 105c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 3 3 4 +--R (270a b c + 90b c)d e + (- 378a c - 567b c )d e + 1022b c d e +--R + +--R 4 4 3 +--R - 556c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (108a c + 216a b c + 18b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 3 4 3 +--R (- 270a b c - 90b c)d e + (- 54a c - 81b c )d e + 546b c d e +--R + +--R 4 5 2 +--R - 408c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 6a c - 9a b )e + (- 54a b c - 18a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (162a c + 324a b c + 27b )d e + (- 810a b c - 270b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (486a c + 729b c )d e - 714b c d e + 222c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 2a b e + (- 2a c - 3a b )d e + (- 18a b c - 6a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (66a c + 132a b c + 11b )d e + (- 390a b c - 130b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (282a c + 423b c )d e - 518b c d e + 214c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 845 +m0:=a0-r0 +--R +--R +--R 3 2 2 2 2 3 3 4 4 +--R (- 18a c - 27b c )d e + 112b c d e - 101c d +--R (4) ---------------------------------------------- +--R 8 +--R 6e +--R Type: Expression(Integer) +--E 254 + +--S 255 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 845 +r0:=c^2*(30*c^2*d^2+9*b^2*e^2-c*e*(35*b*d-6*a*e))*x/e^7-1/2*c^3*_ + (10*c*d-7*b*e)*x^2/e^6+2/3*c^4*x^3/e^5+1/4*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^3/(e^8*(d+e*x)^4)-1/3*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x)^3)+3/2*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))/(e^8*(d+e*x)^2)+_ + (-70*c^4*d^4-b^4*e^4+4*b^2*c*e^3*(5*b*d-3*a*e)+20*c^3*d^2*e*(7*b*d-_ + 3*a*e)-6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))/(e^8*(d+e*x))-_ + 5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 3 2 2 6 3 2 5 +--R (180a b c + 60b c)e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 3 4 +--R - 840c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 3 4 4 4 3 +--R 5040b c d e - 3360c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1080a b c + 360b c)d e + (- 2160a c - 3240b c )d e +--R + +--R 3 4 3 4 5 2 +--R 7560b c d e - 5040c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 5 2 4 6 +--R 5040b c d e - 3360c d e +--R * +--R x +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (180a b c + 60b c)d e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (42b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((72a c + 108b c )e - 252b c d e + 168c d e )x +--R + +--R 3 2 2 6 3 2 5 4 3 4 4 +--R ((288a c + 432b c )d e - 1428b c d e + 1112c d e )x +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 72a c - 144a b c - 12b )e + (720a b c + 240b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 288a c - 432b c )d e - 672b c d e + 1088c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (- 108a c - 216a b c - 18b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1620a b c + 540b c)d e + (- 1512a c - 2268b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2772b c d e - 888c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 8a c - 12a b )e + (- 36a b c - 12a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 72a c - 144a b c - 12b )d e + (1320a b c + 440b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 1488a c - 2232b c )d e + 3528b c d e - 1712c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 3a b e + (- 2a c - 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 18a c - 36a b c - 3b )d e + (375a b c + 125b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 462a c - 693b c )d e + 1197b c d e - 638c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 257 + +--S 258 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 7 3 2 2 6 3 2 5 +--R (180a b c + 60b c)e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 3 4 +--R - 840c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 3 4 4 4 3 +--R 5040b c d e - 3360c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1080a b c + 360b c)d e + (- 2160a c - 3240b c )d e +--R + +--R 3 4 3 4 5 2 +--R 7560b c d e - 5040c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 5 2 4 6 +--R 5040b c d e - 3360c d e +--R * +--R x +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (180a b c + 60b c)d e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (42b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((72a c + 108b c )e - 252b c d e + 168c d e )x +--R + +--R 3 2 2 6 3 2 5 4 3 4 4 +--R ((288a c + 432b c )d e - 1428b c d e + 1112c d e )x +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 72a c - 144a b c - 12b )e + (720a b c + 240b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 288a c - 432b c )d e - 672b c d e + 1088c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (- 108a c - 216a b c - 18b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1620a b c + 540b c)d e + (- 1512a c - 2268b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2772b c d e - 888c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 8a c - 12a b )e + (- 36a b c - 12a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 72a c - 144a b c - 12b )d e + (1320a b c + 440b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 1488a c - 2232b c )d e + 3528b c d e - 1712c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 3a b e + (- 2a c - 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 18a c - 36a b c - 3b )d e + (375a b c + 125b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 462a c - 693b c )d e + 1197b c d e - 638c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 845 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 845 +r0:=e*(8*c^3*d^3-b^3*e^3+b*c*e^2*(4*b*d+3*a*e)-2*c^2*d*e*(3*b*d+4*a*e))*_ + x/c^3+1/2*e^2*(12*c^2*d^2+b^2*e^2-2*c*e*(2*b*d+a*e))*x^2/c^2+1/3*e^3*_ + (8*c*d-b*e)*x^3/c+1/2*e^4*x^4+1/2*(2*c^4*d^4+b^4*e^4-4*b^2*c*e^3*_ + (b*d+a*e)-4*c^3*d^2*e*(b*d+3*a*e)+2*c^2*e^2*(3*b^2*d^2+6*a*b*d*e+_ + a^2*e^2))*log(a+b*x+c*x^2)/c^4-e*(2*c*d-b*e)*(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^4 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 12a b c + 6b )e + (24a c - 24b c)d e + 36b c d e - 24c d e) +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c - 12a b c + 3b )e + (36a b c - 12b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 36a c + 18b c )d e - 12b c d e + 6c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3c e x + (- 2b c e + 16c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 2 +--R ((- 6a c + 3b c )e - 12b c d e + 36c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 +--R ((18a b c - 6b c)e + (- 48a c + 24b c )d e - 36b c d e + 48c d e)x +--R / +--R 4 +--R 6c +--R Type: Expression(Integer) +--E 262 + +--S 263 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 2 3 2 2 2 3 3 +--R ((6a b c - 3b )e + (- 12a c + 12b c)d e - 18b c d e + 12c d e) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c - 12a b c + 3b )e + (36a b c - 12b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 36a c + 18b c )d e - 12b c d e + 6c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3c e x + (- 2b c e + 16c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 2 +--R ((- 6a c + 3b c )e - 12b c d e + 36c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 +--R ((18a b c - 6b c)e + (- 48a c + 24b c )d e - 36b c d e + 48c d e)x +--R / +--R 4 +--R 6c +--R , +--R +--R 3 4 2 2 3 2 2 2 3 3 +--R ((12a b c - 6b )e + (- 24a c + 24b c)d e - 36b c d e + 24c d e) +--R * +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b +--R \|4a c - b atan(------------) +--R 2c x + b +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c - 12a b c + 3b )e + (36a b c - 12b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 36a c + 18b c )d e - 12b c d e + 6c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3c e x + (- 2b c e + 16c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 2 +--R ((- 6a c + 3b c )e - 12b c d e + 36c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 +--R ((18a b c - 6b c)e + (- 48a c + 24b c )d e - 36b c d e + 48c d e)x +--R / +--R 4 +--R 6c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 263 + +--S 264 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((2a b c - b )e + (- 4a c + 4b c)d e - 6b c d e + 4c d e) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((4a b c - 2b )e + (- 8a c + 8b c)d e - 12b c d e + 8c d e) +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 +--R 2c +--R Type: Expression(Integer) +--E 264 + +--S 265 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((2a b c - b )e + (- 4a c + 4b c)d e - 6b c d e + 4c d e) +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((2a b c - b )e + (- 4a c + 4b c)d e - 6b c d e + 4c d e) +--R * +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b +--R \|4a c - b atan(------------) +--R 2c x + b +--R / +--R 4 +--R c +--R Type: Expression(Integer) +--E 266 + +--S 267 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 268 + +--S 269 of 845 +r0:=e*(6*c^2*d^2+b^2*e^2-c*e*(3*b*d+2*a*e))*x/c^2+1/2*e^2*(6*c*d-b*e)*x^2/c+_ + 2/3*e^3*x^3+1/2*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(a+b*x+_ + c*x^2)/c^3-e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^3 +--R +--R +--R (2) +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((6a c - 6b )e + 18b c d e - 18c d e)\|- 4a c + b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((9a b c - 3b )e + (- 18a c + 9b c)d e - 9b c d e + 6c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 3 2 3 3 2 2 +--R 4c e x + (- 3b c e + 18c d e )x +--R + +--R 2 2 3 2 2 3 2 +--R ((- 12a c + 6b c)e - 18b c d e + 36c d e)x +--R / +--R 3 +--R 6c +--R Type: Expression(Integer) +--E 269 + +--S 270 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((3a c - 3b )e + 9b c d e - 9c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((9a b c - 3b )e + (- 18a c + 9b c)d e - 9b c d e + 6c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 3 2 3 3 2 2 +--R 4c e x + (- 3b c e + 18c d e )x +--R + +--R 2 2 3 2 2 3 2 +--R ((- 12a c + 6b c)e - 18b c d e + 36c d e)x +--R / +--R 3 +--R 6c +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R 2 3 2 2 2 | 2 \|4a c - b +--R ((- 6a c + 6b )e - 18b c d e + 18c d e)\|4a c - b atan(------------) +--R 2c x + b +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((9a b c - 3b )e + (- 18a c + 9b c)d e - 9b c d e + 6c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 3 2 3 3 2 2 +--R 4c e x + (- 3b c e + 18c d e )x +--R + +--R 2 2 3 2 2 3 2 +--R ((- 12a c + 6b c)e - 18b c d e + 36c d e)x +--R / +--R 3 +--R 6c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 270 + +--S 271 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((a c - b )e + 3b c d e - 3c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((- 2a c + 2b )e - 6b c d e + 6c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 +--R 2c +--R Type: Expression(Integer) +--E 271 + +--S 272 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((- a c + b )e - 3b c d e + 3c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 3 2 2 2 | 2 \|4a c - b +--R ((- a c + b )e - 3b c d e + 3c d e)\|4a c - b atan(------------) +--R 2c x + b +--R / +--R 3 +--R c +--R Type: Expression(Integer) +--E 273 + +--S 274 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 274 + +)clear all + +--S 275 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 275 + +--S 276 of 845 +r0:=e*(4*d-b*e/c)*x+e^2*x^2+1/2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + log(a+b*x+c*x^2)/c^2-e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*_ + sqrt(b^2-4*a*c)/c^2 +--R +--R +--R (2) +--R +-----------+ +--R 2 | 2 2c x + b +--R (2b e - 4c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d )log(c x + b x + a) + 2c e x +--R + +--R 2 2 +--R (- 2b c e + 8c d e)x +--R / +--R 2 +--R 2c +--R Type: Expression(Integer) +--E 276 + +--S 277 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 | 2 +--R (b e - 2c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d )log(c x + b x + a) + 2c e x +--R + +--R 2 2 +--R (- 2b c e + 8c d e)x +--R / +--R 2 +--R 2c +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 \|4a c - b +--R (- 2b e + 4c d e)\|4a c - b atan(------------) +--R 2c x + b +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d )log(c x + b x + a) + 2c e x +--R + +--R 2 2 +--R (- 2b c e + 8c d e)x +--R / +--R 2 +--R 2c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 277 + +--S 278 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 | 2 +--R (b e - 2c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 2c x + b +--R (- 2b e + 4c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 +--R 2c +--R Type: Expression(Integer) +--E 278 + +--S 279 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 | 2 2c x + b +--R (- b e + 2c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 \|4a c - b +--R (- b e + 2c d e)\|4a c - b atan(------------) +--R 2c x + b +--R / +--R 2 +--R c +--R Type: Expression(Integer) +--E 280 + +--S 281 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 281 + +)clear all + +--S 282 of 845 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) ----------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 282 + +--S 283 of 845 +r0:=2*e*x+1/2*(2*c*d-b*e)*log(a+b*x+c*x^2)/c-e*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c +--R +--R +--R (2) +--R +-----------+ +--R | 2 2c x + b +--R - 2e\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R (- b e + 2c d)log(c x + b x + a) + 4c e x +--R / +--R 2c +--R Type: Expression(Integer) +--E 283 + +--S 284 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | 2 +--R e\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 +--R (- b e + 2c d)log(c x + b x + a) + 4c e x +--R / +--R 2c +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b 2 +--R 2e\|4a c - b atan(------------) + (- b e + 2c d)log(c x + b x + a) +--R 2c x + b +--R + +--R 4c e x +--R / +--R 2c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 284 + +--S 285 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R | 2 +--R e\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R | 2 2c x + b +--R 2e\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2c +--R Type: Expression(Integer) +--E 285 + +--S 286 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 845 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +--R +-----------+ +---------+ | 2 +--R | 2 2c x + b | 2 \|4a c - b +--R e\|- 4a c + b atanh(--------------) + e\|4a c - b atan(------------) +--R +-----------+ 2c x + b +--R | 2 +--R \|- 4a c + b +--R (6) ---------------------------------------------------------------------- +--R c +--R Type: Expression(Integer) +--E 287 + +--S 288 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 845 +t0:=(b+2*c*x)/(a+b*x+c*x^2) +--R +--R +--R 2c x + b +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 289 + +--S 290 of 845 +r0:=log(a+b*x+c*x^2) +--R +--R +--R 2 +--R (2) log(c x + b x + a) +--R Type: Expression(Integer) +--E 290 + +--S 291 of 845 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) log(c x + b x + a) +--R Type: Union(Expression(Integer),...) +--E 291 + +--S 292 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 293 + +)clear all + +--S 294 of 845 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------- +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 294 + +--S 295 of 845 +r0:=-(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)+1/2*(2*c*d-b*e)*log(a+b*x+_ + c*x^2)/(c*d^2-b*d*e+a*e^2)+e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-_ + 4*a*c)/(c*d^2-b*d*e+a*e^2) +--R +--R +--R (2) +--R +-----------+ +--R | 2 2c x + b 2 +--R 2e\|- 4a c + b atanh(--------------) + (- b e + 2c d)log(c x + b x + a) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R (2b e - 4c d)log(e x + d) +--R / +--R 2 2 +--R 2a e - 2b d e + 2c d +--R Type: Expression(Integer) +--E 295 + +--S 296 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | 2 +--R e\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 +--R (- b e + 2c d)log(c x + b x + a) + (2b e - 4c d)log(e x + d) +--R / +--R 2 2 +--R 2a e - 2b d e + 2c d +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b 2 +--R - 2e\|4a c - b atan(------------) + (- b e + 2c d)log(c x + b x + a) +--R 2c x + b +--R + +--R (2b e - 4c d)log(e x + d) +--R / +--R 2 2 +--R 2a e - 2b d e + 2c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 296 + +--S 297 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | 2 2 2 2 +--R | 2 (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R e\|- 4a c + b log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R | 2 2c x + b +--R - 2e\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 2 +--R 2a e - 2b d e + 2c d +--R Type: Expression(Integer) +--E 297 + +--S 298 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 298 + +--S 299 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R +-----------+ +---------+ | 2 +--R | 2 2c x + b | 2 \|4a c - b +--R - e\|- 4a c + b atanh(--------------) - e\|4a c - b atan(------------) +--R +-----------+ 2c x + b +--R | 2 +--R \|- 4a c + b +--R ------------------------------------------------------------------------ +--R 2 2 +--R a e - b d e + c d +--R Type: Expression(Integer) +--E 299 + +--S 300 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 845 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 845 +r0:=(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x))-(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2+1/2*(2*c^2*d^2+_ + b^2*e^2-2*c*e*(b*d+a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2+_ + e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/_ + (c*d^2-b*d*e+a*e^2)^2 +--R +--R +--R (2) +--R +-----------+ +--R 3 2 2 2 | 2 +--R ((- 2b e + 4c d e )x - 2b d e + 4c d e)\|- 4a c + b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d e)x + (- 2a c + b )d e +--R + +--R 2 2 3 +--R - 2b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 2 2 2 2 +--R ((4a c - 2b )e + 4b c d e - 4c d e)x + (4a c - 2b )d e + 4b c d e +--R + +--R 2 3 +--R - 4c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (4a c + 2b )d e - 6b c d e + 4c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R Type: Expression(Integer) +--E 302 + +--S 303 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 2 2 2 | 2 +--R ((b e - 2c d e )x + b d e - 2c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d e)x + (- 2a c + b )d e +--R + +--R 2 2 3 +--R - 2b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 2 2 2 +--R ((4a c - 2b )e + 4b c d e - 4c d e)x + (4a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (4a c + 2b )d e - 6b c d e + 4c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R 3 2 2 2 | 2 \|4a c - b +--R ((2b e - 4c d e )x + 2b d e - 4c d e)\|4a c - b atan(------------) +--R 2c x + b +--R + +--R 2 3 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d e)x + (- 2a c + b )d e +--R + +--R 2 2 3 +--R - 2b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 2 2 2 +--R ((4a c - 2b )e + 4b c d e - 4c d e)x + (4a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (4a c + 2b )d e - 6b c d e + 4c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 303 + +--S 304 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 | 2 +--R (b e - 2c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 2c x + b +--R (2b e - 4c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 4 3 2 2 2 3 2 4 +--R 2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R Type: Expression(Integer) +--E 304 + +--S 305 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 | 2 2c x + b +--R (b e - 2c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 \|4a c - b +--R (b e - 2c d e)\|4a c - b atan(------------) +--R 2c x + b +--R / +--R 2 4 3 2 2 2 3 2 4 +--R a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R Type: Expression(Integer) +--E 306 + +--S 307 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 307 + +)clear all + +--S 308 of 845 +t0:=(b+2*c*x)/((d+e*x)^3*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 308 + +--S 309 of 845 +r0:=1/2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))-(2*c*d-b*e)*(c^2*d^2+_ + b^2*e^2-c*e*(b*d+3*a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*(2*c*d-_ + b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+_ + a*e^2)^3+e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/(c*d^2-b*d*e+a*e^2)^3 +--R +--R +--R (2) +--R 2 5 4 2 2 3 2 +--R ((- 2a c + 2b )e - 6b c d e + 6c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 +--R ((- 4a c + 4b )d e - 12b c d e + 12c d e )x + (- 2a c + 2b )d e +--R + +--R 3 2 2 4 +--R - 6b c d e + 6c d e +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((6a b c - 2b )d e + (- 12a c + 6b c)d e - 6b c d e + 4c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (3a b c - b )d e + (- 6a c + 3b c)d e - 3b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((- 12a b c + 4b )d e + (24a c - 12b c)d e + 12b c d e - 8c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 6a b c + 2b )d e + (12a c - 6b c)d e + 6b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 2 2 5 3 4 2 2 3 2 3 2 3 4 2 5 +--R ((- 4a c + 2a b )e - 2b d e + 6b c d e - 8b c d e + 4c d e)x - a b e +--R + +--R 2 2 4 3 2 3 2 2 3 2 +--R (- 2a c + 4a b )d e + (- 6a b c - 3b )d e + (4a c + 10b c)d e +--R + +--R 2 4 3 5 +--R - 13b c d e + 6c d +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R Type: Expression(Integer) +--E 309 + +--S 310 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 5 4 2 2 3 2 +--R ((a c - b )e + 3b c d e - 3c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 +--R ((2a c - 2b )d e + 6b c d e - 6c d e )x + (a c - b )d e +--R + +--R 3 2 2 4 +--R 3b c d e - 3c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((6a b c - 2b )d e + (- 12a c + 6b c)d e - 6b c d e + 4c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (3a b c - b )d e + (- 6a c + 3b c)d e - 3b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 12a b c + 4b )d e + (24a c - 12b c)d e + 12b c d e +--R + +--R 3 4 +--R - 8c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 6a b c + 2b )d e + (12a c - 6b c)d e + 6b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 2 2 5 3 4 2 2 3 2 3 2 3 4 +--R ((- 4a c + 2a b )e - 2b d e + 6b c d e - 8b c d e + 4c d e)x +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (- 2a c + 4a b )d e + (- 6a b c - 3b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (4a c + 10b c)d e - 13b c d e + 6c d +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R , +--R +--R 2 5 4 2 2 3 2 +--R ((2a c - 2b )e + 6b c d e - 6c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 +--R ((4a c - 4b )d e + 12b c d e - 12c d e )x + (2a c - 2b )d e +--R + +--R 3 2 2 4 +--R 6b c d e - 6c d e +--R * +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b +--R \|4a c - b atan(------------) +--R 2c x + b +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((6a b c - 2b )d e + (- 12a c + 6b c)d e - 6b c d e + 4c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (3a b c - b )d e + (- 6a c + 3b c)d e - 3b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 12a b c + 4b )d e + (24a c - 12b c)d e + 12b c d e +--R + +--R 3 4 +--R - 8c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 6a b c + 2b )d e + (12a c - 6b c)d e + 6b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 2 2 5 3 4 2 2 3 2 3 2 3 4 +--R ((- 4a c + 2a b )e - 2b d e + 6b c d e - 8b c d e + 4c d e)x +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (- 2a c + 4a b )d e + (- 6a b c - 3b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (4a c + 10b c)d e - 13b c d e + 6c d +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 310 + +--S 311 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((a c - b )e + 3b c d e - 3c d e)\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((2a c - 2b )e + 6b c d e - 6c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R Type: Expression(Integer) +--E 311 + +--S 312 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((a c - b )e + 3b c d e - 3c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 3 2 2 2 | 2 \|4a c - b +--R ((a c - b )e + 3b c d e - 3c d e)\|4a c - b atan(------------) +--R 2c x + b +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R Type: Expression(Integer) +--E 313 + +--S 314 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 314 + +)clear all + +--S 315 of 845 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 315 + +--S 316 of 845 +r0:=4*e^3*(3*c*d-b*e)*x/c^2+2*e^4*x^2/c-(d+e*x)^4/(a+b*x+c*x^2)+_ + 2*e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(a+b*x+c*x^2)/c^3-_ + 4*e*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 3 2 2 +--R (- 12a b c + 4b c)e + (24a c - 12b c )d e + 12b c d e +--R + +--R 4 3 +--R - 8c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 3 3 2 2 2 2 +--R (- 12a b c + 4b )e + (24a b c - 12b c)d e + 12b c d e +--R + +--R 3 3 +--R - 8b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (- 12a b c + 4a b )e + (24a c - 12a b c)d e + 12a b c d e +--R + +--R 3 3 +--R - 8a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 2a c + 2b c)e - 6b c d e + 6c d e )x +--R + +--R 3 4 2 3 2 2 2 +--R ((- 2a b c + 2b )e - 6b c d e + 6b c d e )x +--R + +--R 2 2 4 3 2 2 2 +--R (- 2a c + 2a b )e - 6a b c d e + 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 4 4 2 4 3 3 3 +--R c e x + (- 2b c e + 8c d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((2a c - 4b c)e + 12b c d e - 6c d e )x +--R + +--R 4 2 3 3 3 3 4 +--R (- 4a b c e + 12a c d e - 4c d e)x - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 3 | 2 +--R (c x + b c x + a c )\|- 4a c + b +--R Type: Expression(Integer) +--E 316 + +--S 317 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 4 3 2 2 3 3 2 2 +--R (6a b c - 2b c)e + (- 12a c + 6b c )d e - 6b c d e +--R + +--R 4 3 +--R 4c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 3 3 2 2 2 2 +--R (6a b c - 2b )e + (- 12a b c + 6b c)d e - 6b c d e +--R + +--R 3 3 +--R 4b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 3 3 +--R (6a b c - 2a b )e + (- 12a c + 6a b c)d e - 6a b c d e + 4a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 2a c + 2b c)e - 6b c d e + 6c d e )x +--R + +--R 3 4 2 3 2 2 2 +--R ((- 2a b c + 2b )e - 6b c d e + 6b c d e )x +--R + +--R 2 2 4 3 2 2 2 +--R (- 2a c + 2a b )e - 6a b c d e + 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 4 4 2 4 3 3 3 2 2 4 2 3 2 +--R c e x + (- 2b c e + 8c d e )x + ((a c - 3b c)e + 8b c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 5a b c + b )e + (12a c - 4b c)d e + 6b c d e - 4c d e)x +--R + +--R 2 2 4 3 2 2 2 3 4 +--R (- a c + a b )e - 4a b c d e + 6a c d e - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 3 | 2 +--R (c x + b c x + a c )\|- 4a c + b +--R , +--R +--R 2 3 4 3 2 2 3 3 2 2 +--R (12a b c - 4b c)e + (- 24a c + 12b c )d e - 12b c d e +--R + +--R 4 3 +--R 8c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 3 3 2 2 2 2 +--R (12a b c - 4b )e + (- 24a b c + 12b c)d e - 12b c d e +--R + +--R 3 3 +--R 8b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (12a b c - 4a b )e + (- 24a c + 12a b c)d e - 12a b c d e +--R + +--R 3 3 +--R 8a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 2a c + 2b c)e - 6b c d e + 6c d e )x +--R + +--R 3 4 2 3 2 2 2 +--R ((- 2a b c + 2b )e - 6b c d e + 6b c d e )x +--R + +--R 2 2 4 3 2 2 2 +--R (- 2a c + 2a b )e - 6a b c d e + 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 4 4 2 4 3 3 3 2 2 4 2 3 2 +--R c e x + (- 2b c e + 8c d e )x + ((a c - 3b c)e + 8b c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 5a b c + b )e + (12a c - 4b c)d e + 6b c d e - 4c d e)x +--R + +--R 2 2 4 3 2 2 2 3 4 +--R (- a c + a b )e - 4a b c d e + 6a c d e - c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 4 2 3 3 | 2 +--R (c x + b c x + a c )\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 317 + +--S 318 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((12a b c - 4b )e + (- 24a c + 12b c)d e - 12b c d e + 8c d e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((- a c + b )e - 4b c d e + 6c d e )\|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R c \|- 4a c + b +--R Type: Expression(Integer) +--E 318 + +--S 319 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((12a b c - 4b )e + (- 24a c + 12b c)d e - 12b c d e + 8c d e) +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((12a b c - 4b )e + (- 24a c + 12b c)d e - 12b c d e + 8c d e) +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +-----------+ +---------+ +--R 2 4 3 2 2 2 | 2 | 2 +--R ((- a c + b )e - 4b c d e + 6c d e )\|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 320 + +--S 321 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 322 + +--S 323 of 845 +r0:=3*e^3*x/c-(d+e*x)^3/(a+b*x+c*x^2)+3/2*e^2*(2*c*d-b*e)*_ + log(a+b*x+c*x^2)/c^2-3*e*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 2 3 2 2 +--R ((12a c - 6b c)e + 12b c d e - 12c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((12a b c - 6b )e + 12b c d e - 12b c d e)x + (12a c - 6a b )e +--R + +--R 2 2 2 +--R 12a b c d e - 12a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- 3b c e + 6c d e )x + (- 3b e + 6b c d e )x - 3a b e +--R + +--R 2 +--R 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 3 2 2 2 3 2 2 2 3 +--R 4c e x + (6b c e - 6c d e )x + (6a c e - 6c d e)x - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 | 2 +--R (2c x + 2b c x + 2a c )\|- 4a c + b +--R Type: Expression(Integer) +--E 323 + +--S 324 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 3 2 2 +--R ((6a c - 3b c)e + 6b c d e - 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((6a b c - 3b )e + 6b c d e - 6b c d e)x + (6a c - 3a b )e +--R + +--R 2 2 2 +--R 6a b c d e - 6a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2 2 3 2 3 +--R (- 3b c e + 6c d e )x + (- 3b e + 6b c d e )x - 3a b e +--R + +--R 2 +--R 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 3 2 2 3 2 2 2 +--R 4c e x + 4b c e x + ((6a c - 2b )e + 6b c d e - 6c d e)x +--R + +--R 3 2 2 3 +--R - 2a b e + 6a c d e - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 | 2 +--R (2c x + 2b c x + 2a c )\|- 4a c + b +--R , +--R +--R 2 2 3 2 2 3 2 2 +--R ((- 12a c + 6b c)e - 12b c d e + 12c d e)x +--R + +--R 3 3 2 2 2 2 +--R ((- 12a b c + 6b )e - 12b c d e + 12b c d e)x +--R + +--R 2 2 3 2 2 2 +--R (- 12a c + 6a b )e - 12a b c d e + 12a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- 3b c e + 6c d e )x + (- 3b e + 6b c d e )x - 3a b e +--R + +--R 2 +--R 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 3 2 2 3 2 2 2 +--R 4c e x + 4b c e x + ((6a c - 2b )e + 6b c d e - 6c d e)x +--R + +--R 3 2 2 3 +--R - 2a b e + 6a c d e - 2c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 3 2 2 2 | 2 +--R (2c x + 2b c x + 2a c )\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 324 + +--S 325 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 +--R ((6a c - 3b )e + 6b c d e - 6c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 2c x + b +--R ((- 12a c + 6b )e - 12b c d e + 12c d e)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 2 | 2 +--R (- 2b e + 6c d e )\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 325 + +--S 326 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((- 6a c + 3b )e - 6b c d e + 6c d e)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((- 6a c + 3b )e - 6b c d e + 6c d e)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +-----------+ +---------+ +--R 3 2 | 2 | 2 +--R (- b e + 3c d e )\|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 327 + +--S 328 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 328 + +)clear all + +--S 329 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 329 + +--S 330 of 845 +r0:=-(d+e*x)^2/(a+b*x+c*x^2)+e^2*log(a+b*x+c*x^2)/c-2*e*(2*c*d-b*e)*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R ((2b c e - 4c d e)x + (2b e - 4b c d e)x + 2a b e - 4a c d e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 2 2 +--R ((c e x + b e x + a e )log(c x + b x + a) - c e x - 2c d e x - c d ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (c x + b c x + a c)\|- 4a c + b +--R Type: Expression(Integer) +--E 330 + +--S 331 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R ((b c e - 2c d e)x + (b e - 2b c d e)x + a b e - 2a c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 2 +--R (c e x + b e x + a e )log(c x + b x + a) + (b e - 2c d e)x +--R + +--R 2 2 +--R a e - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (c x + b c x + a c)\|- 4a c + b +--R , +--R +--R 2 2 2 2 2 2 +--R ((- 2b c e + 4c d e)x + (- 2b e + 4b c d e)x - 2a b e + 4a c d e) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 2 2 2 +--R (c e x + b e x + a e )log(c x + b x + a) + (b e - 2c d e)x +--R + +--R 2 2 +--R a e - c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 2 2 | 2 +--R (c x + b c x + a c)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 331 + +--S 332 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +--R (b e - 2c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 2c x + b 2 | 2 +--R (- 2b e + 4c d e)atanh(--------------) + e \|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R c\|- 4a c + b +--R Type: Expression(Integer) +--E 332 + +--S 333 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 333 + +--S 334 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 2 | 2 2c x + b +--R (- 2b e + 4c d e)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (- 2b e + 4c d e)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R e \|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R c\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 334 + +--S 335 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 845 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 845 +r0:=(-d-e*x)/(a+b*x+c*x^2)-2*e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c) +--R +--R +--R (2) +--R +-----------+ +--R 2 2c x + b | 2 +--R (- 2c e x - 2b e x - 2a e)atanh(--------------) + (- e x - d)\|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R ---------------------------------------------------------------------------- +--R +-----------+ +--R 2 | 2 +--R (c x + b x + a)\|- 4a c + b +--R Type: Expression(Integer) +--E 337 + +--S 338 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +--R (c e x + b e x + a e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R | 2 +--R (- e x - d)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R (c x + b x + a)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 (2c x + b)\|4a c - b +--R (2c e x + 2b e x + 2a e)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (- e x - d)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R (c x + b x + a)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 338 + +--S 339 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R 2e atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 339 + +--S 340 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +--S 341 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R | 2 2c x + b +--R 2e\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R 2e\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 341 + +--S 342 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 845 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^2 +--R +--R +--R 2c x + b +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 343 + +--S 344 of 845 +r0:=(-1)/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (2) - -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 344 + +--S 345 of 845 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - -------------- +--R 2 +--R c x + b x + a +--R Type: Union(Expression(Integer),...) +--E 345 + +--S 346 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 347 + +)clear all + +--S 348 of 845 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 348 + +--S 349 of 845 +r0:=(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))-e^2*(2*c*d-b*e)*log(d+e*x)/_ + (c*d^2-b*d*e+a*e^2)^2+1/2*e^2*(2*c*d-b*e)*log(a+b*x+c*x^2)/_ + (c*d^2-b*d*e+a*e^2)^2+e*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 2 3 2 2 +--R ((- 4a c + 2b c)e - 4b c d e + 4c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 4a b c + 2b )e - 4b c d e + 4b c d e)x + (- 4a c + 2a b )e +--R + +--R 2 2 2 +--R - 4a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- b c e + 2c d e )x + (- b e + 2b c d e )x - a b e +--R + +--R 2 +--R 2a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 2 3 2 3 +--R (2b c e - 4c d e )x + (2b e - 4b c d e )x + 2a b e +--R + +--R 2 +--R - 4a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 +--R (2a c e - 2b c d e + 2c d e)x + 2a b e + (- 2a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (2a c e - 4a b c d e + (4a c + 2b c)d e - 4b c d e + 2c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 +--R (2a b e - 4a b d e + (4a b c + 2b )d e - 4b c d e + 2b c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R 2a e - 4a b d e + (4a c + 2a b )d e - 4a b c d e + 2a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 349 + +--S 350 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 3 2 2 +--R ((2a c - b c)e + 2b c d e - 2c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((2a b c - b )e + 2b c d e - 2b c d e)x + (2a c - a b )e +--R + +--R 2 2 2 +--R 2a b c d e - 2a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2 2 3 2 3 +--R (- b c e + 2c d e )x + (- b e + 2b c d e )x - a b e +--R + +--R 2 +--R 2a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 2 3 2 3 +--R (2b c e - 4c d e )x + (2b e - 4b c d e )x + 2a b e +--R + +--R 2 +--R - 4a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 +--R (2a c e - 2b c d e + 2c d e)x + 2a b e + (- 2a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (2a c e - 4a b c d e + (4a c + 2b c)d e - 4b c d e + 2c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 +--R (2a b e - 4a b d e + (4a b c + 2b )d e - 4b c d e + 2b c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R 2a e - 4a b d e + (4a c + 2a b )d e - 4a b c d e + 2a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 2 3 2 2 3 2 2 +--R ((4a c - 2b c)e + 4b c d e - 4c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((4a b c - 2b )e + 4b c d e - 4b c d e)x + (4a c - 2a b )e +--R + +--R 2 2 2 +--R 4a b c d e - 4a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- b c e + 2c d e )x + (- b e + 2b c d e )x - a b e +--R + +--R 2 +--R 2a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 2 3 2 3 +--R (2b c e - 4c d e )x + (2b e - 4b c d e )x + 2a b e +--R + +--R 2 +--R - 4a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 +--R (2a c e - 2b c d e + 2c d e)x + 2a b e + (- 2a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 2c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (2a c e - 4a b c d e + (4a c + 2b c)d e - 4b c d e + 2c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 +--R (2a b e - 4a b d e + (4a b c + 2b )d e - 4b c d e + 2b c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R 2a e - 4a b d e + (4a c + 2a b )d e - 4a b c d e + 2a c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 350 + +--S 351 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 +--R ((2a c - b )e + 2b c d e - 2c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 2c x + b +--R ((4a c - 2b )e + 4b c d e - 4c d e)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 351 + +--S 352 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 2 3 2 2 2 | 2 2c x + b +--R ((2a c - b )e + 2b c d e - 2c d e)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((2a c - b )e + 2b c d e - 2c d e)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (a e - 2a b d e + (2a c + b )d e - 2b c d e + c d )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression(Integer) +--E 353 + +--S 354 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 845 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + ((2a c + b )e + 4b c d e + c d )x +--R + +--R 2 2 2 3 +--R (2a b e + (4a c + 2b )d e + 2b c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (a e + 4a b d e + (2a c + b )d )x + (2a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 355 + +--S 356 of 845 +r0:=2*e^2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))+(-(b^2-4*a*c)*_ + (c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*_ + (a+b*x+c*x^2))-2*e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(d+e*x)/_ + (c*d^2-b*d*e+a*e^2)^3+e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*_ + log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3+2*e*(2*c*d-b*e)*(c^2*d^2+_ + b^2*e^2-c*e*(b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + ((c*d^2-b*d*e+a*e^2)^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 5 3 2 2 4 3 2 3 4 3 2 3 +--R ((6a b c - 2b c)e + (- 12a c + 6b c )d e - 6b c d e + 4c d e )x +--R + +--R 2 4 5 2 3 4 3 2 3 +--R (6a b c - 2b )e + (- 6a b c + 4b c)d e - 12a c d e +--R + +--R 3 3 2 4 4 +--R - 2b c d e + 4c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (6a b c - 2a b )e + (- 12a c + 12a b c - 2b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 +--R (- 18a b c + 6b c)d e + (4a c - 6b c )d e + 4b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 2 3 2 3 2 3 4 +--R (6a b c - 2a b )d e + (- 12a c + 6a b c)d e - 6a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((- a c + b c)e - 3b c d e + 3c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((- a b c + b )e + (- a c - 2b c)d e + 3c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- a c + a b )e + (- 4a b c + b )d e + (3a c - 3b c)d e +--R + +--R 2 3 2 +--R 3b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (- a c + a b )d e - 3a b c d e + 3a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((2a c - 2b c)e + 6b c d e - 6c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((2a b c - 2b )e + (2a c + 4b c)d e - 6c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (2a c - 2a b )e + (8a b c - 2b )d e + (- 6a c + 6b c)d e +--R + +--R 2 3 2 +--R - 6b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (2a c - 2a b )d e + 6a b c d e - 6a c d e +--R * +--R log(e x + d) +--R + +--R 5 2 2 4 2 2 3 3 3 2 2 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (a c - 2a b )e + (2a b c + 2b )d e + (2a c - 5b c)d e +--R + +--R 2 3 2 3 4 +--R 2b c d e + c d e +--R * +--R x +--R + +--R 2 5 2 4 3 2 3 2 2 3 2 +--R - a b e + 3a c d e + (- 2a b c + b )d e + (2a c - 3b c)d e +--R + +--R 2 4 3 5 +--R 3b c d e - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 7 2 6 2 2 2 2 5 2 3 3 4 +--R a c e - 3a b c d e + (3a c + 3a b c)d e + (- 6a b c - b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (3a c + 3b c )d e - 3b c d e + c d e +--R * +--R 3 +--R x +--R + +--R 3 7 3 2 2 6 3 2 5 2 2 2 4 3 4 +--R a b e + (a c - 3a b )d e + 3a b d e + (3a c - 3a b c - b )d e +--R + +--R 2 3 4 3 3 5 2 3 6 4 7 +--R (- 3a b c + 2b c)d e + 3a c d e - 2b c d e + c d +--R * +--R 2 +--R x +--R + +--R 4 7 3 6 3 2 5 2 3 3 4 +--R a e - 2a b d e + 3a c d e + (- 3a b c + 2a b )d e +--R + +--R 2 2 2 4 4 3 3 5 2 3 2 2 6 3 7 +--R (3a c - 3a b c - b )d e + 3b c d e + (a c - 3b c )d e + b c d +--R * +--R x +--R + +--R 4 6 3 2 5 3 2 2 3 4 2 3 4 3 +--R a d e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - a b )d e +--R + +--R 2 2 2 5 2 2 6 3 7 +--R (3a c + 3a b c)d e - 3a b c d e + a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 356 + +--S 357 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 5 3 2 2 4 3 2 3 4 3 2 3 +--R ((3a b c - b c)e + (- 6a c + 3b c )d e - 3b c d e + 2c d e )x +--R + +--R 2 4 5 2 3 4 3 2 3 3 3 2 +--R (3a b c - b )e + (- 3a b c + 2b c)d e - 6a c d e - b c d e +--R + +--R 4 4 +--R 2c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (3a b c - a b )e + (- 6a c + 6a b c - b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 +--R (- 9a b c + 3b c)d e + (2a c - 3b c )d e + 2b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 2 3 2 3 2 3 4 +--R (3a b c - a b )d e + (- 6a c + 3a b c)d e - 3a b c d e + 2a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((- a c + b c)e - 3b c d e + 3c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((- a b c + b )e + (- a c - 2b c)d e + 3c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- a c + a b )e + (- 4a b c + b )d e + (3a c - 3b c)d e +--R + +--R 2 3 2 +--R 3b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (- a c + a b )d e - 3a b c d e + 3a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((2a c - 2b c)e + 6b c d e - 6c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((2a b c - 2b )e + (2a c + 4b c)d e - 6c d e )x +--R + +--R 2 2 5 3 4 +--R (2a c - 2a b )e + (8a b c - 2b )d e +--R + +--R 2 2 2 3 2 3 2 +--R (- 6a c + 6b c)d e - 6b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (2a c - 2a b )d e + 6a b c d e - 6a c d e +--R * +--R log(e x + d) +--R + +--R 5 2 2 4 2 2 3 3 3 2 2 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (a c - 2a b )e + (2a b c + 2b )d e + (2a c - 5b c)d e +--R + +--R 2 3 2 3 4 +--R 2b c d e + c d e +--R * +--R x +--R + +--R 2 5 2 4 3 2 3 2 2 3 2 +--R - a b e + 3a c d e + (- 2a b c + b )d e + (2a c - 3b c)d e +--R + +--R 2 4 3 5 +--R 3b c d e - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 7 2 6 2 2 2 2 5 +--R a c e - 3a b c d e + (3a c + 3a b c)d e +--R + +--R 2 3 3 4 3 2 2 4 3 3 5 2 4 6 +--R (- 6a b c - b c)d e + (3a c + 3b c )d e - 3b c d e + c d e +--R * +--R 3 +--R x +--R + +--R 3 7 3 2 2 6 3 2 5 +--R a b e + (a c - 3a b )d e + 3a b d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 3 5 2 +--R (3a c - 3a b c - b )d e + (- 3a b c + 2b c)d e + 3a c d e +--R + +--R 3 6 4 7 +--R - 2b c d e + c d +--R * +--R 2 +--R x +--R + +--R 4 7 3 6 3 2 5 2 3 3 4 +--R a e - 2a b d e + 3a c d e + (- 3a b c + 2a b )d e +--R + +--R 2 2 2 4 4 3 3 5 2 3 2 2 6 3 7 +--R (3a c - 3a b c - b )d e + 3b c d e + (a c - 3b c )d e + b c d +--R * +--R x +--R + +--R 4 6 3 2 5 3 2 2 3 4 2 3 4 3 +--R a d e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - a b )d e +--R + +--R 2 2 2 5 2 2 6 3 7 +--R (3a c + 3a b c)d e - 3a b c d e + a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 3 5 3 2 2 4 3 2 3 +--R (- 6a b c + 2b c)e + (12a c - 6b c )d e + 6b c d e +--R + +--R 4 3 2 +--R - 4c d e +--R * +--R 3 +--R x +--R + +--R 2 4 5 2 3 4 3 2 3 +--R (- 6a b c + 2b )e + (6a b c - 4b c)d e + 12a c d e +--R + +--R 3 3 2 4 4 +--R 2b c d e - 4c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (- 6a b c + 2a b )e + (12a c - 12a b c + 2b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 +--R (18a b c - 6b c)d e + (- 4a c + 6b c )d e - 4b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 2 3 2 3 2 +--R (- 6a b c + 2a b )d e + (12a c - 6a b c)d e + 6a b c d e +--R + +--R 3 4 +--R - 4a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((- a c + b c)e - 3b c d e + 3c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((- a b c + b )e + (- a c - 2b c)d e + 3c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- a c + a b )e + (- 4a b c + b )d e + (3a c - 3b c)d e +--R + +--R 2 3 2 +--R 3b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (- a c + a b )d e - 3a b c d e + 3a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((2a c - 2b c)e + 6b c d e - 6c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((2a b c - 2b )e + (2a c + 4b c)d e - 6c d e )x +--R + +--R 2 2 5 3 4 +--R (2a c - 2a b )e + (8a b c - 2b )d e +--R + +--R 2 2 2 3 2 3 2 +--R (- 6a c + 6b c)d e - 6b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (2a c - 2a b )d e + 6a b c d e - 6a c d e +--R * +--R log(e x + d) +--R + +--R 5 2 2 4 2 2 3 3 3 2 2 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (a c - 2a b )e + (2a b c + 2b )d e + (2a c - 5b c)d e +--R + +--R 2 3 2 3 4 +--R 2b c d e + c d e +--R * +--R x +--R + +--R 2 5 2 4 3 2 3 2 2 3 2 +--R - a b e + 3a c d e + (- 2a b c + b )d e + (2a c - 3b c)d e +--R + +--R 2 4 3 5 +--R 3b c d e - c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 3 7 2 6 2 2 2 2 5 +--R a c e - 3a b c d e + (3a c + 3a b c)d e +--R + +--R 2 3 3 4 3 2 2 4 3 3 5 2 4 6 +--R (- 6a b c - b c)d e + (3a c + 3b c )d e - 3b c d e + c d e +--R * +--R 3 +--R x +--R + +--R 3 7 3 2 2 6 3 2 5 +--R a b e + (a c - 3a b )d e + 3a b d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 3 5 2 +--R (3a c - 3a b c - b )d e + (- 3a b c + 2b c)d e + 3a c d e +--R + +--R 3 6 4 7 +--R - 2b c d e + c d +--R * +--R 2 +--R x +--R + +--R 4 7 3 6 3 2 5 2 3 3 4 +--R a e - 2a b d e + 3a c d e + (- 3a b c + 2a b )d e +--R + +--R 2 2 2 4 4 3 3 5 2 3 2 2 6 3 7 +--R (3a c - 3a b c - b )d e + 3b c d e + (a c - 3b c )d e + b c d +--R * +--R x +--R + +--R 4 6 3 2 5 3 2 2 3 4 2 3 4 3 +--R a d e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - a b )d e +--R + +--R 2 2 2 5 2 2 6 3 7 +--R (3a c + 3a b c)d e - 3a b c d e + a c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 357 + +--S 358 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 358 + +--S 359 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e) +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e) +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 360 + +--S 361 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 361 + +)clear all + +--S 362 of 845 +t0:=(b+2*c*x)*(d+e*x)^5/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R 2c e x + (b e + 10c d e )x + (5b d e + 20c d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10b d e + 20c d e )x + (10b d e + 10c d e)x + (5b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 362 + +--S 363 of 845 +r0:=5*e^3*(3*c^2*d^2+b^2*e^2-c*e*(2*b*d+3*a*e))*x/(c^2*(b^2-4*a*c))+_ + 5/2*e^4*(2*c*d-b*e)*x^2/(c*(b^2-4*a*c))-1/2*(d+e*x)^5/(a+b*x+c*x^2)^2-_ + 5/2*e*(d+e*x)^3*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+_ + 5*e*(2*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(b*d-3*a*e)-6*a*c^2*e^3*(2*b*d+a*e)+_ + 2*b^2*c*e^3*(b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*(b^2-_ + 4*a*c)^(3/2))+5/2*e^4*(2*c*d-b*e)*log(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (60a c - 60a b c + 10b c )e + (120a b c - 20b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R - 120a c d e + 40b c d e - 20c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (120a b c - 120a b c + 20b c)e + (240a b c - 40b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R - 240a b c d e + 80b c d e - 40b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (120a c - 60a b c - 40a b c + 10b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (240a b c + 80a b c - 20b c)d e + (- 240a c - 120a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (80a b c + 40b c )d e + (- 40a c - 20b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (120a b c - 120a b c + 20a b )e + (240a b c - 40a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R - 240a b c d e + 80a b c d e - 40a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (60a c - 60a b c + 10a b )e + (120a b c - 20a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R - 120a c d e + 40a b c d e - 20a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 20a b c + 5b c )e + (40a c - 10b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 40a b c + 10b c)e + (80a b c - 20b c )d e )x +--R + +--R 2 2 3 5 5 +--R (- 40a b c - 10a b c + 5b )e +--R + +--R 2 3 2 2 4 4 +--R (80a c + 20a b c - 10b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 40a b c + 10a b )e + (80a b c - 20a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 20a b c + 5a b )e + (40a c - 10a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 2 3 5 5 +--R (16a c - 4b c )e x +--R + +--R 3 3 2 5 4 2 3 4 4 2 3 +--R (55a b c - 15b c )e + (- 60a c + 25b c )d e - 30b c d e +--R + +--R 5 3 2 +--R 30c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (50a c + 20a b c - 10b c)e + (- 20a b c + 20b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (- 100a c - 20b c )d e + 40b c d e + 10c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 3 2 3 +--R (65a b c - 20a b c)e + (- 40a c + 40a b c )d e - 90a b c d e +--R + +--R 4 2 3 3 2 4 4 +--R (- 20a c + 20b c )d e + 15b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 5 2 2 4 2 3 2 3 +--R (30a c - 10a b c)e + 20a b c d e - 60a c d e +--R + +--R 4 2 3 4 +--R (- 10a c + 10b c )d e +--R * +--R x +--R + +--R 2 3 3 2 3 4 4 2 3 5 +--R - 10a c d e + 5a b c d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 6 2 5 4 5 3 4 3 2 5 2 4 4 3 2 +--R (8a c - 2b c )x + (16a b c - 4b c )x + (16a c + 4a b c - 2b c )x +--R + +--R 2 4 3 3 3 4 2 2 3 +--R (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 363 + +--S 364 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (30a c - 30a b c + 5b c )e + (60a b c - 10b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R - 60a c d e + 20b c d e - 10c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (60a b c - 60a b c + 10b c)e + (120a b c - 20b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R - 120a b c d e + 40b c d e - 20b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (60a c - 30a b c - 20a b c + 5b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (120a b c + 40a b c - 10b c)d e + (- 120a c - 60a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (40a b c + 20b c )d e + (- 20a c - 10b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (60a b c - 60a b c + 10a b )e + (120a b c - 20a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R - 120a b c d e + 40a b c d e - 20a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (30a c - 30a b c + 5a b )e + (60a b c - 10a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R - 60a c d e + 20a b c d e - 10a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 20a b c + 5b c )e + (40a c - 10b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 40a b c + 10b c)e + (80a b c - 20b c )d e )x +--R + +--R 2 2 3 5 5 +--R (- 40a b c - 10a b c + 5b )e +--R + +--R 2 3 2 2 4 4 +--R (80a c + 20a b c - 10b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 40a b c + 10a b )e + (80a b c - 20a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 20a b c + 5a b )e + (40a c - 10a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 2 3 5 5 3 3 2 5 4 +--R (16a c - 4b c )e x + (32a b c - 8b c )e x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (50a c - 26a b c + 4b c)e + (100a b c - 30b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (- 100a c + 40b c )d e - 20b c d e + 10c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (19a b c - 29a b c + 7b )e + (80a c + 50a b c - 25b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (- 30a b c + 30b c )d e + (- 80a c - 10b c )d e + 15b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 3 4 +--R (30a c - 56a b c + 14a b )e + (140a b c - 50a b c)d e +--R + +--R 2 3 2 2 2 3 3 3 2 4 2 3 4 +--R (- 60a c + 60a b c )d e - 60a b c d e + (- 10a c + 10b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 2 2 2 3 +--R (- 23a b c + 7a b )e + (60a c - 25a b c)d e + 30a b c d e +--R + +--R 2 3 3 2 3 4 4 2 3 5 +--R - 40a c d e + 5a b c d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 6 2 5 4 5 3 4 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 5 2 4 4 3 2 2 4 3 3 3 4 2 2 3 +--R (16a c + 4a b c - 2b c )x + (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (- 60a c + 60a b c - 10b c )e + (- 120a b c + 20b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R 120a c d e - 40b c d e + 20c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 +--R (- 120a b c + 120a b c - 20b c)e +--R + +--R 2 3 4 2 4 4 2 3 2 4 3 2 +--R (- 240a b c + 40b c )d e + 240a b c d e - 80b c d e +--R + +--R 5 4 +--R 40b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 120a c + 60a b c + 40a b c - 10b )e +--R + +--R 2 3 3 2 5 4 +--R (- 240a b c - 80a b c + 20b c)d e +--R + +--R 2 4 2 3 2 3 4 3 3 3 2 +--R (240a c + 120a b c )d e + (- 80a b c - 40b c )d e +--R + +--R 5 2 4 4 +--R (40a c + 20b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 +--R (- 120a b c + 120a b c - 20a b )e +--R + +--R 2 2 2 4 4 2 3 2 3 2 3 3 2 +--R (- 240a b c + 40a b c)d e + 240a b c d e - 80a b c d e +--R + +--R 4 4 +--R 40a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (- 60a c + 60a b c - 10a b )e + (- 120a b c + 20a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R 120a c d e - 40a b c d e + 20a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 20a b c + 5b c )e + (40a c - 10b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 40a b c + 10b c)e + (80a b c - 20b c )d e )x +--R + +--R 2 2 3 5 5 +--R (- 40a b c - 10a b c + 5b )e +--R + +--R 2 3 2 2 4 4 +--R (80a c + 20a b c - 10b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 40a b c + 10a b )e + (80a b c - 20a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 20a b c + 5a b )e + (40a c - 10a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 2 3 5 5 3 3 2 5 4 +--R (16a c - 4b c )e x + (32a b c - 8b c )e x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (50a c - 26a b c + 4b c)e + (100a b c - 30b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (- 100a c + 40b c )d e - 20b c d e + 10c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (19a b c - 29a b c + 7b )e + (80a c + 50a b c - 25b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (- 30a b c + 30b c )d e + (- 80a c - 10b c )d e + 15b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 3 4 +--R (30a c - 56a b c + 14a b )e + (140a b c - 50a b c)d e +--R + +--R 2 3 2 2 2 3 3 3 2 4 2 3 4 +--R (- 60a c + 60a b c )d e - 60a b c d e + (- 10a c + 10b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 2 2 2 3 +--R (- 23a b c + 7a b )e + (60a c - 25a b c)d e + 30a b c d e +--R + +--R 2 3 3 2 3 4 4 2 3 5 +--R - 40a c d e + 5a b c d e + (- 4a c + b c )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 6 2 5 4 5 3 4 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 5 2 4 4 3 2 2 4 3 3 3 4 2 2 3 +--R (16a c + 4a b c - 2b c )x + (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 364 + +--S 365 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 4 5 2 3 4 3 2 3 +--R (30a c - 30a b c + 5b )e + (60a b c - 10b c)d e - 60a c d e +--R + +--R 3 3 2 4 4 +--R 20b c d e - 10c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 4 5 2 3 4 +--R (- 60a c + 60a b c - 10b )e + (- 120a b c + 20b c)d e +--R + +--R 3 2 3 3 3 2 4 4 +--R 120a c d e - 40b c d e + 20c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 +--R ((- 23a b c + 7b )e + (60a c - 25b c)d e + 30b c d e - 30c d e ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 | 2 +--R (8a c - 2b c )\|- 4a c + b +--R Type: Expression(Integer) +--E 365 + +--S 366 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 4 5 2 3 4 +--R (- 60a c + 60a b c - 10b )e + (- 120a b c + 20b c)d e +--R + +--R 3 2 3 3 3 2 4 4 +--R 120a c d e - 40b c d e + 20c d e +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 4 5 2 3 4 +--R (- 60a c + 60a b c - 10b )e + (- 120a b c + 20b c)d e +--R + +--R 3 2 3 3 3 2 4 4 +--R 120a c d e - 40b c d e + 20c d e +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 +--R ((- 23a b c + 7b )e + (60a c - 25b c)d e + 30b c d e - 30c d e ) +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R 4 2 3 | 2 | 2 +--R (8a c - 2b c )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 367 + +--S 368 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 368 + +)clear all + +--S 369 of 845 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 369 + +--S 370 of 845 +r0:=2*e^3*(2*c*d-b*e)*x/(c*(b^2-4*a*c))-1/2*(d+e*x)^4/(a+b*x+c*x^2)^2-_ + 2*e*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+_ + 2*e*(2*c*d-b*e)*(2*c^2*d^2-b^2*e^2-2*c*e*(b*d-3*a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(c^2*(b^2-4*a*c)^(3/2))+e^4*log(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 3 3 2 4 4 3 4 2 2 5 3 4 +--R ((24a b c - 4b c )e - 48a c d e + 24b c d e - 16c d e)x +--R + +--R 2 2 4 4 3 3 2 3 2 2 4 3 3 +--R ((48a b c - 8b c)e - 96a b c d e + 48b c d e - 32b c d e)x +--R + +--R 2 2 3 5 4 2 3 2 2 3 +--R (48a b c + 16a b c - 4b )e + (- 96a c - 48a b c )d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (48a b c + 24b c )d e + (- 32a c - 16b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 2 2 2 2 3 3 +--R ((48a b c - 8a b )e - 96a b c d e + 48a b c d e - 32a b c d e)x +--R + +--R 3 2 3 4 3 2 3 2 2 2 2 2 3 3 +--R (24a b c - 4a b )e - 48a c d e + 24a b c d e - 16a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 4 4 2 3 4 3 +--R (8a c - 2b c )e x + (16a b c - 4b c)e x +--R + +--R 2 2 2 4 4 2 2 3 4 +--R (16a c + 4a b c - 2b )e x + (16a b c - 4a b )e x +--R + +--R 3 2 2 4 +--R (8a c - 2a b )e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 12a c + 5b c )e - 12b c d e + 16c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (- 4a b c + 4b c)e + (- 40a c - 8b c )d e + 20b c d e +--R + +--R 4 3 +--R 8c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 2 3 3 2 2 2 2 +--R (- 8a c + 8a b c)e - 36a b c d e + (- 16a c + 10b c )d e +--R + +--R 3 3 +--R 12b c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 2 2 3 2 2 3 +--R (4a b c e - 24a c d e - 4a b c d e + (- 8a c + 8b c )d e)x +--R + +--R 2 2 2 2 2 3 3 2 2 4 +--R - 8a c d e + 4a b c d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 4 4 3 3 3 2 4 2 3 4 2 2 +--R (8a c - 2b c )x + (16a b c - 4b c )x + (16a c + 4a b c - 2b c )x +--R + +--R 2 3 3 2 3 3 2 2 2 +--R (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 370 + +--S 371 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 4 4 3 4 2 2 5 3 4 +--R ((12a b c - 2b c )e - 24a c d e + 12b c d e - 8c d e)x +--R + +--R 2 2 4 4 3 3 2 3 2 2 4 3 3 +--R ((24a b c - 4b c)e - 48a b c d e + 24b c d e - 16b c d e)x +--R + +--R 2 2 3 5 4 2 3 2 2 3 +--R (24a b c + 8a b c - 2b )e + (- 48a c - 24a b c )d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (24a b c + 12b c )d e + (- 16a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 2 2 2 2 3 3 +--R ((24a b c - 4a b )e - 48a b c d e + 24a b c d e - 16a b c d e)x +--R + +--R 3 2 3 4 3 2 3 2 2 2 2 2 3 3 +--R (12a b c - 2a b )e - 24a c d e + 12a b c d e - 8a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 4 4 2 3 4 3 +--R (8a c - 2b c )e x + (16a b c - 4b c)e x +--R + +--R 2 2 2 4 4 2 2 3 4 +--R (16a c + 4a b c - 2b )e x + (16a b c - 4a b )e x +--R + +--R 3 2 2 4 +--R (8a c - 2a b )e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (20a b c - 6b c)e + (- 40a c + 16b c )d e - 12b c d e +--R + +--R 4 3 +--R 8c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 4 2 3 3 +--R (16a c + 10a b c - 5b )e + (- 12a b c + 12b c)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 48a c - 6b c )d e + 12b c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (28a b c - 10a b )e + (- 24a c + 24a b c)d e - 36a b c d e +--R + +--R 3 2 2 3 +--R (- 8a c + 8b c )d e +--R * +--R x +--R + +--R 3 2 2 4 2 3 2 2 2 2 2 3 +--R (12a c - 5a b )e + 12a b c d e - 24a c d e + 4a b c d e +--R + +--R 3 2 2 4 +--R (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 4 4 3 3 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 4 2 3 4 2 2 2 3 3 2 3 3 2 2 2 +--R (16a c + 4a b c - 2b c )x + (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 3 3 2 4 4 3 4 2 2 5 3 4 +--R ((- 24a b c + 4b c )e + 48a c d e - 24b c d e + 16c d e)x +--R + +--R 2 2 4 4 3 3 2 3 2 2 4 3 3 +--R ((- 48a b c + 8b c)e + 96a b c d e - 48b c d e + 32b c d e)x +--R + +--R 2 2 3 5 4 2 3 2 2 3 +--R (- 48a b c - 16a b c + 4b )e + (96a c + 48a b c )d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (- 48a b c - 24b c )d e + (32a c + 16b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 2 2 2 2 +--R (- 48a b c + 8a b )e + 96a b c d e - 48a b c d e +--R + +--R 3 3 +--R 32a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 3 2 2 2 2 2 3 3 +--R (- 24a b c + 4a b )e + 48a c d e - 24a b c d e + 16a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 2 2 4 4 2 3 4 3 +--R (8a c - 2b c )e x + (16a b c - 4b c)e x +--R + +--R 2 2 2 4 4 2 2 3 4 +--R (16a c + 4a b c - 2b )e x + (16a b c - 4a b )e x +--R + +--R 3 2 2 4 +--R (8a c - 2a b )e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (20a b c - 6b c)e + (- 40a c + 16b c )d e - 12b c d e +--R + +--R 4 3 +--R 8c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 4 2 3 3 +--R (16a c + 10a b c - 5b )e + (- 12a b c + 12b c)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 48a c - 6b c )d e + 12b c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (28a b c - 10a b )e + (- 24a c + 24a b c)d e - 36a b c d e +--R + +--R 3 2 2 3 +--R (- 8a c + 8b c )d e +--R * +--R x +--R + +--R 3 2 2 4 2 3 2 2 2 2 2 3 +--R (12a c - 5a b )e + 12a b c d e - 24a c d e + 4a b c d e +--R + +--R 3 2 2 4 +--R (- 4a c + b c )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 5 2 4 4 4 3 3 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 4 2 3 4 2 2 2 3 3 2 3 3 2 2 2 +--R (16a c + 4a b c - 2b c )x + (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 371 + +--S 372 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 2 3 2 2 2 3 3 +--R ((12a b c - 2b )e - 24a c d e + 12b c d e - 8c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 4 2 3 2 2 2 3 3 +--R ((- 24a b c + 4b )e + 48a c d e - 24b c d e + 16c d e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((12a c - 5b )e + 12b c d e - 16c d e )\|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 | 2 +--R (8a c - 2b c )\|- 4a c + b +--R Type: Expression(Integer) +--E 372 + +--S 373 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 3 4 2 3 2 2 2 3 3 | 2 +--R ((- 24a b c + 4b )e + 48a c d e - 24b c d e + 16c d e)\|4a c - b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 4 2 3 2 2 2 3 3 | 2 +--R ((- 24a b c + 4b )e + 48a c d e - 24b c d e + 16c d e)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +-----------+ +---------+ +--R 2 4 3 2 2 2 | 2 | 2 +--R ((12a c - 5b )e + 12b c d e - 16c d e )\|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R 3 2 2 | 2 | 2 +--R (8a c - 2b c )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 374 + +--S 375 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 845 +r0:=-1/2*(d+e*x)^3/(a+b*x+c*x^2)^2-3/2*e*(d+e*x)*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + ((b^2-4*a*c)*(a+b*x+c*x^2))+6*e*(c*d^2-b*d*e+a*e^2)*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 12a c e + 12b c d e - 12c d e)x +--R + +--R 3 2 2 2 2 3 +--R (- 24a b c e + 24b c d e - 24b c d e)x +--R + +--R 2 2 3 3 2 +--R (- 24a c - 12a b )e + (24a b c + 12b )d e +--R + +--R 2 2 2 +--R (- 24a c - 12b c)d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 3 3 2 2 +--R (- 24a b e + 24a b d e - 24a b c d e)x - 12a e + 12a b d e +--R + +--R 2 2 +--R - 12a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 4 2 3 2 2 2 3 +--R (- 3b c e + 6c d e )x + ((- 10a c - 2b )e + 6b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 +--R (- 9a b e + (- 12a c + 3b )d e + 9b c d e)x +--R + +--R 2 3 2 2 2 2 2 2 +--R (- 6a e - 6a b d e + (- 6a c + 6b )d e)x - 6a d e + 3a b d e +--R + +--R 2 3 +--R (- 4a c + b )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 377 + +--S 378 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 4 2 4 +--R (6a c e - 6b c d e + 6c d e)x +--R + +--R 2 3 2 2 2 3 2 3 +--R (12a b c e - 12b c d e + 12b c d e)x +--R + +--R 2 2 2 3 2 3 2 +--R (12a c + 6a b c)e + (- 12a b c - 6b c)d e +--R + +--R 3 2 2 2 +--R (12a c + 6b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 3 2 2 +--R (12a b c e - 12a b c d e + 12a b c d e)x + 6a c e - 6a b c d e +--R + +--R 2 2 2 +--R 6a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 10a c + 4b c)e - 6b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 3a b c + 3b )e + (- 24a c - 3b c)d e + 9b c d e)x +--R + +--R 2 2 3 2 2 2 2 +--R ((- 6a c + 6a b )e - 18a b c d e + (- 6a c + 6b c)d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R 3a b e - 12a c d e + 3a b c d e + (- 4a c + b c)d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 2 3 4 3 3 2 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 3 2 2 4 2 2 2 3 3 2 2 2 +--R (16a c + 4a b c - 2b c)x + (16a b c - 4a b c)x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 3 3 3 2 4 2 4 +--R (12a c e - 12b c d e + 12c d e)x +--R + +--R 2 3 2 2 2 3 2 3 +--R (24a b c e - 24b c d e + 24b c d e)x +--R + +--R 2 2 2 3 2 3 2 +--R (24a c + 12a b c)e + (- 24a b c - 12b c)d e +--R + +--R 3 2 2 2 +--R (24a c + 12b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 3 +--R (24a b c e - 24a b c d e + 24a b c d e)x + 12a c e +--R + +--R 2 2 2 2 2 +--R - 12a b c d e + 12a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 10a c + 4b c)e - 6b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 3a b c + 3b )e + (- 24a c - 3b c)d e + 9b c d e)x +--R + +--R 2 2 3 2 2 2 2 +--R ((- 6a c + 6a b )e - 18a b c d e + (- 6a c + 6b c)d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R 3a b e - 12a c d e + 3a b c d e + (- 4a c + b c)d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 4 2 3 4 3 3 2 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 3 2 2 4 2 2 2 3 3 2 2 2 +--R (16a c + 4a b c - 2b c)x + (16a b c - 4a b c)x + 8a c - 2a b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 378 + +--S 379 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 2 +--R (6a c e - 6b c d e + 6c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2 2c x + b +--R (12a c e - 12b c d e + 12c d e)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 2 | 2 +--R (3b e - 6c d e )\|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (8a c - 2b c)\|- 4a c + b +--R Type: Expression(Integer) +--E 379 + +--S 380 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 3 2 2 2 | 2 2c x + b +--R (12a c e - 12b c d e + 12c d e)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 2 2 2 | 2 +--R (12a c e - 12b c d e + 12c d e)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +-----------+ +---------+ +--R 3 2 | 2 | 2 +--R (3b e - 6c d e )\|- 4a c + b \|4a c - b +--R / +--R +-----------+ +---------+ +--R 2 2 | 2 | 2 +--R (8a c - 2b c)\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 381 + +--S 382 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 382 + +)clear all + +--S 383 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 383 + +--S 384 of 845 +r0:=-1/2*(d+e*x)^2/(a+b*x+c*x^2)^2-e*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*_ + (a+b*x+c*x^2))+2*e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 2 2 3 4 2 2 2 3 +--R (4b c e - 8c d e)x + (8b c e - 16b c d e)x +--R + +--R 3 2 2 2 2 +--R ((8a b c + 4b )e + (- 16a c - 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (8a b e - 16a b c d e)x + 4a b e - 8a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 2 +--R (- 2b c e + 4c d e)x + ((- 8a c - b )e + 6b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 6a b e + (- 4a c + 4b )d e)x - 4a e + 2a b d e + (- 4a c + b )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 384 + +--S 385 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 4 2 2 2 3 +--R (2b c e - 4c d e)x + (4b c e - 8b c d e)x +--R + +--R 3 2 2 2 2 +--R ((4a b c + 2b )e + (- 8a c - 4b c)d e)x +--R + +--R 2 2 2 2 2 +--R (4a b e - 8a b c d e)x + 2a b e - 4a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 2 2 2 +--R (- 2b c e + 4c d e)x + ((- 8a c - b )e + 6b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 6a b e + (- 4a c + 4b )d e)x - 4a e + 2a b d e + (- 4a c + b )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 2 3 4 2 2 2 3 +--R (- 4b c e + 8c d e)x + (- 8b c e + 16b c d e)x +--R + +--R 3 2 2 2 2 +--R ((- 8a b c - 4b )e + (16a c + 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 8a b e + 16a b c d e)x - 4a b e + 8a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 3 2 2 2 +--R (- 2b c e + 4c d e)x + ((- 8a c - b )e + 6b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 6a b e + (- 4a c + 4b )d e)x - 4a e + 2a b d e + (- 4a c + b )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 385 + +--S 386 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +--R (b e - 2c d e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2c x + b +--R (- 2b e + 4c d e)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R (4a c - b )\|- 4a c + b +--R Type: Expression(Integer) +--E 386 + +--S 387 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 2 | 2 2c x + b +--R (- 2b e + 4c d e)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (- 2b e + 4c d e)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R (4a c - b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 388 + +--S 389 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 389 + +)clear all + +--S 390 of 845 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 390 + +--S 391 of 845 +r0:=1/2*(-d-e*x)/(a+b*x+c*x^2)^2-1/2*e*(b+2*c*x)/((b^2-4*a*c)*_ + (a+b*x+c*x^2))+2*c*e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 2 +--R (- 4c e x - 8b c e x + (- 8a c - 4b c)e x - 8a b c e x - 4a c e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 2 +--R (2c e x + 3b c e x + (- 2a c + 2b )e x + a b e + (- 4a c + b )d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 391 + +--S 392 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 3 2 2 2 2 +--R (2c e x + 4b c e x + (4a c + 2b c)e x + 4a b c e x + 2a c e) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 +--R (2c e x + 3b c e x + (- 2a c + 2b )e x + a b e + (- 4a c + b )d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 3 4 2 3 2 2 2 2 +--R (4c e x + 8b c e x + (8a c + 4b c)e x + 8a b c e x + 4a c e) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 3 2 2 2 +--R (2c e x + 3b c e x + (- 2a c + 2b )e x + a b e + (- 4a c + b )d) +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 392 + +--S 393 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R c e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R 2c e atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R (4a c - b )\|- 4a c + b +--R Type: Expression(Integer) +--E 393 + +--S 394 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R | 2 2c x + b +--R 2c e\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R 2c e\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R (4a c - b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 395 + +--S 396 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 of 845 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 397 + +--S 398 of 845 +r0:=(-1/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 1 +--R - +--R 2 +--R (2) - -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 398 + +--S 399 of 845 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------------------------------------- +--R 2 4 3 2 2 2 +--R 2c x + 4b c x + (4a c + 2b )x + 4a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 401 + +)clear all + +--S 402 of 845 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^3) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 7 2 3 6 2 2 2 5 +--R c e x + (3b c e + c d)x + ((3a c + 3b c)e + 3b c d)x +--R + +--R 3 2 2 4 +--R ((6a b c + b )e + (3a c + 3b c)d)x +--R + +--R 2 2 3 3 2 2 2 2 +--R ((3a c + 3a b )e + (6a b c + b )d)x + (3a b e + (3a c + 3a b )d)x +--R + +--R 3 2 3 +--R (a e + 3a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 402 + +--S 403 of 845 +r0:=1/2*(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)-1/2*e*(3*b^2*c*d*e-8*a*c^2*d*e-_ + 2*b^3*e^2-b*c*(c*d^2-7*a*e^2)-2*c*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*(a+b*x+c*x^2))-e*(2*c^4*d^4-b^4*e^4-_ + 4*c^3*d^2*e*(b*d-3*a*e)-6*a*c^2*e^3*(2*b*d+a*e)+2*b^2*c*e^3*_ + (b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((b^2-4*a*c)^(3/2)*_ + (c*d^2-b*d*e+a*e^2)^3)-e^4*(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+_ + 1/2*e^4*(2*c*d-b*e)*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3 +--R +--R +--R (2) +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (- 12a c + 12a b c - 2b c )e + (- 24a b c + 4b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R 24a c d e - 8b c d e + 4c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (- 24a b c + 24a b c - 4b c)e + (- 48a b c + 8b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R 48a b c d e - 16b c d e + 8b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 24a c + 12a b c + 8a b c - 2b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (- 48a b c - 16a b c + 4b c)d e + (48a c + 24a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (- 16a b c - 8b c )d e + (8a c + 4b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (- 24a b c + 24a b c - 4a b )e + (- 48a b c + 8a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R 48a b c d e - 16a b c d e + 8a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (- 12a c + 12a b c - 2a b )e + (- 24a b c + 4a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R 24a c d e - 8a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 4a b c + b c )e + (8a c - 2b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 8a b c + 2b c)e + (16a b c - 4b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((- 8a b c - 2a b c + b )e + (16a c + 4a b c - 2b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 8a b c + 2a b )e + (16a b c - 4a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 4a b c + a b )e + (8a c - 2a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((8a b c - 2b c )e + (- 16a c + 4b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((16a b c - 4b c)e + (- 32a b c + 8b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((16a b c + 4a b c - 2b )e + (- 32a c - 8a b c + 4b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((16a b c - 4a b )e + (- 32a b c + 8a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (8a b c - 2a b )e + (- 16a c + 4a b c)d e +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 5 3 3 2 4 +--R (6a c - 2a b c )e + (- 4a b c + 2b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (4a c - 4b c )d e + 4b c d e - 2c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 4 +--R (13a b c - 4a b c)e + (- 8a c - 8a b c + 4b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (18a b c - 9b c )d e + (- 8a c + 8b c )d e - 3b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 5 4 +--R (10a c + 4a b c - 2a b )e + (- 20a b c + 2b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (12a c + 12a b c - 6b c)d e + (- 12a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (2a c - 2b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (11a b c - 3a b )e + (- 12a c - 11a b c + 4a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (30a b c - 5a b c - b )d e + (- 16a c - 6a b c + 3b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (11a b c - 3b c )d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 3 3 2 2 6 3 3 2 3 2 5 +--R (8a c - 2a b c )e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 4 +--R (24a c + 18a b c - 6a b c )d e +--R + +--R 2 4 3 3 5 2 3 3 +--R (- 48a b c + 4a b c + 2b c )d e +--R + +--R 2 5 2 4 4 3 4 2 5 3 4 5 +--R (24a c + 18a b c - 6b c )d e + (- 24a b c + 6b c )d e +--R + +--R 6 2 5 6 +--R (8a c - 2b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 6 3 2 2 2 4 5 +--R (16a b c - 4a b c)e + (- 48a b c + 12a b c)d e +--R + +--R 3 3 2 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b c)d e +--R + +--R 2 2 3 4 2 6 3 3 +--R (- 96a b c + 8a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 4 2 2 4 4 3 5 +--R (48a b c + 36a b c - 12b c )d e + (- 48a b c + 12b c )d e +--R + +--R 5 3 4 6 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 6 4 2 3 3 2 5 5 +--R (16a c + 4a b c - 2a b )e + (- 48a b c - 12a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 4 +--R (48a c + 60a b c + 6a b c - 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 96a b c - 40a b c + 8a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 4 2 +--R (48a c + 60a b c + 6a b c - 6b c)d e +--R + +--R 2 4 3 3 5 2 5 2 5 2 4 4 3 6 +--R (- 48a b c - 12a b c + 6b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 3 6 4 2 3 4 5 +--R (16a b c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b )d e +--R + +--R 3 2 2 2 4 6 3 3 +--R (- 96a b c + 8a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 2 3 4 2 5 +--R (48a b c + 36a b c - 12a b c)d e + (- 48a b c + 12a b c )d e +--R + +--R 2 4 3 3 6 +--R (16a b c - 4a b c )d +--R * +--R x +--R + +--R 6 5 2 6 5 4 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 5 2 4 2 3 4 2 4 4 2 3 3 2 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2a b )d e +--R + +--R 4 3 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (24a c + 18a b c - 6a b c)d e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 6 +--R (8a c - 2a b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 403 + +--S 404 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (6a c - 6a b c + b c )e + (12a b c - 2b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R - 12a c d e + 4b c d e - 2c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (12a b c - 12a b c + 2b c)e + (24a b c - 4b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R - 24a b c d e + 8b c d e - 4b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (12a c - 6a b c - 4a b c + b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (24a b c + 8a b c - 2b c)d e + (- 24a c - 12a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (8a b c + 4b c )d e + (- 4a c - 2b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (12a b c - 12a b c + 2a b )e + (24a b c - 4a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R - 24a b c d e + 8a b c d e - 4a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 3 3 2 3 +--R (6a c - 6a b c + a b )e + (12a b c - 2a b c)d e - 12a c d e +--R + +--R 2 3 3 2 2 4 4 +--R 4a b c d e - 2a c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 4a b c + b c )e + (8a c - 2b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 8a b c + 2b c)e + (16a b c - 4b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((- 8a b c - 2a b c + b )e + (16a c + 4a b c - 2b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 8a b c + 2a b )e + (16a b c - 4a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 4a b c + a b )e + (8a c - 2a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((8a b c - 2b c )e + (- 16a c + 4b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((16a b c - 4b c)e + (- 32a b c + 8b c )d e )x +--R + +--R 2 2 3 5 5 +--R (16a b c + 4a b c - 2b )e +--R + +--R 2 3 2 2 4 4 +--R (- 32a c - 8a b c + 4b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((16a b c - 4a b )e + (- 32a b c + 8a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (8a b c - 2a b )e + (- 16a c + 4a b c)d e +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 5 3 3 2 4 +--R (6a c - 2a b c )e + (- 4a b c + 2b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (4a c - 4b c )d e + 4b c d e - 2c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 4 +--R (13a b c - 4a b c)e + (- 8a c - 8a b c + 4b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (18a b c - 9b c )d e + (- 8a c + 8b c )d e - 3b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 5 4 +--R (10a c + 4a b c - 2a b )e + (- 20a b c + 2b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (12a c + 12a b c - 6b c)d e + (- 12a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (2a c - 2b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (11a b c - 3a b )e + (- 12a c - 11a b c + 4a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (30a b c - 5a b c - b )d e + (- 16a c - 6a b c + 3b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (11a b c - 3b c )d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 3 3 2 2 6 3 3 2 3 2 5 +--R (8a c - 2a b c )e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 4 +--R (24a c + 18a b c - 6a b c )d e +--R + +--R 2 4 3 3 5 2 3 3 +--R (- 48a b c + 4a b c + 2b c )d e +--R + +--R 2 5 2 4 4 3 4 2 5 3 4 5 +--R (24a c + 18a b c - 6b c )d e + (- 24a b c + 6b c )d e +--R + +--R 6 2 5 6 +--R (8a c - 2b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 6 3 2 2 2 4 5 +--R (16a b c - 4a b c)e + (- 48a b c + 12a b c)d e +--R + +--R 3 3 2 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b c)d e +--R + +--R 2 2 3 4 2 6 3 3 +--R (- 96a b c + 8a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 4 2 2 4 4 3 5 +--R (48a b c + 36a b c - 12b c )d e + (- 48a b c + 12b c )d e +--R + +--R 5 3 4 6 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 6 4 2 3 3 2 5 5 +--R (16a c + 4a b c - 2a b )e + (- 48a b c - 12a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 4 +--R (48a c + 60a b c + 6a b c - 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 96a b c - 40a b c + 8a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 4 2 +--R (48a c + 60a b c + 6a b c - 6b c)d e +--R + +--R 2 4 3 3 5 2 5 2 5 2 4 4 3 6 +--R (- 48a b c - 12a b c + 6b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 3 6 4 2 3 4 5 +--R (16a b c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b )d e +--R + +--R 3 2 2 2 4 6 3 3 +--R (- 96a b c + 8a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 2 3 4 2 5 +--R (48a b c + 36a b c - 12a b c)d e + (- 48a b c + 12a b c )d e +--R + +--R 2 4 3 3 6 +--R (16a b c - 4a b c )d +--R * +--R x +--R + +--R 6 5 2 6 5 4 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 5 2 4 2 3 4 2 4 4 2 3 3 2 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2a b )d e +--R + +--R 4 3 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (24a c + 18a b c - 6a b c)d e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 6 +--R (8a c - 2a b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (12a c - 12a b c + 2b c )e + (24a b c - 4b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R - 24a c d e + 8b c d e - 4c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (24a b c - 24a b c + 4b c)e + (48a b c - 8b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R - 48a b c d e + 16b c d e - 8b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (24a c - 12a b c - 8a b c + 2b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (48a b c + 16a b c - 4b c)d e + (- 48a c - 24a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (16a b c + 8b c )d e + (- 8a c - 4b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (24a b c - 24a b c + 4a b )e + (48a b c - 8a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R - 48a b c d e + 16a b c d e - 8a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 3 3 2 3 +--R (12a c - 12a b c + 2a b )e + (24a b c - 4a b c)d e - 24a c d e +--R + +--R 2 3 3 2 2 4 4 +--R 8a b c d e - 4a c d e +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 4a b c + b c )e + (8a c - 2b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 8a b c + 2b c)e + (16a b c - 4b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((- 8a b c - 2a b c + b )e + (16a c + 4a b c - 2b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 8a b c + 2a b )e + (16a b c - 4a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 4a b c + a b )e + (8a c - 2a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((8a b c - 2b c )e + (- 16a c + 4b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((16a b c - 4b c)e + (- 32a b c + 8b c )d e )x +--R + +--R 2 2 3 5 5 +--R (16a b c + 4a b c - 2b )e +--R + +--R 2 3 2 2 4 4 +--R (- 32a c - 8a b c + 4b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((16a b c - 4a b )e + (- 32a b c + 8a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (8a b c - 2a b )e + (- 16a c + 4a b c)d e +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 5 3 3 2 4 +--R (6a c - 2a b c )e + (- 4a b c + 2b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (4a c - 4b c )d e + 4b c d e - 2c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 4 +--R (13a b c - 4a b c)e + (- 8a c - 8a b c + 4b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (18a b c - 9b c )d e + (- 8a c + 8b c )d e - 3b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 5 4 +--R (10a c + 4a b c - 2a b )e + (- 20a b c + 2b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (12a c + 12a b c - 6b c)d e + (- 12a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (2a c - 2b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (11a b c - 3a b )e + (- 12a c - 11a b c + 4a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (30a b c - 5a b c - b )d e + (- 16a c - 6a b c + 3b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (11a b c - 3b c )d e + (- 4a c + b c )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 4 3 3 2 2 6 3 3 2 3 2 5 +--R (8a c - 2a b c )e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 4 +--R (24a c + 18a b c - 6a b c )d e +--R + +--R 2 4 3 3 5 2 3 3 +--R (- 48a b c + 4a b c + 2b c )d e +--R + +--R 2 5 2 4 4 3 4 2 5 3 4 5 +--R (24a c + 18a b c - 6b c )d e + (- 24a b c + 6b c )d e +--R + +--R 6 2 5 6 +--R (8a c - 2b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 6 3 2 2 2 4 5 +--R (16a b c - 4a b c)e + (- 48a b c + 12a b c)d e +--R + +--R 3 3 2 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b c)d e +--R + +--R 2 2 3 4 2 6 3 3 +--R (- 96a b c + 8a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 4 2 2 4 4 3 5 +--R (48a b c + 36a b c - 12b c )d e + (- 48a b c + 12b c )d e +--R + +--R 5 3 4 6 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 6 4 2 3 3 2 5 5 +--R (16a c + 4a b c - 2a b )e + (- 48a b c - 12a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 4 +--R (48a c + 60a b c + 6a b c - 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 96a b c - 40a b c + 8a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 4 2 +--R (48a c + 60a b c + 6a b c - 6b c)d e +--R + +--R 2 4 3 3 5 2 5 2 5 2 4 4 3 6 +--R (- 48a b c - 12a b c + 6b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 3 6 4 2 3 4 5 +--R (16a b c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b )d e +--R + +--R 3 2 2 2 4 6 3 3 +--R (- 96a b c + 8a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 2 3 4 2 5 +--R (48a b c + 36a b c - 12a b c)d e + (- 48a b c + 12a b c )d e +--R + +--R 2 4 3 3 6 +--R (16a b c - 4a b c )d +--R * +--R x +--R + +--R 6 5 2 6 5 4 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 5 2 4 2 3 4 2 4 4 2 3 3 2 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2a b )d e +--R + +--R 4 3 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (24a c + 18a b c - 6a b c)d e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 6 +--R (8a c - 2a b c )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 404 + +--S 405 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 4 5 2 3 4 3 2 3 +--R (6a c - 6a b c + b )e + (12a b c - 2b c)d e - 12a c d e +--R + +--R 3 3 2 4 4 +--R 4b c d e - 2c d e +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 4 5 2 3 4 3 2 3 +--R (12a c - 12a b c + 2b )e + (24a b c - 4b c)d e - 24a c d e +--R + +--R 3 3 2 4 4 +--R 8b c d e - 4c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 405 + +--S 406 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 4 5 2 3 4 3 2 3 +--R (6a c - 6a b c + b )e + (12a b c - 2b c)d e - 12a c d e +--R + +--R 3 3 2 4 4 +--R 4b c d e - 2c d e +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 4 5 2 3 4 3 2 3 +--R (6a c - 6a b c + b )e + (12a b c - 2b c)d e - 12a c d e +--R + +--R 3 3 2 4 4 +--R 4b c d e - 2c d e +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 407 + +--S 408 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 845 +t0:=(b+2*c*x)*(d+e*x)^4*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 845 +r0:=1/1680*(128*c^4*d^4+105*b^4*e^4-16*c^3*d^2*e*(16*b*d+93*a*e)-_ + 4*b^2*c*e^3*(109*b*d+101*a*e)+4*c^2*e^2*(141*b^2*d^2+372*a*b*d*e+_ + 16*a^2*e^2))*(a+b*x+c*x^2)^(3/2)/c^4+1/35*(4*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(b*d+2*a*e))*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)/c^2+2/21*(2*c*d-b*e)*_ + (d+e*x)^3*(a+b*x+c*x^2)^(3/2)/c+2/7*(d+e*x)^4*(a+b*x+c*x^2)^(3/2)-_ + 1/280*e*(9*b^3*d*e^2+8*a*c*e*(17*c*d^2-4*a*e^2)-4*b*c*d*(2*c*d^2+_ + 15*a*e^2)-b^2*(22*c*d^2*e-12*a*e^3)-(2*c*d-b*e)*(8*c^2*d^2+_ + 21*b^2*e^2-4*c*e*(2*b*d+19*a*e))*x)*(a+b*x+c*x^2)^(3/2)/c^3-_ + 1/256*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(8*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(2*b*d+a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/_ + c^(11/2)+1/128*(b^2-4*a*c)*e*(2*c*d-b*e)*(8*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(2*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 3 3 2 3 2 5 7 4 +--R (- 6720a b c + 8400a b c - 2940a b c + 315b )e +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (13440a c - 30240a b c + 12600a b c - 1470b c)d e +--R + +--R 2 4 3 3 5 2 2 2 +--R (40320a b c - 20160a b c + 2520b c )d e +--R + +--R 2 5 2 4 4 3 3 +--R (- 26880a c + 13440a b c - 1680b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 6 4 6 5 4 6 3 5 +--R 7680c e x + (5120b c e + 35840c d e )x +--R + +--R 5 2 4 4 5 3 6 2 2 4 +--R ((1536a c - 256b c )e + 25088b c d e + 64512c d e )x +--R + +--R 4 3 3 4 5 2 4 3 +--R (- 1408a b c + 288b c )e + (8960a c - 1344b c )d e +--R + +--R 5 2 2 6 3 +--R 48384b c d e + 53760c d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 4 2 4 +--R (- 2048a c + 1984a b c - 336b c )e +--R + +--R 4 3 3 3 5 2 4 2 2 +--R (- 8064a b c + 1568b c )d e + (21504a c - 2688b c )d e +--R + +--R 5 3 6 4 +--R 44800b c d e + 17920c d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 5 4 +--R (4672a b c - 2912a b c + 420b c)e +--R + +--R 2 4 2 3 4 2 3 +--R (- 13440a c + 12096a b c - 1960b c )d e +--R + +--R 4 3 3 2 2 5 2 4 3 +--R (- 18816a b c + 3360b c )d e + (26880a c - 2240b c )d e +--R + +--R 5 4 +--R 17920b c d +--R * +--R x +--R + +--R 3 3 2 2 2 4 6 4 +--R (4096a c - 10976a b c + 5040a b c - 630b )e +--R + +--R 2 3 3 2 5 3 +--R (36288a b c - 21280a b c + 2940b c)d e +--R + +--R 2 4 2 3 4 2 2 2 +--R (- 43008a c + 33600a b c - 5040b c )d e +--R + +--R 4 3 3 3 5 4 +--R (- 22400a b c + 3360b c )d e + 17920a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 26880c \|c +--R Type: Expression(Integer) +--E 410 + +--S 411 of 845 +--a0:=integrate(t0,x) +--E 411 + +--S 412 of 845 +--m0:=a0-r0 +--E 412 + +--S 413 of 845 +--d0:=D(m0,x) +--E 413 + +)clear all + +--S 414 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 414 + +--S 415 of 845 +r0:=1/480*(2*c*d-b*e)*(32*c^2*d^2+35*b^2*e^2-4*c*e*(8*b*d+27*a*e))*_ + (a+b*x+c*x^2)^(3/2)/c^3+1/10*(2*c*d-b*e)*(d+e*x)^2*_ + (a+b*x+c*x^2)^(3/2)/c+1/3*(d+e*x)^3*(a+b*x+c*x^2)^(3/2)+1/80*e*_ + (3*b^2*d*e-28*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+7*b^2*e^2-4*c*e*_ + (2*b*d+5*a*e))*x)*(a+b*x+c*x^2)^(3/2)/c^2-1/512*(b^2-4*a*c)^2*e*_ + (24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)+1/256*(b^2-4*a*c)*e*(24*c^2*d^2+_ + 7*b^2*e^2-4*c*e*(6*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 3 +--R (960a c - 2160a b c + 900a b c - 105b )e +--R + +--R 2 3 3 2 5 2 +--R (5760a b c - 2880a b c + 360b c)d e +--R + +--R 2 4 2 3 4 2 2 +--R (- 5760a c + 2880a b c - 360b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 5 3 5 4 3 5 2 4 +--R 2560c e x + (1792b c e + 9216c d e )x +--R + +--R 4 2 3 3 4 2 5 2 3 +--R ((640a c - 96b c )e + 6912b c d e + 11520c d e)x +--R + +--R 3 3 2 3 4 2 3 2 +--R (- 576a b c + 112b c )e + (3072a c - 384b c )d e +--R + +--R 4 2 5 3 +--R 9600b c d e + 5120c d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 4 3 3 3 2 2 +--R (- 960a c + 864a b c - 140b c)e + (- 2688a b c + 480b c )d e +--R + +--R 4 2 3 2 4 3 +--R (5760a c - 480b c )d e + 5120b c d +--R * +--R x +--R + +--R 2 2 3 5 3 +--R (2592a b c - 1520a b c + 210b )e +--R + +--R 2 3 2 2 4 2 3 3 2 2 +--R (- 6144a c + 4800a b c - 720b c)d e + (- 4800a b c + 720b c )d e +--R + +--R 4 3 +--R 5120a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 415 + +--S 416 of 845 +--a0:=integrate(t0,x) +--E 416 + +--S 417 of 845 +--m0:=a0-r0 +--E 417 + +--S 418 of 845 +--d0:=D(m0,x) +--E 418 + +)clear all + +--S 419 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R +--------------+ +--R 2 3 2 2 2 2 | 2 +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|c x + b x + a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 845 +r0:=1/60*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*(a+b*x+c*x^2)^(3/2)/c^2+_ + 2/5*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)+1/10*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/c-1/64*(b^2-4*a*c)^2*e*(2*c*d-b*e)*atanh(1/2*(b+_ + 2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+1/32*(b^2-4*a*c)*e*(2*c*d-_ + b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 2 3 5 2 2 3 2 2 4 +--R ((240a b c - 120a b c + 15b )e + (- 480a c + 240a b c - 30b c)d e) +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 4 2 4 3 2 4 3 +--R 384c e x + (288b c e + 960c d e)x +--R + +--R 3 2 2 2 3 4 2 2 +--R ((128a c - 16b c )e + 800b c d e + 640c d )x +--R + +--R 2 3 2 3 2 2 3 2 +--R ((- 112a b c + 20b c)e + (480a c - 40b c )d e + 640b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 +--R (- 256a c + 200a b c - 30b )e + (- 400a b c + 60b c)d e + 640a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 960c \|c +--R Type: Expression(Integer) +--E 420 + +--S 421 of 845 +--a0:=integrate(t0,x) +--E 421 + +--S 422 of 845 +--m0:=a0-r0 +--E 422 + +--S 423 of 845 +--d0:=D(m0,x) +--E 423 + +)clear all + +--S 424 of 845 +t0:=(b+2*c*x)*(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (1) (2c e x + (b e + 2c d)x + b d)\|c x + b x + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 845 +r0:=1/12*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/c+1/2*(d+e*x)*(a+b*x+c*x^2)^(3/2)-_ + 1/64*(b^2-4*a*c)^2*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(5/2)+1/32*(b^2-4*a*c)*e*(b+2*c*x)*_ + sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 4 2c x + b +--R (- 48a c + 24a b c - 3b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 3 2 3 2 2 2 2 +--R 96c e x + (80b c e + 128c d)x + ((48a c - 4b c)e + 128b c d)x +--R + +--R 3 2 +--R (- 40a b c + 6b )e + 128a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 425 + +--S 426 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 384a b c - 96a b c + 24b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 2304a b c - 1728a b c + 240a b )e x +--R + +--R 4 2 3 3 2 5 +--R (9216a b c - 4608a b c + 576a b )e x +--R + +--R 5 2 4 2 3 4 +--R (6144a c - 3072a b c + 384a b )e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (- 768a c - 768a b c + 480a b c - 48a b c - 3b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 1536a b c + 384a b c - 96a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 4608a b c + 3456a b c - 480a b )e x +--R + +--R 5 2 4 3 3 5 +--R (- 12288a b c + 6144a b c - 768a b )e x +--R + +--R 6 2 5 2 4 4 +--R (- 6144a c + 3072a b c - 384a b )e +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 5 2 4 4 3 7 +--R (- 1536a c - 2304a b c - 96b c )e x +--R + +--R 2 4 3 3 5 2 +--R (- 13568a b c - 4992a b c - 80b c )e +--R + +--R 2 5 2 4 4 3 +--R (- 2048a c - 3072a b c - 128b c )d +--R * +--R 6 +--R x +--R + +--R 3 4 2 2 3 4 2 6 +--R (- 13056a c - 26688a b c - 2512a b c + 4b c)e +--R + +--R 2 4 3 3 5 2 +--R (- 18432a b c - 7168a b c - 128b c )d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 5 7 +--R (- 40320a b c - 12960a b c + 24a b c - 6b )e +--R + +--R 3 4 2 2 3 4 2 +--R (- 18432a c - 39936a b c - 4224a b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 2 2 4 6 +--R (- 18432a c - 23808a b c + 1024a b c - 144a b )e +--R + +--R 3 3 2 3 2 +--R (- 61440a b c - 23552a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (- 19968a b c + 3840a b c - 480a b )e +--R + +--R 4 3 3 2 2 +--R (- 24576a c - 43008a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 4 2 +--R ((- 6144a c + 3072a b c - 384a b )e - 24576a b c d)x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 5 3 4 8 +--R (3072a b c + 768b c )e x +--R + +--R 2 5 2 4 4 3 5 3 4 7 +--R ((6144a c + 13312a b c + 1408b c )e + (4096a b c + 1024b c )d)x +--R + +--R 2 4 3 3 5 2 +--R (34304a b c + 17664a b c + 608b c )e +--R + +--R 2 5 2 4 4 3 +--R (8192a c + 18432a b c + 2048b c )d +--R * +--R 6 +--R x +--R + +--R 3 4 2 2 3 4 2 6 +--R (21504a c + 52992a b c + 6848a b c + 16b c)e +--R + +--R 2 4 3 3 5 2 +--R (49152a b c + 26624a b c + 1024b c )d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 5 7 +--R (57984a b c + 21600a b c - 104a b c + 42b )e +--R + +--R 3 4 2 2 3 4 2 +--R (30720a c + 82944a b c + 12160a b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 2 2 4 6 +--R (21504a c + 31488a b c - 2368a b c + 336a b )e +--R + +--R 3 3 2 3 2 +--R (86016a b c + 41984a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (23040a b c - 5376a b c + 672a b )e +--R + +--R 4 3 3 2 2 +--R (24576a c + 55296a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 4 2 +--R ((6144a c - 3072a b c + 384a b )e + 24576a b c d)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 3 2 3 2 3 2 2 2 +--R (6144a b c + 1536b c )x + (12288a c + 15360a b c )x +--R + +--R 2 2 3 2 +--R 36864a b c x + 24576a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 4 2 3 4 2 4 +--R (- 3072a c - 4608a b c - 192b c )x +--R + +--R 2 3 3 2 3 3 3 2 2 2 2 +--R (- 24576a b c - 6144a b c )x + (- 24576a c - 30720a b c )x +--R + +--R 3 2 4 2 +--R - 49152a b c x - 24576a c +--R * +--R +-+ +--R \|c +--R , +--R +--R 3 3 2 3 2 5 7 3 +--R (- 1536a b c + 384a b c + 96a b c - 24b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 3072a c - 2304a b c + 1728a b c - 240a b )e x +--R + +--R 4 2 3 3 2 5 +--R (- 9216a b c + 4608a b c - 576a b )e x +--R + +--R 5 2 4 2 3 4 +--R (- 6144a c + 3072a b c - 384a b )e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (768a c + 768a b c - 480a b c + 48a b c + 3b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (6144a b c - 1536a b c - 384a b c + 96a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (6144a c + 4608a b c - 3456a b c + 480a b )e x +--R + +--R 5 2 4 3 3 5 +--R (12288a b c - 6144a b c + 768a b )e x +--R + +--R 6 2 5 2 4 4 +--R (6144a c - 3072a b c + 384a b )e +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 5 2 4 4 3 7 +--R (- 768a c - 1152a b c - 48b c )e x +--R + +--R 2 4 3 3 5 2 +--R (- 6784a b c - 2496a b c - 40b c )e +--R + +--R 2 5 2 4 4 3 +--R (- 1024a c - 1536a b c - 64b c )d +--R * +--R 6 +--R x +--R + +--R 3 4 2 2 3 4 2 6 +--R (- 6528a c - 13344a b c - 1256a b c + 2b c)e +--R + +--R 2 4 3 3 5 2 +--R (- 9216a b c - 3584a b c - 64b c )d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 5 7 +--R (- 20160a b c - 6480a b c + 12a b c - 3b )e +--R + +--R 3 4 2 2 3 4 2 +--R (- 9216a c - 19968a b c - 2112a b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 2 2 4 6 +--R (- 9216a c - 11904a b c + 512a b c - 72a b )e +--R + +--R 3 3 2 3 2 +--R (- 30720a b c - 11776a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (- 9984a b c + 1920a b c - 240a b )e +--R + +--R 4 3 3 2 2 +--R (- 12288a c - 21504a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 4 2 +--R ((- 3072a c + 1536a b c - 192a b )e - 12288a b c d)x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 5 3 4 8 +--R (1536a b c + 384b c )e x +--R + +--R 2 5 2 4 4 3 5 3 4 7 +--R ((3072a c + 6656a b c + 704b c )e + (2048a b c + 512b c )d)x +--R + +--R 2 4 3 3 5 2 +--R (17152a b c + 8832a b c + 304b c )e +--R + +--R 2 5 2 4 4 3 +--R (4096a c + 9216a b c + 1024b c )d +--R * +--R 6 +--R x +--R + +--R 3 4 2 2 3 4 2 6 +--R (10752a c + 26496a b c + 3424a b c + 8b c)e +--R + +--R 2 4 3 3 5 2 +--R (24576a b c + 13312a b c + 512b c )d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 5 7 +--R (28992a b c + 10800a b c - 52a b c + 21b )e +--R + +--R 3 4 2 2 3 4 2 +--R (15360a c + 41472a b c + 6080a b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 2 2 4 6 +--R (10752a c + 15744a b c - 1184a b c + 168a b )e +--R + +--R 3 3 2 3 2 +--R (43008a b c + 20992a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (11520a b c - 2688a b c + 336a b )e +--R + +--R 4 3 3 2 2 +--R (12288a c + 27648a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 4 2 +--R ((3072a c - 1536a b c + 192a b )e + 12288a b c d)x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (3072a b c + 768b c )x + (6144a c + 7680a b c )x + 18432a b c x +--R + +--R 3 2 +--R 12288a c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 4 2 3 4 2 4 +--R (- 1536a c - 2304a b c - 96b c )x +--R + +--R 2 3 3 2 3 3 3 2 2 2 2 +--R (- 12288a b c - 3072a b c )x + (- 12288a c - 15360a b c )x +--R + +--R 3 2 4 2 +--R - 24576a b c x - 12288a c +--R * +--R +---+ +--R \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 426 + +--S 427 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 384a b c - 96a b c + 24b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 2304a b c - 1728a b c + 240a b )e x +--R + +--R 4 2 3 3 2 5 +--R (9216a b c - 4608a b c + 576a b )e x +--R + +--R 5 2 4 2 3 4 +--R (6144a c - 3072a b c + 384a b )e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (- 768a c - 768a b c + 480a b c - 48a b c - 3b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 1536a b c + 384a b c - 96a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 4608a b c + 3456a b c - 480a b )e x +--R + +--R 5 2 4 3 3 5 +--R (- 12288a b c + 6144a b c - 768a b )e x +--R + +--R 6 2 5 2 4 4 +--R (- 6144a c + 3072a b c - 384a b )e +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 384a b c - 96a b c + 24b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 2304a b c - 1728a b c + 240a b )e x +--R + +--R 4 2 3 3 2 5 +--R (9216a b c - 4608a b c + 576a b )e x +--R + +--R 5 2 4 2 3 4 +--R (6144a c - 3072a b c + 384a b )e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (- 768a c - 768a b c + 480a b c - 48a b c - 3b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 1536a b c + 384a b c - 96a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 4608a b c + 3456a b c - 480a b )e x +--R + +--R 5 2 4 3 3 5 +--R (- 12288a b c + 6144a b c - 768a b )e x +--R + +--R 6 2 5 2 4 4 +--R (- 6144a c + 3072a b c - 384a b )e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 4 6 3 3 2 3 2 3 +--R ((- 1280a b c - 128a b c + 48a b )e + (4096a b c + 1024a b c )d)x +--R + +--R 4 2 3 3 2 5 4 3 3 2 2 2 +--R ((- 2560a b c - 2816a b c + 480a b )e + (8192a c + 10240a b c )d)x +--R + +--R 4 2 3 4 4 2 +--R ((- 7680a b c + 1152a b )e + 24576a b c d)x +--R + +--R 5 4 3 5 2 +--R (- 5120a b c + 768a b )e + 16384a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 +--R (640a b c + 864a b c - 104a b c - 6b )e +--R + +--R 3 4 2 2 3 4 2 +--R (- 2048a c - 3072a b c - 128a b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 4 6 +--R (5120a b c + 512a b c - 192a b )e +--R + +--R 3 3 2 3 2 +--R (- 16384a b c - 4096a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (5120a b c + 5632a b c - 960a b )e +--R + +--R 4 3 3 2 2 +--R (- 16384a c - 20480a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 4 2 5 4 3 +--R ((10240a b c - 1536a b )e - 32768a b c d)x + (5120a b c - 768a b )e +--R + +--R 5 2 +--R - 16384a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 3 2 3 2 3 2 2 2 +--R (6144a b c + 1536b c )x + (12288a c + 15360a b c )x +--R + +--R 2 2 3 2 +--R 36864a b c x + 24576a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 4 2 3 4 2 4 +--R (- 3072a c - 4608a b c - 192b c )x +--R + +--R 2 3 3 2 3 3 3 2 2 2 2 +--R (- 24576a b c - 6144a b c )x + (- 24576a c - 30720a b c )x +--R + +--R 3 2 4 2 +--R - 49152a b c x - 24576a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 427 + +--S 428 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 384a b c - 96a b c + 24b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 2304a b c - 1728a b c + 240a b )e x +--R + +--R 4 2 3 3 2 5 +--R (9216a b c - 4608a b c + 576a b )e x +--R + +--R 5 2 4 2 3 4 +--R (6144a c - 3072a b c + 384a b )e +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (- 768a c - 768a b c + 480a b c - 48a b c - 3b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 1536a b c + 384a b c - 96a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 4608a b c + 3456a b c - 480a b )e x +--R + +--R 5 2 4 3 3 5 +--R (- 12288a b c + 6144a b c - 768a b )e x +--R + +--R 6 2 5 2 4 4 +--R (- 6144a c + 3072a b c - 384a b )e +--R * +--R +---+ +--R \|- c +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 +--R (- 3072a b c + 768a b c + 192a b c - 48b )e x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 6144a c - 4608a b c + 3456a b c - 480a b )e x +--R + +--R 4 2 3 3 2 5 +--R (- 18432a b c + 9216a b c - 1152a b )e x +--R + +--R 5 2 4 2 3 4 +--R (- 12288a c + 6144a b c - 768a b )e +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 4 4 3 2 3 2 4 2 6 8 4 +--R (1536a c + 1536a b c - 960a b c + 96a b c + 6b )e x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (12288a b c - 3072a b c - 768a b c + 192a b )e x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (12288a c + 9216a b c - 6912a b c + 960a b )e x +--R + +--R 5 2 4 3 3 5 +--R (24576a b c - 12288a b c + 1536a b )e x +--R + +--R 6 2 5 2 4 4 +--R (12288a c - 6144a b c + 768a b )e +--R * +--R +-+ +--R \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 2 2 2 4 6 3 3 2 3 2 3 +--R ((- 1280a b c - 128a b c + 48a b )e + (4096a b c + 1024a b c )d)x +--R + +--R 4 2 3 3 2 5 4 3 3 2 2 2 +--R ((- 2560a b c - 2816a b c + 480a b )e + (8192a c + 10240a b c )d)x +--R + +--R 4 2 3 4 4 2 +--R ((- 7680a b c + 1152a b )e + 24576a b c d)x +--R + +--R 5 4 3 5 2 +--R (- 5120a b c + 768a b )e + 16384a c d +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 +--R (640a b c + 864a b c - 104a b c - 6b )e +--R + +--R 3 4 2 2 3 4 2 +--R (- 2048a c - 3072a b c - 128a b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 4 6 +--R (5120a b c + 512a b c - 192a b )e +--R + +--R 3 3 2 3 2 +--R (- 16384a b c - 4096a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 +--R (5120a b c + 5632a b c - 960a b )e +--R + +--R 4 3 3 2 2 +--R (- 16384a c - 20480a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 4 2 5 4 3 +--R ((10240a b c - 1536a b )e - 32768a b c d)x + (5120a b c - 768a b )e +--R + +--R 5 2 +--R - 16384a c d +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R / +--R 3 3 2 3 2 3 2 2 2 +--R (6144a b c + 1536b c )x + (12288a c + 15360a b c )x +--R + +--R 2 2 3 2 +--R 36864a b c x + 24576a c +--R * +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R \|- c \|a \|c \|c x + b x + a +--R + +--R 2 4 2 3 4 2 4 +--R (- 3072a c - 4608a b c - 192b c )x +--R + +--R 2 3 3 2 3 3 3 2 2 2 2 +--R (- 24576a b c - 6144a b c )x + (- 24576a c - 30720a b c )x +--R + +--R 3 2 4 2 +--R - 49152a b c x - 24576a c +--R * +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 429 + +--S 430 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R (1) (2c x + b)\|c x + b x + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 845 +r0:=2/3*(a+b*x+c*x^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (2c x + 2b x + 2a)\|c x + b x + a +--R (2) ------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 5 2 2 2 4 4 +--R (- 24a b c - 2b c)x + (- 48a c - 60a b c - 2b )x +--R + +--R 2 3 3 3 2 2 2 3 +--R (- 168a b c - 38a b )x + (- 96a c - 120a b )x - 96a b x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 2 2 6 2 3 5 +--R (16a c + 12b c )x + (96a b c + 24b c)x +--R + +--R 2 2 2 4 4 2 3 3 +--R (96a c + 168a b c + 12b )x + (264a b c + 86a b )x +--R + +--R 3 2 2 2 3 +--R (96a c + 168a b )x + 96a b x +--R * +--R +-+ +--R \|a +--R / +--R +--------------+ +--R 2 2 2 +-+ | 2 +--R ((24a c + 18b )x + 96a b x + 96a )\|a \|c x + b x + a +--R + +--R 3 3 2 2 2 2 3 +--R (- 36a b c - 3b )x + (- 72a c - 54a b )x - 144a b x - 96a +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------------+ +--R 3 2 2 2 3 4 | 2 +--R ((16a c + 12a b )x + 64a b x + 64a )\|c x + b x + a +--R + +--R 2 3 3 3 2 2 2 3 4 +-+ +--R ((- 24a b c - 2a b )x + (- 48a c - 36a b )x - 96a b x - 64a )\|a +--R / +--R +--------------+ +--R 2 2 2 +-+ | 2 +--R ((24a c + 18b )x + 96a b x + 96a )\|a \|c x + b x + a +--R + +--R 3 3 2 2 2 2 3 +--R (- 36a b c - 3b )x + (- 72a c - 54a b )x - 144a b x - 96a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 436 + +--S 437 of 845 +r0:=1/4*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^3*sqrt(c))-(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-_ + b*d*e+a*e^2)/e^3-1/2*(4*c*d-3*b*e-2*c*e*x)*sqrt(a+b*x+c*x^2)/e^2 +--R +--R +--R (2) +--R 2 2 2 2 2c x + b +--R ((4a c + b )e - 8b c d e + 8c d )atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R +-+ | 2 2 +--R (- 4b e + 8c d)\|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +--------------+ +--R 2 2 +-+ | 2 +--R (4c e x + 6b e - 8c d e)\|c \|c x + b x + a +--R / +--R 3 +-+ +--R 4e \|c +--R Type: Expression(Integer) +--E 437 + +--S 438 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 +-+ +-+ +--R ((16b e - 32b c d)x + 32a b e - 64a c d)\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d)x +--R + +--R 2 2 2 +--R (- 32a b e + 64a b c d)x - 32a b e + 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R log +--R +-------------------+ +--R | 2 2 2 +-+ +--R (- 2d x\|a e - b d e + c d + (2d e x + 2d )\|a ) +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2e x + 2d x)\|a \|a e - b d e + c d +--R + +--R 2 2 2 2 2 +--R (- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 2 2 2 3 +--R (- 16a c - 4b c)e x +--R + +--R 3 2 2 2 2 +--R ((- 56a b c - 6b )e + (32a c + 8b c)d e)x +--R + +--R 2 2 2 +--R ((- 32a c - 24a b )e + 32a b c d e)x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 2 4 2 2 2 2 3 +--R 16b c e x + ((32a c + 40b c)e - 32b c d e)x +--R + +--R 3 2 2 2 2 +--R ((72a b c + 18b )e + (- 32a c - 24b c)d e)x +--R + +--R 2 2 2 +--R ((32a c + 24a b )e - 32a b c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 3 +-+ +-+ | 2 +--R (16b e x + 32a e )\|a \|c \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +-+ +--R ((- 16a c - 4b )e x - 32a b e x - 32a e )\|c +--R , +--R +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +---------------------+ +--R 2 | 2 2 +--R ((32b e - 64b c d)x + 64a b e - 128a c d)\|- a e + b d e - c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 32a b c - 8b )e + (64a c + 16b c)d)x +--R + +--R 2 2 2 +--R (- 64a b e + 128a b c d)x - 64a b e + 128a c d +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|c +--R * +--R +--------------+ +--R | 2 +-+ +--R d\|c x + b x + a + (- e x - d)\|a +--R atan(------------------------------------) +--R +---------------------+ +--R | 2 2 +--R x\|- a e + b d e - c d +--R + +--R 2 2 2 3 +--R (- 16a c - 4b c)e x +--R + +--R 3 2 2 2 2 +--R ((- 56a b c - 6b )e + (32a c + 8b c)d e)x +--R + +--R 2 2 2 +--R ((- 32a c - 24a b )e + 32a b c d e)x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 2 4 2 2 2 2 3 +--R 16b c e x + ((32a c + 40b c)e - 32b c d e)x +--R + +--R 3 2 2 2 2 +--R ((72a b c + 18b )e + (- 32a c - 24b c)d e)x +--R + +--R 2 2 2 +--R ((32a c + 24a b )e - 32a b c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 3 +-+ +-+ | 2 +--R (16b e x + 32a e )\|a \|c \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +-+ +--R ((- 16a c - 4b )e x - 32a b e x - 32a e )\|c +--R , +--R +--R 2 +---+ +-+ +--R ((8b e - 16b c d)x + 16a b e - 32a c d)\|- c \|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 8a b c - 2b )e + (16a c + 4b c)d)x +--R + +--R 2 2 2 +--R (- 16a b e + 32a b c d)x - 16a b e + 32a c d +--R * +--R +-------------------+ +--R +---+ | 2 2 +--R \|- c \|a e - b d e + c d +--R * +--R log +--R +-------------------+ +--R | 2 2 2 +-+ +--R (- 2d x\|a e - b d e + c d + (2d e x + 2d )\|a ) +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2e x + 2d x)\|a \|a e - b d e + c d +--R + +--R 2 2 2 2 2 +--R (- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 2 2 3 3 2 2 2 2 +--R (- 8a c - 2b c)e x + ((- 28a b c - 3b )e + (16a c + 4b c)d e)x +--R + +--R 2 2 2 +--R ((- 16a c - 12a b )e + 16a b c d e)x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 2 2 4 2 2 2 2 3 +--R 8b c e x + ((16a c + 20b c)e - 16b c d e)x +--R + +--R 3 2 2 2 2 +--R ((36a b c + 9b )e + (- 16a c - 12b c)d e)x +--R + +--R 2 2 2 +--R ((16a c + 12a b )e - 16a b c d e)x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------------+ +--R 3 3 +---+ +-+ | 2 +--R (8b e x + 16a e )\|- c \|a \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +---+ +--R ((- 8a c - 2b )e x - 16a b e x - 16a e )\|- c +--R , +--R +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R +---------------------+ +--R 2 | 2 2 +--R ((16b e - 32b c d)x + 32a b e - 64a c d)\|- a e + b d e - c d +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d)x +--R + +--R 2 2 2 +--R (- 32a b e + 64a b c d)x - 32a b e + 64a c d +--R * +--R +---------------------+ +--R | 2 2 +---+ +--R \|- a e + b d e - c d \|- c +--R * +--R +--------------+ +--R | 2 +-+ +--R d\|c x + b x + a + (- e x - d)\|a +--R atan(------------------------------------) +--R +---------------------+ +--R | 2 2 +--R x\|- a e + b d e - c d +--R + +--R 2 2 2 3 3 2 2 2 2 +--R (- 8a c - 2b c)e x + ((- 28a b c - 3b )e + (16a c + 4b c)d e)x +--R + +--R 2 2 2 +--R ((- 16a c - 12a b )e + 16a b c d e)x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 2 2 4 2 2 2 2 3 +--R 8b c e x + ((16a c + 20b c)e - 16b c d e)x +--R + +--R 3 2 2 2 2 +--R ((36a b c + 9b )e + (- 16a c - 12b c)d e)x +--R + +--R 2 2 2 +--R ((16a c + 12a b )e - 16a b c d e)x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------------+ +--R 3 3 +---+ +-+ | 2 +--R (8b e x + 16a e )\|- c \|a \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +---+ +--R ((- 8a c - 2b )e x - 16a b e x - 16a e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 438 + +--S 439 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 +-+ +-+ +--R ((16b e - 32b c d)x + 32a b e - 64a c d)\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d)x +--R + +--R 2 2 2 +--R (- 32a b e + 64a b c d)x - 32a b e + 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R log +--R +-------------------+ +--R | 2 2 2 +-+ +--R (- 2d x\|a e - b d e + c d + (2d e x + 2d )\|a ) +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2e x + 2d x)\|a \|a e - b d e + c d +--R + +--R 2 2 2 2 2 +--R (- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R 3 2 2 2 2 +--R ((- 16a b c - 4b )e + 32b c d e - 32b c d )x +--R + +--R 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (16a c + 8a b c + b )e + (- 32a b c - 8b c)d e +--R + +--R 3 2 2 2 +--R (32a c + 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R ((32a b c + 8a b )e - 64a b c d e + 64a b c d )x + (32a c + 8a b )e +--R + +--R 2 2 2 2 +--R - 64a b c d e + 64a c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 +-+ +-+ +--R ((16b e - 32b c d)x + 32a b e - 64a c d)\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d)x +--R + +--R 2 2 2 +--R (- 32a b e + 64a b c d)x - 32a b e + 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +--------------+ +--R 2 2 2 2 2 +-+ | 2 +--R ((24a b e - 32a b c d e)x + 48a b e - 64a c d e)\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 24a b c - 6b )e + (32a c + 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 48a b e + 64a b c d e)x - 48a b e + 64a c d e +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 3 +-+ +-+ | 2 +--R (16b e x + 32a e )\|a \|c \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +-+ +--R ((- 16a c - 4b )e x - 32a b e x - 32a e )\|c +--R Type: Expression(Integer) +--E 439 + +--S 440 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 2 2 2 2 2 2 2 +--R ((16a b c + 4b )e - 32b c d e + 32b c d )x + (32a c + 8a b )e +--R + +--R 2 2 +--R - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (- 16a c - 8a b c - b )e + (32a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R ((- 32a b c - 8a b )e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 2 2 2 2 +--R ((- 16a b c - 4b )e + 32b c d e - 32b c d )x +--R + +--R 2 2 2 2 2 +--R (- 32a c - 8a b )e + 64a b c d e - 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 +--R (16a c + 8a b c + b )e + (- 32a b c - 8b c)d e +--R + +--R 3 2 2 2 +--R (32a c + 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R ((32a b c + 8a b )e - 64a b c d e + 64a b c d )x + (32a c + 8a b )e +--R + +--R 2 2 2 2 +--R - 64a b c d e + 64a c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 +-+ +-+ +--R ((16b e - 32b c d)x + 32a b e - 64a c d)\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d)x +--R + +--R 2 2 2 +--R (- 32a b e + 64a b c d)x - 32a b e + 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +---------------------+ +--R 2 | 2 2 +--R ((32b e - 64b c d)x + 64a b e - 128a c d)\|- a e + b d e - c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 3 2 2 2 +--R ((- 32a b c - 8b )e + (64a c + 16b c)d)x +--R + +--R 2 2 2 +--R (- 64a b e + 128a b c d)x - 64a b e + 128a c d +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|c +--R * +--R +--------------+ +--R | 2 +-+ +--R d\|c x + b x + a + (- e x - d)\|a +--R atan(------------------------------------) +--R +---------------------+ +--R | 2 2 +--R x\|- a e + b d e - c d +--R + +--R +--------------+ +--R 2 2 2 2 2 +-+ | 2 +--R ((24a b e - 32a b c d e)x + 48a b e - 64a c d e)\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 24a b c - 6b )e + (32a c + 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 48a b e + 64a b c d e)x - 48a b e + 64a c d e +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 3 +-+ +-+ | 2 +--R (16b e x + 32a e )\|a \|c \|c x + b x + a +--R + +--R 2 3 2 3 2 3 +-+ +--R ((- 16a c - 4b )e x - 32a b e x - 32a e )\|c +--R Type: Expression(Integer) +--E 441 + +--S 442 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 443 + +--S 444 of 845 +r0:=-2*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*_ + sqrt(c)/e^3+1/2*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*atanh(1/2*_ + (b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (e^3*sqrt(c*d^2-b*d*e+a*e^2))+(4*c*d-b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/_ + (e^2*(d+e*x)) +--R +--R +--R (2) +--R +-------------------+ +--R 2 2 +-+ | 2 2 +--R ((4b e - 8c d e)x + 4b d e - 8c d )\|c \|a e - b d e + c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 +--R ((- 4a c - b )e + 8b c d e - 8c d e)x + (- 4a c - b )d e +--R + +--R 2 2 3 +--R 8b c d e - 8c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R 2 2 | 2 2 | 2 +--R (4c e x - 2b e + 8c d e)\|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 4 3 | 2 2 +--R (2e x + 2d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 444 + +--S 445 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 2 3 2 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d e)x +--R + +--R 2 2 3 3 2 2 +--R (32a c + 8a b )d e + (- 48a b c + 4b )d e +--R + +--R 2 2 3 2 4 +--R (64a c - 32b c)d e + 32b c d +--R * +--R x +--R + +--R 2 2 2 2 3 2 4 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 2 2 4 2 2 +--R (- 32a b c - 8a b )d e + (- 16a c + 56a b c - b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 32a c - 8a b )d e + (32a b c - 8a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d +--R * +--R x +--R + +--R 3 2 2 2 2 2 3 2 2 4 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 2 2 2 2 +--R (16b d e - 32b c d e)x +--R + +--R 2 2 2 3 2 +--R (32a b d e + (- 64a c + 16b )d e - 32b c d )x + 32a b d e +--R + +--R 3 +--R - 64a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ +-+ | 2 2 | 2 +--R \|a \|c \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((- 16a b c - 4b )d e + (32a c + 8b c)d e)x +--R + +--R 2 2 3 2 2 2 3 2 +--R (- 32a b d e + (48a b c - 4b )d e + (32a c + 8b c)d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 32a b d e + (64a c - 32a b )d e + 64a b c d )x - 32a b d e +--R + +--R 2 3 +--R 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x +--R + +--R - 2a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 2 3 +--R (- 16a c - 4b c)d e x +--R + +--R 2 3 3 2 2 2 2 2 +--R (- 8a b e + (8a b c + 2b )d e + (- 32a c - 8b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (- 16a b e + (32a c + 8a b )d e - 32a b c d e)x +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 4 3 3 2 2 3 +--R 16b c d e x + ((8a b c + 2b )e + 32b c d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R (16a b e + (- 24a b c - 6b )d e + (32a c + 24b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (16a b e + (- 32a c - 8a b )d e + 32a b c d e)x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 4 2 4 2 3 2 3 +-+ +--R (8b d e x + (16a d e + 8b d e )x + 16a d e )\|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 2 3 2 +--R (- 8a c - 2b )d e x + (- 16a b d e + (- 8a c - 2b )d e )x +--R + +--R 2 4 2 3 2 2 3 +--R (- 16a d e - 16a b d e )x - 16a d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R , +--R +--R 3 3 2 2 2 2 3 2 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d e)x +--R + +--R 2 2 3 3 2 2 +--R (32a c + 8a b )d e + (- 48a b c + 4b )d e +--R + +--R 2 2 3 2 4 +--R (64a c - 32b c)d e + 32b c d +--R * +--R x +--R + +--R 2 2 2 2 3 2 4 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 2 2 4 2 2 +--R (- 32a b c - 8a b )d e + (- 16a c + 56a b c - b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 32a c - 8a b )d e + (32a b c - 8a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d +--R * +--R x +--R + +--R 3 2 2 2 2 2 3 2 2 4 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 2 2 2 2 +--R (32b d e - 64b c d e)x +--R + +--R 2 2 2 3 2 +--R (64a b d e + (- 128a c + 32b )d e - 64b c d )x + 64a b d e +--R + +--R 3 +--R - 128a c d +--R * +--R +-------------------+ +--------------+ +--R +---+ +-+ | 2 2 | 2 +--R \|- c \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((- 32a b c - 8b )d e + (64a c + 16b c)d e)x +--R + +--R 2 2 3 2 2 2 3 2 +--R (- 64a b d e + (96a b c - 8b )d e + (64a c + 16b c)d )x +--R + +--R 2 2 2 2 2 3 +--R (- 64a b d e + (128a c - 64a b )d e + 128a b c d )x +--R + +--R 2 2 2 3 +--R - 64a b d e + 128a c d +--R * +--R +-------------------+ +--R +---+ | 2 2 +--R \|- c \|a e - b d e + c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|c x + b x + a - \|a +--R atan(------------------------) +--R +---+ +--R x\|- c +--R + +--R 2 2 2 3 +--R (- 16a c - 4b c)d e x +--R + +--R 2 3 3 2 2 2 2 2 +--R (- 8a b e + (8a b c + 2b )d e + (- 32a c - 8b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (- 16a b e + (32a c + 8a b )d e - 32a b c d e)x +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 4 3 3 2 2 3 +--R 16b c d e x + ((8a b c + 2b )e + 32b c d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R (16a b e + (- 24a b c - 6b )d e + (32a c + 24b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (16a b e + (- 32a c - 8a b )d e + 32a b c d e)x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 4 2 4 2 3 2 3 +-+ +--R (8b d e x + (16a d e + 8b d e )x + 16a d e )\|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 2 3 2 +--R (- 8a c - 2b )d e x + (- 16a b d e + (- 8a c - 2b )d e )x +--R + +--R 2 4 2 3 2 2 3 +--R (- 16a d e - 16a b d e )x - 16a d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R , +--R +--R 2 2 2 2 +--R (8b d e - 16b c d e)x +--R + +--R 2 2 2 3 2 +--R (16a b d e + (- 32a c + 8b )d e - 16b c d )x + 16a b d e +--R + +--R 3 +--R - 32a c d +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ +-+ | 2 +--R \|- a e + b d e - c d \|a \|c \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((- 8a b c - 2b )d e + (16a c + 4b c)d e)x +--R + +--R 2 2 3 2 2 2 3 2 +--R (- 16a b d e + (24a b c - 2b )d e + (16a c + 4b c)d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 16a b d e + (32a c - 16a b )d e + 32a b c d )x - 16a b d e +--R + +--R 2 3 +--R 32a c d +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x +--R + +--R - 2a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 3 2 2 2 2 3 2 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d e)x +--R + +--R 2 2 3 3 2 2 +--R (32a c + 8a b )d e + (- 48a b c + 4b )d e +--R + +--R 2 2 3 2 4 +--R (64a c - 32b c)d e + 32b c d +--R * +--R x +--R + +--R 2 2 2 2 3 2 4 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 2 2 4 2 2 +--R (- 32a b c - 8a b )d e + (- 16a c + 56a b c - b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 32a c - 8a b )d e + (32a b c - 8a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d +--R * +--R x +--R + +--R 3 2 2 2 2 2 3 2 2 4 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 2 2 2 3 +--R (- 8a c - 2b c)d e x +--R + +--R 2 3 3 2 2 2 2 2 +--R (- 4a b e + (4a b c + b )d e + (- 16a c - 4b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (- 8a b e + (16a c + 4a b )d e - 16a b c d e)x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 2 4 3 3 2 2 3 +--R 8b c d e x + ((4a b c + b )e + 16b c d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R (8a b e + (- 12a b c - 3b )d e + (16a c + 12b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (8a b e + (- 16a c - 4a b )d e + 16a b c d e)x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / +--R +---------------------+ +--R 4 2 4 2 3 2 3 | 2 2 +--R (4b d e x + (8a d e + 4b d e )x + 8a d e )\|- a e + b d e - c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 4 3 4 2 2 3 2 +--R (- 4a c - b )d e x + (- 8a b d e + (- 4a c - b )d e )x +--R + +--R 2 4 2 3 2 2 3 +--R (- 8a d e - 8a b d e )x - 8a d e +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R , +--R +--R 3 3 2 2 2 2 3 2 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d e)x +--R + +--R 2 2 3 3 2 2 +--R (32a c + 8a b )d e + (- 48a b c + 4b )d e +--R + +--R 2 2 3 2 4 +--R (64a c - 32b c)d e + 32b c d +--R * +--R x +--R + +--R 2 2 2 2 3 2 4 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 2 2 4 2 2 +--R (- 32a b c - 8a b )d e + (- 16a c + 56a b c - b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 32a c - 8a b )d e + (32a b c - 8a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d +--R * +--R x +--R + +--R 3 2 2 2 2 2 3 2 2 4 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 2 2 2 2 +--R (16b d e - 32b c d e)x +--R + +--R 2 2 2 3 2 +--R (32a b d e + (- 64a c + 16b )d e - 32b c d )x + 32a b d e +--R + +--R 3 +--R - 64a c d +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +---+ +-+ | 2 +--R \|- a e + b d e - c d \|- c \|a \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((- 16a b c - 4b )d e + (32a c + 8b c)d e)x +--R + +--R 2 2 3 2 2 2 3 2 +--R (- 32a b d e + (48a b c - 4b )d e + (32a c + 8b c)d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 32a b d e + (64a c - 32a b )d e + 64a b c d )x - 32a b d e +--R + +--R 2 3 +--R 64a c d +--R * +--R +---------------------+ +--R | 2 2 +---+ +--R \|- a e + b d e - c d \|- c +--R * +--R +--------------+ +--R | 2 +-+ +--R \|c x + b x + a - \|a +--R atan(------------------------) +--R +---+ +--R x\|- c +--R + +--R 2 2 2 3 +--R (- 8a c - 2b c)d e x +--R + +--R 2 3 3 2 2 2 2 2 +--R (- 4a b e + (4a b c + b )d e + (- 16a c - 4b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (- 8a b e + (16a c + 4a b )d e - 16a b c d e)x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 2 4 3 3 2 2 3 +--R 8b c d e x + ((4a b c + b )e + 16b c d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R (8a b e + (- 12a b c - 3b )d e + (16a c + 12b c)d e)x +--R + +--R 2 3 2 2 2 2 +--R (8a b e + (- 16a c - 4a b )d e + 16a b c d e)x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / +--R +---------------------+ +--R 4 2 4 2 3 2 3 | 2 2 +--R (4b d e x + (8a d e + 4b d e )x + 8a d e )\|- a e + b d e - c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 4 3 4 2 2 3 2 +--R (- 4a c - b )d e x + (- 8a b d e + (- 4a c - b )d e )x +--R + +--R 2 4 2 3 2 2 3 +--R (- 8a d e - 8a b d e )x - 8a d e +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 445 + +--S 446 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 2 2 3 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d )x +--R + +--R 2 2 2 2 2 3 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R ((- 32a b c - 8a b )d e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 3 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R 2 2 2 +-+ +-+ +--R ((16b d e - 32b c d )x + 32a b d e - 64a c d )\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 16a b c - 4b )d e + (32a c + 8b c)d )x +--R + +--R 2 2 2 2 2 +--R (- 32a b d e + 64a b c d )x - 32a b d e + 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x - 2a +--R log(-------------------------------------------------------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 2 +-+ +-+ +--R ((- 16b d e + 32b c d )x - 32a b d e + 64a c d )\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((16a b c + 4b )d e + (- 32a c - 8b c)d )x +--R + +--R 2 2 2 2 2 +--R (32a b d e - 64a b c d )x + 32a b d e - 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d )x +--R + +--R 2 2 2 2 2 3 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R ((- 32a b c - 8a b )d e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 3 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 8a b e + 32a b c d e)x - 16a b e + 64a c d e) +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((8a b c + 2b )e + (- 32a c - 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (16a b e - 64a b c d e)x + 16a b e - 64a c d e +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 3 3 +-+ | 2 2 | 2 +--R (8b d e x + 16a d e )\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 2 3 2 3 2 3 | 2 2 +--R ((- 8a c - 2b )d e x - 16a b d e x - 16a d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 446 + +--S 447 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 2 2 2 2 3 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d )x +--R + +--R 2 2 2 2 2 3 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R ((- 32a b c - 8a b )d e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 3 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R 2 2 2 +-+ +-+ +--R ((- 16b d e + 32b c d )x - 32a b d e + 64a c d )\|a \|c +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((16a b c + 4b )d e + (- 32a c - 8b c)d )x +--R + +--R 2 2 2 2 2 +--R (32a b d e - 64a b c d )x + 32a b d e - 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|c \|a e - b d e + c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 3 +--R ((16a b c + 4b )d e - 32b c d e + 32b c d )x +--R + +--R 2 2 2 2 2 3 +--R (32a c + 8a b )d e - 64a b c d e + 64a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 2 2 3 2 +--R (- 16a c - 8a b c - b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R ((- 32a b c - 8a b )d e + 64a b c d e - 64a b c d )x +--R + +--R 3 2 2 2 2 2 2 2 3 +--R (- 32a c - 8a b )d e + 64a b c d e - 64a c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 +---+ +-+ +--R ((32b d e - 64b c d )x + 64a b d e - 128a c d )\|- c \|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 32a b c - 8b )d e + (64a c + 16b c)d )x +--R + +--R 2 2 2 2 2 +--R (- 64a b d e + 128a b c d )x - 64a b d e + 128a c d +--R * +--R +-------------------+ +--R +---+ | 2 2 +--R \|- c \|a e - b d e + c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|c x + b x + a - \|a +--R atan(------------------------) +--R +---+ +--R x\|- c +--R + +--R 2 2 2 2 2 +--R ((- 8a b e + 32a b c d e)x - 16a b e + 64a c d e) +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((8a b c + 2b )e + (- 32a c - 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (16a b e - 64a b c d e)x + 16a b e - 64a c d e +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 3 3 +-+ | 2 2 | 2 +--R (8b d e x + 16a d e )\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 2 3 2 3 2 3 | 2 2 +--R ((- 8a c - 2b )d e x - 16a b d e x - 16a d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 448 + +--S 449 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 449 + +)clear all + +--S 450 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 450 + +--S 451 of 845 +r0:=1/2*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+_ + 2*c^(3/2)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/e^3-_ + 1/8*(2*c*d-b*e)*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*atanh(1/2*_ + (b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (e^3*(c*d^2-b*d*e+a*e^2)^(3/2))-1/4*(8*c^2*d^2-6*b*c*d*e-b^2*e^2+_ + 8*a*c*e^2+2*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-_ + b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 4 3 2 2 2 2 +--R (16a c e - 16b c d e + 16c d e )x +--R + +--R 3 2 2 2 3 2 2 3 2 4 +--R (32a c d e - 32b c d e + 32c d e)x + 16a c d e - 16b c d e + 16c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 12a b c + b )e + (24a c + 6b c)d e - 24b c d e + 16c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 24a b c + 2b )d e + (48a c + 12b c)d e - 48b c d e +--R + +--R 3 4 +--R 32c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 12a b c + b )d e + (24a c + 6b c)d e - 24b c d e + 16c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 2 2 2 4 +--R ((- 16a c - 2b )e + 24b c d e - 24c d e )x - 4a b e +--R + +--R 2 3 2 2 2 3 +--R (- 8a c + 2b )d e + 12b c d e - 16c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 7 6 2 5 2 6 2 5 3 4 +--R (8a e - 8b d e + 8c d e )x + (16a d e - 16b d e + 16c d e )x +--R + +--R 2 5 3 4 4 3 +--R 8a d e - 8b d e + 8c d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 451 + +--S 452 of 845 +--a0:=integrate(t0,x) +--E 452 + +--S 453 of 845 +--m0:=a0-r0 +--E 453 + +--S 454 of 845 +--d0:=D(m0,x) +--E 454 + +)clear all + +--S 455 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 455 + +--S 456 of 845 +r0:=1/16*(b^2-4*a*c)^2*e*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+_ + 1/12*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*sqrt(a+b*x+c*x^2)/_ + (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+1/24*(2*c*d-b*e)*(8*c^2*d^2-_ + 3*b^2*e^2-4*c*e*(2*b*d-5*a*e))*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-_ + b*d*e+a*e^2)^2*(d+e*x))-1/3*(4*c*d+b*e+6*c*e*x)*sqrt(a+b*x+c*x^2)/_ + (e^2*(d+e*x)^3) +--R +--R +--R (2) +--R 2 2 2 4 4 3 2 2 2 4 3 2 +--R (- 48a c + 24a b c - 3b )e x + (- 144a c + 72a b c - 9b )d e x +--R + +--R 2 2 2 4 2 2 2 2 2 4 3 +--R (- 144a c + 72a b c - 9b )d e x + (- 48a c + 24a b c - 3b )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 2 2 2 2 3 3 2 +--R ((- 40a b c + 6b )e + (80a c + 4b c)d e - 48b c d e + 32c d )x +--R + +--R 2 2 3 3 2 2 2 2 +--R (- 48a c - 4a b )e + (32a b c + 16b )d e + (48a c - 60b c)d e +--R + +--R 2 3 +--R 32b c d +--R * +--R x +--R + +--R 2 3 2 2 2 3 2 2 3 +--R - 16a b e + (- 16a c + 28a b )d e + (- 24a b c - 6b )d e + 32a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 2 7 6 2 2 5 3 4 2 4 3 3 +--R (48a e - 96a b d e + (96a c + 48b )d e - 96b c d e + 48c d e )x +--R + +--R 2 6 2 5 2 3 4 4 3 +--R 144a d e - 288a b d e + (288a c + 144b )d e - 288b c d e +--R + +--R 2 5 2 +--R 144c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 2 4 3 5 2 +--R 144a d e - 288a b d e + (288a c + 144b )d e - 288b c d e +--R + +--R 2 6 +--R 144c d e +--R * +--R x +--R + +--R 2 3 4 4 3 2 5 2 6 2 7 +--R 48a d e - 96a b d e + (96a c + 48b )d e - 96b c d e + 48c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 456 + +--S 457 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 4 6 3 4 5 +--R (384a c + 96a b c - 120a b c + 18b )d e x +--R + +--R 3 2 2 3 5 3 4 +--R (1536a b c - 768a b c + 96a b )d e +--R + +--R 3 3 2 2 2 4 6 4 3 +--R (1152a c + 288a b c - 360a b c + 54b )d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 2 2 4 3 4 +--R (1536a c - 768a b c + 96a b )d e +--R + +--R 3 2 2 3 5 4 3 +--R (4608a b c - 2304a b c + 288a b )d e +--R + +--R 3 3 2 2 2 4 6 5 2 +--R (1152a c + 288a b c - 360a b c + 54b )d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 3 +--R (4608a c - 2304a b c + 288a b )d e +--R + +--R 3 2 2 3 5 5 2 +--R (4608a b c - 2304a b c + 288a b )d e +--R + +--R 3 3 2 2 2 4 6 6 +--R (384a c + 96a b c - 120a b c + 18b )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 2 2 4 5 2 +--R (4608a c - 2304a b c + 288a b )d e +--R + +--R 3 2 2 3 5 6 +--R (1536a b c - 768a b c + 96a b )d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 6 +--R (1536a c - 768a b c + 96a b )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 4 6 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 4 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e +--R + +--R 3 3 2 3 2 5 7 4 3 +--R (- 1728a b c + 720a b c - 36a b c - 9b )d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 3 2 5 3 4 +--R (- 2304a b c + 1152a b c - 144a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 3 +--R (- 3456a c - 864a b c + 1080a b c - 162a b )d e +--R + +--R 3 3 2 3 2 5 7 5 2 +--R (- 1728a b c + 720a b c - 36a b c - 9b )d e +--R * +--R 4 +--R x +--R + +--R 5 2 4 2 3 4 3 4 +--R (- 1536a c + 768a b c - 96a b )d e +--R + +--R 4 2 3 3 2 5 4 3 +--R (- 6912a b c + 3456a b c - 432a b )d e +--R + +--R 4 3 3 2 2 2 4 6 5 2 +--R (- 3456a c - 864a b c + 1080a b c - 162a b )d e +--R + +--R 3 3 2 3 2 5 7 6 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 4 3 +--R (- 4608a c + 2304a b c - 288a b )d e +--R + +--R 4 2 3 3 2 5 5 2 +--R (- 6912a b c + 3456a b c - 432a b )d e +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 5 2 +--R (- 4608a c + 2304a b c - 288a b )d e +--R + +--R 4 2 3 3 2 5 6 +--R (- 2304a b c + 1152a b c - 144a b )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 6 +--R (- 1536a c + 768a b c - 96a b )d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 4 3 3 6 4 2 3 2 2 4 5 +--R (- 128a b c - 96a b )e + (- 128a c + 128a b c + 168a b )d e +--R + +--R 3 2 2 3 5 2 4 +--R (- 192a b c - 192a b c - 36a b )d e +--R + +--R 3 3 2 2 2 4 6 3 3 +--R (256a c + 672a b c - 32a b c - 6b )d e +--R + +--R 2 3 3 2 5 4 2 2 3 4 2 5 +--R (- 960a b c - 128a b c - 4b c)d e + (576a b c + 48b c )d e +--R + +--R 4 3 3 6 +--R (- 384a b c - 32b c )d +--R * +--R 5 +--R x +--R + +--R 4 2 6 4 3 3 5 +--R - 512a b e + (- 896a b c + 608a b )d e +--R + +--R 4 2 3 2 2 4 2 4 +--R (- 384a c - 384a b c + 312a b )d e +--R + +--R 3 2 2 3 5 3 3 +--R (1984a b c + 96a b c - 212a b )d e +--R + +--R 3 3 2 2 2 4 6 4 2 +--R (- 1152a c - 1344a b c - 296a b c - 16b )d e +--R + +--R 2 3 3 2 5 5 +--R (576a b c + 1536a b c + 60b c)d e +--R + +--R 2 4 2 3 4 2 6 +--R (- 768a c - 960a b c - 32b c )d +--R * +--R 4 +--R x +--R + +--R 5 6 5 4 2 5 +--R - 512a b e + (- 512a c - 640a b )d e +--R + +--R 4 3 3 2 4 +--R (- 2688a b c + 2208a b )d e +--R + +--R 4 2 3 2 2 4 3 3 +--R (1792a c + 1152a b c - 272a b )d e +--R + +--R 3 2 2 3 5 4 2 +--R (- 1920a b c - 2048a b c - 424a b )d e +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 384a c + 3744a b c + 1176a b c + 6b )d e +--R + +--R 2 3 3 2 6 +--R (- 2688a b c - 608a b c )d +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 2 2 4 3 3 3 3 +--R - 1536a b d e + (- 1536a c + 1152a b )d e + 2304a b d e +--R + +--R 4 2 3 2 2 4 4 2 +--R (768a c - 4224a b c - 1680a b )d e +--R + +--R 3 2 2 3 5 5 +--R (2688a b c + 3264a b c + 72a b )d e +--R + +--R 3 3 2 2 2 6 +--R (- 1536a c - 1920a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 2 3 3 4 3 3 4 2 +--R - 1536a b d e + 3072a b d e + (- 3072a b c - 1536a b )d e +--R + +--R 4 2 3 2 2 4 5 3 2 6 +--R (1536a c + 2304a b c + 96a b )d e - 1536a b c d +--R * +--R x +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 6 3 2 2 3 5 5 +--R (192a b c + 16a b )e + (192a b c - 320a b c - 28a b )d e +--R + +--R 2 2 2 4 6 2 4 +--R (288a b c + 96a b c + 6b )d e +--R + +--R 2 3 3 2 5 3 3 +--R (- 704a b c - 224a b c + 36b c)d e +--R + +--R 2 4 2 3 4 2 4 2 4 3 3 5 +--R (640a c + 512a b c + 24b c )d e + (- 384a b c - 288b c )d e +--R + +--R 5 2 4 6 +--R (256a c + 192b c )d +--R * +--R 6 +--R x +--R + +--R 4 3 3 6 4 2 3 2 2 4 5 +--R (384a b c + 288a b )e + (384a c + 192a b c - 456a b )d e +--R + +--R 3 2 2 3 5 2 4 +--R (1152a b c - 384a b c + 24a b )d e +--R + +--R 3 3 2 2 2 4 6 3 3 +--R (- 1152a c - 1632a b c + 264a b c + 54b )d e +--R + +--R 2 3 3 2 5 4 2 +--R (2304a b c + 864a b c + 120b c)d e +--R + +--R 2 4 2 3 4 2 5 4 3 3 6 +--R (384a c - 2112a b c - 648b c )d e + (1536a b c + 384b c )d +--R * +--R 5 +--R x +--R + +--R 4 2 6 4 3 3 5 +--R 768a b e + (1920a b c - 480a b )d e +--R + +--R 4 2 3 2 2 4 2 4 +--R (1152a c + 576a b c - 1176a b )d e +--R + +--R 3 2 2 3 5 3 3 +--R (- 2880a b c - 1056a b c + 444a b )d e +--R + +--R 3 3 2 2 2 4 6 4 2 +--R (768a c + 3744a b c + 1440a b c + 114b )d e +--R + +--R 2 3 3 2 5 5 +--R (- 1344a b c - 4224a b c - 396b c)d e +--R + +--R 2 4 2 3 4 2 6 +--R (1536a c + 2688a b c + 192b c )d +--R * +--R 4 +--R x +--R + +--R 5 6 5 4 2 5 +--R 512a b e + (512a c + 1408a b )d e +--R + +--R 4 3 3 2 4 +--R (4224a b c - 2976a b )d e +--R + +--R 4 2 3 2 2 4 3 3 +--R (- 1792a c - 2688a b c - 496a b )d e +--R + +--R 3 2 2 3 5 4 2 +--R (3072a b c + 4544a b c + 1072a b )d e +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 384a c - 6048a b c - 2568a b c - 30b )d e +--R + +--R 2 3 3 2 6 +--R (4224a b c + 1376a b c )d +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 2 2 4 3 3 3 3 +--R 1536a b d e + (1536a c - 384a b )d e - 3840a b d e +--R + +--R 4 2 3 2 2 4 4 2 +--R (- 768a c + 5760a b c + 2448a b )d e +--R + +--R 3 2 2 3 5 5 +--R (- 3456a b c - 4416a b c - 120a b )d e +--R + +--R 3 3 2 2 2 6 +--R (1536a c + 2688a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 2 3 3 4 3 3 4 2 +--R 1536a b d e - 3072a b d e + (3072a b c + 1536a b )d e +--R + +--R 4 2 3 2 2 4 5 3 2 6 +--R (- 1536a c - 2304a b c - 96a b )d e + 1536a b c d +--R * +--R x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 3 2 2 3 7 2 3 4 6 +--R (384a c + 288a b )d e + (- 768a b c - 576a b )d e +--R + +--R 2 2 2 4 5 5 2 3 6 4 +--R (768a c + 960a b c + 288b )d e + (- 768a b c - 576b c)d e +--R + +--R 3 2 2 7 3 +--R (384a c + 288b c )d e +--R * +--R 5 +--R x +--R + +--R 3 3 7 3 2 2 4 6 +--R 1536a b d e + (1152a c - 2208a b )d e +--R + +--R 2 3 5 5 2 2 2 4 6 4 +--R (768a b c - 192a b )d e + (2304a c - 192a b c + 864b )d e +--R + +--R 2 3 7 3 3 2 2 8 2 +--R (- 768a b c - 1728b c)d e + (1152a c + 864b c )d e +--R * +--R 4 +--R x +--R + +--R 4 3 7 3 4 6 3 2 2 5 5 +--R 1536a d e + 1536a b d e + (4224a c - 6816a b )d e +--R + +--R 2 3 6 4 2 2 2 4 7 3 +--R (3840a b c + 2880a b )d e + (3840a c - 6336a b c + 864b )d e +--R + +--R 2 3 8 2 3 2 2 9 +--R (2304a b c - 1728b c)d e + (1152a c + 864b c )d e +--R * +--R 3 +--R x +--R + +--R 4 4 6 3 5 5 3 2 2 6 4 +--R 4608a d e - 4608a b d e + (9600a c - 4320a b )d e +--R + +--R 2 3 7 3 +--R (- 768a b c + 4032a b )d e +--R + +--R 2 2 2 4 8 2 2 3 9 +--R (5376a c - 8256a b c + 288b )d e + (3840a b c - 576b c)d e +--R + +--R 3 2 2 10 +--R (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 6 4 3 2 2 7 3 +--R 4608a d e - 7680a b d e + (9216a c + 1536a b )d e +--R + +--R 2 3 8 2 2 2 2 9 +--R (- 6144a b c + 1536a b )d e + (4608a c - 3072a b c)d e +--R + +--R 2 10 +--R 1536a b c d +--R * +--R x +--R + +--R 4 6 4 3 7 3 3 2 2 8 2 +--R 1536a d e - 3072a b d e + (3072a c + 1536a b )d e +--R + +--R 2 9 2 2 10 +--R - 3072a b c d e + 1536a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 3 7 2 2 4 4 6 +--R (- 576a b c - 48a b )d e + (1152a b c + 96a b )d e +--R + +--R 2 2 3 5 5 5 2 2 4 6 4 +--R (- 1152a b c - 672a b c - 48b )d e + (1152a b c + 96b c)d e +--R + +--R 3 3 2 7 3 +--R (- 576a b c - 48b c )d e +--R * +--R 6 +--R x +--R + +--R 4 3 2 3 7 3 2 3 4 6 +--R (- 1152a c - 864a b )d e + (576a b c + 1584a b )d e +--R + +--R 3 2 2 2 4 5 5 +--R (- 2304a c + 576a b c - 576a b )d e +--R + +--R 2 2 3 5 6 4 +--R (- 1152a b c - 288a b c - 144b )d e +--R + +--R 2 3 2 2 4 7 3 +--R (- 1152a c + 2592a b c + 288b c)d e +--R + +--R 3 3 2 8 2 +--R (- 1728a b c - 144b c )d e +--R * +--R 5 +--R x +--R + +--R 4 3 7 4 3 2 4 6 +--R - 2304a b d e + (- 3456a c + 2016a b )d e +--R + +--R 3 2 3 5 5 +--R (576a b c + 2736a b )d e +--R + +--R 3 2 2 2 4 6 4 +--R (- 6912a c - 576a b c - 2304a b )d e +--R + +--R 2 2 3 5 7 3 +--R (1152a b c + 3168a b c - 144b )d e +--R + +--R 2 3 2 2 4 8 2 +--R (- 3456a c + 864a b c + 288b c)d e +--R + +--R 3 3 2 9 +--R (- 1728a b c - 144b c )d e +--R * +--R 4 +--R x +--R + +--R 5 3 7 4 4 6 4 3 2 5 5 +--R - 1536a d e - 3840a b d e + (- 6528a c + 9696a b )d e +--R + +--R 3 2 3 6 4 +--R (- 4416a b c - 1776a b )d e +--R + +--R 3 2 2 2 4 7 3 +--R (- 8448a c + 6336a b c - 2496a b )d e +--R + +--R 2 2 3 5 8 2 +--R (- 1152a b c + 4512a b c - 48b )d e +--R + +--R 2 3 2 2 4 9 3 3 2 10 +--R (- 3456a c - 1440a b c + 96b c)d e + (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 5 4 6 4 5 5 4 3 2 6 4 +--R - 4608a d e + 2304a b d e + (- 10368a c + 8352a b )d e +--R + +--R 3 2 3 7 3 +--R (- 2304a b c - 5184a b )d e +--R + +--R 3 2 2 2 4 8 2 +--R (- 6912a c + 10944a b c - 864a b )d e +--R + +--R 2 2 3 9 2 3 2 2 10 +--R (- 4608a b c + 1728a b c)d e + (- 1152a c - 864a b c )d +--R * +--R 2 +--R x +--R + +--R 5 5 5 4 6 4 4 7 3 +--R - 4608a d e + 6912a b d e - 9216a c d e +--R + +--R 3 2 3 8 2 3 2 2 2 9 +--R (4608a b c - 2304a b )d e + (- 4608a c + 4608a b c)d e +--R + +--R 2 2 10 +--R - 2304a b c d +--R * +--R x +--R + +--R 5 6 4 4 7 3 4 3 2 8 2 +--R - 1536a d e + 3072a b d e + (- 3072a c - 1536a b )d e +--R + +--R 3 9 3 2 10 +--R 3072a b c d e - 1536a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R , +--R +--R 3 3 2 2 2 4 6 3 4 5 +--R (384a c + 96a b c - 120a b c + 18b )d e x +--R + +--R 3 2 2 3 5 3 4 +--R (1536a b c - 768a b c + 96a b )d e +--R + +--R 3 3 2 2 2 4 6 4 3 +--R (1152a c + 288a b c - 360a b c + 54b )d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 2 2 4 3 4 +--R (1536a c - 768a b c + 96a b )d e +--R + +--R 3 2 2 3 5 4 3 +--R (4608a b c - 2304a b c + 288a b )d e +--R + +--R 3 3 2 2 2 4 6 5 2 +--R (1152a c + 288a b c - 360a b c + 54b )d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 3 +--R (4608a c - 2304a b c + 288a b )d e +--R + +--R 3 2 2 3 5 5 2 +--R (4608a b c - 2304a b c + 288a b )d e +--R + +--R 3 3 2 2 2 4 6 6 +--R (384a c + 96a b c - 120a b c + 18b )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 2 2 4 5 2 +--R (4608a c - 2304a b c + 288a b )d e +--R + +--R 3 2 2 3 5 6 +--R (1536a b c - 768a b c + 96a b )d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 6 +--R (1536a c - 768a b c + 96a b )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 4 6 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 4 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e +--R + +--R 3 3 2 3 2 5 7 4 3 +--R (- 1728a b c + 720a b c - 36a b c - 9b )d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 3 2 5 3 4 +--R (- 2304a b c + 1152a b c - 144a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 3 +--R (- 3456a c - 864a b c + 1080a b c - 162a b )d e +--R + +--R 3 3 2 3 2 5 7 5 2 +--R (- 1728a b c + 720a b c - 36a b c - 9b )d e +--R * +--R 4 +--R x +--R + +--R 5 2 4 2 3 4 3 4 +--R (- 1536a c + 768a b c - 96a b )d e +--R + +--R 4 2 3 3 2 5 4 3 +--R (- 6912a b c + 3456a b c - 432a b )d e +--R + +--R 4 3 3 2 2 2 4 6 5 2 +--R (- 3456a c - 864a b c + 1080a b c - 162a b )d e +--R + +--R 3 3 2 3 2 5 7 6 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 4 3 +--R (- 4608a c + 2304a b c - 288a b )d e +--R + +--R 4 2 3 3 2 5 5 2 +--R (- 6912a b c + 3456a b c - 432a b )d e +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 5 2 +--R (- 4608a c + 2304a b c - 288a b )d e +--R + +--R 4 2 3 3 2 5 6 +--R (- 2304a b c + 1152a b c - 144a b )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 6 +--R (- 1536a c + 768a b c - 96a b )d e +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 4 3 3 6 4 2 3 2 2 4 5 +--R (- 64a b c - 48a b )e + (- 64a c + 64a b c + 84a b )d e +--R + +--R 3 2 2 3 5 2 4 +--R (- 96a b c - 96a b c - 18a b )d e +--R + +--R 3 3 2 2 2 4 6 3 3 +--R (128a c + 336a b c - 16a b c - 3b )d e +--R + +--R 2 3 3 2 5 4 2 2 3 4 2 5 +--R (- 480a b c - 64a b c - 2b c)d e + (288a b c + 24b c )d e +--R + +--R 4 3 3 6 +--R (- 192a b c - 16b c )d +--R * +--R 5 +--R x +--R + +--R 4 2 6 4 3 3 5 +--R - 256a b e + (- 448a b c + 304a b )d e +--R + +--R 4 2 3 2 2 4 2 4 +--R (- 192a c - 192a b c + 156a b )d e +--R + +--R 3 2 2 3 5 3 3 +--R (992a b c + 48a b c - 106a b )d e +--R + +--R 3 3 2 2 2 4 6 4 2 +--R (- 576a c - 672a b c - 148a b c - 8b )d e +--R + +--R 2 3 3 2 5 5 +--R (288a b c + 768a b c + 30b c)d e +--R + +--R 2 4 2 3 4 2 6 +--R (- 384a c - 480a b c - 16b c )d +--R * +--R 4 +--R x +--R + +--R 5 6 5 4 2 5 +--R - 256a b e + (- 256a c - 320a b )d e +--R + +--R 4 3 3 2 4 +--R (- 1344a b c + 1104a b )d e +--R + +--R 4 2 3 2 2 4 3 3 +--R (896a c + 576a b c - 136a b )d e +--R + +--R 3 2 2 3 5 4 2 +--R (- 960a b c - 1024a b c - 212a b )d e +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 192a c + 1872a b c + 588a b c + 3b )d e +--R + +--R 2 3 3 2 6 +--R (- 1344a b c - 304a b c )d +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 2 2 4 3 3 3 3 +--R - 768a b d e + (- 768a c + 576a b )d e + 1152a b d e +--R + +--R 4 2 3 2 2 4 4 2 +--R (384a c - 2112a b c - 840a b )d e +--R + +--R 3 2 2 3 5 5 3 3 2 2 2 6 +--R (1344a b c + 1632a b c + 36a b )d e + (- 768a c - 960a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 2 3 3 4 3 3 4 2 +--R - 768a b d e + 1536a b d e + (- 1536a b c - 768a b )d e +--R + +--R 4 2 3 2 2 4 5 3 2 6 +--R (768a c + 1152a b c + 48a b )d e - 768a b c d +--R * +--R x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 3 2 2 4 6 3 2 2 3 5 5 +--R (96a b c + 8a b )e + (96a b c - 160a b c - 14a b )d e +--R + +--R 2 2 2 4 6 2 4 +--R (144a b c + 48a b c + 3b )d e +--R + +--R 2 3 3 2 5 3 3 +--R (- 352a b c - 112a b c + 18b c)d e +--R + +--R 2 4 2 3 4 2 4 2 4 3 3 5 +--R (320a c + 256a b c + 12b c )d e + (- 192a b c - 144b c )d e +--R + +--R 5 2 4 6 +--R (128a c + 96b c )d +--R * +--R 6 +--R x +--R + +--R 4 3 3 6 4 2 3 2 2 4 5 +--R (192a b c + 144a b )e + (192a c + 96a b c - 228a b )d e +--R + +--R 3 2 2 3 5 2 4 +--R (576a b c - 192a b c + 12a b )d e +--R + +--R 3 3 2 2 2 4 6 3 3 +--R (- 576a c - 816a b c + 132a b c + 27b )d e +--R + +--R 2 3 3 2 5 4 2 +--R (1152a b c + 432a b c + 60b c)d e +--R + +--R 2 4 2 3 4 2 5 4 3 3 6 +--R (192a c - 1056a b c - 324b c )d e + (768a b c + 192b c )d +--R * +--R 5 +--R x +--R + +--R 4 2 6 4 3 3 5 +--R 384a b e + (960a b c - 240a b )d e +--R + +--R 4 2 3 2 2 4 2 4 +--R (576a c + 288a b c - 588a b )d e +--R + +--R 3 2 2 3 5 3 3 +--R (- 1440a b c - 528a b c + 222a b )d e +--R + +--R 3 3 2 2 2 4 6 4 2 +--R (384a c + 1872a b c + 720a b c + 57b )d e +--R + +--R 2 3 3 2 5 5 +--R (- 672a b c - 2112a b c - 198b c)d e +--R + +--R 2 4 2 3 4 2 6 +--R (768a c + 1344a b c + 96b c )d +--R * +--R 4 +--R x +--R + +--R 5 6 5 4 2 5 4 3 3 2 4 +--R 256a b e + (256a c + 704a b )d e + (2112a b c - 1488a b )d e +--R + +--R 4 2 3 2 2 4 3 3 +--R (- 896a c - 1344a b c - 248a b )d e +--R + +--R 3 2 2 3 5 4 2 +--R (1536a b c + 2272a b c + 536a b )d e +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 192a c - 3024a b c - 1284a b c - 15b )d e +--R + +--R 2 3 3 2 6 +--R (2112a b c + 688a b c )d +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 2 2 4 3 3 3 3 +--R 768a b d e + (768a c - 192a b )d e - 1920a b d e +--R + +--R 4 2 3 2 2 4 4 2 +--R (- 384a c + 2880a b c + 1224a b )d e +--R + +--R 3 2 2 3 5 5 3 3 2 2 2 6 +--R (- 1728a b c - 2208a b c - 60a b )d e + (768a c + 1344a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 2 3 3 4 3 3 4 2 +--R 768a b d e - 1536a b d e + (1536a b c + 768a b )d e +--R + +--R 4 2 3 2 2 4 5 3 2 6 +--R (- 768a c - 1152a b c - 48a b )d e + 768a b c d +--R * +--R x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / +--R 3 2 2 3 7 2 3 4 6 +--R (192a c + 144a b )d e + (- 384a b c - 288a b )d e +--R + +--R 2 2 2 4 5 5 2 3 6 4 +--R (384a c + 480a b c + 144b )d e + (- 384a b c - 288b c)d e +--R + +--R 3 2 2 7 3 +--R (192a c + 144b c )d e +--R * +--R 5 +--R x +--R + +--R 3 3 7 3 2 2 4 6 2 3 5 5 +--R 768a b d e + (576a c - 1104a b )d e + (384a b c - 96a b )d e +--R + +--R 2 2 2 4 6 4 2 3 7 3 +--R (1152a c - 96a b c + 432b )d e + (- 384a b c - 864b c)d e +--R + +--R 3 2 2 8 2 +--R (576a c + 432b c )d e +--R * +--R 4 +--R x +--R + +--R 4 3 7 3 4 6 3 2 2 5 5 +--R 768a d e + 768a b d e + (2112a c - 3408a b )d e +--R + +--R 2 3 6 4 2 2 2 4 7 3 +--R (1920a b c + 1440a b )d e + (1920a c - 3168a b c + 432b )d e +--R + +--R 2 3 8 2 3 2 2 9 +--R (1152a b c - 864b c)d e + (576a c + 432b c )d e +--R * +--R 3 +--R x +--R + +--R 4 4 6 3 5 5 3 2 2 6 4 +--R 2304a d e - 2304a b d e + (4800a c - 2160a b )d e +--R + +--R 2 3 7 3 +--R (- 384a b c + 2016a b )d e +--R + +--R 2 2 2 4 8 2 2 3 9 +--R (2688a c - 4128a b c + 144b )d e + (1920a b c - 288b c)d e +--R + +--R 3 2 2 10 +--R (192a c + 144b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 6 4 3 2 2 7 3 +--R 2304a d e - 3840a b d e + (4608a c + 768a b )d e +--R + +--R 2 3 8 2 2 2 2 9 +--R (- 3072a b c + 768a b )d e + (2304a c - 1536a b c)d e +--R + +--R 2 10 +--R 768a b c d +--R * +--R x +--R + +--R 4 6 4 3 7 3 3 2 2 8 2 2 9 +--R 768a d e - 1536a b d e + (1536a c + 768a b )d e - 1536a b c d e +--R + +--R 2 2 10 +--R 768a c d +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 2 3 3 7 2 2 4 4 6 +--R (- 288a b c - 24a b )d e + (576a b c + 48a b )d e +--R + +--R 2 2 3 5 5 5 2 2 4 6 4 +--R (- 576a b c - 336a b c - 24b )d e + (576a b c + 48b c)d e +--R + +--R 3 3 2 7 3 +--R (- 288a b c - 24b c )d e +--R * +--R 6 +--R x +--R + +--R 4 3 2 3 7 3 2 3 4 6 +--R (- 576a c - 432a b )d e + (288a b c + 792a b )d e +--R + +--R 3 2 2 2 4 5 5 +--R (- 1152a c + 288a b c - 288a b )d e +--R + +--R 2 2 3 5 6 4 +--R (- 576a b c - 144a b c - 72b )d e +--R + +--R 2 3 2 2 4 7 3 +--R (- 576a c + 1296a b c + 144b c)d e +--R + +--R 3 3 2 8 2 +--R (- 864a b c - 72b c )d e +--R * +--R 5 +--R x +--R + +--R 4 3 7 4 3 2 4 6 +--R - 1152a b d e + (- 1728a c + 1008a b )d e +--R + +--R 3 2 3 5 5 +--R (288a b c + 1368a b )d e +--R + +--R 3 2 2 2 4 6 4 +--R (- 3456a c - 288a b c - 1152a b )d e +--R + +--R 2 2 3 5 7 3 +--R (576a b c + 1584a b c - 72b )d e +--R + +--R 2 3 2 2 4 8 2 3 3 2 9 +--R (- 1728a c + 432a b c + 144b c)d e + (- 864a b c - 72b c )d e +--R * +--R 4 +--R x +--R + +--R 5 3 7 4 4 6 4 3 2 5 5 +--R - 768a d e - 1920a b d e + (- 3264a c + 4848a b )d e +--R + +--R 3 2 3 6 4 +--R (- 2208a b c - 888a b )d e +--R + +--R 3 2 2 2 4 7 3 +--R (- 4224a c + 3168a b c - 1248a b )d e +--R + +--R 2 2 3 5 8 2 +--R (- 576a b c + 2256a b c - 24b )d e +--R + +--R 2 3 2 2 4 9 3 3 2 10 +--R (- 1728a c - 720a b c + 48b c)d e + (- 288a b c - 24b c )d +--R * +--R 3 +--R x +--R + +--R 5 4 6 4 5 5 4 3 2 6 4 +--R - 2304a d e + 1152a b d e + (- 5184a c + 4176a b )d e +--R + +--R 3 2 3 7 3 +--R (- 1152a b c - 2592a b )d e +--R + +--R 3 2 2 2 4 8 2 +--R (- 3456a c + 5472a b c - 432a b )d e +--R + +--R 2 2 3 9 2 3 2 2 10 +--R (- 2304a b c + 864a b c)d e + (- 576a c - 432a b c )d +--R * +--R 2 +--R x +--R + +--R 5 5 5 4 6 4 4 7 3 +--R - 2304a d e + 3456a b d e - 4608a c d e +--R + +--R 3 2 3 8 2 3 2 2 2 9 +--R (2304a b c - 1152a b )d e + (- 2304a c + 2304a b c)d e +--R + +--R 2 2 10 +--R - 1152a b c d +--R * +--R x +--R + +--R 5 6 4 4 7 3 4 3 2 8 2 +--R - 768a d e + 1536a b d e + (- 1536a c - 768a b )d e +--R + +--R 3 9 3 2 10 +--R 1536a b c d e - 768a c d +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 457 + +--S 458 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 4 6 3 2 +--R (384a c + 96a b c - 120a b c + 18b )d e x +--R + +--R 3 2 2 3 5 3 +--R (1536a b c - 768a b c + 96a b )d e x +--R + +--R 4 2 3 2 2 4 3 +--R (1536a c - 768a b c + 96a b )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e x +--R + +--R 4 2 3 3 2 5 3 +--R (- 2304a b c + 1152a b c - 144a b )d e x +--R + +--R 5 2 4 2 3 4 3 +--R (- 1536a c + 768a b c - 96a b )d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R 3 3 2 2 2 4 6 3 2 +--R (384a c + 96a b c - 120a b c + 18b )d e x +--R + +--R 3 2 2 3 5 3 +--R (1536a b c - 768a b c + 96a b )d e x +--R + +--R 4 2 3 2 2 4 3 +--R (1536a c - 768a b c + 96a b )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e x +--R + +--R 4 2 3 3 2 5 3 +--R (- 2304a b c + 1152a b c - 144a b )d e x +--R + +--R 5 2 4 2 3 4 3 +--R (- 1536a c + 768a b c - 96a b )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 4 3 3 3 4 2 3 2 2 4 2 +--R (- 128a b c - 96a b )e + (- 128a c + 128a b c + 168a b )d e +--R + +--R 3 2 2 3 5 2 3 3 2 2 2 3 +--R (- 192a b c - 192a b c - 36a b )d e + (256a c + 192a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 3 3 2 +--R - 512a b e + (- 512a b c + 896a b )d e +--R + +--R 3 2 2 4 2 3 2 3 +--R (- 768a b c - 192a b )d e + 1024a b c d +--R * +--R x +--R + +--R 5 3 5 4 2 2 4 3 3 2 +--R - 512a b e + (- 512a c + 896a b )d e + (- 768a b c - 192a b )d e +--R + +--R 4 2 3 +--R 1024a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 3 3 2 2 3 5 2 +--R (192a b c + 16a b )e + (192a b c - 320a b c - 28a b )d e +--R + +--R 2 2 2 4 6 2 2 3 3 2 3 +--R (288a b c + 96a b c + 6b )d e + (- 384a b c - 32a b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 3 4 2 3 2 2 4 2 +--R (384a b c + 288a b )e + (384a c - 384a b c - 504a b )d e +--R + +--R 3 2 2 3 5 2 3 3 2 2 2 3 +--R (576a b c + 576a b c + 108a b )d e + (- 768a c - 576a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 3 3 2 3 2 2 4 2 +--R 768a b e + (768a b c - 1344a b )d e + (1152a b c + 288a b )d e +--R + +--R 3 2 3 +--R - 1536a b c d +--R * +--R x +--R + +--R 5 3 5 4 2 2 4 3 3 2 +--R 512a b e + (512a c - 896a b )d e + (768a b c + 192a b )d e +--R + +--R 4 2 3 +--R - 1024a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 3 2 2 3 4 2 3 4 3 +--R (384a c + 288a b )d e + (- 768a b c - 576a b )d e +--R + +--R 2 2 2 4 5 2 2 3 6 +--R (768a c + 960a b c + 288b )d e + (- 768a b c - 576b c)d e +--R + +--R 3 2 2 7 +--R (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 4 2 2 4 3 2 3 5 2 +--R 1536a b d e - 3072a b d e + (3072a b c + 1536a b )d e +--R + +--R 2 6 2 7 +--R - 3072a b c d e + 1536a b c d +--R * +--R x +--R + +--R 4 3 4 3 4 3 3 2 2 5 2 2 6 +--R 1536a d e - 3072a b d e + (3072a c + 1536a b )d e - 3072a b c d e +--R + +--R 2 2 7 +--R 1536a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 3 4 2 2 4 4 3 +--R (- 576a b c - 48a b )d e + (1152a b c + 96a b )d e +--R + +--R 2 2 3 5 5 2 2 2 4 6 +--R (- 1152a b c - 672a b c - 48b )d e + (1152a b c + 96b c)d e +--R + +--R 3 3 2 7 +--R (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 3 2 3 4 3 +--R (- 1152a c - 864a b )d e + (2304a b c + 1728a b )d e +--R + +--R 3 2 2 2 4 5 2 +--R (- 2304a c - 2880a b c - 864a b )d e +--R + +--R 2 2 3 6 2 3 2 2 7 +--R (2304a b c + 1728a b c)d e + (- 1152a c - 864a b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 4 3 2 4 3 3 2 3 5 2 +--R - 2304a b d e + 4608a b d e + (- 4608a b c - 2304a b )d e +--R + +--R 2 2 6 2 2 7 +--R 4608a b c d e - 2304a b c d +--R * +--R x +--R + +--R 5 3 4 4 4 3 4 3 2 5 2 +--R - 1536a d e + 3072a b d e + (- 3072a c - 1536a b )d e +--R + +--R 3 6 3 2 7 +--R 3072a b c d e - 1536a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 458 + +--S 459 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 4 6 3 2 +--R (384a c + 96a b c - 120a b c + 18b )d e x +--R + +--R 3 2 2 3 5 3 +--R (1536a b c - 768a b c + 96a b )d e x +--R + +--R 4 2 3 2 2 4 3 +--R (1536a c - 768a b c + 96a b )d e +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 576a b c + 240a b c - 12a b c - 3b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (- 1152a c - 288a b c + 360a b c - 54a b )d e x +--R + +--R 4 2 3 3 2 5 3 +--R (- 2304a b c + 1152a b c - 144a b )d e x +--R + +--R 5 2 4 2 3 4 3 +--R (- 1536a c + 768a b c - 96a b )d e +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 2 2 4 6 3 2 +--R (768a c + 192a b c - 240a b c + 36b )d e x +--R + +--R 3 2 2 3 5 3 +--R (3072a b c - 1536a b c + 192a b )d e x +--R + +--R 4 2 3 2 2 4 3 +--R (3072a c - 1536a b c + 192a b )d e +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 1152a b c + 480a b c - 24a b c - 6b )d e x +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (- 2304a c - 576a b c + 720a b c - 108a b )d e x +--R + +--R 4 2 3 3 2 5 3 +--R (- 4608a b c + 2304a b c - 288a b )d e x +--R + +--R 5 2 4 2 3 4 3 +--R (- 3072a c + 1536a b c - 192a b )d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 4 3 3 3 4 2 3 2 2 4 2 +--R (- 128a b c - 96a b )e + (- 128a c + 128a b c + 168a b )d e +--R + +--R 3 2 2 3 5 2 3 3 2 2 2 3 +--R (- 192a b c - 192a b c - 36a b )d e + (256a c + 192a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 3 3 2 +--R - 512a b e + (- 512a b c + 896a b )d e +--R + +--R 3 2 2 4 2 3 2 3 +--R (- 768a b c - 192a b )d e + 1024a b c d +--R * +--R x +--R + +--R 5 3 5 4 2 2 4 3 3 2 +--R - 512a b e + (- 512a c + 896a b )d e + (- 768a b c - 192a b )d e +--R + +--R 4 2 3 +--R 1024a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 | 2 2 | 2 +--R \|- a e + b d e - c d \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 3 3 2 2 3 5 2 +--R (192a b c + 16a b )e + (192a b c - 320a b c - 28a b )d e +--R + +--R 2 2 2 4 6 2 2 3 3 2 3 +--R (288a b c + 96a b c + 6b )d e + (- 384a b c - 32a b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 3 4 2 3 2 2 4 2 +--R (384a b c + 288a b )e + (384a c - 384a b c - 504a b )d e +--R + +--R 3 2 2 3 5 2 3 3 2 2 2 3 +--R (576a b c + 576a b c + 108a b )d e + (- 768a c - 576a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 3 3 2 3 2 2 4 2 +--R 768a b e + (768a b c - 1344a b )d e + (1152a b c + 288a b )d e +--R + +--R 3 2 3 +--R - 1536a b c d +--R * +--R x +--R + +--R 5 3 5 4 2 2 4 3 3 2 +--R 512a b e + (512a c - 896a b )d e + (768a b c + 192a b )d e +--R + +--R 4 2 3 +--R - 1024a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d +--R / +--R 3 2 2 3 4 2 3 4 3 +--R (384a c + 288a b )d e + (- 768a b c - 576a b )d e +--R + +--R 2 2 2 4 5 2 2 3 6 +--R (768a c + 960a b c + 288b )d e + (- 768a b c - 576b c)d e +--R + +--R 3 2 2 7 +--R (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 4 2 2 4 3 2 3 5 2 +--R 1536a b d e - 3072a b d e + (3072a b c + 1536a b )d e +--R + +--R 2 6 2 7 +--R - 3072a b c d e + 1536a b c d +--R * +--R x +--R + +--R 4 3 4 3 4 3 3 2 2 5 2 2 6 +--R 1536a d e - 3072a b d e + (3072a c + 1536a b )d e - 3072a b c d e +--R + +--R 2 2 7 +--R 1536a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 +-+ | 2 2 | 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 3 4 2 2 4 4 3 +--R (- 576a b c - 48a b )d e + (1152a b c + 96a b )d e +--R + +--R 2 2 3 5 5 2 2 2 4 6 +--R (- 1152a b c - 672a b c - 48b )d e + (1152a b c + 96b c)d e +--R + +--R 3 3 2 7 +--R (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 3 2 3 4 3 +--R (- 1152a c - 864a b )d e + (2304a b c + 1728a b )d e +--R + +--R 3 2 2 2 4 5 2 +--R (- 2304a c - 2880a b c - 864a b )d e +--R + +--R 2 2 3 6 2 3 2 2 7 +--R (2304a b c + 1728a b c)d e + (- 1152a c - 864a b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 4 3 2 4 3 3 2 3 5 2 +--R - 2304a b d e + 4608a b d e + (- 4608a b c - 2304a b )d e +--R + +--R 2 2 6 2 2 7 +--R 4608a b c d e - 2304a b c d +--R * +--R x +--R + +--R 5 3 4 4 4 3 4 3 2 5 2 +--R - 1536a d e + 3072a b d e + (- 3072a c - 1536a b )d e +--R + +--R 3 6 3 2 7 +--R 3072a b c d e - 1536a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R Type: Expression(Integer) +--E 460 + +--S 461 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 461 + +)clear all + +--S 462 of 845 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 462 + +--S 463 of 845 +r0:=5/128*(b^2-4*a*c)^2*e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (c*d^2-b*d*e+a*e^2)^(7/2)+1/24*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3)+_ + 1/96*(2*c*d-b*e)*(8*c^2*d^2-5*b^2*e^2-4*c*e*(2*b*d-7*a*e))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^2)+_ + 1/192*(32*c^4*d^4-15*b^4*e^4-16*c^3*d^2*e*(4*b*d-9*a*e)+_ + 20*b^2*c*e^3*(b*d+5*a*e)+4*c^2*e^2*(3*b^2*d^2-36*a*b*d*e-32*a^2*e^2))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)^3*(d+e*x))-1/4*(2*c*d+b*e+_ + 4*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^4) +--R +--R +--R (2) +--R 2 2 3 5 6 +--R (240a b c - 120a b c + 15b )e +--R + +--R 2 3 2 2 4 5 +--R (- 480a c + 240a b c - 30b c)d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 5 +--R (960a b c - 480a b c + 60b )d e +--R + +--R 2 3 2 2 4 2 4 +--R (- 1920a c + 960a b c - 120b c)d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 4 +--R (1440a b c - 720a b c + 90b )d e +--R + +--R 2 3 2 2 4 3 3 +--R (- 2880a c + 1440a b c - 180b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 5 3 3 +--R (960a b c - 480a b c + 60b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (- 1920a c + 960a b c - 120b c)d e +--R * +--R x +--R + +--R 2 2 3 5 4 2 2 3 2 2 4 5 +--R (240a b c - 120a b c + 15b )d e + (- 480a c + 240a b c - 30b c)d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 4 5 2 3 4 +--R (- 256a c + 200a b c - 30b )e + (- 288a b c + 40b c)d e +--R + +--R 3 2 2 2 3 3 3 2 4 4 +--R (288a c + 24b c )d e - 128b c d e + 64c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (- 112a b c + 20a b )e + (- 544a c + 704a b c - 110b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 +--R (- 1296a b c + 148b c)d e + (1152a c + 160b c )d e +--R + +--R 3 4 4 5 +--R - 544b c d e + 256c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 5 2 3 4 +--R (- 256a c - 16a b )e + (608a b c + 72a b )d e +--R + +--R 2 2 2 4 2 3 2 3 3 2 +--R (- 1152a c - 120a b c - 146b )d e + (64a b c + 528b c)d e +--R + +--R 3 2 2 4 3 5 +--R (544a c - 728b c )d e + 256b c d +--R * +--R x +--R + +--R 3 5 3 2 2 4 2 3 2 3 +--R - 96a b e + (- 64a c + 272a b )d e + (- 144a b c - 236a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (- 288a c + 528a b c + 30b )d e + (- 368a b c - 60b c)d e +--R + +--R 3 5 +--R 256a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 3 10 2 9 2 2 2 8 +--R 384a e - 1152a b d e + (1152a c + 1152a b )d e +--R + +--R 3 3 7 2 2 4 6 2 5 5 +--R (- 2304a b c - 384b )d e + (1152a c + 1152b c)d e - 1152b c d e +--R + +--R 3 6 4 +--R 384c d e +--R * +--R 4 +--R x +--R + +--R 3 9 2 2 8 2 2 3 7 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 4 6 2 2 5 5 +--R (- 9216a b c - 1536b )d e + (4608a c + 4608b c)d e +--R + +--R 2 6 4 3 7 3 +--R - 4608b c d e + 1536c d e +--R * +--R 3 +--R x +--R + +--R 3 2 8 2 3 7 2 2 4 6 +--R 2304a d e - 6912a b d e + (6912a c + 6912a b )d e +--R + +--R 3 5 5 2 2 6 4 +--R (- 13824a b c - 2304b )d e + (6912a c + 6912b c)d e +--R + +--R 2 7 3 3 8 2 +--R - 6912b c d e + 2304c d e +--R * +--R 2 +--R x +--R + +--R 3 3 7 2 4 6 2 2 5 5 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 6 4 2 2 7 3 +--R (- 9216a b c - 1536b )d e + (4608a c + 4608b c)d e +--R + +--R 2 8 2 3 9 +--R - 4608b c d e + 1536c d e +--R * +--R x +--R + +--R 3 4 6 2 5 5 2 2 6 4 +--R 384a d e - 1152a b d e + (1152a c + 1152a b )d e +--R + +--R 3 7 3 2 2 8 2 2 9 +--R (- 2304a b c - 384b )d e + (1152a c + 1152b c)d e - 1152b c d e +--R + +--R 3 10 +--R 384c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 463 + +--S 464 of 845 +--a0:=integrate(t0,x) +--E 464 + +--S 465 of 845 +--m0:=a0-r0 +--E 465 + +--S 466 of 845 +--d0:=D(m0,x) +--E 466 + +)clear all + +--S 467 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R 2c e x + (3b c e + 6c d e )x + ((2a c + b )e + 9b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (6a c + 3b )d e + 9b c d e + 2c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R (3a b d e + (6a c + 3b )d e + 3b c d )x + (3a b d e + (2a c + b )d )x +--R + +--R 3 +--R a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 845 +r0:=1/1024*(b^2-4*a*c)*e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*_ + (b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+3/2240*(2*c*d-b*e)*(16*c^2*d^2+_ + 21*b^2*e^2-4*c*e*(4*b*d+17*a*e))*(a+b*x+c*x^2)^(5/2)/c^3+3/56*(2*c*d-_ + b*e)*(d+e*x)^2*(a+b*x+c*x^2)^(5/2)/c+1/4*(d+e*x)^3*(a+b*x+c*x^2)^(5/2)+_ + 1/224*e*(5*b^2*d*e-36*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+9*b^2*e^2-_ + 4*c*e*(2*b*d+7*a*e))*x)*(a+b*x+c*x^2)^(5/2)/c^2+3/16384*(b^2-4*a*c)^3*_ + e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)-3/8192*(b^2-4*a*c)^2*e*(32*c^2*_ + d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 4 4 3 2 3 2 4 2 6 8 3 +--R (26880a c - 80640a b c + 50400a b c - 11760a b c + 945b )e +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (215040a b c - 161280a b c + 40320a b c - 3360b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (- 215040a c + 161280a b c - 40320a b c + 3360b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 7 3 7 6 3 7 2 6 +--R 143360c e x + (256000b c e + 491520c d e )x +--R + +--R 6 2 5 3 6 2 7 2 5 +--R ((215040a c + 104960b c )e + 901120b c d e + 573440c d e)x +--R + +--R 5 3 4 3 6 2 5 2 +--R (144384a b c - 768b c )e + (786432a c + 385024b c )d e +--R + +--R 6 2 7 3 +--R 1089536b c d e + 229376c d +--R * +--R 4 +--R x +--R + +--R 2 5 2 4 4 3 3 +--R (17920a c - 6912a b c + 864b c )e +--R + +--R 5 3 4 2 6 2 5 2 +--R (569344a b c - 3072b c )d e + (1003520a c + 494592b c )d e +--R + +--R 6 3 +--R 458752b c d +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 3 +--R (- 22272a b c + 9088a b c - 1008b c )e +--R + +--R 2 5 2 4 4 3 2 +--R (98304a c - 30720a b c + 3584b c )d e +--R + +--R 5 3 4 2 6 2 5 3 +--R (817152a b c - 3584b c )d e + (458752a c + 229376b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (- 26880a c + 38208a b c - 12656a b c + 1260b c)e +--R + +--R 2 4 3 3 5 2 2 +--R (- 116736a b c + 43008a b c - 4480b c )d e +--R + +--R 2 5 2 4 4 3 2 5 3 +--R (215040a c - 43008a b c + 4480b c )d e + 458752a b c d +--R * +--R x +--R + +--R 3 3 2 3 2 5 7 3 +--R (84864a b c - 75488a b c + 21000a b c - 1890b )e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 196608a c + 236544a b c - 71680a b c + 6720b c)d e +--R + +--R 2 4 3 3 5 2 2 2 5 3 +--R (- 236544a b c + 71680a b c - 6720b c )d e + 229376a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 573440c \|c +--R Type: Expression(Integer) +--E 468 + +--S 469 of 845 +--a0:=integrate(t0,x) +--E 469 + +--S 470 of 845 +--m0:=a0-r0 +--E 470 + +--S 471 of 845 +--d0:=D(m0,x) +--E 471 + +)clear all + +--S 472 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x +--R + +--R 2 +--R a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 845 +r0:=1/96*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3+_ + 1/210*(24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*(a+b*x+c*x^2)^(5/2)/c^2+_ + 2/7*(d+e*x)^2*(a+b*x+c*x^2)^(5/2)+1/21*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(5/2)/c+1/512*(b^2-4*a*c)^3*e*(2*c*d-b*e)*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)-1/256*(b^2-4*a*c)^2*e*_ + (2*c*d-b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 3 3 2 3 2 5 7 2 +--R (6720a b c - 5040a b c + 1260a b c - 105b )e +--R + +--R 3 4 2 2 3 4 2 6 +--R (- 13440a c + 10080a b c - 2520a b c + 210b c)d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 6 2 6 5 2 6 5 +--R 15360c e x + (28160b c e + 35840c d e)x +--R + +--R 5 2 4 2 5 6 2 4 +--R ((24576a c + 12032b c )e + 68096b c d e + 21504c d )x +--R + +--R 4 3 3 2 5 2 4 +--R (17792a b c - 96b c )e + (62720a c + 30912b c )d e +--R + +--R 5 2 +--R 43008b c d +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 4 2 2 4 3 3 +--R (3072a c - 960a b c + 112b c )e + (51072a b c - 224b c )d e +--R + +--R 5 2 4 2 +--R (43008a c + 21504b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 5 2 +--R (- 3648a b c + 1344a b c - 140b c)e +--R + +--R 2 4 2 3 4 2 4 2 +--R (13440a c - 2688a b c + 280b c )d e + 43008a b c d +--R * +--R x +--R + +--R 3 3 2 2 2 4 6 2 +--R (- 6144a c + 7392a b c - 2240a b c + 210b )e +--R + +--R 2 3 3 2 5 2 4 2 +--R (- 14784a b c + 4480a b c - 420b c)d e + 21504a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 53760c \|c +--R Type: Expression(Integer) +--E 473 + +--S 474 of 845 +--a0:=integrate(t0,x) +--E 474 + +--S 475 of 845 +--m0:=a0-r0 +--E 475 + +--S 476 of 845 +--d0:=D(m0,x) +--E 476 + +)clear all + +--S 477 of 845 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 845 +r0:=1/96*(b^2-4*a*c)*e*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^2+1/30*(2*c*d-b*e)*_ + (a+b*x+c*x^2)^(5/2)/c+1/3*(d+e*x)*(a+b*x+c*x^2)^(5/2)+1/512*(b^2-4*a*c)^3*_ + e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-1/256*(b^2-_ + 4*a*c)^2*e*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 2c x + b +--R (- 960a c + 720a b c - 180a b c + 15b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 5 5 4 5 4 +--R 2560c e x + (4864b c e + 3072c d)x +--R + +--R 4 2 3 4 3 +--R ((4480a c + 2208b c )e + 6144b c d)x +--R + +--R 3 3 2 4 2 3 2 +--R ((3648a b c - 16b c )e + (6144a c + 3072b c )d)x +--R + +--R 2 3 2 2 4 3 +--R ((960a c - 192a b c + 20b c)e + 6144a b c d)x +--R + +--R 2 2 3 5 2 3 +--R (- 1056a b c + 320a b c - 30b )e + 3072a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 478 + +--S 479 of 845 +--a0:=integrate(t0,x) +--E 479 + +--S 480 of 845 +--m0:=a0-r0 +--E 480 + +--S 481 of 845 +--d0:=D(m0,x) +--E 481 + +)clear all + +--S 482 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (1) (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 845 +r0:=2/5*(a+b*x+c*x^2)^(5/2) +--R +--R +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (2c x + 4b c x + (4a c + 2b )x + 4a b x + 2a )\|c x + b x + a +--R (2) ------------------------------------------------------------------ +--R 5 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 3 5 2 9 +--R (- 160a b c - 80a b c - 2b c )x +--R + +--R 3 4 2 2 3 4 2 6 8 +--R (- 320a c - 1120a b c - 260a b c - 4b c)x +--R + +--R 3 3 2 3 2 5 7 7 +--R (- 2880a b c - 2720a b c - 284a b c - 2b )x +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (- 1920a c - 8320a b c - 2760a b c - 104a b )x +--R + +--R 4 2 3 3 2 5 5 +--R (- 9760a b c - 9680a b c - 1002a b )x +--R + +--R 5 2 4 2 3 4 4 5 4 3 3 +--R (- 3840a c - 15360a b c - 3920a b )x + (- 10880a b c - 7520a b )x +--R + +--R 6 5 2 2 6 +--R (- 2560a c - 7040a b )x - 2560a b x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 5 2 4 4 3 10 2 4 3 3 5 2 9 +--R (64a c + 160a b c + 20b c )x + (960a b c + 800a b c + 60b c )x +--R + +--R 3 4 2 2 3 4 2 6 8 +--R (960a c + 4320a b c + 1500a b c + 60b c)x +--R + +--R 3 3 2 3 2 5 7 7 +--R (7040a b c + 8320a b c + 1240a b c + 20b )x +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (3520a c + 17760a b c + 7260a b c + 380a b )x +--R + +--R 4 2 3 3 2 5 5 +--R (16160a b c + 18640a b c + 2362a b )x +--R + +--R 5 2 4 2 3 4 4 5 4 3 3 +--R (5120a c + 23360a b c + 6960a b )x + (13440a b c + 10720a b )x +--R + +--R 6 5 2 2 6 +--R (2560a c + 8320a b )x + 2560a b x +--R * +--R +-+ +--R \|a +--R / +--R 2 2 2 4 4 2 3 3 +--R (160a c + 400a b c + 50b )x + (1920a b c + 800a b )x +--R + +--R 3 2 2 2 3 4 +--R (1920a c + 3360a b )x + 5120a b x + 2560a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 3 5 5 3 2 2 2 4 4 +--R (- 400a b c - 200a b c - 5b )x + (- 800a c - 2000a b c - 250a b )x +--R + +--R 3 2 3 3 4 3 2 2 4 5 +--R (- 4800a b c - 2000a b )x + (- 3200a c - 5600a b )x - 6400a b x - 2560a +--R Type: Union(Expression(Integer),...) +--E 484 + +--S 485 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 4 2 3 4 4 5 4 3 3 +--R (64a c + 160a b c + 20a b )x + (768a b c + 320a b )x +--R + +--R 6 5 2 2 6 7 +--R (768a c + 1344a b )x + 2048a b x + 1024a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 4 2 3 3 2 5 5 +--R (- 160a b c - 80a b c - 2a b )x +--R + +--R 5 2 4 2 3 4 4 5 4 3 3 +--R (- 320a c - 800a b c - 100a b )x + (- 1920a b c - 800a b )x +--R + +--R 6 5 2 2 6 7 +--R (- 1280a c - 2240a b )x - 2560a b x - 1024a +--R * +--R +-+ +--R \|a +--R / +--R 2 2 2 4 4 2 3 3 +--R (160a c + 400a b c + 50b )x + (1920a b c + 800a b )x +--R + +--R 3 2 2 2 3 4 +--R (1920a c + 3360a b )x + 5120a b x + 2560a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 3 5 5 3 2 2 2 4 4 +--R (- 400a b c - 200a b c - 5b )x + (- 800a c - 2000a b c - 250a b )x +--R + +--R 3 2 3 3 4 3 2 2 4 5 +--R (- 4800a b c - 2000a b )x + (- 3200a c - 5600a b )x - 6400a b x - 2560a +--R Type: Expression(Integer) +--E 485 + +--S 486 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 486 + +)clear all + +--S 487 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 487 + +--S 488 of 845 +r0:=-1/12*(8*c*d-7*b*e-6*c*e*x)*(a+b*x+c*x^2)^(3/2)/e^2+1/64*(128*c^4*d^4-_ + b^4*e^4-8*b^2*c*e^3*(2*b*d-3*a*e)-64*c^3*d^2*e*(4*b*d-3*a*e)+48*c^2*_ + e^2*(3*b^2*d^2-4*a*b*d*e+a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(c^(3/2)*e^5)-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^(3/2)*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/e^5-1/32*(64*c^3*d^3-b^3*e^3+4*b*c*e^2*(12*b*d-_ + 11*a*e)-16*c^2*d*e*(7*b*d-4*a*e)-2*c*e*(16*c^2*d^2+b^2*e^2-_ + 4*c*e*(4*b*d-3*a*e))*x)*sqrt(a+b*x+c*x^2)/(c*e^4) +--R +--R +--R (2) +--R 2 2 2 4 4 2 3 3 +--R (144a c + 72a b c - 3b )e + (- 576a b c - 48b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (576a c + 432b c )d e - 768b c d e + 384c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 2 3 3 +-+ +--R (- 192a b c e + (384a c + 192b c)d e - 576b c d e + 384c d )\|c +--R * +--R +-------------------+ +--R | 2 2 (b e - 2c d)x + 2a e - b d +--R \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 4 3 2 4 3 3 2 +--R 96c e x + (208b c e - 128c d e )x +--R + +--R 2 2 4 2 3 3 2 2 +--R ((240a c + 124b c)e - 320b c d e + 192c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (376a b c + 6b )e + (- 512a c - 288b c)d e + 672b c d e - 384c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 192c e \|c +--R Type: Expression(Integer) +--E 488 + +--S 489 of 845 +--a0:=integrate(t0,x) +--E 489 + +--S 490 of 845 +--m0:=a0-r0 +--E 490 + +--S 491 of 845 +--d0:=D(m0,x) +--E 491 + +)clear all + +--S 492 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 492 + +--S 493 of 845 +r0:=1/3*(8*c*d-3*b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x))-_ + 1/4*(2*c*d-b*e)*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e^5*sqrt(c))+1/2*(16*c^2*d^2+_ + 3*b^2*e^2-4*c*e*(4*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^5+_ + 1/2*(16*c^2*d^2+5*b^2*e^2-4*c*e*(5*b*d-a*e)-4*c*e*(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/e^4 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((36a b c + 3b )e + (- 72a c - 54b c)d e + 144b c d e - 96c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 4 +--R (36a b c + 3b )d e + (- 72a c - 54b c)d e + 144b c d e - 96c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 +--R ((- 24a c - 18b )e + 96b c d e - 96c d e)x + (- 24a c - 18b )d e +--R + +--R 2 2 3 +--R 96b c d e - 96c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 3 2 +--R 8c e x + (20b c e - 16c d e )x +--R + +--R 2 4 3 2 2 2 4 +--R ((32a c + 18b )e - 64b c d e + 48c d e )x - 12a b e +--R + +--R 2 3 2 2 2 3 +--R (56a c + 30b )d e - 120b c d e + 96c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 6 5 +-+ +--R (12e x + 12d e )\|c +--R Type: Expression(Integer) +--E 493 + +--S 494 of 845 +--a0:=integrate(t0,x) +--E 494 + +--S 495 of 845 +--m0:=a0-r0 +--E 495 + +--S 496 of 845 +--d0:=D(m0,x) +--E 496 + +)clear all + +--S 497 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 497 + +--S 498 of 845 +r0:=1/2*(4*c*d-b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)+_ + 3/4*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e^5-3/8*(2*c*d-b*e)*(16*c^2*d^2+_ + b^2*e^2-4*c*e*(4*b*d-3*a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*sqrt(c*d^2-b*d*e+_ + a*e^2))-3/4*(16*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-a*e)+4*c*e*(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 4 3 2 2 2 2 +--R ((24a c + 18b )e - 96b c d e + 96c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 +--R ((48a c + 36b )d e - 192b c d e + 192c d e)x + (24a c + 18b )d e +--R + +--R 3 2 4 +--R - 96b c d e + 96c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 36a b c - 3b )e + (72a c + 54b c)d e - 144b c d e +--R + +--R 3 3 2 +--R 96c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 72a b c - 6b )d e + (144a c + 108b c)d e - 288b c d e +--R + +--R 3 4 +--R 192c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 36a b c - 3b )d e + (72a c + 54b c)d e - 144b c d e + 96c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 3 2 +--R 8c e x + (28b c e - 32c d e )x +--R + +--R 2 4 3 2 2 2 4 +--R ((- 16a c - 10b )e + 112b c d e - 144c d e )x - 4a b e +--R + +--R 2 3 2 2 2 3 +--R (- 8a c - 6b )d e + 72b c d e - 96c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 7 2 6 2 5 | 2 2 +--R (8e x + 16d e x + 8d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 498 + +--S 499 of 845 +--a0:=integrate(t0,x) +--E 499 + +--S 500 of 845 +--m0:=a0-r0 +--E 500 + +--S 501 of 845 +--d0:=D(m0,x) +--E 501 + +)clear all + +--S 502 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 502 + +--S 503 of 845 +r0:=-1/4*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*(a+b*x+c*x^2)^(3/2)/_ + (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+1/3*(8*c*d-b*e+6*c*e*x)*(a+b*x+_ + c*x^2)^(3/2)/(e^2*(d+e*x)^3)-4*c^(3/2)*(2*c*d-b*e)*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/e^5+1/16*(128*c^4*d^4-b^4*e^4-_ + 8*b^2*c*e^3*(2*b*d-3*a*e)-64*c^3*d^2*e*(4*b*d-3*a*e)+48*c^2*e^2*_ + (3*b^2*d^2-4*a*b*d*e+a^2*e^2))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*(c*d^2-b*d*e+_ + a*e^2)^(3/2))+1/8*(64*c^3*d^3+b^3*e^3+4*b*c*e^2*(4*b*d-5*a*e)-_ + 16*c^2*d*e*(5*b*d-4*a*e)+2*c*e*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-_ + 3*a*e))*x)*sqrt(a+b*x+c*x^2)/(e^4*(c*d^2-b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 6 2 2 5 2 2 4 3 3 3 3 +--R (192a b c e + (- 384a c - 192b c)d e + 576b c d e - 384c d e )x +--R + +--R 5 2 2 2 4 2 3 3 +--R 576a b c d e + (- 1152a c - 576b c)d e + 1728b c d e +--R + +--R 3 4 2 +--R - 1152c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 3 2 4 2 +--R 576a b c d e + (- 1152a c - 576b c)d e + 1728b c d e +--R + +--R 3 5 +--R - 1152c d e +--R * +--R x +--R + +--R 3 3 2 2 4 2 2 5 3 6 +--R 192a b c d e + (- 384a c - 192b c)d e + 576b c d e - 384c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 144a c - 72a b c + 3b )e + (576a b c + 48b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 576a c - 432b c )d e + 768b c d e - 384c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (- 432a c - 216a b c + 9b )d e + (1728a b c + 144b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (- 1728a c - 1296b c )d e + 2304b c d e - 1152c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 432a c - 216a b c + 9b )d e + (1728a b c + 144b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 1728a c - 1296b c )d e + 2304b c d e - 1152c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 144a c - 72a b c + 3b )d e + (576a b c + 48b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 576a c - 432b c )d e + 768b c d e - 384c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 6 2 5 3 2 4 3 +--R (96a c e - 96b c d e + 96c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (- 184a b c - 6b )e + (656a c + 220b c)d e - 912b c d e +--R + +--R 3 3 3 +--R 704c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 48a c - 28a b )e + (- 160a b c + 16b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (816a c + 252b c)d e - 1216b c d e + 960c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 16a b e + (- 16a c + 4a b )d e + (- 72a b c + 6b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (320a c + 96b c)d e - 480b c d e + 384c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 10 9 2 8 3 +--R (48a e - 48b d e + 48c d e )x +--R + +--R 9 2 8 3 7 2 +--R (144a d e - 144b d e + 144c d e )x +--R + +--R 2 8 3 7 4 6 3 7 4 6 5 5 +--R (144a d e - 144b d e + 144c d e )x + 48a d e - 48b d e + 48c d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 503 + +--S 504 of 845 +--a0:=integrate(t0,x) +--E 504 + +--S 505 of 845 +--m0:=a0-r0 +--E 505 + +--S 506 of 845 +--d0:=D(m0,x) +--E 506 + +)clear all + +--S 507 of 845 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 3 8 2 3 3 2 7 +--R 2c e x + (5b c e + 6c d e )x +--R + +--R 2 2 3 2 2 3 2 6 +--R ((4a c + 4b c)e + 15b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (12a c + 12b c)d e + 15b c d e + 2c d )x +--R + +--R 2 2 3 3 2 2 2 2 +--R (2a c + 2a b )e + (18a b c + 3b )d e + (12a c + 12b c)d e +--R + +--R 2 3 +--R 5b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 3 2 2 2 3 3 +--R (a b e + (6a c + 6a b )d e + (18a b c + 3b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 6a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 3 2 3 +--R (3a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 507 + +--S 508 of 845 +r0:=-1/8192*(b^2-4*a*c)^2*e*(40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*_ + (b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^5+1/2560*(b^2-4*a*c)*e*(40*c^2*d^2+_ + 11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^4+_ + 1/6720*(2*c*d-b*e)*(64*c^2*d^2+99*b^2*e^2-4*c*e*(16*b*d+83*a*e))*_ + (a+b*x+c*x^2)^(7/2)/c^3+1/30*(2*c*d-b*e)*(d+e*x)^2*(a+b*x+_ + c*x^2)^(7/2)/c+1/5*(d+e*x)^3*(a+b*x+c*x^2)^(7/2)+1/480*e*(7*b^2*d*e-_ + 44*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+11*b^2*e^2-4*c*e*(2*b*d+_ + 9*a*e))*x)*(a+b*x+c*x^2)^(7/2)/c^2-3/131072*(b^2-4*a*c)^4*e*_ + (40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(13/2)+3/65536*(b^2-4*a*c)^3*e*_ + (40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^6 +--R +--R +--R (2) +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 322560a c - 1209600a b c + 1008000a b c - 352800a b c +--R + +--R 8 10 +--R 56700a b c - 3465b +--R * +--R 3 +--R e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R 3225600a b c - 3225600a b c + 1209600a b c - 201600a b c +--R + +--R 9 +--R 12600b c +--R * +--R 2 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R - 3225600a c + 3225600a b c - 1209600a b c + 201600a b c +--R + +--R 8 2 +--R - 12600b c +--R * +--R 2 +--R d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 9 3 9 8 3 9 2 8 +--R 2752512c e x + (7798784b c e + 9175040c d e )x +--R + +--R 8 2 7 3 8 2 9 2 7 +--R ((7225344a c + 7196672b c )e + 26378240b c d e + 10321920c d e)x +--R + +--R 7 3 6 3 +--R (12836864a b c + 2119680b c )e +--R + +--R 8 2 7 2 8 2 9 3 +--R (24903680a c + 24821760b c )d e + 30228480b c d e + 3932160c d +--R * +--R 6 +--R x +--R + +--R 2 7 2 6 4 5 3 +--R (5332992a c + 5222400a b c - 2560b c )e +--R + +--R 7 3 6 2 +--R (45465600a b c + 7516160b c )d e +--R + +--R 8 2 7 2 8 3 +--R (29245440a c + 29184000b c )d e + 11796480b c d +--R * +--R 5 +--R x +--R + +--R 2 6 3 5 5 4 3 +--R (3502080a b c - 30720a b c + 2816b c )e +--R + +--R 2 7 2 6 4 5 2 +--R (19660800a c + 19292160a b c - 10240b c )d e +--R + +--R 7 3 6 2 8 2 7 3 +--R (55418880a b c + 9185280b c )d e + (11796480a c + 11796480b c )d +--R * +--R 4 +--R x +--R + +--R 3 6 2 2 5 4 4 6 3 3 +--R (215040a c - 145920a b c + 37760a b c - 3168b c )e +--R + +--R 2 6 3 5 5 4 2 +--R (13946880a b c - 133120a b c + 11520b c )d e +--R + +--R 2 7 2 6 4 5 2 +--R (25374720a c + 25036800a b c - 11520b c )d e +--R + +--R 7 3 6 3 +--R (23592960a b c + 3932160b c )d +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (- 332800a b c + 211200a b c - 47808a b c + 3696b c )e +--R + +--R 3 6 2 2 5 4 4 6 3 2 +--R (1310720a c - 706560a b c + 168960a b c - 13440b c )d e +--R + +--R 2 6 3 5 5 4 2 +--R (20367360a b c - 168960a b c + 13440b c )d e +--R + +--R 2 7 2 6 3 +--R (11796480a c + 11796480a b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R - 322560a c + 634880a b c - 320640a b c + 64512a b c +--R + +--R 8 +--R - 4620b c +--R * +--R 3 +--R e +--R + +--R 3 5 2 3 4 5 3 7 2 2 +--R (- 1914880a b c + 1082880a b c - 228480a b c + 16800b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 2 +--R (3225600a c - 1082880a b c + 228480a b c - 16800b c )d e +--R + +--R 2 6 3 +--R 11796480a b c d +--R * +--R x +--R + +--R 4 4 3 3 3 2 5 2 7 +--R 1149440a b c - 1374720a b c + 576576a b c - 104160a b c +--R + +--R 9 +--R 6930b +--R * +--R 3 +--R e +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R - 2621440a c + 4285440a b c - 1962240a b c + 369600a b c +--R + +--R 8 +--R - 25200b c +--R * +--R 2 +--R d e +--R + +--R 3 5 2 3 4 5 3 7 2 2 +--R (- 4285440a b c + 1962240a b c - 369600a b c + 25200b c )d e +--R + +--R 3 6 3 +--R 3932160a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 6 +-+ +--R 13762560c \|c +--R Type: Expression(Integer) +--E 508 + +--S 509 of 845 +--a0:=integrate(t0,x) +--E 509 + +--S 510 of 845 +--m0:=a0-r0 +--E 510 + +--S 511 of 845 +--d0:=D(m0,x) +--E 511 + +)clear all + +--S 512 of 845 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 512 + +--S 513 of 845 +r0:=-5/3072*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+_ + 1/192*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^3+_ + 1/504*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*_ + (a+b*x+c*x^2)^(7/2)/c^2+2/9*(d+e*x)^2*(a+b*x+c*x^2)^(7/2)+_ + 1/36*e*(b*d-2*a*e+(2*c*d-b*e)*x)*(a+b*x+c*x^2)^(7/2)/c-_ + 5/16384*(b^2-4*a*c)^4*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(11/2)+5/8192*(b^2-4*a*c)^3*e*(2*c*d-b*e)*_ + (b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 4 4 3 3 3 2 5 2 7 9 2 +--R (80640a b c - 80640a b c + 30240a b c - 5040a b c + 315b )e +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 +--R (- 161280a c + 161280a b c - 60480a b c + 10080a b c - 630b c)d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 8 2 8 7 2 8 7 +--R 229376c e x + (659456b c e + 516096c d e)x +--R + +--R 7 2 6 2 7 8 2 6 +--R ((622592a c + 620544b c )e + 1511424b c d e + 294912c d )x +--R + +--R 6 3 5 2 7 2 6 +--R (1136640a b c + 187904b c )e + (1462272a c + 1459200b c )d e +--R + +--R 7 2 +--R 884736b c d +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 4 4 2 +--R (491520a c + 482304a b c - 256b c )e +--R + +--R 6 3 5 7 2 6 2 +--R (2770944a b c + 459264b c )d e + (884736a c + 884736b c )d +--R * +--R 4 +--R x +--R + +--R 2 5 3 4 5 3 2 +--R (348672a b c - 3328a b c + 288b c )e +--R + +--R 2 6 2 5 4 4 +--R (1268736a c + 1251840a b c - 576b c )d e +--R + +--R 6 3 5 2 +--R (1769472a b c + 294912b c )d +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (32768a c - 17664a b c + 4224a b c - 336b c )e +--R + +--R 2 5 3 4 5 3 +--R (1018368a b c - 8448a b c + 672b c )d e +--R + +--R 2 6 2 5 2 +--R (884736a c + 884736a b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (- 47872a b c + 27072a b c - 5712a b c + 420b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (161280a c - 54144a b c + 11424a b c - 840b c )d e +--R + +--R 2 5 2 +--R 884736a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 2 4 2 6 8 2 +--R (- 65536a c + 107136a b c - 49056a b c + 9240a b c - 630b )e +--R + +--R 3 4 2 3 3 5 2 7 +--R (- 214272a b c + 98112a b c - 18480a b c + 1260b c)d e +--R + +--R 3 5 2 +--R 294912a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 1032192c \|c +--R Type: Expression(Integer) +--E 513 + +--S 514 of 845 +--a0:=integrate(t0,x) +--E 514 + +--S 515 of 845 +--m0:=a0-r0 +--E 515 + +--S 516 of 845 +--d0:=D(m0,x) +--E 516 + +)clear all + +--S 517 of 845 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 +--R ((6a b c + b )e + (4a c + 4b c)d)x +--R + +--R 2 2 3 2 2 2 2 2 +--R ((2a c + 2a b )e + (6a b c + b )d)x + (a b e + (2a c + 2a b )d)x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 517 + +--S 518 of 845 +r0:=-5/3072*(b^2-4*a*c)^2*e*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3+_ + 1/192*(b^2-4*a*c)*e*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^2+1/56*(2*c*d-b*e)*_ + (a+b*x+c*x^2)^(7/2)/c+1/4*(d+e*x)*(a+b*x+c*x^2)^(7/2)-_ + 5/16384*(b^2-4*a*c)^4*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(9/2)+5/8192*(b^2-4*a*c)^3*e*(b+2*c*x)*_ + sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 4 4 3 2 3 2 4 2 6 8 +--R (- 26880a c + 26880a b c - 10080a b c + 1680a b c - 105b )e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 7 7 6 7 6 +--R 86016c e x + (251904b c e + 98304c d)x +--R + +--R 6 2 5 6 5 +--R ((243712a c + 243200b c )e + 294912b c d)x +--R + +--R 5 3 4 6 2 5 4 +--R ((461824a b c + 76544b c )e + (294912a c + 294912b c )d)x +--R + +--R 2 5 2 4 4 3 +--R (211456a c + 208640a b c - 96b c )e +--R + +--R 5 3 4 +--R (589824a b c + 98304b c )d +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 +--R (169728a b c - 1408a b c + 112b c )e +--R + +--R 2 5 2 4 +--R (294912a c + 294912a b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 3 4 2 6 2 4 +--R ((26880a c - 9024a b c + 1904a b c - 140b c)e + 294912a b c d)x +--R + +--R 3 3 2 3 2 5 7 3 4 +--R (- 35712a b c + 16352a b c - 3080a b c + 210b )e + 98304a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 344064c \|c +--R Type: Expression(Integer) +--E 518 + +--S 519 of 845 +--a0:=integrate(t0,x) +--E 519 + +--S 520 of 845 +--m0:=a0-r0 +--E 520 + +--S 521 of 845 +--d0:=D(m0,x) +--E 521 + +)clear all + +--S 522 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 522 + +--S 523 of 845 +r0:=2/7*(a+b*x+c*x^2)^(7/2) +--R +--R +--R (2) +--R 3 6 2 5 2 2 4 3 3 +--R 2c x + 6b c x + (6a c + 6b c)x + (12a b c + 2b )x +--R + +--R 2 2 2 2 3 +--R (6a c + 6a b )x + 6a b x + 2a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 7 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 3 5 5 4 7 3 13 +--R (- 896a b c - 1120a b c - 168a b c - 2b c )x +--R + +--R 4 6 3 2 5 2 4 4 6 3 8 2 12 +--R (- 1792a c - 12096a b c - 7280a b c - 700a b c - 6b c )x +--R + +--R 4 5 3 3 4 2 5 3 7 2 9 11 +--R (- 29568a b c - 59360a b c - 18760a b c - 1098a b c - 6b c)x +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R - 19712a c - 168000a b c - 141680a b c - 23884a b c +--R + +--R 8 10 +--R - 768a b c - 2b +--R * +--R 10 +--R x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 192640a b c - 451360a b c - 177912a b c - 15014a b c +--R + +--R 9 +--R - 202a b +--R * +--R 9 +--R x +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R - 77056a c - 695744a b c - 626640a b c - 113204a b c +--R + +--R 2 8 +--R - 3730a b +--R * +--R 8 +--R x +--R + +--R 6 3 5 3 2 4 5 3 7 7 +--R (- 515200a b c - 1183392a b c - 435288a b c - 28814a b )x +--R + +--R 7 3 6 2 2 5 4 4 6 6 +--R (- 146944a c - 1233792a b c - 959392a b c - 119784a b )x +--R + +--R 7 2 6 3 5 5 5 +--R (- 666624a b c - 1261568a b c - 298816a b )x +--R + +--R 8 2 7 2 6 4 4 +--R (- 143360a c - 967680a b c - 465920a b )x +--R + +--R 8 7 3 3 9 8 2 2 +--R (- 387072a b c - 448000a b )x + (- 57344a c - 243712a b )x +--R + +--R 9 +--R - 57344a b x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 7 2 2 6 4 5 6 4 14 +--R (256a c + 1344a b c + 560a b c + 28b c )x +--R + +--R 3 6 2 3 5 5 4 7 3 13 +--R (7168a b c + 12544a b c + 3136a b c + 112b c )x +--R + +--R 4 6 3 2 5 2 4 4 6 3 8 2 12 +--R (7168a c + 59136a b c + 47040a b c + 7056a b c + 168b c )x +--R + +--R 4 5 3 3 4 2 5 3 7 2 9 11 +--R (93184a b c + 224000a b c + 90944a b c + 7952a b c + 112b c)x +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 8 +--R 46592a c + 452480a b c + 451360a b c + 96040a b c + 4480a b c +--R + +--R 10 +--R 28b +--R * +--R 10 +--R x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R 408576a b c + 1084160a b c + 501312a b c + 52752a b c +--R + +--R 9 +--R 1008a b +--R * +--R 9 +--R x +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 136192a c + 1356544a b c + 1377600a b c + 290192a b c +--R + +--R 2 8 +--R 11816a b +--R * +--R 8 +--R x +--R + +--R 6 3 5 3 2 4 5 3 7 7 +--R (852096a b c + 2154656a b c + 890904a b c + 68462a b )x +--R + +--R 7 3 6 2 2 5 4 4 6 6 +--R (211456a c + 1927296a b c + 1648864a b c + 231000a b )x +--R + +--R 7 2 6 3 5 5 5 +--R (910336a b c + 1874432a b c + 488768a b )x +--R + +--R 8 2 7 2 6 4 4 +--R (172032a c + 1261568a b c + 663040a b )x +--R + +--R 8 7 3 3 9 8 2 2 9 +--R (444416a b c + 562688a b )x + (57344a c + 272384a b )x + 57344a b x +--R * +--R +-+ +--R \|a +--R / +--R 3 3 2 2 2 4 6 6 +--R (896a c + 4704a b c + 1960a b c + 98b )x +--R + +--R 3 2 2 3 5 5 +--R (21504a b c + 25088a b c + 3136a b )x +--R + +--R 4 2 3 2 2 4 4 4 3 3 3 +--R (21504a c + 96768a b c + 28224a b )x + (143360a b c + 107520a b )x +--R + +--R 5 4 2 2 5 6 +--R (71680a c + 197120a b )x + 172032a b x + 57344a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 7 +--R (- 3136a b c - 3920a b c - 588a b c - 7b )x +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (- 6272a c - 32928a b c - 13720a b c - 686a b )x +--R + +--R 4 2 3 3 2 5 5 +--R (- 75264a b c - 87808a b c - 10976a b )x +--R + +--R 5 2 4 2 3 4 4 +--R (- 50176a c - 225792a b c - 65856a b )x +--R + +--R 5 4 3 3 6 5 2 2 +--R (- 250880a b c - 188160a b )x + (- 100352a c - 275968a b )x +--R + +--R 6 7 +--R - 200704a b x - 57344a +--R Type: Union(Expression(Integer),...) +--E 524 + +--S 525 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 3 6 2 2 5 4 4 6 6 +--R (256a c + 1344a b c + 560a b c + 28a b )x +--R + +--R 7 2 6 3 5 5 5 +--R (6144a b c + 7168a b c + 896a b )x +--R + +--R 8 2 7 2 6 4 4 8 7 3 3 +--R (6144a c + 27648a b c + 8064a b )x + (40960a b c + 30720a b )x +--R + +--R 9 8 2 2 9 10 +--R (20480a c + 56320a b )x + 49152a b x + 16384a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 6 3 5 3 2 4 5 3 7 7 +--R (- 896a b c - 1120a b c - 168a b c - 2a b )x +--R + +--R 7 3 6 2 2 5 4 4 6 6 +--R (- 1792a c - 9408a b c - 3920a b c - 196a b )x +--R + +--R 7 2 6 3 5 5 5 +--R (- 21504a b c - 25088a b c - 3136a b )x +--R + +--R 8 2 7 2 6 4 4 +--R (- 14336a c - 64512a b c - 18816a b )x +--R + +--R 8 7 3 3 9 8 2 2 +--R (- 71680a b c - 53760a b )x + (- 28672a c - 78848a b )x +--R + +--R 9 10 +--R - 57344a b x - 16384a +--R * +--R +-+ +--R \|a +--R / +--R 3 3 2 2 2 4 6 6 +--R (896a c + 4704a b c + 1960a b c + 98b )x +--R + +--R 3 2 2 3 5 5 +--R (21504a b c + 25088a b c + 3136a b )x +--R + +--R 4 2 3 2 2 4 4 4 3 3 3 +--R (21504a c + 96768a b c + 28224a b )x + (143360a b c + 107520a b )x +--R + +--R 5 4 2 2 5 6 +--R (71680a c + 197120a b )x + 172032a b x + 57344a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 7 +--R (- 3136a b c - 3920a b c - 588a b c - 7b )x +--R + +--R 4 3 3 2 2 2 4 6 6 +--R (- 6272a c - 32928a b c - 13720a b c - 686a b )x +--R + +--R 4 2 3 3 2 5 5 +--R (- 75264a b c - 87808a b c - 10976a b )x +--R + +--R 5 2 4 2 3 4 4 +--R (- 50176a c - 225792a b c - 65856a b )x +--R + +--R 5 4 3 3 6 5 2 2 +--R (- 250880a b c - 188160a b )x + (- 100352a c - 275968a b )x +--R + +--R 6 7 +--R - 200704a b x - 57344a +--R Type: Expression(Integer) +--E 525 + +--S 526 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 526 + +)clear all + +--S 527 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R e x + d +--R Type: Expression(Integer) +--E 527 + +--S 528 of 845 +r0:=-1/96*(64*c^3*d^3-b^3*e^3+4*b*c*e^2*(14*b*d-13*a*e)-8*c^2*d*e*_ + (15*b*d-8*a*e)-2*c*e*(24*c^2*d^2+b^2*e^2-4*c*e*(6*b*d-5*a*e))*x)*_ + (a+b*x+c*x^2)^(3/2)/(c*e^4)-1/30*(12*c*d-11*b*e-10*c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/e^2+1/512*(1024*c^6*d^6+b^6*e^6+4*b^4*c*e^5*_ + (2*b*d-5*a*e)-512*c^5*d^4*e*(6*b*d-5*a*e)-320*c^3*e^3*(b*d-a*e)^2*_ + (4*b*d-a*e)+640*c^4*d^2*e^2*(5*b^2*d^2-8*a*b*d*e+3*a^2*e^2)+_ + 40*b^2*c^2*e^4*(3*b^2*d^2-8*a*b*d*e+6*a^2*e^2))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(5/2)*e^7)-(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^(5/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/e^7-1/256*(512*c^5*d^5+b^5*e^5-_ + 128*c^4*d^3*e*(11*b*d-8*a*e)+8*b^3*c*e^4*(b*d-2*a*e)+32*c^3*d*e^2*_ + (40*b^2*d^2-55*a*b*d*e+16*a^2*e^2)-8*b*c^2*e^3*(49*b^2*d^2-_ + 92*a*b*d*e+42*a^2*e^2)-2*c*e*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*_ + (8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/(c^2*e^6) +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 6 +--R (4800a c + 3600a b c - 300a b c + 15b )e +--R + +--R 2 3 3 2 5 5 +--R (- 28800a b c - 4800a b c + 120b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (28800a c + 43200a b c + 1800b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (- 76800a b c - 19200b c )d e + (38400a c + 48000b c )d e +--R + +--R 5 5 6 6 +--R - 46080b c d e + 15360c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 5 2 3 2 2 4 +--R - 7680a b c e + (15360a c + 15360a b c )d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (- 46080a b c - 7680b c )d e + (30720a c + 30720b c )d e +--R + +--R 4 4 5 5 +--R - 38400b c d e + 15360c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 5 6 5 4 6 5 5 4 +--R 2560c e x + (7936b c e - 3072c d e )x +--R + +--R 4 2 3 6 4 5 5 2 4 3 +--R ((8320a c + 8352b c )e - 9984b c d e + 3840c d e )x +--R + +--R 3 3 2 6 4 2 3 5 +--R (18112a b c + 3056b c )e + (- 11264a c - 11392b c )d e +--R + +--R 4 2 4 5 3 3 +--R 13440b c d e - 5120c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 4 6 +--R (10560a c + 10912a b c + 20b c)e +--R + +--R 3 3 2 5 4 2 3 2 4 +--R (- 28544a b c - 4960b c )d e + (17280a c + 17760b c )d e +--R + +--R 4 3 3 5 4 2 +--R - 20480b c d e + 7680c d e +--R * +--R x +--R + +--R 2 2 3 5 6 +--R (17056a b c + 560a b c - 30b )e +--R + +--R 2 3 2 2 4 5 +--R (- 23552a c - 26560a b c - 240b c)d e +--R + +--R 3 3 2 2 4 4 2 3 3 3 +--R (62400a b c + 11760b c )d e + (- 35840a c - 38400b c )d e +--R + +--R 4 4 2 5 5 +--R 42240b c d e - 15360c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 7 +-+ +--R 7680c e \|c +--R Type: Expression(Integer) +--E 528 + +--S 529 of 845 +--a0:=integrate(t0,x) +--E 529 + +--S 530 of 845 +--m0:=a0-r0 +--E 530 + +--S 531 of 845 +--d0:=D(m0,x) +--E 531 + +)clear all + +--S 532 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 532 + +--S 533 of 845 +r0:=1/12*(48*c^2*d^2-66*b*c*d*e+19*b^2*e^2+8*a*c*e^2-18*c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/e^4+1/5*(12*c*d-5*b*e+2*c*e*x)*(a+b*x+c*x^2)^(5/2)/_ + (e^2*(d+e*x))-1/64*(2*c*d-b*e)*(384*c^4*d^4-b^4*e^4-8*b^2*c*e^3*(4*b*d-_ + 5*a*e)-128*c^3*d^2*e*(6*b*d-5*a*e)+16*c^2*e^2*(26*b^2*d^2-40*a*b*d*e+_ + 15*a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*_ + e^7)+1/2*(c*d^2-b*d*e+a*e^2)^(3/2)*(24*c^2*d^2+5*b^2*e^2-4*c*e*_ + (6*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+_ + a*e^2)*sqrt(a+b*x+c*x^2)))/e^7+1/32*(384*c^4*d^4+b^4*e^4-2*b^2*c*e^3*_ + (65*b*d-62*a*e)-32*c^3*d^2*e*(27*b*d-14*a*e)+8*c^2*e^2*(76*b^2*d^2-_ + 67*a*b*d*e+8*a^2*e^2)-2*c*e*(2*c*d-b*e)*(48*c^2*d^2-48*b*c*d*e+_ + b^2*e^2+44*a*c*e^2)*x)*sqrt(a+b*x+c*x^2)/(c*e^6) +--R +--R +--R (2) +--R 2 2 3 5 6 +--R (3600a b c + 600a b c - 15b )e +--R + +--R 2 3 2 2 4 5 +--R (- 7200a c - 10800a b c - 450b c)d e +--R + +--R 3 3 2 2 4 4 2 3 3 3 +--R (28800a b c + 7200b c )d e + (- 19200a c - 24000b c )d e +--R + +--R 4 4 2 5 5 +--R 28800b c d e - 11520c d e +--R * +--R x +--R + +--R 2 2 3 5 5 +--R (3600a b c + 600a b c - 15b )d e +--R + +--R 2 3 2 2 4 2 4 +--R (- 7200a c - 10800a b c - 450b c)d e +--R + +--R 3 3 2 3 3 4 2 3 4 2 +--R (28800a b c + 7200b c )d e + (- 19200a c - 24000b c )d e +--R + +--R 4 5 5 6 +--R 28800b c d e - 11520c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 5 2 3 4 +--R (- 1920a c - 2400a b c)e + (13440a b c + 2400b c)d e +--R + +--R 3 2 2 2 3 3 3 2 4 4 +--R (- 13440a c - 13920b c )d e + 23040b c d e - 11520c d e +--R * +--R x +--R + +--R 2 2 2 4 2 3 2 3 +--R (- 1920a c - 2400a b c)d e + (13440a b c + 2400b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (- 13440a c - 13920b c )d e + 23040b c d e - 11520c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 4 6 5 3 6 4 5 4 +--R 384c e x + (1248b c e - 576c d e )x +--R + +--R 3 2 2 6 3 5 4 2 4 3 +--R ((1408a c + 1424b c )e - 2112b c d e + 960c d e )x +--R + +--R 2 3 6 3 2 2 5 +--R (3568a b c + 620b c)e + (- 2912a c - 3016b c )d e +--R + +--R 3 2 4 4 3 3 +--R 4320b c d e - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 6 2 3 5 +--R (2944a c + 3320a b c + 30b )e + (- 12032a b c - 2320b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (9120a c + 9960b c )d e - 13440b c d e + 5760c d e +--R * +--R x +--R + +--R 2 6 2 2 2 4 5 +--R - 960a b c e + (4864a c + 5240a b c + 30b )d e +--R + +--R 2 3 2 4 3 2 2 3 3 +--R (- 21360a b c - 3900b c)d e + (17280a c + 18240b c )d e +--R + +--R 3 4 2 4 5 +--R - 25920b c d e + 11520c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 8 7 +-+ +--R (960c e x + 960c d e )\|c +--R Type: Expression(Integer) +--E 533 + +--S 534 of 845 +--a0:=integrate(t0,x) +--E 534 + +--S 535 of 845 +--m0:=a0-r0 +--E 535 + +--S 536 of 845 +--d0:=D(m0,x) +--E 536 + +)clear all + +--S 537 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 537 + +--S 538 of 845 +r0:=-5/4*(8*c^2*d^2+b^2*e^2-c*e*(7*b*d-2*a*e)+c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/2*(3*c*d-b*e+c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)+15/64*(128*c^4*d^4+b^4*e^4-_ + 8*b^2*c*e^3*(4*b*d-3*a*e)-128*c^3*d^2*e*(2*b*d-a*e)+16*c^2*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^7*sqrt(c))-15/8*(2*c*d-b*e)*(8*c^2*d^2+b^2*e^2-_ + 4*c*e*(2*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^7-_ + 15/32*(64*c^3*d^3-7*b^3*e^3+4*b*c*e^2*(14*b*d-5*a*e)-16*c^2*d*e*_ + (7*b*d-2*a*e)-2*c*e*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*x)*_ + sqrt(a+b*x+c*x^2)/e^6 +--R +--R +--R (2) +--R 2 2 2 4 6 2 3 5 +--R (240a c + 360a b c + 15b )e + (- 1920a b c - 480b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (1920a c + 2400b c )d e - 3840b c d e + 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 5 2 3 2 4 +--R (480a c + 720a b c + 30b )d e + (- 3840a b c - 960b c)d e +--R + +--R 3 2 2 3 3 3 4 2 4 5 +--R (3840a c + 4800b c )d e - 7680b c d e + 3840c d e +--R * +--R x +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (240a c + 360a b c + 15b )d e + (- 1920a b c - 480b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (1920a c + 2400b c )d e - 3840b c d e + 1920c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 480a b c - 120b )e + (960a c + 1200b c)d e - 2880b c d e +--R + +--R 3 3 2 +--R 1920c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 960a b c - 240b )d e + (1920a c + 2400b c)d e +--R + +--R 2 3 2 3 4 +--R - 5760b c d e + 3840c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 +--R (- 480a b c - 120b )d e + (960a c + 1200b c)d e - 2880b c d e +--R + +--R 3 5 +--R 1920c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 6 5 2 6 3 5 4 +--R 32c e x + (112b c e - 64c d e )x +--R + +--R 2 2 6 2 5 3 2 4 3 +--R ((144a c + 148b c)e - 288b c d e + 160c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (520a b c + 98b )e + (- 608a c - 664b c)d e + 1200b c d e +--R + +--R 3 3 3 +--R - 640c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 128a c - 144a b )e + (1872a b c + 340b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 2480a c - 2620b c)d e + 5120b c d e - 2880c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 32a b e + (- 64a c - 80a b )d e + (1160a b c + 210b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (- 1600a c - 1680b c)d e + 3360b c d e - 1920c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 9 2 8 2 7 +-+ +--R (64e x + 128d e x + 64d e )\|c +--R Type: Expression(Integer) +--E 538 + +--S 539 of 845 +--a0:=integrate(t0,x) +--E 539 + +--S 540 of 845 +--m0:=a0-r0 +--E 540 + +--S 541 of 845 +--d0:=D(m0,x) +--E 541 + +)clear all + +--S 542 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 542 + +--S 543 of 845 +r0:=-5/12*(16*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-a*e)+4*c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(4*c*d-b*e+2*c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)-5/2*(2*c*d-b*e)*(8*c^2*d^2+b^2*e^2-_ + 4*c*e*(2*b*d-a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*_ + sqrt(c)/e^7+5/16*(128*c^4*d^4+b^4*e^4-8*b^2*c*e^3*(4*b*d-3*a*e)-_ + 128*c^3*d^2*e*(2*b*d-a*e)+16*c^2*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2))*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(e^7*sqrt(c*d^2-b*d*e+a*e^2))+5/8*(64*c^3*d^3-_ + b^3*e^3-16*c^2*d*e*(5*b*d-2*a*e)+12*b*c*e^2*(2*b*d-a*e)+2*c*e*_ + (16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 3 6 2 2 5 2 2 4 +--R (480a b c + 120b )e + (- 960a c - 1200b c)d e + 2880b c d e +--R + +--R 3 3 3 +--R - 1920c d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 2 4 +--R (1440a b c + 360b )d e + (- 2880a c - 3600b c)d e +--R + +--R 2 3 3 3 4 2 +--R 8640b c d e - 5760c d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 2 3 3 +--R (1440a b c + 360b )d e + (- 2880a c - 3600b c)d e +--R + +--R 2 4 2 3 5 +--R 8640b c d e - 5760c d e +--R * +--R x +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (480a b c + 120b )d e + (- 960a c - 1200b c)d e + 2880b c d e +--R + +--R 3 6 +--R - 1920c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 240a c - 360a b c - 15b )e + (1920a b c + 480b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 1920a c - 2400b c )d e + 3840b c d e - 1920c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (- 720a c - 1080a b c - 45b )d e + (5760a b c + 1440b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (- 5760a c - 7200b c )d e + 11520b c d e - 5760c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 720a c - 1080a b c - 45b )d e + (5760a b c + 1440b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 5760a c - 7200b c )d e + 11520b c d e - 5760c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 240a c - 360a b c - 15b )d e + (1920a b c + 480b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 1920a c - 2400b c )d e + 3840b c d e - 1920c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 6 5 2 6 3 5 4 +--R 32c e x + (128b c e - 96c d e )x +--R + +--R 2 2 6 2 5 3 2 4 3 +--R ((224a c + 240b c)e - 672b c d e + 480c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (- 328a b c - 66b )e + (1328a c + 1444b c)d e - 4560b c d e +--R + +--R 3 3 3 +--R 3520c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 48a c - 52a b )e + (- 352a b c - 80b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (1680a c + 1860b c)d e - 6080b c d e + 4800c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 16a b e + (- 16a c - 20a b )d e + (- 120a b c - 30b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (640a c + 720b c)d e - 2400b c d e + 1920c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 10 3 9 2 2 8 3 7 | 2 2 +--R (48e x + 144d e x + 144d e x + 48d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 543 + +--S 544 of 845 +--a0:=integrate(t0,x) +--E 544 + +--S 545 of 845 +--m0:=a0-r0 +--E 545 + +--S 546 of 845 +--d0:=D(m0,x) +--E 546 + +)clear all + +--S 547 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 547 + +--S 548 of 845 +r0:=3/64*(b^2-4*a*c)*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+_ + 1/32*(2*c*d-b*e)*(16*c^2*d^2+15*b^2*e^2-4*c*e*(4*b*d+11*a*e))*_ + sqrt(a+b*x+c*x^2)/c^3+1/4*(2*c*d-b*e)*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+_ + 1/2*(d+e*x)^3*sqrt(a+b*x+c*x^2)+1/16*e*(b^2*d*e-20*a*c*d*e+4*b*_ + (c*d^2+a*e^2)+(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*x)*_ + sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 4 3 2 3 2 +--R (48a c - 72a b c + 15b )e + (192a b c - 48b c)d e +--R + +--R 3 2 2 2 +--R (- 192a c + 48b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 32c e x + (- 16b c e + 128c d e )x +--R + +--R 2 2 3 2 2 3 2 3 3 +--R ((- 48a c + 20b c)e - 64b c d e + 192c d e)x + (104a b c - 30b )e +--R + +--R 2 2 2 2 2 3 3 +--R (- 256a c + 96b c)d e - 96b c d e + 128c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 64c \|c +--R Type: Expression(Integer) +--E 548 + +--S 549 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 3 2 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120a b )e +--R + +--R 3 2 3 6 2 3 4 5 2 2 +--R (6144a b c - 384a b c)d e + (- 6144a b c + 384a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (3072a c - 768a b c - 4800a b c + 1200a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (12288a b c + 12288a b c - 3840a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (- 12288a c - 12288a b c + 3840a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (9216a b c - 13824a b c + 2880a b )e +--R + +--R 4 2 2 3 4 2 +--R (36864a b c - 9216a b c)d e +--R + +--R 4 3 3 3 2 2 +--R (- 36864a b c + 9216a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (6144a c - 9216a b c + 1920a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (24576a b c - 6144a b c)d e + (- 24576a c + 6144a b c )d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 3 +--R (- 768a c + 1440a b c - 288a b c - 15b )e +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (- 3072a b c - 3840a b c + 960a b c + 48b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (3072a c + 3840a b c - 960a b c - 48b c )d e +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480a b )e +--R + +--R 3 2 3 6 2 +--R (- 24576a b c + 1536a b c)d e +--R + +--R 3 4 5 2 2 +--R (24576a b c - 1536a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (- 24576a b c - 24576a b c + 7680a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (24576a c + 24576a b c - 7680a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (- 12288a b c + 18432a b c - 3840a b )e +--R + +--R 4 2 2 3 4 2 +--R (- 49152a b c + 12288a b c)d e +--R + +--R 4 3 3 3 2 2 +--R (49152a b c - 12288a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (- 6144a c + 9216a b c - 1920a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (- 24576a b c + 6144a b c)d e + (24576a c - 6144a b c )d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 5 2 4 4 3 3 7 +--R (- 512a c - 768a b c - 32b c )e x +--R + +--R 2 4 3 3 5 2 3 +--R (- 3840a b c - 640a b c + 16b c )e +--R + +--R 2 5 2 4 4 3 2 +--R (- 2048a c - 3072a b c - 128b c )d e +--R * +--R 6 +--R x +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (- 3328a c - 2240a b c + 80a b c - 20b c)e +--R + +--R 2 4 3 3 5 2 2 +--R (- 15360a b c - 2560a b c + 64b c )d e +--R + +--R 2 5 2 4 4 3 2 +--R (- 3072a c - 4608a b c - 192b c )d e +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 5 7 3 +--R (- 1664a b c - 480a b c - 24a b c + 30b )e +--R + +--R 3 4 2 2 3 6 2 +--R (- 12288a c - 7680a b c - 96b c)d e +--R + +--R 2 4 3 3 5 2 2 +--R (- 23040a b c - 3840a b c + 96b c )d e +--R + +--R 2 5 2 4 4 3 3 +--R (- 2048a c - 3072a b c - 128b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 2 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+--R 5 2 4 3 3 5 3 +--R (- 13312a b c - 12800a b c + 4800a b )e +--R + +--R 5 3 4 2 2 3 4 2 +--R (32768a c + 28672a b c - 15360a b c)d e +--R + +--R 4 3 3 3 2 2 4 4 3 2 3 3 +--R (12288a b c + 15360a b c )d e + (- 16384a c - 20480a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 3 5 2 4 3 2 +--R (- 26624a b c + 7680a b )e + (65536a b c - 24576a b c)d e +--R + +--R 4 2 2 2 4 3 3 +--R 24576a b c d e - 32768a b c d +--R * +--R x +--R + +--R 6 5 3 3 6 2 5 2 2 +--R (- 13312a b c + 3840a b )e + (32768a c - 12288a b c)d e +--R + +--R 5 2 2 5 3 3 +--R 12288a b c d e - 16384a c d +--R * +--R +-+ +--R \|c +--R / +--R 2 4 3 3 3 3 4 2 2 3 2 3 3 +--R (2048a b c + 512a b c )x + (4096a c + 5120a b c )x + 12288a b c x +--R + +--R 4 3 +--R 8192a c +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 2 4 3 3 3 +--R (- 1024a c - 1536a b c - 64b c )x + (- 8192a b c - 2048a b c )x +--R + +--R 3 4 2 2 3 2 3 3 4 3 +--R (- 8192a c - 10240a b c )x - 16384a b c x - 8192a c +--R * +--R +-+ +-+ +--R \|a \|c +--R Type: Expression(Integer) +--E 550 + +--S 551 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 551 + +--S 552 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 3 3 2 2 5 7 3 +--R (- 1536a b c + 1920a b c + 96a b c - 120a b )e +--R + +--R 3 2 3 6 2 3 4 5 2 2 +--R (- 6144a b c + 384a b c)d e + (6144a b c - 384a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (- 3072a c + 768a b c + 4800a b c - 1200a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (- 12288a b c - 12288a b c + 3840a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (12288a c + 12288a b c - 3840a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (- 9216a b c + 13824a b c - 2880a b )e +--R + +--R 4 2 2 3 4 2 4 3 3 3 2 2 +--R (- 36864a b c + 9216a b c)d e + (36864a b c - 9216a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (- 6144a c + 9216a b c - 1920a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (- 24576a b c + 6144a b c)d e + (24576a c - 6144a b c )d e +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 3 +--R (768a c - 1440a b c + 288a b c + 15b )e +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (3072a b c + 3840a b c - 960a b c - 48b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (- 3072a c - 3840a b c + 960a b c + 48b c )d e +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (6144a b c - 7680a b c - 384a b c + 480a b )e +--R + +--R 3 2 3 6 2 3 4 5 2 2 +--R (24576a b c - 1536a b c)d e + (- 24576a b c + 1536a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (6144a c - 1536a b c - 9600a b c + 2400a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (24576a b c + 24576a b c - 7680a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (- 24576a c - 24576a b c + 7680a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (12288a b c - 18432a b c + 3840a b )e +--R + +--R 4 2 2 3 4 2 +--R (49152a b c - 12288a b c)d e +--R + +--R 4 3 3 3 2 2 +--R (- 49152a b c + 12288a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (6144a c - 9216a b c + 1920a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (24576a b c - 6144a b c)d e + (- 24576a c + 6144a b c )d e +--R * +--R +---+ +-+ +--R \|- c \|a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (3072a b c - 3840a b c - 192a b c + 240a b )e +--R + +--R 3 2 3 6 2 3 4 5 2 2 +--R (12288a b c - 768a b c)d e + (- 12288a b c + 768a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (6144a c - 1536a b c - 9600a b c + 2400a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (24576a b c + 24576a b c - 7680a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (- 24576a c - 24576a b c + 7680a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (18432a b c - 27648a b c + 5760a b )e +--R + +--R 4 2 2 3 4 2 +--R (73728a b c - 18432a b c)d e +--R + +--R 4 3 3 3 2 2 +--R (- 73728a b c + 18432a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (12288a c - 18432a b c + 3840a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (49152a b c - 12288a b c)d e + (- 49152a c + 12288a b c )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 3 +--R (- 1536a c + 2880a b c - 576a b c - 30b )e +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (- 6144a b c - 7680a b c + 1920a b c + 96b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (6144a c + 7680a b c - 1920a b c - 96b c )d e +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 12288a b c + 15360a b c + 768a b c - 960a b )e +--R + +--R 3 2 3 6 2 3 4 5 2 2 +--R (- 49152a b c + 3072a b c)d e + (49152a b c - 3072a b c )d e +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 2 3 4 2 6 3 +--R (- 12288a c + 3072a b c + 19200a b c - 4800a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (- 49152a b c - 49152a b c + 15360a b c)d e +--R + +--R 4 4 3 2 3 2 4 2 2 +--R (49152a c + 49152a b c - 15360a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (- 24576a b c + 36864a b c - 7680a b )e +--R + +--R 4 2 2 3 4 2 +--R (- 98304a b c + 24576a b c)d e +--R + +--R 4 3 3 3 2 2 +--R (98304a b c - 24576a b c )d e +--R * +--R x +--R + +--R 6 2 5 2 4 4 3 +--R (- 12288a c + 18432a b c - 3840a b )e +--R + +--R 5 2 4 3 2 5 3 4 2 2 2 +--R (- 49152a b c + 12288a b c)d e + (49152a c - 12288a b c )d e +--R * +--R +-+ +-+ +--R \|a \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 2 2 2 4 6 3 +--R (3328a b c - 128a b c - 240a b )e +--R + +--R 3 3 2 3 2 5 2 +--R (- 8192a b c + 1024a b c + 768a b c)d e +--R + +--R 2 2 3 4 2 2 2 4 3 3 3 +--R (- 3072a b c - 768a b c )d e + (4096a b c + 1024a b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 2 5 3 +--R (6656a b c + 6400a b c - 2400a b )e +--R + +--R 4 3 3 2 2 2 4 2 +--R (- 16384a c - 14336a b c + 7680a b c)d e +--R + +--R 3 3 2 3 2 2 3 4 2 2 3 3 +--R (- 6144a b c - 7680a b c )d e + (8192a c + 10240a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 3 4 3 4 2 3 3 2 +--R (19968a b c - 5760a b )e + (- 49152a b c + 18432a b c)d e +--R + +--R 3 2 2 2 3 3 3 +--R - 18432a b c d e + 24576a b c d +--R * +--R x +--R + +--R 5 4 3 3 5 2 4 2 2 +--R (13312a b c - 3840a b )e + (- 32768a c + 12288a b c)d e +--R + +--R 4 2 2 4 3 3 +--R - 12288a b c d e + 16384a c d +--R * +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R \|- c \|a \|c \|c x + b x + a +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 1664a b c - 2016a b c + 616a b c + 30a b )e +--R + +--R 4 4 3 2 3 2 4 2 6 2 +--R (4096a c + 4608a b c - 2048a b c - 96a b c)d e +--R + +--R 3 4 2 3 3 5 2 2 +--R (1536a b c + 2304a b c + 96a b c )d e +--R + +--R 3 5 2 2 4 4 3 3 +--R (- 2048a c - 3072a b c - 128a b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 2 3 4 2 6 3 +--R (- 13312a b c + 512a b c + 960a b )e +--R + +--R 4 3 3 3 2 2 5 2 +--R (32768a b c - 4096a b c - 3072a b c)d e +--R + +--R 3 2 3 2 4 2 2 3 4 2 3 3 3 +--R (12288a b c + 3072a b c )d e + (- 16384a b c - 4096a b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 3 3 5 3 +--R (- 13312a b c - 12800a b c + 4800a b )e +--R + +--R 5 3 4 2 2 3 4 2 +--R (32768a c + 28672a b c - 15360a b c)d e +--R + +--R 4 3 3 3 2 2 4 4 3 2 3 3 +--R (12288a b c + 15360a b c )d e + (- 16384a c - 20480a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 3 5 2 4 3 2 +--R (- 26624a b c + 7680a b )e + (65536a b c - 24576a b c)d e +--R + +--R 4 2 2 2 4 3 3 +--R 24576a b c d e - 32768a b c d +--R * +--R x +--R + +--R 6 5 3 3 6 2 5 2 2 +--R (- 13312a b c + 3840a b )e + (32768a c - 12288a b c)d e +--R + +--R 5 2 2 5 3 3 +--R 12288a b c d e - 16384a c d +--R * +--R +---+ +-+ +--R \|- c \|c +--R / +--R 2 4 3 3 3 3 4 2 2 3 2 3 3 +--R (2048a b c + 512a b c )x + (4096a c + 5120a b c )x + 12288a b c x +--R + +--R 4 3 +--R 8192a c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 2 4 3 3 3 +--R (- 1024a c - 1536a b c - 64b c )x + (- 8192a b c - 2048a b c )x +--R + +--R 3 4 2 2 3 2 3 3 4 3 +--R (- 8192a c - 10240a b c )x - 16384a b c x - 8192a c +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R Type: Expression(Integer) +--E 552 + +--S 553 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 553 + +)clear all + +--S 554 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 554 + +--S 555 of 845 +r0:=1/4*(b^2-4*a*c)*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(5/2)+1/6*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+_ + a*e))*sqrt(a+b*x+c*x^2)/c^2+2/3*(d+e*x)^2*sqrt(a+b*x+c*x^2)+1/3*e*_ + (b*d-2*a*e+(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R 3 2 2 2 2c x + b +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e)atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 2 2 2 2 +--R 8c e x + (- 4b c e + 24c d e)x + (- 16a c + 6b )e - 12b c d e +--R + +--R 2 2 +--R 24c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 +-+ +--R 12c \|c +--R Type: Expression(Integer) +--E 555 + +--S 556 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 5 2 +--R (96a b c + 48a b c - 18b )e +--R + +--R 2 3 2 2 4 +--R (- 192a c - 96a b c + 36b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((384a b c - 96a b )e + (- 768a b c + 192a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (384a b c - 96a b )e + (- 768a c + 192a b c)d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (- 144a b c + 24a b c + 3b )e +--R + +--R 2 3 3 2 5 +--R (288a b c - 48a b c - 6b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (- 288a b c - 144a b c + 54a b )e +--R + +--R 3 3 2 2 2 4 +--R (576a c + 288a b c - 108a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((- 576a b c + 144a b )e + (1152a b c - 288a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (- 384a b c + 96a b )e + (768a c - 192a b c)d e +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 3 2 2 5 +--R (- 96a b c - 8b c )e x +--R + +--R 2 3 2 2 4 2 3 3 2 4 +--R ((- 192a c - 96a b c + 4b c)e + (- 288a b c - 24b c )d e)x +--R + +--R 2 2 3 5 2 +--R (- 96a b c + 16a b c - 6b )e +--R + +--R 2 3 2 2 4 3 3 2 2 +--R (- 576a c - 288a b c + 12b c)d e + (- 288a b c - 24b c )d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R (288a b c - 72a b )e + (- 960a b c + 144a b c)d e +--R + +--R 2 3 2 2 2 +--R (- 384a c - 288a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 2 2 2 2 2 2 +--R ((384a b c - 96a b )e + (- 768a c + 192a b c)d e - 384a b c d )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 4 2 3 2 6 +--R (64a c + 48b c )e x +--R + +--R 3 3 2 2 4 2 3 5 +--R ((288a b c + 24b c )e + (192a c + 144b c )d e)x +--R + +--R 2 3 2 2 4 2 3 3 2 +--R (192a c + 96a b c + 12b c)e + (864a b c + 72b c )d e +--R + +--R 4 2 3 2 +--R (192a c + 144b c )d +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 2 +--R (- 96a b c - 64a b c + 30b )e +--R + +--R 2 3 2 2 4 3 3 2 2 +--R (960a c + 576a b c - 60b c)d e + (672a b c + 120b c )d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R (- 480a b c + 120a b )e + (1344a b c - 240a b c)d e +--R + +--R 2 3 2 2 2 +--R (384a c + 480a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 2 2 2 2 2 2 +--R ((- 384a b c + 96a b )e + (768a c - 192a b c)d e + 384a b c d )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +-+ +-+ | 2 +--R ((96a c + 72b c )x + 384a b c x + 384a c )\|a \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 144a b c - 12b c )x + (- 288a c - 216a b c )x - 576a b c x +--R + +--R 3 2 +--R - 384a c +--R * +--R +-+ +--R \|c +--R , +--R +--R 2 2 3 5 2 +--R (96a b c + 48a b c - 18b )e +--R + +--R 2 3 2 2 4 +--R (- 192a c - 96a b c + 36b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((384a b c - 96a b )e + (- 768a b c + 192a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (384a b c - 96a b )e + (- 768a c + 192a b c)d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (- 144a b c + 24a b c + 3b )e +--R + +--R 2 3 3 2 5 +--R (288a b c - 48a b c - 6b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (- 288a b c - 144a b c + 54a b )e +--R + +--R 3 3 2 2 2 4 +--R (576a c + 288a b c - 108a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((- 576a b c + 144a b )e + (1152a b c - 288a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (- 384a b c + 96a b )e + (768a c - 192a b c)d e +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 3 2 2 5 +--R (- 48a b c - 4b c )e x +--R + +--R 2 3 2 2 4 2 3 3 2 4 +--R ((- 96a c - 48a b c + 2b c)e + (- 144a b c - 12b c )d e)x +--R + +--R 2 2 3 5 2 +--R (- 48a b c + 8a b c - 3b )e +--R + +--R 2 3 2 2 4 3 3 2 2 +--R (- 288a c - 144a b c + 6b c)d e + (- 144a b c - 12b c )d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R (144a b c - 36a b )e + (- 480a b c + 72a b c)d e +--R + +--R 2 3 2 2 2 +--R (- 192a c - 144a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 2 2 2 2 2 2 +--R ((192a b c - 48a b )e + (- 384a c + 96a b c)d e - 192a b c d )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 4 2 3 2 6 +--R (32a c + 24b c )e x +--R + +--R 3 3 2 2 4 2 3 5 +--R ((144a b c + 12b c )e + (96a c + 72b c )d e)x +--R + +--R 2 3 2 2 4 2 3 3 2 +--R (96a c + 48a b c + 6b c)e + (432a b c + 36b c )d e +--R + +--R 4 2 3 2 +--R (96a c + 72b c )d +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 2 +--R (- 48a b c - 32a b c + 15b )e +--R + +--R 2 3 2 2 4 3 3 2 2 +--R (480a c + 288a b c - 30b c)d e + (336a b c + 60b c )d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R (- 240a b c + 60a b )e + (672a b c - 120a b c)d e +--R + +--R 2 3 2 2 2 +--R (192a c + 240a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 2 2 2 2 2 2 +--R ((- 192a b c + 48a b )e + (384a c - 96a b c)d e + 192a b c d )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +---+ +-+ | 2 +--R ((48a c + 36b c )x + 192a b c x + 192a c )\|- c \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 72a b c - 6b c )x + (- 144a c - 108a b c )x - 288a b c x +--R + +--R 3 2 +--R - 192a c +--R * +--R +---+ +--R \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 556 + +--S 557 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 3 5 2 +--R (96a b c + 48a b c - 18b )e +--R + +--R 2 3 2 2 4 +--R (- 192a c - 96a b c + 36b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((384a b c - 96a b )e + (- 768a b c + 192a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (384a b c - 96a b )e + (- 768a c + 192a b c)d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (- 144a b c + 24a b c + 3b )e +--R + +--R 2 3 3 2 5 +--R (288a b c - 48a b c - 6b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (- 288a b c - 144a b c + 54a b )e +--R + +--R 3 3 2 2 2 4 +--R (576a c + 288a b c - 108a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((- 576a b c + 144a b )e + (1152a b c - 288a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (- 384a b c + 96a b )e + (768a c - 192a b c)d e +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 3 5 2 +--R (- 96a b c - 48a b c + 18b )e +--R + +--R 2 3 2 2 4 +--R (192a c + 96a b c - 36b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((- 384a b c + 96a b )e + (768a b c - 192a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (- 384a b c + 96a b )e + (768a c - 192a b c)d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (144a b c - 24a b c - 3b )e +--R + +--R 2 3 3 2 5 +--R (- 288a b c + 48a b c + 6b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (288a b c + 144a b c - 54a b )e +--R + +--R 3 3 2 2 2 4 +--R (- 576a c - 288a b c + 108a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((576a b c - 144a b )e + (- 1152a b c + 288a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (384a b c - 96a b )e + (- 768a c + 192a b c)d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 4 2 2 2 3 +--R (- 128a c - 48a b c + 36a b )e + (- 96a b c - 72a b c)d e +--R + +--R 2 3 2 2 2 +--R (192a c + 144a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 2 2 2 +--R ((- 512a b c + 192a b )e - 384a b c d e + 768a b c d )x +--R + +--R 4 3 2 2 3 3 2 2 +--R (- 512a c + 192a b )e - 384a b c d e + 768a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 2 3 5 2 2 2 4 +--R (192a b c - 56a b c - 6b )e + (144a b c + 12b c)d e +--R + +--R 3 3 2 2 +--R (- 288a b c - 24b c )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 4 2 2 2 3 +--R (384a c + 144a b c - 108a b )e + (288a b c + 216a b c)d e +--R + +--R 2 3 2 2 2 +--R (- 576a c - 432a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 2 2 2 +--R ((768a b c - 288a b )e + 576a b c d e - 1152a b c d )x +--R + +--R 4 3 2 2 3 3 2 2 +--R (512a c - 192a b )e + 384a b c d e - 768a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +-+ +-+ | 2 +--R ((96a c + 72b c )x + 384a b c x + 384a c )\|a \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 144a b c - 12b c )x + (- 288a c - 216a b c )x - 576a b c x +--R + +--R 3 2 +--R - 384a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 557 + +--S 558 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 558 + +--S 559 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 3 5 2 +--R (- 96a b c - 48a b c + 18b )e +--R + +--R 2 3 2 2 4 +--R (192a c + 96a b c - 36b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((- 384a b c + 96a b )e + (768a b c - 192a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (- 384a b c + 96a b )e + (768a c - 192a b c)d e +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (144a b c - 24a b c - 3b )e +--R + +--R 2 3 3 2 5 +--R (- 288a b c + 48a b c + 6b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (288a b c + 144a b c - 54a b )e +--R + +--R 3 3 2 2 2 4 +--R (- 576a c - 288a b c + 108a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((576a b c - 144a b )e + (- 1152a b c + 288a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (384a b c - 96a b )e + (- 768a c + 192a b c)d e +--R * +--R +---+ +--R \|- c +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 3 5 2 +--R (192a b c + 96a b c - 36b )e +--R + +--R 2 3 2 2 4 +--R (- 384a c - 192a b c + 72b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 2 2 3 +--R ((768a b c - 192a b )e + (- 1536a b c + 384a b c)d e)x +--R + +--R 3 2 3 2 3 2 2 2 +--R (768a b c - 192a b )e + (- 1536a c + 384a b c)d e +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 2 2 4 6 2 +--R (- 288a b c + 48a b c + 6b )e +--R + +--R 2 3 3 2 5 +--R (576a b c - 96a b c - 12b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 5 2 +--R (- 576a b c - 288a b c + 108a b )e +--R + +--R 3 3 2 2 2 4 +--R (1152a c + 576a b c - 216a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 2 3 +--R ((- 1152a b c + 288a b )e + (2304a b c - 576a b c)d e)x +--R + +--R 4 3 3 2 4 2 3 2 +--R (- 768a b c + 192a b )e + (1536a c - 384a b c)d e +--R * +--R +-+ +--R \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 2 2 2 4 2 2 2 3 +--R (- 128a c - 48a b c + 36a b )e + (- 96a b c - 72a b c)d e +--R + +--R 2 3 2 2 2 +--R (192a c + 144a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 2 2 2 +--R ((- 512a b c + 192a b )e - 384a b c d e + 768a b c d )x +--R + +--R 4 3 2 2 3 3 2 2 +--R (- 512a c + 192a b )e - 384a b c d e + 768a c d +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 2 2 3 5 2 2 2 4 +--R (192a b c - 56a b c - 6b )e + (144a b c + 12b c)d e +--R + +--R 3 3 2 2 +--R (- 288a b c - 24b c )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 4 2 2 2 3 +--R (384a c + 144a b c - 108a b )e + (288a b c + 216a b c)d e +--R + +--R 2 3 2 2 2 +--R (- 576a c - 432a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 2 2 2 +--R ((768a b c - 288a b )e + 576a b c d e - 1152a b c d )x +--R + +--R 4 3 2 2 3 3 2 2 +--R (512a c - 192a b )e + 384a b c d e - 768a c d +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +-+ +--R ((96a c + 72b c )x + 384a b c x + 384a c )\|- c \|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 144a b c - 12b c )x + (- 288a c - 216a b c )x - 576a b c x +--R + +--R 3 2 +--R - 384a c +--R * +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 559 + +--S 560 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 845 +t0:=(b+2*c*x)*(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) ----------------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 561 + +--S 562 of 845 +r0:=1/4*(b^2-4*a*c)*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/_ + c^(3/2)+1/2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/c+(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R (2) +--R 2 2c x + b +--R (- 4a c + b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R +-+ | 2 +--R (4c e x - 2b e + 8c d)\|c \|c x + b x + a +--R / +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 562 + +--S 563 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R 2 3 3 2 2 | 2 +--R ((16a b c - 4a b )e x + (32a c - 8a b )e)\|c x + b x + a +--R + +--R 2 2 4 2 2 3 +--R (- 16a c + b )e x + (- 32a b c + 8a b )e x +--R + +--R 3 2 2 +--R (- 32a c + 8a b )e +--R * +--R +-+ +--R \|a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 3 3 2 2 2 +--R (- 16a c - 4b c)e x + ((- 24a b c + 2b )e + (- 32a c - 8b c)d)x +--R + +--R 2 2 +--R ((- 32a c + 8a b )e - 32a b c d)x +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 4 2 2 2 2 3 +--R 16a b c e x + ((32a c + 8a b c)e + 32a b c d)x +--R + +--R 2 3 2 2 2 2 +--R ((40a b c - 6a b )e + (32a c + 24a b c)d)x +--R + +--R 3 2 2 2 +--R ((32a c - 8a b )e + 32a b c d)x +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 2 +-+ | 2 +--R (16a b c x + 32a c)\|c \|c x + b x + a +--R + +--R 2 2 2 2 +-+ +-+ +--R ((- 16a c - 4b c)x - 32a b c x - 32a c)\|a \|c +--R , +--R +--R +--------------+ +--R 2 3 3 2 2 | 2 +--R ((- 16a b c + 4a b )e x + (- 32a c + 8a b )e)\|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +-+ +--R ((16a c - b )e x + (32a b c - 8a b )e x + (32a c - 8a b )e)\|a +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 2 3 3 2 2 2 +--R (- 8a c - 2b c)e x + ((- 12a b c + b )e + (- 16a c - 4b c)d)x +--R + +--R 2 2 +--R ((- 16a c + 4a b )e - 16a b c d)x +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 4 2 2 2 2 3 +--R 8a b c e x + ((16a c + 4a b c)e + 16a b c d)x +--R + +--R 2 3 2 2 2 2 +--R ((20a b c - 3a b )e + (16a c + 12a b c)d)x +--R + +--R 3 2 2 2 +--R ((16a c - 4a b )e + 16a b c d)x +--R * +--R +---+ +--R \|- c +--R / +--R +--------------+ +--R 2 +---+ | 2 +--R (8a b c x + 16a c)\|- c \|c x + b x + a +--R + +--R 2 2 2 2 +---+ +-+ +--R ((- 8a c - 2b c)x - 16a b c x - 16a c)\|- c \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 563 + +--S 564 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 3 3 2 2 | 2 +--R ((16a b c - 4a b )e x + (32a c - 8a b )e)\|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +-+ +--R ((- 16a c + b )e x + (- 32a b c + 8a b )e x + (- 32a c + 8a b )e)\|a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +--------------+ +--R 2 3 3 2 2 | 2 +--R ((16a b c - 4a b )e x + (32a c - 8a b )e)\|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +-+ +--R ((- 16a c + b )e x + (- 32a b c + 8a b )e x + (- 32a c + 8a b )e)\|a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R 2 2 2 +-+ +-+ | 2 +--R ((- 8a b e + 32a b c d)x - 16a b e + 64a c d)\|a \|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 2 2 +--R ((8a b c + 2a b )e + (- 32a c - 8a b c)d)x + (16a b e - 64a b c d)x +--R + +--R 3 3 +--R 16a b e - 64a c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 2 +-+ | 2 +--R (16a b c x + 32a c)\|c \|c x + b x + a +--R + +--R 2 2 2 2 +-+ +-+ +--R ((- 16a c - 4b c)x - 32a b c x - 32a c)\|a \|c +--R Type: Expression(Integer) +--E 564 + +--S 565 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 565 + +--S 566 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------------+ +--R 2 3 3 2 2 +---+ | 2 +--R ((16a b c - 4a b )e x + (32a c - 8a b )e)\|- c \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R ((- 16a c + b )e x + (- 32a b c + 8a b )e x + (- 32a c + 8a b )e) +--R * +--R +---+ +-+ +--R \|- c \|a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R 2 3 3 2 2 +-+ | 2 +--R ((- 32a b c + 8a b )e x + (- 64a c + 16a b )e)\|c \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R ((32a c - 2b )e x + (64a b c - 16a b )e x + (64a c - 16a b )e) +--R * +--R +-+ +-+ +--R \|a \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 2 2 +---+ +-+ +-+ +--R ((- 8a b e + 32a b c d)x - 16a b e + 64a c d)\|- c \|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 2 2 +--R ((8a b c + 2a b )e + (- 32a c - 8a b c)d)x + (16a b e - 64a b c d)x +--R + +--R 3 3 +--R 16a b e - 64a c d +--R * +--R +---+ +-+ +--R \|- c \|c +--R / +--R +--------------+ +--R 2 +---+ +-+ | 2 +--R (16a b c x + 32a c)\|- c \|c \|c x + b x + a +--R + +--R 2 2 2 2 +---+ +-+ +-+ +--R ((- 16a c - 4b c)x - 32a b c x - 32a c)\|- c \|a \|c +--R Type: Expression(Integer) +--E 566 + +--S 567 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 845 +t0:=(b+2*c*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2c x + b +--R (1) ----------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 568 + +--S 569 of 845 +r0:=2*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R (2) 2\|c x + b x + a +--R Type: Expression(Integer) +--E 569 + +--S 570 of 845 +a0:=integrate(t0,x) +--R +--R +--R +--------------+ +--R | 2 2 +-+ +--R - 2b x\|c x + b x + a + (4c x + 2b x)\|a +--R (3) -------------------------------------------- +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R Type: Union(Expression(Integer),...) +--E 570 + +--S 571 of 845 +m0:=a0-r0 +--R +--R +--R +--------------+ +--R | 2 +-+ +--R 4a\|c x + b x + a + (- 2b x - 4a)\|a +--R (4) --------------------------------------- +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 572 + +)clear all + +--S 573 of 845 +t0:=(b+2*c*x)/((d+e*x)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) -------------------------- +--R +--------------+ +--R | 2 +--R (e x + d)\|c x + b x + a +--R Type: Expression(Integer) +--E 573 + +--S 574 of 845 +r0:=2*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e-_ + (2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(e*sqrt(c*d^2-b*d*e+a*e^2)) +--R +--R +--R (2) +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R 2\|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R (b e - 2c d)x + 2a e - b d +--R (- b e + 2c d)atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R | 2 2 +--R e\|a e - b d e + c d +--R Type: Expression(Integer) +--E 574 + +--S 575 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (b e - 2c d) +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R +-------------------+ +--R +-+ | 2 2 +--R 2\|c \|a e - b d e + c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x +--R + +--R - 2a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R / +--R +-------------------+ +--R | 2 2 +--R e\|a e - b d e + c d +--R , +--R +--R +---------------------+ +--R | 2 2 +-+ +--R 2\|- a e + b d e - c d \|c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x +--R + +--R - 2a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R (2b e - 4c d) +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R / +--R +---------------------+ +--R | 2 2 +--R e\|- a e + b d e - c d +--R , +--R +--R (b e - 2c d) +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R +--------------+ +--R +-------------------+ | 2 +-+ +--R +---+ | 2 2 \|c x + b x + a - \|a +--R 4\|- c \|a e - b d e + c d atan(------------------------) +--R +---+ +--R x\|- c +--R / +--R +-------------------+ +--R | 2 2 +--R e\|a e - b d e + c d +--R , +--R +--R (2b e - 4c d) +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R +--------------+ +--R +---------------------+ | 2 +-+ +--R | 2 2 +---+ \|c x + b x + a - \|a +--R 4\|- a e + b d e - c d \|- c atan(------------------------) +--R +---+ +--R x\|- c +--R / +--R +---------------------+ +--R | 2 2 +--R e\|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 575 + +--S 576 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R (b e - 2c d) +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R +-------------------+ +--R +-+ | 2 2 +--R 2\|c \|a e - b d e + c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x - 2a +--R log(-------------------------------------------------------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R - 2\|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R (b e - 2c d)x + 2a e - b d +--R (b e - 2c d)atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R | 2 2 +--R e\|a e - b d e + c d +--R Type: Expression(Integer) +--E 576 + +--S 577 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 577 + +--S 578 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R 2\|- a e + b d e - c d \|c \|a e - b d e + c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x - 2a +--R log(-------------------------------------------------------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R - +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R 2\|- a e + b d e - c d \|c \|a e - b d e + c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +--R (b e - 2c d)\|- a e + b d e - c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 +--R (2b e - 4c d)\|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R / +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R e\|- a e + b d e - c d \|a e - b d e + c d +--R Type: Expression(Integer) +--E 578 + +--S 579 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 of 845 +t0:=(b+2*c*x)/((d+e*x)^2*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------- +--R +--------------+ +--R 2 2 2 | 2 +--R (e x + 2d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 580 + +--S 581 of 845 +r0:=-1/2*(b^2-4*a*c)*e*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)+(2*c*d-b*e)*_ + sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 +--R ((- 4a c + b )e x + (- 4a c + b )d e) +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R (- 2b e + 4c d)\|a e - b d e + c d \|c x + b x + a +--R / +--R 3 2 2 2 2 3 +--R ((2a e - 2b d e + 2c d e)x + 2a d e - 2b d e + 2c d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 581 + +--S 582 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R 2 2 2 2 +-+ | 2 +--R ((8a c - 2b )d e x + (8a c - 2b )d e)\|a \|c x + b x + a +--R + +--R 3 2 2 +--R (- 4a b c + b )d e x +--R + +--R 2 2 2 3 2 2 2 2 +--R ((- 8a c + 2a b )d e + (- 4a b c + b )d e)x + (- 8a c + 2a b )d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R +-------------------+ +--R 2 2 2 | 2 2 +--R (- 4a b e + (8a c + 2b )d e - 4b c d )x\|a e - b d e + c d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (2b e - 8b c d e + 8c d )x +--R + +--R 2 2 2 +--R (4a b e + (- 8a c - 2b )d e + 4b c d )x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 3 2 2 3 2 2 3 4 +-+ +--R ((4a d e - 4b d e + 4c d e)x + 4a d e - 4b d e + 4c d )\|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 3 2 +--R (- 2a b d e + 2b d e - 2b c d e)x +--R + +--R 2 3 2 2 2 3 4 2 2 2 +--R (- 4a d e + 2a b d e + (- 4a c + 2b )d e - 2b c d )x - 4a d e +--R + +--R 3 4 +--R 4a b d e - 4a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R , +--R +--R +--------------+ +--R 2 2 2 2 +-+ | 2 +--R ((8a c - 2b )d e x + (8a c - 2b )d e)\|a \|c x + b x + a +--R + +--R 3 2 2 +--R (- 4a b c + b )d e x +--R + +--R 2 2 2 3 2 2 2 2 +--R ((- 8a c + 2a b )d e + (- 4a b c + b )d e)x + (- 8a c + 2a b )d e +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R +---------------------+ +--R 2 2 2 | 2 2 +--R (- 2a b e + (4a c + b )d e - 2b c d )x\|- a e + b d e - c d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (b e - 4b c d e + 4c d )x +--R + +--R 2 2 2 +--R (2a b e + (- 4a c - b )d e + 2b c d )x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / +--R 3 2 2 3 2 2 3 4 +--R ((2a d e - 2b d e + 2c d e)x + 2a d e - 2b d e + 2c d ) +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 2 2 2 3 2 +--R (- a b d e + b d e - b c d e)x +--R + +--R 2 3 2 2 2 3 4 2 2 2 +--R (- 2a d e + a b d e + (- 2a c + b )d e - b c d )x - 2a d e +--R + +--R 3 4 +--R 2a b d e - 2a c d +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 582 + +--S 583 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 +-+ | 2 3 +--R (8a c - 2b )d e\|a \|c x + b x + a + (- 4a b c + b )d e x +--R + +--R 2 2 +--R (- 8a c + 2a b )d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R +--------------+ +--R 2 +-+ | 2 3 +--R (8a c - 2b )d e\|a \|c x + b x + a + (- 4a b c + b )d e x +--R + +--R 2 2 +--R (- 8a c + 2a b )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R (- 4a b e + 8a c d)\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 2 +-+ | 2 2 +--R ((2b e - 4b c d)x + 4a b e - 8a c d)\|a \|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 2 2 3 +-+ | 2 2 | 2 +--R (4a d e - 4b d e + 4c d )\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 3 2 2 2 3 +--R ((- 2a b d e + 2b d e - 2b c d )x - 4a d e + 4a b d e - 4a c d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 583 + +--S 584 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------------------+ +--------------+ +--R 2 | 2 2 +-+ | 2 +--R (8a c - 2b )d e\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R 3 2 2 | 2 2 +--R ((- 4a b c + b )d e x + (- 8a c + 2a b )d e)\|- a e + b d e - c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R 2 +-+ | 2 2 | 2 +--R (16a c - 4b )d e\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 3 2 2 | 2 2 +--R ((- 8a b c + 2b )d e x + (- 16a c + 4a b )d e)\|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R (- 4a b e + 8a c d)\|- a e + b d e - c d \|a e - b d e + c d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R +---------------------+ +--R 2 | 2 2 +-+ +--R ((2b e - 4b c d)x + 4a b e - 8a c d)\|- a e + b d e - c d \|a +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R +---------------------+ +--R 2 2 3 | 2 2 +-+ +--R (4a d e - 4b d e + 4c d )\|- a e + b d e - c d \|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 3 2 2 2 3 +--R ((- 2a b d e + 2b d e - 2b c d )x - 4a d e + 4a b d e - 4a c d ) +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R Type: Expression(Integer) +--E 585 + +--S 586 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 586 + +)clear all + +--S 587 of 845 +t0:=(b+2*c*x)/((d+e*x)^3*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ----------------------------------------------- +--R +--------------+ +--R 3 3 2 2 2 3 | 2 +--R (e x + 3d e x + 3d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 587 + +--S 588 of 845 +r0:=-3/8*(b^2-4*a*c)*e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+_ + 1/2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+_ + 1/4*(4*c^2*d^2+3*b^2*e^2-4*c*e*(b*d+2*a*e))*sqrt(a+b*x+c*x^2)/_ + ((c*d^2-b*d*e+a*e^2)^2*(d+e*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 2 +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e )x +--R + +--R 3 3 2 2 2 2 3 2 2 +--R ((24a b c - 6b )d e + (- 48a c + 12b c)d e )x + (12a b c - 3b )d e +--R + +--R 2 2 3 +--R (- 24a c + 6b c)d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 2 2 2 3 +--R ((- 16a c + 6b )e - 8b c d e + 8c d e)x - 4a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c + 10b )d e - 20b c d e + 16c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 2 6 5 2 2 4 3 3 2 4 2 2 +--R (8a e - 16a b d e + (16a c + 8b )d e - 16b c d e + 8c d e )x +--R + +--R 2 5 2 4 2 3 3 4 2 2 5 +--R (16a d e - 32a b d e + (32a c + 16b )d e - 32b c d e + 16c d e)x +--R + +--R 2 2 4 3 3 2 4 2 5 2 6 +--R 8a d e - 16a b d e + (16a c + 8b )d e - 16b c d e + 8c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 588 + +--S 589 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 4 2 4 2 2 3 3 3 3 +--R ((48a b c - 12a b )d e + (- 96a b c + 24a b c)d e )x +--R + +--R 3 2 3 2 4 +--R (96a b c - 24a b )d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 192a c + 144a b c - 24a b )d e +--R + +--R 2 2 3 4 2 +--R (- 192a b c + 48a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 3 +--R (192a b c - 48a b )d e +--R + +--R 3 2 2 2 4 4 2 +--R (- 384a c + 144a b c - 12a b )d e +--R + +--R 2 2 3 5 +--R (- 96a b c + 24a b c)d e +--R * +--R x +--R + +--R 3 2 3 4 2 3 2 2 2 5 +--R (96a b c - 24a b )d e + (- 192a c + 48a b c)d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 5 2 4 2 3 4 3 3 4 +--R ((- 48a b c + 3b )d e + (96a c - 6b c)d e )x +--R + +--R 2 2 4 2 4 2 2 3 5 3 3 +--R (- 96a b c + 24a b )d e + (96a b c - 48a b c + 6b )d e +--R + +--R 2 3 4 4 2 +--R (192a c - 12b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 4 +--R (- 96a b c + 24a b )d e +--R + +--R 3 2 2 2 4 3 3 +--R (192a c - 240a b c + 48a b )d e +--R + +--R 2 2 3 5 4 2 2 3 4 5 +--R (336a b c - 96a b c + 3b )d e + (96a c - 6b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 3 +--R (- 192a b c + 48a b )d e +--R + +--R 3 2 2 2 4 4 2 2 2 3 5 +--R (384a c - 192a b c + 24a b )d e + (192a b c - 48a b c)d e +--R * +--R x +--R + +--R 3 2 3 4 2 3 2 2 2 5 +--R (- 96a b c + 24a b )d e + (192a c - 48a b c)d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 2 2 2 2 2 2 +--R ((4a e + 4a c d )x + (8a d e + 4a b d )x + 8a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 2 3 2 2 2 3 2 +--R (4a e - 2a b d e + (4a c - 2b )d e + 2b c d )x +--R + +--R 2 2 2 3 +--R (8a d e - 8a b d e + 8a c d )x +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 3 +--R (- 2a b e + (- 4a c + b )d e - 2b c d )x +--R + +--R 2 2 2 2 2 +--R (- 4a e - 4a b d e + (- 8a c - b )d )x +--R + +--R 2 2 2 2 +--R (- 8a d e - 8a b d )x - 8a d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 2a b e + (- 4a c + 2a b )d e + 2a b c d e - 4a c d )x +--R + +--R 3 3 2 2 2 2 2 3 2 +--R (- 4a e - 2a b d e + (- 4a c + 6a b )d e - 6a b c d )x +--R + +--R 3 2 2 2 2 3 +--R (- 8a d e + 8a b d e - 8a c d )x +--R / +--R +--------------+ +--R 2 2 2 | 2 +--R (4a b e x + (8a e + 4a b d)x + 8a d)\|c x + b x + a +--R + +--R 2 3 2 2 +--R (- 4a c - b )e x + (- 8a b e + (- 4a c - b )d)x +--R + +--R 2 2 +--R (- 8a e - 8a b d)x - 8a d +--R * +--R +-+ +--R \|a +--R + +--R 2 2 5 2 3 4 +--R - 16a b e + (- 32a b c + 40a b )d e +--R + +--R 2 2 2 4 2 3 2 3 3 2 +--R (64a c - 88a b c - 6b )d e + (96a b c + 8b c)d e +--R + +--R 3 2 2 4 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 3 2 2 4 2 3 2 3 +--R - 32a b e + (- 64a c + 48a b )d e + (- 80a b c + 36a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (160a c - 128a b c - 10b )d e + (144a b c + 20b c)d e +--R + +--R 3 2 2 5 +--R (- 64a c - 16b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 3 2 +--R - 64a b d e + 128a b d e + (- 224a b c - 40a b )d e +--R + +--R 2 2 2 4 2 5 +--R (192a c + 80a b c)d e - 64a b c d +--R * +--R x +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (16a b c + 4a b )e + (32a c - 32a b c - 10a b )d e +--R + +--R 2 2 3 2 3 2 3 2 2 3 2 +--R (16a b c + 44a b c)d e + (- 64a c - 48a b c )d e +--R + +--R 3 4 +--R 32a b c d e +--R * +--R 4 +--R x +--R + +--R 3 2 5 3 2 3 4 +--R 32a b e + (96a b c - 72a b )d e +--R + +--R 3 2 2 2 4 2 3 2 2 3 3 2 +--R (- 64a c + 64a b c + 4a b )d e + (- 64a b c + 48a b c)d e +--R + +--R 2 3 2 2 4 3 5 +--R (- 64a c - 80a b c )d e + 64a b c d +--R * +--R 3 +--R x +--R + +--R 4 5 4 3 2 4 3 2 3 2 3 +--R 32a b e + (64a c - 16a b )d e + (80a b c - 100a b )d e +--R + +--R 3 2 2 2 4 3 2 +--R (- 160a c + 240a b c + 30a b )d e +--R + +--R 2 2 3 4 2 3 2 2 5 +--R (- 240a b c - 60a b c)d e + (64a c + 48a b c )d +--R * +--R 2 +--R x +--R + +--R 4 4 3 2 2 3 3 2 3 3 2 +--R 64a b d e - 128a b d e + (224a b c + 40a b )d e +--R + +--R 3 2 2 2 4 2 2 5 +--R (- 192a c - 80a b c)d e + 64a b c d +--R * +--R x +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 3 2 6 2 2 3 5 2 3 4 4 2 5 3 +--R 32a b d e - 64a b d e + (64a b c + 32a b )d e - 64a b c d e +--R + +--R 2 6 2 +--R 32a b c d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 3 5 3 2 2 4 4 3 5 3 +--R 64a d e - 64a b d e + (128a c - 64a b )d e + 64a b d e +--R + +--R 2 2 2 6 2 2 7 +--R (64a c - 128a b c)d e + 64a b c d e +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 3 2 2 5 3 +--R 128a d e - 224a b d e + (256a c + 64a b )d e +--R + +--R 2 3 6 2 2 2 2 7 2 8 +--R (- 192a b c + 32a b )d e + (128a c - 64a b c)d e + 32a b c d +--R * +--R x +--R + +--R 4 4 4 3 5 3 3 2 2 6 2 2 7 +--R 64a d e - 128a b d e + (128a c + 64a b )d e - 128a b c d e +--R + +--R 2 2 8 +--R 64a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 6 2 3 3 5 +--R (- 32a c - 8a b )d e + (64a b c + 16a b )d e +--R + +--R 2 2 2 4 4 4 2 3 5 3 +--R (- 64a c - 48a b c - 8b )d e + (64a b c + 16b c)d e +--R + +--R 3 2 2 6 2 +--R (- 32a c - 8b c )d e +--R * +--R 4 +--R x +--R + +--R 3 2 6 3 2 2 3 5 3 4 4 +--R - 64a b d e + (- 64a c + 112a b )d e - 32a b d e +--R + +--R 2 2 2 4 5 3 2 3 6 2 +--R (- 128a c + 32a b c - 16b )d e + (64a b c + 32b c)d e +--R + +--R 3 2 2 7 +--R (- 64a c - 16b c )d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 2 2 4 4 +--R - 64a d e + (- 160a c + 184a b )d e +--R + +--R 2 3 5 3 2 2 2 4 6 2 +--R (- 64a b c - 112a b )d e + (- 128a c + 208a b c - 8b )d e +--R + +--R 2 3 7 3 2 2 8 +--R (- 64a b c + 16b c)d e + (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 3 5 3 +--R - 128a d e + 192a b d e - 256a c d e +--R + +--R 2 3 6 2 2 2 2 7 2 8 +--R (128a b c - 64a b )d e + (- 128a c + 128a b c)d e - 64a b c d +--R * +--R x +--R + +--R 4 4 4 3 5 3 3 2 2 6 2 2 7 +--R - 64a d e + 128a b d e + (- 128a c - 64a b )d e + 128a b c d e +--R + +--R 2 2 8 +--R - 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R , +--R +--R 2 2 4 2 4 2 2 3 3 3 3 +--R ((- 48a b c + 12a b )d e + (96a b c - 24a b c)d e )x +--R + +--R 3 2 3 2 4 +--R (- 96a b c + 24a b )d e +--R + +--R 3 2 2 2 4 3 3 2 2 3 4 2 +--R (192a c - 144a b c + 24a b )d e + (192a b c - 48a b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 3 +--R (- 192a b c + 48a b )d e +--R + +--R 3 2 2 2 4 4 2 2 2 3 5 +--R (384a c - 144a b c + 12a b )d e + (96a b c - 24a b c)d e +--R * +--R x +--R + +--R 3 2 3 4 2 3 2 2 2 5 +--R (- 96a b c + 24a b )d e + (192a c - 48a b c)d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 5 2 4 2 3 4 3 3 4 +--R ((48a b c - 3b )d e + (- 96a c + 6b c)d e )x +--R + +--R 2 2 4 2 4 2 2 3 5 3 3 +--R (96a b c - 24a b )d e + (- 96a b c + 48a b c - 6b )d e +--R + +--R 2 3 4 4 2 +--R (- 192a c + 12b c)d e +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 4 +--R (96a b c - 24a b )d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 192a c + 240a b c - 48a b )d e +--R + +--R 2 2 3 5 4 2 2 3 4 5 +--R (- 336a b c + 96a b c - 3b )d e + (- 96a c + 6b c)d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 3 +--R (192a b c - 48a b )d e +--R + +--R 3 2 2 2 4 4 2 +--R (- 384a c + 192a b c - 24a b )d e +--R + +--R 2 2 3 5 +--R (- 192a b c + 48a b c)d e +--R * +--R x +--R + +--R 3 2 3 4 2 3 2 2 2 5 +--R (96a b c - 24a b )d e + (- 192a c + 48a b c)d e +--R * +--R +-+ +--R \|a +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R d\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +--R (- a e x - a d)\|- a e + b d e - c d +--R / +--R 2 2 +-+ +--R (a e - b d e + c d )x\|a +--R + +--R 2 2 5 2 3 4 +--R - 8a b e + (- 16a b c + 20a b )d e +--R + +--R 2 2 2 4 2 3 2 3 3 2 +--R (32a c - 44a b c - 3b )d e + (48a b c + 4b c)d e +--R + +--R 3 2 2 4 +--R (- 16a c - 4b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 3 2 2 4 2 3 2 3 +--R - 16a b e + (- 32a c + 24a b )d e + (- 40a b c + 18a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (80a c - 64a b c - 5b )d e + (72a b c + 10b c)d e +--R + +--R 3 2 2 5 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 3 2 +--R - 32a b d e + 64a b d e + (- 112a b c - 20a b )d e +--R + +--R 2 2 2 4 2 5 +--R (96a c + 40a b c)d e - 32a b c d +--R * +--R x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (8a b c + 2a b )e + (16a c - 16a b c - 5a b )d e +--R + +--R 2 2 3 2 3 2 3 2 2 3 2 3 4 +--R (8a b c + 22a b c)d e + (- 32a c - 24a b c )d e + 16a b c d e +--R * +--R 4 +--R x +--R + +--R 3 2 5 3 2 3 4 +--R 16a b e + (48a b c - 36a b )d e +--R + +--R 3 2 2 2 4 2 3 2 2 3 3 2 +--R (- 32a c + 32a b c + 2a b )d e + (- 32a b c + 24a b c)d e +--R + +--R 2 3 2 2 4 3 5 +--R (- 32a c - 40a b c )d e + 32a b c d +--R * +--R 3 +--R x +--R + +--R 4 5 4 3 2 4 3 2 3 2 3 +--R 16a b e + (32a c - 8a b )d e + (40a b c - 50a b )d e +--R + +--R 3 2 2 2 4 3 2 2 2 3 4 +--R (- 80a c + 120a b c + 15a b )d e + (- 120a b c - 30a b c)d e +--R + +--R 2 3 2 2 5 +--R (32a c + 24a b c )d +--R * +--R 2 +--R x +--R + +--R 4 4 3 2 2 3 3 2 3 3 2 +--R 32a b d e - 64a b d e + (112a b c + 20a b )d e +--R + +--R 3 2 2 2 4 2 2 5 +--R (- 96a c - 40a b c)d e + 32a b c d +--R * +--R x +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R / +--R 3 2 6 2 2 3 5 2 3 4 4 2 5 3 +--R 16a b d e - 32a b d e + (32a b c + 16a b )d e - 32a b c d e +--R + +--R 2 6 2 +--R 16a b c d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 3 5 3 2 2 4 4 3 5 3 +--R 32a d e - 32a b d e + (64a c - 32a b )d e + 32a b d e +--R + +--R 2 2 2 6 2 2 7 +--R (32a c - 64a b c)d e + 32a b c d e +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 3 2 2 5 3 +--R 64a d e - 112a b d e + (128a c + 32a b )d e +--R + +--R 2 3 6 2 2 2 2 7 2 8 +--R (- 96a b c + 16a b )d e + (64a c - 32a b c)d e + 16a b c d +--R * +--R x +--R + +--R 4 4 4 3 5 3 3 2 2 6 2 2 7 2 2 8 +--R 32a d e - 64a b d e + (64a c + 32a b )d e - 64a b c d e + 32a c d +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 3 2 2 2 6 2 3 3 5 +--R (- 16a c - 4a b )d e + (32a b c + 8a b )d e +--R + +--R 2 2 2 4 4 4 2 3 5 3 +--R (- 32a c - 24a b c - 4b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 6 2 +--R (- 16a c - 4b c )d e +--R * +--R 4 +--R x +--R + +--R 3 2 6 3 2 2 3 5 3 4 4 +--R - 32a b d e + (- 32a c + 56a b )d e - 16a b d e +--R + +--R 2 2 2 4 5 3 2 3 6 2 +--R (- 64a c + 16a b c - 8b )d e + (32a b c + 16b c)d e +--R + +--R 3 2 2 7 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 2 2 4 4 2 3 5 3 +--R - 32a d e + (- 80a c + 92a b )d e + (- 32a b c - 56a b )d e +--R + +--R 2 2 2 4 6 2 2 3 7 +--R (- 64a c + 104a b c - 4b )d e + (- 32a b c + 8b c)d e +--R + +--R 3 2 2 8 +--R (- 16a c - 4b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 3 5 3 2 3 6 2 +--R - 64a d e + 96a b d e - 128a c d e + (64a b c - 32a b )d e +--R + +--R 2 2 2 7 2 8 +--R (- 64a c + 64a b c)d e - 32a b c d +--R * +--R x +--R + +--R 4 4 4 3 5 3 3 2 2 6 2 2 7 +--R - 32a d e + 64a b d e + (- 64a c - 32a b )d e + 64a b c d e +--R + +--R 2 2 8 +--R - 32a c d +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 589 + +--S 590 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 4 2 2 2 2 3 3 +--R ((48a b c - 12a b )d e + (- 96a b c + 24a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (96a b c - 24a b )d e + (- 192a c + 48a b c)d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 5 2 2 2 3 4 3 2 +--R ((- 48a b c + 3b )d e + (96a c - 6b c)d e)x +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((- 96a b c + 24a b )d e + (192a b c - 48a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (- 96a b c + 24a b )d e + (192a c - 48a b c)d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 2 2 2 2 2 2 +--R ((4a e + 4a c d )x + (8a d e + 4a b d )x + 8a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 2 3 2 2 2 3 2 +--R (4a e - 2a b d e + (4a c - 2b )d e + 2b c d )x +--R + +--R 2 2 2 3 +--R (8a d e - 8a b d e + 8a c d )x +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 3 +--R (- 2a b e + (- 4a c + b )d e - 2b c d )x +--R + +--R 2 2 2 2 2 +--R (- 4a e - 4a b d e + (- 8a c - b )d )x +--R + +--R 2 2 2 2 +--R (- 8a d e - 8a b d )x - 8a d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 2a b e + (- 4a c + 2a b )d e + 2a b c d e - 4a c d )x +--R + +--R 3 3 2 2 2 2 2 3 2 +--R (- 4a e - 2a b d e + (- 4a c + 6a b )d e - 6a b c d )x +--R + +--R 3 2 2 2 2 3 +--R (- 8a d e + 8a b d e - 8a c d )x +--R / +--R +--------------+ +--R 2 2 2 | 2 +--R (4a b e x + (8a e + 4a b d)x + 8a d)\|c x + b x + a +--R + +--R 2 3 2 2 +--R (- 4a c - b )e x + (- 8a b e + (- 4a c - b )d)x +--R + +--R 2 2 +--R (- 8a e - 8a b d)x - 8a d +--R * +--R +-+ +--R \|a +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((- 48a b c + 12a b )d e + (96a b c - 24a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (- 96a b c + 24a b )d e + (192a c - 48a b c)d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 5 2 2 2 3 4 3 2 +--R ((48a b c - 3b )d e + (- 96a c + 6b c)d e)x +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((96a b c - 24a b )d e + (- 192a b c + 48a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (96a b c - 24a b )d e + (- 192a c + 48a b c)d e +--R * +--R +-+ +--R \|a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 3 2 3 2 2 2 2 3 +--R (- 16a b e + (- 32a b c + 40a b )d e - 80a b c d e + 64a b c d )x +--R + +--R 3 3 3 2 2 2 2 2 2 2 3 +--R - 32a b e + (- 64a c + 80a b )d e - 160a b c d e + 128a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 3 3 2 2 2 4 2 +--R (16a b c + 4a b )e + (32a c - 32a b c - 10a b )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (80a b c + 20a b c)d e + (- 64a c - 16a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 2 3 2 2 2 2 2 2 3 +--R (32a b e + (64a b c - 80a b )d e + 160a b c d e - 128a b c d )x +--R + +--R 4 3 4 3 2 2 3 2 3 2 3 +--R 32a b e + (64a c - 80a b )d e + 160a b c d e - 128a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 3 2 4 2 2 3 3 2 3 4 2 2 5 +--R 32a b d e - 64a b d e + (64a b c + 32a b )d e - 64a b c d e +--R + +--R 2 6 +--R 32a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 +--R 64a d e - 128a b d e + (128a c + 64a b )d e - 128a b c d e +--R + +--R 2 2 6 +--R 64a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 4 2 3 3 3 +--R (- 32a c - 8a b )d e + (64a b c + 16a b )d e +--R + +--R 2 2 2 4 4 2 2 3 5 +--R (- 64a c - 48a b c - 8b )d e + (64a b c + 16b c)d e +--R + +--R 3 2 2 6 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 2 3 3 2 3 4 2 +--R - 64a b d e + 128a b d e + (- 128a b c - 64a b )d e +--R + +--R 2 5 2 6 +--R 128a b c d e - 64a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 +--R - 64a d e + 128a b d e + (- 128a c - 64a b )d e + 128a b c d e +--R + +--R 2 2 6 +--R - 64a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R Type: Expression(Integer) +--E 590 + +--S 591 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 591 + +--S 592 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 4 2 2 2 2 3 3 +--R ((- 48a b c + 12a b )d e + (96a b c - 24a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (- 96a b c + 24a b )d e + (192a c - 48a b c)d e +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 2 5 2 2 2 3 4 3 2 +--R ((48a b c - 3b )d e + (- 96a c + 6b c)d e)x +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((96a b c - 24a b )d e + (- 192a b c + 48a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (96a b c - 24a b )d e + (- 192a c + 48a b c)d e +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((- 96a b c + 24a b )d e + (192a b c - 48a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (- 192a b c + 48a b )d e + (384a c - 96a b c)d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 5 2 2 2 3 4 3 2 +--R ((96a b c - 6b )d e + (- 192a c + 12b c)d e)x +--R + +--R 2 2 4 2 2 2 2 3 3 +--R ((192a b c - 48a b )d e + (- 384a b c + 96a b c)d e)x +--R + +--R 3 2 3 2 2 3 2 2 2 3 +--R (192a b c - 48a b )d e + (- 384a c + 96a b c)d e +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R d\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +--R (- a e x - a d)\|- a e + b d e - c d +--R / +--R 2 2 +-+ +--R (a e - b d e + c d )x\|a +--R + +--R 2 2 3 2 3 2 2 2 2 3 +--R (- 16a b e + (- 32a b c + 40a b )d e - 80a b c d e + 64a b c d )x +--R + +--R 3 3 3 2 2 2 2 2 2 2 3 +--R - 32a b e + (- 64a c + 80a b )d e - 160a b c d e + 128a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 +-+ | 2 2 | 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 3 3 3 2 2 2 4 2 +--R (16a b c + 4a b )e + (32a c - 32a b c - 10a b )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (80a b c + 20a b c)d e + (- 64a c - 16a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 3 2 3 2 2 2 2 2 2 3 +--R (32a b e + (64a b c - 80a b )d e + 160a b c d e - 128a b c d )x +--R + +--R 4 3 4 3 2 2 3 2 3 2 3 +--R 32a b e + (64a c - 80a b )d e + 160a b c d e - 128a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R / +--R 3 2 4 2 2 3 3 2 3 4 2 2 5 +--R 32a b d e - 64a b d e + (64a b c + 32a b )d e - 64a b c d e +--R + +--R 2 6 +--R 32a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 +--R 64a d e - 128a b d e + (128a c + 64a b )d e - 128a b c d e +--R + +--R 2 2 6 +--R 64a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 | 2 2 | 2 +--R \|- a e + b d e - c d \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 4 2 3 3 3 +--R (- 32a c - 8a b )d e + (64a b c + 16a b )d e +--R + +--R 2 2 2 4 4 2 2 3 5 +--R (- 64a c - 48a b c - 8b )d e + (64a b c + 16b c)d e +--R + +--R 3 2 2 6 +--R (- 32a c - 8b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 2 3 3 2 3 4 2 +--R - 64a b d e + 128a b d e + (- 128a b c - 64a b )d e +--R + +--R 2 5 2 6 +--R 128a b c d e - 64a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 +--R - 64a d e + 128a b d e + (- 128a c - 64a b )d e + 128a b c d e +--R + +--R 2 2 6 +--R - 64a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d +--R Type: Expression(Integer) +--E 592 + +--S 593 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 593 + +)clear all + +--S 594 of 845 +t0:=(b+2*c*x)/((d+e*x)^4*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) --------------------------------------------------------- +--R +--------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 594 + +--S 595 of 845 +r0:=-1/16*(b^2-4*a*c)*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)+1/3*(2*c*d-b*e)*_ + sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^3)+1/12*(8*c^2*d^2+_ + 5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+_ + a*e^2)^2*(d+e*x)^2)+1/24*(2*c*d-b*e)*(8*c^2*d^2+15*b^2*e^2-4*c*e*_ + (2*b*d+13*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^3*(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 4 6 2 3 5 +--R (48a c - 72a b c + 15b )e + (192a b c - 48b c)d e +--R + +--R 3 2 2 2 4 +--R (- 192a c + 48b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 5 2 3 2 4 +--R (144a c - 216a b c + 45b )d e + (576a b c - 144b c)d e +--R + +--R 3 2 2 3 3 +--R (- 576a c + 144b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (144a c - 216a b c + 45b )d e + (576a b c - 144b c)d e +--R + +--R 3 2 2 4 2 +--R (- 576a c + 144b c )d e +--R * +--R x +--R + +--R 2 2 2 4 3 3 2 3 4 2 +--R (48a c - 72a b c + 15b )d e + (192a b c - 48b c)d e +--R + +--R 3 2 2 5 +--R (- 192a c + 48b c )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (104a b c - 30b 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7 2 3 6 2 2 4 5 +--R 144a d e - 432a b d e + (432a c + 432a b )d e +--R + +--R 3 5 4 2 2 6 3 2 7 2 +--R (- 864a b c - 144b )d e + (432a c + 432b c)d e - 432b c d e +--R + +--R 3 8 +--R 144c d e +--R * +--R x +--R + +--R 3 3 6 2 4 5 2 2 5 4 +--R 48a d e - 144a b d e + (144a c + 144a b )d e +--R + +--R 3 6 3 2 2 7 2 2 8 3 9 +--R (- 288a b c - 48b )d e + (144a c + 144b c)d e - 144b c d e + 48c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 595 + +--S 596 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 4 6 3 6 +--R (384a c - 288a b c - 312a b c + 90b )d e +--R + +--R 2 3 3 2 5 4 5 +--R (1536a b c + 768a b c - 288b c)d e +--R + +--R 2 4 2 3 4 2 5 4 +--R (- 1536a c - 768a b c + 288b c )d e +--R * +--R 5 +--R x +--R + +--R 3 2 2 3 5 3 6 +--R (1536a b c - 2304a b c + 480a b )d e +--R + +--R 3 3 2 2 2 4 6 4 5 +--R (1152a c + 5280a b c - 2472a b c + 270b )d e +--R + +--R 2 3 3 2 5 5 4 +--R (- 1536a b c + 3840a b c 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+--R 3 3 2 2 2 4 6 6 3 +--R (18048a c - 22752a b c + 4920a b c - 90b )d e +--R + +--R 2 3 3 2 5 7 2 +--R (16896a b c - 5376a b c + 288b c)d e +--R + +--R 2 4 2 3 4 2 8 +--R (1536a c + 768a b c - 288b c )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 2 2 4 5 4 +--R (- 4608a c + 6912a b c - 1440a b )d e +--R + +--R 3 2 2 3 5 6 3 +--R (- 19968a b c + 6912a b c - 480a b )d e +--R + +--R 3 3 2 2 2 4 7 2 +--R (18432a c - 10752a b c + 1536a b c)d e +--R + +--R 2 3 3 2 8 +--R (6144a b c - 1536a b c )d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 6 3 +--R (- 1536a c + 2304a b c - 480a b )d e +--R + +--R 3 2 2 3 7 2 3 3 2 2 2 8 +--R (- 6144a b c + 1536a b c)d e + (6144a c - 1536a b c )d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 6 +--R (576a b c - 816a b c + 108a b c + 15b )d e +--R + +--R 2 2 3 4 2 6 4 5 +--R (2304a b c - 384a b c - 48b c)d e +--R + +--R 2 4 3 3 5 2 5 4 +--R (- 2304a b c + 384a b c + 48b c )d e +--R * +--R 6 +--R x +--R + +--R 4 3 3 2 2 2 4 6 3 6 +--R (1152a c - 864a b c - 936a b c + 270a b )d e +--R + +--R 3 3 2 3 2 5 7 4 5 +--R (6336a b c - 144a b c - 540a b c + 45b )d e +--R + +--R 3 4 2 2 3 4 2 6 5 4 +--R (- 4608a c + 4608a b c - 288a b c - 144b c)d e +--R + +--R 2 4 3 3 5 2 6 3 +--R (- 6912a b c + 1152a b c + 144b c )d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 3 2 5 3 6 +--R (2304a b c - 3456a b c + 720a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 5 +--R (3456a c + 6624a b c - 5112a b c + 810a b )d e +--R + +--R 3 3 2 3 2 5 7 5 4 +--R (6336a b c + 6768a b c - 2268a b c + 45b )d e +--R + +--R 3 4 4 2 6 6 3 +--R (- 13824a c + 1440a b c - 144b c)d e +--R + +--R 2 4 3 3 5 2 7 2 +--R (- 6912a b c + 1152a b c + 144b c )d e +--R * +--R 4 +--R x +--R + +--R 5 2 4 2 3 4 3 6 +--R (1536a c - 2304a b c + 480a b )d e +--R + +--R 4 2 3 3 2 5 4 5 +--R (13056a b c - 11904a b c + 2160a b )d e +--R + +--R 4 3 3 2 2 2 4 6 5 4 +--R (- 2688a c + 26592a b c - 9720a b c + 810a b )d e +--R + +--R 3 3 2 3 2 5 7 6 3 +--R (- 13248a b c + 13008a b c - 2484a b c + 15b )d e +--R + +--R 3 4 2 2 3 4 2 6 7 2 +--R (- 13824a c - 4608a b c + 2208a b c - 48b c)d e +--R + +--R 2 4 3 3 5 2 8 +--R (- 2304a b c + 384a b c + 48b c )d e +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 4 5 +--R (4608a c - 6912a b c + 1440a b )d e +--R + +--R 4 2 3 3 2 5 5 4 +--R (25344a b c - 14976a b c + 2160a b )d e +--R + +--R 4 3 3 2 2 2 4 6 6 3 +--R (- 17280a c + 31392a b c - 7848a b c + 270a b )d e +--R + +--R 3 3 2 3 2 5 7 2 +--R (- 23040a b c + 9216a b c - 864a b c)d e +--R + +--R 3 4 2 2 3 4 2 8 +--R (- 4608a c - 2304a b c + 864a b c )d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 2 3 4 5 4 +--R (4608a c - 6912a b c + 1440a b )d e +--R + +--R 4 2 3 3 2 5 6 3 +--R (20736a b c - 8064a b c + 720a b )d e +--R + +--R 4 3 3 2 2 2 4 7 2 +--R (- 18432a c + 13824a b c - 2304a b c)d e +--R + +--R 3 3 2 3 2 8 +--R (- 9216a b c + 2304a b c )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 6 3 4 2 3 3 7 2 +--R (1536a c - 2304a b c + 480a b )d e + (6144a b c - 1536a b c)d e +--R + +--R 4 3 3 2 2 8 +--R (- 6144a c + 1536a b c )d e +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 4 3 3 8 4 2 3 2 2 4 7 +--R (- 64a b c - 48a b )e + (- 64a c + 160a b c + 156a b )d e +--R + +--R 3 2 2 3 5 2 6 +--R (96a b c - 192a b c - 198a b )d e +--R + +--R 3 3 2 2 2 4 6 3 5 +--R (- 640a c - 336a b c + 704a b c + 15b )d e +--R + +--R 2 3 3 2 5 4 4 +--R (480a b c - 928a b c - 38b c)d e +--R + +--R 2 4 2 3 4 2 5 3 4 3 3 6 2 +--R (384a c + 576a b c + 24b c )d e + (- 192a b c - 16b c )d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 4 3 3 7 +--R - 256a b e + (- 448a b c + 688a b )d e +--R + +--R 4 2 3 2 2 4 2 6 +--R (- 192a c + 864a b c - 588a b )d e +--R + +--R 3 2 2 3 5 3 5 +--R (- 3232a b c + 1824a b c - 334a b )d e +--R + +--R 3 3 2 2 2 4 6 4 4 +--R (576a c - 2592a b c + 1412a b c + 40b )d e +--R + +--R 2 3 3 2 5 5 3 +--R (2400a b c - 2304a b c - 102b c)d e +--R + +--R 2 4 2 3 4 2 6 2 4 3 3 7 +--R (768a c + 1536a b c + 80b c )d e + (- 576a b c - 48b c )d e +--R * +--R 4 +--R x +--R + +--R 5 8 5 4 2 7 +--R - 256a b e + (- 256a c + 64a b )d e +--R + +--R 4 3 3 2 6 +--R (- 576a b c + 1296a b )d e +--R + +--R 4 2 3 2 2 4 3 5 +--R (- 2176a c + 2496a b c - 2152a b )d e +--R + +--R 3 2 2 3 5 4 4 +--R (- 8064a b c + 5456a b c + 100a b )d e +--R + +--R 3 3 2 2 2 4 6 5 3 +--R (4800a c - 5904a b c + 276a b c + 33b )d e +--R + +--R 2 3 3 2 5 6 2 +--R (4416a b c - 1360a b c - 96b c)d e +--R + +--R 2 3 4 2 7 4 3 3 8 +--R (1152a b c + 96b c )d e + (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 5 7 5 4 2 2 6 3 3 3 5 +--R - 768a b d e + (- 768a c + 1728a b )d e - 576a b d e +--R + +--R 4 2 3 2 2 4 4 4 +--R (- 4224a c + 3456a b c - 1560a b )d e +--R + +--R 3 2 2 3 5 5 3 +--R (- 5952a b c + 4704a b c + 396a b )d e +--R + +--R 3 3 2 2 2 4 6 2 +--R (5376a c - 5952a b c - 1152a b c)d e +--R + +--R 2 3 3 2 7 2 4 2 3 8 +--R (3840a b c + 1152a b c )d e + (- 768a c - 576a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 2 3 5 4 3 3 4 4 +--R - 768a b d e + 2304a b d e + (- 2304a b c - 2304a b )d e +--R + +--R 4 2 3 2 2 4 5 3 +--R (- 768a c + 5760a b c + 528a b )d e +--R + +--R 3 2 2 3 6 2 3 3 2 2 2 7 +--R (- 5376a b c - 1536a b c)d e + (3072a c + 1536a b c )d e +--R + +--R 2 3 8 +--R - 768a b c d +--R * +--R x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 3 2 2 4 8 3 2 2 3 5 7 +--R (96a b c + 8a b )e + (96a b c - 304a b c - 26a b )d e +--R + +--R 2 2 2 4 6 2 6 +--R (- 144a b c + 384a b c + 33b )d e +--R + +--R 2 3 3 2 5 3 5 +--R (1376a b c - 880a b c - 186b c)d e +--R + +--R 2 4 2 3 4 2 4 4 +--R (- 832a c + 832a b c + 324b c )d e +--R + +--R 4 3 3 5 3 5 2 4 6 2 +--R (- 768a b c - 192b c )d e + (128a c + 96b c )d e +--R * +--R 6 +--R x +--R + +--R 4 3 3 8 4 2 3 2 2 4 7 +--R (192a b c + 144a b )e + (192a c - 192a b c - 444a b )d e +--R + +--R 2 3 5 2 6 +--R (- 336a b c + 516a b )d e +--R + +--R 3 3 2 2 2 4 6 3 5 +--R (1728a c + 720a b c - 804a b c + 9b )d e +--R + +--R 2 3 3 2 5 4 4 +--R (1920a b c - 240a b c - 300b c)d e +--R + +--R 2 4 2 3 4 2 5 3 +--R (- 2880a c + 1152a b c + 756b c )d e +--R + +--R 4 3 3 6 2 5 2 4 7 +--R (- 1728a b c - 528b c )d e + (384a c + 288b c )d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 4 3 3 7 +--R 384a b e + (960a b c - 816a b )d e +--R + +--R 4 2 3 2 2 4 2 6 +--R (576a c - 1728a b c + 204a b )d e +--R + +--R 3 2 2 3 5 3 5 +--R (4320a b c - 2208a b c + 1194a b )d e +--R + +--R 3 3 2 2 2 4 6 4 4 +--R (1536a c + 3792a b c - 3360a b c - 141b )d e +--R + +--R 2 3 3 2 5 5 3 +--R (- 2016a b c + 3648a b c + 126b c)d e +--R + +--R 2 4 2 3 4 2 6 2 +--R (- 3456a c - 1440a b c + 384b c )d e +--R + +--R 4 3 3 7 5 2 4 8 +--R (- 576a b c - 432b c )d e + (384a c + 288b c )d +--R * +--R 4 +--R x +--R + +--R 5 8 5 4 2 7 4 3 3 2 6 +--R 256a b e + (256a c + 320a b )d e + (1344a b c - 2256a b )d e +--R + +--R 4 2 3 2 2 4 3 5 +--R (2176a c - 3648a b c + 2728a b )d e +--R + +--R 3 2 2 3 5 4 4 +--R (11328a b c - 6320a b c + 392a b )d e +--R + +--R 3 3 2 2 2 4 6 5 3 +--R (- 4416a c + 5904a b c - 2172a b c - 165b )d e +--R + +--R 2 3 3 2 5 6 2 +--R (- 4416a b c + 4432a b c + 480b c)d e +--R + +--R 2 4 2 3 4 2 7 4 3 3 8 +--R (- 1536a c - 3456a b c - 480b c )d e + (1344a b c + 240b c )d +--R * +--R 3 +--R x +--R + +--R 5 7 5 4 2 2 6 3 3 3 5 +--R 768a b d e + (768a c - 1344a b )d e - 576a b d e +--R + +--R 4 2 3 2 2 4 4 4 +--R (4224a c - 2304a b c + 2712a b )d e +--R + +--R 3 2 2 3 5 5 3 +--R (6336a b c - 7584a b c - 660a b )d e +--R + +--R 3 3 2 2 2 4 6 2 +--R (- 5376a c + 8640a b c + 1920a b c)d e +--R + +--R 2 3 3 2 7 2 4 2 3 8 +--R (- 5376a b c - 1920a b c )d e + (768a c + 960a b c )d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 2 3 5 4 3 3 4 4 +--R 768a b d e - 2304a b d e + (2304a b c + 2304a b )d e +--R + +--R 4 2 3 2 2 4 5 3 +--R (768a c - 5760a b c - 528a b )d e +--R + +--R 3 2 2 3 6 2 3 3 2 2 2 7 +--R (5376a b c + 1536a b c)d e + (- 3072a c - 1536a b c )d e +--R + +--R 2 3 8 +--R 768a b c d +--R * +--R x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / +--R 4 3 2 3 9 3 2 3 4 8 +--R (192a c + 144a b )d e + (- 576a b c - 432a b )d e +--R + +--R 3 2 2 2 4 5 7 +--R (576a c + 1008a b c + 432a b )d e +--R + +--R 2 2 3 5 6 6 +--R (- 1152a b c - 1056a b c - 144b )d e +--R + +--R 2 3 2 2 4 7 5 +--R (576a c + 1008a b c + 432b c)d e +--R + +--R 3 3 2 8 4 4 2 3 9 3 +--R (- 576a b c - 432b c )d e + (192a c + 144b c )d e +--R * +--R 5 +--R x +--R + +--R 4 3 9 4 3 2 4 8 +--R 768a b d e + (576a c - 1872a b )d e +--R + +--R 3 2 3 5 7 +--R (576a b c + 1008a b )d e +--R + +--R 3 2 2 2 4 6 6 +--R (1728a c - 1584a b c + 528a b )d e +--R + +--R 2 2 3 5 7 5 +--R (- 1152a b c - 864a b c - 432b )d e +--R + +--R 2 3 2 2 4 8 4 +--R (1728a c + 720a b c + 1296b c)d e +--R + +--R 3 3 2 9 3 4 2 3 10 2 +--R (- 960a b c - 1296b c )d e + (576a c + 432b c )d e +--R * +--R 4 +--R x +--R + +--R 5 3 9 4 3 2 5 7 +--R 768a d e + (2880a c - 4176a b )d e +--R + +--R 3 2 3 6 6 +--R (576a b c + 4848a b )d e +--R + +--R 3 2 2 2 4 7 5 +--R (4032a c - 8496a b c - 1008a b )d e +--R + +--R 2 2 3 5 8 4 +--R (1152a b c + 3744a b c - 432b )d e +--R + +--R 2 3 2 2 4 9 3 +--R (2496a c - 3888a b c + 1296b c)d e +--R + +--R 3 3 2 10 2 4 2 3 11 +--R (576a b c - 1296b c )d e + (576a c + 432b c )d e +--R * +--R 3 +--R x +--R + +--R 5 4 8 4 5 7 4 3 2 6 6 +--R 2304a d e - 4608a b d e + (7104a c + 144a b )d e +--R + +--R 3 2 3 7 5 +--R (- 7488a b c + 4176a b )d e +--R + +--R 3 2 2 2 4 8 4 +--R (7488a c - 5904a b c - 1872a b )d e +--R + +--R 2 2 3 5 9 3 +--R (- 1152a b c + 5856a b c - 144b )d e +--R + +--R 2 3 2 2 4 10 2 +--R (2880a c - 5904a b c + 432b c)d e +--R + +--R 3 3 2 11 4 2 3 12 +--R (1728a b c - 432b c )d e + (192a c + 144b c )d +--R * +--R 2 +--R x +--R + +--R 5 5 7 4 6 6 4 3 2 7 5 +--R 2304a d e - 6144a b d e + (6912a c + 4608a b )d e +--R + +--R 3 8 4 3 2 2 2 4 9 3 +--R - 11520a b c d e + (6912a c + 2304a b c - 768a b )d e +--R + +--R 2 2 3 10 2 2 3 2 2 11 +--R (- 4608a b c + 2304a b c)d e + (2304a c - 2304a b c )d e +--R + +--R 3 12 +--R 768a b c d +--R * +--R x +--R + +--R 5 6 6 4 7 5 4 3 2 8 4 +--R 768a d e - 2304a b d e + (2304a c + 2304a b )d e +--R + +--R 3 2 3 9 3 3 2 2 2 10 2 +--R (- 4608a b c - 768a b )d e + (2304a c + 2304a b c)d e +--R + +--R 2 2 11 2 3 12 +--R - 2304a b c d e + 768a c d +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 4 3 3 3 9 3 2 2 4 4 8 +--R (- 288a b c - 24a b )d e + (864a b c + 72a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 864a b c - 936a b c - 72a b )d e +--R + +--R 2 2 2 4 6 6 6 +--R (1728a b c + 432a b c + 24b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 864a b c - 936a b c - 72b c)d e +--R + +--R 2 3 4 2 8 4 4 3 3 9 3 +--R (864a b c + 72b c )d e + (- 288a 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+ +--R 2 3 3 2 11 2 4 2 3 12 +--R (- 1728a b c + 1296a b c )d e + (- 576a c - 432a b c )d +--R * +--R 2 +--R x +--R + +--R 6 5 7 5 6 6 5 4 2 7 5 +--R - 2304a d e + 5760a b d e + (- 6912a c - 3456a b )d e +--R + +--R 4 3 3 8 4 4 2 2 4 9 3 +--R (10368a b c - 1152a b )d e + (- 6912a c + 1152a b )d e +--R + +--R 3 2 2 3 10 2 3 3 2 2 2 11 +--R (3456a b c - 3456a b c)d e + (- 2304a c + 3456a b c )d e +--R + +--R 2 3 12 +--R - 1152a b c d +--R * +--R x +--R + +--R 6 6 6 5 7 5 5 4 2 8 4 +--R - 768a d e + 2304a b d e + (- 2304a c - 2304a b )d e +--R + +--R 4 3 3 9 3 4 2 3 2 10 2 +--R (4608a b c + 768a b )d e + (- 2304a c - 2304a b c)d e +--R + +--R 3 2 11 3 3 12 +--R 2304a b c d e - 768a c d +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 596 + +--S 597 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 4 6 3 3 +--R (384a c - 288a b c - 312a b c + 90b )d e +--R + +--R 2 3 3 2 5 4 2 +--R (1536a b c + 768a b 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+--R + +--R 3 4 2 2 3 4 2 5 +--R (- 4608a c - 2304a b c + 864a b c )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 3 3 +--R (2304a b c - 3456a b c + 720a b )d e +--R + +--R 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (9216a b c - 2304a b c)d e + (- 9216a b c + 2304a b c )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 3 3 4 2 3 3 4 2 +--R (1536a c - 2304a b c + 480a b )d e + (6144a b c - 1536a b c)d e +--R + +--R 4 3 3 2 2 5 +--R (- 6144a c + 1536a b c )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 4 3 3 5 4 2 3 2 2 4 4 +--R (- 128a b c - 96a b )e + (- 128a c + 320a b c + 312a b )d e +--R + +--R 3 2 2 3 5 2 3 +--R (192a b c - 384a b c - 396a b )d e +--R + +--R 3 3 2 2 2 4 3 2 +--R (- 1280a c + 576a b c + 1152a b c)d e +--R + +--R 2 3 3 2 4 2 4 2 3 5 +--R (- 1536a b c - 1152a b c )d e + (768a c + 576a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 +--R - 512a b e + (- 512a b c + 1664a b )d e +--R + +--R 3 2 2 4 2 3 3 2 2 3 3 2 +--R (768a b c - 2112a b )d e + (- 5120a b c + 6144a b c)d e +--R + +--R 2 2 2 4 2 3 5 +--R - 6144a b c d e + 3072a b c d +--R * +--R x +--R + +--R 5 5 5 4 2 4 4 3 3 2 3 +--R - 512a b e + (- 512a c + 1664a b )d e + (768a b c - 2112a b )d e +--R + +--R 4 2 3 2 3 2 3 2 4 3 3 5 +--R (- 5120a c + 6144a b c)d e - 6144a b c d e + 3072a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 5 3 2 2 3 5 4 +--R (192a b c + 16a b )e + (192a b c - 608a b c - 52a b )d e +--R + +--R 2 2 2 4 6 2 3 +--R (- 288a b c + 768a b c + 66b )d e +--R + +--R 2 3 3 2 5 3 2 +--R (1920a b c - 2144a b c - 192b c)d e +--R + +--R 2 3 4 2 4 4 3 3 5 +--R (2304a b c + 192b c )d e + (- 1152a b c - 96b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 5 4 2 3 2 2 4 4 +--R (384a b c + 288a b )e + (384a c - 960a b c - 936a b )d e +--R + +--R 3 2 2 3 5 2 3 +--R (- 576a b c + 1152a b c + 1188a b )d e +--R + +--R 3 3 2 2 2 4 3 2 +--R (3840a c - 1728a b c - 3456a b c)d e +--R + +--R 2 3 3 2 4 2 4 2 3 5 +--R (4608a b c + 3456a b c )d e + (- 2304a c - 1728a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 +--R 768a b e + (768a b c - 2496a b )d e +--R + +--R 3 2 2 4 2 3 3 2 2 3 3 2 +--R (- 1152a b c + 3168a b )d e + (7680a b c - 9216a b c)d e +--R + +--R 2 2 2 4 2 3 5 +--R 9216a b c d e - 4608a b c d +--R * +--R x +--R + +--R 5 5 5 4 2 4 4 3 3 2 3 +--R 512a b e + (512a c - 1664a b )d e + (- 768a b c + 2112a b )d e +--R + +--R 4 2 3 2 3 2 3 2 4 3 3 5 +--R (5120a c - 6144a b c)d e + 6144a b c d e - 3072a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 4 3 2 3 6 3 2 3 4 5 +--R (384a c + 288a b )d e + (- 1152a b c - 864a b )d e +--R + +--R 3 2 2 2 4 5 4 +--R (1152a c + 2016a b c + 864a b )d e +--R + +--R 2 2 3 5 6 3 +--R (- 2304a b c - 2112a b c - 288b )d e +--R + +--R 2 3 2 2 4 7 2 +--R (1152a c + 2016a b c + 864b c)d e +--R + +--R 3 3 2 8 4 2 3 9 +--R (- 1152a b c - 864b c )d e + (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 2 4 5 3 2 3 5 4 +--R 1536a b d e - 4608a b d e + (4608a b c + 4608a b )d e +--R + +--R 2 2 4 6 3 2 2 3 7 2 +--R (- 9216a b c - 1536a b )d e + (4608a b c + 4608a b c)d e +--R + +--R 2 2 8 3 9 +--R - 4608a b c d e + 1536a b c d +--R * +--R x +--R + +--R 5 3 6 4 4 5 4 3 2 5 4 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 2 3 6 3 3 2 2 2 7 2 +--R (- 9216a b c - 1536a b )d e + (4608a c + 4608a b c)d e +--R + +--R 2 2 8 2 3 9 +--R - 4608a b c d e + 1536a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 4 3 3 3 6 3 2 2 4 4 5 +--R (- 576a b c - 48a b )d e + (1728a b c + 144a b )d e +--R + +--R 3 2 2 3 5 5 4 +--R (- 1728a b c - 1872a b c - 144a b )d e +--R + +--R 2 2 2 4 6 6 3 +--R (3456a b c + 864a b c + 48b )d e +--R + +--R 2 3 3 2 5 7 2 +--R (- 1728a b c - 1872a b c - 144b c)d e +--R + +--R 2 3 4 2 8 4 3 3 9 +--R (1728a b c + 144b c )d e + (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 5 4 2 3 6 4 3 3 4 5 +--R (- 1152a c - 864a b )d e + (3456a b c + 2592a b )d e +--R + +--R 4 2 3 2 2 4 5 4 +--R (- 3456a c - 6048a b c - 2592a b )d e +--R + +--R 3 2 2 3 5 6 3 +--R (6912a b c + 6336a b c + 864a b )d e +--R + +--R 3 3 2 2 2 4 7 2 +--R (- 3456a c - 6048a b c - 2592a b c)d e +--R + +--R 2 3 3 2 8 2 4 2 3 9 +--R (3456a b c + 2592a b c )d e + (- 1152a c - 864a b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 2 4 5 4 3 3 5 4 +--R - 2304a b d e + 6912a b d e + (- 6912a b c - 6912a b )d e +--R + +--R 3 2 2 4 6 3 3 2 2 3 7 2 +--R (13824a b c + 2304a b )d e + (- 6912a b c - 6912a b c)d e +--R + +--R 2 2 2 8 2 3 9 +--R 6912a b c d e - 2304a b c d +--R * +--R x +--R + +--R 6 3 6 5 4 5 5 4 2 5 4 +--R - 1536a d e + 4608a b d e + (- 4608a c - 4608a b )d e +--R + +--R 4 3 3 6 3 4 2 3 2 7 2 +--R (9216a b c + 1536a b )d e + (- 4608a c - 4608a b c)d e +--R + +--R 3 2 8 3 3 9 +--R 4608a b c d e - 1536a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 597 + +--S 598 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 598 + +--S 599 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 4 6 3 3 +--R (- 384a c + 288a b c + 312a b c - 90b )d e +--R + +--R 2 3 3 2 5 4 2 +--R (- 1536a b c - 768a b c + 288b c)d e +--R + +--R 2 4 2 3 4 2 5 +--R (1536a c + 768a b c - 288b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 3 3 +--R (- 1536a b c + 2304a b c - 480a b )d e +--R + +--R 2 2 2 4 4 2 2 3 3 2 5 +--R (- 6144a b c + 1536a b c)d e + (6144a b c - 1536a b c )d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 3 3 +--R (- 1536a c + 2304a b c - 480a b )d e +--R + +--R 3 2 2 3 4 2 3 3 2 2 2 5 +--R (- 6144a b c + 1536a b c)d e + (6144a c - 1536a b c )d e +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (576a b c - 816a b c + 108a b c + 15b )d e +--R + +--R 2 2 3 4 2 6 4 2 +--R (2304a b c - 384a b c - 48b c)d e +--R + +--R 2 4 3 3 5 2 5 +--R (- 2304a b c + 384a b c + 48b c )d e +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 2 2 4 6 3 3 +--R (1152a c - 864a b c - 936a b c + 270a b )d e +--R + +--R 3 3 2 3 2 5 4 2 +--R (4608a b c + 2304a b c - 864a b c)d e +--R + +--R 3 4 2 2 3 4 2 5 +--R (- 4608a c - 2304a b c + 864a b c )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 3 3 +--R (2304a b c - 3456a b c + 720a b )d e +--R + +--R 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (9216a b c - 2304a b c)d e + (- 9216a b c + 2304a b c )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 3 3 +--R (1536a c - 2304a b c + 480a b )d e +--R + +--R 4 2 3 3 4 2 4 3 3 2 2 5 +--R (6144a b c - 1536a b c)d e + (- 6144a c + 1536a b c )d e +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 2 2 4 6 3 3 +--R (- 768a c + 576a b c + 624a b c - 180b )d e +--R + +--R 2 3 3 2 5 4 2 +--R (- 3072a b c - 1536a b c + 576b c)d e +--R + +--R 2 4 2 3 4 2 5 +--R (3072a c + 1536a b c - 576b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 3 3 +--R (- 3072a b c + 4608a b c - 960a b )d e +--R + +--R 2 2 2 4 4 2 2 3 3 2 5 +--R (- 12288a b c + 3072a b c)d e + (12288a b c - 3072a b c )d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 3 3 +--R (- 3072a c + 4608a b c - 960a b )d e +--R + +--R 3 2 2 3 4 2 3 3 2 2 2 5 +--R (- 12288a b c + 3072a b c)d e + (12288a c - 3072a b c )d e +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (1152a b c - 1632a b c + 216a b c + 30b )d e +--R + +--R 2 2 3 4 2 6 4 2 +--R (4608a b c - 768a b c - 96b c)d e +--R + +--R 2 4 3 3 5 2 5 +--R (- 4608a b c + 768a b c + 96b c )d e +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 2 2 4 6 3 3 +--R (2304a c - 1728a b c - 1872a b c + 540a b )d e +--R + +--R 3 3 2 3 2 5 4 2 +--R (9216a b c + 4608a b c - 1728a b c)d e +--R + +--R 3 4 2 2 3 4 2 5 +--R (- 9216a c - 4608a b c + 1728a b c )d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 3 3 +--R (4608a b c - 6912a b c + 1440a b )d e +--R + +--R 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (18432a b c - 4608a b c)d e + (- 18432a b c + 4608a b c )d e +--R * +--R x +--R + +--R 5 2 4 2 3 4 3 3 +--R (3072a c - 4608a b c + 960a b )d e +--R + +--R 4 2 3 3 4 2 4 3 3 2 2 5 +--R (12288a b c - 3072a b c)d e + (- 12288a c + 3072a b c )d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 4 3 3 5 4 2 3 2 2 4 4 +--R (- 128a b c - 96a b )e + (- 128a c + 320a b c + 312a b )d e +--R + +--R 3 2 2 3 5 2 3 +--R (192a b c - 384a b c - 396a b )d e +--R + +--R 3 3 2 2 2 4 3 2 +--R (- 1280a c + 576a b c + 1152a b c)d e +--R + +--R 2 3 3 2 4 2 4 2 3 5 +--R (- 1536a b c - 1152a b c )d e + (768a c + 576a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 +--R - 512a b e + (- 512a b c + 1664a b )d e +--R + +--R 3 2 2 4 2 3 3 2 2 3 3 2 +--R (768a b c - 2112a b )d e + (- 5120a b c + 6144a b c)d e +--R + +--R 2 2 2 4 2 3 5 +--R - 6144a b c d e + 3072a b c d +--R * +--R x +--R + +--R 5 5 5 4 2 4 4 3 3 2 3 +--R - 512a b e + (- 512a c + 1664a b )d e + (768a b c - 2112a b )d e +--R + +--R 4 2 3 2 3 2 3 2 4 3 3 5 +--R (- 5120a c + 6144a b c)d e - 6144a b c d e + 3072a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 | 2 2 | 2 +--R \|- a e + b d e - c d \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 5 3 2 2 3 5 4 +--R (192a b c + 16a b )e + (192a b c - 608a b c - 52a b )d e +--R + +--R 2 2 2 4 6 2 3 +--R (- 288a b c + 768a b c + 66b )d e +--R + +--R 2 3 3 2 5 3 2 +--R (1920a b c - 2144a b c - 192b c)d e +--R + +--R 2 3 4 2 4 4 3 3 5 +--R (2304a b c + 192b c )d e + (- 1152a b c - 96b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 5 4 2 3 2 2 4 4 +--R (384a b c + 288a b )e + (384a c - 960a b c - 936a b )d e +--R + +--R 3 2 2 3 5 2 3 +--R (- 576a b c + 1152a b c + 1188a b )d e +--R + +--R 3 3 2 2 2 4 3 2 +--R (3840a c - 1728a b c - 3456a b c)d e +--R + +--R 2 3 3 2 4 2 4 2 3 5 +--R (4608a b c + 3456a b c )d e + (- 2304a c - 1728a b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 +--R 768a b e + (768a b c - 2496a b )d e +--R + +--R 3 2 2 4 2 3 3 2 2 3 3 2 +--R (- 1152a b c + 3168a b )d e + (7680a b c - 9216a b c)d e +--R + +--R 2 2 2 4 2 3 5 +--R 9216a b c d e - 4608a b c d +--R * +--R x +--R + +--R 5 5 5 4 2 4 4 3 3 2 3 +--R 512a b e + (512a c - 1664a b )d e + (- 768a b c + 2112a b )d e +--R + +--R 4 2 3 2 3 2 3 2 4 3 3 5 +--R (5120a c - 6144a b c)d e + 6144a b c d e - 3072a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d +--R / +--R 4 3 2 3 6 3 2 3 4 5 +--R (384a c + 288a b )d e + (- 1152a b c - 864a b )d e +--R + +--R 3 2 2 2 4 5 4 +--R (1152a c + 2016a b c + 864a b )d e +--R + +--R 2 2 3 5 6 3 +--R (- 2304a b c - 2112a b c - 288b )d e +--R + +--R 2 3 2 2 4 7 2 +--R (1152a c + 2016a b c + 864b c)d e +--R + +--R 3 3 2 8 4 2 3 9 +--R (- 1152a b c - 864b c )d e + (384a c + 288b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 2 4 5 3 2 3 5 4 +--R 1536a b d e - 4608a b d e + (4608a b c + 4608a b )d e +--R + +--R 2 2 4 6 3 2 2 3 7 2 +--R (- 9216a b c - 1536a b )d e + (4608a b c + 4608a b c)d e +--R + +--R 2 2 8 3 9 +--R - 4608a b c d e + 1536a b c d +--R * +--R x +--R + +--R 5 3 6 4 4 5 4 3 2 5 4 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 2 3 6 3 3 2 2 2 7 2 +--R (- 9216a b c - 1536a b )d e + (4608a c + 4608a b c)d e +--R + +--R 2 2 8 2 3 9 +--R - 4608a b c d e + 1536a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 +-+ | 2 2 | 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 4 3 3 3 6 3 2 2 4 4 5 +--R (- 576a b c - 48a b )d e + (1728a b c + 144a b )d e +--R + +--R 3 2 2 3 5 5 4 +--R (- 1728a b c - 1872a b c - 144a b )d e +--R + +--R 2 2 2 4 6 6 3 +--R (3456a b c + 864a b c + 48b )d e +--R + +--R 2 3 3 2 5 7 2 +--R (- 1728a b c - 1872a b c - 144b c)d e +--R + +--R 2 3 4 2 8 4 3 3 9 +--R (1728a b c + 144b c )d e + (- 576a b c - 48b c )d +--R * +--R 3 +--R x +--R + +--R 5 4 2 3 6 4 3 3 4 5 +--R (- 1152a c - 864a b )d e + (3456a b c + 2592a b )d e +--R + +--R 4 2 3 2 2 4 5 4 +--R (- 3456a c - 6048a b c - 2592a b )d e +--R + +--R 3 2 2 3 5 6 3 +--R (6912a b c + 6336a b c + 864a b )d e +--R + +--R 3 3 2 2 2 4 7 2 +--R (- 3456a c - 6048a b c - 2592a b c)d e +--R + +--R 2 3 3 2 8 2 4 2 3 9 +--R (3456a b c + 2592a b c )d e + (- 1152a c - 864a b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 2 4 5 4 3 3 5 4 +--R - 2304a b d e + 6912a b d e + (- 6912a b c - 6912a b )d e +--R + +--R 3 2 2 4 6 3 3 2 2 3 7 2 +--R (13824a b c + 2304a b )d e + (- 6912a b c - 6912a b c)d e +--R + +--R 2 2 2 8 2 3 9 +--R 6912a b c d e - 2304a b c d +--R * +--R x +--R + +--R 6 3 6 5 4 5 5 4 2 5 4 +--R - 1536a d e + 4608a b d e + (- 4608a c - 4608a b )d e +--R + +--R 4 3 3 6 3 4 2 3 2 7 2 +--R (9216a b c + 1536a b )d e + (- 4608a c - 4608a b c)d e +--R + +--R 3 2 8 3 3 9 +--R 4608a b c d e - 1536a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R Type: Expression(Integer) +--E 599 + +--S 600 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 845 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 601 + +--S 602 of 845 +r0:=1/2*e*(2*c*d-b*e)*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-2*(d+e*x)^4/_ + sqrt(a+b*x+c*x^2)+1/3*e^2*(52*c^2*d^2+15*b^2*e^2-4*c*e*(13*b*d+2*a*e))*_ + sqrt(a+b*x+c*x^2)/c^3+8/3*e^2*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+2/3*e^2*_ + (6*c*d^2-e*(b*d+4*a*e)+5*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((36a b c - 15b )e + (- 72a c + 54b c)d e - 72b c d e + 48c d e) +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 4 4 2 4 3 3 3 +--R 4c e x + (- 4b c e + 24c d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 16a c + 10b c)e - 36b c d e + 72c d e )x +--R + +--R 3 4 2 2 3 2 2 2 +--R (- 52a b c + 30b )e + (72a c - 108b c)d e + 144b c d e +--R + +--R 3 3 +--R - 48c d e +--R * +--R x +--R + +--R 2 2 4 3 2 2 2 3 4 +--R (- 32a c + 30a b )e - 108a b c d e + 144a c d e - 12c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 3 +-+ | 2 +--R 6c \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 602 + +--S 603 of 845 +--a0:=integrate(t0,x) +--E 603 + +--S 604 of 845 +--m0a:=a0.1-r0 +--E 604 + +--S 605 of 845 +--d0a:=D(m0a,x) +--E 605 + +--S 606 of 845 +--m0b:=a0.2-r0 +--E 606 + +--S 607 of 845 +--d0b:=D(m0b,x) +--E 607 + +)clear all + +--S 608 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 608 + +--S 609 of 845 +r0:=3/4*e*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-2*(d+e*x)^3/sqrt(a+b*x+c*x^2)+_ + 9/2*e^2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/c^2+3*e^2*(d+e*x)*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R +--------------+ +--R 2 3 2 2 2 | 2 +--R ((- 12a c + 9b )e - 24b c d e + 24c d e)\|c x + b x + a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 3 3 2 2 2 +--R 4c e x + (- 6b c e + 24c d e )x +--R + +--R 2 3 2 2 2 3 2 +--R ((12a c - 18b )e + 48b c d e - 24c d e)x - 18a b e + 48a c d e +--R + +--R 2 3 +--R - 8c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 2 +-+ | 2 +--R 4c \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 609 + +--S 610 of 845 +--a0:=integrate(t0,x) +--E 610 + +--S 611 of 845 +--m0:=a0-r0 +--E 611 + +--S 612 of 845 +--d0:=D(m0,x) +--E 612 + +)clear all + +--S 613 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 613 + +--S 614 of 845 +r0:=2*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-_ + 2*(d+e*x)^2/sqrt(a+b*x+c*x^2)+4*e^2*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R +--------------+ +--R 2 | 2 2c x + b +--R (- 2b e + 4c d e)\|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 2 2 +-+ +--R (2c e x + (4b e - 4c d e)x + 4a e - 2c d )\|c +--R / +--R +--------------+ +--R +-+ | 2 +--R c\|c \|c x + b x + a +--R Type: Expression(Integer) +--E 614 + +--S 615 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 +--R ((8a b c + 2b )e + (- 16a c - 4b c)d e)x +--R + +--R 2 2 2 2 2 +--R (16a b e - 32a b c d e)x + 16a b e - 32a c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 3 +--R (- 8a b c e + 16a b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R ((- 16a b c - 8a b )e + (32a c + 16a b c)d e)x +--R + +--R 2 2 2 2 3 2 3 +--R (- 24a b e + 48a b c d e)x - 16a b e + 32a c d e +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 3 2 2 2 2 2 2 +--R - 8a b c e x + (- 12a b e + 16a b c d e + (- 8a c - 2b c)d )x +--R + +--R 2 2 2 2 +--R (- 16a b e + 32a c d e - 8a b c d )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 2 2 4 +--R (8a c + 2b c)e x +--R + +--R 3 2 2 2 2 2 3 +--R ((16a b c + 4b )e + (- 16a c - 4b c)d e + 8b c d )x +--R + +--R 2 2 2 2 2 2 +--R (20a b e - 32a b c d e + (8a c + 6b c)d )x +--R + +--R 2 2 2 2 +--R (16a b e - 32a c d e + 8a b c d )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 2 2 2 2 +-+ +-+ | 2 +--R ((4a c + b c)x + 8a b c x + 8a c)\|a \|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 3 +-+ +--R (- 4a b c x + (- 8a c - 4a b c)x - 12a b c x - 8a c)\|c +--R , +--R +--R 3 2 2 2 2 +--R ((- 16a b c - 4b )e + (32a c + 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 32a b e + 64a b c d e)x - 32a b e + 64a c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 3 +--R (16a b c e - 32a b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R ((32a b c + 16a b )e + (- 64a c - 32a b c)d e)x +--R + +--R 2 2 2 2 3 2 3 +--R (48a b e - 96a b c d e)x + 32a b e - 64a c d e +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 3 2 2 2 2 2 2 +--R - 8a b c e x + (- 12a b e + 16a b c d e + (- 8a c - 2b c)d )x +--R + +--R 2 2 2 2 +--R (- 16a b e + 32a c d e - 8a b c d )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 2 2 2 4 +--R (8a c + 2b c)e x +--R + +--R 3 2 2 2 2 2 3 +--R ((16a b c + 4b )e + (- 16a c - 4b c)d e + 8b c d )x +--R + +--R 2 2 2 2 2 2 +--R (20a b e - 32a b c d e + (8a c + 6b c)d )x +--R + +--R 2 2 2 2 +--R (16a b e - 32a c d e + 8a b c d )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------------+ +--R 2 2 2 2 +---+ +-+ | 2 +--R ((4a c + b c)x + 8a b c x + 8a c)\|- c \|a \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 3 +---+ +--R (- 4a b c x + (- 8a c - 4a b c)x - 12a b c x - 8a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 615 + +--S 616 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 2 2 2 | 2 +--R ((8a b e - 16a b c d e)x + 16a b e - 32a c d e)\|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 8a b c - 2b )e + (16a c + 4b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 16a b e + 32a b c d e)x - 16a b e + 32a c d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +--------------+ +--R 2 2 2 2 2 | 2 +--R ((8a b e - 16a b c d e)x + 16a b e - 32a c d e)\|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 8a b c - 2b )e + (16a c + 4b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 16a b e + 32a b c d e)x - 16a b e + 32a c d e +--R * +--R +-+ +--R \|a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R 2 2 2 2 2 +-+ +-+ | 2 +--R ((16a b e - 8b c d )x + 32a e - 16a c d )\|a \|c \|c x + b x + a +--R + +--R 2 2 2 2 2 2 2 +--R ((- 16a c - 4a b )e + (8a c + 2b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (- 32a b e + 16a b c d )x - 32a e + 16a c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 2 +-+ | 2 +--R (4a b c x + 8a c)\|c \|c x + b x + a +--R + +--R 2 2 2 2 +-+ +-+ +--R ((- 4a c - b c)x - 8a b c x - 8a c)\|a \|c +--R Type: Expression(Integer) +--E 616 + +--S 617 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 617 + +--S 618 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +---+ +--R ((8a b e - 16a b c d e)x + 16a b e - 32a c d e)\|- c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((- 8a b c - 2b )e + (16a c + 4b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 16a b e + 32a b c d e)x - 16a b e + 32a c d e +--R * +--R +---+ +-+ +--R \|- c \|a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 2 2 +-+ +--R ((- 16a b e + 32a b c d e)x - 32a b e + 64a c d e)\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((16a b c + 4b )e + (- 32a c - 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (32a b e - 64a b c d e)x + 32a b e - 64a c d e +--R * +--R +-+ +-+ +--R \|a \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 2 2 2 2 +---+ +-+ +-+ +--R ((16a b e - 8b c d )x + 32a e - 16a c d )\|- c \|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 2 2 +--R ((- 16a c - 4a b )e + (8a c + 2b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (- 32a b e + 16a b c d )x - 32a e + 16a c d +--R * +--R +---+ +-+ +--R \|- c \|c +--R / +--R +--------------+ +--R 2 +---+ +-+ | 2 +--R (4a b c x + 8a c)\|- c \|c \|c x + b x + a +--R + +--R 2 2 2 2 +---+ +-+ +-+ +--R ((- 4a c - b c)x - 8a b c x - 8a c)\|- c \|a \|c +--R Type: Expression(Integer) +--E 618 + +--S 619 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 619 + +)clear all + +--S 620 of 845 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 620 + +--S 621 of 845 +r0:=2*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/sqrt(c)-_ + 2*(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 2c x + b +-+ +--R 2e\|c x + b x + a atanh(----------------------) + (- 2e x - 2d)\|c +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R (2) -------------------------------------------------------------------- +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 621 + +--S 622 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R 2 | 2 +--R (2a b e x + 4a e)\|c x + b x + a +--R + +--R 2 2 +-+ +--R (- 4a c e x - 4a b e x - 4a e)\|a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +--------------+ +--R +-+ +-+ | 2 +--R (4a e - 2b d)x\|a \|c \|c x + b x + a +--R + +--R 2 2 +-+ +--R ((- 2a b e + 4a c d)x + (- 4a e + 2a b d)x)\|c +--R / +--R +--------------+ +--R 2 +-+ | 2 2 2 +-+ +-+ +--R (a b x + 2a )\|c \|c x + b x + a + (- 2a c x - 2a b x - 2a )\|a \|c +--R , +--R +--R +--------------+ +--R 2 | 2 +--R (4a b e x + 8a e)\|c x + b x + a +--R + +--R 2 2 +-+ +--R (- 8a c e x - 8a b e x - 8a e)\|a +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R +--------------+ +--R +---+ +-+ | 2 +--R (4a e - 2b d)x\|- c \|a \|c x + b x + a +--R + +--R 2 2 +---+ +--R ((- 2a b e + 4a c d)x + (- 4a e + 2a b d)x)\|- c +--R / +--R +--------------+ +--R 2 +---+ | 2 +--R (a b x + 2a )\|- c \|c x + b x + a +--R + +--R 2 2 +---+ +-+ +--R (- 2a c x - 2a b x - 2a )\|- c \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 622 + +--S 623 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R +-+ | 2 2 +--R (4a e\|a \|c x + b x + a - 2a b e x - 4a e) +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +--------------+ +--R +-+ | 2 2 +--R (- 4a e\|a \|c x + b x + a + 2a b e x + 4a e) +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R +-+ | 2 +-+ +-+ +--R - 4a d\|c \|c x + b x + a + (2b d x + 4a d)\|a \|c +--R / +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R 2a\|a \|c \|c x + b x + a + (- a b x - 2a )\|c +--R Type: Expression(Integer) +--E 623 + +--S 624 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 624 + +--S 625 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------------+ +--R +---+ +-+ | 2 2 +---+ +--R (- 4a e\|- c \|a \|c x + b x + a + (2a b e x + 4a e)\|- c ) +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (8a e\|a \|c \|c x + b x + a + (- 4a b e x - 8a e)\|c ) +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R +--------------+ +--R +---+ +-+ | 2 +---+ +-+ +-+ +--R - 4a d\|- c \|c \|c x + b x + a + (2b d x + 4a d)\|- c \|a \|c +--R / +--R +--------------+ +--R +---+ +-+ +-+ | 2 2 +---+ +-+ +--R 2a\|- c \|a \|c \|c x + b x + a + (- a b x - 2a )\|- c \|c +--R Type: Expression(Integer) +--E 625 + +--S 626 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 626 + +)clear all + +--S 627 of 845 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2c x + b +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 627 + +--S 628 of 845 +r0:=(-2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +--R (2) - ----------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 628 + +--S 629 of 845 +a0:=integrate(t0,x) +--R +--R +--R +--------------+ +--R | 2 2 +-+ +--R - 2b x\|c x + b x + a + (4c x + 2b x)\|a +--R (3) -------------------------------------------------------- +--R +--------------+ +--R +-+ | 2 2 2 +--R (b x + 2a)\|a \|c x + b x + a - 2a c x - 2a b x - 2a +--R Type: Union(Expression(Integer),...) +--E 629 + +--S 630 of 845 +m0:=a0-r0 +--R +--R +--R +--------------+ +--R +-+ | 2 +--R - 4\|a \|c x + b x + a + 2b x + 4a +--R (4) -------------------------------------- +--R +--------------+ +--R | 2 +-+ +--R 2a\|c x + b x + a + (- b x - 2a)\|a +--R Type: Expression(Integer) +--E 630 + +--S 631 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 631 + +)clear all + +--S 632 of 845 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R 2c x + b +--R (1) -------------------------------------------------------------- +--R +--------------+ +--R 3 2 | 2 +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|c x + b x + a +--R Type: Expression(Integer) +--E 632 + +--S 633 of 845 +r0:=-e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)-_ + 2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R +--------------+ +--R 2 | 2 +--R (- b e + 2c d e)\|c x + b x + a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 +--R (2c e x + 2b e - 2c d)\|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 2 2 | 2 2 | 2 +--R (a e - b d e + c d )\|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 633 + +--S 634 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R 2 2 2 2 2 | 2 +--R ((a b e - 2a b c d e)x + 2a b e - 4a c d e)\|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (- 2a b c e + 4a c d e)x + (- 2a b e + 4a b c d e)x +--R + +--R 2 2 2 +--R - 2a b e + 4a c d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 2 2 2 2 2 2 +--R ((4a e + 4a c d )x + (8a d e + 4a b d )x + 8a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 2 3 2 2 2 3 2 +--R (- 4a e + 2a b d e + (- 4a c + 2b )d e - 2b c d )x +--R + +--R 2 2 2 3 +--R (- 8a d e + 8a b d e - 8a c d )x +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 3 +--R (- 2a b e + (- 4a c + b )d e - 2b c d )x +--R + +--R 2 2 2 2 2 +--R (- 4a e - 4a b d e + (- 8a c - b )d )x +--R + +--R 2 2 2 2 +--R (- 8a d e - 8a b d )x - 8a d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (2a b e + (4a c - 2a b )d e - 2a b c d e + 4a c d )x +--R + +--R 3 3 2 2 2 2 2 3 2 +--R (4a e + 2a b d e + (4a c - 6a b )d e + 6a b c d )x +--R + +--R 3 2 2 2 2 3 +--R (8a d e - 8a b d e + 8a c d )x +--R / +--R +--------------+ +--R 2 2 2 | 2 +--R (4a b e x + (8a e + 4a b d)x + 8a d)\|c x + b x + a +--R + +--R 2 3 2 2 +--R (- 4a c - b )e x + (- 8a b e + (- 4a c - b )d)x +--R + +--R 2 2 +--R (- 8a e - 8a b d)x - 8a d +--R * +--R +-+ +--R \|a +--R + +--R +-------------------+ +--------------+ +--R 2 +-+ | 2 2 | 2 +--R ((- 4a c + 2b )e - 2b c d)x\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 2 +--R ((- 2a b c e + 4a c d)x + ((4a c - 2a b )e + 2a b c d)x) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 2 2 2 2 3 2 2 2 2 +--R ((a b e - a b d e + a b c d )x + 2a e - 2a b d e + 2a c d ) +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (- 2a c e + 2a b c d e - 2a c d )x +--R + +--R 2 2 2 2 3 2 2 2 2 +--R (- 2a b e + 2a b d e - 2a b c d )x - 2a e + 2a b d e - 2a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R , +--R +--R +--------------+ +--R 2 2 2 2 2 | 2 +--R ((2a b e - 4a b c d e)x + 4a b e - 8a c d e)\|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (- 4a b c e + 8a c d e)x + (- 4a b e + 8a b c d e)x +--R + +--R 2 2 2 +--R - 4a b e + 8a c d e +--R * +--R +-+ +--R \|a +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R d\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +--R (- a e x - a d)\|- a e + b d e - c d +--R / +--R 2 2 +-+ +--R (a e - b d e + c d )x\|a +--R + +--R +---------------------+ +--R 2 | 2 2 +-+ +--R ((- 4a c + 2b )e - 2b c d)x\|- a e + b d e - c d \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 +--R ((- 2a b c e + 4a c d)x + ((4a c - 2a b )e + 2a b c d)x) +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R / +--R 2 2 2 2 3 2 2 2 2 +--R ((a b e - a b d e + a b c d )x + 2a e - 2a b d e + 2a c d ) +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R (- 2a c e + 2a b c d e - 2a c d )x +--R + +--R 2 2 2 2 3 2 2 2 2 +--R (- 2a b e + 2a b d e - 2a b c d )x - 2a e + 2a b d e - 2a c d +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 634 + +--S 635 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 +-+ | 2 2 2 +--R (2a b e - 4a c d e)\|a \|c x + b x + a + (- a b e + 2a b c d e)x +--R + +--R 2 2 2 +--R - 2a b e + 4a c d e +--R * +--R log +--R 2 2 2 2 2 2 2 2 +--R ((4a e + 4a c d )x + (8a d e + 4a b d )x + 8a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 2 3 2 2 2 3 2 +--R (- 4a e + 2a b d e + (- 4a c + 2b )d e - 2b c d )x +--R + +--R 2 2 2 3 +--R (- 8a d e + 8a b d e - 8a c d )x +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 3 +--R (- 2a b e + (- 4a c + b )d e - 2b c d )x +--R + +--R 2 2 2 2 2 +--R (- 4a e - 4a b d e + (- 8a c - b )d )x +--R + +--R 2 2 2 2 +--R (- 8a d e - 8a b d )x - 8a d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (2a b e + (4a c - 2a b )d e - 2a b c d e + 4a c d )x +--R + +--R 3 3 2 2 2 2 2 3 2 +--R (4a e + 2a b d e + (4a c - 6a b )d e + 6a b c d )x +--R + +--R 3 2 2 2 2 3 +--R (8a d e - 8a b d e + 8a c d )x +--R / +--R +--------------+ +--R 2 2 2 | 2 +--R (4a b e x + (8a e + 4a b d)x + 8a d)\|c x + b x + a +--R + +--R 2 3 2 2 +--R (- 4a c - b )e x + (- 8a b e + (- 4a c - b )d)x +--R + +--R 2 2 +--R (- 8a e - 8a b d)x - 8a d +--R * +--R +-+ +--R \|a +--R + +--R +--------------+ +--R 2 +-+ | 2 2 2 +--R (2a b e - 4a c d e)\|a \|c x + b x + a + (- a b e + 2a b c d e)x +--R + +--R 2 2 2 +--R - 2a b e + 4a c d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R (4a b e - 4a c d)\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 2 +-+ | 2 2 +--R ((- 2b e + 2b c d)x - 4a b e + 4a c d)\|a \|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 2 2 2 +-+ | 2 2 | 2 +--R (2a e - 2a b d e + 2a c d )\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 2 3 2 2 2 2 +--R ((- a b e + a b d e - a b c d )x - 2a e + 2a b d e - 2a c d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 635 + +--S 636 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 636 + +--S 637 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------------------+ +--------------+ +--R 2 | 2 2 +-+ | 2 +--R (2a b e - 4a c d e)\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R 2 2 2 2 2 | 2 2 +--R ((- a b e + 2a b c d e)x - 2a b e + 4a c d e)\|- a e + b d e - c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R 2 +-+ | 2 2 | 2 +--R (4a b e - 8a c d e)\|a \|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 2 2 2 2 2 | 2 2 +--R ((- 2a b e + 4a b c d e)x - 4a b e + 8a c d e)\|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R d\|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +--R (- a e x - a d)\|- a e + b d e - c d +--R / +--R 2 2 +-+ +--R (a e - b d e + c d )x\|a +--R + +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R (4a b e - 4a c d)\|- a e + b d e - c d \|a e - b d e + c d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R +---------------------+ +--R 2 | 2 2 +-+ +--R ((- 2b e + 2b c d)x - 4a b e + 4a c d)\|- a e + b d e - c d \|a +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R +---------------------+ +--R 2 2 2 | 2 2 +-+ +--R (2a e - 2a b d e + 2a c d )\|- a e + b d e - c d \|a +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 2 3 2 2 2 2 +--R ((- a b e + a b d e - a b c d )x - 2a e + 2a b d e - 2a c d ) +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R Type: Expression(Integer) +--E 637 + +--S 638 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 638 + +)clear all + +--S 639 of 845 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x +--R + +--R 2 2 +--R (2a d e + b d )x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 639 + +--S 640 of 845 +r0:=-1/2*e*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (c*d^2-b*d*e+a*e^2)^(5/2)-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*sqrt(a+b*x+c*x^2))+3*e^2*_ + (2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 4 3 2 2 2 2 3 +--R ((- 4a c + 3b )e - 8b c d e + 8c d e )x + (- 4a c + 3b )d e +--R + +--R 2 2 2 3 +--R - 8b c d e + 8c d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 6b c e + 12c d e )x + ((4a c - 6b )e + 8b c d e + 4c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (8a c - 4b )d e + 8b c d e - 4c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 640 + +--S 641 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 4 4 2 3 2 3 +--R (16a c - 8a b c - 3b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 2 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 4 2 2 2 4 2 3 +--R (32a b c - 24a b )d e + (16a c + 56a b c - 3b )d e +--R + +--R 2 3 3 2 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 3 +--R (32a c - 24a b )d e + (96a b c - 24a b )d e +--R + +--R 2 2 2 3 2 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d e +--R * +--R x +--R + +--R 3 2 2 2 3 2 3 2 2 2 4 +--R (32a c - 24a b )d e + 64a b c d e - 64a c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 3 4 2 2 2 3 3 3 2 4 +--R ((- 16a b c + 12a b c)d e - 32a b c d e + 32a b c d e )x +--R + +--R 3 2 2 2 4 4 2 2 3 2 3 +--R (- 32a c + 8a b c + 12a b )d e + (- 80a b c - 20a b c)d e +--R + +--R 2 3 3 2 3 4 +--R 64a c d e + 32a b c d e +--R * +--R 3 +--R x +--R + +--R 3 2 3 4 3 2 2 2 4 2 3 +--R (- 48a b c + 36a b )d e + (- 32a c - 88a b c + 12a b )d e +--R + +--R 2 2 3 3 2 2 3 2 2 4 +--R (32a b c - 32a b c)d e + (64a c + 32a b c )d e +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 3 2 3 2 3 +--R (- 32a c + 24a b )d e + (- 112a b c + 36a b )d e +--R + +--R 3 2 2 2 3 2 2 2 4 +--R (64a c - 96a b c)d e + 96a b c d e +--R * +--R x +--R + +--R 4 3 2 2 3 3 3 2 3 2 4 +--R (- 32a c + 24a b )d e - 64a b c d e + 64a c d e +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x +--R + +--R - 2a d +--R + +--R 2 3 4 2 2 2 4 3 +--R (- 8a b c - 2a b )e + (32a c + 16a b c - 4b )d e +--R + +--R 2 3 2 2 3 2 2 3 +--R (- 16a b c + 8b c)d e + (- 16a c - 4b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R - 16a b e + (88a b c - 10a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 +--R (- 64a c + 24a b c - 4b )d e + (- 16a b c + 8b c)d e +--R + +--R 3 2 2 4 +--R (- 16a c - 4b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 +--R - 16a b e + (32a c + 8a b )d e + (32a b c - 16a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 64a c + 32a b c)d e - 16a b c d +--R * +--R x +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 2 3 3 3 2 2 2 2 +--R 8a b c e + (- 56a b c + 10b c)d e + (48a c - 20b c )d e +--R + +--R 3 3 +--R 16b c d e +--R * +--R 4 +--R x +--R + +--R 2 3 4 2 2 2 4 3 +--R (16a b c + 8a b )e + (- 48a c - 60a b c + 10b )d e +--R + +--R 2 3 2 2 3 2 2 3 3 4 +--R (32a b c - 8b c)d e + (48a c - 12b c )d e + 16b c d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R 24a b e + (- 104a b c + 6a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 +--R (64a c - 40a b c + 12b )d e + (48a b c - 24b c)d e +--R + +--R 3 2 2 4 +--R (16a c + 12b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 +--R 16a b e + (- 32a c - 8a b )d e + (- 32a b c + 16a b )d e +--R + +--R 2 2 2 3 2 4 +--R (64a c - 32a b c)d e + 16a b c d +--R * +--R x +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R / +--R 3 2 2 5 2 3 2 4 +--R (8a c + 2a b )d e + (- 16a b c - 4a b )d e +--R + +--R 2 2 2 4 3 3 2 3 4 2 +--R (16a c + 12a b c + 2b )d e + (- 16a b c - 4b c)d e +--R + +--R 3 2 2 5 +--R (8a c + 2b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 3 2 2 2 4 2 3 3 3 +--R 16a b d e + (8a c - 30a b )d e + (16a b c + 12a b )d e +--R + +--R 2 2 2 4 4 2 3 5 3 2 2 6 +--R (16a c - 20a b c + 2b )d e - 4b c d e + (8a c + 2b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 3 3 4 2 +--R 16a d e - 16a b d e + (32a c - 16a b )d e + 16a b d e +--R + +--R 2 2 2 5 2 6 +--R (16a c - 32a b c)d e + 16a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 2 2 6 +--R 16a d e - 32a b d e + (32a c + 16a b )d e - 32a b c d e + 16a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + 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d e +--R + +--R 3 2 6 +--R - 16a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R , +--R +--R 2 2 2 4 4 2 3 2 3 +--R (16a c - 8a b c - 3b )d e + (32a b c + 8b c)d e +--R + +--R 3 2 2 3 2 +--R (- 32a c - 8b c )d e +--R * +--R 3 +--R x +--R + +--R 2 3 4 2 2 2 4 2 3 +--R (32a b c - 24a b )d e + (16a c + 56a b c - 3b )d e +--R + +--R 2 3 3 2 3 2 2 4 +--R (- 32a b c + 8b c)d e + (- 32a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 4 2 3 2 3 +--R (32a c - 24a b )d e + (96a b c - 24a b )d e +--R + +--R 2 2 2 3 2 2 4 +--R (- 64a c + 64a b c)d e - 64a b c d e +--R * +--R x +--R + +--R 3 2 2 2 3 2 3 2 2 2 4 +--R (32a c - 24a b )d e + 64a b c d e - 64a c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 3 4 2 2 2 3 3 3 2 4 +--R ((- 16a b c + 12a b c)d e - 32a b c d e + 32a b c d e )x +--R + +--R 3 2 2 2 4 4 2 2 3 2 3 +--R (- 32a c + 8a b c + 12a b )d e + (- 80a b c - 20a b c)d e +--R + +--R 2 3 3 2 3 4 +--R 64a c d e + 32a b c d e +--R * +--R 3 +--R x +--R + +--R 3 2 3 4 3 2 2 2 4 2 3 +--R (- 48a b c + 36a b )d e + (- 32a c - 88a b c + 12a b )d e +--R + +--R 2 2 3 3 2 2 3 2 2 4 +--R (32a b c - 32a b c)d e + (64a c + 32a b c )d e +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 3 2 3 2 3 +--R (- 32a c + 24a b )d e + (- 112a b c + 36a b )d e +--R + +--R 3 2 2 2 3 2 2 2 4 +--R (64a c - 96a b c)d e + 96a b c d e +--R * +--R x +--R + +--R 4 3 2 2 3 3 3 2 3 2 4 +--R (- 32a c + 24a b )d e - 64a b c d e + 64a c d e +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 2 3 4 2 2 2 4 3 +--R (- 4a b c - a b )e + (16a c + 8a b c - 2b )d e +--R + +--R 2 3 2 2 3 2 2 3 +--R (- 8a b c + 4b c)d e + (- 8a c - 2b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R - 8a b e + (44a b c - 5a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 +--R (- 32a c + 12a b c - 2b )d e + (- 8a b c + 4b c)d e +--R + +--R 3 2 2 4 +--R (- 8a c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 +--R - 8a b e + (16a c + 4a b )d e + (16a b c - 8a b )d e +--R + +--R 2 2 2 3 2 4 +--R (- 32a c + 16a b c)d e - 8a b c d +--R * +--R x +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 4 2 3 3 3 2 2 2 2 +--R 4a b c e + (- 28a b c + 5b c)d e + (24a c - 10b c )d e +--R + +--R 3 3 +--R 8b c d e +--R * +--R 4 +--R x +--R + +--R 2 3 4 2 2 2 4 3 +--R (8a b c + 4a b )e + (- 24a c - 30a b c + 5b )d e +--R + +--R 2 3 2 2 3 2 2 3 3 4 +--R (16a b c - 4b c)d e + (24a c - 6b c )d e + 8b c d +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 +--R 12a b e + (- 52a b c + 3a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 +--R (32a c - 20a b c + 6b )d e + (24a b c - 12b c)d e +--R + +--R 3 2 2 4 +--R (8a c + 6b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 +--R 8a b e + (- 16a c - 4a b )d e + (- 16a b c + 8a b )d e +--R + +--R 2 2 2 3 2 4 +--R (32a c - 16a b c)d e + 8a b c d +--R * +--R x +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R / +--R 3 2 2 5 2 3 2 4 +--R (4a c + a b )d e + (- 8a b c - 2a b )d e +--R + +--R 2 2 2 4 3 3 2 3 4 2 +--R (8a c + 6a b c + b )d e + (- 8a b c - 2b c)d e +--R + +--R 3 2 2 5 +--R (4a c + b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 3 2 2 2 4 2 3 3 3 +--R 8a b d e + (4a c - 15a b )d e + (8a b c + 6a b )d e +--R + +--R 2 2 2 4 4 2 3 5 3 2 2 6 +--R (8a c - 10a b c + b )d e - 2b c d e + (4a c + b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 3 3 4 2 +--R 8a d e - 8a b d e + (16a c - 8a b )d e + 8a b d e +--R + +--R 2 2 2 5 2 6 +--R (8a c - 16a b c)d e + 8a b c d +--R * +--R x +--R + +--R 4 2 4 3 3 3 3 2 2 4 2 2 5 2 2 6 +--R 8a d e - 16a b d e + (16a c + 8a b )d e - 16a b c d e + 8a c d +--R * +--R +---------------------+ +--------------+ +--R | 2 2 +-+ | 2 +--R \|- a e + b d e - c d \|a \|c x + b x + a +--R + +--R 3 5 2 2 2 4 2 2 3 3 3 +--R - 4a b c d e + 8a b c d e + (- 8a b c - 4a b c)d e +--R + +--R 2 2 4 2 3 5 +--R 8a b c d e - 4a b c d e +--R * +--R 4 +--R x +--R + +--R 4 3 2 5 3 2 3 2 4 +--R (- 8a c - 4a b )d e + (12a b c + 8a b )d e +--R + +--R 3 2 2 2 4 3 3 2 2 3 4 2 +--R (- 16a c - 8a b c - 4a b )d e + (8a b c + 4a b c)d e +--R + +--R 2 3 2 2 5 3 6 +--R (- 8a c + 4a b c )d e - 4a b c d +--R * +--R 3 +--R x +--R + +--R 4 5 4 3 2 2 4 3 2 3 3 3 +--R - 12a b d e + (- 8a c + 20a b )d e + (- 8a b c - 4a b )d e +--R + +--R 3 2 2 2 4 4 2 2 2 3 5 +--R (- 16a c + 8a b c - 4a b )d e + (4a b c + 8a b c)d e +--R + +--R 2 3 2 2 6 +--R (- 8a c - 4a b c )d +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 4 3 2 3 3 +--R - 8a d e + 4a b d e + (- 16a c + 16a b )d e +--R + +--R 3 2 3 4 2 3 2 2 2 5 2 2 6 +--R (- 8a b c - 12a b )d e + (- 8a c + 24a b c)d e - 12a b c d +--R * +--R x +--R + +--R 5 2 4 4 3 3 4 3 2 4 2 3 5 +--R - 8a d e + 16a b d e + (- 16a c - 8a b )d e + 16a b c d e +--R + +--R 3 2 6 +--R - 8a c d +--R * +--R +---------------------+ +--R | 2 2 +--R \|- a e + b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 641 + +--S 642 of 845 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 2 3 +--R ((16a b c - 12a b )d e + 32a b c d e - 32a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (32a c - 24a b )d e + 64a b c d e - 64a c d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c + 8a b c + 3b )d e + (- 32a b c - 8b c)d e +--R + +--R 3 2 2 3 +--R (32a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 3 +--R ((- 32a b c + 24a b )d e - 64a b c d e + 64a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (- 32a c + 24a b )d e - 64a b c d e + 64a c d e +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 2 2 +--R (2d e x + 2d )\|a \|a e - b d e + c d +--R + +--R 2 2 3 +--R (- 2a d e + 2b d e - 2c d )x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 2 2 +--R ((- 2a e + b d e - 2c d )x + (- 2a d e - b d )x - 2a d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R + +--R 3 2 2 2 2 2 3 +-+ +--R ((2a e - 2b d e + 2c d e)x + (2a d e - 2b d e + 2c d )x)\|a +--R / +--R +--------------+ +--R +-+ | 2 2 +--R (2e x + 2d)\|a \|c x + b x + a - b e x + (- 2a e - b d)x - 2a d +--R + +--R 2 3 3 2 2 2 2 3 +--R ((16a b c - 12a b )d e + 32a b c d e - 32a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (32a c - 24a b )d e + 64a b c d e - 64a c d e +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c + 8a b c + 3b )d e + (- 32a b c - 8b c)d e +--R + +--R 3 2 2 3 +--R (32a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 3 +--R ((- 32a b c + 24a b )d e - 64a b c d e + 64a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (- 32a c + 24a b )d e - 64a b c d e + 64a c d e +--R * +--R +-+ +--R \|a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 3 2 2 2 2 3 2 3 +--R (- 8a b e + (32a b c - 16b )d e + 32b c d e - 16b c d )x - 16a b e +--R + +--R 2 2 2 2 2 3 +--R (64a c - 32a b )d e + 64a b c d e - 32a c d +--R * +--R +-------------------+ +--------------+ +--R +-+ | 2 2 | 2 +--R \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 3 2 2 2 4 2 +--R (8a b c + 2a b )e + (- 32a c + 8a b c + 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (- 32a b c - 8b c)d e + (16a c + 4b c )d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 2 2 2 3 +--R (16a b e + (- 64a b c + 32a b )d e - 64a b c d e + 32a b c d )x +--R + +--R 3 3 3 2 2 2 2 2 2 2 3 +--R 16a b e + (- 64a c + 32a b )d e - 64a b c d e + 32a c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 3 4 2 2 2 3 2 3 3 2 2 4 +--R 8a b d e - 16a b d e + (16a b c + 8a b )d e - 16a b c d e +--R + +--R 2 5 +--R 8a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 3 2 2 3 2 2 4 2 2 5 +--R 16a d e - 32a b d e + (32a c + 16a b )d e - 32a b c d e + 16a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 2 3 2 3 +--R (- 8a c - 2a b )d e + (16a b c + 4a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (- 16a c - 12a b c - 2b )d e + (16a b c + 4b c)d e +--R + +--R 3 2 2 5 +--R (- 8a c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 3 2 +--R - 16a b d e + 32a b d e + (- 32a b c - 16a b )d e +--R + +--R 2 4 2 5 +--R 32a b c d e - 16a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 3 2 2 3 2 2 4 +--R - 16a d e + 32a b d e + (- 32a c - 16a b )d e + 32a b c d e +--R + +--R 2 2 5 +--R - 16a c d +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R Type: Expression(Integer) +--E 642 + +--S 643 of 845 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 643 + +--S 644 of 845 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 2 3 +--R ((16a b c - 12a b )d e + 32a b c d e - 32a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (32a c - 24a b )d e + 64a b c d e - 64a c d e +--R * +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R \|- a e + b d e - c d \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 16a c + 8a b c + 3b )d e + (- 32a b c - 8b c)d e +--R + +--R 3 2 2 3 +--R (32a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 3 +--R ((- 32a b c + 24a b )d e - 64a b c d e + 64a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (- 32a c + 24a b )d e - 64a b c d e + 64a c d e +--R * +--R +---------------------+ +--R | 2 2 +-+ +--R \|- a e + b d e - c d \|a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 3 2 2 2 2 3 +--R ((32a b c - 24a b )d e + 64a b c d e - 64a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (64a c - 48a b )d e + 128a b c d e - 128a c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 4 3 2 3 2 2 +--R (- 32a c + 16a b c + 6b )d e + (- 64a b c - 16b c)d e +--R + +--R 3 2 2 3 +--R (64a c + 16b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 3 +--R ((- 64a b c + 48a b )d e - 128a b c d e + 128a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 3 +--R (- 64a c + 48a b )d e - 128a b c d e + 128a c d e +--R * +--R +-------------------+ +--R +-+ | 2 2 +--R \|a \|a e - b d e + c d +--R * +--R atan +--R +---------------------+ +--------------+ +--R | 2 2 | 2 +--R d\|- a e + b d e - c d \|c x + b x + a +--R + +--R +---------------------+ +--R | 2 2 +-+ +--R (- e x - d)\|- a e + b d e - c d \|a +--R / +--R 2 2 +--R (a e - b d e + c d )x +--R + +--R 2 3 3 2 2 2 2 3 2 3 +--R (- 8a b e + (32a b c - 16b )d e + 32b c d e - 16b c d )x - 16a b e +--R + +--R 2 2 2 2 2 3 +--R (64a c - 32a b )d e + 64a b c d e - 32a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 +-+ | 2 2 | 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 3 2 2 2 4 2 +--R (8a b c + 2a b )e + (- 32a c + 8a b c + 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (- 32a b c - 8b c)d e + (16a c + 4b c )d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 2 2 2 3 +--R (16a b e + (- 64a b c + 32a b )d e - 64a b c d e + 32a b c d )x +--R + +--R 3 3 3 2 2 2 2 2 2 2 3 +--R 16a b e + (- 64a c + 32a b )d e - 64a b c d e + 32a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 | 2 2 +--R \|- a e + b d e - c d \|a e - b d e + c d +--R / +--R 3 4 2 2 2 3 2 3 3 2 2 4 +--R 8a b d e - 16a b d e + (16a b c + 8a b )d e - 16a b c d e +--R + +--R 2 5 +--R 8a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 3 2 2 3 2 2 4 2 2 5 +--R 16a d e - 32a b d e + (32a c + 16a b )d e - 32a b c d e + 16a c d +--R * +--R +---------------------+ +-------------------+ +--------------+ +--R | 2 2 | 2 2 | 2 +--R \|- a e + b d e - c d \|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 4 2 3 2 3 +--R (- 8a c - 2a b )d e + (16a b c + 4a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (- 16a c - 12a b c - 2b )d e + (16a b c + 4b c)d e +--R + +--R 3 2 2 5 +--R (- 8a c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 3 2 +--R - 16a b d e + 32a b d e + (- 32a b c - 16a b )d e +--R + +--R 2 4 2 5 +--R 32a b c d e - 16a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 3 2 2 3 2 2 4 +--R - 16a d e + 32a b d e + (- 32a c - 16a b )d e + 32a b c d e +--R + +--R 2 2 5 +--R - 16a c d +--R * +--R +---------------------+ +-------------------+ +--R | 2 2 +-+ | 2 2 +--R \|- a e + b d e - c d \|a \|a e - b d e + c d +--R Type: Expression(Integer) +--E 644 + +--S 645 of 845 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 845 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 845 +r0:=-2/3*(d+e*x)^4/(a+b*x+c*x^2)^(3/2)+4*e^3*(2*c*d-b*e)*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-_ + 16/3*e*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*_ + sqrt(a+b*x+c*x^2))+8/3*e^2*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*_ + sqrt(a+b*x+c*x^2)/(c^2*(b^2-4*a*c))+16/3*e^3*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/(c*(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 2 +--R ((- 48a b c + 12b c)e + (96a c - 24b c )d e )x +--R + +--R 2 4 4 2 3 3 +--R ((- 48a b c + 12b )e + (96a b c - 24b c)d e )x +--R + +--R 2 3 4 2 2 2 3 +--R (- 48a b c + 12a b )e + (96a c - 24a b c)d e +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 4 4 +--R (24a c - 6b c )e x +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (112a b c - 32b c)e + (- 128a c + 56b c )d e - 48b c d e +--R + +--R 4 3 +--R 32c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 4 2 3 3 +--R (96a c + 48a b c - 24b )e + (- 48a b c + 48b c)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 144a c - 36b c )d e + 48b c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (144a b c - 48a b )e + (- 96a c + 96a b c)d e - 144a b c d e +--R + +--R 2 2 3 +--R 24b c d e +--R * +--R x +--R + +--R 3 2 2 4 2 3 2 2 2 2 2 3 +--R (64a c - 24a b )e + 48a b c d e - 96a c d e + 16a b c d e +--R + +--R 3 2 2 4 +--R (- 8a c + 2b c )d +--R * +--R +-+ +--R \|c +--R / +--R 4 2 3 2 3 3 2 2 3 2 2 +-+ +--R ((12a c - 3b c )x + (12a b c - 3b c )x + 12a c - 3a b c )\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 647 + +--S 648 of 845 +--a0:=integrate(t0,x) +--E 648 + +--S 649 of 845 +--m0:=a0-r0 +--E 649 + +--S 650 of 845 +--d0:=D(m0,x) +--E 650 + +)clear all + +--S 651 of 845 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 651 + +--S 652 of 845 +r0:=-2/3*(d+e*x)^3/(a+b*x+c*x^2)^(3/2)+2*e^3*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-4*e*(d+e*x)*(b*d-2*a*e+(2*c*d-_ + b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+4*e^2*(2*c*d-b*e)*sqrt(a+b*x+_ + c*x^2)/(c*(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 3 3 2 2 3 +--R ((24a c - 6b c)e x + (24a b c - 6b )e x + (24a c - 6a b )e ) +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 32a c + 14b c)e - 24b c d e + 24c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 12a b c + 12b )e + (- 72a c - 18b c)d e + 36b c d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R ((- 24a c + 24a b )e - 72a b c d e + 18b c d e)x + 12a b e +--R + +--R 2 2 2 2 2 3 +--R - 48a c d e + 12a b c d e + (- 8a c + 2b c)d +--R * +--R +-+ +--R \|c +--R / +--R 3 2 2 2 2 3 2 2 2 +-+ +--R ((12a c - 3b c )x + (12a b c - 3b c)x + 12a c - 3a b c)\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 652 + +--S 653 of 845 +--a0:=integrate(t0,x) +--E 653 + +--S 654 of 845 +--m0:=a0-r0 +--E 654 + +--S 655 of 845 +--d0:=D(m0,x) +--E 655 + +)clear all + +--S 656 of 845 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 656 + +--S 657 of 845 +r0:=-2/3*(d+e*x)^2/(a+b*x+c*x^2)^(3/2)-8/3*e*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + ((b^2-4*a*c)*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 2 3 2 2 2 +--R (- 8b c e + 16c d e)x + ((- 24a c - 6b )e + 24b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 24a b e + 12b d e)x - 16a e + 8a b d e + (- 8a c + 2b )d +--R / +--R +--------------+ +--R 2 2 2 3 2 2 | 2 +--R ((12a c - 3b c)x + (12a b c - 3b )x + 12a c - 3a b )\|c x + b x + a +--R Type: Expression(Integer) +--E 657 + +--S 658 of 845 +--a0:=integrate(t0,x) +--E 658 + +--S 659 of 845 +--m0:=a0-r0 +--E 659 + +--S 660 of 845 +--d0:=D(m0,x) +--E 660 + +)clear all + +--S 661 of 845 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 661 + +--S 662 of 845 +r0:=-2/3*(d+e*x)/(a+b*x+c*x^2)^(3/2)-4/3*e*(b+2*c*x)/((b^2-4*a*c)*_ + sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 2 +--R 8c e x + 12b c e x + 6b e x + 4a b e + (- 8a c + 2b )d +--R ----------------------------------------------------------------------- +--R +--------------+ +--R 2 2 2 3 2 2 | 2 +--R ((12a c - 3b c)x + (12a b c - 3b )x + 12a c - 3a b )\|c x + b x + a +--R Type: Expression(Integer) +--E 662 + +--S 663 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 3 5 +--R ((- 16a c - 4a b c)e + (- 24a b c - 2b c)d)x +--R + +--R 2 3 2 2 2 4 4 +--R ((- 64a b c - 4a b )e + (- 48a c - 60a b c - 2b )d)x +--R + +--R 3 2 2 2 3 3 +--R ((- 64a c - 40a b )e + (- 168a b c - 38a b )d)x +--R + +--R 3 3 2 2 2 3 +--R (- 48a b e + (- 96a c - 120a b )d)x - 96a b d x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 3 2 2 6 +--R (16a b c e + (16a c + 12b c )d)x +--R + +--R 2 2 2 2 3 5 +--R ((48a c + 36a b c)e + (96a b c + 24b c)d)x +--R + +--R 2 3 2 2 2 4 4 +--R ((120a b c + 18a b )e + (96a c + 168a b c + 12b )d)x +--R + +--R 3 2 2 2 3 3 +--R ((64a c + 64a b )e + (264a b c + 86a b )d)x +--R + +--R 3 3 2 2 2 3 +--R (48a b e + (96a c + 168a b )d)x + 96a b d x +--R * +--R +-+ +--R \|a +--R / +--R 2 2 3 5 3 2 2 2 4 4 +--R (36a b c + 3a b c)x + (72a c + 90a b c + 3a b )x +--R + +--R 3 2 3 3 4 3 2 2 4 5 +--R (252a b c + 57a b )x + (168a c + 198a b )x + 240a b x + 96a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 2 2 6 3 2 2 3 5 +--R (- 24a c - 18a b c )x + (- 144a b c - 36a b c)x +--R + +--R 4 2 3 2 2 4 4 4 3 3 3 +--R (- 144a c - 252a b c - 18a b )x + (- 432a b c - 132a b )x +--R + +--R 5 4 2 2 5 6 +--R (- 216a c - 306a b )x - 288a b x - 96a +--R Type: Union(Expression(Integer),...) +--E 663 + +--S 664 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 4 2 +--R ((32a b c + 24a b )e + (- 64a c - 32a b c + 12b )d)x +--R + +--R 2 2 2 3 3 3 2 2 +--R (128a b e + (- 256a b c + 64a b )d)x + 128a b e + (- 256a c + 64a b )d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 5 3 +--R ((- 48a b c - 4a b )e + (96a b c - 16a b c - 2b )d)x +--R + +--R 3 2 3 3 2 2 2 4 2 +--R ((- 96a b c - 72a b )e + (192a c + 96a b c - 36a b )d)x +--R + +--R 3 2 3 2 3 4 4 3 2 +--R (- 192a b e + (384a b c - 96a b )d)x - 128a b e + (256a c - 64a b )d +--R / +--R 4 2 3 2 2 4 2 4 3 3 5 +--R (96a c + 48a b c - 18a b )x + (384a b c - 96a b )x + 384a c +--R + +--R 4 2 +--R - 96a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 2 2 3 5 3 4 2 3 2 2 4 2 +--R (- 144a b c + 24a b c + 3a b )x + (- 288a c - 144a b c + 54a b )x +--R + +--R 4 3 3 5 4 2 +--R (- 576a b c + 144a b )x - 384a c + 96a b +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 664 + +--S 665 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 665 + +)clear all + +--S 666 of 845 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2c x + b +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 666 + +--S 667 of 845 +r0:=(-2/3)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R (2) - ------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (3c x + 3b x + 3a)\|c x + b x + a +--R Type: Expression(Integer) +--E 667 + +--S 668 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 5 2 2 2 4 4 +--R (- 24a b c - 2b c)x + (- 48a c - 60a b c - 2b )x +--R + +--R 2 3 3 3 2 2 2 3 +--R (- 168a b c - 38a b )x + (- 96a c - 120a b )x - 96a b x +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 2 2 6 2 3 5 +--R (16a c + 12b c )x + (96a b c + 24b c)x +--R + +--R 2 2 2 4 4 2 3 3 +--R (96a c + 168a b c + 12b )x + (264a b c + 86a b )x +--R + +--R 3 2 2 2 3 +--R (96a c + 168a b )x + 96a b x +--R * +--R +-+ +--R \|a +--R / +--R 2 2 3 5 3 2 2 2 4 4 +--R (36a b c + 3a b c)x + (72a c + 90a b c + 3a b )x +--R + +--R 3 2 3 3 4 3 2 2 4 5 +--R (252a b c + 57a b )x + (168a c + 198a b )x + 240a b x + 96a +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 3 3 2 2 2 6 3 2 2 3 5 +--R (- 24a c - 18a b c )x + (- 144a b c - 36a b c)x +--R + +--R 4 2 3 2 2 4 4 4 3 3 3 +--R (- 144a c - 252a b c - 18a b )x + (- 432a b c - 132a b )x +--R + +--R 5 4 2 2 5 6 +--R (- 216a c - 306a b )x - 288a b x - 96a +--R Type: Union(Expression(Integer),...) +--E 668 + +--S 669 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 2 +-+ | 2 +--R ((- 16a c - 12b )x - 64a b x - 64a )\|a \|c x + b x + a +--R + +--R 3 3 2 2 2 2 3 +--R (24a b c + 2b )x + (48a c + 36a b )x + 96a b x + 64a +--R / +--R +--------------+ +--R 3 2 2 2 3 4 | 2 +--R ((24a c + 18a b )x + 96a b x + 96a )\|c x + b x + a +--R + +--R 2 3 3 3 2 2 2 3 4 +-+ +--R ((- 36a b c - 3a b )x + (- 72a c - 54a b )x - 144a b x - 96a )\|a +--R Type: Expression(Integer) +--E 669 + +--S 670 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 670 + +)clear all + +--S 671 of 845 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 671 + +--S 672 of 845 +r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-e^3*(2*c*d-b*e)*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)-2/3*e*(5*b^2*c*d*e-_ + 12*a*c^2*d*e-3*b^3*e^2-2*b*c*(c*d^2-5*a*e^2)-c*(4*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(b*d+2*a*e))*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 2 +--R ((- 12a b c + 3b c)e + (24a c - 6b c )d e )x +--R + +--R 2 4 4 2 3 3 +--R ((- 12a b c + 3b )e + (24a b c - 6b c)d e )x +--R + +--R 2 3 4 2 2 2 3 +--R (- 12a b c + 3a b )e + (24a c - 6a b c)d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 3 3 2 4 2 3 +--R ((16a c - 6b c )e + 8b c d e - 8c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 2 +--R ((36a b c - 12b c)e + (- 24a c + 18b c )d e - 12b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 2 2 2 +--R ((24a c + 12a b c - 6b )e + (- 24a b c + 12b c)d e - 6b c d e)x +--R + +--R 2 3 3 2 2 2 4 2 +--R (28a b c - 8a b )e + (- 32a c + 4a b c + 2b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (12a b c - 4b c)d e + (- 8a c + 2b c )d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 3 2 2 2 4 2 2 3 3 +--R (12a c - 3a b c)e + (- 24a b c + 6a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (24a c + 6a b c - 3b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (12a c - 3b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 2 2 4 3 +--R (12a b c - 3a b )e + (- 24a b c + 6a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (24a b c + 6a b c - 3b )d e + (- 24a b c + 6b c)d e +--R + +--R 3 3 2 4 +--R (12a b c - 3b c )d +--R * +--R x +--R + +--R 4 3 2 4 3 2 3 3 +--R (12a c - 3a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (24a c + 6a b c - 3a b )d e + (- 24a b c + 6a b c)d e +--R + +--R 2 3 2 2 4 +--R (12a c - 3a b c )d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 672 + +--S 673 of 845 +--a0:=integrate(t0,x) +--E 673 + +--S 674 of 845 +--m0:=a0-r0 +--E 674 + +--S 675 of 845 +--d0:=D(m0,x) +--E 675 + +)clear all + +--S 676 of 845 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + ((2a c + b )e + 4b c d e + c d )x +--R + +--R 2 2 2 3 +--R (2a b e + (4a c + 2b )d e + 2b c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (a e + 4a b d e + (2a c + b )d )x + (2a d e + 2a b d )x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 845 +r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(d+e*x)*(a+b*x+c*x^2)^(3/2))-1/2*e^3*(16*c^2*d^2+_ + 5*b^2*e^2-4*c*e*(4*b*d+a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)-_ + 2/3*e*(9*b^2*c*d*e-20*a*c^2*d*e-5*b^3*e^2-4*b*c*(c*d^2-4*a*e^2)-_ + c*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*x)/((b^2-4*a*c)*(c*d^2-_ + b*d*e+a*e^2)^2*(d+e*x)*sqrt(a+b*x+c*x^2))+1/3*e^2*(2*c*d-b*e)*_ + (8*c^2*d^2+15*b^2*e^2-4*c*e*(2*b*d+13*a*e))*sqrt(a+b*x+c*x^2)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)) +--R +--R +--R (2) +--R 2 3 2 2 4 6 3 3 2 5 +--R (- 48a c + 72a b c - 15b c)e + (- 192a b c + 48b c )d e +--R + +--R 4 2 3 2 4 +--R (192a c - 48b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 6 +--R (- 48a b c + 72a b c - 15b )e +--R + +--R 2 3 2 2 4 5 4 2 3 3 3 +--R (- 48a c - 120a b c + 33b c)d e + (192a c - 48b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 6 +--R (- 48a c + 72a b c - 15a b )e +--R + +--R 2 2 3 5 5 +--R (- 240a b c + 120a b c - 15b )d e +--R + +--R 2 3 2 2 4 2 4 3 3 2 3 3 +--R (192a c - 240a b c + 48b c)d e + (192a b c - 48b c )d e +--R * +--R x +--R + +--R 3 2 2 2 4 5 2 2 3 2 4 +--R (- 48a c + 72a b c - 15a b )d e + (- 192a b c + 48a b c)d e +--R + +--R 2 3 2 2 3 3 +--R (192a c - 48a b c )d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 5 4 2 3 4 4 2 3 +--R (- 104a b c + 30b c )e + (208a c - 76b c )d e + 48b c d e +--R + +--R 5 3 2 +--R - 32c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (48a c - 228a b c + 60b c)e + (400a b c - 132b c )d e +--R + +--R 4 2 3 2 3 5 4 +--R (16a c + 44b c )d e - 32c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 5 +--R (- 96a b c - 84a b c + 30b )e +--R + +--R 2 3 2 2 4 4 3 3 2 2 3 +--R (336a c + 12a b c - 36b c)d e + (240a b c - 60b c )d e +--R + +--R 4 2 3 3 2 4 4 +--R (- 144a c + 84b c )d e - 48b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 +--R (64a c - 168a b c + 40a b )e +--R + +--R 2 2 3 5 4 +--R (288a b c - 152a b c + 20b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (48a c + 180a b c - 60b c)d e + (- 112a b c + 60b c )d e +--R + +--R 4 2 3 4 +--R (- 16a c - 20b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (- 24a b c + 6a b )e + (112a c - 132a b c + 28a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (240a b c - 56a b c - 4b )d e + (- 144a c + 12a b c + 12b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (32a b c - 12b c )d e + (- 16a c + 4b c )d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 4 2 3 2 7 3 2 2 3 6 +--R (24a c - 6a b c)e + (- 72a b c + 18a b c)d e +--R + +--R 3 3 2 2 2 4 2 5 +--R (72a c + 54a b c - 18a b c)d e +--R + +--R 2 3 3 2 5 3 4 +--R (- 144a b c + 12a b c + 6b c)d e +--R + +--R 2 4 2 3 4 2 4 3 4 3 3 5 2 +--R (72a c + 54a b c - 18b c )d e + (- 72a b c + 18b c )d e +--R + +--R 5 2 4 6 +--R (24a c - 6b c )d e +--R * +--R 3 +--R x +--R + +--R 4 3 3 7 4 2 3 2 2 4 6 +--R (24a b c - 6a b )e + (24a c - 78a b c + 18a b )d e +--R + +--R 2 3 5 2 5 3 3 2 2 2 4 6 3 4 +--R (72a b c - 18a b )d e + (72a c - 90a b c - 6a b c + 6b )d e +--R + +--R 2 3 3 2 5 4 3 2 4 2 3 5 2 +--R (- 72a b c + 66a b c - 12b c)d e + (72a c - 18a b c )d e +--R + +--R 4 3 3 6 5 2 4 7 +--R (- 48a b c + 12b c )d e + (24a c - 6b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 2 7 4 3 3 6 +--R (24a c - 6a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 2 2 5 3 2 2 3 5 3 4 +--R (72a c - 18a b c)d e + (- 72a b c + 66a b c - 12a b )d e +--R + +--R 3 3 2 2 2 4 6 4 3 3 2 5 5 2 +--R (72a c - 90a b c - 6a b c + 6b )d e + (72a b c - 18b c)d e +--R + +--R 2 4 2 3 4 2 6 4 3 3 7 +--R (24a c - 78a b c + 18b c )d e + (24a b c - 6b c )d +--R * +--R x +--R + +--R 5 4 2 6 4 3 3 2 5 +--R (24a c - 6a b )d e + (- 72a b c + 18a b )d e +--R + +--R 4 2 3 2 2 4 3 4 3 2 2 3 5 4 3 +--R (72a c + 54a b c - 18a b )d e + (- 144a b c + 12a b c + 6a b )d e +--R + +--R 3 3 2 2 2 4 5 2 2 3 3 2 6 +--R (72a c + 54a b c - 18a b c)d e + (- 72a b c + 18a b c )d e +--R + +--R 2 4 2 3 7 +--R (24a c - 6a b c )d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 677 + +--S 678 of 845 +--a0:=integrate(t0,x) +--E 678 + +--S 679 of 845 +--m0:=a0-r0 +--E 679 + +--S 680 of 845 +--d0:=D(m0,x) +--E 680 + +)clear all + +--S 681 of 845 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x +--R + +--R 2 +--R a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 681 + +--S 682 of 845 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(7/2)/e^4+2/9*_ + (6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(9/2)/e^4-6/11*c*_ + (2*c*d-b*e)*(d+e*x)^(11/2)/e^4+4/13*c^2*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 +--R 2772c e x + (4914b c e + 6804c d e )x +--R + +--R 2 6 5 2 2 4 4 +--R ((4004a c + 2002b )e + 12558b c d e + 4452c d e )x +--R + +--R 6 2 5 2 4 2 3 3 3 +--R (2574a b e + (10868a c + 5434b )d e + 8814b c d e + 60c d e )x +--R + +--R 5 2 2 4 3 3 2 4 2 2 +--R (7722a b d e + (8580a c + 4290b )d e + 234b c d e - 72c d e )x +--R + +--R 2 4 2 3 3 4 2 2 5 +--R (7722a b d e + (572a c + 286b )d e - 312b c d e + 96c d e)x +--R + +--R 3 3 2 4 2 5 2 6 +--R 2574a b d e + (- 1144a c - 572b )d e + 624b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 682 + +--S 683 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 6 2 5 5 +--R 2772c e x + (4914b c e + 6804c d e )x +--R + +--R 2 6 5 2 2 4 4 +--R ((4004a c + 2002b )e + 12558b c d e + 4452c d e )x +--R + +--R 6 2 5 2 4 2 3 3 3 +--R (2574a b e + (10868a c + 5434b )d e + 8814b c d e + 60c d e )x +--R + +--R 5 2 2 4 3 3 2 4 2 2 +--R (7722a b d e + (8580a c + 4290b )d e + 234b c d e - 72c d e )x +--R + +--R 2 4 2 3 3 4 2 2 5 +--R (7722a b d e + (572a c + 286b )d e - 312b c d e + 96c d e)x +--R + +--R 3 3 2 4 2 5 2 6 +--R 2574a b d e + (- 1144a c - 572b )d e + 624b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 683 + +--S 684 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 684 + +--S 685 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 685 + +)clear all + +--S 686 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 686 + +--S 687 of 845 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(5/2)/e^4+_ + 2/7*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(7/2)/e^4-_ + 2/3*c*(2*c*d-b*e)*(d+e*x)^(9/2)/e^4+4/11*c^2*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 +--R 420c e x + (770b c e + 560c d e )x +--R + +--R 2 5 4 2 2 3 3 +--R ((660a c + 330b )e + 1100b c d e + 20c d e )x +--R + +--R 5 2 4 2 3 2 3 2 2 +--R (462a b e + (1056a c + 528b )d e + 66b c d e - 24c d e )x +--R + +--R 4 2 2 3 3 2 2 4 +--R (924a b d e + (132a c + 66b )d e - 88b c d e + 32c d e)x +--R + +--R 2 3 2 3 2 4 2 5 +--R 462a b d e + (- 264a c - 132b )d e + 176b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Expression(Integer) +--E 687 + +--S 688 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 5 2 4 4 +--R 420c e x + (770b c e + 560c d e )x +--R + +--R 2 5 4 2 2 3 3 +--R ((660a c + 330b )e + 1100b c d e + 20c d e )x +--R + +--R 5 2 4 2 3 2 3 2 2 +--R (462a b e + (1056a c + 528b )d e + 66b c d e - 24c d e )x +--R + +--R 4 2 2 3 3 2 2 4 +--R (924a b d e + (132a c + 66b )d e - 88b c d e + 32c d e)x +--R + +--R 2 3 2 3 2 4 2 5 +--R 462a b d e + (- 264a c - 132b )d e + 176b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Union(Expression(Integer),...) +--E 688 + +--S 689 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 689 + +--S 690 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)*sqrt(d+e*x) +--R +--R +--R 2 3 2 2 +-------+ +--R (1) (2c x + 3b c x + (2a c + b )x + a b)\|e x + d +--R Type: Expression(Integer) +--E 691 + +--S 692 of 845 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2)/e^4+_ + 2/5*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(5/2)/e^4-_ + 6/7*c*(2*c*d-b*e)*(d+e*x)^(7/2)/e^4+4/9*c^2*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 140c e x + (270b c e + 20c d e )x +--R + +--R 2 4 3 2 2 2 2 +--R ((252a c + 126b )e + 54b c d e - 24c d e )x +--R + +--R 4 2 3 2 2 2 3 3 +--R (210a b e + (84a c + 42b )d e - 72b c d e + 32c d e)x + 210a b d e +--R + +--R 2 2 2 3 2 4 +--R (- 168a c - 84b )d e + 144b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 692 + +--S 693 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 2 3 3 +--R 140c e x + (270b c e + 20c d e )x +--R + +--R 2 4 3 2 2 2 2 +--R ((252a c + 126b )e + 54b c d e - 24c d e )x +--R + +--R 4 2 3 2 2 2 3 3 +--R (210a b e + (84a c + 42b )d e - 72b c d e + 32c d e)x + 210a b d e +--R + +--R 2 2 2 3 2 4 +--R (- 168a c - 84b )d e + 144b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 693 + +--S 694 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 694 + +--S 695 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 695 + +)clear all + +--S 696 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 696 + +--S 697 of 845 +r0:=2/3*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(3/2)/e^4-_ + 6/5*c*(2*c*d-b*e)*(d+e*x)^(5/2)/e^4+4/7*c^2*(d+e*x)^(7/2)/e^4-_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 60c e x + (126b c e - 72c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((140a c + 70b )e - 168b c d e + 96c d e)x + 210a b e +--R + +--R 2 2 2 2 3 +--R (- 280a c - 140b )d e + 336b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 697 + +--S 698 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 +--R 60c e x + (126b c e - 72c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((140a c + 70b )e - 168b c d e + 96c d e)x + 210a b e +--R + +--R 2 2 2 2 3 +--R (- 280a c - 140b )d e + 336b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 698 + +--S 699 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 699 + +--S 700 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 701 + +--S 702 of 845 +r0:=-2*c*(2*c*d-b*e)*(d+e*x)^(3/2)/e^4+4/5*c^2*(d+e*x)^(5/2)/e^4+_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*sqrt(d+e*x))+2*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 4c e x + (10b c e - 8c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((20a c + 10b )e - 40b c d e + 32c d e)x - 10a b e +--R + +--R 2 2 2 2 3 +--R (40a c + 20b )d e - 80b c d e + 64c d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Expression(Integer) +--E 702 + +--S 703 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 +--R 4c e x + (10b c e - 8c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((20a c + 10b )e - 40b c d e + 32c d e)x - 10a b e +--R + +--R 2 2 2 2 3 +--R (40a c + 20b )d e - 80b c d e + 64c d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 706 + +--S 707 of 845 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^(3/2))+_ + 4/3*c^2*(d+e*x)^(3/2)/e^4-2*(6*c^2*d^2+b^2*e^2-2*c*e*_ + (3*b*d-a*e))/(e^4*sqrt(d+e*x))-6*c*(2*c*d-b*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 4c e x + (18b c e - 24c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((- 12a c - 6b )e + 72b c d e - 96c d e)x - 2a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c - 4b )d e + 48b c d e - 64c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 707 + +--S 708 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 +--R 4c e x + (18b c e - 24c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((- 12a c - 6b )e + 72b c d e - 96c d e)x - 2a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c - 4b )d e + 48b c d e - 64c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 709 + +--S 710 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 710 + +)clear all + +--S 711 of 845 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 711 + +--S 712 of 845 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(7/2)/e^6+_ + 4/9*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(9/2)/e^6-2/11*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(11/2)/e^6+8/13*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(13/2)/e^6-2/3*c^2*(2*c*d-b*e)*_ + (d+e*x)^(15/2)/e^6+4/17*c^3*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 3 8 8 2 8 3 7 7 +--R 36036c e x + (102102b c e + 84084c d e )x +--R + +--R 2 2 8 2 7 3 2 6 6 +--R ((94248a c + 94248b c)e + 243474b c d e + 50820c d e )x +--R + +--R 3 8 2 2 7 +--R (167076a b c + 27846b )e + (231336a c + 231336b c)d e +--R + +--R 2 2 6 3 3 5 +--R 152082b c d e + 252c d e +--R * +--R 5 +--R x +--R + +--R 2 2 8 3 7 +--R (68068a c + 68068a b )e + (426972a b c + 71162b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (151368a c + 151368b c)d e + 1190b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 7 +--R 43758a b e + (184756a c + 184756a b )d e +--R + +--R 3 2 6 2 2 3 5 +--R (299676a b c + 49946b )d e + (2040a c + 2040b c)d e +--R + +--R 2 4 4 3 5 3 +--R - 1360b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 2 6 +--R 131274a b d e + (145860a c + 145860a b )d e +--R + +--R 3 3 5 2 2 4 4 +--R (7956a b c + 1326b )d e + (- 2448a c - 2448b c)d e +--R + +--R 2 5 3 3 6 2 +--R 1632b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 2 2 3 5 +--R 131274a b d e + (9724a c + 9724a b )d e +--R + +--R 3 4 4 2 2 5 3 +--R (- 10608a b c - 1768b )d e + (3264a c + 3264b c)d e +--R + +--R 2 6 2 3 7 +--R - 2176b c d e + 512c d e +--R * +--R x +--R + +--R 2 3 5 2 2 4 4 +--R 43758a b d e + (- 19448a c - 19448a b )d e +--R + +--R 3 5 3 2 2 6 2 2 7 +--R (21216a b c + 3536b )d e + (- 6528a c - 6528b c)d e + 4352b c d e +--R + +--R 3 8 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Expression(Integer) +--E 712 + +--S 713 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 8 8 2 8 3 7 7 +--R 36036c e x + (102102b c e + 84084c d e )x +--R + +--R 2 2 8 2 7 3 2 6 6 +--R ((94248a c + 94248b c)e + 243474b c d e + 50820c d e )x +--R + +--R 3 8 2 2 7 +--R (167076a b c + 27846b )e + (231336a c + 231336b c)d e +--R + +--R 2 2 6 3 3 5 +--R 152082b c d e + 252c d e +--R * +--R 5 +--R x +--R + +--R 2 2 8 3 7 +--R (68068a c + 68068a b )e + (426972a b c + 71162b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (151368a c + 151368b c)d e + 1190b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 7 +--R 43758a b e + (184756a c + 184756a b )d e +--R + +--R 3 2 6 2 2 3 5 +--R (299676a b c + 49946b )d e + (2040a c + 2040b c)d e +--R + +--R 2 4 4 3 5 3 +--R - 1360b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 2 6 +--R 131274a b d e + (145860a c + 145860a b )d e +--R + +--R 3 3 5 2 2 4 4 +--R (7956a b c + 1326b )d e + (- 2448a c - 2448b c)d e +--R + +--R 2 5 3 3 6 2 +--R 1632b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 2 2 3 5 +--R 131274a b d e + (9724a c + 9724a b )d e +--R + +--R 3 4 4 2 2 5 3 +--R (- 10608a b c - 1768b )d e + (3264a c + 3264b c)d e +--R + +--R 2 6 2 3 7 +--R - 2176b c d e + 512c d e +--R * +--R x +--R + +--R 2 3 5 2 2 4 4 +--R 43758a b d e + (- 19448a c - 19448a b )d e +--R + +--R 3 5 3 2 2 6 2 2 7 +--R (21216a b c + 3536b )d e + (- 6528a c - 6528b c)d e + 4352b c d e +--R + +--R 3 8 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 714 + +--S 715 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 +--R ((6a b c + b )e + (4a c + 4b c)d)x +--R + +--R 2 2 3 2 2 2 2 2 +--R ((2a c + 2a b )e + (6a b c + b )d)x + (a b e + (2a c + 2a b )d)x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 716 + +--S 717 of 845 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(5/2)/e^6+_ + 4/7*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(7/2)/e^6-2/9*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(9/2)/e^6+8/11*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(11/2)/e^6-10/13*c^2*(2*c*d-b*e)*_ + (d+e*x)^(13/2)/e^6+4/15*c^3*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 3 7 7 2 7 3 6 6 +--R 12012c e x + (34650b c e + 14784c d e )x +--R + +--R 2 2 7 2 6 3 2 5 5 +--R ((32760a c + 32760b c)e + 44100b c d e + 252c d e )x +--R + +--R 3 7 2 2 6 +--R (60060a b c + 10010b )e + (43680a c + 43680b c)d e +--R + +--R 2 2 5 3 3 4 +--R 1050b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 2 7 3 6 +--R (25740a c + 25740a b )e + (85800a b c + 14300b )d e +--R + +--R 2 2 2 5 2 3 4 3 4 3 +--R (1560a c + 1560b c)d e - 1200b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 6 3 2 5 +--R 18018a b e + (41184a c + 41184a b )d e + (5148a b c + 858b )d e +--R + +--R 2 2 3 4 2 4 3 3 5 2 +--R (- 1872a c - 1872b c)d e + 1440b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 2 5 +--R 36036a b d e + (5148a c + 5148a b )d e +--R + +--R 3 3 4 2 2 4 3 +--R (- 6864a b c - 1144b )d e + (2496a c + 2496b c)d e +--R + +--R 2 5 2 3 6 +--R - 1920b c d e + 512c d e +--R * +--R x +--R + +--R 2 2 5 2 2 3 4 +--R 18018a b d e + (- 10296a c - 10296a b )d e +--R + +--R 3 4 3 2 2 5 2 2 6 +--R (13728a b c + 2288b )d e + (- 4992a c - 4992b c)d e + 3840b c d e +--R + +--R 3 7 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 717 + +--S 718 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 2 7 3 6 6 +--R 12012c e x + (34650b c e + 14784c d e )x +--R + +--R 2 2 7 2 6 3 2 5 5 +--R ((32760a c + 32760b c)e + 44100b c d e + 252c d e )x +--R + +--R 3 7 2 2 6 +--R (60060a b c + 10010b )e + (43680a c + 43680b c)d e +--R + +--R 2 2 5 3 3 4 +--R 1050b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 2 7 3 6 +--R (25740a c + 25740a b )e + (85800a b c + 14300b )d e +--R + +--R 2 2 2 5 2 3 4 3 4 3 +--R (1560a c + 1560b c)d e - 1200b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 6 3 2 5 +--R 18018a b e + (41184a c + 41184a b )d e + (5148a b c + 858b )d e +--R + +--R 2 2 3 4 2 4 3 3 5 2 +--R (- 1872a c - 1872b c)d e + 1440b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 2 5 +--R 36036a b d e + (5148a c + 5148a b )d e +--R + +--R 3 3 4 2 2 4 3 +--R (- 6864a b c - 1144b )d e + (2496a c + 2496b c)d e +--R + +--R 2 5 2 3 6 +--R - 1920b c d e + 512c d e +--R * +--R x +--R + +--R 2 2 5 2 2 3 4 +--R 18018a b d e + (- 10296a c - 10296a b )d e +--R + +--R 3 4 3 2 2 5 2 2 6 +--R (13728a b c + 2288b )d e + (- 4992a c - 4992b c)d e + 3840b c d e +--R + +--R 3 7 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 718 + +--S 719 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 719 + +--S 720 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 721 + +--S 722 of 845 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(3/2)/e^6+_ + 4/5*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(5/2)/e^6-2/7*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))*(d+e*x)^(7/2)/e^6+8/9*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(9/2)/e^6-10/11*c^2*(2*c*d-b*e)*_ + (d+e*x)^(11/2)/e^6+4/13*c^3*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 13860c e x + (40950b c e + 1260c d e )x +--R + +--R 2 2 6 2 5 3 2 4 4 +--R ((40040a c + 40040b c)e + 4550b c d e - 1400c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (77220a b c + 12870b )e + (5720a c + 5720b c)d e - 5200b c d e +--R + +--R 3 3 3 +--R 1600c d e +--R * +--R 3 +--R x +--R + +--R 2 2 6 3 5 +--R (36036a c + 36036a b )e + (15444a b c + 2574b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 6864a c - 6864b c)d e + 6240b c d e - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 +--R 30030a b e + (12012a c + 12012a b )d e +--R + +--R 3 2 4 2 2 3 3 +--R (- 20592a b c - 3432b )d e + (9152a c + 9152b c)d e +--R + +--R 2 4 2 3 5 +--R - 8320b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 2 4 +--R 30030a b d e + (- 24024a c - 24024a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (41184a b c + 6864b )d e + (- 18304a c - 18304b c)d e + 16640b c d e +--R + +--R 3 6 +--R - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 722 + +--S 723 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 2 6 3 5 5 +--R 13860c e x + (40950b c e + 1260c d e )x +--R + +--R 2 2 6 2 5 3 2 4 4 +--R ((40040a c + 40040b c)e + 4550b c d e - 1400c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (77220a b c + 12870b )e + (5720a c + 5720b c)d e - 5200b c d e +--R + +--R 3 3 3 +--R 1600c d e +--R * +--R 3 +--R x +--R + +--R 2 2 6 3 5 +--R (36036a c + 36036a b )e + (15444a b c + 2574b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 6864a c - 6864b c)d e + 6240b c d e - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 +--R 30030a b e + (12012a c + 12012a b )d e +--R + +--R 3 2 4 2 2 3 3 +--R (- 20592a b c - 3432b )d e + (9152a c + 9152b c)d e +--R + +--R 2 4 2 3 5 +--R - 8320b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 2 4 +--R 30030a b d e + (- 24024a c - 24024a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (41184a b c + 6864b )d e + (- 18304a c - 18304b c)d e + 16640b c d e +--R + +--R 3 6 +--R - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 723 + +--S 724 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 724 + +--S 725 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 725 + +)clear all + +--S 726 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 726 + +--S 727 of 845 +r0:=4/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(3/2)/e^6-2/5*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(5/2)/e^6+8/7*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(7/2)/e^6-10/9*c^2*(2*c*d-b*e)*_ + (d+e*x)^(9/2)/e^6+4/11*c^3*(d+e*x)^(11/2)/e^6-2*(2*c*d-b*e)*_ + (c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 1260c e x + (3850b c e - 1400c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((3960a c + 3960b c)e - 4400b c d e + 1600c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (8316a b c + 1386b )e + (- 4752a c - 4752b c)d e + 5280b c d e +--R + +--R 3 3 2 +--R - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (4620a c + 4620a b )e + (- 11088a b c - 1848b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (6336a c + 6336b c)d e - 7040b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R 6930a b e + (- 9240a c - 9240a b )d e + (22176a b c + 3696b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12672a c - 12672b c)d e + 14080b c d e - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 727 + +--S 728 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 2 5 3 4 4 +--R 1260c e x + (3850b c e - 1400c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((3960a c + 3960b c)e - 4400b c d e + 1600c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (8316a b c + 1386b )e + (- 4752a c - 4752b c)d e + 5280b c d e +--R + +--R 3 3 2 +--R - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (4620a c + 4620a b )e + (- 11088a b c - 1848b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (6336a c + 6336b c)d e - 7040b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R 6930a b e + (- 9240a c - 9240a b )d e + (22176a b c + 3696b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12672a c - 12672b c)d e + 14080b c d e - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 728 + +--S 729 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 729 + +--S 730 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 730 + +)clear all + +--S 731 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 731 + +--S 732 of 845 +r0:=-2/3*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^(3/2)/e^6+8/5*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(5/2)/e^6-10/7*c^2*(2*c*d-b*e)*(d+e*x)^(7/2)/e^6+4/9*c^3*_ + (d+e*x)^(9/2)/e^6+2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*_ + sqrt(d+e*x))+4*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 140c e x + (450b c e - 200c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((504a c + 504b c)e - 720b c d e + 320c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (1260a b c + 210b )e + (- 1008a c - 1008b c)d e + 1440b c d e +--R + +--R 3 3 2 +--R - 640c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (1260a c + 1260a b )e + (- 5040a b c - 840b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (4032a c + 4032b c)d e - 5760b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 630a b e + (2520a c + 2520a b )d e + (- 10080a b c - 1680b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (8064a c + 8064b c)d e - 11520b c d e + 5120c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 732 + +--S 733 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 2 5 3 4 4 +--R 140c e x + (450b c e - 200c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((504a c + 504b c)e - 720b c d e + 320c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (1260a b c + 210b )e + (- 1008a c - 1008b c)d e + 1440b c d e +--R + +--R 3 3 2 +--R - 640c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (1260a c + 1260a b )e + (- 5040a b c - 840b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (4032a c + 4032b c)d e - 5760b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 630a b e + (2520a c + 2520a b )d e + (- 10080a b c - 1680b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (8064a c + 8064b c)d e - 11520b c d e + 5120c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 733 + +--S 734 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 736 + +--S 737 of 845 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^(3/2))+_ + 8/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(3/2)/e^6-_ + 2*c^2*(2*c*d-b*e)*(d+e*x)^(5/2)/e^6+4/7*c^3*(d+e*x)^(7/2)/e^6-_ + 4*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/(e^6*_ + sqrt(d+e*x))-2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 12c e x + (42b c e - 24c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((56a c + 56b c)e - 112b c d e + 64c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (252a b c + 42b )e + (- 336a c - 336b c)d e + 672b c d e +--R + +--R 3 3 2 +--R - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (- 84a c - 84a b )e + (1008a b c + 168b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (- 1344a c - 1344b c)d e + 2688b c d e - 1536c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 14a b e + (- 56a c - 56a b )d e + (672a b c + 112b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 896a c - 896b c)d e + 1792b c d e - 1024c d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Expression(Integer) +--E 737 + +--S 738 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 2 5 3 4 4 +--R 12c e x + (42b c e - 24c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((56a c + 56b c)e - 112b c d e + 64c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (252a b c + 42b )e + (- 336a c - 336b c)d e + 672b c d e +--R + +--R 3 3 2 +--R - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (- 84a c - 84a b )e + (1008a b c + 168b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (- 1344a c - 1344b c)d e + 2688b c d e - 1536c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 14a b e + (- 56a c - 56a b )d e + (672a b c + 112b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 896a c - 896b c)d e + 1792b c d e - 1024c d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 738 + +--S 739 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 739 + +--S 740 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 740 + +)clear all + +--S 741 of 845 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 2 9 3 2 4 8 +--R 2c e x + (7b c e + 4c d e)x +--R + +--R 3 2 2 2 3 4 2 7 +--R ((6a c + 9b c )e + 14b c d e + 2c d )x +--R + +--R 2 3 2 3 2 2 3 2 6 +--R ((15a b c + 5b c)e + (12a c + 18b c )d e + 7b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 2 2 5 +--R ((6a c + 12a b c + b )e + (30a b c + 10b c)d e + (6a c + 9b c )d )x +--R + +--R 2 3 2 2 2 2 4 +--R (9a b c + 3a b )e + (12a c + 24a b c + 2b )d e +--R + +--R 2 3 2 +--R (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 2 3 2 2 2 4 2 3 +--R ((2a c + 3a b )e + (18a b c + 6a b )d e + (6a c + 12a b c + b )d )x +--R + +--R 3 2 3 2 2 2 3 2 2 +--R (a b e + (4a c + 6a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 2 2 2 3 2 +--R (2a b d e + (2a c + 3a b )d )x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 741 + +--S 742 of 845 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(7/2)/e^8+_ + 2/9*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(9/2)/e^8-6/11*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(11/2)/e^8+2/13*(70*c^4*d^4+_ + b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+_ + 6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(13/2)/e^8-_ + 2/3*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^(15/2)/e^8+6/17*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(17/2)/e^8-14/19*c^3*(2*c*d-b*e)*(d+e*x)^(19/2)/e^8+_ + 4/21*c^4*(d+e*x)^(21/2)/e^8 +--R +--R +--R (2) +--R 4 10 10 3 10 4 9 9 +--R 554268c e x + (2144142b c e + 1254396c d e )x +--R + +--R 3 2 2 10 3 9 4 2 8 8 +--R ((2054052a c + 3081078b c )e + 4918914b c d e + 725868c d e )x +--R + +--R 2 3 10 3 2 2 9 +--R (5819814a b c + 1939938b c)e + (4792788a c + 7189182b c )d e +--R + +--R 3 2 8 4 3 7 +--R 2900898b c d e + 1716c d e +--R * +--R 7 +--R x +--R + +--R 2 2 2 4 10 +--R (2686068a c + 5372136a b c + 447678b )e +--R + +--R 2 3 9 3 2 2 2 8 +--R (13878018a b c + 4626006b c)d e + (2896740a c + 4345110b c )d e +--R + +--R 3 3 7 4 4 6 +--R 9702b c d e - 1848c d e +--R * +--R 6 +--R x +--R + +--R 2 3 10 +--R (4761666a b c + 1587222a b )e +--R + +--R 2 2 2 4 9 +--R (6593076a c + 13186152a b c + 1098846b )d e +--R + +--R 2 3 2 8 3 2 2 3 7 +--R (8668674a b c + 2889558b c)d e + (14364a c + 21546b c )d e +--R + +--R 3 4 6 4 5 5 +--R - 10584b c d e + 2016c d e +--R * +--R 5 +--R x +--R + +--R 3 2 2 10 2 3 9 +--R (1293292a c + 1939938a b )e + (12168702a b c + 4056234a b )d e +--R + +--R 2 2 2 4 2 8 +--R (4313988a c + 8627976a b c + 718998b )d e +--R + +--R 2 3 3 7 3 2 2 4 6 +--R (67830a b c + 22610b c)d e + (- 15960a c - 23940b c )d e +--R + +--R 3 5 5 4 6 4 +--R 11760b c d e - 2240c d e +--R * +--R 4 +--R x +--R + +--R 3 10 3 2 2 9 +--R 831402a b e + (3510364a c + 5265546a b )d e +--R + +--R 2 3 2 8 +--R (8540766a b c + 2846922a b )d e +--R + +--R 2 2 2 4 3 7 +--R (58140a c + 116280a b c + 9690b )d e +--R + +--R 2 3 4 6 3 2 2 5 5 +--R (- 77520a b c - 25840b c)d e + (18240a c + 27360b c )d e +--R + +--R 3 6 4 4 7 3 +--R - 13440b c d e + 2560c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 2 8 +--R 2494206a b d e + (2771340a c + 4157010a b )d e +--R + +--R 2 3 3 7 +--R (226746a b c + 75582a b )d e +--R + +--R 2 2 2 4 4 6 +--R (- 69768a c - 139536a b c - 11628b )d e +--R + +--R 2 3 5 5 3 2 2 6 4 +--R (93024a b c + 31008b c)d e + (- 21888a c - 32832b c )d e +--R + +--R 3 7 3 4 8 2 +--R 16128b c d e - 3072c d e +--R * +--R 2 +--R x +--R + +--R 3 2 8 3 2 2 3 7 +--R 2494206a b d e + (184756a c + 277134a b )d e +--R + +--R 2 3 4 6 +--R (- 302328a b c - 100776a b )d e +--R + +--R 2 2 2 4 5 5 +--R (93024a c + 186048a b c + 15504b )d e +--R + +--R 2 3 6 4 3 2 2 7 3 +--R (- 124032a b c - 41344b c)d e + (29184a c + 43776b c )d e +--R + +--R 3 8 2 4 9 +--R - 21504b c d e + 4096c d e +--R * +--R x +--R + +--R 3 3 7 3 2 2 4 6 +--R 831402a b d e + (- 369512a c - 554268a b )d e +--R + +--R 2 3 5 5 +--R (604656a b c + 201552a b )d e +--R + +--R 2 2 2 4 6 4 +--R (- 186048a c - 372096a b c - 31008b )d e +--R + +--R 2 3 7 3 3 2 2 8 2 +--R (248064a b c + 82688b c)d e + (- 58368a c - 87552b c )d e +--R + +--R 3 9 4 10 +--R 43008b c d e - 8192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Expression(Integer) +--E 742 + +--S 743 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 10 10 3 10 4 9 9 +--R 554268c e x + (2144142b c e + 1254396c d e )x +--R + +--R 3 2 2 10 3 9 4 2 8 8 +--R ((2054052a c + 3081078b c )e + 4918914b c d e + 725868c d e )x +--R + +--R 2 3 10 3 2 2 9 +--R (5819814a b c + 1939938b c)e + (4792788a c + 7189182b c )d e +--R + +--R 3 2 8 4 3 7 +--R 2900898b c d e + 1716c d e +--R * +--R 7 +--R x +--R + +--R 2 2 2 4 10 +--R (2686068a c + 5372136a b c + 447678b )e +--R + +--R 2 3 9 3 2 2 2 8 +--R (13878018a b c + 4626006b c)d e + (2896740a c + 4345110b c )d e +--R + +--R 3 3 7 4 4 6 +--R 9702b c d e - 1848c d e +--R * +--R 6 +--R x +--R + +--R 2 3 10 +--R (4761666a b c + 1587222a b )e +--R + +--R 2 2 2 4 9 +--R (6593076a c + 13186152a b c + 1098846b )d e +--R + +--R 2 3 2 8 3 2 2 3 7 +--R (8668674a b c + 2889558b c)d e + (14364a c + 21546b c )d e +--R + +--R 3 4 6 4 5 5 +--R - 10584b c d e + 2016c d e +--R * +--R 5 +--R x +--R + +--R 3 2 2 10 2 3 9 +--R (1293292a c + 1939938a b )e + (12168702a b c + 4056234a b )d e +--R + +--R 2 2 2 4 2 8 +--R (4313988a c + 8627976a b c + 718998b )d e +--R + +--R 2 3 3 7 3 2 2 4 6 +--R (67830a b c + 22610b c)d e + (- 15960a c - 23940b c )d e +--R + +--R 3 5 5 4 6 4 +--R 11760b c d e - 2240c d e +--R * +--R 4 +--R x +--R + +--R 3 10 3 2 2 9 +--R 831402a b e + (3510364a c + 5265546a b )d e +--R + +--R 2 3 2 8 +--R (8540766a b c + 2846922a b )d e +--R + +--R 2 2 2 4 3 7 +--R (58140a c + 116280a b c + 9690b )d e +--R + +--R 2 3 4 6 3 2 2 5 5 +--R (- 77520a b c - 25840b c)d e + (18240a c + 27360b c )d e +--R + +--R 3 6 4 4 7 3 +--R - 13440b c d e + 2560c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 2 8 +--R 2494206a b d e + (2771340a c + 4157010a b )d e +--R + +--R 2 3 3 7 +--R (226746a b c + 75582a b )d e +--R + +--R 2 2 2 4 4 6 +--R (- 69768a c - 139536a b c - 11628b )d e +--R + +--R 2 3 5 5 3 2 2 6 4 +--R (93024a b c + 31008b c)d e + (- 21888a c - 32832b c )d e +--R + +--R 3 7 3 4 8 2 +--R 16128b c d e - 3072c d e +--R * +--R 2 +--R x +--R + +--R 3 2 8 3 2 2 3 7 +--R 2494206a b d e + (184756a c + 277134a b )d e +--R + +--R 2 3 4 6 +--R (- 302328a b c - 100776a b )d e +--R + +--R 2 2 2 4 5 5 +--R (93024a c + 186048a b c + 15504b )d e +--R + +--R 2 3 6 4 3 2 2 7 3 +--R (- 124032a b c - 41344b c)d e + (29184a c + 43776b c )d e +--R + +--R 3 8 2 4 9 +--R - 21504b c d e + 4096c d e +--R * +--R x +--R + +--R 3 3 7 3 2 2 4 6 +--R 831402a b d e + (- 369512a c - 554268a b )d e +--R + +--R 2 3 5 5 +--R (604656a b c + 201552a b )d e +--R + +--R 2 2 2 4 6 4 +--R (- 186048a c - 372096a b c - 31008b )d e +--R + +--R 2 3 7 3 3 2 2 8 2 +--R (248064a b c + 82688b c)d e + (- 58368a c - 87552b c )d e +--R + +--R 3 9 4 10 +--R 43008b c d e - 8192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Union(Expression(Integer),...) +--E 743 + +--S 744 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 744 + +--S 745 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 745 + +)clear all + +--S 746 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 8 3 4 7 3 2 2 3 6 +--R 2c e x + (7b c e + 2c d)x + ((6a c + 9b c )e + 7b c d)x +--R + +--R 2 3 3 2 2 5 +--R ((15a b c + 5b c)e + (6a c + 9b c )d)x +--R + +--R 2 2 2 4 2 3 4 +--R ((6a c + 12a b c + b )e + (15a b c + 5b c)d)x +--R + +--R 2 3 2 2 2 4 3 +--R ((9a b c + 3a b )e + (6a c + 12a b c + b )d)x +--R + +--R 3 2 2 2 3 2 3 3 2 2 +--R ((2a c + 3a b )e + (9a b c + 3a b )d)x + (a b e + (2a c + 3a b )d)x +--R + +--R 3 +--R a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 746 + +--S 747 of 845 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(5/2)/e^8+_ + 2/7*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(7/2)/e^8-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(9/2)/e^8+2/11*(70*c^4*d^4+_ + b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+_ + 6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(11/2)/e^8-_ + 10/13*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^(13/2)/e^8+2/5*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(15/2)/e^8-14/17*c^3*(2*c*d-b*e)*(d+e*x)^(17/2)/e^8+_ + 4/19*c^4*(d+e*x)^(19/2)/e^8 +--R +--R +--R (2) +--R 4 9 9 3 9 4 8 8 +--R 1021020c e x + (3993990b c e + 1201200c d e )x +--R + +--R 3 2 2 9 3 8 4 2 7 7 +--R ((3879876a c + 5819814b c )e + 4792788b c d e + 12012c d e )x +--R + +--R 2 3 9 3 2 2 8 +--R (11191950a b c + 3730650b c)e + (4775232a c + 7162848b c )d e +--R + +--R 3 2 7 4 3 6 +--R 61446b c d e - 12936c d e +--R * +--R 6 +--R x +--R + +--R 2 2 2 4 9 +--R (5290740a c + 10581480a b c + 881790b )e +--R + +--R 2 3 8 3 2 2 2 7 +--R (14244300a b c + 4748100b c)d e + (81396a c + 122094b c )d e +--R + +--R 3 3 6 4 4 5 +--R - 67032b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 3 9 +--R (9699690a b c + 3233230a b )e +--R + +--R 2 2 2 4 8 +--R (7054320a c + 14108640a b c + 1175720b )d e +--R + +--R 2 3 2 7 3 2 2 3 6 +--R (339150a b c + 113050b c)d e + (- 90440a c - 135660b c )d e +--R + +--R 3 4 5 4 5 4 +--R 74480b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 3 2 2 9 2 3 8 +--R (2771340a c + 4157010a b )e + (13856700a b c + 4618900a b )d e +--R + +--R 2 2 2 4 2 7 +--R (251940a c + 503880a b c + 41990b )d e +--R + +--R 2 3 3 6 3 2 2 4 5 +--R (- 387600a b c - 129200b c)d e + (103360a c + 155040b c )d e +--R + +--R 3 5 4 4 6 3 +--R - 85120b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 8 +--R 1939938a b e + (4434144a c + 6651216a b )d e +--R + +--R 2 3 2 7 +--R (831402a b c + 277134a b )d e +--R + +--R 2 2 2 4 3 6 +--R (- 302328a c - 604656a b c - 50388b )d e +--R + +--R 2 3 4 5 3 2 2 5 4 +--R (465120a b c + 155040b c)d e + (- 124032a c - 186048b c )d e +--R + +--R 3 6 3 4 7 2 +--R 102144b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 2 7 +--R 3879876a b d e + (554268a c + 831402a b )d e +--R + +--R 2 3 3 6 +--R (- 1108536a b c - 369512a b )d e +--R + +--R 2 2 2 4 4 5 +--R (403104a c + 806208a b c + 67184b )d e +--R + +--R 2 3 5 4 3 2 2 6 3 +--R (- 620160a b c - 206720b c)d e + (165376a c + 248064b c )d e +--R + +--R 3 7 2 4 8 +--R - 136192b c d e + 28672c d e +--R * +--R x +--R + +--R 3 2 7 3 2 2 3 6 +--R 1939938a b d e + (- 1108536a c - 1662804a b )d e +--R + +--R 2 3 4 5 +--R (2217072a b c + 739024a b )d e +--R + +--R 2 2 2 4 5 4 +--R (- 806208a c - 1612416a b c - 134368b )d e +--R + +--R 2 3 6 3 3 2 2 7 2 +--R (1240320a b c + 413440b c)d e + (- 330752a c - 496128b c )d e +--R + +--R 3 8 4 9 +--R 272384b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 4849845e +--R Type: Expression(Integer) +--E 747 + +--S 748 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 9 9 3 9 4 8 8 +--R 1021020c e x + (3993990b c e + 1201200c d e )x +--R + +--R 3 2 2 9 3 8 4 2 7 7 +--R ((3879876a c + 5819814b c )e + 4792788b c d e + 12012c d e )x +--R + +--R 2 3 9 3 2 2 8 +--R (11191950a b c + 3730650b c)e + (4775232a c + 7162848b c )d e +--R + +--R 3 2 7 4 3 6 +--R 61446b c d e - 12936c d e +--R * +--R 6 +--R x +--R + +--R 2 2 2 4 9 +--R (5290740a c + 10581480a b c + 881790b )e +--R + +--R 2 3 8 3 2 2 2 7 +--R (14244300a b c + 4748100b c)d e + (81396a c + 122094b c )d e +--R + +--R 3 3 6 4 4 5 +--R - 67032b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 3 9 +--R (9699690a b c + 3233230a b )e +--R + +--R 2 2 2 4 8 +--R (7054320a c + 14108640a b c + 1175720b )d e +--R + +--R 2 3 2 7 3 2 2 3 6 +--R (339150a b c + 113050b c)d e + (- 90440a c - 135660b c )d e +--R + +--R 3 4 5 4 5 4 +--R 74480b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 3 2 2 9 2 3 8 +--R (2771340a c + 4157010a b )e + (13856700a b c + 4618900a b )d e +--R + +--R 2 2 2 4 2 7 +--R (251940a c + 503880a b c + 41990b )d e +--R + +--R 2 3 3 6 3 2 2 4 5 +--R (- 387600a b c - 129200b c)d e + (103360a c + 155040b c )d e +--R + +--R 3 5 4 4 6 3 +--R - 85120b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 8 +--R 1939938a b e + (4434144a c + 6651216a b )d e +--R + +--R 2 3 2 7 +--R (831402a b c + 277134a b )d e +--R + +--R 2 2 2 4 3 6 +--R (- 302328a c - 604656a b c - 50388b )d e +--R + +--R 2 3 4 5 3 2 2 5 4 +--R (465120a b c + 155040b c)d e + (- 124032a c - 186048b c )d e +--R + +--R 3 6 3 4 7 2 +--R 102144b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 2 7 +--R 3879876a b d e + (554268a c + 831402a b )d e +--R + +--R 2 3 3 6 +--R (- 1108536a b c - 369512a b )d e +--R + +--R 2 2 2 4 4 5 +--R (403104a c + 806208a b c + 67184b )d e +--R + +--R 2 3 5 4 3 2 2 6 3 +--R (- 620160a b c - 206720b c)d e + (165376a c + 248064b c )d e +--R + +--R 3 7 2 4 8 +--R - 136192b c d e + 28672c d e +--R * +--R x +--R + +--R 3 2 7 3 2 2 3 6 +--R 1939938a b d e + (- 1108536a c - 1662804a b )d e +--R + +--R 2 3 4 5 +--R (2217072a b c + 739024a b )d e +--R + +--R 2 2 2 4 5 4 +--R (- 806208a c - 1612416a b c - 134368b )d e +--R + +--R 2 3 6 3 3 2 2 7 2 +--R (1240320a b c + 413440b c)d e + (- 330752a c - 496128b c )d e +--R + +--R 3 8 4 9 +--R 272384b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 4849845e +--R Type: Union(Expression(Integer),...) +--E 748 + +--S 749 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 749 + +--S 750 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 751 + +--S 752 of 845 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(3/2)/e^8+_ + 2/5*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(5/2)/e^8-6/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(7/2)/e^8+2/9*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(9/2)/e^8-10/11*c*_ + (2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(11/2)/e^8+_ + 6/13*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(13/2)/e^8-_ + 14/15*c^3*(2*c*d-b*e)*(d+e*x)^(15/2)/e^8+4/17*c^4*(d+e*x)^(17/2)/e^8 +--R +--R +--R (2) +--R 4 8 8 3 8 4 7 7 +--R 180180c e x + (714714b c e + 12012c d e )x +--R + +--R 3 2 2 8 3 7 4 2 6 6 +--R ((706860a c + 1060290b c )e + 54978b c d e - 12936c d e )x +--R + +--R 2 3 8 3 2 2 7 +--R (2088450a b c + 696150b c)e + (64260a c + 96390b c )d e +--R + +--R 3 2 6 4 3 5 +--R - 59976b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 2 2 4 8 +--R (1021020a c + 2042040a b c + 170170b )e +--R + +--R 2 3 7 3 2 2 2 6 +--R (232050a b c + 77350b c)d e + (- 71400a c - 107100b c )d e +--R + +--R 3 3 5 4 4 4 +--R 66640b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 3 8 +--R (1969110a b c + 656370a b )e +--R + +--R 2 2 2 4 7 +--R (145860a c + 291720a b c + 24310b )d e +--R + +--R 2 3 2 6 3 2 2 3 5 +--R (- 265200a b c - 88400b c)d e + (81600a c + 122400b c )d e +--R + +--R 3 4 4 4 5 3 +--R - 76160b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 8 2 3 7 +--R (612612a c + 918918a b )e + (393822a b c + 131274a b )d e +--R + +--R 2 2 2 4 2 6 +--R (- 175032a c - 350064a b c - 29172b )d e +--R + +--R 2 3 3 5 3 2 2 4 4 +--R (318240a b c + 106080b c)d e + (- 97920a c - 146880b c )d e +--R + +--R 3 5 3 4 6 2 +--R 91392b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 7 +--R 510510a b e + (204204a c + 306306a b )d e +--R + +--R 2 3 2 6 +--R (- 525096a b c - 175032a b )d e +--R + +--R 2 2 2 4 3 5 +--R (233376a c + 466752a b c + 38896b )d e +--R + +--R 2 3 4 4 3 2 2 5 3 +--R (- 424320a b c - 141440b c)d e + (130560a c + 195840b c )d e +--R + +--R 3 6 2 4 7 +--R - 121856b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 2 6 +--R 510510a b d e + (- 408408a c - 612612a b )d e +--R + +--R 2 3 3 5 +--R (1050192a b c + 350064a b )d e +--R + +--R 2 2 2 4 4 4 +--R (- 466752a c - 933504a b c - 77792b )d e +--R + +--R 2 3 5 3 3 2 2 6 2 +--R (848640a b c + 282880b c)d e + (- 261120a c - 391680b c )d e +--R + +--R 3 7 4 8 +--R 243712b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Expression(Integer) +--E 752 + +--S 753 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 8 3 8 4 7 7 +--R 180180c e x + (714714b c e + 12012c d e )x +--R + +--R 3 2 2 8 3 7 4 2 6 6 +--R ((706860a c + 1060290b c )e + 54978b c d e - 12936c d e )x +--R + +--R 2 3 8 3 2 2 7 +--R (2088450a b c + 696150b c)e + (64260a c + 96390b c )d e +--R + +--R 3 2 6 4 3 5 +--R - 59976b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 2 2 4 8 +--R (1021020a c + 2042040a b c + 170170b )e +--R + +--R 2 3 7 3 2 2 2 6 +--R (232050a b c + 77350b c)d e + (- 71400a c - 107100b c )d e +--R + +--R 3 3 5 4 4 4 +--R 66640b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 3 8 +--R (1969110a b c + 656370a b )e +--R + +--R 2 2 2 4 7 +--R (145860a c + 291720a b c + 24310b )d e +--R + +--R 2 3 2 6 3 2 2 3 5 +--R (- 265200a b c - 88400b c)d e + (81600a c + 122400b c )d e +--R + +--R 3 4 4 4 5 3 +--R - 76160b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 8 2 3 7 +--R (612612a c + 918918a b )e + (393822a b c + 131274a b )d e +--R + +--R 2 2 2 4 2 6 +--R (- 175032a c - 350064a b c - 29172b )d e +--R + +--R 2 3 3 5 3 2 2 4 4 +--R (318240a b c + 106080b c)d e + (- 97920a c - 146880b c )d e +--R + +--R 3 5 3 4 6 2 +--R 91392b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 7 +--R 510510a b e + (204204a c + 306306a b )d e +--R + +--R 2 3 2 6 +--R (- 525096a b c - 175032a b )d e +--R + +--R 2 2 2 4 3 5 +--R (233376a c + 466752a b c + 38896b )d e +--R + +--R 2 3 4 4 3 2 2 5 3 +--R (- 424320a b c - 141440b c)d e + (130560a c + 195840b c )d e +--R + +--R 3 6 2 4 7 +--R - 121856b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 2 6 +--R 510510a b d e + (- 408408a c - 612612a b )d e +--R + +--R 2 3 3 5 +--R (1050192a b c + 350064a b )d e +--R + +--R 2 2 2 4 4 4 +--R (- 466752a c - 933504a b c - 77792b )d e +--R + +--R 2 3 5 3 3 2 2 6 2 +--R (848640a b c + 282880b c)d e + (- 261120a c - 391680b c )d e +--R + +--R 3 7 4 8 +--R 243712b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Union(Expression(Integer),...) +--E 753 + +--S 754 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 754 + +--S 755 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 756 + +--S 757 of 845 +r0:=2/3*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(3/2)/e^8-6/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5/2)/e^8+2/7*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(7/2)/e^8-10/9*c*(2*c*d-b*e)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(9/2)/e^8+6/11*c^2*_ + (14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(11/2)/e^8-14/13*c^3*_ + (2*c*d-b*e)*(d+e*x)^(13/2)/e^8+4/15*c^4*(d+e*x)^(15/2)/e^8-_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 12012c e x + (48510b c e - 12936c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((49140a c + 73710b c )e - 52920b c d e + 14112c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (150150a b c + 50050b c)e + (- 54600a c - 81900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 58800b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 +--R (77220a c + 154440a b c + 12870b )e +--R + +--R 2 3 6 3 2 2 2 5 +--R (- 171600a b c - 57200b c)d e + (62400a c + 93600b c )d e +--R + +--R 3 3 4 4 4 3 +--R - 67200b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (162162a b c + 54054a b )e +--R + +--R 2 2 2 4 6 +--R (- 92664a c - 185328a b c - 15444b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 74880a c - 112320b c )d e +--R + +--R 3 4 3 4 5 2 +--R 80640b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 216216a b c - 72072a b )d e +--R + +--R 2 2 2 4 2 5 +--R (123552a c + 247104a b c + 20592b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 274560a b c - 91520b c)d e + (99840a c + 149760b c )d e +--R + +--R 3 5 2 4 6 +--R - 107520b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R 90090a b e + (- 120120a c - 180180a b )d e +--R + +--R 2 3 2 5 +--R (432432a b c + 144144a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 247104a c - 494208a b c - 41184b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (549120a b c + 183040b c)d e + (- 199680a c - 299520b c )d e +--R + +--R 3 6 4 7 +--R 215040b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 757 + +--S 758 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 7 3 7 4 6 6 +--R 12012c e x + (48510b c e - 12936c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((49140a c + 73710b c )e - 52920b c d e + 14112c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (150150a b c + 50050b c)e + (- 54600a c - 81900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 58800b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 +--R (77220a c + 154440a b c + 12870b )e +--R + +--R 2 3 6 3 2 2 2 5 +--R (- 171600a b c - 57200b c)d e + (62400a c + 93600b c )d e +--R + +--R 3 3 4 4 4 3 +--R - 67200b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (162162a b c + 54054a b )e +--R + +--R 2 2 2 4 6 +--R (- 92664a c - 185328a b c - 15444b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 74880a c - 112320b c )d e +--R + +--R 3 4 3 4 5 2 +--R 80640b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 216216a b c - 72072a b )d e +--R + +--R 2 2 2 4 2 5 +--R (123552a c + 247104a b c + 20592b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 274560a b c - 91520b c)d e + (99840a c + 149760b c )d e +--R + +--R 3 5 2 4 6 +--R - 107520b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R 90090a b e + (- 120120a c - 180180a b )d e +--R + +--R 2 3 2 5 +--R (432432a b c + 144144a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 247104a c - 494208a b c - 41184b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (549120a b c + 183040b c)d e + (- 199680a c - 299520b c )d e +--R + +--R 3 6 4 7 +--R 215040b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 758 + +--S 759 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 759 + +--S 760 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 760 + +)clear all + +--S 761 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 761 + +--S 762 of 845 +r0:=-2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^(3/2)/e^8+2/5*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(5/2)/e^8-10/7*c*(2*c*d-b*e)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(7/2)/e^8+2/3*c^2*_ + (14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(9/2)/e^8-14/11*c^3*_ + (2*c*d-b*e)*(d+e*x)^(11/2)/e^8+4/13*c^4*(d+e*x)^(13/2)/e^8+_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*sqrt(d+e*x))+2*(c*d^2-_ + b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 4620c e x + (19110b c e - 5880c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((20020a c + 30030b c )e - 25480b c d e + 7840c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (64350a b c + 21450b c)e + (- 28600a c - 42900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 36400b c d e - 11200c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (36036a c + 72072a b c + 6006b )e + (- 102960a b c - 34320b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (45760a c + 68640b c )d e - 58240b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (90090a b c + 30030a b )e +--R + +--R 2 2 2 4 6 +--R (- 72072a c - 144144a b c - 12012b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 91520a c - 137280b c )d e +--R + +--R 3 4 3 4 5 2 +--R 116480b c d e - 35840c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 360360a b c - 120120a b )d e +--R + +--R 2 2 2 4 2 5 +--R (288288a c + 576576a b c + 48048b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 823680a b c - 274560b c)d e + (366080a c + 549120b c )d e +--R + +--R 3 5 2 4 6 +--R - 465920b c d e + 143360c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R - 30030a b e + (120120a c + 180180a b )d e +--R + +--R 2 3 2 5 +--R (- 720720a b c - 240240a b )d e +--R + +--R 2 2 2 4 3 4 +--R (576576a c + 1153152a b c + 96096b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 1647360a b c - 549120b c)d e + (732160a c + 1098240b c )d e +--R + +--R 3 6 4 7 +--R - 931840b c d e + 286720c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Expression(Integer) +--E 762 + +--S 763 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 7 3 7 4 6 6 +--R 4620c e x + (19110b c e - 5880c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((20020a c + 30030b c )e - 25480b c d e + 7840c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (64350a b c + 21450b c)e + (- 28600a c - 42900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 36400b c d e - 11200c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (36036a c + 72072a b c + 6006b )e + (- 102960a b c - 34320b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (45760a c + 68640b c )d e - 58240b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (90090a b c + 30030a b )e +--R + +--R 2 2 2 4 6 +--R (- 72072a c - 144144a b c - 12012b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 91520a c - 137280b c )d e +--R + +--R 3 4 3 4 5 2 +--R 116480b c d e - 35840c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 360360a b c - 120120a b )d e +--R + +--R 2 2 2 4 2 5 +--R (288288a c + 576576a b c + 48048b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 823680a b c - 274560b c)d e + (366080a c + 549120b c )d e +--R + +--R 3 5 2 4 6 +--R - 465920b c d e + 143360c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R - 30030a b e + (120120a c + 180180a b )d e +--R + +--R 2 3 2 5 +--R (- 720720a b c - 240240a b )d e +--R + +--R 2 2 2 4 3 4 +--R (576576a c + 1153152a b c + 96096b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 1647360a b c - 549120b c)d e + (732160a c + 1098240b c )d e +--R + +--R 3 6 4 7 +--R - 931840b c d e + 286720c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 763 + +--S 764 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 764 + +--S 765 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 765 + +)clear all + +--S 766 of 845 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 766 + +--S 767 of 845 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^(3/2))+2/3*_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(3/2)/e^8-_ + 2*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5/2)/_ + e^8+6/7*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(7/2)/_ + e^8-14/9*c^3*(2*c*d-b*e)*(d+e*x)^(9/2)/e^8+4/11*c^4*(d+e*x)^(11/2)/_ + e^8-2*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/_ + (e^8*sqrt(d+e*x))-6*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 252c e x + (1078b c e - 392c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((1188a c + 1782b c )e - 1848b c d e + 672c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (4158a b c + 1386b c)e + (- 2376a c - 3564b c )d e + 3696b c d e +--R + +--R 4 3 4 +--R - 1344c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (2772a c + 5544a b c + 462b )e + (- 11088a b c - 3696b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (6336a c + 9504b c )d e - 9856b c d e + 3584c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (12474a b c + 4158a b )e + (- 16632a c - 33264a b c - 2772b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (66528a b c + 22176b c)d e + (- 38016a c - 57024b c )d e +--R + +--R 3 4 3 4 5 2 +--R 59136b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 2772a c - 4158a b )e + (49896a b c + 16632a b )d e +--R + +--R 2 2 2 4 2 5 +--R (- 66528a c - 133056a b c - 11088b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (266112a b c + 88704b c)d e + (- 152064a c - 228096b c )d e +--R + +--R 3 5 2 4 6 +--R 236544b c d e - 86016c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 462a b e + (- 1848a c - 2772a b )d e + (33264a b c + 11088a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 44352a c - 88704a b c - 7392b )d e + (177408a b c + 59136b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 101376a c - 152064b c )d e + 157696b c d e - 57344c d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Expression(Integer) +--E 767 + +--S 768 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 7 3 7 4 6 6 +--R 252c e x + (1078b c e - 392c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((1188a c + 1782b c )e - 1848b c d e + 672c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (4158a b c + 1386b c)e + (- 2376a c - 3564b c )d e + 3696b c d e +--R + +--R 4 3 4 +--R - 1344c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (2772a c + 5544a b c + 462b )e + (- 11088a b c - 3696b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (6336a c + 9504b c )d e - 9856b c d e + 3584c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (12474a b c + 4158a b )e + (- 16632a c - 33264a b c - 2772b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (66528a b c + 22176b c)d e + (- 38016a c - 57024b c )d e +--R + +--R 3 4 3 4 5 2 +--R 59136b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 2772a c - 4158a b )e + (49896a b c + 16632a b )d e +--R + +--R 2 2 2 4 2 5 +--R (- 66528a c - 133056a b c - 11088b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (266112a b c + 88704b c)d e + (- 152064a c - 228096b c )d e +--R + +--R 3 5 2 4 6 +--R 236544b c d e - 86016c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 462a b e + (- 1848a c - 2772a b )d e + (33264a b c + 11088a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 44352a c - 88704a b c - 7392b )d e + (177408a b c + 59136b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 101376a c - 152064b c )d e + 157696b c d e - 57344c d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 768 + +--S 769 of 845 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 770 + +)clear all + +--S 771 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 771 + +--S 772 of 845 +r0:=4/3*(d+e*x)^(3/2)+2*(2*c*d-b*e)*sqrt(d+e*x)/c-atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c^2*d^2+b^2*_ + e^2-2*c*e*(b*d+a*e)+e*(2*c*d-b*e)*sqrt(b^2-4*a*c))/(c^(3/2)*sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e)-_ + e*(2*c*d-b*e)*sqrt(b^2-4*a*c))/(c^(3/2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R 2 +-+ | 2 +--R (- 3b e + 6c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((6a c - 3b )e + 6b c d e - 6c d )\|2 +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 +-+ | 2 +--R (3b e - 6c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((6a c - 3b )e + 6b c d e - 6c d )\|2 +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R (4c e x - 6b e + 16c d)\|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R +-+ | | 2 | | 2 +--R 3c\|c \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 772 + +--S 773 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 3c +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R log +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- a b c + b )e + (2a c - 5b c)d e + 9b c d e - 6c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e +--R + +--R 3 3 +--R 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 +--R (4a c - 4a b )e + (8a b c + 4b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 8a c - 16b c)d e + 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3c +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R log +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (a b c - b )e + (- 2a c + 5b c)d e - 9b c d e + 6c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (4a c - 4a b )e + (8a b c + 4b )d e + (- 8a c - 16b c)d e +--R + +--R 2 3 3 4 +--R 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R 3c +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R log +--R - +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- a b c + b )e + (2a c - 5b c)d e + 9b c d e - 6c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e +--R + +--R 3 3 +--R 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 +--R (4a c - 4a b )e + (8a b c + 4b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 8a c - 16b c)d e + 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3c +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R log +--R - +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (a b c - b )e + (- 2a c + 5b c)d e - 9b c d e + 6c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (4a c - 4a b )e + (8a b c + 4b )d e + (- 8a c - 16b c)d e +--R + +--R 2 3 3 4 +--R 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-------+ +--R (8c e x - 12b e + 32c d)\|e x + d +--R / +--R 6c +--R Type: Union(Expression(Integer),...) +--E 773 + +--S 774 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R c\|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- a b c + b )e + (2a c - 5b c)d e + 9b c d e - 6c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e +--R + +--R 3 3 +--R 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 +--R (4a c - 4a b )e + (8a b c + 4b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 8a c - 16b c)d e + 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R c\|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (a b c - b )e + (- 2a c + 5b c)d e - 9b c d e + 6c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (4a c - 4a b )e + (8a b c + 4b )d e + (- 8a c - 16b c)d e +--R + +--R 2 3 3 4 +--R 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R c\|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R - +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- a b c + b )e + (2a c - 5b c)d e + 9b c d e - 6c d +--R * +--R ROOT +--R - +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 +--R (72a b c - 18b c )d e +--R + +--R 5 2 4 4 2 +--R (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e +--R + +--R 3 3 +--R 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 +--R (4a c - 4a b )e + (8a b c + 4b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (- 8a c - 16b c)d e + 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R c\|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R - +--R 3 +--R c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (a b c - b )e + (- 2a c + 5b c)d e - 9b c d e + 6c d +--R * +--R ROOT +--R 3 +--R 2c +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 +--R c +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 +--R c +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (4a c - 4a b )e + (8a b c + 4b )d e + (- 8a c - 16b c)d e +--R + +--R 2 3 3 4 +--R 24b c d e - 12c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 2 +-+ | 2 +--R (2b e - 4c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((- 4a c + 2b )e - 4b c d e + 4c d )\|2 +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 +-+ | 2 +--R (- 2b e + 4c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((- 4a c + 2b )e - 4b c d e + 4c d )\|2 +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R +-+ | | 2 | | 2 +--R 2c\|c \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 774 + +--S 775 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 775 + +)clear all + +--S 776 of 845 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 776 + +--S 777 of 845 +r0:=4*sqrt(d+e*x)-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ + sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))/sqrt(c)-_ + atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ + sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/sqrt(c) +--R +--R +--R (2) +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|2 \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|2 \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-+ +-------+ +--R 4\|c \|e x + d +--R / +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 777 + +--S 778 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +--R |---------------------------------- +--R \| c +--R * +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log( |---------------------------------- + 2\|e x + d ) +--R \| c +--R + +--R - +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +--R |------------------------------------ +--R \| c +--R * +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log( |------------------------------------ + 2\|e x + d ) +--R \| c +--R + +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +--R |------------------------------------ +--R \| c +--R * +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log(- |------------------------------------ + 2\|e x + d ) +--R \| c +--R + +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +--R |---------------------------------- +--R \| c +--R * +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log(- |---------------------------------- + 2\|e x + d ) +--R \| c +--R + +--R +-------+ +--R 8\|e x + d +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 778 + +--S 779 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R +-+ | \| c +--R \|c |---------------------------------- +--R \| c +--R * +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log( |---------------------------------- + 2\|e x + d ) +--R \| c +--R + +--R - +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R +-+ | \| c +--R \|c |------------------------------------ +--R \| c +--R * +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log( |------------------------------------ + 2\|e x + d ) +--R \| c +--R + +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R +-+ | \| c +--R \|c |------------------------------------ +--R \| c +--R * +--R +------------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |- 2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log(- |------------------------------------ + 2\|e x + d ) +--R \| c +--R + +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R +-+ | \| c +--R \|c |---------------------------------- +--R \| c +--R * +--R +----------------------------------+ +--R | +---------------+ +--R | | 2 2 +--R | |(- 4a c + b )e +--R |2c |--------------- - 2b e + 4c d +--R | | 2 +--R | \| c +-------+ +--R log(- |---------------------------------- + 2\|e x + d ) +--R \| c +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R 2\|2 \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R +-+ | | 2 \|2 \|c \|e x + d +--R 2\|2 \|e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-+ +--R 2\|c +--R Type: Expression(Integer) +--E 779 + +--S 780 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 780 + +)clear all + +--S 781 of 845 +t0:=(b+2*c*x)/((a+b*x+c*x^2)*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) -------------------------- +--R 2 +-------+ +--R (c x + b x + a)\|e x + d +--R Type: Expression(Integer) +--E 781 + +--S 782 of 845 +r0:=-2*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ + sqrt(2)*sqrt(c)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))-2*atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*_ + sqrt(c)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))) +--R +--R +--R (2) +--R - +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 782 + +--S 783 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (a e - b d e + c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R b e - 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R - +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (a e - b d e + c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R ROOT +--R 2 2 +--R (- 4a c + b )e +--R / +--R 2 4 3 2 2 2 3 +--R a e - 2a b d e + (2a c + b )d e - 2b c d e +--R + +--R 2 4 +--R c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (- a e + b d e - c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R b e - 2c d +--R * +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R - +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (- a e + b d e - c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R ROOT +--R 2 2 +--R (- 4a c + b )e +--R / +--R 2 4 3 2 2 2 3 +--R a e - 2a b d e + (2a c + b )d e - 2b c d e +--R + +--R 2 4 +--R c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 783 + +--S 784 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (a e - b d e + c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R b e - 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R - +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 2 +--R (a e - b d e + c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R ROOT +--R 2 2 +--R (- 4a c + b )e +--R / +--R 2 4 3 2 2 2 3 +--R a e - 2a b d e + (2a c + b )d e - 2b c d e +--R + +--R 2 4 +--R c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 2 +--R (- a e + b d e - c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R b e - 2c d +--R * +--R ROOT +--R 2 2 +--R (- 2a e + 2b d e - 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R - +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R * +--R log +--R 2 2 +--R (- a e + b d e - c d ) +--R * +--R +----------------------------------------------------+ +--R | 2 2 +--R | (- 4a c + b )e +--R |---------------------------------------------------- +--R | 2 4 3 2 2 2 3 2 4 +--R \|a e - 2a b d e + (2a c + b )d e - 2b c d e + c d +--R + +--R - b e + 2c d +--R * +--R ROOT +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R ROOT +--R 2 2 +--R (- 4a c + b )e +--R / +--R 2 4 3 2 2 2 3 +--R a e - 2a b d e + (2a c + b )d e - 2b c d e +--R + +--R 2 4 +--R c d +--R + +--R - 2b e + 4c d +--R / +--R 2 2 +--R a e - b d e + c d +--R + +--R +-------+ +--R 4c\|e x + d +--R + +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 4\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 4\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R 2\|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 784 + +--S 785 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 845 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------------------- +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 786 + +--S 787 of 845 +r0:=2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))+atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b*e*_ + (b+sqrt(b^2-4*a*c))-2*c*(2*a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*_ + (b*e*(b-sqrt(b^2-4*a*c))+2*c*(-2*a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-_ + b*d*e+a*e^2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +-------+ +--R ((b e - 2c d)\|2 \|- 4a c + b + (4a c - b )e\|2 )\|c \|e x + d +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +-------+ +--R ((b e - 2c d)\|2 \|- 4a c + b + (- 4a c + b )e\|2 )\|c \|e x + d +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R (- 2b e + 4c d)\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 2 | 2 +-------+ +--R (a e - b d e + c d )\|- 4a c + b \|e x + d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 787 + +--S 788 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +-------+ +--R (a e - b d e + c d )\|e x + d +--R * +--R ROOT +--R 3 6 2 5 2 2 2 4 +--R 2a e - 6a b d e + (6a c + 6a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (- 12a b c - 2b )d e + (6a c + 6b c)d e - 6b c d e + 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R * +--R log +--R 3 7 3 2 2 6 2 3 2 5 +--R a b e + (- 2a c - 3a b )d e + (9a b c + 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 6a c - 12a b c - b )d e + (15a b c + 5b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 6a c - 9b c )d e + 7b c d e - 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 2 2 2 4 4 2 3 3 +--R (2a c - 3a b c + b )e + (8a b c - 5b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 8a c + 11b c )d e - 12b c d e + 6c d +--R * +--R ROOT +--R 3 6 2 5 2 2 2 4 +--R 2a e - 6a b d e + (6a c + 6a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (- 12a b c - 2b )d e + (6a c + 6b c)d e - 6b c d e +--R + +--R 3 6 +--R 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 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b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 6 2 5 2 2 2 4 +--R 2a e - 6a b d e + (6a c + 6a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (- 12a b c - 2b )d e + (6a c + 6b c)d e - 6b c d e + 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 6 2 5 2 2 2 4 3 3 3 +--R a e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 4 2 2 5 3 6 +--R (3a c + 3b c)d e - 3b c d e + c d +--R * +--R log +--R 3 7 3 2 2 6 2 3 2 5 +--R - a b e + (2a c + 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (6a c + 12a b c + b )d e + (- 15a b c - 5b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (6a c + 9b c )d e - 7b c d e + 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 5 2 4 10 2 +--R (- 30a b c - 20b c )d e + (6a c + 15b c )d e +--R + +--R 5 11 6 12 +--R - 6b c d e + c d +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 2a c + 3a b c - b )e + (- 8a b c + 5b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (8a c - 11b c )d e + 12b c d e - 6c d +--R * +--R ROOT +--R 3 6 2 5 2 2 2 4 +--R 2a e - 6a b d e + (6a c + 6a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (- 12a b c - 2b )d e + (6a c + 6b c)d e - 6b c d e +--R + +--R 3 6 +--R 2c d +--R * +--R ROOT +--R 3 3 2 2 2 4 6 6 +--R (- 4a c + 9a b c - 6a b c + b )e +--R + +--R 2 3 3 2 5 5 +--R (- 24a b c + 30a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (24a c - 66a b c + 15b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (72a b c - 18b c )d e + (- 36a c + 9b c )d e +--R / +--R 6 12 5 11 5 4 2 2 10 +--R a e - 6a b d e + (6a c + 15a b )d e +--R + +--R 4 3 3 3 9 +--R (- 30a b c - 20a b )d e +--R + +--R 4 2 3 2 2 4 4 8 +--R (15a c + 60a b c + 15a b )d e +--R + +--R 3 2 2 3 5 5 7 +--R (- 60a b c - 60a b c - 6a b )d e +--R + +--R 3 3 2 2 2 4 6 6 6 +--R (20a c + 90a b c + 30a b c + b )d e +--R + +--R 2 3 3 2 5 7 5 +--R (- 60a b c - 60a b c - 6b c)d e +--R + +--R 2 4 2 3 4 2 8 4 +--R (15a c + 60a b c + 15b c )d e +--R + +--R 4 3 3 9 3 +--R (- 30a b c - 20b c )d e +--R + +--R 5 2 4 10 2 5 11 6 12 +--R (6a c + 15b c )d e - 6b c d e + c d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d +--R / +--R 3 6 2 5 2 2 2 4 +--R a e - 3a b d e + (3a c + 3a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (- 6a b c - b )d e + (3a c + 3b c)d e - 3b c d e + c d +--R + +--R 3 2 2 2 3 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d )\|e x + d +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +--R ((- 2b e + 4c d)\|2 \|- 4a c + b + (- 8a c + 2b )e\|2 )\|c +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +--R ((- 2b e + 4c d)\|2 \|- 4a c + b + (8a c - 2b )e\|2 )\|c +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 789 + +--S 790 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +)clear all + +--S 791 of 845 +t0:=(b+2*c*x)/((d+e*x)^(5/2)*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x +--R + +--R 2 2 +--R (2a d e + b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 791 + +--S 792 of 845 +r0:=2/3*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+_ + 2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))/((c*d^2-b*d*e+a*e^2)^2*_ + sqrt(d+e*x))-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b^2*e^2*(b+sqrt(b^2-4*a*c))+_ + 2*c^2*d*(4*a*e+d*sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e+b*d*_ + sqrt(b^2-4*a*c)+a*e*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*_ + sqrt(c)*(b^2*e^2*(b-sqrt(b^2-4*a*c))-2*c^2*d*(-4*a*e+d*_ + sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e-b*d*sqrt(b^2-4*a*c)-_ + a*e*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((6a c - 3b )e + 6b c d e - 6c d e)x + (6a c - 3b )d e +--R + +--R 2 2 3 +--R 6b c d e - 6c d +--R * +--R +-----------+ +--R +-+ | 2 +--R \|2 \|- 4a c + b +--R + +--R 3 3 2 2 2 +--R ((- 12a b c + 3b )e + (24a c - 6b c)d e )x +--R + +--R 3 2 2 2 2 +--R (- 12a b c + 3b )d e + (24a c - 6b c)d e +--R * +--R +-+ +--R \|2 +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 2 2 +--R ((6a c - 3b )e + 6b c d e - 6c d e)x + (6a c - 3b )d e +--R + +--R 2 2 3 +--R 6b c d e - 6c d +--R * +--R +-----------+ +--R +-+ | 2 +--R \|2 \|- 4a c + b +--R + +--R 3 3 2 2 2 +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e )x +--R + +--R 3 2 2 2 2 +--R (12a b c - 3b )d e + (- 24a c + 6b c)d e +--R * +--R +-+ +--R \|2 +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 3 +--R ((- 12a c + 6b )e - 12b c d e + 12c d e)x - 2a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c + 8b )d e - 18b c d e + 16c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (3a e - 6a b d e + (6a c + 3b )d e - 6b c d e + 3c d e)x + 3a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 6a b d e + (6a c + 3b )d e - 6b c d e + 3c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-------+ | | 2 +--R \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 792 + +--S 793 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 2 2 3 3 2 2 4 +--R (- 3a e + 6a b d e + (- 6a c - 3b )d e + 6b c d e - 3c d e)x +--R + +--R 2 4 2 3 2 3 2 4 2 5 +--R - 3a d e + 6a b d e + (- 6a c - 3b )d e + 6b c d e - 3c d +--R * +--R +-------+ +--R \|e x + d +--R * +--R ROOT +--R 5 10 4 9 4 3 2 2 8 +--R 2a e - 10a b d e + (10a c + 20a b )d e +--R + +--R 3 2 3 3 7 3 2 2 2 4 4 6 +--R (- 40a b c - 20a b )d e + (20a c + 60a b c + 10a b )d e +--R + +--R 2 2 3 5 5 5 +--R (- 60a b c - 40a b c - 2b )d e +--R + +--R 2 3 2 2 4 6 4 3 3 2 7 3 +--R (20a c + 60a b c + 10b c)d e + (- 40a b c - 20b c )d e +--R + +--R 4 2 3 8 2 4 9 5 10 +--R (10a c + 20b c )d e - 10b c d e + 2c d +--R * +--R ROOT +--R 5 5 4 2 4 3 4 3 2 6 2 8 +--R - 4a c + 25a b c - 50a b c + 35a b c - 10a b c +--R + +--R 10 +--R b +--R * +--R 10 +--R e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 80a b c + 300a b c - 270a b c + 90a b c +--R + +--R 9 +--R - 10b c +--R * +--R 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 8 2 +--R (80a c - 740a b c + 900a b c - 360a b c + 45b c ) +--R * +--R 2 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 3 7 +--R (880a b c - 1660a b c + 840a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 4 6 +--R (- 440a c + 1830a b c - 1270a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 5 5 +--R (- 1200a b c + 1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 9 2 8 8 2 +--R (400a b c - 100b c )d e + (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 14 +--R (120a c + 1260a b c + 1260a b c + 210a b )d e +--R + +--R 6 3 5 3 2 4 5 3 7 7 13 +--R (- 840a b c - 2520a b c - 1260a b c - 120a b )d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 252a c + 3150a b c + 4200a b c + 1260a b c +--R + +--R 8 10 +--R 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10b c +--R * +--R 11 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 12 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 13 7 +--R (- 840a b c - 2520a b c - 1260a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 14 6 +--R (120a c + 1260a b c + 1260a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 15 5 +--R (- 360a b c - 840a b c - 252b c )d e +--R + +--R 2 8 2 7 4 6 16 4 +--R (45a c + 360a b c + 210b c )d e +--R + +--R 8 3 7 17 3 9 2 8 18 2 +--R (- 90a b c - 120b c )d e + (10a c + 45b c )d e +--R + +--R 9 19 10 20 +--R - 10b c d e + c d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (- 10a b c + 10a b c - 2b )e + (20a c - 40a b c + 10b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (60a b c - 20b c )d e + (- 40a c + 20b c )d e - 10b c d e +--R + +--R 5 5 +--R 4c d +--R / +--R 5 10 4 9 4 3 2 2 8 +--R a e - 5a b d e + (5a c + 10a b )d e +--R + +--R 3 2 3 3 7 3 2 2 2 4 4 6 +--R (- 20a b c - 10a b )d e + (10a c + 30a b c + 5a b )d e +--R + +--R 2 2 3 5 5 5 2 3 2 2 4 6 4 +--R (- 30a b c - 20a b c - b )d e + (10a c + 30a b c + 5b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 4 9 +--R (- 20a b c - 10b c )d e + (5a c + 10b c )d e - 5b c d e +--R + +--R 5 10 +--R c d +--R * +--R log +--R 6 5 2 12 5 4 3 11 +--R (a c - a b )e + (- 2a b c + 5a b )d e +--R + +--R 5 2 4 2 3 4 2 10 +--R (2a c - 10a b c - 10a b )d e +--R + +--R 4 2 3 3 2 5 3 9 +--R (10a b c + 40a b c + 10a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 8 +--R (- 5a c - 70a b c - 55a b c - 5a b )d e +--R + +--R 3 3 2 3 2 5 7 5 7 +--R (60a b c + 130a b c + 34a b c + b )d e +--R + +--R 3 4 2 2 3 4 2 6 6 6 +--R (- 20a c - 160a b c - 100a b c - 8b c)d e +--R + +--R 2 4 3 3 5 2 7 5 +--R (100a b c + 160a b c + 28b c )d e +--R + +--R 2 5 2 4 4 3 8 4 +--R (- 25a c - 145a b c - 55b c )d e +--R + +--R 5 3 4 9 3 6 2 5 10 2 +--R (70a b c + 65b c )d e + (- 14a c - 46b c )d e +--R + +--R 6 11 7 12 +--R 18b c d e - 3c d +--R * +--R ROOT +--R 5 5 4 2 4 3 4 3 2 6 2 +--R - 4a c + 25a b c - 50a b c + 35a b c +--R + +--R 8 10 +--R - 10a b c + b +--R * +--R 10 +--R e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 80a b c + 300a b c - 270a b c + 90a b c +--R + +--R 9 +--R - 10b c +--R * +--R 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 80a c - 740a b c + 900a b c - 360a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 2 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 3 7 +--R (880a b c - 1660a b c + 840a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 4 6 +--R (- 440a c + 1830a b c - 1270a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 5 5 +--R (- 1200a b c + 1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 9 2 8 8 2 +--R (400a b c - 100b c )d e + (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 14 +--R (120a c + 1260a b c + 1260a b c + 210a b )d e +--R + +--R 6 3 5 3 2 4 5 3 7 7 13 +--R (- 840a b c - 2520a b c - 1260a b c - 120a b )d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 252a c + 3150a b c + 4200a b c + 1260a b c +--R + +--R 8 10 +--R 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 1260a b c - 4200a b c - 2520a b c +--R + +--R 7 2 9 +--R - 360a b c - 10b c +--R * +--R 11 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 8 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1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 +--R (400a b c - 100b c )d e +--R + +--R 9 2 8 8 2 +--R (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 +--R (120a c + 1260a b c + 1260a b c + 210a b )d +--R * +--R 14 +--R e +--R + +--R 6 3 5 3 2 4 5 +--R - 840a b c - 2520a b c - 1260a b c +--R + +--R 3 7 +--R - 120a b +--R * +--R 7 13 +--R d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 +--R - 1260a b c - 4200a b c - 2520a b c +--R + +--R 2 7 9 +--R - 360a b c - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 +--R 252a c + 3150a 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+--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 14 +--R (120a c + 1260a b c + 1260a b c + 210a b )d e +--R + +--R 6 3 5 3 2 4 5 3 7 7 13 +--R (- 840a b c - 2520a b c - 1260a b c - 120a b )d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 252a c + 3150a b c + 4200a b c + 1260a b c +--R + +--R 8 10 +--R 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 1260a b c - 4200a b c - 2520a b c +--R + +--R 7 2 9 +--R - 360a b c - 10b c +--R * +--R 11 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 12 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 +--R (- 840a b c - 2520a b c - 1260a b c - 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100b c )d e + (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 14 +--R (120a c + 1260a b c + 1260a b c + 210a b )d e +--R + +--R 6 3 5 3 2 4 5 3 7 7 13 +--R (- 840a b c - 2520a b c - 1260a b c - 120a b )d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 252a c + 3150a b c + 4200a b c + 1260a b c +--R + +--R 8 10 +--R 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10b 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50a b c + 35a b c +--R + +--R 8 10 +--R - 10a b c + b +--R * +--R 10 +--R e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R - 80a b c + 300a b c - 270a b c + 90a b c +--R + +--R 9 +--R - 10b c +--R * +--R 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 80a c - 740a b c + 900a b c - 360a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 2 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 3 7 +--R (880a b c - 1660a b c + 840a b c - 120b c )d e +--R + +--R 3 7 2 2 6 4 5 6 4 4 6 +--R (- 440a c + 1830a b c - 1270a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 5 5 +--R (- 1200a b c + 1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 9 2 8 8 2 +--R (400a b c - 100b c )d e + (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e 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20a c - 60a b c - 10b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 +--R (40a b c + 20b c )d e + (- 10a c - 20b c )d e +--R + +--R 4 9 5 10 +--R 10b c d e - 2c d +--R * +--R ROOT +--R 5 5 4 2 4 3 4 3 2 6 2 +--R - 4a c + 25a b c - 50a b c + 35a b c +--R + +--R 8 10 +--R - 10a b c + b +--R * +--R 10 +--R e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 80a b c + 300a b c - 270a b c +--R + +--R 7 2 9 +--R 90a b c - 10b c +--R * +--R 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 80a c - 740a b c + 900a b c - 360a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 2 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 +--R (880a b c - 1660a b c + 840a b c - 120b c ) +--R * +--R 3 7 +--R d e +--R + +--R 3 7 2 2 6 4 5 +--R - 440a c + 1830a b c - 1270a b c +--R + +--R 6 4 +--R 210b c +--R * +--R 4 6 +--R d e +--R + +--R 2 7 3 6 5 5 5 5 +--R (- 1200a b c + 1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 +--R (400a b c - 100b c )d e +--R + +--R 9 2 8 8 2 +--R (- 100a c 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4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 9 2 8 8 2 +--R (400a b c - 100b c )d e + (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 14 +--R (120a c + 1260a b c + 1260a b c + 210a b )d e +--R + +--R 6 3 5 3 2 4 5 3 7 7 13 +--R (- 840a b c - 2520a b c - 1260a b c - 120a b )d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 1260a b c - 4200a b c - 2520a b c - 360a b c +--R + +--R 9 +--R - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 252a c + 3150a b c + 4200a b c + 1260a b c +--R + +--R 8 10 +--R 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 1260a b c - 4200a b c - 2520a b c +--R + +--R 7 2 9 +--R - 360a b c - 10b c +--R * +--R 11 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 12 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 +--R (- 840a b c - 2520a b c - 1260a b c - 120b c ) +--R * +--R 13 7 +--R d e +--R + +--R 3 7 2 2 6 4 5 6 4 14 6 +--R (120a c + 1260a b c + 1260a b c + 210b c )d e +--R + +--R 2 7 3 6 5 5 15 5 +--R (- 360a b c - 840a b c - 252b c )d e +--R + +--R 2 8 2 7 4 6 16 4 +--R (45a c + 360a b c + 210b c )d e +--R + +--R 8 3 7 17 3 9 2 8 18 2 +--R (- 90a b c - 120b c )d e + (10a c + 45b c )d e +--R + +--R 9 19 10 20 +--R - 10b c d e + c d +--R + +--R 3 3 2 3 2 5 7 7 +--R (- 3a b c + 10a b c - 6a b c + b )e +--R + +--R 3 4 2 2 3 4 2 6 6 +--R (6a c - 51a b c + 40a b c - 8b c)d e +--R + +--R 2 4 3 3 5 2 2 5 +--R (93a b c - 109a b c + 28b c )d e +--R + +--R 2 5 2 4 4 3 3 4 +--R (- 62a c + 156a b c - 57b c )d e +--R + +--R 5 3 4 4 3 6 2 5 5 2 6 6 +--R (- 125a b c + 75b c )d e + (50a c - 65b c )d e + 35b c d e +--R + +--R 7 7 +--R - 10c d +--R * +--R ROOT +--R 5 10 4 9 4 3 2 2 8 +--R 2a e - 10a b d e + (10a c + 20a b )d e +--R + +--R 3 2 3 3 7 +--R (- 40a b c - 20a b )d e +--R + +--R 3 2 2 2 4 4 6 +--R (20a c + 60a b c + 10a b )d e +--R + +--R 2 2 3 5 5 5 +--R (- 60a b c - 40a b c - 2b )d e +--R + +--R 2 3 2 2 4 6 4 +--R (20a c + 60a b c + 10b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 +--R (- 40a b c - 20b c )d e + (10a c + 20b c )d e +--R + +--R 4 9 5 10 +--R - 10b c d e + 2c d +--R * +--R ROOT +--R 5 5 4 2 4 3 4 3 2 6 2 +--R - 4a c + 25a b c - 50a b c + 35a b c +--R + +--R 8 10 +--R - 10a b c + b +--R * +--R 10 +--R e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 80a b c + 300a b c - 270a b c +--R + +--R 7 2 9 +--R 90a b c - 10b c +--R * +--R 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R 80a c - 740a b c + 900a b c - 360a b c +--R + +--R 8 2 +--R 45b c +--R * +--R 2 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 7 3 +--R (880a b c - 1660a b c + 840a b c - 120b c ) +--R * +--R 3 7 +--R d e +--R + +--R 3 7 2 2 6 4 5 +--R - 440a c + 1830a b c - 1270a b c +--R + +--R 6 4 +--R 210b c +--R * +--R 4 6 +--R d e +--R + +--R 2 7 3 6 5 5 5 5 +--R (- 1200a b c + 1300a b c - 250b c )d e +--R + +--R 2 8 2 7 4 6 6 4 +--R (400a c - 900a b c + 200b c )d e +--R + +--R 8 3 7 7 3 +--R (400a b c - 100b c )d e +--R + +--R 9 2 8 8 2 +--R (- 100a c + 25b c )d e +--R / +--R 10 20 9 19 9 8 2 2 18 +--R a e - 10a b d e + (10a c + 45a b )d e +--R + +--R 8 7 3 3 17 +--R (- 90a b c - 120a b )d e +--R + +--R 8 2 7 2 6 4 4 16 +--R (45a c + 360a b c + 210a b )d e +--R + +--R 7 2 6 3 5 5 5 15 +--R (- 360a b c - 840a b c - 252a b )d e +--R + +--R 7 3 6 2 2 5 4 4 6 6 +--R (120a c + 1260a b c + 1260a b c + 210a b )d +--R * +--R 14 +--R e +--R + +--R 6 3 5 3 2 4 5 +--R - 840a b c - 2520a b c - 1260a b c +--R + +--R 3 7 +--R - 120a b +--R * +--R 7 13 +--R d e +--R + +--R 6 4 5 2 3 4 4 2 3 6 +--R 210a c + 2520a b c + 3150a b c + 840a b c +--R + +--R 2 8 +--R 45a b +--R * +--R 8 12 +--R d e +--R + +--R 5 4 4 3 3 3 5 2 +--R - 1260a b c - 4200a b c - 2520a b c +--R + +--R 2 7 9 +--R - 360a b c - 10a b +--R * +--R 9 11 +--R d e +--R + +--R 5 5 4 2 4 3 4 3 +--R 252a c + 3150a b c + 4200a b c +--R + +--R 2 6 2 8 10 +--R 1260a b c + 90a b c + b +--R * +--R 10 10 +--R d e +--R + +--R 4 5 3 3 4 2 5 3 +--R - 1260a b c - 4200a b c - 2520a b c +--R + +--R 7 2 9 +--R - 360a b c - 10b c +--R * +--R 11 9 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 +--R 210a c + 2520a b c + 3150a b c +--R + +--R 6 3 8 2 +--R 840a b c + 45b c +--R * +--R 12 8 +--R d e +--R + +--R 3 6 2 3 5 5 4 +--R - 840a b c - 2520a b c - 1260a b c +--R + +--R 7 3 +--R - 120b c +--R * +--R 13 7 +--R d e +--R + +--R 3 7 2 2 6 4 5 6 4 +--R (120a c + 1260a b c + 1260a b c + 210b c ) +--R * +--R 14 6 +--R d e +--R + +--R 2 7 3 6 5 5 15 5 +--R (- 360a b c - 840a b c - 252b c )d e +--R + +--R 2 8 2 7 4 6 16 4 +--R (45a c + 360a b c + 210b c )d e +--R + +--R 8 3 7 17 3 +--R (- 90a b c - 120b c )d e +--R + +--R 9 2 8 18 2 9 19 10 20 +--R (10a c + 45b c )d e - 10b c d e + c d +--R + +--R 2 2 3 5 5 +--R (- 10a b c + 10a b c - 2b )e +--R + +--R 2 3 2 2 4 4 3 3 2 2 3 +--R (20a c - 40a b c + 10b c)d e + (60a b c - 20b c )d e +--R + +--R 4 2 3 3 2 4 4 5 5 +--R (- 40a c + 20b c )d e - 10b c d e + 4c d +--R / +--R 5 10 4 9 4 3 2 2 8 +--R a e - 5a b d e + (5a c + 10a b )d e +--R + +--R 3 2 3 3 7 3 2 2 2 4 4 6 +--R (- 20a b c - 10a b )d e + (10a c + 30a b c + 5a b )d e +--R + +--R 2 2 3 5 5 5 +--R (- 30a b c - 20a b c - b )d e +--R + +--R 2 3 2 2 4 6 4 +--R (10a c + 30a b c + 5b c)d e +--R + +--R 3 3 2 7 3 4 2 3 8 2 +--R (- 20a b c - 10b c )d e + (5a c + 10b c )d e +--R + +--R 4 9 5 10 +--R - 5b c d e + c d +--R + +--R 2 5 2 4 4 3 4 5 3 4 3 +--R (4a c - 12a b c + 4b c )e + (40a b c - 20b c )d e +--R + +--R 6 2 5 2 2 6 3 7 4 +--R (- 40a c + 40b c )d e - 40b c d e + 20c d +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 2 2 2 2 +-+ | 2 +--R ((- 4a c + 2b )e - 4b c d e + 4c d )\|2 \|- 4a c + b +--R + +--R 3 2 2 2 +-+ +--R ((8a b c - 2b )e + (- 16a c + 4b c)d e)\|2 +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 2 2 2 +-+ | 2 +--R ((- 4a c + 2b )e - 4b c d e + 4c d )\|2 \|- 4a c + b +--R + +--R 3 2 2 2 +-+ +--R ((- 8a b c + 2b )e + (16a c - 4b c)d e)\|2 +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d )\|- 4a c + b +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 794 + +--S 795 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 795 + +)clear all + +--S 796 of 845 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 796 + +--S 797 of 845 +r0:=-(d+e*x)^(5/2)/(a+b*x+c*x^2)+5*e^2*sqrt(d+e*x)/c-5*e*atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))/sqrt(b^2-4*a*c))/(c^(3/2)*_ + sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-5*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (-2*c^2*d^2-b^2*e^2+2*c*e*(b*d+a*e))/sqrt(b^2-4*a*c))/(c^(3/2)*_ + sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 2 2 3 2 3 +--R (5b c e - 10c d e )x + (5b e - 10b c d e )x + 5a b e +--R + +--R 2 +--R - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((- 10a c + 5b c)e - 10b c d e + 10c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 10a b c + 5b )e - 10b c d e + 10b c d e)x + (- 10a c + 5a b )e +--R + +--R 2 2 2 +--R - 10a b c d e + 10a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 3 +--R (5b c e - 10c d e )x + (5b e - 10b c d e )x + 5a b e +--R + +--R 2 +--R - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((10a c - 5b c)e + 10b c d e - 10c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((10a b c - 5b )e + 10b c d e - 10b c d e)x + (10a c - 5a b )e +--R + +--R 2 2 2 +--R 10a b c d e - 10a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 2 2 2 2 +-+ | 2 +-+ +--R (4c e x + (5b e - 2c d e)x + 5a e - c d )\|2 \|- 4a c + b \|c +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-------+ | | 2 +--R \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 2 +-+ | 2 +-+ +--R (c x + b c x + a c)\|2 \|- 4a c + b \|c +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 797 + +--S 798 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (c x + b c x + a c) +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R log +--R 4 3 3 5 2 4 +--R ((16a b c - 4b c )e + (- 32a c + 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (- 100a c + 125a b c - 25b )e + (- 300a b c + 75b c)d e +--R + +--R 3 2 2 2 4 +--R (300a c - 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +--R (- c x - b c x - a c) +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R log +--R 4 3 3 5 2 4 +--R ((16a b c - 4b c )e + (- 32a c + 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (100a c - 125a b c + 25b )e + (300a b c - 75b c)d e +--R + +--R 3 2 2 2 4 +--R (- 300a c + 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 +--R (c x + b c x + a c) +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R log +--R 4 3 3 5 2 4 +--R ((- 16a b c + 4b c )e + (32a c - 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (- 100a c + 125a b c - 25b )e + (- 300a b c + 75b c)d e +--R + +--R 3 2 2 2 4 +--R (300a c - 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 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11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (100a c - 125a b c + 25b )e + (300a b c - 75b c)d e +--R + +--R 3 2 2 2 4 +--R (- 300a c + 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 2 2 2 +-------+ +--R (8c e x + (10b e - 4c d e)x + 10a e - 2c d )\|e x + d +--R / +--R 2 2 +--R 2c x + 2b c x + 2a c +--R Type: Union(Expression(Integer),...) +--E 798 + +--S 799 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R c\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 3 3 5 2 4 +--R ((16a b c - 4b c )e + (- 32a c + 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (- 100a c + 125a b c - 25b )e + (- 300a b c + 75b c)d e +--R + +--R 3 2 2 2 4 +--R (300a c - 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R c\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 3 3 5 2 4 +--R ((16a b c - 4b c )e + (- 32a c + 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (100a c - 125a b c + 25b )e + (300a b c - 75b c)d e +--R + +--R 3 2 2 2 4 +--R (- 300a c + 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e +--R + +--R 2 2 3 3 3 2 +--R 75b c d e - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R c\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 3 3 5 2 4 +--R ((- 16a b c + 4b c )e + (32a c - 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (- 100a c + 125a b c - 25b )e + (- 300a b c + 75b c)d e +--R + +--R 3 2 2 2 4 +--R (300a c - 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (- 16a c + 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R c\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (3750a c - 9375b c )d e + 11250b c d e - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e + 75b c d e +--R + +--R 3 3 2 +--R - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 3 3 5 2 4 +--R ((- 16a b c + 4b c )e + (32a c - 8b c )d) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 2 2 2 4 6 2 3 5 +--R (100a c - 125a b c + 25b )e + (300a b c - 75b c)d e +--R + +--R 3 2 2 2 4 +--R (- 300a c + 75b c )d e +--R * +--R ROOT +--R 4 2 3 +--R (16a c - 4b c ) +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- 625a c + 1250a b c - 625b )e +--R + +--R 2 3 9 +--R (- 3750a b c + 3750b c)d e +--R + +--R 3 2 2 2 8 3 3 7 +--R (3750a c - 9375b c )d e + 11250b c d e +--R + +--R 4 4 6 +--R - 5625c d e +--R / +--R 7 2 6 +--R 64a c - 16b c +--R + +--R 3 5 2 2 4 +--R (- 75a b c + 25b )e + (150a c - 75b c)d e +--R + +--R 2 2 3 3 3 2 +--R 75b c d e - 50c d e +--R / +--R 4 2 3 +--R 8a c - 2b c +--R + +--R 2 2 8 3 7 +--R (250a c - 250a b )e + (500a b c + 250b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (- 500a c - 1000b c)d e + 1500b c d e - 750c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 10b e + 20c d e )\|- 4a c + b + (20a c - 10b )e + 20b c d e +--R + +--R 2 2 +--R - 20c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 10b e + 20c d e )\|- 4a c + b + (- 20a c + 10b )e - 20b c d e +--R + +--R 2 2 +--R 20c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R 2c\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 799 + +--S 800 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 800 + +)clear all + +--S 801 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 801 + +--S 802 of 845 +r0:=-(d+e*x)^(3/2)/(a+b*x+c*x^2)-3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ + (sqrt(2)*sqrt(c)*sqrt(b^2-4*a*c))+3*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c)))/(sqrt(2)*sqrt(c)*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R +------------------------------+ +--R | +-----------+ +--R 2 | | 2 +--R (3c e x + 3b e x + 3a e)\|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R | +-----------+ +--R 2 | | 2 +--R (- 3c e x - 3b e x - 3a e)\|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-------+ +--R (- e x - d)\|2 \|- 4a c + b \|c \|e x + d +--R / +--R +-----------+ +--R 2 +-+ | 2 +-+ +--R (c x + b x + a)\|2 \|- 4a c + b \|c +--R Type: Expression(Integer) +--E 802 + +--S 803 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (c x + b x + a) +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R 2 +--R (- c x - b x - a) +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R 2 +--R (c x + b x + a) +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R 2 +--R (- c x - b x - a) +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R +-------+ +--R (- 2e x - 2d)\|e x + d +--R / +--R 2 +--R 2c x + 2b x + 2a +--R Type: Union(Expression(Integer),...) +--E 803 + +--S 804 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-+ | 2 +-+ +--R \|2 \|- 4a c + b \|c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R - +--R +-----------+ +--R +-+ | 2 +-+ +--R \|2 \|- 4a c + b \|c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R \|2 \|- 4a c + b \|c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +--------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(- 16a c + 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |-------------------------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R - +--R +-----------+ +--R +-+ | 2 +-+ +--R \|2 \|- 4a c + b \|c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R | 6 +--R 2 2 | 81e +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +------------------------------------------------------+ +--R | +-----------------+ +--R | | 6 +--R | 2 2 | 81e 3 2 +--R |(16a c - 4b c) |- --------------- + 9b e - 18c d e +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |------------------------------------------------------ +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R 4 +-------+ +--R 27e \|e x + d +--R + +--R - +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R 6e\|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R 6e\|e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R +-+ | 2 +-+ +--R 2\|2 \|- 4a c + b \|c +--R Type: Expression(Integer) +--E 804 + +--S 805 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 805 + +)clear all + +--S 806 of 845 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^2 +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 806 + +--S 807 of 845 +r0:=-sqrt(d+e*x)/(a+b*x+c*x^2)-e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/(sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/_ + (sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +----------------------------+ +--R | +-----------+ +--R 2 +-+ +-+ | | 2 +--R (c e x + b e x + a e)\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R 2 +-+ +-+ | | 2 +--R (- c e x - b e x - a e)\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-------+ | | 2 +--R \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 +--R (c x + b x + a)\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 807 + +--S 808 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (c x + b x + a) +--R * +--R ROOT +--R 2 2 2 3 2 2 2 +--R ((16a c - 4a b )e + (- 16a b c + 4b )d e + (16a c - 4b c)d ) +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c 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+--R * +--R ROOT +--R 2 2 2 3 +--R (16a c - 4a b )e + (- 16a b c + 4b )d e +--R + +--R 2 2 2 +--R (16a c - 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R +-------+ +--R - 2\|e x + d +--R / +--R 2 +--R 2c x + 2b x + 2a +--R Type: Union(Expression(Integer),...) +--E 808 + +--S 809 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 2 3 2 2 2 +--R ((16a c - 4a b )e + (- 16a b c + 4b )d e + (16a c - 4b c)d ) +--R * +--R ROOT +--R - +--R 6 +--R e +--R / 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+--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (16a b c - 4a b )e + (- 32a c - 8a b c + 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (48a b c - 12b c)d e + (- 32a c + 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (- 4a c + b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 +--R (- 128a b c + 32b c)d e +--R + +--R 3 2 2 4 +--R (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e +--R + +--R 2 2 2 +--R (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (- 16a b c + 4a b )e + (32a c + 8a b c - 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (- 48a b c + 12b c)d e + (32a c - 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (4a c - b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (- 16a c + 4a b )e + (16a b c - 4b )d e +--R + +--R 2 2 2 +--R (- 16a c + 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 2 2 2 3 +--R (16a c - 4a b )e + (- 16a b c + 4b )d e +--R + +--R 2 2 2 +--R (16a c - 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e + (8a c - 2b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 2 3 3 2 2 2 4 2 +--R (- 16a b c + 4a b )e + (32a c + 8a b c - 4b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (- 48a b c + 12b c)d e + (32a c - 8b c )d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 2 3 3 +--R (64a c - 16a b )e + (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 128a b c + 32b c)d e + (64a c - 16b c )d +--R + +--R 2 4 +--R (- 4a c + b )e +--R * +--R ROOT +--R 2 2 2 3 +--R (16a c - 4a b )e + (- 16a b c + 4b )d e +--R + +--R 2 2 2 +--R (16a c - 4b c)d +--R * +--R ROOT +--R - +--R 6 +--R e +--R / +--R 3 2 2 4 +--R (64a c - 16a b )e +--R + +--R 2 3 3 +--R (- 128a b c + 32a b )d e +--R + +--R 2 2 2 4 2 2 +--R (128a c + 32a b c - 16b )d e +--R + +--R 2 3 3 +--R (- 128a b c + 32b c)d e +--R + +--R 3 2 2 4 +--R (64a c - 16b c )d +--R + +--R 3 2 +--R b e - 2c d e +--R / +--R 2 2 2 3 +--R (8a c - 2a b )e + (- 8a b c + 2b )d e +--R + +--R 2 2 2 +--R (8a c - 2b c)d +--R + +--R 4 +-------+ +--R 2c e \|e x + d +--R + +--R - +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2e\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2e\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R 2\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 809 + +--S 810 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 810 + +)clear all + +--S 811 of 845 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) -------------------------------------------------------- +--R 2 4 3 2 2 2 +-------+ +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 811 + +--S 812 of 845 +r0:=-((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))+e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(2*c*d-e*(b+_ + sqrt(b^2-4*a*c)))/((c*d^2-e*(b*d-a*e))*sqrt(2)*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(2*c*d-_ + e*(b-sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R 2 2 2 2 | 2 2 2 2 +--R (- c e x - b e x - a e )\|- 4a c + b + (b c e - 2c d e)x +--R + +--R 2 2 2 +--R (b e - 2b c d e)x + a b e - 2a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 2 2 2 | 2 2 2 2 +--R (- c e x - b e x - a e )\|- 4a c + b + (- b c e + 2c d e)x +--R + +--R 2 2 2 +--R (- b e + 2b c d e)x - a b e + 2a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-------+ +--R (c e x + b e - c d)\|2 \|- 4a c + b \|e x + d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (a c e - b c d e + c d )x + (a b e - b d e + b c d )x + a e +--R + +--R 2 +--R - a b d e + a c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 812 + +--S 813 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R (a c e - b c d e + c d )x + (a b e - b d e + b c d )x + a e +--R + +--R 2 +--R - a b d e + a c d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (16a c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (48a c + 36a b c - 12a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 96a b c + 8a b c + 4b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (48a c + 36a b c - 12b c)d e + (- 48a b c + 12b c )d e +--R + +--R 4 2 3 6 +--R (16a c - 4b c )d +--R * +--R ROOT +--R 2 2 2 4 10 2 3 9 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (64a c - 16a b )e + (- 384a b c + 96a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (384a c + 864a b c - 240a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 1920a b c - 800a b c + 320a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (960a c + 3600a b c - 240a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 3840a b c - 2880a b c + 576a b c + 96a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (1280a c + 5440a b c + 480a b c - 416a b c - 16b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 3840a b c - 2880a b c + 576a b c + 96b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (960a c + 3600a b c - 240b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 1920a b c - 800a b c + 320b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (384a c + 864a b c - 240b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 384a b c + 96b c )d e + (64a c - 16b c )d +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 +--R (- 3a b c + b )e + (6a c - 3b c)d e + 3b c d e - 2c d e +--R / +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 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2c d \|e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (16a c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (48a c + 36a b c - 12a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 96a b c + 8a b c + 4b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (48a c + 36a b c - 12b c)d e + (- 48a b c + 12b c )d e +--R + +--R 4 2 3 6 +--R (16a c - 4b c )d +--R * +--R ROOT +--R 2 2 2 4 10 2 3 9 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (64a c - 16a b )e + (- 384a b c + 96a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (384a c + 864a b c - 240a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 1920a b c - 800a b c + 320a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (960a c + 3600a b c - 240a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 3840a b c - 2880a b c + 576a b c + 96a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (1280a c + 5440a b c + 480a b c - 416a b c - 16b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 3840a b c - 2880a b c + 576a b c + 96b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (960a c + 3600a b c - 240b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 1920a b c - 800a b c + 320b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (384a c + 864a b c - 240b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 384a b c + 96b c )d e + (64a c - 16b c )d +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 +--R (- 3a b c + b )e + (6a c - 3b c)d e + 3b c d e - 2c d e +--R / +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (- 32a c + 24a b c - 4a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (64a b c - 64a b c + 12a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (- 64a c + 64a b c + 36a b c - 12a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (- 160a b c + 24a b c + 4b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (240a b c + 20a b c - 20b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (- 192a b c - 128a b c + 44b c )d e +--R + +--R 2 5 2 4 4 3 6 2 +--R (64a c + 192a b c - 52b c )d e +--R + +--R 5 3 4 7 6 2 5 8 +--R (- 128a b c + 32b c )d e + (32a c - 8b c )d +--R * +--R ROOT +--R 2 2 2 4 10 2 3 9 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 8 3 3 7 4 4 6 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (64a c - 16a b )e + (- 384a b c + 96a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (384a c + 864a b c - 240a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 1920a b c - 800a b c + 320a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (960a c + 3600a b c - 240a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 3840a b c - 2880a b c + 576a b c + 96a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 +--R 1280a c + 5440a b c + 480a b c - 416a b c +--R + +--R 8 +--R - 16b +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 3840a b c - 2880a b c + 576a b c + 96b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (960a c + 3600a b c - 240b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 1920a b c - 800a b c + 320b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (384a c + 864a b c - 240b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 384a b c + 96b c )d e + (64a c - 16b c )d +--R + +--R 2 2 3 5 7 2 3 2 2 4 6 +--R (- 4a b c + 5a b c - b )e + (8a c - 22a b c + 5b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (36a b c - 9b c )d e + (- 24a c + 6b c )d e +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (16a c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (48a c + 36a b c - 12a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 96a b c + 8a b c + 4b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (48a c + 36a b c - 12b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (- 48a b c + 12b c )d e + (16a c - 4b c )d +--R * +--R ROOT +--R 2 2 2 4 10 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 9 3 2 2 2 8 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 7 4 4 6 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (64a c - 16a b )e + (- 384a b c + 96a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (384a c + 864a b c - 240a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 1920a b c - 800a b c + 320a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (960a c + 3600a b c - 240a b )d e +--R + +--R 4 3 3 3 2 2 5 +--R - 3840a b c - 2880a b c + 576a b c +--R + +--R 7 +--R 96a b +--R * +--R 5 7 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 6 +--R 1280a c + 5440a b c + 480a b c - 416a b c +--R + +--R 8 +--R - 16b +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 3840a b c - 2880a b c + 576a b c +--R + +--R 7 +--R 96b c +--R * +--R 7 5 +--R d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (960a c + 3600a b c - 240b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 1920a b c - 800a b c + 320b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (384a c + 864a b c - 240b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 384a b c + 96b c )d e + (64a c - 16b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 3a b c + b )e + (6a c - 3b c)d e + 3b c d e +--R + +--R 3 3 2 +--R - 2c d e +--R / +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R + +--R 3 2 2 6 3 5 4 2 4 +-------+ +--R ((2a c - 2b c )e + 6b c d e - 6c d e )\|e x + d +--R + +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 2 +-+ | | 2 +--R (2e \|- 4a c + b - 2b e + 4c d e)\|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 | 2 2 +-+ +--R (2e \|- 4a c + b + 2b e - 4c d e)\|c +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 2 +-+ | 2 +--R (2a e - 2b d e + 2c d )\|2 \|- 4a c + b +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 814 + +--S 815 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 815 + +)clear all + +--S 816 of 845 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 816 + +--S 817 of 845 +r0:=3*e^2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))+(-(b^2-4*a*c)*_ + (c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ + (a+b*x+c*x^2)*sqrt(d+e*x))+3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(2*c^2*d^2+b*e^2*(b+_ + sqrt(b^2-4*a*c))-2*c*e*(b*d+a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+_ + a*e^2)^2*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-_ + 3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c))))*sqrt(c)*(2*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-_ + 2*c*e*(b*d+a*e-d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(2)*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 2 2 3 2 3 +--R (3b c e - 6c d e )x + (3b e - 6b c d e )x + 3a b e +--R + +--R 2 +--R - 6a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((6a c - 3b c)e + 6b c d e - 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((6a b c - 3b )e + 6b c d e - 6b c d e)x + (6a c - 3a b )e +--R + +--R 2 2 2 +--R 6a b c d e - 6a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 3 +--R (3b c e - 6c d e )x + (3b e - 6b c d e )x + 3a b e +--R + +--R 2 +--R - 6a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((- 6a c + 3b c)e - 6b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 6a b c + 3b )e - 6b c d e + 6b c d e)x + (- 6a c + 3a b )e +--R + +--R 2 2 2 +--R - 6a b c d e + 6a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 3b c e + 6c d e )x + ((a c - 3b )e + 5b c d e + c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (5a c - b )d e + 2b c d e - c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (a c e - 2a b c d e + (2a c + b c)d e - 2b c d e + c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 3 4 +--R (a b e - 2a b d e + (2a b c + b )d e - 2b c d e + b c d )x + a e +--R + +--R 2 3 2 2 2 2 3 2 4 +--R - 2a b d e + (2a c + a b )d e - 2a b c d e + a c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 817 + +--S 818 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (a c e - 2a b c d e + (2a c + b c)d e - 2b c d e + c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 3 4 +--R (a b e - 2a b d e + (2a b c + b )d e - 2b c d e + b c d )x + a e +--R + +--R 2 3 2 2 2 2 3 2 4 +--R - 2a b d e + (2a c + a b )d e - 2a b c d e + a c d +--R * +--R +-------+ +--R \|e x + d +--R * +--R ROOT +--R 6 5 2 10 5 4 3 9 +--R (16a c - 4a b )e + (- 80a b c + 20a b )d e +--R + +--R 5 2 4 2 3 4 2 8 +--R (80a c + 140a b c - 40a b )d e +--R + +--R 4 2 3 3 2 5 3 7 +--R (- 320a b c - 80a b c + 40a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 6 +--R (160a c + 440a b c - 40a b c - 20a b )d e +--R + +--R 3 3 2 3 2 5 7 5 5 +--R (- 480a b c - 200a b c + 64a b c + 4b )d e +--R + +--R 3 4 2 2 3 4 2 6 6 4 +--R (160a c + 440a b c - 40a b c - 20b c)d e +--R + +--R 2 4 3 3 5 2 7 3 +--R (- 320a b c - 80a b c + 40b c )d e +--R + +--R 2 5 2 4 4 3 8 2 5 3 4 9 +--R (80a c + 140a b c - 40b c )d e + (- 80a b c + 20b c )d e +--R + +--R 6 2 5 10 +--R (16a c - 4b c )d +--R * +--R ROOT +--R 4 4 3 2 3 2 4 2 6 8 14 +--R (- 81a c + 486a b c - 891a b c + 486a b c - 81b )e +--R + +--R 3 4 2 3 3 5 2 7 13 +--R (- 1620a b c + 5670a b c - 4050a b c + 810b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 12 +--R (1620a c - 14580a b c + 14580a b c - 3645b c )d e +--R + +--R 2 5 3 4 5 3 3 11 +--R (17820a b c - 29160a b c + 9720b c )d e +--R + +--R 2 6 2 5 4 4 4 10 +--R (- 8910a c + 34830a b c - 17010b c )d e +--R + +--R 6 3 5 5 9 +--R (- 24300a b c + 20250b c )d e +--R + +--R 7 2 6 6 8 7 7 7 8 8 6 +--R (8100a c - 16200b c )d e + 8100b c d e - 2025c d e +--R / +--R 11 10 2 20 10 9 3 19 +--R (64a c - 16a b )e + (- 640a b c + 160a b )d e +--R + +--R 10 2 9 2 8 4 2 18 +--R (640a c + 2720a b c - 720a b )d e +--R + +--R 9 2 8 3 7 5 3 17 +--R (- 5760a b c - 6240a b c + 1920a b )d e +--R + +--R 9 3 8 2 2 7 4 6 6 4 16 +--R (2880a c + 22320a b c + 7680a b c - 3360a b )d e +--R + +--R 8 3 7 3 2 6 5 5 7 +--R (- 23040a b c - 48000a b c - 2688a b c + 4032a b ) +--R * +--R 5 15 +--R d e +--R + +--R 8 4 7 2 3 6 4 2 5 6 +--R 7680a c + 78720a b c + 60480a b c - 6720a b c +--R + +--R 4 8 +--R - 3360a b +--R * +--R 6 14 +--R d e +--R + +--R 7 4 6 3 3 5 5 2 +--R - 53760a b c - 147840a b c - 40320a b c +--R + +--R 4 7 3 9 +--R 12480a b c + 1920a b +--R * +--R 7 13 +--R d e +--R + +--R 7 5 6 2 4 5 4 3 +--R 13440a c + 157920a b c + 161280a b c +--R + +--R 4 6 2 3 8 2 10 +--R 3360a b c - 10560a b c - 720a b +--R * +--R 8 12 +--R d e +--R + +--R 6 5 5 3 4 4 5 3 +--R - 80640a b c - 248640a b c - 94080a b c +--R + +--R 3 7 2 2 9 11 +--R 17280a b c + 5120a b c + 160a b +--R * +--R 9 11 +--R d e +--R + +--R 6 6 5 2 5 4 4 4 +--R 16128a c + 197568a b c + 218400a b c +--R + 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8 18 2 +--R (640a c + 2720a b c - 720b c )d e +--R + +--R 10 3 9 19 11 2 10 20 +--R (- 640a b c + 160b c )d e + (64a c - 16b c )d +--R + +--R 2 2 3 5 7 +--R (45a b c - 45a b c + 9b )e +--R + +--R 2 3 2 2 4 6 3 3 2 2 5 +--R (- 90a c + 180a b c - 45b c)d e + (- 270a b c + 90b c )d e +--R + +--R 4 2 3 3 4 4 4 3 5 5 2 +--R (180a c - 90b c )d e + 45b c d e - 18c d e +--R / +--R 6 5 2 10 5 4 3 9 +--R (8a c - 2a b )e + (- 40a b c + 10a b )d e +--R + +--R 5 2 4 2 3 4 2 8 +--R (40a c + 70a b c - 20a b )d e +--R + +--R 4 2 3 3 2 5 3 7 +--R (- 160a b c - 40a b c + 20a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 6 +--R (80a c + 220a b c - 20a b c - 10a b )d e +--R + +--R 3 3 2 3 2 5 7 5 5 +--R (- 240a b c - 100a b c + 32a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 6 4 +--R (80a c + 220a b c - 20a b c - 10b c)d e +--R + +--R 2 4 3 3 5 2 7 3 +--R (- 160a b c - 40a b c + 20b c )d e +--R + +--R 2 5 2 4 4 3 8 2 5 3 4 9 +--R (40a c + 70a b c - 20b c )d e + (- 40a b c + 10b c )d e +--R + +--R 6 2 5 10 +--R (8a c 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c + 1920a b )d e +--R + +--R 9 3 8 2 2 7 4 6 6 4 16 +--R (2880a c + 22320a b c + 7680a b c - 3360a b )d e +--R + +--R 8 3 7 3 2 6 5 +--R - 23040a b c - 48000a b c - 2688a b c +--R + +--R 5 7 +--R 4032a b +--R * +--R 5 15 +--R d e +--R + +--R 8 4 7 2 3 6 4 2 5 6 +--R 7680a c + 78720a b c + 60480a b c - 6720a b c +--R + +--R 4 8 +--R - 3360a b +--R * +--R 6 14 +--R d e +--R + +--R 7 4 6 3 3 5 5 2 +--R - 53760a b c - 147840a b c - 40320a b c +--R + +--R 4 7 3 9 +--R 12480a b c + 1920a b +--R * +--R 7 13 +--R d e +--R + +--R 7 5 6 2 4 5 4 3 +--R 13440a c + 157920a b c + 161280a b c +--R + +--R 4 6 2 3 8 2 10 +--R 3360a b c - 10560a b c - 720a b +--R * +--R 8 12 +--R d e +--R + +--R 6 5 5 3 4 4 5 3 +--R - 80640a b c - 248640a b c - 94080a b c +--R + +--R 3 7 2 2 9 11 +--R 17280a b c + 5120a b c + 160a b +--R * +--R 9 11 +--R d e +--R + +--R 6 6 5 2 5 4 4 4 +--R 16128a c + 197568a b c + 218400a b c +--R + +--R 3 6 3 2 8 2 10 12 +--R 13440a b c - 14400a b c - 1376a b c - 16b +--R * +--R 10 10 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20 +--R (- 640a b c + 160b c )d e + (64a c - 16b c )d +--R + +--R 4 4 3 2 3 2 4 2 6 8 10 +--R (- 36a c + 153a b c - 180a b c + 72a b c - 9b )e +--R + +--R 3 4 2 3 3 5 2 7 9 +--R (- 468a b c + 981a b c - 504a b c + 72b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 8 +--R (468a c - 2241a b c + 1539a b c - 252b c )d e +--R + +--R 2 5 3 4 5 3 3 7 +--R (2520a b c - 2610a b c + 495b c )d e +--R + +--R 2 6 2 5 4 4 4 6 +--R (- 1260a c + 2655a b c - 585b c )d e +--R + +--R 6 3 5 5 5 7 2 6 6 4 +--R (- 1620a b c + 405b c )d e + (540a c - 135b c )d e +--R * +--R ROOT +--R 6 5 2 10 5 4 3 9 +--R (16a c - 4a b )e + (- 80a b c + 20a b )d e +--R + +--R 5 2 4 2 3 4 2 8 +--R (80a c + 140a b c - 40a b )d e +--R + +--R 4 2 3 3 2 5 3 7 +--R (- 320a b c - 80a b c + 40a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 6 +--R (160a c + 440a b c - 40a b c - 20a b )d e +--R + +--R 3 3 2 3 2 5 7 5 5 +--R (- 480a b c - 200a b c + 64a b c + 4b )d e +--R + +--R 3 4 2 2 3 4 2 6 6 4 +--R (160a c + 440a b c - 40a b c - 20b c)d e +--R + +--R 2 4 3 3 5 2 7 3 +--R (- 320a b c - 80a b c + 40b c )d e +--R + +--R 2 5 2 4 4 3 8 2 +--R (80a c + 140a b c - 40b c )d e +--R + +--R 5 3 4 9 6 2 5 10 +--R (- 80a b c + 20b c )d e + (16a c - 4b c )d +--R * +--R ROOT +--R 4 4 3 2 3 2 4 2 6 +--R - 81a c + 486a b c - 891a b c + 486a b c +--R + +--R 8 +--R - 81b +--R * +--R 14 +--R e +--R + +--R 3 4 2 3 3 5 2 +--R - 1620a b c + 5670a b c - 4050a b c +--R + +--R 7 +--R 810b c +--R * +--R 13 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 1620a c - 14580a b c + 14580a b c +--R + +--R 6 2 +--R - 3645b c +--R * +--R 2 12 +--R d e +--R + +--R 2 5 3 4 5 3 3 11 +--R (17820a b c - 29160a b c + 9720b c )d e +--R + +--R 2 6 2 5 4 4 4 10 +--R (- 8910a c + 34830a b c - 17010b c )d e +--R + +--R 6 3 5 5 9 +--R (- 24300a b c + 20250b c )d e +--R + +--R 7 2 6 6 8 7 7 7 +--R (8100a c - 16200b c )d e + 8100b c d e +--R + +--R 8 8 6 +--R - 2025c d e +--R / +--R 11 10 2 20 +--R (64a c - 16a b )e +--R + +--R 10 9 3 19 +--R (- 640a b c + 160a b )d e +--R + +--R 10 2 9 2 8 4 2 18 +--R (640a c + 2720a b c - 720a b )d e +--R + +--R 9 2 8 3 7 5 3 17 +--R (- 5760a b c - 6240a b c + 1920a b )d e +--R + +--R 9 3 8 2 2 7 4 +--R 2880a c + 22320a b c + 7680a b c +--R + +--R 6 6 +--R - 3360a b +--R * +--R 4 16 +--R d e +--R + +--R 8 3 7 3 2 6 5 +--R - 23040a b c - 48000a b c - 2688a b c +--R + +--R 5 7 +--R 4032a b +--R * +--R 5 15 +--R d e +--R + +--R 8 4 7 2 3 6 4 2 +--R 7680a c + 78720a b c + 60480a b c +--R + +--R 5 6 4 8 +--R - 6720a b c - 3360a b +--R * +--R 6 14 +--R d e +--R + +--R 7 4 6 3 3 5 5 2 +--R - 53760a b c - 147840a b c - 40320a b c +--R + +--R 4 7 3 9 +--R 12480a b c + 1920a b +--R * +--R 7 13 +--R d e +--R + +--R 7 5 6 2 4 5 4 3 +--R 13440a c + 157920a b c + 161280a b c +--R + +--R 4 6 2 3 8 2 10 +--R 3360a b c - 10560a b c - 720a b +--R * +--R 8 12 +--R d e +--R + +--R 6 5 5 3 4 4 5 3 +--R - 80640a b c - 248640a b c - 94080a b c +--R + +--R 3 7 2 2 9 11 +--R 17280a b c + 5120a b c + 160a b +--R * +--R 9 11 +--R d e +--R + +--R 6 6 5 2 5 4 4 4 +--R 16128a c + 197568a b c + 218400a b c +--R + +--R 3 6 3 2 8 2 10 12 +--R 13440a b c - 14400a b c - 1376a b c - 16b +--R * +--R 10 10 +--R d e +--R + +--R 5 6 4 3 5 3 5 4 +--R - 80640a b c - 248640a b c - 94080a b c +--R + +--R 2 7 3 9 2 11 +--R 17280a b c + 5120a b c + 160b c +--R * +--R 11 9 +--R d e +--R + +--R 5 7 4 2 6 3 4 5 +--R 13440a c + 157920a b c + 161280a b c +--R + +--R 2 6 4 8 3 10 2 +--R 3360a b c - 10560a b c - 720b c +--R * +--R 12 8 +--R d e +--R + +--R 4 7 3 3 6 2 5 5 +--R - 53760a b c - 147840a b c - 40320a b c +--R + +--R 7 4 9 3 +--R 12480a b c + 1920b c +--R * +--R 13 7 +--R d e +--R + +--R 4 8 3 2 7 2 4 6 +--R 7680a c + 78720a b c + 60480a b c +--R + +--R 6 5 8 4 +--R - 6720a b c - 3360b c +--R * +--R 14 6 +--R d e +--R + +--R 3 8 2 3 7 5 6 +--R - 23040a b c - 48000a b c - 2688a b c +--R + +--R 7 5 +--R 4032b c +--R * +--R 15 5 +--R d e +--R + +--R 3 9 2 2 8 4 7 +--R 2880a c + 22320a b c + 7680a b c +--R + +--R 6 6 +--R - 3360b c +--R * +--R 16 4 +--R d e +--R + +--R 2 9 3 8 5 7 17 3 +--R (- 5760a b c - 6240a b c + 1920b c )d e +--R + +--R 2 10 2 9 4 8 18 2 +--R (640a c + 2720a b c - 720b c )d e +--R + +--R 10 3 9 19 +--R (- 640a b c + 160b c )d e +--R + +--R 11 2 10 20 +--R (64a c - 16b c )d +--R + +--R 2 2 3 5 7 +--R (45a b c - 45a b c + 9b )e +--R + +--R 2 3 2 2 4 6 +--R (- 90a c + 180a b c - 45b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (- 270a b c + 90b c )d e + (180a c - 90b c )d e +--R + +--R 4 4 3 5 5 2 +--R 45b c d e - 18c d e +--R / +--R 6 5 2 10 5 4 3 9 +--R (8a c - 2a b )e + (- 40a b c + 10a b )d e +--R + +--R 5 2 4 2 3 4 2 8 +--R (40a c + 70a b c - 20a b )d e +--R + +--R 4 2 3 3 2 5 3 7 +--R (- 160a b c - 40a b c + 20a b )d e +--R + +--R 4 3 3 2 2 2 4 6 4 6 +--R (80a c + 220a b c - 20a b c - 10a b )d e +--R + +--R 3 3 2 3 2 5 7 5 5 +--R (- 240a b c - 100a b c + 32a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 6 4 +--R (80a c + 220a b c - 20a b c - 10b c)d e +--R + +--R 2 4 3 3 5 2 7 3 +--R (- 160a b c - 40a b c + 20b c )d e +--R + +--R 2 5 2 4 4 3 8 2 +--R (40a c + 70a b c - 20b c )d e +--R + +--R 5 3 4 9 6 2 5 10 +--R (- 40a b c + 10b c )d e + (8a c - 2b c )d +--R + +--R 2 5 2 4 4 3 8 5 3 4 7 +--R (54a c - 162a b c + 54b c )e + (540a b c - 270b c )d e +--R + +--R 6 2 5 2 6 6 3 5 7 4 4 +--R (- 540a c + 540b c )d e - 540b c d e + 270c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 6b e + 12c d e )\|- 4a c + b + (- 12a c + 6b )e - 12b c d e +--R + +--R 2 2 +--R 12c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 6b e + 12c d e )\|- 4a c + b + (12a c - 6b )e + 12b c d e +--R + +--R 2 2 +--R - 12c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 4 3 2 2 2 3 2 4 +-+ +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d )\|2 +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 819 + +--S 820 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 845 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 821 + +--S 822 of 845 +r0:=-1/2*(d+e*x)^(7/2)/(a+b*x+c*x^2)^2-7/4*e*(d+e*x)^(3/2)*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+7/4*e^2*(2*c*d-b*e)*_ + sqrt(d+e*x)/(c*(b^2-4*a*c))+7/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c^2*d^2-b^2*e^2-2*c*e*_ + (b*d-3*a*e))+(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))/_ + sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))+7/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(e*(2*c^2*d^2-b^2*e^2-2*c*e*_ + (b*d-3*a*e))-(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))/_ + sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(2*c*d-e*_ + (b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 42a c + 7b c )e + 14b c d e - 14c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 84a b c + 14b c)e + 28b c d e - 28b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 84a c - 28a b c + 7b )e + (28a b c + 14b c)d e +--R + +--R 3 2 2 2 2 +--R (- 28a c - 14b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 84a b c + 14a b )e + 28a b c d e - 28a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 42a c + 7a b )e + 14a b c d e - 14a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (- 56a b c + 7b c )e + (112a c + 14b c )d e - 84b c d e +--R + +--R 5 3 +--R 56c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (- 112a b c + 14b c)e + (224a b c + 28b c )d e - 168b c d e +--R + +--R 4 3 +--R 112b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 +--R (- 112a b c - 42a b c + 7b )e +--R + +--R 2 3 2 2 4 3 3 3 2 2 2 +--R (224a c + 140a b c + 14b c)d e + (- 168a b c - 84b c )d e +--R + +--R 4 2 3 3 +--R (112a c + 56b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 +--R (- 112a b c + 14a b )e + (224a b c + 28a b c)d e +--R + +--R 2 2 2 2 3 3 +--R - 168a b c d e + 112a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 +--R (- 56a b c + 7a b )e + (112a c + 14a b c)d e - 84a b c d e +--R + +--R 2 3 3 +--R 56a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 42a c + 7b c )e + 14b c d e - 14c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 84a b c + 14b c)e + 28b c d e - 28b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 84a c - 28a b c + 7b )e + (28a b c + 14b c)d e +--R + +--R 3 2 2 2 2 +--R (- 28a c - 14b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 84a b c + 14a b )e + 28a b c d e - 28a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 42a c + 7a b )e + 14a b c d e - 14a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (56a b c - 7b c )e + (- 112a c - 14b c )d e + 84b c d e +--R + +--R 5 3 +--R - 56c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (112a b c - 14b c)e + (- 224a b c - 28b c )d e + 168b c d e +--R + +--R 4 3 +--R - 112b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 +--R (112a b c + 42a b c - 7b )e +--R + +--R 2 3 2 2 4 3 3 3 2 2 2 +--R (- 224a c - 140a b c - 14b c)d e + (168a b c + 84b c )d e +--R + +--R 4 2 3 3 +--R (- 112a c - 56b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 +--R (112a b c - 14a b )e + (- 224a b c - 28a b c)d e +--R + +--R 2 2 2 2 3 3 +--R 168a b c d e - 112a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 +--R (56a b c - 7a b )e + (- 112a c - 14a b c)d e + 84a b c d e +--R + +--R 2 3 3 +--R - 56a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 22a c + 9b c)e - 14b c d e + 14c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 7a b c + 7b )e + (- 52a c - 8b c)d e + 21b c d e)x +--R + +--R 2 2 3 2 2 2 2 +--R ((- 14a c + 14a b )e - 42a b c d e + (- 10a c + 13b c)d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R 7a b e - 28a c d e + 7a b c d e + (- 8a c + 2b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-------+ | | 2 +--R \|2 \|- 4a c + b \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 4 2 3 4 3 3 2 3 2 3 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c )x + (32a c + 8a b c - 4b c)x +--R + +--R 2 2 3 3 2 2 2 +--R (32a b c - 8a b c)x + 16a c - 4a b c +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R \|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 822 + +--S 823 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 4 3 3 2 3 +--R (8a c - 2b c )x + (16a b c - 4b c )x +--R + +--R 2 3 2 2 4 2 2 2 3 3 2 2 2 +--R (16a c + 4a b c - 2b c)x + (16a b c - 4a b c)x + 8a c - 2a b c +--R * +--R ROOT +--R 3 6 2 2 5 4 4 6 3 +--R (4096a c - 3072a b c + 768a b c - 64b c ) +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 3 3 11 +--R (- 216090a c - 36015b c )d e + 120050b c d e +--R + +--R 4 4 10 +--R - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c 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- 9408a b c - 588a b c + 294b c)d e +--R + +--R 2 4 3 3 5 2 2 7 +--R (- 23520a b c + 11760a b c - 1470b c )d e +--R + +--R 2 5 2 4 4 3 3 6 +--R (15680a c - 7840a b c + 980b c )d e +--R * +--R ROOT +--R 3 6 2 2 5 4 4 6 3 +--R (4096a c - 3072a b c + 768a b c - 64b c ) +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 +--R (- 216090a c - 36015b c )d e +--R + +--R 3 3 11 4 4 10 +--R 120050b c d e - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 3 5 7 +--R (2940a b c - 735a b c + 49b )e +--R + +--R 2 3 2 2 4 6 +--R (- 5880a c - 1470a b c + 245b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (8820a b c - 245b c )d e + (- 5880a c - 2450b c )d e +--R + +--R 4 4 3 5 5 2 +--R 3920b c d e - 1568c d e +--R / +--R 3 6 2 2 5 4 4 6 3 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 3 2 2 2 4 12 +--R (111132a c - 27783a b c + 1715a b )e +--R + +--R 2 2 3 5 11 +--R (- 222264a b c + 41846a b c - 1715b )d e +--R + +--R 2 3 2 2 4 2 10 +--R (222264a c + 96726a b c - 12348b c)d e +--R + +--R 3 3 2 3 9 4 2 3 4 8 +--R (- 277144a b c + 686b c )d e + (138572a c + 68257b c )d e +--R + +--R 4 5 7 5 6 6 +--R - 82320b c d e + 27440c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 +-+ | 2 +-+ | | 2 +--R (- 8a c + 2b c)\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 6 2 2 5 4 4 6 3 +--R (- 4096a c + 3072a b c - 768a b c + 64b c ) +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 3 3 11 +--R (- 216090a c - 36015b c )d e + 120050b c d e +--R + +--R 4 4 10 +--R - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 3 5 7 +--R (2940a b c - 735a b c + 49b )e +--R + +--R 2 3 2 2 4 6 +--R (- 5880a c - 1470a b c + 245b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (8820a b c - 245b c )d e + (- 5880a c - 2450b c )d e +--R + +--R 4 4 3 5 5 2 +--R 3920b c d e - 1568c d e +--R / +--R 3 6 2 2 5 4 4 6 3 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 7 3 2 6 2 4 5 6 4 +--R 98304a c - 81920a b c + 24576a b c - 3072a b c +--R + +--R 8 3 +--R 128b c +--R * +--R 2 +--R e +--R + +--R 3 7 2 3 6 5 5 7 4 +--R (- 65536a b c + 49152a b c - 12288a b c + 1024b c )d e +--R + +--R 3 8 2 2 7 4 6 6 5 2 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 3 3 11 +--R (- 216090a c - 36015b c )d e + 120050b c d e +--R + +--R 4 4 10 +--R - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 3 2 3 2 5 7 9 +--R (14112a b c - 8624a b c + 1666a b c - 98b )e +--R + +--R 3 4 2 2 3 4 2 6 8 +--R (- 28224a c + 9408a b c + 588a b c - 294b c)d e +--R + +--R 2 4 3 3 5 2 2 7 +--R (23520a b c - 11760a b c + 1470b c )d e +--R + +--R 2 5 2 4 4 3 3 6 +--R (- 15680a c + 7840a b c - 980b c )d e +--R * +--R ROOT +--R 3 6 2 2 5 4 4 6 3 +--R (- 4096a c + 3072a b c - 768a b c + 64b c ) +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 +--R (- 216090a c - 36015b c )d e +--R + +--R 3 3 11 4 4 10 +--R 120050b c d e - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 3 5 7 +--R (2940a b c - 735a b c + 49b )e +--R + +--R 2 3 2 2 4 6 +--R (- 5880a c - 1470a b c + 245b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (8820a b c - 245b c )d e + (- 5880a c - 2450b c )d e +--R + +--R 4 4 3 5 5 2 +--R 3920b c d e - 1568c d e +--R / +--R 3 6 2 2 5 4 4 6 3 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 3 2 2 2 4 12 +--R (111132a c - 27783a b c + 1715a b )e +--R + +--R 2 2 3 5 11 +--R (- 222264a b c + 41846a b c - 1715b )d e +--R + +--R 2 3 2 2 4 2 10 +--R (222264a c + 96726a b c - 12348b c)d e +--R + +--R 3 3 2 3 9 4 2 3 4 8 +--R (- 277144a b c + 686b c )d e + (138572a c + 68257b c )d e +--R + +--R 4 5 7 5 6 6 +--R - 82320b c d e + 27440c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 +-+ | 2 +-+ | | 2 +--R (8a c - 2b c)\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 6 2 2 5 4 4 6 3 +--R (- 4096a c + 3072a b c - 768a b c + 64b c ) +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 3 3 11 +--R (- 216090a c - 36015b c )d e + 120050b c d e +--R + +--R 4 4 10 +--R - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 3 5 7 +--R (2940a b c - 735a b c + 49b )e +--R + +--R 2 3 2 2 4 6 +--R (- 5880a c - 1470a b c + 245b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (8820a b c - 245b c )d e + (- 5880a c - 2450b c )d e +--R + +--R 4 4 3 5 5 2 +--R 3920b c d e - 1568c d e +--R / +--R 3 6 2 2 5 4 4 6 3 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 7 3 2 6 2 4 5 6 4 +--R - 98304a c + 81920a b c - 24576a b c + 3072a b c +--R + +--R 8 3 +--R - 128b c +--R * +--R 2 +--R e +--R + +--R 3 7 2 3 6 5 5 7 4 +--R (65536a b c - 49152a b c + 12288a b c - 1024b c )d e +--R + +--R 3 8 2 2 7 4 6 6 5 2 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 3 3 11 +--R (- 216090a c - 36015b c )d e + 120050b c d e +--R + +--R 4 4 10 +--R - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 3 2 3 2 5 7 9 +--R (- 14112a b c + 8624a b c - 1666a b c + 98b )e +--R + +--R 3 4 2 2 3 4 2 6 8 +--R (28224a c - 9408a b c - 588a b c + 294b c)d e +--R + +--R 2 4 3 3 5 2 2 7 +--R (- 23520a b c + 11760a b c - 1470b c )d e +--R + +--R 2 5 2 4 4 3 3 6 +--R (15680a c - 7840a b c + 980b c )d e +--R * +--R ROOT +--R 3 6 2 2 5 4 4 6 3 +--R (- 4096a c + 3072a b c - 768a b c + 64b c ) +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 +--R (- 216090a c - 36015b c )d e +--R + +--R 3 3 11 4 4 10 +--R 120050b c d e - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 3 5 7 +--R (2940a b c - 735a b c + 49b )e +--R + +--R 2 3 2 2 4 6 +--R (- 5880a c - 1470a b c + 245b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (8820a b c - 245b c )d e + (- 5880a c - 2450b c )d e +--R + +--R 4 4 3 5 5 2 +--R 3920b c d e - 1568c d e +--R / +--R 3 6 2 2 5 4 4 6 3 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 3 2 2 2 4 12 +--R (111132a c - 27783a b c + 1715a b )e +--R + +--R 2 2 3 5 11 +--R (- 222264a b c + 41846a b c - 1715b )d e +--R + +--R 2 3 2 2 4 2 10 +--R (222264a c + 96726a b c - 12348b c)d e +--R + +--R 3 3 2 3 9 4 2 3 4 8 +--R (- 277144a b c + 686b c )d e + (138572a c + 68257b c )d e +--R + +--R 4 5 7 5 6 6 +--R - 82320b c d e + 27440c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 +-+ | 2 +-+ | | 2 +--R (- 8a c + 2b c)\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 6 2 2 5 4 4 6 3 +--R (4096a c - 3072a b c + 768a b c - 64b c ) +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 3 3 11 +--R (- 216090a c - 36015b c )d e + 120050b c d e +--R + +--R 4 4 10 +--R - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 3 5 7 +--R (2940a b c - 735a b c + 49b )e +--R + +--R 2 3 2 2 4 6 +--R (- 5880a c - 1470a b c + 245b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (8820a b c - 245b c )d e + (- 5880a c - 2450b c )d e +--R + +--R 4 4 3 5 5 2 +--R 3920b c d e - 1568c d e +--R / +--R 3 6 2 2 5 4 4 6 3 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 4 7 3 2 6 2 4 5 6 4 +--R - 98304a c + 81920a b c - 24576a b c + 3072a b c +--R + +--R 8 3 +--R - 128b c +--R * +--R 2 +--R e +--R + +--R 3 7 2 3 6 5 5 7 4 +--R (65536a b c - 49152a b c + 12288a b c - 1024b c )d e +--R + +--R 3 8 2 2 7 4 6 6 5 2 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 3 3 11 +--R (- 216090a c - 36015b c )d e + 120050b c d e +--R + +--R 4 4 10 +--R - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 3 2 3 2 5 7 9 +--R (14112a b c - 8624a b c + 1666a b c - 98b )e +--R + +--R 3 4 2 2 3 4 2 6 8 +--R (- 28224a c + 9408a b c + 588a b c - 294b c)d e +--R + +--R 2 4 3 3 5 2 2 7 +--R (23520a b c - 11760a b c + 1470b c )d e +--R + +--R 2 5 2 4 4 3 3 6 +--R (- 15680a c + 7840a b c - 980b c )d e +--R * +--R ROOT +--R 3 6 2 2 5 4 4 6 3 +--R (4096a c - 3072a b c + 768a b c - 64b c ) +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 194481a c + 43218a b c - 2401b )e +--R + +--R 2 3 13 +--R (216090a b c - 24010b c)d e +--R + +--R 3 2 2 2 12 +--R (- 216090a c - 36015b c )d e +--R + +--R 3 3 11 4 4 10 +--R 120050b c d e - 60025c d e +--R / +--R 3 9 2 2 8 4 7 6 6 +--R 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 3 5 7 +--R (2940a b c - 735a b c + 49b )e +--R + +--R 2 3 2 2 4 6 +--R (- 5880a c - 1470a b c + 245b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 +--R (8820a b c - 245b c )d e + (- 5880a c - 2450b c )d e +--R + +--R 4 4 3 5 5 2 +--R 3920b c d e - 1568c d e +--R / +--R 3 6 2 2 5 4 4 6 3 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 3 2 2 2 4 12 +--R (111132a c - 27783a b c + 1715a b )e +--R + +--R 2 2 3 5 11 +--R (- 222264a b c + 41846a b c - 1715b )d e +--R + +--R 2 3 2 2 4 2 10 +--R (222264a c + 96726a b c - 12348b c)d e +--R + +--R 3 3 2 3 9 4 2 3 4 8 +--R (- 277144a b c + 686b c )d e + (138572a c + 68257b c )d e +--R + +--R 4 5 7 5 6 6 +--R - 82320b c d e + 27440c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((42a c - 7b )e - 14b c d e + 14c d e )\|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (56a b c - 7b )e + (- 112a c - 14b c)d e + 84b c d e - 56c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((42a c - 7b )e - 14b c d e + 14c d e )\|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (- 56a b c + 7b )e + (112a c + 14b c)d e - 84b c d e + 56c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 +-+ | 2 +-+ | | 2 +--R (16a c - 4b c)\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 824 + +--S 825 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 845 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 826 + +--S 827 of 845 +r0:=-1/2*(d+e*x)^(5/2)/(a+b*x+c*x^2)^2-5/4*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + sqrt(d+e*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+5/4*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))/sqrt(b^2-4*a*c))/((b^2-4*a*c)*_ + sqrt(2)*sqrt(c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-5/4*e*_ + atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ + (8*c^2*d^2+b*e^2*(b+sqrt(b^2-4*a*c))-2*c*e*(4*b*d-2*a*e+d*_ + sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(c)*sqrt(2*c*d-e*_ + (b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 3 2 4 2 3 2 2 3 +--R (5b c e - 10c d e )x + (10b c e - 20b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((10a b c + 5b )e + (- 20a c - 10b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (10a b e - 20a b c d e )x + 5a b e - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((20a c + 5b c )e - 40b c d e + 40c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((40a b c + 10b c)e - 80b c d e + 80b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (40a c + 30a b c + 5b )e + (- 80a b c - 40b c)d e +--R + +--R 3 2 2 2 +--R (80a c + 40b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((40a b c + 10a b )e - 80a b c d e + 80a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (20a c + 5a b )e - 40a b c d e + 40a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 3 2 4 2 3 2 2 3 +--R (5b c e - 10c d e )x + (10b c e - 20b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((10a b c + 5b )e + (- 20a c - 10b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (10a b e - 20a b c d e )x + 5a b e - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((- 20a c - 5b c )e + 40b c d e - 40c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((- 40a b c - 10b c)e + 80b c d e - 80b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (- 40a c - 30a b c - 5b )e + (80a b c + 40b c)d e +--R + +--R 3 2 2 2 +--R (- 80a c - 40b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((- 40a b c - 10a b )e + 80a b c d e - 80a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (- 20a c - 5a b )e + 40a b c d e - 40a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 2 2 2 +--R (- 5b c e + 10c d e)x + ((- 18a c - 3b )e + 15b c d e)x +--R + +--R 2 2 2 2 +--R (- 15a b e + (- 6a c + 9b )d e)x - 10a e + 5a b d e +--R + +--R 2 2 +--R (- 8a c + 2b )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-------+ | | 2 +--R \|2 \|- 4a c + b \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c)x + (32a c + 8a b c - 4b )x +--R + +--R 2 3 3 2 2 +--R (32a b c - 8a b )x + 16a c - 4a b +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R \|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 827 + +--S 828 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (32768a b c - 24576a b c + 6144a b c - 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (1600a c - 800a b c + 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R 3 2 2 4 2 3 3 +--R (- 8a c + 2b c )x + (- 16a b c + 4b c)x +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (- 16a c - 4a b c + 2b )x + (- 16a b c + 4a b )x - 8a c + 2a b +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (32768a b c - 24576a b c + 6144a b c - 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (- 1600a c + 800a b c - 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (- 32768a b c + 24576a b c - 6144a b c + 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (1600a c - 800a b c + 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R 3 2 2 4 2 3 3 +--R (- 8a c + 2b c )x + (- 16a b c + 4b c)x +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (- 16a c - 4a b c + 2b )x + (- 16a b c + 4a b )x - 8a c + 2a b +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (- 32768a b c + 24576a b c - 6144a b c + 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (- 1600a c + 800a b c - 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R 2 2 3 2 2 2 +--R (- 5b c e + 10c d e)x + ((- 18a c - 3b )e + 15b c d e)x +--R + +--R 2 2 2 2 +--R (- 15a b e + (- 6a c + 9b )d e)x - 10a e + 5a b d e +--R + +--R 2 2 +--R (- 8a c + 2b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c)x + (32a c + 8a b c - 4b )x +--R + +--R 2 3 3 2 2 +--R (32a b c - 8a b )x + 16a c - 4a b +--R Type: Union(Expression(Integer),...) +--E 828 + +--S 829 of 845 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 +-+ | | 2 +--R (8a c - 2b )\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (32768a b c - 24576a b c + 6144a b c - 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (1600a c - 800a b c + 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 +-+ | | 2 +--R (- 8a c + 2b )\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (32768a b c - 24576a b c + 6144a b c - 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (- 1600a c + 800a b c - 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 +-+ | | 2 +--R (8a c - 2b )\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (- 32768a b c + 24576a b c - 6144a b c + 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (1600a c - 800a b c + 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (- 4096a c + 3072a b c - 768a b c + 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 +-+ | | 2 +--R (- 8a c + 2b )\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 2 2 3 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e + 1200b c d e +--R + +--R 3 3 2 +--R - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 3 4 2 3 3 5 2 7 +--R (- 32768a b c + 24576a b c - 6144a b c + 512b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 2 2 2 4 6 +--R (- 1600a c + 800a b c - 100b )e +--R * +--R ROOT +--R 3 4 2 2 3 4 2 6 +--R (4096a c - 3072a b c + 768a b c - 64b c) +--R * +--R +----------------------------------------------------+ +--R | 10 +--R | 625e +--R |- -------------------------------------------------- +--R | 3 5 2 2 4 4 3 6 2 +--R \| 262144a c - 196608a b c + 49152a b c - 4096b c +--R + +--R 3 5 2 2 4 +--R (300a b c + 25b )e + (- 600a c - 450b c)d e +--R + +--R 2 2 3 3 3 2 +--R 1200b c d e - 800c d e +--R / +--R 3 4 2 2 3 4 2 6 +--R 2048a c - 1536a b c + 384a b c - 32b c +--R + +--R 2 8 7 2 2 6 +-------+ +--R ((500a c + 375b )e - 2000b c d e + 2000c d e )\|e x + d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 5b e + 10c d e )\|- 4a c + b + (- 20a c - 5b )e + 40b c d e +--R + +--R 2 2 +--R - 40c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- 5b e + 10c d e )\|- 4a c + b + (20a c + 5b )e - 40b c d e +--R + +--R 2 2 +--R 40c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 +-+ | | 2 +--R (16a c - 4b )\|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 829 + +--S 830 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 845 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 831 + +--S 832 of 845 +r0:=-1/2*(d+e*x)^(3/2)/(a+b*x+c*x^2)^2-3/4*e*(b+2*c*x)*sqrt(d+e*x)/_ + ((b^2-4*a*c)*(a+b*x+c*x^2))+3/2*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(4*c*d-e*(2*b-_ + sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b-_ + sqrt(b^2-4*a*c))))-3/2*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(4*c*d-e*(2*b+sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 2 4 2 3 2 2 2 2 2 2 +--R (- 6c e x - 12b c e x + (- 12a c - 6b )e x - 12a b e x - 6a e ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 4 2 2 2 3 +--R (- 12b c e + 24c d e)x + (- 24b c e + 48b c d e)x +--R + +--R 3 2 2 2 2 +--R ((- 24a b c - 12b )e + (48a c + 24b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 24a b e + 48a b c d e)x - 12a b e + 24a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 4 2 3 2 2 2 2 2 2 +--R (- 6c e x - 12b c e x + (- 12a c - 6b )e x - 12a b e x - 6a e ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 4 2 2 2 3 +--R (12b c e - 24c d e)x + (24b c e - 48b c d e)x +--R + +--R 3 2 2 2 2 +--R ((24a b c + 12b )e + (- 48a c - 24b c)d e)x +--R + +--R 2 2 2 2 2 +--R (24a b e - 48a b c d e)x + 12a b e - 24a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 +--R (6c e x + 9b c e x + (- 2a c + 5b )e x + 3a b e + (- 8a c + 2b )d) +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c)x + (32a c + 8a b c - 4b )x +--R + +--R 2 3 3 2 2 +--R (32a b c - 8a b )x + 16a c - 4a b +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 832 + +--S 833 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 4096a b c + 3072a b c - 768a b c + 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (4096a c - 3072a b c + 768a b c - 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 6 2 4 +--R (262144a c - 196608a b c + 49152a b c - 4096b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e + 432b c d e +--R + +--R 3 3 2 +--R - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R * +--R log +--R 5 4 4 2 3 2 6 8 4 +--R (32768a c - 16384a b c + 1024a b c - 128a b )e +--R + +--R 4 4 3 3 3 2 5 2 9 3 +--R (- 98304a b c + 65536a b c - 12288a b c + 128b )d e +--R + +--R 4 5 2 4 3 6 2 8 2 2 +--R (98304a c - 36864a b c + 12288a b c - 1152b c)d e +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (- 131072a b c + 98304a b c - 24576a b c + 2048b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 4 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 2 2 3 5 7 +--R (- 288a b c + 144a b c - 18b )e +--R + +--R 2 3 2 2 4 6 +--R (576a c - 288a b c + 36b c)d e +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 4096a b c + 3072a b c - 768a b c + 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (4096a c - 3072a b c + 768a b c - 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 +--R - 524288a b c + 393216a b c +--R + +--R 2 5 7 +--R - 98304a b c + 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 +--R - 524288a b c + 393216a b c +--R + +--R 5 2 7 +--R - 98304a b c + 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 3 5 2 2 4 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e +--R + +--R 2 2 3 3 3 2 +--R 432b c d e - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R + +--R 2 2 8 2 7 3 2 6 +-------+ +--R ((108a c + 81b c)e - 432b c d e + 432c d e )\|e x + d +--R + +--R 3 2 2 4 2 3 3 +--R (- 8a c + 2b c )x + (- 16a b c + 4b c)x +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (- 16a c - 4a b c + 2b )x + (- 16a b c + 4a b )x - 8a c + 2a b +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (4096a b c - 3072a b c + 768a b c - 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 6 2 4 +--R (262144a c - 196608a b c + 49152a b c - 4096b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e + 432b c d e +--R + +--R 3 3 2 +--R - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R * +--R log +--R 5 4 4 2 3 2 6 8 4 +--R (32768a c - 16384a b c + 1024a b c - 128a b )e +--R + +--R 4 4 3 3 3 2 5 2 9 3 +--R (- 98304a b c + 65536a b c - 12288a b c + 128b )d e +--R + +--R 4 5 2 4 3 6 2 8 2 2 +--R (98304a c - 36864a b c + 12288a b c - 1152b c)d e +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (- 131072a b c + 98304a b c - 24576a b c + 2048b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 4 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 2 2 3 5 7 +--R (288a b c - 144a b c + 18b )e +--R + +--R 2 3 2 2 4 6 +--R (- 576a c + 288a b c - 36b c)d e +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (4096a b c - 3072a b c + 768a b c - 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 +--R - 524288a b c + 393216a b c +--R + +--R 2 5 7 +--R - 98304a b c + 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 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98304a b c - 24576a b c + 2048b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 4 +--R (65536a c - 49152a b c + 12288a b c - 1024b c )d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 2 2 3 5 7 +--R (288a b c - 144a b c + 18b )e +--R + +--R 2 3 2 2 4 6 +--R (- 576a c + 288a b c - 36b c)d e +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (4096a b c - 3072a b c + 768a b c - 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 +--R - 524288a b c + 393216a b c +--R + +--R 2 5 7 +--R - 98304a b c + 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 +--R - 524288a b c + 393216a b c +--R + +--R 5 2 7 +--R - 98304a b c + 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 3 5 2 2 4 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e +--R + +--R 2 2 3 3 3 2 +--R 432b c d e - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R + +--R 2 2 8 2 7 3 2 6 +-------+ +--R ((108a c + 81b c)e - 432b c d e + 432c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 | | 2 +--R (4a c - b )\|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (4096a b c - 3072a b c + 768a b c - 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 6 2 4 +--R (262144a c - 196608a b c + 49152a b c - 4096b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e + 432b c d e +--R + +--R 3 3 2 +--R - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 5 4 4 2 3 2 6 8 4 +--R (- 32768a c + 16384a b c - 1024a b c + 128a b )e +--R + +--R 4 4 3 3 3 2 5 2 9 3 +--R (98304a b c - 65536a b c + 12288a b c - 128b )d e +--R + +--R 4 5 2 4 3 6 2 8 2 2 +--R (- 98304a c + 36864a b c - 12288a b c + 1152b c)d e +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (131072a b c - 98304a b c + 24576a b c - 2048b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 4 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 2 2 3 5 7 +--R (- 288a b c + 144a b c - 18b )e +--R + +--R 2 3 2 2 4 6 +--R (576a c - 288a b c + 36b c)d e +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (4096a b c - 3072a b c + 768a b c - 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 4096a c + 3072a b c - 768a b c + 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 +--R - 524288a b c + 393216a b c +--R + +--R 2 5 7 +--R - 98304a b c + 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 +--R - 524288a b c + 393216a b c +--R + +--R 5 2 7 +--R - 98304a b c + 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 3 5 2 2 4 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e +--R + +--R 2 2 3 3 3 2 +--R 432b c d e - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R + +--R 2 2 8 2 7 3 2 6 +-------+ +--R ((108a c + 81b c)e - 432b c d e + 432c d e )\|e x + d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 | | 2 +--R (- 4a c + b )\|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 4096a b c + 3072a b c - 768a b c + 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (4096a c - 3072a b c + 768a b c - 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 6 2 4 +--R (262144a c - 196608a b c + 49152a b c - 4096b c )d +--R + +--R 3 5 2 2 4 2 2 3 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e + 432b c d e +--R + +--R 3 3 2 +--R - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R * +--R log +--R 5 4 4 2 3 2 6 8 4 +--R (- 32768a c + 16384a b c - 1024a b c + 128a b )e +--R + +--R 4 4 3 3 3 2 5 2 9 3 +--R (98304a b c - 65536a b c + 12288a b c - 128b )d e +--R + +--R 4 5 2 4 3 6 2 8 2 2 +--R (- 98304a c + 36864a b c - 12288a b c + 1152b c)d e +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (131072a b c - 98304a b c + 24576a b c - 2048b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 4 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 2 5 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 5 2 +--R - 524288a b c + 393216a b c - 98304a b c +--R + +--R 7 +--R 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 2 2 3 5 7 +--R (288a b c - 144a b c + 18b )e +--R + +--R 2 3 2 2 4 6 +--R (- 576a c + 288a b c - 36b c)d e +--R * +--R ROOT +--R 4 3 3 2 2 2 4 6 2 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 4096a b c + 3072a b c - 768a b c + 64b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (4096a c - 3072a b c + 768a b c - 64b c)d +--R * +--R ROOT +--R - +--R 10 +--R 81e +--R / +--R 5 3 4 2 2 3 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 2 6 +--R - 4096a b +--R * +--R 4 +--R e +--R + +--R 4 3 3 3 2 +--R - 524288a b c + 393216a b c +--R + +--R 2 5 7 +--R - 98304a b c + 8192a b +--R * +--R 3 +--R d e +--R + +--R 4 4 3 2 3 2 4 2 +--R 524288a c - 131072a b c - 98304a b c +--R + +--R 6 8 +--R 40960a b c - 4096b +--R * +--R 2 2 +--R d e +--R + +--R 3 4 2 3 3 +--R - 524288a b c + 393216a b c +--R + +--R 5 2 7 +--R - 98304a b c + 8192b c +--R * +--R 3 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 2 +--R - 4096b c +--R * +--R 4 +--R d +--R + +--R 3 5 2 2 4 +--R (108a b c + 9b )e + (- 216a c - 162b c)d e +--R + +--R 2 2 3 3 3 2 +--R 432b c d e - 288c d e +--R / +--R 4 3 3 2 2 2 4 6 2 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 3 3 2 3 2 5 7 +--R (- 2048a b c + 1536a b c - 384a b c + 32b )d e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (2048a c - 1536a b c + 384a b c - 32b c)d +--R + +--R 2 2 8 2 7 3 2 6 +-------+ +--R ((108a c + 81b c)e - 432b c d e + 432c d e )\|e x + d +--R + +--R +-----------+ +--R 2 | 2 2 +-+ +--R (3e \|- 4a c + b + 6b e - 12c d e)\|c +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 | 2 2 +-+ +--R (3e \|- 4a c + b - 6b e + 12c d e)\|c +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 +-+ | 2 | | 2 +--R (8a c - 2b )\|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 834 + +--S 835 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 845 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R +-------+ +--R (2c x + b)\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 836 + +--S 837 of 845 +r0:=-1/2*sqrt(d+e*x)/(a+b*x+c*x^2)^2-1/4*e*(b*c*d-b^2*e+2*a*c*e+_ + c*(2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ + (a+b*x+c*x^2))+1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^2*d^2-b*e^2*(b+sqrt(b^2-4*a*c))-_ + 2*c*e*(4*b*d-6*a*e-d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-_ + e*(b*d-a*e))*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-_ + 1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^2*d^2-b*e^2*(b-sqrt(b^2-4*a*c))-_ + 2*c*e*(4*b*d-6*a*e+d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-_ + b*d*e+a*e^2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 3 2 4 2 3 2 2 3 +--R (b c e - 2c d e )x + (2b c e - 4b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((2a b c + b )e + (- 4a c - 2b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (2a b e - 4a b c d e )x + a b e - 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((12a c - b c )e - 8b c d e + 8c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((24a b c - 2b c)e - 16b c d e + 16b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (24a c + 10a b c - b )e + (- 16a b c - 8b c)d e +--R + +--R 3 2 2 2 +--R (16a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((24a b c - 2a b )e - 16a b c d e + 16a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (12a c - a b )e - 8a b c d e + 8a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 3 2 4 2 3 2 2 3 +--R (b c e - 2c d e )x + (2b c e - 4b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((2a b c + b )e + (- 4a c - 2b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (2a b e - 4a b c d e )x + a b e - 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((- 12a c + b c )e + 8b c d e - 8c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((- 24a b c + 2b c)e + 16b c d e - 16b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (- 24a c - 10a b c + b )e + (16a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 16a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((- 24a b c + 2a b )e + 16a b c d e - 16a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (- 12a c + a b )e + 8a b c d e - 8a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 3 2 2 2 2 2 +--R (- b c e + 2c d e)x + ((2a c - 2b c)e + 3b c d e)x +--R + +--R 3 2 2 2 2 2 2 +--R ((a b c - b )e + (2a c + b c)d e)x + (- 6a c + a b )e +--R + +--R 3 2 2 2 +--R (9a b c - 2b )d e + (- 8a c + 2b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 3 2 2 2 3 3 2 4 2 3 2 4 +--R ((16a c - 4a b c )e + (- 16a b c + 4b c )d e + (16a c - 4b c )d )x +--R + +--R 2 2 3 2 2 2 4 +--R (32a b c - 8a b c)e + (- 32a b c + 8b c)d e +--R + +--R 3 3 2 2 +--R (32a b c - 8b c )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 4 2 2 2 3 5 +--R (32a c + 8a b c - 4a b )e + (- 32a b c - 8a b c + 4b )d e +--R + +--R 2 3 2 2 4 2 +--R (32a c + 8a b c - 4b c)d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 4 2 2 3 2 +--R ((32a b c - 8a b )e + (- 32a b c + 8a b )d e + (32a b c - 8a b c)d )x +--R + +--R 4 3 2 2 3 2 3 3 2 2 2 2 +--R (16a c - 4a b )e + (- 16a b c + 4a b )d e + (16a c - 4a b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 837 + +--S 838 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 3 3 2 4 2 3 2 4 +--R ((8a c - 2a b c )e + (- 8a b c + 2b c )d e + (8a c - 2b c )d )x +--R + +--R 2 2 3 2 2 2 4 +--R (16a b c - 4a b c)e + (- 16a b c + 4b c)d e +--R + +--R 3 3 2 2 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 4 2 2 2 3 5 +--R (16a c + 4a b c - 2a b )e + (- 16a b c - 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 2 +--R (16a c + 4a b c - 2b c)d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 4 +--R (16a b c - 4a b )e + (- 16a b c + 4a b )d e +--R + +--R 2 2 3 2 +--R (16a b c - 4a b c)d +--R * +--R x +--R + +--R 4 3 2 2 3 2 3 3 2 2 2 2 +--R (8a c - 2a b )e + (- 8a b c + 2a b )d e + (8a c - 2a b c)d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 6 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 5 3 4 3 2 3 5 2 7 5 +--R (- 12288a b c + 9216a b c - 2304a b c + 192a b )d e +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 12288a c + 3072a b c - 6912a b c + 2112a b c +--R + +--R 8 +--R - 192a b +--R * +--R 2 4 +--R d e +--R + +--R 4 4 3 3 3 2 5 2 7 +--R - 24576a b c + 14336a b c - 1536a b c - 384a b c +--R + +--R 9 +--R 64b +--R * +--R 3 3 +--R d e +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R 12288a c + 3072a b c - 6912a b c + 2112a b c +--R + +--R 8 +--R - 192b c +--R * +--R 4 2 +--R d e +--R + +--R 3 5 2 3 4 5 3 7 2 5 +--R (- 12288a b c + 9216a b c - 2304a b c + 192b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 6 +--R (4096a c - 3072a b c + 768a b c - 64b c )d +--R * +--R ROOT +--R 2 2 2 4 14 2 3 13 +--R (- 81a c + 18a b c - b )e + (90a b c - 10b c)d e +--R + +--R 3 2 2 2 12 3 3 11 4 4 10 +--R (- 90a c - 15b c )d e + 50b c d e - 25c d e +--R / +--R 9 3 8 2 2 7 4 6 6 12 +--R (262144a c - 196608a b c + 49152a b c - 4096a b )e +--R + +--R 8 3 7 3 2 6 5 +--R - 1572864a b c + 1179648a b c - 294912a b c +--R + +--R 5 7 +--R 24576a b +--R * +--R 11 +--R d e +--R + +--R 8 4 7 2 3 6 4 2 +--R 1572864a c + 2752512a b c - 2654208a b c +--R + +--R 5 6 4 8 +--R 712704a b c - 61440a b +--R * +--R 2 10 +--R d e +--R + +--R 7 4 6 3 3 5 5 2 +--R - 7864320a b c + 655360a b c + 2457600a b c +--R + +--R 4 7 3 9 +--R - 860160a b c + 81920a b +--R * +--R 3 9 +--R d e +--R + +--R 7 5 6 2 4 5 4 3 +--R 3932160a c + 12779520a b c - 7127040a b c +--R + +--R 4 6 2 3 8 2 10 +--R - 61440a b c + 491520a b c - 61440a b +--R * +--R 4 8 +--R d e +--R + +--R 6 5 5 3 4 4 5 3 +--R - 15728640a b c - 3932160a b c + 7274496a b c +--R + +--R 3 7 2 2 9 11 +--R - 1523712a b c - 49152a b c + 24576a b +--R * +--R 5 7 +--R d e +--R + +--R 6 6 5 2 5 4 4 4 +--R 5242880a c + 19660800a b c - 8847360a b c +--R + +--R 3 6 3 2 8 2 10 +--R - 1294336a b c + 909312a b c - 73728a b c +--R + +--R 12 +--R - 4096b +--R * +--R 6 6 +--R d e +--R + +--R 5 6 4 3 5 3 5 4 +--R - 15728640a b c - 3932160a b c + 7274496a b c +--R + +--R 2 7 3 9 2 11 +--R - 1523712a b c - 49152a b c + 24576b c +--R * +--R 7 5 +--R d e +--R + +--R 5 7 4 2 6 3 4 5 +--R 3932160a c + 12779520a b c - 7127040a b c +--R + +--R 2 6 4 8 3 10 2 +--R - 61440a b c + 491520a b c - 61440b c +--R * +--R 8 4 +--R d e +--R + +--R 4 7 3 3 6 2 5 5 +--R - 7864320a b c + 655360a b c + 2457600a b c +--R + +--R 7 4 9 3 +--R - 860160a b c + 81920b c +--R * +--R 9 3 +--R d e +--R + +--R 4 8 3 2 7 2 4 6 +--R 1572864a c + 2752512a b c - 2654208a b c +--R + +--R 6 5 8 4 +--R 712704a b c - 61440b c +--R * +--R 10 2 +--R d e +--R + +--R 3 8 2 3 7 5 6 +--R - 1572864a b c + 1179648a b c - 294912a b c +--R + +--R 7 5 +--R 24576b c +--R * +--R 11 +--R d e +--R + +--R 3 9 2 2 8 4 7 6 6 12 +--R (262144a c - 196608a b c + 49152a b c - 4096b c )d +--R + +--R 2 2 3 5 7 2 3 2 2 4 6 +--R (60a b c - 15a b c + b )e + (- 120a c - 30a b c + 5b c)d e +--R + +--R 3 3 2 2 5 4 2 3 3 4 4 4 3 +--R (180a b c - 5b c )d e + (- 120a c - 50b c )d e + 80b c d e +--R + +--R 5 5 2 +--R - 32c d e +--R / +--R 6 3 5 2 2 4 4 3 6 6 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 5 3 4 3 2 3 5 2 7 5 +--R (- 6144a b c + 4608a b c - 1152a b c + 96a b )d e +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 2 4 +--R (6144a c + 1536a b c - 3456a b c + 1056a b c - 96a b )d e +--R + +--R 4 4 3 3 3 2 5 2 7 9 3 3 +--R (- 12288a b c + 7168a b c - 768a b c - 192a b c + 32b )d e +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 4 2 +--R (6144a c + 1536a b c - 3456a b c + 1056a b c - 96b c)d e +--R + +--R 3 5 2 3 4 5 3 7 2 5 +--R (- 6144a b c + 4608a b c - 1152a b c + 96b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 6 +--R (2048a c - 1536a b c + 384a b c - 32b c )d +--R * +--R log +--R 7 4 6 3 3 5 5 2 4 7 +--R 65536a b c - 57344a b c + 18432a b c - 2560a b c +--R + +--R 3 9 +--R 128a b +--R * +--R 9 +--R e +--R + +--R 7 5 6 2 4 5 4 3 +--R - 131072a c - 114688a b c + 159744a b c +--R + +--R 4 6 2 3 8 2 10 +--R - 56320a b c + 7936a b c - 384a b +--R * +--R 8 +--R d e +--R + +--R 6 5 5 3 4 4 5 3 +--R 688128a b c - 294912a b c - 61440a b c +--R + +--R 3 7 2 2 9 11 +--R 49152a b c - 8064a b c + 384a b +--R * +--R 2 7 +--R d e +--R + +--R 6 6 5 2 5 4 4 4 +--R - 458752a c - 786432a b c + 696320a b c +--R + +--R 3 6 3 2 8 2 10 12 +--R - 147456a b c - 768a b c + 2560a b c - 128b +--R * +--R 3 6 +--R d e +--R + +--R 5 6 4 3 5 3 5 4 +--R 1474560a b c - 409600a b c - 253952a b c +--R + +--R 2 7 3 9 2 11 +--R 113664a b c - 12416a b c + 128b c +--R * +--R 4 5 +--R d e +--R + +--R 5 7 4 2 6 3 4 5 +--R - 589824a c - 983040a b c + 835584a b c +--R + +--R 2 6 4 8 3 10 2 +--R - 165888a b c - 768a b c + 1920b c +--R * +--R 5 4 +--R d e +--R + +--R 4 7 3 3 6 2 5 5 +--R 1146880a b c - 458752a b c - 86016a b c +--R + +--R 7 4 9 3 +--R 57344a b c - 6272b c +--R * +--R 6 3 +--R d e +--R + +--R 4 8 3 2 7 2 4 6 +--R - 327680a c - 262144a b c + 319488a b c +--R + +--R 6 5 8 4 +--R - 90112a b c + 7936b c +--R * +--R 7 2 +--R d e +--R + +--R 3 8 2 3 7 5 6 7 5 8 +--R (294912a b c - 221184a b c + 55296a b c - 4608b c )d e +--R + +--R 3 9 2 2 8 4 7 6 6 9 +--R (- 65536a c + 49152a b c - 12288a b c + 1024b c )d +--R * +--R ROOT +--R 2 2 2 4 14 +--R (- 81a c + 18a b c - b )e +--R + +--R 2 3 13 3 2 2 2 12 +--R (90a b c - 10b c)d e + (- 90a c - 15b c )d e +--R + +--R 3 3 11 4 4 10 +--R 50b c d e - 25c d e +--R / +--R 9 3 8 2 2 7 4 6 6 +--R (262144a c - 196608a b c + 49152a b c - 4096a b ) +--R * +--R 12 +--R e +--R + +--R 8 3 7 3 2 6 5 +--R - 1572864a b c + 1179648a b c - 294912a b c +--R + +--R 5 7 +--R 24576a b +--R * +--R 11 +--R d e +--R + +--R 8 4 7 2 3 6 4 2 +--R 1572864a c + 2752512a b c - 2654208a b c +--R + +--R 5 6 4 8 +--R 712704a b c - 61440a b +--R * +--R 2 10 +--R d e +--R + +--R 7 4 6 3 3 5 5 2 +--R - 7864320a b c + 655360a b c + 2457600a b c +--R + +--R 4 7 3 9 +--R - 860160a b c + 81920a b +--R * +--R 3 9 +--R d e +--R + +--R 7 5 6 2 4 5 4 3 +--R 3932160a c + 12779520a b c - 7127040a b c +--R + +--R 4 6 2 3 8 2 10 +--R - 61440a b c + 491520a b c - 61440a b +--R * +--R 4 8 +--R d e +--R + +--R 6 5 5 3 4 4 5 3 +--R - 15728640a b c - 3932160a b 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+--R 2 4 2 3 4 2 10 4 3 3 9 +--R (324a c - 81a b c + 5b c )e + (- 324a b c + 41b c )d e +--R + +--R 5 2 4 2 8 5 3 7 6 4 6 +--R (324a c + 39b c )d e - 160b c d e + 80c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- b e + 2c d e )\|- 4a c + b + (- 12a c + b )e + 8b c d e +--R + +--R 2 2 +--R - 8c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 3 2 | 2 2 3 2 +--R (- b e + 2c d e )\|- 4a c + b + (12a c - b )e - 8b c d e +--R + +--R 2 2 +--R 8c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 2 2 3 2 2 2 +-+ +--R ((16a c - 4a b )e + (- 16a b c + 4b )d e + (16a c - 4b c)d )\|2 +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 839 + +--S 840 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 845 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 841 + +--S 842 of 845 +r0:=-1/2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)+1/4*e*(5*a*c*e*_ + (2*c*d-b*e)+(c*d-3*b*e)*(b*c*d-b^2*e+2*a*c*e)+c*(2*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(b*d+5*a*e))*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ + (a+b*x+c*x^2))-1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^3*d^3+3*b^2*e^3*(b+_ + sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-16*a*e-d*sqrt(b^2-4*a*c))-2*c*e^2*_ + (b^2*d+8*a*b*e+b*d*sqrt(b^2-4*a*c)+5*a*e*sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))+1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^3*d^3+3*b^2*e^3*_ + (b-sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-16*a*e+d*sqrt(b^2-4*a*c))-_ + 2*c*e^2*(b^2*d+8*a*b*e-b*d*sqrt(b^2-4*a*c)-5*a*e*sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 10a c + 3b c )e - 2b c d e + 2c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 20a b c + 6b c)e - 4b c d e + 4b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 20a c - 4a b c + 3b )e + (- 4a b c - 2b c)d e +--R + +--R 3 2 2 2 2 +--R (4a c + 2b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 20a b c + 6a b )e - 4a b c d e + 4a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 10a c + 3a b )e - 2a b c d e + 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (16a b c - 3b c )e + (- 32a c + 2b c )d e + 12b c d e +--R + +--R 5 3 +--R - 8c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (32a b c - 6b c)e + (- 64a b c + 4b c )d e + 24b c d e +--R + +--R 4 3 +--R - 16b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 2 3 2 2 4 3 +--R (32a b c + 10a b c - 3b )e + (- 64a c - 28a b c + 2b c)d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (24a b c + 12b c )d e + (- 16a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 2 2 2 2 +--R (32a b c - 6a b )e + (- 64a b c + 4a b c)d e + 24a b c d e +--R + +--R 3 3 +--R - 16a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 2 3 3 +--R (16a b c - 3a b )e + (- 32a c + 2a b c)d e + 12a b c d e - 8a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 10a c + 3b c )e - 2b c d e + 2c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 20a b c + 6b c)e - 4b c d e + 4b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 20a c - 4a b c + 3b )e + (- 4a b c - 2b c)d e +--R + +--R 3 2 2 2 2 +--R (4a c + 2b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 20a b c + 6a b )e - 4a b c d e + 4a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 10a c + 3a b )e - 2a b c d e + 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (- 16a b c + 3b c )e + (32a c - 2b c )d e - 12b c d e +--R + +--R 5 3 +--R 8c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (- 32a b c + 6b c)e + (64a b c - 4b c )d e - 24b c d e +--R + +--R 4 3 +--R 16b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 2 3 2 2 4 3 +--R (- 32a b c - 10a b c + 3b )e + (64a c + 28a b c - 2b c)d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (- 24a b c - 12b c )d e + (16a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 2 2 2 2 +--R (- 32a b c + 6a b )e + (64a b c - 4a b c)d e - 24a b c d e +--R + +--R 3 3 +--R 16a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 2 3 3 +--R (- 16a b c + 3a b )e + (32a c - 2a b c)d e - 12a b c d e + 8a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 3 3 2 4 2 3 +--R ((10a c - 3b c )e + 2b c d e - 2c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 2 +--R ((21a b c - 6b c)e + (- 12a c + 6b c )d e - 3b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (18a c + 6a b c - 3b )e + (- 18a b c + 6b c)d e +--R + +--R 3 2 2 2 +--R (6a c - 3b c )d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 4 2 +--R (19a b c - 5a b )e + (- 20a c - 2a b c + 2b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (15a b c - 4b c)d e + (- 8a c + 2b c )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 3 2 2 2 4 2 3 3 2 3 +--R (16a c - 4a b c )e + (- 32a b c + 8a b c )d e +--R + +--R 2 4 2 3 4 2 2 2 4 3 3 3 +--R (32a c + 8a b c - 4b c )d e + (- 32a b c + 8b c )d e +--R + +--R 5 2 4 4 +--R (16a c - 4b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 4 2 2 2 4 3 +--R (32a b c - 8a b c)e + (- 64a b c + 16a b c)d e +--R + +--R 2 3 3 2 5 2 2 2 3 4 2 3 +--R (64a b c + 16a b c - 8b c)d e + (- 64a b c + 16b c )d e +--R + +--R 4 3 3 4 +--R (32a b c - 8b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 3 2 2 3 5 3 +--R (32a c + 8a b c - 4a b )e + (- 64a b c - 16a b c + 8a b )d e +--R + +--R 3 3 2 2 2 6 2 2 2 3 3 2 5 3 +--R (64a c + 48a b c - 4b )d e + (- 64a b c - 16a b c + 8b c)d e +--R + +--R 2 4 2 3 4 2 4 +--R (32a c + 8a b c - 4b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 3 2 2 4 3 +--R (32a b c - 8a b )e + (- 64a b c + 16a b )d e +--R + +--R 3 2 2 3 5 2 2 2 2 2 4 3 +--R (64a b c + 16a b c - 8a b )d e + (- 64a b c + 16a b c)d e +--R + +--R 2 3 3 2 4 +--R (32a b c - 8a b c )d +--R * +--R x +--R + +--R 5 4 2 4 4 3 3 3 +--R (16a c - 4a b )e + (- 32a b c + 8a b )d e +--R + +--R 4 2 3 2 2 4 2 2 3 2 2 3 3 +--R (32a c + 8a b c - 4a b )d e + (- 32a b c + 8a b c)d e +--R + +--R 3 3 2 2 2 4 +--R (16a c - 4a b c )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 842 + +--S 843 of 845 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 4 2 3 3 2 3 +--R (8a c - 2a b c )e + (- 16a b c + 4a b c )d e +--R + +--R 2 4 2 3 4 2 2 2 4 3 3 3 +--R (16a c + 4a b c - 2b c )d e + (- 16a b c + 4b c )d e +--R + +--R 5 2 4 4 +--R (8a c - 2b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 4 2 2 2 4 3 +--R (16a b c - 4a b c)e + (- 32a b c + 8a b c)d e +--R + +--R 2 3 3 2 5 2 2 2 3 4 2 3 +--R (32a b c + 8a b c - 4b c)d e + (- 32a b c + 8b c )d e +--R + +--R 4 3 3 4 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 3 2 2 3 5 3 +--R (16a c + 4a b c - 2a b )e + (- 32a b c - 8a b c + 4a b )d e +--R + +--R 3 3 2 2 2 6 2 2 2 3 3 2 5 3 +--R (32a c + 24a b c - 2b )d e + (- 32a b c - 8a b c + 4b c)d e +--R + +--R 2 4 2 3 4 2 4 +--R (16a c + 4a b c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 3 2 2 4 3 +--R (16a b c - 4a b )e + (- 32a b c + 8a b )d e +--R + +--R 3 2 2 3 5 2 2 2 2 2 4 3 +--R (32a b c + 8a b c - 4a b )d e + (- 32a b c + 8a b c)d e +--R + +--R 2 3 3 2 4 +--R (16a b c - 4a b c )d +--R * +--R x +--R + +--R 5 4 2 4 4 3 3 3 +--R (8a c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 4 2 3 2 2 4 2 2 3 2 2 3 3 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 3 3 2 2 2 4 +--R (8a c - 2a b c )d +--R * +--R ROOT +--R 8 3 7 2 2 6 4 5 6 10 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 7 3 6 3 2 5 5 4 7 9 +--R (- 20480a b c + 15360a b c - 3840a b c + 320a b )d e +--R + +--R 7 4 6 2 3 5 4 2 4 6 +--R 20480a c + 25600a b c - 26880a b c + 7360a b c +--R + +--R 3 8 +--R - 640a b +--R * +--R 2 8 +--R d e +--R + +--R 6 4 5 3 3 4 5 2 3 7 +--R - 81920a b c + 20480a b c + 15360a b c - 6400a b c +--R + +--R 2 9 +--R 640a b +--R * +--R 3 7 +--R d e +--R + +--R 6 5 5 2 4 4 4 3 3 6 2 +--R 40960a c + 92160a b c - 64000a b c + 7040a b c +--R + +--R 2 8 10 +--R 1920a b c - 320a b +--R * +--R 4 6 +--R d e +--R + +--R 5 5 4 3 4 3 5 3 2 7 2 +--R - 122880a b c + 10240a b c + 34304a b c - 10368a b c +--R + +--R 9 11 +--R 512a b c + 64b +--R * +--R 5 5 +--R d e +--R + +--R 5 6 4 2 5 3 4 4 2 6 3 +--R 40960a c + 92160a b c - 64000a b c + 7040a b c +--R + +--R 8 2 10 +--R 1920a b c - 320b c +--R * +--R 6 4 +--R d e +--R + +--R 4 6 3 3 5 2 5 4 7 3 +--R - 81920a b c + 20480a b c + 15360a b c - 6400a b c +--R + +--R 9 2 +--R 640b c +--R * +--R 7 3 +--R d e +--R + +--R 4 7 3 2 6 2 4 5 6 4 +--R 20480a c + 25600a b c - 26880a b c + 7360a b c +--R + +--R 8 3 +--R - 640b c +--R * +--R 8 2 +--R d e +--R + +--R 3 7 2 3 6 5 5 7 4 9 +--R (- 20480a b 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* +--R 20 +--R d +--R + +--R 5 5 4 3 4 3 5 3 2 7 2 +--R - 10400a b c + 28816a b c - 21098a b c + 6660a b c +--R + +--R 9 11 +--R - 972a b c + 54b +--R * +--R 13 +--R e +--R + +--R 5 6 4 2 5 3 4 4 2 6 3 +--R 20800a c - 120896a b c + 95716a b c - 29946a b c +--R + +--R 8 2 10 +--R 4176a b c - 216b c +--R * +--R 12 +--R d e +--R + +--R 4 6 3 3 5 2 5 4 7 3 +--R 189792a b c - 141072a b c + 36102a b c - 3462a b c +--R + +--R 9 2 +--R 72b c +--R * +--R 2 11 +--R d e +--R + +--R 4 7 3 2 6 2 4 5 6 4 +--R - 126528a c + 29088a b c + 20732a b c - 7912a b c +--R + +--R 8 3 +--R 722b c +--R * +--R 3 10 +--R d e +--R + +--R 3 7 2 3 6 5 5 7 4 4 9 +--R (97440a b c - 63280a b c + 13370a b c - 910b c )d e +--R + +--R 3 8 2 2 7 4 6 6 5 5 8 +--R (- 38976a c + 17472a b c - 1428a b c - 126b c )d e +--R + +--R 2 8 3 7 5 6 6 7 +--R (7840a b c - 3920a b c + 490b c )d e +--R + +--R 2 9 2 8 4 7 7 6 +--R (- 2240a c + 1120a b c - 140b c )d e +--R * +--R ROOT +--R 8 3 7 2 2 6 4 5 6 10 +--R (4096a c - 3072a b c + 768a b c - 64a b )e +--R + +--R 7 3 6 3 2 5 5 4 7 +--R (- 20480a b c + 15360a b c - 3840a b c + 320a b ) +--R * +--R 9 +--R d e +--R + +--R 7 4 6 2 3 5 4 2 4 6 +--R 20480a c + 25600a b c - 26880a b c + 7360a b c +--R + +--R 3 8 +--R - 640a b +--R * +--R 2 8 +--R d e +--R + +--R 6 4 5 3 3 4 5 2 +--R - 81920a b c + 20480a b c + 15360a b c +--R + +--R 3 7 2 9 +--R - 6400a b c + 640a b +--R * +--R 3 7 +--R d e +--R + +--R 6 5 5 2 4 4 4 3 +--R 40960a c + 92160a b c - 64000a b c +--R + +--R 3 6 2 2 8 10 +--R 7040a b c + 1920a b c - 320a b +--R * +--R 4 6 +--R d e +--R + +--R 5 5 4 3 4 3 5 3 +--R - 122880a b c + 10240a b c + 34304a b c +--R + +--R 2 7 2 9 11 +--R - 10368a b c + 512a b c + 64b +--R * +--R 5 5 +--R d e +--R + +--R 5 6 4 2 5 3 4 4 +--R 40960a c + 92160a b c - 64000a b c +--R + +--R 2 6 3 8 2 10 +--R 7040a b c + 1920a b c - 320b c +--R * +--R 6 4 +--R d e +--R + +--R 4 6 3 3 5 2 5 4 +--R - 81920a b c + 20480a b c + 15360a b c +--R + +--R 7 3 9 2 +--R - 6400a b c + 640b c +--R * +--R 7 3 +--R d e +--R + +--R 4 7 3 2 6 2 4 5 +--R 20480a c + 25600a b c - 26880a b c +--R + +--R 6 4 8 3 +--R 7360a b c - 640b c +--R * +--R 8 2 +--R d e +--R + +--R 3 7 2 3 6 5 5 +--R - 20480a b c + 15360a b c - 3840a b c +--R + +--R 7 4 +--R 320b c +--R * +--R 9 +--R d e +--R + +--R 3 8 2 2 7 4 6 6 5 10 +--R (4096a c - 3072a b c + 768a b c - 64b c )d +--R * +--R ROOT +--R 4 4 3 2 3 2 4 2 +--R - 625a c + 2550a b c - 3051a b c +--R + +--R 6 8 +--R 918a b c - 81b +--R * +--R 18 +--R e +--R + +--R 3 4 2 3 3 5 2 +--R - 7700a b c + 16758a b c - 4914a b c +--R + +--R 7 +--R 378b c +--R * +--R 17 +--R d e +--R + +--R 3 5 2 2 4 4 3 +--R 7700a c - 38724a b c + 7812a b c +--R + +--R 6 2 +--R - 189b c +--R * +--R 2 16 +--R d e +--R + +--R 2 5 3 4 5 3 3 15 +--R (43932a b c + 4984a b c - 1848b c )d e +--R + +--R 2 6 2 5 4 4 4 14 +--R (- 21966a c - 29442a b c + 3374b c )d e +--R + +--R 6 3 5 5 13 +--R (32340a b c + 490b c )d e +--R + +--R 7 2 6 6 12 7 7 11 +--R (- 10780a c - 5880b c )d e + 4900b c d e +--R + +--R 8 8 10 +--R - 1225c d e +--R / +--R 13 3 12 2 2 11 4 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 10 6 +--R - 4096a b +--R * +--R 20 +--R e +--R + +--R 12 3 11 3 2 +--R - 2621440a b c + 1966080a b c +--R + +--R 10 5 9 7 +--R - 491520a b c + 40960a b +--R * +--R 19 +--R d e +--R + +--R 12 4 11 2 3 +--R 2621440a c + 9830400a b c +--R + +--R 10 4 2 9 6 8 8 +--R - 8355840a b c + 2170880a b c - 184320a b +--R * +--R 2 18 +--R d e +--R + +--R 11 4 10 3 3 +--R - 23592960a b c - 13762560a b c +--R + +--R 9 5 2 8 7 7 9 +--R 19169280a b c - 5529600a b c + 491520a b +--R * +--R 3 17 +--R d e +--R + +--R 11 5 10 2 4 +--R 11796480a c + 85524480a b c +--R + +--R 9 4 3 8 6 2 +--R - 13516800a b c - 23777280a b c +--R + +--R 7 8 6 10 +--R 8847360a b c - 860160a b +--R * +--R 4 16 +--R d e +--R + +--R 10 5 9 3 4 +--R - 94371840a b c - 149422080a b c +--R + +--R 8 5 3 7 7 2 +--R 81395712a b c + 9732096a b c +--R + +--R 6 9 5 11 +--R - 8945664a b c + 1032192a b +--R * +--R 5 15 +--R d e +--R + +--R 10 6 9 2 5 +--R 31457280a c + 306708480a b c +--R + +--R 8 4 4 7 6 3 +--R 88473600a b c - 131235840a b c +--R + +--R 6 8 2 5 10 4 12 +--R 15482880a b c + 5160960a b c - 860160a b +--R * +--R 6 14 +--R d e +--R + +--R 9 6 8 3 5 +--R - 220200960a b c - 495452160a b c +--R + +--R 7 5 4 6 7 3 +--R 123863040a b c + 95846400a b c +--R + +--R 5 9 2 4 11 3 13 +--R - 28016640a b c - 737280a b c + 491520a b +--R * +--R 7 13 +--R d e +--R + +--R 9 7 8 2 6 +--R 55050240a c + 619315200a b c +--R + +--R 7 4 5 6 6 4 +--R 340623360a b c - 276111360a b c +--R + +--R 5 8 3 4 10 2 +--R - 8847360a b c + 19537920a b c +--R + +--R 3 12 2 14 +--R - 1228800a b c - 184320a b +--R * +--R 8 12 +--R d e +--R + +--R 8 7 7 3 6 +--R - 330301440a b c - 853278720a b c +--R + +--R 6 5 5 5 7 4 +--R 103219200a b c + 199802880a b c +--R + +--R 4 9 3 3 11 2 +--R - 38502400a b c - 5406720a b c +--R + +--R 2 13 15 +--R 983040a b c + 40960a b +--R * +--R 9 11 +--R d e +--R + +--R 8 8 7 2 7 +--R 66060288a c + 776208384a b c +--R + +--R 6 4 6 5 6 5 +--R 494075904a b c - 341655552a b c +--R + +--R 4 8 4 3 10 3 +--R - 30597120a b c + 27295744a b c +--R + +--R 2 12 2 14 16 +--R - 933888a b c - 319488a b c - 4096b +--R * +--R 10 10 +--R d e +--R + +--R 7 8 6 3 7 +--R - 330301440a b c - 853278720a b c +--R + +--R 5 5 6 4 7 5 +--R 103219200a b c + 199802880a b c +--R + +--R 3 9 4 2 11 3 +--R - 38502400a b c - 5406720a b c +--R + +--R 13 2 15 +--R 983040a b c + 40960b c +--R * +--R 11 9 +--R d e +--R + +--R 7 9 6 2 8 +--R 55050240a c + 619315200a b c +--R + +--R 5 4 7 4 6 6 +--R 340623360a b c - 276111360a b c +--R + +--R 3 8 5 2 10 4 +--R - 8847360a b c + 19537920a b c +--R + +--R 12 3 14 2 +--R - 1228800a b c - 184320b c +--R * +--R 12 8 +--R d e +--R + +--R 6 9 5 3 8 +--R - 220200960a b c - 495452160a b c +--R + +--R 4 5 7 3 7 6 +--R 123863040a b c + 95846400a b c +--R + +--R 2 9 5 11 4 13 3 +--R - 28016640a b c - 737280a b c + 491520b c +--R * +--R 13 7 +--R d e +--R + +--R 6 10 5 2 9 +--R 31457280a c + 306708480a b c +--R + +--R 4 4 8 3 6 7 +--R 88473600a b c - 131235840a b c +--R + +--R 2 8 6 10 5 12 4 +--R 15482880a b c + 5160960a b c - 860160b c +--R * +--R 14 6 +--R d e +--R + +--R 5 10 4 3 9 +--R - 94371840a b c - 149422080a b c +--R + +--R 3 5 8 2 7 7 +--R 81395712a b c + 9732096a b c +--R + +--R 9 6 11 5 +--R - 8945664a b c + 1032192b c +--R * +--R 15 5 +--R d e +--R + +--R 5 11 4 2 10 +--R 11796480a c + 85524480a b c +--R + +--R 3 4 9 2 6 8 +--R - 13516800a b c - 23777280a b c +--R + +--R 8 7 10 6 +--R 8847360a b c - 860160b c +--R * +--R 16 4 +--R d e +--R + +--R 4 11 3 3 10 +--R - 23592960a b c - 13762560a b c +--R + +--R 2 5 9 7 8 9 7 +--R 19169280a b c - 5529600a b c + 491520b c +--R * +--R 17 3 +--R d e +--R + +--R 4 12 3 2 11 +--R 2621440a c + 9830400a b c +--R + +--R 2 4 10 6 9 8 8 +--R - 8355840a b c + 2170880a b c - 184320b c +--R * +--R 18 2 +--R d e +--R + +--R 3 12 2 3 11 +--R - 2621440a b c + 1966080a b c +--R + +--R 5 10 7 9 +--R - 491520a b c + 40960b c +--R * +--R 19 +--R d e +--R + +--R 3 13 2 2 12 4 11 +--R 262144a c - 196608a b c + 49152a b c +--R + +--R 6 10 +--R - 4096b c +--R * +--R 20 +--R d +--R + +--R 3 3 2 3 2 5 7 9 +--R (- 420a b c + 385a b c - 105a b c + 9b )e +--R + +--R 3 4 2 2 3 4 2 6 8 +--R (840a c - 1050a b c + 280a b c - 21b c)d e +--R + +--R 2 4 3 3 5 2 2 7 +--R (840a b c - 70a b c - 14b c )d e +--R + +--R 2 5 2 4 4 3 3 6 +--R (- 560a c - 420a b c + 70b c )d e +--R + +--R 5 3 4 4 5 6 2 5 5 4 +--R (700a b c - 35b c )d e + (- 280a c - 98b c )d e +--R + +--R 6 6 3 7 7 2 +--R 112b c d e - 32c d e +--R / +--R 8 3 7 2 2 6 4 5 6 10 +--R (2048a c - 1536a b c + 384a b c - 32a b )e +--R + +--R 7 3 6 3 2 5 5 4 7 9 +--R (- 10240a b c + 7680a b c - 1920a b c + 160a b )d e +--R + +--R 7 4 6 2 3 5 4 2 4 6 +--R 10240a c + 12800a b c - 13440a b c + 3680a b c +--R + +--R 3 8 +--R - 320a b +--R * +--R 2 8 +--R d e +--R + +--R 6 4 5 3 3 4 5 2 3 7 +--R - 40960a b c + 10240a b c + 7680a b c - 3200a b c +--R + +--R 2 9 +--R 320a b +--R * +--R 3 7 +--R d e +--R + +--R 6 5 5 2 4 4 4 3 3 6 2 +--R 20480a c + 46080a b c - 32000a b c + 3520a b c +--R + +--R 2 8 10 +--R 960a b c - 160a b +--R * +--R 4 6 +--R d e +--R + +--R 5 5 4 3 4 3 5 3 2 7 2 +--R - 61440a b c + 5120a b c + 17152a b c - 5184a b c +--R + +--R 9 11 +--R 256a b c + 32b +--R * +--R 5 5 +--R d e +--R + +--R 5 6 4 2 5 3 4 4 2 6 3 +--R 20480a c + 46080a b c - 32000a b c + 3520a b c +--R + +--R 8 2 10 +--R 960a b c - 160b c +--R * +--R 6 4 +--R d e +--R + +--R 4 6 3 3 5 2 5 4 7 3 +--R - 40960a b c + 10240a b c + 7680a b c - 3200a b c +--R + +--R 9 2 +--R 320b c +--R * +--R 7 3 +--R d e +--R + +--R 4 7 3 2 6 2 4 5 6 4 +--R 10240a c + 12800a b c - 13440a b c + 3680a b c +--R + +--R 8 3 +--R - 320b c +--R * +--R 8 2 +--R d e +--R + +--R 3 7 2 3 6 5 5 7 4 9 +--R (- 10240a b c + 7680a b c - 1920a b c + 160b c )d e +--R + +--R 3 8 2 2 7 4 6 6 5 10 +--R (2048a c - 1536a b c + 384a b c - 32b c )d +--R + +--R 3 6 2 2 5 4 4 6 3 12 +--R (2500a c - 5625a b c + 1971a b c - 189b c )e +--R + +--R 2 6 3 5 5 4 11 +--R (15000a b c - 4518a b c + 297b c )d e +--R + +--R 2 7 2 6 4 5 2 10 +--R (- 15000a c - 1446a b c + 774b c )d e +--R + +--R 7 3 6 3 9 8 2 7 4 8 +--R (11928a b c - 1582b c )d e + (- 5964a c - 609b c )d e +--R + +--R 8 5 7 9 6 6 +--R 1680b c d e - 560c d e +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((10a c - 3b )e + 2b c d e - 2c d e )\|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (- 16a b c + 3b )e + (32a c - 2b c)d e - 12b c d e + 8c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 4 3 2 2 2 | 2 +--R ((10a c - 3b )e + 2b c d e - 2c d e )\|- 4a c + b +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (16a b c - 3b )e + (- 32a c + 2b c)d e + 12b c d e - 8c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 2 2 4 2 3 3 +--R (16a c - 4a b )e + (- 32a b c + 8a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 3 2 2 4 +--R (32a c + 8a b c - 4b )d e + (- 32a b c + 8b c)d e + (16a c - 4b c )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 844 + +--S 845 of 845 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich12d.input.pamphlet b/src/input/rich12d.input.pamphlet new file mode 100644 index 0000000..a5bc901 --- /dev/null +++ b/src/input/rich12d.input.pamphlet @@ -0,0 +1,68963 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12d.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 129 matching answers. +\item 151 cases where Axiom answer differs from Rubi +\item 52 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 26 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12d.output +)spool rich12d.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1378 +t0:=(b+2*c*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R +-------+ | 2 +--R (1) (2c x + b)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1378 +--r0:=4/7*(a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)-2/105*(8*c^2*d^2+b^2*e^2-_ +-- c*e*(11*b*d-10*a*e)-3*c*e*(2*c*d-b*e)*x)*sqrt(d+e*x)*sqrt(a+b*x+_ +-- c*x^2)/(c*e^2)-1/105*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(5*c*e*(b*d-2*a*e)^2-_ +-- (2*c*d-b*e)*(4*b*c*d^2-b^2*d*e-2*a*c*d*e-a*b*e^2))+(2*c*d-b*e)*_ +-- (4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e^3*sqrt(a+b*x+_ +-- c*x^2))-1/105*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*e^4*sqrt(a+b*x+c*x^2)) +--E 2 + +--S 3 of 1378 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 1378 +--m0:=a0-r0 +--E 4 + +--S 5 of 1378 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 1378 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1378 +--r0:=-2/15*(8*c*d-7*b*e-6*c*e*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/e^2-_ +-- 1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*(2*c*(7*b^2*d*e+4*a*c*d*e-8*b*(c*d^2+a*e^2))+_ +-- (16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e^3*sqrt(2)*sqrt(a+b*x+_ +-- c*x^2))-1/15*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*e^4*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 7 + +--S 8 of 1378 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 1378 +--m0:=a0-r0 +--E 9 + +--S 10 of 1378 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 1378 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1378 +--r0:=2/3*(8*c*d-3*b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*sqrt(d+e*x))-_ +-- 1/3*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(b*e*(b-4*sqrt(b^2-4*a*c))+c*(-4*a*e+_ +-- 8*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^3*sqrt(c)*sqrt(a+b*x+c*x^2))+4/3*(2*c*d-b*e)*elliptic_e(asin(_ +-- sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^4*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 12 + +--S 13 of 1378 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 1378 +--m0:=a0-r0 +--E 14 + +--S 15 of 1378 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 1378 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1378 +--r0:=2/3*(8*c*d-b*e+6*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/3*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*sqrt(a+b*x+c*x^2)/_ +-- (e^2*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(7*b^2*d*e+_ +-- 4*a*c*d*e-8*b*(c*d^2+a*e^2))+(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-_ +-- 3*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^3*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-_ +-- 4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-_ +-- 4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-_ +-- 4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^4*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 17 + +--S 18 of 1378 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 1378 +--m0:=a0-r0 +--E 19 + +--S 20 of 1378 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 1378 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1378 +--r0:=2/15*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*sqrt(a+b*x+c*x^2)/_ +-- (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))-2/5*(8*c*d+b*e+10*c*e*x)*_ +-- sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^(5/2))+4/15*(2*c*d-b*e)*(4*c^2*d^2-_ +-- b^2*e^2-4*c*e*(b*d-2*a*e))*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*_ +-- e^2)^2*sqrt(d+e*x))+1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+_ +-- e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*_ +-- a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*(b^3*d*e^2-4*a*_ +-- c*e*(c*d^2+5*a*e^2)+4*b*c*d*(2*c*d^2+5*a*e^2)-b^2*(11*c*d^2*e-a*e^3))+_ +-- (2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e^3*(c*d^2-b*d*e+a*e^2)^2*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2))+1/15*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-_ +-- 2*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^4*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 22 + +--S 23 of 1378 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 1378 +--m0:=a0-r0 +--E 24 + +--S 25 of 1378 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 1378 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1378 +--r0:=-2/63*(16*c*d-15*b*e-14*c*e*x)*(a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)/e^2-_ +-- 2/315*(128*c^3*d^3-b^3*e^3+3*b*c*e^2*(37*b*d-36*a*e)-12*c^2*d*_ +-- e*(20*b*d-11*a*e)-3*c*e*(32*c^2*d^2+b^2*e^2-4*c*e*(8*b*d-7*a*e))*x)*_ +-- sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*e^4)-1/315*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*((4*b*c*_ +-- d^2-b^2*d*e-2*a*c*d*e-a*b*e^2)*(32*c^2*d^2+b^2*e^2-4*c*e*(8*b*d-_ +-- 7*a*e))+5*c*e*(b*d-2*a*e)*(15*b^2*d*e+4*a*c*d*e-16*b*(c*d^2+a*e^2)))+_ +-- (128*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(64*b*d-57*a*e)-b^2*c*e^3*(7*b*d-_ +-- 15*a*e)+3*c^2*e^2*(45*b^2*d^2-76*a*b*d*e+28*a^2*e^2))*(b-sqrt(b^2-_ +-- 4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e^5*sqrt(a+b*x+_ +-- c*x^2))-1/315*(128*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(64*b*d-57*a*e)-_ +-- b^2*c*e^3*(7*b*d-15*a*e)+3*c^2*e^2*(45*b^2*d^2-76*a*b*d*e+28*a^2*_ +-- e^2))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*e^6*sqrt(a+b*x+c*x^2)) +--E 27 + +--S 28 of 1378 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 1378 +--m0:=a0-r0 +--E 29 + +--S 30 of 1378 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 1378 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1378 +--r0:=2/7*(16*c*d-7*b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+_ +-- 2/35*(128*c^2*d^2+51*b^2*e^2-4*c*e*(44*b*d-5*a*e)-48*c*e*(2*c*d-_ +-- b*e)*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/e^4+1/35*elliptic_f(asin(_ +-- sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- (-2*c*(51*b^3*d*e^2-8*a*c*e*(8*c*d^2+5*a*e^2)+4*b*c*d*(32*c*d^2+_ +-- 45*a*e^2)-2*b^2*(88*c*d^2*e+27*a*e^3))+(2*c*d-b*e)*(128*c^2*d^2+_ +-- 3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e^5*sqrt(2)*sqrt(a+b*x+c*x^2))+_ +-- 1/35*(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*e^6*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 32 + +--S 33 of 1378 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 1378 +--m0:=a0-r0 +--E 34 + +--S 35 of 1378 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 1378 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1378 +--r0:=2/15*(16*c*d-5*b*e+6*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/15*(128*c^2*d^2+15*b^2*e^2-4*c*e*(28*b*d-9*a*e)+16*c*e*(2*c*d-_ +-- b*e)*x)*sqrt(a+b*x+c*x^2)/(e^4*sqrt(d+e*x))-1/15*elliptic_f(_ +-- asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(b^2*e^2*(8*b-23*sqrt(b^2-4*a*c))-64*c^2*d*(-a*e+2*d*_ +-- sqrt(b^2-4*a*c))-4*c*e*(4*b^2*d+8*a*b*e-32*b*d*sqrt(b^2-4*a*c)+_ +-- 9*a*e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^5*sqrt(c)*sqrt(a+b*x+c*x^2))-1/15*(128*c^2*d^2+23*b^2*e^2-_ +-- 4*c*e*(32*b*d-9*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^6*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 37 + +--S 38 of 1378 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 1378 +--m0:=a0-r0 +--E 39 + +--S 40 of 1378 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 1378 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1378 +--r0:=2/15*(16*c*d-3*b*e+10*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 2/15*(128*c^2*d^2+3*b^2*e^2-20*c*e*(4*b*d-a*e)+48*c*e*(2*c*d-b*e)*x)*_ +-- sqrt(a+b*x+c*x^2)/(e^4*(d+e*x)^(3/2))+2/15*(2*c*d-b*e)*(128*c^2*d^2+_ +-- 3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*sqrt(a+b*x+c*x^2)/(e^4*(c*d^2-_ +-- b*d*e+a*e^2)*sqrt(d+e*x))+1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(-2*c*(51*b^3*d*e^2-_ +-- 8*a*c*e*(8*c*d^2+5*a*e^2)+4*b*c*d*(32*c*d^2+45*a*e^2)-2*b^2*(88*c*_ +-- d^2*e+27*a*e^3))+(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-_ +-- 29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^5*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+_ +-- 1/15*(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^6*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 42 + +--S 43 of 1378 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 1378 +--m0:=a0-r0 +--E 44 + +--S 45 of 1378 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1378 +--r0:=2/7*(2*c*d-b*e)*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)/c+4/7*(d+e*x)^(5/2)*_ +-- sqrt(a+b*x+c*x^2)+4/21*(3*c^2*d^2+2*b^2*e^2-c*e*(3*b*d+5*a*e))*_ +-- sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c^2-1/21*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(4*b^3*_ +-- d*e^2+2*a*c*e*(27*c*d^2-5*a*e^2)-b*c*d*(3*c*d^2+25*a*e^2)-b^2*_ +-- (9*c*d^2*e-4*a*e^3))+(2*c*d-b*e)*(3*c^2*d^2+8*b^2*e^2-c*e*(3*b*d+_ +-- 29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(7/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-1/21*(2*c*d-b*e)*(3*c^2*d^2+_ +-- 8*b^2*e^2-c*e*(3*b*d+29*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(7/2)*_ +-- e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 47 + +--S 48 of 1378 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 1378 +--m0:=a0-r0 +--E 49 + +--S 50 of 1378 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1378 +--r0:=4/5*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)+2/5*(2*c*d-b*e)*sqrt(d+e*x)*_ +-- sqrt(a+b*x+c*x^2)/c+1/5*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*_ +-- d*e+a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e*sqrt(a+b*x+c*x^2))-_ +-- 1/5*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- e^2*sqrt(a+b*x+c*x^2)) +--E 52 + +--S 53 of 1378 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 1378 +--m0:=a0-r0 +--E 54 + +--S 55 of 1378 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 1378 +t0:=(b+2*c*x)*sqrt(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1378 +--r0:=4/3*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)+1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(b*e*(b-_ +-- sqrt(b^2-4*a*c))+2*c*(-2*a*e+d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 57 + +--S 58 of 1378 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 1378 +--m0:=a0-r0 +--E 59 + +--S 60 of 1378 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 1378 +t0:=(b+2*c*x)/(sqrt(d+e*x)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) --------------------------- +--R +--------------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1378 +--r0:=elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/(e*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 62 + +--S 63 of 1378 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 1378 +--m0:=a0-r0 +--E 64 + +--S 65 of 1378 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 1378 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------ +--R +--------------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1378 +--r0:=2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+2*d*sqrt(b^2-_ +-- 4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(2*c*d-b*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 67 + +--S 68 of 1378 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 1378 +--m0:=a0-r0 +--E 69 + +--S 70 of 1378 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 1378 +t0:=(b+2*c*x)/((d+e*x)^(5/2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ----------------------------------------------- +--R +--------------+ +--R 2 2 2 +-------+ | 2 +--R (e x + 2d e x + d )\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1378 +--r0:=2/3*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+_ +-- 4/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-_ +-- b*d*e+a*e^2)^2*sqrt(d+e*x))-1/3*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+_ +-- b^2*d*e-8*a*c*d*e+a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*_ +-- sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+_ +-- 2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*(c*d^2-_ +-- b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2))+1/3*(c^2*d^2+b^2*e^2-_ +-- c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 72 + +--S 73 of 1378 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 1378 +--m0:=a0-r0 +--E 74 + +--S 75 of 1378 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1378 +--r0:=-2*(d+e*x)^(7/2)/sqrt(a+b*x+c*x^2)+14/5*e^2*(d+e*x)^(3/2)*_ +-- sqrt(a+b*x+c*x^2)/c+56/15*e^2*(2*c*d-b*e)*sqrt(d+e*x)*sqrt(a+_ +-- b*x+c*x^2)/c^2-7/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(-2*c*(15*c^2*d^3+4*b*e^2*(b*d+a*e)-_ +-- c*d*e*(11*b*d+17*a*e))+e*(23*c^2*d^2+8*b^2*e^2-c*e*(23*b*d+9*a*e))*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(7/2)*sqrt(2)*sqrt(a+b*x+c*x^2))-7/15*(23*c^2*d^2+8*b^2*e^2-_ +-- c*e*(23*b*d+9*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(7/2)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 77 + +--S 78 of 1378 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 1378 +--m0:=a0-r0 +--E 79 + +--S 80 of 1378 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1378 +--r0:=-2*(d+e*x)^(5/2)/sqrt(a+b*x+c*x^2)+10/3*e^2*sqrt(d+e*x)*_ +-- sqrt(a+b*x+c*x^2)/c-5/3*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*(3*c*d^2-e*(b*d+a*e))+_ +-- e*(2*c*d-b*e)*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(5/2)*sqrt(a+b*x+c*x^2))-5/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- sqrt(a+b*x+c*x^2)) +--E 82 + +--S 83 of 1378 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 1378 +--m0:=a0-r0 +--E 84 + +--S 85 of 1378 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1378 +--r0:=-2*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2)+3*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))^(3/2)*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*sqrt(2)*sqrt(a+b*x+c*x^2))-3*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 87 + +--S 88 of 1378 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 1378 +--m0:=a0-r0 +--E 89 + +--S 90 of 1378 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 1378 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1378 +--r0:=-2*sqrt(d+e*x)/sqrt(a+b*x+c*x^2)+elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/(sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 92 + +--S 93 of 1378 +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 1378 +--m0:=a0-r0 +--E 94 + +--S 95 of 1378 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 1378 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------- +--R +--------------+ +--R 2 +-------+ | 2 +--R (c x + b x + a)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1378 +--r0:=-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ +-- (c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2))-elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))^(3/2)*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+_ +-- c*x^2))+elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 97 + +--S 98 of 1378 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 1378 +--m0:=a0-r0 +--E 99 + +--S 100 of 1378 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 1378 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R 2c x + b +--R ------------------------------------------------------------------------ +--R +--------------+ +--R 3 2 +-------+ | 2 +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1378 +--r0:=-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-_ +-- b*d*e+a*e^2)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))+4*e^2*(2*c*d-b*e)*_ +-- sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))-_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(3*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-_ +-- c*e*(3*b*d+a*e-2*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- ((c*d^2-b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2))+(2*c*d-b*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 102 + +--S 103 of 1378 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 1378 +--m0:=a0-r0 +--E 104 + +--S 105 of 1378 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1378 +--r0:=-2/3*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(3/2)-14/3*e*(d+e*x)^(3/2)*(b*d-_ +-- 2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+14/3*e^2*(2*c*d-_ +-- b*e)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*(b^2-4*a*c))+7/3*e*_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*d*e+a*b*e^2)-_ +-- (c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))-_ +-- 7/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- (b^2-4*a*c)*sqrt(a+b*x+c*x^2)) +--E 107 + +--S 108 of 1378 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 1378 +--m0:=a0-r0 +--E 109 + +--S 110 of 1378 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1378 +--r0:=-2/3*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2)-10/3*e*(b*d-2*a*e+(2*c*d-_ +-- b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+5/3*e*_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+2*d*_ +-- sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*(b^2-_ +-- 4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))-5/3*(2*c*d-b*e)*elliptic_e(_ +-- asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*_ +-- (b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 112 + +--S 113 of 1378 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 1378 +--m0:=a0-r0 +--E 114 + +--S 115 of 1378 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 1378 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1378 +--r0:=-2/3*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2)-2*e*(b+2*c*x)*sqrt(d+e*x)/_ +-- ((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+e*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(sqrt(c)*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2))-_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 117 + +--S 118 of 1378 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 1378 +--m0:=a0-r0 +--E 119 + +--S 120 of 1378 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 1378 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1378 +--r0:=-2/3*sqrt(d+e*x)/(a+b*x+c*x^2)^(3/2)-2/3*e*(b*c*d-b^2*e+2*a*c*e+c*_ +-- (2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(a+b*x+c*x^2))+1/3*e*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+_ +-- 2*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- ((b^2-4*a*c)*(c*d^2-e*(b*d-a*e))*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*(c*d^2-e*(b*d-a*e))*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 122 + +--S 123 of 1378 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 1378 +--m0:=a0-r0 +--E 124 + +--S 125 of 1378 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 1378 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R (1) +--R 2c x + b +--R ------------------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 +-------+ | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1378 +--r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-_ +-- 4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-2/3*e*(3*b^2*c*d*e-_ +-- 8*a*c^2*d*e-2*b^3*e^2-b*c*(c*d^2-7*a*e^2)-2*c*(c^2*d^2+b^2*e^2-_ +-- c*e*(b*d+3*a*e))*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(a+b*x+c*x^2))-1/3*e*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*d*e+_ +-- a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2))+1/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-_ +-- 4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 127 + +--S 128 of 1378 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 1378 +--m0:=a0-r0 +--E 129 + +--S 130 of 1378 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 1378 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 m +--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(e x + d) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1378 +r0:=-(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(b*d-a*e)*(3*b*B*d-_ + 2*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^4*(2+m))-b*(3*b*B*d-A*b*e-2*a*B*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+b^2*B*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 m + 4 +--R (B b m + 6B b m + 11B b m + 6B b )(e x + d) +--R + +--R 2 2 3 2 2 2 +--R ((A b + 2B a b)e - 3B b d)m + ((7A b + 14B a b)e - 21B b d)m +--R + +--R 2 2 2 2 +--R ((14A b + 28B a b)e - 42B b d)m + (8A b + 16B a b)e - 24B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (- 2A b - 4B a b)d e + 3B b d )m +--R + +--R 2 2 2 2 2 2 +--R ((16A a b + 8B a )e + (- 16A b - 32B a b)d e + 24B b d )m +--R + +--R 2 2 2 2 2 +--R ((38A a b + 19B a )e + (- 38A b - 76B a b)d e + 57B b d )m +--R + +--R 2 2 2 2 2 +--R (24A a b + 12B a )e + (- 24A b - 48B a b)d e + 36B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (- 2A a b - B a )d e + (A b + 2B a b)d e - B b d )m +--R + +--R 2 3 2 2 2 2 +--R 9A a e + (- 18A a b - 9B a )d e + (9A b + 18B a b)d e +--R + +--R 2 3 +--R - 9B b d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 2 +--R 26A a e + (- 52A a b - 26B a )d e + (26A b + 52B a b)d e +--R + +--R 2 3 +--R - 26B b d +--R * +--R m +--R + +--R 2 3 2 2 2 2 2 3 +--R 24A a e + (- 48A a b - 24B a )d e + (24A b + 48B a b)d e - 24B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 4 2 2 4 2 4 4 +--R (B b e m + 6B b e m + 11B b e m + 6B b e )x +--R + +--R 2 4 2 3 3 +--R ((A b + 2B a b)e + B b d e )m +--R + +--R 2 4 2 3 2 +--R ((7A b + 14B a b)e + 3B b d e )m +--R + +--R 2 4 2 3 2 4 +--R ((14A b + 28B a b)e + 2B b d e )m + (8A b + 16B a b)e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 3 +--R ((2A a b + B a )e + (A b + 2B a b)d e )m +--R + +--R 2 4 2 3 2 2 2 2 +--R ((16A a b + 8B a )e + (5A b + 10B a b)d e - 3B b d e )m +--R + +--R 2 4 2 3 2 2 2 +--R ((38A a b + 19B a )e + (4A b + 8B a b)d e - 3B b d e )m +--R + +--R 2 4 +--R (24A a b + 12B a )e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 3 +--R (A a e + (2A a b + B a )d e )m +--R + +--R 2 4 2 3 2 2 2 2 +--R (9A a e + (14A a b + 7B a )d e + (- 2A b - 4B a b)d e )m +--R + +--R 2 4 2 3 2 2 2 +--R 26A a e + (24A a b + 12B a )d e + (- 8A b - 16B a b)d e +--R + +--R 2 3 +--R 6B b d e +--R * +--R m +--R + +--R 2 4 +--R 24A a e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 2 2 +--R A a d e m + (9A a d e + (- 2A a b - B a )d e )m +--R + +--R 2 3 2 2 2 2 3 +--R (26A a d e + (- 14A a b - 7B a )d e + (2A b + 4B a b)d e)m +--R + +--R 2 3 2 2 2 2 3 2 4 +--R 24A a d e + (- 24A a b - 12B a )d e + (8A b + 16B a b)d e - 6B b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 3 2 4 2 2 4 2 4 4 +--R (B b e m + 6B b e m + 11B b e m + 6B b e )x +--R + +--R 2 4 2 3 3 +--R ((A b + 2B a b)e + B b d e )m +--R + +--R 2 4 2 3 2 +--R ((7A b + 14B a b)e + 3B b d e )m +--R + +--R 2 4 2 3 2 4 +--R ((14A b + 28B a b)e + 2B b d e )m + (8A b + 16B a b)e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 3 +--R ((2A a b + B a )e + (A b + 2B a b)d e )m +--R + +--R 2 4 2 3 2 2 2 2 +--R ((16A a b + 8B a )e + (5A b + 10B a b)d e - 3B b d e )m +--R + +--R 2 4 2 3 2 2 2 +--R ((38A a b + 19B a )e + (4A b + 8B a b)d e - 3B b d e )m +--R + +--R 2 4 +--R (24A a b + 12B a )e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 3 +--R (A a e + (2A a b + B a )d e )m +--R + +--R 2 4 2 3 2 2 2 2 +--R (9A a e + (14A a b + 7B a )d e + (- 2A b - 4B a b)d e )m +--R + +--R 2 4 2 3 2 2 2 +--R 26A a e + (24A a b + 12B a )d e + (- 8A b - 16B a b)d e +--R + +--R 2 3 +--R 6B b d e +--R * +--R m +--R + +--R 2 4 +--R 24A a e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 2 2 +--R A a d e m + (9A a d e + (- 2A a b - B a )d e )m +--R + +--R 2 3 2 2 2 2 3 +--R (26A a d e + (- 14A a b - 7B a )d e + (2A b + 4B a b)d e)m +--R + +--R 2 3 2 2 2 2 3 2 4 +--R 24A a d e + (- 24A a b - 12B a )d e + (8A b + 16B a b)d e - 6B b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 3 2 2 2 2 m + 4 +--R (- B b m - 6B b m - 11B b m - 6B b )(e x + d) +--R + +--R 2 2 3 2 2 2 +--R ((- A b - 2B a b)e + 3B b d)m + ((- 7A b - 14B a b)e + 21B b d)m +--R + +--R 2 2 2 2 +--R ((- 14A b - 28B a b)e + 42B b d)m + (- 8A b - 16B a b)e + 24B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 2 3 +--R ((- 2A a b - B a )e + (2A b + 4B a b)d e - 3B b d )m +--R + +--R 2 2 2 2 2 2 +--R ((- 16A a b - 8B a )e + (16A b + 32B a b)d e - 24B b d )m +--R + +--R 2 2 2 2 2 +--R ((- 38A a b - 19B a )e + (38A b + 76B a b)d e - 57B b d )m +--R + +--R 2 2 2 2 2 +--R (- 24A a b - 12B a )e + (24A b + 48B a b)d e - 36B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- A a e + (2A a b + B a )d e + (- A b - 2B a b)d e + B b d )m +--R + +--R 2 3 2 2 2 2 +--R - 9A a e + (18A a b + 9B a )d e + (- 9A b - 18B a b)d e +--R + +--R 2 3 +--R 9B b d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 2 +--R - 26A a e + (52A a b + 26B a )d e + (- 26A b - 52B a b)d e +--R + +--R 2 3 +--R 26B b d +--R * +--R m +--R + +--R 2 3 2 2 2 2 +--R - 24A a e + (48A a b + 24B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 24B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1378 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 5 8 2 5 2 4 7 +--R B b e x + ((A b + 2B a b)e + 5B b d e )x +--R + +--R 2 5 2 4 2 2 3 6 +--R ((2A a b + B a )e + (5A b + 10B a b)d e + 10B b d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 5 +--R (A a e + (10A a b + 5B a )d e + (10A b + 20B a b)d e + 10B b d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 4 4 +--R (5A a d e + (20A a b + 10B a )d e + (10A b + 20B a b)d e + 5B b d e)x +--R + +--R 2 2 3 2 3 2 2 4 2 5 3 +--R (10A a d e + (20A a b + 10B a )d e + (5A b + 10B a b)d e + B b d )x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 1378 +r0:=-1/6*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^6/e^4+1/7*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^7/e^4-1/8*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^8/e^4+_ + 1/9*b^2*B*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 2 9 9 1 2 1 9 5 2 8 8 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 9 5 2 10 8 10 2 2 7 7 +--R ((- A a b + - B a )e + (- A b + -- B a b)d e + -- B b d e )x +--R 7 7 7 7 7 +--R + +--R 1 2 9 5 5 2 8 5 2 10 2 7 +--R - A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e +--R 6 3 6 3 3 +--R + +--R 5 2 3 6 +--R - B b d e +--R 3 +--R * +--R 6 +--R x +--R + +--R 2 8 2 2 7 2 3 6 2 4 5 5 +--R (A a d e + (4A a b + 2B a )d e + (2A b + 4B a b)d e + B b d e )x +--R + +--R 5 2 2 7 5 2 3 6 5 2 5 4 5 +--R - A a d e + (5A a b + - B a )d e + (- A b + - B a b)d e +--R 2 2 4 2 +--R + +--R 1 2 5 4 +--R - B b d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 10 2 3 6 10 5 2 4 5 1 2 2 5 4 3 +--R (-- A a d e + (-- A a b + - B a )d e + (- A b + - B a b)d e )x +--R 3 3 3 3 3 +--R + +--R 5 2 4 5 1 2 5 4 2 2 5 4 1 2 6 3 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 1 1 2 7 2 1 2 1 8 1 2 9 +--R (- -- A a b - -- B a )d e + (--- A b + -- B a b)d e - --- B b d +--R 21 42 168 84 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 137 + +--S 138 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 5 9 1 2 1 5 5 2 4 8 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 5 5 2 10 4 10 2 2 3 7 +--R ((- A a b + - B a )e + (- A b + -- B a b)d e + -- B b d e )x +--R 7 7 7 7 7 +--R + +--R 1 2 5 5 5 2 4 5 2 10 2 3 +--R - A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e +--R 6 3 6 3 3 +--R + +--R 5 2 3 2 +--R - B b d e +--R 3 +--R * +--R 6 +--R x +--R + +--R 2 4 2 2 3 2 3 2 2 4 5 +--R (A a d e + (4A a b + 2B a )d e + (2A b + 4B a b)d e + B b d e)x +--R + +--R 5 2 2 3 5 2 3 2 5 2 5 4 1 2 5 4 +--R (- A a d e + (5A a b + - B a )d e + (- A b + - B a b)d e + - B b d )x +--R 2 2 4 2 4 +--R + +--R 10 2 3 2 10 5 2 4 1 2 2 5 3 +--R (-- A a d e + (-- A a b + - B a )d e + (- A b + - B a b)d )x +--R 3 3 3 3 3 +--R + +--R 5 2 4 1 2 5 2 2 5 +--R (- A a d e + (A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 6 3 1 1 2 7 2 1 2 1 8 +--R - - A a d e + (-- A a b + -- B a )d e + (- --- A b - -- B a b)d e +--R 6 21 42 168 84 +--R + +--R 1 2 9 +--R --- B b d +--R 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 139 + +--S 140 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 140 + +)clear all + +--S 141 of 1378 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 7 2 4 2 3 6 +--R B b e x + ((A b + 2B a b)e + 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((2A a b + B a )e + (4A b + 8B a b)d e + 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (A a e + (8A a b + 4B a )d e + (6A b + 12B a b)d e + 4B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 3 +--R (4A a d e + (12A a b + 6B a )d e + (4A b + 8B a b)d e + B b d )x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 141 + +--S 142 of 1378 +r0:=-1/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^5/e^4+1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^6/e^4-1/7*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^7/e^4+_ + 1/8*b^2*B*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 2 8 8 1 2 2 8 4 2 7 7 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 8 7 7 7 +--R + +--R 1 1 2 8 2 2 4 7 2 2 6 6 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + B b d e )x +--R 3 6 3 3 +--R + +--R 1 2 8 8 4 2 7 6 2 12 2 6 +--R - A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e +--R 5 5 5 5 5 +--R + +--R 4 2 3 5 +--R - B b d e +--R 5 +--R * +--R 5 +--R x +--R + +--R 2 7 3 2 2 6 2 3 5 1 2 4 4 4 +--R (A a d e + (3A a b + - B a )d e + (A b + 2B a b)d e + - B b d e )x +--R 2 4 +--R + +--R 2 2 6 8 4 2 3 5 1 2 2 4 4 3 +--R (2A a d e + (- A a b + - B a )d e + (- A b + - B a b)d e )x +--R 3 3 3 3 +--R + +--R 2 3 5 1 2 4 4 2 2 4 4 1 2 5 3 +--R (2A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 5 +--R + +--R 1 1 2 6 2 1 2 2 7 1 2 8 +--R (- -- A a b - -- B a )d e + (--- A b + --- B a b)d e - --- B b d +--R 15 30 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 142 + +--S 143 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 8 1 2 2 4 4 2 3 7 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 8 7 7 7 +--R + +--R 1 1 2 4 2 2 4 3 2 2 2 6 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + B b d e )x +--R 3 6 3 3 +--R + +--R 1 2 4 8 4 2 3 6 2 12 2 2 4 2 3 5 +--R (- A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e + - B b d e)x +--R 5 5 5 5 5 5 +--R + +--R 2 3 3 2 2 2 2 3 1 2 4 4 +--R (A a d e + (3A a b + - B a )d e + (A b + 2B a b)d e + - B b d )x +--R 2 4 +--R + +--R 2 2 2 8 4 2 3 1 2 2 4 3 +--R (2A a d e + (- A a b + - B a )d e + (- A b + - B a b)d )x +--R 3 3 3 3 +--R + +--R 2 3 1 2 4 2 2 4 +--R (2A a d e + (A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 143 + +--S 144 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 5 3 1 1 2 6 2 1 2 2 7 +--R - - A a d e + (-- A a b + -- B a )d e + (- --- A b - --- B a b)d e +--R 5 15 30 105 105 +--R + +--R 1 2 8 +--R --- B b d +--R 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 144 + +--S 145 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 145 + +)clear all + +--S 146 of 1378 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 146 + +--S 147 of 1378 +r0:=-1/4*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^4/e^4+1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^5/e^4-1/6*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^6/e^4+_ + 1/7*b^2*B*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 2 7 7 1 2 1 7 1 2 6 6 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 7 6 3 2 +--R + +--R 2 1 2 7 3 2 6 6 3 2 2 5 5 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + - B b d e )x +--R 5 5 5 5 5 +--R + +--R 1 2 7 3 3 2 6 3 2 3 2 5 +--R - A a e + (- A a b + - B a )d e + (- A b + - B a b)d e +--R 4 2 4 4 2 +--R + +--R 1 2 3 4 +--R - B b d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 1 2 2 3 4 3 +--R (A a d e + (2A a b + B a )d e + (- A b + - B a b)d e )x +--R 3 3 +--R + +--R 3 2 2 5 1 2 3 4 2 2 3 4 1 2 4 3 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 4 +--R + +--R 1 1 2 5 2 1 2 1 6 1 2 7 +--R (- -- A a b - -- B a )d e + (-- A b + -- B a b)d e - --- B b d +--R 10 20 60 30 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 147 + +--S 148 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 3 7 1 2 1 3 1 2 2 6 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 7 6 3 2 +--R + +--R 2 1 2 3 3 2 6 2 3 2 2 5 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + - B b d e)x +--R 5 5 5 5 5 +--R + +--R 1 2 3 3 3 2 2 3 2 3 2 1 2 3 4 +--R (- A a e + (- A a b + - B a )d e + (- A b + - B a b)d e + - B b d )x +--R 4 2 4 4 2 4 +--R + +--R 2 2 2 2 1 2 2 3 3 +--R (A a d e + (2A a b + B a )d e + (- A b + - B a b)d )x +--R 3 3 +--R + +--R 3 2 2 1 2 3 2 2 3 +--R (- A a d e + (A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 148 + +--S 149 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 4 3 1 1 2 5 2 1 2 1 6 +--R - - A a d e + (-- A a b + -- B a )d e + (- -- A b - -- B a b)d e +--R 4 10 20 60 30 +--R + +--R 1 2 7 +--R --- B b d +--R 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 150 + +)clear all + +--S 151 of 1378 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 151 + +--S 152 of 1378 +r0:=1/3*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^3/b^4+1/4*(b*d-a*e)*(b*B*d+2*A*b*e-_ + 3*a*B*e)*(a+b*x)^4/b^4+1/5*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^5/b^4+_ + 1/6*B*e^2*(a+b*x)^6/b^4 +--R +--R +--R (2) +--R 1 6 2 6 1 6 2 5 2 2 6 5 +--R - B b e x + ((- A b + - B a b )e + - B b d e)x +--R 6 5 5 5 +--R + +--R 1 5 1 2 4 2 1 6 5 1 6 2 4 +--R ((- A a b + - B a b )e + (- A b + B a b )d e + - B b d )x +--R 2 4 2 4 +--R + +--R 1 2 4 2 4 5 2 2 4 1 6 2 5 2 3 +--R (- A a b e + (- A a b + - B a b )d e + (- A b + - B a b )d )x +--R 3 3 3 3 3 +--R + +--R 2 4 5 1 2 4 2 2 2 4 2 +--R (A a b d e + (A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 5 1 6 2 1 4 2 1 5 +--R (-- A a b - -- B a )e + (- - A a b + -- B a b)d e +--R 30 60 6 15 +--R + +--R 1 3 3 1 4 2 2 +--R (- A a b - -- B a b )d +--R 3 12 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 152 + +--S 153 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 6 1 2 2 2 2 2 5 +--R - B b e x + ((- A b + - B a b)e + - B b d e)x +--R 6 5 5 5 +--R + +--R 1 1 2 2 1 2 1 2 2 4 +--R ((- A a b + - B a )e + (- A b + B a b)d e + - B b d )x +--R 2 4 2 4 +--R + +--R 1 2 2 4 2 2 1 2 2 2 3 +--R (- A a e + (- A a b + - B a )d e + (- A b + - B a b)d )x +--R 3 3 3 3 3 +--R + +--R 2 1 2 2 2 2 2 +--R (A a d e + (A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 153 + +--S 154 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 5 1 6 2 1 4 2 1 5 +--R (- -- A a b + -- B a )e + (- A a b - -- B a b)d e +--R 30 60 6 15 +--R + +--R 1 3 3 1 4 2 2 +--R (- - A a b + -- B a b )d +--R 3 12 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 154 + +--S 155 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 155 + +)clear all + +--S 156 of 1378 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 156 + +--S 157 of 1378 +r0:=1/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)^3/b^3+1/4*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^4/b^3+1/5*B*e*(a+b*x)^5/b^3 +--R +--R +--R (2) +--R 1 5 5 1 5 1 4 1 5 4 +--R - B b e x + ((- A b + - B a b )e + - B b d)x +--R 5 4 2 4 +--R + +--R 2 4 1 2 3 1 5 2 4 3 +--R ((- A a b + - B a b )e + (- A b + - B a b )d)x +--R 3 3 3 3 +--R + +--R 1 2 3 4 1 2 3 2 2 3 +--R (- A a b e + (A a b + - B a b )d)x + A a b d x +--R 2 2 +--R + +--R 1 4 1 5 1 3 2 1 4 +--R (- -- A a b + -- B a )e + (- A a b - -- B a b)d +--R 12 30 3 12 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 157 + +--S 158 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 5 1 2 1 1 2 4 +--R - B b e x + ((- A b + - B a b)e + - B b d)x +--R 5 4 2 4 +--R + +--R 2 1 2 1 2 2 3 +--R ((- A a b + - B a )e + (- A b + - B a b)d)x +--R 3 3 3 3 +--R + +--R 1 2 1 2 2 2 +--R (- A a e + (A a b + - B a )d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 158 + +--S 159 of 1378 +m0:=a0-r0 +--R +--R +--R 1 4 1 5 1 3 2 1 4 +--R (-- A a b - -- B a )e + (- - A a b + -- B a b)d +--R 12 30 3 12 +--R (4) ------------------------------------------------ +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 159 + +--S 160 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 160 + +)clear all + +--S 161 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 161 + +--S 162 of 1378 +r0:=1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2 +--R +--R +--R (2) +--R 1 4 4 1 4 2 3 3 3 1 2 2 2 2 2 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x + A a b x +--R 4 3 3 2 +--R + +--R 1 3 1 4 +--R - A a b - -- B a +--R 3 12 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +--S 163 of 1378 +a0:=integrate(t0,x) +--R +--R +--R 1 2 4 1 2 2 3 1 2 2 2 +--R (3) - B b x + (- A b + - B a b)x + (A a b + - B a )x + A a x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 163 + +--S 164 of 1378 +m0:=a0-r0 +--R +--R +--R 1 3 1 4 +--R - - A a b + -- B a +--R 3 12 +--R (4) ------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 164 + +--S 165 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 165 + +)clear all + +--S 166 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1378 +r0:=b*(b*d-a*e)*(B*d-A*e)*x/e^3-1/2*(B*d-A*e)*(a+b*x)^2/e^2+_ + 1/3*B*(a+b*x)^3/(b*e)-(b*d-a*e)^2*(B*d-A*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 +--R 6A a b e + (- 12A a b - 6B a b)d e + (6A b + 12B a b )d e +--R + +--R 3 3 +--R - 6B b d +--R * +--R log(e x + d) +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 2B b e x + ((3A b + 6B a b )e - 3B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((12A a b + 6B a b)e + (- 6A b - 12B a b )d e + 6B b d e)x +--R + +--R 2 3 3 2 2 +--R (3A a b + 2B a )e - 3B a b d e +--R / +--R 4 +--R 6b e +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 3 +--R (6A a e + (- 12A a b - 6B a )d e + (6A b + 12B a b)d e - 6B b d ) +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((3A b + 6B a b)e - 3B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((12A a b + 6B a )e + (- 6A b - 12B a b)d e + 6B b d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1378 +m0:=a0-r0 +--R +--R +--R 2 3 2 +--R (- 3A a b - 2B a )e + 3B a b d +--R (4) ------------------------------ +--R 2 +--R 6b e +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1378 +r0:=-b*(2*b*B*d-A*b*e-2*a*B*e)*x/e^3+1/2*b^2*B*x^2/e^2+(b*d-a*e)^2*_ + (B*d-A*e)/(e^4*(d+e*x))+(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 2 +--R ((4A a b + 2B a )e + (- 4A b - 8B a b)d e + 6B b d e)x +--R + +--R 2 2 2 2 2 3 +--R (4A a b + 2B a )d e + (- 4A b - 8B a b)d e + 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 3 2 2 2 +--R B b e x + ((2A b + 4B a b)e - 3B b d e )x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A b + 4B a b)d e - 4B b d e)x - 2A a e + (4A a b + 2B a )d e +--R + +--R 2 2 2 3 +--R (- 2A b - 4B a b)d e + 2B b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 +--R ((4A a b + 2B a )e + (- 4A b - 8B a b)d e + 6B b d e)x +--R + +--R 2 2 2 2 2 3 +--R (4A a b + 2B a )d e + (- 4A b - 8B a b)d e + 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 3 2 2 2 +--R B b e x + ((2A b + 4B a b)e - 3B b d e )x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A b + 4B a b)d e - 4B b d e)x - 2A a e + (4A a b + 2B a )d e +--R + +--R 2 2 2 3 +--R (- 2A b - 4B a b)d e + 2B b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1378 +r0:=b^2*B*x/e^3+1/2*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^2)-(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x))-b*(3*b*B*d-A*b*e-2*a*B*e)*_ + log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R ((2A b + 4B a b)e - 6B b d e )x +--R + +--R 2 2 2 2 2 2 2 3 +--R ((4A b + 8B a b)d e - 12B b d e)x + (2A b + 4B a b)d e - 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 +--R 2B b e x + 4B b d e x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 4A a b - 2B a )e + (4A b + 8B a b)d e - 4B b d e)x - A a e +--R + +--R 2 2 2 2 2 3 +--R (- 2A a b - B a )d e + (3A b + 6B a b)d e - 5B b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 +--R ((2A b + 4B a b)e - 6B b d e )x +--R + +--R 2 2 2 2 2 2 2 3 +--R ((4A b + 8B a b)d e - 12B b d e)x + (2A b + 4B a b)d e - 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 +--R 2B b e x + 4B b d e x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 4A a b - 2B a )e + (4A b + 8B a b)d e - 4B b d e)x - A a e +--R + +--R 2 2 2 2 2 3 +--R (- 2A a b - B a )d e + (3A b + 6B a b)d e - 5B b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1378 +r0:=-1/3*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^3)-1/2*B*(b*d-a*e)^2/_ + (e^4*(d+e*x)^2)+2*b*B*(b*d-a*e)/(e^4*(d+e*x))+b^2*B*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 4 3 3 3 2 3 3 2 2 2 +--R (6B a b e - 6B b d e )x + (18B a b d e - 18B b d e )x +--R + +--R 2 2 2 3 3 2 3 3 4 +--R (18B a b d e - 18B b d e)x + 6B a b d e - 6B b d +--R * +--R log(e x + d) +--R + +--R 3 4 3 3 3 +--R (- 2A b e + 2B b d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 6A a b - 12B a b)e + 30B a b d e - 12B b d e )x +--R + +--R 2 3 4 2 3 2 2 2 3 3 +--R ((- 6A a b - 3B a )e - 9B a b d e + 39B a b d e - 21B b d e)x +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 +--R - 2A a e - B a d e - 3B a b d e + 15B a b d e - 9B b d +--R / +--R 8 7 3 7 2 6 2 2 6 3 5 +--R (6a e - 6b d e )x + (18a d e - 18b d e )x + (18a d e - 18b d e )x +--R + +--R 3 5 4 4 +--R 6a d e - 6b d e +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 2 2 2 3 +--R (6B b e x + 18B b d e x + 18B b d e x + 6B b d )log(e x + d) +--R + +--R 2 3 2 2 2 +--R ((- 6A b - 12B a b)e + 18B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 6A a b - 3B a )e + (- 6A b - 12B a b)d e + 27B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 2A a b - B a )d e + (- 2A b - 4B a b)d e + 11B b d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1378 +m0:=a0-r0 +--R +--R +--R 3 3 +--R A b e - B b d +--R (4) --------------- +--R 5 4 +--R 3a e - 3b d e +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1378 +r0:=-1/4*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^4)+1/12*(3*b*B*d+A*b*e-_ + 4*a*B*e)*(a+b*x)^3/(e*(b*d-a*e)^2*(d+e*x)^3) +--R +--R +--R (2) +--R 1 4 1 3 1 4 4 +--R ((-- A b - - B a b )e + - B b d)x +--R 12 3 4 +--R + +--R 2 2 1 4 2 3 3 +--R (- B a b e + (- A b + - B a b )d)x +--R 3 3 +--R + +--R 1 2 2 3 3 1 2 2 2 +--R ((- - A a b - B a b)e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 2 3 1 4 2 2 1 4 1 3 1 4 +--R ((- - A a b - - B a )e + A a b d)x - - A a e + (- A a b - -- B a )d +--R 3 3 4 3 12 +--R / +--R 2 6 5 2 2 4 4 2 5 2 4 2 3 3 3 +--R (a e - 2a b d e + b d e )x + (4a d e - 8a b d e + 4b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (6a d e - 12a b d e + 6b d e )x + (4a d e - 8a b d e + 4b d e)x +--R + +--R 2 4 2 5 2 6 +--R a d e - 2a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 187 + +--S 188 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R - 12B b e x + ((- 6A b - 12B a b)e - 18B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 8A a b - 4B a )e + (- 4A b - 8B a b)d e - 12B b d e)x - 3A a e +--R + +--R 2 2 2 2 2 3 +--R (- 2A a b - B a )d e + (- A b - 2B a b)d e - 3B b d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1378 +m0:=a0-r0 +--R +--R +--R 4 3 4 +--R (- A b + 4B a b )e - 3B b d +--R (4) ------------------------------ +--R 2 6 5 2 2 4 +--R 12a e - 24a b d e + 12b d e +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1378 +r0:=1/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^5)-1/4*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^4)+1/3*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^3)-_ + 1/2*b^2*B/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 3 3 1 2 2 3 1 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - - B b d e )x +--R 2 3 3 2 +--R + +--R 1 1 2 3 1 2 1 2 1 2 2 +--R ((- - A a b - - B a )e + (- - A b - - B a b)d e - - B b d e)x +--R 2 4 6 3 4 +--R + +--R 1 2 3 1 1 2 2 1 2 1 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A b - -- B a b)d e +--R 5 10 20 30 15 +--R + +--R 1 2 3 +--R - -- B b d +--R 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 192 + +--S 193 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R - 30B b e x + ((- 20A b - 40B a b)e - 30B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 30A a b - 15B a )e + (- 10A b - 20B a b)d e - 15B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 12A a e + (- 6A a b - 3B a )d e + (- 2A b - 4B a b)d e - 3B b d +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1378 +r0:=1/6*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^6)-1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^5)+1/4*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^4)-_ + 1/3*b^2*B/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 3 3 1 2 1 3 1 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - - B b d e )x +--R 3 4 2 4 +--R + +--R 2 1 2 3 1 2 1 2 1 2 2 +--R ((- - A a b - - B a )e + (- -- A b - - B a b)d e - -- B b d e)x +--R 5 5 10 5 10 +--R + +--R 1 2 3 1 1 2 2 1 2 1 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A b - -- B a b)d e +--R 6 15 30 60 30 +--R + +--R 1 2 3 +--R - -- B b d +--R 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 197 + +--S 198 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R - 20B b e x + ((- 15A b - 30B a b)e - 15B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 24A a b - 12B a )e + (- 6A b - 12B a b)d e - 6B b d e)x - 10A a e +--R + +--R 2 2 2 2 2 3 +--R (- 4A a b - 2B a )d e + (- A b - 2B a b)d e - B b d +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 4 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^8 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1378 +r0:=1/7*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^7)-1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^6)+1/5*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^5)-_ + 1/4*b^2*B/(e^4*(d+e*x)^4) +--R +--R +--R (2) +--R 1 2 3 3 1 2 2 3 3 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - -- B b d e )x +--R 4 5 5 20 +--R + +--R 1 1 2 3 1 2 2 2 1 2 2 +--R ((- - A a b - - B a )e + (- -- A b - -- B a b)d e - -- B b d e)x +--R 3 6 15 15 20 +--R + +--R 1 2 3 1 1 2 2 1 2 2 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- --- A b - --- B a b)d e +--R 7 21 42 105 105 +--R + +--R 1 2 3 +--R - --- B b d +--R 140 +--R / +--R 11 7 10 6 2 9 5 3 8 4 4 7 3 5 6 2 6 5 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 4 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 202 + +--S 203 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R - 105B b e x + ((- 84A b - 168B a b)e - 63B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 140A a b - 70B a )e + (- 28A b - 56B a b)d e - 21B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 60A a e + (- 20A a b - 10B a )d e + (- 4A b - 8B a b)d e - 3B b d +--R / +--R 11 7 10 6 2 9 5 3 8 4 4 7 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 6 2 6 5 7 4 +--R 8820d e x + 2940d e x + 420d e +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1378 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1378 +r0:=-(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(1+m)/(e^6*(1+m))+(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^6*(2+m))-2*b*(b*d-a*e)^2*(5*b*B*d-_ + 3*A*b*e-2*a*B*e)*(d+e*x)^(3+m)/(e^6*(3+m))+2*b^2*(b*d-a*e)*(5*b*B*d-_ + 2*A*b*e-3*a*B*e)*(d+e*x)^(4+m)/(e^6*(4+m))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+b^4*B*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 4 5 4 4 4 3 4 2 4 4 +--R (B b m + 15B b m + 85B b m + 225B b m + 274B b m + 120B b ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 4 3 4 5 4 3 4 4 +--R ((A b + 4B a b )e - 5B b d)m + ((16A b + 64B a b )e - 80B b d)m +--R + +--R 4 3 4 3 +--R ((95A b + 380B a b )e - 475B b d)m +--R + +--R 4 3 4 2 +--R ((260A b + 1040B a b )e - 1300B b d)m +--R + +--R 4 3 4 4 3 +--R ((324A b + 1296B a b )e - 1620B b d)m + (144A b + 576B a b )e +--R + +--R 4 +--R - 720B b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (- 4A b - 16B a b )d e + 10B b d )m +--R + +--R 3 2 2 2 4 3 4 2 4 +--R ((68A a b + 102B a b )e + (- 68A b - 272B a b )d e + 170B b d )m +--R + +--R 3 2 2 2 4 3 +--R (428A a b + 642B a b )e + (- 428A b - 1712B a b )d e +--R + +--R 4 2 +--R 1070B b d +--R * +--R 3 +--R m +--R + +--R 3 2 2 2 4 3 +--R (1228A a b + 1842B a b )e + (- 1228A b - 4912B a b )d e +--R + +--R 4 2 +--R 3070B b d +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 4 3 +--R (1584A a b + 2376B a b )e + (- 1584A b - 6336B a b )d e +--R + +--R 4 2 +--R 3960B b d +--R * +--R m +--R + +--R 3 2 2 2 4 3 4 2 +--R (720A a b + 1080B a b )e + (- 720A b - 2880B a b )d e + 1800B b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (- 12A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (6A b + 24B a b )d e - 10B b d +--R * +--R 5 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (108A a b + 72B a b)e + (- 216A a b - 324B a b )d e +--R + +--R 4 3 2 4 3 +--R (108A b + 432B a b )d e - 180B b d +--R * +--R 4 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (726A a b + 484B a b)e + (- 1452A a b - 2178B a b )d e +--R + +--R 4 3 2 4 3 +--R (726A b + 2904B a b )d e - 1210B b d +--R * +--R 3 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (2232A a b + 1488B a b)e + (- 4464A a b - 6696B a b )d e +--R + +--R 4 3 2 4 3 +--R (2232A b + 8928B a b )d e - 3720B b d +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (3048A a b + 2032B a b)e + (- 6096A a b - 9144B a b )d e +--R + +--R 4 3 2 4 3 +--R (3048A b + 12192B a b )d e - 5080B b d +--R * +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (1440A a b + 960B a b)e + (- 2880A a b - 4320B a b )d e +--R + +--R 4 3 2 4 3 +--R (1440A b + 5760B a b )d e - 2400B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (12A a b + 18B a b )d e + (- 4A b - 16B a b )d e + 5B b d +--R * +--R 5 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (76A a b + 19B a )e + (- 228A a b - 152B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (228A a b + 342B a b )d e + (- 76A b - 304B a b )d e + 95B b d +--R * +--R 4 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (548A a b + 137B a )e + (- 1644A a b - 1096B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1644A a b + 2466B a b )d e + (- 548A b - 2192B a b )d e +--R + +--R 4 4 +--R 685B b d +--R * +--R 3 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (1844A a b + 461B a )e + (- 5532A a b - 3688B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (5532A a b + 8298B a b )d e + (- 1844A b - 7376B a b )d e +--R + +--R 4 4 +--R 2305B b d +--R * +--R 2 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (2808A a b + 702B a )e + (- 8424A a b - 5616B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (8424A a b + 12636B a b )d e + (- 2808A b - 11232B a b )d e +--R + +--R 4 4 +--R 3510B b d +--R * +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (1440A a b + 360B a )e + (- 4320A a b - 2880B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (4320A a b + 6480B a b )d e + (- 1440A b - 5760B a b )d e +--R + +--R 4 4 +--R 1800B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (- 4A a b - B a )d e + (6A a b + 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 4A a b - 6B a b )d e + (A b + 4B a b )d e - B b d +--R * +--R 5 +--R m +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 20A a e + (- 80A a b - 20B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 80A a b - 120B a b )d e + (20A b + 80B a b )d e - 20B b d +--R * +--R 4 +--R m +--R + +--R 4 5 3 4 4 +--R 155A a e + (- 620A a b - 155B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (930A a b + 620B a b)d e + (- 620A a b - 930B a b )d e +--R + +--R 4 3 4 4 5 +--R (155A b + 620B a b )d e - 155B b d +--R * +--R 3 +--R m +--R + +--R 4 5 3 4 4 +--R 580A a e + (- 2320A a b - 580B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (3480A a b + 2320B a b)d e + (- 2320A a b - 3480B a b )d e +--R + +--R 4 3 4 4 5 +--R (580A b + 2320B a b )d e - 580B b d +--R * +--R 2 +--R m +--R + +--R 4 5 3 4 4 +--R 1044A a e + (- 4176A a b - 1044B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (6264A a b + 4176B a b)d e + (- 4176A a b - 6264B a b )d e +--R + +--R 4 3 4 4 5 +--R (1044A b + 4176B a b )d e - 1044B b d +--R * +--R m +--R + +--R 4 5 3 4 4 +--R 720A a e + (- 2880A a b - 720B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (4320A a b + 2880B a b)d e + (- 2880A a b - 4320B a b )d e +--R + +--R 4 3 4 4 5 +--R (720A b + 2880B a b )d e - 720B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 5 4 6 4 4 6 3 4 6 2 4 6 +--R B b e m + 15B b e m + 85B b e m + 225B b e m + 274B b e m +--R + +--R 4 6 +--R 120B b e +--R * +--R 6 +--R x +--R + +--R 4 3 6 4 5 5 +--R ((A b + 4B a b )e + B b d e )m +--R + +--R 4 3 6 4 5 4 +--R ((16A b + 64B a b )e + 10B b d e )m +--R + +--R 4 3 6 4 5 3 +--R ((95A b + 380B a b )e + 35B b d e )m +--R + +--R 4 3 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216B a b )d e + (12A b + 48B a b )d e +--R * +--R 3 +--R m +--R + +--R 3 4 6 2 2 3 5 +--R (1844A a b + 461B a )e + (1164A a b + 776B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 492A a b - 738B a b )d e + (84A b + 336B a b )d e +--R + +--R 4 4 2 +--R - 60B b d e +--R * +--R 2 +--R m +--R + +--R 3 4 6 2 2 3 5 +--R (2808A a b + 702B a )e + (720A a b + 480B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 360A a b - 540B a b )d e + (72A b + 288B a b )d e +--R + +--R 4 4 2 +--R - 60B b d e +--R * +--R m +--R + +--R 3 4 6 +--R (1440A a b + 360B a )e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 5 5 +--R (A a e + (4A a b + B a )d e )m +--R + +--R 4 6 3 4 5 2 2 3 2 4 4 +--R (20A a e + (72A a b + 18B a )d e + (- 12A a b - 8B a b)d e )m +--R + +--R 4 6 3 4 5 +--R 155A a e + (476A a b + 119B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 180A a b - 120B a b)d e + (24A a b + 36B a b )d e +--R * +--R 3 +--R m +--R + +--R 4 6 3 4 5 +--R 580A a e + (1368A a b + 342B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 888A a b - 592B a b)d e + (264A a b + 396B a b )d e +--R + +--R 4 3 4 2 +--R (- 24A b - 96B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 6 3 4 5 +--R 1044A a e + (1440A a b + 360B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 1440A a b - 960B a b)d e + (720A a b + 1080B a b )d e +--R + +--R 4 3 4 2 4 5 +--R (- 144A b - 576B a b )d e + 120B b d e +--R * +--R m +--R + +--R 4 6 +--R 720A a e +--R * +--R x +--R + +--R 4 5 5 4 5 3 4 2 4 4 +--R A a d e m + (20A a d e + (- 4A a b - B a )d e )m +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 3 +--R (155A a d e + (- 72A a b - 18B a )d e + (12A a b + 8B a b)d e )m +--R + +--R 4 5 3 4 2 4 +--R 580A a d e + (- 476A a b - 119B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (180A a b + 120B a b)d e + (- 24A a b - 36B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 5 3 4 2 4 +--R 1044A a d e + (- 1368A a b - 342B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (888A a b + 592B a b)d e + (- 264A a b - 396B a b )d e +--R + +--R 4 3 5 +--R (24A b + 96B a b )d e +--R * +--R m +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 720A a d e + (- 1440A a b - 360B a )d e + (1440A a b + 960B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (- 720A a b - 1080B a b )d e + (144A b + 576B a b )d e - 120B b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 6 5 4 6 4 4 6 3 4 6 2 4 6 +--R B b e m + 15B b e m + 85B b e m + 225B b e m + 274B b e m +--R + +--R 4 6 +--R 120B b e +--R * +--R 6 +--R x +--R + +--R 4 3 6 4 5 5 +--R ((A b + 4B a b )e + B b d e )m +--R + +--R 4 3 6 4 5 4 +--R ((16A b + 64B a b )e + 10B b d e )m +--R + +--R 4 3 6 4 5 3 +--R ((95A b + 380B a b )e + 35B b d e )m +--R + +--R 4 3 6 4 5 2 +--R ((260A b + 1040B a b )e + 50B b d e )m +--R + +--R 4 3 6 4 5 4 3 6 +--R ((324A b + 1296B a b )e + 24B b d e )m + (144A b + 576B a b )e +--R * +--R 5 +--R x +--R + +--R 3 2 2 6 4 3 5 5 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d e )m +--R + +--R 3 2 2 6 4 3 5 +--R (68A a b + 102B a b )e + (12A b + 48B a b )d e +--R + +--R 4 2 4 +--R - 5B b d e +--R * +--R 4 +--R m +--R + +--R 3 2 2 6 4 3 5 +--R (428A a b + 642B a b )e + (47A b + 188B a b )d e +--R + +--R 4 2 4 +--R - 30B b d e +--R * +--R 3 +--R m +--R + +--R 3 2 2 6 4 3 5 +--R (1228A a b + 1842B a b )e + (72A b + 288B a b )d e +--R + +--R 4 2 4 +--R - 55B b d e +--R * +--R 2 +--R m +--R + +--R 3 2 2 6 4 3 5 +--R (1584A a b + 2376B a b )e + (36A b + 144B a b )d e +--R + +--R 4 2 4 +--R - 30B b d e +--R * +--R m +--R + +--R 3 2 2 6 +--R (720A a b + 1080B a b )e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 3 2 2 5 5 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d e )m +--R + +--R 2 2 3 6 3 2 2 5 +--R (108A a b + 72B a b)e + (56A a b + 84B a b )d e +--R + +--R 4 3 2 4 +--R (- 4A b - 16B a b )d e +--R * +--R 4 +--R m +--R + +--R 2 2 3 6 3 2 2 5 +--R (726A a b + 484B a b)e + (260A a b + 390B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (- 36A b - 144B a b )d e + 20B b d e +--R * +--R 3 +--R m +--R + +--R 2 2 3 6 3 2 2 5 +--R (2232A a b + 1488B a b)e + (448A a b + 672B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (- 80A b - 320B a b )d e + 60B b d e +--R * +--R 2 +--R m +--R + +--R 2 2 3 6 3 2 2 5 +--R (3048A a b + 2032B a b)e + (240A a b + 360B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (- 48A b - 192B a b )d e + 40B b d e +--R * +--R m +--R + +--R 2 2 3 6 +--R (1440A a b + 960B a b)e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 2 3 5 5 +--R ((4A a b + B a )e + (6A a b + 4B a b)d e )m +--R + +--R 3 4 6 2 2 3 5 +--R (76A a b + 19B a )e + (96A a b + 64B a b)d e +--R + +--R 3 2 2 2 4 +--R (- 12A a b - 18B a b )d e +--R * +--R 4 +--R m +--R + +--R 3 4 6 2 2 3 5 +--R (548A a b + 137B a )e + (534A a b + 356B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 144A a b - 216B a b )d e + (12A b + 48B a b )d e +--R * +--R 3 +--R m +--R + +--R 3 4 6 2 2 3 5 +--R (1844A a b + 461B a )e + (1164A a b + 776B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 492A a b - 738B a b )d e + (84A b + 336B a b )d e +--R + +--R 4 4 2 +--R - 60B b d e +--R * +--R 2 +--R m +--R + +--R 3 4 6 2 2 3 5 +--R (2808A a b + 702B a )e + (720A a b + 480B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 360A a b - 540B a b )d e + (72A b + 288B a b )d e +--R + +--R 4 4 2 +--R - 60B b d e +--R * +--R m +--R + +--R 3 4 6 +--R (1440A a b + 360B a )e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 5 5 +--R (A a e + (4A a b + B a )d e )m +--R + +--R 4 6 3 4 5 2 2 3 2 4 4 +--R (20A a e + (72A a b + 18B a )d e + (- 12A a b - 8B a b)d e )m +--R + +--R 4 6 3 4 5 +--R 155A a e + (476A a b + 119B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 180A a b - 120B a b)d e + (24A a b + 36B a b )d e +--R * +--R 3 +--R m +--R + +--R 4 6 3 4 5 +--R 580A a e + (1368A a b + 342B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 888A a b - 592B a b)d e + (264A a b + 396B a b )d e +--R + +--R 4 3 4 2 +--R (- 24A b - 96B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 6 3 4 5 +--R 1044A a e + (1440A a b + 360B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 1440A a b - 960B a b)d e + (720A a b + 1080B a b )d e +--R + +--R 4 3 4 2 4 5 +--R (- 144A b - 576B a b )d e + 120B b d e +--R * +--R m +--R + +--R 4 6 +--R 720A a e +--R * +--R x +--R + +--R 4 5 5 4 5 3 4 2 4 4 +--R A a d e m + (20A a d e + (- 4A a b - B a )d e )m +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 3 +--R (155A a d e + (- 72A a b - 18B a )d e + (12A a b + 8B a b)d e )m +--R + +--R 4 5 3 4 2 4 +--R 580A a d e + (- 476A a b - 119B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (180A a b + 120B a b)d e + (- 24A a b - 36B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 5 3 4 2 4 +--R 1044A a d e + (- 1368A a b - 342B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (888A a b + 592B a b)d e + (- 264A a b - 396B a b )d e +--R + +--R 4 3 5 +--R (24A b + 96B a b )d e +--R * +--R m +--R + +--R 4 5 3 4 2 4 +--R 720A a d e + (- 1440A a b - 360B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (1440A a b + 960B a b)d e + (- 720A a b - 1080B a b )d e +--R + +--R 4 3 5 4 6 +--R (144A b + 576B a b )d e - 120B b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 4 5 4 4 4 3 4 2 4 4 +--R (- B b m - 15B b m - 85B b m - 225B b m - 274B b m - 120B b ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 4 3 4 5 +--R ((- A b - 4B a b )e + 5B b d)m +--R + +--R 4 3 4 4 +--R ((- 16A b - 64B a b )e + 80B b d)m +--R + +--R 4 3 4 3 +--R ((- 95A b - 380B a b )e + 475B b d)m +--R + +--R 4 3 4 2 +--R ((- 260A b - 1040B a b )e + 1300B b d)m +--R + +--R 4 3 4 4 3 +--R ((- 324A b - 1296B a b )e + 1620B b d)m + (- 144A b - 576B a b )e +--R + +--R 4 +--R 720B b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((- 4A a b - 6B a b )e + (4A b + 16B a b )d e - 10B b d )m +--R + +--R 3 2 2 2 4 3 4 2 4 +--R ((- 68A a b - 102B a b )e + (68A b + 272B a b )d e - 170B b d )m +--R + +--R 3 2 2 2 4 3 +--R (- 428A a b - 642B a b )e + (428A b + 1712B a b )d e +--R + +--R 4 2 +--R - 1070B b d +--R * +--R 3 +--R m +--R + +--R 3 2 2 2 4 3 +--R (- 1228A a b - 1842B a b )e + (1228A b + 4912B a b )d e +--R + +--R 4 2 +--R - 3070B b d +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 4 3 +--R (- 1584A a b - 2376B a b )e + (1584A b + 6336B a b )d e +--R + +--R 4 2 +--R - 3960B b d +--R * +--R m +--R + +--R 3 2 2 2 4 3 4 2 +--R (- 720A a b - 1080B a b )e + (720A b + 2880B a b )d e - 1800B b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 6A a b - 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b - 24B a b )d e + 10B b d +--R * +--R 5 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 108A a b - 72B a b)e + (216A a b + 324B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 108A b - 432B a b )d e + 180B b d +--R * +--R 4 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 726A a b - 484B a b)e + (1452A a b + 2178B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 726A b - 2904B a b )d e + 1210B b d +--R * +--R 3 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 2232A a b - 1488B a b)e + (4464A a b + 6696B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 2232A b - 8928B a b )d e + 3720B b d +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 3048A a b - 2032B a b)e + (6096A a b + 9144B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 3048A b - 12192B a b )d e + 5080B b d +--R * +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1440A a b - 960B a b)e + (2880A a b + 4320B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 1440A b - 5760B a b )d e + 2400B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 4 4 2 2 3 3 +--R (- 4A a b - B a )e + (12A a b + 8B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 12A a b - 18B a b )d e + (4A b + 16B a b )d e - 5B b d +--R * +--R 5 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (- 76A a b - 19B a )e + (228A a b + 152B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 228A a b - 342B a b )d e + (76A b + 304B a b )d e - 95B b d +--R * +--R 4 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (- 548A a b - 137B a )e + (1644A a b + 1096B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 1644A a b - 2466B a b )d e + (548A b + 2192B a b )d e +--R + +--R 4 4 +--R - 685B b d +--R * +--R 3 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (- 1844A a b - 461B a )e + (5532A a b + 3688B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 5532A a b - 8298B a b )d e + (1844A b + 7376B a b )d e +--R + +--R 4 4 +--R - 2305B b d +--R * +--R 2 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (- 2808A a b - 702B a )e + (8424A a b + 5616B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 8424A a b - 12636B a b )d e + (2808A b + 11232B a b )d e +--R + +--R 4 4 +--R - 3510B b d +--R * +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (- 1440A a b - 360B a )e + (4320A a b + 2880B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 4320A a b - 6480B a b )d e + (1440A b + 5760B a b )d e +--R + +--R 4 4 +--R - 1800B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - A a e + (4A a b + B a )d e + (- 6A a b - 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (4A a b + 6B a b )d e + (- A b - 4B a b )d e + B b d +--R * +--R 5 +--R m +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 20A a e + (80A a b + 20B a )d e + (- 120A a b - 80B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (80A a b + 120B a b )d e + (- 20A b - 80B a b )d e + 20B b d +--R * +--R 4 +--R m +--R + +--R 4 5 3 4 4 +--R - 155A a e + (620A a b + 155B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 930A a b - 620B a b)d e + (620A a b + 930B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 155A b - 620B a b )d e + 155B b d +--R * +--R 3 +--R m +--R + +--R 4 5 3 4 4 +--R - 580A a e + (2320A a b + 580B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 3480A a b - 2320B a b)d e + (2320A a b + 3480B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 580A b - 2320B a b )d e + 580B b d +--R * +--R 2 +--R m +--R + +--R 4 5 3 4 4 +--R - 1044A a e + (4176A a b + 1044B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 6264A a b - 4176B a b)d e + (4176A a b + 6264B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 1044A b - 4176B a b )d e + 1044B b d +--R * +--R m +--R + +--R 4 5 3 4 4 +--R - 720A a e + (2880A a b + 720B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 4320A a b - 2880B a b)d e + (2880A a b + 4320B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 720A b - 2880B a b )d e + 720B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1378 +t0:=(A+B*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 7 12 4 3 7 4 6 11 +--R B b e x + ((A b + 4B a b )e + 7B b d e )x +--R + +--R 3 2 2 7 4 3 6 4 2 5 10 +--R ((4A a b + 6B a b )e + (7A b + 28B a b )d e + 21B b d e )x +--R + +--R 2 2 3 7 3 2 2 6 +--R (6A a b + 4B a b)e + (28A a b + 42B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (21A b + 84B a b )d e + 35B b d e +--R * +--R 9 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (4A a b + B a )e + (42A a b + 28B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 4 4 3 +--R (84A a b + 126B a b )d e + (35A b + 140B a b )d e + 35B b d e +--R * +--R 8 +--R x +--R + +--R 4 7 3 4 6 2 2 3 2 5 +--R A a e + (28A a b + 7B a )d e + (126A a b + 84B a b)d e +--R + +--R 3 2 2 3 4 4 3 4 3 4 5 2 +--R (140A a b + 210B a b )d e + (35A b + 140B a b )d e + 21B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 2 5 2 2 3 3 4 +--R 7A a d e + (84A a b + 21B a )d e + (210A a b + 140B a b)d e +--R + +--R 3 2 2 4 3 4 3 5 2 4 6 +--R (140A a b + 210B a b )d e + (21A b + 84B a b )d e + 7B b d e +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 4 3 4 2 2 3 4 3 +--R 21A a d e + (140A a b + 35B a )d e + (210A a b + 140B a b)d e +--R + +--R 3 2 2 5 2 4 3 6 4 7 +--R (84A a b + 126B a b )d e + (7A b + 28B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 3 4 3 4 4 3 2 2 3 5 2 +--R 35A a d e + (140A a b + 35B a )d e + (126A a b + 84B a b)d e +--R + +--R 3 2 2 6 4 3 7 +--R (28A a b + 42B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 4 3 3 4 5 2 2 2 3 6 +--R 35A a d e + (84A a b + 21B a )d e + (42A a b + 28B a b)d e +--R + +--R 3 2 2 7 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 4 6 2 2 3 7 2 +--R (21A a d e + (28A a b + 7B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 6 3 4 7 4 7 +--R (7A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 1378 +r0:=-1/8*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^8/e^6+1/9*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^9/e^6-1/5*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^10/e^6+2/11*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^11/e^6-1/12*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^12/e^6+_ + 1/13*b^4*B*(d+e*x)^13/e^6 +--R +--R +--R (2) +--R 1 4 13 13 1 4 1 3 13 7 4 12 12 +--R -- B b e x + ((-- A b + - B a b )e + -- B b d e )x +--R 13 12 3 12 +--R + +--R 4 3 6 2 2 13 7 4 28 3 12 +--R (-- A a b + -- B a b )e + (-- A b + -- B a b )d e +--R 11 11 11 11 +--R + +--R 21 4 2 11 +--R -- B b d e +--R 11 +--R * +--R 11 +--R x +--R + +--R 3 2 2 2 3 13 14 3 21 2 2 12 +--R (- A a b + - B a b)e + (-- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 21 4 42 3 2 11 7 4 3 10 +--R (-- A b + -- B a b )d e + - B b d e +--R 10 5 2 +--R * +--R 10 +--R x +--R + +--R 4 3 1 4 13 14 2 2 28 3 12 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 9 9 3 9 +--R + +--R 28 3 2 2 2 11 35 4 140 3 3 10 35 4 4 9 +--R (-- A a b + 14B a b )d e + (-- A b + --- B a b )d e + -- B b d e +--R 3 9 9 9 +--R * +--R 9 +--R x +--R + +--R 1 4 13 7 3 7 4 12 63 2 2 21 3 2 11 +--R - A a e + (- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 8 2 8 4 2 +--R + +--R 35 3 105 2 2 3 10 35 4 35 3 4 9 21 4 5 8 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + -- B b d e +--R 2 4 8 2 8 +--R * +--R 8 +--R x +--R + +--R 4 12 3 4 2 11 2 2 3 3 10 +--R A a d e + (12A a b + 3B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 4 9 4 3 5 8 4 6 7 +--R (20A a b + 30B a b )d e + (3A b + 12B a b )d e + B b d e +--R * +--R 7 +--R x +--R + +--R 7 4 2 11 70 3 35 4 3 10 2 2 70 3 4 9 +--R - A a d e + (-- A a b + -- B a )d e + (35A a b + -- B a b)d e +--R 2 3 6 3 +--R + +--R 3 2 2 5 8 7 4 14 3 6 7 1 4 7 6 +--R (14A a b + 21B a b )d e + (- A b + -- B a b )d e + - B b d e +--R 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 3 10 3 4 4 9 126 2 2 84 3 5 8 +--R 7A a d e + (28A a b + 7B a )d e + (--- A a b + -- B a b)d e +--R 5 5 +--R + +--R 28 3 42 2 2 6 7 1 4 4 3 7 6 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 35 4 4 9 3 21 4 5 8 21 2 2 3 6 7 +--R -- A a d e + (21A a b + -- B a )d e + (-- A a b + 7B a b)d e +--R 4 4 2 +--R + +--R 3 3 2 2 7 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 5 8 28 3 7 4 6 7 2 2 4 3 7 6 3 +--R (7A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d e )x +--R 3 3 3 +--R + +--R 7 4 6 7 3 1 4 7 6 2 4 7 6 1 4 8 5 +--R (- A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 8 +--R + +--R 1 3 1 4 9 4 1 2 2 1 3 10 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 18 72 60 90 +--R + +--R 1 3 1 2 2 11 2 1 4 1 3 12 +--R (- --- A a b - --- B a b )d e + (---- A b + --- B a b )d e +--R 330 220 3960 990 +--R + +--R 1 4 13 +--R - ----- B b d +--R 10296 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 212 + +--S 213 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 7 13 1 4 1 3 7 7 4 6 12 +--R -- B b e x + ((-- A b + - B a b )e + -- B b d e )x +--R 13 12 3 12 +--R + +--R 4 3 6 2 2 7 7 4 28 3 6 21 4 2 5 11 +--R ((-- A a b + -- B a b )e + (-- A b + -- B a b )d e + -- B b d e )x +--R 11 11 11 11 11 +--R + +--R 3 2 2 2 3 7 14 3 21 2 2 6 +--R (- A a b + - B a b)e + (-- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 21 4 42 3 2 5 7 4 3 4 +--R (-- A b + -- B a b )d e + - B b d e +--R 10 5 2 +--R * +--R 10 +--R x +--R + +--R 4 3 1 4 7 14 2 2 28 3 6 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 9 9 3 9 +--R + +--R 28 3 2 2 2 5 35 4 140 3 3 4 35 4 4 3 +--R (-- A a b + 14B a b )d e + (-- A b + --- B a b )d e + -- B b d e +--R 3 9 9 9 +--R * +--R 9 +--R x +--R + +--R 1 4 7 7 3 7 4 6 63 2 2 21 3 2 5 +--R - A a e + (- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 8 2 8 4 2 +--R + +--R 35 3 105 2 2 3 4 35 4 35 3 4 3 21 4 5 2 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + -- B b d e +--R 2 4 8 2 8 +--R * +--R 8 +--R x +--R + +--R 4 6 3 4 2 5 2 2 3 3 4 +--R A a d e + (12A a b + 3B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 4 3 4 3 5 2 4 6 +--R (20A a b + 30B a b )d e + (3A b + 12B a b )d e + B b d e +--R * +--R 7 +--R x +--R + +--R 7 4 2 5 70 3 35 4 3 4 2 2 70 3 4 3 +--R - A a d e + (-- A a b + -- B a )d e + (35A a b + -- B a b)d e +--R 2 3 6 3 +--R + +--R 3 2 2 5 2 7 4 14 3 6 1 4 7 +--R (14A a b + 21B a b )d e + (- A b + -- B a b )d e + - B b d +--R 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 3 4 3 4 4 3 126 2 2 84 3 5 2 +--R 7A a d e + (28A a b + 7B a )d e + (--- A a b + -- B a b)d e +--R 5 5 +--R + +--R 28 3 42 2 2 6 1 4 4 3 7 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 35 4 4 3 3 21 4 5 2 21 2 2 3 6 +--R -- A a d e + (21A a b + -- B a )d e + (-- A a b + 7B a b)d e +--R 4 4 2 +--R + +--R 3 3 2 2 7 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 5 2 28 3 7 4 6 2 2 4 3 7 3 +--R (7A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d )x +--R 3 3 3 +--R + +--R 7 4 6 3 1 4 7 2 4 7 +--R (- A a d e + (2A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 4 8 5 1 3 1 4 9 4 1 2 2 1 3 10 3 +--R - - A a d e + (-- A a b + -- B a )d e + (- -- A a b - -- B a b)d e +--R 8 18 72 60 90 +--R + +--R 1 3 1 2 2 11 2 1 4 1 3 12 +--R (--- A a b + --- B a b )d e + (- ---- A b - --- B a b )d e +--R 330 220 3960 990 +--R + +--R 1 4 13 +--R ----- B b d +--R 10296 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 214 + +--S 215 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 215 + +)clear all + +--S 216 of 1378 +t0:=(A+B*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 11 4 3 6 4 5 10 +--R B b e x + ((A b + 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 6 4 3 5 4 2 4 9 +--R ((4A a b + 6B a b )e + (6A b + 24B a b )d e + 15B b d e )x +--R + +--R 2 2 3 6 3 2 2 5 +--R (6A a b + 4B a b)e + (24A a b + 36B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (15A b + 60B a b )d e + 20B b d e +--R * +--R 8 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (4A a b + B a )e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 4 4 2 +--R (60A a b + 90B a b )d e + (20A b + 80B a b )d e + 15B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 5 2 2 3 2 4 +--R A a e + (24A a b + 6B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 3 3 4 3 4 2 4 5 +--R (80A a b + 120B a b )d e + (15A b + 60B a b )d e + 6B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 6A a d e + (60A a b + 15B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (60A a b + 90B a b )d e + (6A b + 24B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A a d e + (80A a b + 20B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 5 4 3 6 +--R (24A a b + 36B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 4 4 2 2 2 3 5 +--R 20A a d e + (60A a b + 15B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 6 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 2 +--R (15A a d e + (24A a b + 6B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 5 3 4 6 4 6 +--R (6A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 1378 +r0:=-1/7*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^7/e^6+1/8*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^8/e^6-2/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^9/e^6+1/5*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^10/e^6-1/11*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^11/e^6+_ + 1/12*b^4*B*(d+e*x)^12/e^6 +--R +--R +--R (2) +--R 1 4 12 12 1 4 4 3 12 6 4 11 11 +--R -- B b e x + ((-- A b + -- B a b )e + -- B b d e )x +--R 12 11 11 11 +--R + +--R 2 3 3 2 2 12 3 4 12 3 11 3 4 2 10 10 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e )x +--R 5 5 5 5 2 +--R + +--R 2 2 2 4 3 12 8 3 2 2 11 +--R (- A a b + - B a b)e + (- A a b + 4B a b )d e +--R 3 9 3 +--R + +--R 5 4 20 3 2 10 20 4 3 9 +--R (- A b + -- B a b )d e + -- B b d e +--R 3 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 1 4 12 9 2 2 3 11 +--R (- A a b + - B a )e + (- A a b + 3B a b)d e +--R 2 8 2 +--R + +--R 15 3 45 2 2 2 10 5 4 3 3 9 15 4 4 8 +--R (-- A a b + -- B a b )d e + (- A b + 10B a b )d e + -- B b d e +--R 2 4 2 8 +--R * +--R 8 +--R x +--R + +--R 1 4 12 24 3 6 4 11 90 2 2 60 3 2 10 +--R - A a e + (-- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 80 3 120 2 2 3 9 15 4 60 3 4 8 6 4 5 7 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 4 11 3 5 4 2 10 2 2 40 3 3 9 +--R A a d e + (10A a b + - B a )d e + (20A a b + -- B a b)d e +--R 2 3 +--R + +--R 3 2 2 4 8 4 3 5 7 1 4 6 6 +--R (10A a b + 15B a b )d e + (A b + 4B a b )d e + - B b d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 4 2 10 3 4 3 9 2 2 3 4 8 +--R 3A a d e + (16A a b + 4B a )d e + (18A a b + 12B a b)d e +--R + +--R 24 3 36 2 2 5 7 1 4 4 3 6 6 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 3 9 3 15 4 4 8 2 2 3 5 7 +--R 5A a d e + (15A a b + -- B a )d e + (9A a b + 6B a b)d e +--R 4 +--R + +--R 3 3 2 2 6 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 4 8 3 4 5 7 2 2 4 3 6 6 3 +--R (5A a d e + (8A a b + 2B a )d e + (2A a b + - B a b)d e )x +--R 3 +--R + +--R 4 5 7 3 1 4 6 6 2 4 6 6 1 4 7 5 +--R (3A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 7 +--R + +--R 1 3 1 4 8 4 1 2 2 1 3 9 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 14 56 42 63 +--R + +--R 1 3 1 2 2 10 2 1 4 2 3 11 +--R (- --- A a b - --- B a b )d e + (---- A b + ---- B a b )d e +--R 210 140 2310 1155 +--R + +--R 1 4 12 +--R - ---- B b d +--R 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 217 + +--S 218 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 6 12 1 4 4 3 6 6 4 5 11 +--R -- B b e x + ((-- A b + -- B a b )e + -- B b d e )x +--R 12 11 11 11 +--R + +--R 2 3 3 2 2 6 3 4 12 3 5 3 4 2 4 10 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e )x +--R 5 5 5 5 2 +--R + +--R 2 2 2 4 3 6 8 3 2 2 5 +--R (- A a b + - B a b)e + (- A a b + 4B a b )d e +--R 3 9 3 +--R + +--R 5 4 20 3 2 4 20 4 3 3 +--R (- A b + -- B a b )d e + -- B b d e +--R 3 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 1 4 6 9 2 2 3 5 +--R (- A a b + - B a )e + (- A a b + 3B a b)d e +--R 2 8 2 +--R + +--R 15 3 45 2 2 2 4 5 4 3 3 3 15 4 4 2 +--R (-- A a b + -- B a b )d e + (- A b + 10B a b )d e + -- B b d e +--R 2 4 2 8 +--R * +--R 8 +--R x +--R + +--R 1 4 6 24 3 6 4 5 90 2 2 60 3 2 4 +--R - A a e + (-- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 80 3 120 2 2 3 3 15 4 60 3 4 2 6 4 5 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 4 5 3 5 4 2 4 2 2 40 3 3 3 +--R A a d e + (10A a b + - B a )d e + (20A a b + -- B a b)d e +--R 2 3 +--R + +--R 3 2 2 4 2 4 3 5 1 4 6 +--R (10A a b + 15B a b )d e + (A b + 4B a b )d e + - B b d +--R 6 +--R * +--R 6 +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 3A a d e + (16A a b + 4B a )d e + (18A a b + 12B a b)d e +--R + +--R 24 3 36 2 2 5 1 4 4 3 6 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 3 3 3 15 4 4 2 2 2 3 5 +--R 5A a d e + (15A a b + -- B a )d e + (9A a b + 6B a b)d e +--R 4 +--R + +--R 3 3 2 2 6 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 4 2 3 4 5 2 2 4 3 6 3 +--R (5A a d e + (8A a b + 2B a )d e + (2A a b + - B a b)d )x +--R 3 +--R + +--R 4 5 3 1 4 6 2 4 6 +--R (3A a d e + (2A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 4 7 5 1 3 1 4 8 4 1 2 2 1 3 9 3 +--R - - A a d e + (-- A a b + -- B a )d e + (- -- A a b - -- B a b)d e +--R 7 14 56 42 63 +--R + +--R 1 3 1 2 2 10 2 1 4 2 3 11 +--R (--- A a b + --- B a b )d e + (- ---- A b - ---- B a b )d e +--R 210 140 2310 1155 +--R + +--R 1 4 12 +--R ---- B b d +--R 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 219 + +--S 220 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 220 + +)clear all + +--S 221 of 1378 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 10 4 3 5 4 4 9 +--R B b e x + ((A b + 4B a b )e + 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 8 +--R ((4A a b + 6B a b )e + (5A b + 20B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (6A a b + 4B a b)e + (20A a b + 30B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (10A b + 40B a b )d e + 10B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b + B a )e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (40A a b + 60B a b )d e + (10A b + 40B a b )d e + 5B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (20A a b + 5B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (40A a b + 60B a b )d e + (5A b + 20B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R 5A a d e + (40A a b + 10B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 4 4 3 5 +--R (20A a b + 30B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 3 2 2 2 3 4 +--R 10A a d e + (40A a b + 10B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 5 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 2 +--R (10A a d e + (20A a b + 5B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 4 3 4 5 4 5 +--R (5A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 1378 +r0:=-1/6*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^6/e^6+1/7*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^7/e^6-1/4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^8/e^6+2/9*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^9/e^6-1/10*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^10/e^6+_ + 1/11*b^4*B*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 4 11 11 1 4 2 3 11 1 4 10 10 +--R -- B b e x + ((-- A b + - B a b )e + - B b d e )x +--R 11 10 5 2 +--R + +--R 4 3 2 2 2 11 5 4 20 3 10 10 4 2 9 9 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + -- B b d e )x +--R 9 3 9 9 9 +--R + +--R 3 2 2 1 3 11 5 3 15 2 2 10 +--R (- A a b + - B a b)e + (- A a b + -- B a b )d e +--R 4 2 2 4 +--R + +--R 5 4 3 2 9 5 4 3 8 +--R (- A b + 5B a b )d e + - B b d e +--R 4 4 +--R * +--R 8 +--R x +--R + +--R 4 3 1 4 11 30 2 2 20 3 10 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 7 7 7 7 +--R + +--R 40 3 60 2 2 2 9 10 4 40 3 3 8 5 4 4 7 +--R (-- A a b + -- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 4 11 10 3 5 4 10 2 2 20 3 2 9 +--R - A a e + (-- A a b + - B a )d e + (10A a b + -- B a b)d e +--R 6 3 6 3 +--R + +--R 20 3 2 2 3 8 5 4 10 3 4 7 1 4 5 6 +--R (-- A a b + 10B a b )d e + (- A b + -- B a b )d e + - B b d e +--R 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 10 3 4 2 9 2 2 3 3 8 +--R A a d e + (8A a b + 2B a )d e + (12A a b + 8B a b)d e +--R + +--R 3 2 2 4 7 1 4 4 3 5 6 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 4 2 9 3 5 4 3 8 15 2 2 3 4 7 +--R - A a d e + (10A a b + - B a )d e + (-- A a b + 5B a b)d e +--R 2 2 2 +--R + +--R 3 3 2 2 5 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 10 4 3 8 20 3 5 4 4 7 2 2 4 3 5 6 3 +--R (-- A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d e )x +--R 3 3 3 3 +--R + +--R 5 4 4 7 3 1 4 5 6 2 4 5 6 1 4 6 5 +--R (- A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 2 3 1 4 7 4 1 2 2 1 3 8 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 21 42 28 42 +--R + +--R 1 3 1 2 2 9 2 1 4 1 3 10 +--R (- --- A a b - -- B a b )d e + (---- A b + --- B a b )d e +--R 126 84 1260 315 +--R + +--R 1 4 11 +--R - ---- B b d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 222 + +--S 223 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 5 11 1 4 2 3 5 1 4 4 10 +--R -- B b e x + ((-- A b + - B a b )e + - B b d e )x +--R 11 10 5 2 +--R + +--R 4 3 2 2 2 5 5 4 20 3 4 10 4 2 3 9 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + -- B b d e )x +--R 9 3 9 9 9 +--R + +--R 3 2 2 1 3 5 5 3 15 2 2 4 +--R (- A a b + - B a b)e + (- A a b + -- B a b )d e +--R 4 2 2 4 +--R + +--R 5 4 3 2 3 5 4 3 2 +--R (- A b + 5B a b )d e + - B b d e +--R 4 4 +--R * +--R 8 +--R x +--R + +--R 4 3 1 4 5 30 2 2 20 3 4 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 7 7 7 7 +--R + +--R 40 3 60 2 2 2 3 10 4 40 3 3 2 5 4 4 +--R (-- A a b + -- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 4 5 10 3 5 4 4 2 2 20 3 2 3 +--R - A a e + (-- A a b + - B a )d e + (10A a b + -- B a b)d e +--R 6 3 6 3 +--R + +--R 20 3 2 2 3 2 5 4 10 3 4 1 4 5 +--R (-- A a b + 10B a b )d e + (- A b + -- B a b )d e + - B b d +--R 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R A a d e + (8A a b + 2B a )d e + (12A a b + 8B a b)d e +--R + +--R 3 2 2 4 1 4 4 3 5 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 4 2 3 3 5 4 3 2 15 2 2 3 4 +--R - A a d e + (10A a b + - B a )d e + (-- A a b + 5B a b)d e +--R 2 2 2 +--R + +--R 3 3 2 2 5 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 10 4 3 2 20 3 5 4 4 2 2 4 3 5 3 +--R (-- A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d )x +--R 3 3 3 3 +--R + +--R 5 4 4 3 1 4 5 2 4 5 +--R (- A a d e + (2A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 4 6 5 2 3 1 4 7 4 1 2 2 1 3 8 3 +--R - - A a d e + (-- A a b + -- B a )d e + (- -- A a b - -- B a b)d e +--R 6 21 42 28 42 +--R + +--R 1 3 1 2 2 9 2 1 4 1 3 10 +--R (--- A a b + -- B a b )d e + (- ---- A b - --- B a b )d e +--R 126 84 1260 315 +--R + +--R 1 4 11 +--R ---- B b d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 224 + +--S 225 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 225 + +)clear all + +--S 226 of 1378 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 4 9 4 3 4 4 3 8 +--R B b e x + ((A b + 4B a b )e + 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((4A a b + 6B a b )e + (4A b + 16B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (6A a b + 4B a b)e + (16A a b + 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (6A b + 24B a b )d e + 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (24A a b + 36B a b )d e + (4A b + 16B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R A a e + (16A a b + 4B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (16A a b + 24B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 4A a d e + (24A a b + 6B a )d e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 4 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (6A a d e + (16A a b + 4B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (4A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 1378 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^4*(a+b*x)^5/b^6+1/6*(b*d-a*e)^3*(b*B*d+4*A*b*e-_ + 5*a*B*e)*(a+b*x)^6/b^6+2/7*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*_ + (a+b*x)^7/b^6+1/4*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^8/_ + b^6+1/9*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^9/b^6+1/10*B*e^4*_ + (a+b*x)^10/b^6 +--R +--R +--R (2) +--R 1 10 4 10 1 10 4 9 4 4 10 3 9 +--R -- B b e x + ((- A b + - B a b )e + - B b d e )x +--R 10 9 9 9 +--R + +--R 1 9 3 2 8 4 1 10 9 3 3 10 2 2 8 +--R ((- A a b + - B a b )e + (- A b + 2B a b )d e + - B b d e )x +--R 2 4 2 4 +--R + +--R 6 2 8 4 3 7 4 16 9 24 2 8 3 +--R (- A a b + - B a b )e + (-- A a b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 6 10 24 9 2 2 4 10 3 +--R (- A b + -- B a b )d e + - B b d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 2 3 7 1 4 6 4 2 8 8 3 7 3 +--R (- A a b + - B a b )e + (4A a b + - B a b )d e +--R 3 6 3 +--R + +--R 9 2 8 2 2 2 10 8 9 3 1 10 4 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d e + - B b d +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 4 6 4 16 3 7 4 4 6 3 36 2 8 24 3 7 2 2 +--R - A a b e + (-- A a b + - B a b )d e + (-- A a b + -- B a b )d e +--R 5 5 5 5 5 +--R + +--R 16 9 24 2 8 3 1 10 4 9 4 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 6 3 3 7 3 4 6 2 2 2 8 3 7 3 +--R A a b d e + (6A a b + - B a b )d e + (6A a b + 4B a b )d e +--R 2 +--R + +--R 9 3 2 8 4 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 6 2 2 16 3 7 4 4 6 3 2 8 4 3 7 4 3 +--R (2A a b d e + (-- A a b + - B a b )d e + (2A a b + - B a b )d )x +--R 3 3 3 +--R + +--R 4 6 3 3 7 1 4 6 4 2 4 6 4 +--R (2A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 9 1 10 4 1 8 2 2 9 3 +--R (--- A a b - ---- B a )e + (- -- A a b + --- B a b)d e +--R 630 1260 70 315 +--R + +--R 2 7 3 3 8 2 2 2 2 6 4 4 7 3 3 +--R (-- A a b - --- B a b )d e + (- -- A a b + --- B a b )d e +--R 35 140 15 105 +--R + +--R 1 5 5 1 6 4 4 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 227 + +--S 228 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 4 10 1 4 4 3 4 4 4 3 9 +--R -- B b e x + ((- A b + - B a b )e + - B b d e )x +--R 10 9 9 9 +--R + +--R 1 3 3 2 2 4 1 4 3 3 3 4 2 2 8 +--R ((- A a b + - B a b )e + (- A b + 2B a b )d e + - B b d e )x +--R 2 4 2 4 +--R + +--R 6 2 2 4 3 4 16 3 24 2 2 3 +--R (- A a b + - B a b)e + (-- A a b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 6 4 24 3 2 2 4 4 3 +--R (- A b + -- B a b )d e + - B b d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 2 3 1 4 4 2 2 8 3 3 +--R (- A a b + - B a )e + (4A a b + - B a b)d e +--R 3 6 3 +--R + +--R 3 2 2 2 2 2 4 8 3 3 1 4 4 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d e + - B b d +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 4 4 16 3 4 4 3 36 2 2 24 3 2 2 +--R - A a e + (-- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 5 5 5 5 5 +--R + +--R 16 3 24 2 2 3 1 4 4 3 4 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 3 3 3 4 2 2 2 2 3 3 +--R A a d e + (6A a b + - B a )d e + (6A a b + 4B a b)d e +--R 2 +--R + +--R 3 3 2 2 4 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 2 2 16 3 4 4 3 2 2 4 3 4 3 +--R (2A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d )x +--R 3 3 3 +--R + +--R 4 3 3 1 4 4 2 4 4 +--R (2A a d e + (2A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 9 1 10 4 1 8 2 2 9 3 +--R (- --- A a b + ---- B a )e + (-- A a b - --- B a b)d e +--R 630 1260 70 315 +--R + +--R 2 7 3 3 8 2 2 2 2 6 4 4 7 3 3 +--R (- -- A a b + --- B a b )d e + (-- A a b - --- B a b )d e +--R 35 140 15 105 +--R + +--R 1 5 5 1 6 4 4 +--R (- - A a b + -- B a b )d +--R 5 30 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 229 + +--S 230 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 230 + +)clear all + +--S 231 of 1378 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e + (12A a b + 18B a b )d e +--R + +--R 4 3 3 +--R (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 1378 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^3*(a+b*x)^5/b^5+1/6*(b*d-a*e)^2*(b*B*d+3*A*b*e-_ + 4*a*B*e)*(a+b*x)^6/b^5+3/7*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^7/b^5+1/8*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^8/b^5+_ + 1/9*B*e^3*(a+b*x)^9/b^5 +--R +--R +--R (2) +--R 1 9 3 9 1 9 1 8 3 3 9 2 8 +--R - B b e x + ((- A b + - B a b )e + - B b d e )x +--R 9 8 2 8 +--R + +--R 4 8 6 2 7 3 3 9 12 8 2 3 9 2 7 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e)x +--R 7 7 7 7 7 +--R + +--R 2 7 2 3 6 3 8 2 7 2 +--R (A a b + - B a b )e + (2A a b + 3B a b )d e +--R 3 +--R + +--R 1 9 8 2 1 9 3 +--R (- A b + 2B a b )d e + - B b d +--R 2 6 +--R * +--R 6 +--R x +--R + +--R 4 3 6 1 4 5 3 18 2 7 12 3 6 2 +--R (- A a b + - B a b )e + (-- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 12 8 18 2 7 2 1 9 4 8 3 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 4 5 3 3 6 3 4 5 2 9 2 7 3 6 2 +--R - A a b e + (3A a b + - B a b )d e + (- A a b + 3B a b )d e +--R 4 4 2 +--R + +--R 8 3 2 7 3 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 5 2 3 6 4 5 2 2 7 4 3 6 3 3 +--R (A a b d e + (4A a b + B a b )d e + (2A a b + - B a b )d )x +--R 3 +--R + +--R 3 4 5 2 3 6 1 4 5 3 2 4 5 3 +--R (- A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 2 +--R + +--R 1 8 1 9 3 1 7 2 3 8 2 +--R (- --- A a b + --- B a )e + (-- A a b - --- B a b)d e +--R 280 630 35 280 +--R + +--R 1 6 3 1 7 2 2 1 5 4 1 6 3 3 +--R (- -- A a b + -- B a b )d e + (- A a b - -- B a b )d +--R 10 35 5 30 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 232 + +--S 233 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 3 9 1 4 1 3 3 3 4 2 8 +--R - B b e x + ((- A b + - B a b )e + - B b d e )x +--R 9 8 2 8 +--R + +--R 4 3 6 2 2 3 3 4 12 3 2 3 4 2 7 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e)x +--R 7 7 7 7 7 +--R + +--R 2 2 2 3 3 3 2 2 2 1 4 3 2 +--R (A a b + - B a b)e + (2A a b + 3B a b )d e + (- A b + 2B a b )d e +--R 3 2 +--R + +--R 1 4 3 +--R - B b d +--R 6 +--R * +--R 6 +--R x +--R + +--R 4 3 1 4 3 18 2 2 12 3 2 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 5 5 5 5 +--R + +--R 12 3 18 2 2 2 1 4 4 3 3 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 4 3 3 3 4 2 9 2 2 3 2 +--R - A a e + (3A a b + - B a )d e + (- A a b + 3B a b)d e +--R 4 4 2 +--R + +--R 3 3 2 2 3 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 2 3 4 2 2 2 4 3 3 3 +--R (A a d e + (4A a b + B a )d e + (2A a b + - B a b)d )x +--R 3 +--R + +--R 3 4 2 3 1 4 3 2 4 3 +--R (- A a d e + (2A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 8 1 9 3 1 7 2 3 8 2 +--R (--- A a b - --- B a )e + (- -- A a b + --- B a b)d e +--R 280 630 35 280 +--R + +--R 1 6 3 1 7 2 2 1 5 4 1 6 3 3 +--R (-- A a b - -- B a b )d e + (- - A a b + -- B a b )d +--R 10 35 5 30 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 234 + +--S 235 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 235 + +)clear all + +--S 236 of 1378 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 236 + +--S 237 of 1378 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^5/b^4+1/6*(b*d-a*e)*(b*B*d+2*A*b*e-_ + 3*a*B*e)*(a+b*x)^6/b^4+1/7*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^7/b^4+_ + 1/8*B*e^2*(a+b*x)^8/b^4 +--R +--R +--R (2) +--R 1 8 2 8 1 8 4 7 2 2 8 7 +--R - B b e x + ((- A b + - B a b )e + - B b d e)x +--R 8 7 7 7 +--R + +--R 2 7 2 6 2 1 8 4 7 1 8 2 6 +--R ((- A a b + B a b )e + (- A b + - B a b )d e + - B b d )x +--R 3 3 3 6 +--R + +--R 6 2 6 4 3 5 2 8 7 12 2 6 +--R (- A a b + - B a b )e + (- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 1 8 4 7 2 +--R (- A b + - B a b )d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 3 5 1 4 4 2 2 6 3 5 +--R (A a b + - B a b )e + (3A a b + 2B a b )d e +--R 4 +--R + +--R 7 3 2 6 2 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 1 4 4 2 8 3 5 2 4 4 2 6 4 3 5 2 3 +--R (- A a b e + (- A a b + - B a b )d e + (2A a b + - B a b )d )x +--R 3 3 3 3 +--R + +--R 4 4 3 5 1 4 4 2 2 4 4 2 +--R (A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 7 1 8 2 1 6 2 2 7 +--R (--- A a b - --- B a )e + (- -- A a b + --- B a b)d e +--R 105 280 15 105 +--R + +--R 1 5 3 1 6 2 2 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 237 + +--S 238 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 2 8 1 4 4 3 2 2 4 7 +--R - B b e x + ((- A b + - B a b )e + - B b d e)x +--R 8 7 7 7 +--R + +--R 2 3 2 2 2 1 4 4 3 1 4 2 6 +--R ((- A a b + B a b )e + (- A b + - B a b )d e + - B b d )x +--R 3 3 3 6 +--R + +--R 6 2 2 4 3 2 8 3 12 2 2 +--R (- A a b + - B a b)e + (- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 1 4 4 3 2 +--R (- A b + - B a b )d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 3 1 4 2 2 2 3 3 3 2 2 2 4 +--R ((A a b + - B a )e + (3A a b + 2B a b)d e + (A a b + - B a b )d )x +--R 4 2 +--R + +--R 1 4 2 8 3 2 4 2 2 4 3 2 3 +--R (- A a e + (- A a b + - B a )d e + (2A a b + - B a b)d )x +--R 3 3 3 3 +--R + +--R 4 3 1 4 2 2 4 2 +--R (A a d e + (2A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 238 + +--S 239 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 7 1 8 2 1 6 2 2 7 +--R (- --- A a b + --- B a )e + (-- A a b - --- B a b)d e +--R 105 280 15 105 +--R + +--R 1 5 3 1 6 2 2 +--R (- - A a b + -- B a b )d +--R 5 30 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 239 + +--S 240 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 240 + +)clear all + +--S 241 of 1378 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R Type: Polynomial(Integer) +--E 241 + +--S 242 of 1378 +r0:=1/5*(A*b-a*B)*(b*d-a*e)*(a+b*x)^5/b^3+1/6*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^6/b^3+1/7*B*e*(a+b*x)^7/b^3 +--R +--R +--R (2) +--R 1 7 7 1 7 2 6 1 7 6 +--R - B b e x + ((- A b + - B a b )e + - B b d)x +--R 7 6 3 6 +--R + +--R 4 6 6 2 5 1 7 4 6 5 +--R ((- A a b + - B a b )e + (- A b + - B a b )d)x +--R 5 5 5 5 +--R + +--R 3 2 5 3 4 6 3 2 5 4 +--R ((- A a b + B a b )e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 3 4 1 4 3 2 5 4 3 4 3 +--R ((- A a b + - B a b )e + (2A a b + - B a b )d)x +--R 3 3 3 +--R + +--R 1 4 3 3 4 1 4 3 2 4 3 +--R (- A a b e + (2A a b + - B a b )d)x + A a b d x +--R 2 2 +--R + +--R 1 6 1 7 1 5 2 1 6 +--R (- -- A a b + --- B a )e + (- A a b - -- B a b)d +--R 30 105 5 30 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 242 + +--S 243 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 7 1 4 2 3 1 4 6 +--R - B b e x + ((- A b + - B a b )e + - B b d)x +--R 7 6 3 6 +--R + +--R 4 3 6 2 2 1 4 4 3 5 +--R ((- A a b + - B a b )e + (- A b + - B a b )d)x +--R 5 5 5 5 +--R + +--R 3 2 2 3 3 3 2 2 4 +--R ((- A a b + B a b)e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 3 1 4 2 2 4 3 3 +--R ((- A a b + - B a )e + (2A a b + - B a b)d)x +--R 3 3 3 +--R + +--R 1 4 3 1 4 2 4 +--R (- A a e + (2A a b + - B a )d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 243 + +--S 244 of 1378 +m0:=a0-r0 +--R +--R +--R 1 6 1 7 1 5 2 1 6 +--R (-- A a b - --- B a )e + (- - A a b + -- B a b)d +--R 30 105 5 30 +--R (4) ------------------------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 244 + +--S 245 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 245 + +)clear all + +--S 246 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 2 2 3 2 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x + (6A a b + 4B a b)x +--R + +--R 3 4 4 +--R (4A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 246 + +--S 247 of 1378 +r0:=1/5*(A*b-a*B)*(a+b*x)^5/b^2+1/6*B*(a+b*x)^6/b^2 +--R +--R +--R (2) +--R 1 6 6 1 6 4 5 5 5 3 2 4 4 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x +--R 6 5 5 2 +--R + +--R 2 4 4 3 3 3 3 3 1 4 2 2 4 2 1 5 +--R (2A a b + - B a b )x + (2A a b + - B a b )x + A a b x + - A a b +--R 3 2 5 +--R + +--R 1 6 +--R - -- B a +--R 30 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 247 + +--S 248 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 6 1 4 4 3 5 3 3 2 2 4 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x +--R 6 5 5 2 +--R + +--R 2 2 4 3 3 3 1 4 2 4 +--R (2A a b + - B a b)x + (2A a b + - B a )x + A a x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 248 + +--S 249 of 1378 +m0:=a0-r0 +--R +--R +--R 1 5 1 6 +--R - - A a b + -- B a +--R 5 30 +--R (4) ------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 249 + +--S 250 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 250 + +)clear all + +--S 251 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1378 +r0:=b*(b*d-a*e)^3*(B*d-A*e)*x/e^5-1/2*(b*d-a*e)^2*(B*d-A*e)*(a+b*x)^2/e^4+_ + 1/3*(b*d-a*e)*(B*d-A*e)*(a+b*x)^3/e^3-1/4*(B*d-A*e)*(a+b*x)^4/e^2+_ + 1/5*B*(a+b*x)^5/(b*e)-(b*d-a*e)^4*(B*d-A*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 3 2 4 4 +--R 60A a b e + (- 240A a b - 60B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (360A a b + 240B a b )d e + (- 240A a b - 360B a b )d e +--R + +--R 5 4 4 5 5 +--R (60A b + 240B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 5 4 5 5 4 4 +--R 12B b e x + ((15A b + 60B a b )e - 15B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 3 +--R ((80A a b + 120B a b )e + (- 20A b - 80B a b )d e + 20B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (180A a b + 120B a b )e + (- 120A a b - 180B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b + 120B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b + 60B a b)e + (- 360A a b - 240B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (240A a b + 360B a b )d e + (- 60A b - 240B a b )d e + 60B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (65A a b + 12B a )e + (- 80A a b - 65B a b)d e +--R + +--R 2 3 3 2 2 3 2 3 3 2 +--R (30A a b + 80B a b )d e - 30B a b d e +--R / +--R 6 +--R 60b e +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 3 4 4 2 2 3 2 3 +--R 60A a e + (- 240A a b - 60B a )d e + (360A a b + 240B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 240A a b - 360B a b )d e + (60A b + 240B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 12B b e x + ((15A b + 60B a b )e - 15B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((80A a b + 120B a b )e + (- 20A b - 80B a b )d e + 20B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (180A a b + 120B a b)e + (- 120A a b - 180B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (30A b + 120B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (240A a b + 60B a )e + (- 360A a b - 240B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (240A a b + 360B a b )d e + (- 60A b - 240B a b )d e + 60B b d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 3 3 2 4 2 +--R (- 65A a b - 12B a )e + (80A a b + 65B a b)d e +--R + +--R 2 3 3 2 2 2 3 3 +--R (- 30A a b - 80B a b )d e + 30B a b d +--R / +--R 4 +--R 60b e +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1378 +r0:=-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*x/e^5+(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x))+b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^2/e^6-1/3*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^3/e^6+1/4*b^4*_ + B*(d+e*x)^4/e^6+(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 4 5 2 2 3 4 +--R (48A a b + 12B a )e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e +--R + +--R 4 4 +--R 60B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 2 3 +--R (48A a b + 12B a )d e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((4A b + 16B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 8A b - 32B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (72A a b + 48B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (24A b + 96B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (16A b + 64B a b )d e - 5B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 12A a e + (48A a b + 12B a )d e + (- 72A a b - 48B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (72A a b + 108B a b )d e + (- 32A b - 128B a b )d e + 55B b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 5 2 2 3 4 +--R (48A a b + 12B a )e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e +--R + +--R 4 4 +--R 60B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 2 3 +--R (48A a b + 12B a )d e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((4A b + 16B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 8A b - 32B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (72A a b + 48B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (24A b + 96B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 96A a b - 144B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (36A b + 144B a b )d e - 48B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 12A a e + (48A a b + 12B a )d e + (- 72A a b - 48B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (48A a b + 72B a b )d e + (- 12A b - 48B a b )d e + 12B b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1378 +m0:=a0-r0 +--R +--R +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 24A a b - 36B a b )d e + (20A b + 80B a b )d e - 43B b d +--R (4) --------------------------------------------------------------- +--R 6 +--R 12e +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1378 +r0:=2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*x/e^5+1/2*(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x)^2)-(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*_ + (d+e*x))-1/2*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^2/e^6+1/3*b^4*B*_ + (d+e*x)^3/e^6-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 3 5 3 2 2 4 +--R (36A a b + 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (36A b + 144B a b )d e - 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 144A a b - 216B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (72A b + 288B a b )d e - 120B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (36A a b + 24B a b)d e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 4 4 5 +--R (36A b + 144B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 2B b e x + ((3A b + 12B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 12A b - 48B a b )d e + 20B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 4 3 2 2 +--R ((48A a b + 72B a b )d e + (- 30A b - 120B a b )d e + 50B b d e )x +--R + +--R 3 4 5 2 2 3 4 +--R (- 24A a b - 6B a )e + (72A a b + 48B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (12A b + 48B a b )d e - 20B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 12A a b - 3B a )d e + (54A a b + 36B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 60A a b - 90B a b )d e + (24A b + 96B a b )d e - 40B b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 5 3 2 2 4 +--R (36A a b + 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (36A b + 144B a b )d e - 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 144A a b - 216B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (72A b + 288B a b )d e - 120B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (36A a b + 24B a b)d e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 4 4 5 +--R (36A b + 144B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 2B b e x + ((3A b + 12B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 12A b - 48B a b )d e + 20B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 4 3 2 2 +--R ((48A a b + 72B a b )d e + (- 33A b - 132B a b )d e + 63B b d e )x +--R + +--R 3 4 5 2 2 3 4 +--R (- 24A a b - 6B a )e + (72A a b + 48B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (6A b + 24B a b )d e + 6B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 12A a b - 3B a )d e + (54A a b + 36B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 60A a b - 90B a b )d e + (21A b + 84B a b )d e - 27B b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1378 +m0:=a0-r0 +--R +--R +--R 4 3 2 4 3 +--R (- 3A b - 12B a b )d e + 13B b d +--R (4) ---------------------------------- +--R 6 +--R 6e +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1378 +r0:=-b^3*(4*b*B*d-A*b*e-4*a*B*e)*x/e^5+1/2*b^4*B*x^2/e^4+1/3*(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x)^3)-1/2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/_ + (e^6*(d+e*x)^2)+2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*(d+_ + e*x))+2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 24A b - 96B a b )d e + 60B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 3 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 4 +--R 180B b d e +--R * +--R x +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (24A a b + 36B a b )d e + (- 24A b - 96B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((6A b + 24B a b )e - 15B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((18A b + 72B a b )d e - 63B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (72A a b + 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 18A b - 72B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 12A a b - 3B a )e + (- 36A a b - 24B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (108A a b + 162B a b )d e + (- 54A b - 216B a b )d e + 81B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 2A a e + (- 4A a b - B a )d e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (44A a b + 66B a b )d e + (- 26A b - 104B a b )d e + 47B b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 24A b - 96B a b )d e + 60B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 3 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 4 +--R 180B b d e +--R * +--R x +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (24A a b + 36B a b )d e + (- 24A b - 96B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((6A b + 24B a b )e - 15B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((18A b + 72B a b )d e - 63B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (72A a b + 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 18A b - 72B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 12A a b - 3B a )e + (- 36A a b - 24B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (108A a b + 162B a b )d e + (- 54A b - 216B a b )d e + 81B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 2A a e + (- 4A a b - B a )d e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (44A a b + 66B a b )d e + (- 26A b - 104B a b )d e + 47B b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1378 +r0:=b^4*B*x/e^5+1/4*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^4)-1/3*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^3)+b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^2)-2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 3 5 4 4 4 +--R ((12A b + 48B a b )e - 60B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((48A b + 192B a b )d e - 240B b d e )x +--R + +--R 4 3 2 3 4 3 2 2 +--R ((72A b + 288B a b )d e - 360B b d e )x +--R + +--R 4 3 3 2 4 4 4 3 4 +--R ((48A b + 192B a b )d e - 240B b d e)x + (12A b + 48B a b )d e +--R + +--R 4 5 +--R - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 4 4 +--R 12B b e x + 48B b d e x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((- 48A a b - 72B a b )e + (48A b + 192B a b )d e - 48B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (108A b + 432B a b )d e - 252B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 16A a b - 4B a )e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (88A b + 352B a b )d e - 248B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 4A a b - B a )d e + (- 6A a b - 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 12A a b - 18B a b )d e + (25A b + 100B a b )d e - 77B b d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 5 4 4 4 +--R ((12A b + 48B a b )e - 60B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((48A b + 192B a b )d e - 240B b d e )x +--R + +--R 4 3 2 3 4 3 2 2 +--R ((72A b + 288B a b )d e - 360B b d e )x +--R + +--R 4 3 3 2 4 4 4 3 4 +--R ((48A b + 192B a b )d e - 240B b d e)x + (12A b + 48B a b )d e +--R + +--R 4 5 +--R - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 4 4 +--R 12B b e x + 48B b d e x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((- 48A a b - 72B a b )e + (48A b + 192B a b )d e - 48B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (108A b + 432B a b )d e - 252B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 16A a b - 4B a )e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (88A b + 352B a b )d e - 248B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 4A a b - B a )d e + (- 6A a b - 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 12A a b - 18B a b )d e + (25A b + 100B a b )d e - 77B b d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^6 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1378 +r0:=-1/5*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^5)-1/4*B*(b*d-a*e)^4/_ + (e^6*(d+e*x)^4)+4/3*b*B*(b*d-a*e)^3/(e^6*(d+e*x)^3)-3*b^2*B*(b*d-_ + a*e)^2/(e^6*(d+e*x)^2)+4*b^3*B*(b*d-a*e)/(e^6*(d+e*x))+b^4*B*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 6 5 5 5 4 5 5 2 4 4 +--R (60B a b e - 60B b d e )x + (300B a b d e - 300B b d e )x +--R + +--R 4 2 4 5 3 3 3 4 3 3 5 4 2 2 +--R (600B a b d e - 600B b d e )x + (600B a b d e - 600B b d e )x +--R + +--R 4 4 2 5 5 4 5 5 6 +--R (300B a b d e - 300B b d e)x + 60B a b d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 5 6 5 5 5 +--R (- 12A b e + 12B b d e )x +--R + +--R 4 2 3 6 4 5 5 2 4 4 +--R ((- 60A a b - 240B a b )e + 540B a b d e - 240B b d e )x +--R + +--R 2 3 3 2 6 2 3 5 4 2 4 +--R (- 120A a b - 180B a b )e - 300B a b d e + 1380B a b d e +--R + +--R 5 3 3 +--R - 780B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 3 2 5 2 3 2 4 +--R (- 120A a b - 80B a b)e - 100B a b d e - 300B a b d e +--R + +--R 4 3 3 5 4 2 +--R 1580B a b d e - 980B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 4 5 3 2 2 4 2 3 3 3 +--R (- 60A a b - 15B a )e - 25B a b d e - 50B a b d e - 150B a b d e +--R + +--R 4 4 2 5 5 +--R 865B a b d e - 565B b d e +--R * +--R x +--R + +--R 5 6 5 5 4 2 4 3 2 3 3 2 3 4 2 +--R - 12A a e - 3B a d e - 5B a b d e - 10B a b d e - 30B a b d e +--R + +--R 4 5 5 6 +--R 185B a b d e - 125B b d +--R / +--R 12 11 5 11 2 10 4 +--R (60a e - 60b d e )x + (300a d e - 300b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (600a d e - 600b d e )x + (600a d e - 600b d e )x +--R + +--R 4 8 5 7 5 7 6 6 +--R (300a d e - 300b d e )x + 60a d e - 60b d e +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 4 4 4 2 3 3 4 3 2 2 +--R 60B b e x + 300B b d e x + 600B b d e x + 600B b d e x +--R + +--R 4 4 4 5 +--R 300B b d e x + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 4 +--R ((- 60A b - 240B a b )e + 300B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 120A a b - 180B a b )e + (- 120A b - 480B a b )d e +--R + +--R 4 2 3 +--R 900B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 120A a b - 80B a b)e + (- 120A a b - 180B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 120A b - 480B a b )d e + 1100B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 60A a b - 15B a )e + (- 60A a b - 40B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 60A a b - 90B a b )d e + (- 60A b - 240B a b )d e + 625B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 12A a e + (- 12A a b - 3B a )d e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 12A a b - 18B a b )d e + (- 12A b - 48B a b )d e + 137B b d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1378 +m0:=a0-r0 +--R +--R +--R 5 5 +--R A b e - B b d +--R (4) --------------- +--R 7 6 +--R 5a e - 5b d e +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1378 +r0:=-1/6*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^6)+1/30*(5*b*B*d+A*b*e-_ + 6*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^5) +--R +--R +--R (2) +--R 1 6 1 5 1 6 6 +--R ((-- A b - - B a b )e + - B b d)x +--R 30 5 6 +--R + +--R 2 4 1 6 4 5 5 +--R (- B a b e + (- A b + - B a b )d)x +--R 5 5 +--R + +--R 1 2 4 3 3 5 3 2 4 4 +--R ((- - A a b - 2B a b )e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 3 3 4 2 2 4 4 3 3 3 +--R ((- - A a b - 2B a b )e + (2A a b + - B a b )d)x +--R 3 3 +--R + +--R 3 4 2 5 3 3 1 4 2 2 +--R ((- - A a b - B a b)e + (2A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 5 1 6 4 2 1 6 1 5 1 6 +--R ((- - A a b - - B a )e + A a b d)x - - A a e + (- A a b - -- B a )d +--R 5 5 6 5 30 +--R / +--R 2 8 7 2 2 6 6 2 7 2 6 2 3 5 5 +--R (a e - 2a b d e + b d e )x + (6a d e - 12a b d e + 6b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (15a d e - 30a b d e + 15b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (20a d e - 40a b d e + 20b d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 2 5 3 6 2 2 7 +--R (15a d e - 30a b d e + 15b d e )x + (6a d e - 12a b d e + 6b d e)x +--R + +--R 2 6 2 7 2 8 +--R a d e - 2a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 282 + +--S 283 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 30B b e x + ((- 15A b - 60B a b )e - 75B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((- 40A a b - 60B a b )e + (- 20A b - 80B a b )d e - 100B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 45A a b - 30B a b)e + (- 30A a b - 45B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 15A b - 60B a b )d e - 75B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 24A a b - 6B a )e + (- 18A a b - 12B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 12A a b - 18B a b )d e + (- 6A b - 24B a b )d e - 30B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 5A a e + (- 4A a b - B a )d e + (- 3A a b - 2B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 2A a b - 3B a b )d e + (- A b - 4B a b )d e - 5B b d +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 +--R 30e x + 180d e x + 450d e x + 600d e x + 450d e x + 180d e x +--R + +--R 6 6 +--R 30d e +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1378 +m0:=a0-r0 +--R +--R +--R 6 5 6 +--R (- A b + 6B a b )e - 5B b d +--R (4) ------------------------------ +--R 2 8 7 2 2 6 +--R 30a e - 60a b d e + 30b d e +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1378 +r0:=-1/7*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^7)+1/42*(5*b*B*d+2*A*b*e-_ + 7*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^6)+1/210*b*(5*b*B*d+2*A*b*e-_ + 7*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 1 7 1 6 2 1 7 7 +--R ((- --- A b + -- B a b )e - -- B b d e)x +--R 105 30 42 +--R + +--R 1 7 7 6 1 7 2 6 +--R ((- -- A b + -- B a b )d e - - B b d )x +--R 15 30 6 +--R + +--R 1 3 4 2 3 2 5 1 7 4 6 2 5 +--R (- - B a b e + - B a b d e + (- - A b - - B a b )d )x +--R 2 2 5 5 +--R + +--R 1 3 4 4 4 3 2 2 5 19 3 4 +--R (- - A a b - - B a b )e + (A a b + -- B a b )d e +--R 3 3 6 +--R + +--R 6 3 2 5 2 +--R (- A a b - - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 3 3 5 2 2 8 3 4 19 4 3 +--R (- A a b - - B a b )e + (- A a b + -- B a b )d e +--R 2 3 6 +--R + +--R 2 5 4 3 4 2 +--R (- 2A a b - - B a b )d +--R 3 +--R * +--R 3 +--R x +--R + +--R 6 5 2 4 6 2 4 3 3 5 2 +--R (- - A a b - - B a b)e + (3A a b + - B a b )d e +--R 5 5 2 +--R + +--R 3 4 1 4 3 2 +--R (- 2A a b - - B a b )d +--R 2 +--R * +--R 2 +--R x +--R + +--R 2 6 1 7 2 8 5 2 7 6 4 3 2 +--R ((- - A a b - - B a )e + (- A a b + -- B a b)d e - A a b d )x +--R 3 6 5 30 +--R + +--R 1 7 2 1 6 1 7 1 5 2 1 6 2 +--R - - A a e + (- A a b - -- B a )d e + (- - A a b + -- B a b)d +--R 7 3 42 5 30 +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (a e - 3a b d e + 3a b d e - b d e )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (7a d e - 21a b d e + 21a b d e - 7b d e )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (21a d e - 63a b d e + 63a b d e - 21b d e )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (35a d e - 105a b d e + 105a b d e - 35b d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (35a d e - 105a b d e + 105a b d e - 35b d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (21a d e - 63a b d e + 63a b d e - 21b d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 2 8 2 +--R (7a d e - 21a b d e + 21a b d e - 7b d e)x + a d e - 3a b d e +--R + +--R 2 9 3 10 +--R 3a b d e - b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 287 + +--S 288 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 105B b e x + ((- 70A b - 280B a b )e - 175B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 210A a b - 315B a b )e + (- 70A b - 280B a b )d e +--R + +--R 4 2 3 +--R - 175B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 252A a b - 168B a b)e + (- 126A a b - 189B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 42A b - 168B a b )d e - 105B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 140A a b - 35B a )e + (- 84A a b - 56B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 42A a b - 63B a b )d e + (- 14A b - 56B a b )d e - 35B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 30A a e + (- 20A a b - 5B a )d e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 6A a b - 9B a b )d e + (- 2A b - 8B a b )d e - 5B b d +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 +--R 210e x + 1470d e x + 4410d e x + 7350d e x + 7350d e x +--R + +--R 5 8 2 6 7 7 6 +--R 4410d e x + 1470d e x + 210d e +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1378 +m0:=a0-r0 +--R +--R +--R 7 6 7 +--R (2A b - 7B a b )e + 5B b d +--R (4) ----------------------------------------------- +--R 3 9 2 8 2 2 7 3 3 6 +--R 210a e - 630a b d e + 630a b d e - 210b d e +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1378 +r0:=-1/8*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^8)+1/56*(5*b*B*d+3*A*b*e-_ + 8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^7)+1/168*b*(5*b*B*d+3*A*b*e-_ + 8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^3*(d+e*x)^6)+1/840*b^2*(5*b*B*d+_ + 3*A*b*e-8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 1 8 1 7 3 1 8 2 8 +--R ((--- A b - --- B a b )e + --- B b d e )x +--R 280 105 168 +--R + +--R 1 8 8 7 2 1 8 2 7 +--R ((-- A b - --- B a b )d e + -- B b d e)x +--R 35 105 21 +--R + +--R 1 8 4 7 2 1 8 3 6 +--R ((-- A b - -- B a b )d e + - B b d )x +--R 10 15 6 +--R + +--R 1 4 4 3 4 3 5 2 2 6 2 1 8 4 7 3 5 +--R (- - B a b e + - B a b d e - 2B a b d e + (- A b + - B a b )d )x +--R 3 3 5 5 +--R + +--R 1 4 4 5 3 3 3 5 43 4 4 2 +--R (- - A a b - B a b )e + (A a b + -- B a b )d e +--R 4 12 +--R + +--R 3 2 6 13 3 5 2 7 3 2 6 3 +--R (- - A a b - -- B a b )d e + (A a b + - B a b )d +--R 2 3 2 +--R * +--R 4 +--R x +--R + +--R 4 5 3 6 6 2 3 4 4 5 3 2 +--R (- - A a b - - B a b )e + (3A a b + 4B a b )d e +--R 5 5 +--R + +--R 3 5 13 4 4 2 2 6 4 3 5 3 +--R (- 4A a b - -- B a b )d e + (2A a b + - B a b )d +--R 3 3 +--R * +--R 3 +--R x +--R + +--R 6 2 2 7 3 18 5 3 31 6 2 2 +--R (- A a b - - B a b)e + (-- A a b + -- B a b )d e +--R 3 5 15 +--R + +--R 9 4 4 5 3 2 3 5 1 4 4 3 +--R (- - A a b - 2B a b )d e + (2A a b + - B a b )d +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 4 7 1 8 3 6 2 8 7 2 +--R (- - A a b - - B a )e + (2A a b + -- B a b)d e +--R 7 7 21 +--R + +--R 12 5 3 4 6 2 2 4 4 3 +--R (- -- A a b - -- B a b )d e + A a b d +--R 5 15 +--R * +--R x +--R + +--R 1 8 3 3 7 1 8 2 1 6 2 1 7 2 +--R - - A a e + (- A a b - -- B a )d e + (- - A a b + -- B a b)d e +--R 8 7 56 2 21 +--R + +--R 1 5 3 1 6 2 3 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 4 12 3 11 2 2 2 10 3 3 9 4 4 8 8 +--R (a e - 4a b d e + 6a b d e - 4a b d e + b d e )x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 4 5 7 7 +--R (8a d e - 32a b d e + 48a b d e - 32a b d e + 8b d e )x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 4 6 6 6 +--R (28a d e - 112a b d e + 168a b d e - 112a b d e + 28b d e )x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 4 7 5 5 +--R (56a d e - 224a b d e + 336a b d e - 224a b d e + 56b d e )x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 8 4 4 +--R (70a d e - 280a b d e + 420a b d e - 280a b d e + 70b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 8 4 4 9 3 3 +--R (56a d e - 224a b d e + 336a b d e - 224a b d e + 56b d e )x +--R + +--R 4 6 6 3 7 5 2 2 8 4 3 9 3 4 10 2 2 +--R (28a d e - 112a b d e + 168a b d e - 112a b d e + 28b d e )x +--R + +--R 4 7 5 3 8 4 2 2 9 3 3 10 2 4 11 4 8 4 +--R (8a d e - 32a b d e + 48a b d e - 32a b d e + 8b d e)x + a d e +--R + +--R 3 9 3 2 2 10 2 3 11 4 12 +--R - 4a b d e + 6a b d e - 4a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 292 + +--S 293 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 280B b e x + ((- 210A b - 840B a b )e - 350B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 672A a b - 1008B a b )e + (- 168A b - 672B a b )d e +--R + +--R 4 2 3 +--R - 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 840A a b - 560B a b)e + (- 336A a b - 504B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 84A b - 336B a b )d e - 140B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 480A a b - 120B a )e + (- 240A a b - 160B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 96A a b - 144B a b )d e + (- 24A b - 96B a b )d e - 40B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 105A a e + (- 60A a b - 15B a )d e + (- 30A a b - 20B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 12A a b - 18B a b )d e + (- 3A b - 12B a b )d e - 5B b d +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 +--R 840e x + 6720d e x + 23520d e x + 47040d e x + 58800d e x +--R + +--R 5 9 3 6 8 2 7 7 8 6 +--R 47040d e x + 23520d e x + 6720d e x + 840d e +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1378 +m0:=a0-r0 +--R +--R +--R 8 7 8 +--R (- 3A b + 8B a b )e - 5B b d +--R (4) ----------------------------------------------------------------- +--R 4 10 3 9 2 2 2 8 3 3 7 4 4 6 +--R 840a e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d e +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^10 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 1378 +r0:=1/9*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^9)-1/8*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^8)+2/7*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^7)-1/3*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^6)+1/5*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^5)-_ + 1/4*b^4*B/(e^6*(d+e*x)^4) +--R +--R +--R (2) +--R 1 4 5 5 1 4 4 3 5 1 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - - B b d e )x +--R 4 5 5 4 +--R + +--R 2 3 2 2 5 2 4 8 3 4 1 4 2 3 3 +--R ((- - A a b - B a b )e + (- -- A b - -- B a b )d e - - B b d e )x +--R 3 15 15 6 +--R + +--R 6 2 2 4 3 5 2 3 3 2 2 4 +--R (- - A a b - - B a b)e + (- - A a b - - B a b )d e +--R 7 7 7 7 +--R + +--R 2 4 8 3 2 3 1 4 3 2 +--R (- -- A b - -- B a b )d e - -- B b d e +--R 35 35 14 +--R * +--R 2 +--R x +--R + +--R 1 3 1 4 5 3 2 2 1 3 4 +--R (- - A a b - - B a )e + (- -- A a b - - B a b)d e +--R 2 8 14 7 +--R + +--R 1 3 3 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- -- A b - -- B a b )d e +--R 14 28 70 35 +--R + +--R 1 4 4 +--R - -- B b d e +--R 56 +--R * +--R x +--R + +--R 1 4 5 1 3 1 4 4 1 2 2 1 3 2 3 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A a b - -- B a b)d e +--R 9 18 72 42 63 +--R + +--R 1 3 1 2 2 3 2 1 4 2 3 4 1 4 5 +--R (- --- A a b - -- B a b )d e + (- --- A b - --- B a b )d e - --- B b d +--R 126 84 630 315 504 +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 5 10 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 9 3 7 8 2 8 7 9 6 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 297 + +--S 298 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 630B b e x + ((- 504A b - 2016B a b )e - 630B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 1680A a b - 2520B a b )e + (- 336A b - 1344B a b )d e +--R + +--R 4 2 3 +--R - 420B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 2160A a b - 1440B a b)e + (- 720A a b - 1080B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 144A b - 576B a b )d e - 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 1260A a b - 315B a )e + (- 540A a b - 360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 180A a b - 270B a b )d e + (- 36A b - 144B a b )d e - 45B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 280A a e + (- 140A a b - 35B a )d e + (- 60A a b - 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 20A a b - 30B a b )d e + (- 4A b - 16B a b )d e - 5B b d +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 +--R 2520e x + 22680d e x + 90720d e x + 211680d e x + 317520d e x +--R + +--R 5 10 4 6 9 3 7 8 2 8 7 9 6 +--R 317520d e x + 211680d e x + 90720d e x + 22680d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^11 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1378 +r0:=1/10*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^10)-1/9*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^9)+1/4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^8)-2/7*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^7)+1/6*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^6)-_ + 1/5*b^4*B/(e^6*(d+e*x)^5) +--R +--R +--R (2) +--R 1 4 5 5 1 4 2 3 5 1 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - - B b d e )x +--R 5 6 3 6 +--R + +--R 4 3 6 2 2 5 2 4 8 3 4 2 4 2 3 3 +--R ((- - A a b - - B a b )e + (- -- A b - -- B a b )d e - -- B b d e )x +--R 7 7 21 21 21 +--R + +--R 3 2 2 1 3 5 3 3 9 2 2 4 +--R (- - A a b - - B a b)e + (- -- A a b - -- B a b )d e +--R 4 2 14 28 +--R + +--R 1 4 1 3 2 3 1 4 3 2 +--R (- -- A b - - B a b )d e - -- B b d e +--R 28 7 28 +--R * +--R 2 +--R x +--R + +--R 4 3 1 4 5 1 2 2 1 3 4 +--R (- - A a b - - B a )e + (- - A a b - - B a b)d e +--R 9 9 6 9 +--R + +--R 1 3 1 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- --- A b - -- B a b )d e +--R 21 14 126 63 +--R + +--R 1 4 4 +--R - --- B b d e +--R 126 +--R * +--R x +--R + +--R 1 4 5 2 3 1 4 4 1 2 2 1 3 2 3 +--R - -- A a e + (- -- A a b - -- B a )d e + (- -- A a b - -- B a b)d e +--R 10 45 90 60 90 +--R + +--R 1 3 1 2 2 3 2 1 4 1 3 4 +--R (- --- A a b - --- B a b )d e + (- ---- A b - --- B a b )d e +--R 210 140 1260 315 +--R + +--R 1 4 5 +--R - ---- B b d +--R 1260 +--R / +--R 16 10 15 9 2 14 8 3 13 7 4 12 6 5 11 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 10 4 7 9 3 8 8 2 9 7 10 6 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 302 + +--S 303 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 252B b e x + ((- 210A b - 840B a b )e - 210B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 720A a b - 1080B a b )e + (- 120A b - 480B a b )d e +--R + +--R 4 2 3 +--R - 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 945A a b - 630B a b)e + (- 270A a b - 405B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 45A b - 180B a b )d e - 45B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 560A a b - 140B a )e + (- 210A a b - 140B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 60A a b - 90B a b )d e + (- 10A b - 40B a b )d e - 10B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 126A a e + (- 56A a b - 14B a )d e + (- 21A a b - 14B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 6A a b - 9B a b )d e + (- A b - 4B a b )d e - B b d +--R / +--R 16 10 15 9 2 14 8 3 13 7 4 12 6 +--R 1260e x + 12600d e x + 56700d e x + 151200d e x + 264600d e x +--R + +--R 5 11 5 6 10 4 7 9 3 8 8 2 9 7 +--R 317520d e x + 264600d e x + 151200d e x + 56700d e x + 12600d e x +--R + +--R 10 6 +--R 1260d e +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^12 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 1378 +r0:=1/11*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^11)-1/10*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^10)+2/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^9)-1/4*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^8)+1/7*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^7)-_ + 1/6*b^4*B/(e^6*(d+e*x)^6) +--R +--R +--R (2) +--R 1 4 5 5 1 4 4 3 5 5 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - -- B b d e )x +--R 6 7 7 42 +--R + +--R 1 3 3 2 2 5 1 4 2 3 4 5 4 2 3 3 +--R ((- - A a b - - B a b )e + (- -- A b - - B a b )d e - -- B b d e )x +--R 2 4 14 7 84 +--R + +--R 2 2 2 4 3 5 1 3 1 2 2 4 +--R (- - A a b - - B a b)e + (- - A a b - - B a b )d e +--R 3 9 6 4 +--R + +--R 1 4 2 3 2 3 5 4 3 2 +--R (- -- A b - -- B a b )d e - --- B b d e +--R 42 21 252 +--R * +--R 2 +--R x +--R + +--R 2 3 1 4 5 2 2 2 4 3 4 +--R (- - A a b - -- B a )e + (- -- A a b - -- B a b)d e +--R 5 10 15 45 +--R + +--R 1 3 1 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- --- A b - --- B a b )d e +--R 30 20 210 105 +--R + +--R 1 4 4 +--R - --- B b d e +--R 252 +--R * +--R x +--R + +--R 1 4 5 2 3 1 4 4 +--R - -- A a e + (- -- A a b - --- B a )d e +--R 11 55 110 +--R + +--R 2 2 2 4 3 2 3 1 3 1 2 2 3 2 +--R (- --- A a b - --- B a b)d e + (- --- A a b - --- B a b )d e +--R 165 495 330 220 +--R + +--R 1 4 2 3 4 1 4 5 +--R (- ---- A b - ---- B a b )d e - ---- B b d +--R 2310 1155 2772 +--R / +--R 17 11 16 10 2 15 9 3 14 8 4 13 7 5 12 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 11 5 7 10 4 8 9 3 9 8 2 10 7 11 6 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 307 + +--S 308 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R - 2310B b e x + ((- 1980A b - 7920B a b )e - 1650B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (- 6930A a b - 10395B a b )e + (- 990A b - 3960B a b )d e +--R + +--R 4 2 3 +--R - 825B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 9240A a b - 6160B a b)e + (- 2310A a b - 3465B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 330A b - 1320B a b )d e - 275B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 5544A a b - 1386B a )e + (- 1848A a b - 1232B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 462A a b - 693B a b )d e + (- 66A b - 264B a b )d e - 55B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 1260A a e + (- 504A a b - 126B a )d e + (- 168A a b - 112B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 42A a b - 63B a b )d e + (- 6A b - 24B a b )d e - 5B b d +--R / +--R 17 11 16 10 2 15 9 3 14 8 +--R 13860e x + 152460d e x + 762300d e x + 2286900d e x +--R + +--R 4 13 7 5 12 6 6 11 5 7 10 4 +--R 4573800d e x + 6403320d e x + 6403320d e x + 4573800d e x +--R + +--R 8 9 3 9 8 2 10 7 11 6 +--R 2286900d e x + 762300d e x + 152460d e x + 13860d e +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1378 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 1378 +r0:=2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*x/b^5-(A*b-a*B)*(b*d-a*e)^4/_ + (b^6*(a+b*x))+e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^2/b^6+_ + 1/3*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^3/b^6+1/4*B*e^4*(a+b*x)^4/b^6+_ + (b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 3 2 4 4 2 3 3 2 3 +--R (- 48A a b + 60B a b)e + (144A a b - 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 144A a b + 216B a b )d e + (48A b - 96B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 60B a )e + (144A a b - 192B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 144A a b + 216B a b )d e + (48A a b - 96B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - 5B a b )e + 16B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 8A a b + 10B a b )e + (24A b - 32B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (24A a b - 30B a b )e + (- 72A a b + 96B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (72A b - 108B a b )d e + 48B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (16A a b - 5B a b)e + (- 72A a b + 64B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 108B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 32A a b + 55B a )e + (72A a b - 128B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A a b + 108B a b )d e + (48A a b - 48B a b )d e +--R + +--R 5 4 4 +--R (- 12A b + 12B a b )d +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 4 2 3 3 2 3 +--R (- 48A a b + 60B a b)e + (144A a b - 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 144A a b + 216B a b )d e + (48A b - 96B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 60B a )e + (144A a b - 192B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 144A a b + 216B a b )d e + (48A a b - 96B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - 5B a b )e + 16B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 8A a b + 10B a b )e + (24A b - 32B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (24A a b - 30B a b )e + (- 72A a b + 96B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (72A b - 108B a b )d e + 48B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (36A a b - 48B a b)e + (- 96A a b + 144B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 144B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 12A a b + 12B a )e + (48A a b - 48B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A a b + 72B a b )d e + (48A a b - 48B a b )d e +--R + +--R 5 4 4 +--R (- 12A b + 12B a b )d +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1378 +m0:=a0-r0 +--R +--R +--R 3 4 4 2 2 3 3 2 2 2 2 +--R (20A a b - 43B a )e + (- 24A a b + 80B a b)d e - 36B a b d e +--R (4) ---------------------------------------------------------------- +--R 6 +--R 12b +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1378 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1378 +r0:=3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*x/b^4-(A*b-a*B)*(b*d-a*e)^3/(b^5*_ + (a+b*x))+1/2*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^2/b^5+1/3*B*e^3*_ + (a+b*x)^3/b^5+(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 24B a b)e + (- 36A a b + 54B a b )d e +--R + +--R 4 3 2 4 3 +--R (18A b - 36B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (18A a b - 24B a )e + (- 36A a b + 54B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A a b - 36B a b )d e + 6B a b d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - 4B a b )e + 9B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 9A a b + 12B a b )e + (18A b - 27B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 9A a b + 8B a b)e + (18A a b - 27B a b )d e + 18B a b d e)x +--R + +--R 3 4 3 2 2 3 2 +--R (9A a b - 16B a )e + (- 18A a b + 27B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A a b - 18B a b )d e + (- 6A b + 6B a b )d +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 24B a b)e + (- 36A a b + 54B a b )d e +--R + +--R 4 3 2 4 3 +--R (18A b - 36B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (18A a b - 24B a )e + (- 36A a b + 54B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A a b - 36B a b )d e + 6B a b d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - 4B a b )e + 9B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 9A a b + 12B a b )e + (18A b - 27B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 18B a b)e + (18A a b - 36B a b )d e + 18B a b d e)x +--R + +--R 3 4 3 2 2 3 2 +--R (6A a b - 6B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A a b - 18B a b )d e + (- 6A b + 6B a b )d +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1378 +m0:=a0-r0 +--R +--R +--R 2 3 3 2 2 +--R (- 3A a b + 10B a )e - 9B a b d e +--R (4) ----------------------------------- +--R 5 +--R 6b +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1378 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 1378 +r0:=e*(2*b*B*d+A*b*e-2*a*B*e)*x/b^3+1/2*B*e^2*x^2/b^2-(A*b-a*B)*_ + (b*d-a*e)^2/(b^4*(a+b*x))+(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((- 4A a b + 6B a b)e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 4A a b + 6B a )e + (4A a b - 8B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((2A a b - 4B a b)e + 4B a b d e)x + (- 2A a b + 2B a )e +--R + +--R 2 2 3 2 2 +--R (4A a b - 4B a b)d e + (- 2A b + 2B a b )d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 +--R ((- 4A a b + 6B a b)e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 4A a b + 6B a )e + (4A a b - 8B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((2A a b - 4B a b)e + 4B a b d e)x + (- 2A a b + 2B a )e +--R + +--R 2 2 3 2 2 +--R (4A a b - 4B a b)d e + (- 2A b + 2B a b )d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 1378 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 1378 +r0:=B*e*x/b^2-(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x))+(b*B*d+A*b*e-2*a*B*e)*_ + log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (((A b - 2B a b)e + B b d)x + (A a b - 2B a )e + B a b d)log(b x + a) +--R + +--R 2 2 2 2 +--R B b e x + B a b e x + (A a b - B a )e + (- A b + B a b)d +--R / +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (((A b - 2B a b)e + B b d)x + (A a b - 2B a )e + B a b d)log(b x + a) +--R + +--R 2 2 2 2 +--R B b e x + B a b e x + (A a b - B a )e + (- A b + B a b)d +--R / +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1378 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R B x + A +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1378 +r0:=(-A*b+a*B)/(b^2*(a+b*x))+B*log(a+b*x)/b^2 +--R +--R +--R (B b x + B a)log(b x + a) - A b + B a +--R (2) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (B b x + B a)log(b x + a) - A b + B a +--R (3) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1378 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (2a b e + b d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 1378 +r0:=(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x))+(B*d-A*e)*log(a+b*x)/(b*d-a*e)^2-_ + (B*d-A*e)*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (2) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(b x + a) + (A a b - B a )e +--R + +--R 2 +--R (- A b + B a b)d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R (a b e - 2a b d e + b d )x + a b e - 2a b d e + a b d +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(b x + a) + (A a b - B a )e +--R + +--R 2 +--R (- A b + B a b)d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R (a b e - 2a b d e + b d )x + a b e - 2a b d e + a b d +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1378 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 1378 +r0:=(-A*b+a*B)/((b*d-a*e)^2*(a+b*x))+(B*d-A*e)/((b*d-a*e)^2*(d+e*x))+_ + (b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^3-(b*B*d-2*A*b*e+a*B*e)*_ + log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 2A b + B a b)e + B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 2A a b + B a )e + (- 2A b + 2B a b)d e + B b d )x +--R + +--R 2 2 +--R (- 2A a b + B a )d e + B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R ((2A b - B a b)e - B b d e)x +--R + +--R 2 2 2 2 2 +--R ((2A a b - B a )e + (2A b - 2B a b)d e - B b d )x +--R + +--R 2 2 +--R (2A a b - B a )d e - B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2A a b + B a )e + 2A b d e - B b d )x - A a e + 2B a d e +--R + +--R 2 2 +--R (A b - 2B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R ((- 2A b + B a b)e + B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 2A a b + B a )e + (- 2A b + 2B a b)d e + B b d )x +--R + +--R 2 2 +--R (- 2A a b + B a )d e + B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R ((2A b - B a b)e - B b d e)x +--R + +--R 2 2 2 2 2 +--R ((2A a b - B a )e + (2A b - 2B a b)d e - B b d )x +--R + +--R 2 2 +--R (2A a b - B a )d e - B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2A a b + B a )e + 2A b d e - B b d )x - A a e + 2B a d e +--R + +--R 2 2 +--R (A b - 2B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1378 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 1378 +r0:=-b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x))+1/2*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^2)+_ + (b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x))+b*(b*B*d-3*A*b*e+2*a*B*e)*_ + log(a+b*x)/(b*d-a*e)^4-b*(b*B*d-3*A*b*e+2*a*B*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((6A b - 4B a b )e - 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (12A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((12A a b - 8B a b)d e + (6A b - 8B a b )d e - 2B b d )x +--R + +--R 2 2 2 2 3 +--R (6A a b - 4B a b)d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((- 6A b + 4B a b )e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 4B a b)e + (- 12A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((- 12A a b + 8B a b)d e + (- 6A b + 8B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 3 +--R (- 6A a b + 4B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (- 6A b + 2B a b )d e + 2B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b - 2B a )e + (6A a b - 5B a b)d e + (- 9A b + 4B a b )d e +--R + +--R 3 3 +--R 3B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - A a e + (6A a b - B a )d e + (- 3A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- 2A b + 5B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 3 +--R ((6A b - 4B a b )e - 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (12A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((12A a b - 8B a b)d e + (6A b - 8B a b )d e - 2B b d )x +--R + +--R 2 2 2 2 3 +--R (6A a b - 4B a b)d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((- 6A b + 4B a b )e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 4B a b)e + (- 12A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((- 12A a b + 8B a b)d e + (- 6A b + 8B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 3 +--R (- 6A a b + 4B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (- 6A b + 2B a b )d e + 2B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b - 2B a )e + (6A a b - 5B a b)d e + (- 9A b + 4B a b )d e +--R + +--R 3 3 +--R 3B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - A a e + (6A a b - B a )d e + (- 3A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- 2A b + 5B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1378 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 1378 +r0:=e^3*(4*b*B*d+A*b*e-4*a*B*e)*x/b^5+1/2*B*e^4*x^2/b^4-1/3*(A*b-a*B)*_ + (b*d-a*e)^4/(b^6*(a+b*x)^3)-1/2*(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)/_ + (b^6*(a+b*x)^2)-2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)/(b^6*(a+b*x))+_ + 2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 24A a b + 60B a b )e + (24A b - 96B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 72A a b + 180B a b )e + (72A a b - 288B a b )d e +--R + +--R 4 2 2 +--R 108B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 72A a b + 180B a b)e + (72A a b - 288B a b )d e +--R + +--R 2 3 2 2 +--R 108B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 3 2 2 2 +--R (- 24A a b + 60B a )e + (24A a b - 96B a b)d e + 36B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((6A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((18A a b - 63B a b )e + 72B a b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 18A a b - 9B a b )e + (72A a b - 72B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 54A a b + 81B a b)e + (108A a b - 216B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 36A a b + 162B a b )d e + (- 12A b - 24B a b )d e - 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 26A a b + 47B a )e + (44A a b - 104B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 12A a b + 66B a b )d e + (- 4A a b - 8B a b )d e +--R + +--R 5 4 4 +--R (- 2A b - B a b )d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 24A a b + 60B a b )e + (24A b - 96B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 72A a b + 180B a b )e + (72A a b - 288B a b )d e +--R + +--R 4 2 2 +--R 108B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 72A a b + 180B a b)e + (72A a b - 288B a b )d e +--R + +--R 2 3 2 2 +--R 108B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 3 2 2 2 +--R (- 24A a b + 60B a )e + (24A a b - 96B a b)d e + 36B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((6A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((18A a b - 63B a b )e + 72B a b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 18A a b - 9B a b )e + (72A a b - 72B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 54A a b + 81B a b)e + (108A a b - 216B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 36A a b + 162B a b )d e + (- 12A b - 24B a b )d e - 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 26A a b + 47B a )e + (44A a b - 104B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 12A a b + 66B a b )d e + (- 4A a b - 8B a b )d e +--R + +--R 5 4 4 +--R (- 2A b - B a b )d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1378 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 1378 +r0:=B*e^3*x/b^4-1/3*(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x)^3)-1/2*(b*d-a*e)^2*_ + (b*B*d+3*A*b*e-4*a*B*e)/(b^5*(a+b*x)^2)-3*e*(b*d-a*e)*(b*B*d+A*b*e-_ + 2*a*B*e)/(b^5*(a+b*x))+e^2*(3*b*B*d+A*b*e-4*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((6A b - 24B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((18A a b - 72B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((18A a b - 72B a b)e + 54B a b d e )x + (6A a b - 24B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 3 +--R 6B b e x + 18B a b e x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((18A a b - 18B a b )e + (- 18A b + 54B a b )d e - 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (27A a b - 54B a b)e + (- 18A a b + 81B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 9A b - 18B a b )d e - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (11A a b - 26B a )e + (- 6A a b + 33B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b - 6B a b )d e + (- 2A b - B a b )d +--R / +--R 8 3 7 2 2 6 3 5 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 3 4 2 3 +--R ((6A b - 24B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((18A a b - 72B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((18A a b - 72B a b)e + 54B a b d e )x + (6A a b - 24B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 3 +--R 6B b e x + 18B a b e x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((18A a b - 18B a b )e + (- 18A b + 54B a b )d e - 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (27A a b - 54B a b)e + (- 18A a b + 81B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 9A b - 18B a b )d e - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (11A a b - 26B a )e + (- 6A a b + 33B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b - 6B a b )d e + (- 2A b - B a b )d +--R / +--R 8 3 7 2 2 6 3 5 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1378 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 1378 +r0:=-1/2*B*(b*d-a*e)^2/(b^4*(a+b*x)^2)-2*B*e*(b*d-a*e)/(b^4*(a+b*x))-_ + 1/3*(A*b-a*B)*(d+e*x)^3/(b*(b*d-a*e)*(a+b*x)^3)+B*e^2*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 4 2 3 2 2 3 3 2 2 +--R (6B a b e - 6B b d e )x + (18B a b e - 18B a b d e )x +--R + +--R 3 3 2 2 2 4 3 3 2 +--R (18B a b e - 18B a b d e )x + 6B a e - 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 3 3 +--R (2A b - 2B a b )e x +--R + +--R 2 2 3 4 3 2 4 2 2 +--R (12B a b e + (6A b - 30B a b )d e + 12B b d e)x +--R + +--R 3 3 2 2 2 4 3 2 4 3 4 3 +--R (21B a b e - 39B a b d e + (6A b + 9B a b )d e + 3B b d )x + 9B a e +--R + +--R 3 2 2 2 2 4 3 3 +--R - 15B a b d e + 3B a b d e + (2A b + B a b )d +--R / +--R 7 8 3 2 6 7 2 3 5 2 6 4 4 +--R (6a b e - 6b d)x + (18a b e - 18a b d)x + (18a b e - 18a b d)x + 6a b e +--R + +--R 3 5 +--R - 6a b d +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 2 2 2 2 3 2 +--R (6B b e x + 18B a b e x + 18B a b e x + 6B a e )log(b x + a) +--R + +--R 3 2 2 3 2 +--R ((- 6A b + 18B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 6A a b + 27B a b)e + (- 6A b - 12B a b )d e - 3B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 2A a b + 11B a )e + (- 2A a b - 4B a b)d e + (- 2A b - B a b )d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 1378 +m0:=a0-r0 +--R +--R +--R 3 +--R (- A b + B a)e +--R (4) --------------- +--R 4 5 +--R 3a b e - 3b d +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 1378 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 1378 +r0:=-1/3*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)^3)+1/2*(-b*B*d-A*b*e+2*a*B*e)/_ + (b^3*(a+b*x)^2)-B*e/(b^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 1 2 1 2 1 1 2 +--R - B b e x + ((- - A b - B a b)e - - B b d)x + (- - A a b - - B a )e +--R 2 2 6 3 +--R + +--R 1 2 1 +--R (- - A b - - B a b)d +--R 3 6 +--R / +--R 6 3 5 2 2 4 3 3 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 367 + +--S 368 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R - 6B b e x + ((- 3A b - 6B a b)e - 3B b d)x + (- A a b - 2B a )e +--R + +--R 2 +--R (- 2A b - B a b)d +--R / +--R 6 3 5 2 2 4 3 3 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 1378 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R B x + A +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 1378 +r0:=1/3*(-A*b+a*B)/(b^2*(a+b*x)^3)-1/2*B/(b^2*(a+b*x)^2) +--R +--R +--R 1 1 1 +--R - - B b x - - A b - - B a +--R 2 3 6 +--R (2) ------------------------------ +--R 5 3 4 2 2 3 3 2 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 372 + +--S 373 of 1378 +a0:=integrate(t0,x) +--R +--R +--R - 3B b x - 2A b - B a +--R (3) ---------------------------------- +--R 5 3 4 2 2 3 3 2 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1378 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 1378 +r0:=1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3)+1/2*(-B*d+A*e)/((b*d-a*e)^2*_ + (a+b*x)^2)+e*(B*d-A*e)/((b*d-a*e)^3*(a+b*x))+e^2*(B*d-A*e)*log(a+b*x)/_ + (b*d-a*e)^4-e^2*(B*d-A*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 4 3 4 2 3 3 3 3 2 2 +--R (6A b e - 6B b d e )x + (18A a b e - 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (18A a b e - 18B a b d e )x + 6A a b e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 2 3 3 3 3 2 2 +--R (- 6A b e + 6B b d e )x + (- 18A a b e + 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (- 18A a b e + 18B a b d e )x - 6A a b e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 4 3 2 4 2 2 +--R (6A a b e + (- 6A b - 6B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 2 2 2 4 3 2 +--R 15A a b e + (- 18A a b - 15B a b )d e + (3A b + 18B a b )d e +--R + +--R 4 3 +--R - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (11A a b - 2B a )e + (- 18A a b - 3B a b)d e + (9A a b + 6B a b )d e +--R + +--R 4 3 3 +--R (- 2A b - B a b )d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 3 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 2 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 7 4 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x + 6a b e +--R + +--R 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 3 3 3 3 2 2 +--R (6A b e - 6B b d e )x + (18A a b e - 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (18A a b e - 18B a b d e )x + 6A a b e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 2 3 3 3 3 2 2 +--R (- 6A b e + 6B b d e )x + (- 18A a b e + 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (- 18A a b e + 18B a b d e )x - 6A a b e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 4 3 2 4 2 2 +--R (6A a b e + (- 6A b - 6B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 2 2 2 4 3 2 +--R 15A a b e + (- 18A a b - 15B a b )d e + (3A b + 18B a b )d e +--R + +--R 4 3 +--R - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (11A a b - 2B a )e + (- 18A a b - 3B a b)d e + (9A a b + 6B a b )d e +--R + +--R 4 3 3 +--R (- 2A b - B a b )d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 3 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 2 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 7 4 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x + 6a b e +--R + +--R 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 1378 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 1378 +r0:=1/3*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^3)+1/2*(-b*B*d+2*A*b*e-a*B*e)/_ + ((b*d-a*e)^3*(a+b*x)^2)+e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(a+b*x))+_ + e^2*(B*d-A*e)/((b*d-a*e)^4*(d+e*x))+e^2*(3*b*B*d-4*A*b*e+a*B*e)*_ + log(a+b*x)/(b*d-a*e)^5-e^2*(3*b*B*d-4*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 24A b + 6B a b )e + 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 72A a b + 18B a b )e + (- 24A b + 60B a b )d e +--R + +--R 4 2 2 +--R 18B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 72A a b + 18B a b)e + (- 72A a b + 72B a b )d e +--R + +--R 3 2 2 +--R 54B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((- 24A a b + 6B a )e + (- 72A a b + 36B a b)d e + 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (- 24A a b + 6B a )d e + 18B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((24A b - 6B a b )e - 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((72A a b - 18B a b )e + (24A b - 60B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 3 2 2 2 +--R ((72A a b - 18B a b)e + (72A a b - 72B a b )d e - 54B a b d e )x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((24A a b - 6B a )e + (72A a b - 36B a b)d e - 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (24A a b - 6B a )d e - 18B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 24A a b + 6B a b )e + (24A b + 12B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 60A a b + 15B a b)e + (48A a b + 33B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 39B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 44A a b + 11B a )e + (12A a b + 30B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (36A a b - 18B a b )d e + (- 4A b - 26B a b )d e + 3B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (- 20A a b + 17B a )d e + (36A a b - 9B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 12A a b - 9B a b )d e + (2A b + B a b )d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 8 5 4 +--R (6a b e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6b d e)x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 18a b e - 84a b d e + 150a b d e - 120a b d e + 30a b d e +--R + +--R 7 5 8 6 +--R 12a b d e - 6b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 18a b e - 72a b d e + 90a b d e - 90a b d e + 72a b d e +--R + +--R 7 6 +--R - 18a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 6a e - 12a b d e - 30a b d e + 120a b d e - 150a b d e +--R + +--R 3 5 5 2 6 6 +--R 84a b d e - 18a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 3 5 6 +--R 6a d e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6a b d +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 4 3 4 +--R ((- 24A b + 6B a b )e + 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 72A a b + 18B a b )e + (- 24A b + 60B a b )d e +--R + +--R 4 2 2 +--R 18B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 72A a b + 18B a b)e + (- 72A a b + 72B a b )d e +--R + +--R 3 2 2 +--R 54B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((- 24A a b + 6B a )e + (- 72A a b + 36B a b)d e + 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (- 24A a b + 6B a )d e + 18B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((24A b - 6B a b )e - 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((72A a b - 18B a b )e + (24A b - 60B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 3 2 2 2 +--R ((72A a b - 18B a b)e + (72A a b - 72B a b )d e - 54B a b d e )x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((24A a b - 6B a )e + (72A a b - 36B a b)d e - 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (24A a b - 6B a )d e - 18B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 24A a b + 6B a b )e + (24A b + 12B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 60A a b + 15B a b)e + (48A a b + 33B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 39B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 44A a b + 11B a )e + (12A a b + 30B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (36A a b - 18B a b )d e + (- 4A b - 26B a b )d e + 3B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (- 20A a b + 17B a )d e + (36A a b - 9B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 12A a b - 9B a b )d e + (2A b + B a b )d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 8 5 4 +--R (6a b e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6b d e)x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 18a b e - 84a b d e + 150a b d e - 120a b d e + 30a b d e +--R + +--R 7 5 8 6 +--R 12a b d e - 6b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 18a b e - 72a b d e + 90a b d e - 90a b d e + 72a b d e +--R + +--R 7 6 +--R - 18a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 6a e - 12a b d e - 30a b d e + 120a b d e - 150a b d e +--R + +--R 3 5 5 2 6 6 +--R 84a b d e - 18a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 3 5 6 +--R 6a d e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6a b d +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 1378 +t0:=(A+B*x)*(d+e*x)^m*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R m | 2 2 2 +--R (1) (B x + A)(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1378 +r0:=(A*b*e*(3+m)-B*(2*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2*(2+m)*(3+m))-(b*d-a*e)*(A*b*e*(3+m)-B*(2*b*d+_ + a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(1+m)*_ + (2+m)*(3+m)*(a+b*x))+B*(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e*(3+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (B b e m + 3B b e m + 2B b e )x +--R + +--R 2 2 2 2 +--R (A b + B a)e m + ((4A b + 4B a)e - 2B b d e)m + (3A b + 3B a)e +--R + +--R - 2B b d e +--R * +--R x +--R + +--R 2 2 2 2 +--R A a e m + (5A a e + (- A b - B a)d e)m + 6A a e + (- 3A b - 3B a)d e +--R + +--R 2 +--R 2B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 3 +--R (B b e m + 3B b e m + 2B b e )x +--R + +--R 3 2 2 3 2 +--R ((A b + B a)e + B b d e )m + ((4A b + 4B a)e + B b d e )m +--R + +--R 3 +--R (3A b + 3B a)e +--R * +--R 2 +--R x +--R + +--R 3 2 2 +--R (A a e + (A b + B a)d e )m +--R + +--R 3 2 2 3 +--R (5A a e + (3A b + 3B a)d e - 2B b d e)m + 6A a e +--R * +--R x +--R + +--R 2 2 2 2 2 +--R A a d e m + (5A a d e + (- A b - B a)d e)m + 6A a d e +--R + +--R 2 3 +--R (- 3A b - 3B a)d e + 2B b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 3 3 3 2 3 3 +--R e m + 6e m + 11e m + 6e +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 3 2 3 4 +--R (B b e m + 3B b e m + 2B b e )x +--R + +--R 2 3 2 2 2 +--R ((A b + 2B a b)e + B b d e )m +--R + +--R 2 3 2 2 2 3 +--R ((4A b + 7B a b)e + B b d e )m + (3A b + 5B a b)e +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d e )m +--R + +--R 2 3 2 2 2 2 +--R ((9A a b + 4B a )e + (3A b + 4B a b)d e - 2B b d e)m +--R + +--R 2 3 +--R (9A a b + 3B a )e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 +--R (A a e + (2A a b + B a )d e )m +--R + +--R 2 3 2 2 2 2 +--R (5A a e + (8A a b + 3B a )d e + (- A b - 3B a b)d e)m +--R + +--R 2 3 2 2 2 2 3 +--R 6A a e + 6A a b d e + (- 3A b - 3B a b)d e + 2B b d +--R * +--R x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R A a d e m + (5A a d e + (- A a b - B a )d e)m + 6A a d e +--R + +--R 2 2 3 +--R (- 3A a b - 3B a )d e + 2B a b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 2 2 2 2 +--R (- B b e m - 3B b e m - 2B b e )x +--R + +--R 2 2 2 +--R (- A b - B a)e m + ((- 4A b - 4B a)e + 2B b d e)m +--R + +--R 2 +--R (- 3A b - 3B a)e + 2B b d e +--R * +--R x +--R + +--R 2 2 2 2 +--R - A a e m + (- 5A a e + (A b + B a)d e)m - 6A a e +--R + +--R 2 +--R (3A b + 3B a)d e - 2B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1378 +t0:=(A+B*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1378 +r0:=-1/42*(2*b*B*d-7*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/210*(b*d-a*e)*(2*b*B*d-7*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/7*B*(a+b*x)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 7 7 7 6 6 +--R 30B b e x + ((35A b + 35B a)e + 140B b d e )x +--R + +--R 7 6 2 5 5 +--R (42A a e + (168A b + 168B a)d e + 252B b d e )x +--R + +--R 6 2 5 3 4 4 +--R (210A a d e + (315A b + 315B a)d e + 210B b d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (420A a d e + (280A b + 280B a)d e + 70B b d e )x +--R + +--R 3 4 4 3 2 4 3 5 2 +--R (420A a d e + (105A b + 105B a)d e )x + 210A a d e x + 42A a d e +--R + +--R 6 7 +--R (- 7A b - 7B a)d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 210b e x + 210a e +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 4 3 6 +--R 30B b e x + ((35A b + 35B a)e + 140B b d e )x +--R + +--R 4 3 2 2 5 +--R (42A a e + (168A b + 168B a)d e + 252B b d e )x +--R + +--R 3 2 2 3 4 +--R (210A a d e + (315A b + 315B a)d e + 210B b d e)x +--R + +--R 2 2 3 4 3 +--R (420A a d e + (280A b + 280B a)d e + 70B b d )x +--R + +--R 3 4 2 4 +--R (420A a d e + (105A b + 105B a)d )x + 210A a d x +--R / +--R 210 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 7 7 6 6 +--R - 30B b e x + ((- 35A b - 35B a)e - 140B b d e )x +--R + +--R 7 6 2 5 5 +--R (- 42A a e + (- 168A b - 168B a)d e - 252B b d e )x +--R + +--R 6 2 5 3 4 4 +--R (- 210A a d e + (- 315A b - 315B a)d e - 210B b d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (- 420A a d e + (- 280A b - 280B a)d e - 70B b d e )x +--R + +--R 3 4 4 3 2 4 3 +--R (- 420A a d e + (- 105A b - 105B a)d e )x - 210A a d e x +--R + +--R 5 2 6 7 +--R - 42A a d e + (7A b + 7B a)d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 7 8 2 7 2 6 7 +--R 30B b e x + ((35A b + 65B a b)e + 140B b d e )x +--R + +--R 2 7 2 6 2 2 5 6 +--R ((77A a b + 35B a )e + (168A b + 308B a b)d e + 252B b d e )x +--R + +--R 2 7 2 6 2 2 5 +--R 42A a e + (378A a b + 168B a )d e + (315A b + 567B a b)d e +--R + +--R 2 3 4 +--R 210B b d e +--R * +--R 5 +--R x +--R + +--R 2 6 2 2 5 2 3 4 +--R 210A a d e + (735A a b + 315B a )d e + (280A b + 490B a b)d e +--R + +--R 2 4 3 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 3 +--R (420A a d e + (700A a b + 280B a )d e + (105A b + 175B a b)d e )x +--R + +--R 2 3 4 2 4 3 2 2 4 3 +--R (420A a d e + (315A a b + 105B a )d e )x + 210A a d e x +--R / +--R 3 3 +--R 210b e x + 210a e +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 6 4 3 5 +--R B b e x + ((A b + B a)e + 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (A a e + (4A b + 4B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (4A a d e + (6A b + 6B a)d e + 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (6A a d e + (4A b + 4B a)d e + B b d )x +--R + +--R 3 4 4 +--R (4A a d e + (A b + B a)d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 7 2 4 2 3 6 +--R - B b e x + ((- A b - 2B a b)e - 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((- 2A a b - B a )e + (- 4A b - 8B a b)d e - 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R - A a e + (- 8A a b - 4B a )d e + (- 6A b - 12B a b)d e +--R + +--R 2 3 +--R - 4B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R - 4A a d e + (- 12A a b - 6B a )d e + (- 4A b - 8B a b)d e +--R + +--R 2 4 +--R - B b d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 3 2 4 2 +--R (- 6A a d e + (- 8A a b - 4B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (- 4A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1378 +t0:=(A+B*x)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1378 +r0:=-1/15*(b*B*d-3*A*b*e+2*a*B*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/60*(b*d-a*e)*(b*B*d-3*A*b*e+2*a*B*e)*(d+e*x)^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/6*B*(a+b*x)*(d+e*x)^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 10B b e x + ((12A b + 12B a)e + 36B b d e )x +--R + +--R 6 5 2 4 4 +--R (15A a e + (45A b + 45B a)d e + 45B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (60A a d e + (60A b + 60B a)d e + 20B b d e )x +--R + +--R 2 4 3 3 2 3 3 4 2 +--R (90A a d e + (30A b + 30B a)d e )x + 60A a d e x + 15A a d e +--R + +--R 5 6 +--R (- 3A b - 3B a)d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 3 2 5 +--R 10B b e x + ((12A b + 12B a)e + 36B b d e )x +--R + +--R 3 2 2 4 +--R (15A a e + (45A b + 45B a)d e + 45B b d e)x +--R + +--R 2 2 3 3 +--R (60A a d e + (60A b + 60B a)d e + 20B b d )x +--R + +--R 2 3 2 3 +--R (90A a d e + (30A b + 30B a)d )x + 60A a d x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 5 +--R - 10B b e x + ((- 12A b - 12B a)e - 36B b d e )x +--R + +--R 6 5 2 4 4 +--R (- 15A a e + (- 45A b - 45B a)d e - 45B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (- 60A a d e + (- 60A b - 60B a)d e - 20B b d e )x +--R + +--R 2 4 3 3 2 3 3 4 2 +--R (- 90A a d e + (- 30A b - 30B a)d e )x - 60A a d e x - 15A a d e +--R + +--R 5 6 +--R (3A b + 3B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 6 7 2 6 2 5 6 +--R 10B b e x + ((12A b + 22B a b)e + 36B b d e )x +--R + +--R 2 6 2 5 2 2 4 5 +--R ((27A a b + 12B a )e + (45A b + 81B a b)d e + 45B b d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 15A a e + (105A a b + 45B a )d e + (60A b + 105B a b)d e +--R + +--R 2 3 3 +--R 20B b d e +--R * +--R 4 +--R x +--R + +--R 2 5 2 2 4 2 3 3 3 +--R (60A a d e + (150A a b + 60B a )d e + (30A b + 50B a b)d e )x +--R + +--R 2 2 4 2 3 3 2 2 3 3 +--R (90A a d e + (90A a b + 30B a )d e )x + 60A a d e x +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 3 2 4 +--R B b e x + ((A b + B a)e + 3B b d e )x +--R + +--R 3 2 2 3 +--R (A a e + (3A b + 3B a)d e + 3B b d e)x +--R + +--R 2 2 3 2 +--R (3A a d e + (3A b + 3B a)d e + B b d )x +--R + +--R 2 3 3 +--R (3A a d e + (A b + B a)d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 6 2 3 2 2 5 +--R - B b e x + ((- A b - 2B a b)e - 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((- 2A a b - B a )e + (- 3A b - 6B a b)d e - 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- A a e + (- 6A a b - 3B a )d e + (- 3A b - 6B a b)d e - B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (- 3A a d e + (- 6A a b - 3B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (- 3A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1378 +t0:=(A+B*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1378 +r0:=-1/20*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/60*(b*d-a*e)*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/5*B*(a+b*x)*(d+e*x)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 12B b e x + ((15A b + 15B a)e + 30B b d e )x +--R + +--R 5 4 2 3 3 +--R (20A a e + (40A b + 40B a)d e + 20B b d e )x +--R + +--R 4 2 3 2 2 3 3 2 +--R (60A a d e + (30A b + 30B a)d e )x + 60A a d e x + 20A a d e +--R + +--R 4 5 +--R (- 5A b - 5B a)d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 +--R 12B b e x + ((15A b + 15B a)e + 30B b d e)x +--R + +--R 2 2 3 +--R (20A a e + (40A b + 40B a)d e + 20B b d )x +--R + +--R 2 2 2 +--R (60A a d e + (30A b + 30B a)d )x + 60A a d x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 4 +--R - 12B b e x + ((- 15A b - 15B a)e - 30B b d e )x +--R + +--R 5 4 2 3 3 +--R (- 20A a e + (- 40A b - 40B a)d e - 20B b d e )x +--R + +--R 4 2 3 2 2 3 3 2 +--R (- 60A a d e + (- 30A b - 30B a)d e )x - 60A a d e x - 20A a d e +--R + +--R 4 5 +--R (5A b + 5B a)d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 5 6 2 5 2 4 5 +--R 12B b e x + ((15A b + 27B a b)e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 4 +--R ((35A a b + 15B a )e + (40A b + 70B a b)d e + 20B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (20A a e + (100A a b + 40B a )d e + (30A b + 50B a b)d e )x +--R + +--R 2 4 2 2 3 2 2 2 3 +--R (60A a d e + (90A a b + 30B a )d e )x + 60A a d e x +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 4 2 3 +--R B b e x + ((A b + B a)e + 2B b d e)x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + B b d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 5 2 2 2 4 +--R - B b e x + ((- A b - 2B a b)e - 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((- 2A a b - B a )e + (- 2A b - 4B a b)d e - B b d )x +--R + +--R 2 2 2 2 2 2 +--R (- A a e + (- 4A a b - 2B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (- 2A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1378 +t0:=(A+B*x)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 | 2 2 2 +--R (1) (B e x + (A e + B d)x + A d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1378 +r0:=1/6*(2*A*b*e-B*(b*d+a*e))*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^3+1/4*(b*d-_ + a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b^3*e)+_ + 1/4*B*(a+b*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 3 3 3 2 3 2 +--R 3B b e x + ((4A b + B a b )e + 4B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((2A a b - B a b)e + (6A b + 2B a b )d)x + (- 2A a b + B a )e +--R + +--R 2 2 +--R (6A a b - 2B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 12b +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 3B b e x + ((4A b + 4B a)e + 4B b d)x + (6A a e + (6A b + 6B a)d)x +--R + +--R 12A a d x +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 +--R - 3B b e x + ((- 4A b - B a b )e - 4B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((- 2A a b + B a b)e + (- 6A b - 2B a b )d)x + (2A a b - B a )e +--R + +--R 2 2 +--R (- 6A a b + 2B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 4 3 4 3 +--R 3B b e x + ((4A b + 4B a b )e + 4B b d)x +--R + +--R 3 4 3 2 3 +--R (6A a b e + (6A b + 6B a b )d)x + 12A a b d x +--R / +--R 3 +--R 12b +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 2 +--R (B b e x + ((A b + B a)e + B b d)x + (A a e + (A b + B a)d)x + A a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 2 3 +--R - B b e x + ((- A b - 2B a b)e - B b d)x +--R + +--R 2 2 2 +--R ((- 2A a b - B a )e + (- A b - 2B a b)d)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (1) (B x + A)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1378 +r0:=1/3*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/b^2 +--R +--R +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R (2B b x + (3A b + B a b)x + 3A a b - B a )\|b x + 2a b x + a +--R (2) ----------------------------------------------------------------- +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1378 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 2B b x + (3A b + 3B a)x + 6A a x +--R (3) ---------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R (- 2B b x + (- 3A b - B a b)x - 3A a b + B a )\|b x + 2a b x + a +--R + +--R 3 3 3 2 2 2 +--R 2B b x + (3A b + 3B a b )x + 6A a b x +--R / +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1378 +r0:=-(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/2*B*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e)+(b*d-a*e)*(B*d-A*e)*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (2A a b e + (- 2A b - 2B a b)d e + 2B b d )log(e x + d) + B b e x +--R + +--R 2 2 2 2 2 +--R ((2A b + 2B a b)e - 2B b d e)x + (2A a b + B a )e - 2B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 3 3 +--R 2b e x + 2a b e +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R (2A a e + (- 2A b - 2B a)d e + 2B b d )log(e x + d) + B b e x +--R + +--R 2 +--R ((2A b + 2B a)e - 2B b d e)x +--R / +--R 3 +--R 2e +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 +--R (- 2A a b e + (2A b + 2B a b)d e - 2B b d )log(e x + d) - B b e x +--R + +--R 2 2 2 2 2 +--R ((- 2A b - 2B a b)e + 2B b d e)x + (- 2A a b - B a )e + 2B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 3 2 2 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + 2A a b e +--R + +--R 2 2 2 2 +--R (- 2A a b - 2B a b)d e + 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b + 3B a b )e - 2B b d e)x +--R + +--R 2 2 2 2 +--R ((2A a b + 2B a b)e - 2B a b d e)x +--R / +--R 2 3 3 +--R 2b e x + 2a b e +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1378 +r0:=(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*(d+e*x))-_ + (2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 +--R (((A b + B a)e - 2B b d e)x + (A b + B a)d e - 2B b d )log(e x + d) +--R + +--R 2 2 2 2 +--R B b e x + ((- A b + B a)e + 2B b d e)x - A a e + 2B a d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (((A b + B a)e - 2B b d e)x + (A b + B a)d e - 2B b d )log(e x + d) +--R + +--R 2 2 2 2 +--R B b e x + B b d e x - A a e + (A b + B a)d e - B b d +--R / +--R 4 3 +--R e x + d e +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 +--R (((- A b - B a)e + 2B b d e)x + (- A b - B a)d e + 2B b d ) +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R - B b e x + ((A b - B a)e - 2B b d e)x + A a e - 2B a d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 2 +--R ((A b + B a b)e - 2B b d e)x +--R + +--R 2 2 2 2 2 2 +--R ((A a b + B a )e + (A b - B a b)d e - 2B b d )x + (A a b + B a )d e +--R + +--R 2 +--R - 2B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 3 2 2 2 +--R B b e x + (B a b e + B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R (- A a b e + (A b + 2B a b)d e - B b d )x - A a e + (A a b + B a )d e +--R + +--R 2 +--R - B a b d +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1378 +r0:=-1/2*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^2)+B*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*_ + (d+e*x))+b*B*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 3 2 2 2 2 2 2 2 +--R (2B a b e - 2B b d e )x + (4B a b d e - 4B b d e)x + 2B a b d e +--R + +--R 2 3 +--R - 2B b d +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- A b e + B b d e )x +--R + +--R 2 3 2 2 2 2 3 2 2 +--R ((- 2A a b - 2B a )e + 6B a b d e - 2B b d e)x - A a e - B a d e +--R + +--R 2 2 3 +--R 4B a b d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 5 3 2 6 5 2 2 4 2 +--R (2a b e - 2b d e )x + (2a e + 2a b d e - 4b d e )x +--R + +--R 2 5 2 4 2 3 3 2 2 4 3 3 +--R (4a d e - 2a b d e - 2b d e )x + 2a d e - 2a b d e +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (2B b e x + 4B b d e x + 2B b d )log(e x + d) +--R + +--R 2 2 2 +--R ((- 2A b - 2B a)e + 4B b d e)x - A a e + (- A b - B a)d e + 3B b d +--R / +--R 5 2 4 2 3 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 2 2 2 2 +--R (- 2B a b e + 2B b d e )x + (- 4B a b d e + 4B b d e)x +--R + +--R 2 2 3 +--R - 2B a b d e + 2B b d +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (A b e - B b d e )x +--R + +--R 2 3 2 2 2 2 3 2 2 +--R ((2A a b + 2B a )e - 6B a b d e + 2B b d e)x + A a e + B a d e +--R + +--R 2 2 3 +--R - 4B a b d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (2B a b e - 2B b d e )x + (2B a b e + 2B a b d e - 4B b d e)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (4B a b d e - 2B a b d e - 2B b d )x + 2B a b d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 2A a b - 2B a b)e + (2A b + 6B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 3 +--R ((- 3A a b - 2B a )e + (2A a b + 5B a b)d e + A b d e - 3B b d )x +--R + +--R 3 3 3 2 2 2 2 2 3 +--R - A a e - B a d e + (A a b + 4B a b)d e - 3B a b d +--R / +--R 6 2 5 3 2 6 5 2 2 4 2 +--R (2a b e - 2b d e )x + (2a e + 2a b d e - 4b d e )x +--R + +--R 2 5 2 4 2 3 3 2 2 4 3 3 +--R (4a d e - 2a b d e - 2b d e )x + 2a d e - 2a b d e +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1378 +r0:=1/3*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^3)+_ + 1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^2) +--R +--R +--R (2) +--R 2 2 2 +--R ((A b - 3B a b)e + 2B b d)x +--R + +--R 2 2 2 2 +--R ((- A a b - 3B a )e + (3A b + B a b)d)x - 2A a e + (3A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 5 4 2 2 3 3 2 4 2 3 2 3 2 2 +--R (6a e - 12a b d e + 6b d e )x + (18a d e - 36a b d e + 18b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (18a d e - 36a b d e + 18b d e)x + 6a d e - 12a b d e + 6b d +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 6B b e x + ((- 3A b - 3B a)e - 6B b d e)x - 2A a e +--R + +--R 2 +--R (- A b - B a)d e - 2B b d +--R / +--R 6 3 5 2 2 4 3 3 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 +--R ((- A b + 3B a b)e - 2B b d e )x +--R + +--R 2 4 2 3 2 4 +--R ((A a b + 3B a )e + (- 3A b - B a b)d e )x + 2A a e +--R + +--R 2 3 +--R (- 3A a b + B a )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 3 2 2 2 +--R (- 6B a b e + 12B a b d e - 6B b d e )x +--R + +--R 2 3 4 2 3 3 2 2 2 +--R (- 3A a b - 3B a )e + 6A a b d e + (- 3A b + 9B a b )d e +--R + +--R 3 3 +--R - 6B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 3 2 3 3 4 +--R - 2A a e + (3A a b - B a )d e + (- A b + 3B a b )d e - 2B b d +--R / +--R 2 8 7 2 2 6 3 2 7 2 6 2 3 5 2 +--R (6a e - 12a b d e + 6b d e )x + (18a d e - 36a b d e + 18b d e )x +--R + +--R 2 2 6 3 5 2 4 4 2 3 5 4 4 2 5 3 +--R (18a d e - 36a b d e + 18b d e )x + 6a d e - 12a b d e + 6b d e +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1378 +r0:=-1/4*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/4*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^3)-1/12*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^3) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a)e - 4B b d e)x - 3A a e +--R + +--R 2 +--R (- A b - B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 5 7 6 4 6 2 5 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 5 3 4 2 3 4 4 3 4 3 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a)e - 4B b d e)x - 3A a e +--R + +--R 2 +--R (- A b - B a)d e - B b d +--R / +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R 6B b e x + ((4A b + 4B a)e + 4B b d e)x + 3A a e + (A b + B a)d e +--R + +--R 2 +--R B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R - 6B b e x + ((- 4A b - 10B a b)e - 4B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 7A a b - 4B a )e + (- A b - 5B a b)d e - B b d )x - 3A a e +--R + +--R 2 2 +--R (- A a b - B a )d e - B a b d +--R / +--R 7 5 7 6 4 6 2 5 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 5 3 4 2 3 4 4 3 4 3 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1378 +r0:=-1/5*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^5)-1/15*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^4)-1/60*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^4) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 20B b e x + ((- 15A b - 15B a)e - 10B b d e)x - 12A a e +--R + +--R 2 +--R (- 3A b - 3B a)d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 6 8 7 5 7 2 6 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 6 3 5 3 3 5 4 4 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 4 5 3 5 3 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 20B b e x + ((- 15A b - 15B a)e - 10B b d e)x - 12A a e +--R + +--R 2 +--R (- 3A b - 3B a)d e - 2B b d +--R / +--R 8 5 7 4 2 6 3 3 5 2 4 4 5 3 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R 20B b e x + ((15A b + 15B a)e + 10B b d e)x + 12A a e +--R + +--R 2 +--R (3A b + 3B a)d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R - 20B b e x + ((- 15A b - 35B a b)e - 10B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 27A a b - 15B a )e + (- 3A b - 13B a b)d e - 2B b d )x - 12A a e +--R + +--R 2 2 +--R (- 3A a b - 3B a )d e - 2B a b d +--R / +--R 8 6 8 7 5 7 2 6 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 6 3 5 3 3 5 4 4 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 4 5 3 5 3 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1378 +r0:=-1/6*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^6)-1/12*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^5)-1/60*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 15B b e x + ((- 12A b - 12B a)e - 6B b d e)x - 10A a e +--R + +--R 2 +--R (- 2A b - 2B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 15B b e x + ((- 12A b - 12B a)e - 6B b d e)x - 10A a e +--R + +--R 2 +--R (- 2A b - 2B a)d e - B b d +--R / +--R 9 6 8 5 2 7 4 3 6 3 4 5 2 5 4 6 3 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R 15B b e x + ((12A b + 12B a)e + 6B b d e)x + 10A a e +--R + +--R 2 +--R (2A b + 2B a)d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R - 15B b e x + ((- 12A b - 27B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 22A a b - 12B a )e + (- 2A b - 8B a b)d e - B b d )x - 10A a e +--R + +--R 2 2 +--R (- 2A a b - 2B a )d e - B a b d +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 1378 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 m +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(e x + d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1378 +r0:=(A*b*e*(5+m)-B*(4*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2*(4+m)*(5+m))+B*(a+b*x)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(b*e*(5+m))+6*(b*d-a*e)^2*(A*b*e*(5+m)-_ + B*(4*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4*_ + (2+m)*(3+m)*(4+m)*(5+m))-6*(b*d-a*e)^3*(A*b*e*(5+m)-B*(4*b*d+a*e*_ + (1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(1+m)*(2+m)*_ + (3+m)*(4+m)*(5+m)*(a+b*x))-3*(b*d-a*e)*(A*b*e*(5+m)-B*(4*b*d+a*e*_ + (1+m)))*(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*_ + (3+m)*(4+m)*(5+m)) +--R +--R +--R (2) +--R 3 4 4 3 4 3 3 4 2 3 4 3 4 4 +--R (B b e m + 10B b e m + 35B b e m + 50B b e m + 24B b e )x +--R + +--R 3 2 4 4 3 2 4 3 3 3 +--R (A b + 3B a b )e m + ((11A b + 33B a b )e - 4B b d e )m +--R + +--R 3 2 4 3 3 2 +--R ((41A b + 123B a b )e - 24B b d e )m +--R + +--R 3 2 4 3 3 3 2 4 +--R ((61A b + 183B a b )e - 44B b d e )m + (30A b + 90B a b )e +--R + +--R 3 3 +--R - 24B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 +--R (3A a b + 3B a b)e m +--R + +--R 2 2 4 3 2 3 3 +--R ((36A a b + 36B a b)e + (- 3A b - 9B a b )d e )m +--R + +--R 2 2 4 3 2 3 +--R (147A a b + 147B a b)e + (- 24A b - 72B a b )d e +--R + +--R 3 2 2 +--R 12B b d e +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 2 3 +--R (234A a b + 234B a b)e + (- 51A b - 153B a b )d e +--R + +--R 3 2 2 +--R 36B b d e +--R * +--R m +--R + +--R 2 2 4 3 2 3 3 2 2 +--R (120A a b + 120B a b)e + (- 30A b - 90B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 +--R (3A a b + B a )e m +--R + +--R 2 3 4 2 2 3 3 +--R ((39A a b + 13B a )e + (- 6A a b - 6B a b)d e )m +--R + +--R 2 3 4 2 2 3 +--R (177A a b + 59B a )e + (- 60A a b - 60B a b)d e +--R + +--R 3 2 2 2 +--R (6A b + 18B a b )d e +--R * +--R 2 +--R m +--R + +--R 2 3 4 2 2 3 +--R (321A a b + 107B a )e + (- 174A a b - 174B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (36A b + 108B a b )d e - 24B b d e +--R * +--R m +--R + +--R 2 3 4 2 2 3 +--R (180A a b + 60B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (30A b + 90B a b )d e - 24B b d e +--R * +--R x +--R + +--R 3 4 4 3 4 2 3 3 3 +--R A a e m + (14A a e + (- 3A a b - B a )d e )m +--R + +--R 3 4 2 3 3 2 2 2 2 2 +--R (71A a e + (- 36A a b - 12B a )d e + (6A a b + 6B a b)d e )m +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 154A a e + (- 141A a b - 47B a )d e + (54A a b + 54B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 18B a b )d e +--R * +--R m +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 120A a e + (- 180A a b - 60B a )d e + (120A a b + 120B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 30A b - 90B a b )d e + 24B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 4 3 5 3 3 5 2 3 5 3 5 5 +--R (B b e m + 10B b e m + 35B b e m + 50B b e m + 24B b e )x +--R + +--R 3 2 5 3 4 4 +--R ((A b + 3B a b )e + B b d e )m +--R + +--R 3 2 5 3 4 3 +--R ((11A b + 33B a b )e + 6B b d e )m +--R + +--R 3 2 5 3 4 2 +--R ((41A b + 123B a b )e + 11B b d e )m +--R + +--R 3 2 5 3 4 3 2 5 +--R ((61A b + 183B a b )e + 6B b d e )m + (30A b + 90B a b )e +--R * +--R 4 +--R x +--R + +--R 2 2 5 3 2 4 4 +--R ((3A a b + 3B a b)e + (A b + 3B a b )d e )m +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((36A a b + 36B a b)e + (8A b + 24B a b )d e - 4B b d e )m +--R + +--R 2 2 5 3 2 4 3 2 3 2 +--R ((147A a b + 147B a b)e + (17A b + 51B a b )d e - 12B b d e )m +--R + +--R 2 2 5 3 2 4 3 2 3 +--R ((234A a b + 234B a b)e + (10A b + 30B a b )d e - 8B b d e )m +--R + +--R 2 2 5 +--R (120A a b + 120B a b)e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 4 4 +--R ((3A a b + B a )e + (3A a b + 3B a b)d e )m +--R + +--R 2 3 5 2 2 4 +--R (39A a b + 13B a )e + (30A a b + 30B a b)d e +--R + +--R 3 2 2 3 +--R (- 3A b - 9B a b )d e +--R * +--R 3 +--R m +--R + +--R 2 3 5 2 2 4 +--R (177A a b + 59B a )e + (87A a b + 87B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 18A b - 54B a b )d e + 12B b d e +--R * +--R 2 +--R m +--R + +--R 2 3 5 2 2 4 +--R (321A a b + 107B a )e + (60A a b + 60B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 15A b - 45B a b )d e + 12B b d e +--R * +--R m +--R + +--R 2 3 5 +--R (180A a b + 60B a )e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 4 +--R (A a e + (3A a b + B a )d e )m +--R + +--R 3 5 2 3 4 2 2 2 3 3 +--R (14A a e + (36A a b + 12B a )d e + (- 6A a b - 6B a b)d e )m +--R + +--R 3 5 2 3 4 2 2 2 3 +--R 71A a e + (141A a b + 47B a )d e + (- 54A a b - 54B a b)d e +--R + +--R 3 2 3 2 +--R (6A b + 18B a b )d e +--R * +--R 2 +--R m +--R + +--R 3 5 2 3 4 +--R 154A a e + (180A a b + 60B a )d e +--R + +--R 2 2 2 3 3 2 3 2 +--R (- 120A a b - 120B a b)d e + (30A b + 90B a b )d e +--R + +--R 3 4 +--R - 24B b d e +--R * +--R m +--R + +--R 3 5 +--R 120A a e +--R * +--R x +--R + +--R 3 4 4 3 4 2 3 2 3 3 +--R A a d e m + (14A a d e + (- 3A a b - B a )d e )m +--R + +--R 3 4 2 3 2 3 2 2 3 2 2 +--R (71A a d e + (- 36A a b - 12B a )d e + (6A a b + 6B a b)d e )m +--R + +--R 3 4 2 3 2 3 2 2 3 2 +--R 154A a d e + (- 141A a b - 47B a )d e + (54A a b + 54B a b)d e +--R + +--R 3 2 4 +--R (- 6A b - 18B a b )d e +--R * +--R m +--R + +--R 3 4 2 3 2 3 2 2 3 2 +--R 120A a d e + (- 180A a b - 60B a )d e + (120A a b + 120B a b)d e +--R + +--R 3 2 4 3 5 +--R (- 30A b - 90B a b )d e + 24B b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R e m + 15e m + 85e m + 225e m + 274e m + 120e +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 4 4 5 3 4 5 2 4 5 4 5 6 +--R (B b e m + 10B b e m + 35B b e m + 50B b e m + 24B b e )x +--R + +--R 4 3 5 4 4 4 +--R ((A b + 4B a b )e + B b d e )m +--R + +--R 4 3 5 4 4 3 +--R ((11A b + 43B a b )e + 6B b d e )m +--R + +--R 4 3 5 4 4 2 +--R ((41A b + 158B a b )e + 11B b d e )m +--R + +--R 4 3 5 4 4 4 3 5 +--R ((61A b + 233B a b )e + 6B b d e )m + (30A b + 114B a b )e +--R * +--R 5 +--R x +--R + +--R 3 2 2 5 4 3 4 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d e )m +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((47A a b + 69B a b )e + (8A b + 30B a b )d e - 4B b d e )m +--R + +--R 3 2 2 5 4 3 4 +--R (188A a b + 270B a b )e + (17A b + 62B a b )d e +--R + +--R 4 2 3 +--R - 12B b d e +--R * +--R 2 +--R m +--R + +--R 3 2 2 5 4 3 4 +--R (295A a b + 417B a b )e + (10A b + 36B a b )d e +--R + +--R 4 2 3 +--R - 8B b d e +--R * +--R m +--R + +--R 3 2 2 5 +--R (150A a b + 210B a b )e +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 3 2 2 4 4 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d e )m +--R + +--R 2 2 3 5 3 2 2 4 +--R (75A a b + 49B a b)e + (38A a b + 54B a b )d e +--R + +--R 4 3 2 3 +--R (- 3A b - 13B a b )d e +--R * +--R 3 +--R m +--R + +--R 2 2 3 5 3 2 2 4 +--R (324A a b + 206B a b)e + (104A a b + 138B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 18A b - 66B a b )d e + 12B b d e +--R * +--R 2 +--R m +--R + +--R 2 2 3 5 3 2 2 4 +--R (555A a b + 341B a b)e + (70A a b + 90B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 15A b - 53B a b )d e + 12B b d e +--R * +--R m +--R + +--R 2 2 3 5 +--R (300A a b + 180B a b)e +--R * +--R 3 +--R x +--R + +--R 3 4 5 2 2 3 4 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d e )m +--R + +--R 3 4 5 2 2 3 4 +--R (53A a b + 13B a )e + (66A a b + 42B a b)d e +--R + +--R 3 2 2 2 3 +--R (- 9A a b - 15B a b )d e +--R * +--R 3 +--R m +--R + +--R 3 4 5 2 2 3 4 +--R (248A a b + 59B a )e + (228A a b + 134B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 72A a b - 108B a b )d e + (6A b + 30B a b )d e +--R * +--R 2 +--R m +--R + +--R 3 4 5 2 2 3 4 +--R (475A a b + 107B a )e + (240A a b + 120B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 135A a b - 165B a b )d e + (30A b + 102B a b )d e +--R + +--R 4 4 +--R - 24B b d e +--R * +--R m +--R + +--R 3 4 5 +--R (300A a b + 60B a )e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 4 4 +--R (A a e + (4A a b + B a )d e )m +--R + +--R 4 5 3 4 4 2 2 3 2 3 3 +--R (14A a e + (50A a b + 12B a )d e + (- 9A a b - 7B a b)d e )m +--R + +--R 4 5 3 4 4 +--R 71A a e + (212A a b + 47B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 90A a b - 66B a b)d e + (12A a b + 24B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 5 3 4 4 +--R 154A a e + (334A a b + 60B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 261A a b - 167B a b)d e + (84A a b + 144B a b )d e +--R + +--R 4 3 4 +--R (- 6A b - 42B a b )d e +--R * +--R m +--R + +--R 4 5 3 4 2 2 3 2 3 +--R 120A a e + 120A a b d e + (- 180A a b - 60B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (120A a b + 120B a b )d e + (- 30A b - 90B a b )d e + 24B b d +--R * +--R x +--R + +--R 4 4 4 4 4 3 4 2 3 3 +--R A a d e m + (14A a d e + (- 3A a b - B a )d e )m +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 2 +--R (71A a d e + (- 36A a b - 12B a )d e + (6A a b + 6B a b)d e )m +--R + +--R 4 4 3 4 2 3 +--R 154A a d e + (- 141A a b - 47B a )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (54A a b + 54B a b)d e + (- 6A a b - 18B a b )d e +--R * +--R m +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R 120A a d e + (- 180A a b - 60B a )d e + (120A a b + 120B a b)d e +--R + +--R 3 2 2 4 3 5 +--R (- 30A a b - 90B a b )d e + 24B a b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 4 4 3 4 3 3 4 2 3 4 3 4 4 +--R (- B b e m - 10B b e m - 35B b e m - 50B b e m - 24B b e )x +--R + +--R 3 2 4 4 3 2 4 3 3 3 +--R (- A b - 3B a b )e m + ((- 11A b - 33B a b )e + 4B b d e )m +--R + +--R 3 2 4 3 3 2 +--R ((- 41A b - 123B a b )e + 24B b d e )m +--R + +--R 3 2 4 3 3 +--R ((- 61A b - 183B a b )e + 44B b d e )m +--R + +--R 3 2 4 3 3 +--R (- 30A b - 90B a b )e + 24B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 +--R (- 3A a b - 3B a b)e m +--R + +--R 2 2 4 3 2 3 3 +--R ((- 36A a b - 36B a b)e + (3A b + 9B a b )d e )m +--R + +--R 2 2 4 3 2 3 +--R (- 147A a b - 147B a b)e + (24A b + 72B a b )d e +--R + +--R 3 2 2 +--R - 12B b d e +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 2 3 +--R (- 234A a b - 234B a b)e + (51A b + 153B a b )d e +--R + +--R 3 2 2 +--R - 36B b d e +--R * +--R m +--R + +--R 2 2 4 3 2 3 3 2 2 +--R (- 120A a b - 120B a b)e + (30A b + 90B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 +--R (- 3A a b - B a )e m +--R + +--R 2 3 4 2 2 3 3 +--R ((- 39A a b - 13B a )e + (6A a b + 6B a b)d e )m +--R + +--R 2 3 4 2 2 3 +--R (- 177A a b - 59B a )e + (60A a b + 60B a b)d e +--R + +--R 3 2 2 2 +--R (- 6A b - 18B a b )d e +--R * +--R 2 +--R m +--R + +--R 2 3 4 2 2 3 +--R (- 321A a b - 107B a )e + (174A a b + 174B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 36A b - 108B a b )d e + 24B b d e +--R * +--R m +--R + +--R 2 3 4 2 2 3 +--R (- 180A a b - 60B a )e + (120A a b + 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 30A b - 90B a b )d e + 24B b d e +--R * +--R x +--R + +--R 3 4 4 3 4 2 3 3 3 +--R - A a e m + (- 14A a e + (3A a b + B a )d e )m +--R + +--R 3 4 2 3 3 2 2 2 2 2 +--R (- 71A a e + (36A a b + 12B a )d e + (- 6A a b - 6B a b)d e )m +--R + +--R 3 4 2 3 3 +--R - 154A a e + (141A a b + 47B a )d e +--R + +--R 2 2 2 2 3 2 3 +--R (- 54A a b - 54B a b)d e + (6A b + 18B a b )d e +--R * +--R m +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 120A a e + (180A a b + 60B a )d e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 3 3 4 +--R (30A b + 90B a b )d e - 24B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 1378 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 5 8 2 5 2 4 7 +--R B b e x + ((A b + 2B a b)e + 5B b d e )x +--R + +--R 2 5 2 4 2 2 3 6 +--R ((2A a b + B a )e + (5A b + 10B a b)d e + 10B b d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 5 +--R (A a e + (10A a b + 5B a )d e + (10A b + 20B a b)d e + 10B b d e )x +--R + +--R 2 4 2 2 3 2 3 2 +--R 5A a d e + (20A a b + 10B a )d e + (10A b + 20B a b)d e +--R + +--R 2 4 +--R 5B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 3 +--R (10A a d e + (20A a b + 10B a )d e + (5A b + 10B a b)d e + B b d )x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1378 +r0:=-1/45*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/10*B*(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-_ + 1/420*(b*d-a*e)^2*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^6*sqrt(a^2+2*a*b*_ + x+b^2*x^2)/(b*e^4)+1/2520*(b*d-a*e)^3*(2*b*B*d-5*A*b*e+3*a*B*e)*_ + (d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))+1/120*(b*d-a*e)*_ + (2*b*B*d-5*A*b*e+3*a*B*e)*(a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 10 10 3 2 10 3 9 9 +--R 252B b e x + ((280A b + 840B a b )e + 1400B b d e )x +--R + +--R 2 2 10 3 2 9 +--R (945A a b + 945B a b)e + (1575A b + 4725B a b )d e +--R + +--R 3 2 8 +--R 3150B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 10 2 2 9 +--R (1080A a b + 360B a )e + (5400A a b + 5400B a b)d e +--R + +--R 3 2 2 8 3 3 7 +--R (3600A b + 10800B a b )d e + 3600B b d e +--R * +--R 7 +--R x +--R + +--R 3 10 2 3 9 +--R 420A a e + (6300A a b + 2100B a )d e +--R + +--R 2 2 2 8 3 2 3 7 +--R (12600A a b + 12600B a b)d e + (4200A b + 12600B a b )d e +--R + +--R 3 4 6 +--R 2100B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 2 8 +--R 2520A a d e + (15120A a b + 5040B a )d e +--R + +--R 2 2 3 7 3 2 4 6 +--R (15120A a b + 15120B a b)d e + (2520A b + 7560B a b )d e +--R + +--R 3 5 5 +--R 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 8 2 3 3 7 +--R 6300A a d e + (18900A a b + 6300B a )d e +--R + +--R 2 2 4 6 3 2 5 5 +--R (9450A a b + 9450B a b)d e + (630A b + 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 3 7 2 3 4 6 +--R 8400A a d e + (12600A a b + 4200B a )d e +--R + +--R 2 2 5 5 +--R (2520A a b + 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 3 5 5 2 3 5 5 +--R (6300A a d e + (3780A a b + 1260B a )d e )x + 2520A a d e x +--R + +--R 3 6 4 2 3 7 3 2 2 8 2 +--R 420A a d e + (- 180A a b - 60B a )d e + (45A a b + 45B a b)d e +--R + +--R 3 2 9 3 10 +--R (- 5A b - 15B a b )d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 10 3 2 5 3 4 9 +--R 252B b e x + ((280A b + 840B a b )e + 1400B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 8 +--R ((945A a b + 945B a b)e + (1575A b + 4725B a b )d e + 3150B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (1080A a b + 360B a )e + (5400A a b + 5400B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (3600A b + 10800B a b )d e + 3600B b d e +--R * +--R 7 +--R x +--R + +--R 3 5 2 3 4 +--R 420A a e + (6300A a b + 2100B a )d e +--R + +--R 2 2 2 3 3 2 3 2 +--R (12600A a b + 12600B a b)d e + (4200A b + 12600B a b )d e +--R + +--R 3 4 +--R 2100B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 2 3 2 3 +--R 2520A a d e + (15120A a b + 5040B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (15120A a b + 15120B a b)d e + (2520A b + 7560B a b )d e + 504B b d +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 3 3 2 +--R 6300A a d e + (18900A a b + 6300B a )d e +--R + +--R 2 2 4 3 2 5 +--R (9450A a b + 9450B a b)d e + (630A b + 1890B a b )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 3 4 +--R 8400A a d e + (12600A a b + 4200B a )d e +--R + +--R 2 2 5 +--R (2520A a b + 2520B a b)d +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 5 2 3 5 +--R (6300A a d e + (3780A a b + 1260B a )d )x + 2520A a d x +--R / +--R 2520 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 10 10 3 2 10 3 9 9 +--R - 252B b e x + ((- 280A b - 840B a b )e - 1400B b d e )x +--R + +--R 2 2 10 3 2 9 +--R (- 945A a b - 945B a b)e + (- 1575A b - 4725B a b )d e +--R + +--R 3 2 8 +--R - 3150B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 10 2 2 9 +--R (- 1080A a b - 360B a )e + (- 5400A a b - 5400B a b)d e +--R + +--R 3 2 2 8 3 3 7 +--R (- 3600A b - 10800B a b )d e - 3600B b d e +--R * +--R 7 +--R x +--R + +--R 3 10 2 3 9 +--R - 420A a e + (- 6300A a b - 2100B a )d e +--R + +--R 2 2 2 8 3 2 3 7 +--R (- 12600A a b - 12600B a b)d e + (- 4200A b - 12600B a b )d e +--R + +--R 3 4 6 +--R - 2100B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 2 8 +--R - 2520A a d e + (- 15120A a b - 5040B a )d e +--R + +--R 2 2 3 7 3 2 4 6 +--R (- 15120A a b - 15120B a b)d e + (- 2520A b - 7560B a b )d e +--R + +--R 3 5 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 8 2 3 3 7 +--R - 6300A a d e + (- 18900A a b - 6300B a )d e +--R + +--R 2 2 4 6 3 2 5 5 +--R (- 9450A a b - 9450B a b)d e + (- 630A b - 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 3 7 2 3 4 6 +--R - 8400A a d e + (- 12600A a b - 4200B a )d e +--R + +--R 2 2 5 5 +--R (- 2520A a b - 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 3 5 5 2 3 5 5 +--R (- 6300A a d e + (- 3780A a b - 1260B a )d e )x - 2520A a d e x +--R + +--R 3 6 4 2 3 7 3 2 2 8 2 +--R - 420A a d e + (180A a b + 60B a )d e + (- 45A a b - 45B a b)d e +--R + +--R 3 2 9 3 10 +--R (5A b + 15B a b )d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 10 11 4 3 10 4 9 10 +--R 252B b e x + ((280A b + 1092B a b )e + 1400B b d e )x +--R + +--R 3 2 2 10 4 3 9 +--R (1225A a b + 1785B a b )e + (1575A b + 6125B a b )d e +--R + +--R 4 2 8 +--R 3150B b d e +--R * +--R 9 +--R x +--R + +--R 2 2 3 10 3 2 2 9 +--R (2025A a b + 1305B a b)e + (6975A a b + 10125B a b )d e +--R + +--R 4 3 2 8 4 3 7 +--R (3600A b + 13950B a b )d e + 3600B b d e +--R * +--R 8 +--R x +--R + +--R 3 4 10 2 2 3 9 +--R (1500A a b + 360B a )e + (11700A a b + 7500B a b)d e +--R + +--R 3 2 2 2 8 4 3 3 7 +--R (16200A a b + 23400B a b )d e + (4200A b + 16200B a b )d e +--R + +--R 4 4 6 +--R 2100B b d e +--R * +--R 7 +--R x +--R + +--R 4 10 3 4 9 +--R 420A a e + (8820A a b + 2100B a )d e +--R + +--R 2 2 3 2 8 3 2 2 3 7 +--R (27720A a b + 17640B a b)d e + (19320A a b + 27720B a b )d e +--R + +--R 4 3 4 6 4 5 5 +--R (2520A b + 9660B a b )d e + 504B b d e +--R * +--R 6 +--R x +--R + +--R 4 9 3 4 2 8 +--R 2520A a d e + (21420A a b + 5040B a )d e +--R + +--R 2 2 3 3 7 3 2 2 4 6 +--R (34020A a b + 21420B a b)d e + (11970A a b + 17010B a b )d e +--R + +--R 4 3 5 5 +--R (630A b + 2394B a b )d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 3 4 3 7 +--R 6300A a d e + (27300A a b + 6300B a )d e +--R + +--R 2 2 3 4 6 3 2 2 5 5 +--R (22050A a b + 13650B a b)d e + (3150A a b + 4410B a b )d e +--R * +--R 4 +--R x +--R + +--R 4 3 7 3 4 4 6 +--R 8400A a d e + (18900A a b + 4200B a )d e +--R + +--R 2 2 3 5 5 +--R (6300A a b + 3780B a b)d e +--R * +--R 3 +--R x +--R + +--R 4 4 6 3 4 5 5 2 4 5 5 +--R (6300A a d e + (6300A a b + 1260B a )d e )x + 2520A a d e x +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 9 3 2 5 3 4 8 +--R B b e x + ((A b + 3B a b )e + 5B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 7 +--R ((3A a b + 3B a b)e + (5A b + 15B a b )d e + 10B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (3A a b + B a )e + (15A a b + 15B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (10A b + 30B a b )d e + 10B b d e +--R * +--R 6 +--R x +--R + +--R 3 5 2 3 4 2 2 2 3 +--R A a e + (15A a b + 5B a )d e + (30A a b + 30B a b)d e +--R + +--R 3 2 3 2 3 4 +--R (10A b + 30B a b )d e + 5B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 2 3 2 2 3 2 +--R 5A a d e + (30A a b + 10B a )d e + (30A a b + 30B a b)d e +--R + +--R 3 2 4 3 5 +--R (5A b + 15B a b )d e + B b d +--R * +--R 4 +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 10A a d e + (30A a b + 10B a )d e + (15A a b + 15B a b)d e +--R + +--R 3 2 5 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 4 2 2 5 2 +--R (10A a d e + (15A a b + 5B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 4 2 3 5 3 5 +--R (5A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 10 4 3 5 4 4 9 +--R - B b e x + ((- A b - 4B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 8 +--R ((- 4A a b - 6B a b )e + (- 5A b - 20B a b )d e - 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 6A a b - 4B a b)e + (- 20A a b - 30B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 10A b - 40B a b )d e - 10B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 4A a b - B a )e + (- 30A a b - 20B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 40A a b - 60B a b )d e + (- 10A b - 40B a b )d e - 5B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - A a e + (- 20A a b - 5B a )d e + (- 60A a b - 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 40A a b - 60B a b )d e + (- 5A b - 20B a b )d e - B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R - 5A a d e + (- 40A a b - 10B a )d e + (- 60A a b - 40B a b)d e +--R + +--R 3 2 2 4 4 3 5 +--R (- 20A a b - 30B a b )d e + (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 3 2 2 2 3 4 +--R - 10A a d e + (- 40A a b - 10B a )d e + (- 30A a b - 20B a b)d e +--R + +--R 3 2 2 5 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 2 +--R (- 10A a d e + (- 20A a b - 5B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 4 3 4 5 4 5 +--R (- 5A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 1378 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 7 2 4 2 3 6 +--R B b e x + ((A b + 2B a b)e + 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((2A a b + B a )e + (4A b + 8B a b)d e + 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (A a e + (8A a b + 4B a )d e + (6A b + 12B a b)d e + 4B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 3 +--R (4A a d e + (12A a b + 6B a )d e + (4A b + 8B a b)d e + B b d )x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1378 +r0:=-1/72*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/9*B*(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-_ + 1/504*(b*d-a*e)^2*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^4)+1/2520*(b*d-a*e)^3*(4*b*B*d-9*A*b*e+5*a*B*e)*_ + (d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))+1/168*(b*d-a*e)*_ + (4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 9 9 3 2 9 3 8 8 +--R 280B b e x + ((315A b + 945B a b )e + 1260B b d e )x +--R + +--R 2 2 9 3 2 8 +--R (1080A a b + 1080B a b)e + (1440A b + 4320B a b )d e +--R + +--R 3 2 7 +--R 2160B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 9 2 2 8 +--R (1260A a b + 420B a )e + (5040A a b + 5040B a b)d e +--R + +--R 3 2 2 7 3 3 6 +--R (2520A b + 7560B a b )d e + 1680B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 8 +--R 504A a e + (6048A a b + 2016B a )d e +--R + +--R 2 2 2 7 3 2 3 6 +--R (9072A a b + 9072B a b)d e + (2016A b + 6048B a b )d e +--R + +--R 3 4 5 +--R 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 2 7 +--R 2520A a d e + (11340A a b + 3780B a )d e +--R + +--R 2 2 3 6 3 2 4 5 +--R (7560A a b + 7560B a b)d e + (630A b + 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 2 7 2 3 3 6 +--R 5040A a d e + (10080A a b + 3360B a )d e +--R + +--R 2 2 4 5 +--R (2520A a b + 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 3 6 2 3 4 5 2 3 4 5 +--R (5040A a d e + (3780A a b + 1260B a )d e )x + 2520A a d e x +--R + +--R 3 5 4 2 3 6 3 2 2 7 2 +--R 504A a d e + (- 252A a b - 84B a )d e + (72A a b + 72B a b)d e +--R + +--R 3 2 8 3 9 +--R (- 9A b - 27B a b )d e + 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 9 3 2 4 3 3 8 +--R 280B b e x + ((315A b + 945B a b )e + 1260B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (1080A a b + 1080B a b)e + (1440A b + 4320B a b )d e +--R + +--R 3 2 2 +--R 2160B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 4 2 2 3 +--R (1260A a b + 420B a )e + (5040A a b + 5040B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (2520A b + 7560B a b )d e + 1680B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 504A a e + (6048A a b + 2016B a )d e + (9072A a b + 9072B a b)d e +--R + +--R 3 2 3 3 4 +--R (2016A b + 6048B a b )d e + 504B b d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 2 +--R 2520A a d e + (11340A a b + 3780B a )d e +--R + +--R 2 2 3 3 2 4 +--R (7560A a b + 7560B a b)d e + (630A b + 1890B a b )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 3 3 +--R 5040A a d e + (10080A a b + 3360B a )d e +--R + +--R 2 2 4 +--R (2520A a b + 2520B a b)d +--R * +--R 3 +--R x +--R + +--R 3 3 2 3 4 2 3 4 +--R (5040A a d e + (3780A a b + 1260B a )d )x + 2520A a d x +--R / +--R 2520 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 9 9 3 2 9 3 8 8 +--R - 280B b e x + ((- 315A b - 945B a b )e - 1260B b d e )x +--R + +--R 2 2 9 3 2 8 +--R (- 1080A a b - 1080B a b)e + (- 1440A b - 4320B a b )d e +--R + +--R 3 2 7 +--R - 2160B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 9 2 2 8 +--R (- 1260A a b - 420B a )e + (- 5040A a b - 5040B a b)d e +--R + +--R 3 2 2 7 3 3 6 +--R (- 2520A b - 7560B a b )d e - 1680B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 8 +--R - 504A a e + (- 6048A a b - 2016B a )d e +--R + +--R 2 2 2 7 3 2 3 6 +--R (- 9072A a b - 9072B a b)d e + (- 2016A b - 6048B a b )d e +--R + +--R 3 4 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 2 7 +--R - 2520A a d e + (- 11340A a b - 3780B a )d e +--R + +--R 2 2 3 6 3 2 4 5 +--R (- 7560A a b - 7560B a b)d e + (- 630A b - 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 2 7 2 3 3 6 +--R - 5040A a d e + (- 10080A a b - 3360B a )d e +--R + +--R 2 2 4 5 +--R (- 2520A a b - 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 3 6 2 3 4 5 2 3 4 5 +--R (- 5040A a d e + (- 3780A a b - 1260B a )d e )x - 2520A a d e x +--R + +--R 3 5 4 2 3 6 3 2 2 7 2 +--R - 504A a d e + (252A a b + 84B a )d e + (- 72A a b - 72B a b)d e +--R + +--R 3 2 8 3 9 +--R (9A b + 27B a b )d e - 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 9 10 4 3 9 4 8 9 +--R 280B b e x + ((315A b + 1225B a b )e + 1260B b d e )x +--R + +--R 3 2 2 9 4 3 8 +--R (1395A a b + 2025B a b )e + (1440A b + 5580B a b )d e +--R + +--R 4 2 7 +--R 2160B b d e +--R * +--R 8 +--R x +--R + +--R 2 2 3 9 3 2 2 8 +--R (2340A a b + 1500B a b)e + (6480A a b + 9360B a b )d e +--R + +--R 4 3 2 7 4 3 6 +--R (2520A b + 9720B a b )d e + 1680B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 9 2 2 3 8 +--R (1764A a b + 420B a )e + (11088A a b + 7056B a b)d e +--R + +--R 3 2 2 2 7 4 3 3 6 +--R (11592A a b + 16632B a b )d e + (2016A b + 7728B a b )d e +--R + +--R 4 4 5 +--R 504B b d e +--R * +--R 6 +--R x +--R + +--R 4 9 3 4 8 +--R 504A a e + (8568A a b + 2016B a )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (20412A a b + 12852B a b)d e + (9576A a b + 13608B a b )d e +--R + +--R 4 3 4 5 +--R (630A b + 2394B a b )d e +--R * +--R 5 +--R x +--R + +--R 4 8 3 4 2 7 +--R 2520A a d e + (16380A a b + 3780B a )d e +--R + +--R 2 2 3 3 6 3 2 2 4 5 +--R (17640A a b + 10920B a b)d e + (3150A a b + 4410B a b )d e +--R * +--R 4 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 5040A a d e + (15120A a b + 3360B a )d e +--R + +--R 2 2 3 4 5 +--R (6300A a b + 3780B a b)d e +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 4 5 2 4 4 5 +--R (5040A a d e + (6300A a b + 1260B a )d e )x + 2520A a d e x +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 8 3 2 4 3 3 7 +--R B b e x + ((A b + 3B a b )e + 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 6 +--R ((3A a b + 3B a b)e + (4A b + 12B a b )d e + 6B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b + B a )e + (12A a b + 12B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (6A b + 18B a b )d e + 4B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A a e + (12A a b + 4B a )d e + (18A a b + 18B a b)d e +--R + +--R 3 2 3 3 4 +--R (4A b + 12B a b )d e + B b d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 3 +--R 4A a d e + (18A a b + 6B a )d e + (12A a b + 12B a b)d e +--R + +--R 3 2 4 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 3 3 2 2 4 2 +--R (6A a d e + (12A a b + 4B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 3 2 3 4 3 4 +--R (4A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 9 4 3 4 4 3 8 +--R - B b e x + ((- A b - 4B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((- 4A a b - 6B a b )e + (- 4A b - 16B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 6A a b - 4B a b)e + (- 16A a b - 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 6A b - 24B a b )d e - 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 4A a b - B a )e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 24A a b - 36B a b )d e + (- 4A b - 16B a b )d e - B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - A a e + (- 16A a b - 4B a )d e + (- 36A a b - 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 16A a b - 24B a b )d e + (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R - 4A a d e + (- 24A a b - 6B a )d e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 4 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (- 6A a d e + (- 16A a b - 4B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (- 4A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 1378 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1378 +r0:=1/14*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/8*B*(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)+_ + 1/70*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^4)-1/280*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))-1/28*(b*d-a*e)*(2*A*b*e-_ + B*(b*d+a*e))*(a+b*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 8 8 3 2 8 3 7 7 +--R 35B b e x + ((40A b + 120B a b )e + 120B b d e )x +--R + +--R 2 2 8 3 2 7 3 2 6 6 +--R ((140A a b + 140B a b)e + (140A b + 420B a b )d e + 140B b d e )x +--R + +--R 2 3 8 2 2 7 +--R (168A a b + 56B a )e + (504A a b + 504B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (168A b + 504B a b )d e + 56B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 70A a e + (630A a b + 210B a )d e + (630A a b + 630B a b)d e +--R + +--R 3 2 3 5 +--R (70A b + 210B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 2 2 3 5 3 +--R (280A a d e + (840A a b + 280B a )d e + (280A a b + 280B a b)d e )x +--R + +--R 3 2 6 2 3 3 5 2 3 3 5 3 4 4 +--R (420A a d e + (420A a b + 140B a )d e )x + 280A a d e x + 70A a d e +--R + +--R 2 3 5 3 2 2 6 2 +--R (- 42A a b - 14B a )d e + (14A a b + 14B a b)d e +--R + +--R 3 2 7 3 8 +--R (- 2A b - 6B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 280b e x + 280a e +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 8 3 2 3 3 2 7 +--R 35B b e x + ((40A b + 120B a b )e + 120B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 6 +--R ((140A a b + 140B a b)e + (140A b + 420B a b )d e + 140B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (168A a b + 56B a )e + (504A a b + 504B a b)d e +--R + +--R 3 2 2 3 3 +--R (168A b + 504B a b )d e + 56B b d +--R * +--R 5 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R 70A a e + (630A a b + 210B a )d e + (630A a b + 630B a b)d e +--R + +--R 3 2 3 +--R (70A b + 210B a b )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 2 2 2 3 3 +--R (280A a d e + (840A a b + 280B a )d e + (280A a b + 280B a b)d )x +--R + +--R 3 2 2 3 3 2 3 3 +--R (420A a d e + (420A a b + 140B a )d )x + 280A a d x +--R / +--R 280 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 8 8 3 2 8 3 7 7 +--R - 35B b e x + ((- 40A b - 120B a b )e - 120B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (- 140A a b - 140B a b)e + (- 140A b - 420B a b )d e +--R + +--R 3 2 6 +--R - 140B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (- 168A a b - 56B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (- 168A b - 504B a b )d e - 56B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R - 70A a e + (- 630A a b - 210B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (- 630A a b - 630B a b)d e + (- 70A b - 210B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 280A a d e + (- 840A a b - 280B a )d e +--R + +--R 2 2 3 5 +--R (- 280A a b - 280B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 2 3 3 5 +--R (- 420A a d e + (- 420A a b - 140B a )d e )x - 280A a d e x +--R + +--R 3 4 4 2 3 5 3 2 2 6 2 +--R - 70A a d e + (42A a b + 14B a )d e + (- 14A a b - 14B a b)d e +--R + +--R 3 2 7 3 8 +--R (2A b + 6B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 8 9 4 3 8 4 7 8 +--R 35B b e x + ((40A b + 155B a b )e + 120B b d e )x +--R + +--R 3 2 2 8 4 3 7 4 2 6 7 +--R ((180A a b + 260B a b )e + (140A b + 540B a b )d e + 140B b d e )x +--R + +--R 2 2 3 8 3 2 2 7 +--R (308A a b + 196B a b)e + (644A a b + 924B a b )d e +--R + +--R 4 3 2 6 4 3 5 +--R (168A b + 644B a b )d e + 56B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 8 2 2 3 7 +--R (238A a b + 56B a )e + (1134A a b + 714B a b)d e +--R + +--R 3 2 2 2 6 4 3 3 5 +--R (798A a b + 1134B a b )d e + (70A b + 266B a b )d e +--R * +--R 5 +--R x +--R + +--R 4 8 3 4 7 2 2 3 2 6 +--R 70A a e + (910A a b + 210B a )d e + (1470A a b + 910B a b)d e +--R + +--R 3 2 2 3 5 +--R (350A a b + 490B a b )d e +--R * +--R 4 +--R x +--R + +--R 4 7 3 4 2 6 2 2 3 3 5 3 +--R (280A a d e + (1260A a b + 280B a )d e + (700A a b + 420B a b)d e )x +--R + +--R 4 2 6 3 4 3 5 2 4 3 5 +--R (420A a d e + (700A a b + 140B a )d e )x + 280A a d e x +--R / +--R 5 5 +--R 280b e x + 280a e +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 3 7 3 2 3 3 2 6 +--R B b e x + ((A b + 3B a b )e + 3B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 5 +--R ((3A a b + 3B a b)e + (3A b + 9B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b + B a )e + (9A a b + 9B a b)d e + (3A b + 9B a b )d e +--R + +--R 3 3 +--R B b d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R A a e + (9A a b + 3B a )d e + (9A a b + 9B a b)d e +--R + +--R 3 2 3 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 3 2 +--R (3A a d e + (9A a b + 3B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 2 3 3 3 3 +--R (3A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 8 4 3 3 4 2 7 +--R - B b e x + ((- A b - 4B a b )e - 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((- 4A a b - 6B a b )e + (- 3A b - 12B a b )d e - 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 6A a b - 4B a b)e + (- 12A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 3A b - 12B a b )d e - B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 4A a b - B a )e + (- 18A a b - 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 12A a b - 18B a b )d e + (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R - A a e + (- 12A a b - 3B a )d e + (- 18A a b - 12B a b)d e +--R + +--R 3 2 2 3 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (- 3A a d e + (- 12A a b - 3B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (- 3A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 1378 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 471 + +--S 472 of 1378 +r0:=-1/84*(b*d-a*e)^2*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b^4*e)-1/42*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(d+_ + e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*e)+1/7*B*(a+b*x)*(d+e*x)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-1/105*(b*d-a*e)*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4 +--R +--R +--R (2) +--R 6 2 6 6 5 2 6 5 +--R 60B b e x + ((70A b + 150B a b )e + 140B b d e)x +--R + +--R 5 2 4 2 6 5 6 2 4 +--R ((182A a b + 102B a b )e + (168A b + 364B a b )d e + 84B b d )x +--R + +--R 2 4 3 3 2 5 2 4 +--R (133A a b + 3B a b )e + (462A a b + 266B a b )d e +--R + +--R 6 5 2 +--R (105A b + 231B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (7A a b - 3B a b )e + (378A a b + 14B a b )d e +--R + +--R 5 2 4 2 +--R (315A a b + 189B a b )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (- 7A a b + 3B a b)e + (42A a b - 14B a b )d e +--R + +--R 2 4 3 3 2 +--R (315A a b + 21B a b )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 3 3 4 2 2 +--R (7A a b - 3B a )e + (- 42A a b + 14B a b)d e + (105A a b - 21B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 420b +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 7 3 2 2 3 6 +--R 60B b e x + ((70A b + 210B a b )e + 140B b d e)x +--R + +--R 2 2 2 3 2 3 2 5 +--R ((252A a b + 252B a b)e + (168A b + 504B a b )d e + 84B b d )x +--R + +--R 2 3 2 2 2 +--R (315A a b + 105B a )e + (630A a b + 630B a b)d e +--R + +--R 3 2 2 +--R (105A b + 315B a b )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 2 2 2 3 +--R (140A a e + (840A a b + 280B a )d e + (420A a b + 420B a b)d )x +--R + +--R 3 2 3 2 2 3 2 +--R (420A a d e + (630A a b + 210B a )d )x + 420A a d x +--R / +--R 420 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 2 6 6 5 2 6 5 +--R - 60B b e x + ((- 70A b - 150B a b )e - 140B b d e)x +--R + +--R 5 2 4 2 6 5 +--R (- 182A a b - 102B a b )e + (- 168A b - 364B a b )d e +--R + +--R 6 2 +--R - 84B b d +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 2 5 2 4 +--R (- 133A a b - 3B a b )e + (- 462A a b - 266B a b )d e +--R + +--R 6 5 2 +--R (- 105A b - 231B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 7A a b + 3B a b )e + (- 378A a b - 14B a b )d e +--R + +--R 5 2 4 2 +--R (- 315A a b - 189B a b )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (7A a b - 3B a b)e + (- 42A a b + 14B a b )d e +--R + +--R 2 4 3 3 2 +--R (- 315A a b - 21B a b )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 7A a b + 3B a )e + (42A a b - 14B a b)d e +--R + +--R 3 3 4 2 2 +--R (- 105A a b + 21B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 2 7 7 6 2 7 6 +--R 60B b e x + ((70A b + 210B a b )e + 140B b d e)x +--R + +--R 6 2 5 2 7 6 7 2 5 +--R ((252A a b + 252B a b )e + (168A b + 504B a b )d e + 84B b d )x +--R + +--R 2 5 3 4 2 6 2 5 +--R (315A a b + 105B a b )e + (630A a b + 630B a b )d e +--R + +--R 7 6 2 +--R (105A b + 315B a b )d +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 5 3 4 6 2 5 2 3 +--R (140A a b e + (840A a b + 280B a b )d e + (420A a b + 420B a b )d )x +--R + +--R 3 4 2 5 3 4 2 2 3 4 2 +--R (420A a b d e + (630A a b + 210B a b )d )x + 420A a b d x +--R / +--R 4 +--R 420b +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 2 6 3 2 2 3 5 +--R B b e x + ((A b + 3B a b )e + 2B b d e)x +--R + +--R 2 2 2 3 2 3 2 4 +--R ((3A a b + 3B a b)e + (2A b + 6B a b )d e + B b d )x +--R + +--R 2 3 2 2 2 3 2 2 3 +--R ((3A a b + B a )e + (6A a b + 6B a b)d e + (A b + 3B a b )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (A a e + (6A a b + 2B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 3 2 3 2 +--R (2A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 2 7 4 3 2 4 6 +--R - B b e x + ((- A b - 4B a b )e - 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((- 4A a b - 6B a b )e + (- 2A b - 8B a b )d e - B b d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 6A a b - 4B a b)e + (- 8A a b - 12B a b )d e +--R + +--R 4 3 2 +--R (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 4A a b - B a )e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 2 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- A a e + (- 8A a b - 2B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (- 2A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 1378 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1378 +r0:=-1/12*(b*d-a*e)*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b^3*e)+1/6*B*(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-1/15*(2*b*B*d-3*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b^3 +--R +--R +--R (2) +--R 5 5 5 4 5 4 +--R 10B b e x + ((12A b + 26B a b )e + 12B b d)x +--R + +--R 4 2 3 5 4 3 +--R ((33A a b + 19B a b )e + (15A b + 33B a b )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((27A a b + B a b )e + (45A a b + 27B a b )d)x +--R + +--R 3 2 4 2 3 3 2 4 5 +--R ((3A a b - B a b)e + (45A a b + 3B a b )d)x + (- 3A a b + B a )e +--R + +--R 3 2 4 +--R (15A a b - 3B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 60b +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 3 2 3 5 +--R 10B b e x + ((12A b + 36B a b )e + 12B b d)x +--R + +--R 2 2 3 2 4 +--R ((45A a b + 45B a b)e + (15A b + 45B a b )d)x +--R + +--R 2 3 2 2 3 +--R ((60A a b + 20B a )e + (60A a b + 60B a b)d)x +--R + +--R 3 2 3 2 3 +--R (30A a e + (90A a b + 30B a )d)x + 60A a d x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 5 4 +--R - 10B b e x + ((- 12A b - 26B a b )e - 12B b d)x +--R + +--R 4 2 3 5 4 3 +--R ((- 33A a b - 19B a b )e + (- 15A b - 33B a b )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((- 27A a b - B a b )e + (- 45A a b - 27B a b )d)x +--R + +--R 3 2 4 2 3 3 2 4 5 +--R ((- 3A a b + B a b)e + (- 45A a b - 3B a b )d)x + (3A a b - B a )e +--R + +--R 3 2 4 +--R (- 15A a b + 3B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 6 5 6 5 +--R 10B b e x + ((12A b + 36B a b )e + 12B b d)x +--R + +--R 5 2 4 6 5 4 +--R ((45A a b + 45B a b )e + (15A b + 45B a b )d)x +--R + +--R 2 4 3 3 5 2 4 3 +--R ((60A a b + 20B a b )e + (60A a b + 60B a b )d)x +--R + +--R 3 3 2 4 3 3 2 3 3 +--R (30A a b e + (90A a b + 30B a b )d)x + 60A a b d x +--R / +--R 3 +--R 60b +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 3 2 3 4 +--R B b e x + ((A b + 3B a b )e + B b d)x +--R + +--R 2 2 3 2 3 +--R ((3A a b + 3B a b)e + (A b + 3B a b )d)x +--R + +--R 2 3 2 2 2 +--R ((3A a b + B a )e + (3A a b + 3B a b)d)x +--R + +--R 3 2 3 3 +--R (A a e + (3A a b + B a )d)x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 4 5 +--R - B b e x + ((- A b - 4B a b )e - B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((- 4A a b - 6B a b )e + (- A b - 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 6A a b - 4B a b)e + (- 4A a b - 6B a b )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 4A a b - B a )e + (- 6A a b - 4B a b)d)x +--R + +--R 4 3 4 4 +--R (- A a e + (- 4A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1378 +r0:=1/4*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+_ + 1/5*B*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2 +--R +--R +--R (2) +--R 4 4 4 3 3 3 2 2 2 +--R 4B b x + (5A b + 11B a b )x + (15A a b + 9B a b )x +--R + +--R 2 2 3 3 4 +--R (15A a b + B a b)x + 5A a b - B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 20b +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 3 2 4 2 2 3 +--R 4B b x + (5A b + 15B a b )x + (20A a b + 20B a b)x +--R + +--R 2 3 2 3 +--R (30A a b + 10B a )x + 20A a x +--R / +--R 20 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 3 3 2 2 2 +--R - 4B b x + (- 5A b - 11B a b )x + (- 15A a b - 9B a b )x +--R + +--R 2 2 3 3 4 +--R (- 15A a b - B a b)x - 5A a b + B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 5 5 4 4 4 2 3 3 +--R 4B b x + (5A b + 15B a b )x + (20A a b + 20B a b )x +--R + +--R 2 3 3 2 2 3 2 +--R (30A a b + 10B a b )x + 20A a b x +--R / +--R 2 +--R 20b +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1378 +r0:=-1/3*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/4*B*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-(b*d-a*e)^2*(B*d-A*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^4+1/2*(b*d-a*e)*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^3+(b*d-a*e)^3*(B*d-A*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 3 3 2 2 2 2 +--R 12A a b e + (- 36A a b - 12B a b)d e + (36A a b + 36B a b )d e +--R + +--R 4 3 3 4 4 +--R (- 12A b - 36B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 3B b e x + ((4A b + 12B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((18A a b + 18B a b )e + (- 6A b - 18B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (36A a b + 12B a b)e + (- 36A a b - 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b + 36B a b )d e - 12B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (22A a b + 3B a )e + (- 30A a b - 22B a b)d e +--R + +--R 3 2 2 2 2 3 3 +--R (12A a b + 30B a b )d e - 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 5 5 +--R 12b e x + 12a b e +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 2 3 3 2 2 2 2 +--R 12A a e + (- 36A a b - 12B a )d e + (36A a b + 36B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 12A b - 36B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 3B b e x + ((4A b + 12B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((18A a b + 18B a b)e + (- 6A b - 18B a b )d e + 6B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (36A a b + 12B a )e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (12A b + 36B a b )d e - 12B b d e +--R * +--R x +--R / +--R 5 +--R 12e +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 3 +--R - 12A a b e + (36A a b + 12B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 36A a b - 36B a b )d e + (12A b + 36B a b )d e - 12B b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 4 3 4 4 3 3 +--R - 3B b e x + ((- 4A b - 12B a b )e + 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((- 18A a b - 18B a b )e + (6A b + 18B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 36A a b - 12B a b)e + (36A a b + 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b - 36B a b )d e + 12B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 22A a b - 3B a )e + (30A a b + 22B a b)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 12A a b - 30B a b )d e + 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 4 2 3 3 2 3 +--R 12A a b e + (- 36A a b - 12B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (36A a b + 36B a b )d e + (- 12A b - 36B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 4 3 2 4 3 2 3 3 2 2 2 +--R 12A a b e + (- 36A a b - 12B a b)d e + (36A a b + 36B a b )d e +--R + +--R 4 2 3 3 4 4 +--R (- 12A a b - 36B a b )d e + 12B a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b + 15B a b )e - 4B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((22A a b + 30B a b )e + (- 6A b - 22B a b )d e + 6B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (54A a b + 30B a b )e + (- 42A a b - 54B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (12A b + 42B a b )d e - 12B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (36A a b + 12B a b)e + (- 36A a b - 36B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (12A a b + 36B a b )d e - 12B a b d e +--R * +--R x +--R / +--R 2 5 5 +--R 12b e x + 12a b e +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1378 +r0:=1/3*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*(d+e*x))+_ + (b*d-a*e)*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-_ + 1/2*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-_ + (b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 3 4 2 2 3 +--R (18A a b + 6B a )e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A b + 54B a b )d e - 24B b d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A a b + 6B a )d e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 3 3 4 +--R (18A b + 54B a b )d e - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 2B b e x + ((3A b + 9B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((18A a b + 18B a b)e + (- 9A b - 27B a b )d e + 12B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (9A a b + 11B a )e + (18A a b - 6B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 18A b - 30B a b )d e + 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (27A a b + 17B a )d e + (- 18A a b - 42B a b)d e +--R + +--R 2 3 +--R 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +--R 6b e x + (6a e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 4 2 2 3 +--R (18A a b + 6B a )e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A b + 54B a b )d e - 24B b d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A a b + 6B a )d e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 3 3 4 +--R (18A b + 54B a b )d e - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 2B b e x + ((3A b + 9B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((18A a b + 18B a b)e + (- 9A b - 27B a b )d e + 12B b d e )x +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((18A a b + 18B a b)d e + (- 12A b - 36B a b )d e + 18B b d e)x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (18A a b + 6B a )d e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 3 3 4 +--R (6A b + 18B a b )d e - 6B b d +--R / +--R 6 5 +--R 6e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 4 2 2 3 +--R (- 18A a b - 6B a )e + (36A a b + 36B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 18A b - 54B a b )d e + 24B b d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (- 18A a b - 6B a )d e + (36A a b + 36B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 18A b - 54B a b )d e + 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R - 2B b e x + ((- 3A b - 9B a b )e + 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 18A a b - 18B a b)e + (9A b + 27B a b )d e - 12B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 9A a b - 11B a )e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A b + 30B a b )d e - 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 6A a e + (- 27A a b - 17B a )d e + (18A a b + 42B a b)d e +--R + +--R 2 3 +--R - 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 4 3 2 2 3 +--R (18A a b + 6B a b)e + (- 36A a b - 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (18A b + 54B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (18A a b + 6B a )e + (- 18A a b - 30B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 18A a b + 18B a b )d e + (18A b + 30B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 +--R (18A a b + 6B a )d e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (18A a b + 54B a b )d e - 24B a b d +--R * +--R log(e x + d) +--R + +--R 4 4 5 4 3 4 4 3 4 +--R 2B b e x + ((3A b + 11B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((21A a b + 27B a b )e + (- 9A b - 31B a b )d e + 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (18A a b + 18B a b)e + (9A a b - 9B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b - 24B a b )d e + 18B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 3 3 3 2 2 2 2 +--R - 6A a b e + (36A a b + 24B a b)d e + (- 30A a b - 54B a b )d e +--R + +--R 4 3 3 4 4 +--R (6A b + 36B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (18A a b + 6B a )d e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (6A a b + 18B a b )d e - 6B a b d +--R / +--R 6 2 6 5 5 +--R 6b e x + (6a e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1378 +r0:=-1/2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^2)-(2*b*B*d-A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*_ + (b*d-a*e)*(d+e*x))-3*b*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*_ + x^2)/e^4+3/2*b*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*_ + x^2)/(e^3*(b*d-a*e))+3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 2 4 3 2 3 3 2 2 2 +--R ((6A a b + 6B a b)e + (- 6A b - 18B a b )d e + 12B b d e )x +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((12A a b + 12B a b)d e + (- 12A b - 36B a b )d e + 24B b d e)x +--R + +--R 2 2 2 2 3 2 3 3 4 +--R (6A a b + 6B a b)d e + (- 6A b - 18B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R B b e x + ((2A b + 6B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 3A a b + 3B a b)e + (9A b + 15B a b )d e - 18B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 6A a b - 2B a )e + (6A a b + 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (6A b - 6B a b )d e - 12B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 3 +--R - A a e + (- 3A a b - B a )d e + (6A a b + 12B a b)d e - 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 2 3 3 2 2 2 +--R ((6A a b + 6B a b)e + (- 6A b - 18B a b )d e + 12B b d e )x +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((12A a b + 12B a b)d e + (- 12A b - 36B a b )d e + 24B b d e)x +--R + +--R 2 2 2 2 3 2 3 3 4 +--R (6A a b + 6B a b)d e + (- 6A b - 18B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R B b e x + ((2A b + 6B a b )e - 4B b d e )x +--R + +--R 3 2 3 3 2 2 2 +--R ((4A b + 12B a b )d e - 11B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 6A a b - 2B a )e + (12A a b + 12B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 4A b - 12B a b )d e + 2B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - A a e + (- 3A a b - B a )d e + (9A a b + 9B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 5A b - 15B a b )d e + 7B b d +--R / +--R 7 2 6 2 5 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 6A a b - 6B a b)e + (6A b + 18B a b )d e - 12B b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R (- 12A a b - 12B a b)d e + (12A b + 36B a b )d e +--R + +--R 3 3 +--R - 24B b d e +--R * +--R x +--R + +--R 2 2 2 2 3 2 3 3 4 +--R (- 6A a b - 6B a b)d e + (6A b + 18B a b )d e - 12B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R - B b e x + ((- 2A b - 6B a b )e + 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((3A a b - 3B a b)e + (- 9A b - 15B a b )d e + 18B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (6A a b + 2B a )e + (- 6A a b - 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 6A b + 6B a b )d e + 12B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 3 +--R A a e + (3A a b + B a )d e + (- 6A a b - 12B a b)d e + 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((6A a b + 6B a b )e + (- 6A b - 18B a b )d e + 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (6A a b + 6B a b)e + (6A a b - 6B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b - 24B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (12A a b + 12B a b)d e + (- 6A a b - 30B a b )d e +--R + +--R 4 3 3 4 4 +--R (- 6A b + 6B a b )d e + 12B b d +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 2 3 3 4 +--R (6A a b + 6B a b)d e + (- 6A a b - 18B a b )d e + 12B a b d +--R * +--R log(e x + d) +--R + +--R 4 4 5 4 3 4 4 3 4 +--R B b e x + ((2A b + 7B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((2A a b + 6B a b )e + (4A b + 8B a b )d e - 11B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 6A a b - 2B a b)e + (16A a b + 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 4A b - 23B a b )d e + 2B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 7A a b - 2B a )e + (9A a b + 11B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (5A a b - 3B a b )d e + (- 5A b - 13B a b )d e + 7B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - A a e + (- 3A a b - B a )d e + (9A a b + 9B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 5A a b - 15B a b )d e + 7B a b d +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 500 + +)clear all + +--S 501 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1378 +r0:=-1/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^3)-1/6*(4*b*B*d-A*b*e-3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^2)+b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(b*d-a*e))-1/2*b*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x))-b^2*(4*b*B*d-A*b*e-_ + 3*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 2 4 3 3 3 +--R ((6A b + 18B a b )e - 24B b d e )x +--R + +--R 3 2 3 3 2 2 2 +--R ((18A b + 54B a b )d e - 72B b d e )x +--R + +--R 3 2 2 2 3 3 3 2 3 +--R ((18A b + 54B a b )d e - 72B b d e)x + (6A b + 18B a b )d e +--R + +--R 3 4 +--R - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((- 11A b - 9B a b )e + 44B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 18A a b - 18B a b)e + (- 15A b + 27B a b )d e + 60B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 9A a b - 3B a )e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 6A b + 54B a b )d e + 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (- 3A a b - B a )d e + (- 6A a b - 6B a b)d e +--R + +--R 2 3 +--R 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 6 3 5 3 5 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 3 3 +--R ((6A b + 18B a b )e - 24B b d e )x +--R + +--R 3 2 3 3 2 2 2 +--R ((18A b + 54B a b )d e - 72B b d e )x +--R + +--R 3 2 2 2 3 3 3 2 3 +--R ((18A b + 54B a b )d e - 72B b d e)x + (6A b + 18B a b )d e +--R + +--R 3 4 +--R - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 3 3 +--R 6B b e x + 18B b d e x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 18A a b - 18B a b)e + (18A b + 54B a b )d e - 18B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 9A a b - 3B a )e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (27A b + 81B a b )d e - 54B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (- 3A a b - B a )d e + (- 6A a b - 6B a b)d e +--R + +--R 3 2 3 3 4 +--R (11A b + 33B a b )d e - 26B b d +--R / +--R 8 3 7 2 2 6 3 5 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 4 3 3 3 +--R ((- 6A b - 18B a b )e + 24B b d e )x +--R + +--R 3 2 3 3 2 2 2 +--R ((- 18A b - 54B a b )d e + 72B b d e )x +--R + +--R 3 2 2 2 3 3 +--R ((- 18A b - 54B a b )d e + 72B b d e)x +--R + +--R 3 2 3 3 4 +--R (- 6A b - 18B a b )d e + 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R - 6B b e x + ((11A b + 9B a b )e - 44B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((18A a b + 18B a b)e + (15A b - 27B a b )d e - 60B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (9A a b + 3B a )e + (18A a b + 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (6A b - 54B a b )d e - 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 3 +--R 2A a e + (3A a b + B a )d e + (6A a b + 6B a b)d e - 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 4 3 4 +--R ((6A b + 18B a b )e - 24B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((6A a b + 18B a b )e + (18A b + 30B a b )d e - 72B b d e )x +--R + +--R 3 2 2 3 4 3 2 2 4 3 2 +--R ((18A a b + 54B a b )d e + (18A b - 18B a b )d e - 72B b d e)x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R ((18A a b + 54B a b )d e + (6A b - 54B a b )d e - 24B b d )x +--R + +--R 3 2 2 3 3 4 +--R (6A a b + 18B a b )d e - 24B a b d +--R * +--R log(e x + d) +--R + +--R 4 4 5 3 4 4 3 4 +--R 6B b e x + (6B a b e + 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 18A a b - 18B a b )e + (18A b + 72B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 2 2 3 4 3 2 2 +--R (- 27A a b - 21B a b)e + 36B a b d e + (27A b + 63B a b )d e +--R + +--R 4 3 +--R - 54B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 11A a b - 3B a )e + (- 21A a b - 19B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (21A a b + 75B a b )d e + (11A b - 21B a b )d e - 26B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 2A a e + (- 3A a b - B a )d e + (- 6A a b - 6B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (11A a b + 33B a b )d e - 26B a b d +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 6 3 5 3 5 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 505 + +)clear all + +--S 506 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1378 +r0:=-1/4*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/3*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^3)-_ + 1/2*b*B*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^2)+b^2*B*_ + (b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))+b^3*B*_ + log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 5 4 4 4 3 4 4 2 3 3 +--R (12B a b e - 12B b d e )x + (48B a b d e - 48B b d e )x +--R + +--R 3 2 3 4 3 2 2 3 3 2 4 4 +--R (72B a b d e - 72B b d e )x + (48B a b d e - 48B b d e)x +--R + +--R 3 4 4 5 +--R 12B a b d e - 12B b d +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 4 +--R ((- 3A b - 10B a b )e + 13B b d e )x +--R + +--R 3 2 2 5 3 4 4 2 3 3 +--R ((- 12A a b - 36B a b )e + 44B a b d e + 4B b d e )x +--R + +--R 2 2 3 5 2 2 4 3 2 3 +--R (- 18A a b - 18B a b)e - 36B a b d e + 102B a b d e +--R + +--R 4 3 2 +--R - 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 3 4 2 2 2 3 3 3 2 +--R (- 12A a b - 4B a )e - 8B a b d e - 24B a b d e + 84B a b d e +--R + +--R 4 4 +--R - 36B b d e +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R - 3A a e - B a d e - 2B a b d e - 6B a b d e + 24B a b d e - 12B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 2 9 5 2 10 9 2 2 8 4 +--R (12a b e - 12b d e )x + (12a e + 36a b d e - 48b d e )x +--R + +--R 2 9 2 8 2 3 7 3 +--R (48a d e + 24a b d e - 72b d e )x +--R + +--R 2 2 8 3 7 2 4 6 2 +--R (72a d e - 24a b d e - 48b d e )x +--R + +--R 2 3 7 4 6 2 5 5 2 4 6 5 5 +--R (48a d e - 36a b d e - 12b d e )x + 12a d e - 12a b d e +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 3 3 3 2 2 2 3 3 3 4 +--R (12B b e x + 48B b d e x + 72B b d e x + 48B b d e x + 12B b d ) +--R * +--R log(e x + d) +--R + +--R 3 2 4 3 3 3 +--R ((- 12A b - 36B a b )e + 48B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 18A a b - 18B a b)e + (- 18A b - 54B a b )d e + 108B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 12A a b - 4B a )e + (- 12A a b - 12B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 12A b - 36B a b )d e + 88B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 3A a e + (- 3A a b - B a )d e + (- 3A a b - 3B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 3A b - 9B a b )d e + 25B b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 5 4 4 4 3 4 4 2 3 3 +--R (- 12B a b e + 12B b d e )x + (- 48B a b d e + 48B b d e )x +--R + +--R 3 2 3 4 3 2 2 3 3 2 4 4 +--R (- 72B a b d e + 72B b d e )x + (- 48B a b d e + 48B b d e)x +--R + +--R 3 4 4 5 +--R - 12B a b d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 4 +--R ((3A b + 10B a b )e - 13B b d e )x +--R + +--R 3 2 2 5 3 4 4 2 3 3 +--R ((12A a b + 36B a b )e - 44B a b d e - 4B b d e )x +--R + +--R 2 2 3 5 2 2 4 3 2 3 +--R (18A a b + 18B a b)e + 36B a b d e - 102B a b d e +--R + +--R 4 3 2 +--R 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 3 4 2 2 2 3 3 3 2 +--R (12A a b + 4B a )e + 8B a b d e + 24B a b d e - 84B a b d e +--R + +--R 4 4 +--R 36B b d e +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 3A a e + B a d e + 2B a b d e + 6B a b d e - 24B a b d e + 12B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 5 4 5 +--R (12B a b e - 12B b d e )x +--R + +--R 2 3 5 4 4 5 2 3 4 +--R (12B a b e + 36B a b d e - 48B b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 3 +--R (48B a b d e + 24B a b d e - 72B b d e )x +--R + +--R 2 3 2 3 4 3 2 5 4 2 +--R (72B a b d e - 24B a b d e - 48B b d e)x +--R + +--R 2 3 3 2 4 4 5 5 2 3 4 4 5 +--R (48B a b d e - 36B a b d e - 12B b d )x + 12B a b d e - 12B a b d +--R * +--R log(e x + d) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 12A a b - 36B a b )e + (12A b + 84B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 30A a b - 54B a b )e + (12A a b + 48B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (18A b + 114B a b )d e - 108B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 3 2 4 4 2 3 2 3 +--R (- 30A a b - 22B a b)e - 44B a b d e + (18A a b + 138B a b )d e +--R + +--R 5 4 3 2 5 4 +--R (12A b + 16B a b )d e - 88B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 4 4 3 2 2 3 +--R (- 15A a b - 4B a )e - 9B a b d e - 26B a b d e +--R + +--R 4 2 3 3 2 5 4 4 5 5 +--R (12A a b + 118B a b )d e + (3A b - 54B a b )d e - 25B b d +--R * +--R x +--R + +--R 5 5 5 4 4 2 3 3 2 3 2 +--R - 3A a e - B a d e - 2B a b d e - 6B a b d e +--R + +--R 4 2 3 4 4 5 +--R (3A a b + 34B a b )d e - 25B a b d +--R / +--R 10 2 9 5 2 10 9 2 2 8 4 +--R (12a b e - 12b d e )x + (12a e + 36a b d e - 48b d e )x +--R + +--R 2 9 2 8 2 3 7 3 +--R (48a d e + 24a b d e - 72b d e )x +--R + +--R 2 2 8 3 7 2 4 6 2 +--R (72a d e - 24a b d e - 48b d e )x +--R + +--R 2 3 7 4 6 2 5 5 2 4 6 5 5 +--R (48a d e - 36a b d e - 12b d e )x + 12a d e - 12a b d e +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1378 +r0:=1/4*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*_ + (d+e*x)^4)+1/5*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*_ + (d+e*x)^5) +--R +--R +--R (2) +--R 4 3 4 4 +--R ((A b - 5B a b )e + 4B b d)x +--R + +--R 3 2 2 4 3 3 +--R ((- A a b - 15B a b )e + (5A b + 11B a b )d)x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 9A a b - 15B a b)e + (15A a b + 9B a b )d)x +--R + +--R 3 4 2 2 3 4 3 4 +--R ((- 11A a b - 5B a )e + (15A a b + B a b)d)x - 4A a e + (5A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 7 6 2 2 5 5 +--R (20a e - 40a b d e + 20b d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (100a d e - 200a b d e + 100b d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (100a d e - 200a b d e + 100b d e)x + 20a d e - 40a b d e + 20b d +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 20B b e x + ((- 10A b - 30B a b )e - 40B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 20A a b - 20B a b)e + (- 10A b - 30B a b )d e - 40B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 15A a b - 5B a )e + (- 10A a b - 10B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 5A b - 15B a b )d e - 20B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 4A a e + (- 3A a b - B a )d e + (- 2A a b - 2B a b)d e +--R + +--R 3 2 3 3 4 +--R (- A b - 3B a b )d e - 4B b d +--R / +--R 10 5 9 4 2 8 3 3 7 2 4 6 5 5 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 6 4 5 4 +--R ((- A b + 5B a b )e - 4B b d e )x +--R + +--R 3 2 2 6 4 3 5 3 +--R ((A a b + 15B a b )e + (- 5A b - 11B a b )d e )x +--R + +--R 2 2 3 6 3 2 2 5 2 +--R ((9A a b + 15B a b)e + (- 15A a b - 9B a b )d e )x +--R + +--R 3 4 6 2 2 3 5 4 6 +--R ((11A a b + 5B a )e + (- 15A a b - B a b)d e )x + 4A a e +--R + +--R 3 4 5 +--R (- 5A a b + B a )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 6 4 5 5 2 4 4 +--R (- 20B a b e + 40B a b d e - 20B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 10A a b - 30B a b )e + (20A a b + 20B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 10A b + 50B a b )d e - 40B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 20A a b - 20B a b)e + (30A a b + 10B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (- 10A b + 50B a b )d e - 40B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 5 5 4 4 2 +--R (- 15A a b - 5B a )e + 20A a b d e + (- 5A b + 25B a b )d e +--R + +--R 5 5 +--R - 20B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 5 4 5 5 6 +--R - 4A a e + (5A a b - B a )d e + (- A b + 5B a b )d e - 4B b d +--R / +--R 2 12 11 2 2 10 5 +--R (20a e - 40a b d e + 20b d e )x +--R + +--R 2 11 2 10 2 3 9 4 +--R (100a d e - 200a b d e + 100b d e )x +--R + +--R 2 2 10 3 9 2 4 8 3 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 3 9 4 8 2 5 7 2 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 4 8 5 7 2 6 6 2 5 7 6 6 2 7 5 +--R (100a d e - 200a b d e + 100b d e )x + 20a d e - 40a b d e + 20b d e +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 515 + +)clear all + +--S 516 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1378 +r0:=-1/6*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^6)+1/12*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^5)+1/60*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 5 4 2 5 5 +--R ((- A b + 3B a b )e - 2B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 4 +--R ((A a b - 3B a b )e + (- 6A b + 20B a b )d e - 12B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (- A a b - 27B a b )e + (6A a b + 70B a b )d e +--R + +--R 5 4 2 +--R (- 15A b - 33B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 19A a b - 33B a b)e + (54A a b + 70B a b )d e +--R + +--R 4 2 3 2 +--R (- 45A a b - 27B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 26A a b - 12B a )e + (66A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 +--R (- 45A a b - 3B a b )d +--R * +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R - 10A a e + (24A a b - 2B a )d e + (- 15A a b + 3B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 9 2 8 2 2 7 3 3 6 6 +--R (60a e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 8 2 2 7 2 3 6 3 4 5 5 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e )x +--R + +--R 3 2 7 2 3 6 2 4 5 3 5 4 4 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (1200a d e - 3600a b d e + 3600a b d e - 1200b d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e)x + 60a d e +--R + +--R 2 7 2 2 8 3 9 +--R - 180a b d e + 180a b d e - 60b d +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 30B b e x + ((- 20A b - 60B a b )e - 40B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 45A a b - 45B a b)e + (- 15A b - 45B a b )d e - 30B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 36A a b - 12B a )e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 6A b - 18B a b )d e - 12B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 6A a b - 2B a )d e + (- 3A a b - 3B a b)d e +--R + +--R 3 2 3 3 4 +--R (- A b - 3B a b )d e - 2B b d +--R / +--R 11 6 10 5 2 9 4 3 8 3 4 7 2 5 6 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 5 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 7 5 6 5 +--R ((A b - 3B a b )e + 2B b d e )x +--R + +--R 4 2 3 7 5 4 6 5 2 5 4 +--R ((- A a b + 3B a b )e + (6A b - 20B a b )d e + 12B b d e )x +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (A a b + 27B a b )e + (- 6A a b - 70B a b )d e +--R + +--R 5 4 2 5 +--R (15A b + 33B a b )d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (19A a b + 33B a b)e + (- 54A a b - 70B a b )d e +--R + +--R 4 2 3 2 5 +--R (45A a b + 27B a b )d e +--R * +--R 2 +--R x +--R + +--R 4 5 7 3 2 4 6 +--R (26A a b + 12B a )e + (- 66A a b - 20B a b)d e +--R + +--R 2 3 3 2 2 5 +--R (45A a b + 3B a b )d e +--R * +--R x +--R + +--R 5 7 4 5 6 3 2 4 2 5 +--R 10A a e + (- 24A a b + 2B a )d e + (15A a b - 3B a b)d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 4 +--R (- 30B a b e + 90B a b d e - 90B a b d e + 30B b d e )x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (- 20A a b - 60B a b )e + (60A a b + 140B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 6 4 3 +--R (- 60A a b - 60B a b )d e + (20A b - 60B a b )d e + 40B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (- 45A a b - 45B a b)e + (120A a b + 90B a b )d e +--R + +--R 2 4 3 3 2 5 6 5 4 3 6 5 2 +--R (- 90A a b - 30B a b )d e + (15A b - 45B a b )d e + 30B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 3 3 2 5 +--R (- 36A a b - 12B a )e + (90A a b + 18B a b)d e - 60A a b d e +--R + +--R 6 5 5 2 6 6 +--R (6A b - 18B a b )d e + 12B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 10A a e + (24A a b - 2B a )d e + (- 15A a b + 3B a b)d e +--R + +--R 6 5 6 6 7 +--R (A b - 3B a b )d e + 2B b d +--R / +--R 3 14 2 13 2 2 12 3 3 11 6 +--R (60a e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 13 2 2 12 2 3 11 3 4 10 5 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e )x +--R + +--R 3 2 12 2 3 11 2 4 10 3 5 9 4 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 3 11 2 4 10 2 5 9 3 6 8 3 +--R (1200a d e - 3600a b d e + 3600a b d e - 1200b d e )x +--R + +--R 3 4 10 2 5 9 2 6 8 3 7 7 2 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 5 9 2 6 8 2 7 7 3 8 6 3 6 8 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e )x + 60a d e +--R + +--R 2 7 7 2 8 6 3 9 5 +--R - 180a b d e + 180a b d e - 60b d e +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 520 + +)clear all + +--S 521 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1378 +r0:=-1/7*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^7)+1/42*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^6)+1/84*b*(4*b*B*d+3*A*b*e-_ + 7*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)^3*_ + (d+e*x)^5)+1/420*b*(4*b*B*d+3*A*b*e-7*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 6 5 3 6 2 6 +--R ((3A b - 7B a b )e + 4B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 5 +--R ((- 3A a b + 7B a b )e + (21A b - 53B a b )d e + 28B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (3A a b - 7B a b )e + (- 21A a b + 53B a b )d e +--R + +--R 6 5 2 6 3 +--R (63A b - 175B a b )d e + 84B b d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (- 3A a b - 133B a b )e + (21A a b + 507B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 63A a b - 665B a b )d e + (105A b + 231B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 102A a b - 182B a b)e + (399A a b + 613B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 567A a b - 665B a b )d e + (315A a b + 189B a b )d +--R * +--R 2 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 150A a b - 70B a )e + (546A a b + 206B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 693A a b - 175B a b )d e + (315A a b + 21B a b )d +--R * +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R - 60A a e + (210A a b - 10B a )d e + (- 252A a b + 28B a b)d e +--R + +--R 3 3 4 2 3 +--R (105A a b - 21B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 11 3 10 2 2 2 9 3 3 8 4 4 7 7 +--R (420a e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e )x +--R + +--R 4 10 3 2 9 2 2 3 8 3 4 7 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 5 6 +--R 2940b d e +--R * +--R 6 +--R x +--R + +--R 4 2 9 3 3 8 2 2 4 7 3 5 6 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 6 5 +--R 8820b d e +--R * +--R 5 +--R x +--R + +--R 4 3 8 3 4 7 2 2 5 6 3 6 5 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 7 4 +--R 14700b d e +--R * +--R 4 +--R x +--R + +--R 4 4 7 3 5 6 2 2 6 5 3 7 4 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 8 3 +--R 14700b d e +--R * +--R 3 +--R x +--R + +--R 4 5 6 3 6 5 2 2 7 4 3 8 3 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 9 2 +--R 8820b d e +--R * +--R 2 +--R x +--R + +--R 4 6 5 3 7 4 2 2 8 3 3 9 2 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 10 +--R 2940b d e +--R * +--R x +--R + +--R 4 7 4 3 8 3 2 2 9 2 3 10 4 11 +--R 420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 140B b e x + ((- 105A b - 315B a b )e - 140B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 252A a b - 252B a b)e + (- 63A b - 189B a b )d e - 84B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 210A a b - 70B a )e + (- 84A a b - 84B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 21A b - 63B a b )d e - 28B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 60A a e + (- 30A a b - 10B a )d e + (- 12A a b - 12B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 3A b - 9B a b )d e - 4B b d +--R / +--R 12 7 11 6 2 10 5 3 9 4 4 8 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 7 2 6 6 7 5 +--R 8820d e x + 2940d e x + 420d e +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 8 6 7 6 +--R ((- 3A b + 7B a b )e - 4B b d e )x +--R + +--R 5 2 4 8 6 5 7 6 2 6 5 +--R ((3A a b - 7B a b )e + (- 21A b + 53B a b )d e - 28B b d e )x +--R + +--R 2 4 3 3 8 5 2 4 7 +--R (- 3A a b + 7B a b )e + (21A a b - 53B a b )d e +--R + +--R 6 5 2 6 6 3 5 +--R (- 63A b + 175B a b )d e - 84B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 8 2 4 3 3 7 +--R (3A a b + 133B a b )e + (- 21A a b - 507B a b )d e +--R + +--R 5 2 4 2 6 6 5 3 5 +--R (63A a b + 665B a b )d e + (- 105A b - 231B a b )d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 8 3 3 4 2 7 +--R (102A a b + 182B a b)e + (- 399A a b - 613B a b )d e +--R + +--R 2 4 3 3 2 6 5 2 4 3 5 +--R (567A a b + 665B a b )d e + (- 315A a b - 189B a b )d e +--R * +--R 2 +--R x +--R + +--R 5 6 8 4 2 5 7 +--R (150A a b + 70B a )e + (- 546A a b - 206B a b)d e +--R + +--R 3 3 4 2 2 6 2 4 3 3 3 5 +--R (693A a b + 175B a b )d e + (- 315A a b - 21B a b )d e +--R * +--R x +--R + +--R 6 8 5 6 7 4 2 5 2 6 +--R 60A a e + (- 210A a b + 10B a )d e + (252A a b - 28B a b)d e +--R + +--R 3 3 4 2 3 5 +--R (- 105A a b + 21B a b )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 +--R - 140B a b e + 560B a b d e - 840B a b d e + 560B a b d e +--R + +--R 7 4 4 +--R - 140B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 8 3 4 4 3 7 +--R (- 105A a b - 315B a b )e + (420A a b + 1120B a b )d e +--R + +--R 2 5 3 4 2 6 6 2 5 3 5 +--R (- 630A a b - 1330B a b )d e + (420A a b + 420B a b )d e +--R + +--R 7 6 4 4 7 5 3 +--R (- 105A b + 245B a b )d e - 140B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 8 4 3 5 2 7 +--R (- 252A a b - 252B a b)e + (945A a b + 819B a b )d e +--R + +--R 3 4 4 3 2 6 2 5 3 4 3 5 +--R (- 1260A a b - 840B a b )d e + (630A a b + 210B a b )d e +--R + +--R 7 6 5 3 7 6 2 +--R (- 63A b + 147B a b )d e - 84B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 8 5 2 6 7 +--R (- 210A a b - 70B a )e + (756A a b + 196B a b)d e +--R + +--R 4 3 5 2 2 6 3 4 3 5 +--R (- 945A a b - 147B a b )d e + 420A a b d e +--R + +--R 7 6 6 2 7 7 +--R (- 21A b + 49B a b )d e - 28B b d e +--R * +--R x +--R + +--R 7 8 6 7 7 5 2 6 2 6 +--R - 60A a e + (210A a b - 10B a )d e + (- 252A a b + 28B a b)d e +--R + +--R 4 3 5 2 3 5 7 6 7 7 8 +--R (105A a b - 21B a b )d e + (- 3A b + 7B a b )d e - 4B b d +--R / +--R 4 16 3 15 2 2 2 14 3 3 13 4 4 12 7 +--R (420a e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e )x +--R + +--R 4 15 3 2 14 2 2 3 13 3 4 12 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 5 11 +--R 2940b d e +--R * +--R 6 +--R x +--R + +--R 4 2 14 3 3 13 2 2 4 12 3 5 11 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 6 10 +--R 8820b d e +--R * +--R 5 +--R x +--R + +--R 4 3 13 3 4 12 2 2 5 11 3 6 10 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 7 9 +--R 14700b d e +--R * +--R 4 +--R x +--R + +--R 4 4 12 3 5 11 2 2 6 10 3 7 9 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 8 8 +--R 14700b d e +--R * +--R 3 +--R x +--R + +--R 4 5 11 3 6 10 2 2 7 9 3 8 8 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 9 7 +--R 8820b d e +--R * +--R 2 +--R x +--R + +--R 4 6 10 3 7 9 2 2 8 8 3 9 7 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 10 6 +--R 2940b d e +--R * +--R x +--R + +--R 4 7 9 3 8 8 2 2 9 7 3 10 6 4 11 5 +--R 420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1378 +r0:=-1/8*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^8)-1/14*(b*B*d+A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^7)-1/28*b*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^6)-1/56*b^2*_ + (b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(b*d-a*e)*_ + (d+e*x)^5)-1/280*b^2*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 70B b e x + ((- 56A b - 168B a b )e - 56B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 140A a b - 140B a b)e + (- 28A b - 84B a b )d e - 28B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 120A a b - 40B a )e + (- 40A a b - 40B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 8A b - 24B a b )d e - 8B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 35A a e + (- 15A a b - 5B a )d e + (- 5A a b - 5B a b)d e +--R + +--R 3 2 3 3 4 +--R (- A b - 3B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 9 13 12 8 12 2 11 7 +--R 280b e x + (280a e + 2240b d e )x + (2240a d e + 7840b d e )x +--R + +--R 2 11 3 10 6 3 10 4 9 5 +--R (7840a d e + 15680b d e )x + (15680a d e + 19600b d e )x +--R + +--R 4 9 5 8 4 5 8 6 7 3 +--R (19600a d e + 15680b d e )x + (15680a d e + 7840b d e )x +--R + +--R 6 7 7 6 2 7 6 8 5 8 5 +--R (7840a d e + 2240b d e )x + (2240a d e + 280b d e )x + 280a d e +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 70B b e x + ((- 56A b - 168B a b )e - 56B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 140A a b - 140B a b)e + (- 28A b - 84B a b )d e - 28B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 120A a b - 40B a )e + (- 40A a b - 40B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 8A b - 24B a b )d e - 8B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 35A a e + (- 15A a b - 5B a )d e + (- 5A a b - 5B a b)d e +--R + +--R 3 2 3 3 4 +--R (- A b - 3B a b )d e - B b d +--R / +--R 13 8 12 7 2 11 6 3 10 5 4 9 4 +--R 280e x + 2240d e x + 7840d e x + 15680d e x + 19600d e x +--R + +--R 5 8 3 6 7 2 7 6 8 5 +--R 15680d e x + 7840d e x + 2240d e x + 280d e +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((56A b + 168B a b )e + 56B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((140A a b + 140B a b)e + (28A b + 84B a b )d e + 28B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (120A a b + 40B a )e + (40A a b + 40B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (8A b + 24B a b )d e + 8B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 35A a e + (15A a b + 5B a )d e + (5A a b + 5B a b)d e +--R + +--R 3 2 3 3 4 +--R (A b + 3B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R - 70B b e x + ((- 56A b - 238B a b )e - 56B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 196A a b - 308B a b )e + (- 28A b - 140B a b )d e - 28B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 260A a b - 180B a b)e + (- 68A a b - 124B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 8A b - 52B a b )d e - 8B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 155A a b - 40B a )e + (- 55A a b - 45B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 13A a b - 29B a b )d e + (- A b - 11B a b )d e - B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 35A a e + (- 15A a b - 5B a )d e + (- 5A a b - 5B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- A a b - 3B a b )d e - B a b d +--R / +--R 13 9 13 12 8 12 2 11 7 +--R 280b e x + (280a e + 2240b d e )x + (2240a d e + 7840b d e )x +--R + +--R 2 11 3 10 6 3 10 4 9 5 +--R (7840a d e + 15680b d e )x + (15680a d e + 19600b d e )x +--R + +--R 4 9 5 8 4 5 8 6 7 3 +--R (19600a d e + 15680b d e )x + (15680a d e + 7840b d e )x +--R + +--R 6 7 7 6 2 7 6 8 5 8 5 +--R (7840a d e + 2240b d e )x + (2240a d e + 280b d e )x + 280a d e +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1378 +r0:=-1/9*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^9)-1/72*(4*b*B*d+5*A*b*e-9*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^8)-1/168*b*(4*b*B*d+5*A*b*e-_ + 9*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^7)-_ + 1/420*b^2*(4*b*B*d+5*A*b*e-9*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^6)-1/2520*b^2*(4*b*B*d+5*A*b*e-9*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 504B b e x + ((- 420A b - 1260B a b )e - 336B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 1080A a b - 1080B a b)e + (- 180A b - 540B a b )d e +--R + +--R 3 2 2 +--R - 144B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 945A a b - 315B a )e + (- 270A a b - 270B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 45A b - 135B a b )d e - 36B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 280A a e + (- 105A a b - 35B a )d e + (- 30A a b - 30B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 5A b - 15B a b )d e - 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 10 14 13 9 +--R 2520b e x + (2520a e + 22680b d e )x +--R + +--R 13 2 12 8 2 12 3 11 7 +--R (22680a d e + 90720b d e )x + (90720a d e + 211680b d e )x +--R + +--R 3 11 4 10 6 4 10 5 9 5 +--R (211680a d e + 317520b d e )x + (317520a d e + 317520b d e )x +--R + +--R 5 9 6 8 4 6 8 7 7 3 +--R (317520a d e + 211680b d e )x + (211680a d e + 90720b d e )x +--R + +--R 7 7 8 6 2 8 6 9 5 9 5 +--R (90720a d e + 22680b d e )x + (22680a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 504B b e x + ((- 420A b - 1260B a b )e - 336B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 1080A a b - 1080B a b)e + (- 180A b - 540B a b )d e +--R + +--R 3 2 2 +--R - 144B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 945A a b - 315B a )e + (- 270A a b - 270B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 45A b - 135B a b )d e - 36B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 280A a e + (- 105A a b - 35B a )d e + (- 30A a b - 30B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 5A b - 15B a b )d e - 4B b d +--R / +--R 14 9 13 8 2 12 7 3 11 6 4 10 5 +--R 2520e x + 22680d e x + 90720d e x + 211680d e x + 317520d e x +--R + +--R 5 9 4 6 8 3 7 7 2 8 6 9 5 +--R 317520d e x + 211680d e x + 90720d e x + 22680d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 533 + +--S 534 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R 504B b e x + ((420A b + 1260B a b )e + 336B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (1080A a b + 1080B a b)e + (180A b + 540B a b )d e +--R + +--R 3 2 2 +--R 144B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (945A a b + 315B a )e + (270A a b + 270B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (45A b + 135B a b )d e + 36B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 280A a e + (105A a b + 35B a )d e + (30A a b + 30B a b)d e +--R + +--R 3 2 3 3 4 +--R (5A b + 15B a b )d e + 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R - 504B b e x + ((- 420A b - 1764B a b )e - 336B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1500A a b - 2340B a b )e + (- 180A b - 876B a b )d e +--R + +--R 4 2 2 +--R - 144B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 2025A a b - 1395B a b)e + (- 450A a b - 810B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 45A b - 279B a b )d e - 36B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 1225A a b - 315B a )e + (- 375A a b - 305B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 75A a b - 165B a b )d e + (- 5A b - 51B a b )d e - 4B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 280A a e + (- 105A a b - 35B a )d e + (- 30A a b - 30B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 5A a b - 15B a b )d e - 4B a b d +--R / +--R 14 10 14 13 9 +--R 2520b e x + (2520a e + 22680b d e )x +--R + +--R 13 2 12 8 2 12 3 11 7 +--R (22680a d e + 90720b d e )x + (90720a d e + 211680b d e )x +--R + +--R 3 11 4 10 6 4 10 5 9 5 +--R (211680a d e + 317520b d e )x + (317520a d e + 317520b d e )x +--R + +--R 5 9 6 8 4 6 8 7 7 3 +--R (317520a d e + 211680b d e )x + (211680a d e + 90720b d e )x +--R + +--R 7 7 8 6 2 8 6 9 5 9 5 +--R (90720a d e + 22680b d e )x + (22680a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 535 + +)clear all + +--S 536 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1378 +r0:=-1/10*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^10)-1/45*(2*b*B*d+3*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^9)-1/120*b*(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^8)-_ + 1/360*b^2*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^7)-1/2520*b^2*(2*b*B*d+3*A*b*e-5*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 420B b e x + ((- 360A b - 1080B a b )e - 240B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 945A a b - 945B a b)e + (- 135A b - 405B a b )d e +--R + +--R 3 2 2 +--R - 90B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 840A a b - 280B a )e + (- 210A a b - 210B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 30A b - 90B a b )d e - 20B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 252A a e + (- 84A a b - 28B a )d e + (- 21A a b - 21B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 3A b - 9B a b )d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 15 11 15 14 10 +--R 2520b e x + (2520a e + 25200b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (25200a d e + 113400b d e )x + (113400a d e + 302400b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (302400a d e + 529200b d e )x + (529200a d e + 635040b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (635040a d e + 529200b d e )x + (529200a d e + 302400b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (302400a d e + 113400b d e )x + (113400a d e + 25200b d e )x +--R + +--R 9 6 10 5 10 5 +--R (25200a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 420B b e x + ((- 360A b - 1080B a b )e - 240B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 945A a b - 945B a b)e + (- 135A b - 405B a b )d e - 90B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 840A a b - 280B a )e + (- 210A a b - 210B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 30A b - 90B a b )d e - 20B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 252A a e + (- 84A a b - 28B a )d e + (- 21A a b - 21B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 3A b - 9B a b )d e - 2B b d +--R / +--R 15 10 14 9 2 13 8 3 12 7 4 11 6 +--R 2520e x + 25200d e x + 113400d e x + 302400d e x + 529200d e x +--R + +--R 5 10 5 6 9 4 7 8 3 8 7 2 9 6 +--R 635040d e x + 529200d e x + 302400d e x + 113400d e x + 25200d e x +--R + +--R 10 5 +--R 2520d e +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R 420B b e x + ((360A b + 1080B a b )e + 240B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((945A a b + 945B a b)e + (135A b + 405B a b )d e + 90B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (840A a b + 280B a )e + (210A a b + 210B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (30A b + 90B a b )d e + 20B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 252A a e + (84A a b + 28B a )d e + (21A a b + 21B a b)d e +--R + +--R 3 2 3 3 4 +--R (3A b + 9B a b )d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R - 420B b e x + ((- 360A b - 1500B a b )e - 240B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1305A a b - 2025B a b )e + (- 135A b - 645B a b )d e +--R + +--R 4 2 2 +--R - 90B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 1785A a b - 1225B a b)e + (- 345A a b - 615B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 30A b - 180B a b )d e - 20B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 1092A a b - 280B a )e + (- 294A a b - 238B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 51A a b - 111B a b )d e + (- 3A b - 29B a b )d e - 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 252A a e + (- 84A a b - 28B a )d e + (- 21A a b - 21B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 3A a b - 9B a b )d e - 2B a b d +--R / +--R 15 11 15 14 10 +--R 2520b e x + (2520a e + 25200b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (25200a d e + 113400b d e )x + (113400a d e + 302400b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (302400a d e + 529200b d e )x + (529200a d e + 635040b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (635040a d e + 529200b d e )x + (529200a d e + 302400b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (302400a d e + 113400b d e )x + (113400a d e + 25200b d e )x +--R + +--R 9 6 10 5 10 5 +--R (25200a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1378 +r0:=-1/11*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^11)-1/110*(4*b*B*d+7*A*b*e-11*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^10)-1/330*b*(4*b*B*d+7*A*b*e-_ + 11*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^9)-_ + 1/1155*b^2*(4*b*B*d+7*A*b*e-11*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^8)-1/9240*b^2*(4*b*B*d+7*A*b*e-11*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 1320B b e x + ((- 1155A b - 3465B a b )e - 660B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 3080A a b - 3080B a b)e + (- 385A b - 1155B a b )d e +--R + +--R 3 2 2 +--R - 220B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 2772A a b - 924B a )e + (- 616A a b - 616B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 77A b - 231B a b )d e - 44B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 840A a e + (- 252A a b - 84B a )d e + (- 56A a b - 56B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 7A b - 21B a b )d e - 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 16 12 16 15 11 +--R 9240b e x + (9240a e + 101640b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (101640a d e + 508200b d e )x + (508200a d e + 1524600b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (1524600a d e + 3049200b d e )x + (3049200a d e + 4268880b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (4268880a d e + 4268880b d e )x + (4268880a d e + 3049200b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (3049200a d e + 1524600b d e )x + (1524600a d e + 508200b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (508200a d e + 101640b d e )x + (101640a d e + 9240b d e )x +--R + +--R 11 5 +--R 9240a d e +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R - 1320B b e x + ((- 1155A b - 3465B a b )e - 660B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 3080A a b - 3080B a b)e + (- 385A b - 1155B a b )d e +--R + +--R 3 2 2 +--R - 220B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 2772A a b - 924B a )e + (- 616A a b - 616B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 77A b - 231B a b )d e - 44B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 840A a e + (- 252A a b - 84B a )d e + (- 56A a b - 56B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 7A b - 21B a b )d e - 4B b d +--R / +--R 16 11 15 10 2 14 9 3 13 8 +--R 9240e x + 101640d e x + 508200d e x + 1524600d e x +--R + +--R 4 12 7 5 11 6 6 10 5 7 9 4 +--R 3049200d e x + 4268880d e x + 4268880d e x + 3049200d e x +--R + +--R 8 8 3 9 7 2 10 6 11 5 +--R 1524600d e x + 508200d e x + 101640d e x + 9240d e +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R 1320B b e x + ((1155A b + 3465B a b )e + 660B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (3080A a b + 3080B a b)e + (385A b + 1155B a b )d e +--R + +--R 3 2 2 +--R 220B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (2772A a b + 924B a )e + (616A a b + 616B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (77A b + 231B a b )d e + 44B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 840A a e + (252A a b + 84B a )d e + (56A a b + 56B a b)d e +--R + +--R 3 2 3 3 4 +--R (7A b + 21B a b )d e + 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R - 1320B b e x + ((- 1155A b - 4785B a b )e - 660B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 4235A a b - 6545B a b )e + (- 385A b - 1815B a b )d e +--R + +--R 4 2 2 +--R - 220B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 5852A a b - 4004B a b)e + (- 1001A a b - 1771B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 77A b - 451B a b )d e - 44B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 3612A a b - 924B a )e + (- 868A a b - 700B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 133A a b - 287B a b )d e + (- 7A b - 65B a b )d e - 4B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 840A a e + (- 252A a b - 84B a )d e + (- 56A a b - 56B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 7A a b - 21B a b )d e - 4B a b d +--R / +--R 16 12 16 15 11 +--R 9240b e x + (9240a e + 101640b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (101640a d e + 508200b d e )x + (508200a d e + 1524600b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (1524600a d e + 3049200b d e )x + (3049200a d e + 4268880b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (4268880a d e + 4268880b d e )x + (4268880a d e + 3049200b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (3049200a d e + 1524600b d e )x + (1524600a d e + 508200b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (508200a d e + 101640b d e )x + (101640a d e + 9240b d e )x +--R + +--R 11 5 +--R 9240a d e +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x +--R + +--R 12 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1378 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R m | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1378 +r0:=20*(b*d-a*e)^2*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4*(4+m)*(5+m)*(6+m)*(7+m))-_ + 5*(b*d-a*e)*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(a+b*x)*(d+e*x)^(1+m)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3*(5+m)*(6+m)*(7+m))+(A*b*e*(7+m)-_ + B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (b*e^2*(6+m)*(7+m))+B*(a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e*(7+m))+120*(b*d-a*e)^4*(A*b*e*(7+m)-B*(6*b*d+_ + a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6*_ + (2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m))-120*(b*d-a*e)^5*(A*b*e*(7+m)-_ + B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^7*(1+m)*(2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)*(a+b*x))-60*(b*d-_ + a*e)^3*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(a+b*x)*(d+e*x)^(1+m)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)) +--R +--R +--R (2) +--R 5 6 6 5 6 5 5 6 4 5 6 3 5 6 2 +--R B b e m + 21B b e m + 175B b e m + 735B b e m + 1624B b e m +--R + +--R 5 6 5 6 +--R 1764B b e m + 720B b e +--R * +--R 6 +--R x +--R + +--R 5 4 6 6 5 4 6 5 5 5 +--R (A b + 5B a b )e m + ((22A b + 110B a b )e - 6B b d e )m +--R + +--R 5 4 6 5 5 4 +--R ((190A b + 950B a b )e - 90B b d e )m +--R + +--R 5 4 6 5 5 3 +--R ((820A b + 4100B a b )e - 510B b d e )m +--R + +--R 5 4 6 5 5 2 +--R ((1849A b + 9245B a b )e - 1350B b d e )m +--R + +--R 5 4 6 5 5 +--R ((2038A b + 10190B a b )e - 1644B b d e )m +--R + +--R 5 4 6 5 5 +--R (840A b + 4200B a b )e - 720B b d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 6 6 +--R (5A a b + 10B a b )e m +--R + +--R 4 2 3 6 5 4 5 5 +--R ((115A a b + 230B a b )e + (- 5A b - 25B a b )d e )m +--R + +--R 4 2 3 6 5 4 5 +--R (1035A a b + 2070B a b )e + (- 85A b - 425B a b )d e +--R + +--R 5 2 4 +--R 30B b d e +--R * +--R 4 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (4625A a b + 9250B a b )e + (- 525A b - 2625B a b )d e +--R + +--R 5 2 4 +--R 300B b d e +--R * +--R 3 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (10720A a b + 21440B a b )e + (- 1475A b - 7375B a b )d e +--R + +--R 5 2 4 +--R 1050B b d e +--R * +--R 2 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (12060A a b + 24120B a b )e + (- 1870A b - 9350B a b )d e +--R + +--R 5 2 4 +--R 1500B b d e +--R * +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (5040A a b + 10080B a b )e + (- 840A b - 4200B a b )d e +--R + +--R 5 2 4 +--R 720B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 6 +--R (10A a b + 10B a b )e m +--R + +--R 2 3 3 2 6 4 2 3 5 5 +--R ((240A a b + 240B a b )e + (- 20A a b - 40B a b )d e )m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2260A a b + 2260B a b )e + (- 380A a b - 760B a b )d e +--R + +--R 5 4 2 4 +--R (20A b + 100B a b )d e +--R * +--R 4 +--R m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (10560A a b + 10560B a b )e + (- 2620A a b - 5240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (260A b + 1300B a b )d e - 120B b d e +--R * +--R 3 +--R m +--R + +--R 2 3 3 2 6 +--R (25450A a b + 25450B a b )e +--R + +--R 4 2 3 5 5 4 2 4 +--R (- 8020A a b - 16040B a b )d e + (1060A b + 5300B a b )d e +--R + +--R 5 3 3 +--R - 720B b d e +--R * +--R 2 +--R m +--R + +--R 2 3 3 2 6 +--R (29520A a b + 29520B a b )e +--R + +--R 4 2 3 5 5 4 2 4 +--R (- 10800A a b - 21600B a b )d e + (1660A b + 8300B a b )d e +--R + +--R 5 3 3 +--R - 1320B b d e +--R * +--R m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (12600A a b + 12600B a b )e + (- 5040A a b - 10080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (840A b + 4200B a b )d e - 720B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 6 +--R (10A a b + 5B a b)e m +--R + +--R 3 2 4 6 2 3 3 2 5 5 +--R ((250A a b + 125B a b)e + (- 30A a b - 30B a b )d e )m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (2470A a b + 1235B a b)e + (- 630A a b - 630B a b )d e +--R + +--R 4 2 3 2 4 +--R (60A a b + 120B a b )d e +--R * +--R 4 +--R m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (12190A a b + 6095B a b)e + (- 4890A a b - 4890B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (960A a b + 1920B a b )d e + (- 60A b - 300B a b )d e +--R * +--R 3 +--R m +--R + +--R 3 2 4 6 +--R (31120A a b + 15560B a b)e +--R + +--R 2 3 3 2 5 +--R (- 17010A a b - 17010B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (4980A a b + 9960B a b )d e + (- 600A b - 3000B a b )d e +--R + +--R 5 4 2 +--R 360B b d e +--R * +--R 2 +--R m +--R + +--R 3 2 4 6 +--R (37960A a b + 18980B a b)e +--R + +--R 2 3 3 2 5 +--R (- 25320A a b - 25320B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (9120A a b + 18240B a b )d e + (- 1380A b - 6900B a b )d e +--R + +--R 5 4 2 +--R 1080B b d e +--R * +--R m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (16800A a b + 8400B a b)e + (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (5040A a b + 10080B a b )d e + (- 840A b - 4200B a b )d e +--R + +--R 5 4 2 +--R 720B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 6 +--R (5A a b + B a )e m +--R + +--R 4 5 6 3 2 4 5 5 +--R ((130A a b + 26B a )e + (- 20A a b - 10B a b)d e )m +--R + +--R 4 5 6 3 2 4 5 +--R (1350A a b + 270B a )e + (- 460A a b - 230B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (60A a b + 60B a b )d e +--R * +--R 4 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (7100A a b + 1420B a )e + (- 4020A a b - 2010B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1140A a b + 1140B a b )d e + (- 120A a b - 240B a b )d e +--R * +--R 3 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (19645A a b + 3929B a )e + (- 16340A a b - 8170B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (7500A a b + 7500B a b )d e + (- 1680A a b - 3360B a b )d e +--R + +--R 5 4 4 2 +--R (120A b + 600B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (26370A a b + 5274B a )e + (- 29560A a b - 14780B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (19020A a b + 19020B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 6600A a b - 13200B a b )d e + (960A b + 4800B a b )d e +--R + +--R 5 5 +--R - 720B b d e +--R * +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (12600A a b + 2520B a )e + (- 16800A a b - 8400B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (12600A a b + 12600B a b )d e + (- 5040A a b - 10080B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (840A b + 4200B a b )d e - 720B b d e +--R * +--R x +--R + +--R 5 6 6 5 6 4 5 5 5 +--R A a e m + (27A a e + (- 5A a b - B a )d e )m +--R + +--R 5 6 4 5 5 3 2 4 2 4 4 +--R (295A a e + (- 125A a b - 25B a )d e + (20A a b + 10B a b)d e )m +--R + +--R 5 6 4 5 5 +--R 1665A a e + (- 1225A a b - 245B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (440A a b + 220B a b)d e + (- 60A a b - 60B a b )d e +--R * +--R 3 +--R m +--R + +--R 5 6 4 5 5 +--R 5104A a e + (- 5875A a b - 1175B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (3580A a b + 1790B a b)d e + (- 1080A a b - 1080B a b )d e +--R + +--R 4 2 3 4 2 +--R (120A a b + 240B a b )d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 5 5 +--R 8028A a e + (- 13770A a b - 2754B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (12760A a b + 6380B a b)d e + (- 6420A a b - 6420B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (1560A a b + 3120B a b )d e + (- 120A b - 600B a b )d e +--R * +--R m +--R + +--R 5 6 4 5 5 +--R 5040A a e + (- 12600A a b - 2520B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (16800A a b + 8400B a b)d e + (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (5040A a b + 10080B a b )d e + (- 840A b - 4200B a b )d e + 720B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m + 13132b e m +--R + +--R 7 7 +--R 13068b e m + 5040b e +--R * +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a e m + 28a e m + 322a e m + 1960a e m + 6769a e m + 13132a e m +--R + +--R 7 7 +--R 13068a e m + 5040a e +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 6 5 7 5 5 7 4 5 7 3 5 7 2 +--R B b e m + 21B b e m + 175B b e m + 735B b e m + 1624B b e m +--R + +--R 5 7 5 7 +--R 1764B b e m + 720B b e +--R * +--R 7 +--R x +--R + +--R 5 4 7 5 6 6 +--R ((A b + 5B a b )e + B b d e )m +--R + +--R 5 4 7 5 6 5 +--R ((22A b + 110B a b )e + 15B b d e )m +--R + +--R 5 4 7 5 6 4 +--R ((190A b + 950B a b )e + 85B b d e )m +--R + +--R 5 4 7 5 6 3 +--R ((820A b + 4100B a b )e + 225B b d e )m +--R + +--R 5 4 7 5 6 2 +--R ((1849A b + 9245B a b )e + 274B b d e )m +--R + +--R 5 4 7 5 6 +--R ((2038A b + 10190B a b )e + 120B b d e )m +--R + +--R 5 4 7 +--R (840A b + 4200B a b )e +--R * +--R 6 +--R x +--R + +--R 4 2 3 7 5 4 6 6 +--R ((5A a b + 10B a b )e + (A b + 5B a b )d e )m +--R + +--R 4 2 3 7 5 4 6 5 2 5 5 +--R ((115A a b + 230B a b )e + (17A b + 85B a b )d e - 6B b d e )m +--R + +--R 4 2 3 7 5 4 6 +--R (1035A a b + 2070B a b )e + (105A b + 525B a b )d e +--R + +--R 5 2 5 +--R - 60B b d e +--R * +--R 4 +--R m +--R + +--R 4 2 3 7 5 4 6 +--R (4625A a b + 9250B a b )e + (295A b + 1475B a b )d e +--R + +--R 5 2 5 +--R - 210B b d e +--R * +--R 3 +--R m +--R + +--R 4 2 3 7 5 4 6 +--R (10720A a b + 21440B a b )e + (374A b + 1870B a b )d e +--R + +--R 5 2 5 +--R - 300B b d e +--R * +--R 2 +--R m +--R + +--R 4 2 3 7 5 4 6 +--R (12060A a b + 24120B a b )e + (168A b + 840B a b )d e +--R + +--R 5 2 5 +--R - 144B b d e +--R * +--R m +--R + +--R 4 2 3 7 +--R (5040A a b + 10080B a b )e +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 7 4 2 3 6 6 +--R ((10A a b + 10B a b )e + (5A a b + 10B a b )d e )m +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (240A a b + 240B a b )e + (95A a b + 190B a b )d e +--R + +--R 5 4 2 5 +--R (- 5A b - 25B a b )d e +--R * +--R 5 +--R m +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (2260A a b + 2260B a b )e + (655A a b + 1310B a b )d e +--R + +--R 5 4 2 5 5 3 4 +--R (- 65A b - 325B a b )d e + 30B b d e +--R * +--R 4 +--R m +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (10560A a b + 10560B a b )e + (2005A a b + 4010B a b )d e +--R + +--R 5 4 2 5 5 3 4 +--R (- 265A b - 1325B a b )d e + 180B b d e +--R * +--R 3 +--R m +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (25450A a b + 25450B a b )e + (2700A a b + 5400B a b )d e +--R + +--R 5 4 2 5 5 3 4 +--R (- 415A b - 2075B a b )d e + 330B b d e +--R * +--R 2 +--R m +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (29520A a b + 29520B a b )e + (1260A a b + 2520B a b )d e +--R + +--R 5 4 2 5 5 3 4 +--R (- 210A b - 1050B a b )d e + 180B b d e +--R * +--R m +--R + +--R 2 3 3 2 7 +--R (12600A a b + 12600B a b )e +--R * +--R 4 +--R x +--R + +--R 3 2 4 7 2 3 3 2 6 6 +--R ((10A a b + 5B a b)e + (10A a b + 10B a b )d e )m +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (250A a b + 125B a b)e + (210A a b + 210B a b )d e +--R + +--R 4 2 3 2 5 +--R (- 20A a b - 40B a b )d e +--R * +--R 5 +--R m +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (2470A a b + 1235B a b)e + (1630A a b + 1630B a b )d e +--R + +--R 4 2 3 2 5 5 4 3 4 +--R (- 320A a b - 640B a b )d e + (20A b + 100B a b )d e +--R * +--R 4 +--R m +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (12190A a b + 6095B a b)e + (5670A a b + 5670B a b )d e +--R + +--R 4 2 3 2 5 5 4 3 4 +--R (- 1660A a b - 3320B a b )d e + 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570B a b )d e + (60A a b + 120B a b )d e +--R * +--R 4 +--R m +--R + +--R 4 5 7 3 2 4 6 +--R (7100A a b + 1420B a )e + (8170A a b + 4085B a b)d e +--R + +--R 2 3 3 2 2 5 4 2 3 3 4 +--R (- 3750A a b - 3750B a b )d e + (840A a b + 1680B a b )d e +--R + +--R 5 4 4 3 +--R (- 60A b - 300B a b )d e +--R * +--R 3 +--R m +--R + +--R 4 5 7 3 2 4 6 +--R (19645A a b + 3929B a )e + (14780A a b + 7390B a b)d e +--R + +--R 2 3 3 2 2 5 4 2 3 3 4 +--R (- 9510A a b - 9510B a b )d e + (3300A a b + 6600B a b )d e +--R + +--R 5 4 4 3 5 5 2 +--R (- 480A b - 2400B a b )d e + 360B b d e +--R * +--R 2 +--R m +--R + +--R 4 5 7 3 2 4 6 +--R (26370A a b + 5274B a )e + (8400A a b + 4200B a b)d e +--R + +--R 2 3 3 2 2 5 4 2 3 3 4 +--R (- 6300A a b - 6300B a b )d e + (2520A a b + 5040B a b )d e +--R + +--R 5 4 4 3 5 5 2 +--R (- 420A b - 2100B a b )d e + 360B b d e +--R * +--R m +--R + +--R 4 5 7 +--R (12600A a b + 2520B a )e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 6 6 +--R (A a e + (5A a b + B a )d e )m +--R + 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b )d e + (- 120A b - 600B a b )d e +--R * +--R m +--R + +--R 5 6 4 5 2 5 +--R 5040A a d e + (- 12600A a b - 2520B a )d e +--R + +--R 3 2 4 3 4 2 3 3 2 4 3 +--R (16800A a b + 8400B a b)d e + (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 5 2 5 4 6 5 7 +--R (5040A a b + 10080B a b )d e + (- 840A b - 4200B a b )d e + 720B b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R e m + 28e m + 322e m + 1960e m + 6769e m + 13132e m + 13068e m +--R + +--R 7 +--R 5040e +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 6 6 7 5 6 7 4 6 7 3 6 7 2 +--R B b e m + 21B b e m + 175B b e m + 735B b e m + 1624B b e m +--R + +--R 6 7 6 7 +--R 1764B b e m + 720B b e +--R * +--R 8 +--R x +--R + +--R 6 5 7 6 6 6 +--R ((A b + 6B a b )e + B b d e )m +--R + +--R 6 5 7 6 6 5 +--R ((22A b + 131B a b )e + 15B b d e )m +--R + +--R 6 5 7 6 6 4 +--R ((190A b + 1125B a b )e + 85B b d e )m +--R + +--R 6 5 7 6 6 3 +--R ((820A b + 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a b + 17640B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 5460A a b - 12180B a b )d e + (840A b + 4560B a b )d e +--R + +--R 6 6 +--R - 720B b d e +--R * +--R m +--R + +--R 5 6 7 +--R (17640A a b + 2520B a )e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 6 6 +--R (A a e + (6A a b + B a )d e )m +--R + +--R 6 7 5 6 6 +--R 27A a e + (152A a b + 25B a )d e +--R + +--R 4 2 5 2 5 +--R (- 25A a b - 11B a b)d e +--R * +--R 5 +--R m +--R + +--R 6 7 5 6 6 +--R 295A a e + (1520A a b + 245B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 565A a b - 245B a b)d e + (80A a b + 70B a b )d e +--R * +--R 4 +--R m +--R + +--R 6 7 5 6 6 +--R 1665A a e + (7540A a b + 1175B a )d e +--R + +--R 4 2 5 2 5 +--R (- 4805A a b - 2035B a b)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (1520A a b + 1300B a b )d e + (- 180A a b - 300B a b )d e +--R * +--R 3 +--R m +--R + +--R 6 7 5 6 6 +--R 5104A a e + (18874A a b + 2754B a )d e +--R + +--R 4 2 5 2 5 +--R (- 18635A a b - 7555B a b)d e +--R + +--R 3 3 4 2 3 4 +--R 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+ +--R 4 2 5 3 4 +--R (20A a b + 10B a b)d e +--R * +--R 4 +--R m +--R + +--R 6 6 5 6 2 5 +--R 1665A a d e + (- 1225A a b - 245B a )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (440A a b + 220B a b)d e + (- 60A a b - 60B a b )d e +--R * +--R 3 +--R m +--R + +--R 6 6 5 6 2 5 +--R 5104A a d e + (- 5875A a b - 1175B a )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (3580A a b + 1790B a b)d e + (- 1080A a b - 1080B a b )d e +--R + +--R 2 4 3 3 5 2 +--R (120A a b + 240B a b )d e +--R * +--R 2 +--R m +--R + +--R 6 6 5 6 2 5 +--R 8028A a d e + (- 13770A a b - 2754B a )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (12760A a b + 6380B a b)d e + (- 6420A a b - 6420B a b )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (1560A a b + 3120B a b )d e + (- 120A a b - 600B a b )d e +--R * +--R m +--R + +--R 6 6 5 6 2 5 +--R 5040A a d e + (- 12600A a b - 2520B a )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (16800A a b + 8400B a b)d e + (- 12600A a b - 12600B a b )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (5040A a b + 10080B a b )d e + (- 840A a b - 4200B a b )d e +--R + +--R 5 7 +--R 720B a b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 5 6 6 5 6 5 5 6 4 5 6 3 +--R - B b e m - 21B b e m - 175B b e m - 735B b e m +--R + +--R 5 6 2 5 6 5 6 +--R - 1624B b e m - 1764B b e m - 720B b e +--R * +--R 6 +--R x +--R + +--R 5 4 6 6 5 4 6 5 5 5 +--R (- A b - 5B a b )e m + ((- 22A b - 110B a b )e + 6B b d e )m +--R + +--R 5 4 6 5 5 4 +--R ((- 190A b - 950B a b )e + 90B b d e )m +--R + +--R 5 4 6 5 5 3 +--R ((- 820A b - 4100B a b )e + 510B b d e )m +--R + +--R 5 4 6 5 5 2 +--R ((- 1849A b - 9245B a b )e + 1350B b d e )m +--R + +--R 5 4 6 5 5 +--R ((- 2038A b - 10190B a b )e + 1644B b d e )m +--R + +--R 5 4 6 5 5 +--R (- 840A b - 4200B a b )e + 720B b d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 6 6 +--R (- 5A a b - 10B a b )e m +--R + +--R 4 2 3 6 5 4 5 5 +--R ((- 115A a b - 230B a b )e + (5A b + 25B a b )d e )m +--R + +--R 4 2 3 6 5 4 5 +--R (- 1035A a b - 2070B a b )e + (85A b + 425B a b )d e +--R + +--R 5 2 4 +--R - 30B b d e +--R * +--R 4 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (- 4625A a b - 9250B a b )e + (525A b + 2625B a b )d e +--R + +--R 5 2 4 +--R - 300B b d e +--R * +--R 3 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (- 10720A a b - 21440B a b )e + (1475A b + 7375B a b )d e +--R + +--R 5 2 4 +--R - 1050B b d e +--R * +--R 2 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (- 12060A a b - 24120B a b )e + (1870A b + 9350B a b )d e +--R + +--R 5 2 4 +--R - 1500B b d e +--R * +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (- 5040A a b - 10080B a b )e + (840A b + 4200B a b )d e +--R + +--R 5 2 4 +--R - 720B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 6 +--R (- 10A a b - 10B a b )e m +--R + +--R 2 3 3 2 6 4 2 3 5 5 +--R ((- 240A a b - 240B a b )e + (20A a b + 40B a b )d e )m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 2260A a b - 2260B a b )e + (380A a b + 760B a b )d e +--R + +--R 5 4 2 4 +--R (- 20A b - 100B a b )d e +--R * +--R 4 +--R m +--R + +--R 2 3 3 2 6 +--R (- 10560A a b - 10560B a b )e +--R + +--R 4 2 3 5 5 4 2 4 +--R (2620A a b + 5240B a b )d e + (- 260A b - 1300B a b )d e +--R + +--R 5 3 3 +--R 120B b d e +--R * +--R 3 +--R m +--R + +--R 2 3 3 2 6 +--R (- 25450A a b - 25450B a b )e +--R + +--R 4 2 3 5 +--R (8020A a b + 16040B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 1060A b - 5300B a b )d e + 720B b d e +--R * +--R 2 +--R m +--R + +--R 2 3 3 2 6 +--R (- 29520A a b - 29520B a b )e +--R + +--R 4 2 3 5 +--R (10800A a b + 21600B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 1660A b - 8300B a b )d e + 1320B b d e +--R * +--R m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 12600A a b - 12600B a b )e + (5040A a b + 10080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 840A b - 4200B a b )d e + 720B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 6 +--R (- 10A a b - 5B a b)e m +--R + +--R 3 2 4 6 2 3 3 2 5 5 +--R ((- 250A a b - 125B a b)e + (30A a b + 30B a b )d e )m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 2470A a b - 1235B a b)e + (630A a b + 630B a b )d e +--R + +--R 4 2 3 2 4 +--R (- 60A a b - 120B a b )d e +--R * +--R 4 +--R m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 12190A a b - 6095B a b)e + (4890A a b + 4890B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 960A a b - 1920B a b )d e + (60A b + 300B a b )d e +--R * +--R 3 +--R m +--R + +--R 3 2 4 6 +--R (- 31120A a b - 15560B a b)e +--R + +--R 2 3 3 2 5 +--R (17010A a b + 17010B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 4980A a b - 9960B a b )d e + (600A b + 3000B a b )d e +--R + +--R 5 4 2 +--R - 360B b d e +--R * +--R 2 +--R m +--R + +--R 3 2 4 6 +--R (- 37960A a b - 18980B a b)e +--R + +--R 2 3 3 2 5 +--R (25320A a b + 25320B a b )d e +--R + +--R 4 2 3 2 4 +--R (- 9120A a b - 18240B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (1380A b + 6900B a b )d e - 1080B b d e +--R * +--R m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 16800A a b - 8400B a b)e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 5040A a b - 10080B a b )d e + (840A b + 4200B a b )d e +--R + +--R 5 4 2 +--R - 720B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 6 +--R (- 5A a b - B a )e m +--R + +--R 4 5 6 3 2 4 5 5 +--R ((- 130A a b - 26B a )e + (20A a b + 10B a b)d e )m +--R + +--R 4 5 6 3 2 4 5 +--R (- 1350A a b - 270B a )e + (460A a b + 230B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 60A a b - 60B a b )d e +--R * +--R 4 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (- 7100A a b - 1420B a )e + (4020A a b + 2010B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 1140A a b - 1140B a b )d e + (120A a b + 240B a b )d e +--R * +--R 3 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (- 19645A a b - 3929B a )e + (16340A a b + 8170B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 7500A a b - 7500B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (1680A a b + 3360B a b )d e + (- 120A b - 600B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (- 26370A a b - 5274B a )e + (29560A a b + 14780B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 19020A a b - 19020B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (6600A a b + 13200B a b )d e + (- 960A b - 4800B a b )d e +--R + +--R 5 5 +--R 720B b d e +--R * +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (- 12600A a b - 2520B a )e + (16800A a b + 8400B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (5040A a b + 10080B a b )d e + (- 840A b - 4200B a b )d e +--R + +--R 5 5 +--R 720B b d e +--R * +--R x +--R + +--R 5 6 6 5 6 4 5 5 5 +--R - A a e m + (- 27A a e + (5A a b + B a )d e )m +--R + +--R 5 6 4 5 5 +--R - 295A a e + (125A a b + 25B a )d e +--R + +--R 3 2 4 2 4 +--R (- 20A a b - 10B a b)d e +--R * +--R 4 +--R m +--R + +--R 5 6 4 5 5 +--R - 1665A a e + (1225A a b + 245B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 440A a b - 220B a b)d e + (60A a b + 60B a b )d e +--R * +--R 3 +--R m +--R + +--R 5 6 4 5 5 +--R - 5104A a e + (5875A a b + 1175B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 3580A a b - 1790B a b)d e + (1080A a b + 1080B a b )d e +--R + +--R 4 2 3 4 2 +--R (- 120A a b - 240B a b )d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 5 5 +--R - 8028A a e + (13770A a b + 2754B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 12760A a b - 6380B a b)d e + (6420A a b + 6420B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 1560A a b - 3120B a b )d e + (120A b + 600B a b )d e +--R * +--R m +--R + +--R 5 6 4 5 5 +--R - 5040A a e + (12600A a b + 2520B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 16800A a b - 8400B a b)d e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 5040A a b - 10080B a b )d e + (840A b + 4200B a b )d e +--R + +--R 5 6 +--R - 720B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m + 13132b e m +--R + +--R 7 7 +--R 13068b e m + 5040b e +--R * +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a e m + 28a e m + 322a e m + 1960a e m + 6769a e m + 13132a e m +--R + +--R 7 7 +--R 13068a e m + 5040a e +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 1378 +t0:=(A+B*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 11 4 3 6 4 5 10 +--R B b e x + ((A b + 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 6 4 3 5 4 2 4 9 +--R ((4A a b + 6B a b )e + (6A b + 24B a b )d e + 15B b d e )x +--R + +--R 2 2 3 6 3 2 2 5 +--R (6A a b + 4B a b)e + (24A a b + 36B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (15A b + 60B a b )d e + 20B b d e +--R * +--R 8 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (4A a b + B a )e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 4 4 2 +--R (60A a b + 90B a b )d e + (20A b + 80B a b )d e + 15B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 5 2 2 3 2 4 +--R A a e + (24A a b + 6B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 3 3 4 3 4 2 4 5 +--R (80A a b + 120B a b )d e + (15A b + 60B a b )d e + 6B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 6A a d e + (60A a b + 15B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (60A a b + 90B a b )d e + (6A b + 24B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A a d e + (80A a b + 20B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 5 4 3 6 +--R (24A a b + 36B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 4 4 2 2 2 3 5 +--R 20A a d e + (60A a b + 15B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 6 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 2 +--R (15A a d e + (24A a b + 6B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 5 3 4 6 4 6 +--R (6A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1378 +r0:=-1/858*(b*d-a*e)^2*(6*b*B*d-13*A*b*e+7*a*B*e)*(d+e*x)^7*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)+5/1716*(b*d-a*e)*(6*b*B*d-13*A*b*e+7*a*B*e)*_ + (a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-1/156*(6*b*B*d-_ + 13*A*b*e+7*a*B*e)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+_ + 1/13*B*(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 1/10296*(b*d-a*e)^4*(6*b*B*d-13*A*b*e+7*a*B*e)*(d+e*x)^7*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^6)+1/72072*(b*d-a*e)^5*(6*b*B*d-13*A*b*e+_ + 7*a*B*e)*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+_ + 1/2574*(b*d-a*e)^3*(6*b*B*d-13*A*b*e+7*a*B*e)*(a+b*x)*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 13 13 5 4 13 5 12 12 +--R 5544B b e x + ((6006A b + 30030B a b )e + 36036B b d e )x +--R + +--R 4 2 3 13 5 4 12 +--R (32760A a b + 65520B a b )e + (39312A b + 196560B a b )d e +--R + +--R 5 2 11 +--R 98280B b d e +--R * +--R 11 +--R x +--R + +--R 2 3 3 2 13 4 2 3 12 +--R (72072A a b + 72072B a b )e + (216216A a b + 432432B a b )d e +--R + +--R 5 4 2 11 5 3 10 +--R (108108A b + 540540B a b )d e + 144144B b d e +--R * +--R 10 +--R x +--R + +--R 3 2 4 13 2 3 3 2 12 +--R (80080A a b + 40040B a b)e + (480480A a b + 480480B a b )d e +--R + +--R 4 2 3 2 11 +--R (600600A a b + 1201200B a b )d e +--R + +--R 5 4 3 10 5 4 9 +--R (160160A b + 800800B a b )d e + 120120B b d e +--R * +--R 9 +--R x +--R + +--R 4 5 13 3 2 4 12 +--R (45045A a b + 9009B a )e + (540540A a b + 270270B a b)d e +--R + +--R 2 3 3 2 2 11 +--R (1351350A a b + 1351350B a b )d e +--R + +--R 4 2 3 3 10 +--R (900900A a b + 1801800B a b )d e +--R + +--R 5 4 4 9 5 5 8 +--R (135135A b + 675675B a b )d e + 54054B b d e +--R * +--R 8 +--R x +--R + +--R 5 13 4 5 12 +--R 10296A a e + (308880A a b + 61776B a )d e +--R + +--R 3 2 4 2 11 +--R (1544400A a b + 772200B a b)d e +--R + +--R 2 3 3 2 3 10 +--R (2059200A a b + 2059200B a b )d e +--R + +--R 4 2 3 4 9 5 4 5 8 +--R (772200A a b + 1544400B a b )d e + (61776A b + 308880B a b )d e +--R + +--R 5 6 7 +--R 10296B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 2 11 +--R 72072A a d e + (900900A a b + 180180B a )d e +--R + +--R 3 2 4 3 10 +--R (2402400A a b + 1201200B a b)d e +--R + +--R 2 3 3 2 4 9 +--R (1801800A a b + 1801800B a b )d e +--R + +--R 4 2 3 5 8 5 4 6 7 +--R (360360A a b + 720720B a b )d e + (12012A b + 60060B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 2 11 4 5 3 10 +--R 216216A a d e + (1441440A a b + 288288B a )d e +--R + +--R 3 2 4 4 9 +--R (2162160A a b + 1081080B a b)d e +--R + +--R 2 3 3 2 5 8 4 2 3 6 7 +--R (864864A a b + 864864B a b )d e + (72072A a b + 144144B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 3 10 4 5 4 9 +--R 360360A a d e + (1351350A a b + 270270B a )d e +--R + +--R 3 2 4 5 8 2 3 3 2 6 7 +--R (1081080A a b + 540540B a b)d e + (180180A a b + 180180B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 4 9 4 5 5 8 +--R 360360A a d e + (720720A a b + 144144B a )d e +--R + +--R 3 2 4 6 7 +--R (240240A a b + 120120B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 5 8 4 5 6 7 2 5 6 7 +--R (216216A a d e + (180180A a b + 36036B a )d e )x + 72072A a d e x +--R + +--R 5 7 6 4 5 8 5 +--R 10296A a d e + (- 6435A a b - 1287B a )d e +--R + +--R 3 2 4 9 4 2 3 3 2 10 3 +--R (2860A a b + 1430B a b)d e + (- 858A a b - 858B a b )d e +--R + +--R 4 2 3 11 2 5 4 12 5 13 +--R (156A a b + 312B a b )d e + (- 13A b - 65B a b )d e + 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 72072b e x + 72072a e +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 13 5 4 6 5 5 12 +--R 5544B b e x + ((6006A b + 30030B a b )e + 36036B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (32760A a b + 65520B a b )e + (39312A b + 196560B a b )d e +--R + +--R 5 2 4 +--R 98280B b d e +--R * +--R 11 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (72072A a b + 72072B a b )e + (216216A a b + 432432B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (108108A b + 540540B a b )d e + 144144B b d e +--R * +--R 10 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (80080A a b + 40040B a b)e + (480480A a b + 480480B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (600600A a b + 1201200B a b )d e + (160160A b + 800800B a b )d e +--R + +--R 5 4 2 +--R 120120B b d e +--R * +--R 9 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (45045A a b + 9009B a )e + (540540A a b + 270270B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (1351350A a b + 1351350B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (900900A a b + 1801800B a b )d e + (135135A b + 675675B a b )d e +--R + +--R 5 5 +--R 54054B b d e +--R * +--R 8 +--R x +--R + +--R 5 6 4 5 5 +--R 10296A a e + (308880A a b + 61776B a )d e +--R + +--R 3 2 4 2 4 +--R (1544400A a b + 772200B a b)d e +--R + +--R 2 3 3 2 3 3 +--R (2059200A a b + 2059200B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (772200A a b + 1544400B a b )d e + (61776A b + 308880B a b )d e +--R + +--R 5 6 +--R 10296B b d +--R * +--R 7 +--R x +--R + +--R 5 5 4 5 2 4 +--R 72072A a d e + (900900A a b + 180180B a )d e +--R + +--R 3 2 4 3 3 +--R (2402400A a b + 1201200B a b)d e +--R + +--R 2 3 3 2 4 2 +--R (1801800A a b + 1801800B a b )d e +--R + +--R 4 2 3 5 5 4 6 +--R (360360A a b + 720720B a b )d e + (12012A b + 60060B a b )d +--R * +--R 6 +--R x +--R + +--R 5 2 4 4 5 3 3 +--R 216216A a d e + (1441440A a b + 288288B a )d e +--R + +--R 3 2 4 4 2 2 3 3 2 5 +--R (2162160A a b + 1081080B a b)d e + (864864A a b + 864864B a b )d e +--R + +--R 4 2 3 6 +--R (72072A a b + 144144B a b )d +--R * +--R 5 +--R x +--R + +--R 5 3 3 4 5 4 2 +--R 360360A a d e + (1351350A a b + 270270B a )d e +--R + +--R 3 2 4 5 2 3 3 2 6 +--R (1081080A a b + 540540B a b)d e + (180180A a b + 180180B a b )d +--R * +--R 4 +--R x +--R + +--R 5 4 2 4 5 5 +--R 360360A a d e + (720720A a b + 144144B a )d e +--R + +--R 3 2 4 6 +--R (240240A a b + 120120B a b)d +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 6 2 5 6 +--R (216216A a d e + (180180A a b + 36036B a )d )x + 72072A a d x +--R / +--R 72072 +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 13 13 +--R - 5544B b e x +--R + +--R 5 4 13 5 12 12 +--R ((- 6006A b - 30030B a b )e - 36036B b d e )x +--R + +--R 4 2 3 13 +--R (- 32760A a b - 65520B a b )e +--R + +--R 5 4 12 5 2 11 +--R (- 39312A b - 196560B a b )d e - 98280B b d e +--R * +--R 11 +--R x +--R + +--R 2 3 3 2 13 +--R (- 72072A a b - 72072B a b )e +--R + +--R 4 2 3 12 +--R (- 216216A a b - 432432B a b )d e +--R + +--R 5 4 2 11 5 3 10 +--R (- 108108A b - 540540B a b )d e - 144144B b d e +--R * +--R 10 +--R x +--R + +--R 3 2 4 13 +--R (- 80080A a b - 40040B a b)e +--R + +--R 2 3 3 2 12 +--R (- 480480A a b - 480480B a b )d e +--R + +--R 4 2 3 2 11 +--R (- 600600A a b - 1201200B a b )d e +--R + +--R 5 4 3 10 5 4 9 +--R (- 160160A b - 800800B a b )d e - 120120B b d e +--R * +--R 9 +--R x +--R + +--R 4 5 13 +--R (- 45045A a b - 9009B a )e +--R + +--R 3 2 4 12 +--R (- 540540A a b - 270270B a b)d e +--R + +--R 2 3 3 2 2 11 +--R (- 1351350A a b - 1351350B a b )d e +--R + +--R 4 2 3 3 10 +--R (- 900900A a b - 1801800B a b )d e +--R + +--R 5 4 4 9 5 5 8 +--R (- 135135A b - 675675B a b )d e - 54054B b d e +--R * +--R 8 +--R x +--R + +--R 5 13 4 5 12 +--R - 10296A a e + (- 308880A a b - 61776B a )d e +--R + +--R 3 2 4 2 11 +--R (- 1544400A a b - 772200B a b)d e +--R + +--R 2 3 3 2 3 10 +--R (- 2059200A a b - 2059200B a b )d e +--R + +--R 4 2 3 4 9 +--R (- 772200A a b - 1544400B a b )d e +--R + +--R 5 4 5 8 5 6 7 +--R (- 61776A b - 308880B a b )d e - 10296B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 2 11 +--R - 72072A a d e + (- 900900A a b - 180180B a )d e +--R + +--R 3 2 4 3 10 +--R (- 2402400A a b - 1201200B a b)d e +--R + +--R 2 3 3 2 4 9 +--R (- 1801800A a b - 1801800B a b )d e +--R + +--R 4 2 3 5 8 +--R (- 360360A a b - 720720B a b )d e +--R + +--R 5 4 6 7 +--R (- 12012A b - 60060B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 2 11 4 5 3 10 +--R - 216216A a d e + (- 1441440A a b - 288288B a )d e +--R + +--R 3 2 4 4 9 +--R (- 2162160A a b - 1081080B a b)d e +--R + +--R 2 3 3 2 5 8 +--R (- 864864A a b - 864864B a b )d e +--R + +--R 4 2 3 6 7 +--R (- 72072A a b - 144144B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 3 10 4 5 4 9 +--R - 360360A a d e + (- 1351350A a b - 270270B a )d e +--R + +--R 3 2 4 5 8 +--R (- 1081080A a b - 540540B a b)d e +--R + +--R 2 3 3 2 6 7 +--R (- 180180A a b - 180180B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 4 9 4 5 5 8 +--R - 360360A a d e + (- 720720A a b - 144144B a )d e +--R + +--R 3 2 4 6 7 +--R (- 240240A a b - 120120B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 5 8 4 5 6 7 2 +--R (- 216216A a d e + (- 180180A a b - 36036B a )d e )x +--R + +--R 5 6 7 5 7 6 4 5 8 5 +--R - 72072A a d e x - 10296A a d e + (6435A a b + 1287B a )d e +--R + +--R 3 2 4 9 4 2 3 3 2 10 3 +--R (- 2860A a b - 1430B a b)d e + (858A a b + 858B a b )d e +--R + +--R 4 2 3 11 2 5 4 12 5 13 +--R (- 156A a b - 312B a b )d e + (13A b + 65B a b )d e - 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 13 14 6 5 13 6 12 13 +--R 5544B b e x + ((6006A b + 35574B a b )e + 36036B b d e )x +--R + +--R 5 2 4 13 6 5 12 +--R (38766A a b + 95550B a b )e + (39312A b + 232596B a b )d e +--R + +--R 6 2 11 +--R 98280B b d e +--R * +--R 12 +--R x +--R + +--R 2 4 3 3 13 5 2 4 12 +--R (104832A a b + 137592B a b )e + (255528A a b + 628992B a b )d e +--R + +--R 6 5 2 11 6 3 10 +--R (108108A b + 638820B a b )d e + 144144B b d e +--R * +--R 11 +--R x +--R + +--R 3 3 4 2 13 2 4 3 3 12 +--R (152152A a b + 112112B a b )e + (696696A a b + 912912B a b )d e +--R + +--R 5 2 4 2 11 +--R (708708A a b + 1741740B a b )d e +--R + +--R 6 5 3 10 6 4 9 +--R (160160A b + 944944B a b )d e + 120120B b d e +--R * +--R 10 +--R x +--R + +--R 4 2 5 13 3 3 4 2 12 +--R (125125A a b + 49049B a b)e + (1021020A a b + 750750B a b )d e +--R + +--R 2 4 3 3 2 11 +--R (1951950A a b + 2552550B a b )d e +--R + +--R 5 2 4 3 10 +--R (1061060A a b + 2602600B a b )d e +--R + +--R 6 5 4 9 6 5 8 +--R (135135A b + 795795B a b )d e + 54054B b d e +--R * +--R 9 +--R x +--R + +--R 5 6 13 4 2 5 12 +--R (55341A a b + 9009B a )e + (849420A a b + 332046B a b)d e +--R + +--R 3 3 4 2 2 11 +--R (2895750A a b + 2123550B a b )d e +--R + +--R 2 4 3 3 3 10 +--R (2960100A a b + 3861000B a b )d e +--R + +--R 5 2 4 4 9 6 5 5 8 +--R (907335A a b + 2220075B a b )d e + (61776A b + 362934B a b )d e +--R + +--R 6 6 7 +--R 10296B b d e +--R * +--R 8 +--R x +--R + +--R 6 13 5 6 12 +--R 10296A a e + (380952A a b + 61776B a )d e +--R + +--R 4 2 5 2 11 +--R (2445300A a b + 952380B a b)d e +--R + +--R 3 3 4 2 3 10 +--R (4461600A a b + 3260400B a b )d e +--R + +--R 2 4 3 3 4 9 +--R (2574000A a b + 3346200B a b )d e +--R + +--R 5 2 4 5 8 6 5 6 7 +--R (422136A a b + 1029600B a b )d e + (12012A b + 70356B a b )d e +--R * +--R 7 +--R x +--R + +--R 6 12 5 6 2 11 +--R 72072A a d e + (1117116A a b + 180180B a )d e +--R + +--R 4 2 5 3 10 +--R (3843840A a b + 1489488B a b)d e +--R + +--R 3 3 4 2 4 9 +--R (3963960A a b + 2882880B a b )d e +--R + +--R 2 4 3 3 5 8 5 2 4 6 7 +--R (1225224A a b + 1585584B a b )d e + (84084A a b + 204204B a b )d e +--R * +--R 6 +--R x +--R + +--R 6 2 11 5 6 3 10 +--R 216216A a d e + (1801800A a b + 288288B a )d e +--R + +--R 4 2 5 4 9 +--R (3513510A a b + 1351350B a b)d e +--R + +--R 3 3 4 2 5 8 2 4 3 3 6 7 +--R (1945944A a b + 1405404B a b )d e + (252252A a b + 324324B a b )d e +--R * +--R 5 +--R x +--R + +--R 6 3 10 5 6 4 9 +--R 360360A a d e + (1711710A a b + 270270B a )d e +--R + +--R 4 2 5 5 8 3 3 4 2 6 7 +--R (1801800A a b + 684684B a b)d e + (420420A a b + 300300B a b )d e +--R * +--R 4 +--R x +--R + +--R 6 4 9 5 6 5 8 +--R 360360A a d e + (936936A a b + 144144B a )d e +--R + +--R 4 2 5 6 7 +--R (420420A a b + 156156B a b)d e +--R * +--R 3 +--R x +--R + +--R 6 5 8 5 6 6 7 2 6 6 7 +--R (216216A a d e + (252252A a b + 36036B a )d e )x + 72072A a d e x +--R / +--R 7 7 +--R 72072b e x + 72072a e +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 12 5 4 6 5 5 11 +--R B b e x + ((A b + 5B a b )e + 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 10 +--R ((5A a b + 10B a b )e + (6A b + 30B a b )d e + 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (10A a b + 10B a b )e + (30A a b + 60B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (15A b + 75B a b )d e + 20B b d e +--R * +--R 9 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (10A a b + 5B a b)e + (60A a b + 60B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (75A a b + 150B a b )d e + (20A b + 100B a b )d e + 15B b d e +--R * +--R 8 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (5A a b + B a )e + (60A a b + 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (150A a b + 150B a b )d e + (100A a b + 200B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (15A b + 75B a b )d e + 6B b d e +--R * +--R 7 +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R A a e + (30A a b + 6B a )d e + (150A a b + 75B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (200A a b + 200B a b )d e + (75A a b + 150B a b )d e +--R + +--R 5 4 5 5 6 +--R (6A b + 30B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 5 5 4 5 2 4 3 2 4 3 3 +--R 6A a d e + (75A a b + 15B a )d e + (200A a b + 100B a b)d e +--R + +--R 2 3 3 2 4 2 4 2 3 5 +--R (150A a b + 150B a b )d e + (30A a b + 60B a b )d e +--R + +--R 5 4 6 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 5 2 4 4 5 3 3 3 2 4 4 2 +--R 15A a d e + (100A a b + 20B a )d e + (150A a b + 75B a b)d e +--R + +--R 2 3 3 2 5 4 2 3 6 +--R (60A a b + 60B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 3 4 5 4 2 3 2 4 5 +--R 20A a d e + (75A a b + 15B a )d e + (60A a b + 30B a b)d e +--R + +--R 2 3 3 2 6 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 4 2 4 5 5 3 2 4 6 2 +--R (15A a d e + (30A a b + 6B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 5 4 5 6 5 6 +--R (6A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 13 6 5 6 6 5 12 +--R - B b e x + ((- A b - 6B a b )e - 6B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 11 +--R ((- 6A a b - 15B a b )e + (- 6A b - 36B a b )d e - 15B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 15A a b - 20B a b )e + (- 36A a b - 90B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 15A b - 90B a b )d e - 20B b d e +--R * +--R 10 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 20A a b - 15B a b )e + (- 90A a b - 120B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (- 90A a b - 225B a b )d e + (- 20A b - 120B a b )d e - 15B b d e +--R * +--R 9 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 15A a b - 6B a b)e + (- 120A a b - 90B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 225A a b - 300B a b )d e + (- 120A a b - 300B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 15A b - 90B a b )d e - 6B b d e +--R * +--R 8 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 6A a b - B a )e + (- 90A a b - 36B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 300A a b - 225B a b )d e + (- 300A a b - 400B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 90A a b - 225B a b )d e + (- 6A b - 36B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - A a e + (- 36A a b - 6B a )d e + (- 225A a b - 90B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 400A a b - 300B a b )d e + (- 225A a b - 300B a b )d e +--R + +--R 5 2 4 5 6 5 6 +--R (- 36A a b - 90B a b )d e + (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 6 5 5 6 2 4 4 2 5 3 3 +--R - 6A a d e + (- 90A a b - 15B a )d e + (- 300A a b - 120B a b)d e +--R + +--R 3 3 4 2 4 2 2 4 3 3 5 +--R (- 300A a b - 225B a b )d e + (- 90A a b - 120B a b )d e +--R + +--R 5 2 4 6 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 6 2 4 5 6 3 3 +--R - 15A a d e + (- 120A a b - 20B a )d e +--R + +--R 4 2 5 4 2 3 3 4 2 5 +--R (- 225A a b - 90B a b)d e + (- 120A a b - 90B a b )d e +--R + +--R 2 4 3 3 6 +--R (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 3 5 6 4 2 4 2 5 5 +--R - 20A a d e + (- 90A a b - 15B a )d e + (- 90A a b - 36B a b)d e +--R + +--R 3 3 4 2 6 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 4 2 5 6 5 4 2 5 6 2 +--R (- 15A a d e + (- 36A a b - 6B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 5 5 6 6 6 6 +--R (- 6A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1378 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 10 4 3 5 4 4 9 +--R B b e x + ((A b + 4B a b )e + 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 8 +--R ((4A a b + 6B a b )e + (5A b + 20B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (6A a b + 4B a b)e + (20A a b + 30B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (10A b + 40B a b )d e + 10B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b + B a )e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (40A a b + 60B a b )d e + (10A b + 40B a b )d e + 5B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (20A a b + 5B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (40A a b + 60B a b )d e + (5A b + 20B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R 5A a d e + (40A a b + 10B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 4 4 3 5 +--R (20A a b + 30B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 3 2 2 2 3 4 +--R 10A a d e + (40A a b + 10B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 5 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 2 +--R (10A a d e + (20A a b + 5B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 4 3 4 5 4 5 +--R (5A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1378 +r0:=1/99*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^6*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)-1/44*(b*d-a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)+1/22*(2*A*b*e-B*(b*d+_ + a*e))*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+1/12*B*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)+1/924*(b*d-a*e)^4*(2*A*b*e-_ + B*(b*d+a*e))*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)-_ + 1/5544*(b*d-a*e)^5*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^7*(a+b*x))-1/264*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*_ + (a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 12 12 5 4 12 5 11 11 +--R 462B b e x + ((504A b + 2520B a b )e + 2520B b d e )x +--R + +--R 4 2 3 12 5 4 11 +--R (2772A a b + 5544B a b )e + (2772A b + 13860B a b )d e +--R + +--R 5 2 10 +--R 5544B b d e +--R * +--R 10 +--R x +--R + +--R 2 3 3 2 12 4 2 3 11 +--R (6160A a b + 6160B a b )e + (15400A a b + 30800B a b )d e +--R + +--R 5 4 2 10 5 3 9 +--R (6160A b + 30800B a b )d e + 6160B b d e +--R * +--R 9 +--R x +--R + +--R 3 2 4 12 2 3 3 2 11 +--R (6930A a b + 3465B a b)e + (34650A a b + 34650B a b )d e +--R + +--R 4 2 3 2 10 5 4 3 9 +--R (34650A a b + 69300B a b )d e + (6930A b + 34650B a b )d e +--R + +--R 5 4 8 +--R 3465B b d e +--R * +--R 8 +--R x +--R + +--R 4 5 12 3 2 4 11 +--R (3960A a b + 792B a )e + (39600A a b + 19800B a b)d e +--R + +--R 2 3 3 2 2 10 4 2 3 3 9 +--R (79200A a b + 79200B a b )d e + (39600A a b + 79200B a b )d e +--R + +--R 5 4 4 8 5 5 7 +--R (3960A b + 19800B a b )d e + 792B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 11 +--R 924A a e + (23100A a b + 4620B a )d e +--R + +--R 3 2 4 2 10 2 3 3 2 3 9 +--R (92400A a b + 46200B a b)d e + (92400A a b + 92400B a b )d e +--R + +--R 4 2 3 4 8 5 4 5 7 +--R (23100A a b + 46200B a b )d e + (924A b + 4620B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 11 4 5 2 10 +--R 5544A a d e + (55440A a b + 11088B a )d e +--R + +--R 3 2 4 3 9 2 3 3 2 4 8 +--R (110880A a b + 55440B a b)d e + (55440A a b + 55440B a b )d e +--R + +--R 4 2 3 5 7 +--R (5544A a b + 11088B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 2 10 4 5 3 9 +--R 13860A a d e + (69300A a b + 13860B a )d e +--R + +--R 3 2 4 4 8 2 3 3 2 5 7 +--R (69300A a b + 34650B a b)d e + (13860A a b + 13860B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 3 9 4 5 4 8 +--R 18480A a d e + (46200A a b + 9240B a )d e +--R + +--R 3 2 4 5 7 +--R (18480A a b + 9240B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 4 8 4 5 5 7 2 5 5 7 +--R (13860A a d e + (13860A a b + 2772B a )d e )x + 5544A a d e x +--R + +--R 5 6 6 4 5 7 5 3 2 4 8 4 +--R 924A a d e + (- 660A a b - 132B a )d e + (330A a b + 165B a b)d e +--R + +--R 2 3 3 2 9 3 4 2 3 10 2 +--R (- 110A a b - 110B a b )d e + (22A a b + 44B a b )d e +--R + +--R 5 4 11 5 12 +--R (- 2A b - 10B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 5544b e x + 5544a e +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 12 5 4 5 5 4 11 +--R 462B b e x + ((504A b + 2520B a b )e + 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (2772A a b + 5544B a b )e + (2772A b + 13860B a b )d e +--R + +--R 5 2 3 +--R 5544B b d e +--R * +--R 10 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (6160A a b + 6160B a b )e + (15400A a b + 30800B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (6160A b + 30800B a b )d e + 6160B b d e +--R * +--R 9 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (6930A a b + 3465B a b)e + (34650A a b + 34650B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (34650A a b + 69300B a b )d e + (6930A b + 34650B a b )d e +--R + +--R 5 4 +--R 3465B b d e +--R * +--R 8 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (3960A a b + 792B a )e + (39600A a b + 19800B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (79200A a b + 79200B a b )d e + (39600A a b + 79200B a b )d e +--R + +--R 5 4 4 5 5 +--R (3960A b + 19800B a b )d e + 792B b d +--R * +--R 7 +--R x +--R + +--R 5 5 4 5 4 +--R 924A a e + (23100A a b + 4620B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (92400A a b + 46200B a b)d e + (92400A a b + 92400B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (23100A a b + 46200B a b )d e + (924A b + 4620B a b )d +--R * +--R 6 +--R x +--R + +--R 5 4 4 5 2 3 +--R 5544A a d e + (55440A a b + 11088B a )d e +--R + +--R 3 2 4 3 2 2 3 3 2 4 +--R (110880A a b + 55440B a b)d e + (55440A a b + 55440B a b )d e +--R + +--R 4 2 3 5 +--R (5544A a b + 11088B a b )d +--R * +--R 5 +--R x +--R + +--R 5 2 3 4 5 3 2 +--R 13860A a d e + (69300A a b + 13860B a )d e +--R + +--R 3 2 4 4 2 3 3 2 5 +--R (69300A a b + 34650B a b)d e + (13860A a b + 13860B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 2 4 5 4 +--R 18480A a d e + (46200A a b + 9240B a )d e +--R + +--R 3 2 4 5 +--R (18480A a b + 9240B a b)d +--R * +--R 3 +--R x +--R + +--R 5 4 4 5 5 2 5 5 +--R (13860A a d e + (13860A a b + 2772B a )d )x + 5544A a d x +--R / +--R 5544 +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 12 12 5 4 12 5 11 11 +--R - 462B b e x + ((- 504A b - 2520B a b )e - 2520B b d e )x +--R + +--R 4 2 3 12 5 4 11 +--R (- 2772A a b - 5544B a b )e + (- 2772A b - 13860B a b )d e +--R + +--R 5 2 10 +--R - 5544B b d e +--R * +--R 10 +--R x +--R + +--R 2 3 3 2 12 +--R (- 6160A a b - 6160B a b )e +--R + +--R 4 2 3 11 +--R (- 15400A a b - 30800B a b )d e +--R + +--R 5 4 2 10 5 3 9 +--R (- 6160A b - 30800B a b )d e - 6160B b d e +--R * +--R 9 +--R x +--R + +--R 3 2 4 12 +--R (- 6930A a b - 3465B a b)e +--R + +--R 2 3 3 2 11 +--R (- 34650A a b - 34650B a b )d e +--R + +--R 4 2 3 2 10 +--R (- 34650A a b - 69300B a b )d e +--R + +--R 5 4 3 9 5 4 8 +--R (- 6930A b - 34650B a b )d e - 3465B b d e +--R * +--R 8 +--R x +--R + +--R 4 5 12 3 2 4 11 +--R (- 3960A a b - 792B a )e + (- 39600A a b - 19800B a b)d e +--R + +--R 2 3 3 2 2 10 +--R (- 79200A a b - 79200B a b )d e +--R + +--R 4 2 3 3 9 +--R (- 39600A a b - 79200B a b )d e +--R + +--R 5 4 4 8 5 5 7 +--R (- 3960A b - 19800B a b )d e - 792B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 11 +--R - 924A a e + (- 23100A a b - 4620B a )d e +--R + +--R 3 2 4 2 10 +--R (- 92400A a b - 46200B a b)d e +--R + +--R 2 3 3 2 3 9 +--R (- 92400A a b - 92400B a b )d e +--R + +--R 4 2 3 4 8 5 4 5 7 +--R (- 23100A a b - 46200B a b )d e + (- 924A b - 4620B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 11 4 5 2 10 +--R - 5544A a d e + (- 55440A a b - 11088B a )d e +--R + +--R 3 2 4 3 9 +--R (- 110880A a b - 55440B a b)d e +--R + +--R 2 3 3 2 4 8 +--R (- 55440A a b - 55440B a b )d e +--R + +--R 4 2 3 5 7 +--R (- 5544A a b - 11088B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 2 10 4 5 3 9 +--R - 13860A a d e + (- 69300A a b - 13860B a )d e +--R + +--R 3 2 4 4 8 +--R (- 69300A a b - 34650B a b)d e +--R + +--R 2 3 3 2 5 7 +--R (- 13860A a b - 13860B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 3 9 4 5 4 8 +--R - 18480A a d e + (- 46200A a b - 9240B a )d e +--R + +--R 3 2 4 5 7 +--R (- 18480A a b - 9240B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 4 8 4 5 5 7 2 5 5 7 +--R (- 13860A a d e + (- 13860A a b - 2772B a )d e )x - 5544A a d e x +--R + +--R 5 6 6 4 5 7 5 +--R - 924A a d e + (660A a b + 132B a )d e +--R + +--R 3 2 4 8 4 2 3 3 2 9 3 +--R (- 330A a b - 165B a b)d e + (110A a b + 110B a b )d e +--R + +--R 4 2 3 10 2 5 4 11 5 12 +--R (- 22A a b - 44B a b )d e + (2A b + 10B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 12 13 6 5 12 6 11 12 +--R 462B b e x + ((504A b + 2982B a b )e + 2520B b d e )x +--R + +--R 5 2 4 12 6 5 11 +--R (3276A a b + 8064B a b )e + (2772A b + 16380B a b )d e +--R + +--R 6 2 10 +--R 5544B b d e +--R * +--R 11 +--R x +--R + +--R 2 4 3 3 12 5 2 4 11 +--R (8932A a b + 11704B a b )e + (18172A a b + 44660B a b )d e +--R + +--R 6 5 2 10 6 3 9 +--R (6160A b + 36344B a b )d e + 6160B b d e +--R * +--R 10 +--R x +--R + +--R 3 3 4 2 12 2 4 3 3 11 +--R (13090A a b + 9625B a b )e + (50050A a b + 65450B a b )d e +--R + +--R 5 2 4 2 10 6 5 3 9 +--R (40810A a b + 100100B a b )d e + (6930A b + 40810B a b )d e +--R + +--R 6 4 8 +--R 3465B b d e +--R * +--R 9 +--R x +--R + +--R 4 2 5 12 3 3 4 2 11 +--R (10890A a b + 4257B a b)e + (74250A a b + 54450B a b )d e +--R + +--R 2 4 3 3 2 10 5 2 4 3 9 +--R (113850A a b + 148500B a b )d e + (46530A a b + 113850B a b )d e +--R + +--R 6 5 4 8 6 5 7 +--R (3960A b + 23265B a b )d e + 792B b d e +--R * +--R 8 +--R x +--R + +--R 5 6 12 4 2 5 11 +--R (4884A a b + 792B a )e + (62700A a b + 24420B a b)d e +--R + +--R 3 3 4 2 2 10 +--R (171600A a b + 125400B a b )d e +--R + +--R 2 4 3 3 3 9 5 2 4 4 8 +--R (132000A a b + 171600B a b )d e + (27060A a b + 66000B a b )d e +--R + +--R 6 5 5 7 +--R (924A b + 5412B a b )d e +--R * +--R 7 +--R x +--R + +--R 6 12 5 6 11 +--R 924A a e + (28644A a b + 4620B a )d e +--R + +--R 4 2 5 2 10 3 3 4 2 3 9 +--R (147840A a b + 57288B a b)d e + (203280A a b + 147840B a b )d e +--R + +--R 2 4 3 3 4 8 5 2 4 5 7 +--R (78540A a b + 101640B a b )d e + (6468A a b + 15708B a b )d e +--R * +--R 6 +--R x +--R + +--R 6 11 5 6 2 10 +--R 5544A a d e + (69300A a b + 11088B a )d e +--R + +--R 4 2 5 3 9 3 3 4 2 4 8 +--R (180180A a b + 69300B a b)d e + (124740A a b + 90090B a b )d e +--R + +--R 2 4 3 3 5 7 +--R (19404A a b + 24948B a b )d e +--R * +--R 5 +--R x +--R + +--R 6 2 10 5 6 3 9 +--R 13860A a d e + (87780A a b + 13860B a )d e +--R + +--R 4 2 5 4 8 3 3 4 2 5 7 +--R (115500A a b + 43890B a b)d e + (32340A a b + 23100B a b )d e +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 6 4 8 +--R 18480A a d e + (60060A a b + 9240B a )d e +--R + +--R 4 2 5 5 7 +--R (32340A a b + 12012B a b)d e +--R * +--R 3 +--R x +--R + +--R 6 4 8 5 6 5 7 2 6 5 7 +--R (13860A a d e + (19404A a b + 2772B a )d e )x + 5544A a d e x +--R / +--R 7 7 +--R 5544b e x + 5544a e +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 5 11 5 4 5 5 4 10 +--R B b e x + ((A b + 5B a b )e + 5B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 9 +--R ((5A a b + 10B a b )e + (5A b + 25B a b )d e + 10B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (10A a b + 10B a b )e + (25A a b + 50B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (10A b + 50B a b )d e + 10B b d e +--R * +--R 8 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (10A a b + 5B a b)e + (50A a b + 50B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (50A a b + 100B a b )d e + (10A b + 50B a b )d e + 5B b d e +--R * +--R 7 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (5A a b + B a )e + (50A a b + 25B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (100A a b + 100B a b )d e + (50A a b + 100B a b )d e +--R + +--R 5 4 4 5 5 +--R (5A b + 25B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R A a e + (25A a b + 5B a )d e + (100A a b + 50B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (100A a b + 100B a b )d e + (25A a b + 50B a b )d e +--R + +--R 5 4 5 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 5A a d e + (50A a b + 10B a )d e + (100A a b + 50B a b)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (50A a b + 50B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 5 3 2 3 2 4 4 +--R 10A a d e + (50A a b + 10B a )d e + (50A a b + 25B a b)d e +--R + +--R 2 3 3 2 5 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 3 2 4 5 4 3 2 4 5 2 +--R (10A a d e + (25A a b + 5B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 4 4 5 5 5 5 +--R (5A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 12 6 5 5 6 4 11 +--R - B b e x + ((- A b - 6B a b )e - 5B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 10 +--R ((- 6A a b - 15B a b )e + (- 5A b - 30B a b )d e - 10B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 15A a b - 20B a b )e + (- 30A a b - 75B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 10A b - 60B a b )d e - 10B b d e +--R * +--R 9 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 20A a b - 15B a b )e + (- 75A a b - 100B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 60A a b - 150B a b )d e + (- 10A b - 60B a b )d e - 5B b d e +--R * +--R 8 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 15A a b - 6B a b)e + (- 100A a b - 75B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 150A a b - 200B a b )d e + (- 60A a b - 150B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 5A b - 30B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 6A a b - B a )e + (- 75A a b - 30B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 200A a b - 150B a b )d e + (- 150A a b - 200B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 30A a b - 75B a b )d e + (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 6 5 5 6 4 4 2 5 2 3 +--R - A a e + (- 30A a b - 5B a )d e + (- 150A a b - 60B a b)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (- 200A a b - 150B a b )d e + (- 75A a b - 100B a b )d e +--R + +--R 5 2 4 5 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 6 4 5 6 2 3 4 2 5 3 2 +--R - 5A a d e + (- 60A a b - 10B a )d e + (- 150A a b - 60B a b)d e +--R + +--R 3 3 4 2 4 2 4 3 3 5 +--R (- 100A a b - 75B a b )d e + (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 2 3 5 6 3 2 4 2 5 4 +--R - 10A a d e + (- 60A a b - 10B a )d e + (- 75A a b - 30B a b)d e +--R + +--R 3 3 4 2 5 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 3 2 5 6 4 4 2 5 5 2 +--R (- 10A a d e + (- 30A a b - 5B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 4 5 6 5 6 5 +--R (- 5A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 1378 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 4 9 4 3 4 4 3 8 +--R B b e x + ((A b + 4B a b )e + 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((4A a b + 6B a b )e + (4A b + 16B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (6A a b + 4B a b)e + (16A a b + 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (6A b + 24B a b )d e + 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (24A a b + 36B a b )d e + (4A b + 16B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R A a e + (16A a b + 4B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (16A a b + 24B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 4A a d e + (24A a b + 6B a )d e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 4 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (6A a d e + (16A a b + 4B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (4A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1378 +r0:=-1/1980*(b*d-a*e)^4*(6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^6*e)-1/660*(b*d-a*e)^2*(6*b*B*d-11*A*b*e+5*a*B*e)*_ + (a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^4*e)-2/495*(b*d-a*e)*_ + (6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^3*e)-1/110*(6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*_ + (d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+1/11*B*(a+b*x)*(d+_ + e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-1/2310*(b*d-a*e)^3*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6 +--R +--R +--R (2) +--R 10 4 10 10 9 4 10 3 9 +--R 1260B b e x + ((1386A b + 5670B a b )e + 5544B b d e )x +--R + +--R 9 2 8 4 10 9 3 +--R (6314A a b + 9730B a b )e + (6160A b + 25256B a b )d e +--R + +--R 10 2 2 +--R 9240B b d e +--R * +--R 8 +--R x +--R + +--R 2 8 3 7 4 9 2 8 3 +--R (11011A a b + 7595B a b )e + (28490A a b + 44044B a b )d e +--R + +--R 10 9 2 2 10 3 +--R (10395A b + 42735B a b )d e + 6930B b d e +--R * +--R 7 +--R x +--R + +--R 3 7 4 6 4 2 8 3 7 3 +--R (8789A a b + 2305B a b )e + (50710A a b + 35156B a b )d e +--R + +--R 9 2 8 2 2 10 9 3 +--R (49005A a b + 76065B a b )d e + (7920A b + 32670B a b )d e +--R + +--R 10 4 +--R 1980B b d +--R * +--R 6 +--R x +--R + +--R 4 6 5 5 4 3 7 4 6 3 +--R (2761A a b + 5B a b )e + (41690A a b + 11044B a b )d e +--R + +--R 2 8 3 7 2 2 9 2 8 3 +--R (89595A a b + 62535B a b )d e + (38280A a b + 59730B a b )d e +--R + +--R 10 9 4 +--R (2310A b + 9570B a b )d +--R * +--R 5 +--R x +--R + +--R 5 5 6 4 4 4 6 5 5 3 +--R (11A a b - 5B a b )e + (13750A a b + 44B a b )d e +--R + +--R 3 7 4 6 2 2 2 8 3 7 3 +--R (76725A a b + 20625B a b )d e + (72600A a b + 51150B a b )d e +--R + +--R 9 2 8 4 +--R (11550A a b + 18150B a b )d +--R * +--R 4 +--R x +--R + +--R 6 4 7 3 4 5 5 6 4 3 +--R (- 11A a b + 5B a b )e + (110A a b - 44B a b )d e +--R + +--R 4 6 5 5 2 2 3 7 4 6 3 +--R (27225A a b + 165B a b )d e + (66000A a b + 18150B a b )d e +--R + +--R 2 8 3 7 4 +--R (23100A a b + 16500B a b )d +--R * +--R 3 +--R x +--R + +--R 7 3 8 2 4 6 4 7 3 3 +--R (11A a b - 5B a b )e + (- 110A a b + 44B a b )d e +--R + +--R 5 5 6 4 2 2 4 6 5 5 3 +--R (495A a b - 165B a b )d e + (26400A a b + 330B a b )d e +--R + +--R 3 7 4 6 4 +--R (23100A a b + 6600B a b )d +--R * +--R 2 +--R x +--R + +--R 8 2 9 4 7 3 8 2 3 +--R (- 11A a b + 5B a b)e + (110A a b - 44B a b )d e +--R + +--R 6 4 7 3 2 2 5 5 6 4 3 +--R (- 495A a b + 165B a b )d e + (1320A a b - 330B a b )d e +--R + +--R 4 6 5 5 4 +--R (11550A a b + 330B a b )d +--R * +--R x +--R + +--R 9 10 4 8 2 9 3 +--R (11A a b - 5B a )e + (- 110A a b + 44B a b)d e +--R + +--R 7 3 8 2 2 2 6 4 7 3 3 +--R (495A a b - 165B a b )d e + (- 1320A a b + 330B a b )d e +--R + +--R 5 5 6 4 4 +--R (2310A a b - 330B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 +--R 13860b +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 11 5 4 4 5 3 10 +--R 1260B b e x + ((1386A b + 6930B a b )e + 5544B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (7700A a b + 15400B a b )e + (6160A b + 30800B a b )d e +--R + +--R 5 2 2 +--R 9240B b d e +--R * +--R 9 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (17325A a b + 17325B a b )e + (34650A a b + 69300B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (10395A b + 51975B a b )d e + 6930B b d e +--R * +--R 8 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (19800A a b + 9900B a b)e + (79200A a b + 79200B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (59400A a b + 118800B a b )d e + (7920A b + 39600B a b )d e +--R + +--R 5 4 +--R 1980B b d +--R * +--R 7 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (11550A a b + 2310B a )e + (92400A a b + 46200B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (138600A a b + 138600B a b )d e + (46200A a b + 92400B a b )d e +--R + +--R 5 4 4 +--R (2310A b + 11550B a b )d +--R * +--R 6 +--R x +--R + +--R 5 4 4 5 3 +--R 2772A a e + (55440A a b + 11088B a )d e +--R + +--R 3 2 4 2 2 2 3 3 2 3 +--R (166320A a b + 83160B a b)d e + (110880A a b + 110880B a b )d e +--R + +--R 4 2 3 4 +--R (13860A a b + 27720B a b )d +--R * +--R 5 +--R x +--R + +--R 5 3 4 5 2 2 +--R 13860A a d e + (103950A a b + 20790B a )d e +--R + +--R 3 2 4 3 2 3 3 2 4 +--R (138600A a b + 69300B a b)d e + (34650A a b + 34650B a b )d +--R * +--R 4 +--R x +--R + +--R 5 2 2 4 5 3 +--R 27720A a d e + (92400A a b + 18480B a )d e +--R + +--R 3 2 4 4 +--R (46200A a b + 23100B a b)d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 4 2 5 4 +--R (27720A a d e + (34650A a b + 6930B a )d )x + 13860A a d x +--R / +--R 13860 +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 10 4 10 10 9 4 10 3 9 +--R - 1260B b e x + ((- 1386A b - 5670B a b )e - 5544B b d e )x +--R + +--R 9 2 8 4 10 9 3 +--R (- 6314A a b - 9730B a b )e + (- 6160A b - 25256B a b )d e +--R + +--R 10 2 2 +--R - 9240B b d e +--R * +--R 8 +--R x +--R + +--R 2 8 3 7 4 +--R (- 11011A a b - 7595B a b )e +--R + +--R 9 2 8 3 +--R (- 28490A a b - 44044B a b )d e +--R + +--R 10 9 2 2 10 3 +--R (- 10395A b - 42735B a b )d e - 6930B b d e +--R * +--R 7 +--R x +--R + +--R 3 7 4 6 4 2 8 3 7 3 +--R (- 8789A a b - 2305B a b )e + (- 50710A a b - 35156B a b )d e +--R + +--R 9 2 8 2 2 +--R (- 49005A a b - 76065B a b )d e +--R + +--R 10 9 3 10 4 +--R (- 7920A b - 32670B a b )d e - 1980B b d +--R * +--R 6 +--R x +--R + +--R 4 6 5 5 4 3 7 4 6 3 +--R (- 2761A a b - 5B a b )e + (- 41690A a b - 11044B a b )d e +--R + +--R 2 8 3 7 2 2 +--R (- 89595A a b - 62535B a b )d e +--R + +--R 9 2 8 3 10 9 4 +--R (- 38280A a b - 59730B a b )d e + (- 2310A b - 9570B a b )d +--R * +--R 5 +--R x +--R + +--R 5 5 6 4 4 4 6 5 5 3 +--R (- 11A a b + 5B a b )e + (- 13750A a b - 44B a b )d e +--R + +--R 3 7 4 6 2 2 +--R (- 76725A a b - 20625B a b )d e +--R + +--R 2 8 3 7 3 9 2 8 4 +--R (- 72600A a b - 51150B a b )d e + (- 11550A a b - 18150B a b )d +--R * +--R 4 +--R x +--R + +--R 6 4 7 3 4 5 5 6 4 3 +--R (11A a b - 5B a b )e + (- 110A a b + 44B a b )d e +--R + +--R 4 6 5 5 2 2 +--R (- 27225A a b - 165B a b )d e +--R + +--R 3 7 4 6 3 2 8 3 7 4 +--R (- 66000A a b - 18150B a b )d e + (- 23100A a b - 16500B a b )d +--R * +--R 3 +--R x +--R + +--R 7 3 8 2 4 6 4 7 3 3 +--R (- 11A a b + 5B a b )e + (110A a b - 44B a b )d e +--R + +--R 5 5 6 4 2 2 4 6 5 5 3 +--R (- 495A a b + 165B a b )d e + (- 26400A a b - 330B a b )d e +--R + +--R 3 7 4 6 4 +--R (- 23100A a b - 6600B a b )d +--R * +--R 2 +--R x +--R + +--R 8 2 9 4 7 3 8 2 3 +--R (11A a b - 5B a b)e + (- 110A a b + 44B a b )d e +--R + +--R 6 4 7 3 2 2 5 5 6 4 3 +--R (495A a b - 165B a b )d e + (- 1320A a b + 330B a b )d e +--R + +--R 4 6 5 5 4 +--R (- 11550A a b - 330B a b )d +--R * +--R x +--R + +--R 9 10 4 8 2 9 3 +--R (- 11A a b + 5B a )e + (110A a b - 44B a b)d e +--R + +--R 7 3 8 2 2 2 6 4 7 3 3 +--R (- 495A a b + 165B a b )d e + (1320A a b - 330B a b )d e +--R + +--R 5 5 6 4 4 +--R (- 2310A a b + 330B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 11 4 11 11 10 4 11 3 10 +--R 1260B b e x + ((1386A b + 6930B a b )e + 5544B b d e )x +--R + +--R 10 2 9 4 11 10 3 +--R (7700A a b + 15400B a b )e + (6160A b + 30800B a b )d e +--R + +--R 11 2 2 +--R 9240B b d e +--R * +--R 9 +--R x +--R + +--R 2 9 3 8 4 10 2 9 3 +--R (17325A a b + 17325B a b )e + (34650A a b + 69300B a b )d e +--R + +--R 11 10 2 2 11 3 +--R (10395A b + 51975B a b )d e + 6930B b d e +--R * +--R 8 +--R x +--R + +--R 3 8 4 7 4 2 9 3 8 3 +--R (19800A a b + 9900B a b )e + (79200A a b + 79200B a b )d e +--R + +--R 10 2 9 2 2 11 10 3 +--R (59400A a b + 118800B a b )d e + (7920A b + 39600B a b )d e +--R + +--R 11 4 +--R 1980B b d +--R * +--R 7 +--R x +--R + +--R 4 7 5 6 4 3 8 4 7 3 +--R (11550A a b + 2310B a b )e + (92400A a b + 46200B a b )d e +--R + +--R 2 9 3 8 2 2 10 2 9 3 +--R (138600A a b + 138600B a b )d e + (46200A a b + 92400B a b )d e +--R + +--R 11 10 4 +--R (2310A b + 11550B a b )d +--R * +--R 6 +--R x +--R + +--R 5 6 4 4 7 5 6 3 +--R 2772A a b e + (55440A a b + 11088B a b )d e +--R + +--R 3 8 4 7 2 2 2 9 3 8 3 +--R (166320A a b + 83160B a b )d e + (110880A a b + 110880B a b )d e +--R + +--R 10 2 9 4 +--R (13860A a b + 27720B a b )d +--R * +--R 5 +--R x +--R + +--R 5 6 3 4 7 5 6 2 2 +--R 13860A a b d e + (103950A a b + 20790B a b )d e +--R + +--R 3 8 4 7 3 2 9 3 8 4 +--R (138600A a b + 69300B a b )d e + (34650A a b + 34650B a b )d +--R * +--R 4 +--R x +--R + +--R 5 6 2 2 4 7 5 6 3 +--R 27720A a b d e + (92400A a b + 18480B a b )d e +--R + +--R 3 8 4 7 4 +--R (46200A a b + 23100B a b )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 7 5 6 4 2 5 6 4 +--R (27720A a b d e + (34650A a b + 6930B a b )d )x + 13860A a b d x +--R / +--R 6 +--R 13860b +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 4 10 5 4 4 5 3 9 +--R B b e x + ((A b + 5B a b )e + 4B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 8 +--R ((5A a b + 10B a b )e + (4A b + 20B a b )d e + 6B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (10A a b + 10B a b )e + (20A a b + 40B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (6A b + 30B a b )d e + 4B b d e +--R * +--R 7 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (10A a b + 5B a b)e + (40A a b + 40B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (30A a b + 60B a b )d e + (4A b + 20B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (5A a b + B a )e + (40A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (60A a b + 60B a b )d e + (20A a b + 40B a b )d e +--R + +--R 5 4 4 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R A a e + (20A a b + 4B a )d e + (60A a b + 30B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (40A a b + 40B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 4 5 2 2 3 2 4 3 +--R 4A a d e + (30A a b + 6B a )d e + (40A a b + 20B a b)d e +--R + +--R 2 3 3 2 4 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 2 4 5 3 3 2 4 4 2 +--R (6A a d e + (20A a b + 4B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 3 4 5 4 5 4 +--R (4A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 4 11 6 5 4 6 3 10 +--R - B b e x + ((- A b - 6B a b )e - 4B b d e )x +--R + +--R 5 2 4 4 6 5 3 6 2 2 9 +--R ((- 6A a b - 15B a b )e + (- 4A b - 24B a b )d e - 6B b d e )x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 15A a b - 20B a b )e + (- 24A a b - 60B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (- 6A b - 36B a b )d e - 4B b d e +--R * +--R 8 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (- 20A a b - 15B a b )e + (- 60A a b - 80B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (- 36A a b - 90B a b )d e + (- 4A b - 24B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 15A a b - 6B a b)e + (- 80A a b - 60B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 90A a b - 120B a b )d e + (- 24A a b - 60B a b )d e +--R + +--R 6 5 4 +--R (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 6A a b - B a )e + (- 60A a b - 24B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 120A a b - 90B a b )d e + (- 60A a b - 80B a b )d e +--R + +--R 5 2 4 4 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R - A a e + (- 24A a b - 4B a )d e + (- 90A a b - 36B a b)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (- 80A a b - 60B a b )d e + (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 5 6 2 2 4 2 5 3 +--R - 4A a d e + (- 36A a b - 6B a )d e + (- 60A a b - 24B a b)d e +--R + +--R 3 3 4 2 4 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 2 5 6 3 4 2 5 4 2 +--R (- 6A a d e + (- 24A a b - 4B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 3 5 6 4 6 4 +--R (- 4A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 565 + +)clear all + +--S 566 of 1378 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1378 +r0:=-1/360*(b*d-a*e)^3*(3*b*B*d-5*A*b*e+2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^5*e)-1/120*(b*d-a*e)*(3*b*B*d-5*A*b*e+2*a*B*e)*_ + (a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^3*e)-1/45*(3*b*B*d-_ + 5*A*b*e+2*a*B*e)*(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+_ + 1/10*B*(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 1/420*(b*d-a*e)^2*(3*b*B*d-5*A*b*e+2*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^5 +--R +--R +--R (2) +--R 9 3 9 9 8 3 9 2 8 +--R 252B b e x + ((280A b + 1148B a b )e + 840B b d e )x +--R + +--R 8 2 7 3 9 8 2 +--R (1295A a b + 2002B a b )e + (945A b + 3885B a b )d e +--R + +--R 9 2 +--R 945B b d e +--R * +--R 7 +--R x +--R + +--R 2 7 3 6 3 8 2 7 2 +--R (2305A a b + 1598B a b )e + (4455A a b + 6915B a b )d e +--R + +--R 9 8 2 9 3 +--R (1080A b + 4455B a b )d e + 360B b d +--R * +--R 6 +--R x +--R + +--R 3 6 4 5 3 2 7 3 6 2 +--R (1895A a b + 502B a b )e + (8145A a b + 5685B a b )d e +--R + +--R 8 2 7 2 9 8 3 +--R (5220A a b + 8145B a b )d e + (420A b + 1740B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 5 4 3 3 6 4 5 2 +--R (625A a b + 2B a b )e + (6975A a b + 1875B a b )d e +--R + +--R 2 7 3 6 2 8 2 7 3 +--R (9900A a b + 6975B a b )d e + (2100A a b + 3300B a b )d +--R * +--R 4 +--R x +--R + +--R 5 4 6 3 3 4 5 5 4 2 +--R (5A a b - 2B a b )e + (2475A a b + 15B a b )d e +--R + +--R 3 6 4 5 2 2 7 3 6 3 +--R (9000A a b + 2475B a b )d e + (4200A a b + 3000B a b )d +--R * +--R 3 +--R x +--R + +--R 6 3 7 2 3 5 4 6 3 2 +--R (- 5A a b + 2B a b )e + (45A a b - 15B a b )d e +--R + +--R 4 5 5 4 2 3 6 4 5 3 +--R (3600A a b + 45B a b )d e + (4200A a b + 1200B a b )d +--R * +--R 2 +--R x +--R + +--R 7 2 8 3 6 3 7 2 2 +--R (5A a b - 2B a b)e + (- 45A a b + 15B a b )d e +--R + +--R 5 4 6 3 2 4 5 5 4 3 +--R (180A a b - 45B a b )d e + (2100A a b + 60B a b )d +--R * +--R x +--R + +--R 8 9 3 7 2 8 2 +--R (- 5A a b + 2B a )e + (45A a b - 15B a b)d e +--R + +--R 6 3 7 2 2 5 4 6 3 3 +--R (- 180A a b + 45B a b )d e + (420A a b - 60B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 2520b +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 10 5 4 3 5 2 9 +--R 252B b e x + ((280A b + 1400B a b )e + 840B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 8 +--R ((1575A a b + 3150B a b )e + (945A b + 4725B a b )d e + 945B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (3600A a b + 3600B a b )e + (5400A a b + 10800B a b )d e +--R + +--R 5 4 2 5 3 +--R (1080A b + 5400B a b )d e + 360B b d +--R * +--R 7 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (4200A a b + 2100B a b)e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (6300A a b + 12600B a b )d e + (420A b + 2100B a b )d +--R * +--R 6 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (2520A a b + 504B a )e + (15120A a b + 7560B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (15120A a b + 15120B a b )d e + (2520A a b + 5040B a b )d +--R * +--R 5 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R 630A a e + (9450A a b + 1890B a )d e + (18900A a b + 9450B a b)d e +--R + +--R 2 3 3 2 3 +--R (6300A a b + 6300B a b )d +--R * +--R 4 +--R x +--R + +--R 5 2 4 5 2 +--R 2520A a d e + (12600A a b + 2520B a )d e +--R + +--R 3 2 4 3 +--R (8400A a b + 4200B a b)d +--R * +--R 3 +--R x +--R + +--R 5 2 4 5 3 2 5 3 +--R (3780A a d e + (6300A a b + 1260B a )d )x + 2520A a d x +--R / +--R 2520 +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 3 9 9 8 3 9 2 8 +--R - 252B b e x + ((- 280A b - 1148B a b )e - 840B b d e )x +--R + +--R 8 2 7 3 9 8 2 +--R (- 1295A a b - 2002B a b )e + (- 945A b - 3885B a b )d e +--R + +--R 9 2 +--R - 945B b d e +--R * +--R 7 +--R x +--R + +--R 2 7 3 6 3 8 2 7 2 +--R (- 2305A a b - 1598B a b )e + (- 4455A a b - 6915B a b )d e +--R + +--R 9 8 2 9 3 +--R (- 1080A b - 4455B a b )d e - 360B b d +--R * +--R 6 +--R x +--R + +--R 3 6 4 5 3 2 7 3 6 2 +--R (- 1895A a b - 502B a b )e + (- 8145A a b - 5685B a b )d e +--R + +--R 8 2 7 2 9 8 3 +--R (- 5220A a b - 8145B a b )d e + (- 420A b - 1740B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 5 4 3 3 6 4 5 2 +--R (- 625A a b - 2B a b )e + (- 6975A a b - 1875B a b )d e +--R + +--R 2 7 3 6 2 8 2 7 3 +--R (- 9900A a b - 6975B a b )d e + (- 2100A a b - 3300B a b )d +--R * +--R 4 +--R x +--R + +--R 5 4 6 3 3 4 5 5 4 2 +--R (- 5A a b + 2B a b )e + (- 2475A a b - 15B a b )d e +--R + +--R 3 6 4 5 2 2 7 3 6 3 +--R (- 9000A a b - 2475B a b )d e + (- 4200A a b - 3000B a b )d +--R * +--R 3 +--R x +--R + +--R 6 3 7 2 3 5 4 6 3 2 +--R (5A a b - 2B a b )e + (- 45A a b + 15B a b )d e +--R + +--R 4 5 5 4 2 3 6 4 5 3 +--R (- 3600A a b - 45B a b )d e + (- 4200A a b - 1200B a b )d +--R * +--R 2 +--R x +--R + +--R 7 2 8 3 6 3 7 2 2 +--R (- 5A a b + 2B a b)e + (45A a b - 15B a b )d e +--R + +--R 5 4 6 3 2 4 5 5 4 3 +--R (- 180A a b + 45B a b )d e + (- 2100A a b - 60B a b )d +--R * +--R x +--R + +--R 8 9 3 7 2 8 2 +--R (5A a b - 2B a )e + (- 45A a b + 15B a b)d e +--R + +--R 6 3 7 2 2 5 4 6 3 3 +--R (180A a b - 45B a b )d e + (- 420A a b + 60B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 10 3 10 10 9 3 10 2 9 +--R 252B b e x + ((280A b + 1400B a b )e + 840B b d e )x +--R + +--R 9 2 8 3 10 9 2 +--R (1575A a b + 3150B a b )e + (945A b + 4725B a b )d e +--R + +--R 10 2 +--R 945B b d e +--R * +--R 8 +--R x +--R + +--R 2 8 3 7 3 9 2 8 2 +--R (3600A a b + 3600B a b )e + (5400A a b + 10800B a b )d e +--R + +--R 10 9 2 10 3 +--R (1080A b + 5400B a b )d e + 360B b d +--R * +--R 7 +--R x +--R + +--R 3 7 4 6 3 2 8 3 7 2 +--R (4200A a b + 2100B a b )e + (12600A a b + 12600B a b )d e +--R + +--R 9 2 8 2 10 9 3 +--R (6300A a b + 12600B a b )d e + (420A b + 2100B a b )d +--R * +--R 6 +--R x +--R + +--R 4 6 5 5 3 3 7 4 6 2 +--R (2520A a b + 504B a b )e + (15120A a b + 7560B a b )d e +--R + +--R 2 8 3 7 2 9 2 8 3 +--R (15120A a b + 15120B a b )d e + (2520A a b + 5040B a b )d +--R * +--R 5 +--R x +--R + +--R 5 5 3 4 6 5 5 2 +--R 630A a b e + (9450A a b + 1890B a b )d e +--R + +--R 3 7 4 6 2 2 8 3 7 3 +--R (18900A a b + 9450B a b )d e + (6300A a b + 6300B a b )d +--R * +--R 4 +--R x +--R + +--R 5 5 2 4 6 5 5 2 +--R 2520A a b d e + (12600A a b + 2520B a b )d e +--R + +--R 3 7 4 6 3 +--R (8400A a b + 4200B a b )d +--R * +--R 3 +--R x +--R + +--R 5 5 2 4 6 5 5 3 2 5 5 3 +--R (3780A a b d e + (6300A a b + 1260B a b )d )x + 2520A a b d x +--R / +--R 5 +--R 2520b +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 3 9 5 4 3 5 2 8 +--R B b e x + ((A b + 5B a b )e + 3B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 7 +--R ((5A a b + 10B a b )e + (3A b + 15B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (10A a b + 10B a b )e + (15A a b + 30B a b )d e +--R + +--R 5 4 2 5 3 +--R (3A b + 15B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (10A a b + 5B a b)e + (30A a b + 30B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (15A a b + 30B a b )d e + (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (5A a b + B a )e + (30A a b + 15B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (30A a b + 30B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A a e + (15A a b + 3B a )d e + (30A a b + 15B a b)d e +--R + +--R 2 3 3 2 3 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 5 2 3 2 4 3 2 +--R (3A a d e + (15A a b + 3B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 2 4 5 3 5 3 +--R (3A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 3 10 6 5 3 6 2 9 +--R - B b e x + ((- A b - 6B a b )e - 3B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 8 +--R ((- 6A a b - 15B a b )e + (- 3A b - 18B a b )d e - 3B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (- 15A a b - 20B a b )e + (- 18A a b - 45B a b )d e +--R + +--R 6 5 2 6 3 +--R (- 3A b - 18B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (- 20A a b - 15B a b )e + (- 45A a b - 60B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 18A a b - 45B a b )d e + (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 15A a b - 6B a b)e + (- 60A a b - 45B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 45A a b - 60B a b )d e + (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 6A a b - B a )e + (- 45A a b - 18B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A a b - 45B a b )d e + (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R - A a e + (- 18A a b - 3B a )d e + (- 45A a b - 18B a b)d e +--R + +--R 3 3 4 2 3 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 2 4 2 5 3 2 +--R (- 3A a d e + (- 18A a b - 3B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 2 5 6 3 6 3 +--R (- 3A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 1378 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1378 +r0:=-1/72*(b*d-a*e)^2*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^4*e)-1/24*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(d+_ + e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+1/9*B*(a+b*x)*(d+e*x)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-1/84*(b*d-a*e)*(2*b*B*d-3*A*b*e+_ + a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4 +--R +--R +--R (2) +--R 8 2 8 8 7 2 8 7 +--R 56B b e x + ((63A b + 259B a b )e + 126B b d e)x +--R + +--R 7 2 6 2 8 7 8 2 6 +--R ((297A a b + 461B a b )e + (144A b + 594B a b )d e + 72B b d )x +--R + +--R 2 6 3 5 2 7 2 6 +--R (543A a b + 379B a b )e + (696A a b + 1086B a b )d e +--R + +--R 8 7 2 +--R (84A b + 348B a b )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (465A a b + 125B a b )e + (1320A a b + 930B a b )d e +--R + +--R 7 2 6 2 +--R (420A a b + 660B a b )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (165A a b + B a b )e + (1200A a b + 330B a b )d e +--R + +--R 2 6 3 5 2 +--R (840A a b + 600B a b )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (3A a b - B a b )e + (480A a b + 6B a b )d e +--R + +--R 3 5 4 4 2 +--R (840A a b + 240B a b )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 3A a b + B a b)e + (24A a b - 6B a b )d e +--R + +--R 4 4 5 3 2 +--R (420A a b + 12B a b )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 5 3 6 2 2 +--R (3A a b - B a )e + (- 24A a b + 6B a b)d e + (84A a b - 12B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 504b +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 9 5 4 2 5 8 +--R 56B b e x + ((63A b + 315B a b )e + 126B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 7 +--R ((360A a b + 720B a b )e + (144A b + 720B a b )d e + 72B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (840A a b + 840B a b )e + (840A a b + 1680B a b )d e +--R + +--R 5 4 2 +--R (84A b + 420B a b )d +--R * +--R 6 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (1008A a b + 504B a b)e + (2016A a b + 2016B a b )d e +--R + +--R 4 2 3 2 +--R (504A a b + 1008B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 2 3 2 4 +--R (630A a b + 126B a )e + (2520A a b + 1260B a b)d e +--R + +--R 2 3 3 2 2 +--R (1260A a b + 1260B a b )d +--R * +--R 4 +--R x +--R + +--R 5 2 4 5 3 2 4 2 3 +--R (168A a e + (1680A a b + 336B a )d e + (1680A a b + 840B a b)d )x +--R + +--R 5 4 5 2 2 5 2 +--R (504A a d e + (1260A a b + 252B a )d )x + 504A a d x +--R / +--R 504 +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 2 8 8 7 2 8 7 +--R - 56B b e x + ((- 63A b - 259B a b )e - 126B b d e)x +--R + +--R 7 2 6 2 8 7 +--R (- 297A a b - 461B a b )e + (- 144A b - 594B a b )d e +--R + +--R 8 2 +--R - 72B b d +--R * +--R 6 +--R x +--R + +--R 2 6 3 5 2 7 2 6 +--R (- 543A a b - 379B a b )e + (- 696A a b - 1086B a b )d e +--R + +--R 8 7 2 +--R (- 84A b - 348B a b )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (- 465A a b - 125B a b )e + (- 1320A a b - 930B a b )d e +--R + +--R 7 2 6 2 +--R (- 420A a b - 660B a b )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (- 165A a b - B a b )e + (- 1200A a b - 330B a b )d e +--R + +--R 2 6 3 5 2 +--R (- 840A a b - 600B a b )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (- 3A a b + B a b )e + (- 480A a b - 6B a b )d e +--R + +--R 3 5 4 4 2 +--R (- 840A a b - 240B a b )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (3A a b - B a b)e + (- 24A a b + 6B a b )d e +--R + +--R 4 4 5 3 2 +--R (- 420A a b - 12B a b )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 +--R (- 3A a b + B a )e + (24A a b - 6B a b)d e +--R + +--R 5 3 6 2 2 +--R (- 84A a b + 12B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 9 2 9 9 8 2 9 8 +--R 56B b e x + ((63A b + 315B a b )e + 126B b d e)x +--R + +--R 8 2 7 2 9 8 9 2 7 +--R ((360A a b + 720B a b )e + (144A b + 720B a b )d e + 72B b d )x +--R + +--R 2 7 3 6 2 8 2 7 +--R (840A a b + 840B a b )e + (840A a b + 1680B a b )d e +--R + +--R 9 8 2 +--R (84A b + 420B a b )d +--R * +--R 6 +--R x +--R + +--R 3 6 4 5 2 2 7 3 6 +--R (1008A a b + 504B a b )e + (2016A a b + 2016B a b )d e +--R + +--R 8 2 7 2 +--R (504A a b + 1008B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 5 4 2 3 6 4 5 +--R (630A a b + 126B a b )e + (2520A a b + 1260B a b )d e +--R + +--R 2 7 3 6 2 +--R (1260A a b + 1260B a b )d +--R * +--R 4 +--R x +--R + +--R 5 4 2 4 5 5 4 +--R 168A a b e + (1680A a b + 336B a b )d e +--R + +--R 3 6 4 5 2 +--R (1680A a b + 840B a b )d +--R * +--R 3 +--R x +--R + +--R 5 4 4 5 5 4 2 2 5 4 2 +--R (504A a b d e + (1260A a b + 252B a b )d )x + 504A a b d x +--R / +--R 4 +--R 504b +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 2 8 5 4 2 5 7 +--R B b e x + ((A b + 5B a b )e + 2B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 6 +--R ((5A a b + 10B a b )e + (2A b + 10B a b )d e + B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (10A a b + 10B a b )e + (10A a b + 20B a b )d e +--R + +--R 5 4 2 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (10A a b + 5B a b)e + (20A a b + 20B a b )d e +--R + +--R 4 2 3 2 +--R (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 4 5 2 3 2 4 +--R (5A a b + B a )e + (20A a b + 10B a b)d e +--R + +--R 2 3 3 2 2 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 5 3 2 4 2 2 +--R (A a e + (10A a b + 2B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 4 5 2 5 2 +--R (2A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 2 9 6 5 2 6 8 +--R - B b e x + ((- A b - 6B a b )e - 2B b d e)x +--R + +--R 5 2 4 2 6 5 6 2 7 +--R ((- 6A a b - 15B a b )e + (- 2A b - 12B a b )d e - B b d )x +--R + +--R 2 4 3 3 2 5 2 4 +--R (- 15A a b - 20B a b )e + (- 12A a b - 30B a b )d e +--R + +--R 6 5 2 +--R (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 20A a b - 15B a b )e + (- 30A a b - 40B a b )d e +--R + +--R 5 2 4 2 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (- 15A a b - 6B a b)e + (- 40A a b - 30B a b )d e +--R + +--R 2 4 3 3 2 +--R (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 6A a b - B a )e + (- 30A a b - 12B a b)d e +--R + +--R 3 3 4 2 2 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 4 2 5 2 2 +--R (- A a e + (- 12A a b - 2B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 5 6 2 6 2 +--R (- 2A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 1378 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1378 +r0:=-1/24*(b*d-a*e)*(3*b*B*d-4*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^3*e)+1/8*B*(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-1/28*(3*b*B*d-4*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^3 +--R +--R +--R (2) +--R 7 7 7 6 7 6 +--R 21B b e x + ((24A b + 99B a b )e + 24B b d)x +--R + +--R 6 2 5 7 6 5 +--R ((116A a b + 181B a b )e + (28A b + 116B a b )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((220A a b + 155B a b )e + (140A a b + 220B a b )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((200A a b + 55B a b )e + (280A a b + 200B a b )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((80A a b + B a b )e + (280A a b + 80B a b )d)x +--R + +--R 5 2 6 4 3 5 2 6 7 +--R ((4A a b - B a b)e + (140A a b + 4B a b )d)x + (- 4A a b + B a )e +--R + +--R 5 2 6 +--R (28A a b - 4B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 168b +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 8 5 4 5 7 +--R 21B b e x + ((24A b + 120B a b )e + 24B b d)x +--R + +--R 4 2 3 5 4 6 +--R ((140A a b + 280B a b )e + (28A b + 140B a b )d)x +--R + +--R 2 3 3 2 4 2 3 5 +--R ((336A a b + 336B a b )e + (168A a b + 336B a b )d)x +--R + +--R 3 2 4 2 3 3 2 4 +--R ((420A a b + 210B a b)e + (420A a b + 420B a b )d)x +--R + +--R 4 5 3 2 4 3 +--R ((280A a b + 56B a )e + (560A a b + 280B a b)d)x +--R + +--R 5 4 5 2 5 +--R (84A a e + (420A a b + 84B a )d)x + 168A a d x +--R / +--R 168 +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 7 7 6 7 6 +--R - 21B b e x + ((- 24A b - 99B a b )e - 24B b d)x +--R + +--R 6 2 5 7 6 5 +--R ((- 116A a b - 181B a b )e + (- 28A b - 116B a b )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((- 220A a b - 155B a b )e + (- 140A a b - 220B a b )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((- 200A a b - 55B a b )e + (- 280A a b - 200B a b )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((- 80A a b - B a b )e + (- 280A a b - 80B a b )d)x +--R + +--R 5 2 6 4 3 5 2 6 7 +--R ((- 4A a b + B a b)e + (- 140A a b - 4B a b )d)x + (4A a b - B a )e +--R + +--R 5 2 6 +--R (- 28A a b + 4B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 8 8 8 7 8 7 +--R 21B b e x + ((24A b + 120B a b )e + 24B b d)x +--R + +--R 7 2 6 8 7 6 +--R ((140A a b + 280B a b )e + (28A b + 140B a b )d)x +--R + +--R 2 6 3 5 7 2 6 5 +--R ((336A a b + 336B a b )e + (168A a b + 336B a b )d)x +--R + +--R 3 5 4 4 2 6 3 5 4 +--R ((420A a b + 210B a b )e + (420A a b + 420B a b )d)x +--R + +--R 4 4 5 3 3 5 4 4 3 +--R ((280A a b + 56B a b )e + (560A a b + 280B a b )d)x +--R + +--R 5 3 4 4 5 3 2 5 3 +--R (84A a b e + (420A a b + 84B a b )d)x + 168A a b d x +--R / +--R 3 +--R 168b +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 7 5 4 5 6 +--R B b e x + ((A b + 5B a b )e + B b d)x +--R + +--R 4 2 3 5 4 5 +--R ((5A a b + 10B a b )e + (A b + 5B a b )d)x +--R + +--R 2 3 3 2 4 2 3 4 +--R ((10A a b + 10B a b )e + (5A a b + 10B a b )d)x +--R + +--R 3 2 4 2 3 3 2 3 +--R ((10A a b + 5B a b)e + (10A a b + 10B a b )d)x +--R + +--R 4 5 3 2 4 2 +--R ((5A a b + B a )e + (10A a b + 5B a b)d)x +--R + +--R 5 4 5 5 +--R (A a e + (5A a b + B a )d)x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 8 6 5 6 7 +--R - B b e x + ((- A b - 6B a b )e - B b d)x +--R + +--R 5 2 4 6 5 6 +--R ((- 6A a b - 15B a b )e + (- A b - 6B a b )d)x +--R + +--R 2 4 3 3 5 2 4 5 +--R ((- 15A a b - 20B a b )e + (- 6A a b - 15B a b )d)x +--R + +--R 3 3 4 2 2 4 3 3 4 +--R ((- 20A a b - 15B a b )e + (- 15A a b - 20B a b )d)x +--R + +--R 4 2 5 3 3 4 2 3 +--R ((- 15A a b - 6B a b)e + (- 20A a b - 15B a b )d)x +--R + +--R 5 6 4 2 5 2 +--R ((- 6A a b - B a )e + (- 15A a b - 6B a b)d)x +--R + +--R 6 5 6 6 +--R (- A a e + (- 6A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1378 +r0:=1/6*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+_ + 1/7*B*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2 +--R +--R +--R (2) +--R 6 6 6 5 5 5 2 4 4 +--R 6B b x + (7A b + 29B a b )x + (35A a b + 55B a b )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 4 2 5 +--R (70A a b + 50B a b )x + (70A a b + 20B a b )x + (35A a b + B a b)x +--R + +--R 5 6 +--R 7A a b - B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 42b +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 5 4 6 4 2 3 5 +--R 6B b x + (7A b + 35B a b )x + (42A a b + 84B a b )x +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (105A a b + 105B a b )x + (140A a b + 70B a b)x +--R + +--R 4 5 2 5 +--R (105A a b + 21B a )x + 42A a x +--R / +--R 42 +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 5 5 2 4 4 +--R - 6B b x + (- 7A b - 29B a b )x + (- 35A a b - 55B a b )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 +--R (- 70A a b - 50B a b )x + (- 70A a b - 20B a b )x +--R + +--R 4 2 5 5 6 +--R (- 35A a b - B a b)x - 7A a b + B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 7 6 6 6 2 5 5 +--R 6B b x + (7A b + 35B a b )x + (42A a b + 84B a b )x +--R + +--R 2 5 3 4 4 3 4 4 3 3 +--R (105A a b + 105B a b )x + (140A a b + 70B a b )x +--R + +--R 4 3 5 2 2 5 2 +--R (105A a b + 21B a b )x + 42A a b x +--R / +--R 2 +--R 42b +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R e x + d +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1378 +r0:=-1/3*(b*d-a*e)^2*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/4*(b*d-a*e)*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/5*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/6*B*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-(b*d-a*e)^4*(B*d-A*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/2*(b*d-a*e)^3*(B*d-A*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+(b*d-a*e)^5*(B*d-A*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 5 +--R 60A a b e + (- 300A a b - 60B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (600A a b + 300B a b )d e + (- 600A a b - 600B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (300A a b + 600B a b )d e + (- 60A b - 300B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 6 5 6 6 5 5 +--R 10B b e x + ((12A b + 60B a b )e - 12B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 4 +--R ((75A a b + 150B a b )e + (- 15A b - 75B a b )d e + 15B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (200A a b + 200B a b )e + (- 100A a b - 200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (20A b + 100B a b )d e - 20B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (300A a b + 150B a b )e + (- 300A a b - 300B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (150A a b + 300B a b )d e + (- 30A b - 150B a b )d e + 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (300A a b + 60B a b)e + (- 600A a b - 300B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (60A b + 300B a b )d e - 60B b d e +--R * +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (137A a b + 10B a )e + (- 385A a b - 137B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (470A a b + 385B a b )d e + (- 270A a b - 470B a b )d e +--R + +--R 5 2 4 4 2 5 5 +--R (60A a b + 270B a b )d e - 60B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 7 7 +--R 60b e x + 60a b e +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 4 5 5 3 2 4 2 4 +--R 60A a e + (- 300A a b - 60B a )d e + (600A a b + 300B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 600A a b - 600B a b )d e + (300A a b + 600B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 60A b - 300B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 10B b e x + ((12A b + 60B a b )e - 12B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((75A a b + 150B a b )e + (- 15A b - 75B a b )d e + 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (200A a b + 200B a b )e + (- 100A a b - 200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (20A b + 100B a b )d e - 20B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (300A a b + 150B a b)e + (- 300A a b - 300B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (150A a b + 300B a b )d e + (- 30A b - 150B a b )d e + 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (300A a b + 60B a )e + (- 600A a b - 300B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (60A b + 300B a b )d e - 60B b d e +--R * +--R x +--R / +--R 7 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 4 2 5 5 +--R - 60A a b e + (300A a b + 60B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 600A a b - 300B a b )d e + (600A a b + 600B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 300A a b - 600B a b )d e + (60A b + 300B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 6 5 6 6 5 5 +--R - 10B b e x + ((- 12A b - 60B a b )e + 12B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 4 +--R ((- 75A a b - 150B a b )e + (15A b + 75B a b )d e - 15B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 200A a b - 200B a b )e + (100A a b + 200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 20A b - 100B a b )d e + 20B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 300A a b - 150B a b )e + (300A a b + 300B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 150A a b - 300B a b )d e + (30A b + 150B a b )d e +--R + +--R 6 4 2 +--R - 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 300A a b - 60B a b)e + (600A a b + 300B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 600A a b - 600B a b )d e + (300A a b + 600B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 60A b - 300B a b )d e + 60B b d e +--R * +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 137A a b - 10B a )e + (385A a b + 137B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 470A a b - 385B a b )d e + (270A a b + 470B a b )d e +--R + +--R 5 2 4 4 2 5 5 +--R (- 60A a b - 270B a b )d e + 60B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 6 4 3 5 2 5 +--R 60A a b e + (- 300A a b - 60B a b )d e +--R + +--R 3 4 4 3 2 4 2 5 3 4 3 3 +--R (600A a b + 300B a b )d e + (- 600A a b - 600B a b )d e +--R + +--R 6 2 5 4 2 7 6 5 7 6 +--R (300A a b + 600B a b )d e + (- 60A b - 300B a b )d e + 60B b d +--R * +--R x +--R + +--R 6 6 5 2 6 5 +--R 60A a b e + (- 300A a b - 60B a b)d e +--R + +--R 4 3 5 2 2 4 3 4 4 3 3 3 +--R (600A a b + 300B a b )d e + (- 600A a b - 600B a b )d e +--R + +--R 2 5 3 4 4 2 6 2 5 5 6 6 +--R (300A a b + 600B a b )d e + (- 60A a b - 300B a b )d e + 60B a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 7 6 6 7 5 6 +--R 10B b e x + ((12A b + 70B a b )e - 12B b d e )x +--R + +--R 6 2 5 6 7 6 5 7 2 4 5 +--R ((87A a b + 210B a b )e + (- 15A b - 87B a b )d e + 15B b d e )x +--R + +--R 2 5 3 4 6 6 2 5 5 +--R (275A a b + 350B a b )e + (- 115A a b - 275B a b )d e +--R + +--R 7 6 2 4 7 3 3 +--R (20A b + 115B a b )d e - 20B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 6 2 5 3 4 5 +--R (500A a b + 350B a b )e + (- 400A a b - 500B a b )d e +--R + +--R 6 2 5 2 4 7 6 3 3 7 4 2 +--R (170A a b + 400B a b )d e + (- 30A b - 170B a b )d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 6 3 4 4 3 5 +--R (600A a b + 210B a b )e + (- 900A a b - 600B a b )d e +--R + +--R 2 5 3 4 2 4 6 2 5 3 3 +--R (750A a b + 900B a b )d e + (- 330A a b - 750B a b )d e +--R + +--R 7 6 4 2 7 5 +--R (60A b + 330B a b )d e - 60B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 6 4 3 5 2 5 +--R (300A a b + 60B a b)e + (- 600A a b - 300B a b )d e +--R + +--R 3 4 4 3 2 4 2 5 3 4 3 3 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 6 2 5 4 2 6 5 +--R (60A a b + 300B a b )d e - 60B a b d e +--R * +--R x +--R / +--R 2 7 7 +--R 60b e x + 60a b e +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1378 +r0:=1/3*(b*d-a*e)*(6*b*B*d-5*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-_ + 1/4*(6*b*B*d-5*A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3+_ + 1/5*(6*b*B*d-5*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x))+_ + (b*d-a*e)^3*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 1/2*(b*d-a*e)^2*(6*b*B*d-5*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^5-(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 5 6 3 2 4 5 +--R (300A a b + 60B a )e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (300A b + 1500B a b )d e - 360B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (300A a b + 60B a )d e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 5 5 6 +--R (300A b + 1500B a b )d e - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 12B b e x + ((15A b + 75B a b )e - 18B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((100A a b + 200B a b )e + (- 25A b - 125B a b )d e + 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (300A a b + 300B a b )e + (- 200A a b - 400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (50A b + 250B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (600A a b + 300B a b)e + (- 900A a b - 900B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (600A a b + 1200B a b )d e + (- 150A b - 750B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (325A a b + 137B a )e + (- 100A a b - 410B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 750A a b - 30B a b )d e + (900A a b + 1080B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 300A b - 1140B a b )d e + 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 60A a e + (625A a b + 197B a )d e + (- 1300A a b - 1010B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (1050A a b + 1770B a b )d e + (- 300A a b - 1320B a b )d e +--R + +--R 4 5 +--R 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +--R 60b e x + (60a e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 6 3 2 4 5 +--R (300A a b + 60B a )e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (300A b + 1500B a b )d e - 360B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (300A a b + 60B a )d e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 5 5 6 +--R (300A b + 1500B a b )d e - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 12B b e x + ((15A b + 75B a b )e - 18B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((100A a b + 200B a b )e + (- 25A b - 125B a b )d e + 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (300A a b + 300B a b )e + (- 200A a b - 400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (50A b + 250B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (600A a b + 300B a b)e + (- 900A a b - 900B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (600A a b + 1200B a b )d e + (- 150A b - 750B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 2 4 +--R (600A a b + 300B a b)d e + (- 1200A a b - 1200B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (900A a b + 1800B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 300B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 60A a e + (300A a b + 60B a )d e + (- 600A a b - 300B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 60B b d +--R / +--R 8 7 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 593 + +--S 594 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 6 3 2 4 5 +--R (- 300A a b - 60B a )e + (1200A a b + 600B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 1800A a b - 1800B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (1200A a b + 2400B a b )d e + (- 300A b - 1500B a b )d e +--R + +--R 5 5 +--R 360B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (- 300A a b - 60B a )d e + (1200A a b + 600B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 1800A a b - 1800B a b )d e + (1200A a b + 2400B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 300A b - 1500B a b )d e + 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R - 12B b e x + ((- 15A b - 75B a b )e + 18B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 100A a b - 200B a b )e + (25A b + 125B a b )d e +--R + +--R 5 2 4 +--R - 30B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 300A a b - 300B a b )e + (200A a b + 400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 50A b - 250B a b )d e + 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 600A a b - 300B a b)e + (900A a b + 900B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 600A a b - 1200B a b )d e + (150A b + 750B a b )d e +--R + +--R 5 4 2 +--R - 180B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 325A a b - 137B a )e + (100A a b + 410B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (750A a b + 30B a b )d e + (- 900A a b - 1080B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (300A b + 1140B a b )d e - 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 60A a e + (- 625A a b - 197B a )d e + (1300A a b + 1010B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 1050A a b - 1770B a b )d e + (300A a b + 1320B a b )d e +--R + +--R 4 5 +--R - 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (300A a b + 60B a b)e + (- 1200A a b - 600B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (300A b + 1500B a b )d e - 360B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (300A a b + 60B a )e + (- 900A a b - 540B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (600A a b + 1200B a b )d e + (600A a b - 600B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (- 900A a b - 900B a b )d e + (300A b + 1140B a b )d e +--R + +--R 6 6 +--R - 360B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 2 4 +--R (300A a b + 60B a )d e + (- 1200A a b - 600B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (300A a b + 1500B a b )d e - 360B a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 12B b e x + ((15A b + 87B a b )e - 18B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((115A a b + 275B a b )e + (- 25A b - 143B a b )d e + 30B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (400A a b + 500B a b )e + (- 225A a b - 525B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (50A b + 280B a b )d e - 60B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (900A a b + 600B a b )e + (- 1100A a b - 1300B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (650A a b + 1450B a b )d e + (- 150A b - 810B a b )d e +--R + +--R 6 4 2 +--R 180B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (600A a b + 300B a b)e + (- 300A a b - 600B a b )d e +--R + +--R 2 4 2 4 5 2 4 3 3 +--R - 600A a b d e + (750A a b + 1050B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 240A b - 1020B a b )d e + 300B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 5 +--R - 60A a b e + (900A a b + 360B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 1800A a b - 1500B a b )d e + (1500A a b + 2400B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 540A a b - 1800B a b )d e + (60A b + 600B a b )d e - 60B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 60A a e + (300A a b + 60B a )d e + (- 600A a b - 300B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (60A a b + 300B a b )d e - 60B a b d +--R / +--R 8 2 8 7 7 +--R 60b e x + (60a e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 595 + +)clear all + +--S 596 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1378 +r0:=-5/3*b*(3*b*B*d-2*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 5/4*b*(3*b*B*d-2*A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e))-1/2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e*(b*d-a*e)*(d+e*x)^2)-(3*b*B*d-2*A*b*e-a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x))-5*b*(b*d-a*e)^2*(3*b*B*d-_ + 2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+5/2*b*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+5*b*_ + (b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 3 2 4 6 2 3 3 2 5 +--R (120A a b + 60B a b)e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 2 4 +--R (240A a b + 120B a b)d e + (- 720A a b - 720B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (720A a b + 1440B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 360B b d e +--R * +--R x +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (120A a b + 60B a b)d e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 3B b e x + ((4A b + 20B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 10A b - 50B a b )d e + 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (120A a b + 120B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (40A b + 200B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (40A a b + 65B a b)e + (240A a b + 60B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 420A a b - 570B a b )d e + (180A b + 720B a b )d e +--R + +--R 5 4 2 +--R - 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 60A a b - 12B a )e + (320A a b + 250B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 240A a b - 600B a b )d e + (- 120A a b + 300B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (120A b + 240B a b )d e - 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 6A a e + (- 30A a b - 6B a )d e + (220A a b + 155B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 300A a b - 480B a b )d e + (120A a b + 510B a b )d e +--R + +--R 4 5 +--R - 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 12b e x + (12a e + 24b d e )x + (24a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 6 2 3 3 2 5 +--R (120A a b + 60B a b)e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 2 4 +--R (240A a b + 120B a b)d e + (- 720A a b - 720B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (720A a b + 1440B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 360B b d e +--R * +--R x +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (120A a b + 60B a b)d e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 3B b e x + ((4A b + 20B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 10A b - 50B a b )d e + 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (120A a b + 120B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (40A b + 200B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 2 4 +--R (240A a b + 240B a b )d e + (- 330A a b - 660B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (126A b + 630B a b )d e - 204B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 60A a b - 12B a )e + (240A a b + 120B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 240A a b - 240B a b )d e + (60A a b + 120B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (12A b + 60B a b )d e - 48B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 6A a e + (- 30A a b - 6B a )d e + (180A a b + 90B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 300A a b - 300B a b )d e + (210A a b + 420B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 54A b - 270B a b )d e + 66B b d +--R / +--R 9 2 8 2 7 +--R 12e x + 24d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 598 + +--S 599 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 4 6 2 3 3 2 5 +--R (- 120A a b - 60B a b)e + (360A a b + 360B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 360A a b - 720B a b )d e + (120A b + 600B a b )d e +--R + +--R 5 4 2 +--R - 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 2 4 +--R (- 240A a b - 120B a b)d e + (720A a b + 720B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 720A a b - 1440B a b )d e + (240A b + 1200B a b )d e +--R + +--R 5 5 +--R - 360B b d e +--R * +--R x +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 120A a b - 60B a b)d e + (360A a b + 360B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 360A a b - 720B a b )d e + (120A b + 600B a b )d e +--R + +--R 5 6 +--R - 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R - 3B b e x + ((- 4A b - 20B a b )e + 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((- 30A a b - 60B a b )e + (10A b + 50B a b )d e - 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 120A a b - 120B a b )e + (120A a b + 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 40A b - 200B a b )d e + 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 40A a b - 65B a b)e + (- 240A a b - 60B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (420A a b + 570B a b )d e + (- 180A b - 720B a b )d e +--R + +--R 5 4 2 +--R 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (60A a b + 12B a )e + (- 320A a b - 250B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (240A a b + 600B a b )d e + (120A a b - 300B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 120A b - 240B a b )d e + 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 6A a e + (30A a b + 6B a )d e + (- 220A a b - 155B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (300A a b + 480B a b )d e + (- 120A a b - 510B a b )d e +--R + +--R 4 5 +--R 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (120A a b + 60B a b )e + (- 360A a b - 360B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e +--R + +--R 6 4 2 +--R 180B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (120A a b + 60B a b)e + (- 120A a b - 240B a b )d e +--R + +--R 2 4 2 4 5 2 4 3 3 +--R - 360A a b d e + (600A a b + 840B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 240A b - 1020B a b )d e + 360B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (240A a b + 120B a b)d e + (- 600A a b - 660B a b )d e +--R + +--R 2 4 3 3 3 3 5 2 4 4 2 +--R (360A a b + 1080B a b )d e + (120A a b - 480B a b )d e +--R + +--R 6 5 5 6 6 +--R (- 120A b - 240B a b )d e + 180B b d +--R * +--R x +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (120A a b + 60B a b)d e + (- 360A a b - 360B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (360A a b + 720B a b )d e + (- 120A a b - 600B a b )d e +--R + +--R 5 6 +--R 180B a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 3B b e x + ((4A b + 23B a b )e - 6B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((34A a b + 80B a b )e + (- 10A b - 56B a b )d e + 15B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (150A a b + 180B a b )e + (- 130A a b - 290B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (40A b + 215B a b )d e - 60B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 5 +--R (120A a b + 120B a b )e + 120A a b d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (- 290A a b - 460B a b )d e + (126A b + 570B a b )d e - 204B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 60A a b - 12B a b)e + (480A a b + 360B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 570A a b - 900B a b )d e + (186A a b + 750B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (12A b - 144B a b )d e - 48B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 66A a b - 12B a )e + (210A a b + 114B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 60A a b - 150B a b )d e + (- 240A a b - 180B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (222A a b + 480B a b )d e + (- 54A b - 318B a b )d e + 66B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 6A a e + (- 30A a b - 6B a )d e + (180A a b + 90B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 300A a b - 300B a b )d e + (210A a b + 420B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- 54A a b - 270B a b )d e + 66B a b d +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 12b e x + (12a e + 24b d e )x + (24a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1378 +r0:=10/3*b^2*(2*b*B*d-A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-_ + a*e))-5/2*b*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x))-1/3*(B*d-A*e)*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^3)-1/2*(2*b*B*d-A*b*e-_ + a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^2)+_ + 10*b^2*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 5*b^2*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-_ + 10*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 2 3 3 2 6 4 2 3 5 +--R (60A a b + 60B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (60A b + 300B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 2 4 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R x +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (60A a b + 60B a b )d e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 120B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 2B b e x + ((3A b + 15B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 15A b - 75B a b )d e + 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 20A a b + 20B a b )e + (160A a b + 200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 110A b - 430B a b )d e + 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (120A a b + 240B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (120A a b - 120B a b )d e + (- 150A b - 390B a b )d e +--R + +--R 5 4 2 +--R 300B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 15A a b - 3B a )e + (- 60A a b - 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (210A a b + 330B a b )d e + (- 60A a b - 480B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b + 60B a b )d e + 120B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 2A a e + (- 5A a b - B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (90A a b + 130B a b )d e + (- 60A a b - 240B a b )d e + 120B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 8 3 7 3 7 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 6 4 2 3 5 +--R (60A a b + 60B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (60A b + 300B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 2 4 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R x +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (60A a b + 60B a b )d e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 120B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 2B b e x + ((3A b + 15B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 15A b - 75B a b )d e + 30B b d e )x +--R + +--R 4 2 3 5 5 4 2 4 5 3 3 3 +--R ((90A a b + 180B a b )d e + (- 63A b - 315B a b )d e + 146B b d e )x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (180A a b + 180B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (- 90A a b - 180B a b )d e + (- 9A b - 45B a b )d e + 78B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 15A a b - 3B a )e + (- 60A a b - 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (270A a b + 270B a b )d e + (- 270A a b - 540B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (81A b + 405B a b )d e - 102B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 2A a e + (- 5A a b - B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (110A a b + 110B a b )d e + (- 130A a b - 260B a b )d e +--R + +--R 5 4 5 5 6 +--R (47A b + 235B a b )d e - 74B b d +--R / +--R 10 3 9 2 2 8 3 7 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 603 + +--S 604 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 3 2 6 4 2 3 5 +--R (- 60A a b - 60B a b )e + (120A a b + 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 60A b - 300B a b )d e + 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 2 4 +--R (- 180A a b - 180B a b )d e + (360A a b + 720B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (- 180A b - 900B a b )d e + 360B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 180A a b - 180B a b )d e + (360A a b + 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 180A b - 900B a b )d e + 360B b d e +--R * +--R x +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 60A a b - 60B a b )d e + (120A a b + 240B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 60A b - 300B a b )d e + 120B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R - 2B b e x + ((- 3A b - 15B a b )e + 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((- 30A a b - 60B a b )e + (15A b + 75B a b )d e - 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (20A a b - 20B a b )e + (- 160A a b - 200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (110A b + 430B a b )d e - 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (60A a b + 30B a b)e + (- 120A a b - 240B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 120A a b + 120B a b )d e + (150A b + 390B a b )d e +--R + +--R 5 4 2 +--R - 300B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (15A a b + 3B a )e + (60A a b + 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 210A a b - 330B a b )d e + (60A a b + 480B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (60A b - 60B a b )d e - 120B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 2A a e + (5A a b + B a )d e + (20A a b + 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 90A a b - 130B a b )d e + (60A a b + 240B a b )d e +--R + +--R 4 5 +--R - 120B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (60A a b + 60B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (60A b + 300B a b )d e - 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (60A a b + 60B a b )e + (60A a b - 60B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 300A a b - 420B a b )d e + (180A b + 780B a b )d e +--R + +--R 6 4 2 +--R - 360B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 2 4 +--R (180A a b + 180B a b )d e + (- 180A a b - 540B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 180A a b + 180B a b )d e + (180A b + 540B a b )d e +--R + +--R 6 5 +--R - 360B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (180A a b + 180B a b )d e + (- 300A a b - 660B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (60A a b + 660B a b )d e + (60A b - 60B a b )d e - 120B b d +--R * +--R x +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (60A a b + 60B a b )d e + (- 120A a b - 240B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (60A a b + 300B a b )d e - 120B a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 2B b e x + ((3A b + 17B a b )e - 6B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((33A a b + 75B a b )e + (- 15A b - 81B a b )d e + 30B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (30A a b + 60B a b )e + (75A a b + 105B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 63A b - 285B a b )d e + 146B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 60A a b - 30B a b )e + (270A a b + 360B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (- 153A a b - 495B a b )d e + (- 9A b + 101B a b )d e + 78B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 75A a b - 33B a b)e + (120A a b + 150B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (180A a b + 90B a b )d e + (- 279A a b - 585B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (81A b + 483B a b )d e - 102B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 17A a b - 3B a )e + (- 65A a b - 31B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (250A a b + 260B a b )d e + (- 160A a b - 430B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 49A a b + 145B a b )d e + (47A b + 133B a b )d e - 74B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 2A a e + (- 5A a b - B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (110A a b + 110B a b )d e + (- 130A a b - 260B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (47A a b + 235B a b )d e - 74B a b d +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 8 3 7 3 7 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 605 + +)clear all + +--S 606 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1378 +r0:=-5/12*b*(3*b*B*d-A*b*e-2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^2)-5/3*b^2*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x))-_ + 1/4*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/6*(3*b*B*d-A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^3)-5*b^3*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^6+5/2*b^3*(3*b*B*d-A*b*e-2*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e))+5*b^3*(b*d-a*e)*(3*b*B*d-_ + A*b*e-2*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 2 3 6 5 4 5 +--R (60A a b + 120B a b )e + (- 60A b - 300B a b )d e +--R + +--R 5 2 4 +--R 180B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 5 5 4 2 4 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 3 3 +--R 720B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 360A b - 1800B a b )d e +--R + +--R 5 4 2 +--R 1080B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 720B b d e +--R * +--R x +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (60A a b + 120B a b )d e + (- 60A b - 300B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 6B b e x + ((12A b + 60B a b )e - 36B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((- 65A a b - 40B a b )e + (125A b + 445B a b )d e - 375B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 120A a b - 120B a b )e + (- 20A a b + 320B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (260A b + 580B a b )d e - 780B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (- 180A a b - 180B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (150A a b + 840B a b )d e + (210A b - 30B a b )d e - 630B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 20A a b - 4B a )e + (- 40A a b - 20B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 120A a b - 120B a b )d e + (180A a b + 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (60A b - 420B a b )d e - 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 3A a e + (- 5A a b - B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (- 30A a b - 30B a b )d e + (60A a b + 210B a b )d e - 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 6 5 4 5 +--R (60A a b + 120B a b )e + (- 60A b - 300B a b )d e +--R + +--R 5 2 4 +--R 180B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 5 5 4 2 4 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 3 3 +--R 720B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 360A b - 1800B a b )d e +--R + +--R 5 4 2 +--R 1080B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 720B b d e +--R * +--R x +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (60A a b + 120B a b )d e + (- 60A b - 300B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 6B b e x + ((12A b + 60B a b )e - 36B b d e )x +--R + +--R 5 4 5 5 2 4 4 +--R ((48A b + 240B a b )d e - 204B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 120A a b - 120B a b )e + (240A a b + 480B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 48A b - 240B a b )d e - 96B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (- 180A a b - 180B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (540A a b + 1080B a b )d e + (- 252A b - 1260B a b )d e +--R + +--R 5 4 2 +--R 396B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 20A a b - 4B a )e + (- 40A a b - 20B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 120A a b - 120B a b )d e + (440A a b + 880B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 248A b - 1240B a b )d e + 504B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 3A a e + (- 5A a b - B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 30A a b - 30B a b )d e + (125A a b + 250B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 77A b - 385B a b )d e + 171B b d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 608 + +--S 609 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 3 6 5 4 5 +--R (- 60A a b - 120B a b )e + (60A b + 300B a b )d e +--R + +--R 5 2 4 +--R - 180B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 5 5 4 2 4 +--R (- 240A a b - 480B a b )d e + (240A b + 1200B a b )d e +--R + +--R 5 3 3 +--R - 720B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 360A a b - 720B a b )d e + (360A b + 1800B a b )d e +--R + +--R 5 4 2 +--R - 1080B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 240A a b - 480B a b )d e + (240A b + 1200B a b )d e +--R + +--R 5 5 +--R - 720B b d e +--R * +--R x +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (- 60A a b - 120B a b )d e + (60A b + 300B a b )d e - 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R - 6B b e x + ((- 12A b - 60B a b )e + 36B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (65A a b + 40B a b )e + (- 125A b - 445B a b )d e +--R + +--R 5 2 4 +--R 375B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (120A a b + 120B a b )e + (20A a b - 320B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 260A b - 580B a b )d e + 780B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (60A a b + 30B a b)e + (180A a b + 180B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 150A a b - 840B a b )d e + (- 210A b + 30B a b )d e +--R + +--R 5 4 2 +--R 630B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (20A a b + 4B a )e + (40A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (120A a b + 120B a b )d e + (- 180A a b - 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b + 420B a b )d e + 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 3A a e + (5A a b + B a )d e + (10A a b + 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (30A a b + 30B a b )d e + (- 60A a b - 210B a b )d e + 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 4 6 6 5 5 +--R (60A a b + 120B a b )e + (- 60A b - 300B a b )d e +--R + +--R 6 2 4 +--R 180B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (60A a b + 120B a b )e + (180A a b + 180B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 240A b - 1020B a b )d e + 720B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 5 2 4 2 4 +--R (240A a b + 480B a b )d e + (120A a b - 480B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 360A b - 1080B a b )d e + 1080B b d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (360A a b + 720B a b )d e + (- 120A a b - 1320B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 240A b - 120B a b )d e + 720B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 3 3 5 2 4 4 2 +--R (240A a b + 480B a b )d e + (- 180A a b - 1080B a b )d e +--R + +--R 6 5 5 6 6 +--R (- 60A b + 420B a b )d e + 180B b d +--R * +--R x +--R + +--R 2 4 3 3 4 2 5 2 4 5 5 6 +--R (60A a b + 120B a b )d e + (- 60A a b - 300B a b )d e + 180B a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 6B b e x + ((12A b + 66B a b )e - 36B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((12A a b + 60B a b )e + (48A b + 204B a b )d e - 204B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 120A a b - 120B a b )e + (288A a b + 720B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 48A b - 444B a b )d e - 96B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 180A a b - 150B a b )e + (60A a b + 300B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (492A a b + 840B a b )d e + (- 252A b - 1356B a b )d e +--R + +--R 6 4 2 +--R 396B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 80A a b - 34B a b)e + (- 220A a b - 200B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (420A a b + 960B a b )d e + (188A a b - 380B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 248A b - 844B a b )d e + 504B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 23A a b - 4B a )e + (- 45A a b - 21B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 130A a b - 125B a b )d e + (410A a b + 850B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 123A a b - 990B a b )d e + (- 77A b + 119B a b )d e + 171B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 3A a e + (- 5A a b - B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 30A a b - 30B a b )d e + (125A a b + 250B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- 77A a b - 385B a b )d e + 171B a b d +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 610 + +)clear all + +--S 611 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^6 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1378 +r0:=-1/12*b*(6*b*B*d-A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e)*(d+e*x)^3)-1/6*b^2*(6*b*B*d-A*b*e-5*a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^2)-1/5*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^5)-_ + 1/20*(6*b*B*d-A*b*e-5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*_ + (b*d-a*e)*(d+e*x)^4)+b^4*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^6*(b*d-a*e))-1/2*b^3*(6*b*B*d-A*b*e-5*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*(d+e*x))-b^4*(6*b*B*d-A*b*e-_ + 5*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 4 6 5 5 5 +--R ((60A b + 300B a b )e - 360B b d e )x +--R + +--R 5 4 5 5 2 4 4 +--R ((300A b + 1500B a b )d e - 1800B b d e )x +--R + +--R 5 4 2 4 5 3 3 3 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 3 3 5 4 2 2 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 4 2 5 5 +--R ((300A b + 1500B a b )d e - 1800B b d e)x +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 60B b e x + ((- 137A b - 325B a b )e + 822B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 300A a b - 600B a b )e + (- 385A b - 125B a b )d e +--R + +--R 5 2 4 +--R 2310B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 300A a b - 300B a b )e + (- 600A a b - 1200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 470A b + 1250B a b )d e + 2820B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 200A a b - 100B a b)e + (- 300A a b - 300B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 600A a b - 1200B a b )d e + (- 270A b + 2250B a b )d e +--R + +--R 5 4 2 +--R 1620B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 75A a b - 15B a )e + (- 100A a b - 50B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 150A a b - 150B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b + 1500B a b )d e + 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 12A a e + (- 15A a b - 3B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (- 30A a b - 30B a b )d e + (- 60A a b - 120B a b )d e + 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 8 5 7 5 7 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 6 5 5 5 +--R ((60A b + 300B a b )e - 360B b d e )x +--R + +--R 5 4 5 5 2 4 4 +--R ((300A b + 1500B a b )d e - 1800B b d e )x +--R + +--R 5 4 2 4 5 3 3 3 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 3 3 5 4 2 2 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 4 2 5 5 5 4 5 +--R ((300A b + 1500B a b )d e - 1800B b d e)x + (60A b + 300B a b )d e +--R + +--R 5 6 +--R - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 5 5 +--R 60B b e x + 300B b d e x +--R + +--R 4 2 3 6 5 4 5 +--R (- 300A a b - 600B a b )e + (300A b + 1500B a b )d e +--R + +--R 5 2 4 +--R - 300B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 300A a b - 300B a b )e + (- 600A a b - 1200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (900A b + 4500B a b )d e - 2400B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 200A a b - 100B a b)e + (- 300A a b - 300B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 600A a b - 1200B a b )d e + (1100A b + 5500B a b )d e +--R + +--R 5 4 2 +--R - 3600B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 75A a b - 15B a )e + (- 100A a b - 50B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 150A a b - 150B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (625A b + 3125B a b )d e - 2250B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 12A a e + (- 15A a b - 3B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 30A a b - 30B a b )d e + (- 60A a b - 120B a b )d e +--R + +--R 5 4 5 5 6 +--R (137A b + 685B a b )d e - 522B b d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 5 7 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 613 + +--S 614 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 6 5 5 5 +--R ((- 60A b - 300B a b )e + 360B b d e )x +--R + +--R 5 4 5 5 2 4 4 +--R ((- 300A b - 1500B a b )d e + 1800B b d e )x +--R + +--R 5 4 2 4 5 3 3 3 +--R ((- 600A b - 3000B a b )d e + 3600B b d e )x +--R + +--R 5 4 3 3 5 4 2 2 +--R ((- 600A b - 3000B a b )d e + 3600B b d e )x +--R + +--R 5 4 4 2 5 5 +--R ((- 300A b - 1500B a b )d e + 1800B b d e)x +--R + +--R 5 4 5 5 6 +--R (- 60A b - 300B a b )d e + 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R - 60B b e x + ((137A b + 325B a b )e - 822B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (300A a b + 600B a b )e + (385A b + 125B a b )d e +--R + +--R 5 2 4 +--R - 2310B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (300A a b + 300B a b )e + (600A a b + 1200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (470A b - 1250B a b )d e - 2820B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (200A a b + 100B a b)e + (300A a b + 300B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (600A a b + 1200B a b )d e + (270A b - 2250B a b )d e +--R + +--R 5 4 2 +--R - 1620B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (75A a b + 15B a )e + (100A a b + 50B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (150A a b + 150B a b )d e + (300A a b + 600B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (60A b - 1500B a b )d e - 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 12A a e + (15A a b + 3B a )d e + (20A a b + 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (30A a b + 30B a b )d e + (60A a b + 120B a b )d e - 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 6 6 5 6 +--R ((60A b + 300B a b )e - 360B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (60A a b + 300B a b )e + (300A b + 1140B a b )d e +--R + +--R 6 2 4 +--R - 1800B b d e +--R * +--R 5 +--R x +--R + +--R 5 2 4 5 6 5 2 4 +--R (300A a b + 1500B a b )d e + (600A b + 1200B a b )d e +--R + +--R 6 3 3 +--R - 3600B b d e +--R * +--R 4 +--R x +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (600A a b + 3000B a b )d e + (600A b - 600B a b )d e +--R + +--R 6 4 2 +--R - 3600B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (600A a b + 3000B a b )d e + (300A b - 2100B a b )d e +--R + +--R 6 5 +--R - 1800B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 4 4 2 6 5 5 +--R (300A a b + 1500B a b )d e + (60A b - 1500B a b )d e +--R + +--R 6 6 +--R - 360B b d +--R * +--R x +--R + +--R 5 2 4 5 5 6 +--R (60A a b + 300B a b )d e - 360B a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 5 6 6 5 6 +--R 60B b e x + (60B a b e + 300B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 300A a b - 600B a b )e + (300A b + 1800B a b )d e +--R + +--R 6 2 4 +--R - 300B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 600A a b - 900B a b )e + (- 300A a b + 300B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (900A b + 4200B a b )d e - 2400B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 500A a b - 400B a b )e + (- 900A a b - 1500B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (300A a b + 3300B a b )d e + (1100A b + 3100B a b )d e +--R + +--R 6 4 2 +--R - 3600B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 275A a b - 115B a b)e + (- 400A a b - 350B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 750A a b - 1350B a b )d e + (800A a b + 4900B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (625A b - 475B a b )d e - 2250B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 87A a b - 15B a )e + (- 115A a b - 53B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 170A a b - 160B a b )d e + (- 330A a b - 630B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (565A a b + 3005B a b )d e + (137A b - 1565B a b )d e - 522B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 12A a e + (- 15A a b - 3B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 30A a b - 30B a b )d e + (- 60A a b - 120B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (137A a b + 685B a b )d e - 522B a b d +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 8 5 7 5 7 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^7 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1378 +r0:=-1/4*b*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^4)-_ + 1/3*b^2*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^3)-1/6*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^6)-_ + 1/5*B*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^5)-1/2*b^3*B*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^2)+b^4*B*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))+b^5*B*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 7 6 6 6 5 6 6 2 5 5 +--R (60B a b e - 60B b d e )x + (360B a b d e - 360B b d e )x +--R + +--R 5 2 5 6 3 4 4 5 3 4 6 4 3 3 +--R (900B a b d e - 900B b d e )x + (1200B a b d e - 1200B b d e )x +--R + +--R 5 4 3 6 5 2 2 5 5 2 6 6 +--R (900B a b d e - 900B b d e )x + (360B a b d e - 360B b d e)x +--R + +--R 5 6 6 7 +--R 60B a b d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 6 5 7 6 6 6 +--R ((- 10A b - 77B a b )e + 87B b d e )x +--R + +--R 5 2 4 7 5 6 6 2 5 5 +--R ((- 60A a b - 300B a b )e + 198B a b d e + 162B b d e )x +--R + +--R 2 4 3 3 7 2 4 6 5 2 5 +--R (- 150A a b - 300B a b )e - 450B a b d e + 945B a b d e +--R + +--R 6 3 4 +--R - 45B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 3 3 6 2 4 2 5 +--R (- 200A a b - 200B a b )e - 200B a b d e - 600B a b d e +--R + +--R 5 3 4 6 4 3 +--R 1660B a b d e - 460B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 4 2 6 3 3 2 5 +--R (- 150A a b - 75B a b)e - 75B a b d e - 150B a b d e +--R + +--R 2 4 3 4 5 4 3 6 5 2 +--R - 450B a b d e + 1470B a b d e - 570B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 5 6 4 2 2 5 3 3 3 4 +--R (- 60A a b - 12B a )e - 18B a b d e - 30B a b d e - 60B a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 180B a b d e + 660B a b d e - 300B b d e +--R * +--R x +--R + +--R 6 7 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 10A a e - 2B a d e - 3B a b d e - 5B a b d e - 10B a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R - 30B a b d e + 120B a b d e - 60B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 2 13 7 2 14 13 2 2 12 6 +--R (60a b e - 60b d e )x + (60a e + 300a b d e - 360b d e )x +--R + +--R 2 13 2 12 2 3 11 5 +--R (360a d e + 540a b d e - 900b d e )x +--R + +--R 2 2 12 3 11 2 4 10 4 +--R (900a d e + 300a b d e - 1200b d e )x +--R + +--R 2 3 11 4 10 2 5 9 3 +--R (1200a d e - 300a b d e - 900b d e )x +--R + +--R 2 4 10 5 9 2 6 8 2 +--R (900a d e - 540a b d e - 360b d e )x +--R + +--R 2 5 9 6 8 2 7 7 2 6 8 7 7 +--R (360a d e - 300a b d e - 60b d e )x + 60a d e - 60a b d e +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 5 5 5 2 4 4 5 3 3 3 +--R 60B b e x + 360B b d e x + 900B b d e x + 1200B b d e x +--R + +--R 5 4 2 2 5 5 5 6 +--R 900B b d e x + 360B b d e x + 60B b d +--R * +--R log(e x + d) +--R + +--R 5 4 6 5 5 5 +--R ((- 60A b - 300B a b )e + 360B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 150A a b - 300B a b )e + (- 150A b - 750B a b )d e +--R + +--R 5 2 4 +--R 1350B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 200A a b - 200B a b )e + (- 200A a b - 400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 200A b - 1000B a b )d e + 2200B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 150A a b - 75B a b)e + (- 150A a b - 150B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 150A a b - 300B a b )d e + (- 150A b - 750B a b )d e +--R + +--R 5 4 2 +--R 1875B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 60A a b - 12B a )e + (- 60A a b - 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 60A a b - 60B a b )d e + (- 60A a b - 120B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b - 300B a b )d e + 822B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 10A a e + (- 10A a b - 2B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 10A a b - 10B a b )d e + (- 10A a b - 20B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 10A b - 50B a b )d e + 147B b d +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 5 8 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 7 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 618 + +--S 619 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 7 6 6 6 5 6 6 2 5 5 +--R (- 60B a b e + 60B b d e )x + (- 360B a b d e + 360B b d e )x +--R + +--R 5 2 5 6 3 4 4 +--R (- 900B a b d e + 900B b d e )x +--R + +--R 5 3 4 6 4 3 3 +--R (- 1200B a b d e + 1200B b d e )x +--R + +--R 5 4 3 6 5 2 2 +--R (- 900B a b d e + 900B b d e )x +--R + +--R 5 5 2 6 6 5 6 6 7 +--R (- 360B a b d e + 360B b d e)x - 60B a b d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 6 5 7 6 6 6 +--R ((10A b + 77B a b )e - 87B b d e )x +--R + +--R 5 2 4 7 5 6 6 2 5 5 +--R ((60A a b + 300B a b )e - 198B a b d e - 162B b d e )x +--R + +--R 2 4 3 3 7 2 4 6 5 2 5 +--R (150A a b + 300B a b )e + 450B a b d e - 945B a b d e +--R + +--R 6 3 4 +--R 45B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 3 3 6 2 4 2 5 +--R (200A a b + 200B a b )e + 200B a b d e + 600B a b d e +--R + +--R 5 3 4 6 4 3 +--R - 1660B a b d e + 460B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 4 2 6 3 3 2 5 +--R (150A a b + 75B a b)e + 75B a b d e + 150B a b d e +--R + +--R 2 4 3 4 5 4 3 6 5 2 +--R 450B a b d e - 1470B a b d e + 570B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 5 6 4 2 2 5 3 3 3 4 +--R (60A a b + 12B a )e + 18B a b d e + 30B a b d e + 60B a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 180B a b d e - 660B a b d e + 300B b d e +--R * +--R x +--R + +--R 6 7 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 10A a e + 2B a d e + 3B a b d e + 5B a b d e + 10B a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R 30B a b d e - 120B a b d e + 60B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 7 6 7 +--R (60B a b e - 60B b d e )x +--R + +--R 2 5 7 6 6 7 2 5 6 +--R (60B a b e + 300B a b d e - 360B b d e )x +--R + +--R 2 5 6 6 2 5 7 3 4 5 +--R (360B a b d e + 540B a b d e - 900B b d e )x +--R + +--R 2 5 2 5 6 3 4 7 4 3 4 +--R (900B a b d e + 300B a b d e - 1200B b d e )x +--R + +--R 2 5 3 4 6 4 3 7 5 2 3 +--R (1200B a b d e - 300B a b d e - 900B b d e )x +--R + +--R 2 5 4 3 6 5 2 7 6 2 +--R (900B a b d e - 540B a b d e - 360B b d e)x +--R + +--R 2 5 5 2 6 6 7 7 2 5 6 6 7 +--R (360B a b d e - 300B a b d e - 60B b d )x + 60B a b d e - 60B a b d +--R * +--R log(e x + d) +--R + +--R 6 2 5 7 7 6 6 7 2 5 6 +--R ((- 60A a b - 300B a b )e + (60A b + 660B a b )d e - 360B b d e )x +--R + +--R 2 5 3 4 7 6 2 5 6 +--R (- 210A a b - 600B a b )e + (60A a b + 210B a b )d e +--R + +--R 7 6 2 5 7 3 4 +--R (150A b + 1740B a b )d e - 1350B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 7 3 4 6 +--R (- 350A a b - 500B a b )e - 650B a b d e +--R + +--R 6 2 5 2 5 7 6 3 4 +--R (150A a b + 1500B a b )d e + (200A b + 1850B a b )d e +--R + +--R 7 4 3 +--R - 2200B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 4 3 6 3 4 2 5 +--R (- 350A a b - 275B a b )e - 275B a b d e - 750B a b d e +--R + +--R 6 2 5 3 4 7 6 4 3 7 5 2 +--R (200A a b + 2750B a b )d e + (150A b + 425B a b )d e - 1875B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 7 5 2 6 4 3 2 5 +--R (- 210A a b - 87B a b)e - 93B a b d e - 180B a b d e +--R + +--R 3 4 3 4 6 2 5 4 3 +--R - 510B a b d e + (150A a b + 2445B a b )d e +--R + +--R 7 6 5 2 7 6 +--R (60A b - 753B a b )d e - 822B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 7 6 6 5 2 2 5 4 3 3 4 +--R (- 70A a b - 12B a )e - 20B a b d e - 33B a b d e - 65B a b d e +--R + +--R 3 4 4 3 6 2 5 5 2 +--R - 190B a b d e + (60A a b + 1092B a b )d e +--R + +--R 7 6 6 7 7 +--R (10A b - 625B a b )d e - 147B b d +--R * +--R x +--R + +--R 7 7 7 6 6 2 5 5 2 3 4 4 3 4 3 +--R - 10A a e - 2B a d e - 3B a b d e - 5B a b d e - 10B a b d e +--R + +--R 3 4 5 2 6 2 5 6 6 7 +--R - 30B a b d e + (10A a b + 197B a b )d e - 147B a b d +--R / +--R 14 2 13 7 2 14 13 2 2 12 6 +--R (60a b e - 60b d e )x + (60a e + 300a b d e - 360b d e )x +--R + +--R 2 13 2 12 2 3 11 5 +--R (360a d e + 540a b d e - 900b d e )x +--R + +--R 2 2 12 3 11 2 4 10 4 +--R (900a d e + 300a b d e - 1200b d e )x +--R + +--R 2 3 11 4 10 2 5 9 3 +--R (1200a d e - 300a b d e - 900b d e )x +--R + +--R 2 4 10 5 9 2 6 8 2 +--R (900a d e - 540a b d e - 360b d e )x +--R + +--R 2 5 9 6 8 2 7 7 2 6 8 7 7 +--R (360a d e - 300a b d e - 60b d e )x + 60a d e - 60a b d e +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 620 + +)clear all + +--S 621 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^8 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1378 +r0:=1/6*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*_ + (d+e*x)^6)+1/7*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*_ + (d+e*x)^7) +--R +--R +--R (2) +--R 6 5 6 6 +--R ((A b - 7B a b )e + 6B b d)x +--R + +--R 5 2 4 6 5 5 +--R ((- A a b - 35B a b )e + (7A b + 29B a b )d)x +--R + +--R 2 4 3 3 5 2 4 4 +--R ((- 20A a b - 70B a b )e + (35A a b + 55B a b )d)x +--R + +--R 3 3 4 2 2 4 3 3 3 +--R ((- 50A a b - 70B a b )e + (70A a b + 50B a b )d)x +--R + +--R 4 2 5 3 3 4 2 2 +--R ((- 55A a b - 35B a b)e + (70A a b + 20B a b )d)x +--R + +--R 5 6 4 2 5 6 5 6 +--R ((- 29A a b - 7B a )e + (35A a b + B a b)d)x - 6A a e + (7A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 9 8 2 2 7 7 +--R (42a e - 84a b d e + 42b d e )x +--R + +--R 2 8 2 7 2 3 6 6 +--R (294a d e - 588a b d e + 294b d e )x +--R + +--R 2 2 7 3 6 2 4 5 5 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 3 6 4 5 2 5 4 4 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 4 5 5 4 2 6 3 3 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 5 4 6 3 2 7 2 2 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 6 3 7 2 2 8 2 7 2 8 2 9 +--R (294a d e - 588a b d e + 294b d e)x + 42a d e - 84a b d e + 42b d +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 42B b e x + ((- 21A b - 105B a b )e - 126B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((- 70A a b - 140B a b )e + (- 35A b - 175B a b )d e - 210B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 105A a b - 105B a b )e + (- 70A a b - 140B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 35A b - 175B a b )d e - 210B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 84A a b - 42B a b)e + (- 63A a b - 63B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (- 42A a b - 84B a b )d e + (- 21A b - 105B a b )d e - 126B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 35A a b - 7B a )e + (- 28A a b - 14B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 21A a b - 21B a b )d e + (- 14A a b - 28B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 7A b - 35B a b )d e - 42B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 6A a e + (- 5A a b - B a )d e + (- 4A a b - 2B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 3A a b - 3B a b )d e + (- 2A a b - 4B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - 6B b d +--R / +--R 14 7 13 6 2 12 5 3 11 4 4 10 3 5 9 2 +--R 42e x + 294d e x + 882d e x + 1470d e x + 1470d e x + 882d e x +--R + +--R 6 8 7 7 +--R 294d e x + 42d e +--R Type: Union(Expression(Integer),...) +--E 623 + +--S 624 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 8 6 7 6 +--R ((- A b + 7B a b )e - 6B b d e )x +--R + +--R 5 2 4 8 6 5 7 5 +--R ((A a b + 35B a b )e + (- 7A b - 29B a b )d e )x +--R + +--R 2 4 3 3 8 5 2 4 7 4 +--R ((20A a b + 70B a b )e + (- 35A a b - 55B a b )d e )x +--R + +--R 3 3 4 2 8 2 4 3 3 7 3 +--R ((50A a b + 70B a b )e + (- 70A a b - 50B a b )d e )x +--R + +--R 4 2 5 8 3 3 4 2 7 2 +--R ((55A a b + 35B a b)e + (- 70A a b - 20B a b )d e )x +--R + +--R 5 6 8 4 2 5 7 6 8 +--R ((29A a b + 7B a )e + (- 35A a b - B a b)d e )x + 6A a e +--R + +--R 5 6 7 +--R (- 7A a b + B a )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 5 8 6 7 7 2 6 6 +--R (- 42B a b e + 84B a b d e - 42B b d e )x +--R + +--R 2 5 3 4 8 6 2 5 7 +--R (- 21A a b - 105B a b )e + (42A a b + 84B a b )d e +--R + +--R 7 6 2 6 7 3 5 +--R (- 21A b + 147B a b )d e - 126B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 8 2 5 3 4 7 +--R (- 70A a b - 140B a b )e + (105A a b + 105B a b )d e +--R + +--R 7 6 3 5 7 4 4 +--R (- 35A b + 245B a b )d e - 210B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 8 3 4 4 3 7 +--R (- 105A a b - 105B a b )e + (140A a b + 70B a b )d e +--R + +--R 7 6 4 4 7 5 3 +--R (- 35A b + 245B a b )d e - 210B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 8 4 3 5 2 7 +--R (- 84A a b - 42B a b)e + (105A a b + 21B a b )d e +--R + +--R 7 6 5 3 7 6 2 +--R (- 21A b + 147B a b )d e - 126B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 8 5 2 7 7 6 6 2 +--R (- 35A a b - 7B a )e + 42A a b d e + (- 7A b + 49B a b )d e +--R + +--R 7 7 +--R - 42B b d e +--R * +--R x +--R + +--R 7 8 6 7 7 7 6 7 7 8 +--R - 6A a e + (7A a b - B a )d e + (- A b + 7B a b )d e - 6B b d +--R / +--R 2 16 15 2 2 14 7 +--R (42a e - 84a b d e + 42b d e )x +--R + +--R 2 15 2 14 2 3 13 6 +--R (294a d e - 588a b d e + 294b d e )x +--R + +--R 2 2 14 3 13 2 4 12 5 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 3 13 4 12 2 5 11 4 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 4 12 5 11 2 6 10 3 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 5 11 6 10 2 7 9 2 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 6 10 7 9 2 8 8 2 7 9 8 8 2 9 7 +--R (294a d e - 588a b d e + 294b d e )x + 42a d e - 84a b d e + 42b d e +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 625 + +)clear all + +--S 626 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^9 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1378 +r0:=-1/8*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^8)+1/24*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^7)+1/168*(3*b*B*d+A*b*e-_ + 4*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^7) +--R +--R +--R (2) +--R 7 6 2 7 7 +--R ((- A b + 4B a b )e - 3B b d e)x +--R + +--R 6 2 5 2 7 6 7 2 6 +--R ((A a b - 4B a b )e + (- 8A b + 35B a b )d e - 24B b d )x +--R + +--R 2 5 3 4 2 6 2 5 +--R (- A a b - 80B a b )e + (8A a b + 217B a b )d e +--R + +--R 7 6 2 +--R (- 28A b - 116B a b )d +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 2 2 5 3 4 +--R (- 55A a b - 200B a b )e + (160A a b + 455B a b )d e +--R + +--R 6 2 5 2 +--R (- 140A a b - 220B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 2 3 4 4 3 +--R (- 155A a b - 220B a b )e + (400A a b + 455B a b )d e +--R + +--R 2 5 3 4 2 +--R (- 280A a b - 200B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 6 2 4 3 5 2 +--R (- 181A a b - 116B a b)e + (440A a b + 217B a b )d e +--R + +--R 3 4 4 3 2 +--R (- 280A a b - 80B a b )d +--R * +--R 2 +--R x +--R + +--R 6 7 2 5 2 6 +--R (- 99A a b - 24B a )e + (232A a b + 35B a b)d e +--R + +--R 4 3 5 2 2 +--R (- 140A a b - 4B a b )d +--R * +--R x +--R + +--R 7 2 6 7 5 2 6 2 +--R - 21A a e + (48A a b - 3B a )d e + (- 28A a b + 4B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 11 2 10 2 2 9 3 3 8 8 +--R (168a e - 504a b d e + 504a b d e - 168b d e )x +--R + +--R 3 10 2 2 9 2 3 8 3 4 7 7 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e )x +--R + +--R 3 2 9 2 3 8 2 4 7 3 5 6 6 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (11760a d e - 35280a b d e + 35280a b d e - 11760b d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e)x + 168a d e +--R + +--R 2 9 2 2 10 3 11 +--R - 504a b d e + 504a b d e - 168b d +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 84B b e x + ((- 56A b - 280B a b )e - 168B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 210A a b - 420B a b )e + (- 70A b - 350B a b )d e +--R + +--R 5 2 4 +--R - 210B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 336A a b - 336B a b )e + (- 168A a b - 336B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 56A b - 280B a b )d e - 168B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 280A a b - 140B a b)e + (- 168A a b - 168B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (- 84A a b - 168B a b )d e + (- 28A b - 140B a b )d e - 84B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 120A a b - 24B a )e + (- 80A a b - 40B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 48A a b - 48B a b )d e + (- 24A a b - 48B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 8A b - 40B a b )d e - 24B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 21A a e + (- 15A a b - 3B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 6A a b - 6B a b )d e + (- 3A a b - 6B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - 3B b d +--R / +--R 15 8 14 7 2 13 6 3 12 5 4 11 4 +--R 168e x + 1344d e x + 4704d e x + 9408d e x + 11760d e x +--R + +--R 5 10 3 6 9 2 7 8 8 7 +--R 9408d e x + 4704d e x + 1344d e x + 168d e +--R Type: Union(Expression(Integer),...) +--E 628 + +--S 629 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 6 9 7 8 7 +--R ((A b - 4B a b )e + 3B b d e )x +--R + +--R 6 2 5 9 7 6 8 7 2 7 6 +--R ((- A a b + 4B a b )e + (8A b - 35B a b )d e + 24B b d e )x +--R + +--R 2 5 3 4 9 6 2 5 8 +--R (A a b + 80B a b )e + (- 8A a b - 217B a b )d e +--R + +--R 7 6 2 7 +--R (28A b + 116B a b )d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 9 2 5 3 4 8 +--R (55A a b + 200B a b )e + (- 160A a b - 455B a b )d e +--R + +--R 6 2 5 2 7 +--R (140A a b + 220B a b )d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 9 3 4 4 3 8 +--R (155A a b + 220B a b )e + (- 400A a b - 455B a b )d e +--R + +--R 2 5 3 4 2 7 +--R (280A a b + 200B a b )d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 9 4 3 5 2 8 +--R (181A a b + 116B a b)e + (- 440A a b - 217B a b )d e +--R + +--R 3 4 4 3 2 7 +--R (280A a b + 80B a b )d e +--R * +--R 2 +--R x +--R + +--R 6 7 9 5 2 6 8 +--R (99A a b + 24B a )e + (- 232A a b - 35B a b)d e +--R + +--R 4 3 5 2 2 7 +--R (140A a b + 4B a b )d e +--R * +--R x +--R + +--R 7 9 6 7 8 5 2 6 2 7 +--R 21A a e + (- 48A a b + 3B a )d e + (28A a b - 4B a b)d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 9 2 6 8 7 2 7 8 3 6 6 +--R (- 84B a b e + 252B a b d e - 252B a b d e + 84B b d e )x +--R + +--R 3 5 4 4 9 2 6 3 5 8 +--R (- 56A a b - 280B a b )e + (168A a b + 672B a b )d e +--R + +--R 7 2 6 2 7 8 7 3 6 8 4 5 +--R (- 168A a b - 336B a b )d e + (56A b - 224B a b )d e + 168B b d e +--R * +--R 5 +--R x +--R + +--R 4 4 5 3 9 3 5 4 4 8 +--R (- 210A a b - 420B a b )e + (560A a b + 910B a b )d e +--R + +--R 2 6 3 5 2 7 8 7 4 5 8 5 4 +--R (- 420A a b - 420B a b )d e + (70A b - 280B a b )d e + 210B b d e +--R * +--R 4 +--R x +--R + +--R 5 3 6 2 9 4 4 5 3 8 +--R (- 336A a b - 336B a b )e + (840A a b + 672B a b )d e +--R + +--R 3 5 4 4 2 7 8 7 5 4 8 6 3 +--R (- 560A a b - 280B a b )d e + (56A b - 224B a b )d e + 168B b d e +--R * +--R 3 +--R x +--R + +--R 6 2 7 9 5 3 6 2 8 +--R (- 280A a b - 140B a b)e + (672A a b + 252B a b )d e +--R + +--R 4 4 5 3 2 7 8 7 6 3 8 7 2 +--R (- 420A a b - 84B a b )d e + (28A b - 112B a b )d e + 84B b d e +--R * +--R 2 +--R x +--R + +--R 7 8 9 6 2 7 8 5 3 2 7 +--R (- 120A a b - 24B a )e + (280A a b + 32B a b)d e - 168A a b d e +--R + +--R 8 7 7 2 8 8 +--R (8A b - 32B a b )d e + 24B b d e +--R * +--R x +--R + +--R 8 9 7 8 8 6 2 7 2 7 +--R - 21A a e + (48A a b - 3B a )d e + (- 28A a b + 4B a b)d e +--R + +--R 8 7 8 8 9 +--R (A b - 4B a b )d e + 3B b d +--R / +--R 3 18 2 17 2 2 16 3 3 15 8 +--R (168a e - 504a b d e + 504a b d e - 168b d e )x +--R + +--R 3 17 2 2 16 2 3 15 3 4 14 7 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e )x +--R + +--R 3 2 16 2 3 15 2 4 14 3 5 13 6 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 3 15 2 4 14 2 5 13 3 6 12 5 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 4 14 2 5 13 2 6 12 3 7 11 4 +--R (11760a d e - 35280a b d e + 35280a b d e - 11760b d e )x +--R + +--R 3 5 13 2 6 12 2 7 11 3 8 10 3 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 6 12 2 7 11 2 8 10 3 9 9 2 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 7 11 2 8 10 2 9 9 3 10 8 3 8 10 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e )x + 168a d e +--R + +--R 2 9 9 2 10 8 3 11 7 +--R - 504a b d e + 504a b d e - 168b d e +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^10 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1378 +r0:=-1/9*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^9)+1/24*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^8)+1/72*b*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)^3*_ + (d+e*x)^7)+1/504*b*(2*b*B*d+A*b*e-3*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^7) +--R +--R +--R (2) +--R 8 7 3 8 2 8 +--R ((A b - 3B a b )e + 2B b d e )x +--R + +--R 7 2 6 3 8 7 2 8 2 7 +--R ((- A a b + 3B a b )e + (9A b - 29B a b )d e + 18B b d e)x +--R + +--R 2 6 3 5 3 7 2 6 2 +--R (A a b - 3B a b )e + (- 9A a b + 29B a b )d e +--R + +--R 8 7 2 8 3 +--R (36A b - 126B a b )d e + 72B b d +--R * +--R 6 +--R x +--R + +--R 3 5 4 4 3 2 6 3 5 2 +--R (- A a b - 165B a b )e + (9A a b + 643B a b )d e +--R + +--R 7 2 6 2 8 7 3 +--R (- 36A a b - 882B a b )d e + (84A b + 348B a b )d +--R * +--R 5 +--R x +--R + +--R 4 4 5 3 3 3 5 4 4 2 +--R (- 125A a b - 465B a b )e + (495A a b + 1625B a b )d e +--R + +--R 2 6 3 5 2 7 2 6 3 +--R (- 720A a b - 1890B a b )d e + (420A a b + 660B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 6 2 3 4 4 5 3 2 +--R (- 379A a b - 543B a b )e + (1395A a b + 1777B a b )d e +--R + +--R 3 5 4 4 2 2 6 3 5 3 +--R (- 1800A a b - 1890B a b )d e + (840A a b + 600B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 7 3 5 3 6 2 2 +--R (- 461A a b - 297B a b)e + (1629A a b + 911B a b )d e +--R + +--R 4 4 5 3 2 3 5 4 4 3 +--R (- 1980A a b - 882B a b )d e + (840A a b + 240B a b )d +--R * +--R 2 +--R x +--R + +--R 7 8 3 6 2 7 2 +--R (- 259A a b - 63B a )e + (891A a b + 169B a b)d e +--R + +--R 5 3 6 2 2 4 4 5 3 3 +--R (- 1044A a b - 126B a b )d e + (420A a b + 12B a b )d +--R * +--R x +--R + +--R 8 3 7 8 2 6 2 7 2 +--R - 56A a e + (189A a b - 7B a )d e + (- 216A a b + 18B a b)d e +--R + +--R 5 3 6 2 3 +--R (84A a b - 12B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 13 3 12 2 2 2 11 3 3 10 4 4 9 9 +--R (504a e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d e )x +--R + +--R 4 12 3 2 11 2 2 3 10 3 4 9 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 5 8 +--R 4536b d e +--R * +--R 8 +--R x +--R + +--R 4 2 11 3 3 10 2 2 4 9 3 5 8 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 6 7 +--R 18144b d e +--R * +--R 7 +--R x +--R + +--R 4 3 10 3 4 9 2 2 5 8 3 6 7 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 7 6 +--R 42336b d e +--R * +--R 6 +--R x +--R + +--R 4 4 9 3 5 8 2 2 6 7 3 7 6 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 8 5 +--R 63504b d e +--R * +--R 5 +--R x +--R + +--R 4 5 8 3 6 7 2 2 7 6 3 8 5 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 9 4 +--R 63504b d e +--R * +--R 4 +--R x +--R + +--R 4 6 7 3 7 6 2 2 8 5 3 9 4 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 10 3 +--R 42336b d e +--R * +--R 3 +--R x +--R + +--R 4 7 6 3 8 5 2 2 9 4 3 10 3 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 11 2 +--R 18144b d e +--R * +--R 2 +--R x +--R + +--R 4 8 5 3 9 4 2 2 10 3 3 11 2 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 12 +--R 4536b d e +--R * +--R x +--R + +--R 4 9 4 3 10 3 2 2 11 2 3 12 4 13 +--R 504a d e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 168B b e x + ((- 126A b - 630B a b )e - 252B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 504A a b - 1008B a b )e + (- 126A b - 630B a b )d e +--R + +--R 5 2 4 +--R - 252B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 840A a b - 840B a b )e + (- 336A a b - 672B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 84A b - 420B a b )d e - 168B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 720A a b - 360B a b)e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (- 144A a b - 288B a b )d e + (- 36A b - 180B a b )d e - 72B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 315A a b - 63B a )e + (- 180A a b - 90B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 90A a b - 90B a b )d e + (- 36A a b - 72B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 9A b - 45B a b )d e - 18B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 56A a e + (- 35A a b - 7B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 10A a b - 10B a b )d e + (- 4A a b - 8B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - 2B b d +--R / +--R 16 9 15 8 2 14 7 3 13 6 4 12 5 +--R 504e x + 4536d e x + 18144d e x + 42336d e x + 63504d e x +--R + +--R 5 11 4 6 10 3 7 9 2 8 8 9 7 +--R 63504d e x + 42336d e x + 18144d e x + 4536d e x + 504d e +--R Type: Union(Expression(Integer),...) +--E 633 + +--S 634 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 7 10 8 9 8 +--R ((- A b + 3B a b )e - 2B b d e )x +--R + +--R 7 2 6 10 8 7 9 8 2 8 7 +--R ((A a b - 3B a b )e + (- 9A b + 29B a b )d e - 18B b d e )x +--R + +--R 2 6 3 5 10 7 2 6 9 +--R (- A a b + 3B a b )e + (9A a b - 29B a b )d e +--R + +--R 8 7 2 8 8 3 7 +--R (- 36A b + 126B a b )d e - 72B b d e +--R * +--R 6 +--R x +--R + +--R 3 5 4 4 10 2 6 3 5 9 +--R (A a b + 165B a b )e + (- 9A a b - 643B a b )d e +--R + +--R 7 2 6 2 8 8 7 3 7 +--R (36A a b + 882B a b )d e + (- 84A b - 348B a b )d e +--R * +--R 5 +--R x +--R + +--R 4 4 5 3 10 3 5 4 4 9 +--R (125A a b + 465B a b )e + (- 495A a b - 1625B a b )d e +--R + +--R 2 6 3 5 2 8 7 2 6 3 7 +--R (720A a b + 1890B a b )d e + (- 420A a b - 660B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 3 6 2 10 4 4 5 3 9 +--R (379A a b + 543B a b )e + (- 1395A a b - 1777B a b )d e +--R + +--R 3 5 4 4 2 8 2 6 3 5 3 7 +--R (1800A a b + 1890B a b )d e + (- 840A a b - 600B a b )d e +--R * +--R 3 +--R x +--R + +--R 6 2 7 10 5 3 6 2 9 +--R (461A a b + 297B a b)e + (- 1629A a b - 911B a b )d e +--R + +--R 4 4 5 3 2 8 3 5 4 4 3 7 +--R (1980A a b + 882B a b )d e + (- 840A a b - 240B a b )d e +--R * +--R 2 +--R x +--R + +--R 7 8 10 6 2 7 9 +--R (259A a b + 63B a )e + (- 891A a b - 169B a b)d e +--R + +--R 5 3 6 2 2 8 4 4 5 3 3 7 +--R (1044A a b + 126B a b )d e + (- 420A a b - 12B a b )d e +--R * +--R x +--R + +--R 8 10 7 8 9 6 2 7 2 8 +--R 56A a e + (- 189A a b + 7B a )d e + (216A a b - 18B a b)d e +--R + +--R 5 3 6 2 3 7 +--R (- 84A a b + 12B a b )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 10 3 6 9 2 7 2 8 8 3 7 +--R - 168B a b e + 672B a b d e - 1008B a b d e + 672B a b d e +--R + +--R 9 4 6 +--R - 168B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 5 4 10 3 6 4 5 9 +--R (- 126A a b - 630B a b )e + (504A a b + 2268B a b )d e +--R + +--R 2 7 3 6 2 8 8 2 7 3 7 +--R (- 756A a b - 2772B a b )d e + (504A a b + 1008B a b )d e +--R + +--R 9 8 4 6 9 5 5 +--R (- 126A b + 378B a b )d e - 252B b d e +--R * +--R 5 +--R x +--R + +--R 5 4 6 3 10 4 5 5 4 9 +--R (- 504A a b - 1008B a b )e + (1890A a b + 3402B a b )d e +--R + +--R 3 6 4 5 2 8 2 7 3 6 3 7 +--R (- 2520A a b - 3780B a b )d e + (1260A a b + 1260B a b )d e +--R + +--R 9 8 5 5 9 6 4 +--R (- 126A b + 378B a b )d e - 252B b d e +--R * +--R 4 +--R x +--R + +--R 6 3 7 2 10 5 4 6 3 9 +--R (- 840A a b - 840B a b )e + (3024A a b + 2688B a b )d e +--R + +--R 4 5 5 4 2 8 3 6 4 5 3 7 +--R (- 3780A a b - 2772B a b )d e + (1680A a b + 840B a b )d e +--R + +--R 9 8 6 4 9 7 3 +--R (- 84A b + 252B a b )d e - 168B b d e +--R * +--R 3 +--R x +--R + +--R 7 2 8 10 6 3 7 2 9 +--R (- 720A a b - 360B a b)e + (2520A a b + 1080B a b )d e +--R + +--R 5 4 6 3 2 8 4 5 5 4 3 7 +--R (- 3024A a b - 1008B a b )d e + (1260A a b + 252B a b )d e +--R + +--R 9 8 7 3 9 8 2 +--R (- 36A b + 108B a b )d e - 72B b d e +--R * +--R 2 +--R x +--R + +--R 8 9 10 7 2 8 9 +--R (- 315A a b - 63B a )e + (1080A a b + 162B a b)d e +--R + +--R 6 3 7 2 2 8 5 4 3 7 +--R (- 1260A a b - 108B a b )d e + 504A a b d e +--R + +--R 9 8 8 2 9 9 +--R (- 9A b + 27B a b )d e - 18B b d e +--R * +--R x +--R + +--R 9 10 8 9 9 7 2 8 2 8 +--R - 56A a e + (189A a b - 7B a )d e + (- 216A a b + 18B a b)d e +--R + +--R 6 3 7 2 3 7 9 8 9 9 10 +--R (84A a b - 12B a b )d e + (- A b + 3B a b )d e - 2B b d +--R / +--R 4 20 3 19 2 2 2 18 3 3 17 4 4 16 9 +--R (504a e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d e )x +--R + +--R 4 19 3 2 18 2 2 3 17 3 4 16 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 5 15 +--R 4536b d e +--R * +--R 8 +--R x +--R + +--R 4 2 18 3 3 17 2 2 4 16 3 5 15 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 6 14 +--R 18144b d e +--R * +--R 7 +--R x +--R + +--R 4 3 17 3 4 16 2 2 5 15 3 6 14 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 7 13 +--R 42336b d e +--R * +--R 6 +--R x +--R + +--R 4 4 16 3 5 15 2 2 6 14 3 7 13 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 8 12 +--R 63504b d e +--R * +--R 5 +--R x +--R + +--R 4 5 15 3 6 14 2 2 7 13 3 8 12 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 9 11 +--R 63504b d e +--R * +--R 4 +--R x +--R + +--R 4 6 14 3 7 13 2 2 8 12 3 9 11 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 10 10 +--R 42336b d e +--R * +--R 3 +--R x +--R + +--R 4 7 13 3 8 12 2 2 9 11 3 10 10 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 11 9 +--R 18144b d e +--R * +--R 2 +--R x +--R + +--R 4 8 12 3 9 11 2 2 10 10 3 11 9 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 12 8 +--R 4536b d e +--R * +--R x +--R + +--R 4 9 11 3 10 10 2 2 11 9 3 12 8 4 13 7 +--R 504a d e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d e +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 635 + +)clear all + +--S 636 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^11 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1378 +r0:=-1/10*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^10)+1/45*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^9)+1/120*b*(3*b*B*d+2*A*b*e-_ + 5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)^3*(d+_ + e*x)^8)+1/360*b^2*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^4*(d+e*x)^7)+1/2520*b^2*(3*b*B*d+2*A*b*e-_ + 5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^7) +--R +--R +--R (2) +--R 9 8 4 9 3 9 +--R ((- 2A b 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b )d +--R * +--R 4 +--R x +--R + +--R 6 3 7 2 4 5 4 6 3 3 +--R (- 1598A a b - 2305B a b )e + (7580A a b + 10153B a b )d e +--R + +--R 4 5 5 4 2 2 3 6 4 5 3 +--R (- 13950A a b - 16755B a b )d e + (12000A a b + 12075B a b )d e +--R + +--R 2 7 3 6 4 +--R (- 4200A a b - 3000B a b )d +--R * +--R 3 +--R x +--R + +--R 7 2 8 4 6 3 7 2 3 +--R (- 2002A a b - 1295B a b)e + (9220A a b + 5447B a b )d e +--R + +--R 5 4 6 3 2 2 4 5 5 4 3 +--R (- 16290A a b - 8445B a b )d e + (13200A a b + 5565B a b )d e +--R + +--R 3 6 4 5 4 +--R (- 4200A a b - 1200B a b )d +--R * +--R 2 +--R x +--R + +--R 8 9 4 7 2 8 3 +--R (- 1148A a b - 280B a )e + (5180A a b + 1078B a b)d e +--R + +--R 6 3 7 2 2 2 5 4 6 3 3 +--R (- 8910A a b - 1455B a b )d e + (6960A a b + 735B a b )d e +--R + +--R 4 5 5 4 4 +--R (- 2100A a b - 60B a b )d +--R * +--R x +--R + +--R 9 4 8 9 3 7 2 8 2 2 +--R - 252A a e + (1120A a b - 28B a )d e + (- 1890A a b + 105B a b)d e +--R + +--R 6 3 7 2 3 5 4 6 3 4 +--R (1440A a b - 135B a b )d e + (- 420A a b + 60B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 15 4 14 3 2 2 13 2 3 3 12 +--R 2520a e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 4 11 5 5 10 +--R 12600a b d e - 2520b d e +--R * +--R 10 +--R x +--R + +--R 5 14 4 2 13 3 2 3 12 2 3 4 11 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 5 10 5 6 9 +--R 126000a b d e - 25200b d e +--R * +--R 9 +--R x +--R + +--R 5 2 13 4 3 12 3 2 4 11 2 3 5 10 +--R 113400a d e - 567000a b d e + 1134000a b d e - 1134000a b d e +--R + +--R 4 6 9 5 7 8 +--R 567000a b d e - 113400b d e +--R * +--R 8 +--R x +--R + +--R 5 3 12 4 4 11 3 2 5 10 2 3 6 9 +--R 302400a d e - 1512000a b d e + 3024000a b d e - 3024000a b d e +--R + +--R 4 7 8 5 8 7 +--R 1512000a b d e - 302400b d e +--R * +--R 7 +--R x +--R + +--R 5 4 11 4 5 10 3 2 6 9 2 3 7 8 +--R 529200a d e - 2646000a b d e + 5292000a b d e - 5292000a b d e +--R + +--R 4 8 7 5 9 6 +--R 2646000a b d e - 529200b d e +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 2 7 8 2 3 8 7 +--R 635040a d e - 3175200a b d e + 6350400a b d e - 6350400a b d e +--R + +--R 4 9 6 5 10 5 +--R 3175200a b d e - 635040b d e +--R * +--R 5 +--R x +--R + +--R 5 6 9 4 7 8 3 2 8 7 2 3 9 6 +--R 529200a d e - 2646000a b d e + 5292000a b d e - 5292000a b d e +--R + +--R 4 10 5 5 11 4 +--R 2646000a b d e - 529200b d e +--R * +--R 4 +--R x +--R + +--R 5 7 8 4 8 7 3 2 9 6 2 3 10 5 +--R 302400a d e - 1512000a b d e + 3024000a b d e - 3024000a b d e +--R + +--R 4 11 4 5 12 3 +--R 1512000a b d e - 302400b d e +--R * +--R 3 +--R x +--R + +--R 5 8 7 4 9 6 3 2 10 5 2 3 11 4 +--R 113400a d e - 567000a b d e + 1134000a b d e - 1134000a b d e +--R + +--R 4 12 3 5 13 2 +--R 567000a b d e - 113400b d e +--R * +--R 2 +--R x +--R + +--R 5 9 6 4 10 5 3 2 11 4 2 3 12 3 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 13 2 5 14 +--R 126000a b d e - 25200b d e +--R * +--R x +--R + +--R 5 10 5 4 11 4 3 2 12 3 2 3 13 2 +--R 2520a d e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 14 5 15 +--R 12600a b d e - 2520b d +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 630B b e x + ((- 504A b - 2520B a b )e - 756B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 2100A a b - 4200B a b )e + (- 420A b - 2100B a b )d e +--R + +--R 5 2 4 +--R - 630B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 3600A a b - 3600B a b )e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 240A b - 1200B a b )d e - 360B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 3150A a b - 1575B a b)e + (- 1350A a b - 1350B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 450A a b - 900B a b )d e + (- 90A b - 450B a b )d e +--R + +--R 5 4 2 +--R - 135B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 1400A a b - 280B a )e + (- 700A a b - 350B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 300A a b - 300B a b )d e + (- 100A a b - 200B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 20A b - 100B a b )d e - 30B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 252A a e + (- 140A a b - 28B a )d e + (- 70A a b - 35B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 30A a b - 30B a b )d e + (- 10A a b - 20B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 2A b - 10B a b )d e - 3B b d +--R / +--R 17 10 16 9 2 15 8 3 14 7 4 13 6 +--R 2520e x + 25200d e x + 113400d e x + 302400d e x + 529200d e x +--R + +--R 5 12 5 6 11 4 7 10 3 8 9 2 9 8 +--R 635040d e x + 529200d e x + 302400d e x + 113400d e x + 25200d e x +--R + +--R 10 7 +--R 2520d e +--R Type: Union(Expression(Integer),...) +--E 638 + +--S 639 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 8 11 9 10 9 +--R ((2A b - 5B a b )e + 3B b d e )x +--R + +--R 8 2 7 11 9 8 10 9 2 9 8 +--R ((- 2A a b + 5B a b )e + (20A b - 53B a b )d e + 30B b d e )x +--R + +--R 2 7 3 6 11 8 2 7 10 +--R (2A a b - 5B a b )e + (- 20A a b + 53B a b )d e +--R + +--R 9 8 2 9 9 3 8 +--R (90A b - 255B a b )d e + 135B b d e +--R * +--R 7 +--R x +--R + +--R 3 6 4 5 11 2 7 3 6 10 +--R (- 2A a b + 5B a b )e + (20A a b - 53B a b )d e +--R + +--R 8 2 7 2 9 9 8 3 8 +--R (- 90A a b + 255B a b )d e + (240A b - 735B a b )d e +--R + +--R 9 4 7 +--R 360B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 5 4 11 3 6 4 5 10 +--R (2A a b + 625B a b )e + (- 20A a b - 3097B a b )d e +--R + +--R 2 7 3 6 2 9 8 2 7 3 8 +--R (90A a b + 6045B a b )d e + (- 240A a b - 5565B a b )d e +--R + +--R 9 8 4 7 +--R (420A b + 1740B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 4 6 3 11 4 5 5 4 10 +--R (502A a b + 1895B a b )e + (- 2500A a b - 8747B a b )d e +--R + +--R 3 6 4 5 2 9 2 7 3 6 3 8 +--R (4950A a b + 15375B a b )d e + (- 4800A a b - 12075B a b )d e +--R + +--R 8 2 7 4 7 +--R (2100A a b + 3300B a b )d e +--R * +--R 4 +--R x +--R + +--R 6 3 7 2 11 5 4 6 3 10 +--R (1598A a b + 2305B a b )e + (- 7580A a b - 10153B a b )d e +--R + +--R 4 5 5 4 2 9 +--R (13950A a b + 16755B a b )d e +--R + +--R 3 6 4 5 3 8 2 7 3 6 4 7 +--R (- 12000A a b - 12075B a b )d e + (4200A a b + 3000B a b )d e +--R * +--R 3 +--R x +--R + +--R 7 2 8 11 6 3 7 2 10 +--R (2002A a b + 1295B a b)e + (- 9220A a b - 5447B a b )d e +--R + +--R 5 4 6 3 2 9 4 5 5 4 3 8 +--R (16290A a b + 8445B a b )d e + (- 13200A a b - 5565B a b )d e +--R + +--R 3 6 4 5 4 7 +--R (4200A a b + 1200B a b )d e +--R * +--R 2 +--R x +--R + +--R 8 9 11 7 2 8 10 +--R (1148A a b + 280B a )e + (- 5180A a b - 1078B a b)d e +--R + +--R 6 3 7 2 2 9 5 4 6 3 3 8 +--R (8910A a b + 1455B a b )d e + (- 6960A a b - 735B a b )d e +--R + +--R 4 5 5 4 4 7 +--R (2100A a b + 60B a b )d e +--R * +--R x +--R + +--R 9 11 8 9 10 +--R 252A a e + (- 1120A a b + 28B a )d e +--R + +--R 7 2 8 2 9 6 3 7 2 3 8 +--R (1890A a b - 105B a b)d e + (- 1440A a b + 135B a b )d e +--R + +--R 5 4 6 3 4 7 +--R (420A a b - 60B a b )d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 5 11 4 6 10 3 7 2 9 2 8 3 8 +--R - 630B a b e + 3150B a b d e - 6300B a b d e + 6300B a b d e +--R + +--R 9 4 7 10 5 6 +--R - 3150B a b d e + 630B b d e +--R * +--R 6 +--R x +--R + +--R 5 5 6 4 11 4 6 5 5 10 +--R (- 504A a b - 2520B a b )e + (2520A a b + 11844B a b )d e +--R + +--R 3 7 4 6 2 9 2 8 3 7 3 8 +--R (- 5040A a b - 21420B a b )d e + (5040A a b + 17640B a b )d e +--R + +--R 9 2 8 4 7 10 9 5 6 +--R (- 2520A a b - 5040B a b )d e + (504A b - 1260B a b )d e +--R + +--R 10 6 5 +--R 756B b d e +--R * +--R 5 +--R x +--R + +--R 6 4 7 3 11 5 5 6 4 10 +--R (- 2100A a b - 4200B a b )e + (10080A a b + 18900B a b )d e +--R + +--R 4 6 5 5 2 9 3 7 4 6 3 8 +--R (- 18900A a b - 32130B a b )d e + (16800A a b + 24150B a b )d e +--R + +--R 2 8 3 7 4 7 10 9 6 5 +--R (- 6300A a b - 6300B a b )d e + (420A b - 1050B a b )d e +--R + +--R 10 7 4 +--R 630B b d e +--R * +--R 4 +--R x +--R + +--R 7 3 8 2 11 6 4 7 3 10 +--R (- 3600A a b - 3600B a b )e + (16800A a b + 15600B a b )d e +--R + +--R 5 5 6 4 2 9 4 6 5 5 3 8 +--R (- 30240A a b - 25200B a b )d e + (25200A a b + 17640B a b )d e +--R + +--R 3 7 4 6 4 7 10 9 7 4 +--R (- 8400A a b - 4200B a b )d e + (240A b - 600B a b )d e +--R + +--R 10 8 3 +--R 360B b d e +--R * +--R 3 +--R x +--R + +--R 8 2 9 11 7 3 8 2 10 +--R (- 3150A a b - 1575B a b)e + (14400A a b + 6525B a b )d e +--R + +--R 6 4 7 3 2 9 5 5 6 4 3 8 +--R (- 25200A a b - 9900B a b )d e + (20160A a b + 6300B a b )d e +--R + +--R 4 6 5 5 4 7 10 9 8 3 +--R (- 6300A a b - 1260B a b )d e + (90A b - 225B a b )d e +--R + +--R 10 9 2 +--R 135B b d e +--R * +--R 2 +--R x +--R + +--R 9 10 11 8 2 9 10 +--R (- 1400A a b - 280B a )e + (6300A a b + 1050B a b)d e +--R + +--R 7 3 8 2 2 9 6 4 7 3 3 8 +--R (- 10800A a b - 1350B a b )d e + (8400A a b + 600B a b )d e +--R + +--R 5 5 4 7 10 9 9 2 10 10 +--R - 2520A a b d e + (20A b - 50B a b )d e + 30B b d e +--R * +--R x +--R + +--R 10 11 9 10 10 +--R - 252A a e + (1120A a b - 28B a )d e +--R + +--R 8 2 9 2 9 7 3 8 2 3 8 +--R (- 1890A a b + 105B a b)d e + (1440A a b - 135B a b )d e +--R + +--R 6 4 7 3 4 7 10 9 10 10 11 +--R (- 420A a b + 60B a b )d e + (2A b - 5B a b )d e + 3B b d +--R / +--R 5 22 4 21 3 2 2 20 2 3 3 19 +--R 2520a e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 4 18 5 5 17 +--R 12600a b d e - 2520b d e +--R * +--R 10 +--R x +--R + +--R 5 21 4 2 20 3 2 3 19 2 3 4 18 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 5 17 5 6 16 +--R 126000a b d e - 25200b d e +--R * +--R 9 +--R x +--R + +--R 5 2 20 4 3 19 3 2 4 18 2 3 5 17 +--R 113400a d e - 567000a b d e + 1134000a b d e - 1134000a b d e +--R + +--R 4 6 16 5 7 15 +--R 567000a b d e - 113400b d e +--R * +--R 8 +--R x +--R + +--R 5 3 19 4 4 18 3 2 5 17 +--R 302400a d e - 1512000a b d e + 3024000a b d e +--R + +--R 2 3 6 16 4 7 15 5 8 14 +--R - 3024000a b d e + 1512000a b d e - 302400b d e +--R * +--R 7 +--R x +--R + +--R 5 4 18 4 5 17 3 2 6 16 +--R 529200a d e - 2646000a b d e + 5292000a b d e +--R + +--R 2 3 7 15 4 8 14 5 9 13 +--R - 5292000a b d e + 2646000a b d e - 529200b d e +--R * +--R 6 +--R x +--R + +--R 5 5 17 4 6 16 3 2 7 15 +--R 635040a d e - 3175200a b d e + 6350400a b d e +--R + +--R 2 3 8 14 4 9 13 5 10 12 +--R - 6350400a b d e + 3175200a b d e - 635040b d e +--R * +--R 5 +--R x +--R + +--R 5 6 16 4 7 15 3 2 8 14 +--R 529200a d e - 2646000a b d e + 5292000a b d e +--R + +--R 2 3 9 13 4 10 12 5 11 11 +--R - 5292000a b d e + 2646000a b d e - 529200b d e +--R * +--R 4 +--R x +--R + +--R 5 7 15 4 8 14 3 2 9 13 +--R 302400a d e - 1512000a b d e + 3024000a b d e +--R + +--R 2 3 10 12 4 11 11 5 12 10 +--R - 3024000a b d e + 1512000a b d e - 302400b d e +--R * +--R 3 +--R x +--R + +--R 5 8 14 4 9 13 3 2 10 12 +--R 113400a d e - 567000a b d e + 1134000a b d e +--R + +--R 2 3 11 11 4 12 10 5 13 9 +--R - 1134000a b d e + 567000a b d e - 113400b d e +--R * +--R 2 +--R x +--R + +--R 5 9 13 4 10 12 3 2 11 11 2 3 12 10 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 13 9 5 14 8 +--R 126000a b d e - 25200b d e +--R * +--R x +--R + +--R 5 10 12 4 11 11 3 2 12 10 2 3 13 9 +--R 2520a d e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 14 8 5 15 7 +--R 12600a b d e - 2520b d e +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 640 + +)clear all + +--S 641 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^12 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1378 +r0:=-1/198*b*(6*b*B*d+5*A*b*e-11*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^9)-1/396*b^2*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^8)-_ + 1/11*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^11)-1/110*(6*b*B*d+5*A*b*e-11*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^10)-1/924*b^3*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*_ + (d+e*x)^7)-1/2310*b^4*(6*b*B*d+5*A*b*e-11*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^6)-1/13860*b^4*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 2772B b e x + ((- 2310A b - 11550B a b )e - 2772B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 9900A a b - 19800B a b )e + (- 1650A b - 8250B a b )d e +--R + +--R 5 2 4 +--R - 1980B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 17325A a b - 17325B a b )e + (- 4950A a b - 9900B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 825A b - 4125B a b )d e - 990B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 15400A a b - 7700B a b)e + (- 5775A a b - 5775B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 1650A a b - 3300B a b )d e + (- 275A b - 1375B a b )d e +--R + +--R 5 4 2 +--R - 330B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 6930A a b - 1386B a )e + (- 3080A a b - 1540B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 1155A a b - 1155B a b )d e + (- 330A a b - 660B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 55A b - 275B a b )d e - 66B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 1260A a e + (- 630A a b - 126B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 280A a b - 140B a b)d e + (- 105A a b - 105B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (- 30A a b - 60B a b )d e + (- 5A b - 25B a b )d e - 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 18 12 18 17 11 +--R 13860b e x + (13860a e + 152460b d e )x +--R + +--R 17 2 16 10 2 16 3 15 9 +--R (152460a d e + 762300b d e )x + (762300a d e + 2286900b d e )x +--R + +--R 3 15 4 14 8 4 14 5 13 7 +--R (2286900a d e + 4573800b d e )x + (4573800a d e + 6403320b d e )x +--R + +--R 5 13 6 12 6 6 12 7 11 5 +--R (6403320a d e + 6403320b d e )x + (6403320a d e + 4573800b d e )x +--R + +--R 7 11 8 10 4 8 10 9 9 3 +--R (4573800a d e + 2286900b d e )x + (2286900a d e + 762300b d e )x +--R + +--R 9 9 10 8 2 10 8 11 7 +--R (762300a d e + 152460b d e )x + (152460a d e + 13860b d e )x +--R + +--R 11 7 +--R 13860a d e +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 2772B b e x + ((- 2310A b - 11550B a b )e - 2772B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 9900A a b - 19800B a b )e + (- 1650A b - 8250B a b )d e +--R + +--R 5 2 4 +--R - 1980B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 17325A a b - 17325B a b )e + (- 4950A a b - 9900B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 825A b - 4125B a b )d e - 990B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 15400A a b - 7700B a b)e + (- 5775A a b - 5775B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 1650A a b - 3300B a b )d e + (- 275A b - 1375B a b )d e +--R + +--R 5 4 2 +--R - 330B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 6930A a b - 1386B a )e + (- 3080A a b - 1540B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 1155A a b - 1155B a b )d e + (- 330A a b - 660B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 55A b - 275B a b )d e - 66B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 1260A a e + (- 630A a b - 126B a )d e + (- 280A a b - 140B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 105A a b - 105B a b )d e + (- 30A a b - 60B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 5A b - 25B a b )d e - 6B b d +--R / +--R 18 11 17 10 2 16 9 3 15 8 +--R 13860e x + 152460d e x + 762300d e x + 2286900d e x +--R + +--R 4 14 7 5 13 6 6 12 5 7 11 4 +--R 4573800d e x + 6403320d e x + 6403320d e x + 4573800d e x +--R + +--R 8 10 3 9 9 2 10 8 11 7 +--R 2286900d e x + 762300d e x + 152460d e x + 13860d e +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R 2772B b e x + ((2310A b + 11550B a b )e + 2772B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (9900A a b + 19800B a b )e + (1650A b + 8250B a b )d e +--R + +--R 5 2 4 +--R 1980B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (17325A a b + 17325B a b )e + (4950A a b + 9900B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (825A b + 4125B a b )d e + 990B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (15400A a b + 7700B a b)e + (5775A a b + 5775B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (1650A a b + 3300B a b )d e + (275A b + 1375B a b )d e +--R + +--R 5 4 2 +--R 330B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (6930A a b + 1386B a )e + (3080A a b + 1540B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1155A a b + 1155B a b )d e + (330A a b + 660B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (55A b + 275B a b )d e + 66B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 1260A a e + (630A a b + 126B a )d e + (280A a b + 140B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (105A a b + 105B a b )d e + (30A a b + 60B a b )d e +--R + +--R 5 4 5 5 6 +--R (5A b + 25B a b )d e + 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R - 2772B b e x + ((- 2310A b - 14322B a b )e - 2772B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 12210A a b - 31350B a b )e + (- 1650A b - 11022B a b )d e +--R + +--R 6 2 4 +--R - 1980B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 27225A a b - 37125B a b )e + (- 6600A a b - 18150B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 825A b - 6105B a b )d e - 990B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 32725A a b - 25025B a b )e + (- 10725A a b - 15675B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 2475A a b - 7425B a b )d e + (- 275A b - 2365B a b )d e +--R + +--R 6 4 2 +--R - 330B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 22330A a b - 9086B a b)e + (- 8855A a b - 7315B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 2805A a b - 4455B a b )d e + (- 605A a b - 2035B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 55A b - 605B a b )d e - 66B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 8190A a b - 1386B a )e + (- 3710A a b - 1666B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 1435A a b - 1295B a b )d e + (- 435A a b - 765B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 85A a b - 335B a b )d e + (- 5A b - 91B a b )d e - 6B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 1260A a e + (- 630A a b - 126B a )d e + (- 280A a b - 140B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 105A a b - 105B a b )d e + (- 30A a b - 60B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- 5A a b - 25B a b )d e - 6B a b d +--R / +--R 18 12 18 17 11 +--R 13860b e x + (13860a e + 152460b d e )x +--R + +--R 17 2 16 10 2 16 3 15 9 +--R (152460a d e + 762300b d e )x + (762300a d e + 2286900b d e )x +--R + +--R 3 15 4 14 8 4 14 5 13 7 +--R (2286900a d e + 4573800b d e )x + (4573800a d e + 6403320b d e )x +--R + +--R 5 13 6 12 6 6 12 7 11 5 +--R (6403320a d e + 6403320b d e )x + (6403320a d e + 4573800b d e )x +--R + +--R 7 11 8 10 4 8 10 9 9 3 +--R (4573800a d e + 2286900b d e )x + (2286900a d e + 762300b d e )x +--R + +--R 9 9 10 8 2 10 8 11 7 +--R (762300a d e + 152460b d e )x + (152460a d e + 13860b d e )x +--R + +--R 11 7 +--R 13860a d e +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x +--R + +--R 12 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^13 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R e x + 13d e x + 78d e x + 286d e x + 715d e x + 1287d e x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 +--R 1716d e x + 1716d e x + 1287d e x + 715d e x + 286d e x + 78d e x +--R + +--R 12 13 +--R 13d e x + d +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1378 +r0:=-1/44*b*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e)*(d+e*x)^10)-1/99*b^2*(b*B*d+A*b*e-2*a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^9)-1/12*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^12)-_ + 1/22*(b*B*d+A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-_ + a*e)*(d+e*x)^11)-1/264*b^3*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*(d+e*x)^8)-1/792*b^4*(b*B*d+A*b*e-_ + 2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^7)-_ + 1/5544*b^4*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*_ + (a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 924B b e x + ((- 792A b - 3960B a b )e - 792B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 3465A a b - 6930B a b )e + (- 495A b - 2475B a b )d e +--R + +--R 5 2 4 +--R - 495B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 6160A a b - 6160B a b )e + (- 1540A a b - 3080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 220A b - 1100B a b )d e - 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 5544A a b - 2772B a b)e + (- 1848A a b - 1848B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 462A a b - 924B a b )d e + (- 66A b - 330B a b )d e +--R + +--R 5 4 2 +--R - 66B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 2520A a b - 504B a )e + (- 1008A a b - 504B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 336A a b - 336B a b )d e + (- 84A a b - 168B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 12A b - 60B a b )d e - 12B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 462A a e + (- 210A a b - 42B a )d e + (- 84A a b - 42B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 28A a b - 28B a b )d e + (- 7A a b - 14B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 19 13 19 18 12 +--R 5544b e x + (5544a e + 66528b d e )x +--R + +--R 18 2 17 11 2 17 3 16 10 +--R (66528a d e + 365904b d e )x + (365904a d e + 1219680b d e )x +--R + +--R 3 16 4 15 9 4 15 5 14 8 +--R (1219680a d e + 2744280b d e )x + (2744280a d e + 4390848b d e )x +--R + +--R 5 14 6 13 7 6 13 7 12 6 +--R (4390848a d e + 5122656b d e )x + (5122656a d e + 4390848b d e )x +--R + +--R 7 12 8 11 5 8 11 9 10 4 +--R (4390848a d e + 2744280b d e )x + (2744280a d e + 1219680b d e )x +--R + +--R 9 10 10 9 3 10 9 11 8 2 +--R (1219680a d e + 365904b d e )x + (365904a d e + 66528b d e )x +--R + +--R 11 8 12 7 12 7 +--R (66528a d e + 5544b d e )x + 5544a d e +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 924B b e x + ((- 792A b - 3960B a b )e - 792B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 3465A a b - 6930B a b )e + (- 495A b - 2475B a b )d e +--R + +--R 5 2 4 +--R - 495B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 6160A a b - 6160B a b )e + (- 1540A a b - 3080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 220A b - 1100B a b )d e - 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 5544A a b - 2772B a b)e + (- 1848A a b - 1848B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (- 462A a b - 924B a b )d e + (- 66A b - 330B a b )d e - 66B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 2520A a b - 504B a )e + (- 1008A a b - 504B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 336A a b - 336B a b )d e + (- 84A a b - 168B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 12A b - 60B a b )d e - 12B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 462A a e + (- 210A a b - 42B a )d e + (- 84A a b - 42B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 28A a b - 28B a b )d e + (- 7A a b - 14B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - B b d +--R / +--R 19 12 18 11 2 17 10 3 16 9 +--R 5544e x + 66528d e x + 365904d e x + 1219680d e x +--R + +--R 4 15 8 5 14 7 6 13 6 7 12 5 +--R 2744280d e x + 4390848d e x + 5122656d e x + 4390848d e x +--R + +--R 8 11 4 9 10 3 10 9 2 11 8 12 7 +--R 2744280d e x + 1219680d e x + 365904d e x + 66528d e x + 5544d e +--R Type: Union(Expression(Integer),...) +--E 648 + +--S 649 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R 924B b e x + ((792A b + 3960B a b )e + 792B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (3465A a b + 6930B a b )e + (495A b + 2475B a b )d e +--R + +--R 5 2 4 +--R 495B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (6160A a b + 6160B a b )e + (1540A a b + 3080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (220A b + 1100B a b )d e + 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (5544A a b + 2772B a b)e + (1848A a b + 1848B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (462A a b + 924B a b )d e + (66A b + 330B a b )d e + 66B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (2520A a b + 504B a )e + (1008A a b + 504B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (336A a b + 336B a b )d e + (84A a b + 168B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (12A b + 60B a b )d e + 12B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 462A a e + (210A a b + 42B a )d e + (84A a b + 42B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (28A a b + 28B a b )d e + (7A a b + 14B a b )d e +--R + +--R 5 4 5 5 6 +--R (A b + 5B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R - 924B b e x + ((- 792A b - 4884B a b )e - 792B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 4257A a b - 10890B a b )e + (- 495A b - 3267B a b )d e +--R + +--R 6 2 4 +--R - 495B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 9625A a b - 13090B a b )e + (- 2035A a b - 5555B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 220A b - 1595B a b )d e - 220B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 11704A a b - 8932B a b )e + (- 3388A a b - 4928B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 682A a b - 2024B a b )d e + (- 66A b - 550B a b )d e +--R + +--R 6 4 2 +--R - 66B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 8064A a b - 3276B a b)e + (- 2856A a b - 2352B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 798A a b - 1260B a b )d e + (- 150A a b - 498B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 12A b - 126B a b )d e - 12B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 2982A a b - 504B a )e + (- 1218A a b - 546B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 420A a b - 378B a b )d e + (- 112A a b - 196B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 19A a b - 74B a b )d e + (- A b - 17B a b )d e - B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 462A a e + (- 210A a b - 42B a )d e + (- 84A a b - 42B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 28A a b - 28B a b )d e + (- 7A a b - 14B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- A a b - 5B a b )d e - B a b d +--R / +--R 19 13 19 18 12 +--R 5544b e x + (5544a e + 66528b d e )x +--R + +--R 18 2 17 11 2 17 3 16 10 +--R (66528a d e + 365904b d e )x + (365904a d e + 1219680b d e )x +--R + +--R 3 16 4 15 9 4 15 5 14 8 +--R (1219680a d e + 2744280b d e )x + (2744280a d e + 4390848b d e )x +--R + +--R 5 14 6 13 7 6 13 7 12 6 +--R (4390848a d e + 5122656b d e )x + (5122656a d e + 4390848b d e )x +--R + +--R 7 12 8 11 5 8 11 9 10 4 +--R (4390848a d e + 2744280b d e )x + (2744280a d e + 1219680b d e )x +--R + +--R 9 10 10 9 3 10 9 11 8 2 +--R (1219680a d e + 365904b d e )x + (365904a d e + 66528b d e )x +--R + +--R 11 8 12 7 12 7 +--R (66528a d e + 5544b d e )x + 5544a d e +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R e x + 13d e x + 78d e x + 286d e x + 715d e x + 1287d e x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 +--R 1716d e x + 1716d e x + 1287d e x + 715d e x + 286d e x +--R + +--R 11 2 2 12 13 +--R 78d e x + 13d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 650 + +)clear all + +--S 651 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^14 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R e x + 14d e x + 91d e x + 364d e x + 1001d e x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002d e x + 3003d e x + 3432d e x + 3003d e x + 2002d e x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001d e x + 364d e x + 91d e x + 14d e x + d +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1378 +r0:=-5/1716*b*(6*b*B*d+7*A*b*e-13*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^11)-1/858*b^2*(6*b*B*d+7*A*b*e-_ + 13*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^10)-_ + 1/13*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^13)-1/156*(6*b*B*d+7*A*b*e-13*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^12)-1/2574*b^3*(6*b*B*d+_ + 7*A*b*e-13*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-_ + a*e)*(d+e*x)^9)-1/9009*b^4*(6*b*B*d+7*A*b*e-13*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^8)-1/72072*b^4*(6*b*B*d+_ + 7*A*b*e-13*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 10296B b e x + ((- 9009A b - 45045B a b )e - 7722B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 40040A a b - 80080B a b )e + (- 5005A b - 25025B a b )d e +--R + +--R 5 2 4 +--R - 4290B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 72072A a b - 72072B a b )e + (- 16016A a b - 32032B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 2002A b - 10010B a b )d e - 1716B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 65520A a b - 32760B a b)e + (- 19656A a b - 19656B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 4368A a b - 8736B a b )d e + (- 546A b - 2730B a b )d e +--R + +--R 5 4 2 +--R - 468B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 30030A a b - 6006B a )e + (- 10920A a b - 5460B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 3276A a b - 3276B a b )d e + (- 728A a b - 1456B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 91A b - 455B a b )d e - 78B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 5544A a e + (- 2310A a b - 462B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 840A a b - 420B a b)d e + (- 252A a b - 252B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (- 56A a b - 112B a b )d e + (- 7A b - 35B a b )d e - 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 20 14 20 19 13 +--R 72072b e x + (72072a e + 936936b d e )x +--R + +--R 19 2 18 12 +--R (936936a d e + 5621616b d e )x +--R + +--R 2 18 3 17 11 +--R (5621616a d e + 20612592b d e )x +--R + +--R 3 17 4 16 10 +--R (20612592a d e + 51531480b d e )x +--R + +--R 4 16 5 15 9 +--R (51531480a d e + 92756664b d e )x +--R + +--R 5 15 6 14 8 +--R (92756664a d e + 123675552b d e )x +--R + +--R 6 14 7 13 7 +--R (123675552a d e + 123675552b d e )x +--R + +--R 7 13 8 12 6 +--R (123675552a d e + 92756664b d e )x +--R + +--R 8 12 9 11 5 +--R (92756664a d e + 51531480b d e )x +--R + +--R 9 11 10 10 4 +--R (51531480a d e + 20612592b d e )x +--R + +--R 10 10 11 9 3 +--R (20612592a d e + 5621616b d e )x +--R + +--R 11 9 12 8 2 12 8 13 7 +--R (5621616a d e + 936936b d e )x + (936936a d e + 72072b d e )x +--R + +--R 13 7 +--R 72072a d e +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R - 10296B b e x + ((- 9009A b - 45045B a b )e - 7722B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 40040A a b - 80080B a b )e + (- 5005A b - 25025B a b )d e +--R + +--R 5 2 4 +--R - 4290B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 72072A a b - 72072B a b )e + (- 16016A a b - 32032B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 2002A b - 10010B a b )d e - 1716B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 65520A a b - 32760B a b)e + (- 19656A a b - 19656B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 4368A a b - 8736B a b )d e + (- 546A b - 2730B a b )d e +--R + +--R 5 4 2 +--R - 468B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 30030A a b - 6006B a )e + (- 10920A a b - 5460B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 3276A a b - 3276B a b )d e + (- 728A a b - 1456B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 91A b - 455B a b )d e - 78B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 5544A a e + (- 2310A a b - 462B a )d e + (- 840A a b - 420B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 252A a b - 252B a b )d e + (- 56A a b - 112B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 7A b - 35B a b )d e - 6B b d +--R / +--R 20 13 19 12 2 18 11 3 17 10 +--R 72072e x + 936936d e x + 5621616d e x + 20612592d e x +--R + +--R 4 16 9 5 15 8 6 14 7 7 13 6 +--R 51531480d e x + 92756664d e x + 123675552d e x + 123675552d e x +--R + +--R 8 12 5 9 11 4 10 10 3 11 9 2 +--R 92756664d e x + 51531480d e x + 20612592d e x + 5621616d e x +--R + +--R 12 8 13 7 +--R 936936d e x + 72072d e +--R Type: Union(Expression(Integer),...) +--E 653 + +--S 654 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R 10296B b e x + ((9009A b + 45045B a b )e + 7722B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (40040A a b + 80080B a b )e + (5005A b + 25025B a b )d e +--R + +--R 5 2 4 +--R 4290B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (72072A a b + 72072B a b )e + (16016A a b + 32032B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2002A b + 10010B a b )d e + 1716B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (65520A a b + 32760B a b)e + (19656A a b + 19656B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (4368A a b + 8736B a b )d e + (546A b + 2730B a b )d e +--R + +--R 5 4 2 +--R 468B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (30030A a b + 6006B a )e + (10920A a b + 5460B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (3276A a b + 3276B a b )d e + (728A a b + 1456B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (91A b + 455B a b )d e + 78B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 5544A a e + (2310A a b + 462B a )d e + (840A a b + 420B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (252A a b + 252B a b )d e + (56A a b + 112B a b )d e +--R + +--R 5 4 5 5 6 +--R (7A b + 35B a b )d e + 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R - 10296B b e x + ((- 9009A b - 55341B a b )e - 7722B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 49049A a b - 125125B a b )e + (- 5005A b - 32747B a b )d e +--R + +--R 6 2 4 +--R - 4290B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 112112A a b - 152152B a b )e + (- 21021A a b - 57057B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 2002A b - 14300B a b )d e - 1716B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 137592A a b - 104832B a b )e + (- 35672A a b - 51688B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 6370A a b - 18746B a b )d e + (- 546A b - 4446B a b )d e +--R + +--R 6 4 2 +--R - 468B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 95550A a b - 38766B a b)e + (- 30576A a b - 25116B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 7644A a b - 12012B a b )d e + (- 1274A a b - 4186B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 91A b - 923B a b )d e - 78B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 35574A a b - 6006B a )e + (- 13230A a b - 5922B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 4116A a b - 3696B a b )d e + (- 980A a b - 1708B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 147A a b - 567B a b )d e + (- 7A b - 113B a b )d e - 6B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 5544A a e + (- 2310A a b - 462B a )d e + (- 840A a b - 420B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 252A a b - 252B a b )d e + (- 56A a b - 112B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- 7A a b - 35B a b )d e - 6B a b d +--R / +--R 20 14 20 19 13 +--R 72072b e x + (72072a e + 936936b d e )x +--R + +--R 19 2 18 12 +--R (936936a d e + 5621616b d e )x +--R + +--R 2 18 3 17 11 +--R (5621616a d e + 20612592b d e )x +--R + +--R 3 17 4 16 10 +--R (20612592a d e + 51531480b d e )x +--R + +--R 4 16 5 15 9 +--R (51531480a d e + 92756664b d e )x +--R + +--R 5 15 6 14 8 +--R (92756664a d e + 123675552b d e )x +--R + +--R 6 14 7 13 7 +--R (123675552a d e + 123675552b d e )x +--R + +--R 7 13 8 12 6 +--R (123675552a d e + 92756664b d e )x +--R + +--R 8 12 9 11 5 +--R (92756664a d e + 51531480b d e )x +--R + +--R 9 11 10 10 4 +--R (51531480a d e + 20612592b d e )x +--R + +--R 10 10 11 9 3 +--R (20612592a d e + 5621616b d e )x +--R + +--R 11 9 12 8 2 12 8 13 7 +--R (5621616a d e + 936936b d e )x + (936936a d e + 72072b d e )x +--R + +--R 13 7 +--R 72072a d e +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R e x + 14d e x + 91d e x + 364d e x + 1001d e x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002d e x + 3003d e x + 3432d e x + 3003d e x + 2002d e x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001d e x + 364d e x + 91d e x + 14d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 655 + +)clear all + +--S 656 of 1378 +t0:=(A+B*x)*(d+e*x)^3/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1378 +r0:=1/2*(A*b-a*B)*(b*d-a*e)*(a+b*x)*(d+e*x)^2/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+1/3*(A*b-a*B)*(a+b*x)*(d+e*x)^3/(b^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+1/4*B*(a+b*x)*(d+e*x)^4/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*(b*d-a*e)^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+(A*b-a*B)*e*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 2 4 4 2 3 3 2 3 +--R (- 12A a b + 12B a b)e + (36A a b - 36B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 36A a b + 36B a b )d e + (12A a b - 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 2A a b + 2B a b )e + (18A b - 6B a b )d e + 18B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (6A a b - 6B a b )e + (- 18A a b + 18B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 18B a b )d e + 12B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (24A a b - 24B a b)e + (- 60A a b + 60B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (42A a b - 42B a b )d e + (10A b + 2B a b )d e + 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (12A a b - 12B a )e + (- 24A a b + 24B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (6A a b - 6B a b )d e + (10A a b - 10B a b )d e + 3B a b d +--R / +--R +------------------+ +--R 5 | 2 2 2 +--R 12b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 2 3 2 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 3B b e x + ((4A b - 4B a b )e + 12B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 6B a b )e + (18A b - 18B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (12A a b - 12B a b)e + (- 36A a b + 36B a b )d e +--R + +--R 4 3 2 4 3 +--R (36A b - 36B a b )d e + 12B b d +--R * +--R x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 658 + +--S 659 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 2 2 3 3 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 3B b e x + ((4A b - 4B a b )e + 12B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((- 6A a b + 6B a b )e + (18A b - 18B a b )d e + 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 12B a b)e + (- 36A a b + 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (36A b - 36B a b )d e + 12B b d e +--R * +--R x +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A a b - 12B a b)e + (- 36A a b + 36B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (36A a b - 36B a b )d e + (- 12A b + 12B a b )d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (12A a b - 12B a )e + (- 36A a b + 36B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (36A a b - 36B a b )d e + (- 12A a b + 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R - 3B b e x + ((- 4A b + B a b )e - 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((2A a b - 2B a b )e + (- 18A b + 6B a b )d e - 18B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 6A a b + 6B a b )e + (18A a b - 18B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 18B a b )d e - 12B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 24A a b + 24B a b)e + (60A a b - 60B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 42A a b + 42B a b )d e + (- 10A b - 2B a b )d e - 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 12A a b + 12B a )e + (24A a b - 24B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 6A a b + 6B a b )d e + (- 10A a b + 10B a b )d e - 3B a b d +--R / +--R +------------------+ +--R 5 | 2 2 2 +--R 12b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 1378 +t0:=(A+B*x)*(d+e*x)^2/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1378 +r0:=1/2*(A*b-a*B)*(a+b*x)*(d+e*x)^2/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 1/3*B*(a+b*x)*(d+e*x)^3/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*_ + (b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*e*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (6A a b - 6B a b)e + (- 12A a b + 12B a b )d e +--R + +--R 4 3 2 +--R (6A b - 6B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (6A a b - 6B a )e + (- 12A a b + 12B a b)d e +--R + +--R 3 2 2 2 +--R (6A a b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 3A a b + 3B a b )e + (12A b - 6B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 12A a b + 12B a b)e + (18A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 3B a b )d e + 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (- 6A a b + 6B a )e + (6A a b - 6B a b)d e + (3A a b - 3B a b )d e +--R + +--R 3 3 +--R 2B a b d +--R / +--R +------------------+ +--R 4 | 2 2 2 +--R 6b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 3 2 2 +--R ((6A a b - 6B a )e + (- 12A a b + 12B a b)d e + (6A b - 6B a b )d ) +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R 2B b e x + ((3A b - 3B a b )e + 6B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (12A b - 12B a b )d e + 6B b d )x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 663 + +--S 664 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 +--R (6A a b - 6B a )e + (- 12A a b + 12B a b)d e +--R + +--R 3 2 2 +--R (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 2B b e x + ((3A b - 3B a b )e + 6B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 6A a b + 6B a b)e + (12A b - 12B a b )d e + 6B b d e)x +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 6A a b + 6B a b)e + (12A a b - 12B a b )d e +--R + +--R 4 3 2 +--R (- 6A b + 6B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 6A a b + 6B a )e + (12A a b - 12B a b)d e +--R + +--R 3 2 2 2 +--R (- 6A a b + 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R - 2B b e x + ((- 3A b + B a b )e - 6B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((3A a b - 3B a b )e + (- 12A b + 6B a b )d e - 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (12A a b - 12B a b)e + (- 18A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 3A b - 3B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (6A a b - 6B a )e + (- 6A a b + 6B a b)d e + (- 3A a b + 3B a b )d e +--R + +--R 3 3 +--R - 2B a b d +--R / +--R +------------------+ +--R 4 | 2 2 2 +--R 6b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 665 + +)clear all + +--S 666 of 1378 +t0:=(A+B*x)*(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1378 +r0:=1/2*B*(a+b*x)*(d+e*x)^2/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*_ + (b*d-a*e)*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-_ + a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3 +--R +--R +--R (2) +--R 2 2 2 3 2 +--R ((- 2A a b + 2B a b)e + (2A b - 2B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (- 2A a b + 2B a )e + (2A a b - 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - B a b )e + 2B b d e)x +--R + +--R 2 2 2 2 3 2 2 3 2 +--R ((4A a b - 4B a b)e + 2B a b d e + B b d )x + (2A a b - 2B a )e +--R + +--R 2 2 +--R B a b d +--R / +--R +------------------+ +--R 3 | 2 2 2 +--R 2b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R ((- 2A a b + 2B a )e + (2A b - 2B a b)d)log(b x + a) + B b e x +--R + +--R 2 2 +--R ((2A b - 2B a b)e + 2B b d)x +--R / +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 668 + +--S 669 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 +--R ((- 2A a b + 2B a )e + (2A b - 2B a b)d e)log(b x + a) + B b e x +--R + +--R 2 2 2 +--R ((2A b - 2B a b)e + 2B b d e)x +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 3 2 2 3 2 +--R ((2A a b - 2B a b)e + (- 2A b + 2B a b )d e)x + (2A a b - 2B a )e +--R + +--R 2 2 +--R (- 2A a b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R - B b e x + ((- 2A b + B a b )e - 2B b d e)x +--R + +--R 2 2 2 2 3 2 2 3 2 +--R ((- 4A a b + 4B a b)e - 2B a b d e - B b d )x + (- 2A a b + 2B a )e +--R + +--R 2 2 +--R - B a b d +--R / +--R +------------------+ +--R 3 | 2 2 2 +--R 2b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 670 + +)clear all + +--S 671 of 1378 +t0:=(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R B x + A +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1378 +r0:=(A*b-a*B)*(a+b*x)*log(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + B*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2 +--R +--R +--R (2) +--R 2 2 2 2 2 +--R ((A b - B a b)x + A a b - B a )log(b x + a) + B b x + 2B a b x + B a +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (A b - B a)log(b x + a) + B b x +--R (3) ------------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 673 + +--S 674 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R | 2 2 2 +--R ((A b - B a)log(b x + a) + B b x)\|b x + 2a b x + a +--R + +--R 2 2 2 2 2 +--R ((- A b + B a b)x - A a b + B a )log(b x + a) - B b x - 2B a b x - B a +--R / +--R +------------------+ +--R 2 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 1378 +t0:=(A+B*x)/((d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1378 +r0:=(A*b-a*B)*(a+b*x)*log(a+b*x)/(b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (B*d-A*e)*(a+b*x)*log(d+e*x)/(e*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 +--R ((- A b + B a b)e x + (- A a b + B a )e)log(b x + a) +--R / +--R +------------------+ +--R 2 2 | 2 2 2 +--R (a b e - b d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (A b e - B b d)log(e x + d) + (- A b + B a)e log(b x + a) +--R (3) --------------------------------------------------------- +--R 2 2 +--R a b e - b d e +--R Type: Union(Expression(Integer),...) +--E 678 + +--S 679 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R ((A b e - B b d)log(e x + d) + (- A b + B a)e log(b x + a)) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(e x + d) +--R + +--R 2 2 +--R ((A b - B a b)e x + (A a b - B a )e)log(b x + a) +--R / +--R +------------------+ +--R 2 2 | 2 2 2 +--R (a b e - b d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 680 + +)clear all + +--S 681 of 1378 +t0:=(A+B*x)/((d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1378 +r0:=-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (- A b + B a b)e x + ((- A a b + B a )e + (- A b + B a b)d e)x +--R + +--R 2 +--R (- A a b + B a )d e +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 2 2 +--R (A b - B a b)e x + ((A a b - B a )e + (A b - B a b)d e)x +--R + +--R 2 +--R (A a b - B a )d e +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R (- A a b e + (A b + B a b)d e - B b d )x - A a e + (A a b + B a )d e +--R + +--R 2 +--R - B a b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R ((- A b + B a)e x + (- A b + B a)d e)log(e x + d) +--R + +--R 2 2 +--R ((A b - B a)e x + (A b - B a)d e)log(b x + a) - A a e + (A b + B a)d e +--R + +--R 2 +--R - B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R (a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e +--R Type: Union(Expression(Integer),...) +--E 683 + +--S 684 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +--R ((- A b + B a)e x + (- A b + B a)d e)log(e x + d) +--R + +--R 2 2 +--R ((A b - B a)e x + (A b - B a)d e)log(b x + a) - A a e +--R + +--R 2 +--R (A b + B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 2 2 2 +--R (A b - B a b)e x + ((A a b - B a )e + (A b - B a b)d e)x +--R + +--R 2 +--R (A a b - B a )d e +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 2 2 +--R (- A b + B a b)e x + ((- A a b + B a )e + (- A b + B a b)d e)x +--R + +--R 2 +--R (- A a b + B a )d e +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R (A a b e + (- A b - B a b)d e + B b d )x + A a e + (- A a b - B a )d e +--R + +--R 2 +--R B a b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R --------------------------------------------------------------------------- +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 685 + +)clear all + +--S 686 of 1378 +t0:=(A+B*x)/((d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1378 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + b*(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b*(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (A*b-a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 +--R (2A b - 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((2A a b - 2B a b)e + (4A b - 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((4A a b - 4B a b)d e + (2A b - 2B a b )d e)x +--R + +--R 2 2 2 +--R (2A a b - 2B a b)d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 +--R (- 2A b + 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 2A a b + 2B a b)e + (- 4A b + 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 4A a b + 4B a b)d e + (- 2A b + 2B a b )d e)x +--R + +--R 2 2 2 +--R (- 2A a b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 3 2 2 2 +--R (2A b - 2B a b )e x + ((4A a b - 4B a b)e + (2A b - 2B a b )d e )x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (A a b - 2B a )e + (6A a b - 3B a b)d e + (- A b - 2B a b )d e +--R + +--R 3 3 +--R B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R - A a e + (4A a b - B a )d e + (- A a b - 2B a b)d e + B a b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 +--R ((2A b - 2B a b)e x + (4A b - 4B a b)d e x + (2A b - 2B a b)d e) +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- 2A b + 2B a b)e x + (- 4A b + 4B a b)d e x +--R + +--R 2 2 +--R (- 2A b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 2 3 +--R ((2A a b - 2B a )e + (- 2A b + 2B a b)d e )x - A a e +--R + +--R 2 2 2 2 2 3 +--R (4A a b - B a )d e - 3A b d e + B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R Type: Union(Expression(Integer),...) +--E 688 + +--S 689 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 +--R (2A b - 2B a b)e x + (4A b - 4B a b)d e x +--R + +--R 2 2 +--R (2A b - 2B a b)d e +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- 2A b + 2B a b)e x + (- 4A b + 4B a b)d e x +--R + +--R 2 2 +--R (- 2A b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 2 3 +--R ((2A a b - 2B a )e + (- 2A b + 2B a b)d e )x - A a e +--R + +--R 2 2 2 2 2 3 +--R (4A a b - B a )d e - 3A b d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 3 +--R (- 2A b + 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 2A a b + 2B a b)e + (- 4A b + 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 4A a b + 4B a b)d e + (- 2A b + 2B a b )d e)x +--R + +--R 2 2 2 +--R (- 2A a b + 2B a b)d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 +--R (2A b - 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((2A a b - 2B a b)e + (4A b - 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((4A a b - 4B a b)d e + (2A b - 2B a b )d e)x +--R + +--R 2 2 2 +--R (2A a b - 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 +--R (- 2A b + 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 4A a b + 4B a b)e + (- 2A b + 2B a b )d e )x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- A a b + 2B a )e + (- 6A a b + 3B a b)d e + (A b + 2B a b )d e +--R + +--R 3 3 +--R - B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R A a e + (- 4A a b + B a )d e + (A a b + 2B a b)d e - B a b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 1378 +t0:=(A+B*x)/((d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1378 +r0:=-1/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 1/2*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + b^2*(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b^2*(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b*(A*b-a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^4*(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 +--R (- 6A b + 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((- 6A a b + 6B a b )e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((- 18A a b + 18B a b )d e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((- 18A a b + 18B a b )d e + (- 6A b + 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (- 6A a b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 +--R (6A b - 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((6A a b - 6B a b )e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((18A a b - 18B a b )d e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((18A a b - 18B a b )d e + (6A b - 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (6A a b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 +--R (- 6A b + 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((- 12A a b + 12B a b )e + (- 12A b + 12B a b )d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 3A a b + 3B a b)e + (- 30A a b + 30B a b )d e +--R + +--R 4 3 2 2 +--R (- 3A b + 3B a b )d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (A a b - 3B a )e + (- 9A a b + 17B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 21A a b + 9B a b )d e + (5A b + 3B a b )d e - 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (5A a b + 3B a b )d e - 2B a b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4 7 +--R 6a d e - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 3 2 3 2 +--R (- 6A b + 6B a b )e x + (- 18A b + 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (- 18A b + 18B a b )d e x + (- 6A b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 3 2 4 3 3 2 3 2 +--R (6A b - 6B a b )e x + (18A b - 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (18A b - 18B a b )d e x + (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 2 2 4 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (6A b - 6B a b )d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b - 3B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 +--R (15A b - 15B a b )d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 3 3 4 +--R (11A b - 3B a b )d e - 2B b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 4 3 5 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x + 6a d e +--R + +--R 3 4 4 2 2 5 3 3 6 2 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R Type: Union(Expression(Integer),...) +--E 693 + +--S 694 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 4 3 3 2 3 2 +--R (- 6A b + 6B a b )e x + (- 18A b + 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (- 18A b + 18B a b )d e x + (- 6A b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 3 2 4 3 3 2 3 2 +--R (6A b - 6B a b )e x + (18A b - 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (18A b - 18B a b )d e x + (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 2 2 4 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (6A b - 6B a b )d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b - 3B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 +--R (15A b - 15B a b )d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 3 3 4 +--R (11A b - 3B a b )d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 4 +--R (6A b - 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((6A a b - 6B a b )e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((18A a b - 18B a b )d e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((18A a b - 18B a b )d e + (6A b - 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (6A a b - 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 +--R (- 6A b + 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((- 6A a b + 6B a b )e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((- 18A a b + 18B a b )d e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((- 18A a b + 18B a b )d e + (- 6A b + 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (- 6A a b + 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 +--R (6A b - 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((12A a b - 12B a b )e + (12A b - 12B a b )d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (3A a b - 3B a b)e + (30A a b - 30B a b )d e +--R + +--R 4 3 2 2 +--R (3A b - 3B a b )d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- A a b + 3B a )e + (9A a b - 17B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (21A a b - 9B a b )d e + (- 5A b - 3B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R 2A a e + (- 9A a b + B a )d e + (18A a b - 6B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 5A a b - 3B a b )d e + 2B a b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4 7 +--R 6a d e - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 695 + +)clear all + +--S 696 of 1378 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1378 +r0:=-1/6*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^4/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/3*B*(a+b*x)*(d+e*x)^5/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+e*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^2/(b^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-2/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^3/_ + (b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*(a+b*x)*log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2*e^2*(b*d-a*e)*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6 +--R +--R +--R (2) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 90A a b + 150B a b )e + (144A a b - 300B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 156B a b )d e - 4B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 108A a b + 180B a b)e + (144A a b - 312B a b )d e +--R + +--R 2 3 2 2 5 4 3 5 4 +--R 96B a b d e + (- 24A b + 40B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 36A a b + 60B a )e + (36A a b - 84B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (18A a b - 6B a b )d e + (- 12A a b + 32B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R / +--R +------------------+ +--R 7 6 | 2 2 2 +--R (6b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 33A a b + 63B a b )e + (48A a b - 132B a b )d e + 72B a b d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (6A a b + 6B a b)e + (- 48A a b + 24B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (72A a b - 72B a b )d e + (- 24A b + 48B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (21A a b - 27B a )e + (- 60A a b + 84B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (54A a b - 90B a b )d e + (- 12A a b + 36B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 698 + +--S 699 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 33A a b + 63B a b )e + (48A a b - 132B a b )d e +--R + +--R 4 2 2 +--R 72B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (6A a b + 6B a b)e + (- 48A a b + 24B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (72A a b - 72B a b )d e + (- 24A b + 48B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (21A a b - 27B a )e + (- 60A a b + 84B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (54A a b - 90B a b )d e + (- 12A a b + 36B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 36A a b + 60B a b )e + (72A a b - 144B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (- 36A b + 108B a b )d e - 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (- 108A a b + 180B a b )e + (216A a b - 432B a b )d e +--R + +--R 5 2 4 2 2 5 3 +--R (- 108A a b + 324B a b )d e - 72B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 108A a b + 180B a b)e + (216A a b - 432B a b )d e +--R + +--R 2 4 3 3 2 2 2 4 3 +--R (- 108A a b + 324B a b )d e - 72B a b d e +--R * +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 36A a b + 60B a )e + (72A a b - 144B a b)d e +--R + +--R 3 3 4 2 2 2 3 3 3 +--R (- 36A a b + 108B a b )d e - 24B a b d e +--R * +--R log(b x + a) +--R + +--R 6 4 6 6 5 4 6 3 5 +--R - 2B b e x + ((- 3A b + 3B a b )e - 12B b d e )x +--R + +--R 5 2 4 4 6 5 3 6 2 2 4 +--R ((9A a b - 15B a b )e + (- 24A b + 36B a b )d e - 36B b d e )x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (102A a b - 170B a b )e + (- 168A a b + 348B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (36A b - 192B a b )d e + 4B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (198A a b - 330B a b )e + (- 288A a b + 612B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (36A a b - 252B a b )d e + (24A b - 36B a b )d e + 6B b d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (144A a b - 240B a b)e + (- 180A a b + 396B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 18A a b - 90B a b )d e + (36A a b - 72B a b )d e +--R + +--R 6 5 4 +--R (3A b + 9B a b )d +--R * +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (36A a b - 60B a )e + (- 36A a b + 84B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 18A a b + 6B a b )d e + (12A a b - 32B a b )d e +--R + +--R 5 2 4 4 +--R (3A a b + 3B a b )d +--R / +--R +------------------+ +--R 8 2 7 2 6 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 5 +--R - B b e x + ((- A b - B a)e - 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (- A a e + (- 4A b - 4B a)d e - 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (- 4A a d e + (- 6A b - 6B a)d e - 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (- 6A a d e + (- 4A b - 4B a)d e - B b d )x +--R + +--R 3 4 4 +--R (- 4A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 1378 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1378 +r0:=-1/2*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*(d+e*x)^3/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/2*B*(a+b*x)*(d+e*x)^4/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-3/2*(b*B*d+A*b*e-2*a*B*e)*(d+e*x)^2/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*B*d+A*b*e-_ + 2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 24B a b)e + (12A a b - 36B a b )d e + 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((15A a b - 30B a b )e + (- 9A b + 33B a b )d e - 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 36B a b)e + (- 6A a b + 30B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 6B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 3 2 3 2 2 2 +--R (6A a b - 12B a )e + 6B a b d e + (- 3A a b + 6B a b )d e +--R + +--R 4 3 3 +--R (- A b - B a b )d +--R / +--R +------------------+ +--R 6 5 | 2 2 2 +--R (2b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 24B a b)e + (12A a b - 36B a b )d e + 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((4A a b - 11B a b )e + 12B a b d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 4A a b + 2B a b)e + (12A a b - 12B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 12B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (- 5A a b + 7B a )e + (9A a b - 15B a b)d e + (- 3A a b + 9B a b )d e +--R + +--R 4 3 3 +--R (- A b - B a b )d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 12A a b + 24B a b)e + (12A a b - 36B a b )d e +--R + +--R 3 2 +--R 12B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((4A a b - 11B a b )e + 12B a b d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 4A a b + 2B a b)e + (12A a b - 12B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 12B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 5A a b + 7B a )e + (9A a b - 15B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b + 9B a b )d e + (- A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((6A a b - 12B a b )e + (- 6A b + 18B a b )d e - 6B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (18A a b - 36B a b )e + (- 18A a b + 54B a b )d e +--R + +--R 4 2 +--R - 18B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 3 2 +--R ((18A a b - 36B a b)e + (- 18A a b + 54B a b )d e - 18B a b d e)x +--R + +--R 4 5 3 3 2 4 2 3 2 2 +--R (6A a b - 12B a )e + (- 6A a b + 18B a b)d e - 6B a b d e +--R * +--R log(b x + a) +--R + +--R 5 3 5 5 4 3 5 2 4 +--R - B b e x + ((- 2A b + 3B a b )e - 6B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((- 17A a b + 34B a b )e + (9A b - 39B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 33A a b + 66B a b )e + (15A a b - 63B a b )d e +--R + +--R 5 4 2 5 3 +--R (6A b - 3B a b )d e + 2B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 24A a b + 48B a b)e + (6A a b - 36B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (9A a b - 12B a b )d e + (A b + 3B a b )d +--R * +--R x +--R + +--R 4 5 3 4 2 2 3 3 2 2 +--R (- 6A a b + 12B a )e - 6B a b d e + (3A a b - 6B a b )d e +--R + +--R 4 2 3 3 +--R (A a b + B a b )d +--R / +--R +------------------+ +--R 7 2 6 2 5 | 2 2 2 +--R (2b x + 4a b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1378 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1378 +r0:=-1/2*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^2/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+B*(a+b*x)*(d+e*x)^3/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + (2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 2 +--R 2B b e x + (- 3A b + 9B a b )e x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 2A a b + 6B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 2 3 2 2 +--R (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R / +--R +------------------+ +--R 5 4 | 2 2 2 +--R (2b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 2 2 +--R 2B b e x + 4B a b e x +--R + +--R 2 2 2 3 2 3 2 +--R ((4A a b - 4B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (3A a b - 5B a )e + (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 2 2 +--R 2B b e x + 4B a b e x +--R + +--R 2 2 2 3 2 3 2 +--R ((4A a b - 4B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (3A a b - 5B a )e + (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 2 4 3 +--R ((- 2A b + 6B a b )e - 4B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((- 6A a b + 18B a b )e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((- 6A a b + 18B a b)e - 12B a b d e)x + (- 2A a b + 6B a )e +--R + +--R 3 +--R - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 4 4 3 2 3 +--R - 2B b e x + (3A b - 11B a b )e x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((5A a b - 15B a b )e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 +--R ((2A a b - 6B a b)e + (6A a b - 14B a b )d e + (A b + 3B a b )d )x +--R + +--R 2 2 3 3 2 2 2 +--R (2A a b - 6B a b)d e + (A a b + B a b )d +--R / +--R +------------------+ +--R 6 2 5 2 4 | 2 2 2 +--R (2b x + 4a b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 710 + +)clear all + +--S 711 of 1378 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1378 +r0:=-1/2*(A*b-a*B)*(a+b*x)*(d+e*x)^2/(b*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-B*(b*d-a*e)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + B*e*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2)),-1/2*B*(a+_ + b*x)*(d+e*x)^2/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*(B*d-A*e)*(a+_ + b*x)*(d+e*x)^2/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-B*(d+e*x)/_ + (b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e*(a+b*x)*log(a+b*x)/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R [ +--R 2 2 3 2 2 2 2 3 2 +--R (2B a b e - 2B b d e)x + (4B a b e - 4B a b d e)x + 2B a e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 2 2 2 3 2 3 2 +--R (A b - B a b )e x + (2B a b e + (2A b - 6B a b )d e + 2B b d )x +--R + +--R 3 2 2 3 2 2 +--R 2B a e - 4B a b d e + (A b + B a b )d +--R / +--R +------------------+ +--R 4 5 2 3 4 | 2 2 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|b x + 2a b x + a +--R , +--R +--R 2 2 3 2 2 2 2 3 2 +--R (2B a b e - 2B b d e)x + (4B a b e - 4B a b d e)x + 2B a e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 3 2 +--R ((A b - 3B a b )e + 2B b d e)x +--R + +--R 2 2 3 2 3 2 2 +--R (- 2B a b e + (2A b - 2B a b )d e + 2B b d )x - 2B a b d e +--R + +--R 3 2 2 +--R (A b + B a b )d +--R / +--R +------------------+ +--R 4 5 2 3 4 | 2 2 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|b x + 2a b x + a +--R ] +--R Type: Tuple(Expression(Integer)) +--E 712 + +--S 713 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (2B b e x + 4B a b e x + 2B a e)log(b x + a) +--R + +--R 2 2 2 2 +--R ((- 2A b + 4B a b)e - 2B b d)x + (- A a b + 3B a )e + (- A b - B a b)d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 3 2 2 2 2 3 2 +--R (2B a b e - 2B b d e)x + (4B a b e - 4B a b d e)x + 2B a e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 2 3 2 +--R ((- 2A a b + 4B a b)e + (2A b - 6B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 3 2 2 +--R (- A a b + 3B a )e - 4B a b d e + (A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 4 3 2 2 2 3 2 +--R (- 2B a b e + 2B b d e)x + (- 6B a b e + 6B a b d e)x +--R + +--R 3 2 2 2 4 2 3 +--R (- 6B a b e + 6B a b d e)x - 2B a e + 2B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 2 3 +--R (- A b + B a b )e x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((- A a b - B a b )e + (- 2A b + 6B a b )d e - 2B b d )x +--R + +--R 3 2 3 2 2 4 3 2 +--R (- 4B a b e + (- 2A a b + 10B a b )d e + (- A b - 3B a b )d )x +--R + +--R 4 2 3 3 2 2 2 +--R - 2B a e + 4B a b d e + (- A a b - B a b )d +--R / +--R 5 6 2 2 4 5 3 3 2 4 +--R ((2a b e - 2b d)x + (4a b e - 4a b d)x + 2a b e - 2a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 1378 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1378 +r0:=-1/2*(a+b*x)*(A+B*x)^2/((A*b-a*B)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 2 2 2 +--R - B x - 2A B x - A +--R (2) --------------------------------------------------------- +--R +------------------+ +--R 2 2 | 2 2 2 +--R ((2A b - 2B a b)x + 2A a b - 2B a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1378 +a0:=integrate(t0,x) +--R +--R +--R - 2B b x - A b - B a +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 718 + +--S 719 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 2 2 2 2 2 | 2 2 2 2 3 3 +--R ((- 2A B b + 2B a b)x - A b + B a )\|b x + 2a b x + a + B b x +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (2A B b + B a b )x + (A b + 2A B a b )x + A a b +--R / +--R 5 4 2 4 2 3 2 3 3 2 +--R ((2A b - 2B a b )x + (4A a b - 4B a b )x + 2A a b - 2B a b ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 1378 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1378 +r0:=-1/2*(A*b-a*B)*(a+b*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + (-B*d+A*e)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(B*d-A*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + e*(B*d-A*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x - 2A a b e +--R + +--R 2 +--R 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R / +--R 3 2 3 2 3 2 4 2 5 3 4 3 3 2 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x + 2a b e - 6a b d e +--R + +--R 2 3 2 4 3 +--R 6a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x - 2A a b e +--R + +--R 2 +--R 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R / +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 3 4 2 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a b e - 6a b d e +--R + +--R 3 3 2 2 4 3 +--R 6a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 723 + +--S 724 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x +--R + +--R 2 2 2 +--R - 2A a b e + 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 2 4 3 3 2 3 2 +--R (- 2A b e + 2B b d e)x + (- 6A a b e + 6B a b d e)x +--R + +--R 2 2 2 2 2 3 2 3 +--R (- 6A a b e + 6B a b d e)x - 2A a b e + 2B a b d e +--R * +--R log(e x + d) +--R + +--R 4 2 4 3 3 2 3 2 +--R (2A b e - 2B b d e)x + (6A a b e - 6B a b d e)x +--R + +--R 2 2 2 2 2 3 2 3 +--R (6A a b e - 6B a b d e)x + 2A a b e - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 4 3 4 2 2 +--R (- 2A a b e + (2A b + 2B a b )d e - 2B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 +--R ((- 5A a b + B a b)e + (6A a b + 2B a b )d e + (- A b - 3B a b )d )x +--R + +--R 3 4 2 2 2 3 2 2 2 +--R (- 3A a b + B a )e + 4A a b d e + (- A a b - B a b )d +--R / +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 3 4 2 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a b e - 6a b d e +--R + +--R 3 3 2 2 4 3 +--R 6a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 725 + +)clear all + +--S 726 of 1378 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1378 +r0:=1/2*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+(-2*b*B*d+3*A*b*e-a*B*e)/((b*d-a*e)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-e*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/_ + ((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(2*b*B*d-3*A*b*e+a*B*e)*_ + (a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e + (3A b - 5B a b )d e +--R + +--R 3 3 +--R - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (2a e - 6a b d e + 4a b d e + 4a b d e - 6a b d e + 2b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e + (3A b - 5B a b )d e +--R + +--R 3 3 +--R - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 728 + +--S 729 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e +--R + +--R 3 2 2 3 3 +--R (3A b - 5B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 3 4 2 4 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 3 +--R ((18A a b - 6B a b )e + (6A b - 14B a b )d e - 4B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 2 +--R ((18A a b - 6B a b)e + (18A a b - 18B a b )d e - 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R ((6A a b - 2B a )e + (18A a b - 10B a b)d e - 12B a b d e)x +--R + +--R 3 4 2 3 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 3 4 2 4 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 3 +--R ((- 18A a b + 6B a b )e + (- 6A b + 14B a b )d e + 4B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 18A a b + 6B a b)e + (- 18A a b + 18B a b )d e +--R + +--R 3 2 +--R 12B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 18A a b + 10B a b)d e + 12B a b d e)x +--R + +--R 3 4 2 3 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 3 4 3 2 4 2 3 +--R ((6A a b - 2B a b )e + (- 6A b - 2B a b )d e + 4B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (15A a b - 5B a b)e + (- 12A a b - 6B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 3A b + 9B a b )d e + 2B b d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (11A a b - 3B a )e + (- 3A a b - 9B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 9A a b + 9B a b )d e + (A b + 3B a b )d +--R * +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 2A a e + (3A a b - 5B a )d e + (- 6A a b + 4B a b)d e +--R + +--R 3 2 2 3 +--R (A a b + B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 730 + +)clear all + +--S 731 of 1378 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1378 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/2*(b*B*d-2*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-3/2*(b*B*d-2*A*b*e+a*B*e)/_ + ((b*d-a*e)^3*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3*b*e*(b*B*d-_ + 2*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*b*e*(b*B*d-2*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*B*d-2*A*b*e+a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/((b*d-a*e)^5*(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 12B a b )e + (24A b - 24B a b )d e - 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (24A a b - 24B a b )d e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((36A a b - 18B a b )e + (12A b - 24B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (30A a b - 15B a b)e + (48A a b - 39B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 6A b - 21B a b )d e + 3B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R (4A a b - 2B a )e + (48A a b - 26B a b)d e - 24B a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 2B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - A a e + (8A a b - B a )d e + (12A a b - 15B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 8A a b + 3B a b )d e + (A b + B a b )d +--R / +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e +--R + +--R 6 5 2 +--R - 2b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 6 3 3 3 4 2 4 4 3 5 5 2 6 6 2 +--R (2a e - 6a b d e + 20a b d e - 30a b d e + 18a b d e - 4b d e)x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5 6 6 7 +--R (4a d e - 18a b d e + 30a b d e - 20a b d e + 6a b d e - 2b d )x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 12B a b )e + (24A b - 24B a b )d e - 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (24A a b - 24B a b )d e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 4 2 2 3 +--R ((12A a b - 6B a b )e - 12A b d e + 6B b d e )x +--R + +--R 2 2 3 4 2 2 3 4 3 2 2 +--R (18A a b - 9B a b)e - 9B a b d e + (- 18A b + 9B a b )d e +--R + +--R 4 3 +--R 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 3 2 2 +--R (4A a b - 2B a )e + (24A a b - 14B a b)d e - 24A a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 14B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 3 2 2 3 2 2 3 +--R - A a e + (8A a b - B a )d e - 9B a b d e + (- 8A a b + 9B a b )d e +--R + +--R 4 3 4 +--R (A b + B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 733 + +--S 734 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (24A a b - 12B a b )e + (24A b - 24B a b )d e +--R + +--R 4 2 2 +--R - 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (24A a b - 12B a b)d e + (24A a b - 24B a b )d e +--R + +--R 3 3 +--R - 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 4 2 2 3 +--R ((12A a b - 6B a b )e - 12A b d e + 6B b d e )x +--R + +--R 2 2 3 4 2 2 3 4 3 2 2 +--R (18A a b - 9B a b)e - 9B a b d e + (- 18A b + 9B a b )d e +--R + +--R 4 3 +--R 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 3 2 2 +--R (4A a b - 2B a )e + (24A a b - 14B a b)d e - 24A a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 14B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 3 2 2 +--R - A a e + (8A a b - B a )d e - 9B a b d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 8A a b + 9B a b )d e + (A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 4 5 3 5 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 36A a b + 18B a b )e + (- 24A b + 30B a b )d e +--R + +--R 5 2 2 +--R 12B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 36A a b + 18B a b )e + (- 72A a b + 54B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 12A b + 42B a b )d e + 6B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 12A a b + 6B a b)e + (- 72A a b + 42B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (- 36A a b + 54B a b )d e + 18B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 36A a b + 30B a b )d e +--R + +--R 2 3 3 +--R 18B a b d e +--R * +--R x +--R + +--R 3 2 4 2 2 3 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 4 5 3 5 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 4 +--R ((36A a b - 18B a b )e + (24A b - 30B a b )d e - 12B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 18B a b )e + (72A a b - 54B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (12A b - 42B a b )d e - 6B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A a b - 6B a b)e + (72A a b - 42B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (36A a b - 54B a b )d e - 18B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (36A a b - 30B a b )d e - 18B a b d e)x +--R + +--R 3 2 4 2 2 3 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 4 5 3 5 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 4 +--R ((- 48A a b + 24B a b )e + (- 12A b + 30B a b )d e + 6B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 66A a b + 33B a b )e + (- 60A a b + 63B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (6A b + 27B a b )d e - 3B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 34A a b + 17B a b)e + (- 96A a b + 65B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (6A a b + 45B a b )d e + (4A b - 5B a b )d e - 2B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 3A a b + 2B a )e + (- 56A a b + 27B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 12A a b + 39B a b )d e + (12A a b - 5B a b )d e +--R + +--R 5 4 4 +--R (- A b - 3B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R A a e + (- 8A a b + B a )d e + (- 12A a b + 15B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (8A a b - 3B a b )d e + (- A a b - B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e +--R + +--R 7 5 2 +--R - 2b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e +--R + +--R 7 6 +--R - 4b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 18a b d e + 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 1378 +t0:=(A+B*x)*(d+e*x)^5/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1378 +r0:=-1/4*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^5/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/2*B*(a+b*x)*(d+e*x)^6/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-5/6*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^3/_ + (b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/12*(2*b*B*d+A*b*e-3*a*B*e)*_ + (d+e*x)^4/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/2*e^2*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(d+e*x)^2/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+5*e^3*(b*d-a*e)*_ + (2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*log(a+b*x)/(b^7*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+5*e^4*(2*b*B*d+A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7 +--R +--R +--R (2) +--R 5 2 4 5 6 5 4 +--R (- 60A a b + 180B a b )e + (60A b - 300B a b )d e +--R + +--R 6 2 3 +--R 120B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 240A a b + 720B a b )e + (240A a b - 1200B a b )d e +--R + +--R 5 2 3 +--R 480B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 360A a b + 1080B a b )e + (360A a b - 1800B a b )d e +--R + +--R 2 4 2 3 +--R 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 720B a b)e + (240A a b - 1200B a b )d e +--R + +--R 3 3 2 3 +--R 480B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 4 2 2 3 +--R (- 60A a b + 180B a )e + (60A a b - 300B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 6B b e x + ((12A b - 36B a b )e + 60B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((185A a b - 555B a b )e + (- 125A b + 745B a b )d e - 160B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (500A a b - 1500B a b )e + (- 260A a b + 1780B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 120A b - 160B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (570A a b - 1710B a b )e + (- 210A a b + 1770B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 180A a b + 120B a b )d e + (- 60A b - 180B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (300A a b - 900B a b)e + (- 60A a b + 780B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 120A a b + 240B a b )d e + (- 40A a b - 120B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 20A b - 20B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 6 5 5 4 3 3 4 2 2 3 +--R (60A a b - 180B a )e + 120B a b d e + (- 30A a b + 90B a b )d e +--R + +--R 2 4 3 3 3 2 5 2 4 4 +--R (- 10A a b - 30B a b )d e + (- 5A a b - 5B a b )d e +--R + +--R 6 5 5 +--R (- 3A b - B a b )d +--R / +--R +------------------+ +--R 10 3 9 2 2 8 3 7 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 5 6 5 4 +--R (- 60A a b + 180B a b )e + (60A b - 300B a b )d e +--R + +--R 6 2 3 +--R 120B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 240A a b + 720B a b )e + (240A a b - 1200B a b )d e +--R + +--R 5 2 3 +--R 480B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 360A a b + 1080B a b )e + (360A a b - 1800B a b )d e +--R + +--R 2 4 2 3 +--R 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 720B a b)e + (240A a b - 1200B a b )d e +--R + +--R 3 3 2 3 +--R 480B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 4 2 2 3 +--R (- 60A a b + 180B a )e + (60A a b - 300B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 6B b e x + ((12A b - 36B a b )e + 60B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((48A a b - 204B a b )e + 240B a b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 48A a b - 96B a b )e + (240A a b - 240B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 120A b + 480B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 252A a b + 396B a b )e + (540A a b - 1260B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 180A a b + 1080B a b )d e + (- 60A b - 180B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 248A a b + 504B a b)e + (440A a b - 1240B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 120A a b + 880B a b )d e + (- 40A a b - 120B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 20A b - 20B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 77A a b + 171B a )e + (125A a b - 385B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 30A a b + 250B a b )d e + (- 10A a b - 30B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 5A a b - 5B a b )d e + (- 3A b - B a b )d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 738 + +--S 739 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 4 5 6 5 4 +--R (- 60A a b + 180B a b )e + (60A b - 300B a b )d e +--R + +--R 6 2 3 +--R 120B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 240A a b + 720B a b )e + (240A a b - 1200B a b )d e +--R + +--R 5 2 3 +--R 480B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 360A a b + 1080B a b )e + (360A a b - 1800B a b )d e +--R + +--R 2 4 2 3 +--R 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 720B a b)e + (240A a b - 1200B a b )d e +--R + +--R 3 3 2 3 +--R 480B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 4 2 2 3 +--R (- 60A a b + 180B a )e + (60A a b - 300B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 6B b e x + ((12A b - 36B a b )e + 60B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((48A a b - 204B a b )e + 240B a b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 48A a b - 96B a b )e + (240A a b - 240B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 120A b + 480B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 252A a b + 396B a b )e + (540A a b - 1260B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 180A a b + 1080B a b )d e + (- 60A b - 180B a b )d e +--R + +--R 6 4 +--R - 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 248A a b + 504B a b)e + (440A a b - 1240B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 120A a b + 880B a b )d e + (- 40A a b - 120B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 20A b - 20B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 77A a b + 171B a )e + (125A a b - 385B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 30A a b + 250B a b )d e + (- 10A a b - 30B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 5A a b - 5B a b )d e + (- 3A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 2 5 5 7 6 4 +--R (60A a b - 180B a b )e + (- 60A b + 300B a b )d e +--R + +--R 7 2 3 +--R - 120B b d e +--R * +--R 5 +--R x +--R + +--R 2 5 3 4 5 6 2 5 4 +--R (300A a b - 900B a b )e + (- 300A a b + 1500B a b )d e +--R + +--R 6 2 3 +--R - 600B a b d e +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 5 2 5 3 4 4 +--R (600A a b - 1800B a b )e + (- 600A a b + 3000B a b )d e +--R + +--R 2 5 2 3 +--R - 1200B a b d e +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 5 3 4 4 3 4 +--R (600A a b - 1800B a b )e + (- 600A a b + 3000B a b )d e +--R + +--R 3 4 2 3 +--R - 1200B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 4 3 5 2 4 +--R (300A a b - 900B a b)e + (- 300A a b + 1500B a b )d e +--R + +--R 4 3 2 3 +--R - 600B a b d e +--R * +--R x +--R + +--R 6 7 5 5 2 6 4 5 2 2 3 +--R (60A a b - 180B a )e + (- 60A a b + 300B a b)d e - 120B a b d e +--R * +--R log(b x + a) +--R + +--R 7 5 7 7 6 5 7 4 6 +--R - 6B b e x + ((- 12A b + 30B a b )e - 60B b d e )x +--R + +--R 6 2 5 5 7 6 4 7 2 3 5 +--R ((- 197A a b + 591B a b )e + (125A b - 805B a b )d e + 160B b d e )x +--R + +--R 2 5 3 4 5 6 2 5 4 +--R (- 685A a b + 2055B a b )e + (385A a b - 2525B a b )d e +--R + +--R 7 6 2 3 7 3 2 +--R (120A b + 320B a b )d e + 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 5 2 5 3 4 4 +--R (- 1070A a b + 3210B a b )e + (470A a b - 3550B a b )d e +--R + +--R 6 2 5 2 3 7 6 3 2 7 4 +--R (300A a b + 40B a b )d e + (60A b + 300B a b )d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 5 3 4 4 3 4 +--R (- 870A a b + 2610B a b )e + (270A a b - 2550B a b )d e +--R + +--R 2 5 3 4 2 3 6 2 5 3 2 +--R (300A a b - 360B a b )d e + (100A a b + 300B a b )d e +--R + +--R 7 6 4 7 5 +--R (20A b + 50B a b )d e + 4B b d +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 4 3 5 2 4 +--R (- 360A a b + 1080B a b)e + (60A a b - 900B a b )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (150A a b - 330B a b )d e + (50A a b + 150B a b )d e +--R + +--R 6 2 5 4 7 6 5 +--R (25A a b + 25B a b )d e + (3A b + 5B a b )d +--R * +--R x +--R + +--R 6 7 5 6 4 4 3 5 2 2 3 +--R (- 60A a b + 180B a )e - 120B a b d e + (30A a b - 90B a b )d e +--R + +--R 3 4 4 3 3 2 2 5 3 4 4 6 2 5 5 +--R (10A a b + 30B a b )d e + (5A a b + 5B a b )d e + (3A a b + B a b )d +--R / +--R +------------------+ +--R 11 4 10 3 2 9 2 3 8 4 7 | 2 2 2 +--R (12b x + 48a b x + 72a b x + 48a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x +--R + +--R 5 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 7 5 4 6 +--R - B b e x + ((- A b - B a)e - 5B b d e )x +--R + +--R 5 4 2 3 5 +--R (- A a e + (- 5A b - 5B a)d e - 10B b d e )x +--R + +--R 4 2 3 3 2 4 +--R (- 5A a d e + (- 10A b - 10B a)d e - 10B b d e )x +--R + +--R 2 3 3 2 4 3 +--R (- 10A a d e + (- 10A b - 10B a)d e - 5B b d e)x +--R + +--R 3 2 4 5 2 +--R (- 10A a d e + (- 5A b - 5B a)d e - B b d )x +--R + +--R 4 5 5 +--R (- 5A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 740 + +)clear all + +--S 741 of 1378 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1378 +r0:=-1/4*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^4/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+B*(a+b*x)*(d+e*x)^5/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))-_ + 1/2*e*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^2/(b^4*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-1/3*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)^3/(b^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))-e^2*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)/(b^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*_ + log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((12A b - 60B a b )e + 48B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((48A a b - 240B a b )e + 192B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((72A a b - 360B a b )e + 288B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((48A a b - 240B a b)e + 192B a b d e )x + (12A a b - 60B a )e +--R + +--R 4 3 +--R 48B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 12B b e x + ((- 25A b + 125B a b )e - 40B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 52A a b + 260B a b )e + (- 48A b + 32B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 42A a b + 210B a b )e + (- 72A a b + 192B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b - 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 12A a b + 60B a b)e + (- 48A a b + 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 24A a b - 72B a b )d e + (- 16A b - 16B a b )d e - 4B b d +--R * +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (- 12A a b + 60B a b)d e + (- 6A a b - 18B a b )d e +--R + +--R 4 2 3 3 5 4 4 +--R (- 4A a b - 4B a b )d e + (- 3A b - B a b )d +--R / +--R +------------------+ +--R 9 3 8 2 2 7 3 6 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 4 5 3 4 +--R ((12A b - 60B a b )e + 48B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((48A a b - 240B a b )e + 192B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((72A a b - 360B a b )e + 288B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((48A a b - 240B a b)e + 192B a b d e )x + (12A a b - 60B a )e +--R + +--R 4 3 +--R 48B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 4 4 4 +--R 12B b e x + 48B a b e x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((48A a b - 48B a b )e + (- 48A b + 192B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (108A a b - 252B a b )e + (- 72A a b + 432B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b - 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (88A a b - 248B a b)e + (- 48A a b + 352B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 24A a b - 72B a b )d e + (- 16A b - 16B a b )d e - 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 77B a )e + (- 12A a b + 100B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 6A a b - 18B a b )d e + (- 4A a b - 4B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - B a b )d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 743 + +--S 744 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((12A b - 60B a b )e + 48B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((48A a b - 240B a b )e + 192B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((72A a b - 360B a b )e + 288B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((48A a b - 240B a b)e + 192B a b d e )x + (12A a b - 60B a )e +--R + +--R 4 3 +--R 48B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 4 4 4 +--R 12B b e x + 48B a b e x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((48A a b - 48B a b )e + (- 48A b + 192B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (108A a b - 252B a b )e + (- 72A a b + 432B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b - 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (88A a b - 248B a b)e + (- 48A a b + 352B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 24A a b - 72B a b )d e + (- 16A b - 16B a b )d e - 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 77B a )e + (- 12A a b + 100B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 6A a b - 18B a b )d e + (- 4A a b - 4B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 4 6 3 5 +--R ((- 12A b + 60B a b )e - 48B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((- 60A a b + 300B a b )e - 240B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((- 120A a b + 600B a b )e - 480B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((- 120A a b + 600B a b )e - 480B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((- 60A a b + 300B a b)e - 240B a b d e )x + (- 12A a b + 60B a )e +--R + +--R 5 3 +--R - 48B a b d e +--R * +--R log(b x + a) +--R + +--R 6 4 6 6 5 4 6 3 5 +--R - 12B b e x + ((25A b - 137B a b )e + 40B b d e )x +--R + +--R 5 2 4 4 6 5 3 6 2 2 4 +--R ((77A a b - 385B a b )e + (48A b + 8B a b )d e + 72B b d e )x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (94A a b - 470B a b )e + (120A a b - 224B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (36A b + 180B a b )d e + 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (54A a b - 270B a b )e + (120A a b - 384B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (60A a b + 180B a b )d e + (16A b + 40B a b )d e + 4B b d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (12A a b - 60B a b)e + (60A a b - 252B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (30A a b + 90B a b )d e + (20A a b + 20B a b )d e +--R + +--R 6 5 4 +--R (3A b + 5B a b )d +--R * +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 2 +--R (12A a b - 60B a b)d e + (6A a b + 18B a b )d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (4A a b + 4B a b )d e + (3A a b + B a b )d +--R / +--R +------------------+ +--R 10 4 9 3 2 8 2 3 7 4 6 | 2 2 2 +--R (12b x + 48a b x + 72a b x + 48a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 5 +--R - B b e x + ((- A b - B a)e - 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (- A a e + (- 4A b - 4B a)d e - 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (- 4A a d e + (- 6A b - 6B a)d e - 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (- 6A a d e + (- 4A b - 4B a)d e - B b d )x +--R + +--R 3 4 4 +--R (- 4A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 745 + +)clear all + +--S 746 of 1378 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1378 +r0:=-1/4*(A*b-a*B)*(a+b*x)*(d+e*x)^4/(b*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/2*B*e*(a+b*x)*(d+e*x)^2/(b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-1/3*B*(d+e*x)^3/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + B*e^2*(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e^3*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)),-1/4*B*(a+b*x)*_ + (d+e*x)^4/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+1/4*(B*d-A*e)*(a+b*x)*_ + (d+e*x)^4/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-1/2*B*e*(a+b*x)*_ + (d+e*x)^2/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/3*B*(d+e*x)^3/(b^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-B*e^2*(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+B*e^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R [ +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12B a b e - 12B b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 +--R (72B a b e - 72B a b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 5 4 4 3 +--R 12B a e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 4 5 3 4 +--R ((3A b - 25B a b )e + 22B b d e )x +--R + +--R 2 3 4 5 4 3 5 2 2 3 +--R (- 52B a b e + (12A b + 4B a b )d e + 36B b d e )x +--R + +--R 3 2 4 2 3 3 5 4 2 2 5 3 2 +--R (- 42B a b e - 30B a b d e + (18A b + 36B a b )d e + 18B b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 5 4 3 +--R - 12B a b e - 36B a b d e + 24B a b d e + (12A b + 8B a b )d e +--R + +--R 5 4 +--R 4B b d +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 5 4 4 +--R - 12B a b d e + 6B a b d e + 2B a b d e + (3A b + B a b )d +--R / +--R 8 9 3 2 7 8 2 3 6 2 7 +--R (12a b e - 12b d)x + (36a b e - 36a b d)x + (36a b e - 36a b d)x +--R + +--R 4 5 3 6 +--R 12a b e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R , +--R +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12B a b e - 12B b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 +--R (72B a b e - 72B a b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 5 4 4 3 +--R 12B a e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 4 5 3 4 +--R ((3A b - 25B a b )e + 22B b d e )x +--R + +--R 2 3 4 5 4 3 5 2 2 3 +--R (- 52B a b e + (12A b + 4B a b )d e + 36B b d e )x +--R + +--R 3 2 4 2 3 3 5 4 2 2 5 3 2 +--R (- 42B a b e - 30B a b d e + (18A b + 36B a b )d e + 18B b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 5 4 3 +--R - 12B a b e - 36B a b d e + 24B a b d e + (12A b + 8B a b )d e +--R + +--R 5 4 +--R 4B b d +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 5 4 4 +--R - 12B a b d e + 6B a b d e + 2B a b d e + (3A b + B a b )d +--R / +--R 8 9 3 2 7 8 2 3 6 2 7 +--R (12a b e - 12b d)x + (36a b e - 36a b d)x + (36a b e - 36a b d)x +--R + +--R 4 5 3 6 +--R 12a b e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R ] +--R Type: Tuple(Expression(Integer)) +--E 747 + +--S 748 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (12B b e x + 48B a b e x + 72B a b e x + 48B a b e x + 12B a e ) +--R * +--R log(b x + a) +--R + +--R 4 3 3 4 2 3 +--R ((- 12A b + 48B a b )e - 36B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 18A a b + 108B a b )e + (- 18A b - 54B a b )d e - 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 12A a b + 88B a b)e + (- 12A a b - 36B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 12A b - 12B a b )d e - 4B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 3A a b + 25B a )e + (- 3A a b - 9B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b - 3B a b )d e + (- 3A b - B a b )d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 748 + +--S 749 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12B a b e - 12B b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 +--R (72B a b e - 72B a b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 5 4 4 3 +--R 12B a e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 48B a b )e + (12A b - 84B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 2 3 3 +--R (- 18A a b + 108B a b )e - 162B a b d e +--R + +--R 5 4 2 2 5 3 +--R (18A b + 36B a b )d e + 18B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 3 2 3 2 3 2 2 +--R (- 12A a b + 88B a b)e - 124B a b d e + 24B a b d e +--R + +--R 5 4 3 5 4 +--R (12A b + 8B a b )d e + 4B b d +--R * +--R x +--R + +--R 4 5 4 4 3 3 2 2 2 2 3 3 +--R (- 3A a b + 25B a )e - 34B a b d e + 6B a b d e + 2B a b d e +--R + +--R 5 4 4 +--R (3A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 6 3 5 2 4 4 5 3 4 +--R (- 12B a b e + 12B b d e )x + (- 60B a b e + 60B a b d e )x +--R + +--R 3 3 4 2 4 3 3 4 2 4 3 3 3 2 +--R (- 120B a b e + 120B a b d e )x + (- 120B a b e + 120B a b d e )x +--R + +--R 5 4 4 2 3 6 4 5 3 +--R (- 60B a b e + 60B a b d e )x - 12B a e + 12B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 4 6 3 5 +--R ((- 3A b + 25B a b )e - 22B b d e )x +--R + +--R 5 2 4 4 6 5 3 6 2 2 4 +--R ((- 3A a b + 77B a b )e + (- 12A b - 26B a b )d e - 36B b d e )x +--R + +--R 3 3 4 5 2 4 3 6 5 2 2 +--R 94B a b e + (- 12A a b + 26B a b )d e + (- 18A b - 72B a b )d e +--R + +--R 6 3 +--R - 18B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 4 3 3 3 5 2 4 2 2 +--R 54B a b e + 66B a b d e + (- 18A a b - 60B a b )d e +--R + +--R 6 5 3 6 4 +--R (- 12A b - 26B a b )d e - 4B b d +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 3 2 2 5 2 4 3 +--R 12B a b e + 48B a b d e - 30B a b d e + (- 12A a b - 10B a b )d e +--R + +--R 6 5 4 +--R (- 3A b - 5B a b )d +--R * +--R x +--R + +--R 5 3 4 2 2 2 3 3 3 5 2 4 4 +--R 12B a b d e - 6B a b d e - 2B a b d e + (- 3A a b - B a b )d +--R / +--R 9 10 4 2 8 9 3 3 7 2 8 2 +--R (12a b e - 12b d)x + (48a b e - 48a b d)x + (72a b e - 72a b d)x +--R + +--R 4 6 3 7 5 5 4 6 +--R (48a b e - 48a b d)x + 12a b e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 1378 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1378 +r0:=-1/4*(A*b-a*B)*(a+b*x)*(d+e*x)^4/((b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/3*(B*d-A*e)*(d+e*x)^3/((b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 4 3 4 4 3 2 2 3 +--R ((A b + 3B a)e - 4B b d e )x + (4A a e + 8B a d e - 12B b d e )x +--R + +--R 3 2 2 3 2 +--R (12A a d e + (- 6A b + 6B a)d e - 12B b d e)x +--R + +--R 2 2 3 4 3 4 +--R (12A a d e - 8A b d e - 4B b d )x + 4A a d e + (- 3A b - B a)d +--R / +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (12a b e - 24a b d e + 12b d )x + (36a b e - 72a b d e + 36a b d )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (36a b e - 72a b d e + 36a b d )x + 12a e - 24a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 2 3 2 +--R - 12B b e x + ((- 6A b - 18B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 4A a b - 12B a b)e + (- 8A b - 8B a b )d e - 4B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- A a b - 3B a )e + (- 2A a b - 2B a b)d e + (- 3A b - B a b )d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 753 + +--S 754 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 4 4 3 5 2 2 3 +--R (- 12B a b e + 24B a b d e - 12B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 6A a b - 18B a b )e + (12A a b + 24B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 6A b + 6B a b )d e - 12B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 3 2 3 4 2 2 5 3 +--R (- 4A a b - 12B a b)e + 16B a b d e + 12A a b d e - 8A b d e +--R + +--R 5 4 +--R - 4B b d +--R * +--R x +--R + +--R 4 5 4 4 3 4 3 5 4 4 +--R (- A a b - 3B a )e + 4B a b d e + 4A a b d e + (- 3A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 4 6 3 5 +--R ((- A b - 3B a b )e + 4B b d e )x +--R + +--R 5 2 4 4 5 3 6 2 2 4 +--R ((- 5A a b - 3B a b )e - 4B a b d e + 12B b d e )x +--R + +--R 2 4 4 5 2 4 3 6 5 2 2 +--R - 4A a b e + (- 12A a b - 8B a b )d e + (6A b + 6B a b )d e +--R + +--R 6 3 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 5 2 4 2 2 6 5 3 +--R - 12A a b d e + (- 6A a b - 6B a b )d e + (8A b + 12B a b )d e +--R + +--R 6 4 +--R 4B b d +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 5 3 6 5 4 2 4 3 +--R (- 12A a b d e + 4A a b d e + (3A b + 5B a b )d )x - 4A a b d e +--R + +--R 5 2 4 4 +--R (3A a b + B a b )d +--R / +--R 2 8 2 9 10 2 4 +--R (12a b e - 24a b d e + 12b d )x +--R + +--R 3 7 2 2 8 9 2 3 +--R (48a b e - 96a b d e + 48a b d )x +--R + +--R 4 6 2 3 7 2 8 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 5 5 2 4 6 3 7 2 6 4 2 5 5 4 6 2 +--R (48a b e - 96a b d e + 48a b d )x + 12a b e - 24a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 1378 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1378 +r0:=1/4*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)/(b^3*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/2*B*(a+b*x)*(d+e*x)^2/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/3*(2*b*B*d-A*b*e-a*B*e)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a b)e - 4B b d)x + (- A a b - B a )e +--R + +--R 2 +--R (- 3A b - B a b)d +--R / +--R +------------------+ +--R 6 3 5 2 2 4 3 3 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a b)e - 4B b d)x + (- A a b - B a )e +--R + +--R 2 +--R (- 3A b - B a b)d +--R / +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 758 + +--S 759 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a b)e - 4B b d)x + (- A a b - B a )e +--R + +--R 2 +--R (- 3A b - B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 3 3 2 3 2 +--R 6B b e x + ((4A b + 10B a b )e + 4B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((5A a b + 5B a b)e + (3A b + 5B a b )d)x + (A a b + B a )e +--R + +--R 2 2 +--R (3A a b + B a b)d +--R / +--R +------------------+ +--R 7 4 6 3 2 5 2 3 4 4 3 | 2 2 2 +--R (12b x + 48a b x + 72a b x + 48a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 760 + +)clear all + +--S 761 of 1378 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1378 +r0:=-1/4*(A*b-a*B)*(a+b*x)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2))-_ + 1/3*B/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R - 4B b x - 3A b - B a +--R (2) ----------------------------------------------------------- +--R +------------------+ +--R 5 3 4 2 2 3 3 2 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1378 +a0:=integrate(t0,x) +--R +--R +--R - 4B b x - 3A b - B a +--R (3) ----------------------------------------------- +--R 6 4 5 3 2 4 2 3 3 4 2 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 763 + +--S 764 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R | 2 2 2 2 2 +--R (- 4B b x - 3A b - B a)\|b x + 2a b x + a + 4B b x +--R + +--R 2 2 +--R (3A b + 5B a b)x + 3A a b + B a +--R / +--R +------------------+ +--R 6 4 5 3 2 4 2 3 3 4 2 | 2 2 2 +--R (12b x + 48a b x + 72a b x + 48a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R ------------------------------------------------------------------------- +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 765 + +)clear all + +--S 766 of 1378 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1378 +r0:=-1/4*(A*b-a*B)*(a+b*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/3*(-B*d+A*e)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/2*e*(B*d-A*e)*(a+b*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + e^2*(B*d-A*e)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(B*d-A*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*_ + (B*d-A*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 3 4 4 4 4 3 3 +--R (12A b e - 12B b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (72A a b e - 72B a b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 4 4 4 3 +--R 12A a b e - 12B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 3 4 4 4 4 3 3 +--R (- 12A b e + 12B b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (- 72A a b e + 72B a b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 4 4 4 3 +--R - 12A a b e + 12B a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 5 4 3 5 2 2 3 +--R (12A a b e + (- 12A b - 12B a b )d e + 12B b d e )x +--R + +--R 2 3 4 4 2 3 3 5 4 2 2 +--R 42A a b e + (- 48A a b - 42B a b )d e + (6A b + 48B a b )d e +--R + +--R 5 3 +--R - 6B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 2 3 4 2 3 2 2 +--R 52A a b e + (- 72A a b - 52B a b )d e + (24A a b + 72B a b )d e +--R + +--R 5 4 3 5 4 +--R (- 4A b - 24B a b )d e + 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 3B a )e + (- 48A a b - 10B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 5 4 4 +--R (36A a b + 18B a b )d e + (- 16A a b - 6B a b )d e + (3A b + B a b )d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 9 5 +--R - 12b d +--R * +--R 3 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 2 7 4 +--R 36a b e - 180a b d e + 360a b d e - 360a b d e + 180a b d e +--R + +--R 8 5 +--R - 36a b d +--R * +--R 2 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 3 6 4 +--R 36a b e - 180a b d e + 360a b d e - 360a b d e + 180a b d e +--R + +--R 2 7 5 +--R - 36a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 4 5 4 3 6 5 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 5 3 4 4 4 4 3 3 +--R (12A b e - 12B b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (72A a b e - 72B a b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 4 4 4 3 +--R 12A a b e - 12B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 3 4 4 4 4 3 3 +--R (- 12A b e + 12B b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (- 72A a b e + 72B a b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 4 4 4 3 +--R - 12A a b e + 12B a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 5 4 3 5 2 2 3 +--R (12A a b e + (- 12A b - 12B a b )d e + 12B b d e )x +--R + +--R 2 3 4 4 2 3 3 5 4 2 2 +--R 42A a b e + (- 48A a b - 42B a b )d e + (6A b + 48B a b )d e +--R + +--R 5 3 +--R - 6B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 2 3 4 2 3 2 2 +--R 52A a b e + (- 72A a b - 52B a b )d e + (24A a b + 72B a b )d e +--R + +--R 5 4 3 5 4 +--R (- 4A b - 24B a b )d e + 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 3B a )e + (- 48A a b - 10B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 5 4 4 +--R (36A a b + 18B a b )d e + (- 16A a b - 6B a b )d e + (3A b + B a b )d +--R / +--R 5 5 5 4 6 4 3 7 2 3 2 8 3 2 9 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 10 5 +--R - 12b d +--R * +--R 4 +--R x +--R + +--R 6 4 5 5 5 4 4 6 2 3 3 7 3 2 2 8 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 9 5 +--R - 48a b d +--R * +--R 3 +--R x +--R + +--R 7 3 5 6 4 4 5 5 2 3 4 6 3 2 3 7 4 +--R 72a b e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 2 8 5 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 4 2 3 5 5 3 2 4 6 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 7 5 +--R - 48a b d +--R * +--R x +--R + +--R 9 5 8 2 4 7 3 2 3 6 4 3 2 5 5 4 4 6 5 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R Type: Union(Expression(Integer),...) +--E 768 + +--S 769 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 5 3 4 4 4 4 3 3 +--R (12A b e - 12B b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (72A a b e - 72B a b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 4 4 4 3 +--R 12A a b e - 12B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 3 4 4 4 4 3 3 +--R (- 12A b e + 12B b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (- 72A a b e + 72B a b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 4 4 4 3 +--R - 12A a b e + 12B a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 5 4 3 5 2 2 3 +--R (12A a b e + (- 12A b - 12B a b )d e + 12B b d e )x +--R + +--R 2 3 4 4 2 3 3 5 4 2 2 +--R 42A a b e + (- 48A a b - 42B a b )d e + (6A b + 48B a b )d e +--R + +--R 5 3 +--R - 6B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 2 3 +--R 52A a b e + (- 72A a b - 52B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (24A a b + 72B a b )d e + (- 4A b - 24B a b )d e + 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 3B a )e + (- 48A a b - 10B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (36A a b + 18B a b )d e + (- 16A a b - 6B a b )d e +--R + +--R 5 4 4 +--R (3A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 4 6 3 5 5 4 5 3 4 +--R (- 12A b e + 12B b d e )x + (- 60A a b e + 60B a b d e )x +--R + +--R 2 4 4 2 4 3 3 3 3 4 3 3 3 2 +--R (- 120A a b e + 120B a b d e )x + (- 120A a b e + 120B a b d e )x +--R + +--R 4 2 4 4 2 3 5 4 5 3 +--R (- 60A a b e + 60B a b d e )x - 12A a b e + 12B a b d e +--R * +--R log(e x + d) +--R + +--R 6 4 6 3 5 5 4 5 3 4 +--R (12A b e - 12B b d e )x + (60A a b e - 60B a b d e )x +--R + +--R 2 4 4 2 4 3 3 3 3 4 3 3 3 2 +--R (120A a b e - 120B a b d e )x + (120A a b e - 120B a b d e )x +--R + +--R 4 2 4 4 2 3 5 4 5 3 +--R (60A a b e - 60B a b d e )x + 12A a b e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 6 5 3 6 2 2 4 +--R (- 12A a b e + (12A b + 12B a b )d e - 12B b d e )x +--R + +--R 2 4 4 5 2 4 3 6 5 2 2 +--R - 54A a b e + (60A a b + 54B a b )d e + (- 6A b - 60B a b )d e +--R + +--R 6 3 +--R 6B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 3 3 3 +--R - 94A a b e + (120A a b + 94B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (- 30A a b - 120B a b )d e + (4A b + 30B a b )d e - 4B b d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 77A a b + 3B a b)e + (120A a b + 62B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 60A a b - 90B a b )d e + (20A a b + 30B a b )d e +--R + +--R 6 5 4 +--R (- 3A b - 5B a b )d +--R * +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 25A a b + 3B a )e + (48A a b + 10B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 36A a b - 18B a b )d e + (16A a b + 6B a b )d e +--R + +--R 5 2 4 4 +--R (- 3A a b - B a b )d +--R / +--R 5 5 5 4 6 4 3 7 2 3 2 8 3 2 9 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 10 5 +--R - 12b d +--R * +--R 4 +--R x +--R + +--R 6 4 5 5 5 4 4 6 2 3 3 7 3 2 2 8 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 9 5 +--R - 48a b d +--R * +--R 3 +--R x +--R + +--R 7 3 5 6 4 4 5 5 2 3 4 6 3 2 3 7 4 +--R 72a b e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 2 8 5 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 4 2 3 5 5 3 2 4 6 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 7 5 +--R - 48a b d +--R * +--R x +--R + +--R 9 5 8 2 4 7 3 2 3 6 4 3 2 5 5 4 4 6 5 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 6 4 5 5 2 3 4 4 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (10a b e + 10a b d)x + (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 770 + +)clear all + +--S 771 of 1378 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1378 +r0:=1/4*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2))+1/3*(-4*b*B*d+5*A*b*e-a*B*e)/((b*d-a*e)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*e*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)/_ + ((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2*(4*b*B*d-5*A*b*e+_ + a*B*e)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+e^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/_ + ((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((- 60A b + 12B a b )e + 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 240A a b + 48B a b )e + (- 60A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 360A a b + 72B a b )e + (- 240A a b + 336B a b )d e +--R + +--R 4 2 3 +--R 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 240A a b + 48B a b)e + (- 360A a b + 264B a b )d e +--R + +--R 2 3 2 3 +--R 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 60A a b + 12B a )e + (- 240A a b + 96B a b)d e +--R + +--R 3 2 2 3 +--R 192B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 60A a b + 12B a )d e + 48B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 12B a b )e - 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((240A a b - 48B a b )e + (60A b - 204B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (360A a b - 72B a b )e + (240A a b - 336B a b )d e +--R + +--R 4 2 3 +--R - 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b - 48B a b)e + (360A a b - 264B a b )d e +--R + +--R 2 3 2 3 +--R - 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 3 2 2 3 +--R ((60A a b - 12B a )e + (240A a b - 96B a b)d e - 192B a b d e )x +--R + +--R 4 5 4 4 2 3 +--R (60A a b - 12B a )d e - 48B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 12B a b )e + (60A b + 36B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 210A a b + 42B a b )e + (180A a b + 132B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b - 150B a b )d e - 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 260A a b + 52B a b)e + (150A a b + 178B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b - 144B a b )d e + (- 10A b - 94B a b )d e + 8B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 125A a b + 25B a )e + (- 20A a b + 104B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 20B a b )d e + (- 40A a b - 136B a b )d e +--R + +--R 5 4 4 5 5 +--R (5A b + 31B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 12A a e + (- 65A a b + 37B a )d e + (120A a b - 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 60A a b - 36B a b )d e + (20A a b + 8B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - B a b )d +--R / +--R 6 3 7 5 4 6 4 5 2 5 3 6 3 4 2 7 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 8 5 2 9 6 +--R - 72a b d e + 12b d e +--R * +--R 4 +--R x +--R + +--R 7 2 7 6 3 6 5 4 2 5 4 5 3 4 3 6 4 3 +--R 36a b e - 204a b d e + 468a b d e - 540a b d e + 300a b d e +--R + +--R 2 7 5 2 8 6 9 7 +--R - 36a b d e - 36a b d e + 12b d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 4 5 4 3 +--R 36a b e - 180a b d e + 324a b d e - 180a b d e - 180a b d e +--R + +--R 3 6 5 2 2 7 6 8 7 +--R 324a b d e - 180a b d e + 36a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 6 7 2 2 5 6 3 3 4 5 4 4 3 +--R 12a e - 36a b d e - 36a b d e + 300a b d e - 540a b d e +--R + +--R 4 5 5 2 3 6 6 2 7 7 +--R 468a b d e - 204a b d e + 36a b d +--R * +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 4 5 6 3 6 7 +--R - 72a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 5 5 4 5 +--R ((- 60A b + 12B a b )e + 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 240A a b + 48B a b )e + (- 60A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 360A a b + 72B a b )e + (- 240A a b + 336B a b )d e +--R + +--R 4 2 3 +--R 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 240A a b + 48B a b)e + (- 360A a b + 264B a b )d e +--R + +--R 2 3 2 3 +--R 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 60A a b + 12B a )e + (- 240A a b + 96B a b)d e +--R + +--R 3 2 2 3 +--R 192B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 60A a b + 12B a )d e + 48B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 12B a b )e - 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((240A a b - 48B a b )e + (60A b - 204B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (360A a b - 72B a b )e + (240A a b - 336B a b )d e +--R + +--R 4 2 3 +--R - 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b - 48B a b)e + (360A a b - 264B a b )d e +--R + +--R 2 3 2 3 +--R - 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 3 2 2 3 +--R ((60A a b - 12B a )e + (240A a b - 96B a b)d e - 192B a b d e )x +--R + +--R 4 5 4 4 2 3 +--R (60A a b - 12B a )d e - 48B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 12B a b )e + (60A b + 36B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 210A a b + 42B a b )e + (180A a b + 132B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b - 150B a b )d e - 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 260A a b + 52B a b)e + (150A a b + 178B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b - 144B a b )d e + (- 10A b - 94B a b )d e + 8B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 125A a b + 25B a )e + (- 20A a b + 104B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 20B a b )d e + (- 40A a b - 136B a b )d e +--R + +--R 5 4 4 5 5 +--R (5A b + 31B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 12A a e + (- 65A a b + 37B a )d e + (120A a b - 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 60A a b - 36B a b )d e + (20A a b + 8B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - B a b )d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 2 8 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 9 5 2 10 6 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 3 7 4 3 +--R 48a b e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 8 5 2 9 6 10 7 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 4 6 4 3 +--R 72a b e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 3 7 5 2 2 8 6 9 7 +--R 288a b d e - 216a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 5 5 4 3 +--R 48a b e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 4 6 5 2 3 7 6 2 8 7 +--R 792a b d e - 384a b d e + 72a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 6 4 4 3 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 5 5 5 2 4 6 6 3 7 7 +--R 648a b d e - 276a b d e + 48a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 5 5 6 4 6 7 +--R - 72a b d e + 12a b d +--R Type: Union(Expression(Integer),...) +--E 773 + +--S 774 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 5 5 4 5 +--R ((- 60A b + 12B a b )e + 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 240A a b + 48B a b )e + (- 60A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 360A a b + 72B a b )e + (- 240A a b + 336B a b )d e +--R + +--R 4 2 3 +--R 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 240A a b + 48B a b)e + (- 360A a b + 264B a b )d e +--R + +--R 2 3 2 3 +--R 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 60A a b + 12B a )e + (- 240A a b + 96B a b)d e +--R + +--R 3 2 2 3 +--R 192B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 60A a b + 12B a )d e + 48B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 12B a b )e - 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (240A a b - 48B a b )e + (60A b - 204B a b )d e +--R + +--R 5 2 3 +--R - 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (360A a b - 72B a b )e + (240A a b - 336B a b )d e +--R + +--R 4 2 3 +--R - 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b - 48B a b)e + (360A a b - 264B a b )d e +--R + +--R 2 3 2 3 +--R - 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (60A a b - 12B a )e + (240A a b - 96B a b)d e +--R + +--R 3 2 2 3 +--R - 192B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (60A a b - 12B a )d e - 48B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 12B a b )e + (60A b + 36B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 210A a b + 42B a b )e + (180A a b + 132B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b - 150B a b )d e - 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 260A a b + 52B a b)e + (150A a b + 178B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b - 144B a b )d e + (- 10A b - 94B a b )d e + 8B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 125A a b + 25B a )e + (- 20A a b + 104B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 20B a b )d e + (- 40A a b - 136B a b )d e +--R + +--R 5 4 4 5 5 +--R (5A b + 31B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 12A a e + (- 65A a b + 37B a )d e + (120A a b - 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 60A a b - 36B a b )d e + (20A a b + 8B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 5 6 4 6 +--R ((60A b - 12B a b )e - 48B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 5 +--R ((300A a b - 60B a b )e + (60A b - 252B a b )d e - 48B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (600A a b - 120B a b )e + (300A a b - 540B a b )d e +--R + +--R 5 2 3 +--R - 240B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (600A a b - 120B a b )e + (600A a b - 600B a b )d e +--R + +--R 2 4 2 3 +--R - 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (300A a b - 60B a b)e + (600A a b - 360B a b )d e +--R + +--R 3 3 2 3 +--R - 480B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 4 2 2 3 +--R ((60A a b - 12B a )e + (300A a b - 108B a b)d e - 240B a b d e )x +--R + +--R 5 6 4 5 2 3 +--R (60A a b - 12B a )d e - 48B a b d e +--R * +--R log(e x + d) +--R + +--R 6 5 5 6 4 6 +--R ((- 60A b + 12B a b )e + 48B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 300A a b + 60B a b )e + (- 60A b + 252B a b )d e +--R + +--R 6 2 3 +--R 48B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 600A a b + 120B a b )e + (- 300A a b + 540B a b )d e +--R + +--R 5 2 3 +--R 240B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 600A a b + 120B a b )e + (- 600A a b + 600B a b )d e +--R + +--R 2 4 2 3 +--R 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 300A a b + 60B a b)e + (- 600A a b + 360B a b )d e +--R + +--R 3 3 2 3 +--R 480B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 60A a b + 12B a )e + (- 300A a b + 108B a b)d e +--R + +--R 4 2 2 3 +--R 240B a b d e +--R * +--R x +--R + +--R 5 6 4 5 2 3 +--R (- 60A a b + 12B a )d e + 48B a b d e +--R * +--R log(b x + a) +--R + +--R 5 2 4 5 6 5 4 6 2 3 5 +--R ((60A a b - 12B a b )e + (- 60A b - 36B a b )d e + 48B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (270A a b - 54B a b )e + (- 240A a b - 168B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 30A b + 198B a b )d e + 24B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (470A a b - 94B a b )e + (- 330A a b - 310B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 150A a b + 294B a b )d e + (10A b + 118B a b )d e - 8B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (385A a b - 77B a b)e + (- 130A a b - 282B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 300A a b + 164B a b )d e + (50A a b + 230B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 5A b - 39B a b )d e + 4B b d +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (137A a b - 25B a )e + (85A a b - 141B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 300A a b + 28B a b )d e + (100A a b + 172B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 25A a b - 39B a b )d e + (3A b + 5B a b )d +--R * +--R x +--R + +--R 6 5 5 6 4 4 2 5 2 3 +--R 12A a e + (65A a b - 37B a )d e + (- 120A a b + 8B a b)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (60A a b + 36B a b )d e + (- 20A a b - 8B a b )d e +--R + +--R 5 2 4 5 +--R (3A a b + B a b )d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 2 8 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 9 5 2 10 6 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 3 7 4 3 +--R 48a b e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 8 5 2 9 6 10 7 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 4 6 4 3 +--R 72a b e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 3 7 5 2 2 8 6 9 7 +--R 288a b d e - 216a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 5 5 4 3 +--R 48a b e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 4 6 5 2 3 7 6 2 8 7 +--R 792a b d e - 384a b d e + 72a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 6 4 4 3 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 5 5 5 2 4 6 6 3 7 7 +--R 648a b d e - 276a b d e + 48a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 5 5 6 4 6 7 +--R - 72a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 775 + +)clear all + +--S 776 of 1378 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1378 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/4*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-5/12*(2*b*B*d-3*A*b*e+a*B*e)/_ + ((b*d-a*e)^3*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5/6*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)*(a+b*x)/((b*d-a*e)^4*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-5/2*e^2*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^5*(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-5*b*e^3*(2*b*B*d-3*A*b*e+a*B*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^7*sqrt(a^2+2*a*b*x+b^2*x^2))+5*b*e^3*_ + (2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^7*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+5*e^4*(2*b*B*d-3*A*b*e+a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/((b*d-a*e)^7*(d+e*x)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (720A a b - 240B a b )e + (360A b - 600B a b )d e +--R + +--R 6 2 4 +--R - 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (1080A a b - 360B a b )e + (1440A a b - 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (180A b - 1020B a b )d e - 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (720A a b - 240B a b )e + (2160A a b - 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (720A a b - 1680B a b )d e - 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (180A a b - 60B a b)e + (1440A a b - 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (1080A a b - 1320B a b )d e - 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (360A a b - 120B a b)d e + (720A a b - 480B a b )d e +--R + +--R 3 3 3 3 +--R - 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (180A a b - 60B a b)d e - 120B a b d e +--R * +--R log(e x + d) +--R + +--R 6 5 6 6 5 6 +--R ((- 180A b + 60B a b )e + 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 720A a b + 240B a b )e + (- 360A b + 600B a b )d e +--R + +--R 6 2 4 +--R 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 1080A a b + 360B a b )e + (- 1440A a b + 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 180A b + 1020B a b )d e + 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 720A a b + 240B a b )e + (- 2160A a b + 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (- 720A a b + 1680B a b )d e + 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 180A a b + 60B a b)e + (- 1440A a b + 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (- 1080A a b + 1320B a b )d e + 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (- 360A a b + 120B a b)d e + (- 720A a b + 480B a b )d e +--R + +--R 3 3 3 3 +--R 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (- 180A a b + 60B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 6 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((900A a b - 300B a b )e + (180A b - 660B a b )d e - 120B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (1710A a b - 570B a b )e + (1080A a b - 1500B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 90A b - 690B a b )d e + 60B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (1500A a b - 500B a b )e + (2340A a b - 1780B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 180A a b - 1500B a b )d e + (- 60A b + 140B a b )d e +--R + +--R 6 4 2 +--R 40B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (555A a b - 185B a b)e + (2280A a b - 1130B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (90A a b - 1550B a b )d e + (- 240A a b + 20B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (15A b + 155B a b )d e - 10B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (36A a b - 12B a )e + (930A a b - 334B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (420A a b - 760B a b )d e + (- 360A a b - 160B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (60A a b + 220B a b )d e + (- 6A b - 38B a b )d e + 4B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 6A a e + (72A a b - 6B a )d e + (285A a b - 185B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 240A a b - 40B a b )d e + (90A a b + 60B a b )d e +--R + +--R 5 2 4 5 6 5 6 +--R (- 24A a b - 10B a b )d e + (3A b + B a b )d +--R / +--R 7 3 9 6 4 8 5 5 2 7 4 6 3 6 3 7 4 5 +--R 12a b e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 2 8 5 4 9 6 3 10 7 2 +--R - 252a b d e + 84a b d e - 12b d e +--R * +--R 5 +--R x +--R + +--R 8 2 9 7 3 8 6 4 2 7 5 5 3 6 4 6 4 5 +--R 36a b e - 228a b d e + 588a b d e - 756a b d e + 420a b d e +--R + +--R 3 7 5 4 2 8 6 3 9 7 2 10 8 +--R 84a b d e - 252a b d e + 132a b d e - 24b d e +--R * +--R 4 +--R x +--R + +--R 9 9 8 2 8 7 3 2 7 6 4 3 6 5 5 4 5 +--R 36a b e - 180a b d e + 264a b d e + 168a b d e - 1008a b d e +--R + +--R 4 6 5 4 3 7 6 3 2 8 7 2 9 8 10 9 +--R 1344a b d e - 840a b d e + 216a b d e + 12a b d e - 12b d +--R * +--R 3 +--R x +--R + +--R 10 9 9 8 8 2 2 7 7 3 3 6 6 4 4 5 +--R 12a e - 12a b d e - 216a b d e + 840a b d e - 1344a b d e +--R + +--R 5 5 5 4 4 6 6 3 3 7 7 2 2 8 8 9 9 +--R 1008a b d e - 168a b d e - 264a b d e + 180a b d e - 36a b d +--R * +--R 2 +--R x +--R + +--R 10 8 9 2 7 8 2 3 6 7 3 4 5 6 4 5 4 +--R 24a d e - 132a b d e + 252a b d e - 84a b d e - 420a b d e +--R + +--R 5 5 6 3 4 6 7 2 3 7 8 2 8 9 +--R 756a b d e - 588a b d e + 228a b d e - 36a b d +--R * +--R x +--R + +--R 10 2 7 9 3 6 8 2 4 5 7 3 5 4 6 4 6 3 +--R 12a d e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 5 5 7 2 4 6 8 3 7 9 +--R - 252a b d e + 84a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 6 6 5 6 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (720A a b - 240B a b )e + (360A b - 600B a b )d e +--R + +--R 6 2 4 +--R - 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (1080A a b - 360B a b )e + (1440A a b - 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (180A b - 1020B a b )d e - 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (720A a b - 240B a b )e + (2160A a b - 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (720A a b - 1680B a b )d e - 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (180A a b - 60B a b)e + (1440A a b - 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (1080A a b - 1320B a b )d e - 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (360A a b - 120B a b)d e + (720A a b - 480B a b )d e +--R + +--R 3 3 3 3 +--R - 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (180A a b - 60B a b)d e - 120B a b d e +--R * +--R log(e x + d) +--R + +--R 6 5 6 6 5 6 +--R ((- 180A b + 60B a b )e + 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 720A a b + 240B a b )e + (- 360A b + 600B a b )d e +--R + +--R 6 2 4 +--R 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 1080A a b + 360B a b )e + (- 1440A a b + 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 180A b + 1020B a b )d e + 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 720A a b + 240B a b )e + (- 2160A a b + 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (- 720A a b + 1680B a b )d e + 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 180A a b + 60B a b)e + (- 1440A a b + 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (- 1080A a b + 1320B a b )d e + 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (- 360A a b + 120B a b)d e + (- 720A a b + 480B a b )d e +--R + +--R 3 3 3 3 +--R 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (- 180A a b + 60B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((180A a b - 60B a b )e + (- 180A b - 60B a b )d e + 120B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (630A a b - 210B a b )e + (- 360A a b - 300B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 270A b + 330B a b )d e + 180B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (780A a b - 260B a b )e + (180A a b - 580B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (- 900A a b + 180B a b )d e + (- 60A b + 620B a b )d e + 40B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (375A a b - 125B a b)e + (840A a b - 530B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 990A a b - 230B a b )d e + (- 240A a b + 740B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (15A b + 155B a b )d e - 10B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (36A a b - 12B a )e + (570A a b - 214B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 300A a b - 280B a b )d e + (- 360A a b + 320B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (60A a b + 220B a b )d e + (- 6A b - 38B a b )d e + 4B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 6A a e + (72A a b - 6B a )d e + (105A a b - 125B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 240A a b + 80B a b )d e + (90A a b + 60B a b )d e +--R + +--R 5 2 4 5 6 5 6 +--R (- 24A a b - 10B a b )d e + (3A b + B a b )d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 3 8 4 5 +--R 12a b e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 2 9 5 4 10 6 3 11 7 2 +--R - 252a b d e + 84a b d e - 12b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 4 7 4 5 +--R 48a b e - 312a b d e + 840a b d e - 1176a b d e + 840a b d e +--R + +--R 3 8 5 4 2 9 6 3 10 7 2 11 8 +--R - 168a b d e - 168a b d e + 120a b d e - 24b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 5 6 4 5 +--R 72a b e - 408a b d e + 852a b d e - 588a b d e - 588a b d e +--R + +--R 4 7 5 4 3 8 6 3 2 9 7 2 10 8 11 9 +--R 1428a b d e - 1092a b d e + 348a b d e - 12a b d e - 12b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 6 5 4 5 +--R 48a b e - 192a b d e + 48a b d e + 1008a b d e - 2352a b d e +--R + +--R 5 6 5 4 4 7 6 3 3 8 7 2 2 9 8 10 9 +--R 2352a b d e - 1008a b d e - 48a b d e + 192a b d e - 48a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5 +--R 12a e + 12a b d e - 348a b d e + 1092a b d e - 1428a b d e +--R + +--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9 +--R 588a b d e + 588a b d e - 852a b d e + 408a b d e - 72a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 7 4 5 4 +--R 24a d e - 120a b d e + 168a b d e + 168a b d e - 840a b d e +--R + +--R 6 5 6 3 5 6 7 2 4 7 8 3 8 9 +--R 1176a b d e - 840a b d e + 312a b d e - 48a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 7 4 6 3 +--R 12a d e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 6 5 7 2 5 6 8 4 7 9 +--R - 252a b d e + 84a b d e - 12a b d +--R Type: Union(Expression(Integer),...) +--E 778 + +--S 779 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 6 6 5 6 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (720A a b - 240B a b )e + (360A b - 600B a b )d e +--R + +--R 6 2 4 +--R - 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (1080A a b - 360B a b )e + (1440A a b - 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (180A b - 1020B a b )d e - 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (720A a b - 240B a b )e + (2160A a b - 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (720A a b - 1680B a b )d e - 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (180A a b - 60B a b)e + (1440A a b - 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (1080A a b - 1320B a b )d e - 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (360A a b - 120B a b)d e + (720A a b - 480B a b )d e +--R + +--R 3 3 3 3 +--R - 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (180A a b - 60B a b)d e - 120B a b d e +--R * +--R log(e x + d) +--R + +--R 6 5 6 6 5 6 +--R ((- 180A b + 60B a b )e + 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 720A a b + 240B a b )e + (- 360A b + 600B a b )d e +--R + +--R 6 2 4 +--R 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 1080A a b + 360B a b )e +--R + +--R 5 2 4 5 +--R (- 1440A a b + 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 180A b + 1020B a b )d e + 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 720A a b + 240B a b )e + (- 2160A a b + 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (- 720A a b + 1680B a b )d e + 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 180A a b + 60B a b)e + (- 1440A a b + 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (- 1080A a b + 1320B a b )d e + 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (- 360A a b + 120B a b)d e + (- 720A a b + 480B a b )d e +--R + +--R 3 3 3 3 +--R 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (- 180A a b + 60B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 5 2 4 6 6 5 5 +--R (180A a b - 60B a b )e + (- 180A b - 60B a b )d e +--R + +--R 6 2 4 +--R 120B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (630A a b - 210B a b )e + (- 360A a b - 300B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 270A b + 330B a b )d e + 180B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (780A a b - 260B a b )e + (180A a b - 580B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 900A a b + 180B a b )d e + (- 60A b + 620B a b )d e +--R + +--R 6 4 2 +--R 40B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (375A a b - 125B a b)e + (840A a b - 530B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 990A a b - 230B a b )d e + (- 240A a b + 740B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (15A b + 155B a b )d e - 10B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (36A a b - 12B a )e + (570A a b - 214B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 300A a b - 280B a b )d e + (- 360A a b + 320B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (60A a b + 220B a b )d e + (- 6A b - 38B a b )d e + 4B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 6A a e + (72A a b - 6B a )d e + (105A a b - 125B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 240A a b + 80B a b )d e + (90A a b + 60B a b )d e +--R + +--R 5 2 4 5 6 5 6 +--R (- 24A a b - 10B a b )d e + (3A b + B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 6 7 5 7 +--R ((- 180A b + 60B a b )e + 120B b d e )x +--R + +--R 6 2 5 6 7 6 5 +--R (- 900A a b + 300B a b )e + (- 360A b + 720B a b )d e +--R + +--R 7 2 4 +--R 240B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 6 6 2 5 5 +--R (- 1800A a b + 600B a b )e + (- 1800A a b + 1800B a b )d e +--R + +--R 7 6 2 4 7 3 3 +--R (- 180A b + 1260B a b )d e + 120B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 6 2 5 3 4 5 +--R (- 1800A a b + 600B a b )e + (- 3600A a b + 2400B a b )d e +--R + +--R 6 2 5 2 4 6 3 3 +--R (- 900A a b + 2700B a b )d e + 600B a b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 6 3 4 4 3 5 +--R (- 900A a b + 300B a b )e + (- 3600A a b + 1800B a b )d e +--R + +--R 2 5 3 4 2 4 2 5 3 3 +--R (- 1800A a b + 3000B a b )d e + 1200B a b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 6 4 3 5 2 5 +--R (- 180A a b + 60B a b)e + (- 1800A a b + 720B a b )d e +--R + +--R 3 4 4 3 2 4 3 4 3 3 +--R (- 1800A a b + 1800B a b )d e + 1200B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 4 3 5 2 2 4 +--R (- 360A a b + 120B a b)d e + (- 900A a b + 540B a b )d e +--R + +--R 4 3 3 3 +--R 600B a b d e +--R * +--R x +--R + +--R 5 2 6 2 4 5 2 3 3 +--R (- 180A a b + 60B a b)d e + 120B a b d e +--R * +--R log(e x + d) +--R + +--R 7 6 6 7 5 7 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 6 2 5 6 7 6 5 +--R (900A a b - 300B a b )e + (360A b - 720B a b )d e +--R + +--R 7 2 4 +--R - 240B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 6 6 2 5 5 +--R (1800A a b - 600B a b )e + (1800A a b - 1800B a b )d e +--R + +--R 7 6 2 4 7 3 3 +--R (180A b - 1260B a b )d e - 120B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 6 2 5 3 4 5 +--R (1800A a b - 600B a b )e + (3600A a b - 2400B a b )d e +--R + +--R 6 2 5 2 4 6 3 3 +--R (900A a b - 2700B a b )d e - 600B a b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 6 3 4 4 3 5 +--R (900A a b - 300B a b )e + (3600A a b - 1800B a b )d e +--R + +--R 2 5 3 4 2 4 2 5 3 3 +--R (1800A a b - 3000B a b )d e - 1200B a b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 6 4 3 5 2 5 +--R (180A a b - 60B a b)e + (1800A a b - 720B a b )d e +--R + +--R 3 4 4 3 2 4 3 4 3 3 +--R (1800A a b - 1800B a b )d e - 1200B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 4 3 5 2 2 4 +--R (360A a b - 120B a b)d e + (900A a b - 540B a b )d e +--R + +--R 4 3 3 3 +--R - 600B a b d e +--R * +--R x +--R + +--R 5 2 6 2 4 5 2 3 3 +--R (180A a b - 60B a b)d e - 120B a b d e +--R * +--R log(b x + a) +--R + +--R 7 6 6 7 5 7 +--R ((- 180A b + 60B a b )e + 120B b d e )x +--R + +--R 6 2 5 6 7 6 5 +--R (- 1080A a b + 360B a b )e + (- 180A b + 780B a b )d e +--R + +--R 7 2 4 +--R 120B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 6 6 2 5 5 +--R (- 2610A a b + 870B a b )e + (- 1260A a b + 2160B a b )d e +--R + +--R 7 6 2 4 7 3 3 +--R (90A b + 810B a b )d e - 60B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 6 2 5 3 4 5 +--R (- 3210A a b + 1070B a b )e + (- 3420A a b + 3280B a b )d e +--R + +--R 6 2 5 2 4 7 6 3 3 7 4 2 +--R (270A a b + 2190B a b )d e + (60A b - 200B a b )d e - 40B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 6 3 4 4 3 5 +--R (- 2055A a b + 685B a b )e + (- 4620A a b + 2910B a b )d e +--R + +--R 2 5 3 4 2 4 6 2 5 3 3 +--R (90A a b + 3050B a b )d e + (300A a b - 160B a b )d e +--R + +--R 7 6 4 2 7 5 +--R (- 15A b - 195B a b )d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 6 4 3 5 2 5 +--R (- 591A a b + 197B a b)e + (- 3210A a b + 1464B a b )d e +--R + +--R 3 4 4 3 2 4 2 5 3 4 3 3 +--R (- 510A a b + 2310B a b )d e + (600A a b + 140B a b )d e +--R + +--R 6 2 5 4 2 7 6 5 7 6 +--R (- 75A a b - 375B a b )d e + (6A b + 48B a b )d e - 4B b d +--R * +--R 2 +--R x +--R + +--R 6 7 6 5 2 6 5 +--R (- 30A a b + 12B a )e + (- 1002A a b + 340B a b)d e +--R + +--R 4 3 5 2 2 4 3 4 4 3 3 3 +--R (- 705A a b + 945B a b )d e + (600A a b + 200B a b )d e +--R + +--R 2 5 3 4 4 2 6 2 5 5 +--R (- 150A a b - 280B a b )d e + (30A a b + 48B a b )d e +--R + +--R 7 6 6 +--R (- 3A b - 5B a b )d +--R * +--R x +--R + +--R 7 6 6 7 5 5 2 6 2 4 +--R 6A a e + (- 72A a b + 6B a )d e + (- 285A a b + 185B a b)d e +--R + +--R 4 3 5 2 3 3 3 4 4 3 4 2 +--R (240A a b + 40B a b )d e + (- 90A a b - 60B a b )d e +--R + +--R 2 5 3 4 5 6 2 5 6 +--R (24A a b + 10B a b )d e + (- 3A a b - B a b )d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 3 8 4 5 +--R 12a b e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 2 9 5 4 10 6 3 11 7 2 +--R - 252a b d e + 84a b d e - 12b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 4 7 4 5 +--R 48a b e - 312a b d e + 840a b d e - 1176a b d e + 840a b d e +--R + +--R 3 8 5 4 2 9 6 3 10 7 2 11 8 +--R - 168a b d e - 168a b d e + 120a b d e - 24b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 5 6 4 5 +--R 72a b e - 408a b d e + 852a b d e - 588a b d e - 588a b d e +--R + +--R 4 7 5 4 3 8 6 3 2 9 7 2 10 8 11 9 +--R 1428a b d e - 1092a b d e + 348a b d e - 12a b d e - 12b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 6 5 4 5 +--R 48a b e - 192a b d e + 48a b d e + 1008a b d e - 2352a b d e +--R + +--R 5 6 5 4 4 7 6 3 3 8 7 2 2 9 8 10 9 +--R 2352a b d e - 1008a b d e - 48a b d e + 192a b d e - 48a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5 +--R 12a e + 12a b d e - 348a b d e + 1092a b d e - 1428a b d e +--R + +--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9 +--R 588a b d e + 588a b d e - 852a b d e + 408a b d e - 72a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 7 4 5 4 +--R 24a d e - 120a b d e + 168a b d e + 168a b d e - 840a b d e +--R + +--R 6 5 6 3 5 6 7 2 4 7 8 3 8 9 +--R 1176a b d e - 840a b d e + 312a b d e - 48a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 7 4 6 3 +--R 12a d e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 6 5 7 2 5 6 8 4 7 9 +--R - 252a b d e + 84a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 780 + +)clear all + +--S 781 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1378 +r0:=-2/9*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(9/2)/e^4+2/11*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^4-2/13*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(13/2)/e^4+2/15*b^2*B*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 2 7 7 2 7 2 6 6 +--R 858B b e x + ((990A b + 1980B a b)e + 3036B b d e )x +--R + +--R 2 7 2 6 +--R (2340A a b + 1170B a )e + (3600A b + 7200B a b)d e +--R + +--R 2 2 5 +--R 3708B b d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 1430A a e + (8840A a b + 4420B a )d e +--R + +--R 2 2 5 2 3 4 +--R (4580A b + 9160B a b)d e + 1600B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 5720A a d e + (11960A a b + 5980B a )d e +--R + +--R 2 3 4 2 4 3 +--R (2120A b + 4240B a b)d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 8580A a d e + (6240A a b + 3120B a )d e + (30A b + 60B a b)d e +--R + +--R 2 5 2 +--R - 12B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 5720A a d e + (260A a b + 130B a )d e + (- 40A b - 80B a b)d e +--R + +--R 2 6 +--R 16B b d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 1430A a d e + (- 520A a b - 260B a )d e + (80A b + 160B a b)d e +--R + +--R 2 7 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 7 2 7 2 6 6 +--R 858B b e x + ((990A b + 1980B a b)e + 3036B b d e )x +--R + +--R 2 7 2 6 +--R (2340A a b + 1170B a )e + (3600A b + 7200B a b)d e +--R + +--R 2 2 5 +--R 3708B b d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 1430A a e + (8840A a b + 4420B a )d e +--R + +--R 2 2 5 2 3 4 +--R (4580A b + 9160B a b)d e + 1600B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 5720A a d e + (11960A a b + 5980B a )d e +--R + +--R 2 3 4 2 4 3 +--R (2120A b + 4240B a b)d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 8580A a d e + (6240A a b + 3120B a )d e + (30A b + 60B a b)d e +--R + +--R 2 5 2 +--R - 12B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 5720A a d e + (260A a b + 130B a )d e + (- 40A b - 80B a b)d e +--R + +--R 2 6 +--R 16B b d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 1430A a d e + (- 520A a b - 260B a )d e + (80A b + 160B a b)d e +--R + +--R 2 7 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Union(Expression(Integer),...) +--E 783 + +--S 784 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1378 +r0:=-2/7*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(7/2)/e^4+2/9*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^4-2/11*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(11/2)/e^4+2/13*b^2*B*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 1386B b e x + ((1638A b + 3276B a b)e + 3402B b d e )x +--R + +--R 2 6 2 5 +--R (4004A a b + 2002B a )e + (4186A b + 8372B a b)d e +--R + +--R 2 2 4 +--R 2226B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 2574A a e + (10868A a b + 5434B a )d e +--R + +--R 2 2 4 2 3 3 +--R (2938A b + 5876B a b)d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 7722A a d e + (8580A a b + 4290B a )d e + (78A b + 156B a b)d e +--R + +--R 2 4 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R 7722A a d e + (572A a b + 286B a )d e +--R + +--R 2 4 2 2 5 +--R (- 104A b - 208B a b)d e + 48B b d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 2574A a d e + (- 1144A a b - 572B a )d e + (208A b + 416B a b)d e +--R + +--R 2 6 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 6 2 5 5 +--R 1386B b e x + ((1638A b + 3276B a b)e + 3402B b d e )x +--R + +--R 2 6 2 5 +--R (4004A a b + 2002B a )e + (4186A b + 8372B a b)d e +--R + +--R 2 2 4 +--R 2226B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 2574A a e + (10868A a b + 5434B a )d e +--R + +--R 2 2 4 2 3 3 +--R (2938A b + 5876B a b)d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 7722A a d e + (8580A a b + 4290B a )d e + (78A b + 156B a b)d e +--R + +--R 2 4 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R 7722A a d e + (572A a b + 286B a )d e +--R + +--R 2 4 2 2 5 +--R (- 104A b - 208B a b)d e + 48B b d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 2574A a d e + (- 1144A a b - 572B a )d e + (208A b + 416B a b)d e +--R + +--R 2 6 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 788 + +--S 789 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +)clear all + +--S 791 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1378 +r0:=-2/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^4-2/9*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(9/2)/e^4+2/11*b^2*B*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B b e x + ((770A b + 1540B a b)e + 840B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A a b + 990B a )e + (1100A b + 2200B a b)d e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 1386A a e + (3168A a b + 1584B a )d e + (66A b + 132B a b)d e +--R + +--R 2 3 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 2772A a d e + (396A a b + 198B a )d e + (- 88A b - 176B a b)d e +--R + +--R 2 4 +--R 48B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 1386A a d e + (- 792A a b - 396B a )d e + (176A b + 352B a b)d e +--R + +--R 2 5 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 630B b e x + ((770A b + 1540B a b)e + 840B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A a b + 990B a )e + (1100A b + 2200B a b)d e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 1386A a e + (3168A a b + 1584B a )d e + (66A b + 132B a b)d e +--R + +--R 2 3 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 2772A a d e + (396A a b + 198B a )d e + (- 88A b - 176B a b)d e +--R + +--R 2 4 +--R 48B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 1386A a d e + (- 792A a b - 396B a )d e + (176A b + 352B a b)d e +--R + +--R 2 5 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 793 + +--S 794 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 795 + +)clear all + +--S 796 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1378 +r0:=-2/3*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^4-2/7*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(7/2)/e^4+2/9*b^2*B*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 2 4 4 2 4 2 3 3 +--R 70B b e x + ((90A b + 180B a b)e + 10B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((252A a b + 126B a )e + (18A b + 36B a b)d e - 12B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 210A a e + (84A a b + 42B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 16B b d e +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 210A a d e + (- 168A a b - 84B a )d e + (48A b + 96B a b)d e +--R + +--R 2 4 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 2 4 2 3 3 +--R 70B b e x + ((90A b + 180B a b)e + 10B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((252A a b + 126B a )e + (18A b + 36B a b)d e - 12B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 210A a e + (84A a b + 42B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 16B b d e +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 210A a d e + (- 168A a b - 84B a )d e + (48A b + 96B a b)d e +--R + +--R 2 4 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 798 + +--S 799 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 800 + +)clear all + +--S 801 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1378 +r0:=2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^4-2/5*b*_ + (3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^4+2/7*b^2*B*(d+e*x)^(7/2)/e^4-_ + 2*(b*d-a*e)^2*(B*d-A*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((42A b + 84B a b)e - 36B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((140A a b + 70B a )e + (- 56A b - 112B a b)d e + 48B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 210A a e + (- 280A a b - 140B a )d e + (112A b + 224B a b)d e +--R + +--R 2 3 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((42A b + 84B a b)e - 36B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((140A a b + 70B a )e + (- 56A b - 112B a b)d e + 48B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 210A a e + (- 280A a b - 140B a )d e + (112A b + 224B a b)d e +--R + +--R 2 3 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 803 + +--S 804 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 805 + +)clear all + +--S 806 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1378 +r0:=-2/3*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^4+2/5*b^2*B*_ + (d+e*x)^(5/2)/e^4+2*(b*d-a*e)^2*(B*d-A*e)/(e^4*sqrt(d+e*x))+_ + 2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((10A b + 20B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((60A a b + 30B a )e + (- 40A b - 80B a b)d e + 48B b d e)x - 30A a e +--R + +--R 2 2 2 2 2 3 +--R (120A a b + 60B a )d e + (- 80A b - 160B a b)d e + 96B b d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((10A b + 20B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((60A a b + 30B a )e + (- 40A b - 80B a b)d e + 48B b d e)x - 30A a e +--R + +--R 2 2 2 2 2 3 +--R (120A a b + 60B a )d e + (- 80A b - 160B a b)d e + 96B b d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 808 + +--S 809 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 810 + +)clear all + +--S 811 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1378 +r0:=2/3*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(3/2))+2/3*b^2*B*_ + (d+e*x)^(3/2)/e^4-2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*_ + sqrt(d+e*x))-2*b*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((6A b + 12B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12A a b - 6B a )e + (24A b + 48B a b)d e - 48B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 8A a b - 4B a )d e + (16A b + 32B a b)d e - 32B b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((6A b + 12B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12A a b - 6B a )e + (24A b + 48B a b)d e - 48B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 8A a b - 4B a )d e + (16A b + 32B a b)d e - 32B b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 813 + +--S 814 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 815 + +)clear all + +--S 816 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1378 +r0:=2/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(5/2))-2/3*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^(3/2))+2*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)/(e^4*sqrt(d+e*x))+2*b^2*B*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((- 30A b - 60B a b)e + 180B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 20A a b - 10B a )e + (- 40A b - 80B a b)d e + 240B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 6A a e + (- 8A a b - 4B a )d e + (- 16A b - 32B a b)d e + 96B b d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((- 30A b - 60B a b)e + 180B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 20A a b - 10B a )e + (- 40A b - 80B a b)d e + 240B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 6A a e + (- 8A a b - 4B a )d e + (- 16A b - 32B a b)d e + 96B b d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 818 + +--S 819 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1378 +r0:=-2/9*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(9/2)/e^6+2/11*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^6-4/13*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^6+4/15*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^6-2/17*b^3*(5*b*B*d-_ + A*b*e-4*a*B*e)*(d+e*x)^(17/2)/e^6+2/19*b^4*B*(d+e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 4 9 9 4 3 9 4 8 8 +--R 218790B b e x + ((244530A b + 978120B a b )e + 746460B b d e )x +--R + +--R 3 2 2 9 +--R (1108536A a b + 1662804B a b )e +--R + +--R 4 3 8 4 2 7 +--R (847704A b + 3390816B a b )d e + 866580B b d e +--R * +--R 7 +--R x +--R + +--R 2 2 3 9 +--R (1918620A a b + 1279080B a b)e +--R + +--R 3 2 2 8 +--R (3922512A a b + 5883768B a b )d e +--R + +--R 4 3 2 7 4 3 6 +--R (1005708A b + 4022832B a b )d e + 345840B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 9 2 2 3 8 +--R (1511640A a b + 377910B a )e + (6976800A a b + 4651200B a b)d e +--R + +--R 3 2 2 2 7 +--R (4790736A a b + 7186104B a b )d e +--R + +--R 4 3 3 6 4 4 5 +--R (414504A b + 1658016B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 4 9 3 4 8 +--R 461890A a e + (5710640A a b + 1427660B a )d e +--R + +--R 2 2 3 2 7 +--R (8876040A a b + 5917360B a b)d e +--R + +--R 3 2 2 3 6 4 3 4 5 +--R (2067200A a b + 3100800B a b )d e + (1330A b + 5320B a b )d e +--R + +--R 4 5 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R 1847560A a d e + (7726160A a b + 1931540B a )d e +--R + +--R 2 2 3 3 6 +--R (4108560A a b + 2739040B a b)d e +--R + +--R 3 2 2 4 5 4 3 5 4 +--R (12920A a b + 19380B a b )d e + (- 1520A b - 6080B a b )d e +--R + +--R 4 6 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 2771340A a d e + (4031040A a b + 1007760B a )d e +--R + +--R 2 2 3 4 5 3 2 2 5 4 +--R (58140A a b + 38760B a b)d e + (- 15504A a b - 23256B a b )d e +--R + +--R 4 3 6 3 4 7 2 +--R (1824A b + 7296B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R 1847560A a d e + (167960A a b + 41990B a )d e +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (- 77520A a b - 51680B a b)d e + (20672A a b + 31008B a b )d e +--R + +--R 4 3 7 2 4 8 +--R (- 2432A b - 9728B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R 461890A a d e + (- 335920A a b - 83980B a )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (155040A a b + 103360B a b)d e + (- 41344A a b - 62016B a b )d e +--R + +--R 4 3 8 4 9 +--R (4864A b + 19456B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 9 9 4 3 9 4 8 8 +--R 218790B b e x + ((244530A b + 978120B a b )e + 746460B b d e )x +--R + +--R 3 2 2 9 +--R (1108536A a b + 1662804B a b )e +--R + +--R 4 3 8 4 2 7 +--R (847704A b + 3390816B a b )d e + 866580B b d e +--R * +--R 7 +--R x +--R + +--R 2 2 3 9 +--R (1918620A a b + 1279080B a b)e +--R + +--R 3 2 2 8 +--R (3922512A a b + 5883768B a b )d e +--R + +--R 4 3 2 7 4 3 6 +--R (1005708A b + 4022832B a b )d e + 345840B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 9 2 2 3 8 +--R (1511640A a b + 377910B a )e + (6976800A a b + 4651200B a b)d e +--R + +--R 3 2 2 2 7 +--R (4790736A a b + 7186104B a b )d e +--R + +--R 4 3 3 6 4 4 5 +--R (414504A b + 1658016B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 4 9 3 4 8 +--R 461890A a e + (5710640A a b + 1427660B a )d e +--R + +--R 2 2 3 2 7 +--R (8876040A a b + 5917360B a b)d e +--R + +--R 3 2 2 3 6 4 3 4 5 +--R (2067200A a b + 3100800B a b )d e + (1330A b + 5320B a b )d e +--R + +--R 4 5 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R 1847560A a d e + (7726160A a b + 1931540B a )d e +--R + +--R 2 2 3 3 6 +--R (4108560A a b + 2739040B a b)d e +--R + +--R 3 2 2 4 5 4 3 5 4 +--R (12920A a b + 19380B a b )d e + (- 1520A b - 6080B a b )d e +--R + +--R 4 6 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 2771340A a d e + (4031040A a b + 1007760B a )d e +--R + +--R 2 2 3 4 5 3 2 2 5 4 +--R (58140A a b + 38760B a b)d e + (- 15504A a b - 23256B a b )d e +--R + +--R 4 3 6 3 4 7 2 +--R (1824A b + 7296B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R 1847560A a d e + (167960A a b + 41990B a )d e +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (- 77520A a b - 51680B a b)d e + (20672A a b + 31008B a b )d e +--R + +--R 4 3 7 2 4 8 +--R (- 2432A b - 9728B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R 461890A a d e + (- 335920A a b - 83980B a )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (155040A a b + 103360B a b)d e + (- 41344A a b - 62016B a b )d e +--R + +--R 4 3 8 4 9 +--R (4864A b + 19456B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Union(Expression(Integer),...) +--E 823 + +--S 824 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1378 +r0:=-2/7*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(7/2)/e^6+2/9*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^6-4/11*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(11/2)/e^6+4/13*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(13/2)/e^6-2/15*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(15/2)/e^6+2/17*b^4*B*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 4 8 8 4 3 8 4 7 7 +--R 90090B b e x + ((102102A b + 408408B a b )e + 210210B b d e )x +--R + +--R 3 2 2 8 4 3 7 +--R (471240A a b + 706860B a b )e + (243474A b + 973896B a b )d e +--R + +--R 4 2 6 +--R 127050B b d e +--R * +--R 6 +--R x +--R + +--R 2 2 3 8 +--R (835380A a b + 556920B a b)e +--R + +--R 3 2 2 7 +--R (1156680A a b + 1735020B a b )d e +--R + +--R 4 3 2 6 4 3 5 +--R (152082A b + 608328B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 8 2 2 3 7 +--R (680680A a b + 170170B a )e + (2134860A a b + 1423240B a b)d e +--R + +--R 3 2 2 2 6 4 3 3 5 +--R (756840A a b + 1135260B a b )d e + (1190A b + 4760B a b )d e +--R + +--R 4 4 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 7 +--R 218790A a e + (1847560A a b + 461890B a )d e +--R + +--R 2 2 3 2 6 3 2 2 3 5 +--R (1498380A a b + 998920B a b)d e + (10200A a b + 15300B a b )d e +--R + +--R 4 3 4 4 4 5 3 +--R (- 1360A b - 5440B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 2 6 +--R 656370A a d e + (1458600A a b + 364650B a )d e +--R + +--R 2 2 3 3 5 3 2 2 4 4 +--R (39780A a b + 26520B a b)d e + (- 12240A a b - 18360B a b )d e +--R + +--R 4 3 5 3 4 6 2 +--R (1632A b + 6528B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 6 3 4 3 5 +--R 656370A a d e + (97240A a b + 24310B a )d e +--R + +--R 2 2 3 4 4 3 2 2 5 3 +--R (- 53040A a b - 35360B a b)d e + (16320A a b + 24480B a b )d e +--R + +--R 4 3 6 2 4 7 +--R (- 2176A b - 8704B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 3 5 3 4 4 4 +--R 218790A a d e + (- 194480A a b - 48620B a )d e +--R + +--R 2 2 3 5 3 3 2 2 6 2 +--R (106080A a b + 70720B a b)d e + (- 32640A a b - 48960B a b )d e +--R + +--R 4 3 7 4 8 +--R (4352A b + 17408B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 8 4 3 8 4 7 7 +--R 90090B b e x + ((102102A b + 408408B a b )e + 210210B b d e )x +--R + +--R 3 2 2 8 4 3 7 +--R (471240A a b + 706860B a b )e + (243474A b + 973896B a b )d e +--R + +--R 4 2 6 +--R 127050B b d e +--R * +--R 6 +--R x +--R + +--R 2 2 3 8 +--R (835380A a b + 556920B a b)e +--R + +--R 3 2 2 7 +--R (1156680A a b + 1735020B a b )d e +--R + +--R 4 3 2 6 4 3 5 +--R (152082A b + 608328B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 8 2 2 3 7 +--R (680680A a b + 170170B a )e + (2134860A a b + 1423240B a b)d e +--R + +--R 3 2 2 2 6 4 3 3 5 +--R (756840A a b + 1135260B a b )d e + (1190A b + 4760B a b )d e +--R + +--R 4 4 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 7 +--R 218790A a e + (1847560A a b + 461890B a )d e +--R + +--R 2 2 3 2 6 3 2 2 3 5 +--R (1498380A a b + 998920B a b)d e + (10200A a b + 15300B a b )d e +--R + +--R 4 3 4 4 4 5 3 +--R (- 1360A b - 5440B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 2 6 +--R 656370A a d e + (1458600A a b + 364650B a )d e +--R + +--R 2 2 3 3 5 3 2 2 4 4 +--R (39780A a b + 26520B a b)d e + (- 12240A a b - 18360B a b )d e +--R + +--R 4 3 5 3 4 6 2 +--R (1632A b + 6528B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 6 3 4 3 5 +--R 656370A a d e + (97240A a b + 24310B a )d e +--R + +--R 2 2 3 4 4 3 2 2 5 3 +--R (- 53040A a b - 35360B a b)d e + (16320A a b + 24480B a b )d e +--R + +--R 4 3 6 2 4 7 +--R (- 2176A b - 8704B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 3 5 3 4 4 4 +--R 218790A a d e + (- 194480A a b - 48620B a )d e +--R + +--R 2 2 3 5 3 3 2 2 6 2 +--R (106080A a b + 70720B a b)d e + (- 32640A a b - 48960B a b )d e +--R + +--R 4 3 7 4 8 +--R (4352A b + 17408B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Union(Expression(Integer),...) +--E 828 + +--S 829 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1378 +r0:=-2/5*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(5/2)/e^6+2/7*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^6-4/9*b*(b*d-a*e)^2*(5*b*B*d-_ + 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2808B a b )d e +--R + +--R 4 3 4 3 4 5 2 +--R (288A b + 1152B a b )d e - 192B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 2 5 +--R 36036A a d e + (10296A a b + 2574B a )d e +--R + +--R 2 2 3 3 4 3 2 2 4 3 +--R (- 6864A a b - 4576B a b)d e + (2496A a b + 3744B a b )d e +--R + +--R 4 3 5 2 4 6 +--R (- 384A b - 1536B a b )d e + 256B b d e +--R * +--R x +--R + +--R 4 2 5 3 4 3 4 +--R 18018A a d e + (- 20592A a b - 5148B a )d e +--R + +--R 2 2 3 4 3 3 2 2 5 2 +--R (13728A a b + 9152B a b)d e + (- 4992A a b - 7488B a b )d e +--R + +--R 4 3 6 4 7 +--R (768A b + 3072B a b )d e - 512B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 7 4 3 7 4 6 6 +--R 6006B b e x + ((6930A b + 27720B a b )e + 7392B b d e )x +--R + +--R 3 2 2 7 4 3 6 +--R (32760A a b + 49140B a b )e + (8820A b + 35280B a b )d e +--R + +--R 4 2 5 +--R 126B b d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 3 2 2 6 +--R (60060A a b + 40040B a b)e + (43680A a b + 65520B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (210A b + 840B a b )d e - 140B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (51480A a b + 12870B a )e + (85800A a b + 57200B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 +--R (1560A a b + 2340B a b )d e + (- 240A b - 960B a b )d e +--R + +--R 4 4 3 +--R 160B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 6 +--R 18018A a e + (82368A a b + 20592B a )d e +--R + +--R 2 2 3 2 5 3 2 2 3 4 +--R (5148A a b + 3432B a b)d e + (- 1872A a b - 2808B a b )d e +--R + +--R 4 3 4 3 4 5 2 +--R (288A b + 1152B a b )d e - 192B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 2 5 +--R 36036A a d e + (10296A a b + 2574B a )d e +--R + +--R 2 2 3 3 4 3 2 2 4 3 +--R (- 6864A a b - 4576B a b)d e + (2496A a b + 3744B a b )d e +--R + +--R 4 3 5 2 4 6 +--R (- 384A b - 1536B a b )d e + 256B b d e +--R * +--R x +--R + +--R 4 2 5 3 4 3 4 +--R 18018A a d e + (- 20592A a b - 5148B a )d e +--R + +--R 2 2 3 4 3 3 2 2 5 2 +--R (13728A a b + 9152B a b)d e + (- 4992A a b - 7488B a b )d e +--R + +--R 4 3 6 4 7 +--R (768A b + 3072B a b )d e - 512B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 833 + +--S 834 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1378 +r0:=-2/3*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(3/2)/e^6+2/5*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^6-4/7*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^6+4/9*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^6-2/11*b^3*_ + (5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(11/2)/e^6+2/13*b^4*B*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 4 6 6 4 3 6 4 5 5 +--R 6930B b e x + ((8190A b + 32760B a b )e + 630B b d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (40040A a b + 60060B a b )e + (910A b + 3640B a b )d e +--R + +--R 4 2 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (77220A a b + 51480B a b)e + (5720A a b + 8580B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (- 1040A b - 4160B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (72072A a b + 18018B a )e + (15444A a b + 10296B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 6864A a b - 10296B a b )d e + (1248A b + 4992B a b )d e +--R + +--R 4 4 2 +--R - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 5 +--R 30030A a e + (24024A a b + 6006B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 20592A a b - 13728B a b)d e + (9152A a b + 13728B a b )d e +--R + +--R 4 3 4 2 4 5 +--R (- 1664A b - 6656B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 2 4 +--R 30030A a d e + (- 48048A a b - 12012B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (41184A a b + 27456B a b)d e + (- 18304A a b - 27456B a b )d e +--R + +--R 4 3 5 4 6 +--R (3328A b + 13312B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 6 4 3 6 4 5 5 +--R 6930B b e x + ((8190A b + 32760B a b )e + 630B b d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (40040A a b + 60060B a b )e + (910A b + 3640B a b )d e +--R + +--R 4 2 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (77220A a b + 51480B a b)e + (5720A a b + 8580B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (- 1040A b - 4160B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (72072A a b + 18018B a )e + (15444A a b + 10296B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 6864A a b - 10296B a b )d e + (1248A b + 4992B a b )d e +--R + +--R 4 4 2 +--R - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 5 +--R 30030A a e + (24024A a b + 6006B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 20592A a b - 13728B a b)d e + (9152A a b + 13728B a b )d e +--R + +--R 4 3 4 2 4 5 +--R (- 1664A b - 6656B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 2 4 +--R 30030A a d e + (- 48048A a b - 12012B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (41184A a b + 27456B a b)d e + (- 18304A a b - 27456B a b )d e +--R + +--R 4 3 5 4 6 +--R (3328A b + 13312B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 838 + +--S 839 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1378 +r0:=2/3*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^6-4/5*b*_ + (b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^6+4/7*b^2*_ + (b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^6-2/9*b^3*_ + (5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(9/2)/e^6+2/11*b^4*B*(d+e*x)^(11/2)/e^6-_ + 2*(b*d-a*e)^4*(B*d-A*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 630B b e x + ((770A b + 3080B a b )e - 700B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (3960A a b + 5940B a b )e + (- 880A b - 3520B a b )d e +--R + +--R 4 2 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (8316A a b + 5544B a b)e + (- 4752A a b - 7128B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (1056A b + 4224B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (9240A a b + 2310B a )e + (- 11088A a b - 7392B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (6336A a b + 9504B a b )d e + (- 1408A b - 5632B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R 6930A a e + (- 18480A a b - 4620B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (22176A a b + 14784B a b)d e + (- 12672A a b - 19008B a b )d e +--R + +--R 4 3 4 4 5 +--R (2816A b + 11264B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R 630B b e x + ((770A b + 3080B a b )e - 700B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (3960A a b + 5940B a b )e + (- 880A b - 3520B a b )d e +--R + +--R 4 2 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (8316A a b + 5544B a b)e + (- 4752A a b - 7128B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (1056A b + 4224B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (9240A a b + 2310B a )e + (- 11088A a b - 7392B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (6336A a b + 9504B a b )d e + (- 1408A b - 5632B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R 6930A a e + (- 18480A a b - 4620B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (22176A a b + 14784B a b)d e + (- 12672A a b - 19008B a b )d e +--R + +--R 4 3 4 4 5 +--R (2816A b + 11264B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 843 + +--S 844 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +)clear all + +--S 846 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1378 +r0:=-4/3*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^6+_ + 4/5*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^6-_ + 2/7*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(7/2)/e^6+2/9*b^4*B*_ + (d+e*x)^(9/2)/e^6+2*(b*d-a*e)^4*(B*d-A*e)/(e^6*sqrt(d+e*x))+_ + 2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 70B b e x + ((90A b + 360B a b )e - 100B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((504A a b + 756B a b )e + (- 144A b - 576B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1008A a b - 1512B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (288A b + 1152B a b )d e - 320B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (2520A a b + 630B a )e + (- 5040A a b - 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (4032A a b + 6048B a b )d e + (- 1152A b - 4608B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R - 630A a e + (5040A a b + 1260B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 10080A a b - 6720B a b)d e + (8064A a b + 12096B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 2304A b - 9216B a b )d e + 2560B b d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R 70B b e x + ((90A b + 360B a b )e - 100B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((504A a b + 756B a b )e + (- 144A b - 576B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1008A a b - 1512B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (288A b + 1152B a b )d e - 320B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (2520A a b + 630B a )e + (- 5040A a b - 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (4032A a b + 6048B a b )d e + (- 1152A b - 4608B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R - 630A a e + (5040A a b + 1260B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 10080A a b - 6720B a b)d e + (8064A a b + 12096B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 2304A b - 9216B a b )d e + 2560B b d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 848 + +--S 849 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1378 +r0:=2/3*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^(3/2))+4/3*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^6-2/5*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(5/2)/e^6+2/7*b^4*B*(d+e*x)^(7/2)/e^6-2*(b*d-_ + a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*sqrt(d+e*x))-4*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 30B b e x + ((42A b + 168B a b )e - 60B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((280A a b + 420B a b )e + (- 112A b - 448B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1680A a b - 2520B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (672A b + 2688B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 840A a b - 210B a )e + (5040A a b + 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 6720A a b - 10080B a b )d e + (2688A b + 10752B a b )d e +--R + +--R 4 4 +--R - 3840B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 70A a e + (- 560A a b - 140B a )d e + (3360A a b + 2240B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 4480A a b - 6720B a b )d e + (1792A b + 7168B a b )d e - 2560B b d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R 30B b e x + ((42A b + 168B a b )e - 60B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((280A a b + 420B a b )e + (- 112A b - 448B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1680A a b - 2520B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (672A b + 2688B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 840A a b - 210B a )e + (5040A a b + 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 6720A a b - 10080B a b )d e + (2688A b + 10752B a b )d e +--R + +--R 4 4 +--R - 3840B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 70A a e + (- 560A a b - 140B a )d e + (3360A a b + 2240B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 4480A a b - 6720B a b )d e + (1792A b + 7168B a b )d e - 2560B b d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 853 + +--S 854 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 855 + +)clear all + +--S 856 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1378 +r0:=2/5*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^(5/2))-2/3*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^(3/2))-2/3*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(3/2)/e^6+2/5*b^4*B*(d+e*x)^(5/2)/e^6+4*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*sqrt(d+e*x))+4*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 6B b e x + ((10A b + 40B a b )e - 20B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((120A a b + 180B a b )e + (- 80A b - 320B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 180A a b - 120B a b)e + (720A a b + 1080B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 480A b - 1920B a b )d e + 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 40A a b - 10B a )e + (- 240A a b - 160B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (960A a b + 1440B a b )d e + (- 640A b - 2560B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 6A a e + (- 16A a b - 4B a )d e + (- 96A a b - 64B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (384A a b + 576B a b )d e + (- 256A b - 1024B a b )d e + 512B b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 857 + +--S 858 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 4 3 5 4 4 4 +--R 6B b e x + ((10A b + 40B a b )e - 20B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((120A a b + 180B a b )e + (- 80A b - 320B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 180A a b - 120B a b)e + (720A a b + 1080B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 480A b - 1920B a b )d e + 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 40A a b - 10B a )e + (- 240A a b - 160B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (960A a b + 1440B a b )d e + (- 640A b - 2560B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 6A a e + (- 16A a b - 4B a )d e + (- 96A a b - 64B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (384A a b + 576B a b )d e + (- 256A b - 1024B a b )d e + 512B b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 858 + +--S 859 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 6 3 10 6 5 3 6 2 9 +--R B b e x + ((A b + 6B a b )e + 3B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 8 +--R ((6A a b + 15B a b )e + (3A b + 18B a b )d e + 3B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (15A a b + 20B a b )e + (18A a b + 45B a b )d e +--R + +--R 6 5 2 6 3 +--R (3A b + 18B a b )d e + B b d +--R * +--R 7 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (20A a b + 15B a b )e + (45A a b + 60B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (18A a b + 45B a b )d e + (A b + 6B a b )d +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (15A a b + 6B a b)e + (60A a b + 45B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (45A a b + 60B a b )d e + (6A a b + 15B a b )d +--R * +--R 5 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (6A a b + B a )e + (45A a b + 18B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (60A a b + 45B a b )d e + (15A a b + 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R A a e + (18A a b + 3B a )d e + (45A a b + 18B a b)d e +--R + +--R 3 3 4 2 3 +--R (20A a b + 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 2 4 2 5 3 2 +--R (3A a d e + (18A a b + 3B a )d e + (15A a b + 6B a b)d )x +--R + +--R 6 2 5 6 3 6 3 +--R (3A a d e + (6A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1378 +r0:=-2/9*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(9/2)/e^8+2/11*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^8-6/13*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^8+2/3*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^8-10/17*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(17/2)/e^8+6/19*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(19/2)/e^8-2/21*b^5*(7*b*B*d-A*b*e-_ + 6*a*B*e)*(d+e*x)^(21/2)/e^8+2/23*b^6*B*(d+e*x)^(23/2)/e^8 +--R +--R +--R (2) +--R 6 11 11 +--R 5819814B b e x +--R + +--R 6 5 11 6 10 10 +--R ((6374082A b + 38244492B a b )e + 19399380B b d e )x +--R + +--R 5 2 4 11 +--R (42270228A a b + 105675570B a b )e +--R + +--R 6 5 10 6 2 9 +--R (21470592A b + 128823552B a b )d e + 21849828B b d e +--R * +--R 9 +--R x +--R + +--R 2 4 3 3 11 +--R (118107990A a b + 157477320B a b )e +--R + +--R 5 2 4 10 +--R (144216072A a b + 360540180B a b )d e +--R + +--R 6 5 2 9 6 3 8 +--R (24509628A b + 147057768B a b )d e + 8360352B b d e +--R * +--R 8 +--R x +--R + +--R 3 3 4 2 11 +--R (178474296A a b + 133855722B a b )e +--R + +--R 2 4 3 3 10 +--R (409441032A a b + 545921376B a b )d e +--R + +--R 5 2 4 2 9 +--R (167423256A a b + 418558140B a b )d e +--R + +--R 6 5 3 8 6 4 7 +--R (9551256A b + 57307536B a b )d e + 6006B b d e +--R * +--R 7 +--R x +--R + +--R 4 2 5 11 +--R (154448910A a b + 61779564B a b)e +--R + +--R 3 3 4 2 10 +--R (631524432A a b + 473643324B a b )d e +--R + +--R 2 4 3 3 2 9 +--R (485756964A a b + 647675952B a b )d e +--R + +--R 5 2 4 3 8 +--R (66816288A a b + 167040720B a b )d e +--R + +--R 6 5 4 7 6 5 6 +--R (10626A b + 63756B a b )d e - 6468B b d e +--R * +--R 6 +--R x +--R + +--R 5 6 11 +--R (73012212A a b + 12168702B a )e +--R + +--R 4 2 5 10 +--R (561632400A a b + 224652960B a b)d e +--R + +--R 3 3 4 2 2 9 +--R (771308496A a b + 578481372B a b )d e +--R + +--R 2 4 3 3 3 8 +--R (200205432A a b + 266940576B a b )d e +--R + +--R 5 2 4 4 7 6 5 5 6 +--R (121716A a b + 304290B a b )d e + (- 11592A b - 69552B a b )d e +--R + +--R 6 6 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 6 11 5 6 10 +--R 14872858A a e + (275823912A a b + 45970652B a )d e +--R + +--R 4 2 5 2 9 +--R (714521220A a b + 285808488B a b)d e +--R + +--R 3 3 4 2 3 8 +--R (332819200A a b + 249614400B a b )d e +--R + +--R 2 4 3 3 4 7 +--R (642390A a b + 856520B a b )d e +--R + +--R 5 2 4 5 6 6 5 6 5 +--R (- 135240A a b - 338100B a b )d e + (12880A b + 77280B a b )d e +--R + +--R 6 7 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 6 10 5 6 2 9 +--R 59491432A a d e + (373173528A a b + 62195588B a )d e +--R + +--R 4 2 5 3 8 +--R (330739080A a b + 132295632B a b)d e +--R + +--R 3 3 4 2 4 7 +--R (2080120A a b + 1560090B a b )d e +--R + +--R 2 4 3 3 5 6 +--R (- 734160A a b - 978880B a b )d e +--R + +--R 5 2 4 6 5 6 5 7 4 +--R (154560A a b + 386400B a b )d e + (- 14720A b - 88320B a b )d e +--R + +--R 6 8 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 6 2 9 5 6 3 8 +--R 89237148A a d e + (194699232A a b + 32449872B a )d e +--R + +--R 4 2 5 4 7 +--R (4680270A a b + 1872108B a b)d e +--R + +--R 3 3 4 2 5 6 +--R (- 2496144A a b - 1872108B a b )d e +--R + +--R 2 4 3 3 6 5 +--R (880992A a b + 1174656B a b )d e +--R + +--R 5 2 4 7 4 +--R (- 185472A a b - 463680B a b )d e +--R + +--R 6 5 8 3 6 9 2 +--R (17664A b + 105984B a b )d e - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 6 3 8 5 6 4 7 +--R 59491432A a d e + (8112468A a b + 1352078B a )d e +--R + +--R 4 2 5 5 6 +--R (- 6240360A a b - 2496144B a b)d e +--R + +--R 3 3 4 2 6 5 +--R (3328192A a b + 2496144B a b )d e +--R + +--R 2 4 3 3 7 4 +--R (- 1174656A a b - 1566208B a b )d e +--R + +--R 5 2 4 8 3 +--R (247296A a b + 618240B a b )d e +--R + +--R 6 5 9 2 6 10 +--R (- 23552A b - 141312B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 4 7 5 6 5 6 +--R 14872858A a d e + (- 16224936A a b - 2704156B a )d e +--R + +--R 4 2 5 6 5 +--R (12480720A a b + 4992288B a b)d e +--R + +--R 3 3 4 2 7 4 +--R (- 6656384A a b - 4992288B a b )d e +--R + +--R 2 4 3 3 8 3 +--R (2349312A a b + 3132416B a b )d e +--R + +--R 5 2 4 9 2 6 5 10 +--R (- 494592A a b - 1236480B a b )d e + (47104A b + 282624B a b )d e +--R + +--R 6 11 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 66927861e +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 11 11 +--R 5819814B b e x +--R + +--R 6 5 11 6 10 10 +--R ((6374082A b + 38244492B a b )e + 19399380B b d e )x +--R + +--R 5 2 4 11 +--R (42270228A a b + 105675570B a b )e +--R + +--R 6 5 10 6 2 9 +--R (21470592A b + 128823552B a b )d e + 21849828B b d e +--R * +--R 9 +--R x +--R + +--R 2 4 3 3 11 +--R (118107990A a b + 157477320B a b )e +--R + +--R 5 2 4 10 +--R (144216072A a b + 360540180B a b )d e +--R + +--R 6 5 2 9 6 3 8 +--R (24509628A b + 147057768B a b )d e + 8360352B b d e +--R * +--R 8 +--R x +--R + +--R 3 3 4 2 11 +--R (178474296A a b + 133855722B a b )e +--R + +--R 2 4 3 3 10 +--R (409441032A a b + 545921376B a b )d e +--R + +--R 5 2 4 2 9 +--R (167423256A a b + 418558140B a b )d e +--R + +--R 6 5 3 8 6 4 7 +--R (9551256A b + 57307536B a b )d e + 6006B b d e +--R * +--R 7 +--R x +--R + +--R 4 2 5 11 +--R (154448910A a b + 61779564B a b)e +--R + +--R 3 3 4 2 10 +--R (631524432A a b + 473643324B a b )d e +--R + +--R 2 4 3 3 2 9 +--R (485756964A a b + 647675952B a b )d e +--R + +--R 5 2 4 3 8 +--R (66816288A a b + 167040720B a b )d e +--R + +--R 6 5 4 7 6 5 6 +--R (10626A b + 63756B a b )d e - 6468B b d e +--R * +--R 6 +--R x +--R + +--R 5 6 11 +--R (73012212A a b + 12168702B a )e +--R + +--R 4 2 5 10 +--R (561632400A a b + 224652960B a b)d e +--R + +--R 3 3 4 2 2 9 +--R (771308496A a b + 578481372B a b )d e +--R + +--R 2 4 3 3 3 8 +--R (200205432A a b + 266940576B a b )d e +--R + +--R 5 2 4 4 7 6 5 5 6 +--R (121716A a b + 304290B a b )d e + (- 11592A b - 69552B a b )d e +--R + +--R 6 6 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 6 11 5 6 10 +--R 14872858A a e + (275823912A a b + 45970652B a )d e +--R + +--R 4 2 5 2 9 +--R (714521220A a b + 285808488B a b)d e +--R + +--R 3 3 4 2 3 8 +--R (332819200A a b + 249614400B a b )d e +--R + +--R 2 4 3 3 4 7 +--R (642390A a b + 856520B a b )d e +--R + +--R 5 2 4 5 6 6 5 6 5 +--R (- 135240A a b - 338100B a b )d e + (12880A b + 77280B a b )d e +--R + +--R 6 7 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 6 10 5 6 2 9 +--R 59491432A a d e + (373173528A a b + 62195588B a )d e +--R + +--R 4 2 5 3 8 +--R (330739080A a b + 132295632B 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5 2 4 8 3 +--R (247296A a b + 618240B a b )d e +--R + +--R 6 5 9 2 6 10 +--R (- 23552A b - 141312B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 4 7 5 6 5 6 +--R 14872858A a d e + (- 16224936A a b - 2704156B a )d e +--R + +--R 4 2 5 6 5 +--R (12480720A a b + 4992288B a b)d e +--R + +--R 3 3 4 2 7 4 +--R (- 6656384A a b - 4992288B a b )d e +--R + +--R 2 4 3 3 8 3 +--R (2349312A a b + 3132416B a b )d e +--R + +--R 5 2 4 9 2 6 5 10 +--R (- 494592A a b - 1236480B a b )d e + (47104A b + 282624B a b )d e +--R + +--R 6 11 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 66927861e +--R Type: Union(Expression(Integer),...) +--E 863 + +--S 864 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +)clear all + +--S 866 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 6 2 9 6 5 2 6 8 +--R B b e x + ((A b + 6B a b 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+--R (- 1555840A a b - 1166880B a b )d e +--R + +--R 2 4 3 3 5 3 +--R (848640A a b + 1131520B a b )d e +--R + +--R 5 2 4 6 2 6 5 7 +--R (- 261120A a b - 652800B a b )d e + (34816A b + 208896B a b )d e +--R + +--R 6 8 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 8 8 6 5 8 6 7 7 +--R 90090B b e x + ((102102A b + 612612B a b )e + 6006B b d e )x +--R + +--R 5 2 4 8 6 5 7 +--R (706860A a b + 1767150B a b )e + (7854A b + 47124B a b )d e +--R + +--R 6 2 6 +--R - 6468B b d e +--R * +--R 6 +--R x +--R + +--R 2 4 3 3 8 +--R (2088450A a b + 2784600B a b )e +--R + +--R 5 2 4 7 6 5 2 6 +--R (64260A a b + 160650B a b )d e + (- 8568A b - 51408B a b )d e +--R + +--R 6 3 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 3 3 4 2 8 +--R (3403400A a b + 2552550B a b )e +--R + +--R 2 4 3 3 7 +--R (232050A a b + 309400B a b )d e +--R + +--R 5 2 4 2 6 6 5 3 5 +--R 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+--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 +--R (150150A a b + 200200B a b )e +--R + +--R 5 2 4 6 6 5 2 5 +--R (- 54600A a b - 136500B a b )d e + (8400A b + 50400B a b )d e +--R + +--R 6 3 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 +--R (257400A a b + 193050B a b )e +--R + +--R 2 4 3 3 6 +--R (- 171600A a b - 228800B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (62400A a b + 156000B a b )d e + (- 9600A b - 57600B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 +--R (270270A a b + 108108B a b)e +--R + +--R 3 3 4 2 6 +--R (- 308880A a b - 231660B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (205920A a b + 274560B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (- 74880A a b - 187200B a b )d e + (11520A b + 69120B a b )d e +--R + +--R 6 5 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (180180A a b + 30030B a )e + (- 360360A a b - 144144B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (411840A a b + 308880B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 274560A a b - 366080B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (99840A a b + 249600B a b )d e + (- 15360A b - 92160B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R 90090A a e + (- 360360A a b - 60060B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (720720A a b + 288288B a b)d e + (- 823680A a b - 617760B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (549120A a b + 732160B a b )d e + (- 199680A a b - 499200B a b )d e +--R + +--R 6 5 6 6 7 +--R (30720A b + 184320B a b )d e - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 883 + +--S 884 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1378 +r0:=-2*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^8+2*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^8-10/7*b^3*_ + (b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(7/2)/e^8+2/3*b^4*_ + (b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(9/2)/e^8-2/11*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(11/2)/e^8+2/13*b^6*B*_ + (d+e*x)^(13/2)/e^8+2*(b*d-a*e)^6*(B*d-A*e)/(e^8*sqrt(d+e*x))+_ + 2*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 462B b e x + ((546A b + 3276B a b )e - 588B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (4004A a b + 10010B a b )e + (- 728A b - 4368B a b )d e +--R + +--R 6 2 5 +--R 784B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (12870A a b + 17160B a b )e + (- 5720A a b - 14300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (1040A b + 6240B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (24024A a b + 18018B a b )e + (- 20592A a b - 27456B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (9152A a b + 22880B a b )d e + (- 1664A b - 9984B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (30030A a b + 12012B a b)e + (- 48048A a b - 36036B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (41184A a b + 54912B a b )d e + (- 18304A a b - 45760B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (3328A b + 19968B a b )d e - 3584B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (36036A a b + 6006B a )e + (- 120120A a b - 48048B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (192192A a b + 144144B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 164736A a b - 219648B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (73216A a b + 183040B a b )d e + (- 13312A b - 79872B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 6006A a e + (72072A a b + 12012B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 240240A a b - 96096B a b)d e + (384384A a b + 288288B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 329472A a b - 439296B a b )d e + (146432A a b + 366080B a b )d e +--R + +--R 6 5 6 6 7 +--R (- 26624A b - 159744B a b )d e + 28672B b d +--R / +--R 8 +-------+ +--R 3003e \|e x + d +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 6 5 7 6 6 6 +--R 462B b e x + ((546A b + 3276B a b )e - 588B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (4004A a b + 10010B a b )e + (- 728A b - 4368B a b )d e +--R + +--R 6 2 5 +--R 784B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (12870A a b + 17160B a b )e + (- 5720A a b - 14300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (1040A b + 6240B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (24024A a b + 18018B a b )e + (- 20592A a b - 27456B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (9152A a b + 22880B a b )d e + (- 1664A b - 9984B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (30030A a b + 12012B a b)e + (- 48048A a b - 36036B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (41184A a b + 54912B a b )d e + (- 18304A a b - 45760B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (3328A b + 19968B a b )d e - 3584B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (36036A a b + 6006B a )e + (- 120120A a b - 48048B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (192192A a b + 144144B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 164736A a b - 219648B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (73216A a b + 183040B a b )d e + (- 13312A b - 79872B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 6006A a e + (72072A a b + 12012B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 240240A a b - 96096B a b)d e + (384384A a b + 288288B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 329472A a b - 439296B a b )d e + (146432A a b + 366080B a b )d e +--R + +--R 6 5 6 6 7 +--R (- 26624A b - 159744B a b )d e + 28672B b d +--R / +--R 8 +-------+ +--R 3003e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 888 + +--S 889 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1378 +r0:=2/3*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^(3/2))+10/3*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^8-2*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(5/2)/e^8+6/7*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(7/2)/e^8-2/9*b^5*(7*b*B*d-A*b*e-_ + 6*a*B*e)*(d+e*x)^(9/2)/e^8+2/11*b^6*B*(d+e*x)^(11/2)/e^8-2*_ + (b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*sqrt(d+e*x))-6*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 126B b e x + ((154A b + 924B a b )e - 196B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (1188A a b + 2970B a b )e + (- 264A b - 1584B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (4158A a b + 5544B a b )e + (- 2376A a b - 5940B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (528A b + 3168B a b )d e - 672B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (9240A a b + 6930B a b )e + (- 11088A a b - 14784B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (6336A a b + 15840B a b )d e + (- 1408A b - 8448B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (20790A a b + 8316B a b)e + (- 55440A a b - 41580B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (66528A a b + 88704B a b )d e + (- 38016A a b - 95040B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (8448A b + 50688B a b )d e - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 8316A a b - 1386B a )e + (83160A a b + 33264B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (- 221760A a b - 166320B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (266112A a b + 354816B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 152064A a b - 380160B a b )d e + (33792A b + 202752B a b )d e +--R + +--R 6 6 +--R - 43008B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 462A a e + (- 5544A a b - 924B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (55440A a b + 22176B a b)d e + (- 147840A a b - 110880B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (177408A a b + 236544B a b )d e + (- 101376A a b - 253440B a b )d e +--R + +--R 6 5 6 6 7 +--R (22528A b + 135168B a b )d e - 28672B b d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 6 5 7 6 6 6 +--R 126B b e x + ((154A b + 924B a b )e - 196B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (1188A a b + 2970B a b )e + (- 264A b - 1584B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (4158A a b + 5544B a b )e + (- 2376A a b - 5940B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (528A b + 3168B a b )d e - 672B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (9240A a b + 6930B a b )e + (- 11088A a b - 14784B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (6336A a b + 15840B a b )d e + (- 1408A b - 8448B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (20790A a b + 8316B a b)e + (- 55440A a b - 41580B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (66528A a b + 88704B a b )d e + (- 38016A a b - 95040B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (8448A b + 50688B a b )d e - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 8316A a b - 1386B a )e + (83160A a b + 33264B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (- 221760A a b - 166320B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (266112A a b + 354816B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 152064A a b - 380160B a b )d e + (33792A b + 202752B a b )d e +--R + +--R 6 6 +--R - 43008B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 462A a e + (- 5544A a b - 924B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (55440A a b + 22176B a b)d e + (- 147840A a b - 110880B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (177408A a b + 236544B a b )d e + (- 101376A a b - 253440B a b )d e +--R + +--R 6 5 6 6 7 +--R (22528A b + 135168B a b )d e - 28672B b d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 893 + +--S 894 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 895 + +)clear all + +--S 896 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1378 +r0:=2/5*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^(5/2))-2/3*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^(3/2))-10/3*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(3/2)/e^8+6/5*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(5/2)/e^8-2/7*b^5*(7*b*B*d-_ + A*b*e-6*a*B*e)*(d+e*x)^(7/2)/e^8+2/9*b^6*B*(d+e*x)^(9/2)/e^8+6*b*_ + (b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*sqrt(d+e*x))+10*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 70B b e x + ((90A b + 540B a b )e - 140B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (756A a b + 1890B a b )e + (- 216A b - 1296B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (3150A a b + 4200B a b )e + (- 2520A a b - 6300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (720A b + 4320B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (12600A a b + 9450B a b )e + (- 25200A a b - 33600B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (20160A a b + 50400B a b )d e + (- 5760A b - 34560B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (- 9450A a b - 3780B a b)e + (75600A a b + 56700B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (- 151200A a b - 201600B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (120960A a b + 302400B a b )d e + (- 34560A b - 207360B a b )d e +--R + +--R 6 5 2 +--R 53760B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 1260A a b - 210B a )e + (- 12600A a b - 5040B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (100800A a b + 75600B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 201600A a b - 268800B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (161280A a b + 403200B a b )d e + (- 46080A b - 276480B a b )d e +--R + +--R 6 6 +--R 71680B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 126A a e + (- 504A a b - 84B a )d e + (- 5040A a b - 2016B a b)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (40320A a b + 30240B a b )d e + (- 80640A a b - 107520B a b )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (64512A a b + 161280B a b )d e + (- 18432A b - 110592B a b )d e +--R + +--R 6 7 +--R 28672B b d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 6 5 7 6 6 6 +--R 70B b e x + ((90A b + 540B a b )e - 140B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (756A a b + 1890B a b )e + (- 216A b - 1296B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (3150A a b + 4200B a b )e + (- 2520A a b - 6300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (720A b + 4320B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (12600A a b + 9450B a b )e + (- 25200A a b - 33600B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (20160A a b + 50400B a b )d e + (- 5760A b - 34560B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (- 9450A a b - 3780B a b)e + (75600A a b + 56700B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (- 151200A a b - 201600B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (120960A a b + 302400B a b )d e + (- 34560A b - 207360B a b )d e +--R + +--R 6 5 2 +--R 53760B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 1260A a b - 210B a )e + (- 12600A a b - 5040B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (100800A a b + 75600B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 201600A a b - 268800B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (161280A a b + 403200B a b )d e + (- 46080A b - 276480B a b )d e +--R + +--R 6 6 +--R 71680B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 126A a e + (- 504A a b - 84B a )d e + (- 5040A a b - 2016B a b)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (40320A a b + 30240B a b )d e + (- 80640A a b - 107520B a b )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (64512A a b + 161280B a b )d e + (- 18432A b - 110592B a b )d e +--R + +--R 6 7 +--R 28672B b d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 898 + +--S 899 of 1378 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1378 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +)clear all + +--S 901 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1378 +r0:=1/3*(b*d-a*e)*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+_ + 1/5*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/b^3+1/7*(2*b*B*d+7*A*b*e-_ + 9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(9/2)/(b*_ + (b*d-a*e)*(a+b*x))-(b*d-a*e)^(5/2)*(2*b*B*d+7*A*b*e-9*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+(b*d-a*e)^2*_ + (2*b*B*d+7*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (- 735A a b + 945B a b)e + (1470A a b - 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 735A b + 1365B a b )d e - 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 735A a b + 945B a )e + (1470A a b - 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 735A a b + 1365B a b )d e - 210B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 54B a b )e + 132B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 98A a b + 126B a b )e + (224A b - 316B a b )d e +--R + +--R 4 2 +--R 244B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (490A a b - 630B a b)e + (- 1176A a b + 1652B a b )d e +--R + +--R 4 3 2 4 3 +--R (812A b - 1380B a b )d e + 352B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1715A a b + 2415B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (1127A a b - 1939B a b )d e + (- 105A b + 457B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 5 +-+ +--R (105b x + 105a b )\|b +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 3 3 2 2 2 +--R (735A a b - 945B a b)e + (- 1470A a b + 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (735A b - 1365B a b )d e + 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1470A a b + 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (735A a b - 1365B a b )d e + 210B a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 60B b e x + ((84A b - 108B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 196A a b + 252B a b )e + (448A b - 632B a b )d e +--R + +--R 4 2 +--R 488B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (980A a b - 1260B a b)e + (- 2352A a b + 3304B a b )d e +--R + +--R 4 3 2 4 3 +--R (1624A b - 2760B a b )d e + 704B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (1470A a b - 1890B a )e + (- 3430A a b + 4830B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (2254A a b - 3878B a b )d e + (- 210A b + 914B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 5 +--R 210b x + 210a b +--R , +--R +--R 2 2 3 3 3 2 2 2 +--R (- 735A a b + 945B a b)e + (1470A a b - 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 735A b + 1365B a b )d e - 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 735A a b + 945B a )e + (1470A a b - 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 735A a b + 1365B a b )d e - 210B a b d +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 54B a b )e + 132B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 98A a b + 126B a b )e + (224A b - 316B a b )d e +--R + +--R 4 2 +--R 244B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (490A a b - 630B a b)e + (- 1176A a b + 1652B a b )d e +--R + +--R 4 3 2 4 3 +--R (812A b - 1380B a b )d e + 352B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1715A a b + 2415B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (1127A a b - 1939B a b )d e + (- 105A b + 457B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 5 +--R 105b x + 105a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 903 + +--S 904 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 +--R (7A a b - 9B a )e + (- 14A a b + 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (7A b - 13B a b )d e + 2B b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 18B a )e + (- 28A a b + 40B a b)d e +--R + +--R 3 2 2 3 3 +--R (14A b - 26B a b )d e + 4B b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 +--R (7A a b - 9B a )e + (- 14A a b + 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (7A b - 13B a b )d e + 2B b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 3 2 2 2 +--R (- 7A a b + 9B a )e + (14A a b - 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 7A b + 13B a b )d e - 2B b d +--R * +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 907 + +)clear all + +--S 908 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1378 +r0:=1/3*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/b^3+1/5*(2*b*B*d+5*A*b*e-_ + 7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(7/2)/(b*_ + (b*d-a*e)*(a+b*x))-(b*d-a*e)^(3/2)*(2*b*B*d+5*A*b*e-7*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+(b*d-a*e)*(2*b*B*d+_ + 5*A*b*e-7*a*B*e)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 14B a b )e + 22B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 50A a b + 70B a b)e + (70A b - 118B a b )d e + 46B b d )x +--R + +--R 2 3 2 2 2 +--R (- 75A a b + 105B a )e + (100A a b - 170B a b)d e +--R + +--R 3 2 2 +--R (- 15A b + 61B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 5 4 +-+ +--R (15b x + 15a b )\|b +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R 12B b e x + ((20A b - 28B a b )e + 44B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 100A a b + 140B a b)e + (140A b - 236B a b )d e + 92B b d )x +--R + +--R 2 3 2 2 2 +--R (- 150A a b + 210B a )e + (200A a b - 340B a b)d e +--R + +--R 3 2 2 +--R (- 30A b + 122B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 30b x + 30a b +--R , +--R +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 14B a b )e + 22B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 50A a b + 70B a b)e + (70A b - 118B a b )d e + 46B b d )x +--R + +--R 2 3 2 2 2 +--R (- 75A a b + 105B a )e + (100A a b - 170B a b)d e +--R + +--R 3 2 2 +--R (- 15A b + 61B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 15b x + 15a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 910 + +--S 911 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 2 |- a e + b d +--R ((5A a b - 7B a )e + (- 5A b + 9B a b)d e - 2B b d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R +-+ \| b +--R \|b log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 +--R ((- 10A a b + 14B a )e + (10A b - 18B a b)d e + 4B b d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +-----------+ +--R ((- 5A a b + 7B a )e + (5A b - 9B a b)d e + 2B b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 2 2 2 +-+ |a e - b d +--R ((5A a b - 7B a )e + (- 5A b + 9B a b)d e - 2B b d )\|b |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 914 + +)clear all + +--S 915 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1378 +r0:=1/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e))-_ + (A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+_ + (2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (((- 9A b + 15B a b)e - 6B b d)x + (- 9A a b + 15B a )e - 6B a b d) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 10B a b)e + 8B b d)x + (9A a b - 15B a )e +--R + +--R 2 +--R (- 3A b + 11B a b)d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((9A b - 15B a b)e + 6B b d)x + (9A a b - 15B a )e + 6B a b d) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 2 2 2 2 +--R 4B b e x + ((12A b - 20B a b)e + 16B b d)x + (18A a b - 30B a )e +--R + +--R 2 +--R (- 6A b + 22B a b)d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +--R 2 2 2 +--R (((- 9A b + 15B a b)e - 6B b d)x + (- 9A a b + 15B a )e - 6B a b d) +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 10B a b)e + 8B b d)x + (9A a b - 15B a )e +--R + +--R 2 +--R (- 3A b + 11B a b)d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 3b x + 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 917 + +--S 918 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- a e + b d +-+ +--R ((3A b - 5B a)e + 2B b d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R ((6A b - 10B a)e + 4B b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R ((3A b - 5B a)e + 2B b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R ((- 3A b + 5B a)e - 2B b d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 921 + +)clear all + +--S 922 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1378 +r0:=-(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+A*b*e-3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))+_ + (2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)) +--R +--R +--R (2) +--R 2 2 2 +--R (((- A b + 3B a b)e - 2B b d)x + (- A a b + 3B a )e - 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (2B b x - A b + 3B a)\|- a e + b d \|b \|e x + d +--R / +--R 3 2 +-----------+ +-+ +--R (b x + a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((A b - 3B a b)e + 2B b d)x + (A a b - 3B a )e + 2B a b d) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (4B b x - 2A b + 6B a)\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 3 2 | 2 +--R (2b x + 2a b )\|- a b e + b d +--R , +--R +--R 2 2 2 +--R (((A b - 3B a b)e + 2B b d)x + (A a b - 3B a )e + 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (2B b x - A b + 3B a)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 3 2 | 2 +--R (b x + a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 924 + +--S 925 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R ((A b - 3B a)e + 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((2A b - 6B a)e + 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R 2b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((A b - 3B a)e + 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b - 3B a)e + 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 928 + +)clear all + +--S 929 of 1378 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1378 +r0:=-(2*b*B*d-A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(3/2)*(b*d-a*e)^(3/2))-(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 +--R (((- A b - B a b)e + 2B b d)x + (- A a b - B a )e + 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (A b - B a)\|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 2 +-----------+ +-+ +--R ((a b e - b d)x + a b e - a b d)\|- a e + b d \|b +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((A b + B a b)e - 2B b d)x + (A a b + B a )e - 2B a b d) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (2A b - 2B a)\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 2 3 2 2 | 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|- a b e + b d +--R , +--R +--R 2 2 2 +--R (((A b + B a b)e - 2B b d)x + (A a b + B a )e - 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (A b - B a)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 2 3 2 2 | 2 +--R ((a b e - b d)x + a b e - a b d)\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 931 + +--S 932 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R ((A b + B a)e - 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((2A b + 2B a)e - 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R (2a b e - 2b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((A b + B a)e - 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b + B a)e - 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R (a b e - b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 935 + +)clear all + +--S 936 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1378 +r0:=-(2*b*B*d-3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(5/2)*sqrt(b))+(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^2*_ + sqrt(d+e*x))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 +-------+ +--R (((3A b - B a b)e - 2B b d)x + (3A a b - B a )e - 2B a b d)\|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R (((- 3A b + B a)e + 2B b d)x - 2A a e + (- A b + 3B a)d)\|- a e + b d \|b +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-----------+ +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((3A b - B a b)e - 2B b d)x + (3A a b - B a )e - 2B a b d) +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R (((- 6A b + 2B a)e + 4B b d)x - 4A a e + (- 2A b + 6B a)d) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +--R ((2a b e - 4a b d e + 2b d )x + 2a e - 4a b d e + 2a b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 2 2 2 +--R (((- 3A b + B a b)e + 2B b d)x + (- 3A a b + B a )e + 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +--R (((- 3A b + B a)e + 2B b d)x - 2A a e + (- A b + 3B a)d)\|a b e - b d +--R / +--R +-----------+ +--R 2 2 2 3 2 3 2 2 2 2 | 2 +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|a b e - b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 938 + +--S 939 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R ((3A b - B a)e - 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((- 6A b + 2B a)e + 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 2 | 2 +-----------+ +-+ +--R (2a e - 4a b d e + 2b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((- 3A b + B a)e + 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((- 3A b + B a)e + 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 2 +-----------+ +-+ | 2 +--R (a e - 2a b d e + b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 942 + +)clear all + +--S 943 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1378 +r0:=1/3*(2*b*B*d-5*A*b*e+3*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+(-A*b+a*B)/_ + (b*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2))-(2*b*B*d-5*A*b*e+3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(7/2)+_ + (2*b*B*d-5*A*b*e+3*a*B*e)/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 15A b + 9B a b)e + 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 15A a b + 9B a )e + (- 15A b + 15B a b)d e + 6B b d )x +--R + +--R 2 2 +--R (- 15A a b + 9B a )d e + 6B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((10A a b - 6B a )e + (20A b - 16B a b)d e - 8B b d )x - 2A a e +--R + +--R 2 2 2 +--R (14A a b - 4B a )d e + (3A b - 11B a b)d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((15A a b - 9B a )e + (15A b - 15B a b)d e - 6B b d )x +--R + +--R 2 2 +--R (15A a b - 9B a )d e - 6B a b d +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R ((30A b - 18B a b)e - 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((20A a b - 12B a )e + (40A b - 32B a b)d e - 16B b d )x - 4A a e +--R + +--R 2 2 2 +--R (28A a b - 8B a )d e + (6A b - 22B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b e - 18a b d e + 18a b d e - 6b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (6a e - 12a b d e + 12a b d e - 6b d )x + 6a d e - 18a b d e +--R + +--R 2 2 3 3 4 +--R 18a b d e - 6a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((15A a b - 9B a )e + (15A b - 15B a b)d e - 6B b d )x +--R + +--R 2 2 +--R (15A a b - 9B a )d e - 6B a b d +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((10A a b - 6B a )e + (20A b - 16B a b)d e - 8B b d )x - 2A a e +--R + +--R 2 2 2 +--R (14A a b - 4B a )d e + (3A b - 11B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 945 + +--S 946 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R ((5A b - 3B a)e - 2B b d)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R ((10A b - 6B a)e - 4B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (2a e - 6a b d e + 6a b d e - 2b d )\|- a e + b d +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R ((5A b - 3B a)e - 2B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R +-----------+ | b +--R ((5A b - 3B a)e - 2B b d)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 949 + +)clear all + +--S 950 of 1378 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1378 +r0:=1/5*(2*b*B*d-7*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+_ + (-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(5/2))+1/3*(2*b*B*d-7*A*b*e+_ + 5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2))-b^(3/2)*(2*b*B*d-7*A*b*e+_ + 5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+_ + b*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((105A b - 75B a b )e - 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((105A a b - 75B a b)e + (210A b - 180B a b )d e - 60B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((210A a b - 150B a b)d e + (105A b - 135B a b )d e - 30B b d )x +--R + +--R 2 2 2 2 3 +--R (105A a b - 75B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 70A a b + 50B a b)e + (- 245A b + 195B a b )d e +--R + +--R 3 2 +--R 70B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 10B a )e + (- 168A a b + 116B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 161A b + 163B a b )d e + 46B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (32A a b - 4B a )d e + (- 116A a b + 48B a b)d e +--R + +--R 3 2 3 +--R (- 15A b + 61B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 3 2 3 +--R ((105A b - 75B a b )e - 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((105A a b - 75B a b)e + (210A b - 180B a b )d e - 60B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((210A a b - 150B a b)d e + (105A b - 135B a b )d e - 30B b d )x +--R + +--R 2 2 2 2 3 +--R (105A a b - 75B a b)d e - 30B a b d +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 3 +--R ((- 210A b + 150B a b )e + 60B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 140A a b + 100B a b)e + (- 490A b + 390B a b )d e +--R + +--R 3 2 +--R 140B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (28A a b - 20B a )e + (- 336A a b + 232B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 322A b + 326B a b )d e + 92B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 12A a e + (64A a b - 8B a )d e + (- 232A a b + 96B a b)d e +--R + +--R 3 2 3 +--R (- 30A b + 122B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (30a b e - 120a b d e + 180a b d e - 120a b d e + 30b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 30a e - 60a b d e - 60a b d e + 240a b d e - 210a b d e +--R + +--R 5 5 +--R 60b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 60a d e - 210a b d e + 240a b d e - 60a b d e - 60a b d e +--R + +--R 5 6 +--R 30b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 30a d e - 120a b d e + 180a b d e - 120a b d e + 30a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 105A a b + 75B a b)e + (- 210A b + 180B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 3 2 2 +--R (- 210A a b + 150B a b)d e + (- 105A b + 135B a b )d e +--R + +--R 3 3 +--R 30B b d +--R * +--R x +--R + +--R 2 2 2 2 3 +--R (- 105A a b + 75B a b)d e + 30B a b d +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 70A a b + 50B a b)e + (- 245A b + 195B a b )d e + 70B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 10B a )e + (- 168A a b + 116B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 161A b + 163B a b )d e + 46B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (32A a b - 4B a )d e + (- 116A a b + 48B a b)d e +--R + +--R 3 2 3 +--R (- 15A b + 61B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 952 + +--S 953 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 +-----------+ | b +--R ((7A b - 5B a b)e - 2B b d)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R ((- 14A b + 10B a b)e + 4B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (2a e - 8a b d e + 12a b d e - 8a b d e + 2b d )\|- a e + b d +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R ((- 7A b + 5B a b)e + 2B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 +-----------+ | b +--R ((- 7A b + 5B a b)e + 2B b d)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (a e - 4a b d e + 6a b d e - 4a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 956 + +)clear all + +--S 957 of 1378 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1378 +r0:=7/8*e^2*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(3/2)/b^5+21/40*e^2*_ + (6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*(b*d-a*e))-3/8*e*_ + (6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(7/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/12*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(9/2)/(b^2*(b*d-a*e)*_ + (a+b*x)^2)-1/3*(A*b-a*B)*(d+e*x)^(11/2)/(b*(b*d-a*e)*(a+b*x)^3)-_ + 21/8*e^2*(b*d-a*e)^(3/2)*(6*b*B*d+5*A*b*e-11*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(13/2)+21/8*e^2*(b*d-a*e)*(6*b*B*d+_ + 5*A*b*e-11*a*B*e)*sqrt(d+e*x)/b^6 +--R +--R +--R (2) +--R 4 2 3 4 5 4 3 +--R (1575A a b - 3465B a b )e + (- 1575A b + 5355B a b )d e +--R + +--R 5 2 2 +--R - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4725A a b - 10395B a b )e + (- 4725A a b + 16065B a b )d e +--R + +--R 4 2 2 +--R - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (4725A a b - 10395B a b)e + (- 4725A a b + 16065B a b )d e +--R + +--R 2 3 2 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (1575A a b - 3465B a )e + (- 1575A a b + 5355B a b)d e +--R + +--R 3 2 2 2 +--R - 1890B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 48B b e x + ((80A b - 176B a b )e + 336B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 720A a b + 1584B a b )e + (1040A b - 3152B a b )d e +--R + +--R 5 2 2 +--R 1728B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 3465A a b + 7623B a b )e + (4770A a b - 14652B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 825A b + 7539B a b )d e - 510B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 4200A a b + 9240B a b)e + (5670A a b - 17514B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 900A a b + 8784B a b )d e + (- 250A b - 530B a b )d e +--R + +--R 5 4 +--R - 60B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 1575A a b + 3465B a )e + (2100A a b - 6510B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 315A a b + 3213B a b )d e + (- 90A a b - 180B a b )d e +--R + +--R 5 4 4 +--R (- 40A b - 20B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 9 3 8 2 2 7 3 6 +-+ +--R (120b x + 360a b x + 360a b x + 120a b )\|b +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 3 4 5 4 3 +--R (- 1575A a b + 3465B a b )e + (1575A b - 5355B a b )d e +--R + +--R 5 2 2 +--R 1890B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 4725A a b + 10395B a b )e + (4725A a b - 16065B a b )d e +--R + +--R 4 2 2 +--R 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 4725A a b + 10395B a b)e + (4725A a b - 16065B a b )d e +--R + +--R 2 3 2 2 +--R 5670B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 1575A a b + 3465B a )e + (1575A a b - 5355B a b)d e +--R + +--R 3 2 2 2 +--R 1890B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 96B b e x + ((160A b - 352B a b )e + 672B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 1440A a b + 3168B a b )e + (2080A b - 6304B a b )d e +--R + +--R 5 2 2 +--R 3456B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 6930A a b + 15246B a b )e + (9540A a b - 29304B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1650A b + 15078B a b )d e - 1020B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 8400A a b + 18480B a b)e + (11340A a b - 35028B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 1800A a b + 17568B a b )d e + (- 500A b - 1060B a b )d e +--R + +--R 5 4 +--R - 120B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 3150A a b + 6930B a )e + (4200A a b - 13020B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 630A a b + 6426B a b )d e + (- 180A a b - 360B a b )d e +--R + +--R 5 4 4 +--R (- 80A b - 40B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 9 3 8 2 2 7 3 6 +--R 240b x + 720a b x + 720a b x + 240a b +--R , +--R +--R 4 2 3 4 5 4 3 +--R (1575A a b - 3465B a b )e + (- 1575A b + 5355B a b )d e +--R + +--R 5 2 2 +--R - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4725A a b - 10395B a b )e + (- 4725A a b + 16065B a b )d e +--R + +--R 4 2 2 +--R - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (4725A a b - 10395B a b)e + (- 4725A a b + 16065B a b )d e +--R + +--R 2 3 2 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (1575A a b - 3465B a )e + (- 1575A a b + 5355B a b)d e +--R + +--R 3 2 2 2 +--R - 1890B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 48B b e x + ((80A b - 176B a b )e + 336B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 720A a b + 1584B a b )e + (1040A b - 3152B a b )d e +--R + +--R 5 2 2 +--R 1728B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 3465A a b + 7623B a b )e + (4770A a b - 14652B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 825A b + 7539B a b )d e - 510B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 4200A a b + 9240B a b)e + (5670A a b - 17514B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 900A a b + 8784B a b )d e + (- 250A b - 530B a b )d e +--R + +--R 5 4 +--R - 60B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 1575A a b + 3465B a )e + (2100A a b - 6510B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 315A a b + 3213B a b )d e + (- 90A a b - 180B a b )d e +--R + +--R 5 4 4 +--R (- 40A b - 20B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 9 3 8 2 2 7 3 6 +--R 120b x + 360a b x + 360a b x + 120a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 959 + +--S 960 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 2 3 2 2 2 +--R ((- 105A a b + 231B a )e + (105A b - 357B a b)d e + 126B b d e ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 4 2 3 2 2 2 +--R ((- 210A a b + 462B a )e + (210A b - 714B a b)d e + 252B b d e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 4 2 3 2 2 2 +--R ((- 105A a b + 231B a )e + (105A b - 357B a b)d e + 126B b d e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 4 2 3 2 2 2 +-+ +--R ((105A a b - 231B a )e + (- 105A b + 357B a b)d e - 126B b d e )\|b +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 6 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 963 + +)clear all + +--S 964 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1378 +r0:=35/24*e^2*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e))-_ + 7/8*e*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(5/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/4*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^3)-35/8*e^2*(2*b*B*d+_ + A*b*e-3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-_ + a*e)/b^(11/2)+35/8*e^2*(2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 105A b + 315B a b )e - 210B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 315A a b + 945B a b )e - 630B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 315A a b + 945B a b)e - 630B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 105A a b + 315B a )e - 210B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 16B b e x + ((48A b - 144B a b )e + 160B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (231A a b - 693B a b )e + (- 87A b + 723B a b )d e +--R + +--R 4 2 +--R - 78B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (280A a b - 840B a b)e + (- 98A a b + 854B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 38A b - 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (105A a b - 315B a )e + (- 35A a b + 315B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 14A a b - 28B a b )d e + (- 8A b - 4B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +-+ +--R (24b x + 72a b x + 72a b x + 24a b )\|b +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((- 105A b + 315B a b )e - 210B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 315A a b + 945B a b )e - 630B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 315A a b + 945B a b)e - 630B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 105A a b + 315B a )e - 210B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 32B b e x + ((96A b - 288B a b )e + 320B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (462A a b - 1386B a b )e + (- 174A b + 1446B a b )d e +--R + +--R 4 2 +--R - 156B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (560A a b - 1680B a b)e + (- 196A a b + 1708B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 76A b - 164B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 630B a )e + (- 70A a b + 630B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 28A a b - 56B a b )d e + (- 16A b - 8B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +--R 48b x + 144a b x + 144a b x + 48a b +--R , +--R +--R 4 3 3 4 2 3 +--R ((- 105A b + 315B a b )e - 210B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 315A a b + 945B a b )e - 630B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 315A a b + 945B a b)e - 630B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 105A a b + 315B a )e - 210B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 16B b e x + ((48A b - 144B a b )e + 160B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (231A a b - 693B a b )e + (- 87A b + 723B a b )d e +--R + +--R 4 2 +--R - 78B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (280A a b - 840B a b)e + (- 98A a b + 854B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 38A b - 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (105A a b - 315B a )e + (- 35A a b + 315B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 14A a b - 28B a b )d e + (- 8A b - 4B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +--R 24b x + 72a b x + 72a b x + 24a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 966 + +--S 967 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 |- a e + b d +-+ +--R ((- 35A b + 105B a)e - 70B b d e ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 2 +-----------+ \|b \|e x + d +--R ((70A b - 210B a)e + 140B b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 +-----------+ \|b \|e x + d +--R ((35A b - 105B a)e + 70B b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 3 2 +-+ |a e - b d \|e x + d +--R ((- 35A b + 105B a)e - 70B b d e )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1378 +r0:=-5/24*e*(6*b*B*d+A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/12*(6*b*B*d+A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^3)-5/8*e^2*_ + (6*b*B*d+A*b*e-7*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(9/2)*sqrt(b*d-a*e))+5/8*e^2*(6*b*B*d+A*b*e-7*a*B*e)*sqrt(d+e*x)/_ + (b^4*(b*d-a*e)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 15A b + 105B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 45A a b + 315B a b )e - 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 45A a b + 315B a b)e - 270B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 15A a b + 105B a )e - 90B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 48B b e x + ((- 33A b + 231B a b )e - 54B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 40A a b + 280B a b)e + (- 26A b - 58B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (- 15A a b + 105B a )e + (- 10A a b - 20B a b)d e +--R + +--R 3 2 2 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 3 6 2 2 5 3 4 +-----------+ +-+ +--R (24b x + 72a b x + 72a b x + 24a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((15A b - 105B a b )e + 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((45A a b - 315B a b )e + 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((45A a b - 315B a b)e + 270B a b d e )x + (15A a b - 105B a )e +--R + +--R 3 2 +--R 90B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R 96B b e x + ((- 66A b + 462B a b )e - 108B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 80A a b + 560B a b)e + (- 52A b - 116B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (- 30A a b + 210B a )e + (- 20A a b - 40B a b)d e +--R + +--R 3 2 2 +--R (- 16A b - 8B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 7 3 6 2 2 5 3 4 | 2 +--R (48b x + 144a b x + 144a b x + 48a b )\|- a b e + b d +--R , +--R +--R 4 3 3 4 2 3 +--R ((15A b - 105B a b )e + 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((45A a b - 315B a b )e + 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((45A a b - 315B a b)e + 270B a b d e )x + (15A a b - 105B a )e +--R + +--R 3 2 +--R 90B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 48B b e x + ((- 33A b + 231B a b )e - 54B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 40A a b + 280B a b)e + (- 26A b - 58B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (- 15A a b + 105B a )e + (- 10A a b - 20B a b)d e +--R + +--R 3 2 2 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 7 3 6 2 2 5 3 4 | 2 +--R (24b x + 72a b x + 72a b x + 24a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 973 + +--S 974 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R ((5A b - 35B a)e + 30B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((10A b - 70B a)e + 60B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 4 | 2 +-----------+ +-+ +--R 16b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +--S 976 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((5A b - 35B a)e + 30B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 +-----------+ +-+ +--R ((5A b - 35B a)e + 30B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 4 +-----------+ +-+ | 2 +--R 8b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 977 + +)clear all + +--S 978 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1378 +r0:=-1/12*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^3)-1/8*e^2*(6*b*B*d-_ + A*b*e-5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*_ + (b*d-a*e)^(3/2))-1/8*e*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*_ + (b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 3A b - 15B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 9A a b - 45B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 9A a b - 45B a b)e + 54B a b d e )x + (- 3A a b - 15B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b - 33B a b )e + 30B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 8A a b - 40B a b)e + (14A b + 22B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 15B a )e + (- 2A a b + 8B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 6 7 3 2 5 6 2 3 4 2 5 +--R (24a b e - 24b d)x + (72a b e - 72a b d)x + (72a b e - 72a b d)x +--R + +--R 4 3 3 4 +--R 24a b e - 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((3A b + 15B a b )e - 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((9A a b + 45B a b )e - 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((9A a b + 45B a b)e - 54B a b d e )x + (3A a b + 15B a )e +--R + +--R 3 2 +--R - 18B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 2 3 2 +--R ((6A b - 66B a b )e + 60B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 16A a b - 80B a b)e + (28A b + 44B a b )d e + 24B b d )x +--R + +--R 2 3 2 2 2 +--R (- 6A a b - 30B a )e + (- 4A a b + 16B a b)d e +--R + +--R 3 2 2 +--R (16A b + 8B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 6 7 3 2 5 6 2 +--R (48a b e - 48b d)x + (144a b e - 144a b d)x +--R + +--R 3 4 2 5 4 3 3 4 +--R (144a b e - 144a b d)x + 48a b e - 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 3 3 4 2 3 +--R ((3A b + 15B a b )e - 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((9A a b + 45B a b )e - 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((9A a b + 45B a b)e - 54B a b d e )x + (3A a b + 15B a )e +--R + +--R 3 2 +--R - 18B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 2 2 3 2 +--R ((3A b - 33B a b )e + 30B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 8A a b - 40B a b)e + (14A b + 22B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 15B a )e + (- 2A a b + 8B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 6 7 3 2 5 6 2 3 4 2 5 +--R (24a b e - 24b d)x + (72a b e - 72a b d)x + (72a b e - 72a b d)x +--R + +--R 4 3 3 4 +--R 24a b e - 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 980 + +--S 981 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R ((A b + 5B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((2A b + 10B a)e - 12B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 4 | 2 +-----------+ +-+ +--R (16a b e - 16b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((A b + 5B a)e - 6B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 +-----------+ +-+ +--R ((A b + 5B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 3 4 +-----------+ +-+ | 2 +--R (8a b e - 8b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 984 + +)clear all + +--S 985 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1378 +r0:=-1/3*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^3)+1/8*e^2*(2*b*B*d-_ + A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*_ + (b*d-a*e)^(5/2))-1/4*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^2*_ + (b*d-a*e)*(a+b*x)^2)-1/8*e*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 3A b - 3B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 9A a b - 9B a b )e + 18B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 9A a b - 9B a b)e + 18B a b d e )x + (- 3A a b - 3B a )e +--R + +--R 3 2 +--R 6B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b + 3B a b )e - 6B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((8A a b - 8B a b)e + (- 2A b + 14B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 3B a )e + (14A a b + 4B a b)d e + (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 5 2 6 7 2 3 +--R (24a b e - 48a b d e + 24b d )x +--R + +--R 3 4 2 2 5 6 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 2 2 4 3 3 4 2 +--R (72a b e - 144a b d e + 72a b d )x + 24a b e - 48a b d e + 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((3A b + 3B a b )e - 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((9A a b + 9B a b )e - 18B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((9A a b + 9B a b)e - 18B a b d e )x + (3A a b + 3B a )e +--R + +--R 3 2 +--R - 6B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 2 3 2 +--R ((6A b + 6B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((16A a b - 16B a b)e + (- 4A b + 28B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (- 6A a b - 6B a )e + (28A a b + 8B a b)d e +--R + +--R 3 2 2 +--R (- 16A b - 8B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 5 2 6 7 2 3 +--R (48a b e - 96a b d e + 48b d )x +--R + +--R 3 4 2 2 5 6 2 2 +--R (144a b e - 288a b d e + 144a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 2 2 4 3 3 4 2 +--R (144a b e - 288a b d e + 144a b d )x + 48a b e - 96a b d e + 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 3 3 4 2 3 +--R ((3A b + 3B a b )e - 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((9A a b + 9B a b )e - 18B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((9A a b + 9B a b)e - 18B a b d e )x + (3A a b + 3B a )e +--R + +--R 3 2 +--R - 6B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 2 2 3 2 +--R ((3A b + 3B a b )e - 6B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((8A a b - 8B a b)e + (- 2A b + 14B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 3B a )e + (14A a b + 4B a b)d e + (- 8A b - 4B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 5 2 6 7 2 3 +--R (24a b e - 48a b d e + 24b d )x +--R + +--R 3 4 2 2 5 6 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 2 2 4 3 3 4 2 +--R (72a b e - 144a b d e + 72a b d )x + 24a b e - 48a b d e + 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 987 + +--S 988 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R ((A b + B a)e - 2B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((2A b + 2B a)e - 4B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 3 4 2 | 2 +-----------+ +-+ +--R (16a b e - 32a b d e + 16b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((A b + B a)e - 2B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 3 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b + B a)e - 2B b d e )\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 3 4 2 +-----------+ +-+ | 2 +--R (8a b e - 16a b d e + 8b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 990 + +--S 991 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 991 + +)clear all + +--S 992 of 1378 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1378 +r0:=-1/8*e^2*(6*b*B*d-5*A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(7/2))-1/3*(A*b-a*B)*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^3)-1/12*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*(a+b*x)^2)+1/8*e*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 15A b - 3B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 45A a b - 9B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 45A a b - 9B a b)e + 54B a b d e )x + (- 15A a b - 3B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((15A b + 3B a b )e - 18B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((40A a b + 8B a b)e + (- 10A b - 50B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (33A a b - 3B a )e + (- 26A a b - 16B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 6 3 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x + 24a b e +--R + +--R 5 2 2 4 3 2 3 4 3 +--R - 72a b d e + 72a b d e - 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((15A b + 3B a b )e - 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((45A a b + 9B a b )e - 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((45A a b + 9B a b)e - 54B a b d e )x + (15A a b + 3B a )e +--R + +--R 3 2 +--R - 18B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 2 3 2 +--R ((30A b + 6B a b )e - 36B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((80A a b + 16B a b)e + (- 20A b - 100B a b )d e + 24B b d )x +--R + +--R 2 3 2 2 2 +--R (66A a b - 6B a )e + (- 52A a b - 32B a b)d e +--R + +--R 3 2 2 +--R (16A b + 8B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (48a b e - 144a b d e + 144a b d e - 48b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 2 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 6 3 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x + 48a b e +--R + +--R 5 2 2 4 3 2 3 4 3 +--R - 144a b d e + 144a b d e - 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 3 3 4 2 3 +--R ((15A b + 3B a b )e - 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((45A a b + 9B a b )e - 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((45A a b + 9B a b)e - 54B a b d e )x + (15A a b + 3B a )e +--R + +--R 3 2 +--R - 18B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 2 2 3 2 +--R ((15A b + 3B a b )e - 18B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((40A a b + 8B a b)e + (- 10A b - 50B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (33A a b - 3B a )e + (- 26A a b - 16B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 6 3 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x + 24a b e +--R + +--R 5 2 2 4 3 2 3 4 3 +--R - 72a b d e + 72a b d e - 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 994 + +--S 995 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R ((5A b + B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((10A b + 2B a)e - 12B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 3 2 2 2 3 2 4 3 | 2 +--R (16a b e - 48a b d e + 48a b d e - 16b d )\|- a b e + b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((5A b + B a)e - 6B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 +-----------+ +-+ +--R ((5A b + B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 3 3 2 2 2 3 2 4 3 +-----------+ +-+ | 2 +--R (8a b e - 24a b d e + 24a b d e - 8b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 998 + +)clear all + +--S 999 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1378 +r0:=-5/8*e^2*(6*b*B*d-7*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(b))+5/8*e^2*(6*b*B*d-7*A*b*e+_ + a*B*e)/(b*(b*d-a*e)^4*sqrt(d+e*x))+1/3*(-A*b+a*B)/(b*(b*d-a*e)*_ + (a+b*x)^3*sqrt(d+e*x))+1/12*(-6*b*B*d+7*A*b*e-a*B*e)/(b*(b*d-a*e)^2*_ + (a+b*x)^2*sqrt(d+e*x))+5/24*e*(6*b*B*d-7*A*b*e+a*B*e)/(b*(b*d-a*e)^3*_ + (a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((105A b - 15B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((315A a b - 45B a b )e - 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((315A a b - 45B a b)e - 270B a b d e )x + (105A a b - 15B a )e +--R + +--R 3 2 +--R - 90B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 15B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 280A a b + 40B a b)e + (- 35A b + 245B a b )d e +--R + +--R 3 2 +--R 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 231A a b + 33B a )e + (- 98A a b + 212B a b)d e +--R + +--R 3 2 2 3 3 +--R (14A b + 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 48A a e + (- 87A a b + 81B a )d e + (38A a b + 28B a b)d e +--R + +--R 3 2 3 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 3 4 2 3 +--R ((105A b - 15B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((315A a b - 45B a b )e - 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((315A a b - 45B a b)e - 270B a b d e )x + (105A a b - 15B a )e +--R + +--R 3 2 +--R - 90B a b d e +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 3 +--R ((- 210A b + 30B a b )e + 180B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 560A a b + 80B a b)e + (- 70A b + 490B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 462A a b + 66B a )e + (- 196A a b + 424B a b)d e +--R + +--R 3 2 2 3 3 +--R (28A b + 164B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 96A a e + (- 174A a b + 162B a )d e + (76A a b + 56B a b)d e +--R + +--R 3 2 3 +--R (- 16A b - 8B a b )d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (48a b e - 192a b d e + 288a b d e - 192a b d e + 48b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 48a e - 192a b d e + 288a b d e - 192a b d e + 48a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 4 3 3 4 2 3 +--R ((- 105A b + 15B a b )e + 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 315A a b + 45B a b )e + 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 315A a b + 45B a b)e + 270B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 105A a b + 15B a )e + 90B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 15B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 280A a b + 40B a b)e + (- 35A b + 245B a b )d e +--R + +--R 3 2 +--R 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 231A a b + 33B a )e + (- 98A a b + 212B a b)d e +--R + +--R 3 2 2 3 3 +--R (14A b + 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 48A a e + (- 87A a b + 81B a )d e + (38A a b + 28B a b)d e +--R + +--R 3 2 3 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1001 + +--S 1002 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R ((35A b - 5B a)e - 30B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((- 70A b + 10B a)e + 60B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 4 4 3 3 2 2 2 2 3 3 4 4 | 2 +--R (16a e - 64a b d e + 96a b d e - 64a b d e + 16b d )\|- a b e + b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 2 | 2 \|b \|e x + d +--R ((- 35A b + 5B a)e + 30B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 +-----------+ +-+ +--R ((- 35A b + 5B a)e + 30B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +-+ +--R (8a e - 32a b d e + 48a b d e - 32a b d e + 8b d )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1378 +r0:=35/24*e^2*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(3/2))+_ + 1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(3/2))+1/4*(-2*b*B*d+_ + 3*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(3/2))+7/8*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(3/2))-35/8*e^2*(2*b*B*d-_ + 3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-_ + a*e)^(11/2)+35/8*e^2*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 315A b + 105B a b )e + 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 945A a b + 315B a b )e + (- 315A b + 735B a b )d e +--R + +--R 4 2 2 +--R 210B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 945A a b + 315B a b)e + (- 945A a b + 945B a b )d e +--R + +--R 3 2 2 +--R 630B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 315A a b + 105B a )e + (- 945A a b + 525B a b)d e +--R + +--R 2 2 2 2 +--R 630B a b d e +--R * +--R x +--R + +--R 3 4 3 3 2 2 +--R (- 315A a b + 105B a )d e + 210B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((315A b - 105B a b )e - 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (840A a b - 280B a b )e + (420A b - 700B a b )d e +--R + +--R 4 2 2 +--R - 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (693A a b - 231B a b)e + (1134A a b - 840B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (63A b - 777B a b )d e - 42B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 48B a )e + (954A a b - 414B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (180A a b - 696B a b )d e + (- 18A b - 114B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 16A a e + (208A a b - 32B a )d e + (165A a b - 247B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 50A a b - 40B a b )d e + (8A b + 4B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 8 5 +--R - 24b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b e - 336a b d e + 600a b d e - 480a b d e + 120a b d e +--R + +--R 7 5 8 6 +--R 48a b d e - 24b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b e - 288a b d e + 360a b d e - 360a b d e + 288a b d e +--R + +--R 7 6 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a e - 48a b d e - 120a b d e + 480a b d e - 600a b d e +--R + +--R 3 5 5 2 6 6 +--R 336a b d e - 72a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 3 5 6 +--R - 24a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 4 4 3 4 +--R ((315A b - 105B a b )e - 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (945A a b - 315B a b )e + (315A b - 735B a b )d e +--R + +--R 4 2 2 +--R - 210B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 315B a b)e + (945A a b - 945B a b )d e +--R + +--R 3 2 2 +--R - 630B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (315A a b - 105B a )e + (945A a b - 525B a b)d e +--R + +--R 2 2 2 2 +--R - 630B a b d e +--R * +--R x +--R + +--R 3 4 3 3 2 2 +--R (315A a b - 105B a )d e - 210B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 4 3 4 +--R ((630A b - 210B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1680A a b - 560B a b )e + (840A b - 1400B a b )d e +--R + +--R 4 2 2 +--R - 560B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (1386A a b - 462B a b)e + (2268A a b - 1680B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (126A b - 1554B a b )d e - 84B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (288A a b - 96B a )e + (1908A a b - 828B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (360A a b - 1392B a b )d e + (- 36A b - 228B a b )d e + 24B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 32A a e + (416A a b - 64B a )d e + (330A a b - 494B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 100A a b - 80B a b )d e + (16A b + 8B a b )d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 +--R 144a b e - 672a b d e + 1200a b d e - 960a b d e +--R + +--R 2 6 4 2 7 5 8 6 +--R 240a b d e + 96a b d e - 48b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 144a b e - 576a b d e + 720a b d e - 720a b d e + 576a b d e +--R + +--R 7 6 +--R - 144a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 48a e - 96a b d e - 240a b d e + 960a b d e - 1200a b d e +--R + +--R 3 5 5 2 6 6 +--R 672a b d e - 144a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 5 6 +--R - 48a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 3 4 4 3 4 +--R ((315A b - 105B a b )e - 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (945A a b - 315B a b )e + (315A b - 735B a b )d e +--R + +--R 4 2 2 +--R - 210B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 315B a b)e + (945A a b - 945B a b )d e +--R + +--R 3 2 2 +--R - 630B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (315A a b - 105B a )e + (945A a b - 525B a b)d e +--R + +--R 2 2 2 2 +--R - 630B a b d e +--R * +--R x +--R + +--R 3 4 3 3 2 2 +--R (315A a b - 105B a )d e - 210B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((315A b - 105B a b )e - 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((840A a b - 280B a b )e + (420A b - 700B a b )d e - 280B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (693A a b - 231B a b)e + (1134A a b - 840B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (63A b - 777B a b )d e - 42B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 48B a )e + (954A a b - 414B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (180A a b - 696B a b )d e + (- 18A b - 114B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 16A a e + (208A a b - 32B a )d e + (165A a b - 247B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 50A a b - 40B a b )d e + (8A b + 4B a b )d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 8 5 +--R - 24b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b e - 336a b d e + 600a b d e - 480a b d e + 120a b d e +--R + +--R 7 5 8 6 +--R 48a b d e - 24b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b e - 288a b d e + 360a b d e - 360a b d e + 288a b d e +--R + +--R 7 6 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a e - 48a b d e - 120a b d e + 480a b d e - 600a b d e +--R + +--R 3 5 5 2 6 6 +--R 336a b d e - 72a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 3 5 6 +--R - 24a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1008 + +--S 1009 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 +-----------+ | b +--R ((105A b - 35B a)e - 70B b d e )\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 2 +-+ \|b \|e x + d +--R ((210A b - 70B a)e - 140B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (16a e - 80a b d e + 160a b d e - 160a b d e + 80a b d e - 16b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 +-+ \|b \|e x + d +--R ((105A b - 35B a)e - 70B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 3 2 +-----------+ | b +--R ((105A b - 35B a)e - 70B b d e )\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (8a e - 40a b d e + 80a b d e - 80a b d e + 40a b d e - 8b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1012 + +)clear all + +--S 1013 of 1378 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1378 +r0:=21/40*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(5/2))+_ + 1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(5/2))+1/12*(-6*b*B*d+_ + 11*A*b*e-5*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(5/2))+3/8*e*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(5/2))+7/8*e^2*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)/((b*d-a*e)^5*(d+e*x)^(3/2))-21/8*b^(3/2)*e^2*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b*d-a*e)^(13/2)+21/8*b*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/((b*d-a*e)^6*_ + sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((3465A b - 1575B a b )e - 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (10395A a b - 4725B a b )e + (6930A b - 8820B a b )d e +--R + +--R 5 2 3 +--R - 3780B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (10395A a b - 4725B a b )e + (20790A a b - 15120B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (3465A b - 12915B a b )d e - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (3465A a b - 1575B a b)e + (20790A a b - 11340B a b )d e +--R + +--R 4 2 3 2 3 4 3 2 +--R (10395A a b - 16065B a b )d e - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 2 3 +--R (6930A a b - 3150B a b)d e + (10395A a b - 8505B a b )d e +--R + +--R 2 3 3 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 2 3 2 +--R (3465A a b - 1575B a b)d e - 1890B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 1575B a b )e + 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 9240A a b + 4200B a b )e + (- 8085A b + 8715B a b )d e +--R + +--R 5 2 3 +--R 4410B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 7623A a b + 3465B a b )e + (- 21714A a b + 14028B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 5313A b + 14259B a b )d e + 2898B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 1584A a b + 720B a b)e + (- 18117A a b + 9099B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 14454A a b + 16452B a b )d e + (- 495A b + 8109B a b )d e +--R + +--R 5 4 +--R 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (176A a b - 80B a )e + (- 3872A a b + 1664B a b)d e +--R + +--R 2 3 3 2 2 3 +--R (- 12309A a b + 7707B a b )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 1430A a b + 7364B a b )d e + (110A b + 730B a b )d e +--R + +--R 5 5 +--R - 60B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 48A a e + (416A a b - 32B a )d e + (- 2768A a b + 704B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 1335A a b + 2553B a b )d e + (310A a b + 260B a b )d e +--R + +--R 5 4 5 +--R (- 40A b - 20B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 120a b e - 720a b d e + 1800a b d e - 2400a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 1800a b d e - 720a b d e + 120b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 360a b e - 1920a b d e + 3960a b d e - 3600a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 600a b d e + 1440a b d e - 1080a b d e + 240b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 360a b e - 1440a b d e + 1200a b d e + 2880a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 7200a b d e + 6240a b d e - 2160a b d e + 120b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 4 5 5 3 +--R 120a e - 2160a b d e + 6240a b d e - 7200a b d e + 2880a b d e +--R + +--R 3 6 6 2 2 7 7 8 8 +--R 1200a b d e - 1440a b d e + 360a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 +--R 240a d e - 1080a b d e + 1440a b d e + 600a b d e +--R + +--R 5 4 5 3 4 5 6 2 3 6 7 2 7 8 +--R - 3600a b d e + 3960a b d e - 1920a b d e + 360a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 120a d e - 720a b d e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 5 7 3 6 8 +--R - 720a b d e + 120a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 5 5 4 5 +--R ((3465A b - 1575B a b )e - 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (10395A a b - 4725B a b )e + (6930A b - 8820B a b )d e +--R + +--R 5 2 3 +--R - 3780B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (10395A a b - 4725B a b )e + (20790A a b - 15120B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (3465A b - 12915B a b )d e - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (3465A a b - 1575B a b)e + (20790A a b - 11340B a b )d e +--R + +--R 4 2 3 2 3 4 3 2 +--R (10395A a b - 16065B a b )d e - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 2 3 +--R (6930A a b - 3150B a b)d e + (10395A a b - 8505B a b )d e +--R + +--R 2 3 3 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 2 3 2 +--R (3465A a b - 1575B a b)d e - 1890B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 5 5 4 5 +--R ((- 6930A b + 3150B a b )e + 3780B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 18480A a b + 8400B a b )e + (- 16170A b + 17430B a b )d e +--R + +--R 5 2 3 +--R 8820B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 15246A a b + 6930B a b )e + (- 43428A a b + 28056B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 10626A b + 28518B a b )d e + 5796B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 3168A a b + 1440B a b)e + (- 36234A a b + 18198B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 28908A a b + 32904B a b )d e + (- 990A b + 16218B a b )d e +--R + +--R 5 4 +--R 540B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (352A a b - 160B a )e + (- 7744A a b + 3328B a b)d e +--R + +--R 2 3 3 2 2 3 +--R (- 24618A a b + 15414B a b )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 2860A a b + 14728B a b )d e + 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12480a b d e - 14400a b d e +--R + +--R 4 5 5 3 3 6 6 2 2 7 7 8 8 +--R 5760a b d e + 2400a b d e - 2880a b d e + 720a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 +--R 480a d e - 2160a b d e + 2880a b d e + 1200a b d e +--R + +--R 5 4 5 3 4 5 6 2 3 6 7 2 7 8 +--R - 7200a b d e + 7920a b d e - 3840a b d e + 720a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 240a d e - 1440a b d e + 3600a b d e - 4800a b d e + 3600a b d e +--R + +--R 4 5 7 3 6 8 +--R - 1440a b d e + 240a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 5 4 5 5 4 5 +--R ((- 3465A b + 1575B a b )e + 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 10395A a b + 4725B a b )e + (- 6930A b + 8820B a b )d e +--R + +--R 5 2 3 +--R 3780B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 +--R (- 10395A a b + 4725B a b )e +--R + +--R 4 2 3 4 +--R (- 20790A a b + 15120B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 3465A b + 12915B a b )d e + 1890B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 +--R (- 3465A a b + 1575B a b)e +--R + +--R 2 3 3 2 4 +--R (- 20790A a b + 11340B a b )d e +--R + +--R 4 2 3 2 3 4 3 2 +--R (- 10395A a b + 16065B a b )d e + 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 +--R (- 6930A a b + 3150B a b)d e +--R + +--R 2 3 3 2 2 3 2 3 3 2 +--R (- 10395A a b + 8505B a b )d e + 5670B a b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 2 3 2 +--R (- 3465A a b + 1575B a b)d e + 1890B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 1575B a b )e + 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 9240A a b + 4200B a b )e + (- 8085A b + 8715B a b )d e +--R + +--R 5 2 3 +--R 4410B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 7623A a b + 3465B a b )e + (- 21714A a b + 14028B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 5313A b + 14259B a b )d e + 2898B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 1584A a b + 720B a b)e + (- 18117A a b + 9099B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 14454A a b + 16452B a b )d e + (- 495A b + 8109B a b )d e +--R + +--R 5 4 +--R 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (176A a b - 80B a )e + (- 3872A a b + 1664B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 12309A a b + 7707B a b )d e + (- 1430A a b + 7364B a b )d e +--R + +--R 5 4 4 5 5 +--R (110A b + 730B a b )d e - 60B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 48A a e + (416A a b - 32B a )d e + (- 2768A a b + 704B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 1335A a b + 2553B a b )d e + (310A a b + 260B a b )d e +--R + +--R 5 4 5 +--R (- 40A b - 20B a b )d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 120a b e - 720a b d e + 1800a b d e - 2400a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 1800a b d e - 720a b d e + 120b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 360a b e - 1920a b d e + 3960a b d e - 3600a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 600a b d e + 1440a b d e - 1080a b d e + 240b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 360a b e - 1440a b d e + 1200a b d e + 2880a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 7200a b d e + 6240a b d e - 2160a b d e + 120b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 +--R 120a e - 2160a b d e + 6240a b d e - 7200a b d e +--R + +--R 4 5 5 3 3 6 6 2 2 7 7 8 8 +--R 2880a b d e + 1200a b d e - 1440a b d e + 360a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 +--R 240a d e - 1080a b d e + 1440a b d e + 600a b d e +--R + +--R 5 4 5 3 4 5 6 2 3 6 7 2 7 8 +--R - 3600a b d e + 3960a b d e - 1920a b d e + 360a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 120a d e - 720a b d e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 5 7 3 6 8 +--R - 720a b d e + 120a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1015 + +--S 1016 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 3 2 2 +-----------+ | b +--R ((231A b - 105B a b)e - 126B b d e )\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 3 2 2 +-+ \|b \|e x + d +--R ((- 462A b + 210B a b)e + 252B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 16a e - 96a b d e + 240a b d e - 320a b d e + 240a b d e +--R + +--R 5 5 6 6 +--R - 96a b d e + 16b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 3 2 2 +-+ \|b \|e x + d +--R ((- 231A b + 105B a b)e + 126B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 3 2 2 +-----------+ | b +--R ((- 231A b + 105B a b)e + 126B b d e )\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 8a e - 48a b d e + 120a b d e - 160a b d e + 120a b d e +--R + +--R 5 5 6 6 +--R - 48a b d e + 8b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1019 + +)clear all + +--S 1020 of 1378 +t0:=(A+B*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1378 +r0:=77/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(3/2)/(b^6*(b*d-a*e))-_ + 231/640*e^3*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(5/2)/(b^5*(b*d-a*e)*_ + (a+b*x))-33/320*e^2*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(7/2)/(b^4*_ + (b*d-a*e)*(a+b*x)^2)-11/240*e*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(9/2)/_ + (b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d+3*A*b*e-13*a*B*e)*_ + (d+e*x)^(11/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(13/2)/_ + (b*(b*d-a*e)*(a+b*x)^5)-231/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(15/2)+_ + 231/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*sqrt(d+e*x)/b^7 +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 10395A b + 45045B a b )e - 34650B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 51975A a b + 225225B a b )e - 173250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 51975A a b + 225225B a b)e - 173250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 10395A a b + 45045B a )e - 34650B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 1280B b e x + ((3840A b - 16640B a b )e + 20480B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (31845A a b - 137995B a b )e + (- 12645A b + 160945B a b )d e +--R + +--R 6 2 3 +--R - 22950B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (78210A a b - 338910B a b )e +--R + +--R 5 2 4 4 +--R (- 29040A a b + 386540B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 10770A b - 50130B a b )d e - 10300B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (88704A a b - 384384B a b )e +--R + +--R 2 4 3 3 4 +--R (- 31482A a b + 432102B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 12078A a b - 52602B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 6744A b - 11036B a b )d e - 3280B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (48510A a b - 210210B a b)e +--R + +--R 3 3 4 2 4 +--R (- 16632A a b + 233772B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 6534A a b - 27126B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3696A a b - 5764B a b )d e + (- 2448A b - 1712B a b )d e +--R + +--R 6 5 +--R - 480B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (10395A a b - 45045B a )e + (- 3465A a b + 49665B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 1386A a b - 5544B a b )d e + (- 792A a b - 1188B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 528A a b - 352B a b )d e + (- 384A b - 96B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 +--R 1920b x + 9600a b x + 19200a b x + 19200a b x + 9600a b x +--R + +--R 5 7 +--R 1920a b +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((- 10395A b + 45045B a b )e - 34650B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 51975A a b + 225225B a b )e - 173250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 51975A a b + 225225B a b)e - 173250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 10395A a b + 45045B a )e - 34650B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 2560B b e x + ((7680A b - 33280B a b )e + 40960B b d e )x +--R + +--R 5 2 4 5 +--R (63690A a b - 275990B a b )e +--R + +--R 6 5 4 6 2 3 +--R (- 25290A b + 321890B a b )d e - 45900B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (156420A a b - 677820B a b )e +--R + +--R 5 2 4 4 +--R (- 58080A a b + 773080B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 21540A b - 100260B a b )d e - 20600B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (177408A a b - 768768B a b )e +--R + +--R 2 4 3 3 4 +--R (- 62964A a b + 864204B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 24156A a b - 105204B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 13488A b - 22072B a b )d e - 6560B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (97020A a b - 420420B a b)e +--R + +--R 3 3 4 2 4 +--R (- 33264A a b + 467544B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 13068A a b - 54252B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 7392A a b - 11528B a b )d e + (- 4896A b - 3424B a b )d e +--R + +--R 6 5 +--R - 960B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (20790A a b - 90090B a )e + (- 6930A a b + 99330B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 2772A a b - 11088B a b )d e + (- 1584A a b - 2376B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 1056A a b - 704B a b )d e + (- 768A b - 192B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 +--R 3840b x + 19200a b x + 38400a b x + 38400a b x + 19200a b x +--R + +--R 5 7 +--R 3840a b +--R , +--R +--R 6 5 5 6 4 5 +--R ((- 10395A b + 45045B a b )e - 34650B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 51975A a b + 225225B a b )e - 173250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 51975A a b + 225225B a b)e - 173250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 10395A a b + 45045B a )e - 34650B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 1280B b e x + ((3840A b - 16640B a b )e + 20480B b d e )x +--R + +--R 5 2 4 5 +--R (31845A a b - 137995B a b )e +--R + +--R 6 5 4 6 2 3 +--R (- 12645A b + 160945B a b )d e - 22950B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (78210A a b - 338910B a b )e +--R + +--R 5 2 4 4 +--R (- 29040A a b + 386540B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 10770A b - 50130B a b )d e - 10300B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (88704A a b - 384384B a b )e +--R + +--R 2 4 3 3 4 +--R (- 31482A a b + 432102B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 12078A a b - 52602B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 6744A b - 11036B a b )d e - 3280B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (48510A a b - 210210B a b)e +--R + +--R 3 3 4 2 4 +--R (- 16632A a b + 233772B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 6534A a b - 27126B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3696A a b - 5764B a b )d e + (- 2448A b - 1712B a b )d e +--R + +--R 6 5 +--R - 480B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (10395A a b - 45045B a )e + (- 3465A a b + 49665B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 1386A a b - 5544B a b )d e + (- 792A a b - 1188B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 528A a b - 352B a b )d e + (- 384A b - 96B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 +--R 1920b x + 9600a b x + 19200a b x + 19200a b x + 9600a b x +--R + +--R 5 7 +--R 1920a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1022 + +--S 1023 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 5 4 |- a e + b d +-+ +--R ((- 693A b + 3003B a)e - 2310B b d e ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 5 4 +-----------+ \|b \|e x + d +--R ((1386A b - 6006B a)e + 4620B b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 +-+ +--R 256b \|b +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 5 4 +-----------+ \|b \|e x + d +--R ((693A b - 3003B a)e + 2310B b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 5 4 +-+ |a e - b d \|e x + d +--R ((- 693A b + 3003B a)e - 2310B b d e )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 7 +-+ +--R 128b \|b +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1026 + +)clear all + +--S 1027 of 1378 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1378 +r0:=-21/128*e^3*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(3/2)/(b^5*(b*d-a*e)*_ + (a+b*x))-21/320*e^2*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*_ + (b*d-a*e)*(a+b*x)^2)-3/80*e*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(7/2)/_ + (b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d+A*b*e-11*a*B*e)*_ + (d+e*x)^(9/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(11/2)/_ + (b*(b*d-a*e)*(a+b*x)^5)-63/128*e^4*(10*b*B*d+A*b*e-11*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(13/2)*sqrt(b*d-a*e))+_ + 63/128*e^4*(10*b*B*d+A*b*e-11*a*B*e)*sqrt(d+e*x)/(b^6*(b*d-a*e)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 315A b + 3465B a b )e - 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 1575A a b + 17325B a b )e - 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 3150A a b + 34650B a b )e - 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 3150A a b + 34650B a b )e - 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 1575A a b + 17325B a b)e - 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 315A a b + 3465B a )e - 3150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 1280B b e x + ((- 965A b + 10615B a b )e - 3250B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 2370A a b + 26070B a b )e + (- 1490A b - 7310B a b )d e +--R + +--R 5 2 2 +--R - 2100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 2688A a b + 29568B a b )e + (- 1734A a b - 7806B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1368A b - 2292B a b )d e - 880B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 1470A a b + 16170B a b)e + (- 966A a b - 4074B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 768A a b - 1212B a b )d e + (- 656A b - 464B a b )d e +--R + +--R 5 4 +--R - 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 315A a b + 3465B a )e + (- 210A a b - 840B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 168A a b - 252B a b )d e + (- 144A a b - 96B a b )d e +--R + +--R 5 4 4 +--R (- 128A b - 32B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R (640b x + 3200a b x + 6400a b x + 6400a b x + 3200a b x + 640a b ) +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((315A b - 3465B a b )e + 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((1575A a b - 17325B a b )e + 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((3150A a b - 34650B a b )e + 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((3150A a b - 34650B a b )e + 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((1575A a b - 17325B a b)e + 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (315A a b - 3465B a )e + 3150B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2560B b e x + ((- 1930A b + 21230B a b )e - 6500B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 4740A a b + 52140B a b )e + (- 2980A b - 14620B a b )d e +--R + +--R 5 2 2 +--R - 4200B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 +--R (- 5376A a b + 59136B a b )e +--R + +--R 4 2 3 3 +--R (- 3468A a b - 15612B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 2736A b - 4584B a b )d e - 1760B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 2940A a b + 32340B a b)e + (- 1932A a b - 8148B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 1536A a b - 2424B a b )d e + (- 1312A b - 928B a b )d e +--R + +--R 5 4 +--R - 320B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 630A a b + 6930B a )e + (- 420A a b - 1680B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 336A a b - 504B a b )d e + (- 288A a b - 192B a b )d e +--R + +--R 5 4 4 +--R (- 256A b - 64B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 +--R 1280b x + 6400a b x + 12800a b x + 12800a b x + 6400a b x +--R + +--R 5 6 +--R 1280a b +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 6 5 5 6 4 5 +--R ((315A b - 3465B a b )e + 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((1575A a b - 17325B a b )e + 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((3150A a b - 34650B a b )e + 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((3150A a b - 34650B a b )e + 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((1575A a b - 17325B a b)e + 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (315A a b - 3465B a )e + 3150B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 1280B b e x + ((- 965A b + 10615B a b )e - 3250B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 2370A a b + 26070B a b )e + (- 1490A b - 7310B a b )d e +--R + +--R 5 2 2 +--R - 2100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 +--R (- 2688A a b + 29568B a b )e +--R + +--R 4 2 3 3 5 4 2 2 +--R (- 1734A a b - 7806B a b )d e + (- 1368A b - 2292B a b )d e +--R + +--R 5 3 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 1470A a b + 16170B a b)e + (- 966A a b - 4074B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 768A a b - 1212B a b )d e + (- 656A b - 464B a b )d e +--R + +--R 5 4 +--R - 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 315A a b + 3465B a )e + (- 210A a b - 840B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 168A a b - 252B a b )d e + (- 144A a b - 96B a b )d e +--R + +--R 5 4 4 +--R (- 128A b - 32B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 +--R 640b x + 3200a b x + 6400a b x + 6400a b x + 3200a b x +--R + +--R 5 6 +--R 640a b +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1029 + +--S 1030 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((63A b - 693B a)e + 630B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((126A b - 1386B a)e + 1260B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 6 | 2 +-----------+ +-+ +--R 256b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((63A b - 693B a)e + 630B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((63A b - 693B a)e + 630B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 6 +-----------+ +-+ | 2 +--R 128b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1033 + +)clear all + +--S 1034 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1378 +r0:=-7/192*e^2*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e)*_ + (a+b*x)^2)-7/240*e*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(5/2)/(b^3*_ + (b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(7/2)/_ + (b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*_ + (a+b*x)^5)-7/128*e^4*(10*b*B*d-A*b*e-9*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(11/2)*(b*d-a*e)^(3/2))-_ + 7/128*e^3*(10*b*B*d-A*b*e-9*a*B*e)*sqrt(d+e*x)/(b^5*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 105A b - 945B a b )e + 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 525A a b - 4725B a b )e + 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 1050A a b - 9450B a b )e + 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 1050A a b - 9450B a b )e + 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 525A a b - 4725B a b)e + 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 105A a b - 945B a )e + 1050B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b - 2895B a b )e + 2790B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 790A a b - 7110B a b )e + (1210A b + 3430B a b )d e +--R + +--R 5 2 2 +--R 3260B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 896A a b - 8064B a b )e + (- 578A a b + 3758B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (2104A b + 1676B a b )d e + 2000B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 490A a b - 4410B a b)e + (- 322A a b + 2002B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 256A a b + 916B a b )d e + (1488A b + 592B a b )d e +--R + +--R 5 4 +--R 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 945B a )e + (- 70A a b + 420B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 56A a b + 196B a b )d e + (- 48A a b + 128B a b )d e +--R + +--R 5 4 4 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 10 11 5 2 9 10 4 +--R (1920a b e - 1920b d)x + (9600a b e - 9600a b d)x +--R + +--R 3 8 2 9 3 4 7 3 8 2 +--R (19200a b e - 19200a b d)x + (19200a b e - 19200a b d)x +--R + +--R 5 6 4 7 6 5 5 6 +--R (9600a b e - 9600a b d)x + 1920a b e - 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((105A b + 945B a b )e - 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((525A a b + 4725B a b )e - 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((1050A a b + 9450B a b )e - 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((1050A a b + 9450B a b )e - 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((525A a b + 4725B a b)e - 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (105A a b + 945B a )e - 1050B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 4 5 3 4 +--R ((210A b - 5790B a b )e + 5580B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 1580A a b - 14220B a b )e + (2420A b + 6860B a b )d e +--R + +--R 5 2 2 +--R 6520B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 +--R (- 1792A a b - 16128B a b )e +--R + +--R 4 2 3 3 5 4 2 2 +--R (- 1156A a b + 7516B a b )d e + (4208A b + 3352B a b )d e +--R + +--R 5 3 +--R 4000B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 980A a b - 8820B a b)e + (- 644A a b + 4004B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 512A a b + 1832B a b )d e + (2976A b + 1184B a b )d e +--R + +--R 5 4 +--R 960B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 210A a b - 1890B a )e + (- 140A a b + 840B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 112A a b + 392B a b )d e + (- 96A a b + 256B a b )d e +--R + +--R 5 4 4 +--R (768A b + 192B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 10 11 5 2 9 10 4 +--R (3840a b e - 3840b d)x + (19200a b e - 19200a b d)x +--R + +--R 3 8 2 9 3 4 7 3 8 2 +--R (38400a b e - 38400a b d)x + (38400a b e - 38400a b d)x +--R + +--R 5 6 4 7 6 5 5 6 +--R (19200a b e - 19200a b d)x + 3840a b e - 3840a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 6 5 5 6 4 5 +--R ((105A b + 945B a b )e - 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((525A a b + 4725B a b )e - 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((1050A a b + 9450B a b )e - 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((1050A a b + 9450B a b )e - 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((525A a b + 4725B a b)e - 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (105A a b + 945B a )e - 1050B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b - 2895B a b )e + 2790B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 790A a b - 7110B a b )e + (1210A b + 3430B a b )d e +--R + +--R 5 2 2 +--R 3260B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 896A a b - 8064B a b )e + (- 578A a b + 3758B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (2104A b + 1676B a b )d e + 2000B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 490A a b - 4410B a b)e + (- 322A a b + 2002B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 256A a b + 916B a b )d e + (1488A b + 592B a b )d e +--R + +--R 5 4 +--R 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 945B a )e + (- 70A a b + 420B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 56A a b + 196B a b )d e + (- 48A a b + 128B a b )d e +--R + +--R 5 4 4 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 10 11 5 2 9 10 4 +--R (1920a b e - 1920b d)x + (9600a b e - 9600a b d)x +--R + +--R 3 8 2 9 3 4 7 3 8 2 +--R (19200a b e - 19200a b d)x + (19200a b e - 19200a b d)x +--R + +--R 5 6 4 7 6 5 5 6 +--R (9600a b e - 9600a b d)x + 1920a b e - 1920a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1036 + +--S 1037 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((7A b + 63B a)e - 70B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((14A b + 126B a)e - 140B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 5 6 | 2 +-----------+ +-+ +--R (256a b e - 256b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((7A b + 63B a)e - 70B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((7A b + 63B a)e - 70B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 5 6 +-----------+ +-+ | 2 +--R (128a b e - 128b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1040 + +)clear all + +--S 1041 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1378 +r0:=-1/48*e*(10*b*B*d-3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*_ + (a+b*x)^3)-1/40*(10*b*B*d-3*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-_ + a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^5)+_ + 1/128*e^4*(10*b*B*d-3*A*b*e-7*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(9/2)*(b*d-a*e)^(5/2))-1/64*e^2*(10*b*B*d-_ + 3*A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)*(a+b*x)^2)-_ + 1/128*e^3*(10*b*B*d-3*A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 45A b - 105B a b )e + 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 225A a b - 525B a b )e + 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 450A a b - 1050B a b )e + 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 450A a b - 1050B a b )e + 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 225A a b - 525B a b)e + 750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 45A a b - 105B a )e + 150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((45A b + 105B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (210A a b - 790B a b )e + (- 30A b + 1790B a b )d e +--R + +--R 5 2 2 +--R - 1180B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 384A a b - 896B a b )e + (1398A a b + 702B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 744A b + 1284B a b )d e - 1360B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 210A a b - 490B a b)e + (- 138A a b + 378B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (1536A a b + 204B a b )d e + (- 1008A b + 208B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 45A a b - 105B a )e + (- 30A a b + 80B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 24A a b + 44B a b )d e + (528A a b + 32B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 9 2 10 11 2 5 +--R (1920a b e - 3840a b d e + 1920b d )x +--R + +--R 3 8 2 2 9 10 2 4 +--R (9600a b e - 19200a b d e + 9600a b d )x +--R + +--R 4 7 2 3 8 2 9 2 3 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 5 6 2 4 7 3 8 2 2 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 6 5 2 5 6 4 7 2 7 4 2 6 5 +--R (9600a b e - 19200a b d e + 9600a b d )x + 1920a b e - 3840a b d e +--R + +--R 5 6 2 +--R 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((45A b + 105B a b )e - 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((225A a b + 525B a b )e - 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((450A a b + 1050B a b )e - 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((450A a b + 1050B a b )e - 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((225A a b + 525B a b)e - 750B a b d e )x + (45A a b + 105B a )e +--R + +--R 5 4 +--R - 150B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 4 5 3 4 +--R ((90A b + 210B a b )e - 300B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (420A a b - 1580B a b )e + (- 60A b + 3580B a b )d e +--R + +--R 5 2 2 +--R - 2360B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 768A a b - 1792B a b )e + (2796A a b + 1404B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1488A b + 2568B a b )d e - 2720B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 420A a b - 980B a b)e + (- 276A a b + 756B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (3072A a b + 408B a b )d e + (- 2016A b + 416B a b )d e +--R + +--R 5 4 +--R - 960B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 90A a b - 210B a )e + (- 60A a b + 160B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 48A a b + 88B a b )d e + (1056A a b + 64B a b )d e +--R + +--R 5 4 4 +--R (- 768A b - 192B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 9 2 10 11 2 5 +--R (3840a b e - 7680a b d e + 3840b d )x +--R + +--R 3 8 2 2 9 10 2 4 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 4 7 2 3 8 2 9 2 3 +--R (38400a b e - 76800a b d e + 38400a b d )x +--R + +--R 5 6 2 4 7 3 8 2 2 +--R (38400a b e - 76800a b d e + 38400a b d )x +--R + +--R 6 5 2 5 6 4 7 2 7 4 2 +--R (19200a b e - 38400a b d e + 19200a b d )x + 3840a b e +--R + +--R 6 5 5 6 2 +--R - 7680a b d e + 3840a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 6 5 5 6 4 5 +--R ((45A b + 105B a b )e - 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((225A a b + 525B a b )e - 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((450A a b + 1050B a b )e - 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((450A a b + 1050B a b )e - 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((225A a b + 525B a b)e - 750B a b d e )x + (45A a b + 105B a )e +--R + +--R 5 4 +--R - 150B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 5 4 4 5 3 4 +--R ((45A b + 105B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (210A a b - 790B a b )e + (- 30A b + 1790B a b )d e +--R + +--R 5 2 2 +--R - 1180B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 384A a b - 896B a b )e + (1398A a b + 702B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 744A b + 1284B a b )d e - 1360B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 210A a b - 490B a b)e + (- 138A a b + 378B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (1536A a b + 204B a b )d e + (- 1008A b + 208B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 45A a b - 105B a )e + (- 30A a b + 80B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 24A a b + 44B a b )d e + (528A a b + 32B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 9 2 10 11 2 5 +--R (1920a b e - 3840a b d e + 1920b d )x +--R + +--R 3 8 2 2 9 10 2 4 +--R (9600a b e - 19200a b d e + 9600a b d )x +--R + +--R 4 7 2 3 8 2 9 2 3 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 5 6 2 4 7 3 8 2 2 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 6 5 2 5 6 4 7 2 7 4 2 6 5 +--R (9600a b e - 19200a b d e + 9600a b d )x + 1920a b e - 3840a b d e +--R + +--R 5 6 2 +--R 1920a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1043 + +--S 1044 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((3A b + 7B a)e - 10B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((6A b + 14B a)e - 20B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 4 2 5 6 2 | 2 +-----------+ +-+ +--R (256a b e - 512a b d e + 256b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((3A b + 7B a)e - 10B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((3A b + 7B a)e - 10B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 4 2 5 6 2 +-----------+ +-+ | 2 +--R (128a b e - 256a b d e + 128b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1047 + +)clear all + +--S 1048 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1378 +r0:=-1/8*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-_ + 1/5*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^5)-3/128*e^4*(2*b*B*d-_ + A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-_ + a*e)^(7/2))-1/16*e*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)*_ + (a+b*x)^3)-1/64*e^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)^2*_ + (a+b*x)^2)+3/128*e^3*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*_ + (b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 15A b - 15B a b )e + 30B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 75A a b - 75B a b )e + 150B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 150A a b - 150B a b )e + 300B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 150A a b - 150B a b )e + 300B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((- 75A a b - 75B a b)e + 150B a b d e )x + (- 15A a b - 15B a )e +--R + +--R 5 4 +--R 30B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((15A b + 15B a b )e - 30B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((70A a b + 70B a b )e + (- 10A b - 150B a b )d e + 20B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (128A a b - 128B a b )e + (- 46A a b + 466B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (8A b - 668B a b )d e + 240B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 70A a b - 70B a b)e + (466A a b + 94B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 512A a b + 92B a b )d e + (176A b - 336B a b )d e + 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 15A a b - 15B a )e + (- 10A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (248A a b + 12B a b )d e + (- 336A a b - 64B a b )d e +--R + +--R 5 4 4 +--R (128A b + 32B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 8 3 2 9 2 10 2 11 3 5 +--R (640a b e - 1920a b d e + 1920a b d e - 640b d )x +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 4 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x +--R + +--R 5 6 3 4 7 2 3 8 2 2 9 3 3 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 6 5 3 5 6 2 4 7 2 3 8 3 2 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 7 4 3 6 5 2 5 6 2 4 7 3 8 3 3 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x + 640a b e +--R + +--R 7 4 2 6 5 2 5 6 3 +--R - 1920a b d e + 1920a b d e - 640a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((15A b + 15B a b )e - 30B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((75A a b + 75B a b )e - 150B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((150A a b + 150B a b )e - 300B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((150A a b + 150B a b )e - 300B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((75A a b + 75B a b)e - 150B a b d e )x + (15A a b + 15B a )e +--R + +--R 5 4 +--R - 30B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 4 5 3 4 +--R ((30A b + 30B a b )e - 60B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (140A a b + 140B a b )e + (- 20A b - 300B a b )d e +--R + +--R 5 2 2 +--R 40B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (256A a b - 256B a b )e + (- 92A a b + 932B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (16A b - 1336B a b )d e + 480B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 140A a b - 140B a b)e + (932A a b + 188B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 1024A a b + 184B a b )d e + (352A b - 672B a b )d e +--R + +--R 5 4 +--R 320B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 30A a b - 30B a )e + (- 20A a b + 40B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (496A a b + 24B a b )d e + (- 672A a b - 128B a b )d e +--R + +--R 5 4 4 +--R (256A b + 64B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 3 8 3 2 9 2 10 2 11 3 5 +--R (1280a b e - 3840a b d e + 3840a b d e - 1280b d )x +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 4 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 5 6 3 4 7 2 3 8 2 2 9 3 3 +--R (12800a b e - 38400a b d e + 38400a b d e - 12800a b d )x +--R + +--R 6 5 3 5 6 2 4 7 2 3 8 3 2 +--R (12800a b e - 38400a b d e + 38400a b d e - 12800a b d )x +--R + +--R 7 4 3 6 5 2 5 6 2 4 7 3 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 8 3 3 7 4 2 6 5 2 5 6 3 +--R 1280a b e - 3840a b d e + 3840a b d e - 1280a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 6 5 5 6 4 5 +--R ((15A b + 15B a b )e - 30B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((75A a b + 75B a b )e - 150B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((150A a b + 150B a b )e - 300B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((150A a b + 150B a b )e - 300B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((75A a b + 75B a b)e - 150B a b d e )x + (15A a b + 15B a )e +--R + +--R 5 4 +--R - 30B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 5 4 4 5 3 4 +--R ((15A b + 15B a b )e - 30B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (70A a b + 70B a b )e + (- 10A b - 150B a b )d e +--R + +--R 5 2 2 +--R 20B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (128A a b - 128B a b )e + (- 46A a b + 466B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (8A b - 668B a b )d e + 240B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 70A a b - 70B a b)e + (466A a b + 94B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 512A a b + 92B a b )d e + (176A b - 336B a b )d e +--R + +--R 5 4 +--R 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 15A a b - 15B a )e + (- 10A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (248A a b + 12B a b )d e + (- 336A a b - 64B a b )d e +--R + +--R 5 4 4 +--R (128A b + 32B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 3 8 3 2 9 2 10 2 11 3 5 +--R (640a b e - 1920a b d e + 1920a b d e - 640b d )x +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 4 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x +--R + +--R 5 6 3 4 7 2 3 8 2 2 9 3 3 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 6 5 3 5 6 2 4 7 2 3 8 3 2 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 7 4 3 6 5 2 5 6 2 4 7 3 8 3 3 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x + 640a b e +--R + +--R 7 4 2 6 5 2 5 6 3 +--R - 1920a b d e + 1920a b d e - 640a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1050 + +--S 1051 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((3A b + 3B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((6A b + 6B a)e - 12B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 3 3 2 4 2 5 2 6 3 | 2 +--R (256a b e - 768a b d e + 768a b d e - 256b d )\|- a b e + b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((3A b + 3B a)e - 6B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((3A b + 3B a)e - 6B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R 3 3 3 2 4 2 5 2 6 3 +-----------+ +-+ +--R (128a b e - 384a b d e + 384a b d e - 128b d )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1054 + +)clear all + +--S 1055 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1378 +r0:=-1/5*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^5)+1/128*e^4*_ + (10*b*B*d-7*A*b*e-3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(5/2)*(b*d-a*e)^(9/2))-1/40*(10*b*B*d-7*A*b*e-3*a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)*(a+b*x)^4)-1/240*e*(10*b*B*d-7*A*b*e-3*a*B*e)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x)^3)+1/192*e^2*(10*b*B*d-7*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^3*(a+b*x)^2)-1/128*e^3*(10*b*B*d-_ + 7*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^4*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 105A b - 45B a b )e + 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 525A a b - 225B a b )e + 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 1050A a b - 450B a b )e + 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 1050A a b - 450B a b )e + 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 525A a b - 225B a b)e + 750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 105A a b - 45B a )e + 150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b + 45B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (490A a b + 210B a b )e + (- 70A b - 730B a b )d e +--R + +--R 5 2 2 +--R 100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (896A a b + 384B a b )e + (- 322A a b - 1418B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (56A b + 484B a b )d e - 80B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (790A a b - 210B a b)e + (- 578A a b + 818B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (256A a b - 2356B a b )d e + (- 48A b + 1808B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 45B a )e + (1210A a b + 120B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 2104A a b - 436B a b )d e + (1488A a b + 352B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 7 4 3 8 3 2 9 2 2 10 3 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e +--R + +--R 11 4 +--R 1920b d +--R * +--R 5 +--R x +--R + +--R 5 6 4 4 7 3 3 8 2 2 2 9 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 10 4 +--R 9600a b d +--R * +--R 4 +--R x +--R + +--R 6 5 4 5 6 3 4 7 2 2 3 8 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 2 9 4 +--R 19200a b d +--R * +--R 3 +--R x +--R + +--R 7 4 4 6 5 3 5 6 2 2 4 7 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 3 8 4 +--R 19200a b d +--R * +--R 2 +--R x +--R + +--R 8 3 4 7 4 3 6 5 2 2 5 6 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 4 7 4 +--R 9600a b d +--R * +--R x +--R + +--R 9 2 4 8 3 3 7 4 2 2 6 5 3 5 6 4 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e + 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((105A b + 45B a b )e - 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((525A a b + 225B a b )e - 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((1050A a b + 450B a b )e - 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((1050A a b + 450B a b )e - 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((525A a b + 225B a b)e - 750B a b d e )x + (105A a b + 45B a )e +--R + +--R 5 4 +--R - 150B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 4 5 3 4 +--R ((210A b + 90B a b )e - 300B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (980A a b + 420B a b )e + (- 140A b - 1460B a b )d e +--R + +--R 5 2 2 +--R 200B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (1792A a b + 768B a b )e + (- 644A a b - 2836B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (112A b + 968B a b )d e - 160B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (1580A a b - 420B a b)e + (- 1156A a b + 1636B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (512A a b - 4712B a b )d e + (- 96A b + 3616B a b )d e +--R + +--R 5 4 +--R - 960B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 210A a b - 90B a )e + (2420A a b + 240B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 4208A a b - 872B a b )d e + (2976A a b + 704B a b )d e +--R + +--R 5 4 4 +--R (- 768A b - 192B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 4 7 4 3 8 3 2 9 2 2 10 3 +--R 3840a b e - 15360a b d e + 23040a b d e - 15360a b d e +--R + +--R 11 4 +--R 3840b d +--R * +--R 5 +--R x +--R + +--R 5 6 4 4 7 3 3 8 2 2 2 9 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 10 4 +--R 19200a b d +--R * +--R 4 +--R x +--R + +--R 6 5 4 5 6 3 4 7 2 2 3 8 3 +--R 38400a b e - 153600a b d e + 230400a b d e - 153600a b d e +--R + +--R 2 9 4 +--R 38400a b d +--R * +--R 3 +--R x +--R + +--R 7 4 4 6 5 3 5 6 2 2 4 7 3 +--R 38400a b e - 153600a b d e + 230400a b d e - 153600a b d e +--R + +--R 3 8 4 +--R 38400a b d +--R * +--R 2 +--R x +--R + +--R 8 3 4 7 4 3 6 5 2 2 5 6 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 4 7 4 +--R 19200a b d +--R * +--R x +--R + +--R 9 2 4 8 3 3 7 4 2 2 6 5 3 5 6 4 +--R 3840a b e - 15360a b d e + 23040a b d e - 15360a b d e + 3840a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 6 5 5 6 4 5 +--R ((105A b + 45B a b )e - 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((525A a b + 225B a b )e - 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((1050A a b + 450B a b )e - 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((1050A a b + 450B a b )e - 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((525A a b + 225B a b)e - 750B a b d e )x + (105A a b + 45B a )e +--R + +--R 5 4 +--R - 150B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b + 45B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (490A a b + 210B a b )e + (- 70A b - 730B a b )d e +--R + +--R 5 2 2 +--R 100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (896A a b + 384B a b )e + (- 322A a b - 1418B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (56A b + 484B a b )d e - 80B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (790A a b - 210B a b)e + (- 578A a b + 818B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (256A a b - 2356B a b )d e + (- 48A b + 1808B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 45B a )e + (1210A a b + 120B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 2104A a b - 436B a b )d e + (1488A a b + 352B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 4 7 4 3 8 3 2 9 2 2 10 3 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e +--R + +--R 11 4 +--R 1920b d +--R * +--R 5 +--R x +--R + +--R 5 6 4 4 7 3 3 8 2 2 2 9 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 10 4 +--R 9600a b d +--R * +--R 4 +--R x +--R + +--R 6 5 4 5 6 3 4 7 2 2 3 8 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 2 9 4 +--R 19200a b d +--R * +--R 3 +--R x +--R + +--R 7 4 4 6 5 3 5 6 2 2 4 7 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 3 8 4 +--R 19200a b d +--R * +--R 2 +--R x +--R + +--R 8 3 4 7 4 3 6 5 2 2 5 6 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 4 7 4 +--R 9600a b d +--R * +--R x +--R + +--R 9 2 4 8 3 3 7 4 2 2 6 5 3 5 6 4 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e + 1920a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1057 + +--S 1058 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((7A b + 3B a)e - 10B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((14A b + 6B a)e - 20B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 +--R (256a b e - 1024a b d e + 1536a b d e - 1024a b d e + 256b d ) +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((7A b + 3B a)e - 10B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((7A b + 3B a)e - 10B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 +--R (128a b e - 512a b d e + 768a b d e - 512a b d e + 128b d ) +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1061 + +)clear all + +--S 1062 of 1378 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x)) +--R +--R +--R (1) +--R B x + A +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1378 +r0:=-7/128*e^4*(10*b*B*d-9*A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(11/2))-1/5*(A*b-a*B)*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^5)-1/40*(10*b*B*d-9*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*(a+b*x)^4)+7/240*e*(10*b*B*d-9*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x)^3)-7/192*e^2*(10*b*B*d-9*A*b*e-_ + a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^4*(a+b*x)^2)+7/128*e^3*(10*b*B*d-_ + 9*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^5*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 945A b - 105B a b )e + 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 4725A a b - 525B a b )e + 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 9450A a b - 1050B a b )e + 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 9450A a b - 1050B a b )e + 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 4725A a b - 525B a b)e + 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 945A a b - 105B a )e + 1050B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((945A b + 105B a b )e - 1050B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (4410A a b + 490B a b )e + (- 630A b - 4970B a b )d e +--R + +--R 5 2 2 +--R 700B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (8064A a b + 896B a b )e + (- 2898A a b - 9282B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (504A b + 3276B a b )d e - 560B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (7110A a b + 790B a b)e + (- 5202A a b - 8478B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (2304A a b + 6036B a b )d e + (- 432A b - 2608B a b )d e +--R + +--R 5 4 +--R 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (2895A a b - 105B a )e + (- 4470A a b - 1580B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (4104A a b + 1156B a b )d e + (- 1968A a b - 512B a b )d e +--R + +--R 5 4 4 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 +--R 1920a b e - 9600a b d e + 19200a b d e - 19200a b d e +--R + +--R 10 4 11 5 +--R 9600a b d e - 1920b d +--R * +--R 5 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R 9600a b e - 48000a b d e + 96000a b d e - 96000a b d e +--R + +--R 2 9 4 10 5 +--R 48000a b d e - 9600a b d +--R * +--R 4 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R 19200a b e - 96000a b d e + 192000a b d e - 192000a b d e +--R + +--R 3 8 4 2 9 5 +--R 96000a b d e - 19200a b d +--R * +--R 3 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 +--R 19200a b e - 96000a b d e + 192000a b d e - 192000a b d e +--R + +--R 4 7 4 3 8 5 +--R 96000a b d e - 19200a b d +--R * +--R 2 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 +--R 9600a b e - 48000a b d e + 96000a b d e - 96000a b d e +--R + +--R 5 6 4 4 7 5 +--R 48000a b d e - 9600a b d +--R * +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 +--R 1920a b e - 9600a b d e + 19200a b d e - 19200a b d e +--R + +--R 6 5 4 5 6 5 +--R 9600a b d e - 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 5 6 4 5 +--R ((945A b + 105B a b )e - 1050B b d e )x +--R + 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2 +--R 1920a b e - 9600a b d e + 19200a b d e - 19200a b d e +--R + +--R 6 5 4 5 6 5 +--R 9600a b d e - 1920a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1064 + +--S 1065 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((63A b + 7B a)e - 70B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((126A b + 14B a)e - 140B b d e )\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e + 1280a b d e +--R + +--R 6 5 +--R - 256b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((63A b + 7B a)e - 70B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((63A b + 7B a)e - 70B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 128a b e - 640a b d e + 1280a b d e - 1280a b d e + 640a b d e +--R + +--R 6 5 +--R - 128b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1068 + +)clear all + +--S 1069 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 7 5 6 6 2 4 5 5 +--R b e x + (6a b e + b d)x + (15a b e + 6a b d)x +--R + +--R 3 3 2 4 4 4 2 3 3 3 5 4 2 2 +--R (20a b e + 15a b d)x + (15a b e + 20a b d)x + (6a b e + 15a b d)x +--R + +--R 6 5 6 +--R (a e + 6a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1378 +r0:=-63/128*e^4*(10*b*B*d-11*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/((b*d-a*e)^(13/2)*sqrt(b))+63/128*e^4*(10*b*B*d-_ + 11*A*b*e+a*B*e)/(b*(b*d-a*e)^6*sqrt(d+e*x))+1/5*(-A*b+a*B)/(b*(b*d-_ + a*e)*(a+b*x)^5*sqrt(d+e*x))+1/40*(-10*b*B*d+11*A*b*e-a*B*e)/(b*(b*d-_ + a*e)^2*(a+b*x)^4*sqrt(d+e*x))+3/80*e*(10*b*B*d-11*A*b*e+a*B*e)/(b*_ + (b*d-a*e)^3*(a+b*x)^3*sqrt(d+e*x))-21/320*e^2*(10*b*B*d-11*A*b*e+_ + a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*sqrt(d+e*x))+21/128*e^3*(10*b*B*d-_ + 11*A*b*e+a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 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4 7 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R x +--R + +--R 11 6 10 5 9 2 2 4 8 3 3 3 +--R 1280a e - 7680a b d e + 19200a b d e - 25600a b d e +--R + +--R 7 4 4 2 6 5 5 5 6 6 +--R 19200a b d e - 7680a b d e + 1280a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 6 5 5 6 4 5 +--R ((- 3465A b + 315B a b )e + 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 17325A a b + 1575B a b )e + 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 34650A a b + 3150B a b )e + 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 34650A a b + 3150B a b )e + 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 17325A a b + 1575B a b)e + 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 3465A a b + 315B a )e + 3150B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 315B a b )e + 3150B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 16170A a b + 1470B a b )e + (- 1155A b + 14805B a b )d e +--R + +--R 5 2 3 +--R 1050B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 +--R (- 29568A a b + 2688B a b )e +--R + +--R 4 2 3 4 5 4 2 3 +--R (- 5544A a b + 27384B a b )d e + (462A b + 4998B a b )d e +--R + +--R 5 3 2 +--R - 420B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 +--R (- 26070A a b + 2370B a b)e +--R + +--R 2 3 3 2 4 +--R (- 10494A a b + 24654B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2178A a b + 9342B a b )d e + (- 264A b - 1956B a b )d e +--R + +--R 5 4 +--R 240B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 10615A a b + 965B a )e + (- 9680A a b + 10530B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (4026A a b + 8434B a b )d e + (- 1232A a b - 3548B a b )d e +--R + +--R 5 4 4 5 5 +--R (176A b + 1104B a b )d e - 160B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 1280A a e + (- 4215A a b + 2245B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (3590A a b + 1760B a b)d e + (- 2248A a b - 732B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (816A a b + 224B a b )d e + (- 128A b - 32B a b )d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R / +--R 6 5 6 5 6 5 4 7 2 4 3 8 3 3 +--R 640a b e - 3840a b d e + 9600a b d e - 12800a b d e +--R + +--R 2 9 4 2 10 5 11 6 +--R 9600a b d e - 3840a b d e + 640b d +--R * +--R 5 +--R x +--R + +--R 7 4 6 6 5 5 5 6 2 4 4 7 3 3 +--R 3200a b e - 19200a b d e + 48000a b d e - 64000a b d e +--R + +--R 3 8 4 2 2 9 5 10 6 +--R 48000a b d e - 19200a b d e + 3200a b d +--R * +--R 4 +--R x +--R + +--R 8 3 6 7 4 5 6 5 2 4 5 6 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 4 7 4 2 3 8 5 2 9 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 3 +--R x +--R + +--R 9 2 6 8 3 5 7 4 2 4 6 5 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 5 6 4 2 4 7 5 3 8 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 2 +--R x +--R + +--R 10 6 9 2 5 8 3 2 4 7 4 3 3 +--R 3200a b e - 19200a b d e + 48000a b d e - 64000a b d e +--R + +--R 6 5 4 2 5 6 5 4 7 6 +--R 48000a b d e - 19200a b d e + 3200a b d +--R * +--R x +--R + +--R 11 6 10 5 9 2 2 4 8 3 3 3 +--R 640a e - 3840a b d e + 9600a b d e - 12800a b d e +--R + +--R 7 4 4 2 6 5 5 5 6 6 +--R 9600a b d e - 3840a b d e + 640a b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1071 + +--S 1072 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R ((693A b - 63B a)e - 630B b d e )\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R 5 4 | 2 +--R ((- 1386A b + 126B a)e + 1260B b d e )\|- a b e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 256a e - 1536a b d e + 3840a b d e - 5120a b d e + 3840a b d e +--R + +--R 5 5 6 6 +--R - 1536a b d e + 256b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 4 | 2 \|b \|e x + d +--R ((- 693A b + 63B a)e + 630B b d e )\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 +-----------+ +-+ +--R ((- 693A b + 63B a)e + 630B b d e )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 128a e - 768a b d e + 1920a b d e - 2560a b d e + 1920a b d e +--R + +--R 5 5 6 6 +--R - 768a b d e + 128b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1075 + +)clear all + +--S 1076 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 2 8 5 2 6 7 2 4 2 5 6 2 6 +--R b e x + (6a b e + 2b d e)x + (15a b e + 12a b d e + b d )x +--R + +--R 3 3 2 2 4 5 2 5 +--R (20a b e + 30a b d e + 6a b d )x +--R + +--R 4 2 2 3 3 2 4 2 4 +--R (15a b e + 40a b d e + 15a b d )x +--R + +--R 5 2 4 2 3 3 2 3 6 2 5 4 2 2 2 +--R (6a b e + 30a b d e + 20a b d )x + (a e + 12a b d e + 15a b d )x +--R + +--R 6 5 2 6 2 +--R (2a d e + 6a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1378 +r0:=77/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^6*(d+e*x)^(3/2))+_ + 1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*(d+e*x)^(3/2))+1/40*(-10*b*B*d+_ + 13*A*b*e-3*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*(d+e*x)^(3/2))+11/240*e*_ + (10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*(d+e*x)^(3/2))-_ + 33/320*e^2*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*_ + (d+e*x)^(3/2))+231/640*e^3*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^5*_ + (a+b*x)*(d+e*x)^(3/2))-231/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(15/2)+_ + 231/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)/((b*d-a*e)^7*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((- 45045A b + 10395B a b )e + 34650B b d e )x +--R + +--R 5 2 4 6 +--R (- 225225A a b + 51975B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 45045A b + 183645B a b )d e + 34650B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 450450A a b + 103950B a b )e +--R + +--R 5 2 4 5 5 2 4 +--R (- 225225A a b + 398475B a b )d e + 173250B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 450450A a b + 103950B a b )e +--R + +--R 2 4 3 3 5 2 4 2 4 +--R (- 450450A a b + 450450B a b )d e + 346500B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 225225A a b + 51975B a b)e +--R + +--R 3 3 4 2 5 3 3 2 4 +--R (- 450450A a b + 277200B a b )d e + 346500B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 45045A a b + 10395B a )e + (- 225225A a b + 86625B a b)d e +--R + +--R 4 2 2 4 +--R 173250B a b d e +--R * +--R x +--R + +--R 5 6 5 5 2 4 +--R (- 45045A a b + 10395B a )d e + 34650B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 6 +--R ((45045A b - 10395B a b )e - 34650B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (210210A a b - 48510B a b )e + (60060A b - 175560B a b )d e +--R + +--R 6 2 4 +--R - 46200B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (384384A a b - 88704B a b )e +--R + +--R 5 2 4 5 6 5 2 4 +--R (282282A a b - 360822B a b )d e + (9009A b - 219219B a b )d e +--R + +--R 6 3 3 +--R - 6930B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (338910A a b - 78210B a b )e +--R + +--R 2 4 3 3 5 +--R (520806A a b - 380886B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (43758A a b - 410718B a b )d e + (- 2574A b - 33066B a b )d e +--R + +--R 6 4 2 +--R 1980B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (137995A a b - 31845B a b)e + (464750A a b - 213400B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (84084A a b - 376904B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 12298A a b - 61842B a b )d e + (1144A b + 9196B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (16640A a b - 3840B a )e + (192790A a b - 57290B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (79170A a b - 166570B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 23114A a b - 55566B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (5408A a b + 16532B a b )d e + (- 624A b - 4016B a b )d e +--R + +--R 6 6 +--R 480B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 1280A a e + (24320A a b - 2560B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (35595A a b - 33125B a b)d e + (- 21070A a b - 12180B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (10024A a b + 3556B a b )d e + (- 2928A a b - 832B a b )d e +--R + +--R 6 5 6 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 5 8 6 6 7 5 7 2 6 4 8 3 5 +--R 1920a b e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 3 9 4 4 2 10 5 3 11 6 2 12 7 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920b d e +--R * +--R 6 +--R x +--R + +--R 8 4 8 7 5 7 6 6 2 6 5 7 3 5 +--R 9600a b e - 65280a b d e + 188160a b d e - 295680a b d e +--R + +--R 4 8 4 4 3 9 5 3 2 10 6 2 11 7 +--R 268800a b d e - 134400a b d e + 26880a b d e + 3840a b d e +--R + +--R 12 8 +--R - 1920b d +--R * +--R 5 +--R x +--R + +--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5 +--R 19200a b e - 124800a b d e + 336000a b d e - 470400a b d e +--R + +--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7 +--R 336000a b d e - 67200a b d e - 67200a b d e + 48000a b d e +--R + +--R 11 8 +--R - 9600a b d +--R * +--R 4 +--R x +--R + +--R 10 2 8 9 3 7 8 4 2 6 7 5 3 5 +--R 19200a b e - 115200a b d e + 268800a b d e - 268800a b d e +--R + +--R 5 7 5 3 4 8 6 2 3 9 7 2 10 8 +--R 268800a b d e - 268800a b d e + 115200a b d e - 19200a b d +--R * +--R 3 +--R x +--R + +--R 11 8 10 2 7 9 3 2 6 8 4 3 5 +--R 9600a b e - 48000a b d e + 67200a b d e + 67200a b d e +--R + +--R 7 5 4 4 6 6 5 3 5 7 6 2 4 8 7 +--R - 336000a b d e + 470400a b d e - 336000a b d e + 124800a b d e +--R + +--R 3 9 8 +--R - 19200a b d +--R * +--R 2 +--R x +--R + +--R 12 8 11 7 10 2 2 6 9 3 3 5 +--R 1920a e - 3840a b d e - 26880a b d e + 134400a b d e +--R + +--R 8 4 4 4 7 5 5 3 6 6 6 2 5 7 7 +--R - 268800a b d e + 295680a b d e - 188160a b d e + 65280a b d e +--R + +--R 4 8 8 +--R - 9600a b d +--R * +--R x +--R + +--R 12 7 11 2 6 10 2 3 5 9 3 4 4 +--R 1920a d e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 8 4 5 3 7 5 6 2 6 6 7 5 7 8 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 6 6 5 6 +--R ((45045A b - 10395B a b )e - 34650B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (225225A a b - 51975B a b )e + (45045A b - 183645B a b )d e +--R + +--R 6 2 4 +--R - 34650B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (450450A a b - 103950B a b )e +--R + +--R 5 2 4 5 5 2 4 +--R (225225A a b - 398475B a b )d e - 173250B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (450450A a b - 103950B a b )e +--R + +--R 2 4 3 3 5 2 4 2 4 +--R (450450A a b - 450450B a b )d e - 346500B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (225225A a b - 51975B a b)e +--R + +--R 3 3 4 2 5 3 3 2 4 +--R (450450A a b - 277200B a b )d e - 346500B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (45045A a b - 10395B a )e + (225225A a b - 86625B a b)d e +--R + +--R 4 2 2 4 +--R - 173250B a b d e +--R * +--R x +--R + +--R 5 6 5 5 2 4 +--R (45045A a b - 10395B a )d e - 34650B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 6 5 6 6 5 6 +--R ((90090A b - 20790B a b )e - 69300B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (420420A a b - 97020B a b )e + (120120A b - 351120B a b )d e +--R + +--R 6 2 4 +--R - 92400B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (768768A a b - 177408B a b )e + (564564A a b - 721644B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (18018A b - 438438B a b )d e - 13860B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (677820A a b - 156420B a b )e +--R + +--R 2 4 3 3 5 +--R (1041612A a b - 761772B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (87516A a b - 821436B a b )d e + (- 5148A b - 66132B a b )d e +--R + +--R 6 4 2 +--R 3960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (275990A a b - 63690B a b)e + (929500A a b - 426800B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (168168A a b - 753808B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 24596A a b - 123684B a b )d e + (2288A b + 18392B a b )d e +--R + +--R 6 5 +--R - 1760B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (33280A a b - 7680B a )e + (385580A a b - 114580B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (158340A a b - 333140B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 46228A a b - 111132B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (10816A a b + 33064B a b )d e + (- 1248A b - 8032B a b )d e +--R + +--R 6 6 +--R 960B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 2560A a e + (48640A a b - 5120B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (71190A a b - 66250B a b)d e + (- 42140A a b - 24360B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (20048A a b + 7112B a b )d e + (- 5856A a b - 1664B a b )d e +--R + +--R 6 5 6 +--R (768A b + 192B a b )d +--R / +--R 7 5 8 6 6 7 5 7 2 6 4 8 3 5 +--R 3840a b e - 26880a b d e + 80640a b d e - 134400a b d e +--R + +--R 3 9 4 4 2 10 5 3 11 6 2 12 7 +--R 134400a b d e - 80640a b d e + 26880a b d e - 3840b d e +--R * +--R 6 +--R x +--R + +--R 8 4 8 7 5 7 6 6 2 6 5 7 3 5 +--R 19200a b e - 130560a b d e + 376320a b d e - 591360a b d e +--R + +--R 4 8 4 4 3 9 5 3 2 10 6 2 11 7 +--R 537600a b d e - 268800a b d e + 53760a b d e + 7680a b d e +--R + +--R 12 8 +--R - 3840b d +--R * +--R 5 +--R x +--R + +--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5 +--R 38400a b e - 249600a b d e + 672000a b d e - 940800a b d e +--R + +--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7 +--R 672000a b d e - 134400a b d e - 134400a b d e + 96000a b d e +--R + +--R 11 8 +--R - 19200a b d +--R * +--R 4 +--R x +--R + +--R 10 2 8 9 3 7 8 4 2 6 7 5 3 5 +--R 38400a b e - 230400a b d e + 537600a b d e - 537600a b d e +--R + +--R 5 7 5 3 4 8 6 2 3 9 7 2 10 8 +--R 537600a b d e - 537600a b d e + 230400a b d e - 38400a b d +--R * +--R 3 +--R x +--R + +--R 11 8 10 2 7 9 3 2 6 8 4 3 5 +--R 19200a b e - 96000a b d e + 134400a b d e + 134400a b d e +--R + +--R 7 5 4 4 6 6 5 3 5 7 6 2 +--R - 672000a b d e + 940800a b d e - 672000a b d e +--R + +--R 4 8 7 3 9 8 +--R 249600a b d e - 38400a b d +--R * +--R 2 +--R x +--R + +--R 12 8 11 7 10 2 2 6 9 3 3 5 +--R 3840a e - 7680a b d e - 53760a b d e + 268800a b d e +--R + +--R 8 4 4 4 7 5 5 3 6 6 6 2 +--R - 537600a b d e + 591360a b d e - 376320a b d e +--R + +--R 5 7 7 4 8 8 +--R 130560a b d e - 19200a b d +--R * +--R x +--R + +--R 12 7 11 2 6 10 2 3 5 9 3 4 4 +--R 3840a d e - 26880a b d e + 80640a b d e - 134400a b d e +--R + +--R 8 4 5 3 7 5 6 2 6 6 7 5 7 8 +--R 134400a b d e - 80640a b d e + 26880a b d e - 3840a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 6 5 6 6 5 6 +--R ((45045A b - 10395B a b )e - 34650B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (225225A a b - 51975B a b )e + (45045A b - 183645B a b )d e +--R + +--R 6 2 4 +--R - 34650B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (450450A a b - 103950B a b )e +--R + +--R 5 2 4 5 5 2 4 +--R (225225A a b - 398475B a b )d e - 173250B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (450450A a b - 103950B a b )e +--R + +--R 2 4 3 3 5 2 4 2 4 +--R (450450A a b - 450450B a b )d e - 346500B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (225225A a b - 51975B a b)e +--R + +--R 3 3 4 2 5 3 3 2 4 +--R (450450A a b - 277200B a b )d e - 346500B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (45045A a b - 10395B a )e + (225225A a b - 86625B a b)d e +--R + +--R 4 2 2 4 +--R - 173250B a b d e +--R * +--R x +--R + +--R 5 6 5 5 2 4 +--R (45045A a b - 10395B a )d e - 34650B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 6 5 6 6 5 6 +--R ((45045A b - 10395B a b )e - 34650B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (210210A a b - 48510B a b )e + (60060A b - 175560B a b )d e +--R + +--R 6 2 4 +--R - 46200B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (384384A a b - 88704B a b )e + (282282A a b - 360822B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (9009A b - 219219B a b )d e - 6930B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (338910A a b - 78210B a b )e + (520806A a b - 380886B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (43758A a b - 410718B a b )d e + (- 2574A b - 33066B a b )d e +--R + +--R 6 4 2 +--R 1980B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (137995A a b - 31845B a b)e + (464750A a b - 213400B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (84084A a b - 376904B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 12298A a b - 61842B a b )d e + (1144A b + 9196B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (16640A a b - 3840B a )e + (192790A a b - 57290B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (79170A a b - 166570B a b )d e +--R + +--R 2 4 3 3 3 3 5 2 4 4 2 +--R (- 23114A a b - 55566B a b )d e + (5408A a b + 16532B a b )d e +--R + +--R 6 5 5 6 6 +--R (- 624A b - 4016B a b )d e + 480B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 1280A a e + (24320A a b - 2560B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (35595A a b - 33125B a b)d e + (- 21070A a b - 12180B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (10024A a b + 3556B a b )d e + (- 2928A a b - 832B a b )d e +--R + +--R 6 5 6 +--R (384A b + 96B a b )d +--R / +--R 7 5 8 6 6 7 5 7 2 6 4 8 3 5 +--R 1920a b e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 3 9 4 4 2 10 5 3 11 6 2 12 7 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920b d e +--R * +--R 6 +--R x +--R + +--R 8 4 8 7 5 7 6 6 2 6 5 7 3 5 +--R 9600a b e - 65280a b d e + 188160a b d e - 295680a b d e +--R + +--R 4 8 4 4 3 9 5 3 2 10 6 2 11 7 +--R 268800a b d e - 134400a b d e + 26880a b d e + 3840a b d e +--R + +--R 12 8 +--R - 1920b d +--R * +--R 5 +--R x +--R + +--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5 +--R 19200a b e - 124800a b d e + 336000a b d e - 470400a b d e +--R + +--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7 +--R 336000a b d e - 67200a b d e - 67200a b d e + 48000a b d e +--R + +--R 11 8 +--R - 9600a b d +--R * +--R 4 +--R x +--R + +--R 10 2 8 9 3 7 8 4 2 6 7 5 3 5 +--R 19200a b e - 115200a b d e + 268800a b d e - 268800a b d e +--R + +--R 5 7 5 3 4 8 6 2 3 9 7 2 10 8 +--R 268800a b d e - 268800a b d e + 115200a b d e - 19200a b d +--R * +--R 3 +--R x +--R + +--R 11 8 10 2 7 9 3 2 6 8 4 3 5 +--R 9600a b e - 48000a b d e + 67200a b d e + 67200a b d e +--R + +--R 7 5 4 4 6 6 5 3 5 7 6 2 +--R - 336000a b d e + 470400a b d e - 336000a b d e +--R + +--R 4 8 7 3 9 8 +--R 124800a b d e - 19200a b d +--R * +--R 2 +--R x +--R + +--R 12 8 11 7 10 2 2 6 9 3 3 5 +--R 1920a e - 3840a b d e - 26880a b d e + 134400a b d e +--R + +--R 8 4 4 4 7 5 5 3 6 6 6 2 5 7 7 +--R - 268800a b d e + 295680a b d e - 188160a b d e + 65280a b d e +--R + +--R 4 8 8 +--R - 9600a b d +--R * +--R x +--R + +--R 12 7 11 2 6 10 2 3 5 9 3 4 4 +--R 1920a d e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 8 4 5 3 7 5 6 2 6 6 7 5 7 8 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1078 + +--S 1079 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 5 4 +-----------+ | b +--R ((3003A b - 693B a)e - 2310B b d e )\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 5 4 +-+ \|b \|e x + d +--R ((6006A b - 1386B a)e - 4620B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 256a e - 1792a b d e + 5376a b d e - 8960a b d e + 8960a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 5376a b d e + 1792a b d e - 256b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 5 4 +-+ \|b \|e x + d +--R ((3003A b - 693B a)e - 2310B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 5 4 +-----------+ | b +--R ((3003A b - 693B a)e - 2310B b d e )\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 128a e - 896a b d e + 2688a b d e - 4480a b d e + 4480a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 2688a b d e + 896a b d e - 128b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1082 + +)clear all + +--S 1083 of 1378 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 3 9 5 3 6 2 8 2 4 3 5 2 6 2 7 +--R b e x + (6a b e + 3b d e )x + (15a b e + 18a b d e + 3b d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (20a b e + 45a b d e + 18a b d e + b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (15a b e + 60a b d e + 45a b d e + 6a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (6a b e + 45a b d e + 60a b d e + 15a b d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (a e + 18a b d e + 45a b d e + 20a b d )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (3a d e + 18a b d e + 15a b d )x + (3a d e + 6a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1378 +r0:=3003/640*e^4*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^6*(d+e*x)^(5/2))+_ + 1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*(d+e*x)^(5/2))+1/8*(-2*b*B*d+_ + 3*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*(d+e*x)^(5/2))+13/48*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*(d+e*x)^(5/2))-143/192*e^2*_ + (2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*(d+e*x)^(5/2))+_ + 429/128*e^3*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*_ + (d+e*x)^(5/2))+1001/128*e^4*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^7*_ + (d+e*x)^(3/2))-3003/128*b^(3/2)*e^4*(2*b*B*d-3*A*b*e+a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(17/2)+_ + 3003/128*b*e^4*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^8*sqrt(d+e*x)) +--R +--R +--R (2) +--R 7 6 7 7 6 7 +--R ((135135A b - 45045B a b )e - 90090B b d e )x +--R + +--R 6 2 5 7 7 6 6 +--R (675675A a b - 225225B a b )e + (270270A b - 540540B a b )d e +--R + +--R 7 2 5 +--R - 180180B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 7 +--R (1351350A a b - 450450B a b )e +--R + +--R 6 2 5 6 +--R (1351350A a b - 1351350B a b )d e +--R + +--R 7 6 2 5 7 3 4 +--R (135135A b - 945945B a b )d e - 90090B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 7 +--R (1351350A a b - 450450B a b )e +--R + +--R 2 5 3 4 6 +--R (2702700A a b - 1801800B a b )d e +--R + +--R 6 2 5 2 5 6 3 4 +--R (675675A a b - 2027025B a b )d e - 450450B a b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 +--R (675675A a b - 225225B a b )e +--R + +--R 3 4 4 3 6 +--R (2702700A a b - 1351350B a b )d e +--R + +--R 2 5 3 4 2 5 2 5 3 4 +--R (1351350A a b - 2252250B a b )d e - 900900B a b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 7 +--R (135135A a b - 45045B a b)e +--R + +--R 4 3 5 2 6 +--R (1351350A a b - 540540B a b )d e +--R + +--R 3 4 4 3 2 5 3 4 3 4 +--R (1351350A a b - 1351350B a b )d e - 900900B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 6 +--R (270270A a b - 90090B a b)d e +--R + +--R 4 3 5 2 2 5 4 3 3 4 +--R (675675A a b - 405405B a b )d e - 450450B a b d e +--R * +--R x +--R + +--R 5 2 6 2 5 5 2 3 4 +--R (135135A a b - 45045B a b)d e - 90090B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 7 6 7 7 6 7 +--R ((- 135135A b + 45045B a b )e + 90090B b d e )x +--R + +--R 6 2 5 7 +--R (- 630630A a b + 210210B a b )e +--R + +--R 7 6 6 7 2 5 +--R (- 315315A b + 525525B a b )d e + 210210B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 7 +--R (- 1153152A a b + 384384B a b )e +--R + +--R 6 2 5 6 +--R (- 1477476A a b + 1261260B a b )d e +--R + +--R 7 6 2 5 7 3 4 +--R (- 207207A b + 1054053B a b )d e + 138138B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 7 +--R (- 1016730A a b + 338910B a b )e +--R + +--R 2 5 3 4 6 +--R (- 2715570A a b + 1583010B a b )d e +--R + +--R 6 2 5 2 5 +--R (- 978120A a b + 2136420B a b )d e +--R + +--R 7 6 3 4 7 4 3 +--R (- 19305A b + 658515B a b )d e + 12870B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 +--R (- 413985A a b + 137995B a b )e +--R + +--R 3 4 4 3 6 +--R (- 2410980A a b + 1079650B a b )d e +--R + +--R 2 5 3 4 2 5 +--R (- 1814670A a b + 2212210B a b )d e +--R + +--R 6 2 5 3 4 +--R (- 94380A a b + 1241240B a b )d e +--R + +--R 7 6 4 3 7 5 2 +--R (4290A b + 61490B a b )d e - 2860B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 7 +--R (- 49920A a b + 16640B a b)e +--R + +--R 4 3 5 2 6 +--R (- 992355A a b + 364065B a b )d e +--R + +--R 3 4 4 3 2 5 +--R (- 1631760A a b + 1205490B a b )d e +--R + +--R 2 5 3 4 3 4 +--R (- 182910A a b + 1148810B a b )d e +--R + +--R 6 2 5 4 3 7 6 5 2 +--R (20670A a b + 115050B a b )d e + (- 1560A b - 13260B a b )d e +--R + +--R 7 6 +--R 1040B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 7 5 2 6 6 +--R (3840A a b - 1280B a )e + (- 122880A a b + 38400B a b)d e +--R + +--R 4 3 5 2 2 5 +--R (- 685155A a b + 310305B a b )d e +--R + +--R 3 4 4 3 3 4 +--R (- 174300A a b + 514870B a b )d e +--R + +--R 2 5 3 4 4 3 +--R (39270A a b + 103110B a b )d e +--R + +--R 6 2 5 5 2 7 6 6 +--R (- 7440A a b - 23700B a b )d 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log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 5 2 4 +-+ \|b \|e x + d +--R ((- 18018A b + 6006B a b)e + 12012B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R 256a e - 2048a b d e + 7168a b d e - 14336a b d e + 17920a b d e +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R - 14336a b d e + 7168a b d e - 2048a b d e + 256b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1378 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 5 2 4 +-+ \|b \|e x + d +--R ((- 9009A b + 3003B a b)e + 6006B b d e )\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 5 2 4 +-----------+ | b +--R ((- 9009A b + 3003B a b)e + 6006B b d e )\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R 128a e - 1024a b d e + 3584a b d e - 7168a b d e + 8960a b d e +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R - 7168a b d e + 3584a b d e - 1024a b d e + 128b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1378 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1089 + +)clear all + +--S 1090 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1378 +r0:=-2/143*(4*b*B*d-13*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/1287*(b*d-a*e)*(4*b*B*d-13*A*b*e+9*a*B*e)*_ + (d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+_ + 2/13*B*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 198B b e x + ((234A b + 234B a)e + 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (286A a e + (884A b + 884B a)d e + 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (1144A a d e + (1196A b + 1196B a)d e + 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (1716A a d e + (624A b + 624B a)d e + 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (1144A a d e + (26A b + 26B a)d e - 8B b d e)x + 286A a d e +--R + +--R 5 6 +--R (- 52A b - 52B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 5 +--R 198B b e x + ((234A b + 234B a)e + 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (286A a e + (884A b + 884B a)d e + 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (1144A a d e + (1196A b + 1196B a)d e + 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (1716A a d e + (624A b + 624B a)d e + 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (1144A a d e + (26A b + 26B a)d e - 8B b d e)x + 286A a d e +--R + +--R 5 6 +--R (- 52A b - 52B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 1287e +--R Type: Union(Expression(Integer),...) +--E 1092 + +--S 1093 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 5 +--R - 198B b e x + ((- 234A b - 234B a)e - 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (- 286A a e + (- 884A b - 884B a)d e - 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (- 1144A a d e + (- 1196A b - 1196B a)d e - 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (- 1716A a d e + (- 624A b - 624B a)d e - 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (- 1144A a d e + (- 26A b - 26B a)d e + 8B b d e)x - 286A a d e +--R + +--R 5 6 +--R (52A b + 52B a)d e - 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 2 6 7 2 6 2 5 6 +--R 198B b e x + ((234A b + 432B a b)e + 720B b d e )x +--R + +--R 2 6 2 5 2 2 4 5 +--R ((520A a b + 234B a )e + (884A b + 1604B a b)d e + 916B b d e )x +--R + +--R 2 6 2 5 +--R 286A a e + (2028A a b + 884B a )d e +--R + +--R 2 2 4 2 3 3 +--R (1196A b + 2112B a b)d e + 424B b d e +--R * +--R 4 +--R x +--R + +--R 2 5 2 2 4 +--R 1144A a d e + (2912A a b + 1196B a )d e +--R + +--R 2 3 3 2 4 2 +--R (624A b + 1048B a b)d e + 6B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R 1716A a d e + (1768A a b + 624B a )d e + (26A b + 32B a b)d e +--R + +--R 2 5 +--R - 8B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 1144A a d e + (312A a b + 26B a )d e + (- 52A b - 60B a b)d e +--R + +--R 2 6 +--R 16B b d +--R * +--R x +--R + +--R 2 4 2 2 5 6 +--R 286A a d e + (- 52A a b - 52B a )d e + 16B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 6 4 3 5 +--R B b e x + ((A b + B a)e + 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (A a e + (4A b + 4B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (4A a d e + (6A b + 6B a)d e + 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (6A a d e + (4A b + 4B a)d e + B b d )x +--R + +--R 3 4 4 +--R (4A a d e + (A b + B a)d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 7 2 4 2 3 6 +--R - B b e x + ((- A b - 2B a b)e - 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((- 2A a b - B a )e + (- 4A b - 8B a b)d e - 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R - A a e + (- 8A a b - 4B a )d e + (- 6A b - 12B a b)d e +--R + +--R 2 3 +--R - 4B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R - 4A a d e + (- 12A a b - 6B a )d e + (- 4A b - 8B a b)d e +--R + +--R 2 4 +--R - B b d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 3 2 4 2 +--R (- 6A a d e + (- 8A a b - 4B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (- 4A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1094 + +)clear all + +--S 1095 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1378 +r0:=-2/99*(4*b*B*d-11*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/693*(b*d-a*e)*(4*b*B*d-11*A*b*e+7*a*B*e)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/11*B*_ + (a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 126B b e x + ((154A b + 154B a)e + 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (198A a e + (418A b + 418B a)d e + 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (594A a d e + (330A b + 330B a)d e + 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (594A a d e + (22A b + 22B a)d e - 8B b d e)x + 198A a d e +--R + +--R 4 5 +--R (- 44A b - 44B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 4 +--R 126B b e x + ((154A b + 154B a)e + 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (198A a e + (418A b + 418B a)d e + 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (594A a d e + (330A b + 330B a)d e + 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (594A a d e + (22A b + 22B a)d e - 8B b d e)x + 198A a d e +--R + +--R 4 5 +--R (- 44A b - 44B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 693e +--R Type: Union(Expression(Integer),...) +--E 1097 + +--S 1098 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 4 +--R - 126B b e x + ((- 154A b - 154B a)e - 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (- 198A a e + (- 418A b - 418B a)d e - 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (- 594A a d e + (- 330A b - 330B a)d e - 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (- 594A a d e + (- 22A b - 22B a)d e + 8B b d e)x - 198A a d e +--R + +--R 4 5 +--R (44A b + 44B a)d e - 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 2 5 6 2 5 2 4 5 +--R 126B b e x + ((154A b + 280B a b)e + 322B b d e )x +--R + +--R 2 5 2 4 2 2 3 4 +--R ((352A a b + 154B a )e + (418A b + 740B a b)d e + 226B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 198A a e + (1012A a b + 418B a )d e + (330A b + 556B a b)d e +--R + +--R 2 3 2 +--R 6B b d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 594A a d e + (924A a b + 330B a )d e + (22A b + 28B a b)d e +--R + +--R 2 4 +--R - 8B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 594A a d e + (220A a b + 22B a )d e + (- 44A b - 52B a b)d e +--R + +--R 2 5 +--R 16B b d +--R * +--R x +--R + +--R 2 3 2 2 4 5 +--R 198A a d e + (- 44A a b - 44B a )d e + 16B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 3 2 4 +--R B b e x + ((A b + B a)e + 3B b d e )x +--R + +--R 3 2 2 3 +--R (A a e + (3A b + 3B a)d e + 3B b d e)x +--R + +--R 2 2 3 2 +--R (3A a d e + (3A b + 3B a)d e + B b d )x +--R + +--R 2 3 3 +--R (3A a d e + (A b + B a)d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 6 2 3 2 2 5 +--R - B b e x + ((- A b - 2B a b)e - 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((- 2A a b - B a )e + (- 3A b - 6B a b)d e - 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- A a e + (- 6A a b - 3B a )d e + (- 3A b - 6B a b)d e - B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (- 3A a d e + (- 6A a b - 3B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (- 3A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1099 + +)clear all + +--S 1100 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (1) (B e x + (A e + B d)x + A d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1378 +r0:=-2/63*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/315*(b*d-a*e)*(4*b*B*d-9*A*b*e+5*a*B*e)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/9*B*_ + (a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B b e x + ((90A b + 90B a)e + 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (126A a e + (144A b + 144B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (252A a d e + (18A b + 18B a)d e - 8B b d e)x + 126A a d e +--R + +--R 3 4 +--R (- 36A b - 36B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 3 +--R 70B b e x + ((90A b + 90B a)e + 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (126A a e + (144A b + 144B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (252A a d e + (18A b + 18B a)d e - 8B b d e)x + 126A a d e +--R + +--R 3 4 +--R (- 36A b - 36B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 1102 + +--S 1103 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 3 +--R - 70B b e x + ((- 90A b - 90B a)e - 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (- 126A a e + (- 144A b - 144B a)d e - 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 252A a d e + (- 18A b - 18B a)d e + 8B b d e)x - 126A a d e +--R + +--R 3 4 +--R (36A b + 36B a)d e - 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 2 4 5 2 4 2 3 4 +--R 70B b e x + ((90A b + 160B a b)e + 100B b d e )x +--R + +--R 2 4 2 3 2 2 2 3 +--R ((216A a b + 90B a )e + (144A b + 244B a b)d e + 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 126A a e + (396A a b + 144B a )d e + (18A b + 24B a b)d e +--R + +--R 2 3 +--R - 8B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 252A a d e + (144A a b + 18B a )d e + (- 36A b - 44B a b)d e +--R + +--R 2 4 +--R 16B b d +--R * +--R x +--R + +--R 2 2 2 2 3 4 +--R 126A a d e + (- 36A a b - 36B a )d e + 16B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 4 2 3 +--R B b e x + ((A b + B a)e + 2B b d e)x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + B b d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 5 2 2 2 4 +--R - B b e x + ((- A b - 2B a b)e - 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((- 2A a b - B a )e + (- 2A b - 4B a b)d e - B b d )x +--R + +--R 2 2 2 2 2 2 +--R (- A a e + (- 4A a b - 2B a )d e + (- A b - 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (- 2A a d e + (- 2A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1104 + +)clear all + +--S 1105 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R +-------+ | 2 2 2 +--R (1) (B x + A)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1378 +r0:=-2/35*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/105*(b*d-a*e)*(4*b*B*d-7*A*b*e+3*a*B*e)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/7*B*_ + (a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B b e x + ((42A b + 42B a)e + 6B b d e )x +--R + +--R 3 2 2 2 +--R (70A a e + (14A b + 14B a)d e - 8B b d e)x + 70A a d e +--R + +--R 2 3 +--R (- 28A b - 28B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B b e x + ((42A b + 42B a)e + 6B b d e )x +--R + +--R 3 2 2 2 +--R (70A a e + (14A b + 14B a)d e - 8B b d e)x + 70A a d e +--R + +--R 2 3 +--R (- 28A b - 28B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 1107 + +--S 1108 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 2 +--R - 30B b e x + ((- 42A b - 42B a)e - 6B b d e )x +--R + +--R 3 2 2 2 +--R (- 70A a e + (- 14A b - 14B a)d e + 8B b d e)x - 70A a d e +--R + +--R 2 3 +--R (28A b + 28B a)d e - 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 2 3 4 2 3 2 2 3 +--R 30B b e x + ((42A b + 72B a b)e + 6B b d e )x +--R + +--R 2 3 2 2 2 2 2 +--R ((112A a b + 42B a )e + (14A b + 20B a b)d e - 8B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 70A a e + (84A a b + 14B a )d e + (- 28A b - 36B a b)d e +--R + +--R 2 3 +--R 16B b d +--R * +--R x +--R + +--R 2 2 2 2 3 +--R 70A a d e + (- 28A a b - 28B a )d e + 16B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 2 +--R (B b e x + ((A b + B a)e + B b d)x + (A a e + (A b + B a)d)x + A a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 2 3 +--R - B b e x + ((- A b - 2B a b)e - B b d)x +--R + +--R 2 2 2 +--R ((- 2A a b - B a )e + (- A b - 2B a b)d)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1109 + +)clear all + +--S 1110 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1378 +r0:=-2/15*(4*b*B*d-5*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/15*(b*d-a*e)*(4*b*B*d-5*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/5*B*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 2 2 2 2 +--R 6B b e x + ((10A b + 10B a)e - 8B b d e)x + 30A a e +--R + +--R 2 +--R (- 20A b - 20B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R 6B b e x + ((10A b + 10B a)e - 8B b d e)x + 30A a e +--R + +--R 2 +--R (- 20A b - 20B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15e +--R Type: Union(Expression(Integer),...) +--E 1112 + +--S 1113 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R - 6B b e x + ((- 10A b - 10B a)e + 8B b d e)x - 30A a e +--R + +--R 2 +--R (20A b + 20B a)d e - 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R 6B b e x + ((10A b + 16B a b)e - 8B b d e)x +--R + +--R 2 2 2 2 2 +--R ((40A a b + 10B a )e + (- 20A b - 28B a b)d e + 16B b d )x +--R + +--R 2 2 2 2 +--R 30A a e + (- 20A a b - 20B a )d e + 16B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1114 + +)clear all + +--S 1115 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1378 +r0:=-2*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+2/3*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^2*(b*d-a*e))-4/3*(4*b*B*d-3*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R 2B b e x + ((6A b + 6B a)e - 8B b d e)x - 6A a e +--R + +--R 2 +--R (12A b + 12B a)d e - 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R 2B b e x + ((6A b + 6B a)e - 8B b d e)x - 6A a e + (12A b + 12B a)d e +--R + +--R 2 +--R - 16B b d +--R / +--R 3 +-------+ +--R 3e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1117 + +--S 1118 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R - 2B b e x + ((- 6A b - 6B a)e + 8B b d e)x + 6A a e +--R + +--R 2 +--R (- 12A b - 12B a)d e + 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R 2B b e x + ((6A b + 8B a b)e - 8B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R (6B a e + (12A b + 4B a b)d e - 16B b d )x - 6A a e +--R + +--R 2 2 +--R (12A a b + 12B a )d e - 16B a b d +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))+2/3*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^2*(b*d-a*e)*sqrt(d+e*x))+4/3*(4*b*B*d-A*b*e-3*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R 6B b e x + ((- 6A b - 6B a)e + 24B b d e)x - 2A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e + 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R 6B b e x + ((- 6A b - 6B a)e + 24B b d e)x - 2A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e + 16B b d +--R / +--R 4 3 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R - 6B b e x + ((6A b + 6B a)e - 24B b d e)x + 2A a e +--R + +--R 2 +--R (4A b + 4B a)d e - 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R 6B b e x + (- 6A b e + 24B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 8A a b - 6B a )e + (- 4A b + 20B a b)d e + 16B b d )x - 2A a e +--R + +--R 2 2 +--R (- 4A a b - 4B a )d e + 16B a b d +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1378 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1378 +r0:=-2/5*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/5*(4*b*B*d+A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/15*(4*b*B*d+A*b*e-5*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 30B b e x + ((- 10A b - 10B a)e - 40B b d e)x - 6A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e - 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 30B b e x + ((- 10A b - 10B a)e - 40B b d e)x - 6A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e - 16B b d +--R / +--R 5 2 4 2 3 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R 30B b e x + ((10A b + 10B a)e + 40B b d e)x + 6A a e +--R + +--R 2 +--R (4A b + 4B a)d e + 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 +--R - 30B b e x + ((- 10A b - 40B a b)e - 40B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 16A a b - 10B a )e + (- 4A b - 44B a b)d e - 16B b d )x - 6A a e +--R + +--R 2 2 +--R (- 4A a b - 4B a )d e - 16B a b d +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 | 2 2 2 2 3 +--R (B b x + (A b + B a)x + A a)\|b x + 2a b x + a - B b x +--R + +--R 2 2 2 2 +--R (- A b - 2B a b)x + (- 2A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1378 +r0:=-2/255*(8*b*B*d-17*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/17*B*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/12155*(b*d-a*e)^2*(8*b*B*d-17*A*b*e+_ + 9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/109395*_ + (b*d-a*e)^3*(8*b*B*d-17*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5*(a+b*x))+4/1105*(b*d-a*e)*(8*b*B*d-17*A*b*e+_ + 9*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 8 8 3 2 8 3 7 7 +--R 12870B b e x + ((14586A b + 43758B a b )e + 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (50490A a b + 50490B a b)e + (51612A b + 154836B a b )d e +--R + +--R 3 2 6 +--R 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (59670A a b + 19890B a )e + (183600A a b + 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (63036A b + 189108B a b )d e + 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R 24310A a e + (225420A a b + 75140B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (233580A a b + 233580B a b)d e + (27200A b + 81600B a b )d e +--R + +--R 3 4 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R 97240A a d e + (304980A a b + 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (108120A a b + 108120B a b)d e + (170A b + 510B a b )d e +--R + +--R 3 5 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R 145860A a d e + (159120A a b + 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (1530A a b + 1530B a b)d e + (- 204A b - 612B a b )d e +--R + +--R 3 6 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R 97240A a d e + (6630A a b + 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (- 2040A a b - 2040B a b)d e + (272A b + 816B a b )d e +--R + +--R 3 7 +--R - 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (4080A a b + 4080B a b)d e + (- 544A b - 1632B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 109395b e x + 109395a e +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 8 8 3 2 8 3 7 7 +--R 12870B b e x + ((14586A b + 43758B a b )e + 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (50490A a b + 50490B a b)e + (51612A b + 154836B a b )d e +--R + +--R 3 2 6 +--R 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (59670A a b + 19890B a )e + (183600A a b + 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (63036A b + 189108B a b )d e + 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R 24310A a e + (225420A a b + 75140B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (233580A a b + 233580B a b)d e + (27200A b + 81600B a b )d e +--R + +--R 3 4 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R 97240A a d e + (304980A a b + 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (108120A a b + 108120B a b)d e + (170A b + 510B a b )d e +--R + +--R 3 5 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R 145860A a d e + (159120A a b + 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (1530A a b + 1530B a b)d e + (- 204A b - 612B a b )d e +--R + +--R 3 6 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R 97240A a d e + (6630A a b + 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (- 2040A a b - 2040B a b)d e + (272A b + 816B a b )d e +--R + +--R 3 7 +--R - 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (4080A a b + 4080B a b)d e + (- 544A b - 1632B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 109395e +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 8 8 3 2 8 3 7 7 +--R - 12870B b e x + ((- 14586A b - 43758B a b )e - 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (- 50490A a b - 50490B a b)e + (- 51612A b - 154836B a b )d e +--R + +--R 3 2 6 +--R - 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (- 59670A a b - 19890B a )e + (- 183600A a b - 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (- 63036A b - 189108B a b )d e - 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R - 24310A a e + (- 225420A a b - 75140B a )d e +--R + +--R 2 2 2 6 +--R (- 233580A a b - 233580B a b)d e +--R + +--R 3 2 3 5 3 4 4 +--R (- 27200A b - 81600B a b )d e - 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 97240A a d e + (- 304980A a b - 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (- 108120A a b - 108120B a b)d e + (- 170A b - 510B a b )d e +--R + +--R 3 5 3 +--R 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 145860A a d e + (- 159120A a b - 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (- 1530A a b - 1530B a b)d e + (204A b + 612B a b )d e +--R + +--R 3 6 2 +--R - 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 97240A a d e + (- 6630A a b - 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (2040A a b + 2040B a b)d e + (- 272A b - 816B a b )d e +--R + +--R 3 7 +--R 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R - 24310A a d e + (13260A a b + 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (- 4080A a b - 4080B a b)d e + (544A b + 1632B a b )d e - 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 4 8 9 4 3 8 4 7 8 +--R 12870B b e x + ((14586A b + 56628B a b )e + 44616B b d e )x +--R + +--R 3 2 2 8 4 3 7 +--R (65076A a b + 94248B a b )e + (51612A b + 199452B a b )d e +--R + +--R 4 2 6 +--R 52932B b d e +--R * +--R 7 +--R x +--R + +--R 2 2 3 8 3 2 2 7 +--R (110160A a b + 70380B a b)e + (235212A a b + 338436B a b )d e +--R + +--R 4 3 2 6 4 3 5 +--R (63036A b + 242040B a b )d e + 21816B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 8 2 2 3 7 +--R (83980A a b + 19890B a )e + (409020A a b + 258740B a b)d e +--R + +--R 3 2 2 2 6 +--R (296616A a b + 422688B a b )d e +--R + +--R 4 3 3 5 4 4 4 +--R (27200A b + 103416B a b )d e + 70B b d e +--R * +--R 5 +--R x +--R + +--R 4 8 3 4 7 +--R 24310A a e + (322660A a b + 75140B a )d e +--R + +--R 2 2 3 2 6 +--R (538560A a b + 335240B a b)d e +--R + +--R 3 2 2 3 5 4 3 4 4 +--R (135320A a b + 189720B a b )d e + (170A b + 580B a b )d e +--R + +--R 4 5 3 +--R - 80B b d e +--R * +--R 4 +--R x +--R + +--R 4 7 3 4 2 6 +--R 97240A a d e + (450840A a b + 101660B a )d e +--R + +--R 2 2 3 3 5 3 2 2 4 4 +--R (267240A a b + 161160B a b)d e + (1700A a b + 2040B a b )d e +--R + +--R 4 3 5 3 4 6 2 +--R (- 204A b - 692B a b )d e + 96B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 4 3 5 +--R 145860A a d e + (256360A a b + 53040B a )d e +--R + +--R 2 2 3 4 4 3 2 2 5 3 +--R (8160A a b + 3740B a b)d e + (- 2244A a b - 2652B a b )d e +--R + +--R 4 3 6 2 4 7 +--R (272A b + 912B a b )d e - 128B b d e +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 4 +--R 97240A a d e + (30940A a b + 2210B a )d e +--R + +--R 2 2 3 5 3 3 2 2 6 2 +--R (- 15300A a b - 6460B a b)d e + (4352A a b + 4896B a b )d e +--R + +--R 4 3 7 4 8 +--R (- 544A b - 1760B a b )d e + 256B b d +--R * +--R x +--R + +--R 4 4 4 3 4 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 3 6 2 3 2 2 7 +--R (4080A a b + 4080B a b)d e + (- 544A a b - 1632B a b )d e +--R + +--R 3 8 +--R 256B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 109395b e x + 109395a e +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 8 3 2 4 3 3 7 +--R B b e x + ((A b + 3B a b )e + 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 6 +--R ((3A a b + 3B a b)e + (4A b + 12B a b )d e + 6B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b + B a )e + (12A a b + 12B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (6A b + 18B a b )d e + 4B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A a e + (12A a b + 4B a )d e + (18A a b + 18B a b)d e +--R + +--R 3 2 3 3 4 +--R (4A b + 12B a b )d e + B b d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 3 +--R 4A a d e + (18A a b + 6B a )d e + (12A a b + 12B a b)d e +--R + +--R 3 2 4 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 3 3 2 2 4 2 +--R (6A a d e + (12A a b + 4B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 3 2 3 4 3 4 +--R (4A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 9 4 3 4 4 3 8 +--R - B b e x + ((- A b - 4B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((- 4A a b - 6B a b )e + (- 4A b - 16B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 6A a b - 4B a b)e + (- 16A a b - 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 6A b - 24B a b )d e - 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 4A a b - B a )e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 24A a b - 36B a b )d e + (- 4A b - 16B a b )d e - B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - A a e + (- 16A a b - 4B a )d e + (- 36A a b - 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 16A a b - 24B a b )d e + (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R - 4A a d e + (- 24A a b - 6B a )d e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 4 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (- 6A a d e + (- 16A a b - 4B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (- 4A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1378 +r0:=-2/195*(8*b*B*d-15*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/15*B*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/6435*(b*d-a*e)^2*(8*b*B*d-15*A*b*e+7*a*B*e)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/45045*(b*d-a*e)^3*_ + (8*b*B*d-15*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/715*(b*d-a*e)*(8*b*B*d-15*A*b*e+7*a*B*e)*(a+b*x)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 7 7 3 2 7 3 6 6 +--R 6006B b e x + ((6930A b + 20790B a b )e + 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (24570A a b + 24570B a b)e + (17010A b + 51030B a b )d e +--R + +--R 3 2 5 +--R 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (30030A a b + 10010B a )e + (62790A a b + 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (11130A b + 33390B a b )d e + 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R 12870A a e + (81510A a b + 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (44070A a b + 44070B a b)d e + (150A b + 450B a b )d e +--R + +--R 3 4 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 38610A a d e + (64350A a b + 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1170A a b + 1170B a b)d e + (- 180A b - 540B a b )d e +--R + +--R 3 5 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 38610A a d e + (4290A a b + 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1560A a b - 1560B a b)d e + (240A b + 720B a b )d e +--R + +--R 3 6 +--R - 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (3120A a b + 3120B a b)d e + (- 480A b - 1440B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 2 7 3 6 6 +--R 6006B b e x + ((6930A b + 20790B a b )e + 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (24570A a b + 24570B a b)e + (17010A b + 51030B a b )d e +--R + +--R 3 2 5 +--R 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (30030A a b + 10010B a )e + (62790A a b + 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (11130A b + 33390B a b )d e + 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R 12870A a e + (81510A a b + 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (44070A a b + 44070B a b)d e + (150A b + 450B a b )d e +--R + +--R 3 4 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 38610A a d e + (64350A a b + 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1170A a b + 1170B a b)d e + (- 180A b - 540B a b )d e +--R + +--R 3 5 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 38610A a d e + (4290A a b + 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1560A a b - 1560B a b)d e + (240A b + 720B a b )d e +--R + +--R 3 6 +--R - 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (3120A a b + 3120B a b)d e + (- 480A b - 1440B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 1137 + +--S 1138 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 7 7 3 2 7 3 6 6 +--R - 6006B b e x + ((- 6930A b - 20790B a b )e - 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (- 24570A a b - 24570B a b)e + (- 17010A b - 51030B a b )d e +--R + +--R 3 2 5 +--R - 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (- 30030A a b - 10010B a )e + (- 62790A a b - 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 11130A b - 33390B a b )d e - 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R - 12870A a e + (- 81510A a b - 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 44070A a b - 44070B a b)d e + (- 150A b - 450B a b )d e +--R + +--R 3 4 3 +--R 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 38610A a d e + (- 64350A a b - 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 1170A a b - 1170B a b)d e + (180A b + 540B a b )d e +--R + +--R 3 5 2 +--R - 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 38610A a d e + (- 4290A a b - 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1560A a b + 1560B a b)d e + (- 240A b - 720B a b )d e +--R + +--R 3 6 +--R 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 12870A a d e + (8580A a b + 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 3120A a b - 3120B a b)d e + (480A b + 1440B a b )d e - 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 4 7 8 4 3 7 4 6 7 +--R 6006B b e x + ((6930A b + 26796B a b )e + 14322B b d e )x +--R + +--R 3 2 2 7 4 3 6 +--R (31500A a b + 45360B a b )e + (17010A b + 65352B a b )d e +--R + +--R 4 2 5 +--R 8946B b d e +--R * +--R 6 +--R x +--R + +--R 2 2 3 7 3 2 2 6 +--R (54600A a b + 34580B a b)e + (79800A a b + 113820B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (11130A b + 42336B a b )d e + 70B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (42900A a b + 10010B a )e + (144300A a b + 89960B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 +--R (55200A a b + 77460B a b )d e + (150A b + 520B a b )d e +--R + +--R 4 4 3 +--R - 80B b d e +--R * +--R 4 +--R x +--R + +--R 4 7 3 4 6 +--R 12870A a e + (120120A a b + 27170B a )d e +--R + +--R 2 2 3 2 5 3 2 2 3 4 +--R (108420A a b + 65520B a b)d e + (1320A a b + 1620B a b )d e +--R + +--R 4 3 4 3 4 5 2 +--R (- 180A b - 620B a b )d e + 96B b d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 4 2 5 +--R 38610A a d e + (102960A a b + 21450B a )d e +--R + +--R 2 2 3 3 4 3 2 2 4 3 +--R (5460A a b + 2600B a b)d e + (- 1740A a b - 2100B a b )d e +--R + +--R 4 3 5 2 4 6 +--R (240A b + 816B a b )d e - 128B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 4 3 4 +--R 38610A a d e + (17160A a b + 1430B a )d e +--R + +--R 2 2 3 4 3 3 2 2 5 2 +--R (- 10140A a b - 4420B a b)d e + (3360A a b + 3840B a b )d e +--R + +--R 4 3 6 4 7 +--R (- 480A b - 1568B a b )d e + 256B b d +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (3120A a b + 3120B a b)d e + (- 480A a b - 1440B a b )d e +--R + +--R 3 7 +--R 256B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 3 7 3 2 3 3 2 6 +--R B b e x + ((A b + 3B a b )e + 3B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 5 +--R ((3A a b + 3B a b)e + (3A b + 9B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b + B a )e + (9A a b + 9B a b)d e + (3A b + 9B a b )d e +--R + +--R 3 3 +--R B b d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R A a e + (9A a b + 3B a )d e + (9A a b + 9B a b)d e +--R + +--R 3 2 3 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 3 2 +--R (3A a d e + (9A a b + 3B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 2 3 3 3 3 +--R (3A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 8 4 3 3 4 2 7 +--R - B b e x + ((- A b - 4B a b )e - 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((- 4A a b - 6B a b )e + (- 3A b - 12B a b )d e - 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 6A a b - 4B a b)e + (- 12A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 3A b - 12B a b )d e - B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 4A a b - B a )e + (- 18A a b - 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 12A a b - 18B a b )d e + (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R - A a e + (- 12A a b - 3B a )d e + (- 18A a b - 12B a b)d e +--R + +--R 3 2 2 3 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (- 3A a d e + (- 12A a b - 3B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (- 3A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1139 + +)clear all + +--S 1140 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1378 +r0:=-2/143*(8*b*B*d-13*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/13*B*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/3003*(b*d-a*e)^2*(8*b*B*d-13*A*b*e+5*a*B*e)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/15015*(b*d-a*e)^3*_ + (8*b*B*d-13*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/429*(b*d-a*e)*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 6 6 3 2 6 3 5 5 +--R 2310B b e x + ((2730A b + 8190B a b )e + 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (10010A a b + 10010B a b)e + (3640A b + 10920B a b )d e +--R + +--R 3 2 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (12870A a b + 4290B a )e + (14300A a b + 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (130A b + 390B a b )d e - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R 6006A a e + (20592A a b + 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 3 4 2 +--R (858A a b + 858B a b)d e + (- 156A b - 468B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R 12012A a d e + (2574A a b + 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 1144A a b - 1144B a b)d e + (208A b + 624B a b )d e +--R + +--R 3 5 +--R - 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (2288A a b + 2288B a b)d e + (- 416A b - 1248B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 3 2 6 3 5 5 +--R 2310B b e x + ((2730A b + 8190B a b )e + 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (10010A a b + 10010B a b)e + (3640A b + 10920B a b )d e +--R + +--R 3 2 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (12870A a b + 4290B a )e + (14300A a b + 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (130A b + 390B a b )d e - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R 6006A a e + (20592A a b + 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 3 4 2 +--R (858A a b + 858B a b)d e + (- 156A b - 468B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R 12012A a d e + (2574A a b + 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 1144A a b - 1144B a b)d e + (208A b + 624B a b )d e +--R + +--R 3 5 +--R - 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (2288A a b + 2288B a b)d e + (- 416A b - 1248B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 15015e +--R Type: Union(Expression(Integer),...) +--E 1142 + +--S 1143 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 6 6 3 2 6 3 5 5 +--R - 2310B b e x + ((- 2730A b - 8190B a b )e - 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (- 10010A a b - 10010B a b)e + (- 3640A b - 10920B a b )d e +--R + +--R 3 2 4 +--R - 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (- 12870A a b - 4290B a )e + (- 14300A a b - 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (- 130A b - 390B a b )d e + 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R - 6006A a e + (- 20592A a b - 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 +--R (- 858A a b - 858B a b)d e + (156A b + 468B a b )d e +--R + +--R 3 4 2 +--R - 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R - 12012A a d e + (- 2574A a b - 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (1144A a b + 1144B a b)d e + (- 208A b - 624B a b )d e +--R + +--R 3 5 +--R 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R - 6006A a d e + (5148A a b + 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (- 2288A a b - 2288B a b)d e + (416A b + 1248B a b )d e - 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 4 6 7 4 3 6 4 5 6 +--R 2310B b e x + ((2730A b + 10500B a b )e + 2940B b d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (12740A a b + 18200B a b )e + (3640A b + 13860B a b )d e +--R + +--R 4 2 4 +--R 70B b d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (22880A a b + 14300B a b)e + (17940A a b + 25220B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (130A b + 460B a b )d e - 80B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (18876A a b + 4290B a )e + (34892A a b + 21164B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (988A a b + 1248B a b )d e + (- 156A b - 548B a b )d e +--R + +--R 4 4 2 +--R 96B b d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 4 5 +--R 6006A a e + (32604A a b + 6864B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (3432A a b + 1716B a b)d e + (- 1300A a b - 1612B a b )d e +--R + +--R 4 3 4 2 4 5 +--R (208A b + 720B a b )d e - 128B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 4 +--R 12012A a d e + (8580A a b + 858B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (- 6292A a b - 2860B a b)d e + (2496A a b + 2912B a b )d e +--R + +--R 4 3 5 4 6 +--R (- 416A b - 1376B a b )d e + 256B b d +--R * +--R x +--R + +--R 4 2 4 3 4 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 3 4 2 3 2 2 5 +--R (2288A a b + 2288B a b)d e + (- 416A a b - 1248B a b )d e +--R + +--R 3 6 +--R 256B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 2 6 3 2 2 3 5 +--R B b e x + ((A b + 3B a b )e + 2B b d e)x +--R + +--R 2 2 2 3 2 3 2 4 +--R ((3A a b + 3B a b)e + (2A b + 6B a b )d e + B b d )x +--R + +--R 2 3 2 2 2 3 2 2 3 +--R ((3A a b + B a )e + (6A a b + 6B a b)d e + (A b + 3B a b )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (A a e + (6A a b + 2B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 3 2 3 2 +--R (2A a d e + (3A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 2 7 4 3 2 4 6 +--R - B b e x + ((- A b - 4B a b )e - 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((- 4A a b - 6B a b )e + (- 2A b - 8B a b )d e - B b d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 6A a b - 4B a b)e + (- 8A a b - 12B a b )d e +--R + +--R 4 3 2 +--R (- A b - 4B a b )d +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 4A a b - B a )e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 2 +--R (- 4A a b - 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- A a e + (- 8A a b - 2B a )d e + (- 6A a b - 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (- 2A a d e + (- 4A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1144 + +)clear all + +--S 1145 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1378 +r0:=-2/99*(8*b*B*d-11*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/11*B*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/1155*(b*d-a*e)^2*(8*b*B*d-11*A*b*e+3*a*B*e)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/3465*(b*d-a*e)^3*_ + (8*b*B*d-11*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/231*(b*d-a*e)*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 5 5 3 2 5 3 4 4 +--R 630B b e x + ((770A b + 2310B a b )e + 70B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((2970A a b + 2970B a b)e + (110A b + 330B a b )d e - 80B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (4158A a b + 1386B a )e + (594A a b + 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 132A b - 396B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R 2310A a e + (1386A a b + 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R (- 792A a b - 792B a b)d e + (176A b + 528B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (1584A a b + 1584B a b)d e + (- 352A b - 1056B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 3 2 5 3 4 4 +--R 630B b e x + ((770A b + 2310B a b )e + 70B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((2970A a b + 2970B a b)e + (110A b + 330B a b )d e - 80B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (4158A a b + 1386B a )e + (594A a b + 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 132A b - 396B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R 2310A a e + (1386A a b + 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R (- 792A a b - 792B a b)d e + (176A b + 528B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (1584A a b + 1584B a b)d e + (- 352A b - 1056B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 1147 + +--S 1148 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 5 5 3 2 5 3 4 4 +--R - 630B b e x + ((- 770A b - 2310B a b )e - 70B b d e )x +--R + +--R 2 2 5 3 2 4 +--R (- 2970A a b - 2970B a b)e + (- 110A b - 330B a b )d e +--R + +--R 3 2 3 +--R 80B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 4 +--R (- 4158A a b - 1386B a )e + (- 594A a b - 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (132A b + 396B a b )d e - 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R - 2310A a e + (- 1386A a b - 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 +--R (792A a b + 792B a b)d e + (- 176A b - 528B a b )d e +--R + +--R 3 4 +--R 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R - 2310A a d e + (2772A a b + 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (- 1584A a b - 1584B a b)d e + (352A b + 1056B a b )d e - 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 4 5 6 4 3 5 4 4 5 +--R 630B b e x + ((770A b + 2940B a b )e + 70B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (3740A a b + 5280B a b )e + (110A b + 400B a b )d e +--R + +--R 4 2 3 +--R - 80B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (7128A a b + 4356B a b)e + (704A a b + 924B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 132A b - 476B a b )d e + 96B b d e +--R * +--R 3 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (6468A a b + 1386B a )e + (1980A a b + 1056B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 924A a b - 1188B a b )d e + (176A b + 624B a b )d e +--R + +--R 4 4 +--R - 128B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 4 +--R 2310A a e + (3696A a b + 462B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 3564A a b - 1716B a b)d e + (1760A a b + 2112B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 352A b - 1184B a b )d e + 256B b d +--R * +--R x +--R + +--R 4 4 3 4 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (1584A a b + 1584B a b)d e + (- 352A a b - 1056B a b )d e +--R + +--R 3 5 +--R 256B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 5 3 2 3 4 +--R B b e x + ((A b + 3B a b )e + B b d)x +--R + +--R 2 2 3 2 3 +--R ((3A a b + 3B a b)e + (A b + 3B a b )d)x +--R + +--R 2 3 2 2 2 +--R ((3A a b + B a )e + (3A a b + 3B a b)d)x +--R + +--R 3 2 3 3 +--R (A a e + (3A a b + B a )d)x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 4 5 +--R - B b e x + ((- A b - 4B a b )e - B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((- 4A a b - 6B a b )e + (- A b - 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 6A a b - 4B a b)e + (- 4A a b - 6B a b )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 4A a b - B a )e + (- 6A a b - 4B a b)d)x +--R + +--R 4 3 4 4 +--R (- A a e + (- 4A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1149 + +)clear all + +--S 1150 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1378 +r0:=-2/63*(8*b*B*d-9*A*b*e+a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(b*e^2)+2/9*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(b*e)-16/315*(b*d-a*e)^2*(8*b*B*d-9*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/315*(b*d-a*e)^3*_ + (8*b*B*d-9*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/105*(b*d-a*e)*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((90A b + 270B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((378A a b + 378B a b)e + (- 108A b - 324B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (630A a b + 210B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (144A b + 432B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 630A a e + (- 1260A a b - 420B a )d e + (1008A a b + 1008B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 288A b - 864B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((90A b + 270B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((378A a b + 378B a b)e + (- 108A b - 324B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (630A a b + 210B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (144A b + 432B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 630A a e + (- 1260A a b - 420B a )d e + (1008A a b + 1008B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 288A b - 864B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 1152 + +--S 1153 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R - 70B b e x + ((- 90A b - 270B a b )e + 80B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 378A a b - 378B a b)e + (108A b + 324B a b )d e +--R + +--R 3 2 2 +--R - 96B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 630A a b - 210B a )e + (504A a b + 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 144A b - 432B a b )d e + 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 +--R - 630A a e + (1260A a b + 420B a )d e +--R + +--R 2 2 2 2 3 2 3 3 4 +--R (- 1008A a b - 1008B a b)d e + (288A b + 864B a b )d e - 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R 70B b e x + ((90A b + 340B a b )e - 80B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (468A a b + 648B a b )e + (- 108A b - 404B a b )d e +--R + +--R 4 2 2 +--R 96B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (1008A a b + 588B a b)e + (- 612A a b - 828B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (144A b + 528B a b )d e - 128B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (1260A a b + 210B a )e + (- 1764A a b - 924B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1152A a b + 1440B a b )d e + (- 288A b - 992B a b )d e +--R + +--R 4 4 +--R 256B b d +--R * +--R x +--R + +--R 4 4 3 4 3 +--R 630A a e + (- 1260A a b - 420B a )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (1008A a b + 1008B a b)d e + (- 288A a b - 864B a b )d e +--R + +--R 3 4 +--R 256B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1154 + +)clear all + +--S 1155 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1378 +r0:=-2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+2/7*(8*b*B*d-7*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(e^2*(b*d-a*e))+16/35*(b*d-a*e)*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-32/35*(b*d-a*e)^2*(8*b*B*d-_ + 7*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-_ + 12/35*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^3 +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((14A b + 42B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((70A a b + 70B a b)e + (- 28A b - 84B a b )d e + 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (210A a b + 70B a )e + (- 280A a b - 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (112A b + 336B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (224A b + 672B a b )d e - 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((14A b + 42B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((70A a b + 70B a b)e + (- 28A b - 84B a b )d e + 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (210A a b + 70B a )e + (- 280A a b - 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (112A b + 336B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (224A b + 672B a b )d e - 256B b d +--R / +--R 5 +-------+ +--R 35e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1157 + +--S 1158 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R - 10B b e x + ((- 14A b - 42B a b )e + 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 70A a b - 70B a b)e + (28A b + 84B a b )d e - 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 210A a b - 70B a )e + (280A a b + 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 112A b - 336B a b )d e + 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 70A a e + (- 420A a b - 140B a )d e + (560A a b + 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 224A b - 672B a b )d e + 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R 10B b e x + ((14A b + 52B a b )e - 16B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((84A a b + 112B a b )e + (- 28A b - 100B a b )d e + 32B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (280A a b + 140B a b)e + (- 308A a b - 364B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (112A b + 368B a b )d e - 128B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (140A a b + 70B a )e + (140A a b - 140B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 448A a b - 224B a b )d e + (224A b + 544B a b )d e - 256B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (224A a b + 672B a b )d e - 256B a b d +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1159 + +)clear all + +--S 1160 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))-2/3*(8*b*B*d-5*A*b*e-3*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*sqrt(d+e*x))-16/15*b*(8*b*B*d-5*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+32/15*b*(b*d-a*e)*_ + (8*b*B*d-5*A*b*e-3*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x))+4/5*b*(8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((10A b + 30B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((90A a b + 90B a b)e + (- 60A b - 180B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 90A a b - 30B a )e + (360A a b + 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 160A b - 480B a b )d e + 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((10A b + 30B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((90A a b + 90B a b)e + (- 60A b - 180B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 90A a b - 30B a )e + (360A a b + 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 160A b - 480B a b )d e + 256B b d +--R / +--R 6 5 +-------+ +--R (15e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1162 + +--S 1163 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R - 6B b e x + ((- 10A b - 30B a b )e + 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (60A b + 180B a b )d e - 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (90A a b + 30B a )e + (- 360A a b - 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 10A a e + (60A a b + 20B a )d e + (- 240A a b - 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (160A b + 480B a b )d e - 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R 6B b e x + ((10A b + 36B a b )e - 16B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((100A a b + 120B a b )e + (- 60A b - 196B a b )d e + 96B b d e )x +--R + +--R 3 4 3 2 2 3 +--R 60B a b e + (300A a b + 180B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 240A b - 624B a b )d e + 384B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R (- 100A a b - 30B a )e + (300A a b + 340B a b)d e - 480B a b d e +--R + +--R 4 3 3 4 4 +--R (- 160A b - 96B a b )d e + 256B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (- 160A a b - 480B a b )d e + 256B a b d +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1164 + +)clear all + +--S 1165 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1378 +r0:=-2/5*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/15*(8*b*B*d-3*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/5*b*(8*b*B*d-_ + 3*A*b*e-5*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*_ + sqrt(d+e*x))+16/15*b^2*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(b*d-a*e))-32/15*b^2*(8*b*B*d-3*A*b*e-_ + 5*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((30A b + 90B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (180A b + 540B a b )d e - 480B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 30A a b - 10B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (96A b + 288B a b )d e - 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((30A b + 90B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (180A b + 540B a b )d e - 480B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 30A a b - 10B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (96A b + 288B a b )d e - 256B b d +--R / +--R 7 2 6 2 5 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1167 + +--S 1168 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 2 4 3 3 3 +--R - 10B b e x + ((- 30A b - 90B a b )e + 80B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (90A a b + 90B a b)e + (- 180A b - 540B a b )d e +--R + +--R 3 2 2 +--R 480B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (30A a b + 10B a )e + (120A a b + 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 6A a e + (12A a b + 4B a )d e + (48A a b + 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 96A b - 288B a b )d e + 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 4 3 4 4 3 4 +--R 10B b e x + ((30A b + 100B a b )e - 80B b d e )x +--R + +--R 3 4 4 3 3 4 2 2 3 +--R (- 60A a b e + (180A b + 460B a b )d e - 480B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 120A a b - 100B a b)e + (60A a b + 420B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (240A b + 240B a b )d e - 640B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 36A a b - 10B a )e + (- 132A a b - 124B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (192A a b + 672B a b )d e + (96A b - 352B a b )d e - 256B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (96A a b + 288B a b )d e - 256B a b d +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1378 +r0:=-32/6783*(b*d-a*e)^2*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+20/2261*(b*d-a*e)*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-_ + 2/133*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/21*B*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/323323*(b*d-a*e)^4*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/2909907*(b*d-a*e)^5*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/29393*(b*d-a*e)^3*_ + (4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 10 10 5 4 10 5 9 9 +--R 277134B b e x + ((306306A b + 1531530B a b )e + 933504B b d e )x +--R + +--R 4 2 3 10 +--R (1711710A a b + 3423420B a b )e +--R + +--R 5 4 9 5 2 8 +--R (1045044A b + 5225220B a b )d e + 1065636B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 3 2 10 +--R (3879876A a b + 3879876B a b )e +--R + +--R 4 2 3 9 +--R (5933928A a b + 11867856B a b )d e +--R + +--R 5 4 2 8 5 3 7 +--R (1213212A b + 6066060B a b )d e + 415272B b d e +--R * +--R 7 +--R x +--R + +--R 3 2 4 10 +--R (4476780A a b + 2238390B a b)e +--R + +--R 2 3 3 2 9 +--R (13728792A a b + 13728792B a b )d e +--R + +--R 4 2 3 2 8 +--R (7039956A a b + 14079912B a b )d e +--R + +--R 5 4 3 7 5 4 6 +--R (484176A b + 2420880B a b )d e + 462B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 10 +--R (2645370A a b + 529074B a )e +--R + +--R 3 2 4 9 +--R (16279200A a b + 8139600B a b)d e +--R + +--R 2 3 3 2 2 8 +--R (16767576A a b + 16767576B a b )d e +--R + +--R 4 2 3 3 7 5 4 4 6 +--R (2901528A a b + 5803056B a b )d e + (882A b + 4410B a b )d e +--R + +--R 5 5 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 5 10 4 5 9 +--R 646646A a e + (9993620A a b + 1998724B a )d e +--R + +--R 3 2 4 2 8 +--R (20710760A a b + 10355380B a b)d e +--R + +--R 2 3 3 2 3 7 +--R (7235200A a b + 7235200B a b )d e +--R + +--R 4 2 3 4 6 5 4 5 5 +--R (9310A a b + 18620B a b )d e + (- 980A b - 4900B a b )d e +--R + +--R 5 6 4 +--R 560B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 2 8 +--R 2586584A a d e + (13520780A a b + 2704156B a )d e +--R + +--R 3 2 4 3 7 +--R (9586640A a b + 4793320B a b)d e +--R + +--R 2 3 3 2 4 6 4 2 3 5 5 +--R (45220A a b + 45220B a b )d e + (- 10640A a b - 21280B a b )d e +--R + +--R 5 4 6 4 5 7 3 +--R (1120A b + 5600B a b )d e - 640B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 8 4 5 3 7 +--R 3879876A a d e + (7054320A a b + 1410864B a )d e +--R + +--R 3 2 4 4 6 2 3 3 2 5 5 +--R (135660A a b + 67830B a b)d e + (- 54264A a b - 54264B a b )d e +--R + +--R 4 2 3 6 4 5 4 7 3 +--R (12768A a b + 25536B a b )d e + (- 1344A b - 6720B a b )d e +--R + +--R 5 8 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 3 7 4 5 4 6 +--R 2586584A a d e + 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b)d e +--R + +--R 3 3 4 2 4 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 2 5 6 3 4 2 5 4 2 +--R (- 6A a d e + (- 24A a b - 4B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 3 5 6 4 6 4 +--R (- 4A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1378 +r0:=-32/12597*(b*d-a*e)^2*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+4/969*(b*d-a*e)*(12*b*B*d-19*A*b*e+_ + 7*a*B*e)*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-_ + 2/323*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/19*B*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/415701*(b*d-a*e)^4*(12*b*B*d-19*A*b*e+_ + 7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/2909907*(b*d-a*e)^5*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/46189*(b*d-a*e)^3*_ + (12*b*B*d-19*A*b*e+7*a*B*e)*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 9 9 5 4 9 5 8 8 +--R 306306B b e x + ((342342A b + 1711710B a b )e + 702702B b d e )x +--R + +--R 4 2 3 9 +--R (1939938A a b + 3879876B a b )e +--R + +--R 5 4 8 5 2 7 +--R (798798A b + 3993990B a b )d e + 414414B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 3 2 9 +--R (4476780A a b + 4476780B a b )e +--R + +--R 4 2 3 8 +--R (4626006A a b + 9252012B a b )d e +--R + +--R 5 4 2 7 5 3 6 +--R (482790A b + 2413950B a b )d e + 1386B b d e +--R * +--R 6 +--R x +--R + +--R 3 2 4 9 +--R (5290740A a b + 2645370B a b)e +--R + +--R 2 3 3 2 8 +--R (10988460A a b + 10988460B a b )d e +--R + +--R 4 2 3 2 7 5 4 3 6 +--R (2889558A a b + 5779116B a b )d e + (2394A b + 11970B a b )d e +--R + +--R 5 4 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 4 5 9 3 2 4 8 +--R (3233230A a b + 646646B a )e + (13520780A a b + 6760390B a b)d e +--R + +--R 2 3 3 2 2 7 +--R (7189980A a b + 7189980B a b )d e +--R + +--R 4 2 3 3 6 5 4 4 5 +--R (22610A a b + 45220B a b )d e + (- 2660A b - 13300B a b )d e +--R + +--R 5 5 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 8 +--R 831402A a e + (8775910A a b + 1755182B a )d e +--R + +--R 3 2 4 2 7 +--R (9489740A a b + 4744870B a b)d e +--R + +--R 2 3 3 2 3 6 4 2 3 4 5 +--R (96900A a b + 96900B a b )d e + (- 25840A a b - 51680B a b )d e +--R + +--R 5 4 5 4 5 6 3 +--R (3040A b + 15200B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 2 7 +--R 2494206A a d e + (6928350A a b + 1385670B a )d e +--R + +--R 3 2 4 3 6 +--R (251940A a b + 125970B a b)d e +--R + +--R 2 3 3 2 4 5 +--R (- 116280A a b - 116280B a b )d e +--R + +--R 4 2 3 5 4 5 4 6 3 +--R (31008A a b + 62016B a b )d e + (- 3648A b - 18240B a b )d e +--R + +--R 5 7 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 7 4 5 3 6 +--R 2494206A a d e + (461890A a b + 92378B a )d e +--R + +--R 3 2 4 4 5 +--R (- 335920A a b - 167960B a b)d e +--R + +--R 2 3 3 2 5 4 +--R (155040A a b + 155040B a b )d e +--R + +--R 4 2 3 6 3 5 4 7 2 +--R (- 41344A a b - 82688B a b )d e + (4864A b + 24320B a b )d e +--R + +--R 5 8 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 3 6 4 5 4 5 +--R 831402A a d e + (- 923780A a b - 184756B a )d e +--R + +--R 3 2 4 5 4 2 3 3 2 6 3 +--R (671840A a b + 335920B a b)d e + (- 310080A a b - 310080B a b )d e +--R + +--R 4 2 3 7 2 5 4 8 +--R (82688A a b + 165376B a b )d e + (- 9728A b - 48640B a b )d e +--R + +--R 5 9 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 2909907b e x + 2909907a e +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 9 9 5 4 9 5 8 8 +--R 306306B b e x + ((342342A b + 1711710B a b )e + 702702B b d e )x +--R + +--R 4 2 3 9 +--R (1939938A a b + 3879876B a b )e +--R + +--R 5 4 8 5 2 7 +--R (798798A b + 3993990B a b )d e + 414414B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 3 2 9 +--R (4476780A a b + 4476780B a b )e +--R + +--R 4 2 3 8 +--R (4626006A a b + 9252012B a b )d e +--R + +--R 5 4 2 7 5 3 6 +--R (482790A b + 2413950B a b )d e + 1386B b d e +--R * +--R 6 +--R x +--R + +--R 3 2 4 9 +--R (5290740A a b + 2645370B a b)e +--R + +--R 2 3 3 2 8 +--R (10988460A a b + 10988460B a b )d e +--R + +--R 4 2 3 2 7 5 4 3 6 +--R (2889558A a b + 5779116B a b )d e + (2394A b + 11970B a b )d e +--R + +--R 5 4 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 4 5 9 3 2 4 8 +--R (3233230A a b + 646646B a )e + (13520780A a b + 6760390B a b)d e +--R + +--R 2 3 3 2 2 7 +--R (7189980A a b + 7189980B a b )d e +--R + +--R 4 2 3 3 6 5 4 4 5 +--R (22610A a b + 45220B a b )d e + (- 2660A b - 13300B a b )d e +--R + +--R 5 5 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 8 +--R 831402A a e + (8775910A a b + 1755182B a )d e +--R + +--R 3 2 4 2 7 +--R (9489740A a b + 4744870B a b)d e +--R + +--R 2 3 3 2 3 6 4 2 3 4 5 +--R (96900A a b + 96900B a b )d e + (- 25840A a b - 51680B a b )d e +--R + +--R 5 4 5 4 5 6 3 +--R (3040A b + 15200B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 2 7 +--R 2494206A a d e + (6928350A a b + 1385670B a )d e +--R + +--R 3 2 4 3 6 +--R (251940A a b + 125970B a b)d e +--R + +--R 2 3 3 2 4 5 +--R (- 116280A a b - 116280B a b )d e +--R + +--R 4 2 3 5 4 5 4 6 3 +--R (31008A a b + 62016B a b )d e + (- 3648A b - 18240B a b )d e +--R + +--R 5 7 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 7 4 5 3 6 +--R 2494206A a d e + (461890A a b + 92378B a )d e +--R + +--R 3 2 4 4 5 +--R (- 335920A a b - 167960B a b)d e +--R + +--R 2 3 3 2 5 4 +--R (155040A a b + 155040B a b )d e +--R + +--R 4 2 3 6 3 5 4 7 2 +--R (- 41344A a b - 82688B a b )d e + (4864A b + 24320B a b )d e +--R + +--R 5 8 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 3 6 4 5 4 5 +--R 831402A a d e + (- 923780A a b - 184756B a )d e +--R + +--R 3 2 4 5 4 2 3 3 2 6 3 +--R (671840A a b + 335920B a b)d e + (- 310080A a b - 310080B a b )d e +--R + +--R 4 2 3 7 2 5 4 8 +--R (82688A a b + 165376B a b )d e + (- 9728A b - 48640B a b )d e +--R + +--R 5 9 +--R 6144B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 2909907e +--R Type: Union(Expression(Integer),...) +--E 1177 + +--S 1178 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 9 9 +--R - 306306B b e x +--R + +--R 5 4 9 5 8 8 +--R ((- 342342A b - 1711710B a b )e - 702702B b d e )x +--R + +--R 4 2 3 9 +--R (- 1939938A a b - 3879876B a b )e +--R + +--R 5 4 8 5 2 7 +--R (- 798798A b - 3993990B a b )d e - 414414B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 3 2 9 +--R (- 4476780A a b - 4476780B a b )e +--R + +--R 4 2 3 8 +--R (- 4626006A a b - 9252012B a b )d e +--R + +--R 5 4 2 7 5 3 6 +--R (- 482790A b - 2413950B a b )d e - 1386B b d e +--R * +--R 6 +--R x +--R + +--R 3 2 4 9 +--R (- 5290740A a b - 2645370B a b)e +--R + +--R 2 3 3 2 8 +--R (- 10988460A a b - 10988460B a b )d e +--R + +--R 4 2 3 2 7 +--R (- 2889558A a b - 5779116B a b )d e +--R + +--R 5 4 3 6 5 4 5 +--R (- 2394A b - 11970B a b )d e + 1512B b d e +--R * +--R 5 +--R x +--R + +--R 4 5 9 +--R (- 3233230A a b - 646646B a )e +--R + +--R 3 2 4 8 +--R (- 13520780A a b - 6760390B a b)d e +--R + +--R 2 3 3 2 2 7 +--R (- 7189980A a b - 7189980B a b )d e +--R + +--R 4 2 3 3 6 5 4 4 5 +--R (- 22610A a b - 45220B a b )d e + (2660A b + 13300B a b )d e +--R + +--R 5 5 4 +--R - 1680B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 8 +--R - 831402A a e + (- 8775910A a b - 1755182B a )d e +--R + +--R 3 2 4 2 7 +--R (- 9489740A a b - 4744870B a b)d e +--R + +--R 2 3 3 2 3 6 +--R (- 96900A a b - 96900B a b )d e +--R + +--R 4 2 3 4 5 5 4 5 4 +--R (25840A a b + 51680B a b )d e + (- 3040A b - 15200B a b )d e +--R + +--R 5 6 3 +--R 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 2 7 +--R - 2494206A a d e + (- 6928350A a b - 1385670B a )d e +--R + +--R 3 2 4 3 6 +--R (- 251940A a b - 125970B a b)d e +--R + +--R 2 3 3 2 4 5 +--R (116280A a b + 116280B a b )d e +--R + +--R 4 2 3 5 4 5 4 6 3 +--R (- 31008A a b - 62016B a b )d e + (3648A b + 18240B a b )d e +--R + +--R 5 7 2 +--R - 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 7 4 5 3 6 +--R - 2494206A a d e + (- 461890A a b - 92378B a )d e +--R + +--R 3 2 4 4 5 +--R (335920A a b + 167960B a b)d e +--R + +--R 2 3 3 2 5 4 +--R (- 155040A a b - 155040B a b )d e +--R + +--R 4 2 3 6 3 5 4 7 2 +--R (41344A a b + 82688B a b )d e + (- 4864A b - 24320B a b )d e +--R + +--R 5 8 +--R 3072B b d e +--R * +--R x +--R + +--R 5 3 6 4 5 4 5 +--R - 831402A a d e + (923780A a b + 184756B a )d e +--R + +--R 3 2 4 5 4 +--R (- 671840A a b - 335920B a b)d e +--R + +--R 2 3 3 2 6 3 +--R (310080A a b + 310080B a b )d e +--R + +--R 4 2 3 7 2 5 4 8 +--R (- 82688A a b - 165376B a b )d e + (9728A b + 48640B a b )d e +--R + +--R 5 9 +--R - 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 6 9 10 6 5 9 6 8 9 +--R 306306B b e x + ((342342A b + 2018016B a b )e + 702702B b d e )x +--R + +--R 5 2 4 9 +--R (2282280A a b + 5591586B a b )e +--R + +--R 6 5 8 6 2 7 +--R (798798A b + 4696692B a b )d e + 414414B b d e +--R * +--R 8 +--R x +--R + +--R 2 4 3 3 9 +--R (6416718A a b + 8356656B a b )e +--R + +--R 5 2 4 8 +--R (5424804A a b + 13246002B a b )d e +--R + +--R 6 5 2 7 6 3 6 +--R (482790A b + 2828364B a b )d e + 1386B b d e +--R * +--R 7 +--R x +--R + +--R 3 3 4 2 9 +--R (9767520A a b + 7122150B a b )e +--R + +--R 2 4 3 3 8 +--R (15614466A a b + 20240472B a b )d e +--R + +--R 5 2 4 2 7 +--R (3372348A a b + 8193066B a b )d e +--R + +--R 6 5 3 6 6 4 5 +--R (2394A b + 13356B a b )d e - 1512B b d e +--R * +--R 6 +--R x +--R + +--R 4 2 5 9 +--R (8523970A a b + 3292016B a b)e +--R + +--R 3 3 4 2 8 +--R (24509240A a b + 17748850B a b )d e +--R + +--R 2 4 3 3 2 7 +--R (10079538A a b + 12969096B a b )d e +--R + +--R 5 2 4 3 6 6 5 4 5 +--R (25004A a b + 57190B a b )d e + (- 2660A b - 14812B a b )d e +--R + +--R 6 5 4 +--R 1680B b d e +--R * +--R 5 +--R x +--R + +--R 5 6 9 +--R (4064632A a b + 646646B a )e +--R + +--R 4 2 5 8 +--R (22296690A a b + 8515572B a b)d e +--R + +--R 3 3 4 2 2 7 +--R (16679720A a b + 11934850B a b )d e +--R + +--R 2 4 3 3 3 6 +--R (119510A a b + 142120B a b )d e +--R + +--R 5 2 4 4 5 6 5 5 4 +--R (- 28500A a b - 64980B a b )d e + (3040A b + 16880B a b )d e +--R + +--R 6 6 3 +--R - 1920B b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 6 8 +--R 831402A a e + (11270116A a b + 1755182B a )d e +--R + +--R 4 2 5 2 7 +--R (16418090A a b + 6130540B a b)d e +--R + +--R 3 3 4 2 3 6 +--R (348840A a b + 222870B a b )d e +--R + +--R 2 4 3 3 4 5 +--R (- 142120A a b - 167960B a b )d e +--R + +--R 5 2 4 5 4 6 5 6 3 +--R (34048A a b + 77216B a b )d e + (- 3648A b - 20160B a b )d e +--R + +--R 6 7 2 +--R 2304B b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 6 2 7 +--R 2494206A a d e + (9422556A a b + 1385670B a )d e +--R + +--R 4 2 5 3 6 +--R (713830A a b + 218348B a b)d e +--R + +--R 3 3 4 2 4 5 +--R (- 452200A a b - 284240B a b )d e +--R + +--R 2 4 3 3 5 4 +--R (186048A a b + 217056B a b )d e +--R + +--R 5 2 4 6 3 6 5 7 2 +--R (- 44992A a b - 100928B a b )d e + (4864A b + 26624B a b )d e +--R + +--R 6 8 +--R - 3072B b d e +--R * +--R 2 +--R x +--R + +--R 6 2 7 5 6 3 6 +--R 2494206A a d e + (1293292A a b + 92378B a )d e +--R + +--R 4 2 5 4 5 +--R (- 1259700A a b - 352716B a b)d e +--R + +--R 3 3 4 2 5 4 +--R (826880A a b + 490960B a b )d e +--R + +--R 2 4 3 3 6 3 +--R (- 351424A a b - 392768B a b )d e +--R + +--R 5 2 4 7 2 6 5 8 +--R (87552A a b + 189696B a b )d e + (- 9728A b - 51712B a b )d e +--R + +--R 6 9 +--R 6144B b d +--R * +--R x +--R + +--R 6 3 6 5 6 4 5 +--R 831402A a d e + (- 923780A a b - 184756B a )d e +--R + +--R 4 2 5 5 4 +--R (671840A a b + 335920B a b)d e +--R + +--R 3 3 4 2 6 3 +--R (- 310080A a b - 310080B a b )d e +--R + +--R 2 4 3 3 7 2 5 2 4 8 +--R (82688A a b + 165376B a b )d e + (- 9728A a b - 48640B a b )d e +--R + +--R 5 9 +--R 6144B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 2909907b e x + 2909907a e +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 3 9 5 4 3 5 2 8 +--R B b e x + ((A b + 5B a b )e + 3B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 7 +--R ((5A a b + 10B a b )e + (3A b + 15B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (10A a b + 10B a b )e + (15A a b + 30B a b )d e +--R + +--R 5 4 2 5 3 +--R (3A b + 15B a b )d e + B b d +--R * +--R 6 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (10A a b + 5B a b)e + (30A a b + 30B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (15A a b + 30B a b )d e + (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (5A a b + B a )e + (30A a b + 15B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (30A a b + 30B a b )d e + (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A a e + (15A a b + 3B a )d e + (30A a b + 15B a b)d e +--R + +--R 2 3 3 2 3 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 5 2 3 2 4 3 2 +--R (3A a d e + (15A a b + 3B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 2 4 5 3 5 3 +--R (3A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 3 10 6 5 3 6 2 9 +--R - B b e x + ((- A b - 6B a b )e - 3B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 8 +--R ((- 6A a b - 15B a b )e + (- 3A b - 18B a b )d e - 3B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (- 15A a b - 20B a b )e + (- 18A a b - 45B a b )d e +--R + +--R 6 5 2 6 3 +--R (- 3A b - 18B a b )d e - B b d +--R * +--R 7 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (- 20A a b - 15B a b )e + (- 45A a b - 60B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 18A a b - 45B a b )d e + (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 15A a b - 6B a b)e + (- 60A a b - 45B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 45A a b - 60B a b )d e + (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 6A a b - B a )e + (- 45A a b - 18B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A a b - 45B a b )d e + (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R - A a e + (- 18A a b - 3B a )d e + (- 45A a b - 18B a b)d e +--R + +--R 3 3 4 2 3 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 2 4 2 5 3 2 +--R (- 3A a d e + (- 18A a b - 3B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 2 5 6 3 6 3 +--R (- 3A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1179 + +)clear all + +--S 1180 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1378 +r0:=-32/7293*(b*d-a*e)^2*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+4/663*(b*d-a*e)*(12*b*B*d-_ + 17*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^3)-2/255*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/17*B*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/153153*(b*d-a*e)^4*(12*b*B*d-17*A*b*e+_ + 5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/765765*(b*d-a*e)^5*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/21879*(b*d-a*e)^3*_ + (12*b*B*d-17*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 8 8 5 4 8 5 7 7 +--R 90090B b e x + ((102102A b + 510510B a b )e + 108108B b d e )x +--R + +--R 4 2 3 8 5 4 7 +--R (589050A a b + 1178100B a b )e + (125664A b + 628320B a b )d e +--R + +--R 5 2 6 +--R 1386B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 8 +--R (1392300A a b + 1392300B a b )e +--R + +--R 4 2 3 7 5 4 2 6 +--R (749700A a b + 1499400B a b )d e + (2142A b + 10710B a b )d e +--R + +--R 5 3 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 4 8 +--R (1701700A a b + 850850B a b)e +--R + +--R 2 3 3 2 7 +--R (1856400A a b + 1856400B a b )d e +--R + +--R 4 2 3 2 6 5 4 3 5 +--R (17850A a b + 35700B a b )d e + (- 2380A b - 11900B a b )d e +--R + +--R 5 4 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 4 5 8 3 2 4 7 +--R (1093950A a b + 218790B a )e + (2431000A a b + 1215500B a b)d e +--R + +--R 2 3 3 2 2 6 4 2 3 3 5 +--R (66300A a b + 66300B a b )d e + (- 20400A a b - 40800B a b )d e +--R + +--R 5 4 4 4 5 5 3 +--R (2720A b + 13600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 7 +--R 306306A a e + (1750320A a b + 350064B a )d e +--R + +--R 3 2 4 2 6 2 3 3 2 3 5 +--R (145860A a b + 72930B a b)d e + (- 79560A a b - 79560B a b )d e +--R + +--R 4 2 3 4 4 5 4 5 3 +--R (24480A a b + 48960B a b )d e + (- 3264A b - 16320B a b )d e +--R + +--R 5 6 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 2 6 +--R 612612A a d e + (218790A a b + 43758B a )d e +--R + +--R 3 2 4 3 5 +--R (- 194480A a b - 97240B a b)d e +--R + +--R 2 3 3 2 4 4 +--R (106080A a b + 106080B a b )d e +--R + +--R 4 2 3 5 3 5 4 6 2 +--R (- 32640A a b - 65280B a b )d e + (4352A b + 21760B a b )d e +--R + +--R 5 7 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 2 6 4 5 3 5 +--R 306306A a d e + (- 437580A a b - 87516B a )d e +--R + +--R 3 2 4 4 4 2 3 3 2 5 3 +--R (388960A a b + 194480B a b)d e + (- 212160A a b - 212160B a b )d e +--R + +--R 4 2 3 6 2 5 4 7 +--R (65280A a b + 130560B a b )d e + (- 8704A b - 43520B a b )d e +--R + +--R 5 8 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 765765b e x + 765765a e +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 8 8 5 4 8 5 7 7 +--R 90090B b e x + ((102102A b + 510510B a b )e + 108108B b d e )x +--R + +--R 4 2 3 8 5 4 7 +--R (589050A a b + 1178100B a b )e + (125664A b + 628320B a b )d e +--R + +--R 5 2 6 +--R 1386B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 8 +--R (1392300A a b + 1392300B a b )e +--R + +--R 4 2 3 7 5 4 2 6 +--R (749700A a b + 1499400B a b )d e + (2142A b + 10710B a b )d e +--R + +--R 5 3 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 4 8 +--R (1701700A a b + 850850B a b)e +--R + +--R 2 3 3 2 7 +--R (1856400A a b + 1856400B a b )d e +--R + +--R 4 2 3 2 6 5 4 3 5 +--R (17850A a b + 35700B a b )d e + (- 2380A b - 11900B a b )d e +--R + +--R 5 4 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 4 5 8 3 2 4 7 +--R (1093950A a b + 218790B a )e + (2431000A a b + 1215500B a b)d e +--R + +--R 2 3 3 2 2 6 4 2 3 3 5 +--R (66300A a b + 66300B a b )d e + (- 20400A a b - 40800B a b )d e +--R + +--R 5 4 4 4 5 5 3 +--R (2720A b + 13600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 7 +--R 306306A a e + (1750320A a b + 350064B a )d e +--R + +--R 3 2 4 2 6 2 3 3 2 3 5 +--R (145860A a b + 72930B a b)d e + (- 79560A a b - 79560B a b )d e +--R + +--R 4 2 3 4 4 5 4 5 3 +--R (24480A a b + 48960B a b )d e + (- 3264A b - 16320B a b )d e +--R + +--R 5 6 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 2 6 +--R 612612A a d e + (218790A a b + 43758B a )d e +--R + +--R 3 2 4 3 5 +--R (- 194480A a b - 97240B a b)d e +--R + +--R 2 3 3 2 4 4 +--R (106080A a b + 106080B a b )d e +--R + +--R 4 2 3 5 3 5 4 6 2 +--R (- 32640A a b - 65280B a b )d e + (4352A b + 21760B a b )d e +--R + +--R 5 7 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 2 6 4 5 3 5 +--R 306306A a d e + (- 437580A a b - 87516B a )d e +--R + +--R 3 2 4 4 4 2 3 3 2 5 3 +--R (388960A a b + 194480B a b)d e + (- 212160A a b - 212160B a b )d e +--R + +--R 4 2 3 6 2 5 4 7 +--R (65280A a b + 130560B a b )d e + (- 8704A b - 43520B a b )d e +--R + +--R 5 8 +--R 6144B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 765765e +--R Type: Union(Expression(Integer),...) +--E 1182 + +--S 1183 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 8 8 +--R - 90090B b e x +--R + +--R 5 4 8 5 7 7 +--R ((- 102102A b - 510510B a b )e - 108108B b d e )x +--R + +--R 4 2 3 8 +--R (- 589050A a b - 1178100B a b )e +--R + +--R 5 4 7 5 2 6 +--R (- 125664A b - 628320B a b )d e - 1386B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 8 +--R (- 1392300A a b - 1392300B a b )e +--R + +--R 4 2 3 7 +--R (- 749700A a b - 1499400B a b )d e +--R + +--R 5 4 2 6 5 3 5 +--R (- 2142A b - 10710B a b )d e + 1512B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 4 8 +--R (- 1701700A a b - 850850B a b)e +--R + +--R 2 3 3 2 7 +--R (- 1856400A a b - 1856400B a b )d e +--R + +--R 4 2 3 2 6 5 4 3 5 +--R (- 17850A a b - 35700B a b )d e + (2380A b + 11900B a b )d e +--R + +--R 5 4 4 +--R - 1680B b d e +--R * +--R 4 +--R x +--R + +--R 4 5 8 +--R (- 1093950A a b - 218790B a )e +--R + +--R 3 2 4 7 +--R (- 2431000A a b - 1215500B a b)d e +--R + +--R 2 3 3 2 2 6 +--R (- 66300A a b - 66300B a b )d e +--R + +--R 4 2 3 3 5 5 4 4 4 +--R (20400A a b + 40800B a b )d e + (- 2720A b - 13600B a b )d e +--R + +--R 5 5 3 +--R 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 7 +--R - 306306A a e + (- 1750320A a b - 350064B a )d e +--R + +--R 3 2 4 2 6 +--R (- 145860A a b - 72930B a b)d e +--R + +--R 2 3 3 2 3 5 +--R (79560A a b + 79560B a b )d e +--R + +--R 4 2 3 4 4 5 4 5 3 +--R (- 24480A a b - 48960B a b )d e + (3264A b + 16320B a b )d e +--R + +--R 5 6 2 +--R - 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 2 6 +--R - 612612A a d e + (- 218790A a b - 43758B a )d e +--R + +--R 3 2 4 3 5 +--R (194480A a b + 97240B a b)d e +--R + +--R 2 3 3 2 4 4 +--R (- 106080A a b - 106080B a b )d e +--R + +--R 4 2 3 5 3 5 4 6 2 +--R (32640A a b + 65280B a b )d e + (- 4352A b - 21760B a b )d e +--R + +--R 5 7 +--R 3072B b d e +--R * +--R x +--R + +--R 5 2 6 4 5 3 5 +--R - 306306A a d e + (437580A a b + 87516B a )d e +--R + +--R 3 2 4 4 4 +--R (- 388960A a b - 194480B a b)d e +--R + +--R 2 3 3 2 5 3 +--R (212160A a b + 212160B a b )d e +--R + +--R 4 2 3 6 2 5 4 7 +--R (- 65280A a b - 130560B a b )d e + (8704A b + 43520B a b )d e +--R + +--R 5 8 +--R - 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 6 8 9 6 5 8 6 7 8 +--R 90090B b e x + ((102102A b + 600600B a b )e + 108108B b d e )x +--R + +--R 5 2 4 8 +--R (691152A a b + 1688610B a b )e +--R + +--R 6 5 7 6 2 6 +--R (125664A b + 736428B a b )d e + 1386B b d e +--R * +--R 7 +--R x +--R + +--R 2 4 3 3 8 +--R (1981350A a b + 2570400B a b )e +--R + +--R 5 2 4 7 6 5 2 6 +--R (875364A a b + 2127720B a b )d e + (2142A b + 12096B a b )d e +--R + +--R 6 3 5 +--R - 1512B b d e +--R * +--R 6 +--R x +--R + +--R 3 3 4 2 8 +--R (3094000A a b + 2243150B a b )e +--R + +--R 2 4 3 3 7 +--R (2606100A a b + 3355800B a b )d e +--R + +--R 5 2 4 2 6 6 5 3 5 +--R (19992A a b + 46410B a b )d e + (- 2380A b - 13412B a b )d e +--R + +--R 6 4 4 +--R 1680B b d e +--R * +--R 5 +--R x +--R + +--R 4 2 5 8 +--R (2795650A a b + 1069640B a b)e +--R + +--R 3 3 4 2 7 +--R (4287400A a b + 3071900B a b )d e +--R + +--R 2 4 3 3 2 6 +--R (84150A a b + 102000B a b )d e +--R + +--R 5 2 4 3 5 6 5 4 4 +--R (- 22780A a b - 52700B a b )d e + (2720A b + 15280B a b )d e +--R + +--R 6 5 3 +--R - 1920B b d e +--R * +--R 4 +--R x +--R + +--R 5 6 8 +--R (1400256A a b + 218790B a )e +--R + +--R 4 2 5 7 +--R (4181320A a b + 1565564B a b)d e +--R + +--R 3 3 4 2 2 6 +--R (212160A a b + 139230B a b )d e +--R + +--R 2 4 3 3 3 5 +--R (- 99960A a b - 120360B a b )d e +--R + +--R 5 2 4 4 4 6 5 5 3 +--R (27200A a b + 62560B a b )d e + (- 3264A b - 18240B a b )d e +--R + +--R 6 6 2 +--R 2304B b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 6 7 +--R 306306A a e + (2362932A a b + 350064B a )d e +--R + +--R 4 2 5 2 6 +--R (364650A a b + 116688B a b)d e +--R + +--R 3 3 4 2 3 5 +--R (- 274040A a b - 176800B a b )d e +--R + +--R 2 4 3 3 4 4 +--R (130560A a b + 155040B a b )d e +--R + +--R 5 2 4 5 3 6 5 6 2 +--R (- 35904A a b - 81600B a b )d e + (4352A b + 24064B a b )d e +--R + +--R 6 7 +--R - 3072B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 2 6 +--R 612612A a d e + (525096A a b + 43758B a )d e +--R + +--R 4 2 5 3 5 +--R (- 632060A a b - 184756B a b)d e +--R + +--R 3 3 4 2 4 4 +--R (495040A a b + 300560B a b )d e +--R + +--R 2 4 3 3 5 3 +--R (- 244800A a b - 277440B a b )d e +--R + +--R 5 2 4 6 2 6 5 7 +--R (69632A a b + 152320B a b )d e + (- 8704A b - 46592B a b )d e +--R + +--R 6 8 +--R 6144B b d +--R * +--R x +--R + +--R 6 2 6 5 6 3 5 +--R 306306A a d e + (- 437580A a b - 87516B a )d e +--R + +--R 4 2 5 4 4 +--R (388960A a b + 194480B a b)d e +--R + +--R 3 3 4 2 5 3 +--R (- 212160A a b - 212160B a b )d e +--R + +--R 2 4 3 3 6 2 5 2 4 7 +--R (65280A a b + 130560B a b )d e + (- 8704A a b - 43520B a b )d e +--R + +--R 5 8 +--R 6144B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 765765b e x + 765765a e +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 2 8 5 4 2 5 7 +--R B b e x + ((A b + 5B a b )e + 2B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 6 +--R ((5A a b + 10B a b )e + (2A b + 10B a b )d e + B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (10A a b + 10B a b )e + (10A a b + 20B a b )d e +--R + +--R 5 4 2 +--R (A b + 5B a b )d +--R * +--R 5 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (10A a b + 5B a b)e + (20A a b + 20B a b )d e +--R + +--R 4 2 3 2 +--R (5A a b + 10B a b )d +--R * +--R 4 +--R x +--R + +--R 4 5 2 3 2 4 +--R (5A a b + B a )e + (20A a b + 10B a b)d e +--R + +--R 2 3 3 2 2 +--R (10A a b + 10B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 5 3 2 4 2 2 +--R (A a e + (10A a b + 2B a )d e + (10A a b + 5B a b)d )x +--R + +--R 5 4 5 2 5 2 +--R (2A a d e + (5A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 2 9 6 5 2 6 8 +--R - B b e x + ((- A b - 6B a b )e - 2B b d e)x +--R + +--R 5 2 4 2 6 5 6 2 7 +--R ((- 6A a b - 15B a b )e + (- 2A b - 12B a b )d e - B b d )x +--R + +--R 2 4 3 3 2 5 2 4 +--R (- 15A a b - 20B a b )e + (- 12A a b - 30B a b )d e +--R + +--R 6 5 2 +--R (- A b - 6B a b )d +--R * +--R 6 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 20A a b - 15B a b )e + (- 30A a b - 40B a b )d e +--R + +--R 5 2 4 2 +--R (- 6A a b - 15B a b )d +--R * +--R 5 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (- 15A a b - 6B a b)e + (- 40A a b - 30B a b )d e +--R + +--R 2 4 3 3 2 +--R (- 15A a b - 20B a b )d +--R * +--R 4 +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 6A a b - B a )e + (- 30A a b - 12B a b)d e +--R + +--R 3 3 4 2 2 +--R (- 20A a b - 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 4 2 5 2 2 +--R (- A a e + (- 12A a b - 2B a )d e + (- 15A a b - 6B a b)d )x +--R + +--R 6 5 6 2 6 2 +--R (- 2A a d e + (- 6A a b - B a )d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1184 + +)clear all + +--S 1185 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1378 +r0:=-32/1287*(b*d-a*e)^2*(4*b*B*d-5*A*b*e+a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)+4/143*(b*d-a*e)*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-2/65*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+_ + 2/15*B*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 256/15015*(b*d-a*e)^4*(4*b*B*d-5*A*b*e+a*B*e)*(d+e*x)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+512/45045*(b*d-a*e)^5*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*_ + (a+b*x))+64/3003*(b*d-a*e)^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 7 7 5 4 7 5 6 6 +--R 6006B b e x + ((6930A b + 34650B a b )e + 462B b d e )x +--R + +--R 4 2 3 7 5 4 6 +--R (40950A a b + 81900B a b )e + (630A b + 3150B a b )d e +--R + +--R 5 2 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (100100A a b + 100100B a b )e + (4550A a b + 9100B a b )d e +--R + +--R 5 4 2 5 5 3 4 +--R (- 700A b - 3500B a b )d e + 560B b d e +--R * +--R 4 +--R x +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (128700A a b + 64350B a b)e + (14300A a b + 14300B a b )d e +--R + +--R 4 2 3 2 5 5 4 3 4 +--R (- 5200A a b - 10400B a b )d e + (800A b + 4000B a b )d e +--R + +--R 5 4 3 +--R - 640B b d e +--R * +--R 3 +--R x +--R + +--R 4 5 7 3 2 4 6 +--R (90090A a b + 18018B a )e + (25740A a b + 12870B a b)d e +--R + +--R 2 3 3 2 2 5 4 2 3 3 4 +--R (- 17160A a b - 17160B a b )d e + (6240A a b + 12480B a b )d e +--R + +--R 5 4 4 3 5 5 2 +--R (- 960A b - 4800B a b )d e + 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 6 +--R 30030A a e + (30030A a b + 6006B a )d e +--R + +--R 3 2 4 2 5 2 3 3 2 3 4 +--R (- 34320A a b - 17160B a b)d e + (22880A a b + 22880B a b )d e +--R + +--R 4 2 3 4 3 5 4 5 2 +--R (- 8320A a b - 16640B a b )d e + (1280A b + 6400B a b )d e +--R + +--R 5 6 +--R - 1024B b d e +--R * +--R x +--R + +--R 5 6 4 5 2 5 +--R 30030A a d e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 3 4 2 3 3 2 4 3 +--R (68640A a b + 34320B a b)d e + (- 45760A a b - 45760B a b )d e +--R + +--R 4 2 3 5 2 5 4 6 +--R (16640A a b + 33280B a b )d e + (- 2560A b - 12800B a b )d e +--R + +--R 5 7 +--R 2048B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 7 5 4 7 5 6 6 +--R 6006B b e x + ((6930A b + 34650B a b )e + 462B b d e )x +--R + +--R 4 2 3 7 5 4 6 +--R (40950A a b + 81900B a b )e + (630A b + 3150B a b )d e +--R + +--R 5 2 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (100100A a b + 100100B a b )e + (4550A a b + 9100B a b )d e +--R + +--R 5 4 2 5 5 3 4 +--R (- 700A b - 3500B a b )d e + 560B b d e +--R * +--R 4 +--R x +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (128700A a b + 64350B a b)e + (14300A a b + 14300B a b )d e +--R + +--R 4 2 3 2 5 5 4 3 4 +--R (- 5200A a b - 10400B a b )d e + (800A b + 4000B a b )d e +--R + +--R 5 4 3 +--R - 640B b d e +--R * +--R 3 +--R x +--R + +--R 4 5 7 3 2 4 6 +--R (90090A a b + 18018B a )e + (25740A a b + 12870B a b)d e +--R + +--R 2 3 3 2 2 5 4 2 3 3 4 +--R (- 17160A a b - 17160B a b )d e + (6240A a b + 12480B a b )d e +--R + +--R 5 4 4 3 5 5 2 +--R (- 960A b - 4800B a b )d e + 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 6 +--R 30030A a e + (30030A a b + 6006B a )d e +--R + +--R 3 2 4 2 5 2 3 3 2 3 4 +--R (- 34320A a b - 17160B a b)d e + (22880A a b + 22880B a b )d e +--R + +--R 4 2 3 4 3 5 4 5 2 +--R (- 8320A a b - 16640B a b )d e + (1280A b + 6400B a b )d e +--R + +--R 5 6 +--R - 1024B b d e +--R * +--R x +--R + +--R 5 6 4 5 2 5 +--R 30030A a d e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 3 4 2 3 3 2 4 3 +--R (68640A a b + 34320B a b)d e + (- 45760A a b - 45760B a b )d e +--R + +--R 4 2 3 5 2 5 4 6 +--R (16640A a b + 33280B a b )d e + (- 2560A b - 12800B a b )d e +--R + +--R 5 7 +--R 2048B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 7 7 5 4 7 5 6 6 +--R - 6006B b e x + ((- 6930A b - 34650B a b )e - 462B b d e )x +--R + +--R 4 2 3 7 5 4 6 +--R (- 40950A a b - 81900B a b )e + (- 630A b - 3150B a b )d e +--R + +--R 5 2 5 +--R 504B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 7 +--R (- 100100A a b - 100100B a b )e +--R + +--R 4 2 3 6 5 4 2 5 +--R (- 4550A a b - 9100B a b )d e + (700A b + 3500B a b )d e +--R + +--R 5 3 4 +--R - 560B b d e +--R * +--R 4 +--R x +--R + +--R 3 2 4 7 +--R (- 128700A a b - 64350B a b)e +--R + +--R 2 3 3 2 6 +--R (- 14300A a b - 14300B a b )d e +--R + +--R 4 2 3 2 5 5 4 3 4 +--R (5200A a b + 10400B a b )d e + (- 800A b - 4000B a b )d e +--R + +--R 5 4 3 +--R 640B b d e +--R * +--R 3 +--R x +--R + +--R 4 5 7 3 2 4 6 +--R (- 90090A a b - 18018B a )e + (- 25740A a b - 12870B a b)d e +--R + +--R 2 3 3 2 2 5 +--R (17160A a b + 17160B a b )d e +--R + +--R 4 2 3 3 4 5 4 4 3 +--R (- 6240A a b - 12480B a b )d e + (960A b + 4800B a b )d e +--R + +--R 5 5 2 +--R - 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 6 +--R - 30030A a e + (- 30030A a b - 6006B a )d e +--R + +--R 3 2 4 2 5 +--R (34320A a b + 17160B a b)d e +--R + +--R 2 3 3 2 3 4 +--R (- 22880A a b - 22880B a b )d e +--R + +--R 4 2 3 4 3 5 4 5 2 +--R (8320A a b + 16640B a b )d e + (- 1280A b - 6400B a b )d e +--R + +--R 5 6 +--R 1024B b d e +--R * +--R x +--R + +--R 5 6 4 5 2 5 +--R - 30030A a d e + (60060A a b + 12012B a )d e +--R + +--R 3 2 4 3 4 2 3 3 2 4 3 +--R (- 68640A a b - 34320B a b)d e + (45760A a b + 45760B a b )d e +--R + +--R 4 2 3 5 2 5 4 6 +--R (- 16640A a b - 33280B a b )d e + (2560A b + 12800B a b )d e +--R + +--R 5 7 +--R - 2048B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 6 7 8 6 5 7 6 6 7 +--R 6006B b e x + ((6930A b + 40656B a b )e + 462B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (47880A a b + 116550B a b )e + (630A b + 3612B a b )d e +--R + +--R 6 2 5 +--R - 504B b d e +--R * +--R 6 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (141050A a b + 182000B a b )e + (5180A a b + 12250B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (- 700A b - 4004B a b )d e + 560B b d e +--R * +--R 5 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (228800A a b + 164450B a b )e + (18850A a b + 23400B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (- 5900A a b - 13900B a b )d e + (800A b + 4560B a b )d e +--R + +--R 6 4 3 +--R - 640B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (218790A a b + 82368B a b)e + (40040A a b + 27170B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (- 22360A a b - 27560B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (7040A a b + 16480B a b )d e + (- 960A b - 5440B a b )d e +--R + +--R 6 5 2 +--R 768B b d e +--R * +--R 3 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (120120A a b + 18018B a )e + (55770A a b + 18876B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (- 51480A a b - 34320B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (29120A a b + 35360B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 9280A a b - 21440B a b )d e + (1280A b + 7168B a b )d e +--R + +--R 6 6 +--R - 1024B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 6 +--R 30030A a e + (60060A a b + 6006B a )d e +--R + +--R 4 2 5 2 5 +--R (- 94380A a b - 29172B a b)d e +--R + +--R 3 3 4 2 3 4 +--R (91520A a b + 57200B a b )d e +--R + +--R 2 4 3 3 4 3 +--R (- 54080A a b - 62400B a b )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (17920A a b + 39680B a b )d e + (- 2560A b - 13824B a b )d e +--R + +--R 6 7 +--R 2048B b d +--R * +--R x +--R + +--R 6 6 5 6 2 5 +--R 30030A a d e + (- 60060A a b - 12012B a )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (68640A a b + 34320B a b)d e + (- 45760A a b - 45760B a b )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (16640A a b + 33280B a b )d e + (- 2560A a b - 12800B a b )d e +--R + +--R 5 7 +--R 2048B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 7 5 4 5 6 +--R B b e x + ((A b + 5B a b )e + B b d)x +--R + +--R 4 2 3 5 4 5 +--R ((5A a b + 10B a b )e + (A b + 5B a b )d)x +--R + +--R 2 3 3 2 4 2 3 4 +--R ((10A a b + 10B a b )e + (5A a b + 10B a b )d)x +--R + +--R 3 2 4 2 3 3 2 3 +--R ((10A a b + 5B a b)e + (10A a b + 10B a b )d)x +--R + +--R 4 5 3 2 4 2 +--R ((5A a b + B a )e + (10A a b + 5B a b)d)x +--R + +--R 5 4 5 5 +--R (A a e + (5A a b + B a )d)x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 8 6 5 6 7 +--R - B b e x + ((- A b - 6B a b )e - B b d)x +--R + +--R 5 2 4 6 5 6 +--R ((- 6A a b - 15B a b )e + (- A b - 6B a b )d)x +--R + +--R 2 4 3 3 5 2 4 5 +--R ((- 15A a b - 20B a b )e + (- 6A a b - 15B a b )d)x +--R + +--R 3 3 4 2 2 4 3 3 4 +--R ((- 20A a b - 15B a b )e + (- 15A a b - 20B a b )d)x +--R + +--R 4 2 5 3 3 4 2 3 +--R ((- 15A a b - 6B a b)e + (- 20A a b - 15B a b )d)x +--R + +--R 5 6 4 2 5 2 +--R ((- 6A a b - B a )e + (- 15A a b - 6B a b)d)x +--R + +--R 6 5 6 6 +--R (- A a e + (- 6A a b - B a )d)x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1378 +r0:=-160/9009*(b*d-a*e)^2*(12*b*B*d-13*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x)/(b*e^4)+20/1287*(b*d-a*e)*(12*b*B*d-_ + 13*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/_ + (b*e^3)-2/143*(12*b*B*d-13*A*b*e+a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x)/(b*e^2)+2/13*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x)/(b*e)-256/9009*(b*d-a*e)^4*(12*b*B*d-13*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+512/9009*(b*d-a*e)^5*_ + (12*b*B*d-13*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^7*(a+b*x))+64/3003*(b*d-a*e)^3*(12*b*B*d-13*A*b*e+a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 1386B b e x + ((1638A b + 8190B a b )e - 1512B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (10010A a b + 20020B a b )e + (- 1820A b - 9100B a b )d e +--R + +--R 5 2 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (25740A a b + 25740B a b )e + (- 11440A a b - 22880B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2080A b + 10400B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (36036A a b + 18018B a b)e + (- 30888A a b - 30888B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (13728A a b + 27456B a b )d e + (- 2496A b - 12480B a b )d e +--R + +--R 5 4 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (30030A a b + 6006B a )e + (- 48048A a b - 24024B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (41184A a b + 41184B a b )d e + (- 18304A a b - 36608B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (3328A b + 16640B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R 18018A a e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (96096A a b + 48048B a b)d e + (- 82368A a b - 82368B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (36608A a b + 73216B a b )d e + (- 6656A b - 33280B a b )d e +--R + +--R 5 6 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 9009b e x + 9009a e +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R 1386B b e x + ((1638A b + 8190B a b )e - 1512B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (10010A a b + 20020B a b )e + (- 1820A b - 9100B a b )d e +--R + +--R 5 2 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (25740A a b + 25740B a b )e + (- 11440A a b - 22880B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2080A b + 10400B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (36036A a b + 18018B a b)e + (- 30888A a b - 30888B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (13728A a b + 27456B a b )d e + (- 2496A b - 12480B a b )d e +--R + +--R 5 4 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (30030A a b + 6006B a )e + (- 48048A a b - 24024B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (41184A a b + 41184B a b )d e + (- 18304A a b - 36608B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (3328A b + 16640B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R 18018A a e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (96096A a b + 48048B a b)d e + (- 82368A a b - 82368B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (36608A a b + 73216B a b )d e + (- 6656A b - 33280B a b )d e +--R + +--R 5 6 +--R 6144B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R - 1386B b e x + ((- 1638A b - 8190B a b )e + 1512B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 10010A a b - 20020B a b )e + (1820A b + 9100B a b )d e +--R + +--R 5 2 4 +--R - 1680B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 25740A a b - 25740B a b )e + (11440A a b + 22880B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 2080A b - 10400B a b )d e + 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 36036A a b - 18018B a b)e + (30888A a b + 30888B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 13728A a b - 27456B a b )d e + (2496A b + 12480B a b )d e +--R + +--R 5 4 2 +--R - 2304B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 30030A a b - 6006B a )e + (48048A a b + 24024B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 41184A a b - 41184B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (18304A a b + 36608B a b )d e + (- 3328A b - 16640B a b )d e +--R + +--R 5 5 +--R 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 18018A a e + (60060A a b + 12012B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 96096A a b - 48048B a b)d e + (82368A a b + 82368B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 36608A a b - 73216B a b )d e + (6656A b + 33280B a b )d e +--R + +--R 5 6 +--R - 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 1386B b e x + ((1638A b + 9576B a b )e - 1512B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (11648A a b + 28210B a b )e + (- 1820A b - 10612B a b )d e +--R + +--R 6 2 4 +--R 1680B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (35750A a b + 45760B a b )e + (- 13260A a b - 31980B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (2080A b + 12080B a b )d e - 1920B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (61776A a b + 43758B a b )e + (- 42328A a b - 53768B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (15808A a b + 37856B a b )d e + (- 2496A b - 14400B a b )d e +--R + +--R 6 4 2 +--R 2304B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (66066A a b + 24024B a b)e + (- 78936A a b - 54912B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (54912A a b + 68640B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 20800A a b - 49088B a b )d e + (3328A b + 18944B a b )d e +--R + +--R 6 5 +--R - 3072B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (48048A a b + 6006B a )e + (- 108108A a b - 36036B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (137280A a b + 89232B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 100672A a b - 118976B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (39936A a b + 89856B a b )d e + (- 6656A b - 36352B a b )d e +--R + +--R 6 6 +--R 6144B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R 18018A a e + (- 60060A a b - 12012B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (96096A a b + 48048B a b)d e + (- 82368A a b - 82368B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (36608A a b + 73216B a b )d e + (- 6656A a b - 33280B a b )d e +--R + +--R 5 6 +--R 6144B a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 9009b e x + 9009a e +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1378 +r0:=-2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+160/693*(b*d-a*e)*(12*b*B*d-11*A*b*e-a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4-20/99*(12*b*B*d-11*A*b*e-_ + a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3+2/11*_ + (12*b*B*d-11*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/_ + (e^2*(b*d-a*e))+256/693*(b*d-a*e)^3*(12*b*B*d-11*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-512/693*(b*d-a*e)^4*_ + (12*b*B*d-11*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x))-64/231*(b*d-a*e)^2*(12*b*B*d-11*A*b*e-a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 126B b e x + ((154A b + 770B a b )e - 168B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (990A a b + 1980B a b )e + (- 220A b - 1100B a b )d e +--R + +--R 5 2 4 +--R 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2772A a b + 2772B a b )e + (- 1584A a b - 3168B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (352A b + 1760B a b )d e - 384B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (4620A a b + 2310B a b)e + (- 5544A a b - 5544B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (3168A a b + 6336B a b )d e + (- 704A b - 3520B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (6930A a b + 1386B a )e + (- 18480A a b - 9240B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (22176A a b + 22176B a b )d e + (- 12672A a b - 25344B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (2816A b + 14080B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 1386A a e + (13860A a b + 2772B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 36960A a b - 18480B a b)d e + (44352A a b + 44352B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 25344A a b - 50688B a b )d e + (5632A b + 28160B a b )d e +--R + +--R 5 6 +--R - 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +-------+ +--R (693b e x + 693a e )\|e x + d +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R 126B b e x + ((154A b + 770B a b )e - 168B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (990A a b + 1980B a b )e + (- 220A b - 1100B a b )d e +--R + +--R 5 2 4 +--R 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2772A a b + 2772B a b )e + (- 1584A a b - 3168B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (352A b + 1760B a b )d e - 384B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (4620A a b + 2310B a b)e + (- 5544A a b - 5544B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (3168A a b + 6336B a b )d e + (- 704A b - 3520B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (6930A a b + 1386B a )e + (- 18480A a b - 9240B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (22176A a b + 22176B a b )d e + (- 12672A a b - 25344B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (2816A b + 14080B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 1386A a e + (13860A a b + 2772B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 36960A a b - 18480B a b)d e + (44352A a b + 44352B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 25344A a b - 50688B a b )d e + (5632A b + 28160B a b )d e +--R + +--R 5 6 +--R - 6144B b d +--R / +--R 7 +-------+ +--R 693e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R - 126B b e x + ((- 154A b - 770B a b )e + 168B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 990A a b - 1980B a b )e + (220A b + 1100B a b )d e +--R + +--R 5 2 4 +--R - 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 2772A a b - 2772B a b )e + (1584A a b + 3168B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 352A b - 1760B a b )d e + 384B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 4620A a b - 2310B a b)e + (5544A a b + 5544B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 3168A a b - 6336B a b )d e + (704A b + 3520B a b )d e +--R + +--R 5 4 2 +--R - 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 6930A a b - 1386B a )e + (18480A a b + 9240B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 22176A a b - 22176B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (12672A a b + 25344B a b )d e + (- 2816A b - 14080B a b )d e +--R + +--R 5 5 +--R 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R 1386A a e + (- 13860A a b - 2772B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (36960A a b + 18480B a b)d e + (- 44352A a b - 44352B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (25344A a b + 50688B a b )d e + (- 5632A b - 28160B a b )d e +--R + +--R 5 6 +--R 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 126B b e x + ((154A b + 896B a b )e - 168B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (1144A a b + 2750B a b )e + (- 220A b - 1268B a b )d e +--R + +--R 6 2 4 +--R 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (3762A a b + 4752B a b )e + (- 1804A a b - 4268B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (352A b + 2000B a b )d e - 384B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (7392A a b + 5082B a b )e + (- 7128A a b - 8712B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (3520A a b + 8096B a b )d e + (- 704A b - 3904B a b )d e +--R + +--R 6 4 2 +--R 768B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (11550A a b + 3696B a b)e + (- 24024A a b - 14784B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (25344A a b + 28512B a b )d e + (- 13376A a b - 28864B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (2816A b + 14848B a b )d e - 3072B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (5544A a b + 1386B a )e + (- 4620A a b - 6468B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 14784A a b + 3696B a b )d e + (31680A a b + 19008B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (- 22528A a b - 36608B a b )d e + (5632A b + 25088B a b )d e +--R + +--R 6 6 +--R - 6144B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 1386A a e + (13860A a b + 2772B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 36960A a b - 18480B a b)d e + (44352A a b + 44352B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (- 25344A a b - 50688B a b )d e + (5632A a b + 28160B a b )d e +--R + +--R 5 6 +--R - 6144B a b d +--R / +--R 7 7 +-------+ +--R (693b e x + 693a e )\|e x + d +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))-2*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(b*d-a*e)*sqrt(d+e*x))-160/63*b*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+20/9*b*(4*b*B*d-3*A*b*e-a*B*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/(e^3*(b*d-a*e))-_ + 256/63*b*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^6+512/63*b*(b*d-a*e)^3*(4*b*B*d-3*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+64/21*b*(b*d-_ + a*e)*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 14B b e x + ((18A b + 90B a b )e - 24B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((126A a b + 252B a b )e + (- 36A b - 180B a b )d e + 48B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (420A a b + 420B a b )e + (- 336A a b - 672B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (96A b + 480B a b )d e - 128B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (1260A a b + 630B a b)e + (- 2520A a b - 2520B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (2016A a b + 4032B a b )d e + (- 576A b - 2880B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 630A a b - 126B a )e + (5040A a b + 2520B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 10080A a b - 10080B a b )d e + (8064A a b + 16128B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 2304A b - 11520B a b )d e + 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 420A a b - 84B a )d e + (3360A a b + 1680B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 6720A a b - 6720B a b )d e + (5376A a b + 10752B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 1536A b - 7680B a b )d e + 2048B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R 14B b e x + ((18A b + 90B a b )e - 24B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((126A a b + 252B a b )e + (- 36A b - 180B a b )d e + 48B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (420A a b + 420B a b )e + (- 336A a b - 672B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (96A b + 480B a b )d e - 128B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (1260A a b + 630B a b)e + (- 2520A a b - 2520B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (2016A a b + 4032B a b )d e + (- 576A b - 2880B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 630A a b - 126B a )e + (5040A a b + 2520B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 10080A a b - 10080B a b )d e + (8064A a b + 16128B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 2304A b - 11520B a b )d e + 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 420A a b - 84B a )d e + (3360A a b + 1680B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 6720A a b - 6720B a b )d e + (5376A a b + 10752B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 1536A b - 7680B a b )d e + 2048B b d +--R / +--R 8 7 +-------+ +--R (63e x + 63d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R - 14B b e x + ((- 18A b - 90B a b )e + 24B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 126A a b - 252B a b )e + (36A b + 180B a b )d e +--R + +--R 5 2 4 +--R - 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 420A a b - 420B a b )e + (336A a b + 672B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 96A b - 480B a b )d e + 128B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 1260A a b - 630B a b)e + (2520A a b + 2520B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 2016A a b - 4032B a b )d e + (576A b + 2880B a b )d e +--R + +--R 5 4 2 +--R - 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (630A a b + 126B a )e + (- 5040A a b - 2520B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (10080A a b + 10080B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 8064A a b - 16128B a b )d e + (2304A b + 11520B a b )d e +--R + +--R 5 5 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 42A a e + (420A a b + 84B a )d e + (- 3360A a b - 1680B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (6720A a b + 6720B a b )d e + (- 5376A a b - 10752B a b )d e +--R + +--R 5 4 5 5 6 +--R (1536A b + 7680B a b )d e - 2048B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 14B b e x + ((18A b + 104B a b )e - 24B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((144A a b + 342B a b )e + (- 36A b - 204B a b )d e + 48B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (546A a b + 672B a b )e + (- 372A a b - 852B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (96A b + 528B a b )d e - 128B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (1680A a b + 1050B a b )e + (- 2856A a b - 3192B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (2112A a b + 4512B a b )d e + (- 576A b - 3008B a b )d e +--R + +--R 6 4 2 +--R 768B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 5 +--R (630A a b + 504B a b)e + 2520A a b d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (- 8064A a b - 6048B a b )d e + (7488A a b + 13248B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 2304A b - 10752B a b )d e + 3072B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 672A a b - 126B a )e + (4620A a b + 2436B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 6720A a b - 8400B a b )d e + (1344A a b + 9408B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (3072A a b - 768B a b )d e + (- 1536A b - 4608B a b )d e +--R + +--R 6 6 +--R 2048B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 42A a e + (- 420A a b - 84B a )d e + (3360A a b + 1680B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 6720A a b - 6720B a b )d e + (5376A a b + 10752B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (- 1536A a b - 7680B a b )d e + 2048B a b d +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1378 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1378 +r0:=-2/5*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/15*(12*b*B*d-7*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/3*b*(12*b*B*d-_ + 7*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*_ + sqrt(d+e*x))+32/21*b^2*(12*b*B*d-7*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x)/(e^4*(b*d-a*e))+256/105*b^2*(b*d-a*e)*_ + (12*b*B*d-7*A*b*e-5*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 512/105*b^2*(b*d-a*e)^2*(12*b*B*d-7*A*b*e-5*a*B*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-64/35*b^2*(12*b*B*d-7*A*b*_ + e-5*a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 30B b e x + ((42A b + 210B a b )e - 72B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (350A a b + 700B a b )e + (- 140A b - 700B a b )d e +--R + +--R 5 2 4 +--R 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2100A a b + 2100B a b )e + (- 2800A a b - 5600B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (1120A b + 5600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 2100A a b - 1050B a b)e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 16800A a b - 33600B a b )d e + (6720A b + 33600B a b )d e +--R + +--R 5 4 2 +--R - 11520B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 350A a b - 70B a )e + (- 2800A a b - 1400B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (16800A a b + 16800B a b )d e + (- 22400A a b - 44800B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (8960A b + 44800B a b )d e - 15360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 140A a b - 28B a )d e + (- 1120A a b - 560B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (6720A a b + 6720B a b )d e + (- 8960A a b - 17920B a b )d e +--R + +--R 5 4 5 5 6 +--R (3584A b + 17920B a b )d e - 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 +--R 105b e x + (105a e + 210b d e )x + (210a d e + 105b d e )x +--R + +--R 2 7 +--R 105a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 4 6 5 5 5 +--R 30B b e x + ((42A b + 210B a b )e - 72B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((350A a b + 700B a b )e + (- 140A b - 700B a b )d e + 240B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2100A a b + 2100B a b )e + (- 2800A a b - 5600B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (1120A b + 5600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 2100A a b - 1050B a b)e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 16800A a b - 33600B a b )d e + (6720A b + 33600B a b )d e +--R + +--R 5 4 2 +--R - 11520B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 350A a b - 70B a )e + (- 2800A a b - 1400B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (16800A a b + 16800B a b )d e + (- 22400A a b - 44800B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (8960A b + 44800B a b )d e - 15360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 140A a b - 28B a )d e + (- 1120A a b - 560B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (6720A a b + 6720B a b )d e + (- 8960A a b - 17920B a b )d e +--R + +--R 5 4 5 5 6 +--R (3584A b + 17920B a b )d e - 6144B b d +--R / +--R 9 2 8 2 7 +-------+ +--R (105e x + 210d e x + 105d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1378 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 4 6 5 5 5 +--R - 30B b e x + ((- 42A b - 210B a b )e + 72B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 350A a b - 700B a b )e + (140A b + 700B a b )d e +--R + +--R 5 2 4 +--R - 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 2100A a b - 2100B a b )e + (2800A a b + 5600B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 1120A b - 5600B a b )d e + 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (2100A a b + 1050B a b)e + (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (16800A a b + 33600B a b )d e + (- 6720A b - 33600B a b )d e +--R + +--R 5 4 2 +--R 11520B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (350A a b + 70B a )e + (2800A a b + 1400B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (- 16800A a b - 16800B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (22400A a b + 44800B a b )d e + (- 8960A b - 44800B a b )d e +--R + +--R 5 5 +--R 15360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R 42A a e + (140A a b + 28B a )d e + (1120A a b + 560B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 6720A a b - 6720B a b )d e + (8960A a b + 17920B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 3584A b - 17920B a b )d e + 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 6 5 6 6 5 6 +--R 30B b e x + ((42A b + 240B a b )e - 72B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((392A a b + 910B a b )e + (- 140A b - 772B a b )d e + 240B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (2450A a b + 2800B a b )e + (- 2940A a b - 6300B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (1120A b + 5840B a b )d e - 1920B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 6 2 4 3 3 5 +--R 1050B a b e + (9800A a b + 7000B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 15680A a b - 28000B a b )d e + (6720A b + 31680B a b )d e +--R + +--R 6 4 2 +--R - 11520B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 2450A a b - 1120B a b)e + (9800A a b + 11200B a b )d e +--R + +--R 3 3 2 4 5 2 4 3 3 +--R - 16800B a b d e + (- 15680A a b - 11200B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (8960A b + 33280B a b )d e - 15360B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 392A a b - 70B a )e + (- 2940A a b - 1428B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (15680A a b + 16240B a b )d e + (- 15680A a b - 38080B a b )d e +--R + +--R 2 4 4 2 6 5 5 6 6 +--R 26880B a b d e + (3584A b + 2560B a b )d e - 6144B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 42A a e + (- 140A a b - 28B a )d e + (- 1120A a b - 560B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (6720A a b + 6720B a b )d e + (- 8960A a b - 17920B a b )d e +--R + +--R 5 2 4 5 5 6 +--R (3584A a b + 17920B a b )d e - 6144B a b d +--R / +--R 9 3 9 8 2 8 2 7 +--R 105b e x + (105a e + 210b d e )x + (210a d e + 105b d e )x +--R + +--R 2 7 +--R 105a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1378 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x +--R + +--R 5 +--R A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 6 5 6 5 2 4 5 +--R - B b x + (- A b - 6B a b )x + (- 6A a b - 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 15A a b - 20B a b )x + (- 20A a b - 15B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 15A a b - 6B a b)x + (- 6A a b - B a )x - A a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1210 + +--S 1211 of 1378 +r0:=2/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/5*(A*b-a*B)*(a+b*x)*(d+e*x)^(5/2)/(b^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/7*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(b*d-a*e)^(5/2)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (- 210A a b + 210B a b)e + (420A a b - 420B a b )d e +--R + +--R 4 3 2 +--R (- 210A b + 210B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 2 +--R (- 210A a b + 210B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 12B a b )e + 90B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 28A a b + 28B a b )e + (154A b - 64B a b )d e + 90B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (140A a b - 140B a b)e + (- 336A a b + 336B a b )d e +--R + +--R 4 3 2 4 3 +--R (322A b - 232B a b )d e + 30B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (322A a b - 322B a b )d e + 30B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 105b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 2 +--R (- 105A a b + 105B a )e + (210A a b - 210B a b)d e +--R + +--R 3 2 2 +--R (- 105A b + 105B a b )d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b e +--R , +--R +--R 2 3 3 2 2 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 +--R (- 210A b + 210B a b )d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1212 + +--S 1213 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 +--R (- 105A a b + 105B a )e + (210A a b - 210B a b)d e +--R + +--R 3 2 2 +--R (- 105A b + 105B a b )d e +--R * +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 3 3 3 2 2 2 +--R (210A a b - 210B a b)e + (- 420A a b + 420B a b )d e +--R + +--R 4 3 2 +--R (210A b - 210B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 210B a )e + (- 420A a b + 420B a b)d e +--R + +--R 3 2 2 2 +--R (210A a b - 210B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R - 30B b e x + ((- 42A b + 12B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((28A a b - 28B a b )e + (- 154A b + 64B a b )d e - 90B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 140A a b + 140B a b)e + (336A a b - 336B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 322A b + 232B a b )d e - 30B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 210B a )e + (490A a b - 490B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 322A a b + 322B a b )d e - 30B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 105b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 +--R 2B b e x + (2A b e + 6B b d e )x + (6A b d e + 6B b d e)x +--R + +--R 2 3 3 +--R (6A b d e + 2B b d )x + 2A b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 4 5 4 3 4 +--R B b e x + ((A b - B a)e + 5B b d e )x +--R + +--R 4 3 2 2 3 +--R (- A a e + (5A b - 3B a)d e + 9B b d e )x +--R + +--R 3 2 2 3 2 +--R (- 3A a d e + (9A b - 3B a)d e + 7B b d e)x +--R + +--R 2 2 3 4 3 4 +--R (- 3A a d e + (7A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 5 2 3 2 2 4 +--R - 2B b e x + ((- 2A b - 2B a b)e - 6B b d e )x +--R + +--R 3 2 2 2 2 3 +--R (- 2A a b e + (- 6A b - 6B a b)d e - 6B b d e)x +--R + +--R 2 2 2 2 3 2 +--R (- 6A a b d e + (- 6A b - 6B a b)d e - 2B b d )x +--R + +--R 2 2 3 3 +--R (- 6A a b d e + (- 2A b - 2B a b)d )x - 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 4 6 2 4 2 3 5 +--R - B b e x + (- A b e - 5B b d e )x +--R + +--R 2 4 2 3 2 2 2 4 +--R (B a e + (- 5A b - 2B a b)d e - 9B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 3 +--R (A a e + (- 2A a b + 3B a )d e + (- 9A b - 6B a b)d e - 7B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 2 +--R (3A a d e + (- 6A a b + 3B a )d e + (- 7A b - 6B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 3 2 4 2 3 +--R (3A a d e + (- 6A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 4 +--R - 2A a b d +--R / +--R 2 2 2 2 +-------+ +--R (b e x + 2b d x - a e + 2a b d)\|e x + d +--R + +--R +-----------+ +--R 2 2 2 |- a e + b d +--R (2b e x + (2a b e + 2b d)x + 2a b d) |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 3 3 3 2 2 2 +--R (210A a b - 210B a b)e + (- 420A a b + 420B a b )d e +--R + +--R 4 3 2 +--R (210A b - 210B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 210B a )e + (- 420A a b + 420B a b)d e +--R + +--R 3 2 2 2 +--R (210A a b - 210B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 3 2 2 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 +--R (- 210A b + 210B a b )d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R - 30B b e x + ((- 42A b + 12B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((28A a b - 28B a b )e + (- 154A b + 64B a b )d e - 90B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 140A a b + 140B a b)e + (336A a b - 336B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 322A b + 232B a b )d e - 30B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 210B a )e + (490A a b - 490B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 322A a b + 322B a b )d e - 30B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 105b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1216 + +)clear all + +--S 1217 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1217 + +--S 1218 of 1378 +r0:=2/3*(A*b-a*B)*(a+b*x)*(d+e*x)^(3/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2/5*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(b*d-a*e)^(3/2)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (b*d-a*e)*(a+b*x)*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 3 2 +--R ((30A a b - 30B a b)e + (- 30A b + 30B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (30A a b - 30B a )e + (- 30A a b + 30B a b)d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 4B a b )e + 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 20A a b + 20B a b)e + (40A b - 28B a b )d e + 6B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A a b - 40B a b)d e + 6B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 15b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 |- a e + b d +--R ((- 15A a b + 15B a )e + (15A b - 15B a b)d e) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b e +--R , +--R +--R +---------+ +--R 2 2 2 |a e - b d +--R ((30A a b - 30B a )e + (- 30A b + 30B a b)d e) |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1219 + +--S 1220 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 |- a e + b d +-+ +--R ((- 15A a b + 15B a )e + (15A b - 15B a b)d e) |----------- \|b +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 3 2 +--R ((- 30A a b + 30B a b)e + (30A b - 30B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (- 30A a b + 30B a )e + (30A a b - 30B a b)d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R - 6B b e x + ((- 10A b + 4B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((20A a b - 20B a b)e + (- 40A b + 28B a b )d e - 6B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (30A a b - 30B a )e + (- 40A a b + 40B a b)d e - 6B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 15b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 3 2 2 2 +--R - 2B b e x + (- 2A b e - 4B b d e)x + (- 4A b d e - 2B b d )x +--R + +--R 2 +--R - 2A b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 3 4 3 2 3 +--R B b e x + ((A b - B a)e + 4B b d e )x +--R + +--R 3 2 2 2 +--R (- A a e + (4A b - 2B a)d e + 5B b d e)x +--R + +--R 2 2 3 2 3 +--R (- 2A a d e + (5A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 4 2 2 2 3 +--R 2B b e x + ((2A b + 2B a b)e + 4B b d e)x +--R + +--R 2 2 2 2 2 +--R (2A a b e + (4A b + 4B a b)d e + 2B b d )x +--R + +--R 2 2 2 +--R (4A a b d e + (2A b + 2B a b)d )x + 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 3 5 2 3 2 2 4 +--R - B b e x + (- A b e - 4B b d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (B a e + (- 4A b - 2B a b)d e - 5B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 2 +--R (A a e + (- 2A a b + 2B a )d e + (- 5A b - 4B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (2A a d e + (- 4A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 3 +--R - 2A a b d +--R / +--R 2 2 2 2 +-------+ +--R (b e x + 2b d x - a e + 2a b d)\|e x + d +--R + +--R +-----------+ +--R 2 2 2 |- a e + b d +--R (- 2b e x + (- 2a b e - 2b d)x - 2a b d) |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 3 2 +--R ((- 30A a b + 30B a b)e + (30A b - 30B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (- 30A a b + 30B a )e + (30A a b - 30B a b)d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 2 +-+ |a e - b d +--R ((30A a b - 30B a )e + (- 30A b + 30B a b)d e)\|b |--------- +--R \| b +--R * +--R +------------------+ +-------+ +--R | 2 2 2 \|e x + d +--R \|b x + 2a b x + a atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R - 6B b e x + ((- 10A b + 4B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((20A a b - 20B a b)e + (- 40A b + 28B a b )d e - 6B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (30A a b - 30B a )e + (- 40A a b + 40B a b)d e - 6B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 15b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1223 + +)clear all + +--S 1224 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1378 +r0:=2/3*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b*d-a*e)/(b^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (a+b*x)*sqrt(d+e*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 +-----------+ +--R ((- 6A b + 6B a b)e x + (- 6A a b + 6B a )e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 4B a b)e + 2B b d)x + (6A a b - 6B a )e +--R + +--R 2B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R 3b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a e + b d +--R (3A b - 3B a)e |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|e x + d +--R / +--R 2 +--R 3b e +--R , +--R +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R (- 6A b + 6B a)e |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +-------+ +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|e x + d +--R / +--R 2 +--R 3b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1226 + +--S 1227 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R (3A b - 3B a)e |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 +-----------+ +--R ((6A b - 6B a b)e x + (6A a b - 6B a )e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|b \|e x + d \|b x + 2a b x + a +--R + +--R 2 2 2 2 2 +--R - 2B b e x + ((- 6A b + 4B a b)e - 2B b d)x + (- 6A a b + 6B a )e +--R + +--R - 2B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R 3b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +-----------+ +--R 2 |- a e + b d +-------+ +--R (- 2B b e x + (- 2A b e - 2B b d)x - 2A b d) |----------- \|e x + d +--R \| b +--R + +--R 2 3 2 2 +--R B b e x + ((A b - B a)e + 3B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (3A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 2 +--R 2B b e x + ((2A b + 2B a b)e + 2B b d)x +--R + +--R 2 +--R (2A a b e + (2A b + 2B a b)d)x + 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 2 4 2 2 2 3 +--R - B b e x + (- A b e - 3B b d e)x +--R + +--R 2 2 2 2 2 2 +--R (B a e + (- 3A b - 2B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (- 2A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 2 +--R - 2A a b d +--R / +--R 2 2 2 2 +-------+ +--R (b e x + 2b d x - a e + 2a b d)\|e x + d +--R + +--R +-----------+ +--R 2 2 2 |- a e + b d +--R (- 2b e x + (- 2a b e - 2b d)x - 2a b d) |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 +-----------+ +--R ((6A b - 6B a b)e x + (6A a b - 6B a )e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R (- 6A b + 6B a)e\|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|b \|e x + d \|b x + 2a b x + a +--R + +--R 2 2 2 2 2 +--R - 2B b e x + ((- 6A b + 4B a b)e - 2B b d)x + (- 6A a b + 6B a )e +--R + +--R - 2B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R 3b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1230 + +)clear all + +--S 1231 of 1378 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1378 +r0:=-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(3/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*B*(a+b*x)*_ + sqrt(d+e*x)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 \|b \|e x + d +--R ((- 2A b + 2B a b)e x + (- 2A a b + 2B a )e)atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (2B b x + 2B a)\|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R b e\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (A b - B a)e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R 2B\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R | 2 +--R b e\|- a b e + b d +--R , +--R +-----------+ +--R | 2 +-------+ +-----------+ +--R \|a b e - b d \|e x + d | 2 +-------+ +--R (2A b - 2B a)e atan(------------------------) + 2B\|a b e - b d \|e x + d +--R a e - b d +--R --------------------------------------------------------------------------] +--R +-----------+ +--R | 2 +--R b e\|a b e - b d +--R Type: Union(List(Expression(Integer)),...) +--E 1233 + +--S 1234 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (A b - B a)e\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R 2 2 | 2 +--R ((2A b - 2B a b)e x + (2A a b - 2B a )e)\|- a b e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R 2B\|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R (- 2B b x - 2B a)\|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R b e\|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 +-------+ +--R ((2B a b e - 2B b d)x + 2A a b e - 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 +--R (- 2B a b e + 2B b d)x +--R + +--R 2 2 3 2 2 2 +--R ((- 2A a b - 2B a b)e + (2A b + 2B a b )d)x - 2A a b e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R +-------------+ +--R 2 2 2 2 | 2 +-------+ +--R (b e x + 2b d x - a e + 2a b d)\|- a b e + b d \|e x + d +--R + +--R 2 2 3 2 2 2 3 2 2 2 2 +--R (2a b e - 2b d e)x + (2a b e - 2b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 2 | 2 +--R ((2A b - 2B a b)e x + (2A a b - 2B a )e)\|a b e - b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (2A b - 2B a)e\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R 2B\|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R (- 2B b x - 2B a)\|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R b e\|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (7) -------------------------------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1237 + +)clear all + +--S 1238 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1378 +r0:=-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(3/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*(B*d-A*e)*_ + (a+b*x)/(e*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 +-------+ \|b \|e x + d +--R ((2A b - 2B a b)e x + (2A a b - 2B a )e)\|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R ((- 2A b e + 2B b d)x - 2A a e + 2B a d)\|- a e + b d \|b +--R / +--R +------------------+ +--R 2 +-----------+ +-+ +-------+ | 2 2 2 +--R (a e - b d e)\|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R (A b - B a)e\|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +--R (- 2A e + 2B d)\|- a b e + b d +--R / +--R +-------------+ +--R 2 | 2 +-------+ +--R (a e - b d e)\|- a b e + b d \|e x + d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R (- 2A b + 2B a)e\|e x + d atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +--R (- 2A e + 2B d)\|a b e - b d +--R / +--R +-----------+ +--R 2 | 2 +-------+ +--R (a e - b d e)\|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1240 + +--S 1241 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R (A b - B a)e\|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R 2 2 | 2 +-------+ +--R ((- 2A b + 2B a b)e x + (- 2A a b + 2B a )e)\|- a b e + b d \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R (- 2A e + 2B d)\|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R + +--R +-------------+ +--R | 2 +-----------+ +-+ +--R ((2A b e - 2B b d)x + 2A a e - 2B a d)\|- a b e + b d \|- a e + b d \|b +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +-------+ +--R (a e - b d e)\|- a b e + b d \|- a e + b d \|b \|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 +-------+ +--R ((- 2B a b e + 2B b d)x - 2A a b e + 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 2 3 2 +--R (2B a b e - 2B b d)x + ((2A a b + 2B a b)e + (- 2A b - 2B a b )d)x +--R + +--R 2 2 +--R 2A a b e - 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (b e x + 3b d e x + (- a e + 2a b d e + 2b d )x - a d e + 2a b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (- 2a b e + 2b d e )x + (- 2a b e - 2a b d e + 4b d e)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (- 4a b d e + 2a b d e + 2b d )x - 2a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 2 | 2 +-------+ +--R ((- 2A b + 2B a b)e x + (- 2A a b + 2B a )e)\|a b e - b d \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R (- 2A b + 2B a)e\|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R (- 2A e + 2B d)\|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R + +--R +-----------+ +--R +-----------+ +-+ | 2 +--R ((2A b e - 2B b d)x + 2A a e - 2B a d)\|- a e + b d \|b \|a b e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +-------+ +--R (a e - b d e)\|- a e + b d \|b \|a b e - b d \|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (7) -------------------------------------------------------------- +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))*sqrt(b)/((b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-_ + a*B)*(a+b*x)/((b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 +--R (- 6A b + 6B a b)e x +--R + +--R 2 2 2 2 +--R ((- 6A a b + 6B a )e + (- 6A b + 6B a b)d e)x + (- 6A a b + 6B a )d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +--R (6A b - 6B a b)e x +--R + +--R 2 2 2 2 2 2 2 +--R ((4A a b - 6B a )e + (8A b - 4B a b)d e - 2B b d )x - 2A a e +--R + +--R 2 2 +--R (8A a b - 4B a )d e - 2B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e) +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 | b +-------+ +--R ((3A b - 3B a)e x + (3A b - 3B a)d e) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R (6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e)\|e x + d +--R , +--R +--R +---------+ +--R 2 | b +-------+ +--R ((6A b - 6B a)e x + (6A b - 6B a)d e) |--------- \|e x + d +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 +--R (6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e)\|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1247 + +--S 1248 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R ((3A b - 3B a)e x + (3A b - 3B a)d e)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 +--R (6A b - 6B a b)e x + ((6A a b - 6B a )e + (6A b - 6B a b)d e)x +--R + +--R 2 +--R (6A a b - 6B a )d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +-----------+ +--R ((6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d )\|- a e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 +--R (- 6A b + 6B a b)e x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 4A a b + 6B a )e + (- 8A b + 4B a b)d e + 2B b d )x + 2A a e +--R + +--R 2 2 +--R (- 8A a b + 4B a )d e + 2B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e) +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 2 +--R (6A b - 6B a b)e x + ((6A a b - 6B a )e + (6A b - 6B a b)d e)x +--R + +--R 2 +--R (6A a b - 6B a )d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 +-----------+ | b +--R ((6A b - 6B a)e x + (6A b - 6B a)d e)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +------------------+ +-------+ +--R +-------+ | 2 2 2 b\|e x + d +--R \|e x + d \|b x + 2a b x + a atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 +-----------+ +--R ((6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d )\|- a e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 +--R (- 6A b + 6B a b)e x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 4A a b + 6B a )e + (- 8A b + 4B a b)d e + 2B b d )x + 2A a e +--R + +--R 2 2 +--R (- 8A a b + 4B a )d e + 2B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e) +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1251 + +)clear all + +--S 1252 of 1378 +t0:=(A+B*x)/((d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 1378 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/3*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-2*b^(3/2)*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2*b*(A*b-a*B)*(a+b*x)/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 +--R (30A b - 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((30A a b - 30B a b)e + (60A b - 60B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((60A a b - 60B a b)d e + (30A b - 30B a b )d e)x +--R + +--R 2 2 2 +--R (30A a b - 30B a b)d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 +--R (- 30A b + 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 20A a b + 20B a b)e + (- 70A b + 70B a b )d e )x +--R + +--R 2 3 3 2 2 2 +--R (4A a b - 10B a )e + (- 48A a b + 66B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 46A b + 28B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (22A a b - 4B a )d e + (- 46A a b + 28B a b)d e +--R + +--R 2 3 +--R 6B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 +--R (15A b - 15B a b)e x + (30A b - 30B a b)d e x +--R + +--R 2 2 +--R (15A b - 15B a b)d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 3 2 2 2 +--R (- 30A b + 30B a b)e x + (- 60A b + 60B a b)d e x +--R + +--R 2 2 +--R (- 30A b + 30B a b)d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1254 + +--S 1255 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 +--R (15A b - 15B a b)e x + (30A b - 30B a b)d e x +--R + +--R 2 2 +--R (15A b - 15B a b)d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 +--R (- 30A b + 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 30A a b + 30B a b)e + (- 60A b + 60B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 60A a b + 60B a b)d e + (- 30A b + 30B a b )d e)x +--R + +--R 2 2 2 +--R (- 30A a b + 30B a b)d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 3 2 3 3 +--R (30A b - 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((20A a b - 20B a b)e + (70A b - 70B a b )d e )x +--R + +--R 2 3 3 2 2 2 +--R (- 4A a b + 10B a )e + (48A a b - 66B a b)d e +--R + +--R 3 2 2 3 3 +--R (46A b - 28B a b )d e - 6B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R 6A a e + (- 22A a b + 4B a )d e + (46A a b - 28B a b)d e - 6B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 2 3 3 +--R (- 30A b + 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 30A a b + 30B a b)e + (- 60A b + 60B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 60A a b + 60B a b)d e + (- 30A b + 30B a b )d e)x +--R + +--R 2 2 2 +--R (- 30A a b + 30B a b)d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 2 2 +--R (- 30A b + 30B a b)e x + (- 60A b + 60B a b)d e x +--R + +--R 2 2 +--R (- 30A b + 30B a b)d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 3 2 3 3 +--R (30A b - 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((20A a b - 20B a b)e + (70A b - 70B a b )d e )x +--R + +--R 2 3 3 2 2 2 +--R (- 4A a b + 10B a )e + (48A a b - 66B a b)d e +--R + +--R 3 2 2 3 3 +--R (46A b - 28B a b )d e - 6B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R 6A a e + (- 22A a b + 4B a )d e + (46A a b - 28B a b)d e - 6B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1258 + +)clear all + +--S 1259 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 1378 +r0:=-1/10*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*(d+e*x)^(7/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+2/5*B*(a+b*x)*(d+e*x)^(9/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+7/12*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-7/20*(4*b*B*d+5*A*b*e-_ + 9*a*B*e)*(d+e*x)^(5/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*e*(b*d-_ + a*e)^(3/2)*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/(b^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*e*(b*d-_ + a*e)*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 5 +-+ | 2 2 2 +--R (60b x + 60a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 4 3 2 +--R (- 525A a b + 945B a b )e + (525A b - 1365B a b )d e +--R + +--R 4 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1050A a b + 1890B a b)e + (1050A a b - 2730B a b )d e +--R + +--R 3 2 +--R 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 525A a b + 945B a )e + (525A a b - 1365B a b)d e + 420B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 48B b e x + ((80A b - 144B a b )e + 256B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 560A a b + 1008B a b )e + (800A b - 1888B a b )d e +--R + +--R 4 2 +--R 928B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1750A a b + 3150B a b)e + (2380A a b - 5684B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 390A b + 2606B a b )d e - 120B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 1050A a b + 1890B a )e + (1400A a b - 3360B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 210A a b + 1498B a b )d e + (- 60A b - 60B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 120b x + 240a b x + 120a b +--R , +--R +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 60b x + 120a b x + 60a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1261 + +--S 1262 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 4 3 2 +--R (- 525A a b + 945B a b )e + (525A b - 1365B a b )d e +--R + +--R 4 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1050A a b + 1890B a b)e + (1050A a b - 2730B a b )d e +--R + +--R 3 2 +--R 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 525A a b + 945B a )e + (525A a b - 1365B a b)d e + 420B a b d e +--R * +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 4 2 3 3 5 4 2 +--R (- 1050A a b + 1890B a b )e + (1050A b - 2730B a b )d e +--R + +--R 5 2 +--R 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 3150A a b + 5670B a b )e + (3150A a b - 8190B a b )d e +--R + +--R 4 2 +--R 2520B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 3150A a b + 5670B a b)e + (3150A a b - 8190B a b )d e +--R + +--R 2 3 2 +--R 2520B a b d e +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 1050A a b + 1890B a )e + (1050A a b - 2730B a b)d e +--R + +--R 3 2 2 +--R 840B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 48B b e x + ((80A b - 144B a b )e + 256B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 560A a b + 1008B a b )e + (800A b - 1888B a b )d e +--R + +--R 4 2 +--R 928B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1750A a b + 3150B a b)e + (2380A a b - 5684B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 390A b + 2606B a b )d e - 120B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 1050A a b + 1890B a )e + (1400A a b - 3360B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 210A a b + 1498B a b )d e + (- 60A b - 60B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 3 5 5 4 3 5 2 4 +--R - 48B b e x + ((- 80A b + 96B a b )e - 256B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (480A a b - 864B a b )e + (- 800A b + 1632B a b )d e +--R + +--R 5 2 +--R - 928B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (2310A a b - 4158B a b )e + (- 3180A a b + 7572B a b )d e +--R + +--R 5 4 2 5 3 +--R (390A b - 3534B a b )d e + 120B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2800A a b - 5040B a b)e + (- 3780A a b + 9044B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (600A a b - 4104B a b )d e + (60A b + 180B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (1050A a b - 1890B a )e + (- 1400A a b + 3360B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (210A a b - 1498B a b )d e + (60A a b + 60B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 7 2 6 2 5 +-+ | 2 2 2 +--R (120b x + 240a b x + 120a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 4 5 4 3 4 +--R - 2B b e x + (- 2A b e - 8B b d e )x +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 8A b d e - 12B b d e )x + (- 12A b d e - 8B b d e)x +--R + +--R 3 4 4 +--R (- 8A b d e - 2B b d )x - 2A b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 5 6 5 4 5 +--R B b e x + ((A b - B a)e + 6B b d e )x +--R + +--R 5 4 2 3 4 +--R (- A a e + (6A b - 4B a)d e + 14B b d e )x +--R + +--R 4 2 3 3 2 3 +--R (- 4A a d e + (14A b - 6B a)d e + 16B b d e )x +--R + +--R 2 3 3 2 4 2 +--R (- 6A a d e + (16A b - 4B a)d e + 9B b d e)x +--R + +--R 3 2 4 5 4 5 +--R (- 4A a d e + (9A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 6 2 4 2 3 5 +--R 2B b e x + ((2A b + 2B a b)e + 8B b d e )x +--R + +--R 4 2 3 2 2 2 4 +--R (2A a b e + (8A b + 8B a b)d e + 12B b d e )x +--R + +--R 3 2 2 2 2 3 3 +--R (8A a b d e + (12A b + 12B a b)d e + 8B b d e)x +--R + +--R 2 2 2 3 2 4 2 +--R (12A a b d e + (8A b + 8B a b)d e + 2B b d )x +--R + +--R 3 2 4 4 +--R (8A a b d e + (2A b + 2B a b)d )x + 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 5 7 2 5 2 4 6 +--R - B b e x + (- A b e - 6B b d e )x +--R + +--R 2 5 2 4 2 2 3 5 +--R (B a e + (- 6A b - 2B a b)d e - 14B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (- 2A a b + 4B a )d e + (- 14A b - 8B a b)d e +--R + +--R 2 3 2 +--R - 16B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 4A a d e + (- 8A a b + 6B a )d e + (- 16A b - 12B a b)d e +--R + +--R 2 4 +--R - 9B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 2 +--R (6A a d e + (- 12A a b + 4B a )d e + (- 9A b - 8B a b)d e - 2B b d )x +--R + +--R 2 3 2 2 4 2 5 2 4 +--R (4A a d e + (- 8A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 5 +--R - 2A a b d +--R / +--R 4 4 3 4 3 3 2 3 2 2 4 +--R b e x + (2a b e + 2b d)x + 6a b d x + (- 2a b e + 6a b d)x - a e +--R + +--R 3 +--R 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 4 4 3 4 3 2 2 3 2 +--R - 2b e x + (- 6a b e - 2b d)x + (- 6a b e - 6a b d)x +--R + +--R 3 2 2 3 +--R (- 2a b e - 6a b d)x - 2a b d +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 2 3 3 5 4 2 +--R (- 525A a b + 945B a b )e + (525A b - 1365B a b )d e +--R + +--R 5 2 +--R 420B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 1575A a b + 2835B a b )e + (1575A a b - 4095B a b )d e +--R + +--R 4 2 +--R 1260B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 1575A a b + 2835B a b)e + (1575A a b - 4095B a b )d e +--R + +--R 2 3 2 +--R 1260B a b d e +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 3 2 2 +--R (- 525A a b + 945B a )e + (525A a b - 1365B a b)d e + 420B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 3 5 5 4 3 5 2 4 +--R - 24B b e x + ((- 40A b + 48B a b )e - 128B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (240A a b - 432B a b )e + (- 400A b + 816B a b )d e +--R + +--R 5 2 +--R - 464B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (1155A a b - 2079B a b )e + (- 1590A a b + 3786B a b )d e +--R + +--R 5 4 2 5 3 +--R (195A b - 1767B a b )d e + 60B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (1400A a b - 2520B a b)e + (- 1890A a b + 4522B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (300A a b - 2052B a b )d e + (30A b + 90B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (525A a b - 945B a )e + (- 700A a b + 1680B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (105A a b - 749B a b )d e + (30A a b + 30B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 7 2 6 2 5 +-+ | 2 2 2 +--R (60b x + 120a b x + 60a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 5 +--R - B b e x + ((- A b - B a)e - 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (- A a e + (- 4A b - 4B a)d e - 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (- 4A a d e + (- 6A b - 6B a)d e - 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (- 6A a d e + (- 4A b - 4B a)d e - B b d )x +--R + +--R 3 4 4 +--R (- 4A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1265 + +)clear all + +--S 1266 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1378 +r0:=-1/6*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*(d+e*x)^(5/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+2/3*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))-5/12*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/_ + (b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/_ + (b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*_ + (a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x + (- 45A a b + 105B a )e +--R + +--R 2 +--R - 60B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 5 4 +-+ | 2 2 2 +--R (12b x + 12a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1267 + +--S 1268 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x +--R + +--R 2 3 2 2 +--R (- 45A a b + 105B a )e - 60B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R 16B b e x + ((48A b - 112B a b )e + 112B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((150A a b - 350B a b)e + (- 54A b + 326B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (90A a b - 210B a )e + (- 30A a b + 190B a b)d e +--R + +--R 3 2 2 +--R (- 12A b - 12B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 24b x + 48a b x + 24a b +--R , +--R +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x +--R + +--R 2 3 2 2 +--R (- 45A a b + 105B a )e - 60B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 12b x + 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1268 + +--S 1269 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x + (- 45A a b + 105B a )e +--R + +--R 2 +--R - 60B a b d e +--R * +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((90A b - 210B a b )e + 120B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((270A a b - 630B a b )e + 360B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((270A a b - 630B a b)e + 360B a b d e)x + (90A a b - 210B a )e +--R + +--R 3 +--R 120B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 16B b e x + ((48A b - 112B a b )e + 112B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((150A a b - 350B a b)e + (- 54A b + 326B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (90A a b - 210B a )e + (- 30A a b + 190B a b)d e +--R + +--R 3 2 2 +--R (- 12A b - 12B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 2 4 4 3 2 4 3 +--R - 16B b e x + ((- 48A b + 96B a b )e - 112B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((- 198A a b + 462B a b )e + (54A b - 438B a b )d e + 24B b d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 240A a b + 560B a b)e + (84A a b - 516B a b )d e +--R + +--R 4 3 2 +--R (12A b + 36B a b )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 90A a b + 210B a )e + (30A a b - 190B a b)d e +--R + +--R 3 2 2 2 +--R (12A a b + 12B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 2 5 2 4 +-+ | 2 2 2 +--R (24b x + 48a b x + 24a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 +--R 2B b e x + (2A b e + 6B b d e )x + (6A b d e + 6B b d e)x +--R + +--R 2 3 3 +--R (6A b d e + 2B b d )x + 2A b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 4 5 4 3 4 +--R B b e x + ((A b - B a)e + 5B b d e )x +--R + +--R 4 3 2 2 3 +--R (- A a e + (5A b - 3B a)d e + 9B b d e )x +--R + +--R 3 2 2 3 2 +--R (- 3A a d e + (9A b - 3B a)d e + 7B b d e)x +--R + +--R 2 2 3 4 3 4 +--R (- 3A a d e + (7A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 5 2 3 2 2 4 +--R - 2B b e x + ((- 2A b - 2B a b)e - 6B b d e )x +--R + +--R 3 2 2 2 2 3 +--R (- 2A a b e + (- 6A b - 6B a b)d e - 6B b d e)x +--R + +--R 2 2 2 2 3 2 +--R (- 6A a b d e + (- 6A b - 6B a b)d e - 2B b d )x +--R + +--R 2 2 3 3 +--R (- 6A a b d e + (- 2A b - 2B a b)d )x - 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 4 6 2 4 2 3 5 +--R - B b e x + (- A b e - 5B b d e )x +--R + +--R 2 4 2 3 2 2 2 4 +--R (B a e + (- 5A b - 2B a b)d e - 9B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 3 +--R (A a e + (- 2A a b + 3B a )d e + (- 9A b - 6B a b)d e - 7B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 2 +--R (3A a d e + (- 6A a b + 3B a )d e + (- 7A b - 6B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 3 2 4 2 3 +--R (3A a d e + (- 6A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 4 +--R - 2A a b d +--R / +--R 4 4 3 4 3 3 2 3 2 2 4 +--R b e x + (2a b e + 2b d)x + 6a b d x + (- 2a b e + 6a b d)x - a e +--R + +--R 3 +--R 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 4 4 3 4 3 2 2 3 2 +--R 2b e x + (6a b e + 2b d)x + (6a b e + 6a b d)x +--R + +--R 3 2 2 3 +--R (2a b e + 6a b d)x + 2a b d +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 2 4 3 +--R ((45A b - 105B a b )e + 60B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((135A a b - 315B a b )e + 180B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((135A a b - 315B a b)e + 180B a b d e)x + (45A a b - 105B a )e +--R + +--R 3 +--R 60B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x + (- 45A a b + 105B a )e +--R + +--R 2 +--R - 60B a b d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 2 4 4 3 2 4 3 +--R - 8B b e x + ((- 24A b + 48B a b )e - 56B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((- 99A a b + 231B a b )e + (27A b - 219B a b )d e + 12B b d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 120A a b + 280B a b)e + (42A a b - 258B a b )d e +--R + +--R 4 3 2 +--R (6A b + 18B a b )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 45A a b + 105B a )e + (15A a b - 95B a b)d e +--R + +--R 3 2 2 2 +--R (6A a b + 6B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 2 5 2 4 +-+ | 2 2 2 +--R (12b x + 24a b x + 12a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1272 + +)clear all + +--S 1273 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1378 +r0:=-1/2*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+2*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-3/4*(4*b*B*d+A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 3A b + 15B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b + 30B a b)e - 24B a b d e)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 4 3 +-----------+ +-+ | 2 2 2 +--R (4b x + 4a b )\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R 16B b e x + ((- 10A b + 50B a b)e - 8B b d)x +--R + +--R 2 2 +--R (- 6A a b + 30B a )e + (- 4A b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 5 2 4 2 3 | 2 +--R (8b x + 16a b x + 8a b )\|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 5 2 4 2 3 | 2 +--R (4b x + 8a b x + 4a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1275 + +--S 1276 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((6A b - 30B a b )e + 24B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((18A a b - 90B a b )e + 72B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((18A a b - 90B a b)e + 72B a b d e)x + (6A a b - 30B a )e +--R + +--R 3 +--R 24B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 16B b e x + ((- 10A b + 50B a b)e - 8B b d)x + (- 6A a b + 30B a )e +--R + +--R 2 +--R (- 4A b - 4B a b)d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 3 3 2 3 2 +--R - 16B b e x + ((10A b - 66B a b )e + 8B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((16A a b - 80B a b)e + (4A b + 12B a b )d)x + (6A a b - 30B a )e +--R + +--R 2 2 +--R (4A a b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +--R 5 2 4 2 3 | 2 +-----------+ +-+ +--R (8b x + 16a b x + 8a b )\|- a b e + b d \|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 3 2 2 3 +--R (2B a b e - 2B b d e )x +--R + +--R 3 2 2 2 2 2 +--R (2A a b e + (- 2A b + 4B a b)d e - 4B b d e)x +--R + +--R 2 2 2 2 3 2 +--R (4A a b d e + (- 4A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 3 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 4 3 2 3 +--R B b e x + ((A b - B a)e + 4B b d e )x +--R + +--R 3 2 2 2 +--R (- A a e + (4A b - 2B a)d e + 5B b d e)x +--R + +--R 2 2 3 2 3 +--R (- 2A a d e + (5A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 3 2 4 +--R (- 2B a b e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 3 +--R ((- 2A a b - 2B a b)e + (2A b - 2B a b )d e + 4B b d e)x +--R + +--R 2 3 2 2 2 3 2 2 +--R - 2A a b e + (- 2A a b - 4B a b)d e + (4A b + 2B a b )d e +--R + +--R 3 3 +--R 2B b d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 2 3 +--R (- 4A a b d e + (2A a b - 2B a b)d e + (2A b + 2B a b )d )x +--R + +--R 2 2 2 3 +--R - 2A a b d e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 5 2 3 2 2 4 +--R - B b e x + (- A b e - 4B b d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (B a e + (- 4A b - 2B a b)d e - 5B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 2 +--R (A a e + (- 2A a b + 2B a )d e + (- 5A b - 4B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (2A a d e + (- 4A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 3 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 4 4 3 4 3 3 2 3 2 2 4 +--R b e x + (2a b e + 2b d)x + 6a b d x + (- 2a b e + 6a b d)x - a e +--R + +--R 3 +--R 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (2a b e - 2b d e)x + (6a b e - 4a b d e - 2b d )x +--R + +--R 3 2 2 4 2 2 4 2 3 2 2 3 2 4 +--R (6a b e - 6a b d )x + (2a b e + 4a b d e - 6a b d )x + 2a b d e +--R + +--R 3 2 2 +--R - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 2 4 3 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((9A a b - 45B a b )e + 36B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((9A a b - 45B a b)e + 36B a b d e)x + (3A a b - 15B a )e +--R + +--R 3 +--R 12B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 3 3 2 3 2 +--R - 8B b e x + ((5A b - 33B a b )e + 4B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((8A a b - 40B a b)e + (2A b + 6B a b )d)x + (3A a b - 15B a )e +--R + +--R 2 2 +--R (2A a b + 2B a b)d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 5 2 4 2 3 +-----------+ +-+ | 2 +--R (4b x + 8a b x + 4a b )\|- a e + b d \|b \|a b e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1378 +r0:=-2*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/2*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-1/4*e*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 2A a b - 6B a b)e + 8B a b d e)x + (- A a b - 3B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e + (2A b + 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 3 4 2 2 3 +-----------+ +-+ | 2 2 2 +--R ((4a b e - 4b d)x + 4a b e - 4a b d)\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R ((2A b - 10B a b)e + 8B b d)x + (- 2A a b - 6B a )e +--R + +--R 2 +--R (4A b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +--R ((8a b e - 8b d)x + (16a b e - 16a b d)x + 8a b e - 8a b d) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 +--R ((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e +--R + +--R 2 +--R (2A b + 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 4 5 2 2 3 4 3 2 2 3 | 2 +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1282 + +--S 1283 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((2A b + 6B a b )e - 8B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((6A a b + 18B a b )e - 24B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((6A a b + 18B a b)e - 24B a b d e)x + (2A a b + 6B a )e +--R + +--R 3 +--R - 8B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +--R ((2A b - 10B a b)e + 8B b d)x + (- 2A a b - 6B a )e +--R + +--R 2 +--R (4A b + 4B a b)d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 +--R ((- 2A b + 10B a b )e - 8B b d)x +--R + +--R 2 3 2 2 3 +--R (16B a b e + (- 4A b - 12B a b )d)x + (2A a b + 6B a )e +--R + +--R 2 2 +--R (- 4A a b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +--R ((8a b e - 8b d)x + (16a b e - 16a b d)x + 8a b e - 8a b d) +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 2 +--R (2B a b e - 2B b d e)x +--R + +--R 2 2 2 2 +--R (2A a b e + (- 2A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 2 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 +--R B b e x + ((A b - B a)e + 3B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (3A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 3 +--R (- 2B a b e + 2B b d e)x +--R + +--R 2 2 2 3 3 2 2 +--R ((- 2A a b - 2B a b)e + 2A b d e + 2B b d )x +--R + +--R 2 2 2 3 2 2 2 +--R (- 2A a b e - 2B a b d e + (2A b + 2B a b )d )x - 2A a b d e +--R + +--R 2 2 +--R 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 4 2 2 2 3 +--R - B b e x + (- A b e - 3B b d e)x +--R + +--R 2 2 2 2 2 2 +--R (B a e + (- 3A b - 2B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (- 2A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 2 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 4 4 3 4 3 3 2 3 2 2 4 +--R b e x + (2a b e + 2b d)x + 6a b d x + (- 2a b e + 6a b d)x - a e +--R + +--R 3 +--R 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (2a b e - 2b d e)x + (6a b e - 4a b d e - 2b d )x +--R + +--R 3 2 2 4 2 2 4 2 3 2 2 3 2 4 +--R (6a b e - 6a b d )x + (2a b e + 4a b d e - 6a b d )x + 2a b d e +--R + +--R 3 2 2 +--R - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 2 4 3 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((3A a b + 9B a b )e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 3 +--R ((3A a b + 9B a b)e - 12B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 +--R (((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e + (2A b + 2B a b)d) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R ((- A b + 5B a b )e - 4B b d)x + (8B a b e + (- 2A b - 6B a b )d)x +--R + +--R 2 3 2 2 +--R (A a b + 3B a )e + (- 2A a b - 2B a b)d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +-----------+ +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|- a e + b d +--R * +--R +-----------+ +------------------+ +--R +-+ | 2 | 2 2 2 +--R \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1286 + +)clear all + +--S 1287 of 1378 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1378 +r0:=-2/3*B*(a+b*x)*sqrt(d+e*x)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/6*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/4*e*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 3A b - B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b - 2B a b)e + 8B a b d e)x + (- 3A a b - B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((3A b + B a b)e - 4B b d)x + (5A a b - B a )e + (- 2A b - 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R ((4a b e - 8a b d e + 4b d )x + 4a b e - 8a b d e + 4a b d ) +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R ((6A b + 2B a b)e - 8B b d)x + (10A a b - 2B a )e +--R + +--R 2 +--R (- 4A b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (8a b e - 16a b d e + 8b d )x + (16a b e - 32a b d e + 16a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 8a b e - 16a b d e + 8a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 +--R ((3A b + B a b)e - 4B b d)x + (5A a b - B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 4a b e - 8a b d e + 4a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1289 + +--S 1290 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((6A b + 2B a b )e - 8B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((18A a b + 6B a b )e - 24B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((18A a b + 6B a b)e - 24B a b d e)x + (6A a b + 2B a )e +--R + +--R 3 +--R - 8B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +--R ((6A b + 2B a b)e - 8B b d)x + (10A a b - 2B a )e +--R + +--R 2 +--R (- 4A b - 4B a b)d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 +--R ((- 6A b - 2B a b )e + 8B b d)x +--R + +--R 2 3 2 2 3 +--R (- 16A a b e + (4A b + 12B a b )d)x + (- 10A a b + 2B a )e +--R + +--R 2 2 +--R (4A a b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (8a b e - 16a b d e + 8b d )x + (16a b e - 32a b d e + 16a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 8a b e - 16a b d e + 8a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (5) +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((6A b + 2B a b )e - 8B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((18A a b + 6B a b )e - 24B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((18A a b + 6B a b)e - 24B a b d e)x + (6A a b + 2B a )e +--R + +--R 3 +--R - 8B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +--R ((6A b + 2B a b)e - 8B b d)x + (10A a b - 2B a )e +--R + +--R 2 +--R (- 4A b - 4B a b)d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 +--R ((- 6A b - 2B a b )e + 8B b d)x +--R + +--R 2 3 2 2 3 +--R (- 16A a b e + (4A b + 12B a b )d)x + (- 10A a b + 2B a )e +--R + +--R 2 2 +--R (4A a b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (8a b e - 16a b d e + 8b d )x + (16a b e - 32a b d e + 16a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 8a b e - 16a b d e + 8a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (6) +--R 2 2 +-------+ +--R ((2B a b e - 2B b d)x + 2A a b e - 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 +--R (- 2B a b e + 2B b d)x +--R + +--R 2 2 3 2 2 2 +--R ((- 2A a b - 2B a b)e + (2A b + 2B a b )d)x - 2A a b e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 4 4 3 4 3 3 2 3 2 2 4 +--R b e x + (2a b e + 2b d)x + 6a b d x + (- 2a b e + 6a b d)x - a e +--R + +--R 3 +--R 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (2a b e - 2b d e)x + (6a b e - 4a b d e - 2b d )x +--R + +--R 3 2 2 4 2 2 4 2 3 2 2 3 2 4 +--R (6a b e - 6a b d )x + (2a b e + 4a b d e - 6a b d )x + 2a b d e +--R + +--R 3 2 2 +--R - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (7) +--R 4 3 2 4 3 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((9A a b + 3B a b )e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 3 +--R ((9A a b + 3B a b)e - 12B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 +--R (((3A b + B a b)e - 4B b d)x + (5A a b - B a )e + (- 2A b - 2B a b)d) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R ((- 3A b - B a b )e + 4B b d)x + (- 8A a b e + (2A b + 6B a b )d)x +--R + +--R 2 3 2 2 +--R (- 5A a b + B a )e + (2A a b + 2B a b)d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 4a b e - 8a b d e + 4a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R (8) -------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1295 + +--S 1296 of 1378 +r0:=-2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x))+1/2*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/(e*_ + (b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+3/4*e*(4*b*B*d-5*A*b*e+_ + a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-_ + a*e)^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-3/4*(4*b*B*d-5*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x - 8A a e +--R + +--R 2 2 2 +--R (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x + 4a e - 12a b d e +--R + +--R 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R ((- 30A b + 6B a b)e + 24B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 50A a b + 10B a )e + (- 10A b + 42B a b)d e + 8B b d )x +--R + +--R 2 2 2 2 2 +--R - 16A a e + (- 18A a b + 26B a )d e + (4A b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (8a b e - 24a b d e + 24a b d e - 8b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (16a b e - 48a b d e + 48a b d e - 16a b d )x + 8a e - 24a b d e +--R + +--R 3 2 2 2 3 3 +--R 24a b d e - 8a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 3 2 2 3 2 +--R ((- 15A b + 3B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 30A a b + 6B a b)e + 24B a b d e)x + (- 15A a b + 3B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x +--R + +--R 2 2 2 2 2 +--R - 8A a e + (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1297 + +--S 1298 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 2 4 3 +--R ((- 30A b + 6B a b )e + 24B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((- 90A a b + 18B a b )e + 72B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((- 90A a b + 18B a b)e + 72B a b d e)x + (- 30A a b + 6B a )e +--R + +--R 3 +--R 24B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 +-------+ \|b \|e x + d +--R \|- a b e + b d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((- 30A b + 6B a b)e + 24B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 50A a b + 10B a )e + (- 10A b + 42B a b)d e + 8B b d )x +--R + +--R 2 2 2 2 2 +--R - 16A a e + (- 18A a b + 26B a )d e + (4A b + 4B a b)d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R + +--R 3 2 2 3 3 +--R ((30A b - 6B a b )e - 24B b d e)x +--R + +--R 2 2 2 3 2 3 2 2 +--R ((80A a b - 16B a b)e + (10A b - 66B a b )d e - 8B b d )x +--R + +--R 2 3 2 2 2 +--R (66A a b - 10B a )e + (28A a b - 68B a b)d e +--R + +--R 3 2 2 +--R (- 4A b - 12B a b )d +--R * +--R x +--R + +--R 3 2 2 3 2 2 2 +--R 16A a e + (18A a b - 26B a )d e + (- 4A a b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (8a b e - 24a b d e + 24a b d e - 8b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (16a b e - 48a b d e + 48a b d e - 16a b d )x + 8a e - 24a b d e +--R + +--R 3 2 2 2 3 3 +--R 24a b d e - 8a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 +-------+ +--R ((- 2B a b e + 2B b d)x - 2A a b e + 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 2 3 2 +--R (2B a b e - 2B b d)x + ((2A a b + 2B a b)e + (- 2A b - 2B a b )d)x +--R + +--R 2 2 +--R 2A a b e - 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 4 2 5 3 2 4 4 3 4 2 3 +--R b e x + (2a b e + 3b d e)x + (8a b d e + 2b d )x +--R + +--R 3 2 2 2 3 2 2 4 2 2 2 2 4 +--R (- 2a b e + 6a b d e + 6a b d )x + (- a e + 6a b d )x - a d e +--R + +--R 3 2 +--R 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 4 3 5 2 5 2 3 3 4 2 5 2 4 +--R (- 2a b e + 2b d e )x + (- 6a b e + 2a b d e + 4b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (- 6a b e - 6a b d e + 10a b d e + 2b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 2 +--R (- 2a b e - 10a b d e + 6a b d e + 6a b d )x +--R + +--R 4 2 3 2 2 2 3 3 4 2 3 2 3 +--R (- 4a b d e - 2a b d e + 6a b d )x - 2a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 2 4 3 +--R ((- 15A b + 3B a b )e + 12B b d e)x +--R + +--R 3 2 2 2 3 2 +--R ((- 45A a b + 9B a b )e + 36B a b d e)x +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((- 45A a b + 9B a b)e + 36B a b d e)x + (- 15A a b + 3B a )e +--R + +--R 3 +--R 12B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 +-------+ \|b \|e x + d +--R \|a b e - b d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((- 15A b + 3B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 30A a b + 6B a b)e + 24B a b d e)x + (- 15A a b + 3B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x - 8A a e +--R + +--R 2 2 2 +--R (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R + +--R 3 2 2 3 3 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 2 +--R ((40A a b - 8B a b)e + (5A b - 33B a b )d e - 4B b d )x +--R + +--R 2 3 2 2 2 +--R (33A a b - 5B a )e + (14A a b - 34B a b)d e +--R + +--R 3 2 2 +--R (- 2A b - 6B a b )d +--R * +--R x +--R + +--R 3 2 2 3 2 2 2 +--R 8A a e + (9A a b - 13B a )d e + (- 2A a b - 2B a b)d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1300 + +--S 1301 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1301 + +)clear all + +--S 1302 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1302 + +--S 1303 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/6*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))+5/4*e*(4*b*B*d-_ + 7*A*b*e+3*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b)/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/12*(4*b*B*d-_ + 7*A*b*e+3*a*B*e)/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 105A b + 45B a b )e + 60B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 210A a b + 90B a b)e + (- 105A b + 165B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 105A a b + 45B a )e + (- 210A a b + 150B a b)d e +--R + +--R 2 2 +--R 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (- 105A a b + 45B a )d e + 60B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (12a e - 36a b d e + 24a b d e + 24a b d e - 36a b d e + 12b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (105A a b - 45B a )e + (210A a b - 150B a b)d e +--R + +--R 2 2 +--R - 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 3 +--R ((210A b - 90B a b )e - 120B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((350A a b - 150B a b)e + (280A b - 320B a b )d e - 160B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (112A a b - 48B a )e + (476A a b - 268B a b)d e +--R + +--R 3 2 2 3 3 +--R (42A b - 290B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 16A a e + (160A a b - 32B a )d e + (78A a b - 166B a b)d e +--R + +--R 3 2 3 +--R (- 12A b - 12B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 48a b e - 168a b d e + 192a b d e - 48a b d e - 48a b d e +--R + +--R 6 5 +--R 24b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 24a e - 48a b d e - 48a b d e + 192a b d e - 168a b d e +--R + +--R 5 5 +--R 48a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 24a d e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (105A a b - 45B a )e + (210A a b - 150B a b)d e +--R + +--R 2 2 +--R - 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e +--R + +--R 5 5 +--R 24a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1304 + +--S 1305 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((105A a b - 45B a )e + (210A a b - 150B a b)d e - 120B a b d e)x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 3 3 4 2 4 +--R ((210A b - 90B a b )e - 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (630A a b - 270B a b )e + (210A b - 450B a b )d e +--R + +--R 4 2 +--R - 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (630A a b - 270B a b)e + (630A a b - 630B a b )d e +--R + +--R 3 2 +--R - 360B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R ((210A a b - 90B a )e + (630A a b - 390B a b)d e - 360B a b d e)x +--R + +--R 3 4 2 3 2 +--R (210A a b - 90B a )d e - 120B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((210A b - 90B a b )e - 120B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((350A a b - 150B a b)e + (280A b - 320B a b )d e - 160B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (112A a b - 48B a )e + (476A a b - 268B a b)d e +--R + +--R 3 2 2 3 3 +--R (42A b - 290B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 16A a e + (160A a b - 32B a )d e + (78A a b - 166B a b)d e +--R + +--R 3 2 3 +--R (- 12A b - 12B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 3 4 2 4 +--R ((- 210A b + 90B a b )e + 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 560A a b + 240B a b )e + (- 280A b + 440B a b )d e +--R + +--R 4 2 +--R 160B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 462A a b + 198B a b)e + (- 756A a b + 588B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 42A b + 450B a b )d e + 24B b d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 96A a b + 48B a )e + (- 636A a b + 300B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 120A a b + 456B a b )d e + (12A b + 36B a b )d +--R * +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 16A a e + (- 160A a b + 32B a )d e + (- 78A a b + 166B a b)d e +--R + +--R 3 2 2 3 +--R (12A a b + 12B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 48a b e - 168a b d e + 192a b d e - 48a b d e - 48a b d e +--R + +--R 6 5 +--R 24b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 24a e - 48a b d e - 48a b d e + 192a b d e - 168a b d e +--R + +--R 5 5 +--R 48a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 24a d e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1305 + +--S 1306 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 3 4 2 4 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 3 +--R ((315A a b - 135B a b )e + (105A b - 225B a b )d e - 60B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (315A a b - 135B a b)e + (315A a b - 315B a b )d e +--R + +--R 3 2 +--R - 180B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R ((105A a b - 45B a )e + (315A a b - 195B a b)d e - 180B a b d e)x +--R + +--R 3 4 2 3 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((105A a b - 45B a )e + (210A a b - 150B a b)d e - 120B a b d e)x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 3 4 2 4 +--R ((- 105A b + 45B a b )e + 60B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 120B a b )e + (- 140A b + 220B a b )d e +--R + +--R 4 2 +--R 80B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 231A a b + 99B a b)e + (- 378A a b + 294B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 21A b + 225B a b )d e + 12B b d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 48A a b + 24B a )e + (- 318A a b + 150B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 60A a b + 228B a b )d e + (6A b + 18B a b )d +--R * +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 8A a e + (- 80A a b + 16B a )d e + (- 39A a b + 83B a b)d e +--R + +--R 3 2 2 3 +--R (6A a b + 6B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e + 24a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1308 + +)clear all + +--S 1309 of 1378 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 1378 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/10*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-7/20*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-7/12*e*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^4*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*b^(3/2)*e*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*b*e*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 5 2 +--R - 60b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 6 3 3 3 4 2 4 4 3 5 5 2 +--R 60a e - 180a b d e + 600a b d e - 900a b d e + 540a b d e +--R + +--R 6 6 +--R - 120b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5 6 +--R 120a d e - 540a b d e + 900a b d e - 600a b d e + 180a b d e +--R + +--R 6 7 +--R - 60b d +--R * +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 5 7 +--R - 60a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 4 3 4 +--R ((- 1890A b + 1050B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3150A a b + 1750B a b )e + (- 4410A b + 3850B a b )d e +--R + +--R 4 2 2 +--R 1960B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 1008A a b + 560B a b)e + (- 7434A a b + 4578B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 2898A b + 4914B a b )d e + 1288B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 80B a )e + (- 2448A a b + 1296B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 4986A a b + 3858B a b )d e + (- 270A b + 2366B a b )d e +--R + +--R 4 4 +--R 120B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 48A a e + (336A a b - 32B a )d e + (- 1728A a b + 544B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 510A a b + 1318B a b )d e + (60A b + 60B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 120a b e - 600a b d e + 1200a b d e - 1200a b d e +--R + +--R 6 4 3 7 5 2 +--R 600a b d e - 120b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 +--R 240a b e - 960a b d e + 1200a b d e - 1200a b d e +--R + +--R 6 5 2 7 6 +--R 960a b d e - 240b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 120a e - 120a b d e - 1080a b d e + 3000a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 3000a b d e + 1080a b d e + 120a b d e - 120b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 +--R 240a d e - 960a b d e + 1200a b d e - 1200a b d e +--R + +--R 2 5 6 6 7 +--R 960a b d e - 240a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 120a d e - 600a b d e + 1200a b d e - 1200a b d e + 600a b d e +--R + +--R 2 5 7 +--R - 120a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1890A a b + 1050B a b )e + (- 1890A b + 1890B a b )d e +--R + +--R 4 2 2 +--R 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 945A a b + 525B a b)e + (- 3780A a b + 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 945A b + 2205B a b )d e + 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 +--R (- 1890A a b + 1050B a b)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 1890A a b + 1890B a b )d e + 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 945A a b + 525B a b)d e + 420B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 7 5 2 +--R - 60b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 120a b e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 7 6 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 60a e - 60a b d e - 540a b d e + 1500a b d e - 1500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 540a b d e + 60a b d e - 60b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 120a d e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 6 7 +--R - 120a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 2 5 7 +--R - 60a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1311 + +--S 1312 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 5 4 4 5 3 5 +--R ((- 1890A b + 1050B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 5670A a b + 3150B a b )e + (- 3780A b + 4620B a b )d e +--R + +--R 5 2 2 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 5670A a b + 3150B a b )e + (- 11340A a b + 8820B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1890A b + 6090B a b )d e + 840B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 1890A a b + 1050B a b)e + (- 11340A a b + 7140B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (- 5670A a b + 8190B a b )d e + 2520B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (- 3780A a b + 2100B a b)d e + (- 5670A a b + 4830B a b )d e +--R + +--R 2 3 3 +--R 2520B a b d e +--R * +--R x +--R + +--R 3 2 4 2 2 3 2 3 +--R (- 1890A a b + 1050B a b)d e + 840B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 1890A b + 1050B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3150A a b + 1750B a b )e + (- 4410A b + 3850B a b )d e +--R + +--R 4 2 2 +--R 1960B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 1008A a b + 560B a b)e + (- 7434A a b + 4578B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 2898A b + 4914B a b )d e + 1288B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 80B a )e + (- 2448A a b + 1296B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 4986A a b + 3858B a b )d e + (- 270A b + 2366B a b )d e +--R + +--R 4 4 +--R 120B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 48A a e + (336A a b - 32B a )d e + (- 1728A a b + 544B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 510A a b + 1318B a b )d e + (60A b + 60B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 5 4 4 5 3 5 +--R ((1890A b - 1050B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (5040A a b - 2800B a b )e + (4410A b - 4690B a b )d e +--R + +--R 5 2 2 +--R - 1960B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4158A a b - 2310B a b )e + (11844A a b - 8428B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (2898A b - 6874B a b )d e - 1288B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (864A a b - 480B a b)e + (9882A a b - 5874B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (7884A a b - 8772B a b )d e + (270A b - 3654B a b )d e +--R + +--R 5 4 +--R - 120B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 96A a b + 80B a )e + (2112A a b - 1264B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (6714A a b - 4402B a b )d e + (780A a b - 3684B a b )d e +--R + +--R 5 4 4 +--R (- 60A b - 180B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R 48A a e + (- 336A a b + 32B a )d e + (1728A a b - 544B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (510A a b - 1318B a b )d e + (- 60A a b - 60B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 120a b e - 600a b d e + 1200a b d e - 1200a b d e + 600a b d e +--R + +--R 7 5 2 +--R - 120b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 240a b e - 960a b d e + 1200a b d e - 1200a b d e + 960a b d e +--R + +--R 7 6 +--R - 240b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 120a e - 120a b d e - 1080a b d e + 3000a b d e - 3000a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 1080a b d e + 120a b d e - 120b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 240a d e - 960a b d e + 1200a b d e - 1200a b d e + 960a b d e +--R + +--R 6 7 +--R - 240a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 120a d e - 600a b d e + 1200a b d e - 1200a b d e + 600a b d e +--R + +--R 2 5 7 +--R - 120a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 4 4 5 3 5 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 2835A a b + 1575B a b )e + (- 1890A b + 2310B a b )d e +--R + +--R 5 2 2 +--R 840B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 2835A a b + 1575B a b )e + (- 5670A a b + 4410B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 945A b + 3045B a b )d e + 420B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 945A a b + 525B a b)e + (- 5670A a b + 3570B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (- 2835A a b + 4095B a b )d e + 1260B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (- 1890A a b + 1050B a b)d e + (- 2835A a b + 2415B a b )d e +--R + +--R 2 3 3 +--R 1260B a b d e +--R * +--R x +--R + +--R 3 2 4 2 2 3 2 3 +--R (- 945A a b + 525B a b)d e + 420B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1890A a b + 1050B a b )e + (- 1890A b + 1890B a b )d e +--R + +--R 4 2 2 +--R 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 945A a b + 525B a b)e + (- 3780A a b + 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 945A b + 2205B a b )d e + 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 1890A a b + 1050B a b)d e + (- 1890A a b + 1890B a b )d e +--R + +--R 3 3 +--R 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 945A a b + 525B a b)d e + 420B a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 5 4 4 5 3 5 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (2520A a b - 1400B a b )e + (2205A b - 2345B a b )d e +--R + +--R 5 2 2 +--R - 980B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (2079A a b - 1155B a b )e + (5922A a b - 4214B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (1449A b - 3437B a b )d e - 644B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (432A a b - 240B a b)e + (4941A a b - 2937B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (3942A a b - 4386B a b )d e + (135A b - 1827B a b )d e +--R + +--R 5 4 +--R - 60B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 40B a )e + (1056A a b - 632B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (3357A a b - 2201B a b )d e + (390A a b - 1842B a b )d e +--R + +--R 5 4 4 +--R (- 30A b - 90B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R 24A a e + (- 168A a b + 16B a )d e + (864A a b - 272B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (255A a b - 659B a b )d e + (- 30A a b - 30B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 7 5 2 +--R - 60b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 120a b e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 7 6 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 60a e - 60a b d e - 540a b d e + 1500a b d e - 1500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 540a b d e + 60a b d e - 60b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 120a d e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 6 7 +--R - 120a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 2 5 7 +--R - 60a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1315 + +)clear all + +--S 1316 of 1378 +t0:=(A+B*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1378 +r0:=-1/20*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*(d+e*x)^(11/2)/(b^2*e*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))+2/5*B*(a+b*x)*(d+e*x)^(13/2)/(b*e*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-33/160*e*(8*b*B*d+5*A*b*e-13*a*B*e)*_ + (a+b*x)*(d+e*x)^(7/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-11/120*_ + (8*b*B*d+5*A*b*e-13*a*B*e)*(d+e*x)^(9/2)/(b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+77/64*e^3*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*(d+_ + e*x)^(3/2)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))-231/320*e^2*(8*b*B*d+_ + 5*A*b*e-13*a*B*e)*(d+e*x)^(5/2)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 231/64*e^3*(b*d-a*e)^(3/2)*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(15/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+231/64*e^3*(b*d-a*e)*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*_ + sqrt(d+e*x)/(b^7*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 2 4 5 6 5 4 +--R (17325A a b - 45045B a b )e + (- 17325A b + 72765B a b )d e +--R + +--R 6 2 3 +--R - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (69300A a b - 180180B a b )e +--R + +--R 5 2 4 4 5 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (103950A a b - 270270B a b )e +--R + +--R 2 4 3 3 4 2 4 2 3 +--R (- 103950A a b + 436590B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (69300A a b - 180180B a b)e +--R + +--R 3 3 4 2 4 3 3 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (17325A a b - 45045B a )e + (- 17325A a b + 72765B a b)d e +--R + +--R 4 2 2 3 +--R - 27720B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 384B b e x + ((640A b - 1664B a b )e + 3328B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 7040A a b + 18304B a b )e + (10240A b - 37888B a b )d e +--R + +--R 6 2 3 +--R 22144B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (- 46035A a b + 119691B a b )e +--R + +--R 5 2 4 4 +--R (63910A a b - 239822B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 11475A b + 132091B a b )d e - 10680B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (- 84315A a b + 219219B a b )e +--R + +--R 2 4 3 3 4 +--R (114840A a b - 433488B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 18975A a b + 233079B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 5150A b - 16970B a b )d e - 2480B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 63525A a b + 165165B a b)e +--R + +--R 3 3 4 2 4 +--R (85470A a b - 323862B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 13365A a b + 171501B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3740A a b - 11660B a b )d e + (- 1640A b - 1720B a b )d e +--R + +--R 6 5 +--R - 320B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 17325A a b + 45045B a )e + (23100A a b - 87780B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 3465A a b + 45969B a b )d e + (- 990A a b - 2970B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 440A a b - 440B a b )d e + (- 240A b - 80B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 10 3 9 2 2 8 3 7 +-+ | 2 2 2 +--R (960b x + 2880a b x + 2880a b x + 960a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 2 4 5 6 5 4 +--R (- 17325A a b + 45045B a b )e + (17325A b - 72765B a b )d e +--R + +--R 6 2 3 +--R 27720B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (- 69300A a b + 180180B a b )e +--R + +--R 5 2 4 4 5 2 3 +--R (69300A a b - 291060B a b )d e + 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (- 103950A a b + 270270B a b )e +--R + +--R 2 4 3 3 4 2 4 2 3 +--R (103950A a b - 436590B a b )d e + 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 69300A a b + 180180B a b)e +--R + +--R 3 3 4 2 4 3 3 2 3 +--R (69300A a b - 291060B a b )d e + 110880B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 17325A a b + 45045B a )e + (17325A a b - 72765B a b)d e +--R + +--R 4 2 2 3 +--R 27720B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b 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+--R +--R (6) +--R 6 2 5 5 7 6 4 +--R (- 17325A a b + 45045B a b )e + (17325A b - 72765B a b )d e +--R + +--R 7 2 3 +--R 27720B b d e +--R * +--R 5 +--R x +--R + +--R 2 5 3 4 5 +--R (- 86625A a b + 225225B a b )e +--R + +--R 6 2 5 4 6 2 3 +--R (86625A a b - 363825B a b )d e + 138600B a b d e +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 5 +--R (- 173250A a b + 450450B a b )e +--R + +--R 2 5 3 4 4 2 5 2 3 +--R (173250A a b - 727650B a b )d e + 277200B a b d e +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 5 +--R (- 173250A a b + 450450B a b )e +--R + +--R 3 4 4 3 4 3 4 2 3 +--R (173250A a b - 727650B a b )d e + 277200B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 +--R (- 86625A a b + 225225B a b)e +--R + +--R 4 3 5 2 4 4 3 2 3 +--R (86625A a b - 363825B a b )d e + 138600B a b d e +--R * +--R x +--R + +--R 6 7 5 5 2 6 4 +--R (- 17325A a b + 45045B a )e + (17325A a b - 72765B a b)d e +--R + +--R 5 2 2 3 +--R 27720B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 2 4 5 6 5 4 +--R (17325A a b - 45045B a b )e + (- 17325A b + 72765B a b )d e +--R + +--R 6 2 3 +--R - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (69300A a b - 180180B a b )e +--R + +--R 5 2 4 4 5 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (103950A a b - 270270B a b )e +--R + +--R 2 4 3 3 4 2 4 2 3 +--R (- 103950A a b + 436590B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (69300A a b - 180180B a b)e +--R + +--R 3 3 4 2 4 3 3 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (17325A a b - 45045B a )e + (- 17325A a b + 72765B a b)d e +--R + +--R 4 2 2 3 +--R - 27720B a b d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 384B b e x + ((640A b - 1664B a b )e + 3328B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 7040A a b + 18304B a b )e + (10240A b - 37888B a b )d e +--R + +--R 6 2 3 +--R 22144B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (- 46035A a b + 119691B a b )e +--R + +--R 5 2 4 4 +--R (63910A a b - 239822B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 11475A b + 132091B a b )d e - 10680B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (- 84315A a b + 219219B a b )e +--R + +--R 2 4 3 3 4 +--R (114840A a b - 433488B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 18975A a b + 233079B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 5150A b - 16970B a b )d e - 2480B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 63525A a b + 165165B a b)e +--R + +--R 3 3 4 2 4 +--R (85470A a b - 323862B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 13365A a b + 171501B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3740A a b - 11660B a b )d e + (- 1640A b - 1720B a b )d e +--R + +--R 6 5 +--R - 320B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 17325A a b + 45045B a )e + (23100A a b - 87780B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 3465A a b + 45969B a b )d e + (- 990A a b - 2970B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 440A a b - 440B a b )d e + (- 240A b - 80B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 7 5 7 7 6 5 7 4 6 +--R - 384B b e x + ((- 640A b + 1280B a b )e - 3328B b d e )x +--R + +--R 6 2 5 5 7 6 4 +--R (6400A a b - 16640B a b )e + (- 10240A b + 34560B a b )d e +--R + +--R 7 2 3 +--R - 22144B b d e +--R * +--R 5 +--R x +--R + +--R 2 5 3 4 5 +--R (53075A a b - 137995B a b )e +--R + +--R 6 2 5 4 +--R (- 74150A a b + 277710B a b )d e +--R + +--R 7 6 2 3 7 3 2 +--R (11475A b - 154235B a b )d e + 10680B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 5 +--R (130350A a b - 338910B a b )e +--R + +--R 2 5 3 4 4 +--R (- 178750A a b + 673310B a b )d e +--R + +--R 6 2 5 2 3 7 6 3 2 +--R (30450A a b - 365170B a b )d e + (5150A b + 27650B a b )d e +--R + +--R 7 4 +--R 2480B b d e +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 5 +--R (147840A a b - 384384B a b )e +--R + +--R 3 4 4 3 4 +--R (- 200310A a b + 757350B a b )d e +--R + +--R 2 5 3 4 2 3 6 2 5 3 2 +--R (32340A a b - 404580B a b )d e + (8890A a b + 28630B a b )d e +--R + +--R 7 6 4 7 5 +--R (1640A b + 4200B a b )d e + 320B b d +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 +--R (80850A a b - 210210B a b)e +--R + +--R 4 3 5 2 4 +--R (- 108570A a b + 411642B a b )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (16830A a b - 217470B a b )d e + (4730A a b + 14630B a b )d e +--R + +--R 6 2 5 4 7 6 5 +--R (2080A a b + 2160B a b )d e + (240A b + 400B a b )d +--R * +--R x +--R + +--R 6 7 5 5 2 6 4 +--R (17325A a b - 45045B a )e + (- 23100A a b + 87780B a b)d e +--R + +--R 4 3 5 2 2 3 3 4 4 3 3 2 +--R (3465A a b - 45969B a b )d e + (990A a b + 2970B a b )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (440A a b + 440B a b )d e + (240A a b + 80B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +-+ +--R (960b x + 3840a b x + 5760a b x + 3840a b x + 960a b )\|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 6 7 6 5 6 5 2 4 5 +--R B e x + (A e + 6B d e )x + (6A d e + 15B d e )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (15A d e + 20B d e )x + (20A d e + 15B d e )x +--R + +--R 4 2 5 2 5 6 6 +--R (15A d e + 6B d e)x + (6A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 8 6 5 7 +--R - B b e x + ((- A b - B a)e - 6B b d e )x +--R + +--R 6 5 2 4 6 +--R (- A a e + (- 6A b - 6B a)d e - 15B b d e )x +--R + +--R 5 2 4 3 3 5 +--R (- 6A a d e + (- 15A b - 15B a)d e - 20B b d e )x +--R + +--R 2 4 3 3 4 2 4 +--R (- 15A a d e + (- 20A b - 20B a)d e - 15B b d e )x +--R + +--R 3 3 4 2 5 3 +--R (- 20A a d e + (- 15A b - 15B a)d e - 6B b d e)x +--R + +--R 4 2 5 6 2 +--R (- 15A a d e + (- 6A b - 6B a)d e - B b d )x +--R + +--R 5 6 6 +--R (- 6A a d e + (- A b - B a)d )x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1322 + +)clear all + +--S 1323 of 1378 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1323 + +--S 1324 of 1378 +r0:=-1/12*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*(d+e*x)^(9/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2))+2/3*B*(a+b*x)*(d+e*x)^(11/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-7/32*e*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*(d+_ + e*x)^(5/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/8*(8*b*B*d+3*A*b*e-_ + 11*a*B*e)*(d+e*x)^(7/2)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 35/64*e^2*(8*b*B*d+3*A*b*e-11*a*B*e)*(d+e*x)^(3/2)/(b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-105/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(13/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+105/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*_ + (a+b*x)*sqrt(d+e*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 128B b e x + ((384A b - 1408B a b )e + 1664B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (2511A a b - 9207B a b )e + (- 975A b + 10271B a b )d e +--R + +--R 5 2 2 +--R - 1320B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4599A a b - 16863B a b )e + (- 1665A a b + 18369B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 630A b - 2130B a b )d e - 400B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (3465A a b - 12705B a b)e + (- 1197A a b + 13629B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 468A a b - 1476B a b )d e + (- 264A b - 280B a b )d e +--R + +--R 5 4 +--R - 64B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (945A a b - 3465B a )e + (- 315A a b + 3675B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 126A a b - 378B a b )d e + (- 72A a b - 72B a b )d e +--R + +--R 5 4 4 +--R (- 48A b - 16B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 9 3 8 2 2 7 3 6 +-+ | 2 2 2 +--R (192b x + 576a b x + 576a b x + 192a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 256B b e x + ((768A b - 2816B a b )e + 3328B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (5022A a b - 18414B a b )e + (- 1950A b + 20542B a b )d e +--R + +--R 5 2 2 +--R - 2640B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (9198A a b - 33726B a b )e + (- 3330A a b + 36738B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1260A b - 4260B a b )d e - 800B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (6930A a b - 25410B a b)e + (- 2394A a b + 27258B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 936A a b - 2952B a b )d e + (- 528A b - 560B a b )d e +--R + +--R 5 4 +--R - 128B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (1890A a b - 6930B a )e + (- 630A a b + 7350B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 252A a b - 756B a b )d e + (- 144A a b - 144B a b )d e +--R + +--R 5 4 4 +--R (- 96A b - 32B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 384b x + 1536a b x + 2304a b x + 1536a b x + 384a b +--R , +--R +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 128B b e x + ((384A b - 1408B a b )e + 1664B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (2511A a b - 9207B a b )e + (- 975A b + 10271B a b )d e +--R + +--R 5 2 2 +--R - 1320B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4599A a b - 16863B a b )e + (- 1665A a b + 18369B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 630A b - 2130B a b )d e - 400B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (3465A a b - 12705B a b)e + (- 1197A a b + 13629B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 468A a b - 1476B a b )d e + (- 264A b - 280B a b )d e +--R + +--R 5 4 +--R - 64B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (945A a b - 3465B a )e + (- 315A a b + 3675B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 126A a b - 378B a b )d e + (- 72A a b - 72B a b )d e +--R + +--R 5 4 4 +--R (- 48A b - 16B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 192b x + 768a b x + 1152a b x + 768a b x + 192a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1325 + +--S 1326 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((1890A b - 6930B a b )e + 5040B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((9450A a b - 34650B a b )e + 25200B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((18900A a b - 69300B a b )e + 50400B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((18900A a b - 69300B a b )e + 50400B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((9450A a b - 34650B a b)e + 25200B a b d e )x +--R + +--R 5 6 4 5 3 +--R (1890A a b - 6930B a )e + 5040B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 256B b e x + ((768A b - 2816B a b )e + 3328B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (5022A a b - 18414B a b )e + (- 1950A b + 20542B a b )d e +--R + +--R 5 2 2 +--R - 2640B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (9198A a b - 33726B a b )e + (- 3330A a b + 36738B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1260A b - 4260B a b )d e - 800B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (6930A a b - 25410B a b)e + (- 2394A a b + 27258B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 936A a b - 2952B a b )d e + (- 528A b - 560B a b )d e +--R + +--R 5 4 +--R - 128B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (1890A a b - 6930B a )e + (- 630A a b + 7350B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 252A a b - 756B a b )d e + (- 144A a b - 144B a b )d e +--R + +--R 5 4 4 +--R (- 96A b - 32B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 6 4 6 6 5 4 6 3 5 +--R - 256B b e x + ((- 768A b + 2560B a b )e - 3328B b d e )x +--R + +--R 5 2 4 4 6 5 3 +--R (- 5790A a b + 21230B a b )e + (1950A b - 23870B a b )d e +--R + +--R 6 2 2 +--R 2640B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 14220A a b + 52140B a b )e + (5280A a b - 57280B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (1260A b + 6900B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (- 16128A a b + 59136B a b )e + (5724A a b - 63996B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 +--R (2196A a b + 7212B a b )d e + (528A b + 1360B a b )d e +--R + +--R 6 4 +--R 128B b d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 8820A a b + 32340B a b)e + (3024A a b - 34608B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (1188A a b + 3708B a b )d e + (672A a b + 704B a b )d e +--R + +--R 6 5 4 +--R (96A b + 160B a b )d +--R * +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 1890A a b + 6930B a )e + (630A a b - 7350B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (252A a b + 756B a b )d e + (144A a b + 144B a b )d e +--R + +--R 5 2 4 4 +--R (96A a b + 32B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +-+ +--R (384b x + 1536a b x + 2304a b x + 1536a b x + 384a b )\|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 5 6 5 4 5 +--R 2B b e x + (2A b e + 10B b d e )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (10A b d e + 20B b d e )x + (20A b d e + 20B b d e )x +--R + +--R 3 2 4 2 4 5 5 +--R (20A b d e + 10B b d e)x + (10A b d e + 2B b d )x + 2A b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 6 7 6 5 6 +--R B b e x + ((A b - B a)e + 7B b d e )x +--R + +--R 6 5 2 4 5 +--R (- A a e + (7A b - 5B a)d e + 20B b d e )x +--R + +--R 5 2 4 3 3 4 +--R (- 5A a d e + (20A b - 10B a)d e + 30B b d e )x +--R + +--R 2 4 3 3 4 2 3 +--R (- 10A a d e + (30A b - 10B a)d e + 25B b d e )x +--R + +--R 3 3 4 2 5 2 +--R (- 10A a d e + (25A b - 5B a)d e + 11B b d e)x +--R + +--R 4 2 5 6 5 6 +--R (- 5A a d e + (11A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 5 7 2 5 2 4 6 +--R - 2B b e x + ((- 2A b - 2B a b)e - 10B b d e )x +--R + +--R 5 2 4 2 2 3 5 +--R (- 2A a b e + (- 10A b - 10B a b)d e - 20B b d e )x +--R + +--R 4 2 2 3 2 3 2 4 +--R (- 10A a b d e + (- 20A b - 20B a b)d e - 20B b d e )x +--R + +--R 2 3 2 3 2 2 4 3 +--R (- 20A a b d e + (- 20A b - 20B a b)d e - 10B b d e)x +--R + +--R 3 2 2 4 2 5 2 +--R (- 20A a b d e + (- 10A b - 10B a b)d e - 2B b d )x +--R + +--R 4 2 5 5 +--R (- 10A a b d e + (- 2A b - 2B a b)d )x - 2A a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 6 8 2 6 2 5 7 +--R - B b e x + (- A b e - 7B b d e )x +--R + +--R 2 6 2 5 2 2 4 6 +--R (B a e + (- 7A b - 2B a b)d e - 20B b d e )x +--R + +--R 2 6 2 5 2 2 4 +--R A a e + (- 2A a b + 5B a )d e + (- 20A b - 10B a b)d e +--R + +--R 2 3 3 +--R - 30B b d e +--R * +--R 5 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 5A a d e + (- 10A a b + 10B a )d e + (- 30A b - 20B a b)d e +--R + +--R 2 4 2 +--R - 25B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R 10A a d e + (- 20A a b + 10B a )d e + (- 25A b - 20B a b)d e +--R + +--R 2 5 +--R - 11B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 10A a d e + (- 20A a b + 5B a )d e + (- 11A b - 10B a b)d e +--R + +--R 2 6 +--R - 2B b d +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 5 2 6 2 5 +--R (5A a d e + (- 10A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 6 +--R - 2A a b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 6 6 5 6 5 2 4 5 4 +--R 2b e x + (10a b e + 2b d)x + (20a b e + 10a b d)x +--R + +--R 3 3 2 4 3 4 2 3 3 2 5 4 2 +--R (20a b e + 20a b d)x + (10a b e + 20a b d)x + (2a b e + 10a b d)x +--R + +--R 5 +--R 2a b d +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1327 + +--S 1328 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((945A b - 3465B a b )e + 2520B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((4725A a b - 17325B a b )e + 12600B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((9450A a b - 34650B a b )e + 25200B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((9450A a b - 34650B a b )e + 25200B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((4725A a b - 17325B a b)e + 12600B a b d e )x +--R + +--R 5 6 4 5 3 +--R (945A a b - 3465B a )e + 2520B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 128B b e x + ((384A b - 1408B a b )e + 1664B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (2511A a b - 9207B a b )e + (- 975A b + 10271B a b )d e +--R + +--R 5 2 2 +--R - 1320B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4599A a b - 16863B a b )e + (- 1665A a b + 18369B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 630A b - 2130B a b )d e - 400B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (3465A a b - 12705B a b)e + (- 1197A a b + 13629B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 468A a b - 1476B a b )d e + (- 264A b - 280B a b )d e +--R + +--R 5 4 +--R - 64B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (945A a b - 3465B a )e + (- 315A a b + 3675B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 126A a b - 378B a b )d e + (- 72A a b - 72B a b )d e +--R + +--R 5 4 4 +--R (- 48A b - 16B a b )d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 6 4 6 6 5 4 6 3 5 +--R - 128B b e x + ((- 384A b + 1280B a b )e - 1664B b d e )x +--R + +--R 5 2 4 4 6 5 3 +--R (- 2895A a b + 10615B a b )e + (975A b - 11935B a b )d e +--R + +--R 6 2 2 +--R 1320B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 7110A a b + 26070B a b )e + (2640A a b - 28640B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (630A b + 3450B a b )d e + 400B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (- 8064A a b + 29568B a b )e + (2862A a b - 31998B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 6 4 +--R (1098A a b + 3606B a b )d e + (264A b + 680B a b )d e + 64B b d +--R * +--R 2 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 4410A a b + 16170B a b)e + (1512A a b - 17304B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (594A a b + 1854B a b )d e + (336A a b + 352B a b )d e +--R + +--R 6 5 4 +--R (48A b + 80B a b )d +--R * +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 945A a b + 3465B a )e + (315A a b - 3675B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (126A a b + 378B a b )d e + (72A a b + 72B a b )d e +--R + +--R 5 2 4 4 +--R (48A a b + 16B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x +--R + +--R 5 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 7 5 4 6 +--R - B b e x + ((- A b - B a)e - 5B b d e )x +--R + +--R 5 4 2 3 5 +--R (- A a e + (- 5A b - 5B a)d e - 10B b d e )x +--R + +--R 4 2 3 3 2 4 +--R (- 5A a d e + (- 10A b - 10B a)d e - 10B b d e )x +--R + +--R 2 3 3 2 4 3 +--R (- 10A a d e + (- 10A b - 10B a)d e - 5B b d e)x +--R + +--R 3 2 4 5 2 +--R (- 10A a d e + (- 5A b - 5B a)d e - B b d )x +--R + +--R 4 5 5 +--R (- 5A a d e + (- A b - B a)d )x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1329 + +)clear all + +--S 1330 of 1378 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1330 + +--S 1331 of 1378 +r0:=-1/4*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*(d+e*x)^(7/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+2*B*(a+b*x)*(d+e*x)^(9/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-35/96*e*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*(d+_ + e*x)^(3/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-7/24*(8*b*B*d+A*b*e-_ + 9*a*B*e)*(d+e*x)^(5/2)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-35/64*e^3*_ + (8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))/(b^(11/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*_ + (8*b*B*d+A*b*e-9*a*B*e)*sqrt(d+e*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 105A b + 945B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 420A a b + 3780B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 630A a b + 5670B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 420A a b + 3780B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 105A a b + 945B a )e - 840B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 384B b e x + ((- 279A b + 2511B a b )e - 696B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 511A a b + 4599B a b )e + (- 326A b - 1154B a b )d e +--R + +--R 4 2 +--R - 304B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 385A a b + 3465B a b)e + (- 252A a b - 812B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 200A b - 216B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 105A a b + 945B a )e + (- 70A a b - 210B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 56A a b - 56B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +-----------+ +-+ +--R (192b x + 576a b x + 576a b x + 192a b )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((105A b - 945B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b - 3780B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b - 5670B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((420A a b - 3780B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (105A a b - 945B a )e + 840B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 768B b e x + ((- 558A b + 5022B a b )e - 1392B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 1022A a b + 9198B a b )e + (- 652A b - 2308B a b )d e +--R + +--R 4 2 +--R - 608B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 770A a b + 6930B a b)e + (- 504A a b - 1624B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 400A b - 432B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 1890B a )e + (- 140A a b - 420B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 112A a b - 112B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 9 4 8 3 2 7 2 3 6 4 5 | 2 +--R (384b x + 1536a b x + 2304a b x + 1536a b x + 384a b )\|- a b e + b d +--R , +--R +--R 5 4 4 5 3 4 +--R ((105A b - 945B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b - 3780B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b - 5670B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((420A a b - 3780B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (105A a b - 945B a )e + 840B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 384B b e x + ((- 279A b + 2511B a b )e - 696B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 511A a b + 4599B a b )e + (- 326A b - 1154B a b )d e +--R + +--R 4 2 +--R - 304B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 385A a b + 3465B a b)e + (- 252A a b - 812B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 200A b - 216B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 105A a b + 945B a )e + (- 70A a b - 210B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 56A a b - 56B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 9 4 8 3 2 7 2 3 6 4 5 | 2 +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1332 + +--S 1333 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((105A b - 945B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b - 3780B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b - 5670B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((420A a b - 3780B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (105A a b - 945B a )e + 840B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((210A b - 1890B a b )e + 1680B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((1050A a b - 9450B a b )e + 8400B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((2100A a b - 18900B a b )e + 16800B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((2100A a b - 18900B a b )e + 16800B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((1050A a b - 9450B a b)e + 8400B a b d e )x +--R + +--R 5 6 4 5 3 +--R (210A a b - 1890B a )e + 1680B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 768B b e x + ((- 558A b + 5022B a b )e - 1392B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 1022A a b + 9198B a b )e + (- 652A b - 2308B a b )d e +--R + +--R 4 2 +--R - 608B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 770A a b + 6930B a b)e + (- 504A a b - 1624B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 400A b - 432B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 1890B a )e + (- 140A a b - 420B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 112A a b - 112B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 3 5 5 4 3 5 2 4 +--R - 768B b e x + ((558A b - 5790B a b )e + 1392B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (1580A a b - 14220B a b )e + (652A b + 3700B a b )d e +--R + +--R 5 2 +--R 608B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (1792A a b - 16128B a b )e + (1156A a b + 3932B a b )d e +--R + +--R 5 4 2 5 3 +--R (400A b + 1040B a b )d e + 128B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (980A a b - 8820B a b)e + (644A a b + 2044B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (512A a b + 544B a b )d e + (96A b + 160B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (210A a b - 1890B a )e + (140A a b + 420B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (112A a b + 112B a b )d e + (96A a b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +--R 9 4 8 3 2 7 2 3 6 4 5 | 2 +--R (384b x + 1536a b x + 2304a b x + 1536a b x + 384a b )\|- a b e + b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 5 2 4 5 +--R (2B a b e - 2B b d e )x +--R + +--R 5 2 4 2 2 3 4 +--R (2A a b e + (- 2A b + 8B a b)d e - 8B b d e )x +--R + +--R 4 2 2 3 2 3 2 3 +--R (8A a b d e + (- 8A b + 12B a b)d e - 12B b d e )x +--R + +--R 2 3 2 3 2 2 4 2 +--R (12A a b d e + (- 12A b + 8B a b)d e - 8B b d e)x +--R + +--R 3 2 2 4 2 5 4 +--R (8A a b d e + (- 8A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 5 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 5 6 5 4 5 +--R B b e x + ((A b - B a)e + 6B b d e )x +--R + +--R 5 4 2 3 4 +--R (- A a e + (6A b - 4B a)d e + 14B b d e )x +--R + +--R 4 2 3 3 2 3 +--R (- 4A a d e + (14A b - 6B a)d e + 16B b d e )x +--R + +--R 2 3 3 2 4 2 +--R (- 6A a d e + (16A b - 4B a)d e + 9B b d e)x +--R + +--R 3 2 4 5 4 5 +--R (- 4A a d e + (9A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 5 3 4 6 +--R (- 2B a b e + 2B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 5 +--R ((- 2A a b - 2B a b)e + (2A b - 6B a b )d e + 8B b d e )x +--R + +--R 2 5 2 2 4 3 2 2 3 +--R - 2A a b e + (- 6A a b - 8B a b)d e + (8A b - 4B a b )d e +--R + +--R 3 3 2 +--R 12B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 2 2 2 3 +--R - 8A a b d e + (- 4A a b - 12B a b)d e +--R + +--R 3 2 3 2 3 4 +--R (12A b + 4B a b )d e + 8B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 2 3 2 3 2 4 +--R - 12A a b d e + (4A a b - 8B a b)d e + (8A b + 6B a b )d e +--R + +--R 3 5 +--R 2B b d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 4 3 2 5 +--R (- 8A a b d e + (6A a b - 2B a b)d e + (2A b + 2B a b )d )x +--R + +--R 2 4 2 5 +--R - 2A a b d e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 5 7 2 5 2 4 6 +--R - B b e x + (- A b e - 6B b d e )x +--R + +--R 2 5 2 4 2 2 3 5 +--R (B a e + (- 6A b - 2B a b)d e - 14B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (- 2A a b + 4B a )d e + (- 14A b - 8B a b)d e +--R + +--R 2 3 2 +--R - 16B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 4A a d e + (- 8A a b + 6B a )d e + (- 16A b - 12B a b)d e +--R + +--R 2 4 +--R - 9B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 6A a d e + (- 12A a b + 4B a )d e + (- 9A b - 8B a b)d e +--R + +--R 2 5 +--R - 2B b d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 4 2 5 2 4 +--R (4A a d e + (- 8A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 5 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 2 7 6 2 5 2 6 7 2 5 +--R (2a b e - 2b d e)x + (10a b e - 8a b d e - 2b d )x +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 2 5 2 3 +--R (20a b e - 10a b d e - 10a b d )x + (20a b e - 20a b d )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (10a b e + 10a b d e - 20a b d )x + (2a b e + 8a b d e - 10a b d )x +--R + +--R 6 5 2 2 +--R 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1334 + +--S 1335 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((105A b - 945B a b )e + 840B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((525A a b - 4725B a b )e + 4200B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((1050A a b - 9450B a b )e + 8400B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((1050A a b - 9450B a b )e + 8400B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((525A a b - 4725B a b)e + 4200B a b d e )x +--R + +--R 5 6 4 5 3 +--R (105A a b - 945B a )e + 840B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b - 945B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b - 3780B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b - 5670B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((420A a b - 3780B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (105A a b - 945B a )e + 840B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 384B b e x + ((- 279A b + 2511B a b )e - 696B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 511A a b + 4599B a b )e + (- 326A b - 1154B a b )d e +--R + +--R 4 2 +--R - 304B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 385A a b + 3465B a b)e + (- 252A a b - 812B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 200A b - 216B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 105A a b + 945B a )e + (- 70A a b - 210B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 56A a b - 56B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 5 3 5 5 4 3 5 2 4 +--R - 384B b e x + ((279A b - 2895B a b )e + 696B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (790A a b - 7110B a b )e + (326A b + 1850B a b )d e +--R + +--R 5 2 +--R 304B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (896A a b - 8064B a b )e + (578A a b + 1966B a b )d e +--R + +--R 5 4 2 5 3 +--R (200A b + 520B a b )d e + 64B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (490A a b - 4410B a b)e + (322A a b + 1022B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (256A a b + 272B a b )d e + (48A b + 80B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (105A a b - 945B a )e + (70A a b + 210B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (56A a b + 56B a b )d e + (48A a b + 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +-----------+ +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|- a e + b d \|b +--R * +--R +-----------+ +------------------+ +--R | 2 | 2 2 2 +--R \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 4 3 5 +--R - B b e x + ((- A b - B a)e - 4B b d e )x +--R + +--R 4 3 2 2 4 +--R (- A a e + (- 4A b - 4B a)d e - 6B b d e )x +--R + +--R 3 2 2 3 3 +--R (- 4A a d e + (- 6A b - 6B a)d e - 4B b d e)x +--R + +--R 2 2 3 4 2 +--R (- 6A a d e + (- 4A b - 4B a)d e - B b d )x +--R + +--R 3 4 4 +--R (- 4A a d e + (- A b - B a)d )x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1336 + +)clear all + +--S 1337 of 1378 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1337 + +--S 1338 of 1378 +r0:=1/4*(8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*(d+e*x)^(5/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-2*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+5/24*(8*b*B*d-A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+5/32*e*(8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/64*e^3*_ + (8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))/(b^(9/2)*(b*d-a*e)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^2*_ + (8*b*B*d-A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 15A b - 105B a b )e + 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 60A a b - 420B a b )e + 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 90A a b - 630B a b )e + 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 60A a b - 420B a b)e + 480B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 15A a b - 105B a )e + 120B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b - 279B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 73A a b - 511B a b )e + (118A b + 258B a b )d e +--R + +--R 4 2 +--R 208B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 55A a b - 385B a b)e + (- 36A a b + 188B a b )d e +--R + +--R 4 3 2 4 3 +--R (136A b + 88B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 105B a )e + (- 10A a b + 50B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 8A a b + 24B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 8 3 2 6 7 2 +--R (192a b e - 192b d)x + (576a b e - 576a b d)x +--R + +--R 3 5 2 6 4 4 3 5 +--R (576a b e - 576a b d)x + 192a b e - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((15A b + 105B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 420B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 630B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 420B a b)e - 480B a b d e )x + (15A a b + 105B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 3 4 2 3 +--R ((30A b - 558B a b )e + 528B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 146A a b - 1022B a b )e + (236A b + 516B a b )d e +--R + +--R 4 2 +--R 416B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 110A a b - 770B a b)e + (- 72A a b + 376B a b )d e +--R + +--R 4 3 2 4 3 +--R (272A b + 176B a b )d e + 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 30A a b - 210B a )e + (- 20A a b + 100B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 16A a b + 48B a b )d e + (96A b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 8 9 4 2 7 8 3 +--R (384a b e - 384b d)x + (1536a b e - 1536a b d)x +--R + +--R 3 6 2 7 2 4 5 3 6 5 4 +--R (2304a b e - 2304a b d)x + (1536a b e - 1536a b d)x + 384a b e +--R + +--R 4 5 +--R - 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 5 4 4 5 3 4 +--R ((15A b + 105B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 420B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 630B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 420B a b)e - 480B a b d e )x + (15A a b + 105B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b - 279B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 73A a b - 511B a b )e + (118A b + 258B a b )d e +--R + +--R 4 2 +--R 208B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 55A a b - 385B a b)e + (- 36A a b + 188B a b )d e +--R + +--R 4 3 2 4 3 +--R (136A b + 88B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 105B a )e + (- 10A a b + 50B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 8A a b + 24B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 8 9 4 2 7 8 3 +--R (192a b e - 192b d)x + (768a b e - 768a b d)x +--R + +--R 3 6 2 7 2 4 5 3 6 5 4 +--R (1152a b e - 1152a b d)x + (768a b e - 768a b d)x + 192a b e +--R + +--R 4 5 +--R - 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1339 + +--S 1340 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((15A b + 105B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 420B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 630B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 420B a b)e - 480B a b d e )x + (15A a b + 105B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((30A b + 210B a b )e - 240B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((150A a b + 1050B a b )e - 1200B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((300A a b + 2100B a b )e - 2400B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((300A a b + 2100B a b )e - 2400B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((150A a b + 1050B a b)e - 1200B a b d e )x + (30A a b + 210B a )e +--R + +--R 5 3 +--R - 240B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((30A b - 558B a b )e + 528B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 146A a b - 1022B a b )e + (236A b + 516B a b )d e +--R + +--R 4 2 +--R 416B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 110A a b - 770B a b)e + (- 72A a b + 376B a b )d e +--R + +--R 4 3 2 4 3 +--R (272A b + 176B a b )d e + 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 30A a b - 210B a )e + (- 20A a b + 100B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 16A a b + 48B a b )d e + (96A b + 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 30A b + 558B a b )e - 528B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (116A a b + 1580B a b )e + (- 236A b - 1044B a b )d e +--R + +--R 5 2 +--R - 416B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (256A a b + 1792B a b )e + (- 164A a b - 892B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 272A b - 592B a b )d e - 128B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (140A a b + 980B a b)e + (92A a b - 476B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 256A a b - 224B a b )d e + (- 96A b - 160B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (30A a b + 210B a )e + (20A a b - 100B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (16A a b - 48B a b )d e + (- 96A a b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 8 9 4 2 7 8 3 +--R (384a b e - 384b d)x + (1536a b e - 1536a b d)x +--R + +--R 3 6 2 7 2 4 5 3 6 5 4 +--R (2304a b e - 2304a b d)x + (1536a b e - 1536a b d)x + 384a b e +--R + +--R 4 5 +--R - 384a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 4 2 3 4 +--R (2B a b e - 2B b d e )x +--R + +--R 4 2 3 2 2 2 3 +--R (2A a b e + (- 2A b + 6B a b)d e - 6B b d e )x +--R + +--R 3 2 2 2 2 3 2 +--R (6A a b d e + (- 6A b + 6B a b)d e - 6B b d e)x +--R + +--R 2 2 2 3 2 4 3 +--R (6A a b d e + (- 6A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 4 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 4 5 4 3 4 +--R B b e x + ((A b - B a)e + 5B b d e )x +--R + +--R 4 3 2 2 3 +--R (- A a e + (5A b - 3B a)d e + 9B b d e )x +--R + +--R 3 2 2 3 2 +--R (- 3A a d e + (9A b - 3B a)d e + 7B b d e)x +--R + +--R 2 2 3 4 3 4 +--R (- 3A a d e + (7A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 3 3 5 +--R (- 2B a b e + 2B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 4 +--R ((- 2A a b - 2B a b)e + (2A b - 4B a b )d e + 6B b d e )x +--R + +--R 2 4 2 2 3 3 2 2 3 3 3 +--R (- 2A a b e + (- 4A a b - 6B a b)d e + 6A b d e + 6B b d e)x +--R + +--R 2 3 2 2 2 3 2 3 3 4 2 +--R (- 6A a b d e - 6B a b d e + (6A b + 4B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 2 3 3 2 4 +--R (- 6A a b d e + (4A a b - 2B a b)d e + (2A b + 2B a b )d )x +--R + +--R 2 3 2 4 +--R - 2A a b d e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 6 2 4 2 3 5 +--R - B b e x + (- A b e - 5B b d e )x +--R + +--R 2 4 2 3 2 2 2 4 +--R (B a e + (- 5A b - 2B a b)d e - 9B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R A a e + (- 2A a b + 3B a )d e + (- 9A b - 6B a b)d e +--R + +--R 2 3 +--R - 7B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 3A a d e + (- 6A a b + 3B a )d e + (- 7A b - 6B a b)d e +--R + +--R 2 4 +--R - 2B b d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 3 2 4 2 3 +--R (3A a d e + (- 6A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 4 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 2 7 6 2 5 2 6 7 2 5 +--R (2a b e - 2b d e)x + (10a b e - 8a b d e - 2b d )x +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 2 5 2 3 +--R (20a b e - 10a b d e - 10a b d )x + (20a b e - 20a b d )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (10a b e + 10a b d e - 20a b d )x + (2a b e + 8a b d e - 10a b d )x +--R + +--R 6 5 2 2 +--R 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((15A b + 105B a b )e - 120B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((75A a b + 525B a b )e - 600B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((150A a b + 1050B a b )e - 1200B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((150A a b + 1050B a b )e - 1200B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((75A a b + 525B a b)e - 600B a b d e )x + (15A a b + 105B a )e +--R + +--R 5 3 +--R - 120B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((15A b + 105B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 420B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 630B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 420B a b)e - 480B a b d e )x + (15A a b + 105B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b - 279B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 73A a b - 511B a b )e + (118A b + 258B a b )d e +--R + +--R 4 2 +--R 208B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 55A a b - 385B a b)e + (- 36A a b + 188B a b )d e +--R + +--R 4 3 2 4 3 +--R (136A b + 88B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 105B a )e + (- 10A a b + 50B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 8A a b + 24B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 15A b + 279B a b )e - 264B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (58A a b + 790B a b )e + (- 118A b - 522B a b )d e +--R + +--R 5 2 +--R - 208B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (128A a b + 896B a b )e + (- 82A a b - 446B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 136A b - 296B a b )d e - 64B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (70A a b + 490B a b)e + (46A a b - 238B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 128A a b - 112B a b )d e + (- 48A b - 80B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (15A a b + 105B a )e + (10A a b - 50B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (8A a b - 24B a b )d e + (- 48A a b - 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 8 9 4 2 7 8 3 +--R (192a b e - 192b d)x + (768a b e - 768a b d)x +--R + +--R 3 6 2 7 2 4 5 3 6 5 4 4 5 +--R (1152a b e - 1152a b d)x + (768a b e - 768a b d)x + 192a b e - 192a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 3 2 4 +--R - B b e x + ((- A b - B a)e - 3B b d e )x +--R + +--R 3 2 2 3 +--R (- A a e + (- 3A b - 3B a)d e - 3B b d e)x +--R + +--R 2 2 3 2 +--R (- 3A a d e + (- 3A b - 3B a)d e - B b d )x +--R + +--R 2 3 3 +--R (- 3A a d e + (- A b - B a)d )x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1343 + +)clear all + +--S 1344 of 1378 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1344 + +--S 1345 of 1378 +r0:=1/12*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-2/3*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/24*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/96*e*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+_ + b*x)*sqrt(d+e*x)/(b^3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/64*e^3*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-1/64*e^2*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*(b*d-_ + a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 9A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 36A a b - 60B a b )e + 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 54A a b - 90B a b )e + 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((- 36A a b - 60B a b)e + 96B a b d e )x + (- 9A a b - 15B a )e +--R + +--R 4 3 +--R 24B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((33A a b - 73B a b )e + (- 6A b + 158B a b )d e - 112B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 33A a b - 55B a b)e + (132A a b + 52B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 72A b + 40B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 9A a b - 15B a )e + (- 6A a b + 14B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (72A a b + 8B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 6 2 7 8 2 3 +--R (192a b e - 384a b d e + 192b d )x +--R + +--R 3 5 2 2 6 7 2 2 +--R (576a b e - 1152a b d e + 576a b d )x +--R + +--R 4 4 2 3 5 2 6 2 5 3 2 4 4 +--R (576a b e - 1152a b d e + 576a b d )x + 192a b e - 384a b d e +--R + +--R 3 5 2 +--R 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((36A a b + 60B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((54A a b + 90B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((36A a b + 60B a b)e - 96B a b d e )x + (9A a b + 15B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 3 4 2 3 +--R ((18A b + 30B a b )e - 48B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (66A a b - 146B a b )e + (- 12A b + 316B a b )d e +--R + +--R 4 2 +--R - 224B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 66A a b - 110B a b)e + (264A a b + 104B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 144A b + 80B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 18A a b - 30B a )e + (- 12A a b + 28B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (144A a b + 16B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 7 2 8 9 2 4 +--R (384a b e - 768a b d e + 384b d )x +--R + +--R 3 6 2 2 7 8 2 3 +--R (1536a b e - 3072a b d e + 1536a b d )x +--R + +--R 4 5 2 3 6 2 7 2 2 +--R (2304a b e - 4608a b d e + 2304a b d )x +--R + +--R 5 4 2 4 5 3 6 2 6 3 2 5 4 +--R (1536a b e - 3072a b d e + 1536a b d )x + 384a b e - 768a b d e +--R + +--R 4 5 2 +--R 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 5 4 4 5 3 4 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((36A a b + 60B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((54A a b + 90B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((36A a b + 60B a b)e - 96B a b d e )x + (9A a b + 15B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (33A a b - 73B a b )e + (- 6A b + 158B a b )d e +--R + +--R 4 2 +--R - 112B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 33A a b - 55B a b)e + (132A a b + 52B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 72A b + 40B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 9A a b - 15B a )e + (- 6A a b + 14B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (72A a b + 8B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 7 2 8 9 2 4 +--R (192a b e - 384a b d e + 192b d )x +--R + +--R 3 6 2 2 7 8 2 3 +--R (768a b e - 1536a b d e + 768a b d )x +--R + +--R 4 5 2 3 6 2 7 2 2 +--R (1152a b e - 2304a b d e + 1152a b d )x +--R + +--R 5 4 2 4 5 3 6 2 6 3 2 5 4 +--R (768a b e - 1536a b d e + 768a b d )x + 192a b e - 384a b d e +--R + +--R 4 5 2 +--R 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1346 + +--S 1347 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((36A a b + 60B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((54A a b + 90B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((36A a b + 60B a b)e - 96B a b d e )x + (9A a b + 15B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((18A b + 30B a b )e - 48B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((90A a b + 150B a b )e - 240B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((180A a b + 300B a b )e - 480B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((180A a b + 300B a b )e - 480B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((90A a b + 150B a b)e - 240B a b d e )x + (18A a b + 30B a )e +--R + +--R 5 3 +--R - 48B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((18A b + 30B a b )e - 48B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (66A a b - 146B a b )e + (- 12A b + 316B a b )d e +--R + +--R 4 2 +--R - 224B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 66A a b - 110B a b)e + (264A a b + 104B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 144A b + 80B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 18A a b - 30B a )e + (- 12A a b + 28B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (144A a b + 16B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 18A b - 30B a b )e + 48B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (- 84A a b + 116B a b )e + (12A b - 268B a b )d e +--R + +--R 5 2 +--R 224B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 3 4 2 3 2 +--R 256B a b e + (- 252A a b - 420B a b )d e +--R + +--R 5 4 2 5 3 +--R (144A b + 144B a b )d e + 128B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (84A a b + 140B a b)e + (- 252A a b - 132B a b )d e +--R + +--R 2 3 2 5 4 3 +--R - 96B a b d e + (96A b + 160B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (18A a b + 30B a )e + (12A a b - 28B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 144A a b - 16B a b )d e + (96A a b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 2 7 2 8 9 2 4 +--R (384a b e - 768a b d e + 384b d )x +--R + +--R 3 6 2 2 7 8 2 3 +--R (1536a b e - 3072a b d e + 1536a b d )x +--R + +--R 4 5 2 3 6 2 7 2 2 +--R (2304a b e - 4608a b d e + 2304a b d )x +--R + +--R 5 4 2 4 5 3 6 2 6 3 2 5 4 +--R (1536a b e - 3072a b d e + 1536a b d )x + 384a b e - 768a b d e +--R + +--R 4 5 2 +--R 384a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 3 2 2 3 +--R (2B a b e - 2B b d e )x +--R + +--R 3 2 2 2 2 2 +--R (2A a b e + (- 2A b + 4B a b)d e - 4B b d e)x +--R + +--R 2 2 2 2 3 2 +--R (4A a b d e + (- 4A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 3 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 4 3 2 3 +--R B b e x + ((A b - B a)e + 4B b d e )x +--R + +--R 3 2 2 2 +--R (- A a e + (4A b - 2B a)d e + 5B b d e)x +--R + +--R 2 2 3 2 3 +--R (- 2A a d e + (5A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 3 2 4 +--R (- 2B a b e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 3 +--R ((- 2A a b - 2B a b)e + (2A b - 2B a b )d e + 4B b d e)x +--R + +--R 2 3 2 2 2 3 2 2 +--R - 2A a b e + (- 2A a b - 4B a b)d e + (4A b + 2B a b )d e +--R + +--R 3 3 +--R 2B b d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 2 3 +--R (- 4A a b d e + (2A a b - 2B a b)d e + (2A b + 2B a b )d )x +--R + +--R 2 2 2 3 +--R - 2A a b d e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 5 2 3 2 2 4 +--R - B b e x + (- A b e - 4B b d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (B a e + (- 4A b - 2B a b)d e - 5B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 2 +--R (A a e + (- 2A a b + 2B a )d e + (- 5A b - 4B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 3 2 2 +--R (2A a d e + (- 4A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 3 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 2 7 6 2 5 2 6 7 2 5 +--R (2a b e - 2b d e)x + (10a b e - 8a b d e - 2b d )x +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 2 5 2 3 +--R (20a b e - 10a b d e - 10a b d )x + (20a b e - 20a b d )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (10a b e + 10a b d e - 20a b d )x + (2a b e + 8a b d e - 10a b d )x +--R + +--R 6 5 2 2 +--R 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((45A a b + 75B a b )e - 120B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((90A a b + 150B a b )e - 240B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((90A a b + 150B a b )e - 240B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((45A a b + 75B a b)e - 120B a b d e )x + (9A a b + 15B a )e +--R + +--R 5 3 +--R - 24B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((36A a b + 60B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((54A a b + 90B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((36A a b + 60B a b)e - 96B a b d e )x + (9A a b + 15B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((33A a b - 73B a b )e + (- 6A b + 158B a b )d e - 112B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 33A a b - 55B a b)e + (132A a b + 52B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 72A b + 40B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 9A a b - 15B a )e + (- 6A a b + 14B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (72A a b + 8B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 9A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((- 42A a b + 58B a b )e + (6A b - 134B a b )d e + 112B b d e)x +--R + +--R 3 2 3 4 2 3 2 +--R 128B a b e + (- 126A a b - 210B a b )d e +--R + +--R 5 4 2 5 3 +--R (72A b + 72B a b )d e + 64B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (42A a b + 70B a b)e + (- 126A a b - 66B a b )d e +--R + +--R 2 3 2 5 4 3 +--R - 48B a b d e + (48A b + 80B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (9A a b + 15B a )e + (6A a b - 14B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 72A a b - 8B a b )d e + (48A a b + 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 2 7 2 8 9 2 4 +--R (192a b e - 384a b d e + 192b d )x +--R + +--R 3 6 2 2 7 8 2 3 +--R (768a b e - 1536a b d e + 768a b d )x +--R + +--R 4 5 2 3 6 2 7 2 2 +--R (1152a b e - 2304a b d e + 1152a b d )x +--R + +--R 5 4 2 4 5 3 6 2 6 3 2 5 4 +--R (768a b e - 1536a b d e + 768a b d )x + 192a b e - 384a b d e +--R + +--R 4 5 2 +--R 192a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R 2 3 2 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 2 3 +--R - B b e x + ((- A b - B a)e - 2B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (- 2A b - 2B a)d e - B b d )x +--R + +--R 2 2 +--R (- 2A a d e + (- A b - B a)d )x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1350 + +)clear all + +--S 1351 of 1378 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1378 +r0:=-2/5*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/20*(8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-1/24*(8*b*B*d-5*A*b*e-3*a*B*e)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/96*e*_ + (8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-1/64*e^3*(8*b*B*d-5*A*b*e-3*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-_ + a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/64*e^2*(8*b*B*d-5*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 15A b - 9B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 60A a b - 36B a b )e + 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 90A a b - 54B a b )e + 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((- 60A a b - 36B a b)e + 96B a b d e )x + (- 15A a b - 9B a )e +--R + +--R 4 3 +--R 24B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((55A a b + 33B a b )e + (- 10A b - 94B a b )d e + 16B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (73A a b - 33B a b)e + (- 36A a b + 92B a b )d e +--R + +--R 4 3 2 4 3 +--R (8A b - 168B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 9B a )e + (118A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 136A a b - 40B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 3 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 2 +--R (576a b e - 1728a b d e + 1728a b d e - 576a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 6 2 3 +--R (576a b e - 1728a b d e + 1728a b d e - 576a b d )x + 192a b e +--R + +--R 5 3 2 4 4 2 3 5 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1352 + +--S 1353 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 36B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 54B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 36B a b)e - 96B a b d e )x + (15A a b + 9B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 3 4 2 3 +--R ((30A b + 18B a b )e - 48B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (110A a b + 66B a b )e + (- 20A b - 188B a b )d e +--R + +--R 4 2 +--R 32B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (146A a b - 66B a b)e + (- 72A a b + 184B a b )d e +--R + +--R 4 3 2 4 3 +--R (16A b - 336B a b )d e + 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 30A a b - 18B a )e + (236A a b + 36B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 272A a b - 80B a b )d e + (96A b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 3 6 3 2 7 2 8 2 9 3 4 +--R (384a b e - 1152a b d e + 1152a b d e - 384b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 2 +--R (2304a b e - 6912a b d e + 6912a b d e - 2304a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 7 2 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x + 384a b e +--R + +--R 6 3 2 5 4 2 4 5 3 +--R - 1152a b d e + 1152a b d e - 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 5 4 4 5 3 4 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 36B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 54B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 36B a b)e - 96B a b d e )x + (15A a b + 9B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((55A a b + 33B a b )e + (- 10A b - 94B a b )d e + 16B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (73A a b - 33B a b)e + (- 36A a b + 92B a b )d e +--R + +--R 4 3 2 4 3 +--R (8A b - 168B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 9B a )e + (118A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 136A a b - 40B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 3 6 3 2 7 2 8 2 9 3 4 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 2 +--R (1152a b e - 3456a b d e + 3456a b d e - 1152a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 7 2 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x + 192a b e +--R + +--R 6 3 2 5 4 2 4 5 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1353 + +--S 1354 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 36B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 54B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 36B a b)e - 96B a b d e )x + (15A a b + 9B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((30A b + 18B a b )e - 48B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((150A a b + 90B a b )e - 240B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((300A a b + 180B a b )e - 480B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((300A a b + 180B a b )e - 480B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((150A a b + 90B a b)e - 240B a b d e )x + (30A a b + 18B a )e +--R + +--R 5 3 +--R - 48B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((30A b + 18B a b )e - 48B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((110A a b + 66B a b )e + (- 20A b - 188B a b )d e + 32B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (146A a b - 66B a b)e + (- 72A a b + 184B a b )d e +--R + +--R 4 3 2 4 3 +--R (16A b - 336B a b )d e + 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 30A a b - 18B a )e + (236A a b + 36B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 272A a b - 80B a b )d e + (96A b + 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 30A b - 18B a b )e + 48B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((- 140A a b - 84B a b )e + (20A b + 236B a b )d e - 32B b d e)x +--R + +--R 2 3 3 4 2 3 2 +--R - 256A a b e + (92A a b + 4B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 16A b + 304B a b )d e - 128B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 116A a b + 84B a b)e + (- 164A a b - 220B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (256A a b + 416B a b )d e + (- 96A b - 160B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (30A a b + 18B a )e + (- 236A a b - 36B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (272A a b + 80B a b )d e + (- 96A a b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 3 6 3 2 7 2 8 2 9 3 4 +--R (384a b e - 1152a b d e + 1152a b d e - 384b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 2 +--R (2304a b e - 6912a b d e + 6912a b d e - 2304a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 7 2 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x + 384a b e +--R + +--R 6 3 2 5 4 2 4 5 3 +--R - 1152a b d e + 1152a b d e - 384a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1354 + +--S 1355 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 2 +--R (2B a b e - 2B b d e)x +--R + +--R 2 2 2 2 +--R (2A a b e + (- 2A b + 2B a b)d e - 2B b d )x + 2A a b d e +--R + +--R 2 2 +--R - 2A b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 +--R B b e x + ((A b - B a)e + 3B b d e)x +--R + +--R 2 2 2 +--R (- A a e + (3A b - B a)d e + 2B b d )x - A a d e + 2A b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 3 +--R (- 2B a b e + 2B b d e)x +--R + +--R 2 2 2 3 3 2 2 +--R ((- 2A a b - 2B a b)e + 2A b d e + 2B b d )x +--R + +--R 2 2 2 3 2 2 2 +--R (- 2A a b e - 2B a b d e + (2A b + 2B a b )d )x - 2A a b d e +--R + +--R 2 2 +--R 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 4 2 2 2 3 +--R - B b e x + (- A b e - 3B b d e)x +--R + +--R 2 2 2 2 2 2 +--R (B a e + (- 3A b - 2B a b)d e - 2B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (- 2A a b + B a )d e + (- 2A b - 2B a b)d )x + A a d e +--R + +--R 2 +--R - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 2 7 6 2 5 2 6 7 2 5 +--R (2a b e - 2b d e)x + (10a b e - 8a b d e - 2b d )x +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 2 5 2 3 +--R (20a b e - 10a b d e - 10a b d )x + (20a b e - 20a b d )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (10a b e + 10a b d e - 20a b d )x + (2a b e + 8a b d e - 10a b d )x +--R + +--R 6 5 2 2 +--R 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1355 + +--S 1356 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((75A a b + 45B a b )e - 120B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((150A a b + 90B a b )e - 240B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((150A a b + 90B a b )e - 240B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((75A a b + 45B a b)e - 120B a b d e )x + (15A a b + 9B a )e +--R + +--R 5 3 +--R - 24B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((60A a b + 36B a b )e - 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((90A a b + 54B a b )e - 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((60A a b + 36B a b)e - 96B a b d e )x + (15A a b + 9B a )e +--R + +--R 4 3 +--R - 24B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((55A a b + 33B a b )e + (- 10A b - 94B a b )d e + 16B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (73A a b - 33B a b)e + (- 36A a b + 92B a b )d e +--R + +--R 4 3 2 4 3 +--R (8A b - 168B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 9B a )e + (118A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 136A a b - 40B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 15A b - 9B a b )e + 24B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((- 70A a b - 42B a b )e + (10A b + 118B a b )d e - 16B b d e)x +--R + +--R 2 3 3 4 2 3 2 +--R - 128A a b e + (46A a b + 2B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 8A b + 152B a b )d e - 64B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 58A a b + 42B a b)e + (- 82A a b - 110B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (128A a b + 208B a b )d e + (- 48A b - 80B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (15A a b + 9B a )e + (- 118A a b - 18B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (136A a b + 40B a b )d e + (- 48A a b - 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 3 6 3 2 7 2 8 2 9 3 4 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 2 +--R (1152a b e - 3456a b d e + 3456a b d e - 1152a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 7 2 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x + 192a b e +--R + +--R 6 3 2 5 4 2 4 5 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 2 | 2 2 2 3 +--R (B e x + (A e + B d)x + A d)\|b x + 2a b x + a - B b e x +--R + +--R 2 +--R ((- A b - B a)e - B b d)x + (- A a e + (- A b - B a)d)x - A a d +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1357 + +)clear all + +--S 1358 of 1378 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1358 + +--S 1359 of 1378 +r0:=-2/7*B*(a+b*x)*sqrt(d+e*x)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/28*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-1/24*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5/96*e*_ + (8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+5/64*e^3*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^2*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 105A b - 15B a b )e + 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 420A a b - 60B a b )e + 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 630A a b - 90B a b )e + 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 420A a b - 60B a b)e + 480B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 105A a b - 15B a )e + 120B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((385A a b + 55B a b )e + (- 70A b - 450B a b )d e + 80B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (511A a b + 73B a b)e + (- 252A a b - 620B a b )d e +--R + +--R 4 3 2 4 3 +--R (56A b + 296B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (279A a b - 15B a )e + (- 326A a b - 146B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (200A a b + 72B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 3 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 2 +--R (576a b e - 2304a b d e + 3456a b d e - 2304a b d e + 576a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 +--R (576a b e - 2304a b d e + 3456a b d e - 2304a b d e + 576a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R 192a b e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1359 + +--S 1360 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b + 60B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b + 90B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((420A a b + 60B a b)e - 480B a b d e )x + (105A a b + 15B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 3 4 2 3 +--R ((210A b + 30B a b )e - 240B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (770A a b + 110B a b )e + (- 140A b - 900B a b )d e +--R + +--R 4 2 +--R 160B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1022A a b + 146B a b)e + (- 504A a b - 1240B a b )d e +--R + +--R 4 3 2 4 3 +--R (112A b + 592B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (558A a b - 30B a )e + (- 652A a b - 292B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (400A a b + 144B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 4 +--R (384a b e - 1536a b d e + 2304a b d e - 1536a b d e + 384b d )x +--R + +--R 5 4 4 4 5 3 3 6 2 2 2 7 3 +--R 1536a b e - 6144a b d e + 9216a b d e - 6144a b d e +--R + +--R 8 4 +--R 1536a b d +--R * +--R 3 +--R x +--R + +--R 6 3 4 5 4 3 4 5 2 2 3 6 3 +--R 2304a b e - 9216a b d e + 13824a b d e - 9216a b d e +--R + +--R 2 7 4 +--R 2304a b d +--R * +--R 2 +--R x +--R + +--R 7 2 4 6 3 3 5 4 2 2 4 5 3 +--R 1536a b e - 6144a b d e + 9216a b d e - 6144a b d e +--R + +--R 3 6 4 +--R 1536a b d +--R * +--R x +--R + +--R 8 4 7 2 3 6 3 2 2 5 4 3 4 5 4 +--R 384a b e - 1536a b d e + 2304a b d e - 1536a b d e + 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 5 4 4 5 3 4 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b + 60B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b + 90B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((420A a b + 60B a b)e - 480B a b d e )x + (105A a b + 15B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (385A a b + 55B a b )e + (- 70A b - 450B a b )d e +--R + +--R 4 2 +--R 80B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (511A a b + 73B a b)e + (- 252A a b - 620B a b )d e +--R + +--R 4 3 2 4 3 +--R (56A b + 296B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (279A a b - 15B a )e + (- 326A a b - 146B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (200A a b + 72B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 4 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 4 4 4 5 3 3 6 2 2 2 7 3 8 4 3 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 6 3 4 5 4 3 4 5 2 2 3 6 3 +--R 1152a b e - 4608a b d e + 6912a b d e - 4608a b d e +--R + +--R 2 7 4 +--R 1152a b d +--R * +--R 2 +--R x +--R + +--R 7 2 4 6 3 3 5 4 2 2 4 5 3 3 6 4 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 8 4 7 2 3 6 3 2 2 5 4 3 4 5 4 +--R 192a b e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1360 + +--S 1361 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b + 60B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b + 90B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((420A a b + 60B a b)e - 480B a b d e )x + (105A a b + 15B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((210A b + 30B a b )e - 240B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((1050A a b + 150B a b )e - 1200B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((2100A a b + 300B a b )e - 2400B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((2100A a b + 300B a b )e - 2400B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((1050A a b + 150B a b)e - 1200B a b d e )x + (210A a b + 30B a )e +--R + +--R 5 3 +--R - 240B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((210A b + 30B a b )e - 240B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (770A a b + 110B a b )e + (- 140A b - 900B a b )d e +--R + +--R 4 2 +--R 160B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1022A a b + 146B a b)e + (- 504A a b - 1240B a b )d e +--R + +--R 4 3 2 4 3 +--R (112A b + 592B a b )d e - 128B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (558A a b - 30B a )e + (- 652A a b - 292B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (400A a b + 144B a b )d e + (- 96A b - 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 210A b - 30B a b )e + 240B b d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (- 980A a b - 140B a b )e + (140A b + 1140B a b )d e +--R + +--R 5 2 +--R - 160B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 1792A a b - 256B a b )e + (644A a b + 2140B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 112A b - 752B a b )d e + 128B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 1580A a b - 116B a b)e + (1156A a b + 1532B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 512A a b - 736B a b )d e + (96A b + 160B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 558A a b + 30B a )e + (652A a b + 292B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 400A a b - 144B a b )d e + (96A a b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 4 +--R (384a b e - 1536a b d e + 2304a b d e - 1536a b d e + 384b d )x +--R + +--R 5 4 4 4 5 3 3 6 2 2 2 7 3 8 4 3 +--R (1536a b e - 6144a b d e + 9216a b d e - 6144a b d e + 1536a b d )x +--R + +--R 6 3 4 5 4 3 4 5 2 2 3 6 3 +--R 2304a b e - 9216a b d e + 13824a b d e - 9216a b d e +--R + +--R 2 7 4 +--R 2304a b d +--R * +--R 2 +--R x +--R + +--R 7 2 4 6 3 3 5 4 2 2 4 5 3 3 6 4 +--R (1536a b e - 6144a b d e + 9216a b d e - 6144a b d e + 1536a b d )x +--R + +--R 8 4 7 2 3 6 3 2 2 5 4 3 4 5 4 +--R 384a b e - 1536a b d e + 2304a b d e - 1536a b d e + 384a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 +-------+ +--R ((2B a b e - 2B b d)x + 2A a b e - 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 +--R (- 2B a b e + 2B b d)x +--R + +--R 2 2 3 2 2 2 +--R ((- 2A a b - 2B a b)e + (2A b + 2B a b )d)x - 2A a b e + 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 6 5 6 5 2 4 5 4 2 4 3 +--R b e x + (4a b e + 2b d)x + (5a b e + 10a b d)x + 20a b d x +--R + +--R 4 2 3 3 2 5 4 2 6 5 +--R (- 5a b e + 20a b d)x + (- 4a b e + 10a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 2 7 6 2 5 2 6 7 2 5 +--R (2a b e - 2b d e)x + (10a b e - 8a b d e - 2b d )x +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 2 5 2 3 +--R (20a b e - 10a b d e - 10a b d )x + (20a b e - 20a b d )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (10a b e + 10a b d e - 20a b d )x + (2a b e + 8a b d e - 10a b d )x +--R + +--R 6 5 2 2 +--R 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1362 + +--S 1363 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((525A a b + 75B a b )e - 600B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((1050A a b + 150B a b )e - 1200B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((1050A a b + 150B a b )e - 1200B a b d e )x +--R + +--R 4 2 5 4 4 2 3 5 6 4 +--R ((525A a b + 75B a b)e - 600B a b d e )x + (105A a b + 15B a )e +--R + +--R 5 3 +--R - 120B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((420A a b + 60B a b )e - 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((630A a b + 90B a b )e - 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((420A a b + 60B a b)e - 480B a b d e )x + (105A a b + 15B a )e +--R + +--R 4 3 +--R - 120B a b d e +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R +-----------+ +-+ | 2 2 2 \|a b e - b d \|e x + d +--R \|- a e + b d \|b \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 4 3 3 4 2 3 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((385A a b + 55B a b )e + (- 70A b - 450B a b )d e + 80B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (511A a b + 73B a b)e + (- 252A a b - 620B a b )d e +--R + +--R 4 3 2 4 3 +--R (56A b + 296B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (279A a b - 15B a )e + (- 326A a b - 146B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (200A a b + 72B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 3 5 2 4 +--R ((- 105A b - 15B a b )e + 120B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 3 +--R ((- 490A a b - 70B a b )e + (70A b + 570B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 896A a b - 128B a b )e + (322A a b + 1070B a b )d e +--R + +--R 5 4 2 5 3 +--R (- 56A b - 376B a b )d e + 64B b d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 790A a b - 58B a b)e + (578A a b + 766B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 256A a b - 368B a b )d e + (48A b + 80B a b )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 279A a b + 15B a )e + (326A a b + 146B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 200A a b - 72B a b )d e + (48A a b + 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 4 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 4 4 4 5 3 3 6 2 2 2 7 3 8 4 3 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 6 3 4 5 4 3 4 5 2 2 3 6 3 2 7 4 2 +--R (1152a b e - 4608a b d e + 6912a b d e - 4608a b d e + 1152a b d )x +--R + +--R 7 2 4 6 3 3 5 4 2 2 4 5 3 3 6 4 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 8 4 7 2 3 6 3 2 2 5 4 3 4 5 4 +--R 192a b e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1364 + +)clear all + +--S 1365 of 1378 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1365 + +--S 1366 of 1378 +r0:=-2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x))+1/4*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/(e*_ + (b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2))-7/24*(8*b*B*d-9*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/96*e*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^4*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+35/64*e^3*(8*b*B*d-9*A*b*e+a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(11/2)*_ + sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*(8*b*B*d-9*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((945A b - 105B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((3780A a b - 420B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((5670A a b - 630B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((3780A a b - 420B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (945A a b - 105B a )e - 840B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3465A a b + 385B a b )e + (- 315A b + 3115B a b )d e +--R + +--R 4 2 2 +--R 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 4599A a b + 511B a b)e + (- 1197A a b + 4221B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (126A b + 1050B a b )d e - 112B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 2511A a b + 279B a )e + (- 1665A a b + 2417B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (468A a b + 1428B a b )d e + (- 72A b - 408B a b )d e + 64B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 384A a e + (- 975A a b + 663B a )d e + (630A a b + 370B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 264A a b - 104B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 5 3 5 4 4 4 3 5 2 3 2 6 3 2 7 4 +--R 192a b e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 8 5 +--R - 192b d +--R * +--R 3 +--R x +--R + +--R 6 2 5 5 3 4 4 4 2 3 3 5 3 2 +--R 576a b e - 2880a b d e + 5760a b d e - 5760a b d e +--R + +--R 2 6 4 7 5 +--R 2880a b d e - 576a b d +--R * +--R 2 +--R x +--R + +--R 7 5 6 2 4 5 3 2 3 4 4 3 2 +--R 576a b e - 2880a b d e + 5760a b d e - 5760a b d e +--R + +--R 3 5 4 2 6 5 +--R 2880a b d e - 576a b d +--R * +--R x +--R + +--R 8 5 7 4 6 2 2 3 5 3 3 2 4 4 4 +--R 192a e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 3 5 5 +--R - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 4 5 3 4 +--R ((945A b - 105B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((3780A a b - 420B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((5670A a b - 630B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((3780A a b - 420B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (945A a b - 105B a )e - 840B a b d e +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 4 3 4 +--R ((- 1890A b + 210B a b )e + 1680B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 6930A a b + 770B a b )e + (- 630A b + 6230B a b )d e +--R + +--R 4 2 2 +--R 560B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 9198A a b + 1022B a b)e + (- 2394A a b + 8442B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (252A b + 2100B a b )d e - 224B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 5022A a b + 558B a )e + (- 3330A a b + 4834B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (936A a b + 2856B a b )d e + (- 144A b - 816B a b )d e +--R + +--R 4 4 +--R 128B b d +--R * +--R x +--R + +--R 4 4 3 4 3 +--R - 768A a e + (- 1950A a b + 1326B a )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (1260A a b + 740B a b)d e + (- 528A a b - 208B a b )d e +--R + +--R 4 3 4 +--R (96A b + 32B a b )d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 +--R 384a b e - 1920a b d e + 3840a b d e - 3840a b d e +--R + +--R 8 4 9 5 +--R 1920a b d e - 384b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 1536a b e - 7680a b d e + 15360a b d e - 15360a b d e +--R + +--R 2 7 4 8 5 +--R 7680a b d e - 1536a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 2304a b e - 11520a b d e + 23040a b d e - 23040a b d e +--R + +--R 3 6 4 2 7 5 +--R 11520a b d e - 2304a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 1536a b e - 7680a b d e + 15360a b d e - 15360a b d e +--R + +--R 4 5 4 3 6 5 +--R 7680a b d e - 1536a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 384a e - 1920a b d e + 3840a b d e - 3840a b d e + 1920a b d e +--R + +--R 4 5 5 +--R - 384a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 5 4 4 5 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 420B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 630B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 420B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 105B a )e + 840B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3465A a b + 385B a b )e + (- 315A b + 3115B a b )d e +--R + +--R 4 2 2 +--R 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 4599A a b + 511B a b)e + (- 1197A a b + 4221B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (126A b + 1050B a b )d e - 112B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 2511A a b + 279B a )e + (- 1665A a b + 2417B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (468A a b + 1428B a b )d e + (- 72A b - 408B a b )d e +--R + +--R 4 4 +--R 64B b d +--R * +--R x +--R + +--R 4 4 3 4 3 +--R - 384A a e + (- 975A a b + 663B a )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (630A a b + 370B a b)d e + (- 264A a b - 104B a b )d e +--R + +--R 4 3 4 +--R (48A b + 16B a b )d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 +--R 192a b e - 960a b d e + 1920a b d e - 1920a b d e +--R + +--R 8 4 9 5 +--R 960a b d e - 192b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 768a b e - 3840a b d e + 7680a b d e - 7680a b d e +--R + +--R 2 7 4 8 5 +--R 3840a b d e - 768a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 1152a b e - 5760a b d e + 11520a b d e - 11520a b d e +--R + +--R 3 6 4 2 7 5 +--R 5760a b d e - 1152a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 768a b e - 3840a b d e + 7680a b d e - 7680a b d e +--R + +--R 4 5 4 3 6 5 +--R 3840a b d e - 768a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 192a e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 4 5 5 +--R - 192a b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1367 + +--S 1368 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 4 5 3 4 +--R ((945A b - 105B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((3780A a b - 420B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((5670A a b - 630B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((3780A a b - 420B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (945A a b - 105B a )e - 840B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 4 6 3 5 +--R ((- 1890A b + 210B a b )e + 1680B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((- 9450A a b + 1050B a b )e + 8400B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((- 18900A a b + 2100B a b )e + 16800B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((- 18900A a b + 2100B a b )e + 16800B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((- 9450A a b + 1050B a b)e + 8400B a b d e )x +--R + +--R 5 6 4 5 3 +--R (- 1890A a b + 210B a )e + 1680B a b d e +--R * +--R +-------------+ +-+ +-------+ +--R | 2 +-------+ \|b \|e x + d +--R \|- a b e + b d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 1890A b + 210B a b )e + 1680B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 6930A a b + 770B a b )e + (- 630A b + 6230B a b )d e +--R + +--R 4 2 2 +--R 560B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 9198A a b + 1022B a b)e + (- 2394A a b + 8442B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (252A b + 2100B a b )d e - 224B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 5022A a b + 558B a )e + (- 3330A a b + 4834B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (936A a b + 2856B a b )d e + (- 144A b - 816B a b )d e +--R + +--R 4 4 +--R 128B b d +--R * +--R x +--R + +--R 4 4 3 4 3 +--R - 768A a e + (- 1950A a b + 1326B a )d e +--R + +--R 2 2 3 2 2 3 2 2 3 +--R (1260A a b + 740B a b)d e + (- 528A a b - 208B a b )d e +--R + +--R 4 3 4 +--R (96A b + 32B a b )d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R + +--R 5 4 4 5 3 5 +--R ((1890A b - 210B a b )e - 1680B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (8820A a b - 980B a b )e + (630A b - 7910B a b )d e +--R + +--R 5 2 2 +--R - 560B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (16128A a b - 1792B a b )e + (3024A a b - 14672B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 252A b - 2660B a b )d e + 224B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (14220A a b - 1580B a b)e + (5724A a b - 13276B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 1188A a b - 4956B a b )d e + (144A b + 1040B a b )d e +--R + +--R 5 4 +--R - 128B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (5790A a b - 558B a )e + (5280A a b - 6160B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 2196A a b - 3596B a b )d e + (672A a b + 1024B a b )d e +--R + +--R 5 4 4 +--R (- 96A b - 160B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 +--R 768A a e + (1950A a b - 1326B a )d e +--R + +--R 3 2 4 2 2 2 3 3 2 3 +--R (- 1260A a b - 740B a b)d e + (528A a b + 208B a b )d e +--R + +--R 4 2 3 4 +--R (- 96A a b - 32B a b )d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 +--R 384a b e - 1920a b d e + 3840a b d e - 3840a b d e +--R + +--R 8 4 9 5 +--R 1920a b d e - 384b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 1536a b e - 7680a b d e + 15360a b d e - 15360a b d e +--R + +--R 2 7 4 8 5 +--R 7680a b d e - 1536a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 2304a b e - 11520a b d e + 23040a b d e - 23040a b d e +--R + +--R 3 6 4 2 7 5 +--R 11520a b d e - 2304a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 1536a b e - 7680a b d e + 15360a b d e - 15360a b d e +--R + +--R 4 5 4 3 6 5 +--R 7680a b d e - 1536a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 384a e - 1920a b d e + 3840a b d e - 3840a b d e + 1920a b d e +--R + +--R 4 5 5 +--R - 384a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 +-------+ +--R ((- 2B a b e + 2B b d)x - 2A a b e + 2A b d)\|e x + d +--R + +--R +-------------+ +--R 2 | 2 +--R (B b e x + ((A b - B a)e + 2B b d)x - A a e + 2A b d)\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 2 3 2 +--R (2B a b e - 2B b d)x + ((2A a b + 2B a b)e + (- 2A b - 2B a b )d)x +--R + +--R 2 2 +--R 2A a b e - 2A a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 2 +--R - B b e x + (- A b e - 2B b d)x + (B a e + (- 2A b - 2B a b)d)x +--R + +--R 2 +--R A a e - 2A a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 6 2 7 5 2 6 6 2 4 2 5 6 2 5 +--R b e x + (4a b e + 3b d e)x + (5a b e + 14a b d e + 2b d )x +--R + +--R 2 4 5 2 4 4 2 2 3 3 2 4 2 3 +--R (25a b d e + 10a b d )x + (- 5a b e + 20a b d e + 20a b d )x +--R + +--R 5 2 4 2 3 3 2 2 +--R (- 4a b e + 5a b d e + 20a b d )x +--R + +--R 6 2 5 4 2 2 6 5 2 +--R (- a e - 2a b d e + 10a b d )x - a d e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 6 3 7 2 7 2 5 3 6 2 7 2 6 +--R (- 2a b e + 2b d e )x + (- 10a b e + 6a b d e + 4b d e)x +--R + +--R 3 4 3 6 2 7 3 5 +--R (- 20a b e + 18a b d e + 2b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 4 +--R (- 20a b e - 20a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 3 +--R (- 10a b e - 30a b d e + 20a b d e + 20a b d )x +--R + +--R 6 3 5 2 2 3 4 3 2 +--R (- 2a b e - 18a b d e + 20a b d )x +--R + +--R 6 2 5 2 2 4 3 3 6 2 5 2 3 +--R (- 4a b d e - 6a b d e + 10a b d )x - 2a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1369 + +--S 1370 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 4 6 3 5 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 5 2 4 4 5 3 4 +--R ((- 4725A a b + 525B a b )e + 4200B a b d e )x +--R + +--R 2 4 3 3 4 2 4 3 3 +--R ((- 9450A a b + 1050B a b )e + 8400B a b d e )x +--R + +--R 3 3 4 2 4 3 3 3 2 +--R ((- 9450A a b + 1050B a b )e + 8400B a b d e )x +--R + +--R 4 2 5 4 4 2 3 +--R ((- 4725A a b + 525B a b)e + 4200B a b d e )x +--R + +--R 5 6 4 5 3 +--R (- 945A a b + 105B a )e + 840B a b d e +--R * +--R +-----------+ +-+ +-------+ +--R | 2 +-------+ \|b \|e x + d +--R \|a b e - b d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 420B a b )e + 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 630B a b )e + 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 420B a b)e + 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 105B a )e + 840B a b d e +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3465A a b + 385B a b )e + (- 315A b + 3115B a b )d e +--R + +--R 4 2 2 +--R 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 4599A a b + 511B a b)e + (- 1197A a b + 4221B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (126A b + 1050B a b )d e - 112B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 2511A a b + 279B a )e + (- 1665A a b + 2417B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (468A a b + 1428B a b )d e + (- 72A b - 408B a b )d e + 64B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 384A a e + (- 975A a b + 663B a )d e + (630A a b + 370B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 264A a b - 104B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R + +--R 5 4 4 5 3 5 +--R ((945A b - 105B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (4410A a b - 490B a b )e + (315A b - 3955B a b )d e +--R + +--R 5 2 2 +--R - 280B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (8064A a b - 896B a b )e + (1512A a b - 7336B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 126A b - 1330B a b )d e + 112B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (7110A a b - 790B a b)e + (2862A a b - 6638B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 594A a b - 2478B a b )d e + (72A b + 520B a b )d e - 64B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (2895A a b - 279B a )e + (2640A a b - 3080B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 1098A a b - 1798B a b )d e + (336A a b + 512B a b )d e +--R + +--R 5 4 4 +--R (- 48A b - 80B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R 384A a e + (975A a b - 663B a )d e + (- 630A a b - 370B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (264A a b + 104B a b )d e + (- 48A a b - 16B a b )d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 192a b e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 9 5 +--R - 192b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 768a b e - 3840a b d e + 7680a b d e - 7680a b d e +--R + +--R 2 7 4 8 5 +--R 3840a b d e - 768a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 1152a b e - 5760a b d e + 11520a b d e - 11520a b d e +--R + +--R 3 6 4 2 7 5 +--R 5760a b d e - 1152a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 768a b e - 3840a b d e + 7680a b d e - 7680a b d e +--R + +--R 4 5 4 3 6 5 +--R 3840a b d e - 768a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 192a e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 4 5 5 +--R - 192a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1370 + +--S 1371 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 6 4 5 5 2 3 4 4 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (10a b e + 10a b d)x + (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1371 + +)clear all + +--S 1372 of 1378 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1372 + +--S 1373 of 1378 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/12*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x))+1/8*(-8*b*B*d+11*A*b*e-_ + 3*a*B*e)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))+_ + 7/32*e*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x))+105/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-_ + a*e)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*(8*b*B*d-11*A*b*e+_ + 3*a*B*e)/((b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 105/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^6*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((- 3465A b + 945B a b )e + 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 13860A a b + 3780B a b )e + (- 3465A b + 11025B a b )d e +--R + +--R 5 2 3 +--R 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 +--R (- 20790A a b + 5670B a b )e +--R + +--R 4 2 3 4 4 2 3 +--R (- 13860A a b + 18900B a b )d e + 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 13860A a b + 3780B a b)e + (- 20790A a b + 15750B a b )d e +--R + +--R 2 3 2 3 +--R 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 3465A a b + 945B a )e + (- 13860A a b + 6300B a b)d e +--R + +--R 3 2 2 3 +--R 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 3465A a b + 945B a )d e + 2520B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (12705A a b - 3465B a b )e + (4620A b - 10500B a b )d e +--R + +--R 5 2 3 +--R - 3360B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (16863A a b - 4599B a b )e + (17094A a b - 16926B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (693A b - 12621B a b )d e - 504B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (9207A a b - 2511B a b)e + (22968A a b - 12960B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2673A a b - 17433B a b )d e + (- 198A b - 1890B a b )d e +--R + +--R 5 4 +--R 144B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (1408A a b - 384B a )e + (12782A a b - 4510B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (3795A a b - 10331B a b )d e + (- 748A a b - 2556B a b )d e +--R + +--R 5 4 4 5 5 +--R (88A b + 520B a b )d e - 64B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 128A a e + (2048A a b - 256B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (2295A a b - 2639B a b)d e + (- 1030A a b - 690B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (328A a b + 136B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 7 5 4 6 4 5 2 5 3 6 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 7 4 3 8 5 2 9 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 4 +--R x +--R + +--R 7 2 7 6 3 6 5 4 2 5 4 5 3 4 +--R 576a b e - 3264a b d e + 7488a b d e - 8640a b d e +--R + +--R 3 6 4 3 2 7 5 2 8 6 9 7 +--R 4800a b d e - 576a b d e - 576a b d e + 192b d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 +--R 576a b e - 2880a b d e + 5184a b d e - 2880a b d e +--R + +--R 4 5 4 3 3 6 5 2 2 7 6 8 7 +--R - 2880a b d e + 5184a b d e - 2880a b d e + 576a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 6 7 2 2 5 6 3 3 4 5 4 4 3 +--R 192a e - 576a b d e - 576a b d e + 4800a b d e - 8640a b d e +--R + +--R 4 5 5 2 3 6 6 2 7 7 +--R 7488a b d e - 3264a b d e + 576a b d +--R * +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e + 2880a b d e +--R + +--R 4 5 6 3 6 7 +--R - 1152a b d e + 192a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1373 + +--S 1374 of 1378 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (13860A a b - 3780B a b )e + (3465A b - 11025B a b )d e +--R + +--R 5 2 3 +--R - 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (20790A a b - 5670B a b )e + (13860A a b - 18900B a b )d e +--R + +--R 4 2 3 +--R - 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (13860A a b - 3780B a b)e + (20790A a b - 15750B a b )d e +--R + +--R 2 3 2 3 +--R - 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (3465A a b - 945B a )e + (13860A a b - 6300B a b)d e +--R + +--R 3 2 2 3 +--R - 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (3465A a b - 945B a )d e - 2520B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 5 4 5 5 4 5 +--R ((6930A b - 1890B a b )e - 5040B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (25410A a b - 6930B a b )e + (9240A b - 21000B a b )d e +--R + +--R 5 2 3 +--R - 6720B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (33726A a b - 9198B a b )e + (34188A a b - 33852B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (1386A b - 25242B a b )d e - 1008B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (18414A a b - 5022B a b)e + (45936A a b - 25920B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (5346A a b - 34866B a b )d e + (- 396A b - 3780B a b )d e +--R + +--R 5 4 +--R 288B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (2816A a b - 768B a )e + (25564A a b - 9020B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (7590A a b - 20662B a b )d e + (- 1496A a b - 5112B a b )d e +--R + +--R 5 4 4 5 5 +--R (176A b + 1040B a b )d e - 128B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 256A a e + (4096A a b - 512B a )d e + (4590A a b - 5278B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 2060A a b - 1380B a b )d e + (656A a b + 272B a b )d e +--R + +--R 5 4 5 +--R (- 96A b - 32B a b )d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 384a b e - 2304a b d e + 5760a b d e - 7680a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 5760a b d e - 2304a b d e + 384b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 1536a b e - 8832a b d e + 20736a b d e - 24960a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 15360a b d e - 3456a b d e - 768a b d e + 384b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 2304a b e - 12288a b d e + 25344a b d e - 23040a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 3840a b d e + 9216a b d e - 6912a b d e + 1536a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 1536a b e - 6912a b d e + 9216a b d e + 3840a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 23040a b d e + 25344a b d e - 12288a b d e + 2304a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 384a e - 768a b d e - 3456a b d e + 15360a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 24960a b d e + 20736a b d e - 8832a b d e + 1536a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 +--R 384a d e - 2304a b d e + 5760a b d e - 7680a b d e +--R + +--R 6 4 5 2 5 5 6 4 6 7 +--R 5760a b d e - 2304a b d e + 384a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (13860A a b - 3780B a b )e + (3465A b - 11025B a b )d e +--R + +--R 5 2 3 +--R - 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (20790A a b - 5670B a b )e + (13860A a b - 18900B a b )d e +--R + +--R 4 2 3 +--R - 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (13860A a b - 3780B a b)e + (20790A a b - 15750B a b )d e +--R + +--R 2 3 2 3 +--R - 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (3465A a b - 945B a )e + (13860A a b - 6300B a b)d e +--R + +--R 3 2 2 3 +--R - 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (3465A a b - 945B a )d e - 2520B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (12705A a b - 3465B a b )e + (4620A b - 10500B a b )d e +--R + +--R 5 2 3 +--R - 3360B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (16863A a b - 4599B a b )e + (17094A a b - 16926B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (693A b - 12621B a b )d e - 504B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (9207A a b - 2511B a b)e + (22968A a b - 12960B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2673A a b - 17433B a b )d e + (- 198A b - 1890B a b )d e +--R + +--R 5 4 +--R 144B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (1408A a b - 384B a )e + (12782A a b - 4510B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (3795A a b - 10331B a b )d e + (- 748A a b - 2556B a b )d e +--R + +--R 5 4 4 5 5 +--R (88A b + 520B a b )d e - 64B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 128A a e + (2048A a b - 256B a )d e + (2295A a b - 2639B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 1030A a b - 690B a b )d e + (328A a b + 136B a b )d e +--R + +--R 5 4 5 +--R (- 48A b - 16B a b )d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 768a b e - 4416a b d e + 10368a b d e - 12480a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 7680a b d e - 1728a b d e - 384a b d e + 192b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 1152a b e - 6144a b d e + 12672a b d e - 11520a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 1920a b d e + 4608a b d e - 3456a b d e + 768a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 768a b e - 3456a b d e + 4608a b d e + 1920a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 11520a b d e + 12672a b d e - 6144a b d e + 1152a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 192a e - 384a b d e - 1728a b d e + 7680a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 12480a b d e + 10368a b d e - 4416a b d e + 768a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 6 4 5 2 5 5 6 4 6 7 +--R 2880a b d e - 1152a b d e + 192a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1374 + +--S 1375 of 1378 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (13860A a b - 3780B a b )e + (3465A b - 11025B a b )d e +--R + +--R 5 2 3 +--R - 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (20790A a b - 5670B a b )e + (13860A a b - 18900B a b )d e +--R + +--R 4 2 3 +--R - 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (13860A a b - 3780B a b)e + (20790A a b - 15750B a b )d e +--R + +--R 2 3 2 3 +--R - 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (3465A a b - 945B a )e + (13860A a b - 6300B a b)d e +--R + +--R 3 2 2 3 +--R - 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (3465A a b - 945B a )d e - 2520B a b d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 6 5 5 6 4 6 +--R ((6930A b - 1890B a b )e - 5040B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (34650A a b - 9450B a b )e + (6930A b - 27090B a b )d e +--R + +--R 6 2 3 +--R - 5040B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (69300A a b - 18900B a b )e + (34650A a b - 59850B a b )d e +--R + +--R 5 2 3 +--R - 25200B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (69300A a b - 18900B a b )e + (69300A a b - 69300B a b )d e +--R + +--R 2 4 2 3 +--R - 50400B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (34650A a b - 9450B a b)e + (69300A a b - 44100B a b )d e +--R + +--R 3 3 2 3 +--R - 50400B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (6930A a b - 1890B a )e + (34650A a b - 14490B a b)d e +--R + +--R 4 2 2 3 +--R - 25200B a b d e +--R * +--R x +--R + +--R 5 6 4 5 2 3 +--R (6930A a b - 1890B a )d e - 5040B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((6930A b - 1890B a b )e - 5040B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (25410A a b - 6930B a b )e + (9240A b - 21000B a b )d e +--R + +--R 5 2 3 +--R - 6720B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (33726A a b - 9198B a b )e + (34188A a b - 33852B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (1386A b - 25242B a b )d e - 1008B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (18414A a b - 5022B a b)e + (45936A a b - 25920B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (5346A a b - 34866B a b )d e + (- 396A b - 3780B a b )d e +--R + +--R 5 4 +--R 288B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (2816A a b - 768B a )e + (25564A a b - 9020B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (7590A a b - 20662B a b )d e + (- 1496A a b - 5112B a b )d e +--R + +--R 5 4 4 5 5 +--R (176A b + 1040B a b )d e - 128B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 256A a e + (4096A a b - 512B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (4590A a b - 5278B a b)d e + (- 2060A a b - 1380B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (656A a b + 272B a b )d e + (- 96A b - 32B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 6 5 5 6 4 6 +--R ((- 6930A b + 1890B a b )e + 5040B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 32340A a b + 8820B a b )e + (- 9240A b + 26040B a b )d e +--R + +--R 6 2 3 +--R 6720B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 +--R (- 59136A a b + 16128B a b )e +--R + +--R 5 2 4 4 +--R (- 43428A a b + 54852B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 1386A b + 31962B a b )d e + 1008B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 +--R (- 52140A a b + 14220B a b )e +--R + +--R 2 4 3 3 4 +--R (- 80124A a b + 59772B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 6732A a b + 60108B a b )d e + (396A b + 4788B a b )d e +--R + +--R 6 4 +--R - 288B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 21230A a b + 5790B a b)e + (- 71500A a b + 34940B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 12936A a b + 55528B a b )d e + (1892A a b + 8892B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 176A b - 1328B a b )d e + 128B b d +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 2560A a b + 768B a )e + (- 29660A a b + 9532B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 12180A a b + 25940B a b )d e + (3556A a b + 6492B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 832A a b - 1312B a b )d e + (96A b + 160B a b )d +--R * +--R x +--R + +--R 6 5 5 6 4 +--R 256A a e + (- 4096A a b + 512B a )d e +--R + +--R 4 2 5 2 3 3 3 4 2 3 2 +--R (- 4590A a b + 5278B a b)d e + (2060A a b + 1380B a b )d e +--R + +--R 2 4 3 3 4 5 2 4 5 +--R (- 656A a b - 272B a b )d e + (96A a b + 32B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 384a b e - 2304a b d e + 5760a b d e - 7680a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 5760a b d e - 2304a b d e + 384b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 1536a b e - 8832a b d e + 20736a b d e - 24960a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 15360a b d e - 3456a b d e - 768a b d e + 384b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 2304a b e - 12288a b d e + 25344a b d e - 23040a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 3840a b d e + 9216a b d e - 6912a b d e + 1536a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 1536a b e - 6912a b d e + 9216a b d e + 3840a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 23040a b d e + 25344a b d e - 12288a b d e + 2304a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 384a e - 768a b d e - 3456a b d e + 15360a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 24960a b d e + 20736a b d e - 8832a b d e + 1536a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 384a d e - 2304a b d e + 5760a b d e - 7680a b d e + 5760a b d e +--R + +--R 5 5 6 4 6 7 +--R - 2304a b d e + 384a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1375 + +--S 1376 of 1378 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1376 + +--S 1377 of 1378 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 5 6 4 6 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (17325A a b - 4725B a b )e + (3465A b - 13545B a b )d e +--R + +--R 6 2 3 +--R - 2520B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (34650A a b - 9450B a b )e + (17325A a b - 29925B a b )d e +--R + +--R 5 2 3 +--R - 12600B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (34650A a b - 9450B a b )e + (34650A a b - 34650B a b )d e +--R + +--R 2 4 2 3 +--R - 25200B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (17325A a b - 4725B a b)e + (34650A a b - 22050B a b )d e +--R + +--R 3 3 2 3 +--R - 25200B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (3465A a b - 945B a )e + (17325A a b - 7245B a b)d e +--R + +--R 4 2 2 3 +--R - 12600B a b d e +--R * +--R x +--R + +--R 5 6 4 5 2 3 +--R (3465A a b - 945B a )d e - 2520B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (13860A a b - 3780B a b )e + (3465A b - 11025B a b )d e +--R + +--R 5 2 3 +--R - 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (20790A a b - 5670B a b )e + (13860A a b - 18900B a b )d e +--R + +--R 4 2 3 +--R - 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (13860A a b - 3780B a b)e + (20790A a b - 15750B a b )d e +--R + +--R 2 3 2 3 +--R - 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (3465A a b - 945B a )e + (13860A a b - 6300B a b)d e +--R + +--R 3 2 2 3 +--R - 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (3465A a b - 945B a )d e - 2520B a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (12705A a b - 3465B a b )e + (4620A b - 10500B a b )d e +--R + +--R 5 2 3 +--R - 3360B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (16863A a b - 4599B a b )e + (17094A a b - 16926B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (693A b - 12621B a b )d e - 504B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (9207A a b - 2511B a b)e + (22968A a b - 12960B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2673A a b - 17433B a b )d e + (- 198A b - 1890B a b )d e +--R + +--R 5 4 +--R 144B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (1408A a b - 384B a )e + (12782A a b - 4510B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (3795A a b - 10331B a b )d e + (- 748A a b - 2556B a b )d e +--R + +--R 5 4 4 5 5 +--R (88A b + 520B a b )d e - 64B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 128A a e + (2048A a b - 256B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (2295A a b - 2639B a b)d e + (- 1030A a b - 690B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (328A a b + 136B a b )d e + (- 48A b - 16B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 6 5 5 6 4 6 +--R ((- 3465A b + 945B a b )e + 2520B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 16170A a b + 4410B a b )e + (- 4620A b + 13020B a b )d e +--R + +--R 6 2 3 +--R 3360B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 +--R (- 29568A a b + 8064B a b )e +--R + +--R 5 2 4 4 6 5 2 3 +--R (- 21714A a b + 27426B a b )d e + (- 693A b + 15981B a b )d e +--R + +--R 6 3 2 +--R 504B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 +--R (- 26070A a b + 7110B a b )e +--R + +--R 2 4 3 3 4 +--R (- 40062A a b + 29886B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 3366A a b + 30054B a b )d e + (198A b + 2394B a b )d e +--R + +--R 6 4 +--R - 144B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 10615A a b + 2895B a b)e + (- 35750A a b + 17470B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 6468A a b + 27764B a b )d e + (946A a b + 4446B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 88A b - 664B a b )d e + 64B b d +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 1280A a b + 384B a )e + (- 14830A a b + 4766B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 6090A a b + 12970B a b )d e + (1778A a b + 3246B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 416A a b - 656B a b )d e + (48A b + 80B a b )d +--R * +--R x +--R + +--R 6 5 5 6 4 +--R 128A a e + (- 2048A a b + 256B a )d e +--R + +--R 4 2 5 2 3 3 3 4 2 3 2 +--R (- 2295A a b + 2639B a b)d e + (1030A a b + 690B a b )d e +--R + +--R 2 4 3 3 4 5 2 4 5 +--R (- 328A a b - 136B a b )d e + (48A a b + 16B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 768a b e - 4416a b d e + 10368a b d e - 12480a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 7680a b d e - 1728a b d e - 384a b d e + 192b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 1152a b e - 6144a b d e + 12672a b d e - 11520a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 1920a b d e + 4608a b d e - 3456a b d e + 768a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 768a b e - 3456a b d e + 4608a b d e + 1920a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 11520a b d e + 12672a b d e - 6144a b d e + 1152a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 192a e - 384a b d e - 1728a b d e + 7680a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 12480a b d e + 10368a b d e - 4416a b d e + 768a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e + 2880a b d e +--R + +--R 5 5 6 4 6 7 +--R - 1152a b d e + 192a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1377 + +--S 1378 of 1378 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1378 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich12e.input.pamphlet b/src/input/rich12e.input.pamphlet new file mode 100644 index 0000000..15e31d2 --- /dev/null +++ b/src/input/rich12e.input.pamphlet @@ -0,0 +1,46858 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12e.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 138 matching answers. +\item 157 cases where Axiom answer differs from Rubi +\item 39 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12e.output +)spool rich12e.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1353 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1353 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/20*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-11/120*(8*b*B*d-13*A*b*e+_ + 5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 33/160*e*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-231/320*e^2*(8*b*B*d-13*A*b*e+5*a*B*e)/_ + ((b*d-a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-77/64*e^3*(8*b*B*d-_ + 13*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+231/64*b^(3/2)*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(15/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-231/64*b*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/_ + ((b*d-a*e)^7*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((45045A b - 17325B a b )e - 27720B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (180180A a b - 69300B a b )e + (90090A b - 145530B a b )d e +--R + +--R 6 2 4 +--R - 55440B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (270270A a b - 103950B a b )e +--R + +--R 5 2 4 5 +--R (360360A a b - 304920B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (45045A b - 239085B a b )d e - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (180180A a b - 69300B a b )e +--R + +--R 2 4 3 3 5 +--R (540540A a b - 318780B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (180180A a b - 401940B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (45045A a b - 17325B a b)e + (360360A a b - 166320B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (270270A a b - 325710B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (90090A a b - 34650B a b)d e +--R + +--R 3 3 4 2 2 4 3 3 3 3 +--R (180180A a b - 124740B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (45045A a b - 17325B a b)d e - 27720B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 165165A a b + 63525B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 105105A b + 142065B a b )d e + 64680B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 219219A a b + 84315B a b )e +--R + +--R 5 2 4 5 +--R (- 387387A a b + 283899B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 69069A b + 264957B a b )d e + 42504B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 119691A a b + 46035B a b )e +--R + +--R 2 4 3 3 5 +--R (- 517803A a b + 272811B a b )d e +--R + +--R 5 2 4 2 4 +--R (- 256971A a b + 417483B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 6435A b + 160611B a b )d e + 3960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 18304A a b + 7040B a b)e +--R + +--R 3 3 4 2 5 +--R (- 285857A a b + 121209B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (- 347919A a b + 309727B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 25025A a b + 223729B a b )d e + (1430A b + 14850B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (1664A a b - 640B a )e + (- 44928A a b + 16256B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (- 196001A a b + 103033B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 35945A a b + 134441B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (5460A a b + 20020B a b )d e + (- 520A b - 3160B a b )d e +--R + +--R 6 6 +--R 320B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 384A a e + (3968A a b - 256B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 32384A a b + 6912B a b)d e + (- 22155A a b + 33619B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (7630A a b + 5530B a b )d e + (- 1960A a b - 840B a b )d e +--R + +--R 6 5 6 +--R (240A b + 80B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 3 9 6 4 8 5 5 2 7 4 6 3 6 +--R 960a b e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 3 7 4 5 2 8 5 4 9 6 3 10 7 2 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960b d e +--R * +--R 5 +--R x +--R + +--R 8 2 9 7 3 8 6 4 2 7 5 5 3 6 +--R 2880a b e - 18240a b d e + 47040a b d e - 60480a b d e +--R + +--R 4 6 4 5 3 7 5 4 2 8 6 3 9 7 2 +--R 33600a b d e + 6720a b d e - 20160a b d e + 10560a b d e +--R + +--R 10 8 +--R - 1920b d e +--R * +--R 4 +--R x +--R + +--R 9 9 8 2 8 7 3 2 7 6 4 3 6 +--R 2880a b e - 14400a b d e + 21120a b d e + 13440a b d e +--R + +--R 5 5 4 5 4 6 5 4 3 7 6 3 2 8 7 2 +--R - 80640a b d e + 107520a b d e - 67200a b d e + 17280a b d e +--R + +--R 9 8 10 9 +--R 960a b d e - 960b d +--R * +--R 3 +--R x +--R + +--R 10 9 9 8 8 2 2 7 7 3 3 6 +--R 960a e - 960a b d e - 17280a b d e + 67200a b d e +--R + +--R 6 4 4 5 5 5 5 4 4 6 6 3 3 7 7 2 +--R - 107520a b d e + 80640a b d e - 13440a b d e - 21120a b d e +--R + +--R 2 8 8 9 9 +--R 14400a b d e - 2880a b d +--R * +--R 2 +--R x +--R + +--R 10 8 9 2 7 8 2 3 6 7 3 4 5 +--R 1920a d e - 10560a b d e + 20160a b d e - 6720a b d e +--R + +--R 6 4 5 4 5 5 6 3 4 6 7 2 3 7 8 +--R - 33600a b d e + 60480a b d e - 47040a b d e + 18240a b d e +--R + +--R 2 8 9 +--R - 2880a b d +--R * +--R x +--R + +--R 10 2 7 9 3 6 8 2 4 5 7 3 5 4 +--R 960a d e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 6 4 6 3 5 5 7 2 4 6 8 3 7 9 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 6 6 5 6 +--R ((45045A b - 17325B a b )e - 27720B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (180180A a b - 69300B a b )e + (90090A b - 145530B a b )d e +--R + +--R 6 2 4 +--R - 55440B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (270270A a b - 103950B a b )e +--R + +--R 5 2 4 5 +--R (360360A a b - 304920B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (45045A b - 239085B a b )d e - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (180180A a b - 69300B a b )e +--R + +--R 2 4 3 3 5 +--R (540540A a b - 318780B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (180180A a b - 401940B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (45045A a b - 17325B a b)e +--R + +--R 3 3 4 2 5 +--R (360360A a b - 166320B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (270270A a b - 325710B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (90090A a b - 34650B a b)d e +--R + +--R 3 3 4 2 2 4 3 3 3 3 +--R (180180A a b - 124740B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (45045A a b - 17325B a b)d e - 27720B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 6 5 6 6 5 6 +--R ((- 90090A b + 34650B a b )e + 55440B b d e )x +--R + +--R 5 2 4 6 +--R (- 330330A a b + 127050B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 210210A b + 284130B a b )d e + 129360B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 438438A a b + 168630B a b )e +--R + +--R 5 2 4 5 +--R (- 774774A a b + 567798B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 138138A b + 529914B a b )d e + 85008B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 239382A a b + 92070B a b )e +--R + +--R 2 4 3 3 5 +--R (- 1035606A a b + 545622B a b )d e +--R + +--R 5 2 4 2 4 +--R (- 513942A a b + 834966B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 12870A b + 321222B a b )d e + 7920B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 36608A a b + 14080B a b)e +--R + +--R 3 3 4 2 5 +--R (- 571714A a b + 242418B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (- 695838A a b + 619454B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 50050A a b + 447458B a b )d e + (2860A b + 29700B a b )d e +--R + +--R 6 5 +--R - 1760B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (3328A a b - 1280B a )e + (- 89856A a b + 32512B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (- 392002A a b + 206066B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 71890A a b + 268882B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (10920A a b + 40040B a b )d e + (- 1040A b - 6320B a b )d e +--R + +--R 6 6 +--R 640B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 768A a e + (7936A a b - 512B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 64768A a b + 13824B a b)d e + (- 44310A a b + 67238B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (15260A a b + 11060B a b )d e + (- 3920A a b - 1680B a b )d e +--R + +--R 6 5 6 +--R (480A b + 160B a b )d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 +--R 1920a b e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 3 8 4 5 2 9 5 4 10 6 3 11 7 2 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 +--R 7680a b e - 49920a b d e + 134400a b d e - 188160a b d e +--R + +--R 4 7 4 5 3 8 5 4 2 9 6 3 10 7 2 +--R 134400a b d e - 26880a b d e - 26880a b d e + 19200a b d e +--R + +--R 11 8 +--R - 3840b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 +--R 11520a b e - 65280a b d e + 136320a b d e - 94080a b d e +--R + +--R 5 6 4 5 4 7 5 4 3 8 6 3 2 9 7 2 +--R - 94080a b d e + 228480a b d e - 174720a b d e + 55680a b d e +--R + +--R 10 8 11 9 +--R - 1920a b d e - 1920b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 +--R 7680a b e - 30720a b d e + 7680a b d e + 161280a b d e +--R + +--R 6 5 4 5 5 6 5 4 4 7 6 3 3 8 7 2 +--R - 376320a b d e + 376320a b d e - 161280a b d e - 7680a b d e +--R + +--R 2 9 8 10 9 +--R 30720a b d e - 7680a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 +--R 1920a e + 1920a b d e - 55680a b d e + 174720a b d e +--R + +--R 7 4 4 5 6 5 5 4 5 6 6 3 4 7 7 2 +--R - 228480a b d e + 94080a b d e + 94080a b d e - 136320a b d e +--R + +--R 3 8 8 2 9 9 +--R 65280a b d e - 11520a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 +--R 3840a d e - 19200a b d e + 26880a b d e + 26880a b d e +--R + +--R 7 4 5 4 6 5 6 3 5 6 7 2 4 7 8 +--R - 134400a b d e + 188160a b d e - 134400a b d e + 49920a b d e +--R + +--R 3 8 9 +--R - 7680a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 +--R 1920a d e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 7 4 6 3 6 5 7 2 5 6 8 4 7 9 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 180180A a b + 69300B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 90090A b + 145530B a b )d e + 55440B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 270270A a b + 103950B a b )e +--R + +--R 5 2 4 5 +--R (- 360360A a b + 304920B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 45045A b + 239085B a b )d e + 27720B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 180180A a b + 69300B a b )e +--R + +--R 2 4 3 3 5 +--R (- 540540A a b + 318780B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (- 180180A a b + 401940B a b )d e + 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 45045A a b + 17325B a b)e +--R + +--R 3 3 4 2 5 +--R (- 360360A a b + 166320B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (- 270270A a b + 325710B a b )d e + 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 90090A a b + 34650B a b)d e +--R + +--R 3 3 4 2 2 4 3 3 3 3 +--R (- 180180A a b + 124740B a b )d e + 110880B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (- 45045A a b + 17325B a b)d e + 27720B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 165165A a b + 63525B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 105105A b + 142065B a b )d e + 64680B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 219219A a b + 84315B a b )e +--R + +--R 5 2 4 5 +--R (- 387387A a b + 283899B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 69069A b + 264957B a b )d e + 42504B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 119691A a b + 46035B a b )e +--R + +--R 2 4 3 3 5 +--R (- 517803A a b + 272811B a b )d e +--R + +--R 5 2 4 2 4 +--R (- 256971A a b + 417483B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 6435A b + 160611B a b )d e + 3960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 18304A a b + 7040B a b)e + (- 285857A a b + 121209B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (- 347919A a b + 309727B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 25025A a b + 223729B a b )d e + (1430A b + 14850B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (1664A a b - 640B a )e + (- 44928A a b + 16256B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (- 196001A a b + 103033B a b )d e +--R + +--R 2 4 3 3 3 3 5 2 4 4 2 +--R (- 35945A a b + 134441B a b )d e + (5460A a b + 20020B a b )d e +--R + +--R 6 5 5 6 6 +--R (- 520A b - 3160B a b )d e + 320B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 384A a e + (3968A a b - 256B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 32384A a b + 6912B a b)d e + (- 22155A a 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* +--R 6 +--R x +--R + +--R 2 5 3 4 6 +--R (- 450450A a b + 173250B a b )e +--R + +--R 6 2 5 5 +--R (- 450450A a b + 450450B a b )d e +--R + +--R 7 6 2 4 7 3 3 +--R (- 45045A b + 294525B a b )d e + 27720B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 6 +--R (- 450450A a b + 173250B a b )e +--R + +--R 2 5 3 4 5 +--R (- 900900A a b + 623700B a b )d e +--R + +--R 6 2 5 2 4 6 3 3 +--R (- 225225A a b + 641025B a b )d e + 138600B a b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 6 +--R (- 225225A a b + 86625B a b )e +--R + +--R 3 4 4 3 5 +--R (- 900900A a b + 485100B a b )d e +--R + +--R 2 5 3 4 2 4 2 5 3 3 +--R (- 450450A a b + 727650B a b )d e + 277200B a b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 6 +--R (- 45045A a b + 17325B a b)e +--R + +--R 4 3 5 2 5 +--R (- 450450A a b + 200970B a b )d e +--R + +--R 3 4 4 3 2 4 3 4 3 3 +--R (- 450450A a b + 450450B a b )d e + 277200B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 5 +--R (- 90090A a b + 34650B a b)d e +--R + +--R 4 3 5 2 2 4 4 3 3 3 +--R (- 225225A a b + 142065B a b )d e + 138600B a b d e +--R * +--R x +--R + +--R 5 2 6 2 4 5 2 3 3 +--R (- 45045A a b + 17325B a b)d e + 27720B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 180180A a b + 69300B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 90090A b + 145530B a b )d e + 55440B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 270270A a b + 103950B a b )e +--R + +--R 5 2 4 5 +--R (- 360360A a b + 304920B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 45045A b + 239085B a b )d e + 27720B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 180180A a b + 69300B a b )e +--R + +--R 2 4 3 3 5 +--R (- 540540A a b + 318780B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (- 180180A a b + 401940B a b )d e + 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 45045A a b + 17325B a b)e +--R + +--R 3 3 4 2 5 +--R (- 360360A a b + 166320B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (- 270270A a b + 325710B a b )d e + 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 90090A a b + 34650B a b)d e +--R + +--R 3 3 4 2 2 4 3 3 3 3 +--R (- 180180A a b + 124740B a b )d e + 110880B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (- 45045A a b + 17325B a b)d e + 27720B a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 165165A a b + 63525B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 105105A b + 142065B a b )d e + 64680B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 219219A a b + 84315B a b )e +--R + +--R 5 2 4 5 +--R (- 387387A a b + 283899B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 69069A b + 264957B a b )d e + 42504B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 119691A a b + 46035B a b )e +--R + +--R 2 4 3 3 5 +--R (- 517803A a b + 272811B a b )d e +--R + +--R 5 2 4 2 4 +--R (- 256971A a b + 417483B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 6435A b + 160611B a b )d e + 3960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 18304A a b + 7040B a b)e +--R + +--R 3 3 4 2 5 +--R (- 285857A a b + 121209B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (- 347919A a b + 309727B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 25025A a b + 223729B a b )d e + (1430A b + 14850B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (1664A a b - 640B a )e + (- 44928A a b + 16256B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (- 196001A a b + 103033B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 35945A a b + 134441B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (5460A a b + 20020B a b )d e + (- 520A b - 3160B a b )d e +--R + +--R 6 6 +--R 320B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 384A a e + (3968A a b - 256B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 32384A a b + 6912B a b)d e + (- 22155A a b + 33619B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (7630A a b + 5530B a b )d e + (- 1960A a b - 840B a b )d e +--R + +--R 6 5 6 +--R (240A b + 80B a b )d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 7 6 6 7 5 7 +--R ((45045A b - 17325B a b )e - 27720B b d e )x +--R + +--R 6 2 5 6 7 6 5 +--R (210210A a b - 80850B a b )e + (105105A b - 169785B a b )d e +--R + +--R 7 2 4 +--R - 64680B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 6 +--R (384384A a b - 147840B a b )e +--R + +--R 6 2 5 5 +--R (492492A a b - 425964B a b )d e +--R + +--R 7 6 2 4 7 3 3 +--R (69069A b - 329637B a b )d e - 42504B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 6 +--R (338910A a b - 130350B a b )e +--R + +--R 2 5 3 4 5 +--R (905190A a b - 556710B a b )d e +--R + +--R 6 2 5 2 4 7 6 3 3 +--R (326040A a b - 682440B a b )d e + (6435A b - 203115B a b )d e +--R + +--R 7 4 2 +--R - 3960B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 6 +--R (137995A a b - 53075B a b )e +--R + +--R 3 4 4 3 5 +--R (803660A a b - 394020B a b )d e +--R + +--R 2 5 3 4 2 4 +--R (604890A a b - 727210B a b )d e +--R + +--R 6 2 5 3 3 7 6 4 2 +--R (31460A a b - 384340B a b )d e + (- 1430A b - 18810B a b )d e +--R + +--R 7 5 +--R 880B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 6 4 3 5 2 5 +--R (16640A a b - 6400B a b)e + (330785A a b - 137465B a b )d e +--R + +--R 3 4 4 3 2 4 +--R (543920A a b - 412760B a b )d e +--R + +--R 2 5 3 4 3 3 +--R (60970A a b - 358170B a b )d e +--R + +--R 6 2 5 4 2 7 6 5 +--R (- 6890A a b - 34870B a b )d e + (520A b + 4040B a b )d e +--R + +--R 7 6 +--R - 320B b d +--R * +--R 2 +--R x +--R + +--R 6 7 6 5 2 6 5 +--R (- 1280A a b + 640B a )e + (40960A a b - 16000B a b)d e +--R + +--R 4 3 5 2 2 4 +--R (228385A a b - 109945B a b )d e +--R + +--R 3 4 4 3 3 3 +--R (58100A a b - 168060B a b )d e +--R + +--R 2 5 3 4 4 2 6 2 5 5 +--R (- 13090A a b - 25550B a b )d e + (2480A a b + 4000B a b )d e +--R + +--R 7 6 6 +--R (- 240A b - 400B a b )d +--R * +--R x +--R + +--R 7 6 6 7 5 +--R 384A a e + (- 3968A a b + 256B a )d e +--R + +--R 5 2 6 2 4 4 3 5 2 3 3 +--R (32384A a b - 6912B a b)d e + (22155A a b - 33619B a b )d e +--R + +--R 3 4 4 3 4 2 2 5 3 4 5 +--R (- 7630A a b - 5530B a b )d e + (1960A a b + 840B a b )d e +--R + +--R 6 2 5 6 +--R (- 240A a b - 80B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 +--R 960a b e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 3 8 4 5 2 9 5 4 10 6 3 11 7 2 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 +--R 3840a b e - 24960a b d e + 67200a b d e - 94080a b d e +--R + +--R 4 7 4 5 3 8 5 4 2 9 6 3 10 7 2 +--R 67200a b d e - 13440a b d e - 13440a b d e + 9600a b d e +--R + +--R 11 8 +--R - 1920b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 +--R 5760a b e - 32640a b d e + 68160a b d e - 47040a b d e +--R + +--R 5 6 4 5 4 7 5 4 3 8 6 3 2 9 7 2 +--R - 47040a b d e + 114240a b d e - 87360a b d e + 27840a b d e +--R + +--R 10 8 11 9 +--R - 960a b d e - 960b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 +--R 3840a b e - 15360a b d e + 3840a b d e + 80640a b d e +--R + +--R 6 5 4 5 5 6 5 4 4 7 6 3 3 8 7 2 +--R - 188160a b d e + 188160a b d e - 80640a b d e - 3840a b d e +--R + +--R 2 9 8 10 9 +--R 15360a b d e - 3840a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 +--R 960a e + 960a b d e - 27840a b d e + 87360a b d e +--R + +--R 7 4 4 5 6 5 5 4 5 6 6 3 4 7 7 2 +--R - 114240a b d e + 47040a b d e + 47040a b d e - 68160a b d e +--R + +--R 3 8 8 2 9 9 +--R 32640a b d e - 5760a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 +--R 1920a d e - 9600a b d e + 13440a b d e + 13440a b d e +--R + +--R 7 4 5 4 6 5 6 3 5 6 7 2 4 7 8 +--R - 67200a b d e + 94080a b d e - 67200a b d e + 24960a b d e +--R + +--R 3 8 9 +--R - 3840a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 +--R 960a d e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 7 4 6 3 6 5 7 2 5 6 8 4 7 9 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a +--R / +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 7 + +)clear all + +--S 8 of 1353 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 m +--R (1) (b x + 3a b x + 3a b x + a )(e x + d) +--R Type: Expression(Integer) +--E 8 + +--S 9 of 1353 +r0:=-(b*d-a*e)^3*(d+e*x)^(1+m)/(e^4*(1+m))+3*b*(b*d-a*e)^2*_ + (d+e*x)^(2+m)/(e^4*(2+m))-3*b^2*(b*d-a*e)*(d+e*x)^(3+m)/(e^4*(3+m))+_ + b^3*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 4 +--R (b m + 6b m + 11b m + 6b )(e x + d) +--R + +--R 2 3 3 2 3 2 2 3 +--R (3a b e - 3b d)m + (21a b e - 21b d)m + (42a b e - 42b d)m +--R + +--R 2 3 +--R 24a b e - 24b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 3 2 2 +--R (3a b e - 6a b d e + 3b d )m + (24a b e - 48a b d e + 24b d )m +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (57a b e - 114a b d e + 57b d )m + 36a b e - 72a b d e + 36b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e - 3a b d e + 3a b d e - b d )m +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (9a e - 27a b d e + 27a b d e - 9b d )m +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (26a e - 78a b d e + 78a b d e - 26b d )m + 24a e - 72a b d e +--R + +--R 2 2 3 3 +--R 72a b d e - 24b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 3 4 2 3 4 3 4 4 +--R (b e m + 6b e m + 11b e m + 6b e )x +--R + +--R 2 4 3 3 3 2 4 3 3 2 +--R (3a b e + b d e )m + (21a b e + 3b d e )m +--R + +--R 2 4 3 3 2 4 +--R (42a b e + 2b d e )m + 24a b e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 3 2 4 2 3 3 2 2 2 +--R (3a b e + 3a b d e )m + (24a b e + 15a b d e - 3b d e )m +--R + +--R 2 4 2 3 3 2 2 2 4 +--R (57a b e + 12a b d e - 3b d e )m + 36a b e +--R * +--R 2 +--R x +--R + +--R 3 4 2 3 3 3 4 2 3 2 2 2 2 +--R (a e + 3a b d e )m + (9a e + 21a b d e - 6a b d e )m +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 +--R (26a e + 36a b d e - 24a b d e + 6b d e)m + 24a e +--R * +--R x +--R + +--R 3 3 3 3 3 2 2 2 2 +--R a d e m + (9a d e - 3a b d e )m +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (26a d e - 21a b d e + 6a b d e)m + 24a d e - 36a b d e + 24a b d e +--R + +--R 3 4 +--R - 6b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 10 + +--S 11 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 3 3 4 2 3 4 3 4 4 +--R (b e m + 6b e m + 11b e m + 6b e )x +--R + +--R 2 4 3 3 3 2 4 3 3 2 +--R (3a b e + b d e )m + (21a b e + 3b d e )m +--R + +--R 2 4 3 3 2 4 +--R (42a b e + 2b d e )m + 24a b e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 3 2 4 2 3 3 2 2 2 +--R (3a b e + 3a b d e )m + (24a b e + 15a b d e - 3b d e )m +--R + +--R 2 4 2 3 3 2 2 2 4 +--R (57a b e + 12a b d e - 3b d e )m + 36a b e +--R * +--R 2 +--R x +--R + +--R 3 4 2 3 3 3 4 2 3 2 2 2 2 +--R (a e + 3a b d e )m + (9a e + 21a b d e - 6a b d e )m +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 +--R (26a e + 36a b d e - 24a b d e + 6b d e)m + 24a e +--R * +--R x +--R + +--R 3 3 3 3 3 2 2 2 2 +--R a d e m + (9a d e - 3a b d e )m +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 +--R (26a d e - 21a b d e + 6a b d e)m + 24a d e - 36a b d e +--R + +--R 2 3 3 4 +--R 24a b d e - 6b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 3 3 2 3 3 m + 4 +--R (- b m - 6b m - 11b m - 6b )(e x + d) +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 3a b e + 3b d)m + (- 21a b e + 21b d)m + (- 42a b e + 42b d)m +--R + +--R 2 3 +--R - 24a b e + 24b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 +--R (- 3a b e + 6a b d e - 3b d )m +--R + +--R 2 2 2 3 2 2 +--R (- 24a b e + 48a b d e - 24b d )m +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (- 57a b e + 114a b d e - 57b d )m - 36a b e + 72a b d e - 36b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a e + 3a b d e - 3a b d e + b d )m +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 9a e + 27a b d e - 27a b d e + 9b d )m +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 26a e + 78a b d e - 78a b d e + 26b d )m - 24a e + 72a b d e +--R + +--R 2 2 3 3 +--R - 72a b d e + 24b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 1353 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 5 8 2 5 3 4 7 2 5 2 4 3 2 3 6 +--R b e x + (3a b e + 5b d e )x + (3a b e + 15a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 5 +--R (a e + 15a b d e + 30a b d e + 10b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 4 +--R (5a d e + 30a b d e + 30a b d e + 5b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (10a d e + 30a b d e + 15a b d e + b d )x +--R + +--R 3 3 2 2 4 2 5 2 3 4 2 5 3 5 +--R (10a d e + 15a b d e + 3a b d )x + (5a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 13 + +--S 14 of 1353 +r0:=-1/6*(b*d-a*e)^3*(d+e*x)^6/e^4+3/7*b*(b*d-a*e)^2*(d+e*x)^7/e^4-_ + 3/8*b^2*(b*d-a*e)*(d+e*x)^8/e^4+1/9*b^3*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 3 9 9 3 2 9 5 3 8 8 +--R - b e x + (- a b e + - b d e )x +--R 9 8 8 +--R + +--R 3 2 9 15 2 8 10 3 2 7 7 +--R (- a b e + -- a b d e + -- b d e )x +--R 7 7 7 +--R + +--R 1 3 9 5 2 8 2 2 7 5 3 3 6 6 +--R (- a e + - a b d e + 5a b d e + - b d e )x +--R 6 2 3 +--R + +--R 3 8 2 2 7 2 3 6 3 4 5 5 +--R (a d e + 6a b d e + 6a b d e + b d e )x +--R + +--R 5 3 2 7 15 2 3 6 15 2 4 5 1 3 5 4 4 +--R (- a d e + -- a b d e + -- a b d e + - b d e )x +--R 2 2 4 4 +--R + +--R 10 3 3 6 2 4 5 2 5 4 3 5 3 4 5 3 2 5 4 2 +--R (-- a d e + 5a b d e + a b d e )x + (- a d e + - a b d e )x +--R 3 2 2 +--R + +--R 3 5 4 1 3 6 3 1 2 7 2 1 2 8 1 3 9 +--R a d e x + - a d e - -- a b d e + -- a b d e - --- b d +--R 6 14 56 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 14 + +--S 15 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 5 9 3 2 5 5 3 4 8 3 2 5 15 2 4 10 3 2 3 7 +--R - b e x + (- a b e + - b d e )x + (- a b e + -- a b d e + -- b d e )x +--R 9 8 8 7 7 7 +--R + +--R 1 3 5 5 2 4 2 2 3 5 3 3 2 6 +--R (- a e + - a b d e + 5a b d e + - b d e )x +--R 6 2 3 +--R + +--R 3 4 2 2 3 2 3 2 3 4 5 +--R (a d e + 6a b d e + 6a b d e + b d e)x +--R + +--R 5 3 2 3 15 2 3 2 15 2 4 1 3 5 4 +--R (- a d e + -- a b d e + -- a b d e + - b d )x +--R 2 2 4 4 +--R + +--R 10 3 3 2 2 4 2 5 3 5 3 4 3 2 5 2 3 5 +--R (-- a d e + 5a b d e + a b d )x + (- a d e + - a b d )x + a d x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 15 + +--S 16 of 1353 +m0:=a0-r0 +--R +--R +--R 1 3 6 3 1 2 7 2 1 2 8 1 3 9 +--R - - a d e + -- a b d e - -- a b d e + --- b d +--R 6 14 56 504 +--R (4) ------------------------------------------------ +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 16 + +--S 17 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 17 + +)clear all + +--S 18 of 1353 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 18 + +--S 19 of 1353 +r0:=-1/5*(b*d-a*e)^3*(d+e*x)^5/e^4+1/2*b*(b*d-a*e)^2*(d+e*x)^6/e^4-_ + 3/7*b^2*(b*d-a*e)*(d+e*x)^7/e^4+1/8*b^3*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 3 8 8 3 2 8 4 3 7 7 1 2 8 2 7 3 2 6 6 +--R - b e x + (- a b e + - b d e )x + (- a b e + 2a b d e + b d e )x +--R 8 7 7 2 +--R + +--R 1 3 8 12 2 7 18 2 2 6 4 3 3 5 5 +--R (- a e + -- a b d e + -- a b d e + - b d e )x +--R 5 5 5 5 +--R + +--R 3 7 9 2 2 6 2 3 5 1 3 4 4 4 +--R (a d e + - a b d e + 3a b d e + - b d e )x +--R 2 4 +--R + +--R 3 2 6 2 3 5 2 4 4 3 3 3 5 3 2 4 4 2 3 4 4 +--R (2a d e + 4a b d e + a b d e )x + (2a d e + - a b d e )x + a d e x +--R 2 +--R + +--R 1 3 5 3 1 2 6 2 1 2 7 1 3 8 +--R - a d e - -- a b d e + -- a b d e - --- b d +--R 5 10 35 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 19 + +--S 20 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 8 3 2 4 4 3 3 7 1 2 4 2 3 3 2 2 6 +--R - b e x + (- a b e + - b d e )x + (- a b e + 2a b d e + b d e )x +--R 8 7 7 2 +--R + +--R 1 3 4 12 2 3 18 2 2 2 4 3 3 5 +--R (- a e + -- a b d e + -- a b d e + - b d e)x +--R 5 5 5 5 +--R + +--R 3 3 9 2 2 2 2 3 1 3 4 4 +--R (a d e + - a b d e + 3a b d e + - b d )x +--R 2 4 +--R + +--R 3 2 2 2 3 2 4 3 3 3 3 2 4 2 3 4 +--R (2a d e + 4a b d e + a b d )x + (2a d e + - a b d )x + a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +--S 21 of 1353 +m0:=a0-r0 +--R +--R +--R 1 3 5 3 1 2 6 2 1 2 7 1 3 8 +--R - - a d e + -- a b d e - -- a b d e + --- b d +--R 5 10 35 280 +--R (4) ------------------------------------------------ +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 21 + +--S 22 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 22 + +)clear all + +--S 23 of 1353 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 23 + +--S 24 of 1353 +r0:=1/4*(b*d-a*e)^3*(a+b*x)^4/b^4+3/5*e*(b*d-a*e)^2*(a+b*x)^5/b^4+_ + 1/2*e^2*(b*d-a*e)*(a+b*x)^6/b^4+1/7*e^3*(a+b*x)^7/b^4 +--R +--R +--R (2) +--R 1 7 3 7 1 6 3 1 7 2 6 3 2 5 3 9 6 2 3 7 2 5 +--R - b e x + (- a b e + - b d e )x + (- a b e + - a b d e + - b d e)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 4 3 9 2 5 2 9 6 2 1 7 3 4 +--R (- a b e + - a b d e + - a b d e + - b d )x +--R 4 4 4 4 +--R + +--R 3 4 2 2 5 2 6 3 3 3 3 4 2 3 2 5 3 2 3 4 3 +--R (a b d e + 3a b d e + a b d )x + (- a b d e + - a b d )x + a b d x +--R 2 2 +--R + +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R - --- a e + -- a b d e - -- a b d e + - a b d +--R 140 20 20 4 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 24 + +--S 25 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 3 7 1 2 3 1 3 2 6 3 2 3 9 2 2 3 3 2 5 +--R - b e x + (- a b e + - b d e )x + (- a b e + - a b d e + - b d e)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 3 9 2 2 9 2 2 1 3 3 4 +--R (- a e + - a b d e + - a b d e + - b d )x +--R 4 4 4 4 +--R + +--R 3 2 2 2 2 3 3 3 3 2 3 2 3 2 3 3 +--R (a d e + 3a b d e + a b d )x + (- a d e + - a b d )x + a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +--S 26 of 1353 +m0:=a0-r0 +--R +--R +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R --- a e - -- a b d e + -- a b d e - - a b d +--R 140 20 20 4 +--R (4) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 26 + +--S 27 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 27 + +)clear all + +--S 28 of 1353 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 28 + +--S 29 of 1353 +r0:=1/4*(b*d-a*e)^2*(a+b*x)^4/b^3+2/5*e*(b*d-a*e)*(a+b*x)^5/b^3+_ + 1/6*e^2*(a+b*x)^6/b^3 +--R +--R +--R (2) +--R 1 6 2 6 3 5 2 2 6 5 3 2 4 2 3 5 1 6 2 4 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 3 2 2 4 5 2 3 3 3 3 2 4 2 2 3 3 2 +--R (- a b e + 2a b d e + a b d )x + (a b d e + - a b d )x + a b d x +--R 3 2 +--R + +--R 1 6 2 1 5 1 4 2 2 +--R -- a e - -- a b d e + - a b d +--R 60 10 4 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 29 + +--S 30 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 6 3 2 2 2 3 5 3 2 2 3 2 1 3 2 4 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 2 2 2 2 3 3 3 2 2 2 3 2 +--R (- a e + 2a b d e + a b d )x + (a d e + - a b d )x + a d x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +--S 31 of 1353 +m0:=a0-r0 +--R +--R +--R 1 6 2 1 5 1 4 2 2 +--R - -- a e + -- a b d e - - a b d +--R 60 10 4 +--R (4) --------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 31 + +--S 32 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 32 + +)clear all + +--S 33 of 1353 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d +--R Type: Polynomial(Integer) +--E 33 + +--S 34 of 1353 +r0:=1/4*(b*d-a*e)*(a+b*x)^4/b^2+1/5*e*(a+b*x)^5/b^2 +--R +--R +--R (2) +--R 1 5 5 3 4 1 5 4 2 3 4 3 +--R - b e x + (- a b e + - b d)x + (a b e + a b d)x +--R 5 4 4 +--R + +--R 1 3 2 3 2 3 2 3 2 1 5 1 4 +--R (- a b e + - a b d)x + a b d x - -- a e + - a b d +--R 2 2 20 4 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 34 + +--S 35 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 5 3 2 1 3 4 2 2 3 1 3 3 2 2 +--R - b e x + (- a b e + - b d)x + (a b e + a b d)x + (- a e + - a b d)x +--R 5 4 4 2 2 +--R + +--R 3 +--R a d x +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +--S 36 of 1353 +m0:=a0-r0 +--R +--R +--R 1 5 1 4 +--R -- a e - - a b d +--R 20 4 +--R (4) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 36 + +--S 37 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 37 + +)clear all + +--S 38 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 38 + +--S 39 of 1353 +r0:=1/4*(a+b*x)^4/b +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - b x + a b x + - a b x + a b x + - a +--R 4 2 4 +--R (2) ----------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 39 + +--S 40 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 3 4 2 3 3 2 2 3 +--R (3) - b x + a b x + - a b x + a x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +--S 41 of 1353 +m0:=a0-r0 +--R +--R +--R 1 4 +--R - a +--R 4 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 41 + +--S 42 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 42 + +)clear all + +--S 43 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 43 + +--S 44 of 1353 +r0:=b*(b*d-a*e)^2*x/e^3-1/2*(b*d-a*e)*(a+b*x)^2/e^2+1/3*(a+b*x)^3/e-_ + (b*d-a*e)^3*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a e - 18a b d e + 18a b d e - 6b d )log(e x + d) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (9a b e - 3b d e )x + (18a b e - 18a b d e + 6b d e)x + 5a e +--R + +--R 2 2 +--R - 3a b d e +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a e - 18a b d e + 18a b d e - 6b d )log(e x + d) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (9a b e - 3b d e )x + (18a b e - 18a b d e + 6b d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 45 + +--S 46 of 1353 +m0:=a0-r0 +--R +--R +--R 3 2 +--R - 5a e + 3a b d +--R (4) --------------- +--R 2 +--R 6e +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 47 + +)clear all + +--S 48 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 48 + +--S 49 of 1353 +r0:=-b^2*(2*b*d-3*a*e)*x/e^3+1/2*b^3*x^2/e^2+(b*d-a*e)^3/(e^4*(d+e*x))+_ + 3*b*(b*d-a*e)^2*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b e - 12a b d e + 6b d e)x + 6a b d e - 12a b d e + 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 3 3 +--R b e x + (6a b e - 3b d e )x + (6a b d e - 4b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 6a b d e + 2b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b e - 12a b d e + 6b d e)x + 6a b d e - 12a b d e + 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 3 3 +--R b e x + (6a b e - 3b d e )x + (6a b d e - 4b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 6a b d e + 2b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 50 + +--S 51 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 52 + +)clear all + +--S 53 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 53 + +--S 54 of 1353 +r0:=b^3*x/e^3+1/2*(b*d-a*e)^3/(e^4*(d+e*x)^2)-3*b*(b*d-a*e)^2/(e^4*(d+e*x))-_ + 3*b^2*(b*d-a*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 2 3 2 2 2 3 3 +--R ((6a b e - 6b d e )x + (12a b d e - 12b d e)x + 6a b d e - 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 3 2 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4b d e x + (- 6a b e + 12a b d e - 4b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 9a b d e - 5b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 2 3 2 2 2 3 3 +--R ((6a b e - 6b d e )x + (12a b d e - 12b d e)x + 6a b d e - 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 3 2 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4b d e x + (- 6a b e + 12a b d e - 4b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 9a b d e - 5b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 55 + +--S 56 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 58 + +--S 59 of 1353 +r0:=1/3*(b*d-a*e)^3/(e^4*(d+e*x)^3)-3/2*b*(b*d-a*e)^2/(e^4*(d+e*x)^2)+_ + 3*b^2*(b*d-a*e)/(e^4*(d+e*x))+b^3*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(e x + d) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 18a b e + 18b d e )x + (- 9a b e - 18a b d e + 27b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e - 6a b d e + 11b d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(e x + d) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 18a b e + 18b d e )x + (- 9a b e - 18a b d e + 27b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e - 6a b d e + 11b d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 60 + +--S 61 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 62 + +)clear all + +--S 63 of 1353 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 m +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )(e x + d) +--R Type: Expression(Integer) +--E 63 + +--S 64 of 1353 +r0:=-(b*d-a*e)^5*(d+e*x)^(1+m)/(e^6*(1+m))+5*b*(b*d-a*e)^4*(d+e*x)^(2+m)/_ + (e^6*(2+m))-10*b^2*(b*d-a*e)^3*(d+e*x)^(3+m)/(e^6*(3+m))+10*b^3*_ + (b*d-a*e)^2*(d+e*x)^(4+m)/(e^6*(4+m))-5*b^4*(b*d-a*e)*(d+e*x)^(5+m)/_ + (e^6*(5+m))+b^5*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 5 5 5 4 5 3 5 2 5 5 m + 6 +--R (b m + 15b m + 85b m + 225b m + 274b m + 120b )(e x + d) +--R + +--R 4 5 5 4 5 4 4 5 3 +--R (5a b e - 5b d)m + (80a b e - 80b d)m + (475a b e - 475b d)m +--R + +--R 4 5 2 4 5 4 5 +--R (1300a b e - 1300b d)m + (1620a b e - 1620b d)m + 720a b e - 720b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 3 2 4 5 2 5 +--R (10a b e - 20a b d e + 10b d )m +--R + +--R 2 3 2 4 5 2 4 +--R (170a b e - 340a b d e + 170b d )m +--R + +--R 2 3 2 4 5 2 3 +--R (1070a b e - 2140a b d e + 1070b d )m +--R + +--R 2 3 2 4 5 2 2 +--R (3070a b e - 6140a b d e + 3070b d )m +--R + +--R 2 3 2 4 5 2 2 3 2 4 +--R (3960a b e - 7920a b d e + 3960b d )m + 1800a b e - 3600a b d e +--R + +--R 5 2 +--R 1800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e - 30a b d e + 30a b d e - 10b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (180a b e - 540a b d e + 540a b d e - 180b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (1210a b e - 3630a b d e + 3630a b d e - 1210b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (3720a b e - 11160a b d e + 11160a b d e - 3720b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 2 3 +--R (5080a b e - 15240a b d e + 15240a b d e - 5080b d )m + 2400a b e +--R + +--R 2 3 2 4 2 5 3 +--R - 7200a b d e + 7200a b d e - 2400b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e - 20a b d e + 30a b d e - 20a b d e + 5b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 4 +--R (95a b e - 380a b d e + 570a b d e - 380a b d e + 95b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (685a b e - 2740a b d e + 4110a b d e - 2740a b d e + 685b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 2305a b e - 9220a b d e + 13830a b d e - 9220a b d e +--R + +--R 5 4 +--R 2305b d +--R * +--R 2 +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 3510a b e - 14040a b d e + 21060a b d e - 14040a b d e +--R + +--R 5 4 +--R 3510b d +--R * +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R 1800a b e - 7200a b d e + 10800a b d e - 7200a b d e + 1800b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e - 5a b d e + 10a b d e - 10a b d e + 5a b d e - b d )m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 20a e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 5 5 +--R - 20b d +--R * +--R 4 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 155a e - 775a b d e + 1550a b d e - 1550a b d e + 775a b d e +--R + +--R 5 5 +--R - 155b d +--R * +--R 3 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R 580a e - 2900a b d e + 5800a b d e - 5800a b d e +--R + +--R 4 4 5 5 +--R 2900a b d e - 580b d +--R * +--R 2 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R 1044a e - 5220a b d e + 10440a b d e - 10440a b d e +--R + +--R 4 4 5 5 +--R 5220a b d e - 1044b d +--R * +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 720a e - 3600a b d e + 7200a b d e - 7200a b d e + 3600a b d e +--R + +--R 5 5 +--R - 720b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 5 6 4 5 6 3 5 6 2 5 6 5 6 6 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x +--R + +--R 4 6 5 5 5 4 6 5 5 4 +--R (5a b e + b d e )m + (80a b e + 10b d e )m +--R + +--R 4 6 5 5 3 4 6 5 5 2 +--R (475a b e + 35b d e )m + (1300a b e + 50b d e )m +--R + +--R 4 6 5 5 4 6 +--R (1620a b e + 24b d e )m + 720a b e +--R * +--R 5 +--R x +--R + +--R 2 3 6 4 5 5 2 3 6 4 5 5 2 4 4 +--R (10a b e + 5a b d e )m + (170a b e + 60a b d e - 5b d e )m +--R + +--R 2 3 6 4 5 5 2 4 3 +--R (1070a b e + 235a b d e - 30b d e )m +--R + +--R 2 3 6 4 5 5 2 4 2 +--R (3070a b e + 360a b d e - 55b d e )m +--R + +--R 2 3 6 4 5 5 2 4 2 3 6 +--R (3960a b e + 180a b d e - 30b d e )m + 1800a b e +--R * +--R 4 +--R x +--R + +--R 3 2 6 2 3 5 5 +--R (10a b e + 10a b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 4 +--R (180a b e + 140a b d e - 20a b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (1210a b e + 650a b d e - 180a b d e + 20b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 2 +--R (3720a b e + 1120a b d e - 400a b d e + 60b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 2 6 +--R (5080a b e + 600a b d e - 240a b d e + 40b d e )m + 2400a b e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 5 4 6 3 2 5 2 3 2 4 4 +--R (5a b e + 10a b d e )m + (95a b e + 160a b d e - 30a b d e )m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 3 +--R (685a b e + 890a b d e - 360a b d e + 60a b d e )m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 2305a b e + 1940a b d e - 1230a b d e + 420a b d e +--R + +--R 5 4 2 +--R - 60b d e +--R * +--R 2 +--R m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 +--R (3510a b e + 1200a b d e - 900a b d e + 360a b d e - 60b d e )m +--R + +--R 4 6 +--R 1800a b e +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 5 5 6 4 5 3 2 2 4 4 +--R (a e + 5a b d e )m + (20a e + 90a b d e - 20a b d e )m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 3 +--R (155a e + 595a b d e - 300a b d e + 60a b d e )m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 580a e + 1710a b d e - 1480a b d e + 660a b d e +--R + +--R 4 4 2 +--R - 120a b d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 1044a e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 4 2 5 5 +--R - 720a b d e + 120b d e +--R * +--R m +--R + +--R 5 6 +--R 720a e +--R * +--R x +--R + +--R 5 5 5 5 5 4 2 4 4 +--R a d e m + (20a d e - 5a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 3 +--R (155a d e - 90a b d e + 20a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 2 +--R (580a d e - 595a b d e + 300a b d e - 60a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R (1044a d e - 1710a b d e + 1480a b d e - 660a b d e + 120a b d e)m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 720a d e - 1800a b d e + 2400a b d e - 1800a b d e + 720a b d e +--R + +--R 5 6 +--R - 120b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Union(Expression(Integer),...) +--E 65 + +--S 66 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 5 5 6 4 5 6 3 5 6 2 5 6 5 6 6 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x +--R + +--R 4 6 5 5 5 4 6 5 5 4 +--R (5a b e + b d e )m + (80a b e + 10b d e )m +--R + +--R 4 6 5 5 3 4 6 5 5 2 +--R (475a b e + 35b d e )m + (1300a b e + 50b d e )m +--R + +--R 4 6 5 5 4 6 +--R (1620a b e + 24b d e )m + 720a b e +--R * +--R 5 +--R x +--R + +--R 2 3 6 4 5 5 2 3 6 4 5 5 2 4 4 +--R (10a b e + 5a b d e )m + (170a b e + 60a b d e - 5b d e )m +--R + +--R 2 3 6 4 5 5 2 4 3 +--R (1070a b e + 235a b d e - 30b d e )m +--R + +--R 2 3 6 4 5 5 2 4 2 +--R (3070a b e + 360a b d e - 55b d e )m +--R + +--R 2 3 6 4 5 5 2 4 2 3 6 +--R (3960a b e + 180a b d e - 30b d e )m + 1800a b e +--R * +--R 4 +--R x +--R + +--R 3 2 6 2 3 5 5 +--R (10a b e + 10a b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 4 +--R (180a b e + 140a b d e - 20a b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (1210a b e + 650a b d e - 180a b d e + 20b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 2 +--R (3720a b e + 1120a b d e - 400a b d e + 60b d e )m +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 2 6 +--R (5080a b e + 600a b d e - 240a b d e + 40b d e )m + 2400a b e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 5 +--R (5a b e + 10a b d e )m +--R + +--R 4 6 3 2 5 2 3 2 4 4 +--R (95a b e + 160a b d e - 30a b d e )m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 3 +--R (685a b e + 890a b d e - 360a b d e + 60a b d e )m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 2305a b e + 1940a b d e - 1230a b d e + 420a b d e +--R + +--R 5 4 2 +--R - 60b d e +--R * +--R 2 +--R m +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 3510a b e + 1200a b d e - 900a b d e + 360a b d e +--R + +--R 5 4 2 +--R - 60b d e +--R * +--R m +--R + +--R 4 6 +--R 1800a b e +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 5 5 6 4 5 3 2 2 4 4 +--R (a e + 5a b d e )m + (20a e + 90a b d e - 20a b d e )m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 3 +--R (155a e + 595a b d e - 300a b d e + 60a b d e )m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 580a e + 1710a b d e - 1480a b d e + 660a b d e +--R + +--R 4 4 2 +--R - 120a b d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 1044a e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 4 2 5 5 +--R - 720a b d e + 120b d e +--R * +--R m +--R + +--R 5 6 +--R 720a e +--R * +--R x +--R + +--R 5 5 5 5 5 4 2 4 4 +--R a d e m + (20a d e - 5a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 3 +--R (155a d e - 90a b d e + 20a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 2 +--R (580a d e - 595a b d e + 300a b d e - 60a b d e )m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 +--R 1044a d e - 1710a b d e + 1480a b d e - 660a b d e +--R + +--R 4 5 +--R 120a b d e +--R * +--R m +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 720a d e - 1800a b d e + 2400a b d e - 1800a b d e + 720a b d e +--R + +--R 5 6 +--R - 120b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 6 +--R (- b m - 15b m - 85b m - 225b m - 274b m - 120b )(e x + d) +--R + +--R 4 5 5 4 5 4 4 5 3 +--R (- 5a b e + 5b d)m + (- 80a b e + 80b d)m + (- 475a b e + 475b d)m +--R + +--R 4 5 2 4 5 4 +--R (- 1300a b e + 1300b d)m + (- 1620a b e + 1620b d)m - 720a b e +--R + +--R 5 +--R 720b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 3 2 4 5 2 5 +--R (- 10a b e + 20a b d e - 10b d )m +--R + +--R 2 3 2 4 5 2 4 +--R (- 170a b e + 340a b d e - 170b d )m +--R + +--R 2 3 2 4 5 2 3 +--R (- 1070a b e + 2140a b d e - 1070b d )m +--R + +--R 2 3 2 4 5 2 2 +--R (- 3070a b e + 6140a b d e - 3070b d )m +--R + +--R 2 3 2 4 5 2 2 3 2 4 +--R (- 3960a b e + 7920a b d e - 3960b d )m - 1800a b e + 3600a b d e +--R + +--R 5 2 +--R - 1800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 10a b e + 30a b d e - 30a b d e + 10b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (- 180a b e + 540a b d e - 540a b d e + 180b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (- 1210a b e + 3630a b d e - 3630a b d e + 1210b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 3720a b e + 11160a b d e - 11160a b d e + 3720b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 +--R (- 5080a b e + 15240a b d e - 15240a b d e + 5080b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 +--R - 2400a b e + 7200a b d e - 7200a b d e + 2400b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (- 5a b e + 20a b d e - 30a b d e + 20a b d e - 5b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 4 +--R (- 95a b e + 380a b d e - 570a b d e + 380a b d e - 95b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (- 685a b e + 2740a b d e - 4110a b d e + 2740a b d e - 685b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R - 2305a b e + 9220a b d e - 13830a b d e + 9220a b d e +--R + +--R 5 4 +--R - 2305b d +--R * +--R 2 +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R - 3510a b e + 14040a b d e - 21060a b d e + 14040a b d e +--R + +--R 5 4 +--R - 3510b d +--R * +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R - 1800a b e + 7200a b d e - 10800a b d e + 7200a b d e - 1800b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (- a e + 5a b d e - 10a b d e + 10a b d e - 5a b d e + b d )m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 20a e + 100a b d e - 200a b d e + 200a b d e - 100a b d e +--R + +--R 5 5 +--R 20b d +--R * +--R 4 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R - 155a e + 775a b d e - 1550a b d e + 1550a b d e +--R + +--R 4 4 5 5 +--R - 775a b d e + 155b d +--R * +--R 3 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R - 580a e + 2900a b d e - 5800a b d e + 5800a b d e +--R + +--R 4 4 5 5 +--R - 2900a b d e + 580b d +--R * +--R 2 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R - 1044a e + 5220a b d e - 10440a b d e + 10440a b d e +--R + +--R 4 4 5 5 +--R - 5220a b d e + 1044b d +--R * +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 720a e + 3600a b d e - 7200a b d e + 7200a b d e - 3600a b d e +--R + +--R 5 5 +--R 720b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 67 + +)clear all + +--S 68 of 1353 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 11 4 6 5 5 10 2 3 6 4 5 5 2 4 9 +--R b e x + (5a b e + 6b d e )x + (10a b e + 30a b d e + 15b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 8 +--R (10a b e + 60a b d e + 75a b d e + 20b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 7 +--R (5a b e + 60a b d e + 150a b d e + 100a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 6 +--R (a e + 30a b d e + 150a b d e + 200a b d e + 75a b d e + 6b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 5 +--R (6a d e + 75a b d e + 200a b d e + 150a b d e + 30a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 4 +--R (15a d e + 100a b d e + 150a b d e + 60a b d e + 5a b d )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 3 +--R (20a d e + 75a b d e + 60a b d e + 10a b d )x +--R + +--R 5 4 2 4 5 3 2 6 2 5 5 4 6 5 6 +--R (15a d e + 30a b d e + 10a b d )x + (6a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 68 + +--S 69 of 1353 +r0:=-1/7*(b*d-a*e)^5*(d+e*x)^7/e^6+5/8*b*(b*d-a*e)^4*(d+e*x)^8/e^6-_ + 10/9*b^2*(b*d-a*e)^3*(d+e*x)^9/e^6+b^3*(b*d-a*e)^2*(d+e*x)^10/e^6-_ + 5/11*b^4*(b*d-a*e)*(d+e*x)^11/e^6+1/12*b^5*(d+e*x)^12/e^6 +--R +--R +--R (2) +--R 1 5 12 12 5 4 12 6 5 11 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 2 3 12 4 11 3 5 2 10 10 +--R (a b e + 3a b d e + - b d e )x +--R 2 +--R + +--R 10 3 2 12 20 2 3 11 25 4 2 10 20 5 3 9 9 +--R (-- a b e + -- a b d e + -- a b d e + -- b d e )x +--R 9 3 3 9 +--R + +--R 5 4 12 15 3 2 11 75 2 3 2 10 25 4 3 9 15 5 4 8 8 +--R (- a b e + -- a b d e + -- a b d e + -- a b d e + -- b d e )x +--R 8 2 4 2 8 +--R + +--R 1 5 12 30 4 11 150 3 2 2 10 200 2 3 3 9 75 4 4 8 +--R - a e + -- a b d e + --- a b d e + --- a b d e + -- a b d e +--R 7 7 7 7 7 +--R + +--R 6 5 5 7 +--R - b d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 5 11 25 4 2 10 100 3 2 3 9 2 3 4 8 4 5 7 +--R a d e + -- a b d e + --- a b d e + 25a b d e + 5a b d e +--R 2 3 +--R + +--R 1 5 6 6 +--R - b d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 2 4 8 2 3 5 7 4 6 6 5 +--R (3a d e + 20a b d e + 30a b d e + 12a b d e + a b d e )x +--R + +--R 5 3 9 75 4 4 8 3 2 5 7 5 2 3 6 6 4 +--R (5a d e + -- a b d e + 15a b d e + - a b d e )x +--R 4 2 +--R + +--R 5 4 8 4 5 7 10 3 2 6 6 3 5 5 7 5 4 6 6 2 +--R (5a d e + 10a b d e + -- a b d e )x + (3a d e + - a b d e )x +--R 3 2 +--R + +--R 5 6 6 1 5 7 5 5 4 8 4 5 3 2 9 3 1 2 3 10 2 +--R a d e x + - a d e - -- a b d e + --- a b d e - -- a b d e +--R 7 56 126 84 +--R + +--R 1 4 11 1 5 12 +--R --- a b d e - ---- b d +--R 462 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 69 + +--S 70 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 6 12 5 4 6 6 5 5 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 2 3 6 4 5 3 5 2 4 10 +--R (a b e + 3a b d e + - b d e )x +--R 2 +--R + +--R 10 3 2 6 20 2 3 5 25 4 2 4 20 5 3 3 9 +--R (-- a b e + -- a b d e + -- a b d e + -- b d e )x +--R 9 3 3 9 +--R + +--R 5 4 6 15 3 2 5 75 2 3 2 4 25 4 3 3 15 5 4 2 8 +--R (- a b e + -- a b d e + -- a b d e + -- a b d e + -- b d e )x +--R 8 2 4 2 8 +--R + +--R 1 5 6 30 4 5 150 3 2 2 4 200 2 3 3 3 75 4 4 2 +--R - a e + -- a b d e + --- a b d e + --- a b d e + -- a b d e +--R 7 7 7 7 7 +--R + +--R 6 5 5 +--R - b d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 5 5 25 4 2 4 100 3 2 3 3 2 3 4 2 4 5 1 5 6 6 +--R (a d e + -- a b d e + --- a b d e + 25a b d e + 5a b d e + - b d )x +--R 2 3 6 +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 5 +--R (3a d e + 20a b d e + 30a b d e + 12a b d e + a b d )x +--R + +--R 5 3 3 75 4 4 2 3 2 5 5 2 3 6 4 +--R (5a d e + -- a b d e + 15a b d e + - a b d )x +--R 4 2 +--R + +--R 5 4 2 4 5 10 3 2 6 3 5 5 5 4 6 2 5 6 +--R (5a d e + 10a b d e + -- a b d )x + (3a d e + - a b d )x + a d x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 70 + +--S 71 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 5 7 5 5 4 8 4 5 3 2 9 3 1 2 3 10 2 1 4 11 +--R - - a d e + -- a b d e - --- a b d e + -- a b d e - --- a b d e +--R 7 56 126 84 462 +--R + +--R 1 5 12 +--R ---- b d +--R 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 71 + +--S 72 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 72 + +)clear all + +--S 73 of 1353 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 5 10 4 5 5 4 9 2 3 5 4 4 5 2 3 8 +--R b e x + (5a b e + 5b d e )x + (10a b e + 25a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 7 +--R (10a b e + 50a b d e + 50a b d e + 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 6 +--R (5a b e + 50a b d e + 100a b d e + 50a b d e + 5b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e + 25a b d e + 100a b d e + 100a b d e + 25a b d e + b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4 +--R (5a d e + 50a b d e + 100a b d e + 50a b d e + 5a b d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 3 +--R (10a d e + 50a b d e + 50a b d e + 10a b d )x +--R + +--R 5 3 2 4 4 3 2 5 2 5 4 4 5 5 5 +--R (10a d e + 25a b d e + 10a b d )x + (5a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 73 + +--S 74 of 1353 +r0:=1/6*(b*d-a*e)^5*(a+b*x)^6/b^6+5/7*e*(b*d-a*e)^4*(a+b*x)^7/b^6+_ + 5/4*e^2*(b*d-a*e)^3*(a+b*x)^8/b^6+10/9*e^3*(b*d-a*e)^2*(a+b*x)^9/b^6+_ + 1/2*e^4*(b*d-a*e)*(a+b*x)^10/b^6+1/11*e^5*(a+b*x)^11/b^6 +--R +--R +--R (2) +--R 1 11 5 11 1 10 5 1 11 4 10 +--R -- b e x + (- a b e + - b d e )x +--R 11 2 2 +--R + +--R 10 2 9 5 25 10 4 10 11 2 3 9 +--R (-- a b e + -- a b d e + -- b d e )x +--R 9 9 9 +--R + +--R 5 3 8 5 25 2 9 4 25 10 2 3 5 11 3 2 8 +--R (- a b e + -- a b d e + -- a b d e + - b d e )x +--R 4 4 4 4 +--R + +--R 5 4 7 5 50 3 8 4 100 2 9 2 3 50 10 3 2 5 11 4 7 +--R (- a b e + -- a b d e + --- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 7 +--R + +--R 1 5 6 5 25 4 7 4 50 3 8 2 3 50 2 9 3 2 25 10 4 +--R - a b e + -- a b d e + -- a b d e + -- a b d e + -- a b d e +--R 6 6 3 3 6 +--R + +--R 1 11 5 +--R - b d +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 6 4 4 7 2 3 3 8 3 2 2 9 4 10 5 5 +--R (a b d e + 10a b d e + 20a b d e + 10a b d e + a b d )x +--R + +--R 5 5 6 2 3 25 4 7 3 2 25 3 8 4 5 2 9 5 4 +--R (- a b d e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 10 5 6 3 2 25 4 7 4 10 3 8 5 3 5 5 6 4 5 4 7 5 2 +--R (-- a b d e + -- a b d e + -- a b d )x + (- a b d e + - a b d )x +--R 3 3 3 2 2 +--R + +--R 5 6 5 1 11 5 1 10 4 5 9 2 2 3 5 8 3 3 2 +--R a b d x - ---- a e + --- a b d e - --- a b d e + -- a b d e +--R 2772 252 252 84 +--R + +--R 5 7 4 4 1 6 5 5 +--R - -- a b d e + - a b d +--R 42 6 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 74 + +--S 75 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 5 11 1 4 5 1 5 4 10 +--R -- b e x + (- a b e + - b d e )x +--R 11 2 2 +--R + +--R 10 2 3 5 25 4 4 10 5 2 3 9 +--R (-- a b e + -- a b d e + -- b d e )x +--R 9 9 9 +--R + +--R 5 3 2 5 25 2 3 4 25 4 2 3 5 5 3 2 8 +--R (- a b e + -- a b d e + -- a b d e + - b d e )x +--R 4 4 4 4 +--R + +--R 5 4 5 50 3 2 4 100 2 3 2 3 50 4 3 2 5 5 4 7 +--R (- a b e + -- a b d e + --- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 7 +--R + +--R 1 5 5 25 4 4 50 3 2 2 3 50 2 3 3 2 25 4 4 1 5 5 6 +--R (- a e + -- a b d e + -- a b d e + -- a b d e + -- a b d e + - b d )x +--R 6 6 3 3 6 6 +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 5 +--R (a d e + 10a b d e + 20a b d e + 10a b d e + a b d )x +--R + +--R 5 5 2 3 25 4 3 2 25 3 2 4 5 2 3 5 4 +--R (- a d e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 10 5 3 2 25 4 4 10 3 2 5 3 5 5 4 5 4 5 2 5 5 +--R (-- a d e + -- a b d e + -- a b d )x + (- a d e + - a b d )x + a d x +--R 3 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 75 + +--S 76 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 11 5 1 10 4 5 9 2 2 3 5 8 3 3 2 5 7 4 4 +--R ---- a e - --- a b d e + --- a b d e - -- a b d e + -- a b d e +--R 2772 252 252 84 42 +--R + +--R 1 6 5 5 +--R - - a b d +--R 6 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 76 + +--S 77 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +)clear all + +--S 78 of 1353 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 78 + +--S 79 of 1353 +r0:=1/6*(b*d-a*e)^4*(a+b*x)^6/b^5+4/7*e*(b*d-a*e)^3*(a+b*x)^7/b^5+3/4*e^2*_ + (b*d-a*e)^2*(a+b*x)^8/b^5+4/9*e^3*(b*d-a*e)*(a+b*x)^9/b^5+1/10*e^4*_ + (a+b*x)^10/b^5 +--R +--R +--R (2) +--R 1 10 4 10 5 9 4 4 10 3 9 +--R -- b e x + (- a b e + - b d e )x +--R 10 9 9 +--R + +--R 5 2 8 4 5 9 3 3 10 2 2 8 +--R (- a b e + - a b d e + - b d e )x +--R 4 2 4 +--R + +--R 10 3 7 4 40 2 8 3 30 9 2 2 4 10 3 7 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 +--R + +--R 5 4 6 4 20 3 7 3 2 8 2 2 10 9 3 1 10 4 6 +--R (- a b e + -- a b d e + 10a b d e + -- a b d e + - b d )x +--R 6 3 3 6 +--R + +--R 1 5 5 4 4 6 3 3 7 2 2 2 8 3 9 4 5 +--R (- a b e + 4a b d e + 12a b d e + 8a b d e + a b d )x +--R 5 +--R + +--R 5 5 3 15 4 6 2 2 3 7 3 5 2 8 4 4 +--R (a b d e + -- a b d e + 10a b d e + - a b d )x +--R 2 2 +--R + +--R 5 5 2 2 20 4 6 3 10 3 7 4 3 5 5 3 5 4 6 4 2 +--R (2a b d e + -- a b d e + -- a b d )x + (2a b d e + - a b d )x +--R 3 3 2 +--R + +--R 5 5 4 1 10 4 1 9 3 1 8 2 2 2 2 7 3 3 1 6 4 4 +--R a b d x + ---- a e - --- a b d e + -- a b d e - -- a b d e + - a b d +--R 1260 126 28 21 6 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 79 + +--S 80 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 4 10 5 4 4 4 5 3 9 5 2 3 4 5 4 3 3 5 2 2 8 +--R -- b e x + (- a b e + - b d e )x + (- a b e + - a b d e + - b d e )x +--R 10 9 9 4 2 4 +--R + +--R 10 3 2 4 40 2 3 3 30 4 2 2 4 5 3 7 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 +--R + +--R 5 4 4 20 3 2 3 2 3 2 2 10 4 3 1 5 4 6 +--R (- a b e + -- a b d e + 10a b d e + -- a b d e + - b d )x +--R 6 3 3 6 +--R + +--R 1 5 4 4 3 3 2 2 2 2 3 3 4 4 5 +--R (- a e + 4a b d e + 12a b d e + 8a b d e + a b d )x +--R 5 +--R + +--R 5 3 15 4 2 2 3 2 3 5 2 3 4 4 +--R (a d e + -- a b d e + 10a b d e + - a b d )x +--R 2 2 +--R + +--R 5 2 2 20 4 3 10 3 2 4 3 5 3 5 4 4 2 5 4 +--R (2a d e + -- a b d e + -- a b d )x + (2a d e + - a b d )x + a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +--S 81 of 1353 +m0:=a0-r0 +--R +--R +--R 1 10 4 1 9 3 1 8 2 2 2 2 7 3 3 1 6 4 4 +--R - ---- a e + --- a b d e - -- a b d e + -- a b d e - - a b d +--R 1260 126 28 21 6 +--R (4) ----------------------------------------------------------------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 81 + +--S 82 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 82 + +)clear all + +--S 83 of 1353 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 83 + +--S 84 of 1353 +r0:=1/6*(b*d-a*e)^3*(a+b*x)^6/b^4+3/7*e*(b*d-a*e)^2*(a+b*x)^7/b^4+_ + 3/8*e^2*(b*d-a*e)*(a+b*x)^8/b^4+1/9*e^3*(a+b*x)^9/b^4 +--R +--R +--R (2) +--R 1 9 3 9 5 8 3 3 9 2 8 +--R - b e x + (- a b e + - b d e )x +--R 9 8 8 +--R + +--R 10 2 7 3 15 8 2 3 9 2 7 +--R (-- a b e + -- a b d e + - b d e)x +--R 7 7 7 +--R + +--R 5 3 6 3 2 7 2 5 8 2 1 9 3 6 +--R (- a b e + 5a b d e + - a b d e + - b d )x +--R 3 2 6 +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (a b e + 6a b d e + 6a b d e + a b d )x +--R + +--R 1 5 4 3 15 4 5 2 15 3 6 2 5 2 7 3 4 +--R (- a b e + -- a b d e + -- a b d e + - a b d )x +--R 4 4 2 2 +--R + +--R 5 4 2 4 5 2 10 3 6 3 3 3 5 4 2 5 4 5 3 2 5 4 3 +--R (a b d e + 5a b d e + -- a b d )x + (- a b d e + - a b d )x + a b d x +--R 3 2 2 +--R + +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R - --- a e + -- a b d e - -- a b d e + - a b d +--R 504 56 14 6 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 84 + +--S 85 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 3 9 5 4 3 3 5 2 8 10 2 3 3 15 4 2 3 5 2 7 +--R - b e x + (- a b e + - b d e )x + (-- a b e + -- a b d e + - b d e)x +--R 9 8 8 7 7 7 +--R + +--R 5 3 2 3 2 3 2 5 4 2 1 5 3 6 +--R (- a b e + 5a b d e + - a b d e + - b d )x +--R 3 2 6 +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 +--R (a b e + 6a b d e + 6a b d e + a b d )x +--R + +--R 1 5 3 15 4 2 15 3 2 2 5 2 3 3 4 +--R (- a e + -- a b d e + -- a b d e + - a b d )x +--R 4 4 2 2 +--R + +--R 5 2 4 2 10 3 2 3 3 3 5 2 5 4 3 2 5 3 +--R (a d e + 5a b d e + -- a b d )x + (- a d e + - a b d )x + a d x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +--S 86 of 1353 +m0:=a0-r0 +--R +--R +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R --- a e - -- a b d e + -- a b d e - - a b d +--R 504 56 14 6 +--R (4) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 86 + +--S 87 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +)clear all + +--S 88 of 1353 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 88 + +--S 89 of 1353 +r0:=1/6*(b*d-a*e)^2*(a+b*x)^6/b^3+2/7*e*(b*d-a*e)*(a+b*x)^7/b^3+_ + 1/8*e^2*(a+b*x)^8/b^3 +--R +--R +--R (2) +--R 1 8 2 8 5 7 2 2 8 7 5 2 6 2 5 7 1 8 2 6 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 8 7 7 3 3 6 +--R + +--R 3 5 2 2 6 7 2 5 5 4 4 2 3 5 5 2 6 2 4 +--R (2a b e + 4a b d e + a b d )x + (- a b e + 5a b d e + - a b d )x +--R 4 2 +--R + +--R 1 5 3 2 10 4 4 10 3 5 2 3 5 3 5 4 4 2 2 5 3 2 +--R (- a b e + -- a b d e + -- a b d )x + (a b d e + - a b d )x + a b d x +--R 3 3 3 2 +--R + +--R 1 8 2 1 7 1 6 2 2 +--R --- a e - -- a b d e + - a b d +--R 168 21 6 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 2 8 5 4 2 2 5 7 5 2 3 2 5 4 1 5 2 6 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 8 7 7 3 3 6 +--R + +--R 3 2 2 2 3 4 2 5 5 4 2 3 2 5 2 3 2 4 +--R (2a b e + 4a b d e + a b d )x + (- a b e + 5a b d e + - a b d )x +--R 4 2 +--R + +--R 1 5 2 10 4 10 3 2 2 3 5 5 4 2 2 5 2 +--R (- a e + -- a b d e + -- a b d )x + (a d e + - a b d )x + a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 90 + +--S 91 of 1353 +m0:=a0-r0 +--R +--R +--R 1 8 2 1 7 1 6 2 2 +--R - --- a e + -- a b d e - - a b d +--R 168 21 6 +--R (4) ---------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 91 + +--S 92 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +)clear all + +--S 93 of 1353 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R Type: Polynomial(Integer) +--E 93 + +--S 94 of 1353 +r0:=1/6*(b*d-a*e)*(a+b*x)^6/b^2+1/7*e*(a+b*x)^7/b^2 +--R +--R +--R (2) +--R 1 7 7 5 6 1 7 6 2 5 6 5 +--R - b e x + (- a b e + - b d)x + (2a b e + a b d)x +--R 7 6 6 +--R + +--R 5 3 4 5 2 5 4 5 4 3 10 3 4 3 1 5 2 5 4 3 2 +--R (- a b e + - a b d)x + (- a b e + -- a b d)x + (- a b e + - a b d)x +--R 2 2 3 3 2 2 +--R + +--R 5 2 1 7 1 6 +--R a b d x - -- a e + - a b d +--R 42 6 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 94 + +--S 95 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 7 5 4 1 5 6 2 3 4 5 5 3 2 5 2 3 4 +--R - b e x + (- a b e + - b d)x + (2a b e + a b d)x + (- a b e + - a b d)x +--R 7 6 6 2 2 +--R + +--R 5 4 10 3 2 3 1 5 5 4 2 5 +--R (- a b e + -- a b d)x + (- a e + - a b d)x + a d x +--R 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 95 + +--S 96 of 1353 +m0:=a0-r0 +--R +--R +--R 1 7 1 6 +--R -- a e - - a b d +--R 42 6 +--R (4) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 96 + +--S 97 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 97 + +)clear all + +--S 98 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Polynomial(Integer) +--E 98 + +--S 99 of 1353 +r0:=1/6*(a+b*x)^6/b +--R +--R +--R 1 6 6 5 5 5 2 4 4 10 3 3 3 5 4 2 2 5 1 6 +--R - b x + a b x + - a b x + -- a b x + - a b x + a b x + - a +--R 6 2 3 2 6 +--R (2) ---------------------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 99 + +--S 100 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 5 6 4 5 5 2 3 4 10 3 2 3 5 4 2 5 +--R (3) - b x + a b x + - a b x + -- a b x + - a b x + a x +--R 6 2 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +--S 101 of 1353 +m0:=a0-r0 +--R +--R +--R 1 6 +--R - a +--R 6 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 101 + +--S 102 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 102 + +)clear all + +--S 103 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 103 + +--S 104 of 1353 +r0:=b*(b*d-a*e)^4*x/e^5-1/2*(b*d-a*e)^3*(a+b*x)^2/e^4+1/3*(b*d-a*e)^2*_ + (a+b*x)^3/e^3-1/4*(b*d-a*e)*(a+b*x)^4/e^2+1/5*(a+b*x)^5/e-(b*d-a*e)^5*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 5 5 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b e x + (75a b e - 15b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b e - 100a b d e + 20b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b e - 300a b d e + 150a b d e - 30b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (300a b e - 600a b d e + 600a b d e - 300a b d e + 60b d e)x + 77a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 +--R - 145a b d e + 110a b d e - 30a b d e +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 5 5 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b e x + (75a b e - 15b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b e - 100a b d e + 20b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b e - 300a b d e + 150a b d e - 30b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (300a b e - 600a b d e + 600a b d e - 300a b d e + 60b d e)x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 105 + +--S 106 of 1353 +m0:=a0-r0 +--R +--R +--R 5 3 4 2 3 2 2 2 3 3 +--R - 77a e + 145a b d e - 110a b d e + 30a b d +--R (4) ---------------------------------------------- +--R 4 +--R 60e +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 107 + +)clear all + +--S 108 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 108 + +--S 109 of 1353 +r0:=-10*b^2*(b*d-a*e)^3*x/e^5+(b*d-a*e)^5/(e^6*(d+e*x))+5*b^3*(b*d-a*e)^2*_ + (d+e*x)^2/e^6-5/3*b^4*(b*d-a*e)*(d+e*x)^3/e^6+1/4*b^5*(d+e*x)^4/e^6+_ + 5*b*(b*d-a*e)^4*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b e x + (20a b e - 5b d e )x + (60a b e - 40a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b e - 180a b d e + 120a b d e - 30b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 5 5 4 4 +--R (120a b d e - 180a b d e + 80a b d e - 5b d e)x - 12a e + 60a b d e +--R + +--R 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 120a b d e + 180a b d e - 160a b d e + 55b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b e x + (20a b e - 5b d e )x + (60a b e - 40a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b e - 180a b d e + 120a b d e - 30b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (120a b d e - 240a b d e + 180a b d e - 48b d e)x - 12a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e - 120a b d e + 120a b d e - 60a b d e + 12b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 110 + +--S 111 of 1353 +m0:=a0-r0 +--R +--R +--R 2 3 2 2 4 3 5 4 +--R - 60a b d e + 100a b d e - 43b d +--R (4) ---------------------------------- +--R 6 +--R 12e +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 112 + +)clear all + +--S 113 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 113 + +--S 114 of 1353 +r0:=10*b^3*(b*d-a*e)^2*x/e^5+1/2*(b*d-a*e)^5/(e^6*(d+e*x)^2)-_ + 5*b*(b*d-a*e)^4/(e^6*(d+e*x))-5/2*b^4*(b*d-a*e)*(d+e*x)^2/e^6+_ + 1/3*b^5*(d+e*x)^3/e^6-10*b^2*(b*d-a*e)^3*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b d e - 360a b d e + 360a b d e - 120b d e)x + 60a b d e +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b e x + (15a b e - 5b d e )x + (60a b e - 60a b d e + 20b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (120a b d e - 150a b d e + 50b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b e + 120a b d e - 120a b d e + 60a b d e - 20b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b d e + 90a b d e - 150a b d e + 120a b d e - 40b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b d e - 360a b d e + 360a b d e - 120b d e)x + 60a b d e +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b e x + (15a b e - 5b d e )x + (60a b e - 60a b d e + 20b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (120a b d e - 165a b d e + 63b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b e + 120a b d e - 120a b d e + 30a b d e + 6b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b d e + 90a b d e - 150a b d e + 105a b d e - 27b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 115 + +--S 116 of 1353 +m0:=a0-r0 +--R +--R +--R 4 2 5 3 +--R - 15a b d e + 13b d +--R (4) -------------------- +--R 6 +--R 6e +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^4 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 of 1353 +r0:=-b^4*(4*b*d-5*a*e)*x/e^5+1/2*b^5*x^2/e^4+1/3*(b*d-a*e)^5/(e^6*(d+e*x)^3)-_ + 5/2*b*(b*d-a*e)^4/(e^6*(d+e*x)^2)+10*b^2*(b*d-a*e)^3/(e^6*(d+e*x))+_ + 10*b^3*(b*d-a*e)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e - 360a b d e + 180b d e )x +--R + +--R 2 3 2 3 4 3 2 5 4 2 3 3 2 4 4 +--R (180a b d e - 360a b d e + 180b d e)x + 60a b d e - 120a b d e +--R + +--R 5 5 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 4 4 5 2 3 3 +--R 3b e x + (30a b e - 15b d e )x + (90a b d e - 63b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 60a b e + 180a b d e - 90a b d e - 9b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 15a b e - 60a b d e + 270a b d e - 270a b d e + 81b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 5a b d e - 20a b d e + 110a b d e - 130a b d e + 47b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e - 360a b d e + 180b d e )x +--R + +--R 2 3 2 3 4 3 2 5 4 2 3 3 2 4 4 +--R (180a b d e - 360a b d e + 180b d e)x + 60a b d e - 120a b d e +--R + +--R 5 5 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 4 4 5 2 3 3 +--R 3b e x + (30a b e - 15b d e )x + (90a b d e - 63b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 60a b e + 180a b d e - 90a b d e - 9b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 15a b e - 60a b d e + 270a b d e - 270a b d e + 81b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 5a b d e - 20a b d e + 110a b d e - 130a b d e + 47b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 120 + +--S 121 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 122 + +)clear all + +--S 123 of 1353 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 123 + +--S 124 of 1353 +r0:=-(b*d-a*e)^7*(d+e*x)^(1+m)/(e^8*(1+m))+7*b*(b*d-a*e)^6*(d+e*x)^(2+m)/_ + (e^8*(2+m))-21*b^2*(b*d-a*e)^5*(d+e*x)^(3+m)/(e^8*(3+m))+35*b^3*_ + (b*d-a*e)^4*(d+e*x)^(4+m)/(e^8*(4+m))-35*b^4*(b*d-a*e)^3*(d+e*x)^(5+m)/_ + (e^8*(5+m))+21*b^5*(b*d-a*e)^2*(d+e*x)^(6+m)/(e^8*(6+m))-7*b^6*(b*d-_ + a*e)*(d+e*x)^(7+m)/(e^8*(7+m))+b^7*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R b m + 28b m + 322b m + 1960b m + 6769b m + 13132b m + 13068b m +--R + +--R 7 +--R 5040b +--R * +--R m + 8 +--R (e x + d) +--R + +--R 6 7 7 6 7 6 6 7 5 +--R (7a b e - 7b d)m + (203a b e - 203b d)m + (2401a b e - 2401b d)m +--R + +--R 6 7 4 6 7 3 +--R (14945a b e - 14945b d)m + (52528a b e - 52528b d)m +--R + +--R 6 7 2 6 7 6 +--R (103292a b e - 103292b d)m + (103824a b e - 103824b d)m + 40320a b e +--R + +--R 7 +--R - 40320b d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 5 2 6 7 2 7 +--R (21a b e - 42a b d e + 21b d )m +--R + +--R 2 5 2 6 7 2 6 +--R (630a b e - 1260a b d e + 630b d )m +--R + +--R 2 5 2 6 7 2 5 +--R (7686a b e - 15372a b d e + 7686b d )m +--R + +--R 2 5 2 6 7 2 4 +--R (49140a b e - 98280a b d e + 49140b d )m +--R + +--R 2 5 2 6 7 2 3 +--R (176589a b e - 353178a b d e + 176589b d )m +--R + +--R 2 5 2 6 7 2 2 +--R (353430a b e - 706860a b d e + 353430b d )m +--R + +--R 2 5 2 6 7 2 2 5 2 +--R (360024a b e - 720048a b d e + 360024b d )m + 141120a b e +--R + +--R 6 7 2 +--R - 282240a b d e + 141120b d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e - 105a b d e + 105a b d e - 35b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 6 +--R (1085a b e - 3255a b d e + 3255a b d e - 1085b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 5 +--R (13685a b e - 41055a b d e + 41055a b d e - 13685b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (90335a b e - 271005a b d e + 271005a b d e - 90335b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (334040a b e - 1002120a b d e + 1002120a b d e - 334040b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 2 +--R (684740a b e - 2054220a b d e + 2054220a b d e - 684740b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R (710640a b e - 2131920a b d e + 2131920a b d e - 710640b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R 282240a b e - 846720a b d e + 846720a b d e - 282240b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (35a b e - 140a b d e + 210a b d e - 140a b d e + 35b d )m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 6 +--R (1120a b e - 4480a b d e + 6720a b d e - 4480a b d e + 1120b d )m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 14630a b e - 58520a b d e + 87780a b d e - 58520a b d e +--R + +--R 7 4 +--R 14630b d +--R * +--R 5 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 100240a b e - 400960a b d e + 601440a b d e - 400960a b d e +--R + +--R 7 4 +--R 100240b d +--R * +--R 4 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 384755a b e - 1539020a b d e + 2308530a b d e - 1539020a b d e +--R + +--R 7 4 +--R 384755b d +--R * +--R 3 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 815920a b e - 3263680a b d e + 4895520a b d e - 3263680a b d e +--R + +--R 7 4 +--R 815920b d +--R * +--R 2 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 870660a b e - 3482640a b d e + 5223960a b d e - 3482640a b d e +--R + +--R 7 4 +--R 870660b d +--R * +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 352800a b e - 1411200a b d e + 2116800a b d e - 1411200a b d e +--R + +--R 7 4 +--R 352800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R 21a b e - 105a b d e + 210a b d e - 210a b d e + 105a b d e +--R + +--R 7 5 +--R - 21b d +--R * +--R 7 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 693a b e - 3465a b d e + 6930a b d e - 6930a b d e +--R + +--R 6 4 7 5 +--R 3465a b d e - 693b d +--R * +--R 6 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 9387a b e - 46935a b d e + 93870a b d e - 93870a b d e +--R + +--R 6 4 7 5 +--R 46935a b d e - 9387b d +--R * +--R 5 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 67095a b e - 335475a b d e + 670950a b d e - 670950a b d e +--R + +--R 6 4 7 5 +--R 335475a b d e - 67095b d +--R * +--R 4 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 270144a b e - 1350720a b d e + 2701440a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 2701440a b d e + 1350720a b d e - 270144b d +--R * +--R 3 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 602532a b e - 3012660a b d e + 6025320a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 6025320a b d e + 3012660a b d e - 602532b d +--R * +--R 2 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 673008a b e - 3365040a b d e + 6730080a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 6730080a b d e + 3365040a b d e - 673008b d +--R * +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 282240a b e - 1411200a b d e + 2822400a b d e - 2822400a b d e +--R + +--R 6 4 7 5 +--R 1411200a b d e - 282240b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 7a b e - 42a b d e + 105a b d e - 140a b d e + 105a b d e +--R + +--R 6 5 7 6 +--R - 42a b d e + 7b d +--R * +--R 7 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 238a b e - 1428a b d e + 3570a b d e - 4760a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 3570a b d e - 1428a b d e + 238b d +--R * +--R 6 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 3346a b e - 20076a b d e + 50190a b d e - 66920a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 50190a b d e - 20076a b d e + 3346b d +--R * +--R 5 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 25060a b e - 150360a b d e + 375900a b d e - 501200a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 375900a b d e - 150360a b d e + 25060b d +--R * +--R 4 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 107023a b e - 642138a b d e + 1605345a b d e - 2140460a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 1605345a b d e - 642138a b d e + 107023b d +--R * +--R 3 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R 256942a b e - 1541652a b d e + 3854130a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R - 5138840a b d e + 3854130a b d e - 1541652a b d e + 256942b d +--R * +--R 2 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R 312984a b e - 1877904a b d e + 4694760a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R - 6259680a b d e + 4694760a b d e - 1877904a b d e + 312984b d +--R * +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 141120a b e - 846720a b d e + 2116800a b d e - 2822400a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 2116800a b d e - 846720a b d e + 141120b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R a e - 7a b d e + 21a b d e - 35a b d e + 35a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 21a b d e + 7a b d e - b d +--R * +--R 7 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 35a e - 245a b d e + 735a b d e - 1225a b d e + 1225a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 735a b d e + 245a b d e - 35b d +--R * +--R 6 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 511a e - 3577a b d e + 10731a b d e - 17885a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 17885a b d e - 10731a b d e + 3577a b d e - 511b d +--R * +--R 5 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 4025a e - 28175a b d e + 84525a b d e - 140875a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 140875a b d e - 84525a b d e + 28175a b d e - 4025b d +--R * +--R 4 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 18424a e - 128968a b d e + 386904a b d e - 644840a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 644840a b d e - 386904a b d e + 128968a b d e - 18424b d +--R * +--R 3 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 48860a e - 342020a b d e + 1026060a b d e - 1710100a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 1710100a b d e - 1026060a b d e + 342020a b d e - 48860b d +--R * +--R 2 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 69264a e - 484848a b d e + 1454544a b d e - 2424240a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 2424240a b d e - 1454544a b d e + 484848a b d e - 69264b d +--R * +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 40320a e - 282240a b d e + 846720a b d e - 1411200a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 1411200a b d e - 846720a b d e + 282240a b d e - 40320b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 8 7 7 8 6 7 8 5 7 8 4 7 8 3 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m +--R + +--R 7 8 2 7 8 7 8 +--R 13132b e m + 13068b e m + 5040b e +--R * +--R 8 +--R x +--R + +--R 6 8 7 7 7 6 8 7 7 6 +--R (7a b e + b d e )m + (203a b e + 21b d e )m +--R + +--R 6 8 7 7 5 6 8 7 7 4 +--R (2401a b e + 175b d e )m + (14945a b e + 735b d e )m +--R + +--R 6 8 7 7 3 6 8 7 7 2 +--R (52528a b e + 1624b d e )m + (103292a b e + 1764b d e )m +--R + +--R 6 8 7 7 6 8 +--R (103824a b e + 720b d e )m + 40320a b e +--R * +--R 7 +--R x +--R + +--R 2 5 8 6 7 7 2 5 8 6 7 7 2 6 6 +--R (21a b e + 7a b d e )m + (630a b e + 161a b d e - 7b d e )m +--R + +--R 2 5 8 6 7 7 2 6 5 +--R (7686a b e + 1435a b d e - 105b d e )m +--R + +--R 2 5 8 6 7 7 2 6 4 +--R (49140a b e + 6335a b d e - 595b d e )m +--R + +--R 2 5 8 6 7 7 2 6 3 +--R (176589a b e + 14518a b d e - 1575b d e )m +--R + +--R 2 5 8 6 7 7 2 6 2 +--R (353430a b e + 16184a b d e - 1918b d e )m +--R + +--R 2 5 8 6 7 7 2 6 2 5 8 +--R (360024a b e + 6720a b d e - 840b d e )m + 141120a b e +--R * +--R 6 +--R x +--R + +--R 3 4 8 2 5 7 7 +--R (35a b e + 21a b d e )m +--R + +--R 3 4 8 2 5 7 6 2 6 6 +--R (1085a b e + 525a b d e - 42a b d e )m +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 5 +--R (13685a b e + 5061a b d e - 756a b d e + 42b d e )m +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 4 +--R (90335a b e + 23835a b d e - 4830a b d e + 420b d e )m +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 3 +--R 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282240a b d e + 141120a b d e - 40320a b d e + 5040b d e +--R * +--R m +--R + +--R 7 8 +--R 40320a e +--R * +--R x +--R + +--R 7 7 7 7 7 6 2 6 6 +--R a d e m + (35a d e - 7a b d e )m +--R + +--R 7 7 6 2 6 5 2 3 5 5 +--R (511a d e - 231a b d e + 42a b d e )m +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 4 +--R (4025a d e - 3115a b d e + 1260a b d e - 210a b d e )m +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 18424a d e - 21945a b d e + 14910a b d e - 5460a b d e +--R + +--R 3 4 5 3 +--R 840a b d e +--R * +--R 3 +--R m +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 48860a d e - 85078a b d e + 86940a b d e - 52710a b d e +--R + +--R 3 4 5 3 2 5 6 2 +--R 17640a b d e - 2520a b d e +--R * +--R 2 +--R m +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 69264a d e - 171864a b d e + 249648a b d e - 223860a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 +--R 122640a b d e - 37800a b d e + 5040a b d e +--R * +--R m +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 40320a d e - 141120a b d e + 282240a b d e - 352800a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 +--R 282240a b d e - 141120a b d e + 40320a b d e - 5040b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R - b m - 28b m - 322b m - 1960b m - 6769b m - 13132b m +--R + +--R 7 7 +--R - 13068b m - 5040b +--R * +--R m + 8 +--R (e x + d) +--R + +--R 6 7 7 6 7 6 +--R (- 7a b e + 7b d)m + (- 203a b e + 203b d)m +--R + +--R 6 7 5 6 7 4 +--R (- 2401a b e + 2401b d)m + (- 14945a b e + 14945b d)m +--R + +--R 6 7 3 6 7 2 +--R (- 52528a b e + 52528b d)m + (- 103292a b e + 103292b d)m +--R + +--R 6 7 6 7 +--R (- 103824a b e + 103824b d)m - 40320a b e + 40320b d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 5 2 6 7 2 7 +--R (- 21a b e + 42a b d e - 21b d )m +--R + +--R 2 5 2 6 7 2 6 +--R (- 630a b e + 1260a b d e - 630b d )m +--R + +--R 2 5 2 6 7 2 5 +--R (- 7686a b e + 15372a b d e - 7686b d )m +--R + +--R 2 5 2 6 7 2 4 +--R (- 49140a b e + 98280a b d e - 49140b d )m +--R + +--R 2 5 2 6 7 2 3 +--R (- 176589a b e + 353178a b d e - 176589b d )m +--R + +--R 2 5 2 6 7 2 2 +--R (- 353430a b e + 706860a b d e - 353430b d )m +--R + +--R 2 5 2 6 7 2 2 5 2 +--R (- 360024a b e + 720048a b d e - 360024b d )m - 141120a b e +--R + +--R 6 7 2 +--R 282240a b d e - 141120b d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (- 35a b e + 105a b d e - 105a b d e + 35b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 6 +--R (- 1085a b e + 3255a b d e - 3255a b d e + 1085b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 5 +--R (- 13685a b e + 41055a b d e - 41055a b d e + 13685b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 90335a b e + 271005a b d e - 271005a b d e + 90335b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (- 334040a b e + 1002120a b d e - 1002120a b d e + 334040b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 2 +--R (- 684740a b e + 2054220a b d e - 2054220a b d e + 684740b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R (- 710640a b e + 2131920a b d e - 2131920a b d e + 710640b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R - 282240a b e + 846720a b d e - 846720a b d e + 282240b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (- 35a b e + 140a b d e - 210a b d e + 140a b d e - 35b d )m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R - 1120a b e + 4480a b d e - 6720a b d e + 4480a b d e +--R + +--R 7 4 +--R - 1120b d +--R * +--R 6 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R - 14630a b e + 58520a b d e - 87780a b d e + 58520a b d e +--R + +--R 7 4 +--R - 14630b d +--R * +--R 5 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R - 100240a b e + 400960a b d e - 601440a b d e + 400960a b d e +--R + +--R 7 4 +--R - 100240b d +--R * +--R 4 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 +--R - 384755a b e + 1539020a b d e - 2308530a b d e +--R + +--R 6 3 7 4 +--R 1539020a b d e - 384755b d +--R * +--R 3 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 +--R - 815920a b e + 3263680a b d e - 4895520a b d e +--R + +--R 6 3 7 4 +--R 3263680a b d e - 815920b d +--R * +--R 2 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 +--R - 870660a b e + 3482640a b d e - 5223960a b d e +--R + +--R 6 3 7 4 +--R 3482640a b d e - 870660b d +--R * +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R - 352800a b e + 1411200a b d e - 2116800a b d e + 1411200a b d e +--R + +--R 7 4 +--R - 352800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R - 21a b e + 105a b d e - 210a b d e + 210a b d e - 105a b d e +--R + +--R 7 5 +--R 21b d +--R * +--R 7 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R - 693a b e + 3465a b d e - 6930a b d e + 6930a b d e +--R + +--R 6 4 7 5 +--R - 3465a b d e + 693b d +--R * +--R 6 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R - 9387a b e + 46935a b d e - 93870a b d e + 93870a b d e +--R + +--R 6 4 7 5 +--R - 46935a b d e + 9387b d +--R * +--R 5 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R - 67095a b e + 335475a b d e - 670950a b d e + 670950a b d e +--R + +--R 6 4 7 5 +--R - 335475a b d e + 67095b d +--R * +--R 4 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R - 270144a b e + 1350720a b d e - 2701440a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R 2701440a b d e - 1350720a b d e + 270144b d +--R * +--R 3 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R - 602532a b e + 3012660a b d e - 6025320a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R 6025320a b d e - 3012660a b d e + 602532b d +--R * +--R 2 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R - 673008a b e + 3365040a b d e - 6730080a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R 6730080a b d e - 3365040a b d e + 673008b d +--R * +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R - 282240a b e + 1411200a b d e - 2822400a b d e + 2822400a b d e +--R + +--R 6 4 7 5 +--R - 1411200a b d e + 282240b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 7a b e + 42a b d e - 105a b d e + 140a b d e - 105a b d e +--R + +--R 6 5 7 6 +--R 42a b d e - 7b d +--R * +--R 7 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 238a b e + 1428a b d e - 3570a b d e + 4760a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 3570a b d e + 1428a b d e - 238b d +--R * +--R 6 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 3346a b e + 20076a b d e - 50190a b d e + 66920a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 50190a b d e + 20076a b d e - 3346b d +--R * +--R 5 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 25060a b e + 150360a b d e - 375900a b d e + 501200a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 375900a b d e + 150360a b d e - 25060b d +--R * +--R 4 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R - 107023a b e + 642138a b d e - 1605345a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R 2140460a b d e - 1605345a b d e + 642138a b d e - 107023b d +--R * +--R 3 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R - 256942a b e + 1541652a b d e - 3854130a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R 5138840a b d e - 3854130a b d e + 1541652a b d e - 256942b d +--R * +--R 2 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R - 312984a b e + 1877904a b d e - 4694760a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R 6259680a b d e - 4694760a b d e + 1877904a b d e - 312984b d +--R * +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 141120a b e + 846720a b d e - 2116800a b d e + 2822400a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 2116800a b d e + 846720a b d e - 141120b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - a e + 7a b d e - 21a b d e + 35a b d e - 35a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 21a b d e - 7a b d e + b d +--R * +--R 7 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 35a e + 245a b d e - 735a b d e + 1225a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 1225a b d e + 735a b d e - 245a b d e + 35b d +--R * +--R 6 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 511a e + 3577a b d e - 10731a b d e + 17885a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 17885a b d e + 10731a b d e - 3577a b d e + 511b d +--R * +--R 5 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 4025a e + 28175a b d e - 84525a b d e + 140875a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 140875a b d e + 84525a b d e - 28175a b d e + 4025b d +--R * +--R 4 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 18424a e + 128968a b d e - 386904a b d e + 644840a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 644840a b d e + 386904a b d e - 128968a b d e + 18424b d +--R * +--R 3 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 48860a e + 342020a b d e - 1026060a b d e + 1710100a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 1710100a b d e + 1026060a b d e - 342020a b d e + 48860b d +--R * +--R 2 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 69264a e + 484848a b d e - 1454544a b d e + 2424240a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 2424240a b d e + 1454544a b d e - 484848a b d e + 69264b d +--R * +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 40320a e + 282240a b d e - 846720a b d e + 1411200a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 1411200a b d e + 846720a b d e - 282240a b d e + 40320b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 127 + +)clear all + +--S 128 of 1353 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 6 13 6 6 7 5 12 2 5 6 6 5 7 2 4 11 +--R b e x + (7a b e + 6b d e )x + (21a b e + 42a b d e + 15b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 10 +--R (35a b e + 126a b d e + 105a b d e + 20b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 9 +--R (35a b e + 210a b d e + 315a b d e + 140a b d e + 15b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 21a b e + 210a b d e + 525a b d e + 420a b d e + 105a b d e +--R + +--R 7 5 +--R 6b d e +--R * +--R 8 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 7a b e + 126a b d e + 525a b d e + 700a b d e + 315a b d e +--R + +--R 6 5 7 6 +--R 42a b d e + b d +--R * +--R 7 +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R a e + 42a b d e + 315a b d e + 700a b d e + 525a b d e +--R + +--R 2 5 5 6 6 +--R 126a b d e + 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 +--R 6a d e + 105a b d e + 420a b d e + 525a b d e + 210a b d e +--R + +--R 2 5 6 +--R 21a b d +--R * +--R 5 +--R x +--R + +--R 7 2 4 6 3 3 5 2 4 2 4 3 5 3 4 6 4 +--R (15a d e + 140a b d e + 315a b d e + 210a b d e + 35a b d )x +--R + +--R 7 3 3 6 4 2 5 2 5 4 3 6 3 +--R (20a d e + 105a b d e + 126a b d e + 35a b d )x +--R + +--R 7 4 2 6 5 5 2 6 2 7 5 6 6 7 6 +--R (15a d e + 42a b d e + 21a b d )x + (6a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 128 + +--S 129 of 1353 +r0:=1/8*(b*d-a*e)^6*(a+b*x)^8/b^7+2/3*e*(b*d-a*e)^5*(a+b*x)^9/b^7+_ + 3/2*e^2*(b*d-a*e)^4*(a+b*x)^10/b^7+20/11*e^3*(b*d-a*e)^3*(a+b*x)^11/b^7+_ + 5/4*e^4*(b*d-a*e)^2*(a+b*x)^12/b^7+6/13*e^5*(b*d-a*e)*(a+b*x)^13/b^7+_ + 1/14*e^6*(a+b*x)^14/b^7 +--R +--R +--R (2) +--R 1 14 6 14 7 13 6 6 14 5 13 +--R -- b e x + (-- a b e + -- b d e )x +--R 14 13 13 +--R + +--R 7 2 12 6 7 13 5 5 14 2 4 12 +--R (- a b e + - a b d e + - b d e )x +--R 4 2 4 +--R + +--R 35 3 11 6 126 2 12 5 105 13 2 4 20 14 3 3 11 +--R (-- a b e + --- a b d e + --- a b d e + -- b d e )x +--R 11 11 11 11 +--R + +--R 7 4 10 6 3 11 5 63 2 12 2 4 13 3 3 3 14 4 2 10 +--R (- a b e + 21a b d e + -- a b d e + 14a b d e + - b d e )x +--R 2 2 2 +--R + +--R 7 5 9 6 70 4 10 5 175 3 11 2 4 140 2 12 3 3 +--R - a b e + -- a b d e + --- a b d e + --- a b d e +--R 3 3 3 3 +--R + +--R 35 13 4 2 2 14 5 +--R -- a b d e + - b d e +--R 3 3 +--R * +--R 9 +--R x +--R + +--R 7 6 8 6 63 5 9 5 525 4 10 2 4 175 3 11 3 3 +--R - a b e + -- a b d e + --- a b d e + --- a b d e +--R 8 4 8 2 +--R + +--R 315 2 12 4 2 21 13 5 1 14 6 +--R --- a b d e + -- a b d e + - b d +--R 8 4 8 +--R * +--R 8 +--R x +--R + +--R 1 7 7 6 6 8 5 5 9 2 4 4 10 3 3 3 11 4 2 +--R - a b e + 6a b d e + 45a b d e + 100a b d e + 75a b d e +--R 7 +--R + +--R 2 12 5 13 6 +--R 18a b d e + a b d +--R * +--R 7 +--R x +--R + +--R 7 7 5 35 6 8 2 4 5 9 3 3 175 4 10 4 2 3 11 5 +--R a b d e + -- a b d e + 70a b d e + --- a b d e + 35a b d e +--R 2 2 +--R + +--R 7 2 12 6 +--R - a b d +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 7 2 4 6 8 3 3 5 9 4 2 4 10 5 3 11 6 5 +--R (3a b d e + 28a b d e + 63a b d e + 42a b d e + 7a b d )x +--R + +--R 7 7 3 3 105 6 8 4 2 63 5 9 5 35 4 10 6 4 +--R (5a b d e + --- a b d e + -- a b d e + -- a b d )x +--R 4 2 4 +--R + +--R 7 7 4 2 6 8 5 5 9 6 3 7 7 5 7 6 8 6 2 7 7 6 +--R (5a b d e + 14a b d e + 7a b d )x + (3a b d e + - a b d )x + a b d x +--R 2 +--R + +--R 1 14 6 1 13 5 1 12 2 2 4 1 11 3 3 3 +--R ----- a e - ---- a b d e + --- a b d e - -- a b d e +--R 24024 1716 264 66 +--R + +--R 1 10 4 4 2 1 9 5 5 1 8 6 6 +--R -- a b d e - -- a b d e + - a b d +--R 24 12 8 +--R / +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 129 + +--S 130 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 6 14 7 6 6 6 7 5 13 +--R -- b e x + (-- a b e + -- b d e )x +--R 14 13 13 +--R + +--R 7 2 5 6 7 6 5 5 7 2 4 12 +--R (- a b e + - a b d e + - b d e )x +--R 4 2 4 +--R + +--R 35 3 4 6 126 2 5 5 105 6 2 4 20 7 3 3 11 +--R (-- a b e + --- a b d e + --- a b d e + -- b d e )x +--R 11 11 11 11 +--R + +--R 7 4 3 6 3 4 5 63 2 5 2 4 6 3 3 3 7 4 2 10 +--R (- a b e + 21a b d e + -- a b d e + 14a b d e + - b d e )x +--R 2 2 2 +--R + +--R 7 5 2 6 70 4 3 5 175 3 4 2 4 140 2 5 3 3 35 6 4 2 +--R - a b e + -- a b d e + --- a b d e + --- a b d e + -- a b d e +--R 3 3 3 3 3 +--R + +--R 2 7 5 +--R - b d e +--R 3 +--R * +--R 9 +--R x +--R + +--R 7 6 6 63 5 2 5 525 4 3 2 4 175 3 4 3 3 315 2 5 4 2 +--R - a b e + -- a b d e + --- a b d e + --- a b d e + --- a b d e +--R 8 4 8 2 8 +--R + +--R 21 6 5 1 7 6 +--R -- a b d e + - b d +--R 4 8 +--R * +--R 8 +--R x +--R + +--R 1 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R - a e + 6a b d e + 45a b d e + 100a b d e + 75a b d e + 18a b d e +--R 7 +--R + +--R 6 6 +--R a b d +--R * +--R 7 +--R x +--R + +--R 7 5 35 6 2 4 5 2 3 3 175 4 3 4 2 3 4 5 7 2 5 6 6 +--R (a d e + -- a b d e + 70a b d e + --- a b d e + 35a b d e + - a b d )x +--R 2 2 2 +--R + +--R 7 2 4 6 3 3 5 2 4 2 4 3 5 3 4 6 5 +--R (3a d e + 28a b d e + 63a b d e + 42a b d e + 7a b d )x +--R + +--R 7 3 3 105 6 4 2 63 5 2 5 35 4 3 6 4 +--R (5a d e + --- a b d e + -- a b d e + -- a b d )x +--R 4 2 4 +--R + +--R 7 4 2 6 5 5 2 6 3 7 5 7 6 6 2 7 6 +--R (5a d e + 14a b d e + 7a b d )x + (3a d e + - a b d )x + a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +--S 131 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 14 6 1 13 5 1 12 2 2 4 1 11 3 3 3 +--R - ----- a e + ---- a b d e - --- a b d e + -- a b d e +--R 24024 1716 264 66 +--R + +--R 1 10 4 4 2 1 9 5 5 1 8 6 6 +--R - -- a b d e + -- a b d e - - a b d +--R 24 12 8 +--R / +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 131 + +--S 132 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 132 + +)clear all + +--S 133 of 1353 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 5 12 6 5 7 4 11 2 5 5 6 4 7 2 3 10 +--R b e x + (7a b e + 5b d e )x + (21a b e + 35a b d e + 10b d e )x +--R + +--R 3 4 5 2 5 4 6 2 3 7 3 2 9 +--R (35a b e + 105a b d e + 70a b d e + 10b d e )x +--R + +--R 4 3 5 3 4 4 2 5 2 3 6 3 2 7 4 8 +--R (35a b e + 175a b d e + 210a b d e + 70a b d e + 5b d e)x +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 7 5 7 +--R (21a b e + 175a b d e + 350a b d e + 210a b d e + 35a b d e + b d )x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 7a b e + 105a b d e + 350a b d e + 350a b d e + 105a b d e +--R + +--R 6 5 +--R 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 5 +--R (a e + 35a b d e + 210a b d e + 350a b d e + 175a b d e + 21a b d )x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 4 +--R (5a d e + 70a b d e + 210a b d e + 175a b d e + 35a b d )x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 3 +--R (10a d e + 70a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 2 6 4 5 2 5 2 7 4 6 5 7 5 +--R (10a d e + 35a b d e + 21a b d )x + (5a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 133 + +--S 134 of 1353 +r0:=1/8*(b*d-a*e)^5*(a+b*x)^8/b^6+5/9*e*(b*d-a*e)^4*(a+b*x)^9/b^6+e^2*_ + (b*d-a*e)^3*(a+b*x)^10/b^6+10/11*e^3*(b*d-a*e)^2*(a+b*x)^11/b^6+_ + 5/12*e^4*(b*d-a*e)*(a+b*x)^12/b^6+1/13*e^5*(a+b*x)^13/b^6 +--R +--R +--R (2) +--R 1 13 5 13 7 12 5 5 13 4 12 +--R -- b e x + (-- a b e + -- b d e )x +--R 13 12 12 +--R + +--R 21 2 11 5 35 12 4 10 13 2 3 11 +--R (-- a b e + -- a b d e + -- b d e )x +--R 11 11 11 +--R + +--R 7 3 10 5 21 2 11 4 12 2 3 13 3 2 10 +--R (- a b e + -- a b d e + 7a b d e + b d e )x +--R 2 2 +--R + +--R 35 4 9 5 175 3 10 4 70 2 11 2 3 70 12 3 2 5 13 4 9 +--R (-- a b e + --- a b d e + -- a b d e + -- a b d e + - b d e)x +--R 9 9 3 9 9 +--R + +--R 21 5 8 5 175 4 9 4 175 3 10 2 3 105 2 11 3 2 +--R -- a b e + --- a b d e + --- a b d e + --- a b d e +--R 8 8 4 4 +--R + +--R 35 12 4 1 13 5 +--R -- a b d e + - b d +--R 8 8 +--R * +--R 8 +--R x +--R + +--R 6 7 5 5 8 4 4 9 2 3 3 10 3 2 2 11 4 12 5 7 +--R (a b e + 15a b d e + 50a b d e + 50a b d e + 15a b d e + a b d )x +--R + +--R 1 7 6 5 35 6 7 4 5 8 2 3 175 4 9 3 2 175 3 10 4 +--R - a b e + -- a b d e + 35a b d e + --- a b d e + --- a b d e +--R 6 6 3 6 +--R + +--R 7 2 11 5 +--R - a b d +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 6 4 6 7 2 3 5 8 3 2 4 9 4 3 10 5 5 +--R (a b d e + 14a b d e + 42a b d e + 35a b d e + 7a b d )x +--R + +--R 5 7 6 2 3 35 6 7 3 2 105 5 8 4 35 4 9 5 4 +--R (- a b d e + -- a b d e + --- a b d e + -- a b d )x +--R 2 2 4 4 +--R + +--R 10 7 6 3 2 35 6 7 4 5 8 5 3 5 7 6 4 7 6 7 5 2 +--R (-- a b d e + -- a b d e + 7a b d )x + (- a b d e + - a b d )x +--R 3 3 2 2 +--R + +--R 7 6 5 1 13 5 1 12 4 1 11 2 2 3 1 10 3 3 2 +--R a b d x - ----- a e + --- a b d e - --- a b d e + -- a b d e +--R 10296 792 132 36 +--R + +--R 5 9 4 4 1 8 5 5 +--R - -- a b d e + - a b d +--R 72 8 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 134 + +--S 135 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 5 13 7 6 5 5 7 4 12 +--R -- b e x + (-- a b e + -- b d e )x +--R 13 12 12 +--R + +--R 21 2 5 5 35 6 4 10 7 2 3 11 +--R (-- a b e + -- a b d e + -- b d e )x +--R 11 11 11 +--R + +--R 7 3 4 5 21 2 5 4 6 2 3 7 3 2 10 +--R (- a b e + -- a b d e + 7a b d e + b d e )x +--R 2 2 +--R + +--R 35 4 3 5 175 3 4 4 70 2 5 2 3 70 6 3 2 5 7 4 9 +--R (-- a b e + --- a b d e + -- a b d e + -- a b d e + - b d e)x +--R 9 9 3 9 9 +--R + +--R 21 5 2 5 175 4 3 4 175 3 4 2 3 105 2 5 3 2 35 6 4 +--R -- a b e + --- a b d e + --- a b d e + --- a b d e + -- a b d e +--R 8 8 4 4 8 +--R + +--R 1 7 5 +--R - b d +--R 8 +--R * +--R 8 +--R x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 6 5 7 +--R (a b e + 15a b d e + 50a b d e + 50a b d e + 15a b d e + a b d )x +--R + +--R 1 7 5 35 6 4 5 2 2 3 175 4 3 3 2 175 3 4 4 +--R - a e + -- a b d e + 35a b d e + --- a b d e + --- a b d e +--R 6 6 3 6 +--R + +--R 7 2 5 5 +--R - a b d +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 5 +--R (a d e + 14a b d e + 42a b d e + 35a b d e + 7a b d )x +--R + +--R 5 7 2 3 35 6 3 2 105 5 2 4 35 4 3 5 4 +--R (- a d e + -- a b d e + --- a b d e + -- a b d )x +--R 2 2 4 4 +--R + +--R 10 7 3 2 35 6 4 5 2 5 3 5 7 4 7 6 5 2 7 5 +--R (-- a d e + -- a b d e + 7a b d )x + (- a d e + - a b d )x + a d x +--R 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +--S 136 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 13 5 1 12 4 1 11 2 2 3 1 10 3 3 2 5 9 4 4 +--R ----- a e - --- a b d e + --- a b d e - -- a b d e + -- a b d e +--R 10296 792 132 36 72 +--R + +--R 1 8 5 5 +--R - - a b d +--R 8 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 136 + +--S 137 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 137 + +)clear all + +--S 138 of 1353 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 4 11 6 4 7 3 10 2 5 4 6 3 7 2 2 9 +--R b e x + (7a b e + 4b d e )x + (21a b e + 28a b d e + 6b d e )x +--R + +--R 3 4 4 2 5 3 6 2 2 7 3 8 +--R (35a b e + 84a b d e + 42a b d e + 4b d e)x +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (35a b e + 140a b d e + 126a b d e + 28a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 6 +--R (21a b e + 140a b d e + 210a b d e + 84a b d e + 7a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 5 +--R (7a b e + 84a b d e + 210a b d e + 140a b d e + 21a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 4 +--R (a e + 28a b d e + 126a b d e + 140a b d e + 35a b d )x +--R + +--R 7 3 6 2 2 5 2 3 4 3 4 3 +--R (4a d e + 42a b d e + 84a b d e + 35a b d )x +--R + +--R 7 2 2 6 3 5 2 4 2 7 3 6 4 7 4 +--R (6a d e + 28a b d e + 21a b d )x + (4a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 138 + +--S 139 of 1353 +r0:=1/8*(b*d-a*e)^4*(a+b*x)^8/b^5+4/9*e*(b*d-a*e)^3*(a+b*x)^9/b^5+3/5*e^2*_ + (b*d-a*e)^2*(a+b*x)^10/b^5+4/11*e^3*(b*d-a*e)*(a+b*x)^11/b^5+1/12*e^4*_ + (a+b*x)^12/b^5 +--R +--R +--R (2) +--R 1 12 4 12 7 11 4 4 12 3 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 21 2 10 4 14 11 3 3 12 2 2 10 +--R (-- a b e + -- a b d e + - b d e )x +--R 10 5 5 +--R + +--R 35 3 9 4 28 2 10 3 14 11 2 2 4 12 3 9 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 9 3 3 9 +--R + +--R 35 4 8 4 35 3 9 3 63 2 10 2 2 7 11 3 1 12 4 8 +--R (-- a b e + -- a b d e + -- a b d e + - a b d e + - b d )x +--R 8 2 4 2 8 +--R + +--R 5 7 4 4 8 3 3 9 2 2 2 10 3 11 4 7 +--R (3a b e + 20a b d e + 30a b d e + 12a b d e + a b d )x +--R + +--R 7 6 6 4 5 7 3 4 8 2 2 70 3 9 3 7 2 10 4 6 +--R (- a b e + 14a b d e + 35a b d e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 1 7 5 4 28 6 6 3 126 5 7 2 2 4 8 3 3 9 4 5 +--R (- a b e + -- a b d e + --- a b d e + 28a b d e + 7a b d )x +--R 5 5 5 +--R + +--R 7 5 3 21 6 6 2 2 5 7 3 35 4 8 4 4 +--R (a b d e + -- a b d e + 21a b d e + -- a b d )x +--R 2 4 +--R + +--R 7 5 2 2 28 6 6 3 5 7 4 3 7 5 3 7 6 6 4 2 7 5 4 +--R (2a b d e + -- a b d e + 7a b d )x + (2a b d e + - a b d )x + a b d x +--R 3 2 +--R + +--R 1 12 4 1 11 3 1 10 2 2 2 1 9 3 3 1 8 4 4 +--R ---- a e - --- a b d e + -- a b d e - -- a b d e + - a b d +--R 3960 330 60 18 8 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 139 + +--S 140 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 4 12 7 6 4 4 7 3 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 21 2 5 4 14 6 3 3 7 2 2 10 +--R (-- a b e + -- a b d e + - b d e )x +--R 10 5 5 +--R + +--R 35 3 4 4 28 2 5 3 14 6 2 2 4 7 3 9 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 9 3 3 9 +--R + +--R 35 4 3 4 35 3 4 3 63 2 5 2 2 7 6 3 1 7 4 8 +--R (-- a b e + -- a b d e + -- a b d e + - a b d e + - b d )x +--R 8 2 4 2 8 +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 7 +--R (3a b e + 20a b d e + 30a b d e + 12a b d e + a b d )x +--R + +--R 7 6 4 5 2 3 4 3 2 2 70 3 4 3 7 2 5 4 6 +--R (- a b e + 14a b d e + 35a b d e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 1 7 4 28 6 3 126 5 2 2 2 4 3 3 3 4 4 5 +--R (- a e + -- a b d e + --- a b d e + 28a b d e + 7a b d )x +--R 5 5 5 +--R + +--R 7 3 21 6 2 2 5 2 3 35 4 3 4 4 +--R (a d e + -- a b d e + 21a b d e + -- a b d )x +--R 2 4 +--R + +--R 7 2 2 28 6 3 5 2 4 3 7 3 7 6 4 2 7 4 +--R (2a d e + -- a b d e + 7a b d )x + (2a d e + - a b d )x + a d x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +--S 141 of 1353 +m0:=a0-r0 +--R +--R +--R 1 12 4 1 11 3 1 10 2 2 2 1 9 3 3 1 8 4 4 +--R - ---- a e + --- a b d e - -- a b d e + -- a b d e - - a b d +--R 3960 330 60 18 8 +--R (4) ------------------------------------------------------------------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 141 + +--S 142 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 142 + +)clear all + +--S 143 of 1353 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 3 10 6 3 7 2 9 2 5 3 6 2 7 2 8 +--R b e x + (7a b e + 3b d e )x + (21a b e + 21a b d e + 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e + 63a b d e + 21a b d e + b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (35a b e + 105a b d e + 63a b d e + 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (21a b e + 105a b d e + 105a b d e + 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (7a b e + 63a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (a e + 21a b d e + 63a b d e + 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (3a d e + 21a b d e + 21a b d )x + (3a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 143 + +--S 144 of 1353 +r0:=1/8*(b*d-a*e)^3*(a+b*x)^8/b^4+1/3*e*(b*d-a*e)^2*(a+b*x)^9/b^4+3/10*e^2*_ + (b*d-a*e)*(a+b*x)^10/b^4+1/11*e^3*(a+b*x)^11/b^4 +--R +--R +--R (2) +--R 1 11 3 11 7 10 3 3 11 2 10 +--R -- b e x + (-- a b e + -- b d e )x +--R 11 10 10 +--R + +--R 7 2 9 3 7 10 2 1 11 2 9 +--R (- a b e + - a b d e + - b d e)x +--R 3 3 3 +--R + +--R 35 3 8 3 63 2 9 2 21 10 2 1 11 3 8 +--R (-- a b e + -- a b d e + -- a b d e + - b d )x +--R 8 8 8 8 +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 7 +--R (5a b e + 15a b d e + 9a b d e + a b d )x +--R + +--R 7 5 6 3 35 4 7 2 35 3 8 2 7 2 9 3 6 +--R (- a b e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 7 6 5 3 63 5 6 2 4 7 2 3 8 3 5 +--R (- a b e + -- a b d e + 21a b d e + 7a b d )x +--R 5 5 +--R + +--R 1 7 4 3 21 6 5 2 63 5 6 2 35 4 7 3 4 +--R (- a b e + -- a b d e + -- a b d e + -- a b d )x +--R 4 4 4 4 +--R + +--R 7 4 2 6 5 2 5 6 3 3 3 7 4 2 7 6 5 3 2 7 4 3 +--R (a b d e + 7a b d e + 7a b d )x + (- a b d e + - a b d )x + a b d x +--R 2 2 +--R + +--R 1 11 3 1 10 2 1 9 2 2 1 8 3 3 +--R - ---- a e + --- a b d e - -- a b d e + - a b d +--R 1320 120 24 8 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 144 + +--S 145 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 3 11 7 6 3 3 7 2 10 +--R -- b e x + (-- a b e + -- b d e )x +--R 11 10 10 +--R + +--R 7 2 5 3 7 6 2 1 7 2 9 +--R (- a b e + - a b d e + - b d e)x +--R 3 3 3 +--R + +--R 35 3 4 3 63 2 5 2 21 6 2 1 7 3 8 +--R (-- a b e + -- a b d e + -- a b d e + - b d )x +--R 8 8 8 8 +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 7 +--R (5a b e + 15a b d e + 9a b d e + a b d )x +--R + +--R 7 5 2 3 35 4 3 2 35 3 4 2 7 2 5 3 6 +--R (- a b e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 7 6 3 63 5 2 2 4 3 2 3 4 3 5 +--R (- a b e + -- a b d e + 21a b d e + 7a b d )x +--R 5 5 +--R + +--R 1 7 3 21 6 2 63 5 2 2 35 4 3 3 4 +--R (- a e + -- a b d e + -- a b d e + -- a b d )x +--R 4 4 4 4 +--R + +--R 7 2 6 2 5 2 3 3 3 7 2 7 6 3 2 7 3 +--R (a d e + 7a b d e + 7a b d )x + (- a d e + - a b d )x + a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 145 + +--S 146 of 1353 +m0:=a0-r0 +--R +--R +--R 1 11 3 1 10 2 1 9 2 2 1 8 3 3 +--R ---- a e - --- a b d e + -- a b d e - - a b d +--R 1320 120 24 8 +--R (4) -------------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 146 + +--S 147 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 147 + +)clear all + +--S 148 of 1353 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R b e x + (7a b e + 2b d e)x + (21a b e + 14a b d e + b d )x +--R + +--R 3 4 2 2 5 6 2 6 4 3 2 3 4 2 5 2 5 +--R (35a b e + 42a b d e + 7a b d )x + (35a b e + 70a b d e + 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 6 2 5 2 4 3 2 3 +--R (21a b e + 70a b d e + 35a b d )x + (7a b e + 42a b d e + 35a b d )x +--R + +--R 7 2 6 5 2 2 2 7 6 2 7 2 +--R (a e + 14a b d e + 21a b d )x + (2a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 148 + +--S 149 of 1353 +r0:=1/8*(b*d-a*e)^2*(a+b*x)^8/b^3+2/9*e*(b*d-a*e)*(a+b*x)^9/b^3+1/10*e^2*_ + (a+b*x)^10/b^3 +--R +--R +--R (2) +--R 1 10 2 10 7 9 2 2 10 9 +--R -- b e x + (- a b e + - b d e)x +--R 10 9 9 +--R + +--R 21 2 8 2 7 9 1 10 2 8 3 7 2 2 8 9 2 7 +--R (-- a b e + - a b d e + - b d )x + (5a b e + 6a b d e + a b d )x +--R 8 4 8 +--R + +--R 35 4 6 2 35 3 7 7 2 8 2 6 +--R (-- a b e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 21 5 5 2 4 6 3 7 2 5 +--R (-- a b e + 14a b d e + 7a b d )x +--R 5 +--R + +--R 7 6 4 2 21 5 5 35 4 6 2 4 +--R (- a b e + -- a b d e + -- a b d )x +--R 4 2 4 +--R + +--R 1 7 3 2 14 6 4 5 5 2 3 7 3 7 6 4 2 2 7 3 2 +--R (- a b e + -- a b d e + 7a b d )x + (a b d e + - a b d )x + a b d x +--R 3 3 2 +--R + +--R 1 10 2 1 9 1 8 2 2 +--R --- a e - -- a b d e + - a b d +--R 360 36 8 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 2 10 7 6 2 2 7 9 21 2 5 2 7 6 1 7 2 8 +--R -- b e x + (- a b e + - b d e)x + (-- a b e + - a b d e + - b d )x +--R 10 9 9 8 4 8 +--R + +--R 3 4 2 2 5 6 2 7 35 4 3 2 35 3 4 7 2 5 2 6 +--R (5a b e + 6a b d e + a b d )x + (-- a b e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 21 5 2 2 4 3 3 4 2 5 7 6 2 21 5 2 35 4 3 2 4 +--R (-- a b e + 14a b d e + 7a b d )x + (- a b e + -- a b d e + -- a b d )x +--R 5 4 2 4 +--R + +--R 1 7 2 14 6 5 2 2 3 7 7 6 2 2 7 2 +--R (- a e + -- a b d e + 7a b d )x + (a d e + - a b d )x + a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 150 + +--S 151 of 1353 +m0:=a0-r0 +--R +--R +--R 1 10 2 1 9 1 8 2 2 +--R - --- a e + -- a b d e - - a b d +--R 360 36 8 +--R (4) ----------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 151 + +--S 152 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 152 + +)clear all + +--S 153 of 1353 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 8 6 7 7 2 5 6 6 3 4 2 5 5 +--R b e x + (7a b e + b d)x + (21a b e + 7a b d)x + (35a b e + 21a b d)x +--R + +--R 4 3 3 4 4 5 2 4 3 3 6 5 2 2 +--R (35a b e + 35a b d)x + (21a b e + 35a b d)x + (7a b e + 21a b d)x +--R + +--R 7 6 7 +--R (a e + 7a b d)x + a d +--R Type: Polynomial(Integer) +--E 153 + +--S 154 of 1353 +r0:=1/8*(b*d-a*e)*(a+b*x)^8/b^2+1/9*e*(a+b*x)^9/b^2 +--R +--R +--R (2) +--R 1 9 9 7 8 1 9 8 2 7 8 7 +--R - b e x + (- a b e + - b d)x + (3a b e + a b d)x +--R 9 8 8 +--R + +--R 35 3 6 7 2 7 6 4 5 3 6 5 21 5 4 35 4 5 4 +--R (-- a b e + - a b d)x + (7a b e + 7a b d)x + (-- a b e + -- a b d)x +--R 6 2 4 4 +--R + +--R 7 6 3 5 4 3 1 7 2 7 6 3 2 7 2 1 9 1 8 +--R (- a b e + 7a b d)x + (- a b e + - a b d)x + a b d x - -- a e + - a b d +--R 3 2 2 72 8 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 154 + +--S 155 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 9 7 6 1 7 8 2 5 6 7 +--R - b e x + (- a b e + - b d)x + (3a b e + a b d)x +--R 9 8 8 +--R + +--R 35 3 4 7 2 5 6 4 3 3 4 5 21 5 2 35 4 3 4 +--R (-- a b e + - a b d)x + (7a b e + 7a b d)x + (-- a b e + -- a b d)x +--R 6 2 4 4 +--R + +--R 7 6 5 2 3 1 7 7 6 2 7 +--R (- a b e + 7a b d)x + (- a e + - a b d)x + a d x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 155 + +--S 156 of 1353 +m0:=a0-r0 +--R +--R +--R 1 9 1 8 +--R -- a e - - a b d +--R 72 8 +--R (4) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 156 + +--S 157 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 157 + +)clear all + +--S 158 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Polynomial(Integer) +--E 158 + +--S 159 of 1353 +r0:=1/8*(a+b*x)^8/b +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - b x + a b x + - a b x + 7a b x + -- a b x + 7a b x + - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R a b x + - a +--R 8 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 159 + +--S 160 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 8 6 7 7 2 5 6 3 4 5 35 4 3 4 5 2 3 7 6 2 7 +--R - b x + a b x + - a b x + 7a b x + -- a b x + 7a b x + - a b x + a x +--R 8 2 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 160 + +--S 161 of 1353 +m0:=a0-r0 +--R +--R +--R 1 8 +--R - a +--R 8 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 161 + +--S 162 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +)clear all + +--S 163 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 of 1353 +r0:=b*(b*d-a*e)^6*x/e^7-1/2*(b*d-a*e)^5*(a+b*x)^2/e^6+1/3*(b*d-a*e)^4*_ + (a+b*x)^3/e^5-1/4*(b*d-a*e)^3*(a+b*x)^4/e^4+1/5*(b*d-a*e)^2*(a+b*x)^5/e^3-_ + 1/6*(b*d-a*e)*(a+b*x)^6/e^2+1/7*(a+b*x)^7/e-(b*d-a*e)^7*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a e - 2940a b d e + 8820a b d e - 14700a b d e + 14700a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 8820a b d e + 2940a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b e x + (490a b e - 70b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (1764a b e - 588a b d e + 84b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (3675a b e - 2205a b d e + 735a b d e - 105b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (4900a b e - 4900a b d e + 2940a b d e - 980a b d e + 140b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4410a b e - 7350a b d e + 7350a b d e - 4410a b d e +--R + +--R 6 4 3 7 5 2 +--R 1470a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 2940a b e - 8820a b d e + 14700a b d e - 14700a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 8820a b d e - 2940a b d e + 420b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 669a e - 2163a b d e + 3339a b d e - 2765a b d e + 1190a b d e +--R + +--R 2 5 5 2 +--R - 210a b d e +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a e - 2940a b d e + 8820a b d e - 14700a b d e + 14700a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 8820a b d e + 2940a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b e x + (490a b e - 70b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (1764a b e - 588a b d e + 84b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (3675a b e - 2205a b d e + 735a b d e - 105b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (4900a b e - 4900a b d e + 2940a b d e - 980a b d e + 140b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4410a b e - 7350a b d e + 7350a b d e - 4410a b d e +--R + +--R 6 4 3 7 5 2 +--R 1470a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 2940a b e - 8820a b d e + 14700a b d e - 14700a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 8820a b d e - 2940a b d e + 420b d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Union(Expression(Integer),...) +--E 165 + +--S 166 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R - 669a e + 2163a b d e - 3339a b d e + 2765a b d e - 1190a b d e +--R + +--R 2 5 5 +--R 210a b d +--R / +--R 6 +--R 420e +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 167 + +)clear all + +--S 168 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 168 + +--S 169 of 1353 +r0:=-21*b^2*(b*d-a*e)^5*x/e^7+(b*d-a*e)^7/(e^8*(d+e*x))+35/2*b^3*_ + (b*d-a*e)^4*(d+e*x)^2/e^8-35/3*b^4*(b*d-a*e)^3*(d+e*x)^3/e^8+_ + 21/4*b^5*(b*d-a*e)^2*(d+e*x)^4/e^8-7/5*b^6*(b*d-a*e)*(d+e*x)^5/e^8+_ + 1/6*b^7*(d+e*x)^6/e^8+7*b*(b*d-a*e)^6*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b d e - 2520a b d e + 420b d e +--R * +--R x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a b d e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 6300a b d e - 2520a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (84a b e - 14b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (315a b e - 126a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (700a b e - 525a b d e + 210a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1050a b e - 1400a b d e + 1050a b d e - 420a b d e + 70b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b e - 3150a b d e + 4200a b d e - 3150a b d e +--R + +--R 6 4 3 7 5 2 +--R 1260a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 1260a b d e - 3150a b d e + 2800a b d e - 525a b d e +--R + +--R 6 5 2 7 6 +--R - 546a b d e + 231b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a e + 420a b d e - 1260a b d e + 3150a b d e - 5600a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 5775a b d e - 3066a b d e + 651b d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b d e - 2520a b d e + 420b d e +--R * +--R x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a b d e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 6300a b d e - 2520a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (84a b e - 14b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (315a b e - 126a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (700a b e - 525a b d e + 210a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1050a b e - 1400a b d e + 1050a b d e - 420a b d e + 70b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b e - 3150a b d e + 4200a b d e - 3150a b d e +--R + +--R 6 4 3 7 5 2 +--R 1260a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 1260a b d e - 4200a b d e + 6300a b d e - 5040a b d e +--R + +--R 6 5 2 7 6 +--R 2100a b d e - 360b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a e + 420a b d e - 1260a b d e + 2100a b d e - 2100a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 1260a b d e - 420a b d e + 60b d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 170 + +--S 171 of 1353 +m0:=a0-r0 +--R +--R +--R 4 3 2 4 3 4 3 3 2 5 4 2 6 5 7 6 +--R - 1050a b d e + 3500a b d e - 4515a b d e + 2646a b d e - 591b d +--R (4) -------------------------------------------------------------------- +--R 8 +--R 60e +--R Type: Expression(Integer) +--E 171 + +--S 172 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 172 + +)clear all + +--S 173 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 173 + +--S 174 of 1353 +r0:=35*b^3*(b*d-a*e)^4*x/e^7+1/2*(b*d-a*e)^7/(e^8*(d+e*x)^2)-_ + 7*b*(b*d-a*e)^6/(e^8*(d+e*x))-35/2*b^4*(b*d-a*e)^3*(d+e*x)^2/e^8+_ + 7*b^5*(b*d-a*e)^2*(d+e*x)^3/e^8-7/4*b^6*(b*d-a*e)*(d+e*x)^4/e^8+_ + 1/5*b^7*(d+e*x)^5/e^8-21*b^2*(b*d-a*e)^5*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 420a b e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 4 3 7 5 2 +--R 2100a b d e - 420b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 840a b d e - 4200a b d e + 8400a b d e - 8400a b d e +--R + +--R 6 5 2 7 6 +--R 4200a b d e - 840b d e +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 420a b d e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 6 7 7 +--R 2100a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 4b e x + (35a b e - 7b d e )x + (140a b e - 70a b d e + 14b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (350a b e - 350a b d e + 175a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (700a b e - 1400a b d e + 1400a b d e - 700a b d e + 140b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (1400a b d e - 3500a b d e + 3500a b d e - 1575a b d e + 259b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 140a b e + 840a b d e - 1400a b d e + 1400a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 1400a b d e + 1050a b d e - 322b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a e - 70a b d e + 630a b d e - 1750a b d e + 2800a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 2800a b d e + 1575a b d e - 371b d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 420a b e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 4 3 7 5 2 +--R 2100a b d e - 420b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 840a b d e - 4200a b d e + 8400a b d e - 8400a b d e +--R + +--R 6 5 2 7 6 +--R 4200a b d e - 840b d e +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 420a b d e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 6 7 7 +--R 2100a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 4b e x + (35a b e - 7b d e )x + (140a b e - 70a b d e + 14b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (350a b e - 350a b d e + 175a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (700a b e - 1400a b d e + 1400a b d e - 700a b d e + 140b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (1400a b d e - 3850a b d e + 4410a b d e - 2380a b d e + 500b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 140a b e + 840a b d e - 1400a b d e + 700a b d e + 420a b d e +--R + +--R 6 5 2 7 6 +--R - 560a b d e + 160b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a e - 70a b d e + 630a b d e - 1750a b d e + 2450a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1890a b d e + 770a b d e - 130b d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 175 + +--S 176 of 1353 +m0:=a0-r0 +--R +--R +--R 3 4 2 3 2 5 3 2 6 4 7 5 +--R - 350a b d e + 910a b d e - 805a b d e + 241b d +--R (4) -------------------------------------------------- +--R 8 +--R 20e +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 178 + +--S 179 of 1353 +r0:=-35*b^4*(b*d-a*e)^3*x/e^7+1/3*(b*d-a*e)^7/(e^8*(d+e*x)^3)-_ + 7/2*b*(b*d-a*e)^6/(e^8*(d+e*x)^2)+21*b^2*(b*d-a*e)^5/(e^8*(d+e*x))+_ + 21/2*b^5*(b*d-a*e)^2*(d+e*x)^2/e^8-7/3*b^6*(b*d-a*e)*(d+e*x)^3/e^8+_ + 1/4*b^7*(d+e*x)^4/e^8+35*b^3*(b*d-a*e)^4*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b e - 1680a b d e + 2520a b d e - 1680a b d e +--R + +--R 7 4 3 +--R 420b d e +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 5 2 +--R 1260b d e +--R * +--R 2 +--R x +--R + +--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 6 +--R 1260b d e +--R * +--R x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 3b e x + (28a b e - 7b d e )x + (126a b e - 84a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b e - 630a b d e + 420a b d e - 105b d e )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1260a b d e - 2520a b d e + 1820a b d e - 455b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 6 4 3 7 5 2 2 +--R (- 252a b e + 1260a b d e - 1260a b d e + 420a b d e - 105b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 42a b e - 252a b d e + 1890a b d e - 3780a b d e + 3780a b d e +--R + +--R 6 5 2 7 6 +--R - 2100a b d e + 525b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e - 14a b d e - 84a b d e + 770a b d e - 1820a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 2100a b d e - 1260a b d e + 315b d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b e - 1680a b d e + 2520a b d e - 1680a b d e +--R + +--R 7 4 3 +--R 420b d e +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 5 2 +--R 1260b d e +--R * +--R 2 +--R x +--R + +--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 6 +--R 1260b d e +--R * +--R x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 3b e x + (28a b e - 7b d e )x + (126a b e - 84a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b e - 630a b d e + 420a b d e - 105b d e )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1260a b d e - 2646a b d e + 2044a b d e - 556b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 252a b e + 1260a b d e - 1260a b d e - 378a b d e +--R + +--R 6 4 3 7 5 2 +--R 1092a b d e - 408b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 42a b e - 252a b d e + 1890a b d e - 3780a b d e + 3402a b d e +--R + +--R 6 5 2 7 6 +--R - 1428a b d e + 222b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e - 14a b d e - 84a b d e + 770a b d e - 1820a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 1974a b d e - 1036a b d e + 214b d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 180 + +--S 181 of 1353 +m0:=a0-r0 +--R +--R +--R 2 5 2 2 6 3 7 4 +--R - 126a b d e + 224a b d e - 101b d +--R (4) ------------------------------------ +--R 8 +--R 12e +--R Type: Expression(Integer) +--E 181 + +--S 182 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 182 + +)clear all + +--S 183 of 1353 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 183 + +--S 184 of 1353 +r0:=e*(b*d-a*e)^3*x/b^4+1/2*(b*d-a*e)^2*(d+e*x)^2/b^3+1/3*(b*d-a*e)*_ + (d+e*x)^3/b^2+1/4*(d+e*x)^4/b+(b*d-a*e)^4*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (- 4a b e + 16b d e )x + (6a b e - 24a b d e + 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 2 2 2 3 3 +--R (- 12a b e + 48a b d e - 72a b d e + 48b d e)x + 6a b d e - 16a b d e +--R + +--R 4 4 +--R 13b d +--R / +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (- 4a b e + 16b d e )x + (6a b e - 24a b d e + 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 +--R (- 12a b e + 48a b d e - 72a b d e + 48b d e)x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 185 + +--S 186 of 1353 +m0:=a0-r0 +--R +--R +--R 2 2 2 3 2 4 +--R - 6a d e + 16a b d e - 13b d +--R (4) ------------------------------ +--R 3 +--R 12b +--R Type: Expression(Integer) +--E 186 + +--S 187 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 187 + +)clear all + +--S 188 of 1353 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 188 + +--S 189 of 1353 +r0:=e*(b*d-a*e)^2*x/b^3+1/2*(b*d-a*e)*(d+e*x)^2/b^2+1/3*(d+e*x)^3/b+_ + (b*d-a*e)^3*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (- 6a e + 18a b d e - 18a b d e + 6b d )log(b x + a) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 2 2 +--R (- 3a b e + 9b d e )x + (6a b e - 18a b d e + 18b d e)x - 3a b d e +--R + +--R 3 3 +--R 5b d +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (- 6a e + 18a b d e - 18a b d e + 6b d )log(b x + a) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (- 3a b e + 9b d e )x + (6a b e - 18a b d e + 18b d e)x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 190 + +--S 191 of 1353 +m0:=a0-r0 +--R +--R +--R 2 3 +--R 3a d e - 5b d +--R (4) -------------- +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 1353 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------ +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 193 + +--S 194 of 1353 +r0:=e*(b*d-a*e)*x/b^2+1/2*(d+e*x)^2/b+(b*d-a*e)^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(b x + a) + b e x + (- 2a b e + 4b d e)x +--R + +--R 2 2 +--R b d +--R / +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(b x + a) + b e x + (- 2a b e + 4b d e)x +--R ----------------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 195 + +--S 196 of 1353 +m0:=a0-r0 +--R +--R +--R 2 +--R d +--R (4) - -- +--R 2b +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 197 + +)clear all + +--S 198 of 1353 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R e x + d +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 198 + +--S 199 of 1353 +r0:=e*x/b+(b*d-a*e)*log(a+b*x)/b^2 +--R +--R +--R (- a e + b d)log(b x + a) + b e x +--R (2) --------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (- a e + b d)log(b x + a) + b e x +--R (3) --------------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 200 + +--S 201 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 202 + +)clear all + +--S 203 of 1353 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 1 +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 203 + +--S 204 of 1353 +r0:=log(a+b*x)/b +--R +--R +--R log(b x + a) +--R (2) ------------ +--R b +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1353 +a0:=integrate(t0,x) +--R +--R +--R log(b x + a) +--R (3) ------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 205 + +--S 206 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 1353 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--R b e x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 208 + +--S 209 of 1353 +r0:=log(a+b*x)/(b*d-a*e)-log(d+e*x)/(b*d-a*e) +--R +--R +--R log(e x + d) - log(b x + a) +--R (2) --------------------------- +--R a e - b d +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1353 +a0:=integrate(t0,x) +--R +--R +--R log(e x + d) - log(b x + a) +--R (3) --------------------------- +--R a e - b d +--R Type: Union(Expression(Integer),...) +--E 210 + +--S 211 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 212 + +)clear all + +--S 213 of 1353 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (a e + 2b d e)x + (2a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 213 + +--S 214 of 1353 +r0:=1/((b*d-a*e)*(d+e*x))+b*log(a+b*x)/(b*d-a*e)^2-b*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (- b e x - b d)log(e x + d) + (b e x + b d)log(b x + a) - a e + b d +--R (2) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a e - 2a b d e + b d e)x + a d e - 2a b d e + b d +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (- b e x - b d)log(e x + d) + (b e x + b d)log(b x + a) - a e + b d +--R (3) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a e - 2a b d e + b d e)x + a d e - 2a b d e + b d +--R Type: Union(Expression(Integer),...) +--E 215 + +--S 216 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 217 + +)clear all + +--S 218 of 1353 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 218 + +--S 219 of 1353 +r0:=1/2/((b*d-a*e)*(d+e*x)^2)+b/((b*d-a*e)^2*(d+e*x))+b^2*log(a+b*x)/_ + (b*d-a*e)^3-b^2*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4b d e x - 2b d )log(b x + a) + (2a b e - 2b d e)x - a e +--R + +--R 2 2 +--R 4a b d e - 3b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a d e - 12a b d e + 12a b d e - 4b d e)x + 2a d e - 6a b d e +--R + +--R 2 4 3 5 +--R 6a b d e - 2b d +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4b d e x - 2b d )log(b x + a) + (2a b e - 2b d e)x - a e +--R + +--R 2 2 +--R 4a b d e - 3b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a d e - 12a b d e + 12a b d e - 4b d e)x + 2a d e - 6a b d e +--R + +--R 2 4 3 5 +--R 6a b d e - 2b d +--R Type: Union(Expression(Integer),...) +--E 220 + +--S 221 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 1353 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 223 + +--S 224 of 1353 +r0:=1/3/((b*d-a*e)*(d+e*x)^3)+1/2*b/((b*d-a*e)^2*(d+e*x)^2)+_ + b^2/((b*d-a*e)^3*(d+e*x))+b^3*log(a+b*x)/(b*d-a*e)^4-_ + b^3*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 3 3 3 2 2 3 2 3 3 +--R (- 6b e x - 18b d e x - 18b d e x - 6b d )log(e x + d) +--R + +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (3a b e - 18a b d e + 15b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 18a b d e + 11b d +--R / +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4 3 4 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e)x + 6a d e +--R + +--R 3 4 3 2 2 5 2 3 6 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 3 2 2 3 2 3 3 +--R (- 6b e x - 18b d e x - 18b d e x - 6b d )log(e x + d) +--R + +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (3a b e - 18a b d e + 15b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 18a b d e + 11b d +--R / +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4 3 4 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e)x + 6a d e +--R + +--R 3 4 3 2 2 5 2 3 6 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d +--R Type: Union(Expression(Integer),...) +--E 225 + +--S 226 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 227 + +)clear all + +--S 228 of 1353 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 228 + +--S 229 of 1353 +r0:=e^3*(4*b*d-3*a*e)*x/b^4+1/2*e^4*x^2/b^3-1/2*(b*d-a*e)^4/(b^5*(a+b*x)^2)-_ + 4*e*(b*d-a*e)^3/(b^5*(a+b*x))+6*e^2*(b*d-a*e)^2*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (24a b e - 48a b d e + 24a b d e )x + 12a e - 24a b d e +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R b e x + (- 4a b e + 8b d e )x + (- 11a b e + 16a b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (2a b e - 16a b d e + 24a b d e - 8b d e)x + 7a e - 20a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 4a b d e - b d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (24a b e - 48a b d e + 24a b d e )x + 12a e - 24a b d e +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R b e x + (- 4a b e + 8b d e )x + (- 11a b e + 16a b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (2a b e - 16a b d e + 24a b d e - 8b d e)x + 7a e - 20a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 4a b d e - b d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 230 + +--S 231 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 232 + +)clear all + +--S 233 of 1353 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 233 + +--S 234 of 1353 +r0:=e^3*x/b^3-1/2*(b*d-a*e)^3/(b^4*(a+b*x)^2)-3*e*(b*d-a*e)^2/(b^4*(a+b*x))+_ + 3*e^2*(b*d-a*e)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b e + 6b d e )x + (- 12a b e + 12a b d e )x - 6a e +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4a b e x + (- 4a b e + 12a b d e - 6b d e)x - 5a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 3a b d e - b d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b e + 6b d e )x + (- 12a b e + 12a b d e )x - 6a e +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4a b e x + (- 4a b e + 12a b d e - 6b d e)x - 5a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 3a b d e - b d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 235 + +--S 236 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 1353 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 238 + +--S 239 of 1353 +r0:=-1/2*(b*d-a*e)^2/(b^3*(a+b*x)^2)-2*e*(b*d-a*e)/(b^3*(a+b*x))+_ + e^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(b x + a) + (4a b e - 4b d e)x + 3a e +--R + +--R 2 2 +--R - 2a b d e - b d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(b x + a) + (4a b e - 4b d e)x + 3a e +--R + +--R 2 2 +--R - 2a b d e - b d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 240 + +--S 241 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 242 + +)clear all + +--S 243 of 1353 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 243 + +--S 244 of 1353 +r0:=-1/2*(d+e*x)^2/((b*d-a*e)*(a+b*x)^2) +--R +--R +--R 1 2 2 1 2 +--R - e x + d e x + - d +--R 2 2 +--R (2) -------------------------------------------------- +--R 2 3 2 2 2 3 2 +--R (a b e - b d)x + (2a b e - 2a b d)x + a e - a b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 244 + +--S 245 of 1353 +a0:=integrate(t0,x) +--R +--R +--R - 2b e x - a e - b d +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 245 + +--S 246 of 1353 +m0:=a0-r0 +--R +--R +--R 2 +--R e +--R (4) - ------------- +--R 2 3 +--R 2a b e - 2b d +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 247 + +)clear all + +--S 248 of 1353 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 1 +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 248 + +--S 249 of 1353 +r0:=(-1/2)/(b*(a+b*x)^2) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ------------------- +--R 3 2 2 2 +--R b x + 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 249 + +--S 250 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------------------- +--R 3 2 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 250 + +--S 251 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 1353 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 253 + +--S 254 of 1353 +r0:=(-1/2)/((b*d-a*e)*(a+b*x)^2)+e/((b*d-a*e)^2*(a+b*x))+_ + e^2*log(a+b*x)/(b*d-a*e)^3-e^2*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4a b e x - 2a e )log(b x + a) + (2a b e - 2b d e)x + 3a e +--R + +--R 2 2 +--R - 4a b d e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a e - 6a b d e +--R + +--R 3 2 2 2 3 3 +--R 6a b d e - 2a b d +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4a b e x - 2a e )log(b x + a) + (2a b e - 2b d e)x + 3a e +--R + +--R 2 2 +--R - 4a b d e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a e - 6a b d e +--R + +--R 3 2 2 2 3 3 +--R 6a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 255 + +--S 256 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 257 + +)clear all + +--S 258 of 1353 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 258 + +--S 259 of 1353 +r0:=-1/2*b/((b*d-a*e)^2*(a+b*x)^2)+2*b*e/((b*d-a*e)^3*(a+b*x))+_ + e^2/((b*d-a*e)^3*(d+e*x))+3*b*e^2*log(a+b*x)/(b*d-a*e)^4-_ + 3*b*e^2*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R - 6b e x + (- 12a b e - 6b d e )x + (- 6a b e - 12a b d e )x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 6b e x + (12a b e + 6b d e )x + (6a b e + 12a b d e )x +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (- 9a b e + 6a b d e + 3b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 6a b d e - b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R - 6b e x + (- 12a b e - 6b d e )x + (- 6a b e - 12a b d e )x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 6b e x + (12a b e + 6b d e )x + (6a b e + 12a b d e )x +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (- 9a b e + 6a b d e + 3b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 6a b d e - b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 260 + +--S 261 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 262 + +)clear all + +--S 263 of 1353 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 263 + +--S 264 of 1353 +r0:=-1/2*b^2/((b*d-a*e)^3*(a+b*x)^2)+3*b^2*e/((b*d-a*e)^4*(a+b*x))+_ + 1/2*e^2/((b*d-a*e)^3*(d+e*x)^2)+3*b*e^2/((b*d-a*e)^4*(d+e*x))+_ + 6*b^2*e^2*log(a+b*x)/(b*d-a*e)^5-6*b^2*e^2*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 12b e x + (24a b e + 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b e + 48a b d e + 12b d e )x + (24a b d e + 24a b d e )x +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b e x + (- 24a b e - 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b e - 48a b d e - 12b d e )x + (- 24a b d e - 24a b d e )x +--R + +--R 2 2 2 2 +--R - 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b e - 12b d e )x + (18a b e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b e + 24a b d e - 24a b d e - 4b d e)x - a e + 8a b d e +--R + +--R 3 3 4 4 +--R - 8a b d e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 12b e x + (24a b e + 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b e + 48a b d e + 12b d e )x + (24a b d e + 24a b d e )x +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b e x + (- 24a b e - 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b e - 48a b d e - 12b d e )x + (- 24a b d e - 24a b d e )x +--R + +--R 2 2 2 2 +--R - 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b e - 12b d e )x + (18a b e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b e + 24a b d e - 24a b d e - 4b d e)x - a e + 8a b d e +--R + +--R 3 3 4 4 +--R - 8a b d e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 265 + +--S 266 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 1353 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 268 + +--S 269 of 1353 +r0:=-1/2*b^3/((b*d-a*e)^4*(a+b*x)^2)+4*b^3*e/((b*d-a*e)^5*(a+b*x))+_ + 1/3*e^2/((b*d-a*e)^3*(d+e*x)^3)+3/2*b*e^2/((b*d-a*e)^4*(d+e*x)^2)+_ + 6*b^2*e^2/((b*d-a*e)^5*(d+e*x))+10*b^3*e^2*log(a+b*x)/(b*d-a*e)^6-_ + 10*b^3*e^2*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 120a b e - 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 60a b e - 360a b d e - 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (- 180a b d e - 360a b d e - 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (- 180a b d e - 120a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (120a b e + 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e + 360a b d e + 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e + 360a b d e + 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (180a b d e + 120a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 90a b e - 60a b d e + 150b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 20a b e - 210a b d e + 120a b d e + 110b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (5a b e - 60a b d e - 120a b d e + 160a b d e + 15b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 15a b d e - 60a b d e + 20a b d e + 30a b d e - 3b d +--R / +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 4 8 6 3 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 12a b e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 198a b d e - 96a b d e + 18b d e +--R * +--R 4 +--R x +--R + +--R 8 9 6 2 2 7 5 3 3 6 4 4 4 5 3 5 5 4 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 2 6 6 3 7 7 2 8 8 +--R 60a b d e - 72a b d e + 18b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4 +--R 18a d e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 5 6 3 2 6 7 2 8 9 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 2 7 7 3 6 6 2 4 5 5 3 5 4 4 4 6 3 +--R 18a d e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 3 5 7 2 2 6 8 7 9 +--R 72a b d e - 54a b d e + 12a b d +--R * +--R x +--R + +--R 8 3 6 7 4 5 6 2 5 4 5 3 6 3 4 4 7 2 3 5 8 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 2 6 9 +--R 6a b d +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 120a b e - 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 60a b e - 360a b d e - 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (- 180a b d e - 360a b d e - 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (- 180a b d e - 120a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (120a b e + 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e + 360a b d e + 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e + 360a b d e + 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (180a b d e + 120a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 90a b e - 60a b d e + 150b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 20a b e - 210a b d e + 120a b d e + 110b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (5a b e - 60a b d e - 120a b d e + 160a b d e + 15b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 15a b d e - 60a b d e + 20a b d e + 30a b d e - 3b d +--R / +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 4 8 6 3 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 12a b e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 198a b d e - 96a b d e + 18b d e +--R * +--R 4 +--R x +--R + +--R 8 9 6 2 2 7 5 3 3 6 4 4 4 5 3 5 5 4 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 2 6 6 3 7 7 2 8 8 +--R 60a b d e - 72a b d e + 18b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4 +--R 18a d e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 5 6 3 2 6 7 2 8 9 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 2 7 7 3 6 6 2 4 5 5 3 5 4 4 4 6 3 +--R 18a d e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 3 5 7 2 2 6 8 7 9 +--R 72a b d e - 54a b d e + 12a b d +--R * +--R x +--R + +--R 8 3 6 7 4 5 6 2 5 4 5 3 6 3 4 4 7 2 3 5 8 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 2 6 9 +--R 6a b d +--R Type: Union(Expression(Integer),...) +--E 270 + +--S 271 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 272 + +)clear all + +--S 273 of 1353 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 273 + +--S 274 of 1353 +r0:=-1/4*(b*d-a*e)^4/(b^5*(a+b*x)^4)-4/3*e*(b*d-a*e)^3/(b^5*(a+b*x)^3)-_ + 3*e^2*(b*d-a*e)^2/(b^5*(a+b*x)^2)-4*e^3*(b*d-a*e)/(b^5*(a+b*x))+_ + e^4*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (48a b e - 48b d e )x + (108a b e - 72a b d e - 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (88a b e - 48a b d e - 24a b d e - 16b d e)x + 25a e - 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 4a b d e - 3b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (48a b e - 48b d e )x + (108a b e - 72a b d e - 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (88a b e - 48a b d e - 24a b d e - 16b d e)x + 25a e - 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 4a b d e - 3b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 275 + +--S 276 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 277 + +)clear all + +--S 278 of 1353 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 278 + +--S 279 of 1353 +r0:=-1/4*(d+e*x)^4/((b*d-a*e)*(a+b*x)^4) +--R +--R +--R (2) +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - e x + d e x + - d e x + d e x + - d +--R 4 2 4 +--R / +--R 4 5 4 2 3 4 3 3 2 2 3 2 +--R (a b e - b d)x + (4a b e - 4a b d)x + (6a b e - 6a b d)x +--R + +--R 4 3 2 5 4 +--R (4a b e - 4a b d)x + a e - a b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 279 + +--S 280 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R - 4b e x + (- 6a b e - 6b d e )x + (- 4a b e - 4a b d e - 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - a e - a b d e - a b d e - b d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 4b x + 16a b x + 24a b x + 16a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 280 + +--S 281 of 1353 +m0:=a0-r0 +--R +--R +--R 4 +--R e +--R (4) - ------------- +--R 4 5 +--R 4a b e - 4b d +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 1353 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 283 + +--S 284 of 1353 +r0:=-1/4*(b*d-a*e)^2/(b^3*(a+b*x)^4)-2/3*e*(b*d-a*e)/(b^3*(a+b*x)^3)-_ + 1/2*e^2/(b^3*(a+b*x)^2) +--R +--R +--R 1 2 2 2 1 2 2 2 1 2 2 1 1 2 2 +--R - - b e x + (- - a b e - - b d e)x - -- a e - - a b d e - - b d +--R 2 3 3 12 6 4 +--R (2) ------------------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 284 + +--S 285 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 6b e x + (- 4a b e - 8b d e)x - a e - 2a b d e - 3b d +--R (3) ----------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 285 + +--S 286 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 287 + +)clear all + +--S 288 of 1353 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 288 + +--S 289 of 1353 +r0:=1/4*(-b*d+a*e)/(b^2*(a+b*x)^4)-1/3*e/(b^2*(a+b*x)^3) +--R +--R +--R 1 1 1 +--R - - b e x - -- a e - - b d +--R 3 12 4 +--R (2) ---------------------------------------- +--R 6 4 5 3 2 4 2 3 3 4 2 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 289 + +--S 290 of 1353 +a0:=integrate(t0,x) +--R +--R +--R - 4b e x - a e - 3b d +--R (3) ----------------------------------------------- +--R 6 4 5 3 2 4 2 3 3 4 2 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 290 + +--S 291 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 292 + +)clear all + +--S 293 of 1353 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 293 + +--S 294 of 1353 +r0:=(-1/4)/(b*(a+b*x)^4) +--R +--R +--R 1 +--R - +--R 4 +--R (2) - --------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 294 + +--S 295 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - -------------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R 4b x + 16a b x + 24a b x + 16a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 295 + +--S 296 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 1353 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 298 + +--S 299 of 1353 +r0:=(-1/4)/((b*d-a*e)*(a+b*x)^4)+1/3*e/((b*d-a*e)^2*(a+b*x)^3)-_ + 1/2*e^2/((b*d-a*e)^3*(a+b*x)^2)+e^3/((b*d-a*e)^4*(a+b*x))+_ + e^4*log(a+b*x)/(b*d-a*e)^5-e^4*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(e x + d) +--R + +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 12b e x - 48a b e x - 72a b e x - 48a b e x - 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (42a b e - 48a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (52a b e - 72a b d e + 24a b d e - 4b d e)x + 25a e - 48a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 36a b d e - 16a b d e + 3b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 9 5 +--R - 12b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 2 7 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 3 6 4 +--R 72a b e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 2 7 5 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 4 5 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 6 5 +--R - 48a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 4 5 5 +--R 12a e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(e x + d) +--R + +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 12b e x - 48a b e x - 72a b e x - 48a b e x - 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (42a b e - 48a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (52a b e - 72a b d e + 24a b d e - 4b d e)x + 25a e - 48a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 36a b d e - 16a b d e + 3b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 9 5 +--R - 12b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 2 7 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 3 6 4 +--R 72a b e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 2 7 5 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 4 5 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 6 5 +--R - 48a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 4 5 5 +--R 12a e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R Type: Union(Expression(Integer),...) +--E 300 + +--S 301 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 302 + +)clear all + +--S 303 of 1353 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 303 + +--S 304 of 1353 +r0:=-1/4*b/((b*d-a*e)^2*(a+b*x)^4)+2/3*b*e/((b*d-a*e)^3*(a+b*x)^3)-_ + 3/2*b*e^2/((b*d-a*e)^4*(a+b*x)^2)+4*b*e^3/((b*d-a*e)^5*(a+b*x))+_ + e^4/((b*d-a*e)^5*(d+e*x))+5*b*e^4*log(a+b*x)/(b*d-a*e)^6-_ + 5*b*e^4*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 240a b e - 60b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (- 360a b e - 240a b d e )x + (- 240a b e - 360a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (- 60a b e - 240a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 3 +--R 60b e x + (240a b e + 60b d e )x + (360a b e + 240a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 4 4 +--R (240a b e + 360a b d e )x + (60a b e + 240a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 210a b e + 180a b d e + 30b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 260a b e + 150a b d e + 120a b d e - 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 125a b e - 20a b d e + 180a b d e - 40a b d e + 5b d e)x - 12a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 65a b d e + 120a b d e - 60a b d e + 20a b d e - 3b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 2 8 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 9 5 2 10 6 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 3 7 4 3 +--R 48a b e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 8 5 2 9 6 10 7 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 4 6 4 3 +--R 72a b e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 3 7 5 2 2 8 6 9 7 +--R 288a b d e - 216a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 5 5 4 3 +--R 48a b e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 4 6 5 2 3 7 6 2 8 7 +--R 792a b d e - 384a b d e + 72a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 6 4 4 3 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 5 5 5 2 4 6 6 3 7 7 +--R 648a b d e - 276a b d e + 48a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 5 5 6 4 6 7 +--R - 72a b d e + 12a b d +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 240a b e - 60b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (- 360a b e - 240a b d e )x + (- 240a b e - 360a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (- 60a b e - 240a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 3 +--R 60b e x + (240a b e + 60b d e )x + (360a b e + 240a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 4 4 +--R (240a b e + 360a b d e )x + (60a b e + 240a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 210a b e + 180a b d e + 30b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 260a b e + 150a b d e + 120a b d e - 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 125a b e - 20a b d e + 180a b d e - 40a b d e + 5b d e)x - 12a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 65a b d e + 120a b d e - 60a b d e + 20a b d e - 3b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 2 8 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 9 5 2 10 6 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 3 7 4 3 +--R 48a b e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 8 5 2 9 6 10 7 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 4 6 4 3 +--R 72a b e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 3 7 5 2 2 8 6 9 7 +--R 288a b d e - 216a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 5 5 4 3 +--R 48a b e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 4 6 5 2 3 7 6 2 8 7 +--R 792a b d e - 384a b d e + 72a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 6 4 4 3 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 5 5 5 2 4 6 6 3 7 7 +--R 648a b d e - 276a b d e + 48a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 5 5 6 4 6 7 +--R - 72a b d e + 12a b d +--R Type: Union(Expression(Integer),...) +--E 305 + +--S 306 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 307 + +)clear all + +--S 308 of 1353 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 308 + +--S 309 of 1353 +r0:=-1/4*b^2/((b*d-a*e)^3*(a+b*x)^4)+b^2*e/((b*d-a*e)^4*(a+b*x)^3)-_ + 3*b^2*e^2/((b*d-a*e)^5*(a+b*x)^2)+10*b^2*e^3/((b*d-a*e)^6*(a+b*x))+_ + 1/2*e^4/((b*d-a*e)^5*(d+e*x)^2)+5*b*e^4/((b*d-a*e)^6*(d+e*x))+_ + 15*b^2*e^4*log(a+b*x)/(b*d-a*e)^7-15*b^2*e^4*log(d+e*x)/(b*d-a*e)^7 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 60b e x + (240a b e + 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (360a b e + 480a b d e + 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (240a b e + 720a b d e + 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (60a b e + 480a b d e + 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (120a b d e + 240a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 60b e x + (- 240a b e - 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 360a b e - 480a b d e - 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (- 240a b e - 720a b d e - 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (- 60a b e - 480a b d e - 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (- 120a b d e - 240a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (210a b e - 120a b d e - 90b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (260a b e + 60a b d e - 300a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (125a b e + 280a b d e - 330a b d e - 80a b d e + 5b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 12a b e + 190a b d e - 100a b d e - 120a b d e + 20a b d e +--R + +--R 6 5 +--R - 2b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e + 24a b d e + 35a b d e - 80a b d e + 30a b d e - 8a b d e +--R + +--R 6 6 +--R b d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 3 8 4 5 +--R 4a b e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 2 9 5 4 10 6 3 11 7 2 +--R - 84a b d e + 28a b d e - 4b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 4 7 4 5 +--R 16a b e - 104a b d e + 280a b d e - 392a b d e + 280a b d e +--R + +--R 3 8 5 4 2 9 6 3 10 7 2 11 8 +--R - 56a b d e - 56a b d e + 40a b d e - 8b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 5 6 4 5 +--R 24a b e - 136a b d e + 284a b d e - 196a b d e - 196a b d e +--R + +--R 4 7 5 4 3 8 6 3 2 9 7 2 10 8 11 9 +--R 476a b d e - 364a b d e + 116a b d e - 4a b d e - 4b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 6 5 4 5 +--R 16a b e - 64a b d e + 16a b d e + 336a b d e - 784a b d e +--R + +--R 5 6 5 4 4 7 6 3 3 8 7 2 2 9 8 10 9 +--R 784a b d e - 336a b d e - 16a b d e + 64a b d e - 16a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5 +--R 4a e + 4a b d e - 116a b d e + 364a b d e - 476a b d e +--R + +--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9 +--R 196a b d e + 196a b d e - 284a b d e + 136a b d e - 24a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 7 4 5 4 +--R 8a d e - 40a b d e + 56a b d e + 56a b d e - 280a b d e +--R + +--R 6 5 6 3 5 6 7 2 4 7 8 3 8 9 +--R 392a b d e - 280a b d e + 104a b d e - 16a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 7 4 6 3 +--R 4a d e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 6 5 7 2 5 6 8 4 7 9 +--R - 84a b d e + 28a b d e - 4a b d +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 60b e x + (240a b e + 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (360a b e + 480a b d e + 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (240a b e + 720a b d e + 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (60a b e + 480a b d e + 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (120a b d e + 240a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 60b e x + (- 240a b e - 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 360a b e - 480a b d e - 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (- 240a b e - 720a b d e - 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (- 60a b e - 480a b d e - 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (- 120a b d e - 240a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (210a b e - 120a b d e - 90b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (260a b e + 60a b d e - 300a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (125a b e + 280a b d e - 330a b d e - 80a b d e + 5b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 12a b e + 190a b d e - 100a b d e - 120a b d e + 20a b d e +--R + +--R 6 5 +--R - 2b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e + 24a b d e + 35a b d e - 80a b d e + 30a b d e - 8a b d e +--R + +--R 6 6 +--R b d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 3 8 4 5 +--R 4a b e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 2 9 5 4 10 6 3 11 7 2 +--R - 84a b d e + 28a b d e - 4b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 4 7 4 5 +--R 16a b e - 104a b d e + 280a b d e - 392a b d e + 280a b d e +--R + +--R 3 8 5 4 2 9 6 3 10 7 2 11 8 +--R - 56a b d e - 56a b d e + 40a b d e - 8b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 5 6 4 5 +--R 24a b e - 136a b d e + 284a b d e - 196a b d e - 196a b d e +--R + +--R 4 7 5 4 3 8 6 3 2 9 7 2 10 8 11 9 +--R 476a b d e - 364a b d e + 116a b d e - 4a b d e - 4b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 6 5 4 5 +--R 16a b e - 64a b d e + 16a b d e + 336a b d e - 784a b d e +--R + +--R 5 6 5 4 4 7 6 3 3 8 7 2 2 9 8 10 9 +--R 784a b d e - 336a b d e - 16a b d e + 64a b d e - 16a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5 +--R 4a e + 4a b d e - 116a b d e + 364a b d e - 476a b d e +--R + +--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9 +--R 196a b d e + 196a b d e - 284a b d e + 136a b d e - 24a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 7 4 5 4 +--R 8a d e - 40a b d e + 56a b d e + 56a b d e - 280a b d e +--R + +--R 6 5 6 3 5 6 7 2 4 7 8 3 8 9 +--R 392a b d e - 280a b d e + 104a b d e - 16a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 7 4 6 3 +--R 4a d e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 6 5 7 2 5 6 8 4 7 9 +--R - 84a b d e + 28a b d e - 4a b d +--R Type: Union(Expression(Integer),...) +--E 310 + +--S 311 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 1353 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 313 + +--S 314 of 1353 +r0:=-1/4*b^3/((b*d-a*e)^4*(a+b*x)^4)+4/3*b^3*e/((b*d-a*e)^5*(a+b*x)^3)-_ + 5*b^3*e^2/((b*d-a*e)^6*(a+b*x)^2)+20*b^3*e^3/((b*d-a*e)^7*(a+b*x))+_ + 1/3*e^4/((b*d-a*e)^5*(d+e*x)^3)+5/2*b*e^4/((b*d-a*e)^6*(d+e*x)^2)+_ + 15*b^2*e^4/((b*d-a*e)^7*(d+e*x))+35*b^3*e^4*log(a+b*x)/(b*d-a*e)^8-_ + 35*b^3*e^4*log(d+e*x)/(b*d-a*e)^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R - 420b e x + (- 1680a b e - 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 2520a b e - 5040a b d e - 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1680a b e - 7560a b d e - 5040a b d e - 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (- 420a b e - 5040a b d e - 7560a b d e - 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (- 1260a b d e - 5040a b d e - 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (- 1260a b d e - 1680a b d e )x - 420a b d e +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 420b e x + (1680a b e + 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2520a b e + 5040a b d e + 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1680a b e + 7560a b d e + 5040a b d e + 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (420a b e + 5040a b d e + 7560a b d e + 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (1260a b d e + 5040a b d e + 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (1260a b d e + 1680a b d e )x + 420a b d e +--R * +--R log(b x + a) +--R + +--R 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R (- 420a b e + 420b d e )x + (- 1470a b e + 420a b d e + 1050b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1820a b e - 1890a b d e + 2940a b d e + 770b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 875a b e - 3780a b d e + 1890a b d e + 2660a b d e + 105b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 84a b e - 2205a b d e - 1260a b d e + 3150a b d e + 420a b d e +--R + +--R 7 5 2 +--R - 21b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 14a b e - 252a b d e - 1575a b d e + 1260a b d e + 630a b d e +--R + +--R 6 5 2 7 6 +--R - 84a b d e + 7b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e + 42a b d e - 252a b d e - 105a b d e + 420a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 126a b d e + 28a b d e - 3b d +--R / +--R 8 4 11 7 5 10 6 6 2 9 5 7 3 8 4 8 4 7 +--R 12a b e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 3 9 5 6 2 10 6 5 11 7 4 12 8 3 +--R - 672a b d e + 336a b d e - 96a b d e + 12b d e +--R * +--R 7 +--R x +--R + +--R 9 3 11 8 4 10 7 5 2 9 6 6 3 8 5 7 4 7 +--R 48a b e - 348a b d e + 1056a b d e - 1680a b d e + 1344a b d e +--R + +--R 4 8 5 6 3 9 6 5 2 10 7 4 11 8 3 12 9 2 +--R - 168a b d e - 672a b d e + 624a b d e - 240a b d e + 36b d e +--R * +--R 6 +--R x +--R + +--R 10 2 11 9 3 10 8 4 2 9 7 5 3 8 6 6 4 7 +--R 72a b e - 432a b d e + 900a b d e - 288a b d e - 2016a b d e +--R + +--R 5 7 5 6 4 8 6 5 3 9 7 4 2 10 8 3 +--R 4032a b d e - 3528a b d e + 1440a b d e - 72a b d e +--R + +--R 11 9 2 12 10 +--R - 144a b d e + 36b d e +--R * +--R 5 +--R x +--R + +--R 11 11 10 2 10 9 3 2 9 8 4 3 8 +--R 48a b e - 168a b d e - 240a b d e + 2220a b d e +--R + +--R 7 5 4 7 6 6 5 6 5 7 6 5 4 8 7 4 +--R - 4800a b d e + 4704a b d e - 1344a b d e - 1560a b d e +--R + +--R 3 9 8 3 2 10 9 2 11 10 12 11 +--R 1680a b d e - 600a b d e + 48a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 12 11 11 10 10 2 2 9 9 3 3 8 8 4 4 7 +--R 12a e + 48a b d e - 600a b d e + 1680a b d e - 1560a b d e +--R + +--R 7 5 5 6 6 6 6 5 5 7 7 4 4 8 8 3 +--R - 1344a b d e + 4704a b d e - 4800a b d e + 2220a b d e +--R + +--R 3 9 9 2 2 10 10 11 11 +--R - 240a b d e - 168a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 12 10 11 2 9 10 2 3 8 9 3 4 7 8 4 5 6 +--R 36a d e - 144a b d e - 72a b d e + 1440a b d e - 3528a b d e +--R + +--R 7 5 6 5 6 6 7 4 5 7 8 3 4 8 9 2 3 9 10 +--R 4032a b d e - 2016a b d e - 288a b d e + 900a b d e - 432a b d e +--R + +--R 2 10 11 +--R 72a b d +--R * +--R 2 +--R x +--R + +--R 12 2 9 11 3 8 10 2 4 7 9 3 5 6 8 4 6 5 +--R 36a d e - 240a b d e + 624a b d e - 672a b d e - 168a b d e +--R + +--R 7 5 7 4 6 6 8 3 5 7 9 2 4 8 10 3 9 11 +--R 1344a b d e - 1680a b d e + 1056a b d e - 348a b d e + 48a b d +--R * +--R x +--R + +--R 12 3 8 11 4 7 10 2 5 6 9 3 6 5 8 4 7 4 +--R 12a d e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 7 5 8 3 6 6 9 2 5 7 10 4 8 11 +--R - 672a b d e + 336a b d e - 96a b d e + 12a b d +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R - 420b e x + (- 1680a b e - 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 2520a b e - 5040a b d e - 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1680a b e - 7560a b d e - 5040a b d e - 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (- 420a b e - 5040a b d e - 7560a b d e - 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (- 1260a b d e - 5040a b d e - 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (- 1260a b d e - 1680a b d e )x - 420a b d e +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 420b e x + (1680a b e + 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2520a b e + 5040a b d e + 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1680a b e + 7560a b d e + 5040a b d e + 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (420a b e + 5040a b d e + 7560a b d e + 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (1260a b d e + 5040a b d e + 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (1260a b d e + 1680a b d e )x + 420a b d e +--R * +--R log(b x + a) +--R + +--R 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R (- 420a b e + 420b d e )x + (- 1470a b e + 420a b d e + 1050b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1820a b e - 1890a b d e + 2940a b d e + 770b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 875a b e - 3780a b d e + 1890a b d e + 2660a b d e + 105b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 84a b e - 2205a b d e - 1260a b d e + 3150a b d e + 420a b d e +--R + +--R 7 5 2 +--R - 21b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 14a b e - 252a b d e - 1575a b d e + 1260a b d e + 630a b d e +--R + +--R 6 5 2 7 6 +--R - 84a b d e + 7b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e + 42a b d e - 252a b d e - 105a b d e + 420a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 126a b d e + 28a b d e - 3b d +--R / +--R 8 4 11 7 5 10 6 6 2 9 5 7 3 8 4 8 4 7 +--R 12a b e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 3 9 5 6 2 10 6 5 11 7 4 12 8 3 +--R - 672a b d e + 336a b d e - 96a b d e + 12b d e +--R * +--R 7 +--R x +--R + +--R 9 3 11 8 4 10 7 5 2 9 6 6 3 8 5 7 4 7 +--R 48a b e - 348a b d e + 1056a b d e - 1680a b d e + 1344a b d e +--R + +--R 4 8 5 6 3 9 6 5 2 10 7 4 11 8 3 12 9 2 +--R - 168a b d e - 672a b d e + 624a b d e - 240a b d e + 36b d e +--R * +--R 6 +--R x +--R + +--R 10 2 11 9 3 10 8 4 2 9 7 5 3 8 6 6 4 7 +--R 72a b e - 432a b d e + 900a b d e - 288a b d e - 2016a b d e +--R + +--R 5 7 5 6 4 8 6 5 3 9 7 4 2 10 8 3 +--R 4032a b d e - 3528a b d e + 1440a b d e - 72a b d e +--R + +--R 11 9 2 12 10 +--R - 144a b d e + 36b d e +--R * +--R 5 +--R x +--R + +--R 11 11 10 2 10 9 3 2 9 8 4 3 8 +--R 48a b e - 168a b d e - 240a b d e + 2220a b d e +--R + +--R 7 5 4 7 6 6 5 6 5 7 6 5 4 8 7 4 +--R - 4800a b d e + 4704a b d e - 1344a b d e - 1560a b d e +--R + +--R 3 9 8 3 2 10 9 2 11 10 12 11 +--R 1680a b d e - 600a b d e + 48a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 12 11 11 10 10 2 2 9 9 3 3 8 8 4 4 7 +--R 12a e + 48a b d e - 600a b d e + 1680a b d e - 1560a b d e +--R + +--R 7 5 5 6 6 6 6 5 5 7 7 4 4 8 8 3 +--R - 1344a b d e + 4704a b d e - 4800a b d e + 2220a b d e +--R + +--R 3 9 9 2 2 10 10 11 11 +--R - 240a b d e - 168a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 12 10 11 2 9 10 2 3 8 9 3 4 7 8 4 5 6 +--R 36a d e - 144a b d e - 72a b d e + 1440a b d e - 3528a b d e +--R + +--R 7 5 6 5 6 6 7 4 5 7 8 3 4 8 9 2 3 9 10 +--R 4032a b d e - 2016a b d e - 288a b d e + 900a b d e - 432a b d e +--R + +--R 2 10 11 +--R 72a b d +--R * +--R 2 +--R x +--R + +--R 12 2 9 11 3 8 10 2 4 7 9 3 5 6 8 4 6 5 +--R 36a d e - 240a b d e + 624a b d e - 672a b d e - 168a b d e +--R + +--R 7 5 7 4 6 6 8 3 5 7 9 2 4 8 10 3 9 11 +--R 1344a b d e - 1680a b d e + 1056a b d e - 348a b d e + 48a b d +--R * +--R x +--R + +--R 12 3 8 11 4 7 10 2 5 6 9 3 6 5 8 4 7 4 +--R 12a d e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 7 5 8 3 6 6 9 2 5 7 10 4 8 11 +--R - 672a b d e + 336a b d e - 96a b d e + 12a b d +--R Type: Union(Expression(Integer),...) +--E 315 + +--S 316 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 317 + +)clear all + +--S 318 of 1353 +t0:=(a+b*x)*(d+e*x)^m*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R m | 2 2 2 +--R (1) (b x + a)(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1353 +r0:=-2*(b*d-a*e)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(2+m)*(3+m))+_ + 2*(b*d-a*e)^2*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(1+m)*_ + (2+m)*(3+m)*(a+b*x))+(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e*(3+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (b e m + 3b e m + 2b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a b e m + (8a b e - 2b d e)m + 6a b e - 2b d e)x + a e m +--R + +--R 2 2 2 2 2 2 +--R (5a e - 2a b d e)m + 6a e - 6a b d e + 2b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 3 3 +--R (b e m + 3b e m + 2b e )x +--R + +--R 3 2 2 2 3 2 2 3 2 +--R ((2a b e + b d e )m + (8a b e + b d e )m + 6a b e )x +--R + +--R 2 3 2 2 2 3 2 2 2 2 3 +--R ((a e + 2a b d e )m + (5a e + 6a b d e - 2b d e)m + 6a e )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 3 +--R a d e m + (5a d e - 2a b d e)m + 6a d e - 6a b d e + 2b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 3 3 3 2 3 3 +--R e m + 6e m + 11e m + 6e +--R Type: Union(Expression(Integer),...) +--E 320 + +--S 321 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 3 3 3 3 4 +--R (b e m + 3b e m + 2b e )x +--R + +--R 2 3 3 2 2 2 3 3 2 2 3 3 +--R ((3a b e + b d e )m + (11a b e + b d e )m + 8a b e )x +--R + +--R 2 3 2 2 2 2 3 2 2 3 2 +--R (3a b e + 3a b d e )m + (13a b e + 7a b d e - 2b d e)m +--R + +--R 2 3 +--R 12a b e +--R * +--R 2 +--R x +--R + +--R 3 3 2 2 2 3 3 2 2 2 2 3 3 +--R (a e + 3a b d e )m + (5a e + 11a b d e - 4a b d e)m + 6a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 6a b d e + 2b d +--R * +--R x +--R + +--R 3 2 2 3 2 2 2 3 2 2 2 2 3 +--R a d e m + (5a d e - 2a b d e)m + 6a d e - 6a b d e + 2a b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 2 2 2 2 2 2 2 +--R (- b e m - 3b e m - 2b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 2a b e m + (- 8a b e + 2b d e)m - 6a b e + 2b d e)x - a e m +--R + +--R 2 2 2 2 2 2 +--R (- 5a e + 2a b d e)m - 6a e + 6a b d e - 2b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x +--R + +--R 3 +--R - a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 322 + +)clear all + +--S 323 of 1353 +t0:=(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b e x + (a e + 5b d e )x + (5a d e + 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a d e + 10b d e )x + (10a d e + 5b d e)x + (5a d e + b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1353 +r0:=-1/28*(b*d-a*e)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 1/168*(b*d-a*e)^2*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 1/8*(a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 8 8 8 2 7 7 +--R 21b e x + (48a b e + 120b d e )x +--R + +--R 2 8 7 2 2 6 6 +--R (28a e + 280a b d e + 280b d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (168a d e + 672a b d e + 336b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (420a d e + 840a b d e + 210b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 2 4 4 5 3 2 +--R (560a d e + 560a b d e + 56b d e )x + (420a d e + 168a b d e )x +--R + +--R 2 5 3 2 6 2 7 2 8 +--R 168a d e x + 28a d e - 8a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 168b e x + 168a e +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 8 5 2 4 7 +--R 21b e x + (48a b e + 120b d e )x +--R + +--R 2 5 4 2 2 3 6 +--R (28a e + 280a b d e + 280b d e )x +--R + +--R 2 4 2 3 2 3 2 5 +--R (168a d e + 672a b d e + 336b d e )x +--R + +--R 2 2 3 3 2 2 4 4 +--R (420a d e + 840a b d e + 210b d e)x +--R + +--R 2 3 2 4 2 5 3 2 4 5 2 2 5 +--R (560a d e + 560a b d e + 56b d )x + (420a d e + 168a b d )x + 168a d x +--R / +--R 168 +--R Type: Union(Expression(Integer),...) +--E 325 + +--S 326 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 8 8 8 2 7 7 +--R - 21b e x + (- 48a b e - 120b d e )x +--R + +--R 2 8 7 2 2 6 6 +--R (- 28a e - 280a b d e - 280b d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (- 168a d e - 672a b d e - 336b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (- 420a d e - 840a b d e - 210b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (- 560a d e - 560a b d e - 56b d e )x +--R + +--R 2 4 4 5 3 2 2 5 3 2 6 2 7 2 8 +--R (- 420a d e - 168a b d e )x - 168a d e x - 28a d e + 8a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 8 9 2 8 3 7 8 +--R 21b e x + (69a b e + 120b d e )x +--R + +--R 2 8 2 7 3 2 6 7 +--R (76a b e + 400a b d e + 280b d e )x +--R + +--R 3 8 2 7 2 2 6 3 3 5 6 +--R (28a e + 448a b d e + 952a b d e + 336b d e )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 5 +--R (168a d e + 1092a b d e + 1176a b d e + 210b d e )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 4 +--R (420a d e + 1400a b d e + 770a b d e + 56b d e )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 3 4 4 2 5 3 2 +--R (560a d e + 980a b d e + 224a b d e )x + (420a d e + 336a b d e )x +--R + +--R 3 5 3 +--R 168a d e x +--R / +--R 3 3 +--R 168b e x + 168a e +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 5 7 5 2 4 6 2 5 4 2 2 3 5 +--R b e x + (2a b e + 5b d e )x + (a e + 10a b d e + 10b d e )x +--R + +--R 2 4 2 3 2 3 2 4 +--R (5a d e + 20a b d e + 10b d e )x +--R + +--R 2 2 3 3 2 2 4 3 2 3 2 4 2 5 2 +--R (10a d e + 20a b d e + 5b d e)x + (10a d e + 10a b d e + b d )x +--R + +--R 2 4 5 2 5 +--R (5a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 5 8 2 5 3 4 7 +--R - b e x + (- 3a b e - 5b d e )x +--R + +--R 2 5 2 4 3 2 3 6 +--R (- 3a b e - 15a b d e - 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 5 +--R (- a e - 15a b d e - 30a b d e - 10b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 4 +--R (- 5a d e - 30a b d e - 30a b d e - 5b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (- 10a d e - 30a b d e - 15a b d e - b d )x +--R + +--R 3 3 2 2 4 2 5 2 3 4 2 5 3 5 +--R (- 10a d e - 15a b d e - 3a b d )x + (- 5a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 1353 +t0:=(a+b*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1353 +r0:=-1/21*(b*d-a*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 1/105*(b*d-a*e)^2*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 1/7*(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 7 7 7 2 6 6 +--R 15b e x + (35a b e + 70b d e )x +--R + +--R 2 7 6 2 2 5 5 +--R (21a e + 168a b d e + 126b d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (105a d e + 315a b d e + 105b d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 2 3 4 4 3 2 +--R (210a d e + 280a b d e + 35b d e )x + (210a d e + 105a b d e )x +--R + +--R 2 4 3 2 5 2 6 2 7 +--R 105a d e x + 21a d e - 7a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 7 4 2 3 6 2 4 3 2 2 2 5 +--R 15b e x + (35a b e + 70b d e )x + (21a e + 168a b d e + 126b d e )x +--R + +--R 2 3 2 2 2 3 4 +--R (105a d e + 315a b d e + 105b d e)x +--R + +--R 2 2 2 3 2 4 3 2 3 4 2 2 4 +--R (210a d e + 280a b d e + 35b d )x + (210a d e + 105a b d )x + 105a d x +--R / +--R 105 +--R Type: Union(Expression(Integer),...) +--E 330 + +--S 331 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 7 7 7 2 6 6 +--R - 15b e x + (- 35a b e - 70b d e )x +--R + +--R 2 7 6 2 2 5 5 +--R (- 21a e - 168a b d e - 126b d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (- 105a d e - 315a b d e - 105b d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 +--R (- 210a d e - 280a b d e - 35b d e )x +--R + +--R 2 3 4 4 3 2 2 4 3 2 5 2 6 2 7 +--R (- 210a d e - 105a b d e )x - 105a d e x - 21a d e + 7a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 7 8 2 7 3 6 7 +--R 15b e x + (50a b e + 70b d e )x +--R + +--R 2 7 2 6 3 2 5 6 +--R (56a b e + 238a b d e + 126b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 5 +--R (21a e + 273a b d e + 441a b d e + 105b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 4 +--R (105a d e + 525a b d e + 385a b d e + 35b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 3 3 4 2 4 3 2 +--R (210a d e + 490a b d e + 140a b d e )x + (210a d e + 210a b d e )x +--R + +--R 3 4 3 +--R 105a d e x +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 4 6 4 2 3 5 2 4 3 2 2 2 4 +--R b e x + (2a b e + 4b d e )x + (a e + 8a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 3 2 2 2 3 2 4 2 +--R (4a d e + 12a b d e + 4b d e)x + (6a d e + 8a b d e + b d )x +--R + +--R 2 3 4 2 4 +--R (4a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R - b e x + (- 3a b e - 4b d e )x + (- 3a b e - 12a b d e - 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (- a e - 12a b d e - 18a b d e - 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (- 4a d e - 18a b d e - 12a b d e - b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (- 6a d e - 12a b d e - 3a b d )x + (- 4a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 332 + +)clear all + +--S 333 of 1353 +t0:=(a+b*x)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1353 +r0:=-1/15*(b*d-a*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/60*(b*d-_ + a*e)^2*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+1/6*(a+b*x)*_ + (d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 2 6 5 2 2 4 4 +--R 10b e x + (24a b e + 36b d e )x + (15a e + 90a b d e + 45b d e )x +--R + +--R 2 5 2 4 2 3 3 3 2 2 4 3 3 2 +--R (60a d e + 120a b d e + 20b d e )x + (90a d e + 60a b d e )x +--R + +--R 2 3 3 2 4 2 5 2 6 +--R 60a d e x + 15a d e - 6a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R 10b e x + (24a b e + 36b d e )x + (15a e + 90a b d e + 45b d e)x +--R + +--R 2 2 2 2 3 3 2 2 3 2 2 3 +--R (60a d e + 120a b d e + 20b d )x + (90a d e + 60a b d )x + 60a d x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 335 + +--S 336 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 6 6 6 2 5 5 +--R - 10b e x + (- 24a b e - 36b d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (- 15a e - 90a b d e - 45b d e )x +--R + +--R 2 5 2 4 2 3 3 3 2 2 4 3 3 2 +--R (- 60a d e - 120a b d e - 20b d e )x + (- 90a d e - 60a b d e )x +--R + +--R 2 3 3 2 4 2 5 2 6 +--R - 60a d e x - 15a d e + 6a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 6 7 2 6 3 5 6 +--R 10b e x + (34a b e + 36b d e )x +--R + +--R 2 6 2 5 3 2 4 5 +--R (39a b e + 126a b d e + 45b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 4 +--R (15a e + 150a b d e + 165a b d e + 20b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 3 2 4 2 3 3 2 +--R (60a d e + 210a b d e + 80a b d e )x + (90a d e + 120a b d e )x +--R + +--R 3 3 3 +--R 60a d e x +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R - b e x + (- 3a b e - 3b d e )x + (- 3a b e - 9a b d e - 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a e - 9a b d e - 9a b d e - b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 3a d e - 9a b d e - 3a b d )x + (- 3a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 337 + +)clear all + +--S 338 of 1353 +t0:=(a+b*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 1353 +r0:=1/30*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^3+1/10*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/5*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/b +--R +--R +--R (2) +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R 6b e x + (9a b e + 15b d e)x + (a b e + 25a b d e + 10b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- a b e + 5a b d e + 20a b d )x + a e - 5a b d e + 10a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 30b +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 6b e x + (15a b e + 15b d e)x + (10a e + 40a b d e + 10b d )x +--R + +--R 2 2 2 2 2 +--R (30a d e + 30a b d )x + 30a d x +--R / +--R 30 +--R Type: Union(Expression(Integer),...) +--E 340 + +--S 341 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 4 3 2 4 3 +--R - 6b e x + (- 9a b e - 15b d e)x +--R + +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (- a b e - 25a b d e - 10b d )x + (a b e - 5a b d e - 20a b d )x +--R + +--R 4 2 3 2 2 2 +--R - a e + 5a b d e - 10a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 6b e x + (15a b e + 15b d e)x + (10a b e + 40a b d e + 10b d )x +--R + +--R 2 3 4 2 2 2 3 2 +--R (30a b d e + 30a b d )x + 30a b d x +--R / +--R 3 +--R 30b +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - b e x + (- 3a b e - 2b d e)x + (- 3a b e - 6a b d e - b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- a e - 6a b d e - 3a b d )x + (- 2a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 1353 +t0:=(a+b*x)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 | 2 2 2 +--R (1) (b e x + (a e + b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1353 +r0:=1/12*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/4*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/b +--R +--R +--R (2) +--R 3 3 2 3 2 2 2 3 2 +--R (3b e x + (5a b e + 4b d)x + (a b e + 8a b d)x - a e + 4a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 12b +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 3 2 2 2 +--R 3b e x + (8a b e + 4b d)x + (6a e + 12a b d)x + 12a d x +--R (3) ---------------------------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 345 + +--S 346 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 3 2 2 2 3 2 +--R (- 3b e x + (- 5a b e - 4b d)x + (- a b e - 8a b d)x + a e - 4a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 3 4 3 2 2 3 2 2 2 +--R 3b e x + (8a b e + 4b d)x + (6a b e + 12a b d)x + 12a b d x +--R / +--R 2 +--R 12b +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + 2a b x + a +--R + +--R 3 4 2 3 3 2 2 2 3 2 +--R - b e x + (- 3a b e - b d)x + (- 3a b e - 3a b d)x + (- a e - 3a b d)x +--R + +--R 3 +--R - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 347 + +)clear all + +--S 348 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (1) (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 348 + +--S 349 of 1353 +r0:=1/3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b +--R +--R +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R (2) ----------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 +--R b x + 3a b x + 3a x +--R (3) --------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 350 + +--S 351 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 +--R (- b x - 2a b x - a )\|b x + 2a b x + a + b x + 3a b x + 3a b x +--R (4) --------------------------------------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 352 + +)clear all + +--S 353 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1353 +r0:=-(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e+(b*d-a*e)^2*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(e x + d) + b e x + (4a b e - 2b d e)x +--R + +--R 2 2 +--R 3a e - 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 2b e x + 2a e +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(e x + d) + b e x + (4a b e - 2b d e)x +--R (3) --------------------------------------------------------------------- +--R 3 +--R 2e +--R Type: Union(Expression(Integer),...) +--E 355 + +--S 356 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 +--R (- 2a e + 4a b d e - 2b d )log(e x + d) - b e x +--R + +--R 2 2 2 2 +--R (- 4a b e + 2b d e)x - 3a e + 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((2a b e - 4a b d e + 2b d )x + 2a e - 4a b d e + 2a b d )log(e x + d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 +--R b e x + (5a b e - 2b d e)x + (4a b e - 2a b d e)x +--R / +--R 3 3 +--R 2b e x + 2a e +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1353 +r0:=2*b*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2-(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e*(d+e*x))-2*b*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((2a b e - 2b d e)x + 2a b d e - 2b d )log(e x + d) + b e x +--R + +--R 2 2 2 +--R 2b d e x - a e + 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 +--R ((2a b e - 2b d e)x + 2a b d e - 2b d )log(e x + d) + b e x + b d e x +--R + +--R 2 2 2 2 +--R - a e + 2a b d e - b d +--R / +--R 4 3 +--R e x + d e +--R Type: Union(Expression(Integer),...) +--E 360 + +--S 361 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 +--R ((- 2a b e + 2b d e)x - 2a b d e + 2b d )log(e x + d) - b e x +--R + +--R 2 2 2 +--R - 2b d e x + a e - 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 3 2 2 2 2 +--R ((2a b e - 2b d e)x + (2a b e - 2b d )x + 2a b d e - 2a b d ) +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 3 2 +--R b e x + (a b e + b d e)x + (- a b e + 3a b d e - b d )x - a e +--R + +--R 2 2 2 +--R 2a b d e - a b d +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 362 + +)clear all + +--S 363 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1353 +r0:=-1/2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^2)+b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x))+b^2*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) - b e x +--R + +--R 2 2 2 2 2 2 +--R (- 4a b e + 2b d e)x - a e - 2a b d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) + (- 4a b e + 4b d e)x - a e +--R + +--R 2 2 +--R - 2a b d e + 3b d +--R / +--R 5 2 4 2 3 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 365 + +--S 366 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4b d e x - 2b d )log(e x + d) + b e x +--R + +--R 2 2 2 2 2 2 +--R (4a b e - 2b d e)x + a e + 2a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 3 2 2 2 +--R (2b e x + (2a b e + 4b d e)x + (4a b d e + 2b d )x + 2a b d ) +--R * +--R log(e x + d) +--R + +--R 2 2 3 2 2 2 2 3 2 3 2 +--R (- 4a b e + 4b d e)x + (- 5a b e + 2a b d e + 3b d )x - a e +--R + +--R 2 2 2 +--R - 2a b d e + 3a b d +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 367 + +)clear all + +--S 368 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1353 +r0:=1/3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^3) +--R +--R +--R (2) +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (- b x - 2a b x - a )\|b x + 2a b x + a +--R / +--R 4 3 3 3 2 2 2 2 2 3 +--R (3a e - 3b d e )x + (9a d e - 9b d e )x + (9a d e - 9b d e)x +--R + +--R 3 4 +--R 3a d e - 3b d +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 3b e x + (- 3a b e - 3b d e)x - a e - a b d e - b d +--R (3) --------------------------------------------------------- +--R 6 3 5 2 2 4 3 3 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 370 + +--S 371 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 3 2 3 2 3 | 2 2 2 2 3 3 2 2 +--R (b e x + 2a b e x + a e )\|b x + 2a b x + a + (- 3a b e + 3b d e )x +--R + +--R 2 3 3 2 3 3 3 3 +--R (- 3a b e + 3b d e)x - a e + b d +--R / +--R 7 6 3 6 2 5 2 2 5 3 4 +--R (3a e - 3b d e )x + (9a d e - 9b d e )x + (9a d e - 9b d e )x +--R + +--R 3 4 4 3 +--R 3a d e - 3b d e +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1353 +r0:=1/4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^4)+_ + 1/12*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^3) +--R +--R +--R (2) +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (- a b e + 4b d)x + (- 5a b e + 8a b d)x - 3a e + 4a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 6 5 2 2 4 4 2 5 2 4 2 3 3 3 +--R (12a e - 24a b d e + 12b d e )x + (48a d e - 96a b d e + 48b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (72a d e - 144a b d e + 72b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (48a d e - 96a b d e + 48b d e)x + 12a d e - 24a b d e + 12b d +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 6b e x + (- 8a b e - 4b d e)x - 3a e - 2a b d e - b d +--R (3) ----------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 375 + +--S 376 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 3 2 4 3 3 2 2 4 2 3 3 4 +--R - b e x + (a b e - 4b d e )x + (5a b e - 8a b d e )x + 3a e +--R + +--R 2 3 +--R - 4a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 4 3 3 4 2 2 2 3 4 2 2 3 4 3 +--R (- 6a b e + 12a b d e - 6b d e )x + (- 8a b e + 12a b d e - 4b d e)x +--R + +--R 4 4 3 3 4 4 +--R - 3a e + 4a b d e - b d +--R / +--R 2 9 8 2 2 7 4 2 8 2 7 2 3 6 3 +--R (12a e - 24a b d e + 12b d e )x + (48a d e - 96a b d e + 48b d e )x +--R + +--R 2 2 7 3 6 2 4 5 2 +--R (72a d e - 144a b d e + 72b d e )x +--R + +--R 2 3 6 4 5 2 5 4 2 4 5 5 4 2 6 3 +--R (48a d e - 96a b d e + 48b d e )x + 12a d e - 24a b d e + 12b d e +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------- +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 377 + +)clear all + +--S 378 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1353 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^5)+_ + 1/10*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^4)+_ + 1/30*b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^3*(d+e*x)^3) +--R +--R +--R (2) +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R - b e x + (a b e - 5b d e)x + (- a b e + 5a b d e - 10b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- 9a b e + 25a b d e - 20a b d )x - 6a e + 15a b d e - 10a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 8 2 7 2 2 6 3 3 5 5 +--R (30a e - 90a b d e + 90a b d e - 30b d e )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 4 +--R (150a d e - 450a b d e + 450a b d e - 150b d e )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 3 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 6 2 2 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 4 4 2 5 3 2 6 2 3 7 3 5 3 +--R (150a d e - 450a b d e + 450a b d e - 150b d e)x + 30a d e +--R + +--R 2 6 2 2 7 3 8 +--R - 90a b d e + 90a b d e - 30b d +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 10b e x + (- 15a b e - 5b d e)x - 6a e - 3a b d e - b d +--R (3) -------------------------------------------------------------- +--R 8 5 7 4 2 6 3 3 5 2 4 4 5 3 +--R 30e x + 150d e x + 300d e x + 300d e x + 150d e x + 30d e +--R Type: Union(Expression(Integer),...) +--E 380 + +--S 381 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 4 3 5 4 4 3 2 2 5 3 4 4 2 3 2 +--R b e x + (- a b e + 5b d e )x + (a b e - 5a b d e + 10b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 5 3 4 2 2 2 3 +--R (9a b e - 25a b d e + 20a b d e )x + 6a e - 15a b d e + 10a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 10a b e + 30a b d e - 30a b d e + 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 5 4 5 5 4 4 +--R (- 15a b e + 40a b d e - 30a b d e + 5b d e)x - 6a e + 15a b d e +--R + +--R 3 2 2 3 5 5 +--R - 10a b d e + b d +--R / +--R 3 11 2 10 2 2 9 3 3 8 5 +--R (30a e - 90a b d e + 90a b d e - 30b d e )x +--R + +--R 3 10 2 2 9 2 3 8 3 4 7 4 +--R (150a d e - 450a b d e + 450a b d e - 150b d e )x +--R + +--R 3 2 9 2 3 8 2 4 7 3 5 6 3 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 3 8 2 4 7 2 5 6 3 6 5 2 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 3 5 6 +--R (150a d e - 450a b d e + 450a b d e - 150b d e )x + 30a d e +--R + +--R 2 6 5 2 7 4 3 8 3 +--R - 90a b d e + 90a b d e - 30b d e +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 382 + +)clear all + +--S 383 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1353 +r0:=-1/6*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^6)-_ + 1/12*b*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^5)-1/60*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 15b e x + (- 24a b e - 6b d e)x - 10a e - 4a b d e - b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R - 15b e x + (- 24a b e - 6b d e)x - 10a e - 4a b d e - b d +--R --------------------------------------------------------------------------- +--R 9 6 8 5 2 7 4 3 6 3 4 5 2 5 4 6 3 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 385 + +--S 386 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (24a b e + 6b d e)x + 10a e + 4a b d e + b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 15b e x + (- 39a b e - 6b d e)x + (- 34a b e - 10a b d e - b d )x +--R + +--R 3 2 2 2 2 +--R - 10a e - 4a b d e - a b d +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1353 +r0:=-1/7*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^7)-_ + 2/35*b*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^6)-1/105*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 21b e x + (- 35a b e - 7b d e)x - 15a e - 5a b d e - b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 8 10 9 7 9 2 8 6 +--R 105b e x + (105a e + 735b d e )x + (735a d e + 2205b d e )x +--R + +--R 2 8 3 7 5 3 7 4 6 4 +--R (2205a d e + 3675b d e )x + (3675a d e + 3675b d e )x +--R + +--R 4 6 5 5 3 5 5 6 4 2 +--R (3675a d e + 2205b d e )x + (2205a d e + 735b d e )x +--R + +--R 6 4 7 3 7 3 +--R (735a d e + 105b d e )x + 105a d e +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R - 21b e x + (- 35a b e - 7b d e)x - 15a e - 5a b d e - b d +--R / +--R 10 7 9 6 2 8 5 3 7 4 4 6 3 5 5 2 +--R 105e x + 735d e x + 2205d e x + 3675d e x + 3675d e x + 2205d e x +--R + +--R 6 4 7 3 +--R 735d e x + 105d e +--R Type: Union(Expression(Integer),...) +--E 390 + +--S 391 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (21b e x + (35a b e + 7b d e)x + 15a e + 5a b d e + b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 21b e x + (- 56a b e - 7b d e)x + (- 50a b e - 12a b d e - b d )x +--R + +--R 3 2 2 2 2 +--R - 15a e - 5a b d e - a b d +--R / +--R 10 8 10 9 7 9 2 8 6 +--R 105b e x + (105a e + 735b d e )x + (735a d e + 2205b d e )x +--R + +--R 2 8 3 7 5 3 7 4 6 4 +--R (2205a d e + 3675b d e )x + (3675a d e + 3675b d e )x +--R + +--R 4 6 5 5 3 5 5 6 4 2 +--R (3675a d e + 2205b d e )x + (2205a d e + 735b d e )x +--R + +--R 6 4 7 3 7 3 +--R (735a d e + 105b d e )x + 105a d e +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 392 + +)clear all + +--S 393 of 1353 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 m | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 393 + +--S 394 of 1353 +r0:=-4*(b*d-a*e)*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(4+m)*(5+m))+_ + (a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(5+m))-_ + 24*(b*d-a*e)^3*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(2+m)*_ + (3+m)*(4+m)*(5+m))+24*(b*d-a*e)^4*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(1+m)*(2+m)*(3+m)*(4+m)*(5+m)*(a+b*x))+12*(b*d-a*e)^2*_ + (a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(3+m)*(4+m)*(5+m)) +--R +--R +--R (2) +--R 4 4 4 4 4 3 4 4 2 4 4 4 4 4 +--R (b e m + 10b e m + 35b e m + 50b e m + 24b e )x +--R + +--R 3 4 4 3 4 4 3 3 3 4 4 3 2 +--R 4a b e m + (44a b e - 4b d e )m + (164a b e - 24b d e )m +--R + +--R 3 4 4 3 3 4 4 3 +--R (244a b e - 44b d e )m + 120a b e - 24b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 2 2 4 3 3 3 +--R 6a b e m + (72a b e - 12a b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (294a b e - 96a b d e + 12b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 2 4 3 3 +--R (468a b e - 204a b d e + 36b d e )m + 240a b e - 120a b d e +--R + +--R 4 2 2 +--R 24b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 4 2 2 3 3 +--R 4a b e m + (52a b e - 12a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 2 +--R (236a b e - 120a b d e + 24a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 4 +--R (428a b e - 348a b d e + 144a b d e - 24b d e)m + 240a b e +--R + +--R 2 2 3 3 2 2 4 3 +--R - 240a b d e + 120a b d e - 24b d e +--R * +--R x +--R + +--R 4 4 4 4 4 3 3 3 4 4 3 3 2 2 2 2 2 +--R a e m + (14a e - 4a b d e )m + (71a e - 48a b d e + 12a b d e )m +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (154a e - 188a b d e + 108a b d e - 24a b d e)m + 120a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 240a b d e + 240a b d e - 120a b d e + 24b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 4 4 5 3 4 5 2 4 5 4 5 5 +--R (b e m + 10b e m + 35b e m + 50b e m + 24b e )x +--R + +--R 3 5 4 4 4 3 5 4 4 3 +--R (4a b e + b d e )m + (44a b e + 6b d e )m +--R + +--R 3 5 4 4 2 3 5 4 4 3 5 +--R (164a b e + 11b d e )m + (244a b e + 6b d e )m + 120a b e +--R * +--R 4 +--R x +--R + +--R 2 2 5 3 4 4 2 2 5 3 4 4 2 3 3 +--R (6a b e + 4a b d e )m + (72a b e + 32a b d e - 4b d e )m +--R + +--R 2 2 5 3 4 4 2 3 2 +--R (294a b e + 68a b d e - 12b d e )m +--R + +--R 2 2 5 3 4 4 2 3 2 2 5 +--R (468a b e + 40a b d e - 8b d e )m + 240a b e +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 4 4 3 5 2 2 4 3 2 3 3 +--R (4a b e + 6a b d e )m + (52a b e + 60a b d e - 12a b d e )m +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (236a b e + 174a b d e - 72a b d e + 12b d e )m +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 5 +--R (428a b e + 120a b d e - 60a b d e + 12b d e )m + 240a b e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 4 4 5 3 4 2 2 2 3 3 +--R (a e + 4a b d e )m + (14a e + 48a b d e - 12a b d e )m +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 2 +--R (71a e + 188a b d e - 108a b d e + 24a b d e )m +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (154a e + 240a b d e - 240a b d e + 120a b d e - 24b d e)m +--R + +--R 4 5 +--R 120a e +--R * +--R x +--R + +--R 4 4 4 4 4 3 2 3 3 +--R a d e m + (14a d e - 4a b d e )m +--R + +--R 4 4 3 2 3 2 2 3 2 2 +--R (71a d e - 48a b d e + 12a b d e )m +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 4 +--R (154a d e - 188a b d e + 108a b d e - 24a b d e)m + 120a d e +--R + +--R 3 2 3 2 2 3 2 3 4 4 5 +--R - 240a b d e + 240a b d e - 120a b d e + 24b d +--R * +--R m log(e x + d) +--R %e +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R e m + 15e m + 85e m + 225e m + 274e m + 120e +--R Type: Union(Expression(Integer),...) +--E 395 + +--S 396 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 4 5 5 3 5 5 2 5 5 5 5 6 +--R (b e m + 10b e m + 35b e m + 50b e m + 24b e )x +--R + +--R 4 5 5 4 4 4 5 5 4 3 +--R (5a b e + b d e )m + (54a b e + 6b d e )m +--R + +--R 4 5 5 4 2 4 5 5 4 4 5 +--R (199a b e + 11b d e )m + (294a b e + 6b d e )m + 144a b e +--R * +--R 5 +--R x +--R + +--R 2 3 5 4 4 4 2 3 5 4 4 5 2 3 3 +--R (10a b e + 5a b d e )m + (116a b e + 38a b d e - 4b d e )m +--R + +--R 2 3 5 4 4 5 2 3 2 +--R (458a b e + 79a b d e - 12b d e )m +--R + +--R 2 3 5 4 4 5 2 3 2 3 5 +--R (712a b e + 46a b d e - 8b d e )m + 360a b e +--R * +--R 4 +--R x +--R + +--R 3 2 5 2 3 4 4 +--R (10a b e + 10a b d e )m +--R + +--R 3 2 5 2 3 4 4 2 3 3 +--R (124a b e + 92a b d e - 16a b d e )m +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (530a b e + 242a b d e - 84a b d e + 12b d e )m +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 2 5 +--R (896a b e + 160a b d e - 68a b d e + 12b d e )m + 480a b e +--R * +--R 3 +--R x +--R + +--R 4 5 3 2 4 4 +--R (5a b e + 10a b d e )m +--R + +--R 4 5 3 2 4 2 3 2 3 3 +--R (66a b e + 108a b d e - 24a b d e )m +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 2 +--R (307a b e + 362a b d e - 180a b d e + 36a b d e )m +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (582a b e + 360a b d e - 300a b d e + 132a b d e - 24b d e)m +--R + +--R 4 5 +--R 360a b e +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 5 5 4 4 3 2 2 3 3 +--R (a e + 5a b d e )m + (14a e + 62a b d e - 16a b d e )m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 2 +--R (71a e + 259a b d e - 156a b d e + 36a b d e )m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R (154a e + 394a b d e - 428a b d e + 228a b d e - 48a b d e)m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 120a e + 120a b d e - 240a b d e + 240a b d e - 120a b d e +--R + +--R 5 5 +--R 24b d +--R * +--R x +--R + +--R 5 4 4 5 4 4 2 3 3 +--R a d e m + (14a d e - 4a b d e )m +--R + +--R 5 4 4 2 3 3 2 3 2 2 +--R (71a d e - 48a b d e + 12a b d e )m +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 5 4 +--R (154a d e - 188a b d e + 108a b d e - 24a b d e)m + 120a d e +--R + +--R 4 2 3 3 2 3 2 2 3 4 4 5 +--R - 240a b d e + 240a b d e - 120a b d e + 24a b d +--R * +--R m log(e x + d) +--R %e +--R + +--R 4 4 4 4 4 3 4 4 2 4 4 4 4 4 +--R (- b e m - 10b e m - 35b e m - 50b e m - 24b e )x +--R + +--R 3 4 4 3 4 4 3 3 +--R - 4a b e m + (- 44a b e + 4b d e )m +--R + +--R 3 4 4 3 2 3 4 4 3 +--R (- 164a b e + 24b d e )m + (- 244a b e + 44b d e )m +--R + +--R 3 4 4 3 +--R - 120a b e + 24b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 2 2 4 3 3 3 +--R - 6a b e m + (- 72a b e + 12a b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 294a b e + 96a b d e - 12b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 2 4 3 3 +--R (- 468a b e + 204a b d e - 36b d e )m - 240a b e + 120a b d e +--R + +--R 4 2 2 +--R - 24b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 4 2 2 3 3 +--R - 4a b e m + (- 52a b e + 12a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 2 +--R (- 236a b e + 120a b d e - 24a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 4 +--R (- 428a b e + 348a b d e - 144a b d e + 24b d e)m - 240a b e +--R + +--R 2 2 3 3 2 2 4 3 +--R 240a b d e - 120a b d e + 24b d e +--R * +--R x +--R + +--R 4 4 4 4 4 3 3 3 +--R - a e m + (- 14a e + 4a b d e )m +--R + +--R 4 4 3 3 2 2 2 2 2 +--R (- 71a e + 48a b d e - 12a b d e )m +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 154a e + 188a b d e - 108a b d e + 24a b d e)m - 120a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 240a b d e - 240a b d e + 120a b d e - 24b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 397 + +)clear all + +--S 398 of 1353 +t0:=(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 7 10 2 7 3 6 9 2 7 2 6 3 2 5 8 +--R b e x + (3a b e + 7b d e )x + (3a b e + 21a b d e + 21b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 7 +--R (a e + 21a b d e + 63a b d e + 35b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 6 +--R (7a d e + 63a b d e + 105a b d e + 35b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 5 +--R (21a d e + 105a b d e + 105a b d e + 21b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 4 +--R (35a d e + 105a b d e + 63a b d e + 7b d e)x +--R + +--R 3 4 3 2 5 2 2 6 3 7 3 +--R (35a d e + 63a b d e + 21a b d e + b d )x +--R + +--R 3 5 2 2 6 2 7 2 3 6 2 7 3 7 +--R (21a d e + 21a b d e + 3a b d )x + (7a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1353 +r0:=-1/33*(b*d-a*e)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/12*(a+b*x)*_ + (d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/495*(b*d-a*e)^3*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/3960*(b*d-a*e)^4*(d+e*x)^8*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/110*(b*d-a*e)^2*(a+b*x)*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 12 12 3 12 4 11 11 +--R 330b e x + (1440a b e + 2520b d e )x +--R + +--R 2 2 12 3 11 4 2 10 10 +--R (2376a b e + 11088a b d e + 8316b d e )x +--R + +--R 3 12 2 2 11 3 2 10 4 3 9 9 +--R (1760a b e + 18480a b d e + 36960a b d e + 15400b d e )x +--R + +--R 4 12 3 11 2 2 2 10 3 3 9 +--R 495a e + 13860a b d e + 62370a b d e + 69300a b d e +--R + +--R 4 4 8 +--R 17325b d e +--R * +--R 8 +--R x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 +--R 3960a d e + 47520a b d e + 118800a b d e + 79200a b d e +--R + +--R 4 5 7 +--R 11880b d e +--R * +--R 7 +--R x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 +--R 13860a d e + 92400a b d e + 138600a b d e + 55440a b d e +--R + +--R 4 6 6 +--R 4620b d e +--R * +--R 6 +--R x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 +--R 27720a d e + 110880a b d e + 99792a b d e + 22176a b d e +--R + +--R 4 7 5 +--R 792b d e +--R * +--R 5 +--R x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 +--R (34650a d e + 83160a b d e + 41580a b d e + 3960a b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 +--R (27720a d e + 36960a b d e + 7920a b d e )x +--R + +--R 4 6 6 3 7 5 2 4 7 5 4 8 4 3 9 3 +--R (13860a d e + 7920a b d e )x + 3960a d e x + 495a d e - 220a b d e +--R + +--R 2 2 10 2 3 11 4 12 +--R 66a b d e - 12a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 3960b e x + 3960a e +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 12 3 7 4 6 11 +--R 330b e x + (1440a b e + 2520b d e )x +--R + +--R 2 2 7 3 6 4 2 5 10 +--R (2376a b e + 11088a b d e + 8316b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 9 +--R (1760a b e + 18480a b d e + 36960a b d e + 15400b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 8 +--R (495a e + 13860a b d e + 62370a b d e + 69300a b d e + 17325b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R 3960a d e + 47520a b d e + 118800a b d e + 79200a b d e +--R + +--R 4 5 2 +--R 11880b d e +--R * +--R 7 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R 13860a d e + 92400a b d e + 138600a b d e + 55440a b d e +--R + +--R 4 6 +--R 4620b d e +--R * +--R 6 +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 5 +--R (27720a d e + 110880a b d e + 99792a b d e + 22176a b d e + 792b d )x +--R + +--R 4 4 3 3 5 2 2 2 6 3 7 4 +--R (34650a d e + 83160a b d e + 41580a b d e + 3960a b d )x +--R + +--R 4 5 2 3 6 2 2 7 3 4 6 3 7 2 +--R (27720a d e + 36960a b d e + 7920a b d )x + (13860a d e + 7920a b d )x +--R + +--R 4 7 +--R 3960a d x +--R / +--R 3960 +--R Type: Union(Expression(Integer),...) +--E 400 + +--S 401 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 12 12 3 12 4 11 11 +--R - 330b e x + (- 1440a b e - 2520b d e )x +--R + +--R 2 2 12 3 11 4 2 10 10 +--R (- 2376a b e - 11088a b d e - 8316b d e )x +--R + +--R 3 12 2 2 11 3 2 10 4 3 9 9 +--R (- 1760a b e - 18480a b d e - 36960a b d e - 15400b d e )x +--R + +--R 4 12 3 11 2 2 2 10 3 3 9 +--R - 495a e - 13860a b d e - 62370a b d e - 69300a b d e +--R + +--R 4 4 8 +--R - 17325b d e +--R * +--R 8 +--R x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 +--R - 3960a d e - 47520a b d e - 118800a b d e - 79200a b d e +--R + +--R 4 5 7 +--R - 11880b d e +--R * +--R 7 +--R x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 +--R - 13860a d e - 92400a b d e - 138600a b d e - 55440a b d e +--R + +--R 4 6 6 +--R - 4620b d e +--R * +--R 6 +--R x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 +--R - 27720a d e - 110880a b d e - 99792a b d e - 22176a b d e +--R + +--R 4 7 5 +--R - 792b d e +--R * +--R 5 +--R x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 +--R (- 34650a d e - 83160a b d e - 41580a b d e - 3960a b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 +--R (- 27720a d e - 36960a b d e - 7920a b d e )x +--R + +--R 4 6 6 3 7 5 2 4 7 5 4 8 4 +--R (- 13860a d e - 7920a b d e )x - 3960a d e x - 495a d e +--R + +--R 3 9 3 2 2 10 2 3 11 4 12 +--R 220a b d e - 66a b d e + 12a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 12 13 4 12 5 11 12 +--R 330b e x + (1770a b e + 2520b d e )x +--R + +--R 2 3 12 4 11 5 2 10 11 +--R (3816a b e + 13608a b d e + 8316b d e )x +--R + +--R 3 2 12 2 3 11 4 2 10 5 3 9 10 +--R (4136a b e + 29568a b d e + 45276a b d e + 15400b d e )x +--R + +--R 4 12 3 2 11 2 3 2 10 4 3 9 +--R 2255a b e + 32340a b d e + 99330a b d e + 84700a b d e +--R + +--R 5 4 8 +--R 17325b d e +--R * +--R 9 +--R x +--R + +--R 5 12 4 11 3 2 2 10 2 3 3 9 +--R 495a e + 17820a b d e + 109890a b d e + 188100a b d e +--R + +--R 4 4 8 5 5 7 +--R 96525a b d e + 11880b d e +--R * +--R 8 +--R x +--R + +--R 5 11 4 2 10 3 2 3 9 2 3 4 8 +--R 3960a d e + 61380a b d e + 211200a b d e + 217800a b d e +--R + +--R 4 5 7 5 6 6 +--R 67320a b d e + 4620b d e +--R * +--R 7 +--R x +--R + +--R 5 2 10 4 3 9 3 2 4 8 2 3 5 7 +--R 13860a d e + 120120a b d e + 249480a b d e + 155232a b d e +--R + +--R 4 6 6 5 7 5 +--R 26796a b d e + 792b d e +--R * +--R 6 +--R x +--R + +--R 5 3 9 4 4 8 3 2 5 7 2 3 6 6 +--R 27720a d e + 145530a b d e + 182952a b d e + 63756a b d e +--R + +--R 4 7 5 +--R 4752a b d e +--R * +--R 5 +--R x +--R + +--R 5 4 8 4 5 7 3 2 6 6 2 3 7 5 4 +--R (34650a d e + 110880a b d e + 78540a b d e + 11880a b d e )x +--R + +--R 5 5 7 4 6 6 3 2 7 5 3 +--R (27720a d e + 50820a b d e + 15840a b d e )x +--R + +--R 5 6 6 4 7 5 2 5 7 5 +--R (13860a d e + 11880a b d e )x + 3960a d e x +--R / +--R 5 5 +--R 3960b e x + 3960a e +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 7 11 3 7 4 6 10 +--R b e x + (4a b e + 7b d e )x +--R + +--R 2 2 7 3 6 4 2 5 9 +--R (6a b e + 28a b d e + 21b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 8 +--R (4a b e + 42a b d e + 84a b d e + 35b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 7 +--R (a e + 28a b d e + 126a b d e + 140a b d e + 35b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6 +--R (7a d e + 84a b d e + 210a b d e + 140a b d e + 21b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 5 +--R (21a d e + 140a b d e + 210a b d e + 84a b d e + 7b d e)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 4 +--R (35a d e + 140a b d e + 126a b d e + 28a b d e + b d )x +--R + +--R 4 4 3 3 5 2 2 2 6 3 7 3 +--R (35a d e + 84a b d e + 42a b d e + 4a b d )x +--R + +--R 4 5 2 3 6 2 2 7 2 4 6 3 7 4 7 +--R (21a d e + 28a b d e + 6a b d )x + (7a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 7 12 4 7 5 6 11 +--R - b e x + (- 5a b e - 7b d e )x +--R + +--R 2 3 7 4 6 5 2 5 10 +--R (- 10a b e - 35a b d e - 21b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 9 +--R (- 10a b e - 70a b d e - 105a b d e - 35b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 8 +--R (- 5a b e - 70a b d e - 210a b d e - 175a b d e - 35b d e )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 +--R - a e - 35a b d e - 210a b d e - 350a b d e - 175a b d e +--R + +--R 5 5 2 +--R - 21b d e +--R * +--R 7 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 +--R - 7a d e - 105a b d e - 350a b d e - 350a b d e - 105a b d e +--R + +--R 5 6 +--R - 7b d e +--R * +--R 6 +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 +--R - 21a d e - 175a b d e - 350a b d e - 210a b d e - 35a b d e +--R + +--R 5 7 +--R - b d +--R * +--R 5 +--R x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 4 +--R (- 35a d e - 175a b d e - 210a b d e - 70a b d e - 5a b d )x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 3 +--R (- 35a d e - 105a b d e - 70a b d e - 10a b d )x +--R + +--R 5 5 2 4 6 3 2 7 2 5 6 4 7 5 7 +--R (- 21a d e - 35a b d e - 10a b d )x + (- 7a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 1353 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 6 9 2 6 3 5 8 2 6 2 5 3 2 4 7 +--R b e x + (3a b e + 6b d e )x + (3a b e + 18a b d e + 15b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 6 +--R (a e + 18a b d e + 45a b d e + 20b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 5 +--R (6a d e + 45a b d e + 60a b d e + 15b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 4 +--R (15a d e + 60a b d e + 45a b d e + 6b d e)x +--R + +--R 3 3 3 2 4 2 2 5 3 6 3 +--R (20a d e + 45a b d e + 18a b d e + b d )x +--R + +--R 3 4 2 2 5 2 6 2 3 5 2 6 3 6 +--R (15a d e + 18a b d e + 3a b d )x + (6a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1353 +r0:=-2/55*(b*d-a*e)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/11*(a+b*x)*_ + (d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/330*(b*d-a*e)^3*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/2310*(b*d-a*e)^4*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/165*(b*d-a*e)^2*(a+b*x)*_ + (d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 11 11 3 11 4 10 10 +--R 210b e x + (924a b e + 1386b d e )x +--R + +--R 2 2 11 3 10 4 2 9 9 +--R (1540a b e + 6160a b d e + 3850b d e )x +--R + +--R 3 11 2 2 10 3 2 9 4 3 8 8 +--R (1155a b e + 10395a b d e + 17325a b d e + 5775b d e )x +--R + +--R 4 11 3 10 2 2 2 9 3 3 8 +--R 330a e + 7920a b d e + 29700a b d e + 26400a b d e +--R + +--R 4 4 7 +--R 4950b d e +--R * +--R 7 +--R x +--R + +--R 4 10 3 2 9 2 2 3 8 3 4 7 +--R 2310a d e + 23100a b d e + 46200a b d e + 23100a b d e +--R + +--R 4 5 6 +--R 2310b d e +--R * +--R 6 +--R x +--R + +--R 4 2 9 3 3 8 2 2 4 7 3 5 6 +--R 6930a d e + 36960a b d e + 41580a b d e + 11088a b d e +--R + +--R 4 6 5 +--R 462b d e +--R * +--R 5 +--R x +--R + +--R 4 3 8 3 4 7 2 2 5 6 3 6 5 4 +--R (11550a d e + 34650a b d e + 20790a b d e + 2310a b d e )x +--R + +--R 4 4 7 3 5 6 2 2 6 5 3 +--R (11550a d e + 18480a b d e + 4620a b d e )x +--R + +--R 4 5 6 3 6 5 2 4 6 5 4 7 4 3 8 3 +--R (6930a d e + 4620a b d e )x + 2310a d e x + 330a d e - 165a b d e +--R + +--R 2 2 9 2 3 10 4 11 +--R 55a b d e - 11a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2310b e x + 2310a e +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 11 3 6 4 5 10 +--R 210b e x + (924a b e + 1386b d e )x +--R + +--R 2 2 6 3 5 4 2 4 9 +--R (1540a b e + 6160a b d e + 3850b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 8 +--R (1155a b e + 10395a b d e + 17325a b d e + 5775b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 7 +--R (330a e + 7920a b d e + 29700a b d e + 26400a b d e + 4950b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 +--R 2310a d e + 23100a b d e + 46200a b d e + 23100a b d e +--R + +--R 4 5 +--R 2310b d e +--R * +--R 6 +--R x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 5 +--R (6930a d e + 36960a b d e + 41580a b d e + 11088a b d e + 462b d )x +--R + +--R 4 3 3 3 4 2 2 2 5 3 6 4 +--R (11550a d e + 34650a b d e + 20790a b d e + 2310a b d )x +--R + +--R 4 4 2 3 5 2 2 6 3 4 5 3 6 2 +--R (11550a d e + 18480a b d e + 4620a b d )x + (6930a d e + 4620a b d )x +--R + +--R 4 6 +--R 2310a d x +--R / +--R 2310 +--R Type: Union(Expression(Integer),...) +--E 405 + +--S 406 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 11 11 3 11 4 10 10 +--R - 210b e x + (- 924a b e - 1386b d e )x +--R + +--R 2 2 11 3 10 4 2 9 9 +--R (- 1540a b e - 6160a b d e - 3850b d e )x +--R + +--R 3 11 2 2 10 3 2 9 4 3 8 8 +--R (- 1155a b e - 10395a b d e - 17325a b d e - 5775b d e )x +--R + +--R 4 11 3 10 2 2 2 9 3 3 8 +--R - 330a e - 7920a b d e - 29700a b d e - 26400a b d e +--R + +--R 4 4 7 +--R - 4950b d e +--R * +--R 7 +--R x +--R + +--R 4 10 3 2 9 2 2 3 8 3 4 7 +--R - 2310a d e - 23100a b d e - 46200a b d e - 23100a b d e +--R + +--R 4 5 6 +--R - 2310b d e +--R * +--R 6 +--R x +--R + +--R 4 2 9 3 3 8 2 2 4 7 3 5 6 +--R - 6930a d e - 36960a b d e - 41580a b d e - 11088a b d e +--R + +--R 4 6 5 +--R - 462b d e +--R * +--R 5 +--R x +--R + +--R 4 3 8 3 4 7 2 2 5 6 3 6 5 4 +--R (- 11550a d e - 34650a b d e - 20790a b d e - 2310a b d e )x +--R + +--R 4 4 7 3 5 6 2 2 6 5 3 +--R (- 11550a d e - 18480a b d e - 4620a b d e )x +--R + +--R 4 5 6 3 6 5 2 4 6 5 4 7 4 +--R (- 6930a d e - 4620a b d e )x - 2310a d e x - 330a d e +--R + +--R 3 8 3 2 2 9 2 3 10 4 11 +--R 165a b d e - 55a b d e + 11a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 11 12 4 11 5 10 11 +--R 210b e x + (1134a b e + 1386b d e )x +--R + +--R 2 3 11 4 10 5 2 9 10 +--R (2464a b e + 7546a b d e + 3850b d e )x +--R + +--R 3 2 11 2 3 10 4 2 9 5 3 8 9 +--R (2695a b e + 16555a b d e + 21175a b d e + 5775b d e )x +--R + +--R 4 11 3 2 10 2 3 2 9 4 3 8 +--R 1485a b e + 18315a b d e + 47025a b d e + 32175a b d e +--R + +--R 5 4 7 +--R 4950b d e +--R * +--R 8 +--R x +--R + +--R 5 11 4 10 3 2 2 9 2 3 3 8 +--R 330a e + 10230a b d e + 52800a b d e + 72600a b d e +--R + +--R 4 4 7 5 5 6 +--R 28050a b d e + 2310b d e +--R * +--R 7 +--R x +--R + +--R 5 10 4 2 9 3 2 3 8 2 3 4 7 +--R 2310a d e + 30030a b d e + 83160a b d e + 64680a b d e +--R + +--R 4 5 6 5 6 5 +--R 13398a b d e + 462b d e +--R * +--R 6 +--R x +--R + +--R 5 2 9 4 3 8 3 2 4 7 2 3 5 6 +--R 6930a d e + 48510a b d e + 76230a b d e + 31878a b d e +--R + +--R 4 6 5 +--R 2772a b d e +--R * +--R 5 +--R x +--R + +--R 5 3 8 4 4 7 3 2 5 6 2 3 6 5 4 +--R (11550a d e + 46200a b d e + 39270a b d e + 6930a b d e )x +--R + +--R 5 4 7 4 5 6 3 2 6 5 3 +--R (11550a d e + 25410a b d e + 9240a b d e )x +--R + +--R 5 5 6 4 6 5 2 5 6 5 +--R (6930a d e + 6930a b d e )x + 2310a d e x +--R / +--R 5 5 +--R 2310b e x + 2310a e +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 6 10 3 6 4 5 9 2 2 6 3 5 4 2 4 8 +--R b e x + (4a b e + 6b d e )x + (6a b e + 24a b d e + 15b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 7 +--R (4a b e + 36a b d e + 60a b d e + 20b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 6 +--R (a e + 24a b d e + 90a b d e + 80a b d e + 15b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 5 +--R (6a d e + 60a b d e + 120a b d e + 60a b d e + 6b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4 +--R (15a d e + 80a b d e + 90a b d e + 24a b d e + b d )x +--R + +--R 4 3 3 3 4 2 2 2 5 3 6 3 +--R (20a d e + 60a b d e + 36a b d e + 4a b d )x +--R + +--R 4 4 2 3 5 2 2 6 2 4 5 3 6 4 6 +--R (15a d e + 24a b d e + 6a b d )x + (6a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 6 11 4 6 5 5 10 +--R - b e x + (- 5a b e - 6b d e )x +--R + +--R 2 3 6 4 5 5 2 4 9 +--R (- 10a b e - 30a b d e - 15b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 8 +--R (- 10a b e - 60a b d e - 75a b d e - 20b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 7 +--R (- 5a b e - 60a b d e - 150a b d e - 100a b d e - 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 6 +--R (- a e - 30a b d e - 150a b d e - 200a b d e - 75a b d e - 6b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 5 +--R (- 6a d e - 75a b d e - 200a b d e - 150a b d e - 30a b d e - b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 4 +--R (- 15a d e - 100a b d e - 150a b d e - 60a b d e - 5a b d )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 3 +--R (- 20a d e - 75a b d e - 60a b d e - 10a b d )x +--R + +--R 5 4 2 4 5 3 2 6 2 5 5 4 6 5 6 +--R (- 15a d e - 30a b d e - 10a b d )x + (- 6a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 407 + +)clear all + +--S 408 of 1353 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 5 8 2 5 3 4 7 2 5 2 4 3 2 3 6 +--R b e x + (3a b e + 5b d e )x + (3a b e + 15a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 5 +--R (a e + 15a b d e + 30a b d e + 10b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 4 +--R (5a d e + 30a b d e + 30a b d e + 5b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (10a d e + 30a b d e + 15a b d e + b d )x +--R + +--R 3 3 2 2 4 2 5 2 3 4 2 5 3 5 +--R (10a d e + 15a b d e + 3a b d )x + (5a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1353 +r0:=-2/45*(b*d-a*e)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/10*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/210*(b*d-a*e)^3*(d+e*x)^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/1260*(b*d-a*e)^4*(d+e*x)^6*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/60*(b*d-a*e)^2*(a+b*x)*(d+e*x)^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 10 10 3 10 4 9 9 +--R 126b e x + (560a b e + 700b d e )x +--R + +--R 2 2 10 3 9 4 2 8 8 +--R (945a b e + 3150a b d e + 1575b d e )x +--R + +--R 3 10 2 2 9 3 2 8 4 3 7 7 +--R (720a b e + 5400a b d e + 7200a b d e + 1800b d e )x +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 4 4 6 6 +--R (210a e + 4200a b d e + 12600a b d e + 8400a b d e + 1050b d e )x +--R + +--R 4 9 3 2 8 2 2 3 7 3 4 6 +--R 1260a d e + 10080a b d e + 15120a b d e + 5040a b d e +--R + +--R 4 5 5 +--R 252b d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 3 3 7 2 2 4 6 3 5 5 4 +--R (3150a d e + 12600a b d e + 9450a b d e + 1260a b d e )x +--R + +--R 4 3 7 3 4 6 2 2 5 5 3 +--R (4200a d e + 8400a b d e + 2520a b d e )x +--R + +--R 4 4 6 3 5 5 2 4 5 5 4 6 4 3 7 3 +--R (3150a d e + 2520a b d e )x + 1260a d e x + 210a d e - 120a b d e +--R + +--R 2 2 8 2 3 9 4 10 +--R 45a b d e - 10a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 1260b e x + 1260a e +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 10 3 5 4 4 9 +--R 126b e x + (560a b e + 700b d e )x +--R + +--R 2 2 5 3 4 4 2 3 8 +--R (945a b e + 3150a b d e + 1575b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 7 +--R (720a b e + 5400a b d e + 7200a b d e + 1800b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 6 +--R (210a e + 4200a b d e + 12600a b d e + 8400a b d e + 1050b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 5 +--R (1260a d e + 10080a b d e + 15120a b d e + 5040a b d e + 252b d )x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 4 +--R (3150a d e + 12600a b d e + 9450a b d e + 1260a b d )x +--R + +--R 4 3 2 3 4 2 2 5 3 4 4 3 5 2 +--R (4200a d e + 8400a b d e + 2520a b d )x + (3150a d e + 2520a b d )x +--R + +--R 4 5 +--R 1260a d x +--R / +--R 1260 +--R Type: Union(Expression(Integer),...) +--E 410 + +--S 411 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 10 10 3 10 4 9 9 +--R - 126b e x + (- 560a b e - 700b d e )x +--R + +--R 2 2 10 3 9 4 2 8 8 +--R (- 945a b e - 3150a b d e - 1575b d e )x +--R + +--R 3 10 2 2 9 3 2 8 4 3 7 7 +--R (- 720a b e - 5400a b d e - 7200a b d e - 1800b d e )x +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 +--R - 210a e - 4200a b d e - 12600a b d e - 8400a b d e +--R + +--R 4 4 6 +--R - 1050b d e +--R * +--R 6 +--R x +--R + +--R 4 9 3 2 8 2 2 3 7 3 4 6 +--R - 1260a d e - 10080a b d e - 15120a b d e - 5040a b d e +--R + +--R 4 5 5 +--R - 252b d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 3 3 7 2 2 4 6 3 5 5 4 +--R (- 3150a d e - 12600a b d e - 9450a b d e - 1260a b d e )x +--R + +--R 4 3 7 3 4 6 2 2 5 5 3 +--R (- 4200a d e - 8400a b d e - 2520a b d e )x +--R + +--R 4 4 6 3 5 5 2 4 5 5 4 6 4 +--R (- 3150a d e - 2520a b d e )x - 1260a d e x - 210a d e +--R + +--R 3 7 3 2 2 8 2 3 9 4 10 +--R 120a b d e - 45a b d e + 10a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 10 11 4 10 5 9 10 +--R 126b e x + (686a b e + 700b d e )x +--R + +--R 2 3 10 4 9 5 2 8 9 +--R (1505a b e + 3850a b d e + 1575b d e )x +--R + +--R 3 2 10 2 3 9 4 2 8 5 3 7 8 +--R (1665a b e + 8550a b d e + 8775a b d e + 1800b d e )x +--R + +--R 4 10 3 2 9 2 3 2 8 4 3 7 +--R 930a b e + 9600a b d e + 19800a b d e + 10200a b d e +--R + +--R 5 4 6 +--R 1050b d e +--R * +--R 7 +--R x +--R + +--R 5 10 4 9 3 2 2 8 2 3 3 7 +--R 210a e + 5460a b d e + 22680a b d e + 23520a b d e +--R + +--R 4 4 6 5 5 5 +--R 6090a b d e + 252b d e +--R * +--R 6 +--R x +--R + +--R 5 9 4 2 8 3 2 3 7 2 3 4 6 +--R 1260a d e + 13230a b d e + 27720a b d e + 14490a b d e +--R + +--R 4 5 5 +--R 1512a b d e +--R * +--R 5 +--R x +--R + +--R 5 2 8 4 3 7 3 2 4 6 2 3 5 5 4 +--R (3150a d e + 16800a b d e + 17850a b d e + 3780a b d e )x +--R + +--R 5 3 7 4 4 6 3 2 5 5 3 +--R (4200a d e + 11550a b d e + 5040a b d e )x +--R + +--R 5 4 6 4 5 5 2 5 5 5 +--R (3150a d e + 3780a b d e )x + 1260a d e x +--R / +--R 5 5 +--R 1260b e x + 1260a e +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 5 9 3 5 4 4 8 2 2 5 3 4 4 2 3 7 +--R b e x + (4a b e + 5b d e )x + (6a b e + 20a b d e + 10b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 6 +--R (4a b e + 30a b d e + 40a b d e + 10b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 5 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 +--R (5a d e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 3 +--R (10a d e + 40a b d e + 30a b d e + 4a b d )x +--R + +--R 4 3 2 3 4 2 2 5 2 4 4 3 5 4 5 +--R (10a d e + 20a b d e + 6a b d )x + (5a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 5 10 4 5 5 4 9 +--R - b e x + (- 5a b e - 5b d e )x +--R + +--R 2 3 5 4 4 5 2 3 8 +--R (- 10a b e - 25a b d e - 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 7 +--R (- 10a b e - 50a b d e - 50a b d e - 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 6 +--R (- 5a b e - 50a b d e - 100a b d e - 50a b d e - 5b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (- a e - 25a b d e - 100a b d e - 100a b d e - 25a b d e - b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4 +--R (- 5a d e - 50a b d e - 100a b d e - 50a b d e - 5a b d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 3 +--R (- 10a d e - 50a b d e - 50a b d e - 10a b d )x +--R + +--R 5 3 2 4 4 3 2 5 2 5 4 4 5 5 5 +--R (- 10a d e - 25a b d e - 10a b d )x + (- 5a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 412 + +)clear all + +--S 413 of 1353 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1353 +r0:=1/630*(b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^5+1/126*(b*d-a*e)^3*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4+1/42*(b*d-a*e)^2*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+1/18*(b*d-a*e)*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/b^2+1/9*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 8 4 8 7 4 8 3 7 +--R 70b e x + (245a b e + 315b d e )x +--R + +--R 2 6 4 7 3 8 2 2 6 +--R (295a b e + 1125a b d e + 540b d e )x +--R + +--R 3 5 4 2 6 3 7 2 2 8 3 5 +--R (125a b e + 1395a b d e + 1980a b d e + 420b d e)x +--R + +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (a b e + 621a b d e + 2556a b d e + 1596a b d e + 126b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (- a b e + 9a b d e + 1224a b d e + 2184a b d e + 504a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (a b e - 9a b d e + 36a b d e + 1176a b d e + 756a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 8 4 +--R (- a b e + 9a b d e - 36a b d e + 84a b d e + 504a b d )x + a e +--R + +--R 7 3 6 2 2 2 5 3 3 4 4 4 +--R - 9a b d e + 36a b d e - 84a b d e + 126a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 630b +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 9 3 4 4 3 8 +--R 70b e x + (315a b e + 315b d e )x +--R + +--R 2 2 4 3 3 4 2 2 7 +--R (540a b e + 1440a b d e + 540b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 6 +--R (420a b e + 2520a b d e + 2520a b d e + 420b d e)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 5 +--R (126a e + 2016a b d e + 4536a b d e + 2016a b d e + 126b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R (630a d e + 3780a b d e + 3780a b d e + 630a b d )x +--R + +--R 4 2 2 3 3 2 2 4 3 4 3 3 4 2 +--R (1260a d e + 3360a b d e + 1260a b d )x + (1260a d e + 1260a b d )x +--R + +--R 4 4 +--R 630a d x +--R / +--R 630 +--R Type: Union(Expression(Integer),...) +--E 415 + +--S 416 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 4 8 7 4 8 3 7 +--R - 70b e x + (- 245a b e - 315b d e )x +--R + +--R 2 6 4 7 3 8 2 2 6 +--R (- 295a b e - 1125a b d e - 540b d e )x +--R + +--R 3 5 4 2 6 3 7 2 2 8 3 5 +--R (- 125a b e - 1395a b d e - 1980a b d e - 420b d e)x +--R + +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (- a b e - 621a b d e - 2556a b d e - 1596a b d e - 126b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (a b e - 9a b d e - 1224a b d e - 2184a b d e - 504a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (- a b e + 9a b d e - 36a b d e - 1176a b d e - 756a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 8 4 +--R (a b e - 9a b d e + 36a b d e - 84a b d e - 504a b d )x - a e +--R + +--R 7 3 6 2 2 2 5 3 3 4 4 4 +--R 9a b d e - 36a b d e + 84a b d e - 126a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 9 4 9 8 4 9 3 8 +--R 70b e x + (315a b e + 315b d e )x +--R + +--R 2 7 4 8 3 9 2 2 7 +--R (540a b e + 1440a b d e + 540b d e )x +--R + +--R 3 6 4 2 7 3 8 2 2 9 3 6 +--R (420a b e + 2520a b d e + 2520a b d e + 420b d e)x +--R + +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 5 +--R (126a b e + 2016a b d e + 4536a b d e + 2016a b d e + 126b d )x +--R + +--R 4 5 3 3 6 2 2 2 7 3 8 4 4 +--R (630a b d e + 3780a b d e + 3780a b d e + 630a b d )x +--R + +--R 4 5 2 2 3 6 3 2 7 4 3 +--R (1260a b d e + 3360a b d e + 1260a b d )x +--R + +--R 4 5 3 3 6 4 2 4 5 4 +--R (1260a b d e + 1260a b d )x + 630a b d x +--R / +--R 5 +--R 630b +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 4 8 3 4 4 3 7 2 2 4 3 3 4 2 2 6 +--R b e x + (4a b e + 4b d e )x + (6a b e + 16a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 5 +--R (4a b e + 24a b d e + 24a b d e + 4b d e)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 16a b d e + 36a b d e + 16a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 24a b d e + 24a b d e + 4a b d )x +--R + +--R 4 2 2 3 3 2 2 4 2 4 3 3 4 4 4 +--R (6a d e + 16a b d e + 6a b d )x + (4a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 9 4 4 5 3 8 +--R - b e x + (- 5a b e - 4b d e )x +--R + +--R 2 3 4 4 3 5 2 2 7 +--R (- 10a b e - 20a b d e - 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (- 10a b e - 40a b d e - 30a b d e - 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (- 5a b e - 40a b d e - 60a b d e - 20a b d e - b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (- a e - 20a b d e - 60a b d e - 40a b d e - 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (- 4a d e - 30a b d e - 40a b d e - 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (- 6a d e - 20a b d e - 10a b d )x + (- 4a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 1353 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1353 +r0:=1/280*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4+1/56*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+3/56*(b*d-a*e)*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/8*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 7 3 7 6 3 7 2 6 +--R 35b e x + (125a b e + 120b d e )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (155a b e + 440a b d e + 140b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (69a b e + 568a b d e + 532a b d e + 56b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (a b e + 272a b d e + 728a b d e + 224a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- a b e + 8a b d e + 392a b d e + 336a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 6 2 +--R (a b e - 8a b d e + 28a b d e + 224a b d )x - a e + 8a b d e +--R + +--R 5 2 2 4 3 3 +--R - 28a b d e + 56a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 280b +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 8 3 3 4 2 7 +--R 35b e x + (160a b e + 120b d e )x +--R + +--R 2 2 3 3 2 4 2 6 +--R (280a b e + 560a b d e + 140b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 5 +--R (224a b e + 1008a b d e + 672a b d e + 56b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 +--R (70a e + 840a b d e + 1260a b d e + 280a b d )x +--R + +--R 4 2 3 2 2 2 3 3 4 2 3 3 2 +--R (280a d e + 1120a b d e + 560a b d )x + (420a d e + 560a b d )x +--R + +--R 4 3 +--R 280a d x +--R / +--R 280 +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 3 7 6 3 7 2 6 +--R - 35b e x + (- 125a b e - 120b d e )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (- 155a b e - 440a b d e - 140b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 69a b e - 568a b d e - 532a b d e - 56b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (- a b e - 272a b d e - 728a b d e - 224a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (a b e - 8a b d e - 392a b d e - 336a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 6 2 +--R (- a b e + 8a b d e - 28a b d e - 224a b d )x + a e - 8a b d e +--R + +--R 5 2 2 4 3 3 +--R 28a b d e - 56a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 8 3 8 7 3 8 2 7 +--R 35b e x + (160a b e + 120b d e )x +--R + +--R 2 6 3 7 2 8 2 6 +--R (280a b e + 560a b d e + 140b d e)x +--R + +--R 3 5 3 2 6 2 7 2 8 3 5 +--R (224a b e + 1008a b d e + 672a b d e + 56b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 4 +--R (70a b e + 840a b d e + 1260a b d e + 280a b d )x +--R + +--R 4 4 2 3 5 2 2 6 3 3 4 4 2 3 5 3 2 +--R (280a b d e + 1120a b d e + 560a b d )x + (420a b d e + 560a b d )x +--R + +--R 4 4 3 +--R 280a b d x +--R / +--R 4 +--R 280b +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R - b e x + (- 5a b e - 3b d e )x + (- 10a b e - 15a b d e - 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 10a b e - 30a b d e - 15a b d e - b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 5a b e - 30a b d e - 30a b d e - 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- a e - 15a b d e - 30a b d e - 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 3a d e - 15a b d e - 10a b d )x + (- 3a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 422 + +)clear all + +--S 423 of 1353 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1353 +r0:=1/105*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+1/21*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/7*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 15b e x + (55a b e + 35b d e)x + (71a b e + 133a b d e + 21b d )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (34a b e + 182a b d e + 84a b d )x +--R + +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (a b e + 98a b d e + 126a b d )x + (- a b e + 7a b d e + 84a b d )x +--R + +--R 6 2 5 4 2 2 +--R a e - 7a b d e + 21a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 105b +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 7 3 2 4 6 2 2 2 3 4 2 5 +--R 15b e x + (70a b e + 35b d e)x + (126a b e + 168a b d e + 21b d )x +--R + +--R 3 2 2 2 3 2 4 +--R (105a b e + 315a b d e + 105a b d )x +--R + +--R 4 2 3 2 2 2 3 4 3 2 2 4 2 +--R (35a e + 280a b d e + 210a b d )x + (105a d e + 210a b d )x + 105a d x +--R / +--R 105 +--R Type: Union(Expression(Integer),...) +--E 425 + +--S 426 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 2 6 5 2 6 5 +--R - 15b e x + (- 55a b e - 35b d e)x +--R + +--R 2 4 2 5 6 2 4 +--R (- 71a b e - 133a b d e - 21b d )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 34a b e - 182a b d e - 84a b d )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- a b e - 98a b d e - 126a b d )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (a b e - 7a b d e - 84a b d )x - a e + 7a b d e - 21a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 2 7 6 2 7 6 2 5 2 6 7 2 5 +--R 15b e x + (70a b e + 35b d e)x + (126a b e + 168a b d e + 21b d )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (105a b e + 315a b d e + 105a b d )x +--R + +--R 4 3 2 3 4 2 5 2 3 4 3 3 4 2 2 +--R (35a b e + 280a b d e + 210a b d )x + (105a b d e + 210a b d )x +--R + +--R 4 3 2 +--R 105a b d x +--R / +--R 3 +--R 105b +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R - b e x + (- 5a b e - 2b d e)x + (- 10a b e - 10a b d e - b d )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 10a b e - 20a b d e - 5a b d )x +--R + +--R 4 2 3 2 2 3 2 3 5 2 4 3 2 2 2 +--R (- 5a b e - 20a b d e - 10a b d )x + (- a e - 10a b d e - 10a b d )x +--R + +--R 5 4 2 5 2 +--R (- 2a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 427 + +)clear all + +--S 428 of 1353 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1353 +r0:=1/30*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/6*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 5 5 4 5 4 2 3 4 3 +--R 5b e x + (19a b e + 6b d)x + (26a b e + 24a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (14a b e + 36a b d)x + (a b e + 24a b d)x - a e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 30b +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 3 4 5 2 2 3 4 +--R 5b e x + (24a b e + 6b d)x + (45a b e + 30a b d)x +--R + +--R 3 2 2 3 4 3 2 4 +--R (40a b e + 60a b d)x + (15a e + 60a b d)x + 30a d x +--R / +--R 30 +--R Type: Union(Expression(Integer),...) +--E 430 + +--S 431 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 4 5 4 2 3 4 3 +--R - 5b e x + (- 19a b e - 6b d)x + (- 26a b e - 24a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 14a b e - 36a b d)x + (- a b e - 24a b d)x + a e - 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 5 6 5 2 4 5 4 +--R 5b e x + (24a b e + 6b d)x + (45a b e + 30a b d)x +--R + +--R 3 3 2 4 3 4 2 3 3 2 4 2 +--R (40a b e + 60a b d)x + (15a b e + 60a b d)x + 30a b d x +--R / +--R 2 +--R 30b +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 6 4 5 5 2 3 4 4 +--R - b e x + (- 5a b e - b d)x + (- 10a b e - 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (- 10a b e - 10a b d)x + (- 5a b e - 10a b d)x + (- a e - 5a b d)x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1353 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R (2) ------------------------------------------------------------- +--R 5b +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 4 5 3 4 2 2 3 3 2 4 +--R b x + 5a b x + 10a b x + 10a b x + 5a x +--R (3) ------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 435 + +--S 436 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (- b x - 4a b x - 6a b x - 4a b x - a )\|b x + 2a b x + a + b x +--R + +--R 4 4 2 3 3 3 2 2 4 +--R 5a b x + 10a b x + 10a b x + 5a b x +--R / +--R 5b +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 437 + +)clear all + +--S 438 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1353 +r0:=-1/3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/4*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/e-(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/2*(b*d-_ + a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3+(b*d-a*e)^4*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (16a b e - 4b d e )x + (36a b e - 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (48a b e - 72a b d e + 48a b d e - 12b d e)x + 25a e - 52a b d e +--R + +--R 2 2 2 2 3 3 +--R 42a b d e - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 12b e x + 12a e +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (16a b e - 4b d e )x + (36a b e - 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 +--R (48a b e - 72a b d e + 48a b d e - 12b d e)x +--R / +--R 5 +--R 12e +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 12a e + 48a b d e - 72a b d e + 48a b d e - 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 3b e x + (- 16a b e + 4b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 36a b e + 24a b d e - 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 48a b e + 72a b d e - 48a b d e + 12b d e)x - 25a e +--R + +--R 3 3 2 2 2 2 3 3 +--R 52a b d e - 42a b d e + 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d )x + 12a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R 3b e x + (19a b e - 4b d e )x + (52a b e - 28a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (84a b e - 96a b d e + 54a b d e - 12b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R (48a b e - 72a b d e + 48a b d e - 12a b d e)x +--R / +--R 5 5 +--R 12b e x + 12a e +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1353 +r0:=4/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2-(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(d+e*x))+4*b*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^4-2*b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-_ + 4*b*(b*d-a*e)^3*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b e - 36a b d e + 36a b d e - 12b d e)x + 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b d e + 36a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (6a b e - 2b d e )x + (18a b e - 18a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (10a b e + 6a b d e - 24a b d e + 12b d e)x - 3a e + 22a b d e +--R + +--R 2 2 2 2 3 3 +--R - 30a b d e + 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +--R 3b e x + (3a e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b e - 36a b d e + 36a b d e - 12b d e)x + 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b d e + 36a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (6a b e - 2b d e )x + (18a b e - 18a b d e + 6b d e )x +--R + +--R 2 2 3 3 2 2 4 3 4 4 3 3 2 2 2 2 +--R (18a b d e - 24a b d e + 9b d e)x - 3a e + 12a b d e - 18a b d e +--R + +--R 3 3 4 4 +--R 12a b d e - 3b d +--R / +--R 6 5 +--R 3e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 445 + +--S 446 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (- 12a b e + 36a b d e - 36a b d e + 12b d e)x - 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 36a b d e - 36a b d e + 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - b e x + (- 6a b e + 2b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 18a b e + 18a b d e - 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 10a b e - 6a b d e + 24a b d e - 12b d e)x + 3a e - 22a b d e +--R + +--R 2 2 2 2 3 3 +--R 30a b d e - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (12a b e - 36a b d e + 36a b d e - 12b d e)x +--R + +--R 4 4 3 2 3 4 3 5 4 4 3 +--R (12a b e - 24a b d e + 24a b d e - 12b d )x + 12a b d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R - 36a b d e + 36a b d e - 12a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R b e x + (7a b e - 2b d e )x + (24a b e - 20a b d e + 6b d e )x +--R + +--R 3 2 4 4 2 2 5 3 2 +--R (18a b e - 18a b d e + 9b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 3a b e + 30a b d e - 42a b d e + 21a b d e - 3b d )x - 3a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R 12a b d e - 18a b d e + 12a b d e - 3a b d +--R / +--R 6 2 6 5 5 +--R 3b e x + (3a e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1353 +r0:=-1/2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^2)-_ + 2*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x))-6*b^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+3*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + e^3+6*b^2*(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 +--R (24a b d e - 48a b d e + 24b d e)x + 12a b d e - 24a b d e +--R + +--R 4 4 +--R 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R b e x + (8a b e - 4b d e )x + (24a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 4 3 4 4 3 3 2 2 2 2 +--R (- 8a b e + 24a b d e - 12b d e)x - a e - 4a b d e + 18a b d e +--R + +--R 3 3 +--R - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 4 4 +--R (24a b d e - 48a b d e + 24b d e)x + 12a b d e - 24a b d e + 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R b e x + (8a b e - 4b d e )x + (16a b d e - 11b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 8a b e + 24a b d e - 16a b d e + 2b d e)x - a e - 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 20a b d e + 7b d +--R / +--R 7 2 6 2 5 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 450 + +--S 451 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 4 3 3 4 2 2 2 +--R (- 12a b e + 24a b d e - 12b d e )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 +--R (- 24a b d e + 48a b d e - 24b d e)x - 12a b d e + 24a b d e +--R + +--R 4 4 +--R - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R - b e x + (- 8a b e + 4b d e )x + (- 24a b d e + 18b d e )x +--R + +--R 3 4 2 2 3 4 3 4 4 3 3 2 2 2 2 +--R (8a b e - 24a b d e + 12b d e)x + a e + 4a b d e - 18a b d e +--R + +--R 3 3 +--R 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 3 2 4 4 2 2 5 3 2 +--R (12a b e - 36a b d e + 24b d e)x +--R + +--R 3 2 3 2 3 2 2 5 4 3 2 2 2 2 3 3 4 4 +--R (24a b d e - 36a b d e + 12b d )x + 12a b d e - 24a b d e + 12a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R b e x + (9a b e - 4b d e )x + (8a b e + 12a b d e - 11b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 8a b e + 40a b d e - 27a b d e + 2b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 9a b e + 20a b d e + 2a b d e - 18a b d e + 7b d )x - a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 4a b d e + 18a b d e - 20a b d e + 7a b d +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 452 + +)clear all + +--S 453 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1353 +r0:=-1/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^3)-_ + 2/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^2)+4*b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^4-2*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+_ + e*x))-4*b^3*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 4 3 3 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (36a b d e - 36b d e )x +--R + +--R 3 2 2 4 3 3 3 4 4 +--R (36a b d e - 36b d e)x + 12a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3b e x + (- 10a b e + 22b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 18a b e + 6a b d e + 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 6a b e - 18a b d e + 24a b d e + 12b d e)x - a e - 2a b d e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e + 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 6 3 5 3 5 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 3 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (36a b d e - 36b d e )x +--R + +--R 3 2 2 4 3 3 3 4 4 +--R (36a b d e - 36b d e)x + 12a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + 9b d e x + (- 18a b e + 36a b d e - 9b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 6a b e - 18a b d e + 54a b d e - 27b d e)x - a e - 2a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e + 22a b d e - 13b d +--R / +--R 8 3 7 2 2 6 3 5 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 455 + +--S 456 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 3 3 3 4 2 2 2 +--R (- 12a b e + 12b d e )x + (- 36a b d e + 36b d e )x +--R + +--R 3 2 2 4 3 3 3 4 4 +--R (- 36a b d e + 36b d e)x - 12a b d e + 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 3b e x + (10a b e - 22b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (18a b e - 6a b d e - 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (6a b e + 18a b d e - 24a b d e - 12b d e)x + a e + 2a b d e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R (12a b e - 12b d e )x + (12a b e + 24a b d e - 36b d e )x +--R + +--R 2 3 3 5 3 2 2 3 2 2 4 3 5 4 +--R (36a b d e - 36b d e)x + (36a b d e - 24a b d e - 12b d )x +--R + +--R 2 3 3 4 4 +--R 12a b d e - 12a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R 3b e x + (3a b e + 9b d e )x + (- 18a b e + 45a b d e - 9b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 24a b e + 18a b d e + 45a b d e - 27b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 7a b e - 20a b d e + 48a b d e - 5a b d e - 13b d )x - a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 2a b d e - 6a b d e + 22a b d e - 13a b d +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 6 3 5 3 5 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 457 + +)clear all + +--S 458 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1353 +r0:=-1/4*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^4)-1/3*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^3)-1/2*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^3*(d+e*x)^2)+b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x)*(d+e*x))+b^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 4 3 3 4 2 2 2 4 3 4 4 +--R (12b e x + 48b d e x + 72b d e x + 48b d e x + 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 13b e x + (- 48a b e - 4b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 36a b e - 72a b d e + 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 16a b e - 24a b d e - 48a b d e + 36b d e)x - 3a e - 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 12a b d e + 12b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 4 3 3 4 2 2 2 4 3 4 4 +--R (12b e x + 48b d e x + 72b d e x + 48b d e x + 12b d )log(e x + d) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (- 48a b e + 48b d e )x + (- 36a b e - 72a b d e + 108b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 16a b e - 24a b d e - 48a b d e + 88b d e)x - 3a e - 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 12a b d e + 25b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 460 + +--S 461 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 4 3 3 4 2 2 2 4 3 4 4 +--R (- 12b e x - 48b d e x - 72b d e x - 48b d e x - 12b d ) +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R 13b e x + (48a b e + 4b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (36a b e + 72a b d e - 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (16a b e + 24a b d e + 48a b d e - 36b d e)x + 3a e + 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 6a b d e + 12a b d e - 12b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 4 3 5 2 2 3 +--R 12b e x + (12a b e + 48b d e )x + (48a b d e + 72b d e )x +--R + +--R 4 2 2 5 3 2 4 3 5 4 4 4 +--R (72a b d e + 48b d e)x + (48a b d e + 12b d )x + 12a b d +--R * +--R log(e x + d) +--R + +--R 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R (- 48a b e + 48b d e )x + (- 84a b e - 24a b d e + 108b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 52a b e - 96a b d e + 60a b d e + 88b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 19a b e - 28a b d e - 54a b d e + 76a b d e + 25b d )x - 3a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 4a b d e - 6a b d e - 12a b d e + 25a b d +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1353 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^5) +--R +--R +--R (2) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (- b x - 4a b x - 6a b x - 4a b x - a )\|b x + 2a b x + a +--R / +--R 6 5 5 5 2 4 4 2 4 3 3 3 +--R (5a e - 5b d e )x + (25a d e - 25b d e )x + (50a d e - 50b d e )x +--R + +--R 3 3 4 2 2 4 2 5 5 6 +--R (50a d e - 50b d e )x + (25a d e - 25b d e)x + 5a d e - 5b d +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 5b e x + (- 10a b e - 10b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 10a b e - 10a b d e - 10b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 5a b e - 5a b d e - 5a b d e - 5b d e)x - a e - a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - a b d e - a b d e - b d +--R / +--R 10 5 9 4 2 8 3 3 7 2 4 6 5 5 +--R 5e x + 25d e x + 50d e x + 50d e x + 25d e x + 5d e +--R Type: Union(Expression(Integer),...) +--E 465 + +--S 466 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 4 5 4 3 5 3 2 2 5 2 3 5 4 5 | 2 2 2 +--R (b e x + 4a b e x + 6a b e x + 4a b e x + a e )\|b x + 2a b x + a +--R + +--R 4 5 5 4 4 2 3 5 5 2 3 3 +--R (- 5a b e + 5b d e )x + (- 10a b e + 10b d e )x +--R + +--R 3 2 5 5 3 2 2 4 5 5 4 5 5 5 5 +--R (- 10a b e + 10b d e )x + (- 5a b e + 5b d e)x - a e + b d +--R / +--R 11 10 5 10 2 9 4 +--R (5a e - 5b d e )x + (25a d e - 25b d e )x +--R + +--R 2 9 3 8 3 3 8 4 7 2 +--R (50a d e - 50b d e )x + (50a d e - 50b d e )x +--R + +--R 4 7 5 6 5 6 6 5 +--R (25a d e - 25b d e )x + 5a d e - 5b d e +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 467 + +)clear all + +--S 468 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1353 +r0:=1/6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^6)+_ + 1/30*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^5) +--R +--R +--R (2) +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (- a b e + 6b d)x + (- 14a b e + 24a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 26a b e + 36a b d)x + (- 19a b e + 24a b d)x - 5a e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 8 7 2 2 6 6 +--R (30a e - 60a b d e + 30b d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (180a d e - 360a b d e + 180b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (600a d e - 1200a b d e + 600b d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 5 3 6 2 2 7 2 6 2 7 2 8 +--R (180a d e - 360a b d e + 180b d e)x + 30a d e - 60a b d e + 30b d +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 15b e x + (- 40a b e - 20b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 45a b e - 30a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 24a b e - 18a b d e - 12a b d e - 6b d e)x - 5a e - 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 3a b d e - 2a b d e - b d +--R / +--R 11 6 10 5 2 9 4 3 8 3 4 7 2 5 6 +--R 30e x + 180d e x + 450d e x + 600d e x + 450d e x + 180d e x +--R + +--R 6 5 +--R 30d e +--R Type: Union(Expression(Integer),...) +--E 470 + +--S 471 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 5 4 6 5 5 4 2 3 6 4 5 3 +--R - b e x + (a b e - 6b d e )x + (14a b e - 24a b d e )x +--R + +--R 3 2 6 2 3 5 2 4 6 3 2 5 5 6 +--R (26a b e - 36a b d e )x + (19a b e - 24a b d e )x + 5a e +--R + +--R 4 5 +--R - 6a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 15a b e + 30a b d e - 15b d e )x +--R + +--R 3 3 6 2 4 5 6 3 3 3 +--R (- 40a b e + 60a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 6 4 2 2 +--R (- 45a b e + 60a b d e - 15b d e )x +--R + +--R 5 6 4 2 5 6 5 6 6 5 5 6 6 +--R (- 24a b e + 30a b d e - 6b d e)x - 5a e + 6a b d e - b d +--R / +--R 2 13 12 2 2 11 6 +--R (30a e - 60a b d e + 30b d e )x +--R + +--R 2 12 2 11 2 3 10 5 +--R (180a d e - 360a b d e + 180b d e )x +--R + +--R 2 2 11 3 10 2 4 9 4 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (600a d e - 1200a b d e + 600b d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 2 8 5 +--R (180a d e - 360a b d e + 180b d e )x + 30a d e - 60a b d e + 30b d e +--R Type: Expression(Integer) +--E 471 + +--S 472 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 472 + +)clear all + +--S 473 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1353 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^7)+_ + 1/21*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^6)+_ + 1/105*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R - b e x + (a b e - 7b d e)x + (- a b e + 7a b d e - 21b d )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 34a b e + 98a b d e - 84a b d )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 71a b e + 182a b d e - 126a b d )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 55a b e + 133a b d e - 84a b d )x - 15a e + 35a b d e - 21a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (105a e - 315a b d e + 315a b d e - 105b d e )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e)x + 105a d e +--R + +--R 2 8 2 2 9 3 10 +--R - 315a b d e + 315a b d e - 105b d +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 35b e x + (- 105a b e - 35b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 126a b e - 63a b d e - 21b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 70a b e - 42a b d e - 21a b d e - 7b d e)x - 15a e - 10a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 3a b d e - b d +--R / +--R 12 7 11 6 2 10 5 3 9 4 4 8 3 +--R 105e x + 735d e x + 2205d e x + 3675d e x + 3675d e x +--R + +--R 5 7 2 6 6 7 5 +--R 2205d e x + 735d e x + 105d e +--R Type: Union(Expression(Integer),...) +--E 475 + +--S 476 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 6 5 7 6 6 5 2 4 7 5 6 6 2 5 4 +--R b e x + (- a b e + 7b d e )x + (a b e - 7a b d e + 21b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 3 +--R (34a b e - 98a b d e + 84a b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 2 +--R (71a b e - 182a b d e + 126a b d e )x +--R + +--R 5 7 4 2 6 3 3 2 5 6 7 5 6 +--R (55a b e - 133a b d e + 84a b d e )x + 15a e - 35a b d e +--R + +--R 4 2 2 5 +--R 21a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 35a b e + 105a b d e - 105a b d e + 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 7 4 3 3 +--R (- 105a b e + 280a b d e - 210a b d e + 35b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 7 5 2 2 +--R (- 126a b e + 315a b d e - 210a b d e + 21b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 7 6 7 7 6 6 +--R (- 70a b e + 168a b d e - 105a b d e + 7b d e)x - 15a e + 35a b d e +--R + +--R 5 2 2 5 7 7 +--R - 21a b d e + b d +--R / +--R 3 15 2 14 2 2 13 3 3 12 7 +--R (105a e - 315a b d e + 315a b d e - 105b d e )x +--R + +--R 3 14 2 2 13 2 3 12 3 4 11 6 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e )x +--R + +--R 3 2 13 2 3 12 2 4 11 3 5 10 5 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 3 12 2 4 11 2 5 10 3 6 9 4 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 4 11 2 5 10 2 6 9 3 7 8 3 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 5 10 2 6 9 2 7 8 3 8 7 2 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 6 9 2 7 8 2 8 7 3 9 6 3 7 8 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e )x + 105a d e +--R + +--R 2 8 7 2 9 6 3 10 5 +--R - 315a b d e + 315a b d e - 105b d e +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1353 +r0:=1/8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^8)+_ + 3/56*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^7)+_ + 1/56*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^6)+_ + 1/280*b^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 7 3 7 6 3 7 2 6 2 5 3 6 2 7 2 5 +--R b e x + (- a b e + 8b d e )x + (a b e - 8a b d e + 28b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- a b e + 8a b d e - 28a b d e + 56b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (- 69a b e + 272a b d e - 392a b d e + 224a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 155a b e + 568a b d e - 728a b d e + 336a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (- 125a b e + 440a b d e - 532a b d e + 224a b d )x - 35a e +--R + +--R 6 2 5 2 2 4 3 3 +--R 120a b d e - 140a b d e + 56a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 12 3 11 2 2 2 10 3 3 9 4 4 8 8 +--R (280a e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d e )x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 +--R 2240a d e - 8960a b d e + 13440a b d e - 8960a b d e +--R + +--R 4 5 7 +--R 2240b d e +--R * +--R 7 +--R x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 6 6 +--R 7840b d e +--R * +--R 6 +--R x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 7 5 +--R 15680b d e +--R * +--R 5 +--R x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 +--R 19600a d e - 78400a b d e + 117600a b d e - 78400a b d e +--R + +--R 4 8 4 +--R 19600b d e +--R * +--R 4 +--R x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 8 4 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 9 3 +--R 15680b d e +--R * +--R 3 +--R x +--R + +--R 4 6 6 3 7 5 2 2 8 4 3 9 3 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 10 2 +--R 7840b d e +--R * +--R 2 +--R x +--R + +--R 4 7 5 3 8 4 2 2 9 3 3 10 2 4 11 +--R (2240a d e - 8960a b d e + 13440a b d e - 8960a b d e + 2240b d e)x +--R + +--R 4 8 4 3 9 3 2 2 10 2 3 11 4 12 +--R 280a d e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 70b e x + (- 224a b e - 56b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 280a b e - 112a b d e - 28b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 160a b e - 80a b d e - 32a b d e - 8b d e)x - 35a e - 20a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 10a b d e - 4a b d e - b d +--R / +--R 13 8 12 7 2 11 6 3 10 5 4 9 4 +--R 280e x + 2240d e x + 7840d e x + 15680d e x + 19600d e x +--R + +--R 5 8 3 6 7 2 7 6 8 5 +--R 15680d e x + 7840d e x + 2240d e x + 280d e +--R Type: Union(Expression(Integer),...) +--E 480 + +--S 481 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 8 7 6 8 7 7 6 2 5 8 6 7 7 2 6 5 +--R - b e x + (a b e - 8b d e )x + (- a b e + 8a b d e - 28b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 4 +--R (a b e - 8a b d e + 28a b d e - 56b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 3 +--R (69a b e - 272a b d e + 392a b d e - 224a b d e )x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 2 +--R (155a b e - 568a b d e + 728a b d e - 336a b d e )x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 7 8 +--R (125a b e - 440a b d e + 532a b d e - 224a b d e )x + 35a e +--R + +--R 6 7 5 2 2 6 4 3 3 5 +--R - 120a b d e + 140a b d e - 56a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 8 4 4 4 +--R (- 70a b e + 280a b d e - 420a b d e + 280a b d e - 70b d e )x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 8 5 3 3 +--R (- 224a b e + 840a b d e - 1120a b d e + 560a b d e - 56b d e )x +--R + +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 8 6 2 2 +--R (- 280a b e + 1008a b d e - 1260a b d e + 560a b d e - 28b d e )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 8 7 +--R (- 160a b e + 560a b d e - 672a b d e + 280a b d e - 8b d e)x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 8 8 +--R - 35a e + 120a b d e - 140a b d e + 56a b d e - b d +--R / +--R 4 17 3 16 2 2 2 15 3 3 14 4 4 13 8 +--R (280a e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d e )x +--R + +--R 4 16 3 2 15 2 2 3 14 3 4 13 +--R 2240a d e - 8960a b d e + 13440a b d e - 8960a b d e +--R + +--R 4 5 12 +--R 2240b d e +--R * +--R 7 +--R x +--R + +--R 4 2 15 3 3 14 2 2 4 13 3 5 12 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 6 11 +--R 7840b d e +--R * +--R 6 +--R x +--R + +--R 4 3 14 3 4 13 2 2 5 12 3 6 11 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 7 10 +--R 15680b d e +--R * +--R 5 +--R x +--R + +--R 4 4 13 3 5 12 2 2 6 11 3 7 10 +--R 19600a d e - 78400a b d e + 117600a b d e - 78400a b d e +--R + +--R 4 8 9 +--R 19600b d e +--R * +--R 4 +--R x +--R + +--R 4 5 12 3 6 11 2 2 7 10 3 8 9 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 9 8 +--R 15680b d e +--R * +--R 3 +--R x +--R + +--R 4 6 11 3 7 10 2 2 8 9 3 9 8 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 10 7 +--R 7840b d e +--R * +--R 2 +--R x +--R + +--R 4 7 10 3 8 9 2 2 9 8 3 10 7 +--R 2240a d e - 8960a b d e + 13440a b d e - 8960a b d e +--R + +--R 4 11 6 +--R 2240b d e +--R * +--R x +--R + +--R 4 8 9 3 9 8 2 2 10 7 3 11 6 4 12 5 +--R 280a d e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d e +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 482 + +)clear all + +--S 483 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1353 +r0:=1/9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^9)+_ + 1/18*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^8)+_ + 1/42*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^7)+_ + 1/126*b^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^6)+_ + 1/630*b^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^5*(d+e*x)^5) +--R +--R +--R (2) +--R 8 4 8 7 4 8 3 7 2 6 4 7 3 8 2 2 6 +--R - b e x + (a b e - 9b d e )x + (- a b e + 9a b d e - 36b d e )x +--R + +--R 3 5 4 2 6 3 7 2 2 8 3 5 +--R (a b e - 9a b d e + 36a b d e - 84b d e)x +--R + +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (- a b e + 9a b d e - 36a b d e + 84a b d e - 126b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (- 125a b e + 621a b d e - 1224a b d e + 1176a b d e - 504a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (- 295a b e + 1395a b d e - 2556a b d e + 2184a b d e - 756a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (- 245a b e + 1125a b d e - 1980a b d e + 1596a b d e - 504a b d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R - 70a e + 315a b d e - 540a b d e + 420a b d e - 126a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 14 4 13 3 2 2 12 2 3 3 11 +--R 630a e - 3150a b d e + 6300a b d e - 6300a b d e +--R + +--R 4 4 10 5 5 9 +--R 3150a b d e - 630b d e +--R * +--R 9 +--R x +--R + +--R 5 13 4 2 12 3 2 3 11 2 3 4 10 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 5 9 5 6 8 +--R 28350a b d e - 5670b d e +--R * +--R 8 +--R x +--R + +--R 5 2 12 4 3 11 3 2 4 10 2 3 5 9 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 6 8 5 7 7 +--R 113400a b d e - 22680b d e +--R * +--R 7 +--R x +--R + +--R 5 3 11 4 4 10 3 2 5 9 2 3 6 8 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 7 7 5 8 6 +--R 264600a b d e - 52920b d e +--R * +--R 6 +--R x +--R + +--R 5 4 10 4 5 9 3 2 6 8 2 3 7 7 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 8 6 5 9 5 +--R 396900a b d e - 79380b d e +--R * +--R 5 +--R x +--R + +--R 5 5 9 4 6 8 3 2 7 7 2 3 8 6 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 9 5 5 10 4 +--R 396900a b d e - 79380b d e +--R * +--R 4 +--R x +--R + +--R 5 6 8 4 7 7 3 2 8 6 2 3 9 5 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 10 4 5 11 3 +--R 264600a b d e - 52920b d e +--R * +--R 3 +--R x +--R + +--R 5 7 7 4 8 6 3 2 9 5 2 3 10 4 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 11 3 5 12 2 +--R 113400a b d e - 22680b d e +--R * +--R 2 +--R x +--R + +--R 5 8 6 4 9 5 3 2 10 4 2 3 11 3 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 12 2 5 13 +--R 28350a b d e - 5670b d e +--R * +--R x +--R + +--R 5 9 5 4 10 4 3 2 11 3 2 3 12 2 4 13 +--R 630a d e - 3150a b d e + 6300a b d e - 6300a b d e + 3150a b d e +--R + +--R 5 14 +--R - 630b d +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 126b e x + (- 420a b e - 84b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 540a b e - 180a b d e - 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 315a b e - 135a b d e - 45a b d e - 9b d e)x - 70a e - 35a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 15a b d e - 5a b d e - b d +--R / +--R 14 9 13 8 2 12 7 3 11 6 4 10 5 +--R 630e x + 5670d e x + 22680d e x + 52920d e x + 79380d e x +--R + +--R 5 9 4 6 8 3 7 7 2 8 6 9 5 +--R 79380d e x + 52920d e x + 22680d e x + 5670d e x + 630d e +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 9 8 7 9 8 8 7 2 6 9 7 8 8 2 7 6 +--R b e x + (- a b e + 9b d e )x + (a b e - 9a b d e + 36b d e )x +--R + +--R 3 5 9 2 6 8 7 2 7 8 3 6 5 +--R (- a b e + 9a b d e - 36a b d e + 84b d e )x +--R + +--R 4 4 9 3 5 8 2 6 2 7 7 3 6 8 4 5 4 +--R (a b e - 9a b d e + 36a b d e - 84a b d e + 126b d e )x +--R + +--R 5 3 9 4 4 8 3 5 2 7 2 6 3 6 +--R 125a b e - 621a b d e + 1224a b d e - 1176a b d e +--R + +--R 7 4 5 +--R 504a b d e +--R * +--R 3 +--R x +--R + +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 +--R 295a b e - 1395a b d e + 2556a b d e - 2184a b d e +--R + +--R 2 6 4 5 +--R 756a b d e +--R * +--R 2 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 +--R 245a b e - 1125a b d e + 1980a b d e - 1596a b d e +--R + +--R 3 5 4 5 +--R 504a b d e +--R * +--R x +--R + +--R 8 9 7 8 6 2 2 7 5 3 3 6 4 4 4 5 +--R 70a e - 315a b d e + 540a b d e - 420a b d e + 126a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 +--R - 126a b e + 630a b d e - 1260a b d e + 1260a b d e - 630a b d e +--R + +--R 9 5 4 +--R 126b d e +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 5 2 7 3 6 3 6 +--R - 420a b e + 2016a b d e - 3780a b d e + 3360a b d e +--R + +--R 2 7 4 5 9 6 3 +--R - 1260a b d e + 84b d e +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 +--R - 540a b e + 2520a b d e - 4536a b d e + 3780a b d e +--R + +--R 3 6 4 5 9 7 2 +--R - 1260a b d e + 36b d e +--R * +--R 2 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 +--R - 315a b e + 1440a b d e - 2520a b d e + 2016a b d e +--R + +--R 4 5 4 5 9 8 +--R - 630a b d e + 9b d e +--R * +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 9 9 +--R - 70a e + 315a b d e - 540a b d e + 420a b d e - 126a b d e + b d +--R / +--R 5 19 4 18 3 2 2 17 2 3 3 16 +--R 630a e - 3150a b d e + 6300a b d e - 6300a b d e +--R + +--R 4 4 15 5 5 14 +--R 3150a b d e - 630b d e +--R * +--R 9 +--R x +--R + +--R 5 18 4 2 17 3 2 3 16 2 3 4 15 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 5 14 5 6 13 +--R 28350a b d e - 5670b d e +--R * +--R 8 +--R x +--R + +--R 5 2 17 4 3 16 3 2 4 15 2 3 5 14 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 6 13 5 7 12 +--R 113400a b d e - 22680b d e +--R * +--R 7 +--R x +--R + +--R 5 3 16 4 4 15 3 2 5 14 2 3 6 13 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 7 12 5 8 11 +--R 264600a b d e - 52920b d e +--R * +--R 6 +--R x +--R + +--R 5 4 15 4 5 14 3 2 6 13 2 3 7 12 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 8 11 5 9 10 +--R 396900a b d e - 79380b d e +--R * +--R 5 +--R x +--R + +--R 5 5 14 4 6 13 3 2 7 12 2 3 8 11 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 9 10 5 10 9 +--R 396900a b d e - 79380b d e +--R * +--R 4 +--R x +--R + +--R 5 6 13 4 7 12 3 2 8 11 2 3 9 10 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 10 9 5 11 8 +--R 264600a b d e - 52920b d e +--R * +--R 3 +--R x +--R + +--R 5 7 12 4 8 11 3 2 9 10 2 3 10 9 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 11 8 5 12 7 +--R 113400a b d e - 22680b d e +--R * +--R 2 +--R x +--R + +--R 5 8 11 4 9 10 3 2 10 9 2 3 11 8 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 12 7 5 13 6 +--R 28350a b d e - 5670b d e +--R * +--R x +--R + +--R 5 9 10 4 10 9 3 2 11 8 2 3 12 7 +--R 630a d e - 3150a b d e + 6300a b d e - 6300a b d e +--R + +--R 4 13 6 5 14 5 +--R 3150a b d e - 630b d e +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 487 + +)clear all + +--S 488 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1353 +r0:=-1/10*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^10)-_ + 2/45*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^9)-1/60*b^2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^8)-1/180*b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(d+e*x)^7)-1/1260*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 210b e x + (- 720a b e - 120b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 945a b e - 270a b d e - 45b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 560a b e - 210a b d e - 60a b d e - 10b d e)x - 126a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 56a b d e - 21a b d e - 6a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 15 11 15 14 10 +--R 1260b e x + (1260a e + 12600b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (12600a d e + 56700b d e )x + (56700a d e + 151200b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (151200a d e + 264600b d e )x + (264600a d e + 317520b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (317520a d e + 264600b d e )x + (264600a d e + 151200b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (151200a d e + 56700b d e )x + (56700a d e + 12600b d e )x +--R + +--R 9 6 10 5 10 5 +--R (12600a d e + 1260b d e )x + 1260a d e +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 210b e x + (- 720a b e - 120b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 945a b e - 270a b d e - 45b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 560a b e - 210a b d e - 60a b d e - 10b d e)x - 126a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 56a b d e - 21a b d e - 6a b d e - b d +--R / +--R 15 10 14 9 2 13 8 3 12 7 4 11 6 +--R 1260e x + 12600d e x + 56700d e x + 151200d e x + 264600d e x +--R + +--R 5 10 5 6 9 4 7 8 3 8 7 2 9 6 +--R 317520d e x + 264600d e x + 151200d e x + 56700d e x + 12600d e x +--R + +--R 10 5 +--R 1260d e +--R Type: Union(Expression(Integer),...) +--E 490 + +--S 491 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R 210b e x + (720a b e + 120b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (945a b e + 270a b d e + 45b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (560a b e + 210a b d e + 60a b d e + 10b d e)x + 126a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 56a b d e + 21a b d e + 6a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 210b e x + (- 930a b e - 120b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 1665a b e - 390a b d e - 45b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 1505a b e - 480a b d e - 105a b d e - 10b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 686a b e - 266a b d e - 81a b d e - 16a b d e - b d )x - 126a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 56a b d e - 21a b d e - 6a b d e - a b d +--R / +--R 15 11 15 14 10 +--R 1260b e x + (1260a e + 12600b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (12600a d e + 56700b d e )x + (56700a d e + 151200b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (151200a d e + 264600b d e )x + (264600a d e + 317520b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (317520a d e + 264600b d e )x + (264600a d e + 151200b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (151200a d e + 56700b d e )x + (56700a d e + 12600b d e )x +--R + +--R 9 6 10 5 10 5 +--R (12600a d e + 1260b d e )x + 1260a d e +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1353 +r0:=-1/11*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^11)-_ + 2/55*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^10)-2/165*b^2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^9)-4/1155*b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(d+e*x)^8)-1/2310*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 330b e x + (- 1155a b e - 165b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1540a b e - 385a b d e - 55b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 924a b e - 308a b d e - 77a b d e - 11b d e)x - 210a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 84a b d e - 28a b d e - 7a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 16 12 16 15 11 +--R 2310b e x + (2310a e + 25410b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (25410a d e + 127050b d e )x + (127050a d e + 381150b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (381150a d e + 762300b d e )x + (762300a d e + 1067220b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (1067220a d e + 1067220b d e )x + (1067220a d e + 762300b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (762300a d e + 381150b d e )x + (381150a d e + 127050b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (127050a d e + 25410b d e )x + (25410a d e + 2310b d e )x +--R + +--R 11 5 +--R 2310a d e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 330b e x + (- 1155a b e - 165b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1540a b e - 385a b d e - 55b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 924a b e - 308a b d e - 77a b d e - 11b d e)x - 210a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 84a b d e - 28a b d e - 7a b d e - b d +--R / +--R 16 11 15 10 2 14 9 3 13 8 +--R 2310e x + 25410d e x + 127050d e x + 381150d e x +--R + +--R 4 12 7 5 11 6 6 10 5 7 9 4 +--R 762300d e x + 1067220d e x + 1067220d e x + 762300d e x +--R + +--R 8 8 3 9 7 2 10 6 11 5 +--R 381150d e x + 127050d e x + 25410d e x + 2310d e +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R 330b e x + (1155a b e + 165b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1540a b e + 385a b d e + 55b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (924a b e + 308a b d e + 77a b d e + 11b d e)x + 210a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 84a b d e + 28a b d e + 7a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 330b e x + (- 1485a b e - 165b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 2695a b e - 550a b d e - 55b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 2464a b e - 693a b d e - 132a b d e - 11b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 1134a b e - 392a b d e - 105a b d e - 18a b d e - b d )x - 210a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 84a b d e - 28a b d e - 7a b d e - a b d +--R / +--R 16 12 16 15 11 +--R 2310b e x + (2310a e + 25410b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (25410a d e + 127050b d e )x + (127050a d e + 381150b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (381150a d e + 762300b d e )x + (762300a d e + 1067220b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (1067220a d e + 1067220b d e )x + (1067220a d e + 762300b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (762300a d e + 381150b d e )x + (381150a d e + 127050b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (127050a d e + 25410b d e )x + (25410a d e + 2310b d e )x +--R + +--R 11 5 +--R 2310a d e +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x +--R + +--R 12 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 1353 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 m +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )(e x + d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1353 +r0:=-120*(b*d-a*e)^3*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(4+m)*_ + (5+m)*(6+m)*(7+m))+30*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(5+m)*(6+m)*(7+m))-6*(b*d-a*e)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(6+m)*(7+m))+(a+b*x)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(7+m))-720*(b*d-a*e)^5*(d+e*x)^(1+m)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m))+_ + 720*(b*d-a*e)^6*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(1+m)*_ + (2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)*(a+b*x))+360*(b*d-a*e)^4*(a+b*x)*_ + (d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)) +--R +--R +--R (2) +--R 6 6 6 6 6 5 6 6 4 6 6 3 6 6 2 6 6 +--R b e m + 21b e m + 175b e m + 735b e m + 1624b e m + 1764b e m +--R + +--R 6 6 +--R 720b e +--R * +--R 6 +--R x +--R + +--R 5 6 6 5 6 6 5 5 5 6 6 5 4 +--R 6a b e m + (132a b e - 6b d e )m + (1140a b e - 90b d e )m +--R + +--R 5 6 6 5 3 5 6 6 5 2 +--R (4920a b e - 510b d e )m + (11094a b e - 1350b d e )m +--R + +--R 5 6 6 5 5 6 6 5 +--R (12228a b e - 1644b d e )m + 5040a b e - 720b d e +--R * +--R 5 +--R x +--R + +--R 2 4 6 6 2 4 6 5 5 5 +--R 15a b e m + (345a b e - 30a b d e )m +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (3105a b e - 510a b d e + 30b d e )m +--R + +--R 2 4 6 5 5 6 2 4 3 +--R (13875a b e - 3150a b d e + 300b d e )m +--R + +--R 2 4 6 5 5 6 2 4 2 +--R (32160a b e - 8850a b d e + 1050b d e )m +--R + +--R 2 4 6 5 5 6 2 4 2 4 6 +--R (36180a b e - 11220a b d e + 1500b d e )m + 15120a b e +--R + +--R 5 5 6 2 4 +--R - 5040a b d e + 720b d e +--R * 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d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 31644a b e + 44340a b d e - 38040a b d e + 19800a b d e +--R + +--R 5 4 2 6 5 +--R - 5760a b d e + 720b d e +--R * +--R m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 15120a b e + 25200a b d e - 25200a b d e + 15120a b d e +--R + +--R 5 4 2 6 5 +--R - 5040a b d e + 720b d e +--R * +--R x +--R + +--R 6 6 6 6 6 5 5 5 +--R - a e m + (- 27a e + 6a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 4 +--R (- 295a e + 150a b d e - 30a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 3 +--R (- 1665a e + 1470a b d e - 660a b d e + 120a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 5104a e + 7050a b d e - 5370a b d e + 2160a b d e +--R + +--R 2 4 4 2 +--R - 360a b d e +--R * +--R 2 +--R m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 8028a e + 16524a b d e - 19140a b d e + 12840a b d e +--R + +--R 2 4 4 2 5 5 +--R - 4680a b d e + 720a b d e +--R * +--R m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 5040a e + 15120a b d e - 25200a b d e + 25200a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 15120a b d e + 5040a b d e - 720b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m + 13132b e m +--R + +--R 7 7 +--R 13068b e m + 5040b e +--R * +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a e m + 28a e m + 322a e m + 1960a e m + 6769a e m + 13132a e m +--R + +--R 7 7 +--R 13068a e m + 5040a e +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x +--R + +--R 7 +--R - a +--R * +--R (m + 1)log(e x + d) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 502 + +)clear all + +--S 503 of 1353 +t0:=(a+b*x)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 9 14 4 9 5 8 13 2 3 9 4 8 5 2 7 12 +--R b e x + (5a b e + 9b d e )x + (10a b e + 45a b d e + 36b d e )x +--R + +--R 3 2 9 2 3 8 4 2 7 5 3 6 11 +--R (10a b e + 90a b d e + 180a b d e + 84b d e )x +--R + +--R 4 9 3 2 8 2 3 2 7 4 3 6 5 4 5 10 +--R (5a b e + 90a b d e + 360a b d e + 420a b d e + 126b d e )x +--R + +--R 5 9 4 8 3 2 2 7 2 3 3 6 4 4 5 +--R a e + 45a b d e + 360a b d e + 840a b d e + 630a b d e +--R + +--R 5 5 4 +--R 126b d e +--R * +--R 9 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 4 5 4 +--R 9a d e + 180a b d e + 840a b d e + 1260a b d e + 630a b d e +--R + +--R 5 6 3 +--R 84b d e +--R * +--R 8 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 4 6 3 +--R 36a d e + 420a b d e + 1260a b d e + 1260a b d e + 420a b d e +--R + +--R 5 7 2 +--R 36b d e +--R * +--R 7 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 4 7 2 +--R 84a d e + 630a b d e + 1260a b d e + 840a b d e + 180a b d e +--R + +--R 5 8 +--R 9b d e +--R * +--R 6 +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 4 8 +--R 126a d e + 630a b d e + 840a b d e + 360a b d e + 45a b d e +--R + +--R 5 9 +--R b d +--R * +--R 5 +--R x +--R + +--R 5 5 4 4 6 3 3 2 7 2 2 3 8 4 9 4 +--R (126a d e + 420a b d e + 360a b d e + 90a b d e + 5a b d )x +--R + +--R 5 6 3 4 7 2 3 2 8 2 3 9 3 +--R (84a d e + 180a b d e + 90a b d e + 10a b d )x +--R + +--R 5 7 2 4 8 3 2 9 2 5 8 4 9 5 9 +--R (36a d e + 45a b d e + 10a b d )x + (9a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1353 +r0:=-1/364*(b*d-a*e)^3*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/112*(b*d-a*e)^2*(a+b*x)*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/40*(b*d-a*e)*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/16*(a+b*x)*_ + (d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/8008*(b*d-a*e)^5*(d+e*x)^10*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/80080*(b*d-a*e)^6*(d+e*x)^10*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/1456*(b*d-a*e)^4*(a+b*x)*(d+e*x)^10*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 16 16 5 16 6 15 15 +--R 5005b e x + (32032a b e + 48048b d e )x +--R + +--R 2 4 16 5 15 6 2 14 14 +--R (85800a b e + 308880a b d e + 205920b d e )x +--R + +--R 3 3 16 2 4 15 5 2 14 6 3 13 13 +--R (123200a b e + 831600a b d e + 1330560a b d e + 517440b d e )x +--R + +--R 4 2 16 3 3 15 2 4 2 14 +--R 100100a b e + 1201200a b d e + 3603600a b d e +--R + +--R 5 3 13 6 4 12 +--R 3363360a b d e + 840840b d e +--R * +--R 12 +--R x +--R + +--R 5 16 4 2 15 3 3 2 14 +--R 43680a b e + 982800a b d e + 5241600a b d e +--R + +--R 2 4 3 13 5 4 12 6 5 11 +--R 9172800a b d e + 5503680a b d e + 917280b d e +--R * +--R 11 +--R x +--R + +--R 6 16 5 15 4 2 2 14 3 3 3 13 +--R 8008a e + 432432a b d e + 4324320a b d e + 13453440a b d e +--R + +--R 2 4 4 12 5 5 11 6 6 10 +--R 15135120a b d e + 6054048a b d e + 672672b d e +--R * +--R 10 +--R x +--R + +--R 6 15 5 2 14 4 2 3 13 +--R 80080a d e + 1921920a b d e + 11211200a b d e +--R + +--R 3 3 4 12 2 4 5 11 5 6 10 +--R 22422400a b d e + 16816800a b d e + 4484480a b d e +--R + +--R 6 7 9 +--R 320320b d e +--R * +--R 9 +--R x +--R + +--R 6 2 14 5 3 13 4 2 4 12 +--R 360360a d e + 5045040a b d e + 18918900a b d e +--R + +--R 3 3 5 11 2 4 6 10 5 7 9 6 8 8 +--R 25225200a b d e + 12612600a b d e + 2162160a b d e + 90090b d e +--R * +--R 8 +--R x +--R + +--R 6 3 13 5 4 12 4 2 5 11 +--R 960960a d e + 8648640a b d e + 21621600a b d e +--R + +--R 3 3 6 10 2 4 7 9 5 8 8 6 9 7 +--R 19219200a b d e + 6177600a b d e + 617760a b d e + 11440b d e +--R * +--R 7 +--R x +--R + +--R 6 4 12 5 5 11 4 2 6 10 +--R 1681680a d e + 10090080a b d e + 16816800a b d e +--R + +--R 3 3 7 9 2 4 8 8 5 9 7 +--R 9609600a b d e + 1801800a b d e + 80080a b d e +--R * +--R 6 +--R x +--R + +--R 6 5 11 5 6 10 4 2 7 9 +--R 2018016a d e + 8072064a b d e + 8648640a b d e +--R + +--R 3 3 8 8 2 4 9 7 +--R 2882880a b d e + 240240a b d e +--R * +--R 5 +--R x +--R + +--R 6 6 10 5 7 9 4 2 8 8 3 3 9 7 4 +--R (1681680a d e + 4324320a b d e + 2702700a b d e + 400400a b d e )x +--R + +--R 6 7 9 5 8 8 4 2 9 7 3 +--R (960960a d e + 1441440a b d e + 400400a b d e )x +--R + +--R 6 8 8 5 9 7 2 6 9 7 6 10 6 +--R (360360a d e + 240240a b d e )x + 80080a d e x + 8008a d e +--R + +--R 5 11 5 4 2 12 4 3 3 13 3 2 4 14 2 +--R - 4368a b d e + 1820a b d e - 560a b d e + 120a b d e +--R + +--R 5 15 6 16 +--R - 16a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 80080b e x + 80080a e +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 9 16 5 9 6 8 15 +--R 5005b e x + (32032a b e + 48048b d e )x +--R + +--R 2 4 9 5 8 6 2 7 14 +--R (85800a b e + 308880a b d e + 205920b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 13 +--R (123200a b e + 831600a b d e + 1330560a b d e + 517440b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 5 3 6 +--R 100100a b e + 1201200a b d e + 3603600a b d e + 3363360a b d e +--R + +--R 6 4 5 +--R 840840b d e +--R * +--R 12 +--R x +--R + +--R 5 9 4 2 8 3 3 2 7 2 4 3 6 +--R 43680a b e + 982800a b d e + 5241600a b d e + 9172800a b d e +--R + +--R 5 4 5 6 5 4 +--R 5503680a b d e + 917280b d e +--R * +--R 11 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 +--R 8008a e + 432432a b d e + 4324320a b d e + 13453440a b d e +--R + +--R 2 4 4 5 5 5 4 6 6 3 +--R 15135120a b d e + 6054048a b d e + 672672b d e +--R * +--R 10 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R 80080a d e + 1921920a b d e + 11211200a b d e + 22422400a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R 16816800a b d e + 4484480a b d e + 320320b d e +--R * +--R 9 +--R x +--R + +--R 6 2 7 5 3 6 4 2 4 5 3 3 5 4 +--R 360360a d e + 5045040a b d e + 18918900a b d e + 25225200a b d e +--R + +--R 2 4 6 3 5 7 2 6 8 +--R 12612600a b d e + 2162160a b d e + 90090b d e +--R * +--R 8 +--R x +--R + +--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 +--R 960960a d e + 8648640a b d e + 21621600a b d e + 19219200a b d e +--R + +--R 2 4 7 2 5 8 6 9 +--R 6177600a b d e + 617760a b d e + 11440b d +--R * +--R 7 +--R x +--R + +--R 6 4 5 5 5 4 4 2 6 3 3 3 7 2 +--R 1681680a d e + 10090080a b d e + 16816800a b d e + 9609600a b d e +--R + +--R 2 4 8 5 9 +--R 1801800a b d e + 80080a b d +--R * +--R 6 +--R x +--R + +--R 6 5 4 5 6 3 4 2 7 2 3 3 8 +--R 2018016a d e + 8072064a b d e + 8648640a b d e + 2882880a b d e +--R + +--R 2 4 9 +--R 240240a b d +--R * +--R 5 +--R x +--R + +--R 6 6 3 5 7 2 4 2 8 3 3 9 4 +--R (1681680a d e + 4324320a b d e + 2702700a b d e + 400400a b d )x +--R + +--R 6 7 2 5 8 4 2 9 3 +--R (960960a d e + 1441440a b d e + 400400a b d )x +--R + +--R 6 8 5 9 2 6 9 +--R (360360a d e + 240240a b d )x + 80080a d x +--R / +--R 80080 +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 16 16 5 16 6 15 15 +--R - 5005b e x + (- 32032a b e - 48048b d e )x +--R + +--R 2 4 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8339760a b d e +--R + +--R 6 8 8 7 9 7 +--R 707850a b d e + 11440b d e +--R * +--R 8 +--R x +--R + +--R 7 3 13 6 4 12 5 2 5 11 +--R 960960a d e + 10330320a b d e + 31711680a b d e +--R + +--R 4 3 6 10 3 4 7 9 2 5 8 8 6 9 7 +--R 36036000a b d e + 15787200a b d e + 2419560a b d e + 91520a b d e +--R * +--R 7 +--R x +--R + +--R 7 4 12 6 5 11 5 2 6 10 +--R 1681680a d e + 12108096a b d e + 24888864a b d e +--R + +--R 4 3 7 9 3 4 8 8 2 5 9 7 +--R 18258240a b d e + 4684680a b d e + 320320a b d e +--R * +--R 6 +--R x +--R + +--R 7 5 11 6 6 10 5 2 7 9 +--R 2018016a d e + 9753744a b d e + 12972960a b d e +--R + +--R 4 3 8 8 3 4 9 7 +--R 5585580a b d e + 640640a b d e +--R * +--R 5 +--R x +--R + +--R 7 6 10 6 7 9 5 2 8 8 4 3 9 7 4 +--R (1681680a d e + 5285280a b d e + 4144140a b d e + 800800a b d e )x +--R + +--R 7 7 9 6 8 8 5 2 9 7 3 +--R (960960a d e + 1801800a b d e + 640640a b d e )x +--R + +--R 7 8 8 6 9 7 2 7 9 7 +--R (360360a d e + 320320a b d e )x + 80080a d e x +--R / +--R 7 7 +--R 80080b e x + 80080a e +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 9 15 5 9 6 8 14 +--R b e x + (6a b e + 9b d e )x +--R + +--R 2 4 9 5 8 6 2 7 13 +--R (15a b e + 54a b d e + 36b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 12 +--R (20a b e + 135a b d e + 216a b d e + 84b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 5 3 6 6 4 5 11 +--R (15a b e + 180a b d e + 540a b d e + 504a b d e + 126b d e )x +--R + +--R 5 9 4 2 8 3 3 2 7 2 4 3 6 5 4 5 +--R 6a b e + 135a b d e + 720a b d e + 1260a b d e + 756a b d e +--R + +--R 6 5 4 +--R 126b d e +--R * +--R 10 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 2 4 4 5 +--R a e + 54a b d e + 540a b d e + 1680a b d e + 1890a b d e +--R + +--R 5 5 4 6 6 3 +--R 756a b d e + 84b d e +--R * +--R 9 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R 9a d e + 216a b d e + 1260a b d e + 2520a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R 1890a b d e + 504a b d e + 36b d e +--R * +--R 8 +--R x +--R + +--R 6 2 7 5 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- 63a b d e - 36b d e )x +--R + +--R 3 4 9 2 5 8 6 2 7 7 3 6 13 +--R (- 35a b e - 189a b d e - 252a b d e - 84b d e )x +--R + +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 7 4 5 12 +--R (- 35a b e - 315a b d e - 756a b d e - 588a b d e - 126b d e )x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 6 4 5 +--R - 21a b e - 315a b d e - 1260a b d e - 1764a b d e - 882a b d e +--R + +--R 7 5 4 +--R - 126b d e +--R * +--R 11 +--R x +--R + +--R 6 9 5 2 8 4 3 2 7 3 4 3 6 2 5 4 5 +--R - 7a b e - 189a b d e - 1260a b d e - 2940a b d e - 2646a b d e +--R + +--R 6 5 4 7 6 3 +--R - 882a b d e - 84b d e +--R * +--R 10 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 3 4 4 5 +--R - a e - 63a b d e - 756a b d e - 2940a b d e - 4410a b d e +--R + +--R 2 5 5 4 6 6 3 7 7 2 +--R - 2646a b d e - 588a b d e - 36b d e +--R * +--R 9 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 3 4 5 4 +--R - 9a d e - 252a b d e - 1764a b d e - 4410a b d e - 4410a b d e +--R + +--R 2 5 6 3 6 7 2 7 8 +--R - 1764a b d e - 252a b d e - 9b d e +--R * +--R 8 +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 +--R - 36a d e - 588a b d e - 2646a b d e - 4410a b d e - 2940a b d e +--R + +--R 2 5 7 2 6 8 7 9 +--R - 756a b d e - 63a b d e - b d +--R * +--R 7 +--R x +--R + +--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2 +--R - 84a d e - 882a b d e - 2646a b d e - 2940a b d e - 1260a b d e +--R + +--R 2 5 8 6 9 +--R - 189a b d e - 7a b d +--R * +--R 6 +--R x +--R + +--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8 +--R - 126a d e - 882a b d e - 1764a b d e - 1260a b d e - 315a b d e +--R + +--R 2 5 9 +--R - 21a b d +--R * +--R 5 +--R x +--R + +--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9 4 +--R (- 126a d e - 588a b d e - 756a b d e - 315a b d e - 35a b d )x +--R + +--R 7 6 3 6 7 2 5 2 8 4 3 9 3 +--R (- 84a d e - 252a b d e - 189a b d e - 35a b d )x +--R + +--R 7 7 2 6 8 5 2 9 2 7 8 6 9 7 9 +--R (- 36a d e - 63a b d e - 21a b d )x + (- 9a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 1353 +t0:=(a+b*x)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 8 13 4 8 5 7 12 2 3 8 4 7 5 2 6 11 +--R b e x + (5a b e + 8b d e )x + (10a b e + 40a b d e + 28b d e )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 10 +--R (10a b e + 80a b d e + 140a b d e + 56b d e )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 5 4 4 9 +--R (5a b e + 80a b d e + 280a b d e + 280a b d e + 70b d e )x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 4 4 4 +--R a e + 40a b d e + 280a b d e + 560a b d e + 350a b d e +--R + +--R 5 5 3 +--R 56b d e +--R * +--R 8 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 4 5 3 +--R 8a d e + 140a b d e + 560a b d e + 700a b d e + 280a b d e +--R + +--R 5 6 2 +--R 28b d e +--R * +--R 7 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 4 6 2 +--R 28a d e + 280a b d e + 700a b d e + 560a b d e + 140a b d e +--R + +--R 5 7 +--R 8b d e +--R * +--R 6 +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 4 7 5 8 5 +--R (56a d e + 350a b d e + 560a b d e + 280a b d e + 40a b d e + b d )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 4 +--R (70a d e + 280a b d e + 280a b d e + 80a b d e + 5a b d )x +--R + +--R 5 5 3 4 6 2 3 2 7 2 3 8 3 +--R (56a d e + 140a b d e + 80a b d e + 10a b d )x +--R + +--R 5 6 2 4 7 3 2 8 2 5 7 4 8 5 8 +--R (28a d e + 40a b d e + 10a b d )x + (8a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1353 +r0:=-1/273*(b*d-a*e)^3*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/91*(b*d-a*e)^2*(a+b*x)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/35*(b*d-a*e)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/15*(a+b*x)*_ + (d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/5005*(b*d-a*e)^5*(d+e*x)^9*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/45045*(b*d-a*e)^6*(d+e*x)^9*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/1001*(b*d-a*e)^4*(a+b*x)*(d+e*x)^9*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 15 15 5 15 6 14 14 +--R 3003b e x + (19305a b e + 25740b d e )x +--R + +--R 2 4 15 5 14 6 2 13 13 +--R (51975a b e + 166320a b d e + 97020b d e )x +--R + +--R 3 3 15 2 4 14 5 2 13 6 3 12 12 +--R (75075a b e + 450450a b d e + 630630a b d e + 210210b d e )x +--R + +--R 4 2 15 3 3 14 2 4 2 13 +--R 61425a b e + 655200a b d e + 1719900a b d e +--R + +--R 5 3 12 6 4 11 +--R 1375920a b d e + 286650b d e +--R * +--R 11 +--R x +--R + +--R 5 15 4 2 14 3 3 2 13 +--R 27027a b e + 540540a b d e + 2522520a b d e +--R + +--R 2 4 3 12 5 4 11 6 5 10 +--R 3783780a b d e + 1891890a b d e + 252252b d e +--R * +--R 10 +--R x +--R + +--R 6 15 5 14 4 2 2 13 3 3 3 12 +--R 5005a e + 240240a b d e + 2102100a b d e + 5605600a b d e +--R + +--R 2 4 4 11 5 5 10 6 6 9 +--R 5255250a b d e + 1681680a b d e + 140140b d e +--R * +--R 9 +--R x +--R + +--R 6 14 5 2 13 4 2 3 12 +--R 45045a d e + 945945a b d e + 4729725a b d e +--R + +--R 3 3 4 11 2 4 5 10 5 6 9 6 7 8 +--R 7882875a b d e + 4729725a b d e + 945945a b d e + 45045b d e +--R * +--R 8 +--R x +--R + +--R 6 2 13 5 3 12 4 2 4 11 +--R 180180a d e + 2162160a b d e + 6756750a b d e +--R + +--R 3 3 5 10 2 4 6 9 5 7 8 6 8 7 +--R 7207200a b d e + 2702700a b d e + 308880a b d e + 6435b d e +--R * +--R 7 +--R x +--R + +--R 6 3 12 5 4 11 4 2 5 10 +--R 420420a d e + 3153150a b d e + 6306300a b d e +--R + +--R 3 3 6 9 2 4 7 8 5 8 7 +--R 4204200a b d e + 900900a b d e + 45045a b d e +--R * +--R 6 +--R x +--R + +--R 6 4 11 5 5 10 4 2 6 9 +--R 630630a d e + 3027024a b d e + 3783780a b d e +--R + +--R 3 3 7 8 2 4 8 7 +--R 1441440a b d e + 135135a b d e +--R * +--R 5 +--R x +--R + +--R 6 5 10 5 6 9 4 2 7 8 3 3 8 7 4 +--R (630630a d e + 1891890a b d e + 1351350a b d e + 225225a b d e )x +--R + +--R 6 6 9 5 7 8 4 2 8 7 3 +--R (420420a d e + 720720a b d e + 225225a b d e )x +--R + +--R 6 7 8 5 8 7 2 6 8 7 6 9 6 +--R (180180a d e + 135135a b d e )x + 45045a d e x + 5005a d e +--R + +--R 5 10 5 4 2 11 4 3 3 12 3 2 4 13 2 +--R - 3003a b d e + 1365a b d e - 455a b d e + 105a b d e +--R + +--R 5 14 6 15 +--R - 15a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 8 15 5 8 6 7 14 +--R 3003b e x + (19305a b e + 25740b d e )x +--R + +--R 2 4 8 5 7 6 2 6 13 +--R (51975a b e + 166320a b d e + 97020b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 12 +--R (75075a b e + 450450a b d e + 630630a b d e + 210210b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 +--R 61425a b e + 655200a b d e + 1719900a b d e + 1375920a b d e +--R + +--R 6 4 4 +--R 286650b d e +--R * +--R 11 +--R x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 +--R 27027a b e + 540540a b d e + 2522520a b d e + 3783780a b d e +--R + +--R 5 4 4 6 5 3 +--R 1891890a b d e + 252252b d e +--R * +--R 10 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 +--R 5005a e + 240240a b d e + 2102100a b d e + 5605600a b d e +--R + +--R 2 4 4 4 5 5 3 6 6 2 +--R 5255250a b d e + 1681680a b d e + 140140b d e +--R * +--R 9 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 +--R 45045a d e + 945945a b d e + 4729725a b d e + 7882875a b d e +--R + +--R 2 4 5 3 5 6 2 6 7 +--R 4729725a b d e + 945945a b d e + 45045b d e +--R * +--R 8 +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R 180180a d e + 2162160a b d e + 6756750a b d e + 7207200a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R 2702700a b d e + 308880a b d e + 6435b d +--R * +--R 7 +--R x +--R + +--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 +--R 420420a d e + 3153150a b d e + 6306300a b d e + 4204200a b d e +--R + +--R 2 4 7 5 8 +--R 900900a b d e + 45045a b d +--R * +--R 6 +--R x +--R + +--R 6 4 4 5 5 3 4 2 6 2 3 3 7 +--R 630630a d e + 3027024a b d e + 3783780a b d e + 1441440a b d e +--R + +--R 2 4 8 +--R 135135a b d +--R * +--R 5 +--R x +--R + +--R 6 5 3 5 6 2 4 2 7 3 3 8 4 +--R (630630a d e + 1891890a b d e + 1351350a b d e + 225225a b d )x +--R + +--R 6 6 2 5 7 4 2 8 3 +--R (420420a d e + 720720a b d e + 225225a b d )x +--R + +--R 6 7 5 8 2 6 8 +--R (180180a d e + 135135a b d )x + 45045a d x +--R / +--R 45045 +--R Type: Union(Expression(Integer),...) +--E 510 + +--S 511 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 15 15 5 15 6 14 14 +--R - 3003b e x + (- 19305a b e - 25740b d e )x +--R + +--R 2 4 15 5 14 6 2 13 13 +--R (- 51975a b e - 166320a b d e - 97020b d e )x +--R + +--R 3 3 15 2 4 14 5 2 13 +--R - 75075a b e - 450450a b d e - 630630a b d e +--R + +--R 6 3 12 +--R - 210210b d e +--R * +--R 12 +--R x +--R + +--R 4 2 15 3 3 14 2 4 2 13 +--R - 61425a b e - 655200a b d e - 1719900a b d e +--R + +--R 5 3 12 6 4 11 +--R - 1375920a b d e - 286650b d e +--R * +--R 11 +--R x +--R + +--R 5 15 4 2 14 3 3 2 13 +--R - 27027a b e - 540540a b d e - 2522520a b d e +--R + +--R 2 4 3 12 5 4 11 6 5 10 +--R - 3783780a b d e - 1891890a b d e - 252252b d e +--R * +--R 10 +--R x +--R + +--R 6 15 5 14 4 2 2 13 +--R - 5005a e - 240240a b d e - 2102100a b d e +--R + +--R 3 3 3 12 2 4 4 11 5 5 10 +--R - 5605600a b d e - 5255250a b d e - 1681680a b d e +--R + +--R 6 6 9 +--R 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x +--R + +--R 6 6 9 5 7 8 4 2 8 7 3 +--R (- 420420a d e - 720720a b d e - 225225a b d e )x +--R + +--R 6 7 8 5 8 7 2 6 8 7 6 9 6 +--R (- 180180a d e - 135135a b d e )x - 45045a d e x - 5005a d e +--R + +--R 5 10 5 4 2 11 4 3 3 12 3 2 4 13 2 +--R 3003a b d e - 1365a b d e + 455a b d e - 105a b d e +--R + +--R 5 14 6 15 +--R 15a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 15 16 6 15 7 14 15 +--R 3003b e x + (22308a b e + 25740b d e )x +--R + +--R 2 5 15 6 14 7 2 13 14 +--R (71280a b e + 192060a b d e + 97020b d e )x +--R + +--R 3 4 15 2 5 14 6 2 13 7 3 12 13 +--R (127050a b e + 616770a b d e + 727650a b d e + 210210b d e )x +--R + +--R 4 3 15 3 4 14 2 5 2 13 +--R 136500a b e + 1105650a b d e + 2350530a b d e +--R + +--R 6 3 12 7 4 11 +--R 1586130a b d e + 286650b d e +--R * +--R 12 +--R x +--R + +--R 5 2 15 4 3 14 3 4 2 13 2 5 3 12 +--R 88452a b e + 1195740a b d e + 4242420a b d e + 5159700a b d e +--R + +--R 6 4 11 7 5 10 +--R 2178540a b d e + 252252b d e +--R * +--R 11 +--R x +--R + +--R 6 15 5 2 14 4 3 2 13 3 4 3 12 +--R 32032a b e + 780780a b d e + 4624620a b d e + 9389380a b d e +--R + +--R 2 5 4 11 6 5 10 7 6 9 +--R 7147140a b d e + 1933932a b d e + 140140b d e +--R * +--R 10 +--R x +--R + +--R 7 15 6 14 5 2 2 13 4 3 3 12 +--R 5005a e + 285285a b d e + 3048045a b d e + 10335325a b d e +--R + +--R 3 4 4 11 2 5 5 10 6 6 9 7 7 8 +--R 13138125a b d e + 6411405a b d e + 1086085a b d e + 45045b d e +--R * +--R 9 +--R x +--R + +--R 7 14 6 2 13 5 2 3 12 +--R 45045a d e + 1126125a b d e + 6891885a b d e +--R + +--R 4 3 4 11 3 4 5 10 2 5 6 9 +--R 14639625a b d e + 11936925a b d e + 3648645a b d e +--R + +--R 6 7 8 7 8 7 +--R 353925a b d e + 6435b d e +--R * +--R 8 +--R x +--R + +--R 7 2 13 6 3 12 5 2 4 11 +--R 180180a d e + 2582580a b d e + 9909900a b d e +--R + +--R 4 3 5 10 3 4 6 9 2 5 7 8 6 8 7 +--R 13513500a b d e + 6906900a b d e + 1209780a b d e + 51480a b d e +--R * +--R 7 +--R x +--R + +--R 7 3 12 6 4 11 5 2 5 10 4 3 6 9 +--R 420420a d e + 3783780a b d e + 9333324a b d e + 7987980a b d e +--R + +--R 3 4 7 8 2 5 8 7 +--R 2342340a b d e + 180180a b d e +--R * +--R 6 +--R x +--R + +--R 7 4 11 6 5 10 5 2 6 9 4 3 7 8 +--R 630630a d e + 3657654a b d e + 5675670a b d e + 2792790a b d e +--R + +--R 3 4 8 7 +--R 360360a b d e +--R * +--R 5 +--R x +--R + +--R 7 5 10 6 6 9 5 2 7 8 4 3 8 7 4 +--R (630630a d e + 2312310a b d e + 2072070a b d e + 450450a b d e )x +--R + +--R 7 6 9 6 7 8 5 2 8 7 3 +--R (420420a d e + 900900a b d e + 360360a b d e )x +--R + +--R 7 7 8 6 8 7 2 7 8 7 +--R (180180a d e + 180180a b d e )x + 45045a d e x +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 8 14 5 8 6 7 13 +--R b e x + (6a b e + 8b d e )x +--R + +--R 2 4 8 5 7 6 2 6 12 +--R (15a b e + 48a b d e + 28b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 11 +--R (20a b e + 120a b d e + 168a b d e + 56b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 6 4 4 10 +--R (15a b e + 160a b d e + 420a b d e + 336a b d e + 70b d e )x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 +--R 6a b e + 120a b d e + 560a b d e + 840a b d e + 420a b d e +--R + +--R 6 5 3 +--R 56b d e +--R * +--R 9 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 2 4 4 4 +--R a e + 48a b d e + 420a b d e + 1120a b d e + 1050a b d e +--R + +--R 5 5 3 6 6 2 +--R 336a b d e + 28b d e +--R * +--R 8 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 +--R 8a d e + 168a b d e + 840a b d e + 1400a b d e + 840a b d e +--R + +--R 5 6 2 6 7 +--R 168a b d e + 8b d e +--R * +--R 7 +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R 28a d e + 336a b d e + 1050a b d e + 1120a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R 420a b d e + 48a b d e + b d +--R * +--R 6 +--R x +--R + +--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7 +--R 56a d e + 420a b d e + 840a b d e + 560a b d e + 120a b d e +--R + +--R 5 8 +--R 6a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8 4 +--R (70a d e + 336a b d e + 420a b d e + 160a b d e + 15a b d )x +--R + +--R 6 5 3 5 6 2 4 2 7 3 3 8 3 +--R (56a d e + 168a b d e + 120a b d e + 20a b d )x +--R + +--R 6 6 2 5 7 4 2 8 2 6 7 5 8 6 8 +--R (28a d e + 48a b d e + 15a b d )x + (8a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 8 15 6 8 7 7 14 +--R - b e x + (- 7a b e - 8b d e )x +--R + +--R 2 5 8 6 7 7 2 6 13 +--R (- 21a b e - 56a b d e - 28b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 12 +--R (- 35a b e - 168a b d e - 196a b d e - 56b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 7 4 4 11 +--R (- 35a b e - 280a b d e - 588a b d e - 392a b d e - 70b d e )x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 6 4 4 +--R - 21a b e - 280a b d e - 980a b d e - 1176a b d e - 490a b d e +--R + +--R 7 5 3 +--R - 56b d e +--R * +--R 10 +--R x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 2 5 4 4 +--R - 7a b e - 168a b d e - 980a b d e - 1960a b d e - 1470a b d e +--R + +--R 6 5 3 7 6 2 +--R - 392a b d e - 28b d e +--R * +--R 9 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 3 4 4 4 +--R - a e - 56a b d e - 588a b d e - 1960a b d e - 2450a b d e +--R + +--R 2 5 5 3 6 6 2 7 7 +--R - 1176a b d e - 196a b d e - 8b d e +--R * +--R 8 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 3 4 5 3 +--R - 8a d e - 196a b d e - 1176a b d e - 2450a b d e - 1960a b d e +--R + +--R 2 5 6 2 6 7 7 8 +--R - 588a b d e - 56a b d e - b d +--R * +--R 7 +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 4 3 5 3 3 4 6 2 +--R - 28a d e - 392a b d e - 1470a b d e - 1960a b d e - 980a b d e +--R + +--R 2 5 7 6 8 +--R - 168a b d e - 7a b d +--R * +--R 6 +--R x +--R + +--R 7 3 5 6 4 4 5 2 5 3 4 3 6 2 3 4 7 +--R - 56a d e - 490a b d e - 1176a b d e - 980a b d e - 280a b d e +--R + +--R 2 5 8 +--R - 21a b d +--R * +--R 5 +--R x +--R + +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 4 +--R (- 70a d e - 392a b d e - 588a b d e - 280a b d e - 35a b d )x +--R + +--R 7 5 3 6 6 2 5 2 7 4 3 8 3 +--R (- 56a d e - 196a b d e - 168a b d e - 35a b d )x +--R + +--R 7 6 2 6 7 5 2 8 2 7 7 6 8 7 8 +--R (- 28a d e - 56a b d e - 21a b d )x + (- 8a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 512 + +)clear all + +--S 513 of 1353 +t0:=(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 7 12 4 7 5 6 11 2 3 7 4 6 5 2 5 10 +--R b e x + (5a b e + 7b d e )x + (10a b e + 35a b d e + 21b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 9 +--R (10a b e + 70a b d e + 105a b d e + 35b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 8 +--R (5a b e + 70a b d e + 210a b d e + 175a b d e + 35b d e )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 +--R a e + 35a b d e + 210a b d e + 350a b d e + 175a b d e +--R + +--R 5 5 2 +--R 21b d e +--R * +--R 7 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 +--R 7a d e + 105a b d e + 350a b d e + 350a b d e + 105a b d e +--R + +--R 5 6 +--R 7b d e +--R * +--R 6 +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 5 7 5 +--R (21a d e + 175a b d e + 350a b d e + 210a b d e + 35a b d e + b d )x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 4 +--R (35a d e + 175a b d e + 210a b d e + 70a b d e + 5a b d )x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 3 +--R (35a d e + 105a b d e + 70a b d e + 10a b d )x +--R + +--R 5 5 2 4 6 3 2 7 2 5 6 4 7 5 7 +--R (21a d e + 35a b d e + 10a b d )x + (7a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1353 +r0:=-5/1001*(b*d-a*e)^3*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 5/364*(b*d-a*e)^2*(a+b*x)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 3/91*(b*d-a*e)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/14*(a+b*x)*_ + (d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/3003*(b*d-a*e)^5*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/24024*(b*d-a*e)^6*(d+e*x)^8*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+3/2002*(b*d-a*e)^4*(a+b*x)*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 14 14 5 14 6 13 13 +--R 1716b e x + (11088a b e + 12936b d e )x +--R + +--R 2 4 14 5 13 6 2 12 12 +--R (30030a b e + 84084a b d e + 42042b d e )x +--R + +--R 3 3 14 2 4 13 5 2 12 6 3 11 11 +--R (43680a b e + 229320a b d e + 275184a b d e + 76440b d e )x +--R + +--R 4 2 14 3 3 13 2 4 2 12 5 3 11 +--R 36036a b e + 336336a b d e + 756756a b d e + 504504a b d e +--R + +--R 6 4 10 +--R 84084b d e +--R * +--R 10 +--R x +--R + +--R 5 14 4 2 13 3 3 2 12 +--R 16016a b e + 280280a b d e + 1121120a b d e +--R + +--R 2 4 3 11 5 4 10 6 5 9 +--R 1401400a b d e + 560560a b d e + 56056b d e +--R * +--R 9 +--R x +--R + +--R 6 14 5 13 4 2 2 12 3 3 3 11 +--R 3003a e + 126126a b d e + 945945a b d e + 2102100a b d e +--R + +--R 2 4 4 10 5 5 9 6 6 8 +--R 1576575a b d e + 378378a b d e + 21021b d e +--R * +--R 8 +--R x +--R + +--R 6 13 5 2 12 4 2 3 11 +--R 24024a d e + 432432a b d e + 1801800a b d e +--R + +--R 3 3 4 10 2 4 5 9 5 6 8 6 7 7 +--R 2402400a b d e + 1081080a b d e + 144144a b d e + 3432b d e +--R * +--R 7 +--R x +--R + +--R 6 2 12 5 3 11 4 2 4 10 3 3 5 9 +--R 84084a d e + 840840a b d e + 2102100a b d e + 1681680a b d e +--R + +--R 2 4 6 8 5 7 7 +--R 420420a b d e + 24024a b d e +--R * +--R 6 +--R x +--R + +--R 6 3 11 5 4 10 4 2 5 9 3 3 6 8 +--R 168168a d e + 1009008a b d e + 1513512a b d e + 672672a b d e +--R + +--R 2 4 7 7 +--R 72072a b d e +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 2 6 8 3 3 7 7 4 +--R (210210a d e + 756756a b d e + 630630a b d e + 120120a b d e )x +--R + +--R 6 5 9 5 6 8 4 2 7 7 3 +--R (168168a d e + 336336a b d e + 120120a b d e )x +--R + +--R 6 6 8 5 7 7 2 6 7 7 6 8 6 +--R (84084a d e + 72072a b d e )x + 24024a d e x + 3003a d e +--R + +--R 5 9 5 4 2 10 4 3 3 11 3 2 4 12 2 +--R - 2002a b d e + 1001a b d e - 364a b d e + 91a b d e +--R + +--R 5 13 6 14 +--R - 14a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 24024b e x + 24024a e +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 14 5 7 6 6 13 +--R 1716b e x + (11088a b e + 12936b d e )x +--R + +--R 2 4 7 5 6 6 2 5 12 +--R (30030a b e + 84084a b d e + 42042b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 11 +--R (43680a b e + 229320a b d e + 275184a b d e + 76440b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 +--R 36036a b e + 336336a b d e + 756756a b d e + 504504a b d e +--R + +--R 6 4 3 +--R 84084b d e +--R * +--R 10 +--R x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 16016a b e + 280280a b d e + 1121120a b d e + 1401400a b d e +--R + +--R 5 4 3 6 5 2 +--R 560560a b d e + 56056b d e +--R * +--R 9 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 3003a e + 126126a b d e + 945945a b d e + 2102100a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 1576575a b d e + 378378a b d e + 21021b d e +--R * +--R 8 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 24024a d e + 432432a b d e + 1801800a b d e + 2402400a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R 1081080a b d e + 144144a b d e + 3432b d +--R * +--R 7 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 +--R 84084a d e + 840840a b d e + 2102100a b d e + 1681680a b d e +--R + +--R 2 4 6 5 7 +--R 420420a b d e + 24024a b d +--R * +--R 6 +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 +--R 168168a d e + 1009008a b d e + 1513512a b d e + 672672a b d e +--R + +--R 2 4 7 +--R 72072a b d +--R * +--R 5 +--R x +--R + +--R 6 4 3 5 5 2 4 2 6 3 3 7 4 +--R (210210a d e + 756756a b d e + 630630a b d e + 120120a b d )x +--R + +--R 6 5 2 5 6 4 2 7 3 +--R (168168a d e + 336336a b d e + 120120a b d )x +--R + +--R 6 6 5 7 2 6 7 +--R (84084a d e + 72072a b d )x + 24024a d x +--R / +--R 24024 +--R Type: Union(Expression(Integer),...) +--E 515 + +--S 516 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 14 14 5 14 6 13 13 +--R - 1716b e x + (- 11088a b e - 12936b d e )x +--R + +--R 2 4 14 5 13 6 2 12 12 +--R (- 30030a b e - 84084a b d e - 42042b d e )x +--R + +--R 3 3 14 2 4 13 5 2 12 6 3 11 +--R (- 43680a b e - 229320a b d e - 275184a b d e - 76440b d e ) +--R * +--R 11 +--R x +--R + +--R 4 2 14 3 3 13 2 4 2 12 +--R - 36036a b e - 336336a b d e - 756756a b d e +--R + +--R 5 3 11 6 4 10 +--R - 504504a b d e - 84084b d e +--R * +--R 10 +--R x +--R + +--R 5 14 4 2 13 3 3 2 12 +--R - 16016a b e - 280280a b d e - 1121120a b d e +--R + +--R 2 4 3 11 5 4 10 6 5 9 +--R - 1401400a b d e - 560560a b d e - 56056b d e +--R * +--R 9 +--R x +--R + +--R 6 14 5 13 4 2 2 12 +--R - 3003a e - 126126a b d e - 945945a b d e +--R + +--R 3 3 3 11 2 4 4 10 5 5 9 +--R - 2102100a b d e - 1576575a b d e - 378378a b d e +--R + +--R 6 6 8 +--R - 21021b d e +--R * +--R 8 +--R x +--R + +--R 6 13 5 2 12 4 2 3 11 +--R - 24024a d e - 432432a b d e - 1801800a b d e +--R + +--R 3 3 4 10 2 4 5 9 5 6 8 6 7 7 +--R - 2402400a b d e - 1081080a b d e - 144144a b d e - 3432b d e +--R * +--R 7 +--R x +--R + +--R 6 2 12 5 3 11 4 2 4 10 +--R - 84084a d e - 840840a b d e - 2102100a b d e +--R + +--R 3 3 5 9 2 4 6 8 5 7 7 +--R - 1681680a b d e - 420420a b d e - 24024a b d e +--R * +--R 6 +--R x +--R + +--R 6 3 11 5 4 10 4 2 5 9 +--R - 168168a d e - 1009008a b d e - 1513512a b d e +--R + +--R 3 3 6 8 2 4 7 7 +--R - 672672a b d e - 72072a b d e +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 2 6 8 +--R - 210210a d e - 756756a b d e - 630630a b d e +--R + +--R 3 3 7 7 +--R - 120120a b d e +--R * +--R 4 +--R x +--R + +--R 6 5 9 5 6 8 4 2 7 7 3 +--R (- 168168a d e - 336336a b d e - 120120a b d e )x +--R + +--R 6 6 8 5 7 7 2 6 7 7 6 8 6 +--R (- 84084a d e - 72072a b d e )x - 24024a d e x - 3003a d e +--R + +--R 5 9 5 4 2 10 4 3 3 11 3 2 4 12 2 +--R 2002a b d e - 1001a b d e + 364a b d e - 91a b d e +--R + +--R 5 13 6 14 +--R 14a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 14 15 6 14 7 13 14 +--R 1716b e x + (12804a b e + 12936b d e )x +--R + +--R 2 5 14 6 13 7 2 12 13 +--R (41118a b e + 97020a b d e + 42042b d e )x +--R + +--R 3 4 14 2 5 13 6 2 12 7 3 11 12 +--R (73710a b e + 313404a b d e + 317226a b d e + 76440b d e )x +--R + +--R 4 3 14 3 4 13 2 5 2 12 6 3 11 +--R 79716a b e + 565656a b d e + 1031940a b d e + 580944a b d e +--R + +--R 7 4 10 +--R 84084b d e +--R * +--R 11 +--R x +--R + +--R 5 2 14 4 3 13 3 4 2 12 2 5 3 11 +--R 52052a b e + 616616a b d e + 1877876a b d e + 1905904a b d e +--R + +--R 6 4 10 7 5 9 +--R 644644a b d e + 56056b d e +--R * +--R 10 +--R x +--R + +--R 6 14 5 2 13 4 3 2 12 3 4 3 11 +--R 19019a b e + 406406a b d e + 2067065a b d e + 3503500a b d e +--R + +--R 2 5 4 10 6 5 9 7 6 8 +--R 2137135a b d e + 434434a b d e + 21021b d e +--R * +--R 9 +--R x +--R + +--R 7 14 6 13 5 2 2 12 4 3 3 11 +--R 3003a e + 150150a b d e + 1378377a b d e + 3903900a b d e +--R + +--R 3 4 4 10 2 5 5 9 6 6 8 7 7 7 +--R 3978975a b d e + 1459458a b d e + 165165a b d e + 3432b d e +--R * +--R 8 +--R x +--R + +--R 7 13 6 2 12 5 2 3 11 4 3 4 10 +--R 24024a d e + 516516a b d e + 2642640a b d e + 4504500a b d e +--R + +--R 3 4 5 9 2 5 6 8 6 7 7 +--R 2762760a b d e + 564564a b d e + 27456a b d e +--R * +--R 7 +--R x +--R + +--R 7 2 12 6 3 11 5 2 4 10 4 3 5 9 +--R 84084a d e + 1009008a b d e + 3111108a b d e + 3195192a b d e +--R + +--R 3 4 6 8 2 5 7 7 +--R 1093092a b d e + 96096a b d e +--R * +--R 6 +--R x +--R + +--R 7 3 11 6 4 10 5 2 5 9 4 3 6 8 +--R 168168a d e + 1219218a b d e + 2270268a b d e + 1303302a b d e +--R + +--R 3 4 7 7 +--R 192192a b d e +--R * +--R 5 +--R x +--R + +--R 7 4 10 6 5 9 5 2 6 8 4 3 7 7 4 +--R (210210a d e + 924924a b d e + 966966a b d e + 240240a b d e )x +--R + +--R 7 5 9 6 6 8 5 2 7 7 3 +--R (168168a d e + 420420a b d e + 192192a b d e )x +--R + +--R 7 6 8 6 7 7 2 7 7 7 +--R (84084a d e + 96096a b d e )x + 24024a d e x +--R / +--R 7 7 +--R 24024b e x + 24024a e +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 7 13 5 7 6 6 12 +--R b e x + (6a b e + 7b d e )x +--R + +--R 2 4 7 5 6 6 2 5 11 +--R (15a b e + 42a b d e + 21b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 10 +--R (20a b e + 105a b d e + 126a b d e + 35b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 6 4 3 9 +--R (15a b e + 140a b d e + 315a b d e + 210a b d e + 35b d e )x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 6a b e + 105a b d e + 420a b d e + 525a b d e + 210a b d e +--R + +--R 6 5 2 +--R 21b d e +--R * +--R 8 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R a e + 42a b d e + 315a b d e + 700a b d e + 525a b d e +--R + +--R 5 5 2 6 6 +--R 126a b d e + 7b d e +--R * +--R 7 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R 7a d e + 126a b d e + 525a b d e + 700a b d e + 315a b d e +--R + +--R 5 6 6 7 +--R 42a b d e + b d +--R * +--R 6 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R 21a d e + 210a b d e + 525a b d e + 420a b d e + 105a b d e +--R + +--R 5 7 +--R 6a b d +--R * +--R 5 +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 4 +--R (35a d e + 210a b d e + 315a b d e + 140a b d e + 15a b d )x +--R + +--R 6 4 3 5 5 2 4 2 6 3 3 7 3 +--R (35a d e + 126a b d e + 105a b d e + 20a b d )x +--R + +--R 6 5 2 5 6 4 2 7 2 6 6 5 7 6 7 +--R (21a d e + 42a b d e + 15a b d )x + (7a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 14 6 7 7 6 13 +--R - b e x + (- 7a b e - 7b d e )x +--R + +--R 2 5 7 6 6 7 2 5 12 +--R (- 21a b e - 49a b d e - 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 11 +--R (- 35a b e - 147a b d e - 147a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 10 +--R (- 35a b e - 245a b d e - 441a b d e - 245a b d e - 35b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 21a b e - 245a b d e - 735a b d e - 735a b d e - 245a b d e +--R + +--R 7 5 2 +--R - 21b d e +--R * +--R 9 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 7a b e - 147a b d e - 735a b d e - 1225a b d e - 735a b d e +--R + +--R 6 5 2 7 6 +--R - 147a b d e - 7b d e +--R * +--R 8 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - a e - 49a b d e - 441a b d e - 1225a b d e - 1225a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 441a b d e - 49a b d e - b d +--R * +--R 7 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 +--R - 7a d e - 147a b d e - 735a b d e - 1225a b d e - 735a b d e +--R + +--R 2 5 6 6 7 +--R - 147a b d e - 7a b d +--R * +--R 6 +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R - 21a d e - 245a b d e - 735a b d e - 735a b d e - 245a b d e +--R + +--R 2 5 7 +--R - 21a b d +--R * +--R 5 +--R x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 4 +--R (- 35a d e - 245a b d e - 441a b d e - 245a b d e - 35a b d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 3 +--R (- 35a d e - 147a b d e - 147a b d e - 35a b d )x +--R + +--R 7 5 2 6 6 5 2 7 2 7 6 6 7 7 7 +--R (- 21a d e - 49a b d e - 21a b d )x + (- 7a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 517 + +)clear all + +--S 518 of 1353 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 11 4 6 5 5 10 2 3 6 4 5 5 2 4 9 +--R b e x + (5a b e + 6b d e )x + (10a b e + 30a b d e + 15b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 8 +--R (10a b e + 60a b d e + 75a b d e + 20b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 7 +--R (5a b e + 60a b d e + 150a b d e + 100a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 6 +--R (a e + 30a b d e + 150a b d e + 200a b d e + 75a b d e + 6b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 5 +--R (6a d e + 75a b d e + 200a b d e + 150a b d e + 30a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 4 +--R (15a d e + 100a b d e + 150a b d e + 60a b d e + 5a b d )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 3 +--R (20a d e + 75a b d e + 60a b d e + 10a b d )x +--R + +--R 5 4 2 4 5 3 2 6 2 5 5 4 6 5 6 +--R (15a d e + 30a b d e + 10a b d )x + (6a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1353 +r0:=1/12012*(b*d-a*e)^6*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^7+1/1716*(b*d-a*e)^5*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6+1/429*(b*d-a*e)^4*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/143*(b*d-a*e)^3*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^4+5/286*(b*d-a*e)^2*(d+e*x)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^3+1/26*(b*d-a*e)*(d+e*x)^5*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/13*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 12 6 12 11 6 12 5 11 +--R 924b e x + (5082a b e + 6006b d e )x +--R + +--R 2 10 6 11 5 12 2 4 10 +--R (11298a b e + 33306a b d e + 16380b d e )x +--R + +--R 3 9 6 2 10 5 11 2 4 12 3 3 9 +--R (12726a b e + 74802a b d e + 91728a b d e + 24024b d e )x +--R + +--R 4 8 6 3 9 5 2 10 2 4 11 3 3 +--R 7294a b e + 85358a b d e + 208572a b d e + 136136a b d e +--R + +--R 12 4 2 +--R 20020b d e +--R * +--R 8 +--R x +--R + +--R 5 7 6 4 8 5 3 9 2 4 2 10 3 3 +--R 1715a b e + 49777a b d e + 241878a b d e + 314314a b d e +--R + +--R 11 4 2 12 5 +--R 115115a b d e + 9009b d e +--R * +--R 7 +--R x +--R + +--R 6 6 6 5 7 5 4 8 2 4 3 9 3 3 +--R a b e + 11999a b d e + 144222a b d e + 372086a b d e +--R + +--R 2 10 4 2 11 5 12 6 +--R 270985a b d e + 52767a b d e + 1716b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 6 6 5 5 7 2 4 4 8 3 3 +--R - a b e + 13a b d e + 35958a b d e + 228514a b d e +--R + +--R 3 9 4 2 2 10 5 11 6 +--R 329615a b d e + 127413a b d e + 10296a b d +--R * +--R 5 +--R x +--R + +--R 8 4 6 7 5 5 6 6 2 4 5 7 3 3 4 8 4 2 +--R a b e - 13a b d e + 78a b d e + 59774a b d e + 210925a b d e +--R + +--R 3 9 5 2 10 6 +--R 160875a b d e + 25740a b d +--R * +--R 4 +--R x +--R + +--R 9 3 6 8 4 5 7 5 2 4 6 6 3 3 5 7 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e + 59345a b d e +--R + +--R 4 8 5 3 9 6 +--R 109395a b d e + 34320a b d +--R * +--R 3 +--R x +--R + +--R 10 2 6 9 3 5 8 4 2 4 7 5 3 3 6 6 4 2 +--R a b e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 5 7 5 4 8 6 +--R 34749a b d e + 25740a b d +--R * +--R 2 +--R x +--R + +--R 11 6 10 2 5 9 3 2 4 8 4 3 3 7 5 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e - 715a b d e +--R + +--R 6 6 5 5 7 6 +--R 1287a b d e + 10296a b d +--R * +--R x +--R + +--R 12 6 11 5 10 2 2 4 9 3 3 3 8 4 4 2 +--R a e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 7 5 5 6 6 6 +--R - 1287a b d e + 1716a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 +--R 12012b +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 13 5 6 6 5 12 +--R 924b e x + (6006a b e + 6006b d e )x +--R + +--R 2 4 6 5 5 6 2 4 11 +--R (16380a b e + 39312a b d e + 16380b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 10 +--R (24024a b e + 108108a b d e + 108108a b d e + 24024b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 20020a b e + 160160a b d e + 300300a b d e + 160160a b d e +--R + +--R 6 4 2 +--R 20020b d e +--R * +--R 9 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 9009a b e + 135135a b d e + 450450a b d e + 450450a b d e +--R + +--R 5 4 2 6 5 +--R 135135a b d e + 9009b d e +--R * +--R 8 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 1716a e + 61776a b d e + 386100a b d e + 686400a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 386100a b d e + 61776a b d e + 1716b d +--R * +--R 7 +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 +--R 12012a d e + 180180a b d e + 600600a b d e + 600600a b d e +--R + +--R 2 4 5 5 6 +--R 180180a b d e + 12012a b d +--R * +--R 6 +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 +--R 36036a d e + 288288a b d e + 540540a b d e + 288288a b d e +--R + +--R 2 4 6 +--R 36036a b d +--R * +--R 5 +--R x +--R + +--R 6 3 3 5 4 2 4 2 5 3 3 6 4 +--R (60060a d e + 270270a b d e + 270270a b d e + 60060a b d )x +--R + +--R 6 4 2 5 5 4 2 6 3 +--R (60060a d e + 144144a b d e + 60060a b d )x +--R + +--R 6 5 5 6 2 6 6 +--R (36036a d e + 36036a b d )x + 12012a d x +--R / +--R 12012 +--R Type: Union(Expression(Integer),...) +--E 520 + +--S 521 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 12 6 12 11 6 12 5 11 +--R - 924b e x + (- 5082a b e - 6006b d e )x +--R + +--R 2 10 6 11 5 12 2 4 10 +--R (- 11298a b e - 33306a b d e - 16380b d e )x +--R + +--R 3 9 6 2 10 5 11 2 4 12 3 3 9 +--R (- 12726a b e - 74802a b d e - 91728a b d e - 24024b d e )x +--R + +--R 4 8 6 3 9 5 2 10 2 4 11 3 3 +--R - 7294a b e - 85358a b d e - 208572a b d e - 136136a b d e +--R + +--R 12 4 2 +--R - 20020b d e +--R * +--R 8 +--R x +--R + +--R 5 7 6 4 8 5 3 9 2 4 2 10 3 3 +--R - 1715a b e - 49777a b d e - 241878a b d e - 314314a b d e +--R + +--R 11 4 2 12 5 +--R - 115115a b d e - 9009b d e +--R * +--R 7 +--R x +--R + +--R 6 6 6 5 7 5 4 8 2 4 3 9 3 3 +--R - a b e - 11999a b d e - 144222a b d e - 372086a b d e +--R + +--R 2 10 4 2 11 5 12 6 +--R - 270985a b d e - 52767a b d e - 1716b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 6 6 5 5 7 2 4 4 8 3 3 +--R a b e - 13a b d e - 35958a b d e - 228514a b d e +--R + +--R 3 9 4 2 2 10 5 11 6 +--R - 329615a b d e - 127413a b d e - 10296a b d +--R * +--R 5 +--R x +--R + +--R 8 4 6 7 5 5 6 6 2 4 5 7 3 3 +--R - a b e + 13a b d e - 78a b d e - 59774a b d e +--R + +--R 4 8 4 2 3 9 5 2 10 6 +--R - 210925a b d e - 160875a b d e - 25740a b d +--R * +--R 4 +--R x +--R + +--R 9 3 6 8 4 5 7 5 2 4 6 6 3 3 5 7 4 2 +--R a b e - 13a b d e + 78a b d e - 286a b d e - 59345a b d e +--R + +--R 4 8 5 3 9 6 +--R - 109395a b d e - 34320a b d +--R * +--R 3 +--R x +--R + +--R 10 2 6 9 3 5 8 4 2 4 7 5 3 3 6 6 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e - 715a b d e +--R + +--R 5 7 5 4 8 6 +--R - 34749a b d e - 25740a b d +--R * +--R 2 +--R x +--R + +--R 11 6 10 2 5 9 3 2 4 8 4 3 3 7 5 4 2 +--R a b e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 6 6 5 5 7 6 +--R - 1287a b d e - 10296a b d +--R * +--R x +--R + +--R 12 6 11 5 10 2 2 4 9 3 3 3 8 4 4 2 +--R - a e + 13a b d e - 78a b d e + 286a b d e - 715a b d e +--R + +--R 7 5 5 6 6 6 +--R 1287a b d e - 1716a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 13 6 13 12 6 13 5 12 +--R 924b e x + (6006a b e + 6006b d e )x +--R + +--R 2 11 6 12 5 13 2 4 11 +--R (16380a b e + 39312a b d e + 16380b d e )x +--R + +--R 3 10 6 2 11 5 12 2 4 13 3 3 10 +--R (24024a b e + 108108a b d e + 108108a b d e + 24024b d e )x +--R + +--R 4 9 6 3 10 5 2 11 2 4 12 3 3 +--R 20020a b e + 160160a b d e + 300300a b d e + 160160a b d e +--R + +--R 13 4 2 +--R 20020b d e +--R * +--R 9 +--R x +--R + +--R 5 8 6 4 9 5 3 10 2 4 2 11 3 3 +--R 9009a b e + 135135a b d e + 450450a b d e + 450450a b d e +--R + +--R 12 4 2 13 5 +--R 135135a b d e + 9009b d e +--R * +--R 8 +--R x +--R + +--R 6 7 6 5 8 5 4 9 2 4 3 10 3 3 +--R 1716a b e + 61776a b d e + 386100a b d e + 686400a b d e +--R + +--R 2 11 4 2 12 5 13 6 +--R 386100a b d e + 61776a b d e + 1716b d +--R * +--R 7 +--R x +--R + +--R 6 7 5 5 8 2 4 4 9 3 3 3 10 4 2 +--R 12012a b d e + 180180a b d e + 600600a b d e + 600600a b d e +--R + +--R 2 11 5 12 6 +--R 180180a b d e + 12012a b d +--R * +--R 6 +--R x +--R + +--R 6 7 2 4 5 8 3 3 4 9 4 2 3 10 5 +--R 36036a b d e + 288288a b d e + 540540a b d e + 288288a b d e +--R + +--R 2 11 6 +--R 36036a b d +--R * +--R 5 +--R x +--R + +--R 6 7 3 3 5 8 4 2 4 9 5 3 10 6 4 +--R (60060a b d e + 270270a b d e + 270270a b d e + 60060a b d )x +--R + +--R 6 7 4 2 5 8 5 4 9 6 3 +--R (60060a b d e + 144144a b d e + 60060a b d )x +--R + +--R 6 7 5 5 8 6 2 6 7 6 +--R (36036a b d e + 36036a b d )x + 12012a b d x +--R / +--R 7 +--R 12012b +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 12 5 6 6 5 11 +--R b e x + (6a b e + 6b d e )x +--R + +--R 2 4 6 5 5 6 2 4 10 +--R (15a b e + 36a b d e + 15b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 9 +--R (20a b e + 90a b d e + 90a b d e + 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 8 +--R (15a b e + 120a b d e + 225a b d e + 120a b d e + 15b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 6a b e + 90a b d e + 300a b d e + 300a b d e + 90a b d e +--R + +--R 6 5 +--R 6b d e +--R * +--R 7 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R a e + 36a b d e + 225a b d e + 400a b d e + 225a b d e +--R + +--R 5 5 6 6 +--R 36a b d e + b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R 6a d e + 90a b d e + 300a b d e + 300a b d e + 90a b d e +--R + +--R 5 6 +--R 6a b d +--R * +--R 5 +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 4 +--R (15a d e + 120a b d e + 225a b d e + 120a b d e + 15a b d )x +--R + +--R 6 3 3 5 4 2 4 2 5 3 3 6 3 +--R (20a d e + 90a b d e + 90a b d e + 20a b d )x +--R + +--R 6 4 2 5 5 4 2 6 2 6 5 5 6 6 6 +--R (15a d e + 36a b d e + 15a b d )x + (6a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 13 6 6 7 5 12 +--R - b e x + (- 7a b e - 6b d e )x +--R + +--R 2 5 6 6 5 7 2 4 11 +--R (- 21a b e - 42a b d e - 15b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 10 +--R (- 35a b e - 126a b d e - 105a b d e - 20b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 9 +--R (- 35a b e - 210a b d e - 315a b d e - 140a b d e - 15b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 21a b e - 210a b d e - 525a b d e - 420a b d e - 105a b d e +--R + +--R 7 5 +--R - 6b d e +--R * +--R 8 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 7a b e - 126a b d e - 525a b d e - 700a b d e - 315a b d e +--R + +--R 6 5 7 6 +--R - 42a b d e - b d +--R * +--R 7 +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - a e - 42a b d e - 315a b d e - 700a b d e - 525a b d e +--R + +--R 2 5 5 6 6 +--R - 126a b d e - 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 +--R - 6a d e - 105a b d e - 420a b d e - 525a b d e - 210a b d e +--R + +--R 2 5 6 +--R - 21a b d +--R * +--R 5 +--R x +--R + +--R 7 2 4 6 3 3 5 2 4 2 4 3 5 3 4 6 4 +--R (- 15a d e - 140a b d e - 315a b d e - 210a b d e - 35a b d )x +--R + +--R 7 3 3 6 4 2 5 2 5 4 3 6 3 +--R (- 20a d e - 105a b d e - 126a b d e - 35a b d )x +--R + +--R 7 4 2 6 5 5 2 6 2 7 5 6 6 7 6 +--R (- 15a d e - 42a b d e - 21a b d )x + (- 6a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 522 + +)clear all + +--S 523 of 1353 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 5 10 4 5 5 4 9 2 3 5 4 4 5 2 3 8 +--R b e x + (5a b e + 5b d e )x + (10a b e + 25a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 7 +--R (10a b e + 50a b d e + 50a b d e + 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 6 +--R (5a b e + 50a b d e + 100a b d e + 50a b d e + 5b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e + 25a b d e + 100a b d e + 100a b d e + 25a b d e + b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4 +--R (5a d e + 50a b d e + 100a b d e + 50a b d e + 5a b d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 3 +--R (10a d e + 50a b d e + 50a b d e + 10a b d )x +--R + +--R 5 3 2 4 4 3 2 5 2 5 4 4 5 5 5 +--R (10a d e + 25a b d e + 10a b d )x + (5a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1353 +r0:=1/5544*(b*d-a*e)^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6+1/792*(b*d-a*e)^4*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/198*(b*d-a*e)^3*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+1/66*(b*d-a*e)^2*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^3+5/132*(b*d-a*e)*(d+e*x)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/12*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 11 5 11 10 5 11 4 10 +--R 462b e x + (2562a b e + 2520b d e )x +--R + +--R 2 9 5 10 4 11 2 3 9 +--R (5754a b e + 14112a b d e + 5544b d e )x +--R + +--R 3 8 5 2 9 4 10 2 3 11 3 2 8 +--R (6566a b e + 32088a b d e + 31416a b d e + 6160b d e )x +--R + +--R 4 7 5 3 8 4 2 9 2 3 10 3 2 +--R 3829a b e + 37212a b d e + 72534a b d e + 35420a b d e +--R + +--R 11 4 +--R 3465b d e +--R * +--R 7 +--R x +--R + +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 +--R 923a b e + 22188a b d e + 85866a b d e + 83380a b d e +--R + +--R 10 4 11 5 +--R 20295a b d e + 792b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R a b e + 5532a b d e + 52734a b d e + 101420a b d e +--R + +--R 2 9 4 10 5 +--R 49005a b d e + 4752a b d +--R * +--R 5 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R - a b e + 12a b d e + 13794a b d e + 64900a b d e +--R + +--R 3 8 4 2 9 5 +--R 61875a b d e + 11880a b d +--R * +--R 4 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 4 7 4 +--R a b e - 12a b d e + 66a b d e + 18260a b d e + 42075a b d e +--R + +--R 3 8 5 +--R 15840a b d +--R * +--R 3 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 5 6 4 +--R - a b e + 12a b d e - 66a b d e + 220a b d e + 13365a b d e +--R + +--R 4 7 5 +--R 11880a b d +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 6 5 4 +--R a b e - 12a b d e + 66a b d e - 220a b d e + 495a b d e +--R + +--R 5 6 5 +--R 4752a b d +--R * +--R x +--R + +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 6 5 5 +--R - a e + 12a b d e - 66a b d e + 220a b d e - 495a b d e + 792a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 +--R 5544b +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 12 5 5 6 4 11 +--R 462b e x + (3024a b e + 2520b d e )x +--R + +--R 2 4 5 5 4 6 2 3 10 +--R (8316a b e + 16632a b d e + 5544b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 9 +--R (12320a b e + 46200a b d e + 36960a b d e + 6160b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 +--R 10395a b e + 69300a b d e + 103950a b d e + 41580a b d e +--R + +--R 6 4 +--R 3465b d e +--R * +--R 8 +--R x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 +--R 4752a b e + 59400a b d e + 158400a b d e + 118800a b d e +--R + +--R 5 4 6 5 +--R 23760a b d e + 792b d +--R * +--R 7 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 +--R 924a e + 27720a b d e + 138600a b d e + 184800a b d e +--R + +--R 2 4 4 5 5 +--R 69300a b d e + 5544a b d +--R * +--R 6 +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 +--R 5544a d e + 66528a b d e + 166320a b d e + 110880a b d e +--R + +--R 2 4 5 +--R 16632a b d +--R * +--R 5 +--R x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 4 +--R (13860a d e + 83160a b d e + 103950a b d e + 27720a b d )x +--R + +--R 6 3 2 5 4 4 2 5 3 +--R (18480a d e + 55440a b d e + 27720a b d )x +--R + +--R 6 4 5 5 2 6 5 +--R (13860a d e + 16632a b d )x + 5544a d x +--R / +--R 5544 +--R Type: Union(Expression(Integer),...) +--E 525 + +--S 526 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 11 5 11 10 5 11 4 10 +--R - 462b e x + (- 2562a b e - 2520b d e )x +--R + +--R 2 9 5 10 4 11 2 3 9 +--R (- 5754a b e - 14112a b d e - 5544b d e )x +--R + +--R 3 8 5 2 9 4 10 2 3 11 3 2 8 +--R (- 6566a b e - 32088a b d e - 31416a b d e - 6160b d e )x +--R + +--R 4 7 5 3 8 4 2 9 2 3 10 3 2 +--R - 3829a b e - 37212a b d e - 72534a b d e - 35420a b d e +--R + +--R 11 4 +--R - 3465b d e +--R * +--R 7 +--R x +--R + +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 +--R - 923a b e - 22188a b d e - 85866a b d e - 83380a b d e +--R + +--R 10 4 11 5 +--R - 20295a b d e - 792b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R - a b e - 5532a b d e - 52734a b d e - 101420a b d e +--R + +--R 2 9 4 10 5 +--R - 49005a b d e - 4752a b d +--R * +--R 5 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R a b e - 12a b d e - 13794a b d e - 64900a b d e +--R + +--R 3 8 4 2 9 5 +--R - 61875a b d e - 11880a b d +--R * +--R 4 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 4 7 4 +--R - a b e + 12a b d e - 66a b d e - 18260a b d e - 42075a b d e +--R + +--R 3 8 5 +--R - 15840a b d +--R * +--R 3 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 5 6 4 +--R a b e - 12a b d e + 66a b d e - 220a b d e - 13365a b d e +--R + +--R 4 7 5 +--R - 11880a b d +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 6 5 4 +--R - a b e + 12a b d e - 66a b d e + 220a b d e - 495a b d e +--R + +--R 5 6 5 +--R - 4752a b d +--R * +--R x +--R + +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 6 5 5 +--R a e - 12a b d e + 66a b d e - 220a b d e + 495a b d e - 792a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 12 5 12 11 5 12 4 11 +--R 462b e x + (3024a b e + 2520b d e )x +--R + +--R 2 10 5 11 4 12 2 3 10 +--R (8316a b e + 16632a b d e + 5544b d e )x +--R + +--R 3 9 5 2 10 4 11 2 3 12 3 2 9 +--R (12320a b e + 46200a b d e + 36960a b d e + 6160b d e )x +--R + +--R 4 8 5 3 9 4 2 10 2 3 11 3 2 +--R 10395a b e + 69300a b d e + 103950a b d e + 41580a b d e +--R + +--R 12 4 +--R 3465b d e +--R * +--R 8 +--R x +--R + +--R 5 7 5 4 8 4 3 9 2 3 2 10 3 2 +--R 4752a b e + 59400a b d e + 158400a b d e + 118800a b d e +--R + +--R 11 4 12 5 +--R 23760a b d e + 792b d +--R * +--R 7 +--R x +--R + +--R 6 6 5 5 7 4 4 8 2 3 3 9 3 2 +--R 924a b e + 27720a b d e + 138600a b d e + 184800a b d e +--R + +--R 2 10 4 11 5 +--R 69300a b d e + 5544a b d +--R * +--R 6 +--R x +--R + +--R 6 6 4 5 7 2 3 4 8 3 2 3 9 4 +--R 5544a b d e + 66528a b d e + 166320a b d e + 110880a b d e +--R + +--R 2 10 5 +--R 16632a b d +--R * +--R 5 +--R x +--R + +--R 6 6 2 3 5 7 3 2 4 8 4 3 9 5 4 +--R (13860a b d e + 83160a b d e + 103950a b d e + 27720a b d )x +--R + +--R 6 6 3 2 5 7 4 4 8 5 3 +--R (18480a b d e + 55440a b d e + 27720a b d )x +--R + +--R 6 6 4 5 7 5 2 6 6 5 +--R (13860a b d e + 16632a b d )x + 5544a b d x +--R / +--R 6 +--R 5544b +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 5 11 5 5 6 4 10 +--R b e x + (6a b e + 5b d e )x +--R + +--R 2 4 5 5 4 6 2 3 9 +--R (15a b e + 30a b d e + 10b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 8 +--R (20a b e + 75a b d e + 60a b d e + 10b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 7 +--R (15a b e + 100a b d e + 150a b d e + 60a b d e + 5b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 6a b e + 75a b d e + 200a b d e + 150a b d e + 30a b d e +--R + +--R 6 5 +--R b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R a e + 30a b d e + 150a b d e + 200a b d e + 75a b d e +--R + +--R 5 5 +--R 6a b d +--R * +--R 5 +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 4 +--R (5a d e + 60a b d e + 150a b d e + 100a b d e + 15a b d )x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 3 +--R (10a d e + 60a b d e + 75a b d e + 20a b d )x +--R + +--R 6 3 2 5 4 4 2 5 2 6 4 5 5 6 5 +--R (10a d e + 30a b d e + 15a b d )x + (5a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 5 12 6 5 7 4 11 +--R - b e x + (- 7a b e - 5b d e )x +--R + +--R 2 5 5 6 4 7 2 3 10 +--R (- 21a b e - 35a b d e - 10b d e )x +--R + +--R 3 4 5 2 5 4 6 2 3 7 3 2 9 +--R (- 35a b e - 105a b d e - 70a b d e - 10b d e )x +--R + +--R 4 3 5 3 4 4 2 5 2 3 6 3 2 7 4 8 +--R (- 35a b e - 175a b d e - 210a b d e - 70a b d e - 5b d e)x +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R - 21a b e - 175a b d e - 350a b d e - 210a b d e - 35a b d e +--R + +--R 7 5 +--R - b d +--R * +--R 7 +--R x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R - 7a b e - 105a b d e - 350a b d e - 350a b d e - 105a b d e +--R + +--R 6 5 +--R - 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R - a e - 35a b d e - 210a b d e - 350a b d e - 175a b d e +--R + +--R 2 5 5 +--R - 21a b d +--R * +--R 5 +--R x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 4 +--R (- 5a d e - 70a b d e - 210a b d e - 175a b d e - 35a b d )x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 3 +--R (- 10a d e - 70a b d e - 105a b d e - 35a b d )x +--R + +--R 7 3 2 6 4 5 2 5 2 7 4 6 5 7 5 +--R (- 10a d e - 35a b d e - 21a b d )x + (- 5a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 527 + +)clear all + +--S 528 of 1353 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1353 +r0:=1/2310*(b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/330*(b*d-a*e)^3*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+2/165*(b*d-a*e)^2*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+2/55*(b*d-a*e)*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/11*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 10 4 10 9 4 10 3 9 +--R 210b e x + (1176a b e + 924b d e )x +--R + +--R 2 8 4 9 3 10 2 2 8 +--R (2674a b e + 5236a b d e + 1540b d e )x +--R + +--R 3 7 4 2 8 3 9 2 2 10 3 7 +--R (3101a b e + 12089a b d e + 8855a b d e + 1155b d e)x +--R + +--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 6 +--R (1849a b e + 14311a b d e + 20845a b d e + 6765a b d e + 330b d )x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R 461a b e + 8789a b d e + 25355a b d e + 16335a b d e +--R + +--R 9 4 +--R 1980a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 2 8 4 4 +--R (a b e + 2299a b d e + 16225a b d e + 20625a b d e + 4950a b d )x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 3 7 4 3 +--R (- a b e + 11a b d e + 4565a b d e + 14025a b d e + 6600a b d )x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 4 6 4 2 +--R (a b e - 11a b d e + 55a b d e + 4455a b d e + 4950a b d )x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 5 5 4 10 4 +--R (- a b e + 11a b d e - 55a b d e + 165a b d e + 1980a b d )x + a e +--R + +--R 9 3 8 2 2 2 7 3 3 6 4 4 +--R - 11a b d e + 55a b d e - 165a b d e + 330a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 2310b +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 4 11 5 4 6 3 10 +--R 210b e x + (1386a b e + 924b d e )x +--R + +--R 2 4 4 5 3 6 2 2 9 +--R (3850a b e + 6160a b d e + 1540b d e )x +--R + +--R 3 3 4 2 4 3 5 2 2 6 3 8 +--R (5775a b e + 17325a b d e + 10395a b d e + 1155b d e)x +--R + +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 7 +--R (4950a b e + 26400a b d e + 29700a b d e + 7920a b d e + 330b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 +--R 2310a b e + 23100a b d e + 46200a b d e + 23100a b d e +--R + +--R 5 4 +--R 2310a b d +--R * +--R 6 +--R x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 5 +--R (462a e + 11088a b d e + 41580a b d e + 36960a b d e + 6930a b d )x +--R + +--R 6 3 5 2 2 4 2 3 3 3 4 4 +--R (2310a d e + 20790a b d e + 34650a b d e + 11550a b d )x +--R + +--R 6 2 2 5 3 4 2 4 3 6 3 5 4 2 +--R (4620a d e + 18480a b d e + 11550a b d )x + (4620a d e + 6930a b d )x +--R + +--R 6 4 +--R 2310a d x +--R / +--R 2310 +--R Type: Union(Expression(Integer),...) +--E 530 + +--S 531 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 10 4 10 9 4 10 3 9 +--R - 210b e x + (- 1176a b e - 924b d e )x +--R + +--R 2 8 4 9 3 10 2 2 8 +--R (- 2674a b e - 5236a b d e - 1540b d e )x +--R + +--R 3 7 4 2 8 3 9 2 2 10 3 7 +--R (- 3101a b e - 12089a b d e - 8855a b d e - 1155b d e)x +--R + +--R 4 6 4 3 7 3 2 8 2 2 9 3 +--R - 1849a b e - 14311a b d e - 20845a b d e - 6765a b d e +--R + +--R 10 4 +--R - 330b d +--R * +--R 6 +--R x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R - 461a b e - 8789a b d e - 25355a b d e - 16335a b d e +--R + +--R 9 4 +--R - 1980a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 +--R - a b e - 2299a b d e - 16225a b d e - 20625a b d e +--R + +--R 2 8 4 +--R - 4950a b d +--R * +--R 4 +--R x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 3 7 4 3 +--R (a b e - 11a b d e - 4565a b d e - 14025a b d e - 6600a b d )x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 4 6 4 2 +--R (- a b e + 11a b d e - 55a b d e - 4455a b d e - 4950a b d )x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 5 5 4 10 4 +--R (a b e - 11a b d e + 55a b d e - 165a b d e - 1980a b d )x - a e +--R + +--R 9 3 8 2 2 2 7 3 3 6 4 4 +--R 11a b d e - 55a b d e + 165a b d e - 330a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 11 4 11 10 4 11 3 10 +--R 210b e x + (1386a b e + 924b d e )x +--R + +--R 2 9 4 10 3 11 2 2 9 +--R (3850a b e + 6160a b d e + 1540b d e )x +--R + +--R 3 8 4 2 9 3 10 2 2 11 3 8 +--R (5775a b e + 17325a b d e + 10395a b d e + 1155b d e)x +--R + +--R 4 7 4 3 8 3 2 9 2 2 10 3 11 4 7 +--R (4950a b e + 26400a b d e + 29700a b d e + 7920a b d e + 330b d )x +--R + +--R 5 6 4 4 7 3 3 8 2 2 2 9 3 +--R 2310a b e + 23100a b d e + 46200a b d e + 23100a b d e +--R + +--R 10 4 +--R 2310a b d +--R * +--R 6 +--R x +--R + +--R 6 5 4 5 6 3 4 7 2 2 3 8 3 2 9 4 5 +--R (462a b e + 11088a b d e + 41580a b d e + 36960a b d e + 6930a b d )x +--R + +--R 6 5 3 5 6 2 2 4 7 3 3 8 4 4 +--R (2310a b d e + 20790a b d e + 34650a b d e + 11550a b d )x +--R + +--R 6 5 2 2 5 6 3 4 7 4 3 +--R (4620a b d e + 18480a b d e + 11550a b d )x +--R + +--R 6 5 3 5 6 4 2 6 5 4 +--R (4620a b d e + 6930a b d )x + 2310a b d x +--R / +--R 5 +--R 2310b +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 4 10 5 4 6 3 9 2 4 4 5 3 6 2 2 8 +--R b e x + (6a b e + 4b d e )x + (15a b e + 24a b d e + 6b d e )x +--R + +--R 3 3 4 2 4 3 5 2 2 6 3 7 +--R (20a b e + 60a b d e + 36a b d e + 4b d e)x +--R + +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 6 +--R (15a b e + 80a b d e + 90a b d e + 24a b d e + b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 5 +--R (6a b e + 60a b d e + 120a b d e + 60a b d e + 6a b d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 4 +--R (a e + 24a b d e + 90a b d e + 80a b d e + 15a b d )x +--R + +--R 6 3 5 2 2 4 2 3 3 3 4 3 +--R (4a d e + 36a b d e + 60a b d e + 20a b d )x +--R + +--R 6 2 2 5 3 4 2 4 2 6 3 5 4 6 4 +--R (6a d e + 24a b d e + 15a b d )x + (4a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 4 11 6 4 7 3 10 +--R - b e x + (- 7a b e - 4b d e )x +--R + +--R 2 5 4 6 3 7 2 2 9 +--R (- 21a b e - 28a b d e - 6b d e )x +--R + +--R 3 4 4 2 5 3 6 2 2 7 3 8 +--R (- 35a b e - 84a b d e - 42a b d e - 4b d e)x +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (- 35a b e - 140a b d e - 126a b d e - 28a b d e - b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 6 +--R (- 21a b e - 140a b d e - 210a b d e - 84a b d e - 7a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 5 +--R (- 7a b e - 84a b d e - 210a b d e - 140a b d e - 21a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 4 +--R (- a e - 28a b d e - 126a b d e - 140a b d e - 35a b d )x +--R + +--R 7 3 6 2 2 5 2 3 4 3 4 3 +--R (- 4a d e - 42a b d e - 84a b d e - 35a b d )x +--R + +--R 7 2 2 6 3 5 2 4 2 7 3 6 4 7 4 +--R (- 6a d e - 28a b d e - 21a b d )x + (- 4a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 532 + +)clear all + +--S 533 of 1353 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1353 +r0:=1/840*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+1/120*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+1/30*(b*d-a*e)*(d+e*x)^2*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^2+1/10*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 9 3 9 8 3 9 2 8 +--R 84b e x + (476a b e + 280b d e )x +--R + +--R 2 7 3 8 2 9 2 7 +--R (1099a b e + 1610a b d e + 315b d e)x +--R + +--R 3 6 3 2 7 2 8 2 9 3 6 +--R (1301a b e + 3790a b d e + 1845a b d e + 120b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (799a b e + 4610a b d e + 4455a b d e + 720a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 4 +--R (209a b e + 2950a b d e + 5625a b d e + 1800a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (a b e + 830a b d e + 3825a b d e + 2400a b d )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (- a b e + 10a b d e + 1215a b d e + 1800a b d )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 8 2 +--R (a b e - 10a b d e + 45a b d e + 720a b d )x - a e + 10a b d e +--R + +--R 7 2 2 6 3 3 +--R - 45a b d e + 120a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 840b +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3 10 5 3 6 2 9 +--R 84b e x + (560a b e + 280b d e )x +--R + +--R 2 4 3 5 2 6 2 8 +--R (1575a b e + 1890a b d e + 315b d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 7 +--R (2400a b e + 5400a b d e + 2160a b d e + 120b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 6 +--R (2100a b e + 8400a b d e + 6300a b d e + 840a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 5 +--R (1008a b e + 7560a b d e + 10080a b d e + 2520a b d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 4 +--R (210a e + 3780a b d e + 9450a b d e + 4200a b d )x +--R + +--R 6 2 5 2 4 2 3 3 6 2 5 3 2 +--R (840a d e + 5040a b d e + 4200a b d )x + (1260a d e + 2520a b d )x +--R + +--R 6 3 +--R 840a d x +--R / +--R 840 +--R Type: Union(Expression(Integer),...) +--E 535 + +--S 536 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 3 9 8 3 9 2 8 +--R - 84b e x + (- 476a b e - 280b d e )x +--R + +--R 2 7 3 8 2 9 2 7 +--R (- 1099a b e - 1610a b d e - 315b d e)x +--R + +--R 3 6 3 2 7 2 8 2 9 3 6 +--R (- 1301a b e - 3790a b d e - 1845a b d e - 120b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (- 799a b e - 4610a b d e - 4455a b d e - 720a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 4 +--R (- 209a b e - 2950a b d e - 5625a b d e - 1800a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (- a b e - 830a b d e - 3825a b d e - 2400a b d )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (a b e - 10a b d e - 1215a b d e - 1800a b d )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 8 2 +--R (- a b e + 10a b d e - 45a b d e - 720a b d )x + a e - 10a b d e +--R + +--R 7 2 2 6 3 3 +--R 45a b d e - 120a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 10 3 10 9 3 10 2 9 +--R 84b e x + (560a b e + 280b d e )x +--R + +--R 2 8 3 9 2 10 2 8 +--R (1575a b e + 1890a b d e + 315b d e)x +--R + +--R 3 7 3 2 8 2 9 2 10 3 7 +--R (2400a b e + 5400a b d e + 2160a b d e + 120b d )x +--R + +--R 4 6 3 3 7 2 2 8 2 9 3 6 +--R (2100a b e + 8400a b d e + 6300a b d e + 840a b d )x +--R + +--R 5 5 3 4 6 2 3 7 2 2 8 3 5 +--R (1008a b e + 7560a b d e + 10080a b d e + 2520a b d )x +--R + +--R 6 4 3 5 5 2 4 6 2 3 7 3 4 +--R (210a b e + 3780a b d e + 9450a b d e + 4200a b d )x +--R + +--R 6 4 2 5 5 2 4 6 3 3 6 4 2 5 5 3 2 +--R (840a b d e + 5040a b d e + 4200a b d )x + (1260a b d e + 2520a b d )x +--R + +--R 6 4 3 +--R 840a b d x +--R / +--R 4 +--R 840b +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 3 9 5 3 6 2 8 2 4 3 5 2 6 2 7 +--R b e x + (6a b e + 3b d e )x + (15a b e + 18a b d e + 3b d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (20a b e + 45a b d e + 18a b d e + b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (15a b e + 60a b d e + 45a b d e + 6a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (6a b e + 45a b d e + 60a b d e + 15a b d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (a e + 18a b d e + 45a b d e + 20a b d )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (3a d e + 18a b d e + 15a b d )x + (3a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 3 10 6 3 7 2 9 +--R - b e x + (- 7a b e - 3b d e )x +--R + +--R 2 5 3 6 2 7 2 8 +--R (- 21a b e - 21a b d e - 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (- 35a b e - 63a b d e - 21a b d e - b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (- 35a b e - 105a b d e - 63a b d e - 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (- 21a b e - 105a b d e - 105a b d e - 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (- 7a b e - 63a b d e - 105a b d e - 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (- a e - 21a b d e - 63a b d e - 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (- 3a d e - 21a b d e - 21a b d )x + (- 3a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1353 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1353 +r0:=1/252*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+1/36*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2+1/9*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 8 2 8 7 2 8 7 +--R 28b e x + (161a b e + 63b d e)x +--R + +--R 2 6 2 7 8 2 6 +--R (379a b e + 369a b d e + 36b d )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (461a b e + 891a b d e + 216a b d )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (295a b e + 1125a b d e + 540a b d )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (83a b e + 765a b d e + 720a b d )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (a b e + 243a b d e + 540a b d )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- a b e + 9a b d e + 216a b d )x + a e - 9a b d e + 36a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 252b +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 9 5 2 6 8 2 4 2 5 6 2 7 +--R 28b e x + (189a b e + 63b d e)x + (540a b e + 432a b d e + 36b d )x +--R + +--R 3 3 2 2 4 5 2 6 +--R (840a b e + 1260a b d e + 252a b d )x +--R + +--R 4 2 2 3 3 2 4 2 5 +--R (756a b e + 2016a b d e + 756a b d )x +--R + +--R 5 2 4 2 3 3 2 4 +--R (378a b e + 1890a b d e + 1260a b d )x +--R + +--R 6 2 5 4 2 2 3 6 5 2 2 6 2 +--R (84a e + 1008a b d e + 1260a b d )x + (252a d e + 756a b d )x + 252a d x +--R / +--R 252 +--R Type: Union(Expression(Integer),...) +--E 540 + +--S 541 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 2 8 7 2 8 7 +--R - 28b e x + (- 161a b e - 63b d e)x +--R + +--R 2 6 2 7 8 2 6 +--R (- 379a b e - 369a b d e - 36b d )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 461a b e - 891a b d e - 216a b d )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 295a b e - 1125a b d e - 540a b d )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 83a b e - 765a b d e - 720a b d )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- a b e - 243a b d e - 540a b d )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (a b e - 9a b d e - 216a b d )x - a e + 9a b d e - 36a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 9 2 9 8 2 9 8 2 7 2 8 9 2 7 +--R 28b e x + (189a b e + 63b d e)x + (540a b e + 432a b d e + 36b d )x +--R + +--R 3 6 2 2 7 8 2 6 +--R (840a b e + 1260a b d e + 252a b d )x +--R + +--R 4 5 2 3 6 2 7 2 5 +--R (756a b e + 2016a b d e + 756a b d )x +--R + +--R 5 4 2 4 5 3 6 2 4 +--R (378a b e + 1890a b d e + 1260a b d )x +--R + +--R 6 3 2 5 4 4 5 2 3 6 3 5 4 2 2 +--R (84a b e + 1008a b d e + 1260a b d )x + (252a b d e + 756a b d )x +--R + +--R 6 3 2 +--R 252a b d x +--R / +--R 3 +--R 252b +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 2 8 5 2 6 7 2 4 2 5 6 2 6 +--R b e x + (6a b e + 2b d e)x + (15a b e + 12a b d e + b d )x +--R + +--R 3 3 2 2 4 5 2 5 +--R (20a b e + 30a b d e + 6a b d )x +--R + +--R 4 2 2 3 3 2 4 2 4 +--R (15a b e + 40a b d e + 15a b d )x +--R + +--R 5 2 4 2 3 3 2 3 6 2 5 4 2 2 2 +--R (6a b e + 30a b d e + 20a b d )x + (a e + 12a b d e + 15a b d )x +--R + +--R 6 5 2 6 2 +--R (2a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R - b e x + (- 7a b e - 2b d e)x + (- 21a b e - 14a b d e - b d )x +--R + +--R 3 4 2 2 5 6 2 6 +--R (- 35a b e - 42a b d e - 7a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 +--R (- 35a b e - 70a b d e - 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 +--R (- 21a b e - 70a b d e - 35a b d )x +--R + +--R 6 2 5 2 4 3 2 3 7 2 6 5 2 2 2 +--R (- 7a b e - 42a b d e - 35a b d )x + (- a e - 14a b d e - 21a b d )x +--R + +--R 7 6 2 7 2 +--R (- 2a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 542 + +)clear all + +--S 543 of 1353 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1353 +r0:=1/56*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2+1/8*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 7 7 6 7 6 2 5 6 5 +--R 7b e x + (41a b e + 8b d)x + (99a b e + 48a b d)x +--R + +--R 3 4 2 5 4 4 3 3 4 3 +--R (125a b e + 120a b d)x + (85a b e + 160a b d)x +--R + +--R 5 2 4 3 2 6 5 2 7 6 +--R (27a b e + 120a b d)x + (a b e + 48a b d)x - a e + 8a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 56b +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 8 5 6 7 2 4 5 6 +--R 7b e x + (48a b e + 8b d)x + (140a b e + 56a b d)x +--R + +--R 3 3 2 4 5 4 2 3 3 4 +--R (224a b e + 168a b d)x + (210a b e + 280a b d)x +--R + +--R 5 4 2 3 6 5 2 6 +--R (112a b e + 280a b d)x + (28a e + 168a b d)x + 56a d x +--R / +--R 56 +--R Type: Union(Expression(Integer),...) +--E 545 + +--S 546 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 7 6 7 6 2 5 6 5 +--R - 7b e x + (- 41a b e - 8b d)x + (- 99a b e - 48a b d)x +--R + +--R 3 4 2 5 4 4 3 3 4 3 +--R (- 125a b e - 120a b d)x + (- 85a b e - 160a b d)x +--R + +--R 5 2 4 3 2 6 5 2 7 6 +--R (- 27a b e - 120a b d)x + (- a b e - 48a b d)x + a e - 8a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 8 8 7 8 7 2 6 7 6 +--R 7b e x + (48a b e + 8b d)x + (140a b e + 56a b d)x +--R + +--R 3 5 2 6 5 4 4 3 5 4 +--R (224a b e + 168a b d)x + (210a b e + 280a b d)x +--R + +--R 5 3 4 4 3 6 2 5 3 2 6 2 +--R (112a b e + 280a b d)x + (28a b e + 168a b d)x + 56a b d x +--R / +--R 2 +--R 56b +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 7 5 6 6 2 4 5 5 +--R b e x + (6a b e + b d)x + (15a b e + 6a b d)x +--R + +--R 3 3 2 4 4 4 2 3 3 3 5 4 2 2 +--R (20a b e + 15a b d)x + (15a b e + 20a b d)x + (6a b e + 15a b d)x +--R + +--R 6 5 6 +--R (a e + 6a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 8 6 7 7 2 5 6 6 +--R - b e x + (- 7a b e - b d)x + (- 21a b e - 7a b d)x +--R + +--R 3 4 2 5 5 4 3 3 4 4 +--R (- 35a b e - 21a b d)x + (- 35a b e - 35a b d)x +--R + +--R 5 2 4 3 3 6 5 2 2 7 6 7 +--R (- 21a b e - 35a b d)x + (- 7a b e - 21a b d)x + (- a e - 7a b d)x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 547 + +)clear all + +--S 548 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1353 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7b +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 6 7 5 6 2 4 5 3 3 4 4 2 3 5 2 6 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a x +--R (3) ----------------------------------------------------------------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 550 + +--S 551 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- b x - 6a b x - 15a b x - 20a b x - 15a b x - 6a b x - a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R / +--R 7b +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1353 +r0:=-1/3*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+1/4*(b*d-a*e)^2*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-1/5*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/e^2+1/6*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-(b*d-_ + a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/2*(b*d-a*e)^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+(b*d-a*e)^6*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 60a e - 360a b d e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 5 5 6 6 +--R - 360a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (72a b e - 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (225a b e - 90a b d e + 15b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b e - 300a b d e + 120a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (450a b e - 600a b d e + 450a b d e - 180a b d e + 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 360a b e - 900a b d e + 1200a b d e - 900a b d e + 360a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 147a e - 522a b d e + 855a b d e - 740a b d e + 330a b d e +--R + +--R 5 5 +--R - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 60a e - 360a b d e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 5 5 6 6 +--R - 360a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (72a b e - 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (225a b e - 90a b d e + 15b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b e - 300a b d e + 120a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (450a b e - 600a b d e + 450a b d e - 180a b d e + 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 360a b e - 900a b d e + 1200a b d e - 900a b d e + 360a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R / +--R 7 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 555 + +--S 556 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 60a e + 360a b d e - 900a b d e + 1200a b d e - 900a b d e +--R + +--R 5 5 6 6 +--R 360a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 10b e x + (- 72a b e + 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 225a b e + 90a b d e - 15b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 400a b e + 300a b d e - 120a b d e + 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 450a b e + 600a b d e - 450a b d e + 180a b d e - 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 360a b e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 5 4 2 6 5 +--R - 360a b d e + 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 147a e + 522a b d e - 855a b d e + 740a b d e - 330a b d e +--R + +--R 5 5 +--R 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 60a b e - 360a b d e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 6 5 7 6 +--R - 360a b d e + 60b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R 60a e - 360a b d e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 2 5 5 6 6 +--R - 360a b d e + 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 +--R 10b e x + (82a b e - 12b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (297a b e - 102a b d e + 15b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (625a b e - 390a b d e + 135a b d e - 20b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (850a b e - 900a b d e + 570a b d e - 200a b d e + 30b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 810a b e - 1500a b d e + 1650a b d e - 1080a b d e + 390a b d e +--R + +--R 7 5 +--R - 60b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 360a b e - 900a b d e + 1200a b d e - 900a b d e + 360a b d e +--R + +--R 6 5 +--R - 60a b d e +--R * +--R x +--R / +--R 7 7 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 557 + +)clear all + +--S 558 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1353 +r0:=2*b*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-3/2*b*(b*d-a*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3+6/5*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/e^2-(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x))+_ + 6*b*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-3*b*(b*d-a*e)^3*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-6*b*(b*d-a*e)^5*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e +--R + +--R 5 4 2 6 5 +--R 300a b d e - 60b d e +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 60a b d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 6 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 2b e x + (15a b e - 3b d e )x + (50a b e - 25a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b e - 100a b d e + 50a b d e - 10b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (150a b e - 300a b d e + 300a b d e - 150a b d e + 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 77a b e - 85a b d e - 130a b d e + 330a b d e - 240a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e + 137a b d e - 385a b d e + 470a b d e - 270a b d e +--R + +--R 5 5 +--R 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +--R 10b e x + (10a e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 60a b d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 6 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 2b e x + (15a b e - 3b d e )x + (50a b e - 25a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b e - 100a b d e + 50a b d e - 10b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (150a b e - 300a b d e + 300a b d e - 150a b d e + 30b d e )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (150a b d e - 400a b d e + 450a b d e - 240a b d e + 50b d e)x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e + 60a b d e - 150a b d e + 200a b d e - 150a b d e +--R + +--R 5 5 6 6 +--R 60a b d e - 10b d +--R / +--R 8 7 +--R 10e x + 10d e +--R Type: Union(Expression(Integer),...) +--E 560 + +--S 561 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 60a b e + 300a b d e - 600a b d e + 600a b d e +--R + +--R 5 4 2 6 5 +--R - 300a b d e + 60b d e +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 60a b d e + 300a b d e - 600a b d e + 600a b d e +--R + +--R 5 5 6 6 +--R - 300a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 2b e x + (- 15a b e + 3b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 50a b e + 25a b d e - 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 100a b e + 100a b d e - 50a b d e + 10b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 150a b e + 300a b d e - 300a b d e + 150a b d e - 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 77a b e + 85a b d e + 130a b d e - 330a b d e + 240a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 10a e - 137a b d e + 385a b d e - 470a b d e + 270a b d e +--R + +--R 5 5 +--R - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 7 5 +--R - 60b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 2 5 4 2 6 5 +--R 60a b e - 240a b d e + 300a b d e - 300a b d e + 240a b d e +--R + +--R 7 6 +--R - 60b d +--R * +--R x +--R + +--R 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R 60a b d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 6 +--R - 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R 2b e x + (17a b e - 3b d e )x + (65a b e - 28a b d e + 5b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (150a b e - 125a b d e + 55a b d e - 10b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (250a b e - 400a b d e + 350a b d e - 160a b d e + 30b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 150a b e - 150a b d e - 100a b d e + 300a b d e - 210a b d e +--R + +--R 7 5 +--R 50b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 10a b e + 210a b d e - 550a b d e + 650a b d e - 390a b d e +--R + +--R 6 5 7 6 +--R 110a b d e - 10b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 10a e + 60a b d e - 150a b d e + 200a b d e - 150a b d e +--R + +--R 2 5 5 6 6 +--R 60a b d e - 10a b d +--R / +--R 8 2 8 7 7 +--R 10b e x + (10a e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 562 + +)clear all + +--S 563 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1353 +r0:=-5*b^2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+15/4*b^2*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-1/2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(d+e*x)^2)-3*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(d+e*x))-15*b^2*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+_ + 15/2*b^2*(b*d-a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+_ + 15*b^2*(b*d-a*e)^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b d e - 480a b d e + 720a b d e - 480a b d e + 120b d e)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (8a b e - 2b d e )x + (30a b e - 20a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b e - 120a b d e + 80a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (35a b e + 100a b d e - 330a b d e + 300a b d e - 90b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b e + 190a b d e - 280a b d e + 60a b d e + 120a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a e - 12a b d e + 125a b d e - 260a b d e + 210a b d e +--R + +--R 5 5 +--R - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 4b e x + (4a e + 8b d e )x + (8a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b d e - 480a b d e + 720a b d e - 480a b d e + 120b d e)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (8a b e - 2b d e )x + (30a b e - 20a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b e - 120a b d e + 80a b d e - 20b d e )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (160a b d e - 330a b d e + 252a b d e - 68b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b e + 120a b d e - 160a b d e + 60a b d e + 24a b d e +--R + +--R 6 5 +--R - 16b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a e - 12a b d e + 90a b d e - 200a b d e + 210a b d e +--R + +--R 5 5 6 6 +--R - 108a b d e + 22b d +--R / +--R 9 2 8 2 7 +--R 4e x + 8d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 565 + +--S 566 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 60a b e + 240a b d e - 360a b d e + 240a b d e +--R + +--R 6 4 2 +--R - 60b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 120a b d e + 480a b d e - 720a b d e + 480a b d e +--R + +--R 6 5 +--R - 120b d e +--R * +--R x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R - 60a b d e + 240a b d e - 360a b d e + 240a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - b e x + (- 8a b e + 2b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 30a b e + 20a b d e - 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 80a b e + 120a b d e - 80a b d e + 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 35a b e - 100a b d e + 330a b d e - 300a b d e + 90b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 24a b e - 190a b d e + 280a b d e - 60a b d e - 120a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 2a e + 12a b d e - 125a b d e + 260a b d e - 210a b d e +--R + +--R 5 5 +--R 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 60a b e - 120a b d e - 120a b d e + 480a b d e - 420a b d e +--R + +--R 7 5 +--R 120b d e +--R * +--R 2 +--R x +--R + +--R 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 120a b d e - 420a b d e + 480a b d e - 120a b d e +--R + +--R 6 5 7 6 +--R - 120a b d e + 60b d +--R * +--R x +--R + +--R 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 6 6 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R b e x + (9a b e - 2b d e )x + (38a b e - 22a b d e + 5b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (110a b e - 140a b d e + 85a b d e - 20b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (80a b e + 40a b d e - 250a b d e + 232a b d e - 68b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 24a b e + 280a b d e - 490a b d e + 312a b d e - 44a b d e +--R + +--R 7 5 +--R - 16b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 26a b e + 108a b d e - 70a b d e - 140a b d e + 234a b d e +--R + +--R 6 5 7 6 +--R - 124a b d e + 22b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 2a e - 12a b d e + 90a b d e - 200a b d e + 210a b d e +--R + +--R 2 5 5 6 6 +--R - 108a b d e + 22a b d +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 4b e x + (4a e + 8b d e )x + (8a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1353 +r0:=20/3*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-5*b^2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(d+e*x))-1/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e*(d+e*x)^3)-b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^2)+20*b^3*_ + (b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-10*b^3*(b*d-a*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-20*b^3*(b*d-a*e)^3*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e )x +--R + +--R 3 3 2 4 2 4 3 3 5 4 2 6 5 3 3 3 3 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e)x + 60a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (9a b e - 3b d e )x + (45a b e - 45a b d e + 15b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (180a b d e - 270a b d e + 110b d e )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 2 +--R (- 45a b e + 180a b d e - 270a b d e + 150b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 6 5 6 6 +--R (- 9a b e - 45a b d e + 270a b d e - 270a b d e + 60b d e)x - a e +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 3a b d e - 15a b d e + 110a b d e - 150a b d e + 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 8 3 7 3 7 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e )x +--R + +--R 3 3 2 4 2 4 3 3 5 4 2 6 5 3 3 3 3 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e)x + 60a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (9a b e - 3b d e )x + (45a b e - 45a b d e + 15b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (135a b d e - 189a b d e + 73b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 45a b e + 180a b d e - 135a b d e - 27a b d e + 39b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 9a b e - 45a b d e + 270a b d e - 405a b d e + 243a b d e +--R + +--R 6 5 +--R - 51b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - a e - 3a b d e - 15a b d e + 110a b d e - 195a b d e + 141a b d e +--R + +--R 6 6 +--R - 37b d +--R / +--R 10 3 9 2 2 8 3 7 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 570 + +--S 571 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 60a b e + 180a b d e - 180a b d e + 60b d e )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 180a b d e + 540a b d e - 540a b d e + 180b d e )x +--R + +--R 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (- 180a b d e + 540a b d e - 540a b d e + 180b d e)x +--R + +--R 3 3 3 3 2 4 4 2 5 5 6 6 +--R - 60a b d e + 180a b d e - 180a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - b e x + (- 9a b e + 3b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 45a b e + 45a b d e - 15b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (- 180a b d e + 270a b d e - 110b d e )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 2 +--R (45a b e - 180a b d e + 270a b d e - 150b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 6 5 6 6 +--R (9a b e + 45a b d e - 270a b d e + 270a b d e - 60b d e)x + a e +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 3a b d e + 15a b d e - 110a b d e + 150a b d e - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 4 3 6 2 5 2 4 6 3 3 7 4 2 3 +--R (60a b e - 360a b d e + 480a b d e - 180b d e )x +--R + +--R 4 3 5 3 4 2 4 6 4 2 7 5 2 +--R (180a b d e - 360a b d e + 360a b d e - 180b d e)x +--R + +--R 4 3 2 4 3 4 3 3 2 5 4 2 7 6 4 3 3 3 +--R (180a b d e - 480a b d e + 360a b d e - 60b d )x + 60a b d e +--R + +--R 3 4 4 2 2 5 5 6 6 +--R - 180a b d e + 180a b d e - 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R b e x + (10a b e - 3b d e )x + (54a b e - 48a b d e + 15b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (45a b e + 90a b d e - 174a b d e + 73b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (- 45a b e + 315a b d e - 324a b d e + 46a b d e + 39b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 54a b e + 135a b d e + 135a b d e - 432a b d e + 282a b d e +--R + +--R 7 5 +--R - 51b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 10a b e - 48a b d e + 255a b d e - 295a b d e + 48a b d e +--R + +--R 6 5 7 6 +--R 90a b d e - 37b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R - a e - 3a b d e - 15a b d e + 110a b d e - 195a b d e + 141a b d e +--R + +--R 6 6 +--R - 37a b d +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 8 3 7 3 7 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 572 + +)clear all + +--S 573 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1353 +r0:=-5/4*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^2)-_ + 5*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x))-1/4*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^4)-1/2*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^3)-15*b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6+15/2*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+_ + 15*b^4*(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 2 4 6 5 5 6 2 4 4 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (240a b d e - 480a b d e + 240b d e )x +--R + +--R 2 4 2 4 5 3 3 6 4 2 2 +--R (360a b d e - 720a b d e + 360b d e )x +--R + +--R 2 4 3 3 5 4 2 6 5 2 4 4 2 5 5 +--R (240a b d e - 480a b d e + 240b d e)x + 60a b d e - 120a b d e +--R + +--R 6 6 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 2b e x + (24a b e - 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 35a b e + 190a b d e - 125b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 80a b e + 100a b d e + 280a b d e - 260b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 30a b e - 120a b d e + 330a b d e + 60a b d e - 210b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 8a b e - 20a b d e - 80a b d e + 300a b d e - 120a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - a e - 2a b d e - 5a b d e - 20a b d e + 90a b d e - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 4b e x + (4a e + 16b d e )x + (16a d e + 24b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (24a d e + 16b d e )x + (16a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 6 5 5 6 2 4 4 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (240a b d e - 480a b d e + 240b d e )x +--R + +--R 2 4 2 4 5 3 3 6 4 2 2 +--R (360a b d e - 720a b d e + 360b d e )x +--R + +--R 2 4 3 3 5 4 2 6 5 2 4 4 2 5 5 +--R (240a b d e - 480a b d e + 240b d e)x + 60a b d e - 120a b d e +--R + +--R 6 6 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 5 5 6 2 4 4 +--R 2b e x + (24a b e - 12b d e )x + (96a b d e - 68b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 80a b e + 240a b d e - 96a b d e - 32b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 30a b e - 120a b d e + 540a b d e - 504a b d e + 132b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 8a b e - 20a b d e - 80a b d e + 440a b d e - 496a b d e +--R + +--R 6 5 +--R 168b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - a e - 2a b d e - 5a b d e - 20a b d e + 125a b d e - 154a b d e +--R + +--R 6 6 +--R 57b d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +--R 4e x + 16d e x + 24d e x + 16d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 575 + +--S 576 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 6 5 5 6 2 4 4 +--R (- 60a b e + 120a b d e - 60b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (- 240a b d e + 480a b d e - 240b d e )x +--R + +--R 2 4 2 4 5 3 3 6 4 2 2 +--R (- 360a b d e + 720a b d e - 360b d e )x +--R + +--R 2 4 3 3 5 4 2 6 5 2 4 4 2 +--R (- 240a b d e + 480a b d e - 240b d e)x - 60a b d e +--R + +--R 5 5 6 6 +--R 120a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 2b e x + (- 24a b e + 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (35a b e - 190a b d e + 125b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b e - 100a b d e - 280a b d e + 260b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (30a b e + 120a b d e - 330a b d e - 60a b d e + 210b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 8a b e + 20a b d e + 80a b d e - 300a b d e + 120a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R a e + 2a b d e + 5a b d e + 20a b d e - 90a b d e + 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (60a b e + 120a b d e - 420a b d e + 240b d e )x +--R + +--R 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (240a b d e - 120a b d e - 480a b d e + 360b d e )x +--R + +--R 3 4 2 4 2 5 3 3 6 4 2 7 5 2 +--R (360a b d e - 480a b d e - 120a b d e + 240b d e)x +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 3 4 4 2 +--R (240a b d e - 420a b d e + 120a b d e + 60b d )x + 60a b d e +--R + +--R 2 5 5 6 6 +--R - 120a b d e + 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R 2b e x + (26a b e - 12b d e )x + (24a b e + 84a b d e - 68b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 80a b e + 336a b d e - 164a b d e - 32b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (- 110a b e + 120a b d e + 444a b d e - 536a b d e + 132b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 38a b e - 140a b d e + 460a b d e - 64a b d e - 364a b d e +--R + +--R 7 5 +--R 168b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 9a b e - 22a b d e - 85a b d e + 420a b d e - 371a b d e +--R + +--R 6 5 7 6 +--R 14a b d e + 57b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R - a e - 2a b d e - 5a b d e - 20a b d e + 125a b d e - 154a b d e +--R + +--R 6 6 +--R 57a b d +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 4b e x + (4a e + 16b d e )x + (16a d e + 24b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (24a d e + 16b d e )x + (16a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 577 + +)clear all + +--S 578 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^6 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1353 +r0:=-1/2*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^3)-_ + b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^2)-1/5*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^5)-3/10*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^4)+6*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 3*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x))-_ + 6*b^5*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 6 5 5 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (300a b d e - 300b d e )x +--R + +--R 5 2 4 6 3 3 3 5 3 3 6 4 2 2 +--R (600a b d e - 600b d e )x + (600a b d e - 600b d e )x +--R + +--R 5 4 2 6 5 5 5 6 6 +--R (300a b d e - 300b d e)x + 60a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (- 77a b e + 137b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 150a b e - 85a b d e + 385b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 100a b e - 300a b d e + 130a b d e + 470b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 50a b e - 100a b d e - 300a b d e + 330a b d e + 270b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 15a b e - 25a b d e - 50a b d e - 150a b d e + 240a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e - 3a b d e - 5a b d e - 10a b d e - 30a b d e + 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 10b e x + (10a e + 50b d e )x + (50a d e + 100b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (100a d e + 100b d e )x + (100a d e + 50b d e )x +--R + +--R 4 8 5 7 5 7 +--R (50a d e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 5 5 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (300a b d e - 300b d e )x +--R + +--R 5 2 4 6 3 3 3 5 3 3 6 4 2 2 +--R (600a b d e - 600b d e )x + (600a b d e - 600b d e )x +--R + +--R 5 4 2 6 5 5 5 6 6 +--R (300a b d e - 300b d e)x + 60a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 10b e x + 50b d e x + (- 150a b e + 300a b d e - 50b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 100a b e - 300a b d e + 900a b d e - 400b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 50a b e - 100a b d e - 300a b d e + 1100a b d e - 600b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 15a b e - 25a b d e - 50a b d e - 150a b d e + 625a b d e +--R + +--R 6 5 +--R - 375b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e - 3a b d e - 5a b d e - 10a b d e - 30a b d e + 137a b d e +--R + +--R 6 6 +--R - 87b d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 5 7 +--R 10e x + 50d e x + 100d e x + 100d e x + 50d e x + 10d e +--R Type: Union(Expression(Integer),...) +--E 580 + +--S 581 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 6 5 5 5 5 6 2 4 4 +--R (- 60a b e + 60b d e )x + (- 300a b d e + 300b d e )x +--R + +--R 5 2 4 6 3 3 3 5 3 3 6 4 2 2 +--R (- 600a b d e + 600b d e )x + (- 600a b d e + 600b d e )x +--R + +--R 5 4 2 6 5 5 5 6 6 +--R (- 300a b d e + 300b d e)x - 60a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 10b e x + (77a b e - 137b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (150a b e + 85a b d e - 385b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b e + 300a b d e - 130a b d e - 470b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (50a b e + 100a b d e + 300a b d e - 330a b d e - 270b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 15a b e + 25a b d e + 50a b d e + 150a b d e - 240a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 2a e + 3a b d e + 5a b d e + 10a b d e + 30a b d e - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R (60a b e - 60b d e )x + (60a b e + 240a b d e - 300b d e )x +--R + +--R 2 5 5 6 2 4 7 3 3 4 +--R (300a b d e + 300a b d e - 600b d e )x +--R + +--R 2 5 2 4 7 4 2 3 +--R (600a b d e - 600b d e )x +--R + +--R 2 5 3 3 6 4 2 7 5 2 +--R (600a b d e - 300a b d e - 300b d e)x +--R + +--R 2 5 4 2 6 5 7 6 2 5 5 6 6 +--R (300a b d e - 240a b d e - 60b d )x + 60a b d e - 60a b d +--R * +--R log(e x + d) +--R + +--R 7 6 7 6 6 7 5 6 +--R 10b e x + (10a b e + 50b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 150a b e + 350a b d e - 50b d e )x +--R + +--R 3 4 6 6 2 4 7 3 3 4 +--R (- 250a b e + 850a b d e - 400b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (- 150a b e - 400a b d e + 600a b d e + 700a b d e - 600b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 65a b e - 125a b d e - 350a b d e + 950a b d e + 25a b d e +--R + +--R 7 5 +--R - 375b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 17a b e - 28a b d e - 55a b d e - 160a b d e + 595a b d e +--R + +--R 6 5 7 6 +--R - 238a b d e - 87b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R - 2a e - 3a b d e - 5a b d e - 10a b d e - 30a b d e + 137a b d e +--R + +--R 6 6 +--R - 87a b d +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 10b e x + (10a e + 50b d e )x + (50a d e + 100b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (100a d e + 100b d e )x + (100a d e + 50b d e )x +--R + +--R 4 8 5 7 5 7 +--R (50a d e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1353 +r0:=-1/4*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^4)-_ + 1/3*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^3)-1/6*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^6)-1/5*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^5)-1/2*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^2)+b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x))+b^6*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 6 6 5 5 6 2 4 4 6 3 3 3 6 4 2 2 +--R 60b e x + 360b d e x + 900b d e x + 1200b d e x + 900b d e x +--R + +--R 6 5 6 6 +--R 360b d e x + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 87b e x + (- 360a b e - 162b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 450a b e - 900a b d e + 45b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 400a b e - 600a b d e - 1200a b d e + 460b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 225a b e - 300a b d e - 450a b d e - 900a b d e + 570b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 72a b e - 90a b d e - 120a b d e - 180a b d e - 360a b d e +--R + +--R 6 5 +--R 300b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e - 12a b d e - 15a b d e - 20a b d e - 30a b d e +--R + +--R 5 5 6 6 +--R - 60a b d e + 60b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 7 13 12 6 12 2 11 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 11 3 10 4 3 10 4 9 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 9 5 8 2 5 8 6 7 6 7 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 6 5 5 6 2 4 4 6 3 3 3 6 4 2 2 +--R 60b e x + 360b d e x + 900b d e x + 1200b d e x + 900b d e x +--R + +--R 6 5 6 6 +--R 360b d e x + 60b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R (- 360a b e + 360b d e )x + (- 450a b e - 900a b d e + 1350b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 400a b e - 600a b d e - 1200a b d e + 2200b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 225a b e - 300a b d e - 450a b d e - 900a b d e + 1875b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 72a b e - 90a b d e - 120a b d e - 180a b d e - 360a b d e +--R + +--R 6 5 +--R 822b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 10a e - 12a b d e - 15a b d e - 20a b d e - 30a b d e - 60a b d e +--R + +--R 6 6 +--R 147b d +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 5 8 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 7 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 585 + +--S 586 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 6 5 5 6 2 4 4 6 3 3 3 +--R - 60b e x - 360b d e x - 900b d e x - 1200b d e x +--R + +--R 6 4 2 2 6 5 6 6 +--R - 900b d e x - 360b d e x - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 87b e x + (360a b e + 162b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (450a b e + 900a b d e - 45b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b e + 600a b d e + 1200a b d e - 460b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (225a b e + 300a b d e + 450a b d e + 900a b d e - 570b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 72a b e + 90a b d e + 120a b d e + 180a b d e + 360a b d e +--R + +--R 6 5 +--R - 300b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 10a e + 12a b d e + 15a b d e + 20a b d e + 30a b d e +--R + +--R 5 5 6 6 +--R 60a b d e - 60b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 6 5 7 2 4 5 +--R 60b e x + (60a b e + 360b d e )x + (360a b d e + 900b d e )x +--R + +--R 6 2 4 7 3 3 4 6 3 3 7 4 2 3 +--R (900a b d e + 1200b d e )x + (1200a b d e + 900b d e )x +--R + +--R 6 4 2 7 5 2 6 5 7 6 6 6 +--R (900a b d e + 360b d e)x + (360a b d e + 60b d )x + 60a b d +--R * +--R log(e x + d) +--R + +--R 6 6 7 5 6 2 5 6 6 5 7 2 4 5 +--R (- 360a b e + 360b d e )x + (- 810a b e - 540a b d e + 1350b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 850a b e - 1500a b d e + 150a b d e + 2200b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (- 625a b e - 900a b d e - 1650a b d e + 1300a b d e + 1875b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R - 297a b e - 390a b d e - 570a b d e - 1080a b d e + 1515a b d e +--R + +--R 7 5 +--R 822b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 82a b e - 102a b d e - 135a b d e - 200a b d e - 390a b d e +--R + +--R 6 5 7 6 +--R 762a b d e + 147b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 2 5 5 +--R - 10a e - 12a b d e - 15a b d e - 20a b d e - 30a b d e - 60a b d e +--R + +--R 6 6 +--R 147a b d +--R / +--R 13 7 13 12 6 12 2 11 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 11 3 10 4 3 10 4 9 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 9 5 8 2 5 8 6 7 6 7 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 587 + +)clear all + +--S 588 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1353 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^7) +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- b x - 6a b x - 15a b x - 20a b x - 15a b x - 6a b x - a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 7 7 7 2 6 6 2 6 3 5 5 +--R (7a e - 7b d e )x + (49a d e - 49b d e )x + (147a d e - 147b d e )x +--R + +--R 3 5 4 4 4 4 4 5 3 3 +--R (245a d e - 245b d e )x + (245a d e - 245b d e )x +--R + +--R 5 3 6 2 2 6 2 7 7 8 +--R (147a d e - 147b d e )x + (49a d e - 49b d e)x + 7a d e - 7b d +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 7b e x + (- 21a b e - 21b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 35a b e - 35a b d e - 35b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 35a b e - 35a b d e - 35a b d e - 35b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 21a b e - 21a b d e - 21a b d e - 21a b d e - 21b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (- 7a b e - 7a b d e - 7a b d e - 7a b d e - 7a b d e - 7b d e)x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R - a e - a b d e - a b d e - a b d e - a b d e - a b d e - b d +--R / +--R 14 7 13 6 2 12 5 3 11 4 4 10 3 5 9 2 +--R 7e x + 49d e x + 147d e x + 245d e x + 245d e x + 147d e x +--R + +--R 6 8 7 7 +--R 49d e x + 7d e +--R Type: Union(Expression(Integer),...) +--E 590 + +--S 591 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 6 5 7 5 2 4 7 4 3 3 7 3 4 2 7 2 5 7 +--R b e x + 6a b e x + 15a b e x + 20a b e x + 15a b e x + 6a b e x +--R + +--R 6 7 +--R a e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 7 7 6 6 2 5 7 7 2 5 5 +--R (- 7a b e + 7b d e )x + (- 21a b e + 21b d e )x +--R + +--R 3 4 7 7 3 4 4 4 3 7 7 4 3 3 +--R (- 35a b e + 35b d e )x + (- 35a b e + 35b d e )x +--R + +--R 5 2 7 7 5 2 2 6 7 7 6 7 7 7 7 +--R (- 21a b e + 21b d e )x + (- 7a b e + 7b d e)x - a e + b d +--R / +--R 15 14 7 14 2 13 6 +--R (7a e - 7b d e )x + (49a d e - 49b d e )x +--R + +--R 2 13 3 12 5 3 12 4 11 4 +--R (147a d e - 147b d e )x + (245a d e - 245b d e )x +--R + +--R 4 11 5 10 3 5 10 6 9 2 +--R (245a d e - 245b d e )x + (147a d e - 147b d e )x +--R + +--R 6 9 7 8 7 8 8 7 +--R (49a d e - 49b d e )x + 7a d e - 7b d e +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 592 + +)clear all + +--S 593 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1353 +r0:=1/8*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^8)+_ + 1/56*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^7) +--R +--R +--R (2) +--R 7 7 6 7 6 2 5 6 5 +--R b e x + (- a b e + 8b d)x + (- 27a b e + 48a b d)x +--R + +--R 3 4 2 5 4 4 3 3 4 3 +--R (- 85a b e + 120a b d)x + (- 125a b e + 160a b d)x +--R + +--R 5 2 4 3 2 6 5 2 7 6 +--R (- 99a b e + 120a b d)x + (- 41a b e + 48a b d)x - 7a e + 8a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 10 9 2 2 8 8 +--R (56a e - 112a b d e + 56b d e )x +--R + +--R 2 9 2 8 2 3 7 7 +--R (448a d e - 896a b d e + 448b d e )x +--R + +--R 2 2 8 3 7 2 4 6 6 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 3 7 4 6 2 5 5 5 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 4 6 5 5 2 6 4 4 +--R (3920a d e - 7840a b d e + 3920b d e )x +--R + +--R 2 5 5 6 4 2 7 3 3 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 6 4 7 3 2 8 2 2 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 7 3 8 2 2 9 2 8 2 9 2 10 +--R (448a d e - 896a b d e + 448b d e)x + 56a d e - 112a b d e + 56b d +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 28b e x + (- 112a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 210a b e - 140a b d e - 70b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 224a b e - 168a b d e - 112a b d e - 56b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 140a b e - 112a b d e - 84a b d e - 56a b d e - 28b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 48a b e - 40a b d e - 32a b d e - 24a b d e - 16a b d e +--R + +--R 6 5 +--R - 8b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R - 7a e - 6a b d e - 5a b d e - 4a b d e - 3a b d e - 2a b d e - b d +--R / +--R 15 8 14 7 2 13 6 3 12 5 4 11 4 +--R 56e x + 448d e x + 1568d e x + 3136d e x + 3920d e x +--R + +--R 5 10 3 6 9 2 7 8 8 7 +--R 3136d e x + 1568d e x + 448d e x + 56d e +--R Type: Union(Expression(Integer),...) +--E 595 + +--S 596 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 8 7 6 8 7 7 6 2 5 8 6 7 5 +--R - b e x + (a b e - 8b d e )x + (27a b e - 48a b d e )x +--R + +--R 3 4 8 2 5 7 4 4 3 8 3 4 7 3 +--R (85a b e - 120a b d e )x + (125a b e - 160a b d e )x +--R + +--R 5 2 8 4 3 7 2 6 8 5 2 7 7 8 +--R (99a b e - 120a b d e )x + (41a b e - 48a b d e )x + 7a e +--R + +--R 6 7 +--R - 8a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 6 8 7 7 8 2 6 6 +--R (- 28a b e + 56a b d e - 28b d e )x +--R + +--R 3 5 8 2 6 7 8 3 5 5 +--R (- 112a b e + 168a b d e - 56b d e )x +--R + +--R 4 4 8 3 5 7 8 4 4 4 +--R (- 210a b e + 280a b d e - 70b d e )x +--R + +--R 5 3 8 4 4 7 8 5 3 3 +--R (- 224a b e + 280a b d e - 56b d e )x +--R + +--R 6 2 8 5 3 7 8 6 2 2 +--R (- 140a b e + 168a b d e - 28b d e )x +--R + +--R 7 8 6 2 7 8 7 8 8 7 7 8 8 +--R (- 48a b e + 56a b d e - 8b d e)x - 7a e + 8a b d e - b d +--R / +--R 2 17 16 2 2 15 8 +--R (56a e - 112a b d e + 56b d e )x +--R + +--R 2 16 2 15 2 3 14 7 +--R (448a d e - 896a b d e + 448b d e )x +--R + +--R 2 2 15 3 14 2 4 13 6 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 3 14 4 13 2 5 12 5 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 4 13 5 12 2 6 11 4 +--R (3920a d e - 7840a b d e + 3920b d e )x +--R + +--R 2 5 12 6 11 2 7 10 3 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 6 11 7 10 2 8 9 2 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 7 10 8 9 2 9 8 2 8 9 9 8 +--R (448a d e - 896a b d e + 448b d e )x + 56a d e - 112a b d e +--R + +--R 2 10 7 +--R 56b d e +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1353 +r0:=1/9*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^9)+_ + 1/36*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^8)+_ + 1/252*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^7) +--R +--R +--R (2) +--R 8 2 8 7 2 8 7 2 6 2 7 8 2 6 +--R - b e x + (a b e - 9b d e)x + (- a b e + 9a b d e - 36b d )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 83a b e + 243a b d e - 216a b d )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 295a b e + 765a b d e - 540a b d )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 461a b e + 1125a b d e - 720a b d )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 379a b e + 891a b d e - 540a b d )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 161a b e + 369a b d e - 216a b d )x - 28a e + 63a b d e - 36a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 12 2 11 2 2 10 3 3 9 9 +--R (252a e - 756a b d e + 756a b d e - 252b d e )x +--R + +--R 3 11 2 2 10 2 3 9 3 4 8 8 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e )x +--R + +--R 3 2 10 2 3 9 2 4 8 3 5 7 7 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 3 9 2 4 8 2 5 7 3 6 6 6 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 4 8 2 5 7 2 6 6 3 7 5 5 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 5 7 2 6 6 2 7 5 3 8 4 4 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 6 6 2 7 5 2 8 4 3 9 3 3 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 7 5 2 8 4 2 9 3 3 10 2 2 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 8 4 2 9 3 2 10 2 3 11 3 9 3 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e)x + 252a d e +--R + +--R 2 10 2 2 11 3 12 +--R - 756a b d e + 756a b d e - 252b d +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 84b e x + (- 378a b e - 126b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 756a b e - 378a b d e - 126b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 840a b e - 504a b d e - 252a b d e - 84b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 540a b e - 360a b d e - 216a b d e - 108a b d e - 36b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 189a b e - 135a b d e - 90a b d e - 54a b d e - 27a b d e +--R + +--R 6 5 +--R - 9b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 28a e - 21a b d e - 15a b d e - 10a b d e - 6a b d e - 3a b d e +--R + +--R 6 6 +--R - b d +--R / +--R 16 9 15 8 2 14 7 3 13 6 4 12 5 +--R 252e x + 2268d e x + 9072d e x + 21168d e x + 31752d e x +--R + +--R 5 11 4 6 10 3 7 9 2 8 8 9 7 +--R 31752d e x + 21168d e x + 9072d e x + 2268d e x + 252d e +--R Type: Union(Expression(Integer),...) +--E 600 + +--S 601 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 9 8 7 9 8 8 7 2 6 9 7 8 8 2 7 6 +--R b e x + (- a b e + 9b d e )x + (a b e - 9a b d e + 36b d e )x +--R + +--R 3 5 9 2 6 8 7 2 7 5 +--R (83a b e - 243a b d e + 216a b d e )x +--R + +--R 4 4 9 3 5 8 2 6 2 7 4 +--R (295a b e - 765a b d e + 540a b d e )x +--R + +--R 5 3 9 4 4 8 3 5 2 7 3 +--R (461a b e - 1125a b d e + 720a b d e )x +--R + +--R 6 2 9 5 3 8 4 4 2 7 2 +--R (379a b e - 891a b d e + 540a b d e )x +--R + +--R 7 9 6 2 8 5 3 2 7 8 9 7 8 +--R (161a b e - 369a b d e + 216a b d e )x + 28a e - 63a b d e +--R + +--R 6 2 2 7 +--R 36a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 6 9 2 7 8 8 2 7 9 3 6 6 +--R (- 84a b e + 252a b d e - 252a b d e + 84b d e )x +--R + +--R 4 5 9 3 6 8 2 7 2 7 9 4 5 5 +--R (- 378a b e + 1008a b d e - 756a b d e + 126b d e )x +--R + +--R 5 4 9 4 5 8 3 6 2 7 9 5 4 4 +--R (- 756a b e + 1890a b d e - 1260a b d e + 126b d e )x +--R + +--R 6 3 9 5 4 8 4 5 2 7 9 6 3 3 +--R (- 840a b e + 2016a b d e - 1260a b d e + 84b d e )x +--R + +--R 7 2 9 6 3 8 5 4 2 7 9 7 2 2 +--R (- 540a b e + 1260a b d e - 756a b d e + 36b d e )x +--R + +--R 8 9 7 2 8 6 3 2 7 9 8 9 9 8 8 +--R (- 189a b e + 432a b d e - 252a b d e + 9b d e)x - 28a e + 63a b d e +--R + +--R 7 2 2 7 9 9 +--R - 36a b d e + b d +--R / +--R 3 19 2 18 2 2 17 3 3 16 9 +--R (252a e - 756a b d e + 756a b d e - 252b d e )x +--R + +--R 3 18 2 2 17 2 3 16 3 4 15 8 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e )x +--R + +--R 3 2 17 2 3 16 2 4 15 3 5 14 7 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 3 16 2 4 15 2 5 14 3 6 13 6 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 4 15 2 5 14 2 6 13 3 7 12 5 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 5 14 2 6 13 2 7 12 3 8 11 4 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 6 13 2 7 12 2 8 11 3 9 10 3 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 7 12 2 8 11 2 9 10 3 10 9 2 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 8 11 2 9 10 2 10 9 3 11 8 3 9 10 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e )x + 252a d e +--R + +--R 2 10 9 2 11 8 3 12 7 +--R - 756a b d e + 756a b d e - 252b d e +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 602 + +)clear all + +--S 603 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1353 +r0:=1/10*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^10)+_ + 1/30*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^9)+_ + 1/120*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^8)+_ + 1/840*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^7) +--R +--R +--R (2) +--R 9 3 9 8 3 9 2 8 2 7 3 8 2 9 2 7 +--R b e x + (- a b e + 10b d e )x + (a b e - 10a b d e + 45b d e)x +--R + +--R 3 6 3 2 7 2 8 2 9 3 6 +--R (- a b e + 10a b d e - 45a b d e + 120b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (- 209a b e + 830a b d e - 1215a b d e + 720a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 4 +--R (- 799a b e + 2950a b d e - 3825a b d e + 1800a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (- 1301a b e + 4610a b d e - 5625a b d e + 2400a b d )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (- 1099a b e + 3790a b d e - 4455a b d e + 1800a b d )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 +--R (- 476a b e + 1610a b d e - 1845a b d e + 720a b d )x - 84a e +--R + +--R 8 2 7 2 2 6 3 3 +--R 280a b d e - 315a b d e + 120a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 14 3 13 2 2 2 12 3 3 11 4 4 10 +--R (840a e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d e ) +--R * +--R 10 +--R x +--R + +--R 4 13 3 2 12 2 2 3 11 3 4 10 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 5 9 +--R 8400b d e +--R * +--R 9 +--R x +--R + +--R 4 2 12 3 3 11 2 2 4 10 3 5 9 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 6 8 +--R 37800b d e +--R * +--R 8 +--R x +--R + +--R 4 3 11 3 4 10 2 2 5 9 3 6 8 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 7 7 +--R 100800b d e +--R * +--R 7 +--R x +--R + +--R 4 4 10 3 5 9 2 2 6 8 3 7 7 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 8 6 +--R 176400b d e +--R * +--R 6 +--R x +--R + +--R 4 5 9 3 6 8 2 2 7 7 3 8 6 +--R 211680a d e - 846720a b d e + 1270080a b d e - 846720a b d e +--R + +--R 4 9 5 +--R 211680b d e +--R * +--R 5 +--R x +--R + +--R 4 6 8 3 7 7 2 2 8 6 3 9 5 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 10 4 +--R 176400b d e +--R * +--R 4 +--R x +--R + +--R 4 7 7 3 8 6 2 2 9 5 3 10 4 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 11 3 +--R 100800b d e +--R * +--R 3 +--R x +--R + +--R 4 8 6 3 9 5 2 2 10 4 3 11 3 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 12 2 +--R 37800b d e +--R * +--R 2 +--R x +--R + +--R 4 9 5 3 10 4 2 2 11 3 3 12 2 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 13 +--R 8400b d e +--R * +--R x +--R + +--R 4 10 4 3 11 3 2 2 12 2 3 13 4 14 +--R 840a d e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 210b e x + (- 1008a b e - 252b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 2100a b e - 840a b d e - 210b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 2400a b e - 1200a b d e - 480a b d e - 120b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 1575a b e - 900a b d e - 450a b d e - 180a b d e - 45b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 560a b e - 350a b d e - 200a b d e - 100a b d e - 40a b d e +--R + +--R 6 5 +--R - 10b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 84a e - 56a b d e - 35a b d e - 20a b d e - 10a b d e - 4a b d e +--R + +--R 6 6 +--R - b d +--R / +--R 17 10 16 9 2 15 8 3 14 7 4 13 6 +--R 840e x + 8400d e x + 37800d e x + 100800d e x + 176400d e x +--R + +--R 5 12 5 6 11 4 7 10 3 8 9 2 9 8 +--R 211680d e x + 176400d e x + 100800d e x + 37800d e x + 8400d e x +--R + +--R 10 7 +--R 840d e +--R Type: Union(Expression(Integer),...) +--E 605 + +--S 606 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 10 9 8 10 9 9 8 +--R - b e x + (a b e - 10b d e )x +--R + +--R 2 7 10 8 9 9 2 8 7 +--R (- a b e + 10a b d e - 45b d e )x +--R + +--R 3 6 10 2 7 9 8 2 8 9 3 7 6 +--R (a b e - 10a b d e + 45a b d e - 120b d e )x +--R + +--R 4 5 10 3 6 9 2 7 2 8 8 3 7 5 +--R (209a b e - 830a b d e + 1215a b d e - 720a b d e )x +--R + +--R 5 4 10 4 5 9 3 6 2 8 2 7 3 7 4 +--R (799a b e - 2950a b d e + 3825a b d e - 1800a b d e )x +--R + +--R 6 3 10 5 4 9 4 5 2 8 3 6 3 7 3 +--R (1301a b e - 4610a b d e + 5625a b d e - 2400a b d e )x +--R + +--R 7 2 10 6 3 9 5 4 2 8 4 5 3 7 2 +--R (1099a b e - 3790a b d e + 4455a b d e - 1800a b d e )x +--R + +--R 8 10 7 2 9 6 3 2 8 5 4 3 7 9 10 +--R (476a b e - 1610a b d e + 1845a b d e - 720a b d e )x + 84a e +--R + +--R 8 9 7 2 2 8 6 3 3 7 +--R - 280a b d e + 315a b d e - 120a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (- 210a b e + 840a b d e - 1260a b d e + 840a b d e - 210b d e )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 1008a b e + 3780a b d e - 5040a b d e + 2520a b d e +--R + +--R 10 5 5 +--R - 252b d e +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 2100a b e + 7560a b d e - 9450a b d e + 4200a b d e +--R + +--R 10 6 4 +--R - 210b d e +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 2400a b e + 8400a b d e - 10080a b d e + 4200a b d e +--R + +--R 10 7 3 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 1575a b e + 5400a b d e - 6300a b d e + 2520a b d e +--R + +--R 10 8 2 +--R - 45b d e +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 10 9 +--R (- 560a b e + 1890a b d e - 2160a b d e + 840a b d e - 10b d e)x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 10 10 +--R - 84a e + 280a b d e - 315a b d e + 120a b d e - b d +--R / +--R 4 21 3 20 2 2 2 19 3 3 18 4 4 17 +--R (840a e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d e ) +--R * +--R 10 +--R x +--R + +--R 4 20 3 2 19 2 2 3 18 3 4 17 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 5 16 +--R 8400b d e +--R * +--R 9 +--R x +--R + +--R 4 2 19 3 3 18 2 2 4 17 3 5 16 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 6 15 +--R 37800b d e +--R * +--R 8 +--R x +--R + +--R 4 3 18 3 4 17 2 2 5 16 3 6 15 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 7 14 +--R 100800b d e +--R * +--R 7 +--R x +--R + +--R 4 4 17 3 5 16 2 2 6 15 3 7 14 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 8 13 +--R 176400b d e +--R * +--R 6 +--R x +--R + +--R 4 5 16 3 6 15 2 2 7 14 3 8 13 +--R 211680a d e - 846720a b d e + 1270080a b d e - 846720a b d e +--R + +--R 4 9 12 +--R 211680b d e +--R * +--R 5 +--R x +--R + +--R 4 6 15 3 7 14 2 2 8 13 3 9 12 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 10 11 +--R 176400b d e +--R * +--R 4 +--R x +--R + +--R 4 7 14 3 8 13 2 2 9 12 3 10 11 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 11 10 +--R 100800b d e +--R * +--R 3 +--R x +--R + +--R 4 8 13 3 9 12 2 2 10 11 3 11 10 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 12 9 +--R 37800b d e +--R * +--R 2 +--R x +--R + +--R 4 9 12 3 10 11 2 2 11 10 3 12 9 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 13 8 +--R 8400b d e +--R * +--R x +--R + +--R 4 10 11 3 11 10 2 2 12 9 3 13 8 4 14 7 +--R 840a d e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d e +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 607 + +)clear all + +--S 608 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1353 +r0:=1/11*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^11)+_ + 2/55*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^10)+_ + 2/165*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^9)+_ + 1/330*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^8)+_ + 1/2310*b^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^7) +--R +--R +--R (2) +--R 10 4 10 9 4 10 3 9 +--R - b e x + (a b e - 11b d e )x +--R + +--R 2 8 4 9 3 10 2 2 8 +--R (- a b e + 11a b d e - 55b d e )x +--R + +--R 3 7 4 2 8 3 9 2 2 10 3 7 +--R (a b e - 11a b d e + 55a b d e - 165b d e)x +--R + +--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 6 +--R (- a b e + 11a b d e - 55a b d e + 165a b d e - 330b d )x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R - 461a b e + 2299a b d e - 4565a b d e + 4455a b d e +--R + +--R 9 4 +--R - 1980a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 +--R - 1849a b e + 8789a b d e - 16225a b d e + 14025a b d e +--R + +--R 2 8 4 +--R - 4950a b d +--R * +--R 4 +--R x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 +--R - 3101a b e + 14311a b d e - 25355a b d e + 20625a b d e +--R + +--R 3 7 4 +--R - 6600a b d +--R * +--R 3 +--R x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 +--R - 2674a b e + 12089a b d e - 20845a b d e + 16335a b d e +--R + +--R 4 6 4 +--R - 4950a b d +--R * +--R 2 +--R x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 +--R - 1176a b e + 5236a b d e - 8855a b d e + 6765a b d e +--R + +--R 5 5 4 +--R - 1980a b d +--R * +--R x +--R + +--R 10 4 9 3 8 2 2 2 7 3 3 6 4 4 +--R - 210a e + 924a b d e - 1540a b d e + 1155a b d e - 330a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 16 4 15 3 2 2 14 2 3 3 13 +--R 2310a e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 4 12 5 5 11 +--R 11550a b d e - 2310b d e +--R * +--R 11 +--R x +--R + +--R 5 15 4 2 14 3 2 3 13 2 3 4 12 +--R 25410a d e - 127050a b d e + 254100a b d e - 254100a b d e +--R + +--R 4 5 11 5 6 10 +--R 127050a b d e - 25410b d e +--R * +--R 10 +--R x +--R + +--R 5 2 14 4 3 13 3 2 4 12 2 3 5 11 +--R 127050a d e - 635250a b d e + 1270500a b d e - 1270500a b d e +--R + +--R 4 6 10 5 7 9 +--R 635250a b d e - 127050b d e +--R * +--R 9 +--R x +--R + +--R 5 3 13 4 4 12 3 2 5 11 +--R 381150a d e - 1905750a b d e + 3811500a b d e +--R + +--R 2 3 6 10 4 7 9 5 8 8 +--R - 3811500a b d e + 1905750a b d e - 381150b d e +--R * +--R 8 +--R x +--R + +--R 5 4 12 4 5 11 3 2 6 10 2 3 7 9 +--R 762300a d e - 3811500a b d e + 7623000a b d e - 7623000a b d e +--R + +--R 4 8 8 5 9 7 +--R 3811500a b d e - 762300b d e +--R * +--R 7 +--R x +--R + +--R 5 5 11 4 6 10 3 2 7 9 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 8 8 4 9 7 5 10 6 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 6 +--R x +--R + +--R 5 6 10 4 7 9 3 2 8 8 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 9 7 4 10 6 5 11 5 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 5 +--R x +--R + +--R 5 7 9 4 8 8 3 2 9 7 2 3 10 6 +--R 762300a d e - 3811500a b d e + 7623000a b d e - 7623000a b d e +--R + +--R 4 11 5 5 12 4 +--R 3811500a b d e - 762300b d e +--R * +--R 4 +--R x +--R + +--R 5 8 8 4 9 7 3 2 10 6 2 3 11 5 +--R 381150a d e - 1905750a b d e + 3811500a b d e - 3811500a b d e +--R + +--R 4 12 4 5 13 3 +--R 1905750a b d e - 381150b d e +--R * +--R 3 +--R x +--R + +--R 5 9 7 4 10 6 3 2 11 5 2 3 12 4 +--R 127050a d e - 635250a b d e + 1270500a b d e - 1270500a b d e +--R + +--R 4 13 3 5 14 2 +--R 635250a b d e - 127050b d e +--R * +--R 2 +--R x +--R + +--R 5 10 6 4 11 5 3 2 12 4 2 3 13 3 +--R 25410a d e - 127050a b d e + 254100a b d e - 254100a b d e +--R + +--R 4 14 2 5 15 +--R 127050a b d e - 25410b d e +--R * +--R x +--R + +--R 5 11 5 4 12 4 3 2 13 3 2 3 14 2 +--R 2310a d e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 15 5 16 +--R 11550a b d e - 2310b d +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 462b e x + (- 2310a b e - 462b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 4950a b e - 1650a b d e - 330b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 5775a b e - 2475a b d e - 825a b d e - 165b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 3850a b e - 1925a b d e - 825a b d e - 275a b d e - 55b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 1386a b e - 770a b d e - 385a b d e - 165a b d e - 55a b d e +--R + +--R 6 5 +--R - 11b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 210a e - 126a b d e - 70a b d e - 35a b d e - 15a b d e - 5a b d e +--R + +--R 6 6 +--R - b d +--R / +--R 18 11 17 10 2 16 9 3 15 8 +--R 2310e x + 25410d e x + 127050d e x + 381150d e x +--R + +--R 4 14 7 5 13 6 6 12 5 7 11 4 +--R 762300d e x + 1067220d e x + 1067220d e x + 762300d e x +--R + +--R 8 10 3 9 9 2 10 8 11 7 +--R 381150d e x + 127050d e x + 25410d e x + 2310d e +--R Type: Union(Expression(Integer),...) +--E 610 + +--S 611 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 10 11 10 9 11 10 10 9 +--R b e x + (- a b e + 11b d e )x +--R + +--R 2 8 11 9 10 10 2 9 8 +--R (a b e - 11a b d e + 55b d e )x +--R + +--R 3 7 11 2 8 10 9 2 9 10 3 8 7 +--R (- a b e + 11a b d e - 55a b d e + 165b d e )x +--R + +--R 4 6 11 3 7 10 2 8 2 9 9 3 8 10 4 7 6 +--R (a b e - 11a b d e + 55a b d e - 165a b d e + 330b d e )x +--R + +--R 5 5 11 4 6 10 3 7 2 9 2 8 3 8 +--R 461a b e - 2299a b d e + 4565a b d e - 4455a b d e +--R + +--R 9 4 7 +--R 1980a b d e +--R * +--R 5 +--R x +--R + +--R 6 4 11 5 5 10 4 6 2 9 3 7 3 8 +--R 1849a b e - 8789a b d e + 16225a b d e - 14025a b d e +--R + +--R 2 8 4 7 +--R 4950a b d e +--R * +--R 4 +--R x +--R + +--R 7 3 11 6 4 10 5 5 2 9 4 6 3 8 +--R 3101a b e - 14311a b d e + 25355a b d e - 20625a b d e +--R + +--R 3 7 4 7 +--R 6600a b d e +--R * +--R 3 +--R x +--R + +--R 8 2 11 7 3 10 6 4 2 9 5 5 3 8 +--R 2674a b e - 12089a b d e + 20845a b d e - 16335a b d e +--R + +--R 4 6 4 7 +--R 4950a b d e +--R * +--R 2 +--R x +--R + +--R 9 11 8 2 10 7 3 2 9 6 4 3 8 +--R 1176a b e - 5236a b d e + 8855a b d e - 6765a b d e +--R + +--R 5 5 4 7 +--R 1980a b d e +--R * +--R x +--R + +--R 10 11 9 10 8 2 2 9 7 3 3 8 6 4 4 7 +--R 210a e - 924a b d e + 1540a b d e - 1155a b d e + 330a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 6 11 4 7 10 3 8 2 9 2 9 3 8 +--R - 462a b e + 2310a b d e - 4620a b d e + 4620a b d e +--R + +--R 10 4 7 11 5 6 +--R - 2310a b d e + 462b d e +--R * +--R 6 +--R x +--R + +--R 6 5 11 5 6 10 4 7 2 9 3 8 3 8 +--R - 2310a b e + 11088a b d e - 20790a b d e + 18480a b d e +--R + +--R 2 9 4 7 11 6 5 +--R - 6930a b d e + 462b d e +--R * +--R 5 +--R x +--R + +--R 7 4 11 6 5 10 5 6 2 9 4 7 3 8 +--R - 4950a b e + 23100a b d e - 41580a b d e + 34650a b d e +--R + +--R 3 8 4 7 11 7 4 +--R - 11550a b d e + 330b d e +--R * +--R 4 +--R x +--R + +--R 8 3 11 7 4 10 6 5 2 9 5 6 3 8 +--R - 5775a b e + 26400a b d e - 46200a b d e + 36960a b d e +--R + +--R 4 7 4 7 11 8 3 +--R - 11550a b d e + 165b d e +--R * +--R 3 +--R x +--R + +--R 9 2 11 8 3 10 7 4 2 9 6 5 3 8 +--R - 3850a b e + 17325a b d e - 29700a b d e + 23100a b d e +--R + +--R 5 6 4 7 11 9 2 +--R - 6930a b d e + 55b d e +--R * +--R 2 +--R x +--R + +--R 10 11 9 2 10 8 3 2 9 7 4 3 8 +--R - 1386a b e + 6160a b d e - 10395a b d e + 7920a b d e +--R + +--R 6 5 4 7 11 10 +--R - 2310a b d e + 11b d e +--R * +--R x +--R + +--R 11 11 10 10 9 2 2 9 8 3 3 8 7 4 4 7 +--R - 210a e + 924a b d e - 1540a b d e + 1155a b d e - 330a b d e +--R + +--R 11 11 +--R b d +--R / +--R 5 23 4 22 3 2 2 21 2 3 3 20 +--R 2310a e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 4 19 5 5 18 +--R 11550a b d e - 2310b d e +--R * +--R 11 +--R x +--R + +--R 5 22 4 2 21 3 2 3 20 2 3 4 19 +--R 25410a d e - 127050a b d e + 254100a b d e - 254100a b d e +--R + +--R 4 5 18 5 6 17 +--R 127050a b d e - 25410b d e +--R * +--R 10 +--R x +--R + +--R 5 2 21 4 3 20 3 2 4 19 2 3 5 18 +--R 127050a d e - 635250a b d e + 1270500a b d e - 1270500a b d e +--R + +--R 4 6 17 5 7 16 +--R 635250a b d e - 127050b d e +--R * +--R 9 +--R x +--R + +--R 5 3 20 4 4 19 3 2 5 18 +--R 381150a d e - 1905750a b d e + 3811500a b d e +--R + +--R 2 3 6 17 4 7 16 5 8 15 +--R - 3811500a b d e + 1905750a b d e - 381150b d e +--R * +--R 8 +--R x +--R + +--R 5 4 19 4 5 18 3 2 6 17 +--R 762300a d e - 3811500a b d e + 7623000a b d e +--R + +--R 2 3 7 16 4 8 15 5 9 14 +--R - 7623000a b d e + 3811500a b d e - 762300b d e +--R * +--R 7 +--R x +--R + +--R 5 5 18 4 6 17 3 2 7 16 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 8 15 4 9 14 5 10 13 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 6 +--R x +--R + +--R 5 6 17 4 7 16 3 2 8 15 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 9 14 4 10 13 5 11 12 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 5 +--R x +--R + +--R 5 7 16 4 8 15 3 2 9 14 +--R 762300a d e - 3811500a b d e + 7623000a b d e +--R + +--R 2 3 10 13 4 11 12 5 12 11 +--R - 7623000a b d e + 3811500a b d e - 762300b d e +--R * +--R 4 +--R x +--R + +--R 5 8 15 4 9 14 3 2 10 13 +--R 381150a d e - 1905750a b d e + 3811500a b d e +--R + +--R 2 3 11 12 4 12 11 5 13 10 +--R - 3811500a b d e + 1905750a b d e - 381150b d e +--R * +--R 3 +--R x +--R + +--R 5 9 14 4 10 13 3 2 11 12 +--R 127050a d e - 635250a b d e + 1270500a b d e +--R + +--R 2 3 12 11 4 13 10 5 14 9 +--R - 1270500a b d e + 635250a b d e - 127050b d e +--R * +--R 2 +--R x +--R + +--R 5 10 13 4 11 12 3 2 12 11 +--R 25410a d e - 127050a b d e + 254100a b d e +--R + +--R 2 3 13 10 4 14 9 5 15 8 +--R - 254100a b d e + 127050a b d e - 25410b d e +--R * +--R x +--R + +--R 5 11 12 4 12 11 3 2 13 10 2 3 14 9 +--R 2310a d e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 15 8 5 16 7 +--R 11550a b d e - 2310b d e +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x +--R + +--R 12 +--R d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^13 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R e x + 13d e x + 78d e x + 286d e x + 715d e x + 1287d e x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 +--R 1716d e x + 1716d e x + 1287d e x + 715d e x + 286d e x + 78d e x +--R + +--R 12 13 +--R 13d e x + d +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1353 +r0:=1/12*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^12)+_ + 5/132*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^11)+_ + 1/66*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^10)+_ + 1/198*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^9)+_ + 1/792*b^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^8)+_ + 1/5544*b^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^6*(d+e*x)^7) +--R +--R +--R (2) +--R 11 5 11 10 5 11 4 10 +--R b e x + (- a b e + 12b d e )x +--R + +--R 2 9 5 10 4 11 2 3 9 +--R (a b e - 12a b d e + 66b d e )x +--R + +--R 3 8 5 2 9 4 10 2 3 11 3 2 8 +--R (- a b e + 12a b d e - 66a b d e + 220b d e )x +--R + +--R 4 7 5 3 8 4 2 9 2 3 10 3 2 11 4 7 +--R (a b e - 12a b d e + 66a b d e - 220a b d e + 495b d e)x +--R + +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 10 4 +--R - a b e + 12a b d e - 66a b d e + 220a b d e - 495a b d e +--R + +--R 11 5 +--R 792b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R - 923a b e + 5532a b d e - 13794a b d e + 18260a b d e +--R + +--R 2 9 4 10 5 +--R - 13365a b d e + 4752a b d +--R * +--R 5 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R - 3829a b e + 22188a b d e - 52734a b d e + 64900a b d e +--R + +--R 3 8 4 2 9 5 +--R - 42075a b d e + 11880a b d +--R * +--R 4 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 +--R - 6566a b e + 37212a b d e - 85866a b d e + 101420a b d e +--R + +--R 4 7 4 3 8 5 +--R - 61875a b d e + 15840a b d +--R * +--R 3 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 +--R - 5754a b e + 32088a b d e - 72534a b d e + 83380a b d e +--R + +--R 5 6 4 4 7 5 +--R - 49005a b d e + 11880a b d +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 +--R - 2562a b e + 14112a b d e - 31416a b d e + 35420a b d e +--R + +--R 6 5 4 5 6 5 +--R - 20295a b d e + 4752a b d +--R * +--R x +--R + +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 +--R - 462a e + 2520a b d e - 5544a b d e + 6160a b d e - 3465a b d e +--R + +--R 6 5 5 +--R 792a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x 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324648324a b d e +--R + +--R 4 3 8 19 3 4 9 18 2 5 10 17 +--R - 541080540a b d e + 541080540a b d e - 324648324a b d e +--R + +--R 6 11 16 7 12 15 +--R 108216108a b d e - 15459444b d e +--R * +--R 8 +--R x +--R + +--R 7 6 21 6 7 20 5 2 8 19 +--R 20612592a d e - 144288144a b d e + 432864432a b d e +--R + +--R 4 3 9 18 3 4 10 17 2 5 11 16 +--R - 721440720a b d e + 721440720a b d e - 432864432a b d e +--R + +--R 6 12 15 7 13 14 +--R 144288144a b d e - 20612592b d e +--R * +--R 7 +--R x +--R + +--R 7 7 20 6 8 19 5 2 9 18 +--R 20612592a d e - 144288144a b d e + 432864432a b d e +--R + +--R 4 3 10 17 3 4 11 16 2 5 12 15 +--R - 721440720a b d e + 721440720a b d e - 432864432a b d e +--R + +--R 6 13 14 7 14 13 +--R 144288144a b d e - 20612592b d e +--R * +--R 6 +--R x +--R + +--R 7 8 19 6 9 18 5 2 10 17 +--R 15459444a d e - 108216108a b d e + 324648324a b d e +--R + +--R 4 3 11 16 3 4 12 15 2 5 13 14 +--R - 541080540a b d e + 541080540a b d e - 324648324a b d e +--R + +--R 6 14 13 7 15 12 +--R 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4 16 11 2 5 17 10 +--R - 5465460a b d e + 5465460a b d e - 3279276a b d e +--R + +--R 6 18 9 7 19 8 +--R 1093092a b d e - 156156b d e +--R * +--R x +--R + +--R 7 13 14 6 14 13 5 2 15 12 4 3 16 11 +--R 12012a d e - 84084a b d e + 252252a b d e - 420420a b d e +--R + +--R 3 4 17 10 2 5 18 9 6 19 8 7 20 7 +--R 420420a b d e - 252252a b d e + 84084a b d e - 12012b d e +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R e x + 14d e x + 91d e x + 364d e x + 1001d e x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002d e x + 3003d e x + 3432d e x + 3003d e x + 2002d e x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001d e x + 364d e x + 91d e x + 14d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 622 + +)clear all + +--S 623 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^15 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 15 15 14 14 2 13 13 3 12 12 4 11 11 +--R e x + 15d e x + 105d e x + 455d e x + 1365d e x +--R + +--R 5 10 10 6 9 9 7 8 8 8 7 7 9 6 6 +--R 3003d e x + 5005d e x + 6435d e x + 6435d e x + 5005d e x +--R + +--R 10 5 5 11 4 4 12 3 3 13 2 2 14 15 +--R 3003d e x + 1365d e x + 455d e x + 105d e x + 15d e x + d +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1353 +r0:=-5/364*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^12)-_ + 5/1001*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^11)-1/14*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^14)-3/91*b*(a^2+2*a*b*x+_ + 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| 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 21 15 21 20 14 +--R 24024b e x + (24024a e + 336336b d e )x +--R + +--R 20 2 19 13 +--R (336336a d e + 2186184b d e )x +--R + +--R 2 19 3 18 12 +--R (2186184a d e + 8744736b d e )x +--R + +--R 3 18 4 17 11 +--R (8744736a d e + 24048024b d e )x +--R + +--R 4 17 5 16 10 +--R (24048024a d e + 48096048b d e )x +--R + +--R 5 16 6 15 9 +--R (48096048a d e + 72144072b d e )x +--R + +--R 6 15 7 14 8 +--R (72144072a d e + 82450368b d e )x +--R + +--R 7 14 8 13 7 +--R (82450368a d e + 72144072b d e )x +--R + +--R 8 13 9 12 6 +--R (72144072a d e + 48096048b d e )x +--R + +--R 9 12 10 11 5 +--R (48096048a d e + 24048024b d e )x +--R + +--R 10 11 11 10 4 +--R (24048024a d e + 8744736b d e )x +--R + +--R 11 10 12 9 3 12 9 13 8 2 +--R (8744736a d e + 2186184b d e )x + (2186184a d e + 336336b d e )x +--R + +--R 13 8 14 7 14 7 +--R (336336a d e + 24024b d e )x + 24024a d e +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 3003b e x + (- 16016a b e - 2002b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 36036a b e - 8008a b d e - 1001b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 43680a b e - 13104a b d e - 2912a b d e - 364b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 30030a b e - 10920a b d e - 3276a b d e - 728a b d e - 91b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 11088a b e - 4620a b d e - 1680a b d e - 504a b d e +--R + +--R 5 4 2 6 5 +--R - 112a b d e - 14b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 1716a e - 792a b d e - 330a b d e - 120a b d e - 36a b d e +--R + +--R 5 5 6 6 +--R - 8a b d e - b d +--R / +--R 21 14 20 13 2 19 12 3 18 11 +--R 24024e x + 336336d e x + 2186184d e x + 8744736d e x +--R + +--R 4 17 10 5 16 9 6 15 8 7 14 7 +--R 24048024d e x + 48096048d e x + 72144072d e x + 82450368d e x +--R + +--R 8 13 6 9 12 5 10 11 4 11 10 3 +--R 72144072d e x + 48096048d e x + 24048024d e x + 8744736d e x +--R + +--R 12 9 2 13 8 14 7 +--R 2186184d e x + 336336d e x + 24024d e +--R Type: Union(Expression(Integer),...) +--E 625 + +--S 626 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R 3003b e x + (16016a b e + 2002b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (36036a b e + 8008a b d e + 1001b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (43680a b e + 13104a b d e + 2912a b d e + 364b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 30030a b e + 10920a b d e + 3276a b d e + 728a b d e +--R + +--R 6 4 2 +--R 91b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 11088a b e + 4620a b d e + 1680a b d e + 504a b d e +--R + +--R 5 4 2 6 5 +--R 112a b d e + 14b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 1716a e + 792a b d e + 330a b d e + 120a b d e + 36a b d e +--R + +--R 5 5 6 6 +--R 8a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R - 3003b e x + (- 19019a b e - 2002b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 52052a b e - 10010a b d e - 1001b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 79716a b e - 21112a b d e - 3913a b d e - 364b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 73710a b e - 24024a b d e - 6188a b d e - 1092a b d e +--R + +--R 7 4 2 +--R - 91b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 41118a b e - 15540a b d e - 4956a b d e - 1232a b d e +--R + +--R 6 4 2 7 5 +--R - 203a b d e - 14b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 12804a b e - 5412a b d e - 2010a b d e - 624a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 148a b d e - 22a b d e - b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 1716a e - 792a b d e - 330a b d e - 120a b d e - 36a b d e +--R + +--R 2 5 5 6 6 +--R - 8a b d e - a b d +--R / +--R 21 15 21 20 14 +--R 24024b e x + (24024a e + 336336b d e )x +--R + +--R 20 2 19 13 +--R (336336a d e + 2186184b d e )x +--R + +--R 2 19 3 18 12 +--R (2186184a d e + 8744736b d e )x +--R + +--R 3 18 4 17 11 +--R (8744736a d e + 24048024b d e )x +--R + +--R 4 17 5 16 10 +--R (24048024a d e + 48096048b d e )x +--R + +--R 5 16 6 15 9 +--R (48096048a d e + 72144072b d e )x +--R + +--R 6 15 7 14 8 +--R (72144072a d e + 82450368b d e )x +--R + +--R 7 14 8 13 7 +--R (82450368a d e + 72144072b d e )x +--R + +--R 8 13 9 12 6 +--R (72144072a d e + 48096048b d e )x +--R + +--R 9 12 10 11 5 +--R (48096048a d e + 24048024b d e )x +--R + +--R 10 11 11 10 4 +--R (24048024a d e + 8744736b d e )x +--R + +--R 11 10 12 9 3 12 9 13 8 2 +--R (8744736a d e + 2186184b d e )x + (2186184a d e + 336336b d e )x +--R + +--R 13 8 14 7 14 7 +--R (336336a d e + 24024b d e )x + 24024a d e +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 15 15 14 14 2 13 13 3 12 12 4 11 11 +--R e x + 15d e x + 105d e x + 455d e x + 1365d e x +--R + +--R 5 10 10 6 9 9 7 8 8 8 7 7 9 6 6 +--R 3003d e x + 5005d e x + 6435d e x + 6435d e x + 5005d e x +--R + +--R 10 5 5 11 4 4 12 3 3 13 2 2 14 15 +--R 3003d e x + 1365d e x + 455d e x + 105d e x + 15d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^16 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 16 16 15 15 2 14 14 3 13 13 4 12 12 +--R e x + 16d e x + 120d e x + 560d e x + 1820d e x +--R + +--R 5 11 11 6 10 10 7 9 9 8 8 8 9 7 7 +--R 4368d e x + 8008d e x + 11440d e x + 12870d e x + 11440d e x +--R + +--R 10 6 6 11 5 5 12 4 4 13 3 3 14 2 2 +--R 8008d e x + 4368d e x + 1820d e x + 560d e x + 120d e x +--R + +--R 15 16 +--R 16d e x + d +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1353 +r0:=-1/91*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^13)-_ + 1/273*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^12)-1/15*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^15)-1/35*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^14)-1/1001*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^11)-2/9009*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^6*(d+e*x)^10)-1/45045*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x)^10) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 5005b e x + (- 27027a b e - 3003b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 61425a b e - 12285a b d e - 1365b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 75075a b e - 20475a b d e - 4095a b d e - 455b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 51975a b e - 17325a b d e - 4725a b d e - 945a b d e +--R + +--R 6 4 2 +--R - 105b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 19305a b e - 7425a b d e - 2475a b d e - 675a b d e +--R + +--R 5 4 2 6 5 +--R - 135a b d e - 15b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 3003a e - 1287a b d e - 495a b d e - 165a b d e - 45a b d e +--R + +--R 5 5 6 6 +--R - 9a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 22 16 22 21 15 +--R 45045b e x + (45045a e + 675675b d e )x +--R + +--R 21 2 20 14 +--R (675675a d e + 4729725b d e )x +--R + +--R 2 20 3 19 13 +--R (4729725a d e + 20495475b d e )x +--R + +--R 3 19 4 18 12 +--R (20495475a d e + 61486425b d e )x +--R + +--R 4 18 5 17 11 +--R (61486425a d e + 135270135b d e )x +--R + +--R 5 17 6 16 10 +--R (135270135a d e + 225450225b d e )x +--R + +--R 6 16 7 15 9 +--R (225450225a d e + 289864575b d e )x +--R + +--R 7 15 8 14 8 +--R (289864575a d e + 289864575b d e )x +--R + +--R 8 14 9 13 7 +--R (289864575a d e + 225450225b d e )x +--R + +--R 9 13 10 12 6 +--R (225450225a d e + 135270135b d e )x +--R + +--R 10 12 11 11 5 +--R (135270135a d e + 61486425b d e )x +--R + +--R 11 11 12 10 4 +--R (61486425a d e + 20495475b d e )x +--R + +--R 12 10 13 9 3 +--R (20495475a d e + 4729725b d e )x +--R + +--R 13 9 14 8 2 14 8 15 7 +--R (4729725a d e + 675675b d e )x + (675675a d e + 45045b d e )x +--R + +--R 15 7 +--R 45045a d e +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 5005b e x + (- 27027a b e - 3003b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 61425a b e - 12285a b d e - 1365b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 75075a b e - 20475a b d e - 4095a b d e - 455b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 51975a b e - 17325a b d e - 4725a b d e - 945a b d e +--R + +--R 6 4 2 +--R - 105b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 19305a b e - 7425a b d e - 2475a b d e - 675a b d e +--R + +--R 5 4 2 6 5 +--R - 135a b d e - 15b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 3003a e - 1287a b d e - 495a b d e - 165a b d e - 45a b d e +--R + +--R 5 5 6 6 +--R - 9a b d e - b d +--R / +--R 22 15 21 14 2 20 13 3 19 12 +--R 45045e x + 675675d e x + 4729725d e x + 20495475d e x +--R + +--R 4 18 11 5 17 10 6 16 9 +--R 61486425d e x + 135270135d e x + 225450225d e x +--R + +--R 7 15 8 8 14 7 9 13 6 +--R 289864575d e x + 289864575d e x + 225450225d e x +--R + +--R 10 12 5 11 11 4 12 10 3 13 9 2 +--R 135270135d e x + 61486425d e x + 20495475d e x + 4729725d e x +--R + +--R 14 8 15 7 +--R 675675d e x + 45045d e +--R Type: Union(Expression(Integer),...) +--E 630 + +--S 631 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R 5005b e x + (27027a b e + 3003b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (61425a b e + 12285a b d e + 1365b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (75075a b e + 20475a b d e + 4095a b d e + 455b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 51975a b e + 17325a b d e + 4725a b d e + 945a b d e +--R + +--R 6 4 2 +--R 105b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 19305a b e + 7425a b d e + 2475a b d e + 675a b d e +--R + +--R 5 4 2 6 5 +--R 135a b d e + 15b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 3003a e + 1287a b d e + 495a b d e + 165a b d e + 45a b d e +--R + +--R 5 5 6 6 +--R 9a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R - 5005b e x + (- 32032a b e - 3003b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 88452a b e - 15288a b d e - 1365b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 136500a b e - 32760a b d e - 5460a b d e - 455b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 127050a b e - 37800a b d e - 8820a b d e - 1400a b d e +--R + +--R 7 4 2 +--R - 105b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 71280a b e - 24750a b d e - 7200a b d e - 1620a b d e +--R + +--R 6 4 2 7 5 +--R - 240a b d e - 15b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 22308a b e - 8712a b d e - 2970a b d e - 840a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 180a b d e - 24a b d e - b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 3003a e - 1287a b d e - 495a b d e - 165a b d e - 45a b d e +--R + +--R 2 5 5 6 6 +--R - 9a b d e - a b d +--R / +--R 22 16 22 21 15 +--R 45045b e x + (45045a e + 675675b d e )x +--R + +--R 21 2 20 14 +--R (675675a d e + 4729725b d e )x +--R + +--R 2 20 3 19 13 +--R (4729725a d e + 20495475b d e )x +--R + +--R 3 19 4 18 12 +--R (20495475a d e + 61486425b d e )x +--R + +--R 4 18 5 17 11 +--R (61486425a d e + 135270135b d e )x +--R + +--R 5 17 6 16 10 +--R (135270135a d e + 225450225b d e )x +--R + +--R 6 16 7 15 9 +--R (225450225a d e + 289864575b d e )x +--R + +--R 7 15 8 14 8 +--R (289864575a d e + 289864575b d e )x +--R + +--R 8 14 9 13 7 +--R (289864575a d e + 225450225b d e )x +--R + +--R 9 13 10 12 6 +--R (225450225a d e + 135270135b d e )x +--R + +--R 10 12 11 11 5 +--R (135270135a d e + 61486425b d e )x +--R + +--R 11 11 12 10 4 +--R (61486425a d e + 20495475b d e )x +--R + +--R 12 10 13 9 3 +--R (20495475a d e + 4729725b d e )x +--R + +--R 13 9 14 8 2 14 8 15 7 +--R (4729725a d e + 675675b d e )x + (675675a d e + 45045b d e )x +--R + +--R 15 7 +--R 45045a d e +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 16 16 15 15 2 14 14 3 13 13 4 12 12 +--R e x + 16d e x + 120d e x + 560d e x + 1820d e x +--R + +--R 5 11 11 6 10 10 7 9 9 8 8 8 9 7 7 +--R 4368d e x + 8008d e x + 11440d e x + 12870d e x + 11440d e x +--R + +--R 10 6 6 11 5 5 12 4 4 13 3 3 14 2 2 +--R 8008d e x + 4368d e x + 1820d e x + 560d e x + 120d e x +--R + +--R 15 16 +--R 16d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 632 + +)clear all + +--S 633 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^17 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 17 17 16 16 2 15 15 3 14 14 4 13 13 +--R e x + 17d e x + 136d e x + 680d e x + 2380d e x +--R + +--R 5 12 12 6 11 11 7 10 10 8 9 9 9 8 8 +--R 6188d e x + 12376d e x + 19448d e x + 24310d e x + 24310d e x +--R + +--R 10 7 7 11 6 6 12 5 5 13 4 4 14 3 3 +--R 19448d e x + 12376d e x + 6188d e x + 2380d e x + 680d e x +--R + +--R 15 2 2 16 17 +--R 136d e x + 17d e x + d +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1353 +r0:=-1/112*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^14)-_ + 1/364*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^13)-1/16*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^16)-1/40*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^15)-1/1456*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^12)-1/7280*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^6*(d+e*x)^11)-1/80080*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x)^11) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 8008b e x + (- 43680a b e - 4368b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 100100a b e - 18200a b d e - 1820b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 123200a b e - 30800a b d e - 5600a b d e - 560b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 85800a b e - 26400a b d e - 6600a b d e - 1200a b d e +--R + +--R 6 4 2 +--R - 120b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 32032a b e - 11440a b d e - 3520a b d e - 880a b d e +--R + +--R 5 4 2 6 5 +--R - 160a b d e - 16b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 5005a e - 2002a b d e - 715a b d e - 220a b d e - 55a b d e +--R + +--R 5 5 6 6 +--R - 10a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 23 17 23 22 16 +--R 80080b e x + (80080a e + 1281280b d e )x +--R + +--R 22 2 21 15 +--R (1281280a d e + 9609600b d e )x +--R + +--R 2 21 3 20 14 +--R (9609600a d e + 44844800b d e )x +--R + +--R 3 20 4 19 13 +--R (44844800a d e + 145745600b d e )x +--R + +--R 4 19 5 18 12 +--R (145745600a d e + 349789440b d e )x +--R + +--R 5 18 6 17 11 +--R (349789440a d e + 641280640b d e )x +--R + +--R 6 17 7 16 10 +--R (641280640a d e + 916115200b d e )x +--R + +--R 7 16 8 15 9 +--R (916115200a d e + 1030629600b d e )x +--R + +--R 8 15 9 14 8 +--R (1030629600a d e + 916115200b d e )x +--R + +--R 9 14 10 13 7 +--R (916115200a d e + 641280640b d e )x +--R + +--R 10 13 11 12 6 +--R (641280640a d e + 349789440b d e )x +--R + +--R 11 12 12 11 5 +--R (349789440a d e + 145745600b d e )x +--R + +--R 12 11 13 10 4 +--R (145745600a d e + 44844800b d e )x +--R + +--R 13 10 14 9 3 +--R (44844800a d e + 9609600b d e )x +--R + +--R 14 9 15 8 2 15 8 16 7 +--R (9609600a d e + 1281280b d e )x + (1281280a d e + 80080b d e )x +--R + +--R 16 7 +--R 80080a d e +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 8008b e x + (- 43680a b e - 4368b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 100100a b e - 18200a b d e - 1820b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 123200a b e - 30800a b d e - 5600a b d e - 560b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 85800a b e - 26400a b d e - 6600a b d e - 1200a b d e +--R + +--R 6 4 2 +--R - 120b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 32032a b e - 11440a b d e - 3520a b d e - 880a b d e +--R + +--R 5 4 2 6 5 +--R - 160a b d e - 16b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 5005a e - 2002a b d e - 715a b d e - 220a b d e - 55a b d e +--R + +--R 5 5 6 6 +--R - 10a b d e - b d +--R / +--R 23 16 22 15 2 21 14 3 20 13 +--R 80080e x + 1281280d e x + 9609600d e x + 44844800d e x +--R + +--R 4 19 12 5 18 11 6 17 10 +--R 145745600d e x + 349789440d e x + 641280640d e x +--R + +--R 7 16 9 8 15 8 9 14 7 +--R 916115200d e x + 1030629600d e x + 916115200d e x +--R + +--R 10 13 6 11 12 5 12 11 4 +--R 641280640d e x + 349789440d e x + 145745600d e x +--R + +--R 13 10 3 14 9 2 15 8 16 7 +--R 44844800d e x + 9609600d e x + 1281280d e x + 80080d e +--R Type: Union(Expression(Integer),...) +--E 635 + +--S 636 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R 8008b e x + (43680a b e + 4368b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (100100a b e + 18200a b d e + 1820b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (123200a b e + 30800a b d e + 5600a b d e + 560b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 85800a b e + 26400a b d e + 6600a b d e + 1200a b d e +--R + +--R 6 4 2 +--R 120b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 32032a b e + 11440a b d e + 3520a b d e + 880a b d e +--R + +--R 5 4 2 6 5 +--R 160a b d e + 16b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 5005a e + 2002a b d e + 715a b d e + 220a b d e + 55a b d e +--R + +--R 5 5 6 6 +--R 10a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R - 8008b e x + (- 51688a b e - 4368b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 143780a b e - 22568a b d e - 1820b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 223300a b e - 49000a b d e - 7420a b d e - 560b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 209000a b e - 57200a b d e - 12200a b d e - 1760a b d e +--R + +--R 7 4 2 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 117832a b e - 37840a b d e - 10120a b d e - 2080a b d e +--R + +--R 6 4 2 7 5 +--R - 280a b d e - 16b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 37037a b e - 13442a b d e - 4235a b d e - 1100a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 215a b d e - 26a b d e - b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 5005a e - 2002a b d e - 715a b d e - 220a b d e - 55a b d e +--R + +--R 2 5 5 6 6 +--R - 10a b d e - a b d +--R / +--R 23 17 23 22 16 +--R 80080b e x + (80080a e + 1281280b d e )x +--R + +--R 22 2 21 15 +--R (1281280a d e + 9609600b d e )x +--R + +--R 2 21 3 20 14 +--R (9609600a d e + 44844800b d e )x +--R + +--R 3 20 4 19 13 +--R (44844800a d e + 145745600b d e )x +--R + +--R 4 19 5 18 12 +--R (145745600a d e + 349789440b d e )x +--R + +--R 5 18 6 17 11 +--R (349789440a d e + 641280640b d e )x +--R + +--R 6 17 7 16 10 +--R (641280640a d e + 916115200b d e )x +--R + +--R 7 16 8 15 9 +--R (916115200a d e + 1030629600b d e )x +--R + +--R 8 15 9 14 8 +--R (1030629600a d e + 916115200b d e )x +--R + +--R 9 14 10 13 7 +--R (916115200a d e + 641280640b d e )x +--R + +--R 10 13 11 12 6 +--R (641280640a d e + 349789440b d e )x +--R + +--R 11 12 12 11 5 +--R (349789440a d e + 145745600b d e )x +--R + +--R 12 11 13 10 4 +--R (145745600a d e + 44844800b d e )x +--R + +--R 13 10 14 9 3 +--R (44844800a d e + 9609600b d e )x +--R + +--R 14 9 15 8 2 15 8 16 7 +--R (9609600a d e + 1281280b d e )x + (1281280a d e + 80080b d e )x +--R + +--R 16 7 +--R 80080a d e +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 17 17 16 16 2 15 15 3 14 14 4 13 13 +--R e x + 17d e x + 136d e x + 680d e x + 2380d e x +--R + +--R 5 12 12 6 11 11 7 10 10 8 9 9 +--R 6188d e x + 12376d e x + 19448d e x + 24310d e x +--R + +--R 9 8 8 10 7 7 11 6 6 12 5 5 13 4 4 +--R 24310d e x + 19448d e x + 12376d e x + 6188d e x + 2380d e x +--R + +--R 14 3 3 15 2 2 16 17 +--R 680d e x + 136d e x + 17d e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 637 + +)clear all + +--S 638 of 1353 +t0:=(a+b*x)*(d+e*x)^m/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R m +--R (b x + a)(e x + d) +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1353 +r0:=(a+b*x)*(d+e*x)^(1+m)/(e*(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R m + 1 +--R (b x + a)(e x + d) +--R (2) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e m + e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1353 +a0:=integrate(t0,x) +--R +--R +--R m log(e x + d) +--R (e x + d)%e +--R (3) ------------------------- +--R e m + e +--R Type: Union(Expression(Integer),...) +--E 640 + +--S 641 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R | 2 2 2 m log(e x + d) m + 1 +--R (e x + d)\|b x + 2a b x + a %e + (- b x - a)(e x + d) +--R -------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (e m + e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 m log(e x + d) +--R (\|b x + 2a b x + a - b x - a)%e +--R (5) ------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 1353 +t0:=(a+b*x)*(d+e*x)^4/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1353 +r0:=1/5*(a+b*x)*(d+e*x)^5/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 6 5 4 5 4 2 3 4 +--R b e x + (a e + 5b d e )x + (5a d e + 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a d e + 10b d e )x + (10a d e + 5b d e)x + (5a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 4 5 3 4 2 2 3 3 2 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d x +--R (3) ------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 645 + +--S 646 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x)\|b x + 2a b x + a +--R + +--R 5 6 5 4 5 4 2 3 4 +--R - b e x + (- a e - 5b d e )x + (- 5a d e - 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (- 10a d e - 10b d e )x + (- 10a d e - 5b d e)x + (- 5a d e - b d )x +--R + +--R 5 +--R - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 647 + +)clear all + +--S 648 of 1353 +t0:=(a+b*x)*(d+e*x)^3/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1353 +r0:=1/4*(a+b*x)*(d+e*x)^4/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 4e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 3 4 2 3 2 2 3 +--R e x + 4d e x + 6d e x + 4d x +--R (3) ------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 650 + +--S 651 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x)\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 4e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 652 + +)clear all + +--S 653 of 1353 +t0:=(a+b*x)*(d+e*x)^2/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R b e x + (a e + 2b d e)x + (2a d e + b d )x + a d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1353 +r0:=1/3*(a+b*x)*(d+e*x)^3/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 +--R e x + 3d e x + 3d x +--R (3) --------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 655 + +--S 656 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 3 3 2 2 2 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x)\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1353 +t0:=(a+b*x)*(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R b e x + (a e + b d)x + a d +--R (1) --------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1353 +r0:=d*x*(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2)+1/2*e*x^2*(a+b*x)/_ + sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 2 +--R b e x + (a e + 2b d)x + 2a d x +--R (2) -------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 2\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R e x + 2d x +--R (3) ----------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 660 + +--S 661 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 | 2 2 2 3 2 +--R (e x + 2d x)\|b x + 2a b x + a - b e x + (- a e - 2b d)x - 2a d x +--R ----------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 2\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 662 + +)clear all + +--S 663 of 1353 +t0:=(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R b x + a +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1353 +r0:=sqrt(a^2+2*a*b*x+b^2*x^2)/b +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (2) --------------------- +--R b +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) x +--R Type: Union(Expression(Integer),...) +--E 665 + +--S 666 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x +--R (4) ----------------------------- +--R b +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 667 + +)clear all + +--S 668 of 1353 +t0:=(a+b*x)/((d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1353 +r0:=(a+b*x)*log(d+e*x)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b x + a)log(e x + d) +--R (2) ---------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1353 +a0:=integrate(t0,x) +--R +--R +--R log(e x + d) +--R (3) ------------ +--R e +--R Type: Union(Expression(Integer),...) +--E 670 + +--S 671 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R log(e x + d)\|b x + 2a b x + a + (- b x - a)log(e x + d) +--R (4) ----------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 1353 +t0:=(a+b*x)/((d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1353 +r0:=(-a-b*x)/(e*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) -------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (e x + d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------- +--R 2 +--R e x + d e +--R Type: Union(Expression(Integer),...) +--E 675 + +--S 676 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) --------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (e x + d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 677 + +)clear all + +--S 678 of 1353 +t0:=(a+b*x)/((d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1353 +r0:=1/2*(-a-b*x)/(e*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) -------------------------------------------- +--R +------------------+ +--R 3 2 2 2 | 2 2 2 +--R (2e x + 4d e x + 2d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------------------- +--R 3 2 2 2 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 680 + +--S 681 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) -------------------------------------------- +--R +------------------+ +--R 3 2 2 2 | 2 2 2 +--R (2e x + 4d e x + 2d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 682 + +)clear all + +--S 683 of 1353 +t0:=(a+b*x)/((d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1353 +r0:=1/3*(-a-b*x)/(e*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) ------------------------------------------------------ +--R +------------------+ +--R 4 3 3 2 2 2 3 | 2 2 2 +--R (3e x + 9d e x + 9d e x + 3d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------------------------- +--R 4 3 3 2 2 2 3 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 685 + +--S 686 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) ------------------------------------------------------ +--R +------------------+ +--R 4 3 3 2 2 2 3 | 2 2 2 +--R (3e x + 9d e x + 9d e x + 3d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 1353 +t0:=(a+b*x)/((d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R b x + a +--R ------------------------------------------------------------------------- +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1353 +r0:=1/4*(-a-b*x)/(e*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R 5 4 4 3 2 3 2 3 2 4 | 2 2 2 +--R (4e x + 16d e x + 24d e x + 16d e x + 4d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - -------------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R 4e x + 16d e x + 24d e x + 16d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 690 + +--S 691 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) ------------------------------------------------------------------- +--R +------------------+ +--R 5 4 4 3 2 3 2 3 2 4 | 2 2 2 +--R (4e x + 16d e x + 24d e x + 16d e x + 4d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R ------------------------------------------------------------------------- +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 692 + +)clear all + +--S 693 of 1353 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1353 +r0:=2*e*(b*d-a*e)*(a+b*x)*(d+e*x)^2/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 4/3*e*(a+b*x)*(d+e*x)^3/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^4/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+4*e*(b*d-a*e)^3*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^2*(b*d-a*e)^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 12a b e + 36a b d e - 36a b d e + 12b d e)x - 12a e +--R + +--R 3 3 2 2 2 2 3 3 +--R 36a b d e - 36a b d e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (- 2a b e + 6b d e )x + (6a b e - 18a b d e + 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (24a b e - 60a b d e + 42a b d e - 2b d e)x + 12a e - 24a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 6a b d e + 10a b d e - 3b d +--R / +--R +------------------+ +--R 5 | 2 2 2 +--R 3b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 12a b e + 36a b d e - 36a b d e + 12b d e)x - 12a e +--R + +--R 3 3 2 2 2 2 3 3 +--R 36a b d e - 36a b d e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (- 2a b e + 6b d e )x + (6a b e - 18a b d e + 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 2 2 2 2 +--R (9a b e - 24a b d e + 18a b d e )x - 3a e + 12a b d e - 18a b d e +--R + +--R 3 3 4 4 +--R 12a b d e - 3b d +--R / +--R 6 5 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 695 + +--S 696 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 12a b e + 36a b d e - 36a b d e + 12b d e)x - 12a e +--R + +--R 3 3 2 2 2 2 3 3 +--R 36a b d e - 36a b d e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 +--R b e x + (- 2a b e + 6b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (6a b e - 18a b d e + 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (9a b e - 24a b d e + 18a b d e )x - 3a e + 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 18a b d e + 12a b d e - 3b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (12a b e - 36a b d e + 36a b d e - 12b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (24a b e - 72a b d e + 72a b d e - 24a b d e)x + 12a e +--R + +--R 4 3 3 2 2 2 2 3 3 +--R - 36a b d e + 36a b d e - 12a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R - b e x + (a b e - 6b d e )x + (- 4a b e + 12a b d e - 18b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 30a b e + 78a b d e - 60a b d e + 2b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 36a b e + 84a b d e - 48a b d e - 8a b d e + 3b d )x - 12a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R 24a b d e - 6a b d e - 10a b d e + 3a b d +--R / +--R +------------------+ +--R 6 5 | 2 2 2 +--R (3b x + 3a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 697 + +)clear all + +--S 698 of 1353 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1353 +r0:=3/2*e*(a+b*x)*(d+e*x)^2/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-(d+e*x)^3/_ + (b*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/_ + (b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b e - 12a b d e + 6b d e)x + 6a e - 12a b d e + 6a b d e) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R b e x + (- 3a b e + 6b d e )x + (- 12a b e + 18a b d e - 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 6a e + 6a b d e + 3a b d e - 2b d +--R / +--R +------------------+ +--R 4 | 2 2 2 +--R 2b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b e - 12a b d e + 6b d e)x + 6a e - 12a b d e + 6a b d e) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 3 +--R b e x + (- 3a b e + 6b d e )x + (- 4a b e + 6a b d e )x + 2a e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e + 6a b d e - 2b d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 700 + +--S 701 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b e - 12a b d e + 6b d e)x + 6a e - 12a b d e + 6a b d e) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 3 +--R b e x + (- 3a b e + 6b d e )x + (- 4a b e + 6a b d e )x + 2a e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e + 6a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 6a b e + 12a b d e - 6b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (- 12a b e + 24a b d e - 12a b d e)x - 6a e + 12a b d e - 6a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R - b e x + (2a b e - 6b d e )x + (15a b e - 24a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 4 3 4 3 3 2 2 2 2 3 3 +--R (18a b e - 24a b d e + 2b d )x + 6a e - 6a b d e - 3a b d e + 2a b d +--R / +--R +------------------+ +--R 5 4 | 2 2 2 +--R (2b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 1353 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1353 +r0:=-(d+e*x)^2/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)*(a+b*x)*_ + log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((- 2a b e + 2b d e)x - 2a e + 2a b d e)log(b x + a) + b e x +--R + +--R 2 2 2 2 2 2 +--R (4a b e - 2b d e)x + 2a e - b d +--R / +--R +------------------+ +--R 3 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 +--R ((- 2a b e + 2b d e)x - 2a e + 2a b d e)log(b x + a) + b e x + a b e x +--R + +--R 2 2 2 2 +--R - a e + 2a b d e - b d +--R / +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 705 + +--S 706 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 +--R ((- 2a b e + 2b d e)x - 2a e + 2a b d e)log(b x + a) + b e x +--R + +--R 2 2 2 2 2 +--R a b e x - a e + 2a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 3 2 2 +--R ((2a b e - 2b d e)x + (4a b e - 4a b d e)x + 2a e - 2a b d e) +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - b e x + (- 5a b e + 2b d e)x + (- 6a b e + 2a b d e + b d )x +--R + +--R 3 2 2 2 +--R - 2a e + a b d +--R / +--R +------------------+ +--R 4 3 | 2 2 2 +--R (b x + a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 707 + +)clear all + +--S 708 of 1353 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1353 +r0:=(-d-e*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(a+b*x)*log(a+b*x)/_ + (b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b e x + a e)log(b x + a) - b e x - b d +--R (2) --------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (b e x + a e)log(b x + a) + a e - b d +--R (3) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 710 + +--S 711 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R | 2 2 2 +--R ((b e x + a e)log(b x + a) + a e - b d)\|b x + 2a b x + a +--R + +--R 2 2 2 2 2 2 +--R (- b e x - 2a b e x - a e)log(b x + a) + b e x + (a b e + b d)x + a b d +--R / +--R +------------------+ +--R 3 2 | 2 2 2 +--R (b x + a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 712 + +)clear all + +--S 713 of 1353 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1353 +r0:=(-1)/(b*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (2) - ---------------------- +--R +------------------+ +--R | 2 2 2 +--R b\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------- +--R 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 715 + +--S 716 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) --------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (b x + a b)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 1353 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1353 +r0:=(-1)/((b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(a+b*x)*log(a+b*x)/_ + ((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(a+b*x)*log(d+e*x)/_ + ((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b e x + a e)log(e x + d) + (- b e x - a e)log(b x + a) + a e - b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R (a e - 2a b d e + b d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (b e x + a e)log(e x + d) + (- b e x - a e)log(b x + a) + a e - b d +--R (3) ------------------------------------------------------------------- +--R 2 2 2 3 2 3 2 2 2 2 +--R (a b e - 2a b d e + b d )x + a e - 2a b d e + a b d +--R Type: Union(Expression(Integer),...) +--E 720 + +--S 721 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R ((b e x + a e)log(e x + d) + (- b e x - a e)log(b x + a) + a e - b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 2 +--R (- b e x - 2a b e x - a e)log(e x + d) +--R + +--R 2 2 2 2 2 +--R (b e x + 2a b e x + a e)log(b x + a) + (- a b e + b d)x - a e + a b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 722 + +)clear all + +--S 723 of 1353 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1353 +r0:=-2*b/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/((b*d-a*e)*(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-2*b*e*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+2*b*e*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (- 2b e x + (- 2a b e - 2b d e)x - 2a b d e)log(e x + d) +--R + +--R 2 2 2 2 2 +--R (2b e x + (2a b e + 2b d e)x + 2a b d e)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b e + 2b d e)x - a e + b d +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 2 3 +--R (a e - 3a b d e + 3a b d e - b d e)x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (- 2b e x + (- 2a b e - 2b d e)x - 2a b d e)log(e x + d) +--R + +--R 2 2 2 2 2 +--R (2b e x + (2a b e + 2b d e)x + 2a b d e)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b e + 2b d e)x - a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Union(Expression(Integer),...) +--E 725 + +--S 726 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 +--R (- 2b e x + (- 2a b e - 2b d e)x - 2a b d e)log(e x + d) +--R + +--R 2 2 2 2 2 +--R (2b e x + (2a b e + 2b d e)x + 2a b d e)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b e + 2b d e)x - a e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 2 +--R (2b e x + (4a b e + 2b d e)x + (2a b e + 4a b d e)x + 2a b d e) +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 +--R - 2b e x + (- 4a b e - 2b d e)x + (- 2a b e - 4a b d e)x +--R + +--R 2 +--R - 2a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 2 2 2 3 2 3 2 2 2 +--R (2a b e - 2b d e)x + (3a b e - 2a b d e - b d )x + a e - a b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 727 + +)clear all + +--S 728 of 1353 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1353 +r0:=-3*b^2/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2/((b*d-a*e)*(d+e*x)^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+3/2*b/((b*d-a*e)^2*(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-3*b^2*e*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*b^2*e*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 2 2 2 +--R (6b e x + (6a b e + 12b d e )x + (12a b d e + 6b d e)x + 6a b d e) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b e x + (- 6a b e - 12b d e )x + (- 12a b d e - 6b d e)x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (3a b e + 6a b d e - 9b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 3a b d e - 2b d +--R / +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (2a e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4 2 4 +--R (4a d e - 16a b d e + 24a b d e - 16a b d e + 4b d e)x + 2a d e +--R + +--R 3 3 3 2 2 4 2 3 5 4 6 +--R - 8a b d e + 12a b d e - 8a b d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 2 3 2 2 2 +--R (6b e x + (6a b e + 12b d e )x + (12a b d e + 6b d e)x + 6a b d e) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b e x + (- 6a b e - 12b d e )x + (- 12a b d e - 6b d e)x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (3a b e + 6a b d e - 9b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 3a b d e - 2b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 730 + +--S 731 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R 6b e x + (6a b e + 12b d e )x + (12a b d e + 6b d e)x +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b e x + (- 6a b e - 12b d e )x + (- 12a b d e - 6b d e)x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (3a b e + 6a b d e - 9b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 3a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 6b e x + (- 12a b e - 12b d e )x +--R + +--R 2 2 3 3 2 4 2 2 2 2 2 3 2 +--R (- 6a b e - 24a b d e - 6b d e)x + (- 12a b d e - 12a b d e)x +--R + +--R 2 2 2 +--R - 6a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R 6b e x + (12a b e + 12b d e )x + (6a b e + 24a b d e + 6b d e)x +--R + +--R 2 2 2 3 2 2 2 2 +--R (12a b d e + 12a b d e)x + 6a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 4 2 3 2 2 3 4 2 2 +--R (- 6a b e + 6b d e )x + (- 9a b e + 9b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (- 2a b e - 12a b d e + 12a b d e + 2b d )x + a e - 6a b d e +--R + +--R 2 2 2 3 3 +--R 3a b d e + 2a b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 732 + +)clear all + +--S 733 of 1353 +t0:=(a+b*x)*(d+e*x)^5/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1353 +r0:=-5/6*e*(a+b*x)*(d+e*x)^4/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^5/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5*e^3*(a+b*x)*_ + (d+e*x)^2/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-10/3*e^2*(d+e*x)^3/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10*e^3*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10*e^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6 +--R +--R +--R (2) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (180a b e - 360a b d e + 180a b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 5 5 4 4 +--R (180a b e - 360a b d e + 180a b d e )x + 60a e - 120a b d e +--R + +--R 3 2 2 3 +--R 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 5 5 4 5 5 4 4 +--R 3b e x + (- 15a b e + 30b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 170a b e + 280a b d e - 80b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 330a b e + 480a b d e - 60a b d e - 60b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 240a b e + 300a b d e + 30a b d e - 60a b d e - 15b d e)x - 60a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e + 30a b d e - 20a b d e - 5a b d e - 2b d +--R / +--R +------------------+ +--R 8 2 7 2 6 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (180a b e - 360a b d e + 180a b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 5 5 4 4 +--R (180a b e - 360a b d e + 180a b d e )x + 60a e - 120a b d e +--R + +--R 3 2 2 3 +--R 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 3 +--R 3b e x + (- 15a b e + 30b d e )x + (- 63a b e + 90a b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 9a b e - 90a b d e + 180a b d e - 60b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (81a b e - 270a b d e + 270a b d e - 60a b d e - 15b d e)x + 47a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 130a b d e + 110a b d e - 20a b d e - 5a b d e - 2b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 735 + +--S 736 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (180a b e - 360a b d e + 180a b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 5 5 4 4 +--R (180a b e - 360a b d e + 180a b d e )x + 60a e - 120a b d e +--R + +--R 3 2 2 3 +--R 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 3 +--R 3b e x + (- 15a b e + 30b d e )x + (- 63a b e + 90a b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 9a b e - 90a b d e + 180a b d e - 60b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (81a b e - 270a b d e + 270a b d e - 60a b d e - 15b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 47a e - 130a b d e + 110a b d e - 20a b d e - 5a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (- 60a b e + 120a b d e - 60b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 3 +--R (- 240a b e + 480a b d e - 240a b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 2 +--R (- 360a b e + 720a b d e - 360a b d e )x +--R + +--R 5 5 4 2 4 3 3 2 3 6 5 5 4 +--R (- 240a b e + 480a b d e - 240a b d e )x - 60a e + 120a b d e +--R + +--R 4 2 2 3 +--R - 60a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 5 5 6 4 5 +--R - 3b e x + (12a b e - 30b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (185a b e - 310a b d e + 80b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 3 +--R (500a b e - 760a b d e + 140a b d e + 60b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 2 +--R (570a b e - 780a b d e + 30a b d e + 120a b d e + 15b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 +--R (300a b e - 360a b d e - 60a b d e + 80a b d e + 20a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R 60a e - 60a b d e - 30a b d e + 20a b d e + 5a b d e + 2a b d +--R / +--R +------------------+ +--R 9 3 8 2 2 7 3 6 | 2 2 2 +--R (6b x + 18a b x + 18a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R + +--R 5 6 5 4 5 4 2 3 4 +--R - b e x + (- a e - 5b d e )x + (- 5a d e - 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 +--R (- 10a d e - 10b d e )x + (- 10a d e - 5b d e)x + (- 5a d e - b d )x +--R + +--R 5 +--R - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 737 + +)clear all + +--S 738 of 1353 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1353 +r0:=-2/3*e*(a+b*x)*(d+e*x)^3/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^4/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-2*e^2*(d+e*x)^2/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^3*(b*d-a*e)*(a+b*x)*log(a+b*x)/(b^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 4 4 3 3 2 2 4 3 3 2 +--R (- 12a b e + 12b d e )x + (- 36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 4 4 3 3 +--R (- 36a b e + 36a b d e )x - 12a e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (34a b e - 22b d e )x + (66a b e - 30a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 2 2 2 2 +--R (48a b e - 12a b d e - 18a b d e - 6b d e)x + 12a e - 6a b d e +--R + +--R 3 3 4 4 +--R - 2a b d e - b d +--R / +--R +------------------+ +--R 7 2 6 2 5 | 2 2 2 +--R (3b x + 6a b x + 3a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 3 2 2 4 3 3 2 +--R (- 12a b e + 12b d e )x + (- 36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 4 4 3 3 +--R (- 36a b e + 36a b d e )x - 12a e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + 9a b e x + (- 9a b e + 36a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 27a b e + 54a b d e - 18a b d e - 6b d e)x - 13a e + 22a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 2a b d e - b d +--R / +--R 8 3 7 2 2 6 3 5 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 740 + +--S 741 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 4 3 3 2 2 4 3 3 2 +--R (- 12a b e + 12b d e )x + (- 36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 4 4 3 3 +--R (- 36a b e + 36a b d e )x - 12a e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + 9a b e x + (- 9a b e + 36a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 27a b e + 54a b d e - 18a b d e - 6b d e)x - 13a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 22a b d e - 6a b d e - 2a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12a b e - 12b d e )x + (48a b e - 48a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 5 4 +--R (72a b e - 72a b d e )x + (48a b e - 48a b d e )x + 12a e +--R + +--R 4 3 +--R - 12a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 4 4 5 3 4 +--R - 3b e x + (- 37a b e + 22b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 100a b e + 52a b d e + 18b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 114a b e + 42a b d e + 36a b d e + 6b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 60a b e + 12a b d e + 24a b d e + 8a b d e + b d )x - 12a e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R 6a b d e + 2a b d e + a b d +--R / +--R +------------------+ +--R 8 3 7 2 2 6 3 5 | 2 2 2 +--R (3b x + 9a b x + 9a b x + 3a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 742 + +)clear all + +--S 743 of 1353 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1353 +r0:=-1/2*e*(a+b*x)*(d+e*x)^2/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^3/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2*(d+e*x)/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(b x + a) - 11b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (- 15a b e - 18b d e )x + (- 6a b e - 18a b d e - 9b d e)x +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e - 3a b d e - 2b d +--R / +--R +------------------+ +--R 6 2 5 2 4 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (18a b e - 18b d e )x + (27a b e - 18a b d e - 9b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e - 3a b d e - 2b d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 745 + +--S 746 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (18a b e - 18b d e )x + (27a b e - 18a b d e - 9b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e - 3a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (- 6b e x - 24a b e x - 36a b e x - 24a b e x - 6a e )log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R 11b e x + (26a b e + 18b d e )x + (21a b e + 36a b d e + 9b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (6a b e + 24a b d e + 12a b d e + 2b d )x + 6a b d e + 3a b d e +--R + +--R 3 3 +--R 2a b d +--R / +--R +------------------+ +--R 7 3 6 2 2 5 3 4 | 2 2 2 +--R (6b x + 18a b x + 18a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 747 + +)clear all + +--S 748 of 1353 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1353 +r0:=-1/3*(d+e*x)^3/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R ----------------------------------------------------------------------------- +--R +------------------+ +--R 2 3 2 2 2 3 2 | 2 2 2 +--R ((3a b e - 3b d)x + (6a b e - 6a b d)x + 3a e - 3a b d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 3b e x + (- 3a b e - 3b d e)x - a e - a b d e - b d +--R (3) --------------------------------------------------------- +--R 6 3 5 2 2 4 3 3 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 750 + +--S 751 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 3 3 2 3 3 3 3 +--R ((- 3a b e + 3b d e )x + (- 3a b e + 3b d e)x - a e + b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 3 2 4 2 2 +--R - b e x + (- a b e - 3b d e )x + (- 3a b d e - 3b d e)x +--R + +--R 3 2 4 3 3 3 +--R (- 3a b d e - b d )x - a b d +--R / +--R 6 7 3 2 5 6 2 3 4 2 5 4 3 +--R (3a b e - 3b d)x + (9a b e - 9a b d)x + (9a b e - 9a b d)x + 3a b e +--R + +--R 3 4 +--R - 3a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 752 + +)clear all + +--S 753 of 1353 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1353 +r0:=-1/6*e*(a+b*x)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/3*(-d-e*x)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R - 3b e x - a e - 2b d +--R (2) ---------------------------------------------- +--R +------------------+ +--R 4 2 3 2 2 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1353 +a0:=integrate(t0,x) +--R +--R +--R - 3b e x - a e - 2b d +--R (3) ---------------------------------- +--R 5 3 4 2 2 3 3 2 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 755 + +--S 756 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R | 2 2 2 2 2 2 +--R (- 3b e x - a e - 2b d)\|b x + 2a b x + a + 3b e x + (4a b e + 2b d)x +--R + +--R 2 +--R a e + 2a b d +--R / +--R +------------------+ +--R 5 3 4 2 2 3 3 2 | 2 2 2 +--R (6b x + 18a b x + 18a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 757 + +)clear all + +--S 758 of 1353 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 1 +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1353 +r0:=(-1/3)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (2) - -------------------------------------------- +--R +------------------+ +--R 3 2 2 2 | 2 2 2 +--R (3b x + 6a b x + 3a b)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------------------------- +--R 4 3 3 2 2 2 3 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 760 + +--S 761 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - \|b x + 2a b x + a + b x + a +--R (4) ------------------------------------------------------ +--R +------------------+ +--R 4 3 3 2 2 2 3 | 2 2 2 +--R (3b x + 9a b x + 9a b x + 3a b)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 762 + +)clear all + +--S 763 of 1353 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1353 +r0:=(-1/3)/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*e*(a+b*x)/_ + ((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(e x + d) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (- 6b e x - 18a b e x - 18a b e x - 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (15a b e - 18a b d e + 3b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 18a b d e + 9a b d e - 2b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 6 4 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12a b d )x + 6a e +--R + +--R 5 3 4 2 2 2 3 3 3 2 4 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(e x + d) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (- 6b e x - 18a b e x - 18a b e x - 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (15a b e - 18a b d e + 3b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 18a b d e + 9a b d e - 2b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 7 4 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x + 6a e +--R + +--R 6 3 5 2 2 2 4 3 3 3 4 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R Type: Union(Expression(Integer),...) +--E 765 + +--S 766 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(e x + d) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (- 6b e x - 18a b e x - 18a b e x - 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (15a b e - 18a b d e + 3b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 18a b d e + 9a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (- 6b e x - 24a b e x - 36a b e x - 24a b e x - 6a e )log(e x + d) +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (6b e x + 24a b e x + 36a b e x + 24a b e x + 6a e )log(b x + a) +--R + +--R 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R (- 6a b e + 6b d e )x + (- 21a b e + 24a b d e - 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (- 26a b e + 36a b d e - 12a b d e + 2b d )x - 11a e + 18a b d e +--R + +--R 2 2 2 3 3 +--R - 9a b d e + 2a b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 7 4 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x + 6a e +--R + +--R 6 3 5 2 2 2 4 3 3 3 4 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 767 + +)clear all + +--S 768 of 1353 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1353 +r0:=-4/3*b/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+2*b*e*(a+b*x)/_ + ((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/((b*d-a*e)*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-4*b*e^2/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-4*b*e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+4*b*e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R - 12b e x + (- 36a b e - 12b d e )x + (- 36a b e - 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (- 12a b e - 36a b d e )x - 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 12b e x + (36a b e + 12b d e )x + (36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (12a b e + 36a b d e )x + 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (- 12a b e + 12b d e )x + (- 30a b e + 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 22a b e + 6a b d e + 18a b d e - 2b d e)x - 3a e - 10a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 6a b d e + b d +--R / +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 3a b e - 15a b d e + 30a b d e - 30a b d e + 15a b d e +--R + +--R 7 5 +--R - 3b d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 6 5 7 6 2 +--R (6a b e - 27a b d e + 45a b d e - 30a b d e + 9a b d e - 3b d )x +--R + +--R 7 6 6 5 4 3 3 3 3 4 4 2 2 5 5 6 6 +--R (3a e - 9a b d e + 30a b d e - 45a b d e + 27a b d e - 6a b d )x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 2 5 6 +--R 3a d e - 15a b d e + 30a b d e - 30a b d e + 15a b d e - 3a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R - 12b e x + (- 36a b e - 12b d e )x + (- 36a b e - 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (- 12a b e - 36a b d e )x - 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 12b e x + (36a b e + 12b d e )x + (36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (12a b e + 36a b d e )x + 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (- 12a b e + 12b d e )x + (- 30a b e + 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 22a b e + 6a b d e + 18a b d e - 2b d e)x - 3a e - 10a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 6a b d e + b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 8 5 4 +--R (3a b e - 15a b d e + 30a b d e - 30a b d e + 15a b d e - 3b d e)x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 9a b e - 42a b d e + 75a b d e - 60a b d e + 15a b d e +--R + +--R 7 5 8 6 +--R 6a b d e - 3b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 7 6 2 +--R (9a b e - 36a b d e + 45a b d e - 45a b d e + 36a b d e - 9a b d )x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5 +--R 3a e - 6a b d e - 15a b d e + 60a b d e - 75a b d e + 42a b d e +--R + +--R 2 6 6 +--R - 9a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 3 5 6 +--R 3a d e - 15a b d e + 30a b d e - 30a b d e + 15a b d e - 3a b d +--R Type: Union(Expression(Integer),...) +--E 770 + +--S 771 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 12b e x + (- 36a b e - 12b d e )x +--R + +--R 2 2 4 3 3 2 3 4 2 2 3 +--R (- 36a b e - 36a b d e )x + (- 12a b e - 36a b d e )x +--R + +--R 3 3 +--R - 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 12b e x + (36a b e + 12b d e )x + (36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (12a b e + 36a b d e )x + 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (- 12a b e + 12b d e )x + (- 30a b e + 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 22a b e + 6a b d e + 18a b d e - 2b d e)x - 3a e - 10a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 6a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 3 +--R 12b e x + (48a b e + 12b d e )x + (72a b e + 48a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 4 3 +--R (48a b e + 72a b d e )x + (12a b e + 48a b d e )x + 12a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 4 3 3 +--R - 12b e x + (- 48a b e - 12b d e )x + (- 72a b e - 48a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 4 3 +--R (- 48a b e - 72a b d e )x + (- 12a b e - 48a b d e )x - 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 5 3 4 2 3 4 4 3 5 2 2 3 +--R (12a b e - 12b d e )x + (42a b e - 36a b d e - 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (52a b e - 30a b d e - 24a b d e + 2b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (25a b e + 4a b d e - 36a b d e + 8a b d e - b d )x + 3a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R 10a b d e - 18a b d e + 6a b d e - a b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 3a b e - 15a b d e + 30a b d e - 30a b d e + 15a b d e +--R + +--R 8 5 +--R - 3b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 9a b e - 42a b d e + 75a b d e - 60a b d e + 15a b d e +--R + +--R 7 5 8 6 +--R 6a b d e - 3b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 9a b e - 36a b d e + 45a b d e - 45a b d e + 36a b d e +--R + +--R 7 6 +--R - 9a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 3a e - 6a b d e - 15a b d e + 60a b d e - 75a b d e +--R + +--R 3 5 5 2 6 6 +--R 42a b d e - 9a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 3 5 6 +--R 3a d e - 15a b d e + 30a b d e - 30a b d e + 15a b d e - 3a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 772 + +)clear all + +--S 773 of 1353 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1353 +r0:=-10/3*b^2/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5*b^2*e*(a+b*x)/_ + ((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2/((b*d-a*e)*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+5/2*b/((b*d-a*e)^2*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-10*b^2*e^2/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 10*b^2*e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 10*b^2*e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (180a b e + 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (180a b e + 360a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (60a b e + 360a b d e + 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (120a b d e + 180a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 180a b e - 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 180a b e - 360a b d e - 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (- 60a b e - 360a b d e - 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (- 120a b d e - 180a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (60a b e - 60b d e )x + (150a b e - 60a b d e - 90b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (110a b e + 120a b d e - 210a b d e - 20b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (15a b e + 160a b d e - 120a b d e - 60a b d e + 5b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 30a b d e + 20a b d e - 60a b d e + 15a b d e - 2b d +--R / +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 2 6 4 4 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 3 8 6 2 +--R - 36a b d e + 6b d e +--R * +--R 4 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R 12a b e - 60a b d e + 108a b d e - 60a b d e - 60a b d e +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 108a b d e - 60a b d e + 12b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R 6a e - 12a b d e - 48a b d e + 204a b d e - 300a b d e +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R 204a b d e - 48a b d e - 12a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R 12a d e - 60a b d e + 108a b d e - 60a b d e - 60a b d e +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 108a b d e - 60a b d e + 12a b d +--R * +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 3 5 7 2 6 8 +--R - 36a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (180a b e + 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (180a b e + 360a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (60a b e + 360a b d e + 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (120a b d e + 180a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 180a b e - 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 180a b e - 360a b d e - 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (- 60a b e - 360a b d e - 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (- 120a b d e - 180a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (60a b e - 60b d e )x + (150a b e - 60a b d e - 90b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (110a b e + 120a b d e - 210a b d e - 20b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (15a b e + 160a b d e - 120a b d e - 60a b d e + 5b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 30a b d e + 20a b d e - 60a b d e + 15a b d e - 2b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 2 7 4 4 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 8 5 3 9 6 2 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 3 6 4 4 +--R 18a b e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 2 7 5 3 8 6 2 9 7 +--R 72a b d e - 54a b d e + 12b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 4 5 4 4 +--R 18a b e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 6 5 3 2 7 6 2 9 8 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 4 5 5 3 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 3 6 6 2 2 7 7 8 8 +--R 60a b d e - 72a b d e + 18a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 5 4 5 3 +--R 12a d e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 4 5 6 2 3 6 7 2 7 8 +--R 198a b d e - 96a b d e + 18a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 4 5 7 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 3 6 8 +--R 6a b d +--R Type: Union(Expression(Integer),...) +--E 775 + +--S 776 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (180a b e + 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (180a b e + 360a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (60a b e + 360a b d e + 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (120a b d e + 180a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 180a b e - 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 180a b e - 360a b d e - 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (- 60a b e - 360a b d e - 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (- 120a b d e - 180a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (60a b e - 60b d e )x + (150a b e - 60a b d e - 90b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (110a b e + 120a b d e - 210a b d e - 20b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (15a b e + 160a b d e - 120a b d e - 60a b d e + 5b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 30a b d e + 20a b d e - 60a b d e + 15a b d e - 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 6 5 6 5 5 6 4 5 +--R - 60b e x + (- 240a b e - 120b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (- 360a b e - 480a b d e - 60b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 3 +--R (- 240a b e - 720a b d e - 240a b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 2 +--R (- 60a b e - 480a b d e - 360a b d e )x +--R + +--R 4 2 4 3 3 2 3 4 2 2 3 +--R (- 120a b d e - 240a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 6 5 6 5 5 6 4 5 +--R 60b e x + (240a b e + 120b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (360a b e + 480a b d e + 60b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 3 +--R (240a b e + 720a b d e + 240a b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 2 +--R (60a b e + 480a b d e + 360a b d e )x +--R + +--R 4 2 4 3 3 2 3 4 2 2 3 +--R (120a b d e + 240a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 5 6 4 5 2 4 5 5 4 6 2 3 4 +--R (- 60a b e + 60b d e )x + (- 210a b e + 120a b d e + 90b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 3 +--R (- 260a b e - 60a b d e + 300a b d e + 20b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 2 +--R (- 125a b e - 280a b d e + 330a b d e + 80a b d e - 5b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R - 12a b e - 190a b d e + 100a b d e + 120a b d e - 20a b d e +--R + +--R 6 5 +--R 2b d +--R * +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R 3a e - 30a b d e - 20a b d e + 60a b d e - 15a b d e + 2a b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 2 7 4 4 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 8 5 3 9 6 2 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 3 6 4 4 +--R 18a b e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 2 7 5 3 8 6 2 9 7 +--R 72a b d e - 54a b d e + 12b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 4 5 4 4 +--R 18a b e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 6 5 3 2 7 6 2 9 8 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 4 5 5 3 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 3 6 6 2 2 7 7 8 8 +--R 60a b d e - 72a b d e + 18a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 5 4 5 3 +--R 12a d e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 4 5 6 2 3 6 7 2 7 8 +--R 198a b d e - 96a b d e + 18a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 4 5 7 3 6 8 +--R - 36a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 777 + +)clear all + +--S 778 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1353 +r0:=-2/9*(b*d-a*e)^3*(d+e*x)^(9/2)/e^4+6/11*b*(b*d-a*e)^2*(d+e*x)^(11/2)/e^4-_ + 6/13*b^2*(b*d-a*e)*(d+e*x)^(13/2)/e^4+2/15*b^3*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 3 7 7 2 7 3 6 6 +--R 858b e x + (2970a b e + 3036b d e )x +--R + +--R 2 7 2 6 3 2 5 5 +--R (3510a b e + 10800a b d e + 3708b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (1430a e + 13260a b d e + 13740a b d e + 1600b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (5720a d e + 17940a b d e + 6360a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (8580a d e + 9360a b d e + 90a b d e - 12b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 3 4 3 +--R (5720a d e + 390a b d e - 120a b d e + 16b d e)x + 1430a d e +--R + +--R 2 5 2 2 6 3 7 +--R - 780a b d e + 240a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 2 7 3 6 6 +--R 858b e x + (2970a b e + 3036b d e )x +--R + +--R 2 7 2 6 3 2 5 5 +--R (3510a b e + 10800a b d e + 3708b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (1430a e + 13260a b d e + 13740a b d e + 1600b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (5720a d e + 17940a b d e + 6360a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (8580a d e + 9360a b d e + 90a b d e - 12b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 3 4 3 +--R (5720a d e + 390a b d e - 120a b d e + 16b d e)x + 1430a d e +--R + +--R 2 5 2 2 6 3 7 +--R - 780a b d e + 240a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Union(Expression(Integer),...) +--E 780 + +--S 781 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 782 + +)clear all + +--S 783 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1353 +r0:=-2/7*(b*d-a*e)^3*(d+e*x)^(7/2)/e^4+2/3*b*(b*d-a*e)^2*(d+e*x)^(9/2)/e^4-_ + 6/11*b^2*(b*d-a*e)*(d+e*x)^(11/2)/e^4+2/13*b^3*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 462b e x + (1638a b e + 1134b d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (2002a b e + 4186a b d e + 742b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (858a e + 5434a b d e + 2938a b d e + 10b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (2574a d e + 4290a b d e + 78a b d e - 12b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (2574a d e + 286a b d e - 104a b d e + 16b d e)x + 858a d e +--R + +--R 2 4 2 2 5 3 6 +--R - 572a b d e + 208a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3003e +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 2 6 3 5 5 +--R 462b e x + (1638a b e + 1134b d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (2002a b e + 4186a b d e + 742b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (858a e + 5434a b d e + 2938a b d e + 10b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (2574a d e + 4290a b d e + 78a b d e - 12b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (2574a d e + 286a b d e - 104a b d e + 16b d e)x + 858a d e +--R + +--R 2 4 2 2 5 3 6 +--R - 572a b d e + 208a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3003e +--R Type: Union(Expression(Integer),...) +--E 785 + +--S 786 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 787 + +)clear all + +--S 788 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1353 +r0:=-2/5*(b*d-a*e)^3*(d+e*x)^(5/2)/e^4+6/7*b*(b*d-a*e)^2*(d+e*x)^(7/2)/e^4-_ + 2/3*b^2*(b*d-a*e)*(d+e*x)^(9/2)/e^4+2/11*b^3*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 210b e x + (770a b e + 280b d e )x +--R + +--R 2 5 2 4 3 2 3 3 +--R (990a b e + 1100a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (462a e + 1584a b d e + 66a b d e - 12b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (924a d e + 198a b d e - 88a b d e + 16b d e)x + 462a d e +--R + +--R 2 3 2 2 4 3 5 +--R - 396a b d e + 176a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 2 5 3 4 4 +--R 210b e x + (770a b e + 280b d e )x +--R + +--R 2 5 2 4 3 2 3 3 +--R (990a b e + 1100a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (462a e + 1584a b d e + 66a b d e - 12b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (924a d e + 198a b d e - 88a b d e + 16b d e)x + 462a d e +--R + +--R 2 3 2 2 4 3 5 +--R - 396a b d e + 176a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Union(Expression(Integer),...) +--E 790 + +--S 791 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 792 + +)clear all + +--S 793 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (1) (b x + 3a b x + 3a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1353 +r0:=-2/3*(b*d-a*e)^3*(d+e*x)^(3/2)/e^4+6/5*b*(b*d-a*e)^2*(d+e*x)^(5/2)/e^4-_ + 6/7*b^2*(b*d-a*e)*(d+e*x)^(7/2)/e^4+2/9*b^3*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 3 4 4 2 4 3 3 3 +--R 70b e x + (270a b e + 10b d e )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (378a b e + 54a b d e - 12b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 +--R (210a e + 126a b d e - 72a b d e + 16b d e)x + 210a d e +--R + +--R 2 2 2 2 3 3 4 +--R - 252a b d e + 144a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 2 4 3 3 3 +--R 70b e x + (270a b e + 10b d e )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (378a b e + 54a b d e - 12b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 +--R (210a e + 126a b d e - 72a b d e + 16b d e)x + 210a d e +--R + +--R 2 2 2 2 3 3 4 +--R - 252a b d e + 144a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 795 + +--S 796 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 797 + +)clear all + +--S 798 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1353 +r0:=2*b*(b*d-a*e)^2*(d+e*x)^(3/2)/e^4-6/5*b^2*(b*d-a*e)*(d+e*x)^(5/2)/e^4+_ + 2/7*b^3*(d+e*x)^(7/2)/e^4-2*(b*d-a*e)^3*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 10b e x + (42a b e - 12b d e )x + (70a b e - 56a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R 70a e - 140a b d e + 112a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 35e +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 10b e x + (42a b e - 12b d e )x + (70a b e - 56a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R 70a e - 140a b d e + 112a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 35e +--R Type: Union(Expression(Integer),...) +--E 800 + +--S 801 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 802 + +)clear all + +--S 803 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1353 +r0:=-2*b^2*(b*d-a*e)*(d+e*x)^(3/2)/e^4+2/5*b^3*(d+e*x)^(5/2)/e^4+_ + 2*(b*d-a*e)^3/(e^4*sqrt(d+e*x))+6*b*(b*d-a*e)^2*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (10a b e - 4b d e )x + (30a b e - 40a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 10a e + 60a b d e - 80a b d e + 32b d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (10a b e - 4b d e )x + (30a b e - 40a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 10a e + 60a b d e - 80a b d e + 32b d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 805 + +--S 806 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 807 + +)clear all + +--S 808 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1353 +r0:=2/3*(b*d-a*e)^3/(e^4*(d+e*x)^(3/2))+2/3*b^3*(d+e*x)^(3/2)/e^4-_ + 6*b*(b*d-a*e)^2/(e^4*sqrt(d+e*x))-6*b^2*(b*d-a*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (18a b e - 12b d e )x + (- 18a b e + 72a b d e - 48b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a e - 12a b d e + 48a b d e - 32b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (18a b e - 12b d e )x + (- 18a b e + 72a b d e - 48b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a e - 12a b d e + 48a b d e - 32b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 810 + +--S 811 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 812 + +)clear all + +--S 813 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1353 +r0:=2/5*(b*d-a*e)^3/(e^4*(d+e*x)^(5/2))-2*b*(b*d-a*e)^2/(e^4*(d+e*x)^(3/2))+_ + 6*b^2*(b*d-a*e)/(e^4*sqrt(d+e*x))+2*b^3*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R 10b e x + (- 30a b e + 60b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 10a b e - 40a b d e + 80b d e)x - 2a e - 4a b d e - 16a b d e +--R + +--R 3 3 +--R 32b d +--R / +--R 6 2 5 2 4 +-------+ +--R (5e x + 10d e x + 5d e )\|e x + d +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 +--R 10b e x + (- 30a b e + 60b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 10a b e - 40a b d e + 80b d e)x - 2a e - 4a b d e - 16a b d e +--R + +--R 3 3 +--R 32b d +--R / +--R 6 2 5 2 4 +-------+ +--R (5e x + 10d e x + 5d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 815 + +--S 816 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 817 + +)clear all + +--S 818 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1353 +r0:=-2/9*(b*d-a*e)^5*(d+e*x)^(9/2)/e^6+10/11*b*(b*d-a*e)^4*(d+e*x)^(11/2)/_ + e^6-20/13*b^2*(b*d-a*e)^3*(d+e*x)^(13/2)/e^6+4/3*b^3*(b*d-a*e)^2*(d+_ + e*x)^(15/2)/e^6-10/17*b^4*(b*d-a*e)*(d+e*x)^(17/2)/e^6+2/19*b^5*(d+_ + e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 5 9 9 4 9 5 8 8 +--R 43758b e x + (244530a b e + 149292b d e )x +--R + +--R 2 3 9 4 8 5 2 7 7 +--R (554268a b e + 847704a b d e + 173316b d e )x +--R + +--R 3 2 9 2 3 8 4 2 7 5 3 6 6 +--R (639540a b e + 1961256a b d e + 1005708a b d e + 69168b d e )x +--R + +--R 4 9 3 2 8 2 3 2 7 4 3 6 +--R 377910a b e + 2325600a b d e + 2395368a b d e + 414504a b d e +--R + +--R 5 4 5 +--R 126b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 8 3 2 2 7 2 3 3 6 +--R 92378a e + 1427660a b d e + 2958680a b d e + 1033600a b d e +--R + +--R 4 4 5 5 5 4 +--R 1330a b d e - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 +--R 369512a d e + 1931540a b d e + 1369520a b d e + 6460a b d e +--R + +--R 4 5 4 5 6 3 +--R - 1520a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 +--R 554268a d e + 1007760a b d e + 19380a b d e - 7752a b d e +--R + +--R 4 6 3 5 7 2 +--R 1824a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 +--R 369512a d e + 41990a b d e - 25840a b d e + 10336a b d e +--R + +--R 4 7 2 5 8 +--R - 2432a b d e + 256b d e +--R * +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 +--R 92378a d e - 83980a b d e + 51680a b d e - 20672a b d e +--R + +--R 4 8 5 9 +--R 4864a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 415701e +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 9 9 4 9 5 8 8 +--R 43758b e x + (244530a b e + 149292b d e )x +--R + +--R 2 3 9 4 8 5 2 7 7 +--R (554268a b e + 847704a b d e + 173316b d e )x +--R + +--R 3 2 9 2 3 8 4 2 7 5 3 6 6 +--R (639540a b e + 1961256a b d e + 1005708a b d e + 69168b d e )x +--R + +--R 4 9 3 2 8 2 3 2 7 4 3 6 +--R 377910a b e + 2325600a b d e + 2395368a b d e + 414504a b d e +--R + +--R 5 4 5 +--R 126b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 8 3 2 2 7 2 3 3 6 +--R 92378a e + 1427660a b d e + 2958680a b d e + 1033600a b d e +--R + +--R 4 4 5 5 5 4 +--R 1330a b d e - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 +--R 369512a d e + 1931540a b d e + 1369520a b d e + 6460a b d e +--R + +--R 4 5 4 5 6 3 +--R - 1520a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 +--R 554268a d e + 1007760a b d e + 19380a b d e - 7752a b d e +--R + +--R 4 6 3 5 7 2 +--R 1824a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 +--R 369512a d e + 41990a b d e - 25840a b d e + 10336a b d e +--R + +--R 4 7 2 5 8 +--R - 2432a b d e + 256b d e +--R * +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 +--R 92378a d e - 83980a b d e + 51680a b d e - 20672a b d e +--R + +--R 4 8 5 9 +--R 4864a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 415701e +--R Type: Union(Expression(Integer),...) +--E 820 + +--S 821 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 822 + +)clear all + +--S 823 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1353 +r0:=-2/7*(b*d-a*e)^5*(d+e*x)^(7/2)/e^6+10/9*b*(b*d-a*e)^4*(d+e*x)^(9/2)/e^6-_ + 20/11*b^2*(b*d-a*e)^3*(d+e*x)^(11/2)/e^6+20/13*b^3*(b*d-a*e)^2*(d+_ + e*x)^(13/2)/e^6-2/3*b^4*(b*d-a*e)*(d+e*x)^(15/2)/e^6+2/17*b^5*(d+_ + e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 5 8 8 4 8 5 7 7 +--R 18018b e x + (102102a b e + 42042b d e )x +--R + +--R 2 3 8 4 7 5 2 6 6 +--R (235620a b e + 243474a b d e + 25410b d e )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 5 +--R (278460a b e + 578340a b d e + 152082a b d e + 126b d e )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 +--R 170170a b e + 711620a b d e + 378420a b d e + 1190a b d e +--R + +--R 5 4 4 +--R - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 +--R 43758a e + 461890a b d e + 499460a b d e + 5100a b d e +--R + +--R 4 4 4 5 5 3 +--R - 1360a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 +--R 131274a d e + 364650a b d e + 13260a b d e - 6120a b d e +--R + +--R 4 5 3 5 6 2 +--R 1632a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 +--R 131274a d e + 24310a b d e - 17680a b d e + 8160a b d e +--R + +--R 4 6 2 5 7 +--R - 2176a b d e + 256b d e +--R * +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 +--R 43758a d e - 48620a b d e + 35360a b d e - 16320a b d e +--R + +--R 4 7 5 8 +--R 4352a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 8 8 4 8 5 7 7 +--R 18018b e x + (102102a b e + 42042b d e )x +--R + +--R 2 3 8 4 7 5 2 6 6 +--R (235620a b e + 243474a b d e + 25410b d e )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 5 +--R (278460a b e + 578340a b d e + 152082a b d e + 126b d e )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 +--R 170170a b e + 711620a b d e + 378420a b d e + 1190a b d e +--R + +--R 5 4 4 +--R - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 +--R 43758a e + 461890a b d e + 499460a b d e + 5100a b d e +--R + +--R 4 4 4 5 5 3 +--R - 1360a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 +--R 131274a d e + 364650a b d e + 13260a b d e - 6120a b d e +--R + +--R 4 5 3 5 6 2 +--R 1632a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 +--R 131274a d e + 24310a b d e - 17680a b d e + 8160a b d e +--R + +--R 4 6 2 5 7 +--R - 2176a b d e + 256b d e +--R * +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 +--R 43758a d e - 48620a b d e + 35360a b d e - 16320a b d e +--R + +--R 4 7 5 8 +--R 4352a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Union(Expression(Integer),...) +--E 825 + +--S 826 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 827 + +)clear all + +--S 828 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1353 +r0:=-2/5*(b*d-a*e)^5*(d+e*x)^(5/2)/e^6+10/7*b*(b*d-a*e)^4*(d+e*x)^(7/2)/e^6-_ + 20/9*b^2*(b*d-a*e)^3*(d+e*x)^(9/2)/e^6+20/11*b^3*(b*d-a*e)^2*(d+_ + e*x)^(11/2)/e^6-10/13*b^4*(b*d-a*e)*(d+e*x)^(13/2)/e^6+2/15*b^5*(d+_ + e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 5 7 7 4 7 5 6 6 +--R 6006b e x + (34650a b e + 7392b d e )x +--R + +--R 2 3 7 4 6 5 2 5 5 +--R (81900a b e + 44100a b d e + 126b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (100100a b e + 109200a b d e + 1050a b d e - 140b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 +--R 64350a b e + 143000a b d e + 3900a b d e - 1200a b d e +--R + +--R 5 4 3 +--R 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 18018a e + 102960a b d e + 8580a b d e - 4680a b d e +--R + +--R 4 4 3 5 5 2 +--R 1440a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 +--R 36036a d e + 12870a b d e - 11440a b d e + 6240a b d e +--R + +--R 4 5 2 5 6 +--R - 1920a b d e + 256b d e +--R * +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 +--R 18018a d e - 25740a b d e + 22880a b d e - 12480a b d e +--R + +--R 4 6 5 7 +--R 3840a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 7 4 7 5 6 6 +--R 6006b e x + (34650a b e + 7392b d e )x +--R + +--R 2 3 7 4 6 5 2 5 5 +--R (81900a b e + 44100a b d e + 126b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (100100a b e + 109200a b d e + 1050a b d e - 140b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 +--R 64350a b e + 143000a b d e + 3900a b d e - 1200a b d e +--R + +--R 5 4 3 +--R 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 18018a e + 102960a b d e + 8580a b d e - 4680a b d e +--R + +--R 4 4 3 5 5 2 +--R 1440a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 +--R 36036a d e + 12870a b d e - 11440a b d e + 6240a b d e +--R + +--R 4 5 2 5 6 +--R - 1920a b d e + 256b d e +--R * +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 +--R 18018a d e - 25740a b d e + 22880a b d e - 12480a b d e +--R + +--R 4 6 5 7 +--R 3840a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 830 + +--S 831 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 832 + +)clear all + +--S 833 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1353 +r0:=-2/3*(b*d-a*e)^5*(d+e*x)^(3/2)/e^6+2*b*(b*d-a*e)^4*(d+e*x)^(5/2)/e^6-_ + 20/7*b^2*(b*d-a*e)^3*(d+e*x)^(7/2)/e^6+20/9*b^3*(b*d-a*e)^2*(d+_ + e*x)^(9/2)/e^6-10/11*b^4*(b*d-a*e)*(d+e*x)^(11/2)/e^6+2/13*b^5*(d+_ + e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 5 6 6 4 6 5 5 5 +--R 1386b e x + (8190a b e + 126b d e )x +--R + +--R 2 3 6 4 5 5 2 4 4 +--R (20020a b e + 910a b d e - 140b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (25740a b e + 2860a b d e - 1040a b d e + 160b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 18018a b e + 5148a b d e - 3432a b d e + 1248a b d e +--R + +--R 5 4 2 +--R - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 6006a e + 6006a b d e - 6864a b d e + 4576a b d e +--R + +--R 4 4 2 5 5 +--R - 1664a b d e + 256b d e +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 6006a d e - 12012a b d e + 13728a b d e - 9152a b d e + 3328a b d e +--R + +--R 5 6 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 9009e +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 4 6 5 5 5 +--R 1386b e x + (8190a b e + 126b d e )x +--R + +--R 2 3 6 4 5 5 2 4 4 +--R (20020a b e + 910a b d e - 140b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (25740a b e + 2860a b d e - 1040a b d e + 160b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 18018a b e + 5148a b d e - 3432a b d e + 1248a b d e +--R + +--R 5 4 2 +--R - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 6006a e + 6006a b d e - 6864a b d e + 4576a b d e +--R + +--R 4 4 2 5 5 +--R - 1664a b d e + 256b d e +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 6006a d e - 12012a b d e + 13728a b d e - 9152a b d e + 3328a b d e +--R + +--R 5 6 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 835 + +--S 836 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 837 + +)clear all + +--S 838 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1353 +r0:=10/3*b*(b*d-a*e)^4*(d+e*x)^(3/2)/e^6-4*b^2*(b*d-a*e)^3*(d+e*x)^(5/2)/e^6+_ + 20/7*b^3*(b*d-a*e)^2*(d+e*x)^(7/2)/e^6-10/9*b^4*(b*d-a*e)*_ + (d+e*x)^(9/2)/e^6+2/11*b^5*(d+e*x)^(11/2)/e^6-2*(b*d-a*e)^5*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 126b e x + (770a b e - 140b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (1980a b e - 880a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (2772a b e - 2376a b d e + 1056a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 1386a e - 4620a b d e + 7392a b d e - 6336a b d e + 2816a b d e +--R + +--R 5 5 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 693e +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 126b e x + (770a b e - 140b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (1980a b e - 880a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (2772a b e - 2376a b d e + 1056a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 1386a e - 4620a b d e + 7392a b d e - 6336a b d e + 2816a b d e +--R + +--R 5 5 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 693e +--R Type: Union(Expression(Integer),...) +--E 840 + +--S 841 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 842 + +)clear all + +--S 843 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1353 +r0:=-20/3*b^2*(b*d-a*e)^3*(d+e*x)^(3/2)/e^6+4*b^3*(b*d-a*e)^2*_ + (d+e*x)^(5/2)/e^6-10/7*b^4*(b*d-a*e)*(d+e*x)^(7/2)/e^6+2/9*b^5*_ + (d+e*x)^(9/2)/e^6+2*(b*d-a*e)^5/(e^6*sqrt(d+e*x))+10*b*(b*d-a*e)^4*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 14b e x + (90a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (252a b e - 144a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 504a b d e + 288a b d e - 64b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (630a b e - 1680a b d e + 2016a b d e - 1152a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 126a e + 1260a b d e - 3360a b d e + 4032a b d e - 2304a b d e +--R + +--R 5 5 +--R 512b d +--R / +--R 6 +-------+ +--R 63e \|e x + d +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 14b e x + (90a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (252a b e - 144a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 504a b d e + 288a b d e - 64b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (630a b e - 1680a b d e + 2016a b d e - 1152a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 126a e + 1260a b d e - 3360a b d e + 4032a b d e - 2304a b d e +--R + +--R 5 5 +--R 512b d +--R / +--R 6 +-------+ +--R 63e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 845 + +--S 846 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1353 +r0:=2/3*(b*d-a*e)^5/(e^6*(d+e*x)^(3/2))+20/3*b^3*(b*d-a*e)^2*_ + (d+e*x)^(3/2)/e^6-2*b^4*(b*d-a*e)*(d+e*x)^(5/2)/e^6+2/7*b^5*_ + (d+e*x)^(7/2)/e^6-10*b*(b*d-a*e)^4/(e^6*sqrt(d+e*x))-20*b^2*_ + (b*d-a*e)^3*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (42a b e - 12b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 840a b d e + 672a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b e + 1680a b d e - 3360a b d e + 2688a b d e - 768b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 14a e - 140a b d e + 1120a b d e - 2240a b d e + 1792a b d e +--R + +--R 5 5 +--R - 512b d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (42a b e - 12b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 840a b d e + 672a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b e + 1680a b d e - 3360a b d e + 2688a b d e - 768b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 14a e - 140a b d e + 1120a b d e - 2240a b d e + 1792a b d e +--R + +--R 5 5 +--R - 512b d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 850 + +--S 851 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 852 + +)clear all + +--S 853 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1353 +r0:=2/5*(b*d-a*e)^5/(e^6*(d+e*x)^(5/2))-10/3*b*(b*d-a*e)^4/(e^6*_ + (d+e*x)^(3/2))-10/3*b^4*(b*d-a*e)*(d+e*x)^(3/2)/e^6+2/5*b^5*_ + (d+e*x)^(5/2)/e^6+20*b^2*(b*d-a*e)^3/(e^6*sqrt(d+e*x))+20*b^3*_ + (b*d-a*e)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (50a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (300a b e - 400a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 300a b e + 1800a b d e - 2400a b d e + 960b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 50a b e - 400a b d e + 2400a b d e - 3200a b d e + 1280b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 6a e - 20a b d e - 160a b d e + 960a b d e - 1280a b d e + 512b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (50a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (300a b e - 400a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 300a b e + 1800a b d e - 2400a b d e + 960b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 50a b e - 400a b d e + 2400a b d e - 3200a b d e + 1280b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 6a e - 20a b d e - 160a b d e + 960a b d e - 1280a b d e + 512b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 855 + +--S 856 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 857 + +)clear all + +--S 858 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 3 10 6 3 7 2 9 2 5 3 6 2 7 2 8 +--R b e x + (7a b e + 3b d e )x + (21a b e + 21a b d e + 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e + 63a b d e + 21a b d e + b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (35a b e + 105a b d e + 63a b d e + 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (21a b e + 105a b d e + 105a b d e + 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (7a b e + 63a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (a e + 21a b d e + 63a b d e + 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (3a d e + 21a b d e + 21a b d )x + (3a d e + 7a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1353 +r0:=-2/9*(b*d-a*e)^7*(d+e*x)^(9/2)/e^8+14/11*b*(b*d-a*e)^6*_ + (d+e*x)^(11/2)/e^8-42/13*b^2*(b*d-a*e)^5*(d+e*x)^(13/2)/e^8+_ + 14/3*b^3*(b*d-a*e)^4*(d+e*x)^(15/2)/e^8-70/17*b^4*(b*d-a*e)^3*_ + (d+e*x)^(17/2)/e^8+42/19*b^5*(b*d-a*e)^2*(d+e*x)^(19/2)/e^8-_ + 2/3*b^6*(b*d-a*e)*(d+e*x)^(21/2)/e^8+2/23*b^7*(d+e*x)^(23/2)/e^8 +--R +--R +--R (2) +--R 7 11 11 6 11 7 10 10 +--R 831402b e x + (6374082a b e + 2771340b d e )x +--R + +--R 2 5 11 6 10 7 2 9 9 +--R (21135114a b e + 21470592a b d e + 3121404b d e )x +--R + +--R 3 4 11 2 5 10 6 2 9 +--R 39369330a b e + 72108036a b d e + 24509628a b d e +--R + +--R 7 3 8 +--R 1194336b d e +--R * +--R 8 +--R x +--R + +--R 4 3 11 3 4 10 2 5 2 9 +--R 44618574a b e + 136480344a b d e + 83711628a b d e +--R + +--R 6 3 8 7 4 7 +--R 9551256a b d e + 858b d e +--R * +--R 7 +--R x +--R + +--R 5 2 11 4 3 10 3 4 2 9 +--R 30889782a b e + 157881108a b d e + 161918988a b d e +--R + +--R 2 5 3 8 6 4 7 7 5 6 +--R 33408144a b d e + 10626a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 6 11 5 2 10 4 3 2 9 +--R 12168702a b e + 112326480a b d e + 192827124a b d e +--R + +--R 3 4 3 8 2 5 4 7 6 5 6 7 6 5 +--R 66735144a b d e + 60858a b d e - 11592a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 7 11 6 10 5 2 2 9 +--R 2124694a e + 45970652a b d e + 142904244a b d e +--R + +--R 4 3 3 8 3 4 4 7 2 5 5 6 6 6 5 +--R 83204800a b d e + 214130a b d e - 67620a b d e + 12880a b d e +--R + +--R 7 7 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 2 9 5 2 3 8 +--R 8498776a d e + 62195588a b d e + 66147816a b d e +--R + +--R 4 3 4 7 3 4 5 6 2 5 6 5 6 7 4 +--R 520030a b d e - 244720a b d e + 77280a b d e - 14720a b d e +--R + +--R 7 8 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 2 4 7 4 3 5 6 +--R 12748164a d e + 32449872a b d e + 936054a b d e - 624036a b d e +--R + +--R 3 4 6 5 2 5 7 4 6 8 3 7 9 2 +--R 293664a b d e - 92736a b d e + 17664a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 3 8 6 4 7 5 2 5 6 4 3 6 5 +--R 8498776a d e + 1352078a b d e - 1248072a b d e + 832048a b d e +--R + +--R 3 4 7 4 2 5 8 3 6 9 2 7 10 +--R - 391552a b d e + 123648a b d e - 23552a b d e + 2048b d e +--R * +--R x +--R + +--R 7 4 7 6 5 6 5 2 6 5 4 3 7 4 +--R 2124694a d e - 2704156a b d e + 2496144a b d e - 1664096a b d e +--R + +--R 3 4 8 3 2 5 9 2 6 10 7 11 +--R 783104a b d e - 247296a b d e + 47104a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 9561123e +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 11 11 6 11 7 10 10 +--R 831402b e x + (6374082a b e + 2771340b d e )x +--R + +--R 2 5 11 6 10 7 2 9 9 +--R (21135114a b e + 21470592a b d e + 3121404b d e )x +--R + +--R 3 4 11 2 5 10 6 2 9 +--R 39369330a b e + 72108036a b d e + 24509628a b d e +--R + +--R 7 3 8 +--R 1194336b d e +--R * +--R 8 +--R x +--R + +--R 4 3 11 3 4 10 2 5 2 9 +--R 44618574a b e + 136480344a b d e + 83711628a b d e +--R + +--R 6 3 8 7 4 7 +--R 9551256a b d e + 858b d e +--R * +--R 7 +--R x +--R + +--R 5 2 11 4 3 10 3 4 2 9 +--R 30889782a b e + 157881108a b d e + 161918988a b d e +--R + +--R 2 5 3 8 6 4 7 7 5 6 +--R 33408144a b d e + 10626a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 6 11 5 2 10 4 3 2 9 +--R 12168702a b e + 112326480a b d e + 192827124a b d e +--R + +--R 3 4 3 8 2 5 4 7 6 5 6 7 6 5 +--R 66735144a b d e + 60858a b d e - 11592a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 7 11 6 10 5 2 2 9 +--R 2124694a e + 45970652a b d e + 142904244a b d e +--R + +--R 4 3 3 8 3 4 4 7 2 5 5 6 6 6 5 +--R 83204800a b d e + 214130a b d e - 67620a b d e + 12880a b d e +--R + +--R 7 7 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 2 9 5 2 3 8 +--R 8498776a d e + 62195588a b d e + 66147816a b d e +--R + +--R 4 3 4 7 3 4 5 6 2 5 6 5 6 7 4 +--R 520030a b d e - 244720a b d e + 77280a b d e - 14720a b d e +--R + +--R 7 8 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 2 4 7 4 3 5 6 +--R 12748164a d e + 32449872a b d e + 936054a b d e - 624036a b d e +--R + +--R 3 4 6 5 2 5 7 4 6 8 3 7 9 2 +--R 293664a b d e - 92736a b d e + 17664a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 3 8 6 4 7 5 2 5 6 4 3 6 5 +--R 8498776a d e + 1352078a b d e - 1248072a b d e + 832048a b d e +--R + +--R 3 4 7 4 2 5 8 3 6 9 2 7 10 +--R - 391552a b d e + 123648a b d e - 23552a b d e + 2048b d e +--R * +--R x +--R + +--R 7 4 7 6 5 6 5 2 6 5 4 3 7 4 +--R 2124694a d e - 2704156a b d e + 2496144a b d e - 1664096a b d e +--R + +--R 3 4 8 3 2 5 9 2 6 10 7 11 +--R 783104a b d e - 247296a b d e + 47104a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 9561123e +--R Type: Union(Expression(Integer),...) +--E 860 + +--S 861 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 862 + +)clear all + +--S 863 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R b e x + (7a b e + 2b d e)x + (21a b e + 14a b d e + b d )x +--R + +--R 3 4 2 2 5 6 2 6 4 3 2 3 4 2 5 2 5 +--R (35a b e + 42a b d e + 7a b d )x + (35a b e + 70a b d e + 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 6 2 5 2 4 3 2 3 +--R (21a b e + 70a b d e + 35a b d )x + (7a b e + 42a b d e + 35a b d )x +--R + +--R 7 2 6 5 2 2 2 7 6 2 7 2 +--R (a e + 14a b d e + 21a b d )x + (2a d e + 7a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1353 +r0:=-2/7*(b*d-a*e)^7*(d+e*x)^(7/2)/e^8+14/9*b*(b*d-a*e)^6*_ + (d+e*x)^(9/2)/e^8-42/11*b^2*(b*d-a*e)^5*(d+e*x)^(11/2)/e^8+_ + 70/13*b^3*(b*d-a*e)^4*(d+e*x)^(13/2)/e^8-14/3*b^4*(b*d-a*e)^3*_ + (d+e*x)^(15/2)/e^8+42/17*b^5*(b*d-a*e)^2*(d+e*x)^(17/2)/e^8-_ + 14/19*b^6*(b*d-a*e)*(d+e*x)^(19/2)/e^8+2/21*b^7*(d+e*x)^(21/2)/e^8 +--R +--R +--R (2) +--R 7 10 10 6 10 7 9 9 +--R 277134b e x + (2144142a b e + 627198b d e )x +--R + +--R 2 5 10 6 9 7 2 8 8 +--R (7189182a b e + 4918914a b d e + 362934b d e )x +--R + +--R 3 4 10 2 5 9 6 2 8 7 3 7 7 +--R (13579566a b e + 16774758a b d e + 2900898a b d e + 858b d e )x +--R + +--R 4 3 10 3 4 9 2 5 2 8 +--R 15668730a b e + 32382042a b d e + 10138590a b d e +--R + +--R 6 3 7 7 4 6 +--R 9702a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 4 2 8 +--R 11110554a b e + 38459610a b d e + 20226906a b d e +--R + +--R 2 5 3 7 6 4 6 7 5 5 +--R 50274a b d e - 10584a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 6 10 5 2 9 4 3 2 8 +--R 4526522a b e + 28393638a b d e + 25164930a b d e +--R + +--R 3 4 3 7 2 5 4 6 6 5 5 7 6 4 +--R 158270a b d e - 55860a b d e + 11760a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 +--R 831402a e + 12286274a b d e + 19928454a b d e + 339150a b d e +--R + +--R 3 4 4 6 2 5 5 5 6 6 4 7 7 3 +--R - 180880a b d e + 63840a b d e - 13440a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 +--R 2494206a d e + 9699690a b d e + 529074a b d e - 406980a b d e +--R + +--R 3 4 5 5 2 5 6 4 6 7 3 7 8 2 +--R 217056a b d e - 76608a b d e + 16128a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 +--R 2494206a d e + 646646a b d e - 705432a b d e + 542640a b d e +--R + +--R 3 4 6 4 2 5 7 3 6 8 2 7 9 +--R - 289408a b d e + 102144a b d e - 21504a b d e + 2048b d e +--R * +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 +--R 831402a d e - 1293292a b d e + 1410864a b d e - 1085280a b d e +--R + +--R 3 4 7 3 2 5 8 2 6 9 7 10 +--R 578816a b d e - 204288a b d e + 43008a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 10 10 6 10 7 9 9 +--R 277134b e x + (2144142a b e + 627198b d e )x +--R + +--R 2 5 10 6 9 7 2 8 8 +--R (7189182a b e + 4918914a b d e + 362934b d e )x +--R + +--R 3 4 10 2 5 9 6 2 8 7 3 7 7 +--R (13579566a b e + 16774758a b d e + 2900898a b d e + 858b d e )x +--R + +--R 4 3 10 3 4 9 2 5 2 8 +--R 15668730a b e + 32382042a b d e + 10138590a b d e +--R + +--R 6 3 7 7 4 6 +--R 9702a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 4 2 8 +--R 11110554a b e + 38459610a b d e + 20226906a b d e +--R + +--R 2 5 3 7 6 4 6 7 5 5 +--R 50274a b d e - 10584a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 6 10 5 2 9 4 3 2 8 +--R 4526522a b e + 28393638a b d e + 25164930a b d e +--R + +--R 3 4 3 7 2 5 4 6 6 5 5 7 6 4 +--R 158270a b d e - 55860a b d e + 11760a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 +--R 831402a e + 12286274a b d e + 19928454a b d e + 339150a b d e +--R + +--R 3 4 4 6 2 5 5 5 6 6 4 7 7 3 +--R - 180880a b d e + 63840a b d e - 13440a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 +--R 2494206a d e + 9699690a b d e + 529074a b d e - 406980a b d e +--R + +--R 3 4 5 5 2 5 6 4 6 7 3 7 8 2 +--R 217056a b d e - 76608a b d e + 16128a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 +--R 2494206a d e + 646646a b d e - 705432a b d e + 542640a b d e +--R + +--R 3 4 6 4 2 5 7 3 6 8 2 7 9 +--R - 289408a b d e + 102144a b d e - 21504a b d e + 2048b d e +--R * +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 +--R 831402a d e - 1293292a b d e + 1410864a b d e - 1085280a b d e +--R + +--R 3 4 7 3 2 5 8 2 6 9 7 10 +--R 578816a b d e - 204288a b d e + 43008a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Union(Expression(Integer),...) +--E 865 + +--S 866 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 8 6 7 7 2 5 6 6 3 4 2 5 5 +--R b e x + (7a b e + b d)x + (21a b e + 7a b d)x + (35a b e + 21a b d)x +--R + +--R 4 3 3 4 4 5 2 4 3 3 6 5 2 2 +--R (35a b e + 35a b d)x + (21a b e + 35a b d)x + (7a b e + 21a b d)x +--R + +--R 7 6 7 +--R (a e + 7a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1353 +r0:=-2/5*(b*d-a*e)^7*(d+e*x)^(5/2)/e^8+2*b*(b*d-a*e)^6*(d+e*x)^(7/2)/e^8-_ + 14/3*b^2*(b*d-a*e)^5*(d+e*x)^(9/2)/e^8+70/11*b^3*(b*d-a*e)^4*_ + (d+e*x)^(11/2)/e^8-70/13*b^4*(b*d-a*e)^3*(d+e*x)^(13/2)/e^8+_ + 14/5*b^5*(b*d-a*e)^2*(d+e*x)^(15/2)/e^8-14/17*b^6*(b*d-a*e)*_ + (d+e*x)^(17/2)/e^8+2/19*b^7*(d+e*x)^(19/2)/e^8 +--R +--R +--R (2) +--R 7 9 9 6 9 7 8 8 +--R 72930b e x + (570570a b e + 85800b d e )x +--R + +--R 2 5 9 6 8 7 2 7 7 +--R (1939938a b e + 684684a b d e + 858b d e )x +--R + +--R 3 4 9 2 5 8 6 2 7 7 3 6 6 +--R (3730650a b e + 2387616a b d e + 8778a b d e - 924b d e )x +--R + +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 +--R 4408950a b e + 4748100a b d e + 40698a b d e - 9576a b d e +--R + +--R 7 4 5 +--R 1008b d e +--R * +--R 5 +--R x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 +--R 3233230a b e + 5878600a b d e + 113050a b d e - 45220a b d e +--R + +--R 6 4 5 7 5 4 +--R 10640a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 2 8 4 3 2 7 3 4 3 6 +--R 1385670a b e + 4618900a b d e + 209950a b d e - 129200a b d e +--R + +--R 2 5 4 5 6 5 4 7 6 3 +--R 51680a b d e - 12160a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 +--R 277134a e + 2217072a b d e + 277134a b d e - 251940a b d e +--R + +--R 3 4 4 5 2 5 5 4 6 6 3 7 7 2 +--R 155040a b d e - 62016a b d e + 14592a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 +--R 554268a d e + 277134a b d e - 369512a b d e + 335920a b d e +--R + +--R 3 4 5 4 2 5 6 3 6 7 2 7 8 +--R - 206720a b d e + 82688a b d e - 19456a b d e + 2048b d e +--R * +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 +--R 277134a d e - 554268a b d e + 739024a b d e - 671840a b d e +--R + +--R 3 4 6 3 2 5 7 2 6 8 7 9 +--R 413440a b d e - 165376a b d e + 38912a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 692835e +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 9 9 6 9 7 8 8 +--R 72930b e x + (570570a b e + 85800b d e )x +--R + +--R 2 5 9 6 8 7 2 7 7 +--R (1939938a b e + 684684a b d e + 858b d e )x +--R + +--R 3 4 9 2 5 8 6 2 7 7 3 6 6 +--R (3730650a b e + 2387616a b d e + 8778a b d e - 924b d e )x +--R + +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 +--R 4408950a b e + 4748100a b d e + 40698a b d e - 9576a b d e +--R + +--R 7 4 5 +--R 1008b d e +--R * +--R 5 +--R x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 +--R 3233230a b e + 5878600a b d e + 113050a b d e - 45220a b d e +--R + +--R 6 4 5 7 5 4 +--R 10640a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 2 8 4 3 2 7 3 4 3 6 +--R 1385670a b e + 4618900a b d e + 209950a b d e - 129200a b d e +--R + +--R 2 5 4 5 6 5 4 7 6 3 +--R 51680a b d e - 12160a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 +--R 277134a e + 2217072a b d e + 277134a b d e - 251940a b d e +--R + +--R 3 4 4 5 2 5 5 4 6 6 3 7 7 2 +--R 155040a b d e - 62016a b d e + 14592a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 +--R 554268a d e + 277134a b d e - 369512a b d e + 335920a b d e +--R + +--R 3 4 5 4 2 5 6 3 6 7 2 7 8 +--R - 206720a b d e + 82688a b d e - 19456a b d e + 2048b d e +--R * +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 +--R 277134a d e - 554268a b d e + 739024a b d e - 671840a b d e +--R + +--R 3 4 6 3 2 5 7 2 6 8 7 9 +--R 413440a b d e - 165376a b d e + 38912a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 692835e +--R Type: Union(Expression(Integer),...) +--E 870 + +--S 871 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 872 + +)clear all + +--S 873 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1353 +r0:=-2/3*(b*d-a*e)^7*(d+e*x)^(3/2)/e^8+14/5*b*(b*d-a*e)^6*(d+e*x)^(5/2)/e^8-_ + 6*b^2*(b*d-a*e)^5*(d+e*x)^(7/2)/e^8+70/9*b^3*(b*d-a*e)^4*_ + (d+e*x)^(9/2)/e^8-70/11*b^4*(b*d-a*e)^3*(d+e*x)^(11/2)/e^8+42/13*b^5*_ + (b*d-a*e)^2*(d+e*x)^(13/2)/e^8-14/15*b^6*(b*d-a*e)*(d+e*x)^(15/2)/e^8+_ + 2/17*b^7*(d+e*x)^(17/2)/e^8 +--R +--R +--R (2) +--R 7 8 8 6 8 7 7 7 +--R 12870b e x + (102102a b e + 858b d e )x +--R + +--R 2 5 8 6 7 7 2 6 6 +--R (353430a b e + 7854a b d e - 924b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 5 +--R (696150a b e + 32130a b d e - 8568a b d e + 1008b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 +--R 850850a b e + 77350a b d e - 35700a b d e + 9520a b d e +--R + +--R 7 4 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 +--R 656370a b e + 121550a b d e - 88400a b d e + 40800a b d e +--R + +--R 6 4 4 7 5 3 +--R - 10880a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 +--R 306306a b e + 131274a b d e - 145860a b d e + 106080a b d e +--R + +--R 2 5 4 4 6 5 3 7 6 2 +--R - 48960a b d e + 13056a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 +--R 72930a e + 102102a b d e - 175032a b d e + 194480a b d e +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 +--R - 141440a b d e + 65280a b d e - 17408a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 72930a d e - 204204a b d e + 350064a b d e - 388960a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 +--R 282880a b d e - 130560a b d e + 34816a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 109395e +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 8 8 6 8 7 7 7 +--R 12870b e x + (102102a b e + 858b d e )x +--R + +--R 2 5 8 6 7 7 2 6 6 +--R (353430a b e + 7854a b d e - 924b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 5 +--R (696150a b e + 32130a b d e - 8568a b d e + 1008b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 +--R 850850a b e + 77350a b d e - 35700a b d e + 9520a b d e +--R + +--R 7 4 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 +--R 656370a b e + 121550a b d e - 88400a b d e + 40800a b d e +--R + +--R 6 4 4 7 5 3 +--R - 10880a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 +--R 306306a b e + 131274a b d e - 145860a b d e + 106080a b d e +--R + +--R 2 5 4 4 6 5 3 7 6 2 +--R - 48960a b d e + 13056a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 +--R 72930a e + 102102a b d e - 175032a b d e + 194480a b d e +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 +--R - 141440a b d e + 65280a b d e - 17408a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 72930a d e - 204204a b d e + 350064a b d e - 388960a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 +--R 282880a b d e - 130560a b d e + 34816a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 109395e +--R Type: Union(Expression(Integer),...) +--E 875 + +--S 876 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 877 + +)clear all + +--S 878 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1353 +r0:=14/3*b*(b*d-a*e)^6*(d+e*x)^(3/2)/e^8-42/5*b^2*(b*d-a*e)^5*_ + (d+e*x)^(5/2)/e^8+10*b^3*(b*d-a*e)^4*(d+e*x)^(7/2)/e^8-70/9*b^4*_ + (b*d-a*e)^3*(d+e*x)^(9/2)/e^8+42/11*b^5*(b*d-a*e)^2*(d+e*x)^(11/2)/e^8-_ + 14/13*b^6*(b*d-a*e)*(d+e*x)^(13/2)/e^8+2/15*b^7*(d+e*x)^(15/2)/e^8-_ + 2*(b*d-a*e)^7*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 858b e x + (6930a b e - 924b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (24570a b e - 7560a b d e + 1008b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (50050a b e - 27300a b d e + 8400a b d e - 1120b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 64350a b e - 57200a b d e + 31200a b d e - 9600a b d e +--R + +--R 7 4 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 54054a b e - 77220a b d e + 68640a b d e - 37440a b d e +--R + +--R 6 4 3 7 5 2 +--R 11520a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 30030a b e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 49920a b d e - 15360a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 12870a e - 60060a b d e + 144144a b d e - 205920a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 183040a b d e - 99840a b d e + 30720a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 6435e +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R 858b e x + (6930a b e - 924b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (24570a b e - 7560a b d e + 1008b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (50050a b e - 27300a b d e + 8400a b d e - 1120b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 64350a b e - 57200a b d e + 31200a b d e - 9600a b d e +--R + +--R 7 4 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 54054a b e - 77220a b d e + 68640a b d e - 37440a b d e +--R + +--R 6 4 3 7 5 2 +--R 11520a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 30030a b e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 49920a b d e - 15360a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 12870a e - 60060a b d e + 144144a b d e - 205920a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 183040a b d e - 99840a b d e + 30720a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 6435e +--R Type: Union(Expression(Integer),...) +--E 880 + +--S 881 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 882 + +)clear all + +--S 883 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1353 +r0:=-14*b^2*(b*d-a*e)^5*(d+e*x)^(3/2)/e^8+14*b^3*(b*d-a*e)^4*_ + (d+e*x)^(5/2)/e^8-10*b^4*(b*d-a*e)^3*(d+e*x)^(7/2)/e^8+14/3*b^5*_ + (b*d-a*e)^2*(d+e*x)^(9/2)/e^8-14/11*b^6*(b*d-a*e)*(d+e*x)^(11/2)/e^8+_ + 2/13*b^7*(d+e*x)^(13/2)/e^8+2*(b*d-a*e)^7/(e^8*sqrt(d+e*x))+_ + 14*b*(b*d-a*e)^6*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 66b e x + (546a b e - 84b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2002a b e - 728a b d e + 112b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (4290a b e - 2860a b d e + 1040a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (6006a b e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 6006a b e - 12012a b d e + 13728a b d e - 9152a b d e +--R + +--R 6 4 3 7 5 2 +--R 3328a b d e - 512b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 6006a b e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 36608a b d e - 13312a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 858a e + 12012a b d e - 48048a b d e + 96096a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 109824a b d e + 73216a b d e - 26624a b d e + 4096b d +--R / +--R 8 +-------+ +--R 429e \|e x + d +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R 66b e x + (546a b e - 84b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2002a b e - 728a b d e + 112b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (4290a b e - 2860a b d e + 1040a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (6006a b e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 6006a b e - 12012a b d e + 13728a b d e - 9152a b d e +--R + +--R 6 4 3 7 5 2 +--R 3328a b d e - 512b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 6006a b e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 36608a b d e - 13312a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 858a e + 12012a b d e - 48048a b d e + 96096a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 109824a b d e + 73216a b d e - 26624a b d e + 4096b d +--R / +--R 8 +-------+ +--R 429e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 885 + +--S 886 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 887 + +)clear all + +--S 888 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1353 +r0:=2/3*(b*d-a*e)^7/(e^8*(d+e*x)^(3/2))+70/3*b^3*(b*d-a*e)^4*_ + (d+e*x)^(3/2)/e^8-14*b^4*(b*d-a*e)^3*(d+e*x)^(5/2)/e^8+6*b^5*_ + (b*d-a*e)^2*(d+e*x)^(7/2)/e^8-14/9*b^6*(b*d-a*e)*(d+e*x)^(9/2)/e^8+_ + 2/11*b^7*(d+e*x)^(11/2)/e^8-14*b*(b*d-a*e)^6/(e^8*sqrt(d+e*x))-_ + 42*b^2*(b*d-a*e)^5*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 18b e x + (154a b e - 28b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (594a b e - 264a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1386a b e - 1188a b d e + 528a b d e - 96b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4158a b e - 13860a b d e + 22176a b d e - 19008a b d e +--R + +--R 6 4 3 7 5 2 +--R 8448a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 1386a b e + 16632a b d e - 55440a b d e + 88704a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 76032a b d e + 33792a b d e - 6144b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 66a e - 924a b d e + 11088a b d e - 36960a b d e + 59136a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 50688a b d e + 22528a b d e - 4096b d +--R / +--R 9 8 +-------+ +--R (99e x + 99d e )\|e x + d +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R 18b e x + (154a b e - 28b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (594a b e - 264a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1386a b e - 1188a b d e + 528a b d e - 96b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4158a b e - 13860a b d e + 22176a b d e - 19008a b d e +--R + +--R 6 4 3 7 5 2 +--R 8448a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 1386a b e + 16632a b d e - 55440a b d e + 88704a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 76032a b d e + 33792a b d e - 6144b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 66a e - 924a b d e + 11088a b d e - 36960a b d e + 59136a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 50688a b d e + 22528a b d e - 4096b d +--R / +--R 9 8 +-------+ +--R (99e x + 99d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 890 + +--S 891 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 892 + +)clear all + +--S 893 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1353 +r0:=2/5*(b*d-a*e)^7/(e^8*(d+e*x)^(5/2))-14/3*b*(b*d-a*e)^6/(e^8*_ + (d+e*x)^(3/2))-70/3*b^4*(b*d-a*e)^3*(d+e*x)^(3/2)/e^8+42/5*b^5*_ + (b*d-a*e)^2*(d+e*x)^(5/2)/e^8-2*b^6*(b*d-a*e)*(d+e*x)^(7/2)/e^8+_ + 2/9*b^7*(d+e*x)^(9/2)/e^8+42*b^2*(b*d-a*e)^5/(e^8*sqrt(d+e*x))+_ + 70*b^3*(b*d-a*e)^4*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (90a b e - 20b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1050a b e - 1260a b d e + 720a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (3150a b e - 8400a b d e + 10080a b d e - 5760a b d e + 1280b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1890a b e + 18900a b d e - 50400a b d e + 60480a b d e +--R + +--R 6 4 3 7 5 2 +--R - 34560a b d e + 7680b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 210a b e - 2520a b d e + 25200a b d e - 67200a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 80640a b d e - 46080a b d e + 10240b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 18a e - 84a b d e - 1008a b d e + 10080a b d e - 26880a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 32256a b d e - 18432a b d e + 4096b d +--R / +--R 10 2 9 2 8 +-------+ +--R (45e x + 90d e x + 45d e )\|e x + d +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (90a b e - 20b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1050a b e - 1260a b d e + 720a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (3150a b e - 8400a b d e + 10080a b d e - 5760a b d e + 1280b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1890a b e + 18900a b d e - 50400a b d e + 60480a b d e +--R + +--R 6 4 3 7 5 2 +--R - 34560a b d e + 7680b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 210a b e - 2520a b d e + 25200a b d e - 67200a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 80640a b d e - 46080a b d e + 10240b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 18a e - 84a b d e - 1008a b d e + 10080a b d e - 26880a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 32256a b d e - 18432a b d e + 4096b d +--R / +--R 10 2 9 2 8 +-------+ +--R (45e x + 90d e x + 45d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 895 + +--S 896 of 1353 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1353 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 897 + +)clear all + +--S 898 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1353 +r0:=2/3*(b*d-a*e)^2*(d+e*x)^(3/2)/b^3+2/5*(b*d-a*e)*(d+e*x)^(5/2)/b^2+_ + 2/7*(d+e*x)^(7/2)/b-2*(b*d-a*e)^(7/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/b^(9/2)+2*(b*d-a*e)^3*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (210a e - 630a b d e + 630a b d e - 210b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (- 42a b e + 132b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 224a b d e + 244b d e)x - 210a e + 700a b d e +--R + +--R 2 2 3 3 +--R - 812a b d e + 352b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 +-+ +--R 105b \|b +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 2 2 2 2 3 3 |- a e + b d +--R (105a e - 315a b d e + 315a b d e - 105b d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (- 42a b e + 132b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 224a b d e + 244b d e)x - 210a e + 700a b d e +--R + +--R 2 2 3 3 +--R - 812a b d e + 352b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b +--R , +--R +--R +---------+ +--R 3 3 2 2 2 2 3 3 |a e - b d +--R (210a e - 630a b d e + 630a b d e - 210b d ) |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (- 42a b e + 132b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 224a b d e + 244b d e)x - 210a e + 700a b d e +--R + +--R 2 2 3 3 +--R - 812a b d e + 352b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 900 + +--S 901 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 2 2 2 2 3 3 |- a e + b d +-+ +--R (a e - 3a b d e + 3a b d e - b d ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|b \|e x + d +--R (- 2a e + 6a b d e - 6a b d e + 2b d )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (- 2a e + 6a b d e - 6a b d e + 2b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 3 3 2 2 2 2 3 3 +-+ |a e - b d \|e x + d +--R (2a e - 6a b d e + 6a b d e - 2b d )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 904 + +)clear all + +--S 905 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R b x + a +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1353 +r0:=2/3*(b*d-a*e)*(d+e*x)^(3/2)/b^2+2/5*(d+e*x)^(5/2)/b-2*(b*d-a*e)^(5/2)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(7/2)+2*(b*d-a*e)^2*_ + sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|e x + d +--R (- 30a e + 60a b d e - 30b d )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (6b e x + (- 10a b e + 22b d e)x + 30a e - 70a b d e + 46b d )\|b +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a e + b d +--R (15a e - 30a b d e + 15b d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 10a b e + 22b d e)x + 30a e - 70a b d e + 46b d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b +--R , +--R +--R +---------+ +-------+ +--R 2 2 2 2 |a e - b d \|e x + d +--R (- 30a e + 60a b d e - 30b d ) |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 10a b e + 22b d e)x + 30a e - 70a b d e + 46b d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 907 + +--S 908 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a e + b d +-+ +--R (a e - 2a b d e + b d ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|e x + d +--R (2a e - 4a b d e + 2b d )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|e x + d +--R (2a e - 4a b d e + 2b d )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a e - b d \|e x + d +--R (- 2a e + 4a b d e - 2b d )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 911 + +)clear all + +--S 912 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------- +--R b x + a +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1353 +r0:=2/3*(d+e*x)^(3/2)/b-2*(b*d-a*e)^(3/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/b^(5/2)+2*(b*d-a*e)*sqrt(d+e*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (6a e - 6b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-+ +-------+ +--R (2b e x - 6a e + 8b d)\|b \|e x + d +--R / +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a e + b d +--R (3a e - 3b d) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R (2b e x - 6a e + 8b d)\|e x + d +--R / +--R 2 +--R 3b +--R , +--R +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R (6a e - 6b d) |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +-------+ +--R (2b e x - 6a e + 8b d)\|e x + d +--R / +--R 2 +--R 3b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 914 + +--S 915 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- a e + b d +-+ +--R (a e - b d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (- 2a e + 2b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (- 2a e + 2b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R (2a e - 2b d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 918 + +)clear all + +--S 919 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ---------- +--R b x + a +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1353 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(3/2)+_ + 2*sqrt(d+e*x)/b +--R +--R +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +-+ +-------+ +--R - 2\|- a e + b d atanh(--------------) + 2\|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) -------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R +-------+ +--R 2\|e x + d +--R / +--R b +--R , +--R +---------+ +-------+ +--R |a e - b d \|e x + d +-------+ +--R - 2 |--------- atan(------------ + 2\|e x + d +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R -----------------------------------------------] +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 921 + +--S 922 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R 2\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +---------+ +-------+ +--R +-----------+ \|b \|e x + d +-+ |a e - b d \|e x + d +--R 2\|- a e + b d atanh(--------------) - 2\|b |--------- atan(------------) +--R +-----------+ \| b +---------+ +--R \|- a e + b d |a e - b d +--R |--------- +--R \| b +--R -------------------------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 925 + +)clear all + +--S 926 of 1353 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|e x + d +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1353 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(sqrt(b)*sqrt(b*d-a*e)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +--R 2atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R (2) - ---------------------- +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R [---------------------------------------------------------------------, +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R 2atan(------------------------) +--R a e - b d +--R -------------------------------] +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R Type: Union(List(Expression(Integer)),...) +--E 928 + +--S 929 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R 2\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R 2\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R 2\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 932 + +)clear all + +--S 933 of 1353 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) --------------------------------------- +--R 2 +-------+ +--R (b e x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1353 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(3/2)+_ + 2/((b*d-a*e)*sqrt(d+e*x)) +--R +--R +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +-----------+ +--R 2\|b \|e x + d atanh(--------------) - 2\|- a e + b d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------ +--R +-----------+ +-------+ +--R (a e - b d)\|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R - 2 +--R / +--R +-------+ +--R (a e - b d)\|e x + d +--R , +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R - 2 |--------- \|e x + d atan(----------------------- - 2 +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R ----------------------------------------------------------] +--R +-------+ +--R (a e - b d)\|e x + d +--R Type: Union(List(Expression(Integer)),...) +--E 935 + +--S 936 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R - 2\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-----------+ +--R (a e - b d)\|- a e + b d +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R - 2\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-----------+ | b b\|e x + d +--R - 2\|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R +-----------+ +--R (a e - b d)\|- a e + b d +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 939 + +)clear all + +--S 940 of 1353 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1353 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2))-2*b^(3/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b*d-a*e)^(5/2)+2*b/((b*d-a*e)^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R (- 6b e x - 6b d)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R (6b e x - 2a e + 8b d)\|- a e + b d +--R / +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e)x + 3a d e - 6a b d e + 3b d ) +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | b +-------+ +--R (3b e x + 3b d) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 6b e x - 2a e + 8b d +--R / +--R 2 3 2 2 2 2 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e)x + 3a d e - 6a b d e + 3b d )\|e x + d +--R , +--R +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R (6b e x + 6b d) |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 6b e x - 2a e + 8b d +--R / +--R 2 3 2 2 2 2 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e)x + 3a d e - 6a b d e + 3b d )\|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 942 + +--S 943 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R b\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R 2b\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 2 2 2 +-----------+ +--R (a e - 2a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R 2b\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-----------+ | b b\|e x + d +--R 2b\|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 2 2 2 2 +-----------+ +--R (a e - 2a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 946 + +)clear all + +--S 947 of 1353 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1353 +r0:=2/5/((b*d-a*e)*(d+e*x)^(5/2))+2/3*b/((b*d-a*e)^2*(d+e*x)^(3/2))-_ + 2*b^(5/2)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(7/2)+_ + 2*b^2/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-+ +-------+ \|b \|e x + d +--R (30b e x + 60b d e x + 30b d )\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 30b e x + (10a b e - 70b d e)x - 6a e + 22a b d e - 46b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (30a d e - 90a b d e + 90a b d e - 30b d e)x + 15a d e - 45a b d e +--R + +--R 2 4 3 5 +--R 45a b d e - 15b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 2 | b +-------+ +--R (15b e x + 30b d e x + 15b d ) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R - 30b e x + (10a b e - 70b d e)x - 6a e + 22a b d e - 46b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30a d e - 90a b d e + 90a b d e - 30b d e)x + 15a d e +--R + +--R 2 3 2 2 4 3 5 +--R - 45a b d e + 45a b d e - 15b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +---------+ +--R 2 2 2 2 2 2 | b +-------+ +--R (- 30b e x - 60b d e x - 30b d ) |--------- \|e x + d +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R - 30b e x + (10a b e - 70b d e)x - 6a e + 22a b d e - 46b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30a d e - 90a b d e + 90a b d e - 30b d e)x + 15a d e +--R + +--R 2 3 2 2 4 3 5 +--R - 45a b d e + 45a b d e - 15b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 949 + +--S 950 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R b \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R - 2b \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R - 2b \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-----------+ | b b\|e x + d +--R - 2b \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 953 + +)clear all + +--S 954 of 1353 +t0:=(a+b*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1353 +r0:=21/4*e^2*(b*d-a*e)*(d+e*x)^(3/2)/b^4+63/20*e^2*(d+e*x)^(5/2)/b^3-_ + 9/4*e*(d+e*x)^(7/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(9/2)/(b*(a+b*x)^2)-_ + 63/4*e^2*(b*d-a*e)^(5/2)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + b^(11/2)+63/4*e^2*(b*d-a*e)^2*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (- 315a b e + 630a b d e - 315b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (- 630a b e + 1260a b d e - 630a b d e )x - 315a e + 630a b d e +--R + +--R 2 2 2 2 +--R - 315a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 8b e x + (- 24a b e + 56b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (168a b e - 408a b d e + 288b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (525a b e - 1239a b d e + 831a b d e - 85b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 735a b d e + 483a b d e - 45a b d e - 10b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 7 2 6 2 5 +-+ +--R (20b x + 40a b x + 20a b )\|b +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 4 3 3 4 2 2 2 +--R (315a b e - 630a b d e + 315b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (630a b e - 1260a b d e + 630a b d e )x + 315a e - 630a b d e +--R + +--R 2 2 2 2 +--R 315a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 16b e x + (- 48a b e + 112b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (336a b e - 816a b d e + 576b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1050a b e - 2478a b d e + 1662a b d e - 170b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1470a b d e + 966a b d e - 90a b d e - 20b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 40b x + 80a b x + 40a b +--R , +--R +--R 2 2 4 3 3 4 2 2 2 +--R (- 315a b e + 630a b d e - 315b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (- 630a b e + 1260a b d e - 630a b d e )x - 315a e + 630a b d e +--R + +--R 2 2 2 2 +--R - 315a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 4 4 3 4 4 3 3 +--R 8b e x + (- 24a b e + 56b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (168a b e - 408a b d e + 288b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (525a b e - 1239a b d e + 831a b d e - 85b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 735a b d e + 483a b d e - 45a b d e - 10b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 20b x + 40a b x + 20a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 956 + +--S 957 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 4 3 2 2 2 |- a e + b d +-+ +--R (63a e - 126a b d e + 63b d e ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 4 3 2 2 2 +-----------+ \|b \|e x + d +--R (126a e - 252a b d e + 126b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 4 3 2 2 2 +-----------+ \|b \|e x + d +--R (63a e - 126a b d e + 63b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 4 3 2 2 2 +-+ |a e - b d \|e x + d +--R (- 63a e + 126a b d e - 63b d e )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1353 +r0:=35/12*e^2*(d+e*x)^(3/2)/b^3-7/4*e*(d+e*x)^(5/2)/(b^2*(a+b*x))-_ + 1/2*(d+e*x)^(7/2)/(b*(a+b*x)^2)-35/4*e^2*(b*d-a*e)^(3/2)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+35/4*e^2*(b*d-a*e)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (105a b e - 105b d e )x + (210a b e - 210a b d e )x + 105a e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 8b e x + (- 56a b e + 80b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 175a b e + 238a b d e - 39b d e)x - 105a e + 140a b d e +--R + +--R 2 2 3 3 +--R - 21a b d e - 6b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 2 5 2 4 +-+ +--R (12b x + 24a b x + 12a b )\|b +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (105a b e - 105b d e )x + (210a b e - 210a b d e )x + 105a e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 16b e x + (- 112a b e + 160b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 350a b e + 476a b d e - 78b d e)x - 210a e + 280a b d e +--R + +--R 2 2 3 3 +--R - 42a b d e - 12b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 24b x + 48a b x + 24a b +--R , +--R +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (105a b e - 105b d e )x + (210a b e - 210a b d e )x + 105a e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 8b e x + (- 56a b e + 80b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 175a b e + 238a b d e - 39b d e)x - 105a e + 140a b d e +--R + +--R 2 2 3 3 +--R - 21a b d e - 6b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 12b x + 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 963 + +--S 964 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 |- a e + b d +-+ +--R (35a e - 35b d e ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 2 +-----------+ \|b \|e x + d +--R (- 70a e + 70b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 +-----------+ \|b \|e x + d +--R (- 35a e + 35b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 3 2 +-+ |a e - b d \|e x + d +--R (35a e - 35b d e )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 967 + +)clear all + +--S 968 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1353 +r0:=-5/4*e*(d+e*x)^(3/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(5/2)/(b*(a+b*x)^2)-_ + 15/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+_ + 15/4*e^2*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-----------+ \|b \|e x + d +--R (- 15b e x - 30a b e x - 15a e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-------+ +--R (8b e x + (25a b e - 9b d e)x + 15a e - 5a b d e - 2b d )\|b \|e x + d +--R / +--R 5 2 4 2 3 +-+ +--R (4b x + 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 2 |- a e + b d +--R (15b e x + 30a b e x + 15a e ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (16b e x + (50a b e - 18b d e)x + 30a e - 10a b d e - 4b d )\|e x + d +--R / +--R 5 2 4 2 3 +--R 8b x + 16a b x + 8a b +--R , +--R +--R +---------+ +-------+ +--R 2 2 2 2 2 2 |a e - b d \|e x + d +--R (- 15b e x - 30a b e x - 15a e ) |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (8b e x + (25a b e - 9b d e)x + 15a e - 5a b d e - 2b d )\|e x + d +--R / +--R 5 2 4 2 3 +--R 4b x + 8a b x + 4a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 970 + +--S 971 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 |- a e + b d +-+ +--R 15e |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-----------+ \|b \|e x + d +--R 30e \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-----------+ \|b \|e x + d +--R 15e \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-+ |a e - b d \|e x + d +--R - 15e \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 974 + +)clear all + +--S 975 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 975 + +--S 976 of 1353 +r0:=-1/2*(d+e*x)^(3/2)/(b*(a+b*x)^2)-3/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))-3/4*e*sqrt(d+e*x)/(b^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- 3b e x - 6a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (- 5b e x - 3a e - 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 4 2 3 2 2 +-----------+ +-+ +--R (4b x + 8a b x + 4a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R (3b e x + 6a b e x + 3a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (- 10b e x - 6a e - 4b d)\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 4 2 3 2 2 | 2 +--R (8b x + 16a b x + 8a b )\|- a b e + b d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 2 2 2 2 2 2 \|a b e - b d \|e x + d +--R (3b e x + 6a b e x + 3a e )atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (- 5b e x - 3a e - 2b d)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 4 2 3 2 2 | 2 +--R (4b x + 8a b x + 4a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 977 + +--S 978 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R 3e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R 6e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R 8b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R 3e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R 3e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R 4b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 981 + +)clear all + +--S 982 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1353 +r0:=1/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + (b*d-a*e)^(3/2))-1/2*sqrt(d+e*x)/(b*(a+b*x)^2)-1/4*e*_ + sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- b e x - 2a b e x - a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (b e x - a e + 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 3 4 2 2 2 3 3 2 2 +-----------+ +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|- a e + b d +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R (b e x + 2a b e x + a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (2b e x - 2a e + 4b d)\|- a b e + b d \|e x + d +--R / +--R 3 4 2 2 2 3 3 2 2 +--R ((8a b e - 8b d)x + (16a b e - 16a b d)x + 8a b e - 8a b d) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 2 2 2 2 2 2 \|a b e - b d \|e x + d +--R (b e x + 2a b e x + a e )atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (b e x - a e + 2b d)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 3 4 2 2 2 3 3 2 2 | 2 +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 984 + +--S 985 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R 2e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R (8a b e - 8b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R (4a b e - 4b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 988 + +)clear all + +--S 989 of 1353 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1353 +r0:=-3/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(5/2)*_ + sqrt(b))-1/2*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^2)+3/4*e*sqrt(d+e*x)/_ + ((b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- 3b e x - 6a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (3b e x + 5a e - 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 2 +--R 4a e - 8a b d e + 4a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 990 + +--S 991 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R (3b e x + 6a b e x + 3a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (6b e x + 10a e - 4b d)\|- a b e + b d \|e x + d +--R / +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (8a b e - 16a b d e + 8b d )x + (16a b e - 32a b d e + 16a b d )x +--R + +--R 4 2 3 2 2 2 +--R 8a e - 16a b d e + 8a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 2 2 2 2 2 2 \|a b e - b d \|e x + d +--R (3b e x + 6a b e x + 3a e )atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (3b e x + 5a e - 2b d)\|a b e - b d \|e x + d +--R / +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 2 +--R 4a e - 8a b d e + 4a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 991 + +--S 992 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R 3e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R 6e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 2 | 2 +-----------+ +-+ +--R (8a e - 16a b d e + 8b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R 3e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R 3e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 2 +-----------+ +-+ | 2 +--R (4a e - 8a b d e + 4b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 1353 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1353 +r0:=-15/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/_ + (b*d-a*e)^(7/2)+15/4*e^2/((b*d-a*e)^3*sqrt(d+e*x))+(-1/2)/((b*d-a*e)*_ + (a+b*x)^2*sqrt(d+e*x))+5/4*e/((b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-+ +-------+ \|b \|e x + d +--R (15b e x + 30a b e x + 15a e )\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 15b e x + (- 25a b e - 5b d e)x - 8a e - 9a b d e + 2b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 2 | b +-------+ +--R (15b e x + 30a b e x + 15a e ) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R - 30b e x + (- 50a b e - 10b d e)x - 16a e - 18a b d e + 4b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (8a b e - 24a b d e + 24a b d e - 8b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (16a b e - 48a b d e + 48a b d e - 16a b d )x + 8a e - 24a b d e +--R + +--R 3 2 2 2 3 3 +--R 24a b d e - 8a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +---------+ +--R 2 2 2 2 2 2 | b +-------+ +--R (- 15b e x - 30a b e x - 15a e ) |--------- \|e x + d +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R - 15b e x + (- 25a b e - 5b d e)x - 8a e - 9a b d e + 2b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 998 + +--S 999 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R 15e \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R - 30e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (8a e - 24a b d e + 24a b d e - 8b d )\|- a e + b d +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R - 15e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-----------+ | b b\|e x + d +--R - 15e \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (4a e - 12a b d e + 12a b d e - 4b d )\|- a e + b d +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1002 + +)clear all + +--S 1003 of 1353 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1353 +r0:=35/12*e^2/((b*d-a*e)^3*(d+e*x)^(3/2))+(-1/2)/((b*d-a*e)*(a+b*x)^2*_ + (d+e*x)^(3/2))+7/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2))-35/4*b^(3/2)*_ + e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+35/4*b*_ + e^2/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 210a b e - 105b d e )x +--R + +--R 2 3 2 2 2 2 +--R (- 105a b e - 210a b d e )x - 105a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (175a b e + 140b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (56a b e + 238a b d e + 21b d e)x - 8a e + 80a b d e + 39a b d e +--R + +--R 3 3 +--R - 6b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e + 24a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 105b e x + (210a b e + 105b d e )x + (105a b e + 210a b d e )x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 210b e x + (350a b e + 280b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (112a b e + 476a b d e + 42b d e)x - 16a e + 160a b d e + 78a b d e +--R + +--R 3 3 +--R - 12b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 48a b e - 168a b d e + 192a b d e - 48a b d e - 48a b d e +--R + +--R 6 5 +--R 24b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 24a e - 48a b d e - 48a b d e + 192a b d e - 168a b d e +--R + +--R 5 5 +--R 48a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 24a d e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 105b e x + (210a b e + 105b d e )x + (105a b e + 210a b d e )x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (175a b e + 140b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (56a b e + 238a b d e + 21b d e)x - 8a e + 80a b d e + 39a b d e +--R + +--R 3 3 +--R - 6b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e +--R + +--R 5 5 +--R 24a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1005 + +--S 1006 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R 35b e \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R 70b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (8a e - 32a b d e + 48a b d e - 32a b d e + 8b d )\|- a e + b d +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R 35b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-----------+ | b b\|e x + d +--R 35b e \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (4a e - 16a b d e + 24a b d e - 16a b d e + 4b d )\|- a e + b d +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1009 + +)clear all + +--S 1010 of 1353 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1353 +r0:=63/20*e^2/((b*d-a*e)^3*(d+e*x)^(5/2))+(-1/2)/((b*d-a*e)*(a+b*x)^2*_ + (d+e*x)^(5/2))+9/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2))+21/4*b*_ + e^2/((b*d-a*e)^4*(d+e*x)^(3/2))-63/4*b^(5/2)*e^2*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(11/2)+63/4*b^2*e^2/((b*d-a*e)^5*_ + sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (630a b e + 630b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (315a b e + 1260a b d e + 315b d e )x +--R + +--R 2 2 3 3 2 2 2 2 2 2 +--R (630a b d e + 630a b d e )x + 315a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 525a b e - 735b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 168a b e - 1239a b d e - 483b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (24a b e - 408a b d e - 831a b d e - 45b d e)x - 8a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 56a b d e - 288a b d e - 85a b d e + 10b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 20a b e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 7 5 2 +--R - 20b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 40a b e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 7 6 +--R - 40b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 20a e - 20a b d e - 180a b d e + 500a b d e - 500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 180a b d e + 20a b d e - 20b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 40a d e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 6 7 +--R - 40a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 20a d e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 2 5 7 +--R - 20a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (630a b e + 630b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (315a b e + 1260a b d e + 315b d e )x +--R + +--R 2 2 3 3 2 2 2 2 2 2 +--R (630a b d e + 630a b d e )x + 315a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R - 630b e x + (- 1050a b e - 1470b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 336a b e - 2478a b d e - 966b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (48a b e - 816a b d e - 1662a b d e - 90b d e)x - 16a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 112a b d e - 576a b d e - 170a b d e + 20b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 40a b e - 200a b d e + 400a b d e - 400a b d e + 200a b d e +--R + +--R 7 5 2 +--R - 40b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 80a b e - 320a b d e + 400a b d e - 400a b d e + 320a b d e +--R + +--R 7 6 +--R - 80b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 40a e - 40a b d e - 360a b d e + 1000a b d e - 1000a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 360a b d e + 40a b d e - 40b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 80a d e - 320a b d e + 400a b d e - 400a b d e + 320a b d e +--R + +--R 6 7 +--R - 80a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 40a d e - 200a b d e + 400a b d e - 400a b d e + 200a b d e +--R + +--R 2 5 7 +--R - 40a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 630a b e - 630b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 315a b e - 1260a b d e - 315b d e )x +--R + +--R 2 2 3 3 2 2 2 2 2 2 +--R (- 630a b d e - 630a b d e )x - 315a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 525a b e - 735b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 168a b e - 1239a b d e - 483b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (24a b e - 408a b d e - 831a b d e - 45b d e)x - 8a e + 56a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 288a b d e - 85a b d e + 10b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 20a b e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 7 5 2 +--R - 20b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 40a b e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 7 6 +--R - 40b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 20a e - 20a b d e - 180a b d e + 500a b d e - 500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 180a b d e + 20a b d e - 20b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 40a d e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 6 7 +--R - 40a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 20a d e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 2 5 7 +--R - 20a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1012 + +--S 1013 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 +-----------+ | b +--R 63b e \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R - 126b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (8a e - 40a b d e + 80a b d e - 80a b d e + 40a b d e - 8b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R - 63b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 2 +-----------+ | b b\|e x + d +--R - 63b e \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (4a e - 20a b d e + 40a b d e - 40a b d e + 20a b d e - 4b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1016 + +)clear all + +--S 1017 of 1353 +t0:=(a+b*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1353 +r0:=385/64*e^4*(d+e*x)^(3/2)/b^5-231/64*e^3*(d+e*x)^(5/2)/(b^4*(a+b*x))-_ + 33/32*e^2*(d+e*x)^(7/2)/(b^3*(a+b*x)^2)-11/24*e*(d+e*x)^(9/2)/(b^2*_ + (a+b*x)^3)-1/4*(d+e*x)^(11/2)/(b*(a+b*x)^4)-1155/64*e^4*(b*d-a*e)^(3/2)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(13/2)+1155/64*e^4*(b*d-_ + a*e)*sqrt(d+e*x)/b^6 +--R +--R +--R (2) +--R 4 5 5 4 4 2 3 5 4 4 3 +--R (3465a b e - 3465b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 +--R (20790a b e - 20790a b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 5 5 4 4 +--R 3465a e - 3465a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R 128b e x + (- 1408a b e + 2048b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 9207a b e + 12782a b d e - 2295b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 16863a b e + 22968a b d e - 3795a b d e - 1030b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 +--R - 12705a b e + 17094a b d e - 2673a b d e - 748a b d e +--R + +--R 5 4 +--R - 328b d e +--R * +--R x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 3465a e + 4620a b d e - 693a b d e - 198a b d e - 88a b d e +--R + +--R 5 5 +--R - 48b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|b +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 5 5 4 4 2 3 5 4 4 3 +--R (3465a b e - 3465b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 +--R (20790a b e - 20790a b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 5 5 4 4 +--R 3465a e - 3465a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 5 5 5 4 5 5 4 4 +--R 256b e x + (- 2816a b e + 4096b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 18414a b e + 25564a b d e - 4590b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 33726a b e + 45936a b d e - 7590a b d e - 2060b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 +--R - 25410a b e + 34188a b d e - 5346a b d e - 1496a b d e +--R + +--R 5 4 +--R - 656b d e +--R * +--R x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 6930a e + 9240a b d e - 1386a b d e - 396a b d e - 176a b d e +--R + +--R 5 5 +--R - 96b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 384b x + 1536a b x + 2304a b x + 1536a b x + 384a b +--R , +--R +--R 4 5 5 4 4 2 3 5 4 4 3 +--R (3465a b e - 3465b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 +--R (20790a b e - 20790a b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 5 5 4 4 +--R 3465a e - 3465a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 5 5 5 4 5 5 4 4 +--R 128b e x + (- 1408a b e + 2048b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 9207a b e + 12782a b d e - 2295b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 16863a b e + 22968a b d e - 3795a b d e - 1030b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 +--R - 12705a b e + 17094a b d e - 2673a b d e - 748a b d e +--R + +--R 5 4 +--R - 328b d e +--R * +--R x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 3465a e + 4620a b d e - 693a b d e - 198a b d e - 88a b d e +--R + +--R 5 5 +--R - 48b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 192b x + 768a b x + 1152a b x + 768a b x + 192a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1019 + +--S 1020 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 5 4 |- a e + b d +-+ +--R (1155a e - 1155b d e ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 5 4 +-----------+ \|b \|e x + d +--R (- 2310a e + 2310b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 +-+ +--R 128b \|b +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 5 4 +-----------+ \|b \|e x + d +--R (- 1155a e + 1155b d e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 5 4 +-+ |a e - b d \|e x + d +--R (1155a e - 1155b d e )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 6 +-+ +--R 64b \|b +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1023 + +)clear all + +--S 1024 of 1353 +t0:=(a+b*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1353 +r0:=-105/64*e^3*(d+e*x)^(3/2)/(b^4*(a+b*x))-21/32*e^2*(d+e*x)^(5/2)/_ + (b^3*(a+b*x)^2)-3/8*e*(d+e*x)^(7/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(9/2)/_ + (b*(a+b*x)^4)-315/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b*d-a*e)/b^(11/2)+315/64*e^4*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 315b e x - 1260a b e x - 1890a b e x - 1260a b e x - 315a e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 128b e x + (837a b e - 325b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1533a b e - 555a b d e - 210b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1155a b e - 399a b d e - 156a b d e - 88b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 105a b d e - 42a b d e - 24a b d e - 16b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +-+ +--R (64b x + 256a b x + 384a b x + 256a b x + 64a b )\|b +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (315b e x + 1260a b e x + 1890a b e x + 1260a b e x + 315a e ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 256b e x + (1674a b e - 650b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (3066a b e - 1110a b d e - 420b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (2310a b e - 798a b d e - 312a b d e - 176b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 210a b d e - 84a b d e - 48a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 128b x + 512a b x + 768a b x + 512a b x + 128a b +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 315b e x - 1260a b e x - 1890a b e x - 1260a b e x - 315a e ) +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 4 4 3 4 4 3 3 +--R 128b e x + (837a b e - 325b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1533a b e - 555a b d e - 210b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1155a b e - 399a b d e - 156a b d e - 88b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 105a b d e - 42a b d e - 24a b d e - 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 64b x + 256a b x + 384a b x + 256a b x + 64a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1026 + +--S 1027 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 |- a e + b d +-+ +--R 315e |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 4 +-----------+ \|b \|e x + d +--R 630e \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 128b \|b +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 +-----------+ \|b \|e x + d +--R 315e \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 4 +-+ |a e - b d \|e x + d +--R - 315e \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R 64b \|b +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1030 + +)clear all + +--S 1031 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1353 +r0:=-35/96*e^2*(d+e*x)^(3/2)/(b^3*(a+b*x)^2)-7/24*e*(d+e*x)^(5/2)/_ + (b^2*(a+b*x)^3)-1/4*(d+e*x)^(7/2)/(b*(a+b*x)^4)-35/64*e^4*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(b*d-a*e))-_ + 35/64*e^3*sqrt(d+e*x)/(b^4*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 105b e x - 420a b e x - 630a b e x - 420a b e x - 105a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 279b e x + (- 511a b e - 326b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 385a b e - 252a b d e - 200b d e)x - 105a e - 70a b d e +--R + +--R 2 2 3 3 +--R - 56a b d e - 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +-----------+ +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (105b e x + 420a b e x + 630a b e x + 420a b e x + 105a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R - 558b e x + (- 1022a b e - 652b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 770a b e - 504a b d e - 400b d e)x - 210a e - 140a b d e +--R + +--R 2 2 3 3 +--R - 112a b d e - 96b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 8 4 7 3 2 6 2 3 5 4 4 | 2 +--R (384b x + 1536a b x + 2304a b x + 1536a b x + 384a b )\|- a b e + b d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (105b e x + 420a b e x + 630a b e x + 420a b e x + 105a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 279b e x + (- 511a b e - 326b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 385a b e - 252a b d e - 200b d e)x - 105a e - 70a b d e +--R + +--R 2 2 3 3 +--R - 56a b d e - 48b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 8 4 7 3 2 6 2 3 5 4 4 | 2 +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1033 + +--S 1034 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 35e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 70e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 4 | 2 +-----------+ +-+ +--R 128b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 35e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b e - b d \|e x + d +--R 35e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 4 +-----------+ +-+ | 2 +--R 64b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1037 + +)clear all + +--S 1038 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1353 +r0:=-5/24*e*(d+e*x)^(3/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(5/2)/(b*(a+b*x)^4)+_ + 5/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*_ + (b*d-a*e)^(3/2))-5/32*e^2*sqrt(d+e*x)/(b^3*(a+b*x)^2)-5/64*e^3*_ + sqrt(d+e*x)/(b^3*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 15b e x - 60a b e x - 90a b e x - 60a b e x - 15a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (- 73a b e + 118b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 55a b e - 36a b d e + 136b d e)x - 15a e - 10a b d e +--R + +--R 2 2 3 3 +--R - 8a b d e + 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 8 4 2 6 7 3 +--R (192a b e - 192b d)x + (768a b e - 768a b d)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 4 4 +--R (1152a b e - 1152a b d)x + (768a b e - 768a b d)x + 192a b e - 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (- 146a b e + 236b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 110a b e - 72a b d e + 272b d e)x - 30a e - 20a b d e +--R + +--R 2 2 3 3 +--R - 16a b d e + 96b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 7 8 4 2 6 7 3 +--R (384a b e - 384b d)x + (1536a b e - 1536a b d)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 +--R (2304a b e - 2304a b d)x + (1536a b e - 1536a b d)x + 384a b e +--R + +--R 4 4 +--R - 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (- 73a b e + 118b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 55a b e - 36a b d e + 136b d e)x - 15a e - 10a b d e +--R + +--R 2 2 3 3 +--R - 8a b d e + 48b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 7 8 4 2 6 7 3 +--R (192a b e - 192b d)x + (768a b e - 768a b d)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 +--R (1152a b e - 1152a b d)x + (768a b e - 768a b d)x + 192a b e +--R + +--R 4 4 +--R - 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1040 + +--S 1041 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 5e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 10e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 4 | 2 +-----------+ +-+ +--R (128a b e - 128b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 5e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b e - b d \|e x + d +--R 5e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 3 4 +-----------+ +-+ | 2 +--R (64a b e - 64b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1353 +r0:=-1/4*(d+e*x)^(3/2)/(b*(a+b*x)^4)-3/64*e^4*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(5/2))-1/8*e*_ + sqrt(d+e*x)/(b^2*(a+b*x)^3)-1/32*e^2*sqrt(d+e*x)/(b^2*(b*d-a*e)*_ + (a+b*x)^2)+3/64*e^3*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 3b e x - 12a b e x - 18a b e x - 12a b e x - 3a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 3b e x + (11a b e - 2b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 11a b e + 44a b d e - 24b d e)x - 3a e - 2a b d e + 24a b d e +--R + +--R 3 3 +--R - 16b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 6 2 7 8 2 4 +--R (64a b e - 128a b d e + 64b d )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (256a b e - 512a b d e + 256a b d )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (384a b e - 768a b d e + 384a b d )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 4 4 2 +--R (256a b e - 512a b d e + 256a b d )x + 64a b e - 128a b d e + 64a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (3b e x + 12a b e x + 18a b e x + 12a b e x + 3a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b e x + (22a b e - 4b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 22a b e + 88a b d e - 48b d e)x - 6a e - 4a b d e +--R + +--R 2 2 3 3 +--R 48a b d e - 32b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 6 2 7 8 2 4 +--R (128a b e - 256a b d e + 128b d )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (512a b e - 1024a b d e + 512a b d )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (768a b e - 1536a b d e + 768a b d )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 +--R (512a b e - 1024a b d e + 512a b d )x + 128a b e - 256a b d e +--R + +--R 4 4 2 +--R 128a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (3b e x + 12a b e x + 18a b e x + 12a b e x + 3a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 3b e x + (11a b e - 2b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 11a b e + 44a b d e - 24b d e)x - 3a e - 2a b d e +--R + +--R 2 2 3 3 +--R 24a b d e - 16b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 6 2 7 8 2 4 +--R (64a b e - 128a b d e + 64b d )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (256a b e - 512a b d e + 256a b d )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (384a b e - 768a b d e + 384a b d )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 +--R (256a b e - 512a b d e + 256a b d )x + 64a b e - 128a b d e +--R + +--R 4 4 2 +--R 64a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1047 + +--S 1048 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 3e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 6e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 3 4 2 | 2 +-----------+ +-+ +--R (128a b e - 256a b d e + 128b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 3e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b e - b d \|e x + d +--R 3e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 3 4 2 +-----------+ +-+ | 2 +--R (64a b e - 128a b d e + 64b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1051 + +)clear all + +--S 1052 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R \|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1353 +r0:=5/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + (b*d-a*e)^(7/2))-1/4*sqrt(d+e*x)/(b*(a+b*x)^4)-1/24*e*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^3)+5/96*e^2*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x)^2)-_ + 5/64*e^3*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 15b e x - 60a b e x - 90a b e x - 60a b e x - 15a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (55a b e - 10b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (73a b e - 36a b d e + 8b d e)x - 15a e + 118a b d e - 136a b d e +--R + +--R 3 3 +--R 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (1152a b e - 3456a b d e + 3456a b d e - 1152a b d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x + 192a b e +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (110a b e - 20b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (146a b e - 72a b d e + 16b d e)x - 30a e + 236a b d e +--R + +--R 2 2 3 3 +--R - 272a b d e + 96b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (384a b e - 1152a b d e + 1152a b d e - 384b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (2304a b e - 6912a b d e + 6912a b d e - 2304a b d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (1536a b e - 4608a b d e + 4608a b d e - 1536a b d )x + 384a b e +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 1152a b d e + 1152a b d e - 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (55a b e - 10b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (73a b e - 36a b d e + 8b d e)x - 15a e + 118a b d e +--R + +--R 2 2 3 3 +--R - 136a b d e + 48b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (1152a b e - 3456a b d e + 3456a b d e - 1152a b d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x + 192a b e +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1054 + +--S 1055 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 5e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 10e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 3 2 2 2 3 2 4 3 | 2 +--R (128a b e - 384a b d e + 384a b d e - 128b d )\|- a b e + b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 5e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b e - b d \|e x + d +--R 5e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R 3 3 2 2 2 3 2 4 3 +-----------+ +-+ +--R (64a b e - 192a b d e + 192a b d e - 64b d )\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1058 + +)clear all + +--S 1059 of 1353 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1353 +r0:=-35/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*_ + sqrt(b))-1/4*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^4)+7/24*e*sqrt(d+e*x)/_ + ((b*d-a*e)^2*(a+b*x)^3)-35/96*e^2*sqrt(d+e*x)/((b*d-a*e)^3*(a+b*x)^2)+_ + 35/64*e^3*sqrt(d+e*x)/((b*d-a*e)^4*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 105b e x - 420a b e x - 630a b e x - 420a b e x - 105a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (385a b e - 70b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (511a b e - 252a b d e + 56b d e)x + 279a e - 326a b d e +--R + +--R 2 2 3 3 +--R 200a b d e - 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (1152a b e - 4608a b d e + 6912a b d e - 4608a b d e + 1152a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 192a e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (105b e x + 420a b e x + 630a b e x + 420a b e x + 105a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 210b e x + (770a b e - 140b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (1022a b e - 504a b d e + 112b d e)x + 558a e - 652a b d e +--R + +--R 2 2 3 3 +--R 400a b d e - 96b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (384a b e - 1536a b d e + 2304a b d e - 1536a b d e + 384b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 +--R 1536a b e - 6144a b d e + 9216a b d e - 6144a b d e +--R + +--R 7 4 +--R 1536a b d +--R * +--R 3 +--R x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 +--R 2304a b e - 9216a b d e + 13824a b d e - 9216a b d e +--R + +--R 2 6 4 +--R 2304a b d +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 +--R 1536a b e - 6144a b d e + 9216a b d e - 6144a b d e +--R + +--R 3 5 4 +--R 1536a b d +--R * +--R x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 384a e - 1536a b d e + 2304a b d e - 1536a b d e + 384a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (105b e x + 420a b e x + 630a b e x + 420a b e x + 105a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (385a b e - 70b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (511a b e - 252a b d e + 56b d e)x + 279a e - 326a b d e +--R + +--R 2 2 3 3 +--R 200a b d e - 48b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 +--R 1152a b e - 4608a b d e + 6912a b d e - 4608a b d e +--R + +--R 2 6 4 +--R 1152a b d +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 192a e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1061 + +--S 1062 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 35e \|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 70e \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (128a e - 512a b d e + 768a b d e - 512a b d e + 128b d ) +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|e x + d +--R 35e \|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b e - b d \|e x + d +--R 35e \|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (64a e - 256a b d e + 384a b d e - 256a b d e + 64b d )\|- a e + b d +--R * +--R +-----------+ +--R +-+ | 2 +--R \|b \|a b e - b d +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1065 + +)clear all + +--S 1066 of 1353 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 6 4 5 5 2 3 4 4 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (10a b e + 10a b d)x + (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1353 +r0:=-315/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-_ + a*e)^(11/2)+315/64*e^4/((b*d-a*e)^5*sqrt(d+e*x))+(-1/4)/((b*d-a*e)*_ + (a+b*x)^4*sqrt(d+e*x))+3/8*e/((b*d-a*e)^2*(a+b*x)^3*sqrt(d+e*x))-_ + 21/32*e^2/((b*d-a*e)^3*(a+b*x)^2*sqrt(d+e*x))+105/64*e^3/((b*d-a*e)^4*_ + (a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +-+ +--R (315b e x + 1260a b e x + 1890a b e x + 1260a b e x + 315a e )\|b +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 1155a b e - 105b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1533a b e - 399a b d e + 42b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 837a b e - 555a b d e + 156a b d e - 24b d e)x - 128a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 325a b d e + 210a b d e - 88a b d e + 16b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 64a b e - 320a b d e + 640a b d e - 640a b d e + 320a b d e +--R + +--R 9 5 +--R - 64b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 2 7 4 8 5 +--R 1280a b d e - 256a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 384a b e - 1920a b d e + 3840a b d e - 3840a b d e +--R + +--R 3 6 4 2 7 5 +--R 1920a b d e - 384a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 4 5 4 3 6 5 +--R 1280a b d e - 256a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 4 5 5 +--R 64a e - 320a b d e + 640a b d e - 640a b d e + 320a b d e - 64a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (315b e x + 1260a b e x + 1890a b e x + 1260a b e x + 315a e ) +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R - 630b e x + (- 2310a b e - 210b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 3066a b e - 798a b d e + 84b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 1674a b e - 1110a b d e + 312a b d e - 48b d e)x - 256a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 650a b d e + 420a b d e - 176a b d e + 32b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 +--R 128a b e - 640a b d e + 1280a b d e - 1280a b d e +--R + +--R 8 4 9 5 +--R 640a b d e - 128b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 512a b e - 2560a b d e + 5120a b d e - 5120a b d e +--R + +--R 2 7 4 8 5 +--R 2560a b d e - 512a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 768a b e - 3840a b d e + 7680a b d e - 7680a b d e +--R + +--R 3 6 4 2 7 5 +--R 3840a b d e - 768a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 512a b e - 2560a b d e + 5120a b d e - 5120a b d e +--R + +--R 4 5 4 3 6 5 +--R 2560a b d e - 512a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 128a e - 640a b d e + 1280a b d e - 1280a b d e + 640a b d e +--R + +--R 4 5 5 +--R - 128a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 315b e x - 1260a b e x - 1890a b e x - 1260a b e x - 315a e ) +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 1155a b e - 105b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1533a b e - 399a b d e + 42b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 837a b e - 555a b d e + 156a b d e - 24b d e)x - 128a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 325a b d e + 210a b d e - 88a b d e + 16b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 64a b e - 320a b d e + 640a b d e - 640a b d e + 320a b d e +--R + +--R 9 5 +--R - 64b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 2 7 4 8 5 +--R 1280a b d e - 256a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 384a b e - 1920a b d e + 3840a b d e - 3840a b d e +--R + +--R 3 6 4 2 7 5 +--R 1920a b d e - 384a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 4 5 4 3 6 5 +--R 1280a b d e - 256a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 64a e - 320a b d e + 640a b d e - 640a b d e + 320a b d e +--R + +--R 4 5 5 +--R - 64a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1068 + +--S 1069 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 +-----------+ | b +--R 315e \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 4 +-+ \|b \|e x + d +--R - 630e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 128a e - 640a b d e + 1280a b d e - 1280a b d e + 640a b d e +--R + +--R 5 5 +--R - 128b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 +-+ \|b \|e x + d +--R - 315e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 4 +-----------+ | b b\|e x + d +--R - 315e \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (64a e - 320a b d e + 640a b d e - 640a b d e + 320a b d e - 64b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1072 + +)clear all + +--S 1073 of 1353 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1353 +r0:=385/64*e^4/((b*d-a*e)^5*(d+e*x)^(3/2))+(-1/4)/((b*d-a*e)*(a+b*x)^4*_ + (d+e*x)^(3/2))+11/24*e/((b*d-a*e)^2*(a+b*x)^3*(d+e*x)^(3/2))-_ + 33/32*e^2/((b*d-a*e)^3*(a+b*x)^2*(d+e*x)^(3/2))+231/64*e^3/((b*d-a*e)^4*_ + (a+b*x)*(d+e*x)^(3/2))-1155/64*b^(3/2)*e^4*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b*d-a*e)^(13/2)+1155/64*b*e^4/((b*d-a*e)^6*sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 3465b e x + (- 13860a b e - 3465b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (- 20790a b e - 13860a b d e )x + (- 13860a b e - 20790a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (- 3465a b e - 13860a b d e )x - 3465a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (12705a b e + 4620b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (16863a b e + 17094a b d e + 693b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (9207a b e + 22968a b d e + 2673a b d e - 198b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (1408a b e + 12782a b d e + 3795a b d e - 748a b d e + 88b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 128a e + 2048a b d e + 2295a b d e - 1030a b d e + 328a b d e +--R + +--R 5 5 +--R - 48b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 768a b e - 4416a b d e + 10368a b d e - 12480a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 7680a b d e - 1728a b d e - 384a b d e + 192b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 1152a b e - 6144a b d e + 12672a b d e - 11520a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 1920a b d e + 4608a b d e - 3456a b d e + 768a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 768a b e - 3456a b d e + 4608a b d e + 1920a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 11520a b d e + 12672a b d e - 6144a b d e + 1152a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 192a e - 384a b d e - 1728a b d e + 7680a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 12480a b d e + 10368a b d e - 4416a b d e + 768a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e + 2880a b d e +--R + +--R 5 5 6 4 6 7 +--R - 1152a b d e + 192a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (13860a b e + 3465b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (20790a b e + 13860a b d e )x + (13860a b e + 20790a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (3465a b e + 13860a b d e )x + 3465a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 5 5 5 4 5 5 4 4 +--R 6930b e x + (25410a b e + 9240b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (33726a b e + 34188a b d e + 1386b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (18414a b e + 45936a b d e + 5346a b d e - 396b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2816a b e + 25564a b d e + 7590a b d e - 1496a b d e + 176b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 256a e + 4096a b d e + 4590a b d e - 2060a b d e + 656a b d e +--R + +--R 5 5 +--R - 96b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 384a b e - 2304a b d e + 5760a b d e - 7680a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 5760a b d e - 2304a b d e + 384b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 1536a b e - 8832a b d e + 20736a b d e - 24960a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 15360a b d e - 3456a b d e - 768a b d e + 384b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 2304a b e - 12288a b d e + 25344a b d e - 23040a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 3840a b d e + 9216a b d e - 6912a b d e + 1536a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 1536a b e - 6912a b d e + 9216a b d e + 3840a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 23040a b d e + 25344a b d e - 12288a b d e + 2304a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 384a e - 768a b d e - 3456a b d e + 15360a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 24960a b d e + 20736a b d e - 8832a b d e + 1536a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 +--R 384a d e - 2304a b d e + 5760a b d e - 7680a b d e +--R + +--R 6 4 5 2 5 5 6 4 6 7 +--R 5760a b d e - 2304a b d e + 384a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (13860a b e + 3465b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (20790a b e + 13860a b d e )x + (13860a b e + 20790a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (3465a b e + 13860a b d e )x + 3465a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (12705a b e + 4620b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (16863a b e + 17094a b d e + 693b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (9207a b e + 22968a b d e + 2673a b d e - 198b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (1408a b e + 12782a b d e + 3795a b d e - 748a b d e + 88b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 128a e + 2048a b d e + 2295a b d e - 1030a b d e + 328a b d e +--R + +--R 5 5 +--R - 48b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 768a b e - 4416a b d e + 10368a b d e - 12480a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 7680a b d e - 1728a b d e - 384a b d e + 192b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 1152a b e - 6144a b d e + 12672a b d e - 11520a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 1920a b d e + 4608a b d e - 3456a b d e + 768a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 768a b e - 3456a b d e + 4608a b d e + 1920a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 11520a b d e + 12672a b d e - 6144a b d e + 1152a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 192a e - 384a b d e - 1728a b d e + 7680a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 12480a b d e + 10368a b d e - 4416a b d e + 768a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 6 4 5 2 5 5 6 4 6 7 +--R 2880a b d e - 1152a b d e + 192a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1075 + +--S 1076 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 +-----------+ | b +--R 1155b e \|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 4 +-+ \|b \|e x + d +--R 2310b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 128a e - 768a b d e + 1920a b d e - 2560a b d e + 1920a b d e +--R + +--R 5 5 6 6 +--R - 768a b d e + 128b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1353 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 +-+ \|b \|e x + d +--R 1155b e \|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 4 +-----------+ | b b\|e x + d +--R 1155b e \|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 64a e - 384a b d e + 960a b d e - 1280a b d e + 960a b d e +--R + +--R 5 5 6 6 +--R - 384a b d e + 64b d +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1353 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1079 + +)clear all + +--S 1080 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1353 +r0:=-8/143*(b*d-a*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/1287*(b*d-a*e)^2*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+_ + b*x))+2/13*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 +--R 198b e x + (468a b e + 720b d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (286a e + 1768a b d e + 916b d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (1144a d e + 2392a b d e + 424b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (1716a d e + 1248a b d e + 6b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (1144a d e + 52a b d e - 8b d e)x + 286a d e - 104a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 6 2 5 5 +--R 198b e x + (468a b e + 720b d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (286a e + 1768a b d e + 916b d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (1144a d e + 2392a b d e + 424b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (1716a d e + 1248a b d e + 6b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (1144a d e + 52a b d e - 8b d e)x + 286a d e - 104a b d e + 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 1287e +--R Type: Union(Expression(Integer),...) +--E 1082 + +--S 1083 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 6 6 6 2 5 5 +--R - 198b e x + (- 468a b e - 720b d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (- 286a e - 1768a b d e - 916b d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (- 1144a d e - 2392a b d e - 424b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (- 1716a d e - 1248a b d e - 6b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (- 1144a d e - 52a b d e + 8b d e)x - 286a d e + 104a b d e - 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 6 7 2 6 3 5 6 +--R 198b e x + (666a b e + 720b d e )x +--R + +--R 2 6 2 5 3 2 4 5 +--R (754a b e + 2488a b d e + 916b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 4 +--R (286a e + 2912a b d e + 3308a b d e + 424b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 +--R (1144a d e + 4108a b d e + 1672a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 2 +--R (1716a d e + 2392a b d e + 58a b d e - 8b d e)x +--R + +--R 3 3 3 2 4 2 2 5 3 6 3 4 2 +--R (1144a d e + 338a b d e - 112a b d e + 16b d )x + 286a d e +--R + +--R 2 5 2 6 +--R - 104a b d e + 16a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 4 6 4 2 3 5 2 4 3 2 2 2 4 +--R b e x + (2a b e + 4b d e )x + (a e + 8a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 3 2 2 2 3 2 4 2 +--R (4a d e + 12a b d e + 4b d e)x + (6a d e + 8a b d e + b d )x +--R + +--R 2 3 4 2 4 +--R (4a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R - b e x + (- 3a b e - 4b d e )x + (- 3a b e - 12a b d e - 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (- a e - 12a b d e - 18a b d e - 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (- 4a d e - 18a b d e - 12a b d e - b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (- 6a d e - 12a b d e - 3a b d )x + (- 4a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1084 + +)clear all + +--S 1085 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1353 +r0:=-8/99*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/693*(b*d-a*e)^2*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+_ + b*x))+2/11*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 +--R 126b e x + (308a b e + 322b d e )x +--R + +--R 2 5 4 2 2 3 3 +--R (198a e + 836a b d e + 226b d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (594a d e + 660a b d e + 6b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (594a d e + 44a b d e - 8b d e)x + 198a d e - 88a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 5 2 4 4 +--R 126b e x + (308a b e + 322b d e )x +--R + +--R 2 5 4 2 2 3 3 +--R (198a e + 836a b d e + 226b d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (594a d e + 660a b d e + 6b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (594a d e + 44a b d e - 8b d e)x + 198a d e - 88a b d e + 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 693e +--R Type: Union(Expression(Integer),...) +--E 1087 + +--S 1088 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5 5 5 2 4 4 +--R - 126b e x + (- 308a b e - 322b d e )x +--R + +--R 2 5 4 2 2 3 3 +--R (- 198a e - 836a b d e - 226b d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (- 594a d e - 660a b d e - 6b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (- 594a d e - 44a b d e + 8b d e)x - 198a d e + 88a b d e - 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 5 6 2 5 3 4 5 +--R 126b e x + (434a b e + 322b d e )x +--R + +--R 2 5 2 4 3 2 3 4 +--R (506a b e + 1158a b d e + 226b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 3 +--R (198a e + 1430a b d e + 886a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 2 +--R (594a d e + 1254a b d e + 50a b d e - 8b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 3 2 +--R (594a d e + 242a b d e - 96a b d e + 16b d )x + 198a d e +--R + +--R 2 4 2 5 +--R - 88a b d e + 16a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R - b e x + (- 3a b e - 3b d e )x + (- 3a b e - 9a b d e - 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a e - 9a b d e - 9a b d e - b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 3a d e - 9a b d e - 3a b d )x + (- 3a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1089 + +)clear all + +--S 1090 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (1) (b e x + (a e + b d)x + a d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1353 +r0:=-8/63*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/315*(b*d-a*e)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 2/9*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 70b e x + (180a b e + 100b d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (126a e + 288a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (252a d e + 36a b d e - 8b d e)x + 126a d e - 72a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 2 3 3 +--R 70b e x + (180a b e + 100b d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (126a e + 288a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (252a d e + 36a b d e - 8b d e)x + 126a d e - 72a b d e + 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 1092 + +--S 1093 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 4 4 2 3 3 +--R - 70b e x + (- 180a b e - 100b d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (- 126a e - 288a b d e - 6b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 252a d e - 36a b d e + 8b d e)x - 126a d e + 72a b d e - 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 4 5 2 4 3 3 4 +--R 70b e x + (250a b e + 100b d e )x +--R + +--R 2 4 2 3 3 2 2 3 +--R (306a b e + 388a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 2 +--R (126a e + 540a b d e + 42a b d e - 8b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 +--R (252a d e + 162a b d e - 80a b d e + 16b d )x + 126a d e +--R + +--R 2 3 2 4 +--R - 72a b d e + 16a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - b e x + (- 3a b e - 2b d e)x + (- 3a b e - 6a b d e - b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- a e - 6a b d e - 3a b d )x + (- 2a d e - 3a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1094 + +)clear all + +--S 1095 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R +-------+ | 2 2 2 +--R (1) (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1353 +r0:=-8/35*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/105*(b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 2/7*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 30b e x + (84a b e + 6b d e )x + (70a e + 28a b d e - 8b d e)x +--R + +--R 2 2 2 2 3 +--R 70a d e - 56a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 30b e x + (84a b e + 6b d e )x + (70a e + 28a b d e - 8b d e)x +--R + +--R 2 2 2 2 3 +--R 70a d e - 56a b d e + 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 1097 + +--S 1098 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 3 3 2 2 2 +--R - 30b e x + (- 84a b e - 6b d e )x +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R (- 70a e - 28a b d e + 8b d e)x - 70a d e + 56a b d e - 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 3 4 2 3 3 2 3 +--R 30b e x + (114a b e + 6b d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (154a b e + 34a b d e - 8b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 +--R (70a e + 98a b d e - 64a b d e + 16b d )x + 70a d e - 56a b d e +--R + +--R 2 3 +--R 16a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + 2a b x + a +--R + +--R 3 4 2 3 3 2 2 2 3 2 +--R - b e x + (- 3a b e - b d)x + (- 3a b e - 3a b d)x + (- a e - 3a b d)x +--R + +--R 3 +--R - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1099 + +)clear all + +--S 1100 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1353 +r0:=-8/15*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+16/15*(b*d-_ + a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/5*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (6b e x + (20a b e - 8b d e)x + 30a e - 40a b d e + 16b d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (6b e x + (20a b e - 8b d e)x + 30a e - 40a b d e + 16b d )\|e x + d +--R ------------------------------------------------------------------------ +--R 3 +--R 15e +--R Type: Union(Expression(Integer),...) +--E 1102 + +--S 1103 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (- 6b e x + (- 20a b e + 8b d e)x - 30a e + 40a b d e - 16b d ) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R 6b e x + (26a b e - 8b d e)x + (50a b e - 48a b d e + 16b d )x +--R + +--R 3 2 2 2 2 +--R 30a e - 40a b d e + 16a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1104 + +)clear all + +--S 1105 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1353 +r0:=-2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*sqrt(d+e*x))+8/3*b*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^2-16/3*b*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2b e x + (12a b e - 8b d e)x - 6a e + 24a b d e - 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R 2b e x + (12a b e - 8b d e)x - 6a e + 24a b d e - 16b d +--R (3) ----------------------------------------------------------- +--R 3 +-------+ +--R 3e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1107 + +--S 1108 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (- 2b e x + (- 12a b e + 8b d e)x + 6a e - 24a b d e + 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 3 2 +--R 2b e x + (14a b e - 8b d e)x + (6a b e + 16a b d e - 16b d )x - 6a e +--R + +--R 2 2 2 +--R 24a b d e - 16a b d +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1109 + +)clear all + +--S 1110 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1353 +r0:=-2/3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^(3/2))+8/3*b*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*sqrt(d+e*x))+16/3*b*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 12a b e + 24b d e)x - 2a e - 8a b d e + 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R 6b e x + (- 12a b e + 24b d e)x - 2a e - 8a b d e + 16b d +--R (3) ------------------------------------------------------------- +--R 4 3 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1112 + +--S 1113 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (- 6b e x + (12a b e - 24b d e)x + 2a e + 8a b d e - 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R 6b e x + (- 6a b e + 24b d e)x + (- 14a b e + 16a b d e + 16b d )x +--R + +--R 3 2 2 2 2 +--R - 2a e - 8a b d e + 16a b d +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1114 + +)clear all + +--S 1115 of 1353 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1353 +r0:=-2/5*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^(5/2))-8/5*b*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^(3/2))-16/15*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 30b e x + (- 20a b e - 40b d e)x - 6a e - 8a b d e - 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 30b e x + (- 20a b e - 40b d e)x - 6a e - 8a b d e - 16b d +--R (3) ---------------------------------------------------------------- +--R 5 2 4 2 3 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1117 + +--S 1118 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R (30b e x + (20a b e + 40b d e)x + 6a e + 8a b d e + 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 30b e x + (- 50a b e - 40b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 26a b e - 48a b d e - 16b d )x - 6a e - 8a b d e - 16a b d +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )\|b x + 2a b x + a - b x - 3a b x - 3a b x - a +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1353 +r0:=-16/195*(b*d-a*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/15*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/6435*(b*d-_ + a*e)^3*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/45045*(b*d-_ + a*e)^4*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/715*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 6006b e x + (27720a b e + 14322b d e )x +--R + +--R 2 2 7 3 6 4 2 5 5 +--R (49140a b e + 68040a b d e + 8946b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 4 +--R (40040a b e + 125580a b d e + 44520a b d e + 70b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (12870a e + 108680a b d e + 88140a b d e + 600a b d e - 80b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (38610a d e + 85800a b d e + 2340a b d e - 720a b d e + 96b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 +--R (38610a d e + 5720a b d e - 3120a b d e + 960a b d e - 128b d e)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 12870a d e - 11440a b d e + 6240a b d e - 1920a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 7 7 3 7 4 6 6 +--R 6006b e x + (27720a b e + 14322b d e )x +--R + +--R 2 2 7 3 6 4 2 5 5 +--R (49140a b e + 68040a b d e + 8946b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 4 +--R (40040a b e + 125580a b d e + 44520a b d e + 70b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (12870a e + 108680a b d e + 88140a b d e + 600a b d e - 80b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (38610a d e + 85800a b d e + 2340a b d e - 720a b d e + 96b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 +--R (38610a d e + 5720a b d e - 3120a b d e + 960a b d e - 128b d e)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 12870a d e - 11440a b d e + 6240a b d e - 1920a b d e + 256b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 7 7 3 7 4 6 6 +--R - 6006b e x + (- 27720a b e - 14322b d e )x +--R + +--R 2 2 7 3 6 4 2 5 5 +--R (- 49140a b e - 68040a b d e - 8946b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 4 +--R (- 40040a b e - 125580a b d e - 44520a b d e - 70b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 12870a e - 108680a b d e - 88140a b d e - 600a b d e +--R + +--R 4 4 3 +--R 80b d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R - 38610a d e - 85800a b d e - 2340a b d e + 720a b d e +--R + +--R 4 5 2 +--R - 96b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R - 38610a d e - 5720a b d e + 3120a b d e - 960a b d e +--R + +--R 4 6 +--R 128b d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R - 12870a d e + 11440a b d e - 6240a b d e + 1920a b d e - 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 5 7 8 4 7 5 6 7 +--R 6006b e x + (33726a b e + 14322b d e )x +--R + +--R 2 3 7 4 6 5 2 5 6 +--R (76860a b e + 82362a b d e + 8946b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 5 +--R (89180a b e + 193620a b d e + 53466a b d e + 70b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 +--R 52910a b e + 234260a b d e + 132660a b d e + 670a b d e +--R + +--R 5 4 3 +--R - 80b d e +--R * +--R 4 +--R x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 12870a e + 147290a b d e + 173940a b d e + 2940a b d e +--R + +--R 4 4 3 5 5 2 +--R - 800a b d e + 96b d e +--R * +--R 3 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 +--R 38610a d e + 124410a b d e + 8060a b d e - 3840a b d e +--R + +--R 4 5 2 5 6 +--R 1056a b d e - 128b d e +--R * +--R 2 +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 +--R 38610a d e + 18590a b d e - 14560a b d e + 7200a b d e +--R + +--R 4 6 5 7 +--R - 2048a b d e + 256b d +--R * +--R x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 +--R 12870a d e - 11440a b d e + 6240a b d e - 1920a b d e + 256a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R - b e x + (- 5a b e - 3b d e )x + (- 10a b e - 15a b d e - 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 10a b e - 30a b d e - 15a b d e - b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 5a b e - 30a b d e - 30a b d e - 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- a e - 15a b d e - 30a b d e - 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 3a d e - 15a b d e - 10a b d )x + (- 3a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1353 +r0:=-16/143*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/13*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/3003*_ + (b*d-a*e)^3*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/15015*_ + (b*d-a*e)^4*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/429*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 6 6 3 6 4 5 5 +--R 2310b e x + (10920a b e + 2940b d e )x +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (20020a b e + 14560a b d e + 70b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (17160a b e + 28600a b d e + 520a b d e - 80b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (6006a e + 27456a b d e + 1716a b d e - 624a b d e + 96b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (12012a d e + 3432a b d e - 2288a b d e + 832a b d e - 128b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 6006a d e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 6 3 6 4 5 5 +--R 2310b e x + (10920a b e + 2940b d e )x +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (20020a b e + 14560a b d e + 70b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (17160a b e + 28600a b d e + 520a b d e - 80b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (6006a e + 27456a b d e + 1716a b d e - 624a b d e + 96b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (12012a d e + 3432a b d e - 2288a b d e + 832a b d e - 128b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 6006a d e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 15015e +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 6 6 3 6 4 5 5 +--R - 2310b e x + (- 10920a b e - 2940b d e )x +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (- 20020a b e - 14560a b d e - 70b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (- 17160a b e - 28600a b d e - 520a b d e + 80b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 +--R - 6006a e - 27456a b d e - 1716a b d e + 624a b d e +--R + +--R 4 4 2 +--R - 96b d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 +--R - 12012a d e - 3432a b d e + 2288a b d e - 832a b d e +--R + +--R 4 5 +--R 128b d e +--R * +--R x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R - 6006a d e + 6864a b d e - 4576a b d e + 1664a b d e - 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 5 6 7 4 6 5 5 6 +--R 2310b e x + (13230a b e + 2940b d e )x +--R + +--R 2 3 6 4 5 5 2 4 5 +--R (30940a b e + 17500a b d e + 70b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 4 +--R (37180a b e + 43160a b d e + 590a b d e - 80b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 23166a b e + 56056a b d e + 2236a b d e - 704a b d e +--R + +--R 5 4 2 +--R 96b d e +--R * +--R 3 +--R x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 6006a e + 39468a b d e + 5148a b d e - 2912a b d e +--R + +--R 4 4 2 5 5 +--R 928a b d e - 128b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 +--R 12012a d e + 9438a b d e - 9152a b d e + 5408a b d e +--R + +--R 4 5 5 6 +--R - 1792a b d e + 256b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 6006a d e - 6864a b d e + 4576a b d e - 1664a b d e + 256a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R - b e x + (- 5a b e - 2b d e)x + (- 10a b e - 10a b d e - b d )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 10a b e - 20a b d e - 5a b d )x +--R + +--R 4 2 3 2 2 3 2 3 5 2 4 3 2 2 2 +--R (- 5a b e - 20a b d e - 10a b d )x + (- a e - 10a b d e - 10a b d )x +--R + +--R 5 4 2 5 2 +--R (- 2a d e - 5a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1353 +r0:=-16/99*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/11*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/1155*_ + (b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/3465*_ + (b*d-a*e)^4*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/231*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 5 5 3 5 4 4 4 +--R 630b e x + (3080a b e + 70b d e )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (5940a b e + 440a b d e - 80b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (5544a b e + 1188a b d e - 528a b d e + 96b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (2310a e + 1848a b d e - 1584a b d e + 704a b d e - 128b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 2310a d e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 3 5 4 4 4 +--R 630b e x + (3080a b e + 70b d e )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (5940a b e + 440a b d e - 80b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (5544a b e + 1188a b d e - 528a b d e + 96b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (2310a e + 1848a b d e - 1584a b d e + 704a b d e - 128b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 2310a d e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 5 3 5 4 4 4 +--R - 630b e x + (- 3080a b e - 70b d e )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (- 5940a b e - 440a b d e + 80b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (- 5544a b e - 1188a b d e + 528a b d e - 96b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (- 2310a e - 1848a b d e + 1584a b d e - 704a b d e + 128b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R - 2310a d e + 3696a b d e - 3168a b d e + 1408a b d e - 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 5 5 6 4 5 5 4 5 +--R 630b e x + (3710a b e + 70b d e )x +--R + +--R 2 3 5 4 4 5 2 3 4 +--R (9020a b e + 510a b d e - 80b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (11484a b e + 1628a b d e - 608a b d e + 96b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (7854a b e + 3036a b d e - 2112a b d e + 800a b d e - 128b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R 2310a e + 4158a b d e - 5280a b d e + 3872a b d e +--R + +--R 4 4 5 5 +--R - 1536a b d e + 256b d +--R * +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 2310a d e - 3696a b d e + 3168a b d e - 1408a b d e + 256a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 6 4 5 5 2 3 4 4 +--R - b e x + (- 5a b e - b d)x + (- 10a b e - 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (- 10a b e - 10a b d)x + (- 5a b e - 10a b d)x + (- a e - 5a b d)x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1353 +r0:=-16/63*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^2+_ + 2/9*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e-_ + 128/315*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+_ + 256/315*(b*d-a*e)^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/105*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (360a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (756a b e - 432a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1680a b d e + 2016a b d e - 1152a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (360a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (756a b e - 432a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1680a b d e + 2016a b d e - 1152a b d e + 256b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 1137 + +--S 1138 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 70b e x + (- 360a b e + 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 756a b e + 432a b d e - 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 840a b e + 1008a b d e - 576a b d e + 128b d e)x - 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 1680a b d e - 2016a b d e + 1152a b d e - 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 70b e x + (430a b e - 80b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (1116a b e - 512a b d e + 96b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (1596a b e - 1440a b d e + 672a b d e - 128b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (1470a b e - 2688a b d e + 2592a b d e - 1280a b d e + 256b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 630a e - 1680a b d e + 2016a b d e - 1152a b d e + 256a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1139 + +)clear all + +--S 1140 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1353 +r0:=-2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*sqrt(d+e*x))+16/7*b*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^2+128/35*b*(b*d-a*e)^2*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-256/35*b*(b*d-a*e)^3*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-96/35*b*(b*d-a*e)*_ + (a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (56a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (280a b e - 560a b d e + 448a b d e - 128b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 560a b d e - 1120a b d e + 896a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (56a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (280a b e - 560a b d e + 448a b d e - 128b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 560a b d e - 1120a b d e + 896a b d e - 256b d +--R / +--R 5 +-------+ +--R 35e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1142 + +--S 1143 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 10b e x + (- 56a b e + 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 140a b e + 112a b d e - 32b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 280a b e + 560a b d e - 448a b d e + 128b d e)x + 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 560a b d e + 1120a b d e - 896a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 10b e x + (66a b e - 16b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (196a b e - 128a b d e + 32b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (420a b e - 672a b d e + 480a b d e - 128b d e)x +--R + +--R 4 4 2 3 2 2 4 3 5 4 5 4 4 3 +--R (210a b e - 672a b d e + 768a b d e - 256b d )x - 70a e + 560a b d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R - 1120a b d e + 896a b d e - 256a b d +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1144 + +)clear all + +--S 1145 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1353 +r0:=-2/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(3/2))-_ + 16/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*sqrt(d+e*x))-_ + 128/15*b^2*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+_ + 256/15*b^2*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*_ + (a+b*x))+32/5*b^2*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 6b e x + (40a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (180a b e - 240a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 120a b e + 720a b d e - 960a b d e + 384b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e + 480a b d e - 640a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 6b e x + (40a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (180a b e - 240a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 120a b e + 720a b d e - 960a b d e + 384b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e + 480a b d e - 640a b d e + 256b d +--R / +--R 6 5 +-------+ +--R (15e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1147 + +--S 1148 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 6b e x + (- 40a b e + 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 180a b e + 240a b d e - 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (120a b e - 720a b d e + 960a b d e - 384b d e)x + 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 80a b d e - 480a b d e + 640a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 6b e x + (46a b e - 16b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (220a b e - 256a b d e + 96b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (60a b e + 480a b d e - 864a b d e + 384b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 130a b e + 640a b d e - 480a b d e - 256a b d e + 256b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R - 10a e - 80a b d e + 480a b d e - 640a b d e + 256a b d +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1149 + +)clear all + +--S 1150 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1353 +r0:=-2/5*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(5/2))-_ + 16/15*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-32/5*b^2*_ + (a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*sqrt(d+e*x))+128/15*b^3*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-256/15*b^3*(b*d-a*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (120a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 180a b e + 720a b d e - 480b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 40a b e - 240a b d e + 960a b d e - 640b d e)x - 6a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 96a b d e + 384a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (120a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 180a b e + 720a b d e - 480b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 40a b e - 240a b d e + 960a b d e - 640b d e)x - 6a e - 16a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 96a b d e + 384a b d e - 256b d +--R / +--R 7 2 6 2 5 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1152 + +--S 1153 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 10b e x + (- 120a b e + 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (180a b e - 720a b d e + 480b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (40a b e + 240a b d e - 960a b d e + 640b d e)x + 6a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 16a b d e + 96a b d e - 384a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 10b e x + (130a b e - 80b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 60a b e + 640a b d e - 480b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 220a b e + 480a b d e + 480a b d e - 640b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 46a b e - 256a b d e + 864a b d e - 256a b d e - 256b d )x - 6a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 96a b d e + 384a b d e - 256a b d +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1154 + +)clear all + +--S 1155 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(9/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1353 +r0:=-2/7*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(7/2))-_ + 16/35*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ + 32/35*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(3/2))+_ + 128/35*b^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*sqrt(d+e*x))+_ + 256/35*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (- 280a b e + 560b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 140a b e - 560a b d e + 1120b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 56a b e - 112a b d e - 448a b d e + 896b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 32a b d e - 128a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 6 3 5 3 5 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (- 280a b e + 560b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 140a b e - 560a b d e + 1120b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 56a b e - 112a b d e - 448a b d e + 896b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 32a b d e - 128a b d e + 256b d +--R / +--R 8 3 7 2 2 6 3 5 +-------+ +--R (35e x + 105d e x + 105d e x + 35d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1157 + +--S 1158 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R - 70b e x + (280a b e - 560b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (140a b e + 560a b d e - 1120b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (56a b e + 112a b d e + 448a b d e - 896b d e)x + 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 16a b d e + 32a b d e + 128a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 2 3 4 5 2 2 3 +--R 70b e x + (- 210a b e + 560b d e )x + (- 420a b e + 1120b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 196a b e - 672a b d e + 672a b d e + 896b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 4 +--R (- 66a b e - 128a b d e - 480a b d e + 768a b d e + 256b d )x - 10a e +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 32a b d e - 128a b d e + 256a b d +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 6 3 5 3 5 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1159 + +)clear all + +--S 1160 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(11/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1353 +r0:=-2/9*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(9/2))-_ + 16/63*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(7/2))-_ + 32/105*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(5/2))-_ + 128/105*b^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(d+e*x)^(3/2))-_ + 256/315*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 630b e x + (- 840a b e - 1680b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 756a b e - 1008a b d e - 2016b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 360a b e - 432a b d e - 576a b d e - 1152b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e - 96a b d e - 128a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 315b e x + (315a e + 1260b d e )x + (1260a d e + 1890b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (1890a d e + 1260b d e )x + (1260a d e + 315b d e )x + 315a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 630b e x + (- 840a b e - 1680b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 756a b e - 1008a b d e - 2016b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 360a b e - 432a b d e - 576a b d e - 1152b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e - 96a b d e - 128a b d e - 256b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +-------+ +--R (315e x + 1260d e x + 1890d e x + 1260d e x + 315d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1162 + +--S 1163 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R 630b e x + (840a b e + 1680b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (756a b e + 1008a b d e + 2016b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (360a b e + 432a b d e + 576a b d e + 1152b d e)x + 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 80a b d e + 96a b d e + 128a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 630b e x + (- 1470a b e - 1680b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 1596a b e - 2688a b d e - 2016b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 1116a b e - 1440a b d e - 2592a b d e - 1152b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 430a b e - 512a b d e - 672a b d e - 1280a b d e - 256b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R - 70a e - 80a b d e - 96a b d e - 128a b d e - 256a b d +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 315b e x + (315a e + 1260b d e )x + (1260a d e + 1890b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (1890a d e + 1260b d e )x + (1260a d e + 315b d e )x + 315a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1164 + +)clear all + +--S 1165 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1353 +r0:=-2/11*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(11/2))-_ + 16/99*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(9/2))-32/231*b^2*_ + (a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(7/2))-128/693*b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(d+e*x)^(5/2))-256/3465*b^3*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 2310b e x + (- 5544a b e - 3696b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 5940a b e - 4752a b d e - 3168b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 3080a b e - 2640a b d e - 2112a b d e - 1408b d e)x - 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 560a b d e - 480a b d e - 384a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 6 10 9 5 +--R 3465b e x + (3465a e + 17325b d e )x +--R + +--R 9 2 8 4 2 8 3 7 3 +--R (17325a d e + 34650b d e )x + (34650a d e + 34650b d e )x +--R + +--R 3 7 4 6 2 4 6 5 5 5 5 +--R (34650a d e + 17325b d e )x + (17325a d e + 3465b d e )x + 3465a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 2310b e x + (- 5544a b e - 3696b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 5940a b e - 4752a b d e - 3168b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 3080a b e - 2640a b d e - 2112a b d e - 1408b d e)x - 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 560a b d e - 480a b d e - 384a b d e - 256b d +--R / +--R 10 5 9 4 2 8 3 3 7 2 4 6 +--R 3465e x + 17325d e x + 34650d e x + 34650d e x + 17325d e x +--R + +--R 5 5 +--R 3465d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1167 + +--S 1168 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 +--R 2310b e x + (5544a b e + 3696b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (5940a b e + 4752a b d e + 3168b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (3080a b e + 2640a b d e + 2112a b d e + 1408b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 560a b d e + 480a b d e + 384a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 2310b e x + (- 7854a b e - 3696b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 11484a b e - 8448a b d e - 3168b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 9020a b e - 7392a b d e - 5280a b d e - 1408b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 3710a b e - 3200a b d e - 2592a b d e - 1792a b d e - 256b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R - 630a e - 560a b d e - 480a b d e - 384a b d e - 256a b d +--R / +--R 10 6 10 9 5 +--R 3465b e x + (3465a e + 17325b d e )x +--R + +--R 9 2 8 4 2 8 3 7 3 +--R (17325a d e + 34650b d e )x + (34650a d e + 34650b d e )x +--R + +--R 3 7 4 6 2 4 6 5 5 5 5 +--R (34650a d e + 17325b d e )x + (17325a d e + 3465b d e )x + 3465a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 5 5 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a - b x +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 5a b x - 10a b x - 10a b x - 5a b x - a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1353 +r0:=-128/4199*(b*d-a*e)^3*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/323*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 24/323*(b*d-a*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/19*_ + (a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/138567*(b*d-_ + a*e)^5*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/969969*(b*d-_ + a*e)^6*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+768/46189*_ + (b*d-a*e)^4*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 9 9 5 9 6 8 8 +--R 102102b e x + (684684a b e + 234234b d e )x +--R + +--R 2 4 9 5 8 6 2 7 7 +--R (1939938a b e + 1597596a b d e + 138138b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 6 +--R (2984520a b e + 4626006a b d e + 965580a b d e + 462b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 5 3 6 +--R 2645370a b e + 7325640a b d e + 2889558a b d e + 4788a b d e +--R + +--R 6 4 5 +--R - 504b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 2 8 3 3 2 7 2 4 3 6 +--R 1293292a b e + 6760390a b d e + 4793320a b d e + 22610a b d e +--R + +--R 5 4 5 6 5 4 +--R - 5320a b d e + 560b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 +--R 277134a e + 3510364a b d e + 4744870a b d e + 64600a b d e +--R + +--R 2 4 4 5 5 5 4 6 6 3 +--R - 25840a b d e + 6080a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R 831402a d e + 2771340a b d e + 125970a b d e - 77520a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R 31008a b d e - 7296a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 2 7 5 3 6 4 2 4 5 3 3 5 4 +--R 831402a d e + 184756a b d e - 167960a b d e + 103360a b d e +--R + +--R 2 4 6 3 5 7 2 6 8 +--R - 41344a b d e + 9728a b d e - 1024b d e +--R * +--R x +--R + +--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 +--R 277134a d e - 369512a b d e + 335920a b d e - 206720a b d e +--R + +--R 2 4 7 2 5 8 6 9 +--R 82688a b d e - 19456a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 969969b e x + 969969a e +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 9 9 5 9 6 8 8 +--R 102102b e x + (684684a b e + 234234b d e )x +--R + +--R 2 4 9 5 8 6 2 7 7 +--R (1939938a b e + 1597596a b d e + 138138b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 6 +--R (2984520a b e + 4626006a b d e + 965580a b d e + 462b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 5 3 6 +--R 2645370a b e + 7325640a b d e + 2889558a b d e + 4788a b d e +--R + +--R 6 4 5 +--R - 504b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 2 8 3 3 2 7 2 4 3 6 +--R 1293292a b e + 6760390a b d e + 4793320a b d e + 22610a b d e +--R + +--R 5 4 5 6 5 4 +--R - 5320a b d e + 560b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 +--R 277134a e + 3510364a b d e + 4744870a b d e + 64600a b d e +--R + +--R 2 4 4 5 5 5 4 6 6 3 +--R - 25840a b d e + 6080a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R 831402a d e + 2771340a b d e + 125970a b d e - 77520a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R 31008a b d e - 7296a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 2 7 5 3 6 4 2 4 5 3 3 5 4 +--R 831402a d e + 184756a b d e - 167960a b d e + 103360a b d e +--R + +--R 2 4 6 3 5 7 2 6 8 +--R - 41344a b d e + 9728a b d e - 1024b d e +--R * +--R x +--R + +--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 +--R 277134a d e - 369512a b d e + 335920a b d e - 206720a b d e +--R + +--R 2 4 7 2 5 8 6 9 +--R 82688a b d e - 19456a b d e + 2048b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 969969e +--R Type: Union(Expression(Integer),...) +--E 1172 + +--S 1173 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 9 9 5 9 6 8 8 +--R - 102102b e x + (- 684684a b e - 234234b d e )x +--R + +--R 2 4 9 5 8 6 2 7 7 +--R (- 1939938a b e - 1597596a b d e - 138138b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 6 +--R (- 2984520a b e - 4626006a b d e - 965580a b d e - 462b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 +--R - 2645370a b e - 7325640a b d e - 2889558a b d e +--R + +--R 5 3 6 6 4 5 +--R - 4788a b d e + 504b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 2 8 3 3 2 7 +--R - 1293292a b e - 6760390a b d e - 4793320a b d e +--R + +--R 2 4 3 6 5 4 5 6 5 4 +--R - 22610a b d e + 5320a b d e - 560b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 +--R - 277134a e - 3510364a b d e - 4744870a b d e - 64600a b d e +--R + +--R 2 4 4 5 5 5 4 6 6 3 +--R 25840a b d e - 6080a b d e + 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R - 831402a d e - 2771340a b d e - 125970a b d e + 77520a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R - 31008a b d e + 7296a b d e - 768b d e +--R * +--R 2 +--R x +--R + +--R 6 2 7 5 3 6 4 2 4 5 3 3 5 4 +--R - 831402a d e - 184756a b d e + 167960a b d e - 103360a b d e +--R + +--R 2 4 6 3 5 7 2 6 8 +--R 41344a b d e - 9728a b d e + 1024b d e +--R * +--R x +--R + +--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 +--R - 277134a d e + 369512a b d e - 335920a b d e + 206720a b d e +--R + +--R 2 4 7 2 5 8 6 9 +--R - 82688a b d e + 19456a b d e - 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 7 9 10 6 9 7 8 9 +--R 102102b e x + (786786a b e + 234234b d e )x +--R + +--R 2 5 9 6 8 7 2 7 8 +--R (2624622a b e + 1831830a b d e + 138138b d e )x +--R + +--R 3 4 9 2 5 8 6 2 7 7 3 6 7 +--R (4924458a b e + 6223602a b d e + 1103718a b d e + 462b d e )x +--R + +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 +--R 5629890a b e + 11951646a b d e + 3855138a b d e + 5250a b d e +--R + +--R 7 4 5 +--R - 504b d e +--R * +--R 6 +--R x +--R + +--R 5 2 9 4 3 8 3 4 2 7 +--R 3938662a b e + 14086030a b d e + 7682878a b d e +--R + +--R 2 5 3 6 6 4 5 7 5 4 +--R 27398a b d e - 5824a b d e + 560b d e +--R * +--R 5 +--R x +--R + +--R 6 9 5 2 8 4 3 2 7 +--R 1570426a b e + 10270754a b d e + 9538190a b d e +--R + +--R 3 4 3 6 2 5 4 5 6 5 4 7 6 3 +--R 87210a b d e - 31160a b d e + 6640a b d e - 640b d e +--R * +--R 4 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 +--R 277134a e + 4341766a b d e + 7516210a b d e + 190570a b d e +--R + +--R 3 4 4 5 2 5 5 4 6 6 3 7 7 2 +--R - 103360a b d e + 37088a b d e - 7936a b d e + 768b d e +--R * +--R 3 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 +--R 831402a d e + 3602742a b d e + 310726a b d e - 245480a b d e +--R + +--R 3 4 5 4 2 5 6 3 6 7 2 7 8 +--R 134368a b d e - 48640a b d e + 10496a b d e - 1024b d e +--R * +--R 2 +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 +--R 831402a d e + 461890a b d e - 537472a b d e + 439280a b d e +--R + +--R 3 4 6 3 2 5 7 2 6 8 7 9 +--R - 248064a b d e + 92416a b d e - 20480a b d e + 2048b d +--R * +--R x +--R + +--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 +--R 277134a d e - 369512a b d e + 335920a b d e - 206720a b d e +--R + +--R 3 4 7 2 2 5 8 6 9 +--R 82688a b d e - 19456a b d e + 2048a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 969969b e x + 969969a e +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 3 9 5 3 6 2 8 2 4 3 5 2 6 2 7 +--R b e x + (6a b e + 3b d e )x + (15a b e + 18a b d e + 3b d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (20a b e + 45a b d e + 18a b d e + b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (15a b e + 60a b d e + 45a b d e + 6a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (6a b e + 45a b d e + 60a b d e + 15a b d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (a e + 18a b d e + 45a b d e + 20a b d )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (3a d e + 18a b d e + 15a b d )x + (3a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 3 10 6 3 7 2 9 +--R - b e x + (- 7a b e - 3b d e )x +--R + +--R 2 5 3 6 2 7 2 8 +--R (- 21a b e - 21a b d e - 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (- 35a b e - 63a b d e - 21a b d e - b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (- 35a b e - 105a b d e - 63a b d e - 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (- 21a b e - 105a b d e - 105a b d e - 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (- 7a b e - 63a b d e - 105a b d e - 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (- a e - 21a b d e - 63a b d e - 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (- 3a d e - 21a b d e - 21a b d )x + (- 3a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1353 +r0:=-128/2431*(b*d-a*e)^3*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/221*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 8/85*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/17*(a+_ + b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/51051*(b*d-a*e)^5*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/255255*(b*d-a*e)^6*(d+_ + e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/7293*(b*d-a*e)^4*_ + (a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 8 8 5 8 6 7 7 +--R 30030b e x + (204204a b e + 36036b d e )x +--R + +--R 2 4 8 5 7 6 2 6 6 +--R (589050a b e + 251328a b d e + 462b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (928200a b e + 749700a b d e + 4284a b d e - 504b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 +--R 850850a b e + 1237600a b d e + 17850a b d e - 4760a b d e +--R + +--R 6 4 4 +--R 560b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 +--R 437580a b e + 1215500a b d e + 44200a b d e - 20400a b d e +--R + +--R 5 4 4 6 5 3 +--R 5440a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 +--R 102102a e + 700128a b d e + 72930a b d e - 53040a b d e +--R + +--R 2 4 4 4 5 5 3 6 6 2 +--R 24480a b d e - 6528a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 +--R 204204a d e + 87516a b d e - 97240a b d e + 70720a b d e +--R + +--R 2 4 5 3 5 6 2 6 7 +--R - 32640a b d e + 8704a b d e - 1024b d e +--R * +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R 102102a d e - 175032a b d e + 194480a b d e - 141440a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R 65280a b d e - 17408a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 255255b e x + 255255a e +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 8 8 5 8 6 7 7 +--R 30030b e x + (204204a b e + 36036b d e )x +--R + +--R 2 4 8 5 7 6 2 6 6 +--R (589050a b e + 251328a b d e + 462b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (928200a b e + 749700a b d e + 4284a b d e - 504b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 +--R 850850a b e + 1237600a b d e + 17850a b d e - 4760a b d e +--R + +--R 6 4 4 +--R 560b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 +--R 437580a b e + 1215500a b d e + 44200a b d e - 20400a b d e +--R + +--R 5 4 4 6 5 3 +--R 5440a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 +--R 102102a e + 700128a b d e + 72930a b d e - 53040a b d e +--R + +--R 2 4 4 4 5 5 3 6 6 2 +--R 24480a b d e - 6528a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 +--R 204204a d e + 87516a b d e - 97240a b d e + 70720a b d e +--R + +--R 2 4 5 3 5 6 2 6 7 +--R - 32640a b d e + 8704a b d e - 1024b d e +--R * +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R 102102a d e - 175032a b d e + 194480a b d e - 141440a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R 65280a b d e - 17408a b d e + 2048b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 255255e +--R Type: Union(Expression(Integer),...) +--E 1177 + +--S 1178 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 8 8 5 8 6 7 7 +--R - 30030b e x + (- 204204a b e - 36036b d e )x +--R + +--R 2 4 8 5 7 6 2 6 6 +--R (- 589050a b e - 251328a b d e - 462b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (- 928200a b e - 749700a b d e - 4284a b d e + 504b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 +--R - 850850a b e - 1237600a b d e - 17850a b d e + 4760a b d e +--R + +--R 6 4 4 +--R - 560b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 +--R - 437580a b e - 1215500a b d e - 44200a b d e + 20400a b d e +--R + +--R 5 4 4 6 5 3 +--R - 5440a b d e + 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 +--R - 102102a e - 700128a b d e - 72930a b d e + 53040a b d e +--R + +--R 2 4 4 4 5 5 3 6 6 2 +--R - 24480a b d e + 6528a b d e - 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 +--R - 204204a d e - 87516a b d e + 97240a b d e - 70720a b d e +--R + +--R 2 4 5 3 5 6 2 6 7 +--R 32640a b d e - 8704a b d e + 1024b d e +--R * +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R - 102102a d e + 175032a b d e - 194480a b d e + 141440a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R - 65280a b d e + 17408a b d e - 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 7 8 9 6 8 7 7 8 +--R 30030b e x + (234234a b e + 36036b d e )x +--R + +--R 2 5 8 6 7 7 2 6 7 +--R (793254a b e + 287364a b d e + 462b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 6 +--R (1517250a b e + 1001028a b d e + 4746a b d e - 504b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 +--R 1779050a b e + 1987300a b d e + 22134a b d e - 5264a b d e +--R + +--R 7 4 4 +--R 560b d e +--R * +--R 5 +--R x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 +--R 1288430a b e + 2453100a b d e + 62050a b d e - 25160a b d e +--R + +--R 6 4 4 7 5 3 +--R 6000a b d e - 640b d e +--R * +--R 4 +--R x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 +--R 539682a b e + 1915628a b d e + 117130a b d e - 73440a b d e +--R + +--R 2 5 4 4 6 5 3 7 6 2 +--R 29920a b d e - 7168a b d e + 768b d e +--R * +--R 3 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 +--R 102102a e + 904332a b d e + 160446a b d e - 150280a b d e +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 +--R 95200a b d e - 39168a b d e + 9472a b d e - 1024b d e +--R * +--R 2 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 204204a d e + 189618a b d e - 272272a b d e + 265200a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 +--R - 174080a b d e + 73984a b d e - 18432a b d e + 2048b d +--R * +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 4 3 5 3 +--R 102102a d e - 175032a b d e + 194480a b d e - 141440a b d e +--R + +--R 3 4 6 2 2 5 7 6 8 +--R 65280a b d e - 17408a b d e + 2048a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 255255b e x + 255255a e +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 2 8 5 2 6 7 2 4 2 5 6 2 6 +--R b e x + (6a b e + 2b d e)x + (15a b e + 12a b d e + b d )x +--R + +--R 3 3 2 2 4 5 2 5 +--R (20a b e + 30a b d e + 6a b d )x +--R + +--R 4 2 2 3 3 2 4 2 4 +--R (15a b e + 40a b d e + 15a b d )x +--R + +--R 5 2 4 2 3 3 2 3 6 2 5 4 2 2 2 +--R (6a b e + 30a b d e + 20a b d )x + (a e + 12a b d e + 15a b d )x +--R + +--R 6 5 2 6 2 +--R (2a d e + 6a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R - b e x + (- 7a b e - 2b d e)x + (- 21a b e - 14a b d e - b d )x +--R + +--R 3 4 2 2 5 6 2 6 +--R (- 35a b e - 42a b d e - 7a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 +--R (- 35a b e - 70a b d e - 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 +--R (- 21a b e - 70a b d e - 35a b d )x +--R + +--R 6 2 5 2 4 3 2 3 7 2 6 5 2 2 2 +--R (- 7a b e - 42a b d e - 35a b d )x + (- a e - 14a b d e - 21a b d )x +--R + +--R 7 6 2 7 2 +--R (- 2a d e - 7a b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1179 + +)clear all + +--S 1180 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1353 +r0:=-128/1287*(b*d-a*e)^3*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/143*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 8/65*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/15*(a+_ + b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/15015*(b*d-_ + a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/45045*(b*d-_ + a*e)^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+_ + 256/3003*(b*d-a*e)^4*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 7 7 5 7 6 6 6 +--R 6006b e x + (41580a b e + 462b d e )x +--R + +--R 2 4 7 5 6 6 2 5 5 +--R (122850a b e + 3780a b d e - 504b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 4 +--R (200200a b e + 13650a b d e - 4200a b d e + 560b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 +--R 193050a b e + 28600a b d e - 15600a b d e + 4800a b d e +--R + +--R 6 4 3 +--R - 640b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 108108a b e + 38610a b d e - 34320a b d e + 18720a b d e +--R + +--R 5 4 3 6 5 2 +--R - 5760a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 30030a e + 36036a b d e - 51480a b d e + 45760a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 24960a b d e + 7680a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 30030a d e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R 49920a b d e - 15360a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 5 7 6 6 6 +--R 6006b e x + (41580a b e + 462b d e )x +--R + +--R 2 4 7 5 6 6 2 5 5 +--R (122850a b e + 3780a b d e - 504b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 4 +--R (200200a b e + 13650a b d e - 4200a b d e + 560b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 +--R 193050a b e + 28600a b d e - 15600a b d e + 4800a b d e +--R + +--R 6 4 3 +--R - 640b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 108108a b e + 38610a b d e - 34320a b d e + 18720a b d e +--R + +--R 5 4 3 6 5 2 +--R - 5760a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 30030a e + 36036a b d e - 51480a b d e + 45760a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 24960a b d e + 7680a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 30030a d e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R 49920a b d e - 15360a b d e + 2048b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 1182 + +--S 1183 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 7 5 7 6 6 6 +--R - 6006b e x + (- 41580a b e - 462b d e )x +--R + +--R 2 4 7 5 6 6 2 5 5 +--R (- 122850a b e - 3780a b d e + 504b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 4 +--R (- 200200a b e - 13650a b d e + 4200a b d e - 560b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 +--R - 193050a b e - 28600a b d e + 15600a b d e - 4800a b d e +--R + +--R 6 4 3 +--R 640b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R - 108108a b e - 38610a b d e + 34320a b d e - 18720a b d e +--R + +--R 5 4 3 6 5 2 +--R 5760a b d e - 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 30030a e - 36036a b d e + 51480a b d e - 45760a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 24960a b d e - 7680a b d e + 1024b d e +--R * +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 30030a d e + 72072a b d e - 102960a b d e + 91520a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R - 49920a b d e + 15360a b d e - 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 7 7 8 6 7 7 6 7 +--R 6006b e x + (47586a b e + 462b d e )x +--R + +--R 2 5 7 6 6 7 2 5 6 +--R (164430a b e + 4242a b d e - 504b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 5 +--R (323050a b e + 17430a b d e - 4704a b d e + 560b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 393250a b e + 42250a b d e - 19800a b d e + 5360a b d e +--R + +--R 7 4 3 +--R - 640b d e +--R * +--R 4 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 301158a b e + 67210a b d e - 49920a b d e + 23520a b d e +--R + +--R 6 4 3 7 5 2 +--R - 6400a b d e + 768b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 138138a b e + 74646a b d e - 85800a b d e + 64480a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 30720a b d e + 8448a b d e - 1024b d e +--R * +--R 2 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 30030a e + 66066a b d e - 123552a b d e + 148720a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 116480a b d e + 57600a b d e - 16384a b d e + 2048b d +--R * +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 +--R 30030a d e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 3 4 5 2 2 5 6 6 7 +--R 49920a b d e - 15360a b d e + 2048a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 7 5 6 6 2 4 5 5 +--R b e x + (6a b e + b d)x + (15a b e + 6a b d)x +--R + +--R 3 3 2 4 4 4 2 3 3 3 5 4 2 2 +--R (20a b e + 15a b d)x + (15a b e + 20a b d)x + (6a b e + 15a b d)x +--R + +--R 6 5 6 +--R (a e + 6a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 8 6 7 7 2 5 6 6 +--R - b e x + (- 7a b e - b d)x + (- 21a b e - 7a b d)x +--R + +--R 3 4 2 5 5 4 3 3 4 4 +--R (- 35a b e - 21a b d)x + (- 35a b e - 35a b d)x +--R + +--R 5 2 4 3 3 6 5 2 2 7 6 7 +--R (- 21a b e - 35a b d)x + (- 7a b e - 21a b d)x + (- a e - 7a b d)x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1184 + +)clear all + +--S 1185 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1353 +r0:=-640/3003*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+_ + 80/429*(b*d-a*e)^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3-_ + 24/143*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e^2+2/13*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e-1024/3003*(b*d-a*e)^5*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/3003*(b*d-a*e)^6*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/1001*(b*d-_ + a*e)^4*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (3276a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (10010a b e - 3640a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (17160a b e - 11440a b d e + 4160a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 18018a b e - 20592a b d e + 13728a b d e - 4992a b d e +--R + +--R 6 4 2 +--R 768b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 12012a b e - 24024a b d e + 27456a b d e - 18304a b d e +--R + +--R 5 4 2 6 5 +--R 6656a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 6006a e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 36608a b d e - 13312a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 3003b e x + 3003a e +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (3276a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (10010a b e - 3640a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (17160a b e - 11440a b d e + 4160a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 18018a b e - 20592a b d e + 13728a b d e - 4992a b d e +--R + +--R 6 4 2 +--R 768b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 12012a b e - 24024a b d e + 27456a b d e - 18304a b d e +--R + +--R 5 4 2 6 5 +--R 6656a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 6006a e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 36608a b d e - 13312a b d e + 2048b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 3003e +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 462b e x + (- 3276a b e + 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 10010a b e + 3640a b d e - 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 17160a b e + 11440a b d e - 4160a b d e + 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 18018a b e + 20592a b d e - 13728a b d e + 4992a b d e +--R + +--R 6 4 2 +--R - 768b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 12012a b e + 24024a b d e - 27456a b d e + 18304a b d e +--R + +--R 5 4 2 6 5 +--R - 6656a b d e + 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 6006a e + 24024a b d e - 48048a b d e + 54912a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 36608a b d e + 13312a b d e - 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 462b e x + (3738a b e - 504b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (13286a b e - 4144a b d e + 560b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (27170a b e - 15080a b d e + 4720a b d e - 640b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R 35178a b e - 32032a b d e + 17888a b d e - 5632a b d e +--R + +--R 7 4 2 +--R 768b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R 30030a b e - 44616a b d e + 41184a b d e - 23296a b d e +--R + +--R 6 4 2 7 5 +--R 7424a b d e - 1024b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 18018a b e - 48048a b d e + 75504a b d e - 73216a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 43264a b d e - 14336a b d e + 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 +--R 6006a e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 3 4 4 2 2 5 5 6 6 +--R 36608a b d e - 13312a b d e + 2048a b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 7 +--R 3003b e x + 3003a e +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1353 +r0:=-2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*sqrt(d+e*x))+640/231*b*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4-80/33*b*(b*d-a*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3+24/11*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e^2+1024/231*b*(b*d-a*e)^4*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-2048/231*b*(b*d-a*e)^5*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-256/77*b*(b*d-a*e)^3*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (308a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (990a b e - 440a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1848a b e - 1584a b d e + 704a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 2772a b e - 9240a b d e + 14784a b d e - 12672a b d e +--R + +--R 5 4 2 6 5 +--R 5632a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 462a e + 5544a b d e - 18480a b d e + 29568a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 25344a b d e + 11264a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +-------+ +--R (231b e x + 231a e )\|e x + d +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (308a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (990a b e - 440a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1848a b e - 1584a b d e + 704a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 2772a b e - 9240a b d e + 14784a b d e - 12672a b d e +--R + +--R 5 4 2 6 5 +--R 5632a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 462a e + 5544a b d e - 18480a b d e + 29568a b d e - 25344a b d e +--R + +--R 5 5 6 6 +--R 11264a b d e - 2048b d +--R / +--R 7 +-------+ +--R 231e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 42b e x + (- 308a b e + 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 990a b e + 440a b d e - 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1848a b e + 1584a b d e - 704a b d e + 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 2310a b e + 3696a b d e - 3168a b d e + 1408a b d e +--R + +--R 6 4 2 +--R - 256b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 2772a b e + 9240a b d e - 14784a b d e + 12672a b d e +--R + +--R 5 4 2 6 5 +--R - 5632a b d e + 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 462a e - 5544a b d e + 18480a b d e - 29568a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 25344a b d e - 11264a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 42b e x + (350a b e - 56b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (1298a b e - 496a b d e + 80b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (2838a b e - 2024a b d e + 784a b d e - 128b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (4158a b e - 5280a b d e + 3872a b d e - 1536a b d e + 256b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R 5082a b e - 12936a b d e + 17952a b d e - 14080a b d e +--R + +--R 6 4 2 7 5 +--R 5888a b d e - 1024b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 2310a b e - 3696a b d e - 3696a b d e + 16896a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 19712a b d e + 10240a b d e - 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 462a e + 5544a b d e - 18480a b d e + 29568a b d e - 25344a b d e +--R + +--R 2 5 5 6 6 +--R 11264a b d e - 2048a b d +--R / +--R 7 7 +-------+ +--R (231b e x + 231a e )\|e x + d +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1353 +r0:=-2/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(3/2))-8*b*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*sqrt(d+e*x))-640/63*b^2*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+80/9*b^2*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3-1024/63*b^2*(b*d-a*e)^3*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/63*b^2*(b*d-a*e)^4*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/21*b^2*(b*d-a*e)^2*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (108a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (1890a b e - 5040a b d e + 6048a b d e - 3456a b d e + 768b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 756a b e + 7560a b d e - 20160a b d e + 24192a b d e +--R + +--R 5 4 2 6 5 +--R - 13824a b d e + 3072b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 504a b d e + 5040a b d e - 13440a b d e + 16128a b d e +--R + +--R 5 5 6 6 +--R - 9216a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (108a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (1890a b e - 5040a b d e + 6048a b d e - 3456a b d e + 768b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 756a b e + 7560a b d e - 20160a b d e + 24192a b d e +--R + +--R 5 4 2 6 5 +--R - 13824a b d e + 3072b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 504a b d e + 5040a b d e - 13440a b d e + 16128a b d e +--R + +--R 5 5 6 6 +--R - 9216a b d e + 2048b d +--R / +--R 8 7 +-------+ +--R (63e x + 63d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 14b e x + (- 108a b e + 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 378a b e + 216a b d e - 48b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 840a b e + 1008a b d e - 576a b d e + 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1890a b e + 5040a b d e - 6048a b d e + 3456a b d e +--R + +--R 6 4 2 +--R - 768b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 756a b e - 7560a b d e + 20160a b d e - 24192a b d e +--R + +--R 5 4 2 6 5 +--R 13824a b d e - 3072b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 42a e + 504a b d e - 5040a b d e + 13440a b d e - 16128a b d e +--R + +--R 5 5 6 6 +--R 9216a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 14b e x + (122a b e - 24b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (486a b e - 240a b d e + 48b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (1218a b e - 1224a b d e + 624a b d e - 128b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (2730a b e - 6048a b d e + 6624a b d e - 3584a b d e + 768b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R 1134a b e + 2520a b d e - 14112a b d e + 20736a b d e +--R + +--R 6 4 2 7 5 +--R - 13056a b d e + 3072b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 798a b e + 7056a b d e - 15120a b d e + 10752a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 2304a b d e - 6144a b d e + 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 42a e - 504a b d e + 5040a b d e - 13440a b d e + 16128a b d e +--R + +--R 2 5 5 6 6 +--R - 9216a b d e + 2048a b d +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1353 +r0:=-2/5*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(5/2))-8/5*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(3/2))-16*b^2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*sqrt(d+e*x))+128/7*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/e^4+1024/35*b^3*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6-2048/35*b^3*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x))-768/35*b^3*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (84a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (350a b e - 280a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1400a b e - 2800a b d e + 2240a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1050a b e + 8400a b d e - 16800a b d e + 13440a b d e +--R + +--R 6 4 2 +--R - 3840b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 140a b e - 1400a b d e + 11200a b d e - 22400a b d e +--R + +--R 5 4 2 6 5 +--R 17920a b d e - 5120b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 56a b d e - 560a b d e + 4480a b d e - 8960a b d e +--R + +--R 5 5 6 6 +--R 7168a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R (35b e x + (35a e + 70b d e )x + (70a d e + 35b d e )x + 35a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (84a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (350a b e - 280a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1400a b e - 2800a b d e + 2240a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1050a b e + 8400a b d e - 16800a b d e + 13440a b d e +--R + +--R 6 4 2 +--R - 3840b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 140a b e - 1400a b d e + 11200a b d e - 22400a b d e +--R + +--R 5 4 2 6 5 +--R 17920a b d e - 5120b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 56a b d e - 560a b d e + 4480a b d e - 8960a b d e +--R + +--R 5 5 6 6 +--R 7168a b d e - 2048b d +--R / +--R 9 2 8 2 7 +-------+ +--R (35e x + 70d e x + 35d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 10b e x + (- 84a b e + 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 350a b e + 280a b d e - 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1400a b e + 2800a b d e - 2240a b d e + 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 1050a b e - 8400a b d e + 16800a b d e - 13440a b d e +--R + +--R 6 4 2 +--R 3840b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 140a b e + 1400a b d e - 11200a b d e + 22400a b d e +--R + +--R 5 4 2 6 5 +--R - 17920a b d e + 5120b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 14a e + 56a b d e + 560a b d e - 4480a b d e + 8960a b d e +--R + +--R 5 5 6 6 +--R - 7168a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 10b e x + (94a b e - 24b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (434a b e - 304a b d e + 80b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (1750a b e - 3080a b d e + 2320a b d e - 640b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 3 +--R (350a b e + 5600a b d e - 14560a b d e + 12800a b d e - 3840b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 1190a b e + 7000a b d e - 5600a b d e - 8960a b d e +--R + +--R 6 4 2 7 5 +--R 14080a b d e - 5120b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 154a b e - 1456a b d e + 10640a b d e - 17920a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 8960a b d e + 2048a b d e - 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 14a e - 56a b d e - 560a b d e + 4480a b d e - 8960a b d e +--R + +--R 2 5 5 6 6 +--R 7168a b d e - 2048a b d +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R (35b e x + (35a e + 70b d e )x + (70a d e + 35b d e )x + 35a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(9/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1353 +r0:=-16/7*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(3/2))-_ + 2/7*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(7/2))-24/35*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(5/2))-128/7*b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^4*sqrt(d+e*x))-1024/35*b^4*(b*d-a*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/35*b^4*(b*d-a*e)^2*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+768/35*b^4*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (140a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (1050a b e - 1400a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1400a b e + 8400a b d e - 11200a b d e + 4480b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 350a b e - 2800a b d e + 16800a b d e - 22400a b d e +--R + +--R 6 4 2 +--R 8960b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 84a b e - 280a b d e - 2240a b d e + 13440a b d e +--R + +--R 5 4 2 6 5 +--R - 17920a b d e + 7168b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e - 24a b d e - 80a b d e - 640a b d e + 3840a b d e +--R + +--R 5 5 6 6 +--R - 5120a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 8 3 7 3 7 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (140a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (1050a b e - 1400a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1400a b e + 8400a b d e - 11200a b d e + 4480b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 350a b e - 2800a b d e + 16800a b d e - 22400a b d e +--R + +--R 6 4 2 +--R 8960b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 84a b e - 280a b d e - 2240a b d e + 13440a b d e +--R + +--R 5 4 2 6 5 +--R - 17920a b d e + 7168b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e - 24a b d e - 80a b d e - 640a b d e + 3840a b d e +--R + +--R 5 5 6 6 +--R - 5120a b d e + 2048b d +--R / +--R 10 3 9 2 2 8 3 7 +-------+ +--R (35e x + 105d e x + 105d e x + 35d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 14b e x + (- 140a b e + 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1050a b e + 1400a b d e - 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1400a b e - 8400a b d e + 11200a b d e - 4480b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 350a b e + 2800a b d e - 16800a b d e + 22400a b d e +--R + +--R 6 4 2 +--R - 8960b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 84a b e + 280a b d e + 2240a b d e - 13440a b d e +--R + +--R 5 4 2 6 5 +--R 17920a b d e - 7168b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 10a e + 24a b d e + 80a b d e + 640a b d e - 3840a b d e +--R + +--R 5 5 6 6 +--R 5120a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 14b e x + (154a b e - 56b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (1190a b e - 1456a b d e + 560b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 350a b e + 7000a b d e - 10640a b d e + 4480b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 1750a b e + 5600a b d e + 5600a b d e - 17920a b d e +--R + +--R 7 4 2 +--R 8960b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 434a b e - 3080a b d e + 14560a b d e - 8960a b d e +--R + +--R 6 4 2 7 5 +--R - 8960a b d e + 7168b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 94a b e - 304a b d e - 2320a b d e + 12800a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 14080a b d e + 2048a b d e + 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 10a e - 24a b d e - 80a b d e - 640a b d e + 3840a b d e +--R + +--R 2 5 5 6 6 +--R - 5120a b d e + 2048a b d +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 8 3 7 3 7 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(11/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1210 + +--S 1211 of 1353 +r0:=-16/21*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(5/2))-_ + 128/63*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(3/2))-2/9*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(9/2))-8/21*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^(7/2))-256/21*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*sqrt(d+e*x))+1024/63*b^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6-2048/63*b^5*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (756a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1890a b e + 7560a b d e - 5040b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 840a b e - 5040a b d e + 20160a b d e - 13440b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 378a b e - 1008a b d e - 6048a b d e + 24192a b d e +--R + +--R 6 4 2 +--R - 16128b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 108a b e - 216a b d e - 576a b d e - 3456a b d e +--R + +--R 5 4 2 6 5 +--R 13824a b d e - 9216b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 24a b d e - 48a b d e - 128a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R 3072a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 63b e x + (63a e + 252b d e )x + (252a d e + 378b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (378a d e + 252b d e )x + (252a d e + 63b d e )x + 63a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (756a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1890a b e + 7560a b d e - 5040b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 840a b e - 5040a b d e + 20160a b d e - 13440b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 378a b e - 1008a b d e - 6048a b d e + 24192a b d e +--R + +--R 6 4 2 +--R - 16128b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 108a b e - 216a b d e - 576a b d e - 3456a b d e +--R + +--R 5 4 2 6 5 +--R 13824a b d e - 9216b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 24a b d e - 48a b d e - 128a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R 3072a b d e - 2048b d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +-------+ +--R (63e x + 252d e x + 378d e x + 252d e x + 63d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1212 + +--S 1213 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 42b e x + (- 756a b e + 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (1890a b e - 7560a b d e + 5040b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (840a b e + 5040a b d e - 20160a b d e + 13440b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 378a b e + 1008a b d e + 6048a b d e - 24192a b d e +--R + +--R 6 4 2 +--R 16128b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 108a b e + 216a b d e + 576a b d e + 3456a b d e +--R + +--R 5 4 2 6 5 +--R - 13824a b d e + 9216b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 14a e + 24a b d e + 48a b d e + 128a b d e + 768a b d e +--R + +--R 5 5 6 6 +--R - 3072a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 42b e x + (798a b e - 504b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 1134a b e + 7056a b d e - 5040b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 2730a b e + 2520a b d e + 15120a b d e - 13440b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 1218a b e - 6048a b d e + 14112a b d e + 10752a b d e +--R + +--R 7 4 2 +--R - 16128b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 486a b e - 1224a b d e - 6624a b d e + 20736a b d e +--R + +--R 6 4 2 7 5 +--R - 2304a b d e - 9216b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 122a b e - 240a b d e - 624a b d e - 3584a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 13056a b d e - 6144a b d e - 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 14a e - 24a b d e - 48a b d e - 128a b d e - 768a b d e +--R + +--R 2 5 5 6 6 +--R 3072a b d e - 2048a b d +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 63b e x + (63a e + 252b d e )x + (252a d e + 378b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (378a d e + 252b d e )x + (252a d e + 63b d e )x + 63a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1353 +r0:=-80/231*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(7/2))-_ + 128/231*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(5/2))-2/11*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(11/2))-8/33*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(9/2))-256/231*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(3/2))+1024/231*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*sqrt(d+e*x))+2048/231*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (- 2772a b e + 5544b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 2310a b e - 9240a b d e + 18480b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1848a b e - 3696a b d e - 14784a b d e + 29568b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 990a b e - 1584a b d e - 3168a b d e - 12672a b d e +--R + +--R 6 4 2 +--R 25344b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 308a b e - 440a b d e - 704a b d e - 1408a b d e +--R + +--R 5 4 2 6 5 +--R - 5632a b d e + 11264b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 56a b d e - 80a b d e - 128a b d e - 256a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 231b e x + (231a e + 1155b d e )x + (1155a d e + 2310b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (2310a d e + 2310b d e )x + (2310a d e + 1155b d e )x +--R + +--R 4 8 5 7 5 7 +--R (1155a d e + 231b d e )x + 231a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (- 2772a b e + 5544b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 2310a b e - 9240a b d e + 18480b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1848a b e - 3696a b d e - 14784a b d e + 29568b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 990a b e - 1584a b d e - 3168a b d e - 12672a b d e +--R + +--R 6 4 2 +--R 25344b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 308a b e - 440a b d e - 704a b d e - 1408a b d e - 5632a b d e +--R + +--R 6 5 +--R 11264b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 56a b d e - 80a b d e - 128a b d e - 256a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e + 2048b d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 5 7 +--R (231e x + 1155d e x + 2310d e x + 2310d e x + 1155d e x + 231d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R - 462b e x + (2772a b e - 5544b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (2310a b e + 9240a b d e - 18480b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1848a b e + 3696a b d e + 14784a b d e - 29568b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 990a b e + 1584a b d e + 3168a b d e + 12672a b d e +--R + +--R 6 4 2 +--R - 25344b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 308a b e + 440a b d e + 704a b d e + 1408a b d e +--R + +--R 5 4 2 6 5 +--R 5632a b d e - 11264b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 42a e + 56a b d e + 80a b d e + 128a b d e + 256a b d e +--R + +--R 5 5 6 6 +--R 1024a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R 462b e x + (- 2310a b e + 5544b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 5082a b e - 3696a b d e + 18480b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 4158a b e - 12936a b d e + 3696a b d e + 29568b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 2838a b e - 5280a b d e - 17952a b d e + 16896a b d e +--R + +--R 7 4 2 +--R 25344b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 1298a b e - 2024a b d e - 3872a b d e - 14080a b d e +--R + +--R 6 4 2 7 5 +--R 19712a b d e + 11264b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R - 350a b e - 496a b d e - 784a b d e - 1536a b d e - 5888a b d e +--R + +--R 6 5 7 6 +--R 10240a b d e + 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 42a e - 56a b d e - 80a b d e - 128a b d e - 256a b d e +--R + +--R 2 5 5 6 6 +--R - 1024a b d e + 2048a b d +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 231b e x + (231a e + 1155b d e )x + (1155a d e + 2310b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (2310a d e + 2310b d e )x + (2310a d e + 1155b d e )x +--R + +--R 4 8 5 7 5 7 +--R (1155a d e + 231b d e )x + 231a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(15/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1353 +r0:=-80/429*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(9/2))-_ + 640/3003*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(7/2))-2/13*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(13/2))-24/143*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(11/2))-256/1001*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(5/2))-1024/1001*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(d+e*x)^(3/2))-2048/3003*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 6006b e x + (- 12012a b e - 24024b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 18018a b e - 24024a b d e - 48048b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 17160a b e - 20592a b d e - 27456a b d e - 54912b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 10010a b e - 11440a b d e - 13728a b d e - 18304a b d e +--R + +--R 6 4 2 +--R - 36608b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 3276a b e - 3640a b d e - 4160a b d e - 4992a b d e +--R + +--R 5 4 2 6 5 +--R - 6656a b d e - 13312b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 462a e - 504a b d e - 560a b d e - 640a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 7 13 12 6 +--R 3003b e x + (3003a e + 18018b d e )x +--R + +--R 12 2 11 5 2 11 3 10 4 +--R (18018a d e + 45045b d e )x + (45045a d e + 60060b d e )x +--R + +--R 3 10 4 9 3 4 9 5 8 2 +--R (60060a d e + 45045b d e )x + (45045a d e + 18018b d e )x +--R + +--R 5 8 6 7 6 7 +--R (18018a d e + 3003b d e )x + 3003a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 6006b e x + (- 12012a b e - 24024b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 18018a b e - 24024a b d e - 48048b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 17160a b e - 20592a b d e - 27456a b d e - 54912b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 10010a b e - 11440a b d e - 13728a b d e - 18304a b d e +--R + +--R 6 4 2 +--R - 36608b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 3276a b e - 3640a b d e - 4160a b d e - 4992a b d e +--R + +--R 5 4 2 6 5 +--R - 6656a b d e - 13312b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 462a e - 504a b d e - 560a b d e - 640a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e - 2048b d +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 +--R 3003e x + 18018d e x + 45045d e x + 60060d e x + 45045d e x +--R + +--R 5 8 6 7 +--R 18018d e x + 3003d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R 6006b e x + (12012a b e + 24024b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (18018a b e + 24024a b d e + 48048b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (17160a b e + 20592a b d e + 27456a b d e + 54912b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 10010a b e + 11440a b d e + 13728a b d e + 18304a b d e +--R + +--R 6 4 2 +--R 36608b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 3276a b e + 3640a b d e + 4160a b d e + 4992a b d e +--R + +--R 5 4 2 6 5 +--R 6656a b d e + 13312b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 462a e + 504a b d e + 560a b d e + 640a b d e + 768a b d e +--R + +--R 5 5 6 6 +--R 1024a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R - 6006b e x + (- 18018a b e - 24024b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 30030a b e - 48048a b d e - 48048b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 35178a b e - 44616a b d e - 75504a b d e - 54912b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 27170a b e - 32032a b d e - 41184a b d e - 73216a b d e +--R + +--R 7 4 2 +--R - 36608b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 13286a b e - 15080a b d e - 17888a b d e - 23296a b d e +--R + +--R 6 4 2 7 5 +--R - 43264a b d e - 13312b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 3738a b e - 4144a b d e - 4720a b d e - 5632a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 7424a b d e - 14336a b d e - 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 462a e - 504a b d e - 560a b d e - 640a b d e - 768a b d e +--R + +--R 2 5 5 6 6 +--R - 1024a b d e - 2048a b d +--R / +--R 13 7 13 12 6 +--R 3003b e x + (3003a e + 18018b d e )x +--R + +--R 12 2 11 5 2 11 3 10 4 +--R (18018a d e + 45045b d e )x + (45045a d e + 60060b d e )x +--R + +--R 3 10 4 9 3 4 9 5 8 2 +--R (60060a d e + 45045b d e )x + (45045a d e + 18018b d e )x +--R + +--R 5 8 6 7 6 7 +--R (18018a d e + 3003b d e )x + 3003a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1353 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(17/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1353 +r0:=-16/143*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(11/2))-_ + 128/1287*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(9/2))-2/15*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(15/2))-8/65*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(13/2))-256/3003*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(7/2))-1024/9009*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(d+e*x)^(5/2))-2048/45045*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 30030b e x + (- 108108a b e - 72072b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 193050a b e - 154440a b d e - 102960b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 200200a b e - 171600a b d e - 137280a b d e - 91520b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 122850a b e - 109200a b d e - 93600a b d e - 74880a b d e +--R + +--R 6 4 2 +--R - 49920b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 41580a b e - 37800a b d e - 33600a b d e - 28800a b d e +--R + +--R 5 4 2 6 5 +--R - 23040a b d e - 15360b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 6006a e - 5544a b d e - 5040a b d e - 4480a b d e - 3840a b d e +--R + +--R 5 5 6 6 +--R - 3072a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 8 14 13 7 +--R 45045b e x + (45045a e + 315315b d e )x +--R + +--R 13 2 12 6 2 12 3 11 5 +--R (315315a d e + 945945b d e )x + (945945a d e + 1576575b d e )x +--R + +--R 3 11 4 10 4 4 10 5 9 3 +--R (1576575a d e + 1576575b d e )x + (1576575a d e + 945945b d e )x +--R + +--R 5 9 6 8 2 6 8 7 7 +--R (945945a d e + 315315b d e )x + (315315a d e + 45045b d e )x +--R + +--R 7 7 +--R 45045a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 30030b e x + (- 108108a b e - 72072b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 193050a b e - 154440a b d e - 102960b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 200200a b e - 171600a b d e - 137280a b d e - 91520b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 122850a b e - 109200a b d e - 93600a b d e - 74880a b d e +--R + +--R 6 4 2 +--R - 49920b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 41580a b e - 37800a b d e - 33600a b d e - 28800a b d e +--R + +--R 5 4 2 6 5 +--R - 23040a b d e - 15360b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 6006a e - 5544a b d e - 5040a b d e - 4480a b d e - 3840a b d e +--R + +--R 5 5 6 6 +--R - 3072a b d e - 2048b d +--R / +--R 14 7 13 6 2 12 5 3 11 4 +--R 45045e x + 315315d e x + 945945d e x + 1576575d e x +--R + +--R 4 10 3 5 9 2 6 8 7 7 +--R 1576575d e x + 945945d e x + 315315d e x + 45045d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 6 6 5 6 6 5 5 +--R 30030b e x + (108108a b e + 72072b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (193050a b e + 154440a b d e + 102960b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (200200a b e + 171600a b d e + 137280a b d e + 91520b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 122850a b e + 109200a b d e + 93600a b d e + 74880a b d e +--R + +--R 6 4 2 +--R 49920b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 41580a b e + 37800a b d e + 33600a b d e + 28800a b d e +--R + +--R 5 4 2 6 5 +--R 23040a b d e + 15360b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 6006a e + 5544a b d e + 5040a b d e + 4480a b d e + 3840a b d e +--R + +--R 5 5 6 6 +--R 3072a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 6 7 6 6 7 5 6 +--R - 30030b e x + (- 138138a b e - 72072b d e )x +--R + +--R 2 5 6 6 5 7 2 4 5 +--R (- 301158a b e - 226512a b d e - 102960b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 4 +--R (- 393250a b e - 326040a b d e - 240240a b d e - 91520b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 +--R - 323050a b e - 280800a b d e - 230880a b d e - 166400a b d e +--R + +--R 7 4 2 +--R - 49920b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 +--R - 164430a b e - 147000a b d e - 127200a b d e - 103680a b d e +--R + +--R 6 4 2 7 5 +--R - 72960a b d e - 15360b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R - 47586a b e - 43344a b d e - 38640a b d e - 33280a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R - 26880a b d e - 18432a b d e - 2048b d +--R * +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R - 6006a e - 5544a b d e - 5040a b d e - 4480a b d e - 3840a b d e +--R + +--R 2 5 5 6 6 +--R - 3072a b d e - 2048a b d +--R / +--R 14 8 14 13 7 +--R 45045b e x + (45045a e + 315315b d e )x +--R + +--R 13 2 12 6 2 12 3 11 5 +--R (315315a d e + 945945b d e )x + (945945a d e + 1576575b d e )x +--R + +--R 3 11 4 10 4 4 10 5 9 3 +--R (1576575a d e + 1576575b d e )x + (1576575a d e + 945945b d e )x +--R + +--R 5 9 6 8 2 6 8 7 7 +--R (945945a d e + 315315b d e )x + (315315a d e + 45045b d e )x +--R + +--R 7 7 +--R 45045a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - b x - 7a b x - 21a b x - 35a b x - 35a b x - 21a b x - 7a b x - a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1353 +r0:=2/9*(a+b*x)*(d+e*x)^(9/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 5 4 3 4 3 2 2 3 +--R 2b e x + (2a e + 8b d e )x + (8a d e + 12b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (12a d e + 8b d e)x + (8a d e + 2b d )x + 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 9e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (2e x + 8d e x + 12d e x + 8d e x + 2d )\|e x + d +--R (3) ----------------------------------------------------- +--R 9e +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (2e x + 8d e x + 12d e x + 8d e x + 2d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - 2b e x + (- 2a e - 8b d e )x + (- 8a d e - 12b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 12a d e - 8b d e)x + (- 8a d e - 2b d )x - 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 9e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1353 +r0:=2/7*(a+b*x)*(d+e*x)^(7/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 4 3 2 3 2 2 2 +--R 2b e x + (2a e + 6b d e )x + (6a d e + 6b d e)x +--R + +--R 2 3 3 +--R (6a d e + 2b d )x + 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 7e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (2e x + 6d e x + 6d e x + 2d )\|e x + d +--R (3) ------------------------------------------ +--R 7e +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (2e x + 6d e x + 6d e x + 2d )\|e x + d \|b x + 2a b x + a +--R + +--R 3 4 3 2 3 2 2 2 +--R - 2b e x + (- 2a e - 6b d e )x + (- 6a d e - 6b d e)x +--R + +--R 2 3 3 +--R (- 6a d e - 2b d )x - 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 7e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (b e x + (a e + b d)x + a d)\|e x + d +--R (1) --------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1240 + +--S 1241 of 1353 +r0:=2/5*(a+b*x)*(d+e*x)^(5/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2b e x + (2a e + 4b d e)x + (4a d e + 2b d )x + 2a d )\|e x + d +--R (2) -------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +-------+ +--R (2e x + 4d e x + 2d )\|e x + d +--R (3) -------------------------------- +--R 5e +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (2e x + 4d e x + 2d )\|e x + d \|b x + 2a b x + a +--R + +--R 2 3 2 2 2 2 +-------+ +--R (- 2b e x + (- 2a e - 4b d e)x + (- 4a d e - 2b d )x - 2a d )\|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (b x + a)\|e x + d +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1353 +r0:=2/3*(a+b*x)*(d+e*x)^(3/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 2 +-------+ +--R (2b e x + (2a e + 2b d)x + 2a d)\|e x + d +--R (2) ------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1353 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R (2e x + 2d)\|e x + d +--R (3) --------------------- +--R 3e +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1353 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R +-------+ | 2 2 2 +--R (2e x + 2d)\|e x + d \|b x + 2a b x + a +--R + +--R 2 +-------+ +--R (- 2b e x + (- 2a e - 2b d)x - 2a d)\|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R (5) -------------------------------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1353 +t0:=(a+b*x)/(sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1353 +r0:=2*(a+b*x)*sqrt(d+e*x)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R +-------+ +--R (2b x + 2a)\|e x + d +--R (2) ---------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1353 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2\|e x + d +--R (3) ----------- +--R e +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R +-------+ | 2 2 2 +-------+ +--R 2\|e x + d \|b x + 2a b x + a + (- 2b x - 2a)\|e x + d +--R (4) ---------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1353 +t0:=(a+b*x)/((d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1353 +r0:=-2*(a+b*x)/(e*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) -------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R e\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - ----------- +--R +-------+ +--R e\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - 2\|b x + 2a b x + a + 2b x + 2a +--R (4) ------------------------------------ +--R +------------------+ +--R +-------+ | 2 2 2 +--R e\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1353 +t0:=(a+b*x)/((d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1353 +r0:=-2/3*(a+b*x)/(e*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) -------------------------------------------- +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (3e x + 3d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - ----------------------- +--R 2 +-------+ +--R (3e x + 3d e)\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - 2\|b x + 2a b x + a + 2b x + 2a +--R (4) -------------------------------------------- +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (3e x + 3d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1353 +t0:=(a+b*x)/((d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1353 +r0:=-2/5*(a+b*x)/(e*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) ------------------------------------------------------- +--R +------------------+ +--R 3 2 2 2 +-------+ | 2 2 2 +--R (5e x + 10d e x + 5d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1353 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - ---------------------------------- +--R 3 2 2 2 +-------+ +--R (5e x + 10d e x + 5d e)\|e x + d +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1353 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R - 2\|b x + 2a b x + a + 2b x + 2a +--R (4) ------------------------------------------------------- +--R +------------------+ +--R 3 2 2 2 +-------+ | 2 2 2 +--R (5e x + 10d e x + 5d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1353 +d0:=normalize(D(m0,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (5) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1353 +r0:=7/3*e*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 7/5*e*(a+b*x)*(d+e*x)^(5/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^(7/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-7*e*(b*d-a*e)^(5/2)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+7*e*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 105a b e + 210a b d e - 105b d e)x - 105a e + 210a b d e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b e x + (- 14a b e + 32b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 168a b d e + 116b d e)x + 105a e - 245a b d e +--R + +--R 2 2 3 3 +--R 161a b d e - 15b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 15b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 3 2 3 3 2 2 +--R (105a b e - 210a b d e + 105b d e)x + 105a e - 210a b d e +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 12b e x + (- 28a b e + 64b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (140a b e - 336a b d e + 232b d e)x + 210a e - 490a b d e +--R + +--R 2 2 3 3 +--R 322a b d e - 30b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 30b x + 30a b +--R , +--R +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 105a b e + 210a b d e - 105b d e)x - 105a e + 210a b d e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b e x + (- 14a b e + 32b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 168a b d e + 116b d e)x + 105a e - 245a b d e +--R + +--R 2 2 3 3 +--R 161a b d e - 15b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 15b x + 15a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1272 + +--S 1273 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 3 2 3 3 2 2 +--R (105a b e - 210a b d e + 105b d e)x + 105a e - 210a b d e +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 3 3 2 4 2 2 +--R (210a b e - 420a b d e + 210b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 +--R (420a b e - 840a b d e + 420a b d e)x + 210a e - 420a b d e +--R + +--R 2 2 2 +--R 210a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 12b e x + (- 28a b e + 64b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (140a b e - 336a b d e + 232b d e)x + 210a e - 490a b d e +--R + +--R 2 2 3 3 +--R 322a b d e - 30b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 12b e x + (16a b e - 64b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 112a b e + 272a b d e - 232b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 350a b e + 826a b d e - 554a b d e + 30b d )x - 210a e +--R + +--R 3 2 2 2 2 3 3 +--R 490a b d e - 322a b d e + 30a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 5 4 +-+ | 2 2 2 +--R (30b x + 30a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b e x - 8b d e x - 12b d e x - 8b d e x - 2b d ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 5 5 5 4 4 4 2 3 3 +--R b e x + (- a e + 6b d e )x + (- 4a d e + 14b d e )x +--R + +--R 2 3 3 2 2 3 2 4 4 5 +--R (- 6a d e + 16b d e )x + (- 4a d e + 9b d e)x - a d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 5 4 2 3 4 3 2 2 2 3 +--R 2b e x + (2a b e + 8b d e )x + (8a b d e + 12b d e )x +--R + +--R 2 2 2 3 2 3 2 4 4 +--R (12a b d e + 8b d e)x + (8a b d e + 2b d )x + 2a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 5 6 2 4 5 2 5 4 2 2 3 4 +--R - b e x - 6b d e x + (a e - 2a b d e - 14b d e )x +--R + +--R 2 4 2 3 2 3 2 3 2 2 3 3 2 2 4 2 +--R (4a d e - 8a b d e - 16b d e )x + (6a d e - 12a b d e - 9b d e)x +--R + +--R 2 3 2 4 2 5 2 4 5 +--R (4a d e - 8a b d e - 2b d )x + a d e - 2a b d +--R / +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (a b e + 2b d)x + (- a b e + 4a b d)x - a e + 2a b d) +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 2 3 2 2 2 2 +--R (- 2b e x + (- 4a b e - 2b d)x + (- 2a b e - 4a b d)x - 2a b d) +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 3 3 2 4 2 2 +--R (105a b e - 210a b d e + 105b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 +--R (210a b e - 420a b d e + 210a b d e)x + 105a e - 210a b d e +--R + +--R 2 2 2 +--R 105a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 105a b e + 210a b d e - 105b d e)x - 105a e + 210a b d e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R \|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b e x + (- 14a b e + 32b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 168a b d e + 116b d e)x + 105a e - 245a b d e +--R + +--R 2 2 3 3 +--R 161a b d e - 15b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 6b e x + (8a b e - 32b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 56a b e + 136a b d e - 116b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 175a b e + 413a b d e - 277a b d e + 15b d )x - 105a e +--R + +--R 3 2 2 2 2 3 3 +--R 245a b d e - 161a b d e + 15a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 5 4 +-+ | 2 2 2 +--R (15b x + 15a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1275 + +--S 1276 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1276 + +)clear all + +--S 1277 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1353 +r0:=5/3*e*(a+b*x)*(d+e*x)^(3/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^(5/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-5*e*(b*d-a*e)^(3/2)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+5*e*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 +-----------+ +--R ((15a b e - 15b d e)x + 15a e - 15a b d e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (2b e x + (- 10a b e + 14b d e)x - 15a e + 20a b d e - 3b d )\|b +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 3b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a e + b d +--R ((15a b e - 15b d e)x + 15a e - 15a b d e) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4b e x + (- 20a b e + 28b d e)x - 30a e + 40a b d e - 6b d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +--R +---------+ +--R 2 2 2 2 |a e - b d +--R ((15a b e - 15b d e)x + 15a e - 15a b d e) |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2b e x + (- 10a b e + 14b d e)x - 15a e + 20a b d e - 3b d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 3b x + 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1279 + +--S 1280 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a e + b d +-+ +--R ((15a b e - 15b d e)x + 15a e - 15a b d e) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +------------------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R | 2 2 2 \| b +--R \|b x + 2a b x + a log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 3 2 2 2 2 3 2 +--R (- 30a b e + 30b d e)x + (- 60a b e + 60a b d e)x - 30a e +--R + +--R 2 +--R 30a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (4b e x + (- 20a b e + 28b d e)x - 30a e + 40a b d e - 6b d )\|b +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 4b e x + (16a b e - 28b d e)x + (50a b e - 68a b d e + 6b d )x +--R + +--R 3 2 2 2 2 +--R 30a e - 40a b d e + 6a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 3 +-+ | 2 2 2 +--R (6b x + 6a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +-----------+ +--R 3 3 2 2 2 3 |- a e + b d +-------+ +--R (2b e x + 6b d e x + 6b d e x + 2b d ) |----------- \|e x + d +--R \| b +--R + +--R 4 4 4 3 3 3 2 2 2 +--R b e x + (- a e + 5b d e )x + (- 3a d e + 9b d e )x +--R + +--R 2 2 3 3 4 +--R (- 3a d e + 7b d e)x - a d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 4 3 2 2 3 2 2 2 2 +--R - 2b e x + (- 2a b e - 6b d e )x + (- 6a b d e - 6b d e)x +--R + +--R 2 2 3 3 +--R (- 6a b d e - 2b d )x - 2a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 4 5 2 3 4 2 4 3 2 2 2 3 +--R - b e x - 5b d e x + (a e - 2a b d e - 9b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 2 3 2 4 2 3 +--R (3a d e - 6a b d e - 7b d e)x + (3a d e - 6a b d e - 2b d )x + a d e +--R + +--R 4 +--R - 2a b d +--R / +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (a b e + 2b d)x + (- a b e + 4a b d)x - a e + 2a b d) +--R * +--R +-------+ +--R \|e x + d +--R + +--R +-----------+ +--R 3 3 2 3 2 2 2 2 |- a e + b d +--R (2b e x + (4a b e + 2b d)x + (2a b e + 4a b d)x + 2a b d) |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 3 2 2 2 2 3 2 +--R (- 15a b e + 15b d e)x + (- 30a b e + 30a b d e)x - 15a e +--R + +--R 2 +--R 15a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 2 2 +-+ |a e - b d +--R ((15a b e - 15b d e)x + 15a e - 15a b d e)\|b |--------- +--R \| b +--R * +--R +------------------+ +-------+ +--R | 2 2 2 \|e x + d +--R \|b x + 2a b x + a atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (2b e x + (- 10a b e + 14b d e)x - 15a e + 20a b d e - 3b d )\|b +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 2b e x + (8a b e - 14b d e)x + (25a b e - 34a b d e + 3b d )x +--R + +--R 3 2 2 2 2 +--R 15a e - 20a b d e + 3a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 3 +-+ | 2 2 2 +--R (3b x + 3a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1283 + +)clear all + +--S 1284 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1353 +r0:=-(d+e*x)^(3/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-3*e*(a+b*x)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*e*(a+b*x)*sqrt(d+e*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (- 3b e x - 3a e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-+ +-------+ +--R (2b e x + 3a e - b d)\|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a e + b d +--R (3b e x + 3a e) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R (4b e x + 6a e - 2b d)\|e x + d +--R / +--R 3 2 +--R 2b x + 2a b +--R , +--R +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R (- 3b e x - 3a e) |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +-------+ +--R (2b e x + 3a e - b d)\|e x + d +--R / +--R 3 2 +--R b x + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1286 + +--S 1287 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +------------------+ +--R |- a e + b d +-+ | 2 2 2 +--R (3b e x + 3a e) |----------- \|b \|b x + 2a b x + a +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 +-----------+ \|b \|e x + d +--R (6b e x + 12a b e x + 6a e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R (4b e x + 6a e - 2b d)\|b \|e x + d \|b x + 2a b x + a +--R + +--R 2 2 2 2 +-+ +-------+ +--R (- 4b e x + (- 10a b e + 2b d)x - 6a e + 2a b d)\|b \|e x + d +--R / +--R +------------------+ +--R 3 2 +-+ | 2 2 2 +--R (2b x + 2a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +-----------+ +--R 2 2 2 |- a e + b d +-------+ 3 3 +--R (- 2b e x - 4b d e x - 2b d ) |----------- \|e x + d + b e x +--R \| b +--R + +--R 3 2 2 2 2 2 3 +--R (- a e + 4b d e )x + (- 2a d e + 5b d e)x - a d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 2 2 2 +--R (2b e x + (2a b e + 4b d e)x + (4a b d e + 2b d )x + 2a b d ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 3 4 2 2 3 2 3 2 2 2 2 +--R - b e x - 4b d e x + (a e - 2a b d e - 5b d e)x +--R + +--R 2 2 2 2 3 2 2 3 +--R (2a d e - 4a b d e - 2b d )x + a d e - 2a b d +--R / +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (a b e + 2b d)x + (- a b e + 4a b d)x - a e + 2a b d) +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 2 3 2 2 2 2 +--R (- 2b e x + (- 4a b e - 2b d)x + (- 2a b e - 4a b d)x - 2a b d) +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 +-----------+ \|b \|e x + d +--R (3b e x + 6a b e x + 3a e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +------------------+ +-------+ +--R +-+ |a e - b d | 2 2 2 \|e x + d +--R (- 3b e x - 3a e)\|b |--------- \|b x + 2a b x + a atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R (2b e x + 3a e - b d)\|b \|e x + d \|b x + 2a b x + a +--R + +--R 2 2 2 2 +-+ +-------+ +--R (- 2b e x + (- 5a b e + b d)x - 3a e + a b d)\|b \|e x + d +--R / +--R +------------------+ +--R 3 2 +-+ | 2 2 2 +--R (b x + a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1290 + +)clear all + +--S 1291 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1353 +r0:=-e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-sqrt(d+e*x)/(b*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +-----------+ +-+ +-------+ +--R (- b e x - a e)atanh(--------------) - \|- a e + b d \|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R b\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (b e x + a e) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 2 | 2 +--R (2b x + 2a b)\|- a b e + b d +--R , +--R +-----------+ +--R | 2 +-------+ +-----------+ +--R \|a b e - b d \|e x + d | 2 +-------+ +--R (b e x + a e)atan(------------------------) - \|a b e - b d \|e x + d +--R a e - b d +--R ----------------------------------------------------------------------] +--R +-----------+ +--R 2 | 2 +--R (b x + a b)\|a b e - b d +--R Type: Union(List(Expression(Integer)),...) +--E 1293 + +--S 1294 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (b e x + a e)\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 2 2 | 2 \|b \|e x + d +--R (2b e x + 4a b e x + 2a e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R - 2\|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R (2b x + 2a)\|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +------------------+ +--R 2 | 2 +-----------+ +-+ | 2 2 2 +--R (2b x + 2a b)\|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 2 2 +-------+ +--R ((2a b e - 2b d e)x + 2a b d e - 2b d )\|e x + d +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +--R (b e x + (- a e + 3b d e)x - a d e + 2b d )\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 3 2 2 2 2 +--R ((- 2a b e + 2b d e)x + (- 2a b e + 2b d )x - 2a b d e + 2a b d ) +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (- b e x - 3b d e x + (a e - 2a b d e - 2b d )x + a d e - 2a b d ) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (a b e + 2b d)x + (- a b e + 4a b d)x - a e + 2a b d) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (2a b e - 2b d e)x + (4a b e - 2a b d e - 2b d )x +--R + +--R 3 2 2 2 3 2 3 2 2 2 +--R (2a b e + 2a b d e - 4a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1295 + +--S 1296 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 2 2 | 2 \|b \|e x + d +--R (b e x + 2a b e x + a e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (b e x + a e)\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R - \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R (b x + a)\|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R +-----------+ +------------------+ +--R 2 +-----------+ +-+ | 2 | 2 2 2 +--R (b x + a b)\|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R (7) -------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1297 + +)clear all + +--S 1298 of 1353 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1353 +r0:=e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(3/2)*_ + sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-sqrt(d+e*x)/((b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +-----------+ +-+ +-------+ +--R (- b e x - a e)atanh(--------------) + \|- a e + b d \|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (a e - b d)\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (b e x + a e) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R 2\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 2 2 | 2 +--R ((2a b e - 2b d)x + 2a e - 2a b d)\|- a b e + b d +--R , +--R +-----------+ +--R | 2 +-------+ +-----------+ +--R \|a b e - b d \|e x + d | 2 +-------+ +--R (b e x + a e)atan(------------------------) + \|a b e - b d \|e x + d +--R a e - b d +--R ----------------------------------------------------------------------] +--R +-----------+ +--R 2 2 | 2 +--R ((a b e - b d)x + a e - a b d)\|a b e - b d +--R Type: Union(List(Expression(Integer)),...) +--E 1300 + +--S 1301 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (b e x + a e)\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 2 2 | 2 \|b \|e x + d +--R (2b e x + 4a b e x + 2a e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R 2\|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R (- 2b x - 2a)\|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +--R 2 2 | 2 +-----------+ +-+ +--R ((2a b e - 2b d)x + 2a e - 2a b d)\|- a b e + b d \|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +-------------+ +--R 2 +-------+ | 2 +--R ((2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 +-------+ +--R ((- 2a b e + 2b d)x - 2a b e + 2a b d)\|e x + d +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +--R (- b e x - 2b d x + a e - 2a b d)\|- a b e + b d +--R / +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (a b e + 2b d)x + (- a b e + 4a b d)x - a e + 2a b d) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (2a b e - 2b d e)x + (4a b e - 2a b d e - 2b d )x +--R + +--R 3 2 2 2 3 2 3 2 2 2 +--R (2a b e + 2a b d e - 4a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1302 + +--S 1303 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 2 2 | 2 \|b \|e x + d +--R (b e x + 2a b e x + a e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (b e x + a e)\|- a e + b d \|b \|b x + 2a b x + a +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R (- b x - a)\|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 2 2 +-----------+ +-+ | 2 +--R ((a b e - b d)x + a e - a b d)\|- a e + b d \|b \|a b e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R (7) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1304 + +)clear all + +--S 1305 of 1353 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------ +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1305 + +--S 1306 of 1353 +r0:=3*e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-_ + a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2/((b*d-a*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-3*b*sqrt(d+e*x)/((b*d-a*e)^2*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R (3b e x + 3a e)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R (- 3b e x - 2a e - b d)\|- a e + b d +--R / +--R +------------------+ +--R 2 2 2 2 +-----------+ +-------+ | 2 2 2 +--R (a e - 2a b d e + b d )\|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | b +-------+ +--R (3b e x + 3a e) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R - 6b e x - 4a e - 2b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-------+ +--R ((2a b e - 4a b d e + 2b d )x + 2a e - 4a b d e + 2a b d )\|e x + d +--R , +--R +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R (- 3b e x - 3a e) |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R - 3b e x - 2a e - b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-------+ +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1307 + +--S 1308 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +-------+ +--R (3b e x + 3a e)\|- a e + b d |- --------- \|e x + d +--R \| a e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 +-+ +-------+ \|b \|e x + d +--R (- 6b e x - 12a b e x - 6a e)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +------------------+ +--R +-----------+ | 2 2 2 +--R (- 6b e x - 4a e - 2b d)\|- a e + b d \|b x + 2a b x + a +--R + +--R 2 2 2 2 +-----------+ +--R (6b e x + (10a b e + 2b d)x + 4a e + 2a b d)\|- a e + b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +--R ((2a b e - 4a b d e + 2b d )x + 2a e - 4a b d e + 2a b d ) +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 +-+ +-------+ \|b \|e x + d +--R (- 3b e x - 6a b e x - 3a e)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R +-----------+ | b +-------+ +--R (- 3b e x - 3a e)\|- a e + b d |--------- \|e x + d +--R \|a e - b d +--R * +--R +------------------+ +-------+ +--R | 2 2 2 b\|e x + d +--R \|b x + 2a b x + a atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R +------------------+ +--R +-----------+ | 2 2 2 +--R (- 3b e x - 2a e - b d)\|- a e + b d \|b x + 2a b x + a +--R + +--R 2 2 2 2 +-----------+ +--R (3b e x + (5a b e + b d)x + 2a e + a b d)\|- a e + b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-----------+ +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|- a e + b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1311 + +)clear all + +--S 1312 of 1353 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1353 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5*b^(3/2)*e*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10/3*b/((b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-5*b^2*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +-+ +-------+ +--R (- 15b e x + (- 15a b e - 15b d e)x - 15a b d e)\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (10a b e + 20b d e)x - 2a e + 14a b d e + 3b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a e - 9a b d e + 9a b d e - 3b d e)x + 3a d e - 9a b d e +--R + +--R 2 3 3 4 +--R 9a b d e - 3b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 | b +--R (15b e x + (15a b e + 15b d e)x + 15a b d e) |- --------- +--R \| a e - b d +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R 30b e x + (20a b e + 40b d e)x - 4a e + 28a b d e + 6b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b e - 18a b d e + 18a b d e - 6b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (6a e - 12a b d e + 12a b d e - 6b d )x + 6a d e - 18a b d e +--R + +--R 2 2 3 3 4 +--R 18a b d e - 6a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +---------+ +--R 2 2 2 2 2 | b +-------+ +--R (15b e x + (15a b e + 15b d e)x + 15a b d e) |--------- \|e x + d +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R 15b e x + (10a b e + 20b d e)x - 2a e + 14a b d e + 3b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1314 + +--S 1315 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 +-----------+ +--R (15b e x + (15a b e + 15b d e)x + 15a b d e)\|- a e + b d +--R * +--R +-----------+ +------------------+ +--R | b +-------+ | 2 2 2 +--R |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 +--R 30b e x + (60a b e + 30b d e)x + (30a b e + 60a b d e)x +--R + +--R 2 +--R 30a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (30b e x + (20a b e + 40b d e)x - 4a e + 28a b d e + 6b d ) +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 30b e x + (- 50a b e - 40b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 16a b e - 68a b d e - 6b d )x + 4a e - 28a b d e - 6a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b e - 18a b d e + 18a b d e - 6b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (6a e - 12a b d e + 12a b d e - 6b d )x + 6a d e - 18a b d e +--R + +--R 2 2 3 3 4 +--R 18a b d e - 6a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 2 3 2 2 3 2 2 2 2 +--R 15b e x + (30a b e + 15b d e)x + (15a b e + 30a b d e)x +--R + +--R 2 +--R 15a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +-----------+ +--R (15b e x + (15a b e + 15b d e)x + 15a b d e)\|- a e + b d +--R * +--R +---------+ +------------------+ +-------+ +--R | b +-------+ | 2 2 2 b\|e x + d +--R |--------- \|e x + d \|b x + 2a b x + a atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (10a b e + 20b d e)x - 2a e + 14a b d e + 3b d ) +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 15b e x + (- 25a b e - 20b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 8a b e - 34a b d e - 3b d )x + 2a e - 14a b d e - 3a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1318 + +)clear all + +--S 1319 of 1353 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 1353 +r0:=2/5/((b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+14/15*b/((b*d-_ + a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7*b^(5/2)*e*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+14/3*b^2/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-7*b^3*sqrt(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R 105b e x + (105a b e + 210b d e )x + (210a b d e + 105b d e)x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 70a b e - 245b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (14a b e - 168a b d e - 161b d e)x - 6a e + 32a b d e +--R + +--R 2 2 3 3 +--R - 116a b d e - 15b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (15a e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (30a d e - 120a b d e + 180a b d e - 120a b d e + 30b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1320 + +--S 1321 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R 105b e x + (105a b e + 210b d e )x + (210a b d e + 105b d e)x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R - 210b e x + (- 140a b e - 490b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (28a b e - 336a b d e - 322b d e)x - 12a e + 64a b d e - 232a b d e +--R + +--R 3 3 +--R - 30b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (30a b e - 120a b d e + 180a b d e - 120a b d e + 30b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 30a e - 60a b d e - 60a b d e + 240a b d e - 210a b d e +--R + +--R 5 5 +--R 60b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 60a d e - 210a b d e + 240a b d e - 60a b d e - 60a b d e +--R + +--R 5 6 +--R 30b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 30a d e - 120a b d e + 180a b d e - 120a b d e + 30a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 105a b e - 210b d e )x +--R + +--R 2 2 3 2 2 2 +--R (- 210a b d e - 105b d e)x - 105a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 70a b e - 245b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (14a b e - 168a b d e - 161b d e)x - 6a e + 32a b d e - 116a b d e +--R + +--R 3 3 +--R - 15b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1321 + +--S 1322 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R 105b e x + (105a b e + 210b d e )x + (210a b d e + 105b d e)x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 210b e x + (- 420a b e - 420b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 210a b e - 840a b d e - 210b d e)x +--R + +--R 2 2 2 3 2 2 2 2 +--R (- 420a b d e - 420a b d e)x - 210a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 210b e x + (- 140a b e - 490b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (28a b e - 336a b d e - 322b d e)x - 12a e + 64a b d e +--R + +--R 2 2 3 3 +--R - 232a b d e - 30b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R 210b e x + (350a b e + 490b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (112a b e + 826a b d e + 322b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 16a b e + 272a b d e + 554a b d e + 30b d )x + 12a e +--R + +--R 3 2 2 2 2 3 3 +--R - 64a b d e + 232a b d e + 30a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (30a b e - 120a b d e + 180a b d e - 120a b d e + 30b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 30a e - 60a b d e - 60a b d e + 240a b d e - 210a b d e +--R + +--R 5 5 +--R 60b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 60a d e - 210a b d e + 240a b d e - 60a b d e - 60a b d e +--R + +--R 5 6 +--R 30b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 30a d e - 120a b d e + 180a b d e - 120a b d e + 30a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1323 + +--S 1324 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 4 3 3 4 2 3 +--R - 105b e x + (- 210a b e - 210b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 105a b e - 420a b d e - 105b d e)x +--R + +--R 2 2 2 3 2 2 2 2 +--R (- 210a b d e - 210a b d e)x - 105a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 105a b e - 210b d e )x +--R + +--R 2 2 3 2 2 2 +--R (- 210a b d e - 105b d e)x - 105a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 70a b e - 245b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (14a b e - 168a b d e - 161b d e)x - 6a e + 32a b d e +--R + +--R 2 2 3 3 +--R - 116a b d e - 15b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R 105b e x + (175a b e + 245b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (56a b e + 413a b d e + 161b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (- 8a b e + 136a b d e + 277a b d e + 15b d )x + 6a e - 32a b d e +--R + +--R 2 2 2 3 3 +--R 116a b d e + 15a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1325 + +)clear all + +--S 1326 of 1353 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1353 +r0:=-7/12*e*(a+b*x)*(d+e*x)^(5/2)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^(7/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-35/24*e^2*_ + (d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-35/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+35/8*e^3*(a+b*x)*sqrt(d+e*x)/(b^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +--R (- 105b e x - 315a b e x - 315a b e x - 105a e )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b e x + (231a b e - 87b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (280a b e - 98a b d e - 38b d e)x + 105a e - 35a b d e +--R + +--R 2 2 3 3 +--R - 14a b d e - 8b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 2 5 2 4 +-+ | 2 2 2 +--R (24b x + 48a b x + 24a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1327 + +--S 1328 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 3 2 3 2 2 3 3 3 |- a e + b d +--R (105b e x + 315a b e x + 315a b e x + 105a e ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 96b e x + (462a b e - 174b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (560a b e - 196a b d e - 76b d e)x + 210a e - 70a b d e +--R + +--R 2 2 3 3 +--R - 28a b d e - 16b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 3 6 2 2 5 3 4 +--R 48b x + 144a b x + 144a b x + 48a b +--R , +--R +--R +---------+ +--R 3 3 3 2 3 2 2 3 3 3 |a e - b d +--R (- 105b e x - 315a b e x - 315a b e x - 105a e ) |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b e x + (231a b e - 87b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (280a b e - 98a b d e - 38b d e)x + 105a e - 35a b d e +--R + +--R 2 2 3 3 +--R - 14a b d e - 8b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 3 6 2 2 5 3 4 +--R 24b x + 72a b x + 72a b x + 24a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1328 + +--S 1329 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 3 2 3 2 2 3 3 3 |- a e + b d +-+ +--R (105b e x + 315a b e x + 315a b e x + 105a e ) |----------- \|b +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (210b e x + 840a b e x + 1260a b e x + 840a b e x + 210a e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 96b e x + (462a b e - 174b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (560a b e - 196a b d e - 76b d e)x + 210a e - 70a b d e +--R + +--R 2 2 3 3 +--R - 28a b d e - 16b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 96b e x + (- 558a b e + 174b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 1022a b e + 370a b d e + 76b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 770a b e + 266a b d e + 104a b d e + 16b d )x - 210a e +--R + +--R 3 2 2 2 2 3 3 +--R 70a b d e + 28a b d e + 16a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 7 3 6 2 2 5 3 4 +-+ | 2 2 2 +--R (48b x + 144a b x + 144a b x + 48a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b e x - 8b d e x - 12b d e x - 8b d e x - 2b d ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 5 5 5 4 4 4 2 3 3 +--R b e x + (- a e + 6b d e )x + (- 4a d e + 14b d e )x +--R + +--R 2 3 3 2 2 3 2 4 4 5 +--R (- 6a d e + 16b d e )x + (- 4a d e + 9b d e)x - a d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 5 4 2 3 4 3 2 2 2 3 +--R 2b e x + (2a b e + 8b d e )x + (8a b d e + 12b d e )x +--R + +--R 2 2 2 3 2 3 2 4 4 +--R (12a b d e + 8b d e)x + (8a b d e + 2b d )x + 2a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R |----------- \|e x + d +--R \| b +--R + +--R 2 5 6 2 4 5 2 5 4 2 2 3 4 +--R - b e x - 6b d e x + (a e - 2a b d e - 14b d e )x +--R + +--R 2 4 2 3 2 3 2 3 2 2 3 3 2 2 4 2 +--R (4a d e - 8a b d e - 16b d e )x + (6a d e - 12a b d e - 9b d e)x +--R + +--R 2 3 2 4 2 5 2 4 5 +--R (4a d e - 8a b d e - 2b d )x + a d e - 2a b d +--R / +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (3a b e + 2b d)x + (2a b e + 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 2a b e + 12a b d)x + (- 3a b e + 8a b d)x - a e + 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 5 5 4 5 4 2 3 4 3 +--R - 2b e x + (- 8a b e - 2b d)x + (- 12a b e - 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 4 +--R (- 8a b e - 12a b d)x + (- 2a b e - 8a b d)x - 2a b d +--R * +--R +-----------+ +--R |- a e + b d +--R |----------- +--R \| b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1330 + +--S 1331 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (105b e x + 420a b e x + 630a b e x + 420a b e x + 105a e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 3 3 3 2 3 2 2 3 3 3 +-+ |a e - b d +--R (- 105b e x - 315a b e x - 315a b e x - 105a e )\|b |--------- +--R \| b +--R * +--R +------------------+ +-------+ +--R | 2 2 2 \|e x + d +--R \|b x + 2a b x + a atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b e x + (231a b e - 87b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (280a b e - 98a b d e - 38b d e)x + 105a e - 35a b d e +--R + +--R 2 2 3 3 +--R - 14a b d e - 8b d +--R * +--R +------------------+ +--R +-+ +-------+ | 2 2 2 +--R \|b \|e x + d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R - 48b e x + (- 279a b e + 87b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 511a b e + 185a b d e + 38b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 385a b e + 133a b d e + 52a b d e + 8b d )x - 105a e +--R + +--R 3 2 2 2 2 3 3 +--R 35a b d e + 14a b d e + 8a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 7 3 6 2 2 5 3 4 +-+ | 2 2 2 +--R (24b x + 72a b x + 72a b x + 24a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 4 5 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 4 3 4 3 2 2 3 2 2 3 2 +--R (- a e - 4b d e )x + (- 4a d e - 6b d e )x + (- 6a d e - 4b d e)x +--R + +--R 3 4 4 +--R (- 4a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1332 + +)clear all + +--S 1333 of 1353 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1353 +r0:=-5/12*e*(a+b*x)*(d+e*x)^(3/2)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^(5/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-5/8*e^2*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 15b e x - 45a b e x - 45a b e x - 15a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 33b e x + (- 40a b e - 26b d e)x - 15a e - 10a b d e - 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 5 2 4 2 3 +-----------+ +-+ | 2 2 2 +--R (24b x + 48a b x + 24a b )\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1334 + +--S 1335 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b e x + 45a b e x + 45a b e x + 15a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 66b e x + (- 80a b e - 52b d e)x - 30a e - 20a b d e - 16b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 6 3 5 2 2 4 3 3 | 2 +--R (48b x + 144a b x + 144a b x + 48a b )\|- a b e + b d +--R , +--R +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b e x + 45a b e x + 45a b e x + 15a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 33b e x + (- 40a b e - 26b d e)x - 15a e - 10a b d e - 8b d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 6 3 5 2 2 4 3 3 | 2 +--R (24b x + 72a b x + 72a b x + 24a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1335 + +--S 1336 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (15b e x + 45a b e x + 45a b e x + 15a e )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (30b e x + 120a b e x + 180a b e x + 120a b e x + 30a e ) +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 66b e x + (- 80a b e - 52b d e)x - 30a e - 20a b d e - 16b d ) +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R 66b e x + (146a b e + 52b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (110a b e + 72a b d e + 16b d )x + 30a e + 20a b d e + 16a b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R +-------------+ +--R 6 3 5 2 2 4 3 3 | 2 +-----------+ +--R (48b x + 144a b x + 144a b x + 48a b )\|- a b e + b d \|- a e + b d +--R * +--R +------------------+ +--R +-+ | 2 2 2 +--R \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 4 2 3 3 3 2 2 2 2 +--R (2a b e - 2b d e )x + (6a b d e - 6b d e )x +--R + +--R 2 2 2 3 3 2 4 +--R (6a b d e - 6b d e)x + 2a b d e - 2b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 4 4 4 3 3 3 2 2 2 +--R b e x + (- a e + 5b d e )x + (- 3a d e + 9b d e )x +--R + +--R 2 2 3 3 4 +--R (- 3a d e + 7b d e)x - a d e + 2b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 4 3 3 4 2 4 2 3 3 2 2 3 +--R (- 2a b e + 2b d e )x + (- 2a b e - 4a b d e + 6b d e )x +--R + +--R 2 3 3 3 2 2 2 2 2 3 3 4 +--R (- 6a b d e + 6b d e)x + (- 6a b d e + 4a b d e + 2b d )x +--R + +--R 2 3 2 4 +--R - 2a b d e + 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 4 5 2 3 4 2 4 3 2 2 2 3 +--R - b e x - 5b d e x + (a e - 2a b d e - 9b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +--R (3a d e - 6a b d e - 7b d e)x + (3a d e - 6a b d e - 2b d )x +--R + +--R 2 3 4 +--R a d e - 2a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (3a b e + 2b d)x + (2a b e + 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 2a b e + 12a b d)x + (- 3a b e + 8a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (2a b e - 2b d e)x + (8a b e - 6a b d e - 2b d )x +--R + +--R 3 3 2 2 4 5 2 3 4 2 2 3 3 2 4 2 2 +--R (12a b e - 4a b d e - 8a b d )x + (8a b e + 4a b d e - 12a b d )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (2a b e + 6a b d e - 8a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1337 + +--S 1338 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e )\|a b e - b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (15b e x + 45a b e x + 45a b e x + 15a e )\|- a e + b d \|b +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R | 2 2 2 \|a b e - b d \|e x + d +--R \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 33b e x + (- 40a b e - 26b d e)x - 15a e - 10a b d e - 8b d ) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R 33b e x + (73a b e + 26b d e)x + (55a b e + 36a b d e + 8b d )x +--R + +--R 3 2 2 2 2 +--R 15a e + 10a b d e + 8a b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 6 3 5 2 2 4 3 3 +-----------+ +-+ | 2 +--R (24b x + 72a b x + 72a b x + 24a b )\|- a e + b d \|b \|a b e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 3 4 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a - b e x +--R + +--R 3 2 3 2 2 2 2 3 3 +--R (- a e - 3b d e )x + (- 3a d e - 3b d e)x + (- 3a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1339 + +)clear all + +--S 1340 of 1353 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1353 +r0:=-1/3*(d+e*x)^(3/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/4*e*(a+b*x)*_ + (d+e*x)^(3/2)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/8*e^3*(a+_ + b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+1/8*e^2*sqrt(d+e*x)/(b^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 3b e x - 9a b e x - 9a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (- 8a b e + 14b d e)x - 3a e - 2a b d e + 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +--R ((24a b e - 24b d)x + (48a b e - 48a b d)x + 24a b e - 24a b d) +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (3b e x + 9a b e x + 9a b e x + 3a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 16a b e + 28b d e)x - 6a e - 4a b d e + 16b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 5 6 3 2 4 5 2 +--R (48a b e - 48b d)x + (144a b e - 144a b d)x +--R + +--R 3 3 2 4 4 2 3 3 +--R (144a b e - 144a b d)x + 48a b e - 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|a b e - b d \|e x + d +--R (3b e x + 9a b e x + 9a b e x + 3a e )atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (- 8a b e + 14b d e)x - 3a e - 2a b d e + 8b d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 5 6 3 2 4 5 2 3 3 2 4 +--R (24a b e - 24b d)x + (72a b e - 72a b d)x + (72a b e - 72a b d)x +--R + +--R 4 2 3 3 +--R 24a b e - 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1342 + +--S 1343 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (3b e x + 9a b e x + 9a b e x + 3a e )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (6b e x + 24a b e x + 36a b e x + 24a b e x + 6a e )\|- a b e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 16a b e + 28b d e)x - 6a e - 4a b d e + 16b d ) +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 6b e x + (10a b e - 28b d e)x + (22a b e - 24a b d e - 16b d )x +--R + +--R 3 2 2 2 2 +--R 6a e + 4a b d e - 16a b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 5 6 3 2 4 5 2 3 3 2 4 +--R (48a b e - 48b d)x + (144a b e - 144a b d)x + (144a b e - 144a b d)x +--R + +--R 4 2 3 3 +--R 48a b e - 48a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 3 2 2 2 2 2 2 2 2 3 +--R ((2a b e - 2b d e )x + (4a b d e - 4b d e)x + 2a b d e - 2b d ) +--R * +--R +-------+ +--R \|e x + d +--R + +--R 3 3 3 2 2 2 2 2 +--R b e x + (- a e + 4b d e )x + (- 2a d e + 5b d e)x - a d e +--R + +--R 3 +--R 2b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (- 2a b e + 2b d e )x + (- 2a b e - 2a b d e + 4b d e)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (- 4a b d e + 2a b d e + 2b d )x - 2a b d e + 2a b d +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 4 2 2 3 2 3 2 2 2 2 +--R - b e x - 4b d e x + (a e - 2a b d e - 5b d e)x +--R + +--R 2 2 2 2 3 2 2 3 +--R (2a d e - 4a b d e - 2b d )x + a d e - 2a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (3a b e + 2b d)x + (2a b e + 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 2a b e + 12a b d)x + (- 3a b e + 8a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (2a b e - 2b d e)x + (8a b e - 6a b d e - 2b d )x +--R + +--R 3 3 2 2 4 5 2 3 4 2 2 3 3 2 4 2 2 +--R (12a b e - 4a b d e - 8a b d )x + (8a b e + 4a b d e - 12a b d )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (2a b e + 6a b d e - 8a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1344 + +--S 1345 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (3b e x + 12a b e x + 18a b e x + 12a b e x + 3a e )\|a b e - b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (3b e x + 9a b e x + 9a b e x + 3a e )\|- a e + b d \|b +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R | 2 2 2 \|a b e - b d \|e x + d +--R \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (- 8a b e + 14b d e)x - 3a e - 2a b d e + 8b d ) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R - 3b e x + (5a b e - 14b d e)x + (11a b e - 12a b d e - 8b d )x +--R + +--R 3 2 2 2 2 +--R 3a e + 2a b d e - 8a b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 5 6 3 2 4 5 2 3 3 2 4 +--R (24a b e - 24b d)x + (72a b e - 72a b d)x + (72a b e - 72a b d)x +--R + +--R 4 2 3 3 +--R 24a b e - 24a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R 2 2 2 | 2 2 2 2 3 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a - b e x + (- a e - 2b d e)x +--R + +--R 2 2 +--R (- 2a d e - b d )x - a d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1346 + +)clear all + +--S 1347 of 1353 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1353 +r0:=-1/3*sqrt(d+e*x)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/12*e*(a+b*x)*_ + sqrt(d+e*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+1/8*e^2*sqrt(d+e*x)/(b*(b*d-a*e)^2*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 3b e x - 9a b e x - 9a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (8a b e - 2b d e)x - 3a e + 14a b d e - 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (24a b e - 48a b d e + 24b d )x + (48a b e - 96a b d e + 48a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 24a b e - 48a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1353 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (3b e x + 9a b e x + 9a b e x + 3a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (16a b e - 4b d e)x - 6a e + 28a b d e - 16b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 4 2 5 6 2 3 +--R (48a b e - 96a b d e + 48b d )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (144a b e - 288a b d e + 144a b d )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (144a b e - 288a b d e + 144a b d )x + 48a b e - 96a b d e + 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|a b e - b d \|e x + d +--R (3b e x + 9a b e x + 9a b e x + 3a e )atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (8a b e - 2b d e)x - 3a e + 14a b d e - 8b d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 4 2 5 6 2 3 +--R (24a b e - 48a b d e + 24b d )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (72a b e - 144a b d e + 72a b d )x + 24a b e - 48a b d e + 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1349 + +--S 1350 of 1353 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (3b e x + 9a b e x + 9a b e x + 3a e )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (6b e x + 24a b e x + 36a b e x + 24a b e x + 6a e )\|- a b e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (16a b e - 4b d e)x - 6a e + 28a b d e - 16b d ) +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 6b e x + (- 22a b e + 4b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 10a b e - 24a b d e + 16b d )x + 6a e - 28a b d e + 16a b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 2 4 2 5 6 2 3 +--R (48a b e - 96a b d e + 48b d )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (144a b e - 288a b d e + 144a b d )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (144a b e - 288a b d e + 144a b d )x + 48a b e - 96a b d e + 48a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1353 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R 2 2 2 2 +-------+ +--R ((2a b e - 2b d e)x + 2a b d e - 2b d )\|e x + d +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +--R (b e x + (- a e + 3b d e)x - a d e + 2b d )\|- a b e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 2 3 2 2 2 3 2 2 2 2 +--R ((- 2a b e + 2b d e)x + (- 2a b e + 2b d )x - 2a b d e + 2a b d ) +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (- b e x - 3b d e x + (a e - 2a b d e - 2b d )x + a d e - 2a b d ) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (3a b e + 2b d)x + (2a b e + 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 2a b e + 12a b d)x + (- 3a b e + 8a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (2a b e - 2b d e)x + (8a b e - 6a b d e - 2b d )x +--R + +--R 3 3 2 2 4 5 2 3 4 2 2 3 3 2 4 2 2 +--R (12a b e - 4a b d e - 8a b d )x + (8a b e + 4a b d e - 12a b d )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (2a b e + 6a b d e - 8a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1353 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (3b e x + 12a b e x + 18a b e x + 12a b e x + 3a e )\|a b e - b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (3b e x + 9a b e x + 9a b e x + 3a e )\|- a e + b d \|b +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R | 2 2 2 \|a b e - b d \|e x + d +--R \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (8a b e - 2b d e)x - 3a e + 14a b d e - 8b d ) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 3b e x + (- 11a b e + 2b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 5a b e - 12a b d e + 8b d )x + 3a e - 14a b d e + 8a b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 2 4 2 5 6 2 3 +--R (24a b e - 48a b d e + 24b d )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (72a b e - 144a b d e + 72a b d )x + 24a b e - 48a b d e + 24a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1352 + +--S 1353 of 1353 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 2 +--R (e x + d)\|b x + 2a b x + a - b e x + (- a e - b d)x - a d +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1353 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich12f.input.pamphlet b/src/input/rich12f.input.pamphlet new file mode 100644 index 0000000..f085ca0 --- /dev/null +++ b/src/input/rich12f.input.pamphlet @@ -0,0 +1,49316 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich12f.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 345 integrals in this file. +\item 345 supplied "optimal results". +\item 275 matching answers. +\item 14 cases where Axiom answer differs from Rubi +\item 13 cases where Axiom supplied 2 results. +\item 9 cases that Axiom failed to integrate. +\item 59 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich12f.output +)spool rich12f.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1751 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1751 +r0:=-1/3*sqrt(d+e*x)/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 5/12*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 5/8*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 5/8*e^2*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 15b e x - 45a b e x - 45a b e x - 15a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (40a b e - 10b d e)x + 33a e - 26a b d e + 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (48a b e - 144a b d e + 144a b d e - 48a b d )x + 24a e - 72a b d e +--R + +--R 3 2 2 2 3 3 +--R 72a b d e - 24a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b e x + 45a b e x + 45a b e x + 15a e ) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (30b e x + (80a b e - 20b d e)x + 66a e - 52a b d e + 16b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (48a b e - 144a b d e + 144a b d e - 48b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x + 48a e +--R + +--R 5 2 4 2 2 3 3 3 +--R - 144a b d e + 144a b d e - 48a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b e x + 45a b e x + 45a b e x + 15a e ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (40a b e - 10b d e)x + 33a e - 26a b d e + 8b d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x + 24a e +--R + +--R 5 2 4 2 2 3 3 3 +--R - 72a b d e + 72a b d e - 24a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 3 + +--S 4 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (15b e x + 45a b e x + 45a b e x + 15a e )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R (30b e x + 120a b e x + 180a b e x + 120a b e x + 30a e ) +--R * +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R \|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (30b e x + (80a b e - 20b d e)x + 66a e - 52a b d e + 16b d ) +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 30b e x + (- 110a b e + 20b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 146a b e + 72a b d e - 16b d )x - 66a e + 52a b d e - 16a b d +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +-------+ +--R \|- a b e + b d \|- a e + b d \|b \|e x + d +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (48a b e - 144a b d e + 144a b d e - 48b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (144a b e - 432a b d e + 432a b d e - 144a b d )x + 48a e +--R + +--R 5 2 4 2 2 3 3 3 +--R - 144a b d e + 144a b d e - 48a b d +--R * +--R +-------------+ +------------------+ +--R | 2 +-----------+ +-+ | 2 2 2 +--R \|- a b e + b d \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +-------------+ +--R 2 +-------+ | 2 +--R ((2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 3 2 2 +-------+ +--R ((- 2a b e + 2b d)x - 2a b e + 2a b d)\|e x + d +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +--R (- b e x - 2b d x + a e - 2a b d)\|- a b e + b d +--R / +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (3a b e + 2b d)x + (2a b e + 8a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 2a b e + 12a b d)x + (- 3a b e + 8a b d)x - a e + 2a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (2a b e - 2b d e)x + (8a b e - 6a b d e - 2b d )x +--R + +--R 3 3 2 2 4 5 2 3 4 2 2 3 3 2 4 2 2 +--R (12a b e - 4a b d e - 8a b d )x + (8a b e + 4a b d e - 12a b d )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (2a b e + 6a b d e - 8a b d )x + 2a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 5 + +--S 6 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 | 2 +--R (15b e x + 60a b e x + 90a b e x + 60a b e x + 15a e )\|a b e - b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +-+ +--R (15b e x + 45a b e x + 45a b e x + 15a e )\|- a e + b d \|b +--R * +--R +-----------+ +--R +------------------+ | 2 +-------+ +--R | 2 2 2 \|a b e - b d \|e x + d +--R \|b x + 2a b x + a atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (40a b e - 10b d e)x + 33a e - 26a b d e + 8b d ) +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 +-------+ | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|e x + d \|b x + 2a b x + a +--R + +--R 3 2 3 2 2 3 2 +--R - 15b e x + (- 55a b e + 10b d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 73a b e + 36a b d e - 8b d )x - 33a e + 26a b d e - 8a b d +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +-------+ +--R \|- a e + b d \|b \|a b e - b d \|e x + d +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x + 24a e - 72a b d e +--R + +--R 4 2 2 3 3 3 +--R 72a b d e - 24a b d +--R * +--R +-----------+ +------------------+ +--R +-----------+ +-+ | 2 | 2 2 2 +--R \|- a e + b d \|b \|a b e - b d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 7 + +)clear all + +--S 8 of 1751 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 8 + +--S 9 of 1751 +r0:=2/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))-_ + 7/3*b*sqrt(d+e*x)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/12*b*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/8*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b)/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 35/8*b*e^2*sqrt(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-+ +-------+ +--R (105b e x + 315a b e x + 315a b e x + 105a e )\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 280a b e - 35b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 231a b e - 98a b d e + 14b d e)x - 48a e - 87a b d e +--R + +--R 2 2 3 3 +--R 38a b d e - 8b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 +--R (48a b e - 192a b d e + 288a b d e - 192a b d e + 48a b d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 3 2 3 2 2 3 3 3 | b +--R (105b e x + 315a b e x + 315a b e x + 105a e ) |- --------- +--R \| a e - b d +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R - 210b e x + (- 560a b e - 70b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 462a b e - 196a b d e + 28b d e)x - 96a e - 174a b d e +--R + +--R 2 2 3 3 +--R 76a b d e - 16b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (48a b e - 192a b d e + 288a b d e - 192a b d e + 48b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 48a e - 192a b d e + 288a b d e - 192a b d e + 48a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +---------+ +--R 3 3 3 2 3 2 2 3 3 3 | b +--R (- 105b e x - 315a b e x - 315a b e x - 105a e ) |--------- +--R \|a e - b d +--R * +--R +-------+ +--R +-------+ b\|e x + d +--R \|e x + d atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 280a b e - 35b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 231a b e - 98a b d e + 14b d e)x - 48a e - 87a b d e + 38a b d e +--R + +--R 3 3 +--R - 8b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 10 + +--S 11 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +--R (105b e x + 315a b e x + 315a b e x + 105a e )\|- a e + b d +--R * +--R +-----------+ +------------------+ +--R | b +-------+ | 2 2 2 +--R |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +-+ +--R (- 210b e x - 840a b e x - 1260a b e x - 840a b e x - 210a e )\|b +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 210b e x + (- 560a b e - 70b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 462a b e - 196a b d e + 28b d e)x - 96a e - 174a b d e +--R + +--R 2 2 3 3 +--R 76a b d e - 16b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R 210b e x + (770a b e + 70b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (1022a b e + 266a b d e - 28b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (558a b e + 370a b d e - 104a b d e + 16b d )x + 96a e +--R + +--R 3 2 2 2 2 3 3 +--R 174a b d e - 76a b d e + 16a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (48a b e - 192a b d e + 288a b d e - 192a b d e + 48b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (144a b e - 576a b d e + 864a b d e - 576a b d e + 144a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 48a e - 192a b d e + 288a b d e - 192a b d e + 48a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +-+ +--R (- 105b e x - 420a b e x - 630a b e x - 420a b e x - 105a e )\|b +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +--R (- 105b e x - 315a b e x - 315a b e x - 105a e )\|- a e + b d +--R * +--R +---------+ +------------------+ +-------+ +--R | b +-------+ | 2 2 2 b\|e x + d +--R |--------- \|e x + d \|b x + 2a b x + a atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 280a b e - 35b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 231a b e - 98a b d e + 14b d e)x - 48a e - 87a b d e +--R + +--R 2 2 3 3 +--R 38a b d e - 8b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R 105b e x + (385a b e + 35b d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (511a b e + 133a b d e - 14b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (279a b e + 185a b d e - 52a b d e + 8b d )x + 48a e + 87a b d e +--R + +--R 2 2 2 3 3 +--R - 38a b d e + 8a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 13 + +--S 14 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 14 + +)clear all + +--S 15 of 1751 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 15 + +--S 16 of 1751 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 6*b/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))-_ + 7*b^2*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/4*b^2*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 105/8*b^(3/2)*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 105/8*b^2*e^2*sqrt(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 945a b e - 315b d e )x +--R + +--R 2 2 4 3 3 2 3 4 2 2 3 +--R (- 945a b e - 945a b d e )x + (- 315a b e - 945a b d e )x +--R + +--R 3 3 +--R - 315a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (840a b e + 420b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (693a b e + 1134a b d e + 63b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (144a b e + 954a b d e + 180a b d e - 18b d e)x - 16a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 208a b d e + 165a b d e - 50a b d e + 8b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 7 5 +--R - 24b d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 6 5 +--R 48a b e - 216a b d e + 360a b d e - 240a b d e + 72a b d e +--R + +--R 7 6 +--R - 24b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 5 4 3 3 3 3 4 4 2 2 5 5 +--R 24a e - 72a b d e + 240a b d e - 360a b d e + 216a b d e +--R + +--R 6 6 +--R - 48a b d +--R * +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 2 5 6 +--R - 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 315b e x + (945a b e + 315b d e )x + (945a b e + 945a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (315a b e + 945a b d e )x + 315a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 630b e x + (1680a b e + 840b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1386a b e + 2268a b d e + 126b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (288a b e + 1908a b d e + 360a b d e - 36b d e)x - 32a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 416a b d e + 330a b d e - 100a b d e + 16b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 +--R 144a b e - 672a b d e + 1200a b d e - 960a b d e +--R + +--R 2 6 4 2 7 5 8 6 +--R 240a b d e + 96a b d e - 48b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 144a b e - 576a b d e + 720a b d e - 720a b d e + 576a b d e +--R + +--R 7 6 +--R - 144a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 48a e - 96a b d e - 240a b d e + 960a b d e - 1200a b d e +--R + +--R 3 5 5 2 6 6 +--R 672a b d e - 144a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 5 6 +--R - 48a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 315b e x + (945a b e + 315b d e )x + (945a b e + 945a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (315a b e + 945a b d e )x + 315a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (840a b e + 420b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (693a b e + 1134a b d e + 63b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (144a b e + 954a b d e + 180a b d e - 18b d e)x - 16a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 208a b d e + 165a b d e - 50a b d e + 8b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 8 5 +--R - 24b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b e - 336a b d e + 600a b d e - 480a b d e + 120a b d e +--R + +--R 7 5 8 6 +--R 48a b d e - 24b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b e - 288a b d e + 360a b d e - 360a b d e + 288a b d e +--R + +--R 7 6 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a e - 48a b d e - 120a b d e + 480a b d e - 600a b d e +--R + +--R 3 5 5 2 6 6 +--R 336a b d e - 72a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 3 5 6 +--R - 24a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 17 + +--S 18 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 315b e x + (945a b e + 315b d e )x + (945a b e + 945a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (315a b e + 945a b d e )x + 315a b d e +--R * +--R +-----------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |- --------- \|e x + d \|b x + 2a b x + a +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 630b e x + (2520a b e + 630b d e )x +--R + +--R 2 3 4 4 3 3 3 2 4 2 3 3 2 +--R (3780a b e + 2520a b d e )x + (2520a b e + 3780a b d e )x +--R + +--R 4 4 3 2 3 4 3 +--R (630a b e + 2520a b d e )x + 630a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 630b e x + (1680a b e + 840b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1386a b e + 2268a b d e + 126b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (288a b e + 1908a b d e + 360a b d e - 36b d e)x - 32a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 416a b d e + 330a b d e - 100a b d e + 16b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 630b e x + (- 2310a b e - 840b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 3066a b e - 3108a b d e - 126b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 1674a b e - 4176a b d e - 486a b d e + 36b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 256a b e - 2324a b d e - 690a b d e + 136a b d e - 16b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 32a e - 416a b d e - 330a b d e + 100a b d e - 16a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 144a b e - 672a b d e + 1200a b d e - 960a b d e + 240a b d e +--R + +--R 7 5 8 6 +--R 96a b d e - 48b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 144a b e - 576a b d e + 720a b d e - 720a b d e + 576a b d e +--R + +--R 7 6 +--R - 144a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 48a e - 96a b d e - 240a b d e + 960a b d e - 1200a b d e +--R + +--R 3 5 5 2 6 6 +--R 672a b d e - 144a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 5 6 +--R - 48a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 18 + +--S 19 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 4 5 4 4 5 3 4 +--R 315b e x + (1260a b e + 315b d e )x +--R + +--R 2 3 4 4 3 3 3 2 4 2 3 3 2 +--R (1890a b e + 1260a b d e )x + (1260a b e + 1890a b d e )x +--R + +--R 4 4 3 2 3 4 3 +--R (315a b e + 1260a b d e )x + 315a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 315b e x + (945a b e + 315b d e )x + (945a b e + 945a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (315a b e + 945a b d e )x + 315a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (840a b e + 420b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (693a b e + 1134a b d e + 63b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (144a b e + 954a b d e + 180a b d e - 18b d e)x - 16a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 208a b d e + 165a b d e - 50a b d e + 8b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R - 315b e x + (- 1155a b e - 420b d e )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (- 1533a b e - 1554a b d e - 63b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 837a b e - 2088a b d e - 243a b d e + 18b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 128a b e - 1162a b d e - 345a b d e + 68a b d e - 8b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 16a e - 208a b d e - 165a b d e + 50a b d e - 8a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 8 5 +--R - 24b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b e - 336a b d e + 600a b d e - 480a b d e + 120a b d e +--R + +--R 7 5 8 6 +--R 48a b d e - 24b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b e - 288a b d e + 360a b d e - 360a b d e + 288a b d e +--R + +--R 7 6 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a e - 48a b d e - 120a b d e + 480a b d e - 600a b d e +--R + +--R 3 5 5 2 6 6 +--R 336a b d e - 72a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 3 5 6 +--R - 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 20 + +--S 21 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 of 1751 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 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4 2 3 5 3 2 2 +--R (- 3168a b e - 36234a b d e - 28908a b d e - 990b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (352a b e - 7744a b d e - 24618a b d e - 2860a b d e + 220b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 96a e + 832a b d e - 5536a b d e - 2670a b d e + 620a b d e +--R + +--R 5 5 +--R - 80b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 6 5 6 5 5 6 4 5 +--R 6930b e x + (25410a b e + 16170b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (33726a b e + 59598a b d e + 10626b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 3 +--R (18414a b e + 79662a b d e + 39534a b d e + 990b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 +--R 2816a b e + 43978a b d e + 53526a b d e + 3850a b d e +--R + +--R 6 4 +--R - 220b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 +--R - 256a b e + 6912a b d e + 30154a b d e + 5530a b d e +--R + +--R 5 4 6 5 +--R - 840a b d e + 80b d +--R * +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 96a e - 832a b d e + 5536a b d e + 2670a b d e - 620a b d e +--R + +--R 5 5 +--R 80a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 240a b e - 1440a b d e + 3600a b d e - 4800a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 3600a b d e - 1440a b d e + 240b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 720a b e - 3840a b d e + 7920a b d e - 7200a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 1200a b d e + 2880a b d e - 2160a b d e + 480b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 720a b e - 2880a b d e + 2400a b d e + 5760a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 14400a b d e + 12480a b d e - 4320a b d e + 240b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 +--R 240a e - 4320a b d e + 12480a b d e - 14400a b d e +--R + +--R 4 5 5 3 3 6 6 2 2 7 7 8 8 +--R 5760a b d e + 2400a b d e - 2880a b d e + 720a b d +--R * +--R 2 +--R x +--R + +--R 9 7 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4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 5 6 5 5 6 4 5 +--R - 3465b e x + (- 13860a b e - 6930b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (- 20790a b e - 27720a b d e - 3465b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 3 +--R (- 13860a b e - 41580a b d e - 13860a b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 2 +--R (- 3465a b e - 27720a b d e - 20790a b d e )x +--R + +--R 4 2 4 3 3 2 3 4 2 2 3 +--R (- 6930a b d e - 13860a b d e )x - 3465a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R - 3465b e x + (- 10395a b e - 6930b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 10395a b e - 20790a b d e - 3465b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (- 3465a b e - 20790a b d e - 10395a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (- 6930a b d e - 10395a b d e )x - 3465a b d e +--R * +--R +---------+ +------------------+ +--R +-----------+ | b +-------+ | 2 2 2 +--R \|- a e + b d |--------- \|e x + d \|b x + 2a b x + a +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 5 5 5 4 5 5 4 4 +--R - 3465b e x + (- 9240a b e - 8085b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 7623a b e - 21714a b d e - 5313b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 1584a b e - 18117a b d e - 14454a b d e - 495b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (176a b e - 3872a b d e - 12309a b d e - 1430a b d e + 110b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 48a e + 416a b d e - 2768a b d e - 1335a b d e + 310a b d e +--R + +--R 5 5 +--R - 40b d +--R * +--R +------------------+ +--R +-----------+ | 2 2 2 +--R \|- a e + b d \|b x + 2a b x + a +--R + +--R 6 5 6 5 5 6 4 5 +--R 3465b e x + (12705a b e + 8085b d e )x +--R + +--R 2 4 5 5 4 6 2 3 4 +--R (16863a b e + 29799a b d e + 5313b d e )x +--R + +--R 3 3 5 2 4 4 5 2 3 6 3 2 3 +--R (9207a b e + 39831a b d e + 19767a b d e + 495b d e )x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 +--R 1408a b e + 21989a b d e + 26763a b d e + 1925a b d e +--R + +--R 6 4 +--R - 110b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 +--R - 128a b e + 3456a b d e + 15077a b d e + 2765a b d e +--R + +--R 5 4 6 5 +--R - 420a b d e + 40b d +--R * +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 48a e - 416a b d e + 2768a b d e + 1335a b d e - 310a b d e +--R + +--R 5 5 +--R 40a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 120a b e - 720a b d e + 1800a b d e - 2400a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 1800a b d e - 720a b d e + 120b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 360a b e - 1920a b d e + 3960a b d e - 3600a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 600a b d e + 1440a b d e - 1080a b d e + 240b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 360a b e - 1440a b d e + 1200a b d e + 2880a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 7200a b d e + 6240a b d e - 2160a b d e + 120b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 4 5 5 3 +--R 120a e - 2160a b d e + 6240a b d e - 7200a b d e + 2880a b d e +--R + +--R 3 6 6 2 2 7 7 8 8 +--R 1200a b d e - 1440a b d e + 360a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 +--R 240a d e - 1080a b d e + 1440a b d e + 600a b d e +--R + +--R 5 4 5 3 4 5 6 2 3 6 7 2 7 8 +--R - 3600a b d e + 3960a b d e - 1920a b d e + 360a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 120a d e - 720a b d e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 5 7 3 6 8 +--R - 720a b d e + 120a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - b x - a +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 28 + +)clear all + +--S 29 of 1751 +t0:=(a+b*x)*(d+e*x)^(-3-2*p)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R - 2p - 3 2 2 2 p +--R (1) (b x + a)(e x + d) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1751 +r0:=1/2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/((b*d-a*e)*(1+p)*(d+e*x)^(2*(1+p))) +--R +--R +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R (2) - --------------------------------------------- +--R 2p + 2 +--R ((2a e - 2b d)p + 2a e - 2b d)(e x + d) +--R Type: Expression(Integer) +--E 30 + +--S 31 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 +--R (- b e x + (- 2a b e - b d)x + (- a e - 2a b d)x - a d) +--R * +--R 2 2 2 +--R (- 2p - 3)log(e x + d) p log(b x + 2a b x + a ) +--R %e %e +--R / +--R (2a e - 2b d)p + 2a e - 2b d +--R Type: Union(Expression(Integer),...) +--E 31 + +--S 32 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 +--R (- b e x + (- 2a b e - b d)x + (- a e - 2a b d)x - a d) +--R * +--R 2 2 2 +--R 2p + 2 (- 2p - 3)log(e x + d) p log(b x + 2a b x + a ) +--R (e x + d) %e %e +--R + +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 2p + 2 +--R ((2a e - 2b d)p + 2a e - 2b d)(e x + d) +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 of 1751 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R 2 2 2 p +--R (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1751 +r0:=3/2*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^4*(1+p)*(2+p)*(3+2*p)*_ + (5+2*p))+3*(b*d-a*e)^2*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^3*(2+p)*_ + (3+2*p)*(5+2*p))+3/2*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/_ + (b^2*(2+p)*(5+2*p))+(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(5+2*p)) +--R +--R +--R (2) +--R 3 3 3 3 3 2 3 3 3 3 3 +--R (4b e p + 18b e p + 26b e p + 12b e )x +--R + +--R 3 2 3 2 3 3 2 2 2 3 3 2 +--R 12b d e p + (- 6a b e + 60b d e )p + (- 15a b e + 93b d e )p +--R + +--R 2 3 3 2 +--R - 9a b e + 45b d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 3 2 2 +--R 12b d e p + (- 12a b d e + 66b d e)p +--R + +--R 2 3 2 2 3 2 2 3 2 2 3 2 +--R (6a b e - 42a b d e + 114b d e)p + 6a b e - 30a b d e + 60b d e +--R * +--R x +--R + +--R 3 3 3 2 2 3 3 2 2 2 2 2 3 3 +--R 4b d p + (- 6a b d e + 24b d )p + (6a b d e - 27a b d e + 47b d )p +--R + +--R 3 3 2 2 2 2 3 3 +--R - 3a e + 15a b d e - 30a b d e + 30b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 4 4 4 3 4 2 4 4 +--R 8b p + 56b p + 142b p + 154b p + 60b +--R Type: Expression(Integer) +--E 35 + +--S 36 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 3 5 3 2 5 3 5 3 5 +--R (4b e p + 18b e p + 26b e p + 12b e )x +--R + +--R 4 3 5 2 3 4 3 5 2 2 +--R (8a b e + 12b d e )p + (30a b e + 60b d e )p +--R + +--R 4 3 5 2 4 3 5 2 +--R (37a b e + 93b d e )p + 15a b e + 45b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 4 2 5 2 3 +--R (4a b e + 24a b d e + 12b d e)p +--R + +--R 2 3 3 4 2 5 2 2 +--R (6a b e + 108a b d e + 66b d e)p +--R + +--R 2 3 3 4 2 5 2 4 2 5 2 +--R (2a b e + 144a b d e + 114b d e)p + 60a b d e + 60b d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 4 2 5 3 3 +--R (12a b d e + 24a b d e + 4b d )p +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 6a b e + 36a b d e + 126a b d e + 24b d )p +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 2 5 3 +--R (- 3a b e + 15a b d e + 201a b d e + 47b d )p + 90a b d e + 30b d +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 3 3 3 2 2 2 3 2 4 3 2 +--R (12a b d e + 8a b d )p + (- 12a b d e + 54a b d e + 48a b d )p +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 3 +--R (6a b e - 30a b d e + 60a b d e + 94a b d )p + 60a b d +--R * +--R x +--R + +--R 2 3 3 3 3 2 2 2 3 3 2 +--R 4a b d p + (- 6a b d e + 24a b d )p +--R + +--R 4 2 3 2 2 2 3 3 5 3 4 2 3 2 2 +--R (6a b d e - 27a b d e + 47a b d )p - 3a e + 15a b d e - 30a b d e +--R + +--R 2 3 3 +--R 30a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R 8b p + 56b p + 142b p + 154b p + 60b +--R Type: Union(Expression(Integer),...) +--E 36 + +--S 37 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 3 3 5 3 2 5 3 5 3 5 +--R (4b e p + 18b e p + 26b e p + 12b e )x +--R + +--R 4 3 5 2 3 4 3 5 2 2 +--R (8a b e + 12b d e )p + (30a b e + 60b d e )p +--R + +--R 4 3 5 2 4 3 5 2 +--R (37a b e + 93b d e )p + 15a b e + 45b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 4 2 5 2 3 +--R (4a b e + 24a b d e + 12b d e)p +--R + +--R 2 3 3 4 2 5 2 2 +--R (6a b e + 108a b d e + 66b d e)p +--R + +--R 2 3 3 4 2 5 2 4 2 5 2 +--R (2a b e + 144a b d e + 114b d e)p + 60a b d e + 60b d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 4 2 5 3 3 +--R (12a b d e + 24a b d e + 4b d )p +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 6a b e + 36a b d e + 126a b d e + 24b d )p +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 2 +--R (- 3a b e + 15a b d e + 201a b d e + 47b d )p + 90a b d e +--R + +--R 5 3 +--R 30b d +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 3 3 3 2 2 2 3 2 4 3 2 +--R (12a b d e + 8a b d )p + (- 12a b d e + 54a b d e + 48a b d )p +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 3 +--R (6a b e - 30a b d e + 60a b d e + 94a b d )p + 60a b d +--R * +--R x +--R + +--R 2 3 3 3 3 2 2 2 3 3 2 +--R 4a b d p + (- 6a b d e + 24a b d )p +--R + +--R 4 2 3 2 2 2 3 3 5 3 4 2 3 2 2 +--R (6a b d e - 27a b d e + 47a b d )p - 3a e + 15a b d e - 30a b d e +--R + +--R 2 3 3 +--R 30a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R + +--R 3 3 3 3 3 2 3 3 3 3 3 +--R (- 4b e p - 18b e p - 26b e p - 12b e )x +--R + +--R 3 2 3 2 3 3 2 2 2 3 3 2 +--R - 12b d e p + (6a b e - 60b d e )p + (15a b e - 93b d e )p +--R + +--R 2 3 3 2 +--R 9a b e - 45b d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 3 2 2 +--R - 12b d e p + (12a b d e - 66b d e)p +--R + +--R 2 3 2 2 3 2 2 3 2 2 +--R (- 6a b e + 42a b d e - 114b d e)p - 6a b e + 30a b d e +--R + +--R 3 2 +--R - 60b d e +--R * +--R x +--R + +--R 3 3 3 2 2 3 3 2 +--R - 4b d p + (6a b d e - 24b d )p +--R + +--R 2 2 2 2 3 3 3 3 2 2 2 2 +--R (- 6a b d e + 27a b d e - 47b d )p + 3a e - 15a b d e + 30a b d e +--R + +--R 3 3 +--R - 30b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 4 4 4 3 4 2 4 4 +--R 8b p + 56b p + 142b p + 154b p + 60b +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 38 + +)clear all + +--S 39 of 1751 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R (1) +--R 2 3 2 2 2 2 2 2 2 p +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1751 +r0:=1/2*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^3*(1+p)*(2+p)*(3+2*p))+_ + (b*d-a*e)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^2*(2+p)*(3+2*p))+_ + 1/2*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(2+p)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (2b e p + 5b e p + 3b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4b d e p + (- 2a b e + 12b d e)p - 2a b e + 8b d e)x + 2b d p +--R + +--R 2 2 2 2 2 2 +--R (- 2a b d e + 7b d )p + a e - 4a b d e + 6b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 3 3 3 2 3 3 +--R 4b p + 18b p + 26b p + 12b +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 2 4 2 4 2 4 +--R (2b e p + 5b e p + 3b e )x +--R + +--R 3 2 4 2 3 2 4 3 2 4 3 +--R ((4a b e + 4b d e)p + (8a b e + 12b d e)p + 4a b e + 8b d e)x +--R + +--R 2 2 2 3 4 2 2 2 2 2 3 4 2 +--R (2a b e + 8a b d e + 2b d )p + (a b e + 22a b d e + 7b d )p +--R + +--R 3 4 2 +--R 12a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 3 2 2 2 3 2 +--R (4a b d e + 4a b d )p + (- 2a b e + 8a b d e + 14a b d )p +--R + +--R 3 2 +--R 12a b d +--R * +--R x +--R + +--R 2 2 2 2 3 2 2 2 4 2 3 2 2 2 +--R 2a b d p + (- 2a b d e + 7a b d )p + a e - 4a b d e + 6a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R / +--R 3 3 3 2 3 3 +--R 4b p + 18b p + 26b p + 12b +--R Type: Union(Expression(Integer),...) +--E 41 + +--S 42 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 2 4 2 4 2 4 +--R (2b e p + 5b e p + 3b e )x +--R + +--R 3 2 4 2 3 2 4 3 2 4 3 +--R ((4a b e + 4b d e)p + (8a b e + 12b d e)p + 4a b e + 8b d e)x +--R + +--R 2 2 2 3 4 2 2 2 2 2 3 4 2 +--R (2a b e + 8a b d e + 2b d )p + (a b e + 22a b d e + 7b d )p +--R + +--R 3 4 2 +--R 12a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 3 2 2 2 3 2 +--R (4a b d e + 4a b d )p + (- 2a b e + 8a b d e + 14a b d )p +--R + +--R 3 2 +--R 12a b d +--R * +--R x +--R + +--R 2 2 2 2 3 2 2 2 4 2 3 2 2 2 +--R 2a b d p + (- 2a b d e + 7a b d )p + a e - 4a b d e + 6a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 2b e p - 5b e p - 3b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 4b d e p + (2a b e - 12b d e)p + 2a b e - 8b d e)x - 2b d p +--R + +--R 2 2 2 2 2 2 +--R (2a b d e - 7b d )p - a e + 4a b d e - 6b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 3 3 3 2 3 3 +--R 4b p + 18b p + 26b p + 12b +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 43 + +)clear all + +--S 44 of 1751 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R 2 2 2 2 p +--R (1) (b e x + (a e + b d)x + a d)(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1751 +r0:=1/2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^2*(1+p)*(3+2*p))+(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(3+2*p)) +--R +--R +--R 2 2 2 p + 1 +--R ((2b e p + 2b e)x + 2b d p - a e + 3b d)(b x + 2a b x + a ) +--R (2) ----------------------------------------------------------------- +--R 2 2 2 2 +--R 4b p + 10b p + 6b +--R Type: Expression(Integer) +--E 45 + +--S 46 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 3 2 +--R (2b e p + 2b e)x + ((4a b e + 2b d)p + 3a b e + 3b d)x +--R + +--R 2 2 2 2 3 2 +--R ((2a b e + 4a b d)p + 6a b d)x + 2a b d p - a e + 3a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R / +--R 2 2 2 2 +--R 4b p + 10b p + 6b +--R Type: Union(Expression(Integer),...) +--E 46 + +--S 47 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 2 3 2 +--R (2b e p + 2b e)x + ((4a b e + 2b d)p + 3a b e + 3b d)x +--R + +--R 2 2 2 2 3 2 +--R ((2a b e + 4a b d)p + 6a b d)x + 2a b d p - a e + 3a b d +--R * +--R 2 2 2 +--R p log(b x + 2a b x + a ) +--R %e +--R + +--R 2 2 2 p + 1 +--R ((- 2b e p - 2b e)x - 2b d p + a e - 3b d)(b x + 2a b x + a ) +--R / +--R 2 2 2 2 +--R 4b p + 10b p + 6b +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 48 + +)clear all + +--S 49 of 1751 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R 2 2 2 p +--R (1) (b x + a)(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1751 +r0:=1/2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(1+p)) +--R +--R +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R (2) ------------------------- +--R 2b p + 2b +--R Type: Expression(Integer) +--E 50 + +--S 51 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2 2 2 p log(b x + 2a b x + a ) +--R (b x + 2a b x + a )%e +--R (3) ----------------------------------------------- +--R 2b p + 2b +--R Type: Union(Expression(Integer),...) +--E 51 + +--S 52 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 +--R 2 2 2 p log(b x + 2a b x + a ) 2 2 2 p + 1 +--R (b x + 2a b x + a )%e - (b x + 2a b x + a ) +--R --------------------------------------------------------------------------- +--R 2b p + 2b +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 53 + +)clear all + +--S 54 of 1751 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p/(d+e*x) +--R +--R +--R 2 2 2 p +--R (b x + a)(b x + 2a b x + a ) +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1751 +--r0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p/(e*(1+2*p))-(a+b*x)*_ +-- (a^2+2*a*b*x+b^2*x^2)^p*hypergeometric(1,1+2*p,2*(1+p),_ +-- -e*(a+b*x)/(b*d-a*e))/(e*(1+2*p)) +--E 55 + +--S 56 of 1751 +--a0:=integrate(t0,x) +--E 56 + +--S 57 of 1751 +--m0:=a0-r0 +--E 57 + +--S 58 of 1751 +--d0:=D(m0,x) +--E 58 + +)clear all + +--S 59 of 1751 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R * +--R m +--R (b c x + a c) +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1751 +r0:=(A*b-a*B)*(a*c+b*c*x)^(7+m)/(b^2*c^7*(7+m))+B*(a*c+b*c*x)^(8+m)/_ + (b^2*c^8*(8+m)) +--R +--R +--R (2) +--R m + 8 +--R (B m + 7B)(b c x + a c) +--R + +--R m + 7 +--R ((A b - B a)c m + (8A b - 8B a)c)(b c x + a c) +--R / +--R 2 8 2 2 8 2 8 +--R b c m + 15b c m + 56b c +--R Type: Expression(Integer) +--E 60 + +--S 61 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 8 8 7 8 7 7 +--R (B b m + 7B b )x + ((A b + 7B a b )m + 8A b + 48B a b )x +--R + +--R 7 2 6 7 2 6 6 +--R ((7A a b + 21B a b )m + 56A a b + 140B a b )x +--R + +--R 2 6 3 5 2 6 3 5 5 +--R ((21A a b + 35B a b )m + 168A a b + 224B a b )x +--R + +--R 3 5 4 4 3 5 4 4 4 +--R ((35A a b + 35B a b )m + 280A a b + 210B a b )x +--R + +--R 4 4 5 3 4 4 5 3 3 +--R ((35A a b + 21B a b )m + 280A a b + 112B a b )x +--R + +--R 5 3 6 2 5 3 6 2 2 +--R ((21A a b + 7B a b )m + 168A a b + 28B a b )x +--R + +--R 6 2 7 6 2 7 7 8 +--R ((7A a b + B a b)m + 56A a b )x + A a b m + 8A a b - B a +--R * +--R m log(b c x + a c) +--R %e +--R / +--R 2 2 2 2 +--R b m + 15b m + 56b +--R Type: Union(Expression(Integer),...) +--E 61 + +--S 62 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8 8 8 8 +--R (B b c m + 7B b c )x +--R + +--R 8 7 8 8 7 8 7 +--R ((A b + 7B a b )c m + (8A b + 48B a b )c )x +--R + +--R 7 2 6 8 7 2 6 8 6 +--R ((7A a b + 21B a b )c m + (56A a b + 140B a b )c )x +--R + +--R 2 6 3 5 8 2 6 3 5 8 5 +--R ((21A a b + 35B a b )c m + (168A a b + 224B a b )c )x +--R + +--R 3 5 4 4 8 3 5 4 4 8 4 +--R ((35A a b + 35B a b )c m + (280A a b + 210B a b )c )x +--R + +--R 4 4 5 3 8 4 4 5 3 8 3 +--R ((35A a b + 21B a b )c m + (280A a b + 112B a b )c )x +--R + +--R 5 3 6 2 8 5 3 6 2 8 2 +--R ((21A a b + 7B a b )c m + (168A a b + 28B a b )c )x +--R + +--R 6 2 7 8 6 2 8 7 8 7 8 8 +--R ((7A a b + B a b)c m + 56A a b c )x + A a b c m + (8A a b - B a )c +--R * +--R m log(b c x + a c) +--R %e +--R + +--R m + 8 +--R (- B m - 7B)(b c x + a c) +--R + +--R m + 7 +--R ((- A b + B a)c m + (- 8A b + 8B a)c)(b c x + a c) +--R / +--R 2 8 2 2 8 2 8 +--R b c m + 15b c m + 56b c +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 1751 +t0:=(A+B*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R m +--R (B x + A)(b c x + a c) +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1751 +r0:=-(A*b-a*B)*c^5*(a*c+b*c*x)^(-5+m)/(b^2*(5-m))-B*c^4*(a*c+b*c*x)^(-4+m)/_ + (b^2*(4-m)) +--R +--R +--R (2) +--R 4 4 m - 4 +--R (B c m - 5B c )(b c x + a c) +--R + +--R 5 5 m - 5 +--R ((A b - B a)c m + (- 4A b + 4B a)c )(b c x + a c) +--R / +--R 2 2 2 2 +--R b m - 9b m + 20b +--R Type: Expression(Integer) +--E 65 + +--S 66 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R m log(b c x + a c) +--R ((B b m - 5B b)x + A b m - 4A b - B a)%e +--R / +--R 7 2 7 7 5 6 2 6 6 4 +--R (b m - 9b m + 20b )x + (5a b m - 45a b m + 100a b )x +--R + +--R 2 5 2 2 5 2 5 3 3 4 2 3 4 3 4 2 +--R (10a b m - 90a b m + 200a b )x + (10a b m - 90a b m + 200a b )x +--R + +--R 4 3 2 4 3 4 3 5 2 2 5 2 5 2 +--R (5a b m - 45a b m + 100a b )x + a b m - 9a b m + 20a b +--R Type: Union(Expression(Integer),...) +--E 66 + +--S 67 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R m log(b c x + a c) +--R ((B b m - 5B b)x + A b m - 4A b - B a)%e +--R + +--R 5 4 5 4 5 4 4 4 4 4 +--R (- B b c m + 5B b c )x + (- 5B a b c m + 25B a b c )x +--R + +--R 2 3 4 2 3 4 3 3 2 4 3 2 4 2 +--R (- 10B a b c m + 50B a b c )x + (- 10B a b c m + 50B a b c )x +--R + +--R 4 4 4 4 5 4 5 4 +--R (- 5B a b c m + 25B a b c )x - B a c m + 5B a c +--R * +--R m - 4 +--R (b c x + a c) +--R + +--R 6 5 5 6 5 5 5 +--R ((- A b + B a b )c m + (4A b - 4B a b )c )x +--R + +--R 5 2 4 5 5 2 4 5 4 +--R ((- 5A a b + 5B a b )c m + (20A a b - 20B a b )c )x +--R + +--R 2 4 3 3 5 2 4 3 3 5 3 +--R ((- 10A a b + 10B a b )c m + (40A a b - 40B a b )c )x +--R + +--R 3 3 4 2 5 3 3 4 2 5 2 +--R ((- 10A a b + 10B a b )c m + (40A a b - 40B a b )c )x +--R + +--R 4 2 5 5 4 2 5 5 +--R ((- 5A a b + 5B a b)c m + (20A a b - 20B a b)c )x +--R + +--R 5 6 5 5 6 5 +--R (- A a b + B a )c m + (4A a b - 4B a )c +--R * +--R m - 5 +--R (b c x + a c) +--R / +--R 7 2 7 7 5 6 2 6 6 4 +--R (b m - 9b m + 20b )x + (5a b m - 45a b m + 100a b )x +--R + +--R 2 5 2 2 5 2 5 3 3 4 2 3 4 3 4 2 +--R (10a b m - 90a b m + 200a b )x + (10a b m - 90a b m + 200a b )x +--R + +--R 4 3 2 4 3 4 3 5 2 2 5 2 5 2 +--R (5a b m - 45a b m + 100a b )x + a b m - 9a b m + 20a b +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 68 + +)clear all + +--S 69 of 1751 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 m +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(b c x + a c) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1751 +r0:=(A*b-a*B)*(a*c+b*c*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*c*(4+m))+_ + B*(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*c^2*(5+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R ((B b m + 4B b )x + (2B a b m + 8B a b)x + B a m + 4B a ) +--R * +--R m + 2 +--R (b c x + a c) +--R + +--R 3 2 3 2 2 +--R ((A b - B a b )c m + (5A b - 5B a b )c)x +--R + +--R 2 2 2 2 +--R ((2A a b - 2B a b)c m + (10A a b - 10B a b)c)x +--R + +--R 2 3 2 3 +--R (A a b - B a )c m + (5A a b - 5B a )c +--R * +--R m + 1 +--R (b c x + a c) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 2 2 2 2 +--R b c m + 9b c m + 20b c +--R Type: Expression(Integer) +--E 70 + +--S 71 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 5 4 5 4 4 +--R (B b m + 4B b )x + ((A b + 4B a b )m + 5A b + 15B a b )x +--R + +--R 4 2 3 4 2 3 3 +--R ((4A a b + 6B a b )m + 20A a b + 20B a b )x +--R + +--R 2 3 3 2 2 3 3 2 2 +--R ((6A a b + 4B a b )m + 30A a b + 10B a b )x +--R + +--R 3 2 4 3 2 4 4 5 +--R ((4A a b + B a b)m + 20A a b )x + A a b m + 5A a b - B a +--R * +--R m log(b c x + a c) +--R %e +--R / +--R 2 2 2 2 +--R b m + 9b m + 20b +--R Type: Union(Expression(Integer),...) +--E 71 + +--S 72 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 5 2 5 +--R (B b c m + 4B b c )x +--R + +--R 5 4 2 5 4 2 4 +--R ((A b + 4B a b )c m + (5A b + 15B a b )c )x +--R + +--R 4 2 3 2 4 2 3 2 3 +--R ((4A a b + 6B a b )c m + (20A a b + 20B a b )c )x +--R + +--R 2 3 3 2 2 2 3 3 2 2 2 +--R ((6A a b + 4B a b )c m + (30A a b + 10B a b )c )x +--R + +--R 3 2 4 2 3 2 2 4 2 4 5 2 +--R ((4A a b + B a b)c m + 20A a b c )x + A a b c m + (5A a b - B a )c +--R * +--R m log(b c x + a c) +--R %e +--R + +--R 2 2 2 2 2 +--R ((- B b m - 4B b )x + (- 2B a b m - 8B a b)x - B a m - 4B a ) +--R * +--R m + 2 +--R (b c x + a c) +--R + +--R 3 2 3 2 2 +--R ((- A b + B a b )c m + (- 5A b + 5B a b )c)x +--R + +--R 2 2 2 2 +--R ((- 2A a b + 2B a b)c m + (- 10A a b + 10B a b)c)x +--R + +--R 2 3 2 3 +--R (- A a b + B a )c m + (- 5A a b + 5B a )c +--R * +--R m + 1 +--R (b c x + a c) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 2 2 2 2 +--R b c m + 9b c m + 20b c +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 4 3 2 3 2 2 2 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 5 4 3 4 3 2 2 3 +--R - B b x + (- A b - 4B a b )x + (- 4A a b - 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 6A a b - 4B a b)x + (- 4A a b - B a )x - A a +--R * +--R m log(b c x + a c) +--R %e +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 73 + +)clear all + +--S 74 of 1751 +t0:=(A+B*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R m +--R (B x + A)(b c x + a c) +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1751 +r0:=-(A*b-a*B)*(a*c+b*c*x)^(1+m)/(b^2*c*(2-m)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + B*(a*c+b*c*x)^(2+m)/(b^2*c^2*(1-m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R m + 2 +--R (B m - 2B)(b c x + a c) +--R + +--R m + 1 +--R ((A b - B a)c m + (- A b + B a)c)(b c x + a c) +--R / +--R 4 2 2 4 2 4 2 2 3 2 2 3 2 3 2 +--R (b c m - 3b c m + 2b c )x + (2a b c m - 6a b c m + 4a b c )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R a b c m - 3a b c m + 2a b c +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 75 + +--S 76 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R m log(b c x + a c) +--R ((B b m - 2B b)x + A b m - A b - B a)%e +--R ----------------------------------------------------------------------------- +--R 4 2 4 4 2 3 2 3 3 2 2 2 2 2 2 2 +--R (b m - 3b m + 2b )x + (2a b m - 6a b m + 4a b )x + a b m - 3a b m + 2a b +--R Type: Union(Expression(Integer),...) +--E 76 + +--S 77 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R ((B b c m - 2B b c )x + A b c m + (- A b - B a)c )\|b x + 2a b x + a +--R * +--R m log(b c x + a c) +--R %e +--R + +--R m + 2 +--R (- B m + 2B)(b c x + a c) +--R + +--R m + 1 +--R ((- A b + B a)c m + (A b - B a)c)(b c x + a c) +--R / +--R 4 2 2 4 2 4 2 2 3 2 2 3 2 3 2 +--R (b c m - 3b c m + 2b c )x + (2a b c m - 6a b c m + 4a b c )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R a b c m - 3a b c m + 2a b c +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +------------------+ +--R | 2 2 2 2 +--R ((B x + A)\|b x + 2a b x + a - B b x + (- A b - B a)x - A a) +--R * +--R m log(b c x + a c) +--R %e +--R / +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 1751 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R m 2 2 2 p +--R (1) (B x + A)(b c x + a c) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1751 +r0:=(A*b-a*B)*(a*c+b*c*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*c*(1+m+2*p))+_ + B*(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*c^2*(2+m+2*p)) +--R +--R +--R (2) +--R m + 2 +--R (2B p + B m + B)(b c x + a c) +--R + +--R m + 1 +--R ((2A b - 2B a)c p + (A b - B a)c m + (2A b - 2B a)c)(b c x + a c) +--R * +--R 2 2 2 p +--R (b x + 2a b x + a ) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +--R 4b c p + (4b c m + 6b c )p + b c m + 3b c m + 2b c +--R Type: Expression(Integer) +--E 80 + +--S 81 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R (2B b p + B b m + B b )x +--R + +--R 2 2 2 +--R ((2A b + 2B a b)p + (A b + B a b)m + 2A b )x + 2A a b p + A a b m +--R + +--R 2 +--R 2A a b - B a +--R * +--R 1 +--R 2p log(b c x + a c) + p log(--) +--R 2 +--R m log(b c x + a c) c +--R %e %e +--R / +--R 2 2 2 2 2 2 2 2 +--R 4b p + (4b m + 6b )p + b m + 3b m + 2b +--R Type: Union(Expression(Integer),...) +--E 81 + +--S 82 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 +--R (2B b c p + B b c m + B b c )x +--R + +--R 2 2 2 2 2 2 2 +--R ((2A b + 2B a b)c p + (A b + B a b)c m + 2A b c )x + 2A a b c p +--R + +--R 2 2 2 +--R A a b c m + (2A a b - B a )c +--R * +--R 1 +--R 2p log(b c x + a c) + p log(--) +--R 2 +--R m log(b c x + a c) c +--R %e %e +--R + +--R m + 2 +--R (- 2B p - B m - B)(b c x + a c) +--R + +--R ((- 2A b + 2B a)c p + (- A b + B a)c m + (- 2A b + 2B a)c) +--R * +--R m + 1 +--R (b c x + a c) +--R * +--R 2 2 2 p +--R (b x + 2a b x + a ) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +--R 4b c p + (4b c m + 6b c )p + b c m + 3b c m + 2b c +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 83 + +)clear all + +--S 84 of 1751 +t0:=(a+b*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R m 2 2 2 p +--R (1) (b x + a)(b c x + a c) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1751 +r0:=(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b*c^2*(2+m+2*p)) +--R +--R +--R m + 2 2 2 2 p +--R (b c x + a c) (b x + 2a b x + a ) +--R (2) --------------------------------------- +--R 2 2 2 +--R 2b c p + b c m + 2b c +--R Type: Expression(Integer) +--E 85 + +--S 86 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 +--R 2p log(b c x + a c) + p log(--) +--R 2 +--R 2 2 2 m log(b c x + a c) c +--R (b x + 2a b x + a )%e %e +--R ------------------------------------------------------------------------- +--R 2b p + b m + 2b +--R Type: Union(Expression(Integer),...) +--E 86 + +--S 87 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 m log(b c x + a c) +--R (b c x + 2a b c x + a c )%e +--R * +--R 1 +--R 2p log(b c x + a c) + p log(--) +--R 2 +--R c +--R %e +--R + +--R m + 2 2 2 2 p +--R - (b c x + a c) (b x + 2a b x + a ) +--R / +--R 2 2 2 +--R 2b c p + b c m + 2b c +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 88 + +)clear all + +--S 89 of 1751 +t0:=(a+b*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R m +--R (b c x + a c) +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1751 +r0:=(a*c+b*c*x)^(8+m)/(b*c^8*(8+m)) +--R +--R +--R m + 8 +--R (b c x + a c) +--R (2) ------------------ +--R 8 8 +--R b c m + 8b c +--R Type: Expression(Integer) +--E 90 + +--S 91 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 8 +--R 8a b x + a +--R * +--R m log(b c x + a c) +--R %e +--R / +--R b m + 8b +--R Type: Union(Expression(Integer),...) +--E 91 + +--S 92 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8 8 7 8 7 2 6 8 6 3 5 8 5 4 4 8 4 +--R b c x + 8a b c x + 28a b c x + 56a b c x + 70a b c x +--R + +--R 5 3 8 3 6 2 8 2 7 8 8 8 +--R 56a b c x + 28a b c x + 8a b c x + a c +--R * +--R m log(b c x + a c) +--R %e +--R + +--R m + 8 +--R - (b c x + a c) +--R / +--R 8 8 +--R b c m + 8b c +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 1751 +t0:=(a+b*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R m +--R (b c x + a c) +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1751 +r0:=-c^4*(a*c+b*c*x)^(-4+m)/(b*(4-m)) +--R +--R +--R 4 m - 4 +--R c (b c x + a c) +--R (2) -------------------- +--R b m - 4b +--R Type: Expression(Integer) +--E 95 + +--S 96 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R m log(b c x + a c) +--R %e +--R / +--R 5 5 4 4 4 3 2 3 2 3 2 +--R (b m - 4b )x + (4a b m - 16a b )x + (6a b m - 24a b )x +--R + +--R 3 2 3 2 4 4 +--R (4a b m - 16a b )x + a b m - 4a b +--R Type: Union(Expression(Integer),...) +--E 96 + +--S 97 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R m log(b c x + a c) +--R %e +--R + +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 m - 4 +--R (- b c x - 4a b c x - 6a b c x - 4a b c x - a c )(b c x + a c) +--R / +--R 5 5 4 4 4 3 2 3 2 3 2 +--R (b m - 4b )x + (4a b m - 16a b )x + (6a b m - 24a b )x +--R + +--R 3 2 3 2 4 4 +--R (4a b m - 16a b )x + a b m - 4a b +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 98 + +)clear all + +--S 99 of 1751 +t0:=x*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (c x + b x + a x)(e x + d) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1751 +r0:=-d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(3*c*d^2-_ + e*(2*b*d-a*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*c*d-b*e)*(d+e*x)^(3+m)/_ + (e^4*(3+m))+c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (c m + 6c m + 11c m + 6c)(e x + d) +--R + +--R 3 2 +--R ((b e - 3c d)m + (7b e - 21c d)m + (14b e - 42c d)m + 8b e - 24c d) +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 2 2 2 +--R (a e - 2b d e + 3c d )m + (8a e - 16b d e + 24c d )m +--R + +--R 2 2 2 2 +--R (19a e - 38b d e + 57c d )m + 12a e - 24b d e + 36c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 2 2 3 2 +--R (- a d e + b d e - c d )m + (- 9a d e + 9b d e - 9c d )m +--R + +--R 2 2 3 2 2 3 +--R (- 26a d e + 26b d e - 26c d )m - 24a d e + 24b d e - 24c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 100 + +--S 101 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (c e m + 6c e m + 11c e m + 6c e )x +--R + +--R 4 3 3 4 3 2 4 3 +--R (b e + c d e )m + (7b e + 3c d e )m + (14b e + 2c d e )m +--R + +--R 4 +--R 8b e +--R * +--R 3 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (a e + b d e )m + (8a e + 5b d e - 3c d e )m +--R + +--R 4 3 2 2 4 +--R (19a e + 4b d e - 3c d e )m + 12a e +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 2 2 3 2 2 3 +--R (a d e m + (7a d e - 2b d e )m + (12a d e - 8b d e + 6c d e)m)x +--R + +--R 2 2 2 2 2 3 2 2 3 4 +--R - a d e m + (- 7a d e + 2b d e)m - 12a d e + 8b d e - 6c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 101 + +--S 102 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (c e m + 6c e m + 11c e m + 6c e )x +--R + +--R 4 3 3 4 3 2 4 3 +--R (b e + c d e )m + (7b e + 3c d e )m + (14b e + 2c d e )m +--R + +--R 4 +--R 8b e +--R * +--R 3 +--R x +--R + +--R 4 3 3 4 3 2 2 2 +--R (a e + b d e )m + (8a e + 5b d e - 3c d e )m +--R + +--R 4 3 2 2 4 +--R (19a e + 4b d e - 3c d e )m + 12a e +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 2 2 3 2 2 3 +--R (a d e m + (7a d e - 2b d e )m + (12a d e - 8b d e + 6c d e)m)x +--R + +--R 2 2 2 2 2 3 2 2 3 4 +--R - a d e m + (- 7a d e + 2b d e)m - 12a d e + 8b d e - 6c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 2 m + 4 +--R (- c m - 6c m - 11c m - 6c)(e x + d) +--R + +--R 3 2 +--R (- b e + 3c d)m + (- 7b e + 21c d)m + (- 14b e + 42c d)m - 8b e +--R + +--R 24c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 2 2 2 +--R (- a e + 2b d e - 3c d )m + (- 8a e + 16b d e - 24c d )m +--R + +--R 2 2 2 2 +--R (- 19a e + 38b d e - 57c d )m - 12a e + 24b d e - 36c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 2 2 3 2 +--R (a d e - b d e + c d )m + (9a d e - 9b d e + 9c d )m +--R + +--R 2 2 3 2 2 3 +--R (26a d e - 26b d e + 26c d )m + 24a d e - 24b d e + 24c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 103 + +)clear all + +--S 104 of 1751 +t0:=x*(d+e*x)^5*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 5 4 2 3 6 +--R c e x + (b e + 5c d e )x + (a e + 5b d e + 10c d e )x +--R + +--R 4 2 3 3 2 5 2 3 3 2 4 4 +--R (5a d e + 10b d e + 10c d e )x + (10a d e + 10b d e + 5c d e)x +--R + +--R 3 2 4 5 3 4 5 2 5 +--R (10a d e + 5b d e + c d )x + (5a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 104 + +--S 105 of 1751 +r0:=-1/6*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^6/e^4+1/7*(3*c*d^2-e*(2*b*d-a*e))*_ + (d+e*x)^7/e^4-1/8*(3*c*d-b*e)*(d+e*x)^8/e^4+1/9*c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 1 9 5 8 10 2 7 7 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + -- c d e )x +--R 9 8 8 7 7 7 +--R + +--R 5 8 5 2 7 5 3 6 6 2 7 3 6 4 5 5 +--R (- a d e + - b d e + - c d e )x + (2a d e + 2b d e + c d e )x +--R 6 3 3 +--R + +--R 5 3 6 5 4 5 1 5 4 4 5 4 5 1 5 4 3 1 5 4 2 +--R (- a d e + - b d e + - c d e )x + (- a d e + - b d e )x + - a d e x +--R 2 4 4 3 3 2 +--R + +--R 1 7 2 1 8 1 9 +--R - -- a d e + --- b d e - --- c d +--R 42 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 105 + +--S 106 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 9 1 5 5 4 8 1 5 5 4 10 2 3 7 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + -- c d e )x +--R 9 8 8 7 7 7 +--R + +--R 5 4 5 2 3 5 3 2 6 2 3 3 2 4 5 +--R (- a d e + - b d e + - c d e )x + (2a d e + 2b d e + c d e)x +--R 6 3 3 +--R + +--R 5 3 2 5 4 1 5 4 5 4 1 5 3 1 5 2 +--R (- a d e + - b d e + - c d )x + (- a d e + - b d )x + - a d x +--R 2 4 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 106 + +--S 107 of 1751 +m0:=a0-r0 +--R +--R +--R 1 7 2 1 8 1 9 +--R -- a d e - --- b d e + --- c d +--R 42 168 504 +--R (4) -------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 107 + +--S 108 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 108 + +)clear all + +--S 109 of 1751 +t0:=x*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 4 3 2 2 5 +--R c e x + (b e + 4c d e )x + (a e + 4b d e + 6c d e )x +--R + +--R 3 2 2 3 4 2 2 3 4 3 +--R (4a d e + 6b d e + 4c d e)x + (6a d e + 4b d e + c d )x +--R + +--R 3 4 2 4 +--R (4a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 109 + +--S 110 of 1751 +r0:=-1/5*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4+1/6*(3*c*d^2-e*(2*b*d-a*e))*_ + (d+e*x)^6/e^4-1/7*(3*c*d-b*e)*(d+e*x)^7/e^4+1/8*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 8 4 7 7 1 8 2 7 2 6 6 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + c d e )x +--R 8 7 7 6 3 +--R + +--R 4 7 6 2 6 4 3 5 5 3 2 6 3 5 1 4 4 4 +--R (- a d e + - b d e + - c d e )x + (- a d e + b d e + - c d e )x +--R 5 5 5 2 4 +--R + +--R 4 3 5 1 4 4 3 1 4 4 2 1 6 2 1 7 1 8 +--R (- a d e + - b d e )x + - a d e x - -- a d e + --- b d e - --- c d +--R 3 3 2 30 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 110 + +--S 111 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 8 1 4 4 3 7 1 4 2 3 2 2 6 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + c d e )x +--R 8 7 7 6 3 +--R + +--R 4 3 6 2 2 4 3 5 3 2 2 3 1 4 4 +--R (- a d e + - b d e + - c d e)x + (- a d e + b d e + - c d )x +--R 5 5 5 2 4 +--R + +--R 4 3 1 4 3 1 4 2 +--R (- a d e + - b d )x + - a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 111 + +--S 112 of 1751 +m0:=a0-r0 +--R +--R +--R 1 6 2 1 7 1 8 +--R -- a d e - --- b d e + --- c d +--R 30 105 280 +--R (4) -------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 112 + +--S 113 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 113 + +)clear all + +--S 114 of 1751 +t0:=x*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 3 2 2 4 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 3 2 3 2 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 114 + +--S 115 of 1751 +r0:=1/2*a*d^3*x^2+1/3*d^2*(b*d+3*a*e)*x^3+1/4*d*(c*d^2+3*e*(b*d+a*e))*x^4+_ + 1/5*e*(3*c*d^2+e*(3*b*d+a*e))*x^5+1/6*e^2*(3*c*d+b*e)*x^6+1/7*c*e^3*x^7 +--R +--R +--R (2) +--R 1 3 7 1 3 1 2 6 1 3 3 2 3 2 5 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + - c d e)x +--R 7 6 2 5 5 5 +--R + +--R 3 2 3 2 1 3 4 2 1 3 3 1 3 2 +--R (- a d e + - b d e + - c d )x + (a d e + - b d )x + - a d x +--R 4 4 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 115 + +--S 116 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 7 1 3 1 2 6 1 3 3 2 3 2 5 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + - c d e)x +--R 7 6 2 5 5 5 +--R + +--R 3 2 3 2 1 3 4 2 1 3 3 1 3 2 +--R (- a d e + - b d e + - c d )x + (a d e + - b d )x + - a d x +--R 4 4 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 116 + +--S 117 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +)clear all + +--S 119 of 1751 +t0:=x*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 2 2 3 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d x +--R Type: Polynomial(Integer) +--E 119 + +--S 120 of 1751 +r0:=1/2*a*d^2*x^2+1/3*d*(b*d+2*a*e)*x^3+1/4*(c*d^2+e*(2*b*d+a*e))*x^4+_ + 1/5*e*(2*c*d+b*e)*x^5+1/6*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - c e x + (- b e + - c d e)x + (- a e + - b d e + - c d )x +--R 6 5 5 4 2 4 +--R + +--R 2 1 2 3 1 2 2 +--R (- a d e + - b d )x + - a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +--S 121 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - c e x + (- b e + - c d e)x + (- a e + - b d e + - c d )x +--R 6 5 5 4 2 4 +--R + +--R 2 1 2 3 1 2 2 +--R (- a d e + - b d )x + - a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 121 + +--S 122 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +)clear all + +--S 124 of 1751 +t0:=x*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R 4 3 2 +--R (1) c e x + (b e + c d)x + (a e + b d)x + a d x +--R Type: Polynomial(Integer) +--E 124 + +--S 125 of 1751 +r0:=1/2*a*d*x^2+1/3*(b*d+a*e)*x^3+1/4*(c*d+b*e)*x^4+1/5*c*e*x^5 +--R +--R +--R 1 5 1 1 4 1 1 3 1 2 +--R (2) - c e x + (- b e + - c d)x + (- a e + - b d)x + - a d x +--R 5 4 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +--S 126 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 1 5 1 1 4 1 1 3 1 2 +--R (3) - c e x + (- b e + - c d)x + (- a e + - b d)x + - a d x +--R 5 4 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 126 + +--S 127 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +)clear all + +--S 129 of 1751 +t0:=x*(a+b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) c x + b x + a x +--R Type: Polynomial(Integer) +--E 129 + +--S 130 of 1751 +r0:=1/2*a*x^2+1/3*b*x^3+1/4*c*x^4 +--R +--R +--R 1 4 1 3 1 2 +--R (2) - c x + - b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +--S 131 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 3 1 2 +--R (3) - c x + - b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 131 + +--S 132 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +)clear all + +--S 134 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ----------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 134 + +--S 135 of 1751 +r0:=(c*d^2-b*d*e+a*e^2)*x/e^3-1/2*(c*d-b*e)*x^2/e^2+1/3*c*x^3/e-_ + d*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 2 3 3 3 3 2 2 +--R (- 6a d e + 6b d e - 6c d )log(e x + d) + 2c e x + (3b e - 3c d e )x +--R + +--R 3 2 2 +--R (6a e - 6b d e + 6c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 135 + +--S 136 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 3 3 2 2 +--R (- 6a d e + 6b d e - 6c d )log(e x + d) + 2c e x + (3b e - 3c d e )x +--R + +--R 3 2 2 +--R (6a e - 6b d e + 6c d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 136 + +--S 137 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 139 + +--S 140 of 1751 +r0:=-(2*c*d-b*e)*x/e^3+1/2*c*x^2/e^2+d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))+_ + (3*c*d^2-e*(2*b*d-a*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((2a e - 4b d e + 6c d e)x + 2a d e - 4b d e + 6c d )log(e x + d) +--R + +--R 3 3 3 2 2 2 2 2 2 +--R c e x + (2b e - 3c d e )x + (2b d e - 4c d e)x + 2a d e - 2b d e +--R + +--R 3 +--R 2c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 140 + +--S 141 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 +--R ((2a e - 4b d e + 6c d e)x + 2a d e - 4b d e + 6c d )log(e x + d) +--R + +--R 3 3 3 2 2 2 2 2 2 +--R c e x + (2b e - 3c d e )x + (2b d e - 4c d e)x + 2a d e - 2b d e +--R + +--R 3 +--R 2c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 141 + +--S 142 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 143 + +)clear all + +--S 144 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 144 + +--S 145 of 1751 +r0:=c*x/e^3+1/2*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (-3*c*d^2+e*(2*b*d-a*e))/(e^4*(d+e*x))-(3*c*d-b*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 +--R ((2b e - 6c d e )x + (4b d e - 12c d e)x + 2b d e - 6c d )log(e x + d) +--R + +--R 3 3 2 2 3 2 2 2 2 +--R 2c e x + 4c d e x + (- 2a e + 4b d e - 4c d e)x - a d e + 3b d e +--R + +--R 3 +--R - 5c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 145 + +--S 146 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 2 3 +--R ((2b e - 6c d e )x + (4b d e - 12c d e)x + 2b d e - 6c d )log(e x + d) +--R + +--R 3 3 2 2 3 2 2 2 2 +--R 2c e x + 4c d e x + (- 2a e + 4b d e - 4c d e)x - a d e + 3b d e +--R + +--R 3 +--R - 5c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 146 + +--S 147 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 148 + +)clear all + +--S 149 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 149 + +--S 150 of 1751 +r0:=1/3*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-3*c*d^2+_ + e*(2*b*d-a*e))/(e^4*(d+e*x)^2)+(3*c*d-b*e)/(e^4*(d+e*x))+c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6c e x + 18c d e x + 18c d e x + 6c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 2 2 +--R (- 6b e + 18c d e )x + (- 3a e - 6b d e + 27c d e)x - a d e - 2b d e +--R + +--R 3 +--R 11c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 150 + +--S 151 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (6c e x + 18c d e x + 18c d e x + 6c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 2 2 +--R (- 6b e + 18c d e )x + (- 3a e - 6b d e + 27c d e)x - a d e - 2b d e +--R + +--R 3 +--R 11c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 151 + +--S 152 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 154 + +--S 155 of 1751 +r0:=1/4*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^3)+1/2*(3*c*d-b*e)/(e^4*(d+e*x)^2)-c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 3 3 2 2 1 3 1 2 2 +--R - c e x + (- - b e - - c d e )x + (- - a e - - b d e - c d e)x +--R 2 2 3 3 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - - c d +--R 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 155 + +--S 156 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 3 2 2 +--R - 12c e x + (- 6b e - 18c d e )x + (- 4a e - 4b d e - 12c d e)x +--R + +--R 2 2 3 +--R - a d e - b d e - 3c d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 156 + +--S 157 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 158 + +)clear all + +--S 159 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 159 + +--S 160 of 1751 +r0:=1/5*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^5)+1/4*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^4)+1/3*(3*c*d-b*e)/(e^4*(d+e*x)^3)-1/2*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 1 3 1 2 1 2 +--R - - c e x + (- - b e - - c d e )x + (- - a e - - b d e - - c d e)x +--R 2 3 2 4 6 4 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - -- c d +--R 20 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 160 + +--S 161 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 3 2 2 +--R - 30c e x + (- 20b e - 30c d e )x + (- 15a e - 10b d e - 15c d e)x +--R + +--R 2 2 3 +--R - 3a d e - 2b d e - 3c d +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 161 + +--S 162 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 163 + +)clear all + +--S 164 of 1751 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R c x + b x + a x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 164 + +--S 165 of 1751 +r0:=1/6*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^6)+1/5*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^5)+1/4*(3*c*d-b*e)/(e^4*(d+e*x)^4)-1/3*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 1 3 1 2 1 2 +--R - - c e x + (- - b e - - c d e )x + (- - a e - -- b d e - -- c d e)x +--R 3 4 4 5 10 10 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - -- c d +--R 30 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 165 + +--S 166 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 3 2 2 +--R - 20c e x + (- 15b e - 15c d e )x + (- 12a e - 6b d e - 6c d e)x +--R + +--R 2 2 3 +--R - 2a d e - b d e - c d +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 4 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 166 + +--S 167 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 1751 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + (A b + B a)x + A a)(e x + d) +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1751 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))-_ + (A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^(2+m)/(e^4*(2+m))-_ + (3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3+m)/(e^4*(3+m))+_ + B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R ((A c + B b)e - 3B c d)m + ((7A c + 7B b)e - 21B c d)m +--R + +--R ((14A c + 14B b)e - 42B c d)m + (8A c + 8B b)e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R ((A b + B a)e + (- 2A c - 2B b)d e + 3B c d )m +--R + +--R 2 2 2 +--R ((8A b + 8B a)e + (- 16A c - 16B b)d e + 24B c d )m +--R + +--R 2 2 +--R ((19A b + 19B a)e + (- 38A c - 38B b)d e + 57B c d )m +--R + +--R 2 2 +--R (12A b + 12B a)e + (- 24A c - 24B b)d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (A a e + (- A b - B a)d e + (A c + B b)d e - B c d )m +--R + +--R 3 2 2 3 2 +--R (9A a e + (- 9A b - 9B a)d e + (9A c + 9B b)d e - 9B c d )m +--R + +--R 3 2 2 3 +--R (26A a e + (- 26A b - 26B a)d e + (26A c + 26B b)d e - 26B c d )m +--R + +--R 3 2 2 3 +--R 24A a e + (- 24A b - 24B a)d e + (24A c + 24B b)d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R ((A c + B b)e + B c d e )m + ((7A c + 7B b)e + 3B c d e )m +--R + +--R 4 3 4 +--R ((14A c + 14B b)e + 2B c d e )m + (8A c + 8B b)e +--R * +--R 3 +--R x +--R + +--R 4 3 3 +--R ((A b + B a)e + (A c + B b)d e )m +--R + +--R 4 3 2 2 2 +--R ((8A b + 8B a)e + (5A c + 5B b)d e - 3B c d e )m +--R + +--R 4 3 2 2 +--R ((19A b + 19B a)e + (4A c + 4B b)d e - 3B c d e )m +--R + +--R 4 +--R (12A b + 12B a)e +--R * +--R 2 +--R x +--R + +--R 4 3 3 +--R (A a e + (A b + B a)d e )m +--R + +--R 4 3 2 2 2 +--R (9A a e + (7A b + 7B a)d e + (- 2A c - 2B b)d e )m +--R + +--R 4 3 2 2 3 +--R (26A a e + (12A b + 12B a)d e + (- 8A c - 8B b)d e + 6B c d e)m +--R + +--R 4 +--R 24A a e +--R * +--R x +--R + +--R 3 3 3 2 2 2 +--R A a d e m + (9A a d e + (- A b - B a)d e )m +--R + +--R 3 2 2 3 3 +--R (26A a d e + (- 7A b - 7B a)d e + (2A c + 2B b)d e)m + 24A a d e +--R + +--R 2 2 3 4 +--R (- 12A b - 12B a)d e + (8A c + 8B b)d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Union(Expression(Integer),...) +--E 171 + +--S 172 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 3 4 3 2 +--R ((A c + B b)e + B c d e )m + ((7A c + 7B b)e + 3B c d e )m +--R + +--R 4 3 4 +--R ((14A c + 14B b)e + 2B c d e )m + (8A c + 8B b)e +--R * +--R 3 +--R x +--R + +--R 4 3 3 +--R ((A b + B a)e + (A c + B b)d e )m +--R + +--R 4 3 2 2 2 +--R ((8A b + 8B a)e + (5A c + 5B b)d e - 3B c d e )m +--R + +--R 4 3 2 2 +--R ((19A b + 19B a)e + (4A c + 4B b)d e - 3B c d e )m +--R + +--R 4 +--R (12A b + 12B a)e +--R * +--R 2 +--R x +--R + +--R 4 3 3 +--R (A a e + (A b + B a)d e )m +--R + +--R 4 3 2 2 2 +--R (9A a e + (7A b + 7B a)d e + (- 2A c - 2B b)d e )m +--R + +--R 4 3 2 2 +--R 26A a e + (12A b + 12B a)d e + (- 8A c - 8B b)d e +--R + +--R 3 +--R 6B c d e +--R * +--R m +--R + +--R 4 +--R 24A a e +--R * +--R x +--R + +--R 3 3 3 2 2 2 +--R A a d e m + (9A a d e + (- A b - B a)d e )m +--R + +--R 3 2 2 3 3 +--R (26A a d e + (- 7A b - 7B a)d e + (2A c + 2B b)d e)m + 24A a d e +--R + +--R 2 2 3 4 +--R (- 12A b - 12B a)d e + (8A c + 8B b)d e - 6B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 2 m + 4 +--R (- B c m - 6B c m - 11B c m - 6B c)(e x + d) +--R + +--R 3 2 +--R ((- A c - B b)e + 3B c d)m + ((- 7A c - 7B b)e + 21B c d)m +--R + +--R ((- 14A c - 14B b)e + 42B c d)m + (- 8A c - 8B b)e + 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R ((- A b - B a)e + (2A c + 2B b)d e - 3B c d )m +--R + +--R 2 2 2 +--R ((- 8A b - 8B a)e + (16A c + 16B b)d e - 24B c d )m +--R + +--R 2 2 +--R ((- 19A b - 19B a)e + (38A c + 38B b)d e - 57B c d )m +--R + +--R 2 2 +--R (- 12A b - 12B a)e + (24A c + 24B b)d e - 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (- A a e + (A b + B a)d e + (- A c - B b)d e + B c d )m +--R + +--R 3 2 2 3 2 +--R (- 9A a e + (9A b + 9B a)d e + (- 9A c - 9B b)d e + 9B c d )m +--R + +--R 3 2 2 3 +--R (- 26A a e + (26A b + 26B a)d e + (- 26A c - 26B b)d e + 26B c d )m +--R + +--R 3 2 2 3 +--R - 24A a e + (24A b + 24B a)d e + (- 24A c - 24B b)d e + 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 173 + +)clear all + +--S 174 of 1751 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 +--R B c e x + ((A c + B b)e + 4B c d e )x +--R + +--R 4 3 2 2 5 +--R ((A b + B a)e + (4A c + 4B b)d e + 6B c d e )x +--R + +--R 4 3 2 2 3 4 +--R (A a e + (4A b + 4B a)d e + (6A c + 6B b)d e + 4B c d e)x +--R + +--R 3 2 2 3 4 3 +--R (4A a d e + (6A b + 6B a)d e + (4A c + 4B b)d e + B c d )x +--R + +--R 2 2 3 4 2 +--R (6A a d e + (4A b + 4B a)d e + (A c + B b)d )x +--R + +--R 3 4 4 +--R (4A a d e + (A b + B a)d )x + A a d +--R Type: Polynomial(Integer) +--E 174 + +--S 175 of 1751 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4-1/6*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^7/e^4+1/8*B*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 1 8 4 7 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 1 8 2 2 7 2 6 6 +--R ((- A b + - B a)e + (- A c + - B b)d e + B c d e )x +--R 6 6 3 3 +--R + +--R 1 8 4 4 7 6 6 2 6 4 3 5 5 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 5 5 +--R + +--R 7 3 3 2 6 3 5 1 4 4 4 +--R (A a d e + (- A b + - B a)d e + (A c + B b)d e + - B c d e )x +--R 2 2 4 +--R + +--R 2 6 4 4 3 5 1 1 4 4 3 +--R (2A a d e + (- A b + - B a)d e + (- A c + - B b)d e )x +--R 3 3 3 3 +--R + +--R 3 5 1 1 4 4 2 4 4 1 5 3 +--R (2A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 5 +--R + +--R 1 1 6 2 1 1 7 1 8 +--R (- -- A b - -- B a)d e + (--- A c + --- B b)d e - --- B c d +--R 30 30 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 175 + +--S 176 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 8 1 1 4 4 3 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 1 4 2 2 3 2 2 6 +--R ((- A b + - B a)e + (- A c + - B b)d e + B c d e )x +--R 6 6 3 3 +--R + +--R 1 4 4 4 3 6 6 2 2 4 3 5 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d e)x +--R 5 5 5 5 5 5 +--R + +--R 3 3 3 2 2 3 1 4 4 +--R (A a d e + (- A b + - B a)d e + (A c + B b)d e + - B c d )x +--R 2 2 4 +--R + +--R 2 2 4 4 3 1 1 4 3 +--R (2A a d e + (- A b + - B a)d e + (- A c + - B b)d )x +--R 3 3 3 3 +--R + +--R 3 1 1 4 2 4 +--R (2A a d e + (- A b + - B a)d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 176 + +--S 177 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 5 3 1 1 6 2 1 1 7 1 8 +--R - - A a d e + (-- A b + -- B a)d e + (- --- A c - --- B b)d e + --- B c d +--R 5 30 30 105 105 280 +--R ---------------------------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 177 + +--S 178 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 178 + +)clear all + +--S 179 of 1751 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R ((A b + B a)e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 3 2 2 3 3 +--R (A a e + (3A b + 3B a)d e + (3A c + 3B b)d e + B c d )x +--R + +--R 2 2 3 2 +--R (3A a d e + (3A b + 3B a)d e + (A c + B b)d )x +--R + +--R 2 3 3 +--R (3A a d e + (A b + B a)d )x + A a d +--R Type: Polynomial(Integer) +--E 179 + +--S 180 of 1751 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4-1/5*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^6/e^4+1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 1 7 1 6 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 1 7 3 3 6 3 2 5 5 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 5 +--R + +--R 1 7 3 3 6 3 3 2 5 1 3 4 4 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d e )x +--R 4 4 4 4 4 4 +--R + +--R 6 2 5 1 1 3 4 3 +--R (A a d e + (A b + B a)d e + (- A c + - B b)d e )x +--R 3 3 +--R + +--R 3 2 5 1 1 3 4 2 3 4 1 4 3 +--R (- A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 2 4 +--R + +--R 1 1 5 2 1 1 6 1 7 +--R (- -- A b - -- B a)d e + (-- A c + -- B b)d e - --- B c d +--R 20 20 60 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 180 + +--S 181 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 7 1 1 3 1 2 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 1 3 3 3 2 3 2 5 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d e)x +--R 5 5 5 5 5 +--R + +--R 1 3 3 3 2 3 3 2 1 3 4 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d )x +--R 4 4 4 4 4 4 +--R + +--R 2 2 1 1 3 3 +--R (A a d e + (A b + B a)d e + (- A c + - B b)d )x +--R 3 3 +--R + +--R 3 2 1 1 3 2 3 +--R (- A a d e + (- A b + - B a)d )x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 181 + +--S 182 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 4 3 1 1 5 2 1 1 6 1 7 +--R - - A a d e + (-- A b + -- B a)d e + (- -- A c - -- B b)d e + --- B c d +--R 4 20 20 60 60 140 +--R -------------------------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 182 + +--S 183 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 183 + +)clear all + +--S 184 of 1751 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 +--R ((A b + B a)e + (2A c + 2B b)d e + B c d )x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + (A c + B b)d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R Type: Polynomial(Integer) +--E 184 + +--S 185 of 1751 +r0:=-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3/e^4-1/4*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^4/e^4-1/5*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^5/e^4+1/6*B*c*(d+e*x)^6/e^4 +--R +--R +--R (2) +--R 1 6 6 1 1 6 2 5 5 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 6 5 5 5 +--R + +--R 1 1 6 1 1 5 1 2 4 4 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d e )x +--R 4 4 2 2 4 +--R + +--R 1 6 2 2 5 1 1 2 4 3 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e )x +--R 3 3 3 3 3 +--R + +--R 5 1 1 2 4 2 2 4 1 3 3 +--R (A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 3 +--R + +--R 1 1 4 2 1 1 5 1 6 +--R (- -- A b - -- B a)d e + (-- A c + -- B b)d e - -- B c d +--R 12 12 30 30 60 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 185 + +--S 186 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 6 1 1 2 2 5 +--R - B c e x + ((- A c + - B b)e + - B c d e)x +--R 6 5 5 5 +--R + +--R 1 1 2 1 1 1 2 4 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d )x +--R 4 4 2 2 4 +--R + +--R 1 2 2 2 1 1 2 3 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d )x +--R 3 3 3 3 3 +--R + +--R 1 1 2 2 2 +--R (A a d e + (- A b + - B a)d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 186 + +--S 187 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 3 1 1 4 2 1 1 5 1 6 +--R - - A a d e + (-- A b + -- B a)d e + (- -- A c - -- B b)d e + -- B c d +--R 3 12 12 30 30 60 +--R ------------------------------------------------------------------------- +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 187 + +--S 188 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 188 + +)clear all + +--S 189 of 1751 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + ((A c + B b)e + B c d)x + ((A b + B a)e + (A c + B b)d)x +--R + +--R (A a e + (A b + B a)d)x + A a d +--R Type: Polynomial(Integer) +--E 189 + +--S 190 of 1751 +r0:=a*A*d*x+1/2*(A*b*d+a*B*d+a*A*e)*x^2+1/3*(b*B*d+A*c*d+A*b*e+a*B*e)*x^3+_ + 1/4*(B*c*d+b*B*e+A*c*e)*x^4+1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 1 3 1 1 1 2 +--R ((- A b + - B a)e + (- A c + - B b)d)x + (- A a e + (- A b + - B a)d)x +--R 3 3 3 3 2 2 2 +--R + +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 190 + +--S 191 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 1 3 1 1 1 2 +--R ((- A b + - B a)e + (- A c + - B b)d)x + (- A a e + (- A b + - B a)d)x +--R 3 3 3 3 2 2 2 +--R + +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 191 + +--S 192 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 192 + +--S 193 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +)clear all + +--S 194 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + (A c + B b)x + (A b + B a)x + A a +--R Type: Polynomial(Integer) +--E 194 + +--S 195 of 1751 +r0:=a*A*x+1/2*(A*b+a*B)*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 1 3 1 1 2 +--R (2) - B c x + (- A c + - B b)x + (- A b + - B a)x + A a x +--R 4 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 195 + +--S 196 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 1 3 1 1 2 +--R (3) - B c x + (- A c + - B b)x + (- A b + - B a)x + A a x +--R 4 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 196 + +--S 197 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +)clear all + +--S 199 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 199 + +--S 200 of 1751 +r0:=-(A*e*(c*d-b*e)-B*(c*d^2-e*(b*d-a*e)))*x/e^3-_ + 1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+1/3*B*c*x^3/e-_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 3 +--R (6A a e + (- 6A b - 6B a)d e + (6A c + 6B b)d e - 6B c d )log(e x + d) +--R + +--R 3 3 3 2 2 +--R 2B c e x + ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R ((6A b + 6B a)e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 200 + +--S 201 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 +--R (6A a e + (- 6A b - 6B a)d e + (6A c + 6B b)d e - 6B c d )log(e x + d) +--R + +--R 3 3 3 2 2 +--R 2B c e x + ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R ((6A b + 6B a)e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Union(Expression(Integer),...) +--E 201 + +--S 202 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 203 + +)clear all + +--S 204 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 204 + +--S 205 of 1751 +r0:=-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))-(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 +--R ((2A b + 2B a)e + (- 4A c - 4B b)d e + 6B c d e)x +--R + +--R 2 2 3 +--R (2A b + 2B a)d e + (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 3 2 +--R ((2A c + 2B b)d e - 4B c d e)x - 2A a e + (2A b + 2B a)d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 205 + +--S 206 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 +--R ((2A b + 2B a)e + (- 4A c - 4B b)d e + 6B c d e)x +--R + +--R 2 2 3 +--R (2A b + 2B a)d e + (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 3 2 +--R ((2A c + 2B b)d e - 4B c d e)x - 2A a e + (2A b + 2B a)d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 206 + +--S 207 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 208 + +)clear all + +--S 209 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 209 + +--S 210 of 1751 +r0:=B*c*x/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x))-_ + (3*B*c*d-b*B*e-A*c*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 +--R 2B c e x + 4B c d e x +--R + +--R 3 2 2 3 +--R ((- 2A b - 2B a)e + (4A c + 4B b)d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 210 + +--S 211 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 +--R 2B c e x + 4B c d e x +--R + +--R 3 2 2 3 +--R ((- 2A b - 2B a)e + (4A c + 4B b)d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 211 + +--S 212 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 214 + +--S 215 of 1751 +r0:=1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+_ + 1/2*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^2)+_ + (3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 3 +--R ((- 3A b - 3B a)e + (- 6A c - 6B b)d e + 27B c d e)x - 2A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 3 +--R ((- 3A b - 3B a)e + (- 6A c - 6B b)d e + 27B c d e)x - 2A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 216 + +--S 217 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 218 + +)clear all + +--S 219 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 219 + +--S 220 of 1751 +r0:=1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^2)-B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 1 3 3 2 2 +--R - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 2 2 +--R + +--R 1 1 3 1 1 2 2 1 3 +--R ((- - A b - - B a)e + (- - A c - - B b)d e - B c d e)x - - A a e +--R 3 3 3 3 4 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - - B c d +--R 12 12 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 220 + +--S 221 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 12B c e x + ((- 6A c - 6B b)e - 18B c d e )x +--R + +--R 3 2 2 3 +--R ((- 4A b - 4B a)e + (- 4A c - 4B b)d e - 12B c d e)x - 3A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (- A c - B b)d e - 3B c d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 221 + +--S 222 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 223 + +)clear all + +--S 224 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 224 + +--S 225 of 1751 +r0:=1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^5)+1/4*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 3 3 2 +--R + +--R 1 1 3 1 1 2 1 2 1 3 +--R ((- - A b - - B a)e + (- - A c - - B b)d e - - B c d e)x - - A a e +--R 4 4 6 6 4 5 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - -- B c d +--R 20 20 30 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 225 + +--S 226 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 30B c e x + ((- 20A c - 20B b)e - 30B c d e )x +--R + +--R 3 2 2 3 +--R ((- 15A b - 15B a)e + (- 10A c - 10B b)d e - 15B c d e)x - 12A a e +--R + +--R 2 2 3 +--R (- 3A b - 3B a)d e + (- 2A c - 2B b)d e - 3B c d +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 226 + +--S 227 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 229 + +--S 230 of 1751 +r0:=1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^6)+1/5*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^5)+1/4*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 3 4 4 4 +--R + +--R 1 1 3 1 1 2 1 2 1 3 +--R ((- - A b - - B a)e + (- -- A c - -- B b)d e - -- B c d e)x - - A a e +--R 5 5 10 10 10 6 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - -- B c d +--R 30 30 60 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 230 + +--S 231 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R - 20B c e x + ((- 15A c - 15B b)e - 15B c d e )x +--R + +--R 3 2 2 3 +--R ((- 12A b - 12B a)e + (- 6A c - 6B b)d e - 6B c d e)x - 10A a e +--R + +--R 2 2 3 +--R (- 2A b - 2B a)d e + (- A c - B b)d e - B c d +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 4 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 231 + +--S 232 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 233 + +)clear all + +--S 234 of 1751 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1751 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))-_ + (c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^(2+m)/(e^6*(2+m))-(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^(4+m)/(e^6*(4+m))-c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((A c + 2B b c)e - 5B c d)m + ((16A c + 32B b c)e - 80B c d)m +--R + +--R 2 2 3 +--R ((95A c + 190B b c)e - 475B c d)m +--R + +--R 2 2 2 +--R ((260A c + 520B b c)e - 1300B c d)m +--R + +--R 2 2 2 2 +--R ((324A c + 648B b c)e - 1620B c d)m + (144A c + 288B b c)e - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R (((2A b + 2B a)c + B b )e + (- 4A c - 8B b c)d e + 10B c d )m +--R + +--R 2 2 2 +--R ((34A b + 34B a)c + 17B b )e + (- 68A c - 136B b c)d e +--R + +--R 2 2 +--R 170B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 +--R ((214A b + 214B a)c + 107B b )e + (- 428A c - 856B b c)d e +--R + +--R 2 2 +--R 1070B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 +--R ((614A b + 614B a)c + 307B b )e + (- 1228A c - 2456B b c)d e +--R + +--R 2 2 +--R 3070B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 +--R ((792A b + 792B a)c + 396B b )e + (- 1584A c - 3168B b c)d e +--R + +--R 2 2 +--R 3960B c d +--R * +--R m +--R + +--R 2 2 2 +--R ((360A b + 360B a)c + 180B b )e + (- 720A c - 1440B b c)d e +--R + +--R 2 2 +--R 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 +--R (2A a c + A b + 2B a b)e + ((- 6A b - 6B a)c - 3B b )d e +--R + +--R 2 2 2 3 +--R (6A c + 12B b c)d e - 10B c d +--R * +--R 5 +--R m +--R + +--R 2 3 +--R (36A a c + 18A b + 36B a b)e +--R + +--R 2 2 2 2 +--R ((- 108A b - 108B a)c - 54B b )d e + (108A c + 216B b c)d e +--R + +--R 2 3 +--R - 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 +--R (242A a c + 121A b + 242B a b)e +--R + +--R 2 2 2 2 +--R ((- 726A b - 726B a)c - 363B b )d e + (726A c + 1452B b c)d e +--R + +--R 2 3 +--R - 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 +--R (744A a c + 372A b + 744B a b)e +--R + +--R 2 2 +--R ((- 2232A b - 2232B a)c - 1116B b )d e +--R + +--R 2 2 2 3 +--R (2232A c + 4464B b c)d e - 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 +--R (1016A a c + 508A b + 1016B a b)e +--R + +--R 2 2 +--R ((- 3048A b - 3048B a)c - 1524B b )d e +--R + +--R 2 2 2 3 +--R (3048A c + 6096B b c)d e - 5080B c d +--R * +--R m +--R + +--R 2 3 +--R (480A a c + 240A b + 480B a b)e +--R + +--R 2 2 2 2 +--R ((- 1440A b - 1440B a)c - 720B b )d e + (1440A c + 2880B b c)d e +--R + +--R 2 3 +--R - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 2 3 +--R (2A a b + B a )e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 2 2 2 3 2 4 +--R ((6A b + 6B a)c + 3B b )d e + (- 4A c - 8B b c)d e + 5B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 +--R (38A a b + 19B a )e + (- 76A a c - 38A b - 76B a b)d e +--R + +--R 2 2 2 2 3 +--R ((114A b + 114B a)c + 57B b )d e + (- 76A c - 152B b c)d e +--R + +--R 2 4 +--R 95B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 +--R (274A a b + 137B a )e + (- 548A a c - 274A b - 548B a b)d e +--R + +--R 2 2 2 2 3 +--R ((822A b + 822B a)c + 411B b )d e + (- 548A c - 1096B b c)d e +--R + +--R 2 4 +--R 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 +--R (922A a b + 461B a )e + (- 1844A a c - 922A b - 1844B a b)d e +--R + +--R 2 2 2 +--R ((2766A b + 2766B a)c + 1383B b )d e +--R + +--R 2 3 2 4 +--R (- 1844A c - 3688B b c)d e + 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 +--R (1404A a b + 702B a )e +--R + +--R 2 3 +--R (- 2808A a c - 1404A b - 2808B a b)d e +--R + +--R 2 2 2 +--R ((4212A b + 4212B a)c + 2106B b )d e +--R + +--R 2 3 2 4 +--R (- 2808A c - 5616B b c)d e + 3510B c d +--R * +--R m +--R + +--R 2 4 2 3 +--R (720A a b + 360B a )e + (- 1440A a c - 720A b - 1440B a b)d e +--R + +--R 2 2 2 2 3 +--R ((2160A b + 2160B a)c + 1080B b )d e + (- 1440A c - 2880B b c)d e +--R + +--R 2 4 +--R 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (- 2A a b - B a )d e + (2A a c + A b + 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 2A b - 2B a)c - B b )d e + (A c + 2B b c)d e - B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 +--R 20A a e + (- 40A a b - 20B a )d e +--R + +--R 2 2 3 +--R (40A a c + 20A b + 40B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 40A b - 40B a)c - 20B b )d e + (20A c + 40B b c)d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 +--R 155A a e + (- 310A a b - 155B a )d e +--R + +--R 2 2 3 +--R (310A a c + 155A b + 310B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 310A b - 310B a)c - 155B b )d e + (155A c + 310B b c)d e +--R + +--R 2 5 +--R - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 +--R 580A a e + (- 1160A a b - 580B a )d e +--R + +--R 2 2 3 +--R (1160A a c + 580A b + 1160B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 1160A b - 1160B a)c - 580B b )d e + (580A c + 1160B b c)d e +--R + +--R 2 5 +--R - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 +--R 1044A a e + (- 2088A a b - 1044B a )d e +--R + +--R 2 2 3 +--R (2088A a c + 1044A b + 2088B a b)d e +--R + +--R 2 3 2 +--R ((- 2088A b - 2088B a)c - 1044B b )d e +--R + +--R 2 4 2 5 +--R (1044A c + 2088B b c)d e - 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 +--R 720A a e + (- 1440A a b - 720B a )d e +--R + +--R 2 2 3 +--R (1440A a c + 720A b + 1440B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 1440A b - 1440B a)c - 720B b )d e + (720A c + 1440B b c)d e +--R + +--R 2 5 +--R - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 235 + +--S 236 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 +--R ((A c + 2B b c)e + B c d e )m +--R + +--R 2 6 2 5 4 +--R ((16A c + 32B b c)e + 10B c d e )m +--R + +--R 2 6 2 5 3 +--R ((95A c + 190B b c)e + 35B c d e )m +--R + +--R 2 6 2 5 2 +--R ((260A c + 520B b c)e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R ((324A c + 648B b c)e + 24B c d e )m + (144A c + 288B b c)e +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 5 +--R (((2A b + 2B a)c + B b )e + (A c + 2B b c)d e )m +--R + +--R 2 6 2 5 +--R ((34A b + 34B a)c + 17B b )e + (12A c + 24B b c)d e +--R + +--R 2 2 4 +--R - 5B c d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R ((214A b + 214B a)c + 107B b )e + (47A c + 94B b c)d e +--R + +--R 2 2 4 +--R - 30B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R ((614A b + 614B a)c + 307B b )e + (72A c + 144B b c)d e +--R + +--R 2 2 4 +--R - 55B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R ((792A b + 792B a)c + 396B b )e + (36A c + 72B b c)d e +--R + +--R 2 2 4 +--R - 30B c d e +--R * +--R m +--R + +--R 2 6 +--R ((360A b + 360B a)c + 180B b )e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A a c + A b + 2B a b)e + ((2A b + 2B a)c + B b )d e )m +--R + +--R 2 6 +--R (36A a c + 18A b + 36B a b)e +--R + +--R 2 5 2 2 4 +--R ((28A b + 28B a)c + 14B b )d e + (- 4A c - 8B b c)d e +--R * +--R 4 +--R m +--R + +--R 2 6 +--R (242A a c + 121A b + 242B a b)e +--R + +--R 2 5 2 2 4 +--R ((130A b + 130B a)c + 65B b )d e + (- 36A c - 72B b c)d e +--R + +--R 2 3 3 +--R 20B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 +--R (744A a c + 372A b + 744B a b)e +--R + +--R 2 5 2 2 4 +--R ((224A b + 224B a)c + 112B b )d e + (- 80A c - 160B b c)d e +--R + +--R 2 3 3 +--R 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 +--R (1016A a c + 508A b + 1016B a b)e +--R + +--R 2 5 2 2 4 +--R ((120A b + 120B a)c + 60B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 3 3 +--R 40B c d e +--R * +--R m +--R + +--R 2 6 +--R (480A a c + 240A b + 480B a b)e +--R * +--R 3 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A a b + B a )e + (2A a c + A b + 2B a b)d e )m +--R + +--R 2 6 2 5 +--R (38A a b + 19B a )e + (32A a c + 16A b + 32B a b)d e +--R + +--R 2 2 4 +--R ((- 6A b - 6B a)c - 3B b )d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R (274A a b + 137B a )e + (178A a c + 89A b + 178B a b)d e +--R + +--R 2 2 4 2 3 3 +--R ((- 72A b - 72B a)c - 36B b )d e + (12A c + 24B b c)d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R (922A a b + 461B a )e + (388A a c + 194A b + 388B a b)d e +--R + +--R 2 2 4 2 3 3 +--R ((- 246A b - 246B a)c - 123B b )d e + (84A c + 168B b c)d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R (1404A a b + 702B a )e + (240A a c + 120A b + 240B a b)d e +--R + +--R 2 2 4 2 3 3 +--R ((- 180A b - 180B a)c - 90B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R m +--R + +--R 2 6 +--R (720A a b + 360B a )e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 5 +--R (A a e + (2A a b + B a )d e )m +--R + +--R 2 6 2 5 +--R 20A a e + (36A a b + 18B a )d e +--R + +--R 2 2 4 +--R (- 4A a c - 2A b - 4B a b)d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R 155A a e + (238A a b + 119B a )d e +--R + +--R 2 2 4 +--R (- 60A a c - 30A b - 60B a b)d e +--R + +--R 2 3 3 +--R ((12A b + 12B a)c + 6B b )d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R 580A a e + (684A a b + 342B a )d e +--R + +--R 2 2 4 +--R (- 296A a c - 148A b - 296B a b)d e +--R + +--R 2 3 3 2 4 2 +--R ((132A b + 132B a)c + 66B b )d e + (- 24A c - 48B b c)d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R 1044A a e + (720A a b + 360B a )d e +--R + +--R 2 2 4 +--R (- 480A a c - 240A b - 480B a b)d e +--R + +--R 2 3 3 2 4 2 +--R ((360A b + 360B a)c + 180B b )d e + (- 144A c - 288B b c)d e +--R + +--R 2 5 +--R 120B c d e +--R * +--R m +--R + +--R 2 6 +--R 720A a e +--R * +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A a d e m + (20A a d e + (- 2A a b - B a )d e )m +--R + +--R 2 5 2 2 4 +--R 155A a d e + (- 36A a b - 18B a )d e +--R + +--R 2 3 3 +--R (4A a c + 2A b + 4B a b)d e +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 +--R 580A a d e + (- 238A a b - 119B a )d e +--R + +--R 2 3 3 2 4 2 +--R (60A a c + 30A b + 60B a b)d e + ((- 12A b - 12B a)c - 6B b )d e +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 1044A a d e + (- 684A a b - 342B a )d e +--R + +--R 2 3 3 +--R (296A a c + 148A b + 296B a b)d e +--R + +--R 2 4 2 2 5 +--R ((- 132A b - 132B a)c - 66B b )d e + (24A c + 48B b c)d e +--R * +--R m +--R + +--R 2 5 2 2 4 +--R 720A a d e + (- 720A a b - 360B a )d e +--R + +--R 2 3 3 +--R (480A a c + 240A b + 480B a b)d e +--R + +--R 2 4 2 2 5 +--R ((- 360A b - 360B a)c - 180B b )d e + (144A c + 288B b c)d e +--R + +--R 2 6 +--R - 120B c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Union(Expression(Integer),...) +--E 236 + +--S 237 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R B c e m + 15B c e m + 85B c e m + 225B c e m + 274B c e m +--R + +--R 2 6 +--R 120B c e +--R * +--R 6 +--R x +--R + +--R 2 6 2 5 5 +--R ((A c + 2B b c)e + B c d e )m +--R + +--R 2 6 2 5 4 +--R ((16A c + 32B b c)e + 10B c d e )m +--R + +--R 2 6 2 5 3 +--R ((95A c + 190B b c)e + 35B c d e )m +--R + +--R 2 6 2 5 2 +--R ((260A c + 520B b c)e + 50B c d e )m +--R + +--R 2 6 2 5 2 6 +--R ((324A c + 648B b c)e + 24B c d e )m + (144A c + 288B b c)e +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 5 +--R (((2A b + 2B a)c + B b )e + (A c + 2B b c)d e )m +--R + +--R 2 6 2 5 +--R ((34A b + 34B a)c + 17B b )e + (12A c + 24B b c)d e +--R + +--R 2 2 4 +--R - 5B c d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R ((214A b + 214B a)c + 107B b )e + (47A c + 94B b c)d e +--R + +--R 2 2 4 +--R - 30B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R ((614A b + 614B a)c + 307B b )e + (72A c + 144B b c)d e +--R + +--R 2 2 4 +--R - 55B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R ((792A b + 792B a)c + 396B b )e + (36A c + 72B b c)d e +--R + +--R 2 2 4 +--R - 30B c d e +--R * +--R m +--R + +--R 2 6 +--R ((360A b + 360B a)c + 180B b )e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A a c + A b + 2B a b)e + ((2A b + 2B a)c + B b )d e )m +--R + +--R 2 6 +--R (36A a c + 18A b + 36B a b)e +--R + +--R 2 5 2 2 4 +--R ((28A b + 28B a)c + 14B b )d e + (- 4A c - 8B b c)d e +--R * +--R 4 +--R m +--R + +--R 2 6 +--R (242A a c + 121A b + 242B a b)e +--R + +--R 2 5 2 2 4 +--R ((130A b + 130B a)c + 65B b )d e + (- 36A c - 72B b c)d e +--R + +--R 2 3 3 +--R 20B c d e +--R * +--R 3 +--R m +--R + +--R 2 6 +--R (744A a c + 372A b + 744B a b)e +--R + +--R 2 5 +--R ((224A b + 224B a)c + 112B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 80A c - 160B b c)d e + 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 +--R (1016A a c + 508A b + 1016B a b)e +--R + +--R 2 5 2 2 4 +--R ((120A b + 120B a)c + 60B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 3 3 +--R 40B c d e +--R * +--R m +--R + +--R 2 6 +--R (480A a c + 240A b + 480B a b)e +--R * +--R 3 +--R x +--R + +--R 2 6 2 5 5 +--R ((2A a b + B a )e + (2A a c + A b + 2B a b)d e )m +--R + +--R 2 6 2 5 +--R (38A a b + 19B a )e + (32A a c + 16A b + 32B a b)d e +--R + +--R 2 2 4 +--R ((- 6A b - 6B a)c - 3B b )d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R (274A a b + 137B a )e + (178A a c + 89A b + 178B a b)d e +--R + +--R 2 2 4 2 3 3 +--R ((- 72A b - 72B a)c - 36B b )d e + (12A c + 24B b c)d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R (922A a b + 461B a )e + (388A a c + 194A b + 388B a b)d e +--R + +--R 2 2 4 +--R ((- 246A b - 246B a)c - 123B b )d e +--R + +--R 2 3 3 2 4 2 +--R (84A c + 168B b c)d e - 60B c d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R (1404A a b + 702B a )e + (240A a c + 120A b + 240B a b)d e +--R + +--R 2 2 4 2 3 3 +--R ((- 180A b - 180B a)c - 90B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 2 +--R - 60B c d e +--R * +--R m +--R + +--R 2 6 +--R (720A a b + 360B a )e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 5 +--R (A a e + (2A a b + B a )d e )m +--R + +--R 2 6 2 5 +--R 20A a e + (36A a b + 18B a )d e +--R + +--R 2 2 4 +--R (- 4A a c - 2A b - 4B a b)d e +--R * +--R 4 +--R m +--R + +--R 2 6 2 5 +--R 155A a e + (238A a b + 119B a )d e +--R + +--R 2 2 4 +--R (- 60A a c - 30A b - 60B a b)d e +--R + +--R 2 3 3 +--R ((12A b + 12B a)c + 6B b )d e +--R * +--R 3 +--R m +--R + +--R 2 6 2 5 +--R 580A a e + (684A a b + 342B a )d e +--R + +--R 2 2 4 +--R (- 296A a c - 148A b - 296B a b)d e +--R + +--R 2 3 3 2 4 2 +--R ((132A b + 132B a)c + 66B b )d e + (- 24A c - 48B b c)d e +--R * +--R 2 +--R m +--R + +--R 2 6 2 5 +--R 1044A a e + (720A a b + 360B a )d e +--R + +--R 2 2 4 +--R (- 480A a c - 240A b - 480B a b)d e +--R + +--R 2 3 3 +--R ((360A b + 360B a)c + 180B b )d e +--R + +--R 2 4 2 2 5 +--R (- 144A c - 288B b c)d e + 120B c d e +--R * +--R m +--R + +--R 2 6 +--R 720A a e +--R * +--R x +--R + +--R 2 5 5 2 5 2 2 4 4 +--R A a d e m + (20A a d e + (- 2A a b - B a )d e )m +--R + +--R 2 5 2 2 4 +--R 155A a d e + (- 36A a b - 18B a )d e +--R + +--R 2 3 3 +--R (4A a c + 2A b + 4B a b)d e +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 +--R 580A a d e + (- 238A a b - 119B a )d e +--R + +--R 2 3 3 2 4 2 +--R (60A a c + 30A b + 60B a b)d e + ((- 12A b - 12B a)c - 6B b )d e +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 1044A a d e + (- 684A a b - 342B a )d e +--R + +--R 2 3 3 +--R (296A a c + 148A b + 296B a b)d e +--R + +--R 2 4 2 2 5 +--R ((- 132A b - 132B a)c - 66B b )d e + (24A c + 48B b c)d e +--R * +--R m +--R + +--R 2 5 2 2 4 +--R 720A a d e + (- 720A a b - 360B a )d e +--R + +--R 2 3 3 +--R (480A a c + 240A b + 480B a b)d e +--R + +--R 2 4 2 2 5 +--R ((- 360A b - 360B a)c - 180B b )d e + (144A c + 288B b c)d e +--R + +--R 2 6 +--R - 120B c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (- B c m - 15B c m - 85B c m - 225B c m - 274B c m - 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((- A c - 2B b c)e + 5B c d)m + ((- 16A c - 32B b c)e + 80B c d)m +--R + +--R 2 2 3 +--R ((- 95A c - 190B b c)e + 475B c d)m +--R + +--R 2 2 2 +--R ((- 260A c - 520B b c)e + 1300B c d)m +--R + +--R 2 2 2 +--R ((- 324A c - 648B b c)e + 1620B c d)m + (- 144A c - 288B b c)e +--R + +--R 2 +--R 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R (((- 2A b - 2B a)c - B b )e + (4A c + 8B b c)d e - 10B c d )m +--R + +--R 2 2 2 +--R ((- 34A b - 34B a)c - 17B b )e + (68A c + 136B b c)d e +--R + +--R 2 2 +--R - 170B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 +--R ((- 214A b - 214B a)c - 107B b )e + (428A c + 856B b c)d e +--R + +--R 2 2 +--R - 1070B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 +--R ((- 614A b - 614B a)c - 307B b )e + (1228A c + 2456B b c)d e +--R + +--R 2 2 +--R - 3070B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 +--R ((- 792A b - 792B a)c - 396B b )e + (1584A c + 3168B b c)d e +--R + +--R 2 2 +--R - 3960B c d +--R * +--R m +--R + +--R 2 2 2 +--R ((- 360A b - 360B a)c - 180B b )e + (720A c + 1440B b c)d e +--R + +--R 2 2 +--R - 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 +--R (- 2A a c - A b - 2B a b)e + ((6A b + 6B a)c + 3B b )d e +--R + +--R 2 2 2 3 +--R (- 6A c - 12B b c)d e + 10B c d +--R * +--R 5 +--R m +--R + +--R 2 3 +--R (- 36A a c - 18A b - 36B a b)e +--R + +--R 2 2 2 2 +--R ((108A b + 108B a)c + 54B b )d e + (- 108A c - 216B b c)d e +--R + +--R 2 3 +--R 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 +--R (- 242A a c - 121A b - 242B a b)e +--R + +--R 2 2 2 2 +--R ((726A b + 726B a)c + 363B b )d e + (- 726A c - 1452B b c)d e +--R + +--R 2 3 +--R 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 +--R (- 744A a c - 372A b - 744B a b)e +--R + +--R 2 2 +--R ((2232A b + 2232B a)c + 1116B b )d e +--R + +--R 2 2 2 3 +--R (- 2232A c - 4464B b c)d e + 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 +--R (- 1016A a c - 508A b - 1016B a b)e +--R + +--R 2 2 +--R ((3048A b + 3048B a)c + 1524B b )d e +--R + +--R 2 2 2 3 +--R (- 3048A c - 6096B b c)d e + 5080B c d +--R * +--R m +--R + +--R 2 3 +--R (- 480A a c - 240A b - 480B a b)e +--R + +--R 2 2 2 2 +--R ((1440A b + 1440B a)c + 720B b )d e + (- 1440A c - 2880B b c)d e +--R + +--R 2 3 +--R 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 2 3 +--R (- 2A a b - B a )e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 2 2 2 3 2 4 +--R ((- 6A b - 6B a)c - 3B b )d e + (4A c + 8B b c)d e - 5B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 +--R (- 38A a b - 19B a )e + (76A a c + 38A b + 76B a b)d e +--R + +--R 2 2 2 2 3 +--R ((- 114A b - 114B a)c - 57B b )d e + (76A c + 152B b c)d e +--R + +--R 2 4 +--R - 95B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 +--R (- 274A a b - 137B a )e + (548A a c + 274A b + 548B a b)d e +--R + +--R 2 2 2 2 3 +--R ((- 822A b - 822B a)c - 411B b )d e + (548A c + 1096B b c)d e +--R + +--R 2 4 +--R - 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 +--R (- 922A a b - 461B a )e + (1844A a c + 922A b + 1844B a b)d e +--R + +--R 2 2 2 +--R ((- 2766A b - 2766B a)c - 1383B b )d e +--R + +--R 2 3 2 4 +--R (1844A c + 3688B b c)d e - 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 +--R (- 1404A a b - 702B a )e +--R + +--R 2 3 +--R (2808A a c + 1404A b + 2808B a b)d e +--R + +--R 2 2 2 +--R ((- 4212A b - 4212B a)c - 2106B b )d e +--R + +--R 2 3 2 4 +--R (2808A c + 5616B b c)d e - 3510B c d +--R * +--R m +--R + +--R 2 4 2 3 +--R (- 720A a b - 360B a )e + (1440A a c + 720A b + 1440B a b)d e +--R + +--R 2 2 2 2 3 +--R ((- 2160A b - 2160B a)c - 1080B b )d e + (1440A c + 2880B b c)d e +--R + +--R 2 4 +--R - 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 +--R - A a e + (2A a b + B a )d e + (- 2A a c - A b - 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((2A b + 2B a)c + B b )d e + (- A c - 2B b c)d e + B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 +--R - 20A a e + (40A a b + 20B a )d e +--R + +--R 2 2 3 +--R (- 40A a c - 20A b - 40B a b)d e +--R + +--R 2 3 2 2 4 +--R ((40A b + 40B a)c + 20B b )d e + (- 20A c - 40B b c)d e +--R + +--R 2 5 +--R 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 +--R - 155A a e + (310A a b + 155B a )d e +--R + +--R 2 2 3 +--R (- 310A a c - 155A b - 310B a b)d e +--R + +--R 2 3 2 2 4 +--R ((310A b + 310B a)c + 155B b )d e + (- 155A c - 310B b c)d e +--R + +--R 2 5 +--R 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 +--R - 580A a e + (1160A a b + 580B a )d e +--R + +--R 2 2 3 +--R (- 1160A a c - 580A b - 1160B a b)d e +--R + +--R 2 3 2 2 4 +--R ((1160A b + 1160B a)c + 580B b )d e + (- 580A c - 1160B b c)d e +--R + +--R 2 5 +--R 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 +--R - 1044A a e + (2088A a b + 1044B a )d e +--R + +--R 2 2 3 +--R (- 2088A a c - 1044A b - 2088B a b)d e +--R + +--R 2 3 2 +--R ((2088A b + 2088B a)c + 1044B b )d e +--R + +--R 2 4 2 5 +--R (- 1044A c - 2088B b c)d e + 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 +--R - 720A a e + (1440A a b + 720B a )d e +--R + +--R 2 2 3 +--R (- 1440A a c - 720A b - 1440B a b)d e +--R + +--R 2 3 2 2 4 +--R ((1440A b + 1440B a)c + 720B b )d e + (- 720A c - 1440B b c)d e +--R + +--R 2 5 +--R 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 238 + +)clear all + +--S 239 of 1751 +t0:=(A+B*x)*(d+e*x)^5*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 10 2 5 2 4 9 +--R B c e x + ((A c + 2B b c)e + 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 8 +--R (((2A b + 2B a)c + B b )e + (5A c + 10B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 +--R (2A a c + A b + 2B a b)e + ((10A b + 10B a)c + 5B b )d e +--R + +--R 2 2 3 2 3 2 +--R (10A c + 20B b c)d e + 10B c d e +--R * +--R 7 +--R x +--R + +--R 2 5 2 4 +--R (2A a b + B a )e + (10A a c + 5A b + 10B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((20A b + 20B a)c + 10B b )d e + (10A c + 20B b c)d e + 5B c d e +--R * +--R 6 +--R x +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (10A a b + 5B a )d e + (20A a c + 10A b + 20B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((20A b + 20B a)c + 10B b )d e + (5A c + 10B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 5A a d e + (20A a b + 10B a )d e + (20A a c + 10A b + 20B a b)d e +--R + +--R 2 4 2 5 +--R ((10A b + 10B a)c + 5B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 10A a d e + (20A a b + 10B a )d e + (10A a c + 5A b + 10B a b)d e +--R + +--R 2 5 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 239 + +--S 240 of 1751 +r0:=-1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^6/e^6-_ + 1/7*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-_ + e*(3*b*d-a*e)))*(d+e*x)^7/e^6-1/8*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^8/e^6-1/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^9/e^6-1/10*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^10/e^6+1/11*B*c^2*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 2 11 11 1 2 1 11 1 2 10 10 +--R -- B c e x + ((-- A c + - B b c)e + - B c d e )x +--R 11 10 5 2 +--R + +--R 2 2 1 2 11 5 2 10 10 +--R ((- A b + - B a)c + - B b )e + (- A c + -- B b c)d e +--R 9 9 9 9 9 +--R + +--R 10 2 2 9 +--R -- B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 1 1 2 1 11 5 5 5 2 10 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 4 8 4 4 4 8 +--R + +--R 5 2 5 2 9 5 2 3 8 +--R (- A c + - B b c)d e + - B c d e +--R 4 2 4 +--R * +--R 8 +--R x +--R + +--R 2 1 2 11 10 5 2 10 10 +--R (- A a b + - B a )e + (-- A a c + - A b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 20 20 10 2 2 9 10 2 20 3 8 +--R ((-- A b + -- B a)c + -- B b )d e + (-- A c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 5 2 4 7 +--R - B c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 1 2 11 5 5 2 10 +--R - A a e + (- A a b + - B a )d e +--R 6 3 6 +--R + +--R 10 5 2 10 2 9 +--R (-- A a c + - A b + -- B a b)d e +--R 3 3 3 +--R + +--R 10 10 5 2 3 8 5 2 5 4 7 1 2 5 6 +--R ((-- A b + -- B a)c + - B b )d e + (- A c + - B b c)d e + - B c d e +--R 3 3 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 2 10 2 2 9 2 3 8 +--R A a d e + (4A a b + 2B a )d e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 4 7 1 2 2 5 6 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 2 2 9 5 2 3 8 5 5 2 5 4 7 +--R - A a d e + (5A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 2 2 2 4 2 +--R + +--R 1 1 1 2 5 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 10 2 3 8 10 5 2 4 7 +--R -- A a d e + (-- A a b + - B a )d e +--R 3 3 3 +--R + +--R 2 1 2 2 5 6 +--R (- A a c + - A b + - B a b)d e +--R 3 3 3 +--R * +--R 3 +--R x +--R + +--R 5 2 4 7 1 2 5 6 2 2 5 6 1 2 6 5 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 1 1 2 7 4 1 1 2 1 8 3 +--R (- -- A a b - -- B a )d e + (-- A a c + --- A b + -- B a b)d e +--R 21 42 84 168 84 +--R + +--R 1 1 1 2 9 2 1 2 1 10 +--R ((- --- A b - --- B a)c - --- B b )d e + (---- A c + --- B b c)d e +--R 252 252 504 1260 630 +--R + +--R 1 2 11 +--R - ---- B c d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 240 + +--S 241 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 5 11 1 2 1 5 1 2 4 10 +--R -- B c e x + ((-- A c + - B b c)e + - B c d e )x +--R 11 10 5 2 +--R + +--R 2 2 1 2 5 5 2 10 4 10 2 2 3 9 +--R (((- A b + - B a)c + - B b )e + (- A c + -- B b c)d e + -- B c d e )x +--R 9 9 9 9 9 9 +--R + +--R 1 1 2 1 5 5 5 5 2 4 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 4 8 4 4 4 8 +--R + +--R 5 2 5 2 3 5 2 3 2 +--R (- A c + - B b c)d e + - B c d e +--R 4 2 4 +--R * +--R 8 +--R x +--R + +--R 2 1 2 5 10 5 2 10 4 +--R (- A a b + - B a )e + (-- A a c + - A b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 20 20 10 2 2 3 10 2 20 3 2 5 2 4 +--R ((-- A b + -- B a)c + -- B b )d e + (-- A c + -- B b c)d e + - B c d e +--R 7 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 5 5 5 2 4 10 5 2 10 2 3 +--R - A a e + (- A a b + - B a )d e + (-- A a c + - A b + -- B a b)d e +--R 6 3 6 3 3 3 +--R + +--R 10 10 5 2 3 2 5 2 5 4 1 2 5 +--R ((-- A b + -- B a)c + - B b )d e + (- A c + - B b c)d e + - B c d +--R 3 3 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R A a d e + (4A a b + 2B a )d e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 4 1 2 2 5 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 2 2 3 5 2 3 2 5 5 2 5 4 +--R - A a d e + (5A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 2 2 2 4 2 +--R + +--R 1 1 1 2 5 +--R ((- A b + - B a)c + - B b )d +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 10 2 3 2 10 5 2 4 2 1 2 2 5 3 +--R (-- A a d e + (-- A a b + - B a )d e + (- A a c + - A b + - B a b)d )x +--R 3 3 3 3 3 3 +--R + +--R 5 2 4 1 2 5 2 2 5 +--R (- A a d e + (A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 241 + +--S 242 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 6 5 1 1 2 7 4 +--R - - A a d e + (-- A a b + -- B a )d e +--R 6 21 42 +--R + +--R 1 1 2 1 8 3 +--R (- -- A a c - --- A b - -- B a b)d e +--R 84 168 84 +--R + +--R 1 1 1 2 9 2 1 2 1 10 +--R ((--- A b + --- B a)c + --- B b )d e + (- ---- A c - --- B b c)d e +--R 252 252 504 1260 630 +--R + +--R 1 2 11 +--R ---- B c d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 242 + +--S 243 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 243 + +)clear all + +--S 244 of 1751 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 +--R B c e x + ((A c + 2B b c)e + 4B c d e )x +--R + +--R 2 4 2 3 2 2 2 7 +--R (((2A b + 2B a)c + B b )e + (4A c + 8B b c)d e + 6B c d e )x +--R + +--R 2 4 2 3 +--R (2A a c + A b + 2B a b)e + ((8A b + 8B a)c + 4B b )d e +--R + +--R 2 2 2 2 3 +--R (6A c + 12B b c)d e + 4B c d e +--R * +--R 6 +--R x +--R + +--R 2 4 2 3 +--R (2A a b + B a )e + (8A a c + 4A b + 8B a b)d e +--R + +--R 2 2 2 2 3 2 4 +--R ((12A b + 12B a)c + 6B b )d e + (4A c + 8B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 3 2 2 2 +--R A a e + (8A a b + 4B a )d e + (12A a c + 6A b + 12B a b)d e +--R + +--R 2 3 2 4 +--R ((8A b + 8B a)c + 4B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 4A a d e + (12A a b + 6B a )d e + (8A a c + 4A b + 8B a b)d e +--R + +--R 2 4 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 244 + +--S 245 of 1751 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^5/e^6-_ + 1/6*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^7/e^6-_ + 1/8*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*_ + (d+e*x)^8/e^6-1/9*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^9/e^6+_ + 1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 2 10 4 2 9 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 1 2 10 1 2 9 3 2 2 8 8 +--R (((- A b + - B a)c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 4 8 2 4 +--R + +--R 2 1 2 2 10 8 8 4 2 9 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 7 7 7 7 7 7 +--R + +--R 6 2 12 2 8 4 2 3 7 +--R (- A c + -- B b c)d e + - B c d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 1 2 10 4 2 2 4 9 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 3 6 3 3 3 +--R + +--R 2 2 8 2 2 4 3 7 1 2 4 6 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d e + - B c d e +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 2 10 8 4 2 9 +--R - A a e + (- A a b + - B a )d e +--R 5 5 5 +--R + +--R 12 6 2 12 2 8 8 8 4 2 3 7 +--R (-- A a c + - A b + -- B a b)d e + ((- A b + - B a)c + - B b )d e +--R 5 5 5 5 5 5 +--R + +--R 1 2 2 4 6 +--R (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 2 9 3 2 2 8 2 3 7 +--R A a d e + (3A a b + - B a )d e + (2A a c + A b + 2B a b)d e +--R 2 +--R + +--R 1 1 1 2 4 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 2 8 8 4 2 3 7 2 1 2 2 4 6 3 +--R (2A a d e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 3 3 +--R + +--R 2 3 7 1 2 4 6 2 2 4 6 1 2 5 5 +--R (2A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 5 +--R + +--R 1 1 2 6 4 2 1 2 2 7 3 +--R (- -- A a b - -- B a )d e + (--- A a c + --- A b + --- B a b)d e +--R 15 30 105 105 105 +--R + +--R 1 1 1 2 8 2 1 2 1 9 +--R ((- --- A b - --- B a)c - --- B b )d e + (--- A c + --- B b c)d e +--R 140 140 280 630 315 +--R + +--R 1 2 10 +--R - ---- B c d +--R 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 245 + +--S 246 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 10 1 2 2 4 4 2 3 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 1 2 4 1 2 3 3 2 2 2 8 +--R (((- A b + - B a)c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 4 8 2 4 +--R + +--R 2 1 2 2 4 8 8 4 2 3 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 7 7 7 7 7 7 +--R + +--R 6 2 12 2 2 4 2 3 +--R (- A c + -- B b c)d e + - B c d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 1 2 4 4 2 2 4 3 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 3 6 3 3 3 +--R + +--R 2 2 2 2 2 4 3 1 2 4 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d e + - B c d +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 2 4 8 4 2 3 12 6 2 12 2 2 +--R - A a e + (- A a b + - B a )d e + (-- A a c + - A b + -- B a b)d e +--R 5 5 5 5 5 5 +--R + +--R 8 8 4 2 3 1 2 2 4 +--R ((- A b + - B a)c + - B b )d e + (- A c + - B b c)d +--R 5 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 2 2 2 3 +--R A a d e + (3A a b + - B a )d e + (2A a c + A b + 2B a b)d e +--R 2 +--R + +--R 1 1 1 2 4 +--R ((- A b + - B a)c + - B b )d +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 2 2 8 4 2 3 2 1 2 2 4 3 +--R (2A a d e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d )x +--R 3 3 3 3 3 +--R + +--R 2 3 1 2 4 2 2 4 +--R (2A a d e + (A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 246 + +--S 247 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 5 5 1 1 2 6 4 +--R - - A a d e + (-- A a b + -- B a )d e +--R 5 15 30 +--R + +--R 2 1 2 2 7 3 +--R (- --- A a c - --- A b - --- B a b)d e +--R 105 105 105 +--R + +--R 1 1 1 2 8 2 1 2 1 9 +--R ((--- A b + --- B a)c + --- B b )d e + (- --- A c - --- B b c)d e +--R 140 140 280 630 315 +--R + +--R 1 2 10 +--R ---- B c d +--R 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 247 + +--S 248 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 248 + +)clear all + +--S 249 of 1751 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R (((2A b + 2B a)c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 +--R (2A a c + A b + 2B a b)e + ((6A b + 6B a)c + 3B b )d e +--R + +--R 2 2 2 3 +--R (3A c + 6B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 3 2 2 +--R (2A a b + B a )e + (6A a c + 3A b + 6B a b)d e +--R + +--R 2 2 2 3 +--R ((6A b + 6B a)c + 3B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 +--R A a e + (6A a b + 3B a )d e + (6A a c + 3A b + 6B a b)d e +--R + +--R 2 3 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 249 + +--S 250 of 1751 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4/e^6-_ + 1/5*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^5/e^6-1/6*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^7/e^6-1/8*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^8/e^6+1/9*B*c^2*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 1 2 9 9 1 2 1 9 3 2 8 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 2 1 2 9 3 2 6 8 3 2 2 7 7 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d e )x +--R 7 7 7 7 7 7 +--R + +--R 1 1 2 1 9 1 2 8 +--R (- A a c + - A b + - B a b)e + ((A b + B a)c + - B b )d e +--R 3 6 3 2 +--R + +--R 1 2 2 7 1 2 3 6 +--R (- A c + B b c)d e + - B c d e +--R 2 6 +--R * +--R 6 +--R x +--R + +--R 2 1 2 9 6 3 2 6 8 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 6 6 3 2 2 7 1 2 2 3 6 +--R ((- A b + - B a)c + - B b )d e + (- A c + - B b c)d e +--R 5 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 2 9 3 3 2 8 3 3 2 3 2 7 +--R - A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 4 2 4 2 4 2 +--R + +--R 1 1 1 2 3 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 7 2 1 2 2 3 6 3 +--R (A a d e + (2A a b + B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 +--R + +--R 3 2 2 7 1 2 3 6 2 2 3 6 1 2 4 5 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 4 +--R + +--R 1 1 2 5 4 1 1 2 1 6 3 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A b + -- B a b)d e +--R 10 20 30 60 30 +--R + +--R 1 1 1 2 7 2 1 2 1 8 +--R ((- -- A b - -- B a)c - --- B b )d e + (--- A c + --- B b c)d e +--R 70 70 140 280 140 +--R + +--R 1 2 9 +--R - --- B c d +--R 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 250 + +--S 251 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 3 9 1 2 1 3 3 2 2 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 2 1 2 3 3 2 6 2 3 2 2 7 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d e)x +--R 7 7 7 7 7 7 +--R + +--R 1 1 2 1 3 1 2 2 +--R (- A a c + - A b + - B a b)e + ((A b + B a)c + - B b )d e +--R 3 6 3 2 +--R + +--R 1 2 2 1 2 3 +--R (- A c + B b c)d e + - B c d +--R 2 6 +--R * +--R 6 +--R x +--R + +--R 2 1 2 3 6 3 2 6 2 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 6 6 3 2 2 1 2 2 3 +--R ((- A b + - B a)c + - B b )d e + (- A c + - B b c)d +--R 5 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 2 3 3 3 2 2 3 3 2 3 2 +--R - A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 4 2 4 2 4 2 +--R + +--R 1 1 1 2 3 +--R ((- A b + - B a)c + - B b )d +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 2 2 2 2 1 2 2 3 3 +--R (A a d e + (2A a b + B a )d e + (- A a c + - A b + - B a b)d )x +--R 3 3 3 +--R + +--R 3 2 2 1 2 3 2 2 3 +--R (- A a d e + (A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 251 + +--S 252 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 4 5 1 1 2 5 4 +--R - - A a d e + (-- A a b + -- B a )d e +--R 4 10 20 +--R + +--R 1 1 2 1 6 3 +--R (- -- A a c - -- A b - -- B a b)d e +--R 30 60 30 +--R + +--R 1 1 1 2 7 2 1 2 1 8 +--R ((-- A b + -- B a)c + --- B b )d e + (- --- A c - --- B b c)d e +--R 70 70 140 280 140 +--R + +--R 1 2 9 +--R --- B c d +--R 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 252 + +--S 253 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 253 + +)clear all + +--S 254 of 1751 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R (((2A b + 2B a)c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 +--R (2A a c + A b + 2B a b)e + ((4A b + 4B a)c + 2B b )d e +--R + +--R 2 2 +--R (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 2 2 +--R (2A a b + B a )e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 2 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 254 + +--S 255 of 1751 +r0:=-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^3/e^6-1/4*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*(d+e*x)^4/e^6-_ + 1/5*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^5/e^6-_ + 1/6*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^7/e^6+_ + 1/8*B*c^2*(d+e*x)^8/e^6 +--R +--R +--R (2) +--R 1 2 8 8 1 2 2 8 2 2 7 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 1 1 2 8 1 2 2 7 1 2 2 6 6 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d e )x +--R 3 3 6 3 3 6 +--R + +--R 2 1 2 2 8 4 4 2 2 7 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 5 5 5 5 5 5 +--R + +--R 1 2 2 2 6 +--R (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 1 1 2 8 1 2 7 +--R (- A a b + - B a )e + (A a c + - A b + B a b)d e +--R 2 4 2 +--R + +--R 1 1 1 2 2 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 1 2 8 4 2 2 7 2 1 2 2 2 6 3 +--R (- A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 3 3 3 +--R + +--R 2 7 1 2 2 6 2 2 2 6 1 2 3 5 +--R (A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 3 +--R + +--R 1 1 2 4 4 1 1 2 1 5 3 +--R (- - A a b - -- B a )d e + (-- A a c + -- A b + -- B a b)d e +--R 6 12 15 30 15 +--R + +--R 1 1 1 2 6 2 1 2 2 7 +--R ((- -- A b - -- B a)c - -- B b )d e + (--- A c + --- B b c)d e +--R 30 30 60 105 105 +--R + +--R 1 2 8 +--R - --- B c d +--R 168 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 255 + +--S 256 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 8 1 2 2 2 2 2 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e)x +--R 8 7 7 7 +--R + +--R 1 1 1 2 2 1 2 2 1 2 2 6 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d )x +--R 3 3 6 3 3 6 +--R + +--R 2 1 2 2 2 4 4 2 2 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 5 5 5 5 5 5 +--R + +--R 1 2 2 2 +--R (- A c + - B b c)d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 1 1 2 2 1 2 +--R (- A a b + - B a )e + (A a c + - A b + B a b)d e +--R 2 4 2 +--R + +--R 1 1 1 2 2 +--R ((- A b + - B a)c + - B b )d +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 1 2 2 4 2 2 2 1 2 2 2 3 +--R (- A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d )x +--R 3 3 3 3 3 3 +--R + +--R 2 1 2 2 2 2 2 +--R (A a d e + (A a b + - B a )d )x + A a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 256 + +--S 257 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 2 3 5 1 1 2 4 4 +--R - - A a d e + (- A a b + -- B a )d e +--R 3 6 12 +--R + +--R 1 1 2 1 5 3 +--R (- -- A a c - -- A b - -- B a b)d e +--R 15 30 15 +--R + +--R 1 1 1 2 6 2 1 2 2 7 +--R ((-- A b + -- B a)c + -- B b )d e + (- --- A c - --- B b c)d e +--R 30 30 60 105 105 +--R + +--R 1 2 8 +--R --- B c d +--R 168 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 257 + +--S 258 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 258 + +)clear all + +--S 259 of 1751 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 +--R (((2A b + 2B a)c + B b )e + (A c + 2B b c)d)x +--R + +--R 2 2 3 +--R ((2A a c + A b + 2B a b)e + ((2A b + 2B a)c + B b )d)x +--R + +--R 2 2 2 +--R ((2A a b + B a )e + (2A a c + A b + 2B a b)d)x +--R + +--R 2 2 2 +--R (A a e + (2A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 259 + +--S 260 of 1751 +r0:=a^2*A*d*x+1/2*a*(2*A*b*d+a*B*d+a*A*e)*x^2+1/3*(a*B*(2*b*d+a*e)+_ + A*(b^2*d+2*a*c*d+2*a*b*e))*x^3+1/4*(b^2*(B*d+A*e)+2*a*c*(B*d+A*e)+_ + 2*b*(A*c*d+a*B*e))*x^4+1/5*(b^2*B*e+2*b*c*(B*d+A*e)+_ + c*(A*c*d+2*a*B*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 2 1 2 1 2 2 5 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 5 +--R + +--R 1 1 2 1 1 1 1 2 4 +--R ((- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d)x +--R 2 4 2 2 2 4 +--R + +--R 2 1 2 2 1 2 2 3 +--R ((- A a b + - B a )e + (- A a c + - A b + - B a b)d)x +--R 3 3 3 3 3 +--R + +--R 1 2 1 2 2 2 +--R (- A a e + (A a b + - B a )d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 260 + +--S 261 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 2 1 2 1 2 2 5 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 5 +--R + +--R 1 1 2 1 1 1 1 2 4 +--R ((- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d)x +--R 2 4 2 2 2 4 +--R + +--R 2 1 2 2 1 2 2 3 +--R ((- A a b + - B a )e + (- A a c + - A b + - B a b)d)x +--R 3 3 3 3 3 +--R + +--R 1 2 1 2 2 2 +--R (- A a e + (A a b + - B a )d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 261 + +--S 262 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 262 + +--S 263 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 263 + +)clear all + +--S 264 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 264 + +--S 265 of 1751 +r0:=a^2*A*x+1/2*a*(2*A*b+a*B)*x^2+1/3*(2*a*b*B+A*(b^2+2*a*c))*x^3+_ + 1/4*(b^2*B+2*A*b*c+2*a*B*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 1 1 2 4 +--R - B c x + (- A c + - B b c)x + ((- A b + - B a)c + - B b )x +--R 6 5 5 2 2 4 +--R + +--R 2 1 2 2 3 1 2 2 2 +--R (- A a c + - A b + - B a b)x + (A a b + - B a )x + A a x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 265 + +--S 266 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 6 1 2 2 5 1 1 1 2 4 +--R - B c x + (- A c + - B b c)x + ((- A b + - B a)c + - B b )x +--R 6 5 5 2 2 4 +--R + +--R 2 1 2 2 3 1 2 2 2 +--R (- A a c + - A b + - B a b)x + (A a b + - B a )x + A a x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 266 + +--S 267 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 267 + +--S 268 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 268 + +)clear all + +--S 269 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 269 + +--S 270 of 1751 +r0:=-(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + x/e^5-1/2*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^2/e^6-1/3*(2*A*c*e*_ + (2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*(d+e*x)^3/e^6-_ + 1/4*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^4/e^6+1/5*B*c^2*(d+e*x)^5/e^6-_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R 60A a e + (- 120A a b - 60B a )d e +--R + +--R 2 2 3 +--R (120A a c + 60A b + 120B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 120A b - 120B a)c - 60B b )d e + (60A c + 120B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((40A b + 40B a)c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 +--R (60A a c + 30A b + 60B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (30A c + 60B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (120A a b + 60B a )e + (- 120A a c - 60A b - 120B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((120A b + 120B a)c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 +--R (60A a c + 30A b + 60B a b)d e + ((- 140A b - 140B a)c - 70B b )d e +--R + +--R 2 4 2 5 +--R (115A c + 230B b c)d e - 163B c d +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 270 + +--S 271 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 +--R 60A a e + (- 120A a b - 60B a )d e +--R + +--R 2 2 3 +--R (120A a c + 60A b + 120B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 120A b - 120B a)c - 60B b )d e + (60A c + 120B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((40A b + 40B a)c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 +--R (60A a c + 30A b + 60B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (30A c + 60B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (120A a b + 60B a )e + (- 120A a c - 60A b - 120B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((120A b + 120B a)c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 271 + +--S 272 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 3 2 3 2 +--R (- 60A a c - 30A b - 60B a b)d e + ((140A b + 140B a)c + 70B b )d e +--R + +--R 2 4 2 5 +--R (- 115A c - 230B b c)d e + 163B c d +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 274 + +--S 275 of 1751 +r0:=-(2*B*(2*c*d-b*e)*(c*d^2-e*(b*d-a*e))-A*e*(3*c^2*d^2+b^2*e^2-_ + 2*c*e*(2*b*d-a*e)))*x/e^5-1/2*(2*A*c*e*(c*d-b*e)-B*(3*c^2*d^2+b^2*e^2-_ + 2*c*e*(2*b*d-a*e)))*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x))-_ + (c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R (24A a b + 12B a )e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 4 2 2 3 +--R (24A a b + 12B a )d e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 +--R (24A a c + 12A b + 24B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (24A c + 48B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R (24A a c + 12A b + 24B a b)d e + ((- 48A b - 48B a)c - 24B b )d e +--R + +--R 2 3 2 2 4 +--R (36A c + 72B b c)d e - 48B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (24A a b + 12B a )d e + (- 24A a c - 12A b - 24B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((24A b + 24B a)c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 +--R (24A a b + 12B a )e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 4 2 2 3 +--R (24A a b + 12B a )d e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 +--R (24A a c + 12A b + 24B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (24A c + 48B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R (24A a c + 12A b + 24B a b)d e + ((- 48A b - 48B a)c - 24B b )d e +--R + +--R 2 3 2 2 4 +--R (36A c + 72B b c)d e - 48B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (24A a b + 12B a )d e + (- 24A a c - 12A b - 24B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((24A b + 24B a)c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 276 + +--S 277 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 278 + +)clear all + +--S 279 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 279 + +--S 280 of 1751 +r0:=-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*x/e^5-_ + 1/2*c*(3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^2)+(c*d^2-b*d*e+a*e^2)*(2*A*e*_ + (2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x))-(B*(10*c^2*d^3+_ + b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-_ + 2*c*e*(3*b*d-a*e)))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R (12A a c + 6A b + 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (36A c + 72B b c)d e - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 +--R (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 72A b - 72B a)c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 +--R (12A a c + 6A b + 12B a b)d e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 4 2 5 +--R (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 +--R ((24A b + 24B a)c + 12B b )d e + (- 33A c - 66B b c)d e +--R + +--R 2 3 2 +--R 63B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 12A a b - 6B a )e + (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((- 24A b - 24B a)c - 12B b )d e + (6A c + 12B b c)d e + 6B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 6A a b - 3B a )d e + (18A a c + 9A b + 18B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 30A b - 30B a)c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 280 + +--S 281 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 +--R (12A a c + 6A b + 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (36A c + 72B b c)d e - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 +--R (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 72A b - 72B a)c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 +--R (12A a c + 6A b + 12B a b)d e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 4 2 5 +--R (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 +--R ((24A b + 24B a)c + 12B b )d e + (- 33A c - 66B b c)d e +--R + +--R 2 3 2 +--R 63B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 12A a b - 6B a )e + (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((- 24A b - 24B a)c - 12B b )d e + (6A c + 12B b c)d e + 6B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 6A a b - 3B a )d e + (18A a c + 9A b + 18B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 30A b - 30B a)c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 281 + +--S 282 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 283 + +)clear all + +--S 284 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 284 + +--S 285 of 1751 +r0:=-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^3)+1/2*(c*d^2-b*d*e+a*e^2)*(2*A*e*_ + (2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^2)+(B*(10*c^2*d^3+_ + b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-_ + 2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(4*b*d-a*e)))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R ((12A b + 12B a)c + 6B b )e + (- 24A c - 48B b c)d e +--R + +--R 2 2 3 +--R 60B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 2 3 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 3 2 +--R 180B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 4 +--R 180B c d e +--R * +--R x +--R + +--R 2 3 2 2 4 2 5 +--R ((12A b + 12B a)c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((36A b + 36B a)c + 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 18A c - 36B b c)d e - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 6A a b - 3B a )e + (- 12A a c - 6A b - 12B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((54A b + 54B a)c + 27B b )d e + (- 54A c - 108B b c)d e + 81B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 2A a e + (- 2A a b - B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((22A b + 22B a)c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 285 + +--S 286 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 +--R ((12A b + 12B a)c + 6B b )e + (- 24A c - 48B b c)d e +--R + +--R 2 2 3 +--R 60B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 2 3 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 3 2 +--R 180B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 4 +--R 180B c d e +--R * +--R x +--R + +--R 2 3 2 2 4 2 5 +--R ((12A b + 12B a)c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((36A b + 36B a)c + 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 18A c - 36B b c)d e - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 6A a b - 3B a )e + (- 12A a c - 6A b - 12B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((54A b + 54B a)c + 27B b )d e + (- 54A c - 108B b c)d e + 81B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 2A a e + (- 2A a b - B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((22A b + 22B a)c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 286 + +--S 287 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 289 + +--S 290 of 1751 +r0:=B*c^2*x/e^5+1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^4)+_ + 1/3*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/_ + (e^6*(d+e*x)^3)+1/2*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-_ + a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^2)+_ + (2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*_ + (d+e*x))-c*(5*B*c*d-2*b*B*e-A*c*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 4 +--R ((12A c + 24B b c)e - 60B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((48A c + 96B b c)d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 +--R ((72A c + 144B b c)d e - 360B c d e )x +--R + +--R 2 3 2 2 4 2 4 +--R ((48A c + 96B b c)d e - 240B c d e)x + (12A c + 24B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 +--R 12B c e x + 48B c d e x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((- 24A b - 24B a)c - 12B b )e + (48A c + 96B b c)d e - 48B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (108A c + 216B b c)d e - 252B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 8A a b - 4B a )e + (- 8A a c - 4A b - 8B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 24A b - 24B a)c - 12B b )d e + (88A c + 176B b c)d e +--R + +--R 2 4 +--R - 248B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 2A a b - B a )d e + (- 2A a c - A b - 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (25A c + 50B b c)d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 4 +--R ((12A c + 24B b c)e - 60B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((48A c + 96B b c)d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 +--R ((72A c + 144B b c)d e - 360B c d e )x +--R + +--R 2 3 2 2 4 2 4 +--R ((48A c + 96B b c)d e - 240B c d e)x + (12A c + 24B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 +--R 12B c e x + 48B c d e x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((- 24A b - 24B a)c - 12B b )e + (48A c + 96B b c)d e - 48B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (108A c + 216B b c)d e - 252B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 8A a b - 4B a )e + (- 8A a c - 4A b - 8B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 24A b - 24B a)c - 12B b )d e + (88A c + 176B b c)d e +--R + +--R 2 4 +--R - 248B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 2A a b - B a )d e + (- 2A a c - A b - 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (25A c + 50B b c)d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 291 + +--S 292 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 293 + +)clear all + +--S 294 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^6 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 294 + +--S 295 of 1751 +r0:=1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^5)+1/4*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^4)+_ + 1/3*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^3)+_ + 1/2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^2)+c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x))+B*c^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R ((- 60A c - 120B b c)e + 300B c d e )x +--R + +--R 2 5 2 4 +--R ((- 60A b - 60B a)c - 30B b )e + (- 120A c - 240B b c)d e +--R + +--R 2 2 3 +--R 900B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 4 +--R (- 40A a c - 20A b - 40B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 120A c - 240B b c)d e + 1100B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 30A a b - 15B a )e + (- 20A a c - 10A b - 20B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 30A b - 30B a)c - 15B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 625B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (- 6A a b - 3B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (- 12A c - 24B b c)d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R ((- 60A c - 120B b c)e + 300B c d e )x +--R + +--R 2 5 2 4 +--R ((- 60A b - 60B a)c - 30B b )e + (- 120A c - 240B b c)d e +--R + +--R 2 2 3 +--R 900B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 4 +--R (- 40A a c - 20A b - 40B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 120A c - 240B b c)d e + 1100B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 30A a b - 15B a )e + (- 20A a c - 10A b - 20B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 30A b - 30B a)c - 15B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 625B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (- 6A a b - 3B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (- 12A c - 24B b c)d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 296 + +--S 297 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 298 + +)clear all + +--S 299 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 299 + +--S 300 of 1751 +r0:=1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^6)+1/5*(c*d^2-_ + b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+_ + e*x)^5)+1/4*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^4)+_ + 1/3*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^3)+1/2*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^2)-_ + B*c^2/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 5 5 1 2 5 5 2 4 4 +--R - B c e x + ((- - A c - B b c)e - - B c d e )x +--R 2 2 +--R + +--R 2 2 1 2 5 2 2 4 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 3 3 3 3 3 +--R + +--R 10 2 2 3 +--R - -- B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 1 1 2 1 5 1 1 1 2 4 +--R (- - A a c - - A b - - B a b)e + ((- - A b - - B a)c - - B b )d e +--R 2 4 2 2 2 4 +--R + +--R 1 2 2 3 5 2 3 2 +--R (- - A c - B b c)d e - - B c d e +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 2 1 2 5 1 1 2 1 4 +--R (- - A a b - - B a )e + (- - A a c - -- A b - - B a b)d e +--R 5 5 5 10 5 +--R + +--R 1 1 1 2 2 3 1 2 2 3 2 2 4 +--R ((- - A b - - B a)c - -- B b )d e + (- - A c - - B b c)d e - B c d e +--R 5 5 10 5 5 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 6 15 30 +--R + +--R 1 1 2 1 2 3 +--R (- -- A a c - -- A b - -- B a b)d e +--R 30 60 30 +--R + +--R 1 1 1 2 3 2 1 2 1 4 1 2 5 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e - - B c d +--R 30 30 60 30 15 6 +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 300 + +--S 301 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 60B c e x + ((- 30A c - 60B b c)e - 150B c d e )x +--R + +--R 2 5 2 4 +--R ((- 40A b - 40B a)c - 20B b )e + (- 40A c - 80B b c)d e +--R + +--R 2 2 3 +--R - 200B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 4 +--R (- 30A a c - 15A b - 30B a b)e + ((- 30A b - 30B a)c - 15B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 30A c - 60B b c)d e - 150B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 24A a b - 12B a )e + (- 12A a c - 6A b - 12B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((- 12A b - 12B a)c - 6B b )d e + (- 12A c - 24B b c)d e - 60B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 10A a e + (- 4A a b - 2B a )d e + (- 2A a c - A b - 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 2A b - 2B a)c - B b )d e + (- 2A c - 4B b c)d e - 10B c d +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 6 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 301 + +--S 302 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 304 + +--S 305 of 1751 +r0:=1/7*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^7)+1/6*(c*d^2-_ + b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*_ + (d+e*x)^6)+1/5*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^5)+_ + 1/4*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^4)+1/3*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^3)-_ + 1/2*B*c^2/(e^6*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 5 5 1 2 2 5 5 2 4 4 +--R - - B c e x + ((- - A c - - B b c)e - - B c d e )x +--R 2 3 3 6 +--R + +--R 1 1 1 2 5 1 2 2 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 2 2 4 3 3 +--R + +--R 5 2 2 3 +--R - - B c d e +--R 6 +--R * +--R 3 +--R x +--R + +--R 2 1 2 2 5 +--R (- - A a c - - A b - - B a b)e +--R 5 5 5 +--R + +--R 3 3 3 2 4 1 2 2 2 3 +--R ((- -- A b - -- B a)c - -- B b )d e + (- - A c - - B b c)d e +--R 10 10 20 5 5 +--R + +--R 1 2 3 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 1 1 2 5 2 1 2 2 4 +--R (- - A a b - - B a )e + (- -- A a c - -- A b - -- B a b)d e +--R 3 6 15 15 15 +--R + +--R 1 1 1 2 2 3 1 2 2 3 2 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e +--R 10 10 20 15 15 +--R + +--R 1 2 4 +--R - - B c d e +--R 6 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 7 21 42 +--R + +--R 2 1 2 2 2 3 +--R (- --- A a c - --- A b - --- B a b)d e +--R 105 105 105 +--R + +--R 1 1 1 2 3 2 1 2 2 4 +--R ((- -- A b - -- B a)c - --- B b )d e + (- --- A c - --- B b c)d e +--R 70 70 140 105 105 +--R + +--R 1 2 5 +--R - -- B c d +--R 42 +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 6 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 305 + +--S 306 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 210B c e x + ((- 140A c - 280B b c)e - 350B c d e )x +--R + +--R 2 5 2 4 +--R ((- 210A b - 210B a)c - 105B b )e + (- 140A c - 280B b c)d e +--R + +--R 2 2 3 +--R - 350B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 +--R (- 168A a c - 84A b - 168B a b)e +--R + +--R 2 4 2 2 3 +--R ((- 126A b - 126B a)c - 63B b )d e + (- 84A c - 168B b c)d e +--R + +--R 2 3 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 140A a b - 70B a )e + (- 56A a c - 28A b - 56B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 42A b - 42B a)c - 21B b )d e + (- 28A c - 56B b c)d e +--R + +--R 2 4 +--R - 70B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 60A a e + (- 20A a b - 10B a )d e + (- 8A a c - 4A b - 8B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (- 4A c - 8B b c)d e - 10B c d +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 8 2 6 7 7 6 +--R 8820d e x + 2940d e x + 420d e +--R Type: Union(Expression(Integer),...) +--E 306 + +--S 307 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 308 + +)clear all + +--S 309 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 309 + +--S 310 of 1751 +r0:=1/8*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^8)+1/7*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^7)+_ + 1/6*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*_ + d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^6)+1/5*(2*A*c*e*(2*c*d-_ + b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*(d+e*x)^5)+_ + 1/4*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^4)-1/3*B*c^2/(e^6*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 5 5 1 2 1 5 5 2 4 4 +--R - - B c e x + ((- - A c - - B b c)e - -- B c d e )x +--R 3 4 2 12 +--R + +--R 2 2 1 2 5 1 2 2 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 5 5 5 5 5 +--R + +--R 1 2 2 3 +--R - - B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 1 1 2 1 5 1 1 1 2 4 +--R (- - A a c - - A b - - B a b)e + ((- - A b - - B a)c - -- B b )d e +--R 3 6 3 5 5 10 +--R + +--R 1 2 1 2 3 1 2 3 2 +--R (- -- A c - - B b c)d e - - B c d e +--R 10 5 6 +--R * +--R 2 +--R x +--R + +--R 2 1 2 5 2 1 2 2 4 +--R (- - A a b - - B a )e + (- -- A a c - -- A b - -- B a b)d e +--R 7 7 21 21 21 +--R + +--R 2 2 1 2 2 3 1 2 2 3 2 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e +--R 35 35 35 35 35 +--R + +--R 1 2 4 +--R - -- B c d e +--R 21 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 8 28 56 +--R + +--R 1 1 2 1 2 3 +--R (- -- A a c - --- A b - -- B a b)d e +--R 84 168 84 +--R + +--R 1 1 1 2 3 2 1 2 1 4 +--R ((- --- A b - --- B a)c - --- B b )d e + (- --- A c - --- B b c)d e +--R 140 140 280 280 140 +--R + +--R 1 2 5 +--R - --- B c d +--R 168 +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 5 9 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 8 2 7 7 8 6 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 310 + +--S 311 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R - 280B c e x + ((- 210A c - 420B b c)e - 350B c d e )x +--R + +--R 2 5 2 4 +--R ((- 336A b - 336B a)c - 168B b )e + (- 168A c - 336B b c)d e +--R + +--R 2 2 3 +--R - 280B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 +--R (- 280A a c - 140A b - 280B a b)e +--R + +--R 2 4 2 2 3 +--R ((- 168A b - 168B a)c - 84B b )d e + (- 84A c - 168B b c)d e +--R + +--R 2 3 2 +--R - 140B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 240A a b - 120B a )e + (- 80A a c - 40A b - 80B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 48A b - 48B a)c - 24B b )d e + (- 24A c - 48B b c)d e +--R + +--R 2 4 +--R - 40B c d e +--R * +--R x +--R + +--R 2 5 2 4 +--R - 105A a e + (- 30A a b - 15B a )d e +--R + +--R 2 2 3 2 3 2 +--R (- 10A a c - 5A b - 10B a b)d e + ((- 6A b - 6B a)c - 3B b )d e +--R + +--R 2 4 2 5 +--R (- 3A c - 6B b c)d e - 5B c d +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 +--R 840e x + 6720d e x + 23520d e x + 47040d e x + 58800d e x +--R + +--R 5 9 3 6 8 2 7 7 8 6 +--R 47040d e x + 23520d e x + 6720d e x + 840d e +--R Type: Union(Expression(Integer),...) +--E 311 + +--S 312 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 313 + +)clear all + +--S 314 of 1751 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1751 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))-_ + (c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*_ + (d+e*x)^(2+m)/(e^8*(2+m))-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*(d+e*x)^(3+m)/(e^8*(3+m))-(A*e*(2*c*d-b*e)*_ + (10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*_ + (4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+_ + a^2*e^2)))*(d+e*x)^(4+m)/(e^8*(4+m))-(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*_ + (5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^(6+m)/(e^8*(6+m))-_ + c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*_ + (d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 2 3 7 3 2 3 6 +--R ((A c + 3B b c )e - 7B c d)m + ((29A c + 87B b c )e - 203B c d)m +--R + +--R 3 2 3 5 +--R ((343A c + 1029B b c )e - 2401B c d)m +--R + +--R 3 2 3 4 +--R ((2135A c + 6405B b c )e - 14945B c d)m +--R + +--R 3 2 3 3 +--R ((7504A c + 22512B b c )e - 52528B c d)m +--R + +--R 3 2 3 2 +--R ((14756A c + 44268B b c )e - 103292B c d)m +--R + +--R 3 2 3 +--R ((14832A c + 44496B b c )e - 103824B c d)m +--R + +--R 3 2 3 +--R (5760A c + 17280B b c )e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 7 +--R (((3A b + 3B a)c + 3B b c)e + (- 6A c - 18B b c )d e + 21B c d )m +--R + +--R 2 2 2 3 2 +--R ((90A b + 90B a)c + 90B b c)e + (- 180A c - 540B b c )d e +--R + +--R 3 2 +--R 630B c d +--R * +--R 6 +--R m +--R + +--R 2 2 2 +--R ((1098A b + 1098B a)c + 1098B b c)e +--R + +--R 3 2 3 2 +--R (- 2196A c - 6588B b c )d e + 7686B c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 +--R ((7020A b + 7020B a)c + 7020B b c)e +--R + +--R 3 2 3 2 +--R (- 14040A c - 42120B b c )d e + 49140B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 +--R ((25227A b + 25227B a)c + 25227B b c)e +--R + +--R 3 2 3 2 +--R (- 50454A c - 151362B b c )d e + 176589B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 +--R ((50490A b + 50490B a)c + 50490B b c)e +--R + +--R 3 2 3 2 +--R (- 100980A c - 302940B b c )d e + 353430B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 +--R ((51432A b + 51432B a)c + 51432B b c)e +--R + +--R 3 2 3 2 +--R (- 102864A c - 308592B b c )d e + 360024B c d +--R * +--R m +--R + +--R 2 2 2 +--R ((20160A b + 20160B a)c + 20160B b c)e +--R + +--R 3 2 3 2 +--R (- 40320A c - 120960B b c )d e + 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 3 3 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 2 3 2 2 +--R ((- 15A b - 15B a)c - 15B b c)d e + (15A c + 45B b c )d e +--R + +--R 3 3 +--R - 35B c d +--R * +--R 7 +--R m +--R + +--R 2 2 3 3 +--R (93A a c + (93A b + 186B a b)c + 31B b )e +--R + +--R 2 2 2 +--R ((- 465A b - 465B a)c - 465B b c)d e +--R + +--R 3 2 2 3 3 +--R (465A c + 1395B b c )d e - 1085B c d +--R * +--R 6 +--R m +--R + +--R 2 2 3 3 +--R (1173A a c + (1173A b + 2346B a b)c + 391B b )e +--R + +--R 2 2 2 +--R ((- 5865A b - 5865B a)c - 5865B b c)d e +--R + +--R 3 2 2 3 3 +--R (5865A c + 17595B b c )d e - 13685B c d +--R * +--R 5 +--R m +--R + +--R 2 2 3 3 +--R (7743A a c + (7743A b + 15486B a b)c + 2581B b )e +--R + +--R 2 2 2 +--R ((- 38715A b - 38715B a)c - 38715B b c)d e +--R + +--R 3 2 2 3 3 +--R (38715A c + 116145B b c )d e - 90335B c d +--R * +--R 4 +--R m +--R + +--R 2 2 3 3 +--R (28632A a c + (28632A b + 57264B a b)c + 9544B b )e +--R + +--R 2 2 2 +--R ((- 143160A b - 143160B a)c - 143160B b c)d e +--R + +--R 3 2 2 3 3 +--R (143160A c + 429480B b c )d e - 334040B c d +--R * +--R 3 +--R m +--R + +--R 2 2 3 3 +--R (58692A a c + (58692A b + 117384B a b)c + 19564B b )e +--R + +--R 2 2 2 +--R ((- 293460A b - 293460B a)c - 293460B b c)d e +--R + +--R 3 2 2 3 3 +--R (293460A c + 880380B b c )d e - 684740B c d +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 +--R (60912A a c + (60912A b + 121824B a b)c + 20304B b )e +--R + +--R 2 2 2 +--R ((- 304560A b - 304560B a)c - 304560B b c)d e +--R + +--R 3 2 2 3 3 +--R (304560A c + 913680B b c )d e - 710640B c d +--R * +--R m +--R + +--R 2 2 3 3 +--R (24192A a c + (24192A b + 48384B a b)c + 8064B b )e +--R + +--R 2 2 2 +--R ((- 120960A b - 120960B a)c - 120960B b c)d e +--R + +--R 3 2 2 3 3 +--R (120960A c + 362880B b c )d e - 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R ((30A b + 30B a)c + 30B b c)d e + (- 20A c - 60B b c )d e +--R + +--R 3 4 +--R 35B c d +--R * +--R 7 +--R m +--R + +--R 2 3 2 4 +--R ((192A a b + 96B a )c + 32A b + 96B a b )e +--R + +--R 2 2 3 3 +--R (- 384A a c + (- 384A b - 768B a b)c - 128B b )d e +--R + +--R 2 2 2 2 +--R ((960A b + 960B a)c + 960B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 640A c - 1920B b c )d e + 1120B c d +--R * +--R 6 +--R m +--R + +--R 2 3 2 4 +--R ((2508A a b + 1254B a )c + 418A b + 1254B a b )e +--R + +--R 2 2 3 3 +--R (- 5016A a c + (- 5016A b - 10032B a b)c - 1672B b )d e +--R + +--R 2 2 2 2 +--R ((12540A b + 12540B a)c + 12540B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 8360A c - 25080B b c )d e + 14630B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 4 +--R ((17184A a b + 8592B a )c + 2864A b + 8592B a b )e +--R + +--R 2 2 3 3 +--R (- 34368A a c + (- 34368A b - 68736B a b)c - 11456B b )d e +--R + +--R 2 2 2 2 +--R ((85920A b + 85920B a)c + 85920B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 57280A c - 171840B b c )d e + 100240B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 4 +--R ((65958A a b + 32979B a )c + 10993A b + 32979B a b )e +--R + +--R 2 2 3 3 +--R (- 131916A a c + (- 131916A b - 263832B a b)c - 43972B b )d e +--R + +--R 2 2 2 2 +--R ((329790A b + 329790B a)c + 329790B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 219860A c - 659580B b c )d e + 384755B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 4 +--R ((139872A a b + 69936B a )c + 23312A b + 69936B a b )e +--R + +--R 2 2 3 3 +--R (- 279744A a c + (- 279744A b - 559488B a b)c - 93248B b )d e +--R + +--R 2 2 2 2 +--R ((699360A b + 699360B a)c + 699360B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 466240A c - 1398720B b c )d e + 815920B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 4 +--R ((149256A a b + 74628B a )c + 24876A b + 74628B a b )e +--R + +--R 2 2 3 3 +--R (- 298512A a c + (- 298512A b - 597024B a b)c - 99504B b )d e +--R + +--R 2 2 2 2 +--R ((746280A b + 746280B a)c + 746280B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 497520A c - 1492560B b c )d e + 870660B c d +--R * +--R m +--R + +--R 2 3 2 4 +--R ((60480A a b + 30240B a )c + 10080A b + 30240B a b )e +--R + +--R 2 2 3 3 +--R (- 120960A a c + (- 120960A b - 241920B a b)c - 40320B b )d e +--R + +--R 2 2 2 2 +--R ((302400A b + 302400B a)c + 302400B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 201600A c - 604800B b c )d e + 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 2 5 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 2 3 +--R (18A a c + (18A b + 36B a b)c + 6B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R ((- 30A b - 30B a)c - 30B b c)d e + (15A c + 45B b c )d e +--R + +--R 3 5 +--R - 21B c d +--R * +--R 7 +--R m +--R + +--R 2 2 2 5 +--R (99A a c + 99A a b + 99B a b)e +--R + +--R 2 3 2 4 +--R ((- 594A a b - 297B a )c - 99A b - 297B a b )d e +--R + +--R 2 2 3 2 3 +--R (594A a c + (594A b + 1188B a b)c + 198B b )d e +--R + +--R 2 2 3 2 +--R ((- 990A b - 990B a)c - 990B b c)d e +--R + +--R 3 2 4 3 5 +--R (495A c + 1485B b c )d e - 693B c d +--R * +--R 6 +--R m +--R + +--R 2 2 2 5 +--R (1341A a c + 1341A a b + 1341B a b)e +--R + +--R 2 3 2 4 +--R ((- 8046A a b - 4023B a )c - 1341A b - 4023B a b )d e +--R + +--R 2 2 3 2 3 +--R (8046A a c + (8046A b + 16092B a b)c + 2682B b )d e +--R + +--R 2 2 3 2 +--R ((- 13410A b - 13410B a)c - 13410B b c)d e +--R + +--R 3 2 4 3 5 +--R (6705A c + 20115B b c )d e - 9387B c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 5 +--R (9585A a c + 9585A a b + 9585B a b)e +--R + +--R 2 3 2 4 +--R ((- 57510A a b - 28755B a )c - 9585A b - 28755B a b )d e +--R + +--R 2 2 3 2 3 +--R (57510A a c + (57510A b + 115020B a b)c + 19170B b )d e +--R + +--R 2 2 3 2 +--R ((- 95850A b - 95850B a)c - 95850B b c)d e +--R + +--R 3 2 4 3 5 +--R (47925A c + 143775B b c )d e - 67095B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 5 +--R (38592A a c + 38592A a b + 38592B a b)e +--R + +--R 2 3 2 4 +--R ((- 231552A a b - 115776B a )c - 38592A b - 115776B a b )d e +--R + +--R 2 2 3 2 3 +--R (231552A a c + (231552A b + 463104B a b)c + 77184B b )d e +--R + +--R 2 2 3 2 +--R ((- 385920A b - 385920B a)c - 385920B b c)d e +--R + +--R 3 2 4 3 5 +--R (192960A c + 578880B b c )d e - 270144B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 5 +--R (86076A a c + 86076A a b + 86076B a b)e +--R + +--R 2 3 2 4 +--R ((- 516456A a b - 258228B a )c - 86076A b - 258228B a b )d e +--R + +--R 2 2 3 2 3 +--R (516456A a c + (516456A b + 1032912B a b)c + 172152B b )d e +--R + +--R 2 2 3 2 +--R ((- 860760A b - 860760B a)c - 860760B b c)d e +--R + +--R 3 2 4 3 5 +--R (430380A c + 1291140B b c )d e - 602532B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 5 +--R 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2 2 3 2 +--R ((990A b + 990B a)c + 990B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 495A c - 1485B b c )d e + 693B c d +--R * +--R 6 +--R m +--R + +--R 2 2 2 5 +--R (- 1341A a c - 1341A a b - 1341B a b)e +--R + +--R 2 3 2 4 +--R ((8046A a b + 4023B a )c + 1341A b + 4023B a b )d e +--R + +--R 2 2 3 2 3 +--R (- 8046A a c + (- 8046A b - 16092B a b)c - 2682B b )d e +--R + +--R 2 2 3 2 +--R ((13410A b + 13410B a)c + 13410B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 6705A c - 20115B b c )d e + 9387B c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 5 +--R (- 9585A a c - 9585A a b - 9585B a b)e +--R + +--R 2 3 2 4 +--R ((57510A a b + 28755B a )c + 9585A b + 28755B a b )d e +--R + +--R 2 2 3 2 3 +--R (- 57510A a c + (- 57510A b - 115020B a b)c - 19170B b )d e +--R + +--R 2 2 3 2 +--R ((95850A b + 95850B a)c + 95850B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 47925A c - 143775B b c )d e + 67095B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 5 +--R (- 38592A a c - 38592A a b - 38592B a b)e +--R + +--R 2 3 2 4 +--R ((231552A a b + 115776B a )c + 38592A b + 115776B a b )d e +--R + +--R 2 2 3 2 3 +--R (- 231552A a c + (- 231552A b - 463104B a b)c - 77184B b )d e +--R + +--R 2 2 3 2 +--R ((385920A b + 385920B a)c + 385920B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 192960A c - 578880B b c )d e + 270144B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 5 +--R (- 86076A a c - 86076A a b - 86076B a b)e +--R + +--R 2 3 2 4 +--R ((516456A a b + 258228B a )c + 86076A b + 258228B a b )d e +--R + +--R 2 2 3 +--R (- 516456A a c + (- 516456A b - 1032912B a b)c - 172152B b ) +--R * +--R 2 3 +--R d e +--R + +--R 2 2 3 2 +--R ((860760A b + 860760B a)c + 860760B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 430380A c - 1291140B b c )d e + 602532B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 5 +--R (- 96144A a c - 96144A a b - 96144B a b)e +--R + +--R 2 3 2 4 +--R ((576864A a b + 288432B a )c + 96144A b + 288432B a b )d e +--R + +--R 2 2 3 +--R (- 576864A a c + (- 576864A b - 1153728B a b)c - 192288B b ) +--R * +--R 2 3 +--R d e +--R 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c)d e +--R + +--R 3 2 5 3 6 +--R (220236A c + 660708B b c )d e - 256942B c d +--R * +--R 2 +--R m +--R + +--R 2 3 6 +--R (- 134136A a b - 44712B a )e +--R + +--R 2 2 2 5 +--R (268272A a c + 268272A a b + 268272B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 804816A a b - 402408B a )c - 134136A b - 402408B a b )d e +--R + +--R 2 2 3 3 3 +--R (536544A a c + (536544A b + 1073088B a b)c + 178848B b )d e +--R + +--R 2 2 4 2 +--R ((- 670680A b - 670680B a)c - 670680B b c)d e +--R + +--R 3 2 5 3 6 +--R (268272A c + 804816B b c )d e - 312984B c d +--R * +--R m +--R + +--R 2 3 6 +--R (- 60480A a b - 20160B a )e +--R + +--R 2 2 2 5 +--R (120960A a c + 120960A a b + 120960B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 362880A a b - 181440B a )c - 60480A b - 181440B a b )d e +--R + +--R 2 2 3 3 3 +--R (241920A a c + (241920A b + 483840B a b)c + 80640B b )d e +--R + +--R 2 2 4 2 +--R ((- 302400A b - 302400B a)c - 302400B b c)d e +--R + +--R 3 2 5 3 6 +--R (120960A c + 362880B b c )d e - 141120B c d +--R * +--R 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b + 1533B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 1533A a c + (- 1533A b - 3066B a b)c - 511B b )d e +--R + +--R 2 2 5 2 +--R ((1533A b + 1533B a)c + 1533B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 511A c - 1533B b c )d e + 511B c d +--R * +--R 5 +--R m +--R + +--R 3 7 2 3 6 +--R - 4025A a e + (12075A a b + 4025B a )d e +--R + +--R 2 2 2 2 5 +--R (- 12075A a c - 12075A a b - 12075B a b)d e +--R + +--R 2 3 2 3 4 +--R ((24150A a b + 12075B a )c + 4025A b + 12075B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12075A a c + (- 12075A b - 24150B a b)c - 4025B b )d e +--R + +--R 2 2 5 2 +--R ((12075A b + 12075B a)c + 12075B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 4025A c - 12075B b c )d e + 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 7 2 3 6 +--R - 18424A a e + (55272A a b + 18424B a )d e +--R + +--R 2 2 2 2 5 +--R (- 55272A a c - 55272A a b - 55272B a b)d e +--R + +--R 2 3 2 3 4 +--R ((110544A a b + 55272B a )c + 18424A b + 55272B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 55272A a c + (- 55272A b - 110544B a b)c - 18424B b )d e +--R + +--R 2 2 5 2 +--R ((55272A b + 55272B a)c + 55272B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 18424A c - 55272B b c )d e + 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 7 2 3 6 +--R - 48860A a e + (146580A a b + 48860B a )d e +--R + +--R 2 2 2 2 5 +--R (- 146580A a c - 146580A a b - 146580B a b)d e +--R + +--R 2 3 2 3 4 +--R ((293160A a b + 146580B a )c + 48860A b + 146580B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 146580A a c + (- 146580A b - 293160B a b)c - 48860B b )d e +--R + +--R 2 2 5 2 +--R ((146580A b + 146580B a)c + 146580B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48860A c - 146580B b c )d e + 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 7 2 3 6 +--R - 69264A a e + (207792A a b + 69264B a )d e +--R + +--R 2 2 2 2 5 +--R (- 207792A a c - 207792A a b - 207792B a b)d e +--R + +--R 2 3 2 3 4 +--R ((415584A a b + 207792B a )c + 69264A b + 207792B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 207792A a c + (- 207792A b - 415584B a b)c - 69264B b )d e +--R + +--R 2 2 5 2 +--R ((207792A b + 207792B a)c + 207792B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 69264A c - 207792B b c )d e + 69264B c d +--R * +--R m +--R + +--R 3 7 2 3 6 +--R - 40320A a e + (120960A a b + 40320B a )d e +--R + +--R 2 2 2 2 5 +--R (- 120960A a c - 120960A a b - 120960B a b)d e +--R + +--R 2 3 2 3 4 +--R ((241920A a b + 120960B a )c + 40320A b + 120960B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 120960A a c + (- 120960A b - 241920B a b)c - 40320B b )d e +--R + +--R 2 2 5 2 +--R ((120960A b + 120960B a)c + 120960B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 40320A c - 120960B b c )d e + 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 of 1751 +t0:=(A+B*x)*(d+e*x)^5*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 5 12 3 2 5 3 4 11 +--R B c e x + ((A c + 3B b c )e + 5B c d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 10 +--R (((3A b + 3B a)c + 3B b c)e + (5A c + 15B b c )d e + 10B c d e )x +--R + +--R 2 2 3 5 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 4 3 2 2 3 3 3 2 +--R ((15A b + 15B a)c + 15B b c)d e + (10A c + 30B b c )d e + 10B c d e +--R * +--R 9 +--R x +--R + +--R 2 3 2 5 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 4 +--R (15A a c + (15A b + 30B a b)c + 5B b )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R ((30A b + 30B a)c + 30B b c)d e + (10A c + 30B b c )d e + 5B c d e +--R * +--R 8 +--R x +--R + +--R 2 2 2 5 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 4 +--R ((30A a b + 15B a )c + 5A b + 15B a b )d e +--R + +--R 2 2 3 2 3 +--R (30A a c + (30A b + 60B a b)c + 10B b )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R ((30A b + 30B a)c + 30B b c)d e + (5A c + 15B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (3A a b + B a )e + (15A a c + 15A a b + 15B a b)d e +--R + +--R 2 3 2 2 3 +--R ((60A a b + 30B a )c + 10A b + 30B a b )d e +--R + +--R 2 2 3 3 2 +--R (30A a c + (30A b + 60B a b)c + 10B b )d e +--R + +--R 2 2 4 3 2 5 +--R ((15A b + 15B a)c + 15B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 5 2 3 4 2 2 2 2 3 +--R A a e + (15A a b + 5B a )d e + (30A a c + 30A a b + 30B a b)d e +--R + +--R 2 3 2 3 2 +--R ((60A a b + 30B a )c + 10A b + 30B a b )d e +--R + +--R 2 2 3 4 +--R (15A a c + (15A b + 30B a b)c + 5B b )d e +--R + +--R 2 2 5 +--R ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 2 3 2 2 2 3 2 +--R 5A a d e + (30A a b + 10B a )d e + (30A a c + 30A a b + 30B a b)d e +--R + +--R 2 3 2 4 +--R ((30A a b + 15B a )c + 5A b + 15B a b )d e +--R + +--R 2 2 3 5 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 2 4 +--R 10A a d e + (30A a b + 10B a )d e + (15A a c + 15A a b + 15B a b)d e +--R + +--R 2 3 2 5 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 4 2 2 2 5 2 +--R (10A a d e + (15A a b + 5B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 4 2 3 5 3 5 +--R (5A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 319 + +--S 320 of 1751 +r0:=-1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^6/e^8-_ + 1/7*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-_ + e*(4*b*d-a*e)))*(d+e*x)^7/e^8-3/8*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*(d+e*x)^8/e^8-1/9*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*_ + (d+e*x)^9/e^8-1/10*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + (d+e*x)^10/e^8-3/11*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-_ + c*e*(6*b*d-a*e)))*(d+e*x)^11/e^8-1/12*c^2*(7*B*c*d-3*b*B*e-A*c*e)*_ + (d+e*x)^12/e^8+1/13*B*c^3*(d+e*x)^13/e^8 +--R +--R +--R (2) +--R 1 3 13 13 1 3 1 2 13 5 3 12 12 +--R -- B c e x + ((-- A c + - B b c )e + -- B c d e )x +--R 13 12 4 12 +--R + +--R 3 3 2 3 2 13 5 3 15 2 12 +--R ((-- A b + -- B a)c + -- B b c)e + (-- A c + -- B b c )d e +--R 11 11 11 11 11 +--R + +--R 10 3 2 11 +--R -- B c d e +--R 11 +--R * +--R 11 +--R x +--R + +--R 3 2 3 2 3 1 3 13 +--R (-- A a c + (-- A b + - B a b)c + -- B b )e +--R 10 10 5 10 +--R + +--R 3 3 2 3 2 12 3 2 2 11 3 3 10 +--R ((- A b + - B a)c + - B b c)d e + (A c + 3B b c )d e + B c d e +--R 2 2 2 +--R * +--R 10 +--R x +--R + +--R 2 1 2 1 3 1 2 13 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 3 3 9 3 +--R + +--R 5 2 5 2 10 5 3 12 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 3 3 3 9 +--R + +--R 10 10 2 10 2 2 11 10 3 10 2 3 10 +--R ((-- A b + -- B a)c + -- B b c)d e + (-- A c + -- B b c )d e +--R 3 3 3 9 3 +--R + +--R 5 3 4 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 3 2 3 2 13 +--R (- A a c + - A a b + - B a b)e +--R 8 8 8 +--R + +--R 15 15 2 5 3 15 2 12 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 4 8 8 8 +--R + +--R 15 2 15 2 15 5 3 2 11 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 4 4 2 4 +--R + +--R 15 15 2 15 2 3 10 5 3 15 2 4 9 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + -- B b c )d e +--R 4 4 4 8 8 +--R + +--R 1 3 5 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 3 2 1 3 13 15 2 15 2 15 2 12 +--R (- A a b + - B a )e + (-- A a c + -- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 60 30 2 10 3 30 2 2 11 +--R ((-- A a b + -- B a )c + -- A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 30 2 30 2 60 10 3 3 10 +--R (-- A a c + (-- A b + -- B a b)c + -- B b )d e +--R 7 7 7 7 +--R + +--R 15 15 2 15 2 4 9 1 3 3 2 5 8 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 13 5 2 5 3 12 +--R - A a e + (- A a b + - B a )d e +--R 6 2 6 +--R + +--R 2 2 2 2 11 +--R (5A a c + 5A a b + 5B a b)d e +--R + +--R 2 5 3 2 3 10 +--R ((10A a b + 5B a )c + - A b + 5B a b )d e +--R 3 +--R + +--R 5 2 5 2 5 3 4 9 +--R (- A a c + (- A b + 5B a b)c + - B b )d e +--R 2 2 6 +--R + +--R 1 1 2 1 2 5 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 12 2 3 2 11 2 2 2 3 10 +--R A a d e + (6A a b + 2B a )d e + (6A a c + 6A a b + 6B a b)d e +--R + +--R 2 3 2 4 9 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 3 2 3 2 6 1 3 5 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 5 3 2 11 15 2 5 3 3 10 +--R - A a d e + (-- A a b + - B a )d e +--R 2 2 2 +--R + +--R 15 2 15 2 15 2 4 9 +--R (-- A a c + -- A a b + -- B a b)d e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 5 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 10 3 3 10 2 5 3 4 9 2 2 2 5 8 3 +--R (-- A a d e + (5A a b + - B a )d e + (A a c + A a b + B a b)d e )x +--R 3 3 +--R + +--R 5 3 4 9 3 2 1 3 5 8 2 3 5 8 1 3 6 7 +--R (- A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 2 6 +--R + +--R 1 2 1 3 7 6 1 2 1 2 1 2 8 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 14 42 56 56 56 +--R + +--R 1 1 2 1 3 1 2 9 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 84 168 504 168 +--R + +--R 1 2 1 2 1 1 3 10 3 +--R (--- A a c + (--- A b + --- B a b)c + ---- B b )d e +--R 420 420 210 1260 +--R + +--R 1 1 2 1 2 11 2 +--R ((- --- A b - --- B a)c - --- B b c)d e +--R 924 924 924 +--R + +--R 1 3 1 2 12 1 3 13 +--R (---- A c + ---- B b c )d e - ----- B c d +--R 5544 1848 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 320 + +--S 321 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 5 13 1 3 1 2 5 5 3 4 12 +--R -- B c e x + ((-- A c + - B b c )e + -- B c d e )x +--R 13 12 4 12 +--R + +--R 3 3 2 3 2 5 5 3 15 2 4 +--R ((-- A b + -- B a)c + -- B b c)e + (-- A c + -- B b c )d e +--R 11 11 11 11 11 +--R + +--R 10 3 2 3 +--R -- B c d e +--R 11 +--R * +--R 11 +--R x +--R + +--R 3 2 3 2 3 1 3 5 +--R (-- A a c + (-- A b + - B a b)c + -- B b )e +--R 10 10 5 10 +--R + +--R 3 3 2 3 2 4 3 2 2 3 3 3 2 +--R ((- A b + - B a)c + - B b c)d e + (A c + 3B b c )d e + B c d e +--R 2 2 2 +--R * +--R 10 +--R x +--R + +--R 2 1 2 1 3 1 2 5 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 3 3 9 3 +--R + +--R 5 2 5 2 10 5 3 4 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 3 3 3 9 +--R + +--R 10 10 2 10 2 2 3 10 3 10 2 3 2 +--R ((-- A b + -- B a)c + -- B b c)d e + (-- A c + -- B b c )d e +--R 3 3 3 9 3 +--R + +--R 5 3 4 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 3 2 3 2 5 +--R (- A a c + - A a b + - B a b)e +--R 8 8 8 +--R + +--R 15 15 2 5 3 15 2 4 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 4 8 8 8 +--R + +--R 15 2 15 2 15 5 3 2 3 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 4 4 2 4 +--R + +--R 15 15 2 15 2 3 2 5 3 15 2 4 1 3 5 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + -- B b c )d e + - B c d +--R 4 4 4 8 8 8 +--R * +--R 8 +--R x +--R + +--R 3 2 1 3 5 15 2 15 2 15 2 4 +--R (- A a b + - B a )e + (-- A a c + -- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 60 30 2 10 3 30 2 2 3 +--R ((-- A a b + -- B a )c + -- A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 30 2 30 2 60 10 3 3 2 +--R (-- A a c + (-- A b + -- B a b)c + -- B b )d e +--R 7 7 7 7 +--R + +--R 15 15 2 15 2 4 1 3 3 2 5 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 5 5 2 5 3 4 2 2 2 2 3 +--R - A a e + (- A a b + - B a )d e + (5A a c + 5A a b + 5B a b)d e +--R 6 2 6 +--R + +--R 2 5 3 2 3 2 +--R ((10A a b + 5B a )c + - A b + 5B a b )d e +--R 3 +--R + +--R 5 2 5 2 5 3 4 +--R (- A a c + (- A b + 5B a b)c + - B b )d e +--R 2 2 6 +--R + +--R 1 1 2 1 2 5 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 4 2 3 2 3 2 2 2 3 2 +--R A a d e + (6A a b + 2B a )d e + (6A a c + 6A a b + 6B a b)d e +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 3 2 3 2 6 1 3 5 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 5 3 2 3 15 2 5 3 3 2 +--R - A a d e + (-- A a b + - B a )d e +--R 2 2 2 +--R + +--R 15 2 15 2 15 2 4 +--R (-- A a c + -- A a b + -- B a b)d e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 5 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 10 3 3 2 2 5 3 4 2 2 2 5 3 +--R (-- A a d e + (5A a b + - B a )d e + (A a c + A a b + B a b)d )x +--R 3 3 +--R + +--R 5 3 4 3 2 1 3 5 2 3 5 +--R (- A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 321 + +--S 322 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 6 7 1 2 1 3 7 6 +--R - - A a d e + (-- A a b + -- B a )d e +--R 6 14 42 +--R + +--R 1 2 1 2 1 2 8 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 56 56 56 +--R + +--R 1 1 2 1 3 1 2 9 4 +--R ((-- A a b + --- B a )c + --- A b + --- B a b )d e +--R 84 168 504 168 +--R + +--R 1 2 1 2 1 1 3 10 3 +--R (- --- A a c + (- --- A b - --- B a b)c - ---- B b )d e +--R 420 420 210 1260 +--R + +--R 1 1 2 1 2 11 2 +--R ((--- A b + --- B a)c + --- B b c)d e +--R 924 924 924 +--R + +--R 1 3 1 2 12 1 3 13 +--R (- ---- A c - ---- B b c )d e + ----- B c d +--R 5544 1848 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 322 + +--S 323 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 323 + +)clear all + +--S 324 of 1751 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 2 4 3 3 10 +--R B c e x + ((A c + 3B b c )e + 4B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 9 +--R (((3A b + 3B a)c + 3B b c)e + (4A c + 12B b c )d e + 6B c d e )x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((12A b + 12B a)c + 12B b c)d e + (6A c + 18B b c )d e + 4B c d e +--R * +--R 8 +--R x +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 3 +--R (12A a c + (12A b + 24B a b)c + 4B b )d e +--R + +--R 2 2 2 2 3 2 3 3 4 +--R ((18A b + 18B a)c + 18B b c)d e + (4A c + 12B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 2 2 4 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 3 +--R ((24A a b + 12B a )c + 4A b + 12B a b )d e +--R + +--R 2 2 3 2 2 +--R (18A a c + (18A b + 36B a b)c + 6B b )d e +--R + +--R 2 2 3 3 2 4 +--R ((12A b + 12B a)c + 12B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 3 4 2 2 2 3 +--R (3A a b + B a )e + (12A a c + 12A a b + 12B a b)d e +--R + +--R 2 3 2 2 2 +--R ((36A a b + 18B a )c + 6A b + 18B a b )d e +--R + +--R 2 2 3 3 +--R (12A a c + (12A b + 24B a b)c + 4B b )d e +--R + +--R 2 2 4 +--R ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 +--R A a e + (12A a b + 4B a )d e + (18A a c + 18A a b + 18B a b)d e +--R + +--R 2 3 2 3 +--R ((24A a b + 12B a )c + 4A b + 12B a b )d e +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R 4A a d e + (18A a b + 6B a )d e + (12A a c + 12A a b + 12B a b)d e +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 3 3 2 2 2 4 2 +--R (6A a d e + (12A a b + 4B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 3 2 3 4 3 4 +--R (4A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 324 + +--S 325 of 1751 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^5/e^8-1/6*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^6/e^8-_ + 3/7*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^7/e^8-_ + 1/8*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^8/e^8-1/9*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*_ + d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^9/e^8-3/10*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^10/e^8-1/11*c^2*(7*B*c*d-_ + 3*b*B*e-A*c*e)*(d+e*x)^11/e^8+1/12*B*c^3*(d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 3 12 12 1 3 3 2 12 4 3 11 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 3 2 3 2 12 2 3 6 2 11 +--R ((-- A b + -- B a)c + -- B b c)e + (- A c + - B b c )d e +--R 10 10 10 5 5 +--R + +--R 3 3 2 10 +--R - B c d e +--R 5 +--R * +--R 10 +--R x +--R + +--R 1 2 1 2 2 1 3 12 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 3 3 3 9 +--R + +--R 4 4 2 4 2 11 2 3 2 2 10 +--R ((- A b + - B a)c + - B b c)d e + (- A c + 2B b c )d e +--R 3 3 3 3 +--R + +--R 4 3 3 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 3 2 1 3 3 2 12 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 4 8 8 8 +--R + +--R 3 2 3 2 1 3 11 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 9 9 2 9 2 2 10 1 3 3 2 3 9 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 4 4 4 2 2 +--R + +--R 1 3 4 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 3 2 3 2 3 2 12 +--R (- A a c + - A a b + - B a b)e +--R 7 7 7 +--R + +--R 24 12 2 4 3 12 2 11 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 18 2 18 2 36 6 3 2 10 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 12 12 2 12 2 3 9 1 3 3 2 4 8 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 12 2 2 2 11 +--R (- A a b + - B a )e + (2A a c + 2A a b + 2B a b)d e +--R 2 6 +--R + +--R 2 3 2 2 10 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 2 2 2 3 3 9 +--R (2A a c + (2A b + 4B a b)c + - B b )d e +--R 3 +--R + +--R 1 1 2 1 2 4 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 1 3 12 12 2 4 3 11 +--R - A a e + (-- A a b + - B a )d e +--R 5 5 5 +--R + +--R 18 2 18 2 18 2 2 10 +--R (-- A a c + -- A a b + -- B a b)d e +--R 5 5 5 +--R + +--R 24 12 2 4 3 12 2 3 9 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 4 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 11 9 2 3 3 2 10 2 2 2 3 9 +--R A a d e + (- A a b + - B a )d e + (3A a c + 3A a b + 3B a b)d e +--R 2 2 +--R + +--R 3 3 2 1 3 3 2 4 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 2 10 2 4 3 3 9 2 2 2 4 8 3 +--R (2A a d e + (4A a b + - B a )d e + (A a c + A a b + B a b)d e )x +--R 3 +--R + +--R 3 3 9 3 2 1 3 4 8 2 3 4 8 1 3 5 7 +--R (2A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 5 +--R + +--R 1 2 1 3 6 6 1 2 1 2 1 2 7 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 10 30 35 35 35 +--R + +--R 3 3 2 1 3 3 2 8 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 280 280 +--R + +--R 1 2 1 2 1 1 3 9 3 +--R (--- A a c + (--- A b + --- B a b)c + --- B b )d e +--R 210 210 105 630 +--R + +--R 1 1 2 1 2 10 2 1 3 1 2 11 +--R ((- --- A b - --- B a)c - --- B b c)d e + (---- A c + --- B b c )d e +--R 420 420 420 2310 770 +--R + +--R 1 3 12 +--R - ---- B c d +--R 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 325 + +--S 326 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 12 1 3 3 2 4 4 3 3 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 3 2 3 2 4 2 3 6 2 3 +--R ((-- A b + -- B a)c + -- B b c)e + (- A c + - B b c )d e +--R 10 10 10 5 5 +--R + +--R 3 3 2 2 +--R - B c d e +--R 5 +--R * +--R 10 +--R x +--R + +--R 1 2 1 2 2 1 3 4 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 3 3 3 9 +--R + +--R 4 4 2 4 2 3 2 3 2 2 2 4 3 3 +--R ((- A b + - B a)c + - B b c)d e + (- A c + 2B b c )d e + - B c d e +--R 3 3 3 3 9 +--R * +--R 9 +--R x +--R + +--R 3 3 2 1 3 3 2 4 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 4 8 8 8 +--R + +--R 3 2 3 2 1 3 3 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 9 9 2 9 2 2 2 1 3 3 2 3 1 3 4 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e + - B c d +--R 4 4 4 2 2 8 +--R * +--R 8 +--R x +--R + +--R 3 2 3 2 3 2 4 +--R (- A a c + - A a b + - B a b)e +--R 7 7 7 +--R + +--R 24 12 2 4 3 12 2 3 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 18 2 18 2 36 6 3 2 2 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 12 12 2 12 2 3 1 3 3 2 4 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 4 2 2 2 3 +--R (- A a b + - B a )e + (2A a c + 2A a b + 2B a b)d e +--R 2 6 +--R + +--R 2 3 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 2 2 2 3 3 +--R (2A a c + (2A b + 4B a b)c + - B b )d e +--R 3 +--R + +--R 1 1 2 1 2 4 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 1 3 4 12 2 4 3 3 +--R - A a e + (-- A a b + - B a )d e +--R 5 5 5 +--R + +--R 18 2 18 2 18 2 2 2 +--R (-- A a c + -- A a b + -- B a b)d e +--R 5 5 5 +--R + +--R 24 12 2 4 3 12 2 3 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 4 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 3 9 2 3 3 2 2 2 2 2 3 +--R A a d e + (- A a b + - B a )d e + (3A a c + 3A a b + 3B a b)d e +--R 2 2 +--R + +--R 3 3 2 1 3 3 2 4 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 4 3 3 2 2 2 4 3 +--R (2A a d e + (4A a b + - B a )d e + (A a c + A a b + B a b)d )x +--R 3 +--R + +--R 3 3 3 2 1 3 4 2 3 4 +--R (2A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 326 + +--S 327 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 5 7 1 2 1 3 6 6 +--R - - A a d e + (-- A a b + -- B a )d e +--R 5 10 30 +--R + +--R 1 2 1 2 1 2 7 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 35 35 35 +--R + +--R 3 3 2 1 3 3 2 8 4 +--R ((--- A a b + --- B a )c + --- A b + --- B a b )d e +--R 140 280 280 280 +--R + +--R 1 2 1 2 1 1 3 9 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 210 210 105 630 +--R + +--R 1 1 2 1 2 10 2 1 3 1 2 11 +--R ((--- A b + --- B a)c + --- B b c)d e + (- ---- A c - --- B b c )d e +--R 420 420 420 2310 770 +--R + +--R 1 3 12 +--R ---- B c d +--R 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 327 + +--S 328 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 328 + +)clear all + +--S 329 of 1751 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 2 3 3 2 9 +--R B c e x + ((A c + 3B b c )e + 3B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 8 +--R (((3A b + 3B a)c + 3B b c)e + (3A c + 9B b c )d e + 3B c d e)x +--R + +--R 2 2 3 3 2 2 2 +--R (3A a c + (3A b + 6B a b)c + B b )e + ((9A b + 9B a)c + 9B b c)d e +--R + +--R 3 2 2 3 3 +--R (3A c + 9B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 3 2 3 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 2 +--R (9A a c + (9A b + 18B a b)c + 3B b )d e +--R + +--R 2 2 2 3 2 3 +--R ((9A b + 9B a)c + 9B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 2 2 3 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 2 +--R ((18A a b + 9B a )c + 3A b + 9B a b )d e +--R + +--R 2 2 3 2 2 2 3 +--R (9A a c + (9A b + 18B a b)c + 3B b )d e + ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (3A a b + B a )e + (9A a c + 9A a b + 9B a b)d e +--R + +--R 2 3 2 2 +--R ((18A a b + 9B a )c + 3A b + 9B a b )d e +--R + +--R 2 2 3 3 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 +--R A a e + (9A a b + 3B a )d e + (9A a c + 9A a b + 9B a b)d e +--R + +--R 2 3 2 3 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 2 3 2 +--R (3A a d e + (9A a b + 3B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 2 2 3 3 3 3 +--R (3A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 329 + +--S 330 of 1751 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^4/e^8-1/5*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^5/e^8-_ + 1/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^6/e^8-_ + 1/7*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^7/e^8-1/8*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^8/e^8-1/3*c*(A*c*e*(2*c*d-_ + b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^9/e^8-1/10*c^2*_ + (7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^10/e^8+1/11*B*c^3*(d+e*x)^11/e^8 +--R +--R +--R (2) +--R 1 3 11 11 1 3 3 2 11 3 3 10 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 1 2 1 2 11 1 3 2 10 +--R ((- A b + - B a)c + - B b c)e + (- A c + B b c )d e +--R 3 3 3 3 +--R + +--R 1 3 2 9 +--R - B c d e +--R 3 +--R * +--R 9 +--R x +--R + +--R 3 2 3 2 3 1 3 11 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 8 8 4 8 +--R + +--R 9 9 2 9 2 10 3 3 9 2 2 9 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 8 8 8 8 8 +--R + +--R 1 3 3 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 6 3 2 1 3 3 2 11 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 7 7 7 7 +--R + +--R 9 2 9 2 18 3 3 10 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 9 9 2 9 2 2 9 1 3 3 2 3 8 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 2 1 2 11 +--R (- A a c + - A a b + - B a b)e +--R 2 2 2 +--R + +--R 3 2 1 3 3 2 10 +--R ((3A a b + - B a )c + - A b + - B a b )d e +--R 2 2 2 +--R + +--R 3 2 3 2 1 3 2 9 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 1 1 2 1 2 3 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 1 3 11 9 2 9 2 9 2 10 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 18 9 2 3 3 9 2 2 9 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 3 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 11 9 2 3 3 10 +--R - A a e + (- A a b + - B a )d e +--R 4 4 4 +--R + +--R 9 2 9 2 9 2 2 9 +--R (- A a c + - A a b + - B a b)d e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 3 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 10 2 3 2 9 2 2 2 3 8 3 +--R (A a d e + (3A a b + B a )d e + (A a c + A a b + B a b)d e )x +--R + +--R 3 3 2 9 3 2 1 3 3 8 2 3 3 8 1 3 4 7 +--R (- A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 2 4 +--R + +--R 3 2 1 3 5 6 1 2 1 2 1 2 6 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 20 20 20 20 20 +--R + +--R 3 3 2 1 3 3 2 7 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 70 140 140 140 +--R + +--R 3 2 3 2 3 1 3 8 3 +--R (--- A a c + (--- A b + --- B a b)c + --- B b )d e +--R 280 280 140 280 +--R + +--R 1 1 2 1 2 9 2 1 3 1 2 10 +--R ((- --- A b - --- B a)c - --- B b c)d e + (--- A c + --- B b c )d e +--R 168 168 168 840 280 +--R + +--R 1 3 11 +--R - ---- B c d +--R 1320 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 330 + +--S 331 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 3 11 1 3 3 2 3 3 3 2 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 1 2 1 2 3 1 3 2 2 1 3 2 9 +--R (((- A b + - B a)c + - B b c)e + (- A c + B b c )d e + - B c d e)x +--R 3 3 3 3 3 +--R + +--R 3 2 3 2 3 1 3 3 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 8 8 4 8 +--R + +--R 9 9 2 9 2 2 3 3 9 2 2 1 3 3 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e + - B c d +--R 8 8 8 8 8 8 +--R * +--R 8 +--R x +--R + +--R 6 3 2 1 3 3 2 3 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 7 7 7 7 +--R + +--R 9 2 9 2 18 3 3 2 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 9 9 2 9 2 2 1 3 3 2 3 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 2 1 2 3 +--R (- A a c + - A a b + - B a b)e +--R 2 2 2 +--R + +--R 3 2 1 3 3 2 2 +--R ((3A a b + - B a )c + - A b + - B a b )d e +--R 2 2 2 +--R + +--R 3 2 3 2 1 3 2 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 1 1 2 1 2 3 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 1 3 3 9 2 9 2 9 2 2 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 18 9 2 3 3 9 2 2 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 3 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 3 9 2 3 3 2 9 2 9 2 9 2 2 +--R - A a e + (- A a b + - B a )d e + (- A a c + - A a b + - B a b)d e +--R 4 4 4 4 4 4 +--R + +--R 3 3 2 1 3 3 2 3 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 2 2 2 2 3 3 +--R (A a d e + (3A a b + B a )d e + (A a c + A a b + B a b)d )x +--R + +--R 3 3 2 3 2 1 3 3 2 3 3 +--R (- A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 331 + +--S 332 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 1 3 4 7 3 2 1 3 5 6 +--R - - A a d e + (-- A a b + -- B a )d e +--R 4 20 20 +--R + +--R 1 2 1 2 1 2 6 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 20 20 20 +--R + +--R 3 3 2 1 3 3 2 7 4 +--R ((-- A a b + --- B a )c + --- A b + --- B a b )d e +--R 70 140 140 140 +--R + +--R 3 2 3 2 3 1 3 8 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 280 280 140 280 +--R + +--R 1 1 2 1 2 9 2 1 3 1 2 10 +--R ((--- A b + --- B a)c + --- B b c)d e + (- --- A c - --- B b c )d e +--R 168 168 168 840 280 +--R + +--R 1 3 11 +--R ---- B c d +--R 1320 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 332 + +--S 333 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 333 + +)clear all + +--S 334 of 1751 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 2 3 8 +--R B c e x + ((A c + 3B b c )e + 2B c d e)x +--R + +--R 2 2 2 3 2 3 2 7 +--R (((3A b + 3B a)c + 3B b c)e + (2A c + 6B b c )d e + B c d )x +--R + +--R 2 2 3 2 2 2 +--R (3A a c + (3A b + 6B a b)c + B b )e + ((6A b + 6B a)c + 6B b c)d e +--R + +--R 3 2 2 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 3 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 2 2 2 +--R (6A a c + (6A b + 12B a b)c + 2B b )d e + ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 2 2 2 2 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 +--R ((12A a b + 6B a )c + 2A b + 6B a b )d e +--R + +--R 2 2 3 2 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 +--R (3A a b + B a )e + (6A a c + 6A a b + 6B a b)d e +--R + +--R 2 3 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (A a e + (6A a b + 2B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 2 3 2 3 2 +--R (2A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 334 + +--S 335 of 1751 +r0:=a^3*A*d^2*x+1/2*a^2*d*(3*A*b*d+a*B*d+2*a*A*e)*x^2+1/3*a*(a*B*d*_ + (3*b*d+2*a*e)+A*(3*b^2*d^2+6*a*b*d*e+a*(3*c*d^2+a*e^2)))*x^3+1/4*(A*_ + (b^3*d^2+6*a*b^2*d*e+6*a^2*c*d*e+3*a*b*(2*c*d^2+a*e^2))+a*B*_ + (3*b^2*d^2+6*a*b*d*e+a*(3*c*d^2+a*e^2)))*x^4+1/5*(b^3*d*(B*d+2*A*e)+_ + 3*b^2*(A*c*d^2+2*a*B*d*e+a*A*e^2)+3*a*c*(A*c*d^2+2*a*B*d*e+a*A*e^2)+_ + 3*a*b*(2*B*c*d^2+4*A*c*d*e+a*B*e^2))*x^5+1/6*(b^3*e*(2*B*d+A*e)+_ + 3*b*c*(A*c*d^2+4*a*B*d*e+2*a*A*e^2)+3*b^2*(B*c*d^2+2*A*c*d*e+a*B*e^2)+_ + 3*a*c*(B*c*d^2+2*A*c*d*e+a*B*e^2))*x^6+1/7*(b^3*B*e^2+3*b^2*c*e*_ + (2*B*d+A*e)+c^2*(A*c*d^2+6*a*B*d*e+3*a*A*e^2)+3*b*c*(B*c*d^2+2*A*c*d*e+_ + 2*a*B*e^2))*x^7+1/8*c*(A*c*e*(2*c*d+3*b*e)+B*(c^2*d^2+3*b^2*e^2+_ + 3*c*e*(2*b*d+a*e)))*x^8+1/9*c^2*e*(2*B*c*d+3*b*B*e+A*c*e)*x^9+_ + 1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 8 4 4 8 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 7 7 7 7 +--R + +--R 6 6 2 6 2 1 3 3 2 2 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 1 2 2 +--R ((A a b + - B a )c + - A b + - B a b )e +--R 2 6 2 +--R + +--R 2 2 1 3 1 1 2 1 2 2 +--R (A a c + (A b + 2B a b)c + - B b )d e + ((- A b + - B a)c + - B b c)d +--R 3 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 3 2 3 2 2 +--R (- A a c + - A a b + - B a b)e +--R 5 5 5 +--R + +--R 12 6 2 2 3 6 2 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 1 3 2 3 2 3 2 3 2 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 4 4 2 2 2 +--R + +--R 3 3 2 1 3 3 2 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 1 3 2 2 2 3 2 2 2 2 3 +--R (- A a e + (2A a b + - B a )d e + (A a c + A a b + B a b)d )x +--R 3 3 +--R + +--R 3 3 2 1 3 2 2 3 2 +--R (A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 335 + +--S 336 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 8 4 4 8 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 7 7 7 7 +--R + +--R 6 6 2 6 2 1 3 3 2 2 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 1 2 2 +--R ((A a b + - B a )c + - A b + - B a b )e +--R 2 6 2 +--R + +--R 2 2 1 3 1 1 2 1 2 2 +--R (A a c + (A b + 2B a b)c + - B b )d e + ((- A b + - B a)c + - B b c)d +--R 3 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 3 2 3 2 2 +--R (- A a c + - A a b + - B a b)e +--R 5 5 5 +--R + +--R 12 6 2 2 3 6 2 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 1 3 2 3 2 3 2 3 2 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 4 4 2 2 2 +--R + +--R 3 3 2 1 3 3 2 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 1 3 2 2 2 3 2 2 2 2 3 +--R (- A a e + (2A a b + - B a )d e + (A a c + A a b + B a b)d )x +--R 3 3 +--R + +--R 3 3 2 1 3 2 2 3 2 +--R (A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 336 + +--S 337 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 337 + +--S 338 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 338 + +)clear all + +--S 339 of 1751 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 2 3 7 +--R B c e x + ((A c + 3B b c )e + B c d)x +--R + +--R 2 2 3 2 6 +--R (((3A b + 3B a)c + 3B b c)e + (A c + 3B b c )d)x +--R + +--R 2 2 3 2 2 5 +--R ((3A a c + (3A b + 6B a b)c + B b )e + ((3A b + 3B a)c + 3B b c)d)x +--R + +--R 2 3 2 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 2 2 2 2 3 2 3 +--R ((3A a c + 3A a b + 3B a b)e + ((6A a b + 3B a )c + A b + 3B a b )d)x +--R + +--R 2 3 2 2 2 2 +--R ((3A a b + B a )e + (3A a c + 3A a b + 3B a b)d)x +--R + +--R 3 2 3 3 +--R (A a e + (3A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 339 + +--S 340 of 1751 +r0:=a^3*A*d*x+1/2*a^2*(3*A*b*d+a*B*d+a*A*e)*x^2+1/3*a*(a*B*(3*b*d+a*e)+_ + 3*A*(b^2*d+a*c*d+a*b*e))*x^3+1/4*(3*a*B*(b^2*d+a*c*d+a*b*e)+A*(b^3*d+_ + 6*a*b*c*d+3*a*b^2*e+3*a^2*c*e))*x^4+1/5*(b^3*(B*d+A*e)+6*a*b*c*(B*d+_ + A*e)+3*b^2*(A*c*d+a*B*e)+3*a*c*(A*c*d+a*B*e))*x^5+1/6*(b^3*B*e+_ + 3*b^2*c*(B*d+A*e)+3*a*c^2*(B*d+A*e)+3*b*c*(A*c*d+2*a*B*e))*x^6+_ + 1/7*c*(3*b^2*B*e+3*b*c*(B*d+A*e)+c*(A*c*d+3*a*B*e))*x^7+_ + 1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 3 2 3 2 1 3 3 2 7 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 7 +--R + +--R 1 2 1 2 1 3 +--R (- A a c + (- A b + B a b)c + - B b )e +--R 2 2 6 +--R + +--R 1 1 2 1 2 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 6 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 3 2 +--R (- A a c + - A a b + - B a b)e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 2 1 3 2 2 2 3 +--R ((A a b + - B a )e + (A a c + A a b + B a b)d)x +--R 3 +--R + +--R 1 3 3 2 1 3 2 3 +--R (- A a e + (- A a b + - B a )d)x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 340 + +--S 341 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 3 2 3 2 1 3 3 2 7 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 7 +--R + +--R 1 2 1 2 1 3 +--R (- A a c + (- A b + B a b)c + - B b )e +--R 2 2 6 +--R + +--R 1 1 2 1 2 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 6 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 3 2 +--R (- A a c + - A a b + - B a b)e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 2 1 3 2 2 2 3 +--R ((A a b + - B a )e + (A a c + A a b + B a b)d)x +--R 3 +--R + +--R 1 3 3 2 1 3 2 3 +--R (- A a e + (- A a b + - B a )d)x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 341 + +--S 342 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 342 + +--S 343 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 343 + +)clear all + +--S 344 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 344 + +--S 345 of 1751 +r0:=a^3*A*x+1/2*a^2*(3*A*b+a*B)*x^2+a*(a*b*B+A*(b^2+a*c))*x^3+_ + 1/4*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^4+1/5*(b^3*B+3*A*b^2*c+_ + 6*a*b*B*c+3*a*A*c^2)*x^5+1/2*c*(b^2*B+A*b*c+a*B*c)*x^6+_ + 1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8 +--R +--R +--R (2) +--R 1 3 8 1 3 3 2 7 1 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + ((- A b + - B a)c + - B b c)x +--R 8 7 7 2 2 2 +--R + +--R 3 2 3 2 6 1 3 5 +--R (- A a c + (- A b + - B a b)c + - B b )x +--R 5 5 5 5 +--R + +--R 3 3 2 1 3 3 2 4 2 2 2 3 +--R ((- A a b + - B a )c + - A b + - B a b )x + (A a c + A a b + B a b)x +--R 2 4 4 4 +--R + +--R 3 2 1 3 2 3 +--R (- A a b + - B a )x + A a x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 345 + +--S 346 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 8 1 3 3 2 7 1 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + ((- A b + - B a)c + - B b c)x +--R 8 7 7 2 2 2 +--R + +--R 3 2 3 2 6 1 3 5 +--R (- A a c + (- A b + - B a b)c + - B b )x +--R 5 5 5 5 +--R + +--R 3 3 2 1 3 3 2 4 2 2 2 3 +--R ((- A a b + - B a )c + - A b + - B a b )x + (A a c + A a b + B a b)x +--R 2 4 4 4 +--R + +--R 3 2 1 3 2 3 +--R (- A a b + - B a )x + A a x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 346 + +--S 347 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 347 + +--S 348 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 348 + +)clear all + +--S 349 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 349 + +--S 350 of 1751 +r0:=-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*_ + (4*b*d-a*e)))*x/e^7-3/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*_ + (8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))*(d+e*x)^2/e^8-1/3*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^3/e^8-_ + 1/4*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^4/e^8-_ + 3/5*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*_ + (d+e*x)^5/e^8-1/6*c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^6/e^8+1/7*B*c^3*_ + (d+e*x)^7/e^8-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 3 6 +--R 420A a e + (- 1260A a b - 420B a )d e +--R + +--R 2 2 2 2 5 +--R (1260A a c + 1260A a b + 1260B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 2520A a b - 1260B a )c - 420A b - 1260B a b )d e +--R + +--R 2 2 3 4 3 +--R (1260A a c + (1260A b + 2520B a b)c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 1260A b - 1260B a)c - 1260B b c)d e + (420A c + 1260B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((252A b + 252B a)c + 252B b c)e + (- 84A c - 252B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (315A a c + (315A b + 630B a b)c + 105B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 315A b - 315B a)c - 315B b c)d e + (105A c + 315B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((840A a b + 420B a )c + 140A b + 420B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((420A b + 420B a)c + 420B b c)d e + (- 140A c - 420B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (630A a c + 630A a b + 630B a b)e +--R + +--R 2 3 2 6 +--R ((- 1260A a b - 630B a )c - 210A b - 630B a b )d e +--R + +--R 2 2 3 2 5 +--R (630A a c + (630A b + 1260B a b)c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 630A b - 630B a)c - 630B b c)d e + (210A c + 630B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (1260A a b + 420B a )e + (- 1260A a c - 1260A a b - 1260B a b)d e +--R + +--R 2 3 2 2 5 +--R ((2520A a b + 1260B a )c + 420A b + 1260B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 1260A a c + (- 1260A b - 2520B a b)c - 420B b )d e +--R + +--R 2 2 4 3 +--R ((1260A b + 1260B a)c + 1260B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 420A c - 1260B b c )d e + 420B c d e +--R * +--R x +--R + +--R 2 2 2 2 5 +--R (630A a c + 630A a b + 630B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 2940A a b - 1470B a )c - 490A b - 1470B a b )d e +--R + +--R 2 2 3 4 3 +--R (2415A a c + (2415A b + 4830B a b)c + 805B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 3423A b - 3423B a)c - 3423B b c)d e + (1491A c + 4473B b c )d e +--R + +--R 3 7 +--R - 1851B c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 2 3 6 +--R 420A a e + (- 1260A a b - 420B a )d e +--R + +--R 2 2 2 2 5 +--R (1260A a c + 1260A a b + 1260B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 2520A a b - 1260B a )c - 420A b - 1260B a b )d e +--R + +--R 2 2 3 4 3 +--R (1260A a c + (1260A b + 2520B a b)c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 1260A b - 1260B a)c - 1260B b c)d e + (420A c + 1260B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((252A b + 252B a)c + 252B b c)e + (- 84A c - 252B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (315A a c + (315A b + 630B a b)c + 105B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 315A b - 315B a)c - 315B b c)d e + (105A c + 315B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((840A a b + 420B a )c + 140A b + 420B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((420A b + 420B a)c + 420B b c)d e + (- 140A c - 420B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (630A a c + 630A a b + 630B a b)e +--R + +--R 2 3 2 6 +--R ((- 1260A a b - 630B a )c - 210A b - 630B a b )d e +--R + +--R 2 2 3 2 5 +--R (630A a c + (630A b + 1260B a b)c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 630A b - 630B a)c - 630B b c)d e + (210A c + 630B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (1260A a b + 420B a )e + (- 1260A a c - 1260A a b - 1260B a b)d e +--R + +--R 2 3 2 2 5 +--R ((2520A a b + 1260B a )c + 420A b + 1260B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 1260A a c + (- 1260A b - 2520B a b)c - 420B b )d e +--R + +--R 2 2 4 3 +--R ((1260A b + 1260B a)c + 1260B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 420A c - 1260B b c )d e + 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Union(Expression(Integer),...) +--E 351 + +--S 352 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 5 +--R (- 630A a c - 630A a b - 630B a b)d e +--R + +--R 2 3 2 3 4 +--R ((2940A a b + 1470B a )c + 490A b + 1470B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 2415A a c + (- 2415A b - 4830B a b)c - 805B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((3423A b + 3423B a)c + 3423B b c)d e + (- 1491A c - 4473B b c )d e +--R + +--R 3 7 +--R 1851B c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 353 + +)clear all + +--S 354 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 354 + +--S 355 of 1751 +r0:=-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*_ + (2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*x/e^7+(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x))-1/2*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*_ + (d+e*x)^2/e^8-1/3*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + (d+e*x)^3/e^8-3/4*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))*(d+e*x)^4/e^8-1/5*c^2*(7*B*c*d-3*b*B*e-A*c*e)*_ + (d+e*x)^5/e^8+1/6*B*c^3*(d+e*x)^6/e^8-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*_ + (2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 2 2 2 6 +--R (180A a b + 60B a )e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 2 5 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 4 3 +--R ((900A b + 900B a)c + 900B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 360A c - 1080B b c )d e + 420B c d e +--R * +--R x +--R + +--R 2 3 6 2 2 2 2 5 +--R (180A a b + 60B a )d e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 3 4 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((900A b + 900B a)c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((45A b + 45B a)c + 45B b c)e + (- 18A c - 54B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (60A a c + (60A b + 120B a b)c + 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 75A b - 75B a)c - 75B b c)d e + (30A c + 90B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((180A a b + 90B a )c + 30A b + 90B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((150A b + 150B a)c + 150B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 4 3 +--R 70B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (180A a c + 180A a b + 180B a b)e +--R + +--R 2 3 2 6 +--R ((- 540A a b - 270B a )c - 90A b - 270B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (180A a c + 180A a b + 180B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 540A a b - 270B a )c - 90A b - 270B a b )d e +--R + +--R 2 2 3 3 4 +--R (240A a c + (240A b + 480B a b)c + 80B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 75A b - 75B a)c - 75B b c)d e + (- 78A c - 234B b c )d e +--R + +--R 3 6 +--R 231B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (180A a b + 60B a )d e +--R + +--R 2 2 2 2 5 +--R (- 180A a c - 180A a b - 180B a b)d e +--R + +--R 2 3 2 3 4 +--R ((540A a b + 270B a )c + 90A b + 270B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 480A a c + (- 480A b - 960B a b)c - 160B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((825A b + 825B a)c + 825B b c)d e + (- 438A c - 1314B b c )d e +--R + +--R 3 7 +--R 651B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 355 + +--S 356 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 7 2 2 2 6 +--R (180A a b + 60B a )e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 2 5 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 4 3 +--R ((900A b + 900B a)c + 900B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 360A c - 1080B b c )d e + 420B c d e +--R * +--R x +--R + +--R 2 3 6 2 2 2 2 5 +--R (180A a b + 60B a )d e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 3 4 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((900A b + 900B a)c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((45A b + 45B a)c + 45B b c)e + (- 18A c - 54B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (60A a c + (60A b + 120B a b)c + 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 75A b - 75B a)c - 75B b c)d e + (30A c + 90B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((180A a b + 90B a )c + 30A b + 90B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((150A b + 150B a)c + 150B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 4 3 +--R 70B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (180A a c + 180A a b + 180B a b)e +--R + +--R 2 3 2 6 +--R ((- 540A a b - 270B a )c - 90A b - 270B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (180A a c + 180A a b + 180B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 720A a b - 360B a )c - 120A b - 360B a b )d e +--R + +--R 2 2 3 3 4 +--R (540A a c + (540A b + 1080B a b)c + 180B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 720A b - 720B a)c - 720B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 6 +--R - 360B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (180A a b + 60B a )d e +--R + +--R 2 2 2 2 5 +--R (- 180A a c - 180A a b - 180B a b)d e +--R + +--R 2 3 2 3 4 +--R ((360A a b + 180B a )c + 60A b + 180B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 180A a c + (- 180A b - 360B a b)c - 60B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((180A b + 180B a)c + 180B b c)d e + (- 60A c - 180B b c )d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Union(Expression(Integer),...) +--E 356 + +--S 357 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 4 +--R ((- 180A a b - 90B a )c - 30A b - 90B a b )d e +--R + +--R 2 2 3 3 3 +--R (300A a c + (300A b + 600B a b)c + 100B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R ((- 645A b - 645B a)c - 645B b c)d e + (378A c + 1134B b c )d e +--R + +--R 3 6 +--R - 591B c d +--R / +--R 8 +--R 60e +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 358 + +)clear all + +--S 359 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 359 + +--S 360 of 1751 +r0:=-(A*e*(10*c^3*d^3-b^3*e^3+3*b*c*e^2*(3*b*d-2*a*e)-9*c^2*d*e*(2*b*d-a*e))-_ + 3*B*(5*c^3*d^4-2*c^2*d^2*e*(5*b*d-3*a*e)-b^2*e^3*(b*d-a*e)+c*e^2*_ + (6*b^2*d^2-6*a*b*d*e+a^2*e^2)))*x/e^7-1/2*(B*(10*c^3*d^3-b^3*e^3+_ + 3*b*c*e^2*(3*b*d-2*a*e)-9*c^2*d*e*(2*b*d-a*e))-3*A*c*e*(2*c^2*d^2+_ + b^2*e^2-c*e*(3*b*d-a*e)))*x^2/e^6-c*(A*c*e*(c*d-b*e)-B*(2*c^2*d^2+_ + b^2*e^2-c*e*(3*b*d-a*e)))*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*_ + x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*_ + (d+e*x)^2)+(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-_ + e*(4*b*d-a*e)))/(e^8*(d+e*x))-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 2 7 +--R (60A a c + 60A a b + 60B a b)e +--R + +--R 2 3 2 6 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (300A c + 900B b c )d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 720A a b - 360B a )c - 120A b - 360B a b )d e +--R + +--R 2 2 3 3 4 +--R (720A a c + (720A b + 1440B a b)c + 240B b )d e +--R + +--R 2 2 4 3 +--R ((- 1200A b - 1200B a)c - 1200B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (600A c + 1800B b c )d e - 840B c d e +--R * +--R x +--R + +--R 2 2 2 2 5 +--R (60A a c + 60A a b + 60B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 4 3 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 600A b - 600B a)c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((20A b + 20B a)c + 20B b c)e + (- 10A c - 30B b c )d e +--R + +--R 3 2 5 +--R 14B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (30A a c + (30A b + 60B a b)c + 10B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 50A b - 50B a)c - 50B b c)d e + (25A c + 75B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((120A a b + 60B a )c + 20A b + 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((200A b + 200B a)c + 200B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((240A a b + 120B a )c + 40A b + 120B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 330A a c + (- 330A b - 660B a b)c - 110B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((630A b + 630B a)c + 630B b c)d e + (- 340A c - 1020B b c )d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 60A a b - 20B a )e + (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 240A a b - 120B a )c - 40A b - 120B a b )d e +--R + +--R 2 2 3 3 4 +--R (60A a c + (60A b + 120B a b)c + 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((60A b + 60B a)c + 60B b c)d e + (- 80A c - 240B b c )d e +--R + +--R 3 6 +--R 160B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 10A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (90A a c + 90A a b + 90B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 300A a b - 150B a )c - 50A b - 150B a b )d e +--R + +--R 2 2 3 4 3 +--R (210A a c + (210A b + 420B a b)c + 70B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 270A b - 270B a)c - 270B b c)d e + (110A c + 330B b c )d e +--R + +--R 3 7 +--R - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 7 +--R (60A a c + 60A a b + 60B a b)e +--R + +--R 2 3 2 6 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (300A c + 900B b c )d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 720A a b - 360B a )c - 120A b - 360B a b )d e +--R + +--R 2 2 3 3 4 +--R (720A a c + (720A b + 1440B a b)c + 240B b )d e +--R + +--R 2 2 4 3 +--R ((- 1200A b - 1200B a)c - 1200B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (600A c + 1800B b c )d e - 840B c d e +--R * +--R x +--R + +--R 2 2 2 2 5 +--R (60A a c + 60A a b + 60B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 4 3 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 600A b - 600B a)c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((20A b + 20B a)c + 20B b c)e + (- 10A c - 30B b c )d e +--R + +--R 3 2 5 +--R 14B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (30A a c + (30A b + 60B a b)c + 10B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 50A b - 50B a)c - 50B b c)d e + (25A c + 75B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((120A a b + 60B a )c + 20A b + 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((200A b + 200B a)c + 200B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((240A a b + 120B a )c + 40A b + 120B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 330A a c + (- 330A b - 660B a b)c - 110B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((630A b + 630B a)c + 630B b c)d e + (- 340A c - 1020B b c )d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 60A a b - 20B a )e + (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 240A a b - 120B a )c - 40A b - 120B a b )d e +--R + +--R 2 2 3 3 4 +--R (60A a c + (60A b + 120B a b)c + 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((60A b + 60B a)c + 60B b c)d e + (- 80A c - 240B b c )d e +--R + +--R 3 6 +--R 160B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 10A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (90A a c + 90A a b + 90B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 300A a b - 150B a )c - 50A b - 150B a b )d e +--R + +--R 2 2 3 4 3 +--R (210A a c + (210A b + 420B a b)c + 70B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 270A b - 270B a)c - 270B b c)d e + (110A c + 330B b c )d e +--R + +--R 3 7 +--R - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 361 + +--S 362 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 364 + +--S 365 of 1751 +r0:=-(B*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + A*c*e*(10*c^2*d^2+3*b^2*e^2-3*c*e*(4*b*d-a*e)))*x/e^7-1/2*c*(A*c*e*_ + (4*c*d-3*b*e)-B*(10*c^2*d^2+3*b^2*e^2-3*c*e*(4*b*d-a*e)))*x^2/e^6-_ + 1/3*c^2*(4*B*c*d-3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+_ + 1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^3)+1/2*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^2)+3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x))-(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+_ + 3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 2 7 +--R ((72A a b + 36B a )c + 12A b + 36B a b )e +--R + +--R 2 2 3 6 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 2 5 +--R ((360A b + 360B a)c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 3 4 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 5 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 4 3 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R x +--R + +--R 2 3 2 3 4 +--R ((72A a b + 36B a )c + 12A b + 36B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((360A b + 360B a)c + 360B b c)d e + (- 240A c - 720B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((18A b + 18B a)c + 18B b c)e + (- 12A c - 36B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 90A b - 90B a)c - 90B b c)d e + (60A c + 180B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (108A a c + (108A b + 216B a b)c + 36B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 378A b - 378B a)c - 378B b c)d e + (292A c + 876B b c )d e +--R + +--R 3 4 3 +--R - 556B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 36A a c - 36A a b - 36B a b)e +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 108A a c + (- 108A b - 216B a b)c - 36B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 54A b - 54B a)c - 54B b c)d e + (156A c + 468B b c )d e +--R + +--R 3 5 2 +--R - 408B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 18A a b - 6B a )e + (- 36A a c - 36A a b - 36B a b)d e +--R + +--R 2 3 2 2 5 +--R ((324A a b + 162B a )c + 54A b + 162B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 324A a c + (- 324A b - 648B a b)c - 108B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((486A b + 486B a)c + 486B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 6 +--R 222B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 6A a b - 2B a )d e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((132A a b + 66B a )c + 22A b + 66B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 156A a c + (- 156A b - 312B a b)c - 52B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((282A b + 282B a)c + 282B b c)d e + (- 148A c - 444B b c )d e +--R + +--R 3 7 +--R 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 7 +--R ((72A a b + 36B a )c + 12A b + 36B a b )e +--R + +--R 2 2 3 6 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 2 5 +--R ((360A b + 360B a)c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 3 4 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 5 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 4 3 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R x +--R + +--R 2 3 2 3 4 +--R ((72A a b + 36B a )c + 12A b + 36B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((360A b + 360B a)c + 360B b c)d e + (- 240A c - 720B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((18A b + 18B a)c + 18B b c)e + (- 12A c - 36B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 90A b - 90B a)c - 90B b c)d e + (60A c + 180B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (108A a c + (108A b + 216B a b)c + 36B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 378A b - 378B a)c - 378B b c)d e + (292A c + 876B b c )d e +--R + +--R 3 4 3 +--R - 556B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 36A a c - 36A a b - 36B a b)e +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 108A a c + (- 108A b - 216B a b)c - 36B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 54A b - 54B a)c - 54B b c)d e + (156A c + 468B b c )d e +--R + +--R 3 5 2 +--R - 408B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 18A a b - 6B a )e + (- 36A a c - 36A a b - 36B a b)d e +--R + +--R 2 3 2 2 5 +--R ((324A a b + 162B a )c + 54A b + 162B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 324A a c + (- 324A b - 648B a b)c - 108B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((486A b + 486B a)c + 486B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 6 +--R 222B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 6A a b - 2B a )d e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((132A a b + 66B a )c + 22A b + 66B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 156A a c + (- 156A b - 312B a b)c - 52B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((282A b + 282B a)c + 282B b c)d e + (- 148A c - 444B b c )d e +--R + +--R 3 7 +--R 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 366 + +--S 367 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 368 + +)clear all + +--S 369 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 369 + +--S 370 of 1751 +r0:=-c*(A*c*e*(5*c*d-3*b*e)-3*B*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*x/e^7-_ + 1/2*c^2*(5*B*c*d-3*b*B*e-A*c*e)*x^2/e^6+1/3*B*c^3*x^3/e^5+1/4*_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^4)+1/3*_ + (c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/_ + (e^8*(d+e*x)^3)+3/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*_ + (8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))/(e^8*(d+e*x)^2)+(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/_ + (e^8*(d+e*x))-(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (180A c + 540B b c )d e - 420B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 5 +--R (216A a c + (216A b + 432B a b)c + 72B b )d e +--R + +--R 2 2 3 4 +--R ((- 1080A b - 1080B a)c - 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (1080A c + 3240B b c )d e - 2520B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 4 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 4 3 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R x +--R + +--R 2 2 3 4 3 +--R (36A a c + (36A b + 72B a b)c + 12B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((6A c + 18B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((36A b + 36B a)c + 36B b c)e + (- 36A c - 108B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 3 2 2 5 +--R ((144A b + 144B a)c + 144B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 3 4 +--R 556B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )e +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 144A b - 144B a)c - 144B b c)d e + (- 96A c - 288B b c )d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 18A a c - 18A a b - 18B a b)e +--R + +--R 2 3 2 6 +--R ((- 108A a b - 54B a )c - 18A b - 54B a b )d e +--R + +--R 2 2 3 2 5 +--R (324A a c + (324A b + 648B a b)c + 108B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 756A b - 756B a)c - 756B b c)d e + (396A c + 1188B b c )d e +--R + +--R 3 5 2 +--R - 444B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 12A a b - 4B a )e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )d e +--R + +--R 2 2 3 3 4 +--R (264A a c + (264A b + 528B a b)c + 88B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 744A b - 744B a)c - 744B b c)d e + (504A c + 1512B b c )d e +--R + +--R 3 6 +--R - 856B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 3A a e + (- 3A a b - B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (75A a c + (75A b + 150B a b)c + 25B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 231A b - 231B a)c - 231B b c)d e + (171A c + 513B b c )d e +--R + +--R 3 7 +--R - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (180A c + 540B b c )d e - 420B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 5 +--R (216A a c + (216A b + 432B a b)c + 72B b )d e +--R + +--R 2 2 3 4 +--R ((- 1080A b - 1080B a)c - 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (1080A c + 3240B b c )d e - 2520B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 4 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 4 3 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R x +--R + +--R 2 2 3 4 3 +--R (36A a c + (36A b + 72B a b)c + 12B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((6A c + 18B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((36A b + 36B a)c + 36B b c)e + (- 36A c - 108B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 3 2 2 5 +--R ((144A b + 144B a)c + 144B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 3 4 +--R 556B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )e +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 144A b - 144B a)c - 144B b c)d e + (- 96A c - 288B b c )d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 18A a c - 18A a b - 18B a b)e +--R + +--R 2 3 2 6 +--R ((- 108A a b - 54B a )c - 18A b - 54B a b )d e +--R + +--R 2 2 3 2 5 +--R (324A a c + (324A b + 648B a b)c + 108B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 756A b - 756B a)c - 756B b c)d e + (396A c + 1188B b c )d e +--R + +--R 3 5 2 +--R - 444B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 12A a b - 4B a )e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )d e +--R + +--R 2 2 3 3 4 +--R (264A a c + (264A b + 528B a b)c + 88B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 744A b - 744B a)c - 744B b c)d e + (504A c + 1512B b c )d e +--R + +--R 3 6 +--R - 856B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 3A a e + (- 3A a b - B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (75A a c + (75A b + 150B a b)c + 25B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 231A b - 231B a)c - 231B b c)d e + (171A c + 513B b c )d e +--R + +--R 3 7 +--R - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 371 + +--S 372 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 373 + +)clear all + +--S 374 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^6 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 374 + +--S 375 of 1751 +r0:=-c^2*(6*B*c*d-3*b*B*e-A*c*e)*x/e^7+1/2*B*c^3*x^2/e^6+1/5*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^5)+1/4*(c*d^2-b*d*e+a*e^2)^2*_ + (3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^4)+_ + (c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*_ + (2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^3)+_ + 1/2*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+_ + 3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^2)+_ + (B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-_ + 3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x))-_ + 3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 7 3 2 6 +--R ((60A b + 60B a)c + 60B b c)e + (- 120A c - 360B b c )d e +--R + +--R 3 2 5 +--R 420B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 5 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 3 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 2 6 +--R ((60A b + 60B a)c + 60B b c)d e + (- 120A c - 360B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((20A c + 60B b c )e - 70B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((100A c + 300B b c )d e - 500B c d e )x +--R + +--R 2 2 3 7 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((300A b + 300B a)c + 300B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 3 4 +--R - 400B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((900A b + 900B a)c + 900B b c)d e + (- 800A c - 2400B b c )d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 20A a c - 20A a b - 20B a b)e +--R + +--R 2 3 2 6 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 3 4 +--R ((1100A b + 1100B a)c + 1100B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 15A a b - 5B a )e + (- 10A a c - 10A a b - 10B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 30A a b - 15B a )c - 5A b - 15B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((625A b + 625B a)c + 625B b c)d e + (- 750A c - 2250B b c )d e +--R + +--R 3 6 +--R 1875B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 3A a b - B a )d e + (- 2A a c - 2A a b - 2B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((137A b + 137B a)c + 137B b c)d e + (- 174A c - 522B b c )d e +--R + +--R 3 7 +--R 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 7 3 2 6 +--R ((60A b + 60B a)c + 60B b c)e + (- 120A c - 360B b c )d e +--R + +--R 3 2 5 +--R 420B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 5 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 3 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 2 6 +--R ((60A b + 60B a)c + 60B b c)d e + (- 120A c - 360B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((20A c + 60B b c )e - 70B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((100A c + 300B b c )d e - 500B c d e )x +--R + +--R 2 2 3 7 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((300A b + 300B a)c + 300B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 3 4 +--R - 400B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((900A b + 900B a)c + 900B b c)d e + (- 800A c - 2400B b c )d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 20A a c - 20A a b - 20B a b)e +--R + +--R 2 3 2 6 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 3 4 +--R ((1100A b + 1100B a)c + 1100B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 15A a b - 5B a )e + (- 10A a c - 10A a b - 10B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 30A a b - 15B a )c - 5A b - 15B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((625A b + 625B a)c + 625B b c)d e + (- 750A c - 2250B b c )d e +--R + +--R 3 6 +--R 1875B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 3A a b - B a )d e + (- 2A a c - 2A a b - 2B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((137A b + 137B a)c + 137B b c)d e + (- 174A c - 522B b c )d e +--R + +--R 3 7 +--R 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 376 + +--S 377 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^7 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 379 + +--S 380 of 1751 +r0:=B*c^3*x/e^7+1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^6)+_ + 1/5*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-_ + a*e)))/(e^8*(d+e*x)^5)+3/4*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^4)+1/3*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/_ + (e^8*(d+e*x)^3)+1/2*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/_ + (e^8*(d+e*x)^2)+3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x))-c^2*(7*B*c*d-3*b*B*e-A*c*e)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 7 3 6 6 +--R ((60A c + 180B b c )e - 420B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((360A c + 1080B b c )d e - 2520B c d e )x +--R + +--R 3 2 2 5 3 3 4 4 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 3 4 3 4 3 3 +--R ((1200A c + 3600B b c )d e - 8400B c d e )x +--R + +--R 3 2 4 3 3 5 2 2 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 5 2 3 6 3 2 6 +--R ((360A c + 1080B b c )d e - 2520B c d e)x + (60A c + 180B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 2 7 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)e + (360A c + 1080B b c )d e +--R + +--R 3 2 5 +--R - 360B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1350A c + 4050B b c )d e +--R + +--R 3 3 4 +--R - 4050B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 120A a b - 60B a )c - 20A b - 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e + (2200A c + 6600B b c )d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 45A a c - 45A a b - 45B a b)e +--R + +--R 2 3 2 6 +--R ((- 90A a b - 45B a )c - 15A b - 45B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1875A c + 5625B b c )d e +--R + +--R 3 5 2 +--R - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 36A a b - 12B a )e + (- 18A a c - 18A a b - 18B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 36A a b - 18B a )c - 6A b - 18B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 36A a c + (- 36A b - 72B a b)c - 12B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 180A b - 180B a)c - 180B b c)d e + (822A c + 2466B b c )d e +--R + +--R 3 6 +--R - 3594B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 10A a e + (- 6A a b - 2B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 6A a c + (- 6A b - 12B a b)c - 2B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 30A b - 30B a)c - 30B b c)d e + (147A c + 441B b c )d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 7 3 6 6 +--R ((60A c + 180B b c )e - 420B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((360A c + 1080B b c )d e - 2520B c d e )x +--R + +--R 3 2 2 5 3 3 4 4 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 3 4 3 4 3 3 +--R ((1200A c + 3600B b c )d e - 8400B c d e )x +--R + +--R 3 2 4 3 3 5 2 2 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 5 2 3 6 3 2 6 +--R ((360A c + 1080B b c )d e - 2520B c d e)x + (60A c + 180B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 2 7 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)e + (360A c + 1080B b c )d e +--R + +--R 3 2 5 +--R - 360B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1350A c + 4050B b c )d e +--R + +--R 3 3 4 +--R - 4050B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 120A a b - 60B a )c - 20A b - 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e + (2200A c + 6600B b c )d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 45A a c - 45A a b - 45B a b)e +--R + +--R 2 3 2 6 +--R ((- 90A a b - 45B a )c - 15A b - 45B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1875A c + 5625B b c )d e +--R + +--R 3 5 2 +--R - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 36A a b - 12B a )e + (- 18A a c - 18A a b - 18B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 36A a b - 18B a )c - 6A b - 18B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 36A a c + (- 36A b - 72B a b)c - 12B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 180A b - 180B a)c - 180B b c)d e + (822A c + 2466B b c )d e +--R + +--R 3 6 +--R - 3594B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 10A a e + (- 6A a b - 2B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 6A a c + (- 6A b - 12B a b)c - 2B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 30A b - 30B a)c - 30B b c)d e + (147A c + 441B b c )d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 383 + +)clear all + +--S 384 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^8 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 384 + +--S 385 of 1751 +r0:=1/7*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^7)+1/6*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+3/5*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^5)+1/4*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^4)+_ + 1/3*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^3)+3/2*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x)^2)+c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*_ + (d+e*x))+B*c^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 2 7 3 6 6 +--R ((- 420A c - 1260B b c )e + 2940B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((- 630A b - 630B a)c - 630B b c)e + (- 1260A c - 3780B b c )d e +--R + +--R 3 2 5 +--R 13230B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )e +--R + +--R 2 2 6 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 2100A c - 6300B b c )d e + 26950B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 630A a b - 315B a )c - 105A b - 315B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 2100A c - 6300B b c )d e + 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 252A a c - 252A a b - 252B a b)e +--R + +--R 2 3 2 6 +--R ((- 378A a b - 189B a )c - 63A b - 189B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 252A a c + (- 252A b - 504B a b)c - 84B b )d e +--R + +--R 2 2 3 4 +--R ((- 630A b - 630B a)c - 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1260A c - 3780B b c )d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 210A a b - 70B a )e + (- 84A a c - 84A a b - 84B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 126A a b - 63B a )c - 21A b - 63B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 84A a c + (- 84A b - 168B a b)c - 28B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 210A b - 210B a)c - 210B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 7203B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 30A b - 30B a)c - 30B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 7 +--R 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 2 7 3 6 6 +--R ((- 420A c - 1260B b c )e + 2940B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((- 630A b - 630B a)c - 630B b c)e + (- 1260A c - 3780B b c )d e +--R + +--R 3 2 5 +--R 13230B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )e +--R + +--R 2 2 6 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 2100A c - 6300B b c )d e + 26950B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 630A a b - 315B a )c - 105A b - 315B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 2100A c - 6300B b c )d e + 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 252A a c - 252A a b - 252B a b)e +--R + +--R 2 3 2 6 +--R ((- 378A a b - 189B a )c - 63A b - 189B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 252A a c + (- 252A b - 504B a b)c - 84B b )d e +--R + +--R 2 2 3 4 +--R ((- 630A b - 630B a)c - 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1260A c - 3780B b c )d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 210A a b - 70B a )e + (- 84A a c - 84A a b - 84B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 126A a b - 63B a )c - 21A b - 63B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 84A a c + (- 84A b - 168B a b)c - 28B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 210A b - 210B a)c - 210B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 7203B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 30A b - 30B a)c - 30B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 7 +--R 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 388 + +)clear all + +--S 389 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^9 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 389 + +--S 390 of 1751 +r0:=1/8*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^8)+1/7*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^7)+1/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+1/5*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^5)+_ + 1/4*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-_ + a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^4)+c*_ + (A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*_ + (d+e*x)^3)+1/2*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^2)-B*c^3/_ + (e^8*(d+e*x)) +--R +--R +--R (2) +--R 3 7 7 1 3 3 2 7 7 3 6 6 +--R - B c e x + ((- - A c - - B b c )e - - B c d e )x +--R 2 2 2 +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R (((- A b - B a)c - B b c)e + (- A c - 3B b c )d e - 7B c d e )x +--R + +--R 3 2 3 2 3 1 3 7 +--R (- - A a c + (- - A b - - B a b)c - - B b )e +--R 4 4 2 4 +--R + +--R 5 5 2 5 2 6 5 3 15 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - -- B b c )d e +--R 4 4 4 4 4 +--R + +--R 35 3 3 4 +--R - -- B c d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 6 3 2 1 3 3 2 7 +--R ((- - A a b - - B a )c - - A b - - B a b )e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 6 +--R (- - A a c + (- - A b - - B a b)c - - B b )d e +--R 5 5 5 5 +--R + +--R 2 2 2 5 3 2 3 4 3 4 3 +--R ((- A b - B a)c - B b c)d e + (- A c - 3B b c )d e - 7B c d e +--R * +--R 3 +--R x +--R + +--R 1 2 1 2 1 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 2 2 2 +--R + +--R 3 3 2 1 3 3 2 6 +--R ((- - A a b - -- B a )c - -- A b - -- B a b )d e +--R 5 10 10 10 +--R + +--R 3 2 3 2 3 1 3 2 5 +--R (- -- A a c + (- -- A b - - B a b)c - -- B b )d e +--R 10 10 5 10 +--R + +--R 1 1 2 1 2 3 4 1 3 3 2 4 3 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 2 2 2 2 2 +--R + +--R 7 3 5 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 3 2 1 3 7 1 2 1 2 1 2 6 +--R (- - A a b - - B a )e + (- - A a c - - A a b - - B a b)d e +--R 7 7 7 7 7 +--R + +--R 6 3 2 1 3 3 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 35 35 35 35 +--R + +--R 3 2 3 2 6 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 35 35 35 35 +--R + +--R 1 1 2 1 2 4 3 1 3 3 2 5 2 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 7 7 7 7 7 +--R + +--R 3 6 +--R - B c d e +--R * +--R x +--R + +--R 1 3 7 3 2 1 3 6 +--R - - A a e + (- -- A a b - -- B a )d e +--R 8 56 56 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 56 56 56 +--R + +--R 3 3 2 1 3 3 2 3 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 280 280 +--R + +--R 3 2 3 2 3 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 280 280 140 280 +--R + +--R 1 1 2 1 2 5 2 1 3 3 2 6 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 56 56 56 56 56 +--R + +--R 1 3 7 +--R - - B c d +--R 8 +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 10 2 7 9 8 8 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 390 + +--S 391 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 2 7 3 6 6 +--R - 280B c e x + ((- 140A c - 420B b c )e - 980B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((- 280A b - 280B a)c - 280B b c)e + (- 280A c - 840B b c )d e +--R + +--R 3 2 5 +--R - 1960B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 210A a c + (- 210A b - 420B a b)c - 70B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 350A b - 350B a)c - 350B b c)d e + (- 350A c - 1050B b c )d e +--R + +--R 3 3 4 +--R - 2450B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 336A a b - 168B a )c - 56A b - 168B a b )e +--R + +--R 2 2 3 6 +--R (- 168A a c + (- 168A b - 336B a b)c - 56B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 280A b - 280B a)c - 280B b c)d e + (- 280A c - 840B b c )d e +--R + +--R 3 4 3 +--R - 1960B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 140A a c - 140A a b - 140B a b)e +--R + +--R 2 3 2 6 +--R ((- 168A a b - 84B a )c - 28A b - 84B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 84A a c + (- 84A b - 168B a b)c - 28B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 140A b - 140B a)c - 140B b c)d e + (- 140A c - 420B b c )d e +--R + +--R 3 5 2 +--R - 980B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 120A a b - 40B a )e + (- 40A a c - 40A a b - 40B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 48A a b - 24B a )c - 8A b - 24B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 24A a c + (- 24A b - 48B a b)c - 8B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 40A b - 40B a)c - 40B b c)d e + (- 40A c - 120B b c )d e +--R + +--R 3 6 +--R - 280B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 35A a e + (- 15A a b - 5B a )d e + (- 5A a c - 5A a b - 5B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 3A a c + (- 3A b - 6B a b)c - B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 5A b - 5B a)c - 5B b c)d e + (- 5A c - 15B b c )d e - 35B c d +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 +--R 280e x + 2240d e x + 7840d e x + 15680d e x + 19600d e x +--R + +--R 5 11 3 6 10 2 7 9 8 8 +--R 15680d e x + 7840d e x + 2240d e x + 280d e +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^10 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 394 + +--S 395 of 1751 +r0:=1/9*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^9)+1/8*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^8)+_ + 3/7*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^7)+_ + 1/6*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^6)+1/5*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^5)+3/4*c*(A*c*e*_ + (2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*(d+e*x)^4)+_ + 1/3*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^3)-1/2*B*c^3/(e^8*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 7 7 1 3 2 7 7 3 6 6 +--R - - B c e x + ((- - A c - B b c )e - - B c d e )x +--R 2 3 6 +--R + +--R 3 3 2 3 2 7 1 3 3 2 6 +--R ((- - A b - - B a)c - - B b c)e + (- - A c - - B b c )d e +--R 4 4 4 2 2 +--R + +--R 7 3 2 5 +--R - - B c d e +--R 4 +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 6 1 3 7 +--R (- - A a c + (- - A b - - B a b)c - - B b )e +--R 5 5 5 5 +--R + +--R 3 3 2 3 2 6 1 3 3 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 4 4 4 2 2 +--R + +--R 7 3 3 4 +--R - - B c d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 1 2 1 3 1 2 7 +--R ((- A a b - - B a )c - - A b - - B a b )e +--R 2 6 2 +--R + +--R 2 2 2 2 4 2 3 6 +--R (- - A a c + (- - A b - - B a b)c - -- B b )d e +--R 5 5 5 15 +--R + +--R 1 1 2 1 2 2 5 1 3 2 3 4 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - B b c )d e +--R 2 2 2 3 +--R + +--R 7 3 4 3 +--R - - B c d e +--R 6 +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 3 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 7 7 7 +--R + +--R 3 3 2 1 3 3 2 6 +--R ((- - A a b - -- B a )c - -- A b - -- B a b )d e +--R 7 14 14 14 +--R + +--R 6 2 6 2 12 2 3 2 5 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 35 35 35 35 +--R + +--R 3 3 2 3 2 3 4 1 3 3 2 4 3 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- - A c - - B b c )d e +--R 14 14 14 7 7 +--R + +--R 1 3 5 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 3 2 1 3 7 3 2 3 2 3 2 6 +--R (- - A a b - - B a )e + (- -- A a c - -- A a b - -- B a b)d e +--R 8 8 28 28 28 +--R + +--R 3 3 2 1 3 3 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 28 56 56 56 +--R + +--R 3 2 3 2 3 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 70 70 35 70 +--R + +--R 3 3 2 3 2 4 3 1 3 3 2 5 2 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 56 56 56 28 28 +--R + +--R 1 3 6 +--R - - B c d e +--R 8 +--R * +--R x +--R + +--R 1 3 7 1 2 1 3 6 +--R - - A a e + (- -- A a b - -- B a )d e +--R 9 24 72 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 84 84 84 +--R + +--R 1 1 2 1 3 1 2 3 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 84 168 504 168 +--R + +--R 1 2 1 2 1 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 210 210 105 630 +--R + +--R 1 1 2 1 2 5 2 1 3 1 2 6 +--R ((- --- A b - --- B a)c - --- B b c)d e + (- --- A c - -- B b c )d e +--R 168 168 168 252 84 +--R + +--R 1 3 7 +--R - -- B c d +--R 72 +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 5 12 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 11 3 7 10 2 8 9 9 8 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 395 + +--S 396 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 2 7 3 6 6 +--R - 1260B c e x + ((- 840A c - 2520B b c )e - 2940B c d e )x +--R + +--R 2 2 7 +--R ((- 1890A b - 1890B a)c - 1890B b c)e +--R + +--R 3 2 6 3 2 5 +--R (- 1260A c - 3780B b c )d e - 4410B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 1512A a c + (- 1512A b - 3024B a b)c - 504B b )e +--R + +--R 2 2 6 +--R ((- 1890A b - 1890B a)c - 1890B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 1260A c - 3780B b c )d e - 4410B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 2520A a b - 1260B a )c - 420A b - 1260B a b )e +--R + +--R 2 2 3 6 +--R (- 1008A a c + (- 1008A b - 2016B a b)c - 336B b )d e +--R + +--R 2 2 2 5 +--R ((- 1260A b - 1260B a)c - 1260B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 840A c - 2520B b c )d e - 2940B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 1080A a c - 1080A a b - 1080B a b)e +--R + +--R 2 3 2 6 +--R ((- 1080A a b - 540B a )c - 180A b - 540B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 540A b - 540B a)c - 540B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 5 2 +--R - 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 945A a b - 315B a )e + (- 270A a c - 270A a b - 270B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 270A a b - 135B a )c - 45A b - 135B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 108A a c + (- 108A b - 216B a b)c - 36B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 135A b - 135B a)c - 135B b c)d e + (- 90A c - 270B b c )d e +--R + +--R 3 6 +--R - 315B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 280A a e + (- 105A a b - 35B a )d e +--R + +--R 2 2 2 2 5 +--R (- 30A a c - 30A a b - 30B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 30A a b - 15B a )c - 5A b - 15B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 15A b - 15B a)c - 15B b c)d e + (- 10A c - 30B b c )d e - 35B c d +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 +--R 2520e x + 22680d e x + 90720d e x + 211680d e x + 317520d e x +--R + +--R 5 12 4 6 11 3 7 10 2 8 9 9 8 +--R 317520d e x + 211680d e x + 90720d e x + 22680d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 398 + +)clear all + +--S 399 of 1751 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^11 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 399 + +--S 400 of 1751 +r0:=1/10*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^10)+1/9*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^9)+3/8*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^8)+1/7*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^7)+_ + 1/6*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+3/5*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x)^5)+1/4*c^2*(7*B*c*d-3*b*B*e-A*c*e)/_ + (e^8*(d+e*x)^4)-1/3*B*c^3/(e^8*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 7 7 1 3 3 2 7 7 3 6 6 +--R - - B c e x + ((- - A c - - B b c )e - -- B c d e )x +--R 3 4 4 12 +--R + +--R 3 3 2 3 2 7 3 3 9 2 6 +--R ((- - A b - - B a)c - - B b c)e + (- -- A c - -- B b c )d e +--R 5 5 5 10 10 +--R + +--R 7 3 2 5 +--R - -- B c d e +--R 10 +--R * +--R 5 +--R x +--R + +--R 1 2 1 2 1 3 7 +--R (- - A a c + (- - A b - B a b)c - - B b )e +--R 2 2 6 +--R + +--R 1 1 2 1 2 6 1 3 3 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 2 2 2 4 4 +--R + +--R 7 3 3 4 +--R - -- B c d e +--R 12 +--R * +--R 4 +--R x +--R + +--R 6 3 2 1 3 3 2 7 +--R ((- - A a b - - B a )c - - A b - - B a b )e +--R 7 7 7 7 +--R + +--R 2 2 2 2 4 2 3 6 +--R (- - A a c + (- - A b - - B a b)c - -- B b )d e +--R 7 7 7 21 +--R + +--R 2 2 2 2 2 2 5 1 3 3 2 3 4 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 7 7 7 7 7 +--R + +--R 1 3 4 3 +--R - - B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 3 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 8 8 8 +--R + +--R 9 9 2 3 3 9 2 6 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 28 56 56 56 +--R + +--R 3 2 3 2 3 1 3 2 5 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 28 28 14 28 +--R + +--R 3 3 2 3 2 3 4 3 3 9 2 4 3 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 28 28 28 56 56 +--R + +--R 1 3 5 2 +--R - - B c d e +--R 8 +--R * +--R 2 +--R x +--R + +--R 1 2 1 3 7 1 2 1 2 1 2 6 +--R (- - A a b - - B a )e + (- -- A a c - -- A a b - -- B a b)d e +--R 3 9 12 12 12 +--R + +--R 1 1 2 1 3 1 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 14 28 84 28 +--R + +--R 1 2 1 2 1 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - --- B b )d e +--R 42 42 21 126 +--R + +--R 1 1 2 1 2 4 3 1 3 1 2 5 2 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 42 42 42 84 28 +--R + +--R 1 3 6 +--R - -- B c d e +--R 36 +--R * +--R x +--R + +--R 1 3 7 1 2 1 3 6 +--R - -- A a e + (- -- A a b - -- B a )d e +--R 10 30 90 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- --- A a c - --- A a b - --- B a b)d e +--R 120 120 120 +--R + +--R 1 1 2 1 3 1 2 3 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 840 280 +--R + +--R 1 2 1 2 1 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - ---- B b )d e +--R 420 420 210 1260 +--R + +--R 1 1 2 1 2 5 2 1 3 1 2 6 +--R ((- --- A b - --- B a)c - --- B b c)d e + (- --- A c - --- B b c )d e +--R 420 420 420 840 280 +--R + +--R 1 3 7 +--R - --- B c d +--R 360 +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 5 13 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 12 4 7 11 3 8 10 2 9 9 10 8 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 400 + +--S 401 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 2 7 3 6 6 +--R - 840B c e x + ((- 630A c - 1890B b c )e - 1470B c d e )x +--R + +--R 2 2 7 +--R ((- 1512A b - 1512B a)c - 1512B b c)e +--R + +--R 3 2 6 3 2 5 +--R (- 756A c - 2268B b c )d e - 1764B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 1260A a c + (- 1260A b - 2520B a b)c - 420B b )e +--R + +--R 2 2 6 +--R ((- 1260A b - 1260B a)c - 1260B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 630A c - 1890B b c )d e - 1470B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 2160A a b - 1080B a )c - 360A b - 1080B a b )e +--R + +--R 2 2 3 6 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 720A b - 720B a)c - 720B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 4 3 +--R - 840B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 945A a c - 945A a b - 945B a b)e +--R + +--R 2 3 2 6 +--R ((- 810A a b - 405B a )c - 135A b - 405B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 270A a c + (- 270A b - 540B a b)c - 90B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 270A b - 270B a)c - 270B b c)d e + (- 135A c - 405B b c )d e +--R + +--R 3 5 2 +--R - 315B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 840A a b - 280B a )e + (- 210A a c - 210A a b - 210B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 180A a b - 90B a )c - 30A b - 90B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 60A b - 60B a)c - 60B b c)d e + (- 30A c - 90B b c )d e +--R + +--R 3 6 +--R - 70B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 252A a e + (- 84A a b - 28B a )d e +--R + +--R 2 2 2 2 5 +--R (- 21A a c - 21A a b - 21B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 6A a c + (- 6A b - 12B a b)c - 2B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 6A b - 6B a)c - 6B b c)d e + (- 3A c - 9B b c )d e - 7B c d +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 +--R 2520e x + 25200d e x + 113400d e x + 302400d e x + 529200d e x +--R + +--R 5 13 5 6 12 4 7 11 3 8 10 2 +--R 635040d e x + 529200d e x + 302400d e x + 113400d e x +--R + +--R 9 9 10 8 +--R 25200d e x + 2520d e +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 403 + +)clear all + +--S 404 of 1751 +t0:=(e*x)^m*(A+B*x) +--R +--R +--R m +--R (1) (B x + A)(e x) +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1751 +r0:=A*(e*x)^(1+m)/(e*(1+m))+B*(e*x)^(2+m)/(e^2*(2+m)) +--R +--R +--R m + 2 m + 1 +--R (B m + B)(e x) + (A e m + 2A e)(e x) +--R (2) ---------------------------------------------- +--R 2 2 2 2 +--R e m + 3e m + 2e +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 2 m log(e x) +--R ((B m + B)x + (A m + 2A)x)%e +--R (3) --------------------------------------- +--R 2 +--R m + 3m + 2 +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 m log(e x) m + 2 +--R ((B e m + B e )x + (A e m + 2A e )x)%e + (- B m - B)(e x) +--R + +--R m + 1 +--R (- A e m - 2A e)(e x) +--R / +--R 2 2 2 2 +--R e m + 3e m + 2e +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 1751 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + (A b + B a)x + A a)(e x) +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1751 +r0:=a*A*(e*x)^(1+m)/(e*(1+m))+(A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+(b*B+A*c)*_ + (e*x)^(3+m)/(e^3*(3+m))+B*c*(e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x) +--R + +--R 3 2 +--R (A c + B b)e m + (7A c + 7B b)e m + (14A c + 14B b)e m +--R + +--R (8A c + 8B b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 2 2 2 +--R (A b + B a)e m + (8A b + 8B a)e m + (19A b + 19B a)e m +--R + +--R 2 +--R (12A b + 12B a)e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 3 3 2 3 3 m + 1 +--R (A a e m + 9A a e m + 26A a e m + 24A a e )(e x) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 +--R (B c m + 6B c m + 11B c m + 6B c)x +--R + +--R 3 2 3 +--R ((A c + B b)m + (7A c + 7B b)m + (14A c + 14B b)m + 8A c + 8B b)x +--R + +--R 3 2 2 +--R ((A b + B a)m + (8A b + 8B a)m + (19A b + 19B a)m + 12A b + 12B a)x +--R + +--R 3 2 +--R (A a m + 9A a m + 26A a m + 24A a)x +--R * +--R m log(e x) +--R %e +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (B c e m + 6B c e m + 11B c e m + 6B c e )x +--R + +--R 4 3 4 2 4 +--R (A c + B b)e m + (7A c + 7B b)e m + (14A c + 14B b)e m +--R + +--R 4 +--R (8A c + 8B b)e +--R * +--R 3 +--R x +--R + +--R 4 3 4 2 4 +--R (A b + B a)e m + (8A b + 8B a)e m + (19A b + 19B a)e m +--R + +--R 4 +--R (12A b + 12B a)e +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 4 4 +--R (A a e m + 9A a e m + 26A a e m + 24A a e )x +--R * +--R m log(e x) +--R %e +--R + +--R 3 2 m + 4 +--R (- B c m - 6B c m - 11B c m - 6B c)(e x) +--R + +--R 3 2 +--R (- A c - B b)e m + (- 7A c - 7B b)e m + (- 14A c - 14B b)e m +--R + +--R (- 8A c - 8B b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 2 2 2 +--R (- A b - B a)e m + (- 8A b - 8B a)e m + (- 19A b - 19B a)e m +--R + +--R 2 +--R (- 12A b - 12B a)e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- A a e m - 9A a e m - 26A a e m - 24A a e )(e x) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 413 + +)clear all + +--S 414 of 1751 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R * +--R m +--R (e x) +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1751 +r0:=a^2*A*(e*x)^(1+m)/(e*(1+m))+a*(2*A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+_ + (2*a*b*B+A*(b^2+2*a*c))*(e*x)^(3+m)/(e^3*(3+m))+(b^2*B+2*A*b*c+2*a*B*c)*_ + (e*x)^(4+m)/(e^4*(4+m))+c*(2*b*B+A*c)*(e*x)^(5+m)/(e^5*(5+m))+_ + B*c^2*(e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 m + 6 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c )(e x) +--R + +--R 2 5 2 4 +--R (A c + 2B b c)e m + (16A c + 32B b c)e m +--R + +--R 2 3 2 2 +--R (95A c + 190B b c)e m + (260A c + 520B b c)e m +--R + +--R 2 2 +--R (324A c + 648B b c)e m + (144A c + 288B b c)e +--R * +--R m + 5 +--R (e x) +--R + +--R 2 2 5 2 2 4 +--R ((2A b + 2B a)c + B b )e m + ((34A b + 34B a)c + 17B b )e m +--R + +--R 2 2 3 +--R ((214A b + 214B a)c + 107B b )e m +--R + +--R 2 2 2 +--R ((614A b + 614B a)c + 307B b )e m +--R + +--R 2 2 2 2 +--R ((792A b + 792B a)c + 396B b )e m + ((360A b + 360B a)c + 180B b )e +--R * +--R m + 4 +--R (e x) +--R + +--R 2 3 5 2 3 4 +--R (2A a c + A b + 2B a b)e m + (36A a c + 18A b + 36B a b)e m +--R + +--R 2 3 3 +--R (242A a c + 121A b + 242B a b)e m +--R + +--R 2 3 2 +--R (744A a c + 372A b + 744B a b)e m +--R + +--R 2 3 +--R (1016A a c + 508A b + 1016B a b)e m +--R + +--R 2 3 +--R (480A a c + 240A b + 480B a b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 4 5 2 4 4 +--R (2A a b + B a )e m + (38A a b + 19B a )e m +--R + +--R 2 4 3 2 4 2 +--R (274A a b + 137B a )e m + (922A a b + 461B a )e m +--R + +--R 2 4 2 4 +--R (1404A a b + 702B a )e m + (720A a b + 360B a )e +--R * +--R m + 2 +--R (e x) +--R + +--R 2 5 5 2 5 4 2 5 3 2 5 2 2 5 +--R A a e m + 20A a e m + 155A a e m + 580A a e m + 1044A a e m +--R + +--R 2 5 +--R 720A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 4 2 3 2 2 2 2 6 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c )x +--R + +--R 2 5 2 4 2 3 +--R (A c + 2B b c)m + (16A c + 32B b c)m + (95A c + 190B b c)m +--R + +--R 2 2 2 2 +--R (260A c + 520B b c)m + (324A c + 648B b c)m + 144A c + 288B b c +--R * +--R 5 +--R x +--R + +--R 2 5 2 4 +--R ((2A b + 2B a)c + B b )m + ((34A b + 34B a)c + 17B b )m +--R + +--R 2 3 2 2 +--R ((214A b + 214B a)c + 107B b )m + ((614A b + 614B a)c + 307B b )m +--R + +--R 2 2 +--R ((792A b + 792B a)c + 396B b )m + (360A b + 360B a)c + 180B b +--R * +--R 4 +--R x +--R + +--R 2 5 2 4 +--R (2A a c + A b + 2B a b)m + (36A a c + 18A b + 36B a b)m +--R + +--R 2 3 +--R (242A a c + 121A b + 242B a b)m +--R + +--R 2 2 +--R (744A a c + 372A b + 744B a b)m +--R + +--R 2 2 +--R (1016A a c + 508A b + 1016B a b)m + 480A a c + 240A b + 480B a b +--R * +--R 3 +--R x +--R + +--R 2 5 2 4 2 3 +--R (2A a b + B a )m + (38A a b + 19B a )m + (274A a b + 137B a )m +--R + +--R 2 2 2 2 +--R (922A a b + 461B a )m + (1404A a b + 702B a )m + 720A a b + 360B a +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (A a m + 20A a m + 155A a m + 580A a m + 1044A a m + 720A a )x +--R * +--R m log(e x) 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3 +--R (242A a c + 121A b + 242B a b)e m +--R + +--R 2 6 2 +--R (744A a c + 372A b + 744B a b)e m +--R + +--R 2 6 +--R (1016A a c + 508A b + 1016B a b)e m +--R + +--R 2 6 +--R (480A a c + 240A b + 480B a b)e +--R * +--R 3 +--R x +--R + +--R 2 6 5 2 6 4 +--R (2A a b + B a )e m + (38A a b + 19B a )e m +--R + +--R 2 6 3 2 6 2 +--R (274A a b + 137B a )e m + (922A a b + 461B a )e m +--R + +--R 2 6 2 6 +--R (1404A a b + 702B a )e m + (720A a b + 360B a )e +--R * +--R 2 +--R x +--R + +--R 2 6 5 2 6 4 2 6 3 2 6 2 2 6 +--R A a e m + 20A a e m + 155A a e m + 580A a e m + 1044A a e m +--R + +--R 2 6 +--R 720A a e +--R * +--R x +--R * +--R m log(e x) +--R %e +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (- B c m - 15B c m - 85B c m - 225B c m - 274B c m - 120B c ) +--R * +--R m + 6 +--R (e x) +--R + +--R 2 5 2 4 +--R (- A c - 2B b c)e m + (- 16A c - 32B b c)e m +--R + +--R 2 3 2 2 +--R (- 95A c - 190B b c)e m + (- 260A c - 520B b c)e m +--R + +--R 2 2 +--R (- 324A c - 648B b c)e m + (- 144A c - 288B b c)e 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+--R + +--R 2 5 5 2 5 4 2 5 3 2 5 2 2 5 +--R - A a e m - 20A a e m - 155A a e m - 580A a e m - 1044A a e m +--R + +--R 2 5 +--R - 720A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 418 + +)clear all + +--S 419 of 1751 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R m +--R (e x) +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1751 +r0:=a^3*A*(e*x)^(1+m)/(e*(1+m))+a^2*(3*A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+_ + 3*a*(a*b*B+A*(b^2+a*c))*(e*x)^(3+m)/(e^3*(3+m))+(3*a*B*(b^2+a*c)+A*_ + (b^3+6*a*b*c))*(e*x)^(4+m)/(e^4*(4+m))+(b^3*B+3*A*b^2*c+6*a*b*B*c+_ + 3*a*A*c^2)*(e*x)^(5+m)/(e^5*(5+m))+3*c*(b^2*B+A*b*c+a*B*c)*_ + (e*x)^(6+m)/(e^6*(6+m))+c^2*(3*b*B+A*c)*(e*x)^(7+m)/(e^7*(7+m))+_ + B*c^3*(e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x) +--R + +--R 3 2 7 3 2 6 +--R (A c + 3B b c )e m + (29A c + 87B b c )e m +--R + +--R 3 2 5 3 2 4 +--R (343A c + 1029B b c )e m + (2135A c + 6405B b c )e m +--R + +--R 3 2 3 3 2 2 +--R (7504A c + 22512B b c )e m + (14756A c + 44268B b c )e m +--R + +--R 3 2 3 2 +--R (14832A c + 44496B b c )e m + (5760A c + 17280B b c )e +--R * +--R m + 7 +--R (e x) +--R + +--R 2 2 2 7 2 2 2 6 +--R ((3A b + 3B a)c + 3B b c)e m + ((90A b + 90B a)c + 90B b c)e m +--R + +--R 2 2 2 5 +--R ((1098A b + 1098B a)c + 1098B b c)e m 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+ 86076B a b)e m +--R + +--R 2 2 2 5 +--R (96144A a c + 96144A a b + 96144B a b)e m +--R + +--R 2 2 2 5 +--R (40320A a c + 40320A a b + 40320B a b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 6 7 2 3 6 6 +--R (3A a b + B a )e m + (102A a b + 34B a )e m +--R + +--R 2 3 6 5 2 3 6 4 +--R (1434A a b + 478B a )e m + (10740A a b + 3580B a )e m +--R + +--R 2 3 6 3 2 3 6 2 +--R (45867A a b + 15289B a )e m + (110118A a b + 36706B a )e m +--R + +--R 2 3 6 2 3 6 +--R (134136A a b + 44712B a )e m + (60480A a b + 20160B a )e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 7 7 3 7 6 3 7 5 3 7 4 3 7 3 +--R A a e m + 35A a e m + 511A a e m + 4025A a e m + 18424A a e m +--R + +--R 3 7 2 3 7 3 7 +--R 48860A a e m + 69264A a e m + 40320A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1751 +a0:=integrate(t0,x) +--R +--R 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+--R 3 7 3 6 3 5 3 4 3 3 +--R A a m + 35A a m + 511A a m + 4025A a m + 18424A a m +--R + +--R 3 2 3 3 +--R 48860A a m + 69264A a m + 40320A a +--R * +--R x +--R * +--R m log(e x) +--R %e +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 8 7 3 8 6 3 8 5 3 8 4 3 8 3 +--R B c e m + 28B c e m + 322B c e m + 1960B c e m + 6769B c e m +--R + +--R 3 8 2 3 8 3 8 +--R 13132B c e m + 13068B c e m + 5040B c e +--R * +--R 8 +--R x +--R + +--R 3 2 8 7 3 2 8 6 +--R (A c + 3B b c )e m + (29A c + 87B b c )e m +--R + +--R 3 2 8 5 3 2 8 4 +--R (343A c + 1029B b c )e m + (2135A c + 6405B b c )e m +--R + +--R 3 2 8 3 3 2 8 2 +--R (7504A c + 22512B b c )e m + (14756A c + 44268B b c )e m +--R + +--R 3 2 8 3 2 8 +--R (14832A c + 44496B b c )e m + (5760A c + 17280B b c )e +--R * +--R 7 +--R x +--R + +--R 2 2 8 7 +--R ((3A b + 3B a)c + 3B b c)e m +--R + +--R 2 2 8 6 +--R ((90A b + 90B a)c + 90B b c)e m +--R + +--R 2 2 8 5 +--R ((1098A b + 1098B a)c + 1098B b c)e m +--R + +--R 2 2 8 4 +--R ((7020A b + 7020B a)c + 7020B b c)e m +--R + +--R 2 2 8 3 +--R ((25227A b + 25227B a)c + 25227B b c)e m +--R + +--R 2 2 8 2 +--R ((50490A b + 50490B a)c + 50490B b c)e m +--R + +--R 2 2 8 +--R ((51432A b + 51432B a)c + 51432B b c)e m +--R + +--R 2 2 8 +--R ((20160A b + 20160B a)c + 20160B b c)e +--R * +--R 6 +--R x +--R + +--R 2 2 3 8 7 +--R (3A a c + (3A b + 6B a b)c + B b )e m +--R + +--R 2 2 3 8 6 +--R (93A a c + (93A b + 186B a b)c + 31B b )e m +--R + +--R 2 2 3 8 5 +--R (1173A a c + (1173A b + 2346B a b)c + 391B b )e m +--R + +--R 2 2 3 8 4 +--R (7743A a c + (7743A b + 15486B a b)c + 2581B b )e m +--R + +--R 2 2 3 8 3 +--R (28632A a c + (28632A b + 57264B a b)c + 9544B b )e m +--R + +--R 2 2 3 8 2 +--R (58692A a c + (58692A b + 117384B a b)c + 19564B b )e m +--R + +--R 2 2 3 8 +--R (60912A a c + (60912A b + 121824B a b)c + 20304B b )e m +--R + +--R 2 2 3 8 +--R (24192A a c + (24192A b + 48384B a b)c + 8064B b )e +--R * +--R 5 +--R x +--R + +--R 2 3 2 8 7 +--R ((6A a b + 3B a )c + A b + 3B a b )e m +--R + +--R 2 3 2 8 6 +--R ((192A a b + 96B a )c + 32A b + 96B a b )e m +--R + +--R 2 3 2 8 5 +--R ((2508A a b + 1254B a )c + 418A b + 1254B a b )e m +--R + +--R 2 3 2 8 4 +--R ((17184A a b + 8592B a )c + 2864A b + 8592B a b )e m +--R + +--R 2 3 2 8 3 +--R ((65958A a b + 32979B a )c + 10993A b + 32979B a b )e m +--R + +--R 2 3 2 8 2 +--R ((139872A a b + 69936B a )c + 23312A b + 69936B a b )e m +--R + +--R 2 3 2 8 +--R ((149256A a b + 74628B a )c + 24876A b + 74628B a b )e m +--R + +--R 2 3 2 8 +--R ((60480A a b + 30240B a )c + 10080A b + 30240B a b )e +--R * +--R 4 +--R x +--R + +--R 2 2 2 8 7 +--R (3A a c + 3A a b + 3B a b)e m +--R + +--R 2 2 2 8 6 +--R (99A a c + 99A a b + 99B a b)e m +--R + +--R 2 2 2 8 5 +--R (1341A a c + 1341A a b + 1341B a b)e m +--R + +--R 2 2 2 8 4 +--R (9585A a c + 9585A a b + 9585B a b)e m +--R + +--R 2 2 2 8 3 +--R (38592A a c + 38592A a b + 38592B a b)e m +--R + +--R 2 2 2 8 2 +--R (86076A a c + 86076A a b + 86076B a b)e m +--R + +--R 2 2 2 8 +--R (96144A a c + 96144A a b + 96144B a b)e m +--R + +--R 2 2 2 8 +--R (40320A a c + 40320A a b + 40320B a b)e +--R * +--R 3 +--R x +--R + +--R 2 3 8 7 2 3 8 6 +--R (3A a b + B a )e m + (102A a b + 34B a )e m +--R + +--R 2 3 8 5 2 3 8 4 +--R (1434A a b + 478B a )e m + (10740A a b + 3580B a )e m +--R + +--R 2 3 8 3 2 3 8 2 +--R (45867A a b + 15289B a )e m + (110118A a b + 36706B a )e m +--R + +--R 2 3 8 2 3 8 +--R (134136A a b + 44712B a )e m + (60480A a b + 20160B a )e +--R * +--R 2 +--R x +--R + +--R 3 8 7 3 8 6 3 8 5 3 8 4 +--R A a e m + 35A a e m + 511A a e m + 4025A a e m +--R + +--R 3 8 3 3 8 2 3 8 3 8 +--R 18424A a e m + 48860A a e m + 69264A a e m + 40320A a e +--R * +--R x +--R * +--R m log(e x) +--R %e +--R + +--R 3 7 3 6 3 5 3 4 3 3 +--R - B c m - 28B c m - 322B c m - 1960B c m - 6769B c m +--R + +--R 3 2 3 3 +--R - 13132B c m - 13068B c m - 5040B c +--R * +--R m + 8 +--R (e x) +--R + +--R 3 2 7 3 2 6 +--R (- A c - 3B b c )e m + (- 29A c - 87B b c )e m +--R + +--R 3 2 5 3 2 4 +--R (- 343A c - 1029B b c )e m + (- 2135A c - 6405B b c )e m +--R + +--R 3 2 3 3 2 2 +--R (- 7504A c - 22512B b c )e m + (- 14756A c - 44268B b c )e m +--R + +--R 3 2 3 2 +--R (- 14832A c - 44496B b c )e m + (- 5760A c - 17280B b c )e +--R * +--R m + 7 +--R (e x) +--R + +--R 2 2 2 7 +--R ((- 3A b - 3B a)c - 3B b c)e m +--R + +--R 2 2 2 6 +--R ((- 90A b - 90B a)c - 90B b c)e m +--R + +--R 2 2 2 5 +--R ((- 1098A b - 1098B a)c - 1098B b c)e m +--R + +--R 2 2 2 4 +--R ((- 7020A b - 7020B a)c - 7020B b c)e m +--R + +--R 2 2 2 3 +--R ((- 25227A b - 25227B a)c - 25227B b c)e m +--R + +--R 2 2 2 2 +--R ((- 50490A b - 50490B a)c - 50490B b c)e m +--R + +--R 2 2 2 +--R ((- 51432A b - 51432B a)c - 51432B b c)e m +--R + +--R 2 2 2 +--R ((- 20160A b - 20160B a)c - 20160B b c)e +--R * +--R m + 6 +--R (e x) +--R + +--R 2 2 3 3 7 +--R (- 3A a c + (- 3A b - 6B a b)c - B b )e m +--R + +--R 2 2 3 3 6 +--R (- 93A a c + (- 93A b - 186B a b)c - 31B b )e m +--R + +--R 2 2 3 3 5 +--R (- 1173A a c + (- 1173A b - 2346B a b)c - 391B b )e m +--R + +--R 2 2 3 3 4 +--R (- 7743A a c + (- 7743A b - 15486B a b)c - 2581B b )e m +--R + +--R 2 2 3 3 3 +--R (- 28632A a c + (- 28632A b - 57264B a b)c - 9544B b )e m +--R + +--R 2 2 3 3 2 +--R (- 58692A a c + (- 58692A b - 117384B a b)c - 19564B b )e m +--R + +--R 2 2 3 3 +--R (- 60912A a c + (- 60912A b - 121824B a b)c - 20304B b )e m +--R + +--R 2 2 3 3 +--R (- 24192A a c + (- 24192A b - 48384B a b)c - 8064B b )e +--R * +--R m + 5 +--R (e x) +--R + +--R 2 3 2 4 7 +--R ((- 6A a b - 3B a )c - A b - 3B a b )e m +--R + +--R 2 3 2 4 6 +--R ((- 192A a b - 96B a )c - 32A b - 96B a b )e m +--R + +--R 2 3 2 4 5 +--R ((- 2508A a b - 1254B a )c - 418A b - 1254B a b )e m +--R + +--R 2 3 2 4 4 +--R ((- 17184A a b - 8592B a )c - 2864A b - 8592B a b )e m +--R + +--R 2 3 2 4 3 +--R ((- 65958A a b - 32979B a )c - 10993A b - 32979B a b )e m +--R + +--R 2 3 2 4 2 +--R ((- 139872A a b - 69936B a )c - 23312A b - 69936B a b )e m +--R + +--R 2 3 2 4 +--R ((- 149256A a b - 74628B a )c - 24876A b - 74628B a b )e m +--R + +--R 2 3 2 4 +--R ((- 60480A a b - 30240B a )c - 10080A b - 30240B a b )e +--R * +--R m + 4 +--R (e x) +--R + +--R 2 2 2 5 7 +--R (- 3A a c - 3A a b - 3B a b)e m +--R + +--R 2 2 2 5 6 +--R (- 99A a c - 99A a b - 99B a b)e m +--R + +--R 2 2 2 5 5 +--R (- 1341A a c - 1341A a b - 1341B a b)e m +--R + +--R 2 2 2 5 4 +--R (- 9585A a c - 9585A a b - 9585B a b)e m +--R + +--R 2 2 2 5 3 +--R (- 38592A a c - 38592A a b - 38592B a b)e m +--R + +--R 2 2 2 5 2 +--R (- 86076A a c - 86076A a b - 86076B a b)e m +--R + +--R 2 2 2 5 +--R (- 96144A a c - 96144A a b - 96144B a b)e m +--R + +--R 2 2 2 5 +--R (- 40320A a c - 40320A a b - 40320B a b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 6 7 2 3 6 6 +--R (- 3A a b - B a )e m + (- 102A a b - 34B a )e m +--R + +--R 2 3 6 5 2 3 6 4 +--R (- 1434A a b - 478B a )e m + (- 10740A a b - 3580B a )e m +--R + +--R 2 3 6 3 2 3 6 2 +--R (- 45867A a b - 15289B a )e m + (- 110118A a b - 36706B a )e m +--R + +--R 2 3 6 2 3 6 +--R (- 134136A a b - 44712B a )e m + (- 60480A a b - 20160B a )e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 7 7 3 7 6 3 7 5 3 7 4 3 7 3 +--R - A a e m - 35A a e m - 511A a e m - 4025A a e m - 18424A a e m +--R + +--R 3 7 2 3 7 3 7 +--R - 48860A a e m - 69264A a e m - 40320A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 1751 +t0:=(A+B*x)*(d+e*x)^m/(a+b*x+c*x^2) +--R +--R +--R m +--R (B x + A)(e x + d) +--R (1) ------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1751 +--r0:=-(d+e*x)^(1+m)*hypergeometric(1,1+m,2+m,2*c*(d+e*x)/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/((1+m)*_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))-(d+e*x)^(1+m)*hypergeometric(1,1+m,_ +-- 2+m,2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(B+(b*B-2*A*c)/_ +-- sqrt(b^2-4*a*c))/((1+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--E 425 + +--S 426 of 1751 +--a0:=integrate(t0,x) +--E 426 + +--S 427 of 1751 +--m0:=a0-r0 +--E 427 + +--S 428 of 1751 +--d0:=D(m0,x) +--E 428 + +)clear all + +--S 429 of 1751 +t0:=(A+B*x)*(d+e*x)^(1+m)/(a+b*x+c*x^2) +--R +--R +--R m + 1 +--R (B x + A)(e x + d) +--R (1) ----------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1751 +--r0:=-(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,2*c*(d+e*x)/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/((2+m)*_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))-(d+e*x)^(2+m)*_ +-- hypergeometric(1,2+m,3+m,2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- (B+(b*B-2*A*c)/sqrt(b^2-4*a*c))/((2+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--E 430 + +--S 431 of 1751 +--a0:=integrate(t0,x) +--E 431 + +--S 432 of 1751 +--m0:=a0-r0 +--E 432 + +--S 433 of 1751 +--d0:=D(m0,x) +--E 433 + +)clear all + +--S 434 of 1751 +t0:=(A+B*x)*(d+e*x)^2/(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 434 + +--S 435 of 1751 +r0:=e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+1/2*(A*c*e*(2*c*d-b*e)+_ + B*(c^2*d^2+b^2*e^2-c*e*(2*b*d+a*e)))*log(a+b*x+c*x^2)/c^3+(b^3*B*e^2-_ + b^2*c*e*(2*B*d+A*e)-2*c^2*(A*c*d^2-2*a*B*d*e-a*A*e^2)+b*c*(B*c*d^2+_ + 2*A*c*d*e-3*a*B*e^2))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-_ + 4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 +--R (4A a c + (- 2A b - 6B a b)c + 2B b )e +--R + +--R 2 2 3 2 2 +--R ((4A b + 8B a)c - 4B b c)d e + (- 4A c + 2B b c )d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 +--R (((- A b - B a)c + B b )e + (2A c - 2B b c)d e + B c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 2 2 2 2 +--R B c e x + ((2A c - 2B b c)e + 4B c d e)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 435 + +--S 436 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 +--R (2A a c + (- A b - 3B a b)c + B b )e +--R + +--R 2 2 3 2 2 +--R ((2A b + 4B a)c - 2B b c)d e + (- 2A c + B b c )d +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 +--R (((- A b - B a)c + B b )e + (2A c - 2B b c)d e + B c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 2 2 2 2 +--R B c e x + ((2A c - 2B b c)e + 4B c d e)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R 2 2 3 2 +--R (- 4A a c + (2A b + 6B a b)c - 2B b )e +--R + +--R 2 2 3 2 2 +--R ((- 4A b - 8B a)c + 4B b c)d e + (4A c - 2B b c )d +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 2 2 +--R (((- A b - B a)c + B b )e + (2A c - 2B b c)d e + B c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 2 2 2 2 +--R B c e x + ((2A c - 2B b c)e + 4B c d e)x +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 3 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 436 + +--S 437 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 3 2 +--R (2A a c + (- A b - 3B a b)c + B b )e +--R + +--R 2 2 3 2 2 +--R ((2A b + 4B a)c - 2B b c)d e + (- 2A c + B b c )d +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 2 +--R (- 4A a c + (2A b + 6B a b)c - 2B b )e +--R + +--R 2 2 3 2 2 +--R ((- 4A b - 8B a)c + 4B b c)d e + (4A c - 2B b c )d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 3 2 +--R (- 2A a c + (A b + 3B a b)c - B b )e +--R + +--R 2 2 3 2 2 +--R ((- 2A b - 4B a)c + 2B b c)d e + (2A c - B b c )d +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 +--R (- 2A a c + (A b + 3B a b)c - B b )e +--R + +--R 2 2 3 2 2 +--R ((- 2A b - 4B a)c + 2B b c)d e + (2A c - B b c )d +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1751 +t0:=(A+B*x)*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 1751 +r0:=B*e*x/c+1/2*(B*c*d-b*B*e+A*c*e)*log(a+b*x+c*x^2)/c^2-(b^2*B*e-b*c*_ + (B*d+A*e)+2*c*(A*c*d-a*B*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (c^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2c x + b +--R (((2A b + 4B a)c - 2B b )e + (- 4A c + 2B b c)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R (((A c - B b)e + B c d)log(c x + b x + a) + 2B c e x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (((A b + 2B a)c - B b )e + (- 2A c + B b c)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R (((A c - B b)e + B c d)log(c x + b x + a) + 2B c e x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R 2 2 +--R (((- 2A b - 4B a)c + 2B b )e + (4A c - 2B b c)d) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (((A c - B b)e + B c d)log(c x + b x + a) + 2B c e x)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 443 + +--S 444 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 +--R (((A b + 2B a)c - B b )e + (- 2A c + B b c)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2c x + b +--R (((- 2A b - 4B a)c + 2B b )e + (4A c - 2B b c)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R 2 2 | 2 +--R (((- A b - 2B a)c + B b )e + (2A c - B b c)d)\|4a c - b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 2 | 2 +--R (((- A b - 2B a)c + B b )e + (2A c - B b c)d)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 1751 +t0:=(A+B*x)/(a+b*x+c*x^2) +--R +--R +--R B x + A +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 448 + +--S 449 of 1751 +r0:=1/2*B*log(a+b*x+c*x^2)/c+(b*B-2*A*c)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (c*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R +-----------+ +--R 2c x + b 2 | 2 +--R (- 4A c + 2B b)atanh(--------------) + B log(c x + b x + a)\|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R -------------------------------------------------------------------------- +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (2A c - B b) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R B log(c x + b x + a)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R (4A c - 2B b)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R B log(c x + b x + a)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2c\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 450 + +--S 451 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R (2A c - B b) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R (4A c - 2B b)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R | 2 2c x + b +--R (2A c - B b)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R (2A c - B b)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R c\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 454 + +)clear all + +--S 455 of 1751 +t0:=(A+B*x)/((d+e*x)*(a+b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 455 + +--S 456 of 1751 +r0:=-(B*d-A*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)+1/2*(B*d-A*e)*_ + log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)+(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2c x + b +--R ((2A b - 4B a)e + (- 4A c + 2B b)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R ((- A e + B d)log(c x + b x + a) + (2A e - 2B d)log(e x + d)) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R ((A b - 2B a)e + (- 2A c + B b)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 +--R ((- A e + B d)log(c x + b x + a) + (2A e - 2B d)log(e x + d)) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R ((- 2A b + 4B a)e + (4A c - 2B b)d)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 +--R ((- A e + B d)log(c x + b x + a) + (2A e - 2B d)log(e x + d)) +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 2 2 | 2 +--R (2a e - 2b d e + 2c d )\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 457 + +--S 458 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R ((A b - 2B a)e + (- 2A c + B b)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R ((- 2A b + 4B a)e + (4A c - 2B b)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +---------+ +--R | 2 2c x + b +--R ((- A b + 2B a)e + (2A c - B b)d)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R ((- A b + 2B a)e + (2A c - B b)d)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 2 | 2 | 2 +--R (a e - b d e + c d )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 461 + +)clear all + +--S 462 of 1751 +t0:=(A+B*x)/((d+e*x)^2*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R Type: Fraction(Polynomial(Integer)) +--E 462 + +--S 463 of 1751 +r0:=(B*d-A*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x))+(A*e*(2*c*d-b*e)-_ + B*(c*d^2-a*e^2))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2-1/2*(A*e*(2*c*d-b*e)-_ + B*(c*d^2-a*e^2))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2-(A*b^2*e^2+_ + 2*c*(A*c*d^2+2*a*B*d*e-a*A*e^2)-b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 2 +--R (4A a c - 2A b + 2B a b)e + (4A b - 8B a)c d e +--R + +--R 2 2 +--R (- 4A c + 2B b c)d e +--R * +--R x +--R + +--R 2 2 2 +--R (4A a c - 2A b + 2B a b)d e + (4A b - 8B a)c d e +--R + +--R 2 3 +--R (- 4A c + 2B b c)d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 +--R ((A b - B a)e - 2A c d e + B c d e)x + (A b - B a)d e +--R + +--R 2 3 +--R - 2A c d e + B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 +--R ((- 2A b + 2B a)e + 4A c d e - 2B c d e)x + (- 2A b + 2B a)d e +--R + +--R 2 3 +--R 4A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + (2A b + 2B a)d e + (- 2A c - 2B b)d e + 2B c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 +--R (2A a c - A b + B a b)e + (2A b - 4B a)c d e +--R + +--R 2 2 +--R (- 2A c + B b c)d e +--R * +--R x +--R + +--R 2 2 2 +--R (2A a c - A b + B a b)d e + (2A b - 4B a)c d e +--R + +--R 2 3 +--R (- 2A c + B b c)d +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2 +--R ((A b - B a)e - 2A c d e + B c d e)x + (A b - B a)d e +--R + +--R 2 3 +--R - 2A c d e + B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 +--R ((- 2A b + 2B a)e + 4A c d e - 2B c d e)x +--R + +--R 2 2 3 +--R (- 2A b + 2B a)d e + 4A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + (2A b + 2B a)d e + (- 2A c - 2B b)d e + 2B c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 5 4 2 2 3 3 2 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x +--R + +--R 2 4 2 3 2 3 2 4 2 5 +--R 2a d e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 3 2 +--R (- 4A a c + 2A b - 2B a b)e + (- 4A b + 8B a)c d e +--R + +--R 2 2 +--R (4A c - 2B b c)d e +--R * +--R x +--R + +--R 2 2 2 +--R (- 4A a c + 2A b - 2B a b)d e + (- 4A b + 8B a)c d e +--R + +--R 2 3 +--R (4A c - 2B b c)d +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 2 2 2 +--R ((A b - B a)e - 2A c d e + B c d e)x + (A b - B a)d e +--R + +--R 2 3 +--R - 2A c d e + B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 +--R ((- 2A b + 2B a)e + 4A c d e - 2B c d e)x +--R + +--R 2 2 3 +--R (- 2A b + 2B a)d e + 4A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + (2A b + 2B a)d e + (- 2A c - 2B b)d e + 2B c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 2 5 4 2 2 3 3 2 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x +--R + +--R 2 4 2 3 2 3 2 4 2 5 +--R 2a d e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 464 + +--S 465 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R ((2A a c - A b + B a b)e + (2A b - 4B a)c d e + (- 2A c + B b c)d ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 +--R (- 4A a c + 2A b - 2B a b)e + (- 4A b + 8B a)c d e +--R + +--R 2 2 +--R (4A c - 2B b c)d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 +--R (- 2A a c + A b - B a b)e + (- 2A b + 4B a)c d e +--R + +--R 2 2 +--R (2A c - B b c)d +--R * +--R +---------+ +--R | 2 2c x + b +--R \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 +--R (- 2A a c + A b - B a b)e + (- 2A b + 4B a)c d e +--R + +--R 2 2 +--R (2A c - B b c)d +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (a e - 2a b d e + (2a c + b )d e - 2b c d e + c d )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1751 +t0:=(A+B*x)/((d+e*x)^3*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 469 + +--S 470 of 1751 +r0:=1/2*(B*d-A*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+(-A*e*(2*c*d-b*e)+_ + B*(c*d^2-a*e^2))/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))-(B*(c^2*d^3-_ + 3*a*c*d*e^2+a*b*e^3)-A*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*_ + log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*(B*(c^2*d^3-3*a*c*d*e^2+a*b*e^3)-_ + A*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*log(a+b*x+c*x^2)/(c*d^2-_ + b*d*e+a*e^2)^3+(A*b^3*e^3-b^2*e^2*(3*A*c*d+a*B*e)+b*c*(B*c*d^3+_ + 3*A*c*d^2*e+3*a*B*d*e^2-3*a*A*e^3)-2*c*(A*c*d*(c*d^2-3*a*e^2)+_ + a*B*e*(3*c*d^2-a*e^2)))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + ((c*d^2-b*d*e+a*e^2)^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 2 5 +--R ((- 6A a b + 4B a )c + 2A b - 2B a b )e +--R + +--R 2 2 4 2 2 3 +--R (12A a c + (- 6A b + 6B a b)c)d e + (6A b - 12B a)c d e +--R + +--R 3 2 3 2 +--R (- 4A c + 2B b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 +--R ((- 12A a b + 8B a )c + 4A b - 4B a b )d e +--R + +--R 2 2 2 3 2 3 2 +--R (24A a c + (- 12A b + 12B a b)c)d e + (12A b - 24B a)c d e +--R + +--R 3 2 4 +--R (- 8A c + 4B b c )d e +--R * +--R x +--R + +--R 2 3 2 2 3 +--R ((- 6A a b + 4B a )c + 2A b - 2B a b )d e +--R + +--R 2 2 3 2 2 4 +--R (12A a c + (- 6A b + 6B a b)c)d e + (6A b - 12B a)c d e +--R + +--R 3 2 5 +--R (- 4A c + 2B b c )d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 5 4 2 2 3 +--R (A a c - A b + B a b)e + (3A b - 3B a)c d e - 3A c d e +--R + +--R 2 3 2 +--R B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 +--R (2A a c - 2A b + 2B a b)d e + (6A b - 6B a)c d e +--R + +--R 2 3 2 2 4 +--R - 6A c d e + 2B c d e +--R * +--R x +--R + +--R 2 2 3 3 2 2 4 +--R (A a c - A b + B a b)d e + (3A b - 3B a)c d e - 3A c d e +--R + +--R 2 5 +--R B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 5 4 +--R (- 2A a c + 2A b - 2B a b)e + (- 6A b + 6B a)c d e +--R + +--R 2 2 3 2 3 2 +--R 6A c d e - 2B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 +--R (- 4A a c + 4A b - 4B a b)d e + (- 12A b + 12B a)c d e +--R + +--R 2 3 2 2 4 +--R 12A c d e - 4B c d e +--R * +--R x +--R + +--R 2 2 3 3 2 +--R (- 2A a c + 2A b - 2B a b)d e + (- 6A b + 6B a)c d e +--R + +--R 2 4 2 5 +--R 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 +--R (2A a b - 2B a )e + (- 4A a c - 2A b + 2B a b)d e +--R + +--R 2 3 2 3 2 2 4 +--R 6A b c d e + (- 4A c - 2B b c)d e + 2B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - A a e + (4A a b - B a )d e + (- 6A a c - 3A b )d e +--R + +--R 2 3 2 2 4 2 5 +--R ((8A b + 2B a)c + B b )d e + (- 5A c - 4B b c)d e + 3B c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1751 +--a0:=integrate(t0,x) +--E 471 + +--S 472 of 1751 +--m0a:=a0.1-r0 +--E 472 + +--S 473 of 1751 +--d0a:=D(m0a,x) +--E 473 + +--S 474 of 1751 +--m0b:=a0.2-r0 +--E 474 + +--S 475 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (4) 0 +--R Type: Polynomial(Integer) +--E 475 + +)clear all + +--S 476 of 1751 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 1751 +r0:=11576/81*x+1156/27*x^2+32/27*x^3-4/3*x^4-6*log(1+x)+10625/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R 10625log(3x + 2) - 1458log(x + 1) - 324x + 288x + 10404x + 34728x +--R (2) -------------------------------------------------------------------- +--R 243 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 10625log(3x + 2) - 1458log(x + 1) - 324x + 288x + 10404x + 34728x +--R (3) -------------------------------------------------------------------- +--R 243 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1751 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 1751 +r0:=922/27*x+26/9*x^2-8/9*x^3-6*log(1+x)+2125/81*log(2+3*x) +--R +--R +--R 3 2 +--R 2125log(3x + 2) - 486log(x + 1) - 72x + 234x + 2766x +--R (2) ------------------------------------------------------ +--R 81 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 2125log(3x + 2) - 486log(x + 1) - 72x + 234x + 2766x +--R (3) ------------------------------------------------------ +--R 81 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1751 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 1751 +r0:=44/9*x-2/3*x^2-6*log(1+x)+425/27*log(2+3*x) +--R +--R +--R 2 +--R 425log(3x + 2) - 162log(x + 1) - 18x + 132x +--R (2) -------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 425log(3x + 2) - 162log(x + 1) - 18x + 132x +--R (3) -------------------------------------------- +--R 27 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 1751 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1751 +r0:=-2/3*x-6*log(1+x)+85/9*log(2+3*x) +--R +--R +--R 85log(3x + 2) - 54log(x + 1) - 6x +--R (2) --------------------------------- +--R 9 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 85log(3x + 2) - 54log(x + 1) - 6x +--R (3) --------------------------------- +--R 9 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1751 +t0:=(5-x)/(2+5*x+3*x^2) +--R +--R +--R - x + 5 +--R (1) ------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 1751 +r0:=-6*log(1+x)+17/3*log(2+3*x) +--R +--R +--R 17log(3x + 2) - 18log(x + 1) +--R (2) ---------------------------- +--R 3 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 17log(3x + 2) - 18log(x + 1) +--R (3) ---------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)clear all + +--S 501 of 1751 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) -------------------- +--R 3 2 +--R 6x + 19x + 19x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 501 + +--S 502 of 1751 +r0:=-6*log(1+x)+13/5*log(3+2*x)+17/5*log(2+3*x) +--R +--R +--R 17log(3x + 2) + 13log(2x + 3) - 30log(x + 1) +--R (2) -------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 17log(3x + 2) + 13log(2x + 3) - 30log(x + 1) +--R (3) -------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 505 + +)clear all + +--S 506 of 1751 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------- +--R 4 3 2 +--R 12x + 56x + 95x + 69x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 506 + +--S 507 of 1751 +r0:=(-13/5)/(3+2*x)-6*log(1+x)+99/25*log(3+2*x)+51/25*log(2+3*x) +--R +--R +--R (2) +--R (102x + 153)log(3x + 2) + (198x + 297)log(2x + 3) +--R + +--R (- 300x - 450)log(x + 1) - 65 +--R / +--R 50x + 75 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (102x + 153)log(3x + 2) + (198x + 297)log(2x + 3) +--R + +--R (- 300x - 450)log(x + 1) - 65 +--R / +--R 50x + 75 +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1751 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 24x + 148x + 358x + 423x + 243x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 511 + +--S 512 of 1751 +r0:=(-13/10)/(3+2*x)^2+(-99/25)/(3+2*x)-6*log(1+x)+597/125*log(3+2*x)+_ + 153/125*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (1224x + 3672x + 2754)log(3x + 2) + (4776x + 14328x + 10746)log(2x + 3) +--R + +--R 2 +--R (- 6000x - 18000x - 13500)log(x + 1) - 1980x - 3295 +--R / +--R 2 +--R 1000x + 3000x + 2250 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (1224x + 3672x + 2754)log(3x + 2) + (4776x + 14328x + 10746)log(2x + 3) +--R + +--R 2 +--R (- 6000x - 18000x - 13500)log(x + 1) - 1980x - 3295 +--R / +--R 2 +--R 1000x + 3000x + 2250 +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 515 + +)clear all + +--S 516 of 1751 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------- +--R 6 5 4 3 2 +--R 48x + 368x + 1160x + 1920x + 1755x + 837x + 162 +--R Type: Fraction(Polynomial(Integer)) +--E 516 + +--S 517 of 1751 +r0:=(-13/15)/(3+2*x)^3+(-99/50)/(3+2*x)^2+(-597/125)/(3+2*x)-6*log(1+x)+_ + 3291/625*log(3+2*x)+459/625*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (22032x + 99144x + 148716x + 74358)log(3x + 2) +--R + +--R 3 2 +--R (157968x + 710856x + 1066284x + 533142)log(2x + 3) +--R + +--R 3 2 2 +--R (- 180000x - 810000x - 1215000x - 607500)log(x + 1) - 71640x - 229770x +--R + +--R - 186715 +--R / +--R 3 2 +--R 30000x + 135000x + 202500x + 101250 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (22032x + 99144x + 148716x + 74358)log(3x + 2) +--R + +--R 3 2 +--R (157968x + 710856x + 1066284x + 533142)log(2x + 3) +--R + +--R 3 2 2 +--R (- 180000x - 810000x - 1215000x - 607500)log(x + 1) - 71640x - 229770x +--R + +--R - 186715 +--R / +--R 3 2 +--R 30000x + 135000x + 202500x + 101250 +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 520 + +)clear all + +--S 521 of 1751 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^2 +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 521 + +--S 522 of 1751 +r0:=15496/9*x+2888/3*x^2+560/3*x^3-(3+2*x)^4*(29+35*x)/(2+5*x+3*x^2)+_ + 83*log(1+x)-1625/27*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 4875x - 8125x - 3250)log(3x + 2) + (6723x + 11205x + 4482)log(x + 1) +--R + +--R 4 3 2 +--R - 72x + 216x - 88824x - 152697x - 63423 +--R / +--R 2 +--R 81x + 135x + 54 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 14625x - 24375x - 9750)log(3x + 2) +--R + +--R 2 4 3 2 +--R (20169x + 33615x + 13446)log(x + 1) - 216x + 648x + 1536x - 11411x +--R + +--R - 11597 +--R / +--R 2 +--R 243x + 405x + 162 +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 1751 +m0:=a0-r0 +--R +--R +--R 89336 +--R (4) ----- +--R 81 +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1751 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^2 +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 526 + +--S 527 of 1751 +r0:=3068/9*x+280/3*x^2-(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)+71*log(1+x)-_ + 1825/27*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 5475x - 9125x - 3650)log(3x + 2) + (5751x + 9585x + 3834)log(x + 1) +--R + +--R 3 2 +--R - 72x - 28158x - 49389x - 21141 +--R / +--R 2 +--R 81x + 135x + 54 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 5475x - 9125x - 3650)log(3x + 2) + (5751x + 9585x + 3834)log(x + 1) +--R + +--R 3 2 +--R - 72x - 120x - 2659x - 2449 +--R / +--R 2 +--R 81x + 135x + 54 +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1751 +m0:=a0-r0 +--R +--R +--R 9346 +--R (4) ---- +--R 27 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1751 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^2 +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 531 + +--S 532 of 1751 +r0:=140/3*x-(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)+59*log(1+x)-535/9*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 1605x - 2675x - 1070)log(3x + 2) + (1593x + 2655x + 1062)log(x + 1) +--R + +--R 2 +--R - 2724x - 5127x - 2349 +--R / +--R 2 +--R 27x + 45x + 18 +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 1605x - 2675x - 1070)log(3x + 2) + (1593x + 2655x + 1062)log(x + 1) +--R + +--R - 587x - 533 +--R / +--R 2 +--R 27x + 45x + 18 +--R Type: Union(Expression(Integer),...) +--E 533 + +--S 534 of 1751 +m0:=a0-r0 +--R +--R +--R 908 +--R (4) --- +--R 9 +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +)clear all + +--S 536 of 1751 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^2 +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 536 + +--S 537 of 1751 +r0:=-(3+2*x)*(29+35*x)/(2+5*x+3*x^2)+94*atanh(5+6*x) +--R +--R +--R 2 2 +--R (282x + 470x + 188)atanh(6x + 5) - 70x - 163x - 87 +--R (2) ---------------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 423x - 705x - 282)log(3x + 2) + (423x + 705x + 282)log(x + 1) - 139x +--R + +--R - 121 +--R / +--R 2 +--R 9x + 15x + 6 +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 1751 +m0:=a0-r0 +--R +--R +--R - 141log(3x + 2) + 141log(x + 1) - 282atanh(6x + 5) + 70 +--R (4) -------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1751 +t0:=(5-x)/(2+5*x+3*x^2)^2 +--R +--R +--R - x + 5 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 541 + +--S 542 of 1751 +r0:=(-29-35*x)/(2+5*x+3*x^2)+70*atanh(5+6*x) +--R +--R +--R 2 +--R (210x + 350x + 140)atanh(6x + 5) - 35x - 29 +--R (2) -------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 105x - 175x - 70)log(3x + 2) + (105x + 175x + 70)log(x + 1) - 35x - 29 +--R --------------------------------------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 1751 +m0:=a0-r0 +--R +--R +--R (4) - 35log(3x + 2) + 35log(x + 1) - 70atanh(6x + 5) +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1751 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R 5 4 3 2 +--R 18x + 87x + 164x + 151x + 68x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 1751 +r0:=-3/5*(37+47*x)/(2+5*x+3*x^2)+23*log(1+x)+52/25*log(3+2*x)-627/25*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 1881x - 3135x - 1254)log(3x + 2) + (156x + 260x + 104)log(2x + 3) +--R + +--R 2 +--R (1725x + 2875x + 1150)log(x + 1) - 705x - 555 +--R / +--R 2 +--R 75x + 125x + 50 +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 1881x - 3135x - 1254)log(3x + 2) + (156x + 260x + 104)log(2x + 3) +--R + +--R 2 +--R (1725x + 2875x + 1150)log(x + 1) - 705x - 555 +--R / +--R 2 +--R 75x + 125x + 50 +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 1751 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------ +--R 6 5 4 3 2 +--R 36x + 228x + 589x + 794x + 589x + 228x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 1751 +r0:=(-454/25)/(3+2*x)-3/5*(37+47*x)/((3+2*x)*(2+5*x+3*x^2))+11*log(1+x)+_ + 812/125*log(3+2*x)-2187/125*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (- 13122x - 41553x - 41553x - 13122)log(3x + 2) +--R + +--R 3 2 +--R (4872x + 15428x + 15428x + 4872)log(2x + 3) +--R + +--R 3 2 2 +--R (8250x + 26125x + 26125x + 8250)log(x + 1) - 6810x - 14875x - 7315 +--R / +--R 3 2 +--R 750x + 2375x + 2375x + 750 +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 13122x - 41553x - 41553x - 13122)log(3x + 2) +--R + +--R 3 2 +--R (4872x + 15428x + 15428x + 4872)log(2x + 3) +--R + +--R 3 2 2 +--R (8250x + 26125x + 26125x + 8250)log(x + 1) - 6810x - 14875x - 7315 +--R / +--R 3 2 +--R 750x + 2375x + 2375x + 750 +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1751 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 1751 +r0:=(-428/25)/(3+2*x)^2+(-2618/125)/(3+2*x)-3/5*(37+47*x)/((3+2*x)^2*_ + (2+5*x+3*x^2))-log(1+x)+8104/625*log(3+2*x)-7479/625*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 89748x - 418824x - 710505x - 516051x - 134622)log(3x + 2) +--R + +--R 4 3 2 +--R (97248x + 453824x + 769880x + 559176x + 145872)log(2x + 3) +--R + +--R 4 3 2 3 +--R (- 7500x - 35000x - 59375x - 43125x - 11250)log(x + 1) - 78540x +--R + +--R 2 +--R - 280810x - 319835x - 113815 +--R / +--R 4 3 2 +--R 7500x + 35000x + 59375x + 43125x + 11250 +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 89748x - 418824x - 710505x - 516051x - 134622)log(3x + 2) +--R + +--R 4 3 2 +--R (97248x + 453824x + 769880x + 559176x + 145872)log(2x + 3) +--R + +--R 4 3 2 3 +--R (- 7500x - 35000x - 59375x - 43125x - 11250)log(x + 1) - 78540x +--R + +--R 2 +--R - 280810x - 319835x - 113815 +--R / +--R 4 3 2 +--R 7500x + 35000x + 59375x + 43125x + 11250 +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 1751 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^2) +--R +--R +--R (1) +--R - x + 5 +--R ---------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 144x + 1344x + 5416x + 12296x + 17185x + 15126x + 8181x + 2484x + 324 +--R Type: Fraction(Polynomial(Integer)) +--E 561 + +--S 562 of 1751 +r0:=(-1258/75)/(3+2*x)^3+(-2212/125)/(3+2*x)^2+(-16522/625)/(3+2*x)-_ + 3/5*(37+47*x)/((3+2*x)^3*(2+5*x+3*x^2))-13*log(1+x)+65816/3125*_ + log(3+2*x)-25191/3125*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 1813752x - 11184804x - 27055134x - 31967379x - 18364239x +--R + +--R - 4080942 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 4738752x + 29222304x + 70686384x + 83520504x + 47979864x +--R + +--R 10662192 +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 2925000x - 18037500x - 43631250x - 51553125x - 29615625x +--R + +--R - 6581250 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R - 2973960x - 14873880x - 27167700x - 21302995x - 5978965 +--R / +--R 5 4 3 2 +--R 225000x + 1387500x + 3356250x + 3965625x + 2278125x + 506250 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 1813752x - 11184804x - 27055134x - 31967379x - 18364239x +--R + +--R - 4080942 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 4738752x + 29222304x + 70686384x + 83520504x + 47979864x +--R + +--R 10662192 +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 2925000x - 18037500x - 43631250x - 51553125x - 29615625x +--R + +--R - 6581250 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R - 2973960x - 14873880x - 27167700x - 21302995x - 5978965 +--R / +--R 5 4 3 2 +--R 225000x + 1387500x + 3356250x + 3965625x + 2278125x + 506250 +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 565 + +)clear all + +--S 566 of 1751 +t0:=(5-x)*(3+2*x)^5/(2+5*x+3*x^2)^3 +--R +--R +--R 6 5 4 3 2 +--R - 32x - 80x + 480x + 2520x + 4590x + 3807x + 1215 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 566 + +--S 567 of 1751 +r0:=-182920/9*x-34760/3*x^2-6800/3*x^3-1/2*(3+2*x)^5*(29+35*x)/_ + (2+5*x+3*x^2)^2+5/2*(3+2*x)^4*(137+170*x)/(2+5*x+3*x^2)-_ + 1085*log(1+x)+29375/27*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (528750x + 1762500x + 2173750x + 1175000x + 235000)log(3x + 2) +--R + +--R 4 3 2 +--R (- 527310x - 1757700x - 2167830x - 1171800x - 234360)log(x + 1) +--R + +--R 5 4 3 2 +--R - 576x + 6126120x + 20591850x + 25603665x + 13944270x + 2805921 +--R / +--R 4 3 2 +--R 486x + 1620x + 1998x + 1080x + 216 +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1586250x + 5287500x + 6521250x + 3525000x + 705000)log(3x + 2) +--R + +--R 4 3 2 +--R (- 1581930x - 5273100x - 6503490x - 3515400x - 703080)log(x + 1) +--R + +--R 5 4 3 2 +--R - 1728x - 5760x + 495150x + 1231835x + 979210x + 247043 +--R / +--R 4 3 2 +--R 1458x + 4860x + 5994x + 3240x + 648 +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 1751 +m0:=a0-r0 +--R +--R +--R 1021340 +--R (4) - ------- +--R 81 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 1751 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^3 +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 of 1751 +r0:=-36892/9*x-3392/3*x^2-1/2*(3+2*x)^4*(29+35*x)/(2+5*x+3*x^2)^2+_ + 1/2*(3+2*x)^3*(695+848*x)/(2+5*x+3*x^2)-883*log(1+x)+23825/27*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (428850x + 1429500x + 1763050x + 953000x + 190600)log(3x + 2) +--R + +--R 4 3 2 +--R (- 429138x - 1430460x - 1764234x - 953640x - 190728)log(x + 1) +--R + +--R 4 3 2 +--R 1971108x + 6712446x + 8456811x + 4665198x + 949887 +--R / +--R 4 3 2 +--R 486x + 1620x + 1998x + 1080x + 216 +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (428850x + 1429500x + 1763050x + 953000x + 190600)log(3x + 2) +--R + +--R 4 3 2 +--R (- 429138x - 1430460x - 1764234x - 953640x - 190728)log(x + 1) +--R + +--R 3 2 +--R 142086x + 353367x + 284958x + 73839 +--R / +--R 4 3 2 +--R 486x + 1620x + 1998x + 1080x + 216 +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 1751 +m0:=a0-r0 +--R +--R +--R 36502 +--R (4) - ----- +--R 9 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 1751 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^3 +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 1751 +r0:=-1/2*(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)^2+141/2*(3+2*x)*(7+8*x)/_ + (2+5*x+3*x^2)-1410*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 4 +--R (- 25380x - 84600x - 104340x - 56400x - 11280)atanh(6x + 5) + 6488x +--R + +--R 3 2 +--R 25862x + 37251x + 23010x + 5139 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (114210x + 380700x + 469530x + 253800x + 50760)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 114210x - 380700x - 469530x - 253800x - 50760)log(x + 1) + 38118x +--R + +--R 2 +--R 95203x + 77330x + 20299 +--R / +--R 4 3 2 +--R 162x + 540x + 666x + 360x + 72 +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 1751 +m0:=a0-r0 +--R +--R +--R 6345log(3x + 2) - 6345log(x + 1) + 12690atanh(6x + 5) - 3244 +--R (4) ------------------------------------------------------------ +--R 9 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 1751 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^3 +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 581 + +--S 582 of 1751 +r0:=-1/2*(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)^2+1/2*(7+8*x)*(199+70*x)/_ + (2+5*x+3*x^2)-1102*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 4 +--R (- 19836x - 66120x - 81548x - 44080x - 8816)atanh(6x + 5) + 1680x +--R + +--R 3 2 +--R 8906x + 15173x + 10466x + 2525 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (29754x + 99180x + 122322x + 66120x + 13224)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 29754x - 99180x - 122322x - 66120x - 13224)log(x + 1) + 9918x +--R + +--R 2 +--R 24799x + 20198x + 5335 +--R / +--R 4 3 2 +--R 54x + 180x + 222x + 120x + 24 +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 1751 +m0:=a0-r0 +--R +--R +--R 1653log(3x + 2) - 1653log(x + 1) + 3306atanh(6x + 5) - 280 +--R (4) ---------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1751 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^3 +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 1751 +r0:=-1/2*(3+2*x)*(29+35*x)/(2+5*x+3*x^2)^2+1/2*(725+842*x)/(2+5*x+3*x^2)-_ + 842*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (- 15156x - 50520x - 62308x - 33680x - 6736)atanh(6x + 5) + 2526x +--R + +--R 2 +--R 6315x + 5146x + 1363 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (7578x + 25260x + 31154x + 16840x + 3368)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 7578x - 25260x - 31154x - 16840x - 3368)log(x + 1) + 2526x +--R + +--R 2 +--R 6315x + 5146x + 1363 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 421log(3x + 2) - 421log(x + 1) + 842atanh(6x + 5) +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1751 +t0:=(5-x)/(2+5*x+3*x^2)^3 +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 591 + +--S 592 of 1751 +r0:=1/2*(-29-35*x)/(2+5*x+3*x^2)^2+105/2*(5+6*x)/(2+5*x+3*x^2)-630*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (- 11340x - 37800x - 46620x - 25200x - 5040)atanh(6x + 5) + 1890x +--R + +--R 2 +--R 4725x + 3850x + 1021 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (5670x + 18900x + 23310x + 12600x + 2520)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 5670x - 18900x - 23310x - 12600x - 2520)log(x + 1) + 1890x +--R + +--R 2 +--R 4725x + 3850x + 1021 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Union(Expression(Integer),...) +--E 593 + +--S 594 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 315log(3x + 2) - 315log(x + 1) + 630atanh(6x + 5) +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +)clear all + +--S 596 of 1751 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 54x + 351x + 963x + 1447x + 1287x + 678x + 196x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 596 + +--S 597 of 1751 +r0:=-3/10*(37+47*x)/(2+5*x+3*x^2)^2+1/50*(9587+11442*x)/(2+5*x+3*x^2)-_ + 233*log(1+x)+208/125*log(3+2*x)+28917/125*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (520506x + 1735020x + 2139858x + 1156680x + 231336)log(3x + 2) +--R + +--R 4 3 2 +--R (3744x + 12480x + 15392x + 8320x + 1664)log(2x + 3) +--R + +--R 4 3 2 +--R (- 524250x - 1747500x - 2155250x - 1165000x - 233000)log(x + 1) +--R + +--R 3 2 +--R 171630x + 429855x + 350570x + 93095 +--R / +--R 4 3 2 +--R 2250x + 7500x + 9250x + 5000x + 1000 +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (520506x + 1735020x + 2139858x + 1156680x + 231336)log(3x + 2) +--R + +--R 4 3 2 +--R (3744x + 12480x + 15392x + 8320x + 1664)log(2x + 3) +--R + +--R 4 3 2 +--R (- 524250x - 1747500x - 2155250x - 1165000x - 233000)log(x + 1) +--R + +--R 3 2 +--R 171630x + 429855x + 350570x + 93095 +--R / +--R 4 3 2 +--R 2250x + 7500x + 9250x + 5000x + 1000 +--R Type: Union(Expression(Integer),...) +--E 598 + +--S 599 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 1751 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 108x + 864x + 2979x + 5783x + 6915x + 5217x + 2426x + 636x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 601 + +--S 602 of 1751 +r0:=12946/125/(3+2*x)-3/10*(37+47*x)/((3+2*x)*(2+5*x+3*x^2)^2)+_ + 1/50*(9293+10848*x)/((3+2*x)*(2+5*x+3*x^2))-175*log(1+x)+_ + 4912/625*log(3+2*x)+104463/625*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3760668x + 18176562x + 34263864x + 31547826x + 14206968x +--R + +--R 2507112 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (176832x + 854688x + 1611136x + 1483424x + 668032x + 117888) +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 3937500x - 19031250x - 35875000x - 33031250x - 14875000x +--R + +--R - 2625000 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R 1165140x + 4697400x + 6842995x + 4275600x + 968615 +--R / +--R 5 4 3 2 +--R 22500x + 108750x + 205000x + 188750x + 85000x + 15000 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 3760668x + 18176562x + 34263864x + 31547826x + 14206968x +--R + +--R 2507112 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (176832x + 854688x + 1611136x + 1483424x + 668032x + 117888) +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 3937500x - 19031250x - 35875000x - 33031250x - 14875000x +--R + +--R - 2625000 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R 1165140x + 4697400x + 6842995x + 4275600x + 968615 +--R / +--R 5 4 3 2 +--R 22500x + 108750x + 205000x + 188750x + 85000x + 15000 +--R Type: Union(Expression(Integer),...) +--E 603 + +--S 604 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 605 + +)clear all + +--S 606 of 1751 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 9 8 7 6 5 4 3 2 +--R 216x + 2052x + 8550x + 20503x + 31179x + 31179x + 20503x + 8550x +--R + +--R 2052x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 606 + +--S 607 of 1751 +r0:=11856/125/(3+2*x)^2+35886/625/(3+2*x)-3/10*(37+47*x)/((3+2*x)^2*_ + (2+5*x+3*x^2)^2)+1/50*(8999+10254*x)/((3+2*x)^2*(2+5*x+3*x^2))-_ + 141*log(1+x)+68592/3125*log(3+2*x)+372033/3125*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 26786376x + 169647048x + 438254874x + 590788404x + 438254874x +--R + +--R 169647048x + 26786376 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R 4938624x + 31277952x + 80801376x + 108924096x + 80801376x +--R + +--R 31277952x + 4938624 +--R * +--R log(2x + 3) +--R + +--R 6 5 4 3 2 +--R - 31725000x - 200925000x - 519056250x - 699712500x - 519056250x +--R + +--R - 200925000x - 31725000 +--R * +--R log(x + 1) +--R + +--R 5 4 3 2 +--R 6459480x + 36556020x + 80482290x + 85904835x + 44358230x + 8857895 +--R / +--R 6 5 4 3 2 +--R 225000x + 1425000x + 3681250x + 4962500x + 3681250x + 1425000x +--R + +--R 225000 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 26786376x + 169647048x + 438254874x + 590788404x + 438254874x +--R + +--R 169647048x + 26786376 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R 4938624x + 31277952x + 80801376x + 108924096x + 80801376x +--R + +--R 31277952x + 4938624 +--R * +--R log(2x + 3) +--R + +--R 6 5 4 3 2 +--R - 31725000x - 200925000x - 519056250x - 699712500x - 519056250x +--R + +--R - 200925000x - 31725000 +--R * +--R log(x + 1) +--R + +--R 5 4 3 2 +--R 6459480x + 36556020x + 80482290x + 85904835x + 44358230x + 8857895 +--R / +--R 6 5 4 3 2 +--R 225000x + 1425000x + 3681250x + 4962500x + 3681250x + 1425000x +--R + +--R 225000 +--R Type: Union(Expression(Integer),...) +--E 608 + +--S 609 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 610 + +)clear all + +--S 611 of 1751 +t0:=x/((-1+x)^3*(3+5*x+4*x^2)^2) +--R +--R +--R x +--R (1) ----------------------------------------------- +--R 7 6 5 4 3 2 +--R 16x - 8x - 23x - 13x + 26x + 14x - 3x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 611 + +--S 612 of 1751 +r0:=(-21/736)/(1-x)^2+(-97/4416)/(1-x)+1/276*(39+44*x)/((1-x)^2*_ + (3+5*x+4*x^2))+11/2304*log(1-x)-11/4608*log(3+5*x+4*x^2)+_ + 6023/52992*atan((5+8*x)/sqrt(23))/sqrt(23) +--R +--R +--R (2) +--R 4 3 2 +--+ 2 +--R (- 1012x + 759x + 759x + 253x - 759)\|23 log(4x + 5x + 3) +--R + +--R 4 3 2 +--+ +--R (2024x - 1518x - 1518x - 506x + 1518)\|23 log(- x + 1) +--R + +--R +--+ +--R 4 3 2 (8x + 5)\|23 +--R (48184x - 36138x - 36138x - 12046x + 36138)atan(-------------) +--R 23 +--R + +--R 3 2 +--+ +--R (9312x - 9768x - 2880x - 1080)\|23 +--R / +--R 4 3 2 +--+ +--R (423936x - 317952x - 317952x - 105984x + 317952)\|23 +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--+ 2 +--R (- 1012x + 759x + 759x + 253x - 759)\|23 log(4x + 5x + 3) +--R + +--R 4 3 2 +--+ +--R (2024x - 1518x - 1518x - 506x + 1518)\|23 log(x - 1) +--R + +--R +--+ +--R 4 3 2 (8x + 5)\|23 +--R (48184x - 36138x - 36138x - 12046x + 36138)atan(-------------) +--R 23 +--R + +--R 3 2 +--+ +--R (9312x - 9768x - 2880x - 1080)\|23 +--R / +--R 4 3 2 +--+ +--R (423936x - 317952x - 317952x - 105984x + 317952)\|23 +--R Type: Union(Expression(Integer),...) +--E 613 + +--S 614 of 1751 +m0:=a0-r0 +--R +--R +--R 11log(x - 1) - 11log(- x + 1) +--R (4) ----------------------------- +--R 2304 +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 1751 +t0:=(x^2+x^3)/(-2+x+x^2) +--R +--R +--R 3 2 +--R x + x +--R (1) ---------- +--R 2 +--R x + x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 616 + +--S 617 of 1751 +r0:=1/2*x^2+2/3*log(1-x)+4/3*log(2+x) +--R +--R +--R 2 +--R 8log(x + 2) + 4log(- x + 1) + 3x +--R (2) --------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 8log(x + 2) + 4log(x - 1) + 3x +--R (3) ------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 618 + +--S 619 of 1751 +m0:=a0-r0 +--R +--R +--R 2log(x - 1) - 2log(- x + 1) +--R (4) 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(2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 7 6 5 4 3 +--R 4148064x - 4657872x - 114284804x - 339936502x - 427075232x +--R + +--R 2 +--R - 246418304x - 53656576x +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 8 7 6 5 4 +--R - 5080320x + 1471104x + 144794208x + 532838896x + 868175930x +--R + +--R 3 2 +--R 733421344x + 313489024x + 53656576x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (3386880x + 8239104x + 6635520x + 1769472)\|2 \|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 8296128x - 27095040x - 32956416x - 17694720x - 3538944)\|3 +--R Type: Union(Expression(Integer),...) +--E 638 + +--S 639 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R 3 2 +-+ | 2 +--R (1095640x + 2665312x + 2146560x + 572416)\|2 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R - 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17694720x - 3538944)\|3 +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 640 + +)clear all + +--S 641 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 +--R (1) (- x + 5)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1751 +r0:=-1/9*(2+5*x+3*x^2)^(3/2)-35/144*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)+35/72*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 6x + 5 2 +-+ | 2 +--R - 35atanh(--------------------) + (- 48x + 340x + 318)\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R -------------------------------------------------------------------------- +--R +-+ +--R 144\|3 +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 2 +-+ | 2 3 2 +--R (6930x + 11200x + 4480)\|2 \|3x + 5x + 2 - 16975x - 41580x +--R + +--R - 33600x - 8960 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R 5 4 3 2 +-+ | 2 +--R (23280x - 107876x - 512070x - 565968x - 188800x)\|3 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +-+ +-+ +--R (- 28512x + 108360x + 737652x + 1213630x + 801968x + 188800x)\|2 \|3 +--R / +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (28512x + 46080x + 18432)\|2 \|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 69840x - 171072x - 138240x - 36864)\|3 +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R 2 +-+ | 2 3 2 +--R (6930x + 11200x + 4480)\|2 \|3x + 5x + 2 - 16975x - 41580x +--R + +--R - 33600x - 8960 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R 2 +-+ | 2 3 2 +--R (6930x + 11200x + 4480)\|2 \|3x + 5x + 2 - 16975x - 41580x +--R + +--R - 33600x - 8960 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 2 +-+ | 2 +--R (125928x + 203520x + 81408)\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ +--R (- 154230x - 377784x - 305280x - 81408)\|2 \|3 +--R / +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (28512x + 46080x + 18432)\|2 \|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 69840x - 171072x - 138240x - 36864)\|3 +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2x + 3 +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1751 +r0:=-311/48*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 13/8*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+_ + 1/24*(73-6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +-+ +-+ 8x + 7 +--R - 311atanh(--------------------) + 78\|3 \|5 atanh(--------------------) +--R +------------+ +------------+ +--R +-+ | 2 +-+ | 2 +--R 2\|3 \|3x + 5x + 2 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (- 12x + 146)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 48\|3 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R +-+ | 2 2 +--R ((6220x + 4976)\|2 \|3x + 5x + 2 - 15239x - 24880x - 9952) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ +-+ +-+ | 2 +--R (1560x + 1248)\|2 \|3 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +-+ +--R (- 3822x - 6240x - 2496)\|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (- 6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (4x + 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (588x - 6194x - 5456x)\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 720x + 6984x + 13014x + 5456x)\|2 \|3 +--R / +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R (960x + 768)\|2 \|3 \|3x + 5x + 2 + (- 2352x - 3840x - 1536)\|3 +--R Type: Union(Expression(Integer),...) +--E 648 + +--S 649 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 2 +--R ((6220x + 4976)\|2 \|3x + 5x + 2 - 15239x - 24880x - 9952) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ +-+ +-+ | 2 +--R (1560x + 1248)\|2 \|3 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +-+ +--R (- 3822x - 6240x - 2496)\|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (- 6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (4x + 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R +-+ | 2 2 +--R ((6220x + 4976)\|2 \|3x + 5x + 2 - 15239x - 24880x - 9952) +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ +-+ | 2 +--R (- 1560x - 1248)\|2 \|3 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +-+ +--R (3822x + 6240x + 2496)\|3 \|5 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R (5840x + 4672)\|3 \|3x + 5x + 2 + (- 7154x - 11680x - 4672)\|2 \|3 +--R / +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R (960x + 768)\|2 \|3 \|3x + 5x + 2 + (- 2352x - 3840x - 1536)\|3 +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 650 + +)clear all + +--S 651 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1751 +r0:=43/8*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 57/8*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/2*(8+x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-+ 6x + 5 +--R (86x + 129)\|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ 8x + 7 +--R (- 114x - 171)\|3 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (- 4x - 32)\|3 \|5 \|3x + 5x + 2 +--R / +--R +-+ +-+ +--R (16x + 24)\|3 \|5 +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (6840x + 15732x + 8208)\|2 \|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 16758x - 52497x - 51984x - 16416)\|3 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 + 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (- 20x - 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (5160x + 11868x + 6192)\|2 \|5 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 12642x - 39603x - 39216x - 12384)\|5 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (588x + 3104x + 2176x)\|3 \|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +-+ +--R (- 720x - 4400x - 5824x - 2176x)\|2 \|3 \|5 +--R / +--R +------------+ +--R 2 +-+ +-+ +-+ | 2 +--R (960x + 2208x + 1152)\|2 \|3 \|5 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ +--R (- 2352x - 7368x - 7296x - 2304)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 653 + +--S 654 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ +-+ | 2 +--R (3420x + 2736)\|2 \|3 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (- 8379x - 13680x - 5472)\|3 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 + 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (- 20x - 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (2580x + 2064)\|2 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (- 6321x - 10320x - 4128)\|5 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (- 2580x - 2064)\|2 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (6321x + 10320x + 4128)\|5 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (3420x + 2736)\|2 \|3 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (- 8379x - 13680x - 5472)\|3 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (- 1280x - 1024)\|3 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +-+ +-+ +--R (1568x + 2560x + 1024)\|2 \|3 \|5 +--R / +--R +------------+ +--R +-+ +-+ +-+ | 2 2 +-+ +-+ +--R (480x + 384)\|2 \|3 \|5 \|3x + 5x + 2 + (- 1176x - 1920x - 768)\|3 \|5 +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 655 + +)clear all + +--S 656 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^3 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1751 +r0:=-13/10*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/8*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+27/80*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3/40*(25+26*x)*sqrt(2+5*x+3*x^2)/_ + (3+2*x) +--R +--R +--R (2) +--R 2 +-+ +-+ 6x + 5 +--R (- 40x - 120x - 90)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 2 8x + 7 +--R (108x + 324x + 243)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (248x + 242)\|5 \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (320x + 960x + 720)\|5 +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 3 2 +-+ | 2 4 +--R (19440x + 73872x + 90396x + 34992)\|2 \|3x + 5x + 2 - 47628x +--R + +--R 3 2 +--R - 220644x - 371547x - 268272x - 69984 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 3 2 +-+ +-+ +-+ | 2 +--R (7200x + 27360x + 33480x + 12960)\|2 \|3 \|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 17640x - 81720x - 137610x - 99360x - 25920)\|3 \|5 +--R * +--R +------------+ +--R +-+ +-+ | 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+------------+ +--R 3 2 | 2 +--R (1) (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1751 +r0:=35/144*(5+6*x)*(2+5*x+3*x^2)^(3/2)-1/15*(2+5*x+3*x^2)^(5/2)+_ + 35/2304*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 35/1152*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 175atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (- 6912x + 27360x + 97584x + 86140x + 23178)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 11520\|3 +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (3395350x + 11032000x + 13372800x + 7168000x + 1433600)\|2 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 8316875x - 33953500x - 55160000x - 44576000x - 17920000x +--R + +--R - 2867200 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 9 8 7 6 +--R 328492800x + 40782240x - 7767404400x - 29890298540x +--R + +--R 5 4 3 2 +--R - 54834244450x - 58293938720x - 36765872000x - 12781112320x +--R + +--R - 1886003200x +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 10 9 8 7 +--R - 402319872x - 385214400x + 9477053280x + 44531601000x +--R + +--R 6 5 4 3 +--R 97535832740x + 126958985650x + 103925540960x + 52683324800x +--R + +--R 2 +--R 15138616320x + 1886003200x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R 4 3 2 +-+ +--R (223511040x + 726220800x + 880312320x + 471859200x + 94371840)\|2 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 547488000x - 2235110400x - 3631104000x - 2934374400x +--R + +--R - 1179648000x - 188743680 +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 2 +-+ +--R (3395350x + 11032000x + 13372800x + 7168000x + 1433600)\|2 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 8316875x - 33953500x - 55160000x - 44576000x - 17920000x +--R + +--R - 2867200 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 4 3 2 +-+ +--R (- 3395350x - 11032000x - 13372800x - 7168000x - 1433600)\|2 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R 8316875x + 33953500x + 55160000x + 44576000x + 17920000x + 2867200 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R (899399112x + 2922282240x + 3542340096x + 1898741760x + 379748352) +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 1101534450x - 4496995560x - 7305705600x - 5903900160x +--R + +--R - 2373427200x - 379748352 +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R 4 3 2 +-+ +--R (223511040x + 726220800x + 880312320x + 471859200x + 94371840)\|2 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 547488000x - 2235110400x - 3631104000x - 2934374400x +--R + +--R - 1179648000x - 188743680 +--R * +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1751 +r0:=1/48*(47-6*x)*(2+5*x+3*x^2)^(3/2)-2011/256*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+65/32*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+1/128*(175-414*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 6033atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R 1560\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 288x + 1776x + 1084x + 2554)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 768\|3 +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 3 2 +-+ | 2 +--R (11824680x + 28765344x + 23166720x + 6177792)\|2 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R - 28964433x - 94597440x - 115061376x - 61777920x - 12355584 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 3 2 +-+ +-+ +-+ +--R (3057600x + 7438080x + 5990400x + 1597440)\|2 \|3 \|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 7489560x - 24460800x - 29752320x - 15974400x - 3194880)\|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (- 6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (4x + 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R 7 6 5 4 3 +--R 1382688x - 4010736x - 27559228x - 60181626x - 68305504x +--R + +--R 2 +--R - 39092352x - 8758272x +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 8 7 6 5 4 +--R - 1693440x + 3500928x + 37869984x + 101746832x + 144683990x +--R + +--R 3 2 +--R 116897248x + 50040192x + 8758272x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (1505280x + 3661824x + 2949120x + 786432)\|2 \|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 3687168x - 12042240x - 14647296x - 7864320x - 1572864)\|3 +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R 3 2 +-+ | 2 +--R (11824680x + 28765344x + 23166720x + 6177792)\|2 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R - 28964433x - 94597440x - 115061376x - 61777920x - 12355584 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 3 2 +-+ +-+ +-+ +--R (3057600x + 7438080x + 5990400x + 1597440)\|2 \|3 \|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 7489560x - 24460800x - 29752320x - 15974400x - 3194880)\|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (- 6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (4x + 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (11824680x + 28765344x + 23166720x + 6177792)\|2 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R - 28964433x - 94597440x - 115061376x - 61777920x - 12355584 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ +-+ +--R (- 3057600x - 7438080x - 5990400x - 1597440)\|2 \|3 \|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (7489560x + 24460800x + 29752320x + 15974400x + 3194880)\|3 \|5 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (10011680x + 24354944x + 19614720x + 5230592)\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 12261754x - 40046720x - 48709888x - 26152960x - 5230592)\|2 \|3 +--R / +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (1505280x + 3661824x + 2949120x + 786432)\|2 \|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 3687168x - 12042240x - 14647296x - 7864320x - 1572864)\|3 +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 710 + +)clear all + +--S 711 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1751 +r0:=-1/6*(21+x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)+3743/192*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-161/32*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)-1/96*(361-726*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R (7486x + 11229)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R (- 1932x - 2898)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 96x + 728x - 512x - 3510)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R (384x + 576)\|3 +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +-+ +--R (3786720x + 14891856x + 21236544x + 13106688x + 2967552)\|2 \|3 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 9275532x - 44207058x - 82287744x - 75054336x - 33632256x +--R + +--R - 5935104 +--R * +--R +-+ +-+ +--R \|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (- 4x - 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R 4 3 2 +-+ +--R (14672560x + 57702088x + 82286112x + 50785024x + 11498496)\|2 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 35940286x - 171290909x - 318843712x - 290816128x - 130316288x +--R + +--R - 22996992 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R 7 6 5 4 3 +--R 460896x - 1989848x - 7126016x + 2805494x + 21470112x +--R + +--R 2 +--R 19252096x + 5241856x +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R + +--R 8 7 6 5 4 +--R - 564480x + 1966656x + 10766272x + 3796564x - 29246266x +--R + +--R 3 2 +--R - 45371424x - 25804416x - 5241856x +--R * +--R +-+ +-+ +--R \|2 \|3 +--R / +--R 4 3 2 +-+ +-+ +--R (752640x + 2959872x + 4220928x + 2605056x + 589824)\|2 \|3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 1843584x - 8786496x - 16355328x - 14917632x - 6684672x +--R + +--R - 1179648 +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 +-+ +-+ +-+ +--R (1893360x + 4605888x + 3709440x + 989184)\|2 \|3 \|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 4637766x - 15146880x - 18423552x - 9891840x - 1978368)\|3 \|5 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (6x\|5 + (12x + 18)\|2 )\|3x + 5x + 2 + (- 4x - 6x)\|2 \|5 +--R + +--R 2 +--R - 40x - 69x - 36 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (7336280x + 17846624x + 14373120x + 3832832)\|2 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R - 17970143x - 58690240x - 71386496x - 38328320x - 7665664 +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 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22314240x + 11980800x + 2396160)\|2 \|3 +--R / +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (376320x + 915456x + 737280x + 196608)\|2 \|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 921792x - 3010560x - 3661824x - 1966080x - 393216)\|3 +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1751 +r0:=-1/4*(8+x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-343/64*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+1329/64*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3/16*(93+43*x)*sqrt(2+5*x+3*x^2)/_ + (3+2*x) +--R +--R +--R (2) +--R 2 +-+ +-+ 6x + 5 +--R (- 1372x - 4116x - 3087)\|3 \|5 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1751 +r0:=35/6*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 1/3*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 6x + 5 +-+ | 2 +--R 35atanh(--------------------) - 2\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ---------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R +-+ | 2 +--R (70\|2 \|3x + 5x + 2 - 175x - 140) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R 10x\|3 \|3x + 5x + 2 + (- 12x - 10x)\|2 \|3 +--R / +--R +------------+ +--R +-+ +-+ | 2 +-+ +--R 12\|2 \|3 \|3x + 5x + 2 + (- 30x - 24)\|3 +--R Type: Union(Expression(Integer),...) +--E 833 + +--S 834 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 +--R (70\|2 \|3x + 5x + 2 - 175x - 140) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 - 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 + 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ | 2 6x + 5 +--R (- 70\|2 \|3x + 5x + 2 + 175x + 140)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +-+ +-+ +--R - 8\|3 \|3x + 5x + 2 + (10x + 8)\|2 \|3 +--R / +--R +------------+ +--R +-+ +-+ | 2 +-+ +--R 12\|2 \|3 \|3x + 5x + 2 + (- 30x - 24)\|3 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 1751 +t0:=(5-x)/((3+2*x)*sqrt(2+5*x+3*x^2)) +--R +--R +--R 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13\|3 atanh(--------------------) +--R +------------+ +------------+ +--R +-+ | 2 +-+ | 2 +--R 2\|3 \|3x + 5x + 2 2\|5 \|3x + 5x + 2 +--R / +--R +-+ +-+ +--R 2\|3 \|5 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 1751 +t0:=(5-x)/((3+2*x)^2*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------ +--R +------------+ +--R 2 | 2 +--R (4x + 12x + 9)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1751 +r0:=47/10*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/5*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R +------------+ +--R 8x + 7 +-+ | 2 +--R (94x + 141)atanh(--------------------) - 26\|5 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R (2) -------------------------------------------------------------- +--R +-+ +--R (20x + 30)\|5 +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R +-+ | 2 2 +--R ((564x + 846)\|2 \|3x + 5x + 2 - 1410x - 3243x - 1692) +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R 182x\|5 \|3x + 5x + 2 + (- 208x - 182x)\|2 \|5 +--R / +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R (120x + 180)\|2 \|5 \|3x + 5x + 2 + (- 300x - 690x - 360)\|5 +--R Type: Union(Expression(Integer),...) +--E 843 + +--S 844 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 +--R (282\|2 \|3x + 5x + 2 - 705x - 564) +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R +-+ | 2 8x + 7 +--R (- 282\|2 \|3x + 5x + 2 + 705x + 564)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +-+ +-+ +--R - 104\|5 \|3x + 5x + 2 + (130x + 104)\|2 \|5 +--R / +--R +------------+ +--R +-+ +-+ | 2 +-+ +--R 60\|2 \|5 \|3x + 5x + 2 + (- 150x - 120)\|5 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +)clear all + +--S 846 of 1751 +t0:=(5-x)/((3+2*x)^3*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R +------------+ +--R 3 2 | 2 +--R (8x + 36x + 54x + 27)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1751 +r0:=389/100*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/10*sqrt(2+5*x+3*x^2)/(3+2*x)^2-73/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 8x + 7 +--R (1556x + 4668x + 3501)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (- 584x - 1006)\|5 \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (400x + 1200x + 900)\|5 +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 3 2 | 2 +--R (560160x + 2128608x + 2604744x + 1008288)\|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 686196x - 3178908x - 5353029x - 3865104x - 1008288)\|2 +--R * +--R log +--R +------------+ +--R 2 +-+ 2 +-+ | 2 +--R ((280x + 552x + 288)\|5 + (- 230x - 240x)\|2 )\|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ 3 2 +--R (- 344x - 961x - 912x - 288)\|2 \|5 + 560x + 1060x + 480x +--R / +--R +------------+ +--R 2 | 2 +--R (80x + 184x + 96)\|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 98x - 307x - 304x - 96)\|2 +--R + +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (96584x + 252478x + 144048x)\|2 \|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 236368x - 815360x - 865076x - 288096x)\|5 +--R / +--R +------------+ +--R 3 2 +-+ | 2 +--R (144000x + 547200x + 669600x + 259200)\|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 176400x - 817200x - 1376100x - 993600x - 259200)\|2 \|5 +--R Type: Union(Expression(Integer),...) +--E 848 + +--S 849 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R | 2 +--R (140040x + 112032)\|3x + 5x + 2 +--R + +--R 2 +-+ +--R (- 171549x - 280080x - 112032)\|2 +--R * +--R log +--R +------------+ +--R 2 +-+ 2 +-+ | 2 +--R ((280x + 552x + 288)\|5 + (- 230x - 240x)\|2 )\|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ 3 2 +--R (- 344x - 961x - 912x - 288)\|2 \|5 + 560x + 1060x + 480x +--R / +--R +------------+ +--R 2 | 2 +--R (80x + 184x + 96)\|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 98x - 307x - 304x - 96)\|2 +--R + +--R +------------+ +--R | 2 +--R (- 140040x - 112032)\|3x + 5x + 2 +--R + +--R 2 +-+ +--R (171549x + 280080x + 112032)\|2 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R (- 40240x - 32192)\|2 \|5 \|3x + 5x + 2 + (98588x + 160960x + 64384)\|5 +--R / +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R (36000x + 28800)\|5 \|3x + 5x + 2 + (- 44100x - 72000x - 28800)\|2 \|5 +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 1751 +t0:=(5-x)/((3+2*x)^4*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------ +--R +------------+ +--R 4 3 2 | 2 +--R (16x + 96x + 216x + 216x + 81)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1751 +r0:=331/100*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/15*sqrt(2+5*x+3*x^2)/(3+2*x)^3-49/30*sqrt(2+5*x+3*x^2)/(3+2*x)^2-_ + 72/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 8x + 7 +--R (7944x + 35748x + 53622x + 26811)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 2 +-+ | 2 +--R (- 3456x - 11348x - 9506)\|5 \|3x + 5x + 2 +--R / +--R 3 2 +-+ +--R (2400x + 10800x + 16200x + 8100)\|5 +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 42468624x + 259744968x + 622980396x + 730170774x + 416964672x +--R + +--R 92658816 +--R * +--R +------------+ +--R +-+ | 2 +--R \|2 \|3x + 5x + 2 +--R + +--R 6 5 4 3 +--R - 104026680x - 722931804x - 2054741418x - 3052566405x +--R + +--R 2 +--R - 2496962052x - 1065576384x - 185317632 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R 5 4 3 2 +-+ +--R (15141312x + 75268460x + 136296206x + 105169680x + 29158272x)\|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R - 18544048x - 107637840x - 243491160x - 266847110x - 141617520x +--R + +--R - 29158272x +--R * +--R +-+ +-+ +--R \|2 \|5 +--R / +--R 5 4 3 2 +--R 12830400x + 78472800x + 188211600x + 220595400x + 125971200x +--R + +--R 27993600 +--R * +--R +------------+ +--R +-+ +-+ | 2 +--R \|2 \|5 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R - 31428000x - 218408400x - 620767800x - 922225500x - 754369200x +--R + +--R - 321926400x - 55987200 +--R * +--R +-+ +--R \|5 +--R Type: Union(Expression(Integer),...) +--E 853 + +--S 854 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R 2 +-+ | 2 3 +--R (5308578x + 8579520x + 3431808)\|2 \|3x + 5x + 2 - 13003335x +--R + +--R 2 +--R - 31851468x - 25738560x - 6863616 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R 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log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R 2 +-+ | 2 3 2 +--R (- 48906x - 79040x - 31616)\|2 \|3x + 5x + 2 + 119795x + 293436x +--R + +--R 237120x + 63232 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 2 +-+ | 2 +--R (- 312444x - 504960x - 201984)\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ +--R (382665x + 937332x + 757440x + 201984)\|2 \|3 +--R / +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (1782x + 2880x + 1152)\|2 \|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 4365x - 10692x - 8640x - 2304)\|3 +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 875 + +)clear all + +--S 876 of 1751 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1751 +r0:=2*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-2*(3+2*x)^2*_ + (29+35*x)/sqrt(2+5*x+3*x^2)+184/3*sqrt(2+5*x+3*x^2)+140/3*(3+2*x)*_ + sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R +-+ | 2 6x + 5 2 +--R 6\|3 \|3x + 5x + 2 atanh(--------------------) - 4x - 398x - 358 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ------------------------------------------------------------------ +--R +------------+ +--R | 2 +--R 3\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 2 +-+ +-+ | 2 +--R (294x + 480x + 192)\|2 \|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 720x - 1776x - 1440x - 384)\|3 +--R * +--R +------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|3 + 2\|2 )\|3x + 5x + 2 + 2x\|2 \|3 - 6x - 5x - 4 +--R log(-------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R 3 2 | 2 +--R (160x - 1494x - 1584x)\|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 196x + 1658x + 3474x + 1584x)\|2 +--R / +--R +------------+ +--R 2 +-+ | 2 3 2 +--R (147x + 240x + 96)\|2 \|3x + 5x + 2 - 360x - 888x - 720x - 192 +--R Type: Union(Expression(Integer),...) +--E 878 + +--S 879 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R ((240x + 192)\|3 \|3x + 5x + 2 + (- 294x - 480x - 192)\|2 \|3 ) +--R * +--R +------------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- 2x\|3 + 2\|2 )\|3x + 5x + 2 + 2x\|2 \|3 - 6x - 5x - 4 +--R log(-------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R ((- 240x - 192)\|3 \|3x + 5x + 2 + (294x + 480x + 192)\|2 \|3 ) +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 2 +--R (- 7160x - 5728)\|2 \|3x + 5x + 2 + 17542x + 28640x + 11456 +--R / +--R +------------+ +--R | 2 2 +-+ +--R (120x + 96)\|3x + 5x + 2 + (- 147x - 240x - 96)\|2 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 880 + +)clear all + +--S 881 of 1751 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1751 +r0:=-2/3*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 2*(3+2*x)*(29+35*x)/sqrt(2+5*x+3*x^2)+140/3*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 6x + 5 +-+ +--R - 2\|3x + 5x + 2 atanh(--------------------) + (- 278x - 242)\|3 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ------------------------------------------------------------------ +--R +------------+ +--R +-+ | 2 +--R 3\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R | 2 2 +-+ +--R ((10x + 8)\|3x + 5x + 2 + (- 12x - 20x - 8)\|2 ) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R - 49x\|2 \|3 \|3x + 5x + 2 + (62x + 98x)\|3 +--R / +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R (15x + 12)\|3 \|3x + 5x + 2 + (- 18x - 30x - 12)\|2 \|3 +--R Type: Union(Expression(Integer),...) +--E 883 + +--S 884 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 +--R (4\|2 \|3x + 5x + 2 - 10x - 8) +--R * +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (2\|2 \|3 + 6x)\|3x + 5x + 2 + (- 6x - 5x - 4)\|3 - 6x\|2 +--R log(---------------------------------------------------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|2 \|3x + 5x + 2 - 5x - 4 +--R + +--R +------------+ +--R +-+ | 2 6x + 5 +--R (4\|2 \|3x + 5x + 2 - 10x - 8)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +-+ +-+ +--R - 484\|3 \|3x + 5x + 2 + (605x + 484)\|2 \|3 +--R / +--R +------------+ +--R +-+ +-+ | 2 +-+ +--R 6\|2 \|3 \|3x + 5x + 2 + (- 15x - 12)\|3 +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 1751 +t0:=(5-x)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R - x + 5 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1751 +r0:=-2*(29+35*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R - 70x - 58 +--R (2) --------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1751 +a0:=integrate(t0,x) +--R +--R +--R +------------+ +--R | 2 2 +-+ +--R - 10x\|3x + 5x + 2 + (- 2x + 10x)\|2 +--R (3) -------------------------------------------- +--R +------------+ +--R +-+ | 2 2 +--R (5x + 4)\|2 \|3x + 5x + 2 - 12x - 20x - 8 +--R Type: Union(Expression(Integer),...) +--E 888 + +--S 889 of 1751 +m0:=a0-r0 +--R +--R +--R +------------+ +--R +-+ | 2 +--R - 116\|2 \|3x + 5x + 2 + 290x + 232 +--R (4) ------------------------------------- +--R +------------+ +--R | 2 +-+ +--R 4\|3x + 5x + 2 + (- 5x - 4)\|2 +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 1751 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------- +--R +------------+ +--R 3 2 | 2 +--R (6x + 19x + 19x + 6)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1751 +r0:=26/5*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 8x + 7 +-+ +--R 26\|3x + 5x + 2 atanh(--------------------) + (- 282x - 222)\|5 +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R (2) ----------------------------------------------------------------- +--R +------------+ +--R +-+ | 2 +--R 5\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R | 2 2 +-+ +--R ((130x + 104)\|3x + 5x + 2 + (- 156x - 260x - 104)\|2 ) +--R * +--R log +--R +------------+ +--R 2 +-+ 2 +-+ | 2 +--R ((280x + 552x + 288)\|5 + (- 230x - 240x)\|2 )\|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ 3 2 +--R (- 344x - 961x - 912x - 288)\|2 \|5 + 560x + 1060x + 480x +--R / +--R +------------+ +--R 2 | 2 +--R (80x + 184x + 96)\|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 98x - 307x - 304x - 96)\|2 +--R + +--R +------------+ +--R +-+ +-+ | 2 2 +-+ +--R 9x\|2 \|5 \|3x + 5x + 2 + (- 78x - 18x)\|5 +--R / +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R (25x + 20)\|5 \|3x + 5x + 2 + (- 30x - 50x - 20)\|2 \|5 +--R Type: Union(Expression(Integer),...) +--E 893 + +--S 894 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +-+ | 2 +--R (52\|2 \|3x + 5x + 2 - 130x - 104) +--R * +--R log +--R +------------+ +--R 2 +-+ 2 +-+ | 2 +--R ((280x + 552x + 288)\|5 + (- 230x - 240x)\|2 )\|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ 3 2 +--R (- 344x - 961x - 912x - 288)\|2 \|5 + 560x + 1060x + 480x +--R / +--R +------------+ +--R 2 | 2 +--R (80x + 184x + 96)\|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 98x - 307x - 304x - 96)\|2 +--R + +--R +------------+ +--R +-+ | 2 8x + 7 +--R (- 52\|2 \|3x + 5x + 2 + 130x + 104)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +-+ +-+ +--R - 444\|5 \|3x + 5x + 2 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Expression(Integer) +--E 897 + +--S 898 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R 3 2 +-+ | 2 4 +--R (88788x + 278142x + 275424x + 86976)\|2 \|3x + 5x + 2 - 217440x +--R + +--R 3 2 +--R - 862512x - 1239408x - 768288x - 173952 +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (31604x + 62974x + 26992x)\|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (- 38856x - 109478x - 96714x - 26992x)\|2 \|5 +--R / +--R +------------+ +--R 3 2 +-+ +-+ | 2 +--R (7350x + 23025x + 22800x + 7200)\|2 \|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 18000x - 71400x - 102600x - 63600x - 14400)\|5 +--R Type: Union(Expression(Integer),...) +--E 898 + +--S 899 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R | 2 2 +-+ +--R ((36240x + 28992)\|3x + 5x + 2 + (- 44394x - 72480x - 28992)\|2 ) +--R * +--R log +--R +------------+ +--R +-+ +-+ | 2 +--R ((12x + 18)\|2 \|5 - 30x)\|3x + 5x + 2 +--R + +--R 2 +-+ 2 +-+ +--R (- 40x - 69x - 36)\|5 + (20x + 30x)\|2 +--R / +--R +------------+ +--R +-+ | 2 2 +--R (4x + 6)\|2 \|3x + 5x + 2 - 10x - 23x - 12 +--R + +--R +------------+ +--R | 2 2 +-+ +--R ((- 36240x - 28992)\|3x + 5x + 2 + (44394x + 72480x + 28992)\|2 ) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (- 56440x - 45152)\|2 \|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (138278x + 225760x + 90304)\|5 +--R / +--R +------------+ +--R +-+ | 2 2 +-+ +-+ +--R (3000x + 2400)\|5 \|3x + 5x + 2 + (- 3675x - 6000x - 2400)\|2 \|5 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +)clear all + +--S 901 of 1751 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 | 2 +--R (24x + 148x + 358x + 423x + 243x + 54)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1751 +r0:=483/25*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/((3+2*x)^2*sqrt(2+5*x+3*x^2))-166/5*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2-864/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R 2 | 2 8x + 7 +--R (1932x + 5796x + 4347)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 5184x - 18906x - 21976x - 7954)\|5 +--R / +--R +------------+ +--R 2 +-+ | 2 +--R (100x + 300x + 225)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 8433180x + 45956484x + 97637967x + 101006892x + 50912064x +--R + +--R 10015488 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4 3 2 +--R - 20592x - 30096x + 447048x + 2029120x + 3733305x + 3496257x +--R + +--R 1636821x + 301887 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 6435 +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2) +--R +--R +--R 5 4 3 2 +------+ +--R (1) (- 12x + 4x + 185x + 406x + 327x + 90)\|2x + 3 +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1751 +r0:=65/56*(3+2*x)^(7/2)-109/72*(3+2*x)^(9/2)+47/88*(3+2*x)^(11/2)-_ + 3/104*(3+2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 16632x + 4284x + 375242x + 1116057x + 1364067x + 758349x +--R + +--R 157383 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 9009 +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 16632x + 4284x + 375242x + 1116057x + 1364067x + 758349x +--R + +--R 157383 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 9009 +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +------+ +--R (1) (- 6x + 11x + 76x + 89x + 30)\|2x + 3 +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1751 +r0:=13/8*(3+2*x)^(5/2)-109/56*(3+2*x)^(7/2)+47/72*(3+2*x)^(9/2)-_ + 3/88*(3+2*x)^(11/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 756x + 1568x + 15627x + 28143x + 19251x + 4617)\|2x + 3 +--R (2) --------------------------------------------------------------- +--R 693 +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +------+ +--R (- 756x + 1568x + 15627x + 28143x + 19251x + 4617)\|2x + 3 +--R (3) --------------------------------------------------------------- +--R 693 +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)*sqrt(3+2*x) +--R +--R +--R 3 2 +------+ +--R (1) (- 3x + 10x + 23x + 10)\|2x + 3 +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1751 +r0:=65/24*(3+2*x)^(3/2)-109/40*(3+2*x)^(5/2)+47/56*(3+2*x)^(7/2)-_ + 1/24*(3+2*x)^(9/2) +--R +--R +--R 4 3 2 +------+ +--R (- 70x + 285x + 1083x + 949x + 303)\|2x + 3 +--R (2) ----------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +------+ +--R (- 70x + 285x + 1083x + 949x + 303)\|2x + 3 +--R (3) ----------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)/sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ----------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1751 +r0:=-109/24*(3+2*x)^(3/2)+47/40*(3+2*x)^(5/2)-3/56*(3+2*x)^(7/2)+_ + 65/8*sqrt(3+2*x) +--R +--R +--R 3 2 +------+ +--R (- 45x + 291x + 223x + 381)\|2x + 3 +--R (2) -------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +------+ +--R (- 45x + 291x + 223x + 381)\|2x + 3 +--R (3) -------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(3/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ----------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1751 +r0:=47/24*(3+2*x)^(3/2)-3/40*(3+2*x)^(5/2)+(-65/8)/sqrt(3+2*x)-_ + 109/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 9x + 77x - 117x - 501 +--R (2) ------------------------- +--R +------+ +--R 15\|2x + 3 +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 9x + 77x - 117x - 501 +--R (3) ------------------------- +--R +------+ +--R 15\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 988 + +--S 989 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(5/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ------------------------ +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1751 +r0:=(-65/24)/(3+2*x)^(3/2)-1/8*(3+2*x)^(3/2)+109/8/sqrt(3+2*x)+_ + 47/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 3x + 57x + 273x + 263 +--R (2) ------------------------- +--R +------+ +--R (6x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 3x + 57x + 273x + 263 +--R (3) ------------------------- +--R +------+ +--R (6x + 9)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(7/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1751 +r0:=(-13/8)/(3+2*x)^(5/2)+109/24/(3+2*x)^(3/2)+(-47/8)/sqrt(3+2*x)-_ + 3/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 9x - 111x - 245x - 153 +--R (2) -------------------------- +--R 2 +------+ +--R (12x + 36x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 9x - 111x - 245x - 153 +--R (3) -------------------------- +--R 2 +------+ +--R (12x + 36x + 27)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 998 + +--S 999 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1000 + +)clear all + +--S 1001 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 72x - 204x + 958x + 5955x + 13215x + 15577x + 10359x + 3672x +--R + +--R 540 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1751 +r0:=325/288*(3+2*x)^(9/2)-1065/352*(3+2*x)^(11/2)+651/208*(3+2*x)^(13/2)-_ + 359/240*(3+2*x)^(15/2)+165/544*(3+2*x)^(17/2)-9/608*(3+2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R - 15752880x - 51274080x + 262729896x + 1939330008x + 5196312621x +--R + +--R 4 3 2 +--R 7690154020x + 6844462215x + 3651616134x + 1077299892x + 135278424 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 2078505 +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 +--R - 15752880x - 51274080x + 262729896x + 1939330008x + 5196312621x +--R + +--R 4 3 2 +--R 7690154020x + 6844462215x + 3651616134x + 1077299892x + 135278424 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 2078505 +--R Type: Union(Expression(Integer),...) +--E 1003 + +--S 1004 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^2 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +------+ +--R (- 36x - 48x + 551x + 2151x + 3381x + 2717x + 1104x + 180)\|2x + 3 +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1751 +r0:=325/224*(3+2*x)^(7/2)-355/96*(3+2*x)^(9/2)+651/176*(3+2*x)^(11/2)-_ + 359/208*(3+2*x)^(13/2)+11/32*(3+2*x)^(15/2)-9/544*(3+2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 216216x - 348348x + 4324782x + 20560239x + 40692820x +--R + +--R 3 2 +--R 43843941x + 26848368x + 8789688x + 1198476 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 51051 +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R - 216216x - 348348x + 4324782x + 20560239x + 40692820x +--R + +--R 3 2 +--R 43843941x + 26848368x + 8789688x + 1198476 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 51051 +--R Type: Union(Expression(Integer),...) +--E 1008 + +--S 1009 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1010 + +)clear all + +--S 1011 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^2 +--R +--R +--R 6 5 4 3 2 +------+ +--R (1) (- 18x + 3x + 271x + 669x + 687x + 328x + 60)\|2x + 3 +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1751 +r0:=65/32*(3+2*x)^(5/2)-1065/224*(3+2*x)^(7/2)+217/48*(3+2*x)^(9/2)-_ + 359/176*(3+2*x)^(11/2)+165/416*(3+2*x)^(13/2)-3/160*(3+2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 36036x + 2772x + 747579x + 2342620x + 3236325x + 2333766x +--R + +--R 857988x + 128736 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15015 +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 36036x + 2772x + 747579x + 2342620x + 3236325x + 2333766x +--R + +--R 857988x + 128736 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15015 +--R Type: Union(Expression(Integer),...) +--E 1013 + +--S 1014 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1015 + +)clear all + +--S 1016 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^2*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +------+ +--R (1) (- 9x + 15x + 113x + 165x + 96x + 20)\|2x + 3 +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1751 +r0:=325/96*(3+2*x)^(3/2)-213/32*(3+2*x)^(5/2)+93/16*(3+2*x)^(7/2)-_ + 359/144*(3+2*x)^(9/2)+15/32*(3+2*x)^(11/2)-9/416*(3+2*x)^(13/2) +--R +--R +--R 6 5 4 3 2 +------+ +--R (- 162x + 297x + 3028x + 5991x + 5292x + 2208x + 396)\|2x + 3 +--R (2) ------------------------------------------------------------------- +--R 117 +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 6 5 4 3 2 +------+ +--R (- 162x + 297x + 3028x + 5991x + 5292x + 2208x + 396)\|2x + 3 +--R (3) ------------------------------------------------------------------- +--R 117 +--R Type: Union(Expression(Integer),...) +--E 1018 + +--S 1019 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^2/sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1751 +r0:=-355/32*(3+2*x)^(3/2)+651/80*(3+2*x)^(5/2)-359/112*(3+2*x)^(7/2)+_ + 55/96*(3+2*x)^(9/2)-9/352*(3+2*x)^(11/2)+325/32*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +------+ +--R (- 945x + 3500x + 12645x + 15354x + 6252x + 4344)\|2x + 3 +--R (2) -------------------------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +------+ +--R (- 945x + 3500x + 12645x + 15354x + 6252x + 4344)\|2x + 3 +--R (3) -------------------------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 1023 + +--S 1024 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1025 + +)clear all + +--S 1026 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1751 +r0:=217/16*(3+2*x)^(3/2)-359/80*(3+2*x)^(5/2)+165/224*(3+2*x)^(7/2)-_ + 1/32*(3+2*x)^(9/2)+(-325/32)/sqrt(3+2*x)-1065/32*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 35x + 150x + 431x + 632x - 432x - 1996 +--R (2) -------------------------------------------- +--R +------+ +--R 35\|2x + 3 +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 35x + 150x + 431x + 632x - 432x - 1996 +--R (3) -------------------------------------------- +--R +------+ +--R 35\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1028 + +--S 1029 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1030 + +)clear all + +--S 1031 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(5/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1751 +r0:=(-325/96)/(3+2*x)^(3/2)-359/48*(3+2*x)^(3/2)+33/32*(3+2*x)^(5/2)-_ + 9/224*(3+2*x)^(7/2)+1065/32/sqrt(3+2*x)+651/16*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 27x + 144x + 215x + 1530x + 7164x + 7024 +--R (2) ---------------------------------------------- +--R +------+ +--R (42x + 63)\|2x + 3 +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 27x + 144x + 215x + 1530x + 7164x + 7024 +--R (3) ---------------------------------------------- +--R +------+ +--R (42x + 63)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1033 + +--S 1034 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1035 + +)clear all + +--S 1036 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(7/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1751 +r0:=(-65/32)/(3+2*x)^(5/2)+355/32/(3+2*x)^(3/2)+55/32*(3+2*x)^(3/2)-_ + 9/160*(3+2*x)^(5/2)+(-651/16)/sqrt(3+2*x)-359/16*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 9x + 70x - 275x - 3300x - 6760x - 4076 +--R (2) -------------------------------------------- +--R 2 +------+ +--R (20x + 60x + 45)\|2x + 3 +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 9x + 70x - 275x - 3300x - 6760x - 4076 +--R (3) -------------------------------------------- +--R 2 +------+ +--R (20x + 60x + 45)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1038 + +--S 1039 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1040 + +)clear all + +--S 1041 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 216x - 972x + 1710x + 22247x + 71336x + 124716x + 135392x +--R + +--R 3 2 +--R 93965x + 40698x + 10044x + 1080 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1751 +r0:=1625/1152*(3+2*x)^(9/2)-7925/1408*(3+2*x)^(11/2)+_ + 16005/1664*(3+2*x)^(13/2)-17201/1920*(3+2*x)^(15/2)+_ + 10475/2176*(3+2*x)^(17/2)-3519/2432*(3+2*x)^(19/2)+_ + 27/128*(3+2*x)^(21/2)-27/2944*(3+2*x)^(23/2) +--R +--R +--R (2) +--R 11 10 9 8 +--R - 897914160x - 4489570800x + 8356902840x + 126274674240x +--R + +--R 7 6 5 4 +--R 465368338149x + 952484547267x + 1244240822034x + 1081998930520x +--R + +--R 3 2 +--R 626194644675x + 232269229971x + 50041179918x + 4766652846 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 47805615 +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 10 9 8 +--R - 897914160x - 4489570800x + 8356902840x + 126274674240x +--R + +--R 7 6 5 4 +--R 465368338149x + 952484547267x + 1244240822034x + 1081998930520x +--R + +--R 3 2 +--R 626194644675x + 232269229971x + 50041179918x + 4766652846 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 47805615 +--R Type: Union(Expression(Integer),...) +--E 1043 + +--S 1044 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1045 + +)clear all + +--S 1046 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 108x - 324x + 1341x + 9112x + 22000x + 29358x + 23659x + 11494x +--R + +--R 3108x + 360 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1751 +r0:=1625/896*(3+2*x)^(7/2)-7925/1152*(3+2*x)^(9/2)+_ + 1455/128*(3+2*x)^(11/2)-17201/1664*(3+2*x)^(13/2)+_ + 2095/384*(3+2*x)^(15/2)-207/128*(3+2*x)^(17/2)+_ + 567/2432*(3+2*x)^(19/2)-9/896*(3+2*x)^(21/2) +--R +--R +--R (2) +--R 10 9 8 7 6 +--R - 160056x - 543348x + 2428218x + 19193889x + 54383679x +--R + +--R 5 4 3 2 +--R 87436314x + 88365578x + 57400347x + 23339691x + 5418846x + 549342 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15561 +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 7 6 +--R - 160056x - 543348x + 2428218x + 19193889x + 54383679x +--R + +--R 5 4 3 2 +--R 87436314x + 88365578x + 57400347x + 23339691x + 5418846x + 549342 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15561 +--R Type: Union(Expression(Integer),...) +--E 1048 + +--S 1049 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1050 + +)clear all + +--S 1051 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (- 54x - 81x + 792x + 3368x + 5948x + 5757x + 3194x + 956x + 120) +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1751 +r0:=325/128*(3+2*x)^(5/2)-7925/896*(3+2*x)^(7/2)+_ + 5335/384*(3+2*x)^(9/2)-17201/1408*(3+2*x)^(11/2)+_ + 10475/1664*(3+2*x)^(13/2)-1173/640*(3+2*x)^(15/2)+_ + 567/2176*(3+2*x)^(17/2)-27/2432*(3+2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R - 27567540x - 48648600x + 511413903x + 2573238129x + 5488936698x +--R + +--R 4 3 2 +--R 6671966560x + 4954126305x + 2231396337x + 561646746x + 61003962 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 4849845 +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 +--R - 27567540x - 48648600x + 511413903x + 2573238129x + 5488936698x +--R + +--R 4 3 2 +--R 6671966560x + 4954126305x + 2231396337x + 561646746x + 61003962 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 4849845 +--R Type: Union(Expression(Integer),...) +--E 1053 + +--S 1054 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1055 + +)clear all + +--S 1056 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^3*sqrt(3+2*x) +--R +--R +--R 7 5 4 3 2 +------+ +--R (1) (- 27x + 396x + 1090x + 1339x + 870x + 292x + 40)\|2x + 3 +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1751 +r0:=1625/384*(3+2*x)^(3/2)-1585/128*(3+2*x)^(5/2)+_ + 16005/896*(3+2*x)^(7/2)-17201/1152*(3+2*x)^(9/2)+_ + 10475/1408*(3+2*x)^(11/2)-3519/1664*(3+2*x)^(13/2)+_ + 189/640*(3+2*x)^(15/2)-27/2176*(3+2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 2432430x - 243243x + 47045691x + 157479462x + 243619810x +--R + +--R 3 2 +--R 212153055x + 107295183x + 29433414x + 3591558 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 765765 +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R - 2432430x - 243243x + 47045691x + 157479462x + 243619810x +--R + +--R 3 2 +--R 212153055x + 107295183x + 29433414x + 3591558 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 765765 +--R Type: Union(Expression(Integer),...) +--E 1058 + +--S 1059 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1060 + +)clear all + +--S 1061 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^3/sqrt(3+2*x) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1061 + +--S 1062 of 1751 +r0:=-7925/384*(3+2*x)^(3/2)+3201/128*(3+2*x)^(5/2)-17201/896*(3+2*x)^(7/2)+_ + 10475/1152*(3+2*x)^(9/2)-3519/1408*(3+2*x)^(11/2)+567/1664*(3+2*x)^(13/2)-_ + 9/640*(3+2*x)^(15/2)+1625/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 81081x + 130977x + 1407294x + 3109960x + 3285105x + 1924641x +--R + +--R 535098x + 196506 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 45045 +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 81081x + 130977x + 1407294x + 3109960x + 3285105x + 1924641x +--R + +--R 535098x + 196506 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 45045 +--R Type: Union(Expression(Integer),...) +--E 1063 + +--S 1064 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1065 + +)clear all + +--S 1066 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(3/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1751 +r0:=5335/128*(3+2*x)^(3/2)-17201/640*(3+2*x)^(5/2)+10475/896*(3+2*x)^(7/2)-_ + 391/128*(3+2*x)^(9/2)+567/1408*(3+2*x)^(11/2)-27/1664*(3+2*x)^(13/2)+_ + (-1625/128)/sqrt(3+2*x)-7925/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 10395x + 19845x + 180530x + 392500x + 398339x + 256433x - 77138x +--R + +--R - 431614 +--R / +--R +------+ +--R 5005\|2x + 3 +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 10395x + 19845x + 180530x + 392500x + 398339x + 256433x - 77138x +--R + +--R - 431614 +--R / +--R +------+ +--R 5005\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1068 + +--S 1069 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1070 + +)clear all + +--S 1071 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(5/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1751 +r0:=(-1625/384)/(3+2*x)^(3/2)-17201/384*(3+2*x)^(3/2)+2095/128*(3+2*x)^(5/2)-_ + 3519/896*(3+2*x)^(7/2)+63/128*(3+2*x)^(9/2)-27/1408*(3+2*x)^(11/2)+_ + 7925/128/sqrt(3+2*x)+16005/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 567x + 1323x + 9666x + 21360x + 17663x + 42003x + 184566x + 181486 +--R -------------------------------------------------------------------------- +--R +------+ +--R (462x + 693)\|2x + 3 +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 567x + 1323x + 9666x + 21360x + 17663x + 42003x + 184566x + 181486 +--R -------------------------------------------------------------------------- +--R +------+ +--R (462x + 693)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1073 + +--S 1074 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1075 + +)clear all + +--S 1076 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(7/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1751 +r0:=(-325/128)/(3+2*x)^(5/2)+7925/384/(3+2*x)^(3/2)+10475/384*(3+2*x)^(3/2)-_ + 3519/640*(3+2*x)^(5/2)+81/128*(3+2*x)^(7/2)-3/128*(3+2*x)^(9/2)+_ + (-16005/128)/sqrt(3+2*x)-17201/128*sqrt(3+2*x) +--R +--R +--R 7 6 5 4 3 2 +--R - 45x + 135x + 702x + 1940x - 3195x - 41805x - 85070x - 51162 +--R (2) ------------------------------------------------------------------- +--R 2 +------+ +--R (60x + 180x + 135)\|2x + 3 +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 7 6 5 4 3 2 +--R - 45x + 135x + 702x + 1940x - 3195x - 41805x - 85070x - 51162 +--R (3) ------------------------------------------------------------------- +--R 2 +------+ +--R (60x + 180x + 135)\|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1078 + +--S 1079 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +)clear all + +--S 1081 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1751 +r0:=526/81*(3+2*x)^(3/2)+62/45*(3+2*x)^(5/2)-2/21*(3+2*x)^(7/2)+_ + 12*atanh(sqrt(3+2*x))-4250/81*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+_ + 3278/81*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 34020\|3 atanh(\|2x + 3 ) - 148750\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (- 2160x + 5904x + 69112x + 197824)\|3 \|2x + 3 +--R / +--R +-+ +--R 2835\|3 +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +------+ +--R 17010\|3 log(\|2x + 3 + 1) - 17010\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +--R 74375\|5 log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (- 2160x + 5904x + 69112x + 197824)\|3 \|2x + 3 +--R / +--R +-+ +--R 2835\|3 +--R Type: Union(Expression(Integer),...) +--E 1083 + +--S 1084 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 486\|3 log(\|2x + 3 + 1) - 486\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 2125\|5 log(-------------------------------) - 972\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 4250\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1751 +r0:=62/27*(3+2*x)^(3/2)-2/15*(3+2*x)^(5/2)+12*atanh(sqrt(3+2*x))-_ + 850/27*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+526/27*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 1620\|3 atanh(\|2x + 3 ) - 4250\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +------+ +--R (- 72x + 404x + 3398)\|3 \|2x + 3 +--R / +--R +-+ +--R 135\|3 +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +------+ +--R 810\|3 log(\|2x + 3 + 1) - 810\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +--R 2125\|5 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +--R (- 72x + 404x + 3398)\|3 \|2x + 3 +--R / +--R +-+ +--R 135\|3 +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 162\|3 log(\|2x + 3 + 1) - 162\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 425\|5 log(-------------------------------) - 324\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 850\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1751 +r0:=-2/9*(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-170/9*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(5/3)+62/9*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 108\|3 atanh(\|2x + 3 ) - 170\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +------+ +--R (- 4x + 56)\|3 \|2x + 3 +--R / +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +------+ +--R 54\|3 log(\|2x + 3 + 1) - 54\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 85\|5 log(-------------------------------) + (- 4x + 56)\|3 \|2x + 3 +--R 3x + 2 +--R / +--R +-+ +--R 9\|3 +--R Type: Union(Expression(Integer),...) +--E 1093 + +--S 1094 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 54\|3 log(\|2x + 3 + 1) - 54\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 85\|5 log(-------------------------------) - 108\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 170\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 1751 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ------------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1751 +r0:=12*atanh(sqrt(3+2*x))-34/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-_ + 2/3*sqrt(3+2*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +-+ +------+ +--R 36\|3 atanh(\|2x + 3 ) - 34\|5 atanh(-------------) - 2\|3 \|2x + 3 +--R +-+ +--R \|5 +--R (2) -------------------------------------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +------+ +--R 18\|3 log(\|2x + 3 + 1) - 18\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 17\|5 log(-------------------------------) - 2\|3 \|2x + 3 +--R 3x + 2 +--R / +--R +-+ +--R 3\|3 +--R Type: Union(Expression(Integer),...) +--E 1098 + +--S 1099 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 18\|3 log(\|2x + 3 + 1) - 18\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 17\|5 log(-------------------------------) - 36\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 34\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1100 + +)clear all + +--S 1101 of 1751 +t0:=(5-x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) ----------------------- +--R 2 +------+ +--R (3x + 5x + 2)\|2x + 3 +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1751 +r0:=12*atanh(sqrt(3+2*x))-34*atanh(sqrt(3/5)*sqrt(3+2*x))/sqrt(15) +--R +--R +--R +-+ +------+ +--R +--+ +------+ \|3 \|2x + 3 +--R 12\|15 atanh(\|2x + 3 ) - 34atanh(-------------) +--R +-+ +--R \|5 +--R (2) ------------------------------------------------ +--R +--+ +--R \|15 +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +------+ +--+ +------+ +--R 6\|15 log(\|2x + 3 + 1) - 6\|15 log(\|2x + 3 - 1) +--R + +--R +------+ +--+ +--R - 15\|2x + 3 + (3x + 7)\|15 +--R 17log(-----------------------------) +--R 3x + 2 +--R / +--R +--+ +--R \|15 +--R Type: Union(Expression(Integer),...) +--E 1103 + +--S 1104 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +------+ +--+ +------+ +--R 6\|15 log(\|2x + 3 + 1) - 6\|15 log(\|2x + 3 - 1) +--R + +--R +------+ +--+ +--R - 15\|2x + 3 + (3x + 7)\|15 +--+ +------+ +--R 17log(-----------------------------) - 12\|15 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R \|3 \|2x + 3 +--R 34atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +--+ +--R \|15 +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-+ +-+ +--+ +------+ +--+ +-+ +-+ +--R (17\|3 \|5 \|15 - 255)\|2x + 3 + (51x + 119)\|15 + (- 51x - 119)\|3 \|5 +--R --------------------------------------------------------------------------- +--R 2 +--+ +------+ 2 +--R (9x + 27x + 14)\|15 \|2x + 3 - 90x - 195x - 90 +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------- +--R 3 2 +------+ +--R (6x + 19x + 19x + 6)\|2x + 3 +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1751 +r0:=12*atanh(sqrt(3+2*x))-34/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-26/5)/sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +------+ +-+ +------+ \|3 \|2x + 3 +--R 60\|5 \|2x + 3 atanh(\|2x + 3 ) - 34\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +--R - 26\|5 +--R / +--R +-+ +------+ +--R 5\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +------+ +-+ +------+ +------+ +--R 30\|5 \|2x + 3 log(\|2x + 3 + 1) - 30\|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ +------+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +--R 17\|3 \|2x + 3 log(-------------------------------) - 26\|5 +--R 3x + 2 +--R / +--R +-+ +------+ +--R 5\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1108 + +--S 1109 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 30\|5 log(\|2x + 3 + 1) - 30\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 17\|3 log(-------------------------------) - 60\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 34\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 5\|5 +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1110 + +)clear all + +--S 1111 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------- +--R 4 3 2 +------+ +--R (12x + 56x + 95x + 69x + 18)\|2x + 3 +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1751 +r0:=(-26/15)/(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-102/25*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(3/5)+(-198/25)/sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +------+ +--R (1800x + 2700)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +-+ +--R (- 612x - 918)\|3 \|2x + 3 atanh(-------------) + (- 1188x - 1912)\|5 +--R +-+ +--R \|5 +--R / +--R +-+ +------+ +--R (150x + 225)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1112 + +--S 1113 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +------+ +--R (900x + 1350)\|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R +-+ +------+ +------+ +--R (- 900x - 1350)\|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ +------+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R (306x + 459)\|3 \|2x + 3 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--R (- 1188x - 1912)\|5 +--R / +--R +-+ +------+ +--R (150x + 225)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1113 + +--S 1114 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 150\|5 log(\|2x + 3 + 1) - 150\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 51\|3 log(-------------------------------) - 300\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 102\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1115 + +)clear all + +--S 1116 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------- +--R 5 4 3 2 +------+ +--R (24x + 148x + 358x + 423x + 243x + 54)\|2x + 3 +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1751 +r0:=(-26/25)/(3+2*x)^(5/2)+(-66/25)/(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-_ + 306/125*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-1194/125)/sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +------+ +--R (6000x + 18000x + 13500)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ +------+ \|3 \|2x + 3 +--R (- 1224x - 3672x - 2754)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +--R (- 4776x - 14988x - 11866)\|5 +--R / +--R 2 +-+ +------+ +--R (500x + 1500x + 1125)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +------+ +------+ +--R (3000x + 9000x + 6750)\|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +------+ +--R (- 3000x - 9000x - 6750)\|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R 2 +-+ +------+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R (612x + 1836x + 1377)\|3 \|2x + 3 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--R (- 4776x - 14988x - 11866)\|5 +--R / +--R 2 +-+ +------+ +--R (500x + 1500x + 1125)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1118 + +--S 1119 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 750\|5 log(\|2x + 3 + 1) - 750\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 153\|3 log(-------------------------------) - 1500\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 306\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 125\|5 +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1120 + +)clear all + +--S 1121 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1751 +r0:=826/27*(3+2*x)^(3/2)+70/3*(3+2*x)^(5/2)-(3+2*x)^(7/2)*(29+35*x)/_ + (2+5*x+3*x^2)-154*atanh(sqrt(3+2*x))+2800/27*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(5/3)+1358/27*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 12474x - 20790x - 8316)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (8400x + 14000x + 5600)\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (- 48x + 400x - 1843x - 2129)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (81x + 135x + 54)\|3 +--R Type: Expression(Integer) +--E 1122 + +--S 1123 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +--R 2 +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +--R (4200x + 7000x + 2800)\|5 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +--R (- 6237x - 10395x - 4158)\|3 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +--R (6237x + 10395x + 4158)\|3 log(\|2x + 3 - 1) +--R + +--R 3 2 +-+ +------+ +--R (- 48x + 400x - 1843x - 2129)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (81x + 135x + 54)\|3 +--R Type: Union(Expression(Integer),...) +--E 1123 + +--S 1124 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 1400\|5 log(-----------------------------) - 2079\|3 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 2079\|3 log(\|2x + 3 - 1) + 4158\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 2800\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1125 + +)clear all + +--S 1126 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1751 +r0:=70/3*(3+2*x)^(3/2)-(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)-_ + 130*atanh(sqrt(3+2*x))+100*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+_ + 30*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 1170x - 1950x - 780)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (900x + 1500x + 600)\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +------+ +--R (- 8x - 209x - 183)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Expression(Integer) +--E 1127 + +--S 1128 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +--R 2 +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +--R (450x + 750x + 300)\|5 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +--R (- 585x - 975x - 390)\|3 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +--R (585x + 975x + 390)\|3 log(\|2x + 3 - 1) +--R + +--R 2 +-+ +------+ +--R (- 8x - 209x - 183)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Union(Expression(Integer),...) +--E 1128 + +--S 1129 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 50\|5 log(-----------------------------) - 65\|3 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 65\|3 log(\|2x + 3 - 1) + 130\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 100\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1751 +r0:=-(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)-106*atanh(sqrt(3+2*x))+_ + 248/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+70/3*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 954x - 1590x - 636)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +-+ +------+ +--R (744x + 1240x + 496)\|5 atanh(-------------) + (- 139x - 121)\|3 \|2x + 3 +--R +-+ +--R \|5 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +--R 2 +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +--R (372x + 620x + 248)\|5 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +--R (- 477x - 795x - 318)\|3 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +-+ +------+ +--R (477x + 795x + 318)\|3 log(\|2x + 3 - 1) + (- 139x - 121)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 124\|5 log(-----------------------------) - 159\|3 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 159\|3 log(\|2x + 3 - 1) + 318\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 248\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 1751 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2 +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1751 +r0:=-82*atanh(sqrt(3+2*x))+316*atanh(sqrt(3/5)*sqrt(3+2*x))/sqrt(15)-_ + (29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 2 +--+ +------+ +--R (- 246x - 410x - 164)\|15 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 \|3 \|2x + 3 +--+ +------+ +--R (948x + 1580x + 632)atanh(-------------) + (- 35x - 29)\|15 \|2x + 3 +--R +-+ +--R \|5 +--R / +--R 2 +--+ +--R (3x + 5x + 2)\|15 +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--+ +------+ +--R (- 123x - 205x - 82)\|15 log(\|2x + 3 + 1) +--R + +--R 2 +--+ +------+ +--R (123x + 205x + 82)\|15 log(\|2x + 3 - 1) +--R + +--R +------+ +--+ +--R 2 15\|2x + 3 + (3x + 7)\|15 +--R (474x + 790x + 316)log(---------------------------) +--R 3x + 2 +--R + +--R +--+ +------+ +--R (- 35x - 29)\|15 \|2x + 3 +--R / +--R 2 +--+ +--R (3x + 5x + 2)\|15 +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +------+ +--+ +------+ +--R - 41\|15 log(\|2x + 3 + 1) + 41\|15 log(\|2x + 3 - 1) +--R + +--R +------+ +--+ +--R 15\|2x + 3 + (3x + 7)\|15 +--+ +------+ +--R 158log(---------------------------) + 82\|15 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R \|3 \|2x + 3 +--R - 316atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +--+ +--R \|15 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-+ +-+ +--+ +------+ +--+ +--R (158\|3 \|5 \|15 - 2370)\|2x + 3 + (- 474x - 1106)\|15 +--R + +--R +-+ +-+ +--R (474x + 1106)\|3 \|5 +--R / +--R 2 +--+ +------+ 2 +--R (9x + 27x + 14)\|15 \|2x + 3 + 90x + 195x + 90 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 1751 +t0:=(5-x)/((2+5*x+3*x^2)^2*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R 4 3 2 +------+ +--R (9x + 30x + 37x + 20x + 4)\|2x + 3 +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1751 +r0:=-58*atanh(sqrt(3+2*x))+384/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 3/5*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 870x - 1450x - 580)\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (1152x + 1920x + 768)\|3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +------+ +--R (- 141x - 111)\|5 \|2x + 3 +--R / +--R 2 +-+ +--R (15x + 25x + 10)\|5 +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +--R 2 +-+ 5\|3 \|2x + 3 + (3x + 7)\|5 +--R (576x + 960x + 384)\|3 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +--R (- 435x - 725x - 290)\|5 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +-+ +------+ +--R (435x + 725x + 290)\|5 log(\|2x + 3 - 1) + (- 141x - 111)\|5 \|2x + 3 +--R / +--R 2 +-+ +--R (15x + 25x + 10)\|5 +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 192\|3 log(-----------------------------) - 145\|5 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 145\|5 log(\|2x + 3 - 1) + 290\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 384\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 5\|5 +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +------+ +--R (18x + 87x + 164x + 151x + 68x + 12)\|2x + 3 +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1751 +r0:=-34*atanh(sqrt(3+2*x))+1356/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-506/25)/sqrt(3+2*x)-3/5*(37+47*x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R (2) +--R 2 +-+ +------+ +------+ +--R (- 2550x - 4250x - 1700)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ +------+ \|3 \|2x + 3 +--R (4068x + 6780x + 2712)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +--R (- 1518x - 3235x - 1567)\|5 +--R / +--R 2 +-+ +------+ +--R (75x + 125x + 50)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +------+ +-+ +--R 2 +-+ +------+ 5\|3 \|2x + 3 + (3x + 7)\|5 +--R (2034x + 3390x + 1356)\|3 \|2x + 3 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +------+ +------+ +--R (- 1275x - 2125x - 850)\|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R 2 +-+ +------+ +------+ +--R (1275x + 2125x + 850)\|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R 2 +-+ +--R (- 1518x - 3235x - 1567)\|5 +--R / +--R 2 +-+ +------+ +--R (75x + 125x + 50)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1148 + +--S 1149 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 678\|3 log(-----------------------------) - 425\|5 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 425\|5 log(\|2x + 3 - 1) + 850\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 1356\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1150 + +)clear all + +--S 1151 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (36x + 228x + 589x + 794x + 589x + 228x + 36)\|2x + 3 +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1751 +r0:=(-262/15)/(3+2*x)^(3/2)-3/5*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2))-_ + 10*atanh(sqrt(3+2*x))+936/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-686/25)/sqrt(3+2*x) +--R +--R +--R (2) +--R 3 2 +-+ +------+ +------+ +--R (- 4500x - 14250x - 14250x - 4500)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 3 2 +-+ +------+ \|3 \|2x + 3 +--R (16848x + 53352x + 53352x + 16848)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +--R (- 12348x - 43032x - 47767x - 16633)\|5 +--R / +--R 3 2 +-+ +------+ +--R (450x + 1425x + 1425x + 450)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +------+ +--R (8424x + 26676x + 26676x + 8424)\|3 \|2x + 3 +--R * +--R +-+ +------+ +-+ +--R 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +------+ +--R (- 2250x - 7125x - 7125x - 2250)\|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R 3 2 +-+ +------+ +------+ +--R (2250x + 7125x + 7125x + 2250)\|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R 3 2 +-+ +--R (- 12348x - 43032x - 47767x - 16633)\|5 +--R / +--R 3 2 +-+ +------+ +--R (450x + 1425x + 1425x + 450)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1153 + +--S 1154 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 468\|3 log(-----------------------------) - 125\|5 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R 125\|5 log(\|2x + 3 - 1) + 250\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 936\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1155 + +)clear all + +--S 1156 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^2) +--R +--R +--R (1) +--R - x + 5 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +------+ +--R (72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108)\|2x + 3 +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1751 +r0:=(-2114/125)/(3+2*x)^(5/2)+(-7042/375)/(3+2*x)^(3/2)-3/5*(37+47*x)/_ + ((3+2*x)^(5/2)*(2+5*x+3*x^2))+14*atanh(sqrt(3+2*x))+_ + 15876/625*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-24626/625)/sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (315000x + 1470000x + 2493750x + 1811250x + 472500)\|5 \|2x + 3 +--R * +--R +------+ +--R atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +------+ +--R (571536x + 2667168x + 4524660x + 3286332x + 857304)\|3 \|2x + 3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +--R (- 886536x - 4348428x - 7782530x - 5977997x - 1646109)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (22500x + 105000x + 178125x + 129375x + 33750)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (285768x + 1333584x + 2262330x + 1643166x + 428652)\|3 \|2x + 3 +--R * +--R +-+ +------+ +-+ +--R 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +------+ +--R (157500x + 735000x + 1246875x + 905625x + 236250)\|5 \|2x + 3 +--R * +--R +------+ +--R log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 157500x - 735000x - 1246875x - 905625x - 236250)\|5 \|2x + 3 +--R * +--R +------+ +--R log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (- 886536x - 4348428x - 7782530x - 5977997x - 1646109)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (22500x + 105000x + 178125x + 129375x + 33750)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1158 + +--S 1159 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +--R +-+ 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 7938\|3 log(-----------------------------) + 4375\|5 log(\|2x + 3 + 1) +--R 3x + 2 +--R + +--R +-+ +------+ +-+ +------+ +--R - 4375\|5 log(\|2x + 3 - 1) - 8750\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R - 15876\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 1751 +t0:=(5-x)*(3+2*x)^(9/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 5 4 3 2 +------+ +--R (- 16x - 16x + 264x + 864x + 999x + 405)\|2x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1751 +r0:=-3151/9*(3+2*x)^(3/2)-283*(3+2*x)^(5/2)-1/2*(3+2*x)^(9/2)*(29+35*x)/_ + (2+5*x+3*x^2)^2+3/2*(3+2*x)^(7/2)*(230+283*x)/(2+5*x+3*x^2)+_ + 1962*atanh(sqrt(3+2*x))-13675/9*atanh(sqrt(3/5)*sqrt(3+2*x))*_ + sqrt(5/3)-3983/9*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (317844x + 1059480x + 1306692x + 706320x + 141264)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 246150x - 820500x - 1011950x - 547000x - 109400)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +------+ +--R (- 192x + 45083x + 112467x + 90465x + 23327)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (162x + 540x + 666x + 360x + 72)\|3 +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (158922x + 529740x + 653346x + 353160x + 70632)\|3 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +--R (- 158922x - 529740x - 653346x - 353160x - 70632)\|3 +--R * +--R +------+ +--R log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (123075x + 410250x + 505975x + 273500x + 54700)\|5 +--R * +--R +-+ +------+ +-+ +--R - 3\|5 \|2x + 3 + (3x + 7)\|3 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +------+ +--R (- 192x + 45083x + 112467x + 90465x + 23327)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (162x + 540x + 666x + 360x + 72)\|3 +--R Type: Union(Expression(Integer),...) +--E 1163 + +--S 1164 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 17658\|3 log(\|2x + 3 + 1) - 17658\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 13675\|5 log(-------------------------------) - 35316\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 27350\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1165 + +)clear all + +--S 1166 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1751 +r0:=-847/3*(3+2*x)^(3/2)-1/2*(3+2*x)^(7/2)*(29+35*x)/(2+5*x+3*x^2)^2+_ + 7/2*(3+2*x)^(5/2)*(100+121*x)/(2+5*x+3*x^2)+1582*atanh(sqrt(3+2*x))-_ + 1225*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-357*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (85428x + 284760x + 351204x + 189840x + 37968)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 66150x - 220500x - 271950x - 147000x - 29400)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (12443x + 30979x + 25073x + 6555)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (42714x + 142380x + 175602x + 94920x + 18984)\|3 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 42714x - 142380x - 175602x - 94920x - 18984)\|3 log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (33075x + 110250x + 135975x + 73500x + 14700)\|5 +--R * +--R +-+ +------+ +-+ +--R - 3\|5 \|2x + 3 + (3x + 7)\|3 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (12443x + 30979x + 25073x + 6555)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Union(Expression(Integer),...) +--E 1168 + +--S 1169 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 1582\|3 log(\|2x + 3 + 1) - 1582\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 1225\|5 log(-------------------------------) - 3164\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 2450\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 2\|3 +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1170 + +)clear all + +--S 1171 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1751 +r0:=-1/2*(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)^2+5/2*(3+2*x)^(3/2)*_ + (142+169*x)/(2+5*x+3*x^2)+1250*atanh(sqrt(3+2*x))-_ + 2905/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-845/3*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (67500x + 225000x + 277500x + 150000x + 30000)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 52290x - 174300x - 214970x - 116200x - 23240)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (9825x + 24497x + 19891x + 5237)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (33750x + 112500x + 138750x + 75000x + 15000)\|3 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 33750x - 112500x - 138750x - 75000x - 15000)\|3 log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (26145x + 87150x + 107485x + 58100x + 11620)\|5 +--R * +--R +-+ +------+ +-+ +--R - 3\|5 \|2x + 3 + (3x + 7)\|3 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (9825x + 24497x + 19891x + 5237)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Union(Expression(Integer),...) +--E 1173 + +--S 1174 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 3750\|3 log(\|2x + 3 + 1) - 3750\|3 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 3\|5 \|2x + 3 + (3x + 7)\|3 +-+ +------+ +--R 2905\|5 log(-------------------------------) - 7500\|3 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 5810\|5 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1175 + +)clear all + +--S 1176 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1751 +r0:=-1/2*(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)^2+966*atanh(sqrt(3+2*x))-_ + 1247*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+3/2*(240+281*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (17388x + 57960x + 71484x + 38640x + 7728)\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 4 3 2 +-+ \|3 \|2x + 3 +--R (- 22446x - 74820x - 92278x - 49880x - 9976)\|3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (2529x + 6305x + 5123x + 1353)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (18x + 60x + 74x + 40x + 8)\|5 +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (8694x + 28980x + 35742x + 19320x + 3864)\|5 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 8694x - 28980x - 35742x - 19320x - 3864)\|5 log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (11223x + 37410x + 46139x + 24940x + 4988)\|3 +--R * +--R +-+ +------+ +-+ +--R - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (2529x + 6305x + 5123x + 1353)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (18x + 60x + 74x + 40x + 8)\|5 +--R Type: Union(Expression(Integer),...) +--E 1178 + +--S 1179 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 966\|5 log(\|2x + 3 + 1) - 966\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 1247\|3 log(-------------------------------) - 1932\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 2494\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 2\|5 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1180 + +)clear all + +--S 1181 of 1751 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^3 +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1751 +r0:=730*atanh(sqrt(3+2*x))-4713/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 1/2*(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+3/10*(878+1063*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (65700x + 219000x + 270100x + 146000x + 29200)\|5 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 84834x - 282780x - 348762x - 188520x - 37704)\|3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (9567x + 23847x + 19373x + 5123)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (90x + 300x + 370x + 200x + 40)\|5 +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (32850x + 109500x + 135050x + 73000x + 14600)\|5 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 32850x - 109500x - 135050x - 73000x - 14600)\|5 log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (42417x + 141390x + 174381x + 94260x + 18852)\|3 +--R * +--R +-+ +------+ +-+ +--R - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (9567x + 23847x + 19373x + 5123)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (90x + 300x + 370x + 200x + 40)\|5 +--R Type: Union(Expression(Integer),...) +--E 1183 + +--S 1184 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 3650\|5 log(\|2x + 3 + 1) - 3650\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 4713\|3 log(-------------------------------) - 7300\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 9426\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 10\|5 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 1751 +t0:=(5-x)/((2+5*x+3*x^2)^3*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (27x + 135x + 279x + 305x + 186x + 60x + 8)\|2x + 3 +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1751 +r0:=542*atanh(sqrt(3+2*x))-17463/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 3/10*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+1/50*(9734+11739*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (243900x + 813000x + 1002700x + 542000x + 108400)\|5 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 314334x - 1047780x - 1292262x - 698520x - 139704)\|3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (35217x + 87897x + 71443x + 18913)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (121950x + 406500x + 501350x + 271000x + 54200)\|5 log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +--R (- 121950x - 406500x - 501350x - 271000x - 54200)\|5 +--R * +--R +------+ +--R log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +--R (157167x + 523890x + 646131x + 349260x + 69852)\|3 +--R * +--R +-+ +------+ +-+ +--R - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +------+ +--R (35217x + 87897x + 71443x + 18913)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 +--R Type: Union(Expression(Integer),...) +--E 1188 + +--S 1189 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 13550\|5 log(\|2x + 3 + 1) - 13550\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 17463\|3 log(-------------------------------) - 27100\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 34926\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 50\|5 +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +------+ +--R (54x + 351x + 963x + 1447x + 1287x + 678x + 196x + 24)\|2x + 3 +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1751 +r0:=402*atanh(sqrt(3+2*x))-12717/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + 2667/25/sqrt(3+2*x)-3/10*(37+47*x)/((2+5*x+3*x^2)^2*sqrt(3+2*x))+_ + 1/10*(1888+2229*x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (180900x + 603000x + 743700x + 402000x + 80400)\|5 \|2x + 3 +--R * +--R +------+ +--R atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +------+ +--R (- 228906x - 763020x - 941058x - 508680x - 101736)\|3 \|2x + 3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +--R (48006x + 193455x + 281403x + 175465x + 39661)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +------+ +--R (90450x + 301500x + 371850x + 201000x + 40200)\|5 \|2x + 3 +--R * +--R +------+ +--R log(\|2x + 3 + 1) +--R + +--R 4 3 2 +-+ +------+ +--R (- 90450x - 301500x - 371850x - 201000x - 40200)\|5 \|2x + 3 +--R * +--R +------+ +--R log(\|2x + 3 - 1) +--R + +--R 4 3 2 +-+ +------+ +--R (114453x + 381510x + 470529x + 254340x + 50868)\|3 \|2x + 3 +--R * +--R +-+ +------+ +-+ +--R - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--R (48006x + 193455x + 281403x + 175465x + 39661)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 10050\|5 log(\|2x + 3 + 1) - 10050\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 12717\|3 log(-------------------------------) - 20100\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 25434\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 50\|5 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 8 7 6 5 4 3 2 +--R (108x + 864x + 2979x + 5783x + 6915x + 5217x + 2426x + 636x + 72) +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1751 +r0:=7451/75/(3+2*x)^(3/2)-3/10*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^2)+_ + 1/50*(9146+10551*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2))+310*_ + atanh(sqrt(3+2*x))-45603/125*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + 6853/125/sqrt(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 4185000x + 20227500x + 38130000x + 35107500x + 15810000x +--R + +--R 2790000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R 5 4 3 2 +--R - 4925124x - 23804766x - 44873352x - 41316318x - 18606024x +--R + +--R - 3283416 +--R * +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +--R \|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 5 4 3 2 +-+ +--R (740124x + 4247856x + 9453447x + 10168583x + 5278129x + 1057511)\|5 +--R / +--R 5 4 3 2 +-+ +------+ +--R (13500x + 65250x + 123000x + 113250x + 51000x + 9000)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (2092500x + 10113750x + 19065000x + 17553750x + 7905000x + 1395000) +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R 5 4 3 2 +--R - 2092500x - 10113750x - 19065000x - 17553750x - 7905000x +--R + +--R - 1395000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R 5 4 3 2 +--R (2462562x + 11902383x + 22436676x + 20658159x + 9303012x + 1641708) +--R * +--R +-+ +------+ +-+ +--R +-+ +------+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R \|3 \|2x + 3 log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--R (740124x + 4247856x + 9453447x + 10168583x + 5278129x + 1057511)\|5 +--R / +--R 5 4 3 2 +-+ +------+ +--R (13500x + 65250x + 123000x + 113250x + 51000x + 9000)\|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1198 + +--S 1199 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 38750\|5 log(\|2x + 3 + 1) - 38750\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +-+ +------+ +--R 45603\|3 log(-------------------------------) - 77500\|5 atanh(\|2x + 3 ) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ \|3 \|2x + 3 +--R 91206\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 250\|5 +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +)clear all + +--S 1201 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 9 8 7 6 5 4 3 +--R 216x + 2052x + 8550x + 20503x + 31179x + 31179x + 20503x +--R + +--R 2 +--R 8550x + 2052x + 216 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1751 +r0:=56399/625/(3+2*x)^(5/2)+102697/1875/(3+2*x)^(3/2)-3/10*(37+47*x)/_ + ((3+2*x)^(5/2)*(2+5*x+3*x^2)^2)+1/50*(8852+9957*x)/((3+2*x)^(5/2)*_ + (2+5*x+3*x^2))+266*atanh(sqrt(3+2*x))-806841/3125*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(3/5)+(-24409/3125)/sqrt(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 179550000x + 1137150000x + 2937637500x + 3960075000x +--R + +--R 2 +--R 2937637500x + 1137150000x + 179550000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R 6 5 4 3 +--R - 174277656x - 1103758488x - 2851376094x - 3843790524x +--R + +--R 2 +--R - 2851376094x - 1103758488x - 174277656 +--R * +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +--R \|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 6 5 4 3 2 +--R - 5272344x - 14906052x + 18312714x + 114099329x + 160041829x +--R + +--R 94082723x + 20250051 +--R * +--R +-+ +--R \|5 +--R / +--R 6 5 4 3 2 +--R 675000x + 4275000x + 11043750x + 14887500x + 11043750x + 4275000x +--R + +--R 675000 +--R * +--R +-+ +------+ +--R \|5 \|2x + 3 +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 89775000x + 568575000x + 1468818750x + 1980037500x + 1468818750x +--R + +--R 568575000x + 89775000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 log(\|2x + 3 + 1) +--R + +--R 6 5 4 3 +--R - 89775000x - 568575000x - 1468818750x - 1980037500x +--R + +--R 2 +--R - 1468818750x - 568575000x - 89775000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 log(\|2x + 3 - 1) +--R + +--R 6 5 4 3 2 +--R 87138828x + 551879244x + 1425688047x + 1921895262x + 1425688047x +--R + +--R 551879244x + 87138828 +--R * +--R +-+ +------+ +-+ +--R +-+ +------+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R \|3 \|2x + 3 log(-------------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R - 5272344x - 14906052x + 18312714x + 114099329x + 160041829x +--R + +--R 94082723x + 20250051 +--R * +--R +-+ +--R \|5 +--R / +--R 6 5 4 3 2 +--R 675000x + 4275000x + 11043750x + 14887500x + 11043750x + 4275000x +--R + +--R 675000 +--R * +--R +-+ +------+ +--R \|5 \|2x + 3 +--R Type: Union(Expression(Integer),...) +--E 1203 + +--S 1204 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +-+ +------+ +--R 831250\|5 log(\|2x + 3 + 1) - 831250\|5 log(\|2x + 3 - 1) +--R + +--R +-+ +------+ +-+ +--R +-+ - 5\|3 \|2x + 3 + (3x + 7)\|5 +--R 806841\|3 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R - 1662500\|5 atanh(\|2x + 3 ) + 1613682\|3 atanh(-------------) +--R +-+ +--R \|5 +--R / +--R +-+ +--R 6250\|5 +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1205 + +)clear all + +--S 1206 of 1751 +t0:=(5+10*x+sqrt(35))/((2+3*x+5*x^2)*sqrt(1+2*x)) +--R +--R +--R +--+ +--R \|35 + 10x + 5 +--R (1) ----------------------- +--R 2 +------+ +--R (5x + 3x + 2)\|2x + 1 +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1751 +r0:=-2*atan((-sqrt(10+20*x)+sqrt(2+sqrt(35)))/sqrt(-2+sqrt(35)))*_ + sqrt(10/(-2+sqrt(35)))+2*atan((sqrt(10+20*x)+sqrt(2+sqrt(35)))/_ + sqrt(-2+sqrt(35)))*sqrt(10/(-2+sqrt(35))),-2*atan((-10*sqrt(1+2*x)+_ + sqrt(10*(2+sqrt(35))))/sqrt(10*(-2+sqrt(35))))*sqrt(10/(-2+sqrt(35)))+_ + 2*atan((10*sqrt(1+2*x)+sqrt(10*(2+sqrt(35))))/sqrt(10*(-2+sqrt(35))))*_ + sqrt(10/(-2+sqrt(35))) +--R +--R +--R (2) +--R [ +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 + \|20x + 10 +--R 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R + +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 - \|20x + 10 +--R - 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R / +--R +--+ +--R \|31 +--R , +--R +--R +------------+ +--R +------------+ | +--+ +------+ +--R | +--+ \|10\|35 + 20 + 10\|2x + 1 +--R 2\|10\|35 + 20 atan(-----------------------------) +--R +------------+ +--R | +--+ +--R \|10\|35 - 20 +--R + +--R +------------+ +--R +------------+ | +--+ +------+ +--R | +--+ \|10\|35 + 20 - 10\|2x + 1 +--R - 2\|10\|35 + 20 atan(-----------------------------) +--R +------------+ +--R | +--+ +--R \|10\|35 - 20 +--R / +--R +--+ +--R \|31 +--R ] +--R Type: Tuple(Expression(Integer)) +--E 1207 + +--S 1208 of 1751 +a0:=integrate(t0,x) +--R +--R +--R +------------+ +--R +------------+ +--+ +------+ | +--+ +--R | +--+ (31\|35 + 62)\|2x + 1 \|10\|35 + 20 +--R 2\|10\|35 + 20 atan(---------------------------------------) +--R +--+ +--+ +--+ +--R (40x - 19)\|31 \|35 + (390x + 55)\|31 +--R (3) - ------------------------------------------------------------- +--R +--+ +--R \|31 +--R Type: Union(Expression(Integer),...) +--E 1208 + +--S 1209 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R +------------+ +--R +------------+ +--+ +------+ | +--+ +--R | +--+ (31\|35 + 62)\|2x + 1 \|10\|35 + 20 +--R - 2\|10\|35 + 20 atan(---------------------------------------) +--R +--+ +--+ +--+ +--R (40x - 19)\|31 \|35 + (390x + 55)\|31 +--R + +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 + \|20x + 10 +--R - 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R + +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 - \|20x + 10 +--R 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R / +--R +--+ +--R \|31 +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +--+ +--+ +--+ +------+ +--R ((- 3120x - 3641)\|31 \|35 + (- 20810x - 21325)\|31 )\|2x + 1 +--R * +--R +---------+ +------------+ +--R +--------+ | +--+ | +--+ +--R \|20x + 10 \|\|35 - 2 \|10\|35 + 20 +--R + +--R 2 +--+ 2 +--R (1934400x + 3224620x + 1128710)\|35 + 12902200x + 19672600x + 6610750 +--R / +--R 3 2 +--+ 3 2 +--R (967200x + 1063920x + 677040x + 193440)\|35 + 6451100x + 7096210x +--R + +--R 4515770x + 1290220 +--R * +--R +------+ +--R \|2x + 1 +--R Type: Expression(Integer) +--E 1210 + +)clear all + +--S 1211 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 3 2 +------+ | 2 +--R (1) (- 4x + 8x + 51x + 45)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1751 +--r0:=730/891*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)-2/33*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(3/2)+12130/6237*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 32567/48114*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-63541/168399*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+_ +-- 1/56133*(250447+280359*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1212 + +--S 1213 of 1751 +--a0:=integrate(t0,x) +--E 1213 + +--S 1214 of 1751 +--m0:=a0-r0 +--E 1214 + +--S 1215 of 1751 +--d0:=D(m0,x) +--E 1215 + +)clear all + +--S 1216 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 2 +------+ | 2 +--R (1) (- 2x + 7x + 15)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1751 +--r0:=-2/27*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)+202/189*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+4729/1458*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-7892/5103*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+1/8505*(27914+30033*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1217 + +--S 1218 of 1751 +--a0:=integrate(t0,x) +--E 1218 + +--S 1219 of 1751 +--m0:=a0-r0 +--E 1219 + +--S 1220 of 1751 +--d0:=D(m0,x) +--E 1220 + +)clear all + +--S 1221 of 1751 +t0:=(5-x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R +------+ | 2 +--R (1) (- x + 5)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1751 +--r0:=-2/21*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+697/162*elliptic_e(asin(sqrt(3+_ +-- 2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 881/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1/945*(2327+2169*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1222 + +--S 1223 of 1751 +--a0:=integrate(t0,x) +--E 1223 + +--S 1224 of 1751 +--m0:=a0-r0 +--E 1224 + +--S 1225 of 1751 +--d0:=D(m0,x) +--E 1225 + +)clear all + +--S 1226 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1751 +--r0:=761/54*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-94/27*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/45*(88-9*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1227 + +--S 1228 of 1751 +--a0:=integrate(t0,x) +--E 1228 + +--S 1229 of 1751 +--m0:=a0-r0 +--E 1229 + +--S 1230 of 1751 +--d0:=D(m0,x) +--E 1230 + +)clear all + +--S 1231 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1751 +--r0:=61/9*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-121/18*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-1/3*(21+x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1232 + +--S 1233 of 1751 +--a0:=integrate(t0,x) +--E 1233 + +--S 1234 of 1751 +--m0:=a0-r0 +--E 1234 + +--S 1235 of 1751 +--d0:=D(m0,x) +--E 1235 + +)clear all + +--S 1236 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1751 +--r0:=67/6*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-8/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-1/3*(11+3*x)*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+67/15*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1237 + +--S 1238 of 1751 +--a0:=integrate(t0,x) +--E 1238 + +--S 1239 of 1751 +--m0:=a0-r0 +--E 1239 + +--S 1240 of 1751 +--d0:=D(m0,x) +--E 1240 + +)clear all + +--S 1241 of 1751 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1751 +--r0:=49/50*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-11/25*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+9/25*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+1/5*(1+5*x)*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(5/2)+49/125*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1242 + +--S 1243 of 1751 +--a0:=integrate(t0,x) +--E 1243 + +--S 1244 of 1751 +--m0:=a0-r0 +--E 1244 + +--S 1245 of 1751 +--d0:=D(m0,x) +--E 1245 + +)clear all + +--S 1246 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R (1) +--R 6 5 4 3 2 +------+ +--R (- 24x - 28x + 382x + 1367x + 1872x + 1161x + 270)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1751 +--r0:=2086/1989*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)+42/85*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(5/2)-2/51*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2)+_ +-- 1/196911*(591064+699377*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 108934/65637*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-2200387/21266388*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1284593/10633194*elliptic_f(asin(sqrt(3+_ +-- 2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/17721990*(6668831+8076357*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1247 + +--S 1248 of 1751 +--a0:=integrate(t0,x) +--E 1248 + +--S 1249 of 1751 +--m0:=a0-r0 +--E 1249 + +--S 1250 of 1751 +--d0:=D(m0,x) +--E 1250 + +)clear all + +--S 1251 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (1) (- 12x + 4x + 185x + 406x + 327x + 90)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1751 +--r0:=202/351*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)-2/45*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(5/2)+1/243243*(534271+629153*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+13318/11583*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+_ +-- 207851/3752892*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+397651/6567561*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-1/21891870*(6006884+7817373*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1252 + +--S 1253 of 1751 +--a0:=integrate(t0,x) +--E 1253 + +--S 1254 of 1751 +--m0:=a0-r0 +--E 1254 + +--S 1255 of 1751 +--d0:=D(m0,x) +--E 1255 + +)clear all + +--S 1256 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (1) (- 6x + 11x + 76x + 89x + 30)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1751 +--r0:=-2/39*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)+1/27027*(43822+50771*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+886/1287*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+152657/416988*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 35611/1459458*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-1/2432430*(486863+783711*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1257 + +--S 1258 of 1751 +--a0:=integrate(t0,x) +--E 1258 + +--S 1259 of 1751 +--m0:=a0-r0 +--E 1259 + +--S 1260 of 1751 +--d0:=D(m0,x) +--E 1260 + +)clear all + +--S 1261 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x) +--R +--R +--R +------------+ +--R 3 2 +------+ | 2 +--R (1) (- 3x + 10x + 23x + 10)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1751 +--r0:=1/99*(119+127*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-_ +-- 2/33*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+15283/10692*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-706/2673*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/8910*(1246+3987*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1262 + +--S 1263 of 1751 +--a0:=integrate(t0,x) +--E 1263 + +--S 1264 of 1751 +--m0:=a0-r0 +--E 1264 + +--S 1265 of 1751 +--d0:=D(m0,x) +--E 1265 + +)clear all + +--S 1266 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1751 +--r0:=1/63*(52-7*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+11123/972*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-8179/3402*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/5670*(107+12429*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1267 + +--S 1268 of 1751 +--a0:=integrate(t0,x) +--E 1268 + +--S 1269 of 1751 +--m0:=a0-r0 +--E 1269 + +--S 1270 of 1751 +--d0:=D(m0,x) +--E 1270 + +)clear all + +--S 1271 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1751 +--r0:=-1/7*(47+x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x)-2411/36*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+899/63*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/210*(136-2493*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1272 + +--S 1273 of 1751 +--a0:=integrate(t0,x) +--E 1273 + +--S 1274 of 1751 +--m0:=a0-r0 +--E 1274 + +--S 1275 of 1751 +--d0:=D(m0,x) +--E 1275 + +)clear all + +--S 1276 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1751 +--r0:=-1/15*(37+3*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2)+367/4*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-39/2*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/10*(241+69*x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1277 + +--S 1278 of 1751 +--a0:=integrate(t0,x) +--E 1278 + +--S 1279 of 1751 +--m0:=a0-r0 +--E 1279 + +--S 1280 of 1751 +--d0:=D(m0,x) +--E 1280 + +)clear all + +--S 1281 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1751 +--r0:=-1/15*(27+5*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2)-2779/60*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+148/15*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/30*(707+411*x)*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-2779/150*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1282 + +--S 1283 of 1751 +--a0:=integrate(t0,x) +--E 1283 + +--S 1284 of 1751 +--m0:=a0-r0 +--E 1284 + +--S 1285 of 1751 +--d0:=D(m0,x) +--E 1285 + +)clear all + +--S 1286 of 1751 +t0:=(5-x)*(3+2*x)^(9/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 144x - 624x + 1304x + 14784x + 44295x + 70799x + 67449x +--R + +--R 2 +--R 38421x + 12096x + 1620 +--R * +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1751 +--r0:=222422/200583*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)+25418/35397*_ +-- (3+2*x)^(5/2)*(2+5*x+3*x^2)^(7/2)+1538/4347*(3+2*x)^(7/2)*_ +-- (2+5*x+3*x^2)^(7/2)-2/69*(3+2*x)^(9/2)*(2+5*x+3*x^2)^(7/2)-_ +-- 5/97580821338*(5514025312+6580844291*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+1/2323352889*(6295010279+7506271641*x)*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+8515726/5415741*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+_ +-- 12104518303/1505532672072*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-18804590219/5269364352252*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1/1756454784084*(62607985973+_ +-- 65705093631*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1287 + +--S 1288 of 1751 +--a0:=integrate(t0,x) +--E 1288 + +--S 1289 of 1751 +--m0:=a0-r0 +--E 1289 + +--S 1290 of 1751 +--d0:=D(m0,x) +--E 1290 + +)clear all + +--S 1291 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 72x - 204x + 958x + 5955x + 13215x + 15577x + 10359x + 3672x +--R + +--R 540 +--R * +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1751 +--r0:=2218/2907*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)+202/513*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(7/2)-2/63*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(7/2)-_ +-- 5/108785754*(4498331+5420233*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 1/2590137*(5130052+6113283*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+_ +-- 89294/78489*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+18269789/1678408776*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-10791761/2937215358*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1/1958143572*(51436624+44779653*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1292 + +--S 1293 of 1751 +--a0:=integrate(t0,x) +--E 1293 + +--S 1294 of 1751 +--m0:=a0-r0 +--E 1294 + +--S 1295 of 1751 +--d0:=D(m0,x) +--E 1295 + +)clear all + +--S 1296 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +------+ +--R (- 36x - 48x + 551x + 2151x + 3381x + 2717x + 1104x + 180)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1751 +--r0:=430/969*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)-2/57*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(7/2)-125/52378326*(64006+79583*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+25/1247103*(72737+86493*x)*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+2350/2907*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+_ +-- 16503475/808122744*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-15117425/2828429604*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+25/942809868*(749099+216603*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1297 + +--S 1298 of 1751 +--a0:=integrate(t0,x) +--E 1298 + +--S 1299 of 1751 +--m0:=a0-r0 +--E 1299 + +--S 1300 of 1751 +--d0:=D(m0,x) +--E 1300 + +)clear all + +--S 1301 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R +------------+ +--R 6 5 4 3 2 +------+ | 2 +--R (- 18x + 3x + 271x + 669x + 687x + 328x + 60)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1751 +--r0:=-2/51*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)-1/8270262*(949997+1332121*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/984555*(1063774+1253571*x)*_ +-- (2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+1166/2295*(2+5*x+3*x^2)^(7/2)*_ +-- sqrt(3+2*x)+34355693/127598328*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6809266/111648537*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+1/744323580*(12174838-22593339*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1302 + +--S 1303 of 1751 +--a0:=integrate(t0,x) +--E 1303 + +--S 1304 of 1751 +--m0:=a0-r0 +--E 1304 + +--S 1305 of 1751 +--d0:=D(m0,x) +--E 1305 + +)clear all + +--S 1306 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x) +--R +--R +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (1) (- 9x + 15x + 113x + 165x + 96x + 20)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1751 +--r0:=-1/162162*(15076+34643*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/19305*_ +-- (15467+17193*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-_ +-- 2/45*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+2742319/2501928*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-2066087/8756748*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 1/14594580*(287729-2667537*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1307 + +--S 1308 of 1751 +--a0:=integrate(t0,x) +--E 1308 + +--S 1309 of 1751 +--m0:=a0-r0 +--E 1309 + +--S 1310 of 1751 +--d0:=D(m0,x) +--E 1310 + +)clear all + +--S 1311 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1751 +--r0:=-5/18018*(563+4669*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 1/429*(224-33*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+651617/277992*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-242783/486486*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+_ +-- 1/324324*(34372-676791*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1312 + +--S 1313 of 1751 +--a0:=integrate(t0,x) +--E 1313 + +--S 1314 of 1751 +--m0:=a0-r0 +--E 1314 + +--S 1315 of 1751 +--d0:=D(m0,x) +--E 1315 + +)clear all + +--S 1316 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1751 +--r0:=-1/11*(73+x)*(2+5*x+3*x^2)^(5/2)/sqrt(3+2*x)+5/1386*(218+3031*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-451331/21384*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+336013/74844*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-_ +-- 1/24948*(21871-471213*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1317 + +--S 1318 of 1751 +--a0:=integrate(t0,x) +--E 1318 + +--S 1319 of 1751 +--m0:=a0-r0 +--E 1319 + +--S 1320 of 1751 +--d0:=D(m0,x) +--E 1320 + +)clear all + +--S 1321 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1751 +--r0:=-1/9*(21+x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(3/2)+5/126*(745+121*x)*_ +-- (2+5*x+3*x^2)^(3/2)/sqrt(3+2*x)+33335/648*elliptic_e(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-_ +-- 6205/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+5/756*(326-6957*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1322 + +--S 1323 of 1751 +--a0:=integrate(t0,x) +--E 1323 + +--S 1324 of 1751 +--m0:=a0-r0 +--E 1324 + +--S 1325 of 1751 +--d0:=D(m0,x) +--E 1325 + +)clear all + +--S 1326 of 1751 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1751 +--r0:=1/210*(2291+879*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2)-1/35*(53+5*x)*_ +-- (2+5*x+3*x^2)^(5/2)/(3+2*x)^(5/2)-2333/8*elliptic_e(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1737/28*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-1/140*(10763+3117*x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1327 + +--S 1328 of 1751 +--a0:=integrate(t0,x) +--E 1328 + +--S 1329 of 1751 +--m0:=a0-r0 +--E 1329 + +--S 1330 of 1751 +--d0:=D(m0,x) +--E 1330 + +)clear all + +--S 1331 of 1751 +t0:=(A+B*x)*(d+e*x)^(1/2)/(a+b*x+c*x^2)^(1/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1751 +--r0:=2/3*B*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c-1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*_ +-- (b*B*d-3*A*c*d+a*B*e)+(B*c*d-2*b*B*e+3*A*c*e)*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(B*c*d-2*b*B*e+3*A*c*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (c^(5/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 1332 + +--S 1333 of 1751 +--a0:=integrate(t0,x) +--E 1333 + +--S 1334 of 1751 +--m0:=a0-r0 +--E 1334 + +--S 1335 of 1751 +--d0:=D(m0,x) +--E 1335 + +)clear all + +--S 1336 of 1751 +t0:=(A+B*x)/((d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)) +--R +--R +--R B x + A +--R (1) --------------------------- +--R +--------------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1751 +--r0:=-elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*B-2*A*c-B*sqrt(b^2-4*a*c))*sqrt(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- B*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 1337 + +--S 1338 of 1751 +--a0:=integrate(t0,x) +--E 1338 + +--S 1339 of 1751 +--m0:=a0-r0 +--E 1339 + +--S 1340 of 1751 +--d0:=D(m0,x) +--E 1340 + +)clear all + +--S 1341 of 1751 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^(1/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------ +--R +--------------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1751 +--r0:=2*(B*d-A*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))+_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c))))*(-2*(b*B*d-A*c*d-a*B*e)+(B*d-A*e)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(B*d-A*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 1342 + +--S 1343 of 1751 +--a0:=integrate(t0,x) +--E 1343 + +--S 1344 of 1751 +--m0:=a0-r0 +--E 1344 + +--S 1345 of 1751 +--d0:=D(m0,x) +--E 1345 + +)clear all + +--S 1346 of 1751 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1751 +--r0:=-2*(A*b-2*a*B-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/((b^2-4*a*c)*_ +-- sqrt(a+b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/_ +-- (c*(b^2-4*a*c))+elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(b^2*B*d-2*a*c*(3*B*d+A*e)+_ +-- b*(A*c*d+a*B*e))+(b*B*c*d-2*A*c^2*d-2*b^2*B*e+A*b*c*e+6*a*B*c*e)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(5/2)*(b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))-(2*b^2*B*e-_ +-- b*c*(B*d+A*e)+2*c*(A*c*d-3*a*B*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (c^(5/2)*(b^2-4*a*c)*e*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 1347 + +--S 1348 of 1751 +--a0:=integrate(t0,x) +--E 1348 + +--S 1349 of 1751 +--m0:=a0-r0 +--E 1349 + +--S 1350 of 1751 +--d0:=D(m0,x) +--E 1350 + +)clear all + +--S 1351 of 1751 +t0:=(A+B*x)*(d+e*x)^(1/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1751 +--r0:=-2*(A*b-2*a*B-(b*B-2*A*c)*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ +-- sqrt(a+b*x+c*x^2))+elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*A*b*c-4*a*B*c+(b*B-2*A*c)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))+(b*B-2*A*c)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*(b^2-4*a*c)*e*_ +-- sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 1352 + +--S 1353 of 1751 +--a0:=integrate(t0,x) +--E 1353 + +--S 1354 of 1751 +--m0:=a0-r0 +--E 1354 + +--S 1355 of 1751 +--d0:=D(m0,x) +--E 1355 + +)clear all + +--S 1356 of 1751 +t0:=(A+B*x)/((d+e*x)^(1/2)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +--------------+ +--R 2 +-------+ | 2 +--R (c x + b x + a)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1751 +--r0:=2*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-_ +-- 2*a*B*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(a+b*x+c*x^2))-elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*b^2*B*d-4*a*c*(B*d-A*e)-_ +-- 2*b*(A*c*d+a*B*e)-(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(b*(B*d+A*e)-2*(A*c*d+a*B*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*e*(c*d^2-e*(b*d-a*e))*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 1357 + +--S 1358 of 1751 +--a0:=integrate(t0,x) +--E 1358 + +--S 1359 of 1751 +--m0:=a0-r0 +--E 1359 + +--S 1360 of 1751 +--d0:=D(m0,x) +--E 1360 + +)clear all + +--S 1361 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1751 +--r0:=-865/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+4540/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+10/7*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)-2/21*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)+_ +-- 1010/189*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1362 + +--S 1363 of 1751 +--a0:=integrate(t0,x) +--E 1363 + +--S 1364 of 1751 +--m0:=a0-r0 +--E 1364 + +--S 1365 of 1751 +--d0:=D(m0,x) +--E 1365 + +)clear all + +--S 1366 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1751 +--r0:=-2743/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+2254/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2/15*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+326/135*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1367 + +--S 1368 of 1751 +--a0:=integrate(t0,x) +--E 1368 + +--S 1369 of 1751 +--m0:=a0-r0 +--E 1369 + +--S 1370 of 1751 +--d0:=D(m0,x) +--E 1370 + +)clear all + +--S 1371 of 1751 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ------------------ +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1371 + +--S 1372 of 1751 +--r0:=-101/27*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+104/27*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-2/9*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1372 + +--S 1373 of 1751 +--a0:=integrate(t0,x) +--E 1373 + +--S 1374 of 1751 +--m0:=a0-r0 +--E 1374 + +--S 1375 of 1751 +--d0:=D(m0,x) +--E 1375 + +)clear all + +--S 1376 of 1751 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------ +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1376 + +--S 1377 of 1751 +--r0:=34/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1/3*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2) +--E 1377 + +--S 1378 of 1751 +--a0:=integrate(t0,x) +--E 1378 + +--S 1379 of 1751 +--m0:=a0-r0 +--E 1379 + +--S 1380 of 1751 +--d0:=D(m0,x) +--E 1380 + +)clear all + +--S 1381 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------- +--R +------------+ +--R +------+ | 2 +--R (2x + 3)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1381 + +--S 1382 of 1751 +--r0:=-13*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+12*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 26/5*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1382 + +--S 1383 of 1751 +--a0:=integrate(t0,x) +--E 1383 + +--S 1384 of 1751 +--m0:=a0-r0 +--E 1384 + +--S 1385 of 1751 +--d0:=D(m0,x) +--E 1385 + +)clear all + +--S 1386 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------- +--R +------------+ +--R 2 +------+ | 2 +--R (4x + 12x + 9)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1386 + +--S 1387 of 1751 +--r0:=-193/15*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+154/15*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 26/15*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-386/75*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1387 + +--S 1388 of 1751 +--a0:=integrate(t0,x) +--E 1388 + +--S 1389 of 1751 +--m0:=a0-r0 +--E 1389 + +--S 1390 of 1751 +--d0:=D(m0,x) +--E 1390 + +)clear all + +--S 1391 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------- +--R +------------+ +--R 3 2 +------+ | 2 +--R (8x + 36x + 54x + 27)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1391 + +--S 1392 of 1751 +--r0:=-4501/375*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+3328/375*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-26/25*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-_ +-- 782/375*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-9002/1875*sqrt(2+5*x+3*x^2)/_ +-- sqrt(3+2*x) +--E 1392 + +--S 1393 of 1751 +--a0:=integrate(t0,x) +--E 1393 + +--S 1394 of 1751 +--m0:=a0-r0 +--E 1394 + +--S 1395 of 1751 +--d0:=D(m0,x) +--E 1395 + +)clear all + +--S 1396 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1396 + +--S 1397 of 1751 +--r0:=-2*(3+2*x)^(7/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-34174/81*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+16072/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+308/5*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+140/3*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)+_ +-- 12068/135*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1397 + +--S 1398 of 1751 +--a0:=integrate(t0,x) +--E 1398 + +--S 1399 of 1751 +--m0:=a0-r0 +--E 1399 + +--S 1400 of 1751 +--d0:=D(m0,x) +--E 1400 + +)clear all + +--S 1401 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1401 + +--S 1402 of 1751 +--r0:=-2*(3+2*x)^(5/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-3830/81*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1340/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+140/3*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+1660/27*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1402 + +--S 1403 of 1751 +--a0:=integrate(t0,x) +--E 1403 + +--S 1404 of 1751 +--m0:=a0-r0 +--E 1404 + +--S 1405 of 1751 +--d0:=D(m0,x) +--E 1405 + +)clear all + +--S 1406 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1406 + +--S 1407 of 1751 +--r0:=-2*(3+2*x)^(3/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-274/9*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- sqrt(2+5*x+3*x^2)+64/9*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+140/3*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1407 + +--S 1408 of 1751 +--a0:=integrate(t0,x) +--E 1408 + +--S 1409 of 1751 +--m0:=a0-r0 +--E 1409 + +--S 1410 of 1751 +--d0:=D(m0,x) +--E 1410 + +)clear all + +--S 1411 of 1751 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1411 + +--S 1412 of 1751 +--r0:=68/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-70/3*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-2*(29+35*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 1412 + +--S 1413 of 1751 +--a0:=integrate(t0,x) +--E 1413 + +--S 1414 of 1751 +--m0:=a0-r0 +--E 1414 + +--S 1415 of 1751 +--d0:=D(m0,x) +--E 1415 + +)clear all + +--S 1416 of 1751 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R +------------+ +--R 2 +------+ | 2 +--R (3x + 5x + 2)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1416 + +--S 1417 of 1751 +--r0:=-94*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+24*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6/5*(37+47*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 1417 + +--S 1418 of 1751 +--a0:=integrate(t0,x) +--E 1418 + +--S 1419 of 1751 +--m0:=a0-r0 +--E 1419 + +--S 1420 of 1751 +--d0:=D(m0,x) +--E 1420 + +)clear all + +--S 1421 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------- +--R +------------+ +--R 3 2 +------+ | 2 +--R (6x + 19x + 19x + 6)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1421 + +--S 1422 of 1751 +--r0:=-454/5*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+172/5*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6/5*(37+47*x)/_ +-- (sqrt(3+2*x)*sqrt(2+5*x+3*x^2))-908/25*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1422 + +--S 1423 of 1751 +--a0:=integrate(t0,x) +--E 1423 + +--S 1424 of 1751 +--m0:=a0-r0 +--E 1424 + +--S 1425 of 1751 +--d0:=D(m0,x) +--E 1425 + +)clear all + +--S 1426 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------- +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (12x + 56x + 95x + 69x + 18)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1426 + +--S 1427 of 1751 +--r0:=-6/5*(37+47*x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2))-7438/75*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+3664/75*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2516/75*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-14876/375*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1427 + +--S 1428 of 1751 +--a0:=integrate(t0,x) +--E 1428 + +--S 1429 of 1751 +--m0:=a0-r0 +--E 1429 + +--S 1430 of 1751 +--d0:=D(m0,x) +--E 1430 + +)clear all + +--S 1431 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------------ +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (24x + 148x + 358x + 423x + 243x + 54)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1431 + +--S 1432 of 1751 +--r0:=-6/5*(37+47*x)/((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2))-213374/1875*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+121172/1875*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-4124/125*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-61468/1875*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(3/2)-426748/9375*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1432 + +--S 1433 of 1751 +--a0:=integrate(t0,x) +--E 1433 + +--S 1434 of 1751 +--m0:=a0-r0 +--E 1434 + +--S 1435 of 1751 +--d0:=D(m0,x) +--E 1435 + +)clear all + +--S 1436 of 1751 +t0:=(5-x)*(3+2*x)^(9/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 16x - 16x + 264x + 864x + 999x + 405)\|2x + 3 +--R (1) ----------------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1436 + +--S 1437 of 1751 +--r0:=-2/3*(3+2*x)^(9/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+4/3*(3+2*x)^(7/2)*_ +-- (445+569*x)/sqrt(2+5*x+3*x^2)+110516/243*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-21248/243*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-5416/9*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)-_ +-- 4552/9*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)-59512/81*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 1437 + +--S 1438 of 1751 +--a0:=integrate(t0,x) +--E 1438 + +--S 1439 of 1751 +--m0:=a0-r0 +--E 1439 + +--S 1440 of 1751 +--d0:=D(m0,x) +--E 1440 + +)clear all + +--S 1441 of 1751 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1441 + +--S 1442 of 1751 +--r0:=-2/3*(3+2*x)^(7/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+28/3*(3+2*x)^(5/2)*_ +-- (65+81*x)/sqrt(2+5*x+3*x^2)+31892/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-6776/81*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-504*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)-_ +-- 16744/27*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1442 + +--S 1443 of 1751 +--a0:=integrate(t0,x) +--E 1443 + +--S 1444 of 1751 +--m0:=a0-r0 +--E 1444 + +--S 1445 of 1751 +--d0:=D(m0,x) +--E 1445 + +)clear all + +--S 1446 of 1751 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1446 + +--S 1447 of 1751 +--r0:=-2/3*(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+20/3*(3+2*x)^(3/2)*_ +-- (93+113*x)/sqrt(2+5*x+3*x^2)+8620/27*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-1840/27*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- sqrt(2+5*x+3*x^2)-4520/9*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 1447 + +--S 1448 of 1751 +--a0:=integrate(t0,x) +--E 1448 + +--S 1449 of 1751 +--m0:=a0-r0 +--E 1449 + +--S 1450 of 1751 +--d0:=D(m0,x) +--E 1450 + +)clear all + +--S 1451 of 1751 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1451 + +--S 1452 of 1751 +--r0:=-2/3*(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)-2392/9*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+2252/9*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+4/3*(475+563*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 1452 + +--S 1453 of 1751 +--a0:=integrate(t0,x) +--E 1453 + +--S 1454 of 1751 +--m0:=a0-r0 +--E 1454 + +--S 1455 of 1751 +--d0:=D(m0,x) +--E 1455 + +)clear all + +--S 1456 of 1751 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1456 + +--S 1457 of 1751 +--r0:=-2/3*(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+2852/3*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-608/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/15*(1759+2139*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 1457 + +--S 1458 of 1751 +--a0:=integrate(t0,x) +--E 1458 + +--S 1459 of 1751 +--m0:=a0-r0 +--E 1459 + +--S 1460 of 1751 +--d0:=D(m0,x) +--E 1460 + +)clear all + +--S 1461 of 1751 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------- +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (9x + 30x + 37x + 20x + 4)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1461 + +--S 1462 of 1751 +--r0:=-2/5*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+3476/5*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-728/5*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/25*(2152+2607*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 1462 + +--S 1463 of 1751 +--a0:=integrate(t0,x) +--E 1463 + +--S 1464 of 1751 +--m0:=a0-r0 +--E 1464 + +--S 1465 of 1751 +--d0:=D(m0,x) +--E 1465 + +)clear all + +--S 1466 of 1751 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (18x + 87x + 164x + 151x + 68x + 12)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1466 + +--S 1467 of 1751 +--r0:=-2/5*(37+47*x)/((2+5*x+3*x^2)^(3/2)*sqrt(3+2*x))+11732/25*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-2096/25*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/25*(2054+2409*x)/(sqrt(3+2*x)*sqrt(2+5*x+3*x^2))+_ +-- 23464/125*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1467 + +--S 1468 of 1751 +--a0:=integrate(t0,x) +--E 1468 + +--S 1469 of 1751 +--m0:=a0-r0 +--E 1469 + +--S 1470 of 1751 +--d0:=D(m0,x) +--E 1470 + +)clear all + +--S 1471 of 1751 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R -------------------------------------------------------------------------- +--R +------------+ +--R 6 5 4 3 2 +------+ | 2 +--R (36x + 228x + 589x + 794x + 589x + 228x + 36)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1471 + +--S 1472 of 1751 +--r0:=-2/5*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2))+_ +-- 12/25*(652+737*x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2))+_ +-- 95396/375*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2888/375*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+61672/375*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(3/2)+190792/1875*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1472 + +--S 1473 of 1751 +--a0:=integrate(t0,x) +--E 1473 + +--S 1474 of 1751 +--m0:=a0-r0 +--E 1474 + +--S 1475 of 1751 +--d0:=D(m0,x) +--E 1475 + +)clear all + +--S 1476 of 1751 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 7 6 5 4 3 2 +------+ +--R (72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 1476 + +--S 1477 of 1751 +--r0:=-2/5*(37+47*x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2))+4/25*(1858+2013*x)/_ +-- ((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2))+107548/3125*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+280256/3125*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+87144/625*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(5/2)+258536/3125*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+_ +-- 215096/15625*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 1477 + +--S 1478 of 1751 +--a0:=integrate(t0,x) +--E 1478 + +--S 1479 of 1751 +--m0:=a0-r0 +--E 1479 + +--S 1480 of 1751 +--d0:=D(m0,x) +--E 1480 + +)clear all + +--S 1481 of 1751 +t0:=sqrt(x)/((1+x^2)*sqrt(1+x)) +--R +--R +--R +-+ +--R \|x +--R (1) ---------------- +--R 2 +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 1481 + +--S 1482 of 1751 +r0:=-1/2*(1-%i)^(3/2)*atanh(sqrt(1-%i)*sqrt(x)/sqrt(1+x))-_ + 1/2*(1+%i)^(3/2)*atanh(sqrt(1+%i)*sqrt(x)/sqrt(1+x)) +--R +--R +--R +------+ +-+ +------+ +-+ +--R +------+ \|1 + %i \|x +------+ \|1 - %i \|x +--R - %i\|1 + %i atanh(-------------) - \|1 - %i atanh(-------------) +--R +-----+ +-----+ +--R \|x + 1 \|x + 1 +--R (2) ----------------------------------------------------------------- +--R 1 + %i +--R Type: Expression(Complex(Integer)) +--E 1482 + +--S 1483 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R +-+4+-+ %pi +-+4+-+ %pi +-+ +-----+ +--R (\|2 \|2 sin(---) + \|2 \|2 cos(---) + 2x)\|x \|x + 1 +--R 8 8 +--R + +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) + (x - 1)\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R (x + 1)\|2 \|2 cos(---) + 2x + x + 1 +--R 8 +--R + +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R +-+4+-+ %pi +-+4+-+ %pi +-+ +-----+ +--R (- \|2 \|2 sin(---) - \|2 \|2 cos(---) + 2x)\|x \|x + 1 +--R 8 8 +--R + +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) + (- x + 1)\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R (- x - 1)\|2 \|2 cos(---) + 2x + x + 1 +--R 8 +--R + +--R - +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) + \|2 +--R 8 8 +--R atan(------------------------------------------------------) +--R +-+ +-+ +-----+ 4+-+ %pi 4+-+ %pi +-+ +--R \|2 \|x \|x + 1 - \|2 sin(---) - \|2 cos(---) + x\|2 +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) - \|2 +--R 4+-+ %pi 8 8 +--R - 2\|2 sin(---)atan(------------------------------------------------------) +--R 8 +-+ +-+ +-----+ 4+-+ %pi 4+-+ %pi +-+ +--R \|2 \|x \|x + 1 + \|2 sin(---) + \|2 cos(---) + x\|2 +--R 8 8 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 1483 + +--S 1484 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R +-+4+-+ %pi +-+4+-+ %pi +-+ +-----+ +--R (\|2 \|2 sin(---) + \|2 \|2 cos(---) + 2x)\|x \|x + 1 +--R 8 8 +--R + +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) + (x - 1)\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R (x + 1)\|2 \|2 cos(---) + 2x + x + 1 +--R 8 +--R + +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R +-+4+-+ %pi +-+4+-+ %pi +-+ +-----+ +--R (- \|2 \|2 sin(---) - \|2 \|2 cos(---) + 2x)\|x \|x + 1 +--R 8 8 +--R + +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) + (- x + 1)\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R (- x - 1)\|2 \|2 cos(---) + 2x + x + 1 +--R 8 +--R + +--R +------+ +-+ +--R +------+ +-+ \|1 + %i \|x +--R (1 + %i)\|1 + %i \|2 atanh(-------------) +--R +-----+ +--R \|x + 1 +--R + +--R +------+ +-+ +--R +------+ +-+ \|1 - %i \|x +--R (1 - %i)\|1 - %i \|2 atanh(-------------) +--R +-----+ +--R \|x + 1 +--R + +--R - +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) + \|2 +--R 8 8 +--R atan(------------------------------------------------------) +--R +-+ +-+ +-----+ 4+-+ %pi 4+-+ %pi +-+ +--R \|2 \|x \|x + 1 - \|2 sin(---) - \|2 cos(---) + x\|2 +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) - \|2 +--R 4+-+ %pi 8 8 +--R - 2\|2 sin(---)atan(------------------------------------------------------) +--R 8 +-+ +-+ +-----+ 4+-+ %pi 4+-+ %pi +-+ +--R \|2 \|x \|x + 1 + \|2 sin(---) + \|2 cos(---) + x\|2 +--R 8 8 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Complex(Integer)) +--E 1484 + +--S 1485 of 1751 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 3 2 %pi 12 3 2 %pi %pi 11 +--R (- 8x - 4x - 4)sin(---) + (- 32x - 16x - 16)cos(---)sin(---) +--R 8 8 8 +--R + +--R 3 2 %pi 2 +--R (- 80x - 40x - 40)cos(---) +--R 8 +--R + +--R 5 3 2 4+-+2 +--R (48x - 10x + 18x - 26x + 2)\|2 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 3 +--R (- 160x - 80x - 80)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (160x - 64x - 124x - 4x - 124x - 4)\|2 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 4 +--R (- 248x - 124x - 124)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 7 +--R (592x + 128x - 166x + 110x - 214x - 34)\|2 cos(---) - 64x +--R 8 +--R + +--R 6 5 4 3 2 +--R 544x + 668x + 230x + 332x + 84x - 2 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 5 +--R (- 320x - 160x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (1152x + 512x - 112x + 304x - 240x - 80)\|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi +--R (- 1024x + 512x + 1472x + 96x + 512x + 160x - 64x)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 6 +--R (- 352x - 176x - 176)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (1696x + 1024x + 52x + 540x - 172x - 132)\|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi 2 +--R (- 3584x - 768x + 2336x - 848x - 80x - 80x - 432x)cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R - 128x - 896x - 544x + 768x + 471x 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+--R + +--R 3 2 +--R 2552x + 840x - 11x - 3 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 2048x - 6912x - 12160x - 11520x - 7304x - 2962x - 192x +--R + +--R 3 2 +--R 20x + 8x - 2x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 9 +--R (- 160x - 80x - 80)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 7 +--R (1408x + 1536x + 688x + 784x + 304x - 112)\|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 9216x - 13824x - 4160x - 288x + 960x + 2336x + 640x +--R + +--R - 128 +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 17920x + 19968x - 13184x - 25728x - 18916x - 11796x +--R + +--R 3 2 +--R - 2400x + 672x + 68x - 12 +--R * +--R 4+-+2 %pi 3 +--R \|2 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R 8192x + 45056x + 78336x + 62208x + 29984x + 7792x +--R + +--R 5 4 3 2 +--R - 2712x - 1280x + 368x + 144x + 8x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 10 +--R (- 80x - 40x - 40)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 8 +--R (816x + 1024x + 534x + 530x + 262x - 62)\|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 6656x - 12544x - 8096x - 4464x - 1776x + 848x + 624x +--R + +--R - 64 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 11904x + 28032x + 18336x - 512x - 6267x - 6923x +--R + +--R 3 2 +--R - 3656x - 280x + 83x - 13 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 28672x - 38912x + 33024x + 93312x + 86160x + 53704x +--R + +--R 5 4 3 2 +--R 20012x + 2560x + 168x + 184x + 28x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 +--R - 4096x - 16384x - 32256x - 36352x - 27408x +--R + +--R 8 7 6 5 4 3 2 +--R - 15840x - 6890x - 2446x - 648x - 128x - 14x - 2x +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 11 +--R (- 32x - 16x - 16)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 9 +--R (288x + 448x + 276x + 236x + 148x - 20)\|2 cos(---) +--R 8 +--R + 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+--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 1152x + 4992x + 7968x + 7168x + 4913x + 2409x + 472x +--R + +--R 2 +--R - 24x + 7x - 1 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 4096x - 16384x - 30208x - 32512x - 23312x - 12320x +--R + +--R 5 4 3 +--R - 4218x - 480x + 68x + 6x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 4096x + 16384x + 28160x + 26112x + 14352x + 4448x +--R + +--R 7 6 5 4 3 2 +--R - 166x - 890x - 504x - 176x - 34x - 6x +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 7 +--R 8192x + 24576x + 35840x + 34816x + 24352x + 12832x + 5156x +--R + +--R 6 5 4 3 +--R 1552x + 344x + 48x + 4x +--R * +--R +-+ +-----+ +--R \|x \|x + 1 +--R + +--R 4 3 2 %pi 12 +--R (- 8x - 8x - 8x - 8x)sin(---) +--R 8 +--R + +--R 4 3 2 %pi %pi 11 +--R (- 32x - 32x - 32x - 32x)cos(---)sin(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (- 80x - 80x - 80x - 80x)cos(---) +--R 8 +--R + +--R 6 5 4 3 4+-+2 +--R (48x + 24x - 16x + 16x - 8x)\|2 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (- 160x - 160x - 160x - 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi +--R (160x + 16x - 176x - 48x - 80x - 64x)\|2 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (- 248x - 248x - 248x - 248x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 2 8 +--R (592x + 424x - 176x + 48x - 128x - 184x)\|2 cos(---) - 64x +--R 8 +--R + +--R 7 6 5 4 3 2 +--R 512x + 948x + 492x + 400x + 240x - 36x + 4x +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (- 320x - 320x - 320x - 320x)cos(---) +--R 8 +--R + +--R 6 5 3 2 4+-+2 %pi 3 +--R (1152x + 1088x + 256x - 128x - 320x)\|2 cos(---) +--R 8 +--R + +--R 8 6 5 4 3 2 %pi +--R (- 1024x + 1856x + 704x + 448x + 448x - 128x )cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (- 352x - 352x - 352x - 352x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 4 +--R (1696x + 1872x + 352x + 544x - 64x - 432x)\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (- 3584x - 2560x + 2400x + 192x - 704x + 64x - 544x - 128x) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 128x - 960x - 976x + 600x + 872x + 496x + 416x + 56x +--R + +--R 2 +--R 8x +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 7 +--R (- 320x - 320x - 320x - 320x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 5 +--R (2112x + 2720x + 992x + 992x + 160x - 448x)\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R - 5632x - 3072x + 8160x + 6880x + 3392x + 2112x - 416x +--R + +--R - 416x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R 1792x + 640x - 1824x + 3312x + 6984x + 5256x + 2976x +--R + +--R 3 2 +--R 720x - 8x - 8x +--R * +--R 4+-+2 %pi +--R \|2 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 8 +--R (- 248x - 248x - 248x - 248x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 6 +--R (1888x + 2736x + 1312x + 1120x + 320x - 336x)\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R - 11648x - 16896x - 1544x + 4136x + 3040x + 3872x + 744x +--R + +--R - 520x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R 1408x - 12992x - 36368x - 33096x - 16152x - 4336x + 2528x +--R + +--R 3 2 +--R 2008x + 136x - 32x +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 5 +--R - 2048x - 7936x - 15360x - 16864x - 11896x - 5720x - 1152x +--R + +--R 4 3 2 +--R 64x - 8x - 8x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 9 +--R (- 160x - 160x - 160x - 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 7 +--R (1408x + 2240x + 1280x + 1024x + 384x - 192x)\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R - 9216x - 18432x - 9920x - 1216x + 832x + 2880x + 1280x +--R + +--R - 256x +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R 17920x + 28928x - 5440x - 33696x - 29584x - 19152x +--R + +--R 4 3 2 +--R - 6848x + 288x + 272x - 48x +--R * +--R 4+-+2 %pi 3 +--R \|2 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 8192x + 49152x + 99840x + 96256x + 53792x + 18368x +--R + +--R 6 5 4 3 2 +--R - 672x - 2816x + 96x + 320x + 32x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 10 +--R (- 80x - 80x - 80x - 80x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 8 +--R (816x + 1432x + 944x + 720x + 320x - 72x)\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (- 6656x - 15872x - 13536x - 7360x - 3520x + 320x + 800x ) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R 11904x + 33984x + 30864x + 5896x - 7528x - 9616x - 6560x +--R + +--R 3 2 +--R - 1496x + 56x - 32x +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R - 28672x - 53248x + 17152x + 112896x + 127376x + 87920x +--R + +--R 6 5 4 3 2 +--R 40160x + 8832x + 560x + 272x + 96x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 4096x - 18432x - 39936x - 50688x - 42416x - 26488x +--R + +--R 8 7 6 5 4 +--R - 12760x - 4816x - 1472x - 312x - 56x +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 11 +--R (- 32x - 32x - 32x - 32x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 9 +--R (288x + 592x + 464x + 336x + 176x )\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R - 2560x - 7168x - 7648x - 5216x - 3136x - 832x + 160x +--R + +--R 32x +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R 6912x + 22656x + 29024x + 20272x + 9224x + 1288x - 1888x +--R + +--R 3 2 +--R - 1008x - 72x - 8x +--R * +--R 4+-+2 %pi 5 +--R \|2 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R - 16384x - 65536x - 96256x - 58880x - 3520x + 22208x +--R + +--R 6 5 4 3 2 +--R 23616x + 12288x + 2880x + 320x + 64x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R 8192x + 20480x + 2048x - 46080x - 77216x - 72144x +--R + +--R 8 7 6 5 4 3 +--R - 46848x - 22384x - 8128x - 2192x - 416x - 48x +--R * +--R 4+-+2 %pi 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64x - 16x +--R * +--R 4+-+2 %pi 5 +--R \|2 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R - 9216x - 52224x - 109824x - 138240x - 133384x - 90856x +--R + +--R 6 5 4 3 2 +--R - 33560x - 5112x - 760x - 280x + 24x - 8x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 +--R 20480x + 71680x + 124672x + 157056x + 149328x +--R + +--R 9 8 7 6 5 4 3 2 +--R 100984x + 48344x + 15976x + 3240x + 392x + 40x + 24x + 8x +--R * +--R 4+-+2 %pi +--R \|2 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 12 +--R (- 8x - 8x - 8x - 8x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 10 +--R (32x + 80x + 80x + 80x + 48x )\|2 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 %pi 8 +--R (- 192x - 896x - 1464x - 1544x - 1360x - 656x - 88x - 8x)cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 3 +--R 512x + 2560x + 5728x + 7552x + 7328x + 5312x + 2144x + 320x +--R + +--R 2 +--R 32x +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R - 2304x - 11008x - 26432x - 40704x - 44674x - 37258x +--R + +--R 6 5 4 3 2 +--R - 22070x - 7806x - 1534x - 246x - 10x - 2x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R 2048x + 15360x + 40320x + 63936x + 76424x + 69164x +--R + +--R 8 7 6 5 4 3 2 +--R 45868x + 22564x + 8052x + 2004x + 340x + 28x + 4x +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 16 15 14 13 12 11 +--R - 8192x - 32768x - 68608x - 103424x - 119584x - 107840x +--R + +--R 10 9 8 7 6 5 4 3 +--R - 77156x - 43892x - 19884x - 7100x - 1948x - 396x - 52x - 4x +--R Type: Expression(Complex(Integer)) +--E 1485 + +)clear all + +--S 1486 of 1751 +t0:=(-1+2*x^2)/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 2 +--R 2x - 1 +--R (1) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 1486 + +--S 1487 of 1751 +r0:=x*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R (2) x\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 1487 + +--S 1488 of 1751 +a0:=integrate(t0,x) +--R +--R +--R +-----+ +-----+ +--R (3) x\|x - 1 \|x + 1 +--R Type: Union(Expression(Integer),...) +--E 1488 + +--S 1489 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1489 + +--S 1490 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1490 + +)clear all + +--S 1491 of 1751 +t0:=(a+c*x^2)/(sqrt(d+e*x)*sqrt(f+g*x)) +--R +--R +--R 2 +--R c x + a +--R (1) -------------------- +--R +-------+ +-------+ +--R \|e x + d \|g x + f +--R Type: Expression(Integer) +--E 1491 + +--S 1492 of 1751 +r0:=-1/4*c*(4*d*e*f*g-3*(e*f+d*g)^2)*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*_ + sqrt(f+g*x)))/(e^(5/2)*g^(5/2))+2*a*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*_ + sqrt(f+g*x)))/(sqrt(e)*sqrt(g))-3/4*c*(e*f+d*g)*sqrt(d+e*x)*_ + sqrt(f+g*x)/(e^2*g^2)+1/2*c*x*sqrt(d+e*x)*sqrt(f+g*x)/(e*g) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 \|g \|e x + d +--R ((8a e + 3c d )g + 2c d e f g + 3c e f )atanh(--------------) +--R +-+ +-------+ +--R \|e \|g x + f +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2c e g x - 3c d g - 3c e f)\|e \|g \|e x + d \|g x + f +--R / +--R 2 2 +-+ +-+ +--R 4e g \|e \|g +--R Type: Expression(Integer) +--E 1492 + +--S 1493 of 1751 +--a0:=integrate(t0,x) +--E 1493 + +--S 1494 of 1751 +--m0:=a0-r0 +--E 1494 + +--S 1495 of 1751 +--d0:=D(m0,x) +--E 1495 + +)clear all + +--S 1496 of 1751 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - e g x + (- 3d e g - 2e f g)x + (- 3d e g - 6d e f g - e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- d g - 6d e f g - 3d e f )x + (- 2d f g - 3d e f )x - d f +--R / +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1496 + +--S 1497 of 1751 +r0:=-d^2*(7*e^2*f^2+16*d*e*f*g+8*d^2*g^2)*x/e^2-d*(2*e^2*f^2+7*d*e*f*g+_ + 4*d^2*g^2)*x^2/e-1/3*(e*f+d*g)*(e*f+7*d*g)*x^3-1/2*e*g*(e*f+2*d*g)*x^4-_ + 1/5*e^2*g^2*x^5-8*d^3*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 5 2 4 3 2 2 5 2 5 +--R (- 240d g - 480d e f g - 240d e f )log(- e x + d) - 6e g x +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (- 30d e g - 15e f g)x + (- 70d e g - 80d e f g - 10e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 120d e g - 210d e f g - 60d e f )x +--R + +--R 4 2 3 2 2 3 2 +--R (- 240d e g - 480d e f g - 210d e f )x +--R / +--R 3 +--R 30e +--R Type: Expression(Integer) +--E 1497 + +--S 1498 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 3 2 2 5 2 5 +--R (- 240d g - 480d e f g - 240d e f )log(e x - d) - 6e g x +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (- 30d e g - 15e f g)x + (- 70d e g - 80d e f g - 10e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 120d e g - 210d e f g - 60d e f )x +--R + +--R 4 2 3 2 2 3 2 +--R (- 240d e g - 480d e f g - 210d e f )x +--R / +--R 3 +--R 30e +--R Type: Union(Expression(Integer),...) +--E 1498 + +--S 1499 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 4 3 2 2 +--R (- 8d g - 16d e f g - 8d e f )log(e x - d) +--R + +--R 5 2 4 3 2 2 +--R (8d g + 16d e f g + 8d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1499 + +--S 1500 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1500 + +)clear all + +--S 1501 of 1751 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R - e g x + (- 2d e g - 2e f g)x + (- d g - 4d e f g - e f )x +--R + +--R 2 2 2 2 +--R (- 2d f g - 2d e f )x - d f +--R / +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1501 + +--S 1502 of 1751 +r0:=-d*(e*f+2*d*g)*(3*e*f+2*d*g)*x/e^2-1/2*(e^2*f^2+6*d*e*f*g+_ + 4*d^2*g^2)*x^2/e-1/3*g*(2*e*f+3*d*g)*x^3-1/4*e*g^2*x^4-_ + 4*d^2*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 3 2 2 2 4 2 4 +--R (- 48d g - 96d e f g - 48d e f )log(- e x + d) - 3e g x +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (- 12d e g - 8e f g)x + (- 24d e g - 36d e f g - 6e f )x +--R + +--R 3 2 2 2 3 2 +--R (- 48d e g - 96d e f g - 36d e f )x +--R / +--R 3 +--R 12e +--R Type: Expression(Integer) +--E 1502 + +--S 1503 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 2 2 2 4 2 4 +--R (- 48d g - 96d e f g - 48d e f )log(e x - d) - 3e g x +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (- 12d e g - 8e f g)x + (- 24d e g - 36d e f g - 6e f )x +--R + +--R 3 2 2 2 3 2 +--R (- 48d e g - 96d e f g - 36d e f )x +--R / +--R 3 +--R 12e +--R Type: Union(Expression(Integer),...) +--E 1503 + +--S 1504 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 3 2 2 2 +--R (- 4d g - 8d e f g - 4d e f )log(e x - d) +--R + +--R 4 2 3 2 2 2 +--R (4d g + 8d e f g + 4d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1504 + +--S 1505 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1505 + +)clear all + +--S 1506 of 1751 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R - e g x + (- d g - 2e f g)x + (- 2d f g - e f )x - d f +--R (1) ---------------------------------------------------------- +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1506 + +--S 1507 of 1751 +r0:=-2*d*g*(e*f+d*g)*x/e^2-d*(f+g*x)^2/e-1/3*(f+g*x)^3/g-_ + 2*d*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 +--R (- 6d g - 12d e f g - 6d e f g)log(- e x + d) - e g x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 2 2 +--R (- 3d e g - 3e f g )x + (- 6d e g - 12d e f g - 3e f g)x - 3d e f g +--R + +--R 3 3 +--R - e f +--R / +--R 3 +--R 3e g +--R Type: Expression(Integer) +--E 1507 + +--S 1508 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 2 3 +--R (- 6d g - 12d e f g - 6d e f )log(e x - d) - e g x +--R + +--R 2 2 3 2 2 2 2 3 2 +--R (- 3d e g - 3e f g)x + (- 6d e g - 12d e f g - 3e f )x +--R / +--R 3 +--R 3e +--R Type: Union(Expression(Integer),...) +--E 1508 + +--S 1509 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 +--R (- 6d g - 12d e f g - 6d e f g)log(e x - d) +--R + +--R 3 3 2 2 2 2 2 2 3 3 +--R (6d g + 12d e f g + 6d e f g)log(- e x + d) + 3d e f g + e f +--R / +--R 3 +--R 3e g +--R Type: Expression(Integer) +--E 1509 + +--S 1510 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1510 + +)clear all + +--S 1511 of 1751 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------- +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1511 + +--S 1512 of 1751 +r0:=-g*(e*f+d*g)*x/e^2-1/2*(f+g*x)^2/e-(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (- 2d g - 4d e f g - 2e f )log(- e x + d) - e g x +--R + +--R 2 2 2 2 +--R (- 2d e g - 4e f g)x - e f +--R / +--R 3 +--R 2e +--R Type: Expression(Integer) +--E 1512 + +--S 1513 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R (- 2d g - 4d e f g - 2e f )log(e x - d) - e g x + (- 2d e g - 4e f g)x +--R ------------------------------------------------------------------------- +--R 3 +--R 2e +--R Type: Union(Expression(Integer),...) +--E 1513 + +--S 1514 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- 2d g - 4d e f g - 2e f )log(e x - d) +--R + +--R 2 2 2 2 2 2 +--R (2d g + 4d e f g + 2e f )log(- e x + d) + e f +--R / +--R 3 +--R 2e +--R Type: Expression(Integer) +--E 1514 + +--S 1515 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1515 + +)clear all + +--S 1516 of 1751 +t0:=(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------- +--R 2 2 2 +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1516 + +--S 1517 of 1751 +r0:=-g^2*x/e^2-1/2*(e*f+d*g)^2*log(d-e*x)/(d*e^3)+_ + 1/2*(e*f-d*g)^2*log(d+e*x)/(d*e^3) +--R +--R +--R (2) +--R 2 2 2 2 +--R (d g - 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 2 +--R (- d g - 2d e f g - e f )log(- e x + d) - 2d e g x +--R / +--R 3 +--R 2d e +--R Type: Expression(Integer) +--E 1517 + +--S 1518 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R (d g - 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) - 2d e g x +--R / +--R 3 +--R 2d e +--R Type: Union(Expression(Integer),...) +--E 1518 + +--S 1519 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 +--R (d g + 2d e f g + e f )log(- e x + d) +--R / +--R 3 +--R 2d e +--R Type: Expression(Integer) +--E 1519 + +--S 1520 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1520 + +)clear all + +--S 1521 of 1751 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------------- +--R 3 3 2 2 2 3 +--R e x + d e x - d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1521 + +--S 1522 of 1751 +r0:=-1/2*(e*f-d*g)^2/(d*e^3*(d+e*x))-1/4*(e*f+d*g)^2*log(d-e*x)/(d^2*e^3)+_ + 1/4*(e*f-d*g)*(e*f+3*d*g)*log(d+e*x)/(d^2*e^3) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3d e g + 2d e f g + e f )x - 3d g + 2d e f g + d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- d e g - 2d e f g - e f )x - d g - 2d e f g - d e f )log(- e x + d) +--R + +--R 3 2 2 2 2 +--R - 2d g + 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x + 4d e +--R Type: Expression(Integer) +--E 1522 + +--S 1523 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3d e g + 2d e f g + e f )x - 3d g + 2d e f g + d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- d e g - 2d e f g - e f )x - d g - 2d e f g - d e f )log(e x - d) +--R + +--R 3 2 2 2 2 +--R - 2d g + 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 1523 + +--S 1524 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 +--R (d g + 2d e f g + e f )log(- e x + d) +--R / +--R 2 3 +--R 4d e +--R Type: Expression(Integer) +--E 1524 + +--S 1525 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1525 + +)clear all + +--S 1526 of 1751 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 4 4 3 3 3 4 +--R e x + 2d e x - 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1526 + +--S 1527 of 1751 +r0:=-1/4*(e*f-d*g)^2/(d*e^3*(d+e*x)^2)-1/4*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x))+1/4*(e*f+d*g)^2*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 4 2 +--R (d e g + 2d e f g + e f )x + (2d e g + 4d e f g + 2d e f )x + d g +--R + +--R 3 2 2 2 +--R 2d e f g + d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (3d e g - 2d e f g - d e f )x + 2d g - 2d e f +--R / +--R 3 5 2 4 4 5 3 +--R 4d e x + 8d e x + 4d e +--R Type: Expression(Integer) +--E 1527 + +--S 1528 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 4 2 +--R (d e g + 2d e f g + e f )x + (2d e g + 4d e f g + 2d e f )x + d g +--R + +--R 3 2 2 2 +--R 2d e f g + d e f +--R * +--R log(e x + d) +--R + +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (- d e g - 2d e f g - e f )x + (- 2d e g - 4d e f g - 2d e f )x +--R + +--R 4 2 3 2 2 2 +--R - d g - 2d e f g - d e f +--R * +--R log(e x - d) +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (6d e g - 4d e f g - 2d e f )x + 4d g - 4d e f +--R / +--R 3 5 2 4 4 5 3 +--R 8d e x + 16d e x + 8d e +--R Type: Union(Expression(Integer),...) +--E 1528 + +--S 1529 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g + 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g - 4d e f g - 2e f )atanh(---) +--R d +--R / +--R 3 3 +--R 8d e +--R Type: Expression(Integer) +--E 1529 + +--S 1530 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1530 + +)clear all + +--S 1531 of 1751 +t0:=(f+g*x)^2/((d+e*x)^3*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 3d e x + 2d e x - 2d e x - 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1531 + +--S 1532 of 1751 +r0:=-1/6*(e*f-d*g)^2/(d*e^3*(d+e*x)^3)-1/8*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x)^2)-1/8*(e*f+d*g)^2/(d^3*e^3*(d+e*x))+_ + 1/8*(e*f+d*g)^2*atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (3d e g + 6d e f g + 3e f )x + (9d e g + 18d e f g + 9d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (9d e g + 18d e f g + 9d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (- 3d e g - 6d e f g - 3d e f )x + (3d e g - 18d e f g - 9d e f )x +--R + +--R 5 2 4 3 2 2 +--R 2d g - 4d e f g - 10d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 24d e x + 72d e x + 72d e x + 24d e +--R Type: Expression(Integer) +--E 1532 + +--S 1533 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (3d e g + 6d e f g + 3e f )x + (9d e g + 18d e f g + 9d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (9d e g + 18d e f g + 9d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R log(e x + d) +--R + +--R 2 3 2 4 5 2 3 +--R (- 3d e g - 6d e f g - 3e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 9d e g - 18d e f g - 9d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 9d e g - 18d e f g - 9d e f )x - 3d g - 6d e f g - 3d e f +--R * +--R log(e x - d) +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (- 6d e g - 12d e f g - 6d e f )x + (6d e g - 36d e f g - 18d e f )x +--R + +--R 5 2 4 3 2 2 +--R 4d g - 8d e f g - 20d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 48d e x + 144d e x + 144d e x + 48d e +--R Type: Union(Expression(Integer),...) +--E 1533 + +--S 1534 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g + 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g - 4d e f g - 2e f )atanh(---) +--R d +--R / +--R 4 3 +--R 16d e +--R Type: Expression(Integer) +--E 1534 + +--S 1535 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1535 + +)clear all + +--S 1536 of 1751 +t0:=(f+g*x)^2/((d+e*x)^4*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------ +--R 6 6 5 5 2 4 4 4 2 2 5 6 +--R e x + 4d e x + 5d e x - 5d e x - 4d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1536 + +--S 1537 of 1751 +r0:=-1/8*(e*f-d*g)^2/(d*e^3*(d+e*x)^4)-1/12*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x)^3)-1/16*(e*f+d*g)^2/(d^3*e^3*(d+e*x)^2)-_ + 1/16*(e*f+d*g)^2/(d^4*e^3*(d+e*x))+1/16*(e*f+d*g)^2*atanh(e*x/d)/(d^5*e^3) +--R +--R +--R (2) +--R 2 4 2 5 6 2 4 3 3 2 2 4 5 2 3 +--R (3d e g + 6d e f g + 3e f )x + (12d e g + 24d e f g + 12d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (18d e g + 36d e f g + 18d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (12d e g + 24d e f g + 12d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 3d e g - 6d e f g - 3d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 12d e g - 24d e f g - 12d e f )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (- 3d e g - 38d e f g - 19d e f )x - 8d e f g - 16d e f +--R / +--R 5 7 4 6 6 3 7 5 2 8 4 9 3 +--R 48d e x + 192d e x + 288d e x + 192d e x + 48d e +--R Type: Expression(Integer) +--E 1537 + +--S 1538 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 5 6 2 4 3 3 2 2 4 5 2 3 +--R (3d e g + 6d e f g + 3e f )x + (12d e g + 24d e f g + 12d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (18d e g + 36d e f g + 18d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (12d e g + 24d e f g + 12d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R log(e x + d) +--R + +--R 2 4 2 5 6 2 4 +--R (- 3d e g - 6d e f g - 3e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 12d e g - 24d e f g - 12d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 18d e g - 36d e f g - 18d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 12d e g - 24d e f g - 12d e f )x - 3d g - 6d e f g - 3d e f +--R * +--R log(e x - d) +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 6d e g - 12d e f g - 6d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 24d e g - 48d e f g - 24d e f )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (- 6d e g - 76d e f g - 38d e f )x - 16d e f g - 32d e f +--R / +--R 5 7 4 6 6 3 7 5 2 8 4 9 3 +--R 96d e x + 384d e x + 576d e x + 384d e x + 96d e +--R Type: Union(Expression(Integer),...) +--E 1538 + +--S 1539 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g + 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g - 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g - 4d e f g - 2e f )atanh(---) +--R d +--R / +--R 5 3 +--R 32d e +--R Type: Expression(Integer) +--E 1539 + +--S 1540 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1540 + +)clear all + +--S 1541 of 1751 +t0:=(d+e*x)^7*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R e g x + (5d e g + 2e f g)x + (10d e g + 10d e f g + e f )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10d e g + 20d e f g + 5d e f )x + (5d e g + 20d e f g + 10d e f )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (d g + 10d e f g + 10d e f )x + (2d f g + 5d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1541 + +--S 1542 of 1751 +r0:=d^3*(49*e^2*f^2+160*d*e*f*g+112*d^2*g^2)*x/e^2+1/2*d^2*(23*e^2*f^2+_ + 98*d*e*f*g+80*d^2*g^2)*x^2/e+1/3*d*(7*e^2*f^2+46*d*e*f*g+49*d^2*g^2)*_ + x^3+1/4*e*(e^2*f^2+14*d*e*f*g+23*d^2*g^2)*x^4+1/5*e^2*g*(2*e*f+7*d*g)*_ + x^5+1/6*e^3*g^2*x^6+32*d^5*(e*f+d*g)^2/(e^3*(d-e*x))+_ + 16*d^4*(e*f+d*g)*(5*e*f+9*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 6 2 5 2 4 3 2 7 2 6 +--R (8640d e g + 13440d e f g + 4800d e f )x - 8640d g - 13440d e f g +--R + +--R 5 2 2 +--R - 4800d e f +--R * +--R log(- e x + d) +--R + +--R 7 2 7 6 2 7 6 2 5 2 6 7 2 5 +--R 10e g x + (74d e g + 24e f g)x + (261d e g + 186d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (635d e g + 710d e f g + 125d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (1420d e g + 2020d e f g + 550d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (4320d e g + 6660d e f g + 2250d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 +--R (- 6720d e g - 9600d e f g - 2940d e f )x - 1920d g - 3840d e f g +--R + +--R 5 2 2 +--R - 1920d e f +--R / +--R 4 3 +--R 60e x - 60d e +--R Type: Expression(Integer) +--E 1542 + +--S 1543 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 5 2 4 3 2 7 2 6 +--R (8640d e g + 13440d e f g + 4800d e f )x - 8640d g - 13440d e f g +--R + +--R 5 2 2 +--R - 4800d e f +--R * +--R log(e x - d) +--R + +--R 7 2 7 6 2 7 6 2 5 2 6 7 2 5 +--R 10e g x + (74d e g + 24e f g)x + (261d e g + 186d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (635d e g + 710d e f g + 125d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (1420d e g + 2020d e f g + 550d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (4320d e g + 6660d e f g + 2250d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 +--R (- 6720d e g - 9600d e f g - 2940d e f )x - 1920d g - 3840d e f g +--R + +--R 5 2 2 +--R - 1920d e f +--R / +--R 4 3 +--R 60e x - 60d e +--R Type: Union(Expression(Integer),...) +--E 1543 + +--S 1544 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 2 5 4 2 2 +--R (144d g + 224d e f g + 80d e f )log(e x - d) +--R + +--R 6 2 5 4 2 2 +--R (- 144d g - 224d e f g - 80d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1544 + +--S 1545 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1545 + +)clear all + +--S 1546 of 1751 +t0:=(d+e*x)^6*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R e g x + (4d e g + 2e f g)x + (6d e g + 8d e f g + e f )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4d e g + 12d e f g + 4d e f )x + (d g + 8d e f g + 6d e f )x +--R + +--R 4 3 2 4 2 +--R (2d f g + 4d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1546 + +--S 1547 of 1751 +r0:=d^2*(17*e^2*f^2+64*d*e*f*g+48*d^2*g^2)*x/e^2+d*(3*e^2*f^2+17*d*e*f*g+_ + 16*d^2*g^2)*x^2/e+1/3*(e^2*f^2+12*d*e*f*g+17*d^2*g^2)*x^3+_ + 1/2*e*g*(e*f+3*d*g)*x^4+1/5*e^2*g^2*x^5+16*d^4*(e*f+d*g)^2/(e^3*(d-e*x))+_ + 32*d^3*(e*f+d*g)*(e*f+2*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 5 2 4 2 3 3 2 6 2 5 +--R (1920d e g + 2880d e f g + 960d e f )x - 1920d g - 2880d e f g +--R + +--R 4 2 2 +--R - 960d e f +--R * +--R log(- e x + d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 6e g x + (39d e g + 15e f g)x + (125d e g + 105d e f g + 10e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (310d e g + 390d e f g + 80d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (960d e g + 1410d e f g + 420d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (- 1440d e g - 1920d e f g - 510d e f )x - 480d g - 960d e f g +--R + +--R 4 2 2 +--R - 480d e f +--R / +--R 4 3 +--R 30e x - 30d e +--R Type: Expression(Integer) +--E 1547 + +--S 1548 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 2 3 3 2 6 2 5 +--R (1920d e g + 2880d e f g + 960d e f )x - 1920d g - 2880d e f g +--R + +--R 4 2 2 +--R - 960d e f +--R * +--R log(e x - d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 6e g x + (39d e g + 15e f g)x + (125d e g + 105d e f g + 10e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (310d e g + 390d e f g + 80d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (960d e g + 1410d e f g + 420d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (- 1440d e g - 1920d e f g - 510d e f )x - 480d g - 960d e f g +--R + +--R 4 2 2 +--R - 480d e f +--R / +--R 4 3 +--R 30e x - 30d e +--R Type: Union(Expression(Integer),...) +--E 1548 + +--S 1549 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 4 3 2 2 +--R (64d g + 96d e f g + 32d e f )log(e x - d) +--R + +--R 5 2 4 3 2 2 +--R (- 64d g - 96d e f g - 32d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1549 + +--S 1550 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1550 + +)clear all + +--S 1551 of 1751 +t0:=(d+e*x)^5*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R e g x + (3d e g + 2e f g)x + (3d e g + 6d e f g + e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (d g + 6d e f g + 3d e f )x + (2d f g + 3d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1551 + +--S 1552 of 1751 +r0:=d*(5*e^2*f^2+24*d*e*f*g+20*d^2*g^2)*x/e^2+1/2*(e^2*f^2+_ + 10*d*e*f*g+12*d^2*g^2)*x^2/e+1/3*g*(2*e*f+5*d*g)*x^3+1/4*e*g^2*x^4+_ + 8*d^3*(e*f+d*g)^2/(e^3*(d-e*x))+4*d^2*(e*f+d*g)*(3*e*f+7*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 3 2 2 3 2 5 2 4 +--R (336d e g + 480d e f g + 144d e f )x - 336d g - 480d e f g +--R + +--R 3 2 2 +--R - 144d e f +--R * +--R log(- e x + d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 3e g x + (17d e g + 8e f g)x + (52d e g + 52d e f g + 6e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (168d e g + 228d e f g + 54d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 240d e g - 288d e f g - 60d e f )x - 96d g - 192d e f g - 96d e f +--R / +--R 4 3 +--R 12e x - 12d e +--R Type: Expression(Integer) +--E 1552 + +--S 1553 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 2 2 3 2 5 2 4 +--R (336d e g + 480d e f g + 144d e f )x - 336d g - 480d e f g +--R + +--R 3 2 2 +--R - 144d e f +--R * +--R log(e x - d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 3e g x + (17d e g + 8e f g)x + (52d e g + 52d e f g + 6e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (168d e g + 228d e f g + 54d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 240d e g - 288d e f g - 60d e f )x - 96d g - 192d e f g - 96d e f +--R / +--R 4 3 +--R 12e x - 12d e +--R Type: Union(Expression(Integer),...) +--E 1553 + +--S 1554 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 3 2 2 2 +--R (28d g + 40d e f g + 12d e f )log(e x - d) +--R + +--R 4 2 3 2 2 2 +--R (- 28d g - 40d e f g - 12d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1554 + +--S 1555 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1555 + +)clear all + +--S 1556 of 1751 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R e g x + (2d e g + 2e f g)x + (d g + 4d e f g + e f )x +--R + +--R 2 2 2 2 +--R (2d f g + 2d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1556 + +--S 1557 of 1751 +r0:=(e^2*f^2+8*d*e*f*g+8*d^2*g^2)*x/e^2+g*(e*f+2*d*g)*x^2/e+1/3*g^2*x^3+_ + 4*d^2*(e*f+d*g)^2/(e^3*(d-e*x))+4*d*(e*f+d*g)*(e*f+3*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R ((36d e g + 48d e f g + 12d e f )x - 36d g - 48d e f g - 12d e f ) +--R * +--R log(- e x + d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R e g x + (5d e g + 3e f g)x + (18d e g + 21d e f g + 3e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- 24d e g - 24d e f g - 3d e f )x - 12d g - 24d e f g - 12d e f +--R / +--R 4 3 +--R 3e x - 3d e +--R Type: Expression(Integer) +--E 1557 + +--S 1558 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R ((36d e g + 48d e f g + 12d e f )x - 36d g - 48d e f g - 12d e f ) +--R * +--R log(e x - d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R e g x + (5d e g + 3e f g)x + (18d e g + 21d e f g + 3e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- 24d e g - 24d e f g - 3d e f )x - 12d g - 24d e f g - 12d e f +--R / +--R 4 3 +--R 3e x - 3d e +--R Type: Union(Expression(Integer),...) +--E 1558 + +--S 1559 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 2 2 +--R (12d g + 16d e f g + 4d e f )log(e x - d) +--R + +--R 3 2 2 2 2 +--R (- 12d g - 16d e f g - 4d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1559 + +--S 1560 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1560 + +)clear all + +--S 1561 of 1751 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R e g x + (d g + 2e f g)x + (2d f g + e f )x + d f +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1561 + +--S 1562 of 1751 +r0:=g*(2*e*f+3*d*g)*x/e^2+1/2*g^2*x^2/e+2*d*(e*f+d*g)^2/(e^3*(d-e*x))+_ + (e*f+d*g)*(e*f+5*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((10d e g + 12d e f g + 2e f )x - 10d g - 12d e f g - 2d e f ) +--R * +--R log(- e x + d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R e g x + (5d e g + 4e f g)x + (- 6d e g - 4d e f g)x - 4d g +--R + +--R 2 2 2 +--R - 8d e f g - 4d e f +--R / +--R 4 3 +--R 2e x - 2d e +--R Type: Expression(Integer) +--E 1562 + +--S 1563 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((10d e g + 12d e f g + 2e f )x - 10d g - 12d e f g - 2d e f ) +--R * +--R log(e x - d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R e g x + (5d e g + 4e f g)x + (- 6d e g - 4d e f g)x - 4d g +--R + +--R 2 2 2 +--R - 8d e f g - 4d e f +--R / +--R 4 3 +--R 2e x - 2d e +--R Type: Union(Expression(Integer),...) +--E 1563 + +--S 1564 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (5d g + 6d e f g + e f )log(e x - d) +--R + +--R 2 2 2 2 +--R (- 5d g - 6d e f g - e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1564 + +--S 1565 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1565 + +)clear all + +--S 1566 of 1751 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------ +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1566 + +--S 1567 of 1751 +r0:=g^2*x/e^2+(e*f+d*g)^2/(e^3*(d-e*x))+2*g*(e*f+d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R ((2d e g + 2e f g)x - 2d g - 2d e f g)log(- e x + d) + e g x - d e g x +--R + +--R 2 2 2 2 +--R - d g - 2d e f g - e f +--R / +--R 4 3 +--R e x - d e +--R Type: Expression(Integer) +--E 1567 + +--S 1568 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 +--R ((2d e g + 2e f g)x - 2d g - 2d e f g)log(e x - d) + e g x - d e g x +--R + +--R 2 2 2 2 +--R - d g - 2d e f g - e f +--R / +--R 4 3 +--R e x - d e +--R Type: Union(Expression(Integer),...) +--E 1568 + +--S 1569 of 1751 +m0:=a0-r0 +--R +--R +--R 2 2 +--R (2d g + 2e f g)log(e x - d) + (- 2d g - 2e f g)log(- e x + d) +--R (4) --------------------------------------------------------------- +--R 3 +--R e +--R Type: Expression(Integer) +--E 1569 + +--S 1570 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1570 + +)clear all + +--S 1571 of 1751 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) -------------------------- +--R 3 3 2 2 2 3 +--R e x - d e x - d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1571 + +--S 1572 of 1751 +r0:=1/2*(e*f+d*g)^2/(d*e^3*(d-e*x))-1/4*(e*f-3*d*g)*(e*f+d*g)*_ + log(d-e*x)/(d^2*e^3)+1/4*(e*f-d*g)^2*log(d+e*x)/(d^2*e^3) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((d e g - 2d e f g + e f )x - d g + 2d e f g - d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((3d e g + 2d e f g - e f )x - 3d g - 2d e f g + d e f )log(- e x + d) +--R + +--R 3 2 2 2 2 +--R - 2d g - 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x - 4d e +--R Type: Expression(Integer) +--E 1572 + +--S 1573 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((d e g - 2d e f g + e f )x - d g + 2d e f g - d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((3d e g + 2d e f g - e f )x - 3d g - 2d e f g + d e f )log(e x - d) +--R + +--R 3 2 2 2 2 +--R - 2d g - 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x - 4d e +--R Type: Union(Expression(Integer),...) +--E 1573 + +--S 1574 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (3d g + 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 +--R (- 3d g - 2d e f g + e f )log(- e x + d) +--R / +--R 2 3 +--R 4d e +--R Type: Expression(Integer) +--E 1574 + +--S 1575 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1575 + +)clear all + +--S 1576 of 1751 +t0:=(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------- +--R 4 4 2 2 2 4 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1576 + +--S 1577 of 1751 +r0:=1/2*(d^2*g+e^2*f*x)*(f+g*x)/(d^2*e^2*(d^2-e^2*x^2))+1/2*(e*f-d*g)*_ + (e*f+d*g)*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 4 2 2 4 2 2 2 2 e x 3 2 +--R ((- d e g + e f )x + d g - d e f )atanh(---) - d e f g x +--R d +--R + +--R 3 2 3 2 3 +--R (- d e g - d e f )x - d e f g +--R / +--R 3 5 2 5 3 +--R 2d e x - 2d e +--R Type: Expression(Integer) +--E 1577 + +--S 1578 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 4 2 2 4 2 2 2 2 +--R ((- d e g + e f )x + d g - d e f )log(e x + d) +--R + +--R 2 2 2 4 2 2 4 2 2 2 2 3 2 3 2 +--R ((d e g - e f )x - d g + d e f )log(e x - d) + (- 2d e g - 2d e f )x +--R + +--R 3 +--R - 4d e f g +--R / +--R 3 5 2 5 3 +--R 4d e x - 4d e +--R Type: Union(Expression(Integer),...) +--E 1578 + +--S 1579 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 +--R (- d g + e f )log(e x + d) + (d g - e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g - 2e f )atanh(---) + 2d e f g +--R d +--R / +--R 3 3 +--R 4d e +--R Type: Expression(Integer) +--E 1579 + +--S 1580 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1580 + +)clear all + +--S 1581 of 1751 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ---------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + d e x - 2d e x - 2d e x + d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1581 + +--S 1582 of 1751 +r0:=1/8*(e*f+d*g)^2/(d^3*e^3*(d-e*x))-1/8*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^2)+_ + 1/4*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x))+1/8*(3*e*f-d*g)*(e*f+d*g)*_ + atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g + 2d e f g + 3e f )x + (- d e g + 2d e f g + 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g - 2d e f g - 3d e f )x + d g - 2d e f g - 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (d e g - 2d e f g - 3d e f )x + (- 3d e g - 2d e f g - 3d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 2d g - 4d e f g + 2d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 8d e x + 8d e x - 8d e x - 8d e +--R Type: Expression(Integer) +--E 1582 + +--S 1583 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g + 2d e f g + 3e f )x + (- d e g + 2d e f g + 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g - 2d e f g - 3d e f )x + d g - 2d e f g - 3d e f +--R * +--R log(e x + d) +--R + +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (d e g - 2d e f g - 3e f )x + (d e g - 2d e f g - 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- d e g + 2d e f g + 3d e f )x - d g + 2d e f g + 3d e f +--R * +--R log(e x - d) +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (2d e g - 4d e f g - 6d e f )x + (- 6d e g - 4d e f g - 6d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 4d g - 8d e f g + 4d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 16d e x + 16d e x - 16d e x - 16d e +--R Type: Union(Expression(Integer),...) +--E 1583 + +--S 1584 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g + 2d e f g + 3e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (d g - 2d e f g - 3e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g - 4d e f g - 6e f )atanh(---) +--R d +--R / +--R 4 3 +--R 16d e +--R Type: Expression(Integer) +--E 1584 + +--S 1585 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1585 + +)clear all + +--S 1586 of 1751 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) -------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 2d e x - d e x - 4d e x - d e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1586 + +--S 1587 of 1751 +r0:=1/16*(e*f+d*g)^2/(d^4*e^3*(d-e*x))-1/12*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^3)+_ + 1/8*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^2)-1/16*(3*e*f-d*g)*(e*f+d*g)/_ + (d^4*e^3*(d+e*x))+1/4*f*(e*f+d*g)*atanh(e*x/d)/(d^5*e^2) +--R +--R +--R (2) +--R 5 6 2 4 2 4 5 2 3 +--R (3d e f g + 3e f )x + (6d e f g + 6d e f )x +--R + +--R 4 2 3 3 2 5 4 2 2 +--R (- 6d e f g - 6d e f )x - 3d e f g - 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 2 4 5 2 3 3 3 2 4 2 2 +--R (- 3d e f g - 3d e f )x + (- 6d e f g - 6d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 4d e g - d e f g - d e f )x - 2d g - 2d e f g + 4d e f +--R / +--R 5 7 4 6 6 3 8 4 9 3 +--R 12d e x + 24d e x - 24d e x - 12d e +--R Type: Expression(Integer) +--E 1587 + +--S 1588 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 2 4 2 4 5 2 3 +--R (3d e f g + 3e f )x + (6d e f g + 6d e f )x +--R + +--R 4 2 3 3 2 5 4 2 2 +--R (- 6d e f g - 6d e f )x - 3d e f g - 3d e f +--R * +--R log(e x + d) +--R + +--R 5 6 2 4 2 4 5 2 3 +--R (- 3d e f g - 3e f )x + (- 6d e f g - 6d e f )x +--R + +--R 4 2 3 3 2 5 4 2 2 +--R (6d e f g + 6d e f )x + 3d e f g + 3d e f +--R * +--R log(e x - d) +--R + +--R 2 4 5 2 3 3 3 2 4 2 2 +--R (- 6d e f g - 6d e f )x + (- 12d e f g - 12d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 8d e g - 2d e f g - 2d e f )x - 4d g - 4d e f g + 8d e f +--R / +--R 5 7 4 6 6 3 8 4 9 3 +--R 24d e x + 48d e x - 48d e x - 24d e +--R Type: Union(Expression(Integer),...) +--E 1588 + +--S 1589 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 +--R (d f g + e f )log(e x + d) + (- d f g - e f )log(e x - d) +--R + +--R 2 e x +--R (- 2d f g - 2e f )atanh(---) +--R d +--R / +--R 5 2 +--R 8d e +--R Type: Expression(Integer) +--E 1589 + +--S 1590 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1590 + +)clear all + +--S 1591 of 1751 +t0:=(f+g*x)^2/((d+e*x)^3*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 3d e x + d e x - 5d e x - 5d e x + d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1591 + +--S 1592 of 1751 +r0:=1/32*(e*f+d*g)^2/(d^5*e^3*(d-e*x))-1/16*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^4)+_ + 1/12*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^3)-1/32*(3*e*f-d*g)*(e*f+d*g)/_ + (d^4*e^3*(d+e*x)^2)-1/8*f*(e*f+d*g)/(d^5*e^2*(d+e*x))+1/32*(e*f+d*g)*_ + (5*e*f+d*g)*atanh(e*x/d)/(d^6*e^3) +--R +--R +--R (2) +--R 2 5 2 6 7 2 5 3 4 2 2 5 6 2 4 +--R (3d e g + 18d e f g + 15e f )x + (9d e g + 54d e f g + 45d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g + 36d e f g + 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 6d e g - 36d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 9d e g - 54d e f g - 45d e f )x - 3d g - 18d e f g - 15d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 3d e g - 18d e f g - 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 9d e g - 54d e f g - 45d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 7d e g - 42d e f g - 35d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 5 2 2 +--R (- 21d e g + 18d e f g + 15d e f )x - 8d g + 32d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 96d e x + 288d e x + 192d e x - 192d e x - 288d e x - 96d e +--R Type: Expression(Integer) +--E 1592 + +--S 1593 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 6 7 2 5 3 4 2 2 5 6 2 4 +--R (3d e g + 18d e f g + 15e f )x + (9d e g + 54d e f g + 45d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g + 36d e f g + 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 6d e g - 36d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 9d e g - 54d e f g - 45d e f )x - 3d g - 18d e f g - 15d e f +--R * +--R log(e x + d) +--R + +--R 2 5 2 6 7 2 5 +--R (- 3d e g - 18d e f g - 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 9d e g - 54d e f g - 45d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 6d e g - 36d e f g - 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (6d e g + 36d e f g + 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (9d e g + 54d e f g + 45d e f )x + 3d g + 18d e f g + 15d e f +--R * +--R log(e x - d) +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 6d e g - 36d e f g - 30d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 18d e g - 108d e f g - 90d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 14d e g - 84d e f g - 70d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 5 2 2 +--R (- 42d e g + 36d e f g + 30d e f )x - 16d g + 64d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 192d e x + 576d e x + 384d e x - 384d e x - 576d e x - 192d e +--R Type: Union(Expression(Integer),...) +--E 1593 + +--S 1594 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g + 6d e f g + 5e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g - 6d e f g - 5e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g - 12d e f g - 10e f )atanh(---) +--R d +--R / +--R 6 3 +--R 64d e +--R Type: Expression(Integer) +--E 1594 + +--S 1595 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1595 + +)clear all + +--S 1596 of 1751 +t0:=(f+g*x)^2/((d+e*x)^4*(d^2-e^2*x^2)^2) +--R +--R +--R (1) +--R 2 2 2 +--R g x + 2f g x + f +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 4d e x + 4d e x - 4d e x - 10d e x - 4d e x + 4d e x +--R + +--R 7 8 +--R 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1596 + +--S 1597 of 1751 +r0:=1/64*(e*f+d*g)^2/(d^6*e^3*(d-e*x))-1/20*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^5)+_ + 1/16*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^4)-1/48*(3*e*f-d*g)*_ + (e*f+d*g)/(d^4*e^3*(d+e*x)^3)-1/16*f*(e*f+d*g)/(d^5*e^2*(d+e*x)^2)-_ + 1/64*(e*f+d*g)*(5*e*f+d*g)/(d^6*e^3*(d+e*x))+1/32*(e*f+d*g)*_ + (3*e*f+d*g)*atanh(e*x/d)/(d^7*e^3) +--R +--R +--R (2) +--R 2 6 2 7 8 2 6 +--R (15d e g + 60d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (60d e g + 240d e f g + 180d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (75d e g + 300d e f g + 225d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 75d e g - 300d e f g - 225d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 60d e g - 240d e f g - 180d e f )x - 15d g - 60d e f g - 45d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 15d e g - 60d e f g - 45d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 60d e g - 240d e f g - 180d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 80d e g - 320d e f g - 240d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 20d e g - 80d e f g - 60d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 49d e g + 188d e f g + 141d e f )x - 16d g + 32d e f g + 144d e f +--R / +--R 7 9 6 8 8 5 9 7 4 11 5 2 12 4 13 3 +--R 480d e x + 1920d e x + 2400d e x - 2400d e x - 1920d e x - 480d e +--R Type: Expression(Integer) +--E 1597 + +--S 1598 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 2 7 8 2 6 +--R (15d e g + 60d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (60d e g + 240d e f g + 180d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (75d e g + 300d e f g + 225d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 75d e g - 300d e f g - 225d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 60d e g - 240d e f g - 180d e f )x - 15d g - 60d e f g - 45d e f +--R * +--R log(e x + d) +--R + +--R 2 6 2 7 8 2 6 +--R (- 15d e g - 60d e f g - 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 60d e g - 240d e f g - 180d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 75d e g - 300d e f g - 225d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (75d e g + 300d e f g + 225d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (60d e g + 240d e f g + 180d e f )x + 15d g + 60d e f g + 45d e f +--R * +--R log(e x - d) +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 30d e g - 120d e f g - 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 120d e g - 480d e f g - 360d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 160d e g - 640d e f g - 480d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 40d e g - 160d e f g - 120d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 98d e g + 376d e f g + 282d e f )x - 32d g + 64d e f g + 288d e f +--R / +--R 7 9 6 8 8 5 9 7 4 11 5 2 12 4 13 3 +--R 960d e x + 3840d e x + 4800d e x - 4800d e x - 3840d e x - 960d e +--R Type: Union(Expression(Integer),...) +--E 1598 + +--S 1599 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g + 4d e f g + 3e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g - 4d e f g - 3e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g - 8d e f g - 6e f )atanh(---) +--R d +--R / +--R 7 3 +--R 64d e +--R Type: Expression(Integer) +--E 1599 + +--S 1600 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1600 + +)clear all + +--S 1601 of 1751 +t0:=(d+e*x)^7*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R - e g x + (- 4d e g - 2e f g)x + (- 6d e g - 8d e f g - e f )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (- 4d e g - 12d e f g - 4d e f )x + (- d g - 8d e f g - 6d e f )x +--R + +--R 4 3 2 4 2 +--R (- 2d f g - 4d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1601 + +--S 1602 of 1751 +r0:=-d*(7*e^2*f^2+48*d*e*f*g+56*d^2*g^2)*x/e^2-1/2*(e*f+2*d*g)*(e*f+12*d*g)*_ + x^2/e-1/3*g*(2*e*f+7*d*g)*x^3-1/4*e*g^2*x^4+8*d^4*(e*f+d*g)^2/(e^3*_ + (d-e*x)^2)-32*d^3*(e*f+d*g)*(e*f+2*d*g)/(e^3*(d-e*x))-8*d^2*(3*e^2*f^2+_ + 14*d*e*f*g+13*d^2*g^2)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 2 3 3 2 4 2 2 +--R (- 1248d e g - 1344d e f g - 288d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (2496d e g + 2688d e f g + 576d e f )x - 1248d g - 1344d e f g +--R + +--R 4 2 2 +--R - 288d e f +--R * +--R log(- e x + d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R - 3e g x + (- 22d e g - 8e f g)x + (- 91d e g - 68d e f g - 6e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 412d e g - 416d e f g - 72d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (1200d e g + 1068d e f g + 162d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (96d e g + 576d e f g + 300d e f )x - 672d g - 960d e f g - 288d e f +--R / +--R 5 2 4 2 3 +--R 12e x - 24d e x + 12d e +--R Type: Expression(Integer) +--E 1602 + +--S 1603 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 2 3 3 2 4 2 2 +--R (- 1248d e g - 1344d e f g - 288d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (2496d e g + 2688d e f g + 576d e f )x - 1248d g - 1344d e f g +--R + +--R 4 2 2 +--R - 288d e f +--R * +--R log(e x - d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R - 3e g x + (- 22d e g - 8e f g)x + (- 91d e g - 68d e f g - 6e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 412d e g - 416d e f g - 72d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (1200d e g + 1068d e f g + 162d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (96d e g + 576d e f g + 300d e f )x - 672d g - 960d e f g - 288d e f +--R / +--R 5 2 4 2 3 +--R 12e x - 24d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1603 + +--S 1604 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 3 2 2 2 +--R (- 104d g - 112d e f g - 24d e f )log(e x - d) +--R + +--R 4 2 3 2 2 2 +--R (104d g + 112d e f g + 24d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1604 + +--S 1605 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1605 + +)clear all + +--S 1606 of 1751 +t0:=(d+e*x)^6*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - e g x + (- 3d e g - 2e f g)x + (- 3d e g - 6d e f g - e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- d g - 6d e f g - 3d e f )x + (- 2d f g - 3d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1606 + +--S 1607 of 1751 +r0:=-(e^2*f^2+12*d*e*f*g+18*d^2*g^2)*x/e^2-g*(e*f+3*d*g)*x^2/e-1/3*g^2*x^3+_ + 4*d^3*(e*f+d*g)^2/(e^3*(d-e*x)^2)-4*d^2*(e*f+d*g)*(3*e*f+7*d*g)/(e^3*_ + (d-e*x))-2*d*(3*e^2*f^2+18*d*e*f*g+19*d^2*g^2)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 2 2 2 3 4 2 2 +--R (- 114d e g - 108d e f g - 18d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (228d e g + 216d e f g + 36d e f )x - 114d g - 108d e f g - 18d e f +--R * +--R log(- e x + d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R - e g x + (- 7d e g - 3e f g)x + (- 37d e g - 30d e f g - 3e f )x +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (99d e g + 69d e f g + 6d e f )x + (30d e g + 84d e f g + 33d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 72d g - 96d e f g - 24d e f +--R / +--R 5 2 4 2 3 +--R 3e x - 6d e x + 3d e +--R Type: Expression(Integer) +--E 1607 + +--S 1608 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 3 4 2 2 +--R (- 114d e g - 108d e f g - 18d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (228d e g + 216d e f g + 36d e f )x - 114d g - 108d e f g - 18d e f +--R * +--R log(e x - d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R - e g x + (- 7d e g - 3e f g)x + (- 37d e g - 30d e f g - 3e f )x +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (99d e g + 69d e f g + 6d e f )x + (30d e g + 84d e f g + 33d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 72d g - 96d e f g - 24d e f +--R / +--R 5 2 4 2 3 +--R 3e x - 6d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 1608 + +--S 1609 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 2 2 +--R (- 38d g - 36d e f g - 6d e f )log(e x - d) +--R + +--R 3 2 2 2 2 +--R (38d g + 36d e f g + 6d e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1609 + +--S 1610 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1610 + +)clear all + +--S 1611 of 1751 +t0:=(d+e*x)^5*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R - e g x + (- 2d e g - 2e f g)x + (- d g - 4d e f g - e f )x +--R + +--R 2 2 2 2 +--R (- 2d f g - 2d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1611 + +--S 1612 of 1751 +r0:=-g*(2*e*f+5*d*g)*x/e^2-1/2*g^2*x^2/e+2*d^2*(e*f+d*g)^2/(e^3*(d-e*x)^2)-_ + 4*d*(e*f+d*g)*(e*f+3*d*g)/(e^3*(d-e*x))-(e^2*f^2+10*d*e*f*g+13*d^2*g^2)*_ + log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 +--R (- 26d e g - 20d e f g - 2e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (52d e g + 40d e f g + 4d e f )x - 26d g - 20d e f g - 2d e f +--R * +--R log(- e x + d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 2 +--R - e g x + (- 8d e g - 4e f g)x + (19d e g + 8d e f g)x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (14d e g + 28d e f g + 8d e f )x - 20d g - 24d e f g - 4d e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Expression(Integer) +--E 1612 + +--S 1613 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 2 +--R (- 26d e g - 20d e f g - 2e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (52d e g + 40d e f g + 4d e f )x - 26d g - 20d e f g - 2d e f +--R * +--R log(e x - d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 2 +--R - e g x + (- 8d e g - 4e f g)x + (19d e g + 8d e f g)x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (14d e g + 28d e f g + 8d e f )x - 20d g - 24d e f g - 4d e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 1613 + +--S 1614 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- 13d g - 10d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 +--R (13d g + 10d e f g + e f )log(- e x + d) +--R / +--R 3 +--R e +--R Type: Expression(Integer) +--E 1614 + +--S 1615 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1615 + +)clear all + +--S 1616 of 1751 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R - e g x + (- d g - 2e f g)x + (- 2d f g - e f )x - d f +--R (1) ---------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1616 + +--S 1617 of 1751 +r0:=-g^2*x/e^2+d*(e*f+d*g)^2/(e^3*(d-e*x)^2)-(e*f+d*g)*(e*f+5*d*g)/(e^3*_ + (d-e*x))-2*g*(e*f+2*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 3 2 2 2 2 3 2 2 +--R ((- 4d e g - 2e f g)x + (8d e g + 4d e f g)x - 4d g - 2d e f g) +--R * +--R log(- e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 3 2 3 2 2 +--R - e g x + 2d e g x + (4d e g + 6d e f g + e f )x - 4d g - 4d e f g +--R / +--R 5 2 4 2 3 +--R e x - 2d e x + d e +--R Type: Expression(Integer) +--E 1617 + +--S 1618 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 2 2 2 2 3 2 2 +--R ((- 4d e g - 2e f g)x + (8d e g + 4d e f g)x - 4d g - 2d e f g) +--R * +--R log(e x - d) +--R + +--R 3 2 3 2 2 2 2 2 2 3 2 3 2 2 +--R - e g x + 2d e g x + (4d e g + 6d e f g + e f )x - 4d g - 4d e f g +--R / +--R 5 2 4 2 3 +--R e x - 2d e x + d e +--R Type: Union(Expression(Integer),...) +--E 1618 + +--S 1619 of 1751 +m0:=a0-r0 +--R +--R +--R 2 2 +--R (- 4d g - 2e f g)log(e x - d) + (4d g + 2e f g)log(- e x + d) +--R (4) --------------------------------------------------------------- +--R 3 +--R e +--R Type: Expression(Integer) +--E 1619 + +--S 1620 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1620 + +)clear all + +--S 1621 of 1751 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1621 + +--S 1622 of 1751 +r0:=1/2*(e*f+d*g)^2/(e^3*(d-e*x)^2)-2*g*(e*f+d*g)/(e^3*(d-e*x))-_ + g^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (- 2e g x + 4d e g x - 2d g )log(- e x + d) + (4d e g + 4e f g)x +--R + +--R 2 2 2 2 +--R - 3d g - 2d e f g + e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Expression(Integer) +--E 1622 + +--S 1623 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2e g x + 4d e g x - 2d g )log(e x - d) + (4d e g + 4e f g)x - 3d g +--R + +--R 2 2 +--R - 2d e f g + e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 1623 + +--S 1624 of 1751 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - g log(e x - d) + g log(- e x + d) +--R (4) ----------------------------------- +--R 3 +--R e +--R Type: Expression(Integer) +--E 1624 + +--S 1625 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1625 + +)clear all + +--S 1626 of 1751 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 4 4 3 3 3 4 +--R e x - 2d e x + 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1626 + +--S 1627 of 1751 +r0:=1/4*(e*f+d*g)^2/(d*e^3*(d-e*x)^2)+1/4*(e*f-3*d*g)*(e*f+d*g)/_ + (d^2*e^3*(d-e*x))+1/4*(e*f-d*g)^2*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (d e g - 2d e f g + e f )x + (- 2d e g + 4d e f g - 2d e f )x +--R + +--R 4 2 3 2 2 2 +--R d g - 2d e f g + d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (3d e g + 2d e f g - d e f )x - 2d g + 2d e f +--R / +--R 3 5 2 4 4 5 3 +--R 4d e x - 8d e x + 4d e +--R Type: Expression(Integer) +--E 1627 + +--S 1628 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (d e g - 2d e f g + e f )x + (- 2d e g + 4d e f g - 2d e f )x +--R + +--R 4 2 3 2 2 2 +--R d g - 2d e f g + d e f +--R * +--R log(e x + d) +--R + +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (- d e g + 2d e f g - e f )x + (2d e g - 4d e f g + 2d e f )x +--R + +--R 4 2 3 2 2 2 +--R - d g + 2d e f g - d e f +--R * +--R log(e x - d) +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (6d e g + 4d e f g - 2d e f )x - 4d g + 4d e f +--R / +--R 3 5 2 4 4 5 3 +--R 8d e x - 16d e x + 8d e +--R Type: Union(Expression(Integer),...) +--E 1628 + +--S 1629 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (d g - 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (- d g + 2d e f g - e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (- 2d g + 4d e f g - 2e f )atanh(---) +--R d +--R / +--R 3 3 +--R 8d e +--R Type: Expression(Integer) +--E 1629 + +--S 1630 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1630 + +)clear all + +--S 1631 of 1751 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x - d e x - 2d e x + 2d e x + d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1631 + +--S 1632 of 1751 +r0:=1/8*(e*f+d*g)^2/(d^2*e^3*(d-e*x)^2)+1/4*(e^2*f^2-d^2*g^2)/(d^3*e^3*_ + (d-e*x))-1/8*(e*f-d*g)^2/(d^3*e^3*(d+e*x))+1/8*(e*f-d*g)*(3*e*f+d*g)*_ + atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g - 2d e f g + 3e f )x + (d e g + 2d e f g - 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g + 2d e f g - 3d e f )x - d g - 2d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 5 2 +--R (d e g + 2d e f g - 3d e f )x + (3d e g - 2d e f g + 3d e f )x - 2d g +--R + +--R 4 3 2 2 +--R 4d e f g + 2d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 8d e x - 8d e x - 8d e x + 8d e +--R Type: Expression(Integer) +--E 1632 + +--S 1633 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g - 2d e f g + 3e f )x + (d e g + 2d e f g - 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g + 2d e f g - 3d e f )x - d g - 2d e f g + 3d e f +--R * +--R log(e x + d) +--R + +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (d e g + 2d e f g - 3e f )x + (- d e g - 2d e f g + 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- d e g - 2d e f g + 3d e f )x + d g + 2d e f g - 3d e f +--R * +--R log(e x - d) +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (2d e g + 4d e f g - 6d e f )x + (6d e g - 4d e f g + 6d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 4d g + 8d e f g + 4d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 16d e x - 16d e x - 16d e x + 16d e +--R Type: Union(Expression(Integer),...) +--E 1633 + +--S 1634 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g - 2d e f g + 3e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (d g + 2d e f g - 3e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g + 4d e f g - 6e f )atanh(---) +--R d +--R / +--R 4 3 +--R 16d e +--R Type: Expression(Integer) +--E 1634 + +--S 1635 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1635 + +)clear all + +--S 1636 of 1751 +t0:=(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ----------------------------- +--R 6 6 2 4 4 4 2 2 6 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1636 + +--S 1637 of 1751 +r0:=-1/4*(d^2*g-e^2*f*x)*(f+g*x)^3/(d^2*(e^2*f^2-d^2*g^2)*(d^2-e^2*x^2)^2)+_ + 1/8*(3*e^2*f^2-d^2*g^2)*(d^2*g+e^2*f*x)*(f+g*x)/(d^4*e^2*_ + (e^2*f^2-d^2*g^2)*(d^2-e^2*x^2))+1/8*(3*e^2*f^2-d^2*g^2)*atanh(e*x/d)/_ + (d^5*e^3) +--R +--R +--R (2) +--R 2 4 2 6 2 4 4 2 2 2 4 2 2 6 2 4 2 2 e x +--R ((- d e g + 3e f )x + (2d e g - 6d e f )x - d g + 3d e f )atanh(---) +--R d +--R + +--R 5 4 3 3 2 5 2 3 3 3 2 5 2 3 3 2 +--R - 3d e f g x + (d e g - 3d e f )x + 6d e f g x + (d e g + 5d e f )x +--R + +--R 5 +--R d e f g +--R / +--R 5 7 4 7 5 2 9 3 +--R 8d e x - 16d e x + 8d e +--R Type: Expression(Integer) +--E 1637 + +--S 1638 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 6 2 4 4 2 2 2 4 2 2 6 2 4 2 2 +--R ((- d e g + 3e f )x + (2d e g - 6d e f )x - d g + 3d e f ) +--R * +--R log(e x + d) +--R + +--R 2 4 2 6 2 4 4 2 2 2 4 2 2 6 2 4 2 2 +--R ((d e g - 3e f )x + (- 2d e g + 6d e f )x + d g - 3d e f ) +--R * +--R log(e x - d) +--R + +--R 3 3 2 5 2 3 5 2 3 3 2 5 +--R (2d e g - 6d e f )x + (2d e g + 10d e f )x + 8d e f g +--R / +--R 5 7 4 7 5 2 9 3 +--R 16d e x - 32d e x + 16d e +--R Type: Union(Expression(Integer),...) +--E 1638 + +--S 1639 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 +--R (- d g + 3e f )log(e x + d) + (d g - 3e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g - 6e f )atanh(---) + 6d e f g +--R d +--R / +--R 5 3 +--R 16d e +--R Type: Expression(Integer) +--E 1639 + +--S 1640 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1640 + +)clear all + +--S 1641 of 1751 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)^3) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + d e x - 3d e x - 3d e x + 3d e x + 3d e x - d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1641 + +--S 1642 of 1751 +r0:=1/32*(e*f+d*g)^2/(d^4*e^3*(d-e*x)^2)+1/8*f*(e*f+d*g)/(d^5*e^2*(d-e*x))-_ + 1/24*(e*f-d*g)^2/(d^3*e^3*(d+e*x)^3)-1/32*(e*f-d*g)*(3*e*f+d*g)/_ + (d^4*e^3*(d+e*x)^2)+1/16*(-3*e^2*f^2+d^2*g^2)/(d^5*e^3*(d+e*x))+_ + 1/16*(5*e^2*f^2+2*d*e*f*g-d^2*g^2)*atanh(e*x/d)/(d^6*e^3) +--R +--R +--R (2) +--R 2 5 2 6 7 2 5 +--R (- 3d e g + 6d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 3d e g + 6d e f g + 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 3d e g + 6d e f g + 15d e f )x - 3d g + 6d e f g + 15d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 3 4 2 5 2 3 +--R (3d e g - 6d e f g - 15d e f )x + (3d e g - 6d e f g - 15d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (- 5d e g + 10d e f g + 25d e f )x + (7d e g + 10d e f g + 25d e f )x +--R + +--R 7 2 6 5 2 2 +--R 4d g + 16d e f g - 8d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 48d e x + 48d e x - 96d e x - 96d e x + 48d e x + 48d e +--R Type: Expression(Integer) +--E 1642 + +--S 1643 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 6 7 2 5 +--R (- 3d e g + 6d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 3d e g + 6d e f g + 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 3d e g + 6d e f g + 15d e f )x - 3d g + 6d e f g + 15d e f +--R * +--R log(e x + d) +--R + +--R 2 5 2 6 7 2 5 3 4 2 2 5 6 2 4 +--R (3d e g - 6d e f g - 15e f )x + (3d e g - 6d e f g - 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 6d e g + 12d e f g + 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 6d e g + 12d e f g + 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (3d e g - 6d e f g - 15d e f )x + 3d g - 6d e f g - 15d e f +--R * +--R log(e x - d) +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 3 4 2 5 2 3 +--R (6d e g - 12d e f g - 30d e f )x + (6d e g - 12d e f g - 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 10d e g + 20d e f g + 50d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (14d e g + 20d e f g + 50d e f )x + 8d g + 32d e f g - 16d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 96d e x + 96d e x - 192d e x - 192d e x + 96d e x + 96d e +--R Type: Union(Expression(Integer),...) +--E 1643 + +--S 1644 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g + 2d e f g + 5e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (d g - 2d e f g - 5e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g - 4d e f g - 10e f )atanh(---) +--R d +--R / +--R 6 3 +--R 32d e +--R Type: Expression(Integer) +--E 1644 + +--S 1645 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1645 + +)clear all + +--S 1646 of 1751 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)^3) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------------------------------------------------------- +--R 8 8 7 7 2 6 6 3 5 5 5 3 3 6 2 2 7 8 +--R e x + 2d e x - 2d e x - 6d e x + 6d e x + 2d e x - 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 1646 + +--S 1647 of 1751 +r0:=1/64*(e*f+d*g)^2/(d^5*e^3*(d-e*x)^2)+1/64*(e*f+d*g)*(5*e*f+d*g)/_ + (d^6*e^3*(d-e*x))-1/32*(e*f-d*g)^2/(d^3*e^3*(d+e*x)^4)-1/48*(e*f-d*g)*_ + (3*e*f+d*g)/(d^4*e^3*(d+e*x)^3)+1/32*(-3*e^2*f^2+d^2*g^2)/(d^5*e^3*_ + (d+e*x)^2)+1/32*(-5*e^2*f^2-2*d*e*f*g+d^2*g^2)/(d^6*e^3*(d+e*x))+_ + 1/64*(15*e^2*f^2+10*d*e*f*g-d^2*g^2)*atanh(e*x/d)/(d^7*e^3) +--R +--R +--R (2) +--R 2 6 2 7 8 2 6 +--R (- 3d e g + 30d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 6d e g + 60d e f g + 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (12d e g - 120d e f g - 180d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 6d e g + 60d e f g + 90d e f )x - 3d g + 30d e f g + 45d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 5 2 2 6 7 2 5 4 4 2 3 5 2 6 2 4 +--R (3d e g - 30d e f g - 45d e f )x + (6d e g - 60d e f g - 90d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 2d e g + 20d e f g + 30d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 10d e g + 100d e f g + 150d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (35d e g + 34d e f g + 51d e f )x + 16d g + 32d e f g - 48d e f +--R / +--R 7 9 6 8 8 5 9 7 4 10 6 3 11 5 2 12 4 +--R 192d e x + 384d e x - 192d e x - 768d e x - 192d e x + 384d e x +--R + +--R 13 3 +--R 192d e +--R Type: Expression(Integer) +--E 1647 + +--S 1648 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 2 7 8 2 6 +--R (- 3d e g + 30d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 6d e g + 60d e f g + 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (12d e g - 120d e f g - 180d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 6d e g + 60d e f g + 90d e f )x - 3d g + 30d e f g + 45d e f +--R * +--R log(e x + d) +--R + +--R 2 6 2 7 8 2 6 3 5 2 2 6 7 2 5 +--R (3d e g - 30d e f g - 45e f )x + (6d e g - 60d e f g - 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 3d e g + 30d e f g + 45d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 12d e g + 120d e f g + 180d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 3d e g + 30d e f g + 45d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (6d e g - 60d e f g - 90d e f )x + 3d g - 30d e f g - 45d e f +--R * +--R log(e x - d) +--R + +--R 3 5 2 2 6 7 2 5 +--R (6d e g - 60d e f g - 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (12d e g - 120d e f g - 180d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 4d e g + 40d e f g + 60d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 20d e g + 200d e f g + 300d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (70d e g + 68d e f g + 102d e f )x + 32d g + 64d e f g - 96d e f +--R / +--R 7 9 6 8 8 5 9 7 4 10 6 3 11 5 2 12 4 +--R 384d e x + 768d e x - 384d e x - 1536d e x - 384d e x + 768d e x +--R + +--R 13 3 +--R 384d e +--R Type: Union(Expression(Integer),...) +--E 1648 + +--S 1649 of 1751 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- d g + 10d e f g + 15e f )log(e x + d) +--R + +--R 2 2 2 2 +--R (d g - 10d e f g - 15e f )log(e x - d) +--R + +--R 2 2 2 2 e x +--R (2d g - 20d e f g - 30e f )atanh(---) +--R d +--R / +--R 7 3 +--R 128d e +--R Type: Expression(Integer) +--E 1649 + +--S 1650 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1650 + +)clear all + +--S 1651 of 1751 +t0:=(a+b*x+c*x^2)/((d+e*x)*(f+g*x)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) --------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 1651 + +--S 1652 of 1751 +r0:=c*x/(e*g)+(c*d^2-b*d*e+a*e^2)*log(d+e*x)/(e^2*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))*log(f+g*x)/(g^2*(e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (a e g - b e f g + c e f )log(g x + f) +--R + +--R 2 2 2 2 2 +--R (- a e + b d e - c d )g log(e x + d) + (c d e g - c e f g)x +--R / +--R 2 3 3 2 +--R d e g - e f g +--R Type: Expression(Integer) +--E 1652 + +--S 1653 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (a e g - b e f g + c e f )log(g x + f) +--R + +--R 2 2 2 2 2 +--R (- a e + b d e - c d )g log(e x + d) + (c d e g - c e f g)x +--R / +--R 2 3 3 2 +--R d e g - e f g +--R Type: Union(Expression(Integer),...) +--E 1653 + +--S 1654 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1654 + +--S 1655 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1655 + +)clear all + +--S 1656 of 1751 +t0:=(a+b*x+c*x^2)^2/((d+e*x)*(f+g*x)) +--R +--R +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R (1) -------------------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 1656 + +--S 1657 of 1751 +r0:=(b^2*e^2*g^2-2*c*e*g*(b*e*f+b*d*g-a*e*g)+c^2*(e^2*f^2+d*e*f*g+_ + d^2*g^2))*x/(e^3*g^3)-1/2*c*(c*e*f+c*d*g-2*b*e*g)*x^2/(e^2*g^2)+_ + 1/3*c^2*x^3/(e*g)+(c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/(e^4*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))^2*log(f+g*x)/(g^4*(e*f-d*g)) +--R +--R +--R (2) +--R 2 4 4 4 3 2 4 2 2 4 3 2 4 4 +--R (6a e g - 12a b e f g + (12a c + 6b )e f g - 12b c e f g + 6c e f ) +--R * +--R log(g x + f) +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (- 6a e + 12a b d e + (- 12a c - 6b )d e + 12b c d e - 6c d )g +--R * +--R log(e x + d) +--R + +--R 2 3 4 2 4 3 3 +--R (2c d e g - 2c e f g )x +--R + +--R 3 2 2 2 4 4 3 2 4 2 2 2 +--R ((6b c d e - 3c d e )g - 6b c e f g + 3c e f g )x +--R + +--R 2 3 2 2 2 3 4 2 4 3 +--R ((12a c + 6b )d e - 12b c d e + 6c d e)g + (- 12a c - 6b )e f g +--R + +--R 4 2 2 2 4 3 +--R 12b c e f g - 6c e f g +--R * +--R x +--R / +--R 4 5 5 4 +--R 6d e g - 6e f g +--R Type: Expression(Integer) +--E 1657 + +--S 1658 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 3 2 4 2 2 4 3 2 4 4 +--R (6a e g - 12a b e f g + (12a c + 6b )e f g - 12b c e f g + 6c e f ) +--R * +--R log(g x + f) +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (- 6a e + 12a b d e + (- 12a c - 6b )d e + 12b c d e - 6c d )g +--R * +--R log(e x + d) +--R + +--R 2 3 4 2 4 3 3 +--R (2c d e g - 2c e f g )x +--R + +--R 3 2 2 2 4 4 3 2 4 2 2 2 +--R ((6b c d e - 3c d e )g - 6b c e f g + 3c e f g )x +--R + +--R 2 3 2 2 2 3 4 2 4 3 +--R ((12a c + 6b )d e - 12b c d e + 6c d e)g + (- 12a c - 6b )e f g +--R + +--R 4 2 2 2 4 3 +--R 12b c e f g - 6c e f g +--R * +--R x +--R / +--R 4 5 5 4 +--R 6d e g - 6e f g +--R Type: Union(Expression(Integer),...) +--E 1658 + +--S 1659 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1659 + +--S 1660 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1660 + +)clear all + +--S 1661 of 1751 +t0:=(a+b*x+c*x^2)^3/((d+e*x)*(f+g*x)) +--R +--R +--R (1) +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R / +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 1661 + +--S 1662 of 1751 +r0:=-(b^2*e^3*g^3*(b*e*f+b*d*g-3*a*e*g)-c^3*(e^4*f^4+d*e^3*f^3*g+_ + d^2*e^2*f^2*g^2+d^3*e*f*g^3+d^4*g^4)-3*c*e^2*g^2*(a^2*e^2*g^2-_ + 2*a*b*e*g*(e*f+d*g)+b^2*(e^2*f^2+d*e*f*g+d^2*g^2))-3*c^2*e*g*(a*e*g*_ + (e^2*f^2+d*e*f*g+d^2*g^2)-b*(e^3*f^3+d*e^2*f^2*g+d^2*e*f*g^2+d^3*g^3)))*_ + x/(e^5*g^5)+1/2*(b^3*e^3*g^3-3*b*c*e^2*g^2*(b*e*f+b*d*g-2*a*e*g)-c^3*_ + (e^3*f^3+d*e^2*f^2*g+d^2*e*f*g^2+d^3*g^3)-3*c^2*e*g*(a*e*g*(e*f+d*g)-_ + b*(e^2*f^2+d*e*f*g+d^2*g^2)))*x^2/(e^4*g^4)+1/3*c*(3*b^2*e^2*g^2-_ + 3*c*e*g*(b*e*f+b*d*g-a*e*g)+c^2*(e^2*f^2+d*e*f*g+d^2*g^2))*_ + x^3/(e^3*g^3)-1/4*c^2*(c*e*f+c*d*g-3*b*e*g)*x^4/(e^2*g^2)+_ + 1/5*c^3*x^5/(e*g)+(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/(e^6*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))^3*log(f+g*x)/(g^6*(e*f-d*g)) +--R +--R +--R (2) +--R 3 6 6 2 6 5 2 2 6 2 4 +--R 60a e g - 180a b e f g + (180a c + 180a b )e f g +--R + +--R 3 6 3 3 2 2 6 4 2 2 6 5 +--R (- 360a b c - 60b )e f g + (180a c + 180b c)e f g - 180b c e f g +--R + +--R 3 6 6 +--R 60c e f +--R * +--R log(g x + f) +--R + +--R 3 6 2 5 2 2 2 4 +--R - 60a e + 180a b d e + (- 180a c - 180a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (360a b c + 60b )d e + (- 180a c - 180b c)d e + 180b c d e - 60c d +--R * +--R 6 +--R g log(e x + d) +--R + +--R 3 5 6 3 6 5 5 +--R (12c d e g - 12c e f g )x +--R + +--R 2 5 3 2 4 6 2 6 5 3 6 2 4 4 +--R ((45b c d e - 15c d e )g - 45b c e f g + 15c e f g )x +--R + +--R 2 2 5 2 2 4 3 3 3 6 +--R ((60a c + 60b c)d e - 60b c d e + 20c d e )g +--R + +--R 2 2 6 5 2 6 2 4 3 6 3 3 +--R (- 60a c - 60b c)e f g + 60b c e f g - 20c e f g +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 2 4 2 3 3 +--R (180a b c + 30b )d e + (- 90a c - 90b c)d e + 90b c d e +--R + +--R 3 4 2 +--R - 30c d e +--R * +--R 6 +--R g +--R + +--R 3 6 5 2 2 6 2 4 2 6 3 3 +--R (- 180a b c - 30b )e f g + (90a c + 90b c)e f g - 90b c e f g +--R + +--R 3 6 4 2 +--R 30c e f g +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 2 4 +--R (180a c + 180a b )d e + (- 360a b c - 60b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (180a c + 180b c)d e - 180b c d e + 60c d e +--R * +--R 6 +--R g +--R + +--R 2 2 6 5 3 6 2 4 +--R (- 180a c - 180a b )e f g + (360a b c + 60b )e f g +--R + +--R 2 2 6 3 3 2 6 4 2 3 6 5 +--R (- 180a c - 180b c)e f g + 180b c e f g - 60c e f g +--R * +--R x +--R / +--R 6 7 7 6 +--R 60d e g - 60e f g +--R Type: Expression(Integer) +--E 1662 + +--S 1663 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 2 6 5 2 2 6 2 4 +--R 60a e g - 180a b e f g + (180a c + 180a b )e f g +--R + +--R 3 6 3 3 2 2 6 4 2 2 6 5 +--R (- 360a b c - 60b )e f g + (180a c + 180b c)e f g - 180b c e f g +--R + +--R 3 6 6 +--R 60c e f +--R * +--R log(g x + f) +--R + +--R 3 6 2 5 2 2 2 4 +--R - 60a e + 180a b d e + (- 180a c - 180a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (360a b c + 60b )d e + (- 180a c - 180b c)d e + 180b c d e - 60c d +--R * +--R 6 +--R g log(e x + d) +--R + +--R 3 5 6 3 6 5 5 +--R (12c d e g - 12c e f g )x +--R + +--R 2 5 3 2 4 6 2 6 5 3 6 2 4 4 +--R ((45b c d e - 15c d e )g - 45b c e f g + 15c e f g )x +--R + +--R 2 2 5 2 2 4 3 3 3 6 +--R ((60a c + 60b c)d e - 60b c d e + 20c d e )g +--R + +--R 2 2 6 5 2 6 2 4 3 6 3 3 +--R (- 60a c - 60b c)e f g + 60b c e f g - 20c e f g +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 2 4 2 3 3 +--R (180a b c + 30b )d e + (- 90a c - 90b c)d e + 90b c d e +--R + +--R 3 4 2 +--R - 30c d e +--R * +--R 6 +--R g +--R + +--R 3 6 5 2 2 6 2 4 2 6 3 3 +--R (- 180a b c - 30b )e f g + (90a c + 90b c)e f g - 90b c e f g +--R + +--R 3 6 4 2 +--R 30c e f g +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 2 4 +--R (180a c + 180a b )d e + (- 360a b c - 60b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (180a c + 180b c)d e - 180b c d e + 60c d e +--R * +--R 6 +--R g +--R + +--R 2 2 6 5 3 6 2 4 +--R (- 180a c - 180a b )e f g + (360a b c + 60b )e f g +--R + +--R 2 2 6 3 3 2 6 4 2 3 6 5 +--R (- 180a c - 180b c)e f g + 180b c e f g - 60c e f g +--R * +--R x +--R / +--R 6 7 7 6 +--R 60d e g - 60e f g +--R Type: Union(Expression(Integer),...) +--E 1663 + +--S 1664 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1664 + +--S 1665 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1665 + +)clear all + +--S 1666 of 1751 +t0:=1/((d+e*x)*(f+g*x)*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 3 2 +--R c e g x + ((b e + c d)g + c e f)x + ((a e + b d)g + (b e + c d)f)x +--R + +--R (a d g + (a e + b d)f)x + a d f +--R Type: Fraction(Polynomial(Integer)) +--E 1666 + +--S 1667 of 1751 +r0:=e^2*log(d+e*x)/((c*d^2-b*d*e+a*e^2)*(e*f-d*g))-g^2*log(f+g*x)/_ + ((e*f-d*g)*(c*f^2-g*(b*f-a*g)))-1/2*(c*e*f+c*d*g-b*e*g)*_ + log(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g)))-_ + (2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g))*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((4a c - 2b )d e + 2b c d )g + ((- 4a c + 2b )e - 4c d )f g +--R + +--R 2 2 2 +--R (- 2b c e + 4c d e)f +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 +--R ((b d e - c d )g - b e f g + c e f )log(c x + b x + a) +--R + +--R 2 2 2 +--R (2a e - 2b d e + 2c d )g log(g x + f) +--R + +--R 2 2 2 2 2 +--R (- 2a e g + 2b e f g - 2c e f )log(e x + d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 2 2 3 3 +--R (2a d e - 2a b d e + 2a c d )g +--R + +--R 2 3 2 2 3 2 +--R (- 2a e + (- 2a c + 2b )d e - 2b c d )f g +--R + +--R 3 2 2 2 3 2 +--R (2a b e + (2a c - 2b )d e + 2c d )f g +--R + +--R 3 2 2 2 3 +--R (- 2a c e + 2b c d e - 2c d e)f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1667 + +--S 1668 of 1751 +--a0:=integrate(t0,x) +--E 1668 + +--S 1669 of 1751 +--m0:=a0-r0 +--E 1669 + +--S 1670 of 1751 +--d0:=D(m0,x) +--E 1670 + +)clear all + +--S 1671 of 1751 +t0:=1/((d+e*x)*(f+g*x)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 6 2 2 5 +--R c e g x + ((2b c e + c d)g + c e f)x +--R + +--R 2 2 4 +--R (((2a c + b )e + 2b c d)g + (2b c e + c d)f)x +--R + +--R 2 2 3 +--R ((2a b e + (2a c + b )d)g + ((2a c + b )e + 2b c d)f)x +--R + +--R 2 2 2 +--R ((a e + 2a b d)g + (2a b e + (2a c + b )d)f)x +--R + +--R 2 2 2 +--R (a d g + (a e + 2a b d)f)x + a d f +--R Type: Fraction(Polynomial(Integer)) +--E 1671 + +--S 1672 of 1751 +r0:=(-b^3*e*g+b^2*c*(e*f+d*g)-2*a*c^2*(e*f+d*g)-b*c*(c*d*f-3*a*e*g)-_ + c*(2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g))*(a+b*x+c*x^2))+2*c*_ + (2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)*(c*f^2-_ + g*(b*f-a*g)))+e^4*log(d+e*x)/((c*d^2-b*d*e+a*e^2)^2*(e*f-d*g))-_ + g^4*log(f+g*x)/((e*f-d*g)*(c*f^2-g*(b*f-a*g))^2)-1/2*(c*e*f+c*d*g-_ + b*e*g)*(c*(e^2*f^2+d^2*g^2)+e*g*(2*a*e*g-b*(e*f+d*g)))*log(a+b*x+_ + c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(c*f^2-g*(b*f-a*g))^2)+(b^2*e^2*g^2*_ + (b*e*f+b*d*g-2*a*e*g)-2*c^3*d*f*(e^2*f^2+d*e*f*g+d^2*g^2)+2*c*e*g*_ + (a^2*e^2*g^2+a*b*e*g*(e*f+d*g)-b^2*(e*f+d*g)^2)-c^2*(4*a*d*e^2*f*g^2-_ + b*(e^3*f^3+5*d*e^2*f^2*g+5*d^2*e*f*g^2+d^3*g^3)))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*(c*f^2-g*(b*f-a*g))^2*_ + sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 3 3 2 2 2 4 3 +--R (24a c - 24a b c + 4a b c)d e +--R + +--R 2 3 3 2 5 2 2 +--R (12a b c + 8a b c - 2b c)d e +--R + +--R 2 4 2 3 4 2 3 4 3 3 4 +--R (8a c - 24a b c + 4b c )d e + (12a b c - 2b c )d +--R * +--R 4 +--R g +--R + +--R 3 3 2 2 2 4 4 2 4 2 2 4 3 +--R (- 24a c + 24a b c - 4a b c)e - 48a c d e + 32a b c d e +--R + +--R 5 4 +--R - 24a c d +--R * +--R 3 +--R f g +--R + +--R 2 3 3 2 5 4 2 4 3 +--R (- 12a b c - 8a b c + 2b c)e + 48a c d e +--R + +--R 5 2 4 3 5 4 +--R (16a c - 16b c )d e + 12b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 4 2 3 4 2 4 4 3 +--R (- 8a c + 24a b c - 4b c )e - 32a b c d e +--R + +--R 5 2 4 2 2 6 4 +--R (- 16a c + 16b c )d e - 8c d +--R * +--R 3 +--R f g +--R + +--R 4 3 3 4 5 3 5 2 2 6 3 4 +--R ((- 12a b c + 2b c )e + 24a c d e - 12b c d e + 8c d e)f +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 3 +--R (24a b c - 24a b c + 4a b )d e +--R + +--R 2 2 2 4 6 2 2 +--R (12a b c + 8a b c - 2b )d e +--R + +--R 2 3 3 2 5 3 2 3 4 2 4 +--R (8a b c - 24a b c + 4b c)d e + (12a b c - 2b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 2 3 5 4 2 3 2 2 2 3 3 +--R (- 24a b c + 24a b c - 4a b )e - 48a b c d e + 32a b c d e +--R + +--R 4 4 +--R - 24a b c d +--R * +--R 3 +--R f g +--R + +--R 2 2 2 4 6 4 2 3 3 +--R (- 12a b c - 8a b c + 2b )e + 48a b c d e +--R + +--R 4 3 3 3 2 4 4 +--R (16a b c - 16b c )d e + 12b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 3 3 2 5 4 2 3 3 +--R (- 8a b c + 24a b c - 4b c)e - 32a b c d e +--R + +--R 4 3 3 2 2 5 4 +--R (- 16a b c + 16b c )d e - 8b c d +--R * +--R 3 +--R f g +--R + +--R 2 3 4 2 4 4 3 2 4 2 2 5 3 4 +--R ((- 12a b c + 2b c )e + 24a b c d e - 12b c d e + 8b c d e)f +--R * +--R x +--R + +--R 4 2 3 2 2 4 3 3 2 2 3 5 2 2 +--R (24a c - 24a b c + 4a b )d e + (12a b c + 8a b c - 2a b )d e +--R + +--R 3 3 2 2 2 4 3 2 3 3 2 4 +--R (8a c - 24a b c + 4a b c)d e + (12a b c - 2a b c )d +--R * +--R 4 +--R g +--R + +--R 4 2 3 2 2 4 4 3 3 2 2 2 3 3 +--R (- 24a c + 24a b c - 4a b )e - 48a c d e + 32a b c d e +--R + +--R 2 4 4 +--R - 24a c d +--R * +--R 3 +--R f g +--R + +--R 3 2 2 3 5 4 3 3 3 +--R (- 12a b c - 8a b c + 2a b )e + 48a c d e +--R + +--R 2 4 2 3 3 4 4 +--R (16a c - 16a b c )d e + 12a b c d +--R * +--R 2 2 +--R f g +--R + +--R 3 3 2 2 2 4 4 2 3 3 +--R (- 8a c + 24a b c - 4a b c)e - 32a b c d e +--R + +--R 2 4 2 3 2 2 5 4 +--R (- 16a c + 16a b c )d e - 8a c d +--R * +--R 3 +--R f g +--R + +--R 2 3 3 2 4 2 4 3 4 2 2 5 3 4 +--R ((- 12a b c + 2a b c )e + 24a c d e - 12a b c d e + 8a c d e)f +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 3 2 3 2 2 4 2 2 +--R (8a b c - 2a b c)d e + (- 8a c - 2a b c + b c)d e +--R + +--R 3 3 2 3 4 2 3 4 +--R (8a b c - 2b c )d e + (- 4a c + b c )d +--R * +--R 4 +--R g +--R + +--R 2 2 3 4 3 2 3 2 2 4 4 2 2 +--R (- 8a b c + 2a b c)e f g + (8a c + 2a b c - b c)e f g +--R + +--R 3 3 2 4 3 4 2 3 4 4 +--R (- 8a b c + 2b c )e f g + (4a c - b c )e f +--R * +--R 2 +--R x +--R + +--R 2 2 4 3 2 2 3 5 2 2 +--R (8a b c - 2a b )d e + (- 8a b c - 2a b c + b )d e +--R + +--R 2 2 4 3 3 3 2 4 +--R (8a b c - 2b c)d e + (- 4a b c + b c )d +--R * +--R 4 +--R g +--R + +--R 2 2 4 4 3 2 2 3 5 4 2 2 +--R (- 8a b c + 2a b )e f g + (8a b c + 2a b c - b )e f g +--R + +--R 2 2 4 4 3 3 3 2 4 4 +--R (- 8a b c + 2b c)e f g + (4a b c - b c )e f +--R * +--R x +--R + +--R 3 2 3 3 3 2 2 2 4 2 2 +--R (8a b c - 2a b )d e + (- 8a c - 2a b c + a b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (8a b c - 2a b c)d e + (- 4a c + a b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 3 4 3 3 2 2 2 4 4 2 2 +--R (- 8a b c + 2a b )e f g + (8a c + 2a b c - a b )e f g +--R + +--R 2 2 3 4 3 2 3 2 2 4 4 +--R (- 8a b c + 2a b c)e f g + (4a c - a b c )e f +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 4 2 2 3 3 +--R (8a c - 2a b c)e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (16a c + 4a b c - 2b c)d e + (- 16a b c + 4b c )d e +--R + +--R 4 2 3 4 +--R (8a c - 2b c )d +--R * +--R 4 2 +--R g x +--R + +--R 3 2 3 4 2 2 4 3 +--R (8a b c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (16a b c + 4a b c - 2b )d e + (- 16a b c + 4b c)d e +--R + +--R 3 3 2 4 +--R (8a b c - 2b c )d +--R * +--R 4 +--R g x +--R + +--R 4 3 2 4 3 2 3 3 +--R (8a c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 +--R (8a c - 2a b c )d +--R * +--R 4 +--R g +--R * +--R log(g x + f) +--R + +--R 3 2 2 2 4 4 2 2 3 4 3 +--R (- 8a c + 2a b c)e g + (16a b c - 4a b c)e f g +--R + +--R 2 3 2 2 4 4 2 2 3 3 2 4 3 +--R (- 16a c - 4a b c + 2b c)e f g + (16a b c - 4b c )e f g +--R + +--R 4 2 3 4 4 +--R (- 8a c + 2b c )e f +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 4 2 2 4 4 3 +--R (- 8a b c + 2a b )e g + (16a b c - 4a b )e f g +--R + +--R 2 2 3 5 4 2 2 2 2 4 4 3 +--R (- 16a b c - 4a b c + 2b )e f g + (16a b c - 4b c)e f g +--R + +--R 3 3 2 4 4 +--R (- 8a b c + 2b c )e f +--R * +--R x +--R + +--R 4 3 2 4 4 3 2 3 4 3 +--R (- 8a c + 2a b )e g + (16a b c - 4a b )e f g +--R + +--R 3 2 2 2 4 4 2 2 2 2 3 4 3 +--R (- 16a c - 4a b c + 2a b )e f g + (16a b c - 4a b c)e f g +--R + +--R 2 3 2 2 4 4 +--R (- 8a c + 2a b c )e f +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 3 2 2 +--R (- 4a c + 2a b c)d e + (2a b c - 2a b c)d e +--R + +--R 2 3 2 2 3 3 4 +--R (- 4a c + 4a b c )d e - 2a b c d +--R * +--R 4 +--R g +--R + +--R 3 2 2 2 4 2 3 2 2 4 2 2 3 2 3 +--R (4a c - 2a b c)e + (8a c - 4a b c + 2b c)d e - 4b c d e +--R + +--R 4 2 3 4 +--R (4a c + 2b c )d +--R * +--R 3 +--R f g +--R + +--R 2 2 3 4 2 3 2 2 4 3 +--R (- 2a b c + 2a b c)e + (- 8a c + 4a b c - 2b c)d e +--R + +--R 4 2 3 3 4 4 +--R (- 8a c + 8b c )d e - 6b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 3 2 2 4 3 2 3 4 2 3 2 2 5 4 +--R ((4a c - 4a b c )e + 4b c d e + (8a c - 8b c )d e + 4c d ) +--R * +--R 3 +--R f g +--R + +--R 3 4 4 2 3 3 4 2 2 5 3 4 +--R (2a b c e + (- 4a c - 2b c )d e + 6b c d e - 4c d e)f +--R * +--R x +--R + +--R 3 2 3 3 3 2 2 2 4 2 2 +--R (- 6a b c + 2a b )d e + (4a c + 4a b c - 2a b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 10a b c + 4a b c)d e + (4a c - 2a b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 3 4 2 2 3 5 2 2 +--R (6a b c - 2a b )e + (4a b c - 6a b c + 2b )d e +--R + +--R 2 2 4 3 3 3 2 4 +--R (8a b c - 4b c)d e + (- 2a b c + 2b c )d +--R * +--R 3 +--R f g +--R + +--R 3 2 2 2 4 4 2 2 3 5 3 +--R (- 4a c - 4a b c + 2a b )e + (- 4a b c + 6a b c - 2b )d e +--R + +--R 3 3 2 3 4 2 3 4 +--R (- 12a b c + 6b c )d e + (4a c - 4b c )d +--R * +--R 2 2 +--R f g +--R + +--R 2 2 3 4 2 2 4 3 +--R (10a b c - 4a b c)e + (- 8a b c + 4b c)d e +--R + +--R 3 3 2 2 2 4 4 +--R (12a b c - 6b c )d e + 2b c d +--R * +--R 3 +--R f g +--R + +--R 2 3 2 2 4 3 3 2 3 +--R (- 4a c + 2a b c )e + (2a b c - 2b c )d e +--R + +--R 4 2 3 2 2 4 3 +--R (- 4a c + 4b c )d e - 2b c d e +--R * +--R 4 +--R f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 2 4 4 2 3 3 2 3 +--R (8a c - 2a b c)d e + (- 16a b c + 4a b c)d e +--R + +--R 4 3 3 2 2 2 4 3 2 3 3 2 3 2 4 +--R (16a c + 4a b c - 2a b c)d e + (- 16a b c + 4a b c )d e +--R + +--R 3 4 2 2 3 5 +--R (8a c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 5 2 4 2 5 4 3 3 2 2 2 4 2 3 +--R (- 8a c + 2a b c)e + (- 16a c + 28a b c - 6a b c)d e +--R + +--R 3 3 2 3 2 5 3 2 +--R (- 16a b c - 12a b c + 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 4 2 4 3 3 5 +--R (- 8a c + 34a b c - 8a b c )d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 2 3 3 5 4 3 3 2 2 2 4 4 +--R (16a b c - 4a b c)e + (16a c - 28a b c + 6a b c)d e +--R + +--R 3 4 2 2 3 4 2 6 3 2 +--R (32a c - 8a b c + 8a b c - 2b c)d e +--R + +--R 2 4 3 3 5 2 4 2 5 2 4 4 3 5 +--R (- 16a b c - 12a b c + 4b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 3 +--R f g +--R + +--R 4 3 3 2 2 2 4 5 +--R (- 16a c - 4a b c + 2a b c)e +--R + +--R 3 3 2 3 2 5 4 +--R (16a b c + 12a b c - 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 6 2 3 +--R (- 32a c + 8a b c - 8a b c + 2b c)d e +--R + +--R 2 5 2 4 4 3 4 5 3 4 5 +--R (- 16a c + 28a b c - 6b c )d e + (- 16a b c + 4b c )d +--R * +--R 3 2 +--R f g +--R + +--R 3 3 2 3 2 5 3 4 2 2 3 4 2 4 +--R (16a b c - 4a b c )e + (8a c - 34a b c + 8a b c )d e +--R + +--R 2 4 3 3 5 2 2 3 +--R (16a b c + 12a b c - 4b c )d e +--R + +--R 2 5 2 4 4 3 3 2 6 2 5 5 +--R (16a c - 28a b c + 6b c )d e + (8a c - 2b c )d +--R * +--R 4 +--R f g +--R + +--R 3 4 2 2 3 5 2 4 3 3 4 +--R (- 8a c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 2 5 2 4 4 3 2 3 5 3 4 3 2 +--R (- 16a c - 4a b c + 2b c )d e + (16a b c - 4b c )d e +--R + +--R 6 2 5 4 +--R (- 8a c + 2b c )d e +--R * +--R 5 +--R f +--R * +--R 2 +--R x +--R + +--R 5 4 3 4 4 2 3 4 2 3 +--R (8a b c - 2a b )d e + (- 16a b c + 4a b )d e +--R + +--R 4 2 3 3 2 5 3 2 3 2 2 2 4 4 +--R (16a b c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 3 3 2 3 2 5 +--R (8a b c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 5 4 3 5 4 2 3 3 2 5 2 3 +--R (- 8a b c + 2a b )e + (- 16a b c + 28a b c - 6a b )d e +--R + +--R 3 2 2 2 4 6 3 2 +--R (- 16a b c - 12a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 3 4 2 5 +--R (- 8a b c + 34a b c - 8a b c)d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 2 3 4 5 4 2 3 3 2 5 4 +--R (16a b c - 4a b )e + (16a b c - 28a b c + 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 2 +--R (32a b c - 8a b c + 8a b c - 2b )d e +--R + +--R 2 2 3 4 2 6 4 +--R (- 16a b c - 12a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 5 +--R (16a b c + 4a b c - 2b c )d +--R * +--R 2 3 +--R f g +--R + +--R 4 2 3 3 2 5 5 +--R (- 16a b c - 4a b c + 2a b )e +--R + +--R 3 2 2 2 4 6 4 +--R (16a b c + 12a b c - 4a b )d e +--R + +--R 3 3 2 3 2 5 7 2 3 +--R (- 32a b c + 8a b c - 8a b c + 2b )d e +--R + +--R 2 4 3 3 5 2 4 2 4 4 3 5 +--R (- 16a b c + 28a b c - 6b c )d e + (- 16a b c + 4b c )d +--R * +--R 3 2 +--R f g +--R + +--R 3 2 2 2 4 5 3 3 2 3 2 5 4 +--R (16a b c - 4a b c)e + (8a b c - 34a b c + 8a b c)d e +--R + +--R 2 2 3 4 2 6 2 3 +--R (16a b c + 12a b c - 4b c)d e +--R + +--R 2 4 3 3 5 2 3 2 5 3 4 5 +--R (16a b c - 28a b c + 6b c )d e + (8a b c - 2b c )d +--R * +--R 4 +--R f g +--R + +--R 3 3 2 3 2 5 2 2 3 4 2 4 +--R (- 8a b c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 2 4 3 3 5 2 2 3 2 4 4 3 3 2 +--R (- 16a b c - 4a b c + 2b c )d e + (16a b c - 4b c )d e +--R + +--R 5 3 4 4 +--R (- 8a b c + 2b c )d e +--R * +--R 5 +--R f +--R * +--R x +--R + +--R 6 5 2 4 5 4 3 2 3 +--R (8a c - 2a b )d e + (- 16a b c + 4a b )d e +--R + +--R 5 2 4 2 3 4 3 2 4 2 3 3 4 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 4 3 3 2 2 5 +--R (8a c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 6 5 2 5 5 2 4 2 3 4 2 3 +--R (- 8a c + 2a b )e + (- 16a c + 28a b c - 6a b )d e +--R + +--R 4 2 3 3 2 5 3 2 +--R (- 16a b c - 12a b c + 4a b )d e +--R + +--R 4 3 3 2 2 2 4 4 3 3 2 3 2 5 +--R (- 8a c + 34a b c - 8a b c)d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 5 4 3 5 5 2 4 2 3 4 4 +--R (16a b c - 4a b )e + (16a c - 28a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (32a c - 8a b c + 8a b c - 2a b )d e +--R + +--R 3 3 2 3 2 5 4 3 4 2 2 3 4 2 5 +--R (- 16a b c - 12a b c + 4a b c)d e + (16a c + 4a b c - 2a b c )d +--R * +--R 2 3 +--R f g +--R + +--R 5 2 4 2 3 4 5 4 2 3 3 2 5 4 +--R (- 16a c - 4a b c + 2a b )e + (16a b c + 12a b c - 4a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 3 +--R (- 32a c + 8a b c - 8a b c + 2a b )d e +--R + +--R 3 4 2 2 3 4 2 4 2 4 3 3 5 +--R (- 16a c + 28a b c - 6a b c )d e + (- 16a b c + 4a b c )d +--R * +--R 3 2 +--R f g +--R + +--R 4 2 3 3 5 4 3 3 2 2 2 4 4 +--R (16a b c - 4a b c)e + (8a c - 34a b c + 8a b c)d e +--R + +--R 3 3 2 3 2 5 2 3 +--R (16a b c + 12a b c - 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 3 2 2 5 2 4 5 +--R (16a c - 28a b c + 6a b c )d e + (8a c - 2a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 3 3 2 2 5 3 3 2 3 2 4 +--R (- 8a c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 3 2 4 3 3 3 2 +--R (- 16a c - 4a b c + 2a b c )d e + (16a b c - 4a b c )d e +--R + +--R 2 5 2 4 4 +--R (- 8a c + 2a b c )d e +--R * +--R 5 +--R f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1672 + +--S 1673 of 1751 +--a0:=integrate(t0,x) +--E 1673 + +--S 1674 of 1751 +--m0:=a0-r0 +--E 1674 + +--S 1675 of 1751 +--d0:=D(m0,x) +--E 1675 + +)clear all + +--S 1676 of 1751 +t0:=sqrt(a+b*x+c*x^2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R (1) --------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 1676 + +--S 1677 of 1751 +r0:=atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/(e*g)+_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/(e*(e*f-d*g))-atanh(1/2*_ + (b*f-2*a*g+(2*c*f-b*g)*x)/(sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))*_ + sqrt(c*f^2-b*f*g+a*g^2)/(g*(e*f-d*g)) +--R +--R +--R (2) +--R +-+ 2c x + b +--R (d g - e f)\|c atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 (b e - 2c d)x + 2a e - b d +--R g\|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 (b g - 2c f)x + 2a g - b f +--R - e\|a g - b f g + c f atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R / +--R 2 2 +--R d e g - e f g +--R Type: Expression(Integer) +--E 1677 + +--S 1678 of 1751 +--a0:=integrate(t0,x) +--E 1678 + +--S 1679 of 1751 +--m0:=a0-r0 +--E 1679 + +--S 1680 of 1751 +--d0:=D(m0,x) +--E 1680 + +)clear all + +--S 1681 of 1751 +t0:=(a+b*x+c*x^2)^(3/2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R (1) --------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 1681 + +--S 1682 of 1751 +r0:=(c*d^2-b*d*e+a*e^2)^(3/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^3*(e*f-d*g))-_ + (c*f^2-b*f*g+a*g^2)^(3/2)*atanh(1/2*(b*f-2*a*g+(2*c*f-b*g)*x)/_ + (sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))/(g^3*(e*f-d*g))-_ + 1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^3*(e*f-d*g)*sqrt(c))+1/8*(8*c^2*e*f^3+b*g^2*_ + (3*b*e*f+b*d*g-4*a*e*g)-4*c*g*(3*b*e*f^2-a*g*(3*e*f-d*g)))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e*g^3*(e*f-d*g)*_ + sqrt(c))+(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)/(e^2*(e*f-d*g))-_ + 1/4*(4*c*e*f^2-g*(5*b*e*f-b*d*g-4*a*e*g)-2*c*g*(e*f-d*g)*x)*_ + sqrt(a+b*x+c*x^2)/(e*g^2*(e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 2 3 3 2 3 2 +--R ((12a c + 3b )d e - 12b c d e + 8c d )g + (- 12a c - 3b )e f g +--R + +--R 3 2 2 3 3 +--R 12b c e f g - 8c e f +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R 2 2 3 +-+ | 2 2 +--R (8a e - 8b d e + 8c d )g \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 3 2 3 3 2 +-+ | 2 2 +--R (- 8a e g + 8b e f g - 8c e f )\|c \|a g - b f g + c f +--R * +--R (b g - 2c f)x + 2a g - b f +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (4c d e g - 4c e f g )x + (10b d e - 8c d e)g - 10b e f g +--R + +--R 3 2 +--R 8c e f g +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 4 4 3 +-+ +--R (8d e g - 8e f g )\|c +--R Type: Expression(Integer) +--E 1682 + +--S 1683 of 1751 +--a0:=integrate(t0,x) +--E 1683 + +--S 1684 of 1751 +--m0:=a0-r0 +--E 1684 + +--S 1685 of 1751 +--d0:=D(m0,x) +--E 1685 + +)clear all + +--S 1686 of 1751 +t0:=(a+b*x+c*x^2)^(5/2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R (1) --------------------------------------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 1686 + +--S 1687 of 1751 +r0:=1/3*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2)/(e^2*(e*f-d*g))-_ + 1/24*(8*c*e*f^2-g*(11*b*e*f-3*b*d*g-8*a*e*g)-6*c*g*(e*f-d*g)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e*g^2*(e*f-d*g))-1/16*(2*c*d-b*e)*(c*d^2-b*d*e+_ + a*e^2)*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*e^5*(e*f-d*g))+1/128*_ + (128*c^4*e*f^5-320*c^3*e*f^3*g*(b*f-a*g)-b^3*g^4*(5*b*e*f+3*b*d*g-_ + 8*a*e*g)+48*c^2*g^2*(5*b^2*e*f^3-10*a*b*e*f^2*g+a^2*g^2*(5*e*f-d*g))-_ + 8*b*c*g^3*(5*b^2*e*f^2+12*a^2*e*g^2-3*a*b*g*(5*e*f+d*g)))*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*e*g^5*(e*f-d*g))+_ + (c*d^2-b*d*e+a*e^2)^(5/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*(e*f-d*g))-_ + (c*f^2-b*f*g+a*g^2)^(5/2)*atanh(1/2*(b*f-2*a*g+(2*c*f-b*g)*x)/_ + (sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))/(g^5*(e*f-d*g))+_ + 1/8*(c*d^2-b*d*e+a*e^2)*(8*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-4*a*e)-_ + 2*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(c*e^4*(e*f-d*g))-_ + 1/64*(64*c^3*e*f^4-16*c^2*e*f^2*g*(9*b*f-8*a*g)-b^2*g^3*(5*b*e*f+_ + 3*b*d*g-8*a*e*g)+4*c*g^2*(22*b^2*e*f^2+16*a^2*e*g^2-3*a*b*g*(13*e*f-_ + d*g))-2*c*g*(16*c^2*e*f^3+b*g^2*(5*b*e*f+3*b*d*g-8*a*e*g)-_ + 4*c*g*(6*b*e*f^2-a*g*(7*e*f-3*d*g)))*x)*sqrt(a+b*x+c*x^2)/(c*e*g^4*_ + (e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 4 4 2 3 2 3 +--R (720a c + 360a b c - 15b )d e + (- 1440a b c - 120b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (960a c + 720b c )d e - 960b c d e + 384c d +--R * +--R 5 +--R g +--R + +--R 2 2 2 4 5 4 2 3 5 2 3 +--R (- 720a c - 360a b c + 15b )e f g + (1440a b c + 120b c)e f g +--R + +--R 3 2 2 5 3 2 3 5 4 4 5 5 +--R (- 960a c - 720b c )e f g + 960b c e f g - 384c e f +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 4 3 2 2 2 2 2 3 +--R 384a c e - 768a b c d e + (768a c + 384b c)d e - 768b c d e +--R + +--R 3 4 +--R 384c d +--R * +--R +-------------------+ +--R 5 +-+ | 2 2 +--R g \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 5 4 5 3 2 2 5 2 2 +--R - 384a c e g + 768a b c e f g + (- 768a c - 384b c)e f g +--R + +--R 2 5 3 3 5 4 +--R 768b c e f g - 384c e f +--R * +--R +-------------------+ +--R +-+ | 2 2 (b g - 2c f)x + 2a g - b f +--R \|c \|a g - b f g + c f atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R + +--R 3 4 5 3 5 4 3 +--R (96c d e g - 96c e f g )x +--R + +--R 2 4 3 2 3 5 2 5 4 3 5 2 3 2 +--R ((272b c d e - 128c d e )g - 272b c e f g + 128c e f g )x +--R + +--R 2 2 4 2 2 3 3 3 2 5 +--R ((432a c + 236b c)d e - 416b c d e + 192c d e )g +--R + +--R 2 2 5 4 2 5 2 3 3 5 3 2 +--R (- 432a c - 236b c)e f g + 416b c e f g - 192c e f g +--R * +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (1112a b c + 30b )d e + (- 896a c - 528b c)d e + 864b c d e +--R + +--R 3 4 +--R - 384c d e +--R * +--R 5 +--R g +--R + +--R 3 5 4 2 2 5 2 3 2 5 3 2 +--R (- 1112a b c - 30b )e f g + (896a c + 528b c)e f g - 864b c e f g +--R + +--R 3 5 4 +--R 384c e f g +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 6 6 5 +-+ +--R (384c d e g - 384c e f g )\|c +--R Type: Expression(Integer) +--E 1687 + +--S 1688 of 1751 +--a0:=integrate(t0,x) +--E 1688 + +--S 1689 of 1751 +--m0:=a0-r0 +--E 1689 + +--S 1690 of 1751 +--d0:=D(m0,x) +--E 1690 + +)clear all + +--S 1691 of 1751 +t0:=(d+e*x)^m*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 2 m +--R (c x + b x + a)(e x + d) +--R (1) -------------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1691 + +--S 1692 of 1751 +--r0:=2*a*(d+e*x)^(1+m)/((e^2-d*f)*sqrt(e+f*x))+2*c*e^2*(d+e*x)^(1+m)/_ +-- (f^2*(e^2-d*f)*sqrt(e+f*x))-2*b*e*(d+e*x)^(1+m)/(f*(e^2-d*f)*_ +-- sqrt(e+f*x))+2*c*(d+e*x)^(1+m)*sqrt(e+f*x)/(e*f^2*(3+2*m))-_ +-- 2*a*e*(1+2*m)*(d+e*x)^m*hypergeometric(1/2,-m,3/2,e*(e+f*x)/_ +-- (e^2-d*f))*sqrt(e+f*x)/(f*(e^2-d*f)*(-f*(d+e*x)/(e^2-d*f))^m)-_ +-- 2*b*(d*f-2*e^2*(1+m))*(d+e*x)^m*hypergeometric(1/2,-m,3/2,_ +-- e*(e+f*x)/(e^2-d*f))*sqrt(e+f*x)/(f^2*(e^2-d*f)*(-f*(d+e*x)/_ +-- (e^2-d*f))^m)+2*c*(d^2*f^2+4*d*e^2*f*(1+m)-4*e^4*(2+3*m+m^2))*_ +-- (d+e*x)^m*hypergeometric(1/2,-m,3/2,e*(e+f*x)/(e^2-d*f))*_ +-- sqrt(e+f*x)/(e*f^3*(e^2-d*f)*(3+2*m)*(-f*(d+e*x)/(e^2-d*f))^m) +--E 1692 + +--S 1693 of 1751 +--a0:=integrate(t0,x) +--E 1693 + +--S 1694 of 1751 +--m0:=a0-r0 +--E 1694 + +--S 1695 of 1751 +--d0:=D(m0,x) +--E 1695 + +)clear all + +--S 1696 of 1751 +t0:=(d+e*x)^3*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R (1) +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R / +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1696 + +--S 1697 of 1751 +r0:=2/3*(e^2-d*f)*(3*e*f*(2*b*e^2-b*d*f-a*e*f)-c*(10*e^4-8*d*e^2*f+_ + d^2*f^2))*(e+f*x)^(3/2)/f^6-2/5*e*(e*f*(4*b*e^2-3*b*d*f-a*e*f)-_ + c*(10*e^4-12*d*e^2*f+3*d^2*f^2))*(e+f*x)^(5/2)/f^6-2/7*e^2*(5*c*e^2-_ + 3*c*d*f-b*e*f)*(e+f*x)^(7/2)/f^6+2/9*c*e^3*(e+f*x)^(9/2)/f^6+_ + 2*(e^2-d*f)^3*(c*e^2-f*(b*e-a*f))/(f^6*sqrt(e+f*x))-2*(e^2-d*f)^2*_ + (f*(4*b*e^2-b*d*f-3*a*e*f)-c*(5*e^3-2*d*e*f))*sqrt(e+f*x)/f^6 +--R +--R +--R (2) +--R 3 5 5 3 2 5 4 4 4 +--R 70c e f x + ((90b e + 270c d e )f - 100c e f )x +--R + +--R 3 2 2 5 4 3 4 +--R (126a e + 378b d e + 378c d e)f + (- 144b e - 432c d e )f +--R + +--R 5 3 +--R 160c e f +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 +--R (630a d e + 630b d e + 210c d )f +--R + +--R 4 3 2 2 4 5 4 3 +--R (- 252a e - 756b d e - 756c d e )f + (288b e + 864c d e )f +--R + +--R 6 2 +--R - 320c e f +--R * +--R 2 +--R x +--R + +--R 2 3 5 3 2 2 3 4 +--R (1890a d e + 630b d )f + (- 2520a d e - 2520b d e - 840c d e)f +--R + +--R 5 4 2 3 3 6 5 2 +--R (1008a e + 3024b d e + 3024c d e )f + (- 1152b e - 3456c d e )f +--R + +--R 7 +--R 1280c e f +--R * +--R x +--R + +--R 3 5 2 2 3 4 +--R - 630a d f + (3780a d e + 1260b d e)f +--R + +--R 4 2 3 3 2 3 +--R (- 5040a d e - 5040b d e - 1680c d e )f +--R + +--R 6 5 2 4 2 7 6 +--R (2016a e + 6048b d e + 6048c d e )f + (- 2304b e - 6912c d e )f +--R + +--R 8 +--R 2560c e +--R / +--R 6 +-------+ +--R 315f \|f x + e +--R Type: Expression(Integer) +--E 1697 + +--S 1698 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 3 2 5 4 4 4 +--R 70c e f x + ((90b e + 270c d e )f - 100c e f )x +--R + +--R 3 2 2 5 4 3 4 +--R (126a e + 378b d e + 378c d e)f + (- 144b e - 432c d e )f +--R + +--R 5 3 +--R 160c e f +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 +--R (630a d e + 630b d e + 210c d )f +--R + +--R 4 3 2 2 4 5 4 3 +--R (- 252a e - 756b d e - 756c d e )f + (288b e + 864c d e )f +--R + +--R 6 2 +--R - 320c e f +--R * +--R 2 +--R x +--R + +--R 2 3 5 3 2 2 3 4 +--R (1890a d e + 630b d )f + (- 2520a d e - 2520b d e - 840c d e)f +--R + +--R 5 4 2 3 3 6 5 2 +--R (1008a e + 3024b d e + 3024c d e )f + (- 1152b e - 3456c d e )f +--R + +--R 7 +--R 1280c e f +--R * +--R x +--R + +--R 3 5 2 2 3 4 +--R - 630a d f + (3780a d e + 1260b d e)f +--R + +--R 4 2 3 3 2 3 +--R (- 5040a d e - 5040b d e - 1680c d e )f +--R + +--R 6 5 2 4 2 7 6 +--R (2016a e + 6048b d e + 6048c d e )f + (- 2304b e - 6912c d e )f +--R + +--R 8 +--R 2560c e +--R / +--R 6 +-------+ +--R 315f \|f x + e +--R Type: Union(Expression(Integer),...) +--E 1698 + +--S 1699 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1699 + +--S 1700 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1700 + +)clear all + +--S 1701 of 1751 +t0:=(d+e*x)^2*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R / +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1701 + +--S 1702 of 1751 +r0:=-2/3*(e*f*(3*b*e^2-2*b*d*f-a*e*f)-c*(6*e^4-6*d*e^2*f+d^2*f^2))*_ + (e+f*x)^(3/2)/f^5-2/5*e*(4*c*e^2-2*c*d*f-b*e*f)*(e+f*x)^(5/2)/f^5+_ + 2/7*c*e^2*(e+f*x)^(7/2)/f^5-2*(e^2-d*f)^2*(c*e^2-f*(b*e-a*f))/_ + (f^5*sqrt(e+f*x))+2*(e^2-d*f)*(f*(3*b*e^2-b*d*f-2*a*e*f)-_ + c*(4*e^3-2*d*e*f))*sqrt(e+f*x)/f^5 +--R +--R +--R (2) +--R 2 4 4 2 4 3 3 3 +--R 30c e f x + ((42b e + 84c d e)f - 48c e f )x +--R + +--R 2 2 4 3 2 3 4 2 2 +--R ((70a e + 140b d e + 70c d )f + (- 84b e - 168c d e )f + 96c e f )x +--R + +--R 2 4 3 2 2 3 +--R (420a d e + 210b d )f + (- 280a e - 560b d e - 280c d e)f +--R + +--R 4 3 2 5 +--R (336b e + 672c d e )f - 384c e f +--R * +--R x +--R + +--R 2 4 2 2 3 +--R - 210a d f + (840a d e + 420b d e)f +--R + +--R 4 3 2 2 2 5 4 6 +--R (- 560a e - 1120b d e - 560c d e )f + (672b e + 1344c d e )f - 768c e +--R / +--R 5 +-------+ +--R 105f \|f x + e +--R Type: Expression(Integer) +--E 1702 + +--S 1703 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 2 4 3 3 3 +--R 30c e f x + ((42b e + 84c d e)f - 48c e f )x +--R + +--R 2 2 4 3 2 3 4 2 2 +--R ((70a e + 140b d e + 70c d )f + (- 84b e - 168c d e )f + 96c e f )x +--R + +--R 2 4 3 2 2 3 +--R (420a d e + 210b d )f + (- 280a e - 560b d e - 280c d e)f +--R + +--R 4 3 2 5 +--R (336b e + 672c d e )f - 384c e f +--R * +--R x +--R + +--R 2 4 2 2 3 +--R - 210a d f + (840a d e + 420b d e)f +--R + +--R 4 3 2 2 2 5 4 6 +--R (- 560a e - 1120b d e - 560c d e )f + (672b e + 1344c d e )f - 768c e +--R / +--R 5 +-------+ +--R 105f \|f x + e +--R Type: Union(Expression(Integer),...) +--E 1703 + +--S 1704 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1704 + +--S 1705 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1705 + +)clear all + +--S 1706 of 1751 +t0:=(d+e*x)*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R (1) ------------------------------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1706 + +--S 1707 of 1751 +r0:=-2/3*(3*c*e^2-c*d*f-b*e*f)*(e+f*x)^(3/2)/f^4+2/5*c*e*(e+f*x)^(5/2)/f^4+_ + 2*(e^2-d*f)*(c*e^2-f*(b*e-a*f))/(f^4*sqrt(e+f*x))-2*(f*(2*b*e^2-_ + b*d*f-a*e*f)-c*(3*e^3-2*d*e*f))*sqrt(e+f*x)/f^4 +--R +--R +--R (2) +--R 3 3 3 2 2 2 +--R 6c e f x + ((10b e + 10c d)f - 12c e f )x +--R + +--R 3 2 2 3 3 +--R ((30a e + 30b d)f + (- 40b e - 40c d e)f + 48c e f)x - 30a d f +--R + +--R 2 2 3 2 4 +--R (60a e + 60b d e)f + (- 80b e - 80c d e )f + 96c e +--R / +--R 4 +-------+ +--R 15f \|f x + e +--R Type: Expression(Integer) +--E 1707 + +--S 1708 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 2 +--R 6c e f x + ((10b e + 10c d)f - 12c e f )x +--R + +--R 3 2 2 3 3 +--R ((30a e + 30b d)f + (- 40b e - 40c d e)f + 48c e f)x - 30a d f +--R + +--R 2 2 3 2 4 +--R (60a e + 60b d e)f + (- 80b e - 80c d e )f + 96c e +--R / +--R 4 +-------+ +--R 15f \|f x + e +--R Type: Union(Expression(Integer),...) +--E 1708 + +--S 1709 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1709 + +--S 1710 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1710 + +)clear all + +--S 1711 of 1751 +t0:=(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 2 +--R c x + b x + a +--R (1) ------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1711 + +--S 1712 of 1751 +r0:=2/3*c*(e+f*x)^(3/2)/f^3-2*(c*e^2-f*(b*e-a*f))/(f^3*sqrt(e+f*x))-_ + 2*(2*c*e-b*f)*sqrt(e+f*x)/f^3 +--R +--R +--R 2 2 2 2 2 +--R 2c f x + (6b f - 8c e f)x - 6a f + 12b e f - 16c e +--R (2) ------------------------------------------------------ +--R 3 +-------+ +--R 3f \|f x + e +--R Type: Expression(Integer) +--E 1712 + +--S 1713 of 1751 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 +--R 2c f x + (6b f - 8c e f)x - 6a f + 12b e f - 16c e +--R (3) ------------------------------------------------------ +--R 3 +-------+ +--R 3f \|f x + e +--R Type: Union(Expression(Integer),...) +--E 1713 + +--S 1714 of 1751 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1714 + +--S 1715 of 1751 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1715 + +)clear all + +--S 1716 of 1751 +t0:=(a+b*x+c*x^2)/((d+e*x)*(e+f*x)^(3/2)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) -------------------------------------- +--R 2 2 +-------+ +--R (e f x + (d f + e )x + d e)\|f x + e +--R Type: Expression(Integer) +--E 1716 + +--S 1717 of 1751 +r0:=-2*(c*d^2-b*d*e+a*e^2)*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(3/2))+2*(c*e^2-f*(b*e-a*f))/(f^2*(e^2-d*f)*_ + sqrt(e+f*x))+2*c*sqrt(e+f*x)/(e*f^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-------+ \|e \|f x + e +--R (2a e - 2b d e + 2c d )f \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 2 2 2 2 3 +--R ((2c d f - 2c e f)x - 2a e f + (2b e + 2c d e)f - 4c e ) +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R +----------+ +--R 3 3 2 | 2 +-+ +-------+ +--R (d e f - e f )\|- d f + e \|e \|f x + e +--R Type: Expression(Integer) +--E 1717 + +--S 1718 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +-------+ +--R (a e - b d e + c d )f \|f x + e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 2 3 +--R ((2c d f - 2c e f)x - 2a e f + (2b e + 2c d e)f - 4c e ) +--R * +--R +------------+ +--R | 3 +--R \|- d e f + e +--R / +--R +------------+ +--R 3 3 2 | 3 +-------+ +--R (d e f - e f )\|- d e f + e \|f x + e +--R , +--R +--R +----------+ +--R | 3 +-------+ +--R 2 2 2 +-------+ \|d e f - e \|f x + e +--R (- 2a e + 2b d e - 2c d )f \|f x + e atan(-----------------------) +--R 2 +--R d f - e +--R + +--R +----------+ +--R 2 2 2 2 3 | 3 +--R ((2c d f - 2c e f)x - 2a e f + (2b e + 2c d e)f - 4c e )\|d e f - e +--R / +--R +----------+ +--R 3 3 2 | 3 +-------+ +--R (d e f - e f )\|d e f - e \|f x + e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1718 + +--S 1719 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 2 2 | 2 +-+ +--R (a e - b d e + c d )\|- d f + e \|e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R +------------+ +-+ +-------+ +--R 2 2 | 3 \|e \|f x + e +--R (- 2a e + 2b d e - 2c d )\|- d e f + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R / +--R +------------+ +----------+ +--R 3 | 3 | 2 +-+ +--R (d e f - e )\|- d e f + e \|- d f + e \|e +--R Type: Expression(Integer) +--E 1719 + +--S 1720 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1720 + +--S 1721 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------+ +-+ +-------+ +--R 2 2 | 3 \|e \|f x + e +--R (- 2a e + 2b d e - 2c d )\|d e f - e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R +----------+ +--R +----------+ | 3 +-------+ +--R 2 2 | 2 +-+ \|d e f - e \|f x + e +--R (- 2a e + 2b d e - 2c d )\|- d f + e \|e atan(-----------------------) +--R 2 +--R d f - e +--R / +--R +----------+ +----------+ +--R 3 | 2 +-+ | 3 +--R (d e f - e )\|- d f + e \|e \|d e f - e +--R Type: Expression(Integer) +--E 1721 + +--S 1722 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1722 + +)clear all + +--S 1723 of 1751 +t0:=(a+b*x+c*x^2)/((d+e*x)^2*(e+f*x)^(3/2)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) ----------------------------------------------------------- +--R 2 3 3 2 2 2 2 +-------+ +--R (e f x + (2d e f + e )x + (d f + 2d e )x + d e)\|f x + e +--R Type: Expression(Integer) +--E 1723 + +--S 1724 of 1751 +r0:=(c*d^2-b*d*e+a*e^2)*f*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(5/2))-2*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/(e^(3/2)*(e^2-d*f)^(5/2))-_ + 2*(c*e^2-f*(b*e-a*f))/(f*(e^2-d*f)^2*sqrt(e+f*x))+(c*d^2-b*d*e+a*e^2)*_ + f*sqrt(e+f*x)/(e*(e^2-d*f)^2*(e^2-d*f-e*(e+f*x))) +--R +--R +--R (2) +--R 3 2 2 2 4 3 +--R ((3a e - b d e - c d e)f + (- 2b e + 4c d e )f)x +--R + +--R 2 2 3 2 3 2 2 +--R (3a d e - b d e - c d )f + (- 2b d e + 4c d e )f +--R * +--R +-+ +-------+ +--R +-------+ \|e \|f x + e +--R \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 2 2 2 3 4 2 +--R ((- 3a e + b d e - c d )f + 2b e f - 2c e )x - 2a d e f +--R + +--R 3 2 2 3 +--R (- a e + 3b d e - c d e)f - 2c d e +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R +----------+ +--R 2 2 3 4 2 6 3 3 2 3 2 5 | 2 +-+ +--R ((d e f - 2d e f + e f)x + d e f - 2d e f + d e f)\|- d f + e \|e +--R * +--R +-------+ +--R \|f x + e +--R Type: Expression(Integer) +--E 1724 + +--S 1725 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 4 3 +--R ((3a e - b d e - c d e)f + (- 2b e + 4c d e )f)x +--R + +--R 2 2 3 2 3 2 2 +--R (3a d e - b d e - c d )f + (- 2b d e + 4c d e )f +--R * +--R +-------+ +--R \|f x + e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 3 4 2 +--R ((- 6a e + 2b d e - 2c d )f + 4b e f - 4c e )x - 4a d e f +--R + +--R 3 2 2 3 +--R (- 2a e + 6b d e - 2c d e)f - 4c d e +--R * +--R +------------+ +--R | 3 +--R \|- d e f + e +--R / +--R 2 2 3 4 2 6 3 3 2 3 2 5 +--R ((2d e f - 4d e f + 2e f)x + 2d e f - 4d e f + 2d e f) +--R * +--R +------------+ +--R | 3 +-------+ +--R \|- d e f + e \|f x + e +--R , +--R +--R 3 2 2 2 4 3 +--R ((- 3a e + b d e + c d e)f + (2b e - 4c d e )f)x +--R + +--R 2 2 3 2 3 2 2 +--R (- 3a d e + b d e + c d )f + (2b d e - 4c d e )f +--R * +--R +----------+ +--R | 3 +-------+ +--R +-------+ \|d e f - e \|f x + e +--R \|f x + e atan(-----------------------) +--R 2 +--R d f - e +--R + +--R 2 2 2 3 4 2 +--R ((- 3a e + b d e - c d )f + 2b e f - 2c e )x - 2a d e f +--R + +--R 3 2 2 3 +--R (- a e + 3b d e - c d e)f - 2c d e +--R * +--R +----------+ +--R | 3 +--R \|d e f - e +--R / +--R +----------+ +--R 2 2 3 4 2 6 3 3 2 3 2 5 | 3 +--R ((d e f - 2d e f + e f)x + d e f - 2d e f + d e f)\|d e f - e +--R * +--R +-------+ +--R \|f x + e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1725 + +--S 1726 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 2 2 3 2 | 2 +-+ +--R ((3a e - b d e - c d )f - 2b e + 4c d e )\|- d f + e \|e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R +------------+ +--R 2 2 3 2 | 3 +--R ((- 6a e + 2b d e + 2c d )f + 4b e - 8c d e )\|- d e f + e +--R * +--R +-+ +-------+ +--R \|e \|f x + e +--R atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R / +--R +------------+ +----------+ +--R 2 2 3 5 | 3 | 2 +-+ +--R (2d e f - 4d e f + 2e )\|- d e f + e \|- d f + e \|e +--R Type: Expression(Integer) +--E 1726 + +--S 1727 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1727 + +--S 1728 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------+ +--R 2 2 3 2 | 3 +--R ((- 3a e + b d e + c d )f + 2b e - 4c d e )\|d e f - e +--R * +--R +-+ +-------+ +--R \|e \|f x + e +--R atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R +----------+ +--R 2 2 3 2 | 2 +-+ +--R ((- 3a e + b d e + c d )f + 2b e - 4c d e )\|- d f + e \|e +--R * +--R +----------+ +--R | 3 +-------+ +--R \|d e f - e \|f x + e +--R atan(-----------------------) +--R 2 +--R d f - e +--R / +--R +----------+ +----------+ +--R 2 2 3 5 | 2 +-+ | 3 +--R (d e f - 2d e f + e )\|- d f + e \|e \|d e f - e +--R Type: Expression(Integer) +--E 1728 + +--S 1729 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1729 + +)clear all + +--S 1730 of 1751 +t0:=(a+b*x+c*x^2)/((d+e*x)^3*(e+f*x)^(3/2)) +--R +--R +--R (1) +--R 2 +--R c x + b x + a +--R / +--R 3 4 2 4 3 2 3 2 3 2 2 3 +--R (e f x + (3d e f + e )x + (3d e f + 3d e )x + (d f + 3d e )x + d e) +--R * +--R +-------+ +--R \|f x + e +--R Type: Expression(Integer) +--E 1730 + +--S 1731 of 1751 +r0:=-3/4*(c*d^2-b*d*e+a*e^2)*f^2*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(7/2))+f*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/(e^(3/2)*(e^2-d*f)^(7/2))-_ + 2*(c*e^2-f*(b*e-a*f))*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))*_ + sqrt(e)/(e^2-d*f)^(7/2)+2*(c*e^2-f*(b*e-a*f))/((e^2-d*f)^3*_ + sqrt(e+f*x))-1/2*(c*d^2-b*d*e+a*e^2)*f^2*sqrt(e+f*x)/(e*(e^2-d*f)^2*_ + (e^2-d*f-e*(e+f*x))^2)-3/4*(c*d^2-b*d*e+a*e^2)*f^2*sqrt(e+f*x)/_ + (e*(e^2-d*f)^3*(e^2-d*f-e*(e+f*x)))+f*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + sqrt(e+f*x)/(e*(e^2-d*f)^3*(e^2-d*f-e*(e+f*x))) +--R +--R +--R (2) +--R 4 3 2 2 2 5 4 6 2 +--R ((15a e - 3b d e - c d e )f + (- 12b e + 8c d e )f + 8c e )x +--R + +--R 3 2 2 3 2 4 2 3 +--R (30a d e - 6b d e - 2c d e)f + (- 24b d e + 16c d e )f +--R + +--R 5 +--R 16c d e +--R * +--R x +--R + +--R 2 2 3 4 2 2 3 3 2 2 4 +--R (15a d e - 3b d e - c d )f + (- 12b d e + 8c d e )f + 8c d e +--R * +--R +-+ +-------+ +--R +-------+ \|e \|f x + e +--R \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 3 2 2 2 4 3 5 2 +--R ((- 15a e + 3b d e + c d e)f + (12b e - 8c d e )f - 8c e )x +--R + +--R 2 2 3 2 4 3 2 2 +--R (- 25a d e + 5b d e - c d )f + (- 5a e + 21b d e - 5c d e )f +--R + +--R 5 4 +--R 4b e - 24c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 5 4 +--R - 8a d e f + (- 9a d e + 13b d e - c d e)f + 2a e + 2b d e +--R + +--R 2 3 +--R - 14c d e +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R 3 3 3 2 5 2 7 9 2 +--R (4d e f - 12d e f + 12d e f - 4e )x +--R + +--R 4 2 3 3 4 2 2 6 8 5 3 4 3 2 3 5 +--R (8d e f - 24d e f + 24d e f - 8d e )x + 4d e f - 12d e f + 12d e f +--R + +--R 2 7 +--R - 4d e +--R * +--R +----------+ +--R | 2 +-+ +-------+ +--R \|- d f + e \|e \|f x + e +--R Type: Expression(Integer) +--E 1731 + +--S 1732 of 1751 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 2 2 2 5 4 6 2 +--R ((15a e - 3b d e - c d e )f + (- 12b e + 8c d e )f + 8c e )x +--R + +--R 3 2 2 3 2 4 2 3 +--R (30a d e - 6b d e - 2c d e)f + (- 24b d e + 16c d e )f +--R + +--R 5 +--R 16c d e +--R * +--R x +--R + +--R 2 2 3 4 2 2 3 3 2 2 4 +--R (15a d e - 3b d e - c d )f + (- 12b d e + 8c d e )f + 8c d e +--R * +--R +-------+ +--R \|f x + e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R 3 2 2 2 4 3 5 2 +--R ((- 30a e + 6b d e + 2c d e)f + (24b e - 16c d e )f - 16c e )x +--R + +--R 2 2 3 2 +--R (- 50a d e + 10b d e - 2c d )f +--R + +--R 4 3 2 2 5 4 +--R (- 10a e + 42b d e - 10c d e )f + 8b e - 48c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 5 4 +--R - 16a d e f + (- 18a d e + 26b d e - 2c d e)f + 4a e + 4b d e +--R + +--R 2 3 +--R - 28c d e +--R * +--R +------------+ +--R | 3 +--R \|- d e f + e +--R / +--R 3 3 3 2 5 2 7 9 2 +--R (8d e f - 24d e f + 24d e f - 8e )x +--R + +--R 4 2 3 3 4 2 2 6 8 5 3 4 3 2 +--R (16d e f - 48d e f + 48d e f - 16d e )x + 8d e f - 24d e f +--R + +--R 3 5 2 7 +--R 24d e f - 8d e +--R * +--R +------------+ +--R | 3 +-------+ +--R \|- d e f + e \|f x + e +--R , +--R +--R 4 3 2 2 2 5 4 6 2 +--R ((- 15a e + 3b d e + c d e )f + (12b e - 8c d e )f - 8c e )x +--R + +--R 3 2 2 3 2 4 2 3 +--R (- 30a d e + 6b d e + 2c d e)f + (24b d e - 16c d e )f +--R + +--R 5 +--R - 16c d e +--R * +--R x +--R + +--R 2 2 3 4 2 2 3 3 2 2 4 +--R (- 15a d e + 3b d e + c d )f + (12b d e - 8c d e )f - 8c d e +--R * +--R +----------+ +--R | 3 +-------+ +--R +-------+ \|d e f - e \|f x + e +--R \|f x + e atan(-----------------------) +--R 2 +--R d f - e +--R + +--R 3 2 2 2 4 3 5 2 +--R ((- 15a e + 3b d e + c d e)f + (12b e - 8c d e )f - 8c e )x +--R + +--R 2 2 3 2 +--R (- 25a d e + 5b d e - c d )f +--R + +--R 4 3 2 2 5 4 +--R (- 5a e + 21b d e - 5c d e )f + 4b e - 24c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 5 4 +--R - 8a d e f + (- 9a d e + 13b d e - c d e)f + 2a e + 2b d e +--R + +--R 2 3 +--R - 14c d e +--R * +--R +----------+ +--R | 3 +--R \|d e f - e +--R / +--R 3 3 3 2 5 2 7 9 2 +--R (4d e f - 12d e f + 12d e f - 4e )x +--R + +--R 4 2 3 3 4 2 2 6 8 5 3 4 3 2 +--R (8d e f - 24d e f + 24d e f - 8d e )x + 4d e f - 12d e f +--R + +--R 3 5 2 7 +--R 12d e f - 4d e +--R * +--R +----------+ +--R | 3 +-------+ +--R \|d e f - e \|f x + e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1732 + +--S 1733 of 1751 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 3 2 4 +--R ((15a e - 3b d e - c d )f + (- 12b e + 8c d e )f + 8c e ) +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R * +--R +------------+ +--R 3 +-------+ 2 | 3 +--R (- 2d e f + 2e )\|f x + e + (e f x - d f + 2e )\|- d e f + e +--R log(---------------------------------------------------------------) +--R e x + d +--R + +--R 2 2 2 3 2 4 +--R ((- 30a e + 6b d e + 2c d )f + (24b e - 16c d e )f - 16c e ) +--R * +--R +------------+ +-+ +-------+ +--R | 3 \|e \|f x + e +--R \|- d e f + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R / +--R +------------+ +----------+ +--R 3 3 2 3 2 5 7 | 3 | 2 +-+ +--R (8d e f - 24d e f + 24d e f - 8e )\|- d e f + e \|- d f + e \|e +--R Type: Expression(Integer) +--E 1733 + +--S 1734 of 1751 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1734 + +--S 1735 of 1751 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 3 2 4 +--R ((- 15a e + 3b d e + c d )f + (12b e - 8c d e )f - 8c e ) +--R * +--R +----------+ +-+ +-------+ +--R | 3 \|e \|f x + e +--R \|d e f - e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 2 2 2 3 2 4 +--R ((- 15a e + 3b d e + c d )f + (12b e - 8c d e )f - 8c e ) +--R * +--R +----------+ +--R +----------+ | 3 +-------+ +--R | 2 +-+ \|d e f - e \|f x + e +--R \|- d f + e \|e atan(-----------------------) +--R 2 +--R d f - e +--R / +--R +----------+ +----------+ +--R 3 3 2 3 2 5 7 | 2 +-+ | 3 +--R (4d e f - 12d e f + 12d e f - 4e )\|- d f + e \|e \|d e f - e +--R Type: Expression(Integer) +--E 1735 + +--S 1736 of 1751 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1736 + +)clear all + +--S 1737 of 1751 +t0:=x^m*(1-a^2*x^2)^p/(1+a*x) +--R +--R +--R 2 2 p m +--R (- a x + 1) x +--R (1) --------------- +--R a x + 1 +--R Type: Expression(Integer) +--E 1737 + +--S 1738 of 1751 +--r0:=x^(1+m)*AppellF1(1+m,-p,1-p,2+m,a*x,-a*x)/(1+m) +--E 1738 + +--S 1739 of 1751 +--a0:=integrate(t0,x) +--E 1739 + +--S 1740 of 1751 +--m0:=a0-r0 +--E 1740 + +--S 1741 of 1751 +--d0:=D(m0,x) +--E 1741 + +)clear all + +--S 1742 of 1751 +t0:=sqrt(-1+x)*sqrt(1+x)/(1+x-x^2) +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (1) - ---------------- +--R 2 +--R x - x - 1 +--R Type: Expression(Integer) +--E 1742 + +--S 1743 of 1751 +r0:=-acosh(x)-atan(sqrt(-1+x)*sqrt(-2+sqrt(5))/sqrt(1+x))*_ + sqrt(2/5*(-1+sqrt(5)))+atanh(sqrt(-1+x)*sqrt(2+sqrt(5))/sqrt(1+x))*_ + sqrt(2/5*(1+sqrt(5))) +--R +--R +--R (2) +--R +--------+ +--R +---------+ +-----+ | +-+ +--R | +-+ \|x - 1 \|\|5 + 2 +--R \|2\|5 + 2 atanh(-------------------) +--R +-----+ +--R \|x + 1 +--R + +--R +--------+ +--R +---------+ +-----+ | +-+ +--R | +-+ \|x - 1 \|\|5 - 2 +-+ +--R - \|2\|5 - 2 atan(-------------------) - \|5 acosh(x) +--R +-----+ +--R \|x + 1 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 1743 + +--S 1744 of 1751 +--a0:=integrate(t0,x) +--E 1744 + +--S 1745 of 1751 +--m0:=a0-r0 +--E 1745 + +--S 1746 of 1751 +--d0:=D(m0,x) +--E 1746 + +)clear all + +--S 1747 of 1751 +t0:=(a+b*x+c*x^2)/(sqrt(d+e*x)*sqrt(f+g*x)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) -------------------- +--R +-------+ +-------+ +--R \|e x + d \|g x + f +--R Type: Expression(Integer) +--E 1747 + +--S 1748 of 1751 +r0:=-b*(e*f+d*g)*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/_ + (e^(3/2)*g^(3/2))-1/4*c*(4*d*e*f*g-3*(e*f+d*g)^2)*atanh(sqrt(g)*_ + sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/(e^(5/2)*g^(5/2))+2*a*atanh(sqrt(g)*_ + sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/(sqrt(e)*sqrt(g))+b*sqrt(d+e*x)*_ + sqrt(f+g*x)/(e*g)-3/4*c*(e*f+d*g)*sqrt(d+e*x)*sqrt(f+g*x)/(e^2*g^2)+_ + 1/2*c*x*sqrt(d+e*x)*sqrt(f+g*x)/(e*g) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R ((8a e - 4b d e + 3c d )g + (- 4b e + 2c d e)f g + 3c e f ) +--R * +--R +-+ +-------+ +--R \|g \|e x + d +--R atanh(--------------) +--R +-+ +-------+ +--R \|e \|g x + f +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2c e g x + (4b e - 3c d)g - 3c e f)\|e \|g \|e x + d \|g x + f +--R / +--R 2 2 +-+ +-+ +--R 4e g \|e \|g +--R Type: Expression(Integer) +--E 1748 + +--S 1749 of 1751 +--a0:=integrate(t0,x) +--E 1749 + +--S 1750 of 1751 +--m0:=a0-r0 +--E 1750 + +--S 1751 of 1751 +--d0:=D(m0,x) +--E 1751 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/richder12a.input.pamphlet b/src/input/richder12a.input.pamphlet new file mode 100644 index 0000000..5476ecd --- /dev/null +++ b/src/input/richder12a.input.pamphlet @@ -0,0 +1,19660 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +All derivatives match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12a.output +)spool richder12a.output +)set message test on +)set message auto off +)clear all + +--S 1 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + A b x)(e x + d) +--R Type: Expression(Integer) +--E 1 + +--S 2 OF 765 +r0:=-d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R ((A c + B b)e - 3B c d)m + ((7A c + 7B b)e - 21B c d)m +--R + +--R ((14A c + 14B b)e - 42B c d)m + (8A c + 8B b)e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R (A b e + (- 2A c - 2B b)d e + 3B c d )m +--R + +--R 2 2 2 +--R (8A b e + (- 16A c - 16B b)d e + 24B c d )m +--R + +--R 2 2 2 +--R (19A b e + (- 38A c - 38B b)d e + 57B c d )m + 12A b e +--R + +--R 2 +--R (- 24A c - 24B b)d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 +--R (- A b d e + (A c + B b)d e - B c d )m +--R + +--R 2 2 3 2 +--R (- 9A b d e + (9A c + 9B b)d e - 9B c d )m +--R + +--R 2 2 3 2 +--R (- 26A b d e + (26A c + 26B b)d e - 26B c d )m - 24A b d e +--R + +--R 2 3 +--R (24A c + 24B b)d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 2 + +--S 3 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 3 + +)clear all + +--S 4 OF 765 +t0:=(A+B*x)*(d+e*x)^5*(b*x+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 +--R B c e x + ((A c + B b)e + 5B c d e )x +--R + +--R 5 4 2 3 6 +--R (A b e + (5A c + 5B b)d e + 10B c d e )x +--R + +--R 4 2 3 3 2 5 +--R (5A b d e + (10A c + 10B b)d e + 10B c d e )x +--R + +--R 2 3 3 2 4 4 +--R (10A b d e + (10A c + 10B b)d e + 5B c d e)x +--R + +--R 3 2 4 5 3 4 5 2 +--R (10A b d e + (5A c + 5B b)d e + B c d )x + (5A b d e + (A c + B b)d )x +--R + +--R 5 +--R A b d x +--R Type: Polynomial(Integer) +--E 4 + +--S 5 OF 765 +r0:=-1/6*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^6/e^4+1/7*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^7/e^4-1/8*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^8/e^4+_ + 1/9*B*c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 1 9 5 8 8 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 9 8 8 8 +--R + +--R 1 9 5 5 8 10 2 7 7 +--R (- A b e + (- A c + - B b)d e + -- B c d e )x +--R 7 7 7 7 +--R + +--R 5 8 5 5 2 7 5 3 6 6 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 6 3 3 3 +--R + +--R 2 7 3 6 4 5 5 +--R (2A b d e + (2A c + 2B b)d e + B c d e )x +--R + +--R 5 3 6 5 5 4 5 1 5 4 4 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 2 4 4 4 +--R + +--R 5 4 5 1 1 5 4 3 1 5 4 2 1 7 2 +--R (- A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 3 2 42 +--R + +--R 1 1 8 1 9 +--R (--- A c + --- B b)d e - --- B c d +--R 168 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 5 + +--S 6 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 6 + +)clear all + +--S 7 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 +--R B c e x + ((A c + B b)e + 4B c d e )x +--R + +--R 4 3 2 2 5 +--R (A b e + (4A c + 4B b)d e + 6B c d e )x +--R + +--R 3 2 2 3 4 +--R (4A b d e + (6A c + 6B b)d e + 4B c d e)x +--R + +--R 2 2 3 4 3 3 4 2 +--R (6A b d e + (4A c + 4B b)d e + B c d )x + (4A b d e + (A c + B b)d )x +--R + +--R 4 +--R A b d x +--R Type: Polynomial(Integer) +--E 7 + +--S 8 OF 765 +r0:=-1/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^5/e^4+1/6*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^7/e^4+_ + 1/8*B*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 1 8 4 7 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 8 2 2 7 2 6 6 +--R (- A b e + (- A c + - B b)d e + B c d e )x +--R 6 3 3 +--R + +--R 4 7 6 6 2 6 4 3 5 5 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 3 2 6 3 5 1 4 4 4 +--R (- A b d e + (A c + B b)d e + - B c d e )x +--R 2 4 +--R + +--R 4 3 5 1 1 4 4 3 1 4 4 2 1 6 2 +--R (- A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 3 2 30 +--R + +--R 1 1 7 1 8 +--R (--- A c + --- B b)d e - --- B c d +--R 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 8 + +--S 9 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 9 + +)clear all + +--S 10 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R (A b e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 2 2 3 3 2 3 2 +--R (3A b d e + (3A c + 3B b)d e + B c d )x + (3A b d e + (A c + B b)d )x +--R + +--R 3 +--R A b d x +--R Type: Polynomial(Integer) +--E 10 + +--S 11 OF 765 +r0:=-1/4*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^4/e^4+1/5*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^6/e^4+_ + 1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 1 7 1 6 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 7 3 3 6 3 2 5 5 +--R (- A b e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 3 6 3 3 2 5 1 3 4 4 +--R (- A b d e + (- A c + - B b)d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 2 5 1 1 3 4 3 1 3 4 2 1 5 2 +--R (A b d e + (- A c + - B b)d e )x + - A b d e x - -- A b d e +--R 3 3 2 20 +--R + +--R 1 1 6 1 7 +--R (-- A c + -- B b)d e - --- B c d +--R 60 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 11 + +--S 12 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R Type: Polynomial(Integer) +--E 13 + +--S 14 OF 765 +r0:=1/2*A*b*d^2*x^2+1/3*d*(b*B*d+A*c*d+2*A*b*e)*x^3+1/4*(A*e*(2*c*d+b*e)+_ + B*d*(c*d+2*b*e))*x^4+1/5*e*(2*B*c*d+b*B*e+A*c*e)*x^5+1/6*B*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 1 2 2 5 +--R - B c e x + ((- A c + - B b)e + - B c d e)x +--R 6 5 5 5 +--R + +--R 1 2 1 1 1 2 4 +--R (- A b e + (- A c + - B b)d e + - B c d )x +--R 4 2 2 4 +--R + +--R 2 1 1 2 3 1 2 2 +--R (- A b d e + (- A c + - B b)d )x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 14 + +--S 15 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 OF 765 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x +--R Type: Polynomial(Integer) +--E 16 + +--S 17 OF 765 +r0:=1/2*A*b*d*x^2+1/3*(b*B*d+A*c*d+A*b*e)*x^3+1/4*(B*c*d+b*B*e+A*c*e)*x^4+_ + 1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 3 1 2 +--R (- A b e + (- A c + - B b)d)x + - A b d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 18 + +)clear all + +--S 19 OF 765 +t0:=(A+B*x)*(b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + (A c + B b)x + A b x +--R Type: Polynomial(Integer) +--E 19 + +--S 20 OF 765 +r0:=1/2*A*b*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 1 3 1 2 +--R (2) - B c x + (- A c + - B b)x + - A b x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +--S 21 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 22 + +--S 23 OF 765 +r0:=(B*d-A*e)*(c*d-b*e)*x/e^3-1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+_ + 1/3*B*c*x^3/e-d*(B*d-A*e)*(c*d-b*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 2 3 3 3 +--R (- 6A b d e + (6A c + 6B b)d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 +--R ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R (6A b e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 23 + +--S 24 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 24 + +)clear all + +--S 25 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 25 + +--S 26 OF 765 +r0:=-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+d*(B*d-A*e)*_ + (c*d-b*e)/(e^4*(d+e*x))+(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 +--R (2A b e + (- 4A c - 4B b)d e + 6B c d e)x + 2A b d e +--R + +--R 2 3 +--R (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 2 2 3 +--R ((2A c + 2B b)d e - 4B c d e)x + 2A b d e + (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 26 + +--S 27 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 27 + +)clear all + +--S 28 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 28 + +--S 29 OF 765 +r0:=B*c*x/e^3+1/2*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^2)+(-B*d*(3*c*d-_ + 2*b*e)+A*e*(2*c*d-b*e))/(e^4*(d+e*x))-(3*B*c*d-b*B*e-A*c*e)*log(d+_ + e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 +--R 2B c e x + 4B c d e x + (- 2A b e + (4A c + 4B b)d e - 4B c d e)x +--R + +--R 2 2 3 +--R - A b d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 29 + +--S 30 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 OF 765 +r0:=1/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^3)+1/2*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^2)+(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+_ + B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 2 +--R (- 3A b e + (- 6A c - 6B b)d e + 27B c d e)x - A b d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 32 + +--S 33 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 34 + +--S 35 OF 765 +r0:=1/4*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^4)+1/3*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^2)-B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 1 3 3 2 2 +--R - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 2 2 +--R + +--R 1 3 1 1 2 2 1 2 +--R (- - A b e + (- - A c - - B b)d e - B c d e)x - -- A b d e +--R 3 3 3 12 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - - B c d +--R 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 35 + +--S 36 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 36 + +)clear all + +--S 37 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 37 + +--S 38 OF 765 +r0:=1/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^5)+1/4*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 3 3 2 +--R + +--R 1 3 1 1 2 1 2 1 2 +--R (- - A b e + (- - A c - - B b)d e - - B c d e)x - -- A b d e +--R 4 6 6 4 20 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - -- B c d +--R 30 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 38 + +--S 39 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 39 + +)clear all + +--S 40 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 40 + +--S 41 OF 765 +r0:=1/6*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^6)+1/5*(-B*d*(3*c*d-2*b*e)+_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^5)+1/4*(3*B*c*d-b*B*e-A*c*e)/(e^4*_ + (d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 3 4 4 4 +--R + +--R 1 3 1 1 2 1 2 1 2 +--R (- - A b e + (- -- A c - -- B b)d e - -- B c d e)x - -- A b d e +--R 5 10 10 10 30 +--R + +--R 1 1 2 1 3 +--R (- -- A c - -- B b)d e - -- B c d +--R 60 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 41 + +--S 42 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 42 + +)clear all + +--S 43 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 m +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )(e x + d) +--R Type: Expression(Integer) +--E 43 + +--S 44 OF 765 +r0:=-d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(1+m)/(e^6*(1+m))+d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^6*(2+m))+_ + (A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(4+m)/(e^6*(4+m))-_ + c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*_ + (d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((A c + 2B b c)e - 5B c d)m + ((16A c + 32B b c)e - 80B c d)m +--R + +--R 2 2 3 +--R ((95A c + 190B b c)e - 475B c d)m +--R + +--R 2 2 2 +--R ((260A c + 520B b c)e - 1300B c d)m +--R + +--R 2 2 2 2 +--R ((324A c + 648B b c)e - 1620B c d)m + (144A c + 288B b c)e - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (- 4A c - 8B b c)d e + 10B c d )m +--R + +--R 2 2 2 2 2 4 +--R ((34A b c + 17B b )e + (- 68A c - 136B b c)d e + 170B c d )m +--R + +--R 2 2 2 2 2 3 +--R ((214A b c + 107B b )e + (- 428A c - 856B b c)d e + 1070B c d )m +--R + +--R 2 2 2 2 2 2 +--R ((614A b c + 307B b )e + (- 1228A c - 2456B b c)d e + 3070B c d )m +--R + +--R 2 2 2 2 2 +--R ((792A b c + 396B b )e + (- 1584A c - 3168B b c)d e + 3960B c d )m +--R + +--R 2 2 2 2 2 +--R (360A b c + 180B b )e + (- 720A c - 1440B b c)d e + 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (- 6A b c - 3B b )d e + (6A c + 12B b c)d e - 10B c d )m +--R + +--R 2 3 2 2 2 2 +--R 18A b e + (- 108A b c - 54B b )d e + (108A c + 216B b c)d e +--R + +--R 2 3 +--R - 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 2 2 +--R 121A b e + (- 726A b c - 363B b )d e + (726A c + 1452B b c)d e +--R + +--R 2 3 +--R - 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 +--R 372A b e + (- 2232A b c - 1116B b )d e +--R + +--R 2 2 2 3 +--R (2232A c + 4464B b c)d e - 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 +--R 508A b e + (- 3048A b c - 1524B b )d e +--R + +--R 2 2 2 3 +--R (3048A c + 6096B b c)d e - 5080B c d +--R * +--R m +--R + +--R 2 3 2 2 2 2 +--R 240A b e + (- 1440A b c - 720B b )d e + (1440A c + 2880B b c)d e +--R + +--R 2 3 +--R - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 3 +--R - 2A b d e + (6A b c + 3B b )d e + (- 4A c - 8B b c)d e +--R + +--R 2 4 +--R 5B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 2 2 2 3 +--R - 38A b d e + (114A b c + 57B b )d e + (- 76A c - 152B b c)d e +--R + +--R 2 4 +--R 95B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 2 2 +--R - 274A b d e + (822A b c + 411B b )d e +--R + +--R 2 3 2 4 +--R (- 548A c - 1096B b c)d e + 685B c d +--R * +--R 3 +--R m +--R + +--R 2 3 2 2 2 +--R - 922A b d e + (2766A b c + 1383B b )d e +--R + +--R 2 3 2 4 +--R (- 1844A c - 3688B b c)d e + 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 +--R - 1404A b d e + (4212A b c + 2106B b )d e +--R + +--R 2 3 2 4 +--R (- 2808A c - 5616B b c)d e + 3510B c d +--R * +--R m +--R + +--R 2 3 2 2 2 +--R - 720A b d e + (2160A b c + 1080B b )d e +--R + +--R 2 3 2 4 +--R (- 1440A c - 2880B b c)d e + 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 2 3 2 2 4 2 5 5 +--R (A b d e + (- 2A b c - B b )d e + (A c + 2B b c)d e - B c d )m +--R + +--R 2 2 3 2 3 2 2 4 +--R 20A b d e + (- 40A b c - 20B b )d e + (20A c + 40B b c)d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 2 3 2 3 2 +--R 155A b d e + (- 310A b c - 155B b )d e +--R + +--R 2 4 2 5 +--R (155A c + 310B b c)d e - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 2 3 2 3 2 +--R 580A b d e + (- 1160A b c - 580B b )d e +--R + +--R 2 4 2 5 +--R (580A c + 1160B b c)d e - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 2 3 2 3 2 +--R 1044A b d e + (- 2088A b c - 1044B b )d e +--R + +--R 2 4 2 5 +--R (1044A c + 2088B b c)d e - 1044B c d +--R * +--R m +--R + +--R 2 2 3 2 3 2 2 4 +--R 720A b d e + (- 1440A b c - 720B b )d e + (720A c + 1440B b c)d e +--R + +--R 2 5 +--R - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 44 + +--S 45 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 +--R B c e x + ((A c + 2B b c)e + 4B c d e )x +--R + +--R 2 4 2 3 2 2 2 7 +--R ((2A b c + B b )e + (4A c + 8B b c)d e + 6B c d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 6 +--R (A b e + (8A b c + 4B b )d e + (6A c + 12B b c)d e + 4B c d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 5 +--R (4A b d e + (12A b c + 6B b )d e + (4A c + 8B b c)d e + B c d )x +--R + +--R 2 2 2 2 3 2 4 4 +--R (6A b d e + (8A b c + 4B b )d e + (A c + 2B b c)d )x +--R + +--R 2 3 2 4 3 2 4 2 +--R (4A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 46 + +--S 47 OF 765 +r0:=-1/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^5/e^6+1/6*d*(c*d-b*e)*(B*d*_ + (5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^6/e^6+1/7*(A*e*(6*c^2*d^2-_ + 6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^7/e^6-1/8*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+_ + b^2*e^2))*(d+e*x)^8/e^6-1/9*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^9/e^6+1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 2 10 4 2 9 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 2 10 1 2 9 3 2 2 8 8 +--R ((- A b c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 8 2 4 +--R + +--R 1 2 10 8 4 2 9 6 2 12 2 8 +--R - A b e + (- A b c + - B b )d e + (- A c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 4 2 3 7 +--R - B c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 2 2 9 2 2 8 2 2 4 3 7 +--R - A b d e + (2A b c + B b )d e + (- A c + - B b c)d e +--R 3 3 3 +--R + +--R 1 2 4 6 +--R - B c d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 6 2 2 8 8 4 2 3 7 1 2 2 4 6 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d e )x +--R 5 5 5 5 5 +--R + +--R 2 3 7 1 1 2 4 6 4 1 2 4 6 3 1 2 7 3 +--R (A b d e + (- A b c + - B b )d e )x + - A b d e x + --- A b d e +--R 2 4 3 105 +--R + +--R 1 1 2 8 2 1 2 1 9 1 2 10 +--R (- --- A b c - --- B b )d e + (--- A c + --- B b c)d e - ---- B c d +--R 140 280 630 315 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 48 + +)clear all + +--S 49 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R ((2A b c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (6A b c + 3B b )d e + (3A c + 6B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 3 4 +--R (3A b d e + (6A b c + 3B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 3 2 3 2 +--R (3A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 49 + +--S 50 OF 765 +r0:=1/3*A*b^2*d^3*x^3+1/4*b*d^2*(b*B*d+2*A*c*d+3*A*b*e)*x^4+1/5*d*(A*c^2*_ + d^2+3*b^2*e*(B*d+A*e)+2*b*c*d*(B*d+3*A*e))*x^5+1/6*(A*e*(3*c^2*d^2+_ + 6*b*c*d*e+b^2*e^2)+B*d*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^6+1/7*e*_ + (A*c*e*(3*c*d+2*b*e)+B*(3*c^2*d^2+6*b*c*d*e+b^2*e^2))*x^7+_ + 1/8*c*e^2*(3*B*c*d+2*b*B*e+A*c*e)*x^8+1/9*B*c^2*e^3*x^9 +--R +--R +--R (2) +--R 1 2 3 9 1 2 1 3 3 2 2 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 3 3 2 6 2 3 2 2 7 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d e)x +--R 7 7 7 7 7 +--R + +--R 1 2 3 1 2 2 1 2 2 1 2 3 6 +--R (- A b e + (A b c + - B b )d e + (- A c + B b c)d e + - B c d )x +--R 6 2 2 6 +--R + +--R 3 2 2 6 3 2 2 1 2 2 3 5 +--R (- A b d e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 3 2 2 1 1 2 3 4 1 2 3 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 50 + +--S 51 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 51 + +)clear all + +--S 52 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 52 + +--S 53 OF 765 +r0:=1/3*A*b^2*d^2*x^3+1/4*b*d*(b*B*d+2*A*c*d+2*A*b*e)*x^4+1/5*(A*c^2*d^2+_ + b^2*e*(2*B*d+A*e)+2*b*c*d*(B*d+2*A*e))*x^5+1/6*(2*A*c*e*(c*d+b*e)+_ + B*(c^2*d^2+4*b*c*d*e+b^2*e^2))*x^6+1/7*c*e*(A*c*e+2*B*(c*d+b*e))*_ + x^7+1/8*B*c^2*e^2*x^8 +--R +--R +--R (2) +--R 1 2 2 8 1 2 2 2 2 2 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e)x +--R 8 7 7 7 +--R + +--R 1 1 2 2 1 2 2 1 2 2 6 +--R ((- A b c + - B b )e + (- A c + - B b c)d e + - B c d )x +--R 3 6 3 3 6 +--R + +--R 1 2 2 4 2 2 1 2 2 2 5 +--R (- A b e + (- A b c + - B b )d e + (- A c + - B b c)d )x +--R 5 5 5 5 5 +--R + +--R 1 2 1 1 2 2 4 1 2 2 3 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 2 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 53 + +--S 54 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 54 + +)clear all + +--S 55 OF 765 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R Type: Polynomial(Integer) +--E 55 + +--S 56 OF 765 +r0:=1/3*A*b^2*d*x^3+1/4*b*(b*B*d+2*A*c*d+A*b*e)*x^4+1/5*(A*c^2*d+b^2*B*e+_ + 2*b*c*(B*d+A*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 1 2 1 2 2 5 +--R ((- A b c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 +--R + +--R 1 2 1 1 2 4 1 2 3 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 4 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 56 + +--S 57 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R (1) B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R Type: Polynomial(Integer) +--E 58 + +--S 59 OF 765 +r0:=1/3*A*b^2*x^3+1/4*b*(b*B+2*A*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6 +--R +--R +--R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 +--R (2) - B c x + (- A c + - B b c)x + (- A b c + - B b )x + - A b x +--R 6 5 5 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 59 + +--S 60 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 OF 765 +r0:=d*(B*d-A*e)*(c*d-b*e)^2*x/e^5-1/2*(B*d-A*e)*(c*d-b*e)^2*x^2/e^4-_ + 1/3*(A*c*e*(c*d-2*b*e)-B*(c*d-b*e)^2)*x^3/e^3-1/4*c*(B*c*d-2*b*B*e-_ + A*c*e)*x^4/e^2+1/5*B*c^2*x^5/e-d^2*(B*d-A*e)*(c*d-b*e)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 3 2 3 2 2 4 +--R 60A b d e + (- 120A b c - 60B b )d e + (60A c + 120B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((40A b c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 60A b c - 30B b )d e + (30A c + 60B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 60A b d e + (120A b c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 62 + +--S 63 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 64 + +--S 65 OF 765 +r0:=-(c*d-b*e)*(2*B*d*(2*c*d-b*e)-A*e*(3*c*d-b*e))*x/e^5+1/2*(c*d-b*e)*_ + (3*B*c*d-b*B*e-2*A*c*e)*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x))+d*_ + (c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 4 2 2 3 2 3 2 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 24A b d e + (72A b c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 12A b e + (- 36A b c - 18B b )d e + (24A c + 48B b c)d e +--R + +--R 2 3 2 +--R - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 48A b c - 24B b )d e + (36A c + 72B b c)d e +--R + +--R 2 4 +--R - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 12A b d e + (24A b c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 65 + +--S 66 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 66 + +)clear all + +--S 67 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 67 + +--S 68 OF 765 +r0:=-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2-6*b*c*d*e+b^2*e^2))*x/e^5-1/2*c*_ + (3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*(d+e*x)^2)-d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*_ + (2*c*d-b*e))/(e^6*(d+e*x))+(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-_ + B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 +--R 6A b e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e +--R + +--R 2 3 2 +--R - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 72A b c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 6A b d e + (- 36A b c - 18B b )d e + (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((24A b c + 12B b )d e + (- 33A c - 66B b c)d e + 63B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 +--R 12A b d e + (- 24A b c - 12B b )d e + (6A c + 12B b c)d e +--R + +--R 2 4 +--R 6B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R 9A b d e + (- 30A b c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 68 + +--S 69 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 69 + +)clear all + +--S 70 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 70 + +--S 71 OF 765 +r0:=-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*(d+e*x)^3)-1/2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-_ + 2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^2)+(-A*e*(6*c^2*d^2-6*b*c*d*e+_ + b^2*e^2)+B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*(d+e*x))-_ + (2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 3 +--R ((12A b c + 6B b )e + (- 24A c - 48B b c)d e + 60B c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e )x +--R + +--R 2 2 3 2 3 2 2 4 +--R ((36A b c + 18B b )d e + (- 72A c - 144B b c)d e + 180B c d e)x +--R + +--R 2 3 2 2 4 2 5 +--R (12A b c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 6A b e + (36A b c + 18B b )d e + (- 18A c - 36B b c)d e +--R + +--R 2 3 2 +--R - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 6A b d e + (54A b c + 27B b )d e + (- 54A c - 108B b c)d e +--R + +--R 2 4 +--R 81B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 +--R - 2A b d e + (22A b c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 71 + +--S 72 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 73 + +--S 74 OF 765 +r0:=-d^3*(B*d-A*e)*(c*d-b*e)^3*(d+e*x)^(1+m)/(e^8*(1+m))+d^2*(c*d-b*e)^2*_ + (B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^8*(2+m))+_ + 3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-_ + 8*b*c*d*e+2*b^2*e^2))*(d+e*x)^(3+m)/(e^8*(3+m))+(B*d*(35*c^3*d^3-_ + 60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-A*e*(20*c^3*d^3-30*b*c^2*_ + d^2*e+12*b^2*c*d*e^2-b^3*e^3))*(d+e*x)^(4+m)/(e^8*(4+m))+(3*A*c*e*_ + (5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*(35*c^3*d^3-45*b*c^2*d^2*e+15*b^2*_ + c*d*e^2-b^3*e^3))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2-6*b*c*d*e+b^2*e^2))*(d+e*x)^(6+m)/(e^8*(6+m))-c^2*_ + (7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*_ + (d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 2 3 7 3 2 3 6 +--R ((A c + 3B b c )e - 7B c d)m + ((29A c + 87B b c )e - 203B c d)m +--R + +--R 3 2 3 5 +--R ((343A c + 1029B b c )e - 2401B c d)m +--R + +--R 3 2 3 4 +--R ((2135A c + 6405B b c )e - 14945B c d)m +--R + +--R 3 2 3 3 +--R ((7504A c + 22512B b c )e - 52528B c d)m +--R + +--R 3 2 3 2 +--R ((14756A c + 44268B b c )e - 103292B c d)m +--R + +--R 3 2 3 +--R ((14832A c + 44496B b c )e - 103824B c d)m +--R + +--R 3 2 3 +--R (5760A c + 17280B b c )e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 7 +--R ((3A b c + 3B b c)e + (- 6A c - 18B b c )d e + 21B c d )m +--R + +--R 2 2 2 3 2 3 2 6 +--R ((90A b c + 90B b c)e + (- 180A c - 540B b c )d e + 630B c d )m +--R + +--R 2 2 2 3 2 +--R (1098A b c + 1098B b c)e + (- 2196A c - 6588B b c )d e +--R + +--R 3 2 +--R 7686B c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 3 2 +--R (7020A b c + 7020B b c)e + (- 14040A c - 42120B b c )d e +--R + +--R 3 2 +--R 49140B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 3 2 +--R (25227A b c + 25227B b c)e + (- 50454A c - 151362B b c )d e +--R + +--R 3 2 +--R 176589B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 3 2 +--R (50490A b c + 50490B b c)e + (- 100980A c - 302940B b c )d e +--R + +--R 3 2 +--R 353430B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 3 2 +--R (51432A b c + 51432B b c)e + (- 102864A c - 308592B b c )d e +--R + +--R 3 2 +--R 360024B c d +--R * +--R m +--R + +--R 2 2 2 3 2 +--R (20160A b c + 20160B b c)e + (- 40320A c - 120960B b c )d e +--R + +--R 3 2 +--R 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 3 2 2 2 +--R (3A b c + B b )e + (- 15A b c - 15B b c)d e +--R + +--R 3 2 2 3 3 +--R (15A c + 45B b c )d e - 35B c d +--R * +--R 7 +--R m +--R + +--R 2 3 3 2 2 2 +--R (93A b c + 31B b )e + (- 465A b c - 465B b c)d e +--R + +--R 3 2 2 3 3 +--R (465A c + 1395B b c )d e - 1085B c d +--R * +--R 6 +--R m +--R + +--R 2 3 3 2 2 2 +--R (1173A b c + 391B b )e + (- 5865A b c - 5865B b c)d e +--R + +--R 3 2 2 3 3 +--R (5865A c + 17595B b c )d e - 13685B c d +--R * +--R 5 +--R m +--R + +--R 2 3 3 2 2 2 +--R (7743A b c + 2581B b )e + (- 38715A b c - 38715B b c)d e +--R + +--R 3 2 2 3 3 +--R (38715A c + 116145B b c )d e - 90335B c d +--R * +--R 4 +--R m +--R + +--R 2 3 3 2 2 2 +--R (28632A b c + 9544B b )e + (- 143160A b c - 143160B b c)d e +--R + +--R 3 2 2 3 3 +--R (143160A c + 429480B b c )d e - 334040B c d +--R * +--R 3 +--R m +--R + +--R 2 3 3 2 2 2 +--R (58692A b c + 19564B b )e + (- 293460A b c - 293460B b c)d e +--R + +--R 3 2 2 3 3 +--R (293460A c + 880380B b c )d e - 684740B c d +--R * +--R 2 +--R m +--R + +--R 2 3 3 2 2 2 +--R (60912A b c + 20304B b )e + (- 304560A b c - 304560B b c)d e +--R + +--R 3 2 2 3 3 +--R (304560A c + 913680B b c )d e - 710640B c d +--R * +--R m +--R + +--R 2 3 3 2 2 2 +--R (24192A b c + 8064B b )e + (- 120960A b c - 120960B b c)d e +--R + +--R 3 2 2 3 3 +--R (120960A c + 362880B b c )d e - 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (- 12A b c - 4B b )d e + (30A b c + 30B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 20A c - 60B b c )d e + 35B c d +--R * +--R 7 +--R m +--R + +--R 3 4 2 3 3 +--R 32A b e + (- 384A b c - 128B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (960A b c + 960B b c)d e + (- 640A c - 1920B b c )d e +--R + +--R 3 4 +--R 1120B c d +--R * +--R 6 +--R m +--R + +--R 3 4 2 3 3 +--R 418A b e + (- 5016A b c - 1672B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (12540A b c + 12540B b c)d e + (- 8360A c - 25080B b c )d e +--R + +--R 3 4 +--R 14630B c d +--R * +--R 5 +--R m +--R + +--R 3 4 2 3 3 +--R 2864A b e + (- 34368A b c - 11456B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (85920A b c + 85920B b c)d e + (- 57280A c - 171840B b c )d e +--R + +--R 3 4 +--R 100240B c d +--R * +--R 4 +--R m +--R + +--R 3 4 2 3 3 +--R 10993A b e + (- 131916A b c - 43972B b )d e +--R + +--R 2 2 2 2 +--R (329790A b c + 329790B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 219860A c - 659580B b c )d e + 384755B c d +--R * +--R 3 +--R m +--R + +--R 3 4 2 3 3 +--R 23312A b e + (- 279744A b c - 93248B b )d e +--R + +--R 2 2 2 2 +--R (699360A b c + 699360B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 466240A c - 1398720B b c )d e + 815920B c d +--R * +--R 2 +--R m +--R + +--R 3 4 2 3 3 +--R 24876A b e + (- 298512A b c - 99504B b )d e +--R + +--R 2 2 2 2 +--R (746280A b c + 746280B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 497520A c - 1492560B b c )d e + 870660B c d +--R * +--R m +--R + +--R 3 4 2 3 3 +--R 10080A b e + (- 120960A b c - 40320B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R (302400A b c + 302400B b c)d e + (- 201600A c - 604800B b c )d e +--R + +--R 3 4 +--R 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 4 2 3 2 3 2 2 3 2 +--R - 3A b d e + (18A b c + 6B b )d e + (- 30A b c - 30B b c)d e +--R + +--R 3 2 4 3 5 +--R (15A c + 45B b c )d e - 21B c d +--R * +--R 7 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 99A b d e + (594A b c + 198B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (- 990A b c - 990B b c)d e + (495A c + 1485B b c )d e +--R + +--R 3 5 +--R - 693B c d +--R * +--R 6 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 1341A b d e + (8046A b c + 2682B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (- 13410A b c - 13410B b c)d e + (6705A c + 20115B b c )d e +--R + +--R 3 5 +--R - 9387B c d +--R * +--R 5 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 9585A b d e + (57510A b c + 19170B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (- 95850A b c - 95850B b c)d e + (47925A c + 143775B b c )d e +--R + +--R 3 5 +--R - 67095B c d +--R * +--R 4 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 38592A b d e + (231552A b c + 77184B b )d e +--R + +--R 2 2 3 2 +--R (- 385920A b c - 385920B b c)d e +--R + +--R 3 2 4 3 5 +--R (192960A c + 578880B b c )d e - 270144B c d +--R * +--R 3 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 86076A b d e + (516456A b c + 172152B b )d e +--R + +--R 2 2 3 2 +--R (- 860760A b c - 860760B b c)d e +--R + +--R 3 2 4 3 5 +--R (430380A c + 1291140B b c )d e - 602532B c d +--R * +--R 2 +--R m +--R + +--R 3 4 2 3 2 3 +--R - 96144A b d e + (576864A b c + 192288B b )d e +--R + +--R 2 2 3 2 +--R (- 961440A b c - 961440B b c)d e +--R + +--R 3 2 4 3 5 +--R (480720A c + 1442160B b c )d e - 673008B c d +--R * +--R m +--R + +--R 3 4 2 3 2 3 +--R - 40320A b d e + (241920A b c + 80640B b )d e +--R + +--R 2 2 3 2 3 2 4 +--R (- 403200A b c - 403200B b c)d e + (201600A c + 604800B b c )d e +--R + +--R 3 5 +--R - 282240B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 2 4 2 3 3 3 2 2 4 2 +--R 3A b d e + (- 12A b c - 4B b )d e + (15A b c + 15B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 6A c - 18B b c )d e + 7B c d +--R * +--R 7 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 102A b d e + (- 408A b c - 136B b )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (510A b c + 510B b c)d e + (- 204A c - 612B b c )d e + 238B c d +--R * +--R 6 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 1434A b d e + (- 5736A b c - 1912B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (7170A b c + 7170B b c)d e + (- 2868A c - 8604B b c )d e +--R + +--R 3 6 +--R 3346B c d +--R * +--R 5 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 10740A b d e + (- 42960A b c - 14320B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (53700A b c + 53700B b c)d e + (- 21480A c - 64440B b c )d e +--R + +--R 3 6 +--R 25060B c d +--R * +--R 4 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 45867A b d e + (- 183468A b c - 61156B b )d e +--R + +--R 2 2 4 2 +--R (229335A b c + 229335B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 91734A c - 275202B b c )d e + 107023B c d +--R * +--R 3 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 110118A b d e + (- 440472A b c - 146824B b )d e +--R + +--R 2 2 4 2 +--R (550590A b c + 550590B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 220236A c - 660708B b c )d e + 256942B c d +--R * +--R 2 +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 134136A b d e + (- 536544A b c - 178848B b )d e +--R + +--R 2 2 4 2 +--R (670680A b c + 670680B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 268272A c - 804816B b c )d e + 312984B c d +--R * +--R m +--R + +--R 3 2 4 2 3 3 3 +--R 60480A b d e + (- 241920A b c - 80640B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (302400A b c + 302400B b c)d e + (- 120960A c - 362880B b c )d e +--R + +--R 3 6 +--R 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - A b d e + (3A b c + B b )d e + (- 3A b c - 3B b c)d e +--R + +--R 3 2 6 3 7 +--R (A c + 3B b c )d e - B c d +--R * +--R 7 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 35A b d e + (105A b c + 35B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 105A b c - 105B b c)d e + (35A c + 105B b c )d e - 35B c d +--R * +--R 6 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 511A b d e + (1533A b c + 511B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (- 1533A b c - 1533B b c)d e + (511A c + 1533B b c )d e +--R + +--R 3 7 +--R - 511B c d +--R * +--R 5 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 4025A b d e + (12075A b c + 4025B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (- 12075A b c - 12075B b c)d e + (4025A c + 12075B b c )d e +--R + +--R 3 7 +--R - 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 18424A b d e + (55272A b c + 18424B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (- 55272A b c - 55272B b c)d e + (18424A c + 55272B b c )d e +--R + +--R 3 7 +--R - 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 48860A b d e + (146580A b c + 48860B b )d e +--R + +--R 2 2 5 2 +--R (- 146580A b c - 146580B b c)d e +--R + +--R 3 2 6 3 7 +--R (48860A c + 146580B b c )d e - 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 69264A b d e + (207792A b c + 69264B b )d e +--R + +--R 2 2 5 2 +--R (- 207792A b c - 207792B b c)d e +--R + +--R 3 2 6 3 7 +--R (69264A c + 207792B b c )d e - 69264B c d +--R * +--R m +--R + +--R 3 3 4 2 3 4 3 +--R - 40320A b d e + (120960A b c + 40320B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R (- 120960A b c - 120960B b c)d e + (40320A c + 120960B b c )d e +--R + +--R 3 7 +--R - 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 74 + +--S 75 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 2 4 3 3 10 +--R B c e x + ((A c + 3B b c )e + 4B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 9 +--R ((3A b c + 3B b c)e + (4A c + 12B b c )d e + 6B c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 2 +--R (3A b c + B b )e + (12A b c + 12B b c)d e + (6A c + 18B b c )d e +--R + +--R 3 3 +--R 4B c d e +--R * +--R 8 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R A b e + (12A b c + 4B b )d e + (18A b c + 18B b c)d e +--R + +--R 3 2 3 3 4 +--R (4A c + 12B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 3 3 2 3 2 2 2 2 3 +--R 4A b d e + (18A b c + 6B b )d e + (12A b c + 12B b c)d e +--R + +--R 3 2 4 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 2 2 2 3 3 2 2 4 5 +--R (6A b d e + (12A b c + 4B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 3 2 3 4 4 3 4 3 +--R (4A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 OF 765 +r0:=1/4*A*b^3*d^4*x^4+1/5*b^2*d^3*(b*B*d+3*A*c*d+4*A*b*e)*x^5+1/6*b*d^2*_ + (3*A*c^2*d^2+2*b^2*e*(2*B*d+3*A*e)+3*b*c*d*(B*d+4*A*e))*x^6+1/7*d*_ + (A*c^3*d^3+2*b^3*e^2*(3*B*d+2*A*e)+6*b^2*c*d*e*(2*B*d+3*A*e)+3*b*_ + c^2*d^2*(B*d+4*A*e))*x^7+1/8*(A*e*(4*c^3*d^3+18*b*c^2*d^2*e+12*_ + b^2*c*d*e^2+b^3*e^3)+B*d*(c^3*d^3+12*b*c^2*d^2*e+18*b^2*c*d*e^2+4*_ + b^3*e^3))*x^8+1/9*e*(3*A*c*e*(2*c^2*d^2+4*b*c*d*e+b^2*e^2)+B*_ + (4*c^3*d^3+18*b*c^2*d^2*e+12*b^2*c*d*e^2+b^3*e^3))*x^9+1/10*c*e^2*_ + (A*c*e*(4*c*d+3*b*e)+3*B*(2*c^2*d^2+4*b*c*d*e+b^2*e^2))*x^10+1/11*_ + c^2*e^3*(4*B*c*d+3*b*B*e+A*c*e)*x^11+1/12*B*c^3*e^4*x^12 +--R +--R +--R (2) +--R 1 3 4 12 1 3 3 2 4 4 3 3 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 2 3 2 4 2 3 6 2 3 3 3 2 2 10 +--R ((-- A b c + -- B b c)e + (- A c + - B b c )d e + - B c d e )x +--R 10 10 5 5 5 +--R + +--R 1 2 1 3 4 4 2 4 2 3 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 3 9 3 3 +--R + +--R 2 3 2 2 2 4 3 3 +--R (- A c + 2B b c )d e + - B c d e +--R 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 4 3 2 1 3 3 9 2 9 2 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 8 2 2 4 4 +--R + +--R 1 3 3 2 3 1 3 4 +--R (- A c + - B b c )d e + - B c d +--R 2 2 8 +--R * +--R 8 +--R x +--R + +--R 4 3 3 18 2 6 3 2 2 12 2 12 2 3 +--R - A b d e + (-- A b c + - B b )d e + (-- A b c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 4 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 2 2 2 3 3 1 2 1 2 4 6 +--R (A b d e + (2A b c + - B b )d e + (- A b c + - B b c)d )x +--R 3 2 2 +--R + +--R 4 3 3 3 2 1 3 4 5 1 3 4 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 77 + +--S 78 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 2 3 3 2 9 +--R B c e x + ((A c + 3B b c )e + 3B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 8 +--R ((3A b c + 3B b c)e + (3A c + 9B b c )d e + 3B c d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A b c + B b )e + (9A b c + 9B b c)d e + (3A c + 9B b c )d e +--R + +--R 3 3 +--R B c d +--R * +--R 7 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R A b e + (9A b c + 3B b )d e + (9A b c + 9B b c)d e +--R + +--R 3 2 3 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 2 2 3 2 2 2 3 5 +--R (3A b d e + (9A b c + 3B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 2 2 3 3 4 3 3 3 +--R (3A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 79 + +--S 80 OF 765 +r0:=1/4*A*b^3*d^3*x^4+1/5*b^2*d^2*(b*B*d+3*A*c*d+3*A*b*e)*x^5+1/2*b*d*_ + (A*c^2*d^2+b^2*e*(B*d+A*e)+b*c*d*(B*d+3*A*e))*x^6+1/7*(A*c^3*d^3+_ + 9*b^2*c*d*e*(B*d+A*e)+b^3*e^2*(3*B*d+A*e)+3*b*c^2*d^2*(B*d+3*A*e))*_ + x^7+1/8*(3*A*c*e*(c^2*d^2+3*b*c*d*e+b^2*e^2)+B*(c^3*d^3+9*b*c^2*d^2*e+_ + 9*b^2*c*d*e^2+b^3*e^3))*x^8+1/3*c*e*(A*c*e*(c*d+b*e)+B*(c^2*d^2+_ + 3*b*c*d*e+b^2*e^2))*x^9+1/10*c^2*e^2*(A*c*e+3*B*(c*d+b*e))*x^10+_ + 1/11*B*c^3*e^3*x^11 +--R +--R +--R (2) +--R 1 3 3 11 1 3 3 2 3 3 3 2 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 2 1 2 3 1 3 2 2 1 3 2 9 +--R ((- A b c + - B b c)e + (- A c + B b c )d e + - B c d e)x +--R 3 3 3 3 +--R + +--R 3 2 1 3 3 9 2 9 2 2 +--R (- A b c + - B b )e + (- A b c + - B b c)d e +--R 8 8 8 8 +--R + +--R 3 3 9 2 2 1 3 3 +--R (- A c + - B b c )d e + - B c d +--R 8 8 8 +--R * +--R 8 +--R x +--R + +--R 1 3 3 9 2 3 3 2 9 2 9 2 2 +--R - A b e + (- A b c + - B b )d e + (- A b c + - B b c)d e +--R 7 7 7 7 7 +--R + +--R 1 3 3 2 3 +--R (- A c + - B b c )d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 2 3 2 1 3 2 1 2 1 2 3 6 +--R (- A b d e + (- A b c + - B b )d e + (- A b c + - B b c)d )x +--R 2 2 2 2 2 +--R + +--R 3 3 2 3 2 1 3 3 5 1 3 3 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +--S 81 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 2 3 8 +--R B c e x + ((A c + 3B b c )e + 2B c d e)x +--R + +--R 2 2 2 3 2 3 2 7 +--R ((3A b c + 3B b c)e + (2A c + 6B b c )d e + B c d )x +--R + +--R 2 3 2 2 2 3 2 2 6 +--R ((3A b c + B b )e + (6A b c + 6B b c)d e + (A c + 3B b c )d )x +--R + +--R 3 2 2 3 2 2 2 5 +--R (A b e + (6A b c + 2B b )d e + (3A b c + 3B b c)d )x +--R + +--R 3 2 3 2 4 3 2 3 +--R (2A b d e + (3A b c + B b )d )x + A b d x +--R Type: Polynomial(Integer) +--E 82 + +--S 83 OF 765 +r0:=1/4*A*b^3*d^2*x^4+1/5*b^2*d*(b*B*d+3*A*c*d+2*A*b*e)*x^5+1/6*b*_ + (3*A*c^2*d^2+b^2*e*(2*B*d+A*e)+3*b*c*d*(B*d+2*A*e))*x^6+1/7*_ + (A*c^3*d^2+b^3*B*e^2+3*b^2*c*e*(2*B*d+A*e)+3*b*c^2*d*(B*d+2*A*e))*x^7+_ + 1/8*c*(A*c*e*(2*c*d+3*b*e)+B*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^8+_ + 1/9*c^2*e*(2*B*c*d+3*b*B*e+A*c*e)*x^9+1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R ((- A b c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 4 4 8 +--R + +--R 3 2 1 3 2 6 2 6 2 1 3 3 2 2 7 +--R ((- A b c + - B b )e + (- A b c + - B b c)d e + (- A c + - B b c )d )x +--R 7 7 7 7 7 7 +--R + +--R 1 3 2 2 1 3 1 2 1 2 2 6 +--R (- A b e + (A b c + - B b )d e + (- A b c + - B b c)d )x +--R 6 3 2 2 +--R + +--R 2 3 3 2 1 3 2 5 1 3 2 4 +--R (- A b d e + (- A b c + - B b )d )x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 OF 765 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 2 3 7 +--R B c e x + ((A c + 3B b c )e + B c d)x +--R + +--R 2 2 3 2 6 +--R ((3A b c + 3B b c)e + (A c + 3B b c )d)x +--R + +--R 2 3 2 2 5 3 2 3 4 +--R ((3A b c + B b )e + (3A b c + 3B b c)d)x + (A b e + (3A b c + B b )d)x +--R + +--R 3 3 +--R A b d x +--R Type: Polynomial(Integer) +--E 85 + +--S 86 OF 765 +r0:=1/4*A*b^3*d*x^4+1/5*b^2*(b*B*d+3*A*c*d+A*b*e)*x^5+1/6*b*(3*A*c^2*d+_ + b^2*B*e+3*b*c*(B*d+A*e))*x^6+1/7*c*(A*c^2*d+3*b^2*B*e+3*b*c*(B*d+_ + A*e))*x^7+1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 2 3 2 1 3 3 2 7 +--R ((- A b c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 +--R + +--R 1 2 1 3 1 2 1 2 6 +--R ((- A b c + - B b )e + (- A b c + - B b c)d)x +--R 2 6 2 2 +--R + +--R 1 3 3 2 1 3 5 1 3 4 +--R (- A b e + (- A b c + - B b )d)x + - A b d x +--R 5 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 86 + +--S 87 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R Type: Polynomial(Integer) +--E 88 + +--S 89 OF 765 +r0:=1/4*A*b^3*x^4+1/5*b^2*(b*B+3*A*c)*x^5+1/2*b*c*(b*B+A*c)*x^6+_ + 1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8 +--R +--R +--R (2) +--R 1 3 8 1 3 3 2 7 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + (- A b c + - B b c)x +--R 8 7 7 2 2 +--R + +--R 3 2 1 3 5 1 3 4 +--R (- A b c + - B b )x + - A b x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 89 + +--S 90 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 OF 765 +r0:=d^2*(B*d-A*e)*(c*d-b*e)^3*x/e^7-1/2*d*(B*d-A*e)*(c*d-b*e)^3*x^2/e^6+_ + 1/3*(B*d-A*e)*(c*d-b*e)^3*x^3/e^5-1/4*(B*(c*d-b*e)^3-A*c*e*(c^2*d^2-_ + 3*b*c*d*e+3*b^2*e^2))*x^4/e^4-1/5*c*(A*c*e*(c*d-3*b*e)-B*(c^2*d^2-_ + 3*b*c*d*e+3*b^2*e^2))*x^5/e^3-1/6*c^2*(B*c*d-3*b*B*e-A*c*e)*x^6/e^2+_ + 1/7*B*c^3*x^7/e-d^3*(B*d-A*e)*(c*d-b*e)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 3 4 2 3 4 3 +--R - 420A b d e + (1260A b c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 1260A b c - 1260B b c)d e + (420A c + 1260B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((252A b c + 252B b c)e + (- 84A c - 252B b c )d e + 84B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (315A b c + 105B b )e + (- 315A b c - 315B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (105A c + 315B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 140A b e + (- 420A b c - 140B b )d e + (420A b c + 420B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 140A c - 420B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 210A b d e + (630A b c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 630A b c - 630B b c)d e + (210A c + 630B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 420A b d e + (- 1260A b c - 420B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1260A b c + 1260B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 92 + +--S 93 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 94 + +--S 95 OF 765 +r0:=d*(c*d-b*e)^2*(A*e*(5*c*d-2*b*e)-3*B*d*(2*c*d-b*e))*x/e^7+_ + 1/2*(c*d-b*e)^2*(B*d*(5*c*d-2*b*e)-A*e*(4*c*d-b*e))*x^2/e^6-_ + 1/3*(c*d-b*e)^2*(4*B*c*d-b*B*e-3*A*c*e)*x^3/e^5-1/4*c*(A*c*e*_ + (2*c*d-3*b*e)-3*B*(c*d-b*e)^2)*x^4/e^4-1/5*c^2*(2*B*c*d-3*b*B*e-_ + A*c*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*_ + (d+e*x))+d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 5 2 3 3 4 +--R 180A b d e + (- 720A b c - 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (900A b c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 6 +--R 420B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 180A b d e + (- 720A b c - 240B b )d e + (900A b c + 900B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 360A c - 1080B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((45A b c + 45B b c)e + (- 18A c - 54B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (60A b c + 20B b )e + (- 75A b c - 75B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (30A c + 90B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 30A b e + (- 120A b c - 40B b )d e + (150A b c + 150B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 60A c - 180B b c )d e + 70B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 90A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 3 5 2 +--R (- 450A b c - 450B b c)d e + (180A c + 540B b c )d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (540A b c + 180B b )d e +--R + +--R 2 2 4 3 3 2 5 2 3 6 +--R (- 720A b c - 720B b c)d e + (300A c + 900B b c )d e - 360B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 60A b d e + (- 180A b c - 60B b )d e + (180A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 60A c - 180B b c )d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 95 + +--S 96 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 97 + +--S 98 OF 765 +r0:=-(c*d-b*e)*(A*e*(10*c^2*d^2-8*b*c*d*e+b^2*e^2)-3*B*d*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2))*x/e^7+1/2*(c*d-b*e)*(3*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*x^2/e^6+c*(c*d-b*e)*(2*B*c*d-b*B*e-_ + A*c*e)*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*x^4/e^4+1/5*B*c^3*_ + x^5/e^3+1/2*d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*(d+e*x)^2)-d^2*_ + (c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))/(e^8*(d+e*x))+_ + 3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-_ + 8*b*c*d*e+2*b^2*e^2))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 6 2 3 2 5 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 5 2 +--R - 420B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 120A b d e + (720A b c + 240B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1200A b c - 1200B b c)d e + (600A c + 1800B b c )d e +--R + +--R 3 6 +--R - 840B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 60A b d e + (360A b c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 600A b c - 600B b c)d e + (300A c + 900B b c )d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((20A b c + 20B b c)e + (- 10A c - 30B b c )d e + 14B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (30A b c + 10B b )e + (- 50A b c - 50B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (25A c + 75B b c )d e - 35B c d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R 20A b e + (- 120A b c - 40B b )d e + (200A b c + 200B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 100A c - 300B b c )d e + 140B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 40A b d e + (- 330A b c - 110B b )d e + (630A b c + 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 340A c - 1020B b c )d e + 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R - 40A b d e + (60A b c + 20B b )d e + (60A b c + 60B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 80A c - 240B b c )d e + 160B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 50A b d e + (210A b c + 70B b )d e + (- 270A b c - 270B b c)d e +--R + +--R 3 2 6 3 7 +--R (110A c + 330B b c )d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 98 + +--S 99 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B c x + (A c + 3B b c )x + (3A b c + 3B b c)x + (3A b c + B b )x +--R + +--R 3 3 +--R A b x +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 100 + +--S 101 OF 765 +r0:=(A*c*e*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2)-B*(20*c^3*d^3-30*b*c^2*d^2*e+_ + 12*b^2*c*d*e^2-b^3*e^3))*x/e^7-1/2*c*(A*c*e*(4*c*d-3*b*e)-_ + B*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*x^2/e^6-1/3*c^2*(4*B*c*d-_ + 3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*d^3*(B*d-A*e)*_ + (c*d-b*e)^3/(e^8*(d+e*x)^3)-1/2*d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-_ + 3*A*e*(2*c*d-b*e))/(e^8*(d+e*x)^2)-3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-8*b*c*d*e+2*b^2*e^2))/(e^8*_ + (d+e*x))+(B*d*(35*c^3*d^3-60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-_ + A*e*(20*c^3*d^3-30*b*c^2*d^2*e+12*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 3 6 2 2 2 5 +--R 12A b e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 36A b d e + (- 432A b c - 144B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (1080A b c + 1080B b c)d e + (- 720A c - 2160B b c )d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 12A b d e + (- 144A b c - 48B b )d e + (360A b c + 360B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 240A c - 720B b c )d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R ((18A b c + 18B b c)e + (- 12A c - 36B b c )d e + 21B c d e )x +--R + +--R 2 3 7 2 2 6 +--R (36A b c + 12B b )e + (- 90A b c - 90B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (60A c + 180B b c )d e - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 2 5 +--R (108A b c + 36B b )d e + (- 378A b c - 378B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (292A c + 876B b c )d e - 556B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 2 2 3 4 +--R 36A b d e + (- 108A b c - 36B b )d e + (- 54A b c - 54B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (156A c + 468B b c )d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 2 2 4 3 +--R 54A b d e + (- 324A b c - 108B b )d e + (486A b c + 486B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 204A c - 612B b c )d e + 222B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R 22A b d e + (- 156A b c - 52B b )d e + (282A b c + 282B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 148A c - 444B b c )d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 101 + +--S 102 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 103 + +--S 104 OF 765 +r0:=e*(A*c*e*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)+B*(4*c^3*d^3-6*b*c^2*d^2*e+_ + 4*b^2*c*d*e^2-b^3*e^3))*x/c^4+1/2*e^2*(A*c*e*(4*c*d-b*e)+B*_ + (6*c^2*d^2-4*b*c*d*e+b^2*e^2))*x^2/c^3+1/3*e^3*(4*B*c*d-b*B*e+_ + A*c*e)*x^3/c^2+1/4*B*e^4*x^4/c+A*d^4*log(x)/b+(b*B-A*c)*_ + (c*d-b*e)^4*log(b+c*x)/(b*c^5) +--R +--R +--R (2) +--R 4 5 4 3 2 4 3 +--R (- 12A b c + 12B b )e + (48A b c - 48B b c)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A b c + 72B b c )d e + (48A b c - 48B b c )d e +--R + +--R 5 4 4 +--R (- 12A c + 12B b c )d +--R * +--R log(c x + b) +--R + +--R 5 4 4 4 4 4 2 3 4 4 3 3 +--R 12A c d log(x) + 3B b c e x + ((4A b c - 4B b c )e + 16B b c d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 6A b c + 6B b c )e + (24A b c - 24B b c )d e + 36B b c d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A b c - 12B b c)e + (- 48A b c + 48B b c )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A b c - 72B b c )d e + 48B b c d e +--R * +--R x +--R / +--R 5 +--R 12b c +--R Type: Expression(Integer) +--E 104 + +--S 105 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 OF 765 +r0:=e*(A*c*e*(3*c*d-b*e)+B*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*x/c^3+_ + 1/2*e^2*(3*B*c*d-b*B*e+A*c*e)*x^2/c^2+1/3*B*e^3*x^3/c+A*d^3*_ + log(x)/b+(b*B-A*c)*(c*d-b*e)^3*log(b+c*x)/(b*c^4) +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (6A b c - 6B b )e + (- 18A b c + 18B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A b c - 18B b c )d e + (- 6A c + 6B b c )d +--R * +--R log(c x + b) +--R + +--R 4 3 3 3 3 3 2 2 3 3 2 2 +--R 6A c d log(x) + 2B b c e x + ((3A b c - 3B b c )e + 9B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 6A b c + 6B b c)e + (18A b c - 18B b c )d e + 18B b c d e)x +--R / +--R 4 +--R 6b c +--R Type: Expression(Integer) +--E 107 + +--S 108 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 109 + +--S 110 OF 765 +r0:=e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+A*d^2*log(x)/b+_ + (b*B-A*c)*(c*d-b*e)^2*log(b+c*x)/(b*c^3) +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 +--R ((- 2A b c + 2B b )e + (4A b c - 4B b c)d e + (- 2A c + 2B b c )d ) +--R * +--R log(c x + b) +--R + +--R 3 2 2 2 2 2 2 2 2 +--R 2A c d log(x) + B b c e x + ((2A b c - 2B b c)e + 4B b c d e)x +--R / +--R 3 +--R 2b c +--R Type: Expression(Integer) +--E 110 + +--S 111 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 OF 765 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 112 + +--S 113 OF 765 +r0:=B*e*x/c+A*d*log(x)/b+(b*B-A*c)*(c*d-b*e)*log(b+c*x)/(b*c^2) +--R +--R +--R (2) +--R 2 2 2 +--R ((A b c - B b )e + (- A c + B b c)d)log(c x + b) + A c d log(x) + B b c e x +--R ---------------------------------------------------------------------------- +--R 2 +--R b c +--R Type: Expression(Integer) +--E 113 + +--S 114 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 OF 765 +t0:=(A+B*x)/(b*x+c*x^2) +--R +--R +--R B x + A +--R (1) ---------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 OF 765 +r0:=A*log(x)/b+(b*B-A*c)*log(b+c*x)/(b*c) +--R +--R +--R (- A c + B b)log(c x + b) + A c log(x) +--R (2) -------------------------------------- +--R b c +--R Type: Expression(Integer) +--E 116 + +--S 117 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 OF 765 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R 3 2 +--R c e x + (b e + c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 OF 765 +r0:=A*log(x)/(b*d)+(b*B-A*c)*log(b+c*x)/(b*(c*d-b*e))-_ + (B*d-A*e)*log(d+e*x)/(d*(c*d-b*e)) +--R +--R +--R (2) +--R (- A b e + B b d)log(e x + d) + (A c - B b)d log(c x + b) +--R + +--R (A b e - A c d)log(x) +--R / +--R 2 2 +--R b d e - b c d +--R Type: Expression(Integer) +--E 119 + +--S 120 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------ +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 OF 765 +r0:=(B*d-A*e)/(d*(c*d-b*e)*(d+e*x))+A*log(x)/(b*d^2)+c*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^2)-(B*c*d^2-A*e*(2*c*d-b*e))*log(d+e*x)/_ + (d^2*(c*d-b*e)^2) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R (- A b e + 2A b c d e - B b c d e)x - A b d e + 2A b c d e +--R + +--R 3 +--R - B b c d +--R * +--R log(e x + d) +--R + +--R 2 2 2 3 +--R ((- A c + B b c)d e x + (- A c + B b c)d )log(c x + b) +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((A b e - 2A b c d e + A c d e)x + A b d e - 2A b c d e + A c d ) +--R * +--R log(x) +--R + +--R 2 2 2 2 3 +--R A b d e + (- A b c - B b )d e + B b c d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d +--R Type: Expression(Integer) +--E 122 + +--S 123 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 OF 765 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R Type: Fraction(Polynomial(Integer)) +--E 124 + +--S 125 OF 765 +r0:=1/2*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^2)+(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x))+A*log(x)/(b*d^3)+c^2*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^3)-(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+_ + b^2*e^2))*log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (- 2A b e + 6A b c d e - 6A b c d e + 2B b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 2 4 3 2 3 +--R (- 4A b d e + 12A b c d e - 12A b c d e + 4B b c d e)x - 2A b d e +--R + +--R 2 3 2 2 4 2 5 +--R 6A b c d e - 6A b c d e + 2B b c d +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 3 2 4 +--R (2A c - 2B b c )d e x + (4A c - 4B b c )d e x +--R + +--R 3 2 5 +--R (2A c - 2B b c )d +--R * +--R log(c x + b) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2A b e - 6A b c d e + 6A b c d e - 2A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (4A b d e - 12A b c d e + 12A b c d e - 4A c d e)x + 2A b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 6A b c d e + 6A b c d e - 2A c d +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 2 3 2 2 4 +--R (2A b d e - 6A b c d e + (4A b c + 2B b c)d e - 2B b c d e)x +--R + +--R 3 2 3 2 3 3 2 2 2 4 2 5 +--R 3A b d e + (- 8A b c - B b )d e + (5A b c + 4B b c)d e - 3B b c d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e)x + 2b d e - 6b c d e +--R + +--R 2 2 7 3 8 +--R 6b c d e - 2b c d +--R Type: Expression(Integer) +--E 125 + +--S 126 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 OF 765 +t0:=(A+B*x)/((d+e*x)^4*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 6 4 3 5 3 2 2 4 +--R c e x + (b e + 4c d e )x + (4b d e + 6c d e )x +--R + +--R 2 2 3 3 3 4 2 4 +--R (6b d e + 4c d e)x + (4b d e + c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 127 + +--S 128 OF 765 +r0:=1/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^3)+1/2*(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x)^2)+(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+_ + b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x))+A*log(x)/(b*d^4)+c^3*(b*B-A*c)*_ + log(b+c*x)/(b*(c*d-b*e)^4)-(B*c^3*d^4-A*e*(4*c^3*d^3-_ + 6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 6A b e + 24A b c d e - 36A b c d e + 24A b c d e +--R + +--R 3 4 3 +--R - 6B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R - 18A b d e + 72A b c d e - 108A b c d e + 72A b c d e +--R + +--R 3 5 2 +--R - 18B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R - 18A b d e + 72A b c d e - 108A b c d e + 72A b c d e +--R + +--R 3 6 +--R - 18B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 3 7 +--R - 6A b d e + 24A b c d e - 36A b c d e + 24A b c d e - 6B b c d +--R * +--R log(e x + d) +--R + +--R 4 3 4 3 3 4 3 5 2 2 +--R (- 6A c + 6B b c )d e x + (- 18A c + 18B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (- 18A c + 18B b c )d e x + (- 6A c + 6B b c )d +--R * +--R log(c x + b) +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (6A b e - 24A b c d e + 36A b c d e - 24A b c d e + 6A c d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R 18A b d e - 72A b c d e + 108A b c d e - 72A b c d e +--R + +--R 4 5 2 +--R 18A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R 18A b d e - 72A b c d e + 108A b c d e - 72A b c d e +--R + +--R 4 6 +--R 18A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 6A b d e - 24A b c d e + 36A b c d e - 24A b c d e + 6A c d +--R * +--R log(x) +--R + +--R 4 6 3 2 5 2 2 3 4 3 2 2 4 3 +--R 6A b d e - 24A b c d e + 36A b c d e + (- 18A b c - 6B b c )d e +--R + +--R 3 5 2 +--R 6B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 15A b d e - 60A b c d e + (87A b c + 3B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 42A b c - 18B b c )d e + 15B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 2 2 3 5 2 +--R 11A b d e + (- 42A b c - 2B b )d e + (57A b c + 9B b c)d e +--R + +--R 3 2 2 6 3 7 +--R (- 26A b c - 18B b c )d e + 11B b c d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (6b d e - 24b c d e + 36b c d e - 24b c d e + 6b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 4 9 2 2 +--R (18b d e - 72b c d e + 108b c d e - 72b c d e + 18b c d e )x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 4 10 +--R (18b d e - 72b c d e + 108b c d e - 72b c d e + 18b c d e)x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 6b d e - 24b c d e + 36b c d e - 24b c d e + 6b c d +--R Type: Expression(Integer) +--E 128 + +--S 129 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 130 + +--S 131 OF 765 +r0:=-A*d^4/(b^2*x)+e^3*(4*B*c*d-2*b*B*e+A*c*e)*x/c^3+1/2*B*e^4*x^2/c^2+_ + (b*B-A*c)*(c*d-b*e)^4/(b^2*c^4*(b+c*x))+d^3*(b*B*d-2*A*c*d+_ + 4*A*b*e)*log(x)/b^3+(c*d-b*e)^3*(2*A*c^2*d-3*b^2*B*e-b*c*(B*d-_ + 2*A*e))*log(b+c*x)/(b^3*c^4) +--R +--R +--R (2) +--R 4 2 5 4 3 3 4 2 3 3 3 2 2 +--R (- 4A b c + 6B b c)e + (8A b c - 16B b c )d e + 12B b c d e +--R + +--R 5 3 6 5 4 +--R - 8A b c d e + (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 4 2 2 2 +--R (- 4A b c + 6B b )e + (8A b c - 16B b c)d e + 12B b c d e +--R + +--R 2 4 3 5 2 4 4 +--R - 8A b c d e + (4A b c - 2B b c )d +--R * +--R x +--R * +--R log(c x + b) +--R + +--R 5 3 6 5 4 2 +--R (8A b c d e + (- 4A c + 2B b c )d )x +--R + +--R 2 4 3 5 2 4 4 +--R (8A b c d e + (- 4A b c + 2B b c )d )x +--R * +--R log(x) +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 3 3 +--R B b c e x + ((2A b c - 3B b c )e + 8B b c d e )x +--R + +--R 4 2 5 4 4 2 3 2 +--R ((2A b c - 4B b c)e + 8B b c d e )x +--R + +--R 5 6 4 4 2 5 3 +--R (- 2A b c + 2B b )e + (8A b c - 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 12A b c + 12B b c )d e + (8A b c - 8B b c )d e +--R + +--R 5 2 4 4 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 2 4 4 +--R - 2A b c d +--R / +--R 3 5 2 4 4 +--R 2b c x + 2b c x +--R Type: Expression(Integer) +--E 131 + +--S 132 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 133 + +--S 134 OF 765 +r0:=-A*d^3/(b^2*x)+B*e^3*x/c^2+(b*B-A*c)*(c*d-b*e)^3/(b^2*c^3*(b+c*x))+_ + d^2*(b*B*d-2*A*c*d+3*A*b*e)*log(x)/b^3-(c*d-b*e)^2*(b*B*c*d-_ + 2*A*c^2*d+2*b^2*B*e-A*b*c*e)*log(b+c*x)/(b^3*c^3) +--R +--R +--R (2) +--R 3 2 4 3 3 2 2 4 2 +--R (A b c - 2B b c)e + 3B b c d e - 3A b c d e +--R + +--R 5 4 3 +--R (2A c - B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 2 3 2 4 2 3 3 +--R ((A b c - 2B b )e + 3B b c d e - 3A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 4 2 5 4 3 2 +--R (3A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (3A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 3 3 4 3 2 +--R B b c e x + B b c e x +--R + +--R 4 5 3 3 2 4 2 2 3 3 2 2 +--R (A b c - B b )e + (- 3A b c + 3B b c)d e + (3A b c - 3B b c )d e +--R + +--R 4 2 3 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - A b c d +--R / +--R 3 4 2 4 3 +--R b c x + b c x +--R Type: Expression(Integer) +--E 134 + +--S 135 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 OF 765 +r0:=-A*d^2/(b^2*x)+(b*B-A*c)*(c*d-b*e)^2/(b^2*c^2*(b+c*x))+d*_ + (b*B*d-2*A*c*d+2*A*b*e)*log(x)/b^3-(c*d-b*e)*(b*B*c*d-2*A*c^2*d+_ + b^2*B*e)*log(b+c*x)/(b^3*c^2) +--R +--R +--R (2) +--R 3 2 3 4 3 2 2 +--R (B b c e - 2A b c d e + (2A c - B b c )d )x +--R + +--R 4 2 2 2 3 2 2 2 +--R (B b e - 2A b c d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 4 3 2 2 +--R (2A b c d e + (- 2A c + B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (2A b c d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((- A b c + B b )e + (2A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 2 2 2 +--R - A b c d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R Type: Expression(Integer) +--E 137 + +--S 138 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 OF 765 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 139 + +--S 140 OF 765 +r0:=-A*d/(b^2*x)+(b*B-A*c)*(c*d-b*e)/(b^2*c*(b+c*x))+(b*B*d-2*A*c*d+A*b*e)*_ + log(x)/b^3-(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^3 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((- A b c e + (2A c - B b c )d)x + (- A b c e + (2A b c - B b c)d)x) +--R * +--R log(c x + b) +--R + +--R 2 3 2 2 2 2 2 +--R ((A b c e + (- 2A c + B b c )d)x + (A b c e + (- 2A b c + B b c)d)x) +--R * +--R log(x) +--R + +--R 2 3 2 2 2 +--R ((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R Type: Expression(Integer) +--E 140 + +--S 141 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 OF 765 +t0:=(A+B*x)/(b*x+c*x^2)^2 +--R +--R +--R B x + A +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 142 + +--S 143 OF 765 +r0:=-A/(b^2*x)+(b*B-A*c)/(b^2*(b+c*x))+(b*B-2*A*c)*log(x)/b^3-(b*B-2*A*c)*_ + log(b+c*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R ((2A c - B b c)x + (2A b c - B b )x)log(c x + b) +--R + +--R 2 2 2 2 +--R ((- 2A c + B b c)x + (- 2A b c + B b )x)log(x) + (- 2A b c + B b )x +--R + +--R 2 +--R - A b +--R / +--R 3 2 4 +--R b c x + b x +--R Type: Expression(Integer) +--E 143 + +--S 144 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 OF 765 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +--R c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 145 + +--S 146 OF 765 +r0:=-A/(b^2*d*x)+c*(b*B-A*c)/(b^2*(c*d-b*e)*(b+c*x))+(b*B*d-2*A*c*d-A*b*e)*_ + log(x)/(b^3*d^2)+c*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+3*A*e))*log(b+c*x)/_ + (b^3*(c*d-b*e)^2)-e^2*(B*d-A*e)*log(d+e*x)/(d^2*(c*d-b*e)^2) +--R +--R +--R (2) +--R 3 3 3 2 2 4 3 4 2 +--R ((A b c e - B b c d e )x + (A b e - B b d e )x)log(e x + d) +--R + +--R 3 2 2 2 4 3 3 2 +--R ((- 3A b c + 2B b c )d e + (2A c - B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((- 3A b c + 2B b c)d e + (2A b c - B b c )d )x +--R * +--R log(c x + b) +--R + +--R 3 3 3 2 3 2 2 2 +--R - A b c e + B b c d e + (3A b c - 2B b c )d e +--R + +--R 4 3 3 +--R (- 2A c + B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 2 2 3 2 3 2 2 3 +--R (- A b e + B b d e + (3A b c - 2B b c)d e + (- 2A b c + B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 2 2 3 +--R (- A b c d e + (3A b c - B b c)d e + (- 2A b c + B b c )d )x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R (b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x +--R Type: Expression(Integer) +--E 146 + +--S 147 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 148 + +--S 149 OF 765 +r0:=-A/(b^2*d^2*x)+c^2*(b*B-A*c)/(b^2*(c*d-b*e)^2*(b+c*x))+e^2*(B*d-A*e)/_ + (d^2*(c*d-b*e)^2*(d+e*x))+(b*B*d-2*A*c*d-2*A*b*e)*log(x)/(b^3*d^3)+_ + c^2*(2*A*c^2*d+3*b^2*B*e-b*c*(B*d+4*A*e))*log(b+c*x)/(b^3*_ + (c*d-b*e)^3)+e^2*(2*A*e*(2*c*d-b*e)-B*d*(3*c*d-b*e))*log(d+e*x)/_ + (d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 4 5 3 2 4 4 3 2 2 3 3 +--R (2A b c e + (- 4A b c - B b c)d e + 3B b c d e )x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 2A b e + (- 2A b c - B b )d e + (- 4A b c + 2B b c)d e +--R + +--R 3 2 3 2 +--R 3B b c d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R (2A b d e + (- 4A b c - B b )d e + 3B b c d e )x +--R * +--R log(e x + d) +--R + +--R 4 2 3 3 2 5 4 4 3 +--R ((4A b c - 3B b c )d e + (- 2A c + B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (4A b c - 3B b c )d e + (2A b c - 2B b c )d e +--R + +--R 5 4 5 +--R (- 2A c + B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((4A b c - 3B b c )d e + (- 2A b c + B b c )d )x +--R * +--R log(c x + b) +--R + +--R 4 5 3 2 4 4 3 2 2 3 +--R - 2A b c e + (4A b c + B b c)d e - 3B b c d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 4A b c + 3B b c )d e + (2A c - B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 2A b e + (2A b c + B b )d e + (4A b c - 2B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R - 4A b c d e + (- 2A b c + 2B b c )d e + (2A c - B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R - 2A b d e + (4A b c + B b )d e - 3B b c d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (- 4A b c + 3B b c )d e + (2A b c - B b c )d +--R * +--R x +--R * +--R log(x) +--R + +--R 4 4 3 2 4 2 3 2 3 3 2 +--R - 2A b c d e + (4A b c + B b c)d e - 4A b c d e +--R + +--R 4 2 3 4 +--R (2A b c - B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 4 3 2 +--R - 2A b d e + (3A b c + B b )d e - B b c d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (- 3A b c + B b c )d e + (2A b c - B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - A b d e + 3A b c d e - 3A b c d e + A b c d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (b c d e - 3b c d e + 3b c d e - b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (b d e - 2b c d e + 2b c d e - b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (b d e - 3b c d e + 3b c d e - b c d )x +--R Type: Expression(Integer) +--E 149 + +--S 150 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 OF 765 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 OF 765 +r0:=-A/(b^2*d^3*x)+c^3*(b*B-A*c)/(b^2*(c*d-b*e)^3*(b+c*x))+1/2*e^2*_ + (B*d-A*e)/(d^2*(c*d-b*e)^2*(d+e*x)^2)-e^2*(2*A*e*(2*c*d-b*e)-B*d*_ + (3*c*d-b*e))/(d^3*(c*d-b*e)^3*(d+e*x))+(b*B*d-2*A*c*d-3*A*b*e)*_ + log(x)/(b^3*d^4)+c^3*(2*A*c^2*d+4*b^2*B*e-b*c*(B*d+5*A*e))*log(b+_ + c*x)/(b^3*(c*d-b*e)^4)-e^2*(B*d*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)-_ + A*e*(10*c^2*d^2-10*b*c*d*e+3*b^2*e^2))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 5 7 4 2 5 6 3 3 4 2 2 5 +--R 6A b c e + (- 20A b c - 2B b c)d e + (20A b c + 8B b c )d e +--R + +--R 3 3 3 4 +--R - 12B b c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R 6A b e + (- 8A b c - 2B b )d e + (- 20A b c + 4B b c)d e +--R + +--R 3 3 4 2 3 4 3 3 4 3 +--R (40A b c + 4B b c )d e - 24B b c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R 12A b d e + (- 34A b c - 4B b )d e + (20A b c + 14B b c)d e +--R + +--R 3 3 4 2 4 3 3 3 5 2 +--R (20A b c - 16B b c )d e - 12B b c d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R 6A b d e + (- 20A b c - 2B b )d e + (20A b c + 8B b c)d e +--R + +--R 4 2 5 2 +--R - 12B b c d e +--R * +--R x +--R * +--R log(e x + d) +--R + +--R 5 2 4 4 3 6 5 5 2 4 +--R ((- 10A b c + 8B b c )d e + (4A c - 2B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 10A b c + 8B b c )d e + (- 16A b c + 14B b c )d e +--R + +--R 6 5 6 +--R (8A c - 4B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 20A b c + 16B b c )d e + (- 2A b c + 4B b c )d e +--R + +--R 6 5 7 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((- 10A b c + 8B b c )d e + (4A b c - 2B b c )d )x +--R * +--R log(c x + b) +--R + +--R 5 7 4 2 5 6 +--R - 6A b c e + (20A b c + 2B b c)d e +--R + +--R 3 3 4 2 2 5 3 3 3 4 +--R (- 20A b c - 8B b c )d e + 12B b c d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (10A b c - 8B b c )d e + (- 4A c + 2B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 6A b e + (8A b c + 2B b )d e + (20A b c - 4B b c)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (- 40A b c - 4B b c )d e + (10A b c + 16B b c )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (16A b c - 14B b c )d e + (- 8A c + 4B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R - 12A b d e + (34A b c + 4B b )d e + (- 20A b c - 14B b c)d e +--R + +--R 3 3 4 2 4 3 2 4 3 3 5 2 +--R (- 20A b c + 16B b c )d e + (20A b c - 4B b c )d e +--R + +--R 5 2 4 6 6 5 7 +--R (2A b c - 4B b c )d e + (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R - 6A b d e + (20A b c + 2B b )d e + (- 20A b c - 8B b c)d e +--R + +--R 4 2 5 2 2 4 3 3 6 5 2 4 7 +--R 12B b c d e + (10A b c - 8B b c )d e + (- 4A b c + 2B b c )d +--R * +--R x +--R * +--R log(x) +--R + +--R 5 6 4 2 5 2 5 3 3 4 2 3 4 +--R - 6A b c d e + (20A b c + 2B b c)d e + (- 20A b c - 8B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (10A b c + 4B b c )d e + (- 4A b c + 2B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 4 2 5 3 4 +--R - 6A b d e + (11A b c + 2B b )d e + (10A b c - 5B b c)d e +--R + +--R 3 3 4 2 4 3 2 4 3 3 5 2 +--R (- 25A b c - 4B b c )d e + (18A b c + 3B b c )d e +--R + +--R 5 2 4 6 +--R (- 8A b c + 4B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 4 2 5 4 3 +--R - 9A b d e + (28A b c + 3B b )d e + (- 25A b c - 10B b c)d e +--R + +--R 3 3 4 2 5 2 2 4 3 3 6 +--R (4A b c + 7B b c )d e + (6A b c - 2B b c )d e +--R + +--R 5 2 4 7 +--R (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 2A b d e + 8A b c d e - 12A b c d e + 8A b c d e - 2A b c d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (2b c d e - 8b c d e + 12b c d e - 8b c d e + 2b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3 +--R (2b d e - 4b c d e - 4b c d e + 16b c d e - 14b c d e + 4b c d e)x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2 +--R (4b d e - 14b c d e + 16b c d e - 4b c d e - 4b c d e + 2b c d )x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )x +--R Type: Expression(Integer) +--E 152 + +--S 153 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 OF 765 +t0:=(A+B*x)*(d+e*x)^5/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 154 + +--S 155 OF 765 +r0:=-1/2*A*d^5/(b^3*x^2)-d^4*(b*B*d-3*A*c*d+5*A*b*e)/(b^4*x)+B*e^5*x/c^3-_ + 1/2*(b*B-A*c)*(c*d-b*e)^5/(b^3*c^4*(b+c*x)^2)-(c*d-b*e)^4*(2*b*B*c*d-_ + 3*A*c^2*d+3*b^2*B*e-2*A*b*c*e)/(b^4*c^4*(b+c*x))+d^3*(6*A*c^2*d^2+_ + 5*b^2*e*(B*d+2*A*e)-3*b*c*d*(B*d+5*A*e))*log(x)/b^5-(c*d-b*e)^3*_ + (6*A*c^3*d^2-3*b^3*B*e^2-3*b*c^2*d*(B*d-A*e)-b^2*c*e*(4*B*d-A*e))*_ + log(b+c*x)/(b^5*c^4) +--R +--R +--R (2) +--R 5 3 6 2 5 5 3 4 2 6 3 2 +--R (2A b c - 6B b c )e + 10B b c d e - 20A b c d e +--R + +--R 7 2 6 4 8 7 5 +--R (30A b c - 10B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 2 7 5 6 2 4 3 5 3 2 +--R (4A b c - 12B b c)e + 20B b c d e - 40A b c d e +--R + +--R 2 6 3 5 4 7 2 6 5 +--R (60A b c - 20B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 7 4 4 4 3 2 +--R (2A b c - 6B b )e + 10B b c d e - 20A b c d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (30A b c - 10B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 6 3 2 7 2 6 4 8 7 5 4 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 5 3 2 2 6 3 5 4 +--R 40A b c d e + (- 60A b c + 20B b c )d e +--R + +--R 7 2 6 5 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 3 2 3 5 4 4 4 2 6 3 5 5 2 +--R (20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 5 5 6 2 5 4 +--R 2B b c e x + 4B b c e x +--R + +--R 6 2 7 5 5 3 6 2 4 5 3 2 3 +--R (4A b c - 4B b c)e + (- 10A b c + 20B b c )d e - 20B b c d e +--R + +--R 3 5 3 2 2 6 3 5 4 7 2 6 5 +--R 20A b c d e + (- 30A b c + 10B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 7 8 5 6 2 7 4 +--R (3A b c - 5B b )e + (- 5A b c + 15B b c)d e +--R + +--R 5 3 6 2 2 3 4 4 5 3 3 2 +--R (- 10A b c - 10B b c )d e + (30A b c - 10B b c )d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (- 45A b c + 15B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 5 4 4 5 4 4 5 +--R (- 10A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 6 4 6 5 3 7 4 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 155 + +--S 156 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 157 + +--S 158 OF 765 +r0:=-1/2*A*d^4/(b^3*x^2)-d^3*(b*B*d-3*A*c*d+4*A*b*e)/(b^4*x)-1/2*(b*B-_ + A*c)*(c*d-b*e)^4/(b^3*c^3*(b+c*x)^2)+(c*d-b*e)^3*(3*A*c^2*d-2*b^2*_ + B*e-b*c*(2*B*d-A*e))/(b^4*c^3*(b+c*x))+d^2*(6*A*c^2*d^2+2*b^2*e*_ + (2*B*d+3*A*e)-3*b*c*d*(B*d+4*A*e))*log(x)/b^5+(c*d-b*e)^2*(3*b*B*_ + c^2*d^2-6*A*c^3*d^2+2*b^2*B*c*d*e+b^3*B*e^2)*log(b+c*x)/(b^5*c^3) +--R +--R +--R (2) +--R 5 2 4 2 5 2 2 6 2 5 3 +--R 2B b c e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 7 6 4 +--R (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 4 3 4 2 2 2 5 3 4 3 +--R 4B b c e - 24A b c d e + (48A b c - 16B b c )d e +--R + +--R 6 2 5 4 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 4 4 3 2 2 3 4 4 3 3 +--R 2B b e - 12A b c d e + (24A b c - 8B b c )d e +--R + +--R 2 5 3 4 4 +--R (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 2 5 2 2 6 2 5 3 7 6 4 4 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 4 2 2 2 5 3 4 3 +--R 24A b c d e + (- 48A b c + 16B b c )d e +--R + +--R 6 2 5 4 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 2 3 4 4 3 3 2 5 3 4 4 2 +--R (12A b c d e + (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 2 6 4 5 2 3 3 4 2 2 +--R (- 2A b c + 4B b c)e - 8B b c d e + 12A b c d e +--R + +--R 2 5 3 4 3 6 2 5 4 +--R (- 24A b c + 8B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- A b c + 3B b )e + (- 4A b c - 4B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (18A b c - 6B b c )d e + (- 36A b c + 12B b c )d e +--R + +--R 2 5 3 4 4 +--R (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 3 4 4 3 4 +--R (- 8A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 5 4 6 4 3 7 3 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 158 + +--S 159 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 OF 765 +r0:=-1/2*A*d^3/(b^3*x^2)-d^2*(b*B*d-3*A*c*d+3*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)^3/(b^3*c^2*(b+c*x)^2)-(c*d-b*e)^2*(2*b*B*c*d-3*A*c^2*d+_ + b^2*B*e)/(b^4*c^2*(b+c*x))-3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*_ + log(x)/b^5+3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 12A b c d e + (36A b c - 12B b c )d e +--R + +--R 5 2 4 3 +--R (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (- 6A b c d e + (18A b c - 6B b c )d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 4 2 5 2 4 2 6 5 3 4 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 3 2 2 4 3 3 2 +--R 12A b c d e + (- 36A b c + 12B b c )d e +--R + +--R 5 2 4 3 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 2 4 3 3 3 2 +--R (6A b c d e + (- 18A b c + 6B b c )d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 5 3 3 3 2 2 4 3 3 2 +--R - 2B b c e + 6A b c d e + (- 18A b c + 6B b c )d e +--R + +--R 5 2 4 3 +--R (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - B b )e + (9A b c - 3B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 27A b c + 9B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 6A b c d e + (4A b c - 2B b c )d )x - A b c d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 161 + +--S 162 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 OF 765 +r0:=-1/2*A*d^2/(b^3*x^2)-d*(b*B*d-3*A*c*d+2*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)^2/(b^3*c*(b+c*x)^2)-(c*d-b*e)*(2*b*B*d-3*A*c*d+A*b*e)/_ + (b^4*(b+c*x))+(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*_ + log(x)/b^5-(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*_ + log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 3 2 4 2 3 5 4 2 4 +--R (- 2A b c e + (12A b c - 4B b c )d e + (- 12A c + 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- 4A b c e + (24A b c - 8B b c )d e + (- 24A b c + 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 2A b c e + (12A b c - 4B b c)d e + (- 12A b c + 6B b c )d )x +--R * +--R log(c x + b) +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A c - 6B b c )d )x +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (4A b c e + (- 24A b c + 8B b c )d e + (24A b c - 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (2A b c e + (- 12A b c + 4B b c)d e + (12A b c - 6B b c )d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (2A b c e + (- 12A b c + 4B b c )d e + (12A b c - 6B b c )d )x +--R + +--R 4 5 2 3 2 4 2 3 3 2 2 2 +--R ((3A b c - B b )e + (- 18A b c + 6B b c)d e + (18A b c - 9B b c )d )x +--R + +--R 4 3 2 4 2 4 2 +--R (- 4A b c d e + (4A b c - 2B b c)d )x - A b c d +--R / +--R 5 3 4 6 2 3 7 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 164 + +--S 165 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 OF 765 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^3 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 OF 765 +r0:=-1/2*A*d/(b^3*x^2)+(-b*B*d+3*A*c*d-A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_ + (c*d-b*e)/(b^3*(b+c*x)^2)+(3*A*c^2*d+b^2*B*e-2*b*c*(B*d+A*e))/_ + (b^4*(b+c*x))+(6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(x)/b^5-_ + (6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 3 2 2 4 3 4 +--R ((6A b c - 2B b c )e + (- 12A c + 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((12A b c - 4B b c)e + (- 24A b c + 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((6A b c - 2B b )e + (- 12A b c + 6B b c)d)x +--R * +--R log(c x + b) +--R + +--R 3 2 2 4 3 4 +--R ((- 6A b c + 2B b c )e + (12A c - 6B b c )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 4B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 6A b c + 2B b )e + (12A b c - 6B b c)d)x +--R * +--R log(x) +--R + +--R 2 2 3 3 2 2 3 +--R ((- 6A b c + 2B b c)e + (12A b c - 6B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 9A b c + 3B b )e + (18A b c - 9B b c)d)x +--R + +--R 4 3 4 4 +--R (- 2A b e + (4A b c - 2B b )d)x - A b d +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 167 + +--S 168 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 OF 765 +t0:=(A+B*x)/(b*x+c*x^2)^3 +--R +--R +--R B x + A +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 169 + +--S 170 OF 765 +r0:=-1/2*A/(b^3*x^2)+(-b*B+3*A*c)/(b^4*x)-1/2*c*(b*B-A*c)/(b^3*(b+c*x)^2)-_ + c*(2*b*B-3*A*c)/(b^4*(b+c*x))-3*c*(b*B-2*A*c)*log(x)/b^5+3*c*(b*B-_ + 2*A*c)*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 4 3 4 3 2 2 3 +--R (- 12A c + 6B b c )x + (- 24A b c + 12B b c )x +--R + +--R 2 2 3 2 +--R (- 12A b c + 6B b c)x +--R * +--R log(c x + b) +--R + +--R 4 3 4 3 2 2 3 +--R (12A c - 6B b c )x + (24A b c - 12B b c )x +--R + +--R 2 2 3 2 +--R (12A b c - 6B b c)x +--R * +--R log(x) +--R + +--R 3 2 2 3 2 2 3 2 3 4 4 +--R (12A b c - 6B b c )x + (18A b c - 9B b c)x + (4A b c - 2B b )x - A b +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 170 + +--S 171 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 OF 765 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R --------------------------------------------------------------------------- +--R 3 7 2 3 6 2 2 5 3 2 4 3 3 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 172 + +--S 173 OF 765 +r0:=-1/2*A/(b^3*d*x^2)+(-b*B*d+3*A*c*d+A*b*e)/(b^4*d^2*x)-1/2*c^2*(b*B-_ + A*c)/(b^3*(c*d-b*e)*(b+c*x)^2)+c^2*(3*A*c^2*d+3*b^2*B*e-2*b*c*(B*d+_ + 2*A*e))/(b^4*(c*d-b*e)^2*(b+c*x))+(6*A*c^2*d^2-3*b*c*d*(B*d-A*e)-_ + b^2*e*(B*d-A*e))*log(x)/(b^5*d^3)-c^2*(6*A*c^3*d^2-6*b^3*B*e^2-_ + 3*b*c^2*d*(B*d+5*A*e)+2*b^2*c*e*(4*B*d+5*A*e))*log(b+c*x)/(b^5*(c*d-_ + b*e)^3)-e^4*(B*d-A*e)*log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 5 2 5 5 2 4 4 6 5 6 4 3 +--R (- 2A b c e + 2B b c d e )x + (- 4A b c e + 4B b c d e )x +--R + +--R 7 5 7 4 2 +--R (- 2A b e + 2B b d e )x +--R * +--R log(e x + d) +--R + +--R 2 5 3 4 3 2 6 2 5 4 +--R (20A b c - 12B b c )d e + (- 30A b c + 16B b c )d e +--R + +--R 7 6 5 +--R (12A c - 6B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 3 2 2 5 3 4 4 +--R (40A b c - 24B b c )d e + (- 60A b c + 32B b c )d e +--R + +--R 6 2 5 5 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (20A b c - 12B b c )d e + (- 30A b c + 16B b c )d e +--R + +--R 2 5 3 4 5 +--R (12A b c - 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 5 2 5 5 2 4 2 5 3 4 3 2 +--R 2A b c e - 2B b c d e + (- 20A b c + 12B b c )d e +--R + +--R 6 2 5 4 7 6 5 +--R (30A b c - 16B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 6 5 6 4 3 4 4 3 3 2 +--R 4A b c e - 4B b c d e + (- 40A b c + 24B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (60A b c - 32B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 7 4 4 3 5 2 3 2 +--R 2A b e - 2B b d e + (- 20A b c + 12B b c )d e +--R + +--R 3 4 4 3 4 2 5 3 4 5 +--R (30A b c - 16B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(x) +--R + +--R 5 2 4 5 2 2 3 3 4 4 3 3 2 +--R 2A b c d e - 2B b c d e + (- 20A b c + 12B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (30A b c - 16B b c )d e + (- 12A b c + 6B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 2 6 2 3 4 3 5 2 3 2 +--R 4A b c d e + (- A b c - 4B b c)d e + (- 30A b c + 19B b c )d e +--R + +--R 3 4 4 3 4 2 5 3 4 5 +--R (45A b c - 24B b c )d e + (- 18A b c + 9B b c )d +--R * +--R 2 +--R x +--R + +--R 7 4 6 7 2 3 5 2 6 3 2 +--R 2A b d e + (- 2A b c - 2B b )d e + (- 6A b c + 6B b c)d e +--R + +--R 4 3 5 2 4 3 4 4 3 5 +--R (10A b c - 6B b c )d e + (- 4A b c + 2B b c )d +--R * +--R x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - A b d e + 3A b c d e - 3A b c d e + A b c d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (2b c d e - 6b c d e + 6b c d e - 2b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d )x +--R Type: Expression(Integer) +--E 173 + +--S 174 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 OF 765 +r0:=-1/2*A/(b^3*d^2*x^2)+(-b*B*d+3*A*c*d+2*A*b*e)/(b^4*d^3*x)-1/2*c^3*(b*B-_ + A*c)/(b^3*(c*d-b*e)^2*(b+c*x)^2)-c^3*(2*b*B*c*d-3*A*c^2*d-4*b^2*B*e+_ + 5*A*b*c*e)/(b^4*(c*d-b*e)^3*(b+c*x))+e^4*(B*d-A*e)/(d^3*(c*d-b*e)^3*_ + (d+e*x))+(6*A*c^2*d^2-b^2*e*(2*B*d-3*A*e)-3*b*c*d*(B*d-2*A*e))*_ + log(x)/(b^5*d^4)-c^3*(6*A*c^3*d^2-10*b^3*B*e^2+5*b^2*c*e*(2*B*d+_ + 3*A*e)-3*b*c^2*d*(B*d+6*A*e))*log(b+c*x)/(b^5*(c*d-b*e)^4)-e^4*_ + (B*d*(5*c*d-2*b*e)-3*A*e*(2*c*d-b*e))*log(d+e*x)/(d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 6 2 7 5 3 6 2 6 5 3 2 5 5 +--R (- 6A b c e + (12A b c + 4B b c )d e - 10B b c d e )x +--R + +--R 7 7 6 2 7 6 +--R - 12A b c e + (18A b c + 8B b c)d e +--R + +--R 5 3 6 2 2 5 5 3 3 4 +--R (12A b c - 16B b c )d e - 10B b c d e +--R * +--R 4 +--R x +--R + +--R 8 7 8 6 6 2 7 2 5 6 2 3 4 3 +--R (- 6A b e + 4B b d e + (24A b c - 2B b c)d e - 20B b c d e )x +--R + +--R 8 6 7 8 2 5 7 3 4 2 +--R (- 6A b d e + (12A b c + 4B b )d e - 10B b c d e )x +--R * +--R log(e x + d) +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 30A b c + 20B b c )d e + (36A b c - 20B b c )d e +--R + +--R 8 7 6 +--R (- 12A c + 6B b c )d e +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 60A b c + 40B b c )d e + (42A b c - 20B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (12A b c - 8B b c )d e + (- 12A c + 6B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (- 30A b c + 20B b c )d e + (- 24A b c + 20B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (60A b c - 34B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (- 30A b c + 20B b c )d e + (36A b c - 20B b c )d e +--R + +--R 2 6 3 5 7 +--R (- 12A b c + 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(c x + b) +--R + +--R 6 2 7 5 3 6 2 6 5 3 2 5 +--R 6A b c e + (- 12A b c - 4B b c )d e + 10B b c d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 8 7 6 +--R (12A c - 6B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R 12A b c e + (- 18A b c - 8B b c)d e +--R + +--R 5 3 6 2 2 5 5 3 3 4 +--R (- 12A b c + 16B b c )d e + 10B b c d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (60A b c - 40B b c )d e + (- 42A b c + 20B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (- 12A b c + 8B b c )d e + (12A c - 6B b c )d +--R * +--R 4 +--R x +--R + +--R 8 7 8 6 6 2 7 2 5 6 2 3 4 +--R 6A b e - 4B b d e + (- 24A b c + 2B b c)d e + 20B b c d e +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (30A b c - 20B b c )d e + (24A b c - 20B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 60A b c + 34B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 7 3 4 +--R 6A b d e + (- 12A b c - 4B b )d e + 10B b c d e +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 2 6 3 5 7 +--R (12A b c - 6B b c )d +--R * +--R 2 +--R x +--R * +--R log(x) +--R + +--R 6 2 6 5 3 6 2 2 5 5 3 3 4 +--R 6A b c d e + (- 12A b c - 4B b c )d e + 10B b c d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (30A b c - 20B b c )d e + (- 36A b c + 20B b c )d e +--R + +--R 7 2 6 6 +--R (12A b c - 6B b c )d e +--R * +--R 4 +--R x +--R + +--R 7 6 6 2 7 2 5 5 3 6 2 3 4 +--R 12A b c d e + (- 21A b c - 8B b c)d e + (- 6A b c + 18B b c )d e +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (45A b c - 25B b c )d e + (- 24A b c + 10B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 18A b c + 11B b c )d e + (12A b c - 6B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 6 2 7 3 4 +--R 6A b d e + (- 6A b c - 4B b )d e + (- 13A b c + 6B b c)d e +--R + +--R 5 3 6 2 4 3 4 4 5 3 5 2 +--R (12A b c + 4B b c )d e + (33A b c - 25B b c )d e +--R + +--R 3 5 4 4 6 2 6 3 5 7 +--R (- 50A b c + 28B b c )d e + (18A b c - 9B b c )d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 8 3 4 6 2 7 4 3 +--R 3A b d e + (- 8A b c - 2B b )d e + (2A b c + 8B b c)d e +--R + +--R 5 3 6 2 5 2 4 4 5 3 6 +--R (12A b c - 12B b c )d e + (- 13A b c + 8B b c )d e +--R + +--R 3 5 4 4 7 +--R (4A b c - 2B b c )d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - A b d e + 4A b c d e - 6A b c d e + 4A b c d e - A b c d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (2b c d e - 8b c d e + 12b c d e - 8b c d e + 2b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 5 6 9 4 +--R (4b c d e - 14b c d e + 16b c d e - 4b c d e - 4b c d e + 2b c d )x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 6 5 9 3 +--R (2b d e - 4b c d e - 4b c d e + 16b c d e - 14b c d e + 4b c d )x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )x +--R Type: Expression(Integer) +--E 176 + +--S 177 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 OF 765 +t0:=(A+B*x)*(d+e*x)^3*sqrt(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 178 + +--S 179 OF 765 +r0:=1/960*(4*A*c*e*(132*c^2*d^2-132*b*c*d*e+35*b^2*e^2)+B*(64*c^3*d^3-_ + 360*b*c^2*d^2*e+366*b^2*c*d*e^2-105*b^3*e^3))*(b*x+c*x^2)^(3/2)/c^4+_ + 1/20*(2*B*c*d-3*b*B*e+4*A*c*e)*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c^2+_ + 1/6*B*(d+e*x)^3*(b*x+c*x^2)^(3/2)/c-1/160*e*(d*(16*b*B*c*d-40*A*c^2*d-_ + 9*b^2*B*e+12*A*b*c*e)-(28*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-36*b*c*d*e+_ + 21*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/c^3-1/512*b^2*(128*A*c^4*d^3+_ + 21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-28*b^3*c*e^2*(3*B*d+A*e)-_ + 64*b*c^3*d^2*(B*d+3*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+_ + 1/512*b*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-_ + 28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/c^5+_ + 1/256*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-_ + 28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*x*sqrt(b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 5 6 3 4 2 5 2 +--R (420A b c - 315B b )e + (- 1800A b c + 1260B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (2880A b c - 1800B b c )d e + (- 1920A b c + 960B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 3 5 5 4 3 5 2 4 +--R 1280B c e x + ((1536A c + 128B b c )e + 4608B c d e )x +--R + +--R 4 2 3 3 5 4 2 +--R (192A b c - 144B b c )e + (5760A c + 576B b c )d e +--R + +--R 5 2 +--R 5760B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (- 224A b c + 168B b c )e + (960A b c - 672B b c )d e +--R + +--R 5 4 2 5 3 +--R (7680A c + 960B b c )d e + 2560B c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (280A b c - 210B b c)e + (- 1200A b c + 840B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (1920A b c - 1200B b c )d e + (3840A c + 640B b c )d +--R * +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 420A b c + 315B b )e + (1800A b c - 1260B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 2880A b c + 1800B b c )d e + (1920A b c - 960B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 179 + +--S 180 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 OF 765 +t0:=(A+B*x)*(d+e*x)^2*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R 2 3 2 2 2 2 | 2 +--R (1) (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|c x + b x +--R Type: Expression(Integer) +--E 181 + +--S 182 OF 765 +r0:=1/240*(50*A*c*e*(2*c*d-b*e)+B*(32*c^2*d^2-82*b*c*d*e+35*b^2*e^2))*_ + (b*x+c*x^2)^(3/2)/c^3+1/5*B*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c-1/40*e*_ + ((3*b*B-10*A*c)*d-(4*B*c*d-7*b*B*e+10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/c^2-_ + 1/128*b^2*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-_ + 16*b*c^2*d*(B*d+2*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)+_ + 1/128*b*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*_ + d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/c^4+1/64*(32*A*c^3*d^2-7*b^3*B*e^2+_ + 10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 4 5 2 3 2 4 +--R (- 150A b c + 105B b )e + (480A b c - 300B b c)d e +--R + +--R 2 3 3 2 2 +--R (- 480A b c + 240B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 2 4 4 3 2 4 3 +--R 384B c e x + ((480A c + 48B b c )e + 960B c d e)x +--R + +--R 3 2 2 2 4 3 4 2 2 +--R ((80A b c - 56B b c )e + (1280A c + 160B b c )d e + 640B c d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 100A b c + 70B b c)e + (320A b c - 200B b c )d e +--R + +--R 4 3 2 +--R (960A c + 160B b c )d +--R * +--R x +--R + +--R 3 4 2 2 2 3 +--R (150A b c - 105B b )e + (- 480A b c + 300B b c)d e +--R + +--R 3 2 2 2 +--R (480A b c - 240B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 1920c \|c +--R Type: Expression(Integer) +--E 182 + +--S 183 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 OF 765 +t0:=(A+B*x)*(d+e*x)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (1) (B e x + (A e + B d)x + A d)\|c x + b x +--R Type: Expression(Integer) +--E 184 + +--S 185 OF 765 +r0:=1/24*(2*B*c*d-5*b*B*e+8*A*c*e)*(b*x+c*x^2)^(3/2)/c^2+1/4*B*(d+e*x)*_ + (b*x+c*x^2)^(3/2)/c-1/64*b^2*(16*A*c^2*d+5*b^2*B*e-8*b*c*(B*d+A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/64*b*(16*A*c^2*d+5*b^2*B*e-_ + 8*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^3+1/32*(16*A*c^2*d+5*b^2*B*e-_ + 8*b*c*(B*d+A*e))*x*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 3 4 2 2 3 x\|c +--R ((24A b c - 15B b )e + (- 48A b c + 24B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 3 3 2 3 2 +--R 48B c e x + ((64A c + 8B b c )e + 64B c d)x +--R + +--R 2 2 3 2 +--R ((16A b c - 10B b c)e + (96A c + 16B b c )d)x +--R + +--R 2 3 2 2 +--R (- 24A b c + 15B b )e + (48A b c - 24B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 185 + +--S 186 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R | 2 +--R (1) (B x + A)\|c x + b x +--R Type: Expression(Integer) +--E 187 + +--S 188 OF 765 +r0:=1/3*B*(b*x+c*x^2)^(3/2)/c+1/8*b^2*(b*B-2*A*c)*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/c^(5/2)-1/8*b*(b*B-2*A*c)*sqrt(b*x+c*x^2)/c^2-_ + 1/4*(b*B-2*A*c)*x*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 2 3 x\|c +--R (- 6A b c + 3B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R 2 2 2 2 +-+ | 2 +--R (8B c x + (12A c + 2B b c)x + 6A b c - 3B b )\|c \|c x + b x +--R / +--R 2 +-+ +--R 24c \|c +--R Type: Expression(Integer) +--E 188 + +--S 189 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R e x + d +--R Type: Expression(Integer) +--E 190 + +--S 191 OF 765 +r0:=-1/4*(4*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-4*b*c*d*e-b^2*e^2))*atanh(x*_ + sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^3)-(B*d-A*e)*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*_ + sqrt(c*d-b*e)/e^3-1/4*(4*B*c*d-b*B*e-4*A*c*e-2*B*c*e*x)*sqrt(b*x+_ + c*x^2)/(c*e^2) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 2 2 x\|c +--R ((4A b c - B b )e + (- 8A c - 4B b c)d e + 8B c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ +--R (- 4A c e + 4B c d)\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R 2 2 +-+ | 2 +--R (2B c e x + (4A c + B b)e - 4B c d e)\|c \|c x + b x +--R / +--R 3 +-+ +--R 4c e \|c +--R Type: Expression(Integer) +--E 191 + +--S 192 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 193 + +--S 194 OF 765 +r0:=-(4*B*c*d-b*B*e-2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^3*sqrt(c))+_ + 1/2*(B*d*(4*c*d-3*b*e)-A*e*(2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^3*sqrt(d)*sqrt(c*d-b*e))+_ + (2*B*d-A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)) +--R +--R +--R (2) +--R 2 2 +--R (((4A c + 2B b)e - 8B c d e)x + (4A c + 2B b)d e - 8B c d ) +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 2 2 +--R (- A b e + (2A c + 3B b)d e - 4B c d e)x - A b d e +--R + +--R 2 3 +--R (2A c + 3B b)d e - 4B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R 2 2 +-----------+ +-+ +-+ | 2 +--R (2B e x - 2A e + 4B d e)\|- b e + c d \|c \|d \|c x + b x +--R / +--R 4 3 +-----------+ +-+ +-+ +--R (2e x + 2d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 194 + +--S 195 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 196 + +--S 197 OF 765 +r0:=1/2*(B*d-A*e)*(b*x+c*x^2)^(3/2)/(d*(c*d-b*e)*(d+e*x)^2)-1/8*(A*b^2*e^3+_ + B*d*(8*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*e^3*(c*d-b*e)^(3/2))+_ + 2*B*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^3+1/4*(A*b*e^2-B*d*_ + (4*c*d-3*b*e)-2*c*e*(B*d-A*e)*x)*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 3 +--R (16B b d e - 16B c d e )x + (32B b d e - 32B c d e)x + 16B b d e +--R + +--R 4 +--R - 16B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 4 2 3 2 3 2 2 +--R (- A b e - 3B b d e + 12B b c d e - 8B c d e )x +--R + +--R 2 4 2 2 3 3 2 2 4 2 2 3 +--R (- 2A b d e - 6B b d e + 24B b c d e - 16B c d e)x - A b d e +--R + +--R 2 3 2 4 2 5 +--R - 3B b d e + 12B b c d e - 8B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 3 2 2 3 +--R (2A b e + (- 4A c - 10B b)d e + 12B c d e )x - 2A b d e +--R + +--R 2 2 3 +--R - 6B b d e + 8B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 6 2 5 2 2 5 3 4 3 4 4 3 +--R ((8b d e - 8c d e )x + (16b d e - 16c d e )x + 8b d e - 8c d e ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 197 + +--S 198 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 199 + +--S 200 OF 765 +r0:=1/16*b^2*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+1/12*(B*_ + d*(4*c*d-5*b*e)+A*e*(2*c*d-b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*_ + (d+e*x)^2)+1/24*(B*d*(8*c^2*d^2-14*b*c*d*e+3*b^2*e^2)+A*e*(4*c^2*_ + d^2-4*b*c*d*e+3*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*_ + (d+e*x))-1/3*(2*B*d+A*e+3*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)^3) +--R +--R +--R (2) +--R 3 4 2 3 3 3 +--R (- 3A b e + (6A b c - 3B b )d e )x +--R + +--R 3 3 2 3 2 2 2 +--R (- 9A b d e + (18A b c - 9B b )d e )x +--R + +--R 3 2 2 2 3 3 3 3 2 3 4 +--R (- 9A b d e + (18A b c - 9B b )d e)x - 3A b d e + (6A b c - 3B b )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 2 +--R 6A b e + (- 8A b c + 6B b )d e + (8A c - 28B b c)d e +--R + +--R 2 3 +--R 16B c d +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 3 +--R (16A b d e + (- 28A b c - 16B b )d e + (24A c + 4B b c)d )x +--R + +--R 2 2 2 3 +--R - 6A b d e + (12A b c - 6B b )d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (48b d e - 96b c d e + 48c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (144b d e - 288b c d e + 144c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (144b d e - 288b c d e + 144c d e)x + 48b d e - 96b c d e + 48c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 200 + +--S 201 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 202 + +--S 203 OF 765 +r0:=-1/128*b^2*(16*A*c^2*d^2-8*b*c*d*(B*d+2*A*e)+b^2*e*(3*B*d+5*A*e))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+1/24*(B*d*(2*c*d-3*b*e)+A*e*(2*c*d-_ + b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)^3)+1/96*(B*d*_ + (8*c^2*d^2-16*b*c*d*e+3*b^2*e^2)+A*e*(8*c^2*d^2-8*b*c*d*e+_ + 5*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*(d+e*x)^2)+_ + 1/192*(A*e*(16*c^3*d^3-24*b*c^2*d^2*e+38*b^2*c*d*e^2-15*b^3*e^3)+_ + B*d*(16*c^3*d^3-40*b*c^2*d^2*e+18*b^2*c*d*e^2-9*b^3*e^3))*_ + sqrt(b*x+c*x^2)/(d^3*e^2*(c*d-b*e)^3*(d+e*x))-1/4*(B*d+A*e+_ + 2*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)^4) +--R +--R +--R (2) +--R 4 6 3 4 5 2 2 3 2 4 4 +--R (- 15A b e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d e )x +--R + +--R 4 5 3 4 2 4 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 3 3 +--R (- 192A b c + 96B b c)d e +--R * +--R 3 +--R x +--R + +--R 4 2 4 3 4 3 3 +--R - 90A b d e + (288A b c - 54B b )d e +--R + +--R 2 2 3 4 2 +--R (- 288A b c + 144B b c)d e +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 2 +--R - 60A b d e + (192A b c - 36B b )d e +--R + +--R 2 2 3 5 +--R (- 192A b c + 96B b c)d e +--R * +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 +--R - 15A b d e + (48A b c - 9B b )d e + (- 48A b c + 24B b c)d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 5 2 3 4 2 2 2 3 +--R 30A b e + (- 76A b c + 18B b )d e + (48A b c - 36B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 32A c + 80B b c )d e - 32B c d e +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 3 +--R 110A b d e + (- 280A b c + 66B b )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (208A b c - 184B b c)d e + (- 128A c + 336B b c )d e - 128B c d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 3 3 2 +--R 146A b d e + (- 396A b c - 66B b )d e +--R + +--R 2 2 4 3 2 5 +--R (352A b c + 188B b c)d e + (- 192A c - 32B b c )d +--R * +--R x +--R + +--R 3 3 2 2 3 4 2 2 5 +--R - 30A b d e + (96A b c - 18B b )d e + (- 96A b c + 48B b c)d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (384b d e - 1152b c d e + 1152b c d e - 384c d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (2304b d e - 6912b c d e + 6912b c d e - 2304c d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (1536b d e - 4608b c d e + 4608b c d e - 1536c d e)x + 384b d e +--R + +--R 2 8 2 2 9 3 10 +--R - 1152b c d e + 1152b c d e - 384c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 203 + +--S 204 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 205 + +--S 206 OF 765 +r0:=1/192*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+_ + 2*A*e))*x*(b*x+c*x^2)^(3/2)/c^3+1/840*(98*A*c*e*(2*c*d-b*e)+B*(48*_ + c^2*d^2-146*b*c*d*e+63*b^2*e^2))*(b*x+c*x^2)^(5/2)/c^3+1/7*B*_ + (d+e*x)^2*(b*x+c*x^2)^(5/2)/c-1/84*e*((5*b*B-14*A*c)*d-(4*B*c*d-_ + 9*b*B*e+14*A*c*e)*x)*(b*x+c*x^2)^(5/2)/c^2+1/1024*b^4*(48*A*c^3*d^2-_ + 9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)-1/1024*b^3*(48*A*c^3*d^2-_ + 9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*sqrt(b*x+_ + c*x^2)/c^5+1/1536*b^2*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+_ + A*e)-24*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^4+1/384*b*_ + (48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+_ + 2*A*e))*x^2*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 6 7 2 5 2 6 +--R (1470A b c - 945B b )e + (- 5040A b c + 2940B b c)d e +--R + +--R 4 3 5 2 2 +--R (5040A b c - 2520B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 2 6 6 5 2 6 5 +--R 15360B c e x + ((17920A c + 19200B b c )e + 35840B c d e)x +--R + +--R 5 2 4 2 6 5 +--R (23296A b c + 384B b c )e + (43008A c + 46592B b c )d e +--R + +--R 6 2 +--R 21504B c d +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 2 5 2 4 +--R (672A b c - 432B b c )e + (59136A b c + 1344B b c )d e +--R + +--R 6 5 2 +--R (26880A c + 29568B b c )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (- 784A b c + 504B b c )e + (2688A b c - 1568B b c )d e +--R + +--R 5 2 4 2 +--R (40320A b c + 1344B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (980A b c - 630B b c)e + (- 3360A b c + 1960B b c )d e +--R + +--R 2 4 3 3 2 +--R (3360A b c - 1680B b c )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 +--R (- 1470A b c + 945B b )e + (5040A b c - 2940B b c)d e +--R + +--R 3 3 4 2 2 +--R (- 5040A b c + 2520B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 107520c \|c +--R Type: Expression(Integer) +--E 206 + +--S 207 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 OF 765 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 4 3 2 +--R (B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x) +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 208 + +--S 209 OF 765 +r0:=1/96*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x*(b*x+c*x^2)^(3/2)/c^2+_ + 1/60*(2*B*c*d-7*b*B*e+12*A*c*e)*(b*x+c*x^2)^(5/2)/c^2+1/6*B*(d+e*x)*_ + (b*x+c*x^2)^(5/2)/c+1/512*b^4*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+_ + A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-1/512*b^3*_ + (24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^4+_ + 1/768*b^2*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x*sqrt(b*x+_ + c*x^2)/c^3+1/192*b*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x^2*_ + sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 5 6 4 2 5 x\|c +--R ((- 180A b c + 105B b )e + (360A b c - 180B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 5 5 4 5 4 +--R 1280B c e x + ((1536A c + 1664B b c )e + 1536B c d)x +--R + +--R 4 2 3 5 4 3 +--R ((2112A b c + 48B b c )e + (1920A c + 2112B b c )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((96A b c - 56B b c )e + (2880A b c + 96B b c )d)x +--R + +--R 3 2 4 2 3 3 2 +--R ((- 120A b c + 70B b c)e + (240A b c - 120B b c )d)x +--R + +--R 4 5 3 2 4 +--R (180A b c - 105B b )e + (- 360A b c + 180B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 209 + +--S 210 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (1) (B c x + (A c + B b)x + A b x)\|c x + b x +--R Type: Expression(Integer) +--E 211 + +--S 212 OF 765 +r0:=-1/8*(b*B-2*A*c)*x*(b*x+c*x^2)^(3/2)/c+1/5*B*(b*x+c*x^2)^(5/2)/c-_ + 3/128*b^4*(b*B-2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+_ + 3/128*b^3*(b*B-2*A*c)*sqrt(b*x+c*x^2)/c^3-1/64*b^2*(b*B-2*A*c)*x*_ + sqrt(b*x+c*x^2)/c^2-1/16*b*(b*B-2*A*c)*x^2*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 4 5 x\|c +--R (30A b c - 15B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 4 4 3 3 3 2 2 2 +--R 128B c x + (160A c + 176B b c )x + (240A b c + 8B b c )x +--R + +--R 2 2 3 3 4 +--R (20A b c - 10B b c)x - 30A b c + 15B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 640c \|c +--R Type: Expression(Integer) +--E 212 + +--S 213 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 214 + +--S 215 OF 765 +r0:=-1/24*(8*B*c*d-3*b*B*e-8*A*c*e-6*B*c*e*x)*(b*x+c*x^2)^(3/2)/(c*e^2)-_ + 1/64*(8*A*c*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3)-_ + B*(128*c^4*d^4-192*b*c^3*d^3*e+48*b^2*c^2*d^2*e^2+8*b^3*c*d*e^3+_ + 3*b^4*e^4))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^5)-d^(3/2)*_ + (B*d-A*e)*(c*d-b*e)^(3/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^5+1/64*(8*A*c*e*(8*c^2*d^2-_ + 10*b*c*d*e+b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+8*b^2*c*d*e^2+_ + 3*b^3*e^3)-2*c*e*(8*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-8*b*c*d*e-_ + 3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^4) +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 +--R (- 24A b c + 9B b )e + (- 144A b c + 24B b c)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (576A b c + 144B b c )d e + (- 384A c - 576B b c )d e + 384B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 2 2 3 3 +-----------+ +--R (192A b c d e + (- 192A c - 192B b c )d e + 192B c d )\|- b e + c d +--R * +--R +-+ +-+ (b e - 2c d)x - b d +--R \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 4 3 3 2 4 3 3 2 +--R 48B c e x + ((64A c + 72B b c )e - 64B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 +--R ((112A b c + 6B b c)e + (- 96A c - 112B b c )d e + 96B c d e )x +--R + +--R 2 3 4 2 2 3 +--R (24A b c - 9B b )e + (- 240A b c - 24B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (192A c + 240B b c )d e - 192B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 5 +-+ +--R 192c e \|c +--R Type: Expression(Integer) +--E 215 + +--S 216 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 217 + +--S 218 OF 765 +r0:=1/3*(4*B*d-3*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x))+1/8*(4*b*c*e*_ + (4*B*d-3*A*e)*(2*c*d-b*e)-(8*B*c*d-b*B*e-6*A*c*e)*(8*c^2*d^2-_ + 4*b*c*d*e-b^2*e^2))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^5)+_ + 1/2*(B*d*(8*c*d-5*b*e)-3*A*e*(2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-_ + b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-_ + b*e)/e^5-1/8*(6*A*c*e*(4*c*d-3*b*e)-B*(32*c^2*d^2-28*b*c*d*e+_ + b^2*e^2)+2*c*e*(8*B*c*d-b*B*e-6*A*c*e)*x)*sqrt(b*x+c*x^2)/(c*e^4) +--R +--R +--R (2) +--R 2 3 4 2 2 3 +--R (18A b c - 3B b )e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (144A c + 216B b c )d e - 192B c d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A b c - 3B b )d e + (- 144A b c - 36B b c)d e +--R + +--R 3 2 3 3 4 +--R (144A c + 216B b c )d e - 192B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 2 2 2 2 +--R (- 36A b c e + (72A c + 60B b c)d e - 96B c d e)x - 36A b c d e +--R + +--R 2 2 2 3 +--R (72A c + 60B b c)d e - 96B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 4 3 2 4 2 3 2 +--R 8B c e x + ((12A c + 14B b c)e - 16B c d e )x +--R + +--R 2 4 2 3 2 2 2 +--R ((30A b c + 3B b )e + (- 36A c - 46B b c)d e + 48B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (54A b c + 3B b )d e + (- 72A c - 84B b c)d e + 96B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 5 +-+ +--R (24c e x + 24c d e )\|c +--R Type: Expression(Integer) +--E 218 + +--S 219 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 220 + +--S 221 OF 765 +r0:=1/2*(2*B*d-A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)-3/4*(4*A*c*e*_ + (2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+b^2*e^2))*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/(e^5*sqrt(c))+3/8*(A*e*(8*c^2*d^2-8*b*c*d*e+_ + b^2*e^2)-B*d*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2))*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^5*_ + sqrt(d)*sqrt(c*d-b*e))-3/4*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+_ + e*(4*B*c*d-b*B*e-2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 +--R ((24A b c + 6B b )e + (- 48A c - 72B b c)d e + 96B c d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((48A b c + 12B b )d e + (- 96A c - 144B b c)d e + 192B c d e)x +--R + +--R 2 2 2 2 3 2 4 +--R (24A b c + 6B b )d e + (- 48A c - 72B b c)d e + 96B c d +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A b e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 3 2 +--R 48B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 6A b d e + (48A b c + 30B b )d e + (- 48A c - 120B b c)d e +--R + +--R 2 4 +--R 96B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 3A b d e + (24A b c + 15B b )d e + (- 24A c - 60B b c)d e +--R + +--R 2 5 +--R 48B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 3 4 3 2 +--R 4B c e x + ((8A c + 10B b)e - 16B c d e )x +--R + +--R 4 3 2 2 3 +--R (- 10A b e + (36A c + 38B b)d e - 72B c d e )x - 6A b d e +--R + +--R 2 2 3 +--R (24A c + 24B b)d e - 48B c d e +--R * +--R +----------+ +--R +-----------+ +-+ +-+ | 2 +--R \|- b e + c d \|c \|d \|c x + b x +--R / +--R 7 2 6 2 5 +-----------+ +-+ +-+ +--R (8e x + 16d e x + 8d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 221 + +--S 222 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +--)clear all +--R +--S 223 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (4) --------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 223 + +--S 224 OF 765 +r0:=-1/4*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*(b*x+c*x^2)^(3/2)/(d*e^2*_ + (c*d-b*e)*(d+e*x)^2)+1/3*(4*B*d-A*e+3*B*e*x)*(b*x+c*x^2)^(3/2)/_ + (e^2*(d+e*x)^3)+1/16*(B*d*(64*c^3*d^3-120*b*c^2*d^2*e+60*b^2*c*d*e^2-_ + 5*b^3*e^3)-A*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(3/2)*e^5*(c*d-b*e)^(3/2))-(8*B*c*d-3*b*B*e-2*A*c*e)*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^5-1/8*(A*e*(8*c^2*d^2-_ + 6*b*c*d*e-b^2*e^2)-B*d*(32*c^2*d^2-36*b*c*d*e+5*b^2*e^2)-_ + 2*c*e*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*x)*sqrt(b*x+c*x^2)/_ + (d*e^4*(c*d-b*e)*(d+e*x)) +--R +--R +--R (5) +--R 2 5 2 2 4 2 3 3 3 +--R ((96A b c + 144B b )d e + (- 96A c - 528B b c)d e + 384B c d e )x +--R + +--R 2 2 4 2 3 3 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 4 2 +--R 1152B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 2 +--R (288A b c + 432B b )d e + (- 288A c - 1584B b c)d e +--R + +--R 2 5 +--R 1152B c d e +--R * +--R x +--R + +--R 2 4 2 2 5 2 6 +--R (96A b c + 144B b )d e + (- 96A c - 528B b c)d e + 384B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 7 2 3 6 2 2 2 5 +--R - 3A b e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 48A c - 360B b c )d e + 192B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 5 2 +--R 576B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 9A b d e + (- 54A b c - 45B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (216A b c + 540B b c)d e + (- 144A c - 1080B b c )d e +--R + +--R 3 6 +--R 576B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 2 2 5 2 +--R - 3A b d e + (- 18A b c - 15B b )d e + (72A b c + 180B b c)d e +--R + +--R 3 2 6 3 7 +--R (- 48A c - 360B b c )d e + 192B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 2 2 4 3 +--R (48B b c d e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 +--R 6A b e + (- 88A b c - 66B b )d e + (88A c + 412B b c)d e +--R + +--R 2 3 3 +--R - 352B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 16A b d e + (- 92A b c - 80B b )d e +--R + +--R 2 3 3 2 4 2 +--R (120A c + 548B b c)d e - 480B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 6A b d e + (- 36A b c - 30B b )d e + (48A c + 216B b c)d e +--R + +--R 2 5 +--R - 192B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 9 2 8 3 2 8 3 7 2 +--R (48b d e - 48c d e )x + (144b d e - 144c d e )x +--R + +--R 3 7 4 6 4 6 5 5 +--R (144b d e - 144c d e )x + 48b d e - 48c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 224 + +--S 225 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 226 + +--S 227 OF 765 +r0:=1/32*(3*A*b^2*e^3+B*d*(16*c^2*d^2-24*b*c*d*e+5*b^2*e^2))*_ + (b*x+c*x^2)^(3/2)/(d^2*e^2*(c*d-b*e)^2*(d+e*x)^2)+1/24*(3*A*b*e^2-_ + B*d*(8*c*d-5*b*e)-6*c*e*(B*d-A*e)*x)*(b*x+c*x^2)^(3/2)/(d*e^2*_ + (c*d-b*e)*(d+e*x)^3)+1/4*(B*d-A*e)*(b*x+c*x^2)^(5/2)/(d*(c*d-b*e)*_ + (d+e*x)^4)+2*B*c^(3/2)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/e^5+_ + 1/128*(3*A*b^4*e^5-B*d*(128*c^4*d^4-320*b*c^3*d^3*e+240*b^2*c^2*_ + d^2*e^2-40*b^3*c*d*e^3-5*b^4*e^4))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*e^5*_ + (c*d-b*e)^(5/2))-1/64*(3*A*b^3*e^4+B*d*(64*c^3*d^3-112*b*c^2*_ + d^2*e+40*b^2*c*d*e^2+5*b^3*e^3)+2*c*e*(3*A*b^2*e^3+B*d*(16*c^2*_ + d^2-24*b*c*d*e+5*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d^2*e^4*_ + (c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 2 6 2 3 5 3 4 4 4 +--R (768B b c d e - 1536B b c d e + 768B c d e )x +--R + +--R 2 3 5 2 4 4 3 5 3 3 +--R (3072B b c d e - 6144B b c d e + 3072B c d e )x +--R + +--R 2 4 4 2 5 3 3 6 2 2 +--R (4608B b c d e - 9216B b c d e + 4608B c d e )x +--R + +--R 2 5 3 2 6 2 3 7 2 6 2 +--R (3072B b c d e - 6144B b c d e + 3072B c d e)x + 768B b c d e +--R + +--R 2 7 3 8 +--R - 1536B b c d e + 768B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 9 4 8 3 2 7 2 2 3 6 +--R - 9A b e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 4 5 4 5 4 +--R - 960B b c d e + 384B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 4 2 7 3 3 6 2 2 4 5 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 5 4 4 6 3 +--R - 3840B b c d e + 1536B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 4 3 6 3 4 5 2 2 5 4 +--R - 54A b d e - 90B b d e - 720B b c d e + 4320B b c d e +--R + +--R 3 6 3 4 7 2 +--R - 5760B b c d e + 2304B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 4 4 5 3 5 4 2 2 6 3 +--R - 36A b d e - 60B b d e - 480B b c d e + 2880B b c d e +--R + +--R 3 7 2 4 8 +--R - 3840B b c d e + 1536B c d e +--R * +--R x +--R + +--R 4 4 5 4 5 4 3 6 3 2 2 7 2 +--R - 9A b d e - 15B b d e - 120B b c d e + 720B b c d e +--R + +--R 3 8 4 9 +--R - 960B b c d e + 384B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 18A b e + (12A b c + 30B b )d e + (- 144A b c - 764B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (96A c + 1552B b c )d e - 800B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R 66A b d e + (- 264A b c - 146B b )d e +--R + +--R 2 2 3 5 2 4 4 3 5 3 +--R (144A b c - 1096B b c)d e + 2960B b c d e - 1664B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 2 4 4 +--R - 66A b d e + (12A b c - 110B b )d e - 860B b c d e +--R + +--R 2 5 3 3 6 2 +--R 2368B b c d e - 1344B c d e +--R * +--R x +--R + +--R 3 3 5 3 4 4 2 5 3 2 6 2 3 7 +--R - 18A b d e - 30B b d e - 240B b c d e + 672B b c d e - 384B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 11 3 10 2 4 9 4 +--R (384b d e - 768b c d e + 384c d e )x +--R + +--R 2 3 10 4 9 2 5 8 3 +--R (1536b d e - 3072b c d e + 1536c d e )x +--R + +--R 2 4 9 5 8 2 6 7 2 +--R (2304b d e - 4608b c d e + 2304c d e )x +--R + +--R 2 5 8 6 7 2 7 6 2 6 7 7 6 +--R (1536b d e - 3072b c d e + 1536c d e )x + 384b d e - 768b c d e +--R + +--R 2 8 5 +--R 384c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 227 + +--S 228 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 229 + +--S 230 OF 765 +r0:=-1/5*(4*B*d+A*e+5*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^5)-_ + 3/256*b^4*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+_ + 1/80*(A*e*(4*c^2*d^2-4*b*c*d*e-b^2*e^2)+B*d*(16*c^2*d^2-26*b*c*d*e+_ + 11*b^2*e^2))*sqrt(b*x+c*x^2)/(d*e^4*(c*d-b*e)*(d+e*x)^3)+1/320*_ + (A*e*(16*c^3*d^3-24*b*c^2*d^2*e-2*b^2*c*d*e^2+5*b^3*e^3)+B*d*_ + (64*c^3*d^3-136*b*c^2*d^2*e+72*b^2*c*d*e^2+5*b^3*e^3))*_ + sqrt(b*x+c*x^2)/(d^2*e^4*(c*d-b*e)^2*(d+e*x)^2)+1/640*(B*d*_ + (128*c^4*d^4-336*b*c^3*d^3*e+248*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-_ + 15*b^4*e^4)+A*e*(32*c^4*d^4-64*b*c^3*d^3*e+12*b^2*c^2*d^2*e^2+_ + 20*b^3*c*d*e^3-15*b^4*e^4))*sqrt(b*x+c*x^2)/(d^3*e^4*(c*d-b*e)^3*_ + (d+e*x))-3/40*(B*d*(8*c*d-b*e)+A*e*(2*c*d+b*e)+2*e*(8*B*c*d-_ + 5*b*B*e+2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x)^4) +--R +--R +--R (2) +--R 5 6 4 5 5 5 +--R (- 15A b e + (30A b c - 15B b )d e )x +--R + +--R 5 5 4 5 2 4 4 +--R (- 75A b d e + (150A b c - 75B b )d e )x +--R + +--R 5 2 4 4 5 3 3 3 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 3 3 4 5 4 2 2 +--R (- 150A b d e + (300A b c - 150B b )d e )x +--R + +--R 5 4 2 4 5 5 5 5 +--R (- 75A b d e + (150A b c - 75B b )d e)x - 15A b d e +--R + +--R 4 5 6 +--R (30A b c - 15B b )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 30A b e + (- 40A b c + 30B b )d e + (- 24A b c + 20B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (128A b c - 496B b c )d e + (- 64A c + 672B b c )d e - 256B c d +--R * +--R 4 +--R x +--R + +--R 4 4 3 4 2 3 +--R 140A b d e + (- 188A b c + 140B b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 184A b c - 932B b c)d e + (672A b c + 1024B b c )d e +--R + +--R 4 3 5 +--R (- 320A c - 352B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 3 4 3 2 +--R 256A b d e + (- 932A b c - 256B b )d e +--R + +--R 2 2 3 4 3 2 2 5 +--R (1336A b c + 92B b c)d e + (- 480A b c - 16B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 +--R (- 140A b d e + (300A b c - 140B b )d e + (- 40A b c + 20B b c)d )x +--R + +--R 4 4 3 4 5 +--R - 30A b d e + (60A b c - 30B b )d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (1280b d e - 3840b c d e + 3840b c d e - 1280c d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (12800b d e - 38400b c d e + 38400b c d e - 12800c d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (6400b d e - 19200b c d e + 19200b c d e - 6400c d e)x + 1280b d e +--R + +--R 2 9 2 2 10 3 11 +--R - 3840b c d e + 3840b c d e - 1280c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 230 + +--S 231 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 232 + +--S 233 OF 765 +r0:=1/768*b*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*_ + (B*d+2*A*e))*x^2*(b*x+c*x^2)^(3/2)/c^3+1/384*(64*A*c^3*d^2-11*b^3*_ + B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*x*(b*x+_ + c*x^2)^(5/2)/c^3+1/2016*(162*A*c*e*(2*c*d-b*e)+B*(64*c^2*d^2-_ + 226*b*c*d*e+99*b^2*e^2))*(b*x+c*x^2)^(7/2)/c^3+1/9*B*(d+e*x)^2*_ + (b*x+c*x^2)^(7/2)/c-1/144*e*((7*b*B-18*A*c)*d-(4*B*c*d-11*b*B*e+_ + 18*A*c*e)*x)*(b*x+c*x^2)^(7/2)/c^2-5/32768*b^6*(64*A*c^3*d^2-_ + 11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(13/2)+5/32768*b^5*(64*A*c^3*_ + d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*_ + sqrt(b*x+c*x^2)/c^6-5/49152*b^4*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*_ + c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^5+_ + 1/12288*b^3*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-_ + 32*b*c^2*d*(B*d+2*A*e))*x^2*sqrt(b*x+c*x^2)/c^4+1/2048*b^2*_ + (64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*_ + (B*d+2*A*e))*x^3*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 8 9 2 7 2 8 +--R (- 5670A b c + 3465B b )e + (20160A b c - 11340B b c)d e +--R + +--R 6 3 7 2 2 +--R (- 20160A b c + 10080B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 8 2 8 8 7 2 8 7 +--R 229376B c e x + ((258048A c + 530432B b c )e + 516096B c d e)x +--R + +--R 7 2 6 2 8 7 +--R (608256A b c + 316416B b c )e + (589824A c + 1216512B b c )d e +--R + +--R 8 2 +--R 294912B c d +--R * +--R 6 +--R x +--R + +--R 2 6 3 5 2 7 2 6 +--R (373248A b c + 1280B b c )e + (1425408A b c + 746496B b c )d e +--R + +--R 8 7 2 +--R (344064A c + 712704B b c )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (2304A b c - 1408B b c )e + (909312A b c + 4608B b c )d e +--R + +--R 7 2 6 2 +--R (860160A b c + 454656B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (- 2592A b c + 1584B b c )e + (9216A b c - 5184B b c )d e +--R + +--R 2 6 3 5 2 +--R (580608A b c + 4608B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (3024A b c - 1848B b c )e + (- 10752A b c + 6048B b c )d e +--R + +--R 3 5 4 4 2 +--R (10752A b c - 5376B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 3780A b c + 2310B b c)e + (13440A b c - 7560B b c )d e +--R + +--R 4 4 5 3 2 +--R (- 13440A b c + 6720B b c )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 +--R (5670A b c - 3465B b )e + (- 20160A b c + 11340B b c)d e +--R + +--R 5 3 6 2 2 +--R (20160A b c - 10080B b c )d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 +-+ +--R 2064384c \|c +--R Type: Expression(Integer) +--E 233 + +--S 234 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 OF 765 +t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 235 + +--S 236 OF 765 +r0:=1/384*b*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^2*_ + (b*x+c*x^2)^(3/2)/c^2+1/192*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*_ + x*(b*x+c*x^2)^(5/2)/c^2+1/112*(2*B*c*d-9*b*B*e+16*A*c*e)*_ + (b*x+c*x^2)^(7/2)/c^2+1/8*B*(d+e*x)*(b*x+c*x^2)^(7/2)/c-_ + 5/16384*b^6*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*atanh(x*_ + sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+5/16384*b^5*(32*A*c^2*d+9*b^2*B*e-_ + 16*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^5-5/24576*b^4*(32*A*c^2*d+_ + 9*b^2*B*e-16*b*c*(B*d+A*e))*x*sqrt(b*x+c*x^2)/c^4+1/6144*b^3*_ + (32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^2*sqrt(b*x+c*x^2)/c^3+_ + 1/1024*b^2*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^3*_ + sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 7 8 6 2 7 +--R ((1680A b c - 945B b )e + (- 3360A b c + 1680B b c)d) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 7 7 7 6 7 6 +--R 43008B c e x + ((49152A c + 101376B b c )e + 49152B c d)x +--R + +--R 6 2 5 7 6 5 +--R ((118784A b c + 62208B b c )e + (57344A c + 118784B b c )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((75776A b c + 384B b c )e + (143360A b c + 75776B b c )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((768A b c - 432B b c )e + (96768A b c + 768B b c )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((- 896A b c + 504B b c )e + (1792A b c - 896B b c )d)x +--R + +--R 5 2 6 4 3 5 2 +--R ((1120A b c - 630B b c)e + (- 2240A b c + 1120B b c )d)x +--R + +--R 6 7 5 2 6 +--R (- 1680A b c + 945B b )e + (3360A b c - 1680B b c)d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 344064c \|c +--R Type: Expression(Integer) +--E 236 + +--S 237 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2) +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R Type: Expression(Integer) +--E 238 + +--S 239 OF 765 +r0:=-1/24*b*(b*B-2*A*c)*x^2*(b*x+c*x^2)^(3/2)/c-1/12*(b*B-2*A*c)*x*_ + (b*x+c*x^2)^(5/2)/c+1/7*B*(b*x+c*x^2)^(7/2)/c+5/1024*b^6*(b*B-_ + 2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-5/1024*b^5*(b*B-_ + 2*A*c)*sqrt(b*x+c*x^2)/c^4+5/1536*b^4*(b*B-2*A*c)*x*sqrt(b*x+_ + c*x^2)/c^3-1/384*b^3*(b*B-2*A*c)*x^2*sqrt(b*x+c*x^2)/c^2-1/64*b^2*_ + (b*B-2*A*c)*x^3*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 6 7 x\|c +--R (- 210A b c + 105B b )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 6 6 5 5 5 2 4 4 +--R 3072B c x + (3584A c + 7424B b c )x + (8960A b c + 4736B b c )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 +--R (6048A b c + 48B b c )x + (112A b c - 56B b c )x +--R + +--R 4 2 5 5 6 +--R (- 140A b c + 70B b c)x + 210A b c - 105B b +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 21504c \|c +--R Type: Expression(Integer) +--E 239 + +--S 240 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x) +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 241 + +--S 242 OF 765 +r0:=1/192*(4*A*c*e*(16*c^2*d^2-22*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-_ + 88*b*c^2*d^2*e+12*b^2*c*d*e^2+5*b^3*e^3)-2*c*e*(12*A*c*e*(2*c*d-_ + b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/_ + (c^2*e^4)-1/60*(12*B*c*d-5*b*B*e-12*A*c*e-10*B*c*e*x)*(b*x+_ + c*x^2)^(5/2)/(c*e^2)-1/512*(4*A*c*e*(256*c^5*d^5-640*b*c^4*d^4*e+_ + 480*b^2*c^3*d^3*e^2-80*b^3*c^2*d^2*e^3-10*b^4*c*d*e^4-3*b^5*e^5)-_ + B*(1024*c^6*d^6-2560*b*c^5*d^5*e+1920*b^2*c^4*d^4*e^2-320*b^3*_ + c^3*d^3*e^3-40*b^4*c^2*d^2*e^4-12*b^5*c*d*e^5-5*b^6*e^6))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(7/2)*e^7)-d^(5/2)*(B*d-A*e)*_ + (c*d-b*e)^(5/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7+1/1536*(3*(4*A*c*e*(128*c^4*d^4-_ + 288*b*c^3*d^3*e+176*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-3*b^4*e^4)-_ + B*(512*c^5*d^5-1152*b*c^4*d^4*e+704*b^2*c^3*d^3*e^2-40*b^3*c^2*_ + d^2*e^3-12*b^4*c*d*e^4-5*b^5*e^5))-2*c*e*(8*b*c*d*e*(2*c*d-b*e)*_ + (12*B*c*d-5*b*B*e-12*A*c*e)+(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2)*_ + (12*A*c*e*(2*c*d-b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2)))*x)*_ + sqrt(b*x+c*x^2)/(c^3*e^6) +--R +--R +--R (2) +--R 5 6 6 4 2 5 5 +--R (180A b c - 75B b )e + (600A b c - 180B b c)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (4800A b c - 600B b c )d e + (- 28800A b c - 4800B b c )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (38400A b c + 28800B b c )d e + (- 15360A c - 38400B b c )d e +--R + +--R 6 6 +--R 15360B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 3 4 2 3 3 2 +--R - 7680A b c d e + (15360A b c + 7680B b c )d e +--R + +--R 5 4 4 5 5 +--R (- 7680A c - 15360B b c )d e + 7680B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 5 6 5 5 4 6 5 5 4 +--R 1280B c e x + ((1536A c + 3200B b c )e - 1536B c d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (4032A b c + 2160B b c )e + (- 1920A c - 4032B b c )d e +--R + +--R 5 2 4 +--R 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2976A b c + 40B b c )e + (- 5440A b c - 2976B b c )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2560A c + 5440B b c )d e - 2560B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (120A b c - 50B b c)e + (- 4720A b c - 120B b c )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (8320A b c + 4720B b c )d e + (- 3840A c - 8320B b c )d e +--R + +--R 5 4 2 +--R 3840B c d e +--R * +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 180A b c + 75B b )e + (- 600A b c + 180B b c)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (10560A b c + 600B b c )d e + (- 17280A b c - 10560B b c )d e +--R + +--R 5 4 4 2 5 5 +--R (7680A c + 17280B b c )d e - 7680B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 7 +-+ +--R 7680c e \|c +--R Type: Expression(Integer) +--E 242 + +--S 243 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 244 + +--S 245 OF 765 +r0:=-1/48*(10*A*c*e*(8*c*d-7*b*e)-B*(96*c^2*d^2-92*b*c*d*e+3*b^2*e^2)+_ + 6*c*e*(12*B*c*d-b*B*e-10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(c*e^4)+_ + 1/5*(6*B*d-5*A*e+B*e*x)*(b*x+c*x^2)^(5/2)/(e^2*(d+e*x))+_ + 1/128*(10*A*c*e*(128*c^4*d^4-256*b*c^3*d^3*e+144*b^2*c^2*d^2*e^2-_ + 16*b^3*c*d*e^3-b^4*e^4)-B*(1536*c^5*d^5-3200*b*c^4*d^4*e+_ + 1920*b^2*c^3*d^3*e^2-240*b^3*c^2*d^2*e^3-20*b^4*c*d*e^4-3*b^5*e^5))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^7)+1/2*d^(3/2)*_ + (c*d-b*e)^(3/2)*(B*d*(12*c*d-7*b*e)-5*A*e*(2*c*d-b*e))*atanh(1/2*_ + (b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7-_ + 1/128*(10*A*c*e*(64*c^3*d^3-112*b*c^2*d^2*e+48*b^2*c*d*e^2-b^3*e^3)-_ + B*(768*c^4*d^4-1408*b*c^3*d^3*e+656*b^2*c^2*d^2*e^2-20*b^3*c*d*e^3-_ + 3*b^4*e^4)-2*c*e*(8*b*c*e*(6*B*d-5*A*e)*(2*c*d-b*e)-(12*B*c*d-b*B*e-_ + 10*A*c*e)*(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^6) +--R +--R +--R (2) +--R 4 5 6 3 2 4 5 +--R (- 150A b c + 45B b )e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 2 4 +--R (21600A b c + 3600B b c )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 38400A b c - 28800B b c )d e + (19200A c + 48000B b c )d e +--R + +--R 5 5 +--R - 23040B c d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (- 150A b c + 45B b )d e + (- 2400A b c + 300B b c)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (21600A b c + 3600B b c )d e + (- 38400A b c - 28800B b c )d e +--R + +--R 5 4 5 5 6 +--R (19200A c + 48000B b c )d e - 23040B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 4 3 2 2 2 3 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 3 2 4 4 +--R (9600A c + 18240B b c )d e - 11520B c d e +--R * +--R x +--R + +--R 2 2 2 3 3 2 2 3 2 +--R 4800A b c d e + (- 14400A b c - 6720B b c )d e +--R + +--R 4 3 4 4 5 +--R (9600A c + 18240B b c )d e - 11520B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 6 5 4 3 6 4 5 4 +--R 384B c e x + ((480A c + 1008B b c )e - 576B c d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (1360A b c + 744B b c )e + (- 800A c - 1712B b c )d e +--R + +--R 4 2 4 +--R 960B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (1180A b c + 30B b c)e + (- 2800A b c - 1616B b c )d e +--R + +--R 4 3 2 4 4 3 3 +--R (1600A c + 3520B b c )d e - 1920B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (150A b c - 45B b )e + (- 4100A b c - 270B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (8800A b c + 5560B b c )d e + (- 4800A c - 11040B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (150A b c - 45B b )d e + (- 7200A b c - 300B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (16800A b c + 9840B b c )d e + (- 9600A c - 21120B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 8 2 7 +-+ +--R (1920c e x + 1920c d e )\|c +--R Type: Expression(Integer) +--E 245 + +--S 246 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 247 + +--S 248 OF 765 +r0:=-5/24*(B*d*(24*c*d-13*b*e)-2*A*e*(8*c*d-3*b*e)+e*(6*B*c*d-b*B*e-_ + 4*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/4*(3*B*d-2*A*e+B*e*x)*_ + (b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)-5/64*(8*A*c*e*(32*c^3*d^3-48*b*c^2*_ + d^2*e+18*b^2*c*d*e^2-b^3*e^3)-B*(384*c^4*d^4-640*b*c^3*d^3*e+288*b^2*_ + c^2*d^2*e^2-24*b^3*c*d*e^3-b^4*e^4))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/_ + (c^(3/2)*e^7)+5/8*(A*e*(16*c^2*d^2-16*b*c*d*e+3*b^2*e^2)-B*d*(24*c^2*_ + d^2-28*b*c*d*e+7*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-b*e)/e^7+5/64*_ + (8*A*c*e*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2)-B*(192*c^3*d^3-272*b*c^2*_ + d^2*e+88*b^2*c*d*e^2-b^3*e^3)-2*c*e*(16*A*c*e*(2*c*d-b*e)-B*(48*c^2*_ + d^2-32*b*c*d*e+b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c*e^6) +--R +--R +--R (2) +--R 3 4 6 2 2 3 5 +--R (120A b c - 15B b )e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 4 2 +--R 5760B c d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 2 4 +--R (240A b c - 30B b )d e + (- 4320A b c - 720B b c)d e +--R + +--R 3 2 2 3 3 4 3 4 2 +--R (11520A b c + 8640B b c )d e + (- 7680A c - 19200B b c )d e +--R + +--R 4 5 +--R 11520B c d e +--R * +--R x +--R + +--R 3 4 2 4 2 2 3 3 3 +--R (120A b c - 15B b )d e + (- 2160A b c - 360B b c)d e +--R + +--R 3 2 2 4 2 4 3 5 +--R (5760A b c + 4320B b c )d e + (- 3840A c - 9600B b c )d e +--R + +--R 4 6 +--R 5760B c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 5 2 2 4 +--R - 360A b c e + (1920A b c + 840B b c)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 1920A c - 3360B b c )d e + 2880B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 2 3 +--R - 720A b c d e + (3840A b c + 1680B b c)d e +--R + +--R 3 2 3 2 3 4 +--R (- 3840A c - 6720B b c )d e + 5760B c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 2 +--R - 360A b c d e + (1920A b c + 840B b c)d e +--R + +--R 3 2 4 3 5 +--R (- 1920A c - 3360B b c )d e + 2880B c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 6 5 3 2 6 3 5 4 +--R 48B c e x + ((64A c + 136B b c )e - 96B c d e )x +--R + +--R 2 2 6 3 2 5 +--R (208A b c + 118B b c)e + (- 160A c - 352B b c )d e +--R + +--R 3 2 4 +--R 240B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 6 2 2 5 +--R (264A b c + 15B b )e + (- 880A b c - 556B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (640A c + 1480B b c )d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (960A b c + 30B b )d e + (- 3680A b c - 2090B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 6240B b c )d e - 4320B c d e +--R * +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (600A b c + 15B b )d e + (- 2400A b c - 1320B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (1920A c + 4080B b c )d e - 2880B c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 9 2 8 2 7 +-+ +--R (192c e x + 384c d e x + 192c d e )\|c +--R Type: Expression(Integer) +--E 248 + +--S 249 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 250 + +--S 251 OF 765 +r0:=-5/12*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+e*(4*B*c*d-b*B*e-2*A*c*e)*x)*_ + (b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(2*B*d-A*e+B*e*x)*_ + (b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)+5/8*(2*A*c*e*(16*c^2*d^2-_ + 16*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+24*b^2*c*d*e^2-_ + b^3*e^3))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^7*sqrt(c))+5/16*(B*d*_ + (64*c^3*d^3-112*b*c^2*d^2*e+56*b^2*c*d*e^2-7*b^3*e^3)-A*e*(32*c^3*d^3-_ + 48*b*c^2*d^2*e+18*b^2*c*d*e^2-b^3*e^3))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^7*sqrt(d)*sqrt(c*d-b*e))-_ + 5/8*(A*e*(16*c^2*d^2-12*b*c*d*e+b^2*e^2)-2*B*d*(16*c^2*d^2-_ + 16*b*c*d*e+3*b^2*e^2)+e*(4*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+_ + b^2*e^2))*x)*sqrt(b*x+c*x^2)/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 3 6 2 2 5 +--R (180A b c + 30B b )e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 2 4 3 3 3 +--R (960A c + 2400B b c )d e - 1920B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 3 3 3 4 2 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 2 2 3 3 +--R (540A b c + 90B b )d e + (- 2880A b c - 2160B b c)d e +--R + +--R 3 2 4 2 3 5 +--R (2880A c + 7200B b c )d e - 5760B c d e +--R * +--R x +--R + +--R 2 3 3 3 2 2 4 2 +--R (180A b c + 30B b )d e + (- 960A b c - 720B b c)d e +--R + +--R 3 2 5 3 6 +--R (960A c + 2400B b c )d e - 1920B c d +--R * +--R +-+ +--R +-----------+ +-+ x\|c +--R \|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 7 2 3 6 +--R - 15A b e + (270A b c + 105B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e +--R + +--R 3 4 3 +--R - 960B c d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 5 2 +--R - 2880B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R - 45A b d e + (810A b c + 315B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 2160A b c - 2520B b c)d e + (1440A c + 5040B b c )d e +--R + +--R 3 6 +--R - 2880B c d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R - 15A b d e + (270A b c + 105B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (- 720A b c - 840B b c)d e + (480A c + 1680B b c )d e - 960B c d +--R * +--R +-+ (b e - 2c d)x - b d +--R \|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 6 5 2 6 2 5 4 +--R 16B c e x + ((24A c + 52B b c)e - 48B c d e )x +--R + +--R 2 6 2 5 2 2 4 3 +--R ((108A b c + 66B b )e + (- 120A c - 276B b c)d e + 240B c d e )x +--R + +--R 2 6 2 5 +--R - 66A b e + (700A b c + 372B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 880A c - 1840B b c)d e + 1760B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 2 4 +--R - 80A b d e + (920A b c + 470B b )d e +--R + +--R 2 3 3 2 4 2 +--R (- 1200A c - 2440B b c)d e + 2400B c d e +--R * +--R x +--R + +--R 2 2 4 2 3 3 2 4 2 +--R - 30A b d e + (360A b c + 180B b )d e + (- 480A c - 960B b c)d e +--R + +--R 2 5 +--R 960B c d e +--R * +--R +----------+ +--R +-----------+ +-+ +-+ | 2 +--R \|- b e + c d \|c \|d \|c x + b x +--R / +--R 10 3 9 2 2 8 3 7 +-----------+ +-+ +-+ +--R (48e x + 144d e x + 144d e x + 48d e )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 251 + +--S 252 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|c x + b x +--R (1) ---------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 253 + +--S 254 OF 765 +r0:=-5/32*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*d^2-64*b*c*d*e+_ + 17*b^2*e^2))*(b*x+c*x^2)^(3/2)/(d*e^4*(c*d-b*e)*(d+e*x)^2)-5/24*_ + (B*d*(24*c*d-11*b*e)-A*e*(8*c*d-b*e)+6*e*(3*B*c*d-b*B*e-A*c*e)*x)*_ + (b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^3)+1/4*(3*B*d-A*e+2*B*e*x)*(b*x+_ + c*x^2)^(5/2)/(e^2*(d+e*x)^4)+5/128*(A*e*(128*c^4*d^4-256*b*c^3*d^3*e+_ + 144*b^2*c^2*d^2*e^2-16*b^3*c*d*e^3-b^4*e^4)-B*d*(384*c^4*d^4-_ + 896*b*c^3*d^3*e+672*b^2*c^2*d^2*e^2-168*b^3*c*d*e^3+7*b^4*e^4))*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(d^(3/2)*e^7*(c*d-b*e)^(3/2))-5/4*(4*A*c*e*(2*c*d-b*e)-_ + B*(24*c^2*d^2-20*b*c*d*e+3*b^2*e^2))*atanh(x*sqrt(c)/sqrt(b*x+_ + c*x^2))*sqrt(c)/e^7-5/64*(B*d*(192*c^3*d^3-304*b*c^2*d^2*e+120*_ + b^2*c*d*e^2-7*b^3*e^3)-A*e*(64*c^3*d^3-80*b*c^2*d^2*e+16*b^2*c*d*_ + e^2+b^3*e^3)-2*c*e*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*_ + d^2-64*b*c*d*e+17*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d*e^6*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 3 7 2 2 2 6 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 3 5 3 4 4 +--R (3840A c + 21120B b c )d e - 11520B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 6 2 2 3 5 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 4 4 3 5 3 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 5 2 2 4 4 +--R (11520A b c + 8640B b )d e + (- 34560A b c - 66240B b c)d e +--R + +--R 3 2 5 3 3 6 2 +--R (23040A c + 126720B b c )d e - 69120B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 2 2 5 3 +--R (7680A b c + 5760B b )d e + (- 23040A b c - 44160B b c)d e +--R + +--R 3 2 6 2 3 7 +--R (15360A c + 84480B b c )d e - 46080B c d e +--R * +--R x +--R + +--R 2 3 5 3 2 2 6 2 +--R (1920A b c + 1440B b )d e + (- 5760A b c - 11040B b c)d e +--R + +--R 3 2 7 3 8 +--R (3840A c + 21120B b c )d e - 11520B c d +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 9 3 4 8 +--R - 15A b e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 2 7 3 2 2 3 6 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 4 5 4 5 4 +--R (1920A c + 13440B b c )d e - 5760B c d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 3 6 3 2 2 4 5 +--R (8640A b c + 10080B b c)d e + (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 5 4 4 6 3 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R - 90A b d e + (- 1440A b c - 630B b )d e +--R + +--R 2 2 3 4 5 +--R (12960A b c + 15120B b c)d e +--R + +--R 3 2 2 5 4 4 3 6 3 +--R (- 23040A b c - 60480B b c )d e + (11520A c + 80640B b c )d e +--R + +--R 4 7 2 +--R - 34560B c d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R - 60A b d e + (- 960A b c - 420B b )d e +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (8640A b c + 10080B b c)d e + (- 15360A b c - 40320B b c )d e +--R + +--R 4 3 7 2 4 8 +--R (7680A c + 53760B b c )d e - 23040B c d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R - 15A b d e + (- 240A b c - 105B b )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (2160A b c + 2520B b c)d e + (- 3840A b c - 10080B b c )d e +--R + +--R 4 3 8 4 9 +--R (1920A c + 13440B b c )d e - 5760B c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 7 3 2 6 5 +--R (192B b c d e - 192B c d e )x +--R + +--R 2 2 7 3 2 2 6 +--R (384A b c + 864B b c)d e + (- 384A c - 2016B b c )d e +--R + +--R 3 3 5 +--R 1152B c d e +--R * +--R 4 +--R x +--R + +--R 3 8 2 3 7 +--R 30A b e + (- 1292A b c - 558B b )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (5232A b c + 8284B b c)d e + (- 4000A c - 19696B b c )d e +--R + +--R 3 4 4 +--R 12000B c d e +--R * +--R 3 +--R x +--R + +--R 3 7 2 3 2 6 +--R - 146A b d e + (- 2264A b c - 1022B b )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (10640A b c + 16392B b c)d e + (- 8320A c - 40240B b c )d e +--R + +--R 3 5 3 +--R 24960B c d e +--R * +--R 2 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R - 110A b d e + (- 1740A b c - 770B b )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (8480A b c + 12860B b c)d e + (- 6720A c - 32160B b c )d e +--R + +--R 3 6 2 +--R 20160B c d e +--R * +--R x +--R + +--R 3 3 5 2 3 4 4 +--R - 30A b d e + (- 480A b c - 210B b )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (2400A b c + 3600B b c)d e + (- 1920A c - 9120B b c )d e +--R + +--R 3 7 +--R 5760B c d e +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 12 2 11 4 2 11 3 10 3 +--R (384b d e - 384c d e )x + (1536b d e - 1536c d e )x +--R + +--R 3 10 4 9 2 4 9 5 8 5 8 +--R (2304b d e - 2304c d e )x + (1536b d e - 1536c d e )x + 384b d e +--R + +--R 6 7 +--R - 384c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 254 + +--S 255 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 OF 765 +t0:=(A+B*x)*(d+e*x)^3/sqrt(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 256 + +--S 257 OF 765 +r0:=1/64*(128*A*c^4*d^3+35*b^4*B*e^3+144*b^2*c^2*d*e*(B*d+A*e)-40*b^3*_ + c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/c^(9/2)+1/192*(8*A*c*e*(52*c^2*d^2-52*b*c*d*e+_ + 15*b^2*e^2)+B*(96*c^3*d^3-352*b*c^2*d^2*e+346*b^2*c*d*e^2-105*_ + b^3*e^3))*sqrt(b*x+c*x^2)/c^4+1/24*(6*B*c*d-7*b*B*e+8*A*c*e)*_ + (d+e*x)^2*sqrt(b*x+c*x^2)/c^2+1/4*B*(d+e*x)^3*sqrt(b*x+c*x^2)/c-_ + 1/96*e*(d*(12*b*B*c*d-48*A*c^2*d-7*b^2*B*e+8*A*b*c*e)-(40*A*c*e*_ + (2*c*d-b*e)+B*(24*c^2*d^2-64*b*c*d*e+35*b^2*e^2))*x)*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (- 120A b c + 105B b )e + (432A b c - 360B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 576A b c + 432B b c )d e + (384A c - 192B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B c e x + ((64A c - 56B b c )e + 192B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 80A b c + 70B b c)e + (288A c - 240B b c )d e + 288B c d e)x +--R + +--R 2 3 3 2 2 2 +--R (120A b c - 105B b )e + (- 432A b c + 360B b c)d e +--R + +--R 3 2 2 3 3 +--R (576A c - 432B b c )d e + 192B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 257 + +--S 258 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 OF 765 +t0:=(A+B*x)*(d+e*x)^2/sqrt(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 259 + +--S 260 OF 765 +r0:=1/8*(16*A*c^3*d^2-5*b^3*B*e^2+6*b^2*c*e*(2*B*d+A*e)-8*b*c^2*d*_ + (B*d+2*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/24*(18*A*c*_ + e*(2*c*d-b*e)+B*(16*c^2*d^2-34*b*c*d*e+15*b^2*e^2))*sqrt(b*x+_ + c*x^2)/c^3+1/3*B*(d+e*x)^2*sqrt(b*x+c*x^2)/c-1/12*e*((b*B-6*A*c)*_ + d-(4*B*c*d-5*b*B*e+6*A*c*e)*x)*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R (18A b c - 15B b )e + (- 48A b c + 36B b c)d e +--R + +--R 3 2 2 +--R (48A c - 24B b c )d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 2 2 +--R 8B c e x + ((12A c - 10B b c)e + 24B c d e)x +--R + +--R 2 2 2 2 2 +--R (- 18A b c + 15B b )e + (48A c - 36B b c)d e + 24B c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 24c \|c +--R Type: Expression(Integer) +--E 260 + +--S 261 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 OF 765 +t0:=(A+B*x)*(d+e*x)/sqrt(b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 262 + +--S 263 OF 765 +r0:=1/4*(8*A*c^2*d+3*b^2*B*e-4*b*c*(B*d+A*e))*atanh(x*sqrt(c)/sqrt(b*x+_ + c*x^2))/c^(5/2)+1/4*(2*B*c*d-3*b*B*e+4*A*c*e)*sqrt(b*x+c*x^2)/c^2+_ + 1/2*B*(d+e*x)*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 2 2 x\|c +--R ((- 4A b c + 3B b )e + (8A c - 4B b c)d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +-+ | 2 +--R (2B c e x + (4A c - 3B b)e + 4B c d)\|c \|c x + b x +--R / +--R 2 +-+ +--R 4c \|c +--R Type: Expression(Integer) +--E 263 + +--S 264 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 OF 765 +t0:=(A+B*x)/sqrt(b*x+c*x^2) +--R +--R +--R B x + A +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 265 + +--S 266 OF 765 +r0:=-(b*B-2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+B*sqrt(b*x+c*x^2)/c +--R +--R +--R +-+ +----------+ +--R x\|c +-+ | 2 +--R (2A c - B b)atanh(-------------) + B\|c \|c x + b x +--R +----------+ +--R | 2 +--R \|c x + b x +--R (2) ----------------------------------------------------- +--R +-+ +--R c\|c +--R Type: Expression(Integer) +--E 266 + +--S 267 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 OF 765 +t0:=(A+B*x)/((d+e*x)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ---------------------- +--R +----------+ +--R | 2 +--R (e x + d)\|c x + b x +--R Type: Expression(Integer) +--E 268 + +--S 269 OF 765 +r0:=2*B*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e*sqrt(c))-(B*d-A*e)*atanh(1/2*_ + (b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/_ + (e*sqrt(d)*sqrt(c*d-b*e)) +--R +--R +--R (2) +--R +-+ +--R +-----------+ +-+ x\|c +--R 2B\|- b e + c d \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-+ (b e - 2c d)x - b d +--R (- A e + B d)\|c atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +-----------+ +-+ +-+ +--R e\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 269 + +--S 270 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 OF 765 +t0:=(A+B*x)/((d+e*x)^2*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (e x + 2d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 271 + +--S 272 OF 765 +r0:=-1/2*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))+(B*d-A*e)*_ + sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 2 +--R ((- A b e + (2A c - B b)d e)x - A b d e + (2A c - B b)d ) +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +-----------+ +-+ | 2 +--R (2A e - 2B d)\|- b e + c d \|d \|c x + b x +--R / +--R 2 2 2 3 +-----------+ +-+ +--R ((2b d e - 2c d e)x + 2b d e - 2c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 272 + +--S 273 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 OF 765 +t0:=(A+B*x)/((d+e*x)^3*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +----------+ +--R 3 3 2 2 2 3 | 2 +--R (e x + 3d e x + 3d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 274 + +--S 275 OF 765 +r0:=1/8*(8*A*c^2*d^2-4*b*c*d*(B*d+2*A*e)+b^2*e*(B*d+3*A*e))*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*_ + (c*d-b*e)^(5/2))+1/2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ + (d+e*x)^2)-1/4*(3*A*e*(2*c*d-b*e)-B*d*(2*c*d+b*e))*sqrt(b*x+c*x^2)/_ + (d^2*(c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 +--R (- 3A b e + (8A b c - B b )d e + (- 8A c + 4B b c)d e )x +--R + +--R 2 3 2 2 2 2 3 +--R (- 6A b d e + (16A b c - 2B b )d e + (- 16A c + 8B b c)d e)x +--R + +--R 2 2 2 2 3 2 4 +--R - 3A b d e + (8A b c - B b )d e + (- 8A c + 4B b c)d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 2 2 +--R (6A b e + (- 12A c + 2B b)d e + 4B c d e)x + 10A b d e +--R + +--R 2 3 +--R (- 16A c - 2B b)d e + 8B c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (8b d e - 16b c d e + 8c d e )x + (16b d e - 32b c d e + 16c d e)x +--R + +--R 2 4 2 5 2 6 +--R 8b d e - 16b c d e + 8c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 275 + +--S 276 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 OF 765 +t0:=(A+B*x)/((d+e*x)^4*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R +----------+ +--R 4 4 3 3 2 2 2 3 4 | 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 277 + +--S 278 OF 765 +r0:=1/16*(16*A*c^3*d^3-8*b*c^2*d^2*(B*d+3*A*e)-b^3*e^2*(B*d+5*A*e)+_ + 2*b^2*c*d*e*(2*B*d+9*A*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+_ + 1/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^3)-_ + 1/12*(5*A*e*(2*c*d-b*e)-B*d*(4*c*d+b*e))*sqrt(b*x+c*x^2)/(d^2*_ + (c*d-b*e)^2*(d+e*x)^2)+1/24*(B*d*(8*c^2*d^2+10*b*c*d*e-3*b^2*e^2)-_ + A*e*(44*c^2*d^2-44*b*c*d*e+15*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*_ + (c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 3 6 2 3 5 2 2 2 4 +--R - 15A b e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 3 3 +--R (48A c - 24B b c )d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 2 4 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 3 +--R - 45A b d e + (162A b c - 9B b )d e +--R + +--R 2 2 4 2 3 2 5 +--R (- 216A b c + 36B b c)d e + (144A c - 72B b c )d e +--R * +--R x +--R + +--R 3 3 3 2 3 4 2 2 2 5 +--R - 15A b d e + (54A b c - 3B b )d e + (- 72A b c + 12B b c)d e +--R + +--R 3 2 6 +--R (48A c - 24B b c )d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 5 2 4 2 2 3 +--R 30A b e + (- 88A b c + 6B b )d e + (88A c - 20B b c)d e +--R + +--R 2 3 2 +--R - 16B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 80A b d e + (- 236A b c + 16B b )d e + (216A c - 28B b c)d e +--R + +--R 2 4 +--R - 48B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 66A b d e + (- 180A b c - 6B b )d e + (144A c + 24B b c)d e +--R + +--R 2 5 +--R - 48B c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (48b d e - 144b c d e + 144b c d e - 48c d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (144b d e - 432b c d e + 432b c d e - 144c d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (144b d e - 432b c d e + 432b c d e - 144c d e)x + 48b d e +--R + +--R 2 7 2 2 8 3 9 +--R - 144b c d e + 144b c d e - 48c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 278 + +--S 279 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 280 + +--S 281 OF 765 +r0:=3/4*e*(4*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-12*b*c*d*e+5*b^2*e^2))*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-2*(A*b-(b*B-2*A*c)*x)*_ + (d+e*x)^3/(b^2*sqrt(b*x+c*x^2))+1/4*e*(32*A*c^3*d^2-15*b^3*B*e^2-_ + 16*b*c^2*d*(B*d+2*A*e)+2*b^2*c*e*(17*B*d+6*A*e))*sqrt(b*x+c*x^2)/_ + (b^2*c^3)-2*(b*B-2*A*c)*e*(d+e*x)^2*sqrt(b*x+c*x^2)/(b^2*c)+_ + 1/2*e^2*(b*(b*B+4*A*c)*d+(8*A*c^2*d+5*b^2*B*e-4*b*c*(B*d+A*e))*x)*_ + sqrt(b*x+c*x^2)/(b^2*c^2) +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 2 2 2 +--R ((- 12A b c + 15B b )e + (24A b c - 36B b c)d e + 24B b c d e) +--R * +--R +----------+ +-+ +--R | 2 x\|c +--R \|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 3 3 2 2 3 3 2 2 2 2 +--R 2B b c e x + ((4A b c - 5B b c)e + 12B b c d e )x +--R + +--R 3 4 3 2 2 3 2 +--R (12A b c - 15B b )e + (- 24A b c + 36B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (24A b c - 24B b c )d e + (- 16A c + 8B b c )d +--R * +--R x +--R + +--R 3 3 +--R - 8A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 3 +-+ | 2 +--R 4b c \|c \|c x + b x +--R Type: Expression(Integer) +--E 281 + +--S 282 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 283 + +--S 284 OF 765 +r0:=e*(4*B*c*d-3*b*B*e+2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-_ + 2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*sqrt(b*x+c*x^2))+e*(8*A*c^2*d+_ + 3*b^2*B*e-4*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/(b^2*c^2)+2*e^2*(A*b-_ + (b*B-2*A*c)*x)*sqrt(b*x+c*x^2)/(b^2*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 2 3 2 2 | 2 x\|c +--R ((2A b c - 3B b )e + 4B b c d e)\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 +--R B b c e x +--R + +--R 2 3 2 2 2 +--R (- 2A b c + 3B b )e + (4A b c - 4B b c)d e +--R + +--R 3 2 2 +--R (- 4A c + 2B b c )d +--R * +--R x +--R + +--R 2 2 +--R - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 2 2 +-+ | 2 +--R b c \|c \|c x + b x +--R Type: Expression(Integer) +--E 284 + +--S 285 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 OF 765 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 286 + +--S 287 OF 765 +r0:=2*B*e*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)-2*(A*b-(b*B-2*A*c)*x)*_ + (d+e*x)/(b^2*sqrt(b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(b*x+c*x^2)/(b^2*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 2 | 2 x\|c +--R 2B b e\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 +-+ +--R (((2A b c - 2B b )e + (- 4A c + 2B b c)d)x - 2A b c d)\|c +--R / +--R +----------+ +--R 2 +-+ | 2 +--R b c\|c \|c x + b x +--R Type: Expression(Integer) +--E 287 + +--S 288 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 OF 765 +t0:=(A+B*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R B x + A +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 289 + +--S 290 OF 765 +r0:=-2*(A*b-(b*B-2*A*c)*x)/(b^2*sqrt(b*x+c*x^2)) +--R +--R +--R (- 4A c + 2B b)x - 2A b +--R (2) ----------------------- +--R +----------+ +--R 2 | 2 +--R b \|c x + b x +--R Type: Expression(Integer) +--E 290 + +--S 291 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 OF 765 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------- +--R +----------+ +--R 3 2 | 2 +--R (c e x + (b e + c d)x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 292 + +--S 293 OF 765 +r0:=-e*(B*d-A*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))-2*(A*b*(c*d-b*e)+_ + c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R +----------+ +--R 2 2 2 | 2 (b e - 2c d)x - b d +--R (A b e - B b d e)\|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +--R ((- 2A b c e + (4A c - 2B b c)d)x - 2A b e + 2A b c d)\|- b e + c d \|d +--R / +--R +----------+ +--R 3 2 2 +-----------+ +-+ | 2 +--R (b d e - b c d )\|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 293 + +--S 294 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------------------------- +--R +----------+ +--R 2 4 2 3 2 2 2 | 2 +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 295 + +--S 296 OF 765 +r0:=1/2*e*(3*A*e*(2*c*d-b*e)-B*d*(4*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-_ + b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-_ + b*e)^(5/2))-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*_ + (c*d-b*e)*(d+e*x)*sqrt(b*x+c*x^2))-e*(4*A*c^2*d^2-b^2*e*(B*d-_ + 3*A*e)-2*b*c*d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 3 4 2 3 3 2 2 2 3 3 +--R (3A b e + (- 6A b c - B b )d e + 4B b c d e )x + 3A b d e +--R + +--R 2 3 2 2 2 3 +--R (- 6A b c - B b )d e + 4B b c d e +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 3 2 2 2 +--R (- 6A b c e + (8A b c + 2B b c)d e + (- 8A c + 4B b c )d e)x +--R + +--R 3 3 2 3 2 2 2 +--R - 6A b e + (4A b c + 2B b )d e + 4A b c d e +--R + +--R 3 2 3 +--R (- 8A c + 4B b c )d +--R * +--R x +--R + +--R 3 2 2 2 2 3 +--R - 4A b d e + 8A b c d e - 4A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((2b d e - 4b c d e + 2b c d e)x + 2b d e - 4b c d e + 2b c d ) +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 296 + +--S 297 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 OF 765 +t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 298 + +--S 299 OF 765 +r0:=-3/8*e*(B*d*(8*c^2*d^2-4*b*c*d*e+b^2*e^2)-A*e*(16*c^2*d^2-16*b*c*d*e+_ + 5*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))-2*(A*b*(c*d-b*e)+_ + c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)^2*sqrt(b*x+_ + c*x^2))-1/2*e*(8*A*c^2*d^2-b^2*e*(B*d-5*A*e)-4*b*c*d*(B*d+2*A*e))*_ + sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^2)-1/4*e*(16*A*c^3*d^3-_ + 2*b^2*c*d*e*(5*B*d-19*A*e)+3*b^3*e^2*(B*d-5*A*e)-8*b*c^2*d^2*_ + (B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 4 6 3 4 5 2 2 3 2 4 +--R 15A b e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 30A b d e + (- 96A b c - 6B b )d e + (96A b c + 24B b c)d e +--R + +--R 2 2 4 2 +--R - 48B b c d e +--R * +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A b d e + (- 48A b c - 3B b )d e + (48A b c + 12B b c)d e +--R + +--R 2 2 5 +--R - 24B b c d e +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 5 2 2 3 4 +--R - 30A b c e + (76A b c + 6B b c)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 48A b c - 20B b c )d e + (32A c - 16B b c )d e +--R * +--R 3 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 30A b e + (26A b c + 6B b )d e + (80A b c - 10B b c)d e +--R + +--R 3 2 2 3 2 4 3 4 +--R (- 80A b c - 24B b c )d e + (64A c - 32B b c )d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 4 2 3 +--R - 50A b d e + (112A b c + 10B b )d e +--R + +--R 2 2 3 3 2 3 4 4 3 5 +--R (- 48A b c - 24B b c)d e - 16A b c d e + (32A c - 16B b c )d +--R * +--R x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 16A b d e + 48A b c d e - 48A b c d e + 16A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (16b d e - 48b c d e + 48b c d e - 16b c d e)x + 8b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 24b c d e + 24b c d e - 8b c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 299 + +--S 300 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 301 + +--S 302 OF 765 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^4/(b^2*(b*x+c*x^2)^(3/2))+e^3*(8*B*c*d-_ + 5*b*B*e+2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-8/3*_ + (d+e*x)^3*(b*(b*B*d-2*A*c*d+2*A*b*e)-(4*A*c^2*d-b^2*B*e-2*b*c*(B*d+_ + A*e))*x)/(b^4*sqrt(b*x+c*x^2))-1/3*e*(64*A*c^4*d^3-15*b^4*B*e^3-_ + 32*b*c^3*d^2*(B*d+3*A*e)+2*b^3*c*e^2*(11*B*d+3*A*e)+4*b^2*c^2*d*_ + e*(4*B*d+5*A*e))*sqrt(b*x+c*x^2)/(b^4*c^3)-8/3*e*(4*A*c^2*d-b^2*B*e-_ + 2*b*c*(B*d+A*e))*(d+e*x)^2*sqrt(b*x+c*x^2)/(b^4*c)+2/3*e^2*(b*d*_ + (4*b*B*c*d-8*A*c^2*d-b^2*B*e+10*A*b*c*e)-(16*A*c^3*d^2+5*b^3*B*e^2-_ + 2*A*b^2*c*e^2-8*b*c^2*d*(B*d+2*A*e))*x)*sqrt(b*x+c*x^2)/(b^4*c^2) +--R +--R +--R (2) +--R 4 2 5 4 4 2 3 2 +--R ((6A b c - 15B b c)e + 24B b c d e )x +--R + +--R 5 6 4 5 3 +--R ((6A b c - 15B b )e + 24B b c d e )x +--R * +--R +----------+ +-+ +--R | 2 x\|c +--R \|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 2 4 4 +--R 3B b c e x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 8A b c + 20B b c)e + (8A b c - 32B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (24A b c + 12B b c )d e + (- 64A b c + 16B b c )d e +--R + +--R 6 5 4 +--R (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 4 5 3 3 3 2 2 +--R (- 6A b c + 15B b )e - 24B b c d e + 36A b c d e +--R + +--R 2 4 3 3 3 5 2 4 4 +--R (- 96A b c + 24B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 4 3 3 4 3 3 4 +--R (- 24A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 4 2 5 3 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R Type: Expression(Integer) +--E 302 + +--S 303 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 304 + +--S 305 OF 765 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^3/(b^2*(b*x+c*x^2)^(3/2))+2*B*e^3*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-4/3*(d+e*x)^2*(b*(2*b*B*d-_ + 4*A*c*d+3*A*b*e)-(8*A*c^2*d-b^2*B*e-4*b*c*(B*d+A*e))*x)/(b^4*_ + sqrt(b*x+c*x^2))-2/3*e*(32*A*c^3*d^2+3*b^3*B*e^2-16*b*c^2*d*(B*d+_ + 2*A*e)+2*b^2*c*e*(2*B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^4*c^2)+4/3*e^2*_ + (b*(2*b*B*d-4*A*c*d+3*A*b*e)-(8*A*c^2*d-b^2*B*e-4*b*c*(B*d+A*e))*x)*_ + sqrt(b*x+c*x^2)/(b^4*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 4 3 2 5 3 | 2 x\|c +--R (6B b c e x + 6B b e x)\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2A b c - 8B b c)e + (12A b c + 6B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 48A b c + 12B b c )d e + (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 3 2 2 2 3 3 2 2 +--R - 6B b e + 18A b c d e + (- 72A b c + 18B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 3 2 3 3 2 3 +--R (- 18A b c d e + (12A b c - 6B b c )d )x - 2A b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 3 2 5 2 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R Type: Expression(Integer) +--E 305 + +--S 306 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 307 + +--S 308 OF 765 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*(b*x+c*x^2)^(3/2))-_ + 8/3*(b*B*d-2*A*c*d+A*b*e)*(b*d+(2*c*d-b*e)*x)/(b^4*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 3 +--R ((4A b c + 2B b )e + (- 32A b c + 8B b c)d e + (32A c - 16B b c )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (6A b e + (- 48A b c + 12B b )d e + (48A b c - 24B b c)d )x +--R + +--R 3 2 3 2 3 2 +--R (- 12A b d e + (12A b c - 6B b )d )x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 308 + +--S 309 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 OF 765 +t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 310 + +--S 311 OF 765 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))-_ + 4/3*(b*(2*b*B*d-4*A*c*d+A*b*e)-(8*A*c^2*d+b^2*B*e-_ + 4*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R 2 2 3 2 3 +--R ((- 16A b c + 4B b c)e + (32A c - 16B b c )d)x +--R + +--R 2 3 2 2 2 +--R ((- 24A b c + 6B b )e + (48A b c - 24B b c)d)x +--R + +--R 3 2 3 3 +--R (- 6A b e + (12A b c - 6B b )d)x - 2A b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 311 + +--S 312 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 OF 765 +t0:=(A+B*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R B x + A +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 313 + +--S 314 OF 765 +r0:=-2/3*(A*b-(b*B-2*A*c)*x)/(b^2*(b*x+c*x^2)^(3/2))+8/3*(b*B-2*A*c)/_ + (b^3*sqrt(b*x+c*x^2))-16/3*(b*B-2*A*c)*sqrt(b*x+c*x^2)/(b^4*x) +--R +--R +--R (2) +--R 3 2 3 2 2 2 2 3 3 +--R (32A c - 16B b c )x + (48A b c - 24B b c)x + (12A b c - 6B b )x - 2A b +--R --------------------------------------------------------------------------- +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 314 + +--S 315 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 OF 765 +t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^(5/2)) +--R +--R +--R B x + A +--R (1) -------------------------------------------------------------------- +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|c x + b x +--R Type: Expression(Integer) +--E 316 + +--S 317 OF 765 +r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ + (b*x+c*x^2)^(3/2))-e^3*(B*d-A*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+_ + 2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+3*b^2*e*(B*d-A*e)-4*b*c*d*(B*d+A*e))+_ + c*(16*A*c^3*d^3-3*b^3*e^2*(B*d-A*e)+2*b^2*c*d*e*(7*B*d+A*e)-_ + 8*b*c^2*d^2*(B*d+3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R +----------+ +--R 4 4 4 3 2 5 4 5 3 | 2 +--R ((- 3A b c e + 3B b c d e )x + (- 3A b e + 3B b d e )x)\|c x + b x +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 3 2 3 3 2 2 4 2 3 2 +--R 6A b c e + (4A b c - 6B b c )d e + (- 48A b c + 28B b c )d e +--R + +--R 5 4 3 +--R (32A c - 16B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 3 2 4 2 2 3 3 2 2 +--R 12A b c e + (6A b c - 12B b c)d e + (- 72A b c + 42B b c )d e +--R + +--R 4 2 3 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R + +--R 5 3 5 2 3 2 4 2 +--R 6A b e - 6B b d e + (- 18A b c + 12B b c)d e +--R + +--R 2 3 3 2 3 +--R (12A b c - 6B b c )d +--R * +--R x +--R + +--R 5 2 4 2 3 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 317 + +--S 318 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 319 + +--S 320 OF 765 +r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ + (d+e*x)*(b*x+c*x^2)^(3/2))-1/2*e^3*(B*d*(8*c*d-3*b*e)-5*A*e*_ + (2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+2/3*(b*(c*d-b*e)*_ + (8*A*c^2*d^2+b^2*e*(3*B*d-5*A*e)-2*b*c*d*(2*B*d+A*e))+c*(16*A*c^3*d^3-_ + b^3*e^2*(3*B*d-5*A*e)+2*b^2*c*d*e*(8*B*d-A*e)-8*b*c^2*d^2*(B*d+_ + 3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*(d+e*x)*sqrt(b*x+c*x^2))+1/3*e*_ + (32*A*c^4*d^4-2*b^3*c*d*e^2*(9*B*d-10*A*e)+3*b^4*e^3*(3*B*d-5*A*e)+_ + 4*b^2*c^2*d^2*e*(10*B*d+3*A*e)-16*b*c^3*d^3*(B*d+4*A*e))*sqrt(b*x+_ + c*x^2)/(b^4*d^3*(c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 5 4 2 2 4 3 +--R (- 15A b c e + (30A b c + 9B b c)d e - 24B b c d e )x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 15A b e + (15A b c + 9B b )d e + (30A b c - 15B b c)d e +--R + +--R 4 2 3 3 +--R - 24B b c d e +--R * +--R 2 +--R x +--R + +--R 6 5 5 6 2 4 5 3 3 +--R (- 15A b d e + (30A b c + 9B b )d e - 24B b c d e )x +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 2 5 3 3 4 2 4 +--R 30A b c e + (- 40A b c - 18B b c )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 24A b c + 36B b c )d e + (128A b c - 80B b c )d e +--R + +--R 6 5 4 +--R (- 64A c + 32B b c )d e +--R * +--R 4 +--R x +--R + +--R 5 5 4 2 5 4 +--R 60A b c e + (- 60A b c - 36B b c)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 76A b c + 60B b c )d e + (168A b c - 84B b c )d e +--R + +--R 5 2 4 4 6 5 5 +--R (32A b c - 32B b c )d e + (- 64A c + 32B b c )d +--R * +--R 3 +--R x +--R + +--R 6 5 6 4 4 2 5 2 3 +--R 30A b e - 18B b d e + (- 84A b c + 12B b c)d e +--R + +--R 3 3 4 2 3 2 2 4 3 3 4 +--R (12A b c + 36B b c )d e + (168A b c - 108B b c )d e +--R + +--R 5 2 4 5 +--R (- 96A b c + 48B b c )d +--R * +--R 2 +--R x +--R + +--R 6 4 5 6 2 3 +--R 20A b d e + (- 36A b c - 12B b )d e +--R + +--R 4 2 5 3 2 3 3 4 2 4 +--R (- 12A b c + 36B b c)d e + (52A b c - 36B b c )d e +--R + +--R 2 4 3 3 5 +--R (- 24A b c + 12B b c )d +--R * +--R x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 4A b d e + 12A b c d e - 12A b c d e + 4A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 320 + +--S 321 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R (A b e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 2 2 3 3 2 3 2 +--R (3A b d e + (3A c + 3B b)d e + B c d )x + (3A b d e + (A c + B b)d )x +--R + +--R 3 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 322 + +--S 323 OF 765 +r0:=-2/9*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(9/2)/e^4+2/11*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^4-2/13*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(13/2)/e^4+2/15*B*c*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 7 7 7 6 6 +--R 858B c e x + ((990A c + 990B b)e + 3036B c d e )x +--R + +--R 7 6 2 5 5 +--R (1170A b e + (3600A c + 3600B b)d e + 3708B c d e )x +--R + +--R 6 2 5 3 4 4 +--R (4420A b d e + (4580A c + 4580B b)d e + 1600B c d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (5980A b d e + (2120A c + 2120B b)d e + 10B c d e )x +--R + +--R 3 4 4 3 5 2 2 +--R (3120A b d e + (30A c + 30B b)d e - 12B c d e )x +--R + +--R 4 3 5 2 6 5 2 +--R (130A b d e + (- 40A c - 40B b)d e + 16B c d e)x - 260A b d e +--R + +--R 6 7 +--R (80A c + 80B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 323 + +--S 324 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 2 2 +--R (A b e + (2A c + 2B b)d e + B c d )x + (2A b d e + (A c + B b)d )x +--R + +--R 2 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 325 + +--S 326 OF 765 +r0:=-2/7*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(7/2)/e^4+2/9*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^4-2/11*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(11/2)/e^4+2/13*B*c*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 1386B c e x + ((1638A c + 1638B b)e + 3402B c d e )x +--R + +--R 6 5 2 4 4 +--R (2002A b e + (4186A c + 4186B b)d e + 2226B c d e )x +--R + +--R 5 2 4 3 3 3 +--R (5434A b d e + (2938A c + 2938B b)d e + 30B c d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (4290A b d e + (78A c + 78B b)d e - 36B c d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (286A b d e + (- 104A c - 104B b)d e + 48B c d e)x - 572A b d e +--R + +--R 5 6 +--R (208A c + 208B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 326 + +--S 327 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R (B c e x + ((A c + B b)e + B c d)x + (A b e + (A c + B b)d)x + A b d x) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 328 + +--S 329 OF 765 +r0:=-2/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(5/2)/e^4+2/7*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^4-2/9*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(9/2)/e^4+2/11*B*c*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 630B c e x + ((770A c + 770B b)e + 840B c d e )x +--R + +--R 5 4 2 3 3 +--R (990A b e + (1100A c + 1100B b)d e + 30B c d e )x +--R + +--R 4 2 3 3 2 2 +--R (1584A b d e + (66A c + 66B b)d e - 36B c d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (198A b d e + (- 88A c - 88B b)d e + 48B c d e)x - 396A b d e +--R + +--R 4 5 +--R (176A c + 176B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 329 + +--S 330 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)*sqrt(d+e*x) +--R +--R +--R 3 2 +-------+ +--R (1) (B c x + (A c + B b)x + A b x)\|e x + d +--R Type: Expression(Integer) +--E 331 + +--S 332 OF 765 +r0:=-2/3*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(3/2)/e^4+2/5*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^4-2/7*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B c e x + ((90A c + 90B b)e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126A b e + (18A c + 18B b)d e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (42A b d e + (- 24A c - 24B b)d e + 16B c d e)x - 84A b d e +--R + +--R 3 4 +--R (48A c + 48B b)d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 332 + +--S 333 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 334 + +--S 335 OF 765 +r0:=2/3*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^4-2/5*(3*B*c*d-_ + b*B*e-A*c*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-2*d*_ + (B*d-A*e)*(c*d-b*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + ((42A c + 42B b)e - 36B c d e )x +--R + +--R 3 2 2 2 +--R (70A b e + (- 56A c - 56B b)d e + 48B c d e)x - 140A b d e +--R + +--R 2 3 +--R (112A c + 112B b)d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 335 + +--S 336 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 336 + +)clear all + +--S 337 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 337 + +--S 338 OF 765 +r0:=-2/3*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+_ + 2*d*(B*d-A*e)*(c*d-b*e)/(e^4*sqrt(d+e*x))+2*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 6B c e x + ((10A c + 10B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (30A b e + (- 40A c - 40B b)d e + 48B c d e)x + 60A b d e +--R + +--R 2 3 +--R (- 80A c - 80B b)d e + 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 338 + +--S 339 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 339 + +)clear all + +--S 340 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 340 + +--S 341 OF 765 +r0:=2/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(3/2))+2/3*B*c*(d+e*x)^(3/2)/e^4-_ + 2*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))/(e^4*sqrt(d+e*x))-_ + 2*(3*B*c*d-b*B*e-A*c*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 2B c e x + ((6A c + 6B b)e - 12B c d e )x +--R + +--R 3 2 2 2 +--R (- 6A b e + (24A c + 24B b)d e - 48B c d e)x - 4A b d e +--R + +--R 2 3 +--R (16A c + 16B b)d e - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 341 + +--S 342 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + A b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 343 + +--S 344 OF 765 +r0:=2/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(5/2))-2/3*(B*d*(3*c*d-2*b*e)-_ + A*e*(2*c*d-b*e))/(e^4*(d+e*x)^(3/2))+2*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + ((- 30A c - 30B b)e + 180B c d e )x +--R + +--R 3 2 2 2 +--R (- 10A b e + (- 40A c - 40B b)d e + 240B c d e)x - 4A b d e +--R + +--R 2 3 +--R (- 16A c - 16B b)d e + 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 344 + +--S 345 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R ((2A b c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (A b e + (6A b c + 3B b )d e + (3A c + 6B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 3 4 +--R (3A b d e + (6A b c + 3B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 3 2 3 2 +--R (3A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 346 + +--S 347 OF 765 +r0:=-2/9*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(9/2)/e^6+2/11*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^6+_ + 2/13*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(15/2)/e^6-2/17*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(17/2)/e^6+2/19*B*c^2*(d+e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 2 9 9 2 9 2 8 8 +--R 218790B c e x + ((244530A c + 489060B b c)e + 746460B c d e )x +--R + +--R 2 9 2 8 +--R (554268A b c + 277134B b )e + (847704A c + 1695408B b c)d e +--R + +--R 2 2 7 +--R 866580B c d e +--R * +--R 7 +--R x +--R + +--R 2 9 2 8 +--R 319770A b e + (1961256A b c + 980628B b )d e +--R + +--R 2 2 7 2 3 6 +--R (1005708A c + 2011416B b c)d e + 345840B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 2 7 +--R 1162800A b d e + (2395368A b c + 1197684B b )d e +--R + +--R 2 3 6 2 4 5 +--R (414504A c + 829008B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 7 2 3 6 +--R 1479340A b d e + (1033600A b c + 516800B b )d e +--R + +--R 2 4 5 2 5 4 +--R (1330A c + 2660B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 4 5 +--R 684760A b d e + (6460A b c + 3230B b )d e +--R + +--R 2 5 4 2 6 3 +--R (- 1520A c - 3040B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 5 2 5 4 +--R 9690A b d e + (- 7752A b c - 3876B b )d e +--R + +--R 2 6 3 2 7 2 +--R (1824A c + 3648B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 4 2 6 3 +--R - 12920A b d e + (10336A b c + 5168B b )d e +--R + +--R 2 7 2 2 8 +--R (- 2432A c - 4864B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 6 3 2 7 2 +--R 25840A b d e + (- 20672A b c - 10336B b )d e +--R + +--R 2 8 2 9 +--R (4864A c + 9728B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Expression(Integer) +--E 347 + +--S 348 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R ((2A b c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 2 2 4 +--R (A b e + (4A b c + 2B b )d e + (A c + 2B b c)d )x +--R + +--R 2 2 2 3 2 2 2 +--R (2A b d e + (2A b c + B b )d )x + A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 349 + +--S 350 OF 765 +r0:=-2/7*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(7/2)/e^6+2/9*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^6+2/11*_ + (A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*(2*A*c*e*(2*c*d-b*e)-_ + B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(15/2)/e^6+2/17*B*c^2*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 2 8 8 2 8 2 7 7 +--R 90090B c e x + ((102102A c + 204204B b c)e + 210210B c d e )x +--R + +--R 2 8 2 7 +--R (235620A b c + 117810B b )e + (243474A c + 486948B b c)d e +--R + +--R 2 2 6 +--R 127050B c d e +--R * +--R 6 +--R x +--R + +--R 2 8 2 7 +--R 139230A b e + (578340A b c + 289170B b )d e +--R + +--R 2 2 6 2 3 5 +--R (152082A c + 304164B b c)d e + 630B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 2 6 +--R 355810A b d e + (378420A b c + 189210B b )d e +--R + +--R 2 3 5 2 4 4 +--R (1190A c + 2380B b c)d e - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 6 2 3 5 +--R 249730A b d e + (5100A b c + 2550B b )d e +--R + +--R 2 4 4 2 5 3 +--R (- 1360A c - 2720B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 4 4 +--R 6630A b d e + (- 6120A b c - 3060B b )d e +--R + +--R 2 5 3 2 6 2 +--R (1632A c + 3264B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 5 3 +--R - 8840A b d e + (8160A b c + 4080B b )d e +--R + +--R 2 6 2 2 7 +--R (- 2176A c - 4352B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 3 2 6 2 +--R 17680A b d e + (- 16320A b c - 8160B b )d e +--R + +--R 2 7 2 8 +--R (4352A c + 8704B b c)d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Expression(Integer) +--E 350 + +--S 351 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 2 2 3 +--R ((2A b c + B b )e + (A c + 2B b c)d)x + (A b e + (2A b c + B b )d)x +--R + +--R 2 2 +--R A b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 352 + +--S 353 OF 765 +r0:=-2/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(5/2)/e^6+2/7*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^6+2/9*(A*e*_ + (6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^(9/2)/e^6-2/11*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+_ + b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(13/2)/e^6+2/15*B*c^2*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 2 7 7 2 7 2 6 6 +--R 6006B c e x + ((6930A c + 13860B b c)e + 7392B c d e )x +--R + +--R 2 7 2 6 +--R (16380A b c + 8190B b )e + (8820A c + 17640B b c)d e +--R + +--R 2 2 5 +--R 126B c d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 10010A b e + (21840A b c + 10920B b )d e +--R + +--R 2 2 5 2 3 4 +--R (210A c + 420B b c)d e - 140B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 14300A b d e + (780A b c + 390B b )d e +--R + +--R 2 3 4 2 4 3 +--R (- 240A c - 480B b c)d e + 160B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 858A b d e + (- 936A b c - 468B b )d e + (288A c + 576B b c)d e +--R + +--R 2 5 2 +--R - 192B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 +--R - 1144A b d e + (1248A b c + 624B b )d e +--R + +--R 2 5 2 2 6 +--R (- 384A c - 768B b c)d e + 256B c d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 2288A b d e + (- 2496A b c - 1248B b )d e + (768A c + 1536B b c)d e +--R + +--R 2 7 +--R - 512B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 353 + +--S 354 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +-------+ +--R (1) (B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x )\|e x + d +--R Type: Expression(Integer) +--E 355 + +--S 356 OF 765 +r0:=-2/3*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(3/2)/e^6+2/5*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^6+2/7*(A*e*_ + (6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_ + (d+e*x)^(7/2)/e^6-2/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(9/2)/e^6-2/11*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + ((8190A c + 16380B b c)e + 630B c d e )x +--R + +--R 2 6 2 5 +--R (20020A b c + 10010B b )e + (910A c + 1820B b c)d e +--R + +--R 2 2 4 +--R - 700B c d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 12870A b e + (2860A b c + 1430B b )d e +--R + +--R 2 2 4 2 3 3 +--R (- 1040A c - 2080B b c)d e + 800B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 +--R 2574A b d e + (- 3432A b c - 1716B b )d e +--R + +--R 2 3 3 2 4 2 +--R (1248A c + 2496B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R - 3432A b d e + (4576A b c + 2288B b )d e +--R + +--R 2 4 2 2 5 +--R (- 1664A c - 3328B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 6864A b d e + (- 9152A b c - 4576B b )d e + (3328A c + 6656B b c)d e +--R + +--R 2 6 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 356 + +--S 357 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 358 + +--S 359 OF 765 +r0:=2/3*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^6+_ + 2/5*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(7/2)/e^6-2/9*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(9/2)/e^6+2/11*B*c^2*(d+e*x)^(11/2)/e^6-2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + ((770A c + 1540B b c)e - 700B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A b c + 990B b )e + (- 880A c - 1760B b c)d e + 800B c d e )x +--R + +--R 2 5 2 4 +--R 1386A b e + (- 2376A b c - 1188B b )d e +--R + +--R 2 2 3 2 3 2 +--R (1056A c + 2112B b c)d e - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 1848A b d e + (3168A b c + 1584B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1408A c - 2816B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 3696A b d e + (- 6336A b c - 3168B b )d e + (2816A c + 5632B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 359 + +--S 360 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 361 + +--S 362 OF 765 +r0:=2/3*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+2*d^2*(B*d-A*e)*_ + (c*d-b*e)^2/(e^6*sqrt(d+e*x))+2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-_ + 2*A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + ((90A c + 180B b c)e - 100B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((252A b c + 126B b )e + (- 144A c - 288B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 504A b c - 252B b )d e + (288A c + 576B b c)d e +--R + +--R 2 3 2 +--R - 320B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R - 840A b d e + (2016A b c + 1008B b )d e +--R + +--R 2 3 2 2 4 +--R (- 1152A c - 2304B b c)d e + 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 1680A b d e + (4032A b c + 2016B b )d e + (- 2304A c - 4608B b c)d e +--R + +--R 2 5 +--R 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 362 + +--S 363 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 364 + +--S 365 OF 765 +r0:=2/3*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(3/2))-2/3*(2*A*c*e*(2*c*d-_ + b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-_ + 2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*sqrt(d+e*x))+_ + 2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + ((42A c + 84B b c)e - 60B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((140A b c + 70B b )e + (- 112A c - 224B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 210A b e + (- 840A b c - 420B b )d e + (672A c + 1344B b c)d e +--R + +--R 2 3 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R 840A b d e + (- 3360A b c - 1680B b )d e +--R + +--R 2 3 2 2 4 +--R (2688A c + 5376B b c)d e - 3840B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 560A b d e + (- 2240A b c - 1120B b )d e + (1792A c + 3584B b c)d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 365 + +--S 366 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R B c x + (A c + 2B b c)x + (2A b c + B b )x + A b x +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 367 + +--S 368 OF 765 +r0:=2/5*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(5/2))-2/3*d*(c*d-b*e)*_ + (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^(3/2))-2/3*c*_ + (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6-_ + 2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_ + 3*b^2*e^2))/(e^6*sqrt(d+e*x))-2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + ((10A c + 20B b c)e - 20B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((60A b c + 30B b )e + (- 80A c - 160B b c)d e + 160B c d e )x +--R + +--R 2 5 2 4 2 2 3 +--R - 30A b e + (360A b c + 180B b )d e + (- 480A c - 960B b c)d e +--R + +--R 2 3 2 +--R 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R - 40A b d e + (480A b c + 240B b )d e + (- 640A c - 1280B b c)d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R - 16A b d e + (192A b c + 96B b )d e + (- 256A c - 512B b c)d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 368 + +--S 369 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 370 + +--S 371 OF 765 +r0:=2/3*(B*(c*d-b*e)^2+A*c*e*(2*c*d-b*e))*(d+e*x)^(3/2)/c^3+2/5*_ + (B*c*d-b*B*e+A*c*e)*(d+e*x)^(5/2)/c^2+2/7*B*(d+e*x)^(7/2)/c-_ + 2*A*d^(7/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(7/2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(9/2))+2*(B*(c*d-b*e)^3+_ + A*c*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/c^4 +--R +--R +--R (2) +--R 3 4 3 2 2 3 2 +--R (- 210A b c + 210B b )e + (630A b c - 630B b c)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 630A b c + 630B b c )d e + (210A c - 210B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 4 3 +-+ +-+ \|e x + d +--R - 210A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 3 3 2 2 3 3 2 2 +--R 30B b c e x + ((42A b c - 42B b c )e + 132B b c d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 70A b c + 70B b c)e + (224A b c - 224B b c )d e +--R + +--R 3 2 +--R 244B b c d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A b c - 210B b )e + (- 700A b c + 700B b c)d e +--R + +--R 3 2 2 2 3 3 +--R (812A b c - 812B b c )d e + 352B b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 4 +-+ +--R 105b c \|c +--R Type: Expression(Integer) +--E 371 + +--S 372 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 373 + +--S 374 OF 765 +r0:=2/3*(B*c*d-b*B*e+A*c*e)*(d+e*x)^(3/2)/c^2+2/5*B*(d+e*x)^(5/2)/c-_ + 2*A*d^(5/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(5/2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(7/2))+2*(B*(c*d-b*e)^2+_ + A*c*e*(2*c*d-b*e))*sqrt(d+e*x)/c^3 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R (30A b c - 30B b )e + (- 60A b c + 60B b c)d e +--R + +--R 3 2 2 +--R (30A c - 30B b c )d +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 2 +-+ +-+ \|e x + d +--R - 30A c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 2 2 2 2 +--R 6B b c e x + ((10A b c - 10B b c)e + 22B b c d e)x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A b c + 30B b )e + (70A b c - 70B b c)d e + 46B b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 +-+ +--R 15b c \|c +--R Type: Expression(Integer) +--E 374 + +--S 375 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 376 + +--S 377 OF 765 +r0:=2/3*B*(d+e*x)^(3/2)/c-2*A*d^(3/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-_ + 2*(b*B-A*c)*(c*d-b*e)^(3/2)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*c^(5/2))+2*(B*c*d-b*B*e+A*c*e)*sqrt(d+e*x)/c^2 +--R +--R +--R (2) +--R 2 2 +-----------+ +--R ((- 6A b c + 6B b )e + (6A c - 6B b c)d)\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 +-+ +-+ \|e x + d +--R - 6A c d\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 +-+ +-------+ +--R (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|c \|e x + d +--R / +--R 2 +-+ +--R 3b c \|c +--R Type: Expression(Integer) +--E 377 + +--S 378 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 379 + +--S 380 OF 765 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b*c^(3/2))+2*B*sqrt(d+e*x)/c +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R (2A c - 2B b)\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-+ +-+ \|e x + d +-+ +-------+ +--R - 2A c\|c \|d atanh(----------) + 2B b\|c \|e x + d +--R +-+ +--R \|d +--R / +--R +-+ +--R b c\|c +--R Type: Expression(Integer) +--E 380 + +--S 381 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 OF 765 +t0:=(A+B*x)/((b*x+c*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ---------------------- +--R 2 +-------+ +--R (c x + b x)\|e x + d +--R Type: Expression(Integer) +--E 382 + +--S 383 OF 765 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*sqrt(d))-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b*sqrt(c)*sqrt(c*d-b*e)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R (2A c - 2B b)\|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R - 2A\|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R / +--R +-----------+ +-+ +-+ +--R b\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 383 + +--S 384 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------ +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 385 + +--S 386 OF 765 +r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(3/2))-2*(b*B-A*c)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b*(c*d-b*e)^(3/2))+_ + 2*(B*d-A*e)/(d*(c*d-b*e)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R (- 2A c + 2B b)d\|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R (- 2A b e + 2A c d)\|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R +-----------+ +-+ +--R (2A b e - 2B b d)\|- b e + c d \|d +--R / +--R 2 2 +-----------+ +-+ +-------+ +--R (b d e - b c d )\|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 386 + +--S 387 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 OF 765 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------------ +--R 2 4 2 3 2 2 2 +-------+ +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 388 + +--S 389 OF 765 +r0:=2/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(3/2))-2*A*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b*d^(5/2))-2*c^(3/2)*(b*B-A*c)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*(c*d-b*e)^(5/2))+2*(B*c*d^2-A*e*(2*c*d-b*e))/(d^2*_ + (c*d-b*e)^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 3 +-+ +-+ +-------+ +--R ((6A c - 6B b c)d e x + (6A c - 6B b c)d )\|c \|d \|e x + d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 2 2 2 2 2 +--R (- 6A b e + 12A b c d e - 6A c d e)x - 6A b d e + 12A b c d e +--R + +--R 2 3 +--R - 6A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 2 +--R (6A b e - 12A b c d e + 6B b c d e)x + 8A b d e +--R + +--R 2 2 3 +--R (- 14A b c - 2B b )d e + 8B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 389 + +--S 390 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 OF 765 +t0:=(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 391 + +--S 392 OF 765 +r0:=2/5*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(5/2))+2/3*(B*c*d^2-A*e*(2*c*d-_ + b*e))/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-2*A*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b*d^(7/2))-2*c^(5/2)*(b*B-A*c)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b*(c*d-b*e)^(7/2))+2*(B*c^2*d^3-A*e*(3*c^2*d^2-_ + 3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 2 2 3 2 4 +--R (- 30A c + 30B b c )d e x + (- 60A c + 60B b c )d e x +--R + +--R 3 2 5 +--R (- 30A c + 30B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30A b e + 90A b c d e - 90A b c d e + 30A c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 +--R (- 60A b d e + 180A b c d e - 180A b c d e + 60A c d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R - 30A b d e + 90A b c d e - 90A b c d e + 30A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 +--R (30A b e - 90A b c d e + 90A b c d e - 30B b c d e )x +--R + +--R 3 4 2 2 3 2 2 3 2 +--R 70A b d e - 210A b c d e + (200A b c + 10B b c)d e +--R + +--R 2 4 +--R - 70B b c d e +--R * +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 4 +--R 46A b d e + (- 132A b c - 6B b )d e + (116A b c + 22B b c)d e +--R + +--R 2 5 +--R - 46B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 392 + +--S 393 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 OF 765 +t0:=(A+B*x)/((d+e*x)^(9/2)*(b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 6 4 3 5 3 2 2 4 +--R c e x + (b e + 4c d e )x + (4b d e + 6c d e )x +--R + +--R 2 2 3 3 3 4 2 4 +--R (6b d e + 4c d e)x + (4b d e + c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 394 + +--S 395 OF 765 +r0:=2/7*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(7/2))+2/5*(B*c*d^2-A*e*(2*c*d-b*e))/_ + (d^2*(c*d-b*e)^2*(d+e*x)^(5/2))+2/3*(B*c^2*d^3-A*e*(3*c^2*d^2-_ + 3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x)^(3/2))-_ + 2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(9/2))-2*c^(7/2)*(b*B-A*c)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*(c*d-b*e)^(9/2))+_ + 2*(B*c^3*d^4-A*e*(4*c^3*d^3-6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))/_ + (d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 3 3 4 3 5 2 2 +--R (210A c - 210B b c )d e x + (630A c - 630B b c )d e x +--R + +--R 4 3 6 4 3 7 +--R (630A c - 630B b c )d e x + (210A c - 210B b c )d +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 210A b e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 4 3 +--R - 210A c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 +--R - 630A b d e + 2520A b c d e - 3780A b c d e + 2520A b c d e +--R + +--R 4 5 2 +--R - 630A c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 +--R - 630A b d e + 2520A b c d e - 3780A b c d e + 2520A b c d e +--R + +--R 4 6 +--R - 630A c d e +--R * +--R x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 +--R - 210A b d e + 840A b c d e - 1260A b c d e + 840A b c d e +--R + +--R 4 7 +--R - 210A c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 210A b e - 840A b c d e + 1260A b c d e - 840A b c d e +--R + +--R 3 4 3 +--R 210B b c d e +--R * +--R 3 +--R x +--R + +--R 4 6 3 2 5 2 2 3 4 +--R 700A b d e - 2800A b c d e + 4200A b c d e +--R + +--R 3 2 2 4 3 3 5 2 +--R (- 2730A b c - 70B b c )d e + 700B b c d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 3 3 4 2 2 3 4 3 +--R 812A b d e - 3248A b c d e + (4830A b c + 42B b c)d e +--R + +--R 3 2 2 5 2 3 6 +--R (- 3024A b c - 224B b c )d e + 812B b c d e +--R * +--R x +--R + +--R 4 3 4 3 4 4 3 +--R 352A b d e + (- 1378A b c - 30B b )d e +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (1980A b c + 132B b c)d e + (- 1164A b c - 244B b c )d e +--R + +--R 3 7 +--R 352B b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 4 8 3 3 +--R (105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d e )x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 315b d e - 1260b c d e + 1890b c d e - 1260b c d e +--R + +--R 4 9 2 +--R 315b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 4 10 +--R (315b d e - 1260b c d e + 1890b c d e - 1260b c d e + 315b c d e)x +--R + +--R 5 7 4 4 8 3 3 2 9 2 2 3 10 4 11 +--R 105b d e - 420b c d e + 630b c d e - 420b c d e + 105b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 395 + +--S 396 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 OF 765 +t0:=(A+B*x)*(d+e*x)^(9/2)/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 397 + +--S 398 OF 765 +r0:=1/3*e*(6*A*c^3*d^2-7*b^3*B*e^2-3*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ + (12*B*d+5*A*e))*(d+e*x)^(3/2)/(b^2*c^3)+1/5*e*(10*A*c^2*d+7*b^2*B*e-_ + 5*b*c*(B*d+A*e))*(d+e*x)^(5/2)/(b^2*c^2)+(b*B-2*A*c)*(c*d-b*e)*_ + (d+e*x)^(7/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(9/2)/(b*x*(b+c*x))-_ + d^(7/2)*(2*b*B*d-4*A*c*d+9*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/b^3-_ + (c*d-b*e)^(7/2)*(4*A*c^2*d-7*b^2*B*e-b*c*(2*B*d-5*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(9/2))+_ + e*(2*A*c^4*d^3+7*b^4*B*e^3-b*c^3*d^2*(B*d+3*A*e)-b^3*c*e^2*_ + (19*B*d+5*A*e)+b^2*c^2*d*e*(15*B*d+11*A*e))*sqrt(d+e*x)/(b^2*c^4) +--R +--R +--R (2) +--R 4 2 5 4 3 3 4 2 3 +--R (75A b c - 105B b c)e + (- 165A b c + 285B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (45A b c - 225B b c )d e + (105A b c + 15B b c )d e +--R + +--R 6 5 4 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (75A b c - 105B b )e + (- 165A b c + 285B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (45A b c - 225B b c )d e + (105A b c + 15B b c )d e +--R + +--R 5 2 4 4 +--R (- 60A b c + 30B b c )d +--R * +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 3 6 5 4 2 +--R (- 135A b c d e + (60A c - 30B b c )d )x +--R + +--R 2 4 3 5 2 4 4 +--R (- 135A b c d e + (60A b c - 30B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 3 3 +--R 6B b c e x + ((10A b c - 14B b c )e + 42B b c d e )x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 50A b c + 70B b c)e + (130A b c - 218B b c )d e +--R + +--R 3 3 2 2 +--R 216B b c d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 75A b c + 105B b )e + (190A b c - 320B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 90A b c + 306B b c )d e + (60A b c - 60B b c )d e +--R + +--R 5 2 4 4 +--R (- 30A b c + 15B b c )d +--R * +--R x +--R + +--R 2 4 4 +--R - 15A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 5 2 4 4 +-+ +--R (15b c x + 15b c x)\|c +--R Type: Expression(Integer) +--E 398 + +--S 399 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 400 + +--S 401 OF 765 +r0:=1/3*e*(6*A*c^2*d+5*b^2*B*e-3*b*c*(B*d+A*e))*(d+e*x)^(3/2)/(b^2*c^2)+_ + (b*B-2*A*c)*(c*d-b*e)*(d+e*x)^(5/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(7/2)/_ + (b*x*(b+c*x))-d^(5/2)*(2*b*B*d-4*A*c*d+7*A*b*e)*atanh(sqrt(d+e*x)/_ + sqrt(d))/b^3+(c*d-b*e)^(5/2)*(2*b*B*c*d-4*A*c^2*d+5*b^2*B*e-_ + 3*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(7/2))+_ + e*(2*A*c^3*d^2-5*b^3*B*e^2-b*c^2*d*(B*d+2*A*e)+b^2*c*e*(8*B*d+_ + 3*A*e))*sqrt(d+e*x)/(b^2*c^3) +--R +--R +--R (2) +--R 3 2 4 3 2 3 3 2 2 +--R (- 9A b c + 15B b c)e + (6A b c - 24B b c )d e +--R + +--R 4 2 3 2 5 4 3 +--R (15A b c + 3B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 9A b c + 15B b )e + (6A b c - 24B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (15A b c + 3B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 2 5 4 3 2 +--R (- 21A b c d e + (12A c - 6B b c )d )x +--R + +--R 2 3 2 4 2 3 3 +--R (- 21A b c d e + (12A b c - 6B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 3 3 3 2 4 3 3 2 2 2 +--R 2B b c e x + ((6A b c - 10B b c)e + 20B b c d e )x +--R + +--R 4 5 3 3 2 4 2 +--R (9A b c - 15B b )e + (- 9A b c + 29B b c)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (9A b c - 9B b c )d e + (- 6A b c + 3B b c )d +--R * +--R x +--R + +--R 2 3 3 +--R - 3A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 4 2 4 3 +-+ +--R (3b c x + 3b c x)\|c +--R Type: Expression(Integer) +--E 401 + +--S 402 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 403 + +--S 404 OF 765 +r0:=(b*B-2*A*c)*(c*d-b*e)*(d+e*x)^(3/2)/(b^2*c*(b+c*x))-A*(d+e*x)^(5/2)/_ + (b*x*(b+c*x))-d^(3/2)*(2*b*B*d-4*A*c*d+5*A*b*e)*atanh(sqrt(d+e*x)/_ + sqrt(d))/b^3-(c*d-b*e)^(3/2)*(4*A*c^2*d-3*b^2*B*e-b*c*(2*B*d-A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(5/2))+e*(2*A*c^2*d+_ + 3*b^2*B*e-b*c*(B*d+A*e))*sqrt(d+e*x)/(b^2*c^2) +--R +--R +--R (2) +--R 2 2 3 2 3 2 2 +--R (A b c - 3B b c)e + (3A b c + B b c )d e +--R + +--R 4 3 2 +--R (- 4A c + 2B b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 3 2 2 2 +--R ((A b c - 3B b )e + (3A b c + B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 4 3 2 2 +--R (- 5A b c d e + (4A c - 2B b c )d )x +--R + +--R 2 2 3 2 2 2 +--R (- 5A b c d e + (4A b c - 2B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 +--R 2B b c e x +--R + +--R 3 4 2 2 2 3 +--R (- A b c + 3B b )e + (2A b c - 2B b c)d e +--R + +--R 3 2 2 2 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 2 2 2 +--R - A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 3 2 4 2 +-+ +--R (b c x + b c x)\|c +--R Type: Expression(Integer) +--E 404 + +--S 405 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 406 + +--S 407 OF 765 +r0:=-A*(d+e*x)^(3/2)/(b*x*(b+c*x))-(2*b*B*d-4*A*c*d+3*A*b*e)*_ + atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b^3-(4*A*c^2*d-b^2*B*e-_ + b*c*(2*B*d+A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*_ + sqrt(c*d-b*e)/(b^3*c^(3/2))+(b*B-2*A*c)*(c*d-b*e)*sqrt(d+e*x)/_ + (b^2*c*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 +--R ((A b c + B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((A b c + B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 2 +--R (- 3A b c e + (4A c - 2B b c )d)x +--R + +--R 2 2 2 +--R (- 3A b c e + (4A b c - 2B b c)d)x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 +-+ +-------+ +--R (((A b c - B b )e + (- 2A b c + B b c)d)x - A b c d)\|c \|e x + d +--R / +--R 3 2 2 4 +-+ +--R (b c x + b c x)\|c +--R Type: Expression(Integer) +--E 407 + +--S 408 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 409 + +--S 410 OF 765 +r0:=-(2*b*B*d-4*A*c*d+A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*sqrt(d))+_ + (2*b*B*c*d-4*A*c^2*d-b^2*B*e+3*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b^3*sqrt(c)*sqrt(c*d-b*e))+(b*B-2*A*c)*sqrt(d+e*x)/_ + (b^2*(b+c*x))-A*sqrt(d+e*x)/(b*x*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 +--R ((3A b c - B b c)e + (- 4A c + 2B b c )d)x +--R + +--R 2 3 2 2 +--R ((3A b c - B b )e + (- 4A b c + 2B b c)d)x +--R * +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 +--R ((- A b c e + (4A c - 2B b c)d)x + (- A b e + (4A b c - 2B b )d)x) +--R * +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 +-----------+ +-+ +-+ +-------+ +--R ((- 2A b c + B b )x - A b )\|- b e + c d \|c \|d \|e x + d +--R / +--R 3 2 4 +-----------+ +-+ +-+ +--R (b c x + b x)\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 410 + +--S 411 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 OF 765 +t0:=(A+B*x)/((b*x+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (c x + 2b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 412 + +--S 413 OF 765 +r0:=-(2*b*B*d-4*A*c*d-A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(3/2))+_ + (2*b*B*c*d-4*A*c^2*d-3*b^2*B*e+5*A*b*c*e)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))*sqrt(c)/(b^3*(c*d-b*e)^(3/2))+c*(b*B*d-2*A*c*d+A*b*e)*_ + sqrt(d+e*x)/(b^2*d*(c*d-b*e)*(b+c*x))-A*sqrt(d+e*x)/(b*d*x*(b+c*x)) +--R +--R +--R (2) +--R 2 2 3 2 2 2 +--R ((- 5A b c + 3B b c)d e + (4A c - 2B b c )d )x +--R + +--R 2 3 2 2 2 +--R ((- 5A b c + 3B b )d e + (4A b c - 2B b c)d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 2 3 2 2 2 +--R (A b c e + (3A b c - 2B b c)d e + (- 4A c + 2B b c )d )x +--R + +--R 3 2 2 3 2 2 2 +--R (A b e + (3A b c - 2B b )d e + (- 4A b c + 2B b c)d )x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 3 2 +-----------+ +-+ +--R ((- A b c e + (2A b c - B b c)d)x - A b e + A b c d)\|- b e + c d \|d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-----------+ +-+ +--R ((b c d e - b c d )x + (b d e - b c d )x)\|- b e + c d \|d +--R Type: Expression(Integer) +--E 413 + +--S 414 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R Type: Expression(Integer) +--E 415 + +--S 416 OF 765 +r0:=-(2*b*B*d-4*A*c*d-3*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(5/2))-_ + c^(3/2)*(4*A*c^2*d+5*b^2*B*e-b*c*(2*B*d+7*A*e))*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(5/2))-e*(2*A*c^2*d^2-_ + b^2*e*(2*B*d-3*A*e)-b*c*d*(B*d+2*A*e))/(b^2*d^2*(c*d-b*e)^2*_ + sqrt(d+e*x))+c*(b*B*d-2*A*c*d+A*b*e)/(b^2*d*(c*d-b*e)*(b+c*x)*_ + sqrt(d+e*x))-A/(b*d*x*(b+c*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 2 4 3 3 2 +--R ((7A b c - 5B b c )d e + (- 4A c + 2B b c )d )x +--R + +--R 2 2 3 2 3 2 2 3 +--R ((7A b c - 5B b c)d e + (- 4A b c + 2B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 2 3 2 3 2 2 2 +--R 3A b c e + (- 2A b c - 2B b c)d e + (- 5A b c + 4B b c )d e +--R + +--R 4 3 3 +--R (4A c - 2B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R 3A b e + (- 2A b c - 2B b )d e + (- 5A b c + 4B b c)d e +--R + +--R 3 2 2 3 +--R (4A b c - 2B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 2 2 3 2 3 2 2 2 2 +--R (- 3A b c e + (2A b c + 2B b c)d e + (- 2A b c + B b c )d e)x +--R + +--R 4 3 3 4 2 2 2 2 +--R - 3A b e + (A b c + 2B b )d e + A b c d e +--R + +--R 3 2 2 3 +--R (- 2A b c + B b c )d +--R * +--R x +--R + +--R 4 2 3 2 2 2 3 +--R - A b d e + 2A b c d e - A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x) +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 416 + +--S 417 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 OF 765 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 418 + +--S 419 OF 765 +r0:=-1/3*e*(6*A*c^2*d^2-b^2*e*(2*B*d-5*A*e)-3*b*c*d*(B*d+2*A*e))/_ + (b^2*d^2*(c*d-b*e)^2*(d+e*x)^(3/2))+c*(b*B*d-2*A*c*d+A*b*e)/_ + (b^2*d*(c*d-b*e)*(b+c*x)*(d+e*x)^(3/2))-A/(b*d*x*(b+c*x)*_ + (d+e*x)^(3/2))-(2*b*B*d-4*A*c*d-5*A*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^3*d^(7/2))+c^(5/2)*(2*b*B*c*d-4*A*c^2*d-7*b^2*B*e+9*A*b*c*e)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(7/2))-_ + e*(2*A*c^3*d^3-b^2*c*d*e*(6*B*d-11*A*e)+b^3*e^2*(2*B*d-5*A*e)-_ + b*c^2*d^2*(B*d+3*A*e))/(b^2*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 2 3 3 2 5 4 4 3 +--R ((- 27A b c + 21B b c )d e + (12A c - 6B b c )d e)x +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 27A b c + 21B b c )d e + (- 15A b c + 15B b c )d e +--R + +--R 5 4 5 +--R (12A c - 6B b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 4 4 2 3 5 +--R ((- 27A b c + 21B b c )d e + (12A b c - 6B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 5 3 2 4 4 2 3 3 2 2 3 +--R 15A b c e + (- 33A b c - 6B b c)d e + (9A b c + 18B b c )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (21A b c - 18B b c )d e + (- 12A c + 6B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R 15A b e + (- 18A b c - 6B b )d e + (- 24A b c + 12B b c)d e +--R + +--R 2 3 3 2 4 2 3 4 5 4 5 +--R 30A b c d e + (9A b c - 12B b c )d e + (- 12A c + 6B b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R 15A b d e + (- 33A b c - 6B b )d e + (9A b c + 18B b c)d e +--R + +--R 2 3 3 2 4 4 2 3 5 +--R (21A b c - 18B b c )d e + (- 12A b c + 6B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 5 3 2 4 4 +--R - 15A b c e + (33A b c + 6B b c)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 9A b c - 18B b c )d e + (6A b c - 3B b c )d e +--R * +--R 3 +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 15A b e + (13A b c + 6B b )d e + (35A b c - 10B b c)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 15A b c - 20B b c )d e + (12A b c - 6B b c )d e +--R * +--R 2 +--R x +--R + +--R 5 4 4 5 2 3 3 2 4 3 2 +--R - 20A b d e + (41A b c + 8B b )d e + (- 9A b c - 20B b c)d e +--R + +--R 2 3 4 4 2 3 5 +--R - 3A b c d e + (6A b c - 3B b c )d +--R * +--R x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 3A b d e + 9A b c d e - 9A b c d e + 3A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 419 + +--S 420 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 OF 765 +t0:=(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 421 + +--S 422 OF 765 +r0:=-1/5*e*(10*A*c^2*d^2-b^2*e*(2*B*d-7*A*e)-5*b*c*d*(B*d+2*A*e))/_ + (b^2*d^2*(c*d-b*e)^2*(d+e*x)^(5/2))+c*(b*B*d-2*A*c*d+A*b*e)/_ + (b^2*d*(c*d-b*e)*(b+c*x)*(d+e*x)^(5/2))-A/(b*d*x*(b+c*x)*_ + (d+e*x)^(5/2))-1/3*e*(6*A*c^3*d^3-b^2*c*d*e*(6*B*d-17*A*e)+_ + b^3*e^2*(2*B*d-7*A*e)-3*b*c^2*d^2*(B*d+3*A*e))/(b^2*d^3*_ + (c*d-b*e)^3*(d+e*x)^(3/2))-(2*b*B*d-4*A*c*d-7*A*b*e)*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(9/2))-c^(7/2)*(4*A*c^2*d+9*b^2*B*e-_ + b*c*(2*B*d+11*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^3*(c*d-b*e)^(9/2))-e*(2*A*c^4*d^4-2*b^2*c^2*d^2*e*(6*B*d-13*A*e)-_ + b^4*e^3*(2*B*d-7*A*e)+8*b^3*c*d*e^2*(B*d-3*A*e)-b*c^3*d^3*_ + (B*d+4*A*e))/(b^2*d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 2 4 4 3 6 5 5 2 4 +--R ((165A b c - 135B b c )d e + (- 60A c + 30B b c )d e )x +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (165A b c - 135B b c )d e + (270A b c - 240B b c )d e +--R + +--R 6 5 6 +--R (- 120A c + 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (330A b c - 270B b c )d e + (45A b c - 75B b c )d e +--R + +--R 6 5 7 +--R (- 60A c + 30B b c )d +--R * +--R 2 +--R x +--R + +--R 2 4 3 3 6 5 2 4 7 +--R ((165A b c - 135B b c )d e + (- 60A b c + 30B b c )d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 7 4 2 5 6 +--R 105A b c e + (- 360A b c - 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (390A b c + 120B b c )d e + (- 60A b c - 180B b c )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 135A b c + 120B b c )d e + (60A c - 30B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 +--R 105A b e + (- 150A b c - 30B b )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 330A b c + 60B b c)d e + (720A b c + 60B b c )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 255A b c - 240B b c )d e + (- 210A b c + 210B b c )d e +--R + +--R 6 5 6 +--R (120A c - 60B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R 210A b d e + (- 615A b c - 60B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (420A b c + 210B b c)d e + (270A b c - 240B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (- 330A b c + 60B b c )d e + (- 15A b c + 60B b c )d e +--R + +--R 6 5 7 +--R (60A c - 30B b c )d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R 105A b d e + (- 360A b c - 30B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (390A b c + 120B b c)d e + (- 60A b c - 180B b c )d e +--R + +--R 2 4 3 3 6 5 2 4 7 +--R (- 135A b c + 120B b c )d e + (60A b c - 30B b c )d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 7 4 2 5 6 +--R - 105A b c e + (360A b c + 30B b c)d e +--R + +--R 3 3 4 2 2 5 2 4 3 3 3 4 +--R (- 390A b c - 120B b c )d e + (60A b c + 180B b c )d e +--R + +--R 5 2 4 4 3 +--R (- 30A b c + 15B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 105A b e + (115A b c + 30B b )d e + (450A b c - 50B b c)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (- 850A b c - 100B b c )d e + (165A b c + 390B b c )d e +--R + +--R 5 2 4 5 2 +--R (- 90A b c + 45B b c )d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 6 2 5 +--R - 245A b d e + (679A b c + 70B b )d e +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 358A b c - 234B b c)d e + (- 436A b c + 218B b c )d e +--R + +--R 2 4 3 3 5 2 5 2 4 6 +--R (135A b c + 216B b c )d e + (- 90A b c + 45B b c )d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 6 3 4 +--R - 161A b d e + (537A b c + 46B b )d e +--R + +--R 4 2 5 4 3 3 3 4 2 5 2 +--R (- 556A b c - 172B b c)d e + (90A b c + 216B b c )d e +--R + +--R 2 4 6 5 2 4 7 +--R 15A b c d e + (- 30A b c + 15B b c )d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 15A b d e + 60A b c d e - 90A b c d e + 60A b c d e - 15A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (15b c d e - 60b c d e + 90b c d e - 60b c d e + 15b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 15b d e - 30b c d e - 30b c d e + 120b c d e - 105b c d e +--R + +--R 3 5 9 +--R 30b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 30b d e - 105b c d e + 120b c d e - 30b c d e - 30b c d e +--R + +--R 3 5 10 +--R 15b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (15b d e - 60b c d e + 90b c d e - 60b c d e + 15b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 422 + +--S 423 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 OF 765 +t0:=(A+B*x)*(d+e*x)^(9/2)/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 424 + +--S 425 OF 765 +r0:=1/4*(c*d-b*e)*(24*A*c^3*d^2+5*b^3*B*e^2+b^2*c*e*(3*B*d-A*e)-_ + 12*b*c^2*d*(B*d+2*A*e))*(d+e*x)^(3/2)/(b^4*c^2*(b+c*x))-_ + 1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+13*A*b*c*e)*_ + (d+e*x)^(5/2)/(b^3*c*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+9*A*b*e)*_ + (d+e*x)^(7/2)/(b^2*x*(b+c*x)^2)-1/2*A*(d+e*x)^(9/2)/(b*x^2*_ + (b+c*x)^2)-3/4*d^(5/2)*(16*A*c^2*d^2+3*b^2*e*(4*B*d+7*A*e)-_ + 4*b*c*d*(2*B*d+9*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/b^5+_ + 3/4*(c*d-b*e)^(5/2)*(16*A*c^3*d^2-5*b^3*B*e^2-4*b*c^2*d*_ + (2*B*d-A*e)-b^2*c*e*(8*B*d-A*e))*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b^5*c^(7/2))-3/4*e*(8*A*c^4*d^3-5*b^4*B*e^3+_ + b^3*c*e^2*(2*B*d+A*e)+b^2*c^2*d*e*(3*B*d+2*A*e)-4*b*c^3*d^2*_ + (B*d+3*A*e))*sqrt(d+e*x)/(b^4*c^3) +--R +--R +--R (2) +--R 4 3 5 2 4 3 4 4 3 3 +--R (3A b c - 15B b c )e + (6A b c + 6B b c )d e +--R + +--R 2 5 3 4 2 2 6 2 5 3 +--R (27A b c + 9B b c )d e + (- 84A b c + 24B b c )d e +--R + +--R 7 6 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (6A b c - 30B b c)e + (12A b c + 12B b c )d e +--R + +--R 3 4 4 3 2 2 2 5 3 4 3 +--R (54A b c + 18B b c )d e + (- 168A b c + 48B b c )d e +--R + +--R 6 2 5 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (3A b c - 15B b )e + (6A b c + 6B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (27A b c + 9B b c )d e + (- 84A b c + 24B b c )d e +--R + +--R 2 5 3 4 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 5 2 2 6 2 5 3 +--R - 63A b c d e + (108A b c - 36B b c )d e +--R + +--R 7 6 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 2 5 3 4 3 +--R - 126A b c d e + (216A b c - 72B b c )d e +--R + +--R 6 2 5 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 2 3 4 4 3 3 +--R - 63A b c d e + (108A b c - 36B b c )d e +--R + +--R 2 5 3 4 4 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 2 4 4 +--R 8B b c e x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (- 5A b c + 25B b c)e + (3A b c - 19B b c )d e +--R + +--R 3 4 4 3 2 2 2 5 3 4 3 +--R (21A b c + 3B b c )d e + (- 48A b c + 15B b c )d e +--R + +--R 6 2 5 4 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- 3A b c + 15B b )e + (- 5A b c - 11B b c)d e +--R + +--R 4 3 5 2 2 2 3 4 4 3 3 +--R (33A b c - 9B b c )d e + (- 73A b c + 23B b c )d e +--R + +--R 2 5 3 4 4 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 3 4 4 3 4 4 3 4 +--R (- 17A b c d e + (8A b c - 4B b c )d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 5 4 6 4 3 7 3 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 425 + +--S 426 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 427 + +--S 428 OF 765 +r0:=-1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+11*A*b*c*e)*_ + (d+e*x)^(3/2)/(b^3*c*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+7*A*b*e)*_ + (d+e*x)^(5/2)/(b^2*x*(b+c*x)^2)-1/2*A*(d+e*x)^(7/2)/(b*x^2*_ + (b+c*x)^2)-1/4*d^(3/2)*(48*A*c^2*d^2+7*b^2*e*(4*B*d+5*A*e)-_ + 12*b*c*d*(2*B*d+7*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/b^5+1/4*_ + (c*d-b*e)^(3/2)*(48*A*c^3*d^2-3*b^3*B*e^2-12*b*c^2*d*(2*B*d+A*e)-_ + b^2*c*e*(8*B*d+A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^5*c^(5/2))+1/4*(c*d-b*e)*(24*A*c^3*d^2+3*b^3*B*e^2+b^2*c*e*_ + (5*B*d+A*e)-12*b*c^2*d*(B*d+2*A*e))*sqrt(d+e*x)/(b^4*c^2*(b+c*x)) +--R +--R +--R (2) +--R 3 3 4 2 3 2 4 3 3 2 +--R (A b c + 3B b c )e + (11A b c + 5B b c )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 60A b c + 16B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (2A b c + 6B b c)e + (22A b c + 10B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 120A b c + 32B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (A b c + 3B b )e + (11A b c + 5B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 60A b c + 16B b c )d e + (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 4 2 5 2 4 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 6 5 3 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 2 4 3 3 2 +--R - 70A b c d e + (168A b c - 56B b c )d e +--R + +--R 5 2 4 3 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 3 4 2 2 +--R - 35A b c d e + (84A b c - 28B b c )d e +--R + +--R 2 4 3 3 3 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (A b c - 5B b c)e + (10A b c + 2B b c )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 36A b c + 11B b c )d e + (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- A b c - 3B b )e + (16A b c - 4B b c)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 55A b c + 17B b c )d e + (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 2 2 3 3 4 2 3 4 2 3 +--R (- 13A b c d e + (8A b c - 4B b c )d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 428 + +--S 429 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 430 + +--S 431 OF 765 +r0:=-1/4*(4*b*B*d-8*A*c*d+5*A*b*e)*(d+e*x)^(3/2)/(b^2*x*(b+c*x)^2)-_ + 1/2*A*(d+e*x)^(5/2)/(b*x^2*(b+c*x)^2)-1/4*(48*A*c^2*d^2+5*b^2*e*_ + (4*B*d+3*A*e)-12*b*c*d*(2*B*d+5*A*e))*atanh(sqrt(d+e*x)/sqrt(d))*_ + sqrt(d)/b^5+1/4*(48*A*c^3*d^2+b^3*B*e^2-12*b*c^2*d*(2*B*d+3*A*e)+_ + b^2*c*e*(8*B*d+3*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*_ + sqrt(c*d-b*e)/(b^5*c^(3/2))-1/4*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-_ + 2*b^2*B*e+9*A*b*c*e)*sqrt(d+e*x)/(b^3*c*(b+c*x)^2)+1/4*_ + (24*A*c^3*d^2+b^3*B*e^2-12*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ + (7*B*d+3*A*e))*sqrt(d+e*x)/(b^4*c*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 +--R (3A b c + B b c )e + (- 36A b c + 8B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (6A b c + 2B b c)e + (- 72A b c + 16B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (3A b c + B b )e + (- 36A b c + 8B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 4 2 3 5 4 2 4 +--R (- 15A b c e + (60A b c - 20B b c )d e + (- 48A c + 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 +--R - 30A b c e + (120A b c - 40B b c )d e +--R + +--R 4 2 3 2 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 15A b c e + (60A b c - 20B b c)d e + (- 48A b c + 24B b c )d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 4 2 2 3 3 2 +--R (3A b c + B b c)e + (- 24A b c + 7B b c )d e +--R + +--R 4 2 3 2 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (5A b c - B b )e + (- 37A b c + 11B b c)d e +--R + +--R 2 3 3 2 2 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 2 4 2 4 2 +--R (- 9A b c d e + (8A b c - 4B b c)d )x - 2A b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 431 + +--S 432 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 433 + +--S 434 OF 765 +r0:=-1/2*A*(d+e*x)^(3/2)/(b*x^2*(b+c*x)^2)-3/4*(16*A*c^2*d^2+b^2*e*_ + (4*B*d+A*e)-4*b*c*d*(2*B*d+3*A*e))*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^5*sqrt(d))+3/4*(16*A*c^3*d^2-b^3*B*e^2-4*b*c^2*d*(2*B*d+5*A*e)+_ + b^2*c*e*(8*B*d+5*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^5*sqrt(c)*sqrt(c*d-b*e))-1/4*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+_ + 7*A*b*c*e)*sqrt(d+e*x)/(b^3*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d+3*A*b*e)*_ + sqrt(d+e*x)/(b^2*x*(b+c*x)^2)+3/4*(8*A*c^2*d+b^2*B*e-4*b*c*(B*d+A*e))*_ + sqrt(d+e*x)/(b^4*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 +--R (15A b c - 3B b c )e + (- 60A b c + 24B b c )d e +--R + +--R 5 4 2 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (30A b c - 6B b c)e + (- 120A b c + 48B b c )d e +--R + +--R 4 2 3 2 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 +--R (15A b c - 3B b )e + (- 60A b c + 24B b c)d e +--R + +--R 2 3 3 2 2 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ \|c \|e x + d +--R \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 2 2 4 3 2 4 +--R (- 3A b c e + (36A b c - 12B b c )d e + (- 48A c + 24B b c )d )x +--R + +--R 3 2 2 2 3 3 2 2 2 3 +--R (- 6A b c e + (72A b c - 24B b c)d e + (- 96A b c + 48B b c )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (- 3A b e + (36A b c - 12B b )d e + (- 48A b c + 24B b c)d )x +--R * +--R +-------+ +--R +-----------+ +-+ \|e x + d +--R \|- b e + c d \|c atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 3 3 2 2 3 +--R ((- 12A b c + 3B b c)e + (24A b c - 12B b c )d)x +--R + +--R 3 4 2 2 3 2 +--R ((- 19A b c + 5B b )e + (36A b c - 18B b c)d)x +--R + +--R 4 3 4 4 +--R (- 5A b e + (8A b c - 4B b )d)x - 2A b d +--R * +--R +-----------+ +-+ +-+ +-------+ +--R \|- b e + c d \|c \|d \|e x + d +--R / +--R 5 2 4 6 3 7 2 +-----------+ +-+ +-+ +--R (4b c x + 8b c x + 4b x )\|- b e + c d \|c \|d +--R Type: Expression(Integer) +--E 434 + +--S 435 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 436 + +--S 437 OF 765 +r0:=-1/4*(48*A*c^2*d^2+b^2*e*(4*B*d-A*e)-12*b*c*d*(2*B*d+A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(3/2))+1/4*(48*A*c^3*d^2-_ + 15*b^3*B*e^2-12*b*c^2*d*(2*B*d+7*A*e)+5*b^2*c*e*(8*B*d+7*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b^5*_ + (c*d-b*e)^(3/2))-1/4*c*(6*b*B*d-12*A*c*d+A*b*e)*sqrt(d+e*x)/_ + (b^3*d*(b+c*x)^2)-1/2*A*sqrt(d+e*x)/(b*x^2*(b+c*x)^2)-_ + 1/4*(4*b*B*d-8*A*c*d+A*b*e)*sqrt(d+e*x)/(b^2*d*x*(b+c*x)^2)+_ + 1/4*c*(24*A*c^2*d^2+b^2*e*(11*B*d+A*e)-12*b*c*d*(B*d+2*A*e))*_ + sqrt(d+e*x)/(b^4*d*(c*d-b*e)*(b+c*x)) +--R +--R +--R (2) +--R 2 3 3 2 2 4 2 3 2 +--R (- 35A b c + 15B b c )d e + (84A b c - 40B b c )d e +--R + +--R 5 4 3 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 2 3 3 2 2 +--R (- 70A b c + 30B b c)d e + (168A b c - 80B b c )d e +--R + +--R 4 2 3 3 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 2 4 2 +--R (- 35A b c + 15B b )d e + (84A b c - 40B b c)d e +--R + +--R 2 3 3 2 3 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 2 3 2 3 3 2 2 4 2 3 2 +--R A b c e + (11A b c - 4B b c )d e + (- 60A b c + 28B b c )d e +--R + +--R 5 4 3 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 2 4 2 2 3 3 2 2 +--R 2A b c e + (22A b c - 8B b c)d e + (- 120A b c + 56B b c )d e +--R + +--R 4 2 3 3 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R A b e + (11A b c - 4B b )d e + (- 60A b c + 28B b c)d e +--R + +--R 2 3 3 2 3 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- A b c e + (24A b c - 11B b c )d e + (- 24A b c + 12B b c )d )x +--R + +--R 4 2 3 2 4 2 3 3 2 2 2 +--R (- 2A b c e + (37A b c - 17B b c)d e + (- 36A b c + 18B b c )d )x +--R + +--R 5 2 4 5 3 2 4 2 5 +--R (- A b e + (9A b c - 4B b )d e + (- 8A b c + 4B b c)d )x - 2A b d e +--R + +--R 4 2 +--R 2A b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 8 7 2 2 +--R ((4b c d e - 4b c d )x + (8b c d e - 8b c d )x + (4b d e - 4b c d )x ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 437 + +--S 438 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 OF 765 +t0:=(A+B*x)/((b*x+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R 3 6 2 5 2 4 3 3 +-------+ +--R (c x + 3b c x + 3b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 439 + +--S 440 OF 765 +r0:=-1/4*(48*A*c^2*d^2-b^2*e*(4*B*d-3*A*e)-12*b*c*d*(2*B*d-A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(5/2))+1/4*c^(3/2)*_ + (48*A*c^3*d^2-35*b^3*B*e^2-12*b*c^2*d*(2*B*d+9*A*e)+7*b^2*c*e*_ + (8*B*d+9*A*e))*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*_ + (c*d-b*e)^(5/2))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-3*A*e)-b*c*d*_ + (6*B*d+7*A*e))*sqrt(d+e*x)/(b^3*d^2*(c*d-b*e)*(b+c*x)^2)-1/2*A*_ + sqrt(d+e*x)/(b*d*x^2*(b+c*x)^2)-1/4*(4*b*B*d-8*A*c*d-3*A*b*e)*_ + sqrt(d+e*x)/(b^2*d^2*x*(b+c*x)^2)+1/4*c*(24*A*c^3*d^3-b^3*e^2*_ + (4*B*d-3*A*e)-12*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(19*B*d+6*A*e))*_ + sqrt(d+e*x)/(b^4*d^2*(c*d-b*e)^2*(b+c*x)) +--R +--R +--R (2) +--R 2 4 3 3 2 2 5 2 4 3 +--R (63A b c - 35B b c )d e + (- 108A b c + 56B b c )d e +--R + +--R 6 5 4 +--R (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (126A b c - 70B b c )d e + (- 216A b c + 112B b c )d e +--R + +--R 5 2 4 4 +--R (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (63A b c - 35B b c)d e + (- 108A b c + 56B b c )d e +--R + +--R 2 4 3 3 4 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 2 4 3 3 4 2 3 +--R - 3A b c e + (- 6A b c + 4B b c )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 27A b c + 16B b c )d e + (84A b c - 44B b c )d e +--R + +--R 6 5 4 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 5 4 4 2 5 3 +--R - 6A b c e + (- 12A b c + 8B b c)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 54A b c + 32B b c )d e + (168A b c - 88B b c )d e +--R + +--R 5 2 4 4 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 6 4 5 6 3 4 2 5 2 2 +--R - 3A b e + (- 6A b c + 4B b )d e + (- 27A b c + 16B b c)d e +--R + +--R 3 3 4 2 3 2 4 3 3 4 +--R (84A b c - 44B b c )d e + (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 3 3 3 4 2 2 2 4 3 3 2 +--R 3A b c e + (6A b c - 4B b c )d e + (- 36A b c + 19B b c )d e +--R + +--R 5 2 4 3 +--R (24A b c - 12B b c )d +--R * +--R 3 +--R x +--R + +--R 5 3 4 2 5 2 3 3 4 2 2 +--R 6A b c e + (10A b c - 8B b c)d e + (- 55A b c + 29B b c )d e +--R + +--R 2 4 3 3 3 +--R (36A b c - 18B b c )d +--R * +--R 2 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R 3A b e + (2A b c - 4B b )d e + (- 13A b c + 8B b c)d e +--R + +--R 3 3 4 2 3 +--R (8A b c - 4B b c )d +--R * +--R x +--R + +--R 6 2 5 2 4 2 3 +--R - 2A b d e + 4A b c d e - 2A b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (4b c d e - 8b c d e + 4b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 9 2 2 8 3 7 2 4 2 +--R (8b c d e - 16b c d e + 8b c d )x + (4b d e - 8b c d e + 4b c d )x +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 440 + +--S 441 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 441 + +)clear all + +--S 442 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 7 2 3 6 2 2 5 3 2 4 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x +--R + +--R 3 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 442 + +--S 443 OF 765 +r0:=-3/4*(16*A*c^2*d^2-b^2*e*(4*B*d-5*A*e)-4*b*c*d*(2*B*d-3*A*e))*_ + atanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(7/2))+3/4*c^(5/2)*(16*A*c^3*d^2-_ + 21*b^3*B*e^2-4*b*c^2*d*(2*B*d+11*A*e)+3*b^2*c*e*(8*B*d+11*A*e))*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(7/2))+_ + 3/4*e*(8*A*c^4*d^4+b^4*e^3*(4*B*d-5*A*e)-b^3*c*d*e^2*(4*B*d-3*A*e)-_ + 4*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*e*(9*B*d+5*A*e))/(b^4*d^3*_ + (c*d-b*e)^3*sqrt(d+e*x))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-5*A*e)-_ + b*c*d*(6*B*d+5*A*e))/(b^3*d^2*(c*d-b*e)*(b+c*x)^2*sqrt(d+e*x))-_ + 1/2*A/(b*d*x^2*(b+c*x)^2*sqrt(d+e*x))+1/4*(-4*b*B*d+8*A*c*d+_ + 5*A*b*e)/(b^2*d^2*x*(b+c*x)^2*sqrt(d+e*x))+1/4*c*(24*A*c^3*d^3-_ + b^3*e^2*(4*B*d-5*A*e)+b^2*c*d*e*(21*B*d+2*A*e)-12*b*c^2*d^2*(B*d+_ + 3*A*e))/(b^4*d^2*(c*d-b*e)^2*(b+c*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 5 3 4 3 2 6 2 5 4 +--R (- 99A b c + 63B b c )d e + (132A b c - 72B b c )d e +--R + +--R 7 6 5 +--R (- 48A c + 24B b c )d +--R * +--R 4 +--R x +--R + +--R 3 4 4 3 3 2 2 5 3 4 4 +--R (- 198A b c + 126B b c )d e + (264A b c - 144B b c )d e +--R + +--R 6 2 5 5 +--R (- 96A b c + 48B b c )d +--R * +--R 3 +--R x +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (- 99A b c + 63B b c )d e + (132A b c - 72B b c )d e +--R + +--R 2 5 3 4 5 +--R (- 48A b c + 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 2 5 4 3 5 2 4 +--R - 15A b c e + (9A b c + 12B b c )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (15A b c - 12B b c )d e + (51A b c - 36B b c )d e +--R + +--R 6 2 5 4 7 6 5 +--R (- 108A b c + 60B b c )d e + (48A c - 24B b c )d +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 6 4 +--R - 30A b c e + (18A b c + 24B b c)d e +--R + +--R 4 3 5 2 2 3 3 4 4 3 3 2 +--R (30A b c - 24B b c )d e + (102A b c - 72B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (- 216A b c + 120B b c )d e + (96A b c - 48B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 6 7 4 5 2 6 2 3 +--R - 15A b e + (9A b c + 12B b )d e + (15A b c - 12B b c)d e +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (51A b c - 36B b c )d e + (- 108A b c + 60B b c )d e +--R + +--R 2 5 3 4 5 +--R (48A b c - 24B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 2 5 4 3 5 2 4 +--R 15A b c e + (- 9A b c - 12B b c )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (- 15A b c + 12B b c )d e + (48A b c - 27B b c )d e +--R + +--R 6 2 5 4 +--R (- 24A b c + 12B b c )d e +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 6 4 +--R 30A b c e + (- 13A b c - 24B b c)d e +--R + +--R 4 3 5 2 2 3 3 4 4 3 3 2 +--R (- 33A b c + 20B b c )d e + (58A b c - 29B b c )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (12A b c - 9B b c )d e + (- 24A b c + 12B b c )d +--R * +--R 3 +--R x +--R + +--R 7 5 6 7 4 5 2 6 2 3 +--R 15A b e + (A b c - 12B b )d e + (- 23A b c + 4B b c)d e +--R + +--R 4 3 5 2 3 2 3 4 4 3 4 +--R (- 7A b c + 12B b c )d e + (65A b c - 37B b c )d e +--R + +--R 2 5 3 4 5 +--R (- 36A b c + 18B b c )d +--R * +--R 2 +--R x +--R + +--R 7 4 6 7 2 3 5 2 6 3 2 +--R 5A b d e + (- 7A b c - 4B b )d e + (- 9A b c + 12B b c)d e +--R + +--R 4 3 5 2 4 3 4 4 3 5 +--R (19A b c - 12B b c )d e + (- 8A b c + 4B b c )d +--R * +--R x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - 2A b d e + 6A b c d e - 6A b c d e + 2A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (8b c d e - 24b c d e + 24b c d e - 8b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 443 + +--S 444 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 OF 765 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 445 + +--S 446 OF 765 +r0:=1/12*e*(72*A*c^4*d^4+5*b^4*e^3*(4*B*d-7*A*e)-9*b^3*c*d*e^2*(4*B*d-_ + 5*A*e)-36*b*c^3*d^3*(B*d+4*A*e)+3*b^2*c^2*d^2*e*(29*B*d+9*A*e))/(b^4*_ + d^3*(c*d-b*e)^3*(d+e*x)^(3/2))+1/4*c*(12*A*c^2*d^2+b^2*e*(4*B*d-7*A*e)-_ + 3*b*c*d*(2*B*d+A*e))/(b^3*d^2*(c*d-b*e)*(b+c*x)^2*(d+e*x)^(3/2))-_ + 1/2*A/(b*d*x^2*(b+c*x)^2*(d+e*x)^(3/2))+1/4*(-4*b*B*d+8*A*c*d+7*A*b*e)/_ + (b^2*d^2*x*(b+c*x)^2*(d+e*x)^(3/2))+1/4*c*(24*A*c^3*d^3-b^3*e^2*_ + (4*B*d-7*A*e)+b^2*c*d*e*(23*B*d-2*A*e)-12*b*c^2*d^2*(B*d+3*A*e))/_ + (b^4*d^2*(c*d-b*e)^2*(b+c*x)*(d+e*x)^(3/2))-1/4*(48*A*c^2*d^2-_ + 5*b^2*e*(4*B*d-7*A*e)-12*b*c*d*(2*B*d-5*A*e))*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b^5*d^(9/2))+1/4*c^(7/2)*(48*A*c^3*d^2-99*b^3*B*e^2-_ + 12*b*c^2*d*(2*B*d+13*A*e)+11*b^2*c*e*(8*B*d+13*A*e))*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(9/2))+1/4*e*(24*A*c^5*d^5+_ + 8*b^4*c*d*e^3*(7*B*d-10*A*e)-5*b^5*e^4*(4*B*d-7*A*e)-6*b^3*_ + c^2*d^2*e^2*(4*B*d-3*A*e)+7*b^2*c^3*d^3*e*(5*B*d+4*A*e)-12*b*c^4*d^4*_ + (B*d+5*A*e))/(b^4*d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (429A b c - 297B b c )d e + (- 468A b c + 264B b c )d e +--R + +--R 8 7 6 +--R (144A c - 72B b c )d e +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (858A b c - 594B b c )d e + (- 507A b c + 231B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (- 180A b c + 120B b c )d e + (144A c - 72B b c )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 4 3 3 5 4 4 5 2 +--R (429A b c - 297B b c )d e + (390A b c - 330B b c )d e +--R + +--R 2 6 3 5 6 7 2 6 7 +--R (- 792A b c + 456B b c )d e + (288A b c - 144B b c )d +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (429A b c - 297B b c )d e + (- 468A b c + 264B b c )d e +--R + +--R 2 6 3 5 7 +--R (144A b c - 72B b c )d +--R * +--R 2 +--R x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 6 2 7 5 3 6 2 6 +--R - 105A b c e + (240A b c + 60B b c )d e +--R + +--R 4 4 5 3 2 5 3 5 4 4 3 4 +--R (- 54A b c - 168B b c )d e + (- 84A b c + 72B b c )d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 249A b c + 192B b c )d e + (396A b c - 228B b c )d e +--R + +--R 8 7 6 +--R (- 144A c + 72B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R - 210A b c e + (375A b c + 120B b c)d e +--R + +--R 5 3 6 2 2 5 4 4 5 3 3 4 +--R (132A b c - 276B b c )d e + (- 222A b c - 24B b c )d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 582A b c + 456B b c )d e + (543A b c - 264B b c )d e +--R + +--R 7 2 6 6 8 7 7 +--R (108A b c - 84B b c )d e + (- 144A c + 72B b c )d +--R * +--R 4 +--R x +--R + +--R 8 7 7 8 6 6 2 7 2 5 +--R - 105A b e + (30A b c + 60B b )d e + (426A b c - 48B b c)d e +--R + +--R 5 3 6 2 3 4 4 4 5 3 4 3 +--R (- 192A b c - 264B b c )d e + (- 417A b c + 336B b c )d e +--R + +--R 3 5 4 4 5 2 2 6 3 5 6 +--R (- 102A b c + 156B b c )d e + (648A b c - 384B b c )d e +--R + +--R 7 2 6 7 +--R (- 288A b c + 144B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 +--R - 105A b d e + (240A b c + 60B b )d e +--R + +--R 6 2 7 3 4 5 3 6 2 4 3 +--R (- 54A b c - 168B b c)d e + (- 84A b c + 72B b c )d e +--R + +--R 4 4 5 3 5 2 3 5 4 4 6 +--R (- 249A b c + 192B b c )d e + (396A b c - 228B b c )d e +--R + +--R 2 6 3 5 7 +--R (- 144A b c + 72B b c )d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 6 2 7 5 3 6 2 6 +--R 105A b c e + (- 240A b c - 60B b c )d e +--R + +--R 4 4 5 3 2 5 3 5 4 4 3 4 +--R (54A b c + 168B b c )d e + (84A b c - 72B b c )d e +--R + +--R 2 6 3 5 4 3 7 2 6 5 2 +--R (- 180A b c + 105B b c )d e + (72A b c - 36B b c )d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 7 6 +--R 210A b c e + (- 340A b c - 120B b c)d e +--R + +--R 5 3 6 2 2 5 4 4 5 3 3 4 +--R (- 212A b c + 256B b c )d e + (240A b c + 80B b c )d e +--R + +--R 3 5 4 4 4 3 2 6 3 5 5 2 +--R (- 105A b c + 15B b c )d e + (- 252A b c + 156B b c )d e +--R + +--R 7 2 6 6 +--R (144A b c - 72B b c )d e +--R * +--R 4 +--R x +--R + +--R 8 7 7 8 6 6 2 7 2 5 +--R 105A b e + (40A b c - 60B b )d e + (- 565A b c + 8B b c)d e +--R + +--R 5 3 6 2 3 4 4 4 5 3 4 3 +--R (180A b c + 364B b c )d e + (255A b c - 192B b c )d e +--R + +--R 3 5 4 4 5 2 2 6 3 5 6 +--R (- 438A b c + 234B b c )d e + (36A b c - 3B b c )d e +--R + +--R 7 2 6 7 +--R (72A b c - 36B b c )d +--R * +--R 3 +--R x +--R + +--R 8 6 7 8 2 5 +--R 140A b d e + (- 278A b c - 80B b )d e +--R + +--R 6 2 7 3 4 5 3 6 2 4 3 +--R (- 30A b c + 200B b c)d e + (180A b c - 48B b c )d e +--R + +--R 5 3 5 2 3 5 4 4 6 +--R - 48B b c d e + (- 225A b c + 135B b c )d e +--R + +--R 2 6 3 5 7 +--R (108A b c - 54B b c )d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 8 3 4 6 2 7 4 3 +--R 21A b d e + (- 60A b c - 12B b )d e + (30A b c + 48B b c)d e +--R + +--R 5 3 6 2 5 2 4 4 5 3 6 +--R (60A b c - 72B b c )d e + (- 75A b c + 48B b c )d e +--R + +--R 3 5 4 4 7 +--R (24A b c - 12B b c )d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - 6A b d e + 24A b c d e - 36A b c d e + 24A b c d e - 6A b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (12b c d e - 48b c d e + 72b c d e - 48b c d e + 12b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 +--R 24b c d e - 84b c d e + 96b c d e - 24b c d e - 24b c d e +--R + +--R 5 6 9 +--R 12b c d +--R * +--R 4 +--R x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 +--R 12b d e - 24b c d e - 24b c d e + 96b c d e - 84b c d e +--R + +--R 6 5 9 +--R 24b c d +--R * +--R 3 +--R x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (12b d e - 48b c d e + 72b c d e - 48b c d e + 12b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 446 + +--S 447 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 OF 765 +t0:=(A+B*x)*(d+e*x)^(1/2)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R +-------+ | 2 +--R (1) (B x + A)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 448 + +--S 449 OF 765 +--r0:=2/7*B*(b*x+c*x^2)^(3/2)*sqrt(d+e*x)/c-2/105*(14*A*c*e*(c^2*d^2-_ +-- b*c*d*e+b^2*e^2)-B*(8*c^3*d^3-5*b*c^2*d^2*e-5*b^2*c*d*e^2+8*_ +-- b^3*e^3))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^3*e^(5/2)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/105*(-b)^(3/2)*_ +-- (c*d-b*e)*(7*A*c*e*(c*d-2*b*e)-B*(4*c^2*d^2+b*c*d*e-8*b^2*e^2))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*e^2*sqrt(d+e*x)*sqrt(b*x+_ +-- c*x^2))+2/105*(7*A*c*e*(c*d+b*e)-B*(4*c^2*d^2-2*b*c*d*e+4*b^2*e^2)+_ +-- 3*c*e*(B*c*d-4*b*B*e+7*A*c*e)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^2) +--E 449 + +--S 450 OF 765 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 451 + +--S 452 OF 765 +--r0:=-2/15*(5*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^2*e^(5/2)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*(-b)^(3/2)*(c*d-b*e)*(4*B*c*d+_ +-- 2*b*B*e-5*A*c*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*e^2*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(4*B*c*d-b*B*e-5*A*c*e-3*B*c*e*x)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c*e^2) +--E 452 + +--S 453 OF 765 +--d0:=D(m0,x) +--E 453 + +)clear all + +--S 454 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 454 + +--S 455 OF 765 +--r0:=-2/3*(8*B*c*d-b*B*e-6*A*c*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (c*e^(5/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*(-b)^(3/2)*(4*B*c*d-b*B*e-3*A*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+_ +-- e*x)/d)/(c^(3/2)*e^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(4*B*d-_ +-- 3*A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*sqrt(d+e*x)) +--E 455 + +--S 456 OF 765 +--d0:=D(m0,x) +--E 456 + +)clear all + +--S 457 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 457 + +--S 458 OF 765 +--r0:=-2/3*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(e^(5/2)*(c*d-b*e)*sqrt(-d)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(-b)^(3/2)*(4*B*d-A*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*e^2*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*(4*B*d-A*e+3*B*e*x)*sqrt(b*x+c*x^2)/(e^2*_ +-- (d+e*x)^(3/2))-2/3*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*_ +-- sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*sqrt(d+e*x)) +--E 458 + +--S 459 OF 765 +--d0:=D(m0,x) +--E 459 + +)clear all + +--S 460 OF 765 +t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R | 2 +--R (B x + A)\|c x + b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 460 + +--S 461 OF 765 +--r0:=-2/15*(2*A*e*(c^2*d^2-b*c*d*e+b^2*e^2)+B*d*(8*c^2*d^2-13*b*c*d*e+_ +-- 3*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(3/2)*e^(5/2)*(c*d-b*e)^2*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(-b)^(3/2)*(B*d*_ +-- (4*c*d-3*b*e)+A*e*(c*d-2*b*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*_ +-- e^2*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*(B*d*(8*c*d-_ +-- 9*b*e)+A*e*(2*c*d-b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+_ +-- e*x)^(3/2))-2/5*(4*B*d+A*e+5*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+_ +-- e*x)^(5/2))+2/15*(2*A*e*(c^2*d^2-b*c*d*e+b^2*e^2)+B*d*(8*c^2*d^2-_ +-- 13*b*c*d*e+3*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 461 + +--S 462 OF 765 +--d0:=D(m0,x) +--E 462 + +)clear all + +--S 463 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(1/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 463 + +--S 464 OF 765 +--r0:=-2/63*(8*B*c*d-3*b*B*e-9*A*c*e-7*B*c*e*x)*(b*x+c*x^2)^(3/2)*_ +-- sqrt(d+e*x)/(c*e^2)-2/315*(18*A*c*e*(8*c^3*d^3-12*b*c^2*d^2*e+_ +-- 2*b^2*c*d*e^2+b^3*e^3)-B*(128*c^4*d^4-184*b*c^3*d^3*e+27*_ +-- b^2*c^2*d^2*e^2+11*b^3*c*d*e^3+8*b^4*e^4))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^3*e^(9/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/315*(-b)^(3/2)*(c*d-b*e)*(9*A*c*e*(8*c^2*d^2-_ +-- 5*b*c*d*e-2*b^2*e^2)-B*(64*c^3*d^3-36*b*c^2*d^2*e-15*b^2*c*d*e^2-_ +-- 8*b^3*e^3))*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*e^4*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/315*(9*A*c*e*(8*c^2*d^2-11*b*c*d*e+b^2*e^2)-_ +-- 2*B*(32*c^3*d^3-42*b*c^2*d^2*e+3*b^2*c*d*e^2+2*b^3*e^3)-3*c*e*_ +-- (9*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-7*b*c*d*e-4*b^2*e^2))*x)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^4) +--E 464 + +--S 465 OF 765 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 466 + +--S 467 OF 765 +--r0:=2/7*(8*B*d-7*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+2/35*_ +-- (5*b*c*e*(8*B*d-7*A*e)*(2*c*d-b*e)-(16*B*c*d-b*B*e-14*A*c*e)*_ +-- (8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (c^2*e^(9/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/35*_ +-- (-b)^(3/2)*(c*d-b*e)*(7*A*c*e*(8*c*d-b*e)-2*B*(32*c^2*d^2-6*b*c*d*e-_ +-- b^2*e^2))*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*e^4*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/35*(7*A*c*e*(8*c*d-7*b*e)-B*(64*c^2*d^2-60*b*c*_ +-- d*e+b^2*e^2)+3*c*e*(16*B*c*d-b*B*e-14*A*c*e)*x)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/(c*e^4) +--E 467 + +--S 468 OF 765 +--d0:=D(m0,x) +--E 468 + +)clear all + +--S 469 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 469 + +--S 470 OF 765 +--r0:=2/15*(8*B*d-5*A*e+3*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/15*(40*A*c*e*(2*c*d-b*e)-B*(128*c^2*d^2-88*b*c*d*e+3*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c*e^(9/2)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(-b)^(3/2)*(5*A*c*e*(8*c*d-5*b*e)-_ +-- B*(64*c^2*d^2-52*b*c*d*e+3*b^2*e^2))*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(3/2)*e^4*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/15*(4*B*d*(16*c*d-9*b*e)-5*A*e*(8*c*d-3*b*e)+e*(16*B*c*d-_ +-- 3*b*B*e-10*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*sqrt(d+e*x)) +--E 470 + +--S 471 OF 765 +--d0:=D(m0,x) +--E 471 + +)clear all + +--S 472 OF 765 +t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (B c x + (A c + B b)x + A b x)\|c x + b x +--R (1) --------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 472 + +--S 473 OF 765 +--r0:=2/15*(8*B*d-3*A*e+5*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 2/15*(3*A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(128*c^2*d^2-_ +-- 168*b*c*d*e+43*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/(e^(9/2)*(c*d-b*e)*_ +-- sqrt(-d)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/15*(-b)^(3/2)*(4*B*d*(16*c*d-7*b*e)-3*A*e*(8*c*d-b*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*e^4*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/15*(4*B*d*(16*c*d-7*b*e)-3*A*e*(8*c*d-b*e)+_ +-- 3*e*(16*B*c*d-5*b*B*e-6*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*_ +-- (d+e*x)^(3/2))-2/15*(3*A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*_ +-- (128*c^2*d^2-168*b*c*d*e+43*b^2*e^2))*sqrt(b*x+c*x^2)/(d*e^4*_ +-- (c*d-b*e)*sqrt(d+e*x)) +--E 473 + +--S 474 OF 765 +--d0:=D(m0,x) +--E 474 + +)clear all + +--S 475 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/sqrt(b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 475 + +--S 476 OF 765 +--r0:=2/105*(7*A*c*e*(23*c^2*d^2-23*b*c*d*e+8*b^2*e^2)+B*(15*c^3*d^3-_ +-- 103*b*c^2*d^2*e+128*b^2*c*d*e^2-48*b^3*e^3))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^4*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/105*(c*d-b*e)*(105*A*c^3*d^2-48*b^3*B*e^2+_ +-- 8*b^2*c*e*(13*B*d+7*A*e)-b*c^2*d*(60*B*d+133*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/35*(5*B*c*d-6*b*B*e+7*A*c*e)*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/c^2+2/7*B*(d+e*x)^(5/2)*sqrt(b*x+c*x^2)/c+2/105*_ +-- (28*A*c*e*(2*c*d-b*e)+B*(15*c^2*d^2-43*b*c*d*e+24*b^2*e^2))*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/c^3 +--E 476 + +--S 477 OF 765 +--d0:=D(m0,x) +--E 477 + +)clear all + +--S 478 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 478 + +--S 479 OF 765 +--r0:=2/15*(10*A*c*e*(2*c*d-b*e)+B*(3*c^2*d^2-13*b*c*d*e+8*b^2*e^2))*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^3*sqrt(e)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(c*d-b*e)*(9*b*B*c*d-15*A*c^2*d-_ +-- 8*b^2*B*e+10*A*b*c*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (c^(7/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*B*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/c+2/15*(3*B*c*d-4*b*B*e+5*A*c*e)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/c^2 +--E 479 + +--S 480 OF 765 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(b*x+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 481 + +--S 482 OF 765 +--r0:=2/3*(B*c*d-2*b*B*e+3*A*c*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^2*_ +-- sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*(2*b*B-_ +-- 3*A*c)*(c*d-b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (c^(5/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*B*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/c +--E 482 + +--S 483 OF 765 +--d0:=D(m0,x) +--E 483 + +)clear all + +--S 484 OF 765 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------- +--R +----------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 484 + +--S 485 OF 765 +--r0:=2*B*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c*sqrt(e)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(b*B-A*c)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(3/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 485 + +--S 486 OF 765 +--d0:=D(m0,x) +--E 486 + +)clear all + +--S 487 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) -------------------------------- +--R +----------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 487 + +--S 488 OF 765 +--r0:=2*(B*d-A*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((c*d-b*e)*sqrt(-d)*sqrt(e)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*A*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*sqrt(d+e*x)) +--E 488 + +--S 489 OF 765 +--d0:=D(m0,x) +--E 489 + +)clear all + +--S 490 OF 765 +t0:=(A+B*x)/((d+e*x)^(5/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +----------+ +--R 2 2 2 +-------+ | 2 +--R (e x + 2d e x + d )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 490 + +--S 491 OF 765 +--r0:=2/3*(2*A*e*(2*c*d-b*e)-B*d*(c*d+b*e))*(b+c*x)*elliptic_e(asin(_ +-- sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/_ +-- ((-d)^(3/2)*(c*d-b*e)^2*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/3*(b*B*d-3*A*c*d+2*A*b*e)*elliptic_f(asin(_ +-- sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ +-- (d+e*x)^(3/2))-2/3*(2*A*e*(2*c*d-b*e)-B*d*(c*d+b*e))*sqrt(b*x+_ +-- c*x^2)/(d^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 491 + +--S 492 OF 765 +--d0:=D(m0,x) +--E 492 + +)clear all + +--S 493 OF 765 +t0:=(A+B*x)/((d+e*x)^(7/2)*sqrt(b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R +----------+ +--R 3 3 2 2 2 3 +-------+ | 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 493 + +--S 494 OF 765 +--r0:=2/15*(B*d*(3*c^2*d^2+7*b*c*d*e-2*b^2*e^2)-A*e*(23*c^2*d^2-_ +-- 23*b*c*d*e+8*b^2*e^2))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(5/2)*_ +-- (c*d-b*e)^3*sqrt(e)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+_ +-- 2/15*(15*A*c^2*d^2+2*b^2*e*(B*d+4*A*e)-b*c*d*(6*B*d+19*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^3*(c*d-b*e)^2*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*(B*d-A*e)*sqrt(b*x+c*x^2)/_ +-- (d*(c*d-b*e)*(d+e*x)^(5/2))-2/15*(4*A*e*(2*c*d-b*e)-B*d*(3*c*d+_ +-- b*e))*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))+2/15*(B*d*_ +-- (3*c^2*d^2+7*b*c*d*e-2*b^2*e^2)-A*e*(23*c^2*d^2-23*b*c*d*e+_ +-- 8*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 494 + +--S 495 OF 765 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 496 + +--S 497 OF 765 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(7/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2/15*(30*A*c^4*d^3+48*b^4*B*e^3-15*b*c^3*d^2*(B*d+3*A*e)-_ +-- 8*b^3*c*e^2*(16*B*d+5*A*e)+b^2*c^2*d*e*(103*B*d+95*A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^4*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*e*(c*d-b*e)*(15*A*c^3*d^2-_ +-- 48*b^3*B*e^2-15*b*c^2*d*(4*B*d+5*A*e)+8*b^2*c*e*(13*B*d+5*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/5*e*(10*A*c^2*d+6*b^2*B*e-5*b*c*(B*d+A*e))*_ +-- (d+e*x)^(3/2)*sqrt(b*x+c*x^2)/(b^2*c^2)-2*(b*B-2*A*c)*e*_ +-- (d+e*x)^(5/2)*sqrt(b*x+c*x^2)/(b^2*c)+2/15*e*(30*A*c^3*d^2-_ +-- 24*b^3*B*e^2-15*b*c^2*d*(B*d+2*A*e)+b^2*c*e*(43*B*d+20*A*e))*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c^3) +--E 497 + +--S 498 OF 765 +--d0:=D(m0,x) +--E 498 + +)clear all + +--S 499 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 499 + +--S 500 OF 765 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(5/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2/3*(6*A*c^3*d^2-8*b^3*B*e^2-3*b*c^2*d*(B*d+2*A*e)+b^2*c*e*_ +-- (13*B*d+6*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^3*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(c*d-b*e)*_ +-- (9*b*B*c*d-3*A*c^2*d-8*b^2*B*e+6*A*b*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(7/2)*sqrt(-b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2*(b*B-2*A*c)*e*(d+e*x)^(3/2)*sqrt(b*x+c*x^2)/(b^2*c)+2/3*e*_ +-- (6*A*c^2*d+4*b^2*B*e-3*b*c*(B*d+A*e))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/_ +-- (b^2*c^2) +--E 500 + +--S 501 OF 765 +--d0:=D(m0,x) +--E 501 + +)clear all + +--S 502 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 502 + +--S 503 OF 765 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^2*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(2*b*B-A*c)*e*(c*d-b*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c) +--E 503 + +--S 504 OF 765 +--d0:=D(m0,x) +--E 504 + +)clear all + +--S 505 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 505 + +--S 506 OF 765 +--r0:=-2*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*sqrt(b*x+c*x^2))-_ +-- 2*(b*B-2*A*c)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*(b*B-A*c)*e*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(3/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)) +--E 506 + +--S 507 OF 765 +--d0:=D(m0,x) +--E 507 + +)clear all + +--S 508 OF 765 +t0:=(A+B*x)/((b*x+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ----------------------------------- +--R +----------+ +--R 2 +-------+ | 2 +--R (c x + b x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 508 + +--S 509 OF 765 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*d*_ +-- (c*d-b*e)*sqrt(b*x+c*x^2))+2*(b*B*d-2*A*c*d+A*b*e)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^2*(c*d-b*e)*sqrt(-d)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*A*e*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(d*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 509 + +--S 510 OF 765 +--d0:=D(m0,x) +--E 510 + +)clear all + +--S 511 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------- +--R +----------+ +--R 3 2 +-------+ | 2 +--R (c e x + (b e + c d)x + b d x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 511 + +--S 512 OF 765 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*(2*A*c^2*d^2-b^2*e*(B*d-2*A*e)-_ +-- b*c*d*(B*d+2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (b^2*(-d)^(3/2)*(c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*e*(b*B*d+A*c*d-2*A*b*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(d^2*(c*d-b*e)*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2*e*(2*A*c^2*d^2-b^2*e*(B*d-2*A*e)-b*c*d*(B*d+_ +-- 2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 512 + +--S 513 OF 765 +--d0:=D(m0,x) +--E 513 + +)clear all + +--S 514 OF 765 +t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 4 2 3 2 2 2 +-------+ +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 514 + +--S 515 OF 765 +--r0:=-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- (d+e*x)^(3/2)*sqrt(b*x+c*x^2))-2/3*(6*A*c^3*d^3-b^2*c*d*e*(7*B*d-_ +-- 19*A*e)+2*b^3*e^2*(B*d-4*A*e)-3*b*c^2*d^2*(B*d+3*A*e))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^2*(-d)^(5/2)*(c*d-b*e)^3*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(3*A*c^2*d^2+3*b*c*d*(2*B*d-_ +-- 5*A*e)-2*b^2*e*(B*d-4*A*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (d^3*(c*d-b*e)^2*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*e*(6*A*c^2*d^2-b^2*e*(B*d-4*A*e)-3*b*c*d*(B*d+2*A*e))*_ +-- sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-_ +-- 2/3*e*(6*A*c^3*d^3-b^2*c*d*e*(7*B*d-19*A*e)+2*b^3*e^2*(B*d-4*A*e)-_ +-- 3*b*c^2*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*_ +-- sqrt(d+e*x)) +--E 515 + +--S 516 OF 765 +--d0:=D(m0,x) +--E 516 + +)clear all + +--S 517 OF 765 +t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 517 + +--S 518 OF 765 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(7/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(d+e*x)^(5/2)*(b*(4*b*B*d-8*A*c*d+7*A*b*e)-(16*A*c^2*d-_ +-- 3*b^2*B*e-8*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^4*d^3-8*b^4*B*e^3+b^3*c*e^2*(5*B*d+2*A*e)-8*b*c^3*d^2*_ +-- (B*d+3*A*e)+b^2*c^2*d*e*(5*B*d+4*A*e))*(b+c*x)*elliptic_e(asin(_ +-- sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(b^4*c^3*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+_ +-- c*x^2))-2/3*e*(c*d-b*e)*(8*A*c^3*d^2+8*b^3*B*e^2-b^2*c*e*(B*d+_ +-- 2*A*e)-b*c^2*d*(4*B*d+5*A*e))*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- ((-b)^(5/2)*c^(7/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*_ +-- (16*A*c^2*d-3*b^2*B*e-8*b*c*(B*d+A*e))*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/(b^4*c)-2/3*e*(16*A*c^3*d^2+4*b^3*B*e^2+b^2*c*e*_ +-- (B*d-A*e)-8*b*c^2*d*(B*d+2*A*e))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^4*c^2) +--E 518 + +--S 519 OF 765 +--d0:=D(m0,x) +--E 519 + +)clear all + +--S 520 OF 765 +t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 520 + +--S 521 OF 765 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(5/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(d+e*x)^(3/2)*(b*(4*b*B*d-8*A*c*d+5*A*b*e)-(16*A*c^2*d-_ +-- b^2*B*e-8*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^3*d^2+2*b^3*B*e^2+b^2*c*e*(3*B*d+A*e)-8*b*c^2*d*(B*d+_ +-- 2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/_ +-- (b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*c^2*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(c*d-b*e)*_ +-- (8*A*c^2*d-2*b^2*B*e-b*c*(4*B*d+A*e))*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/((-b)^(5/2)*c^(5/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/3*e*(16*A*c^2*d-b^2*B*e-8*b*c*(B*d+A*e))*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/(b^4*c) +--E 521 + +--S 522 OF 765 +--d0:=D(m0,x) +--E 522 + +)clear all + +--S 523 OF 765 +t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 523 + +--S 524 OF 765 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(b*(4*b*B*d-8*A*c*d+3*A*b*e)-(16*A*c^2*d+b^2*B*e-8*b*c*_ +-- (B*d+A*e))*x)*sqrt(d+e*x)/(b^4*sqrt(b*x+c*x^2))-2/3*(16*A*c^2*d+_ +-- b^2*B*e-8*b*c*(B*d+A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (b^4*c*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*_ +-- (4*b*B*c*d-8*A*c^2*d-b^2*B*e+5*A*b*c*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/((-b)^(5/2)*c^(3/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 524 + +--S 525 OF 765 +--d0:=D(m0,x) +--E 525 + +)clear all + +--S 526 OF 765 +t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 526 + +--S 527 OF 765 +--r0:=-2/3*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))-_ +-- 2/3*(b*(c*d-b*e)*(4*b*B*d-8*A*c*d+A*b*e)-c*(16*A*c^2*d^2+b^2*e*_ +-- (7*B*d+A*e)-8*b*c*d*(B*d+2*A*e))*x)*sqrt(d+e*x)/(b^4*d*(c*d-b*e)*_ +-- sqrt(b*x+c*x^2))+2/3*(16*A*c^2*d^2+b^2*e*(7*B*d+A*e)-8*b*c*d*_ +-- (B*d+2*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*(c*d-b*e)*sqrt(-d)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(4*b*B*d-_ +-- 8*A*c*d+A*b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 527 + +--S 528 OF 765 +--d0:=D(m0,x) +--E 528 + +)clear all + +--S 529 OF 765 +t0:=(A+B*x)/((b*x+c*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ---------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 +-------+ | 2 +--R (c x + 2b c x + b x )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 529 + +--S 530 OF 765 +--r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/_ +-- (b^2*d*(c*d-b*e)*(b*x+c*x^2)^(3/2))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+_ +-- b^2*e*(3*B*d-2*A*e)-b*c*d*(4*B*d+5*A*e))+c*(16*A*c^3*d^3-b^3*e^2*_ +-- (3*B*d-2*A*e)-8*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(13*B*d+4*A*e))*x)*_ +-- sqrt(d+e*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2))-2/3*_ +-- (16*A*c^3*d^3-b^3*e^2*(3*B*d-2*A*e)-8*b*c^2*d^2*(B*d+3*A*e)+_ +-- b^2*c*d*e*(13*B*d+4*A*e))*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*(-d)^(3/2)*_ +-- (c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*_ +-- (8*A*c^2*d^2+b^2*e*(3*B*d-2*A*e)-b*c*d*(4*B*d+5*A*e))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d^2*(c*d-b*e)*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 530 + +--S 531 OF 765 +--d0:=D(m0,x) +--E 531 + +)clear all + +--S 532 OF 765 +t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 5 2 4 2 3 2 2 +-------+ +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 532 + +--S 533 OF 765 +--r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_ +-- (b*x+c*x^2)^(3/2)*sqrt(d+e*x))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+b^2*_ +-- e*(3*B*d-4*A*e)-b*c*d*(4*B*d+3*A*e))+c*(16*A*c^3*d^3+15*b^2*B*_ +-- c*d^2*e-b^3*e^2*(3*B*d-4*A*e)-8*b*c^2*d^2*(B*d+3*A*e))*x)/_ +-- (b^4*d^2*(c*d-b*e)^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*_ +-- (16*A*c^4*d^4-b^3*c*d*e^2*(9*B*d-7*A*e)-8*b*c^3*d^3*(B*d+4*A*e)+_ +-- b^2*c^2*d^2*e*(19*B*d+9*A*e)+b^4*(6*B*d*e^3-8*A*e^4))*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^4*(-d)^(5/2)*(c*d-b*e)^3*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(8*A*c^3*d^3+3*b^2*c*d*e*_ +-- (2*B*d-A*e)-b*c^2*d^2*(4*B*d+9*A*e)-b^3*(6*B*d*e^2-8*A*e^3))*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d^3*(c*d-b*e)^2*_ +-- sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(16*A*c^4*d^4-_ +-- b^3*c*d*e^2*(9*B*d-7*A*e)-8*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*_ +-- e*(19*B*d+9*A*e)+b^4*(6*B*d*e^3-8*A*e^4))*sqrt(b*x+c*x^2)/_ +-- (b^4*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 533 + +--S 534 OF 765 +--d0:=D(m0,x) +--E 534 + +)clear all + +--S 535 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + A c x + B a x + A a)(e x + d) +--R Type: Expression(Integer) +--E 535 + +--S 536 OF 765 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(3*B*c*d^2-2*A*_ + c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^4*(2+m))-c*(3*B*d-A*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R (A c e - 3B c d)m + (7A c e - 21B c d)m + (14A c e - 42B c d)m +--R + +--R 8A c e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 2 2 2 +--R (B a e - 2A c d e + 3B c d )m + (8B a e - 16A c d e + 24B c d )m +--R + +--R 2 2 2 2 +--R (19B a e - 38A c d e + 57B c d )m + 12B a e - 24A c d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (A a e - B a d e + A c d e - B c d )m +--R + +--R 3 2 2 3 2 +--R (9A a e - 9B a d e + 9A c d e - 9B c d )m +--R + +--R 3 2 2 3 3 +--R (26A a e - 26B a d e + 26A c d e - 26B c d )m + 24A a e +--R + +--R 2 2 3 +--R - 24B a d e + 24A c d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 536 + +--S 537 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 OF 765 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 5 4 2 3 6 +--R B c e x + (A c e + 5B c d e )x + (B a e + 5A c d e + 10B c d e )x +--R + +--R 5 4 2 3 3 2 5 +--R (A a e + 5B a d e + 10A c d e + 10B c d e )x +--R + +--R 4 2 3 3 2 4 4 +--R (5A a d e + 10B a d e + 10A c d e + 5B c d e)x +--R + +--R 2 3 3 2 4 5 3 +--R (10A a d e + 10B a d e + 5A c d e + B c d )x +--R + +--R 3 2 4 5 2 4 5 5 +--R (10A a d e + 5B a d e + A c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 538 + +--S 539 OF 765 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^6/e^4+1/7*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^7/e^4-1/8*c*(3*B*d-A*e)*(d+e*x)^8/e^4+1/9*B*_ + c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 1 9 5 8 10 2 7 7 +--R (- B a e + - A c d e + -- B c d e )x +--R 7 7 7 +--R + +--R 1 9 5 8 5 2 7 5 3 6 6 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 6 6 3 3 +--R + +--R 8 2 7 3 6 4 5 5 +--R (A a d e + 2B a d e + 2A c d e + B c d e )x +--R + +--R 5 2 7 5 3 6 5 4 5 1 5 4 4 +--R (- A a d e + - B a d e + - A c d e + - B c d e )x +--R 2 2 4 4 +--R + +--R 10 3 6 5 4 5 1 5 4 3 5 4 5 1 5 4 2 +--R (-- A a d e + - B a d e + - A c d e )x + (- A a d e + - B a d e )x +--R 3 3 3 2 2 +--R + +--R 5 4 1 6 3 1 7 2 1 8 1 9 +--R A a d e x + - A a d e - -- B a d e + --- A c d e - --- B c d +--R 6 42 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 539 + +--S 540 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 4 3 2 2 5 +--R B c e x + (A c e + 4B c d e )x + (B a e + 4A c d e + 6B c d e )x +--R + +--R 4 3 2 2 3 4 +--R (A a e + 4B a d e + 6A c d e + 4B c d e)x +--R + +--R 3 2 2 3 4 3 +--R (4A a d e + 6B a d e + 4A c d e + B c d )x +--R + +--R 2 2 3 4 2 3 4 4 +--R (6A a d e + 4B a d e + A c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 541 + +--S 542 OF 765 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^5/e^4+1/6*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^6/e^4-1/7*c*(3*B*d-A*e)*(d+e*x)^7/e^4+1/8*B*c*_ + (d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 8 4 7 7 +--R - B c e x + (- A c e + - B c d e )x +--R 8 7 7 +--R + +--R 1 8 2 7 2 6 6 +--R (- B a e + - A c d e + B c d e )x +--R 6 3 +--R + +--R 1 8 4 7 6 2 6 4 3 5 5 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 5 5 5 5 +--R + +--R 7 3 2 6 3 5 1 4 4 4 +--R (A a d e + - B a d e + A c d e + - B c d e )x +--R 2 4 +--R + +--R 2 6 4 3 5 1 4 4 3 3 5 1 4 4 2 +--R (2A a d e + - B a d e + - A c d e )x + (2A a d e + - B a d e )x +--R 3 3 2 +--R + +--R 4 4 1 5 3 1 6 2 1 7 1 8 +--R A a d e x + - A a d e - -- B a d e + --- A c d e - --- B c d +--R 5 30 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 542 + +--S 543 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 3 2 2 4 +--R B c e x + (A c e + 3B c d e )x + (B a e + 3A c d e + 3B c d e)x +--R + +--R 3 2 2 3 3 +--R (A a e + 3B a d e + 3A c d e + B c d )x +--R + +--R 2 2 3 2 2 3 3 +--R (3A a d e + 3B a d e + A c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 544 + +--S 545 OF 765 +r0:=-1/4*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^4/e^4+1/5*(3*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^5/e^4-1/6*c*(3*B*d-A*e)*(d+e*x)^6/e^4+_ + 1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 7 1 6 6 +--R - B c e x + (- A c e + - B c d e )x +--R 7 6 2 +--R + +--R 1 7 3 6 3 2 5 5 +--R (- B a e + - A c d e + - B c d e )x +--R 5 5 5 +--R + +--R 1 7 3 6 3 2 5 1 3 4 4 +--R (- A a e + - B a d e + - A c d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 6 2 5 1 3 4 3 3 2 5 1 3 4 2 +--R (A a d e + B a d e + - A c d e )x + (- A a d e + - B a d e )x +--R 3 2 2 +--R + +--R 3 4 1 4 3 1 5 2 1 6 1 7 +--R A a d e x + - A a d e - -- B a d e + -- A c d e - --- B c d +--R 4 20 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 545 + +--S 546 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 546 + +)clear all + +--S 547 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 2 2 3 +--R B c e x + (A c e + 2B c d e)x + (B a e + 2A c d e + B c d )x +--R + +--R 2 2 2 2 2 +--R (A a e + 2B a d e + A c d )x + (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 547 + +--S 548 OF 765 +r0:=a*A*d^2*x+1/2*a*d*(B*d+2*A*e)*x^2+1/3*(A*c*d^2+2*a*B*d*e+a*A*e^2)*x^3+_ + 1/4*(B*c*d^2+2*A*c*d*e+a*B*e^2)*x^4+1/5*c*e*(2*B*d+A*e)*x^5+_ + 1/6*B*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - B c e x + (- A c e + - B c d e)x + (- B a e + - A c d e + - B c d )x +--R 6 5 5 4 2 4 +--R + +--R 1 2 2 1 2 3 1 2 2 2 +--R (- A a e + - B a d e + - A c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 548 + +--S 549 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 OF 765 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + (A c e + B c d)x + (B a e + A c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 550 + +--S 551 OF 765 +r0:=a*A*d*x+1/2*a*(B*d+A*e)*x^2+1/3*(A*c*d+a*B*e)*x^3+1/4*c*(B*d+A*e)*x^4+_ + 1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 4 1 1 3 +--R - B c e x + (- A c e + - B c d)x + (- B a e + - A c d)x +--R 5 4 4 3 3 +--R + +--R 1 1 2 +--R (- A a e + - B a d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 551 + +--S 552 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 OF 765 +t0:=(A+B*x)*(a+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + A c x + B a x + A a +--R Type: Polynomial(Integer) +--E 553 + +--S 554 OF 765 +r0:=a*A*x+1/2*a*B*x^2+1/3*A*c*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 3 1 2 +--R (2) - B c x + - A c x + - B a x + A a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 554 + +--S 555 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 OF 765 +r0:=(B*c*d^2-A*c*d*e+a*B*e^2)*x/e^3-1/2*c*(B*d-A*e)*x^2/e^2+1/3*B*c*x^3/e-_ + (B*d-A*e)*(c*d^2+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 3 3 3 +--R (6A a e - 6B a d e + 6A c d e - 6B c d )log(e x + d) + 2B c e x +--R + +--R 3 2 2 3 2 2 +--R (3A c e - 3B c d e )x + (6B a e - 6A c d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 557 + +--S 558 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 559 + +--S 560 OF 765 +r0:=-c*(2*B*d-A*e)*x/e^3+1/2*B*c*x^2/e^2+(B*d-A*e)*(c*d^2+a*e^2)/_ + (e^4*(d+e*x))+(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((2B a e - 4A c d e + 6B c d e)x + 2B a d e - 4A c d e + 6B c d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 2 2 3 +--R B c e x + (2A c e - 3B c d e )x + (2A c d e - 4B c d e)x - 2A a e +--R + +--R 2 2 3 +--R 2B a d e - 2A c d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 560 + +--S 561 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 561 + +)clear all + +--S 562 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 562 + +--S 563 OF 765 +r0:=B*c*x/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^2)+(-3*B*c*d^2+_ + 2*A*c*d*e-a*B*e^2)/(e^4*(d+e*x))-c*(3*B*d-A*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 +--R (2A c e - 6B c d e )x + (4A c d e - 12B c d e)x + 2A c d e +--R + +--R 3 +--R - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 2 2 3 +--R 2B c e x + 4B c d e x + (- 2B a e + 4A c d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R - B a d e + 3A c d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 563 + +--S 564 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 565 + +--S 566 OF 765 +r0:=1/3*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^2)+c*(3*B*d-A*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 +--R (- 6A c e + 18B c d e )x + (- 3B a e - 6A c d e + 27B c d e)x +--R + +--R 3 2 2 3 +--R - 2A a e - B a d e - 2A c d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 566 + +--S 567 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 568 + +--S 569 OF 765 +r0:=1/4*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^3)+1/2*c*(3*B*d-A*e)/(e^4*(d+e*x)^2)-_ + B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 3 3 2 2 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 1 3 1 2 2 1 3 1 2 +--R (- - B a e - - A c d e - B c d e)x - - A a e - -- B a d e +--R 3 3 4 12 +--R + +--R 1 2 1 3 +--R - -- A c d e - - B c d +--R 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 569 + +--S 570 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 OF 765 +r0:=1/5*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^5)+1/4*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^4)+1/3*c*(3*B*d-A*e)/(e^4*(d+e*x)^3)-_ + 1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 2 +--R + +--R 1 3 1 2 1 2 1 3 1 2 +--R (- - B a e - - A c d e - - B c d e)x - - A a e - -- B a d e +--R 4 6 4 5 20 +--R + +--R 1 2 1 3 +--R - -- A c d e - -- B c d +--R 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 572 + +--S 573 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 OF 765 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + A c x + B a x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 574 + +--S 575 OF 765 +r0:=1/6*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^6)+1/5*(-3*B*c*d^2+2*A*c*d*e-_ + a*B*e^2)/(e^4*(d+e*x)^5)+1/4*c*(3*B*d-A*e)/(e^4*(d+e*x)^4)-_ + 1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 +--R - - B c e x + (- - A c e - - B c d e )x +--R 3 4 4 +--R + +--R 1 3 1 2 1 2 1 3 1 2 +--R (- - B a e - -- A c d e - -- B c d e)x - - A a e - -- B a d e +--R 5 10 10 6 30 +--R + +--R 1 2 1 3 +--R - -- A c d e - -- B c d +--R 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 575 + +--S 576 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 576 + +)clear all + +--S 577 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 m +--R (1) (B c x + A c x + 2B a c x + 2A a c x + B a x + A a )(e x + d) +--R Type: Expression(Integer) +--E 577 + +--S 578 OF 765 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))+(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^6*(2+m))-2*c*_ + (5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3+m)/(e^6*_ + (3+m))+2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(4+m)/(e^6*(4+m))-_ + c^2*(5*B*d-A*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 2 2 3 +--R (A c e - 5B c d)m + (16A c e - 80B c d)m + (95A c e - 475B c d)m +--R + +--R 2 2 2 2 2 2 +--R (260A c e - 1300B c d)m + (324A c e - 1620B c d)m + 144A c e +--R + +--R 2 +--R - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 5 +--R (2B a c e - 4A c d e + 10B c d )m +--R + +--R 2 2 2 2 4 +--R (34B a c e - 68A c d e + 170B c d )m +--R + +--R 2 2 2 2 3 +--R (214B a c e - 428A c d e + 1070B c d )m +--R + +--R 2 2 2 2 2 +--R (614B a c e - 1228A c d e + 3070B c d )m +--R + +--R 2 2 2 2 2 2 +--R (792B a c e - 1584A c d e + 3960B c d )m + 360B a c e - 720A c d e +--R + +--R 2 2 +--R 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 5 +--R (2A a c e - 6B a c d e + 6A c d e - 10B c d )m +--R + +--R 3 2 2 2 2 3 4 +--R (36A a c e - 108B a c d e + 108A c d e - 180B c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (242A a c e - 726B a c d e + 726A c d e - 1210B c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (744A a c e - 2232B a c d e + 2232A c d e - 3720B c d )m +--R + +--R 3 2 2 2 2 3 +--R (1016A a c e - 3048B a c d e + 3048A c d e - 5080B c d )m +--R + +--R 3 2 2 2 2 3 +--R 480A a c e - 1440B a c d e + 1440A c d e - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 3 2 2 2 3 2 4 5 +--R (B a e - 4A a c d e + 6B a c d e - 4A c d e + 5B c d )m +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (19B a e - 76A a c d e + 114B a c d e - 76A c d e + 95B c d )m +--R + +--R 2 4 3 2 2 2 3 +--R 137B a e - 548A a c d e + 822B a c d e - 548A c d e +--R + +--R 2 4 +--R 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R 461B a e - 1844A a c d e + 2766B a c d e - 1844A c d e +--R + +--R 2 4 +--R 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 3 2 2 2 3 +--R 702B a e - 2808A a c d e + 4212B a c d e - 2808A c d e +--R + +--R 2 4 +--R 3510B c d +--R * +--R m +--R + +--R 2 4 3 2 2 2 3 2 4 +--R 360B a e - 1440A a c d e + 2160B a c d e - 1440A c d e + 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 5 +--R (A a e - B a d e + 2A a c d e - 2B a c d e + A c d e - B c d )m +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R 20A a e - 20B a d e + 40A a c d e - 40B a c d e + 20A c d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 155A a e - 155B a d e + 310A a c d e - 310B a c d e +--R + +--R 2 4 2 5 +--R 155A c d e - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 580A a e - 580B a d e + 1160A a c d e - 1160B a c d e +--R + +--R 2 4 2 5 +--R 580A c d e - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 1044A a e - 1044B a d e + 2088A a c d e - 2088B a c d e +--R + +--R 2 4 2 5 +--R 1044A c d e - 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 2 3 3 2 +--R 720A a e - 720B a d e + 1440A a c d e - 1440B a c d e +--R + +--R 2 4 2 5 +--R 720A c d e - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 578 + +--S 579 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 OF 765 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 10 2 5 2 4 9 5 2 4 2 2 3 8 +--R B c e x + (A c e + 5B c d e )x + (2B a c e + 5A c d e + 10B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 7 +--R (2A a c e + 10B a c d e + 10A c d e + 10B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 6 +--R (B a e + 10A a c d e + 20B a c d e + 10A c d e + 5B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 5 +--R (A a e + 5B a d e + 20A a c d e + 20B a c d e + 5A c d e + B c d )x +--R + +--R 2 4 2 2 3 3 2 4 2 5 4 +--R (5A a d e + 10B a d e + 20A a c d e + 10B a c d e + A c d )x +--R + +--R 2 2 3 2 3 2 4 5 3 +--R (10A a d e + 10B a d e + 10A a c d e + 2B a c d )x +--R + +--R 2 3 2 2 4 5 2 2 4 2 5 2 5 +--R (10A a d e + 5B a d e + 2A a c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 580 + +--S 581 OF 765 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^6/e^6+1/7*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^6-1/4*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^8/e^6+2/9*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^9/e^6-1/10*c^2*(5*B*d-A*e)*(d+e*x)^10/e^6+_ + 1/11*B*c^2*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 2 11 11 1 2 11 1 2 10 10 +--R -- B c e x + (-- A c e + - B c d e )x +--R 11 10 2 +--R + +--R 2 11 5 2 10 10 2 2 9 9 +--R (- B a c e + - A c d e + -- B c d e )x +--R 9 9 9 +--R + +--R 1 11 5 10 5 2 2 9 5 2 3 8 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 4 4 4 4 +--R + +--R 1 2 11 10 10 20 2 9 10 2 3 8 5 2 4 7 7 +--R (- B a e + -- A a c d e + -- B a c d e + -- A c d e + - B c d e )x +--R 7 7 7 7 7 +--R + +--R 1 2 11 5 2 10 10 2 9 10 3 8 5 2 4 7 +--R - A a e + - B a d e + -- A a c d e + -- B a c d e + - A c d e +--R 6 6 3 3 6 +--R + +--R 1 2 5 6 +--R - B c d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 2 10 2 2 9 3 8 4 7 1 2 5 6 5 +--R (A a d e + 2B a d e + 4A a c d e + 2B a c d e + - A c d e )x +--R 5 +--R + +--R 5 2 2 9 5 2 3 8 5 4 7 1 5 6 4 +--R (- A a d e + - B a d e + - A a c d e + - B a c d e )x +--R 2 2 2 2 +--R + +--R 10 2 3 8 5 2 4 7 2 5 6 3 5 2 4 7 1 2 5 6 2 +--R (-- A a d e + - B a d e + - A a c d e )x + (- A a d e + - B a d e )x +--R 3 3 3 2 2 +--R + +--R 2 5 6 1 2 6 5 1 2 7 4 1 8 3 1 9 2 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 6 42 84 252 +--R + +--R 1 2 10 1 2 11 +--R ---- A c d e - ---- B c d +--R 1260 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 581 + +--S 582 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 4 2 3 2 2 2 7 +--R B c e x + (A c e + 4B c d e )x + (2B a c e + 4A c d e + 6B c d e )x +--R + +--R 4 3 2 2 2 2 3 6 +--R (2A a c e + 8B a c d e + 6A c d e + 4B c d e)x +--R + +--R 2 4 3 2 2 2 3 2 4 5 +--R (B a e + 8A a c d e + 12B a c d e + 4A c d e + B c d )x +--R + +--R 2 4 2 3 2 2 3 2 4 4 +--R (A a e + 4B a d e + 12A a c d e + 8B a c d e + A c d )x +--R + +--R 2 3 2 2 2 3 4 3 +--R (4A a d e + 6B a d e + 8A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 3 4 2 2 3 2 4 2 4 +--R (6A a d e + 4B a d e + 2A a c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 583 + +--S 584 OF 765 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^5/e^6+1/6*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^6-2/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^7/e^6+1/4*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^8/e^6-1/9*c^2*(5*B*d-A*e)*(d+e*x)^9/e^6+_ + 1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 10 4 2 9 9 +--R -- B c e x + (- A c e + - B c d e )x +--R 10 9 9 +--R + +--R 1 10 1 2 9 3 2 2 8 8 +--R (- B a c e + - A c d e + - B c d e )x +--R 4 2 4 +--R + +--R 2 10 8 9 6 2 2 8 4 2 3 7 7 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 7 7 7 7 +--R + +--R 1 2 10 4 9 2 8 2 2 3 7 1 2 4 6 6 +--R (- B a e + - A a c d e + 2B a c d e + - A c d e + - B c d e )x +--R 6 3 3 6 +--R + +--R 1 2 10 4 2 9 12 2 8 8 3 7 1 2 4 6 5 +--R (- A a e + - B a d e + -- A a c d e + - B a c d e + - A c d e )x +--R 5 5 5 5 5 +--R + +--R 2 9 3 2 2 8 3 7 1 4 6 4 +--R (A a d e + - B a d e + 2A a c d e + - B a c d e )x +--R 2 2 +--R + +--R 2 2 8 4 2 3 7 2 4 6 3 2 3 7 1 2 4 6 2 +--R (2A a d e + - B a d e + - A a c d e )x + (2A a d e + - B a d e )x +--R 3 3 2 +--R + +--R 2 4 6 1 2 5 5 1 2 6 4 2 7 3 1 8 2 +--R A a d e x + - A a d e - -- B a d e + --- A a c d e - --- B a c d e +--R 5 30 105 140 +--R + +--R 1 2 9 1 2 10 +--R --- A c d e - ---- B c d +--R 630 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 584 + +--S 585 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 3 2 2 2 2 6 +--R B c e x + (A c e + 3B c d e )x + (2B a c e + 3A c d e + 3B c d e)x +--R + +--R 3 2 2 2 2 3 5 +--R (2A a c e + 6B a c d e + 3A c d e + B c d )x +--R + +--R 2 3 2 2 2 3 4 +--R (B a e + 6A a c d e + 6B a c d e + A c d )x +--R + +--R 2 3 2 2 2 3 3 +--R (A a e + 3B a d e + 6A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 3 2 2 2 2 3 2 3 +--R (3A a d e + 3B a d e + 2A a c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 586 + +--S 587 OF 765 +r0:=-1/4*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^4/e^6+1/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^5/e^6-1/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^6/e^6+2/7*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^6-1/8*c^2*(5*B*d-A*e)*(d+e*x)^8/e^6+_ + 1/9*B*c^2*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 1 2 9 9 1 2 9 3 2 8 8 +--R - B c e x + (- A c e + - B c d e )x +--R 9 8 8 +--R + +--R 2 9 3 2 8 3 2 2 7 7 +--R (- B a c e + - A c d e + - B c d e )x +--R 7 7 7 +--R + +--R 1 9 8 1 2 2 7 1 2 3 6 6 +--R (- A a c e + B a c d e + - A c d e + - B c d e )x +--R 3 2 6 +--R + +--R 1 2 9 6 8 6 2 7 1 2 3 6 5 +--R (- B a e + - A a c d e + - B a c d e + - A c d e )x +--R 5 5 5 5 +--R + +--R 1 2 9 3 2 8 3 2 7 1 3 6 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d e )x +--R 4 4 2 2 +--R + +--R 2 8 2 2 7 2 3 6 3 3 2 2 7 1 2 3 6 2 +--R (A a d e + B a d e + - A a c d e )x + (- A a d e + - B a d e )x +--R 3 2 2 +--R + +--R 2 3 6 1 2 4 5 1 2 5 4 1 6 3 1 7 2 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - -- B a c d e +--R 4 20 30 70 +--R + +--R 1 2 8 1 2 9 +--R --- A c d e - --- B c d +--R 280 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 587 + +--S 588 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 2 2 2 2 5 +--R B c e x + (A c e + 2B c d e)x + (2B a c e + 2A c d e + B c d )x +--R + +--R 2 2 2 4 2 2 2 3 +--R (2A a c e + 4B a c d e + A c d )x + (B a e + 4A a c d e + 2B a c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (A a e + 2B a d e + 2A a c d )x + (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 589 + +--S 590 OF 765 +r0:=a^2*A*d^2*x+1/2*a^2*d*(B*d+2*A*e)*x^2+1/3*a*(2*A*c*d^2+2*a*B*d*e+_ + a*A*e^2)*x^3+1/4*a*(2*B*c*d^2+4*A*c*d*e+a*B*e^2)*x^4+1/5*c*(A*c*d^2+_ + 4*a*B*d*e+2*a*A*e^2)*x^5+1/6*c*(B*c*d^2+2*A*c*d*e+2*a*B*e^2)*x^6+_ + 1/7*c^2*e*(2*B*d+A*e)*x^7+1/8*B*c^2*e^2*x^8 +--R +--R +--R (2) +--R 1 2 2 8 1 2 2 2 2 7 +--R - B c e x + (- A c e + - B c d e)x +--R 8 7 7 +--R + +--R 1 2 1 2 1 2 2 6 +--R (- B a c e + - A c d e + - B c d )x +--R 3 3 6 +--R + +--R 2 2 4 1 2 2 5 +--R (- A a c e + - B a c d e + - A c d )x +--R 5 5 5 +--R + +--R 1 2 2 1 2 4 +--R (- B a e + A a c d e + - B a c d )x +--R 4 2 +--R + +--R 1 2 2 2 2 2 2 3 2 1 2 2 2 2 2 +--R (- A a e + - B a d e + - A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 590 + +--S 591 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 591 + +)clear all + +--S 592 OF 765 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 2 4 +--R B c e x + (A c e + B c d)x + (2B a c e + A c d)x +--R + +--R 3 2 2 2 2 2 +--R (2A a c e + 2B a c d)x + (B a e + 2A a c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 592 + +--S 593 OF 765 +r0:=a^2*A*d*x+1/2*a^2*(B*d+A*e)*x^2+1/3*a*(2*A*c*d+a*B*e)*x^3+1/2*a*c*_ + (B*d+A*e)*x^4+1/5*c*(A*c*d+2*a*B*e)*x^5+1/6*c^2*(B*d+A*e)*x^6+_ + 1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 2 6 2 1 2 5 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 7 6 6 5 5 +--R + +--R 1 1 4 1 2 2 3 1 2 1 2 2 +--R (- A a c e + - B a c d)x + (- B a e + - A a c d)x + (- A a e + - B a d)x +--R 2 2 3 3 2 2 +--R + +--R 2 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 593 + +--S 594 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R (1) B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R Type: Polynomial(Integer) +--E 595 + +--S 596 OF 765 +r0:=a^2*A*x+2/3*a*A*c*x^3+1/5*A*c^2*x^5+1/6*B*(a+c*x^2)^3/c +--R +--R +--R (2) +--R 1 3 6 1 3 5 1 2 4 2 2 3 1 2 2 2 1 3 +--R - B c x + - A c x + - B a c x + - A a c x + - B a c x + A a c x + - B a +--R 6 5 2 3 2 6 +--R ----------------------------------------------------------------------------- +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 596 + +--S 597 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 598 + +--S 599 OF 765 +r0:=(B*(c*d^2+a*e^2)^2-A*c*d*e*(c*d^2+2*a*e^2))*x/e^5-1/2*c*(B*d-A*e)*_ + (c*d^2+2*a*e^2)*x^2/e^4+1/3*c*(B*c*d^2-A*c*d*e+2*a*B*e^2)*x^3/e^3-_ + 1/4*c^2*(B*d-A*e)*x^4/e^2+1/5*B*c^2*x^5/e-(B*d-A*e)*(c*d^2+a*e^2)^2*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 2 3 3 2 2 4 +--R 60A a e - 60B a d e + 120A a c d e - 120B a c d e + 60A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + (15A c e - 15B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (40B a c e - 20A c d e + 20B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (60A a c e - 60B a c d e + 30A c d e - 30B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (60B a e - 120A a c d e + 120B a c d e - 60A c d e + 60B c d e)x +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 599 + +--S 600 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 601 + +--S 602 OF 765 +r0:=-c*(4*B*c*d^3-3*A*c*d^2*e+4*a*B*d*e^2-2*a*A*e^3)*x/e^5+1/2*c*_ + (3*B*c*d^2-2*A*c*d*e+2*a*B*e^2)*x^2/e^4-1/3*c^2*(2*B*d-A*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x))+_ + (c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 4 2 3 2 3 2 2 4 +--R (12B a e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d e)x +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 48A a c d e + 72B a c d e - 48A c d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + (4A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 8A c d e + 10B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (24A a c e - 36B a c d e + 24A c d e - 30B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 5 +--R (24A a c d e - 48B a c d e + 36A c d e - 48B c d e)x - 12A a e +--R + +--R 2 4 2 3 3 2 2 4 2 5 +--R 12B a d e - 24A a c d e + 24B a c d e - 12A c d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 602 + +--S 603 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^3 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 604 + +--S 605 OF 765 +r0:=c*(6*B*c*d^2-3*A*c*d*e+2*a*B*e^2)*x/e^5-1/2*c^2*(3*B*d-A*e)*x^2/e^4+_ + 1/3*B*c^2*x^3/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^2)-_ + (c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x))-_ + 2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 4 2 2 3 2 3 2 2 +--R (12A a c e - 36B a c d e + 36A c d e - 60B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (24A a c d e - 72B a c d e + 72A c d e - 120B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R 12A a c d e - 36B a c d e + 36A c d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + (3A c e - 5B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (12B a c e - 12A c d e + 20B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (24B a c d e - 33A c d e + 63B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 6B a e + 24A a c d e - 24B a c d e + 6A c d e + 6B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - 3B a d e + 18A a c d e - 30B a c d e + 21A c d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 605 + +--S 606 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 606 + +)clear all + +--S 607 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^4 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 607 + +--S 608 OF 765 +r0:=-c^2*(4*B*d-A*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*(B*d-A*e)*(c*d^2+_ + a*e^2)^2/(e^6*(d+e*x)^3)-1/2*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+_ + a*B*e^2)/(e^6*(d+e*x)^2)+2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-_ + a*A*e^3)/(e^6*(d+e*x))+2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 2 4 2 2 3 3 +--R (12B a c e - 24A c d e + 60B c d e )x +--R + +--R 4 2 2 3 2 3 2 2 +--R (36B a c d e - 72A c d e + 180B c d e )x +--R + +--R 2 3 2 3 2 2 4 3 2 2 4 +--R (36B a c d e - 72A c d e + 180B c d e)x + 12B a c d e - 24A c d e +--R + +--R 2 5 +--R 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 2 4 2 2 3 3 +--R 3B c e x + (6A c e - 15B c d e )x + (18A c d e - 63B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e + 36B a c d e - 18A c d e - 9B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 3B a e - 12A a c d e + 54B a c d e - 54A c d e + 81B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 2A a e - B a d e - 4A a c d e + 22B a c d e - 26A c d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 608 + +--S 609 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^5 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 610 + +--S 611 OF 765 +r0:=B*c^2*x/e^5+1/4*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^4)-1/3*(c*d^2+_ + a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^3)+c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^2)-2*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x))-c^2*(5*B*d-A*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 4 2 4 2 2 3 3 +--R (12A c e - 60B c d e )x + (48A c d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 2 3 2 2 4 2 4 +--R (72A c d e - 360B c d e )x + (48A c d e - 240B c d e)x + 12A c d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 5 2 4 2 2 3 3 +--R 12B c e x + 48B c d e x + (- 24B a c e + 48A c d e - 48B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 12A a c e - 36B a c d e + 108A c d e - 252B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 4B a e - 8A a c d e - 24B a c d e + 88A c d e - 248B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 3A a e - B a d e - 2A a c d e - 6B a c d e + 25A c d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 611 + +--S 612 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^6 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 613 + +--S 614 OF 765 +r0:=1/5*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^5)-1/4*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^4)+2/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^3)-c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^2)+c^2*(5*B*d-A*e)/(e^6*(d+e*x))+_ + B*c^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R (- 60A c e + 300B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 60B a c e - 120A c d e + 900B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 40A a c e - 60B a c d e - 120A c d e + 1100B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 15B a e - 20A a c d e - 30B a c d e - 60A c d e + 625B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 2 5 +--R - 12A a e - 3B a d e - 4A a c d e - 6B a c d e - 12A c d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Expression(Integer) +--E 614 + +--S 615 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 616 + +--S 617 OF 765 +r0:=1/6*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^6)-1/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^5)+1/2*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^4)-2/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^3)+1/2*c^2*(5*B*d-A*e)/_ + (e^6*(d+e*x)^2)-B*c^2/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 5 5 1 2 5 5 2 4 4 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 2 5 2 2 4 10 2 2 3 3 +--R (- - B a c e - - A c d e - -- B c d e )x +--R 3 3 3 +--R + +--R 1 5 1 4 1 2 2 3 5 2 3 2 2 +--R (- - A a c e - - B a c d e - - A c d e - - B c d e )x +--R 2 2 2 2 +--R + +--R 1 2 5 1 4 1 2 3 1 2 3 2 2 4 +--R (- - B a e - - A a c d e - - B a c d e - - A c d e - B c d e)x +--R 5 5 5 5 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - -- A a c d e - -- B a c d e - -- A c d e +--R 6 30 30 30 30 +--R + +--R 1 2 5 +--R - - B c d +--R 6 +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 617 + +--S 618 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 619 + +--S 620 OF 765 +r0:=1/7*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^7)-1/6*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^6)+2/5*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^5)-1/2*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^4)+1/3*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^3)-1/2*B*c^2/(e^6*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 5 2 4 4 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 6 +--R + +--R 1 5 1 2 4 5 2 2 3 3 +--R (- - B a c e - - A c d e - - B c d e )x +--R 2 3 6 +--R + +--R 2 5 3 4 1 2 2 3 1 2 3 2 2 +--R (- - A a c e - -- B a c d e - - A c d e - - B c d e )x +--R 5 10 5 2 +--R + +--R 1 2 5 2 4 1 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - - B c d e)x +--R 6 15 10 15 6 +--R + +--R 1 2 5 1 2 4 2 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - --- A a c d e - -- B a c d e - --- A c d e +--R 7 42 105 70 105 +--R + +--R 1 2 5 +--R - -- B c d +--R 42 +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 6 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 620 + +--S 621 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 622 + +--S 623 OF 765 +r0:=1/8*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^8)-1/7*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^7)+1/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^6)-2/5*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^5)+1/4*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^4)-1/3*B*c^2/(e^6*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 5 2 4 4 +--R - - B c e x + (- - A c e - -- B c d e )x +--R 3 4 12 +--R + +--R 2 5 1 2 4 1 2 2 3 3 +--R (- - B a c e - - A c d e - - B c d e )x +--R 5 5 3 +--R + +--R 1 5 1 4 1 2 2 3 1 2 3 2 2 +--R (- - A a c e - - B a c d e - -- A c d e - - B c d e )x +--R 3 5 10 6 +--R + +--R 1 2 5 2 4 2 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - -- B c d e)x +--R 7 21 35 35 21 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e - --- A c d e +--R 8 56 84 140 280 +--R + +--R 1 2 5 +--R - --- B c d +--R 168 +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 5 9 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 8 2 7 7 8 6 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 623 + +--S 624 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 OF 765 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^10 +--R +--R +--R (1) +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 625 + +--S 626 OF 765 +r0:=1/9*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^9)-1/8*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^8)+2/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^7)-1/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^6)+1/5*c^2*(5*B*d-A*e)/(e^6*_ + (d+e*x)^5)-1/4*B*c^2/(e^6*(d+e*x)^4) +--R +--R +--R (2) +--R 1 2 5 5 1 2 5 1 2 4 4 +--R - - B c e x + (- - A c e - - B c d e )x +--R 4 5 4 +--R + +--R 1 5 2 2 4 1 2 2 3 3 +--R (- - B a c e - -- A c d e - - B c d e )x +--R 3 15 6 +--R + +--R 2 5 1 4 2 2 2 3 1 2 3 2 2 +--R (- - A a c e - - B a c d e - -- A c d e - -- B c d e )x +--R 7 7 35 14 +--R + +--R 1 2 5 1 4 1 2 3 1 2 3 2 1 2 4 +--R (- - B a e - -- A a c d e - -- B a c d e - -- A c d e - -- B c d e)x +--R 8 14 28 70 56 +--R + +--R 1 2 5 1 2 4 1 2 3 1 3 2 1 2 4 +--R - - A a e - -- B a d e - --- A a c d e - --- B a c d e - --- A c d e +--R 9 72 126 252 630 +--R + +--R 1 2 5 +--R - --- B c d +--R 504 +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 5 10 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 9 3 7 8 2 8 7 9 6 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 626 + +--S 627 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 OF 765 +t0:=(A+B*x)*(d+e*x)^m*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 628 + +--S 629 OF 765 +r0:=-(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))+(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^8*(2+m))-3*c*(c*d^2+_ + a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3+m)/_ + (e^8*(3+m))-c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*_ + c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(4+m)/(e^8*(4+m))-c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(5+m)/(e^8*(5+m))+_ + 3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(6+m)/(e^8*(6+m))-_ + c^3*(7*B*d-A*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 3 7 3 3 6 +--R (A c e - 7B c d)m + (29A c e - 203B c d)m +--R + +--R 3 3 5 3 3 4 +--R (343A c e - 2401B c d)m + (2135A c e - 14945B c d)m +--R + +--R 3 3 3 3 3 2 +--R (7504A c e - 52528B c d)m + (14756A c e - 103292B c d)m +--R + +--R 3 3 3 3 +--R (14832A c e - 103824B c d)m + 5760A c e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 3 3 2 7 +--R (3B a c e - 6A c d e + 21B c d )m +--R + +--R 2 2 3 3 2 6 +--R (90B a c e - 180A c d e + 630B c d )m +--R + +--R 2 2 3 3 2 5 +--R (1098B a c e - 2196A c d e + 7686B c d )m +--R + +--R 2 2 3 3 2 4 +--R (7020B a c e - 14040A c d e + 49140B c d )m +--R + +--R 2 2 3 3 2 3 +--R (25227B a c e - 50454A c d e + 176589B c d )m +--R + +--R 2 2 3 3 2 2 +--R (50490B a c e - 100980A c d e + 353430B c d )m +--R + +--R 2 2 3 3 2 2 2 +--R (51432B a c e - 102864A c d e + 360024B c d )m + 20160B a c e +--R + +--R 3 3 2 +--R - 40320A c d e + 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 2 2 3 2 3 3 7 +--R (3A a c e - 15B a c d e + 15A c d e - 35B c d )m +--R + +--R 2 3 2 2 3 2 3 3 6 +--R (93A a c e - 465B a c d e + 465A c d e - 1085B c d )m +--R + +--R 2 3 2 2 3 2 3 3 5 +--R (1173A a c e - 5865B a c d e + 5865A c d e - 13685B c d )m +--R + +--R 2 3 2 2 3 2 3 3 4 +--R (7743A a c e - 38715B a c d e + 38715A c d e - 90335B c d )m +--R + +--R 2 3 2 2 3 2 3 3 3 +--R (28632A a c e - 143160B a c d e + 143160A c d e - 334040B c d )m +--R + +--R 2 3 2 2 3 2 3 3 2 +--R (58692A a c e - 293460B a c d e + 293460A c d e - 684740B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R (60912A a c e - 304560B a c d e + 304560A c d e - 710640B c d )m +--R + +--R 2 3 2 2 3 2 3 3 +--R 24192A a c e - 120960B a c d e + 120960A c d e - 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 4 2 3 2 2 2 3 3 3 4 7 +--R (3B a c e - 12A a c d e + 30B a c d e - 20A c d e + 35B c d )m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 96B a c e - 384A a c d e + 960B a c d e - 640A c d e +--R + +--R 3 4 +--R 1120B c d +--R * +--R 6 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 1254B a c e - 5016A a c d e + 12540B a c d e - 8360A c d e +--R + +--R 3 4 +--R 14630B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 8592B a c e - 34368A a c d e + 85920B a c d e - 57280A c d e +--R + +--R 3 4 +--R 100240B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 32979B a c e - 131916A a c d e + 329790B a c d e +--R + +--R 3 3 3 4 +--R - 219860A c d e + 384755B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 69936B a c e - 279744A a c d e + 699360B a c d e +--R + +--R 3 3 3 4 +--R - 466240A c d e + 815920B c d +--R * +--R 2 +--R m +--R + +--R 2 4 2 3 2 2 2 +--R 74628B a c e - 298512A a c d e + 746280B a c d e +--R + +--R 3 3 3 4 +--R - 497520A c d e + 870660B c d +--R * +--R m +--R + +--R 2 4 2 3 2 2 2 3 3 +--R 30240B a c e - 120960A a c d e + 302400B a c d e - 201600A c d e +--R + +--R 3 4 +--R 352800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 +--R 3A a c e - 9B a c d e + 18A a c d e - 30B a c d e + 15A c d e +--R + +--R 3 5 +--R - 21B c d +--R * +--R 7 +--R m +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 99A a c e - 297B a c d e + 594A a c d e - 990B a c d e +--R + +--R 3 4 3 5 +--R 495A c d e - 693B c d +--R * +--R 6 +--R m +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 1341A a c e - 4023B a c d e + 8046A a c d e - 13410B a c d e +--R + +--R 3 4 3 5 +--R 6705A c d e - 9387B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 9585A a c e - 28755B a c d e + 57510A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 95850B a c d e + 47925A c d e - 67095B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 38592A a c e - 115776B a c d e + 231552A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 385920B a c d e + 192960A c d e - 270144B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 86076A a c e - 258228B a c d e + 516456A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 860760B a c d e + 430380A c d e - 602532B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 96144A a c e - 288432B a c d e + 576864A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 961440B a c d e + 480720A c d e - 673008B c d +--R * +--R m +--R + +--R 2 5 2 4 2 2 3 +--R 40320A a c e - 120960B a c d e + 241920A a c d e +--R + +--R 2 3 2 3 4 3 5 +--R - 403200B a c d e + 201600A c d e - 282240B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 6 2 5 2 2 4 2 3 3 2 4 2 +--R B a e - 6A a c d e + 9B a c d e - 12A a c d e + 15B a c d e +--R + +--R 3 5 3 6 +--R - 6A c d e + 7B c d +--R * +--R 7 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 34B a e - 204A a c d e + 306B a c d e - 408A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 510B a c d e - 204A c d e + 238B c d +--R * +--R 6 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 478B a e - 2868A a c d e + 4302B a c d e - 5736A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 7170B a c d e - 2868A c d e + 3346B c d +--R * +--R 5 +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 3580B a e - 21480A a c d e + 32220B a c d e - 42960A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 53700B a c d e - 21480A c d e + 25060B c d +--R * +--R 4 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 15289B a e - 91734A a c d e + 137601B a c d e +--R + +--R 2 3 3 2 4 2 3 5 3 6 +--R - 183468A a c d e + 229335B a c d e - 91734A c d e + 107023B c d +--R * +--R 3 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 36706B a e - 220236A a c d e + 330354B a c d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 440472A a c d e + 550590B a c d e - 220236A c d e +--R + +--R 3 6 +--R 256942B c d +--R * +--R 2 +--R m +--R + +--R 3 6 2 5 2 2 4 +--R 44712B a e - 268272A a c d e + 402408B a c d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 536544A a c d e + 670680B a c d e - 268272A c d e +--R + +--R 3 6 +--R 312984B c d +--R * +--R m +--R + +--R 3 6 2 5 2 2 4 2 3 3 +--R 20160B a e - 120960A a c d e + 181440B a c d e - 241920A a c d e +--R + +--R 2 4 2 3 5 3 6 +--R 302400B a c d e - 120960A c d e + 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R A a e - B a d e + 3A a c d e - 3B a c d e + 3A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 3B a c d e + A c d e - B c d +--R * +--R 7 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 35A a e - 35B a d e + 105A a c d e - 105B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 105A a c d e - 105B a c d e + 35A c d e - 35B c d +--R * +--R 6 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 511A a e - 511B a d e + 1533A a c d e - 1533B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 1533A a c d e - 1533B a c d e + 511A c d e - 511B c d +--R * +--R 5 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 4025A a e - 4025B a d e + 12075A a c d e - 12075B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 12075A a c d e - 12075B a c d e + 4025A c d e - 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 18424A a e - 18424B a d e + 55272A a c d e - 55272B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 55272A a c d e - 55272B a c d e + 18424A c d e - 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 48860A a e - 48860B a d e + 146580A a c d e - 146580B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 146580A a c d e - 146580B a c d e + 48860A c d e - 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 69264A a e - 69264B a d e + 207792A a c d e - 207792B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 207792A a c d e - 207792B a c d e + 69264A c d e - 69264B c d +--R * +--R m +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 40320A a e - 40320B a d e + 120960A a c d e - 120960B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 120960A a c d e - 120960B a c d e + 40320A c d e - 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 629 + +--S 630 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 OF 765 +t0:=(A+B*x)*(d+e*x)^5*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 5 12 3 5 3 4 11 +--R B c e x + (A c e + 5B c d e )x +--R + +--R 2 5 3 4 3 2 3 10 +--R (3B a c e + 5A c d e + 10B c d e )x +--R + +--R 2 5 2 4 3 2 3 3 3 2 9 +--R (3A a c e + 15B a c d e + 10A c d e + 10B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 3 2 3 4 8 +--R (3B a c e + 15A a c d e + 30B a c d e + 10A c d e + 5B c d e)x +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 +--R 3A a c e + 15B a c d e + 30A a c d e + 30B a c d e + 5A c d e +--R + +--R 3 5 +--R B c d +--R * +--R 7 +--R x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R B a e + 15A a c d e + 30B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R 6 +--R x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R A a e + 5B a d e + 30A a c d e + 30B a c d e + 15A a c d e +--R + +--R 2 5 +--R 3B a c d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 4 +--R (5A a d e + 10B a d e + 30A a c d e + 15B a c d e + 3A a c d )x +--R + +--R 3 2 3 3 3 2 2 4 2 5 3 +--R (10A a d e + 10B a d e + 15A a c d e + 3B a c d )x +--R + +--R 3 3 2 3 4 2 5 2 3 4 3 5 3 5 +--R (10A a d e + 5B a d e + 3A a c d )x + (5A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 631 + +--S 632 OF 765 +r0:=-1/6*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^6/e^8+1/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^8-3/8*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^8/e^8-1/9*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))*(d+e*x)^9/e^8-1/10*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*_ + B*d*e^2-3*a*A*e^3)*(d+e*x)^10/e^8+3/11*c^2*(7*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)*(d+e*x)^11/e^8-1/12*c^3*(7*B*d-A*e)*(d+e*x)^12/e^8+1/13*_ + B*c^3*(d+e*x)^13/e^8 +--R +--R +--R (2) +--R 1 3 13 13 1 3 13 5 3 12 12 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 13 12 12 +--R + +--R 3 2 13 5 3 12 10 3 2 11 11 +--R (-- B a c e + -- A c d e + -- B c d e )x +--R 11 11 11 +--R + +--R 3 2 13 3 2 12 3 2 11 3 3 10 10 +--R (-- A a c e + - B a c d e + A c d e + B c d e )x +--R 10 2 +--R + +--R 1 2 13 5 2 12 10 2 2 11 10 3 3 10 +--R - B a c e + - A a c d e + -- B a c d e + -- A c d e +--R 3 3 3 9 +--R + +--R 5 3 4 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 13 15 2 12 15 2 2 11 15 2 3 10 +--R - A a c e + -- B a c d e + -- A a c d e + -- B a c d e +--R 8 8 4 4 +--R + +--R 5 3 4 9 1 3 5 8 +--R - A c d e + - B c d e +--R 8 8 +--R * +--R 8 +--R x +--R + +--R 1 3 13 15 2 12 30 2 2 11 30 2 3 10 +--R - B a e + -- A a c d e + -- B a c d e + -- A a c d e +--R 7 7 7 7 +--R + +--R 15 2 4 9 1 3 5 8 +--R -- B a c d e + - A c d e +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 13 5 3 12 2 2 11 2 3 10 5 2 4 9 +--R - A a e + - B a d e + 5A a c d e + 5B a c d e + - A a c d e +--R 6 6 2 +--R + +--R 1 2 5 8 +--R - B a c d e +--R 2 +--R * +--R 6 +--R x +--R + +--R 3 12 3 2 11 2 3 10 2 4 9 3 2 5 8 5 +--R (A a d e + 2B a d e + 6A a c d e + 3B a c d e + - A a c d e )x +--R 5 +--R + +--R 5 3 2 11 5 3 3 10 15 2 4 9 3 2 5 8 4 +--R (- A a d e + - B a d e + -- A a c d e + - B a c d e )x +--R 2 2 4 4 +--R + +--R 10 3 3 10 5 3 4 9 2 5 8 3 5 3 4 9 1 3 5 8 2 +--R (-- A a d e + - B a d e + A a c d e )x + (- A a d e + - B a d e )x +--R 3 3 2 2 +--R + +--R 3 5 8 1 3 6 7 1 3 7 6 1 2 8 5 1 2 9 4 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 6 42 56 168 +--R + +--R 1 2 10 3 1 2 11 2 1 3 12 1 3 13 +--R --- A a c d e - --- B a c d e + ---- A c d e - ----- B c d +--R 420 924 5544 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 632 + +--S 633 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 OF 765 +t0:=(A+B*x)*(d+e*x)^4*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 4 3 3 10 2 4 3 3 3 2 2 9 +--R B c e x + (A c e + 4B c d e )x + (3B a c e + 4A c d e + 6B c d e )x +--R + +--R 2 4 2 3 3 2 2 3 3 8 +--R (3A a c e + 12B a c d e + 6A c d e + 4B c d e)x +--R + +--R 2 4 2 3 2 2 2 3 3 3 4 7 +--R (3B a c e + 12A a c d e + 18B a c d e + 4A c d e + B c d )x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 6 +--R (3A a c e + 12B a c d e + 18A a c d e + 12B a c d e + A c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 5 +--R (B a e + 12A a c d e + 18B a c d e + 12A a c d e + 3B a c d )x +--R + +--R 3 4 3 3 2 2 2 2 3 2 4 4 +--R (A a e + 4B a d e + 18A a c d e + 12B a c d e + 3A a c d )x +--R + +--R 3 3 3 2 2 2 3 2 4 3 +--R (4A a d e + 6B a d e + 12A a c d e + 3B a c d )x +--R + +--R 3 2 2 3 3 2 4 2 3 3 3 4 3 4 +--R (6A a d e + 4B a d e + 3A a c d )x + (4A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 634 + +--S 635 OF 765 +r0:=-1/5*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^5/e^8+1/6*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^8-3/7*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^7/e^8-1/8*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))*(d+e*x)^8/e^8-1/9*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)*(d+e*x)^9/e^8+3/10*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*_ + (d+e*x)^10/e^8-1/11*c^3*(7*B*d-A*e)*(d+e*x)^11/e^8+1/12*B*c^3*_ + (d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 3 12 12 1 3 12 4 3 11 11 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 12 11 11 +--R + +--R 3 2 12 2 3 11 3 3 2 10 10 +--R (-- B a c e + - A c d e + - B c d e )x +--R 10 5 5 +--R + +--R 1 2 12 4 2 11 2 3 2 10 4 3 3 9 9 +--R (- A a c e + - B a c d e + - A c d e + - B c d e )x +--R 3 3 3 9 +--R + +--R 3 2 12 3 2 11 9 2 2 10 1 3 3 9 1 3 4 8 8 +--R (- B a c e + - A a c d e + - B a c d e + - A c d e + - B c d e )x +--R 8 2 4 2 8 +--R + +--R 3 2 12 12 2 11 18 2 2 10 12 2 3 9 +--R - A a c e + -- B a c d e + -- A a c d e + -- B a c d e +--R 7 7 7 7 +--R + +--R 1 3 4 8 +--R - A c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 1 3 12 2 11 2 2 10 2 3 9 1 2 4 8 6 +--R (- B a e + 2A a c d e + 3B a c d e + 2A a c d e + - B a c d e )x +--R 6 2 +--R + +--R 1 3 12 4 3 11 18 2 2 10 12 2 3 9 +--R - A a e + - B a d e + -- A a c d e + -- B a c d e +--R 5 5 5 5 +--R + +--R 3 2 4 8 +--R - A a c d e +--R 5 +--R * +--R 5 +--R x +--R + +--R 3 11 3 3 2 10 2 3 9 3 2 4 8 4 +--R (A a d e + - B a d e + 3A a c d e + - B a c d e )x +--R 2 4 +--R + +--R 3 2 10 4 3 3 9 2 4 8 3 3 3 9 1 3 4 8 2 +--R (2A a d e + - B a d e + A a c d e )x + (2A a d e + - B a d e )x +--R 3 2 +--R + +--R 3 4 8 1 3 5 7 1 3 6 6 1 2 7 5 3 2 8 4 +--R A a d e x + - A a d e - -- B a d e + -- A a c d e - --- B a c d e +--R 5 30 35 280 +--R + +--R 1 2 9 3 1 2 10 2 1 3 11 1 3 12 +--R --- A a c d e - --- B a c d e + ---- A c d e - ---- B c d +--R 210 420 2310 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 635 + +--S 636 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 OF 765 +t0:=(A+B*x)*(d+e*x)^3*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 3 3 2 9 2 3 3 2 3 2 8 +--R B c e x + (A c e + 3B c d e )x + (3B a c e + 3A c d e + 3B c d e)x +--R + +--R 2 3 2 2 3 2 3 3 7 +--R (3A a c e + 9B a c d e + 3A c d e + B c d )x +--R + +--R 2 3 2 2 2 2 3 3 6 +--R (3B a c e + 9A a c d e + 9B a c d e + A c d )x +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (3A a c e + 9B a c d e + 9A a c d e + 3B a c d )x +--R + +--R 3 3 2 2 2 2 2 3 4 +--R (B a e + 9A a c d e + 9B a c d e + 3A a c d )x +--R + +--R 3 3 3 2 2 2 2 3 3 +--R (A a e + 3B a d e + 9A a c d e + 3B a c d )x +--R + +--R 3 2 3 2 2 3 2 3 2 3 3 3 3 +--R (3A a d e + 3B a d e + 3A a c d )x + (3A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 637 + +--S 638 OF 765 +r0:=a^3*A*d^3*x+1/2*a^3*d^2*(B*d+3*A*e)*x^2+a^2*d*(A*c*d^2+a*B*d*e+_ + a*A*e^2)*x^3+1/4*a^2*(3*B*c*d^3+9*A*c*d^2*e+3*a*B*d*e^2+a*A*e^3)*_ + x^4+1/5*a*(a*B*e*(9*c*d^2+a*e^2)+3*A*c*d*(c*d^2+3*a*e^2))*x^5+_ + 1/2*a*c*(B*c*d^3+3*A*c*d^2*e+3*a*B*d*e^2+a*A*e^3)*x^6+1/7*c*(3*a*_ + B*e*(3*c*d^2+a*e^2)+A*c*d*(c*d^2+9*a*e^2))*x^7+1/8*c^2*(B*c*d^3+3*_ + A*c*d^2*e+9*a*B*d*e^2+3*a*A*e^3)*x^8+1/3*c^2*e*(B*c*d^2+A*c*d*e+_ + a*B*e^2)*x^9+1/10*c^3*e^2*(3*B*d+A*e)*x^10+1/11*B*c^3*e^3*x^11 +--R +--R +--R (2) +--R 1 3 3 11 1 3 3 3 3 2 10 +--R -- B c e x + (-- A c e + -- B c d e )x +--R 11 10 10 +--R + +--R 1 2 3 1 3 2 1 3 2 9 +--R (- B a c e + - A c d e + - B c d e)x +--R 3 3 3 +--R + +--R 3 2 3 9 2 2 3 3 2 1 3 3 8 +--R (- A a c e + - B a c d e + - A c d e + - B c d )x +--R 8 8 8 8 +--R + +--R 3 2 3 9 2 2 9 2 2 1 3 3 7 +--R (- B a c e + - A a c d e + - B a c d e + - A c d )x +--R 7 7 7 7 +--R + +--R 1 2 3 3 2 2 3 2 2 1 2 3 6 +--R (- A a c e + - B a c d e + - A a c d e + - B a c d )x +--R 2 2 2 2 +--R + +--R 1 3 3 9 2 2 9 2 2 3 2 3 5 +--R (- B a e + - A a c d e + - B a c d e + - A a c d )x +--R 5 5 5 5 +--R + +--R 1 3 3 3 3 2 9 2 2 3 2 3 4 +--R (- A a e + - B a d e + - A a c d e + - B a c d )x +--R 4 4 4 4 +--R + +--R 3 2 3 2 2 3 3 3 3 2 1 3 3 2 3 3 +--R (A a d e + B a d e + A a c d )x + (- A a d e + - B a d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 638 + +--S 639 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 OF 765 +t0:=(A+B*x)*(d+e*x)^2*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 3 8 2 2 3 3 2 7 +--R B c e x + (A c e + 2B c d e)x + (3B a c e + 2A c d e + B c d )x +--R + +--R 2 2 2 3 2 6 +--R (3A a c e + 6B a c d e + A c d )x +--R + +--R 2 2 2 2 2 5 +--R (3B a c e + 6A a c d e + 3B a c d )x +--R + +--R 2 2 2 2 2 4 +--R (3A a c e + 6B a c d e + 3A a c d )x +--R + +--R 3 2 2 2 2 3 3 2 3 2 2 2 +--R (B a e + 6A a c d e + 3B a c d )x + (A a e + 2B a d e + 3A a c d )x +--R + +--R 3 3 2 3 2 +--R (2A a d e + B a d )x + A a d +--R Type: Polynomial(Integer) +--E 640 + +--S 641 OF 765 +r0:=a^3*A*d^2*x+1/2*a^3*d*(B*d+2*A*e)*x^2+1/3*a^2*(3*A*c*d^2+2*a*B*d*e+_ + a*A*e^2)*x^3+1/4*a^2*(3*B*c*d^2+6*A*c*d*e+a*B*e^2)*x^4+3/5*a*c*_ + (A*c*d^2+2*a*B*d*e+a*A*e^2)*x^5+1/2*a*c*(B*c*d^2+2*A*c*d*e+a*B*_ + e^2)*x^6+1/7*c^2*(A*c*d^2+6*a*B*d*e+3*a*A*e^2)*x^7+1/8*c^2*(B*c*d^2+_ + 2*A*c*d*e+3*a*B*e^2)*x^8+1/9*c^3*e*(2*B*d+A*e)*x^9+1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 2 2 3 9 +--R -- B c e x + (- A c e + - B c d e)x +--R 10 9 9 +--R + +--R 3 2 2 1 3 1 3 2 8 +--R (- B a c e + - A c d e + - B c d )x +--R 8 4 8 +--R + +--R 3 2 2 6 2 1 3 2 7 +--R (- A a c e + - B a c d e + - A c d )x +--R 7 7 7 +--R + +--R 1 2 2 2 1 2 2 6 +--R (- B a c e + A a c d e + - B a c d )x +--R 2 2 +--R + +--R 3 2 2 6 2 3 2 2 5 +--R (- A a c e + - B a c d e + - A a c d )x +--R 5 5 5 +--R + +--R 1 3 2 3 2 3 2 2 4 +--R (- B a e + - A a c d e + - B a c d )x +--R 4 2 4 +--R + +--R 1 3 2 2 3 2 2 3 3 1 3 2 2 3 2 +--R (- A a e + - B a d e + A a c d )x + (A a d e + - B a d )x + A a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 641 + +--S 642 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 OF 765 +t0:=(A+B*x)*(d+e*x)*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 3 7 2 3 6 +--R B c e x + (A c e + B c d)x + (3B a c e + A c d)x +--R + +--R 2 2 5 2 2 4 2 2 3 +--R (3A a c e + 3B a c d)x + (3B a c e + 3A a c d)x + (3A a c e + 3B a c d)x +--R + +--R 3 2 2 3 3 3 +--R (B a e + 3A a c d)x + (A a e + B a d)x + A a d +--R Type: Polynomial(Integer) +--E 643 + +--S 644 OF 765 +r0:=a^3*A*d*x+1/2*a^3*(B*d+A*e)*x^2+1/3*a^2*(3*A*c*d+a*B*e)*x^3+3/4*_ + a^2*c*(B*d+A*e)*x^4+3/5*a*c*(A*c*d+a*B*e)*x^5+1/2*a*c^2*(B*d+A*e)*_ + x^6+1/7*c^2*(A*c*d+3*a*B*e)*x^7+1/8*c^3*(B*d+A*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 1 3 8 3 2 1 3 7 +--R - B c e x + (- A c e + - B c d)x + (- B a c e + - A c d)x +--R 9 8 8 7 7 +--R + +--R 1 2 1 2 6 3 2 3 2 5 +--R (- A a c e + - B a c d)x + (- B a c e + - A a c d)x +--R 2 2 5 5 +--R + +--R 3 2 3 2 4 1 3 2 3 1 3 1 3 2 +--R (- A a c e + - B a c d)x + (- B a e + A a c d)x + (- A a e + - B a d)x +--R 4 4 3 2 2 +--R + +--R 3 +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 644 + +--S 645 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R Type: Polynomial(Integer) +--E 646 + +--S 647 OF 765 +r0:=a^3*A*x+a^2*A*c*x^3+3/5*a*A*c^2*x^5+1/7*A*c^3*x^7+1/8*B*(a+c*x^2)^4/c +--R +--R +--R (2) +--R 1 4 8 1 4 7 1 3 6 3 3 5 3 2 2 4 2 2 3 +--R - B c x + - A c x + - B a c x + - A a c x + - B a c x + A a c x +--R 8 7 2 5 4 +--R + +--R 1 3 2 3 1 4 +--R - B a c x + A a c x + - B a +--R 2 8 +--R / +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 647 + +--S 648 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 649 + +--S 650 OF 765 +r0:=(B*(c*d^2+a*e^2)^3-A*c*d*e*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4))*x/e^7-_ + 1/2*c*(B*d-A*e)*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4)*x^2/e^6-1/3*c*_ + (A*c*d*e*(c*d^2+3*a*e^2)-B*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4))*_ + x^3/e^5-1/4*c^2*(B*d-A*e)*(c*d^2+3*a*e^2)*x^4/e^4+1/5*c^2*(B*c*_ + d^2-A*c*d*e+3*a*B*e^2)*x^5/e^3-1/6*c^3*(B*d-A*e)*x^6/e^2+1/7*B*_ + c^3*x^7/e-(B*d-A*e)*(c*d^2+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 6 2 2 5 2 3 4 +--R 420A a e - 420B a d e + 1260A a c d e - 1260B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 1260A a c d e - 1260B a c d e + 420A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 60B c e x + (70A c e - 70B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (252B a c e - 84A c d e + 84B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (315A a c e - 315B a c d e + 105A c d e - 105B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 420B a c e - 420A a c d e + 420B a c d e - 140A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 630A a c e - 630B a c d e + 630A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R 210A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 420B a e - 1260A a c d e + 1260B a c d e - 1260A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 1260B a c d e - 420A c d e + 420B c d e +--R * +--R x +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 650 + +--S 651 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 652 + +--S 653 OF 765 +r0:=-c*(6*B*d*(c*d^2+a*e^2)^2-A*e*(5*c^2*d^4+9*a*c*d^2*e^2+3*a^2*e^4))*_ + x/e^7-1/2*c*(2*A*c*d*e*(2*c*d^2+3*a*e^2)-B*(5*c^2*d^4+9*a*c*d^2*e^2+_ + 3*a^2*e^4))*x^2/e^6+1/3*c^2*(3*A*e*(c*d^2+a*e^2)-B*(4*c*d^3+_ + 6*a*d*e^2))*x^3/e^5-1/4*c^2*(2*A*c*d*e-3*B*(c*d^2+a*e^2))*x^4/e^4-_ + 1/5*c^3*(2*B*d-A*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+(B*d-A*e)*(c*d^2+_ + a*e^2)^3/(e^8*(d+e*x))+(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+_ + a*B*e^2)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 6 2 2 5 2 3 4 +--R 60B a e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 900B a c d e - 360A c d e + 420B c d e +--R * +--R x +--R + +--R 3 6 2 2 5 2 3 4 2 4 3 +--R 60B a d e - 360A a c d e + 540B a c d e - 720A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 900B a c d e - 360A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (12A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (45B a c e - 18A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (60A a c e - 75B a c d e + 30A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 3 4 3 3 +--R (90B a c e - 120A a c d e + 150B a c d e - 60A c d e + 70B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 180A a c e - 270B a c d e + 360A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 180A c d e - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 180A a c d e - 360B a c d e + 540A a c d e - 720B a c d e +--R + +--R 3 5 2 3 6 +--R 300A c d e - 360B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e + 60B a d e - 180A a c d e + 180B a c d e - 180A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 180B a c d e - 60A c d e + 60B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 653 + +--S 654 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 655 + +--S 656 OF 765 +r0:=-c*(A*c*d*e*(10*c*d^2+9*a*e^2)-3*B*(5*c^2*d^4+6*a*c*d^2*e^2+_ + a^2*e^4))*x/e^7-1/2*c^2*(10*B*c*d^3-6*A*c*d^2*e+9*a*B*d*e^2-_ + 3*a*A*e^3)*x^2/e^6+c^2*(2*B*c*d^2-A*c*d*e+a*B*e^2)*x^3/e^5-_ + 1/4*c^3*(3*B*d-A*e)*x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*(B*d-A*e)*_ + (c*d^2+a*e^2)^3/(e^8*(d+e*x)^2)-(c*d^2+a*e^2)^2*(7*B*c*d^2-_ + 6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x))-3*c*(c*d^2+a*e^2)*(7*B*c*d^3-_ + 5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 2 2 5 2 3 4 +--R 60A a c e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 4 3 3 5 2 +--R 300A c d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 2 3 4 2 4 3 +--R 120A a c d e - 360B a c d e + 720A a c d e - 1200B a c d e +--R + +--R 3 5 2 3 6 +--R 600A c d e - 840B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 2 5 2 +--R 60A a c d e - 180B a c d e + 360A a c d e - 600B a c d e +--R + +--R 3 6 3 7 +--R 300A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (5A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (20B a c e - 10A c d e + 14B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30A a c e - 50B a c d e + 25A c d e - 35B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 60B a c e - 120A a c d e + 200B a c d e - 100A c d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 120B a c d e - 330A a c d e + 630B a c d e - 340A c d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 20B a e + 120A a c d e - 120B a c d e + 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 60B a c d e - 80A c d e + 160B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 10B a d e + 90A a c d e - 150B a c d e + 210A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 270B a c d e + 110A c d e - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 656 + +--S 657 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 658 + +--S 659 OF 765 +r0:=-c^2*(20*B*c*d^3-10*A*c*d^2*e+12*a*B*d*e^2-3*a*A*e^3)*x/e^7+1/2*_ + c^2*(10*B*c*d^2-4*A*c*d*e+3*a*B*e^2)*x^2/e^6-1/3*c^3*(4*B*d-A*e)*_ + x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+_ + e*x)^3)-1/2*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*_ + (d+e*x)^2)+3*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-_ + a*A*e^3)/(e^8*(d+e*x))-c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*_ + d^4+30*a*c*d^2*e^2+3*a^2*e^4))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 2 2 5 3 3 4 +--R 36B a c e - 144A a c d e + 360B a c d e - 240A c d e +--R + +--R 3 4 3 +--R 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 6 2 2 5 2 3 4 3 4 3 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 5 2 +--R 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 3 5 2 +--R 108B a c d e - 432A a c d e + 1080B a c d e - 720A c d e +--R + +--R 3 6 +--R 1260B c d e +--R * +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 3 6 3 7 +--R 36B a c d e - 144A a c d e + 360B a c d e - 240A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 3B c e x + (4A c e - 7B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (18B a c e - 12A c d e + 21B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 90B a c d e + 60A c d e - 105B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (108A a c d e - 378B a c d e + 292A c d e - 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 36A a c e + 108B a c d e - 108A a c d e - 54B a c d e +--R + +--R 3 4 3 3 5 2 +--R 156A c d e - 408B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6B a e - 36A a c d e + 162B a c d e - 324A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 486B a c d e - 204A c d e + 222B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - 2B a d e - 12A a c d e + 66B a c d e - 156A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 282B a c d e - 148A c d e + 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 659 + +--S 660 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 661 + +--S 662 OF 765 +r0:=-c^2*(5*A*c*d*e-3*B*(5*c*d^2+a*e^2))*x/e^7-1/2*c^3*(5*B*d-A*e)*_ + x^2/e^6+1/3*B*c^3*x^3/e^5+1/4*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*_ + (d+e*x)^4)-1/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^3)+3/2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*_ + d*e^2-a*A*e^3)/(e^8*(d+e*x)^2)+c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*_ + (35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x))-c^2*(35*B*c*_ + d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (36A a c e - 180B a c d e + 180A c d e - 420B c d e )x +--R + +--R 2 6 2 2 5 3 3 4 3 4 3 3 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e )x +--R + +--R 2 2 5 2 3 4 3 4 3 3 5 2 2 +--R (216A a c d e - 1080B a c d e + 1080A c d e - 2520B c d e )x +--R + +--R 2 3 4 2 4 3 3 5 2 3 6 +--R (144A a c d e - 720B a c d e + 720A c d e - 1680B c d e)x +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 36A a c d e - 180B a c d e + 180A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 +--R 4B c e x + (6A c e - 14B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (36B a c e - 36A c d e + 84B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (144B a c d e - 204A c d e + 556B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 36B a c e + 144A a c d e - 144B a c d e - 96A c d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 18A a c e - 54B a c d e + 324A a c d e - 756B a c d e +--R + +--R 3 4 3 3 5 2 +--R 396A c d e - 444B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 4B a e - 12A a c d e - 36B a c d e + 264A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 744B a c d e + 504A c d e - 856B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 3A a e - B a d e - 3A a c d e - 9B a c d e + 75A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 231B a c d e + 171A c d e - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 662 + +--S 663 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^6 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 664 + +--S 665 OF 765 +r0:=-c^3*(6*B*d-A*e)*x/e^7+1/2*B*c^3*x^2/e^6+1/5*(B*d-A*e)*(c*d^2+_ + a*e^2)^3/(e^8*(d+e*x)^5)-1/4*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+_ + a*B*e^2)/(e^8*(d+e*x)^4)+c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+_ + 3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^3)+1/2*c*(4*A*c*d*e*(5*c*d^2+_ + 3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^2)+_ + c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*(d+e*x))+_ + 3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 7 3 6 3 2 5 5 +--R (60B a c e - 120A c d e + 420B c d e )x +--R + +--R 2 6 3 2 5 3 3 4 4 +--R (300B a c d e - 600A c d e + 2100B c d e )x +--R + +--R 2 2 5 3 3 4 3 4 3 3 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 3 4 3 4 3 3 5 2 2 +--R (600B a c d e - 1200A c d e + 4200B c d e )x +--R + +--R 2 4 3 3 5 2 3 6 2 5 2 +--R (300B a c d e - 600A c d e + 2100B c d e)x + 60B a c d e +--R + +--R 3 6 3 7 +--R - 120A c d e + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 7 3 6 6 3 6 3 2 5 5 +--R 10B c e x + (20A c e - 70B c d e )x + (100A c d e - 500B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 60A a c e + 300B a c d e - 100A c d e - 400B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 30B a c e - 120A a c d e + 900B a c d e - 800A c d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 20A a c e - 30B a c d e - 120A a c d e + 1100B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1200A c d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 5B a e - 10A a c d e - 15B a c d e - 60A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 625B a c d e - 750A c d e + 1875B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 4A a e - B a d e - 2A a c d e - 3B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 137B a c d e - 174A c d e + 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Expression(Integer) +--E 665 + +--S 666 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^7 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 667 + +--S 668 OF 765 +r0:=B*c^3*x/e^7+1/6*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^6)-1/5*(c*d^2+_ + a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^5)+3/4*c*(c*d^2+_ + a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^4)+_ + 1/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))/(e^8*(d+e*x)^3)+1/2*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*_ + d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^2)-3*c^2*(7*B*c*d^2-2*A*c*d*e+a*_ + B*e^2)/(e^8*(d+e*x))-c^3*(7*B*d-A*e)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 6 6 3 6 3 2 5 5 +--R (60A c e - 420B c d e )x + (360A c d e - 2520B c d e )x +--R + +--R 3 2 5 3 3 4 4 3 3 4 3 4 3 3 +--R (900A c d e - 6300B c d e )x + (1200A c d e - 8400B c d e )x +--R + +--R 3 4 3 3 5 2 2 3 5 2 3 6 +--R (900A c d e - 6300B c d e )x + (360A c d e - 2520B c d e)x +--R + +--R 3 6 3 7 +--R 60A c d e - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 180B a c e + 360A c d e - 360B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 90A a c e - 450B a c d e + 1350A c d e - 4050B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 60B a c e - 120A a c d e - 600B a c d e + 2200A c d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 45A a c e - 45B a c d e - 90A a c d e - 450B a c d e +--R + +--R 3 4 3 3 5 2 +--R 1875A c d e - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 12B a e - 18A a c d e - 18B a c d e - 36A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 180B a c d e + 822A c d e - 3594B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 2B a d e - 3A a c d e - 3B a c d e - 6A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e + 147A c d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Expression(Integer) +--E 668 + +--S 669 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^8 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 670 + +--S 671 OF 765 +r0:=1/7*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^7)-1/6*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^6)+3/5*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^5)+1/4*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^4)+1/3*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^3)-3/2*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^2)+c^3*(7*B*d-A*e)/(e^8*(d+e*x))+B*c^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 3 6 6 +--R (- 420A c e + 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (- 630B a c e - 1260A c d e + 13230B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 420A a c e - 1050B a c d e - 2100A c d e + 26950B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 315B a c e - 420A a c d e - 1050B a c d e - 2100A c d e +--R + +--R 3 4 3 +--R 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 252A a c e - 189B a c d e - 252A a c d e - 630B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 1260A c d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 70B a e - 84A a c d e - 63B a c d e - 84A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 210B a c d e - 420A c d e + 7203B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 60A a e - 10B a d e - 12A a c d e - 9B a c d e - 12A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 30B a c d e - 60A c d e + 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Expression(Integer) +--E 671 + +--S 672 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^9 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 673 + +--S 674 OF 765 +r0:=1/8*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^8)-1/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^7)+1/2*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^6)+1/5*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^5)+1/4*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^4)-c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^8*_ + (d+e*x)^3)+1/2*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^2)-B*c^3/(e^8*(d+e*x)) +--R +--R +--R (2) +--R 3 7 7 1 3 7 7 3 6 6 +--R - B c e x + (- - A c e - - B c d e )x +--R 2 2 +--R + +--R 2 7 3 6 3 2 5 5 +--R (- B a c e - A c d e - 7B c d e )x +--R + +--R 3 2 7 5 2 6 5 3 2 5 35 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - -- B c d e )x +--R 4 4 4 4 +--R + +--R 3 2 7 3 2 6 2 2 5 3 3 4 3 4 3 3 +--R (- - B a c e - - A a c d e - B a c d e - A c d e - 7B c d e )x +--R 5 5 +--R + +--R 1 2 7 3 2 6 3 2 2 5 1 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - - B a c d e +--R 2 10 10 2 +--R + +--R 1 3 4 3 7 3 5 2 +--R - - A c d e - - B c d e +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 1 3 7 1 2 6 3 2 2 5 3 2 3 4 +--R - - B a e - - A a c d e - -- B a c d e - -- A a c d e +--R 7 7 35 35 +--R + +--R 1 2 4 3 1 3 5 2 3 6 +--R - - B a c d e - - A c d e - B c d e +--R 7 7 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 3 2 3 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e +--R 8 56 56 280 +--R + +--R 3 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - -- B a c d e - -- A c d e - - B c d +--R 280 56 56 8 +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 10 2 7 9 8 8 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 674 + +--S 675 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^10 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 676 + +--S 677 OF 765 +r0:=1/9*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^9)-1/8*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^8)+3/7*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^7)+1/6*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*_ + a^2*e^4))/(e^8*(d+e*x)^6)+1/5*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*_ + d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^5)-3/4*c^2*(7*B*c*d^2-2*A*c*d*e+_ + a*B*e^2)/(e^8*(d+e*x)^4)+1/3*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^3)-_ + 1/2*B*c^3/(e^8*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 7 7 1 3 7 7 3 6 6 +--R - - B c e x + (- - A c e - - B c d e )x +--R 2 3 6 +--R + +--R 3 2 7 1 3 6 7 3 2 5 5 +--R (- - B a c e - - A c d e - - B c d e )x +--R 4 2 4 +--R + +--R 3 2 7 3 2 6 1 3 2 5 7 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - - B c d e )x +--R 5 4 2 4 +--R + +--R 1 2 7 2 2 6 1 2 2 5 1 3 3 4 7 3 4 3 3 +--R (- - B a c e - - A a c d e - - B a c d e - - A c d e - - B c d e )x +--R 2 5 2 3 6 +--R + +--R 3 2 7 3 2 6 6 2 2 5 3 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - -- B a c d e +--R 7 14 35 14 +--R + +--R 1 3 4 3 1 3 5 2 +--R - - A c d e - - B c d e +--R 7 2 +--R * +--R 2 +--R x +--R + +--R 1 3 7 3 2 6 3 2 2 5 3 2 3 4 +--R - - B a e - -- A a c d e - -- B a c d e - -- A a c d e +--R 8 28 56 70 +--R + +--R 3 2 4 3 1 3 5 2 1 3 6 +--R - -- B a c d e - -- A c d e - - B c d e +--R 56 28 8 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 1 2 3 4 +--R - - A a e - -- B a d e - -- A a c d e - --- B a c d e +--R 9 72 84 168 +--R + +--R 1 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - --- B a c d e - --- A c d e - -- B c d +--R 210 168 252 72 +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 5 12 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 11 3 7 10 2 8 9 9 8 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 677 + +--S 678 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 678 + +)clear all + +--S 679 OF 765 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^11 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 679 + +--S 680 OF 765 +r0:=1/10*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^10)-1/9*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^9)+3/8*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^8)+1/7*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*_ + e^4))/(e^8*(d+e*x)^7)+1/6*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)/(e^8*(d+e*x)^6)-3/5*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/_ + (e^8*(d+e*x)^5)+1/4*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^4)-1/3*B*c^3/_ + (e^8*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 7 7 1 3 7 7 3 6 6 +--R - - B c e x + (- - A c e - -- B c d e )x +--R 3 4 12 +--R + +--R 3 2 7 3 3 6 7 3 2 5 5 +--R (- - B a c e - -- A c d e - -- B c d e )x +--R 5 10 10 +--R + +--R 1 2 7 1 2 6 1 3 2 5 7 3 3 4 4 +--R (- - A a c e - - B a c d e - - A c d e - -- B c d e )x +--R 2 2 4 12 +--R + +--R 3 2 7 2 2 6 2 2 2 5 1 3 3 4 1 3 4 3 3 +--R (- - B a c e - - A a c d e - - B a c d e - - A c d e - - B c d e )x +--R 7 7 7 7 3 +--R + +--R 3 2 7 9 2 6 3 2 2 5 3 2 3 4 +--R - - A a c e - -- B a c d e - -- A a c d e - -- B a c d e +--R 8 56 28 28 +--R + +--R 3 3 4 3 1 3 5 2 +--R - -- A c d e - - B c d e +--R 56 8 +--R * +--R 2 +--R x +--R + +--R 1 3 7 1 2 6 1 2 2 5 1 2 3 4 +--R - - B a e - -- A a c d e - -- B a c d e - -- A a c d e +--R 9 12 28 42 +--R + +--R 1 2 4 3 1 3 5 2 1 3 6 +--R - -- B a c d e - -- A c d e - -- B c d e +--R 42 84 36 +--R * +--R x +--R + +--R 1 3 7 1 3 6 1 2 2 5 1 2 3 4 +--R - -- A a e - -- B a d e - --- A a c d e - --- B a c d e +--R 10 90 120 280 +--R + +--R 1 2 4 3 1 2 5 2 1 3 6 1 3 7 +--R - --- A a c d e - --- B a c d e - --- A c d e - --- B c d +--R 420 420 840 360 +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 5 13 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 12 4 7 11 3 8 10 2 9 9 10 8 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 680 + +--S 681 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 OF 765 +t0:=(A+B*x)*(d+e*x)^m/(a+c*x^2) +--R +--R +--R m +--R (B x + A)(e x + d) +--R (1) ------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 682 + +--S 683 OF 765 +--r0:=-1/2*(d+e*x)^(1+m)*hypergeometric(1,1+m,2+m,(d+e*x)*sqrt(c)/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(A+B*sqrt(-a)/sqrt(c))/((1+m)*sqrt(-a)*_ +-- (e*sqrt(-a)+d*sqrt(c)))-1/2*(d+e*x)^(1+m)*hypergeometric(1,1+m,2+_ +-- m,(d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*B+A*sqrt(-a)*sqrt(c))/_ +-- (a*(1+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c))) +--E 683 + +--S 684 OF 765 +--d0:=D(m0,x) +--E 684 + +)clear all + +--S 685 OF 765 +t0:=(A+B*x)*(d+e*x)^(1+m)/(a+c*x^2) +--R +--R +--R m + 1 +--R (B x + A)(e x + d) +--R (1) ----------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 685 + +--S 686 OF 765 +--r0:=-1/2*(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,(d+e*x)*sqrt(c)/(e*_ +-- sqrt(-a)+d*sqrt(c)))*(A+B*sqrt(-a)/sqrt(c))/((2+m)*sqrt(-a)*(e*_ +-- sqrt(-a)+d*sqrt(c)))-1/2*(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,_ +-- (d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*B+A*sqrt(-a)*sqrt(c))/_ +-- (a*(2+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c))) +--E 686 + +--S 687 OF 765 +--d0:=D(m0,x) +--E 687 + +)clear all + +--S 688 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 688 + +--S 689 OF 765 +r0:=e*(4*B*c*d^3+6*A*c*d^2*e-4*a*B*d*e^2-a*A*e^3)*x/c^2+1/2*e^2*(6*B*c*d^2+_ + 4*A*c*d*e-a*B*e^2)*x^2/c^2+1/3*e^3*(4*B*d+A*e)*x^3/c+1/4*B*e^4*x^4/c+_ + 1/2*(4*A*c*d*e*(c*d^2-a*e^2)+B*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*_ + log(a+c*x^2)/c^3-(4*a*B*d*e*(c*d^2-a*e^2)-A*(c^2*d^4-6*a*c*d^2*_ + e^2+a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (12A a c e + 48B a c d e - 72A a c d e - 48B a c d e + 12A c d ) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 3 2 2 2 3 2 4 +--R (6B a e - 24A a c d e - 36B a c d e + 24A c d e + 6B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R 3B c e x + (4A c e + 16B c d e )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 6B a c e + 24A c d e + 36B c d e )x +--R + +--R 4 3 2 2 2 2 3 +--R (- 12A a c e - 48B a c d e + 72A c d e + 48B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 +-+ +-+ +--R 12c \|a \|c +--R Type: Expression(Integer) +--E 689 + +--S 690 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 691 + +--S 692 OF 765 +r0:=e*(3*B*c*d^2+3*A*c*d*e-a*B*e^2)*x/c^2+1/2*e^2*(3*B*d+A*e)*x^2/c+_ + 1/3*B*e^3*x^3/c+1/2*(B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*_ + log(a+c*x^2)/c^2+(A*c*d*(c*d^2-3*a*e^2)-a*B*e*(3*c*d^2-a*e^2))*_ + atan(x*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R 2 3 2 2 2 3 x\|c +--R (6B a e - 18A a c d e - 18B a c d e + 6A c d )atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 3 2 3 3 +--R (- 3A a e - 9B a d e + 9A c d e + 3B c d )log(c x + a) + 2B c e x +--R + +--R 3 2 2 3 2 2 +--R (3A c e + 9B c d e )x + (- 6B a e + 18A c d e + 18B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 +-+ +-+ +--R 6c \|a \|c +--R Type: Expression(Integer) +--E 692 + +--S 693 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 694 + +--S 695 OF 765 +r0:=e*(2*B*d+A*e)*x/c+1/2*B*e^2*x^2/c+1/2*(B*c*d^2+2*A*c*d*e-a*B*e^2)*_ + log(a+c*x^2)/c^2+(A*c*d^2-2*a*B*d*e-a*A*e^2)*atan(x*sqrt(c)/_ + sqrt(a))/(c^(3/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 x\|c +--R (- 2A a c e - 4B a c d e + 2A c d )atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 +--R (- B a e + 2A c d e + B c d )log(c x + a) + B c e x +--R + +--R 2 +--R (2A c e + 4B c d e)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 +-+ +-+ +--R 2c \|a \|c +--R Type: Expression(Integer) +--E 695 + +--S 696 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 OF 765 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 697 + +--S 698 OF 765 +r0:=B*e*x/c+1/2*(B*d+A*e)*log(a+c*x^2)/c+(A*c*d-a*B*e)*atan(x*sqrt(c)/_ + sqrt(a))/(c^(3/2)*sqrt(a)) +--R +--R +--R (2) +--R +-+ +--R x\|c 2 +-+ +-+ +--R (- 2B a e + 2A c d)atan(-----) + ((A e + B d)log(c x + a) + 2B e x)\|a \|c +--R +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +-+ +--R 2c\|a \|c +--R Type: Expression(Integer) +--E 698 + +--S 699 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 OF 765 +t0:=(A+B*x)/(a+c*x^2) +--R +--R +--R B x + A +--R (1) -------- +--R 2 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 700 + +--S 701 OF 765 +r0:=1/2*B*log(a+c*x^2)/c+A*atan(x*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c)) +--R +--R +--R +-+ +--R x\|c 2 +-+ +-+ +--R 2A c atan(-----) + B log(c x + a)\|a \|c +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R +-+ +-+ +--R 2c\|a \|c +--R Type: Expression(Integer) +--E 701 + +--S 702 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 OF 765 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------- +--R 3 2 +--R c e x + c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 703 + +--S 704 OF 765 +r0:=-(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)+1/2*(B*d-A*e)*log(a+c*x^2)/_ + (c*d^2+a*e^2)+(A*c*d+a*B*e)*atan(x*sqrt(c)/sqrt(a))/((c*d^2+a*e^2)*_ + sqrt(a)*sqrt(c)) +--R +--R +--R (2) +--R +-+ +--R x\|c +--R (2B a e + 2A c d)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-+ +-+ +--R ((- A e + B d)log(c x + a) + (2A e - 2B d)log(e x + d))\|a \|c +--R / +--R 2 2 +-+ +-+ +--R (2a e + 2c d )\|a \|c +--R Type: Expression(Integer) +--E 704 + +--S 705 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------ +--R 2 4 3 2 2 2 2 +--R c e x + 2c d e x + (a e + c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 706 + +--S 707 OF 765 +r0:=(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x))-(B*c*d^2-2*A*c*d*e-a*B*e^2)*_ + log(d+e*x)/(c*d^2+a*e^2)^2+1/2*(B*c*d^2-2*A*c*d*e-a*B*e^2)*_ + log(a+c*x^2)/(c*d^2+a*e^2)^2+(A*c*d^2+2*a*B*d*e-a*A*e^2)*_ + atan(x*sqrt(c)/sqrt(a))*sqrt(c)/((c*d^2+a*e^2)^2*sqrt(a)) +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((- 2A a e + 4B a d e + 2A c d e)x - 2A a d e + 4B a d e + 2A c d ) +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 2 3 +--R ((- B a e - 2A c d e + B c d e)x - B a d e - 2A c d e + B c d ) +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 2 2 2 +--R (2B a e + 4A c d e - 2B c d e)x + 2B a d e + 4A c d e +--R + +--R 3 +--R - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + 2B a d e - 2A c d e + 2B c d +--R * +--R +-+ +--R \|a +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +-+ +--R ((2a e + 4a c d e + 2c d e)x + 2a d e + 4a c d e + 2c d )\|a +--R Type: Expression(Integer) +--E 707 + +--S 708 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 OF 765 +t0:=(A+B*x)/((d+e*x)^3*(a+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------------- +--R 3 5 2 4 3 2 3 2 3 2 2 3 +--R c e x + 3c d e x + (a e + 3c d e)x + (3a d e + c d )x + 3a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 709 + +--S 710 OF 765 +r0:=1/2*(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x)^2)+(B*c*d^2-2*A*c*d*e-a*B*e^2)/_ + ((c*d^2+a*e^2)^2*(d+e*x))-c*(B*c*d^3-3*A*c*d^2*e-3*a*B*d*e^2+_ + a*A*e^3)*log(d+e*x)/(c*d^2+a*e^2)^3+1/2*c*(B*c*d^3-3*A*c*d^2*e-_ + 3*a*B*d*e^2+a*A*e^3)*log(a+c*x^2)/(c*d^2+a*e^2)^3+(A*c*d*(c*d^2-_ + 3*a*e^2)+a*B*e*(3*c*d^2-a*e^2))*atan(x*sqrt(c)/sqrt(a))*sqrt(c)/_ + ((c*d^2+a*e^2)^3*sqrt(a)) +--R +--R +--R (2) +--R 2 5 4 2 3 2 3 2 2 +--R (- 2B a e - 6A a c d e + 6B a c d e + 2A c d e )x +--R + +--R 2 4 2 3 3 2 2 4 2 2 3 +--R (- 4B a d e - 12A a c d e + 12B a c d e + 4A c d e)x - 2B a d e +--R + +--R 3 2 4 2 5 +--R - 6A a c d e + 6B a c d e + 2A c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (A a c e - 3B a c d e - 3A c d e + B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 2 3 +--R (2A a c d e - 6B a c d e - 6A c d e + 2B c d e)x + A a c d e +--R + +--R 3 2 2 4 2 5 +--R - 3B a c d e - 3A c d e + B c d +--R * +--R 2 +--R log(c x + a) +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 2A a c e + 6B a c d e + 6A c d e - 2B c d e )x +--R + +--R 4 2 3 2 3 2 2 4 +--R (- 4A a c d e + 12B a c d e + 12A c d e - 4B c d e)x +--R + +--R 2 3 3 2 2 4 2 5 +--R - 2A a c d e + 6B a c d e + 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 4 2 3 2 2 4 2 5 2 4 +--R (- 2B a e - 4A a c d e - 4A c d e + 2B c d e)x - A a e - B a d e +--R + +--R 2 3 3 2 2 4 2 5 +--R - 6A a c d e + 2B a c d e - 5A c d e + 3B c d +--R * +--R +-+ +--R \|a +--R / +--R 3 8 2 2 6 2 4 4 3 6 2 2 +--R (2a e + 6a c d e + 6a c d e + 2c d e )x +--R + +--R 3 7 2 3 5 2 5 3 3 7 3 2 6 2 4 4 +--R (4a d e + 12a c d e + 12a c d e + 4c d e)x + 2a d e + 6a c d e +--R + +--R 2 6 2 3 8 +--R 6a c d e + 2c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 710 + +--S 711 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 711 + +)clear all + +--S 712 OF 765 +t0:=(A+B*x)*(d+e*x)^5/(a+c*x^2)^2 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 712 + +--S 713 OF 765 +r0:=-5/2*e^2*(A*c*d*(2*c*d^2-3*a*e^2)-a*B*e*(6*c*d^2-a*e^2))*x/(a*c^3)-_ + e^3*(5*A*c*d^2-5*a*B*d*e-a*A*e^2)*x^2/(a*c^2)-5/6*e^4*(3*A*c*d-a*B*e)*_ + x^3/(a*c^2)-1/2*A*e^5*x^4/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^5/(a*c*_ + (a+c*x^2))+1/2*(A*c*d*(c^2*d^4+10*a*c*d^2*e^2-15*a^2*e^4)+5*a*B*_ + e*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(3/2)*c^(7/2))+e^2*(5*B*c*d^3+5*A*c*d^2*e-5*a*B*d*e^2-a*A*e^3)*_ + log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 15B a c e - 45A a c d e - 90B a c d e + 30A a c d e +--R + +--R 3 4 4 5 +--R 15B a c d e + 3A c d +--R * +--R 2 +--R x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 15B a e - 45A a c d e - 90B a c d e + 30A a c d e + 15B a c d e +--R + +--R 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 2 3 2 3 2 2 +--R (- 6A a c e - 30B a c d e + 30A a c d e + 30B a c d e )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 +--R - 6A a e - 30B a d e + 30A a c d e + 30B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B a c e x + (3A a c e + 15B a c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (- 10B a c e + 30A a c d e + 60B a c d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 +--R 6A a c e + 30B a c d e - 30A a c d e - 30B a c d e +--R + +--R 3 4 +--R 15A c d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 4 2 2 3 2 3 2 +--R - 15B a e + 45A a c d e + 90B a c d e - 30A a c d e +--R + +--R 2 4 3 5 +--R - 15B a c d e + 3A c d +--R * +--R x +--R + +--R 2 5 +--R - 3B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 +-+ +-+ +--R (6a c x + 6a c )\|a \|c +--R Type: Expression(Integer) +--E 713 + +--S 714 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 715 + +--S 716 OF 765 +r0:=-3/2*e^2*(2*A*c*d^2-4*a*B*d*e-a*A*e^2)*x/(a*c^2)-e^3*(2*A*c*d-a*B*e)*_ + x^2/(a*c^2)-1/2*A*e^4*x^3/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^4/(a*c*_ + (a+c*x^2))+1/2*(4*a*B*d*e*(c*d^2-3*a*e^2)+A*(c^2*d^4+6*a*c*d^2*_ + e^2-3*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(5/2))+e^2*_ + (3*B*c*d^2+2*A*c*d*e-a*B*e^2)*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 2 +--R (- 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A c d )x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R - 3A a c e - 12B a c d e + 6A a c d e + 4B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (- 2B a c e + 4A a c d e + 6B a c d e )x - 2B a e +--R + +--R 2 3 2 2 2 +--R 4A a c d e + 6B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 4 4 2 4 2 3 3 +--R B a c e x + (2A a c e + 8B a c d e )x +--R + +--R 2 4 2 3 2 2 2 3 3 2 +--R (2B a c e - 4A a c d e - 6B a c d e + 4A c d e)x +--R + +--R 2 4 2 3 2 2 2 2 3 3 4 +--R (3A a c e + 12B a c d e - 6A a c d e - 4B a c d e + A c d )x +--R + +--R 2 4 +--R - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 716 + +--S 717 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 718 + +--S 719 OF 765 +r0:=-3/2*e^2*(A*c*d-a*B*e)*x/(a*c^2)-1/2*A*e^3*x^2/(a*c)-1/2*(a*B-A*c*x)*_ + (d+e*x)^3/(a*c*(a+c*x^2))+1/2*(3*a*B*e*(c*d^2-a*e^2)+A*c*d*_ + (c*d^2+3*a*e^2))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(5/2))+1/2*_ + e^2*(3*B*d+A*e)*log(a+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 3B a c e + 3A a c d e + 3B a c d e + A c d )x - 3B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e + 3B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((A a c e + 3B a c d e )x + A a e + 3B a d e )log(c x + a) +--R + +--R 3 3 3 2 2 2 2 +--R 2B a c e x + (- A a c e - 3B a c d e + 3A c d e)x +--R + +--R 2 3 2 2 2 3 3 +--R (3B a e - 3A a c d e - 3B a c d e + A c d )x - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 719 + +--S 720 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 721 + +--S 722 OF 765 +r0:=-1/2*A*e^2*x/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^2/(a*c*(a+c*x^2))+_ + 1/2*(A*c*d^2+2*a*B*d*e+a*A*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*_ + c^(3/2))+1/2*B*e^2*log(a+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 3 2 2 2 2 2 2 2 +--R ((A a c e + 2B a c d e + A c d )x + A a c e + 2B a c d e + A a c d ) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 2 2 2 +--R (B a c e x + B a e )log(c x + a) + (- B a c e + 2A c d e)x +--R + +--R 2 2 2 2 +--R (- A a c e - 2B a c d e + A c d )x - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 +-+ +-+ +--R (2a c x + 2a c )\|a \|c +--R Type: Expression(Integer) +--E 722 + +--S 723 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 OF 765 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 724 + +--S 725 OF 765 +r0:=-1/2*(a*B-A*c*x)*(d+e*x)/(a*c*(a+c*x^2))+1/2*(A*c*d+a*B*e)*_ + atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(3/2)) +--R +--R +--R (2) +--R +-+ +--R 2 2 2 x\|c +--R ((B a c e + A c d)x + B a e + A a c d)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 +-+ +-+ +--R (A c e x + (- B a e + A c d)x - B a d)\|a \|c +--R / +--R 2 2 2 +-+ +-+ +--R (2a c x + 2a c)\|a \|c +--R Type: Expression(Integer) +--E 725 + +--S 726 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 726 + +)clear all + +--S 727 OF 765 +t0:=(A+B*x)/(a+c*x^2)^2 +--R +--R +--R B x + A +--R (1) ------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 727 + +--S 728 OF 765 +r0:=1/2*(-a*B+A*c*x)/(a*c*(a+c*x^2))+1/2*A*atan(x*sqrt(c)/sqrt(a))/_ + (a^(3/2)*sqrt(c)) +--R +--R +--R +-+ +--R 2 2 x\|c +-+ +-+ +--R (A c x + A a c)atan(-----) + (A c x - B a)\|a \|c +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 2 2 2 +-+ +-+ +--R (2a c x + 2a c)\|a \|c +--R Type: Expression(Integer) +--E 728 + +--S 729 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 OF 765 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------- +--R 2 5 2 4 3 2 2 2 +--R c e x + c d x + 2a c e x + 2a c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 730 + +--S 731 OF 765 +r0:=1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2))-_ + e^2*(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)^2+1/2*e^2*(B*d-A*e)*log(a+_ + c*x^2)/(c*d^2+a*e^2)^2-1/2*(a*B*e*(c*d^2-a*e^2)-A*c*d*(c*d^2+_ + 3*a*e^2))*atan(x*sqrt(c)/sqrt(a))/(a^(3/2)*(c*d^2+a*e^2)^2*sqrt(c)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (B a c e + 3A a c d e - B a c d e + A c d )x + B a e +--R + +--R 2 2 2 2 2 3 +--R 3A a c d e - B a c d e + A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 3 2 2 2 +--R ((- A a c e + B a c d e )x - A a e + B a d e )log(c x + a) +--R + +--R 3 2 2 2 3 2 2 +--R ((2A a c e - 2B a c d e )x + 2A a e - 2B a d e )log(e x + d) +--R + +--R 2 3 2 2 2 3 2 3 2 2 +--R (B a e + A a c d e + B a c d e + A c d )x + A a e - B a d e +--R + +--R 2 3 +--R A a c d e - B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +-+ +-+ +--R ((2a c e + 4a c d e + 2a c d )x + 2a e + 4a c d e + 2a c d )\|a \|c +--R Type: Expression(Integer) +--E 731 + +--S 732 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 732 + +)clear all + +--S 733 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 6 2 5 2 2 2 4 3 +--R c e x + 2c d e x + (2a c e + c d )x + 4a c d e x +--R + +--R 2 2 2 2 2 2 2 +--R (a e + 2a c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 733 + +--S 734 OF 765 +r0:=1/2*e*(A*c*d^2+4*a*B*d*e-3*a*A*e^2)/(a*(c*d^2+a*e^2)^2*(d+e*x))+_ + 1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(d+e*x)*_ + (a+c*x^2))-e^2*(3*B*c*d^2-4*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+_ + a*e^2)^3+1/2*e^2*(3*B*c*d^2-4*A*c*d*e-a*B*e^2)*log(a+c*x^2)/_ + (c*d^2+a*e^2)^3-1/2*(2*a*B*d*e*(c*d^2-3*a*e^2)-A*(c^2*d^4+6*a*_ + c*d^2*e^2-3*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))*sqrt(c)/(a^(3/2)*_ + (c*d^2+a*e^2)^3) +--R +--R +--R (2) +--R 2 5 2 4 2 2 3 2 3 2 3 4 3 +--R (- 3A a c e + 6B a c d e + 6A a c d e - 2B a c d e + A c d e)x +--R + +--R 2 4 2 2 3 2 3 2 2 4 3 5 2 +--R (- 3A a c d e + 6B a c d e + 6A a c d e - 2B a c d e + A c d )x +--R + +--R 3 5 3 4 2 2 3 2 3 2 2 4 +--R (- 3A a e + 6B a d e + 6A a c d e - 2B a c d e + A a c d e)x +--R + +--R 3 4 3 2 3 2 3 2 2 4 2 5 +--R - 3A a d e + 6B a d e + 6A a c d e - 2B a c d e + A a c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 2 4 2 2 3 3 +--R (- B a c e - 4A a c d e + 3B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (- B a c d e - 4A a c d e + 3B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (- B a e - 4A a c d e + 3B a c d e )x - B a d e - 4A a c d e +--R + +--R 2 3 2 +--R 3B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 5 2 4 2 2 3 3 +--R (2B a c e + 8A a c d e - 6B a c d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 +--R (2B a c d e + 8A a c d e - 6B a c d e )x +--R + +--R 3 5 2 4 2 2 3 3 4 2 2 3 +--R (2B a e + 8A a c d e - 6B a c d e )x + 2B a d e + 8A a c d e +--R + +--R 2 3 2 +--R - 6B a c d e +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 2 2 3 2 3 2 3 4 2 +--R (- 3A a c e + 4B a c d e - 2A a c d e + 4B a c d e + A c d e)x +--R + +--R 3 5 2 4 2 2 3 2 3 2 2 4 +--R B a e + A a c d e + 2B a c d e + 2A a c d e + B a c d e +--R + +--R 3 5 +--R A c d +--R * +--R x +--R + +--R 3 5 3 4 2 3 2 2 4 2 5 +--R - 2A a e + 3B a d e + 2B a c d e + 2A a c d e - B a c d +--R * +--R +-+ +--R \|a +--R / +--R 4 7 3 2 2 5 2 3 4 3 4 6 3 +--R (2a c e + 6a c d e + 6a c d e + 2a c d e)x +--R + +--R 4 6 3 2 3 4 2 3 5 2 4 7 2 +--R (2a c d e + 6a c d e + 6a c d e + 2a c d )x +--R + +--R 5 7 4 2 5 3 2 4 3 2 3 6 5 6 4 3 4 +--R (2a e + 6a c d e + 6a c d e + 2a c d e)x + 2a d e + 6a c d e +--R + +--R 3 2 5 2 2 3 7 +--R 6a c d e + 2a c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 734 + +--S 735 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 OF 765 +t0:=(A+B*x)*(d+e*x)^5/(a+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 736 + +--S 737 OF 765 +r0:=-3/8*e^2*(5*a*B*e*(2*c*d^2-a*e^2)+A*c*d*(6*c*d^2+5*a*e^2))*x/(a^2*c^3)-_ + 1/2*e^3*(3*A*c*d^2+5*a*B*d*e+a*A*e^2)*x^2/(a^2*c^2)-1/8*e^4*(3*A*_ + c*d+5*a*B*e)*x^3/(a^2*c^2)-1/4*(a*B-A*c*x)*(d+e*x)^5/(a*c*(a+_ + c*x^2)^2)+1/8*(d+e*x)^4*(2*a*A*e+(3*A*c*d+5*a*B*e)*x)/(a^2*c*(a+_ + c*x^2))+1/8*(5*a*B*e*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4)+A*c*d*_ + (3*c^2*d^4+10*a*c*d^2*e^2+15*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(5/2)*c^(7/2))+1/2*e^4*(5*B*d+A*e)*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 +--R - 15B a c e + 15A a c d e + 30B a c d e + 10A a c d e +--R + +--R 4 4 5 5 +--R 5B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R - 30B a c e + 30A a c d e + 60B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R 10B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R - 15B a e + 15A a c d e + 30B a c d e + 10A a c d e + 5B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (4A a c e + 20B a c d e )x + (8A a c e + 40B a c d e )x +--R + +--R 4 5 4 4 +--R 4A a e + 20B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 5 +--R 8B a c e x +--R + +--R 2 2 5 2 2 4 3 2 3 3 3 2 +--R - 6A a c e - 30B a c d e + 20A a c d e + 20B a c d e +--R + +--R 4 4 +--R 12A c d e +--R * +--R 4 +--R x +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 +--R 25B a c e - 25A a c d e - 50B a c d e + 10A a c d e +--R + +--R 3 4 4 5 +--R 5B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 3 4 2 +--R (- 4A a c e - 20B a c d e + 24A a c d e)x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 +--R 15B a e - 15A a c d e - 30B a c d e - 10A a c d e +--R + +--R 2 2 4 3 5 +--R - 5B a c d e + 5A a c d +--R * +--R x +--R + +--R 2 2 4 2 2 5 +--R 2A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 5 4 3 4 2 4 3 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 737 + +--S 738 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 738 + +)clear all + +--S 739 OF 765 +t0:=(A+B*x)*(d+e*x)^4/(a+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 739 + +--S 740 OF 765 +r0:=-3/8*e^2*(3*A*c*d^2+4*a*B*d*e+a*A*e^2)*x/(a^2*c^2)-1/8*e^3*(3*A*c*d+_ + 4*a*B*e)*x^2/(a^2*c^2)-1/4*(a*B-A*c*x)*(d+e*x)^4/(a*c*(a+c*x^2)^2)+_ + 1/8*(d+e*x)^3*(a*A*e+(3*A*c*d+4*a*B*e)*x)/(a^2*c*(a+c*x^2))+_ + 1/8*(3*A*(c*d^2+a*e^2)^2+4*a*B*d*e*(c*d^2+3*a*e^2))*atan(x*_ + sqrt(c)/sqrt(a))/(a^(5/2)*c^(5/2))+1/2*B*e^4*log(a+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 3 4 2 3 3 4 2 2 4 3 5 4 4 +--R (3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 2 4 3 2 3 2 3 2 2 2 3 3 4 4 2 +--R (6A a c e + 24B a c d e + 12A a c d e + 8B a c d e + 6A a c d )x +--R + +--R 4 4 4 3 3 2 2 2 3 2 3 2 3 4 +--R 3A a c e + 12B a c d e + 6A a c d e + 4B a c d e + 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 4 4 3 4 2 4 4 2 +--R (4B a c e x + 8B a c e x + 4B a e )log(c x + a) +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 6B a c e + 8A a c d e + 12B a c d e + 9A c d e)x +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 4 4 3 +--R (- 5A a c e - 20B a c d e + 6A a c d e + 4B a c d e + 3A c d )x +--R + +--R 3 4 3 3 2 +--R (- 4B a c e + 18A a c d e)x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 3 4 +--R (- 3A a c e - 12B a c d e - 6A a c d e - 4B a c d e + 5A a c d )x +--R + +--R 2 2 3 2 2 4 +--R A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 5 4 3 4 2 4 3 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 740 + +--S 741 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 741 + +)clear all + +--S 742 OF 765 +t0:=(A+B*x)*(d+e*x)^3/(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 742 + +--S 743 OF 765 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^3/(a*c*(a+c*x^2)^2)-3/8*(A*c*d+a*B*e)*_ + (a*e-c*d*x)*(d+e*x)/(a^2*c^2*(a+c*x^2))+3/8*(A*c*d+a*B*e)*(c*d^2+_ + a*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(5/2)) +--R +--R +--R (2) +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 6A a c d e + 6B a c d e + 6A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 3A a c d e + 3B a c d e + 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 2 3 2 4 +--R (2A a c e + 3B a c d e + 3A c d e)x +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 5B a c e + 3A a c d e + 3B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 +--R (- 6B a c d e + 6A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 2 +--R (- 3B a e - 3A a c d e - 3B a c d e + 5A a c d )x - 3B a d e +--R + +--R 2 2 2 3 +--R - 3A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 4 4 3 3 2 4 2 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 743 + +--S 744 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 744 + +)clear all + +--S 745 OF 765 +t0:=(A+B*x)*(d+e*x)^2/(a+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 745 + +--S 746 OF 765 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^2/(a*c*(a+c*x^2)^2)-1/8*(a*e-c*d*x)*_ + (3*A*c*d+2*a*B*e+A*c*e*x)/(a^2*c^2*(a+c*x^2))+1/8*(3*A*c*d^2+2*a*_ + B*d*e+a*A*e^2)*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(3/2)) +--R +--R +--R (2) +--R 3 2 3 4 2 4 +--R (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 3 2 2 3 2 3 +--R (2A a c e + 4B a c d e + 6A a c d )x + A a c e + 2B a c d e +--R + +--R 2 2 2 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 3 4 2 2 2 3 2 3 +--R A c d e x + (A a c e + 2B a c d e + 3A c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 4B a c e + 2A a c d e)x + (- A a c e - 2B a c d e + 5A a c d )x +--R + +--R 3 2 2 2 2 +--R - 2B a e - 3A a c d e - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 4 4 3 3 2 4 2 +-+ +-+ +--R (8a c x + 16a c x + 8a c )\|a \|c +--R Type: Expression(Integer) +--E 746 + +--S 747 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 747 + +)clear all + +--S 748 OF 765 +t0:=(A+B*x)*(d+e*x)/(a+c*x^2)^3 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 748 + +--S 749 OF 765 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)/(a*c*(a+c*x^2)^2)+1/8*(-2*a*A*e+(3*A*c*d+_ + a*B*e)*x)/(a^2*c*(a+c*x^2))+1/8*(3*A*c*d+a*B*e)*atan(x*sqrt(c)/_ + sqrt(a))/(a^(5/2)*c^(3/2)) +--R +--R +--R (2) +--R 2 3 4 2 2 2 3 2 +--R ((B a c e + 3A c d)x + (2B a c e + 6A a c d)x + B a e + 3A a c d) +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 2 2 +-+ +-+ +--R ((B a c e + 3A c d)x + (- B a e + 5A a c d)x - 2A a e - 2B a d)\|a \|c +--R / +--R 2 3 4 3 2 2 4 +-+ +-+ +--R (8a c x + 16a c x + 8a c)\|a \|c +--R Type: Expression(Integer) +--E 749 + +--S 750 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 OF 765 +t0:=(A+B*x)/(a+c*x^2)^3 +--R +--R +--R B x + A +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 751 + +--S 752 OF 765 +r0:=1/4*(-a*B+A*c*x)/(a*c*(a+c*x^2)^2)+3/8*A*x/(a^2*(a+c*x^2))+_ + 3/8*A*atan(x*sqrt(c)/sqrt(a))/(a^(5/2)*sqrt(c)) +--R +--R +--R (2) +--R +-+ +--R 3 4 2 2 2 x\|c +--R (3A c x + 6A a c x + 3A a c)atan(-----) +--R +-+ +--R \|a +--R + +--R 2 3 2 +-+ +-+ +--R (3A c x + 5A a c x - 2B a )\|a \|c +--R / +--R 2 3 4 3 2 2 4 +-+ +-+ +--R (8a c x + 16a c x + 8a c)\|a \|c +--R Type: Expression(Integer) +--E 752 + +--S 753 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 OF 765 +t0:=(A+B*x)/((d+e*x)*(a+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------------- +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 3 +--R c e x + c d x + 3a c e x + 3a c d x + 3a c e x + 3a c d x + a e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 754 + +--S 755 OF 765 +r0:=1/4*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2)^2)+_ + 1/8*(-4*a^2*e^2*(B*d-A*e)-(a*B*e*(c*d^2-3*a*e^2)-A*c*d*(3*c*d^2+7*_ + a*e^2))*x)/(a^2*(c*d^2+a*e^2)^2*(a+c*x^2))-e^4*(B*d-A*e)*log(d+_ + e*x)/(c*d^2+a*e^2)^3+1/2*e^4*(B*d-A*e)*log(a+c*x^2)/(c*d^2+_ + a*e^2)^3-1/8*(a*B*e*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4)-A*c*d*_ + (3*c^2*d^4+10*a*c*d^2*e^2+15*a^2*e^4))*atan(x*sqrt(c)/sqrt(a))/_ + (a^(5/2)*(c*d^2+a*e^2)^3*sqrt(c)) +--R +--R +--R (2) +--R 3 2 5 2 3 4 2 3 2 3 4 3 2 4 4 +--R 3B a c e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 5 5 +--R 3A c d +--R * +--R 4 +--R x +--R + +--R 4 5 3 2 4 3 2 2 3 2 3 3 2 +--R 6B a c e + 30A a c d e - 12B a c d e + 20A a c d e +--R + +--R 2 3 4 4 5 +--R - 2B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 5 4 4 4 2 3 3 2 3 2 3 2 4 +--R 3B a e + 15A a c d e - 6B a c d e + 10A a c d e - B a c d e +--R + +--R 2 3 5 +--R 3A a c d +--R * +--R +-+ +--R x\|c +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (- 4A a c e + 4B a c d e )x + (- 8A a c e + 8B a c d e )x +--R + +--R 4 5 4 4 +--R - 4A a e + 4B a d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 2 2 5 2 2 4 4 3 5 3 4 2 +--R (8A a c e - 8B a c d e )x + (16A a c e - 16B a c d e )x +--R + +--R 4 5 4 4 +--R 8A a e - 8B a d e +--R * +--R log(e x + d) +--R + +--R 3 5 2 2 4 2 2 2 3 3 3 2 3 4 +--R 3B a c e + 7A a c d e + 2B a c d e + 10A a c d e - B a c d e +--R + +--R 4 5 +--R 3A c d +--R * +--R 3 +--R x +--R + +--R 3 5 3 4 2 2 2 3 2 2 3 2 2 +--R (4A a c e - 4B a c d e + 4A a c d e - 4B a c d e )x +--R + +--R 4 5 3 4 3 2 3 2 2 3 2 2 2 4 +--R 5B a e + 9A a c d e + 6B a c d e + 14A a c d e + B a c d e +--R + +--R 3 5 +--R 5A a c d +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 3 3 2 2 2 4 +--R 6A a e - 6B a d e + 8A a c d e - 8B a c d e + 2A a c d e +--R + +--R 2 2 5 +--R - 2B a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 2 6 4 3 2 4 3 4 4 2 2 5 6 4 +--R (8a c e + 24a c d e + 24a c d e + 8a c d )x +--R + +--R 6 6 5 2 2 4 4 3 4 2 3 4 6 2 7 6 6 2 4 +--R (16a c e + 48a c d e + 48a c d e + 16a c d )x + 8a e + 24a c d e +--R + +--R 5 2 4 2 4 3 6 +--R 24a c d e + 8a c d +--R * +--R +-+ +-+ +--R \|a \|c +--R Type: Expression(Integer) +--E 755 + +--S 756 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 756 + +)clear all + +--S 757 OF 765 +t0:=(A+B*x)/((d+e*x)^2*(a+c*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 8 3 7 2 2 3 2 6 2 5 +--R c e x + 2c d e x + (3a c e + c d )x + 6a c d e x +--R + +--R 2 2 2 2 4 2 3 3 2 2 2 2 3 3 2 +--R (3a c e + 3a c d )x + 6a c d e x + (a e + 3a c d )x + 2a d e x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 757 + +--S 758 OF 765 +r0:=-1/8*e*(2*a*B*d*e*(c*d^2-11*a*e^2)-3*A*(c^2*d^4+4*a*c*d^2*e^2-_ + 5*a^2*e^4))/(a^2*(c*d^2+a*e^2)^3*(d+e*x))+1/4*(-a*(B*d-A*e)+_ + (A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(d+e*x)*(a+c*x^2)^2)+1/8*(-a*_ + e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)-(2*a*B*e*(c*d^2-2*a*e^2)-3*A*c*d*_ + (c*d^2+3*a*e^2))*x)/(a^2*(c*d^2+a*e^2)^2*(d+e*x)*(a+c*x^2))-e^4*_ + (5*B*c*d^2-6*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+a*e^2)^4+1/2*e^4*_ + (5*B*c*d^2-6*A*c*d*e-a*B*e^2)*log(a+c*x^2)/(c*d^2+a*e^2)^4-1/8*_ + (2*a*B*d*e*(c^2*d^4+10*a*c*d^2*e^2-15*a^2*e^4)-3*A*(c^3*d^6+_ + 5*a*c^2*d^4*e^2+15*a^2*c*d^2*e^4-5*a^3*e^6))*atan(x*sqrt(c)/_ + sqrt(a))*sqrt(c)/(a^(5/2)*(c*d^2+a*e^2)^4) +--R +--R +--R (2) +--R 3 2 7 3 2 6 2 3 2 5 2 3 3 4 +--R - 15A a c e + 30B a c d e + 45A a c d e - 20B a c d e +--R + +--R 4 4 3 4 5 2 5 6 +--R 15A a c d e - 2B a c d e + 3A c d e +--R * +--R 5 +--R x +--R + +--R 3 2 6 3 2 2 5 2 3 3 4 2 3 4 3 +--R - 15A a c d e + 30B a c d e + 45A a c d e - 20B a c d e +--R + +--R 4 5 2 4 6 5 7 +--R 15A a c d e - 2B a c d e + 3A c d +--R * +--R 4 +--R x +--R + +--R 4 7 4 6 3 2 2 5 3 2 3 4 +--R - 30A a c e + 60B a c d e + 90A a c d e - 40B a c d e +--R + +--R 2 3 4 3 2 3 5 2 4 6 +--R 30A a c d e - 4B a c d e + 6A a c d e +--R * +--R 3 +--R x +--R + +--R 4 6 4 2 5 3 2 3 4 3 2 4 3 +--R - 30A a c d e + 60B a c d e + 90A a c d e - 40B a c d e +--R + +--R 2 3 5 2 2 3 6 4 7 +--R 30A a c d e - 4B a c d e + 6A a c d +--R * +--R 2 +--R x +--R + +--R 5 7 5 6 4 2 5 4 3 4 +--R - 15A a e + 30B a d e + 45A a c d e - 20B a c d e +--R + +--R 3 2 4 3 3 2 5 2 2 3 6 +--R 15A a c d e - 2B a c d e + 3A a c d e +--R * +--R x +--R + +--R 5 6 5 2 5 4 3 4 4 4 3 +--R - 15A a d e + 30B a d e + 45A a c d e - 20B a c d e +--R + +--R 3 2 5 2 3 2 6 2 3 7 +--R 15A a c d e - 2B a c d e + 3A a c d +--R * +--R +-+ +--R +-+ x\|c +--R \|c atan(-----) +--R +-+ +--R \|a +--R + +--R 3 2 7 2 3 6 2 3 2 5 5 +--R (- 4B a c e - 24A a c d e + 20B a c d e )x +--R + +--R 3 2 6 2 3 2 5 2 3 3 4 4 +--R (- 4B a c d e - 24A a c d e + 20B a c d e )x +--R + +--R 4 7 3 2 6 3 2 2 5 3 +--R (- 8B a c e - 48A a c d e + 40B a c d e )x +--R + +--R 4 6 3 2 2 5 3 2 3 4 2 +--R (- 8B a c d e - 48A a c d e + 40B a c d e )x +--R + +--R 5 7 4 6 4 2 5 5 6 +--R (- 4B a e - 24A a c d e + 20B a c d e )x - 4B a d e +--R + +--R 4 2 5 4 3 4 +--R - 24A a c d e + 20B a c d e +--R * +--R 2 +--R log(c x + a) +--R + +--R 3 2 7 2 3 6 2 3 2 5 5 +--R (8B a c e + 48A a c d e - 40B a c d e )x +--R + +--R 3 2 6 2 3 2 5 2 3 3 4 4 +--R (8B a c d e + 48A a c d e - 40B a c d e )x +--R + +--R 4 7 3 2 6 3 2 2 5 3 +--R (16B a c e + 96A a c d e - 80B a c d e )x +--R + +--R 4 6 3 2 2 5 3 2 3 4 2 +--R (16B a c d e + 96A a c d e - 80B a c d e )x +--R + +--R 5 7 4 6 4 2 5 5 6 +--R (8B a e + 48A a c d e - 40B a c d e )x + 8B a d e +--R + +--R 4 2 5 4 3 4 +--R 48A a c d e - 40B a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 7 3 2 6 2 3 2 5 2 3 3 4 +--R - 15A a c e + 22B a c d e - 3A a c d e + 20B a c d e +--R + +--R 4 4 3 4 5 2 5 6 +--R 15A a c d e - 2B a c d e + 3A c d e +--R * +--R 4 +--R x +--R + +--R 4 7 3 2 6 3 2 2 5 2 3 3 4 +--R 4B a c e + 9A a c d e + 6B a c d e + 21A a c d e +--R + +--R 4 5 2 4 6 5 7 +--R 15A a c d e - 2B a c d e + 3A c d +--R * +--R 3 +--R x +--R + +--R 4 7 4 6 3 2 2 5 3 2 3 4 +--R - 25A a c e + 38B a c d e + 3A a c d e + 28B a c d e +--R + +--R 2 3 4 3 2 3 5 2 4 6 +--R 33A a c d e - 10B a c d e + 5A a c d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 6 4 2 5 3 2 3 4 +--R 6B a e + 11A a c d e + 12B a c d e + 27A a c d e +--R + +--R 3 2 4 3 2 3 5 2 4 7 +--R 6B a c d e + 21A a c d e + 5A a c d +--R * +--R x +--R + +--R 5 7 5 6 4 2 5 4 3 4 3 2 4 3 +--R - 8A a e + 14B a d e + 12A a c d e + 2B a c d e + 24A a c d e +--R + +--R 3 2 5 2 2 3 6 2 3 7 +--R - 14B a c d e + 4A a c d e - 2B a c d +--R * +--R +-+ +--R \|a +--R / +--R 6 2 9 5 3 2 7 4 4 4 5 3 5 6 3 2 6 8 5 +--R (8a c e + 32a c d e + 48a c d e + 32a c d e + 8a c d e)x +--R + +--R 6 2 8 5 3 3 6 4 4 5 4 3 5 7 2 2 6 9 4 +--R (8a c d e + 32a c d e + 48a c d e + 32a c d e + 8a c d )x +--R + +--R 7 9 6 2 2 7 5 3 4 5 4 4 6 3 3 5 8 3 +--R (16a c e + 64a c d e + 96a c d e + 64a c d e + 16a c d e)x +--R + +--R 7 8 6 2 3 6 5 3 5 4 4 4 7 2 3 5 9 2 +--R (16a c d e + 64a c d e + 96a c d e + 64a c d e + 16a c d )x +--R + +--R 8 9 7 2 7 6 2 4 5 5 3 6 3 4 4 8 8 8 +--R (8a e + 32a c d e + 48a c d e + 32a c d e + 8a c d e)x + 8a d e +--R + +--R 7 3 6 6 2 5 4 5 3 7 2 4 4 9 +--R 32a c d e + 48a c d e + 32a c d e + 8a c d +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 758 + +--S 759 OF 765 +--d0:=D(m0,x) +--E 759 + +)clear all + +--S 760 OF 765 +t0:=(-11+6*x)/((-1+2*x)*(-1+x^2)) +--R +--R +--R 6x - 11 +--R (1) ----------------- +--R 3 2 +--R 2x - x - 2x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 760 + +--S 761 OF 765 +r0:=16/3*log(1-2*x)-5/2*log(1-x)-17/6*log(1+x) +--R +--R +--R - 17log(x + 1) - 15log(- x + 1) + 32log(- 2x + 1) +--R (2) ------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 761 + +--S 762 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 762 + +)clear all + +--S 763 OF 765 +t0:=(5-x)*(3+2*x)^4*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (1) (- 16x - 16x + 264x + 864x + 999x + 405)\|3x + 2 +--R Type: Expression(Integer) +--E 763 + +--S 764 OF 765 +r0:=8275/162*(2+3*x^2)^(3/2)+923/315*(3+2*x)^2*(2+3*x^2)^(3/2)+29/63*_ + (3+2*x)^3*(2+3*x^2)^(3/2)-1/21*(3+2*x)^4*(2+3*x^2)^(3/2)+1/270*_ + (4583+6132*x)*(2+3*x^2)^(3/2)+2341/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 2341/18*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 12960x - 15120x + 297648x + 1222200x + 1956174x + 1558935x +--R + +--R 1167988 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1474830asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 5670\|3 +--R Type: Expression(Integer) +--E 764 + +--S 765 OF 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 765 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/richder12b.input.pamphlet b/src/input/richder12b.input.pamphlet new file mode 100644 index 0000000..5052ab0 --- /dev/null +++ b/src/input/richder12b.input.pamphlet @@ -0,0 +1,5677 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12b.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There is 1 derivative that did not match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12b.output +)spool richder12b.output +)set message test on +)set message auto off +)clear all + +--S 1 of 300 +t0:=(5-x)*(3+2*x)^3*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 4 3 2 | 2 +--R (1) (- 8x + 4x + 126x + 243x + 135)\|3x + 2 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 300 +r0:=875/54*(2+3*x^2)^(3/2)+17/30*(3+2*x)^2*(2+3*x^2)^(3/2)-1/18*(3+2*x)^3*_ + (2+3*x^2)^(3/2)+7/90*(91+89*x)*(2+3*x^2)^(3/2)+1022/9*asinh(x*_ + sqrt(3/2))/sqrt(3)+511/9*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 360x + 216x + 8445x + 21918x + 21120x + 14516)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 30660asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 270\|3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 3 + +)clear all + +--S 4 of 300 +t0:=(5-x)*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (1) (- 4x + 8x + 51x + 45)\|3x + 2 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 300 +r0:=205/54*(2+3*x^2)^(3/2)-1/15*(3+2*x)^2*(2+3*x^2)^(3/2)+1/90*(233+132*x)*_ + (2+3*x^2)^(3/2)+131/3*asinh(x*sqrt(3/2))/sqrt(3)+131/6*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +-+ +--R 4 3 2 +-+ | 2 x\|3 +--R (- 216x + 540x + 4542x + 6255x + 3124)\|3 \|3x + 2 + 11790asinh(-----) +--R +-+ +--R \|2 +--R --------------------------------------------------------------------------- +--R +-+ +--R 270\|3 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 6 + +)clear all + +--S 7 of 300 +t0:=(5-x)*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (1) (- 2x + 7x + 15)\|3x + 2 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 300 +r0:=37/36*(2+3*x^2)^(3/2)-1/12*(3+2*x)*(2+3*x^2)^(3/2)+46/3*asinh(x*_ + sqrt(3/2))/sqrt(3)+23/3*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 3 2 +-+ | 2 x\|3 +--R (- 9x + 42x + 132x + 28)\|3 \|3x + 2 + 276asinh(-----) +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------------- +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 8 + +--S 9 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 9 + +)clear all + +--S 10 of 300 +t0:=(5-x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) (- x + 5)\|3x + 2 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 300 +r0:=-1/9*(2+3*x^2)^(3/2)+5*asinh(x*sqrt(3/2))/sqrt(3)+_ + 5/2*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 2 +-+ | 2 x\|3 +--R (- 6x + 45x - 4)\|3 \|3x + 2 + 90asinh(-----) +--R +-+ +--R \|2 +--R (2) ------------------------------------------------ +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 13 + +--S 14 of 300 +r0:=-121/8*asinh(x*sqrt(3/2))/sqrt(3)-13/8*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))*sqrt(35)+1/4*(13-x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R +-+ +--+ 9x - 4 +-+ | 2 +--R 13\|3 \|35 atanh(---------------) + (- 2x + 26)\|3 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R - 121asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 8\|3 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 300 +r0:=2*asinh(x*sqrt(3/2))*sqrt(3)+19*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)-1/2*(8+x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 9x - 4 +--+ | 2 +--R (- 76x - 114)atanh(---------------) + (- x - 8)\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-+ +--R +-+ +--+ x\|3 +--R (8x + 12)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R +--+ +--R (4x + 6)\|35 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 18 + +)clear all + +--S 19 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^3 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) --------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 300 +r0:=-13/70*(2+3*x^2)^(3/2)/(3+2*x)^2-1/8*asinh(x*sqrt(3/2))*sqrt(3)-_ + 471/280*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/140*(35+39*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 9x - 4 +--R (1884x + 5652x + 4239)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R +--+ | 2 2 +-+ +--+ x\|3 +--R (374x + 106)\|35 \|3x + 2 + (- 140x - 420x - 315)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 2 +--+ +--R (1120x + 3360x + 2520)\|35 +--R Type: Expression(Integer) +--E 20 + +--S 21 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^4 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------------------- +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 300 +r0:=-123/1225*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 1/6*(2-3*x)*sqrt(2+3*x^2)/(3+2*x)^3+1/70*sqrt(2+3*x^2)/(3+2*x)^2-_ + 43/2450*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 9x - 4 +--R (5904x + 26568x + 39852x + 19926)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (- 516x + 2337x - 3296)\|35 \|3x + 2 +--R / +--R 3 2 +--+ +--R (58800x + 264600x + 396900x + 198450)\|35 +--R Type: Expression(Integer) +--E 23 + +--S 24 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 24 + +)clear all + +--S 25 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^5 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 300 +r0:=-198/8575*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 1/16*(7-4*x)*sqrt(2+3*x^2)/(3+2*x)^4+47/1680*sqrt(2+3*x^2)/(3+2*x)^3-_ + 3/3920*sqrt(2+3*x^2)/(3+2*x)^2-739/137200*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 9x - 4 +--R (19008x + 114048x + 256608x + 256608x + 96228)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 2217x - 10134x + 304x - 26028)\|35 \|3x + 2 +--R / +--R 4 3 2 +--+ +--R (823200x + 4939200x + 11113200x + 11113200x + 4167450)\|35 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 27 + +)clear all + +--S 28 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^6 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 28 + +--S 29 of 300 +r0:=-1017/214375*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 1/30*(12-5*x)*sqrt(2+3*x^2)/(3+2*x)^5+11/525*sqrt(2+3*x^2)/(3+2*x)^4+_ + 1/875*sqrt(2+3*x^2)/(3+2*x)^3-12/6125*sqrt(2+3*x^2)/(3+2*x)^2-_ + 366/214375*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (65088x + 488160x + 1464480x + 2196720x + 1647540x + 494262) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 4 3 2 +--+ | 2 +--R (- 11712x - 76992x - 186392x - 108167x - 222112)\|35 \|3x + 2 +--R / +--R 5 4 3 2 +--R 13720000x + 102900000x + 308700000x + 463050000x + 347287500x +--R + +--R 104186250 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 300 +t0:=(5-x)*sqrt(2+3*x^2)/(3+2*x)^7 +--R +--R +--R +-------+ +--R | 2 +--R (- x + 5)\|3x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 300 +r0:=-6102/7503125*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 1/48*(17-6*x)*sqrt(2+3*x^2)/(3+2*x)^6+43/2800*sqrt(2+3*x^2)/(3+2*x)^5+_ + 127/98000*sqrt(2+3*x^2)/(3+2*x)^4-479/490000*sqrt(2+3*x^2)/(3+2*x)^3-_ + 2727/3430000*sqrt(2+3*x^2)/(3+2*x)^2-53511/120050000*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 2343168x + 21088512x + 79081920x + 158163840x + 177934320x +--R + +--R 106760592x + 26690148 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 642132x - 5388660x - 18236055x - 30753930x - 18651300x +--R + +--R - 22308548 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R / +--R 6 5 4 3 +--R 2881200000x + 25930800000x + 97240500000x + 194481000000x +--R + +--R 2 +--R 218791125000x + 131274675000x + 32818668750 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 of 300 +t0:=(5-x)*(3+2*x)^4*(2+3*x^2)^(3/2) +--R +--R +--R (1) +--R +-------+ +--R 7 6 5 4 3 2 | 2 +--R (- 48x - 48x + 760x + 2560x + 3525x + 2943x + 1998x + 810)\|3x + 2 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 300 +r0:=2777/36*x*(2+3*x^2)^(3/2)+193027/7290*(2+3*x^2)^(5/2)+_ + 4421/2268*(3+2*x)^2*(2+3*x^2)^(5/2)+13/36*(3+2*x)^3*(2+3*x^2)^(5/2)-_ + 1/27*(3+2*x)^4*(2+3*x^2)^(5/2)+1/10206*(126712+136053*x)*_ + (2+3*x^2)^(5/2)+2777/6*asinh(x*sqrt(3/2))/sqrt(3)+2777/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 181440x - 204120x + 3676320x + 14492520x + 24490404x +--R + +--R 3 2 +--R 27468315x + 27537072x + 19683405x + 8598544 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 15745590asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 34020\|3 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 36 + +)clear all + +--S 37 of 300 +t0:=(5-x)*(3+2*x)^3*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (1) (- 24x + 12x + 362x + 737x + 657x + 486x + 270)\|3x + 2 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 300 +r0:=1087/36*x*(2+3*x^2)^(3/2)+4687/540*(2+3*x^2)^(5/2)+71/168*(3+2*x)^2*_ + (2+3*x^2)^(5/2)-1/24*(3+2*x)^3*(2+3*x^2)^(5/2)+1/756*(3622+3243*x)*_ + (2+3*x^2)^(5/2)+1087/6*asinh(x*sqrt(3/2))/sqrt(3)+1087/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 3780x + 2160x + 75600x + 186012x + 219975x + 245136x +--R + +--R 226065x + 81392 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 228270asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 1260\|3 +--R Type: Expression(Integer) +--E 38 + +--S 39 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 39 + +)clear all + +--S 40 of 300 +t0:=(5-x)*(3+2*x)^2*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (1) (- 12x + 24x + 145x + 151x + 102x + 90)\|3x + 2 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 300 +r0:=397/36*x*(2+3*x^2)^(3/2)+293/135*(2+3*x^2)^(5/2)-1/21*(3+2*x)^2*_ + (2+3*x^2)^(5/2)+1/189*(323+192*x)*(2+3*x^2)^(5/2)+_ + 397/6*asinh(x*sqrt(3/2))/sqrt(3)+397/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 6 5 4 3 2 +-+ +--R (- 2160x + 5040x + 36252x + 48405x + 51216x + 71715x + 17392)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 83370asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 1260\|3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 42 + +)clear all + +--S 43 of 300 +t0:=(5-x)*(3+2*x)*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 4 3 2 | 2 +--R (1) (- 6x + 21x + 41x + 14x + 30)\|3x + 2 +--R Type: Expression(Integer) +--E 43 + +--S 44 of 300 +r0:=137/36*x*(2+3*x^2)^(3/2)+19/30*(2+3*x^2)^(5/2)-1/18*(3+2*x)*_ + (2+3*x^2)^(5/2)+137/6*asinh(x*sqrt(3/2))/sqrt(3)+137/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 60x + 252x + 605x + 336x + 1115x + 112)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1370asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 60\|3 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (1) (- 3x + 15x - 2x + 10)\|3x + 2 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 300 +r0:=5/4*x*(2+3*x^2)^(3/2)-1/15*(2+3*x^2)^(5/2)+5/2*asinh(x*sqrt(3/2))*_ + sqrt(3)+15/4*x*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 4 3 2 | 2 +-+ x\|3 +--R (- 36x + 225x - 48x + 375x - 16)\|3x + 2 + 150\|3 asinh(-----) +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------------- +--R 60 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 48 + +)clear all + +--S 49 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x) +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 300 +r0:=1/24*(26-3*x)*(2+3*x^2)^(3/2)-1529/32*asinh(x*sqrt(3/2))*sqrt(3)-_ + 455/32*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+_ + 1/16*(455-123*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R 1365\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R 3 2 | 2 +-+ x\|3 +--R (- 36x + 312x - 762x + 2938)\|3x + 2 - 4587\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 96 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 51 + +)clear all + +--S 52 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 300 +r0:=-1/6*(21+x)*(2+3*x^2)^(3/2)/(3+2*x)+663/16*asinh(x*sqrt(3/2))*_ + sqrt(3)+193/16*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)-_ + 1/8*(193-63*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R (- 1158x - 1737)\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +-+ +--R 3 2 | 2 +-+ x\|3 +--R (- 24x + 252x - 1198x - 3810)\|3x + 2 + (3978x + 5967)\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 96x + 144 +--R Type: Expression(Integer) +--E 53 + +--S 54 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 54 + +)clear all + +--S 55 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^3 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 300 +r0:=-1/4*(8+x)*(2+3*x^2)^(3/2)/(3+2*x)^2-111/8*asinh(x*sqrt(3/2))*_ + sqrt(3)-1143/8*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 3/4*(37+12*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 9x - 4 +--R (4572x + 13716x + 10287)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 6x + 96x + 656x + 634)\|35 \|3x + 2 +--R + +--R +-+ +--R 2 +-+ +--+ x\|3 +--R (- 444x - 1332x - 999)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 2 +--+ +--R (32x + 96x + 72)\|35 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^4 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ---------------------------------- +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 58 + +--S 59 of 300 +r0:=111/140*(2+3*x^2)^(3/2)/(3+2*x)^2-1/6*(11+3*x)*(2+3*x^2)^(3/2)/_ + (3+2*x)^3+33/16*asinh(x*sqrt(3/2))*sqrt(3)+11727/560*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-3/280*(385+111*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 9x - 4 +--R (- 281448x - 1266516x - 1899774x - 949887)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 2520x - 48948x - 97494x - 60538)\|35 \|3x + 2 +--R + +--R +-+ +--R 3 2 +-+ +--+ x\|3 +--R (27720x + 124740x + 187110x + 93555)\|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 3 2 +--+ +--R (13440x + 60480x + 90720x + 45360)\|35 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^5 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 300 +r0:=-549/9800*(2+3*x^2)^(3/2)/(3+2*x)^2+1/840*(70+117*x)*_ + (2+3*x^2)^(3/2)/(3+2*x)^3-13/140*(2+3*x^2)^(5/2)/(3+2*x)^4-_ + 3/32*asinh(x*sqrt(3/2))*sqrt(3)-39663/39200*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+3/19600*(1225+549*x)*_ + sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1903824x + 11422944x + 25701624x + 25701624x + 9638109) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (501204x + 1119528x + 1436882x + 491886)\|35 \|3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (- 176400x - 1058400x - 2381400x - 2381400x - 893025)\|3 \|35 +--R * +--R +-+ +--R x\|3 +--R asinh(-----) +--R +-+ +--R \|2 +--R / +--R 4 3 2 +--+ +--R (1881600x + 11289600x + 25401600x + 25401600x + 9525600)\|35 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^6 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 300 +r0:=1/10*(1+5*x)*(2+3*x^2)^(3/2)/(3+2*x)^5-1107/85750*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-3/160*(11-12*x)*sqrt(2+3*x^2)/_ + (3+2*x)^4+51/5600*sqrt(2+3*x^2)/(3+2*x)^3-117/39200*sqrt(2+3*x^2)/_ + (3+2*x)^2-5301/1372000*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (70848x + 531360x + 1594080x + 2391120x + 1793340x + 538002) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 4 3 2 +--+ | 2 +--R (- 10602x + 189543x - 26682x + 64493x - 125252)\|35 \|3x + 2 +--R / +--R 5 4 3 2 +--R 5488000x + 41160000x + 123480000x + 185220000x + 138915000x +--R + +--R 41674500 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 66 + +)clear all + +--S 67 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^7 +--R +--R +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 300 +r0:=-1/12*(2-3*x)*(2+3*x^2)^(3/2)/(3+2*x)^6-27/8750*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+37/1400*sqrt(2+3*x^2)/(3+2*x)^4+_ + 51/7000*sqrt(2+3*x^2)/(3+2*x)^3+9/7000*sqrt(2+3*x^2)/(3+2*x)^2-_ + 9/35000*sqrt(2+3*x^2)/(3+2*x)-1/20*(6+5*x)*sqrt(2+3*x^2)/(3+2*x)^5 +--R +--R +--R (2) +--R 6 5 4 3 2 +--R (10368x + 93312x + 349920x + 699840x + 787320x + 472392x + 118098) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 +--+ | 2 +--R (- 432x - 2160x + 39195x - 33180x - 3675x - 39748)\|35 \|3x + 2 +--R / +--R 6 5 4 3 2 +--R 3360000x + 30240000x + 113400000x + 226800000x + 255150000x +--R + +--R 153090000x + 38272500 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 68 + +--S 69 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 69 + +)clear all + +--S 70 of 300 +t0:=(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^8 +--R +--R +--R (1) +--R +-------+ +--R 3 2 | 2 +--R (- 3x + 15x - 2x + 10)\|3x + 2 +--R / +--R 8 7 6 5 4 3 2 +--R 256x + 3072x + 16128x + 48384x + 90720x + 108864x + 81648x +--R + +--R 34992x + 6561 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 300 +r0:=-1/42*(9-7*x)*(2+3*x^2)^(3/2)/(3+2*x)^7-72603/105043750*_ + atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+627/39200*_ + sqrt(2+3*x^2)/(3+2*x)^5+6703/1372000*sqrt(2+3*x^2)/(3+2*x)^4+_ + 7569/6860000*sqrt(2+3*x^2)/(3+2*x)^3+3897/48020000*sqrt(2+3*x^2)/_ + (3+2*x)^2-212679/1680700000*sqrt(2+3*x^2)/(3+2*x)-1/672*(137+162*x)*_ + sqrt(2+3*x^2)/(3+2*x)^6 +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 55759104x + 585470592x + 2634617664x + 6586544160x + 9879816240x +--R + +--R 2 +--R 8891834616x + 4445917308x + 952696566 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 5104296x - 44301924x - 148868010x + 98810025x - 740031210x +--R + +--R - 256388969x - 471103116 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R / +--R 7 6 5 4 +--R 80673600000x + 847072800000x + 3811827600000x + 9529569000000x +--R + +--R 3 2 +--R 14294353500000x + 12864918150000x + 6432459075000x + 1378384087500 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 of 300 +t0:=(5-x)*(3+2*x)^4*(2+3*x^2)^(5/2) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 144x - 144x + 2184x + 7584x + 12095x + 13949x + 13044x + 8316x +--R + +--R 3996x + 1620 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 73 + +--S 74 of 300 +r0:=4991/36*x*(2+3*x^2)^(3/2)+4991/90*x*(2+3*x^2)^(5/2)+_ + 928171/53460*(2+3*x^2)^(7/2)+6433/4455*(3+2*x)^2*(2+3*x^2)^(7/2)+_ + 49/165*(3+2*x)^3*(2+3*x^2)^(7/2)-1/33*(3+2*x)^4*(2+3*x^2)^(7/2)+_ + 7/53460*(74539+71136*x)*(2+3*x^2)^(7/2)+4991/6*asinh(x*_ + sqrt(3/2))/sqrt(3)+4991/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 10 9 8 7 6 +--R - 699840x - 769824x + 12921120x + 50615928x + 93646260x +--R + +--R 5 4 3 2 +--R 129966606x + 150762600x + 127123425x + 92160240x + 64370295x +--R + +--R 19537120 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 44469810asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 53460\|3 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 300 +t0:=(5-x)*(3+2*x)^3*(2+3*x^2)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (- 72x + 36x + 1038x + 2235x + 2695x + 2932x + 2124x + 972x + 540) +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 300 +r0:=3731/72*x*(2+3*x^2)^(3/2)+3731/180*x*(2+3*x^2)^(5/2)+_ + 9371/1620*(2+3*x^2)^(7/2)+91/270*(3+2*x)^2*(2+3*x^2)^(7/2)-_ + 1/30*(3+2*x)^3*(2+3*x^2)^(7/2)+7/1620*(839+711*x)*(2+3*x^2)^(7/2)+_ + 3731/12*asinh(x*sqrt(3/2))/sqrt(3)+3731/24*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 9 8 7 6 5 4 +--R - 23328x + 12960x + 418446x + 1035720x + 1503522x + 2036880x +--R + +--R 3 2 +--R 1922805x + 1350240x + 1245915x + 299200 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1007370asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 3240\|3 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 300 +t0:=(5-x)*(3+2*x)^2*(2+3*x^2)^(5/2) +--R +--R +--R +-------+ +--R 7 6 5 4 3 2 | 2 +--R (1) (- 36x + 72x + 411x + 501x + 596x + 572x + 204x + 180)\|3x + 2 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 300 +r0:=665/36*x*(2+3*x^2)^(3/2)+133/18*x*(2+3*x^2)^(5/2)+491/324*_ + (2+3*x^2)^(7/2)-1/27*(3+2*x)^2*(2+3*x^2)^(7/2)+7/324*(59+36*x)*_ + (2+3*x^2)^(7/2)+665/6*asinh(x*sqrt(3/2))/sqrt(3)+665/12*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 8 7 6 5 4 3 2 +--R - 1296x + 2916x + 18900x + 27378x + 41256x + 50571x + 28272x +--R + +--R 40365x + 6368 +--R * +--R +-------+ +--R +-+ | 2 +--R \|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 35910asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 324\|3 +--R Type: Expression(Integer) +--E 80 + +--S 81 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 of 300 +t0:=(5-x)*(3+2*x)*(2+3*x^2)^(5/2) +--R +--R +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (1) (- 18x + 63x + 111x + 84x + 172x + 28x + 60)\|3x + 2 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 300 +r0:=455/72*x*(2+3*x^2)^(3/2)+91/36*x*(2+3*x^2)^(5/2)+11/24*_ + (2+3*x^2)^(7/2)-1/24*(3+2*x)*(2+3*x^2)^(7/2)+455/12*_ + asinh(x*sqrt(3/2))/sqrt(3)+455/24*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +-+ +--R (- 54x + 216x + 438x + 432x + 1111x + 288x + 985x + 64)\|3 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 910asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 24\|3 +--R Type: Expression(Integer) +--E 83 + +--S 84 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (1) (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R Type: Expression(Integer) +--E 85 + +--S 86 of 300 +r0:=25/12*x*(2+3*x^2)^(3/2)+5/6*x*(2+3*x^2)^(5/2)-1/21*(2+3*x^2)^(7/2)+_ + 25/2*asinh(x*sqrt(3/2))/sqrt(3)+25/4*x*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 6 5 4 3 2 +-+ | 2 +--R (- 108x + 630x - 216x + 1365x - 144x + 1155x - 32)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 1050asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 84\|3 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x) +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 2x + 3 +--R Type: Expression(Integer) +--E 88 + +--S 89 of 300 +r0:=7/96*(130-53*x)*(2+3*x^2)^(3/2)+1/60*(39-5*x)*(2+3*x^2)^(5/2)-_ + 162673/128*asinh(x*sqrt(3/2))/sqrt(3)-15925/128*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+7/64*(2275-691*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +--+ 9x - 4 +--R 238875\|3 \|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 1440x + 11232x - 24180x + 69576x - 160590x + 519142)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R - 2440095asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 1920\|3 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^2 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 300 +r0:=-1/24*(310-153*x)*(2+3*x^2)^(3/2)-1/10*(34+x)*(2+3*x^2)^(5/2)/(3+2*x)+_ + 18543/32*asinh(x*sqrt(3/2))*sqrt(3)+5425/32*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))*sqrt(35)-7/16*(775-243*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +--+ 9x - 4 +--R (- 162750x - 244125)\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 432x + 3672x - 10236x + 38916x - 179042x - 531978)\|3x + 2 +--R + +--R +-+ +--R +-+ x\|3 +--R (556290x + 834435)\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 960x + 1440 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^3 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 300 +r0:=5/32*(178+29*x)*(2+3*x^2)^(3/2)/(3+2*x)-1/16*(29+2*x)*_ + (2+3*x^2)^(5/2)/(3+2*x)^2-43995/128*asinh(x*sqrt(3/2))*sqrt(3)-_ + 12885/128*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+15/64*_ + (859-267*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R 2 +--+ 9x - 4 +--R (51540x + 154620x + 115965)\|35 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 144x + 1392x - 5652x + 38536x + 254806x + 252362)\|3x + 2 +--R + +--R +-+ +--R 2 +-+ x\|3 +--R (- 175980x - 527940x - 395955)\|3 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 2 +--R 512x + 1536x + 1152 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^4 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 300 +r0:=5/12*(37+12*x)*(2+3*x^2)^(3/2)/(3+2*x)^2-1/6*(8+x)*(2+3*x^2)^(5/2)/_ + (3+2*x)^3+3657/16*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(5/7)+_ + 1785/16*asinh(x*sqrt(3/2))*sqrt(3)-15/8*(119+37*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 +-+ 9x - 4 +--R (- 87768x - 394956x - 592434x - 296217)\|5 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 5 4 3 2 +-+ | 2 +--R (- 72x + 864x - 6816x - 75948x - 154122x - 92206)\|7 \|3x + 2 +--R + +--R +-+ +--R 3 2 +-+ +-+ x\|3 +--R (42840x + 192780x + 289170x + 144585)\|3 \|7 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 3 2 +-+ +--R (384x + 1728x + 2592x + 1296)\|7 +--R Type: Expression(Integer) +--E 98 + +--S 99 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R +-+ +-+ +--+ +--R 3657\|5 \|7 \|35 - 127995 +--R (3) -------------------------- +--R +-------+ +--R | 2 +--R (224x + 336)\|3x + 2 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^5 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ------------------------------------------------ +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 100 + +--S 101 of 300 +r0:=-1917/224*(2+3*x^2)^(3/2)/(3+2*x)^2+5/96*(350+171*x)*(2+3*x^2)^(3/2)/_ + (3+2*x)^3-1/16*(19+4*x)*(2+3*x^2)^(5/2)/(3+2*x)^4-2625/128*asinh(x*_ + sqrt(3/2))*sqrt(3)-188379/896*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)+3/448*(6125+1917*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (9042192x + 54253152x + 122069592x + 122069592x + 45776097) +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--+ +--R (- 6048x + 114912x + 1797468x + 5525640x + 6670018x + 2843910)\|35 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (- 882000x - 5292000x - 11907000x - 11907000x - 4465125)\|3 \|35 +--R * +--R +-+ +--R x\|3 +--R asinh(-----) +--R +-+ +--R \|2 +--R / +--R 4 3 2 +--+ +--R (43008x + 258048x + 580608x + 580608x + 217728)\|35 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^6 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 103 + +--S 104 of 300 +r0:=7929/9800*(2+3*x^2)^(3/2)/(3+2*x)^2-1/280*(490+219*x)*(2+3*x^2)^(3/2)/_ + (3+2*x)^3+73/140*(2+3*x^2)^(5/2)/(3+2*x)^4-1/10*(14+5*x)*_ + (2+3*x^2)^(5/2)/(3+2*x)^5+63/32*asinh(x*sqrt(3/2))*sqrt(3)+_ + 789723/39200*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 9/19600*(8575+2643*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 25271136x - 189533520x - 568600560x - 852900840x - 639675630x +--R + +--R - 191902689 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 176400x - 5480376x - 22735476x - 41822596x - 35880926x +--R + +--R - 11998726 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R 2469600x + 18522000x + 55566000x + 83349000x + 62511750x +--R + +--R 18753525 +--R * +--R +-+ +--R +-+ +--+ x\|3 +--R \|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 5 4 3 2 +--R (1254400x + 9408000x + 28224000x + 42336000x + 31752000x + 9525600) +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^7 +--R +--R +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 300 +r0:=-1737/54880*(2+3*x^2)^(3/2)/(3+2*x)^2+1/1568*(98+69*x)*_ + (2+3*x^2)^(3/2)/(3+2*x)^3-23/784*(2+3*x^2)^(5/2)/(3+2*x)^4+_ + 1/140*(7+13*x)*(2+3*x^2)^(5/2)/(3+2*x)^5-13/210*(2+3*x^2)^(7/2)/_ + (3+2*x)^6-9/128*asinh(x*sqrt(3/2))*sqrt(3)-159759/219520*_ + atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+9/109760*_ + (1715+579*x)*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 30673728x + 276063552x + 1035238320x + 2070476640x + 2329286220x +--R + +--R 1397571732x + 349392933 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R 8739216x + 37830672x + 94907604x + 118513176x + 79687218x +--R + +--R 20723614 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 2963520x - 26671680x - 100018800x - 200037600x - 225042300x +--R + +--R - 135025380x - 33756345 +--R * +--R +-+ +--R +-+ +--+ x\|3 +--R \|3 \|35 asinh(-----) +--R +-+ +--R \|2 +--R / +--R 6 5 4 3 2 +--R 42147840x + 379330560x + 1422489600x + 2844979200x + 3200601600x +--R + +--R 1920360960x + 480090240 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 300 +t0:=(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^8 +--R +--R +--R (1) +--R +-------+ +--R 5 4 3 2 | 2 +--R (- 9x + 45x - 12x + 60x - 4x + 20)\|3x + 2 +--R / +--R 8 7 6 5 4 3 2 +--R 256x + 3072x + 16128x + 48384x + 90720x + 108864x + 81648x +--R + +--R 34992x + 6561 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 300 +r0:=5/84*(11+18*x)*(2+3*x^2)^(3/2)/(3+2*x)^6+1/14*(4+7*x)*_ + (2+3*x^2)^(5/2)/(3+2*x)^7-1107/600250*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)-1/56*(3-55*x)*sqrt(2+3*x^2)/(3+2*x)^5-_ + 193/7840*sqrt(2+3*x^2)/(3+2*x)^4-639/39200*sqrt(2+3*x^2)/(3+2*x)^3-_ + 2007/274400*sqrt(2+3*x^2)/(3+2*x)^2-27351/9604000*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 850176x + 8926848x + 40170816x + 100427040x + 150640560x +--R + +--R 2 +--R 135576504x + 67788252x + 14526054 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 656424x + 9455994x + 2997810x + 15015225x - 3488490x + 593639x +--R + +--R - 4499004 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R / +--R 7 6 5 4 +--R 460992000x + 4840416000x + 21781872000x + 54454680000x +--R + +--R 3 2 +--R 81682020000x + 73513818000x + 36756909000x + 7876480500 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 300 +t0:=(5-x)*(3+2*x)^4/sqrt(2+3*x^2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 300 +r0:=343/3*asinh(x*sqrt(3/2))/sqrt(3)+16660/81*sqrt(2+3*x^2)+_ + 1477/270*(3+2*x)^2*sqrt(2+3*x^2)+19/30*(3+2*x)^3*sqrt(2+3*x^2)-_ + 1/15*(3+2*x)^4*sqrt(2+3*x^2)+49/81*(43+99*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 4 3 2 +-+ | 2 +--R (- 432x - 540x + 12264x + 58860x + 118513)\|3 \|3x + 2 +--R + +--R +-+ +--R x\|3 +--R 46305asinh(-----) +--R +-+ +--R \|2 +--R / +--R +-+ +--R 405\|3 +--R Type: Expression(Integer) +--E 113 + +--S 114 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 300 +t0:=(5-x)*(3+2*x)^3/sqrt(2+3*x^2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 115 + +--S 116 of 300 +r0:=275/3*asinh(x*sqrt(3/2))/sqrt(3)+3305/54*sqrt(2+3*x^2)+_ + 31/36*(3+2*x)^2*sqrt(2+3*x^2)-1/12*(3+2*x)^3*sqrt(2+3*x^2)+_ + 5/54*(148+171*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 3 2 +-+ | 2 x\|3 +--R (- 18x + 12x + 585x + 2171)\|3 \|3x + 2 + 2475asinh(-----) +--R +-+ +--R \|2 +--R (2) -------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 300 +t0:=(5-x)*(3+2*x)^2/sqrt(2+3*x^2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 118 + +--S 119 of 300 +r0:=127/3*asinh(x*sqrt(3/2))/sqrt(3)+359/27*sqrt(2+3*x^2)-_ + 1/9*(3+2*x)^2*sqrt(2+3*x^2)+1/27*(143+72*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R 2 +-+ | 2 x\|3 +--R (- 12x + 36x + 475)\|3 \|3x + 2 + 1143asinh(-----) +--R +-+ +--R \|2 +--R (2) ----------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 300 +t0:=(5-x)*(3+2*x)/sqrt(2+3*x^2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 300 +r0:=47/3*asinh(x*sqrt(3/2))/sqrt(3)+17/6*sqrt(2+3*x^2)-_ + 1/6*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R +-+ | 2 x\|3 +--R (- x + 7)\|3 \|3x + 2 + 47asinh(-----) +--R +-+ +--R \|2 +--R (2) ---------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 300 +t0:=(5-x)/sqrt(2+3*x^2) +--R +--R +--R - x + 5 +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 300 +r0:=5*asinh(x*sqrt(3/2))/sqrt(3)-1/3*sqrt(2+3*x^2) +--R +--R +--R +-------+ +-+ +--R +-+ | 2 x\|3 +--R - \|3 \|3x + 2 + 15asinh(-----) +--R +-+ +--R \|2 +--R (2) --------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 125 + +--S 126 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 of 300 +t0:=(5-x)/((3+2*x)*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------ +--R +-------+ +--R | 2 +--R (2x + 3)\|3x + 2 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 300 +r0:=-1/2*asinh(x*sqrt(3/2))/sqrt(3)-13/2*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35) +--R +--R +--R +-+ +--R +-+ 9x - 4 +--+ x\|3 +--R 13\|3 atanh(---------------) - \|35 asinh(-----) +--R +-------+ +-+ +--R +--+ | 2 \|2 +--R \|35 \|3x + 2 +--R (2) ------------------------------------------------ +--R +-+ +--+ +--R 2\|3 \|35 +--R Type: Expression(Integer) +--E 128 + +--S 129 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 300 +t0:=(5-x)/((3+2*x)^2*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------- +--R +-------+ +--R 2 | 2 +--R (4x + 12x + 9)\|3x + 2 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 300 +r0:=-41/35*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/35*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R +-------+ +--R 9x - 4 +--+ | 2 +--R (82x + 123)atanh(---------------) - 13\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R (2) ----------------------------------------------------- +--R +--+ +--R (70x + 105)\|35 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 300 +t0:=(5-x)/((3+2*x)^3*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------- +--R +-------+ +--R 3 2 | 2 +--R (8x + 36x + 54x + 27)\|3x + 2 +--R Type: Expression(Integer) +--E 133 + +--S 134 of 300 +r0:=-291/1225*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/70*sqrt(2+3*x^2)/(3+2*x)^2-281/2450*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 2 9x - 4 +--+ | 2 +--R (1164x + 3492x + 2619)atanh(---------------) + (- 281x - 649)\|35 \|3x + 2 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R ----------------------------------------------------------------------------- +--R 2 +--+ +--R (4900x + 14700x + 11025)\|35 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 300 +t0:=(5-x)/((3+2*x)^4*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------- +--R +-------+ +--R 4 3 2 | 2 +--R (16x + 96x + 216x + 216x + 81)\|3x + 2 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 300 +r0:=-57/1715*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/105*sqrt(2+3*x^2)/(3+2*x)^3-16/245*sqrt(2+3*x^2)/(3+2*x)^2-_ + 10/343*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 9x - 4 +--R (1368x + 6156x + 9234x + 4617)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 2 +--+ | 2 +--R (- 600x - 2472x - 2995)\|35 \|3x + 2 +--R / +--R 3 2 +--+ +--R (41160x + 185220x + 277830x + 138915)\|35 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 300 +t0:=(5-x)/((3+2*x)^5*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------ +--R +-------+ +--R 5 4 3 2 | 2 +--R (32x + 240x + 720x + 1080x + 810x + 243)\|3x + 2 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 300 +r0:=27/42875*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/140*sqrt(2+3*x^2)/(3+2*x)^4-97/2100*sqrt(2+3*x^2)/(3+2*x)^3-_ + 87/4900*sqrt(2+3*x^2)/(3+2*x)^2-991/171500*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 9x - 4 +--R (- 1296x - 7776x - 17496x - 17496x - 6561)atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 3 2 +--+ | 2 +--R (- 5946x - 35892x - 79423x - 70389)\|35 \|3x + 2 +--R / +--R 4 3 2 +--+ +--R (2058000x + 12348000x + 27783000x + 27783000x + 10418625)\|35 +--R Type: Expression(Integer) +--E 140 + +--S 141 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 of 300 +t0:=(5-x)/((3+2*x)^6*sqrt(2+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------------- +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (64x + 576x + 2160x + 4320x + 4860x + 2916x + 729)\|3x + 2 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 300 +r0:=19737/7503125*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-_ + 13/175*sqrt(2+3*x^2)/(3+2*x)^5-439/12250*sqrt(2+3*x^2)/(3+2*x)^4-_ + 797/61250*sqrt(2+3*x^2)/(3+2*x)^3-1611/428750*sqrt(2+3*x^2)/(3+2*x)^2-_ + 10023/15006250*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 631584x - 4736880x - 14210640x - 21315960x - 15986970x +--R + +--R - 4796091 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R +-------+ +--R 4 3 2 +--+ | 2 +--R (- 80184x - 706644x - 2487944x - 4314244x - 3409859)\|35 \|3x + 2 +--R / +--R 5 4 3 2 +--R 240100000x + 1800750000x + 5402250000x + 8103375000x + 6077531250x +--R + +--R 1823259375 +--R * +--R +--+ +--R \|35 +--R Type: Expression(Integer) +--E 143 + +--S 144 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 300 +t0:=(5-x)*(3+2*x)^4/(2+3*x^2)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 145 + +--S 146 of 300 +r0:=880/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^4*(2+15*x)/sqrt(2+3*x^2)+_ + 1255/81*sqrt(2+3*x^2)-115/9*(3+2*x)*sqrt(2+3*x^2)-_ + 151/27*(3+2*x)^2*sqrt(2+3*x^2)-5/3*(3+2*x)^3*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R x\|3 | 2 +--R 47520asinh(-----)\|3x + 2 +--R +-+ +--R \|2 +--R + +--R 4 3 2 +-+ +--R (- 288x - 432x + 15024x - 14715x - 33914)\|3 +--R / +--R +-------+ +--R +-+ | 2 +--R 162\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 300 +t0:=(5-x)*(3+2*x)^3/(2+3*x^2)^(3/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 148 + +--S 149 of 300 +r0:=134/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^3*(2+15*x)/sqrt(2+3*x^2)-_ + 109/9*sqrt(2+3*x^2)-17/3*(3+2*x)*sqrt(2+3*x^2)-5/3*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 3 2 +-+ +--R 804asinh(-----)\|3x + 2 + (- 24x + 24x + 411x - 1426)\|3 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------- +--R +-------+ +--R +-+ | 2 +--R 18\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 300 +t0:=(5-x)*(3+2*x)^2/(2+3*x^2)^(3/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 300 +r0:=8/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)^2*(2+15*x)/sqrt(2+3*x^2)-_ + 53/9*sqrt(2+3*x^2)-5/3*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 2 +-+ +--R 48asinh(-----)\|3x + 2 + (- 24x + 357x - 338)\|3 +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------- +--R +-------+ +--R +-+ | 2 +--R 18\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 300 +t0:=(5-x)*(3+2*x)/(2+3*x^2)^(3/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 300 +r0:=-2/3*asinh(x*sqrt(3/2))/sqrt(3)+1/6*(3+2*x)*(2+15*x)/sqrt(2+3*x^2)-_ + 5/3*sqrt(2+3*x^2) +--R +--R +--R +-+ +-------+ +--R x\|3 | 2 +-+ +--R - 4asinh(-----)\|3x + 2 + (49x - 14)\|3 +--R +-+ +--R \|2 +--R (2) ------------------------------------------ +--R +-------+ +--R +-+ | 2 +--R 6\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 300 +t0:=(5-x)/(2+3*x^2)^(3/2) +--R +--R +--R - x + 5 +--R (1) ------------------- +--R +-------+ +--R 2 | 2 +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 300 +r0:=1/6*(2+15*x)/sqrt(2+3*x^2) +--R +--R +--R 15x + 2 +--R (2) ----------- +--R +-------+ +--R | 2 +--R 6\|3x + 2 +--R Type: Expression(Integer) +--E 158 + +--S 159 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 300 +t0:=(5-x)/((3+2*x)*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------ +--R +-------+ +--R 3 2 | 2 +--R (6x + 9x + 4x + 6)\|3x + 2 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 300 +r0:=-26/35*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/sqrt(2+3*x^2) +--R +--R +--R +-------+ +--R | 2 9x - 4 +--+ +--R 52\|3x + 2 atanh(---------------) + (41x + 26)\|35 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R (2) ---------------------------------------------------- +--R +-------+ +--R +--+ | 2 +--R 70\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 300 +t0:=(5-x)/((3+2*x)^2*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------- +--R +-------+ +--R 4 3 2 | 2 +--R (12x + 36x + 35x + 24x + 18)\|3x + 2 +--R Type: Expression(Integer) +--E 163 + +--S 164 of 300 +r0:=-632/1225*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)*sqrt(2+3*x^2))+19/1225*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R | 2 9x - 4 2 +--+ +--R (2528x + 3792)\|3x + 2 atanh(---------------) + (114x + 1435x + 986)\|35 +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R --------------------------------------------------------------------------- +--R +-------+ +--R +--+ | 2 +--R (4900x + 7350)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 300 +t0:=(5-x)/((3+2*x)^3*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------- +--R +-------+ +--R 5 4 3 2 | 2 +--R (24x + 108x + 178x + 153x + 108x + 54)\|3x + 2 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 300 +r0:=-1962/8575*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^2*sqrt(2+3*x^2))+9/245*sqrt(2+3*x^2)/(3+2*x)^2-_ + 331/8575*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 2 | 2 9x - 4 +--R (15696x + 47088x + 35316)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 3 2 +--+ +--R (- 3972x - 4068x + 7397x + 3658)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 +--R (68600x + 205800x + 154350)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 300 +t0:=(5-x)/((3+2*x)^4*(2+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------- +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (48x + 288x + 680x + 840x + 675x + 432x + 162)\|3x + 2 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 300 +r0:=-3312/42875*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^3*sqrt(2+3*x^2))+23/525*sqrt(2+3*x^2)/_ + (3+2*x)^3-27/1225*sqrt(2+3*x^2)/(3+2*x)^2-1051/42875*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 3 2 | 2 9x - 4 +--R (158976x + 715392x + 1073088x + 536544)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 4 3 2 +--+ +--R (- 75672x - 261036x - 237930x - 23349x - 29438)\|35 +--R / +--R +-------+ +--R 3 2 +--+ | 2 +--R (2058000x + 9261000x + 13891500x + 6945750)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 300 +t0:=(5-x)/((3+2*x)^5*(2+3*x^2)^(3/2)) +--R +--R +--R (1) +--R - x + 5 +--R -------------------------------------------------------------------------- +--R +-------+ +--R 7 6 5 4 3 2 | 2 +--R (96x + 720x + 2224x + 3720x + 3870x + 2889x + 1620x + 486)\|3x + 2 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 300 +r0:=-30078/1500625*atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+_ + 1/70*(26+41*x)/((3+2*x)^4*sqrt(2+3*x^2))+58/1225*sqrt(2+3*x^2)/_ + (3+2*x)^4-298/18375*sqrt(2+3*x^2)/(3+2*x)^3-708/42875*_ + sqrt(2+3*x^2)/(3+2*x)^2-14944/1500625*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 4 3 2 | 2 +--R (2887488x + 17324928x + 38981088x + 38981088x + 14617908)\|3x + 2 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--R - 2151936x - 11467872x - 22188792x - 18957672x - 8562487x +--R + +--R - 4197366 +--R * +--R +--+ +--R \|35 +--R / +--R 4 3 2 +--+ +--R (144060000x + 864360000x + 1944810000x + 1944810000x + 729303750)\|35 +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 173 + +--S 174 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 300 +t0:=(5-x)*(3+2*x)^4/(2+3*x^2)^(5/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 175 + +--S 176 of 300 +r0:=1/18*(3+2*x)^4*(2+15*x)/(2+3*x^2)^(3/2)-16/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 1/18*(3+2*x)^3*(20+37*x)/sqrt(2+3*x^2)-2027/81*sqrt(2+3*x^2)-_ + 19/3*(3+2*x)*sqrt(2+3*x^2)-37/27*(3+2*x)^2*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 x\|3 | 2 +--R (- 864x - 576)asinh(-----)\|3x + 2 +--R +-+ +--R \|2 +--R + +--R 4 3 2 +-+ +--R (- 864x + 57285x - 16560x + 33381x - 25342)\|3 +--R / +--R +-------+ +--R 2 +-+ | 2 +--R (486x + 324)\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 300 +t0:=(5-x)*(3+2*x)^3/(2+3*x^2)^(5/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 178 + +--S 179 of 300 +r0:=1/18*(3+2*x)^3*(2+15*x)/(2+3*x^2)^(3/2)-8/9*asinh(x*sqrt(3/2))/sqrt(3)+_ + 1/18*(3+2*x)^2*(10+39*x)/sqrt(2+3*x^2)-157/27*sqrt(2+3*x^2)-_ + 13/9*(3+2*x)*sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 x\|3 | 2 3 2 +-+ +--R (- 144x - 96)asinh(-----)\|3x + 2 + (4971x - 72x + 3741x - 1490)\|3 +--R +-+ +--R \|2 +--R ------------------------------------------------------------------------- +--R +-------+ +--R 2 +-+ | 2 +--R (162x + 108)\|3 \|3x + 2 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 300 +t0:=(5-x)*(3+2*x)^2/(2+3*x^2)^(5/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 300 +r0:=1/18*(3+2*x)^2*(2+15*x)/(2+3*x^2)^(3/2)-41/54*(4-9*x)/sqrt(2+3*x^2) +--R +--R +--R 3 2 +--R 1287x + 72x + 1215x - 274 +--R (2) --------------------------- +--R +-------+ +--R 2 | 2 +--R (162x + 108)\|3x + 2 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 of 300 +t0:=(5-x)*(3+2*x)/(2+3*x^2)^(5/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 300 +r0:=1/18*(3+2*x)*(2+15*x)/(2+3*x^2)^(3/2)+1/18*(-10+43*x)/sqrt(2+3*x^2) +--R +--R +--R 3 +--R 129x + 135x - 14 +--R (2) --------------------- +--R +-------+ +--R 2 | 2 +--R (54x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 185 + +--S 186 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 300 +t0:=(5-x)/(2+3*x^2)^(5/2) +--R +--R +--R - x + 5 +--R (1) -------------------------- +--R +-------+ +--R 4 2 | 2 +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 300 +r0:=1/18*(2+15*x)/(2+3*x^2)^(3/2)+5/6*x/sqrt(2+3*x^2) +--R +--R +--R 3 +--R 45x + 45x + 2 +--R (2) --------------------- +--R +-------+ +--R 2 | 2 +--R (54x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 188 + +--S 189 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 300 +t0:=(5-x)/((3+2*x)*(2+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------- +--R +-------+ +--R 5 4 3 2 | 2 +--R (18x + 27x + 24x + 36x + 8x + 12)\|3x + 2 +--R Type: Expression(Integer) +--E 190 + +--S 191 of 300 +r0:=1/210*(26+41*x)/(2+3*x^2)^(3/2)-104/1225*atanh((4-9*x)/(sqrt(35)*_ + sqrt(2+3*x^2)))/sqrt(35)+1/7350*(312+2137*x)/sqrt(2+3*x^2) +--R +--R +--R (2) +--R +-------+ +--R 2 | 2 9x - 4 +--R (1872x + 1248)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 3 2 +--+ +--R (6411x + 936x + 5709x + 1534)\|35 +--R / +--R +-------+ +--R 2 +--+ | 2 +--R (22050x + 14700)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 300 +t0:=(5-x)/((3+2*x)^2*(2+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------- +--R +-------+ +--R 6 5 4 3 2 | 2 +--R (36x + 108x + 129x + 144x + 124x + 48x + 36)\|3x + 2 +--R Type: Expression(Integer) +--E 193 + +--S 194 of 300 +r0:=1/210*(26+41*x)/((3+2*x)*(2+3*x^2)^(3/2))-176/1715*atanh((4-9*x)/_ + (sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/1470*(34+507*x)/((3+2*x)*_ + sqrt(2+3*x^2))+277/5145*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 3 2 | 2 9x - 4 +--R (6336x + 9504x + 4224x + 6336)\|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 4 3 2 +--+ +--R (4986x + 10647x + 7362x + 9107x + 3966)\|35 +--R / +--R +-------+ +--R 3 2 +--+ | 2 +--R (61740x + 92610x + 41160x + 61740)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 300 +t0:=(5-x)/((3+2*x)^3*(2+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------------------- +--R +-------+ +--R 7 6 5 4 3 2 | 2 +--R (72x + 324x + 582x + 675x + 680x + 468x + 216x + 108)\|3x + 2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 300 +r0:=1/210*(26+41*x)/((3+2*x)^2*(2+3*x^2)^(3/2))-3072/42875*_ + atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/1050*(4+419*x)/_ + ((3+2*x)^2*sqrt(2+3*x^2))+83/1225*sqrt(2+3*x^2)/(3+2*x)^2+_ + 857/128625*sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-------+ +--R 4 3 2 | 2 +--R (73728x + 221184x + 215040x + 147456x + 110592)\|3x + 2 +--R * +--R 9x - 4 +--R atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 5 4 3 2 +--+ +--R (10284x + 67716x + 116367x + 91268x + 89749x + 41366)\|35 +--R / +--R +-------+ +--R 4 3 2 +--+ | 2 +--R (1029000x + 3087000x + 3001250x + 2058000x + 1543500)\|35 \|3x + 2 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 300 +t0:=(5-x)/((3+2*x)^4*(2+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 8 7 6 5 4 3 2 +--R (144x + 864x + 2136x + 3096x + 3385x + 2976x + 1836x + 864x + 324) +--R * +--R +-------+ +--R | 2 +--R \|3x + 2 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 300 +r0:=1/210*(26+41*x)/((3+2*x)^3*(2+3*x^2)^(3/2))-55344/1500625*_ + atanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/7350*(-114+_ + 3331*x)/((3+2*x)^3*sqrt(2+3*x^2))+1471/18375*sqrt(2+3*x^2)/_ + (3+2*x)^3+541/42875*sqrt(2+3*x^2)/(3+2*x)^2-5987/1500625*_ + sqrt(2+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 7969536x + 35862912x + 59107392x + 50805792x + 35862912x +--R + +--R 17931456 +--R * +--R +-------+ +--R | 2 9x - 4 +--R \|3x + 2 atanh(---------------) +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R + +--R 6 5 4 3 2 +--R - 1293192x - 1834596x + 4920642x + 9795297x + 7866162x +--R + +--R 9103449x + 3788738 +--R * +--R +--+ +--R \|35 +--R / +--R 5 4 3 2 +--R 216090000x + 972405000x + 1602667500x + 1377573750x + 972405000x +--R + +--R 486202500 +--R * +--R +-------+ +--R +--+ | 2 +--R \|35 \|3x + 2 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 300 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + (A c e + B c d)x + (B a e + A c d)x + (A a e + B a d)x +--R + +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 202 + +--S 203 of 300 +r0:=-2/5*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(5/2)/e^4+2/7*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(7/2)/e^4-2/9*c*(3*B*d-A*e)*_ + (d+e*x)^(9/2)/e^4+2/11*B*c*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 630B c e x + (770A c e + 840B c d e )x +--R + +--R 5 4 2 3 3 +--R (990B a e + 1100A c d e + 30B c d e )x +--R + +--R 5 4 2 3 3 2 2 +--R (1386A a e + 1584B a d e + 66A c d e - 36B c d e )x +--R + +--R 4 2 3 3 2 4 2 3 +--R (2772A a d e + 198B a d e - 88A c d e + 48B c d e)x + 1386A a d e +--R + +--R 3 2 4 5 +--R - 396B a d e + 176A c d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 203 + +--S 204 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 300 +t0:=(A+B*x)*(a+c*x^2)*sqrt(d+e*x) +--R +--R +--R 3 2 +-------+ +--R (1) (B c x + A c x + B a x + A a)\|e x + d +--R Type: Expression(Integer) +--E 205 + +--S 206 of 300 +r0:=-2/3*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(3/2)/e^4+2/5*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^4-2/7*c*(3*B*d-A*e)*_ + (d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B c e x + (90A c e + 10B c d e )x +--R + +--R 4 3 2 2 2 +--R (126B a e + 18A c d e - 12B c d e )x +--R + +--R 4 3 2 2 3 3 +--R (210A a e + 42B a d e - 24A c d e + 16B c d e)x + 210A a d e +--R + +--R 2 2 3 4 +--R - 84B a d e + 48A c d e - 32B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 206 + +--S 207 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 300 +t0:=(A+B*x)*(a+c*x^2)/sqrt(d+e*x) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 208 + +--S 209 of 300 +r0:=2/3*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^4-_ + 2/5*c*(3*B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-_ + 2*(B*d-A*e)*(c*d^2+a*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + (42A c e - 36B c d e )x +--R + +--R 3 2 2 3 2 +--R (70B a e - 56A c d e + 48B c d e)x + 210A a e - 140B a d e +--R + +--R 2 3 +--R 112A c d e - 96B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 209 + +--S 210 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 300 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ----------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 211 + +--S 212 of 300 +r0:=-2/3*c*(3*B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*sqrt(d+e*x))+2*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 6B c e x + (10A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (30B a e - 40A c d e + 48B c d e)x - 30A a e + 60B a d e - 80A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 212 + +--S 213 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 300 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 214 + +--S 215 of 300 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^(3/2))+2/3*B*c*_ + (d+e*x)^(3/2)/e^4-2*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^4*sqrt(d+e*x))-_ + 2*c*(3*B*d-A*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 2B c e x + (6A c e - 12B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 6B a e + 24A c d e - 48B c d e)x - 2A a e - 4B a d e + 16A c d e +--R + +--R 3 +--R - 32B c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 215 + +--S 216 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 300 +t0:=(A+B*x)*(a+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 2 +--R B c x + A c x + B a x + A a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 217 + +--S 218 of 300 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^(5/2))-2/3*(3*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)/(e^4*(d+e*x)^(3/2))+2*c*(3*B*d-A*e)/_ + (e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B c e x + (- 30A c e + 180B c d e )x +--R + +--R 3 2 2 3 2 2 +--R (- 10B a e - 40A c d e + 240B c d e)x - 6A a e - 4B a d e - 16A c d e +--R + +--R 3 +--R 96B c d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 218 + +--S 219 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 300 +t0:=(A+B*x)*(a+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +-------+ +--R (1) (B c x + A c x + 2B a c x + 2A a c x + B a x + A a )\|e x + d +--R Type: Expression(Integer) +--E 220 + +--S 221 of 300 +r0:=-2/3*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^(3/2)/e^6+2/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^6-4/7*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(7/2)/e^6+4/9*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(9/2)/e^6-2/11*c^2*(5*B*d-A*e)*_ + (d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 6930B c e x + (8190A c e + 630B c d e )x +--R + +--R 6 2 5 2 2 4 4 +--R (20020B a c e + 910A c d e - 700B c d e )x +--R + +--R 6 5 2 2 4 2 3 3 3 +--R (25740A a c e + 2860B a c d e - 1040A c d e + 800B c d e )x +--R + +--R 2 6 5 2 4 2 3 3 +--R 18018B a e + 5148A a c d e - 3432B a c d e + 1248A c d e +--R + +--R 2 4 2 +--R - 960B c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 5 2 4 3 3 +--R 30030A a e + 6006B a d e - 6864A a c d e + 4576B a c d e +--R + +--R 2 4 2 2 5 +--R - 1664A c d e + 1280B c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 3 4 2 +--R 30030A a d e - 12012B a d e + 13728A a c d e - 9152B a c d e +--R + +--R 2 5 2 6 +--R 3328A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 221 + +--S 222 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 300 +t0:=(A+B*x)*(a+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 223 + +--S 224 of 300 +r0:=2/3*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^6-_ + 4/5*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(5/2)/e^6+_ + 4/7*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(7/2)/e^6-_ + 2/9*c^2*(5*B*d-A*e)*(d+e*x)^(9/2)/e^6+2/11*B*c^2*_ + (d+e*x)^(11/2)/e^6-2*(B*d-A*e)*(c*d^2+a*e^2)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B c e x + (770A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (1980B a c e - 880A c d e + 800B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (2772A a c e - 2376B a c d e + 1056A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 2310B a e - 3696A a c d e + 3168B a c d e - 1408A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R 6930A a e - 4620B a d e + 7392A a c d e - 6336B a c d e +--R + +--R 2 4 2 5 +--R 2816A c d e - 2560B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 224 + +--S 225 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 300 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 226 + +--S 227 of 300 +r0:=-4/3*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3/2)/e^6+_ + 4/5*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^6-_ + 2/7*c^2*(5*B*d-A*e)*(d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*sqrt(d+e*x))+2*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (90A c e - 100B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (252B a c e - 144A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 504B a c d e + 288A c d e - 320B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R 630B a e - 1680A a c d e + 2016B a c d e - 1152A c d e +--R + +--R 2 4 +--R 1280B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 +--R - 630A a e + 1260B a d e - 3360A a c d e + 4032B a c d e +--R + +--R 2 4 2 5 +--R - 2304A c d e + 2560B c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 227 + +--S 228 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 300 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 229 + +--S 230 of 300 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(3/2))+4/3*c*(5*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^6-2/5*c^2*(5*B*d-A*e)*_ + (d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-2*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*sqrt(d+e*x))-4*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 30B c e x + (42A c e - 60B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (140B a c e - 112A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (420A a c e - 840B a c d e + 672A c d e - 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 210B a e + 1680A a c d e - 3360B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 3840B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 70A a e - 140B a d e + 1120A a c d e - 2240B a c d e + 1792A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 230 + +--S 231 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 of 300 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 232 + +--S 233 of 300 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(5/2))-2/3*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^(3/2))-2/3*c^2*_ + (5*B*d-A*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6+4*c*_ + (5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*sqrt(d+e*x))+4*c*_ + (5*B*c*d^2-2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 6B c e x + (10A c e - 20B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (60B a c e - 80A c d e + 160B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 60A a c e + 360B a c d e - 480A c d e + 960B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 2 4 +--R (- 10B a e - 80A a c d e + 480B a c d e - 640A c d e + 1280B c d e)x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 6A a e - 4B a d e - 32A a c d e + 192B a c d e - 256A c d e +--R + +--R 2 5 +--R 512B c d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 233 + +--S 234 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 300 +t0:=(A+B*x)*(a+c*x^2)^2/(d+e*x)^(9/2) +--R +--R +--R 2 5 2 4 3 2 2 2 +--R B c x + A c x + 2B a c x + 2A a c x + B a x + A a +--R (1) ------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 235 + +--S 236 of 300 +r0:=2/7*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(7/2))-2/5*(c*d^2+a*e^2)*_ + (5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^(5/2))+4/3*c*(5*B*c*d^3-_ + 3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^(3/2))+2/3*B*c^2*_ + (d+e*x)^(3/2)/e^6-4*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*_ + sqrt(d+e*x))-2*c^2*(5*B*d-A*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 70B c e x + (210A c e - 700B c d e )x +--R + +--R 5 2 4 2 2 3 3 +--R (- 420B a c e + 1680A c d e - 5600B c d e )x +--R + +--R 5 4 2 2 3 2 3 2 2 +--R (- 140A a c e - 840B a c d e + 3360A c d e - 11200B c d e )x +--R + +--R 2 5 4 2 3 2 3 2 +--R - 42B a e - 112A a c d e - 672B a c d e + 2688A c d e +--R + +--R 2 4 +--R - 8960B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 3 3 2 2 4 +--R - 30A a e - 12B a d e - 32A a c d e - 192B a c d e + 768A c d e +--R + +--R 2 5 +--R - 2560B c d +--R / +--R 9 3 8 2 2 7 3 6 +-------+ +--R (105e x + 315d e x + 315d e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 236 + +--S 237 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 238 + +--S 239 of 300 +r0:=2/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^8-_ + 6/5*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*_ + (d+e*x)^(5/2)/e^8-2/7*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+_ + 30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(7/2)/e^8-2/9*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(9/2)/e^8+6/11*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(11/2)/e^8-2/13*c^3*_ + (7*B*d-A*e)*(d+e*x)^(13/2)/e^8+2/15*B*c^3*(d+e*x)^(15/2)/e^8-_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^3*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 6006B c e x + (6930A c e - 6468B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (24570B a c e - 7560A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (30030A a c e - 27300B a c d e + 8400A c d e - 7840B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 38610B a c e - 34320A a c d e + 31200B a c d e - 9600A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 54054A a c e - 46332B a c d e + 41184A a c d e - 37440B a c d e +--R + +--R 3 4 3 3 5 2 +--R 11520A c d e - 10752B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 72072A a c d e + 61776B a c d e - 54912A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 49920B a c d e - 15360A c d e + 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R 90090A a e - 60060B a d e + 144144A a c d e - 123552B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 109824A a c d e - 99840B a c d e + 30720A c d e - 28672B c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 239 + +--S 240 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 241 + +--S 242 of 300 +r0:=-2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*_ + (d+e*x)^(3/2)/e^8-2/5*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+_ + 30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(5/2)/e^8-2/7*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(7/2)/e^8+2/3*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(9/2)/e^8-2/11*c^3*_ + (7*B*d-A*e)*(d+e*x)^(11/2)/e^8+2/13*B*c^3*(d+e*x)^(13/2)/e^8+_ + 2*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*sqrt(d+e*x))+2*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 2310B c e x + (2730A c e - 2940B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (10010B a c e - 3640A c d e + 3920B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (12870A a c e - 14300B a c d e + 5200A c d e - 5600B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 18018B a c e - 20592A a c d e + 22880B a c d e - 8320A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 30030A a c e - 36036B a c d e + 41184A a c d e - 45760B a c d e +--R + +--R 3 4 3 3 5 2 +--R 16640A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R 30030B a e - 120120A a c d e + 144144B a c d e - 164736A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 183040B a c d e - 66560A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 30030A a e + 60060B a d e - 240240A a c d e + 288288B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 329472A a c d e + 366080B a c d e - 133120A c d e + 143360B c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Expression(Integer) +--E 242 + +--S 243 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 244 + +--S 245 of 300 +r0:=2/3*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(3/2))-2/3*c*(4*A*c*d*e*_ + (5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*_ + (d+e*x)^(3/2)/e^8-2/5*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-_ + 3*a*A*e^3)*(d+e*x)^(5/2)/e^8+6/7*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*_ + (d+e*x)^(7/2)/e^8-2/9*c^3*(7*B*d-A*e)*(d+e*x)^(9/2)/e^8+_ + 2/11*B*c^3*(d+e*x)^(11/2)/e^8-2*(c*d^2+a*e^2)^2*(7*B*c*d^2-_ + 6*A*c*d*e+a*B*e^2)/(e^8*sqrt(d+e*x))-6*c*(c*d^2+a*e^2)*(7*B*c*d^3-_ + 5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 630B c e x + (770A c e - 980B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (2970B a c e - 1320A c d e + 1680B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (4158A a c e - 5940B a c d e + 2640A c d e - 3360B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 6930B a c e - 11088A a c d e + 15840B a c d e - 7040A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R 20790A a c e - 41580B a c d e + 66528A a c d e - 95040B a c d e +--R + +--R 3 4 3 3 5 2 +--R 42240A c d e - 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 6930B a e + 83160A a c d e - 166320B a c d e + 266112A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 380160B a c d e + 168960A c d e - 215040B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 2310A a e - 4620B a d e + 55440A a c d e - 110880B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R 177408A a c d e - 253440B a c d e + 112640A c d e - 143360B c d +--R / +--R 9 8 +-------+ +--R (3465e x + 3465d e )\|e x + d +--R Type: Expression(Integer) +--E 245 + +--S 246 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 247 + +--S 248 of 300 +r0:=2/5*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(5/2))-2/3*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(3/2))-2/3*c^2*(35*B*c*d^3-_ + 15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(3/2)/e^8+6/5*c^2*_ + (7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^8-2/7*c^3*(7*B*d-A*e)*_ + (d+e*x)^(7/2)/e^8+2/9*B*c^3*(d+e*x)^(9/2)/e^8+6*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*sqrt(d+e*x))-_ + 2*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 70B c e x + (90A c e - 140B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (378B a c e - 216A c d e + 336B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (630A a c e - 1260B a c d e + 720A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R 1890B a c e - 5040A a c d e + 10080B a c d e - 5760A c d e +--R + +--R 3 4 3 +--R 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 1890A a c e + 11340B a c d e - 30240A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 34560A c d e + 53760B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 210B a e - 2520A a c d e + 15120B a c d e - 40320A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 80640B a c d e - 46080A c d e + 71680B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 +--R - 126A a e - 84B a d e - 1008A a c d e + 6048B a c d e +--R + +--R 2 4 3 2 5 2 3 6 3 7 +--R - 16128A a c d e + 32256B a c d e - 18432A c d e + 28672B c d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 248 + +--S 249 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(9/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 250 + +--S 251 of 300 +r0:=2/7*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(7/2))-2/5*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(5/2))+2*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^(3/2))+_ + 2*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^8-2/5*c^3*_ + (7*B*d-A*e)*(d+e*x)^(5/2)/e^8+2/7*B*c^3*(d+e*x)^(7/2)/e^8+2*c*_ + (4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))/(e^8*sqrt(d+e*x))-2*c^2*(35*B*c*d^3-15*A*c*d^2*e+_ + 15*a*B*d*e^2-3*a*A*e^3)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 10B c e x + (14A c e - 28B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (70B a c e - 56A c d e + 112B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (210A a c e - 700B a c d e + 560A c d e - 1120B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 210B a c e + 1680A a c d e - 5600B a c d e + 4480A c d e +--R + +--R 3 4 3 +--R - 8960B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 70A a c e - 420B a c d e + 3360A a c d e - 11200B a c d e +--R + +--R 3 4 3 3 5 2 +--R 8960A c d e - 17920B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 14B a e - 56A a c d e - 336B a c d e + 2688A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R - 8960B a c d e + 7168A c d e - 14336B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 10A a e - 4B a d e - 16A a c d e - 96B a c d e + 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R - 2560B a c d e + 2048A c d e - 4096B c d +--R / +--R 11 3 10 2 2 9 3 8 +-------+ +--R (35e x + 105d e x + 105d e x + 35d e )\|e x + d +--R Type: Expression(Integer) +--E 251 + +--S 252 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 300 +t0:=(A+B*x)*(a+c*x^2)^3/(d+e*x)^(11/2) +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 +--R B c x + A c x + 3B a c x + 3A a c x + 3B a c x + 3A a c x + B a x +--R + +--R 3 +--R A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 253 + +--S 254 of 300 +r0:=2/9*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(9/2))-2/7*(c*d^2+a*e^2)^2*_ + (7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(7/2))+6/5*c*(c*d^2+a*e^2)*_ + (7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^(5/2))+_ + 2/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+_ + 3*a^2*e^4))/(e^8*(d+e*x)^(3/2))-2/3*c^3*(7*B*d-A*e)*(d+e*x)^(3/2)/_ + e^8+2/5*B*c^3*(d+e*x)^(5/2)/e^8+2*c^2*(35*B*c*d^3-15*A*c*d^2*e+_ + 15*a*B*d*e^2-3*a*A*e^3)/(e^8*sqrt(d+e*x))+6*c^2*(7*B*c*d^2-_ + 2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 7 3 6 6 +--R 126B c e x + (210A c e - 588B c d e )x +--R + +--R 2 7 3 6 3 2 5 5 +--R (1890B a c e - 2520A c d e + 7056B c d e )x +--R + +--R 2 7 2 6 3 2 5 3 3 4 4 +--R (- 1890A a c e + 18900B a c d e - 25200A c d e + 70560B c d e )x +--R + +--R 2 7 2 6 2 2 5 3 3 4 +--R - 630B a c e - 5040A a c d e + 50400B a c d e - 67200A c d e +--R + +--R 3 4 3 +--R 188160B c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 6 2 2 5 2 3 4 +--R - 378A a c e - 756B a c d e - 6048A a c d e + 60480B a c d e +--R + +--R 3 4 3 3 5 2 +--R - 80640A c d e + 225792B c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 6 2 2 5 2 3 4 +--R - 90B a e - 216A a c d e - 432B a c d e - 3456A a c d e +--R + +--R 2 4 3 3 5 2 3 6 +--R 34560B a c d e - 46080A c d e + 129024B c d e +--R * +--R x +--R + +--R 3 7 3 6 2 2 5 2 3 4 2 4 3 +--R - 70A a e - 20B a d e - 48A a c d e - 96B a c d e - 768A a c d e +--R + +--R 2 5 2 3 6 3 7 +--R 7680B a c d e - 10240A c d e + 28672B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +-------+ +--R (315e x + 1260d e x + 1890d e x + 1260d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 254 + +--S 255 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 300 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 300 +r0:=2/3*(B*d+A*e)*(d+e*x)^(3/2)/c+2/5*B*(d+e*x)^(5/2)/c+2*(B*c*d^2+_ + 2*A*c*d*e-a*B*e^2)*sqrt(d+e*x)/c^2-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ + sqrt(-a)+d*sqrt(c)))*((-A*c*d*(c*d^2-3*a*e^2)+a*B*e*(3*c*d^2-a*e^2))/_ + sqrt(-a)+(B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*sqrt(c))/(c^(9/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+_ + d*sqrt(c)))*((A*c*d*(c*d^2-3*a*e^2)-a*B*e*(3*c*d^2-a*e^2))/sqrt(-a)+_ + (B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*sqrt(c))/(c^(9/4)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 3 +---+ +-+ 2 3 +--R (15A a e + 45B a d e - 45A c d e - 15B c d )\|- a \|c + 15B a e +--R + +--R 2 2 2 3 +--R - 45A a c d e - 45B a c d e + 15A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 3 +---+ +-+ 2 3 +--R (15A a e + 45B a d e - 45A c d e - 15B c d )\|- a \|c - 15B a e +--R + +--R 2 2 2 3 +--R 45A a c d e + 45B a c d e - 15A c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 2 2 +--R (6B c e x + (10A c e + 22B c d e)x - 30B a e + 70A c d e + 46B c d ) +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R 15c \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 257 + +--S 258 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 300 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 300 +r0:=2/3*B*(d+e*x)^(3/2)/c+2*(B*d+A*e)*sqrt(d+e*x)/c-atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2+2*A*c*d*e-_ + a*B*e^2-(A*c*d^2-2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/(c^(7/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*_ + sqrt(-a)+d*sqrt(c)))*(B*c*d^2+2*A*c*d*e-a*B*e^2+(A*c*d^2-2*a*B*d*e-_ + a*A*e^2)*sqrt(c)/sqrt(-a))/(c^(7/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 +-+ +--R (- 3A a e - 6B a d e + 3A c d )\|c +--R + +--R 2 2 +---+ +--R (3B a e - 6A c d e - 3B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 +-+ +--R (3A a e + 6B a d e - 3A c d )\|c +--R + +--R 2 2 +---+ +--R (3B a e - 6A c d e - 3B c d )\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ +--R (2B e x + 6A e + 8B d)\|- a \|c \|e x + d \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R 3c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 260 + +--S 261 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 300 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 +--R c x + a +--R Type: Expression(Integer) +--E 262 + +--S 263 of 300 +r0:=2*B*sqrt(d+e*x)/c-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((-A*c*d+a*B*e)/sqrt(-a)+(B*d+A*e)*sqrt(c))/(c^(5/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*_ + sqrt(-a)+d*sqrt(c)))*((A*c*d-a*B*e)/sqrt(-a)+(B*d+A*e)*sqrt(c))/_ + (c^(5/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- A e - B d)\|- a \|c - B a e + A c d)\|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ | +-+ +---+ +--R ((- A e - B d)\|- a \|c + B a e - A c d)\|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R 2B\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R c\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 263 + +--S 264 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 300 +t0:=(A+B*x)/((a+c*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) -------------------- +--R 2 +-------+ +--R (c x + a)\|e x + d +--R Type: Expression(Integer) +--E 265 + +--S 266 of 300 +r0:=-atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (B+a*A*sqrt(c)/(-a)^(3/2))/(c^(3/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(B+A*sqrt(c)/_ + sqrt(-a))/(c^(3/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (A\|c - B\|- a )\|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ 4+-+ +-------+ +--R +-+ +---+ | +-+ +---+ \|c \|e x + d +--R (- A\|c - B\|- a )\|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 266 + +--S 267 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 300 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R 3 2 +-------+ +--R (c e x + c d x + a e x + a d)\|e x + d +--R Type: Expression(Integer) +--E 268 + +--S 269 of 300 +r0:=2*(B*d-A*e)/((c*d^2+a*e^2)*sqrt(d+e*x))-atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))*((-A*c*d-a*B*e)/sqrt(-a)+(B*d-A*e)*_ + sqrt(c))/(c^(1/4)*(c*d^2+a*e^2)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*_ + ((A*c*d+a*B*e)/sqrt(-a)+(B*d-A*e)*sqrt(c))/(c^(1/4)*(c*d^2+a*e^2)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R +---------------+ +--R +---+ +-+ +-------+ | +-+ +---+ +--R ((A e - B d)\|- a \|c + B a e + A c d)\|e x + d \|d\|c + e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R +---------------+ +--R +---+ +-+ +-------+ | +-+ +---+ +--R ((A e - B d)\|- a \|c - B a e - A c d)\|e x + d \|d\|c - e\|- a +--R * +--R 4+-+ +-------+ +--R \|c \|e x + d +--R atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (- 2A e + 2B d)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R (a e + c d )\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 300 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------------ +--R 2 4 3 2 2 2 2 +-------+ +--R (c e x + 2c d e x + (a e + c d )x + 2a d e x + a d )\|e x + d +--R Type: Expression(Integer) +--E 271 + +--S 272 of 300 +r0:=2/3*(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x)^(3/2))+2*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2)/((c*d^2+a*e^2)^2*sqrt(d+e*x))-c^(1/4)*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2-(A*c*d^2+2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/((c*d^2+_ + a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))-c^(1/4)*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(B*c*d^2-2*A*c*d*e-_ + a*B*e^2+(A*c*d^2+2*a*B*d*e-a*A*e^2)*sqrt(c)/sqrt(-a))/((c*d^2+_ + a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 +--R (- 3A a e + 6B a d e + 3A c d e)x - 3A a d e + 6B a d e +--R + +--R 3 +--R 3A c d +--R * +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 +--R (3B a e + 6A c d e - 3B c d e)x + 3B a d e + 6A c d e +--R + +--R 3 +--R - 3B c d +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ +-------+ | +-+ +---+ \|c \|e x + d +--R \|c \|e x + d \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 +--R (3A a e - 6B a d e - 3A c d e)x + 3A a d e - 6B a d e +--R + +--R 3 +--R - 3A c d +--R * +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 +--R (3B a e + 6A c d e - 3B c d e)x + 3B a d e + 6A c d e +--R + +--R 3 +--R - 3B c d +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R 4+-+ +-------+ | +-+ +---+ \|c \|e x + d +--R \|c \|e x + d \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 3 2 2 3 2 +--R (- 6B a e - 12A c d e + 6B c d e)x - 2A a e - 4B a d e +--R + +--R 2 3 +--R - 14A c d e + 8B c d +--R * +--R +---------------+ +---------------+ +--R +---+ | +-+ +---+ | +-+ +---+ +--R \|- a \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 2 5 2 3 2 4 2 4 3 2 2 5 +---+ +--R ((3a e + 6a c d e + 3c d e)x + 3a d e + 6a c d e + 3c d )\|- a +--R * +--R +---------------+ +---------------+ +--R +-------+ | +-+ +---+ | +-+ +---+ +--R \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 272 + +--S 273 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 300 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 274 + +--S 275 of 300 +r0:=-1/2*A*e*(d+e*x)^(3/2)/(a*c)-1/2*(a*B-A*c*x)*(d+e*x)^(5/2)/(a*c*_ + (a+c*x^2))-1/2*e*(A*c*d-5*a*B*e)*sqrt(d+e*x)/(a*c^2)-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + ((-5*a*B*e*(c*d^2-a*e^2)-2*A*c*d*(c*d^2+2*a*e^2))/sqrt(-a)+_ + e*(A*c*d^2+10*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a*c^(9/4)*sqrt(-e*_ + sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+_ + d*sqrt(c)))*((5*a*B*e*(c*d^2-a*e^2)+2*A*c*d*(c*d^2+2*a*e^2))/_ + sqrt(-a)+e*(A*c*d^2+10*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a*c^(9/4)*_ + sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 2 2 +--R (- 3A a c e - 10B a c d e - A c d e)x - 3A a e - 10B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 5B a c e + 4A a c d e + 5B a c d e + 2A c d )x - 5B a e +--R + +--R 2 2 2 2 2 3 +--R 4A a c d e + 5B a c d e + 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 3A a c e - 10B a c d e - A c d e)x - 3A a e - 10B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (5B a c e - 4A a c d e - 5B a c d e - 2A c d )x + 5B a e +--R + +--R 2 2 2 2 2 3 +--R - 4A a c d e - 5B a c d e - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R 8B a c e x + (- 2A a c e - 4B a c d e + 2A c d )x + 10B a e +--R + +--R 2 +--R - 4A a c d e - 2B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 3 2 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c )\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 300 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 300 +r0:=-1/2*(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*(a+c*x^2))-1/2*A*e*sqrt(d+e*x)/(a*c)-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(e*(A*c*d+_ + 3*a*B*e)+a*(2*A*c*d^2+3*a*B*d*e+a*A*e^2)*sqrt(c)/(-a)^(3/2))/(a*_ + c^(7/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(A*c*d+3*a*B*e)+(2*A*c*d^2+_ + 3*a*B*d*e+a*A*e^2)*sqrt(c)/sqrt(-a))/(a*c^(7/4)*sqrt(e*sqrt(-a)+_ + d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (A a c e + 3B a c d e + 2A c d )x + A a e + 3B a d e +--R + +--R 2 +--R 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- 3B a c e - A c d e)x - 3B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R (- A a c e - 3B a c d e - 2A c d )x - A a e - 3B a d e +--R + +--R 2 +--R - 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- 3B a c e - A c d e)x - 3B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---+4+-+3 +-------+ +--R ((- 2B a e + 2A c d)x - 2A a e - 2B a d)\|- a \|c \|e x + d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 2 +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 278 + +--S 279 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 300 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 4 2 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 300 +r0:=-1/2*(a*B-A*c*x)*sqrt(d+e*x)/(a*c*(a+c*x^2))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*((-2*A*c*d-a*B*e)/sqrt(-a)+_ + A*e*sqrt(c))/(a*c^(5/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*((2*A*c*d+a*B*e)/sqrt(-a)+_ + A*e*sqrt(c))/(a*c^(5/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 +---+ +-+ 2 2 2 +--R (- A c e x - A a e)\|- a \|c + (B a c e + 2A c d)x + B a e +--R + +--R 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 +---+ +-+ 2 2 2 +--R (- A c e x - A a e)\|- a \|c + (- B a c e - 2A c d)x - B a e +--R + +--R - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R (2A c x - 2B a)\|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +---------------+ +--R 2 2 2 +---+4+-+ | +-+ +---+ | +-+ +---+ +--R (4a c x + 4a c)\|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 281 + +--S 282 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 300 +t0:=(A+B*x)/((a+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R 2 4 2 2 +-------+ +--R (c x + 2a c x + a )\|e x + d +--R Type: Expression(Integer) +--E 283 + +--S 284 of 300 +r0:=-1/2*(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ + (a+c*x^2))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (e*(A*c*d+a*B*e)-(2*A*c*d^2-a*B*d*e+3*a*A*e^2)*sqrt(c)/sqrt(-a))/_ + (a*c^(3/4)*(c*d^2+a*e^2)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + 1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*_ + (e*(A*c*d+a*B*e)+(2*A*c*d^2-a*B*d*e+3*a*A*e^2)*sqrt(c)/sqrt(-a))/_ + (a*c^(3/4)*(c*d^2+a*e^2)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (3A a c e - B a c d e + 2A c d )x + 3A a e - B a d e +--R + +--R 2 +--R 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- B a c e - A c d e)x - B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 2 2 2 2 +--R (- 3A a c e + B a c d e - 2A c d )x - 3A a e + B a d e +--R + +--R 2 +--R - 2A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 2 2 2 +---+ +--R ((- B a c e - A c d e)x - B a e - A a c d e)\|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R +---+4+-+3 +-------+ +--R ((2B a e + 2A c d)x + 2A a e - 2B a d)\|- a \|c \|e x + d +--R * +--R +---------------+ +---------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 2 2 2 2 3 2 2 2 +---+4+-+3 | +-+ +---+ +--R ((4a c e + 4a c d )x + 4a e + 4a c d )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 300 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+c*x^2)^2) +--R +--R +--R B x + A +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 3 2 2 2 +-------+ +--R (c e x + c d x + 2a c e x + 2a c d x + a e x + a d)\|e x + d +--R Type: Expression(Integer) +--E 286 + +--S 287 of 300 +r0:=1/2*e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)/(a*(c*d^2+a*e^2)^2*sqrt(d+e*x))+_ + 1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2)*_ + sqrt(d+e*x))-1/4*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((3*a*B*e*(c*d^2-a*e^2)-2*A*c*d*(c*d^2+4*a*e^2))/_ + sqrt(-a)+e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)*sqrt(c))/(a*c^(1/4)*_ + (c*d^2+a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/4*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*((-3*a*B*e*(c*d^2-a*e^2)+_ + 2*A*c*d*(c*d^2+4*a*e^2))/sqrt(-a)+e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)*_ + sqrt(c))/(a*c^(1/4)*(c*d^2+a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 2 2 +--R (5A a c e - 6B a c d e - A c d e)x + 5A a e - 6B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (3B a c e + 8A a c d e - 3B a c d e + 2A c d )x + 3B a e +--R + +--R 2 2 2 2 2 3 +--R 8A a c d e - 3B a c d e + 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R +-------+ | +-+ +---+ \|c \|e x + d +--R \|e x + d \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (5A a c e - 6B a c d e - A c d e)x + 5A a e - 6B a d e +--R + +--R 2 +--R - A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 3 2 2 2 2 3 3 2 3 3 +--R (- 3B a c e - 8A a c d e + 3B a c d e - 2A c d )x - 3B a e +--R + +--R 2 2 2 2 2 3 +--R - 8A a c d e + 3B a c d e - 2A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R +-------+ | +-+ +---+ \|c \|e x + d +--R \|e x + d \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 3 2 2 2 2 +--R (- 10A a c e + 12B a c d e + 2A c d e)x +--R + +--R 2 3 2 2 2 3 2 3 +--R (2B a e + 2A a c d e + 2B a c d e + 2A c d )x - 8A a e +--R + +--R 2 2 2 3 +--R 10B a d e + 4A a c d e - 2B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 3 4 2 2 2 2 3 4 2 4 4 3 2 2 2 2 4 +---+ +--R ((4a c e + 8a c d e + 4a c d )x + 4a e + 8a c d e + 4a c d )\|- a +--R * +--R +---------------+ +---------------+ +--R 4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 300 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 300 +r0:=-1/16*e*(6*A*c*d+7*a*B*e)*(d+e*x)^(3/2)/(a^2*c^2)-1/4*(a*B-A*c*x)*_ + (d+e*x)^(7/2)/(a*c*(a+c*x^2)^2)+1/16*(d+e*x)^(5/2)*(a*A*e+(6*A*c*d+_ + 7*a*B*e)*x)/(a^2*c*(a+c*x^2))-1/16*e*(6*A*c*d^2+7*a*B*d*e+5*a*A*e^2)*_ + sqrt(d+e*x)/(a^2*c^2)-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*(e*(7*a*B*e*(c*d^2+3*a*e^2)+2*A*c*d*(3*c*d^2+4*a*e^2))+_ + a*(14*a*B*d*e*(c*d^2+2*a*e^2)+A*(12*c^2*d^4+19*a*c*d^2*e^2+5*a^2*e^4))*_ + sqrt(c)/(-a)^(3/2))/(a^2*c^(11/4)*sqrt(-e*sqrt(-a)+d*sqrt(c)))-_ + 1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(7*a*B*_ + e*(c*d^2+3*a*e^2)+2*A*c*d*(3*c*d^2+4*a*e^2))+(14*a*B*d*e*(c*d^2+_ + 2*a*e^2)+A*(12*c^2*d^4+19*a*c*d^2*e^2+5*a^2*e^4))*sqrt(c)/sqrt(-a))/_ + (a^2*c^(11/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 +--R 5A a c e + 28B a c d e + 19A a c d e + 14B a c d e +--R + +--R 4 4 +--R 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R 10A a c e + 56B a c d e + 38A a c d e + 28B a c d e +--R + +--R 3 4 +--R 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R 5A a e + 28B a d e + 19A a c d e + 14B a c d e + 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 21B a c e - 8A a c d e - 7B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 42B a c e - 16A a c d e - 14B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 21B a e - 8A a c d e - 7B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 +--R - 5A a c e - 28B a c d e - 19A a c d e - 14B a c d e +--R + +--R 4 4 +--R - 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 10A a c e - 56B a c d e - 38A a c d e - 28B a c d e +--R + +--R 3 4 +--R - 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R - 5A a e - 28B a d e - 19A a c d e - 14B a c d e - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 21B a c e - 8A a c d e - 7B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 42B a c e - 16A a c d e - 14B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 21B a e - 8A a c d e - 7B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (- 22B a c e + 16A a c d e + 14B a c d e + 12A c d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 18A a c e - 52B a c d e + 2A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (- 14B a e - 8A a c d e - 10B a c d e + 20A a c d )x - 10A a e +--R + +--R 3 2 2 2 2 3 +--R - 28B a d e - 22A a c d e - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 4 4 3 3 2 4 2 +---+4+-+3 | +-+ +---+ +--R (32a c x + 64a c x + 32a c )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 290 + +--S 291 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 300 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+c*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 300 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^(5/2)/(a*c*(a+c*x^2)^2)-1/16*(d+e*x)^(3/2)*_ + (a*A*e-(6*A*c*d+5*a*B*e)*x)/(a^2*c*(a+c*x^2))-1/16*e*(6*A*c*d+5*a*B*e)*_ + sqrt(d+e*x)/(a^2*c^2)-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ + d*sqrt(c)))*((-5*a*B*e*(2*c*d^2+a*e^2)-3*A*c*d*(4*c*d^2+3*a*e^2))/_ + sqrt(-a)+e*(6*A*c*d^2+5*a*B*d*e+3*a*A*e^2)*sqrt(c))/(a^2*c^(9/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*((5*a*B*e*(2*c*d^2+a*e^2)+3*A*c*d*(4*c*d^2+_ + 3*a*e^2))/sqrt(-a)+e*(6*A*c*d^2+5*a*B*d*e+3*a*A*e^2)*sqrt(c))/_ + (a^2*c^(9/4)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 3A a c e - 5B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 6A a c e - 10B a c d e - 12A a c d e)x - 3A a e +--R + +--R 3 2 2 2 +--R - 5B a d e - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (5B a c e + 9A a c d e + 10B a c d e + 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (10B a c e + 18A a c d e + 20B a c d e + 24A a c d )x + 5B a e +--R + +--R 3 2 3 2 2 2 3 +--R 9A a c d e + 10B a c d e + 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 3 2 2 3 2 4 +--R (- 3A a c e - 5B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 6A a c e - 10B a c d e - 12A a c d e)x - 3A a e +--R + +--R 3 2 2 2 +--R - 5B a d e - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (- 5B a c e - 9A a c d e - 10B a c d e - 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (- 10B a c e - 18A a c d e - 20B a c d e - 24A a c d )x - 5B a e +--R + +--R 3 2 3 2 2 2 3 +--R - 9A a c d e - 10B a c d e - 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 3 2 3 +--R (6A a c e + 10B a c d e + 12A c d )x +--R + +--R 2 2 2 2 +--R (- 18B a c e + 2A a c d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R (- 2A a c e - 6B a c d e + 20A a c d )x - 10B a e - 14A a c d e +--R + +--R 2 2 +--R - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 4 4 3 3 2 4 2 +---+4+-+ | +-+ +---+ +--R (32a c x + 64a c x + 32a c )\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 293 + +--S 294 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 300 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 295 + +--S 296 of 300 +r0:=-1/4*(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*(a+c*x^2)^2)-3/16*(a*A*e-_ + (2*A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a^2*c*(a+c*x^2))-3/32*atanh(c^(1/4)*_ + sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*(e*(2*A*c*d+a*B*e)+a*_ + (4*A*c*d^2+2*a*B*d*e+a*A*e^2)*sqrt(c)/(-a)^(3/2))/(a^2*c^(7/4)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-3/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(2*A*c*d+a*B*e)+(4*A*c*d^2+_ + 2*a*B*d*e+a*A*e^2)*sqrt(c)/sqrt(-a))/(a^2*c^(7/4)*sqrt(e*sqrt(-a)+_ + d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 2 3 2 4 +--R (3A a c e + 6B a c d e + 12A c d )x +--R + +--R 2 2 2 2 2 2 3 2 3 +--R (6A a c e + 12B a c d e + 24A a c d )x + 3A a e + 6B a d e +--R + +--R 2 2 +--R 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 3 4 2 2 2 2 +--R (- 3B a c e - 6A c d e)x + (- 6B a c e - 12A a c d e)x +--R + +--R 3 2 2 +--R - 3B a e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 2 3 2 4 +--R (- 3A a c e - 6B a c d e - 12A c d )x +--R + +--R 2 2 2 2 2 2 3 2 3 +--R (- 6A a c e - 12B a c d e - 24A a c d )x - 3A a e - 6B a d e +--R + +--R 2 2 +--R - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 3 4 2 2 2 2 +--R (- 3B a c e - 6A c d e)x + (- 6B a c e - 12A a c d e)x +--R + +--R 3 2 2 +--R - 3B a e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 +--R (6B a c e + 12A c d)x + 2A a c e x + (- 2B a e + 20A a c d)x +--R + +--R 2 2 +--R - 6A a e - 8B a d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R +---------------+ +--R 2 3 4 3 2 2 4 +---+4+-+3 | +-+ +---+ +--R (32a c x + 64a c x + 32a c)\|- a \|c \|d\|c - e\|- a +--R * +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 300 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 300 +r0:=-1/4*(a*B-A*c*x)*sqrt(d+e*x)/(a*c*(a+c*x^2)^2)+1/16*(a*e*(A*c*d+a*B*e)+_ + c*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*x)*sqrt(d+e*x)/(a^2*c*(c*d^2+a*e^2)*_ + (a+c*x^2))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + ((-a*B*e*(2*c*d^2+3*a*e^2)-A*c*d*(12*c*d^2+13*a*e^2))/sqrt(-a)+_ + e*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*sqrt(c))/(a^2*c^(5/4)*(c*d^2+a*e^2)*_ + sqrt(-e*sqrt(-a)+d*sqrt(c)))-1/32*atanh(c^(1/4)*sqrt(d+e*x)/_ + sqrt(e*sqrt(-a)+d*sqrt(c)))*((a*B*e*(2*c*d^2+3*a*e^2)+A*c*d*(12*c*d^2+_ + 13*a*e^2))/sqrt(-a)+e*(6*A*c*d^2+a*B*d*e+5*a*A*e^2)*sqrt(c))/_ + (a^2*c^(5/4)*(c*d^2+a*e^2)*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 5A a c e - B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 +--R (- 10A a c e - 2B a c d e - 12A a c d e)x - 5A a e - B a d e +--R + +--R 2 2 +--R - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (3B a c e + 13A a c d e + 2B a c d e + 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (6B a c e + 26A a c d e + 4B a c d e + 24A a c d )x + 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R 13A a c d e + 2B a c d e + 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 3 2 2 3 2 4 +--R (- 5A a c e - B a c d e - 6A c d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 +--R (- 10A a c e - 2B a c d e - 12A a c d e)x - 5A a e - B a d e +--R + +--R 2 2 +--R - 6A a c d e +--R * +--R +---+ +-+ +--R \|- a \|c +--R + +--R 2 2 3 3 2 3 2 4 3 4 +--R (- 3B a c e - 13A a c d e - 2B a c d e - 12A c d )x +--R + +--R 3 3 2 2 2 2 2 2 3 3 2 4 3 +--R (- 6B a c e - 26A a c d e - 4B a c d e - 24A a c d )x - 3B a e +--R + +--R 3 2 3 2 2 2 3 +--R - 13A a c d e - 2B a c d e - 12A a c d +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (10A a c e + 2B a c d e + 12A c d )x + (2B a c e + 2A a c d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R (18A a c e + 2B a c d e + 20A a c d )x - 6B a e + 2A a c d e +--R + +--R 2 2 +--R - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 3 3 2 2 4 2 4 4 2 2 3 3 2 2 5 2 4 2 2 +--R ((32a c e + 32a c d )x + (64a c e + 64a c d )x + 32a c e + 32a c d ) +--R * +--R +---------------+ +---------------+ +--R +---+4+-+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 299 + +--S 300 of 300 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/richder12c.input.pamphlet b/src/input/richder12c.input.pamphlet new file mode 100644 index 0000000..0ae9ec1 --- /dev/null +++ b/src/input/richder12c.input.pamphlet @@ -0,0 +1,13664 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12c.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +All derivatives match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12c.output +)spool richder12c.output +)set message test on +)set message auto off +)clear all + +--S 1 of 465 +t0:=(A+B*x)/((a+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R 3 6 2 4 2 2 3 +-------+ +--R (c x + 3a c x + 3a c x + a )\|e x + d +--R Type: Expression(Integer) +--E 1 + +--S 2 of 465 +r0:=-1/4*(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ + (a+c*x^2)^2)+1/16*(a*e*(A*c*d^2-6*a*B*d*e+7*a*A*e^2)-(a*B*e*(c*d^2-_ + 5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))*x)*sqrt(d+e*x)/(a^2*(c*d^2+a*e^2)^2*_ + (a+c*x^2))+1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c)))*_ + (e*(a*B*e*(c*d^2-5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))-(2*a*B*d*e*(c*d^2+_ + 4*a*e^2)-3*A*(4*c^2*d^4+9*a*c*d^2*e^2+7*a^2*e^4))*sqrt(c)/sqrt(-a))/_ + (a^2*c^(3/4)*(c*d^2+a*e^2)^2*sqrt(-e*sqrt(-a)+d*sqrt(c)))+_ + 1/32*atanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c)))*(e*(a*B*e*_ + (c*d^2-5*a*e^2)-6*A*c*d*(c*d^2+2*a*e^2))+(2*a*B*d*e*(c*d^2+4*a*e^2)-_ + 3*A*(4*c^2*d^4+9*a*c*d^2*e^2+7*a^2*e^4))*sqrt(c)/sqrt(-a))/(a^2*c^(3/4)*_ + (c*d^2+a*e^2)^2*sqrt(e*sqrt(-a)+d*sqrt(c))) +--R +--R +--R (2) +--R 2 2 4 2 2 3 3 2 2 3 3 +--R 21A a c e - 8B a c d e + 27A a c d e - 2B a c d e +--R + +--R 4 4 +--R 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R 42A a c e - 16B a c d e + 54A a c d e - 4B a c d e +--R + +--R 3 4 +--R 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R 21A a e - 8B a d e + 27A a c d e - 2B a c d e + 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 5B a c e - 12A a c d e + B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 10B a c e - 24A a c d e + 2B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 5B a e - 12A a c d e + B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c + e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c - e\|- a +--R + +--R 2 2 4 2 2 3 3 2 2 3 3 +--R - 21A a c e + 8B a c d e - 27A a c d e + 2B a c d e +--R + +--R 4 4 +--R - 12A c d +--R * +--R 4 +--R x +--R + +--R 3 4 3 3 2 2 2 2 2 2 3 +--R - 42A a c e + 16B a c d e - 54A a c d e + 4B a c d e +--R + +--R 3 4 +--R - 24A a c d +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 2 2 3 3 2 2 4 +--R - 21A a e + 8B a d e - 27A a c d e + 2B a c d e - 12A a c d +--R * +--R +-+ +--R \|c +--R + +--R 2 2 4 3 3 3 2 2 4 3 4 +--R (- 5B a c e - 12A a c d e + B a c d e - 6A c d e)x +--R + +--R 3 4 2 2 3 2 2 2 2 3 3 2 +--R (- 10B a c e - 24A a c d e + 2B a c d e - 12A a c d e)x +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 5B a e - 12A a c d e + B a c d e - 6A a c d e +--R * +--R +---+ +--R \|- a +--R * +--R +---------------+ 4+-+ +-------+ +--R | +-+ +---+ \|c \|e x + d +--R \|d\|c - e\|- a atanh(------------------) +--R +---------------+ +--R | +-+ +---+ +--R \|d\|c + e\|- a +--R + +--R 2 3 2 2 2 2 3 3 3 +--R (10B a c e + 24A a c d e - 2B a c d e + 12A c d )x +--R + +--R 2 3 2 2 2 2 2 +--R (14A a c e - 12B a c d e + 2A a c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 3 +--R (18B a e + 32A a c d e + 6B a c d e + 20A a c d )x + 22A a e +--R + +--R 3 2 2 2 2 3 +--R - 20B a d e + 10A a c d e - 8B a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 +-------+ | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|e x + d \|d\|c - e\|- a \|d\|c + e\|- a +--R / +--R 4 2 4 3 3 2 2 2 4 4 4 +--R (32a c e + 64a c d e + 32a c d )x +--R + +--R 5 4 4 2 2 2 3 3 4 2 6 4 5 2 2 4 2 4 +--R (64a c e + 128a c d e + 64a c d )x + 32a e + 64a c d e + 32a c d +--R * +--R +---------------+ +---------------+ +--R +---+4+-+3 | +-+ +---+ | +-+ +---+ +--R \|- a \|c \|d\|c - e\|- a \|d\|c + e\|- a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 3 + +)clear all + +--S 4 of 465 +t0:=x*sqrt(1+x)/(1+x^2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (1) --------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 465 +r0:=-atanh(sqrt(1+x)/sqrt(1-%i))*sqrt(1-%i)-atanh(sqrt(1+x)/sqrt(1+%i))*_ + sqrt(1+%i)+2*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R +------+ \|x + 1 +------+ \|x + 1 +-----+ +--R (2) - \|1 - %i atanh(---------) - \|1 + %i atanh(---------) + 2\|x + 1 +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 5 + +--S 6 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Complex(Integer)) +--E 6 + +)clear all + +--S 7 of 465 +t0:=(1-x)*sqrt(1+x)/(1+x^2) +--R +--R +--R +-----+ +--R (- x + 1)\|x + 1 +--R (1) ----------------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 465 +r0:=(1-%i)^(3/2)*atanh(sqrt(1+x)/sqrt(1-%i))+(1+%i)^(3/2)*_ + atanh(sqrt(1+x)/sqrt(1+%i))-2*sqrt(1+x) +--R +--R +--R (2) +--R +-----+ +-----+ +--R +------+ \|x + 1 +------+ \|x + 1 +--R (1 - %i)\|1 - %i atanh(---------) + (1 + %i)\|1 + %i atanh(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R + +--R +-----+ +--R - 2\|x + 1 +--R Type: Expression(Complex(Integer)) +--E 8 + +--S 9 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Complex(Integer)) +--E 9 + +)clear all + +--S 10 of 465 +t0:=(A+B*x)*sqrt(d+e*x)*sqrt(a+c*x^2) +--R +--R +--R +--------+ +--R +-------+ | 2 +--R (1) (B x + A)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 10 + +--S 11 of 465 +--r0:=2/7*B*(a+c*x^2)^(3/2)*sqrt(d+e*x)/c-2/105*(4*B*c*d^2-7*A*c*d*e+_ +-- 5*a*B*e^2-3*c*e*(B*d+7*A*e)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/(c*e^2)+_ +-- 4/105*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*_ +-- (4*c^(3/2)*d^3-c*d^2*e*sqrt(-a)-5*a*e^3*sqrt(-a)+8*a*d*e^2*sqrt(c))+_ +-- 7*A*e*sqrt(c)*(c*d^2-3*a*e^2-4*d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*e^3*_ +-- sqrt(a+c*x^2))-4/105*(4*B*c*d^3-7*A*c*d^2*e+8*a*B*d*e^2+21*a*A*e^3)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^4*sqrt(a+c*x^2)) +--E 11 + +--S 12 of 465 +--d0:=D(m0,x) +--E 12 + +)clear all + +--S 13 of 465 +t0:=(A+B*x)*sqrt(a+c*x^2)/sqrt(d+e*x) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) -------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 13 + +--S 14 of 465 +--r0:=-2/15*(4*B*d-5*A*e-3*B*e*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^2-_ +-- 4/15*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(4*B*c*d^2-_ +-- 5*A*c*d*e+3*a*B*e^2-B*d*e*sqrt(-a)*sqrt(c)+5*A*e^2*sqrt(-a)*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(3/4)*e^3*sqrt(a+c*x^2))-4/15*(4*B*c*d^2-5*A*c*d*e+3*a*B*e^2)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^4*sqrt(a+c*x^2)) +--E 14 + +--S 15 of 465 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 465 +t0:=(A+B*x)*sqrt(a+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) -------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 16 + +--S 17 of 465 +--r0:=2/3*(4*B*d-3*A*e+B*e*x)*sqrt(a+c*x^2)/(e^2*sqrt(d+e*x))+_ +-- 4/3*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*e*_ +-- sqrt(-a)+4*B*d*sqrt(c)-3*A*e*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e^3*sqrt(a+c*x^2))+_ +-- 4/3*c^(1/4)*(4*B*d-3*A*e)*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^4*sqrt(a+c*x^2)) +--E 17 + +--S 18 of 465 +--d0:=D(m0,x) +--E 18 + +)clear all + +--S 19 of 465 +t0:=(A+B*x)*sqrt(a+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R (B x + A)\|c x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 19 + +--S 20 of 465 +--r0:=2/3*(4*B*d-A*e+3*B*e*x)*sqrt(a+c*x^2)/(e^2*(d+e*x)^(3/2))-_ +-- 4/3*(4*B*c*d^2-A*c*d*e+3*a*B*e^2)*sqrt(a+c*x^2)/(e^2*(c*d^2+a*e^2)*_ +-- sqrt(d+e*x))-4/3*c^(1/4)*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-a)*(4*B*c*d^2-A*c*d*e+3*a*B*e^2-B*d*e*sqrt(-a)*sqrt(c)+A*e^2*_ +-- sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-_ +-- x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*_ +-- sqrt(-a)+d*sqrt(c)))/(e^3*(c*d^2+a*e^2)*sqrt(a+c*x^2))-4/3*c^(1/4)*_ +-- (4*B*c*d^2-A*c*d*e+3*a*B*e^2)*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^4*(c*d^2+a*e^2)*sqrt(a+c*x^2)) +--E 20 + +--S 21 of 465 +--d0:=D(m0,x) +--E 21 + +)clear all + +--S 22 of 465 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 22 + +--S 23 of 465 +--r0:=-2/63*(8*B*d-9*A*e-7*B*e*x)*(a+c*x^2)^(3/2)*sqrt(d+e*x)/e^2-_ +-- 4/315*(32*B*c*d^3-36*A*c*d^2*e+33*a*B*d*e^2-45*a*A*e^3-3*e*(8*B*c*d^2-_ +-- 9*A*c*d*e+7*a*B*e^2)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^4+8/315*_ +-- elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(9*A*e*_ +-- sqrt(c)*(4*c^(3/2)*d^3+5*(-a)^(3/2)*e^3-c*d^2*e*sqrt(-a)+_ +-- 8*a*d*e^2*sqrt(c))-B*(32*c^2*d^4+57*a*c*d^2*e^2+21*a^2*e^4-8*c^(3/2)*_ +-- d^3*e*sqrt(-a)-12*a*d*e^3*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^5*_ +-- sqrt(a+c*x^2))+8/315*(36*A*c*d*e*(c*d^2+2*a*e^2)-B*(32*c^2*d^4+_ +-- 57*a*c*d^2*e^2+21*a^2*e^4))*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^6*sqrt(a+c*x^2)) +--E 23 + +--S 24 of 465 +--d0:=D(m0,x) +--E 24 + +)clear all + +--S 25 of 465 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 25 + +--S 26 of 465 +--r0:=2/7*(8*B*d-7*A*e+B*e*x)*(a+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+_ +-- 4/35*(5*a*B*e^2+4*c*d*(8*B*d-7*A*e)-3*c*e*(8*B*d-7*A*e)*x)*_ +-- sqrt(d+e*x)*sqrt(a+c*x^2)/e^4-8/35*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(-B*(32*c^(3/2)*d^3-8*c*d^2*e*_ +-- sqrt(-a)-5*a*e^3*sqrt(-a)+29*a*d*e^2*sqrt(c))+7*A*e*sqrt(c)*(4*c*d^2+_ +-- 3*a*e^2-d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e^5*sqrt(a+c*x^2))+_ +-- 8/35*c^(1/4)*(32*B*c*d^3-28*A*c*d^2*e+29*a*B*d*e^2-21*a*A*e^3)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(e^6*sqrt(a+c*x^2)) +--E 26 + +--S 27 of 465 +--d0:=D(m0,x) +--E 27 + +)clear all + +--S 28 of 465 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 28 + +--S 29 of 465 +--r0:=2/15*(8*B*d-5*A*e+3*B*e*x)*(a+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 4/15*(9*a*B*e^2+4*c*d*(8*B*d-5*A*e)+c*e*(8*B*d-5*A*e)*x)*_ +-- sqrt(a+c*x^2)/(e^4*sqrt(d+e*x))-8/15*c^(1/4)*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*(32*B*c*d^2-20*A*c*d*e+9*a*B*e^2-_ +-- 8*B*d*e*sqrt(-a)*sqrt(c)+5*A*e^2*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^5*_ +-- sqrt(a+c*x^2))-8/15*c^(1/4)*(9*a*B*e^2+4*c*d*(8*B*d-5*A*e))*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(e^6*sqrt(a+c*x^2)) +--E 29 + +--S 30 of 465 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 465 +t0:=(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +--------+ +--R 3 2 | 2 +--R (B c x + A c x + B a x + A a)\|c x + a +--R (1) ------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 31 + +--S 32 of 465 +--r0:=2/15*(8*B*d-3*A*e+5*B*e*x)*(a+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 4/15*(5*a*B*e^2+4*c*d*(8*B*d-3*A*e)+3*c*e*(8*B*d-3*A*e)*x)*_ +-- sqrt(a+c*x^2)/(e^4*(d+e*x)^(3/2))+8/15*c*(32*B*c*d^3-12*A*c*d^2*e+_ +-- 29*a*B*d*e^2-9*a*A*e^3)*sqrt(a+c*x^2)/(e^4*(c*d^2+a*e^2)*sqrt(d+e*x))-_ +-- 8/15*c^(3/4)*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-a)*_ +-- (-B*(32*c^(3/2)*d^3-8*c*d^2*e*sqrt(-a)-5*a*e^3*sqrt(-a)+29*a*d*e^2*_ +-- sqrt(c))+3*A*e*sqrt(c)*(4*c*d^2+3*a*e^2-d*e*sqrt(-a)*sqrt(c)))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (e^5*(c*d^2+a*e^2)*sqrt(a+c*x^2))+8/15*c^(5/4)*(32*B*c*d^3-_ +-- 12*A*c*d^2*e+29*a*B*d*e^2-9*a*A*e^3)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^6*(c*d^2+_ +-- a*e^2)*sqrt(a+c*x^2)) +--E 32 + +--S 33 of 465 +--d0:=D(m0,x) +--E 33 + +)clear all + +--S 34 of 465 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(a+c*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------+ +--R | 2 +--R \|c x + a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 465 +--r0:=2/5*B*(d+e*x)^(3/2)*sqrt(a+c*x^2)/c+2/15*(3*B*d+5*A*e)*sqrt(d+e*x)*_ +-- sqrt(a+c*x^2)/c-2/15*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- (3*B*(3*(-a)^(3/2)*e^2+c*d^2*sqrt(-a)+4*a*d*e*sqrt(c))-5*A*sqrt(c)*_ +-- (3*c*d^2-a*e^2-4*d*e*sqrt(-a)*sqrt(c)))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(7/4)*e*sqrt(a+c*x^2))-_ +-- 2/15*(3*B*c*d^2+20*A*c*d*e-9*a*B*e^2)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(7/4)*e^2*_ +-- sqrt(a+c*x^2)) +--E 35 + +--S 36 of 465 +--d0:=D(m0,x) +--E 36 + +)clear all + +--S 37 of 465 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(a+c*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +--------+ +--R | 2 +--R \|c x + a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 465 +--r0:=2/3*B*sqrt(d+e*x)*sqrt(a+c*x^2)/c-2/3*elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(-3*A*c*d+a*B*e+B*d*sqrt(-a)*sqrt(c)+3*A*e*_ +-- sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-_ +-- x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*e*sqrt(a+c*x^2))-2/3*(B*d+3*A*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(c^(3/4)*e^2*sqrt(a+c*x^2)) +--E 38 + +--S 39 of 465 +--d0:=D(m0,x) +--E 39 + +)clear all + +--S 40 of 465 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(a+c*x^2)) +--R +--R +--R B x + A +--R (1) --------------------- +--R +--------+ +--R +-------+ | 2 +--R \|e x + d \|c x + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 465 +--r0:=-2*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(B*sqrt(-a)-A*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(3/4)*e*sqrt(a+c*x^2))-2*B*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*e^2*sqrt(a+c*x^2)) +--E 41 + +--S 42 of 465 +--d0:=D(m0,x) +--E 42 + +)clear all + +--S 43 of 465 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(a+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R +--------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 43 + +--S 44 of 465 +--r0:=2*(B*d-A*e)*sqrt(a+c*x^2)/((c*d^2+a*e^2)*sqrt(d+e*x))+_ +-- 2*elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),_ +-- (-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(A*c*d+a*B*e+B*d*_ +-- sqrt(-a)*sqrt(c)-A*e*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(1/4)*e*(c*d^2+a*e^2)*_ +-- sqrt(a+c*x^2))+2*c^(1/4)*(B*d-A*e)*elliptic_e(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/_ +-- (-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(e^2*(c*d^2+_ +-- a*e^2)*sqrt(a+c*x^2)) +--E 44 + +--S 45 of 465 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 465 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------+ +--R 2 | 2 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 465 +--r0:=-(a*B-A*c*x)*(d+e*x)^(3/2)/(a*c*sqrt(a+c*x^2))-A*e*sqrt(d+e*x)*_ +-- sqrt(a+c*x^2)/(a*c)+elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*_ +-- sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- (-A*c*d+3*a*B*e+3*B*d*sqrt(-a)*sqrt(c)+A*e*sqrt(-a)*sqrt(c))*_ +-- sqrt(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+_ +-- d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/_ +-- (c^(7/4)*sqrt(-a)*sqrt(a+c*x^2))+(A*c*d-3*a*B*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(a*c^(7/4)*e*sqrt(a+c*x^2)) +--E 47 + +--S 48 of 465 +--d0:=D(m0,x) +--E 48 + +)clear all + +--S 49 of 465 +t0:=(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 465 +--r0:=-(a*B-A*c*x)*sqrt(d+e*x)/(a*c*sqrt(a+c*x^2))+elliptic_f(asin(c^(1/4)*_ +-- sqrt(d+e*x)/sqrt(-e*sqrt(-a)+d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*(B*sqrt(-a)-A*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(5/4)*_ +-- sqrt(-a)*sqrt(a+c*x^2))+A*elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/_ +-- sqrt(e*sqrt(-a)+d*sqrt(c))),(e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))*(-e*sqrt(-a)+d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*_ +-- sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+_ +-- x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(a*c^(3/4)*e*sqrt(a+c*x^2)) +--E 50 + +--S 51 of 465 +--d0:=D(m0,x) +--E 51 + +)clear all + +--S 52 of 465 +t0:=(A+B*x)/((a+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R +--------+ +--R 2 +-------+ | 2 +--R (c x + a)\|e x + d \|c x + a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 465 +--r0:=-(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*_ +-- sqrt(a+c*x^2))-elliptic_f(asin(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))),(-e*sqrt(-a)+d*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*(A*c*d+_ +-- a*B*e+B*d*sqrt(-a)*sqrt(c)-A*e*sqrt(-a)*sqrt(c))*sqrt(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/(e*sqrt(-a)+d*sqrt(c)))*_ +-- sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))/(c^(3/4)*_ +-- (c*d^2+a*e^2)*sqrt(-a)*sqrt(a+c*x^2))+(A*c*d+a*B*e)*_ +-- elliptic_e(asin(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(-a)+d*sqrt(c))),_ +-- (e*sqrt(-a)+d*sqrt(c))/(-e*sqrt(-a)+d*sqrt(c)))*(-e*sqrt(-a)+_ +-- d*sqrt(c))*sqrt(e*sqrt(-a)+d*sqrt(c))*sqrt(e*(sqrt(-a)-x*sqrt(c))/_ +-- (e*sqrt(-a)+d*sqrt(c)))*sqrt(-e*(sqrt(-a)+x*sqrt(c))/(-e*sqrt(-a)+_ +-- d*sqrt(c)))/(a*c^(3/4)*e*(c*d^2+a*e^2)*sqrt(a+c*x^2)) +--E 53 + +--S 54 of 465 +--d0:=D(m0,x) +--E 54 + +)clear all + +--S 55 of 465 +t0:=(-a*e+c*d*x)*(d+e*x)^(-3-2*p)*(a+c*x^2)^p +--R +--R +--R - 2p - 3 2 p +--R (1) (c d x - a e)(e x + d) (c x + a) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 465 +r0:=1/2*(a+c*x^2)^(1+p)/((1+p)*(d+e*x)^(2*(1+p))) +--R +--R +--R 2 p + 1 +--R (c x + a) +--R (2) ----------------------- +--R 2p + 2 +--R (2p + 2)(e x + d) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 465 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 m +--R (1) (2c x + 3b c x + (2a c + b )x + a b)(e x + d) +--R Type: Expression(Integer) +--E 58 + +--S 59 of 465 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(2+m)/(e^4*(2+m))-3*c*(2*c*d-b*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+2*c^2*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 m + 4 +--R (2c m + 12c m + 22c m + 12c )(e x + d) +--R + +--R 2 3 2 2 2 +--R (3b c e - 6c d)m + (21b c e - 42c d)m + (42b c e - 84c d)m +--R + +--R 2 +--R 24b c e - 48c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 3 +--R ((2a c + b )e - 6b c d e + 6c d )m +--R + +--R 2 2 2 2 2 +--R ((16a c + 8b )e - 48b c d e + 48c d )m +--R + +--R 2 2 2 2 2 2 +--R ((38a c + 19b )e - 114b c d e + 114c d )m + (24a c + 12b )e +--R + +--R 2 2 +--R - 72b c d e + 72c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (- 2a c - b )d e + 3b c d e - 2c d )m +--R + +--R 3 2 2 2 2 3 2 +--R (9a b e + (- 18a c - 9b )d e + 27b c d e - 18c d )m +--R + +--R 3 2 2 2 2 3 3 +--R (26a b e + (- 52a c - 26b )d e + 78b c d e - 52c d )m + 24a b e +--R + +--R 2 2 2 2 3 +--R (- 48a c - 24b )d e + 72b c d e - 48c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 59 + +--S 60 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 465 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 7 4 2 3 6 2 4 3 2 2 2 5 +--R 2c e x + (3b c e + 8c d e )x + ((2a c + b )e + 12b c d e + 12c d e )x +--R + +--R 4 2 3 2 2 2 3 4 +--R (a b e + (8a c + 4b )d e + 18b c d e + 8c d e)x +--R + +--R 3 2 2 2 3 2 4 3 +--R (4a b d e + (12a c + 6b )d e + 12b c d e + 2c d )x +--R + +--R 2 2 2 3 4 2 3 2 4 +--R (6a b d e + (8a c + 4b )d e + 3b c d )x + (4a b d e + (2a c + b )d )x +--R + +--R 4 +--R a b d +--R Type: Polynomial(Integer) +--E 61 + +--S 62 of 465 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4+1/6*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^6/e^4-3/7*c*(2*c*d-b*e)*(d+e*x)^7/e^4+_ + 1/4*c^2*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 2 8 8 3 8 8 2 7 7 +--R - c e x + (- b c e + - c d e )x +--R 4 7 7 +--R + +--R 1 1 2 8 7 2 2 6 6 +--R ((- a c + - b )e + 2b c d e + 2c d e )x +--R 3 6 +--R + +--R 1 8 8 4 2 7 18 2 6 8 2 3 5 5 +--R (- a b e + (- a c + - b )d e + -- b c d e + - c d e )x +--R 5 5 5 5 5 +--R + +--R 7 3 2 2 6 3 5 1 2 4 4 4 +--R (a b d e + (3a c + - b )d e + 3b c d e + - c d e )x +--R 2 2 +--R + +--R 2 6 8 4 2 3 5 4 4 3 +--R (2a b d e + (- a c + - b )d e + b c d e )x +--R 3 3 +--R + +--R 3 5 1 2 4 4 2 4 4 1 5 3 +--R (2a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 5 +--R + +--R 1 1 2 6 2 1 7 1 2 8 +--R (- -- a c - -- b )d e + -- b c d e - --- c d +--R 15 30 35 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R 2c e x + (3b c e + 6c d e )x + ((2a c + b )e + 9b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (6a c + 3b )d e + 9b c d e + 2c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R (3a b d e + (6a c + 3b )d e + 3b c d )x + (3a b d e + (2a c + b )d )x +--R + +--R 3 +--R a b d +--R Type: Polynomial(Integer) +--E 64 + +--S 65 of 465 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4+1/5*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^5/e^4-1/2*c*(2*c*d-b*e)*(d+e*x)^6/e^4+_ + 2/7*c^2*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 2 2 7 7 1 7 2 6 6 +--R - c e x + (- b c e + c d e )x +--R 7 2 +--R + +--R 2 1 2 7 9 6 6 2 2 5 5 +--R ((- a c + - b )e + - b c d e + - c d e )x +--R 5 5 5 5 +--R + +--R 1 7 3 3 2 6 9 2 5 1 2 3 4 4 +--R (- a b e + (- a c + - b )d e + - b c d e + - c d e )x +--R 4 2 4 4 2 +--R + +--R 6 2 2 5 3 4 3 +--R (a b d e + (2a c + b )d e + b c d e )x +--R + +--R 3 2 5 1 2 3 4 2 3 4 1 4 3 +--R (- a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 2 4 +--R + +--R 1 1 2 5 2 1 6 1 2 7 +--R (- -- a c - -- b )d e + -- b c d e - -- c d +--R 10 20 20 70 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 65 + +--S 66 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 66 + +)clear all + +--S 67 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x + a b d +--R Type: Polynomial(Integer) +--E 67 + +--S 68 of 465 +r0:=-1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3/e^4+1/4*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^4/e^4-3/5*c*(2*c*d-b*e)*_ + (d+e*x)^5/e^4+1/3*c^2*(d+e*x)^6/e^4 +--R +--R +--R (2) +--R 1 2 6 6 3 6 4 2 5 5 +--R - c e x + (- b c e + - c d e )x +--R 3 5 5 +--R + +--R 1 1 2 6 3 5 1 2 2 4 4 +--R ((- a c + - b )e + - b c d e + - c d e )x +--R 2 4 2 2 +--R + +--R 1 6 4 2 2 5 2 4 3 +--R (- a b e + (- a c + - b )d e + b c d e )x +--R 3 3 3 +--R + +--R 5 1 2 2 4 2 2 4 1 3 3 +--R (a b d e + (a c + - b )d e )x + a b d e x + - a b d e +--R 2 3 +--R + +--R 1 1 2 4 2 1 5 1 2 6 +--R (- - a c - -- b )d e + -- b c d e - -- c d +--R 6 12 10 30 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 68 + +--S 69 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 69 + +)clear all + +--S 70 of 465 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R Type: Polynomial(Integer) +--E 70 + +--S 71 of 465 +r0:=a*b*d*x+1/2*(b^2*d+2*a*c*d+a*b*e)*x^2+1/3*(3*b*c*d+b^2*e+2*a*c*e)*x^3+_ + 1/4*c*(2*c*d+3*b*e)*x^4+2/5*c^2*e*x^5 +--R +--R +--R (2) +--R 2 2 5 3 1 2 4 2 1 2 3 +--R - c e x + (- b c e + - c d)x + ((- a c + - b )e + b c d)x +--R 5 4 2 3 3 +--R + +--R 1 1 2 2 +--R (- a b e + (a c + - b )d)x + a b d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 71 + +--S 72 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 +--R (1) 2c x + 3b c x + (2a c + b )x + a b +--R Type: Polynomial(Integer) +--E 73 + +--S 74 of 465 +r0:=1/2*(a+b*x+c*x^2)^2 +--R +--R +--R 1 2 4 3 1 2 2 1 2 +--R (2) - c x + b c x + (a c + - b )x + a b x + - a +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 465 +r0:=(2*c^2*d^2+b^2*e^2-c*e*(3*b*d-2*a*e))*x/e^3-1/2*c*(2*c*d-3*b*e)*x^2/e^2+_ + 2/3*c^2*x^3/e-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R (6a b e + (- 12a c - 6b )d e + 18b c d e - 12c d )log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 4c e x + (9b c e - 6c d e )x + ((12a c + 6b )e - 18b c d e + 12c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 77 + +--S 78 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 79 + +--S 80 of 465 +r0:=-c*(4*c*d-3*b*e)*x/e^3+c^2*x^2/e^2+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/_ + (e^4*(d+e*x))+(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 2 +--R ((2a c + b )e - 6b c d e + 6c d e)x + (2a c + b )d e - 6b c d e +--R + +--R 2 3 +--R 6c d +--R * +--R log(e x + d) +--R + +--R 2 3 3 3 2 2 2 2 2 2 3 +--R c e x + (3b c e - 3c d e )x + (3b c d e - 4c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (2a c + b )d e - 3b c d e + 2c d +--R / +--R 5 4 +--R e x + d e +--R Type: Expression(Integer) +--E 80 + +--S 81 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 82 + +--S 83 of 465 +r0:=2*c^2*x/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x))-3*c*(2*c*d-b*e)*_ + log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 2 2 2 3 +--R ((6b c e - 12c d e )x + (12b c d e - 24c d e)x + 6b c d e - 12c d ) +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 2 3 2 2 2 3 +--R 4c e x + 8c d e x + ((- 4a c - 2b )e + 12b c d e - 8c d e)x - a b e +--R + +--R 2 2 2 2 3 +--R (- 2a c - b )d e + 9b c d e - 10c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 83 + +--S 84 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 85 + +--S 86 of 465 +r0:=1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+_ + 1/2*(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x)^2)+_ + 3*c*(2*c*d-b*e)/(e^4*(d+e*x))+2*c^2*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 2 2 2 3 +--R (12c e x + 36c d e x + 36c d e x + 12c d )log(e x + d) +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 18b c e + 36c d e )x + ((- 6a c - 3b )e - 18b c d e + 54c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (- 2a c - b )d e - 6b c d e + 22c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 86 + +--S 87 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 88 + +--S 89 of 465 +r0:=1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+_ + 1/3*(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x)^3)+_ + 3/2*c*(2*c*d-b*e)/(e^4*(d+e*x)^2)-2*c^2/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 3 3 3 3 2 2 2 +--R - 2c e x + (- - b c e - 3c d e )x +--R 2 +--R + +--R 2 1 2 3 2 2 2 1 3 +--R ((- - a c - - b )e - b c d e - 2c d e)x - - a b e +--R 3 3 4 +--R + +--R 1 1 2 2 1 2 1 2 3 +--R (- - a c - -- b )d e - - b c d e - - c d +--R 6 12 4 2 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 465 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 465 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))+_ + 2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(2+m)/(e^6*(2+m))-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(3+m)/(e^6*(3+m))+4*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(4+m)/(e^6*(4+m))-5*c^2*(2*c*d-b*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+2*c^3*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 3 5 3 4 3 3 3 2 3 3 m + 6 +--R (2c m + 30c m + 170c m + 450c m + 548c m + 240c )(e x + d) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R (5b c e - 10c d)m + (80b c e - 160c d)m + (475b c e - 950c d)m +--R + +--R 2 3 2 2 3 2 3 +--R (1300b c e - 2600c d)m + (1620b c e - 3240c d)m + 720b c e - 1440c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 3 2 5 +--R ((4a c + 4b c)e - 20b c d e + 20c d )m +--R + +--R 2 2 2 2 3 2 4 +--R ((68a c + 68b c)e - 340b c d e + 340c d )m +--R + +--R 2 2 2 2 3 2 3 +--R ((428a c + 428b c)e - 2140b c d e + 2140c d )m +--R + +--R 2 2 2 2 3 2 2 +--R ((1228a c + 1228b c)e - 6140b c d e + 6140c d )m +--R + +--R 2 2 2 2 3 2 +--R ((1584a c + 1584b c)e - 7920b c d e + 7920c d )m +--R + +--R 2 2 2 2 3 2 +--R (720a c + 720b c)e - 3600b c d e + 3600c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (- 12a c - 12b c)d e + 30b c d e - 20c d )m +--R + +--R 3 3 2 2 2 2 2 +--R (108a b c + 18b )e + (- 216a c - 216b c)d e + 540b c d e +--R + +--R 3 3 +--R - 360c d +--R * +--R 4 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (726a b c + 121b )e + (- 1452a c - 1452b c)d e + 3630b c d e +--R + +--R 3 3 +--R - 2420c d +--R * +--R 3 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (2232a b c + 372b )e + (- 4464a c - 4464b c)d e + 11160b c d e +--R + +--R 3 3 +--R - 7440c d +--R * +--R 2 +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (3048a b c + 508b )e + (- 6096a c - 6096b c)d e + 15240b c d e +--R + +--R 3 3 +--R - 10160c d +--R * +--R m +--R + +--R 3 3 2 2 2 2 2 +--R (1440a b c + 240b )e + (- 2880a c - 2880b c)d e + 7200b c d e +--R + +--R 3 3 +--R - 4800c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (2a c + 2a b )e + (- 12a b c - 2b )d e + (12a c + 12b c)d e +--R + +--R 2 3 3 4 +--R - 20b c d e + 10c d +--R * +--R 5 +--R m +--R + +--R 2 2 4 3 3 +--R (38a c + 38a b )e + (- 228a b c - 38b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (228a c + 228b c)d e - 380b c d e + 190c d +--R * +--R 4 +--R m +--R + +--R 2 2 4 3 3 +--R (274a c + 274a b )e + (- 1644a b c - 274b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (1644a c + 1644b c)d e - 2740b c d e + 1370c d +--R * +--R 3 +--R m +--R + +--R 2 2 4 3 3 +--R (922a c + 922a b )e + (- 5532a b c - 922b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (5532a c + 5532b c)d e - 9220b c d e + 4610c d +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 3 +--R (1404a c + 1404a b )e + (- 8424a b c - 1404b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (8424a c + 8424b c)d e - 14040b c d e + 7020c d +--R * +--R m +--R + +--R 2 2 4 3 3 +--R (720a c + 720a b )e + (- 4320a b c - 720b )d e +--R + +--R 2 2 2 2 2 3 3 4 +--R (4320a c + 4320b c)d e - 7200b c d e + 3600c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 2 4 3 2 3 +--R a b e + (- 2a c - 2a b )d e + (6a b c + b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 4a c - 4b c)d e + 5b c d e - 2c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 20a b e + (- 40a c - 40a b )d e + (120a b c + 20b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 80a c - 80b c)d e + 100b c d e - 40c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 155a b e + (- 310a c - 310a b )d e + (930a b c + 155b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 620a c - 620b c)d e + 775b c d e - 310c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 580a b e + (- 1160a c - 1160a b )d e + (3480a b c + 580b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 2320a c - 2320b c)d e + 2900b c d e - 1160c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 2 4 +--R 1044a b e + (- 2088a c - 2088a b )d e +--R + +--R 3 2 3 2 2 3 2 +--R (6264a b c + 1044b )d e + (- 4176a c - 4176b c)d e +--R + +--R 2 4 3 5 +--R 5220b c d e - 2088c d +--R * +--R m +--R + +--R 2 5 2 2 4 3 2 3 +--R 720a b e + (- 1440a c - 1440a b )d e + (4320a b c + 720b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 2880a c - 2880b c)d e + 3600b c d e - 1440c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 92 + +--S 93 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 465 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 9 2 4 3 3 8 +--R 2c e x + (5b c e + 8c d e )x +--R + +--R 2 2 4 2 3 3 2 2 7 +--R ((4a c + 4b c)e + 20b c d e + 12c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 6 +--R ((6a b c + b )e + (16a c + 16b c)d e + 30b c d e + 8c d e)x +--R + +--R 2 2 4 3 3 2 2 2 2 +--R (2a c + 2a b )e + (24a b c + 4b )d e + (24a c + 24b c)d e +--R + +--R 2 3 3 4 +--R 20b c d e + 2c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 2 3 3 2 2 2 2 3 +--R a b e + (8a c + 8a b )d e + (36a b c + 6b )d e + (16a c + 16b c)d e +--R + +--R 2 4 +--R 5b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 3 +--R 4a b d e + (12a c + 12a b )d e + (24a b c + 4b )d e +--R + +--R 2 2 4 +--R (4a c + 4b c)d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 3 3 4 2 +--R (6a b d e + (8a c + 8a b )d e + (6a b c + b )d )x +--R + +--R 2 3 2 2 4 2 4 +--R (4a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 94 + +--S 95 of 465 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^5/e^6+1/3*(c*d^2-b*d*e+_ + a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^6/e^6-1/7*(2*c*d-_ + b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^7/e^6+1/2*c*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^8/e^6-5/9*c^2*(2*c*d-b*e)*_ + (d+e*x)^9/e^6+1/5*c^3*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 3 10 10 5 2 10 8 3 9 9 +--R - c e x + (- b c e + - c d e )x +--R 5 9 9 +--R + +--R 1 2 1 2 10 5 2 9 3 3 2 8 8 +--R ((- a c + - b c)e + - b c d e + - c d e )x +--R 2 2 2 2 +--R + +--R 6 1 3 10 16 2 16 2 9 30 2 2 8 8 3 3 7 7 +--R ((- a b c + - b )e + (-- a c + -- b c)d e + -- b c d e + - c d e )x +--R 7 7 7 7 7 7 +--R + +--R 1 2 1 2 10 2 3 9 2 2 2 8 +--R (- a c + - a b )e + (4a b c + - b )d e + (4a c + 4b c)d e +--R 3 3 3 +--R + +--R 10 2 3 7 1 3 4 6 +--R -- b c d e + - c d e +--R 3 3 +--R * +--R 6 +--R x +--R + +--R 1 2 10 8 2 8 2 9 36 6 3 2 8 +--R - a b e + (- a c + - a b )d e + (-- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 16 2 16 2 3 7 2 4 6 +--R (-- a c + -- b c)d e + b c d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 2 9 2 2 2 8 3 3 7 2 2 4 6 4 +--R (a b d e + (3a c + 3a b )d e + (6a b c + b )d e + (a c + b c)d e )x +--R + +--R 2 2 8 8 2 8 2 3 7 1 3 4 6 3 +--R (2a b d e + (- a c + - a b )d e + (2a b c + - b )d e )x +--R 3 3 3 +--R + +--R 2 3 7 2 2 4 6 2 2 4 6 1 2 5 5 +--R (2a b d e + (a c + a b )d e )x + a b d e x + - a b d e +--R 5 +--R + +--R 1 2 1 2 6 4 2 1 3 7 3 +--R (- -- a c - -- a b )d e + (-- a b c + --- b )d e +--R 15 15 35 105 +--R + +--R 1 2 1 2 8 2 1 2 9 1 3 10 +--R (- -- a c - -- b c)d e + --- b c d e - --- c d +--R 70 70 126 630 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 95 + +--S 96 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 3 8 2 3 3 2 7 +--R 2c e x + (5b c e + 6c d e )x +--R + +--R 2 2 3 2 2 3 2 6 +--R ((4a c + 4b c)e + 15b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (12a c + 12b c)d e + 15b c d e + 2c d )x +--R + +--R 2 2 3 3 2 2 2 2 2 3 4 +--R ((2a c + 2a b )e + (18a b c + 3b )d e + (12a c + 12b c)d e + 5b c d )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 3 +--R (a b e + (6a c + 6a b )d e + (18a b c + 3b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 6a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 3 2 3 +--R (3a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 97 + +--S 98 of 465 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4/e^6+2/5*(c*d^2-_ + b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^5/e^6-_ + 1/6*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^6/e^6+4/7*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^7/e^6-5/8*c^2*(2*c*d-b*e)*(d+e*x)^8/e^6+2/9*c^3*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 2 3 9 9 5 2 9 3 3 8 8 +--R - c e x + (- b c e + - c d e )x +--R 9 8 4 +--R + +--R 4 2 4 2 9 15 2 8 6 3 2 7 7 +--R ((- a c + - b c)e + -- b c d e + - c d e )x +--R 7 7 7 7 +--R + +--R 1 3 9 2 2 8 5 2 2 7 1 3 3 6 6 +--R ((a b c + - b )e + (2a c + 2b c)d e + - b c d e + - c d e )x +--R 6 2 3 +--R + +--R 2 2 2 2 9 18 3 3 8 12 2 12 2 2 7 +--R (- a c + - a b )e + (-- a b c + - b )d e + (-- a c + -- b c)d e +--R 5 5 5 5 5 5 +--R + +--R 2 3 6 +--R b c d e +--R * +--R 5 +--R x +--R + +--R 1 2 9 3 2 3 2 8 9 3 3 2 7 +--R - a b e + (- a c + - a b )d e + (- a b c + - b )d e +--R 4 2 2 2 4 +--R + +--R 2 2 3 6 +--R (a c + b c)d e +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 2 7 1 3 3 6 3 +--R (a b d e + (2a c + 2a b )d e + (2a b c + - b )d e )x +--R 3 +--R + +--R 3 2 2 7 2 2 3 6 2 2 3 6 1 2 4 5 +--R (- a b d e + (a c + a b )d e )x + a b d e x + - a b d e +--R 2 4 +--R + +--R 1 2 1 2 5 4 1 1 3 6 3 +--R (- -- a c - -- a b )d e + (-- a b c + -- b )d e +--R 10 10 10 60 +--R + +--R 1 2 1 2 7 2 1 2 8 1 3 9 +--R (- -- a c - -- b c)d e + -- b c d e - --- c d +--R 35 35 56 252 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 98 + +--S 99 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 100 + +--S 101 of 465 +r0:=a^2*b*d^2*x+a*d*(b^2*d+a*c*d+a*b*e)*x^2+1/3*(b^3*d^2+4*a*b^2*d*e+_ + 4*a^2*c*d*e+a*b*(6*c*d^2+a*e^2))*x^3+1/2*(b^3*d*e+6*a*b*c*d*e+b^2*_ + (2*c*d^2+a*e^2)+a*c*(2*c*d^2+a*e^2))*x^4+1/5*(8*b^2*c*d*e+_ + 8*a*c^2*d*e+b^3*e^2+b*c*(5*c*d^2+6*a*e^2))*x^5+1/3*c*(c^2*d^2+_ + 2*b^2*e^2+c*e*(5*b*d+2*a*e))*x^6+1/7*c^2*e*(4*c*d+5*b*e)*x^7+_ + 1/4*c^3*e^2*x^8 +--R +--R +--R (2) +--R 1 3 2 8 5 2 2 4 3 7 +--R - c e x + (- b c e + - c d e)x +--R 4 7 7 +--R + +--R 2 2 2 2 2 5 2 1 3 2 6 +--R ((- a c + - b c)e + - b c d e + - c d )x +--R 3 3 3 3 +--R + +--R 6 1 3 2 8 2 8 2 2 2 5 +--R ((- a b c + - b )e + (- a c + - b c)d e + b c d )x +--R 5 5 5 5 +--R + +--R 1 2 1 2 2 1 3 2 2 2 4 +--R ((- a c + - a b )e + (3a b c + - b )d e + (a c + b c)d )x +--R 2 2 2 +--R + +--R 1 2 2 4 2 4 2 1 3 2 3 +--R (- a b e + (- a c + - a b )d e + (2a b c + - b )d )x +--R 3 3 3 3 +--R + +--R 2 2 2 2 2 2 2 +--R (a b d e + (a c + a b )d )x + a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 101 + +--S 102 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 465 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 2 2 3 2 +--R ((6a b c + b )e + (4a c + 4b c)d)x + ((2a c + 2a b )e + (6a b c + b )d)x +--R + +--R 2 2 2 2 +--R (a b e + (2a c + 2a b )d)x + a b d +--R Type: Polynomial(Integer) +--E 103 + +--S 104 of 465 +r0:=a^2*b*d*x+1/2*a*(2*b^2*d+2*a*c*d+a*b*e)*x^2+1/3*(b^3*d+6*a*b*c*d+_ + 2*a*b^2*e+2*a^2*c*e)*x^3+1/4*(4*b^2*c*d+4*a*c^2*d+b^3*e+6*a*b*c*e)*x^4+_ + 1/5*c*(5*b*c*d+4*b^2*e+4*a*c*e)*x^5+1/6*c^2*(2*c*d+5*b*e)*x^6+2/7*c^3*e*x^7 +--R +--R +--R (2) +--R 2 3 7 5 2 1 3 6 4 2 4 2 2 5 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c)e + b c d)x +--R 7 6 3 5 5 +--R + +--R 3 1 3 2 2 4 +--R ((- a b c + - b )e + (a c + b c)d)x +--R 2 4 +--R + +--R 2 2 2 2 1 3 3 1 2 2 2 2 +--R ((- a c + - a b )e + (2a b c + - b )d)x + (- a b e + (a c + a b )d)x +--R 3 3 3 2 +--R + +--R 2 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 104 + +--S 105 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 465 +r0:=1/3*(a+b*x+c*x^2)^3 +--R +--R +--R (2) +--R 1 3 6 2 5 2 2 4 1 3 3 2 2 2 +--R - c x + b c x + (a c + b c)x + (2a b c + - b )x + (a c + a b )x +--R 3 3 +--R + +--R 2 1 3 +--R a b x + - a +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 107 + +--S 108 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 109 + +--S 110 of 465 +r0:=2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*x/e^5-_ + 1/2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^2/e^6+4/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^3/e^6-_ + 5/4*c^2*(2*c*d-b*e)*(d+e*x)^4/e^6+2/5*c^3*(d+e*x)^5/e^6-(2*c*d-b*e)*_ + (c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 2 4 3 2 3 +--R 60a b e + (- 120a c - 120a b )d e + (360a b c + 60b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 240a c - 240b c)d e + 300b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 24c e x + (75b c e - 30c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((80a c + 80b c)e - 100b c d e + 40c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (180a b c + 30b )e + (- 120a c - 120b c)d e + 150b c d e +--R + +--R 3 3 2 +--R - 60c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (120a c + 120a b )e + (- 360a b c - 60b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (240a c + 240b c)d e - 300b c d e + 120c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (180a b c + 30b )d e + (- 280a c - 280b c)d e + 575b c d e - 326c d +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 110 + +--S 111 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 112 + +--S 113 of 465 +r0:=-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*x/e^5+_ + (2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x))+2*c*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^2/e^6-5/3*c^2*(2*c*d-b*e)*_ + (d+e*x)^3/e^6+1/2*c^3*(d+e*x)^4/e^6+2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 5 3 4 +--R (12a c + 12a b )e + (- 72a b c - 12b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (72a c + 72b c)d e - 120b c d e + 60c d e +--R * +--R x +--R + +--R 2 2 4 3 2 3 2 2 3 2 +--R (12a c + 12a b )d e + (- 72a b c - 12b )d e + (72a c + 72b c)d e +--R + +--R 2 4 3 5 +--R - 120b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 3c e x + (10b c e - 5c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 20b c d e + 10c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((36a b c + 6b )e + (- 36a c - 36b c)d e + 60b c d e - 30c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((36a b c + 6b )d e + (- 36a c - 36b c)d e + 40b c d e - 5c d e)x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 6a b e + (12a c + 12a b )d e + (- 36a b c - 6b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (36a c + 36b c)d e - 80b c d e + 55c d +--R / +--R 7 6 +--R 6e x + 6d e +--R Type: Expression(Integer) +--E 113 + +--S 114 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 of 465 +r0:=c*(12*c^2*d^2+4*b^2*e^2-c*e*(15*b*d-4*a*e))*x/e^5-1/2*c^2*(6*c*d-_ + 5*b*e)*x^2/e^4+2/3*c^3*x^3/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+_ + a*e^2)^2/(e^6*(d+e*x)^2)-2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))/(e^6*(d+e*x))-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 2 2 4 2 2 3 +--R (36a b c + 6b )e + (- 72a c - 72b c)d e + 180b c d e +--R + +--R 3 3 2 +--R - 120c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (72a b c + 12b )d e + (- 144a c - 144b c)d e + 360b c d e +--R + +--R 3 4 +--R - 240c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (36a b c + 6b )d e + (- 72a c - 72b c)d e + 180b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 +--R 4c e x + (15b c e - 10c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((24a c + 24b c)e - 60b c d e + 40c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((48a c + 48b c)d e - 165b c d e + 126c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 12a c - 12a b )e + (72a b c + 12b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 30b c d e + 12c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 6a c - 6a b )d e + (54a b c + 9b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 60a c - 60b c)d e + 105b c d e - 54c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 116 + +--S 117 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 of 465 +r0:=-c^2*(8*c*d-5*b*e)*x/e^5+c^3*x^2/e^4+1/3*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^2/(e^6*(d+e*x)^3)-(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+_ + b^2*e^2-c*e*(5*b*d-a*e))/(e^6*(d+e*x)^2)+(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))/(e^6*(d+e*x))+4*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 5 2 4 3 2 3 3 +--R ((12a c + 12b c)e - 60b c d e + 60c d e )x +--R + +--R 2 2 4 2 2 3 3 3 2 2 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e )x +--R + +--R 2 2 2 3 2 3 2 3 4 +--R ((36a c + 36b c)d e - 180b c d e + 180c d e)x +--R + +--R 2 2 3 2 2 4 3 5 +--R (12a c + 12b c)d e - 60b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 5 3 4 4 2 4 3 2 3 3 +--R 3c e x + (15b c e - 15c d e )x + (45b c d e - 63c d e )x +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 18a b c - 3b )e + (36a c + 36b c)d e - 45b c d e - 9c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 3a c - 3a b )e + (- 18a b c - 3b )d e + (54a c + 54b c)d e +--R + +--R 2 3 2 3 4 +--R - 135b c d e + 81c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - a b e + (- a c - a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (22a c + 22b c)d e - 65b c d e + 47c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Expression(Integer) +--E 119 + +--S 120 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 465 +r0:=2*c^3*x/e^5+1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^4)-_ + 2/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/_ + (e^6*(d+e*x)^3)+1/2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-_ + 3*a*e))/(e^6*(d+e*x)^2)-4*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/_ + (e^6*(d+e*x))-5*c^2*(2*c*d-b*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 3 4 4 2 4 3 2 3 3 +--R (60b c e - 120c d e )x + (240b c d e - 480c d e )x +--R + +--R 2 2 3 3 3 2 2 2 3 2 3 4 2 4 +--R (360b c d e - 720c d e )x + (240b c d e - 480c d e)x + 60b c d e +--R + +--R 3 5 +--R - 120c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 3 4 4 2 2 5 2 4 3 2 3 3 +--R 24c e x + 96c d e x + ((- 48a c - 48b c)e + 240b c d e - 96c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 36a b c - 6b )e + (- 72a c - 72b c)d e + 540b c d e +--R + +--R 3 3 2 +--R - 504c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- 8a c - 8a b )e + (- 24a b c - 4b )d e + (- 48a c - 48b c)d e +--R + +--R 2 3 2 3 4 +--R 440b c d e - 496c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 3a b e + (- 2a c - 2a b )d e + (- 6a b c - b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12a c - 12b c)d e + 125b c d e - 154c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 122 + +--S 123 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 465 +t0:=(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 124 + +--S 125 of 465 +r0:=-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))+_ + (c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(2+m)/(e^8*(2+m))-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(3+m)/(e^8*(3+m))+_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*_ + (7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*_ + (d+e*x)^(4+m)/(e^8*(4+m))-5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^(5+m)/(e^8*(5+m))+3*c^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(6+m)/(e^8*(6+m))-_ + 7*c^3*(2*c*d-b*e)*(d+e*x)^(7+m)/(e^8*(7+m))+2*c^4*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 4 7 4 6 4 5 4 4 4 3 4 2 +--R 2c m + 56c m + 644c m + 3920c m + 13538c m + 26264c m +--R + +--R 4 4 +--R 26136c m + 10080c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 4 7 3 4 6 3 4 5 +--R (7b c e - 14c d)m + (203b c e - 406c d)m + (2401b c e - 4802c d)m +--R + +--R 3 4 4 3 4 3 +--R (14945b c e - 29890c d)m + (52528b c e - 105056c d)m +--R + +--R 3 4 2 3 4 3 +--R (103292b c e - 206584c d)m + (103824b c e - 207648c d)m + 40320b c e +--R + +--R 4 +--R - 80640c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 3 2 2 2 3 4 2 7 +--R ((6a c + 9b c )e - 42b c d e + 42c d )m +--R + +--R 3 2 2 2 3 4 2 6 +--R ((180a c + 270b c )e - 1260b c d e + 1260c d )m +--R + +--R 3 2 2 2 3 4 2 5 +--R ((2196a c + 3294b c )e - 15372b c d e + 15372c d )m +--R + +--R 3 2 2 2 3 4 2 4 +--R ((14040a c + 21060b c )e - 98280b c d e + 98280c d )m +--R + +--R 3 2 2 2 3 4 2 3 +--R ((50454a c + 75681b c )e - 353178b c d e + 353178c d )m +--R + +--R 3 2 2 2 3 4 2 2 +--R ((100980a c + 151470b c )e - 706860b c d e + 706860c d )m +--R + +--R 3 2 2 2 3 4 2 +--R ((102864a c + 154296b c )e - 720048b c d e + 720048c d )m +--R + +--R 3 2 2 2 3 4 2 +--R (40320a c + 60480b c )e - 282240b c d e + 282240c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 3 3 3 2 2 2 3 2 +--R (15a b c + 5b c)e + (- 30a c - 45b c )d e + 105b c d e +--R + +--R 4 3 +--R - 70c d +--R * +--R 7 +--R m +--R + +--R 2 3 3 3 2 2 2 3 2 +--R (465a b c + 155b c)e + (- 930a c - 1395b c )d e + 3255b c d e +--R + +--R 4 3 +--R - 2170c d +--R * +--R 6 +--R m +--R + +--R 2 3 3 3 2 2 2 +--R (5865a b c + 1955b c)e + (- 11730a c - 17595b c )d e 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e + (- 1980a c - 2970b c )d e +--R + +--R 3 4 4 5 +--R 3465b c d e - 1386c d +--R * +--R 6 +--R m +--R + +--R 2 3 5 2 2 2 4 4 +--R (4023a b c + 1341a b )e + (- 8046a c - 16092a b c - 1341b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 +--R (40230a b c + 13410b c)d e + (- 26820a c - 40230b c )d e +--R + +--R 3 4 4 5 +--R 46935b c d e - 18774c d +--R * +--R 5 +--R m +--R + +--R 2 3 5 +--R (28755a b c + 9585a b )e +--R + +--R 2 2 2 4 4 +--R (- 57510a c - 115020a b c - 9585b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 +--R (287550a b c + 95850b c)d e + (- 191700a c - 287550b c )d e +--R + +--R 3 4 4 5 +--R 335475b c d e - 134190c d +--R * +--R 4 +--R m +--R + +--R 2 3 5 +--R (115776a b c + 38592a b )e +--R + +--R 2 2 2 4 4 +--R (- 231552a c - 463104a b c - 38592b )d e +--R + +--R 2 3 2 3 +--R (1157760a b c + 385920b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (- 771840a c - 1157760b c )d e + 1350720b c d e - 540288c d +--R * +--R 3 +--R m +--R + +--R 2 3 5 +--R (258228a b c + 86076a b )e +--R + +--R 2 2 2 4 4 +--R (- 516456a c - 1032912a b c - 86076b )d e +--R + +--R 2 3 2 3 +--R (2582280a b c + 860760b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (- 1721520a c - 2582280b c )d e + 3012660b c d e - 1205064c d +--R * +--R 2 +--R m +--R + +--R 2 3 5 +--R (288432a b c + 96144a b )e +--R + +--R 2 2 2 4 4 +--R (- 576864a c - 1153728a b c - 96144b )d e +--R + +--R 2 3 2 3 +--R (2884320a b c + 961440b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (- 1922880a c - 2884320b c )d e + 3365040b c d e - 1346016c d +--R * +--R m +--R + +--R 2 3 5 +--R (120960a b c + 40320a b )e +--R + +--R 2 2 2 4 4 +--R (- 241920a c - 483840a b c - 40320b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 +--R (1209600a b c + 403200b c)d e + (- 806400a c - 1209600b c )d e +--R + +--R 3 4 4 5 +--R 1411200b c d e - 564480c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 2 2 6 2 3 5 +--R (2a c + 3a b )e + (- 18a b c - 6a b )d e +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (18a c + 36a b c + 3b )d e + (- 60a b c - 20b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (30a c + 45b c )d e - 42b c d e + 14c d +--R * +--R 7 +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (68a c + 102a b )e + (- 612a b c - 204a b )d e +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (612a c + 1224a b c + 102b )d e + (- 2040a b c - 680b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (1020a c + 1530b c )d e - 1428b c d e + 476c d +--R * +--R 6 +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (956a c + 1434a b )e + (- 8604a b c - 2868a b )d e +--R + +--R 2 2 2 4 2 4 +--R (8604a c + 17208a b c + 1434b )d e +--R + +--R 2 3 3 3 3 2 2 4 2 +--R (- 28680a b c - 9560b c)d e + (14340a c + 21510b c )d e +--R + +--R 3 5 4 6 +--R - 20076b c d e + 6692c d +--R * +--R 5 +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (7160a c + 10740a b )e + (- 64440a b c - 21480a b )d e +--R + +--R 2 2 2 4 2 4 +--R (64440a c + 128880a b c + 10740b )d e +--R + +--R 2 3 3 3 3 2 2 4 2 +--R (- 214800a b c - 71600b c)d e + (107400a c + 161100b c )d e +--R + +--R 3 5 4 6 +--R - 150360b c d e + 50120c d +--R * +--R 4 +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (30578a c + 45867a b )e + (- 275202a b c - 91734a b )d e +--R + +--R 2 2 2 4 2 4 +--R (275202a c + 550404a b c + 45867b )d e +--R + +--R 2 3 3 3 3 2 2 4 2 +--R (- 917340a b c - 305780b c)d e + (458670a c + 688005b c )d e +--R + +--R 3 5 4 6 +--R - 642138b c d e + 214046c d +--R * +--R 3 +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (73412a c + 110118a b )e + (- 660708a b c - 220236a b )d e +--R + +--R 2 2 2 4 2 4 +--R (660708a c + 1321416a b c + 110118b )d e +--R + +--R 2 3 3 3 +--R (- 2202360a b c - 734120b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (1101180a c + 1651770b c )d e - 1541652b c d e + 513884c d +--R * +--R 2 +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (89424a c + 134136a b )e + (- 804816a b c - 268272a b )d e +--R + +--R 2 2 2 4 2 4 +--R (804816a c + 1609632a b c + 134136b )d e +--R + +--R 2 3 3 3 +--R (- 2682720a b c - 894240b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (1341360a c + 2012040b c )d e - 1877904b c d e + 625968c d +--R * +--R m +--R + +--R 3 2 2 6 2 3 5 +--R (40320a c + 60480a b )e + (- 362880a b c - 120960a b )d e +--R + +--R 2 2 2 4 2 4 +--R (362880a c + 725760a b c + 60480b )d e +--R + +--R 2 3 3 3 3 2 2 4 2 +--R (- 1209600a b c - 403200b c)d e + (604800a c + 907200b c )d e +--R + +--R 3 5 4 6 +--R - 846720b c d e + 282240c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R a b e + (- 2a c - 3a b )d e + (9a b c + 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 6a c - 12a b c - b )d e + (15a b c + 5b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 6a c - 9b c )d e + 7b c d e - 2c d +--R * +--R 7 +--R m +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R 35a b e + (- 70a c - 105a b )d e + (315a b c + 105a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 210a c - 420a b c - 35b )d e + (525a b c + 175b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 210a c - 315b c )d e + 245b c d e - 70c d +--R * +--R 6 +--R m +--R + +--R 3 7 3 2 2 6 +--R 511a b e + (- 1022a c - 1533a b )d e +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (4599a b c + 1533a b )d e + (- 3066a c - 6132a b c - 511b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (7665a b c + 2555b c)d e + (- 3066a c - 4599b c )d e +--R + +--R 3 6 4 7 +--R 3577b c d e - 1022c d +--R * +--R 5 +--R m +--R + +--R 3 7 3 2 2 6 +--R 4025a b e + (- 8050a c - 12075a b )d e +--R + +--R 2 3 2 5 +--R (36225a b c + 12075a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 24150a c - 48300a b c - 4025b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (60375a b c + 20125b c)d e + (- 24150a c - 36225b c )d e +--R + +--R 3 6 4 7 +--R 28175b c d e - 8050c d +--R * +--R 4 +--R m +--R + +--R 3 7 3 2 2 6 +--R 18424a b e + (- 36848a c - 55272a b )d e +--R + +--R 2 3 2 5 +--R (165816a b c + 55272a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 110544a c - 221088a b c - 18424b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (276360a b c + 92120b c)d e + (- 110544a c - 165816b c )d e +--R + +--R 3 6 4 7 +--R 128968b c d e - 36848c d +--R * +--R 3 +--R m +--R + +--R 3 7 3 2 2 6 +--R 48860a b e + (- 97720a c - 146580a b )d e +--R + +--R 2 3 2 5 +--R (439740a b c + 146580a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 293160a c - 586320a b c - 48860b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (732900a b c + 244300b c)d e + (- 293160a c - 439740b c )d e +--R + +--R 3 6 4 7 +--R 342020b c d e - 97720c d +--R * +--R 2 +--R m +--R + +--R 3 7 3 2 2 6 +--R 69264a b e + (- 138528a c - 207792a b )d e +--R + +--R 2 3 2 5 +--R (623376a b c + 207792a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 415584a c - 831168a b c - 69264b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (1038960a b c + 346320b c)d e + (- 415584a c - 623376b c )d e +--R + +--R 3 6 4 7 +--R 484848b c d e - 138528c d +--R * +--R m +--R + +--R 3 7 3 2 2 6 +--R 40320a b e + (- 80640a c - 120960a b )d e +--R + +--R 2 3 2 5 +--R (362880a b c + 120960a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 241920a c - 483840a b c - 40320b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (604800a b c + 201600b c)d e + (- 241920a c - 362880b c )d e +--R + +--R 3 6 4 7 +--R 282240b c d e - 80640c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 125 + +--S 126 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 of 465 +t0:=(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 4 11 3 4 4 3 10 +--R 2c e x + (7b c e + 8c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 9 +--R ((6a c + 9b c )e + 28b c d e + 12c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 8 +--R ((15a b c + 5b c)e + (24a c + 36b c )d e + 42b c d e + 8c d e)x +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c + 12a b c + b )e + (60a b c + 20b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (36a c + 54b c )d e + 28b c d e + 2c d +--R * +--R 7 +--R x +--R + +--R 2 3 4 2 2 2 4 3 +--R (9a b c + 3a b )e + (24a c + 48a b c + 4b )d e +--R + +--R 2 3 2 2 3 2 2 3 3 4 +--R (90a b c + 30b c)d e + (24a c + 36b c )d e + 7b c d +--R * +--R 6 +--R x +--R + +--R 3 2 2 4 2 3 3 +--R (2a c + 3a b )e + (36a b c + 12a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 3 2 2 4 +--R (36a c + 72a b c + 6b )d e + (60a b c + 20b c)d e + (6a c + 9b c )d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 +--R a b e + (8a c + 12a b )d e + (54a b c + 18a b )d e +--R + +--R 2 2 2 4 3 2 3 4 +--R (24a c + 48a b c + 4b )d e + (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 3 3 2 2 2 2 2 3 3 +--R 4a b d e + (12a c + 18a b )d e + (36a b c + 12a b )d e +--R + +--R 2 2 2 4 4 +--R (6a c + 12a b c + b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 3 2 3 4 2 +--R (6a b d e + (8a c + 12a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 3 2 2 4 3 4 +--R (4a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 127 + +--S 128 of 465 +r0:=-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^5/e^8+1/6*(c*d^2-b*d*e+_ + a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^6/e^8-_ + 3/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^7/e^8+1/8*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+_ + a^2*e^2))*(d+e*x)^8/e^8-5/9*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^9/e^8+3/10*c^2*(14*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(7*b*d-a*e))*(d+e*x)^10/e^8-7/11*c^3*(2*c*d-b*e)*_ + (d+e*x)^11/e^8+1/6*c^4*(d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 4 12 12 7 3 12 8 4 11 11 +--R - c e x + (-- b c e + -- c d e )x +--R 6 11 11 +--R + +--R 3 3 9 2 2 12 14 3 11 6 4 2 10 10 +--R ((- a c + -- b c )e + -- b c d e + - c d e )x +--R 5 10 5 5 +--R + +--R 5 2 5 3 12 8 3 2 2 11 14 3 2 10 +--R (- a b c + - b c)e + (- a c + 4b c )d e + -- b c d e +--R 3 9 3 3 +--R + +--R 8 4 3 9 +--R - c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 2 3 2 1 4 12 15 2 5 3 11 +--R (- a c + - a b c + - b )e + (-- a b c + - b c)d e +--R 4 2 8 2 2 +--R + +--R 9 3 27 2 2 2 10 7 3 3 9 1 4 4 8 +--R (- a c + -- b c )d e + - b c d e + - c d e +--R 2 4 2 4 +--R * +--R 8 +--R x +--R + +--R 9 2 3 3 12 24 2 2 48 2 4 4 11 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 7 7 7 7 7 +--R + +--R 90 2 30 3 2 10 24 3 36 2 2 3 9 3 4 8 +--R (-- a b c + -- b c)d e + (-- a c + -- b c )d e + b c d e +--R 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 1 2 2 12 2 3 11 +--R (- a c + - a b )e + (6a b c + 2a b )d e +--R 3 2 +--R + +--R 2 2 2 4 2 10 2 10 3 3 9 +--R (6a c + 12a b c + b )d e + (10a b c + -- b c)d e +--R 3 +--R + +--R 3 3 2 2 4 8 +--R (a c + - b c )d e +--R 2 +--R * +--R 6 +--R x +--R + +--R 1 3 12 8 3 12 2 2 11 54 2 18 3 2 10 +--R - a b e + (- a c + -- a b )d e + (-- a b c + -- a b )d e +--R 5 5 5 5 5 +--R + +--R 24 2 2 48 2 4 4 3 9 2 3 4 8 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d e +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 11 3 9 2 2 2 10 2 3 3 9 +--R a b d e + (3a c + - a b )d e + (9a b c + 3a b )d e +--R 2 +--R + +--R 3 2 2 2 1 4 4 8 +--R (- a c + 3a b c + - b )d e +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 2 10 8 3 2 2 3 9 2 3 4 8 3 +--R (2a b d e + (- a c + 4a b )d e + (3a b c + a b )d e )x +--R 3 +--R + +--R 3 3 9 3 3 2 2 4 8 2 3 4 8 1 3 5 7 +--R (2a b d e + (a c + - a b )d e )x + a b d e x + - a b d e +--R 2 5 +--R + +--R 1 3 1 2 2 6 6 3 2 1 3 7 5 +--R (- -- a c - -- a b )d e + (-- a b c + -- a b )d e +--R 15 10 35 35 +--R + +--R 3 2 2 3 2 1 4 8 4 1 2 1 3 9 3 +--R (- --- a c - -- a b c - --- b )d e + (-- a b c + --- b c)d e +--R 140 70 280 42 126 +--R + +--R 1 3 1 2 2 10 2 1 3 11 1 4 12 +--R (- --- a c - --- b c )d e + --- b c d e - ---- c d +--R 210 140 330 1980 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 128 + +--S 129 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 3 10 3 3 4 2 9 +--R 2c e x + (7b c e + 6c d e )x +--R + +--R 3 2 2 3 3 2 4 2 8 +--R ((6a c + 9b c )e + 21b c d e + 6c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 4 3 7 +--R ((15a b c + 5b c)e + (18a c + 27b c )d e + 21b c d e + 2c d )x +--R + +--R 2 2 2 4 3 2 3 2 +--R (6a c + 12a b c + b )e + (45a b c + 15b c)d e +--R + +--R 3 2 2 2 3 3 +--R (18a c + 27b c )d e + 7b c d +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 2 2 4 2 +--R (9a b c + 3a b )e + (18a c + 36a b c + 3b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (45a b c + 15b c)d e + (6a c + 9b c )d +--R * +--R 5 +--R x +--R + +--R 3 2 2 3 2 3 2 2 2 2 4 2 +--R (2a c + 3a b )e + (27a b c + 9a b )d e + (18a c + 36a b c + 3b )d e +--R + +--R 2 3 3 +--R (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 3 3 2 2 2 2 3 2 +--R a b e + (6a c + 9a b )d e + (27a b c + 9a b )d e +--R + +--R 2 2 2 4 3 +--R (6a c + 12a b c + b )d +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 9a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 2 3 2 2 3 3 3 +--R (3a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 130 + +--S 131 of 465 +r0:=-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^4/e^8+1/5*(c*d^2-b*d*e+_ + a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^5/e^8-_ + 1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^6/e^8+1/7*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-_ + 10*a*b*d*e+a^2*e^2))*(d+e*x)^7/e^8-5/8*c*(2*c*d-b*e)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^8/e^8+1/3*c^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^9/e^8-7/10*c^3*(2*c*d-b*e)*_ + (d+e*x)^10/e^8+2/11*c^4*(d+e*x)^11/e^8 +--R +--R +--R (2) +--R 2 4 11 11 7 3 11 3 4 10 10 +--R -- c e x + (-- b c e + - c d e )x +--R 11 10 5 +--R + +--R 2 3 2 2 11 7 3 10 2 4 2 9 9 +--R ((- a c + b c )e + - b c d e + - c d e )x +--R 3 3 3 +--R + +--R 15 2 5 3 11 9 3 27 2 2 10 21 3 2 9 +--R (-- a b c + - b c)e + (- a c + -- b c )d e + -- b c d e +--R 8 8 4 8 8 +--R + +--R 1 4 3 8 +--R - c d e +--R 4 +--R * +--R 8 +--R x +--R + +--R 6 2 2 12 2 1 4 11 45 2 15 3 10 +--R (- a c + -- a b c + - b )e + (-- a b c + -- b c)d e +--R 7 7 7 7 7 +--R + +--R 18 3 27 2 2 2 9 3 3 8 +--R (-- a c + -- b c )d e + b c d e +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 3 2 1 3 11 2 2 2 1 4 10 +--R (- a b c + - a b )e + (3a c + 6a b c + - b )d e +--R 2 2 2 +--R + +--R 15 2 5 3 2 9 3 3 2 2 3 8 +--R (-- a b c + - b c)d e + (a c + - b c )d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 2 11 27 2 9 3 10 +--R (- a c + - a b )e + (-- a b c + - a b )d e +--R 5 5 5 5 +--R + +--R 18 2 2 36 2 3 4 2 9 2 3 3 8 +--R (-- a c + -- a b c + - b )d e + (3a b c + b c)d e +--R 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 11 3 3 9 2 2 10 27 2 9 3 2 9 +--R - a b e + (- a c + - a b )d e + (-- a b c + - a b )d e +--R 4 2 4 4 4 +--R + +--R 3 2 2 2 1 4 3 8 +--R (- a c + 3a b c + - b )d e +--R 2 4 +--R * +--R 4 +--R x +--R + +--R 3 10 3 2 2 2 9 2 3 3 8 3 +--R (a b d e + (2a c + 3a b )d e + (3a b c + a b )d e )x +--R + +--R 3 3 2 9 3 3 2 2 3 8 2 3 3 8 1 3 4 7 +--R (- a b d e + (a c + - a b )d e )x + a b d e x + - a b d e +--R 2 2 4 +--R + +--R 1 3 3 2 2 5 6 3 2 1 3 6 5 +--R (- -- a c - -- a b )d e + (-- a b c + -- a b )d e +--R 10 20 20 20 +--R + +--R 3 2 2 3 2 1 4 7 4 3 2 1 3 8 3 +--R (- -- a c - -- a b c - --- b )d e + (-- a b c + -- b c)d e +--R 70 35 140 56 56 +--R + +--R 1 3 1 2 2 9 2 1 3 10 1 4 11 +--R (- -- a c - -- b c )d e + --- b c d e - --- c d +--R 84 56 120 660 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 131 + +--S 132 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 2 9 3 2 4 8 3 2 2 2 3 4 2 7 +--R 2c e x + (7b c e + 4c d e)x + ((6a c + 9b c )e + 14b c d e + 2c d )x +--R + +--R 2 3 2 3 2 2 3 2 6 +--R ((15a b c + 5b c)e + (12a c + 18b c )d e + 7b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 2 2 5 +--R ((6a c + 12a b c + b )e + (30a b c + 10b c)d e + (6a c + 9b c )d )x +--R + +--R 2 3 2 2 2 2 4 2 3 2 4 +--R ((9a b c + 3a b )e + (12a c + 24a b c + 2b )d e + (15a b c + 5b c)d )x +--R + +--R 3 2 2 2 2 3 2 2 2 4 2 3 +--R ((2a c + 3a b )e + (18a b c + 6a b )d e + (6a c + 12a b c + b )d )x +--R + +--R 3 2 3 2 2 2 3 2 2 +--R (a b e + (4a c + 6a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 2 2 2 3 2 +--R (2a b d e + (2a c + 3a b )d )x + a b d +--R Type: Polynomial(Integer) +--E 133 + +--S 134 of 465 +r0:=a^3*b*d^2*x+1/2*a^2*d*(3*b^2*d+2*a*c*d+2*a*b*e)*x^2+1/3*a*(3*b^3*d^2+_ + 6*a*b^2*d*e+4*a^2*c*d*e+a*b*(9*c*d^2+a*e^2))*x^3+1/4*(b^4*d^2+_ + 6*a*b^3*d*e+18*a^2*b*c*d*e+2*a^2*c*(3*c*d^2+a*e^2)+3*a*b^2*(4*c*d^2+_ + a*e^2))*x^4+1/5*(2*b^4*d*e+24*a*b^2*c*d*e+12*a^2*c^2*d*e+b^3*_ + (5*c*d^2+3*a*e^2)+3*a*b*c*(5*c*d^2+3*a*e^2))*x^5+1/6*(10*b^3*c*d*e+_ + 30*a*b*c^2*d*e+b^4*e^2+6*a*c^2*(c*d^2+a*e^2)+3*b^2*c*(3*c*d^2+_ + 4*a*e^2))*x^6+1/7*c*(18*b^2*c*d*e+12*a*c^2*d*e+5*b^3*e^2+b*c*_ + (7*c*d^2+15*a*e^2))*x^7+1/8*c^2*(2*c^2*d^2+9*b^2*e^2+2*c*e*_ + (7*b*d+3*a*e))*x^8+1/9*c^3*e*(4*c*d+7*b*e)*x^9+1/5*c^4*e^2*x^10 +--R +--R +--R (2) +--R 1 4 2 10 7 3 2 4 4 9 +--R - c e x + (- b c e + - c d e)x +--R 5 9 9 +--R + +--R 3 3 9 2 2 2 7 3 1 4 2 8 +--R ((- a c + - b c )e + - b c d e + - c d )x +--R 4 8 4 4 +--R + +--R 15 2 5 3 2 12 3 18 2 2 3 2 7 +--R ((-- a b c + - b c)e + (-- a c + -- b c )d e + b c d )x +--R 7 7 7 7 +--R + +--R 2 2 2 1 4 2 2 5 3 3 3 2 2 2 6 +--R ((a c + 2a b c + - b )e + (5a b c + - b c)d e + (a c + - b c )d )x +--R 6 3 2 +--R + +--R 9 2 3 3 2 12 2 2 24 2 2 4 +--R (- a b c + - a b )e + (-- a c + -- a b c + - b )d e +--R 5 5 5 5 5 +--R + +--R 2 3 2 +--R (3a b c + b c)d +--R * +--R 5 +--R x +--R + +--R 1 3 3 2 2 2 9 2 3 3 3 2 2 2 1 4 2 4 +--R ((- a c + - a b )e + (- a b c + - a b )d e + (- a c + 3a b c + - b )d )x +--R 2 4 2 2 2 4 +--R + +--R 1 3 2 4 3 2 2 2 3 2 3 +--R (- a b e + (- a c + 2a b )d e + (3a b c + a b )d )x +--R 3 3 +--R + +--R 3 3 3 2 2 2 2 3 2 +--R (a b d e + (a c + - a b )d )x + a b d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 465 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 8 3 4 7 3 2 2 3 6 +--R 2c e x + (7b c e + 2c d)x + ((6a c + 9b c )e + 7b c d)x +--R + +--R 2 3 3 2 2 5 +--R ((15a b c + 5b c)e + (6a c + 9b c )d)x +--R + +--R 2 2 2 4 2 3 4 +--R ((6a c + 12a b c + b )e + (15a b c + 5b c)d)x +--R + +--R 2 3 2 2 2 4 3 +--R ((9a b c + 3a b )e + (6a c + 12a b c + b )d)x +--R + +--R 3 2 2 2 3 2 3 3 2 2 3 +--R ((2a c + 3a b )e + (9a b c + 3a b )d)x + (a b e + (2a c + 3a b )d)x + a b d +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 465 +r0:=a^3*b*d*x+1/2*a^2*(3*b^2*d+2*a*c*d+a*b*e)*x^2+1/3*a*(3*b^3*d+_ + 9*a*b*c*d+3*a*b^2*e+2*a^2*c*e)*x^3+1/4*(b^4*d+12*a*b^2*c*d+_ + 6*a^2*c^2*d+3*a*b^3*e+9*a^2*b*c*e)*x^4+1/5*(5*b^3*c*d+15*a*b*c^2*d+_ + b^4*e+12*a*b^2*c*e+6*a^2*c^2*e)*x^5+1/6*c*(9*b^2*c*d+6*a*c^2*d+_ + 5*b^3*e+15*a*b*c*e)*x^6+1/7*c^2*(7*b*c*d+9*b^2*e+6*a*c*e)*x^7+_ + 1/8*c^3*(2*c*d+7*b*e)*x^8+2/9*c^4*e*x^9 +--R +--R +--R (2) +--R 2 4 9 7 3 1 4 8 6 3 9 2 2 3 7 +--R - c e x + (- b c e + - c d)x + ((- a c + - b c )e + b c d)x +--R 9 8 4 7 7 +--R + +--R 5 2 5 3 3 3 2 2 6 +--R ((- a b c + - b c)e + (a c + - b c )d)x +--R 2 6 2 +--R + +--R 6 2 2 12 2 1 4 2 3 5 +--R ((- a c + -- a b c + - b )e + (3a b c + b c)d)x +--R 5 5 5 +--R + +--R 9 2 3 3 3 2 2 2 1 4 4 +--R ((- a b c + - a b )e + (- a c + 3a b c + - b )d)x +--R 4 4 2 4 +--R + +--R 2 3 2 2 2 3 3 1 3 3 3 2 2 2 +--R ((- a c + a b )e + (3a b c + a b )d)x + (- a b e + (a c + - a b )d)x +--R 3 2 2 +--R + +--R 3 +--R a b d x +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R Type: Polynomial(Integer) +--E 139 + +--S 140 of 465 +r0:=1/4*(a+b*x+c*x^2)^4 +--R +--R +--R (2) +--R 1 4 8 3 7 3 3 2 2 6 2 3 5 +--R - c x + b c x + (a c + - b c )x + (3a b c + b c)x +--R 4 2 +--R + +--R 3 2 2 2 1 4 4 2 3 3 3 3 2 2 2 3 +--R (- a c + 3a b c + - b )x + (3a b c + a b )x + (a c + - a b )x + a b x +--R 2 4 2 +--R + +--R 1 4 +--R - a +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +--S 141 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 142 + +--S 143 of 465 +r0:=(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*x/e^7-_ + 3/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*(d+e*x)^2/e^8+1/3*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-_ + 3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+_ + a^2*e^2))*(d+e*x)^3/e^8-5/4*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^4/e^8+3/5*c^2*(14*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(7*b*d-a*e))*(d+e*x)^5/e^8-7/6*c^3*(2*c*d-b*e)*(d+e*x)^6/e^8+_ + 2/7*c^4*(d+e*x)^7/e^8-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 3 2 2 6 2 3 2 5 +--R 420a b e + (- 840a c - 1260a b )d e + (3780a b c + 1260a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 2520a c - 5040a b c - 420b )d e + (6300a b c + 2100b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 2520a c - 3780b c )d e + 2940b c d e - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 120c e x + (490b c e - 140c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((504a c + 756b c )e - 588b c d e + 168c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (1575a b c + 525b c)e + (- 630a c - 945b c )d e + 735b c d e +--R + +--R 4 3 4 +--R - 210c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (840a c + 1680a b c + 140b )e + (- 2100a b c - 700b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (840a c + 1260b c )d e - 980b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (1890a b c + 630a b )e + (- 1260a c - 2520a b c - 210b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (3150a b c + 1050b c)d e + (- 1260a c - 1890b c )d e +--R + +--R 3 4 3 4 5 2 +--R 1470b c d e - 420c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (840a c + 1260a b )e + (- 3780a b c - 1260a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (2520a c + 5040a b c + 420b )d e + (- 6300a b c - 2100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (2520a c + 3780b c )d e - 2940b c d e + 840c d e +--R * +--R x +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (1890a b c + 630a b )d e + (- 2940a c - 5880a b c - 490b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (12075a b c + 4025b c)d e + (- 6846a c - 10269b c )d e + 10437b c d e +--R + +--R 4 7 +--R - 3702c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 143 + +--S 144 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 145 + +--S 146 of 465 +r0:=-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))*x/e^7+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x))+1/2*_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^2/e^8-_ + 5/3*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^3/e^8+3/4*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^4/e^8-7/5*c^3*(2*c*d-b*e)*(d+e*x)^5/e^8+1/3*c^4*_ + (d+e*x)^6/e^8+(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*_ + (7*b*d-a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 2 7 2 3 6 +--R (120a c + 180a b )e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d e +--R * +--R x +--R + +--R 3 2 2 6 2 3 2 5 +--R (120a c + 180a b )d e + (- 1080a b c - 360a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (1080a c + 2160a b c + 180b )d e + (- 3600a b c - 1200b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (1800a c + 2700b c )d e - 2520b c d e + 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 20c e x + (84b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((90a c + 135b c )e - 126b c d e + 42c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (300a b c + 100b c)e + (- 150a c - 225b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (180a c + 360a b c + 30b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (300a c + 450b c )d e - 420b c d e + 140c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (540a b c + 180a b )e + (- 540a c - 1080a b c - 90b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 3 4 3 +--R (1800a b c + 600b c)d e + (- 900a c - 1350b c )d e + 1260b c d e +--R + +--R 4 5 2 +--R - 420c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (540a b c + 180a b )d e + (- 540a c - 1080a b c - 90b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 3 5 2 +--R (1200a b c + 400b c)d e + (- 150a c - 225b c )d e - 546b c d e +--R + +--R 4 6 +--R 462c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 60a b e + (120a c + 180a b )d e + (- 540a b c - 180a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (540a c + 1080a b c + 90b )d e + (- 2400a b c - 800b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (1650a c + 2475b c )d e - 3066b c d e + 1302c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 146 + +--S 147 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 148 + +--S 149 of 465 +r0:=(30*c^4*d^4+b^4*e^4-2*c^3*d^2*e*(35*b*d-18*a*e)-3*b^2*c*e^3*_ + (5*b*d-4*a*e)+3*c^2*e^2*(18*b^2*d^2-15*a*b*d*e+2*a^2*e^2))*x/e^7-_ + 1/2*c*(20*c^3*d^3-5*b^3*e^3+3*b*c*e^2*(9*b*d-5*a*e)-6*c^2*d*e*(7*b*d-_ + 3*a*e))*x^2/e^6+c^2*(4*c^2*d^2+3*b^2*e^2-c*e*(7*b*d-2*a*e))*x^3/e^5-_ + 1/4*c^3*(6*c*d-7*b*e)*x^4/e^4+2/5*c^4*x^5/e^3+1/2*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^3/(e^8*(d+e*x)^2)-(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x))-3*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 2 2 2 4 6 +--R (180a b c + 60a b )e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2100b c d e - 840c d e +--R * +--R 2 +--R x +--R + +--R 2 3 6 2 2 2 4 2 5 +--R (360a b c + 120a b )d e + (- 720a c - 1440a b c - 120b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (3600a b c + 1200b c)d e + (- 2400a c - 3600b c )d e +--R + +--R 3 5 2 4 6 +--R 4200b c d e - 1680c d e +--R * +--R x +--R + +--R 2 3 2 5 2 2 2 4 3 4 +--R (180a b c + 60a b )d e + (- 360a c - 720a b c - 60b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (1800a b c + 600b c)d e + (- 1200a c - 1800b c )d e + 2100b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (35b c e - 14c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((40a c + 60b c )e - 70b c d e + 28c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (150a b c + 50b c)e + (- 100a c - 150b c )d e + 175b c d e +--R + +--R 4 3 4 +--R - 70c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (120a c + 240a b c + 20b )e + (- 600a b c - 200b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (400a c + 600b c )d e - 700b c d e + 280c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (240a c + 480a b c + 40b )d e + (- 1650a b c - 550b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1260a c + 1890b c )d e - 2380b c d e + 1000c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 40a c - 60a b )e + (360a b c + 120a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 240a c - 480a b c - 40b )d e + (300a b c + 100b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (120a c + 180b c )d e - 560b c d e + 320c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 10a b e + (- 20a c - 30a b )d e + (270a b c + 90a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 300a c - 600a b c - 50b )d e + (1050a b c + 350b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 540a c - 810b c )d e + 770b c d e - 260c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 149 + +--S 150 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 465 +r0:=-5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*x/e^7+_ + 1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^3)-1/2*(c*d^2-_ + b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x)^2)+_ + 3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-_ + 3*a*e))/(e^8*(d+e*x))+3/2*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^2/e^8-7/3*c^3*(2*c*d-b*e)*(d+e*x)^3/e^8+1/2*c^4*(d+e*x)^4/e^8+_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 2 4 7 2 3 6 +--R (36a c + 72a b c + 6b )e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (360a c + 540b c )d e - 840b c d e + 420c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (108a c + 216a b c + 18b )d e + (- 1080a b c - 360b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (1080a c + 1620b c )d e - 2520b c d e + 1260c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (36a c + 72a b c + 6b )d e + (- 360a b c - 120b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (360a c + 540b c )d e - 840b c d e + 420c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 3c e x + (14b c e - 7c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((18a c + 27b c )e - 42b c d e + 21c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (90a b c + 30b c)e + (- 90a c - 135b c )d e + 210b c d e +--R + +--R 4 3 4 +--R - 105c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 3 3 4 +--R (270a b c + 90b c)d e + (- 360a c - 540b c )d e + 910b c d e +--R + +--R 4 4 3 +--R - 455c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (108a c + 216a b c + 18b )d e +--R + +--R 2 3 2 5 3 4 3 4 5 2 +--R (- 270a b c - 90b c)d e + 210b c d e - 105c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 6a c - 9a b )e + (- 54a b c - 18a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (162a c + 324a b c + 27b )d e + (- 810a b c - 270b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (540a c + 810b c )d e - 1050b c d e + 525c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 2a b e + (- 2a c - 3a b )d e + (- 18a b c - 6a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (66a c + 132a b c + 11b )d e + (- 390a b c - 130b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (300a c + 450b c )d e - 630b c d e + 315c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 152 + +--S 153 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 154 + +--S 155 of 465 +r0:=c^2*(30*c^2*d^2+9*b^2*e^2-c*e*(35*b*d-6*a*e))*x/e^7-1/2*c^3*_ + (10*c*d-7*b*e)*x^2/e^6+2/3*c^4*x^3/e^5+1/4*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^3/(e^8*(d+e*x)^4)-1/3*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+_ + 3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x)^3)+3/2*(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))/(e^8*(d+e*x)^2)+_ + (-70*c^4*d^4-b^4*e^4+4*b^2*c*e^3*(5*b*d-3*a*e)+20*c^3*d^2*e*(7*b*d-_ + 3*a*e)-6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))/(e^8*(d+e*x))-_ + 5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 3 2 2 6 3 2 5 +--R (180a b c + 60b c)e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 3 4 +--R - 840c d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 3 2 2 2 5 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 3 4 4 4 3 +--R 5040b c d e - 3360c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1080a b c + 360b c)d e + (- 2160a c - 3240b c )d e +--R + +--R 3 4 3 4 5 2 +--R 7560b c d e - 5040c d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (720a b c + 240b c)d e + (- 1440a c - 2160b c )d e +--R + +--R 3 5 2 4 6 +--R 5040b c d e - 3360c d e +--R * +--R x +--R + +--R 2 3 4 3 3 2 2 5 2 3 6 +--R (180a b c + 60b c)d e + (- 360a c - 540b c )d e + 1260b c d e +--R + +--R 4 7 +--R - 840c d +--R * +--R log(e x + d) +--R + +--R 4 7 7 3 7 4 6 6 +--R 8c e x + (42b c e - 28c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((72a c + 108b c )e - 252b c d e + 168c d e )x +--R + +--R 3 2 2 6 3 2 5 4 3 4 4 +--R ((288a c + 432b c )d e - 1428b c d e + 1112c d e )x +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 72a c - 144a b c - 12b )e + (720a b c + 240b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 288a c - 432b c )d e - 672b c d e + 1088c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (- 54a b c - 18a b )e + (- 108a c - 216a b c - 18b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (1620a b c + 540b c)d e + (- 1512a c - 2268b c )d e +--R + +--R 3 4 3 4 5 2 +--R 2772b c d e - 888c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 8a c - 12a b )e + (- 36a b c - 12a b )d e +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 72a c - 144a b c - 12b )d e + (1320a b c + 440b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 1488a c - 2232b c )d e + 3528b c d e - 1712c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 3a b e + (- 2a c - 3a b )d e + (- 9a b c - 3a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 18a c - 36a b c - 3b )d e + (375a b c + 125b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 462a c - 693b c )d e + 1197b c d e - 638c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 155 + +--S 156 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 465 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 157 + +--S 158 of 465 +r0:=e*(8*c^3*d^3-b^3*e^3+b*c*e^2*(4*b*d+3*a*e)-2*c^2*d*e*(3*b*d+4*a*e))*_ + x/c^3+1/2*e^2*(12*c^2*d^2+b^2*e^2-2*c*e*(2*b*d+a*e))*x^2/c^2+1/3*e^3*_ + (8*c*d-b*e)*x^3/c+1/2*e^4*x^4+1/2*(2*c^4*d^4+b^4*e^4-4*b^2*c*e^3*_ + (b*d+a*e)-4*c^3*d^2*e*(b*d+3*a*e)+2*c^2*e^2*(3*b^2*d^2+6*a*b*d*e+_ + a^2*e^2))*log(a+b*x+c*x^2)/c^4-e*(2*c*d-b*e)*(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^4 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((- 12a b c + 6b )e + (24a c - 24b c)d e + 36b c d e - 24c d e) +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 4 4 2 3 3 +--R (6a c - 12a b c + 3b )e + (36a b c - 12b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (- 36a c + 18b c )d e - 12b c d e + 6c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3c e x + (- 2b c e + 16c d e )x +--R + +--R 3 2 2 4 3 3 4 2 2 2 +--R ((- 6a c + 3b c )e - 12b c d e + 36c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 4 3 +--R ((18a b c - 6b c)e + (- 48a c + 24b c )d e - 36b c d e + 48c d e)x +--R / +--R 4 +--R 6c +--R Type: Expression(Integer) +--E 158 + +--S 159 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 of 465 +r0:=e*(6*c^2*d^2+b^2*e^2-c*e*(3*b*d+2*a*e))*x/c^2+1/2*e^2*(6*c*d-b*e)*x^2/c+_ + 2/3*e^3*x^3+1/2*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(a+b*x+_ + c*x^2)/c^3-e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^3 +--R +--R +--R (2) +--R +-----------+ +--R 2 3 2 2 2 | 2 +--R ((6a c - 6b )e + 18b c d e - 18c d e)\|- 4a c + b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((9a b c - 3b )e + (- 18a c + 9b c)d e - 9b c d e + 6c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 3 2 3 3 2 2 +--R 4c e x + (- 3b c e + 18c d e )x +--R + +--R 2 2 3 2 2 3 2 +--R ((- 12a c + 6b c)e - 18b c d e + 36c d e)x +--R / +--R 3 +--R 6c +--R Type: Expression(Integer) +--E 161 + +--S 162 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 of 465 +r0:=e*(4*d-b*e/c)*x+e^2*x^2+1/2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + log(a+b*x+c*x^2)/c^2-e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*_ + sqrt(b^2-4*a*c)/c^2 +--R +--R +--R (2) +--R +-----------+ +--R 2 | 2 2c x + b +--R (2b e - 4c d e)\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d )log(c x + b x + a) + 2c e x +--R + +--R 2 2 +--R (- 2b c e + 8c d e)x +--R / +--R 2 +--R 2c +--R Type: Expression(Integer) +--E 164 + +--S 165 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 465 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) ----------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 465 +r0:=2*e*x+1/2*(2*c*d-b*e)*log(a+b*x+c*x^2)/c-e*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c +--R +--R +--R (2) +--R +-----------+ +--R | 2 2c x + b +--R - 2e\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R (- b e + 2c d)log(c x + b x + a) + 4c e x +--R / +--R 2c +--R Type: Expression(Integer) +--E 167 + +--S 168 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 465 +t0:=(b+2*c*x)/(a+b*x+c*x^2) +--R +--R +--R 2c x + b +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 169 + +--S 170 of 465 +r0:=log(a+b*x+c*x^2) +--R +--R +--R 2 +--R (2) log(c x + b x + a) +--R Type: Expression(Integer) +--E 170 + +--S 171 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 465 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------- +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 172 + +--S 173 of 465 +r0:=-(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)+1/2*(2*c*d-b*e)*log(a+b*x+_ + c*x^2)/(c*d^2-b*d*e+a*e^2)+e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-_ + 4*a*c)/(c*d^2-b*d*e+a*e^2) +--R +--R +--R (2) +--R +-----------+ +--R | 2 2c x + b 2 +--R 2e\|- 4a c + b atanh(--------------) + (- b e + 2c d)log(c x + b x + a) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R (2b e - 4c d)log(e x + d) +--R / +--R 2 2 +--R 2a e - 2b d e + 2c d +--R Type: Expression(Integer) +--E 173 + +--S 174 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 465 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 of 465 +r0:=(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x))-(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2+1/2*(2*c^2*d^2+_ + b^2*e^2-2*c*e*(b*d+a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2+_ + e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/_ + (c*d^2-b*d*e+a*e^2)^2 +--R +--R +--R (2) +--R +-----------+ +--R 3 2 2 2 | 2 +--R ((- 2b e + 4c d e )x - 2b d e + 4c d e)\|- 4a c + b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 2 2 2 +--R ((- 2a c + b )e - 2b c d e + 2c d e)x + (- 2a c + b )d e +--R + +--R 2 2 3 +--R - 2b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 2 2 2 2 +--R ((4a c - 2b )e + 4b c d e - 4c d e)x + (4a c - 2b )d e + 4b c d e +--R + +--R 2 3 +--R - 4c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (4a c + 2b )d e - 6b c d e + 4c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R Type: Expression(Integer) +--E 176 + +--S 177 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 465 +t0:=(b+2*c*x)/((d+e*x)^3*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 178 + +--S 179 of 465 +r0:=1/2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))-(2*c*d-b*e)*(c^2*d^2+_ + b^2*e^2-c*e*(b*d+3*a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*(2*c*d-_ + b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+_ + a*e^2)^3+e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/(c*d^2-b*d*e+a*e^2)^3 +--R +--R +--R (2) +--R 2 5 4 2 2 3 2 +--R ((- 2a c + 2b )e - 6b c d e + 6c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 +--R ((- 4a c + 4b )d e - 12b c d e + 12c d e )x + (- 2a c + 2b )d e +--R + +--R 3 2 2 4 +--R - 6b c d e + 6c d e +--R * +--R +-----------+ +--R | 2 2c x + b +--R \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((6a b c - 2b )d e + (- 12a c + 6b c)d e - 6b c d e + 4c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (3a b c - b )d e + (- 6a c + 3b c)d e - 3b c d e + 2c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 3 4 +--R ((- 12a b c + 4b )d e + (24a c - 12b c)d e + 12b c d e - 8c d e)x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 6a b c + 2b )d e + (12a c - 6b c)d e + 6b c d e - 4c d +--R * +--R log(e x + d) +--R + +--R 2 2 5 3 4 2 2 3 2 3 2 3 4 2 5 +--R ((- 4a c + 2a b )e - 2b d e + 6b c d e - 8b c d e + 4c d e)x - a b e +--R + +--R 2 2 4 3 2 3 2 2 3 2 +--R (- 2a c + 4a b )d e + (- 6a b c - 3b )d e + (4a c + 10b c)d e +--R + +--R 2 4 3 5 +--R - 13b c d e + 6c d +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R Type: Expression(Integer) +--E 179 + +--S 180 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 465 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 465 +r0:=4*e^3*(3*c*d-b*e)*x/c^2+2*e^4*x^2/c-(d+e*x)^4/(a+b*x+c*x^2)+_ + 2*e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(a+b*x+c*x^2)/c^3-_ + 4*e*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 3 2 2 +--R (- 12a b c + 4b c)e + (24a c - 12b c )d e + 12b c d e +--R + +--R 4 3 +--R - 8c d e +--R * +--R 2 +--R x +--R + +--R 2 4 4 2 3 3 2 2 2 2 +--R (- 12a b c + 4b )e + (24a b c - 12b c)d e + 12b c d e +--R + +--R 3 3 +--R - 8b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (- 12a b c + 4a b )e + (24a c - 12a b c)d e + 12a b c d e +--R + +--R 3 3 +--R - 8a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 2a c + 2b c)e - 6b c d e + 6c d e )x +--R + +--R 3 4 2 3 2 2 2 +--R ((- 2a b c + 2b )e - 6b c d e + 6b c d e )x +--R + +--R 2 2 4 3 2 2 2 +--R (- 2a c + 2a b )e - 6a b c d e + 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 4 4 2 4 3 3 3 +--R c e x + (- 2b c e + 8c d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((2a c - 4b c)e + 12b c d e - 6c d e )x +--R + +--R 4 2 3 3 3 3 4 +--R (- 4a b c e + 12a c d e - 4c d e)x - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 3 | 2 +--R (c x + b c x + a c )\|- 4a c + b +--R Type: Expression(Integer) +--E 182 + +--S 183 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 184 + +--S 185 of 465 +r0:=3*e^3*x/c-(d+e*x)^3/(a+b*x+c*x^2)+3/2*e^2*(2*c*d-b*e)*_ + log(a+b*x+c*x^2)/c^2-3*e*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 2 3 2 2 +--R ((12a c - 6b c)e + 12b c d e - 12c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((12a b c - 6b )e + 12b c d e - 12b c d e)x + (12a c - 6a b )e +--R + +--R 2 2 2 +--R 12a b c d e - 12a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- 3b c e + 6c d e )x + (- 3b e + 6b c d e )x - 3a b e +--R + +--R 2 +--R 6a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 3 2 2 2 3 2 2 2 3 +--R 4c e x + (6b c e - 6c d e )x + (6a c e - 6c d e)x - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 | 2 +--R (2c x + 2b c x + 2a c )\|- 4a c + b +--R Type: Expression(Integer) +--E 185 + +--S 186 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 187 + +--S 188 of 465 +r0:=-(d+e*x)^2/(a+b*x+c*x^2)+e^2*log(a+b*x+c*x^2)/c-2*e*(2*c*d-b*e)*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R ((2b c e - 4c d e)x + (2b e - 4b c d e)x + 2a b e - 4a c d e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 2 2 +--R ((c e x + b e x + a e )log(c x + b x + a) - c e x - 2c d e x - c d ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (c x + b c x + a c)\|- 4a c + b +--R Type: Expression(Integer) +--E 188 + +--S 189 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 465 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 190 + +--S 191 of 465 +r0:=(-d-e*x)/(a+b*x+c*x^2)-2*e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c) +--R +--R +--R (2) +--R +-----------+ +--R 2 2c x + b | 2 +--R (- 2c e x - 2b e x - 2a e)atanh(--------------) + (- e x - d)\|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R ---------------------------------------------------------------------------- +--R +-----------+ +--R 2 | 2 +--R (c x + b x + a)\|- 4a c + b +--R Type: Expression(Integer) +--E 191 + +--S 192 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 465 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^2 +--R +--R +--R 2c x + b +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 193 + +--S 194 of 465 +r0:=(-1)/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (2) - -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 194 + +--S 195 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 465 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 465 +r0:=(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))-e^2*(2*c*d-b*e)*log(d+e*x)/_ + (c*d^2-b*d*e+a*e^2)^2+1/2*e^2*(2*c*d-b*e)*log(a+b*x+c*x^2)/_ + (c*d^2-b*d*e+a*e^2)^2+e*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 2 3 2 2 +--R ((- 4a c + 2b c)e - 4b c d e + 4c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 4a b c + 2b )e - 4b c d e + 4b c d e)x + (- 4a c + 2a b )e +--R + +--R 2 2 2 +--R - 4a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 2 3 2 3 +--R (- b c e + 2c d e )x + (- b e + 2b c d e )x - a b e +--R + +--R 2 +--R 2a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 2 3 2 3 +--R (2b c e - 4c d e )x + (2b e - 4b c d e )x + 2a b e +--R + +--R 2 +--R - 4a c d e +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 +--R (2a c e - 2b c d e + 2c d e)x + 2a b e + (- 2a c - 2b )d e +--R + +--R 2 2 3 +--R 4b c d e - 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (2a c e - 4a b c d e + (4a c + 2b c)d e - 4b c d e + 2c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 +--R (2a b e - 4a b d e + (4a b c + 2b )d e - 4b c d e + 2b c d )x +--R + +--R 3 4 2 3 2 2 2 2 3 2 4 +--R 2a e - 4a b d e + (4a c + 2a b )d e - 4a b c d e + 2a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 197 + +--S 198 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 465 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + ((2a c + b )e + 4b c d e + c d )x +--R + +--R 2 2 2 3 +--R (2a b e + (4a c + 2b )d e + 2b c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (a e + 4a b d e + (2a c + b )d )x + (2a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 199 + +--S 200 of 465 +r0:=2*e^2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))+(-(b^2-4*a*c)*_ + (c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*_ + (a+b*x+c*x^2))-2*e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(d+e*x)/_ + (c*d^2-b*d*e+a*e^2)^3+e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*_ + log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3+2*e*(2*c*d-b*e)*(c^2*d^2+_ + b^2*e^2-c*e*(b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + ((c*d^2-b*d*e+a*e^2)^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 5 3 2 2 4 3 2 3 4 3 2 3 +--R ((6a b c - 2b c)e + (- 12a c + 6b c )d e - 6b c d e + 4c d e )x +--R + +--R 2 4 5 2 3 4 3 2 3 +--R (6a b c - 2b )e + (- 6a b c + 4b c)d e - 12a c d e +--R + +--R 3 3 2 4 4 +--R - 2b c d e + 4c d e +--R * +--R 2 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (6a b c - 2a b )e + (- 12a c + 12a b c - 2b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 3 4 +--R (- 18a b c + 6b c)d e + (4a c - 6b c )d e + 4b c d e +--R * +--R x +--R + +--R 2 3 4 2 2 2 2 3 2 3 2 3 4 +--R (6a b c - 2a b )d e + (- 12a c + 6a b c)d e - 6a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((- a c + b c)e - 3b c d e + 3c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((- a b c + b )e + (- a c - 2b c)d e + 3c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (- a c + a b )e + (- 4a b c + b )d e + (3a c - 3b c)d e +--R + +--R 2 3 2 +--R 3b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (- a c + a b )d e - 3a b c d e + 3a c d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((2a c - 2b c)e + 6b c d e - 6c d e )x +--R + +--R 3 5 2 2 4 3 3 2 2 +--R ((2a b c - 2b )e + (2a c + 4b c)d e - 6c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (2a c - 2a b )e + (8a b c - 2b )d e + (- 6a c + 6b c)d e +--R + +--R 2 3 2 +--R - 6b c d e +--R * +--R x +--R + +--R 2 2 4 2 3 2 3 2 +--R (2a c - 2a b )d e + 6a b c d e - 6a c d e +--R * +--R log(e x + d) +--R + +--R 5 2 2 4 2 2 3 3 3 2 2 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d e )x +--R + +--R 2 2 5 3 4 2 2 2 3 +--R (a c - 2a b )e + (2a b c + 2b )d e + (2a c - 5b c)d e +--R + +--R 2 3 2 3 4 +--R 2b c d e + c d e +--R * +--R x +--R + +--R 2 5 2 4 3 2 3 2 2 3 2 +--R - a b e + 3a c d e + (- 2a b c + b )d e + (2a c - 3b c)d e +--R + +--R 2 4 3 5 +--R 3b c d e - c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 7 2 6 2 2 2 2 5 2 3 3 4 +--R a c e - 3a b c d e + (3a c + 3a b c)d e + (- 6a b c - b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (3a c + 3b c )d e - 3b c d e + c d e +--R * +--R 3 +--R x +--R + +--R 3 7 3 2 2 6 3 2 5 2 2 2 4 3 4 +--R a b e + (a c - 3a b )d e + 3a b d e + (3a c - 3a b c - b )d e +--R + +--R 2 3 4 3 3 5 2 3 6 4 7 +--R (- 3a b c + 2b c)d e + 3a c d e - 2b c d e + c d +--R * +--R 2 +--R x +--R + +--R 4 7 3 6 3 2 5 2 3 3 4 +--R a e - 2a b d e + 3a c d e + (- 3a b c + 2a b )d e +--R + +--R 2 2 2 4 4 3 3 5 2 3 2 2 6 3 7 +--R (3a c - 3a b c - b )d e + 3b c d e + (a c - 3b c )d e + b c d +--R * +--R x +--R + +--R 4 6 3 2 5 3 2 2 3 4 2 3 4 3 +--R a d e - 3a b d e + (3a c + 3a b )d e + (- 6a b c - a b )d e +--R + +--R 2 2 2 5 2 2 6 3 7 +--R (3a c + 3a b c)d e - 3a b c d e + a c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 200 + +--S 201 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 465 +t0:=(b+2*c*x)*(d+e*x)^5/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R 2c e x + (b e + 10c d e )x + (5b d e + 20c d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10b d e + 20c d e )x + (10b d e + 10c d e)x + (5b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 202 + +--S 203 of 465 +r0:=5*e^3*(3*c^2*d^2+b^2*e^2-c*e*(2*b*d+3*a*e))*x/(c^2*(b^2-4*a*c))+_ + 5/2*e^4*(2*c*d-b*e)*x^2/(c*(b^2-4*a*c))-1/2*(d+e*x)^5/(a+b*x+c*x^2)^2-_ + 5/2*e*(d+e*x)^3*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+_ + 5*e*(2*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(b*d-3*a*e)-6*a*c^2*e^3*(2*b*d+a*e)+_ + 2*b^2*c*e^3*(b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*(b^2-_ + 4*a*c)^(3/2))+5/2*e^4*(2*c*d-b*e)*log(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (60a c - 60a b c + 10b c )e + (120a b c - 20b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R - 120a c d e + 40b c d e - 20c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (120a b c - 120a b c + 20b c)e + (240a b c - 40b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R - 240a b c d e + 80b c d e - 40b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (120a c - 60a b c - 40a b c + 10b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (240a b c + 80a b c - 20b c)d e + (- 240a c - 120a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (80a b c + 40b c )d e + (- 40a c - 20b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (120a b c - 120a b c + 20a b )e + (240a b c - 40a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R - 240a b c d e + 80a b c d e - 40a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (60a c - 60a b c + 10a b )e + (120a b c - 20a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R - 120a c d e + 40a b c d e - 20a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 20a b c + 5b c )e + (40a c - 10b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 40a b c + 10b c)e + (80a b c - 20b c )d e )x +--R + +--R 2 2 3 5 5 +--R (- 40a b c - 10a b c + 5b )e +--R + +--R 2 3 2 2 4 4 +--R (80a c + 20a b c - 10b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 40a b c + 10a b )e + (80a b c - 20a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 20a b c + 5a b )e + (40a c - 10a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 2 3 5 5 +--R (16a c - 4b c )e x +--R + +--R 3 3 2 5 4 2 3 4 4 2 3 +--R (55a b c - 15b c )e + (- 60a c + 25b c )d e - 30b c d e +--R + +--R 5 3 2 +--R 30c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (50a c + 20a b c - 10b c)e + (- 20a b c + 20b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (- 100a c - 20b c )d e + 40b c d e + 10c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 3 2 3 +--R (65a b c - 20a b c)e + (- 40a c + 40a b c )d e - 90a b c d e +--R + +--R 4 2 3 3 2 4 4 +--R (- 20a c + 20b c )d e + 15b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 5 2 2 4 2 3 2 3 +--R (30a c - 10a b c)e + 20a b c d e - 60a c d e +--R + +--R 4 2 3 4 +--R (- 10a c + 10b c )d e +--R * +--R x +--R + +--R 2 3 3 2 3 4 4 2 3 5 +--R - 10a c d e + 5a b c d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 6 2 5 4 5 3 4 3 2 5 2 4 4 3 2 +--R (8a c - 2b c )x + (16a b c - 4b c )x + (16a c + 4a b c - 2b c )x +--R + +--R 2 4 3 3 3 4 2 2 3 +--R (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 203 + +--S 204 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 465 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 205 + +--S 206 of 465 +r0:=2*e^3*(2*c*d-b*e)*x/(c*(b^2-4*a*c))-1/2*(d+e*x)^4/(a+b*x+c*x^2)^2-_ + 2*e*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+_ + 2*e*(2*c*d-b*e)*(2*c^2*d^2-b^2*e^2-2*c*e*(b*d-3*a*e))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(c^2*(b^2-4*a*c)^(3/2))+e^4*log(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 3 3 2 4 4 3 4 2 2 5 3 4 +--R ((24a b c - 4b c )e - 48a c d e + 24b c d e - 16c d e)x +--R + +--R 2 2 4 4 3 3 2 3 2 2 4 3 3 +--R ((48a b c - 8b c)e - 96a b c d e + 48b c d e - 32b c d e)x +--R + +--R 2 2 3 5 4 2 3 2 2 3 +--R (48a b c + 16a b c - 4b )e + (- 96a c - 48a b c )d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (48a b c + 24b c )d e + (- 32a c - 16b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 2 2 2 2 3 3 +--R ((48a b c - 8a b )e - 96a b c d e + 48a b c d e - 32a b c d e)x +--R + +--R 3 2 3 4 3 2 3 2 2 2 2 2 3 3 +--R (24a b c - 4a b )e - 48a c d e + 24a b c d e - 16a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 4 4 2 3 4 3 +--R (8a c - 2b c )e x + (16a b c - 4b c)e x +--R + +--R 2 2 2 4 4 2 2 3 4 +--R (16a c + 4a b c - 2b )e x + (16a b c - 4a b )e x +--R + +--R 3 2 2 4 +--R (8a c - 2a b )e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 12a c + 5b c )e - 12b c d e + 16c d e )x +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (- 4a b c + 4b c)e + (- 40a c - 8b c )d e + 20b c d e +--R + +--R 4 3 +--R 8c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 2 3 3 2 2 2 2 +--R (- 8a c + 8a b c)e - 36a b c d e + (- 16a c + 10b c )d e +--R + +--R 3 3 +--R 12b c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 2 2 3 2 2 3 +--R (4a b c e - 24a c d e - 4a b c d e + (- 8a c + 8b c )d e)x +--R + +--R 2 2 2 2 2 3 3 2 2 4 +--R - 8a c d e + 4a b c d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 4 4 3 3 3 2 4 2 3 4 2 2 +--R (8a c - 2b c )x + (16a b c - 4b c )x + (16a c + 4a b c - 2b c )x +--R + +--R 2 3 3 2 3 3 2 2 2 +--R (16a b c - 4a b c )x + 8a c - 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 206 + +--S 207 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 208 + +--S 209 of 465 +r0:=-1/2*(d+e*x)^3/(a+b*x+c*x^2)^2-3/2*e*(d+e*x)*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + ((b^2-4*a*c)*(a+b*x+c*x^2))+6*e*(c*d^2-b*d*e+a*e^2)*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 2 3 2 2 3 2 4 +--R (- 12a c e + 12b c d e - 12c d e)x +--R + +--R 3 2 2 2 2 3 +--R (- 24a b c e + 24b c d e - 24b c d e)x +--R + +--R 2 2 3 3 2 +--R (- 24a c - 12a b )e + (24a b c + 12b )d e +--R + +--R 2 2 2 +--R (- 24a c - 12b c)d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 3 3 2 2 +--R (- 24a b e + 24a b d e - 24a b c d e)x - 12a e + 12a b d e +--R + +--R 2 2 +--R - 12a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 4 2 3 2 2 2 3 +--R (- 3b c e + 6c d e )x + ((- 10a c - 2b )e + 6b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 +--R (- 9a b e + (- 12a c + 3b )d e + 9b c d e)x +--R + +--R 2 3 2 2 2 2 2 2 +--R (- 6a e - 6a b d e + (- 6a c + 6b )d e)x - 6a d e + 3a b d e +--R + +--R 2 3 +--R (- 4a c + b )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 209 + +--S 210 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 465 +r0:=-1/2*(d+e*x)^2/(a+b*x+c*x^2)^2-e*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*_ + (a+b*x+c*x^2))+2*e*(2*c*d-b*e)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 2 2 3 4 2 2 2 3 +--R (4b c e - 8c d e)x + (8b c e - 16b c d e)x +--R + +--R 3 2 2 2 2 +--R ((8a b c + 4b )e + (- 16a c - 8b c)d e)x +--R + +--R 2 2 2 2 2 +--R (8a b e - 16a b c d e)x + 4a b e - 8a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 2 +--R (- 2b c e + 4c d e)x + ((- 8a c - b )e + 6b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 6a b e + (- 4a c + 4b )d e)x - 4a e + 2a b d e + (- 4a c + b )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 212 + +--S 213 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 465 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 214 + +--S 215 of 465 +r0:=1/2*(-d-e*x)/(a+b*x+c*x^2)^2-1/2*e*(b+2*c*x)/((b^2-4*a*c)*_ + (a+b*x+c*x^2))+2*c*e*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 2 +--R (- 4c e x - 8b c e x + (- 8a c - 4b c)e x - 8a b c e x - 4a c e) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 2 +--R (2c e x + 3b c e x + (- 2a c + 2b )e x + a b e + (- 4a c + b )d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (8a c - 2b c )x + (16a b c - 4b c)x + (16a c + 4a b c - 2b )x +--R + +--R 2 3 3 2 2 +--R (16a b c - 4a b )x + 8a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 215 + +--S 216 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 465 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 217 + +--S 218 of 465 +r0:=(-1/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 1 +--R - +--R 2 +--R (2) - -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 218 + +--S 219 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 465 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^3) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 7 2 3 6 2 2 2 5 +--R c e x + (3b c e + c d)x + ((3a c + 3b c)e + 3b c d)x +--R + +--R 3 2 2 4 +--R ((6a b c + b )e + (3a c + 3b c)d)x +--R + +--R 2 2 3 3 2 2 2 2 +--R ((3a c + 3a b )e + (6a b c + b )d)x + (3a b e + (3a c + 3a b )d)x +--R + +--R 3 2 3 +--R (a e + 3a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 220 + +--S 221 of 465 +r0:=1/2*(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)-1/2*e*(3*b^2*c*d*e-8*a*c^2*d*e-_ + 2*b^3*e^2-b*c*(c*d^2-7*a*e^2)-2*c*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*(a+b*x+c*x^2))-e*(2*c^4*d^4-b^4*e^4-_ + 4*c^3*d^2*e*(b*d-3*a*e)-6*a*c^2*e^3*(2*b*d+a*e)+2*b^2*c*e^3*_ + (b*d+3*a*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((b^2-4*a*c)^(3/2)*_ + (c*d^2-b*d*e+a*e^2)^3)-e^4*(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+_ + 1/2*e^4*(2*c*d-b*e)*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3 +--R +--R +--R (2) +--R 2 4 2 3 4 2 5 4 3 3 4 +--R (- 12a c + 12a b c - 2b c )e + (- 24a b c + 4b c )d e +--R + +--R 5 2 3 5 3 2 6 4 +--R 24a c d e - 8b c d e + 4c d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 5 2 3 4 2 4 +--R (- 24a b c + 24a b c - 4b c)e + (- 48a b c + 8b c )d e +--R + +--R 4 2 3 2 4 3 2 5 4 +--R 48a b c d e - 16b c d e + 8b c d e +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 2 4 6 5 +--R (- 24a c + 12a b c + 8a b c - 2b )e +--R + +--R 2 3 3 2 5 4 2 4 2 3 2 3 +--R (- 48a b c - 16a b c + 4b c)d e + (48a c + 24a b c )d e +--R + +--R 4 3 3 3 2 5 2 4 4 +--R (- 16a b c - 8b c )d e + (8a c + 4b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 5 2 2 2 4 4 +--R (- 24a b c + 24a b c - 4a b )e + (- 48a b c + 8a b c)d e +--R + +--R 2 3 2 3 2 3 3 2 4 4 +--R 48a b c d e - 16a b c d e + 8a b c d e +--R * +--R x +--R + +--R 4 2 3 2 2 4 5 3 2 2 3 4 +--R (- 12a c + 12a b c - 2a b )e + (- 24a b c + 4a b c)d e +--R + +--R 3 3 2 3 2 3 3 2 2 4 4 +--R 24a c d e - 8a b c d e + 4a c d e +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((- 4a b c + b c )e + (8a c - 2b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((- 8a b c + 2b c)e + (16a b c - 4b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((- 8a b c - 2a b c + b )e + (16a c + 4a b c - 2b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((- 8a b c + 2a b )e + (16a b c - 4a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (- 4a b c + a b )e + (8a c - 2a b c)d e +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 3 2 5 4 2 3 4 4 +--R ((8a b c - 2b c )e + (- 16a c + 4b c )d e )x +--R + +--R 2 2 4 5 3 3 2 4 3 +--R ((16a b c - 4b c)e + (- 32a b c + 8b c )d e )x +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 2 +--R ((16a b c + 4a b c - 2b )e + (- 32a c - 8a b c + 4b c)d e )x +--R + +--R 2 2 4 5 2 2 3 4 +--R ((16a b c - 4a b )e + (- 32a b c + 8a b c)d e )x +--R + +--R 3 2 3 5 3 2 2 2 4 +--R (8a b c - 2a b )e + (- 16a c + 4a b c)d e +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 5 3 3 2 4 +--R (6a c - 2a b c )e + (- 4a b c + 2b c )d e +--R + +--R 4 2 3 2 3 4 3 2 5 4 +--R (4a c - 4b c )d e + 4b c d e - 2c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 4 4 +--R (13a b c - 4a b c)e + (- 8a c - 8a b c + 4b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 4 4 +--R (18a b c - 9b c )d e + (- 8a c + 8b c )d e - 3b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 2 2 5 4 +--R (10a c + 4a b c - 2a b )e + (- 20a b c + 2b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (12a c + 12a b c - 6b c)d e + (- 12a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (2a c - 2b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (11a b c - 3a b )e + (- 12a c - 11a b c + 4a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (30a b c - 5a b c - b )d e + (- 16a c - 6a b c + 3b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (11a b c - 3b c )d e + (- 4a c + b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 4 3 3 2 2 6 3 3 2 3 2 5 +--R (8a c - 2a b c )e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 4 +--R (24a c + 18a b c - 6a b c )d e +--R + +--R 2 4 3 3 5 2 3 3 +--R (- 48a b c + 4a b c + 2b c )d e +--R + +--R 2 5 2 4 4 3 4 2 5 3 4 5 +--R (24a c + 18a b c - 6b c )d e + (- 24a b c + 6b c )d e +--R + +--R 6 2 5 6 +--R (8a c - 2b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 6 3 2 2 2 4 5 +--R (16a b c - 4a b c)e + (- 48a b c + 12a b c)d e +--R + +--R 3 3 2 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b c)d e +--R + +--R 2 2 3 4 2 6 3 3 +--R (- 96a b c + 8a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 4 2 2 4 4 3 5 +--R (48a b c + 36a b c - 12b c )d e + (- 48a b c + 12b c )d e +--R + +--R 5 3 4 6 +--R (16a b c - 4b c )d +--R * +--R 3 +--R x +--R + +--R 5 2 4 2 3 4 6 4 2 3 3 2 5 5 +--R (16a c + 4a b c - 2a b )e + (- 48a b c - 12a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 4 +--R (48a c + 60a b c + 6a b c - 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 3 +--R (- 96a b c - 40a b c + 8a b c + 2b )d e +--R + +--R 3 4 2 2 3 4 2 6 4 2 +--R (48a c + 60a b c + 6a b c - 6b c)d e +--R + +--R 2 4 3 3 5 2 5 2 5 2 4 4 3 6 +--R (- 48a b c - 12a b c + 6b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 3 6 4 2 3 4 5 +--R (16a b c - 4a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 3 2 5 2 4 +--R (48a b c + 36a b c - 12a b )d e +--R + +--R 3 2 2 2 4 6 3 3 +--R (- 96a b c + 8a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 2 3 4 2 5 +--R (48a b c + 36a b c - 12a b c)d e + (- 48a b c + 12a b c )d e +--R + +--R 2 4 3 3 6 +--R (16a b c - 4a b c )d +--R * +--R x +--R + +--R 6 5 2 6 5 4 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 5 2 4 2 3 4 2 4 4 2 3 3 2 5 3 3 +--R (24a c + 18a b c - 6a b )d e + (- 48a b c + 4a b c + 2a b )d e +--R + +--R 4 3 3 2 2 2 4 4 2 3 3 2 3 2 5 +--R (24a c + 18a b c - 6a b c)d e + (- 24a b c + 6a b c )d e +--R + +--R 3 4 2 2 3 6 +--R (8a c - 2a b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 221 + +--S 222 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 465 +t0:=(b+2*c*x)*(d+e*x)^4*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 223 + +--S 224 of 465 +r0:=1/1680*(128*c^4*d^4+105*b^4*e^4-16*c^3*d^2*e*(16*b*d+93*a*e)-_ + 4*b^2*c*e^3*(109*b*d+101*a*e)+4*c^2*e^2*(141*b^2*d^2+372*a*b*d*e+_ + 16*a^2*e^2))*(a+b*x+c*x^2)^(3/2)/c^4+1/35*(4*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(b*d+2*a*e))*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)/c^2+2/21*(2*c*d-b*e)*_ + (d+e*x)^3*(a+b*x+c*x^2)^(3/2)/c+2/7*(d+e*x)^4*(a+b*x+c*x^2)^(3/2)-_ + 1/280*e*(9*b^3*d*e^2+8*a*c*e*(17*c*d^2-4*a*e^2)-4*b*c*d*(2*c*d^2+_ + 15*a*e^2)-b^2*(22*c*d^2*e-12*a*e^3)-(2*c*d-b*e)*(8*c^2*d^2+_ + 21*b^2*e^2-4*c*e*(2*b*d+19*a*e))*x)*(a+b*x+c*x^2)^(3/2)/c^3-_ + 1/256*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(8*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(2*b*d+a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/_ + c^(11/2)+1/128*(b^2-4*a*c)*e*(2*c*d-b*e)*(8*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(2*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 3 3 2 3 2 5 7 4 +--R (- 6720a b c + 8400a b c - 2940a b c + 315b )e +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (13440a c - 30240a b c + 12600a b c - 1470b c)d e +--R + +--R 2 4 3 3 5 2 2 2 +--R (40320a b c - 20160a b c + 2520b c )d e +--R + +--R 2 5 2 4 4 3 3 +--R (- 26880a c + 13440a b c - 1680b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 6 4 6 5 4 6 3 5 +--R 7680c e x + (5120b c e + 35840c d e )x +--R + +--R 5 2 4 4 5 3 6 2 2 4 +--R ((1536a c - 256b c )e + 25088b c d e + 64512c d e )x +--R + +--R 4 3 3 4 5 2 4 3 +--R (- 1408a b c + 288b c )e + (8960a c - 1344b c )d e +--R + +--R 5 2 2 6 3 +--R 48384b c d e + 53760c d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 4 2 4 +--R (- 2048a c + 1984a b c - 336b c )e +--R + +--R 4 3 3 3 5 2 4 2 2 +--R (- 8064a b c + 1568b c )d e + (21504a c - 2688b c )d e +--R + +--R 5 3 6 4 +--R 44800b c d e + 17920c d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 5 4 +--R (4672a b c - 2912a b c + 420b c)e +--R + +--R 2 4 2 3 4 2 3 +--R (- 13440a c + 12096a b c - 1960b c )d e +--R + +--R 4 3 3 2 2 5 2 4 3 +--R (- 18816a b c + 3360b c )d e + (26880a c - 2240b c )d e +--R + +--R 5 4 +--R 17920b c d +--R * +--R x +--R + +--R 3 3 2 2 2 4 6 4 +--R (4096a c - 10976a b c + 5040a b c - 630b )e +--R + +--R 2 3 3 2 5 3 +--R (36288a b c - 21280a b c + 2940b c)d e +--R + +--R 2 4 2 3 4 2 2 2 +--R (- 43008a c + 33600a b c - 5040b c )d e +--R + +--R 4 3 3 3 5 4 +--R (- 22400a b c + 3360b c )d e + 17920a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 26880c \|c +--R Type: Expression(Integer) +--E 224 + +--S 225 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 465 +r0:=1/480*(2*c*d-b*e)*(32*c^2*d^2+35*b^2*e^2-4*c*e*(8*b*d+27*a*e))*_ + (a+b*x+c*x^2)^(3/2)/c^3+1/10*(2*c*d-b*e)*(d+e*x)^2*_ + (a+b*x+c*x^2)^(3/2)/c+1/3*(d+e*x)^3*(a+b*x+c*x^2)^(3/2)+1/80*e*_ + (3*b^2*d*e-28*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+7*b^2*e^2-4*c*e*_ + (2*b*d+5*a*e))*x)*(a+b*x+c*x^2)^(3/2)/c^2-1/512*(b^2-4*a*c)^2*e*_ + (24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)+1/256*(b^2-4*a*c)*e*(24*c^2*d^2+_ + 7*b^2*e^2-4*c*e*(6*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 3 +--R (960a c - 2160a b c + 900a b c - 105b )e +--R + +--R 2 3 3 2 5 2 +--R (5760a b c - 2880a b c + 360b c)d e +--R + +--R 2 4 2 3 4 2 2 +--R (- 5760a c + 2880a b c - 360b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 5 3 5 4 3 5 2 4 +--R 2560c e x + (1792b c e + 9216c d e )x +--R + +--R 4 2 3 3 4 2 5 2 3 +--R ((640a c - 96b c )e + 6912b c d e + 11520c d e)x +--R + +--R 3 3 2 3 4 2 3 2 +--R (- 576a b c + 112b c )e + (3072a c - 384b c )d e +--R + +--R 4 2 5 3 +--R 9600b c d e + 5120c d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 4 3 3 3 2 2 +--R (- 960a c + 864a b c - 140b c)e + (- 2688a b c + 480b c )d e +--R + +--R 4 2 3 2 4 3 +--R (5760a c - 480b c )d e + 5120b c d +--R * +--R x +--R + +--R 2 2 3 5 3 +--R (2592a b c - 1520a b c + 210b )e +--R + +--R 2 3 2 2 4 2 3 3 2 2 +--R (- 6144a c + 4800a b c - 720b c)d e + (- 4800a b c + 720b c )d e +--R + +--R 4 3 +--R 5120a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 227 + +--S 228 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R +--------------+ +--R 2 3 2 2 2 2 | 2 +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|c x + b x + a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 465 +r0:=1/60*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*(a+b*x+c*x^2)^(3/2)/c^2+_ + 2/5*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)+1/10*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/c-1/64*(b^2-4*a*c)^2*e*(2*c*d-b*e)*atanh(1/2*(b+_ + 2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+1/32*(b^2-4*a*c)*e*(2*c*d-_ + b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 2 2 3 5 2 2 3 2 2 4 +--R ((240a b c - 120a b c + 15b )e + (- 480a c + 240a b c - 30b c)d e) +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 4 2 4 3 2 4 3 +--R 384c e x + (288b c e + 960c d e)x +--R + +--R 3 2 2 2 3 4 2 2 +--R ((128a c - 16b c )e + 800b c d e + 640c d )x +--R + +--R 2 3 2 3 2 2 3 2 +--R ((- 112a b c + 20b c)e + (480a c - 40b c )d e + 640b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 +--R (- 256a c + 200a b c - 30b )e + (- 400a b c + 60b c)d e + 640a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 960c \|c +--R Type: Expression(Integer) +--E 230 + +--S 231 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 of 465 +t0:=(b+2*c*x)*(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (1) (2c e x + (b e + 2c d)x + b d)\|c x + b x + a +--R Type: Expression(Integer) +--E 232 + +--S 233 of 465 +r0:=1/12*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/c+1/2*(d+e*x)*(a+b*x+c*x^2)^(3/2)-_ + 1/64*(b^2-4*a*c)^2*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(5/2)+1/32*(b^2-4*a*c)*e*(b+2*c*x)*_ + sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 4 2c x + b +--R (- 48a c + 24a b c - 3b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 3 2 3 2 2 2 2 +--R 96c e x + (80b c e + 128c d)x + ((48a c - 4b c)e + 128b c d)x +--R + +--R 3 2 +--R (- 40a b c + 6b )e + 128a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 233 + +--S 234 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R (1) (2c x + b)\|c x + b x + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 465 +r0:=2/3*(a+b*x+c*x^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (2c x + 2b x + 2a)\|c x + b x + a +--R (2) ------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 238 + +--S 239 of 465 +r0:=1/4*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^3*sqrt(c))-(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-_ + b*d*e+a*e^2)/e^3-1/2*(4*c*d-3*b*e-2*c*e*x)*sqrt(a+b*x+c*x^2)/e^2 +--R +--R +--R (2) +--R 2 2 2 2 2c x + b +--R ((4a c + b )e - 8b c d e + 8c d )atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R +-+ | 2 2 +--R (- 4b e + 8c d)\|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +--------------+ +--R 2 2 +-+ | 2 +--R (4c e x + 6b e - 8c d e)\|c \|c x + b x + a +--R / +--R 3 +-+ +--R 4e \|c +--R Type: Expression(Integer) +--E 239 + +--S 240 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 241 + +--S 242 of 465 +r0:=-2*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*_ + sqrt(c)/e^3+1/2*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*atanh(1/2*_ + (b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (e^3*sqrt(c*d^2-b*d*e+a*e^2))+(4*c*d-b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/_ + (e^2*(d+e*x)) +--R +--R +--R (2) +--R +-------------------+ +--R 2 2 +-+ | 2 2 +--R ((4b e - 8c d e)x + 4b d e - 8c d )\|c \|a e - b d e + c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 +--R ((- 4a c - b )e + 8b c d e - 8c d e)x + (- 4a c - b )d e +--R + +--R 2 2 3 +--R 8b c d e - 8c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R 2 2 | 2 2 | 2 +--R (4c e x - 2b e + 8c d e)\|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 4 3 | 2 2 +--R (2e x + 2d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 242 + +--S 243 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 244 + +--S 245 of 465 +r0:=1/2*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+_ + 2*c^(3/2)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/e^3-_ + 1/8*(2*c*d-b*e)*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*atanh(1/2*_ + (b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (e^3*(c*d^2-b*d*e+a*e^2)^(3/2))-1/4*(8*c^2*d^2-6*b*c*d*e-b^2*e^2+_ + 8*a*c*e^2+2*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-_ + b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 4 3 2 2 2 2 +--R (16a c e - 16b c d e + 16c d e )x +--R + +--R 3 2 2 2 3 2 2 3 2 4 +--R (32a c d e - 32b c d e + 32c d e)x + 16a c d e - 16b c d e + 16c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 3 3 2 2 +--R ((- 12a b c + b )e + (24a c + 6b c)d e - 24b c d e + 16c d e )x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 24a b c + 2b )d e + (48a c + 12b c)d e - 48b c d e +--R + +--R 3 4 +--R 32c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 12a b c + b )d e + (24a c + 6b c)d e - 24b c d e + 16c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 2 2 2 4 +--R ((- 16a c - 2b )e + 24b c d e - 24c d e )x - 4a b e +--R + +--R 2 3 2 2 2 3 +--R (- 8a c + 2b )d e + 12b c d e - 16c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 7 6 2 5 2 6 2 5 3 4 +--R (8a e - 8b d e + 8c d e )x + (16a d e - 16b d e + 16c d e )x +--R + +--R 2 5 3 4 4 3 +--R 8a d e - 8b d e + 8c d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 245 + +--S 246 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 247 + +--S 248 of 465 +r0:=1/16*(b^2-4*a*c)^2*e*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+_ + 1/12*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*sqrt(a+b*x+c*x^2)/_ + (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+1/24*(2*c*d-b*e)*(8*c^2*d^2-_ + 3*b^2*e^2-4*c*e*(2*b*d-5*a*e))*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-_ + b*d*e+a*e^2)^2*(d+e*x))-1/3*(4*c*d+b*e+6*c*e*x)*sqrt(a+b*x+c*x^2)/_ + (e^2*(d+e*x)^3) +--R +--R +--R (2) +--R 2 2 2 4 4 3 2 2 2 4 3 2 +--R (- 48a c + 24a b c - 3b )e x + (- 144a c + 72a b c - 9b )d e x +--R + +--R 2 2 2 4 2 2 2 2 2 4 3 +--R (- 144a c + 72a b c - 9b )d e x + (- 48a c + 24a b c - 3b )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 2 2 2 2 3 3 2 +--R ((- 40a b c + 6b )e + (80a c + 4b c)d e - 48b c d e + 32c d )x +--R + +--R 2 2 3 3 2 2 2 2 +--R (- 48a c - 4a b )e + (32a b c + 16b )d e + (48a c - 60b c)d e +--R + +--R 2 3 +--R 32b c d +--R * +--R x +--R + +--R 2 3 2 2 2 3 2 2 3 +--R - 16a b e + (- 16a c + 28a b )d e + (- 24a b c - 6b )d e + 32a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 2 7 6 2 2 5 3 4 2 4 3 3 +--R (48a e - 96a b d e + (96a c + 48b )d e - 96b c d e + 48c d e )x +--R + +--R 2 6 2 5 2 3 4 4 3 +--R 144a d e - 288a b d e + (288a c + 144b )d e - 288b c d e +--R + +--R 2 5 2 +--R 144c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 2 4 3 5 2 +--R 144a d e - 288a b d e + (288a c + 144b )d e - 288b c d e +--R + +--R 2 6 +--R 144c d e +--R * +--R x +--R + +--R 2 3 4 4 3 2 5 2 6 2 7 +--R 48a d e - 96a b d e + (96a c + 48b )d e - 96b c d e + 48c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 248 + +--S 249 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 465 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 250 + +--S 251 of 465 +r0:=5/128*(b^2-4*a*c)^2*e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (c*d^2-b*d*e+a*e^2)^(7/2)+1/24*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3)+_ + 1/96*(2*c*d-b*e)*(8*c^2*d^2-5*b^2*e^2-4*c*e*(2*b*d-7*a*e))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^2)+_ + 1/192*(32*c^4*d^4-15*b^4*e^4-16*c^3*d^2*e*(4*b*d-9*a*e)+_ + 20*b^2*c*e^3*(b*d+5*a*e)+4*c^2*e^2*(3*b^2*d^2-36*a*b*d*e-32*a^2*e^2))*_ + sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)^3*(d+e*x))-1/4*(2*c*d+b*e+_ + 4*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^4) +--R +--R +--R (2) +--R 2 2 3 5 6 +--R (240a b c - 120a b c + 15b )e +--R + +--R 2 3 2 2 4 5 +--R (- 480a c + 240a b c - 30b c)d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 5 5 +--R (960a b c - 480a b c + 60b )d e +--R + +--R 2 3 2 2 4 2 4 +--R (- 1920a c + 960a b c - 120b c)d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 4 +--R (1440a b c - 720a b c + 90b )d e +--R + +--R 2 3 2 2 4 3 3 +--R (- 2880a c + 1440a b c - 180b c)d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 5 3 3 +--R (960a b c - 480a b c + 60b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (- 1920a c + 960a b c - 120b c)d e +--R * +--R x +--R + +--R 2 2 3 5 4 2 2 3 2 2 4 5 +--R (240a b c - 120a b c + 15b )d e + (- 480a c + 240a b c - 30b c)d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 2 2 4 5 2 3 4 +--R (- 256a c + 200a b c - 30b )e + (- 288a b c + 40b c)d e +--R + +--R 3 2 2 2 3 3 3 2 4 4 +--R (288a c + 24b c )d e - 128b c d e + 64c d e +--R * +--R 3 +--R x +--R + +--R 2 3 5 2 2 2 4 4 +--R (- 112a b c + 20a b )e + (- 544a c + 704a b c - 110b )d e +--R + +--R 2 3 2 3 3 2 2 3 2 +--R (- 1296a b c + 148b c)d e + (1152a c + 160b c )d e +--R + +--R 3 4 4 5 +--R - 544b c d e + 256c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 5 2 3 4 +--R (- 256a c - 16a b )e + (608a b c + 72a b )d e +--R + +--R 2 2 2 4 2 3 2 3 3 2 +--R (- 1152a c - 120a b c - 146b )d e + (64a b c + 528b c)d e +--R + +--R 3 2 2 4 3 5 +--R (544a c - 728b c )d e + 256b c d +--R * +--R x +--R + +--R 3 5 3 2 2 4 2 3 2 3 +--R - 96a b e + (- 64a c + 272a b )d e + (- 144a b c - 236a b )d e +--R + +--R 2 2 2 4 3 2 2 3 4 +--R (- 288a c + 528a b c + 30b )d e + (- 368a b c - 60b c)d e +--R + +--R 3 5 +--R 256a c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 3 10 2 9 2 2 2 8 +--R 384a e - 1152a b d e + (1152a c + 1152a b )d e +--R + +--R 3 3 7 2 2 4 6 2 5 5 +--R (- 2304a b c - 384b )d e + (1152a c + 1152b c)d e - 1152b c d e +--R + +--R 3 6 4 +--R 384c d e +--R * +--R 4 +--R x +--R + +--R 3 9 2 2 8 2 2 3 7 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 4 6 2 2 5 5 +--R (- 9216a b c - 1536b )d e + (4608a c + 4608b c)d e +--R + +--R 2 6 4 3 7 3 +--R - 4608b c d e + 1536c d e +--R * +--R 3 +--R x +--R + +--R 3 2 8 2 3 7 2 2 4 6 +--R 2304a d e - 6912a b d e + (6912a c + 6912a b )d e +--R + +--R 3 5 5 2 2 6 4 +--R (- 13824a b c - 2304b )d e + (6912a c + 6912b c)d e +--R + +--R 2 7 3 3 8 2 +--R - 6912b c d e + 2304c d e +--R * +--R 2 +--R x +--R + +--R 3 3 7 2 4 6 2 2 5 5 +--R 1536a d e - 4608a b d e + (4608a c + 4608a b )d e +--R + +--R 3 6 4 2 2 7 3 +--R (- 9216a b c - 1536b )d e + (4608a c + 4608b c)d e +--R + +--R 2 8 2 3 9 +--R - 4608b c d e + 1536c d e +--R * +--R x +--R + +--R 3 4 6 2 5 5 2 2 6 4 +--R 384a d e - 1152a b d e + (1152a c + 1152a b )d e +--R + +--R 3 7 3 2 2 8 2 2 9 +--R (- 2304a b c - 384b )d e + (1152a c + 1152b c)d e - 1152b c d e +--R + +--R 3 10 +--R 384c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 251 + +--S 252 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R 2c e x + (3b c e + 6c d e )x + ((2a c + b )e + 9b c d e + 6c d e)x +--R + +--R 3 2 2 2 2 3 3 +--R (a b e + (6a c + 3b )d e + 9b c d e + 2c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R (3a b d e + (6a c + 3b )d e + 3b c d )x + (3a b d e + (2a c + b )d )x +--R + +--R 3 +--R a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 465 +r0:=1/1024*(b^2-4*a*c)*e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*_ + (b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+3/2240*(2*c*d-b*e)*(16*c^2*d^2+_ + 21*b^2*e^2-4*c*e*(4*b*d+17*a*e))*(a+b*x+c*x^2)^(5/2)/c^3+3/56*(2*c*d-_ + b*e)*(d+e*x)^2*(a+b*x+c*x^2)^(5/2)/c+1/4*(d+e*x)^3*(a+b*x+c*x^2)^(5/2)+_ + 1/224*e*(5*b^2*d*e-36*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+9*b^2*e^2-_ + 4*c*e*(2*b*d+7*a*e))*x)*(a+b*x+c*x^2)^(5/2)/c^2+3/16384*(b^2-4*a*c)^3*_ + e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)-3/8192*(b^2-4*a*c)^2*e*(32*c^2*_ + d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 4 4 3 2 3 2 4 2 6 8 3 +--R (26880a c - 80640a b c + 50400a b c - 11760a b c + 945b )e +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (215040a b c - 161280a b c + 40320a b c - 3360b c)d e +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (- 215040a c + 161280a b c - 40320a b c + 3360b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 7 3 7 6 3 7 2 6 +--R 143360c e x + (256000b c e + 491520c d e )x +--R + +--R 6 2 5 3 6 2 7 2 5 +--R ((215040a c + 104960b c )e + 901120b c d e + 573440c d e)x +--R + +--R 5 3 4 3 6 2 5 2 +--R (144384a b c - 768b c )e + (786432a c + 385024b c )d e +--R + +--R 6 2 7 3 +--R 1089536b c d e + 229376c d +--R * +--R 4 +--R x +--R + +--R 2 5 2 4 4 3 3 +--R (17920a c - 6912a b c + 864b c )e +--R + +--R 5 3 4 2 6 2 5 2 +--R (569344a b c - 3072b c )d e + (1003520a c + 494592b c )d e +--R + +--R 6 3 +--R 458752b c d +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 3 +--R (- 22272a b c + 9088a b c - 1008b c )e +--R + +--R 2 5 2 4 4 3 2 +--R (98304a c - 30720a b c + 3584b c )d e +--R + +--R 5 3 4 2 6 2 5 3 +--R (817152a b c - 3584b c )d e + (458752a c + 229376b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (- 26880a c + 38208a b c - 12656a b c + 1260b c)e +--R + +--R 2 4 3 3 5 2 2 +--R (- 116736a b c + 43008a b c - 4480b c )d e +--R + +--R 2 5 2 4 4 3 2 5 3 +--R (215040a c - 43008a b c + 4480b c )d e + 458752a b c d +--R * +--R x +--R + +--R 3 3 2 3 2 5 7 3 +--R (84864a b c - 75488a b c + 21000a b c - 1890b )e +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 196608a c + 236544a b c - 71680a b c + 6720b c)d e +--R + +--R 2 4 3 3 5 2 2 2 5 3 +--R (- 236544a b c + 71680a b c - 6720b c )d e + 229376a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 573440c \|c +--R Type: Expression(Integer) +--E 254 + +--S 255 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x +--R + +--R 2 +--R a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 465 +r0:=1/96*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3+_ + 1/210*(24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*(a+b*x+c*x^2)^(5/2)/c^2+_ + 2/7*(d+e*x)^2*(a+b*x+c*x^2)^(5/2)+1/21*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(5/2)/c+1/512*(b^2-4*a*c)^3*e*(2*c*d-b*e)*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)-1/256*(b^2-4*a*c)^2*e*_ + (2*c*d-b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 3 3 2 3 2 5 7 2 +--R (6720a b c - 5040a b c + 1260a b c - 105b )e +--R + +--R 3 4 2 2 3 4 2 6 +--R (- 13440a c + 10080a b c - 2520a b c + 210b c)d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 6 2 6 5 2 6 5 +--R 15360c e x + (28160b c e + 35840c d e)x +--R + +--R 5 2 4 2 5 6 2 4 +--R ((24576a c + 12032b c )e + 68096b c d e + 21504c d )x +--R + +--R 4 3 3 2 5 2 4 +--R (17792a b c - 96b c )e + (62720a c + 30912b c )d e +--R + +--R 5 2 +--R 43008b c d +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 4 2 2 4 3 3 +--R (3072a c - 960a b c + 112b c )e + (51072a b c - 224b c )d e +--R + +--R 5 2 4 2 +--R (43008a c + 21504b c )d +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 5 2 +--R (- 3648a b c + 1344a b c - 140b c)e +--R + +--R 2 4 2 3 4 2 4 2 +--R (13440a c - 2688a b c + 280b c )d e + 43008a b c d +--R * +--R x +--R + +--R 3 3 2 2 2 4 6 2 +--R (- 6144a c + 7392a b c - 2240a b c + 210b )e +--R + +--R 2 3 3 2 5 2 4 2 +--R (- 14784a b c + 4480a b c - 420b c)d e + 21504a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 53760c \|c +--R Type: Expression(Integer) +--E 257 + +--S 258 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 465 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 465 +r0:=1/96*(b^2-4*a*c)*e*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^2+1/30*(2*c*d-b*e)*_ + (a+b*x+c*x^2)^(5/2)/c+1/3*(d+e*x)*(a+b*x+c*x^2)^(5/2)+1/512*(b^2-4*a*c)^3*_ + e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-1/256*(b^2-_ + 4*a*c)^2*e*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 2c x + b +--R (- 960a c + 720a b c - 180a b c + 15b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 5 5 4 5 4 +--R 2560c e x + (4864b c e + 3072c d)x +--R + +--R 4 2 3 4 3 +--R ((4480a c + 2208b c )e + 6144b c d)x +--R + +--R 3 3 2 4 2 3 2 +--R ((3648a b c - 16b c )e + (6144a c + 3072b c )d)x +--R + +--R 2 3 2 2 4 3 +--R ((960a c - 192a b c + 20b c)e + 6144a b c d)x +--R + +--R 2 2 3 5 2 3 +--R (- 1056a b c + 320a b c - 30b )e + 3072a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 260 + +--S 261 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (1) (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R Type: Expression(Integer) +--E 262 + +--S 263 of 465 +r0:=2/5*(a+b*x+c*x^2)^(5/2) +--R +--R +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (2c x + 4b c x + (4a c + 2b )x + 4a b x + 2a )\|c x + b x + a +--R (2) ------------------------------------------------------------------ +--R 5 +--R Type: Expression(Integer) +--E 263 + +--S 264 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 265 + +--S 266 of 465 +r0:=-1/12*(8*c*d-7*b*e-6*c*e*x)*(a+b*x+c*x^2)^(3/2)/e^2+1/64*(128*c^4*d^4-_ + b^4*e^4-8*b^2*c*e^3*(2*b*d-3*a*e)-64*c^3*d^2*e*(4*b*d-3*a*e)+48*c^2*_ + e^2*(3*b^2*d^2-4*a*b*d*e+a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(c^(3/2)*e^5)-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^(3/2)*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/e^5-1/32*(64*c^3*d^3-b^3*e^3+4*b*c*e^2*(12*b*d-_ + 11*a*e)-16*c^2*d*e*(7*b*d-4*a*e)-2*c*e*(16*c^2*d^2+b^2*e^2-_ + 4*c*e*(4*b*d-3*a*e))*x)*sqrt(a+b*x+c*x^2)/(c*e^4) +--R +--R +--R (2) +--R 2 2 2 4 4 2 3 3 +--R (144a c + 72a b c - 3b )e + (- 576a b c - 48b c)d e +--R + +--R 3 2 2 2 2 3 3 4 4 +--R (576a c + 432b c )d e - 768b c d e + 384c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 2 2 2 3 3 +-+ +--R (- 192a b c e + (384a c + 192b c)d e - 576b c d e + 384c d )\|c +--R * +--R +-------------------+ +--R | 2 2 (b e - 2c d)x + 2a e - b d +--R \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 4 3 2 4 3 3 2 +--R 96c e x + (208b c e - 128c d e )x +--R + +--R 2 2 4 2 3 3 2 2 +--R ((240a c + 124b c)e - 320b c d e + 192c d e )x +--R + +--R 3 4 2 2 3 2 2 2 3 3 +--R (376a b c + 6b )e + (- 512a c - 288b c)d e + 672b c d e - 384c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 192c e \|c +--R Type: Expression(Integer) +--E 266 + +--S 267 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 268 + +--S 269 of 465 +r0:=1/3*(8*c*d-3*b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x))-_ + 1/4*(2*c*d-b*e)*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e^5*sqrt(c))+1/2*(16*c^2*d^2+_ + 3*b^2*e^2-4*c*e*(4*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^5+_ + 1/2*(16*c^2*d^2+5*b^2*e^2-4*c*e*(5*b*d-a*e)-4*c*e*(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/e^4 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((36a b c + 3b )e + (- 72a c - 54b c)d e + 144b c d e - 96c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 4 +--R (36a b c + 3b )d e + (- 72a c - 54b c)d e + 144b c d e - 96c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 2 2 2 2 2 +--R ((- 24a c - 18b )e + 96b c d e - 96c d e)x + (- 24a c - 18b )d e +--R + +--R 2 2 3 +--R 96b c d e - 96c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 3 2 +--R 8c e x + (20b c e - 16c d e )x +--R + +--R 2 4 3 2 2 2 4 +--R ((32a c + 18b )e - 64b c d e + 48c d e )x - 12a b e +--R + +--R 2 3 2 2 2 3 +--R (56a c + 30b )d e - 120b c d e + 96c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 6 5 +-+ +--R (12e x + 12d e )\|c +--R Type: Expression(Integer) +--E 269 + +--S 270 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 271 + +--S 272 of 465 +r0:=1/2*(4*c*d-b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)+_ + 3/4*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e^5-3/8*(2*c*d-b*e)*(16*c^2*d^2+_ + b^2*e^2-4*c*e*(4*b*d-3*a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*sqrt(c*d^2-b*d*e+_ + a*e^2))-3/4*(16*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-a*e)+4*c*e*(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 2 4 3 2 2 2 2 +--R ((24a c + 18b )e - 96b c d e + 96c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 +--R ((48a c + 36b )d e - 192b c d e + 192c d e)x + (24a c + 18b )d e +--R + +--R 3 2 4 +--R - 96b c d e + 96c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 36a b c - 3b )e + (72a c + 54b c)d e - 144b c d e +--R + +--R 3 3 2 +--R 96c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (- 72a b c - 6b )d e + (144a c + 108b c)d e - 288b c d e +--R + +--R 3 4 +--R 192c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 3 5 +--R (- 36a b c - 3b )d e + (72a c + 54b c)d e - 144b c d e + 96c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 4 3 4 2 3 2 +--R 8c e x + (28b c e - 32c d e )x +--R + +--R 2 4 3 2 2 2 4 +--R ((- 16a c - 10b )e + 112b c d e - 144c d e )x - 4a b e +--R + +--R 2 3 2 2 2 3 +--R (- 8a c - 6b )d e + 72b c d e - 96c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 7 2 6 2 5 | 2 2 +--R (8e x + 16d e x + 8d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 272 + +--S 273 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 274 + +--S 275 of 465 +r0:=-1/4*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*(a+b*x+c*x^2)^(3/2)/_ + (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+1/3*(8*c*d-b*e+6*c*e*x)*(a+b*x+_ + c*x^2)^(3/2)/(e^2*(d+e*x)^3)-4*c^(3/2)*(2*c*d-b*e)*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/e^5+1/16*(128*c^4*d^4-b^4*e^4-_ + 8*b^2*c*e^3*(2*b*d-3*a*e)-64*c^3*d^2*e*(4*b*d-3*a*e)+48*c^2*e^2*_ + (3*b^2*d^2-4*a*b*d*e+a^2*e^2))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*(c*d^2-b*d*e+_ + a*e^2)^(3/2))+1/8*(64*c^3*d^3+b^3*e^3+4*b*c*e^2*(4*b*d-5*a*e)-_ + 16*c^2*d*e*(5*b*d-4*a*e)+2*c*e*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-_ + 3*a*e))*x)*sqrt(a+b*x+c*x^2)/(e^4*(c*d^2-b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 6 2 2 5 2 2 4 3 3 3 3 +--R (192a b c e + (- 384a c - 192b c)d e + 576b c d e - 384c d e )x +--R + +--R 5 2 2 2 4 2 3 3 +--R 576a b c d e + (- 1152a c - 576b c)d e + 1728b c d e +--R + +--R 3 4 2 +--R - 1152c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 3 2 4 2 +--R 576a b c d e + (- 1152a c - 576b c)d e + 1728b c d e +--R + +--R 3 5 +--R - 1152c d e +--R * +--R x +--R + +--R 3 3 2 2 4 2 2 5 3 6 +--R 192a b c d e + (- 384a c - 192b c)d e + 576b c d e - 384c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 144a c - 72a b c + 3b )e + (576a b c + 48b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 576a c - 432b c )d e + 768b c d e - 384c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (- 432a c - 216a b c + 9b )d e + (1728a b c + 144b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (- 1728a c - 1296b c )d e + 2304b c d e - 1152c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 432a c - 216a b c + 9b )d e + (1728a b c + 144b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 1728a c - 1296b c )d e + 2304b c d e - 1152c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 144a c - 72a b c + 3b )d e + (576a b c + 48b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 576a c - 432b c )d e + 768b c d e - 384c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 6 2 5 3 2 4 3 +--R (96a c e - 96b c d e + 96c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (- 184a b c - 6b )e + (656a c + 220b c)d e - 912b c d e +--R + +--R 3 3 3 +--R 704c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 48a c - 28a b )e + (- 160a b c + 16b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (816a c + 252b c)d e - 1216b c d e + 960c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 16a b e + (- 16a c + 4a b )d e + (- 72a b c + 6b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (320a c + 96b c)d e - 480b c d e + 384c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 10 9 2 8 3 +--R (48a e - 48b d e + 48c d e )x +--R + +--R 9 2 8 3 7 2 +--R (144a d e - 144b d e + 144c d e )x +--R + +--R 2 8 3 7 4 6 3 7 4 6 5 5 +--R (144a d e - 144b d e + 144c d e )x + 48a d e - 48b d e + 48c d e +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 275 + +--S 276 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 465 +t0:=(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 3 8 2 3 3 2 7 +--R 2c e x + (5b c e + 6c d e )x +--R + +--R 2 2 3 2 2 3 2 6 +--R ((4a c + 4b c)e + 15b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 3 3 5 +--R ((6a b c + b )e + (12a c + 12b c)d e + 15b c d e + 2c d )x +--R + +--R 2 2 3 3 2 2 2 2 +--R (2a c + 2a b )e + (18a b c + 3b )d e + (12a c + 12b c)d e +--R + +--R 2 3 +--R 5b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 3 2 2 2 3 3 +--R (a b e + (6a c + 6a b )d e + (18a b c + 3b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 2 3 3 2 +--R (3a b d e + (6a c + 6a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 3 2 3 +--R (3a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 465 +r0:=-1/8192*(b^2-4*a*c)^2*e*(40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*_ + (b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^5+1/2560*(b^2-4*a*c)*e*(40*c^2*d^2+_ + 11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^4+_ + 1/6720*(2*c*d-b*e)*(64*c^2*d^2+99*b^2*e^2-4*c*e*(16*b*d+83*a*e))*_ + (a+b*x+c*x^2)^(7/2)/c^3+1/30*(2*c*d-b*e)*(d+e*x)^2*(a+b*x+_ + c*x^2)^(7/2)/c+1/5*(d+e*x)^3*(a+b*x+c*x^2)^(7/2)+1/480*e*(7*b^2*d*e-_ + 44*a*c*d*e+4*b*(c*d^2+a*e^2)+(8*c^2*d^2+11*b^2*e^2-4*c*e*(2*b*d+_ + 9*a*e))*x)*(a+b*x+c*x^2)^(7/2)/c^2-3/131072*(b^2-4*a*c)^4*e*_ + (40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(13/2)+3/65536*(b^2-4*a*c)^3*e*_ + (40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^6 +--R +--R +--R (2) +--R 5 5 4 2 4 3 4 3 2 6 2 +--R 322560a c - 1209600a b c + 1008000a b c - 352800a b c +--R + +--R 8 10 +--R 56700a b c - 3465b +--R * +--R 3 +--R e +--R + +--R 4 5 3 3 4 2 5 3 7 2 +--R 3225600a b c - 3225600a b c + 1209600a b c - 201600a b c +--R + +--R 9 +--R 12600b c +--R * +--R 2 +--R d e +--R + +--R 4 6 3 2 5 2 4 4 6 3 +--R - 3225600a c + 3225600a b c - 1209600a b c + 201600a b c +--R + +--R 8 2 +--R - 12600b c +--R * +--R 2 +--R d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 9 3 9 8 3 9 2 8 +--R 2752512c e x + (7798784b c e + 9175040c d e )x +--R + +--R 8 2 7 3 8 2 9 2 7 +--R ((7225344a c + 7196672b c )e + 26378240b c d e + 10321920c d e)x +--R + +--R 7 3 6 3 +--R (12836864a b c + 2119680b c )e +--R + +--R 8 2 7 2 8 2 9 3 +--R (24903680a c + 24821760b c )d e + 30228480b c d e + 3932160c d +--R * +--R 6 +--R x +--R + +--R 2 7 2 6 4 5 3 +--R (5332992a c + 5222400a b c - 2560b c )e +--R + +--R 7 3 6 2 +--R (45465600a b c + 7516160b c )d e +--R + +--R 8 2 7 2 8 3 +--R (29245440a c + 29184000b c )d e + 11796480b c d +--R * +--R 5 +--R x +--R + +--R 2 6 3 5 5 4 3 +--R (3502080a b c - 30720a b c + 2816b c )e +--R + +--R 2 7 2 6 4 5 2 +--R (19660800a c + 19292160a b c - 10240b c )d e +--R + +--R 7 3 6 2 8 2 7 3 +--R (55418880a b c + 9185280b c )d e + (11796480a c + 11796480b c )d +--R * +--R 4 +--R x +--R + +--R 3 6 2 2 5 4 4 6 3 3 +--R (215040a c - 145920a b c + 37760a b c - 3168b c )e +--R + +--R 2 6 3 5 5 4 2 +--R (13946880a b c - 133120a b c + 11520b c )d e +--R + +--R 2 7 2 6 4 5 2 +--R (25374720a c + 25036800a b c - 11520b c )d e +--R + +--R 7 3 6 3 +--R (23592960a b c + 3932160b c )d +--R * +--R 3 +--R x +--R + +--R 3 5 2 3 4 5 3 7 2 3 +--R (- 332800a b c + 211200a b c - 47808a b c + 3696b c )e +--R + +--R 3 6 2 2 5 4 4 6 3 2 +--R (1310720a c - 706560a b c + 168960a b c - 13440b c )d e +--R + +--R 2 6 3 5 5 4 2 +--R (20367360a b c - 168960a b c + 13440b c )d e +--R + +--R 2 7 2 6 3 +--R (11796480a c + 11796480a b c )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R - 322560a c + 634880a b c - 320640a b c + 64512a b c +--R + +--R 8 +--R - 4620b c +--R * +--R 3 +--R e +--R + +--R 3 5 2 3 4 5 3 7 2 2 +--R (- 1914880a b c + 1082880a b c - 228480a b c + 16800b c )d e +--R + +--R 3 6 2 2 5 4 4 6 3 2 +--R (3225600a c - 1082880a b c + 228480a b c - 16800b c )d e +--R + +--R 2 6 3 +--R 11796480a b c d +--R * +--R x +--R + +--R 4 4 3 3 3 2 5 2 7 +--R 1149440a b c - 1374720a b c + 576576a b c - 104160a b c +--R + +--R 9 +--R 6930b +--R * +--R 3 +--R e +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R - 2621440a c + 4285440a b c - 1962240a b c + 369600a b c +--R + +--R 8 +--R - 25200b c +--R * +--R 2 +--R d e +--R + +--R 3 5 2 3 4 5 3 7 2 2 +--R (- 4285440a b c + 1962240a b c - 369600a b c + 25200b c )d e +--R + +--R 3 6 3 +--R 3932160a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 6 +-+ +--R 13762560c \|c +--R Type: Expression(Integer) +--E 278 + +--S 279 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 465 +t0:=(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 465 +r0:=-5/3072*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+_ + 1/192*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^3+_ + 1/504*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*_ + (a+b*x+c*x^2)^(7/2)/c^2+2/9*(d+e*x)^2*(a+b*x+c*x^2)^(7/2)+_ + 1/36*e*(b*d-2*a*e+(2*c*d-b*e)*x)*(a+b*x+c*x^2)^(7/2)/c-_ + 5/16384*(b^2-4*a*c)^4*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(11/2)+5/8192*(b^2-4*a*c)^3*e*(2*c*d-b*e)*_ + (b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5 +--R +--R +--R (2) +--R 4 4 3 3 3 2 5 2 7 9 2 +--R (80640a b c - 80640a b c + 30240a b c - 5040a b c + 315b )e +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 +--R (- 161280a c + 161280a b c - 60480a b c + 10080a b c - 630b c)d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 8 2 8 7 2 8 7 +--R 229376c e x + (659456b c e + 516096c d e)x +--R + +--R 7 2 6 2 7 8 2 6 +--R ((622592a c + 620544b c )e + 1511424b c d e + 294912c d )x +--R + +--R 6 3 5 2 7 2 6 +--R (1136640a b c + 187904b c )e + (1462272a c + 1459200b c )d e +--R + +--R 7 2 +--R 884736b c d +--R * +--R 5 +--R x +--R + +--R 2 6 2 5 4 4 2 +--R (491520a c + 482304a b c - 256b c )e +--R + +--R 6 3 5 7 2 6 2 +--R (2770944a b c + 459264b c )d e + (884736a c + 884736b c )d +--R * +--R 4 +--R x +--R + +--R 2 5 3 4 5 3 2 +--R (348672a b c - 3328a b c + 288b c )e +--R + +--R 2 6 2 5 4 4 +--R (1268736a c + 1251840a b c - 576b c )d e +--R + +--R 6 3 5 2 +--R (1769472a b c + 294912b c )d +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (32768a c - 17664a b c + 4224a b c - 336b c )e +--R + +--R 2 5 3 4 5 3 +--R (1018368a b c - 8448a b c + 672b c )d e +--R + +--R 2 6 2 5 2 +--R (884736a c + 884736a b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 3 3 5 2 7 2 +--R (- 47872a b c + 27072a b c - 5712a b c + 420b c)e +--R + +--R 3 5 2 2 4 4 3 6 2 +--R (161280a c - 54144a b c + 11424a b c - 840b c )d e +--R + +--R 2 5 2 +--R 884736a b c d +--R * +--R x +--R + +--R 4 4 3 2 3 2 4 2 6 8 2 +--R (- 65536a c + 107136a b c - 49056a b c + 9240a b c - 630b )e +--R + +--R 3 4 2 3 3 5 2 7 +--R (- 214272a b c + 98112a b c - 18480a b c + 1260b c)d e +--R + +--R 3 5 2 +--R 294912a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 +-+ +--R 1032192c \|c +--R Type: Expression(Integer) +--E 281 + +--S 282 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 465 +t0:=(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 +--R ((6a b c + b )e + (4a c + 4b c)d)x +--R + +--R 2 2 3 2 2 2 2 2 +--R ((2a c + 2a b )e + (6a b c + b )d)x + (a b e + (2a c + 2a b )d)x + a b d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 465 +r0:=-5/3072*(b^2-4*a*c)^2*e*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3+_ + 1/192*(b^2-4*a*c)*e*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^2+1/56*(2*c*d-b*e)*_ + (a+b*x+c*x^2)^(7/2)/c+1/4*(d+e*x)*(a+b*x+c*x^2)^(7/2)-_ + 5/16384*(b^2-4*a*c)^4*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(9/2)+5/8192*(b^2-4*a*c)^3*e*(b+2*c*x)*_ + sqrt(a+b*x+c*x^2)/c^4 +--R +--R +--R (2) +--R 4 4 3 2 3 2 4 2 6 8 +--R (- 26880a c + 26880a b c - 10080a b c + 1680a b c - 105b )e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 7 7 6 7 6 +--R 86016c e x + (251904b c e + 98304c d)x +--R + +--R 6 2 5 6 5 +--R ((243712a c + 243200b c )e + 294912b c d)x +--R + +--R 5 3 4 6 2 5 4 +--R ((461824a b c + 76544b c )e + (294912a c + 294912b c )d)x +--R + +--R 2 5 2 4 4 3 +--R (211456a c + 208640a b c - 96b c )e +--R + +--R 5 3 4 +--R (589824a b c + 98304b c )d +--R * +--R 3 +--R x +--R + +--R 2 4 3 3 5 2 +--R (169728a b c - 1408a b c + 112b c )e +--R + +--R 2 5 2 4 +--R (294912a c + 294912a b c )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 3 4 2 6 2 4 +--R ((26880a c - 9024a b c + 1904a b c - 140b c)e + 294912a b c d)x +--R + +--R 3 3 2 3 2 5 7 3 4 +--R (- 35712a b c + 16352a b c - 3080a b c + 210b )e + 98304a c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 344064c \|c +--R Type: Expression(Integer) +--E 284 + +--S 285 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 465 +r0:=2/7*(a+b*x+c*x^2)^(7/2) +--R +--R +--R (2) +--R 3 6 2 5 2 2 4 3 3 +--R 2c x + 6b c x + (6a c + 6b c)x + (12a b c + 2b )x +--R + +--R 2 2 2 2 3 +--R (6a c + 6a b )x + 6a b x + 2a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 7 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R e x + d +--R Type: Expression(Integer) +--E 289 + +--S 290 of 465 +r0:=-1/96*(64*c^3*d^3-b^3*e^3+4*b*c*e^2*(14*b*d-13*a*e)-8*c^2*d*e*_ + (15*b*d-8*a*e)-2*c*e*(24*c^2*d^2+b^2*e^2-4*c*e*(6*b*d-5*a*e))*x)*_ + (a+b*x+c*x^2)^(3/2)/(c*e^4)-1/30*(12*c*d-11*b*e-10*c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/e^2+1/512*(1024*c^6*d^6+b^6*e^6+4*b^4*c*e^5*_ + (2*b*d-5*a*e)-512*c^5*d^4*e*(6*b*d-5*a*e)-320*c^3*e^3*(b*d-a*e)^2*_ + (4*b*d-a*e)+640*c^4*d^2*e^2*(5*b^2*d^2-8*a*b*d*e+3*a^2*e^2)+_ + 40*b^2*c^2*e^4*(3*b^2*d^2-8*a*b*d*e+6*a^2*e^2))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(5/2)*e^7)-(2*c*d-b*e)*(c*d^2-_ + b*d*e+a*e^2)^(5/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/e^7-1/256*(512*c^5*d^5+b^5*e^5-_ + 128*c^4*d^3*e*(11*b*d-8*a*e)+8*b^3*c*e^4*(b*d-2*a*e)+32*c^3*d*e^2*_ + (40*b^2*d^2-55*a*b*d*e+16*a^2*e^2)-8*b*c^2*e^3*(49*b^2*d^2-_ + 92*a*b*d*e+42*a^2*e^2)-2*c*e*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*_ + (8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/(c^2*e^6) +--R +--R +--R (2) +--R 3 3 2 2 2 4 6 6 +--R (4800a c + 3600a b c - 300a b c + 15b )e +--R + +--R 2 3 3 2 5 5 +--R (- 28800a b c - 4800a b c + 120b c)d e +--R + +--R 2 4 2 3 4 2 2 4 +--R (28800a c + 43200a b c + 1800b c )d e +--R + +--R 4 3 3 3 3 5 2 4 4 2 +--R (- 76800a b c - 19200b c )d e + (38400a c + 48000b c )d e +--R + +--R 5 5 6 6 +--R - 46080b c d e + 15360c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 5 2 3 2 2 4 +--R - 7680a b c e + (15360a c + 15360a b c )d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (- 46080a b c - 7680b c )d e + (30720a c + 30720b c )d e +--R + +--R 4 4 5 5 +--R - 38400b c d e + 15360c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 5 6 5 4 6 5 5 4 +--R 2560c e x + (7936b c e - 3072c d e )x +--R + +--R 4 2 3 6 4 5 5 2 4 3 +--R ((8320a c + 8352b c )e - 9984b c d e + 3840c d e )x +--R + +--R 3 3 2 6 4 2 3 5 +--R (18112a b c + 3056b c )e + (- 11264a c - 11392b c )d e +--R + +--R 4 2 4 5 3 3 +--R 13440b c d e - 5120c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 4 6 +--R (10560a c + 10912a b c + 20b c)e +--R + +--R 3 3 2 5 4 2 3 2 4 +--R (- 28544a b c - 4960b c )d e + (17280a c + 17760b c )d e +--R + +--R 4 3 3 5 4 2 +--R - 20480b c d e + 7680c d e +--R * +--R x +--R + +--R 2 2 3 5 6 +--R (17056a b c + 560a b c - 30b )e +--R + +--R 2 3 2 2 4 5 +--R (- 23552a c - 26560a b c - 240b c)d e +--R + +--R 3 3 2 2 4 4 2 3 3 3 +--R (62400a b c + 11760b c )d e + (- 35840a c - 38400b c )d e +--R + +--R 4 4 2 5 5 +--R 42240b c d e - 15360c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 7 +-+ +--R 7680c e \|c +--R Type: Expression(Integer) +--E 290 + +--S 291 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 292 + +--S 293 of 465 +r0:=1/12*(48*c^2*d^2-66*b*c*d*e+19*b^2*e^2+8*a*c*e^2-18*c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/e^4+1/5*(12*c*d-5*b*e+2*c*e*x)*(a+b*x+c*x^2)^(5/2)/_ + (e^2*(d+e*x))-1/64*(2*c*d-b*e)*(384*c^4*d^4-b^4*e^4-8*b^2*c*e^3*(4*b*d-_ + 5*a*e)-128*c^3*d^2*e*(6*b*d-5*a*e)+16*c^2*e^2*(26*b^2*d^2-40*a*b*d*e+_ + 15*a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*_ + e^7)+1/2*(c*d^2-b*d*e+a*e^2)^(3/2)*(24*c^2*d^2+5*b^2*e^2-4*c*e*_ + (6*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+_ + a*e^2)*sqrt(a+b*x+c*x^2)))/e^7+1/32*(384*c^4*d^4+b^4*e^4-2*b^2*c*e^3*_ + (65*b*d-62*a*e)-32*c^3*d^2*e*(27*b*d-14*a*e)+8*c^2*e^2*(76*b^2*d^2-_ + 67*a*b*d*e+8*a^2*e^2)-2*c*e*(2*c*d-b*e)*(48*c^2*d^2-48*b*c*d*e+_ + b^2*e^2+44*a*c*e^2)*x)*sqrt(a+b*x+c*x^2)/(c*e^6) +--R +--R +--R (2) +--R 2 2 3 5 6 +--R (3600a b c + 600a b c - 15b )e +--R + +--R 2 3 2 2 4 5 +--R (- 7200a c - 10800a b c - 450b c)d e +--R + +--R 3 3 2 2 4 4 2 3 3 3 +--R (28800a b c + 7200b c )d e + (- 19200a c - 24000b c )d e +--R + +--R 4 4 2 5 5 +--R 28800b c d e - 11520c d e +--R * +--R x +--R + +--R 2 2 3 5 5 +--R (3600a b c + 600a b c - 15b )d e +--R + +--R 2 3 2 2 4 2 4 +--R (- 7200a c - 10800a b c - 450b c)d e +--R + +--R 3 3 2 3 3 4 2 3 4 2 +--R (28800a b c + 7200b c )d e + (- 19200a c - 24000b c )d e +--R + +--R 4 5 5 6 +--R 28800b c d e - 11520c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 5 2 3 4 +--R (- 1920a c - 2400a b c)e + (13440a b c + 2400b c)d e +--R + +--R 3 2 2 2 3 3 3 2 4 4 +--R (- 13440a c - 13920b c )d e + 23040b c d e - 11520c d e +--R * +--R x +--R + +--R 2 2 2 4 2 3 2 3 +--R (- 1920a c - 2400a b c)d e + (13440a b c + 2400b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (- 13440a c - 13920b c )d e + 23040b c d e - 11520c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 4 6 5 3 6 4 5 4 +--R 384c e x + (1248b c e - 576c d e )x +--R + +--R 3 2 2 6 3 5 4 2 4 3 +--R ((1408a c + 1424b c )e - 2112b c d e + 960c d e )x +--R + +--R 2 3 6 3 2 2 5 +--R (3568a b c + 620b c)e + (- 2912a c - 3016b c )d e +--R + +--R 3 2 4 4 3 3 +--R 4320b c d e - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 6 2 3 5 +--R (2944a c + 3320a b c + 30b )e + (- 12032a b c - 2320b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (9120a c + 9960b c )d e - 13440b c d e + 5760c d e +--R * +--R x +--R + +--R 2 6 2 2 2 4 5 +--R - 960a b c e + (4864a c + 5240a b c + 30b )d e +--R + +--R 2 3 2 4 3 2 2 3 3 +--R (- 21360a b c - 3900b c)d e + (17280a c + 18240b c )d e +--R + +--R 3 4 2 4 5 +--R - 25920b c d e + 11520c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 8 7 +-+ +--R (960c e x + 960c d e )\|c +--R Type: Expression(Integer) +--E 293 + +--S 294 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 295 + +--S 296 of 465 +r0:=-5/4*(8*c^2*d^2+b^2*e^2-c*e*(7*b*d-2*a*e)+c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/2*(3*c*d-b*e+c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)+15/64*(128*c^4*d^4+b^4*e^4-_ + 8*b^2*c*e^3*(4*b*d-3*a*e)-128*c^3*d^2*e*(2*b*d-a*e)+16*c^2*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2))*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^7*sqrt(c))-15/8*(2*c*d-b*e)*(8*c^2*d^2+b^2*e^2-_ + 4*c*e*(2*b*d-a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^7-_ + 15/32*(64*c^3*d^3-7*b^3*e^3+4*b*c*e^2*(14*b*d-5*a*e)-16*c^2*d*e*_ + (7*b*d-2*a*e)-2*c*e*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*x)*_ + sqrt(a+b*x+c*x^2)/e^6 +--R +--R +--R (2) +--R 2 2 2 4 6 2 3 5 +--R (240a c + 360a b c + 15b )e + (- 1920a b c - 480b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (1920a c + 2400b c )d e - 3840b c d e + 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 5 2 3 2 4 +--R (480a c + 720a b c + 30b )d e + (- 3840a b c - 960b c)d e +--R + +--R 3 2 2 3 3 3 4 2 4 5 +--R (3840a c + 4800b c )d e - 7680b c d e + 3840c d e +--R * +--R x +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (240a c + 360a b c + 15b )d e + (- 1920a b c - 480b c)d e +--R + +--R 3 2 2 4 2 3 5 4 6 +--R (1920a c + 2400b c )d e - 3840b c d e + 1920c d +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (- 480a b c - 120b )e + (960a c + 1200b c)d e - 2880b c d e +--R + +--R 3 3 2 +--R 1920c d e +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 960a b c - 240b )d e + (1920a c + 2400b c)d e +--R + +--R 2 3 2 3 4 +--R - 5760b c d e + 3840c d e +--R * +--R x +--R + +--R 3 2 3 2 2 3 2 2 4 +--R (- 480a b c - 120b )d e + (960a c + 1200b c)d e - 2880b c d e +--R + +--R 3 5 +--R 1920c d +--R * +--R +-------------------+ +--R +-+ | 2 2 (b e - 2c d)x + 2a e - b d +--R \|c \|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 6 5 2 6 3 5 4 +--R 32c e x + (112b c e - 64c d e )x +--R + +--R 2 2 6 2 5 3 2 4 3 +--R ((144a c + 148b c)e - 288b c d e + 160c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (520a b c + 98b )e + (- 608a c - 664b c)d e + 1200b c d e +--R + +--R 3 3 3 +--R - 640c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 128a c - 144a b )e + (1872a b c + 340b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 2480a c - 2620b c)d e + 5120b c d e - 2880c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 32a b e + (- 64a c - 80a b )d e + (1160a b c + 210b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (- 1600a c - 1680b c)d e + 3360b c d e - 1920c d e +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 9 2 8 2 7 +-+ +--R (64e x + 128d e x + 64d e )\|c +--R Type: Expression(Integer) +--E 296 + +--S 297 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 298 + +--S 299 of 465 +r0:=-5/12*(16*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-a*e)+4*c*e*(2*c*d-b*e)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(4*c*d-b*e+2*c*e*x)*_ + (a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)-5/2*(2*c*d-b*e)*(8*c^2*d^2+b^2*e^2-_ + 4*c*e*(2*b*d-a*e))*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*_ + sqrt(c)/e^7+5/16*(128*c^4*d^4+b^4*e^4-8*b^2*c*e^3*(4*b*d-3*a*e)-_ + 128*c^3*d^2*e*(2*b*d-a*e)+16*c^2*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2))*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(e^7*sqrt(c*d^2-b*d*e+a*e^2))+5/8*(64*c^3*d^3-_ + b^3*e^3-16*c^2*d*e*(5*b*d-2*a*e)+12*b*c*e^2*(2*b*d-a*e)+2*c*e*_ + (16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 3 6 2 2 5 2 2 4 +--R (480a b c + 120b )e + (- 960a c - 1200b c)d e + 2880b c d e +--R + +--R 3 3 3 +--R - 1920c d e +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 2 4 +--R (1440a b c + 360b )d e + (- 2880a c - 3600b c)d e +--R + +--R 2 3 3 3 4 2 +--R 8640b c d e - 5760c d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 2 3 3 +--R (1440a b c + 360b )d e + (- 2880a c - 3600b c)d e +--R + +--R 2 4 2 3 5 +--R 8640b c d e - 5760c d e +--R * +--R x +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (480a b c + 120b )d e + (- 960a c - 1200b c)d e + 2880b c d e +--R + +--R 3 6 +--R - 1920c d +--R * +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R \|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 4 7 2 3 6 +--R (- 240a c - 360a b c - 15b )e + (1920a b c + 480b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (- 1920a c - 2400b c )d e + 3840b c d e - 1920c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 6 2 3 2 5 +--R (- 720a c - 1080a b c - 45b )d e + (5760a b c + 1440b c)d e +--R + +--R 3 2 2 3 4 3 4 3 4 5 2 +--R (- 5760a c - 7200b c )d e + 11520b c d e - 5760c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 5 2 3 3 4 +--R (- 720a c - 1080a b c - 45b )d e + (5760a b c + 1440b c)d e +--R + +--R 3 2 2 4 3 3 5 2 4 6 +--R (- 5760a c - 7200b c )d e + 11520b c d e - 5760c d e +--R * +--R x +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 240a c - 360a b c - 15b )d e + (1920a b c + 480b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 1920a c - 2400b c )d e + 3840b c d e - 1920c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 6 5 2 6 3 5 4 +--R 32c e x + (128b c e - 96c d e )x +--R + +--R 2 2 6 2 5 3 2 4 3 +--R ((224a c + 240b c)e - 672b c d e + 480c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (- 328a b c - 66b )e + (1328a c + 1444b c)d e - 4560b c d e +--R + +--R 3 3 3 +--R 3520c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 3 5 +--R (- 48a c - 52a b )e + (- 352a b c - 80b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (1680a c + 1860b c)d e - 6080b c d e + 4800c d e +--R * +--R x +--R + +--R 2 6 2 2 5 3 2 4 +--R - 16a b e + (- 16a c - 20a b )d e + (- 120a b c - 30b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (640a c + 720b c)d e - 2400b c d e + 1920c d e +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R 10 3 9 2 2 8 3 7 | 2 2 +--R (48e x + 144d e x + 144d e x + 48d e )\|a e - b d e + c d +--R Type: Expression(Integer) +--E 299 + +--S 300 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/sqrt(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 465 +r0:=3/64*(b^2-4*a*c)*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+_ + 1/32*(2*c*d-b*e)*(16*c^2*d^2+15*b^2*e^2-4*c*e*(4*b*d+11*a*e))*_ + sqrt(a+b*x+c*x^2)/c^3+1/4*(2*c*d-b*e)*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+_ + 1/2*(d+e*x)^3*sqrt(a+b*x+c*x^2)+1/16*e*(b^2*d*e-20*a*c*d*e+4*b*_ + (c*d^2+a*e^2)+(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*x)*_ + sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 2 2 2 4 3 2 3 2 +--R (48a c - 72a b c + 15b )e + (192a b c - 48b c)d e +--R + +--R 3 2 2 2 +--R (- 192a c + 48b c )d e +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 32c e x + (- 16b c e + 128c d e )x +--R + +--R 2 2 3 2 2 3 2 3 3 +--R ((- 48a c + 20b c)e - 64b c d e + 192c d e)x + (104a b c - 30b )e +--R + +--R 2 2 2 2 2 3 3 +--R (- 256a c + 96b c)d e - 96b c d e + 128c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 +-+ +--R 64c \|c +--R Type: Expression(Integer) +--E 302 + +--S 303 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 304 + +--S 305 of 465 +r0:=1/4*(b^2-4*a*c)*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/c^(5/2)+1/6*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+_ + a*e))*sqrt(a+b*x+c*x^2)/c^2+2/3*(d+e*x)^2*sqrt(a+b*x+c*x^2)+1/3*e*_ + (b*d-2*a*e+(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R 3 2 2 2 2c x + b +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e)atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 2 2 2 2 +--R 8c e x + (- 4b c e + 24c d e)x + (- 16a c + 6b )e - 12b c d e +--R + +--R 2 2 +--R 24c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 2 +-+ +--R 12c \|c +--R Type: Expression(Integer) +--E 305 + +--S 306 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 465 +t0:=(b+2*c*x)*(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) ----------------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 465 +r0:=1/4*(b^2-4*a*c)*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/_ + c^(3/2)+1/2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/c+(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R (2) +--R 2 2c x + b +--R (- 4a c + b )e atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +--------------+ +--R +-+ | 2 +--R (4c e x - 2b e + 8c d)\|c \|c x + b x + a +--R / +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 308 + +--S 309 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 465 +t0:=(b+2*c*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2c x + b +--R (1) ----------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 465 +r0:=2*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R (2) 2\|c x + b x + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 465 +t0:=(b+2*c*x)/((d+e*x)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) -------------------------- +--R +--------------+ +--R | 2 +--R (e x + d)\|c x + b x + a +--R Type: Expression(Integer) +--E 313 + +--S 314 of 465 +r0:=2*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e-_ + (2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(e*sqrt(c*d^2-b*d*e+a*e^2)) +--R +--R +--R (2) +--R +-------------------+ +--R +-+ | 2 2 2c x + b +--R 2\|c \|a e - b d e + c d atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R (b e - 2c d)x + 2a e - b d +--R (- b e + 2c d)atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R / +--R +-------------------+ +--R | 2 2 +--R e\|a e - b d e + c d +--R Type: Expression(Integer) +--E 314 + +--S 315 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 465 +t0:=(b+2*c*x)/((d+e*x)^2*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------- +--R +--------------+ +--R 2 2 2 | 2 +--R (e x + 2d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 465 +r0:=-1/2*(b^2-4*a*c)*e*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-_ + b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)+(2*c*d-b*e)*_ + sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 +--R ((- 4a c + b )e x + (- 4a c + b )d e) +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R (- 2b e + 4c d)\|a e - b d e + c d \|c x + b x + a +--R / +--R 3 2 2 2 2 3 +--R ((2a e - 2b d e + 2c d e)x + 2a d e - 2b d e + 2c d ) +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 317 + +--S 318 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 of 465 +t0:=(b+2*c*x)/((d+e*x)^3*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ----------------------------------------------- +--R +--------------+ +--R 3 3 2 2 2 3 | 2 +--R (e x + 3d e x + 3d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 465 +r0:=-3/8*(b^2-4*a*c)*e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+_ + 1/2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+_ + 1/4*(4*c^2*d^2+3*b^2*e^2-4*c*e*(b*d+2*a*e))*sqrt(a+b*x+c*x^2)/_ + ((c*d^2-b*d*e+a*e^2)^2*(d+e*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 2 +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e )x +--R + +--R 3 3 2 2 2 2 3 2 2 +--R ((24a b c - 6b )d e + (- 48a c + 12b c)d e )x + (12a b c - 3b )d e +--R + +--R 2 2 3 +--R (- 24a c + 6b c)d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 3 2 2 2 3 +--R ((- 16a c + 6b )e - 8b c d e + 8c d e)x - 4a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c + 10b )d e - 20b c d e + 16c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 2 6 5 2 2 4 3 3 2 4 2 2 +--R (8a e - 16a b d e + (16a c + 8b )d e - 16b c d e + 8c d e )x +--R + +--R 2 5 2 4 2 3 3 4 2 2 5 +--R (16a d e - 32a b d e + (32a c + 16b )d e - 32b c d e + 16c d e)x +--R + +--R 2 2 4 3 3 2 4 2 5 2 6 +--R 8a d e - 16a b d e + (16a c + 8b )d e - 16b c d e + 8c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 320 + +--S 321 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 465 +t0:=(b+2*c*x)/((d+e*x)^4*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) --------------------------------------------------------- +--R +--------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|c x + b x + a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 465 +r0:=-1/16*(b^2-4*a*c)*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)+1/3*(2*c*d-b*e)*_ + sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^3)+1/12*(8*c^2*d^2+_ + 5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+_ + a*e^2)^2*(d+e*x)^2)+1/24*(2*c*d-b*e)*(8*c^2*d^2+15*b^2*e^2-4*c*e*_ + (2*b*d+13*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^3*(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 4 6 2 3 5 +--R (48a c - 72a b c + 15b )e + (192a b c - 48b c)d e +--R + +--R 3 2 2 2 4 +--R (- 192a c + 48b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 5 2 3 2 4 +--R (144a c - 216a b c + 45b )d e + (576a b c - 144b c)d e +--R + +--R 3 2 2 3 3 +--R (- 576a c + 144b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 4 2 4 2 3 3 3 +--R (144a c - 216a b c + 45b )d e + (576a b c - 144b c)d e +--R + +--R 3 2 2 4 2 +--R (- 576a c + 144b c )d e +--R * +--R x +--R + +--R 2 2 2 4 3 3 2 3 4 2 +--R (48a c - 72a b c + 15b )d e + (192a b c - 48b c)d e +--R + +--R 3 2 2 5 +--R (- 192a c + 48b c )d e +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 5 2 2 4 2 2 3 +--R (104a b c - 30b )e + (- 208a c + 76b c)d e - 48b c d e +--R + +--R 3 3 2 +--R 32c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (- 48a c + 20a b )e + (224a b c - 80b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (- 432a c + 204b c)d e - 160b c d e + 96c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 16a b e + (- 16a c + 52a b )d e + (24a b c - 66b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 160a c + 192b c)d e - 192b c d e + 96c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R / +--R 3 9 2 8 2 2 2 7 +--R 48a e - 144a b d e + (144a c + 144a b )d e +--R + +--R 3 3 6 2 2 4 5 2 5 4 +--R (- 288a b c - 48b )d e + (144a c + 144b c)d e - 144b c d e +--R + +--R 3 6 3 +--R 48c d e +--R * +--R 3 +--R x +--R + +--R 3 8 2 2 7 2 2 3 6 +--R 144a d e - 432a b d e + (432a c + 432a b )d e +--R + +--R 3 4 5 2 2 5 4 2 6 3 +--R (- 864a b c - 144b )d e + (432a c + 432b c)d e - 432b c d e +--R + +--R 3 7 2 +--R 144c d e +--R * +--R 2 +--R x +--R + +--R 3 2 7 2 3 6 2 2 4 5 +--R 144a d e - 432a b d e + (432a c + 432a b )d e +--R + +--R 3 5 4 2 2 6 3 2 7 2 +--R (- 864a b c - 144b )d e + (432a c + 432b c)d e - 432b c d e +--R + +--R 3 8 +--R 144c d e +--R * +--R x +--R + +--R 3 3 6 2 4 5 2 2 5 4 +--R 48a d e - 144a b d e + (144a c + 144a b )d e +--R + +--R 3 6 3 2 2 7 2 2 8 3 9 +--R (- 288a b c - 48b )d e + (144a c + 144b c)d e - 144b c d e + 48c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R Type: Expression(Integer) +--E 323 + +--S 324 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 of 465 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 465 +r0:=1/2*e*(2*c*d-b*e)*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-2*(d+e*x)^4/_ + sqrt(a+b*x+c*x^2)+1/3*e^2*(52*c^2*d^2+15*b^2*e^2-4*c*e*(13*b*d+2*a*e))*_ + sqrt(a+b*x+c*x^2)/c^3+8/3*e^2*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+2/3*e^2*_ + (6*c*d^2-e*(b*d+4*a*e)+5*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R 3 4 2 2 3 2 2 2 3 3 +--R ((36a b c - 15b )e + (- 72a c + 54b c)d e - 72b c d e + 48c d e) +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 4 4 2 4 3 3 3 +--R 4c e x + (- 4b c e + 24c d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 16a c + 10b c)e - 36b c d e + 72c d e )x +--R + +--R 3 4 2 2 3 2 2 2 +--R (- 52a b c + 30b )e + (72a c - 108b c)d e + 144b c d e +--R + +--R 3 3 +--R - 48c d e +--R * +--R x +--R + +--R 2 2 4 3 2 2 2 3 4 +--R (- 32a c + 30a b )e - 108a b c d e + 144a c d e - 12c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 3 +-+ | 2 +--R 6c \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 465 +r0:=3/4*e*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-2*(d+e*x)^3/sqrt(a+b*x+c*x^2)+_ + 9/2*e^2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/c^2+3*e^2*(d+e*x)*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R +--------------+ +--R 2 3 2 2 2 | 2 +--R ((- 12a c + 9b )e - 24b c d e + 24c d e)\|c x + b x + a +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 3 3 3 2 2 2 +--R 4c e x + (- 6b c e + 24c d e )x +--R + +--R 2 3 2 2 2 3 2 +--R ((12a c - 18b )e + 48b c d e - 24c d e)x - 18a b e + 48a c d e +--R + +--R 2 3 +--R - 8c d +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 2 +-+ | 2 +--R 4c \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 329 + +--S 330 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) ------------------------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 465 +r0:=2*e*(2*c*d-b*e)*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-_ + 2*(d+e*x)^2/sqrt(a+b*x+c*x^2)+4*e^2*sqrt(a+b*x+c*x^2)/c +--R +--R +--R (2) +--R +--------------+ +--R 2 | 2 2c x + b +--R (- 2b e + 4c d e)\|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 2 2 2 +-+ +--R (2c e x + (4b e - 4c d e)x + 4a e - 2c d )\|c +--R / +--R +--------------+ +--R +-+ | 2 +--R c\|c \|c x + b x + a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 465 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 465 +r0:=2*e*atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/sqrt(c)-_ + 2*(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R | 2 2c x + b +-+ +--R 2e\|c x + b x + a atanh(----------------------) + (- 2e x - 2d)\|c +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R (2) -------------------------------------------------------------------- +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 336 + +)clear all + +--S 337 of 465 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2c x + b +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 465 +r0:=(-2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +--R (2) - ----------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 339 + +)clear all + +--S 340 of 465 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R 2c x + b +--R (1) -------------------------------------------------------------- +--R +--------------+ +--R 3 2 | 2 +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|c x + b x + a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 465 +r0:=-e*(2*c*d-b*e)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)-_ + 2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R +--------------+ +--R 2 | 2 +--R (- b e + 2c d e)\|c x + b x + a +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 +--R (2c e x + 2b e - 2c d)\|a e - b d e + c d +--R / +--R +-------------------+ +--------------+ +--R 2 2 | 2 2 | 2 +--R (a e - b d e + c d )\|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 465 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x +--R + +--R 2 2 +--R (2a d e + b d )x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 465 +r0:=-1/2*e*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*atanh(1/2*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/_ + (c*d^2-b*d*e+a*e^2)^(5/2)-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*sqrt(a+b*x+c*x^2))+3*e^2*_ + (2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 4 3 2 2 2 2 3 +--R ((- 4a c + 3b )e - 8b c d e + 8c d e )x + (- 4a c + 3b )d e +--R + +--R 2 2 2 3 +--R - 8b c d e + 8c d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 6b c e + 12c d e )x + ((4a c - 6b )e + 8b c d e + 4c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (8a c - 4b )d e + 8b c d e - 4c d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 465 +t0:=(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R 2c e x + (b e + 8c d e )x + (4b d e + 12c d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6b d e + 8c d e)x + (4b d e + 2c d )x + b d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 465 +r0:=-2/3*(d+e*x)^4/(a+b*x+c*x^2)^(3/2)+4*e^3*(2*c*d-b*e)*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-_ + 16/3*e*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*_ + sqrt(a+b*x+c*x^2))+8/3*e^2*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*_ + sqrt(a+b*x+c*x^2)/(c^2*(b^2-4*a*c))+16/3*e^3*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + sqrt(a+b*x+c*x^2)/(c*(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 2 +--R ((- 48a b c + 12b c)e + (96a c - 24b c )d e )x +--R + +--R 2 4 4 2 3 3 +--R ((- 48a b c + 12b )e + (96a b c - 24b c)d e )x +--R + +--R 2 3 4 2 2 2 3 +--R (- 48a b c + 12a b )e + (96a c - 24a b c)d e +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 3 2 2 4 4 +--R (24a c - 6b c )e x +--R + +--R 2 3 4 3 2 2 3 3 2 2 +--R (112a b c - 32b c)e + (- 128a c + 56b c )d e - 48b c d e +--R + +--R 4 3 +--R 32c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 4 4 2 3 3 +--R (96a c + 48a b c - 24b )e + (- 48a b c + 48b c)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 144a c - 36b c )d e + 48b c d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 2 3 2 2 2 +--R (144a b c - 48a b )e + (- 96a c + 96a b c)d e - 144a b c d e +--R + +--R 2 2 3 +--R 24b c d e +--R * +--R x +--R + +--R 3 2 2 4 2 3 2 2 2 2 2 3 +--R (64a c - 24a b )e + 48a b c d e - 96a c d e + 16a b c d e +--R + +--R 3 2 2 4 +--R (- 8a c + 2b c )d +--R * +--R +-+ +--R \|c +--R / +--R 4 2 3 2 3 3 2 2 3 2 2 +-+ +--R ((12a c - 3b c )x + (12a b c - 3b c )x + 12a c - 3a b c )\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 465 +t0:=(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 465 +r0:=-2/3*(d+e*x)^3/(a+b*x+c*x^2)^(3/2)+2*e^3*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-4*e*(d+e*x)*(b*d-2*a*e+(2*c*d-_ + b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+4*e^2*(2*c*d-b*e)*sqrt(a+b*x+_ + c*x^2)/(c*(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 3 3 2 2 3 +--R ((24a c - 6b c)e x + (24a b c - 6b )e x + (24a c - 6a b )e ) +--R * +--R +--------------+ +--R | 2 2c x + b +--R \|c x + b x + a atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 32a c + 14b c)e - 24b c d e + 24c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 12a b c + 12b )e + (- 72a c - 18b c)d e + 36b c d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R ((- 24a c + 24a b )e - 72a b c d e + 18b c d e)x + 12a b e +--R + +--R 2 2 2 2 2 3 +--R - 48a c d e + 12a b c d e + (- 8a c + 2b c)d +--R * +--R +-+ +--R \|c +--R / +--R 3 2 2 2 2 3 2 2 2 +-+ +--R ((12a c - 3b c )x + (12a b c - 3b c)x + 12a c - 3a b c)\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 of 465 +t0:=(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R 2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 465 +r0:=-2/3*(d+e*x)^2/(a+b*x+c*x^2)^(3/2)-8/3*e*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + ((b^2-4*a*c)*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 2 3 2 2 2 +--R (- 8b c e + 16c d e)x + ((- 24a c - 6b )e + 24b c d e)x +--R + +--R 2 2 2 2 2 2 +--R (- 24a b e + 12b d e)x - 16a e + 8a b d e + (- 8a c + 2b )d +--R / +--R +--------------+ +--R 2 2 2 3 2 2 | 2 +--R ((12a c - 3b c)x + (12a b c - 3b )x + 12a c - 3a b )\|c x + b x + a +--R Type: Expression(Integer) +--E 353 + +--S 354 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 465 +t0:=(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 +--R 2c e x + (b e + 2c d)x + b d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 355 + +--S 356 of 465 +r0:=-2/3*(d+e*x)/(a+b*x+c*x^2)^(3/2)-4/3*e*(b+2*c*x)/((b^2-4*a*c)*_ + sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 2 +--R 8c e x + 12b c e x + 6b e x + 4a b e + (- 8a c + 2b )d +--R ----------------------------------------------------------------------- +--R +--------------+ +--R 2 2 2 3 2 2 | 2 +--R ((12a c - 3b c)x + (12a b c - 3b )x + 12a c - 3a b )\|c x + b x + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 465 +t0:=(b+2*c*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2c x + b +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 358 + +--S 359 of 465 +r0:=(-2/3)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +--R (2) - ------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (3c x + 3b x + 3a)\|c x + b x + a +--R Type: Expression(Integer) +--E 359 + +--S 360 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 465 +t0:=(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 465 +r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-e^3*(2*c*d-b*e)*_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)-2/3*e*(5*b^2*c*d*e-_ + 12*a*c^2*d*e-3*b^3*e^2-2*b*c*(c*d^2-5*a*e^2)-c*(4*c^2*d^2+3*b^2*e^2-_ + 4*c*e*(b*d+2*a*e))*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2)) +--R +--R +--R (2) +--R 2 3 4 3 2 2 3 2 +--R ((- 12a b c + 3b c)e + (24a c - 6b c )d e )x +--R + +--R 2 4 4 2 3 3 +--R ((- 12a b c + 3b )e + (24a b c - 6b c)d e )x +--R + +--R 2 3 4 2 2 2 3 +--R (- 12a b c + 3a b )e + (24a c - 6a b c)d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 2 2 3 3 2 4 2 3 +--R ((16a c - 6b c )e + 8b c d e - 8c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 2 +--R ((36a b c - 12b c)e + (- 24a c + 18b c )d e - 12b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 2 2 2 +--R ((24a c + 12a b c - 6b )e + (- 24a b c + 12b c)d e - 6b c d e)x +--R + +--R 2 3 3 2 2 2 4 2 +--R (28a b c - 8a b )e + (- 32a c + 4a b c + 2b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (12a b c - 4b c)d e + (- 8a c + 2b c )d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 3 2 2 2 4 2 2 3 3 +--R (12a c - 3a b c)e + (- 24a b c + 6a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (24a c + 6a b c - 3b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 4 +--R (12a c - 3b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 2 2 4 3 +--R (12a b c - 3a b )e + (- 24a b c + 6a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (24a b c + 6a b c - 3b )d e + (- 24a b c + 6b c)d e +--R + +--R 3 3 2 4 +--R (12a b c - 3b c )d +--R * +--R x +--R + +--R 4 3 2 4 3 2 3 3 +--R (12a c - 3a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (24a c + 6a b c - 3a b )d e + (- 24a b c + 6a b c)d e +--R + +--R 2 3 2 2 4 +--R (12a c - 3a b c )d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 362 + +--S 363 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 465 +t0:=(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + ((2a c + b )e + 4b c d e + c d )x +--R + +--R 2 2 2 3 +--R (2a b e + (4a c + 2b )d e + 2b c d )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (a e + 4a b d e + (2a c + b )d )x + (2a d e + 2a b d )x + a d +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 364 + +--S 365 of 465 +r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(d+e*x)*(a+b*x+c*x^2)^(3/2))-1/2*e^3*(16*c^2*d^2+_ + 5*b^2*e^2-4*c*e*(4*b*d+a*e))*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)-_ + 2/3*e*(9*b^2*c*d*e-20*a*c^2*d*e-5*b^3*e^2-4*b*c*(c*d^2-4*a*e^2)-_ + c*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*x)/((b^2-4*a*c)*(c*d^2-_ + b*d*e+a*e^2)^2*(d+e*x)*sqrt(a+b*x+c*x^2))+1/3*e^2*(2*c*d-b*e)*_ + (8*c^2*d^2+15*b^2*e^2-4*c*e*(2*b*d+13*a*e))*sqrt(a+b*x+c*x^2)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)) +--R +--R +--R (2) +--R 2 3 2 2 4 6 3 3 2 5 +--R (- 48a c + 72a b c - 15b c)e + (- 192a b c + 48b c )d e +--R + +--R 4 2 3 2 4 +--R (192a c - 48b c )d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 6 +--R (- 48a b c + 72a b c - 15b )e +--R + +--R 2 3 2 2 4 5 4 2 3 3 3 +--R (- 48a c - 120a b c + 33b c)d e + (192a c - 48b c )d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 6 +--R (- 48a c + 72a b c - 15a b )e +--R + +--R 2 2 3 5 5 +--R (- 240a b c + 120a b c - 15b )d e +--R + +--R 2 3 2 2 4 2 4 3 3 2 3 3 +--R (192a c - 240a b c + 48b c)d e + (192a b c - 48b c )d e +--R * +--R x +--R + +--R 3 2 2 2 4 5 2 2 3 2 4 +--R (- 48a c + 72a b c - 15a b )d e + (- 192a b c + 48a b c)d e +--R + +--R 2 3 2 2 3 3 +--R (192a c - 48a b c )d e +--R * +--R +--------------+ +--R | 2 (b e - 2c d)x + 2a e - b d +--R \|c x + b x + a atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 3 3 2 5 4 2 3 4 4 2 3 +--R (- 104a b c + 30b c )e + (208a c - 76b c )d e + 48b c d e +--R + +--R 5 3 2 +--R - 32c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 4 5 3 3 2 4 +--R (48a c - 228a b c + 60b c)e + (400a b c - 132b c )d e +--R + +--R 4 2 3 2 3 5 4 +--R (16a c + 44b c )d e - 32c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 5 +--R (- 96a b c - 84a b c + 30b )e +--R + +--R 2 3 2 2 4 4 3 3 2 2 3 +--R (336a c + 12a b c - 36b c)d e + (240a b c - 60b c )d e +--R + +--R 4 2 3 3 2 4 4 +--R (- 144a c + 84b c )d e - 48b c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 4 5 +--R (64a c - 168a b c + 40a b )e +--R + +--R 2 2 3 5 4 +--R (288a b c - 152a b c + 20b )d e +--R + +--R 2 3 2 2 4 2 3 3 3 2 3 2 +--R (48a c + 180a b c - 60b c)d e + (- 112a b c + 60b c )d e +--R + +--R 4 2 3 4 +--R (- 16a c - 20b c )d e +--R * +--R x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (- 24a b c + 6a b )e + (112a c - 132a b c + 28a b )d e +--R + +--R 2 2 3 5 2 3 2 3 2 2 4 3 2 +--R (240a b c - 56a b c - 4b )d e + (- 144a c + 12a b c + 12b c)d e +--R + +--R 3 3 2 4 4 2 3 5 +--R (32a b c - 12b c )d e + (- 16a c + 4b c )d +--R * +--R +-------------------+ +--R | 2 2 +--R \|a e - b d e + c d +--R / +--R 4 2 3 2 7 3 2 2 3 6 +--R (24a c - 6a b c)e + (- 72a b c + 18a b c)d e +--R + +--R 3 3 2 2 2 4 2 5 +--R (72a c + 54a b c - 18a b c)d e +--R + +--R 2 3 3 2 5 3 4 +--R (- 144a b c + 12a b c + 6b c)d e +--R + +--R 2 4 2 3 4 2 4 3 4 3 3 5 2 +--R (72a c + 54a b c - 18b c )d e + (- 72a b c + 18b c )d e +--R + +--R 5 2 4 6 +--R (24a c - 6b c )d e +--R * +--R 3 +--R x +--R + +--R 4 3 3 7 4 2 3 2 2 4 6 +--R (24a b c - 6a b )e + (24a c - 78a b c + 18a b )d e +--R + +--R 2 3 5 2 5 3 3 2 2 2 4 6 3 4 +--R (72a b c - 18a b )d e + (72a c - 90a b c - 6a b c + 6b )d e +--R + +--R 2 3 3 2 5 4 3 2 4 2 3 5 2 +--R (- 72a b c + 66a b c - 12b c)d e + (72a c - 18a b c )d e +--R + +--R 4 3 3 6 5 2 4 7 +--R (- 48a b c + 12b c )d e + (24a c - 6b c )d +--R * +--R 2 +--R x +--R + +--R 5 4 2 7 4 3 3 6 +--R (24a c - 6a b )e + (- 48a b c + 12a b )d e +--R + +--R 4 2 3 2 2 5 3 2 2 3 5 3 4 +--R (72a c - 18a b c)d e + (- 72a b c + 66a b c - 12a b )d e +--R + +--R 3 3 2 2 2 4 6 4 3 3 2 5 5 2 +--R (72a c - 90a b c - 6a b c + 6b )d e + (72a b c - 18b c)d e +--R + +--R 2 4 2 3 4 2 6 4 3 3 7 +--R (24a c - 78a b c + 18b c )d e + (24a b c - 6b c )d +--R * +--R x +--R + +--R 5 4 2 6 4 3 3 2 5 +--R (24a c - 6a b )d e + (- 72a b c + 18a b )d e +--R + +--R 4 2 3 2 2 4 3 4 3 2 2 3 5 4 3 +--R (72a c + 54a b c - 18a b )d e + (- 144a b c + 12a b c + 6a b )d e +--R + +--R 3 3 2 2 2 4 5 2 2 3 3 2 6 +--R (72a c + 54a b c - 18a b c)d e + (- 72a b c + 18a b c )d e +--R + +--R 2 4 2 3 7 +--R (24a c - 6a b c )d +--R * +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R \|a e - b d e + c d \|c x + b x + a +--R Type: Expression(Integer) +--E 365 + +--S 366 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 of 465 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 4 2 2 2 2 3 +--R 2c e x + (3b c e + 4c d e)x + ((2a c + b )e + 6b c d e + 2c d )x +--R + +--R 2 2 2 2 2 2 +--R (a b e + (4a c + 2b )d e + 3b c d )x + (2a b d e + (2a c + b )d )x +--R + +--R 2 +--R a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 367 + +--S 368 of 465 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(7/2)/e^4+2/9*_ + (6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(9/2)/e^4-6/11*c*_ + (2*c*d-b*e)*(d+e*x)^(11/2)/e^4+4/13*c^2*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 +--R 2772c e x + (4914b c e + 6804c d e )x +--R + +--R 2 6 5 2 2 4 4 +--R ((4004a c + 2002b )e + 12558b c d e + 4452c d e )x +--R + +--R 6 2 5 2 4 2 3 3 3 +--R (2574a b e + (10868a c + 5434b )d e + 8814b c d e + 60c d e )x +--R + +--R 5 2 2 4 3 3 2 4 2 2 +--R (7722a b d e + (8580a c + 4290b )d e + 234b c d e - 72c d e )x +--R + +--R 2 4 2 3 3 4 2 2 5 +--R (7722a b d e + (572a c + 286b )d e - 312b c d e + 96c d e)x +--R + +--R 3 3 2 4 2 5 2 6 +--R 2574a b d e + (- 1144a c - 572b )d e + 624b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 368 + +--S 369 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 +--R 2c e x + (3b c e + 2c d)x + ((2a c + b )e + 3b c d)x +--R + +--R 2 +--R (a b e + (2a c + b )d)x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 370 + +--S 371 of 465 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(5/2)/e^4+_ + 2/7*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(7/2)/e^4-_ + 2/3*c*(2*c*d-b*e)*(d+e*x)^(9/2)/e^4+4/11*c^2*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 +--R 420c e x + (770b c e + 560c d e )x +--R + +--R 2 5 4 2 2 3 3 +--R ((660a c + 330b )e + 1100b c d e + 20c d e )x +--R + +--R 5 2 4 2 3 2 3 2 2 +--R (462a b e + (1056a c + 528b )d e + 66b c d e - 24c d e )x +--R + +--R 4 2 2 3 3 2 2 4 +--R (924a b d e + (132a c + 66b )d e - 88b c d e + 32c d e)x +--R + +--R 2 3 2 3 2 4 2 5 +--R 462a b d e + (- 264a c - 132b )d e + 176b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Expression(Integer) +--E 371 + +--S 372 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)*sqrt(d+e*x) +--R +--R +--R 2 3 2 2 +-------+ +--R (1) (2c x + 3b c x + (2a c + b )x + a b)\|e x + d +--R Type: Expression(Integer) +--E 373 + +--S 374 of 465 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2)/e^4+_ + 2/5*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(5/2)/e^4-_ + 6/7*c*(2*c*d-b*e)*(d+e*x)^(7/2)/e^4+4/9*c^2*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 140c e x + (270b c e + 20c d e )x +--R + +--R 2 4 3 2 2 2 2 +--R ((252a c + 126b )e + 54b c d e - 24c d e )x +--R + +--R 4 2 3 2 2 2 3 3 +--R (210a b e + (84a c + 42b )d e - 72b c d e + 32c d e)x + 210a b d e +--R + +--R 2 2 2 3 2 4 +--R (- 168a c - 84b )d e + 144b c d e - 64c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 374 + +--S 375 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 376 + +--S 377 of 465 +r0:=2/3*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(3/2)/e^4-_ + 6/5*c*(2*c*d-b*e)*(d+e*x)^(5/2)/e^4+4/7*c^2*(d+e*x)^(7/2)/e^4-_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 60c e x + (126b c e - 72c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((140a c + 70b )e - 168b c d e + 96c d e)x + 210a b e +--R + +--R 2 2 2 2 3 +--R (- 280a c - 140b )d e + 336b c d e - 192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 377 + +--S 378 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 379 + +--S 380 of 465 +r0:=-2*c*(2*c*d-b*e)*(d+e*x)^(3/2)/e^4+4/5*c^2*(d+e*x)^(5/2)/e^4+_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*sqrt(d+e*x))+2*(6*c^2*d^2+_ + b^2*e^2-2*c*e*(3*b*d-a*e))*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 4c e x + (10b c e - 8c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((20a c + 10b )e - 40b c d e + 32c d e)x - 10a b e +--R + +--R 2 2 2 2 3 +--R (40a c + 20b )d e - 80b c d e + 64c d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Expression(Integer) +--E 380 + +--S 381 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 +--R 2c x + 3b c x + (2a c + b )x + a b +--R (1) ------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 382 + +--S 383 of 465 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^(3/2))+_ + 4/3*c^2*(d+e*x)^(3/2)/e^4-2*(6*c^2*d^2+b^2*e^2-2*c*e*_ + (3*b*d-a*e))/(e^4*sqrt(d+e*x))-6*c*(2*c*d-b*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 +--R 4c e x + (18b c e - 24c d e )x +--R + +--R 2 3 2 2 2 3 +--R ((- 12a c - 6b )e + 72b c d e - 96c d e)x - 2a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c - 4b )d e + 48b c d e - 64c d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 383 + +--S 384 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 of 465 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 2 7 2 2 3 6 2 2 2 2 3 2 5 +--R 2c e x + (5b c e + 4c d e)x + ((4a c + 4b c)e + 10b c d e + 2c d )x +--R + +--R 3 2 2 2 2 2 4 +--R ((6a b c + b )e + (8a c + 8b c)d e + 5b c d )x +--R + +--R 2 2 2 3 2 2 2 3 +--R ((2a c + 2a b )e + (12a b c + 2b )d e + (4a c + 4b c)d )x +--R + +--R 2 2 2 2 3 2 2 +--R (a b e + (4a c + 4a b )d e + (6a b c + b )d )x +--R + +--R 2 2 2 2 2 2 +--R (2a b d e + (2a c + 2a b )d )x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 385 + +--S 386 of 465 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(7/2)/e^6+_ + 4/9*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(9/2)/e^6-2/11*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(11/2)/e^6+8/13*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(13/2)/e^6-2/3*c^2*(2*c*d-b*e)*_ + (d+e*x)^(15/2)/e^6+4/17*c^3*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 3 8 8 2 8 3 7 7 +--R 36036c e x + (102102b c e + 84084c d e )x +--R + +--R 2 2 8 2 7 3 2 6 6 +--R ((94248a c + 94248b c)e + 243474b c d e + 50820c d e )x +--R + +--R 3 8 2 2 7 +--R (167076a b c + 27846b )e + (231336a c + 231336b c)d e +--R + +--R 2 2 6 3 3 5 +--R 152082b c d e + 252c d e +--R * +--R 5 +--R x +--R + +--R 2 2 8 3 7 +--R (68068a c + 68068a b )e + (426972a b c + 71162b )d e +--R + +--R 2 2 2 6 2 3 5 3 4 4 +--R (151368a c + 151368b c)d e + 1190b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 7 +--R 43758a b e + (184756a c + 184756a b )d e +--R + +--R 3 2 6 2 2 3 5 +--R (299676a b c + 49946b )d e + (2040a c + 2040b c)d e +--R + +--R 2 4 4 3 5 3 +--R - 1360b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 2 6 +--R 131274a b d e + (145860a c + 145860a b )d e +--R + +--R 3 3 5 2 2 4 4 +--R (7956a b c + 1326b )d e + (- 2448a c - 2448b c)d e +--R + +--R 2 5 3 3 6 2 +--R 1632b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 6 2 2 3 5 +--R 131274a b d e + (9724a c + 9724a b )d e +--R + +--R 3 4 4 2 2 5 3 +--R (- 10608a b c - 1768b )d e + (3264a c + 3264b c)d e +--R + +--R 2 6 2 3 7 +--R - 2176b c d e + 512c d e +--R * +--R x +--R + +--R 2 3 5 2 2 4 4 +--R 43758a b d e + (- 19448a c - 19448a b )d e +--R + +--R 3 5 3 2 2 6 2 2 7 +--R (21216a b c + 3536b )d e + (- 6528a c - 6528b c)d e + 4352b c d e +--R + +--R 3 8 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Expression(Integer) +--E 386 + +--S 387 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 3 6 2 3 5 2 2 2 4 +--R 2c e x + (5b c e + 2c d)x + ((4a c + 4b c)e + 5b c d)x +--R + +--R 3 2 2 3 +--R ((6a b c + b )e + (4a c + 4b c)d)x +--R + +--R 2 2 3 2 2 2 2 2 +--R ((2a c + 2a b )e + (6a b c + b )d)x + (a b e + (2a c + 2a b )d)x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 388 + +--S 389 of 465 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(5/2)/e^6+_ + 4/7*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(7/2)/e^6-2/9*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(9/2)/e^6+8/11*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(11/2)/e^6-10/13*c^2*(2*c*d-b*e)*_ + (d+e*x)^(13/2)/e^6+4/15*c^3*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 3 7 7 2 7 3 6 6 +--R 12012c e x + (34650b c e + 14784c d e )x +--R + +--R 2 2 7 2 6 3 2 5 5 +--R ((32760a c + 32760b c)e + 44100b c d e + 252c d e )x +--R + +--R 3 7 2 2 6 +--R (60060a b c + 10010b )e + (43680a c + 43680b c)d e +--R + +--R 2 2 5 3 3 4 +--R 1050b c d e - 280c d e +--R * +--R 4 +--R x +--R + +--R 2 2 7 3 6 +--R (25740a c + 25740a b )e + (85800a b c + 14300b )d e +--R + +--R 2 2 2 5 2 3 4 3 4 3 +--R (1560a c + 1560b c)d e - 1200b c d e + 320c d e +--R * +--R 3 +--R x +--R + +--R 2 7 2 2 6 3 2 5 +--R 18018a b e + (41184a c + 41184a b )d e + (5148a b c + 858b )d e +--R + +--R 2 2 3 4 2 4 3 3 5 2 +--R (- 1872a c - 1872b c)d e + 1440b c d e - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 2 5 +--R 36036a b d e + (5148a c + 5148a b )d e +--R + +--R 3 3 4 2 2 4 3 +--R (- 6864a b c - 1144b )d e + (2496a c + 2496b c)d e +--R + +--R 2 5 2 3 6 +--R - 1920b c d e + 512c d e +--R * +--R x +--R + +--R 2 2 5 2 2 3 4 +--R 18018a b d e + (- 10296a c - 10296a b )d e +--R + +--R 3 4 3 2 2 5 2 2 6 +--R (13728a b c + 2288b )d e + (- 4992a c - 4992b c)d e + 3840b c d e +--R + +--R 3 7 +--R - 1024c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 389 + +--S 390 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x +--R + +--R 2 +--R a b +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 391 + +--S 392 of 465 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(3/2)/e^6+_ + 4/5*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(5/2)/e^6-2/7*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))*(d+e*x)^(7/2)/e^6+8/9*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(9/2)/e^6-10/11*c^2*(2*c*d-b*e)*_ + (d+e*x)^(11/2)/e^6+4/13*c^3*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 13860c e x + (40950b c e + 1260c d e )x +--R + +--R 2 2 6 2 5 3 2 4 4 +--R ((40040a c + 40040b c)e + 4550b c d e - 1400c d e )x +--R + +--R 3 6 2 2 5 2 2 4 +--R (77220a b c + 12870b )e + (5720a c + 5720b c)d e - 5200b c d e +--R + +--R 3 3 3 +--R 1600c d e +--R * +--R 3 +--R x +--R + +--R 2 2 6 3 5 +--R (36036a c + 36036a b )e + (15444a b c + 2574b )d e +--R + +--R 2 2 2 4 2 3 3 3 4 2 +--R (- 6864a c - 6864b c)d e + 6240b c d e - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 6 2 2 5 +--R 30030a b e + (12012a c + 12012a b )d e +--R + +--R 3 2 4 2 2 3 3 +--R (- 20592a b c - 3432b )d e + (9152a c + 9152b c)d e +--R + +--R 2 4 2 3 5 +--R - 8320b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 2 4 +--R 30030a b d e + (- 24024a c - 24024a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 +--R (41184a b c + 6864b )d e + (- 18304a c - 18304b c)d e + 16640b c d e +--R + +--R 3 6 +--R - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 392 + +--S 393 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 394 + +--S 395 of 465 +r0:=4/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(3/2)/e^6-2/5*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))*(d+e*x)^(5/2)/e^6+8/7*c*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e))*(d+e*x)^(7/2)/e^6-10/9*c^2*(2*c*d-b*e)*_ + (d+e*x)^(9/2)/e^6+4/11*c^3*(d+e*x)^(11/2)/e^6-2*(2*c*d-b*e)*_ + (c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 1260c e x + (3850b c e - 1400c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((3960a c + 3960b c)e - 4400b c d e + 1600c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (8316a b c + 1386b )e + (- 4752a c - 4752b c)d e + 5280b c d e +--R + +--R 3 3 2 +--R - 1920c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (4620a c + 4620a b )e + (- 11088a b c - 1848b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (6336a c + 6336b c)d e - 7040b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R 6930a b e + (- 9240a c - 9240a b )d e + (22176a b c + 3696b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 12672a c - 12672b c)d e + 14080b c d e - 5120c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 395 + +--S 396 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 397 + +--S 398 of 465 +r0:=-2/3*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + (d+e*x)^(3/2)/e^6+8/5*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + (d+e*x)^(5/2)/e^6-10/7*c^2*(2*c*d-b*e)*(d+e*x)^(7/2)/e^6+4/9*c^3*_ + (d+e*x)^(9/2)/e^6+2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*_ + sqrt(d+e*x))+4*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 140c e x + (450b c e - 200c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((504a c + 504b c)e - 720b c d e + 320c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (1260a b c + 210b )e + (- 1008a c - 1008b c)d e + 1440b c d e +--R + +--R 3 3 2 +--R - 640c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (1260a c + 1260a b )e + (- 5040a b c - 840b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (4032a c + 4032b c)d e - 5760b c d e + 2560c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 630a b e + (2520a c + 2520a b )d e + (- 10080a b c - 1680b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (8064a c + 8064b c)d e - 11520b c d e + 5120c d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 398 + +--S 399 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 3 5 2 4 2 2 3 3 2 2 2 2 +--R 2c x + 5b c x + (4a c + 4b c)x + (6a b c + b )x + (2a c + 2a b )x + a b +--R ---------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 400 + +--S 401 of 465 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^(3/2))+_ + 8/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(3/2)/e^6-_ + 2*c^2*(2*c*d-b*e)*(d+e*x)^(5/2)/e^6+4/7*c^3*(d+e*x)^(7/2)/e^6-_ + 4*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/(e^6*_ + sqrt(d+e*x))-2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 12c e x + (42b c e - 24c d e )x +--R + +--R 2 2 5 2 4 3 2 3 3 +--R ((56a c + 56b c)e - 112b c d e + 64c d e )x +--R + +--R 3 5 2 2 4 2 2 3 +--R (252a b c + 42b )e + (- 336a c - 336b c)d e + 672b c d e +--R + +--R 3 3 2 +--R - 384c d e +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 4 +--R (- 84a c - 84a b )e + (1008a b c + 168b )d e +--R + +--R 2 2 2 3 2 3 2 3 4 +--R (- 1344a c - 1344b c)d e + 2688b c d e - 1536c d e +--R * +--R x +--R + +--R 2 5 2 2 4 3 2 3 +--R - 14a b e + (- 56a c - 56a b )d e + (672a b c + 112b )d e +--R + +--R 2 2 3 2 2 4 3 5 +--R (- 896a c - 896b c)d e + 1792b c d e - 1024c d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Expression(Integer) +--E 401 + +--S 402 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 465 +t0:=(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 2 9 3 2 4 8 +--R 2c e x + (7b c e + 4c d e)x +--R + +--R 3 2 2 2 3 4 2 7 +--R ((6a c + 9b c )e + 14b c d e + 2c d )x +--R + +--R 2 3 2 3 2 2 3 2 6 +--R ((15a b c + 5b c)e + (12a c + 18b c )d e + 7b c d )x +--R + +--R 2 2 2 4 2 2 3 3 2 2 2 5 +--R ((6a c + 12a b c + b )e + (30a b c + 10b c)d e + (6a c + 9b c )d )x +--R + +--R 2 3 2 2 2 2 4 +--R (9a b c + 3a b )e + (12a c + 24a b c + 2b )d e +--R + +--R 2 3 2 +--R (15a b c + 5b c)d +--R * +--R 4 +--R x +--R + +--R 3 2 2 2 2 3 2 2 2 4 2 3 +--R ((2a c + 3a b )e + (18a b c + 6a b )d e + (6a c + 12a b c + b )d )x +--R + +--R 3 2 3 2 2 2 3 2 2 +--R (a b e + (4a c + 6a b )d e + (9a b c + 3a b )d )x +--R + +--R 3 3 2 2 2 3 2 +--R (2a b d e + (2a c + 3a b )d )x + a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 403 + +--S 404 of 465 +r0:=-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(7/2)/e^8+_ + 2/9*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(9/2)/e^8-6/11*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(11/2)/e^8+2/13*(70*c^4*d^4+_ + b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+_ + 6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(13/2)/e^8-_ + 2/3*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^(15/2)/e^8+6/17*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(17/2)/e^8-14/19*c^3*(2*c*d-b*e)*(d+e*x)^(19/2)/e^8+_ + 4/21*c^4*(d+e*x)^(21/2)/e^8 +--R +--R +--R (2) +--R 4 10 10 3 10 4 9 9 +--R 554268c e x + (2144142b c e + 1254396c d e )x +--R + +--R 3 2 2 10 3 9 4 2 8 8 +--R ((2054052a c + 3081078b c )e + 4918914b c d e + 725868c d e )x +--R + +--R 2 3 10 3 2 2 9 +--R (5819814a b c + 1939938b c)e + (4792788a c + 7189182b c )d e +--R + +--R 3 2 8 4 3 7 +--R 2900898b c d e + 1716c d e +--R * +--R 7 +--R x +--R + +--R 2 2 2 4 10 +--R (2686068a c + 5372136a b c + 447678b )e +--R + +--R 2 3 9 3 2 2 2 8 +--R (13878018a b c + 4626006b c)d e + (2896740a c + 4345110b c )d e +--R + +--R 3 3 7 4 4 6 +--R 9702b c d e - 1848c d e +--R * +--R 6 +--R x +--R + +--R 2 3 10 +--R (4761666a b c + 1587222a b )e +--R + +--R 2 2 2 4 9 +--R (6593076a c + 13186152a b c + 1098846b )d e +--R + +--R 2 3 2 8 3 2 2 3 7 +--R (8668674a b c + 2889558b c)d e + (14364a c + 21546b c )d e +--R + +--R 3 4 6 4 5 5 +--R - 10584b c d e + 2016c d e +--R * +--R 5 +--R x +--R + +--R 3 2 2 10 2 3 9 +--R (1293292a c + 1939938a b )e + (12168702a b c + 4056234a b )d e +--R + +--R 2 2 2 4 2 8 +--R (4313988a c + 8627976a b c + 718998b )d e +--R + +--R 2 3 3 7 3 2 2 4 6 +--R (67830a b c + 22610b c)d e + (- 15960a c - 23940b c )d e +--R + +--R 3 5 5 4 6 4 +--R 11760b c d e - 2240c d e +--R * +--R 4 +--R x +--R + +--R 3 10 3 2 2 9 +--R 831402a b e + (3510364a c + 5265546a b )d e +--R + +--R 2 3 2 8 +--R (8540766a b c + 2846922a b )d e +--R + +--R 2 2 2 4 3 7 +--R (58140a c + 116280a b c + 9690b )d e +--R + +--R 2 3 4 6 3 2 2 5 5 +--R (- 77520a b c - 25840b c)d e + (18240a c + 27360b c )d e +--R + +--R 3 6 4 4 7 3 +--R - 13440b c d e + 2560c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 2 8 +--R 2494206a b d e + (2771340a c + 4157010a b )d e +--R + +--R 2 3 3 7 +--R (226746a b c + 75582a b )d e +--R + +--R 2 2 2 4 4 6 +--R (- 69768a c - 139536a b c - 11628b )d e +--R + +--R 2 3 5 5 3 2 2 6 4 +--R (93024a b c + 31008b c)d e + (- 21888a c - 32832b c )d e +--R + +--R 3 7 3 4 8 2 +--R 16128b c d e - 3072c d e +--R * +--R 2 +--R x +--R + +--R 3 2 8 3 2 2 3 7 +--R 2494206a b d e + (184756a c + 277134a b )d e +--R + +--R 2 3 4 6 +--R (- 302328a b c - 100776a b )d e +--R + +--R 2 2 2 4 5 5 +--R (93024a c + 186048a b c + 15504b )d e +--R + +--R 2 3 6 4 3 2 2 7 3 +--R (- 124032a b c - 41344b c)d e + (29184a c + 43776b c )d e +--R + +--R 3 8 2 4 9 +--R - 21504b c d e + 4096c d e +--R * +--R x +--R + +--R 3 3 7 3 2 2 4 6 +--R 831402a b d e + (- 369512a c - 554268a b )d e +--R + +--R 2 3 5 5 +--R (604656a b c + 201552a b )d e +--R + +--R 2 2 2 4 6 4 +--R (- 186048a c - 372096a b c - 31008b )d e +--R + +--R 2 3 7 3 3 2 2 8 2 +--R (248064a b c + 82688b c)d e + (- 58368a c - 87552b c )d e +--R + +--R 3 9 4 10 +--R 43008b c d e - 8192c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Expression(Integer) +--E 404 + +--S 405 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 4 8 3 4 7 3 2 2 3 6 +--R 2c e x + (7b c e + 2c d)x + ((6a c + 9b c )e + 7b c d)x +--R + +--R 2 3 3 2 2 5 +--R ((15a b c + 5b c)e + (6a c + 9b c )d)x +--R + +--R 2 2 2 4 2 3 4 +--R ((6a c + 12a b c + b )e + (15a b c + 5b c)d)x +--R + +--R 2 3 2 2 2 4 3 +--R ((9a b c + 3a b )e + (6a c + 12a b c + b )d)x +--R + +--R 3 2 2 2 3 2 3 3 2 2 +--R ((2a c + 3a b )e + (9a b c + 3a b )d)x + (a b e + (2a c + 3a b )d)x +--R + +--R 3 +--R a b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 406 + +--S 407 of 465 +r0:=-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(5/2)/e^8+_ + 2/7*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(7/2)/e^8-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(9/2)/e^8+2/11*(70*c^4*d^4+_ + b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+_ + 6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(11/2)/e^8-_ + 10/13*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*_ + (d+e*x)^(13/2)/e^8+2/5*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(15/2)/e^8-14/17*c^3*(2*c*d-b*e)*(d+e*x)^(17/2)/e^8+_ + 4/19*c^4*(d+e*x)^(19/2)/e^8 +--R +--R +--R (2) +--R 4 9 9 3 9 4 8 8 +--R 1021020c e x + (3993990b c e + 1201200c d e )x +--R + +--R 3 2 2 9 3 8 4 2 7 7 +--R ((3879876a c + 5819814b c )e + 4792788b c d e + 12012c d e )x +--R + +--R 2 3 9 3 2 2 8 +--R (11191950a b c + 3730650b c)e + (4775232a c + 7162848b c )d e +--R + +--R 3 2 7 4 3 6 +--R 61446b c d e - 12936c d e +--R * +--R 6 +--R x +--R + +--R 2 2 2 4 9 +--R (5290740a c + 10581480a b c + 881790b )e +--R + +--R 2 3 8 3 2 2 2 7 +--R (14244300a b c + 4748100b c)d e + (81396a c + 122094b c )d e +--R + +--R 3 3 6 4 4 5 +--R - 67032b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 3 9 +--R (9699690a b c + 3233230a b )e +--R + +--R 2 2 2 4 8 +--R (7054320a c + 14108640a b c + 1175720b )d e +--R + +--R 2 3 2 7 3 2 2 3 6 +--R (339150a b c + 113050b c)d e + (- 90440a c - 135660b c )d e +--R + +--R 3 4 5 4 5 4 +--R 74480b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 3 2 2 9 2 3 8 +--R (2771340a c + 4157010a b )e + (13856700a b c + 4618900a b )d e +--R + +--R 2 2 2 4 2 7 +--R (251940a c + 503880a b c + 41990b )d e +--R + +--R 2 3 3 6 3 2 2 4 5 +--R (- 387600a b c - 129200b c)d e + (103360a c + 155040b c )d e +--R + +--R 3 5 4 4 6 3 +--R - 85120b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 9 3 2 2 8 +--R 1939938a b e + (4434144a c + 6651216a b )d e +--R + +--R 2 3 2 7 +--R (831402a b c + 277134a b )d e +--R + +--R 2 2 2 4 3 6 +--R (- 302328a c - 604656a b c - 50388b )d e +--R + +--R 2 3 4 5 3 2 2 5 4 +--R (465120a b c + 155040b c)d e + (- 124032a c - 186048b c )d e +--R + +--R 3 6 3 4 7 2 +--R 102144b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 2 7 +--R 3879876a b d e + (554268a c + 831402a b )d e +--R + +--R 2 3 3 6 +--R (- 1108536a b c - 369512a b )d e +--R + +--R 2 2 2 4 4 5 +--R (403104a c + 806208a b c + 67184b )d e +--R + +--R 2 3 5 4 3 2 2 6 3 +--R (- 620160a b c - 206720b c)d e + (165376a c + 248064b c )d e +--R + +--R 3 7 2 4 8 +--R - 136192b c d e + 28672c d e +--R * +--R x +--R + +--R 3 2 7 3 2 2 3 6 +--R 1939938a b d e + (- 1108536a c - 1662804a b )d e +--R + +--R 2 3 4 5 +--R (2217072a b c + 739024a b )d e +--R + +--R 2 2 2 4 5 4 +--R (- 806208a c - 1612416a b c - 134368b )d e +--R + +--R 2 3 6 3 3 2 2 7 2 +--R (1240320a b c + 413440b c)d e + (- 330752a c - 496128b c )d e +--R + +--R 3 8 4 9 +--R 272384b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 4849845e +--R Type: Expression(Integer) +--E 407 + +--S 408 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 409 + +--S 410 of 465 +r0:=-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(3/2)/e^8+_ + 2/5*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(5/2)/e^8-6/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(7/2)/e^8+2/9*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(9/2)/e^8-10/11*c*_ + (2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(11/2)/e^8+_ + 6/13*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(13/2)/e^8-_ + 14/15*c^3*(2*c*d-b*e)*(d+e*x)^(15/2)/e^8+4/17*c^4*(d+e*x)^(17/2)/e^8 +--R +--R +--R (2) +--R 4 8 8 3 8 4 7 7 +--R 180180c e x + (714714b c e + 12012c d e )x +--R + +--R 3 2 2 8 3 7 4 2 6 6 +--R ((706860a c + 1060290b c )e + 54978b c d e - 12936c d e )x +--R + +--R 2 3 8 3 2 2 7 +--R (2088450a b c + 696150b c)e + (64260a c + 96390b c )d e +--R + +--R 3 2 6 4 3 5 +--R - 59976b c d e + 14112c d e +--R * +--R 5 +--R x +--R + +--R 2 2 2 4 8 +--R (1021020a c + 2042040a b c + 170170b )e +--R + +--R 2 3 7 3 2 2 2 6 +--R (232050a b c + 77350b c)d e + (- 71400a c - 107100b c )d e +--R + +--R 3 3 5 4 4 4 +--R 66640b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 3 8 +--R (1969110a b c + 656370a b )e +--R + +--R 2 2 2 4 7 +--R (145860a c + 291720a b c + 24310b )d e +--R + +--R 2 3 2 6 3 2 2 3 5 +--R (- 265200a b c - 88400b c)d e + (81600a c + 122400b c )d e +--R + +--R 3 4 4 4 5 3 +--R - 76160b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 8 2 3 7 +--R (612612a c + 918918a b )e + (393822a b c + 131274a b )d e +--R + +--R 2 2 2 4 2 6 +--R (- 175032a c - 350064a b c - 29172b )d e +--R + +--R 2 3 3 5 3 2 2 4 4 +--R (318240a b c + 106080b c)d e + (- 97920a c - 146880b c )d e +--R + +--R 3 5 3 4 6 2 +--R 91392b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 8 3 2 2 7 +--R 510510a b e + (204204a c + 306306a b )d e +--R + +--R 2 3 2 6 +--R (- 525096a b c - 175032a b )d e +--R + +--R 2 2 2 4 3 5 +--R (233376a c + 466752a b c + 38896b )d e +--R + +--R 2 3 4 4 3 2 2 5 3 +--R (- 424320a b c - 141440b c)d e + (130560a c + 195840b c )d e +--R + +--R 3 6 2 4 7 +--R - 121856b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 2 6 +--R 510510a b d e + (- 408408a c - 612612a b )d e +--R + +--R 2 3 3 5 +--R (1050192a b c + 350064a b )d e +--R + +--R 2 2 2 4 4 4 +--R (- 466752a c - 933504a b c - 77792b )d e +--R + +--R 2 3 5 3 3 2 2 6 2 +--R (848640a b c + 282880b c)d e + (- 261120a c - 391680b c )d e +--R + +--R 3 7 4 8 +--R 243712b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Expression(Integer) +--E 410 + +--S 411 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 412 + +--S 413 of 465 +r0:=2/3*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*_ + (d+e*x)^(3/2)/e^8-6/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5/2)/e^8+2/7*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(7/2)/e^8-10/9*c*(2*c*d-b*e)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(9/2)/e^8+6/11*c^2*_ + (14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(11/2)/e^8-14/13*c^3*_ + (2*c*d-b*e)*(d+e*x)^(13/2)/e^8+4/15*c^4*(d+e*x)^(15/2)/e^8-_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 12012c e x + (48510b c e - 12936c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((49140a c + 73710b c )e - 52920b c d e + 14112c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (150150a b c + 50050b c)e + (- 54600a c - 81900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 58800b c d e - 15680c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 +--R (77220a c + 154440a b c + 12870b )e +--R + +--R 2 3 6 3 2 2 2 5 +--R (- 171600a b c - 57200b c)d e + (62400a c + 93600b c )d e +--R + +--R 3 3 4 4 4 3 +--R - 67200b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (162162a b c + 54054a b )e +--R + +--R 2 2 2 4 6 +--R (- 92664a c - 185328a b c - 15444b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 74880a c - 112320b c )d e +--R + +--R 3 4 3 4 5 2 +--R 80640b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 216216a b c - 72072a b )d e +--R + +--R 2 2 2 4 2 5 +--R (123552a c + 247104a b c + 20592b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 274560a b c - 91520b c)d e + (99840a c + 149760b c )d e +--R + +--R 3 5 2 4 6 +--R - 107520b c d e + 28672c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R 90090a b e + (- 120120a c - 180180a b )d e +--R + +--R 2 3 2 5 +--R (432432a b c + 144144a b )d e +--R + +--R 2 2 2 4 3 4 +--R (- 247104a c - 494208a b c - 41184b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (549120a b c + 183040b c)d e + (- 199680a c - 299520b c )d e +--R + +--R 3 6 4 7 +--R 215040b c d e - 57344c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 413 + +--S 414 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 415 + +--S 416 of 465 +r0:=-2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-_ + c*e*(7*b*d-3*a*e))*(d+e*x)^(3/2)/e^8+2/5*(70*c^4*d^4+b^4*e^4-_ + 4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*_ + (15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(5/2)/e^8-10/7*c*(2*c*d-b*e)*_ + (7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(7/2)/e^8+2/3*c^2*_ + (14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(9/2)/e^8-14/11*c^3*_ + (2*c*d-b*e)*(d+e*x)^(11/2)/e^8+4/13*c^4*(d+e*x)^(13/2)/e^8+_ + 2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*sqrt(d+e*x))+2*(c*d^2-_ + b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 4620c e x + (19110b c e - 5880c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((20020a c + 30030b c )e - 25480b c d e + 7840c d e )x +--R + +--R 2 3 7 3 2 2 6 +--R (64350a b c + 21450b c)e + (- 28600a c - 42900b c )d e +--R + +--R 3 2 5 4 3 4 +--R 36400b c d e - 11200c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (36036a c + 72072a b c + 6006b )e + (- 102960a b c - 34320b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (45760a c + 68640b c )d e - 58240b c d e + 17920c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 +--R (90090a b c + 30030a b )e +--R + +--R 2 2 2 4 6 +--R (- 72072a c - 144144a b c - 12012b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (205920a b c + 68640b c)d e + (- 91520a c - 137280b c )d e +--R + +--R 3 4 3 4 5 2 +--R 116480b c d e - 35840c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (60060a c + 90090a b )e + (- 360360a b c - 120120a b )d e +--R + +--R 2 2 2 4 2 5 +--R (288288a c + 576576a b c + 48048b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (- 823680a b c - 274560b c)d e + (366080a c + 549120b c )d e +--R + +--R 3 5 2 4 6 +--R - 465920b c d e + 143360c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 +--R - 30030a b e + (120120a c + 180180a b )d e +--R + +--R 2 3 2 5 +--R (- 720720a b c - 240240a b )d e +--R + +--R 2 2 2 4 3 4 +--R (576576a c + 1153152a b c + 96096b )d e +--R + +--R 2 3 4 3 3 2 2 5 2 +--R (- 1647360a b c - 549120b c)d e + (732160a c + 1098240b c )d e +--R + +--R 3 6 4 7 +--R - 931840b c d e + 286720c d +--R / +--R 8 +-------+ +--R 15015e \|e x + d +--R Type: Expression(Integer) +--E 416 + +--S 417 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 465 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 7 3 6 3 2 2 5 2 3 4 +--R 2c x + 7b c x + (6a c + 9b c )x + (15a b c + 5b c)x +--R + +--R 2 2 2 4 3 2 3 2 3 2 2 3 +--R (6a c + 12a b c + b )x + (9a b c + 3a b )x + (2a c + 3a b )x + a b +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 418 + +--S 419 of 465 +r0:=2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^(3/2))+2/3*_ + (70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-_ + 3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(3/2)/e^8-_ + 2*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5/2)/_ + e^8+6/7*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(7/2)/_ + e^8-14/9*c^3*(2*c*d-b*e)*(d+e*x)^(9/2)/e^8+4/11*c^4*(d+e*x)^(11/2)/_ + e^8-2*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/_ + (e^8*sqrt(d+e*x))-6*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+_ + b^2*e^2-c*e*(7*b*d-3*a*e))*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 252c e x + (1078b c e - 392c d e )x +--R + +--R 3 2 2 7 3 6 4 2 5 5 +--R ((1188a c + 1782b c )e - 1848b c d e + 672c d e )x +--R + +--R 2 3 7 3 2 2 6 3 2 5 +--R (4158a b c + 1386b c)e + (- 2376a c - 3564b c )d e + 3696b c d e +--R + +--R 4 3 4 +--R - 1344c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 4 7 2 3 6 +--R (2772a c + 5544a b c + 462b )e + (- 11088a b c - 3696b c)d e +--R + +--R 3 2 2 2 5 3 3 4 4 4 3 +--R (6336a c + 9504b c )d e - 9856b c d e + 3584c d e +--R * +--R 3 +--R x +--R + +--R 2 3 7 2 2 2 4 6 +--R (12474a b c + 4158a b )e + (- 16632a c - 33264a b c - 2772b )d e +--R + +--R 2 3 2 5 3 2 2 3 4 +--R (66528a b c + 22176b c)d e + (- 38016a c - 57024b c )d e +--R + +--R 3 4 3 4 5 2 +--R 59136b c d e - 21504c d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 7 2 3 6 +--R (- 2772a c - 4158a b )e + (49896a b c + 16632a b )d e +--R + +--R 2 2 2 4 2 5 +--R (- 66528a c - 133056a b c - 11088b )d e +--R + +--R 2 3 3 4 3 2 2 4 3 +--R (266112a b c + 88704b c)d e + (- 152064a c - 228096b c )d e +--R + +--R 3 5 2 4 6 +--R 236544b c d e - 86016c d e +--R * +--R x +--R + +--R 3 7 3 2 2 6 2 3 2 5 +--R - 462a b e + (- 1848a c - 2772a b )d e + (33264a b c + 11088a b )d e +--R + +--R 2 2 2 4 3 4 2 3 4 3 +--R (- 44352a c - 88704a b c - 7392b )d e + (177408a b c + 59136b c)d e +--R + +--R 3 2 2 5 2 3 6 4 7 +--R (- 101376a c - 152064b c )d e + 157696b c d e - 57344c d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Expression(Integer) +--E 419 + +--S 420 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 465 +r0:=4/3*(d+e*x)^(3/2)+2*(2*c*d-b*e)*sqrt(d+e*x)/c-atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c^2*d^2+b^2*_ + e^2-2*c*e*(b*d+a*e)+e*(2*c*d-b*e)*sqrt(b^2-4*a*c))/(c^(3/2)*sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e)-_ + e*(2*c*d-b*e)*sqrt(b^2-4*a*c))/(c^(3/2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R 2 +-+ | 2 +--R (- 3b e + 6c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((6a c - 3b )e + 6b c d e - 6c d )\|2 +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 +-+ | 2 +--R (3b e - 6c d e)\|2 \|- 4a c + b +--R + +--R 2 2 2 2 +-+ +--R ((6a c - 3b )e + 6b c d e - 6c d )\|2 +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R (4c e x - 6b e + 16c d)\|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R +-+ | | 2 | | 2 +--R 3c\|c \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 422 + +--S 423 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 465 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 465 +r0:=4*sqrt(d+e*x)-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ + sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))/sqrt(c)-_ + atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ + sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/sqrt(c) +--R +--R +--R (2) +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|2 \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|2 \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-+ +-------+ +--R 4\|c \|e x + d +--R / +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 425 + +--S 426 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 of 465 +t0:=(b+2*c*x)/((a+b*x+c*x^2)*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) -------------------------- +--R 2 +-------+ +--R (c x + b x + a)\|e x + d +--R Type: Expression(Integer) +--E 427 + +--S 428 of 465 +r0:=-2*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ + sqrt(2)*sqrt(c)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))-2*atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*_ + sqrt(c)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))) +--R +--R +--R (2) +--R - +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-+ | | 2 +--R 2\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 428 + +--S 429 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 of 465 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------------------- +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 430 + +--S 431 of 465 +r0:=2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))+atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b*e*_ + (b+sqrt(b^2-4*a*c))-2*c*(2*a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*_ + (b*e*(b-sqrt(b^2-4*a*c))+2*c*(-2*a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-_ + b*d*e+a*e^2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +-------+ +--R ((b e - 2c d)\|2 \|- 4a c + b + (4a c - b )e\|2 )\|c \|e x + d +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +-------+ +--R ((b e - 2c d)\|2 \|- 4a c + b + (- 4a c + b )e\|2 )\|c \|e x + d +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R (- 2b e + 4c d)\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 2 | 2 +-------+ +--R (a e - b d e + c d )\|- 4a c + b \|e x + d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 431 + +--S 432 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 465 +t0:=(b+2*c*x)/((d+e*x)^(5/2)*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x +--R + +--R 2 2 +--R (2a d e + b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 433 + +--S 434 of 465 +r0:=2/3*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+_ + 2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))/((c*d^2-b*d*e+a*e^2)^2*_ + sqrt(d+e*x))-atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b^2*e^2*(b+sqrt(b^2-4*a*c))+_ + 2*c^2*d*(4*a*e+d*sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e+b*d*_ + sqrt(b^2-4*a*c)+a*e*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*_ + sqrt(c)*(b^2*e^2*(b-sqrt(b^2-4*a*c))-2*c^2*d*(-4*a*e+d*_ + sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e-b*d*sqrt(b^2-4*a*c)-_ + a*e*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((6a c - 3b )e + 6b c d e - 6c d e)x + (6a c - 3b )d e +--R + +--R 2 2 3 +--R 6b c d e - 6c d +--R * +--R +-----------+ +--R +-+ | 2 +--R \|2 \|- 4a c + b +--R + +--R 3 3 2 2 2 +--R ((- 12a b c + 3b )e + (24a c - 6b c)d e )x +--R + +--R 3 2 2 2 2 +--R (- 12a b c + 3b )d e + (24a c - 6b c)d e +--R * +--R +-+ +--R \|2 +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 2 2 +--R ((6a c - 3b )e + 6b c d e - 6c d e)x + (6a c - 3b )d e +--R + +--R 2 2 3 +--R 6b c d e - 6c d +--R * +--R +-----------+ +--R +-+ | 2 +--R \|2 \|- 4a c + b +--R + +--R 3 3 2 2 2 +--R ((12a b c - 3b )e + (- 24a c + 6b c)d e )x +--R + +--R 3 2 2 2 2 +--R (12a b c - 3b )d e + (- 24a c + 6b c)d e +--R * +--R +-+ +--R \|2 +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 3 +--R ((- 12a c + 6b )e - 12b c d e + 12c d e)x - 2a b e +--R + +--R 2 2 2 2 3 +--R (- 8a c + 8b )d e - 18b c d e + 16c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (3a e - 6a b d e + (6a c + 3b )d e - 6b c d e + 3c d e)x + 3a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 6a b d e + (6a c + 3b )d e - 6b c d e + 3c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-------+ | | 2 +--R \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 434 + +--S 435 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 465 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 465 +r0:=-(d+e*x)^(5/2)/(a+b*x+c*x^2)+5*e^2*sqrt(d+e*x)/c-5*e*atanh(sqrt(2)*_ + sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))/sqrt(b^2-4*a*c))/(c^(3/2)*_ + sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-5*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (-2*c^2*d^2-b^2*e^2+2*c*e*(b*d+a*e))/sqrt(b^2-4*a*c))/(c^(3/2)*_ + sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 2 2 3 2 3 +--R (5b c e - 10c d e )x + (5b e - 10b c d e )x + 5a b e +--R + +--R 2 +--R - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((- 10a c + 5b c)e - 10b c d e + 10c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 10a b c + 5b )e - 10b c d e + 10b c d e)x + (- 10a c + 5a b )e +--R + +--R 2 2 2 +--R - 10a b c d e + 10a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 3 +--R (5b c e - 10c d e )x + (5b e - 10b c d e )x + 5a b e +--R + +--R 2 +--R - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((10a c - 5b c)e + 10b c d e - 10c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((10a b c - 5b )e + 10b c d e - 10b c d e)x + (10a c - 5a b )e +--R + +--R 2 2 2 +--R 10a b c d e - 10a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 2 2 2 2 +-+ | 2 +-+ +--R (4c e x + (5b e - 2c d e)x + 5a e - c d )\|2 \|- 4a c + b \|c +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-------+ | | 2 +--R \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +-----------+ +--R 2 2 +-+ | 2 +-+ +--R (c x + b c x + a c)\|2 \|- 4a c + b \|c +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 437 + +--S 438 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^2 +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 465 +r0:=-(d+e*x)^(3/2)/(a+b*x+c*x^2)-3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ + (sqrt(2)*sqrt(c)*sqrt(b^2-4*a*c))+3*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c)))/(sqrt(2)*sqrt(c)*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R +------------------------------+ +--R | +-----------+ +--R 2 | | 2 +--R (3c e x + 3b e x + 3a e)\|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R | +-----------+ +--R 2 | | 2 +--R (- 3c e x - 3b e x - 3a e)\|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-------+ +--R (- e x - d)\|2 \|- 4a c + b \|c \|e x + d +--R / +--R +-----------+ +--R 2 +-+ | 2 +-+ +--R (c x + b x + a)\|2 \|- 4a c + b \|c +--R Type: Expression(Integer) +--E 440 + +--S 441 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 441 + +)clear all + +--S 442 of 465 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^2 +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 465 +r0:=-sqrt(d+e*x)/(a+b*x+c*x^2)-e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/(sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/_ + (sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +----------------------------+ +--R | +-----------+ +--R 2 +-+ +-+ | | 2 +--R (c e x + b e x + a e)\|2 \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +------------------------------+ +--R | +-----------+ +--R 2 +-+ +-+ | | 2 +--R (- c e x - b e x - a e)\|2 \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R - +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-------+ | | 2 +--R \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 +--R (c x + b x + a)\|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 443 + +--S 444 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 465 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) -------------------------------------------------------- +--R 2 4 3 2 2 2 +-------+ +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 445 + +--S 446 of 465 +r0:=-((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))+e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(2*c*d-e*(b+_ + sqrt(b^2-4*a*c)))/((c*d^2-e*(b*d-a*e))*sqrt(2)*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(2*c*d-_ + e*(b-sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(b^2-4*a*c)*_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R +-----------+ +--R 2 2 2 2 | 2 2 2 2 +--R (- c e x - b e x - a e )\|- 4a c + b + (b c e - 2c d e)x +--R + +--R 2 2 2 +--R (b e - 2b c d e)x + a b e - 2a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R 2 2 2 2 | 2 2 2 2 +--R (- c e x - b e x - a e )\|- 4a c + b + (- b c e + 2c d e)x +--R + +--R 2 2 2 +--R (- b e + 2b c d e)x - a b e + 2a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-------+ +--R (c e x + b e - c d)\|2 \|- 4a c + b \|e x + d +--R * +--R +------------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (a c e - b c d e + c d )x + (a b e - b d e + b c d )x + a e +--R + +--R 2 +--R - a b d e + a c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 446 + +--S 447 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 465 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 448 + +--S 449 of 465 +r0:=3*e^2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))+(-(b^2-4*a*c)*_ + (c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ + (a+b*x+c*x^2)*sqrt(d+e*x))+3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(2*c^2*d^2+b*e^2*(b+_ + sqrt(b^2-4*a*c))-2*c*e*(b*d+a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+_ + a*e^2)^2*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-_ + 3*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c))))*sqrt(c)*(2*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-_ + 2*c*e*(b*d+a*e-d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(2)*_ + sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 2 2 3 2 3 +--R (3b c e - 6c d e )x + (3b e - 6b c d e )x + 3a b e +--R + +--R 2 +--R - 6a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((6a c - 3b c)e + 6b c d e - 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((6a b c - 3b )e + 6b c d e - 6b c d e)x + (6a c - 3a b )e +--R + +--R 2 2 2 +--R 6a b c d e - 6a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 3 +--R (3b c e - 6c d e )x + (3b e - 6b c d e )x + 3a b e +--R + +--R 2 +--R - 6a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 2 3 2 2 +--R ((- 6a c + 3b c)e - 6b c d e + 6c d e)x +--R + +--R 3 3 2 2 2 2 2 2 3 +--R ((- 6a b c + 3b )e - 6b c d e + 6b c d e)x + (- 6a c + 3a b )e +--R + +--R 2 2 2 +--R - 6a b c d e + 6a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ +-------+ | | 2 +--R \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 2 2 3 2 2 2 +--R (- 3b c e + 6c d e )x + ((a c - 3b )e + 5b c d e + c d e)x +--R + +--R 3 2 2 2 2 3 +--R - 2a b e + (5a c - b )d e + 2b c d e - c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 4 3 2 2 2 2 2 3 3 4 2 +--R (a c e - 2a b c d e + (2a c + b c)d e - 2b c d e + c d )x +--R + +--R 2 4 2 3 3 2 2 2 3 2 4 3 4 +--R (a b e - 2a b d e + (2a b c + b )d e - 2b c d e + b c d )x + a e +--R + +--R 2 3 2 2 2 2 3 2 4 +--R - 2a b d e + (2a c + a b )d e - 2a b c d e + a c d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 449 + +--S 450 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 465 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 465 +r0:=-1/2*(d+e*x)^(7/2)/(a+b*x+c*x^2)^2-7/4*e*(d+e*x)^(3/2)*(b*d-2*a*e+_ + (2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+7/4*e^2*(2*c*d-b*e)*_ + sqrt(d+e*x)/(c*(b^2-4*a*c))+7/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c^2*d^2-b^2*e^2-2*c*e*_ + (b*d-3*a*e))+(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))/_ + sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))+7/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(e*(2*c^2*d^2-b^2*e^2-2*c*e*_ + (b*d-3*a*e))-(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))/_ + sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(2*c*d-e*_ + (b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 42a c + 7b c )e + 14b c d e - 14c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 84a b c + 14b c)e + 28b c d e - 28b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 84a c - 28a b c + 7b )e + (28a b c + 14b c)d e +--R + +--R 3 2 2 2 2 +--R (- 28a c - 14b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 84a b c + 14a b )e + 28a b c d e - 28a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 42a c + 7a b )e + 14a b c d e - 14a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (- 56a b c + 7b c )e + (112a c + 14b c )d e - 84b c d e +--R + +--R 5 3 +--R 56c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (- 112a b c + 14b c)e + (224a b c + 28b c )d e - 168b c d e +--R + +--R 4 3 +--R 112b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 +--R (- 112a b c - 42a b c + 7b )e +--R + +--R 2 3 2 2 4 3 3 3 2 2 2 +--R (224a c + 140a b c + 14b c)d e + (- 168a b c - 84b c )d e +--R + +--R 4 2 3 3 +--R (112a c + 56b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 +--R (- 112a b c + 14a b )e + (224a b c + 28a b c)d e +--R + +--R 2 2 2 2 3 3 +--R - 168a b c d e + 112a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 +--R (- 56a b c + 7a b )e + (112a c + 14a b c)d e - 84a b c d e +--R + +--R 2 3 3 +--R 56a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 42a c + 7b c )e + 14b c d e - 14c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 84a b c + 14b c)e + 28b c d e - 28b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 84a c - 28a b c + 7b )e + (28a b c + 14b c)d e +--R + +--R 3 2 2 2 2 +--R (- 28a c - 14b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 84a b c + 14a b )e + 28a b c d e - 28a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 42a c + 7a b )e + 14a b c d e - 14a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (56a b c - 7b c )e + (- 112a c - 14b c )d e + 84b c d e +--R + +--R 5 3 +--R - 56c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (112a b c - 14b c)e + (- 224a b c - 28b c )d e + 168b c d e +--R + +--R 4 3 +--R - 112b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 +--R (112a b c + 42a b c - 7b )e +--R + +--R 2 3 2 2 4 3 3 3 2 2 2 +--R (- 224a c - 140a b c - 14b c)d e + (168a b c + 84b c )d e +--R + +--R 4 2 3 3 +--R (- 112a c - 56b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 +--R (112a b c - 14a b )e + (- 224a b c - 28a b c)d e +--R + +--R 2 2 2 2 3 3 +--R 168a b c d e - 112a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 +--R (56a b c - 7a b )e + (- 112a c - 14a b c)d e + 84a b c d e +--R + +--R 2 3 3 +--R - 56a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 2 2 3 2 3 +--R ((- 22a c + 9b c)e - 14b c d e + 14c d e)x +--R + +--R 3 3 2 2 2 2 2 2 +--R ((- 7a b c + 7b )e + (- 52a c - 8b c)d e + 21b c d e)x +--R + +--R 2 2 3 2 2 2 2 +--R ((- 14a c + 14a b )e - 42a b c d e + (- 10a c + 13b c)d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R 7a b e - 28a c d e + 7a b c d e + (- 8a c + 2b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-------+ | | 2 +--R \|2 \|- 4a c + b \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 4 2 3 4 3 3 2 3 2 3 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c )x + (32a c + 8a b c - 4b c)x +--R + +--R 2 2 3 3 2 2 2 +--R (32a b c - 8a b c)x + 16a c - 4a b c +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R \|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 452 + +--S 453 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 465 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 465 +r0:=-1/2*(d+e*x)^(5/2)/(a+b*x+c*x^2)^2-5/4*e*(b*d-2*a*e+(2*c*d-b*e)*x)*_ + sqrt(d+e*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+5/4*e*atanh(sqrt(2)*sqrt(c)*_ + sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(2*c*d-b*e)+_ + (8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))/sqrt(b^2-4*a*c))/((b^2-4*a*c)*_ + sqrt(2)*sqrt(c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-5/4*e*_ + atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ + (8*c^2*d^2+b*e^2*(b+sqrt(b^2-4*a*c))-2*c*e*(4*b*d-2*a*e+d*_ + sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(c)*sqrt(2*c*d-e*_ + (b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 3 2 4 2 3 2 2 3 +--R (5b c e - 10c d e )x + (10b c e - 20b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((10a b c + 5b )e + (- 20a c - 10b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (10a b e - 20a b c d e )x + 5a b e - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((20a c + 5b c )e - 40b c d e + 40c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((40a b c + 10b c)e - 80b c d e + 80b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (40a c + 30a b c + 5b )e + (- 80a b c - 40b c)d e +--R + +--R 3 2 2 2 +--R (80a c + 40b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((40a b c + 10a b )e - 80a b c d e + 80a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (20a c + 5a b )e - 40a b c d e + 40a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 3 2 4 2 3 2 2 3 +--R (5b c e - 10c d e )x + (10b c e - 20b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((10a b c + 5b )e + (- 20a c - 10b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (10a b e - 20a b c d e )x + 5a b e - 10a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((- 20a c - 5b c )e + 40b c d e - 40c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((- 40a b c - 10b c)e + 80b c d e - 80b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (- 40a c - 30a b c - 5b )e + (80a b c + 40b c)d e +--R + +--R 3 2 2 2 +--R (- 80a c - 40b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((- 40a b c - 10a b )e + 80a b c d e - 80a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (- 20a c - 5a b )e + 40a b c d e - 40a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|- e\|- 4a c + b - b e + 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 2 2 2 +--R (- 5b c e + 10c d e)x + ((- 18a c - 3b )e + 15b c d e)x +--R + +--R 2 2 2 2 +--R (- 15a b e + (- 6a c + 9b )d e)x - 10a e + 5a b d e +--R + +--R 2 2 +--R (- 8a c + 2b )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-------+ | | 2 +--R \|2 \|- 4a c + b \|c \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c)x + (32a c + 8a b c - 4b )x +--R + +--R 2 3 3 2 2 +--R (32a b c - 8a b )x + 16a c - 4a b +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R \|2 \|- 4a c + b \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 455 + +--S 456 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 456 + +)clear all + +--S 457 of 465 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 465 +r0:=-1/2*(d+e*x)^(3/2)/(a+b*x+c*x^2)^2-3/4*e*(b+2*c*x)*sqrt(d+e*x)/_ + ((b^2-4*a*c)*(a+b*x+c*x^2))+3/2*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(4*c*d-e*(2*b-_ + sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b-_ + sqrt(b^2-4*a*c))))-3/2*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(4*c*d-e*(2*b+sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 2 4 2 3 2 2 2 2 2 2 +--R (- 6c e x - 12b c e x + (- 12a c - 6b )e x - 12a b e x - 6a e ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 4 2 2 2 3 +--R (- 12b c e + 24c d e)x + (- 24b c e + 48b c d e)x +--R + +--R 3 2 2 2 2 +--R ((- 24a b c - 12b )e + (48a c + 24b c)d e)x +--R + +--R 2 2 2 2 2 +--R (- 24a b e + 48a b c d e)x - 12a b e + 24a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 4 2 3 2 2 2 2 2 2 +--R (- 6c e x - 12b c e x + (- 12a c - 6b )e x - 12a b e x - 6a e ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 4 2 2 2 3 +--R (12b c e - 24c d e)x + (24b c e - 48b c d e)x +--R + +--R 3 2 2 2 2 +--R ((24a b c + 12b )e + (- 48a c - 24b c)d e)x +--R + +--R 2 2 2 2 2 +--R (24a b e - 48a b c d e)x + 12a b e - 24a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 2 2 2 +--R (6c e x + 9b c e x + (- 2a c + 5b )e x + 3a b e + (- 8a c + 2b )d) +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (16a c - 4b c )x + (32a b c - 8b c)x + (32a c + 8a b c - 4b )x +--R + +--R 2 3 3 2 2 +--R (32a b c - 8a b )x + 16a c - 4a b +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 458 + +--S 459 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 465 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R +-------+ +--R (2c x + b)\|e x + d +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Expression(Integer) +--E 460 + +--S 461 of 465 +r0:=-1/2*sqrt(d+e*x)/(a+b*x+c*x^2)^2-1/4*e*(b*c*d-b^2*e+2*a*c*e+_ + c*(2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ + (a+b*x+c*x^2))+1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ + (b-sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^2*d^2-b*e^2*(b+sqrt(b^2-4*a*c))-_ + 2*c*e*(4*b*d-6*a*e-d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-_ + e*(b*d-a*e))*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-_ + 1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ + sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^2*d^2-b*e^2*(b-sqrt(b^2-4*a*c))-_ + 2*c*e*(4*b*d-6*a*e+d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-_ + b*d*e+a*e^2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 2 3 3 2 4 2 3 2 2 3 +--R (b c e - 2c d e )x + (2b c e - 4b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((2a b c + b )e + (- 4a c - 2b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (2a b e - 4a b c d e )x + a b e - 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((12a c - b c )e - 8b c d e + 8c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((24a b c - 2b c)e - 16b c d e + 16b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (24a c + 10a b c - b )e + (- 16a b c - 8b c)d e +--R + +--R 3 2 2 2 +--R (16a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((24a b c - 2a b )e - 16a b c d e + 16a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (12a c - a b )e - 8a b c d e + 8a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 2 3 3 2 4 2 3 2 2 3 +--R (b c e - 2c d e )x + (2b c e - 4b c d e )x +--R + +--R 3 3 2 2 2 2 +--R ((2a b c + b )e + (- 4a c - 2b c)d e )x +--R + +--R 2 3 2 2 3 2 2 +--R (2a b e - 4a b c d e )x + a b e - 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 3 3 2 4 2 4 +--R ((- 12a c + b c )e + 8b c d e - 8c d e)x +--R + +--R 2 3 3 2 2 2 3 2 3 +--R ((- 24a b c + 2b c)e + 16b c d e - 16b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (- 24a c - 10a b c + b )e + (16a b c + 8b c)d e +--R + +--R 3 2 2 2 +--R (- 16a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R ((- 24a b c + 2a b )e + 16a b c d e - 16a b c d e)x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (- 12a c + a b )e + 8a b c d e - 8a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 2 2 3 3 2 2 2 2 2 +--R (- b c e + 2c d e)x + ((2a c - 2b c)e + 3b c d e)x +--R + +--R 3 2 2 2 2 2 2 +--R ((a b c - b )e + (2a c + b c)d e)x + (- 6a c + a b )e +--R + +--R 3 2 2 2 +--R (9a b c - 2b )d e + (- 8a c + 2b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 2 3 2 2 2 3 3 2 4 2 3 2 4 +--R ((16a c - 4a b c )e + (- 16a b c + 4b c )d e + (16a c - 4b c )d )x +--R + +--R 2 2 3 2 2 2 4 +--R (32a b c - 8a b c)e + (- 32a b c + 8b c)d e +--R + +--R 3 3 2 2 +--R (32a b c - 8b c )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 4 2 2 2 3 5 +--R (32a c + 8a b c - 4a b )e + (- 32a b c - 8a b c + 4b )d e +--R + +--R 2 3 2 2 4 2 +--R (32a c + 8a b c - 4b c)d +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 2 4 2 2 3 2 +--R ((32a b c - 8a b )e + (- 32a b c + 8a b )d e + (32a b c - 8a b c)d )x +--R + +--R 4 3 2 2 3 2 3 3 2 2 2 2 +--R (16a c - 4a b )e + (- 16a b c + 4a b )d e + (16a c - 4a b c)d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 461 + +--S 462 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 465 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R (1) +--R 2c x + b +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 463 + +--S 464 of 465 +r0:=-1/2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/_ + ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)+1/4*e*(5*a*c*e*_ + (2*c*d-b*e)+(c*d-3*b*e)*(b*c*d-b^2*e+2*a*c*e)+c*(2*c^2*d^2+3*b^2*e^2-_ + 2*c*e*(b*d+5*a*e))*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ + (a+b*x+c*x^2))-1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^3*d^3+3*b^2*e^3*(b+_ + sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-16*a*e-d*sqrt(b^2-4*a*c))-2*c*e^2*_ + (b^2*d+8*a*b*e+b*d*sqrt(b^2-4*a*c)+5*a*e*sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(2*c*d-_ + e*(b-sqrt(b^2-4*a*c))))+1/4*e*atanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ + sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^3*d^3+3*b^2*e^3*_ + (b-sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-16*a*e+d*sqrt(b^2-4*a*c))-_ + 2*c*e^2*(b^2*d+8*a*b*e-b*d*sqrt(b^2-4*a*c)-5*a*e*sqrt(b^2-4*a*c)))/_ + ((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(2*c*d-_ + e*(b+sqrt(b^2-4*a*c)))) +--R +--R +--R (2) +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 10a c + 3b c )e - 2b c d e + 2c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 20a b c + 6b c)e - 4b c d e + 4b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 20a c - 4a b c + 3b )e + (- 4a b c - 2b c)d e +--R + +--R 3 2 2 2 2 +--R (4a c + 2b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 20a b c + 6a b )e - 4a b c d e + 4a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 10a c + 3a b )e - 2a b c d e + 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (16a b c - 3b c )e + (- 32a c + 2b c )d e + 12b c d e +--R + +--R 5 3 +--R - 8c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (32a b c - 6b c)e + (- 64a b c + 4b c )d e + 24b c d e +--R + +--R 4 3 +--R - 16b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 2 3 2 2 4 3 +--R (32a b c + 10a b c - 3b )e + (- 64a c - 28a b c + 2b c)d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (24a b c + 12b c )d e + (- 16a c - 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 2 2 2 2 +--R (32a b c - 6a b )e + (- 64a b c + 4a b c)d e + 24a b c d e +--R + +--R 3 3 +--R - 16a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 2 3 3 +--R (16a b c - 3a b )e + (- 32a c + 2a b c)d e + 12a b c d e - 8a c d e +--R * +--R +----------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(---------------------------------) +--R +------------------------------+ +--R | +-----------+ +--R | | 2 +--R \|- e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 4 3 3 4 2 2 4 +--R ((- 10a c + 3b c )e - 2b c d e + 2c d e )x +--R + +--R 2 3 4 2 2 3 3 2 2 3 +--R ((- 20a b c + 6b c)e - 4b c d e + 4b c d e )x +--R + +--R 2 2 2 4 4 2 3 3 +--R (- 20a c - 4a b c + 3b )e + (- 4a b c - 2b c)d e +--R + +--R 3 2 2 2 2 +--R (4a c + 2b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 3 2 2 2 +--R ((- 20a b c + 6a b )e - 4a b c d e + 4a b c d e )x +--R + +--R 3 2 2 4 2 3 2 2 2 2 +--R (- 10a c + 3a b )e - 2a b c d e + 2a c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 4 4 2 3 3 4 2 2 +--R (- 16a b c + 3b c )e + (32a c - 2b c )d e - 12b c d e +--R + +--R 5 3 +--R 8c d e +--R * +--R 4 +--R x +--R + +--R 2 2 4 4 3 3 2 3 2 3 2 2 +--R (- 32a b c + 6b c)e + (64a b c - 4b c )d e - 24b c d e +--R + +--R 4 3 +--R 16b c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 2 3 2 2 4 3 +--R (- 32a b c - 10a b c + 3b )e + (64a c + 28a b c - 2b c)d e +--R + +--R 3 3 2 2 2 4 2 3 3 +--R (- 24a b c - 12b c )d e + (16a c + 8b c )d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 4 2 2 3 3 2 2 2 2 +--R (- 32a b c + 6a b )e + (64a b c - 4a b c)d e - 24a b c d e +--R + +--R 3 3 +--R 16a b c d e +--R * +--R x +--R + +--R 3 2 3 4 3 2 2 2 3 2 2 2 2 2 3 3 +--R (- 16a b c + 3a b )e + (32a c - 2a b c)d e - 12a b c d e + 8a c d e +--R * +--R +------------------------------+ +--R | +-----------+ +--R +-+ | | 2 +--R \|c \|- e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R 3 2 2 3 3 2 4 2 3 +--R ((10a c - 3b c )e + 2b c d e - 2c d e)x +--R + +--R 2 3 3 3 2 2 2 3 2 2 +--R ((21a b c - 6b c)e + (- 12a c + 6b c )d e - 3b c d e)x +--R + +--R 2 2 2 4 3 2 3 2 +--R (18a c + 6a b c - 3b )e + (- 18a b c + 6b c)d e +--R + +--R 3 2 2 2 +--R (6a c - 3b c )d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 4 2 +--R (19a b c - 5a b )e + (- 20a c - 2a b c + 2b )d e +--R + +--R 2 3 2 3 2 2 3 +--R (15a b c - 4b c)d e + (- 8a c + 2b c )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-------+ | | 2 +--R \|2 \|- 4a c + b \|e x + d \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R / +--R 3 3 2 2 2 4 2 3 3 2 3 +--R (16a c - 4a b c )e + (- 32a b c + 8a b c )d e +--R + +--R 2 4 2 3 4 2 2 2 4 3 3 3 +--R (32a c + 8a b c - 4b c )d e + (- 32a b c + 8b c )d e +--R + +--R 5 2 4 4 +--R (16a c - 4b c )d +--R * +--R 4 +--R x +--R + +--R 3 2 2 3 4 2 2 2 4 3 +--R (32a b c - 8a b c)e + (- 64a b c + 16a b c)d e +--R + +--R 2 3 3 2 5 2 2 2 3 4 2 3 +--R (64a b c + 16a b c - 8b c)d e + (- 64a b c + 16b c )d e +--R + +--R 4 3 3 4 +--R (32a b c - 8b c )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 2 4 4 3 2 2 3 5 3 +--R (32a c + 8a b c - 4a b )e + (- 64a b c - 16a b c + 8a b )d e +--R + +--R 3 3 2 2 2 6 2 2 2 3 3 2 5 3 +--R (64a c + 48a b c - 4b )d e + (- 64a b c - 16a b c + 8b c)d e +--R + +--R 2 4 2 3 4 2 4 +--R (32a c + 8a b c - 4b c )d +--R * +--R 2 +--R x +--R + +--R 4 3 3 4 3 2 2 4 3 +--R (32a b c - 8a b )e + (- 64a b c + 16a b )d e +--R + +--R 3 2 2 3 5 2 2 2 2 2 4 3 +--R (64a b c + 16a b c - 8a b )d e + (- 64a b c + 16a b c)d e +--R + +--R 2 3 3 2 4 +--R (32a b c - 8a b c )d +--R * +--R x +--R + +--R 5 4 2 4 4 3 3 3 +--R (16a c - 4a b )e + (- 32a b c + 8a b )d e +--R + +--R 4 2 3 2 2 4 2 2 3 2 2 3 3 +--R (32a c + 8a b c - 4a b )d e + (- 32a b c + 8a b c)d e +--R + +--R 3 3 2 2 2 4 +--R (16a c - 4a b c )d +--R * +--R +------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 | | 2 +--R \|2 \|- 4a c + b \|- e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R Type: Expression(Integer) +--E 464 + +--S 465 of 465 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 465 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/richder12d.input.pamphlet b/src/input/richder12d.input.pamphlet new file mode 100644 index 0000000..c4c5460 --- /dev/null +++ b/src/input/richder12d.input.pamphlet @@ -0,0 +1,23660 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12d.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +All derivatives match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12d.output +)spool richder12d.output +)set message test on +)set message auto off +)clear all + +--S 1 of 764 +t0:=(b+2*c*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2) +--R +--R +--R +--------------+ +--R +-------+ | 2 +--R (1) (2c x + b)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 764 +--r0:=4/7*(a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)-2/105*(8*c^2*d^2+b^2*e^2-_ +-- c*e*(11*b*d-10*a*e)-3*c*e*(2*c*d-b*e)*x)*sqrt(d+e*x)*sqrt(a+b*x+_ +-- c*x^2)/(c*e^2)-1/105*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(5*c*e*(b*d-2*a*e)^2-_ +-- (2*c*d-b*e)*(4*b*c*d^2-b^2*d*e-2*a*c*d*e-a*b*e^2))+(2*c*d-b*e)*_ +-- (4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e^3*sqrt(a+b*x+_ +-- c*x^2))-1/105*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*e^4*sqrt(a+b*x+c*x^2)) +--E 2 + +--S 3 of 764 +--d0:=D(m0,x) +--E 3 + +)clear all + +--S 4 of 764 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 4 + +--S 5 of 764 +--r0:=-2/15*(8*c*d-7*b*e-6*c*e*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/e^2-_ +-- 1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*(2*c*(7*b^2*d*e+4*a*c*d*e-8*b*(c*d^2+a*e^2))+_ +-- (16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e^3*sqrt(2)*sqrt(a+b*x+_ +-- c*x^2))-1/15*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*e^4*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 5 + +--S 6 of 764 +--d0:=D(m0,x) +--E 6 + +)clear all + +--S 7 of 764 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) --------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 7 + +--S 8 of 764 +--r0:=2/3*(8*c*d-3*b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*sqrt(d+e*x))-_ +-- 1/3*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(b*e*(b-4*sqrt(b^2-4*a*c))+c*(-4*a*e+_ +-- 8*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^3*sqrt(c)*sqrt(a+b*x+c*x^2))+4/3*(2*c*d-b*e)*elliptic_e(asin(_ +-- sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^4*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 8 + +--S 9 of 764 +--d0:=D(m0,x) +--E 9 + +)clear all + +--S 10 of 764 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 10 + +--S 11 of 764 +--r0:=2/3*(8*c*d-b*e+6*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/3*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*sqrt(a+b*x+c*x^2)/_ +-- (e^2*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(7*b^2*d*e+_ +-- 4*a*c*d*e-8*b*(c*d^2+a*e^2))+(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-_ +-- 3*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^3*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-_ +-- 4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-_ +-- 4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-_ +-- 4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^4*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 11 + +--S 12 of 764 +--d0:=D(m0,x) +--E 12 + +)clear all + +--S 13 of 764 +t0:=(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R +--------------+ +--R | 2 +--R (2c x + b)\|c x + b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 13 + +--S 14 of 764 +--r0:=2/15*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*sqrt(a+b*x+c*x^2)/_ +-- (e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))-2/5*(8*c*d+b*e+10*c*e*x)*_ +-- sqrt(a+b*x+c*x^2)/(e^2*(d+e*x)^(5/2))+4/15*(2*c*d-b*e)*(4*c^2*d^2-_ +-- b^2*e^2-4*c*e*(b*d-2*a*e))*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*_ +-- e^2)^2*sqrt(d+e*x))+1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+_ +-- e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*_ +-- a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*(b^3*d*e^2-4*a*_ +-- c*e*(c*d^2+5*a*e^2)+4*b*c*d*(2*c*d^2+5*a*e^2)-b^2*(11*c*d^2*e-a*e^3))+_ +-- (2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e^3*(c*d^2-b*d*e+a*e^2)^2*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2))+1/15*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-_ +-- 2*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^4*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 14 + +--S 15 of 764 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 764 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 16 + +--S 17 of 764 +--r0:=-2/63*(16*c*d-15*b*e-14*c*e*x)*(a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)/e^2-_ +-- 2/315*(128*c^3*d^3-b^3*e^3+3*b*c*e^2*(37*b*d-36*a*e)-12*c^2*d*_ +-- e*(20*b*d-11*a*e)-3*c*e*(32*c^2*d^2+b^2*e^2-4*c*e*(8*b*d-7*a*e))*x)*_ +-- sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*e^4)-1/315*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*((4*b*c*_ +-- d^2-b^2*d*e-2*a*c*d*e-a*b*e^2)*(32*c^2*d^2+b^2*e^2-4*c*e*(8*b*d-_ +-- 7*a*e))+5*c*e*(b*d-2*a*e)*(15*b^2*d*e+4*a*c*d*e-16*b*(c*d^2+a*e^2)))+_ +-- (128*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(64*b*d-57*a*e)-b^2*c*e^3*(7*b*d-_ +-- 15*a*e)+3*c^2*e^2*(45*b^2*d^2-76*a*b*d*e+28*a^2*e^2))*(b-sqrt(b^2-_ +-- 4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e^5*sqrt(a+b*x+_ +-- c*x^2))-1/315*(128*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(64*b*d-57*a*e)-_ +-- b^2*c*e^3*(7*b*d-15*a*e)+3*c^2*e^2*(45*b^2*d^2-76*a*b*d*e+28*a^2*_ +-- e^2))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*e^6*sqrt(a+b*x+c*x^2)) +--E 17 + +--S 18 of 764 +--d0:=D(m0,x) +--E 18 + +)clear all + +--S 19 of 764 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 19 + +--S 20 of 764 +--r0:=2/7*(16*c*d-7*b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+_ +-- 2/35*(128*c^2*d^2+51*b^2*e^2-4*c*e*(44*b*d-5*a*e)-48*c*e*(2*c*d-_ +-- b*e)*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/e^4+1/35*elliptic_f(asin(_ +-- sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- (-2*c*(51*b^3*d*e^2-8*a*c*e*(8*c*d^2+5*a*e^2)+4*b*c*d*(32*c*d^2+_ +-- 45*a*e^2)-2*b^2*(88*c*d^2*e+27*a*e^3))+(2*c*d-b*e)*(128*c^2*d^2+_ +-- 3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e^5*sqrt(2)*sqrt(a+b*x+c*x^2))+_ +-- 1/35*(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*e^6*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 20 + +--S 21 of 764 +--d0:=D(m0,x) +--E 21 + +)clear all + +--S 22 of 764 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 22 + +--S 23 of 764 +--r0:=2/15*(16*c*d-5*b*e+6*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-_ +-- 2/15*(128*c^2*d^2+15*b^2*e^2-4*c*e*(28*b*d-9*a*e)+16*c*e*(2*c*d-_ +-- b*e)*x)*sqrt(a+b*x+c*x^2)/(e^4*sqrt(d+e*x))-1/15*elliptic_f(_ +-- asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(b^2*e^2*(8*b-23*sqrt(b^2-4*a*c))-64*c^2*d*(-a*e+2*d*_ +-- sqrt(b^2-4*a*c))-4*c*e*(4*b^2*d+8*a*b*e-32*b*d*sqrt(b^2-4*a*c)+_ +-- 9*a*e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^5*sqrt(c)*sqrt(a+b*x+c*x^2))-1/15*(128*c^2*d^2+23*b^2*e^2-_ +-- 4*c*e*(32*b*d-9*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^6*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 23 + +--S 24 of 764 +--d0:=D(m0,x) +--E 24 + +)clear all + +--S 25 of 764 +t0:=(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +--------------+ +--R 2 3 2 2 | 2 +--R (2c x + 3b c x + (2a c + b )x + a b)\|c x + b x + a +--R (1) ------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 25 + +--S 26 of 764 +--r0:=2/15*(16*c*d-3*b*e+10*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ +-- 2/15*(128*c^2*d^2+3*b^2*e^2-20*c*e*(4*b*d-a*e)+48*c*e*(2*c*d-b*e)*x)*_ +-- sqrt(a+b*x+c*x^2)/(e^4*(d+e*x)^(3/2))+2/15*(2*c*d-b*e)*(128*c^2*d^2+_ +-- 3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*sqrt(a+b*x+c*x^2)/(e^4*(c*d^2-_ +-- b*d*e+a*e^2)*sqrt(d+e*x))+1/15*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(-2*c*(51*b^3*d*e^2-_ +-- 8*a*c*e*(8*c*d^2+5*a*e^2)+4*b*c*d*(32*c*d^2+45*a*e^2)-2*b^2*(88*c*_ +-- d^2*e+27*a*e^3))+(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-_ +-- 29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e^5*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+_ +-- 1/15*(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^6*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 26 + +--S 27 of 764 +--d0:=D(m0,x) +--E 27 + +)clear all + +--S 28 of 764 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 28 + +--S 29 of 764 +--r0:=2/7*(2*c*d-b*e)*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)/c+4/7*(d+e*x)^(5/2)*_ +-- sqrt(a+b*x+c*x^2)+4/21*(3*c^2*d^2+2*b^2*e^2-c*e*(3*b*d+5*a*e))*_ +-- sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c^2-1/21*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(4*b^3*_ +-- d*e^2+2*a*c*e*(27*c*d^2-5*a*e^2)-b*c*d*(3*c*d^2+25*a*e^2)-b^2*_ +-- (9*c*d^2*e-4*a*e^3))+(2*c*d-b*e)*(3*c^2*d^2+8*b^2*e^2-c*e*(3*b*d+_ +-- 29*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(7/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-1/21*(2*c*d-b*e)*(3*c^2*d^2+_ +-- 8*b^2*e^2-c*e*(3*b*d+29*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(7/2)*_ +-- e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 29 + +--S 30 of 764 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 764 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 31 + +--S 32 of 764 +--r0:=4/5*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)+2/5*(2*c*d-b*e)*sqrt(d+e*x)*_ +-- sqrt(a+b*x+c*x^2)/c+1/5*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*_ +-- d*e+a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e*sqrt(a+b*x+c*x^2))-_ +-- 1/5*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- e^2*sqrt(a+b*x+c*x^2)) +--E 32 + +--S 33 of 764 +--d0:=D(m0,x) +--E 33 + +)clear all + +--S 34 of 764 +t0:=(b+2*c*x)*sqrt(d+e*x)/sqrt(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) -------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 764 +--r0:=4/3*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)+1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(b*e*(b-_ +-- sqrt(b^2-4*a*c))+2*c*(-2*a*e+d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 35 + +--S 36 of 764 +--d0:=D(m0,x) +--E 36 + +)clear all + +--S 37 of 764 +t0:=(b+2*c*x)/(sqrt(d+e*x)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) --------------------------- +--R +--------------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 764 +--r0:=elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/(e*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 38 + +--S 39 of 764 +--d0:=D(m0,x) +--E 39 + +)clear all + +--S 40 of 764 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------ +--R +--------------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 764 +--r0:=2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+2*d*sqrt(b^2-_ +-- 4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-_ +-- 4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-_ +-- 4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(2*c*d-b*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 41 + +--S 42 of 764 +--d0:=D(m0,x) +--E 42 + +)clear all + +--S 43 of 764 +t0:=(b+2*c*x)/((d+e*x)^(5/2)*sqrt(a+b*x+c*x^2)) +--R +--R +--R 2c x + b +--R (1) ----------------------------------------------- +--R +--------------+ +--R 2 2 2 +-------+ | 2 +--R (e x + 2d e x + d )\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 43 + +--S 44 of 764 +--r0:=2/3*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+_ +-- 4/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-_ +-- b*d*e+a*e^2)^2*sqrt(d+e*x))-1/3*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+_ +-- b^2*d*e-8*a*c*d*e+a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*_ +-- sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+_ +-- 2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*(c*d^2-_ +-- b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2))+1/3*(c^2*d^2+b^2*e^2-_ +-- c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 44 + +--S 45 of 764 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 764 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 764 +--r0:=-2*(d+e*x)^(7/2)/sqrt(a+b*x+c*x^2)+14/5*e^2*(d+e*x)^(3/2)*_ +-- sqrt(a+b*x+c*x^2)/c+56/15*e^2*(2*c*d-b*e)*sqrt(d+e*x)*sqrt(a+_ +-- b*x+c*x^2)/c^2-7/15*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(-2*c*(15*c^2*d^3+4*b*e^2*(b*d+a*e)-_ +-- c*d*e*(11*b*d+17*a*e))+e*(23*c^2*d^2+8*b^2*e^2-c*e*(23*b*d+9*a*e))*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(7/2)*sqrt(2)*sqrt(a+b*x+c*x^2))-7/15*(23*c^2*d^2+8*b^2*e^2-_ +-- c*e*(23*b*d+9*a*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(7/2)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 47 + +--S 48 of 764 +--d0:=D(m0,x) +--E 48 + +)clear all + +--S 49 of 764 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 764 +--r0:=-2*(d+e*x)^(5/2)/sqrt(a+b*x+c*x^2)+10/3*e^2*sqrt(d+e*x)*_ +-- sqrt(a+b*x+c*x^2)/c-5/3*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(-c*(3*c*d^2-e*(b*d+a*e))+_ +-- e*(2*c*d-b*e)*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(5/2)*sqrt(a+b*x+c*x^2))-5/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- sqrt(a+b*x+c*x^2)) +--E 50 + +--S 51 of 764 +--d0:=D(m0,x) +--E 51 + +)clear all + +--S 52 of 764 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) ----------------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 764 +--r0:=-2*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2)+3*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))^(3/2)*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*sqrt(2)*sqrt(a+b*x+c*x^2))-3*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(c^(3/2)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 53 + +--S 54 of 764 +--d0:=D(m0,x) +--E 54 + +)clear all + +--S 55 of 764 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 55 + +--S 56 of 764 +--r0:=-2*sqrt(d+e*x)/sqrt(a+b*x+c*x^2)+elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/(sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 56 + +--S 57 of 764 +--d0:=D(m0,x) +--E 57 + +)clear all + +--S 58 of 764 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R 2c x + b +--R (1) ------------------------------------------- +--R +--------------+ +--R 2 +-------+ | 2 +--R (c x + b x + a)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 58 + +--S 59 of 764 +--r0:=-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ +-- (c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2))-elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))^(3/2)*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+_ +-- c*x^2))+elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 59 + +--S 60 of 764 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 764 +t0:=(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R 2c x + b +--R ------------------------------------------------------------------------ +--R +--------------+ +--R 3 2 +-------+ | 2 +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 764 +--r0:=-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-_ +-- b*d*e+a*e^2)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))+4*e^2*(2*c*d-b*e)*_ +-- sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))-_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(3*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-_ +-- c*e*(3*b*d+a*e-2*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- ((c*d^2-b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2))+(2*c*d-b*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(c)*_ +-- sqrt(a+b*x+c*x^2)) +--E 62 + +--S 63 of 764 +--d0:=D(m0,x) +--E 63 + +)clear all + +--S 64 of 764 +t0:=(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R 2c e x + (b e + 6c d e )x + (3b d e + 6c d e)x + (3b d e + 2c d )x +--R + +--R 3 +--R b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 764 +--r0:=-2/3*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(3/2)-14/3*e*(d+e*x)^(3/2)*(b*d-_ +-- 2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+14/3*e^2*(2*c*d-_ +-- b*e)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*(b^2-4*a*c))+7/3*e*_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*d*e+a*b*e^2)-_ +-- (c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))-_ +-- 7/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*elliptic_e(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(5/2)*_ +-- (b^2-4*a*c)*sqrt(a+b*x+c*x^2)) +--E 65 + +--S 66 of 764 +--d0:=D(m0,x) +--E 66 + +)clear all + +--S 67 of 764 +t0:=(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2c e x + (b e + 4c d e)x + (2b d e + 2c d )x + b d )\|e x + d +--R (1) ------------------------------------------------------------------ +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 764 +--r0:=-2/3*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2)-10/3*e*(b*d-2*a*e+(2*c*d-_ +-- b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+5/3*e*_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+2*d*_ +-- sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-_ +-- sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+_ +-- sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*(b^2-_ +-- 4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))-5/3*(2*c*d-b*e)*elliptic_e(_ +-- asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*_ +-- (b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 68 + +--S 69 of 764 +--d0:=D(m0,x) +--E 69 + +)clear all + +--S 70 of 764 +t0:=(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (2c e x + (b e + 2c d)x + b d)\|e x + d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 70 + +--S 71 of 764 +--r0:=-2/3*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2)-2*e*(b+2*c*x)*sqrt(d+e*x)/_ +-- ((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+e*elliptic_f(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(sqrt(c)*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2))-_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c))))*sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 71 + +--S 72 of 764 +--d0:=D(m0,x) +--E 72 + +)clear all + +--S 73 of 764 +t0:=(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^(5/2) +--R +--R +--R +-------+ +--R (2c x + b)\|e x + d +--R (1) --------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R Type: Expression(Integer) +--E 73 + +--S 74 of 764 +--r0:=-2/3*sqrt(d+e*x)/(a+b*x+c*x^2)^(3/2)-2/3*e*(b*c*d-b^2*e+2*a*c*e+c*_ +-- (2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(a+b*x+c*x^2))+1/3*e*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(b*e*(b-sqrt(b^2-4*a*c))+c*(-4*a*e+_ +-- 2*d*sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- ((b^2-4*a*c)*(c*d^2-e*(b*d-a*e))*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(2*c*d-b*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*(c*d^2-e*(b*d-a*e))*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 74 + +--S 75 of 764 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 764 +t0:=(b+2*c*x)/((a+b*x+c*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R (1) +--R 2c x + b +--R ------------------------------------------------------------------------- +--R +--------------+ +--R 2 4 3 2 2 2 +-------+ | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 764 +--r0:=-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-_ +-- 4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-2/3*e*(3*b^2*c*d*e-_ +-- 8*a*c^2*d*e-2*b^3*e^2-b*c*(c*d^2-7*a*e^2)-2*c*(c^2*d^2+b^2*e^2-_ +-- c*e*(b*d+3*a*e))*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(a+b*x+c*x^2))-1/3*e*elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(c*(b*c*d^2+b^2*d*e-8*a*c*d*e+_ +-- a*b*e^2)-(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*_ +-- sqrt(c)*sqrt(a+b*x+c*x^2))+1/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-_ +-- 4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*_ +-- sqrt(2)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- ((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 77 + +--S 78 of 764 +--d0:=D(m0,x) +--E 78 + +)clear all + +--S 79 of 764 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 m +--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(e x + d) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 764 +r0:=-(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(b*d-a*e)*(3*b*B*d-_ + 2*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^4*(2+m))-b*(3*b*B*d-A*b*e-2*a*B*e)*_ + (d+e*x)^(3+m)/(e^4*(3+m))+b^2*B*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 m + 4 +--R (B b m + 6B b m + 11B b m + 6B b )(e x + d) +--R + +--R 2 2 3 2 2 2 +--R ((A b + 2B a b)e - 3B b d)m + ((7A b + 14B a b)e - 21B b d)m +--R + +--R 2 2 2 2 +--R ((14A b + 28B a b)e - 42B b d)m + (8A b + 16B a b)e - 24B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (- 2A b - 4B a b)d e + 3B b d )m +--R + +--R 2 2 2 2 2 2 +--R ((16A a b + 8B a )e + (- 16A b - 32B a b)d e + 24B b d )m +--R + +--R 2 2 2 2 2 +--R ((38A a b + 19B a )e + (- 38A b - 76B a b)d e + 57B b d )m +--R + +--R 2 2 2 2 2 +--R (24A a b + 12B a )e + (- 24A b - 48B a b)d e + 36B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (- 2A a b - B a )d e + (A b + 2B a b)d e - B b d )m +--R + +--R 2 3 2 2 2 2 +--R 9A a e + (- 18A a b - 9B a )d e + (9A b + 18B a b)d e +--R + +--R 2 3 +--R - 9B b d +--R * +--R 2 +--R m +--R + +--R 2 3 2 2 2 2 +--R 26A a e + (- 52A a b - 26B a )d e + (26A b + 52B a b)d e +--R + +--R 2 3 +--R - 26B b d +--R * +--R m +--R + +--R 2 3 2 2 2 2 2 3 +--R 24A a e + (- 48A a b - 24B a )d e + (24A b + 48B a b)d e - 24B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 80 + +--S 81 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 of 764 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 5 8 2 5 2 4 7 +--R B b e x + ((A b + 2B a b)e + 5B b d e )x +--R + +--R 2 5 2 4 2 2 3 6 +--R ((2A a b + B a )e + (5A b + 10B a b)d e + 10B b d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 5 +--R (A a e + (10A a b + 5B a )d e + (10A b + 20B a b)d e + 10B b d e )x +--R + +--R 2 4 2 2 3 2 3 2 2 4 4 +--R (5A a d e + (20A a b + 10B a )d e + (10A b + 20B a b)d e + 5B b d e)x +--R + +--R 2 2 3 2 3 2 2 4 2 5 3 +--R (10A a d e + (20A a b + 10B a )d e + (5A b + 10B a b)d e + B b d )x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 82 + +--S 83 of 764 +r0:=-1/6*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^6/e^4+1/7*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^7/e^4-1/8*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^8/e^4+_ + 1/9*b^2*B*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 2 9 9 1 2 1 9 5 2 8 8 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 9 8 4 8 +--R + +--R 2 1 2 9 5 2 10 8 10 2 2 7 7 +--R ((- A a b + - B a )e + (- A b + -- B a b)d e + -- B b d e )x +--R 7 7 7 7 7 +--R + +--R 1 2 9 5 5 2 8 5 2 10 2 7 +--R - A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e +--R 6 3 6 3 3 +--R + +--R 5 2 3 6 +--R - B b d e +--R 3 +--R * +--R 6 +--R x +--R + +--R 2 8 2 2 7 2 3 6 2 4 5 5 +--R (A a d e + (4A a b + 2B a )d e + (2A b + 4B a b)d e + B b d e )x +--R + +--R 5 2 2 7 5 2 3 6 5 2 5 4 5 +--R - A a d e + (5A a b + - B a )d e + (- A b + - B a b)d e +--R 2 2 4 2 +--R + +--R 1 2 5 4 +--R - B b d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 10 2 3 6 10 5 2 4 5 1 2 2 5 4 3 +--R (-- A a d e + (-- A a b + - B a )d e + (- A b + - B a b)d e )x +--R 3 3 3 3 3 +--R + +--R 5 2 4 5 1 2 5 4 2 2 5 4 1 2 6 3 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 1 1 2 7 2 1 2 1 8 1 2 9 +--R (- -- A a b - -- B a )d e + (--- A b + -- B a b)d e - --- B b d +--R 21 42 168 84 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 83 + +--S 84 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 764 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 7 2 4 2 3 6 +--R B b e x + ((A b + 2B a b)e + 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((2A a b + B a )e + (4A b + 8B a b)d e + 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (A a e + (8A a b + 4B a )d e + (6A b + 12B a b)d e + 4B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 3 +--R (4A a d e + (12A a b + 6B a )d e + (4A b + 8B a b)d e + B b d )x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 85 + +--S 86 of 764 +r0:=-1/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^5/e^4+1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^6/e^4-1/7*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^7/e^4+_ + 1/8*b^2*B*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 2 8 8 1 2 2 8 4 2 7 7 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 8 7 7 7 +--R + +--R 1 1 2 8 2 2 4 7 2 2 6 6 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + B b d e )x +--R 3 6 3 3 +--R + +--R 1 2 8 8 4 2 7 6 2 12 2 6 +--R - A a e + (- A a b + - B a )d e + (- A b + -- B a b)d e +--R 5 5 5 5 5 +--R + +--R 4 2 3 5 +--R - B b d e +--R 5 +--R * +--R 5 +--R x +--R + +--R 2 7 3 2 2 6 2 3 5 1 2 4 4 4 +--R (A a d e + (3A a b + - B a )d e + (A b + 2B a b)d e + - B b d e )x +--R 2 4 +--R + +--R 2 2 6 8 4 2 3 5 1 2 2 4 4 3 +--R (2A a d e + (- A a b + - B a )d e + (- A b + - B a b)d e )x +--R 3 3 3 3 +--R + +--R 2 3 5 1 2 4 4 2 2 4 4 1 2 5 3 +--R (2A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 5 +--R + +--R 1 1 2 6 2 1 2 2 7 1 2 8 +--R (- -- A a b - -- B a )d e + (--- A b + --- B a b)d e - --- B b d +--R 15 30 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 86 + +--S 87 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 764 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 88 + +--S 89 of 764 +r0:=-1/4*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^4/e^4+1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)*(d+e*x)^5/e^4-1/6*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^6/e^4+_ + 1/7*b^2*B*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 2 7 7 1 2 1 7 1 2 6 6 +--R - B b e x + ((- A b + - B a b)e + - B b d e )x +--R 7 6 3 2 +--R + +--R 2 1 2 7 3 2 6 6 3 2 2 5 5 +--R ((- A a b + - B a )e + (- A b + - B a b)d e + - B b d e )x +--R 5 5 5 5 5 +--R + +--R 1 2 7 3 3 2 6 3 2 3 2 5 +--R - A a e + (- A a b + - B a )d e + (- A b + - B a b)d e +--R 4 2 4 4 2 +--R + +--R 1 2 3 4 +--R - B b d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 1 2 2 3 4 3 +--R (A a d e + (2A a b + B a )d e + (- A b + - B a b)d e )x +--R 3 3 +--R + +--R 3 2 2 5 1 2 3 4 2 2 3 4 1 2 4 3 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 4 +--R + +--R 1 1 2 5 2 1 2 1 6 1 2 7 +--R (- -- A a b - -- B a )d e + (-- A b + -- B a b)d e - --- B b d +--R 10 20 60 30 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 764 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 764 +r0:=1/3*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^3/b^4+1/4*(b*d-a*e)*(b*B*d+2*A*b*e-_ + 3*a*B*e)*(a+b*x)^4/b^4+1/5*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^5/b^4+_ + 1/6*B*e^2*(a+b*x)^6/b^4 +--R +--R +--R (2) +--R 1 6 2 6 1 6 2 5 2 2 6 5 +--R - B b e x + ((- A b + - B a b )e + - B b d e)x +--R 6 5 5 5 +--R + +--R 1 5 1 2 4 2 1 6 5 1 6 2 4 +--R ((- A a b + - B a b )e + (- A b + B a b )d e + - B b d )x +--R 2 4 2 4 +--R + +--R 1 2 4 2 4 5 2 2 4 1 6 2 5 2 3 +--R (- A a b e + (- A a b + - B a b )d e + (- A b + - B a b )d )x +--R 3 3 3 3 3 +--R + +--R 2 4 5 1 2 4 2 2 2 4 2 +--R (A a b d e + (A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 5 1 6 2 1 4 2 1 5 +--R (-- A a b - -- B a )e + (- - A a b + -- B a b)d e +--R 30 60 6 15 +--R + +--R 1 3 3 1 4 2 2 +--R (- A a b - -- B a b )d +--R 3 12 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 764 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 94 + +--S 95 of 764 +r0:=1/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)^3/b^3+1/4*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^4/b^3+1/5*B*e*(a+b*x)^5/b^3 +--R +--R +--R (2) +--R 1 5 5 1 5 1 4 1 5 4 +--R - B b e x + ((- A b + - B a b )e + - B b d)x +--R 5 4 2 4 +--R + +--R 2 4 1 2 3 1 5 2 4 3 +--R ((- A a b + - B a b )e + (- A b + - B a b )d)x +--R 3 3 3 3 +--R + +--R 1 2 3 4 1 2 3 2 2 3 +--R (- A a b e + (A a b + - B a b )d)x + A a b d x +--R 2 2 +--R + +--R 1 4 1 5 1 3 2 1 4 +--R (- -- A a b + -- B a )e + (- A a b - -- B a b)d +--R 12 30 3 12 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 95 + +--S 96 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 97 + +--S 98 of 764 +r0:=1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2 +--R +--R +--R (2) +--R 1 4 4 1 4 2 3 3 3 1 2 2 2 2 2 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x + A a b x +--R 4 3 3 2 +--R + +--R 1 3 1 4 +--R - A a b - -- B a +--R 3 12 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 98 + +--S 99 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 100 + +--S 101 of 764 +r0:=b*(b*d-a*e)*(B*d-A*e)*x/e^3-1/2*(B*d-A*e)*(a+b*x)^2/e^2+_ + 1/3*B*(a+b*x)^3/(b*e)-(b*d-a*e)^2*(B*d-A*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 +--R 6A a b e + (- 12A a b - 6B a b)d e + (6A b + 12B a b )d e +--R + +--R 3 3 +--R - 6B b d +--R * +--R log(e x + d) +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 2B b e x + ((3A b + 6B a b )e - 3B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((12A a b + 6B a b)e + (- 6A b - 12B a b )d e + 6B b d e)x +--R + +--R 2 3 3 2 2 +--R (3A a b + 2B a )e - 3B a b d e +--R / +--R 4 +--R 6b e +--R Type: Expression(Integer) +--E 101 + +--S 102 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 103 + +--S 104 of 764 +r0:=-b*(2*b*B*d-A*b*e-2*a*B*e)*x/e^3+1/2*b^2*B*x^2/e^2+(b*d-a*e)^2*_ + (B*d-A*e)/(e^4*(d+e*x))+(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 2 +--R ((4A a b + 2B a )e + (- 4A b - 8B a b)d e + 6B b d e)x +--R + +--R 2 2 2 2 2 3 +--R (4A a b + 2B a )d e + (- 4A b - 8B a b)d e + 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 3 2 2 2 +--R B b e x + ((2A b + 4B a b)e - 3B b d e )x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A b + 4B a b)d e - 4B b d e)x - 2A a e + (4A a b + 2B a )d e +--R + +--R 2 2 2 3 +--R (- 2A b - 4B a b)d e + 2B b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 104 + +--S 105 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 764 +r0:=b^2*B*x/e^3+1/2*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^2)-(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x))-b*(3*b*B*d-A*b*e-2*a*B*e)*_ + log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 +--R ((2A b + 4B a b)e - 6B b d e )x +--R + +--R 2 2 2 2 2 2 2 3 +--R ((4A b + 8B a b)d e - 12B b d e)x + (2A b + 4B a b)d e - 6B b d +--R * +--R log(e x + d) +--R + +--R 2 3 3 2 2 2 +--R 2B b e x + 4B b d e x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 4A a b - 2B a )e + (4A b + 8B a b)d e - 4B b d e)x - A a e +--R + +--R 2 2 2 2 2 3 +--R (- 2A a b - B a )d e + (3A b + 6B a b)d e - 5B b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 107 + +--S 108 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 109 + +--S 110 of 764 +r0:=-1/3*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^3)-1/2*B*(b*d-a*e)^2/_ + (e^4*(d+e*x)^2)+2*b*B*(b*d-a*e)/(e^4*(d+e*x))+b^2*B*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 4 3 3 3 2 3 3 2 2 2 +--R (6B a b e - 6B b d e )x + (18B a b d e - 18B b d e )x +--R + +--R 2 2 2 3 3 2 3 3 4 +--R (18B a b d e - 18B b d e)x + 6B a b d e - 6B b d +--R * +--R log(e x + d) +--R + +--R 3 4 3 3 3 +--R (- 2A b e + 2B b d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 6A a b - 12B a b)e + 30B a b d e - 12B b d e )x +--R + +--R 2 3 4 2 3 2 2 2 3 3 +--R ((- 6A a b - 3B a )e - 9B a b d e + 39B a b d e - 21B b d e)x +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 +--R - 2A a e - B a d e - 3B a b d e + 15B a b d e - 9B b d +--R / +--R 8 7 3 7 2 6 2 2 6 3 5 +--R (6a e - 6b d e )x + (18a d e - 18b d e )x + (18a d e - 18b d e )x +--R + +--R 3 5 4 4 +--R 6a d e - 6b d e +--R Type: Expression(Integer) +--E 110 + +--S 111 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 112 + +--S 113 of 764 +r0:=-1/4*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^4)+1/12*(3*b*B*d+A*b*e-_ + 4*a*B*e)*(a+b*x)^3/(e*(b*d-a*e)^2*(d+e*x)^3) +--R +--R +--R (2) +--R 1 4 1 3 1 4 4 +--R ((-- A b - - B a b )e + - B b d)x +--R 12 3 4 +--R + +--R 2 2 1 4 2 3 3 +--R (- B a b e + (- A b + - B a b )d)x +--R 3 3 +--R + +--R 1 2 2 3 3 1 2 2 2 +--R ((- - A a b - B a b)e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 2 3 1 4 2 2 1 4 1 3 1 4 +--R ((- - A a b - - B a )e + A a b d)x - - A a e + (- A a b - -- B a )d +--R 3 3 4 3 12 +--R / +--R 2 6 5 2 2 4 4 2 5 2 4 2 3 3 3 +--R (a e - 2a b d e + b d e )x + (4a d e - 8a b d e + 4b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (6a d e - 12a b d e + 6b d e )x + (4a d e - 8a b d e + 4b d e)x +--R + +--R 2 4 2 5 2 6 +--R a d e - 2a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 113 + +--S 114 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 of 764 +r0:=1/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^5)-1/4*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^4)+1/3*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^3)-_ + 1/2*b^2*B/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 3 3 1 2 2 3 1 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - - B b d e )x +--R 2 3 3 2 +--R + +--R 1 1 2 3 1 2 1 2 1 2 2 +--R ((- - A a b - - B a )e + (- - A b - - B a b)d e - - B b d e)x +--R 2 4 6 3 4 +--R + +--R 1 2 3 1 1 2 2 1 2 1 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A b - -- B a b)d e +--R 5 10 20 30 15 +--R + +--R 1 2 3 +--R - -- B b d +--R 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 116 + +--S 117 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 of 764 +r0:=1/6*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^6)-1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^5)+1/4*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^4)-_ + 1/3*b^2*B/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 3 3 1 2 1 3 1 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - - B b d e )x +--R 3 4 2 4 +--R + +--R 2 1 2 3 1 2 1 2 1 2 2 +--R ((- - A a b - - B a )e + (- -- A b - - B a b)d e - -- B b d e)x +--R 5 5 10 5 10 +--R + +--R 1 2 3 1 1 2 2 1 2 1 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A b - -- B a b)d e +--R 6 15 30 60 30 +--R + +--R 1 2 3 +--R - -- B b d +--R 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 119 + +--S 120 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^8 +--R +--R +--R (1) +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 764 +r0:=1/7*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^7)-1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-_ + a*B*e)/(e^4*(d+e*x)^6)+1/5*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^5)-_ + 1/4*b^2*B/(e^4*(d+e*x)^4) +--R +--R +--R (2) +--R 1 2 3 3 1 2 2 3 3 2 2 2 +--R - - B b e x + ((- - A b - - B a b)e - -- B b d e )x +--R 4 5 5 20 +--R + +--R 1 1 2 3 1 2 2 2 1 2 2 +--R ((- - A a b - - B a )e + (- -- A b - -- B a b)d e - -- B b d e)x +--R 3 6 15 15 20 +--R + +--R 1 2 3 1 1 2 2 1 2 2 2 +--R - - A a e + (- -- A a b - -- B a )d e + (- --- A b - --- B a b)d e +--R 7 21 42 105 105 +--R + +--R 1 2 3 +--R - --- B b d +--R 140 +--R / +--R 11 7 10 6 2 9 5 3 8 4 4 7 3 5 6 2 6 5 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 4 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 122 + +--S 123 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 764 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 124 + +--S 125 of 764 +r0:=-(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(1+m)/(e^6*(1+m))+(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^6*(2+m))-2*b*(b*d-a*e)^2*(5*b*B*d-_ + 3*A*b*e-2*a*B*e)*(d+e*x)^(3+m)/(e^6*(3+m))+2*b^2*(b*d-a*e)*(5*b*B*d-_ + 2*A*b*e-3*a*B*e)*(d+e*x)^(4+m)/(e^6*(4+m))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+b^4*B*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 4 5 4 4 4 3 4 2 4 4 +--R (B b m + 15B b m + 85B b m + 225B b m + 274B b m + 120B b ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 4 3 4 5 4 3 4 4 +--R ((A b + 4B a b )e - 5B b d)m + ((16A b + 64B a b )e - 80B b d)m +--R + +--R 4 3 4 3 +--R ((95A b + 380B a b )e - 475B b d)m +--R + +--R 4 3 4 2 +--R ((260A b + 1040B a b )e - 1300B b d)m +--R + +--R 4 3 4 4 3 +--R ((324A b + 1296B a b )e - 1620B b d)m + (144A b + 576B a b )e +--R + +--R 4 +--R - 720B b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (- 4A b - 16B a b )d e + 10B b d )m +--R + +--R 3 2 2 2 4 3 4 2 4 +--R ((68A a b + 102B a b )e + (- 68A b - 272B a b )d e + 170B b d )m +--R + +--R 3 2 2 2 4 3 +--R (428A a b + 642B a b )e + (- 428A b - 1712B a b )d e +--R + +--R 4 2 +--R 1070B b d +--R * +--R 3 +--R m +--R + +--R 3 2 2 2 4 3 +--R (1228A a b + 1842B a b )e + (- 1228A b - 4912B a b )d e +--R + +--R 4 2 +--R 3070B b d +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 4 3 +--R (1584A a b + 2376B a b )e + (- 1584A b - 6336B a b )d e +--R + +--R 4 2 +--R 3960B b d +--R * +--R m +--R + +--R 3 2 2 2 4 3 4 2 +--R (720A a b + 1080B a b )e + (- 720A b - 2880B a b )d e + 1800B b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (- 12A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (6A b + 24B a b )d e - 10B b d +--R * +--R 5 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (108A a b + 72B a b)e + (- 216A a b - 324B a b )d e +--R + +--R 4 3 2 4 3 +--R (108A b + 432B a b )d e - 180B b d +--R * +--R 4 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (726A a b + 484B a b)e + (- 1452A a b - 2178B a b )d e +--R + +--R 4 3 2 4 3 +--R (726A b + 2904B a b )d e - 1210B b d +--R * +--R 3 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (2232A a b + 1488B a b)e + (- 4464A a b - 6696B a b )d e +--R + +--R 4 3 2 4 3 +--R (2232A b + 8928B a b )d e - 3720B b d +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (3048A a b + 2032B a b)e + (- 6096A a b - 9144B a b )d e +--R + +--R 4 3 2 4 3 +--R (3048A b + 12192B a b )d e - 5080B b d +--R * +--R m +--R + +--R 2 2 3 3 3 2 2 2 +--R (1440A a b + 960B a b)e + (- 2880A a b - 4320B a b )d e +--R + +--R 4 3 2 4 3 +--R (1440A b + 5760B a b )d e - 2400B b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (12A a b + 18B a b )d e + (- 4A b - 16B a b )d e + 5B b d +--R * +--R 5 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (76A a b + 19B a )e + (- 228A a b - 152B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (228A a b + 342B a b )d e + (- 76A b - 304B a b )d e + 95B b d +--R * +--R 4 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (548A a b + 137B a )e + (- 1644A a b - 1096B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1644A a b + 2466B a b )d e + (- 548A b - 2192B a b )d e +--R + +--R 4 4 +--R 685B b d +--R * +--R 3 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (1844A a b + 461B a )e + (- 5532A a b - 3688B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (5532A a b + 8298B a b )d e + (- 1844A b - 7376B a b )d e +--R + +--R 4 4 +--R 2305B b d +--R * +--R 2 +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (2808A a b + 702B a )e + (- 8424A a b - 5616B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (8424A a b + 12636B a b )d e + (- 2808A b - 11232B a b )d e +--R + +--R 4 4 +--R 3510B b d +--R * +--R m +--R + +--R 3 4 4 2 2 3 3 +--R (1440A a b + 360B a )e + (- 4320A a b - 2880B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (4320A a b + 6480B a b )d e + (- 1440A b - 5760B a b )d e +--R + +--R 4 4 +--R 1800B b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (- 4A a b - B a )d e + (6A a b + 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 4A a b - 6B a b )d e + (A b + 4B a b )d e - B b d +--R * +--R 5 +--R m +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R 20A a e + (- 80A a b - 20B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 80A a b - 120B a b )d e + (20A b + 80B a b )d e - 20B b d +--R * +--R 4 +--R m +--R + +--R 4 5 3 4 4 +--R 155A a e + (- 620A a b - 155B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (930A a b + 620B a b)d e + (- 620A a b - 930B a b )d e +--R + +--R 4 3 4 4 5 +--R (155A b + 620B a b )d e - 155B b d +--R * +--R 3 +--R m +--R + +--R 4 5 3 4 4 +--R 580A a e + (- 2320A a b - 580B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (3480A a b + 2320B a b)d e + (- 2320A a b - 3480B a b )d e +--R + +--R 4 3 4 4 5 +--R (580A b + 2320B a b )d e - 580B b d +--R * +--R 2 +--R m +--R + +--R 4 5 3 4 4 +--R 1044A a e + (- 4176A a b - 1044B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (6264A a b + 4176B a b)d e + (- 4176A a b - 6264B a b )d e +--R + +--R 4 3 4 4 5 +--R (1044A b + 4176B a b )d e - 1044B b d +--R * +--R m +--R + +--R 4 5 3 4 4 +--R 720A a e + (- 2880A a b - 720B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (4320A a b + 2880B a b)d e + (- 2880A a b - 4320B a b )d e +--R + +--R 4 3 4 4 5 +--R (720A b + 2880B a b )d e - 720B b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 125 + +--S 126 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 of 764 +t0:=(A+B*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 7 12 4 3 7 4 6 11 +--R B b e x + ((A b + 4B a b )e + 7B b d e )x +--R + +--R 3 2 2 7 4 3 6 4 2 5 10 +--R ((4A a b + 6B a b )e + (7A b + 28B a b )d e + 21B b d e )x +--R + +--R 2 2 3 7 3 2 2 6 +--R (6A a b + 4B a b)e + (28A a b + 42B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (21A b + 84B a b )d e + 35B b d e +--R * +--R 9 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (4A a b + B a )e + (42A a b + 28B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 4 4 3 +--R (84A a b + 126B a b )d e + (35A b + 140B a b )d e + 35B b d e +--R * +--R 8 +--R x +--R + +--R 4 7 3 4 6 2 2 3 2 5 +--R A a e + (28A a b + 7B a )d e + (126A a b + 84B a b)d e +--R + +--R 3 2 2 3 4 4 3 4 3 4 5 2 +--R (140A a b + 210B a b )d e + (35A b + 140B a b )d e + 21B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 2 5 2 2 3 3 4 +--R 7A a d e + (84A a b + 21B a )d e + (210A a b + 140B a b)d e +--R + +--R 3 2 2 4 3 4 3 5 2 4 6 +--R (140A a b + 210B a b )d e + (21A b + 84B a b )d e + 7B b d e +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 4 3 4 2 2 3 4 3 +--R 21A a d e + (140A a b + 35B a )d e + (210A a b + 140B a b)d e +--R + +--R 3 2 2 5 2 4 3 6 4 7 +--R (84A a b + 126B a b )d e + (7A b + 28B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 3 4 3 4 4 3 2 2 3 5 2 +--R 35A a d e + (140A a b + 35B a )d e + (126A a b + 84B a b)d e +--R + +--R 3 2 2 6 4 3 7 +--R (28A a b + 42B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 4 3 3 4 5 2 2 2 3 6 +--R 35A a d e + (84A a b + 21B a )d e + (42A a b + 28B a b)d e +--R + +--R 3 2 2 7 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 5 2 3 4 6 2 2 3 7 2 +--R (21A a d e + (28A a b + 7B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 6 3 4 7 4 7 +--R (7A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 127 + +--S 128 of 764 +r0:=-1/8*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^8/e^6+1/9*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^9/e^6-1/5*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^10/e^6+2/11*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^11/e^6-1/12*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^12/e^6+_ + 1/13*b^4*B*(d+e*x)^13/e^6 +--R +--R +--R (2) +--R 1 4 13 13 1 4 1 3 13 7 4 12 12 +--R -- B b e x + ((-- A b + - B a b )e + -- B b d e )x +--R 13 12 3 12 +--R + +--R 4 3 6 2 2 13 7 4 28 3 12 +--R (-- A a b + -- B a b )e + (-- A b + -- B a b )d e +--R 11 11 11 11 +--R + +--R 21 4 2 11 +--R -- B b d e +--R 11 +--R * +--R 11 +--R x +--R + +--R 3 2 2 2 3 13 14 3 21 2 2 12 +--R (- A a b + - B a b)e + (-- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 21 4 42 3 2 11 7 4 3 10 +--R (-- A b + -- B a b )d e + - B b d e +--R 10 5 2 +--R * +--R 10 +--R x +--R + +--R 4 3 1 4 13 14 2 2 28 3 12 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 9 9 3 9 +--R + +--R 28 3 2 2 2 11 35 4 140 3 3 10 35 4 4 9 +--R (-- A a b + 14B a b )d e + (-- A b + --- B a b )d e + -- B b d e +--R 3 9 9 9 +--R * +--R 9 +--R x +--R + +--R 1 4 13 7 3 7 4 12 63 2 2 21 3 2 11 +--R - A a e + (- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 8 2 8 4 2 +--R + +--R 35 3 105 2 2 3 10 35 4 35 3 4 9 21 4 5 8 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + -- B b d e +--R 2 4 8 2 8 +--R * +--R 8 +--R x +--R + +--R 4 12 3 4 2 11 2 2 3 3 10 +--R A a d e + (12A a b + 3B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 4 9 4 3 5 8 4 6 7 +--R (20A a b + 30B a b )d e + (3A b + 12B a b )d e + B b d e +--R * +--R 7 +--R x +--R + +--R 7 4 2 11 70 3 35 4 3 10 2 2 70 3 4 9 +--R - A a d e + (-- A a b + -- B a )d e + (35A a b + -- B a b)d e +--R 2 3 6 3 +--R + +--R 3 2 2 5 8 7 4 14 3 6 7 1 4 7 6 +--R (14A a b + 21B a b )d e + (- A b + -- B a b )d e + - B b d e +--R 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 3 10 3 4 4 9 126 2 2 84 3 5 8 +--R 7A a d e + (28A a b + 7B a )d e + (--- A a b + -- B a b)d e +--R 5 5 +--R + +--R 28 3 42 2 2 6 7 1 4 4 3 7 6 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 35 4 4 9 3 21 4 5 8 21 2 2 3 6 7 +--R -- A a d e + (21A a b + -- B a )d e + (-- A a b + 7B a b)d e +--R 4 4 2 +--R + +--R 3 3 2 2 7 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 5 8 28 3 7 4 6 7 2 2 4 3 7 6 3 +--R (7A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d e )x +--R 3 3 3 +--R + +--R 7 4 6 7 3 1 4 7 6 2 4 7 6 1 4 8 5 +--R (- A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 8 +--R + +--R 1 3 1 4 9 4 1 2 2 1 3 10 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 18 72 60 90 +--R + +--R 1 3 1 2 2 11 2 1 4 1 3 12 +--R (- --- A a b - --- B a b )d e + (---- A b + --- B a b )d e +--R 330 220 3960 990 +--R + +--R 1 4 13 +--R - ----- B b d +--R 10296 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 128 + +--S 129 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 764 +t0:=(A+B*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 11 4 3 6 4 5 10 +--R B b e x + ((A b + 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 6 4 3 5 4 2 4 9 +--R ((4A a b + 6B a b )e + (6A b + 24B a b )d e + 15B b d e )x +--R + +--R 2 2 3 6 3 2 2 5 +--R (6A a b + 4B a b)e + (24A a b + 36B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (15A b + 60B a b )d e + 20B b d e +--R * +--R 8 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (4A a b + B a )e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 4 4 2 +--R (60A a b + 90B a b )d e + (20A b + 80B a b )d e + 15B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 5 2 2 3 2 4 +--R A a e + (24A a b + 6B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 3 3 4 3 4 2 4 5 +--R (80A a b + 120B a b )d e + (15A b + 60B a b )d e + 6B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 6A a d e + (60A a b + 15B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (60A a b + 90B a b )d e + (6A b + 24B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A a d e + (80A a b + 20B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 5 4 3 6 +--R (24A a b + 36B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 4 4 2 2 2 3 5 +--R 20A a d e + (60A a b + 15B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 6 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 2 +--R (15A a d e + (24A a b + 6B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 5 3 4 6 4 6 +--R (6A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 130 + +--S 131 of 764 +r0:=-1/7*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^7/e^6+1/8*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^8/e^6-2/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^9/e^6+1/5*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^10/e^6-1/11*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^11/e^6+_ + 1/12*b^4*B*(d+e*x)^12/e^6 +--R +--R +--R (2) +--R 1 4 12 12 1 4 4 3 12 6 4 11 11 +--R -- B b e x + ((-- A b + -- B a b )e + -- B b d e )x +--R 12 11 11 11 +--R + +--R 2 3 3 2 2 12 3 4 12 3 11 3 4 2 10 10 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e )x +--R 5 5 5 5 2 +--R + +--R 2 2 2 4 3 12 8 3 2 2 11 +--R (- A a b + - B a b)e + (- A a b + 4B a b )d e +--R 3 9 3 +--R + +--R 5 4 20 3 2 10 20 4 3 9 +--R (- A b + -- B a b )d e + -- B b d e +--R 3 3 9 +--R * +--R 9 +--R x +--R + +--R 1 3 1 4 12 9 2 2 3 11 +--R (- A a b + - B a )e + (- A a b + 3B a b)d e +--R 2 8 2 +--R + +--R 15 3 45 2 2 2 10 5 4 3 3 9 15 4 4 8 +--R (-- A a b + -- B a b )d e + (- A b + 10B a b )d e + -- B b d e +--R 2 4 2 8 +--R * +--R 8 +--R x +--R + +--R 1 4 12 24 3 6 4 11 90 2 2 60 3 2 10 +--R - A a e + (-- A a b + - B a )d e + (-- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 80 3 120 2 2 3 9 15 4 60 3 4 8 6 4 5 7 +--R (-- A a b + --- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 4 11 3 5 4 2 10 2 2 40 3 3 9 +--R A a d e + (10A a b + - B a )d e + (20A a b + -- B a b)d e +--R 2 3 +--R + +--R 3 2 2 4 8 4 3 5 7 1 4 6 6 +--R (10A a b + 15B a b )d e + (A b + 4B a b )d e + - B b d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 4 2 10 3 4 3 9 2 2 3 4 8 +--R 3A a d e + (16A a b + 4B a )d e + (18A a b + 12B a b)d e +--R + +--R 24 3 36 2 2 5 7 1 4 4 3 6 6 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 3 9 3 15 4 4 8 2 2 3 5 7 +--R 5A a d e + (15A a b + -- B a )d e + (9A a b + 6B a b)d e +--R 4 +--R + +--R 3 3 2 2 6 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 4 8 3 4 5 7 2 2 4 3 6 6 3 +--R (5A a d e + (8A a b + 2B a )d e + (2A a b + - B a b)d e )x +--R 3 +--R + +--R 4 5 7 3 1 4 6 6 2 4 6 6 1 4 7 5 +--R (3A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 7 +--R + +--R 1 3 1 4 8 4 1 2 2 1 3 9 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 14 56 42 63 +--R + +--R 1 3 1 2 2 10 2 1 4 2 3 11 +--R (- --- A a b - --- B a b )d e + (---- A b + ---- B a b )d e +--R 210 140 2310 1155 +--R + +--R 1 4 12 +--R - ---- B b d +--R 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 131 + +--S 132 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 764 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 10 4 3 5 4 4 9 +--R B b e x + ((A b + 4B a b )e + 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 8 +--R ((4A a b + 6B a b )e + (5A b + 20B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (6A a b + 4B a b)e + (20A a b + 30B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (10A b + 40B a b )d e + 10B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b + B a )e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (40A a b + 60B a b )d e + (10A b + 40B a b )d e + 5B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (20A a b + 5B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (40A a b + 60B a b )d e + (5A b + 20B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R 5A a d e + (40A a b + 10B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 4 4 3 5 +--R (20A a b + 30B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 3 2 2 2 3 4 +--R 10A a d e + (40A a b + 10B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 5 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 2 +--R (10A a d e + (20A a b + 5B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 4 3 4 5 4 5 +--R (5A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 133 + +--S 134 of 764 +r0:=-1/6*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^6/e^6+1/7*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)*(d+e*x)^7/e^6-1/4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)*(d+e*x)^8/e^6+2/9*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^9/e^6-1/10*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^10/e^6+_ + 1/11*b^4*B*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 4 11 11 1 4 2 3 11 1 4 10 10 +--R -- B b e x + ((-- A b + - B a b )e + - B b d e )x +--R 11 10 5 2 +--R + +--R 4 3 2 2 2 11 5 4 20 3 10 10 4 2 9 9 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + -- B b d e )x +--R 9 3 9 9 9 +--R + +--R 3 2 2 1 3 11 5 3 15 2 2 10 +--R (- A a b + - B a b)e + (- A a b + -- B a b )d e +--R 4 2 2 4 +--R + +--R 5 4 3 2 9 5 4 3 8 +--R (- A b + 5B a b )d e + - B b d e +--R 4 4 +--R * +--R 8 +--R x +--R + +--R 4 3 1 4 11 30 2 2 20 3 10 +--R (- A a b + - B a )e + (-- A a b + -- B a b)d e +--R 7 7 7 7 +--R + +--R 40 3 60 2 2 2 9 10 4 40 3 3 8 5 4 4 7 +--R (-- A a b + -- B a b )d e + (-- A b + -- B a b )d e + - B b d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 4 11 10 3 5 4 10 2 2 20 3 2 9 +--R - A a e + (-- A a b + - B a )d e + (10A a b + -- B a b)d e +--R 6 3 6 3 +--R + +--R 20 3 2 2 3 8 5 4 10 3 4 7 1 4 5 6 +--R (-- A a b + 10B a b )d e + (- A b + -- B a b )d e + - B b d e +--R 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 4 10 3 4 2 9 2 2 3 3 8 +--R A a d e + (8A a b + 2B a )d e + (12A a b + 8B a b)d e +--R + +--R 3 2 2 4 7 1 4 4 3 5 6 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 4 2 9 3 5 4 3 8 15 2 2 3 4 7 +--R - A a d e + (10A a b + - B a )d e + (-- A a b + 5B a b)d e +--R 2 2 2 +--R + +--R 3 3 2 2 5 6 +--R (A a b + - B a b )d e +--R 2 +--R * +--R 4 +--R x +--R + +--R 10 4 3 8 20 3 5 4 4 7 2 2 4 3 5 6 3 +--R (-- A a d e + (-- A a b + - B a )d e + (2A a b + - B a b)d e )x +--R 3 3 3 3 +--R + +--R 5 4 4 7 3 1 4 5 6 2 4 5 6 1 4 6 5 +--R (- A a d e + (2A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 2 3 1 4 7 4 1 2 2 1 3 8 3 +--R (- -- A a b - -- B a )d e + (-- A a b + -- B a b)d e +--R 21 42 28 42 +--R + +--R 1 3 1 2 2 9 2 1 4 1 3 10 +--R (- --- A a b - -- B a b )d e + (---- A b + --- B a b )d e +--R 126 84 1260 315 +--R + +--R 1 4 11 +--R - ---- B b d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 134 + +--S 135 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 764 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 4 9 4 3 4 4 3 8 +--R B b e x + ((A b + 4B a b )e + 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((4A a b + 6B a b )e + (4A b + 16B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (6A a b + 4B a b)e + (16A a b + 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (6A b + 24B a b )d e + 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (24A a b + 36B a b )d e + (4A b + 16B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R A a e + (16A a b + 4B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (16A a b + 24B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 4A a d e + (24A a b + 6B a )d e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 4 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (6A a d e + (16A a b + 4B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (4A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 764 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^4*(a+b*x)^5/b^6+1/6*(b*d-a*e)^3*(b*B*d+4*A*b*e-_ + 5*a*B*e)*(a+b*x)^6/b^6+2/7*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*_ + (a+b*x)^7/b^6+1/4*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^8/_ + b^6+1/9*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^9/b^6+1/10*B*e^4*_ + (a+b*x)^10/b^6 +--R +--R +--R (2) +--R 1 10 4 10 1 10 4 9 4 4 10 3 9 +--R -- B b e x + ((- A b + - B a b )e + - B b d e )x +--R 10 9 9 9 +--R + +--R 1 9 3 2 8 4 1 10 9 3 3 10 2 2 8 +--R ((- A a b + - B a b )e + (- A b + 2B a b )d e + - B b d e )x +--R 2 4 2 4 +--R + +--R 6 2 8 4 3 7 4 16 9 24 2 8 3 +--R (- A a b + - B a b )e + (-- A a b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 6 10 24 9 2 2 4 10 3 +--R (- A b + -- B a b )d e + - B b d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 2 3 7 1 4 6 4 2 8 8 3 7 3 +--R (- A a b + - B a b )e + (4A a b + - B a b )d e +--R 3 6 3 +--R + +--R 9 2 8 2 2 2 10 8 9 3 1 10 4 +--R (4A a b + 6B a b )d e + (- A b + - B a b )d e + - B b d +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 4 6 4 16 3 7 4 4 6 3 36 2 8 24 3 7 2 2 +--R - A a b e + (-- A a b + - B a b )d e + (-- A a b + -- B a b )d e +--R 5 5 5 5 5 +--R + +--R 16 9 24 2 8 3 1 10 4 9 4 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 4 6 3 3 7 3 4 6 2 2 2 8 3 7 3 +--R A a b d e + (6A a b + - B a b )d e + (6A a b + 4B a b )d e +--R 2 +--R + +--R 9 3 2 8 4 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 6 2 2 16 3 7 4 4 6 3 2 8 4 3 7 4 3 +--R (2A a b d e + (-- A a b + - B a b )d e + (2A a b + - B a b )d )x +--R 3 3 3 +--R + +--R 4 6 3 3 7 1 4 6 4 2 4 6 4 +--R (2A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 9 1 10 4 1 8 2 2 9 3 +--R (--- A a b - ---- B a )e + (- -- A a b + --- B a b)d e +--R 630 1260 70 315 +--R + +--R 2 7 3 3 8 2 2 2 2 6 4 4 7 3 3 +--R (-- A a b - --- B a b )d e + (- -- A a b + --- B a b )d e +--R 35 140 15 105 +--R + +--R 1 5 5 1 6 4 4 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 137 + +--S 138 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 764 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e + (12A a b + 18B a b )d e +--R + +--R 4 3 3 +--R (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 139 + +--S 140 of 764 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^3*(a+b*x)^5/b^5+1/6*(b*d-a*e)^2*(b*B*d+3*A*b*e-_ + 4*a*B*e)*(a+b*x)^6/b^5+3/7*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^7/b^5+1/8*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^8/b^5+_ + 1/9*B*e^3*(a+b*x)^9/b^5 +--R +--R +--R (2) +--R 1 9 3 9 1 9 1 8 3 3 9 2 8 +--R - B b e x + ((- A b + - B a b )e + - B b d e )x +--R 9 8 2 8 +--R + +--R 4 8 6 2 7 3 3 9 12 8 2 3 9 2 7 +--R ((- A a b + - B a b )e + (- A b + -- B a b )d e + - B b d e)x +--R 7 7 7 7 7 +--R + +--R 2 7 2 3 6 3 8 2 7 2 +--R (A a b + - B a b )e + (2A a b + 3B a b )d e +--R 3 +--R + +--R 1 9 8 2 1 9 3 +--R (- A b + 2B a b )d e + - B b d +--R 2 6 +--R * +--R 6 +--R x +--R + +--R 4 3 6 1 4 5 3 18 2 7 12 3 6 2 +--R (- A a b + - B a b )e + (-- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 12 8 18 2 7 2 1 9 4 8 3 +--R (-- A a b + -- B a b )d e + (- A b + - B a b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 4 5 3 3 6 3 4 5 2 9 2 7 3 6 2 +--R - A a b e + (3A a b + - B a b )d e + (- A a b + 3B a b )d e +--R 4 4 2 +--R + +--R 8 3 2 7 3 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 5 2 3 6 4 5 2 2 7 4 3 6 3 3 +--R (A a b d e + (4A a b + B a b )d e + (2A a b + - B a b )d )x +--R 3 +--R + +--R 3 4 5 2 3 6 1 4 5 3 2 4 5 3 +--R (- A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 2 +--R + +--R 1 8 1 9 3 1 7 2 3 8 2 +--R (- --- A a b + --- B a )e + (-- A a b - --- B a b)d e +--R 280 630 35 280 +--R + +--R 1 6 3 1 7 2 2 1 5 4 1 6 3 3 +--R (- -- A a b + -- B a b )d e + (- A a b - -- B a b )d +--R 10 35 5 30 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 140 + +--S 141 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 of 764 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 142 + +--S 143 of 764 +r0:=1/5*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^5/b^4+1/6*(b*d-a*e)*(b*B*d+2*A*b*e-_ + 3*a*B*e)*(a+b*x)^6/b^4+1/7*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^7/b^4+_ + 1/8*B*e^2*(a+b*x)^8/b^4 +--R +--R +--R (2) +--R 1 8 2 8 1 8 4 7 2 2 8 7 +--R - B b e x + ((- A b + - B a b )e + - B b d e)x +--R 8 7 7 7 +--R + +--R 2 7 2 6 2 1 8 4 7 1 8 2 6 +--R ((- A a b + B a b )e + (- A b + - B a b )d e + - B b d )x +--R 3 3 3 6 +--R + +--R 6 2 6 4 3 5 2 8 7 12 2 6 +--R (- A a b + - B a b )e + (- A a b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 1 8 4 7 2 +--R (- A b + - B a b )d +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 3 5 1 4 4 2 2 6 3 5 +--R (A a b + - B a b )e + (3A a b + 2B a b )d e +--R 4 +--R + +--R 7 3 2 6 2 +--R (A a b + - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 1 4 4 2 8 3 5 2 4 4 2 6 4 3 5 2 3 +--R (- A a b e + (- A a b + - B a b )d e + (2A a b + - B a b )d )x +--R 3 3 3 3 +--R + +--R 4 4 3 5 1 4 4 2 2 4 4 2 +--R (A a b d e + (2A a b + - B a b )d )x + A a b d x +--R 2 +--R + +--R 1 7 1 8 2 1 6 2 2 7 +--R (--- A a b - --- B a )e + (- -- A a b + --- B a b)d e +--R 105 280 15 105 +--R + +--R 1 5 3 1 6 2 2 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 143 + +--S 144 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 764 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R Type: Polynomial(Integer) +--E 145 + +--S 146 of 764 +r0:=1/5*(A*b-a*B)*(b*d-a*e)*(a+b*x)^5/b^3+1/6*(b*B*d+A*b*e-2*a*B*e)*_ + (a+b*x)^6/b^3+1/7*B*e*(a+b*x)^7/b^3 +--R +--R +--R (2) +--R 1 7 7 1 7 2 6 1 7 6 +--R - B b e x + ((- A b + - B a b )e + - B b d)x +--R 7 6 3 6 +--R + +--R 4 6 6 2 5 1 7 4 6 5 +--R ((- A a b + - B a b )e + (- A b + - B a b )d)x +--R 5 5 5 5 +--R + +--R 3 2 5 3 4 6 3 2 5 4 +--R ((- A a b + B a b )e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 3 4 1 4 3 2 5 4 3 4 3 +--R ((- A a b + - B a b )e + (2A a b + - B a b )d)x +--R 3 3 3 +--R + +--R 1 4 3 3 4 1 4 3 2 4 3 +--R (- A a b e + (2A a b + - B a b )d)x + A a b d x +--R 2 2 +--R + +--R 1 6 1 7 1 5 2 1 6 +--R (- -- A a b + --- B a )e + (- A a b - -- B a b)d +--R 30 105 5 30 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 146 + +--S 147 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 2 2 3 2 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x + (6A a b + 4B a b)x +--R + +--R 3 4 4 +--R (4A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 148 + +--S 149 of 764 +r0:=1/5*(A*b-a*B)*(a+b*x)^5/b^2+1/6*B*(a+b*x)^6/b^2 +--R +--R +--R (2) +--R 1 6 6 1 6 4 5 5 5 3 2 4 4 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x +--R 6 5 5 2 +--R + +--R 2 4 4 3 3 3 3 3 1 4 2 2 4 2 1 5 +--R (2A a b + - B a b )x + (2A a b + - B a b )x + A a b x + - A a b +--R 3 2 5 +--R + +--R 1 6 +--R - -- B a +--R 30 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 764 +r0:=b*(b*d-a*e)^3*(B*d-A*e)*x/e^5-1/2*(b*d-a*e)^2*(B*d-A*e)*(a+b*x)^2/e^4+_ + 1/3*(b*d-a*e)*(B*d-A*e)*(a+b*x)^3/e^3-1/4*(B*d-A*e)*(a+b*x)^4/e^2+_ + 1/5*B*(a+b*x)^5/(b*e)-(b*d-a*e)^4*(B*d-A*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 3 2 4 4 +--R 60A a b e + (- 240A a b - 60B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (360A a b + 240B a b )d e + (- 240A a b - 360B a b )d e +--R + +--R 5 4 4 5 5 +--R (60A b + 240B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 5 4 5 5 4 4 +--R 12B b e x + ((15A b + 60B a b )e - 15B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 3 +--R ((80A a b + 120B a b )e + (- 20A b - 80B a b )d e + 20B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (180A a b + 120B a b )e + (- 120A a b - 180B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b + 120B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b + 60B a b)e + (- 360A a b - 240B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (240A a b + 360B a b )d e + (- 60A b - 240B a b )d e + 60B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (65A a b + 12B a )e + (- 80A a b - 65B a b)d e +--R + +--R 2 3 3 2 2 3 2 3 3 2 +--R (30A a b + 80B a b )d e - 30B a b d e +--R / +--R 6 +--R 60b e +--R Type: Expression(Integer) +--E 152 + +--S 153 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 154 + +--S 155 of 764 +r0:=-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*x/e^5+(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x))+b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (d+e*x)^2/e^6-1/3*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^3/e^6+1/4*b^4*_ + B*(d+e*x)^4/e^6+(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 4 5 2 2 3 4 +--R (48A a b + 12B a )e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e +--R + +--R 4 4 +--R 60B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 2 3 +--R (48A a b + 12B a )d e + (- 144A a b - 96B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (144A a b + 216B a b )d e + (- 48A b - 192B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((4A b + 16B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 8A b - 32B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (72A a b + 48B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (24A b + 96B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (16A b + 64B a b )d e - 5B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 12A a e + (48A a b + 12B a )d e + (- 72A a b - 48B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (72A a b + 108B a b )d e + (- 32A b - 128B a b )d e + 55B b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 155 + +--S 156 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 157 + +--S 158 of 764 +r0:=2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*x/e^5+1/2*(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x)^2)-(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*_ + (d+e*x))-1/2*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^2/e^6+1/3*b^4*B*_ + (d+e*x)^3/e^6-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 2 3 5 3 2 2 4 +--R (36A a b + 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (36A b + 144B a b )d e - 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 2 3 +--R (72A a b + 48B a b)d e + (- 144A a b - 216B a b )d e +--R + +--R 4 3 3 2 4 4 +--R (72A b + 288B a b )d e - 120B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (36A a b + 24B a b)d e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 4 4 5 +--R (36A b + 144B a b )d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 2B b e x + ((3A b + 12B a b )e - 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 12A b - 48B a b )d e + 20B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 4 3 2 2 +--R ((48A a b + 72B a b )d e + (- 30A b - 120B a b )d e + 50B b d e )x +--R + +--R 3 4 5 2 2 3 4 +--R (- 24A a b - 6B a )e + (72A a b + 48B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (12A b + 48B a b )d e - 20B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 12A a b - 3B a )d e + (54A a b + 36B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 60A a b - 90B a b )d e + (24A b + 96B a b )d e - 40B b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 158 + +--S 159 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 of 764 +r0:=-b^3*(4*b*B*d-A*b*e-4*a*B*e)*x/e^5+1/2*b^4*B*x^2/e^4+1/3*(b*d-a*e)^4*_ + (B*d-A*e)/(e^6*(d+e*x)^3)-1/2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/_ + (e^6*(d+e*x)^2)+2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*(d+_ + e*x))+2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((24A a b + 36B a b )e + (- 24A b - 96B a b )d e + 60B b d e )x +--R + +--R 3 2 2 4 4 3 2 3 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 3 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (72A a b + 108B a b )d e + (- 72A b - 288B a b )d e +--R + +--R 4 4 +--R 180B b d e +--R * +--R x +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (24A a b + 36B a b )d e + (- 24A b - 96B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 3 5 4 4 4 +--R 3B b e x + ((6A b + 24B a b )e - 15B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((18A b + 72B a b )d e - 63B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (72A a b + 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 18A b - 72B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 12A a b - 3B a )e + (- 36A a b - 24B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (108A a b + 162B a b )d e + (- 54A b - 216B a b )d e + 81B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 2A a e + (- 4A a b - B a )d e + (- 12A a b - 8B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (44A a b + 66B a b )d e + (- 26A b - 104B a b )d e + 47B b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 161 + +--S 162 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 of 764 +r0:=b^4*B*x/e^5+1/4*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^4)-1/3*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^3)+b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^2)-2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 3 5 4 4 4 +--R ((12A b + 48B a b )e - 60B b d e )x +--R + +--R 4 3 4 4 2 3 3 +--R ((48A b + 192B a b )d e - 240B b d e )x +--R + +--R 4 3 2 3 4 3 2 2 +--R ((72A b + 288B a b )d e - 360B b d e )x +--R + +--R 4 3 3 2 4 4 4 3 4 +--R ((48A b + 192B a b )d e - 240B b d e)x + (12A b + 48B a b )d e +--R + +--R 4 5 +--R - 60B b d +--R * +--R log(e x + d) +--R + +--R 4 5 5 4 4 4 +--R 12B b e x + 48B b d e x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((- 48A a b - 72B a b )e + (48A b + 192B a b )d e - 48B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 36A a b - 24B a b)e + (- 72A a b - 108B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (108A b + 432B a b )d e - 252B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 16A a b - 4B a )e + (- 24A a b - 16B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (- 48A a b - 72B a b )d e + (88A b + 352B a b )d e - 248B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (- 4A a b - B a )d e + (- 6A a b - 4B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 12A a b - 18B a b )d e + (25A b + 100B a b )d e - 77B b d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 164 + +--S 165 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^6 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 764 +r0:=-1/5*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^5)-1/4*B*(b*d-a*e)^4/_ + (e^6*(d+e*x)^4)+4/3*b*B*(b*d-a*e)^3/(e^6*(d+e*x)^3)-3*b^2*B*(b*d-_ + a*e)^2/(e^6*(d+e*x)^2)+4*b^3*B*(b*d-a*e)/(e^6*(d+e*x))+b^4*B*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 6 5 5 5 4 5 5 2 4 4 +--R (60B a b e - 60B b d e )x + (300B a b d e - 300B b d e )x +--R + +--R 4 2 4 5 3 3 3 4 3 3 5 4 2 2 +--R (600B a b d e - 600B b d e )x + (600B a b d e - 600B b d e )x +--R + +--R 4 4 2 5 5 4 5 5 6 +--R (300B a b d e - 300B b d e)x + 60B a b d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 5 6 5 5 5 +--R (- 12A b e + 12B b d e )x +--R + +--R 4 2 3 6 4 5 5 2 4 4 +--R ((- 60A a b - 240B a b )e + 540B a b d e - 240B b d e )x +--R + +--R 2 3 3 2 6 2 3 5 4 2 4 +--R (- 120A a b - 180B a b )e - 300B a b d e + 1380B a b d e +--R + +--R 5 3 3 +--R - 780B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 3 2 5 2 3 2 4 +--R (- 120A a b - 80B a b)e - 100B a b d e - 300B a b d e +--R + +--R 4 3 3 5 4 2 +--R 1580B a b d e - 980B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 4 5 3 2 2 4 2 3 3 3 +--R (- 60A a b - 15B a )e - 25B a b d e - 50B a b d e - 150B a b d e +--R + +--R 4 4 2 5 5 +--R 865B a b d e - 565B b d e +--R * +--R x +--R + +--R 5 6 5 5 4 2 4 3 2 3 3 2 3 4 2 +--R - 12A a e - 3B a d e - 5B a b d e - 10B a b d e - 30B a b d e +--R + +--R 4 5 5 6 +--R 185B a b d e - 125B b d +--R / +--R 12 11 5 11 2 10 4 +--R (60a e - 60b d e )x + (300a d e - 300b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (600a d e - 600b d e )x + (600a d e - 600b d e )x +--R + +--R 4 8 5 7 5 7 6 6 +--R (300a d e - 300b d e )x + 60a d e - 60b d e +--R Type: Expression(Integer) +--E 167 + +--S 168 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 169 + +--S 170 of 764 +r0:=-1/6*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^6)+1/30*(5*b*B*d+A*b*e-_ + 6*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^5) +--R +--R +--R (2) +--R 1 6 1 5 1 6 6 +--R ((-- A b - - B a b )e + - B b d)x +--R 30 5 6 +--R + +--R 2 4 1 6 4 5 5 +--R (- B a b e + (- A b + - B a b )d)x +--R 5 5 +--R + +--R 1 2 4 3 3 5 3 2 4 4 +--R ((- - A a b - 2B a b )e + (A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 3 3 4 2 2 4 4 3 3 3 +--R ((- - A a b - 2B a b )e + (2A a b + - B a b )d)x +--R 3 3 +--R + +--R 3 4 2 5 3 3 1 4 2 2 +--R ((- - A a b - B a b)e + (2A a b + - B a b )d)x +--R 2 2 +--R + +--R 4 5 1 6 4 2 1 6 1 5 1 6 +--R ((- - A a b - - B a )e + A a b d)x - - A a e + (- A a b - -- B a )d +--R 5 5 6 5 30 +--R / +--R 2 8 7 2 2 6 6 2 7 2 6 2 3 5 5 +--R (a e - 2a b d e + b d e )x + (6a d e - 12a b d e + 6b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (15a d e - 30a b d e + 15b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (20a d e - 40a b d e + 20b d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 2 5 3 6 2 2 7 +--R (15a d e - 30a b d e + 15b d e )x + (6a d e - 12a b d e + 6b d e)x +--R + +--R 2 6 2 7 2 8 +--R a d e - 2a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 170 + +--S 171 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 172 + +--S 173 of 764 +r0:=-1/7*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^7)+1/42*(5*b*B*d+2*A*b*e-_ + 7*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^6)+1/210*b*(5*b*B*d+2*A*b*e-_ + 7*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 1 7 1 6 2 1 7 7 +--R ((- --- A b + -- B a b )e - -- B b d e)x +--R 105 30 42 +--R + +--R 1 7 7 6 1 7 2 6 +--R ((- -- A b + -- B a b )d e - - B b d )x +--R 15 30 6 +--R + +--R 1 3 4 2 3 2 5 1 7 4 6 2 5 +--R (- - B a b e + - B a b d e + (- - A b - - B a b )d )x +--R 2 2 5 5 +--R + +--R 1 3 4 4 4 3 2 2 5 19 3 4 +--R (- - A a b - - B a b )e + (A a b + -- B a b )d e +--R 3 3 6 +--R + +--R 6 3 2 5 2 +--R (- A a b - - B a b )d +--R 2 +--R * +--R 4 +--R x +--R + +--R 4 3 3 5 2 2 8 3 4 19 4 3 +--R (- A a b - - B a b )e + (- A a b + -- B a b )d e +--R 2 3 6 +--R + +--R 2 5 4 3 4 2 +--R (- 2A a b - - B a b )d +--R 3 +--R * +--R 3 +--R x +--R + +--R 6 5 2 4 6 2 4 3 3 5 2 +--R (- - A a b - - B a b)e + (3A a b + - B a b )d e +--R 5 5 2 +--R + +--R 3 4 1 4 3 2 +--R (- 2A a b - - B a b )d +--R 2 +--R * +--R 2 +--R x +--R + +--R 2 6 1 7 2 8 5 2 7 6 4 3 2 +--R ((- - A a b - - B a )e + (- A a b + -- B a b)d e - A a b d )x +--R 3 6 5 30 +--R + +--R 1 7 2 1 6 1 7 1 5 2 1 6 2 +--R - - A a e + (- A a b - -- B a )d e + (- - A a b + -- B a b)d +--R 7 3 42 5 30 +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (a e - 3a b d e + 3a b d e - b d e )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (7a d e - 21a b d e + 21a b d e - 7b d e )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (21a d e - 63a b d e + 63a b d e - 21b d e )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (35a d e - 105a b d e + 105a b d e - 35b d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (35a d e - 105a b d e + 105a b d e - 35b d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (21a d e - 63a b d e + 63a b d e - 21b d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 2 8 2 +--R (7a d e - 21a b d e + 21a b d e - 7b d e)x + a d e - 3a b d e +--R + +--R 2 9 3 10 +--R 3a b d e - b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 173 + +--S 174 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 of 764 +r0:=-1/8*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^8)+1/56*(5*b*B*d+3*A*b*e-_ + 8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^7)+1/168*b*(5*b*B*d+3*A*b*e-_ + 8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^3*(d+e*x)^6)+1/840*b^2*(5*b*B*d+_ + 3*A*b*e-8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 1 8 1 7 3 1 8 2 8 +--R ((--- A b - --- B a b )e + --- B b d e )x +--R 280 105 168 +--R + +--R 1 8 8 7 2 1 8 2 7 +--R ((-- A b - --- B a b )d e + -- B b d e)x +--R 35 105 21 +--R + +--R 1 8 4 7 2 1 8 3 6 +--R ((-- A b - -- B a b )d e + - B b d )x +--R 10 15 6 +--R + +--R 1 4 4 3 4 3 5 2 2 6 2 1 8 4 7 3 5 +--R (- - B a b e + - B a b d e - 2B a b d e + (- A b + - B a b )d )x +--R 3 3 5 5 +--R + +--R 1 4 4 5 3 3 3 5 43 4 4 2 +--R (- - A a b - B a b )e + (A a b + -- B a b )d e +--R 4 12 +--R + +--R 3 2 6 13 3 5 2 7 3 2 6 3 +--R (- - A a b - -- B a b )d e + (A a b + - B a b )d +--R 2 3 2 +--R * +--R 4 +--R x +--R + +--R 4 5 3 6 6 2 3 4 4 5 3 2 +--R (- - A a b - - B a b )e + (3A a b + 4B a b )d e +--R 5 5 +--R + +--R 3 5 13 4 4 2 2 6 4 3 5 3 +--R (- 4A a b - -- B a b )d e + (2A a b + - B a b )d +--R 3 3 +--R * +--R 3 +--R x +--R + +--R 6 2 2 7 3 18 5 3 31 6 2 2 +--R (- A a b - - B a b)e + (-- A a b + -- B a b )d e +--R 3 5 15 +--R + +--R 9 4 4 5 3 2 3 5 1 4 4 3 +--R (- - A a b - 2B a b )d e + (2A a b + - B a b )d +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 4 7 1 8 3 6 2 8 7 2 +--R (- - A a b - - B a )e + (2A a b + -- B a b)d e +--R 7 7 21 +--R + +--R 12 5 3 4 6 2 2 4 4 3 +--R (- -- A a b - -- B a b )d e + A a b d +--R 5 15 +--R * +--R x +--R + +--R 1 8 3 3 7 1 8 2 1 6 2 1 7 2 +--R - - A a e + (- A a b - -- B a )d e + (- - A a b + -- B a b)d e +--R 8 7 56 2 21 +--R + +--R 1 5 3 1 6 2 3 +--R (- A a b - -- B a b )d +--R 5 30 +--R / +--R 4 12 3 11 2 2 2 10 3 3 9 4 4 8 8 +--R (a e - 4a b d e + 6a b d e - 4a b d e + b d e )x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 4 5 7 7 +--R (8a d e - 32a b d e + 48a b d e - 32a b d e + 8b d e )x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 4 6 6 6 +--R (28a d e - 112a b d e + 168a b d e - 112a b d e + 28b d e )x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 4 7 5 5 +--R (56a d e - 224a b d e + 336a b d e - 224a b d e + 56b d e )x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 8 4 4 +--R (70a d e - 280a b d e + 420a b d e - 280a b d e + 70b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 8 4 4 9 3 3 +--R (56a d e - 224a b d e + 336a b d e - 224a b d e + 56b d e )x +--R + +--R 4 6 6 3 7 5 2 2 8 4 3 9 3 4 10 2 2 +--R (28a d e - 112a b d e + 168a b d e - 112a b d e + 28b d e )x +--R + +--R 4 7 5 3 8 4 2 2 9 3 3 10 2 4 11 4 8 4 +--R (8a d e - 32a b d e + 48a b d e - 32a b d e + 8b d e)x + a d e +--R + +--R 3 9 3 2 2 10 2 3 11 4 12 +--R - 4a b d e + 6a b d e - 4a b d e + b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 176 + +--S 177 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^10 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 178 + +--S 179 of 764 +r0:=1/9*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^9)-1/8*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^8)+2/7*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^7)-1/3*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^6)+1/5*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^5)-_ + 1/4*b^4*B/(e^6*(d+e*x)^4) +--R +--R +--R (2) +--R 1 4 5 5 1 4 4 3 5 1 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - - B b d e )x +--R 4 5 5 4 +--R + +--R 2 3 2 2 5 2 4 8 3 4 1 4 2 3 3 +--R ((- - A a b - B a b )e + (- -- A b - -- B a b )d e - - B b d e )x +--R 3 15 15 6 +--R + +--R 6 2 2 4 3 5 2 3 3 2 2 4 +--R (- - A a b - - B a b)e + (- - A a b - - B a b )d e +--R 7 7 7 7 +--R + +--R 2 4 8 3 2 3 1 4 3 2 +--R (- -- A b - -- B a b )d e - -- B b d e +--R 35 35 14 +--R * +--R 2 +--R x +--R + +--R 1 3 1 4 5 3 2 2 1 3 4 +--R (- - A a b - - B a )e + (- -- A a b - - B a b)d e +--R 2 8 14 7 +--R + +--R 1 3 3 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- -- A b - -- B a b )d e +--R 14 28 70 35 +--R + +--R 1 4 4 +--R - -- B b d e +--R 56 +--R * +--R x +--R + +--R 1 4 5 1 3 1 4 4 1 2 2 1 3 2 3 +--R - - A a e + (- -- A a b - -- B a )d e + (- -- A a b - -- B a b)d e +--R 9 18 72 42 63 +--R + +--R 1 3 1 2 2 3 2 1 4 2 3 4 1 4 5 +--R (- --- A a b - -- B a b )d e + (- --- A b - --- B a b )d e - --- B b d +--R 126 84 630 315 504 +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 5 10 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 9 3 7 8 2 8 7 9 6 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 179 + +--S 180 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^11 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 764 +r0:=1/10*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^10)-1/9*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^9)+1/4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^8)-2/7*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^7)+1/6*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^6)-_ + 1/5*b^4*B/(e^6*(d+e*x)^5) +--R +--R +--R (2) +--R 1 4 5 5 1 4 2 3 5 1 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - - B b d e )x +--R 5 6 3 6 +--R + +--R 4 3 6 2 2 5 2 4 8 3 4 2 4 2 3 3 +--R ((- - A a b - - B a b )e + (- -- A b - -- B a b )d e - -- B b d e )x +--R 7 7 21 21 21 +--R + +--R 3 2 2 1 3 5 3 3 9 2 2 4 +--R (- - A a b - - B a b)e + (- -- A a b - -- B a b )d e +--R 4 2 14 28 +--R + +--R 1 4 1 3 2 3 1 4 3 2 +--R (- -- A b - - B a b )d e - -- B b d e +--R 28 7 28 +--R * +--R 2 +--R x +--R + +--R 4 3 1 4 5 1 2 2 1 3 4 +--R (- - A a b - - B a )e + (- - A a b - - B a b)d e +--R 9 9 6 9 +--R + +--R 1 3 1 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- --- A b - -- B a b )d e +--R 21 14 126 63 +--R + +--R 1 4 4 +--R - --- B b d e +--R 126 +--R * +--R x +--R + +--R 1 4 5 2 3 1 4 4 1 2 2 1 3 2 3 +--R - -- A a e + (- -- A a b - -- B a )d e + (- -- A a b - -- B a b)d e +--R 10 45 90 60 90 +--R + +--R 1 3 1 2 2 3 2 1 4 1 3 4 +--R (- --- A a b - --- B a b )d e + (- ---- A b - --- B a b )d e +--R 210 140 1260 315 +--R + +--R 1 4 5 +--R - ---- B b d +--R 1260 +--R / +--R 16 10 15 9 2 14 8 3 13 7 4 12 6 5 11 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 10 4 7 9 3 8 8 2 9 7 10 6 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 182 + +--S 183 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^12 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 184 + +--S 185 of 764 +r0:=1/11*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^11)-1/10*(b*d-a*e)^3*(5*b*B*d-_ + 4*A*b*e-a*B*e)/(e^6*(d+e*x)^10)+2/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-_ + 2*a*B*e)/(e^6*(d+e*x)^9)-1/4*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/_ + (e^6*(d+e*x)^8)+1/7*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^7)-_ + 1/6*b^4*B/(e^6*(d+e*x)^6) +--R +--R +--R (2) +--R 1 4 5 5 1 4 4 3 5 5 4 4 4 +--R - - B b e x + ((- - A b - - B a b )e - -- B b d e )x +--R 6 7 7 42 +--R + +--R 1 3 3 2 2 5 1 4 2 3 4 5 4 2 3 3 +--R ((- - A a b - - B a b )e + (- -- A b - - B a b )d e - -- B b d e )x +--R 2 4 14 7 84 +--R + +--R 2 2 2 4 3 5 1 3 1 2 2 4 +--R (- - A a b - - B a b)e + (- - A a b - - B a b )d e +--R 3 9 6 4 +--R + +--R 1 4 2 3 2 3 5 4 3 2 +--R (- -- A b - -- B a b )d e - --- B b d e +--R 42 21 252 +--R * +--R 2 +--R x +--R + +--R 2 3 1 4 5 2 2 2 4 3 4 +--R (- - A a b - -- B a )e + (- -- A a b - -- B a b)d e +--R 5 10 15 45 +--R + +--R 1 3 1 2 2 2 3 1 4 2 3 3 2 +--R (- -- A a b - -- B a b )d e + (- --- A b - --- B a b )d e +--R 30 20 210 105 +--R + +--R 1 4 4 +--R - --- B b d e +--R 252 +--R * +--R x +--R + +--R 1 4 5 2 3 1 4 4 +--R - -- A a e + (- -- A a b - --- B a )d e +--R 11 55 110 +--R + +--R 2 2 2 4 3 2 3 1 3 1 2 2 3 2 +--R (- --- A a b - --- B a b)d e + (- --- A a b - --- B a b )d e +--R 165 495 330 220 +--R + +--R 1 4 2 3 4 1 4 5 +--R (- ---- A b - ---- B a b )d e - ---- B b d +--R 2310 1155 2772 +--R / +--R 17 11 16 10 2 15 9 3 14 8 4 13 7 5 12 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 11 5 7 10 4 8 9 3 9 8 2 10 7 11 6 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 185 + +--S 186 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 764 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 187 + +--S 188 of 764 +r0:=2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*x/b^5-(A*b-a*B)*(b*d-a*e)^4/_ + (b^6*(a+b*x))+e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^2/b^6+_ + 1/3*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^3/b^6+1/4*B*e^4*(a+b*x)^4/b^6+_ + (b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 3 2 4 4 2 3 3 2 3 +--R (- 48A a b + 60B a b)e + (144A a b - 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 144A a b + 216B a b )d e + (48A b - 96B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 60B a )e + (144A a b - 192B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 144A a b + 216B a b )d e + (48A a b - 96B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - 5B a b )e + 16B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 8A a b + 10B a b )e + (24A b - 32B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (24A a b - 30B a b )e + (- 72A a b + 96B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (72A b - 108B a b )d e + 48B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (16A a b - 5B a b)e + (- 72A a b + 64B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 108B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 32A a b + 55B a )e + (72A a b - 128B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A a b + 108B a b )d e + (48A a b - 48B a b )d e +--R + +--R 5 4 4 +--R (- 12A b + 12B a b )d +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 188 + +--S 189 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 764 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 190 + +--S 191 of 764 +r0:=3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*x/b^4-(A*b-a*B)*(b*d-a*e)^3/(b^5*_ + (a+b*x))+1/2*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^2/b^5+1/3*B*e^3*_ + (a+b*x)^3/b^5+(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 24B a b)e + (- 36A a b + 54B a b )d e +--R + +--R 4 3 2 4 3 +--R (18A b - 36B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (18A a b - 24B a )e + (- 36A a b + 54B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A a b - 36B a b )d e + 6B a b d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - 4B a b )e + 9B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 9A a b + 12B a b )e + (18A b - 27B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 9A a b + 8B a b)e + (18A a b - 27B a b )d e + 18B a b d e)x +--R + +--R 3 4 3 2 2 3 2 +--R (9A a b - 16B a )e + (- 18A a b + 27B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A a b - 18B a b )d e + (- 6A b + 6B a b )d +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Expression(Integer) +--E 191 + +--S 192 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 764 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 193 + +--S 194 of 764 +r0:=e*(2*b*B*d+A*b*e-2*a*B*e)*x/b^3+1/2*B*e^2*x^2/b^2-(A*b-a*B)*_ + (b*d-a*e)^2/(b^4*(a+b*x))+(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((- 4A a b + 6B a b)e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 4A a b + 6B a )e + (4A a b - 8B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((2A a b - 4B a b)e + 4B a b d e)x + (- 2A a b + 2B a )e +--R + +--R 2 2 3 2 2 +--R (4A a b - 4B a b)d e + (- 2A b + 2B a b )d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 194 + +--S 195 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 764 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 764 +r0:=B*e*x/b^2-(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x))+(b*B*d+A*b*e-2*a*B*e)*_ + log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (((A b - 2B a b)e + B b d)x + (A a b - 2B a )e + B a b d)log(b x + a) +--R + +--R 2 2 2 2 +--R B b e x + B a b e x + (A a b - B a )e + (- A b + B a b)d +--R / +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 197 + +--S 198 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 764 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R B x + A +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 199 + +--S 200 of 764 +r0:=(-A*b+a*B)/(b^2*(a+b*x))+B*log(a+b*x)/b^2 +--R +--R +--R (B b x + B a)log(b x + a) - A b + B a +--R (2) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 200 + +--S 201 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 764 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (2a b e + b d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 202 + +--S 203 of 764 +r0:=(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x))+(B*d-A*e)*log(a+b*x)/(b*d-a*e)^2-_ + (B*d-A*e)*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (2) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(b x + a) + (A a b - B a )e +--R + +--R 2 +--R (- A b + B a b)d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R (a b e - 2a b d e + b d )x + a b e - 2a b d e + a b d +--R Type: Expression(Integer) +--E 203 + +--S 204 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 764 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 205 + +--S 206 of 764 +r0:=(-A*b+a*B)/((b*d-a*e)^2*(a+b*x))+(B*d-A*e)/((b*d-a*e)^2*(d+e*x))+_ + (b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^3-(b*B*d-2*A*b*e+a*B*e)*_ + log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 2A b + B a b)e + B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 2A a b + B a )e + (- 2A b + 2B a b)d e + B b d )x +--R + +--R 2 2 +--R (- 2A a b + B a )d e + B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R ((2A b - B a b)e - B b d e)x +--R + +--R 2 2 2 2 2 +--R ((2A a b - B a )e + (2A b - 2B a b)d e - B b d )x +--R + +--R 2 2 +--R (2A a b - B a )d e - B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2A a b + B a )e + 2A b d e - B b d )x - A a e + 2B a d e +--R + +--R 2 2 +--R (A b - 2B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Expression(Integer) +--E 206 + +--S 207 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 764 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 208 + +--S 209 of 764 +r0:=-b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x))+1/2*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^2)+_ + (b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x))+b*(b*B*d-3*A*b*e+2*a*B*e)*_ + log(a+b*x)/(b*d-a*e)^4-b*(b*B*d-3*A*b*e+2*a*B*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((6A b - 4B a b )e - 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (12A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((12A a b - 8B a b)d e + (6A b - 8B a b )d e - 2B b d )x +--R + +--R 2 2 2 2 3 +--R (6A a b - 4B a b)d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((- 6A b + 4B a b )e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 4B a b)e + (- 12A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((- 12A a b + 8B a b)d e + (- 6A b + 8B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 3 +--R (- 6A a b + 4B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (- 6A b + 2B a b )d e + 2B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b - 2B a )e + (6A a b - 5B a b)d e + (- 9A b + 4B a b )d e +--R + +--R 3 3 +--R 3B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - A a e + (6A a b - B a )d e + (- 3A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- 2A b + 5B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 209 + +--S 210 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 764 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 764 +r0:=e^3*(4*b*B*d+A*b*e-4*a*B*e)*x/b^5+1/2*B*e^4*x^2/b^4-1/3*(A*b-a*B)*_ + (b*d-a*e)^4/(b^6*(a+b*x)^3)-1/2*(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)/_ + (b^6*(a+b*x)^2)-2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)/(b^6*(a+b*x))+_ + 2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 24A a b + 60B a b )e + (24A b - 96B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 72A a b + 180B a b )e + (72A a b - 288B a b )d e +--R + +--R 4 2 2 +--R 108B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 72A a b + 180B a b)e + (72A a b - 288B a b )d e +--R + +--R 2 3 2 2 +--R 108B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 3 2 2 2 +--R (- 24A a b + 60B a )e + (24A a b - 96B a b)d e + 36B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((6A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((18A a b - 63B a b )e + 72B a b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 18A a b - 9B a b )e + (72A a b - 72B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 54A a b + 81B a b)e + (108A a b - 216B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 36A a b + 162B a b )d e + (- 12A b - 24B a b )d e - 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 26A a b + 47B a )e + (44A a b - 104B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 12A a b + 66B a b )d e + (- 4A a b - 8B a b )d e +--R + +--R 5 4 4 +--R (- 2A b - B a b )d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 212 + +--S 213 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 764 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 214 + +--S 215 of 764 +r0:=B*e^3*x/b^4-1/3*(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x)^3)-1/2*(b*d-a*e)^2*_ + (b*B*d+3*A*b*e-4*a*B*e)/(b^5*(a+b*x)^2)-3*e*(b*d-a*e)*(b*B*d+A*b*e-_ + 2*a*B*e)/(b^5*(a+b*x))+e^2*(3*b*B*d+A*b*e-4*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((6A b - 24B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((18A a b - 72B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((18A a b - 72B a b)e + 54B a b d e )x + (6A a b - 24B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 3 +--R 6B b e x + 18B a b e x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((18A a b - 18B a b )e + (- 18A b + 54B a b )d e - 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (27A a b - 54B a b)e + (- 18A a b + 81B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 9A b - 18B a b )d e - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (11A a b - 26B a )e + (- 6A a b + 33B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b - 6B a b )d e + (- 2A b - B a b )d +--R / +--R 8 3 7 2 2 6 3 5 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 215 + +--S 216 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 764 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 217 + +--S 218 of 764 +r0:=-1/2*B*(b*d-a*e)^2/(b^4*(a+b*x)^2)-2*B*e*(b*d-a*e)/(b^4*(a+b*x))-_ + 1/3*(A*b-a*B)*(d+e*x)^3/(b*(b*d-a*e)*(a+b*x)^3)+B*e^2*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 4 2 3 2 2 3 3 2 2 +--R (6B a b e - 6B b d e )x + (18B a b e - 18B a b d e )x +--R + +--R 3 3 2 2 2 4 3 3 2 +--R (18B a b e - 18B a b d e )x + 6B a e - 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 3 3 +--R (2A b - 2B a b )e x +--R + +--R 2 2 3 4 3 2 4 2 2 +--R (12B a b e + (6A b - 30B a b )d e + 12B b d e)x +--R + +--R 3 3 2 2 2 4 3 2 4 3 4 3 +--R (21B a b e - 39B a b d e + (6A b + 9B a b )d e + 3B b d )x + 9B a e +--R + +--R 3 2 2 2 2 4 3 3 +--R - 15B a b d e + 3B a b d e + (2A b + B a b )d +--R / +--R 7 8 3 2 6 7 2 3 5 2 6 4 4 +--R (6a b e - 6b d)x + (18a b e - 18a b d)x + (18a b e - 18a b d)x + 6a b e +--R + +--R 3 5 +--R - 6a b d +--R Type: Expression(Integer) +--E 218 + +--S 219 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 764 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 220 + +--S 221 of 764 +r0:=-1/3*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)^3)+1/2*(-b*B*d-A*b*e+2*a*B*e)/_ + (b^3*(a+b*x)^2)-B*e/(b^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 1 2 1 2 1 1 2 +--R - B b e x + ((- - A b - B a b)e - - B b d)x + (- - A a b - - B a )e +--R 2 2 6 3 +--R + +--R 1 2 1 +--R (- - A b - - B a b)d +--R 3 6 +--R / +--R 6 3 5 2 2 4 3 3 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 221 + +--S 222 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 764 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R B x + A +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 223 + +--S 224 of 764 +r0:=1/3*(-A*b+a*B)/(b^2*(a+b*x)^3)-1/2*B/(b^2*(a+b*x)^2) +--R +--R +--R 1 1 1 +--R - - B b x - - A b - - B a +--R 2 3 6 +--R (2) ------------------------------ +--R 5 3 4 2 2 3 3 2 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 224 + +--S 225 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 764 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 764 +r0:=1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3)+1/2*(-B*d+A*e)/((b*d-a*e)^2*_ + (a+b*x)^2)+e*(B*d-A*e)/((b*d-a*e)^3*(a+b*x))+e^2*(B*d-A*e)*log(a+b*x)/_ + (b*d-a*e)^4-e^2*(B*d-A*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 4 3 4 2 3 3 3 3 2 2 +--R (6A b e - 6B b d e )x + (18A a b e - 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (18A a b e - 18B a b d e )x + 6A a b e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 2 3 3 3 3 2 2 +--R (- 6A b e + 6B b d e )x + (- 18A a b e + 18B a b d e )x +--R + +--R 2 2 3 2 2 2 3 3 3 2 +--R (- 18A a b e + 18B a b d e )x - 6A a b e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 4 3 2 4 2 2 +--R (6A a b e + (- 6A b - 6B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 2 2 2 4 3 2 +--R 15A a b e + (- 18A a b - 15B a b )d e + (3A b + 18B a b )d e +--R + +--R 4 3 +--R - 3B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (11A a b - 2B a )e + (- 18A a b - 3B a b)d e + (9A a b + 6B a b )d e +--R + +--R 4 3 3 +--R (- 2A b - B a b )d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 3 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 2 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 7 4 +--R (18a b e - 72a b d e + 108a b d e - 72a b d e + 18a b d )x + 6a b e +--R + +--R 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R Type: Expression(Integer) +--E 227 + +--S 228 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 764 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 229 + +--S 230 of 764 +r0:=1/3*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^3)+1/2*(-b*B*d+2*A*b*e-a*B*e)/_ + ((b*d-a*e)^3*(a+b*x)^2)+e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(a+b*x))+_ + e^2*(B*d-A*e)/((b*d-a*e)^4*(d+e*x))+e^2*(3*b*B*d-4*A*b*e+a*B*e)*_ + log(a+b*x)/(b*d-a*e)^5-e^2*(3*b*B*d-4*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 24A b + 6B a b )e + 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 72A a b + 18B a b )e + (- 24A b + 60B a b )d e +--R + +--R 4 2 2 +--R 18B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 72A a b + 18B a b)e + (- 72A a b + 72B a b )d e +--R + +--R 3 2 2 +--R 54B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((- 24A a b + 6B a )e + (- 72A a b + 36B a b)d e + 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (- 24A a b + 6B a )d e + 18B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((24A b - 6B a b )e - 18B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((72A a b - 18B a b )e + (24A b - 60B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 3 2 2 2 +--R ((72A a b - 18B a b)e + (72A a b - 72B a b )d e - 54B a b d e )x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R ((24A a b - 6B a )e + (72A a b - 36B a b)d e - 54B a b d e )x +--R + +--R 3 4 3 3 2 2 +--R (24A a b - 6B a )d e - 18B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 24A a b + 6B a b )e + (24A b + 12B a b )d e - 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 60A a b + 15B a b)e + (48A a b + 33B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 39B a b )d e - 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 44A a b + 11B a )e + (12A a b + 30B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (36A a b - 18B a b )d e + (- 4A b - 26B a b )d e + 3B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (- 20A a b + 17B a )d e + (36A a b - 9B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 12A a b - 9B a b )d e + (2A b + B a b )d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 8 5 4 +--R (6a b e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6b d e)x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 18a b e - 84a b d e + 150a b d e - 120a b d e + 30a b d e +--R + +--R 7 5 8 6 +--R 12a b d e - 6b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 18a b e - 72a b d e + 90a b d e - 90a b d e + 72a b d e +--R + +--R 7 6 +--R - 18a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 6a e - 12a b d e - 30a b d e + 120a b d e - 150a b d e +--R + +--R 3 5 5 2 6 6 +--R 84a b d e - 18a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 3 5 6 +--R 6a d e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6a b d +--R Type: Expression(Integer) +--E 230 + +--S 231 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 of 764 +t0:=(A+B*x)*(d+e*x)^m*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R m | 2 2 2 +--R (1) (B x + A)(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 232 + +--S 233 of 764 +r0:=(A*b*e*(3+m)-B*(2*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2*(2+m)*(3+m))-(b*d-a*e)*(A*b*e*(3+m)-B*(2*b*d+_ + a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(1+m)*_ + (2+m)*(3+m)*(a+b*x))+B*(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e*(3+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (B b e m + 3B b e m + 2B b e )x +--R + +--R 2 2 2 2 +--R (A b + B a)e m + ((4A b + 4B a)e - 2B b d e)m + (3A b + 3B a)e +--R + +--R - 2B b d e +--R * +--R x +--R + +--R 2 2 2 2 +--R A a e m + (5A a e + (- A b - B a)d e)m + 6A a e + (- 3A b - 3B a)d e +--R + +--R 2 +--R 2B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 233 + +--S 234 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 764 +t0:=(A+B*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 764 +r0:=-1/42*(2*b*B*d-7*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/210*(b*d-a*e)*(2*b*B*d-7*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/7*B*(a+b*x)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 7 7 7 6 6 +--R 30B b e x + ((35A b + 35B a)e + 140B b d e )x +--R + +--R 7 6 2 5 5 +--R (42A a e + (168A b + 168B a)d e + 252B b d e )x +--R + +--R 6 2 5 3 4 4 +--R (210A a d e + (315A b + 315B a)d e + 210B b d e )x +--R + +--R 2 5 3 4 4 3 3 +--R (420A a d e + (280A b + 280B a)d e + 70B b d e )x +--R + +--R 3 4 4 3 2 4 3 5 2 +--R (420A a d e + (105A b + 105B a)d e )x + 210A a d e x + 42A a d e +--R + +--R 6 7 +--R (- 7A b - 7B a)d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 210b e x + 210a e +--R Type: Expression(Integer) +--E 236 + +--S 237 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 764 +t0:=(A+B*x)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 764 +r0:=-1/15*(b*B*d-3*A*b*e+2*a*B*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/60*(b*d-a*e)*(b*B*d-3*A*b*e+2*a*B*e)*(d+e*x)^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/6*B*(a+b*x)*(d+e*x)^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 10B b e x + ((12A b + 12B a)e + 36B b d e )x +--R + +--R 6 5 2 4 4 +--R (15A a e + (45A b + 45B a)d e + 45B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (60A a d e + (60A b + 60B a)d e + 20B b d e )x +--R + +--R 2 4 3 3 2 3 3 4 2 +--R (90A a d e + (30A b + 30B a)d e )x + 60A a d e x + 15A a d e +--R + +--R 5 6 +--R (- 3A b - 3B a)d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 239 + +--S 240 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 764 +t0:=(A+B*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 764 +r0:=-1/20*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^2)+1/60*(b*d-a*e)*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+1/5*B*(a+b*x)*(d+e*x)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 12B b e x + ((15A b + 15B a)e + 30B b d e )x +--R + +--R 5 4 2 3 3 +--R (20A a e + (40A b + 40B a)d e + 20B b d e )x +--R + +--R 4 2 3 2 2 3 3 2 +--R (60A a d e + (30A b + 30B a)d e )x + 60A a d e x + 20A a d e +--R + +--R 4 5 +--R (- 5A b - 5B a)d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 242 + +--S 243 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 764 +t0:=(A+B*x)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 | 2 2 2 +--R (1) (B e x + (A e + B d)x + A d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 764 +r0:=1/6*(2*A*b*e-B*(b*d+a*e))*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^3+1/4*(b*d-_ + a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b^3*e)+_ + 1/4*B*(a+b*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 3 3 3 2 3 2 +--R 3B b e x + ((4A b + B a b )e + 4B b d)x +--R + +--R 2 2 3 2 2 3 +--R ((2A a b - B a b)e + (6A b + 2B a b )d)x + (- 2A a b + B a )e +--R + +--R 2 2 +--R (6A a b - 2B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 12b +--R Type: Expression(Integer) +--E 245 + +--S 246 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (1) (B x + A)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 764 +r0:=1/3*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/b^2 +--R +--R +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R (2B b x + (3A b + B a b)x + 3A a b - B a )\|b x + 2a b x + a +--R (2) ----------------------------------------------------------------- +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 248 + +--S 249 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 250 + +--S 251 of 764 +r0:=-(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/2*B*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e)+(b*d-a*e)*(B*d-A*e)*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (2A a b e + (- 2A b - 2B a b)d e + 2B b d )log(e x + d) + B b e x +--R + +--R 2 2 2 2 2 +--R ((2A b + 2B a b)e - 2B b d e)x + (2A a b + B a )e - 2B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 3 3 +--R 2b e x + 2a b e +--R Type: Expression(Integer) +--E 251 + +--S 252 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 253 + +--S 254 of 764 +r0:=(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*(d+e*x))-_ + (2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 +--R (((A b + B a)e - 2B b d e)x + (A b + B a)d e - 2B b d )log(e x + d) +--R + +--R 2 2 2 2 +--R B b e x + ((- A b + B a)e + 2B b d e)x - A a e + 2B a d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 254 + +--S 255 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 256 + +--S 257 of 764 +r0:=-1/2*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^2)+B*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*_ + (d+e*x))+b*B*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 3 2 2 2 2 2 2 2 +--R (2B a b e - 2B b d e )x + (4B a b d e - 4B b d e)x + 2B a b d e +--R + +--R 2 3 +--R - 2B b d +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- A b e + B b d e )x +--R + +--R 2 3 2 2 2 2 3 2 2 +--R ((- 2A a b - 2B a )e + 6B a b d e - 2B b d e)x - A a e - B a d e +--R + +--R 2 2 3 +--R 4B a b d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 5 3 2 6 5 2 2 4 2 +--R (2a b e - 2b d e )x + (2a e + 2a b d e - 4b d e )x +--R + +--R 2 5 2 4 2 3 3 2 2 4 3 3 +--R (4a d e - 2a b d e - 2b d e )x + 2a d e - 2a b d e +--R Type: Expression(Integer) +--E 257 + +--S 258 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 259 + +--S 260 of 764 +r0:=1/3*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^3)+_ + 1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^2) +--R +--R +--R (2) +--R 2 2 2 +--R ((A b - 3B a b)e + 2B b d)x +--R + +--R 2 2 2 2 +--R ((- A a b - 3B a )e + (3A b + B a b)d)x - 2A a e + (3A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 5 4 2 2 3 3 2 4 2 3 2 3 2 2 +--R (6a e - 12a b d e + 6b d e )x + (18a d e - 36a b d e + 18b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (18a d e - 36a b d e + 18b d e)x + 6a d e - 12a b d e + 6b d +--R Type: Expression(Integer) +--E 260 + +--S 261 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 262 + +--S 263 of 764 +r0:=-1/4*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/4*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^3)-1/12*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^3) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a)e - 4B b d e)x - 3A a e +--R + +--R 2 +--R (- A b - B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 5 7 6 4 6 2 5 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 5 3 4 2 3 4 4 3 4 3 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 263 + +--S 264 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 265 + +--S 266 of 764 +r0:=-1/5*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^5)-1/15*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^4)-1/60*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^4) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 20B b e x + ((- 15A b - 15B a)e - 10B b d e)x - 12A a e +--R + +--R 2 +--R (- 3A b - 3B a)d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 6 8 7 5 7 2 6 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 6 3 5 3 3 5 4 4 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 4 5 3 5 3 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 266 + +--S 267 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 268 + +--S 269 of 764 +r0:=-1/6*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^6)-1/12*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^2*(b*d-a*e)*(d+e*x)^5)-1/60*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 15B b e x + ((- 12A b - 12B a)e - 6B b d e)x - 10A a e +--R + +--R 2 +--R (- 2A b - 2B a)d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 269 + +--S 270 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 764 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 m +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(e x + d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 764 +r0:=(A*b*e*(5+m)-B*(4*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2*(4+m)*(5+m))+B*(a+b*x)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(b*e*(5+m))+6*(b*d-a*e)^2*(A*b*e*(5+m)-_ + B*(4*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4*_ + (2+m)*(3+m)*(4+m)*(5+m))-6*(b*d-a*e)^3*(A*b*e*(5+m)-B*(4*b*d+a*e*_ + (1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(1+m)*(2+m)*_ + (3+m)*(4+m)*(5+m)*(a+b*x))-3*(b*d-a*e)*(A*b*e*(5+m)-B*(4*b*d+a*e*_ + (1+m)))*(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*_ + (3+m)*(4+m)*(5+m)) +--R +--R +--R (2) +--R 3 4 4 3 4 3 3 4 2 3 4 3 4 4 +--R (B b e m + 10B b e m + 35B b e m + 50B b e m + 24B b e )x +--R + +--R 3 2 4 4 3 2 4 3 3 3 +--R (A b + 3B a b )e m + ((11A b + 33B a b )e - 4B b d e )m +--R + +--R 3 2 4 3 3 2 +--R ((41A b + 123B a b )e - 24B b d e )m +--R + +--R 3 2 4 3 3 3 2 4 +--R ((61A b + 183B a b )e - 44B b d e )m + (30A b + 90B a b )e +--R + +--R 3 3 +--R - 24B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 +--R (3A a b + 3B a b)e m +--R + +--R 2 2 4 3 2 3 3 +--R ((36A a b + 36B a b)e + (- 3A b - 9B a b )d e )m +--R + +--R 2 2 4 3 2 3 +--R (147A a b + 147B a b)e + (- 24A b - 72B a b )d e +--R + +--R 3 2 2 +--R 12B b d e +--R * +--R 2 +--R m +--R + +--R 2 2 4 3 2 3 +--R (234A a b + 234B a b)e + (- 51A b - 153B a b )d e +--R + +--R 3 2 2 +--R 36B b d e +--R * +--R m +--R + +--R 2 2 4 3 2 3 3 2 2 +--R (120A a b + 120B a b)e + (- 30A b - 90B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 4 +--R (3A a b + B a )e m +--R + +--R 2 3 4 2 2 3 3 +--R ((39A a b + 13B a )e + (- 6A a b - 6B a b)d e )m +--R + +--R 2 3 4 2 2 3 +--R (177A a b + 59B a )e + (- 60A a b - 60B a b)d e +--R + +--R 3 2 2 2 +--R (6A b + 18B a b )d e +--R * +--R 2 +--R m +--R + +--R 2 3 4 2 2 3 +--R (321A a b + 107B a )e + (- 174A a b - 174B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (36A b + 108B a b )d e - 24B b d e +--R * +--R m +--R + +--R 2 3 4 2 2 3 +--R (180A a b + 60B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (30A b + 90B a b )d e - 24B b d e +--R * +--R x +--R + +--R 3 4 4 3 4 2 3 3 3 +--R A a e m + (14A a e + (- 3A a b - B a )d e )m +--R + +--R 3 4 2 3 3 2 2 2 2 2 +--R (71A a e + (- 36A a b - 12B a )d e + (6A a b + 6B a b)d e )m +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 154A a e + (- 141A a b - 47B a )d e + (54A a b + 54B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 18B a b )d e +--R * +--R m +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 120A a e + (- 180A a b - 60B a )d e + (120A a b + 120B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 30A b - 90B a b )d e + 24B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 272 + +--S 273 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 764 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 5 8 2 5 2 4 7 +--R B b e x + ((A b + 2B a b)e + 5B b d e )x +--R + +--R 2 5 2 4 2 2 3 6 +--R ((2A a b + B a )e + (5A b + 10B a b)d e + 10B b d e )x +--R + +--R 2 5 2 4 2 2 3 2 3 2 5 +--R (A a e + (10A a b + 5B a )d e + (10A b + 20B a b)d e + 10B b d e )x +--R + +--R 2 4 2 2 3 2 3 2 +--R 5A a d e + (20A a b + 10B a )d e + (10A b + 20B a b)d e +--R + +--R 2 4 +--R 5B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 2 3 2 2 4 2 5 3 +--R (10A a d e + (20A a b + 10B a )d e + (5A b + 10B a b)d e + B b d )x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 274 + +--S 275 of 764 +r0:=-1/45*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/10*B*(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-_ + 1/420*(b*d-a*e)^2*(2*b*B*d-5*A*b*e+3*a*B*e)*(d+e*x)^6*sqrt(a^2+2*a*b*_ + x+b^2*x^2)/(b*e^4)+1/2520*(b*d-a*e)^3*(2*b*B*d-5*A*b*e+3*a*B*e)*_ + (d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))+1/120*(b*d-a*e)*_ + (2*b*B*d-5*A*b*e+3*a*B*e)*(a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 10 10 3 2 10 3 9 9 +--R 252B b e x + ((280A b + 840B a b )e + 1400B b d e )x +--R + +--R 2 2 10 3 2 9 +--R (945A a b + 945B a b)e + (1575A b + 4725B a b )d e +--R + +--R 3 2 8 +--R 3150B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 10 2 2 9 +--R (1080A a b + 360B a )e + (5400A a b + 5400B a b)d e +--R + +--R 3 2 2 8 3 3 7 +--R (3600A b + 10800B a b )d e + 3600B b d e +--R * +--R 7 +--R x +--R + +--R 3 10 2 3 9 +--R 420A a e + (6300A a b + 2100B a )d e +--R + +--R 2 2 2 8 3 2 3 7 +--R (12600A a b + 12600B a b)d e + (4200A b + 12600B a b )d e +--R + +--R 3 4 6 +--R 2100B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 2 8 +--R 2520A a d e + (15120A a b + 5040B a )d e +--R + +--R 2 2 3 7 3 2 4 6 +--R (15120A a b + 15120B a b)d e + (2520A b + 7560B a b )d e +--R + +--R 3 5 5 +--R 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 8 2 3 3 7 +--R 6300A a d e + (18900A a b + 6300B a )d e +--R + +--R 2 2 4 6 3 2 5 5 +--R (9450A a b + 9450B a b)d e + (630A b + 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 3 7 2 3 4 6 +--R 8400A a d e + (12600A a b + 4200B a )d e +--R + +--R 2 2 5 5 +--R (2520A a b + 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 3 5 5 2 3 5 5 +--R (6300A a d e + (3780A a b + 1260B a )d e )x + 2520A a d e x +--R + +--R 3 6 4 2 3 7 3 2 2 8 2 +--R 420A a d e + (- 180A a b - 60B a )d e + (45A a b + 45B a b)d e +--R + +--R 3 2 9 3 10 +--R (- 5A b - 15B a b )d e + 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 275 + +--S 276 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 764 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 7 2 4 2 3 6 +--R B b e x + ((A b + 2B a b)e + 4B b d e )x +--R + +--R 2 4 2 3 2 2 2 5 +--R ((2A a b + B a )e + (4A b + 8B a b)d e + 6B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 3 4 +--R (A a e + (8A a b + 4B a )d e + (6A b + 12B a b)d e + 4B b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 3 +--R (4A a d e + (12A a b + 6B a )d e + (4A b + 8B a b)d e + B b d )x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 764 +r0:=-1/72*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/9*B*(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-_ + 1/504*(b*d-a*e)^2*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^4)+1/2520*(b*d-a*e)^3*(4*b*B*d-9*A*b*e+5*a*B*e)*_ + (d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))+1/168*(b*d-a*e)*_ + (4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 9 9 3 2 9 3 8 8 +--R 280B b e x + ((315A b + 945B a b )e + 1260B b d e )x +--R + +--R 2 2 9 3 2 8 +--R (1080A a b + 1080B a b)e + (1440A b + 4320B a b )d e +--R + +--R 3 2 7 +--R 2160B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 9 2 2 8 +--R (1260A a b + 420B a )e + (5040A a b + 5040B a b)d e +--R + +--R 3 2 2 7 3 3 6 +--R (2520A b + 7560B a b )d e + 1680B b d e +--R * +--R 6 +--R x +--R + +--R 3 9 2 3 8 +--R 504A a e + (6048A a b + 2016B a )d e +--R + +--R 2 2 2 7 3 2 3 6 +--R (9072A a b + 9072B a b)d e + (2016A b + 6048B a b )d e +--R + +--R 3 4 5 +--R 504B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 2 7 +--R 2520A a d e + (11340A a b + 3780B a )d e +--R + +--R 2 2 3 6 3 2 4 5 +--R (7560A a b + 7560B a b)d e + (630A b + 1890B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 2 7 2 3 3 6 +--R 5040A a d e + (10080A a b + 3360B a )d e +--R + +--R 2 2 4 5 +--R (2520A a b + 2520B a b)d e +--R * +--R 3 +--R x +--R + +--R 3 3 6 2 3 4 5 2 3 4 5 +--R (5040A a d e + (3780A a b + 1260B a )d e )x + 2520A a d e x +--R + +--R 3 5 4 2 3 6 3 2 2 7 2 +--R 504A a d e + (- 252A a b - 84B a )d e + (72A a b + 72B a b)d e +--R + +--R 3 2 8 3 9 +--R (- 9A b - 27B a b )d e + 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2520b e x + 2520a e +--R Type: Expression(Integer) +--E 278 + +--S 279 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 764 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 764 +r0:=1/14*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^2)+1/8*B*(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)+_ + 1/70*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^4)-1/280*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(a+b*x))-1/28*(b*d-a*e)*(2*A*b*e-_ + B*(b*d+a*e))*(a+b*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 8 8 3 2 8 3 7 7 +--R 35B b e x + ((40A b + 120B a b )e + 120B b d e )x +--R + +--R 2 2 8 3 2 7 3 2 6 6 +--R ((140A a b + 140B a b)e + (140A b + 420B a b )d e + 140B b d e )x +--R + +--R 2 3 8 2 2 7 +--R (168A a b + 56B a )e + (504A a b + 504B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (168A b + 504B a b )d e + 56B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 2 2 2 6 +--R 70A a e + (630A a b + 210B a )d e + (630A a b + 630B a b)d e +--R + +--R 3 2 3 5 +--R (70A b + 210B a b )d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 2 2 3 5 3 +--R (280A a d e + (840A a b + 280B a )d e + (280A a b + 280B a b)d e )x +--R + +--R 3 2 6 2 3 3 5 2 3 3 5 3 4 4 +--R (420A a d e + (420A a b + 140B a )d e )x + 280A a d e x + 70A a d e +--R + +--R 2 3 5 3 2 2 6 2 +--R (- 42A a b - 14B a )d e + (14A a b + 14B a b)d e +--R + +--R 3 2 7 3 8 +--R (- 2A b - 6B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 280b e x + 280a e +--R Type: Expression(Integer) +--E 281 + +--S 282 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 764 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 764 +r0:=-1/84*(b*d-a*e)^2*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b^4*e)-1/42*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(d+_ + e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*e)+1/7*B*(a+b*x)*(d+e*x)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-1/105*(b*d-a*e)*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4 +--R +--R +--R (2) +--R 6 2 6 6 5 2 6 5 +--R 60B b e x + ((70A b + 150B a b )e + 140B b d e)x +--R + +--R 5 2 4 2 6 5 6 2 4 +--R ((182A a b + 102B a b )e + (168A b + 364B a b )d e + 84B b d )x +--R + +--R 2 4 3 3 2 5 2 4 +--R (133A a b + 3B a b )e + (462A a b + 266B a b )d e +--R + +--R 6 5 2 +--R (105A b + 231B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 +--R (7A a b - 3B a b )e + (378A a b + 14B a b )d e +--R + +--R 5 2 4 2 +--R (315A a b + 189B a b )d +--R * +--R 2 +--R x +--R + +--R 4 2 5 2 3 3 4 2 +--R (- 7A a b + 3B a b)e + (42A a b - 14B a b )d e +--R + +--R 2 4 3 3 2 +--R (315A a b + 21B a b )d +--R * +--R x +--R + +--R 5 6 2 4 2 5 3 3 4 2 2 +--R (7A a b - 3B a )e + (- 42A a b + 14B a b)d e + (105A a b - 21B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 420b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 764 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 764 +r0:=-1/12*(b*d-a*e)*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b^3*e)+1/6*B*(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-1/15*(2*b*B*d-3*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b^3 +--R +--R +--R (2) +--R 5 5 5 4 5 4 +--R 10B b e x + ((12A b + 26B a b )e + 12B b d)x +--R + +--R 4 2 3 5 4 3 +--R ((33A a b + 19B a b )e + (15A b + 33B a b )d)x +--R + +--R 2 3 3 2 4 2 3 2 +--R ((27A a b + B a b )e + (45A a b + 27B a b )d)x +--R + +--R 3 2 4 2 3 3 2 4 5 +--R ((3A a b - B a b)e + (45A a b + 3B a b )d)x + (- 3A a b + B a )e +--R + +--R 3 2 4 +--R (15A a b - 3B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 60b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 764 +r0:=1/4*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+_ + 1/5*B*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2 +--R +--R +--R (2) +--R 4 4 4 3 3 3 2 2 2 +--R 4B b x + (5A b + 11B a b )x + (15A a b + 9B a b )x +--R + +--R 2 2 3 3 4 +--R (15A a b + B a b)x + 5A a b - B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 20b +--R Type: Expression(Integer) +--E 290 + +--S 291 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 292 + +--S 293 of 764 +r0:=-1/3*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/4*B*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e)-(b*d-a*e)^2*(B*d-A*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^4+1/2*(b*d-a*e)*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^3+(b*d-a*e)^3*(B*d-A*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 3 3 2 2 2 2 +--R 12A a b e + (- 36A a b - 12B a b)d e + (36A a b + 36B a b )d e +--R + +--R 4 3 3 4 4 +--R (- 12A b - 36B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 3B b e x + ((4A b + 12B a b )e - 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((18A a b + 18B a b )e + (- 6A b - 18B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (36A a b + 12B a b)e + (- 36A a b - 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b + 36B a b )d e - 12B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (22A a b + 3B a )e + (- 30A a b - 22B a b)d e +--R + +--R 3 2 2 2 2 3 3 +--R (12A a b + 30B a b )d e - 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 5 5 +--R 12b e x + 12a b e +--R Type: Expression(Integer) +--E 293 + +--S 294 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 295 + +--S 296 of 764 +r0:=1/3*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*(d+e*x))+_ + (b*d-a*e)*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-_ + 1/2*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-_ + (b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 3 4 2 2 3 +--R (18A a b + 6B a )e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A b + 54B a b )d e - 24B b d e +--R * +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (18A a b + 6B a )d e + (- 36A a b - 36B a b)d e +--R + +--R 3 2 3 3 4 +--R (18A b + 54B a b )d e - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 2B b e x + ((3A b + 9B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((18A a b + 18B a b)e + (- 9A b - 27B a b )d e + 12B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (9A a b + 11B a )e + (18A a b - 6B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 18A b - 30B a b )d e + 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (27A a b + 17B a )d e + (- 18A a b - 42B a b)d e +--R + +--R 2 3 +--R 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +--R 6b e x + (6a e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 296 + +--S 297 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 298 + +--S 299 of 764 +r0:=-1/2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^2)-(2*b*B*d-A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*_ + (b*d-a*e)*(d+e*x))-3*b*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*_ + x^2)/e^4+3/2*b*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*_ + x^2)/(e^3*(b*d-a*e))+3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 2 4 3 2 3 3 2 2 2 +--R ((6A a b + 6B a b)e + (- 6A b - 18B a b )d e + 12B b d e )x +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((12A a b + 12B a b)d e + (- 12A b - 36B a b )d e + 24B b d e)x +--R + +--R 2 2 2 2 3 2 3 3 4 +--R (6A a b + 6B a b)d e + (- 6A b - 18B a b )d e + 12B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R B b e x + ((2A b + 6B a b )e - 4B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 3A a b + 3B a b)e + (9A b + 15B a b )d e - 18B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 6A a b - 2B a )e + (6A a b + 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (6A b - 6B a b )d e - 12B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 3 +--R - A a e + (- 3A a b - B a )d e + (6A a b + 12B a b)d e - 12B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 299 + +--S 300 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 301 + +--S 302 of 764 +r0:=-1/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^3)-1/6*(4*b*B*d-A*b*e-3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^2)+b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(b*d-a*e))-1/2*b*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x))-b^2*(4*b*B*d-A*b*e-_ + 3*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 2 4 3 3 3 +--R ((6A b + 18B a b )e - 24B b d e )x +--R + +--R 3 2 3 3 2 2 2 +--R ((18A b + 54B a b )d e - 72B b d e )x +--R + +--R 3 2 2 2 3 3 3 2 3 +--R ((18A b + 54B a b )d e - 72B b d e)x + (6A b + 18B a b )d e +--R + +--R 3 4 +--R - 24B b d +--R * +--R log(e x + d) +--R + +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((- 11A b - 9B a b )e + 44B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 18A a b - 18B a b)e + (- 15A b + 27B a b )d e + 60B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 9A a b - 3B a )e + (- 18A a b - 18B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 6A b + 54B a b )d e + 24B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (- 3A a b - B a )d e + (- 6A a b - 6B a b)d e +--R + +--R 2 3 +--R 24B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 6 3 5 3 5 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 302 + +--S 303 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 304 + +--S 305 of 764 +r0:=-1/4*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/3*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^3)-_ + 1/2*b*B*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^2)+b^2*B*_ + (b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))+b^3*B*_ + log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 5 4 4 4 3 4 4 2 3 3 +--R (12B a b e - 12B b d e )x + (48B a b d e - 48B b d e )x +--R + +--R 3 2 3 4 3 2 2 3 3 2 4 4 +--R (72B a b d e - 72B b d e )x + (48B a b d e - 48B b d e)x +--R + +--R 3 4 4 5 +--R 12B a b d e - 12B b d +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 4 +--R ((- 3A b - 10B a b )e + 13B b d e )x +--R + +--R 3 2 2 5 3 4 4 2 3 3 +--R ((- 12A a b - 36B a b )e + 44B a b d e + 4B b d e )x +--R + +--R 2 2 3 5 2 2 4 3 2 3 +--R (- 18A a b - 18B a b)e - 36B a b d e + 102B a b d e +--R + +--R 4 3 2 +--R - 30B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 3 4 2 2 2 3 3 3 2 +--R (- 12A a b - 4B a )e - 8B a b d e - 24B a b d e + 84B a b d e +--R + +--R 4 4 +--R - 36B b d e +--R * +--R x +--R + +--R 4 5 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R - 3A a e - B a d e - 2B a b d e - 6B a b d e + 24B a b d e - 12B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 2 9 5 2 10 9 2 2 8 4 +--R (12a b e - 12b d e )x + (12a e + 36a b d e - 48b d e )x +--R + +--R 2 9 2 8 2 3 7 3 +--R (48a d e + 24a b d e - 72b d e )x +--R + +--R 2 2 8 3 7 2 4 6 2 +--R (72a d e - 24a b d e - 48b d e )x +--R + +--R 2 3 7 4 6 2 5 5 2 4 6 5 5 +--R (48a d e - 36a b d e - 12b d e )x + 12a d e - 12a b d e +--R Type: Expression(Integer) +--E 305 + +--S 306 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 307 + +--S 308 of 764 +r0:=1/4*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*_ + (d+e*x)^4)+1/5*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*_ + (d+e*x)^5) +--R +--R +--R (2) +--R 4 3 4 4 +--R ((A b - 5B a b )e + 4B b d)x +--R + +--R 3 2 2 4 3 3 +--R ((- A a b - 15B a b )e + (5A b + 11B a b )d)x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 9A a b - 15B a b)e + (15A a b + 9B a b )d)x +--R + +--R 3 4 2 2 3 4 3 4 +--R ((- 11A a b - 5B a )e + (15A a b + B a b)d)x - 4A a e + (5A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 7 6 2 2 5 5 +--R (20a e - 40a b d e + 20b d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (100a d e - 200a b d e + 100b d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (200a d e - 400a b d e + 200b d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (100a d e - 200a b d e + 100b d e)x + 20a d e - 40a b d e + 20b d +--R Type: Expression(Integer) +--E 308 + +--S 309 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 310 + +--S 311 of 764 +r0:=-1/6*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^6)+1/12*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^5)+1/60*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 5 4 2 5 5 +--R ((- A b + 3B a b )e - 2B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 4 +--R ((A a b - 3B a b )e + (- 6A b + 20B a b )d e - 12B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (- A a b - 27B a b )e + (6A a b + 70B a b )d e +--R + +--R 5 4 2 +--R (- 15A b - 33B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 19A a b - 33B a b)e + (54A a b + 70B a b )d e +--R + +--R 4 2 3 2 +--R (- 45A a b - 27B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 26A a b - 12B a )e + (66A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 +--R (- 45A a b - 3B a b )d +--R * +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R - 10A a e + (24A a b - 2B a )d e + (- 15A a b + 3B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 9 2 8 2 2 7 3 3 6 6 +--R (60a e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 8 2 2 7 2 3 6 3 4 5 5 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e )x +--R + +--R 3 2 7 2 3 6 2 4 5 3 5 4 4 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (1200a d e - 3600a b d e + 3600a b d e - 1200b d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (900a d e - 2700a b d e + 2700a b d e - 900b d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (360a d e - 1080a b d e + 1080a b d e - 360b d e)x + 60a d e +--R + +--R 2 7 2 2 8 3 9 +--R - 180a b d e + 180a b d e - 60b d +--R Type: Expression(Integer) +--E 311 + +--S 312 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 313 + +--S 314 of 764 +r0:=-1/7*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^7)+1/42*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^6)+1/84*b*(4*b*B*d+3*A*b*e-_ + 7*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)^3*_ + (d+e*x)^5)+1/420*b*(4*b*B*d+3*A*b*e-7*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 6 5 3 6 2 6 +--R ((3A b - 7B a b )e + 4B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 5 +--R ((- 3A a b + 7B a b )e + (21A b - 53B a b )d e + 28B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (3A a b - 7B a b )e + (- 21A a b + 53B a b )d e +--R + +--R 6 5 2 6 3 +--R (63A b - 175B a b )d e + 84B b d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (- 3A a b - 133B a b )e + (21A a b + 507B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 63A a b - 665B a b )d e + (105A b + 231B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 102A a b - 182B a b)e + (399A a b + 613B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 567A a b - 665B a b )d e + (315A a b + 189B a b )d +--R * +--R 2 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 150A a b - 70B a )e + (546A a b + 206B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 693A a b - 175B a b )d e + (315A a b + 21B a b )d +--R * +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R - 60A a e + (210A a b - 10B a )d e + (- 252A a b + 28B a b)d e +--R + +--R 3 3 4 2 3 +--R (105A a b - 21B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 11 3 10 2 2 2 9 3 3 8 4 4 7 7 +--R (420a e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e )x +--R + +--R 4 10 3 2 9 2 2 3 8 3 4 7 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 5 6 +--R 2940b d e +--R * +--R 6 +--R x +--R + +--R 4 2 9 3 3 8 2 2 4 7 3 5 6 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 6 5 +--R 8820b d e +--R * +--R 5 +--R x +--R + +--R 4 3 8 3 4 7 2 2 5 6 3 6 5 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 7 4 +--R 14700b d e +--R * +--R 4 +--R x +--R + +--R 4 4 7 3 5 6 2 2 6 5 3 7 4 +--R 14700a d e - 58800a b d e + 88200a b d e - 58800a b d e +--R + +--R 4 8 3 +--R 14700b d e +--R * +--R 3 +--R x +--R + +--R 4 5 6 3 6 5 2 2 7 4 3 8 3 +--R 8820a d e - 35280a b d e + 52920a b d e - 35280a b d e +--R + +--R 4 9 2 +--R 8820b d e +--R * +--R 2 +--R x +--R + +--R 4 6 5 3 7 4 2 2 8 3 3 9 2 +--R 2940a d e - 11760a b d e + 17640a b d e - 11760a b d e +--R + +--R 4 10 +--R 2940b d e +--R * +--R x +--R + +--R 4 7 4 3 8 3 2 2 9 2 3 10 4 11 +--R 420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R Type: Expression(Integer) +--E 314 + +--S 315 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 316 + +--S 317 of 764 +r0:=-1/8*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^8)-1/14*(b*B*d+A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^7)-1/28*b*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^6)-1/56*b^2*_ + (b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(b*d-a*e)*_ + (d+e*x)^5)-1/280*b^2*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 70B b e x + ((- 56A b - 168B a b )e - 56B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 140A a b - 140B a b)e + (- 28A b - 84B a b )d e - 28B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 120A a b - 40B a )e + (- 40A a b - 40B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 8A b - 24B a b )d e - 8B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 35A a e + (- 15A a b - 5B a )d e + (- 5A a b - 5B a b)d e +--R + +--R 3 2 3 3 4 +--R (- A b - 3B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 9 13 12 8 12 2 11 7 +--R 280b e x + (280a e + 2240b d e )x + (2240a d e + 7840b d e )x +--R + +--R 2 11 3 10 6 3 10 4 9 5 +--R (7840a d e + 15680b d e )x + (15680a d e + 19600b d e )x +--R + +--R 4 9 5 8 4 5 8 6 7 3 +--R (19600a d e + 15680b d e )x + (15680a d e + 7840b d e )x +--R + +--R 6 7 7 6 2 7 6 8 5 8 5 +--R (7840a d e + 2240b d e )x + (2240a d e + 280b d e )x + 280a d e +--R Type: Expression(Integer) +--E 317 + +--S 318 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 319 + +--S 320 of 764 +r0:=-1/9*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^9)-1/72*(4*b*B*d+5*A*b*e-9*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^8)-1/168*b*(4*b*B*d+5*A*b*e-_ + 9*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^7)-_ + 1/420*b^2*(4*b*B*d+5*A*b*e-9*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^6)-1/2520*b^2*(4*b*B*d+5*A*b*e-9*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 504B b e x + ((- 420A b - 1260B a b )e - 336B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 1080A a b - 1080B a b)e + (- 180A b - 540B a b )d e +--R + +--R 3 2 2 +--R - 144B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 945A a b - 315B a )e + (- 270A a b - 270B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 45A b - 135B a b )d e - 36B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 280A a e + (- 105A a b - 35B a )d e + (- 30A a b - 30B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 5A b - 15B a b )d e - 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 10 14 13 9 +--R 2520b e x + (2520a e + 22680b d e )x +--R + +--R 13 2 12 8 2 12 3 11 7 +--R (22680a d e + 90720b d e )x + (90720a d e + 211680b d e )x +--R + +--R 3 11 4 10 6 4 10 5 9 5 +--R (211680a d e + 317520b d e )x + (317520a d e + 317520b d e )x +--R + +--R 5 9 6 8 4 6 8 7 7 3 +--R (317520a d e + 211680b d e )x + (211680a d e + 90720b d e )x +--R + +--R 7 7 8 6 2 8 6 9 5 9 5 +--R (90720a d e + 22680b d e )x + (22680a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 320 + +--S 321 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 322 + +--S 323 of 764 +r0:=-1/10*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^10)-1/45*(2*b*B*d+3*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^9)-1/120*b*(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^8)-_ + 1/360*b^2*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^7)-1/2520*b^2*(2*b*B*d+3*A*b*e-5*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 420B b e x + ((- 360A b - 1080B a b )e - 240B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 945A a b - 945B a b)e + (- 135A b - 405B a b )d e +--R + +--R 3 2 2 +--R - 90B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 840A a b - 280B a )e + (- 210A a b - 210B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 30A b - 90B a b )d e - 20B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 252A a e + (- 84A a b - 28B a )d e + (- 21A a b - 21B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 3A b - 9B a b )d e - 2B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 15 11 15 14 10 +--R 2520b e x + (2520a e + 25200b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (25200a d e + 113400b d e )x + (113400a d e + 302400b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (302400a d e + 529200b d e )x + (529200a d e + 635040b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (635040a d e + 529200b d e )x + (529200a d e + 302400b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (302400a d e + 113400b d e )x + (113400a d e + 25200b d e )x +--R + +--R 9 6 10 5 10 5 +--R (25200a d e + 2520b d e )x + 2520a d e +--R Type: Expression(Integer) +--E 323 + +--S 324 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 325 + +--S 326 of 764 +r0:=-1/11*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^11)-1/110*(4*b*B*d+7*A*b*e-11*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^10)-1/330*b*(4*b*B*d+7*A*b*e-_ + 11*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*(d+e*x)^9)-_ + 1/1155*b^2*(4*b*B*d+7*A*b*e-11*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^4*(b*d-a*e)*(d+e*x)^8)-1/9240*b^2*(4*b*B*d+7*A*b*e-11*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R - 1320B b e x + ((- 1155A b - 3465B a b )e - 660B b d e )x +--R + +--R 2 2 4 3 2 3 +--R (- 3080A a b - 3080B a b)e + (- 385A b - 1155B a b )d e +--R + +--R 3 2 2 +--R - 220B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 2 3 +--R (- 2772A a b - 924B a )e + (- 616A a b - 616B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 77A b - 231B a b )d e - 44B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 840A a e + (- 252A a b - 84B a )d e + (- 56A a b - 56B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 7A b - 21B a b )d e - 4B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 16 12 16 15 11 +--R 9240b e x + (9240a e + 101640b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (101640a d e + 508200b d e )x + (508200a d e + 1524600b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (1524600a d e + 3049200b d e )x + (3049200a d e + 4268880b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (4268880a d e + 4268880b d e )x + (4268880a d e + 3049200b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (3049200a d e + 1524600b d e )x + (1524600a d e + 508200b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (508200a d e + 101640b d e )x + (101640a d e + 9240b d e )x +--R + +--R 11 5 +--R 9240a d e +--R Type: Expression(Integer) +--E 326 + +--S 327 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 764 +t0:=(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R m | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 764 +r0:=20*(b*d-a*e)^2*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4*(4+m)*(5+m)*(6+m)*(7+m))-_ + 5*(b*d-a*e)*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(a+b*x)*(d+e*x)^(1+m)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3*(5+m)*(6+m)*(7+m))+(A*b*e*(7+m)-_ + B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (b*e^2*(6+m)*(7+m))+B*(a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e*(7+m))+120*(b*d-a*e)^4*(A*b*e*(7+m)-B*(6*b*d+_ + a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6*_ + (2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m))-120*(b*d-a*e)^5*(A*b*e*(7+m)-_ + B*(6*b*d+a*e*(1+m)))*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^7*(1+m)*(2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)*(a+b*x))-60*(b*d-_ + a*e)^3*(A*b*e*(7+m)-B*(6*b*d+a*e*(1+m)))*(a+b*x)*(d+e*x)^(1+m)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)) +--R +--R +--R (2) +--R 5 6 6 5 6 5 5 6 4 5 6 3 5 6 2 +--R B b e m + 21B b e m + 175B b e m + 735B b e m + 1624B b e m +--R + +--R 5 6 5 6 +--R 1764B b e m + 720B b e +--R * +--R 6 +--R x +--R + +--R 5 4 6 6 5 4 6 5 5 5 +--R (A b + 5B a b )e m + ((22A b + 110B a b )e - 6B b d e )m +--R + +--R 5 4 6 5 5 4 +--R ((190A b + 950B a b )e - 90B b d e )m +--R + +--R 5 4 6 5 5 3 +--R ((820A b + 4100B a b )e - 510B b d e )m +--R + +--R 5 4 6 5 5 2 +--R ((1849A b + 9245B a b )e - 1350B b d e )m +--R + +--R 5 4 6 5 5 +--R ((2038A b + 10190B a b )e - 1644B b d e )m +--R + +--R 5 4 6 5 5 +--R (840A b + 4200B a b )e - 720B b d e +--R * +--R 5 +--R x +--R + +--R 4 2 3 6 6 +--R (5A a b + 10B a b )e m +--R + +--R 4 2 3 6 5 4 5 5 +--R ((115A a b + 230B a b )e + (- 5A b - 25B a b )d e )m +--R + +--R 4 2 3 6 5 4 5 +--R (1035A a b + 2070B a b )e + (- 85A b - 425B a b )d e +--R + +--R 5 2 4 +--R 30B b d e +--R * +--R 4 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (4625A a b + 9250B a b )e + (- 525A b - 2625B a b )d e +--R + +--R 5 2 4 +--R 300B b d e +--R * +--R 3 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (10720A a b + 21440B a b )e + (- 1475A b - 7375B a b )d e +--R + +--R 5 2 4 +--R 1050B b d e +--R * +--R 2 +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (12060A a b + 24120B a b )e + (- 1870A b - 9350B a b )d e +--R + +--R 5 2 4 +--R 1500B b d e +--R * +--R m +--R + +--R 4 2 3 6 5 4 5 +--R (5040A a b + 10080B a b )e + (- 840A b - 4200B a b )d e +--R + +--R 5 2 4 +--R 720B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 6 +--R (10A a b + 10B a b )e m +--R + +--R 2 3 3 2 6 4 2 3 5 5 +--R ((240A a b + 240B a b )e + (- 20A a b - 40B a b )d e )m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2260A a b + 2260B a b )e + (- 380A a b - 760B a b )d e +--R + +--R 5 4 2 4 +--R (20A b + 100B a b )d e +--R * +--R 4 +--R m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (10560A a b + 10560B a b )e + (- 2620A a b - 5240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (260A b + 1300B a b )d e - 120B b d e +--R * +--R 3 +--R m +--R + +--R 2 3 3 2 6 +--R (25450A a b + 25450B a b )e +--R + +--R 4 2 3 5 5 4 2 4 +--R (- 8020A a b - 16040B a b )d e + (1060A b + 5300B a b )d e +--R + +--R 5 3 3 +--R - 720B b d e +--R * +--R 2 +--R m +--R + +--R 2 3 3 2 6 +--R (29520A a b + 29520B a b )e +--R + +--R 4 2 3 5 5 4 2 4 +--R (- 10800A a b - 21600B a b )d e + (1660A b + 8300B a b )d e +--R + +--R 5 3 3 +--R - 1320B b d e +--R * +--R m +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (12600A a b + 12600B a b )e + (- 5040A a b - 10080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (840A b + 4200B a b )d e - 720B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 6 +--R (10A a b + 5B a b)e m +--R + +--R 3 2 4 6 2 3 3 2 5 5 +--R ((250A a b + 125B a b)e + (- 30A a b - 30B a b )d e )m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (2470A a b + 1235B a b)e + (- 630A a b - 630B a b )d e +--R + +--R 4 2 3 2 4 +--R (60A a b + 120B a b )d e +--R * +--R 4 +--R m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (12190A a b + 6095B a b)e + (- 4890A a b - 4890B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (960A a b + 1920B a b )d e + (- 60A b - 300B a b )d e +--R * +--R 3 +--R m +--R + +--R 3 2 4 6 +--R (31120A a b + 15560B a b)e +--R + +--R 2 3 3 2 5 +--R (- 17010A a b - 17010B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (4980A a b + 9960B a b )d e + (- 600A b - 3000B a b )d e +--R + +--R 5 4 2 +--R 360B b d e +--R * +--R 2 +--R m +--R + +--R 3 2 4 6 +--R (37960A a b + 18980B a b)e +--R + +--R 2 3 3 2 5 +--R (- 25320A a b - 25320B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (9120A a b + 18240B a b )d e + (- 1380A b - 6900B a b )d e +--R + +--R 5 4 2 +--R 1080B b d e +--R * +--R m +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (16800A a b + 8400B a b)e + (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (5040A a b + 10080B a b )d e + (- 840A b - 4200B a b )d e +--R + +--R 5 4 2 +--R 720B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 6 +--R (5A a b + B a )e m +--R + +--R 4 5 6 3 2 4 5 5 +--R ((130A a b + 26B a )e + (- 20A a b - 10B a b)d e )m +--R + +--R 4 5 6 3 2 4 5 +--R (1350A a b + 270B a )e + (- 460A a b - 230B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (60A a b + 60B a b )d e +--R * +--R 4 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (7100A a b + 1420B a )e + (- 4020A a b - 2010B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1140A a b + 1140B a b )d e + (- 120A a b - 240B a b )d e +--R * +--R 3 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (19645A a b + 3929B a )e + (- 16340A a b - 8170B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (7500A a b + 7500B a b )d e + (- 1680A a b - 3360B a b )d e +--R + +--R 5 4 4 2 +--R (120A b + 600B a b )d e +--R * +--R 2 +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (26370A a b + 5274B a )e + (- 29560A a b - 14780B a b)d e +--R + +--R 2 3 3 2 2 4 +--R (19020A a b + 19020B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (- 6600A a b - 13200B a b )d e + (960A b + 4800B a b )d e +--R + +--R 5 5 +--R - 720B b d e +--R * +--R m +--R + +--R 4 5 6 3 2 4 5 +--R (12600A a b + 2520B a )e + (- 16800A a b - 8400B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (12600A a b + 12600B a b )d e + (- 5040A a b - 10080B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (840A b + 4200B a b )d e - 720B b d e +--R * +--R x +--R + +--R 5 6 6 5 6 4 5 5 5 +--R A a e m + (27A a e + (- 5A a b - B a )d e )m +--R + +--R 5 6 4 5 5 3 2 4 2 4 4 +--R (295A a e + (- 125A a b - 25B a )d e + (20A a b + 10B a b)d e )m +--R + +--R 5 6 4 5 5 +--R 1665A a e + (- 1225A a b - 245B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (440A a b + 220B a b)d e + (- 60A a b - 60B a b )d e +--R * +--R 3 +--R m +--R + +--R 5 6 4 5 5 +--R 5104A a e + (- 5875A a b - 1175B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (3580A a b + 1790B a b)d e + (- 1080A a b - 1080B a b )d e +--R + +--R 4 2 3 4 2 +--R (120A a b + 240B a b )d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 5 5 +--R 8028A a e + (- 13770A a b - 2754B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (12760A a b + 6380B a b)d e + (- 6420A a b - 6420B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (1560A a b + 3120B a b )d e + (- 120A b - 600B a b )d e +--R * +--R m +--R + +--R 5 6 4 5 5 +--R 5040A a e + (- 12600A a b - 2520B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (16800A a b + 8400B a b)d e + (- 12600A a b - 12600B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (5040A a b + 10080B a b )d e + (- 840A b - 4200B a b )d e + 720B b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m + 13132b e m +--R + +--R 7 7 +--R 13068b e m + 5040b e +--R * +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a e m + 28a e m + 322a e m + 1960a e m + 6769a e m + 13132a e m +--R + +--R 7 7 +--R 13068a e m + 5040a e +--R Type: Expression(Integer) +--E 329 + +--S 330 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 764 +t0:=(A+B*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 11 4 3 6 4 5 10 +--R B b e x + ((A b + 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 6 4 3 5 4 2 4 9 +--R ((4A a b + 6B a b )e + (6A b + 24B a b )d e + 15B b d e )x +--R + +--R 2 2 3 6 3 2 2 5 +--R (6A a b + 4B a b)e + (24A a b + 36B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (15A b + 60B a b )d e + 20B b d e +--R * +--R 8 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (4A a b + B a )e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 4 4 2 +--R (60A a b + 90B a b )d e + (20A b + 80B a b )d e + 15B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 3 4 5 2 2 3 2 4 +--R A a e + (24A a b + 6B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 3 3 4 3 4 2 4 5 +--R (80A a b + 120B a b )d e + (15A b + 60B a b )d e + 6B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 2 4 2 2 3 3 3 +--R 6A a d e + (60A a b + 15B a )d e + (120A a b + 80B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (60A a b + 90B a b )d e + (6A b + 24B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 2 4 3 4 3 3 2 2 3 4 2 +--R 15A a d e + (80A a b + 20B a )d e + (90A a b + 60B a b)d e +--R + +--R 3 2 2 5 4 3 6 +--R (24A a b + 36B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 3 4 4 2 2 2 3 5 +--R 20A a d e + (60A a b + 15B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 6 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 4 2 3 4 5 2 2 3 6 2 +--R (15A a d e + (24A a b + 6B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 5 3 4 6 4 6 +--R (6A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 764 +r0:=-1/858*(b*d-a*e)^2*(6*b*B*d-13*A*b*e+7*a*B*e)*(d+e*x)^7*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)+5/1716*(b*d-a*e)*(6*b*B*d-13*A*b*e+7*a*B*e)*_ + (a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-1/156*(6*b*B*d-_ + 13*A*b*e+7*a*B*e)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+_ + 1/13*B*(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 1/10296*(b*d-a*e)^4*(6*b*B*d-13*A*b*e+7*a*B*e)*(d+e*x)^7*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(b*e^6)+1/72072*(b*d-a*e)^5*(6*b*B*d-13*A*b*e+_ + 7*a*B*e)*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+_ + 1/2574*(b*d-a*e)^3*(6*b*B*d-13*A*b*e+7*a*B*e)*(a+b*x)*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 13 13 5 4 13 5 12 12 +--R 5544B b e x + ((6006A b + 30030B a b )e + 36036B b d e )x +--R + +--R 4 2 3 13 5 4 12 +--R (32760A a b + 65520B a b )e + (39312A b + 196560B a b )d e +--R + +--R 5 2 11 +--R 98280B b d e +--R * +--R 11 +--R x +--R + +--R 2 3 3 2 13 4 2 3 12 +--R (72072A a b + 72072B a b )e + (216216A a b + 432432B a b )d e +--R + +--R 5 4 2 11 5 3 10 +--R (108108A b + 540540B a b )d e + 144144B b d e +--R * +--R 10 +--R x +--R + +--R 3 2 4 13 2 3 3 2 12 +--R (80080A a b + 40040B a b)e + (480480A a b + 480480B a b )d e +--R + +--R 4 2 3 2 11 +--R (600600A a b + 1201200B a b )d e +--R + +--R 5 4 3 10 5 4 9 +--R (160160A b + 800800B a b )d e + 120120B b d e +--R * +--R 9 +--R x +--R + +--R 4 5 13 3 2 4 12 +--R (45045A a b + 9009B a )e + (540540A a b + 270270B a b)d e +--R + +--R 2 3 3 2 2 11 +--R (1351350A a b + 1351350B a b )d e +--R + +--R 4 2 3 3 10 +--R (900900A a b + 1801800B a b )d e +--R + +--R 5 4 4 9 5 5 8 +--R (135135A b + 675675B a b )d e + 54054B b d e +--R * +--R 8 +--R x +--R + +--R 5 13 4 5 12 +--R 10296A a e + (308880A a b + 61776B a )d e +--R + +--R 3 2 4 2 11 +--R (1544400A a b + 772200B a b)d e +--R + +--R 2 3 3 2 3 10 +--R (2059200A a b + 2059200B a b )d e +--R + +--R 4 2 3 4 9 5 4 5 8 +--R (772200A a b + 1544400B a b )d e + (61776A b + 308880B a b )d e +--R + +--R 5 6 7 +--R 10296B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 2 11 +--R 72072A a d e + (900900A a b + 180180B a )d e +--R + +--R 3 2 4 3 10 +--R (2402400A a b + 1201200B a b)d e +--R + +--R 2 3 3 2 4 9 +--R (1801800A a b + 1801800B a b )d e +--R + +--R 4 2 3 5 8 5 4 6 7 +--R (360360A a b + 720720B a b )d e + (12012A b + 60060B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 2 11 4 5 3 10 +--R 216216A a d e + (1441440A a b + 288288B a )d e +--R + +--R 3 2 4 4 9 +--R (2162160A a b + 1081080B a b)d e +--R + +--R 2 3 3 2 5 8 4 2 3 6 7 +--R (864864A a b + 864864B a b )d e + (72072A a b + 144144B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 3 10 4 5 4 9 +--R 360360A a d e + (1351350A a b + 270270B a )d e +--R + +--R 3 2 4 5 8 2 3 3 2 6 7 +--R (1081080A a b + 540540B a b)d e + (180180A a b + 180180B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 4 9 4 5 5 8 +--R 360360A a d e + (720720A a b + 144144B a )d e +--R + +--R 3 2 4 6 7 +--R (240240A a b + 120120B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 5 8 4 5 6 7 2 5 6 7 +--R (216216A a d e + (180180A a b + 36036B a )d e )x + 72072A a d e x +--R + +--R 5 7 6 4 5 8 5 +--R 10296A a d e + (- 6435A a b - 1287B a )d e +--R + +--R 3 2 4 9 4 2 3 3 2 10 3 +--R (2860A a b + 1430B a b)d e + (- 858A a b - 858B a b )d e +--R + +--R 4 2 3 11 2 5 4 12 5 13 +--R (156A a b + 312B a b )d e + (- 13A b - 65B a b )d e + 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 72072b e x + 72072a e +--R Type: Expression(Integer) +--E 332 + +--S 333 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 764 +t0:=(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 10 4 3 5 4 4 9 +--R B b e x + ((A b + 4B a b )e + 5B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 8 +--R ((4A a b + 6B a b )e + (5A b + 20B a b )d e + 10B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (6A a b + 4B a b)e + (20A a b + 30B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (10A b + 40B a b )d e + 10B b d e +--R * +--R 7 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b + B a )e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 4 4 +--R (40A a b + 60B a b )d e + (10A b + 40B a b )d e + 5B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R A a e + (20A a b + 5B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (40A a b + 60B a b )d e + (5A b + 20B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 2 3 2 2 3 3 2 +--R 5A a d e + (40A a b + 10B a )d e + (60A a b + 40B a b)d e +--R + +--R 3 2 2 4 4 3 5 +--R (20A a b + 30B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 3 2 2 2 3 4 +--R 10A a d e + (40A a b + 10B a )d e + (30A a b + 20B a b)d e +--R + +--R 3 2 2 5 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 3 2 3 4 4 2 2 3 5 2 +--R (10A a d e + (20A a b + 5B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 4 3 4 5 4 5 +--R (5A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 764 +r0:=1/99*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^6*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)-1/44*(b*d-a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)+1/22*(2*A*b*e-B*(b*d+_ + a*e))*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+1/12*B*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)+1/924*(b*d-a*e)^4*(2*A*b*e-_ + B*(b*d+a*e))*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)-_ + 1/5544*(b*d-a*e)^5*(2*A*b*e-B*(b*d+a*e))*(d+e*x)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^7*(a+b*x))-1/264*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*_ + (a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 12 12 5 4 12 5 11 11 +--R 462B b e x + ((504A b + 2520B a b )e + 2520B b d e )x +--R + +--R 4 2 3 12 5 4 11 +--R (2772A a b + 5544B a b )e + (2772A b + 13860B a b )d e +--R + +--R 5 2 10 +--R 5544B b d e +--R * +--R 10 +--R x +--R + +--R 2 3 3 2 12 4 2 3 11 +--R (6160A a b + 6160B a b )e + (15400A a b + 30800B a b )d e +--R + +--R 5 4 2 10 5 3 9 +--R (6160A b + 30800B a b )d e + 6160B b d e +--R * +--R 9 +--R x +--R + +--R 3 2 4 12 2 3 3 2 11 +--R (6930A a b + 3465B a b)e + (34650A a b + 34650B a b )d e +--R + +--R 4 2 3 2 10 5 4 3 9 +--R (34650A a b + 69300B a b )d e + (6930A b + 34650B a b )d e +--R + +--R 5 4 8 +--R 3465B b d e +--R * +--R 8 +--R x +--R + +--R 4 5 12 3 2 4 11 +--R (3960A a b + 792B a )e + (39600A a b + 19800B a b)d e +--R + +--R 2 3 3 2 2 10 4 2 3 3 9 +--R (79200A a b + 79200B a b )d e + (39600A a b + 79200B a b )d e +--R + +--R 5 4 4 8 5 5 7 +--R (3960A b + 19800B a b )d e + 792B b d e +--R * +--R 7 +--R x +--R + +--R 5 12 4 5 11 +--R 924A a e + (23100A a b + 4620B a )d e +--R + +--R 3 2 4 2 10 2 3 3 2 3 9 +--R (92400A a b + 46200B a b)d e + (92400A a b + 92400B a b )d e +--R + +--R 4 2 3 4 8 5 4 5 7 +--R (23100A a b + 46200B a b )d e + (924A b + 4620B a b )d e +--R * +--R 6 +--R x +--R + +--R 5 11 4 5 2 10 +--R 5544A a d e + (55440A a b + 11088B a )d e +--R + +--R 3 2 4 3 9 2 3 3 2 4 8 +--R (110880A a b + 55440B a b)d e + (55440A a b + 55440B a b )d e +--R + +--R 4 2 3 5 7 +--R (5544A a b + 11088B a b )d e +--R * +--R 5 +--R x +--R + +--R 5 2 10 4 5 3 9 +--R 13860A a d e + (69300A a b + 13860B a )d e +--R + +--R 3 2 4 4 8 2 3 3 2 5 7 +--R (69300A a b + 34650B a b)d e + (13860A a b + 13860B a b )d e +--R * +--R 4 +--R x +--R + +--R 5 3 9 4 5 4 8 +--R 18480A a d e + (46200A a b + 9240B a )d e +--R + +--R 3 2 4 5 7 +--R (18480A a b + 9240B a b)d e +--R * +--R 3 +--R x +--R + +--R 5 4 8 4 5 5 7 2 5 5 7 +--R (13860A a d e + (13860A a b + 2772B a )d e )x + 5544A a d e x +--R + +--R 5 6 6 4 5 7 5 3 2 4 8 4 +--R 924A a d e + (- 660A a b - 132B a )d e + (330A a b + 165B a b)d e +--R + +--R 2 3 3 2 9 3 4 2 3 10 2 +--R (- 110A a b - 110B a b )d e + (22A a b + 44B a b )d e +--R + +--R 5 4 11 5 12 +--R (- 2A b - 10B a b )d e + B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 5544b e x + 5544a e +--R Type: Expression(Integer) +--E 335 + +--S 336 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 336 + +)clear all + +--S 337 of 764 +t0:=(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 4 9 4 3 4 4 3 8 +--R B b e x + ((A b + 4B a b )e + 4B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 7 +--R ((4A a b + 6B a b )e + (4A b + 16B a b )d e + 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (6A a b + 4B a b)e + (16A a b + 24B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (6A b + 24B a b )d e + 4B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b + B a )e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (24A a b + 36B a b )d e + (4A b + 16B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R A a e + (16A a b + 4B a )d e + (36A a b + 24B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (16A a b + 24B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 4A a d e + (24A a b + 6B a )d e + (24A a b + 16B a b)d e +--R + +--R 3 2 2 4 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 2 3 4 3 2 2 3 4 2 +--R (6A a d e + (16A a b + 4B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 3 4 4 4 4 +--R (4A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 764 +r0:=-1/1980*(b*d-a*e)^4*(6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^6*e)-1/660*(b*d-a*e)^2*(6*b*B*d-11*A*b*e+5*a*B*e)*_ + (a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^4*e)-2/495*(b*d-a*e)*_ + (6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^3*e)-1/110*(6*b*B*d-11*A*b*e+5*a*B*e)*(a+b*x)*_ + (d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+1/11*B*(a+b*x)*(d+_ + e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-1/2310*(b*d-a*e)^3*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6 +--R +--R +--R (2) +--R 10 4 10 10 9 4 10 3 9 +--R 1260B b e x + ((1386A b + 5670B a b )e + 5544B b d e )x +--R + +--R 9 2 8 4 10 9 3 +--R (6314A a b + 9730B a b )e + (6160A b + 25256B a b )d e +--R + +--R 10 2 2 +--R 9240B b d e +--R * +--R 8 +--R x +--R + +--R 2 8 3 7 4 9 2 8 3 +--R (11011A a b + 7595B a b )e + (28490A a b + 44044B a b )d e +--R + +--R 10 9 2 2 10 3 +--R (10395A b + 42735B a b )d e + 6930B b d e +--R * +--R 7 +--R x +--R + +--R 3 7 4 6 4 2 8 3 7 3 +--R (8789A a b + 2305B a b )e + (50710A a b + 35156B a b )d e +--R + +--R 9 2 8 2 2 10 9 3 +--R (49005A a b + 76065B a b )d e + (7920A b + 32670B a b )d e +--R + +--R 10 4 +--R 1980B b d +--R * +--R 6 +--R x +--R + +--R 4 6 5 5 4 3 7 4 6 3 +--R (2761A a b + 5B a b )e + (41690A a b + 11044B a b )d e +--R + +--R 2 8 3 7 2 2 9 2 8 3 +--R (89595A a b + 62535B a b )d e + (38280A a b + 59730B a b )d e +--R + +--R 10 9 4 +--R (2310A b + 9570B a b )d +--R * +--R 5 +--R x +--R + +--R 5 5 6 4 4 4 6 5 5 3 +--R (11A a b - 5B a b )e + (13750A a b + 44B a b )d e +--R + +--R 3 7 4 6 2 2 2 8 3 7 3 +--R (76725A a b + 20625B a b )d e + (72600A a b + 51150B a b )d e +--R + +--R 9 2 8 4 +--R (11550A a b + 18150B a b )d +--R * +--R 4 +--R x +--R + +--R 6 4 7 3 4 5 5 6 4 3 +--R (- 11A a b + 5B a b )e + (110A a b - 44B a b )d e +--R + +--R 4 6 5 5 2 2 3 7 4 6 3 +--R (27225A a b + 165B a b )d e + (66000A a b + 18150B a b )d e +--R + +--R 2 8 3 7 4 +--R (23100A a b + 16500B a b )d +--R * +--R 3 +--R x +--R + +--R 7 3 8 2 4 6 4 7 3 3 +--R (11A a b - 5B a b )e + (- 110A a b + 44B a b )d e +--R + +--R 5 5 6 4 2 2 4 6 5 5 3 +--R (495A a b - 165B a b )d e + (26400A a b + 330B a b )d e +--R + +--R 3 7 4 6 4 +--R (23100A a b + 6600B a b )d +--R * +--R 2 +--R x +--R + +--R 8 2 9 4 7 3 8 2 3 +--R (- 11A a b + 5B a b)e + (110A a b - 44B a b )d e +--R + +--R 6 4 7 3 2 2 5 5 6 4 3 +--R (- 495A a b + 165B a b )d e + (1320A a b - 330B a b )d e +--R + +--R 4 6 5 5 4 +--R (11550A a b + 330B a b )d +--R * +--R x +--R + +--R 9 10 4 8 2 9 3 +--R (11A a b - 5B a )e + (- 110A a b + 44B a b)d e +--R + +--R 7 3 8 2 2 2 6 4 7 3 3 +--R (495A a b - 165B a b )d e + (- 1320A a b + 330B a b )d e +--R + +--R 5 5 6 4 4 +--R (2310A a b - 330B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 +--R 13860b +--R Type: Expression(Integer) +--E 338 + +--S 339 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 339 + +)clear all + +--S 340 of 764 +t0:=(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 764 +r0:=-1/360*(b*d-a*e)^3*(3*b*B*d-5*A*b*e+2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^5*e)-1/120*(b*d-a*e)*(3*b*B*d-5*A*b*e+2*a*B*e)*_ + (a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^3*e)-1/45*(3*b*B*d-_ + 5*A*b*e+2*a*B*e)*(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+_ + 1/10*B*(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 1/420*(b*d-a*e)^2*(3*b*B*d-5*A*b*e+2*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^5 +--R +--R +--R (2) +--R 9 3 9 9 8 3 9 2 8 +--R 252B b e x + ((280A b + 1148B a b )e + 840B b d e )x +--R + +--R 8 2 7 3 9 8 2 +--R (1295A a b + 2002B a b )e + (945A b + 3885B a b )d e +--R + +--R 9 2 +--R 945B b d e +--R * +--R 7 +--R x +--R + +--R 2 7 3 6 3 8 2 7 2 +--R (2305A a b + 1598B a b )e + (4455A a b + 6915B a b )d e +--R + +--R 9 8 2 9 3 +--R (1080A b + 4455B a b )d e + 360B b d +--R * +--R 6 +--R x +--R + +--R 3 6 4 5 3 2 7 3 6 2 +--R (1895A a b + 502B a b )e + (8145A a b + 5685B a b )d e +--R + +--R 8 2 7 2 9 8 3 +--R (5220A a b + 8145B a b )d e + (420A b + 1740B a b )d +--R * +--R 5 +--R x +--R + +--R 4 5 5 4 3 3 6 4 5 2 +--R (625A a b + 2B a b )e + (6975A a b + 1875B a b )d e +--R + +--R 2 7 3 6 2 8 2 7 3 +--R (9900A a b + 6975B a b )d e + (2100A a b + 3300B a b )d +--R * +--R 4 +--R x +--R + +--R 5 4 6 3 3 4 5 5 4 2 +--R (5A a b - 2B a b )e + (2475A a b + 15B a b )d e +--R + +--R 3 6 4 5 2 2 7 3 6 3 +--R (9000A a b + 2475B a b )d e + (4200A a b + 3000B a b )d +--R * +--R 3 +--R x +--R + +--R 6 3 7 2 3 5 4 6 3 2 +--R (- 5A a b + 2B a b )e + (45A a b - 15B a b )d e +--R + +--R 4 5 5 4 2 3 6 4 5 3 +--R (3600A a b + 45B a b )d e + (4200A a b + 1200B a b )d +--R * +--R 2 +--R x +--R + +--R 7 2 8 3 6 3 7 2 2 +--R (5A a b - 2B a b)e + (- 45A a b + 15B a b )d e +--R + +--R 5 4 6 3 2 4 5 5 4 3 +--R (180A a b - 45B a b )d e + (2100A a b + 60B a b )d +--R * +--R x +--R + +--R 8 9 3 7 2 8 2 +--R (- 5A a b + 2B a )e + (45A a b - 15B a b)d e +--R + +--R 6 3 7 2 2 5 4 6 3 3 +--R (- 180A a b + 45B a b )d e + (420A a b - 60B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 2520b +--R Type: Expression(Integer) +--E 341 + +--S 342 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 764 +t0:=(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 764 +r0:=-1/72*(b*d-a*e)^2*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^4*e)-1/24*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*(d+_ + e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b^2*e)+1/9*B*(a+b*x)*(d+e*x)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-1/84*(b*d-a*e)*(2*b*B*d-3*A*b*e+_ + a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4 +--R +--R +--R (2) +--R 8 2 8 8 7 2 8 7 +--R 56B b e x + ((63A b + 259B a b )e + 126B b d e)x +--R + +--R 7 2 6 2 8 7 8 2 6 +--R ((297A a b + 461B a b )e + (144A b + 594B a b )d e + 72B b d )x +--R + +--R 2 6 3 5 2 7 2 6 +--R (543A a b + 379B a b )e + (696A a b + 1086B a b )d e +--R + +--R 8 7 2 +--R (84A b + 348B a b )d +--R * +--R 5 +--R x +--R + +--R 3 5 4 4 2 2 6 3 5 +--R (465A a b + 125B a b )e + (1320A a b + 930B a b )d e +--R + +--R 7 2 6 2 +--R (420A a b + 660B a b )d +--R * +--R 4 +--R x +--R + +--R 4 4 5 3 2 3 5 4 4 +--R (165A a b + B a b )e + (1200A a b + 330B a b )d e +--R + +--R 2 6 3 5 2 +--R (840A a b + 600B a b )d +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 2 4 4 5 3 +--R (3A a b - B a b )e + (480A a b + 6B a b )d e +--R + +--R 3 5 4 4 2 +--R (840A a b + 240B a b )d +--R * +--R 2 +--R x +--R + +--R 6 2 7 2 5 3 6 2 +--R (- 3A a b + B a b)e + (24A a b - 6B a b )d e +--R + +--R 4 4 5 3 2 +--R (420A a b + 12B a b )d +--R * +--R x +--R + +--R 7 8 2 6 2 7 5 3 6 2 2 +--R (3A a b - B a )e + (- 24A a b + 6B a b)d e + (84A a b - 12B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 504b +--R Type: Expression(Integer) +--E 344 + +--S 345 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 764 +t0:=(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 764 +r0:=-1/24*(b*d-a*e)*(3*b*B*d-4*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b^3*e)+1/8*B*(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-1/28*(3*b*B*d-4*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^3 +--R +--R +--R (2) +--R 7 7 7 6 7 6 +--R 21B b e x + ((24A b + 99B a b )e + 24B b d)x +--R + +--R 6 2 5 7 6 5 +--R ((116A a b + 181B a b )e + (28A b + 116B a b )d)x +--R + +--R 2 5 3 4 6 2 5 4 +--R ((220A a b + 155B a b )e + (140A a b + 220B a b )d)x +--R + +--R 3 4 4 3 2 5 3 4 3 +--R ((200A a b + 55B a b )e + (280A a b + 200B a b )d)x +--R + +--R 4 3 5 2 3 4 4 3 2 +--R ((80A a b + B a b )e + (280A a b + 80B a b )d)x +--R + +--R 5 2 6 4 3 5 2 6 7 +--R ((4A a b - B a b)e + (140A a b + 4B a b )d)x + (- 4A a b + B a )e +--R + +--R 5 2 6 +--R (28A a b - 4B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 168b +--R Type: Expression(Integer) +--E 347 + +--S 348 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 764 +r0:=1/6*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+_ + 1/7*B*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2 +--R +--R +--R (2) +--R 6 6 6 5 5 5 2 4 4 +--R 6B b x + (7A b + 29B a b )x + (35A a b + 55B a b )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 4 2 5 +--R (70A a b + 50B a b )x + (70A a b + 20B a b )x + (35A a b + B a b)x +--R + +--R 5 6 +--R 7A a b - B a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 42b +--R Type: Expression(Integer) +--E 350 + +--S 351 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R e x + d +--R Type: Expression(Integer) +--E 352 + +--S 353 of 764 +r0:=-1/3*(b*d-a*e)^2*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/4*(b*d-a*e)*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/5*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/6*B*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-(b*d-a*e)^4*(B*d-A*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/2*(b*d-a*e)^3*(B*d-A*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+(b*d-a*e)^5*(B*d-A*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 5 +--R 60A a b e + (- 300A a b - 60B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (600A a b + 300B a b )d e + (- 600A a b - 600B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (300A a b + 600B a b )d e + (- 60A b - 300B a b )d e + 60B b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 6 5 6 6 5 5 +--R 10B b e x + ((12A b + 60B a b )e - 12B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 4 +--R ((75A a b + 150B a b )e + (- 15A b - 75B a b )d e + 15B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (200A a b + 200B a b )e + (- 100A a b - 200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (20A b + 100B a b )d e - 20B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (300A a b + 150B a b )e + (- 300A a b - 300B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (150A a b + 300B a b )d e + (- 30A b - 150B a b )d e + 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (300A a b + 60B a b)e + (- 600A a b - 300B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (600A a b + 600B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (60A b + 300B a b )d e - 60B b d e +--R * +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (137A a b + 10B a )e + (- 385A a b - 137B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (470A a b + 385B a b )d e + (- 270A a b - 470B a b )d e +--R + +--R 5 2 4 4 2 5 5 +--R (60A a b + 270B a b )d e - 60B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 7 7 +--R 60b e x + 60a b e +--R Type: Expression(Integer) +--E 353 + +--S 354 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 355 + +--S 356 of 764 +r0:=1/3*(b*d-a*e)*(6*b*B*d-5*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-_ + 1/4*(6*b*B*d-5*A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3+_ + 1/5*(6*b*B*d-5*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-a*e))-_ + (B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x))+_ + (b*d-a*e)^3*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 1/2*(b*d-a*e)^2*(6*b*B*d-5*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^5-(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 5 6 3 2 4 5 +--R (300A a b + 60B a )e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (300A b + 1500B a b )d e - 360B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 2 4 +--R (300A a b + 60B a )d e + (- 1200A a b - 600B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (1800A a b + 1800B a b )d e + (- 1200A a b - 2400B a b )d e +--R + +--R 5 4 5 5 6 +--R (300A b + 1500B a b )d e - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 12B b e x + ((15A b + 75B a b )e - 18B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((100A a b + 200B a b )e + (- 25A b - 125B a b )d e + 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (300A a b + 300B a b )e + (- 200A a b - 400B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (50A b + 250B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (600A a b + 300B a b)e + (- 900A a b - 900B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (600A a b + 1200B a b )d e + (- 150A b - 750B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (325A a b + 137B a )e + (- 100A a b - 410B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 750A a b - 30B a b )d e + (900A a b + 1080B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 300A b - 1140B a b )d e + 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 60A a e + (625A a b + 197B a )d e + (- 1300A a b - 1010B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (1050A a b + 1770B a b )d e + (- 300A a b - 1320B a b )d e +--R + +--R 4 5 +--R 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +--R 60b e x + (60a e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 356 + +--S 357 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 358 + +--S 359 of 764 +r0:=-5/3*b*(3*b*B*d-2*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 5/4*b*(3*b*B*d-2*A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e))-1/2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e*(b*d-a*e)*(d+e*x)^2)-(3*b*B*d-2*A*b*e-a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x))-5*b*(b*d-a*e)^2*(3*b*B*d-_ + 2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+5/2*b*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+5*b*_ + (b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 3 2 4 6 2 3 3 2 5 +--R (120A a b + 60B a b)e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e +--R + +--R 5 4 2 +--R 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 2 4 +--R (240A a b + 120B a b)d e + (- 720A a b - 720B a b )d e +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (720A a b + 1440B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 360B b d e +--R * +--R x +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (120A a b + 60B a b)d e + (- 360A a b - 360B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (360A a b + 720B a b )d e + (- 120A b - 600B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 3B b e x + ((4A b + 20B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 10A b - 50B a b )d e + 15B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (120A a b + 120B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (40A b + 200B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (40A a b + 65B a b)e + (240A a b + 60B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 420A a b - 570B a b )d e + (180A b + 720B a b )d e +--R + +--R 5 4 2 +--R - 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 60A a b - 12B a )e + (320A a b + 250B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 240A a b - 600B a b )d e + (- 120A a b + 300B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (120A b + 240B a b )d e - 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 6A a e + (- 30A a b - 6B a )d e + (220A a b + 155B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 300A a b - 480B a b )d e + (120A a b + 510B a b )d e +--R + +--R 4 5 +--R - 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 12b e x + (12a e + 24b d e )x + (24a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 359 + +--S 360 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 361 + +--S 362 of 764 +r0:=10/3*b^2*(2*b*B*d-A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-_ + a*e))-5/2*b*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x))-1/3*(B*d-A*e)*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^3)-1/2*(2*b*B*d-A*b*e-_ + a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^2)+_ + 10*b^2*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 5*b^2*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-_ + 10*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 2 3 3 2 6 4 2 3 5 +--R (60A a b + 60B a b )e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (60A b + 300B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 2 4 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 3 3 5 4 2 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (180A a b + 180B a b )d e + (- 360A a b - 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (180A b + 900B a b )d e - 360B b d e +--R * +--R x +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (60A a b + 60B a b )d e + (- 120A a b - 240B a b )d e +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 120B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 2B b e x + ((3A b + 15B a b )e - 6B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((30A a b + 60B a b )e + (- 15A b - 75B a b )d e + 30B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 20A a b + 20B a b )e + (160A a b + 200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 110A b - 430B a b )d e + 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (120A a b + 240B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (120A a b - 120B a b )d e + (- 150A b - 390B a b )d e +--R + +--R 5 4 2 +--R 300B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 15A a b - 3B a )e + (- 60A a b - 30B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (210A a b + 330B a b )d e + (- 60A a b - 480B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b + 60B a b )d e + 120B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 2A a e + (- 5A a b - B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (90A a b + 130B a b )d e + (- 60A a b - 240B a b )d e + 120B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 6b e x + (6a e + 18b d e )x + (18a d e + 18b d e )x +--R + +--R 2 8 3 7 3 7 +--R (18a d e + 6b d e )x + 6a d e +--R Type: Expression(Integer) +--E 362 + +--S 363 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 364 + +--S 365 of 764 +r0:=-5/12*b*(3*b*B*d-A*b*e-2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^2)-5/3*b^2*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x))-_ + 1/4*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^4)-1/6*(3*b*B*d-A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(b*d-a*e)*(d+e*x)^3)-5*b^3*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^6+5/2*b^3*(3*b*B*d-A*b*e-2*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e))+5*b^3*(b*d-a*e)*(3*b*B*d-_ + A*b*e-2*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 2 3 6 5 4 5 +--R (60A a b + 120B a b )e + (- 60A b - 300B a b )d e +--R + +--R 5 2 4 +--R 180B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 5 5 4 2 4 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 3 3 +--R 720B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (360A a b + 720B a b )d e + (- 360A b - 1800B a b )d e +--R + +--R 5 4 2 +--R 1080B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 3 5 4 4 2 +--R (240A a b + 480B a b )d e + (- 240A b - 1200B a b )d e +--R + +--R 5 5 +--R 720B b d e +--R * +--R x +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (60A a b + 120B a b )d e + (- 60A b - 300B a b )d e + 180B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 6B b e x + ((12A b + 60B a b )e - 36B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((- 65A a b - 40B a b )e + (125A b + 445B a b )d e - 375B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 120A a b - 120B a b )e + (- 20A a b + 320B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (260A b + 580B a b )d e - 780B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 60A a b - 30B a b)e + (- 180A a b - 180B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 5 4 2 +--R (150A a b + 840B a b )d e + (210A b - 30B a b )d e - 630B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 20A a b - 4B a )e + (- 40A a b - 20B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 120A a b - 120B a b )d e + (180A a b + 720B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (60A b - 420B a b )d e - 180B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 3A a e + (- 5A a b - B a )d e + (- 10A a b - 5B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (- 30A a b - 30B a b )d e + (60A a b + 210B a b )d e - 180B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 365 + +--S 366 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^6 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 367 + +--S 368 of 764 +r0:=-1/12*b*(6*b*B*d-A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e)*(d+e*x)^3)-1/6*b^2*(6*b*B*d-A*b*e-5*a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^2)-1/5*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^5)-_ + 1/20*(6*b*B*d-A*b*e-5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*_ + (b*d-a*e)*(d+e*x)^4)+b^4*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^6*(b*d-a*e))-1/2*b^3*(6*b*B*d-A*b*e-5*a*B*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*(d+e*x))-b^4*(6*b*B*d-A*b*e-_ + 5*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 4 6 5 5 5 +--R ((60A b + 300B a b )e - 360B b d e )x +--R + +--R 5 4 5 5 2 4 4 +--R ((300A b + 1500B a b )d e - 1800B b d e )x +--R + +--R 5 4 2 4 5 3 3 3 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 3 3 5 4 2 2 +--R ((600A b + 3000B a b )d e - 3600B b d e )x +--R + +--R 5 4 4 2 5 5 +--R ((300A b + 1500B a b )d e - 1800B b d e)x +--R + +--R 5 4 5 5 6 +--R (60A b + 300B a b )d e - 360B b d +--R * +--R log(e x + d) +--R + +--R 5 6 6 5 4 6 5 5 5 +--R 60B b e x + ((- 137A b - 325B a b )e + 822B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 300A a b - 600B a b )e + (- 385A b - 125B a b )d e +--R + +--R 5 2 4 +--R 2310B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 300A a b - 300B a b )e + (- 600A a b - 1200B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 470A b + 1250B a b )d e + 2820B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 200A a b - 100B a b)e + (- 300A a b - 300B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 600A a b - 1200B a b )d e + (- 270A b + 2250B a b )d e +--R + +--R 5 4 2 +--R 1620B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 75A a b - 15B a )e + (- 100A a b - 50B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 150A a b - 150B a b )d e + (- 300A a b - 600B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 60A b + 1500B a b )d e + 360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 12A a e + (- 15A a b - 3B a )d e + (- 20A a b - 10B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 4 5 +--R (- 30A a b - 30B a b )d e + (- 60A a b - 120B a b )d e + 360B a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 60b e x + (60a e + 300b d e )x + (300a d e + 600b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (600a d e + 600b d e )x + (600a d e + 300b d e )x +--R + +--R 4 8 5 7 5 7 +--R (300a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 368 + +--S 369 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^7 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 370 + +--S 371 of 764 +r0:=-1/4*b*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^4)-_ + 1/3*b^2*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^3)-1/6*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^6)-_ + 1/5*B*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^5)-1/2*b^3*B*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^2)+b^4*B*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))+b^5*B*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 7 6 6 6 5 6 6 2 5 5 +--R (60B a b e - 60B b d e )x + (360B a b d e - 360B b d e )x +--R + +--R 5 2 5 6 3 4 4 5 3 4 6 4 3 3 +--R (900B a b d e - 900B b d e )x + (1200B a b d e - 1200B b d e )x +--R + +--R 5 4 3 6 5 2 2 5 5 2 6 6 +--R (900B a b d e - 900B b d e )x + (360B a b d e - 360B b d e)x +--R + +--R 5 6 6 7 +--R 60B a b d e - 60B b d +--R * +--R log(e x + d) +--R + +--R 6 5 7 6 6 6 +--R ((- 10A b - 77B a b )e + 87B b d e )x +--R + +--R 5 2 4 7 5 6 6 2 5 5 +--R ((- 60A a b - 300B a b )e + 198B a b d e + 162B b d e )x +--R + +--R 2 4 3 3 7 2 4 6 5 2 5 +--R (- 150A a b - 300B a b )e - 450B a b d e + 945B a b d e +--R + +--R 6 3 4 +--R - 45B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 3 3 6 2 4 2 5 +--R (- 200A a b - 200B a b )e - 200B a b d e - 600B a b d e +--R + +--R 5 3 4 6 4 3 +--R 1660B a b d e - 460B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 4 2 6 3 3 2 5 +--R (- 150A a b - 75B a b)e - 75B a b d e - 150B a b d e +--R + +--R 2 4 3 4 5 4 3 6 5 2 +--R - 450B a b d e + 1470B a b d e - 570B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 5 6 4 2 2 5 3 3 3 4 +--R (- 60A a b - 12B a )e - 18B a b d e - 30B a b d e - 60B a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 180B a b d e + 660B a b d e - 300B b d e +--R * +--R x +--R + +--R 6 7 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 10A a e - 2B a d e - 3B a b d e - 5B a b d e - 10B a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R - 30B a b d e + 120B a b d e - 60B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 2 13 7 2 14 13 2 2 12 6 +--R (60a b e - 60b d e )x + (60a e + 300a b d e - 360b d e )x +--R + +--R 2 13 2 12 2 3 11 5 +--R (360a d e + 540a b d e - 900b d e )x +--R + +--R 2 2 12 3 11 2 4 10 4 +--R (900a d e + 300a b d e - 1200b d e )x +--R + +--R 2 3 11 4 10 2 5 9 3 +--R (1200a d e - 300a b d e - 900b d e )x +--R + +--R 2 4 10 5 9 2 6 8 2 +--R (900a d e - 540a b d e - 360b d e )x +--R + +--R 2 5 9 6 8 2 7 7 2 6 8 7 7 +--R (360a d e - 300a b d e - 60b d e )x + 60a d e - 60a b d e +--R Type: Expression(Integer) +--E 371 + +--S 372 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^8 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 373 + +--S 374 of 764 +r0:=1/6*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*_ + (d+e*x)^6)+1/7*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*_ + (d+e*x)^7) +--R +--R +--R (2) +--R 6 5 6 6 +--R ((A b - 7B a b )e + 6B b d)x +--R + +--R 5 2 4 6 5 5 +--R ((- A a b - 35B a b )e + (7A b + 29B a b )d)x +--R + +--R 2 4 3 3 5 2 4 4 +--R ((- 20A a b - 70B a b )e + (35A a b + 55B a b )d)x +--R + +--R 3 3 4 2 2 4 3 3 3 +--R ((- 50A a b - 70B a b )e + (70A a b + 50B a b )d)x +--R + +--R 4 2 5 3 3 4 2 2 +--R ((- 55A a b - 35B a b)e + (70A a b + 20B a b )d)x +--R + +--R 5 6 4 2 5 6 5 6 +--R ((- 29A a b - 7B a )e + (35A a b + B a b)d)x - 6A a e + (7A a b - B a )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 9 8 2 2 7 7 +--R (42a e - 84a b d e + 42b d e )x +--R + +--R 2 8 2 7 2 3 6 6 +--R (294a d e - 588a b d e + 294b d e )x +--R + +--R 2 2 7 3 6 2 4 5 5 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 3 6 4 5 2 5 4 4 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 4 5 5 4 2 6 3 3 +--R (1470a d e - 2940a b d e + 1470b d e )x +--R + +--R 2 5 4 6 3 2 7 2 2 +--R (882a d e - 1764a b d e + 882b d e )x +--R + +--R 2 6 3 7 2 2 8 2 7 2 8 2 9 +--R (294a d e - 588a b d e + 294b d e)x + 42a d e - 84a b d e + 42b d +--R Type: Expression(Integer) +--E 374 + +--S 375 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^9 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 376 + +--S 377 of 764 +r0:=-1/8*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^8)+1/24*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^7)+1/168*(3*b*B*d+A*b*e-_ + 4*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^7) +--R +--R +--R (2) +--R 7 6 2 7 7 +--R ((- A b + 4B a b )e - 3B b d e)x +--R + +--R 6 2 5 2 7 6 7 2 6 +--R ((A a b - 4B a b )e + (- 8A b + 35B a b )d e - 24B b d )x +--R + +--R 2 5 3 4 2 6 2 5 +--R (- A a b - 80B a b )e + (8A a b + 217B a b )d e +--R + +--R 7 6 2 +--R (- 28A b - 116B a b )d +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 2 2 5 3 4 +--R (- 55A a b - 200B a b )e + (160A a b + 455B a b )d e +--R + +--R 6 2 5 2 +--R (- 140A a b - 220B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 2 3 4 4 3 +--R (- 155A a b - 220B a b )e + (400A a b + 455B a b )d e +--R + +--R 2 5 3 4 2 +--R (- 280A a b - 200B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 6 2 4 3 5 2 +--R (- 181A a b - 116B a b)e + (440A a b + 217B a b )d e +--R + +--R 3 4 4 3 2 +--R (- 280A a b - 80B a b )d +--R * +--R 2 +--R x +--R + +--R 6 7 2 5 2 6 +--R (- 99A a b - 24B a )e + (232A a b + 35B a b)d e +--R + +--R 4 3 5 2 2 +--R (- 140A a b - 4B a b )d +--R * +--R x +--R + +--R 7 2 6 7 5 2 6 2 +--R - 21A a e + (48A a b - 3B a )d e + (- 28A a b + 4B a b)d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 11 2 10 2 2 9 3 3 8 8 +--R (168a e - 504a b d e + 504a b d e - 168b d e )x +--R + +--R 3 10 2 2 9 2 3 8 3 4 7 7 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e )x +--R + +--R 3 2 9 2 3 8 2 4 7 3 5 6 6 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 3 8 2 4 7 2 5 6 3 6 5 5 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (11760a d e - 35280a b d e + 35280a b d e - 11760b d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (9408a d e - 28224a b d e + 28224a b d e - 9408b d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (4704a d e - 14112a b d e + 14112a b d e - 4704b d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (1344a d e - 4032a b d e + 4032a b d e - 1344b d e)x + 168a d e +--R + +--R 2 9 2 2 10 3 11 +--R - 504a b d e + 504a b d e - 168b d +--R Type: Expression(Integer) +--E 377 + +--S 378 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^10 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 379 + +--S 380 of 764 +r0:=-1/9*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^9)+1/24*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^8)+1/72*b*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)^3*_ + (d+e*x)^7)+1/504*b*(2*b*B*d+A*b*e-3*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^7) +--R +--R +--R (2) +--R 8 7 3 8 2 8 +--R ((A b - 3B a b )e + 2B b d e )x +--R + +--R 7 2 6 3 8 7 2 8 2 7 +--R ((- A a b + 3B a b )e + (9A b - 29B a b )d e + 18B b d e)x +--R + +--R 2 6 3 5 3 7 2 6 2 +--R (A a b - 3B a b )e + (- 9A a b + 29B a b )d e +--R + +--R 8 7 2 8 3 +--R (36A b - 126B a b )d e + 72B b d +--R * +--R 6 +--R x +--R + +--R 3 5 4 4 3 2 6 3 5 2 +--R (- A a b - 165B a b )e + (9A a b + 643B a b )d e +--R + +--R 7 2 6 2 8 7 3 +--R (- 36A a b - 882B a b )d e + (84A b + 348B a b )d +--R * +--R 5 +--R x +--R + +--R 4 4 5 3 3 3 5 4 4 2 +--R (- 125A a b - 465B a b )e + (495A a b + 1625B a b )d e +--R + +--R 2 6 3 5 2 7 2 6 3 +--R (- 720A a b - 1890B a b )d e + (420A a b + 660B a b )d +--R * +--R 4 +--R x +--R + +--R 5 3 6 2 3 4 4 5 3 2 +--R (- 379A a b - 543B a b )e + (1395A a b + 1777B a b )d e +--R + +--R 3 5 4 4 2 2 6 3 5 3 +--R (- 1800A a b - 1890B a b )d e + (840A a b + 600B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 7 3 5 3 6 2 2 +--R (- 461A a b - 297B a b)e + (1629A a b + 911B a b )d e +--R + +--R 4 4 5 3 2 3 5 4 4 3 +--R (- 1980A a b - 882B a b )d e + (840A a b + 240B a b )d +--R * +--R 2 +--R x +--R + +--R 7 8 3 6 2 7 2 +--R (- 259A a b - 63B a )e + (891A a b + 169B a b)d e +--R + +--R 5 3 6 2 2 4 4 5 3 3 +--R (- 1044A a b - 126B a b )d e + (420A a b + 12B a b )d +--R * +--R x +--R + +--R 8 3 7 8 2 6 2 7 2 +--R - 56A a e + (189A a b - 7B a )d e + (- 216A a b + 18B a b)d e +--R + +--R 5 3 6 2 3 +--R (84A a b - 12B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 13 3 12 2 2 2 11 3 3 10 4 4 9 9 +--R (504a e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d e )x +--R + +--R 4 12 3 2 11 2 2 3 10 3 4 9 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 5 8 +--R 4536b d e +--R * +--R 8 +--R x +--R + +--R 4 2 11 3 3 10 2 2 4 9 3 5 8 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 6 7 +--R 18144b d e +--R * +--R 7 +--R x +--R + +--R 4 3 10 3 4 9 2 2 5 8 3 6 7 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 7 6 +--R 42336b d e +--R * +--R 6 +--R x +--R + +--R 4 4 9 3 5 8 2 2 6 7 3 7 6 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 8 5 +--R 63504b d e +--R * +--R 5 +--R x +--R + +--R 4 5 8 3 6 7 2 2 7 6 3 8 5 +--R 63504a d e - 254016a b d e + 381024a b d e - 254016a b d e +--R + +--R 4 9 4 +--R 63504b d e +--R * +--R 4 +--R x +--R + +--R 4 6 7 3 7 6 2 2 8 5 3 9 4 +--R 42336a d e - 169344a b d e + 254016a b d e - 169344a b d e +--R + +--R 4 10 3 +--R 42336b d e +--R * +--R 3 +--R x +--R + +--R 4 7 6 3 8 5 2 2 9 4 3 10 3 +--R 18144a d e - 72576a b d e + 108864a b d e - 72576a b d e +--R + +--R 4 11 2 +--R 18144b d e +--R * +--R 2 +--R x +--R + +--R 4 8 5 3 9 4 2 2 10 3 3 11 2 +--R 4536a d e - 18144a b d e + 27216a b d e - 18144a b d e +--R + +--R 4 12 +--R 4536b d e +--R * +--R x +--R + +--R 4 9 4 3 10 3 2 2 11 2 3 12 4 13 +--R 504a d e - 2016a b d e + 3024a b d e - 2016a b d e + 504b d +--R Type: Expression(Integer) +--E 380 + +--S 381 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^11 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 382 + +--S 383 of 764 +r0:=-1/10*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^10)+1/45*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^9)+1/120*b*(3*b*B*d+2*A*b*e-_ + 5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)^3*(d+_ + e*x)^8)+1/360*b^2*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(b*d-a*e)^4*(d+e*x)^7)+1/2520*b^2*(3*b*B*d+2*A*b*e-_ + 5*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^7) +--R +--R +--R (2) +--R 9 8 4 9 3 9 +--R ((- 2A b + 5B a b )e - 3B b d e )x +--R + +--R 8 2 7 4 9 8 3 9 2 2 8 +--R ((2A a b - 5B a b )e + (- 20A b + 53B a b )d e - 30B b d e )x +--R + +--R 2 7 3 6 4 8 2 7 3 +--R (- 2A a b + 5B a b )e + (20A a b - 53B a b )d e +--R + +--R 9 8 2 2 9 3 +--R (- 90A b + 255B a b )d e - 135B b d e +--R * +--R 7 +--R x +--R + +--R 3 6 4 5 4 2 7 3 6 3 +--R (2A a b - 5B a b )e + (- 20A a b + 53B a b )d e +--R + +--R 8 2 7 2 2 9 8 3 9 4 +--R (90A a b - 255B a b )d e + (- 240A b + 735B a b )d e - 360B b d +--R * +--R 6 +--R x +--R + +--R 4 5 5 4 4 3 6 4 5 3 +--R (- 2A a b - 625B a b )e + (20A a b + 3097B a b )d e +--R + +--R 2 7 3 6 2 2 8 2 7 3 +--R (- 90A a b - 6045B a b )d e + (240A a b + 5565B a b )d e +--R + +--R 9 8 4 +--R (- 420A b - 1740B a b )d +--R * +--R 5 +--R x +--R + +--R 5 4 6 3 4 4 5 5 4 3 +--R (- 502A a b - 1895B a b )e + (2500A a b + 8747B a b )d e +--R + +--R 3 6 4 5 2 2 2 7 3 6 3 +--R (- 4950A a b - 15375B a b )d e + (4800A a b + 12075B a b )d e +--R + +--R 8 2 7 4 +--R (- 2100A a b - 3300B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 7 2 4 5 4 6 3 3 +--R (- 1598A a b - 2305B a b )e + (7580A a b + 10153B a b )d e +--R + +--R 4 5 5 4 2 2 3 6 4 5 3 +--R (- 13950A a b - 16755B a b )d e + (12000A a b + 12075B a b )d e +--R + +--R 2 7 3 6 4 +--R (- 4200A a b - 3000B a b )d +--R * +--R 3 +--R x +--R + +--R 7 2 8 4 6 3 7 2 3 +--R (- 2002A a b - 1295B a b)e + (9220A a b + 5447B a b )d e +--R + +--R 5 4 6 3 2 2 4 5 5 4 3 +--R (- 16290A a b - 8445B a b )d e + (13200A a b + 5565B a b )d e +--R + +--R 3 6 4 5 4 +--R (- 4200A a b - 1200B a b )d +--R * +--R 2 +--R x +--R + +--R 8 9 4 7 2 8 3 +--R (- 1148A a b - 280B a )e + (5180A a b + 1078B a b)d e +--R + +--R 6 3 7 2 2 2 5 4 6 3 3 +--R (- 8910A a b - 1455B a b )d e + (6960A a b + 735B a b )d e +--R + +--R 4 5 5 4 4 +--R (- 2100A a b - 60B a b )d +--R * +--R x +--R + +--R 9 4 8 9 3 7 2 8 2 2 +--R - 252A a e + (1120A a b - 28B a )d e + (- 1890A a b + 105B a b)d e +--R + +--R 6 3 7 2 3 5 4 6 3 4 +--R (1440A a b - 135B a b )d e + (- 420A a b + 60B a b )d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 15 4 14 3 2 2 13 2 3 3 12 +--R 2520a e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 4 11 5 5 10 +--R 12600a b d e - 2520b d e +--R * +--R 10 +--R x +--R + +--R 5 14 4 2 13 3 2 3 12 2 3 4 11 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 5 10 5 6 9 +--R 126000a b d e - 25200b d e +--R * +--R 9 +--R x +--R + +--R 5 2 13 4 3 12 3 2 4 11 2 3 5 10 +--R 113400a d e - 567000a b d e + 1134000a b d e - 1134000a b d e +--R + +--R 4 6 9 5 7 8 +--R 567000a b d e - 113400b d e +--R * +--R 8 +--R x +--R + +--R 5 3 12 4 4 11 3 2 5 10 2 3 6 9 +--R 302400a d e - 1512000a b d e + 3024000a b d e - 3024000a b d e +--R + +--R 4 7 8 5 8 7 +--R 1512000a b d e - 302400b d e +--R * +--R 7 +--R x +--R + +--R 5 4 11 4 5 10 3 2 6 9 2 3 7 8 +--R 529200a d e - 2646000a b d e + 5292000a b d e - 5292000a b d e +--R + +--R 4 8 7 5 9 6 +--R 2646000a b d e - 529200b d e +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 2 7 8 2 3 8 7 +--R 635040a d e - 3175200a b d e + 6350400a b d e - 6350400a b d e +--R + +--R 4 9 6 5 10 5 +--R 3175200a b d e - 635040b d e +--R * +--R 5 +--R x +--R + +--R 5 6 9 4 7 8 3 2 8 7 2 3 9 6 +--R 529200a d e - 2646000a b d e + 5292000a b d e - 5292000a b d e +--R + +--R 4 10 5 5 11 4 +--R 2646000a b d e - 529200b d e +--R * +--R 4 +--R x +--R + +--R 5 7 8 4 8 7 3 2 9 6 2 3 10 5 +--R 302400a d e - 1512000a b d e + 3024000a b d e - 3024000a b d e +--R + +--R 4 11 4 5 12 3 +--R 1512000a b d e - 302400b d e +--R * +--R 3 +--R x +--R + +--R 5 8 7 4 9 6 3 2 10 5 2 3 11 4 +--R 113400a d e - 567000a b d e + 1134000a b d e - 1134000a b d e +--R + +--R 4 12 3 5 13 2 +--R 567000a b d e - 113400b d e +--R * +--R 2 +--R x +--R + +--R 5 9 6 4 10 5 3 2 11 4 2 3 12 3 +--R 25200a d e - 126000a b d e + 252000a b d e - 252000a b d e +--R + +--R 4 13 2 5 14 +--R 126000a b d e - 25200b d e +--R * +--R x +--R + +--R 5 10 5 4 11 4 3 2 12 3 2 3 13 2 +--R 2520a d e - 12600a b d e + 25200a b d e - 25200a b d e +--R + +--R 4 14 5 15 +--R 12600a b d e - 2520b d +--R Type: Expression(Integer) +--E 383 + +--S 384 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^12 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 385 + +--S 386 of 764 +r0:=-1/198*b*(6*b*B*d+5*A*b*e-11*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^9)-1/396*b^2*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^8)-_ + 1/11*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^11)-1/110*(6*b*B*d+5*A*b*e-11*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^10)-1/924*b^3*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*_ + (d+e*x)^7)-1/2310*b^4*(6*b*B*d+5*A*b*e-11*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^6)-1/13860*b^4*(6*b*B*d+5*A*b*e-_ + 11*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 2772B b e x + ((- 2310A b - 11550B a b )e - 2772B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 9900A a b - 19800B a b )e + (- 1650A b - 8250B a b )d e +--R + +--R 5 2 4 +--R - 1980B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 17325A a b - 17325B a b )e + (- 4950A a b - 9900B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 825A b - 4125B a b )d e - 990B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 15400A a b - 7700B a b)e + (- 5775A a b - 5775B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 1650A a b - 3300B a b )d e + (- 275A b - 1375B a b )d e +--R + +--R 5 4 2 +--R - 330B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 6930A a b - 1386B a )e + (- 3080A a b - 1540B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 1155A a b - 1155B a b )d e + (- 330A a b - 660B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 55A b - 275B a b )d e - 66B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 1260A a e + (- 630A a b - 126B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 280A a b - 140B a b)d e + (- 105A a b - 105B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (- 30A a b - 60B a b )d e + (- 5A b - 25B a b )d e - 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 18 12 18 17 11 +--R 13860b e x + (13860a e + 152460b d e )x +--R + +--R 17 2 16 10 2 16 3 15 9 +--R (152460a d e + 762300b d e )x + (762300a d e + 2286900b d e )x +--R + +--R 3 15 4 14 8 4 14 5 13 7 +--R (2286900a d e + 4573800b d e )x + (4573800a d e + 6403320b d e )x +--R + +--R 5 13 6 12 6 6 12 7 11 5 +--R (6403320a d e + 6403320b d e )x + (6403320a d e + 4573800b d e )x +--R + +--R 7 11 8 10 4 8 10 9 9 3 +--R (4573800a d e + 2286900b d e )x + (2286900a d e + 762300b d e )x +--R + +--R 9 9 10 8 2 10 8 11 7 +--R (762300a d e + 152460b d e )x + (152460a d e + 13860b d e )x +--R + +--R 11 7 +--R 13860a d e +--R Type: Expression(Integer) +--E 386 + +--S 387 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^13 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R e x + 13d e x + 78d e x + 286d e x + 715d e x + 1287d e x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 +--R 1716d e x + 1716d e x + 1287d e x + 715d e x + 286d e x + 78d e x +--R + +--R 12 13 +--R 13d e x + d +--R Type: Expression(Integer) +--E 388 + +--S 389 of 764 +r0:=-1/44*b*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (e^3*(b*d-a*e)*(d+e*x)^10)-1/99*b^2*(b*B*d+A*b*e-2*a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^9)-1/12*(B*d-A*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*(d+e*x)^12)-_ + 1/22*(b*B*d+A*b*e-2*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(b*d-_ + a*e)*(d+e*x)^11)-1/264*b^3*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(b*d-a*e)*(d+e*x)^8)-1/792*b^4*(b*B*d+A*b*e-_ + 2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^7)-_ + 1/5544*b^4*(b*B*d+A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*_ + (a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 924B b e x + ((- 792A b - 3960B a b )e - 792B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 3465A a b - 6930B a b )e + (- 495A b - 2475B a b )d e +--R + +--R 5 2 4 +--R - 495B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 6160A a b - 6160B a b )e + (- 1540A a b - 3080B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 220A b - 1100B a b )d e - 220B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 5544A a b - 2772B a b)e + (- 1848A a b - 1848B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 462A a b - 924B a b )d e + (- 66A b - 330B a b )d e +--R + +--R 5 4 2 +--R - 66B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 2520A a b - 504B a )e + (- 1008A a b - 504B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 336A a b - 336B a b )d e + (- 84A a b - 168B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 12A b - 60B a b )d e - 12B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 462A a e + (- 210A a b - 42B a )d e + (- 84A a b - 42B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 28A a b - 28B a b )d e + (- 7A a b - 14B a b )d e +--R + +--R 5 4 5 5 6 +--R (- A b - 5B a b )d e - B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 19 13 19 18 12 +--R 5544b e x + (5544a e + 66528b d e )x +--R + +--R 18 2 17 11 2 17 3 16 10 +--R (66528a d e + 365904b d e )x + (365904a d e + 1219680b d e )x +--R + +--R 3 16 4 15 9 4 15 5 14 8 +--R (1219680a d e + 2744280b d e )x + (2744280a d e + 4390848b d e )x +--R + +--R 5 14 6 13 7 6 13 7 12 6 +--R (4390848a d e + 5122656b d e )x + (5122656a d e + 4390848b d e )x +--R + +--R 7 12 8 11 5 8 11 9 10 4 +--R (4390848a d e + 2744280b d e )x + (2744280a d e + 1219680b d e )x +--R + +--R 9 10 10 9 3 10 9 11 8 2 +--R (1219680a d e + 365904b d e )x + (365904a d e + 66528b d e )x +--R + +--R 11 8 12 7 12 7 +--R (66528a d e + 5544b d e )x + 5544a d e +--R Type: Expression(Integer) +--E 389 + +--S 390 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^14 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R e x + 14d e x + 91d e x + 364d e x + 1001d e x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002d e x + 3003d e x + 3432d e x + 3003d e x + 2002d e x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001d e x + 364d e x + 91d e x + 14d e x + d +--R Type: Expression(Integer) +--E 391 + +--S 392 of 764 +r0:=-5/1716*b*(6*b*B*d+7*A*b*e-13*a*B*e)*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*(d+e*x)^11)-1/858*b^2*(6*b*B*d+7*A*b*e-_ + 13*a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(b*d-a*e)*(d+e*x)^10)-_ + 1/13*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^13)-1/156*(6*b*B*d+7*A*b*e-13*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^12)-1/2574*b^3*(6*b*B*d+_ + 7*A*b*e-13*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(b*d-_ + a*e)*(d+e*x)^9)-1/9009*b^4*(6*b*B*d+7*A*b*e-13*a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(b*d-a*e)*(d+e*x)^8)-1/72072*b^4*(6*b*B*d+_ + 7*A*b*e-13*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R - 10296B b e x + ((- 9009A b - 45045B a b )e - 7722B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (- 40040A a b - 80080B a b )e + (- 5005A b - 25025B a b )d e +--R + +--R 5 2 4 +--R - 4290B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (- 72072A a b - 72072B a b )e + (- 16016A a b - 32032B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (- 2002A b - 10010B a b )d e - 1716B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 65520A a b - 32760B a b)e + (- 19656A a b - 19656B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 4368A a b - 8736B a b )d e + (- 546A b - 2730B a b )d e +--R + +--R 5 4 2 +--R - 468B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 30030A a b - 6006B a )e + (- 10920A a b - 5460B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 3276A a b - 3276B a b )d e + (- 728A a b - 1456B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 91A b - 455B a b )d e - 78B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 5544A a e + (- 2310A a b - 462B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 840A a b - 420B a b)d e + (- 252A a b - 252B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 5 6 +--R (- 56A a b - 112B a b )d e + (- 7A b - 35B a b )d e - 6B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 20 14 20 19 13 +--R 72072b e x + (72072a e + 936936b d e )x +--R + +--R 19 2 18 12 +--R (936936a d e + 5621616b d e )x +--R + +--R 2 18 3 17 11 +--R (5621616a d e + 20612592b d e )x +--R + +--R 3 17 4 16 10 +--R (20612592a d e + 51531480b d e )x +--R + +--R 4 16 5 15 9 +--R (51531480a d e + 92756664b d e )x +--R + +--R 5 15 6 14 8 +--R (92756664a d e + 123675552b d e )x +--R + +--R 6 14 7 13 7 +--R (123675552a d e + 123675552b d e )x +--R + +--R 7 13 8 12 6 +--R (123675552a d e + 92756664b d e )x +--R + +--R 8 12 9 11 5 +--R (92756664a d e + 51531480b d e )x +--R + +--R 9 11 10 10 4 +--R (51531480a d e + 20612592b d e )x +--R + +--R 10 10 11 9 3 +--R (20612592a d e + 5621616b d e )x +--R + +--R 11 9 12 8 2 12 8 13 7 +--R (5621616a d e + 936936b d e )x + (936936a d e + 72072b d e )x +--R + +--R 13 7 +--R 72072a d e +--R Type: Expression(Integer) +--E 392 + +--S 393 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 764 +t0:=(A+B*x)*(d+e*x)^3/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 764 +r0:=1/2*(A*b-a*B)*(b*d-a*e)*(a+b*x)*(d+e*x)^2/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+1/3*(A*b-a*B)*(a+b*x)*(d+e*x)^3/(b^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+1/4*B*(a+b*x)*(d+e*x)^4/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*(b*d-a*e)^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+(A*b-a*B)*e*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 2 4 4 2 3 3 2 3 +--R (- 12A a b + 12B a b)e + (36A a b - 36B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 36A a b + 36B a b )d e + (12A a b - 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 2A a b + 2B a b )e + (18A b - 6B a b )d e + 18B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (6A a b - 6B a b )e + (- 18A a b + 18B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 18B a b )d e + 12B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (24A a b - 24B a b)e + (- 60A a b + 60B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (42A a b - 42B a b )d e + (10A b + 2B a b )d e + 3B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (12A a b - 12B a )e + (- 24A a b + 24B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (6A a b - 6B a b )d e + (10A a b - 10B a b )d e + 3B a b d +--R / +--R +------------------+ +--R 5 | 2 2 2 +--R 12b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 395 + +--S 396 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 of 764 +t0:=(A+B*x)*(d+e*x)^2/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 764 +r0:=1/2*(A*b-a*B)*(a+b*x)*(d+e*x)^2/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 1/3*B*(a+b*x)*(d+e*x)^3/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*_ + (b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*e*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (6A a b - 6B a b)e + (- 12A a b + 12B a b )d e +--R + +--R 4 3 2 +--R (6A b - 6B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (6A a b - 6B a )e + (- 12A a b + 12B a b)d e +--R + +--R 3 2 2 2 +--R (6A a b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 3A a b + 3B a b )e + (12A b - 6B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 12A a b + 12B a b)e + (18A a b - 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 3B a b )d e + 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (- 6A a b + 6B a )e + (6A a b - 6B a b)d e + (3A a b - 3B a b )d e +--R + +--R 3 3 +--R 2B a b d +--R / +--R +------------------+ +--R 4 | 2 2 2 +--R 6b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 398 + +--S 399 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 of 764 +t0:=(A+B*x)*(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 400 + +--S 401 of 764 +r0:=1/2*B*(a+b*x)*(d+e*x)^2/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*_ + (b*d-a*e)*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-_ + a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3 +--R +--R +--R (2) +--R 2 2 2 3 2 +--R ((- 2A a b + 2B a b)e + (2A b - 2B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (- 2A a b + 2B a )e + (2A a b - 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - B a b )e + 2B b d e)x +--R + +--R 2 2 2 2 3 2 2 3 2 +--R ((4A a b - 4B a b)e + 2B a b d e + B b d )x + (2A a b - 2B a )e +--R + +--R 2 2 +--R B a b d +--R / +--R +------------------+ +--R 3 | 2 2 2 +--R 2b e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 764 +t0:=(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R B x + A +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 764 +r0:=(A*b-a*B)*(a+b*x)*log(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + B*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2 +--R +--R +--R (2) +--R 2 2 2 2 2 +--R ((A b - B a b)x + A a b - B a )log(b x + a) + B b x + 2B a b x + B a +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 404 + +--S 405 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 764 +t0:=(A+B*x)/((d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 764 +r0:=(A*b-a*B)*(a+b*x)*log(a+b*x)/(b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (B*d-A*e)*(a+b*x)*log(d+e*x)/(e*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 +--R ((- A b + B a b)e x + (- A a b + B a )e)log(b x + a) +--R / +--R +------------------+ +--R 2 2 | 2 2 2 +--R (a b e - b d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 407 + +--S 408 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 764 +t0:=(A+B*x)/((d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 764 +r0:=-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + (A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (- A b + B a b)e x + ((- A a b + B a )e + (- A b + B a b)d e)x +--R + +--R 2 +--R (- A a b + B a )d e +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 2 2 +--R (A b - B a b)e x + ((A a b - B a )e + (A b - B a b)d e)x +--R + +--R 2 +--R (A a b - B a )d e +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R (- A a b e + (A b + B a b)d e - B b d )x - A a e + (A a b + B a )d e +--R + +--R 2 +--R - B a b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 of 764 +t0:=(A+B*x)/((d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 412 + +--S 413 of 764 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + b*(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b*(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (A*b-a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 +--R (2A b - 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((2A a b - 2B a b)e + (4A b - 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((4A a b - 4B a b)d e + (2A b - 2B a b )d e)x +--R + +--R 2 2 2 +--R (2A a b - 2B a b)d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 +--R (- 2A b + 2B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 2A a b + 2B a b)e + (- 4A b + 4B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 4A a b + 4B a b)d e + (- 2A b + 2B a b )d e)x +--R + +--R 2 2 2 +--R (- 2A a b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 3 2 2 2 +--R (2A b - 2B a b )e x + ((4A a b - 4B a b)e + (2A b - 2B a b )d e )x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (A a b - 2B a )e + (6A a b - 3B a b)d e + (- A b - 2B a b )d e +--R + +--R 3 3 +--R B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R - A a e + (4A a b - B a )d e + (- A a b - 2B a b)d e + B a b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 764 +t0:=(A+B*x)/((d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 415 + +--S 416 of 764 +r0:=-1/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 1/2*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + b^2*(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b^2*(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + b*(A*b-a*B)*e*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^4*(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 +--R (- 6A b + 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((- 6A a b + 6B a b )e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((- 18A a b + 18B a b )d e + (- 18A b + 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((- 18A a b + 18B a b )d e + (- 6A b + 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (- 6A a b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 +--R (6A b - 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((6A a b - 6B a b )e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 3 4 3 2 2 2 +--R ((18A a b - 18B a b )d e + (18A b - 18B a b )d e )x +--R + +--R 3 2 2 2 2 4 3 3 +--R ((18A a b - 18B a b )d e + (6A b - 6B a b )d e)x +--R + +--R 3 2 2 3 +--R (6A a b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 +--R (- 6A b + 6B a b )e x +--R + +--R 3 2 2 4 4 3 3 3 +--R ((- 12A a b + 12B a b )e + (- 12A b + 12B a b )d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 3A a b + 3B a b)e + (- 30A a b + 30B a b )d e +--R + +--R 4 3 2 2 +--R (- 3A b + 3B a b )d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (A a b - 3B a )e + (- 9A a b + 17B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 21A a b + 9B a b )d e + (5A b + 3B a b )d e - 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 2 3 3 4 +--R (5A a b + 3B a b )d e - 2B a b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4 7 +--R 6a d e - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 416 + +--S 417 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 764 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 418 + +--S 419 of 764 +r0:=-1/6*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^4/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/3*B*(a+b*x)*(d+e*x)^5/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+e*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^2/(b^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-2/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^3/_ + (b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*(a+b*x)*log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2*e^2*(b*d-a*e)*(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6 +--R +--R +--R (2) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 90A a b + 150B a b )e + (144A a b - 300B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b + 156B a b )d e - 4B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 108A a b + 180B a b)e + (144A a b - 312B a b )d e +--R + +--R 2 3 2 2 5 4 3 5 4 +--R 96B a b d e + (- 24A b + 40B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 36A a b + 60B a )e + (36A a b - 84B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (18A a b - 6B a b )d e + (- 12A a b + 32B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R / +--R +------------------+ +--R 7 6 | 2 2 2 +--R (6b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 764 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 764 +r0:=-1/2*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*(d+e*x)^3/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/2*B*(a+b*x)*(d+e*x)^4/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-3/2*(b*B*d+A*b*e-2*a*B*e)*(d+e*x)^2/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*B*d+A*b*e-_ + 2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 24B a b)e + (12A a b - 36B a b )d e + 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((15A a b - 30B a b )e + (- 9A b + 33B a b )d e - 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 36B a b)e + (- 6A a b + 30B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 6B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 3 2 3 2 2 2 +--R (6A a b - 12B a )e + 6B a b d e + (- 3A a b + 6B a b )d e +--R + +--R 4 3 3 +--R (- A b - B a b )d +--R / +--R +------------------+ +--R 6 5 | 2 2 2 +--R (2b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 764 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 764 +r0:=-1/2*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^2/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+B*(a+b*x)*(d+e*x)^3/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + (2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 2 +--R 2B b e x + (- 3A b + 9B a b )e x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 2A a b + 6B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 2 3 2 2 +--R (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R / +--R +------------------+ +--R 5 4 | 2 2 2 +--R (2b x + 2a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 425 + +--S 426 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 of 764 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 764 +r0:=-1/2*(A*b-a*B)*(a+b*x)*(d+e*x)^2/(b*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-B*(b*d-a*e)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + B*e*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2)),-1/2*B*(a+_ + b*x)*(d+e*x)^2/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*(B*d-A*e)*(a+_ + b*x)*(d+e*x)^2/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-B*(d+e*x)/_ + (b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e*(a+b*x)*log(a+b*x)/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R [ +--R 2 2 3 2 2 2 2 3 2 +--R (2B a b e - 2B b d e)x + (4B a b e - 4B a b d e)x + 2B a e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 2 2 2 3 2 3 2 +--R (A b - B a b )e x + (2B a b e + (2A b - 6B a b )d e + 2B b d )x +--R + +--R 3 2 2 3 2 2 +--R 2B a e - 4B a b d e + (A b + B a b )d +--R / +--R +------------------+ +--R 4 5 2 3 4 | 2 2 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|b x + 2a b x + a +--R , +--R +--R 2 2 3 2 2 2 2 3 2 +--R (2B a b e - 2B b d e)x + (4B a b e - 4B a b d e)x + 2B a e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 3 2 +--R ((A b - 3B a b )e + 2B b d e)x +--R + +--R 2 2 3 2 3 2 2 +--R (- 2B a b e + (2A b - 2B a b )d e + 2B b d )x - 2B a b d e +--R + +--R 3 2 2 +--R (A b + B a b )d +--R / +--R +------------------+ +--R 4 5 2 3 4 | 2 2 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|b x + 2a b x + a +--R ] +--R Type: Tuple(Expression(Integer)) +--E 428 + +--S 429 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 of 764 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R B x + A +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 430 + +--S 431 of 764 +r0:=-1/2*(a+b*x)*(A+B*x)^2/((A*b-a*B)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 2 2 2 +--R - B x - 2A B x - A +--R (2) --------------------------------------------------------- +--R +------------------+ +--R 2 2 | 2 2 2 +--R ((2A b - 2B a b)x + 2A a b - 2B a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 764 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R ------------------------------------------------------------------------ +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 433 + +--S 434 of 764 +r0:=-1/2*(A*b-a*B)*(a+b*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + (-B*d+A*e)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(B*d-A*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + e*(B*d-A*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x - 2A a b e +--R + +--R 2 +--R 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R / +--R 3 2 3 2 3 2 4 2 5 3 4 3 3 2 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x + 2a b e - 6a b d e +--R + +--R 2 3 2 4 3 +--R 6a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 764 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 764 +r0:=1/2*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+(-2*b*B*d+3*A*b*e-a*B*e)/((b*d-a*e)^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-e*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/_ + ((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(2*b*B*d-3*A*b*e+a*B*e)*_ + (a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e + (3A b - 5B a b )d e +--R + +--R 3 3 +--R - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (2a e - 6a b d e + 4a b d e + 4a b d e - 6a b d e + 2b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 764 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 764 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/2*(b*B*d-2*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-3/2*(b*B*d-2*A*b*e+a*B*e)/_ + ((b*d-a*e)^3*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3*b*e*(b*B*d-_ + 2*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*b*e*(b*B*d-2*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*B*d-2*A*b*e+a*B*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/((b*d-a*e)^5*(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 12B a b )e + (24A b - 24B a b )d e - 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (24A a b - 24B a b )d e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((36A a b - 18B a b )e + (12A b - 24B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (30A a b - 15B a b)e + (48A a b - 39B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 6A b - 21B a b )d e + 3B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 2 2 2 2 +--R (4A a b - 2B a )e + (48A a b - 26B a b)d e - 24B a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 2B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - A a e + (8A a b - B a )d e + (12A a b - 15B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 8A a b + 3B a b )d e + (A b + B a b )d +--R / +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e +--R + +--R 6 5 2 +--R - 2b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 6 3 3 3 4 2 4 4 3 5 5 2 6 6 2 +--R (2a e - 6a b d e + 20a b d e - 30a b d e + 18a b d e - 4b d e)x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5 6 6 7 +--R (4a d e - 18a b d e + 30a b d e - 20a b d e + 6a b d e - 2b d )x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 440 + +--S 441 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 441 + +)clear all + +--S 442 of 764 +t0:=(A+B*x)*(d+e*x)^5/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 764 +r0:=-1/4*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^5/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/2*B*(a+b*x)*(d+e*x)^6/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-5/6*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^3/_ + (b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/12*(2*b*B*d+A*b*e-3*a*B*e)*_ + (d+e*x)^4/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/2*e^2*(2*b*B*d+A*b*e-_ + 3*a*B*e)*(d+e*x)^2/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+5*e^3*(b*d-a*e)*_ + (2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*log(a+b*x)/(b^7*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+5*e^4*(2*b*B*d+A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7 +--R +--R +--R (2) +--R 5 2 4 5 6 5 4 +--R (- 60A a b + 180B a b )e + (60A b - 300B a b )d e +--R + +--R 6 2 3 +--R 120B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (- 240A a b + 720B a b )e + (240A a b - 1200B a b )d e +--R + +--R 5 2 3 +--R 480B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 360A a b + 1080B a b )e + (360A a b - 1800B a b )d e +--R + +--R 2 4 2 3 +--R 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 720B a b)e + (240A a b - 1200B a b )d e +--R + +--R 3 3 2 3 +--R 480B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 4 2 2 3 +--R (- 60A a b + 180B a )e + (60A a b - 300B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 6B b e x + ((12A b - 36B a b )e + 60B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((185A a b - 555B a b )e + (- 125A b + 745B a b )d e - 160B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (500A a b - 1500B a b )e + (- 260A a b + 1780B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 120A b - 160B a b )d e - 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (570A a b - 1710B a b )e + (- 210A a b + 1770B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 180A a b + 120B a b )d e + (- 60A b - 180B a b )d e - 30B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (300A a b - 900B a b)e + (- 60A a b + 780B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 120A a b + 240B a b )d e + (- 40A a b - 120B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 20A b - 20B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 6 5 5 4 3 3 4 2 2 3 +--R (60A a b - 180B a )e + 120B a b d e + (- 30A a b + 90B a b )d e +--R + +--R 2 4 3 3 3 2 5 2 4 4 +--R (- 10A a b - 30B a b )d e + (- 5A a b - 5B a b )d e +--R + +--R 6 5 5 +--R (- 3A b - B a b )d +--R / +--R +------------------+ +--R 10 3 9 2 2 8 3 7 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 443 + +--S 444 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 764 +t0:=(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 764 +r0:=-1/4*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^4/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+B*(a+b*x)*(d+e*x)^5/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))-_ + 1/2*e*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^2/(b^4*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-1/3*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)^3/(b^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))-e^2*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)/(b^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*_ + log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((12A b - 60B a b )e + 48B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((48A a b - 240B a b )e + 192B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((72A a b - 360B a b )e + 288B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((48A a b - 240B a b)e + 192B a b d e )x + (12A a b - 60B a )e +--R + +--R 4 3 +--R 48B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 12B b e x + ((- 25A b + 125B a b )e - 40B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 52A a b + 260B a b )e + (- 48A b + 32B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 42A a b + 210B a b )e + (- 72A a b + 192B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 36A b - 108B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 12A a b + 60B a b)e + (- 48A a b + 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 24A a b - 72B a b )d e + (- 16A b - 16B a b )d e - 4B b d +--R * +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (- 12A a b + 60B a b)d e + (- 6A a b - 18B a b )d e +--R + +--R 4 2 3 3 5 4 4 +--R (- 4A a b - 4B a b )d e + (- 3A b - B a b )d +--R / +--R +------------------+ +--R 9 3 8 2 2 7 3 6 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 446 + +--S 447 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 764 +t0:=(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 448 + +--S 449 of 764 +r0:=-1/4*(A*b-a*B)*(a+b*x)*(d+e*x)^4/(b*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/2*B*e*(a+b*x)*(d+e*x)^2/(b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-1/3*B*(d+e*x)^3/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + B*e^2*(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e^3*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)),-1/4*B*(a+b*x)*_ + (d+e*x)^4/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+1/4*(B*d-A*e)*(a+b*x)*_ + (d+e*x)^4/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-1/2*B*e*(a+b*x)*_ + (d+e*x)^2/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/3*B*(d+e*x)^3/(b^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-B*e^2*(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+B*e^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R [ +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12B a b e - 12B b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 +--R (72B a b e - 72B a b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 5 4 4 3 +--R 12B a e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 4 5 3 4 +--R ((3A b - 25B a b )e + 22B b d e )x +--R + +--R 2 3 4 5 4 3 5 2 2 3 +--R (- 52B a b e + (12A b + 4B a b )d e + 36B b d e )x +--R + +--R 3 2 4 2 3 3 5 4 2 2 5 3 2 +--R (- 42B a b e - 30B a b d e + (18A b + 36B a b )d e + 18B b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 5 4 3 +--R - 12B a b e - 36B a b d e + 24B a b d e + (12A b + 8B a b )d e +--R + +--R 5 4 +--R 4B b d +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 5 4 4 +--R - 12B a b d e + 6B a b d e + 2B a b d e + (3A b + B a b )d +--R / +--R 8 9 3 2 7 8 2 3 6 2 7 +--R (12a b e - 12b d)x + (36a b e - 36a b d)x + (36a b e - 36a b d)x +--R + +--R 4 5 3 6 +--R 12a b e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R , +--R +--R 4 4 5 3 4 2 3 4 4 3 3 +--R (12B a b e - 12B b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 3 2 4 2 3 3 2 4 4 3 2 3 +--R (72B a b e - 72B a b d e )x + (48B a b e - 48B a b d e )x +--R + +--R 5 4 4 3 +--R 12B a e - 12B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 4 5 3 4 +--R ((3A b - 25B a b )e + 22B b d e )x +--R + +--R 2 3 4 5 4 3 5 2 2 3 +--R (- 52B a b e + (12A b + 4B a b )d e + 36B b d e )x +--R + +--R 3 2 4 2 3 3 5 4 2 2 5 3 2 +--R (- 42B a b e - 30B a b d e + (18A b + 36B a b )d e + 18B b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 5 4 3 +--R - 12B a b e - 36B a b d e + 24B a b d e + (12A b + 8B a b )d e +--R + +--R 5 4 +--R 4B b d +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 5 4 4 +--R - 12B a b d e + 6B a b d e + 2B a b d e + (3A b + B a b )d +--R / +--R 8 9 3 2 7 8 2 3 6 2 7 +--R (12a b e - 12b d)x + (36a b e - 36a b d)x + (36a b e - 36a b d)x +--R + +--R 4 5 3 6 +--R 12a b e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R ] +--R Type: Tuple(Expression(Integer)) +--E 449 + +--S 450 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 764 +t0:=(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 764 +r0:=-1/4*(A*b-a*B)*(a+b*x)*(d+e*x)^4/((b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/3*(B*d-A*e)*(d+e*x)^3/((b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 4 3 4 4 3 2 2 3 +--R ((A b + 3B a)e - 4B b d e )x + (4A a e + 8B a d e - 12B b d e )x +--R + +--R 3 2 2 3 2 +--R (12A a d e + (- 6A b + 6B a)d e - 12B b d e)x +--R + +--R 2 2 3 4 3 4 +--R (12A a d e - 8A b d e - 4B b d )x + 4A a d e + (- 3A b - B a)d +--R / +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (12a b e - 24a b d e + 12b d )x + (36a b e - 72a b d e + 36a b d )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (36a b e - 72a b d e + 36a b d )x + 12a e - 24a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 764 +t0:=(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 764 +r0:=1/4*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(a+b*x)/(b^3*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-1/2*B*(a+b*x)*(d+e*x)^2/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/3*(2*b*B*d-A*b*e-a*B*e)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R - 6B b e x + ((- 4A b - 4B a b)e - 4B b d)x + (- A a b - B a )e +--R + +--R 2 +--R (- 3A b - B a b)d +--R / +--R +------------------+ +--R 6 3 5 2 2 4 3 3 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 455 + +--S 456 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 456 + +)clear all + +--S 457 of 764 +t0:=(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 764 +r0:=-1/4*(A*b-a*B)*(a+b*x)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2))-_ + 1/3*B/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R - 4B b x - 3A b - B a +--R (2) ----------------------------------------------------------- +--R +------------------+ +--R 5 3 4 2 2 3 3 2 | 2 2 2 +--R (12b x + 36a b x + 36a b x + 12a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 458 + +--S 459 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 764 +t0:=(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 460 + +--S 461 of 764 +r0:=-1/4*(A*b-a*B)*(a+b*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/3*(-B*d+A*e)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/2*e*(B*d-A*e)*(a+b*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + e^2*(B*d-A*e)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(B*d-A*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*_ + (B*d-A*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 3 4 4 4 4 3 3 +--R (12A b e - 12B b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (72A a b e - 72B a b d e )x + (48A a b e - 48B a b d e )x +--R + +--R 4 4 4 3 +--R 12A a b e - 12B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 3 4 4 4 4 3 3 +--R (- 12A b e + 12B b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 2 3 4 2 3 3 2 3 2 4 3 2 3 +--R (- 72A a b e + 72B a b d e )x + (- 48A a b e + 48B a b d e )x +--R + +--R 4 4 4 3 +--R - 12A a b e + 12B a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 5 4 3 5 2 2 3 +--R (12A a b e + (- 12A b - 12B a b )d e + 12B b d e )x +--R + +--R 2 3 4 4 2 3 3 5 4 2 2 +--R 42A a b e + (- 48A a b - 42B a b )d e + (6A b + 48B a b )d e +--R + +--R 5 3 +--R - 6B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 2 3 3 2 3 4 2 3 2 2 +--R 52A a b e + (- 72A a b - 52B a b )d e + (24A a b + 72B a b )d e +--R + +--R 5 4 3 5 4 +--R (- 4A b - 24B a b )d e + 4B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (25A a b - 3B a )e + (- 48A a b - 10B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 5 4 4 +--R (36A a b + 18B a b )d e + (- 16A a b - 6B a b )d e + (3A b + B a b )d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 9 5 +--R - 12b d +--R * +--R 3 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 2 7 4 +--R 36a b e - 180a b d e + 360a b d e - 360a b d e + 180a b d e +--R + +--R 8 5 +--R - 36a b d +--R * +--R 2 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 3 6 4 +--R 36a b e - 180a b d e + 360a b d e - 360a b d e + 180a b d e +--R + +--R 2 7 5 +--R - 36a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 4 5 4 3 6 5 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 764 +t0:=(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 463 + +--S 464 of 764 +r0:=1/4*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2))+1/3*(-4*b*B*d+5*A*b*e-a*B*e)/((b*d-a*e)^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*e*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)/_ + ((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2*(4*b*B*d-5*A*b*e+_ + a*B*e)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+e^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/_ + ((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((- 60A b + 12B a b )e + 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 240A a b + 48B a b )e + (- 60A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 360A a b + 72B a b )e + (- 240A a b + 336B a b )d e +--R + +--R 4 2 3 +--R 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 240A a b + 48B a b)e + (- 360A a b + 264B a b )d e +--R + +--R 2 3 2 3 +--R 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 60A a b + 12B a )e + (- 240A a b + 96B a b)d e +--R + +--R 3 2 2 3 +--R 192B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 60A a b + 12B a )d e + 48B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 12B a b )e - 48B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((240A a b - 48B a b )e + (60A b - 204B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (360A a b - 72B a b )e + (240A a b - 336B a b )d e +--R + +--R 4 2 3 +--R - 192B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (240A a b - 48B a b)e + (360A a b - 264B a b )d e +--R + +--R 2 3 2 3 +--R - 288B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 3 2 2 3 +--R ((60A a b - 12B a )e + (240A a b - 96B a b)d e - 192B a b d e )x +--R + +--R 4 5 4 4 2 3 +--R (60A a b - 12B a )d e - 48B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 12B a b )e + (60A b + 36B a b )d e - 48B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 210A a b + 42B a b )e + (180A a b + 132B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (30A b - 150B a b )d e - 24B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 260A a b + 52B a b)e + (150A a b + 178B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b - 144B a b )d e + (- 10A b - 94B a b )d e + 8B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 125A a b + 25B a )e + (- 20A a b + 104B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 20B a b )d e + (- 40A a b - 136B a b )d e +--R + +--R 5 4 4 5 5 +--R (5A b + 31B a b )d e - 4B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 12A a e + (- 65A a b + 37B a )d e + (120A a b - 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 60A a b - 36B a b )d e + (20A a b + 8B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - B a b )d +--R / +--R 6 3 7 5 4 6 4 5 2 5 3 6 3 4 2 7 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 8 5 2 9 6 +--R - 72a b d e + 12b d e +--R * +--R 4 +--R x +--R + +--R 7 2 7 6 3 6 5 4 2 5 4 5 3 4 3 6 4 3 +--R 36a b e - 204a b d e + 468a b d e - 540a b d e + 300a b d e +--R + +--R 2 7 5 2 8 6 9 7 +--R - 36a b d e - 36a b d e + 12b d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 4 5 4 3 +--R 36a b e - 180a b d e + 324a b d e - 180a b d e - 180a b d e +--R + +--R 3 6 5 2 2 7 6 8 7 +--R 324a b d e - 180a b d e + 36a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 6 7 2 2 5 6 3 3 4 5 4 4 3 +--R 12a e - 36a b d e - 36a b d e + 300a b d e - 540a b d e +--R + +--R 4 5 5 2 3 6 6 2 7 7 +--R 468a b d e - 204a b d e + 36a b d +--R * +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 4 5 6 3 6 7 +--R - 72a b d e + 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 464 + +--S 465 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 764 +t0:=(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 764 +r0:=-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/4*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-5/12*(2*b*B*d-3*A*b*e+a*B*e)/_ + ((b*d-a*e)^3*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5/6*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)*(a+b*x)/((b*d-a*e)^4*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-5/2*e^2*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^5*(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-5*b*e^3*(2*b*B*d-3*A*b*e+a*B*e)*_ + (a+b*x)*log(a+b*x)/((b*d-a*e)^7*sqrt(a^2+2*a*b*x+b^2*x^2))+5*b*e^3*_ + (2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^7*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+5*e^4*(2*b*B*d-3*A*b*e+a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/((b*d-a*e)^7*(d+e*x)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (720A a b - 240B a b )e + (360A b - 600B a b )d e +--R + +--R 6 2 4 +--R - 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (1080A a b - 360B a b )e + (1440A a b - 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (180A b - 1020B a b )d e - 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (720A a b - 240B a b )e + (2160A a b - 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (720A a b - 1680B a b )d e - 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (180A a b - 60B a b)e + (1440A a b - 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (1080A a b - 1320B a b )d e - 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (360A a b - 120B a b)d e + (720A a b - 480B a b )d e +--R + +--R 3 3 3 3 +--R - 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (180A a b - 60B a b)d e - 120B a b d e +--R * +--R log(e x + d) +--R + +--R 6 5 6 6 5 6 +--R ((- 180A b + 60B a b )e + 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (- 720A a b + 240B a b )e + (- 360A b + 600B a b )d e +--R + +--R 6 2 4 +--R 240B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (- 1080A a b + 360B a b )e + (- 1440A a b + 1200B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 180A b + 1020B a b )d e + 120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 720A a b + 240B a b )e + (- 2160A a b + 1200B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (- 720A a b + 1680B a b )d e + 480B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 180A a b + 60B a b)e + (- 1440A a b + 600B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (- 1080A a b + 1320B a b )d e + 720B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 2 4 +--R (- 360A a b + 120B a b)d e + (- 720A a b + 480B a b )d e +--R + +--R 3 3 3 3 +--R 480B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (- 180A a b + 60B a b)d e + 120B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 6 +--R ((180A b - 60B a b )e - 120B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 5 +--R ((900A a b - 300B a b )e + (180A b - 660B a b )d e - 120B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (1710A a b - 570B a b )e + (1080A a b - 1500B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 90A b - 690B a b )d e + 60B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (1500A a b - 500B a b )e + (2340A a b - 1780B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (- 180A a b - 1500B a b )d e + (- 60A b + 140B a b )d e +--R + +--R 6 4 2 +--R 40B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (555A a b - 185B a b)e + (2280A a b - 1130B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (90A a b - 1550B a b )d e + (- 240A a b + 20B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (15A b + 155B a b )d e - 10B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (36A a b - 12B a )e + (930A a b - 334B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (420A a b - 760B a b )d e + (- 360A a b - 160B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (60A a b + 220B a b )d e + (- 6A b - 38B a b )d e + 4B b d +--R * +--R x +--R + +--R 6 6 5 6 5 4 2 5 2 4 +--R - 6A a e + (72A a b - 6B a )d e + (285A a b - 185B a b)d e +--R + +--R 3 3 4 2 3 3 2 4 3 3 4 2 +--R (- 240A a b - 40B a b )d e + (90A a b + 60B a b )d e +--R + +--R 5 2 4 5 6 5 6 +--R (- 24A a b - 10B a b )d e + (3A b + B a b )d +--R / +--R 7 3 9 6 4 8 5 5 2 7 4 6 3 6 3 7 4 5 +--R 12a b e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 2 8 5 4 9 6 3 10 7 2 +--R - 252a b d e + 84a b d e - 12b d e +--R * +--R 5 +--R x +--R + +--R 8 2 9 7 3 8 6 4 2 7 5 5 3 6 4 6 4 5 +--R 36a b e - 228a b d e + 588a b d e - 756a b d e + 420a b d e +--R + +--R 3 7 5 4 2 8 6 3 9 7 2 10 8 +--R 84a b d e - 252a b d e + 132a b d e - 24b d e +--R * +--R 4 +--R x +--R + +--R 9 9 8 2 8 7 3 2 7 6 4 3 6 5 5 4 5 +--R 36a b e - 180a b d e + 264a b d e + 168a b d e - 1008a b d e +--R + +--R 4 6 5 4 3 7 6 3 2 8 7 2 9 8 10 9 +--R 1344a b d e - 840a b d e + 216a b d e + 12a b d e - 12b d +--R * +--R 3 +--R x +--R + +--R 10 9 9 8 8 2 2 7 7 3 3 6 6 4 4 5 +--R 12a e - 12a b d e - 216a b d e + 840a b d e - 1344a b d e +--R + +--R 5 5 5 4 4 6 6 3 3 7 7 2 2 8 8 9 9 +--R 1008a b d e - 168a b d e - 264a b d e + 180a b d e - 36a b d +--R * +--R 2 +--R x +--R + +--R 10 8 9 2 7 8 2 3 6 7 3 4 5 6 4 5 4 +--R 24a d e - 132a b d e + 252a b d e - 84a b d e - 420a b d e +--R + +--R 5 5 6 3 4 6 7 2 3 7 8 2 8 9 +--R 756a b d e - 588a b d e + 228a b d e - 36a b d +--R * +--R x +--R + +--R 10 2 7 9 3 6 8 2 4 5 7 3 5 4 6 4 6 3 +--R 12a d e - 84a b d e + 252a b d e - 420a b d e + 420a b d e +--R + +--R 5 5 7 2 4 6 8 3 7 9 +--R - 252a b d e + 84a b d e - 12a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 469 + +--S 470 of 764 +r0:=-2/9*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(9/2)/e^4+2/11*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^4-2/13*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(13/2)/e^4+2/15*b^2*B*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 2 7 7 2 7 2 6 6 +--R 858B b e x + ((990A b + 1980B a b)e + 3036B b d e )x +--R + +--R 2 7 2 6 +--R (2340A a b + 1170B a )e + (3600A b + 7200B a b)d e +--R + +--R 2 2 5 +--R 3708B b d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 1430A a e + (8840A a b + 4420B a )d e +--R + +--R 2 2 5 2 3 4 +--R (4580A b + 9160B a b)d e + 1600B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 5720A a d e + (11960A a b + 5980B a )d e +--R + +--R 2 3 4 2 4 3 +--R (2120A b + 4240B a b)d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 8580A a d e + (6240A a b + 3120B a )d e + (30A b + 60B a b)d e +--R + +--R 2 5 2 +--R - 12B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 5720A a d e + (260A a b + 130B a )d e + (- 40A b - 80B a b)d e +--R + +--R 2 6 +--R 16B b d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 1430A a d e + (- 520A a b - 260B a )d e + (80A b + 160B a b)d e +--R + +--R 2 7 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 470 + +--S 471 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 471 + +)clear all + +--S 472 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 472 + +--S 473 of 764 +r0:=-2/7*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(7/2)/e^4+2/9*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^4-2/11*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(11/2)/e^4+2/13*b^2*B*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 1386B b e x + ((1638A b + 3276B a b)e + 3402B b d e )x +--R + +--R 2 6 2 5 +--R (4004A a b + 2002B a )e + (4186A b + 8372B a b)d e +--R + +--R 2 2 4 +--R 2226B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 2574A a e + (10868A a b + 5434B a )d e +--R + +--R 2 2 4 2 3 3 +--R (2938A b + 5876B a b)d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 7722A a d e + (8580A a b + 4290B a )d e + (78A b + 156B a b)d e +--R + +--R 2 4 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R 7722A a d e + (572A a b + 286B a )d e +--R + +--R 2 4 2 2 5 +--R (- 104A b - 208B a b)d e + 48B b d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 2574A a d e + (- 1144A a b - 572B a )d e + (208A b + 416B a b)d e +--R + +--R 2 6 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 473 + +--S 474 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 474 + +)clear all + +--S 475 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 475 + +--S 476 of 764 +r0:=-2/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^4-2/9*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(9/2)/e^4+2/11*b^2*B*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B b e x + ((770A b + 1540B a b)e + 840B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A a b + 990B a )e + (1100A b + 2200B a b)d e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 1386A a e + (3168A a b + 1584B a )d e + (66A b + 132B a b)d e +--R + +--R 2 3 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 2772A a d e + (396A a b + 198B a )d e + (- 88A b - 176B a b)d e +--R + +--R 2 4 +--R 48B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 1386A a d e + (- 792A a b - 396B a )d e + (176A b + 352B a b)d e +--R + +--R 2 5 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 476 + +--S 477 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--R Type: Expression(Integer) +--E 478 + +--S 479 of 764 +r0:=-2/3*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^4-2/7*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)*(d+e*x)^(7/2)/e^4+2/9*b^2*B*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 2 4 4 2 4 2 3 3 +--R 70B b e x + ((90A b + 180B a b)e + 10B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((252A a b + 126B a )e + (18A b + 36B a b)d e - 12B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 210A a e + (84A a b + 42B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 16B b d e +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 210A a d e + (- 168A a b - 84B a )d e + (48A b + 96B a b)d e +--R + +--R 2 4 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 479 + +--S 480 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 481 + +--S 482 of 764 +r0:=2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^4-2/5*b*_ + (3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^4+2/7*b^2*B*(d+e*x)^(7/2)/e^4-_ + 2*(b*d-a*e)^2*(B*d-A*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((42A b + 84B a b)e - 36B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((140A a b + 70B a )e + (- 56A b - 112B a b)d e + 48B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 210A a e + (- 280A a b - 140B a )d e + (112A b + 224B a b)d e +--R + +--R 2 3 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 482 + +--S 483 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 484 + +--S 485 of 764 +r0:=-2/3*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^4+2/5*b^2*B*_ + (d+e*x)^(5/2)/e^4+2*(b*d-a*e)^2*(B*d-A*e)/(e^4*sqrt(d+e*x))+_ + 2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((10A b + 20B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((60A a b + 30B a )e + (- 40A b - 80B a b)d e + 48B b d e)x - 30A a e +--R + +--R 2 2 2 2 2 3 +--R (120A a b + 60B a )d e + (- 80A b - 160B a b)d e + 96B b d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 485 + +--S 486 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 486 + +)clear all + +--S 487 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 487 + +--S 488 of 764 +r0:=2/3*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(3/2))+2/3*b^2*B*_ + (d+e*x)^(3/2)/e^4-2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*_ + sqrt(d+e*x))-2*b*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((6A b + 12B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12A a b - 6B a )e + (24A b + 48B a b)d e - 48B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 8A a b - 4B a )d e + (16A b + 32B a b)d e - 32B b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 488 + +--S 489 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 489 + +)clear all + +--S 490 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 490 + +--S 491 of 764 +r0:=2/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(5/2))-2/3*(b*d-a*e)*_ + (3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^(3/2))+2*b*(3*b*B*d-A*b*e-_ + 2*a*B*e)/(e^4*sqrt(d+e*x))+2*b^2*B*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((- 30A b - 60B a b)e + 180B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 20A a b - 10B a )e + (- 40A b - 80B a b)d e + 240B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 6A a e + (- 8A a b - 4B a )d e + (- 16A b - 32B a b)d e + 96B b d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 491 + +--S 492 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 493 + +--S 494 of 764 +r0:=-2/9*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(9/2)/e^6+2/11*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^6-4/13*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^6+4/15*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^6-2/17*b^3*(5*b*B*d-_ + A*b*e-4*a*B*e)*(d+e*x)^(17/2)/e^6+2/19*b^4*B*(d+e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 4 9 9 4 3 9 4 8 8 +--R 218790B b e x + ((244530A b + 978120B a b )e + 746460B b d e )x +--R + +--R 3 2 2 9 +--R (1108536A a b + 1662804B a b )e +--R + +--R 4 3 8 4 2 7 +--R (847704A b + 3390816B a b )d e + 866580B b d e +--R * +--R 7 +--R x +--R + +--R 2 2 3 9 +--R (1918620A a b + 1279080B a b)e +--R + +--R 3 2 2 8 +--R (3922512A a b + 5883768B a b )d e +--R + +--R 4 3 2 7 4 3 6 +--R (1005708A b + 4022832B a b )d e + 345840B b d e +--R * +--R 6 +--R x +--R + +--R 3 4 9 2 2 3 8 +--R (1511640A a b + 377910B a )e + (6976800A a b + 4651200B a b)d e +--R + +--R 3 2 2 2 7 +--R (4790736A a b + 7186104B a b )d e +--R + +--R 4 3 3 6 4 4 5 +--R (414504A b + 1658016B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 4 9 3 4 8 +--R 461890A a e + (5710640A a b + 1427660B a )d e +--R + +--R 2 2 3 2 7 +--R (8876040A a b + 5917360B a b)d e +--R + +--R 3 2 2 3 6 4 3 4 5 +--R (2067200A a b + 3100800B a b )d e + (1330A b + 5320B a b )d e +--R + +--R 4 5 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 2 7 +--R 1847560A a d e + (7726160A a b + 1931540B a )d e +--R + +--R 2 2 3 3 6 +--R (4108560A a b + 2739040B a b)d e +--R + +--R 3 2 2 4 5 4 3 5 4 +--R (12920A a b + 19380B a b )d e + (- 1520A b - 6080B a b )d e +--R + +--R 4 6 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 7 3 4 3 6 +--R 2771340A a d e + (4031040A a b + 1007760B a )d e +--R + +--R 2 2 3 4 5 3 2 2 5 4 +--R (58140A a b + 38760B a b)d e + (- 15504A a b - 23256B a b )d e +--R + +--R 4 3 6 3 4 7 2 +--R (1824A b + 7296B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 3 6 3 4 4 5 +--R 1847560A a d e + (167960A a b + 41990B a )d e +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (- 77520A a b - 51680B a b)d e + (20672A a b + 31008B a b )d e +--R + +--R 4 3 7 2 4 8 +--R (- 2432A b - 9728B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 4 5 3 4 5 4 +--R 461890A a d e + (- 335920A a b - 83980B a )d e +--R + +--R 2 2 3 6 3 3 2 2 7 2 +--R (155040A a b + 103360B a b)d e + (- 41344A a b - 62016B a b )d e +--R + +--R 4 3 8 4 9 +--R (4864A b + 19456B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 2078505e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 496 + +--S 497 of 764 +r0:=-2/7*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(7/2)/e^6+2/9*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^6-4/11*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(11/2)/e^6+4/13*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(13/2)/e^6-2/15*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(15/2)/e^6+2/17*b^4*B*(d+e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 4 8 8 4 3 8 4 7 7 +--R 90090B b e x + ((102102A b + 408408B a b )e + 210210B b d e )x +--R + +--R 3 2 2 8 4 3 7 +--R (471240A a b + 706860B a b )e + (243474A b + 973896B a b )d e +--R + +--R 4 2 6 +--R 127050B b d e +--R * +--R 6 +--R x +--R + +--R 2 2 3 8 +--R (835380A a b + 556920B a b)e +--R + +--R 3 2 2 7 +--R (1156680A a b + 1735020B a b )d e +--R + +--R 4 3 2 6 4 3 5 +--R (152082A b + 608328B a b )d e + 630B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 8 2 2 3 7 +--R (680680A a b + 170170B a )e + (2134860A a b + 1423240B a b)d e +--R + +--R 3 2 2 2 6 4 3 3 5 +--R (756840A a b + 1135260B a b )d e + (1190A b + 4760B a b )d e +--R + +--R 4 4 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 4 8 3 4 7 +--R 218790A a e + (1847560A a b + 461890B a )d e +--R + +--R 2 2 3 2 6 3 2 2 3 5 +--R (1498380A a b + 998920B a b)d e + (10200A a b + 15300B a b )d e +--R + +--R 4 3 4 4 4 5 3 +--R (- 1360A b - 5440B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 2 6 +--R 656370A a d e + (1458600A a b + 364650B a )d e +--R + +--R 2 2 3 3 5 3 2 2 4 4 +--R (39780A a b + 26520B a b)d e + (- 12240A a b - 18360B a b )d e +--R + +--R 4 3 5 3 4 6 2 +--R (1632A b + 6528B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 6 3 4 3 5 +--R 656370A a d e + (97240A a b + 24310B a )d e +--R + +--R 2 2 3 4 4 3 2 2 5 3 +--R (- 53040A a b - 35360B a b)d e + (16320A a b + 24480B a b )d e +--R + +--R 4 3 6 2 4 7 +--R (- 2176A b - 8704B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 3 5 3 4 4 4 +--R 218790A a d e + (- 194480A a b - 48620B a )d e +--R + +--R 2 2 3 5 3 3 2 2 6 2 +--R (106080A a b + 70720B a b)d e + (- 32640A a b - 48960B a b )d e +--R + +--R 4 3 7 4 8 +--R (4352A b + 17408B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 765765e +--R Type: Expression(Integer) +--E 497 + +--S 498 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 499 + +--S 500 of 764 +r0:=-2/5*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(5/2)/e^6+2/7*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^6-4/9*b*(b*d-a*e)^2*(5*b*B*d-_ + 3*A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^6+4/11*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-_ + 3*a*B*e)*(d+e*x)^(11/2)/e^6-2/13*b^3*(5*b*B*d-A*b*e-4*a*B*e)*_ + (d+e*x)^(13/2)/e^6+2/15*b^4*B*(d+e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 4 7 7 4 3 7 4 6 6 +--R 6006B b e x + ((6930A b + 27720B a b )e + 7392B b d e )x +--R + +--R 3 2 2 7 4 3 6 +--R (32760A a b + 49140B a b )e + (8820A b + 35280B a b )d e +--R + +--R 4 2 5 +--R 126B b d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 3 2 2 6 +--R (60060A a b + 40040B a b)e + (43680A a b + 65520B a b )d e +--R + +--R 4 3 2 5 4 3 4 +--R (210A b + 840B a b )d e - 140B b d e +--R * +--R 4 +--R x +--R + +--R 3 4 7 2 2 3 6 +--R (51480A a b + 12870B a )e + (85800A a b + 57200B a b)d e +--R + +--R 3 2 2 2 5 4 3 3 4 +--R (1560A a b + 2340B a b )d e + (- 240A b - 960B a b )d e +--R + +--R 4 4 3 +--R 160B b d e +--R * +--R 3 +--R x +--R + +--R 4 7 3 4 6 +--R 18018A a e + (82368A a b + 20592B a )d e +--R + +--R 2 2 3 2 5 3 2 2 3 4 +--R (5148A a b + 3432B a b)d e + (- 1872A a b - 2808B a b )d e +--R + +--R 4 3 4 3 4 5 2 +--R (288A b + 1152B a b )d e - 192B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 2 5 +--R 36036A a d e + (10296A a b + 2574B a )d e +--R + +--R 2 2 3 3 4 3 2 2 4 3 +--R (- 6864A a b - 4576B a b)d e + (2496A a b + 3744B a b )d e +--R + +--R 4 3 5 2 4 6 +--R (- 384A b - 1536B a b )d e + 256B b d e +--R * +--R x +--R + +--R 4 2 5 3 4 3 4 +--R 18018A a d e + (- 20592A a b - 5148B a )d e +--R + +--R 2 2 3 4 3 3 2 2 5 2 +--R (13728A a b + 9152B a b)d e + (- 4992A a b - 7488B a b )d e +--R + +--R 4 3 6 4 7 +--R (768A b + 3072B a b )d e - 512B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 500 + +--S 501 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 501 + +)clear all + +--S 502 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 502 + +--S 503 of 764 +r0:=-2/3*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(3/2)/e^6+2/5*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^6-4/7*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^6+4/9*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^6-2/11*b^3*_ + (5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(11/2)/e^6+2/13*b^4*B*(d+e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 4 6 6 4 3 6 4 5 5 +--R 6930B b e x + ((8190A b + 32760B a b )e + 630B b d e )x +--R + +--R 3 2 2 6 4 3 5 +--R (40040A a b + 60060B a b )e + (910A b + 3640B a b )d e +--R + +--R 4 2 4 +--R - 700B b d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 3 2 2 5 +--R (77220A a b + 51480B a b)e + (5720A a b + 8580B a b )d e +--R + +--R 4 3 2 4 4 3 3 +--R (- 1040A b - 4160B a b )d e + 800B b d e +--R * +--R 3 +--R x +--R + +--R 3 4 6 2 2 3 5 +--R (72072A a b + 18018B a )e + (15444A a b + 10296B a b)d e +--R + +--R 3 2 2 2 4 4 3 3 3 +--R (- 6864A a b - 10296B a b )d e + (1248A b + 4992B a b )d e +--R + +--R 4 4 2 +--R - 960B b d e +--R * +--R 2 +--R x +--R + +--R 4 6 3 4 5 +--R 30030A a e + (24024A a b + 6006B a )d e +--R + +--R 2 2 3 2 4 3 2 2 3 3 +--R (- 20592A a b - 13728B a b)d e + (9152A a b + 13728B a b )d e +--R + +--R 4 3 4 2 4 5 +--R (- 1664A b - 6656B a b )d e + 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 2 4 +--R 30030A a d e + (- 48048A a b - 12012B a )d e +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (41184A a b + 27456B a b)d e + (- 18304A a b - 27456B a b )d e +--R + +--R 4 3 5 4 6 +--R (3328A b + 13312B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 503 + +--S 504 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 504 + +)clear all + +--S 505 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 505 + +--S 506 of 764 +r0:=2/3*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^6-4/5*b*_ + (b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^6+4/7*b^2*_ + (b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^6-2/9*b^3*_ + (5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(9/2)/e^6+2/11*b^4*B*(d+e*x)^(11/2)/e^6-_ + 2*(b*d-a*e)^4*(B*d-A*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 630B b e x + ((770A b + 3080B a b )e - 700B b d e )x +--R + +--R 3 2 2 5 4 3 4 +--R (3960A a b + 5940B a b )e + (- 880A b - 3520B a b )d e +--R + +--R 4 2 3 +--R 800B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 2 2 4 +--R (8316A a b + 5544B a b)e + (- 4752A a b - 7128B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (1056A b + 4224B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (9240A a b + 2310B a )e + (- 11088A a b - 7392B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (6336A a b + 9504B a b )d e + (- 1408A b - 5632B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R 6930A a e + (- 18480A a b - 4620B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (22176A a b + 14784B a b)d e + (- 12672A a b - 19008B a b )d e +--R + +--R 4 3 4 4 5 +--R (2816A b + 11264B a b )d e - 2560B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 3465e +--R Type: Expression(Integer) +--E 506 + +--S 507 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 508 + +--S 509 of 764 +r0:=-4/3*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^6+_ + 4/5*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^6-_ + 2/7*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(7/2)/e^6+2/9*b^4*B*_ + (d+e*x)^(9/2)/e^6+2*(b*d-a*e)^4*(B*d-A*e)/(e^6*sqrt(d+e*x))+_ + 2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 70B b e x + ((90A b + 360B a b )e - 100B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((504A a b + 756B a b )e + (- 144A b - 576B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1008A a b - 1512B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (288A b + 1152B a b )d e - 320B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (2520A a b + 630B a )e + (- 5040A a b - 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (4032A a b + 6048B a b )d e + (- 1152A b - 4608B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 +--R - 630A a e + (5040A a b + 1260B a )d e +--R + +--R 2 2 3 2 3 3 2 2 3 2 +--R (- 10080A a b - 6720B a b)d e + (8064A a b + 12096B a b )d e +--R + +--R 4 3 4 4 5 +--R (- 2304A b - 9216B a b )d e + 2560B b d +--R / +--R 6 +-------+ +--R 315e \|e x + d +--R Type: Expression(Integer) +--E 509 + +--S 510 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 511 + +--S 512 of 764 +r0:=2/3*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^(3/2))+4/3*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^6-2/5*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(5/2)/e^6+2/7*b^4*B*(d+e*x)^(7/2)/e^6-2*(b*d-_ + a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*sqrt(d+e*x))-4*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 30B b e x + ((42A b + 168B a b )e - 60B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((280A a b + 420B a b )e + (- 112A b - 448B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (1260A a b + 840B a b)e + (- 1680A a b - 2520B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (672A b + 2688B a b )d e - 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 840A a b - 210B a )e + (5040A a b + 3360B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (- 6720A a b - 10080B a b )d e + (2688A b + 10752B a b )d e +--R + +--R 4 4 +--R - 3840B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 70A a e + (- 560A a b - 140B a )d e + (3360A a b + 2240B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (- 4480A a b - 6720B a b )d e + (1792A b + 7168B a b )d e - 2560B b d +--R / +--R 7 6 +-------+ +--R (105e x + 105d e )\|e x + d +--R Type: Expression(Integer) +--E 512 + +--S 513 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 514 + +--S 515 of 764 +r0:=2/5*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^(5/2))-2/3*(b*d-a*e)^3*_ + (5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^(3/2))-2/3*b^3*(5*b*B*d-A*b*e-_ + 4*a*B*e)*(d+e*x)^(3/2)/e^6+2/5*b^4*B*(d+e*x)^(5/2)/e^6+4*b*(b*d-a*e)^2*_ + (5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*sqrt(d+e*x))+4*b^2*(b*d-a*e)*_ + (5*b*B*d-2*A*b*e-3*a*B*e)*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 5 4 3 5 4 4 4 +--R 6B b e x + ((10A b + 40B a b )e - 20B b d e )x +--R + +--R 3 2 2 5 4 3 4 4 2 3 3 +--R ((120A a b + 180B a b )e + (- 80A b - 320B a b )d e + 160B b d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 180A a b - 120B a b)e + (720A a b + 1080B a b )d e +--R + +--R 4 3 2 3 4 3 2 +--R (- 480A b - 1920B a b )d e + 960B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (- 40A a b - 10B a )e + (- 240A a b - 160B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (960A a b + 1440B a b )d e + (- 640A b - 2560B a b )d e +--R + +--R 4 4 +--R 1280B b d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 6A a e + (- 16A a b - 4B a )d e + (- 96A a b - 64B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (384A a b + 576B a b )d e + (- 256A b - 1024B a b )d e + 512B b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 515 + +--S 516 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 516 + +)clear all + +--S 517 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 6 3 10 6 5 3 6 2 9 +--R B b e x + ((A b + 6B a b )e + 3B b d e )x +--R + +--R 5 2 4 3 6 5 2 6 2 8 +--R ((6A a b + 15B a b )e + (3A b + 18B a b )d e + 3B b d e)x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (15A a b + 20B a b )e + (18A a b + 45B a b )d e +--R + +--R 6 5 2 6 3 +--R (3A b + 18B a b )d e + B b d +--R * +--R 7 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (20A a b + 15B a b )e + (45A a b + 60B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (18A a b + 45B a b )d e + (A b + 6B a b )d +--R * +--R 6 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (15A a b + 6B a b)e + (60A a b + 45B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (45A a b + 60B a b )d e + (6A a b + 15B a b )d +--R * +--R 5 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (6A a b + B a )e + (45A a b + 18B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (60A a b + 45B a b )d e + (15A a b + 20B a b )d +--R * +--R 4 +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R A a e + (18A a b + 3B a )d e + (45A a b + 18B a b)d e +--R + +--R 3 3 4 2 3 +--R (20A a b + 15B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 5 6 2 4 2 5 3 2 +--R (3A a d e + (18A a b + 3B a )d e + (15A a b + 6B a b)d )x +--R + +--R 6 2 5 6 3 6 3 +--R (3A a d e + (6A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 517 + +--S 518 of 764 +r0:=-2/9*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(9/2)/e^8+2/11*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^8-6/13*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^8+2/3*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^8-10/17*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(17/2)/e^8+6/19*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(19/2)/e^8-2/21*b^5*(7*b*B*d-A*b*e-_ + 6*a*B*e)*(d+e*x)^(21/2)/e^8+2/23*b^6*B*(d+e*x)^(23/2)/e^8 +--R +--R +--R (2) +--R 6 11 11 +--R 5819814B b e x +--R + +--R 6 5 11 6 10 10 +--R ((6374082A b + 38244492B a b )e + 19399380B b d e )x +--R + +--R 5 2 4 11 +--R (42270228A a b + 105675570B a b )e +--R + +--R 6 5 10 6 2 9 +--R (21470592A b + 128823552B a b )d e + 21849828B b d e +--R * +--R 9 +--R x +--R + +--R 2 4 3 3 11 +--R (118107990A a b + 157477320B a b )e +--R + +--R 5 2 4 10 +--R (144216072A a b + 360540180B a b )d e +--R + +--R 6 5 2 9 6 3 8 +--R (24509628A b + 147057768B a b )d e + 8360352B b d e +--R * +--R 8 +--R x +--R + +--R 3 3 4 2 11 +--R (178474296A a b + 133855722B a b )e +--R + +--R 2 4 3 3 10 +--R (409441032A a b + 545921376B a b )d e +--R + +--R 5 2 4 2 9 +--R (167423256A a b + 418558140B a b )d e +--R + +--R 6 5 3 8 6 4 7 +--R (9551256A b + 57307536B a b )d e + 6006B b d e +--R * +--R 7 +--R x +--R + +--R 4 2 5 11 +--R (154448910A a b + 61779564B a b)e +--R + +--R 3 3 4 2 10 +--R (631524432A a b + 473643324B a b )d e +--R + +--R 2 4 3 3 2 9 +--R (485756964A a b + 647675952B a b )d e +--R + +--R 5 2 4 3 8 +--R (66816288A a b + 167040720B a b )d e +--R + +--R 6 5 4 7 6 5 6 +--R (10626A b + 63756B a b )d e - 6468B b d e +--R * +--R 6 +--R x +--R + +--R 5 6 11 +--R (73012212A a b + 12168702B a )e +--R + +--R 4 2 5 10 +--R (561632400A a b + 224652960B a b)d e +--R + +--R 3 3 4 2 2 9 +--R (771308496A a b + 578481372B a b )d e +--R + +--R 2 4 3 3 3 8 +--R (200205432A a b + 266940576B a b )d e +--R + +--R 5 2 4 4 7 6 5 5 6 +--R (121716A a b + 304290B a b )d e + (- 11592A b - 69552B a b )d e +--R + +--R 6 6 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 6 11 5 6 10 +--R 14872858A a e + (275823912A a b + 45970652B a )d e +--R + +--R 4 2 5 2 9 +--R (714521220A a b + 285808488B a b)d e +--R + +--R 3 3 4 2 3 8 +--R (332819200A a b + 249614400B a b )d e +--R + +--R 2 4 3 3 4 7 +--R (642390A a b + 856520B a b )d e +--R + +--R 5 2 4 5 6 6 5 6 5 +--R (- 135240A a b - 338100B a b )d e + (12880A b + 77280B a b )d e +--R + +--R 6 7 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 6 10 5 6 2 9 +--R 59491432A a d e + (373173528A a b + 62195588B a )d e +--R + +--R 4 2 5 3 8 +--R (330739080A a b + 132295632B a b)d e +--R + +--R 3 3 4 2 4 7 +--R (2080120A a b + 1560090B a b )d e +--R + +--R 2 4 3 3 5 6 +--R (- 734160A a b - 978880B a b )d e +--R + +--R 5 2 4 6 5 6 5 7 4 +--R (154560A a b + 386400B a b )d e + (- 14720A b - 88320B a b )d e +--R + +--R 6 8 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 6 2 9 5 6 3 8 +--R 89237148A a d e + (194699232A a b + 32449872B a )d e +--R + +--R 4 2 5 4 7 +--R (4680270A a b + 1872108B a b)d e +--R + +--R 3 3 4 2 5 6 +--R (- 2496144A a b - 1872108B a b )d e +--R + +--R 2 4 3 3 6 5 +--R (880992A a b + 1174656B a b )d e +--R + +--R 5 2 4 7 4 +--R (- 185472A a b - 463680B a b )d e +--R + +--R 6 5 8 3 6 9 2 +--R (17664A b + 105984B a b )d e - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 6 3 8 5 6 4 7 +--R 59491432A a d e + (8112468A a b + 1352078B a )d e +--R + +--R 4 2 5 5 6 +--R (- 6240360A a b - 2496144B a b)d e +--R + +--R 3 3 4 2 6 5 +--R (3328192A a b + 2496144B a b )d e +--R + +--R 2 4 3 3 7 4 +--R (- 1174656A a b - 1566208B a b )d e +--R + +--R 5 2 4 8 3 +--R (247296A a b + 618240B a b )d e +--R + +--R 6 5 9 2 6 10 +--R (- 23552A b - 141312B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 4 7 5 6 5 6 +--R 14872858A a d e + (- 16224936A a b - 2704156B a )d e +--R + +--R 4 2 5 6 5 +--R (12480720A a b + 4992288B a b)d e +--R + +--R 3 3 4 2 7 4 +--R (- 6656384A a b - 4992288B a b )d e +--R + +--R 2 4 3 3 8 3 +--R (2349312A a b + 3132416B a b )d e +--R + +--R 5 2 4 9 2 6 5 10 +--R (- 494592A a b - 1236480B a b )d e + (47104A b + 282624B a b )d e +--R + +--R 6 11 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 66927861e +--R Type: Expression(Integer) +--E 518 + +--S 519 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 519 + +)clear all + 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15B a b )e + (A b + 6B a b )d)x +--R + +--R 2 4 3 3 5 2 4 5 +--R ((15A a b + 20B a b )e + (6A a b + 15B a b )d)x +--R + +--R 3 3 4 2 2 4 3 3 4 +--R ((20A a b + 15B a b )e + (15A a b + 20B a b )d)x +--R + +--R 4 2 5 3 3 4 2 3 +--R ((15A a b + 6B a b)e + (20A a b + 15B a b )d)x +--R + +--R 5 6 4 2 5 2 6 5 6 +--R ((6A a b + B a )e + (15A a b + 6B a b)d)x + (A a e + (6A a b + B a )d)x +--R + +--R 6 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 523 + +--S 524 of 764 +r0:=-2/5*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(5/2)/e^8+2/7*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^8-2/3*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^8+10/11*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(11/2)/e^8-10/13*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(13/2)/e^8+2/5*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(15/2)/e^8-2/17*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(17/2)/e^8+2/19*b^6*B*(d+e*x)^(19/2)/e^8 +--R +--R +--R (2) +--R 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63840B a b )d e +--R + +--R 6 5 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 5 6 9 +--R (8314020A a b + 1385670B a )e +--R + +--R 4 2 5 8 +--R (23094500A a b + 9237800B a b)d e +--R + +--R 3 3 4 2 2 7 +--R (839800A a b + 629850B a b )d e +--R + +--R 2 4 3 3 3 6 +--R (- 387600A a b - 516800B a b )d e +--R + +--R 5 2 4 4 5 6 5 5 4 +--R (103360A a b + 258400B a b )d e + (- 12160A b - 72960B a b )d e +--R + +--R 6 6 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 6 9 5 6 8 +--R 1939938A a e + (13302432A a b + 2217072B a )d e +--R + +--R 4 2 5 2 7 +--R (1385670A a b + 554268B a b)d e +--R + +--R 3 3 4 2 3 6 +--R (- 1007760A a b - 755820B a b )d e +--R + +--R 2 4 3 3 4 5 +--R (465120A a b + 620160B a b )d e +--R + +--R 5 2 4 5 4 6 5 6 3 +--R (- 124032A a b - 310080B a b )d e + (14592A b + 87552B a b )d e +--R + +--R 6 7 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 6 8 5 6 2 7 +--R 3879876A a d e + (1662804A a b + 277134B a )d e +--R + +--R 4 2 5 3 6 +--R (- 1847560A a b - 739024B a b)d e +--R + +--R 3 3 4 2 4 5 +--R (1343680A a b + 1007760B a b )d e +--R + +--R 2 4 3 3 5 4 +--R (- 620160A a b - 826880B a b )d e +--R + +--R 5 2 4 6 3 +--R (165376A a b + 413440B a b )d e +--R + +--R 6 5 7 2 6 8 +--R (- 19456A b - 116736B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 2 7 5 6 3 6 +--R 1939938A a d e + (- 3325608A a b - 554268B a )d e +--R + +--R 4 2 5 4 5 +--R (3695120A a b + 1478048B a b)d e +--R + +--R 3 3 4 2 5 4 +--R (- 2687360A a b - 2015520B a b )d e +--R + +--R 2 4 3 3 6 3 +--R (1240320A a b + 1653760B a b )d e +--R + +--R 5 2 4 7 2 6 5 8 +--R (- 330752A a b - 826880B a b )d e + (38912A b + 233472B a b )d e +--R + +--R 6 9 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 4849845e +--R Type: Expression(Integer) +--E 524 + +--S 525 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 526 + +--S 527 of 764 +r0:=-2/3*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(3/2)/e^8+2/5*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^8-6/7*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^8+10/9*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^8-10/11*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(11/2)/e^8+6/13*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(13/2)/e^8-2/15*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(15/2)/e^8+2/17*b^6*B*(d+e*x)^(17/2)/e^8 +--R +--R +--R (2) +--R 6 8 8 6 5 8 6 7 7 +--R 90090B b e x + ((102102A b + 612612B a b )e + 6006B b d e )x +--R + +--R 5 2 4 8 6 5 7 +--R (706860A a b + 1767150B a b )e + (7854A b + 47124B a b )d e +--R + +--R 6 2 6 +--R - 6468B b d e +--R * +--R 6 +--R x +--R + +--R 2 4 3 3 8 +--R (2088450A a b + 2784600B a b )e +--R + +--R 5 2 4 7 6 5 2 6 +--R (64260A a b + 160650B a b )d e + (- 8568A b - 51408B a b )d e +--R + +--R 6 3 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 3 3 4 2 8 +--R (3403400A a b + 2552550B a b )e +--R + +--R 2 4 3 3 7 +--R (232050A a b + 309400B a b )d e +--R + +--R 5 2 4 2 6 6 5 3 5 +--R (- 71400A a b - 178500B a b )d e + (9520A b + 57120B a b )d e +--R + +--R 6 4 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 5 8 +--R (3281850A a b + 1312740B a b)e +--R + +--R 3 3 4 2 7 +--R (486200A a b + 364650B a b )d e +--R + +--R 2 4 3 3 2 6 +--R (- 265200A a b - 353600B a b )d e +--R + +--R 5 2 4 3 5 6 5 4 4 +--R (81600A a b + 204000B a b )d e + (- 10880A b - 65280B a b )d e +--R + +--R 6 5 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 5 6 8 4 2 5 7 +--R (1837836A a b + 306306B a )e + (656370A a b + 262548B a b)d e +--R + +--R 3 3 4 2 2 6 +--R (- 583440A a b - 437580B a b )d e +--R + +--R 2 4 3 3 3 5 +--R (318240A a b + 424320B a b )d e +--R + +--R 5 2 4 4 4 6 5 5 3 +--R (- 97920A a b - 244800B a b )d e + (13056A b + 78336B a b )d e +--R + +--R 6 6 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 6 8 5 6 7 +--R 510510A a e + (612612A a b + 102102B a )d e +--R + +--R 4 2 5 2 6 +--R (- 875160A a b - 350064B a b)d e +--R + +--R 3 3 4 2 3 5 +--R (777920A a b + 583440B a b )d e +--R + +--R 2 4 3 3 4 4 +--R (- 424320A a b - 565760B a b )d e +--R + +--R 5 2 4 5 3 +--R (130560A a b + 326400B a b )d e +--R + +--R 6 5 6 2 6 7 +--R (- 17408A b - 104448B a b )d e + 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 2 6 +--R 510510A a d e + (- 1225224A a b - 204204B a )d e +--R + +--R 4 2 5 3 5 +--R (1750320A a b + 700128B a b)d e +--R + +--R 3 3 4 2 4 4 +--R (- 1555840A a b - 1166880B a b )d e +--R + +--R 2 4 3 3 5 3 +--R (848640A a b + 1131520B a b )d e +--R + +--R 5 2 4 6 2 6 5 7 +--R (- 261120A a b - 652800B a b )d e + (34816A b + 208896B a b )d e +--R + +--R 6 8 +--R - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 765765e +--R Type: Expression(Integer) +--E 527 + +--S 528 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 528 + +)clear all + +--S 529 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 529 + +--S 530 of 764 +r0:=2/3*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^8-6/5*b*_ + (b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^8+10/7*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^8-10/9*b^3*_ + (b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(9/2)/e^8+6/11*b^4*_ + (b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(11/2)/e^8-2/13*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(13/2)/e^8+2/15*b^6*B*_ + (d+e*x)^(15/2)/e^8-2*(b*d-a*e)^6*(B*d-A*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 6006B b e x + ((6930A b + 41580B a b )e - 6468B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (49140A a b + 122850B a b )e + (- 7560A b - 45360B a b )d e +--R + +--R 6 2 5 +--R 7056B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 +--R (150150A a b + 200200B a b )e +--R + +--R 5 2 4 6 6 5 2 5 +--R (- 54600A a b - 136500B a b )d e + (8400A b + 50400B a b )d e +--R + +--R 6 3 4 +--R - 7840B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 +--R (257400A a b + 193050B a b )e +--R + +--R 2 4 3 3 6 +--R (- 171600A a b - 228800B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (62400A a b + 156000B a b )d e + (- 9600A b - 57600B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 +--R (270270A a b + 108108B a b)e +--R + +--R 3 3 4 2 6 +--R (- 308880A a b - 231660B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (205920A a b + 274560B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (- 74880A a b - 187200B a b )d e + (11520A b + 69120B a b )d e +--R + +--R 6 5 2 +--R - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (180180A a b + 30030B a )e + (- 360360A a b - 144144B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (411840A a b + 308880B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 274560A a b - 366080B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (99840A a b + 249600B a b )d e + (- 15360A b - 92160B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R 90090A a e + (- 360360A a b - 60060B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (720720A a b + 288288B a b)d e + (- 823680A a b - 617760B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (549120A a b + 732160B a b )d e + (- 199680A a b - 499200B a b )d e +--R + +--R 6 5 6 6 7 +--R (30720A b + 184320B a b )d e - 28672B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 45045e +--R Type: Expression(Integer) +--E 530 + +--S 531 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 531 + +)clear all + +--S 532 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 532 + +--S 533 of 764 +r0:=-2*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^8+2*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^8-10/7*b^3*_ + (b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(7/2)/e^8+2/3*b^4*_ + (b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(9/2)/e^8-2/11*b^5*_ + (7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(11/2)/e^8+2/13*b^6*B*_ + (d+e*x)^(13/2)/e^8+2*(b*d-a*e)^6*(B*d-A*e)/(e^8*sqrt(d+e*x))+_ + 2*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 462B b e x + ((546A b + 3276B a b )e - 588B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (4004A a b + 10010B a b )e + (- 728A b - 4368B a b )d e +--R + +--R 6 2 5 +--R 784B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (12870A a b + 17160B a b )e + (- 5720A a b - 14300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (1040A b + 6240B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (24024A a b + 18018B a b )e + (- 20592A a b - 27456B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (9152A a b + 22880B a b )d e + (- 1664A b - 9984B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (30030A a b + 12012B a b)e + (- 48048A a b - 36036B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (41184A a b + 54912B a b )d e + (- 18304A a b - 45760B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (3328A b + 19968B a b )d e - 3584B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (36036A a b + 6006B a )e + (- 120120A a b - 48048B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (192192A a b + 144144B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 164736A a b - 219648B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (73216A a b + 183040B a b )d e + (- 13312A b - 79872B a b )d e +--R + +--R 6 6 +--R 14336B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 6006A a e + (72072A a b + 12012B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (- 240240A a b - 96096B a b)d e + (384384A a b + 288288B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (- 329472A a b - 439296B a b )d e + (146432A a b + 366080B a b )d e +--R + +--R 6 5 6 6 7 +--R (- 26624A b - 159744B a b )d e + 28672B b d +--R / +--R 8 +-------+ +--R 3003e \|e x + d +--R Type: Expression(Integer) +--E 533 + +--S 534 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 534 + +)clear all + +--S 535 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 535 + +--S 536 of 764 +r0:=2/3*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^(3/2))+10/3*b^2*(b*d-a*e)^3*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^8-2*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(5/2)/e^8+6/7*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(7/2)/e^8-2/9*b^5*(7*b*B*d-A*b*e-_ + 6*a*B*e)*(d+e*x)^(9/2)/e^8+2/11*b^6*B*(d+e*x)^(11/2)/e^8-2*_ + (b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*sqrt(d+e*x))-6*b*(b*d-a*e)^4*_ + (7*b*B*d-5*A*b*e-2*a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 126B b e x + ((154A b + 924B a b )e - 196B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (1188A a b + 2970B a b )e + (- 264A b - 1584B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (4158A a b + 5544B a b )e + (- 2376A a b - 5940B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (528A b + 3168B a b )d e - 672B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (9240A a b + 6930B a b )e + (- 11088A a b - 14784B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (6336A a b + 15840B a b )d e + (- 1408A b - 8448B a b )d e +--R + +--R 6 4 3 +--R 1792B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (20790A a b + 8316B a b)e + (- 55440A a b - 41580B a b )d e +--R + +--R 2 4 3 3 2 5 5 2 4 3 4 +--R (66528A a b + 88704B a b )d e + (- 38016A a b - 95040B a b )d e +--R + +--R 6 5 4 3 6 5 2 +--R (8448A b + 50688B a b )d e - 10752B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 8316A a b - 1386B a )e + (83160A a b + 33264B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (- 221760A a b - 166320B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (266112A a b + 354816B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (- 152064A a b - 380160B a b )d e + (33792A b + 202752B a b )d e +--R + +--R 6 6 +--R - 43008B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 +--R - 462A a e + (- 5544A a b - 924B a )d e +--R + +--R 4 2 5 2 5 3 3 4 2 3 4 +--R (55440A a b + 22176B a b)d e + (- 147840A a b - 110880B a b )d e +--R + +--R 2 4 3 3 4 3 5 2 4 5 2 +--R (177408A a b + 236544B a b )d e + (- 101376A a b - 253440B a b )d e +--R + +--R 6 5 6 6 7 +--R (22528A b + 135168B a b )d e - 28672B b d +--R / +--R 9 8 +-------+ +--R (693e x + 693d e )\|e x + d +--R Type: Expression(Integer) +--E 536 + +--S 537 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 538 + +--S 539 of 764 +r0:=2/5*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^(5/2))-2/3*(b*d-a*e)^5*_ + (7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^(3/2))-10/3*b^3*(b*d-a*e)^2*_ + (7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(3/2)/e^8+6/5*b^4*(b*d-a*e)*_ + (7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(5/2)/e^8-2/7*b^5*(7*b*B*d-_ + A*b*e-6*a*B*e)*(d+e*x)^(7/2)/e^8+2/9*b^6*B*(d+e*x)^(9/2)/e^8+6*b*_ + (b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*sqrt(d+e*x))+10*b^2*_ + (b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 7 6 5 7 6 6 6 +--R 70B b e x + ((90A b + 540B a b )e - 140B b d e )x +--R + +--R 5 2 4 7 6 5 6 +--R (756A a b + 1890B a b )e + (- 216A b - 1296B a b )d e +--R + +--R 6 2 5 +--R 336B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 2 4 6 +--R (3150A a b + 4200B a b )e + (- 2520A a b - 6300B a b )d e +--R + +--R 6 5 2 5 6 3 4 +--R (720A b + 4320B a b )d e - 1120B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 2 4 3 3 6 +--R (12600A a b + 9450B a b )e + (- 25200A a b - 33600B a b )d e +--R + +--R 5 2 4 2 5 6 5 3 4 +--R (20160A a b + 50400B a b )d e + (- 5760A b - 34560B a b )d e +--R + +--R 6 4 3 +--R 8960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 4 2 6 +--R (- 9450A a b - 3780B a b)e + (75600A a b + 56700B a b )d e +--R + +--R 2 4 3 3 2 5 +--R (- 151200A a b - 201600B a b )d e +--R + +--R 5 2 4 3 4 6 5 4 3 +--R (120960A a b + 302400B a b )d e + (- 34560A b - 207360B a b )d e +--R + +--R 6 5 2 +--R 53760B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 2 5 6 +--R (- 1260A a b - 210B a )e + (- 12600A a b - 5040B a b)d e +--R + +--R 3 3 4 2 2 5 +--R (100800A a b + 75600B a b )d e +--R + +--R 2 4 3 3 3 4 +--R (- 201600A a b - 268800B a b )d e +--R + +--R 5 2 4 4 3 6 5 5 2 +--R (161280A a b + 403200B a b )d e + (- 46080A b - 276480B a b )d e +--R + +--R 6 6 +--R 71680B b d e +--R * +--R x +--R + +--R 6 7 5 6 6 4 2 5 2 5 +--R - 126A a e + (- 504A a b - 84B a )d e + (- 5040A a b - 2016B a b)d e +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (40320A a b + 30240B a b )d e + (- 80640A a b - 107520B a b )d e +--R + +--R 5 2 4 5 2 6 5 6 +--R (64512A a b + 161280B a b )d e + (- 18432A b - 110592B a b )d e +--R + +--R 6 7 +--R 28672B b d +--R / +--R 10 2 9 2 8 +-------+ +--R (315e x + 630d e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 539 + +--S 540 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 541 + +--S 542 of 764 +r0:=1/3*(b*d-a*e)*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+_ + 1/5*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/b^3+1/7*(2*b*B*d+7*A*b*e-_ + 9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(9/2)/(b*_ + (b*d-a*e)*(a+b*x))-(b*d-a*e)^(5/2)*(2*b*B*d+7*A*b*e-9*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+(b*d-a*e)^2*_ + (2*b*B*d+7*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (- 735A a b + 945B a b)e + (1470A a b - 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 735A b + 1365B a b )d e - 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 735A a b + 945B a )e + (1470A a b - 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 735A a b + 1365B a b )d e - 210B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 54B a b )e + 132B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 98A a b + 126B a b )e + (224A b - 316B a b )d e +--R + +--R 4 2 +--R 244B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (490A a b - 630B a b)e + (- 1176A a b + 1652B a b )d e +--R + +--R 4 3 2 4 3 +--R (812A b - 1380B a b )d e + 352B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1715A a b + 2415B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (1127A a b - 1939B a b )d e + (- 105A b + 457B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 5 +-+ +--R (105b x + 105a b )\|b +--R Type: Expression(Integer) +--E 542 + +--S 543 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 544 + +--S 545 of 764 +r0:=1/3*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/b^3+1/5*(2*b*B*d+5*A*b*e-_ + 7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(7/2)/(b*_ + (b*d-a*e)*(a+b*x))-(b*d-a*e)^(3/2)*(2*b*B*d+5*A*b*e-7*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+(b*d-a*e)*(2*b*B*d+_ + 5*A*b*e-7*a*B*e)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 14B a b )e + 22B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 50A a b + 70B a b)e + (70A b - 118B a b )d e + 46B b d )x +--R + +--R 2 3 2 2 2 +--R (- 75A a b + 105B a )e + (100A a b - 170B a b)d e +--R + +--R 3 2 2 +--R (- 15A b + 61B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 5 4 +-+ +--R (15b x + 15a b )\|b +--R Type: Expression(Integer) +--E 545 + +--S 546 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 546 + +)clear all + +--S 547 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 547 + +--S 548 of 764 +r0:=1/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e))-_ + (A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+3*A*b*e-_ + 5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+_ + (2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (((- 9A b + 15B a b)e - 6B b d)x + (- 9A a b + 15B a )e - 6B a b d) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 10B a b)e + 8B b d)x + (9A a b - 15B a )e +--R + +--R 2 +--R (- 3A b + 11B a b)d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 548 + +--S 549 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 550 + +--S 551 of 764 +r0:=-(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+A*b*e-3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))+_ + (2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)) +--R +--R +--R (2) +--R 2 2 2 +--R (((- A b + 3B a b)e - 2B b d)x + (- A a b + 3B a )e - 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (2B b x - A b + 3B a)\|- a e + b d \|b \|e x + d +--R / +--R 3 2 +-----------+ +-+ +--R (b x + a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 551 + +--S 552 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 764 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 553 + +--S 554 of 764 +r0:=-(2*b*B*d-A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(3/2)*(b*d-a*e)^(3/2))-(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 +--R (((- A b - B a b)e + 2B b d)x + (- A a b - B a )e + 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (A b - B a)\|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 2 +-----------+ +-+ +--R ((a b e - b d)x + a b e - a b d)\|- a e + b d \|b +--R Type: Expression(Integer) +--E 554 + +--S 555 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 556 + +--S 557 of 764 +r0:=-(2*b*B*d-3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(5/2)*sqrt(b))+(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^2*_ + sqrt(d+e*x))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 +-------+ +--R (((3A b - B a b)e - 2B b d)x + (3A a b - B a )e - 2B a b d)\|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R (((- 3A b + B a)e + 2B b d)x - 2A a e + (- A b + 3B a)d)\|- a e + b d \|b +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-----------+ +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R Type: Expression(Integer) +--E 557 + +--S 558 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 559 + +--S 560 of 764 +r0:=1/3*(2*b*B*d-5*A*b*e+3*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+(-A*b+a*B)/_ + (b*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2))-(2*b*B*d-5*A*b*e+3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(7/2)+_ + (2*b*B*d-5*A*b*e+3*a*B*e)/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 15A b + 9B a b)e + 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 15A a b + 9B a )e + (- 15A b + 15B a b)d e + 6B b d )x +--R + +--R 2 2 +--R (- 15A a b + 9B a )d e + 6B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((10A a b - 6B a )e + (20A b - 16B a b)d e - 8B b d )x - 2A a e +--R + +--R 2 2 2 +--R (14A a b - 4B a )d e + (3A b - 11B a b)d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 560 + +--S 561 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 561 + +)clear all + +--S 562 of 764 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 562 + +--S 563 of 764 +r0:=1/5*(2*b*B*d-7*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+_ + (-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(5/2))+1/3*(2*b*B*d-7*A*b*e+_ + 5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2))-b^(3/2)*(2*b*B*d-7*A*b*e+_ + 5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+_ + b*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((105A b - 75B a b )e - 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((105A a b - 75B a b)e + (210A b - 180B a b )d e - 60B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((210A a b - 150B a b)d e + (105A b - 135B a b )d e - 30B b d )x +--R + +--R 2 2 2 2 3 +--R (105A a b - 75B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 70A a b + 50B a b)e + (- 245A b + 195B a b )d e +--R + +--R 3 2 +--R 70B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 10B a )e + (- 168A a b + 116B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 161A b + 163B a b )d e + 46B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (32A a b - 4B a )d e + (- 116A a b + 48B a b)d e +--R + +--R 3 2 3 +--R (- 15A b + 61B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 563 + +--S 564 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 of 764 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 565 + +--S 566 of 764 +r0:=7/8*e^2*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(3/2)/b^5+21/40*e^2*_ + (6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*(b*d-a*e))-3/8*e*_ + (6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(7/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/12*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(9/2)/(b^2*(b*d-a*e)*_ + (a+b*x)^2)-1/3*(A*b-a*B)*(d+e*x)^(11/2)/(b*(b*d-a*e)*(a+b*x)^3)-_ + 21/8*e^2*(b*d-a*e)^(3/2)*(6*b*B*d+5*A*b*e-11*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(13/2)+21/8*e^2*(b*d-a*e)*(6*b*B*d+_ + 5*A*b*e-11*a*B*e)*sqrt(d+e*x)/b^6 +--R +--R +--R (2) +--R 4 2 3 4 5 4 3 +--R (1575A a b - 3465B a b )e + (- 1575A b + 5355B a b )d e +--R + +--R 5 2 2 +--R - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4725A a b - 10395B a b )e + (- 4725A a b + 16065B a b )d e +--R + +--R 4 2 2 +--R - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (4725A a b - 10395B a b)e + (- 4725A a b + 16065B a b )d e +--R + +--R 2 3 2 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (1575A a b - 3465B a )e + (- 1575A a b + 5355B a b)d e +--R + +--R 3 2 2 2 +--R - 1890B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 48B b e x + ((80A b - 176B a b )e + 336B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 720A a b + 1584B a b )e + (1040A b - 3152B a b )d e +--R + +--R 5 2 2 +--R 1728B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 3465A a b + 7623B a b )e + (4770A a b - 14652B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 825A b + 7539B a b )d e - 510B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 4200A a b + 9240B a b)e + (5670A a b - 17514B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 900A a b + 8784B a b )d e + (- 250A b - 530B a b )d e +--R + +--R 5 4 +--R - 60B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 1575A a b + 3465B a )e + (2100A a b - 6510B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 315A a b + 3213B a b )d e + (- 90A a b - 180B a b )d e +--R + +--R 5 4 4 +--R (- 40A b - 20B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 9 3 8 2 2 7 3 6 +-+ +--R (120b x + 360a b x + 360a b x + 120a b )\|b +--R Type: Expression(Integer) +--E 566 + +--S 567 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 568 + +--S 569 of 764 +r0:=35/24*e^2*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e))-_ + 7/8*e*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(5/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/4*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^3)-35/8*e^2*(2*b*B*d+_ + A*b*e-3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-_ + a*e)/b^(11/2)+35/8*e^2*(2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 105A b + 315B a b )e - 210B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 315A a b + 945B a b )e - 630B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 315A a b + 945B a b)e - 630B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 105A a b + 315B a )e - 210B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 16B b e x + ((48A b - 144B a b )e + 160B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (231A a b - 693B a b )e + (- 87A b + 723B a b )d e +--R + +--R 4 2 +--R - 78B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (280A a b - 840B a b)e + (- 98A a b + 854B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 38A b - 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (105A a b - 315B a )e + (- 35A a b + 315B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 14A a b - 28B a b )d e + (- 8A b - 4B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +-+ +--R (24b x + 72a b x + 72a b x + 24a b )\|b +--R Type: Expression(Integer) +--E 569 + +--S 570 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 764 +r0:=-5/24*e*(6*b*B*d+A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a+b*x))-_ + 1/12*(6*b*B*d+A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^3)-5/8*e^2*_ + (6*b*B*d+A*b*e-7*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(9/2)*sqrt(b*d-a*e))+5/8*e^2*(6*b*B*d+A*b*e-7*a*B*e)*sqrt(d+e*x)/_ + (b^4*(b*d-a*e)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 15A b + 105B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 45A a b + 315B a b )e - 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 45A a b + 315B a b)e - 270B a b d e )x +--R + +--R 3 4 3 3 2 +--R (- 15A a b + 105B a )e - 90B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 48B b e x + ((- 33A b + 231B a b )e - 54B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 40A a b + 280B a b)e + (- 26A b - 58B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (- 15A a b + 105B a )e + (- 10A a b - 20B a b)d e +--R + +--R 3 2 2 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 3 6 2 2 5 3 4 +-----------+ +-+ +--R (24b x + 72a b x + 72a b x + 24a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 572 + +--S 573 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 574 + +--S 575 of 764 +r0:=-1/12*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-_ + 1/3*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^3)-1/8*e^2*(6*b*B*d-_ + A*b*e-5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*_ + (b*d-a*e)^(3/2))-1/8*e*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*_ + (b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 3A b - 15B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 9A a b - 45B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 9A a b - 45B a b)e + 54B a b d e )x + (- 3A a b - 15B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b - 33B a b )e + 30B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 8A a b - 40B a b)e + (14A b + 22B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 15B a )e + (- 2A a b + 8B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 6 7 3 2 5 6 2 3 4 2 5 +--R (24a b e - 24b d)x + (72a b e - 72a b d)x + (72a b e - 72a b d)x +--R + +--R 4 3 3 4 +--R 24a b e - 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 575 + +--S 576 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 576 + +)clear all + +--S 577 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 577 + +--S 578 of 764 +r0:=-1/3*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^3)+1/8*e^2*(2*b*B*d-_ + A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*_ + (b*d-a*e)^(5/2))-1/4*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^2*_ + (b*d-a*e)*(a+b*x)^2)-1/8*e*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 3A b - 3B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 9A a b - 9B a b )e + 18B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 9A a b - 9B a b)e + 18B a b d e )x + (- 3A a b - 3B a )e +--R + +--R 3 2 +--R 6B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((3A b + 3B a b )e - 6B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((8A a b - 8B a b)e + (- 2A b + 14B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 3A a b - 3B a )e + (14A a b + 4B a b)d e + (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 5 2 6 7 2 3 +--R (24a b e - 48a b d e + 24b d )x +--R + +--R 3 4 2 2 5 6 2 2 +--R (72a b e - 144a b d e + 72a b d )x +--R + +--R 4 3 2 3 4 2 5 2 5 2 2 4 3 3 4 2 +--R (72a b e - 144a b d e + 72a b d )x + 24a b e - 48a b d e + 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 578 + +--S 579 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 of 764 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 580 + +--S 581 of 764 +r0:=-1/8*e^2*(6*b*B*d-5*A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(7/2))-1/3*(A*b-a*B)*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^3)-1/12*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*(a+b*x)^2)+1/8*e*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((- 15A b - 3B a b )e + 18B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((- 45A a b - 9B a b )e + 54B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((- 45A a b - 9B a b)e + 54B a b d e )x + (- 15A a b - 3B a )e +--R + +--R 3 2 +--R 18B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 2 3 2 +--R ((15A b + 3B a b )e - 18B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((40A a b + 8B a b)e + (- 10A b - 50B a b )d e + 12B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (33A a b - 3B a )e + (- 26A a b - 16B a b)d e + (8A b + 4B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 2 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 6 3 +--R (72a b e - 216a b d e + 216a b d e - 72a b d )x + 24a b e +--R + +--R 5 2 2 4 3 2 3 4 3 +--R - 72a b d e + 72a b d e - 24a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 581 + +--S 582 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 583 + +--S 584 of 764 +r0:=-5/8*e^2*(6*b*B*d-7*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(b))+5/8*e^2*(6*b*B*d-7*A*b*e+_ + a*B*e)/(b*(b*d-a*e)^4*sqrt(d+e*x))+1/3*(-A*b+a*B)/(b*(b*d-a*e)*_ + (a+b*x)^3*sqrt(d+e*x))+1/12*(-6*b*B*d+7*A*b*e-a*B*e)/(b*(b*d-a*e)^2*_ + (a+b*x)^2*sqrt(d+e*x))+5/24*e*(6*b*B*d-7*A*b*e+a*B*e)/(b*(b*d-a*e)^3*_ + (a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 3 4 2 3 +--R ((105A b - 15B a b )e - 90B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((315A a b - 45B a b )e - 270B a b d e )x +--R + +--R 2 2 3 3 2 2 2 3 4 3 +--R ((315A a b - 45B a b)e - 270B a b d e )x + (105A a b - 15B a )e +--R + +--R 3 2 +--R - 90B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 15B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 280A a b + 40B a b)e + (- 35A b + 245B a b )d e +--R + +--R 3 2 +--R 30B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 231A a b + 33B a )e + (- 98A a b + 212B a b)d e +--R + +--R 3 2 2 3 3 +--R (14A b + 82B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 48A a e + (- 87A a b + 81B a )d e + (38A a b + 28B a b)d e +--R + +--R 3 2 3 +--R (- 8A b - 4B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b e - 288a b d e + 432a b d e - 288a b d e + 72a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 584 + +--S 585 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 586 + +--S 587 of 764 +r0:=35/24*e^2*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(3/2))+_ + 1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(3/2))+1/4*(-2*b*B*d+_ + 3*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(3/2))+7/8*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(3/2))-35/8*e^2*(2*b*B*d-_ + 3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-_ + a*e)^(11/2)+35/8*e^2*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 315A b + 105B a b )e + 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 945A a b + 315B a b )e + (- 315A b + 735B a b )d e +--R + +--R 4 2 2 +--R 210B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 945A a b + 315B a b)e + (- 945A a b + 945B a b )d e +--R + +--R 3 2 2 +--R 630B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 315A a b + 105B a )e + (- 945A a b + 525B a b)d e +--R + +--R 2 2 2 2 +--R 630B a b d e +--R * +--R x +--R + +--R 3 4 3 3 2 2 +--R (- 315A a b + 105B a )d e + 210B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((315A b - 105B a b )e - 210B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (840A a b - 280B a b )e + (420A b - 700B a b )d e +--R + +--R 4 2 2 +--R - 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (693A a b - 231B a b)e + (1134A a b - 840B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (63A b - 777B a b )d e - 42B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 48B a )e + (954A a b - 414B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (180A a b - 696B a b )d e + (- 18A b - 114B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 16A a e + (208A a b - 32B a )d e + (165A a b - 247B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 50A a b - 40B a b )d e + (8A b + 4B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 8 5 +--R - 24b d e +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b e - 336a b d e + 600a b d e - 480a b d e + 120a b d e +--R + +--R 7 5 8 6 +--R 48a b d e - 24b d +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b e - 288a b d e + 360a b d e - 360a b d e + 288a b d e +--R + +--R 7 6 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a e - 48a b d e - 120a b d e + 480a b d e - 600a b d e +--R + +--R 3 5 5 2 6 6 +--R 336a b d e - 72a b d +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 3 5 6 +--R - 24a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 587 + +--S 588 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 of 764 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 589 + +--S 590 of 764 +r0:=21/40*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(5/2))+_ + 1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(5/2))+1/12*(-6*b*B*d+_ + 11*A*b*e-5*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(5/2))+3/8*e*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(5/2))+7/8*e^2*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)/((b*d-a*e)^5*(d+e*x)^(3/2))-21/8*b^(3/2)*e^2*(6*b*B*d-_ + 11*A*b*e+5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b*d-a*e)^(13/2)+21/8*b*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/((b*d-a*e)^6*_ + sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((3465A b - 1575B a b )e - 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (10395A a b - 4725B a b )e + (6930A b - 8820B a b )d e +--R + +--R 5 2 3 +--R - 3780B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (10395A a b - 4725B a b )e + (20790A a b - 15120B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (3465A b - 12915B a b )d e - 1890B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (3465A a b - 1575B a b)e + (20790A a b - 11340B a b )d e +--R + +--R 4 2 3 2 3 4 3 2 +--R (10395A a b - 16065B a b )d e - 5670B a b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 2 3 +--R (6930A a b - 3150B a b)d e + (10395A a b - 8505B a b )d e +--R + +--R 2 3 3 2 +--R - 5670B a b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 2 3 2 +--R (3465A a b - 1575B a b)d e - 1890B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 1575B a b )e + 1890B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 9240A a b + 4200B a b )e + (- 8085A b + 8715B a b )d e +--R + +--R 5 2 3 +--R 4410B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 7623A a b + 3465B a b )e + (- 21714A a b + 14028B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 5313A b + 14259B a b )d e + 2898B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 1584A a b + 720B a b)e + (- 18117A a b + 9099B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 14454A a b + 16452B a b )d e + (- 495A b + 8109B a b )d e +--R + +--R 5 4 +--R 270B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (176A a b - 80B a )e + (- 3872A a b + 1664B a b)d e +--R + +--R 2 3 3 2 2 3 +--R (- 12309A a b + 7707B a b )d e +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 1430A a b + 7364B a b )d e + (110A b + 730B a b )d e +--R + +--R 5 5 +--R - 60B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 48A a e + (416A a b - 32B a )d e + (- 2768A a b + 704B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (- 1335A a b + 2553B a b )d e + (310A a b + 260B a b )d e +--R + +--R 5 4 5 +--R (- 40A b - 20B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 8 5 4 7 4 5 2 6 3 6 3 5 +--R 120a b e - 720a b d e + 1800a b d e - 2400a b d e +--R + +--R 2 7 4 4 8 5 3 9 6 2 +--R 1800a b d e - 720a b d e + 120b d e +--R * +--R 5 +--R x +--R + +--R 7 2 8 6 3 7 5 4 2 6 4 5 3 5 +--R 360a b e - 1920a b d e + 3960a b d e - 3600a b d e +--R + +--R 3 6 4 4 2 7 5 3 8 6 2 9 7 +--R 600a b d e + 1440a b d e - 1080a b d e + 240b d e +--R * +--R 4 +--R x +--R + +--R 8 8 7 2 7 6 3 2 6 5 4 3 5 +--R 360a b e - 1440a b d e + 1200a b d e + 2880a b d e +--R + +--R 4 5 4 4 3 6 5 3 2 7 6 2 9 8 +--R - 7200a b d e + 6240a b d e - 2160a b d e + 120b d +--R * +--R 3 +--R x +--R + +--R 9 8 7 2 2 6 6 3 3 5 5 4 4 4 4 5 5 3 +--R 120a e - 2160a b d e + 6240a b d e - 7200a b d e + 2880a b d e +--R + +--R 3 6 6 2 2 7 7 8 8 +--R 1200a b d e - 1440a b d e + 360a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 2 6 7 2 3 5 6 3 4 4 +--R 240a d e - 1080a b d e + 1440a b d e + 600a b d e +--R + +--R 5 4 5 3 4 5 6 2 3 6 7 2 7 8 +--R - 3600a b d e + 3960a b d e - 1920a b d e + 360a b d +--R * +--R x +--R + +--R 9 2 6 8 3 5 7 2 4 4 6 3 5 3 5 4 6 2 +--R 120a d e - 720a b d e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 4 5 7 3 6 8 +--R - 720a b d e + 120a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 590 + +--S 591 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 591 + +)clear all + +--S 592 of 764 +t0:=(A+B*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 592 + +--S 593 of 764 +r0:=77/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(3/2)/(b^6*(b*d-a*e))-_ + 231/640*e^3*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(5/2)/(b^5*(b*d-a*e)*_ + (a+b*x))-33/320*e^2*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(7/2)/(b^4*_ + (b*d-a*e)*(a+b*x)^2)-11/240*e*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(9/2)/_ + (b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d+3*A*b*e-13*a*B*e)*_ + (d+e*x)^(11/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(13/2)/_ + (b*(b*d-a*e)*(a+b*x)^5)-231/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(15/2)+_ + 231/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*sqrt(d+e*x)/b^7 +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 10395A b + 45045B a b )e - 34650B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 51975A a b + 225225B a b )e - 173250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 103950A a b + 450450B a b )e - 346500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 51975A a b + 225225B a b)e - 173250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 10395A a b + 45045B a )e - 34650B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 1280B b e x + ((3840A b - 16640B a b )e + 20480B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (31845A a b - 137995B a b )e + (- 12645A b + 160945B a b )d e +--R + +--R 6 2 3 +--R - 22950B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (78210A a b - 338910B a b )e +--R + +--R 5 2 4 4 +--R (- 29040A a b + 386540B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 10770A b - 50130B a b )d e - 10300B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (88704A a b - 384384B a b )e +--R + +--R 2 4 3 3 4 +--R (- 31482A a b + 432102B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 12078A a b - 52602B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 6744A b - 11036B a b )d e - 3280B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (48510A a b - 210210B a b)e +--R + +--R 3 3 4 2 4 +--R (- 16632A a b + 233772B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 6534A a b - 27126B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3696A a b - 5764B a b )d e + (- 2448A b - 1712B a b )d e +--R + +--R 6 5 +--R - 480B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (10395A a b - 45045B a )e + (- 3465A a b + 49665B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 1386A a b - 5544B a b )d e + (- 792A a b - 1188B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 528A a b - 352B a b )d e + (- 384A b - 96B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 +--R 1920b x + 9600a b x + 19200a b x + 19200a b x + 9600a b x +--R + +--R 5 7 +--R 1920a b +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 593 + +--S 594 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 of 764 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 595 + +--S 596 of 764 +r0:=-21/128*e^3*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(3/2)/(b^5*(b*d-a*e)*_ + (a+b*x))-21/320*e^2*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*_ + (b*d-a*e)*(a+b*x)^2)-3/80*e*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(7/2)/_ + (b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d+A*b*e-11*a*B*e)*_ + (d+e*x)^(9/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(11/2)/_ + (b*(b*d-a*e)*(a+b*x)^5)-63/128*e^4*(10*b*B*d+A*b*e-11*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(13/2)*sqrt(b*d-a*e))+_ + 63/128*e^4*(10*b*B*d+A*b*e-11*a*B*e)*sqrt(d+e*x)/(b^6*(b*d-a*e)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 315A b + 3465B a b )e - 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 1575A a b + 17325B a b )e - 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 3150A a b + 34650B a b )e - 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 3150A a b + 34650B a b )e - 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 1575A a b + 17325B a b)e - 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 315A a b + 3465B a )e - 3150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 1280B b e x + ((- 965A b + 10615B a b )e - 3250B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 2370A a b + 26070B a b )e + (- 1490A b - 7310B a b )d e +--R + +--R 5 2 2 +--R - 2100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 2688A a b + 29568B a b )e + (- 1734A a b - 7806B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 1368A b - 2292B a b )d e - 880B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 1470A a b + 16170B a b)e + (- 966A a b - 4074B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 768A a b - 1212B a b )d e + (- 656A b - 464B a b )d e +--R + +--R 5 4 +--R - 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 315A a b + 3465B a )e + (- 210A a b - 840B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 168A a b - 252B a b )d e + (- 144A a b - 96B a b )d e +--R + +--R 5 4 4 +--R (- 128A b - 32B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R (640b x + 3200a b x + 6400a b x + 6400a b x + 3200a b x + 640a b ) +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 596 + +--S 597 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 598 + +--S 599 of 764 +r0:=-7/192*e^2*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e)*_ + (a+b*x)^2)-7/240*e*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(5/2)/(b^3*_ + (b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(7/2)/_ + (b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*_ + (a+b*x)^5)-7/128*e^4*(10*b*B*d-A*b*e-9*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(11/2)*(b*d-a*e)^(3/2))-_ + 7/128*e^3*(10*b*B*d-A*b*e-9*a*B*e)*sqrt(d+e*x)/(b^5*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 105A b - 945B a b )e + 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 525A a b - 4725B a b )e + 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 1050A a b - 9450B a b )e + 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 1050A a b - 9450B a b )e + 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 525A a b - 4725B a b)e + 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 105A a b - 945B a )e + 1050B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b - 2895B a b )e + 2790B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 790A a b - 7110B a b )e + (1210A b + 3430B a b )d e +--R + +--R 5 2 2 +--R 3260B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 896A a b - 8064B a b )e + (- 578A a b + 3758B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (2104A b + 1676B a b )d e + 2000B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 490A a b - 4410B a b)e + (- 322A a b + 2002B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 256A a b + 916B a b )d e + (1488A b + 592B a b )d e +--R + +--R 5 4 +--R 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 945B a )e + (- 70A a b + 420B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 56A a b + 196B a b )d e + (- 48A a b + 128B a b )d e +--R + +--R 5 4 4 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 10 11 5 2 9 10 4 +--R (1920a b e - 1920b d)x + (9600a b e - 9600a b d)x +--R + +--R 3 8 2 9 3 4 7 3 8 2 +--R (19200a b e - 19200a b d)x + (19200a b e - 19200a b d)x +--R + +--R 5 6 4 7 6 5 5 6 +--R (9600a b e - 9600a b d)x + 1920a b e - 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 599 + +--S 600 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 601 + +--S 602 of 764 +r0:=-1/48*e*(10*b*B*d-3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*_ + (a+b*x)^3)-1/40*(10*b*B*d-3*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-_ + a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^5)+_ + 1/128*e^4*(10*b*B*d-3*A*b*e-7*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(9/2)*(b*d-a*e)^(5/2))-1/64*e^2*(10*b*B*d-_ + 3*A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)*(a+b*x)^2)-_ + 1/128*e^3*(10*b*B*d-3*A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 45A b - 105B a b )e + 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 225A a b - 525B a b )e + 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 450A a b - 1050B a b )e + 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 450A a b - 1050B a b )e + 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 225A a b - 525B a b)e + 750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 45A a b - 105B a )e + 150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((45A b + 105B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (210A a b - 790B a b )e + (- 30A b + 1790B a b )d e +--R + +--R 5 2 2 +--R - 1180B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 384A a b - 896B a b )e + (1398A a b + 702B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 744A b + 1284B a b )d e - 1360B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 210A a b - 490B a b)e + (- 138A a b + 378B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (1536A a b + 204B a b )d e + (- 1008A b + 208B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 45A a b - 105B a )e + (- 30A a b + 80B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 24A a b + 44B a b )d e + (528A a b + 32B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 9 2 10 11 2 5 +--R (1920a b e - 3840a b d e + 1920b d )x +--R + +--R 3 8 2 2 9 10 2 4 +--R (9600a b e - 19200a b d e + 9600a b d )x +--R + +--R 4 7 2 3 8 2 9 2 3 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 5 6 2 4 7 3 8 2 2 +--R (19200a b e - 38400a b d e + 19200a b d )x +--R + +--R 6 5 2 5 6 4 7 2 7 4 2 6 5 +--R (9600a b e - 19200a b d e + 9600a b d )x + 1920a b e - 3840a b d e +--R + +--R 5 6 2 +--R 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 602 + +--S 603 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 604 + +--S 605 of 764 +r0:=-1/8*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-_ + 1/5*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^5)-3/128*e^4*(2*b*B*d-_ + A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-_ + a*e)^(7/2))-1/16*e*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)*_ + (a+b*x)^3)-1/64*e^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)^2*_ + (a+b*x)^2)+3/128*e^3*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*_ + (b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 15A b - 15B a b )e + 30B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 75A a b - 75B a b )e + 150B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 150A a b - 150B a b )e + 300B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 150A a b - 150B a b )e + 300B a b d e )x +--R + +--R 4 2 5 5 4 2 4 5 6 5 +--R ((- 75A a b - 75B a b)e + 150B a b d e )x + (- 15A a b - 15B a )e +--R + +--R 5 4 +--R 30B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((15A b + 15B a b )e - 30B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((70A a b + 70B a b )e + (- 10A b - 150B a b )d e + 20B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (128A a b - 128B a b )e + (- 46A a b + 466B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (8A b - 668B a b )d e + 240B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 70A a b - 70B a b)e + (466A a b + 94B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 512A a b + 92B a b )d e + (176A b - 336B a b )d e + 160B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 15A a b - 15B a )e + (- 10A a b + 20B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (248A a b + 12B a b )d e + (- 336A a b - 64B a b )d e +--R + +--R 5 4 4 +--R (128A b + 32B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 8 3 2 9 2 10 2 11 3 5 +--R (640a b e - 1920a b d e + 1920a b d e - 640b d )x +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 4 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x +--R + +--R 5 6 3 4 7 2 3 8 2 2 9 3 3 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 6 5 3 5 6 2 4 7 2 3 8 3 2 +--R (6400a b e - 19200a b d e + 19200a b d e - 6400a b d )x +--R + +--R 7 4 3 6 5 2 5 6 2 4 7 3 8 3 3 +--R (3200a b e - 9600a b d e + 9600a b d e - 3200a b d )x + 640a b e +--R + +--R 7 4 2 6 5 2 5 6 3 +--R - 1920a b d e + 1920a b d e - 640a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 605 + +--S 606 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 606 + +)clear all + +--S 607 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 607 + +--S 608 of 764 +r0:=-1/5*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^5)+1/128*e^4*_ + (10*b*B*d-7*A*b*e-3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(5/2)*(b*d-a*e)^(9/2))-1/40*(10*b*B*d-7*A*b*e-3*a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)*(a+b*x)^4)-1/240*e*(10*b*B*d-7*A*b*e-3*a*B*e)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x)^3)+1/192*e^2*(10*b*B*d-7*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^3*(a+b*x)^2)-1/128*e^3*(10*b*B*d-_ + 7*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^4*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 105A b - 45B a b )e + 150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 525A a b - 225B a b )e + 750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 1050A a b - 450B a b )e + 1500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 1050A a b - 450B a b )e + 1500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 525A a b - 225B a b)e + 750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 105A a b - 45B a )e + 150B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((105A b + 45B a b )e - 150B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (490A a b + 210B a b )e + (- 70A b - 730B a b )d e +--R + +--R 5 2 2 +--R 100B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (896A a b + 384B a b )e + (- 322A a b - 1418B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (56A b + 484B a b )d e - 80B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (790A a b - 210B a b)e + (- 578A a b + 818B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (256A a b - 2356B a b )d e + (- 48A b + 1808B a b )d e +--R + +--R 5 4 +--R - 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 105A a b - 45B a )e + (1210A a b + 120B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 2104A a b - 436B a b )d e + (1488A a b + 352B a b )d e +--R + +--R 5 4 4 +--R (- 384A b - 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 7 4 3 8 3 2 9 2 2 10 3 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e +--R + +--R 11 4 +--R 1920b d +--R * +--R 5 +--R x +--R + +--R 5 6 4 4 7 3 3 8 2 2 2 9 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 10 4 +--R 9600a b d +--R * +--R 4 +--R x +--R + +--R 6 5 4 5 6 3 4 7 2 2 3 8 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 2 9 4 +--R 19200a b d +--R * +--R 3 +--R x +--R + +--R 7 4 4 6 5 3 5 6 2 2 4 7 3 +--R 19200a b e - 76800a b d e + 115200a b d e - 76800a b d e +--R + +--R 3 8 4 +--R 19200a b d +--R * +--R 2 +--R x +--R + +--R 8 3 4 7 4 3 6 5 2 2 5 6 3 +--R 9600a b e - 38400a b d e + 57600a b d e - 38400a b d e +--R + +--R 4 7 4 +--R 9600a b d +--R * +--R x +--R + +--R 9 2 4 8 3 3 7 4 2 2 6 5 3 5 6 4 +--R 1920a b e - 7680a b d e + 11520a b d e - 7680a b d e + 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 608 + +--S 609 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 764 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x)) +--R +--R +--R (1) +--R B x + A +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 610 + +--S 611 of 764 +r0:=-7/128*e^4*(10*b*B*d-9*A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(11/2))-1/5*(A*b-a*B)*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^5)-1/40*(10*b*B*d-9*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*(a+b*x)^4)+7/240*e*(10*b*B*d-9*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x)^3)-7/192*e^2*(10*b*B*d-9*A*b*e-_ + a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^4*(a+b*x)^2)+7/128*e^3*(10*b*B*d-_ + 9*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^5*(a+b*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((- 945A b - 105B a b )e + 1050B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((- 4725A a b - 525B a b )e + 5250B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((- 9450A a b - 1050B a b )e + 10500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((- 9450A a b - 1050B a b )e + 10500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((- 4725A a b - 525B a b)e + 5250B a b d e )x +--R + +--R 5 6 5 5 4 +--R (- 945A a b - 105B a )e + 1050B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 4 5 3 4 +--R ((945A b + 105B a b )e - 1050B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (4410A a b + 490B a b )e + (- 630A b - 4970B a b )d e +--R + +--R 5 2 2 +--R 700B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (8064A a b + 896B a b )e + (- 2898A a b - 9282B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (504A b + 3276B a b )d e - 560B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (7110A a b + 790B a b)e + (- 5202A a b - 8478B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (2304A a b + 6036B a b )d e + (- 432A b - 2608B a b )d e +--R + +--R 5 4 +--R 480B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (2895A a b - 105B a )e + (- 4470A a b - 1580B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (4104A a b + 1156B a b )d e + (- 1968A a b - 512B a b )d e +--R + +--R 5 4 4 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 +--R 1920a b e - 9600a b d e + 19200a b d e - 19200a b d e +--R + +--R 10 4 11 5 +--R 9600a b d e - 1920b d +--R * +--R 5 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R 9600a b e - 48000a b d e + 96000a b d e - 96000a b d e +--R + +--R 2 9 4 10 5 +--R 48000a b d e - 9600a b d +--R * +--R 4 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R 19200a b e - 96000a b d e + 192000a b d e - 192000a b d e +--R + +--R 3 8 4 2 9 5 +--R 96000a b d e - 19200a b d +--R * +--R 3 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 +--R 19200a b e - 96000a b d e + 192000a b d e - 192000a b d e +--R + +--R 4 7 4 3 8 5 +--R 96000a b d e - 19200a b d +--R * +--R 2 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 +--R 9600a b e - 48000a b d e + 96000a b d e - 96000a b d e +--R + +--R 5 6 4 4 7 5 +--R 48000a b d e - 9600a b d +--R * +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 +--R 1920a b e - 9600a b d e + 19200a b d e - 19200a b d e +--R + +--R 6 5 4 5 6 5 +--R 9600a b d e - 1920a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 611 + +--S 612 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 7 5 6 6 2 4 5 5 +--R b e x + (6a b e + b d)x + (15a b e + 6a b d)x +--R + +--R 3 3 2 4 4 4 2 3 3 3 5 4 2 2 +--R (20a b e + 15a b d)x + (15a b e + 20a b d)x + (6a b e + 15a b d)x +--R + +--R 6 5 6 +--R (a e + 6a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 613 + +--S 614 of 764 +r0:=-63/128*e^4*(10*b*B*d-11*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/((b*d-a*e)^(13/2)*sqrt(b))+63/128*e^4*(10*b*B*d-_ + 11*A*b*e+a*B*e)/(b*(b*d-a*e)^6*sqrt(d+e*x))+1/5*(-A*b+a*B)/(b*(b*d-_ + a*e)*(a+b*x)^5*sqrt(d+e*x))+1/40*(-10*b*B*d+11*A*b*e-a*B*e)/(b*(b*d-_ + a*e)^2*(a+b*x)^4*sqrt(d+e*x))+3/80*e*(10*b*B*d-11*A*b*e+a*B*e)/(b*_ + (b*d-a*e)^3*(a+b*x)^3*sqrt(d+e*x))-21/320*e^2*(10*b*B*d-11*A*b*e+_ + a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*sqrt(d+e*x))+21/128*e^3*(10*b*B*d-_ + 11*A*b*e+a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 5 5 6 4 5 +--R ((3465A b - 315B a b )e - 3150B b d e )x +--R + +--R 5 2 4 5 5 4 4 +--R ((17325A a b - 1575B a b )e - 15750B a b d e )x +--R + +--R 2 4 3 3 5 2 4 4 3 +--R ((34650A a b - 3150B a b )e - 31500B a b d e )x +--R + +--R 3 3 4 2 5 3 3 4 2 +--R ((34650A a b - 3150B a b )e - 31500B a b d e )x +--R + +--R 4 2 5 5 4 2 4 +--R ((17325A a b - 1575B a b)e - 15750B a b d e )x +--R + +--R 5 6 5 5 4 +--R (3465A a b - 315B a )e - 3150B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((- 3465A b + 315B a b )e + 3150B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 16170A a b + 1470B a b )e + (- 1155A b + 14805B a b )d e +--R + +--R 5 2 3 +--R 1050B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 29568A a b + 2688B a b )e + (- 5544A a b + 27384B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (462A b + 4998B a b )d e - 420B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 26070A a b + 2370B a b)e + (- 10494A a b + 24654B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2178A a b + 9342B a b )d e + (- 264A b - 1956B a b )d e +--R + +--R 5 4 +--R 240B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 10615A a b + 965B a )e + (- 9680A a b + 10530B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (4026A a b + 8434B a b )d e + (- 1232A a b - 3548B a b )d e +--R + +--R 5 4 4 5 5 +--R (176A b + 1104B a b )d e - 160B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 1280A a e + (- 4215A a b + 2245B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (3590A a b + 1760B a b)d e + (- 2248A a b - 732B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (816A a b + 224B a b )d e + (- 128A b - 32B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 6 5 6 5 6 5 4 7 2 4 3 8 3 3 +--R 640a b e - 3840a b d e + 9600a b d e - 12800a b d e +--R + +--R 2 9 4 2 10 5 11 6 +--R 9600a b d e - 3840a b d e + 640b d +--R * +--R 5 +--R x +--R + +--R 7 4 6 6 5 5 5 6 2 4 4 7 3 3 +--R 3200a b e - 19200a b d e + 48000a b d e - 64000a b d e +--R + +--R 3 8 4 2 2 9 5 10 6 +--R 48000a b d e - 19200a b d e + 3200a b d +--R * +--R 4 +--R x +--R + +--R 8 3 6 7 4 5 6 5 2 4 5 6 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 4 7 4 2 3 8 5 2 9 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 3 +--R x +--R + +--R 9 2 6 8 3 5 7 4 2 4 6 5 3 3 +--R 6400a b e - 38400a b d e + 96000a b d e - 128000a b d e +--R + +--R 5 6 4 2 4 7 5 3 8 6 +--R 96000a b d e - 38400a b d e + 6400a b d +--R * +--R 2 +--R x +--R + +--R 10 6 9 2 5 8 3 2 4 7 4 3 3 +--R 3200a b e - 19200a b d e + 48000a b d e - 64000a b d e +--R + +--R 6 5 4 2 5 6 5 4 7 6 +--R 48000a b d e - 19200a b d e + 3200a b d +--R * +--R x +--R + +--R 11 6 10 5 9 2 2 4 8 3 3 3 7 4 4 2 +--R 640a e - 3840a b d e + 9600a b d e - 12800a b d e + 9600a b d e +--R + +--R 6 5 5 5 6 6 +--R - 3840a b d e + 640a b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 614 + +--S 615 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 2 8 5 2 6 7 2 4 2 5 6 2 6 +--R b e x + (6a b e + 2b d e)x + (15a b e + 12a b d e + b d )x +--R + +--R 3 3 2 2 4 5 2 5 +--R (20a b e + 30a b d e + 6a b d )x +--R + +--R 4 2 2 3 3 2 4 2 4 +--R (15a b e + 40a b d e + 15a b d )x +--R + +--R 5 2 4 2 3 3 2 3 6 2 5 4 2 2 2 +--R (6a b e + 30a b d e + 20a b d )x + (a e + 12a b d e + 15a b d )x +--R + +--R 6 5 2 6 2 +--R (2a d e + 6a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 616 + +--S 617 of 764 +r0:=77/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^6*(d+e*x)^(3/2))+_ + 1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*(d+e*x)^(3/2))+1/40*(-10*b*B*d+_ + 13*A*b*e-3*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*(d+e*x)^(3/2))+11/240*e*_ + (10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*(d+e*x)^(3/2))-_ + 33/320*e^2*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*_ + (d+e*x)^(3/2))+231/640*e^3*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^5*_ + (a+b*x)*(d+e*x)^(3/2))-231/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(15/2)+_ + 231/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)/((b*d-a*e)^7*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((- 45045A b + 10395B a b )e + 34650B b d e )x +--R + +--R 5 2 4 6 +--R (- 225225A a b + 51975B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 45045A b + 183645B a b )d e + 34650B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 450450A a b + 103950B a b )e +--R + +--R 5 2 4 5 5 2 4 +--R (- 225225A a b + 398475B a b )d e + 173250B a b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 450450A a b + 103950B a b )e +--R + +--R 2 4 3 3 5 2 4 2 4 +--R (- 450450A a b + 450450B a b )d e + 346500B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 225225A a b + 51975B a b)e +--R + +--R 3 3 4 2 5 3 3 2 4 +--R (- 450450A a b + 277200B a b )d e + 346500B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (- 45045A a b + 10395B a )e + (- 225225A a b + 86625B a b)d e +--R + +--R 4 2 2 4 +--R 173250B a b d e +--R * +--R x +--R + +--R 5 6 5 5 2 4 +--R (- 45045A a b + 10395B a )d e + 34650B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 6 +--R ((45045A b - 10395B a b )e - 34650B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (210210A a b - 48510B a b )e + (60060A b - 175560B a b )d e +--R + +--R 6 2 4 +--R - 46200B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (384384A a b - 88704B a b )e +--R + +--R 5 2 4 5 6 5 2 4 +--R (282282A a b - 360822B a b )d e + (9009A b - 219219B a b )d e +--R + +--R 6 3 3 +--R - 6930B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (338910A a b - 78210B a b )e +--R + +--R 2 4 3 3 5 +--R (520806A a b - 380886B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (43758A a b - 410718B a b )d e + (- 2574A b - 33066B a b )d e +--R + +--R 6 4 2 +--R 1980B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (137995A a b - 31845B a b)e + (464750A a b - 213400B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (84084A a b - 376904B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 12298A a b - 61842B a b )d e + (1144A b + 9196B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (16640A a b - 3840B a )e + (192790A a b - 57290B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (79170A a b - 166570B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 23114A a b - 55566B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (5408A a b + 16532B a b )d e + (- 624A b - 4016B a b )d e +--R + +--R 6 6 +--R 480B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 1280A a e + (24320A a b - 2560B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (35595A a b - 33125B a b)d e + (- 21070A a b - 12180B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (10024A a b + 3556B a b )d e + (- 2928A a b - 832B a b )d e +--R + +--R 6 5 6 +--R (384A b + 96B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 5 8 6 6 7 5 7 2 6 4 8 3 5 +--R 1920a b e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 3 9 4 4 2 10 5 3 11 6 2 12 7 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920b d e +--R * +--R 6 +--R x +--R + +--R 8 4 8 7 5 7 6 6 2 6 5 7 3 5 +--R 9600a b e - 65280a b d e + 188160a b d e - 295680a b d e +--R + +--R 4 8 4 4 3 9 5 3 2 10 6 2 11 7 +--R 268800a b d e - 134400a b d e + 26880a b d e + 3840a b d e +--R + +--R 12 8 +--R - 1920b d +--R * +--R 5 +--R x +--R + +--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5 +--R 19200a b e - 124800a b d e + 336000a b d e - 470400a b d e +--R + +--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7 +--R 336000a b d e - 67200a b d e - 67200a b d e + 48000a b d e +--R + +--R 11 8 +--R - 9600a b d +--R * +--R 4 +--R x +--R + +--R 10 2 8 9 3 7 8 4 2 6 7 5 3 5 +--R 19200a b e - 115200a b d e + 268800a b d e - 268800a b d e +--R + +--R 5 7 5 3 4 8 6 2 3 9 7 2 10 8 +--R 268800a b d e - 268800a b d e + 115200a b d e - 19200a b d +--R * +--R 3 +--R x +--R + +--R 11 8 10 2 7 9 3 2 6 8 4 3 5 +--R 9600a b e - 48000a b d e + 67200a b d e + 67200a b d e +--R + +--R 7 5 4 4 6 6 5 3 5 7 6 2 4 8 7 +--R - 336000a b d e + 470400a b d e - 336000a b d e + 124800a b d e +--R + +--R 3 9 8 +--R - 19200a b d +--R * +--R 2 +--R x +--R + +--R 12 8 11 7 10 2 2 6 9 3 3 5 +--R 1920a e - 3840a b d e - 26880a b d e + 134400a b d e +--R + +--R 8 4 4 4 7 5 5 3 6 6 6 2 5 7 7 +--R - 268800a b d e + 295680a b d e - 188160a b d e + 65280a b d e +--R + +--R 4 8 8 +--R - 9600a b d +--R * +--R x +--R + +--R 12 7 11 2 6 10 2 3 5 9 3 4 4 +--R 1920a d e - 13440a b d e + 40320a b d e - 67200a b d e +--R + +--R 8 4 5 3 7 5 6 2 6 6 7 5 7 8 +--R 67200a b d e - 40320a b d e + 13440a b d e - 1920a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 617 + +--S 618 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 764 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 6 3 9 5 3 6 2 8 2 4 3 5 2 6 2 7 +--R b e x + (6a b e + 3b d e )x + (15a b e + 18a b d e + 3b d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (20a b e + 45a b d e + 18a b d e + b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (15a b e + 60a b d e + 45a b d e + 6a b d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (6a b e + 45a b d e + 60a b d e + 15a b d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (a e + 18a b d e + 45a b d e + 20a b d )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (3a d e + 18a b d e + 15a b d )x + (3a d e + 6a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 619 + +--S 620 of 764 +r0:=3003/640*e^4*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^6*(d+e*x)^(5/2))+_ + 1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*(d+e*x)^(5/2))+1/8*(-2*b*B*d+_ + 3*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*(d+e*x)^(5/2))+13/48*e*(2*b*B*d-_ + 3*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*(d+e*x)^(5/2))-143/192*e^2*_ + (2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*(d+e*x)^(5/2))+_ + 429/128*e^3*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*_ + (d+e*x)^(5/2))+1001/128*e^4*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^7*_ + (d+e*x)^(3/2))-3003/128*b^(3/2)*e^4*(2*b*B*d-3*A*b*e+a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(17/2)+_ + 3003/128*b*e^4*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^8*sqrt(d+e*x)) +--R +--R +--R (2) +--R 7 6 7 7 6 7 +--R ((135135A b - 45045B a b )e - 90090B b d e )x +--R + +--R 6 2 5 7 7 6 6 +--R (675675A a b - 225225B a b )e + (270270A b - 540540B a b )d e +--R + +--R 7 2 5 +--R - 180180B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 7 +--R (1351350A a b - 450450B a b )e +--R + +--R 6 2 5 6 +--R (1351350A a b - 1351350B a b )d e +--R + +--R 7 6 2 5 7 3 4 +--R (135135A b - 945945B a b )d e - 90090B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 7 +--R (1351350A a b - 450450B a b )e +--R + +--R 2 5 3 4 6 +--R (2702700A a b - 1801800B a b )d e +--R + +--R 6 2 5 2 5 6 3 4 +--R (675675A a b - 2027025B a b )d e - 450450B a b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 +--R (675675A a b - 225225B a b )e +--R + +--R 3 4 4 3 6 +--R (2702700A a b - 1351350B a b )d e +--R + +--R 2 5 3 4 2 5 2 5 3 4 +--R (1351350A a b - 2252250B a b )d e - 900900B a b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 7 +--R (135135A a b - 45045B a b)e +--R + +--R 4 3 5 2 6 +--R (1351350A a b - 540540B a b )d e +--R + +--R 3 4 4 3 2 5 3 4 3 4 +--R (1351350A a b - 1351350B a b )d e - 900900B a b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 6 +--R (270270A a b - 90090B a b)d e +--R + +--R 4 3 5 2 2 5 4 3 3 4 +--R (675675A a b - 405405B a b )d e - 450450B a b d e +--R * +--R x +--R + +--R 5 2 6 2 5 5 2 3 4 +--R (135135A a b - 45045B a b)d e - 90090B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 7 6 7 7 6 7 +--R ((- 135135A b + 45045B a b )e + 90090B b d e )x +--R + +--R 6 2 5 7 +--R (- 630630A a b + 210210B a b )e +--R + +--R 7 6 6 7 2 5 +--R (- 315315A b + 525525B a b )d e + 210210B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 7 +--R (- 1153152A a b + 384384B a b )e +--R + +--R 6 2 5 6 +--R (- 1477476A a b + 1261260B a b )d e +--R + +--R 7 6 2 5 7 3 4 +--R (- 207207A b + 1054053B a b )d e + 138138B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 7 +--R (- 1016730A a b + 338910B a b )e +--R + +--R 2 5 3 4 6 +--R (- 2715570A a b + 1583010B a b )d e +--R + +--R 6 2 5 2 5 +--R (- 978120A a b + 2136420B a b )d e +--R + +--R 7 6 3 4 7 4 3 +--R (- 19305A b + 658515B a b )d e + 12870B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 +--R (- 413985A a b + 137995B a b )e +--R + +--R 3 4 4 3 6 +--R (- 2410980A a b + 1079650B a b )d e +--R + +--R 2 5 3 4 2 5 +--R (- 1814670A a b + 2212210B a b )d e +--R + +--R 6 2 5 3 4 +--R (- 94380A a b + 1241240B a b )d e +--R + +--R 7 6 4 3 7 5 2 +--R (4290A b + 61490B a b )d e - 2860B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 7 +--R (- 49920A a b + 16640B a b)e +--R + +--R 4 3 5 2 6 +--R (- 992355A a b + 364065B a b )d e +--R + +--R 3 4 4 3 2 5 +--R (- 1631760A a b + 1205490B a b )d e +--R + +--R 2 5 3 4 3 4 +--R (- 182910A a b + 1148810B a b )d e +--R + +--R 6 2 5 4 3 7 6 5 2 +--R (20670A a b + 115050B a b )d e + (- 1560A b - 13260B a b )d e +--R + +--R 7 6 +--R 1040B b d e +--R * +--R 2 +--R x +--R + +--R 6 7 7 5 2 6 6 +--R (3840A a b - 1280B a )e + (- 122880A a b + 38400B a b)d e +--R + +--R 4 3 5 2 2 5 +--R (- 685155A a b + 310305B a b )d e +--R + +--R 3 4 4 3 3 4 +--R (- 174300A a b + 514870B a b )d e +--R + +--R 2 5 3 4 4 3 +--R (39270A a b + 103110B a b )d e +--R + +--R 6 2 5 5 2 7 6 6 +--R (- 7440A a b - 23700B a b )d e + (720A b + 4720B a b )d e +--R + +--R 7 7 +--R - 480B b d +--R * +--R x +--R + +--R 7 7 6 7 6 +--R - 768A a e + (9216A a b - 512B a )d e +--R + +--R 5 2 6 2 5 4 3 5 2 3 4 +--R (- 89088A a b + 16384B a b)d e + (- 79905A a b + 100363B a b )d e +--R + +--R 3 4 4 3 4 3 2 5 3 4 5 2 +--R (36330A a b + 23240B a b )d e + (- 13944A a b - 5236B a b )d e +--R + +--R 6 2 5 6 7 6 7 +--R (3408A a b + 992B a b )d e + (- 384A b - 96B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 8 5 10 7 6 9 6 7 2 8 5 8 3 7 +--R 1920a b e - 15360a b d e + 53760a b d e - 107520a b d e +--R + +--R 4 9 4 6 3 10 5 5 2 11 6 4 12 7 3 +--R 134400a b d e - 107520a b d e + 53760a b d e - 15360a b d e +--R + +--R 13 8 2 +--R 1920b d e +--R * +--R 7 +--R x +--R + +--R 9 4 10 8 5 9 7 6 2 8 6 7 3 7 +--R 9600a b e - 72960a b d e + 238080a b d e - 430080a b d e +--R + +--R 5 8 4 6 4 9 5 5 3 10 6 4 2 11 7 3 +--R 456960a b d e - 268800a b d e + 53760a b d e + 30720a b d e +--R + +--R 12 8 2 13 9 +--R - 21120a b d e + 3840b d e +--R * +--R 6 +--R x +--R + +--R 10 3 10 9 4 9 8 5 2 8 7 6 3 7 +--R 19200a b e - 134400a b d e + 385920a b d e - 552960a b d e +--R + +--R 6 7 4 6 5 8 5 5 4 9 6 4 3 10 7 3 +--R 322560a b d e + 161280a b d e - 403200a b d e + 276480a b d e +--R + +--R 2 11 8 2 12 9 13 10 +--R - 80640a b d e + 3840a b d e + 1920b d +--R * +--R 5 +--R x +--R + +--R 11 2 10 10 3 9 9 4 2 8 8 5 3 7 +--R 19200a b e - 115200a b d e + 240000a b d e - 76800a b d e +--R + +--R 7 6 4 6 6 7 5 5 5 8 6 4 +--R - 537600a b d e + 1075200a b d e - 940800a b d e +--R + +--R 4 9 7 3 3 10 8 2 2 11 9 12 10 +--R 384000a b d e - 19200a b d e - 38400a b d e + 9600a b d +--R * +--R 4 +--R x +--R + +--R 12 10 11 2 9 10 3 2 8 9 4 3 7 +--R 9600a b e - 38400a b d e - 19200a b d e + 384000a b d e +--R + +--R 8 5 4 6 7 6 5 5 6 7 6 4 5 8 7 3 +--R - 940800a b d e + 1075200a b d e - 537600a b d e - 76800a b d e +--R + +--R 4 9 8 2 3 10 9 2 11 10 +--R 240000a b d e - 115200a b d e + 19200a b d +--R * +--R 3 +--R x +--R + +--R 13 10 12 9 11 2 2 8 10 3 3 7 +--R 1920a e + 3840a b d e - 80640a b d e + 276480a b d e +--R + +--R 9 4 4 6 8 5 5 5 7 6 6 4 6 7 7 3 +--R - 403200a b d e + 161280a b d e + 322560a b d e - 552960a b d e +--R + +--R 5 8 8 2 4 9 9 3 10 10 +--R 385920a b d e - 134400a b d e + 19200a b d +--R * +--R 2 +--R x +--R + +--R 13 9 12 2 8 11 2 3 7 10 3 4 6 +--R 3840a d e - 21120a b d e + 30720a b d e + 53760a b d e +--R + +--R 9 4 5 5 8 5 6 4 7 6 7 3 6 7 8 2 +--R - 268800a b d e + 456960a b d e - 430080a b d e + 238080a b d e +--R + +--R 5 8 9 4 9 10 +--R - 72960a b d e + 9600a b d +--R * +--R x +--R + +--R 13 2 8 12 3 7 11 2 4 6 10 3 5 5 +--R 1920a d e - 15360a b d e + 53760a b d e - 107520a b d e +--R + +--R 9 4 6 4 8 5 7 3 7 6 8 2 6 7 9 +--R 134400a b d e - 107520a b d e + 53760a b d e - 15360a b d e +--R + +--R 5 8 10 +--R 1920a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 620 + +--S 621 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 622 + +--S 623 of 764 +r0:=-2/143*(4*b*B*d-13*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/1287*(b*d-a*e)*(4*b*B*d-13*A*b*e+9*a*B*e)*_ + (d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+_ + 2/13*B*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 198B b e x + ((234A b + 234B a)e + 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (286A a e + (884A b + 884B a)d e + 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (1144A a d e + (1196A b + 1196B a)d e + 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (1716A a d e + (624A b + 624B a)d e + 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (1144A a d e + (26A b + 26B a)d e - 8B b d e)x + 286A a d e +--R + +--R 5 6 +--R (- 52A b - 52B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 623 + +--S 624 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 625 + +--S 626 of 764 +r0:=-2/99*(4*b*B*d-11*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/693*(b*d-a*e)*(4*b*B*d-11*A*b*e+7*a*B*e)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/11*B*_ + (a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 126B b e x + ((154A b + 154B a)e + 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (198A a e + (418A b + 418B a)d e + 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (594A a d e + (330A b + 330B a)d e + 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (594A a d e + (22A b + 22B a)d e - 8B b d e)x + 198A a d e +--R + +--R 4 5 +--R (- 44A b - 44B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 626 + +--S 627 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (1) (B e x + (A e + B d)x + A d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 628 + +--S 629 of 764 +r0:=-2/63*(4*b*B*d-9*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/315*(b*d-a*e)*(4*b*B*d-9*A*b*e+5*a*B*e)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/9*B*_ + (a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B b e x + ((90A b + 90B a)e + 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (126A a e + (144A b + 144B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (252A a d e + (18A b + 18B a)d e - 8B b d e)x + 126A a d e +--R + +--R 3 4 +--R (- 36A b - 36B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 629 + +--S 630 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 764 +t0:=(A+B*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R +-------+ | 2 2 2 +--R (1) (B x + A)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 631 + +--S 632 of 764 +r0:=-2/35*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/105*(b*d-a*e)*(4*b*B*d-7*A*b*e+3*a*B*e)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/7*B*_ + (a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B b e x + ((42A b + 42B a)e + 6B b d e )x +--R + +--R 3 2 2 2 +--R (70A a e + (14A b + 14B a)d e - 8B b d e)x + 70A a d e +--R + +--R 2 3 +--R (- 28A b - 28B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 632 + +--S 633 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 634 + +--S 635 of 764 +r0:=-2/15*(4*b*B*d-5*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^2)+4/15*(b*d-a*e)*(4*b*B*d-5*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3*(a+b*x))+2/5*B*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e) +--R +--R +--R (2) +--R 2 2 2 2 +--R 6B b e x + ((10A b + 10B a)e - 8B b d e)x + 30A a e +--R + +--R 2 +--R (- 20A b - 20B a)d e + 16B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 635 + +--S 636 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 637 + +--S 638 of 764 +r0:=-2*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+2/3*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^2*(b*d-a*e))-4/3*(4*b*B*d-3*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R 2B b e x + ((6A b + 6B a)e - 8B b d e)x - 6A a e +--R + +--R 2 +--R (12A b + 12B a)d e - 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 638 + +--S 639 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 640 + +--S 641 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))+2/3*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^2*(b*d-a*e)*sqrt(d+e*x))+4/3*(4*b*B*d-A*b*e-3*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R 6B b e x + ((- 6A b - 6B a)e + 24B b d e)x - 2A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e + 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 641 + +--S 642 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 764 +t0:=(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (B x + A)\|b x + 2a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 643 + +--S 644 of 764 +r0:=-2/5*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/5*(4*b*B*d+A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/15*(4*b*B*d+A*b*e-5*a*B*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 30B b e x + ((- 10A b - 10B a)e - 40B b d e)x - 6A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e - 16B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 644 + +--S 645 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 764 +r0:=-2/255*(8*b*B*d-17*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/17*B*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/12155*(b*d-a*e)^2*(8*b*B*d-17*A*b*e+_ + 9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/109395*_ + (b*d-a*e)^3*(8*b*B*d-17*A*b*e+9*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5*(a+b*x))+4/1105*(b*d-a*e)*(8*b*B*d-17*A*b*e+_ + 9*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 8 8 3 2 8 3 7 7 +--R 12870B b e x + ((14586A b + 43758B a b )e + 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (50490A a b + 50490B a b)e + (51612A b + 154836B a b )d e +--R + +--R 3 2 6 +--R 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (59670A a b + 19890B a )e + (183600A a b + 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (63036A b + 189108B a b )d e + 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R 24310A a e + (225420A a b + 75140B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (233580A a b + 233580B a b)d e + (27200A b + 81600B a b )d e +--R + +--R 3 4 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R 97240A a d e + (304980A a b + 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (108120A a b + 108120B a b)d e + (170A b + 510B a b )d e +--R + +--R 3 5 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R 145860A a d e + (159120A a b + 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (1530A a b + 1530B a b)d e + (- 204A b - 612B a b )d e +--R + +--R 3 6 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R 97240A a d e + (6630A a b + 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (- 2040A a b - 2040B a b)d e + (272A b + 816B a b )d e +--R + +--R 3 7 +--R - 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (4080A a b + 4080B a b)d e + (- 544A b - 1632B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 109395b e x + 109395a e +--R Type: Expression(Integer) +--E 647 + +--S 648 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 649 + +--S 650 of 764 +r0:=-2/195*(8*b*B*d-15*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/15*B*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/6435*(b*d-a*e)^2*(8*b*B*d-15*A*b*e+7*a*B*e)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/45045*(b*d-a*e)^3*_ + (8*b*B*d-15*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/715*(b*d-a*e)*(8*b*B*d-15*A*b*e+7*a*B*e)*(a+b*x)*_ + (d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 7 7 3 2 7 3 6 6 +--R 6006B b e x + ((6930A b + 20790B a b )e + 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (24570A a b + 24570B a b)e + (17010A b + 51030B a b )d e +--R + +--R 3 2 5 +--R 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (30030A a b + 10010B a )e + (62790A a b + 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (11130A b + 33390B a b )d e + 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R 12870A a e + (81510A a b + 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (44070A a b + 44070B a b)d e + (150A b + 450B a b )d e +--R + +--R 3 4 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 38610A a d e + (64350A a b + 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1170A a b + 1170B a b)d e + (- 180A b - 540B a b )d e +--R + +--R 3 5 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 38610A a d e + (4290A a b + 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1560A a b - 1560B a b)d e + (240A b + 720B a b )d e +--R + +--R 3 6 +--R - 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (3120A a b + 3120B a b)d e + (- 480A b - 1440B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 650 + +--S 651 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 652 + +--S 653 of 764 +r0:=-2/143*(8*b*B*d-13*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/13*B*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/3003*(b*d-a*e)^2*(8*b*B*d-13*A*b*e+5*a*B*e)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/15015*(b*d-a*e)^3*_ + (8*b*B*d-13*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/429*(b*d-a*e)*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 6 6 3 2 6 3 5 5 +--R 2310B b e x + ((2730A b + 8190B a b )e + 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (10010A a b + 10010B a b)e + (3640A b + 10920B a b )d e +--R + +--R 3 2 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (12870A a b + 4290B a )e + (14300A a b + 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (130A b + 390B a b )d e - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R 6006A a e + (20592A a b + 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 3 4 2 +--R (858A a b + 858B a b)d e + (- 156A b - 468B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R 12012A a d e + (2574A a b + 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 1144A a b - 1144B a b)d e + (208A b + 624B a b )d e +--R + +--R 3 5 +--R - 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (2288A a b + 2288B a b)d e + (- 416A b - 1248B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 653 + +--S 654 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 655 + +--S 656 of 764 +r0:=-2/99*(8*b*B*d-11*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^2)+2/11*B*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e)-16/1155*(b*d-a*e)^2*(8*b*B*d-11*A*b*e+3*a*B*e)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/3465*(b*d-a*e)^3*_ + (8*b*B*d-11*A*b*e+3*a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/231*(b*d-a*e)*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 5 5 3 2 5 3 4 4 +--R 630B b e x + ((770A b + 2310B a b )e + 70B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((2970A a b + 2970B a b)e + (110A b + 330B a b )d e - 80B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (4158A a b + 1386B a )e + (594A a b + 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 132A b - 396B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R 2310A a e + (1386A a b + 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R (- 792A a b - 792B a b)d e + (176A b + 528B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (1584A a b + 1584B a b)d e + (- 352A b - 1056B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 656 + +--S 657 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 658 + +--S 659 of 764 +r0:=-2/63*(8*b*B*d-9*A*b*e+a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(b*e^2)+2/9*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(b*e)-16/315*(b*d-a*e)^2*(8*b*B*d-9*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^4)+32/315*(b*d-a*e)^3*_ + (8*b*B*d-9*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^5*(a+b*x))+4/105*(b*d-a*e)*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^3) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((90A b + 270B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((378A a b + 378B a b)e + (- 108A b - 324B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (630A a b + 210B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (144A b + 432B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 630A a e + (- 1260A a b - 420B a )d e + (1008A a b + 1008B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 288A b - 864B a b )d e + 256B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 659 + +--S 660 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 661 + +--S 662 of 764 +r0:=-2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+2/7*(8*b*B*d-7*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/(e^2*(b*d-a*e))+16/35*(b*d-a*e)*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-32/35*(b*d-a*e)^2*(8*b*B*d-_ + 7*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-_ + 12/35*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^3 +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((14A b + 42B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((70A a b + 70B a b)e + (- 28A b - 84B a b )d e + 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (210A a b + 70B a )e + (- 280A a b - 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (112A b + 336B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (224A b + 672B a b )d e - 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 662 + +--S 663 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 664 + +--S 665 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))-2/3*(8*b*B*d-5*A*b*e-3*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*sqrt(d+e*x))-16/15*b*(8*b*B*d-5*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+32/15*b*(b*d-a*e)*_ + (8*b*B*d-5*A*b*e-3*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x))+4/5*b*(8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((10A b + 30B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((90A a b + 90B a b)e + (- 60A b - 180B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 90A a b - 30B a )e + (360A a b + 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 160A b - 480B a b )d e + 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 665 + +--S 666 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + 2a b x + a +--R --------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 667 + +--S 668 of 764 +r0:=-2/5*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/15*(8*b*B*d-3*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/5*b*(8*b*B*d-_ + 3*A*b*e-5*a*B*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(b*d-a*e)*_ + sqrt(d+e*x))+16/15*b^2*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(b*d-a*e))-32/15*b^2*(8*b*B*d-3*A*b*e-_ + 5*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((30A b + 90B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (180A b + 540B a b )d e - 480B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 30A a b - 10B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (96A b + 288B a b )d e - 256B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 668 + +--S 669 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 3 8 4 3 3 4 2 7 +--R B b e x + ((A b + 4B a b )e + 3B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 6 +--R ((4A a b + 6B a b )e + (3A b + 12B a b )d e + 3B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (6A a b + 4B a b)e + (12A a b + 18B a b )d e +--R + +--R 4 3 2 4 3 +--R (3A b + 12B a b )d e + B b d +--R * +--R 5 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (4A a b + B a )e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (12A a b + 18B a b )d e + (A b + 4B a b )d +--R * +--R 4 +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R A a e + (12A a b + 3B a )d e + (18A a b + 12B a b)d e +--R + +--R 3 2 2 3 +--R (4A a b + 6B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 3 4 2 2 2 3 3 2 +--R (3A a d e + (12A a b + 3B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 2 3 4 3 4 3 +--R (3A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 670 + +--S 671 of 764 +r0:=-32/6783*(b*d-a*e)^2*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+20/2261*(b*d-a*e)*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-_ + 2/133*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/21*B*(a+b*x)*(d+e*x)^(9/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/323323*(b*d-a*e)^4*(4*b*B*d-7*A*b*e+_ + 3*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/2909907*(b*d-a*e)^5*(4*b*B*d-7*A*b*e+3*a*B*e)*(d+e*x)^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/29393*(b*d-a*e)^3*_ + (4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 10 10 5 4 10 5 9 9 +--R 277134B b e x + ((306306A b + 1531530B a b )e + 933504B b d e )x +--R + +--R 4 2 3 10 +--R (1711710A a b + 3423420B a b )e +--R + +--R 5 4 9 5 2 8 +--R (1045044A b + 5225220B a b )d e + 1065636B b d e +--R * +--R 8 +--R x +--R + +--R 2 3 3 2 10 +--R (3879876A a b + 3879876B a b )e +--R + +--R 4 2 3 9 +--R (5933928A a b + 11867856B a b )d e +--R + +--R 5 4 2 8 5 3 7 +--R (1213212A b + 6066060B a b )d e + 415272B b d e +--R * +--R 7 +--R x +--R + +--R 3 2 4 10 +--R (4476780A a b + 2238390B a b)e +--R + +--R 2 3 3 2 9 +--R (13728792A a b + 13728792B a b )d e +--R + +--R 4 2 3 2 8 +--R (7039956A a b + 14079912B a b )d e +--R + +--R 5 4 3 7 5 4 6 +--R (484176A b + 2420880B a b )d e + 462B b d e +--R * +--R 6 +--R x +--R + +--R 4 5 10 +--R (2645370A a b + 529074B a )e +--R + +--R 3 2 4 9 +--R (16279200A a b + 8139600B a b)d e +--R + +--R 2 3 3 2 2 8 +--R (16767576A a b + 16767576B a b )d e +--R + +--R 4 2 3 3 7 5 4 4 6 +--R (2901528A a b + 5803056B a b )d e + (882A b + 4410B a b )d e +--R + +--R 5 5 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 5 10 4 5 9 +--R 646646A a e + (9993620A a b + 1998724B a )d e +--R + +--R 3 2 4 2 8 +--R (20710760A a b + 10355380B a b)d e +--R + +--R 2 3 3 2 3 7 +--R (7235200A a b + 7235200B a b )d e +--R + +--R 4 2 3 4 6 5 4 5 5 +--R (9310A a b + 18620B a b )d e + (- 980A b - 4900B a b )d e +--R + +--R 5 6 4 +--R 560B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 2 8 +--R 2586584A a d e + (13520780A a b + 2704156B a )d e +--R + +--R 3 2 4 3 7 +--R (9586640A a b + 4793320B a b)d e +--R + +--R 2 3 3 2 4 6 4 2 3 5 5 +--R (45220A a b + 45220B a b )d e + (- 10640A a b - 21280B a b )d e +--R + +--R 5 4 6 4 5 7 3 +--R (1120A b + 5600B a b )d e - 640B b d e +--R * +--R 3 +--R x +--R + +--R 5 2 8 4 5 3 7 +--R 3879876A a d e + (7054320A a b + 1410864B a )d e +--R + +--R 3 2 4 4 6 2 3 3 2 5 5 +--R (135660A a b + 67830B a b)d e + (- 54264A a b - 54264B a b )d e +--R + +--R 4 2 3 6 4 5 4 7 3 +--R (12768A a b + 25536B a b )d e + (- 1344A b - 6720B a b )d e +--R + +--R 5 8 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 3 7 4 5 4 6 +--R 2586584A a d e + (293930A a b + 58786B a )d e +--R + +--R 3 2 4 5 5 2 3 3 2 6 4 +--R (- 180880A a b - 90440B a b)d e + (72352A a b + 72352B a b )d e +--R + +--R 4 2 3 7 3 5 4 8 2 +--R (- 17024A a b - 34048B a b )d e + (1792A b + 8960B a b )d e +--R + +--R 5 9 +--R - 1024B b d e +--R * +--R x +--R + +--R 5 4 6 4 5 5 5 +--R 646646A a d e + (- 587860A a b - 117572B a )d e +--R + +--R 3 2 4 6 4 2 3 3 2 7 3 +--R (361760A a b + 180880B a b)d e + (- 144704A a b - 144704B a b )d e +--R + +--R 4 2 3 8 2 5 4 9 +--R (34048A a b + 68096B a b )d e + (- 3584A b - 17920B a b )d e +--R + +--R 5 10 +--R 2048B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 2909907b e x + 2909907a e +--R Type: Expression(Integer) +--E 671 + +--S 672 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 2 7 4 3 2 4 6 +--R B b e x + ((A b + 4B a b )e + 2B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 5 +--R ((4A a b + 6B a b )e + (2A b + 8B a b )d e + B b d )x +--R + +--R 2 2 3 2 3 2 2 4 3 2 4 +--R ((6A a b + 4B a b)e + (8A a b + 12B a b )d e + (A b + 4B a b )d )x +--R + +--R 3 4 2 2 2 3 3 2 2 2 3 +--R ((4A a b + B a )e + (12A a b + 8B a b)d e + (4A a b + 6B a b )d )x +--R + +--R 4 2 3 4 2 2 3 2 2 +--R (A a e + (8A a b + 2B a )d e + (6A a b + 4B a b)d )x +--R + +--R 4 3 4 2 4 2 +--R (2A a d e + (4A a b + B a )d )x + A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 673 + +--S 674 of 764 +r0:=-32/12597*(b*d-a*e)^2*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+4/969*(b*d-a*e)*(12*b*B*d-19*A*b*e+_ + 7*a*B*e)*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-_ + 2/323*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/19*B*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/415701*(b*d-a*e)^4*(12*b*B*d-19*A*b*e+_ + 7*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/2909907*(b*d-a*e)^5*(12*b*B*d-19*A*b*e+7*a*B*e)*(d+e*x)^(7/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/46189*(b*d-a*e)^3*_ + (12*b*B*d-19*A*b*e+7*a*B*e)*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 9 9 5 4 9 5 8 8 +--R 306306B b e x + ((342342A b + 1711710B a b )e + 702702B b d e )x +--R + +--R 4 2 3 9 +--R (1939938A a b + 3879876B a b )e +--R + +--R 5 4 8 5 2 7 +--R (798798A b + 3993990B a b )d e + 414414B b d e +--R * +--R 7 +--R x +--R + +--R 2 3 3 2 9 +--R (4476780A a b + 4476780B a b )e +--R + +--R 4 2 3 8 +--R (4626006A a b + 9252012B a b )d e +--R + +--R 5 4 2 7 5 3 6 +--R (482790A b + 2413950B a b )d e + 1386B b d e +--R * +--R 6 +--R x +--R + +--R 3 2 4 9 +--R (5290740A a b + 2645370B a b)e +--R + +--R 2 3 3 2 8 +--R (10988460A a b + 10988460B a b )d e +--R + +--R 4 2 3 2 7 5 4 3 6 +--R (2889558A a b + 5779116B a b )d e + (2394A b + 11970B a b )d e +--R + +--R 5 4 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 4 5 9 3 2 4 8 +--R (3233230A a b + 646646B a )e + (13520780A a b + 6760390B a b)d e +--R + +--R 2 3 3 2 2 7 +--R (7189980A a b + 7189980B a b )d e +--R + +--R 4 2 3 3 6 5 4 4 5 +--R (22610A a b + 45220B a b )d e + (- 2660A b - 13300B a b )d e +--R + +--R 5 5 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 5 8 +--R 831402A a e + (8775910A a b + 1755182B a )d e +--R + +--R 3 2 4 2 7 +--R (9489740A a b + 4744870B a b)d e +--R + +--R 2 3 3 2 3 6 4 2 3 4 5 +--R (96900A a b + 96900B a b )d e + (- 25840A a b - 51680B a b )d e +--R + +--R 5 4 5 4 5 6 3 +--R (3040A b + 15200B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 2 7 +--R 2494206A a d e + (6928350A a b + 1385670B a )d e +--R + +--R 3 2 4 3 6 +--R (251940A a b + 125970B a b)d e +--R + +--R 2 3 3 2 4 5 +--R (- 116280A a b - 116280B a b )d e +--R + +--R 4 2 3 5 4 5 4 6 3 +--R (31008A a b + 62016B a b )d e + (- 3648A b - 18240B a b )d e +--R + +--R 5 7 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 2 7 4 5 3 6 +--R 2494206A a d e + (461890A a b + 92378B a )d e +--R + +--R 3 2 4 4 5 +--R (- 335920A a b - 167960B a b)d e +--R + +--R 2 3 3 2 5 4 +--R (155040A a b + 155040B a b )d e +--R + +--R 4 2 3 6 3 5 4 7 2 +--R (- 41344A a b - 82688B a b )d e + (4864A b + 24320B a b )d e +--R + +--R 5 8 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 3 6 4 5 4 5 +--R 831402A a d e + (- 923780A a b - 184756B a )d e +--R + +--R 3 2 4 5 4 2 3 3 2 6 3 +--R (671840A a b + 335920B a b)d e + (- 310080A a b - 310080B a b )d e +--R + +--R 4 2 3 7 2 5 4 8 +--R (82688A a b + 165376B a b )d e + (- 9728A b - 48640B a b )d e +--R + +--R 5 9 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 2909907b e x + 2909907a e +--R Type: Expression(Integer) +--E 674 + +--S 675 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 6 4 3 4 5 +--R B b e x + ((A b + 4B a b )e + B b d)x +--R + +--R 3 2 2 4 3 4 +--R ((4A a b + 6B a b )e + (A b + 4B a b )d)x +--R + +--R 2 2 3 3 2 2 3 +--R ((6A a b + 4B a b)e + (4A a b + 6B a b )d)x +--R + +--R 3 4 2 2 3 2 4 3 4 +--R ((4A a b + B a )e + (6A a b + 4B a b)d)x + (A a e + (4A a b + B a )d)x +--R + +--R 4 +--R A a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 764 +r0:=-32/7293*(b*d-a*e)^2*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^4)+4/663*(b*d-a*e)*(12*b*B*d-_ + 17*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/_ + (b*e^3)-2/255*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e^2)+2/17*B*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(b*e)-256/153153*(b*d-a*e)^4*(12*b*B*d-17*A*b*e+_ + 5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+_ + 512/765765*(b*d-a*e)^5*(12*b*B*d-17*A*b*e+5*a*B*e)*(d+e*x)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*(a+b*x))+64/21879*(b*d-a*e)^3*_ + (12*b*B*d-17*A*b*e+5*a*B*e)*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 8 8 5 4 8 5 7 7 +--R 90090B b e x + ((102102A b + 510510B a b )e + 108108B b d e )x +--R + +--R 4 2 3 8 5 4 7 +--R (589050A a b + 1178100B a b )e + (125664A b + 628320B a b )d e +--R + +--R 5 2 6 +--R 1386B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 3 2 8 +--R (1392300A a b + 1392300B a b )e +--R + +--R 4 2 3 7 5 4 2 6 +--R (749700A a b + 1499400B a b )d e + (2142A b + 10710B a b )d e +--R + +--R 5 3 5 +--R - 1512B b d e +--R * +--R 5 +--R x +--R + +--R 3 2 4 8 +--R (1701700A a b + 850850B a b)e +--R + +--R 2 3 3 2 7 +--R (1856400A a b + 1856400B a b )d e +--R + +--R 4 2 3 2 6 5 4 3 5 +--R (17850A a b + 35700B a b )d e + (- 2380A b - 11900B a b )d e +--R + +--R 5 4 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 4 5 8 3 2 4 7 +--R (1093950A a b + 218790B a )e + (2431000A a b + 1215500B a b)d e +--R + +--R 2 3 3 2 2 6 4 2 3 3 5 +--R (66300A a b + 66300B a b )d e + (- 20400A a b - 40800B a b )d e +--R + +--R 5 4 4 4 5 5 3 +--R (2720A b + 13600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 5 8 4 5 7 +--R 306306A a e + (1750320A a b + 350064B a )d e +--R + +--R 3 2 4 2 6 2 3 3 2 3 5 +--R (145860A a b + 72930B a b)d e + (- 79560A a b - 79560B a b )d e +--R + +--R 4 2 3 4 4 5 4 5 3 +--R (24480A a b + 48960B a b )d e + (- 3264A b - 16320B a b )d e +--R + +--R 5 6 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 2 6 +--R 612612A a d e + (218790A a b + 43758B a )d e +--R + +--R 3 2 4 3 5 +--R (- 194480A a b - 97240B a b)d e +--R + +--R 2 3 3 2 4 4 +--R (106080A a b + 106080B a b )d e +--R + +--R 4 2 3 5 3 5 4 6 2 +--R (- 32640A a b - 65280B a b )d e + (4352A b + 21760B a b )d e +--R + +--R 5 7 +--R - 3072B b d e +--R * +--R x +--R + +--R 5 2 6 4 5 3 5 +--R 306306A a d e + (- 437580A a b - 87516B a )d e +--R + +--R 3 2 4 4 4 2 3 3 2 5 3 +--R (388960A a b + 194480B a b)d e + (- 212160A a b - 212160B a b )d e +--R + +--R 4 2 3 6 2 5 4 7 +--R (65280A a b + 130560B a b )d e + (- 8704A b - 43520B a b )d e +--R + +--R 5 8 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 765765b e x + 765765a e +--R Type: Expression(Integer) +--E 677 + +--S 678 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 678 + +)clear all + +--S 679 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 679 + +--S 680 of 764 +r0:=-32/1287*(b*d-a*e)^2*(4*b*B*d-5*A*b*e+a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(b*e^4)+4/143*(b*d-a*e)*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b*e^3)-2/65*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e^2)+_ + 2/15*B*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(b*e)-_ + 256/15015*(b*d-a*e)^4*(4*b*B*d-5*A*b*e+a*B*e)*(d+e*x)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+512/45045*(b*d-a*e)^5*(4*b*B*d-_ + 5*A*b*e+a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^7*_ + (a+b*x))+64/3003*(b*d-a*e)^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 7 7 5 4 7 5 6 6 +--R 6006B b e x + ((6930A b + 34650B a b )e + 462B b d e )x +--R + +--R 4 2 3 7 5 4 6 +--R (40950A a b + 81900B a b )e + (630A b + 3150B a b )d e +--R + +--R 5 2 5 +--R - 504B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 7 4 2 3 6 +--R (100100A a b + 100100B a b )e + (4550A a b + 9100B a b )d e +--R + +--R 5 4 2 5 5 3 4 +--R (- 700A b - 3500B a b )d e + 560B b d e +--R * +--R 4 +--R x +--R + +--R 3 2 4 7 2 3 3 2 6 +--R (128700A a b + 64350B a b)e + (14300A a b + 14300B a b )d e +--R + +--R 4 2 3 2 5 5 4 3 4 +--R (- 5200A a b - 10400B a b )d e + (800A b + 4000B a b )d e +--R + +--R 5 4 3 +--R - 640B b d e +--R * +--R 3 +--R x +--R + +--R 4 5 7 3 2 4 6 +--R (90090A a b + 18018B a )e + (25740A a b + 12870B a b)d e +--R + +--R 2 3 3 2 2 5 4 2 3 3 4 +--R (- 17160A a b - 17160B a b )d e + (6240A a b + 12480B a b )d e +--R + +--R 5 4 4 3 5 5 2 +--R (- 960A b - 4800B a b )d e + 768B b d e +--R * +--R 2 +--R x +--R + +--R 5 7 4 5 6 +--R 30030A a e + (30030A a b + 6006B a )d e +--R + +--R 3 2 4 2 5 2 3 3 2 3 4 +--R (- 34320A a b - 17160B a b)d e + (22880A a b + 22880B a b )d e +--R + +--R 4 2 3 4 3 5 4 5 2 +--R (- 8320A a b - 16640B a b )d e + (1280A b + 6400B a b )d e +--R + +--R 5 6 +--R - 1024B b d e +--R * +--R x +--R + +--R 5 6 4 5 2 5 +--R 30030A a d e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 3 4 2 3 3 2 4 3 +--R (68640A a b + 34320B a b)d e + (- 45760A a b - 45760B a b )d e +--R + +--R 4 2 3 5 2 5 4 6 +--R (16640A a b + 33280B a b )d e + (- 2560A b - 12800B a b )d e +--R + +--R 5 7 +--R 2048B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 680 + +--S 681 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 682 + +--S 683 of 764 +r0:=-160/9009*(b*d-a*e)^2*(12*b*B*d-13*A*b*e+a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x)/(b*e^4)+20/1287*(b*d-a*e)*(12*b*B*d-_ + 13*A*b*e+a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/_ + (b*e^3)-2/143*(12*b*B*d-13*A*b*e+a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x)/(b*e^2)+2/13*B*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x)/(b*e)-256/9009*(b*d-a*e)^4*(12*b*B*d-13*A*b*e+a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^6)+512/9009*(b*d-a*e)^5*_ + (12*b*B*d-13*A*b*e+a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (b*e^7*(a+b*x))+64/3003*(b*d-a*e)^3*(12*b*B*d-13*A*b*e+a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e^5) +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 1386B b e x + ((1638A b + 8190B a b )e - 1512B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (10010A a b + 20020B a b )e + (- 1820A b - 9100B a b )d e +--R + +--R 5 2 4 +--R 1680B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (25740A a b + 25740B a b )e + (- 11440A a b - 22880B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (2080A b + 10400B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (36036A a b + 18018B a b)e + (- 30888A a b - 30888B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (13728A a b + 27456B a b )d e + (- 2496A b - 12480B a b )d e +--R + +--R 5 4 2 +--R 2304B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (30030A a b + 6006B a )e + (- 48048A a b - 24024B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (41184A a b + 41184B a b )d e + (- 18304A a b - 36608B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (3328A b + 16640B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R 18018A a e + (- 60060A a b - 12012B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (96096A a b + 48048B a b)d e + (- 82368A a b - 82368B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (36608A a b + 73216B a b )d e + (- 6656A b - 33280B a b )d e +--R + +--R 5 6 +--R 6144B b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 9009b e x + 9009a e +--R Type: Expression(Integer) +--E 683 + +--S 684 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 685 + +--S 686 of 764 +r0:=-2*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + sqrt(d+e*x))+160/693*(b*d-a*e)*(12*b*B*d-11*A*b*e-a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4-20/99*(12*b*B*d-11*A*b*e-_ + a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3+2/11*_ + (12*b*B*d-11*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/_ + (e^2*(b*d-a*e))+256/693*(b*d-a*e)^3*(12*b*B*d-11*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-512/693*(b*d-a*e)^4*_ + (12*b*B*d-11*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x))-64/231*(b*d-a*e)^2*(12*b*B*d-11*A*b*e-a*B*e)*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 126B b e x + ((154A b + 770B a b )e - 168B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (990A a b + 1980B a b )e + (- 220A b - 1100B a b )d e +--R + +--R 5 2 4 +--R 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2772A a b + 2772B a b )e + (- 1584A a b - 3168B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (352A b + 1760B a b )d e - 384B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (4620A a b + 2310B a b)e + (- 5544A a b - 5544B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (3168A a b + 6336B a b )d e + (- 704A b - 3520B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (6930A a b + 1386B a )e + (- 18480A a b - 9240B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (22176A a b + 22176B a b )d e + (- 12672A a b - 25344B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (2816A b + 14080B a b )d e - 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 +--R - 1386A a e + (13860A a b + 2772B a )d e +--R + +--R 3 2 4 2 4 2 3 3 2 3 3 +--R (- 36960A a b - 18480B a b)d e + (44352A a b + 44352B a b )d e +--R + +--R 4 2 3 4 2 5 4 5 +--R (- 25344A a b - 50688B a b )d e + (5632A b + 28160B a b )d e +--R + +--R 5 6 +--R - 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +-------+ +--R (693b e x + 693a e )\|e x + d +--R Type: Expression(Integer) +--E 686 + +--S 687 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 688 + +--S 689 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^(3/2))-2*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(b*d-a*e)*sqrt(d+e*x))-160/63*b*(4*b*B*d-3*A*b*e-a*B*e)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+20/9*b*(4*b*B*d-3*A*b*e-a*B*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/(e^3*(b*d-a*e))-_ + 256/63*b*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^6+512/63*b*(b*d-a*e)^3*(4*b*B*d-3*A*b*e-a*B*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+64/21*b*(b*d-_ + a*e)*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 14B b e x + ((18A b + 90B a b )e - 24B b d e )x +--R + +--R 4 2 3 6 5 4 5 5 2 4 4 +--R ((126A a b + 252B a b )e + (- 36A b - 180B a b )d e + 48B b d e )x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (420A a b + 420B a b )e + (- 336A a b - 672B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (96A b + 480B a b )d e - 128B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (1260A a b + 630B a b)e + (- 2520A a b - 2520B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (2016A a b + 4032B a b )d e + (- 576A b - 2880B a b )d e +--R + +--R 5 4 2 +--R 768B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 630A a b - 126B a )e + (5040A a b + 2520B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (- 10080A a b - 10080B a b )d e + (8064A a b + 16128B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (- 2304A b - 11520B a b )d e + 3072B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 420A a b - 84B a )d e + (3360A a b + 1680B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (- 6720A a b - 6720B a b )d e + (5376A a b + 10752B a b )d e +--R + +--R 5 4 5 5 6 +--R (- 1536A b - 7680B a b )d e + 2048B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 689 + +--S 690 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 764 +t0:=(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B b x + (A b + 4B a b )x + (4A a b + 6B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A a b + 4B a b)x + (4A a b + B a )x + A a +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 691 + +--S 692 of 764 +r0:=-2/5*(B*d-A*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(b*d-a*e)*_ + (d+e*x)^(5/2))-2/15*(12*b*B*d-7*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-4/3*b*(12*b*B*d-_ + 7*A*b*e-5*a*B*e)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(b*d-a*e)*_ + sqrt(d+e*x))+32/21*b^2*(12*b*B*d-7*A*b*e-5*a*B*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x)/(e^4*(b*d-a*e))+256/105*b^2*(b*d-a*e)*_ + (12*b*B*d-7*A*b*e-5*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 512/105*b^2*(b*d-a*e)^2*(12*b*B*d-7*A*b*e-5*a*B*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-64/35*b^2*(12*b*B*d-7*A*b*_ + e-5*a*B*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 5 6 6 5 4 6 5 5 5 +--R 30B b e x + ((42A b + 210B a b )e - 72B b d e )x +--R + +--R 4 2 3 6 5 4 5 +--R (350A a b + 700B a b )e + (- 140A b - 700B a b )d e +--R + +--R 5 2 4 +--R 240B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 2 3 5 +--R (2100A a b + 2100B a b )e + (- 2800A a b - 5600B a b )d e +--R + +--R 5 4 2 4 5 3 3 +--R (1120A b + 5600B a b )d e - 1920B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 3 3 2 5 +--R (- 2100A a b - 1050B a b)e + (12600A a b + 12600B a b )d e +--R + +--R 4 2 3 2 4 5 4 3 3 +--R (- 16800A a b - 33600B a b )d e + (6720A b + 33600B a b )d e +--R + +--R 5 4 2 +--R - 11520B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 2 4 5 +--R (- 350A a b - 70B a )e + (- 2800A a b - 1400B a b)d e +--R + +--R 2 3 3 2 2 4 4 2 3 3 3 +--R (16800A a b + 16800B a b )d e + (- 22400A a b - 44800B a b )d e +--R + +--R 5 4 4 2 5 5 +--R (8960A b + 44800B a b )d e - 15360B b d e +--R * +--R x +--R + +--R 5 6 4 5 5 3 2 4 2 4 +--R - 42A a e + (- 140A a b - 28B a )d e + (- 1120A a b - 560B a b)d e +--R + +--R 2 3 3 2 3 3 4 2 3 4 2 +--R (6720A a b + 6720B a b )d e + (- 8960A a b - 17920B a b )d e +--R + +--R 5 4 5 5 6 +--R (3584A b + 17920B a b )d e - 6144B b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 +--R 105b e x + (105a e + 210b d e )x + (210a d e + 105b d e )x +--R + +--R 2 7 +--R 105a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 692 + +--S 693 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 694 + +--S 695 of 764 +r0:=2/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/5*(A*b-a*B)*(a+b*x)*(d+e*x)^(5/2)/(b^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/7*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(b*d-a*e)^(5/2)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (- 210A a b + 210B a b)e + (420A a b - 420B a b )d e +--R + +--R 4 3 2 +--R (- 210A b + 210B a b )d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 2 +--R (- 210A a b + 210B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 12B a b )e + 90B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 28A a b + 28B a b )e + (154A b - 64B a b )d e + 90B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (140A a b - 140B a b)e + (- 336A a b + 336B a b )d e +--R + +--R 4 3 2 4 3 +--R (322A b - 232B a b )d e + 30B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (322A a b - 322B a b )d e + 30B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 105b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 695 + +--S 696 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 697 + +--S 698 of 764 +r0:=2/3*(A*b-a*B)*(a+b*x)*(d+e*x)^(3/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2/5*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(b*d-a*e)^(3/2)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (b*d-a*e)*(a+b*x)*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 3 2 +--R ((30A a b - 30B a b)e + (- 30A b + 30B a b )d e)x +--R + +--R 2 3 2 2 2 +--R (30A a b - 30B a )e + (- 30A a b + 30B a b)d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 4B a b )e + 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 20A a b + 20B a b)e + (40A b - 28B a b )d e + 6B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A a b - 40B a b)d e + 6B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 15b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 698 + +--S 699 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 700 + +--S 701 of 764 +r0:=2/3*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b*d-a*e)/(b^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*_ + (a+b*x)*sqrt(d+e*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 +-----------+ +--R ((- 6A b + 6B a b)e x + (- 6A a b + 6B a )e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 4B a b)e + 2B b d)x + (6A a b - 6B a )e +--R + +--R 2B a b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R 3b e\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 701 + +--S 702 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 764 +t0:=(A+B*x)/(sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 703 + +--S 704 of 764 +r0:=-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(3/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*B*(a+b*x)*_ + sqrt(d+e*x)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 \|b \|e x + d +--R ((- 2A b + 2B a b)e x + (- 2A a b + 2B a )e)atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (2B b x + 2B a)\|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R b e\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 704 + +--S 705 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 764 +r0:=-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(3/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*(B*d-A*e)*_ + (a+b*x)/(e*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 +-------+ \|b \|e x + d +--R ((2A b - 2B a b)e x + (2A a b - 2B a )e)\|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R ((- 2A b e + 2B b d)x - 2A a e + 2B a d)\|- a e + b d \|b +--R / +--R +------------------+ +--R 2 +-----------+ +-+ +-------+ | 2 2 2 +--R (a e - b d e)\|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 707 + +--S 708 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 709 + +--S 710 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-2*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))*sqrt(b)/((b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-_ + a*B)*(a+b*x)/((b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 +--R (- 6A b + 6B a b)e x +--R + +--R 2 2 2 2 +--R ((- 6A a b + 6B a )e + (- 6A b + 6B a b)d e)x + (- 6A a b + 6B a )d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +--R (6A b - 6B a b)e x +--R + +--R 2 2 2 2 2 2 2 +--R ((4A a b - 6B a )e + (8A b - 4B a b)d e - 2B b d )x - 2A a e +--R + +--R 2 2 +--R (8A a b - 4B a )d e - 2B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e) +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 710 + +--S 711 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 711 + +)clear all + +--S 712 of 764 +t0:=(A+B*x)/((d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 712 + +--S 713 of 764 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+2/3*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-2*b^(3/2)*(A*b-a*B)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 2*b*(A*b-a*B)*(a+b*x)/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 +--R (30A b - 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((30A a b - 30B a b)e + (60A b - 60B a b )d e )x +--R + +--R 2 2 2 3 2 2 +--R ((60A a b - 60B a b)d e + (30A b - 30B a b )d e)x +--R + +--R 2 2 2 +--R (30A a b - 30B a b)d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 +--R (- 30A b + 30B a b )e x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 20A a b + 20B a b)e + (- 70A b + 70B a b )d e )x +--R + +--R 2 3 3 2 2 2 +--R (4A a b - 10B a )e + (- 48A a b + 66B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 46A b + 28B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (22A a b - 4B a )d e + (- 46A a b + 28B a b)d e +--R + +--R 2 3 +--R 6B a b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 713 + +--S 714 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 715 + +--S 716 of 764 +r0:=-1/10*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*(d+e*x)^(7/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+2/5*B*(a+b*x)*(d+e*x)^(9/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+7/12*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-7/20*(4*b*B*d+5*A*b*e-_ + 9*a*B*e)*(d+e*x)^(5/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*e*(b*d-_ + a*e)^(3/2)*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/(b^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*e*(b*d-_ + a*e)*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 5 +-+ | 2 2 2 +--R (60b x + 60a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 718 + +--S 719 of 764 +r0:=-1/6*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*(d+e*x)^(5/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+2/3*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))-5/12*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/_ + (b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/_ + (b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*_ + (a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x + (- 45A a b + 105B a )e +--R + +--R 2 +--R - 60B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 5 4 +-+ | 2 2 2 +--R (12b x + 12a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 719 + +--S 720 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 721 + +--S 722 of 764 +r0:=-1/2*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+2*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-3/4*(4*b*B*d+A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 3A b + 15B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b + 30B a b)e - 24B a b d e)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 4 3 +-----------+ +-+ | 2 2 2 +--R (4b x + 4a b )\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 722 + +--S 723 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 764 +r0:=-2*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/2*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-1/4*e*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/_ + (b^2*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 2A a b - 6B a b)e + 8B a b d e)x + (- A a b - 3B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e + (2A b + 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 3 4 2 2 3 +-----------+ +-+ | 2 2 2 +--R ((4a b e - 4b d)x + 4a b e - 4a b d)\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 725 + +--S 726 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 726 + +)clear all + +--S 727 of 764 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (b x + 2a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 727 + +--S 728 of 764 +r0:=-2/3*B*(a+b*x)*sqrt(d+e*x)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/6*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/4*e*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/_ + (b*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 3A b - B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b - 2B a b)e + 8B a b d e)x + (- 3A a b - B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((3A b + B a b)e - 4B b d)x + (5A a b - B a )e + (- 2A b - 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R ((4a b e - 8a b d e + 4b d )x + 4a b e - 8a b d e + 4a b d ) +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 728 + +)clear all + +--S 729 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 729 + +--S 730 of 764 +r0:=-2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x))+1/2*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/(e*_ + (b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+3/4*e*(4*b*B*d-5*A*b*e+_ + a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-_ + a*e)^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-3/4*(4*b*B*d-5*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x - 8A a e +--R + +--R 2 2 2 +--R (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x + 4a e - 12a b d e +--R + +--R 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 730 + +--S 731 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 731 + +)clear all + +--S 732 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 732 + +--S 733 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/6*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))+5/4*e*(4*b*B*d-_ + 7*A*b*e+3*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b)/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/12*(4*b*B*d-_ + 7*A*b*e+3*a*B*e)/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 105A b + 45B a b )e + 60B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 210A a b + 90B a b)e + (- 105A b + 165B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 105A a b + 45B a )e + (- 210A a b + 150B a b)d e +--R + +--R 2 2 +--R 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (- 105A a b + 45B a )d e + 60B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (12a e - 36a b d e + 24a b d e + 24a b d e - 36a b d e + 12b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 734 + +)clear all + +--S 735 of 764 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 735 + +--S 736 of 764 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+1/10*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-7/20*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-7/12*e*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^4*_ + (d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*b^(3/2)*e*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*b*e*(4*b*B*d-_ + 9*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 5 2 +--R - 60b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 6 3 3 3 4 2 4 4 3 5 5 2 +--R 60a e - 180a b d e + 600a b d e - 900a b d e + 540a b d e +--R + +--R 6 6 +--R - 120b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5 6 +--R 120a d e - 540a b d e + 900a b d e - 600a b d e + 180a b d e +--R + +--R 6 7 +--R - 60b d +--R * +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 5 7 +--R - 60a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 736 + +--S 737 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 737 + +)clear all + +--S 738 of 764 +t0:=(A+B*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 738 + +--S 739 of 764 +r0:=-1/20*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*(d+e*x)^(11/2)/(b^2*e*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))+2/5*B*(a+b*x)*(d+e*x)^(13/2)/(b*e*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-33/160*e*(8*b*B*d+5*A*b*e-13*a*B*e)*_ + (a+b*x)*(d+e*x)^(7/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-11/120*_ + (8*b*B*d+5*A*b*e-13*a*B*e)*(d+e*x)^(9/2)/(b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))+77/64*e^3*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*(d+_ + e*x)^(3/2)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))-231/320*e^2*(8*b*B*d+_ + 5*A*b*e-13*a*B*e)*(d+e*x)^(5/2)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 231/64*e^3*(b*d-a*e)^(3/2)*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(15/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+231/64*e^3*(b*d-a*e)*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*_ + sqrt(d+e*x)/(b^7*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 2 4 5 6 5 4 +--R (17325A a b - 45045B a b )e + (- 17325A b + 72765B a b )d e +--R + +--R 6 2 3 +--R - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (69300A a b - 180180B a b )e +--R + +--R 5 2 4 4 5 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (103950A a b - 270270B a b )e +--R + +--R 2 4 3 3 4 2 4 2 3 +--R (- 103950A a b + 436590B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (69300A a b - 180180B a b)e +--R + +--R 3 3 4 2 4 3 3 2 3 +--R (- 69300A a b + 291060B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (17325A a b - 45045B a )e + (- 17325A a b + 72765B a b)d e +--R + +--R 4 2 2 3 +--R - 27720B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 384B b e x + ((640A b - 1664B a b )e + 3328B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 7040A a b + 18304B a b )e + (10240A b - 37888B a b )d e +--R + +--R 6 2 3 +--R 22144B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 5 +--R (- 46035A a b + 119691B a b )e +--R + +--R 5 2 4 4 +--R (63910A a b - 239822B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (- 11475A b + 132091B a b )d e - 10680B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (- 84315A a b + 219219B a b )e +--R + +--R 2 4 3 3 4 +--R (114840A a b - 433488B a b )d e +--R + +--R 5 2 4 2 3 +--R (- 18975A a b + 233079B a b )d e +--R + +--R 6 5 3 2 6 4 +--R (- 5150A b - 16970B a b )d e - 2480B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (- 63525A a b + 165165B a b)e +--R + +--R 3 3 4 2 4 +--R (85470A a b - 323862B a b )d e +--R + +--R 2 4 3 3 2 3 +--R (- 13365A a b + 171501B a b )d e +--R + +--R 5 2 4 3 2 6 5 4 +--R (- 3740A a b - 11660B a b )d e + (- 1640A b - 1720B a b )d e +--R + +--R 6 5 +--R - 320B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 17325A a b + 45045B a )e + (23100A a b - 87780B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 3465A a b + 45969B a b )d e + (- 990A a b - 2970B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 440A a b - 440B a b )d e + (- 240A b - 80B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 10 3 9 2 2 8 3 7 +-+ | 2 2 2 +--R (960b x + 2880a b x + 2880a b x + 960a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 739 + +--S 740 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 740 + +)clear all + +--S 741 of 764 +t0:=(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 741 + +--S 742 of 764 +r0:=-1/12*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*(d+e*x)^(9/2)/(b^2*e*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2))+2/3*B*(a+b*x)*(d+e*x)^(11/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-7/32*e*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*(d+_ + e*x)^(5/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/8*(8*b*B*d+3*A*b*e-_ + 11*a*B*e)*(d+e*x)^(7/2)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 35/64*e^2*(8*b*B*d+3*A*b*e-11*a*B*e)*(d+e*x)^(3/2)/(b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-105/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(13/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+105/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*_ + (a+b*x)*sqrt(d+e*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 945A b + 3465B a b )e - 2520B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 3780A a b + 13860B a b )e - 10080B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 5670A a b + 20790B a b )e - 15120B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 3780A a b + 13860B a b)e - 10080B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 945A a b + 3465B a )e - 2520B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 128B b e x + ((384A b - 1408B a b )e + 1664B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (2511A a b - 9207B a b )e + (- 975A b + 10271B a b )d e +--R + +--R 5 2 2 +--R - 1320B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (4599A a b - 16863B a b )e + (- 1665A a b + 18369B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 630A b - 2130B a b )d e - 400B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (3465A a b - 12705B a b)e + (- 1197A a b + 13629B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (- 468A a b - 1476B a b )d e + (- 264A b - 280B a b )d e +--R + +--R 5 4 +--R - 64B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (945A a b - 3465B a )e + (- 315A a b + 3675B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 126A a b - 378B a b )d e + (- 72A a b - 72B a b )d e +--R + +--R 5 4 4 +--R (- 48A b - 16B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 9 3 8 2 2 7 3 6 +-+ | 2 2 2 +--R (192b x + 576a b x + 576a b x + 192a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 742 + +--S 743 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 764 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 744 + +--S 745 of 764 +r0:=-1/4*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*(d+e*x)^(7/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+2*B*(a+b*x)*(d+e*x)^(9/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-35/96*e*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*(d+_ + e*x)^(3/2)/(b^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))-7/24*(8*b*B*d+A*b*e-_ + 9*a*B*e)*(d+e*x)^(5/2)/(b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))-35/64*e^3*_ + (8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))/(b^(11/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*_ + (8*b*B*d+A*b*e-9*a*B*e)*sqrt(d+e*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 105A b + 945B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 420A a b + 3780B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 630A a b + 5670B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 420A a b + 3780B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 105A a b + 945B a )e - 840B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 384B b e x + ((- 279A b + 2511B a b )e - 696B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 511A a b + 4599B a b )e + (- 326A b - 1154B a b )d e +--R + +--R 4 2 +--R - 304B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 385A a b + 3465B a b)e + (- 252A a b - 812B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 200A b - 216B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 105A a b + 945B a )e + (- 70A a b - 210B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 56A a b - 56B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 8 3 7 2 2 6 3 5 +-----------+ +-+ +--R (192b x + 576a b x + 576a b x + 192a b )\|- a e + b d \|b +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 745 + +--S 746 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 746 + +)clear all + +--S 747 of 764 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 747 + +--S 748 of 764 +r0:=1/4*(8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*(d+e*x)^(5/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-2*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+5/24*(8*b*B*d-A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+5/32*e*(8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*_ + (d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/64*e^3*_ + (8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-_ + a*e))/(b^(9/2)*(b*d-a*e)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^2*_ + (8*b*B*d-A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 15A b - 105B a b )e + 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 60A a b - 420B a b )e + 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 90A a b - 630B a b )e + 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 60A a b - 420B a b)e + 480B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 15A a b - 105B a )e + 120B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b - 279B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 73A a b - 511B a b )e + (118A b + 258B a b )d e +--R + +--R 4 2 +--R 208B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 55A a b - 385B a b)e + (- 36A a b + 188B a b )d e +--R + +--R 4 3 2 4 3 +--R (136A b + 88B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 105B a )e + (- 10A a b + 50B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 8A a b + 24B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 8 3 2 6 7 2 +--R (192a b e - 192b d)x + (576a b e - 576a b d)x +--R + +--R 3 5 2 6 4 4 3 5 +--R (576a b e - 576a b d)x + 192a b e - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 748 + +--S 749 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 749 + +)clear all + +--S 750 of 764 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 750 + +--S 751 of 764 +r0:=1/12*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^2*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))-2/3*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/24*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+1/96*e*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+_ + b*x)*sqrt(d+e*x)/(b^3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/64*e^3*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+b*x)*atanh(sqrt(b)*sqrt(d+_ + e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-1/64*e^2*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*(b*d-_ + a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 9A b - 15B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 36A a b - 60B a b )e + 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 54A a b - 90B a b )e + 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((- 36A a b - 60B a b)e + 96B a b d e )x + (- 9A a b - 15B a )e +--R + +--R 4 3 +--R 24B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((9A b + 15B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((33A a b - 73B a b )e + (- 6A b + 158B a b )d e - 112B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 33A a b - 55B a b)e + (132A a b + 52B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 72A b + 40B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 9A a b - 15B a )e + (- 6A a b + 14B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (72A a b + 8B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 6 2 7 8 2 3 +--R (192a b e - 384a b d e + 192b d )x +--R + +--R 3 5 2 2 6 7 2 2 +--R (576a b e - 1152a b d e + 576a b d )x +--R + +--R 4 4 2 3 5 2 6 2 5 3 2 4 4 +--R (576a b e - 1152a b d e + 576a b d )x + 192a b e - 384a b d e +--R + +--R 3 5 2 +--R 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 751 + +--S 752 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 752 + +)clear all + +--S 753 of 764 +t0:=(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 753 + +--S 754 of 764 +r0:=-2/5*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/20*(8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-1/24*(8*b*B*d-5*A*b*e-3*a*B*e)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/96*e*_ + (8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-1/64*e^3*(8*b*B*d-5*A*b*e-3*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-_ + a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/64*e^2*(8*b*B*d-5*A*b*e-_ + 3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 15A b - 9B a b )e + 24B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 60A a b - 36B a b )e + 96B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 90A a b - 54B a b )e + 144B a b d e )x +--R + +--R 3 2 4 4 3 2 3 4 5 4 +--R ((- 60A a b - 36B a b)e + 96B a b d e )x + (- 15A a b - 9B a )e +--R + +--R 4 3 +--R 24B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((15A b + 9B a b )e - 24B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((55A a b + 33B a b )e + (- 10A b - 94B a b )d e + 16B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (73A a b - 33B a b)e + (- 36A a b + 92B a b )d e +--R + +--R 4 3 2 4 3 +--R (8A b - 168B a b )d e + 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 15A a b - 9B a )e + (118A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 136A a b - 40B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 3 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 2 +--R (576a b e - 1728a b d e + 1728a b d e - 576a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 6 2 3 +--R (576a b e - 1728a b d e + 1728a b d e - 576a b d )x + 192a b e +--R + +--R 5 3 2 4 4 2 3 5 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 754 + +--S 755 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 764 +t0:=(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 +-------+ | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 756 + +--S 757 of 764 +r0:=-2/7*B*(a+b*x)*sqrt(d+e*x)/(b*e*(a^2+2*a*b*x+b^2*x^2)^(5/2))+_ + 1/28*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*e*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2))-1/24*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5/96*e*_ + (8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2))+5/64*e^3*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^2*(8*b*B*d-7*A*b*e-a*B*e)*_ + sqrt(d+e*x)/(b*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((- 105A b - 15B a b )e + 120B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((- 420A a b - 60B a b )e + 480B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((- 630A a b - 90B a b )e + 720B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((- 420A a b - 60B a b)e + 480B a b d e )x +--R + +--R 4 5 4 4 3 +--R (- 105A a b - 15B a )e + 120B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 3 4 2 3 +--R ((105A b + 15B a b )e - 120B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((385A a b + 55B a b )e + (- 70A b - 450B a b )d e + 80B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (511A a b + 73B a b)e + (- 252A a b - 620B a b )d e +--R + +--R 4 3 2 4 3 +--R (56A b + 296B a b )d e - 64B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (279A a b - 15B a )e + (- 326A a b - 146B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (200A a b + 72B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 3 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 2 +--R (576a b e - 2304a b d e + 3456a b d e - 2304a b d e + 576a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 +--R (576a b e - 2304a b d e + 3456a b d e - 2304a b d e + 576a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R 192a b e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 757 + +--S 758 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 758 + +)clear all + +--S 759 of 764 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b e x + (4a b e + b d)x + (6a b e + 4a b d)x + (4a b e + 6a b d)x +--R + +--R 4 3 4 +--R (a e + 4a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 759 + +--S 760 of 764 +r0:=-2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*_ + sqrt(d+e*x))+1/4*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/(e*_ + (b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2))-7/24*(8*b*B*d-9*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/96*e*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^4*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+35/64*e^3*(8*b*B*d-9*A*b*e+a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(11/2)*_ + sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*(8*b*B*d-9*A*b*e+_ + a*B*e)*sqrt(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 4 5 3 4 +--R ((945A b - 105B a b )e - 840B b d e )x +--R + +--R 4 2 3 4 4 3 3 +--R ((3780A a b - 420B a b )e - 3360B a b d e )x +--R + +--R 2 3 3 2 4 2 3 3 2 +--R ((5670A a b - 630B a b )e - 5040B a b d e )x +--R + +--R 3 2 4 4 3 2 3 +--R ((3780A a b - 420B a b)e - 3360B a b d e )x +--R + +--R 4 5 4 4 3 +--R (945A a b - 105B a )e - 840B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 105B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3465A a b + 385B a b )e + (- 315A b + 3115B a b )d e +--R + +--R 4 2 2 +--R 280B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 4599A a b + 511B a b)e + (- 1197A a b + 4221B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (126A b + 1050B a b )d e - 112B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 2511A a b + 279B a )e + (- 1665A a b + 2417B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (468A a b + 1428B a b )d e + (- 72A b - 408B a b )d e + 64B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 384A a e + (- 975A a b + 663B a )d e + (630A a b + 370B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 264A a b - 104B a b )d e + (48A b + 16B a b )d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 5 3 5 4 4 4 3 5 2 3 2 6 3 2 7 4 +--R 192a b e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 8 5 +--R - 192b d +--R * +--R 3 +--R x +--R + +--R 6 2 5 5 3 4 4 4 2 3 3 5 3 2 +--R 576a b e - 2880a b d e + 5760a b d e - 5760a b d e +--R + +--R 2 6 4 7 5 +--R 2880a b d e - 576a b d +--R * +--R 2 +--R x +--R + +--R 7 5 6 2 4 5 3 2 3 4 4 3 2 +--R 576a b e - 2880a b d e + 5760a b d e - 5760a b d e +--R + +--R 3 5 4 2 6 5 +--R 2880a b d e - 576a b d +--R * +--R x +--R + +--R 8 5 7 4 6 2 2 3 5 3 3 2 4 4 4 +--R 192a e - 960a b d e + 1920a b d e - 1920a b d e + 960a b d e +--R + +--R 3 5 5 +--R - 192a b d +--R * +--R +------------------+ +--R +-----------+ +-+ +-------+ | 2 2 2 +--R \|- a e + b d \|b \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 760 + +--S 761 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 761 + +)clear all + +--S 762 of 764 +t0:=(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b e x + (4a b e + 2b d e)x + (6a b e + 8a b d e + b d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b e + 12a b d e + 4a b d )x + (a e + 8a b d e + 6a b d )x +--R + +--R 4 3 2 4 2 +--R (2a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 762 + +--S 763 of 764 +r0:=-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/12*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/(e*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x))+1/8*(-8*b*B*d+11*A*b*e-_ + 3*a*B*e)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))+_ + 7/32*e*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)*sqrt(d+e*x))+105/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-_ + a*e)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^2*(8*b*B*d-11*A*b*e+_ + 3*a*B*e)/((b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 105/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^6*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((- 3465A b + 945B a b )e + 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 13860A a b + 3780B a b )e + (- 3465A b + 11025B a b )d e +--R + +--R 5 2 3 +--R 2520B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 +--R (- 20790A a b + 5670B a b )e +--R + +--R 4 2 3 4 4 2 3 +--R (- 13860A a b + 18900B a b )d e + 10080B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 13860A a b + 3780B a b)e + (- 20790A a b + 15750B a b )d e +--R + +--R 2 3 2 3 +--R 15120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 3465A a b + 945B a )e + (- 13860A a b + 6300B a b)d e +--R + +--R 3 2 2 3 +--R 10080B a b d e +--R * +--R x +--R + +--R 4 5 4 4 2 3 +--R (- 3465A a b + 945B a )d e + 2520B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 4 5 5 4 5 +--R ((3465A b - 945B a b )e - 2520B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (12705A a b - 3465B a b )e + (4620A b - 10500B a b )d e +--R + +--R 5 2 3 +--R - 3360B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (16863A a b - 4599B a b )e + (17094A a b - 16926B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (693A b - 12621B a b )d e - 504B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (9207A a b - 2511B a b)e + (22968A a b - 12960B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (2673A a b - 17433B a b )d e + (- 198A b - 1890B a b )d e +--R + +--R 5 4 +--R 144B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (1408A a b - 384B a )e + (12782A a b - 4510B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (3795A a b - 10331B a b )d e + (- 748A a b - 2556B a b )d e +--R + +--R 5 4 4 5 5 +--R (88A b + 520B a b )d e - 64B b d +--R * +--R x +--R + +--R 5 5 4 5 4 +--R - 128A a e + (2048A a b - 256B a )d e +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (2295A a b - 2639B a b)d e + (- 1030A a b - 690B a b )d e +--R + +--R 4 2 3 4 5 4 5 +--R (328A a b + 136B a b )d e + (- 48A b - 16B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 3 7 5 4 6 4 5 2 5 3 6 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 7 4 3 8 5 2 9 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 4 +--R x +--R + +--R 7 2 7 6 3 6 5 4 2 5 4 5 3 4 +--R 576a b e - 3264a b d e + 7488a b d e - 8640a b d e +--R + +--R 3 6 4 3 2 7 5 2 8 6 9 7 +--R 4800a b d e - 576a b d e - 576a b d e + 192b d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 +--R 576a b e - 2880a b d e + 5184a b d e - 2880a b d e +--R + +--R 4 5 4 3 3 6 5 2 2 7 6 8 7 +--R - 2880a b d e + 5184a b d e - 2880a b d e + 576a b d +--R * +--R 2 +--R x +--R + +--R 9 7 8 6 7 2 2 5 6 3 3 4 5 4 4 3 +--R 192a e - 576a b d e - 576a b d e + 4800a b d e - 8640a b d e +--R + +--R 4 5 5 2 3 6 6 2 7 7 +--R 7488a b d e - 3264a b d e + 576a b d +--R * +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e + 2880a b d e +--R + +--R 4 5 6 3 6 7 +--R - 1152a b d e + 192a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 763 + +--S 764 of 764 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 764 + + + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/richder12e.input.pamphlet b/src/input/richder12e.input.pamphlet new file mode 100644 index 0000000..4663f7a --- /dev/null +++ b/src/input/richder12e.input.pamphlet @@ -0,0 +1,17949 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12e.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +All derivatives match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12e.output +)spool richder12e.output +)set message test on +)set message auto off +)clear all + +--S 1 of 765 +t0:=(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b e x + (4a b e + 3b d e )x + (6a b e + 12a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b e + 18a b d e + 12a b d e + b d )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a e + 12a b d e + 18a b d e + 4a b d )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a d e + 12a b d e + 6a b d )x + (3a d e + 4a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 765 +r0:=-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2))+1/20*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/(e*(b*d-a*e)^2*_ + (d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2))-11/120*(8*b*B*d-13*A*b*e+_ + 5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 33/160*e*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-231/320*e^2*(8*b*B*d-13*A*b*e+5*a*B*e)/_ + ((b*d-a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-77/64*e^3*(8*b*B*d-_ + 13*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+231/64*b^(3/2)*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(15/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-231/64*b*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/_ + ((b*d-a*e)^7*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 6 5 6 6 5 6 +--R ((45045A b - 17325B a b )e - 27720B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (180180A a b - 69300B a b )e + (90090A b - 145530B a b )d e +--R + +--R 6 2 4 +--R - 55440B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (270270A a b - 103950B a b )e +--R + +--R 5 2 4 5 +--R (360360A a b - 304920B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (45045A b - 239085B a b )d e - 27720B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (180180A a b - 69300B a b )e +--R + +--R 2 4 3 3 5 +--R (540540A a b - 318780B a b )d e +--R + +--R 5 2 4 2 4 5 3 3 +--R (180180A a b - 401940B a b )d e - 110880B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (45045A a b - 17325B a b)e + (360360A a b - 166320B a b )d e +--R + +--R 2 4 3 3 2 4 2 4 3 3 +--R (270270A a b - 325710B a b )d e - 166320B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 +--R (90090A a b - 34650B a b)d e +--R + +--R 3 3 4 2 2 4 3 3 3 3 +--R (180180A a b - 124740B a b )d e - 110880B a b d e +--R * +--R x +--R + +--R 4 2 5 2 4 4 2 3 3 +--R (45045A a b - 17325B a b)d e - 27720B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 6 5 6 6 5 6 +--R ((- 45045A b + 17325B a b )e + 27720B b d e )x +--R + +--R 5 2 4 6 +--R (- 165165A a b + 63525B a b )e +--R + +--R 6 5 5 6 2 4 +--R (- 105105A b + 142065B a b )d e + 64680B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 6 +--R (- 219219A a b + 84315B a b )e +--R + +--R 5 2 4 5 +--R (- 387387A a b + 283899B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (- 69069A b + 264957B a b )d e + 42504B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 6 +--R (- 119691A a b + 46035B a b )e +--R + +--R 2 4 3 3 5 +--R (- 517803A a b + 272811B a b )d e +--R + +--R 5 2 4 2 4 +--R (- 256971A a b + 417483B a b )d e +--R + +--R 6 5 3 3 6 4 2 +--R (- 6435A b + 160611B a b )d e + 3960B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 6 +--R (- 18304A a b + 7040B a b)e +--R + +--R 3 3 4 2 5 +--R (- 285857A a b + 121209B a b )d e +--R + +--R 2 4 3 3 2 4 +--R (- 347919A a b + 309727B a b )d e +--R + +--R 5 2 4 3 3 6 5 4 2 +--R (- 25025A a b + 223729B a b )d e + (1430A b + 14850B a b )d e +--R + +--R 6 5 +--R - 880B b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (1664A a b - 640B a )e + (- 44928A a b + 16256B a b)d e +--R + +--R 3 3 4 2 2 4 +--R (- 196001A a b + 103033B a b )d e +--R + +--R 2 4 3 3 3 3 +--R (- 35945A a b + 134441B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (5460A a b + 20020B a b )d e + (- 520A b - 3160B a b )d e +--R + +--R 6 6 +--R 320B b d +--R * +--R x +--R + +--R 6 6 5 6 5 +--R - 384A a e + (3968A a b - 256B a )d e +--R + +--R 4 2 5 2 4 3 3 4 2 3 3 +--R (- 32384A a b + 6912B a b)d e + (- 22155A a b + 33619B a b )d e +--R + +--R 2 4 3 3 4 2 5 2 4 5 +--R (7630A a b + 5530B a b )d e + (- 1960A a b - 840B a b )d e +--R + +--R 6 5 6 +--R (240A b + 80B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 7 3 9 6 4 8 5 5 2 7 4 6 3 6 +--R 960a b e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 3 7 4 5 2 8 5 4 9 6 3 10 7 2 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960b d e +--R * +--R 5 +--R x +--R + +--R 8 2 9 7 3 8 6 4 2 7 5 5 3 6 +--R 2880a b e - 18240a b d e + 47040a b d e - 60480a b d e +--R + +--R 4 6 4 5 3 7 5 4 2 8 6 3 9 7 2 +--R 33600a b d e + 6720a b d e - 20160a b d e + 10560a b d e +--R + +--R 10 8 +--R - 1920b d e +--R * +--R 4 +--R x +--R + +--R 9 9 8 2 8 7 3 2 7 6 4 3 6 +--R 2880a b e - 14400a b d e + 21120a b d e + 13440a b d e +--R + +--R 5 5 4 5 4 6 5 4 3 7 6 3 2 8 7 2 +--R - 80640a b d e + 107520a b d e - 67200a b d e + 17280a b d e +--R + +--R 9 8 10 9 +--R 960a b d e - 960b d +--R * +--R 3 +--R x +--R + +--R 10 9 9 8 8 2 2 7 7 3 3 6 +--R 960a e - 960a b d e - 17280a b d e + 67200a b d e +--R + +--R 6 4 4 5 5 5 5 4 4 6 6 3 3 7 7 2 +--R - 107520a b d e + 80640a b d e - 13440a b d e - 21120a b d e +--R + +--R 2 8 8 9 9 +--R 14400a b d e - 2880a b d +--R * +--R 2 +--R x +--R + +--R 10 8 9 2 7 8 2 3 6 7 3 4 5 +--R 1920a d e - 10560a b d e + 20160a b d e - 6720a b d e +--R + +--R 6 4 5 4 5 5 6 3 4 6 7 2 3 7 8 +--R - 33600a b d e + 60480a b d e - 47040a b d e + 18240a b d e +--R + +--R 2 8 9 +--R - 2880a b d +--R * +--R x +--R + +--R 10 2 7 9 3 6 8 2 4 5 7 3 5 4 +--R 960a d e - 6720a b d e + 20160a b d e - 33600a b d e +--R + +--R 6 4 6 3 5 5 7 2 4 6 8 3 7 9 +--R 33600a b d e - 20160a b d e + 6720a b d e - 960a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 3 + +)clear all + +--S 4 of 765 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 m +--R (1) (b x + 3a b x + 3a b x + a )(e x + d) +--R Type: Expression(Integer) +--E 4 + +--S 5 of 765 +r0:=-(b*d-a*e)^3*(d+e*x)^(1+m)/(e^4*(1+m))+3*b*(b*d-a*e)^2*_ + (d+e*x)^(2+m)/(e^4*(2+m))-3*b^2*(b*d-a*e)*(d+e*x)^(3+m)/(e^4*(3+m))+_ + b^3*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 4 +--R (b m + 6b m + 11b m + 6b )(e x + d) +--R + +--R 2 3 3 2 3 2 2 3 +--R (3a b e - 3b d)m + (21a b e - 21b d)m + (42a b e - 42b d)m +--R + +--R 2 3 +--R 24a b e - 24b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 3 2 2 +--R (3a b e - 6a b d e + 3b d )m + (24a b e - 48a b d e + 24b d )m +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (57a b e - 114a b d e + 57b d )m + 36a b e - 72a b d e + 36b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e - 3a b d e + 3a b d e - b d )m +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (9a e - 27a b d e + 27a b d e - 9b d )m +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (26a e - 78a b d e + 78a b d e - 26b d )m + 24a e - 72a b d e +--R + +--R 2 2 3 3 +--R 72a b d e - 24b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 5 + +--S 6 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 6 + +)clear all + +--S 7 of 765 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 5 8 2 5 3 4 7 2 5 2 4 3 2 3 6 +--R b e x + (3a b e + 5b d e )x + (3a b e + 15a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 5 +--R (a e + 15a b d e + 30a b d e + 10b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 4 +--R (5a d e + 30a b d e + 30a b d e + 5b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (10a d e + 30a b d e + 15a b d e + b d )x +--R + +--R 3 3 2 2 4 2 5 2 3 4 2 5 3 5 +--R (10a d e + 15a b d e + 3a b d )x + (5a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 7 + +--S 8 of 765 +r0:=-1/6*(b*d-a*e)^3*(d+e*x)^6/e^4+3/7*b*(b*d-a*e)^2*(d+e*x)^7/e^4-_ + 3/8*b^2*(b*d-a*e)*(d+e*x)^8/e^4+1/9*b^3*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 3 9 9 3 2 9 5 3 8 8 +--R - b e x + (- a b e + - b d e )x +--R 9 8 8 +--R + +--R 3 2 9 15 2 8 10 3 2 7 7 +--R (- a b e + -- a b d e + -- b d e )x +--R 7 7 7 +--R + +--R 1 3 9 5 2 8 2 2 7 5 3 3 6 6 +--R (- a e + - a b d e + 5a b d e + - b d e )x +--R 6 2 3 +--R + +--R 3 8 2 2 7 2 3 6 3 4 5 5 +--R (a d e + 6a b d e + 6a b d e + b d e )x +--R + +--R 5 3 2 7 15 2 3 6 15 2 4 5 1 3 5 4 4 +--R (- a d e + -- a b d e + -- a b d e + - b d e )x +--R 2 2 4 4 +--R + +--R 10 3 3 6 2 4 5 2 5 4 3 5 3 4 5 3 2 5 4 2 +--R (-- a d e + 5a b d e + a b d e )x + (- a d e + - a b d e )x +--R 3 2 2 +--R + +--R 3 5 4 1 3 6 3 1 2 7 2 1 2 8 1 3 9 +--R a d e x + - a d e - -- a b d e + -- a b d e - --- b d +--R 6 14 56 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 8 + +--S 9 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 9 + +)clear all + +--S 10 of 765 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 10 + +--S 11 of 765 +r0:=-1/5*(b*d-a*e)^3*(d+e*x)^5/e^4+1/2*b*(b*d-a*e)^2*(d+e*x)^6/e^4-_ + 3/7*b^2*(b*d-a*e)*(d+e*x)^7/e^4+1/8*b^3*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 3 8 8 3 2 8 4 3 7 7 1 2 8 2 7 3 2 6 6 +--R - b e x + (- a b e + - b d e )x + (- a b e + 2a b d e + b d e )x +--R 8 7 7 2 +--R + +--R 1 3 8 12 2 7 18 2 2 6 4 3 3 5 5 +--R (- a e + -- a b d e + -- a b d e + - b d e )x +--R 5 5 5 5 +--R + +--R 3 7 9 2 2 6 2 3 5 1 3 4 4 4 +--R (a d e + - a b d e + 3a b d e + - b d e )x +--R 2 4 +--R + +--R 3 2 6 2 3 5 2 4 4 3 3 3 5 3 2 4 4 2 3 4 4 +--R (2a d e + 4a b d e + a b d e )x + (2a d e + - a b d e )x + a d e x +--R 2 +--R + +--R 1 3 5 3 1 2 6 2 1 2 7 1 3 8 +--R - a d e - -- a b d e + -- a b d e - --- b d +--R 5 10 35 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 11 + +--S 12 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 765 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 13 + +--S 14 of 765 +r0:=1/4*(b*d-a*e)^3*(a+b*x)^4/b^4+3/5*e*(b*d-a*e)^2*(a+b*x)^5/b^4+_ + 1/2*e^2*(b*d-a*e)*(a+b*x)^6/b^4+1/7*e^3*(a+b*x)^7/b^4 +--R +--R +--R (2) +--R 1 7 3 7 1 6 3 1 7 2 6 3 2 5 3 9 6 2 3 7 2 5 +--R - b e x + (- a b e + - b d e )x + (- a b e + - a b d e + - b d e)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 4 3 9 2 5 2 9 6 2 1 7 3 4 +--R (- a b e + - a b d e + - a b d e + - b d )x +--R 4 4 4 4 +--R + +--R 3 4 2 2 5 2 6 3 3 3 3 4 2 3 2 5 3 2 3 4 3 +--R (a b d e + 3a b d e + a b d )x + (- a b d e + - a b d )x + a b d x +--R 2 2 +--R + +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R - --- a e + -- a b d e - -- a b d e + - a b d +--R 140 20 20 4 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 14 + +--S 15 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 765 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 765 +r0:=1/4*(b*d-a*e)^2*(a+b*x)^4/b^3+2/5*e*(b*d-a*e)*(a+b*x)^5/b^3+_ + 1/6*e^2*(a+b*x)^6/b^3 +--R +--R +--R (2) +--R 1 6 2 6 3 5 2 2 6 5 3 2 4 2 3 5 1 6 2 4 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 3 2 2 4 5 2 3 3 3 3 2 4 2 2 3 3 2 +--R (- a b e + 2a b d e + a b d )x + (a b d e + - a b d )x + a b d x +--R 3 2 +--R + +--R 1 6 2 1 5 1 4 2 2 +--R -- a e - -- a b d e + - a b d +--R 60 10 4 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 17 + +--S 18 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 18 + +)clear all + +--S 19 of 765 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d +--R Type: Polynomial(Integer) +--E 19 + +--S 20 of 765 +r0:=1/4*(b*d-a*e)*(a+b*x)^4/b^2+1/5*e*(a+b*x)^5/b^2 +--R +--R +--R (2) +--R 1 5 5 3 4 1 5 4 2 3 4 3 +--R - b e x + (- a b e + - b d)x + (a b e + a b d)x +--R 5 4 4 +--R + +--R 1 3 2 3 2 3 2 3 2 1 5 1 4 +--R (- a b e + - a b d)x + a b d x - -- a e + - a b d +--R 2 2 20 4 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 20 + +--S 21 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 22 + +--S 23 of 765 +r0:=1/4*(a+b*x)^4/b +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - b x + a b x + - a b x + a b x + - a +--R 4 2 4 +--R (2) ----------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 23 + +--S 24 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 24 + +)clear all + +--S 25 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 25 + +--S 26 of 765 +r0:=b*(b*d-a*e)^2*x/e^3-1/2*(b*d-a*e)*(a+b*x)^2/e^2+1/3*(a+b*x)^3/e-_ + (b*d-a*e)^3*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a e - 18a b d e + 18a b d e - 6b d )log(e x + d) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (9a b e - 3b d e )x + (18a b e - 18a b d e + 6b d e)x + 5a e +--R + +--R 2 2 +--R - 3a b d e +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 26 + +--S 27 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 27 + +)clear all + +--S 28 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 28 + +--S 29 of 765 +r0:=-b^2*(2*b*d-3*a*e)*x/e^3+1/2*b^3*x^2/e^2+(b*d-a*e)^3/(e^4*(d+e*x))+_ + 3*b*(b*d-a*e)^2*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b e - 12a b d e + 6b d e)x + 6a b d e - 12a b d e + 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 3 3 +--R b e x + (6a b e - 3b d e )x + (6a b d e - 4b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 6a b d e + 2b d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 29 + +--S 30 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 765 +r0:=b^3*x/e^3+1/2*(b*d-a*e)^3/(e^4*(d+e*x)^2)-3*b*(b*d-a*e)^2/(e^4*(d+e*x))-_ + 3*b^2*(b*d-a*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 2 3 2 2 2 3 3 +--R ((6a b e - 6b d e )x + (12a b d e - 12b d e)x + 6a b d e - 6b d ) +--R * +--R log(e x + d) +--R + +--R 3 3 3 3 2 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4b d e x + (- 6a b e + 12a b d e - 4b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 9a b d e - 5b d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 32 + +--S 33 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 34 + +--S 35 of 765 +r0:=1/3*(b*d-a*e)^3/(e^4*(d+e*x)^3)-3/2*b*(b*d-a*e)^2/(e^4*(d+e*x)^2)+_ + 3*b^2*(b*d-a*e)/(e^4*(d+e*x))+b^3*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(e x + d) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 18a b e + 18b d e )x + (- 9a b e - 18a b d e + 27b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e - 6a b d e + 11b d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 35 + +--S 36 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 36 + +)clear all + +--S 37 of 765 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 m +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )(e x + d) +--R Type: Expression(Integer) +--E 37 + +--S 38 of 765 +r0:=-(b*d-a*e)^5*(d+e*x)^(1+m)/(e^6*(1+m))+5*b*(b*d-a*e)^4*(d+e*x)^(2+m)/_ + (e^6*(2+m))-10*b^2*(b*d-a*e)^3*(d+e*x)^(3+m)/(e^6*(3+m))+10*b^3*_ + (b*d-a*e)^2*(d+e*x)^(4+m)/(e^6*(4+m))-5*b^4*(b*d-a*e)*(d+e*x)^(5+m)/_ + (e^6*(5+m))+b^5*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 5 5 5 4 5 3 5 2 5 5 m + 6 +--R (b m + 15b m + 85b m + 225b m + 274b m + 120b )(e x + d) +--R + +--R 4 5 5 4 5 4 4 5 3 +--R (5a b e - 5b d)m + (80a b e - 80b d)m + (475a b e - 475b d)m +--R + +--R 4 5 2 4 5 4 5 +--R (1300a b e - 1300b d)m + (1620a b e - 1620b d)m + 720a b e - 720b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 3 2 4 5 2 5 +--R (10a b e - 20a b d e + 10b d )m +--R + +--R 2 3 2 4 5 2 4 +--R (170a b e - 340a b d e + 170b d )m +--R + +--R 2 3 2 4 5 2 3 +--R (1070a b e - 2140a b d e + 1070b d )m +--R + +--R 2 3 2 4 5 2 2 +--R (3070a b e - 6140a b d e + 3070b d )m +--R + +--R 2 3 2 4 5 2 2 3 2 4 +--R (3960a b e - 7920a b d e + 3960b d )m + 1800a b e - 3600a b d e +--R + +--R 5 2 +--R 1800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e - 30a b d e + 30a b d e - 10b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (180a b e - 540a b d e + 540a b d e - 180b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (1210a b e - 3630a b d e + 3630a b d e - 1210b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (3720a b e - 11160a b d e + 11160a b d e - 3720b d )m +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 2 3 +--R (5080a b e - 15240a b d e + 15240a b d e - 5080b d )m + 2400a b e +--R + +--R 2 3 2 4 2 5 3 +--R - 7200a b d e + 7200a b d e - 2400b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e - 20a b d e + 30a b d e - 20a b d e + 5b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 4 +--R (95a b e - 380a b d e + 570a b d e - 380a b d e + 95b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (685a b e - 2740a b d e + 4110a b d e - 2740a b d e + 685b d )m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 2305a b e - 9220a b d e + 13830a b d e - 9220a b d e +--R + +--R 5 4 +--R 2305b d +--R * +--R 2 +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 3510a b e - 14040a b d e + 21060a b d e - 14040a b d e +--R + +--R 5 4 +--R 3510b d +--R * +--R m +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R 1800a b e - 7200a b d e + 10800a b d e - 7200a b d e + 1800b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e - 5a b d e + 10a b d e - 10a b d e + 5a b d e - b d )m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 20a e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 5 5 +--R - 20b d +--R * +--R 4 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 155a e - 775a b d e + 1550a b d e - 1550a b d e + 775a b d e +--R + +--R 5 5 +--R - 155b d +--R * +--R 3 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R 580a e - 2900a b d e + 5800a b d e - 5800a b d e +--R + +--R 4 4 5 5 +--R 2900a b d e - 580b d +--R * +--R 2 +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R 1044a e - 5220a b d e + 10440a b d e - 10440a b d e +--R + +--R 4 4 5 5 +--R 5220a b d e - 1044b d +--R * +--R m +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 720a e - 3600a b d e + 7200a b d e - 7200a b d e + 3600a b d e +--R + +--R 5 5 +--R - 720b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 38 + +--S 39 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 39 + +)clear all + +--S 40 of 765 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 11 4 6 5 5 10 2 3 6 4 5 5 2 4 9 +--R b e x + (5a b e + 6b d e )x + (10a b e + 30a b d e + 15b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 8 +--R (10a b e + 60a b d e + 75a b d e + 20b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 7 +--R (5a b e + 60a b d e + 150a b d e + 100a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 6 +--R (a e + 30a b d e + 150a b d e + 200a b d e + 75a b d e + 6b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 5 +--R (6a d e + 75a b d e + 200a b d e + 150a b d e + 30a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 4 +--R (15a d e + 100a b d e + 150a b d e + 60a b d e + 5a b d )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 3 +--R (20a d e + 75a b d e + 60a b d e + 10a b d )x +--R + +--R 5 4 2 4 5 3 2 6 2 5 5 4 6 5 6 +--R (15a d e + 30a b d e + 10a b d )x + (6a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 40 + +--S 41 of 765 +r0:=-1/7*(b*d-a*e)^5*(d+e*x)^7/e^6+5/8*b*(b*d-a*e)^4*(d+e*x)^8/e^6-_ + 10/9*b^2*(b*d-a*e)^3*(d+e*x)^9/e^6+b^3*(b*d-a*e)^2*(d+e*x)^10/e^6-_ + 5/11*b^4*(b*d-a*e)*(d+e*x)^11/e^6+1/12*b^5*(d+e*x)^12/e^6 +--R +--R +--R (2) +--R 1 5 12 12 5 4 12 6 5 11 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 2 3 12 4 11 3 5 2 10 10 +--R (a b e + 3a b d e + - b d e )x +--R 2 +--R + +--R 10 3 2 12 20 2 3 11 25 4 2 10 20 5 3 9 9 +--R (-- a b e + -- a b d e + -- a b d e + -- b d e )x +--R 9 3 3 9 +--R + +--R 5 4 12 15 3 2 11 75 2 3 2 10 25 4 3 9 15 5 4 8 8 +--R (- a b e + -- a b d e + -- a b d e + -- a b d e + -- b d e )x +--R 8 2 4 2 8 +--R + +--R 1 5 12 30 4 11 150 3 2 2 10 200 2 3 3 9 75 4 4 8 +--R - a e + -- a b d e + --- a b d e + --- a b d e + -- a b d e +--R 7 7 7 7 7 +--R + +--R 6 5 5 7 +--R - b d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 5 11 25 4 2 10 100 3 2 3 9 2 3 4 8 4 5 7 +--R a d e + -- a b d e + --- a b d e + 25a b d e + 5a b d e +--R 2 3 +--R + +--R 1 5 6 6 +--R - b d e +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 2 4 8 2 3 5 7 4 6 6 5 +--R (3a d e + 20a b d e + 30a b d e + 12a b d e + a b d e )x +--R + +--R 5 3 9 75 4 4 8 3 2 5 7 5 2 3 6 6 4 +--R (5a d e + -- a b d e + 15a b d e + - a b d e )x +--R 4 2 +--R + +--R 5 4 8 4 5 7 10 3 2 6 6 3 5 5 7 5 4 6 6 2 +--R (5a d e + 10a b d e + -- a b d e )x + (3a d e + - a b d e )x +--R 3 2 +--R + +--R 5 6 6 1 5 7 5 5 4 8 4 5 3 2 9 3 1 2 3 10 2 +--R a d e x + - a d e - -- a b d e + --- a b d e - -- a b d e +--R 7 56 126 84 +--R + +--R 1 4 11 1 5 12 +--R --- a b d e - ---- b d +--R 462 5544 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 41 + +--S 42 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 42 + +)clear all + +--S 43 of 765 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 5 10 4 5 5 4 9 2 3 5 4 4 5 2 3 8 +--R b e x + (5a b e + 5b d e )x + (10a b e + 25a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 7 +--R (10a b e + 50a b d e + 50a b d e + 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 6 +--R (5a b e + 50a b d e + 100a b d e + 50a b d e + 5b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e + 25a b d e + 100a b d e + 100a b d e + 25a b d e + b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4 +--R (5a d e + 50a b d e + 100a b d e + 50a b d e + 5a b d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 3 +--R (10a d e + 50a b d e + 50a b d e + 10a b d )x +--R + +--R 5 3 2 4 4 3 2 5 2 5 4 4 5 5 5 +--R (10a d e + 25a b d e + 10a b d )x + (5a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 43 + +--S 44 of 765 +r0:=1/6*(b*d-a*e)^5*(a+b*x)^6/b^6+5/7*e*(b*d-a*e)^4*(a+b*x)^7/b^6+_ + 5/4*e^2*(b*d-a*e)^3*(a+b*x)^8/b^6+10/9*e^3*(b*d-a*e)^2*(a+b*x)^9/b^6+_ + 1/2*e^4*(b*d-a*e)*(a+b*x)^10/b^6+1/11*e^5*(a+b*x)^11/b^6 +--R +--R +--R (2) +--R 1 11 5 11 1 10 5 1 11 4 10 +--R -- b e x + (- a b e + - b d e )x +--R 11 2 2 +--R + +--R 10 2 9 5 25 10 4 10 11 2 3 9 +--R (-- a b e + -- a b d e + -- b d e )x +--R 9 9 9 +--R + +--R 5 3 8 5 25 2 9 4 25 10 2 3 5 11 3 2 8 +--R (- a b e + -- a b d e + -- a b d e + - b d e )x +--R 4 4 4 4 +--R + +--R 5 4 7 5 50 3 8 4 100 2 9 2 3 50 10 3 2 5 11 4 7 +--R (- a b e + -- a b d e + --- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 7 +--R + +--R 1 5 6 5 25 4 7 4 50 3 8 2 3 50 2 9 3 2 25 10 4 +--R - a b e + -- a b d e + -- a b d e + -- a b d e + -- a b d e +--R 6 6 3 3 6 +--R + +--R 1 11 5 +--R - b d +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 6 4 4 7 2 3 3 8 3 2 2 9 4 10 5 5 +--R (a b d e + 10a b d e + 20a b d e + 10a b d e + a b d )x +--R + +--R 5 5 6 2 3 25 4 7 3 2 25 3 8 4 5 2 9 5 4 +--R (- a b d e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 10 5 6 3 2 25 4 7 4 10 3 8 5 3 5 5 6 4 5 4 7 5 2 +--R (-- a b d e + -- a b d e + -- a b d )x + (- a b d e + - a b d )x +--R 3 3 3 2 2 +--R + +--R 5 6 5 1 11 5 1 10 4 5 9 2 2 3 5 8 3 3 2 +--R a b d x - ---- a e + --- a b d e - --- a b d e + -- a b d e +--R 2772 252 252 84 +--R + +--R 5 7 4 4 1 6 5 5 +--R - -- a b d e + - a b d +--R 42 6 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 44 + +--S 45 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 765 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 46 + +--S 47 of 765 +r0:=1/6*(b*d-a*e)^4*(a+b*x)^6/b^5+4/7*e*(b*d-a*e)^3*(a+b*x)^7/b^5+3/4*e^2*_ + (b*d-a*e)^2*(a+b*x)^8/b^5+4/9*e^3*(b*d-a*e)*(a+b*x)^9/b^5+1/10*e^4*_ + (a+b*x)^10/b^5 +--R +--R +--R (2) +--R 1 10 4 10 5 9 4 4 10 3 9 +--R -- b e x + (- a b e + - b d e )x +--R 10 9 9 +--R + +--R 5 2 8 4 5 9 3 3 10 2 2 8 +--R (- a b e + - a b d e + - b d e )x +--R 4 2 4 +--R + +--R 10 3 7 4 40 2 8 3 30 9 2 2 4 10 3 7 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 7 7 7 7 +--R + +--R 5 4 6 4 20 3 7 3 2 8 2 2 10 9 3 1 10 4 6 +--R (- a b e + -- a b d e + 10a b d e + -- a b d e + - b d )x +--R 6 3 3 6 +--R + +--R 1 5 5 4 4 6 3 3 7 2 2 2 8 3 9 4 5 +--R (- a b e + 4a b d e + 12a b d e + 8a b d e + a b d )x +--R 5 +--R + +--R 5 5 3 15 4 6 2 2 3 7 3 5 2 8 4 4 +--R (a b d e + -- a b d e + 10a b d e + - a b d )x +--R 2 2 +--R + +--R 5 5 2 2 20 4 6 3 10 3 7 4 3 5 5 3 5 4 6 4 2 +--R (2a b d e + -- a b d e + -- a b d )x + (2a b d e + - a b d )x +--R 3 3 2 +--R + +--R 5 5 4 1 10 4 1 9 3 1 8 2 2 2 2 7 3 3 1 6 4 4 +--R a b d x + ---- a e - --- a b d e + -- a b d e - -- a b d e + - a b d +--R 1260 126 28 21 6 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 48 + +)clear all + +--S 49 of 765 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 49 + +--S 50 of 765 +r0:=1/6*(b*d-a*e)^3*(a+b*x)^6/b^4+3/7*e*(b*d-a*e)^2*(a+b*x)^7/b^4+_ + 3/8*e^2*(b*d-a*e)*(a+b*x)^8/b^4+1/9*e^3*(a+b*x)^9/b^4 +--R +--R +--R (2) +--R 1 9 3 9 5 8 3 3 9 2 8 +--R - b e x + (- a b e + - b d e )x +--R 9 8 8 +--R + +--R 10 2 7 3 15 8 2 3 9 2 7 +--R (-- a b e + -- a b d e + - b d e)x +--R 7 7 7 +--R + +--R 5 3 6 3 2 7 2 5 8 2 1 9 3 6 +--R (- a b e + 5a b d e + - a b d e + - b d )x +--R 3 2 6 +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (a b e + 6a b d e + 6a b d e + a b d )x +--R + +--R 1 5 4 3 15 4 5 2 15 3 6 2 5 2 7 3 4 +--R (- a b e + -- a b d e + -- a b d e + - a b d )x +--R 4 4 2 2 +--R + +--R 5 4 2 4 5 2 10 3 6 3 3 3 5 4 2 5 4 5 3 2 5 4 3 +--R (a b d e + 5a b d e + -- a b d )x + (- a b d e + - a b d )x + a b d x +--R 3 2 2 +--R + +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R - --- a e + -- a b d e - -- a b d e + - a b d +--R 504 56 14 6 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 50 + +--S 51 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 51 + +)clear all + +--S 52 of 765 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R Type: Polynomial(Integer) +--E 52 + +--S 53 of 765 +r0:=1/6*(b*d-a*e)^2*(a+b*x)^6/b^3+2/7*e*(b*d-a*e)*(a+b*x)^7/b^3+_ + 1/8*e^2*(a+b*x)^8/b^3 +--R +--R +--R (2) +--R 1 8 2 8 5 7 2 2 8 7 5 2 6 2 5 7 1 8 2 6 +--R - b e x + (- a b e + - b d e)x + (- a b e + - a b d e + - b d )x +--R 8 7 7 3 3 6 +--R + +--R 3 5 2 2 6 7 2 5 5 4 4 2 3 5 5 2 6 2 4 +--R (2a b e + 4a b d e + a b d )x + (- a b e + 5a b d e + - a b d )x +--R 4 2 +--R + +--R 1 5 3 2 10 4 4 10 3 5 2 3 5 3 5 4 4 2 2 5 3 2 +--R (- a b e + -- a b d e + -- a b d )x + (a b d e + - a b d )x + a b d x +--R 3 3 3 2 +--R + +--R 1 8 2 1 7 1 6 2 2 +--R --- a e - -- a b d e + - a b d +--R 168 21 6 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 53 + +--S 54 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 54 + +)clear all + +--S 55 of 765 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R Type: Polynomial(Integer) +--E 55 + +--S 56 of 765 +r0:=1/6*(b*d-a*e)*(a+b*x)^6/b^2+1/7*e*(a+b*x)^7/b^2 +--R +--R +--R (2) +--R 1 7 7 5 6 1 7 6 2 5 6 5 +--R - b e x + (- a b e + - b d)x + (2a b e + a b d)x +--R 7 6 6 +--R + +--R 5 3 4 5 2 5 4 5 4 3 10 3 4 3 1 5 2 5 4 3 2 +--R (- a b e + - a b d)x + (- a b e + -- a b d)x + (- a b e + - a b d)x +--R 2 2 3 3 2 2 +--R + +--R 5 2 1 7 1 6 +--R a b d x - -- a e + - a b d +--R 42 6 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 56 + +--S 57 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Polynomial(Integer) +--E 58 + +--S 59 of 765 +r0:=1/6*(a+b*x)^6/b +--R +--R +--R 1 6 6 5 5 5 2 4 4 10 3 3 3 5 4 2 2 5 1 6 +--R - b x + a b x + - a b x + -- a b x + - a b x + a b x + - a +--R 6 2 3 2 6 +--R (2) ---------------------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 59 + +--S 60 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 765 +r0:=b*(b*d-a*e)^4*x/e^5-1/2*(b*d-a*e)^3*(a+b*x)^2/e^4+1/3*(b*d-a*e)^2*_ + (a+b*x)^3/e^3-1/4*(b*d-a*e)*(a+b*x)^4/e^2+1/5*(a+b*x)^5/e-(b*d-a*e)^5*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 5 5 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b e x + (75a b e - 15b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b e - 100a b d e + 20b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b e - 300a b d e + 150a b d e - 30b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (300a b e - 600a b d e + 600a b d e - 300a b d e + 60b d e)x + 77a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 +--R - 145a b d e + 110a b d e - 30a b d e +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 62 + +--S 63 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 64 + +--S 65 of 765 +r0:=-10*b^2*(b*d-a*e)^3*x/e^5+(b*d-a*e)^5/(e^6*(d+e*x))+5*b^3*(b*d-a*e)^2*_ + (d+e*x)^2/e^6-5/3*b^4*(b*d-a*e)*(d+e*x)^3/e^6+1/4*b^5*(d+e*x)^4/e^6+_ + 5*b*(b*d-a*e)^4*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b e x + (20a b e - 5b d e )x + (60a b e - 40a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b e - 180a b d e + 120a b d e - 30b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 5 5 4 4 +--R (120a b d e - 180a b d e + 80a b d e - 5b d e)x - 12a e + 60a b d e +--R + +--R 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 120a b d e + 180a b d e - 160a b d e + 55b d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 65 + +--S 66 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 66 + +)clear all + +--S 67 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 67 + +--S 68 of 765 +r0:=10*b^3*(b*d-a*e)^2*x/e^5+1/2*(b*d-a*e)^5/(e^6*(d+e*x)^2)-_ + 5*b*(b*d-a*e)^4/(e^6*(d+e*x))-5/2*b^4*(b*d-a*e)*(d+e*x)^2/e^6+_ + 1/3*b^5*(d+e*x)^3/e^6-10*b^2*(b*d-a*e)^3*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b d e - 360a b d e + 360a b d e - 120b d e)x + 60a b d e +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b e x + (15a b e - 5b d e )x + (60a b e - 60a b d e + 20b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (120a b d e - 150a b d e + 50b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b e + 120a b d e - 120a b d e + 60a b d e - 20b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b d e + 90a b d e - 150a b d e + 120a b d e - 40b d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 68 + +--S 69 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 69 + +)clear all + +--S 70 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^4 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 70 + +--S 71 of 765 +r0:=-b^4*(4*b*d-5*a*e)*x/e^5+1/2*b^5*x^2/e^4+1/3*(b*d-a*e)^5/(e^6*(d+e*x)^3)-_ + 5/2*b*(b*d-a*e)^4/(e^6*(d+e*x)^2)+10*b^2*(b*d-a*e)^3/(e^6*(d+e*x))+_ + 10*b^3*(b*d-a*e)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e - 360a b d e + 180b d e )x +--R + +--R 2 3 2 3 4 3 2 5 4 2 3 3 2 4 4 +--R (180a b d e - 360a b d e + 180b d e)x + 60a b d e - 120a b d e +--R + +--R 5 5 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 4 4 5 2 3 3 +--R 3b e x + (30a b e - 15b d e )x + (90a b d e - 63b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 60a b e + 180a b d e - 90a b d e - 9b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 15a b e - 60a b d e + 270a b d e - 270a b d e + 81b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 5a b d e - 20a b d e + 110a b d e - 130a b d e + 47b d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 71 + +--S 72 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 of 765 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 73 + +--S 74 of 765 +r0:=-(b*d-a*e)^7*(d+e*x)^(1+m)/(e^8*(1+m))+7*b*(b*d-a*e)^6*(d+e*x)^(2+m)/_ + (e^8*(2+m))-21*b^2*(b*d-a*e)^5*(d+e*x)^(3+m)/(e^8*(3+m))+35*b^3*_ + (b*d-a*e)^4*(d+e*x)^(4+m)/(e^8*(4+m))-35*b^4*(b*d-a*e)^3*(d+e*x)^(5+m)/_ + (e^8*(5+m))+21*b^5*(b*d-a*e)^2*(d+e*x)^(6+m)/(e^8*(6+m))-7*b^6*(b*d-_ + a*e)*(d+e*x)^(7+m)/(e^8*(7+m))+b^7*(d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R b m + 28b m + 322b m + 1960b m + 6769b m + 13132b m + 13068b m +--R + +--R 7 +--R 5040b +--R * +--R m + 8 +--R (e x + d) +--R + +--R 6 7 7 6 7 6 6 7 5 +--R (7a b e - 7b d)m + (203a b e - 203b d)m + (2401a b e - 2401b d)m +--R + +--R 6 7 4 6 7 3 +--R (14945a b e - 14945b d)m + (52528a b e - 52528b d)m +--R + +--R 6 7 2 6 7 6 +--R (103292a b e - 103292b d)m + (103824a b e - 103824b d)m + 40320a b e +--R + +--R 7 +--R - 40320b d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 5 2 6 7 2 7 +--R (21a b e - 42a b d e + 21b d )m +--R + +--R 2 5 2 6 7 2 6 +--R (630a b e - 1260a b d e + 630b d )m +--R + +--R 2 5 2 6 7 2 5 +--R (7686a b e - 15372a b d e + 7686b d )m +--R + +--R 2 5 2 6 7 2 4 +--R (49140a b e - 98280a b d e + 49140b d )m +--R + +--R 2 5 2 6 7 2 3 +--R (176589a b e - 353178a b d e + 176589b d )m +--R + +--R 2 5 2 6 7 2 2 +--R (353430a b e - 706860a b d e + 353430b d )m +--R + +--R 2 5 2 6 7 2 2 5 2 +--R (360024a b e - 720048a b d e + 360024b d )m + 141120a b e +--R + +--R 6 7 2 +--R - 282240a b d e + 141120b d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e - 105a b d e + 105a b d e - 35b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 6 +--R (1085a b e - 3255a b d e + 3255a b d e - 1085b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 5 +--R (13685a b e - 41055a b d e + 41055a b d e - 13685b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (90335a b e - 271005a b d e + 271005a b d e - 90335b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 3 +--R (334040a b e - 1002120a b d e + 1002120a b d e - 334040b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 2 +--R (684740a b e - 2054220a b d e + 2054220a b d e - 684740b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R (710640a b e - 2131920a b d e + 2131920a b d e - 710640b d )m +--R + +--R 3 4 3 2 5 2 6 2 7 3 +--R 282240a b e - 846720a b d e + 846720a b d e - 282240b d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (35a b e - 140a b d e + 210a b d e - 140a b d e + 35b d )m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 6 +--R (1120a b e - 4480a b d e + 6720a b d e - 4480a b d e + 1120b d )m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 14630a b e - 58520a b d e + 87780a b d e - 58520a b d e +--R + +--R 7 4 +--R 14630b d +--R * +--R 5 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 100240a b e - 400960a b d e + 601440a b d e - 400960a b d e +--R + +--R 7 4 +--R 100240b d +--R * +--R 4 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 384755a b e - 1539020a b d e + 2308530a b d e - 1539020a b d e +--R + +--R 7 4 +--R 384755b d +--R * +--R 3 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 815920a b e - 3263680a b d e + 4895520a b d e - 3263680a b d e +--R + +--R 7 4 +--R 815920b d +--R * +--R 2 +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 870660a b e - 3482640a b d e + 5223960a b d e - 3482640a b d e +--R + +--R 7 4 +--R 870660b d +--R * +--R m +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 +--R 352800a b e - 1411200a b d e + 2116800a b d e - 1411200a b d e +--R + +--R 7 4 +--R 352800b d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R 21a b e - 105a b d e + 210a b d e - 210a b d e + 105a b d e +--R + +--R 7 5 +--R - 21b d +--R * +--R 7 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 693a b e - 3465a b d e + 6930a b d e - 6930a b d e +--R + +--R 6 4 7 5 +--R 3465a b d e - 693b d +--R * +--R 6 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 9387a b e - 46935a b d e + 93870a b d e - 93870a b d e +--R + +--R 6 4 7 5 +--R 46935a b d e - 9387b d +--R * +--R 5 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 67095a b e - 335475a b d e + 670950a b d e - 670950a b d e +--R + +--R 6 4 7 5 +--R 335475a b d e - 67095b d +--R * +--R 4 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 270144a b e - 1350720a b d e + 2701440a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 2701440a b d e + 1350720a b d e - 270144b d +--R * +--R 3 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 602532a b e - 3012660a b d e + 6025320a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 6025320a b d e + 3012660a b d e - 602532b d +--R * +--R 2 +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 +--R 673008a b e - 3365040a b d e + 6730080a b d e +--R + +--R 2 5 3 2 6 4 7 5 +--R - 6730080a b d e + 3365040a b d e - 673008b d +--R * +--R m +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 +--R 282240a b e - 1411200a b d e + 2822400a b d e - 2822400a b d e +--R + +--R 6 4 7 5 +--R 1411200a b d e - 282240b d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 7a b e - 42a b d e + 105a b d e - 140a b d e + 105a b d e +--R + +--R 6 5 7 6 +--R - 42a b d e + 7b d +--R * +--R 7 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 238a b e - 1428a b d e + 3570a b d e - 4760a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 3570a b d e - 1428a b d e + 238b d +--R * +--R 6 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 3346a b e - 20076a b d e + 50190a b d e - 66920a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 50190a b d e - 20076a b d e + 3346b d +--R * +--R 5 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 25060a b e - 150360a b d e + 375900a b d e - 501200a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 375900a b d e - 150360a b d e + 25060b d +--R * +--R 4 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 107023a b e - 642138a b d e + 1605345a b d e - 2140460a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 1605345a b d e - 642138a b d e + 107023b d +--R * +--R 3 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R 256942a b e - 1541652a b d e + 3854130a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R - 5138840a b d e + 3854130a b d e - 1541652a b d e + 256942b d +--R * +--R 2 +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 +--R 312984a b e - 1877904a b d e + 4694760a b d e +--R + +--R 3 4 3 3 2 5 4 2 6 5 7 6 +--R - 6259680a b d e + 4694760a b d e - 1877904a b d e + 312984b d +--R * +--R m +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 +--R 141120a b e - 846720a b d e + 2116800a b d e - 2822400a b d e +--R + +--R 2 5 4 2 6 5 7 6 +--R 2116800a b d e - 846720a b d e + 141120b d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R a e - 7a b d e + 21a b d e - 35a b d e + 35a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 21a b d e + 7a b d e - b d +--R * +--R 7 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 35a e - 245a b d e + 735a b d e - 1225a b d e + 1225a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 735a b d e + 245a b d e - 35b d +--R * +--R 6 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 511a e - 3577a b d e + 10731a b d e - 17885a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 17885a b d e - 10731a b d e + 3577a b d e - 511b d +--R * +--R 5 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 4025a e - 28175a b d e + 84525a b d e - 140875a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 140875a b d e - 84525a b d e + 28175a b d e - 4025b d +--R * +--R 4 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 18424a e - 128968a b d e + 386904a b d e - 644840a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 644840a b d e - 386904a b d e + 128968a b d e - 18424b d +--R * +--R 3 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 48860a e - 342020a b d e + 1026060a b d e - 1710100a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 1710100a b d e - 1026060a b d e + 342020a b d e - 48860b d +--R * +--R 2 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 69264a e - 484848a b d e + 1454544a b d e - 2424240a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 2424240a b d e - 1454544a b d e + 484848a b d e - 69264b d +--R * +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 40320a e - 282240a b d e + 846720a b d e - 1411200a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 1411200a b d e - 846720a b d e + 282240a b d e - 40320b d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 74 + +--S 75 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 765 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 6 13 6 6 7 5 12 2 5 6 6 5 7 2 4 11 +--R b e x + (7a b e + 6b d e )x + (21a b e + 42a b d e + 15b d e )x +--R + +--R 3 4 6 2 5 5 6 2 4 7 3 3 10 +--R (35a b e + 126a b d e + 105a b d e + 20b d e )x +--R + +--R 4 3 6 3 4 5 2 5 2 4 6 3 3 7 4 2 9 +--R (35a b e + 210a b d e + 315a b d e + 140a b d e + 15b d e )x +--R + +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 21a b e + 210a b d e + 525a b d e + 420a b d e + 105a b d e +--R + +--R 7 5 +--R 6b d e +--R * +--R 8 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2 +--R 7a b e + 126a b d e + 525a b d e + 700a b d e + 315a b d e +--R + +--R 6 5 7 6 +--R 42a b d e + b d +--R * +--R 7 +--R x +--R + +--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2 +--R a e + 42a b d e + 315a b d e + 700a b d e + 525a b d e +--R + +--R 2 5 5 6 6 +--R 126a b d e + 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 +--R 6a d e + 105a b d e + 420a b d e + 525a b d e + 210a b d e +--R + +--R 2 5 6 +--R 21a b d +--R * +--R 5 +--R x +--R + +--R 7 2 4 6 3 3 5 2 4 2 4 3 5 3 4 6 4 +--R (15a d e + 140a b d e + 315a b d e + 210a b d e + 35a b d )x +--R + +--R 7 3 3 6 4 2 5 2 5 4 3 6 3 +--R (20a d e + 105a b d e + 126a b d e + 35a b d )x +--R + +--R 7 4 2 6 5 5 2 6 2 7 5 6 6 7 6 +--R (15a d e + 42a b d e + 21a b d )x + (6a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 765 +r0:=1/8*(b*d-a*e)^6*(a+b*x)^8/b^7+2/3*e*(b*d-a*e)^5*(a+b*x)^9/b^7+_ + 3/2*e^2*(b*d-a*e)^4*(a+b*x)^10/b^7+20/11*e^3*(b*d-a*e)^3*(a+b*x)^11/b^7+_ + 5/4*e^4*(b*d-a*e)^2*(a+b*x)^12/b^7+6/13*e^5*(b*d-a*e)*(a+b*x)^13/b^7+_ + 1/14*e^6*(a+b*x)^14/b^7 +--R +--R +--R (2) +--R 1 14 6 14 7 13 6 6 14 5 13 +--R -- b e x + (-- a b e + -- b d e )x +--R 14 13 13 +--R + +--R 7 2 12 6 7 13 5 5 14 2 4 12 +--R (- a b e + - a b d e + - b d e )x +--R 4 2 4 +--R + +--R 35 3 11 6 126 2 12 5 105 13 2 4 20 14 3 3 11 +--R (-- a b e + --- a b d e + --- a b d e + -- b d e )x +--R 11 11 11 11 +--R + +--R 7 4 10 6 3 11 5 63 2 12 2 4 13 3 3 3 14 4 2 10 +--R (- a b e + 21a b d e + -- a b d e + 14a b d e + - b d e )x +--R 2 2 2 +--R + +--R 7 5 9 6 70 4 10 5 175 3 11 2 4 140 2 12 3 3 +--R - a b e + -- a b d e + --- a b d e + --- a b d e +--R 3 3 3 3 +--R + +--R 35 13 4 2 2 14 5 +--R -- a b d e + - b d e +--R 3 3 +--R * +--R 9 +--R x +--R + +--R 7 6 8 6 63 5 9 5 525 4 10 2 4 175 3 11 3 3 +--R - a b e + -- a b d e + --- a b d e + --- a b d e +--R 8 4 8 2 +--R + +--R 315 2 12 4 2 21 13 5 1 14 6 +--R --- a b d e + -- a b d e + - b d +--R 8 4 8 +--R * +--R 8 +--R x +--R + +--R 1 7 7 6 6 8 5 5 9 2 4 4 10 3 3 3 11 4 2 +--R - a b e + 6a b d e + 45a b d e + 100a b d e + 75a b d e +--R 7 +--R + +--R 2 12 5 13 6 +--R 18a b d e + a b d +--R * +--R 7 +--R x +--R + +--R 7 7 5 35 6 8 2 4 5 9 3 3 175 4 10 4 2 3 11 5 +--R a b d e + -- a b d e + 70a b d e + --- a b d e + 35a b d e +--R 2 2 +--R + +--R 7 2 12 6 +--R - a b d +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 7 2 4 6 8 3 3 5 9 4 2 4 10 5 3 11 6 5 +--R (3a b d e + 28a b d e + 63a b d e + 42a b d e + 7a b d )x +--R + +--R 7 7 3 3 105 6 8 4 2 63 5 9 5 35 4 10 6 4 +--R (5a b d e + --- a b d e + -- a b d e + -- a b d )x +--R 4 2 4 +--R + +--R 7 7 4 2 6 8 5 5 9 6 3 7 7 5 7 6 8 6 2 7 7 6 +--R (5a b d e + 14a b d e + 7a b d )x + (3a b d e + - a b d )x + a b d x +--R 2 +--R + +--R 1 14 6 1 13 5 1 12 2 2 4 1 11 3 3 3 +--R ----- a e - ---- a b d e + --- a b d e - -- a b d e +--R 24024 1716 264 66 +--R + +--R 1 10 4 4 2 1 9 5 5 1 8 6 6 +--R -- a b d e - -- a b d e + - a b d +--R 24 12 8 +--R / +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 765 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 5 12 6 5 7 4 11 2 5 5 6 4 7 2 3 10 +--R b e x + (7a b e + 5b d e )x + (21a b e + 35a b d e + 10b d e )x +--R + +--R 3 4 5 2 5 4 6 2 3 7 3 2 9 +--R (35a b e + 105a b d e + 70a b d e + 10b d e )x +--R + +--R 4 3 5 3 4 4 2 5 2 3 6 3 2 7 4 8 +--R (35a b e + 175a b d e + 210a b d e + 70a b d e + 5b d e)x +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 7 5 7 +--R (21a b e + 175a b d e + 350a b d e + 210a b d e + 35a b d e + b d )x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 7a b e + 105a b d e + 350a b d e + 350a b d e + 105a b d e +--R + +--R 6 5 +--R 7a b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 5 +--R (a e + 35a b d e + 210a b d e + 350a b d e + 175a b d e + 21a b d )x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 4 +--R (5a d e + 70a b d e + 210a b d e + 175a b d e + 35a b d )x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 3 +--R (10a d e + 70a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 2 6 4 5 2 5 2 7 4 6 5 7 5 +--R (10a d e + 35a b d e + 21a b d )x + (5a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 79 + +--S 80 of 765 +r0:=1/8*(b*d-a*e)^5*(a+b*x)^8/b^6+5/9*e*(b*d-a*e)^4*(a+b*x)^9/b^6+e^2*_ + (b*d-a*e)^3*(a+b*x)^10/b^6+10/11*e^3*(b*d-a*e)^2*(a+b*x)^11/b^6+_ + 5/12*e^4*(b*d-a*e)*(a+b*x)^12/b^6+1/13*e^5*(a+b*x)^13/b^6 +--R +--R +--R (2) +--R 1 13 5 13 7 12 5 5 13 4 12 +--R -- b e x + (-- a b e + -- b d e )x +--R 13 12 12 +--R + +--R 21 2 11 5 35 12 4 10 13 2 3 11 +--R (-- a b e + -- a b d e + -- b d e )x +--R 11 11 11 +--R + +--R 7 3 10 5 21 2 11 4 12 2 3 13 3 2 10 +--R (- a b e + -- a b d e + 7a b d e + b d e )x +--R 2 2 +--R + +--R 35 4 9 5 175 3 10 4 70 2 11 2 3 70 12 3 2 5 13 4 9 +--R (-- a b e + --- a b d e + -- a b d e + -- a b d e + - b d e)x +--R 9 9 3 9 9 +--R + +--R 21 5 8 5 175 4 9 4 175 3 10 2 3 105 2 11 3 2 +--R -- a b e + --- a b d e + --- a b d e + --- a b d e +--R 8 8 4 4 +--R + +--R 35 12 4 1 13 5 +--R -- a b d e + - b d +--R 8 8 +--R * +--R 8 +--R x +--R + +--R 6 7 5 5 8 4 4 9 2 3 3 10 3 2 2 11 4 12 5 7 +--R (a b e + 15a b d e + 50a b d e + 50a b d e + 15a b d e + a b d )x +--R + +--R 1 7 6 5 35 6 7 4 5 8 2 3 175 4 9 3 2 175 3 10 4 +--R - a b e + -- a b d e + 35a b d e + --- a b d e + --- a b d e +--R 6 6 3 6 +--R + +--R 7 2 11 5 +--R - a b d +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 6 4 6 7 2 3 5 8 3 2 4 9 4 3 10 5 5 +--R (a b d e + 14a b d e + 42a b d e + 35a b d e + 7a b d )x +--R + +--R 5 7 6 2 3 35 6 7 3 2 105 5 8 4 35 4 9 5 4 +--R (- a b d e + -- a b d e + --- a b d e + -- a b d )x +--R 2 2 4 4 +--R + +--R 10 7 6 3 2 35 6 7 4 5 8 5 3 5 7 6 4 7 6 7 5 2 +--R (-- a b d e + -- a b d e + 7a b d )x + (- a b d e + - a b d )x +--R 3 3 2 2 +--R + +--R 7 6 5 1 13 5 1 12 4 1 11 2 2 3 1 10 3 3 2 +--R a b d x - ----- a e + --- a b d e - --- a b d e + -- a b d e +--R 10296 792 132 36 +--R + +--R 5 9 4 4 1 8 5 5 +--R - -- a b d e + - a b d +--R 72 8 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 80 + +--S 81 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 of 765 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 4 11 6 4 7 3 10 2 5 4 6 3 7 2 2 9 +--R b e x + (7a b e + 4b d e )x + (21a b e + 28a b d e + 6b d e )x +--R + +--R 3 4 4 2 5 3 6 2 2 7 3 8 +--R (35a b e + 84a b d e + 42a b d e + 4b d e)x +--R + +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7 +--R (35a b e + 140a b d e + 126a b d e + 28a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 6 +--R (21a b e + 140a b d e + 210a b d e + 84a b d e + 7a b d )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 5 +--R (7a b e + 84a b d e + 210a b d e + 140a b d e + 21a b d )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 4 +--R (a e + 28a b d e + 126a b d e + 140a b d e + 35a b d )x +--R + +--R 7 3 6 2 2 5 2 3 4 3 4 3 +--R (4a d e + 42a b d e + 84a b d e + 35a b d )x +--R + +--R 7 2 2 6 3 5 2 4 2 7 3 6 4 7 4 +--R (6a d e + 28a b d e + 21a b d )x + (4a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 82 + +--S 83 of 765 +r0:=1/8*(b*d-a*e)^4*(a+b*x)^8/b^5+4/9*e*(b*d-a*e)^3*(a+b*x)^9/b^5+3/5*e^2*_ + (b*d-a*e)^2*(a+b*x)^10/b^5+4/11*e^3*(b*d-a*e)*(a+b*x)^11/b^5+1/12*e^4*_ + (a+b*x)^12/b^5 +--R +--R +--R (2) +--R 1 12 4 12 7 11 4 4 12 3 11 +--R -- b e x + (-- a b e + -- b d e )x +--R 12 11 11 +--R + +--R 21 2 10 4 14 11 3 3 12 2 2 10 +--R (-- a b e + -- a b d e + - b d e )x +--R 10 5 5 +--R + +--R 35 3 9 4 28 2 10 3 14 11 2 2 4 12 3 9 +--R (-- a b e + -- a b d e + -- a b d e + - b d e)x +--R 9 3 3 9 +--R + +--R 35 4 8 4 35 3 9 3 63 2 10 2 2 7 11 3 1 12 4 8 +--R (-- a b e + -- a b d e + -- a b d e + - a b d e + - b d )x +--R 8 2 4 2 8 +--R + +--R 5 7 4 4 8 3 3 9 2 2 2 10 3 11 4 7 +--R (3a b e + 20a b d e + 30a b d e + 12a b d e + a b d )x +--R + +--R 7 6 6 4 5 7 3 4 8 2 2 70 3 9 3 7 2 10 4 6 +--R (- a b e + 14a b d e + 35a b d e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 1 7 5 4 28 6 6 3 126 5 7 2 2 4 8 3 3 9 4 5 +--R (- a b e + -- a b d e + --- a b d e + 28a b d e + 7a b d )x +--R 5 5 5 +--R + +--R 7 5 3 21 6 6 2 2 5 7 3 35 4 8 4 4 +--R (a b d e + -- a b d e + 21a b d e + -- a b d )x +--R 2 4 +--R + +--R 7 5 2 2 28 6 6 3 5 7 4 3 7 5 3 7 6 6 4 2 7 5 4 +--R (2a b d e + -- a b d e + 7a b d )x + (2a b d e + - a b d )x + a b d x +--R 3 2 +--R + +--R 1 12 4 1 11 3 1 10 2 2 2 1 9 3 3 1 8 4 4 +--R ---- a e - --- a b d e + -- a b d e - -- a b d e + - a b d +--R 3960 330 60 18 8 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 83 + +--S 84 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 765 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 3 10 6 3 7 2 9 2 5 3 6 2 7 2 8 +--R b e x + (7a b e + 3b d e )x + (21a b e + 21a b d e + 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e + 63a b d e + 21a b d e + b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (35a b e + 105a b d e + 63a b d e + 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (21a b e + 105a b d e + 105a b d e + 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (7a b e + 63a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (a e + 21a b d e + 63a b d e + 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (3a d e + 21a b d e + 21a b d )x + (3a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 85 + +--S 86 of 765 +r0:=1/8*(b*d-a*e)^3*(a+b*x)^8/b^4+1/3*e*(b*d-a*e)^2*(a+b*x)^9/b^4+3/10*e^2*_ + (b*d-a*e)*(a+b*x)^10/b^4+1/11*e^3*(a+b*x)^11/b^4 +--R +--R +--R (2) +--R 1 11 3 11 7 10 3 3 11 2 10 +--R -- b e x + (-- a b e + -- b d e )x +--R 11 10 10 +--R + +--R 7 2 9 3 7 10 2 1 11 2 9 +--R (- a b e + - a b d e + - b d e)x +--R 3 3 3 +--R + +--R 35 3 8 3 63 2 9 2 21 10 2 1 11 3 8 +--R (-- a b e + -- a b d e + -- a b d e + - b d )x +--R 8 8 8 8 +--R + +--R 4 7 3 3 8 2 2 9 2 10 3 7 +--R (5a b e + 15a b d e + 9a b d e + a b d )x +--R + +--R 7 5 6 3 35 4 7 2 35 3 8 2 7 2 9 3 6 +--R (- a b e + -- a b d e + -- a b d e + - a b d )x +--R 2 2 2 2 +--R + +--R 7 6 5 3 63 5 6 2 4 7 2 3 8 3 5 +--R (- a b e + -- a b d e + 21a b d e + 7a b d )x +--R 5 5 +--R + +--R 1 7 4 3 21 6 5 2 63 5 6 2 35 4 7 3 4 +--R (- a b e + -- a b d e + -- a b d e + -- a b d )x +--R 4 4 4 4 +--R + +--R 7 4 2 6 5 2 5 6 3 3 3 7 4 2 7 6 5 3 2 7 4 3 +--R (a b d e + 7a b d e + 7a b d )x + (- a b d e + - a b d )x + a b d x +--R 2 2 +--R + +--R 1 11 3 1 10 2 1 9 2 2 1 8 3 3 +--R - ---- a e + --- a b d e - -- a b d e + - a b d +--R 1320 120 24 8 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 86 + +--S 87 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 765 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R b e x + (7a b e + 2b d e)x + (21a b e + 14a b d e + b d )x +--R + +--R 3 4 2 2 5 6 2 6 4 3 2 3 4 2 5 2 5 +--R (35a b e + 42a b d e + 7a b d )x + (35a b e + 70a b d e + 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 6 2 5 2 4 3 2 3 +--R (21a b e + 70a b d e + 35a b d )x + (7a b e + 42a b d e + 35a b d )x +--R + +--R 7 2 6 5 2 2 2 7 6 2 7 2 +--R (a e + 14a b d e + 21a b d )x + (2a d e + 7a b d )x + a d +--R Type: Polynomial(Integer) +--E 88 + +--S 89 of 765 +r0:=1/8*(b*d-a*e)^2*(a+b*x)^8/b^3+2/9*e*(b*d-a*e)*(a+b*x)^9/b^3+1/10*e^2*_ + (a+b*x)^10/b^3 +--R +--R +--R (2) +--R 1 10 2 10 7 9 2 2 10 9 +--R -- b e x + (- a b e + - b d e)x +--R 10 9 9 +--R + +--R 21 2 8 2 7 9 1 10 2 8 3 7 2 2 8 9 2 7 +--R (-- a b e + - a b d e + - b d )x + (5a b e + 6a b d e + a b d )x +--R 8 4 8 +--R + +--R 35 4 6 2 35 3 7 7 2 8 2 6 +--R (-- a b e + -- a b d e + - a b d )x +--R 6 3 2 +--R + +--R 21 5 5 2 4 6 3 7 2 5 +--R (-- a b e + 14a b d e + 7a b d )x +--R 5 +--R + +--R 7 6 4 2 21 5 5 35 4 6 2 4 +--R (- a b e + -- a b d e + -- a b d )x +--R 4 2 4 +--R + +--R 1 7 3 2 14 6 4 5 5 2 3 7 3 7 6 4 2 2 7 3 2 +--R (- a b e + -- a b d e + 7a b d )x + (a b d e + - a b d )x + a b d x +--R 3 3 2 +--R + +--R 1 10 2 1 9 1 8 2 2 +--R --- a e - -- a b d e + - a b d +--R 360 36 8 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 765 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 8 6 7 7 2 5 6 6 3 4 2 5 5 +--R b e x + (7a b e + b d)x + (21a b e + 7a b d)x + (35a b e + 21a b d)x +--R + +--R 4 3 3 4 4 5 2 4 3 3 6 5 2 2 +--R (35a b e + 35a b d)x + (21a b e + 35a b d)x + (7a b e + 21a b d)x +--R + +--R 7 6 7 +--R (a e + 7a b d)x + a d +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 765 +r0:=1/8*(b*d-a*e)*(a+b*x)^8/b^2+1/9*e*(a+b*x)^9/b^2 +--R +--R +--R (2) +--R 1 9 9 7 8 1 9 8 2 7 8 7 +--R - b e x + (- a b e + - b d)x + (3a b e + a b d)x +--R 9 8 8 +--R + +--R 35 3 6 7 2 7 6 4 5 3 6 5 21 5 4 35 4 5 4 +--R (-- a b e + - a b d)x + (7a b e + 7a b d)x + (-- a b e + -- a b d)x +--R 6 2 4 4 +--R + +--R 7 6 3 5 4 3 1 7 2 7 6 3 2 7 2 1 9 1 8 +--R (- a b e + 7a b d)x + (- a b e + - a b d)x + a b d x - -- a e + - a b d +--R 3 2 2 72 8 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Polynomial(Integer) +--E 94 + +--S 95 of 765 +r0:=1/8*(a+b*x)^8/b +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - b x + a b x + - a b x + 7a b x + -- a b x + 7a b x + - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R a b x + - a +--R 8 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 95 + +--S 96 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 97 + +--S 98 of 765 +r0:=b*(b*d-a*e)^6*x/e^7-1/2*(b*d-a*e)^5*(a+b*x)^2/e^6+1/3*(b*d-a*e)^4*_ + (a+b*x)^3/e^5-1/4*(b*d-a*e)^3*(a+b*x)^4/e^4+1/5*(b*d-a*e)^2*(a+b*x)^5/e^3-_ + 1/6*(b*d-a*e)*(a+b*x)^6/e^2+1/7*(a+b*x)^7/e-(b*d-a*e)^7*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a e - 2940a b d e + 8820a b d e - 14700a b d e + 14700a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 8820a b d e + 2940a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b e x + (490a b e - 70b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (1764a b e - 588a b d e + 84b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (3675a b e - 2205a b d e + 735a b d e - 105b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (4900a b e - 4900a b d e + 2940a b d e - 980a b d e + 140b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4410a b e - 7350a b d e + 7350a b d e - 4410a b d e +--R + +--R 6 4 3 7 5 2 +--R 1470a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 2940a b e - 8820a b d e + 14700a b d e - 14700a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 8820a b d e - 2940a b d e + 420b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 669a e - 2163a b d e + 3339a b d e - 2765a b d e + 1190a b d e +--R + +--R 2 5 5 2 +--R - 210a b d e +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 98 + +--S 99 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 100 + +--S 101 of 765 +r0:=-21*b^2*(b*d-a*e)^5*x/e^7+(b*d-a*e)^7/(e^8*(d+e*x))+35/2*b^3*_ + (b*d-a*e)^4*(d+e*x)^2/e^8-35/3*b^4*(b*d-a*e)^3*(d+e*x)^3/e^8+_ + 21/4*b^5*(b*d-a*e)^2*(d+e*x)^4/e^8-7/5*b^6*(b*d-a*e)*(d+e*x)^5/e^8+_ + 1/6*b^7*(d+e*x)^6/e^8+7*b*(b*d-a*e)^6*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b d e - 2520a b d e + 420b d e +--R * +--R x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a b d e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 6300a b d e - 2520a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (84a b e - 14b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (315a b e - 126a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (700a b e - 525a b d e + 210a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1050a b e - 1400a b d e + 1050a b d e - 420a b d e + 70b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b e - 3150a b d e + 4200a b d e - 3150a b d e +--R + +--R 6 4 3 7 5 2 +--R 1260a b d e - 210b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 1260a b d e - 3150a b d e + 2800a b d e - 525a b d e +--R + +--R 6 5 2 7 6 +--R - 546a b d e + 231b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a e + 420a b d e - 1260a b d e + 3150a b d e - 5600a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 5775a b d e - 3066a b d e + 651b d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 101 + +--S 102 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 103 + +--S 104 of 765 +r0:=35*b^3*(b*d-a*e)^4*x/e^7+1/2*(b*d-a*e)^7/(e^8*(d+e*x)^2)-_ + 7*b*(b*d-a*e)^6/(e^8*(d+e*x))-35/2*b^4*(b*d-a*e)^3*(d+e*x)^2/e^8+_ + 7*b^5*(b*d-a*e)^2*(d+e*x)^3/e^8-7/4*b^6*(b*d-a*e)*(d+e*x)^4/e^8+_ + 1/5*b^7*(d+e*x)^5/e^8-21*b^2*(b*d-a*e)^5*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 420a b e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 4 3 7 5 2 +--R 2100a b d e - 420b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 840a b d e - 4200a b d e + 8400a b d e - 8400a b d e +--R + +--R 6 5 2 7 6 +--R 4200a b d e - 840b d e +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 420a b d e - 2100a b d e + 4200a b d e - 4200a b d e +--R + +--R 6 6 7 7 +--R 2100a b d e - 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 4b e x + (35a b e - 7b d e )x + (140a b e - 70a b d e + 14b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (350a b e - 350a b d e + 175a b d e - 35b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (700a b e - 1400a b d e + 1400a b d e - 700a b d e + 140b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (1400a b d e - 3500a b d e + 3500a b d e - 1575a b d e + 259b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 140a b e + 840a b d e - 1400a b d e + 1400a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 1400a b d e + 1050a b d e - 322b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a e - 70a b d e + 630a b d e - 1750a b d e + 2800a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 2800a b d e + 1575a b d e - 371b d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 104 + +--S 105 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 765 +r0:=-35*b^4*(b*d-a*e)^3*x/e^7+1/3*(b*d-a*e)^7/(e^8*(d+e*x)^3)-_ + 7/2*b*(b*d-a*e)^6/(e^8*(d+e*x)^2)+21*b^2*(b*d-a*e)^5/(e^8*(d+e*x))+_ + 21/2*b^5*(b*d-a*e)^2*(d+e*x)^2/e^8-7/3*b^6*(b*d-a*e)*(d+e*x)^3/e^8+_ + 1/4*b^7*(d+e*x)^4/e^8+35*b^3*(b*d-a*e)^4*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b e - 1680a b d e + 2520a b d e - 1680a b d e +--R + +--R 7 4 3 +--R 420b d e +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 5 2 +--R 1260b d e +--R * +--R 2 +--R x +--R + +--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 1260a b d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 7 6 +--R 1260b d e +--R * +--R x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 3b e x + (28a b e - 7b d e )x + (126a b e - 84a b d e + 21b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b e - 630a b d e + 420a b d e - 105b d e )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1260a b d e - 2520a b d e + 1820a b d e - 455b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 6 4 3 7 5 2 2 +--R (- 252a b e + 1260a b d e - 1260a b d e + 420a b d e - 105b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 42a b e - 252a b d e + 1890a b d e - 3780a b d e + 3780a b d e +--R + +--R 6 5 2 7 6 +--R - 2100a b d e + 525b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e - 14a b d e - 84a b d e + 770a b d e - 1820a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 2100a b d e - 1260a b d e + 315b d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 107 + +--S 108 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 765 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 109 + +--S 110 of 765 +r0:=e*(b*d-a*e)^3*x/b^4+1/2*(b*d-a*e)^2*(d+e*x)^2/b^3+1/3*(b*d-a*e)*_ + (d+e*x)^3/b^2+1/4*(d+e*x)^4/b+(b*d-a*e)^4*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (- 4a b e + 16b d e )x + (6a b e - 24a b d e + 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 2 2 2 3 3 +--R (- 12a b e + 48a b d e - 72a b d e + 48b d e)x + 6a b d e - 16a b d e +--R + +--R 4 4 +--R 13b d +--R / +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 110 + +--S 111 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 765 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 112 + +--S 113 of 765 +r0:=e*(b*d-a*e)^2*x/b^3+1/2*(b*d-a*e)*(d+e*x)^2/b^2+1/3*(d+e*x)^3/b+_ + (b*d-a*e)^3*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (- 6a e + 18a b d e - 18a b d e + 6b d )log(b x + a) + 2b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 2 2 +--R (- 3a b e + 9b d e )x + (6a b e - 18a b d e + 18b d e)x - 3a b d e +--R + +--R 3 3 +--R 5b d +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 113 + +--S 114 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 765 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------ +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 of 765 +r0:=e*(b*d-a*e)*x/b^2+1/2*(d+e*x)^2/b+(b*d-a*e)^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(b x + a) + b e x + (- 2a b e + 4b d e)x +--R + +--R 2 2 +--R b d +--R / +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 116 + +--S 117 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 765 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R e x + d +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 of 765 +r0:=e*x/b+(b*d-a*e)*log(a+b*x)/b^2 +--R +--R +--R (- a e + b d)log(b x + a) + b e x +--R (2) --------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 119 + +--S 120 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 765 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 1 +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 765 +r0:=log(a+b*x)/b +--R +--R +--R log(b x + a) +--R (2) ------------ +--R b +--R Type: Expression(Integer) +--E 122 + +--S 123 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 765 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--R b e x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 124 + +--S 125 of 765 +r0:=log(a+b*x)/(b*d-a*e)-log(d+e*x)/(b*d-a*e) +--R +--R +--R log(e x + d) - log(b x + a) +--R (2) --------------------------- +--R a e - b d +--R Type: Expression(Integer) +--E 125 + +--S 126 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 of 765 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (a e + 2b d e)x + (2a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 127 + +--S 128 of 765 +r0:=1/((b*d-a*e)*(d+e*x))+b*log(a+b*x)/(b*d-a*e)^2-b*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (- b e x - b d)log(e x + d) + (b e x + b d)log(b x + a) - a e + b d +--R (2) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a e - 2a b d e + b d e)x + a d e - 2a b d e + b d +--R Type: Expression(Integer) +--E 128 + +--S 129 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 765 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 130 + +--S 131 of 765 +r0:=1/2/((b*d-a*e)*(d+e*x)^2)+b/((b*d-a*e)^2*(d+e*x))+b^2*log(a+b*x)/_ + (b*d-a*e)^3-b^2*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4b d e x - 2b d )log(b x + a) + (2a b e - 2b d e)x - a e +--R + +--R 2 2 +--R 4a b d e - 3b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a d e - 12a b d e + 12a b d e - 4b d e)x + 2a d e - 6a b d e +--R + +--R 2 4 3 5 +--R 6a b d e - 2b d +--R Type: Expression(Integer) +--E 131 + +--S 132 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 765 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 133 + +--S 134 of 765 +r0:=1/3/((b*d-a*e)*(d+e*x)^3)+1/2*b/((b*d-a*e)^2*(d+e*x)^2)+_ + b^2/((b*d-a*e)^3*(d+e*x))+b^3*log(a+b*x)/(b*d-a*e)^4-_ + b^3*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 3 3 3 2 2 3 2 3 3 +--R (- 6b e x - 18b d e x - 18b d e x - 6b d )log(e x + d) +--R + +--R 3 3 3 3 2 2 3 2 3 3 +--R (6b e x + 18b d e x + 18b d e x + 6b d )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (3a b e - 18a b d e + 15b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 18a b d e + 11b d +--R / +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4 3 4 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e)x + 6a d e +--R + +--R 3 4 3 2 2 5 2 3 6 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d +--R Type: Expression(Integer) +--E 134 + +--S 135 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 765 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 765 +r0:=e^3*(4*b*d-3*a*e)*x/b^4+1/2*e^4*x^2/b^3-1/2*(b*d-a*e)^4/(b^5*(a+b*x)^2)-_ + 4*e*(b*d-a*e)^3/(b^5*(a+b*x))+6*e^2*(b*d-a*e)^2*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (24a b e - 48a b d e + 24a b d e )x + 12a e - 24a b d e +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R b e x + (- 4a b e + 8b d e )x + (- 11a b e + 16a b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (2a b e - 16a b d e + 24a b d e - 8b d e)x + 7a e - 20a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 4a b d e - b d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 137 + +--S 138 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 765 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 139 + +--S 140 of 765 +r0:=e^3*x/b^3-1/2*(b*d-a*e)^3/(b^4*(a+b*x)^2)-3*e*(b*d-a*e)^2/(b^4*(a+b*x))+_ + 3*e^2*(b*d-a*e)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b e + 6b d e )x + (- 12a b e + 12a b d e )x - 6a e +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b e x + 4a b e x + (- 4a b e + 12a b d e - 6b d e)x - 5a e +--R + +--R 2 2 2 2 3 3 +--R 9a b d e - 3a b d e - b d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 140 + +--S 141 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 of 765 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 142 + +--S 143 of 765 +r0:=-1/2*(b*d-a*e)^2/(b^3*(a+b*x)^2)-2*e*(b*d-a*e)/(b^3*(a+b*x))+_ + e^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(b x + a) + (4a b e - 4b d e)x + 3a e +--R + +--R 2 2 +--R - 2a b d e - b d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 143 + +--S 144 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 765 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 145 + +--S 146 of 765 +r0:=-1/2*(d+e*x)^2/((b*d-a*e)*(a+b*x)^2) +--R +--R +--R 1 2 2 1 2 +--R - e x + d e x + - d +--R 2 2 +--R (2) -------------------------------------------------- +--R 2 3 2 2 2 3 2 +--R (a b e - b d)x + (2a b e - 2a b d)x + a e - a b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 146 + +--S 147 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 765 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 1 +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 148 + +--S 149 of 765 +r0:=(-1/2)/(b*(a+b*x)^2) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ------------------- +--R 3 2 2 2 +--R b x + 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 765 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 765 +r0:=(-1/2)/((b*d-a*e)*(a+b*x)^2)+e/((b*d-a*e)^2*(a+b*x))+_ + e^2*log(a+b*x)/(b*d-a*e)^3-e^2*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b e x + 4a b e x + 2a e )log(e x + d) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b e x - 4a b e x - 2a e )log(b x + a) + (2a b e - 2b d e)x + 3a e +--R + +--R 2 2 +--R - 4a b d e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a e - 6a b d e +--R + +--R 3 2 2 2 3 3 +--R 6a b d e - 2a b d +--R Type: Expression(Integer) +--E 152 + +--S 153 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 765 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 154 + +--S 155 of 765 +r0:=-1/2*b/((b*d-a*e)^2*(a+b*x)^2)+2*b*e/((b*d-a*e)^3*(a+b*x))+_ + e^2/((b*d-a*e)^3*(d+e*x))+3*b*e^2*log(a+b*x)/(b*d-a*e)^4-_ + 3*b*e^2*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R - 6b e x + (- 12a b e - 6b d e )x + (- 6a b e - 12a b d e )x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 6b e x + (12a b e + 6b d e )x + (6a b e + 12a b d e )x +--R + +--R 2 2 +--R 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b e + 6b d e )x + (- 9a b e + 6a b d e + 3b d e)x - 2a e +--R + +--R 2 2 2 2 3 3 +--R - 3a b d e + 6a b d e - b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 155 + +--S 156 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 765 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 157 + +--S 158 of 765 +r0:=-1/2*b^2/((b*d-a*e)^3*(a+b*x)^2)+3*b^2*e/((b*d-a*e)^4*(a+b*x))+_ + 1/2*e^2/((b*d-a*e)^3*(d+e*x)^2)+3*b*e^2/((b*d-a*e)^4*(d+e*x))+_ + 6*b^2*e^2*log(a+b*x)/(b*d-a*e)^5-6*b^2*e^2*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 12b e x + (24a b e + 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b e + 48a b d e + 12b d e )x + (24a b d e + 24a b d e )x +--R + +--R 2 2 2 2 +--R 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b e x + (- 24a b e - 24b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b e - 48a b d e - 12b d e )x + (- 24a b d e - 24a b d e )x +--R + +--R 2 2 2 2 +--R - 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b e - 12b d e )x + (18a b e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b e + 24a b d e - 24a b d e - 4b d e)x - a e + 8a b d e +--R + +--R 3 3 4 4 +--R - 8a b d e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Expression(Integer) +--E 158 + +--S 159 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 765 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 of 765 +r0:=-1/2*b^3/((b*d-a*e)^4*(a+b*x)^2)+4*b^3*e/((b*d-a*e)^5*(a+b*x))+_ + 1/3*e^2/((b*d-a*e)^3*(d+e*x)^3)+3/2*b*e^2/((b*d-a*e)^4*(d+e*x)^2)+_ + 6*b^2*e^2/((b*d-a*e)^5*(d+e*x))+10*b^3*e^2*log(a+b*x)/(b*d-a*e)^6-_ + 10*b^3*e^2*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 120a b e - 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 60a b e - 360a b d e - 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (- 180a b d e - 360a b d e - 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (- 180a b d e - 120a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (120a b e + 180b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e + 360a b d e + 180b d e )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (180a b d e + 360a b d e + 60b d e )x +--R + +--R 2 3 2 3 4 3 2 2 3 3 2 +--R (180a b d e + 120a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 90a b e - 60a b d e + 150b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 20a b e - 210a b d e + 120a b d e + 110b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (5a b e - 60a b d e - 120a b d e + 160a b d e + 15b d e)x - 2a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 15a b d e - 60a b d e + 20a b d e + 30a b d e - 3b d +--R / +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 4 8 6 3 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 12a b e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 198a b d e - 96a b d e + 18b d e +--R * +--R 4 +--R x +--R + +--R 8 9 6 2 2 7 5 3 3 6 4 4 4 5 3 5 5 4 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 2 6 6 3 7 7 2 8 8 +--R 60a b d e - 72a b d e + 18b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4 +--R 18a d e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 5 6 3 2 6 7 2 8 9 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 2 7 7 3 6 6 2 4 5 5 3 5 4 4 4 6 3 +--R 18a d e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 3 5 7 2 2 6 8 7 9 +--R 72a b d e - 54a b d e + 12a b d +--R * +--R x +--R + +--R 8 3 6 7 4 5 6 2 5 4 5 3 6 3 4 4 7 2 3 5 8 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 2 6 9 +--R 6a b d +--R Type: Expression(Integer) +--E 161 + +--S 162 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 765 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 of 765 +r0:=-1/4*(b*d-a*e)^4/(b^5*(a+b*x)^4)-4/3*e*(b*d-a*e)^3/(b^5*(a+b*x)^3)-_ + 3*e^2*(b*d-a*e)^2/(b^5*(a+b*x)^2)-4*e^3*(b*d-a*e)/(b^5*(a+b*x))+_ + e^4*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (48a b e - 48b d e )x + (108a b e - 72a b d e - 36b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (88a b e - 48a b d e - 24a b d e - 16b d e)x + 25a e - 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 4a b d e - 3b d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Expression(Integer) +--E 164 + +--S 165 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 765 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 765 +r0:=-1/4*(d+e*x)^4/((b*d-a*e)*(a+b*x)^4) +--R +--R +--R (2) +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - e x + d e x + - d e x + d e x + - d +--R 4 2 4 +--R / +--R 4 5 4 2 3 4 3 3 2 2 3 2 +--R (a b e - b d)x + (4a b e - 4a b d)x + (6a b e - 6a b d)x +--R + +--R 4 3 2 5 4 +--R (4a b e - 4a b d)x + a e - a b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 167 + +--S 168 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 765 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 169 + +--S 170 of 765 +r0:=-1/4*(b*d-a*e)^2/(b^3*(a+b*x)^4)-2/3*e*(b*d-a*e)/(b^3*(a+b*x)^3)-_ + 1/2*e^2/(b^3*(a+b*x)^2) +--R +--R +--R 1 2 2 2 1 2 2 2 1 2 2 1 1 2 2 +--R - - b e x + (- - a b e - - b d e)x - -- a e - - a b d e - - b d +--R 2 3 3 12 6 4 +--R (2) ------------------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 170 + +--S 171 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 765 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 172 + +--S 173 of 765 +r0:=1/4*(-b*d+a*e)/(b^2*(a+b*x)^4)-1/3*e/(b^2*(a+b*x)^3) +--R +--R +--R 1 1 1 +--R - - b e x - -- a e - - b d +--R 3 12 4 +--R (2) ---------------------------------------- +--R 6 4 5 3 2 4 2 3 3 4 2 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 173 + +--S 174 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 765 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 of 765 +r0:=(-1/4)/(b*(a+b*x)^4) +--R +--R +--R 1 +--R - +--R 4 +--R (2) - --------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 176 + +--S 177 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 765 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 178 + +--S 179 of 765 +r0:=(-1/4)/((b*d-a*e)*(a+b*x)^4)+1/3*e/((b*d-a*e)^2*(a+b*x)^3)-_ + 1/2*e^2/((b*d-a*e)^3*(a+b*x)^2)+e^3/((b*d-a*e)^4*(a+b*x))+_ + e^4*log(a+b*x)/(b*d-a*e)^5-e^4*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (12b e x + 48a b e x + 72a b e x + 48a b e x + 12a e )log(e x + d) +--R + +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 12b e x - 48a b e x - 72a b e x - 48a b e x - 12a e )log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (42a b e - 48a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (52a b e - 72a b d e + 24a b d e - 4b d e)x + 25a e - 48a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 36a b d e - 16a b d e + 3b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 12a b e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 9 5 +--R - 12b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 2 7 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 8 5 +--R - 48a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 3 6 4 +--R 72a b e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 2 7 5 +--R - 72a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 4 5 4 +--R 48a b e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 3 6 5 +--R - 48a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 4 5 5 +--R 12a e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12a b d +--R Type: Expression(Integer) +--E 179 + +--S 180 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 765 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 765 +r0:=-1/4*b/((b*d-a*e)^2*(a+b*x)^4)+2/3*b*e/((b*d-a*e)^3*(a+b*x)^3)-_ + 3/2*b*e^2/((b*d-a*e)^4*(a+b*x)^2)+4*b*e^3/((b*d-a*e)^5*(a+b*x))+_ + e^4/((b*d-a*e)^5*(d+e*x))+5*b*e^4*log(a+b*x)/(b*d-a*e)^6-_ + 5*b*e^4*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 240a b e - 60b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (- 360a b e - 240a b d e )x + (- 240a b e - 360a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (- 60a b e - 240a b d e )x - 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 3 +--R 60b e x + (240a b e + 60b d e )x + (360a b e + 240a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 4 4 +--R (240a b e + 360a b d e )x + (60a b e + 240a b d e )x + 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (- 60a b e + 60b d e )x + (- 210a b e + 180a b d e + 30b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 260a b e + 150a b d e + 120a b d e - 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 125a b e - 20a b d e + 180a b d e - 40a b d e + 5b d e)x - 12a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 65a b d e + 120a b d e - 60a b d e + 20a b d e - 3b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 2 8 4 3 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 9 5 2 10 6 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 3 7 4 3 +--R 48a b e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 8 5 2 9 6 10 7 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 4 6 4 3 +--R 72a b e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 3 7 5 2 2 8 6 9 7 +--R 288a b d e - 216a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 5 5 4 3 +--R 48a b e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 4 6 5 2 3 7 6 2 8 7 +--R 792a b d e - 384a b d e + 72a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 6 4 4 3 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 5 5 5 2 4 6 6 3 7 7 +--R 648a b d e - 276a b d e + 48a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 5 5 6 4 6 7 +--R - 72a b d e + 12a b d +--R Type: Expression(Integer) +--E 182 + +--S 183 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 of 765 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 184 + +--S 185 of 765 +r0:=-1/4*b^2/((b*d-a*e)^3*(a+b*x)^4)+b^2*e/((b*d-a*e)^4*(a+b*x)^3)-_ + 3*b^2*e^2/((b*d-a*e)^5*(a+b*x)^2)+10*b^2*e^3/((b*d-a*e)^6*(a+b*x))+_ + 1/2*e^4/((b*d-a*e)^5*(d+e*x)^2)+5*b*e^4/((b*d-a*e)^6*(d+e*x))+_ + 15*b^2*e^4*log(a+b*x)/(b*d-a*e)^7-15*b^2*e^4*log(d+e*x)/(b*d-a*e)^7 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 60b e x + (240a b e + 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (360a b e + 480a b d e + 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (240a b e + 720a b d e + 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (60a b e + 480a b d e + 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (120a b d e + 240a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 60b e x + (- 240a b e - 120b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 360a b e - 480a b d e - 60b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 3 +--R (- 240a b e - 720a b d e - 240a b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 2 +--R (- 60a b e - 480a b d e - 360a b d e )x +--R + +--R 4 2 5 3 3 2 4 4 2 2 4 +--R (- 120a b d e - 240a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (210a b e - 120a b d e - 90b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (260a b e + 60a b d e - 300a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (125a b e + 280a b d e - 330a b d e - 80a b d e + 5b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 12a b e + 190a b d e - 100a b d e - 120a b d e + 20a b d e +--R + +--R 6 5 +--R - 2b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e + 24a b d e + 35a b d e - 80a b d e + 30a b d e - 8a b d e +--R + +--R 6 6 +--R b d +--R / +--R 7 4 9 6 5 8 5 6 2 7 4 7 3 6 3 8 4 5 +--R 4a b e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 2 9 5 4 10 6 3 11 7 2 +--R - 84a b d e + 28a b d e - 4b d e +--R * +--R 6 +--R x +--R + +--R 8 3 9 7 4 8 6 5 2 7 5 6 3 6 4 7 4 5 +--R 16a b e - 104a b d e + 280a b d e - 392a b d e + 280a b d e +--R + +--R 3 8 5 4 2 9 6 3 10 7 2 11 8 +--R - 56a b d e - 56a b d e + 40a b d e - 8b d e +--R * +--R 5 +--R x +--R + +--R 9 2 9 8 3 8 7 4 2 7 6 5 3 6 5 6 4 5 +--R 24a b e - 136a b d e + 284a b d e - 196a b d e - 196a b d e +--R + +--R 4 7 5 4 3 8 6 3 2 9 7 2 10 8 11 9 +--R 476a b d e - 364a b d e + 116a b d e - 4a b d e - 4b d +--R * +--R 4 +--R x +--R + +--R 10 9 9 2 8 8 3 2 7 7 4 3 6 6 5 4 5 +--R 16a b e - 64a b d e + 16a b d e + 336a b d e - 784a b d e +--R + +--R 5 6 5 4 4 7 6 3 3 8 7 2 2 9 8 10 9 +--R 784a b d e - 336a b d e - 16a b d e + 64a b d e - 16a b d +--R * +--R 3 +--R x +--R + +--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5 +--R 4a e + 4a b d e - 116a b d e + 364a b d e - 476a b d e +--R + +--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9 +--R 196a b d e + 196a b d e - 284a b d e + 136a b d e - 24a b d +--R * +--R 2 +--R x +--R + +--R 11 8 10 2 7 9 2 3 6 8 3 4 5 7 4 5 4 +--R 8a d e - 40a b d e + 56a b d e + 56a b d e - 280a b d e +--R + +--R 6 5 6 3 5 6 7 2 4 7 8 3 8 9 +--R 392a b d e - 280a b d e + 104a b d e - 16a b d +--R * +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 7 4 6 3 +--R 4a d e - 28a b d e + 84a b d e - 140a b d e + 140a b d e +--R + +--R 6 5 7 2 5 6 8 4 7 9 +--R - 84a b d e + 28a b d e - 4a b d +--R Type: Expression(Integer) +--E 185 + +--S 186 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 765 +t0:=(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 187 + +--S 188 of 765 +r0:=-1/4*b^3/((b*d-a*e)^4*(a+b*x)^4)+4/3*b^3*e/((b*d-a*e)^5*(a+b*x)^3)-_ + 5*b^3*e^2/((b*d-a*e)^6*(a+b*x)^2)+20*b^3*e^3/((b*d-a*e)^7*(a+b*x))+_ + 1/3*e^4/((b*d-a*e)^5*(d+e*x)^3)+5/2*b*e^4/((b*d-a*e)^6*(d+e*x)^2)+_ + 15*b^2*e^4/((b*d-a*e)^7*(d+e*x))+35*b^3*e^4*log(a+b*x)/(b*d-a*e)^8-_ + 35*b^3*e^4*log(d+e*x)/(b*d-a*e)^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R - 420b e x + (- 1680a b e - 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 2520a b e - 5040a b d e - 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1680a b e - 7560a b d e - 5040a b d e - 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (- 420a b e - 5040a b d e - 7560a b d e - 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (- 1260a b d e - 5040a b d e - 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (- 1260a b d e - 1680a b d e )x - 420a b d e +--R * +--R log(e x + d) +--R + +--R 7 7 7 6 7 7 6 6 +--R 420b e x + (1680a b e + 1260b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2520a b e + 5040a b d e + 1260b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1680a b e + 7560a b d e + 5040a b d e + 420b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (420a b e + 5040a b d e + 7560a b d e + 1680a b d e )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 2 +--R (1260a b d e + 5040a b d e + 2520a b d e )x +--R + +--R 4 3 2 5 3 4 3 4 4 3 3 4 +--R (1260a b d e + 1680a b d e )x + 420a b d e +--R * +--R log(b x + a) +--R + +--R 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R (- 420a b e + 420b d e )x + (- 1470a b e + 420a b d e + 1050b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1820a b e - 1890a b d e + 2940a b d e + 770b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 875a b e - 3780a b d e + 1890a b d e + 2660a b d e + 105b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 84a b e - 2205a b d e - 1260a b d e + 3150a b d e + 420a b d e +--R + +--R 7 5 2 +--R - 21b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 14a b e - 252a b d e - 1575a b d e + 1260a b d e + 630a b d e +--R + +--R 6 5 2 7 6 +--R - 84a b d e + 7b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a e + 42a b d e - 252a b d e - 105a b d e + 420a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 126a b d e + 28a b d e - 3b d +--R / +--R 8 4 11 7 5 10 6 6 2 9 5 7 3 8 4 8 4 7 +--R 12a b e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 3 9 5 6 2 10 6 5 11 7 4 12 8 3 +--R - 672a b d e + 336a b d e - 96a b d e + 12b d e +--R * +--R 7 +--R x +--R + +--R 9 3 11 8 4 10 7 5 2 9 6 6 3 8 5 7 4 7 +--R 48a b e - 348a b d e + 1056a b d e - 1680a b d e + 1344a b d e +--R + +--R 4 8 5 6 3 9 6 5 2 10 7 4 11 8 3 12 9 2 +--R - 168a b d e - 672a b d e + 624a b d e - 240a b d e + 36b d e +--R * +--R 6 +--R x +--R + +--R 10 2 11 9 3 10 8 4 2 9 7 5 3 8 6 6 4 7 +--R 72a b e - 432a b d e + 900a b d e - 288a b d e - 2016a b d e +--R + +--R 5 7 5 6 4 8 6 5 3 9 7 4 2 10 8 3 +--R 4032a b d e - 3528a b d e + 1440a b d e - 72a b d e +--R + +--R 11 9 2 12 10 +--R - 144a b d e + 36b d e +--R * +--R 5 +--R x +--R + +--R 11 11 10 2 10 9 3 2 9 8 4 3 8 +--R 48a b e - 168a b d e - 240a b d e + 2220a b d e +--R + +--R 7 5 4 7 6 6 5 6 5 7 6 5 4 8 7 4 +--R - 4800a b d e + 4704a b d e - 1344a b d e - 1560a b d e +--R + +--R 3 9 8 3 2 10 9 2 11 10 12 11 +--R 1680a b d e - 600a b d e + 48a b d e + 12b d +--R * +--R 4 +--R x +--R + +--R 12 11 11 10 10 2 2 9 9 3 3 8 8 4 4 7 +--R 12a e + 48a b d e - 600a b d e + 1680a b d e - 1560a b d e +--R + +--R 7 5 5 6 6 6 6 5 5 7 7 4 4 8 8 3 +--R - 1344a b d e + 4704a b d e - 4800a b d e + 2220a b d e +--R + +--R 3 9 9 2 2 10 10 11 11 +--R - 240a b d e - 168a b d e + 48a b d +--R * +--R 3 +--R x +--R + +--R 12 10 11 2 9 10 2 3 8 9 3 4 7 8 4 5 6 +--R 36a d e - 144a b d e - 72a b d e + 1440a b d e - 3528a b d e +--R + +--R 7 5 6 5 6 6 7 4 5 7 8 3 4 8 9 2 3 9 10 +--R 4032a b d e - 2016a b d e - 288a b d e + 900a b d e - 432a b d e +--R + +--R 2 10 11 +--R 72a b d +--R * +--R 2 +--R x +--R + +--R 12 2 9 11 3 8 10 2 4 7 9 3 5 6 8 4 6 5 +--R 36a d e - 240a b d e + 624a b d e - 672a b d e - 168a b d e +--R + +--R 7 5 7 4 6 6 8 3 5 7 9 2 4 8 10 3 9 11 +--R 1344a b d e - 1680a b d e + 1056a b d e - 348a b d e + 48a b d +--R * +--R x +--R + +--R 12 3 8 11 4 7 10 2 5 6 9 3 6 5 8 4 7 4 +--R 12a d e - 96a b d e + 336a b d e - 672a b d e + 840a b d e +--R + +--R 7 5 8 3 6 6 9 2 5 7 10 4 8 11 +--R - 672a b d e + 336a b d e - 96a b d e + 12a b d +--R Type: Expression(Integer) +--E 188 + +--S 189 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 765 +t0:=(a+b*x)*(d+e*x)^m*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R m | 2 2 2 +--R (1) (b x + a)(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 765 +r0:=-2*(b*d-a*e)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(2+m)*(3+m))+_ + 2*(b*d-a*e)^2*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(1+m)*_ + (2+m)*(3+m)*(a+b*x))+(a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e*(3+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (b e m + 3b e m + 2b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a b e m + (8a b e - 2b d e)m + 6a b e - 2b d e)x + a e m +--R + +--R 2 2 2 2 2 2 +--R (5a e - 2a b d e)m + 6a e - 6a b d e + 2b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 3 3 3 2 3 3 3 3 3 2 3 3 +--R (b e m + 6b e m + 11b e m + 6b e )x + a e m + 6a e m + 11a e m + 6a e +--R Type: Expression(Integer) +--E 191 + +--S 192 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 765 +t0:=(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b e x + (a e + 5b d e )x + (5a d e + 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a d e + 10b d e )x + (10a d e + 5b d e)x + (5a d e + b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 193 + +--S 194 of 765 +r0:=-1/28*(b*d-a*e)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 1/168*(b*d-a*e)^2*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 1/8*(a+b*x)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 8 8 8 2 7 7 +--R 21b e x + (48a b e + 120b d e )x +--R + +--R 2 8 7 2 2 6 6 +--R (28a e + 280a b d e + 280b d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (168a d e + 672a b d e + 336b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (420a d e + 840a b d e + 210b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 2 4 4 5 3 2 +--R (560a d e + 560a b d e + 56b d e )x + (420a d e + 168a b d e )x +--R + +--R 2 5 3 2 6 2 7 2 8 +--R 168a d e x + 28a d e - 8a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 168b e x + 168a e +--R Type: Expression(Integer) +--E 194 + +--S 195 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 765 +t0:=(a+b*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 196 + +--S 197 of 765 +r0:=-1/21*(b*d-a*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 1/105*(b*d-a*e)^2*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 1/7*(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 7 7 7 2 6 6 +--R 15b e x + (35a b e + 70b d e )x +--R + +--R 2 7 6 2 2 5 5 +--R (21a e + 168a b d e + 126b d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (105a d e + 315a b d e + 105b d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 2 3 4 4 3 2 +--R (210a d e + 280a b d e + 35b d e )x + (210a d e + 105a b d e )x +--R + +--R 2 4 3 2 5 2 6 2 7 +--R 105a d e x + 21a d e - 7a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 197 + +--S 198 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 765 +t0:=(a+b*x)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 765 +r0:=-1/15*(b*d-a*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/60*(b*d-_ + a*e)^2*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+1/6*(a+b*x)*_ + (d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 2 6 5 2 2 4 4 +--R 10b e x + (24a b e + 36b d e )x + (15a e + 90a b d e + 45b d e )x +--R + +--R 2 5 2 4 2 3 3 3 2 2 4 3 3 2 +--R (60a d e + 120a b d e + 20b d e )x + (90a d e + 60a b d e )x +--R + +--R 2 3 3 2 4 2 5 2 6 +--R 60a d e x + 15a d e - 6a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 200 + +--S 201 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 765 +t0:=(a+b*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 202 + +--S 203 of 765 +r0:=1/30*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^3+1/10*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/5*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/b +--R +--R +--R (2) +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R 6b e x + (9a b e + 15b d e)x + (a b e + 25a b d e + 10b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- a b e + 5a b d e + 20a b d )x + a e - 5a b d e + 10a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 30b +--R Type: Expression(Integer) +--E 203 + +--S 204 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 765 +t0:=(a+b*x)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 | 2 2 2 +--R (1) (b e x + (a e + b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 205 + +--S 206 of 765 +r0:=1/12*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/4*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/b +--R +--R +--R (2) +--R 3 3 2 3 2 2 2 3 2 +--R (3b e x + (5a b e + 4b d)x + (a b e + 8a b d)x - a e + 4a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 12b +--R Type: Expression(Integer) +--E 206 + +--S 207 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (1) (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 208 + +--S 209 of 765 +r0:=1/3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b +--R +--R +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R (2) ----------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 209 + +--S 210 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 211 + +--S 212 of 765 +r0:=-(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e+(b*d-a*e)^2*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2a e - 4a b d e + 2b d )log(e x + d) + b e x + (4a b e - 2b d e)x +--R + +--R 2 2 +--R 3a e - 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 2b e x + 2a e +--R Type: Expression(Integer) +--E 212 + +--S 213 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 214 + +--S 215 of 765 +r0:=2*b*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2-(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e*(d+e*x))-2*b*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((2a b e - 2b d e)x + 2a b d e - 2b d )log(e x + d) + b e x +--R + +--R 2 2 2 +--R 2b d e x - a e + 2a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +--R b e x + (a e + b d e )x + a d e +--R Type: Expression(Integer) +--E 215 + +--S 216 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 217 + +--S 218 of 765 +r0:=-1/2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^2)+b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x))+b^2*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2b e x + 4b d e x + 2b d )log(e x + d) - b e x +--R + +--R 2 2 2 2 2 2 +--R (- 4a b e + 2b d e)x - a e - 2a b d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 218 + +--S 219 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 220 + +--S 221 of 765 +r0:=1/3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^3) +--R +--R +--R (2) +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (- b x - 2a b x - a )\|b x + 2a b x + a +--R / +--R 4 3 3 3 2 2 2 2 2 3 +--R (3a e - 3b d e )x + (9a d e - 9b d e )x + (9a d e - 9b d e)x +--R + +--R 3 4 +--R 3a d e - 3b d +--R Type: Expression(Integer) +--E 221 + +--S 222 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 223 + +--S 224 of 765 +r0:=1/4*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^4)+_ + 1/12*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^3) +--R +--R +--R (2) +--R 3 3 2 3 2 2 2 3 2 +--R (b e x + (- a b e + 4b d)x + (- 5a b e + 8a b d)x - 3a e + 4a b d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 6 5 2 2 4 4 2 5 2 4 2 3 3 3 +--R (12a e - 24a b d e + 12b d e )x + (48a d e - 96a b d e + 48b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (72a d e - 144a b d e + 72b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (48a d e - 96a b d e + 48b d e)x + 12a d e - 24a b d e + 12b d +--R Type: Expression(Integer) +--E 224 + +--S 225 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 226 + +--S 227 of 765 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^5)+_ + 1/10*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^4)+_ + 1/30*b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^3*(d+e*x)^3) +--R +--R +--R (2) +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R - b e x + (a b e - 5b d e)x + (- a b e + 5a b d e - 10b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- 9a b e + 25a b d e - 20a b d )x - 6a e + 15a b d e - 10a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 8 2 7 2 2 6 3 3 5 5 +--R (30a e - 90a b d e + 90a b d e - 30b d e )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 4 +--R (150a d e - 450a b d e + 450a b d e - 150b d e )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 3 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 6 2 2 +--R (300a d e - 900a b d e + 900a b d e - 300b d e )x +--R + +--R 3 4 4 2 5 3 2 6 2 3 7 3 5 3 +--R (150a d e - 450a b d e + 450a b d e - 150b d e)x + 30a d e +--R + +--R 2 6 2 2 7 3 8 +--R - 90a b d e + 90a b d e - 30b d +--R Type: Expression(Integer) +--E 227 + +--S 228 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 229 + +--S 230 of 765 +r0:=-1/6*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^6)-_ + 1/12*b*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^5)-1/60*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 15b e x + (- 24a b e - 6b d e)x - 10a e - 4a b d e - b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 7 9 8 6 8 2 7 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 7 3 6 4 3 6 4 5 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 5 5 4 2 5 4 6 3 6 3 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 230 + +--S 231 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 232 + +--S 233 of 765 +r0:=-1/7*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^7)-_ + 2/35*b*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^6)-1/105*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^6) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 21b e x + (- 35a b e - 7b d e)x - 15a e - 5a b d e - b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 8 10 9 7 9 2 8 6 +--R 105b e x + (105a e + 735b d e )x + (735a d e + 2205b d e )x +--R + +--R 2 8 3 7 5 3 7 4 6 4 +--R (2205a d e + 3675b d e )x + (3675a d e + 3675b d e )x +--R + +--R 4 6 5 5 3 5 5 6 4 2 +--R (3675a d e + 2205b d e )x + (2205a d e + 735b d e )x +--R + +--R 6 4 7 3 7 3 +--R (735a d e + 105b d e )x + 105a d e +--R Type: Expression(Integer) +--E 233 + +--S 234 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 765 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 m | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )(e x + d) \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 765 +r0:=-4*(b*d-a*e)*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(4+m)*(5+m))+_ + (a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(5+m))-_ + 24*(b*d-a*e)^3*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(2+m)*_ + (3+m)*(4+m)*(5+m))+24*(b*d-a*e)^4*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(1+m)*(2+m)*(3+m)*(4+m)*(5+m)*(a+b*x))+12*(b*d-a*e)^2*_ + (a+b*x)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(3+m)*(4+m)*(5+m)) +--R +--R +--R (2) +--R 4 4 4 4 4 3 4 4 2 4 4 4 4 4 +--R (b e m + 10b e m + 35b e m + 50b e m + 24b e )x +--R + +--R 3 4 4 3 4 4 3 3 3 4 4 3 2 +--R 4a b e m + (44a b e - 4b d e )m + (164a b e - 24b d e )m +--R + +--R 3 4 4 3 3 4 4 3 +--R (244a b e - 44b d e )m + 120a b e - 24b d e +--R * +--R 3 +--R x +--R + +--R 2 2 4 4 2 2 4 3 3 3 +--R 6a b e m + (72a b e - 12a b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (294a b e - 96a b d e + 12b d e )m +--R + +--R 2 2 4 3 3 4 2 2 2 2 4 3 3 +--R (468a b e - 204a b d e + 36b d e )m + 240a b e - 120a b d e +--R + +--R 4 2 2 +--R 24b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 4 2 2 3 3 +--R 4a b e m + (52a b e - 12a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 2 +--R (236a b e - 120a b d e + 24a b d e )m +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 4 +--R (428a b e - 348a b d e + 144a b d e - 24b d e)m + 240a b e +--R + +--R 2 2 3 3 2 2 4 3 +--R - 240a b d e + 120a b d e - 24b d e +--R * +--R x +--R + +--R 4 4 4 4 4 3 3 3 4 4 3 3 2 2 2 2 2 +--R a e m + (14a e - 4a b d e )m + (71a e - 48a b d e + 12a b d e )m +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (154a e - 188a b d e + 108a b d e - 24a b d e)m + 120a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 240a b d e + 240a b d e - 120a b d e + 24b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 5 5 5 4 5 3 5 2 5 5 5 5 +--R (b e m + 15b e m + 85b e m + 225b e m + 274b e m + 120b e )x + a e m +--R + +--R 5 4 5 3 5 2 5 5 +--R 15a e m + 85a e m + 225a e m + 274a e m + 120a e +--R Type: Expression(Integer) +--E 236 + +--S 237 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 765 +t0:=(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 7 10 2 7 3 6 9 2 7 2 6 3 2 5 8 +--R b e x + (3a b e + 7b d e )x + (3a b e + 21a b d e + 21b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 7 +--R (a e + 21a b d e + 63a b d e + 35b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 6 +--R (7a d e + 63a b d e + 105a b d e + 35b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 5 +--R (21a d e + 105a b d e + 105a b d e + 21b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 4 +--R (35a d e + 105a b d e + 63a b d e + 7b d e)x +--R + +--R 3 4 3 2 5 2 2 6 3 7 3 +--R (35a d e + 63a b d e + 21a b d e + b d )x +--R + +--R 3 5 2 2 6 2 7 2 3 6 2 7 3 7 +--R (21a d e + 21a b d e + 3a b d )x + (7a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 765 +r0:=-1/33*(b*d-a*e)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/12*(a+b*x)*_ + (d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/495*(b*d-a*e)^3*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/3960*(b*d-a*e)^4*(d+e*x)^8*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/110*(b*d-a*e)^2*(a+b*x)*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 12 12 3 12 4 11 11 +--R 330b e x + (1440a b e + 2520b d e )x +--R + +--R 2 2 12 3 11 4 2 10 10 +--R (2376a b e + 11088a b d e + 8316b d e )x +--R + +--R 3 12 2 2 11 3 2 10 4 3 9 9 +--R (1760a b e + 18480a b d e + 36960a b d e + 15400b d e )x +--R + +--R 4 12 3 11 2 2 2 10 3 3 9 +--R 495a e + 13860a b d e + 62370a b d e + 69300a b d e +--R + +--R 4 4 8 +--R 17325b d e +--R * +--R 8 +--R x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 +--R 3960a d e + 47520a b d e + 118800a b d e + 79200a b d e +--R + +--R 4 5 7 +--R 11880b d e +--R * +--R 7 +--R x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 +--R 13860a d e + 92400a b d e + 138600a b d e + 55440a b d e +--R + +--R 4 6 6 +--R 4620b d e +--R * +--R 6 +--R x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 +--R 27720a d e + 110880a b d e + 99792a b d e + 22176a b d e +--R + +--R 4 7 5 +--R 792b d e +--R * +--R 5 +--R x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 +--R (34650a d e + 83160a b d e + 41580a b d e + 3960a b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 +--R (27720a d e + 36960a b d e + 7920a b d e )x +--R + +--R 4 6 6 3 7 5 2 4 7 5 4 8 4 3 9 3 +--R (13860a d e + 7920a b d e )x + 3960a d e x + 495a d e - 220a b d e +--R + +--R 2 2 10 2 3 11 4 12 +--R 66a b d e - 12a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 3960b e x + 3960a e +--R Type: Expression(Integer) +--E 239 + +--S 240 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 765 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 6 9 2 6 3 5 8 2 6 2 5 3 2 4 7 +--R b e x + (3a b e + 6b d e )x + (3a b e + 18a b d e + 15b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 6 +--R (a e + 18a b d e + 45a b d e + 20b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 5 +--R (6a d e + 45a b d e + 60a b d e + 15b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 4 +--R (15a d e + 60a b d e + 45a b d e + 6b d e)x +--R + +--R 3 3 3 2 4 2 2 5 3 6 3 +--R (20a d e + 45a b d e + 18a b d e + b d )x +--R + +--R 3 4 2 2 5 2 6 2 3 5 2 6 3 6 +--R (15a d e + 18a b d e + 3a b d )x + (6a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 765 +r0:=-2/55*(b*d-a*e)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/11*(a+b*x)*_ + (d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/330*(b*d-a*e)^3*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/2310*(b*d-a*e)^4*(d+e*x)^7*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/165*(b*d-a*e)^2*(a+b*x)*_ + (d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 11 11 3 11 4 10 10 +--R 210b e x + (924a b e + 1386b d e )x +--R + +--R 2 2 11 3 10 4 2 9 9 +--R (1540a b e + 6160a b d e + 3850b d e )x +--R + +--R 3 11 2 2 10 3 2 9 4 3 8 8 +--R (1155a b e + 10395a b d e + 17325a b d e + 5775b d e )x +--R + +--R 4 11 3 10 2 2 2 9 3 3 8 +--R 330a e + 7920a b d e + 29700a b d e + 26400a b d e +--R + +--R 4 4 7 +--R 4950b d e +--R * +--R 7 +--R x +--R + +--R 4 10 3 2 9 2 2 3 8 3 4 7 +--R 2310a d e + 23100a b d e + 46200a b d e + 23100a b d e +--R + +--R 4 5 6 +--R 2310b d e +--R * +--R 6 +--R x +--R + +--R 4 2 9 3 3 8 2 2 4 7 3 5 6 +--R 6930a d e + 36960a b d e + 41580a b d e + 11088a b d e +--R + +--R 4 6 5 +--R 462b d e +--R * +--R 5 +--R x +--R + +--R 4 3 8 3 4 7 2 2 5 6 3 6 5 4 +--R (11550a d e + 34650a b d e + 20790a b d e + 2310a b d e )x +--R + +--R 4 4 7 3 5 6 2 2 6 5 3 +--R (11550a d e + 18480a b d e + 4620a b d e )x +--R + +--R 4 5 6 3 6 5 2 4 6 5 4 7 4 3 8 3 +--R (6930a d e + 4620a b d e )x + 2310a d e x + 330a d e - 165a b d e +--R + +--R 2 2 9 2 3 10 4 11 +--R 55a b d e - 11a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 2310b e x + 2310a e +--R Type: Expression(Integer) +--E 242 + +--S 243 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 765 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 5 8 2 5 3 4 7 2 5 2 4 3 2 3 6 +--R b e x + (3a b e + 5b d e )x + (3a b e + 15a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 5 +--R (a e + 15a b d e + 30a b d e + 10b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 4 +--R (5a d e + 30a b d e + 30a b d e + 5b d e)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (10a d e + 30a b d e + 15a b d e + b d )x +--R + +--R 3 3 2 2 4 2 5 2 3 4 2 5 3 5 +--R (10a d e + 15a b d e + 3a b d )x + (5a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 765 +r0:=-2/45*(b*d-a*e)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/10*(a+b*x)*_ + (d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-1/210*(b*d-a*e)^3*(d+e*x)^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/1260*(b*d-a*e)^4*(d+e*x)^6*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/60*(b*d-a*e)^2*(a+b*x)*(d+e*x)^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 10 10 3 10 4 9 9 +--R 126b e x + (560a b e + 700b d e )x +--R + +--R 2 2 10 3 9 4 2 8 8 +--R (945a b e + 3150a b d e + 1575b d e )x +--R + +--R 3 10 2 2 9 3 2 8 4 3 7 7 +--R (720a b e + 5400a b d e + 7200a b d e + 1800b d e )x +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 4 4 6 6 +--R (210a e + 4200a b d e + 12600a b d e + 8400a b d e + 1050b d e )x +--R + +--R 4 9 3 2 8 2 2 3 7 3 4 6 +--R 1260a d e + 10080a b d e + 15120a b d e + 5040a b d e +--R + +--R 4 5 5 +--R 252b d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 3 3 7 2 2 4 6 3 5 5 4 +--R (3150a d e + 12600a b d e + 9450a b d e + 1260a b d e )x +--R + +--R 4 3 7 3 4 6 2 2 5 5 3 +--R (4200a d e + 8400a b d e + 2520a b d e )x +--R + +--R 4 4 6 3 5 5 2 4 5 5 4 6 4 3 7 3 +--R (3150a d e + 2520a b d e )x + 1260a d e x + 210a d e - 120a b d e +--R + +--R 2 2 8 2 3 9 4 10 +--R 45a b d e - 10a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 1260b e x + 1260a e +--R Type: Expression(Integer) +--E 245 + +--S 246 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 of 765 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 765 +r0:=1/630*(b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^5+1/126*(b*d-a*e)^3*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4+1/42*(b*d-a*e)^2*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+1/18*(b*d-a*e)*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/b^2+1/9*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 8 4 8 7 4 8 3 7 +--R 70b e x + (245a b e + 315b d e )x +--R + +--R 2 6 4 7 3 8 2 2 6 +--R (295a b e + 1125a b d e + 540b d e )x +--R + +--R 3 5 4 2 6 3 7 2 2 8 3 5 +--R (125a b e + 1395a b d e + 1980a b d e + 420b d e)x +--R + +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (a b e + 621a b d e + 2556a b d e + 1596a b d e + 126b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (- a b e + 9a b d e + 1224a b d e + 2184a b d e + 504a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (a b e - 9a b d e + 36a b d e + 1176a b d e + 756a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 8 4 +--R (- a b e + 9a b d e - 36a b d e + 84a b d e + 504a b d )x + a e +--R + +--R 7 3 6 2 2 2 5 3 3 4 4 4 +--R - 9a b d e + 36a b d e - 84a b d e + 126a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 630b +--R Type: Expression(Integer) +--E 248 + +--S 249 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 765 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 765 +r0:=1/280*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^4+1/56*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+3/56*(b*d-a*e)*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/8*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 7 3 7 6 3 7 2 6 +--R 35b e x + (125a b e + 120b d e )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (155a b e + 440a b d e + 140b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (69a b e + 568a b d e + 532a b d e + 56b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (a b e + 272a b d e + 728a b d e + 224a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- a b e + 8a b d e + 392a b d e + 336a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 6 2 +--R (a b e - 8a b d e + 28a b d e + 224a b d )x - a e + 8a b d e +--R + +--R 5 2 2 4 3 3 +--R - 28a b d e + 56a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 280b +--R Type: Expression(Integer) +--E 251 + +--S 252 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 765 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 765 +r0:=1/105*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^3+1/21*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/7*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 15b e x + (55a b e + 35b d e)x + (71a b e + 133a b d e + 21b d )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (34a b e + 182a b d e + 84a b d )x +--R + +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (a b e + 98a b d e + 126a b d )x + (- a b e + 7a b d e + 84a b d )x +--R + +--R 6 2 5 4 2 2 +--R a e - 7a b d e + 21a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 105b +--R Type: Expression(Integer) +--E 254 + +--S 255 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 765 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 765 +r0:=1/30*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/6*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R (2) +--R 5 5 4 5 4 2 3 4 3 +--R 5b e x + (19a b e + 6b d)x + (26a b e + 24a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (14a b e + 36a b d)x + (a b e + 24a b d)x - a e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 30b +--R Type: Expression(Integer) +--E 257 + +--S 258 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 765 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b +--R +--R +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + 2a b x + a +--R (2) ------------------------------------------------------------- +--R 5b +--R Type: Expression(Integer) +--E 260 + +--S 261 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 262 + +--S 263 of 765 +r0:=-1/3*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+1/4*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/e-(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/2*(b*d-_ + a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3+(b*d-a*e)^4*log(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a e - 48a b d e + 72a b d e - 48a b d e + 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (16a b e - 4b d e )x + (36a b e - 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (48a b e - 72a b d e + 48a b d e - 12b d e)x + 25a e - 52a b d e +--R + +--R 2 2 2 2 3 3 +--R 42a b d e - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +--R 12b e x + 12a e +--R Type: Expression(Integer) +--E 263 + +--S 264 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 265 + +--S 266 of 765 +r0:=4/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2-(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e*(d+e*x))+4*b*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^4-2*b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-_ + 4*b*(b*d-a*e)^3*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b e - 36a b d e + 36a b d e - 12b d e)x + 12a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b d e + 36a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (6a b e - 2b d e )x + (18a b e - 18a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (10a b e + 6a b d e - 24a b d e + 12b d e)x - 3a e + 22a b d e +--R + +--R 2 2 2 2 3 3 +--R - 30a b d e + 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +--R 3b e x + (3a e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 266 + +--S 267 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 268 + +--S 269 of 765 +r0:=-1/2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^2)-_ + 2*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x))-6*b^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+3*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + e^3+6*b^2*(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b e - 24a b d e + 12b d e )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 +--R (24a b d e - 48a b d e + 24b d e)x + 12a b d e - 24a b d e +--R + +--R 4 4 +--R 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R b e x + (8a b e - 4b d e )x + (24a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 4 3 4 4 3 3 2 2 2 2 +--R (- 8a b e + 24a b d e - 12b d e)x - a e - 4a b d e + 18a b d e +--R + +--R 3 3 +--R - 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R 2b e x + (2a e + 4b d e )x + (4a d e + 2b d e )x + 2a d e +--R Type: Expression(Integer) +--E 269 + +--S 270 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^4 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 271 + +--S 272 of 765 +r0:=-1/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^3)-_ + 2/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^2)+4*b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/e^4-2*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+_ + e*x))-4*b^3*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 3 4 4 3 3 3 3 4 2 2 2 +--R (12a b e - 12b d e )x + (36a b d e - 36b d e )x +--R + +--R 3 2 2 4 3 3 3 4 4 +--R (36a b d e - 36b d e)x + 12a b d e - 12b d +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R 3b e x + (- 10a b e + 22b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 18a b e + 6a b d e + 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 6a b e - 18a b d e + 24a b d e + 12b d e)x - a e - 2a b d e +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e + 12a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 6 3 5 3 5 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 272 + +--S 273 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^5 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 274 + +--S 275 of 765 +r0:=-1/4*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^4)-1/3*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^3)-1/2*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^3*(d+e*x)^2)+b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x)*(d+e*x))+b^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 4 3 3 4 2 2 2 4 3 4 4 +--R (12b e x + 48b d e x + 72b d e x + 48b d e x + 12b d )log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 13b e x + (- 48a b e - 4b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 36a b e - 72a b d e + 30b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 16a b e - 24a b d e - 48a b d e + 36b d e)x - 3a e - 4a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b d e - 12a b d e + 12b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 12b e x + (12a e + 48b d e )x + (48a d e + 72b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (72a d e + 48b d e )x + (48a d e + 12b d e )x + 12a d e +--R Type: Expression(Integer) +--E 275 + +--S 276 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^6 +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 277 + +--S 278 of 765 +r0:=1/5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^5) +--R +--R +--R (2) +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (- b x - 4a b x - 6a b x - 4a b x - a )\|b x + 2a b x + a +--R / +--R 6 5 5 5 2 4 4 2 4 3 3 3 +--R (5a e - 5b d e )x + (25a d e - 25b d e )x + (50a d e - 50b d e )x +--R + +--R 3 3 4 2 2 4 2 5 5 6 +--R (50a d e - 50b d e )x + (25a d e - 25b d e)x + 5a d e - 5b d +--R Type: Expression(Integer) +--E 278 + +--S 279 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 280 + +--S 281 of 765 +r0:=1/6*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^6)+_ + 1/30*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^5) +--R +--R +--R (2) +--R 5 5 4 5 4 2 3 4 3 +--R b e x + (- a b e + 6b d)x + (- 14a b e + 24a b d)x +--R + +--R 3 2 2 3 2 4 3 2 5 4 +--R (- 26a b e + 36a b d)x + (- 19a b e + 24a b d)x - 5a e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 8 7 2 2 6 6 +--R (30a e - 60a b d e + 30b d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (180a d e - 360a b d e + 180b d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (600a d e - 1200a b d e + 600b d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 +--R (450a d e - 900a b d e + 450b d e )x +--R + +--R 2 5 3 6 2 2 7 2 6 2 7 2 8 +--R (180a d e - 360a b d e + 180b d e)x + 30a d e - 60a b d e + 30b d +--R Type: Expression(Integer) +--E 281 + +--S 282 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 283 + +--S 284 of 765 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^7)+_ + 1/21*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^6)+_ + 1/105*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^5) +--R +--R +--R (2) +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R - b e x + (a b e - 7b d e)x + (- a b e + 7a b d e - 21b d )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 34a b e + 98a b d e - 84a b d )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 71a b e + 182a b d e - 126a b d )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 55a b e + 133a b d e - 84a b d )x - 15a e + 35a b d e - 21a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (105a e - 315a b d e + 315a b d e - 105b d e )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (3675a d e - 11025a b d e + 11025a b d e - 3675b d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (2205a d e - 6615a b d e + 6615a b d e - 2205b d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 +--R (735a d e - 2205a b d e + 2205a b d e - 735b d e)x + 105a d e +--R + +--R 2 8 2 2 9 3 10 +--R - 315a b d e + 315a b d e - 105b d +--R Type: Expression(Integer) +--E 284 + +--S 285 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 286 + +--S 287 of 765 +r0:=1/8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^8)+_ + 3/56*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^7)+_ + 1/56*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^6)+_ + 1/280*b^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^5) +--R +--R +--R (2) +--R 7 3 7 6 3 7 2 6 2 5 3 6 2 7 2 5 +--R b e x + (- a b e + 8b d e )x + (a b e - 8a b d e + 28b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- a b e + 8a b d e - 28a b d e + 56b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (- 69a b e + 272a b d e - 392a b d e + 224a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 155a b e + 568a b d e - 728a b d e + 336a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (- 125a b e + 440a b d e - 532a b d e + 224a b d )x - 35a e +--R + +--R 6 2 5 2 2 4 3 3 +--R 120a b d e - 140a b d e + 56a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 12 3 11 2 2 2 10 3 3 9 4 4 8 8 +--R (280a e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d e )x +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 +--R 2240a d e - 8960a b d e + 13440a b d e - 8960a b d e +--R + +--R 4 5 7 +--R 2240b d e +--R * +--R 7 +--R x +--R + +--R 4 2 10 3 3 9 2 2 4 8 3 5 7 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 6 6 +--R 7840b d e +--R * +--R 6 +--R x +--R + +--R 4 3 9 3 4 8 2 2 5 7 3 6 6 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 7 5 +--R 15680b d e +--R * +--R 5 +--R x +--R + +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 +--R 19600a d e - 78400a b d e + 117600a b d e - 78400a b d e +--R + +--R 4 8 4 +--R 19600b d e +--R * +--R 4 +--R x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 8 4 +--R 15680a d e - 62720a b d e + 94080a b d e - 62720a b d e +--R + +--R 4 9 3 +--R 15680b d e +--R * +--R 3 +--R x +--R + +--R 4 6 6 3 7 5 2 2 8 4 3 9 3 +--R 7840a d e - 31360a b d e + 47040a b d e - 31360a b d e +--R + +--R 4 10 2 +--R 7840b d e +--R * +--R 2 +--R x +--R + +--R 4 7 5 3 8 4 2 2 9 3 3 10 2 4 11 +--R (2240a d e - 8960a b d e + 13440a b d e - 8960a b d e + 2240b d e)x +--R + +--R 4 8 4 3 9 3 2 2 10 2 3 11 4 12 +--R 280a d e - 1120a b d e + 1680a b d e - 1120a b d e + 280b d +--R Type: Expression(Integer) +--E 287 + +--S 288 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 289 + +--S 290 of 765 +r0:=1/9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^9)+_ + 1/18*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^8)+_ + 1/42*b^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^3*(d+e*x)^7)+_ + 1/126*b^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^4*(d+e*x)^6)+_ + 1/630*b^4*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^5*(d+e*x)^5) +--R +--R +--R (2) +--R 8 4 8 7 4 8 3 7 2 6 4 7 3 8 2 2 6 +--R - b e x + (a b e - 9b d e )x + (- a b e + 9a b d e - 36b d e )x +--R + +--R 3 5 4 2 6 3 7 2 2 8 3 5 +--R (a b e - 9a b d e + 36a b d e - 84b d e)x +--R + +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (- a b e + 9a b d e - 36a b d e + 84a b d e - 126b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (- 125a b e + 621a b d e - 1224a b d e + 1176a b d e - 504a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (- 295a b e + 1395a b d e - 2556a b d e + 2184a b d e - 756a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (- 245a b e + 1125a b d e - 1980a b d e + 1596a b d e - 504a b d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R - 70a e + 315a b d e - 540a b d e + 420a b d e - 126a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 14 4 13 3 2 2 12 2 3 3 11 +--R 630a e - 3150a b d e + 6300a b d e - 6300a b d e +--R + +--R 4 4 10 5 5 9 +--R 3150a b d e - 630b d e +--R * +--R 9 +--R x +--R + +--R 5 13 4 2 12 3 2 3 11 2 3 4 10 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 5 9 5 6 8 +--R 28350a b d e - 5670b d e +--R * +--R 8 +--R x +--R + +--R 5 2 12 4 3 11 3 2 4 10 2 3 5 9 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 6 8 5 7 7 +--R 113400a b d e - 22680b d e +--R * +--R 7 +--R x +--R + +--R 5 3 11 4 4 10 3 2 5 9 2 3 6 8 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 7 7 5 8 6 +--R 264600a b d e - 52920b d e +--R * +--R 6 +--R x +--R + +--R 5 4 10 4 5 9 3 2 6 8 2 3 7 7 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 8 6 5 9 5 +--R 396900a b d e - 79380b d e +--R * +--R 5 +--R x +--R + +--R 5 5 9 4 6 8 3 2 7 7 2 3 8 6 +--R 79380a d e - 396900a b d e + 793800a b d e - 793800a b d e +--R + +--R 4 9 5 5 10 4 +--R 396900a b d e - 79380b d e +--R * +--R 4 +--R x +--R + +--R 5 6 8 4 7 7 3 2 8 6 2 3 9 5 +--R 52920a d e - 264600a b d e + 529200a b d e - 529200a b d e +--R + +--R 4 10 4 5 11 3 +--R 264600a b d e - 52920b d e +--R * +--R 3 +--R x +--R + +--R 5 7 7 4 8 6 3 2 9 5 2 3 10 4 +--R 22680a d e - 113400a b d e + 226800a b d e - 226800a b d e +--R + +--R 4 11 3 5 12 2 +--R 113400a b d e - 22680b d e +--R * +--R 2 +--R x +--R + +--R 5 8 6 4 9 5 3 2 10 4 2 3 11 3 +--R 5670a d e - 28350a b d e + 56700a b d e - 56700a b d e +--R + +--R 4 12 2 5 13 +--R 28350a b d e - 5670b d e +--R * +--R x +--R + +--R 5 9 5 4 10 4 3 2 11 3 2 3 12 2 4 13 +--R 630a d e - 3150a b d e + 6300a b d e - 6300a b d e + 3150a b d e +--R + +--R 5 14 +--R - 630b d +--R Type: Expression(Integer) +--E 290 + +--S 291 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 292 + +--S 293 of 765 +r0:=-1/10*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^10)-_ + 2/45*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^9)-1/60*b^2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^8)-1/180*b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(d+e*x)^7)-1/1260*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 210b e x + (- 720a b e - 120b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 945a b e - 270a b d e - 45b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 560a b e - 210a b d e - 60a b d e - 10b d e)x - 126a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 56a b d e - 21a b d e - 6a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 15 11 15 14 10 +--R 1260b e x + (1260a e + 12600b d e )x +--R + +--R 14 2 13 9 2 13 3 12 8 +--R (12600a d e + 56700b d e )x + (56700a d e + 151200b d e )x +--R + +--R 3 12 4 11 7 4 11 5 10 6 +--R (151200a d e + 264600b d e )x + (264600a d e + 317520b d e )x +--R + +--R 5 10 6 9 5 6 9 7 8 4 +--R (317520a d e + 264600b d e )x + (264600a d e + 151200b d e )x +--R + +--R 7 8 8 7 3 8 7 9 6 2 +--R (151200a d e + 56700b d e )x + (56700a d e + 12600b d e )x +--R + +--R 9 6 10 5 10 5 +--R (12600a d e + 1260b d e )x + 1260a d e +--R Type: Expression(Integer) +--E 293 + +--S 294 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 295 + +--S 296 of 765 +r0:=-1/11*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^11)-_ + 2/55*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^10)-2/165*b^2*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^9)-4/1155*b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^4*(d+e*x)^8)-1/2310*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 330b e x + (- 1155a b e - 165b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1540a b e - 385a b d e - 55b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 924a b e - 308a b d e - 77a b d e - 11b d e)x - 210a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 84a b d e - 28a b d e - 7a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 16 12 16 15 11 +--R 2310b e x + (2310a e + 25410b d e )x +--R + +--R 15 2 14 10 2 14 3 13 9 +--R (25410a d e + 127050b d e )x + (127050a d e + 381150b d e )x +--R + +--R 3 13 4 12 8 4 12 5 11 7 +--R (381150a d e + 762300b d e )x + (762300a d e + 1067220b d e )x +--R + +--R 5 11 6 10 6 6 10 7 9 5 +--R (1067220a d e + 1067220b d e )x + (1067220a d e + 762300b d e )x +--R + +--R 7 9 8 8 4 8 8 9 7 3 +--R (762300a d e + 381150b d e )x + (381150a d e + 127050b d e )x +--R + +--R 9 7 10 6 2 10 6 11 5 +--R (127050a d e + 25410b d e )x + (25410a d e + 2310b d e )x +--R + +--R 11 5 +--R 2310a d e +--R Type: Expression(Integer) +--E 296 + +--S 297 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 765 +t0:=(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 m +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )(e x + d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 765 +r0:=-120*(b*d-a*e)^3*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(4+m)*_ + (5+m)*(6+m)*(7+m))+30*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(5+m)*(6+m)*(7+m))-6*(b*d-a*e)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(6+m)*(7+m))+(a+b*x)*(d+e*x)^(1+m)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(7+m))-720*(b*d-a*e)^5*(d+e*x)^(1+m)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m))+_ + 720*(b*d-a*e)^6*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(1+m)*_ + (2+m)*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)*(a+b*x))+360*(b*d-a*e)^4*(a+b*x)*_ + (d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(3+m)*(4+m)*(5+m)*(6+m)*(7+m)) +--R +--R +--R (2) +--R 6 6 6 6 6 5 6 6 4 6 6 3 6 6 2 6 6 +--R b e m + 21b e m + 175b e m + 735b e m + 1624b e m + 1764b e m +--R + +--R 6 6 +--R 720b e +--R * +--R 6 +--R x +--R + +--R 5 6 6 5 6 6 5 5 5 6 6 5 4 +--R 6a b e m + (132a b e - 6b d e )m + (1140a b e - 90b d e )m +--R + +--R 5 6 6 5 3 5 6 6 5 2 +--R (4920a b e - 510b d e )m + (11094a b e - 1350b d e )m +--R + +--R 5 6 6 5 5 6 6 5 +--R (12228a b e - 1644b d e )m + 5040a b e - 720b d e +--R * +--R 5 +--R x +--R + +--R 2 4 6 6 2 4 6 5 5 5 +--R 15a b e m + (345a b e - 30a b d e )m +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (3105a b e - 510a b d e + 30b d e )m +--R + +--R 2 4 6 5 5 6 2 4 3 +--R (13875a b e - 3150a b d e + 300b d e )m +--R + +--R 2 4 6 5 5 6 2 4 2 +--R (32160a b e - 8850a b d e + 1050b d e )m +--R + +--R 2 4 6 5 5 6 2 4 2 4 6 +--R (36180a b e - 11220a b d e + 1500b d e )m + 15120a b e +--R + +--R 5 5 6 2 4 +--R - 5040a b d e + 720b d e +--R * +--R 4 +--R x +--R + +--R 3 3 6 6 3 3 6 2 4 5 5 +--R 20a b e m + (480a b e - 60a b d e )m +--R + +--R 3 3 6 2 4 5 5 2 4 4 +--R (4520a b e - 1140a b d e + 120a b d e )m +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (21120a b e - 7860a b d e + 1560a b d e - 120b d e )m +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 2 +--R (50900a b e - 24060a b d e + 6360a b d e - 720b d e )m +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 +--R (59040a b e - 32400a b d e + 9960a b d e - 1320b d e )m +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 +--R 25200a b e - 15120a b d e + 5040a b d e - 720b d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 6 4 2 6 3 3 5 5 +--R 15a b e m + (375a b e - 60a b d e )m +--R + +--R 4 2 6 3 3 5 2 4 2 4 4 +--R (3705a b e - 1260a b d e + 180a b d e )m +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 3 +--R (18285a b e - 9780a b d e + 2880a b d e - 360a b d e )m +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 46680a b e - 34020a b d e + 14940a b d e - 3600a b d e +--R + +--R 6 4 2 +--R 360b d e +--R * +--R 2 +--R m +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 56940a b e - 50640a b d e + 27360a b d e - 8280a b d e +--R + +--R 6 4 2 +--R 1080b d e +--R * +--R m +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 25200a b e - 25200a b d e + 15120a b d e - 5040a b d e +--R + +--R 6 4 2 +--R 720b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 5 6 4 2 5 5 +--R 6a b e m + (156a b e - 30a b d e )m +--R + +--R 5 6 4 2 5 3 3 2 4 4 +--R (1620a b e - 690a b d e + 120a b d e )m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 3 +--R (8520a b e - 6030a b d e + 2280a b d e - 360a b d e )m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 23574a b e - 24510a b d e + 15000a b d e - 5040a b d e +--R + +--R 5 4 2 +--R 720a b d e +--R * +--R 2 +--R m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 31644a b e - 44340a b d e + 38040a b d e - 19800a b d e +--R + +--R 5 4 2 6 5 +--R 5760a b d e - 720b d e +--R * +--R m +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 15120a b e - 25200a b d e + 25200a b d e - 15120a b d e +--R + +--R 5 4 2 6 5 +--R 5040a b d e - 720b d e +--R * +--R x +--R + +--R 6 6 6 6 6 5 5 5 +--R a e m + (27a e - 6a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 4 +--R (295a e - 150a b d e + 30a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 3 +--R (1665a e - 1470a b d e + 660a b d e - 120a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 2 +--R (5104a e - 7050a b d e + 5370a b d e - 2160a b d e + 360a b d e )m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 8028a e - 16524a b d e + 19140a b d e - 12840a b d e +--R + +--R 2 4 4 2 5 5 +--R 4680a b d e - 720a b d e +--R * +--R m +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 5040a e - 15120a b d e + 25200a b d e - 25200a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 15120a b d e - 5040a b d e + 720b d +--R * +--R +------------------+ +--R m + 1 | 2 2 2 +--R (e x + d) \|b x + 2a b x + a +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b e m + 28b e m + 322b e m + 1960b e m + 6769b e m + 13132b e m +--R + +--R 7 7 +--R 13068b e m + 5040b e +--R * +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a e m + 28a e m + 322a e m + 1960a e m + 6769a e m + 13132a e m +--R + +--R 7 7 +--R 13068a e m + 5040a e +--R Type: Expression(Integer) +--E 299 + +--S 300 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 765 +t0:=(a+b*x)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 9 14 4 9 5 8 13 2 3 9 4 8 5 2 7 12 +--R b e x + (5a b e + 9b d e )x + (10a b e + 45a b d e + 36b d e )x +--R + +--R 3 2 9 2 3 8 4 2 7 5 3 6 11 +--R (10a b e + 90a b d e + 180a b d e + 84b d e )x +--R + +--R 4 9 3 2 8 2 3 2 7 4 3 6 5 4 5 10 +--R (5a b e + 90a b d e + 360a b d e + 420a b d e + 126b d e )x +--R + +--R 5 9 4 8 3 2 2 7 2 3 3 6 4 4 5 +--R a e + 45a b d e + 360a b d e + 840a b d e + 630a b d e +--R + +--R 5 5 4 +--R 126b d e +--R * +--R 9 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 4 5 4 +--R 9a d e + 180a b d e + 840a b d e + 1260a b d e + 630a b d e +--R + +--R 5 6 3 +--R 84b d e +--R * +--R 8 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 4 6 3 +--R 36a d e + 420a b d e + 1260a b d e + 1260a b d e + 420a b d e +--R + +--R 5 7 2 +--R 36b d e +--R * +--R 7 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 4 7 2 +--R 84a d e + 630a b d e + 1260a b d e + 840a b d e + 180a b d e +--R + +--R 5 8 +--R 9b d e +--R * +--R 6 +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 4 8 +--R 126a d e + 630a b d e + 840a b d e + 360a b d e + 45a b d e +--R + +--R 5 9 +--R b d +--R * +--R 5 +--R x +--R + +--R 5 5 4 4 6 3 3 2 7 2 2 3 8 4 9 4 +--R (126a d e + 420a b d e + 360a b d e + 90a b d e + 5a b d )x +--R + +--R 5 6 3 4 7 2 3 2 8 2 3 9 3 +--R (84a d e + 180a b d e + 90a b d e + 10a b d )x +--R + +--R 5 7 2 4 8 3 2 9 2 5 8 4 9 5 9 +--R (36a d e + 45a b d e + 10a b d )x + (9a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 765 +r0:=-1/364*(b*d-a*e)^3*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/112*(b*d-a*e)^2*(a+b*x)*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/40*(b*d-a*e)*(d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/16*(a+b*x)*_ + (d+e*x)^10*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/8008*(b*d-a*e)^5*(d+e*x)^10*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/80080*(b*d-a*e)^6*(d+e*x)^10*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/1456*(b*d-a*e)^4*(a+b*x)*(d+e*x)^10*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 16 16 5 16 6 15 15 +--R 5005b e x + (32032a b e + 48048b d e )x +--R + +--R 2 4 16 5 15 6 2 14 14 +--R (85800a b e + 308880a b d e + 205920b d e )x +--R + +--R 3 3 16 2 4 15 5 2 14 6 3 13 13 +--R (123200a b e + 831600a b d e + 1330560a b d e + 517440b d e )x +--R + +--R 4 2 16 3 3 15 2 4 2 14 +--R 100100a b e + 1201200a b d e + 3603600a b d e +--R + +--R 5 3 13 6 4 12 +--R 3363360a b d e + 840840b d e +--R * +--R 12 +--R x +--R + +--R 5 16 4 2 15 3 3 2 14 +--R 43680a b e + 982800a b d e + 5241600a b d e +--R + +--R 2 4 3 13 5 4 12 6 5 11 +--R 9172800a b d e + 5503680a b d e + 917280b d e +--R * +--R 11 +--R x +--R + +--R 6 16 5 15 4 2 2 14 3 3 3 13 +--R 8008a e + 432432a b d e + 4324320a b d e + 13453440a b d e +--R + +--R 2 4 4 12 5 5 11 6 6 10 +--R 15135120a b d e + 6054048a b d e + 672672b d e +--R * +--R 10 +--R x +--R + +--R 6 15 5 2 14 4 2 3 13 +--R 80080a d e + 1921920a b d e + 11211200a b d e +--R + +--R 3 3 4 12 2 4 5 11 5 6 10 +--R 22422400a b d e + 16816800a b d e + 4484480a b d e +--R + +--R 6 7 9 +--R 320320b d e +--R * +--R 9 +--R x +--R + +--R 6 2 14 5 3 13 4 2 4 12 +--R 360360a d e + 5045040a b d e + 18918900a b d e +--R + +--R 3 3 5 11 2 4 6 10 5 7 9 6 8 8 +--R 25225200a b d e + 12612600a b d e + 2162160a b d e + 90090b d e +--R * +--R 8 +--R x +--R + +--R 6 3 13 5 4 12 4 2 5 11 +--R 960960a d e + 8648640a b d e + 21621600a b d e +--R + +--R 3 3 6 10 2 4 7 9 5 8 8 6 9 7 +--R 19219200a b d e + 6177600a b d e + 617760a b d e + 11440b d e +--R * +--R 7 +--R x +--R + +--R 6 4 12 5 5 11 4 2 6 10 +--R 1681680a d e + 10090080a b d e + 16816800a b d e +--R + +--R 3 3 7 9 2 4 8 8 5 9 7 +--R 9609600a b d e + 1801800a b d e + 80080a b d e +--R * +--R 6 +--R x +--R + +--R 6 5 11 5 6 10 4 2 7 9 +--R 2018016a d e + 8072064a b d e + 8648640a b d e +--R + +--R 3 3 8 8 2 4 9 7 +--R 2882880a b d e + 240240a b d e +--R * +--R 5 +--R x +--R + +--R 6 6 10 5 7 9 4 2 8 8 3 3 9 7 4 +--R (1681680a d e + 4324320a b d e + 2702700a b d e + 400400a b d e )x +--R + +--R 6 7 9 5 8 8 4 2 9 7 3 +--R (960960a d e + 1441440a b d e + 400400a b d e )x +--R + +--R 6 8 8 5 9 7 2 6 9 7 6 10 6 +--R (360360a d e + 240240a b d e )x + 80080a d e x + 8008a d e +--R + +--R 5 11 5 4 2 12 4 3 3 13 3 2 4 14 2 +--R - 4368a b d e + 1820a b d e - 560a b d e + 120a b d e +--R + +--R 5 15 6 16 +--R - 16a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 80080b e x + 80080a e +--R Type: Expression(Integer) +--E 302 + +--S 303 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 765 +t0:=(a+b*x)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 8 13 4 8 5 7 12 2 3 8 4 7 5 2 6 11 +--R b e x + (5a b e + 8b d e )x + (10a b e + 40a b d e + 28b d e )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 10 +--R (10a b e + 80a b d e + 140a b d e + 56b d e )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 5 4 4 9 +--R (5a b e + 80a b d e + 280a b d e + 280a b d e + 70b d e )x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 4 4 4 +--R a e + 40a b d e + 280a b d e + 560a b d e + 350a b d e +--R + +--R 5 5 3 +--R 56b d e +--R * +--R 8 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 4 5 3 +--R 8a d e + 140a b d e + 560a b d e + 700a b d e + 280a b d e +--R + +--R 5 6 2 +--R 28b d e +--R * +--R 7 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 4 6 2 +--R 28a d e + 280a b d e + 700a b d e + 560a b d e + 140a b d e +--R + +--R 5 7 +--R 8b d e +--R * +--R 6 +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 4 7 5 8 5 +--R (56a d e + 350a b d e + 560a b d e + 280a b d e + 40a b d e + b d )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 4 +--R (70a d e + 280a b d e + 280a b d e + 80a b d e + 5a b d )x +--R + +--R 5 5 3 4 6 2 3 2 7 2 3 8 3 +--R (56a d e + 140a b d e + 80a b d e + 10a b d )x +--R + +--R 5 6 2 4 7 3 2 8 2 5 7 4 8 5 8 +--R (28a d e + 40a b d e + 10a b d )x + (8a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 304 + +--S 305 of 765 +r0:=-1/273*(b*d-a*e)^3*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 1/91*(b*d-a*e)^2*(a+b*x)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 1/35*(b*d-a*e)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/15*(a+b*x)*_ + (d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/5005*(b*d-a*e)^5*(d+e*x)^9*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/45045*(b*d-a*e)^6*(d+e*x)^9*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/1001*(b*d-a*e)^4*(a+b*x)*(d+e*x)^9*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 15 15 5 15 6 14 14 +--R 3003b e x + (19305a b e + 25740b d e )x +--R + +--R 2 4 15 5 14 6 2 13 13 +--R (51975a b e + 166320a b d e + 97020b d e )x +--R + +--R 3 3 15 2 4 14 5 2 13 6 3 12 12 +--R (75075a b e + 450450a b d e + 630630a b d e + 210210b d e )x +--R + +--R 4 2 15 3 3 14 2 4 2 13 +--R 61425a b e + 655200a b d e + 1719900a b d e +--R + +--R 5 3 12 6 4 11 +--R 1375920a b d e + 286650b d e +--R * +--R 11 +--R x +--R + +--R 5 15 4 2 14 3 3 2 13 +--R 27027a b e + 540540a b d e + 2522520a b d e +--R + +--R 2 4 3 12 5 4 11 6 5 10 +--R 3783780a b d e + 1891890a b d e + 252252b d e +--R * +--R 10 +--R x +--R + +--R 6 15 5 14 4 2 2 13 3 3 3 12 +--R 5005a e + 240240a b d e + 2102100a b d e + 5605600a b d e +--R + +--R 2 4 4 11 5 5 10 6 6 9 +--R 5255250a b d e + 1681680a b d e + 140140b d e +--R * +--R 9 +--R x +--R + +--R 6 14 5 2 13 4 2 3 12 +--R 45045a d e + 945945a b d e + 4729725a b d e +--R + +--R 3 3 4 11 2 4 5 10 5 6 9 6 7 8 +--R 7882875a b d e + 4729725a b d e + 945945a b d e + 45045b d e +--R * +--R 8 +--R x +--R + +--R 6 2 13 5 3 12 4 2 4 11 +--R 180180a d e + 2162160a b d e + 6756750a b d e +--R + +--R 3 3 5 10 2 4 6 9 5 7 8 6 8 7 +--R 7207200a b d e + 2702700a b d e + 308880a b d e + 6435b d e +--R * +--R 7 +--R x +--R + +--R 6 3 12 5 4 11 4 2 5 10 +--R 420420a d e + 3153150a b d e + 6306300a b d e +--R + +--R 3 3 6 9 2 4 7 8 5 8 7 +--R 4204200a b d e + 900900a b d e + 45045a b d e +--R * +--R 6 +--R x +--R + +--R 6 4 11 5 5 10 4 2 6 9 +--R 630630a d e + 3027024a b d e + 3783780a b d e +--R + +--R 3 3 7 8 2 4 8 7 +--R 1441440a b d e + 135135a b d e +--R * +--R 5 +--R x +--R + +--R 6 5 10 5 6 9 4 2 7 8 3 3 8 7 4 +--R (630630a d e + 1891890a b d e + 1351350a b d e + 225225a b d e )x +--R + +--R 6 6 9 5 7 8 4 2 8 7 3 +--R (420420a d e + 720720a b d e + 225225a b d e )x +--R + +--R 6 7 8 5 8 7 2 6 8 7 6 9 6 +--R (180180a d e + 135135a b d e )x + 45045a d e x + 5005a d e +--R + +--R 5 10 5 4 2 11 4 3 3 12 3 2 4 13 2 +--R - 3003a b d e + 1365a b d e - 455a b d e + 105a b d e +--R + +--R 5 14 6 15 +--R - 15a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 305 + +--S 306 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 765 +t0:=(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 7 12 4 7 5 6 11 2 3 7 4 6 5 2 5 10 +--R b e x + (5a b e + 7b d e )x + (10a b e + 35a b d e + 21b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 9 +--R (10a b e + 70a b d e + 105a b d e + 35b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 8 +--R (5a b e + 70a b d e + 210a b d e + 175a b d e + 35b d e )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 +--R a e + 35a b d e + 210a b d e + 350a b d e + 175a b d e +--R + +--R 5 5 2 +--R 21b d e +--R * +--R 7 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 +--R 7a d e + 105a b d e + 350a b d e + 350a b d e + 105a b d e +--R + +--R 5 6 +--R 7b d e +--R * +--R 6 +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 5 7 5 +--R (21a d e + 175a b d e + 350a b d e + 210a b d e + 35a b d e + b d )x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 4 +--R (35a d e + 175a b d e + 210a b d e + 70a b d e + 5a b d )x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 3 +--R (35a d e + 105a b d e + 70a b d e + 10a b d )x +--R + +--R 5 5 2 4 6 3 2 7 2 5 6 4 7 5 7 +--R (21a d e + 35a b d e + 10a b d )x + (7a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 765 +r0:=-5/1001*(b*d-a*e)^3*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 5/364*(b*d-a*e)^2*(a+b*x)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 3/91*(b*d-a*e)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+1/14*(a+b*x)*_ + (d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1/3003*(b*d-a*e)^5*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/24024*(b*d-a*e)^6*(d+e*x)^8*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+3/2002*(b*d-a*e)^4*(a+b*x)*(d+e*x)^8*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 14 14 5 14 6 13 13 +--R 1716b e x + (11088a b e + 12936b d e )x +--R + +--R 2 4 14 5 13 6 2 12 12 +--R (30030a b e + 84084a b d e + 42042b d e )x +--R + +--R 3 3 14 2 4 13 5 2 12 6 3 11 11 +--R (43680a b e + 229320a b d e + 275184a b d e + 76440b d e )x +--R + +--R 4 2 14 3 3 13 2 4 2 12 5 3 11 +--R 36036a b e + 336336a b d e + 756756a b d e + 504504a b d e +--R + +--R 6 4 10 +--R 84084b d e +--R * +--R 10 +--R x +--R + +--R 5 14 4 2 13 3 3 2 12 +--R 16016a b e + 280280a b d e + 1121120a b d e +--R + +--R 2 4 3 11 5 4 10 6 5 9 +--R 1401400a b d e + 560560a b d e + 56056b d e +--R * +--R 9 +--R x +--R + +--R 6 14 5 13 4 2 2 12 3 3 3 11 +--R 3003a e + 126126a b d e + 945945a b d e + 2102100a b d e +--R + +--R 2 4 4 10 5 5 9 6 6 8 +--R 1576575a b d e + 378378a b d e + 21021b d e +--R * +--R 8 +--R x +--R + +--R 6 13 5 2 12 4 2 3 11 +--R 24024a d e + 432432a b d e + 1801800a b d e +--R + +--R 3 3 4 10 2 4 5 9 5 6 8 6 7 7 +--R 2402400a b d e + 1081080a b d e + 144144a b d e + 3432b d e +--R * +--R 7 +--R x +--R + +--R 6 2 12 5 3 11 4 2 4 10 3 3 5 9 +--R 84084a d e + 840840a b d e + 2102100a b d e + 1681680a b d e +--R + +--R 2 4 6 8 5 7 7 +--R 420420a b d e + 24024a b d e +--R * +--R 6 +--R x +--R + +--R 6 3 11 5 4 10 4 2 5 9 3 3 6 8 +--R 168168a d e + 1009008a b d e + 1513512a b d e + 672672a b d e +--R + +--R 2 4 7 7 +--R 72072a b d e +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 2 6 8 3 3 7 7 4 +--R (210210a d e + 756756a b d e + 630630a b d e + 120120a b d e )x +--R + +--R 6 5 9 5 6 8 4 2 7 7 3 +--R (168168a d e + 336336a b d e + 120120a b d e )x +--R + +--R 6 6 8 5 7 7 2 6 7 7 6 8 6 +--R (84084a d e + 72072a b d e )x + 24024a d e x + 3003a d e +--R + +--R 5 9 5 4 2 10 4 3 3 11 3 2 4 12 2 +--R - 2002a b d e + 1001a b d e - 364a b d e + 91a b d e +--R + +--R 5 13 6 14 +--R - 14a b d e + b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 24024b e x + 24024a e +--R Type: Expression(Integer) +--E 308 + +--S 309 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 765 +t0:=(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 11 4 6 5 5 10 2 3 6 4 5 5 2 4 9 +--R b e x + (5a b e + 6b d e )x + (10a b e + 30a b d e + 15b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 8 +--R (10a b e + 60a b d e + 75a b d e + 20b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 7 +--R (5a b e + 60a b d e + 150a b d e + 100a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 6 +--R (a e + 30a b d e + 150a b d e + 200a b d e + 75a b d e + 6b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 5 +--R (6a d e + 75a b d e + 200a b d e + 150a b d e + 30a b d e + b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 4 +--R (15a d e + 100a b d e + 150a b d e + 60a b d e + 5a b d )x +--R + +--R 5 3 3 4 4 2 3 2 5 2 3 6 3 +--R (20a d e + 75a b d e + 60a b d e + 10a b d )x +--R + +--R 5 4 2 4 5 3 2 6 2 5 5 4 6 5 6 +--R (15a d e + 30a b d e + 10a b d )x + (6a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 765 +r0:=1/12012*(b*d-a*e)^6*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^7+1/1716*(b*d-a*e)^5*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6+1/429*(b*d-a*e)^4*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/143*(b*d-a*e)^3*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^4+5/286*(b*d-a*e)^2*(d+e*x)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^3+1/26*(b*d-a*e)*(d+e*x)^5*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/13*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 12 6 12 11 6 12 5 11 +--R 924b e x + (5082a b e + 6006b d e )x +--R + +--R 2 10 6 11 5 12 2 4 10 +--R (11298a b e + 33306a b d e + 16380b d e )x +--R + +--R 3 9 6 2 10 5 11 2 4 12 3 3 9 +--R (12726a b e + 74802a b d e + 91728a b d e + 24024b d e )x +--R + +--R 4 8 6 3 9 5 2 10 2 4 11 3 3 +--R 7294a b e + 85358a b d e + 208572a b d e + 136136a b d e +--R + +--R 12 4 2 +--R 20020b d e +--R * +--R 8 +--R x +--R + +--R 5 7 6 4 8 5 3 9 2 4 2 10 3 3 +--R 1715a b e + 49777a b d e + 241878a b d e + 314314a b d e +--R + +--R 11 4 2 12 5 +--R 115115a b d e + 9009b d e +--R * +--R 7 +--R x +--R + +--R 6 6 6 5 7 5 4 8 2 4 3 9 3 3 +--R a b e + 11999a b d e + 144222a b d e + 372086a b d e +--R + +--R 2 10 4 2 11 5 12 6 +--R 270985a b d e + 52767a b d e + 1716b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 6 6 5 5 7 2 4 4 8 3 3 +--R - a b e + 13a b d e + 35958a b d e + 228514a b d e +--R + +--R 3 9 4 2 2 10 5 11 6 +--R 329615a b d e + 127413a b d e + 10296a b d +--R * +--R 5 +--R x +--R + +--R 8 4 6 7 5 5 6 6 2 4 5 7 3 3 4 8 4 2 +--R a b e - 13a b d e + 78a b d e + 59774a b d e + 210925a b d e +--R + +--R 3 9 5 2 10 6 +--R 160875a b d e + 25740a b d +--R * +--R 4 +--R x +--R + +--R 9 3 6 8 4 5 7 5 2 4 6 6 3 3 5 7 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e + 59345a b d e +--R + +--R 4 8 5 3 9 6 +--R 109395a b d e + 34320a b d +--R * +--R 3 +--R x +--R + +--R 10 2 6 9 3 5 8 4 2 4 7 5 3 3 6 6 4 2 +--R a b e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 5 7 5 4 8 6 +--R 34749a b d e + 25740a b d +--R * +--R 2 +--R x +--R + +--R 11 6 10 2 5 9 3 2 4 8 4 3 3 7 5 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e - 715a b d e +--R + +--R 6 6 5 5 7 6 +--R 1287a b d e + 10296a b d +--R * +--R x +--R + +--R 12 6 11 5 10 2 2 4 9 3 3 3 8 4 4 2 +--R a e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 7 5 5 6 6 6 +--R - 1287a b d e + 1716a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 +--R 12012b +--R Type: Expression(Integer) +--E 311 + +--S 312 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 765 +t0:=(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 5 10 4 5 5 4 9 2 3 5 4 4 5 2 3 8 +--R b e x + (5a b e + 5b d e )x + (10a b e + 25a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 7 +--R (10a b e + 50a b d e + 50a b d e + 10b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 6 +--R (5a b e + 50a b d e + 100a b d e + 50a b d e + 5b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 +--R (a e + 25a b d e + 100a b d e + 100a b d e + 25a b d e + b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4 +--R (5a d e + 50a b d e + 100a b d e + 50a b d e + 5a b d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 3 +--R (10a d e + 50a b d e + 50a b d e + 10a b d )x +--R + +--R 5 3 2 4 4 3 2 5 2 5 4 4 5 5 5 +--R (10a d e + 25a b d e + 10a b d )x + (5a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 313 + +--S 314 of 765 +r0:=1/5544*(b*d-a*e)^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^6+1/792*(b*d-a*e)^4*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/198*(b*d-a*e)^3*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+1/66*(b*d-a*e)^2*(d+e*x)^3*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^3+5/132*(b*d-a*e)*(d+e*x)^4*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/12*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 11 5 11 10 5 11 4 10 +--R 462b e x + (2562a b e + 2520b d e )x +--R + +--R 2 9 5 10 4 11 2 3 9 +--R (5754a b e + 14112a b d e + 5544b d e )x +--R + +--R 3 8 5 2 9 4 10 2 3 11 3 2 8 +--R (6566a b e + 32088a b d e + 31416a b d e + 6160b d e )x +--R + +--R 4 7 5 3 8 4 2 9 2 3 10 3 2 +--R 3829a b e + 37212a b d e + 72534a b d e + 35420a b d e +--R + +--R 11 4 +--R 3465b d e +--R * +--R 7 +--R x +--R + +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 +--R 923a b e + 22188a b d e + 85866a b d e + 83380a b d e +--R + +--R 10 4 11 5 +--R 20295a b d e + 792b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R a b e + 5532a b d e + 52734a b d e + 101420a b d e +--R + +--R 2 9 4 10 5 +--R 49005a b d e + 4752a b d +--R * +--R 5 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R - a b e + 12a b d e + 13794a b d e + 64900a b d e +--R + +--R 3 8 4 2 9 5 +--R 61875a b d e + 11880a b d +--R * +--R 4 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 4 7 4 +--R a b e - 12a b d e + 66a b d e + 18260a b d e + 42075a b d e +--R + +--R 3 8 5 +--R 15840a b d +--R * +--R 3 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 5 6 4 +--R - a b e + 12a b d e - 66a b d e + 220a b d e + 13365a b d e +--R + +--R 4 7 5 +--R 11880a b d +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 6 5 4 +--R a b e - 12a b d e + 66a b d e - 220a b d e + 495a b d e +--R + +--R 5 6 5 +--R 4752a b d +--R * +--R x +--R + +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 6 5 5 +--R - a e + 12a b d e - 66a b d e + 220a b d e - 495a b d e + 792a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 +--R 5544b +--R Type: Expression(Integer) +--E 314 + +--S 315 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 765 +t0:=(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 4 9 4 4 5 3 8 2 3 4 4 3 5 2 2 7 +--R b e x + (5a b e + 4b d e )x + (10a b e + 20a b d e + 6b d e )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 6 +--R (10a b e + 40a b d e + 30a b d e + 4b d e)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5 +--R (5a b e + 40a b d e + 60a b d e + 20a b d e + b d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a e + 20a b d e + 60a b d e + 40a b d e + 5a b d )x +--R + +--R 5 3 4 2 2 3 2 3 2 3 4 3 +--R (4a d e + 30a b d e + 40a b d e + 10a b d )x +--R + +--R 5 2 2 4 3 3 2 4 2 5 3 4 4 5 4 +--R (6a d e + 20a b d e + 10a b d )x + (4a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 765 +r0:=1/2310*(b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^5+1/330*(b*d-a*e)^3*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+2/165*(b*d-a*e)^2*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+2/55*(b*d-a*e)*(d+e*x)^3*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b^2+1/11*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 10 4 10 9 4 10 3 9 +--R 210b e x + (1176a b e + 924b d e )x +--R + +--R 2 8 4 9 3 10 2 2 8 +--R (2674a b e + 5236a b d e + 1540b d e )x +--R + +--R 3 7 4 2 8 3 9 2 2 10 3 7 +--R (3101a b e + 12089a b d e + 8855a b d e + 1155b d e)x +--R + +--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 6 +--R (1849a b e + 14311a b d e + 20845a b d e + 6765a b d e + 330b d )x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R 461a b e + 8789a b d e + 25355a b d e + 16335a b d e +--R + +--R 9 4 +--R 1980a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 2 8 4 4 +--R (a b e + 2299a b d e + 16225a b d e + 20625a b d e + 4950a b d )x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 3 7 4 3 +--R (- a b e + 11a b d e + 4565a b d e + 14025a b d e + 6600a b d )x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 4 6 4 2 +--R (a b e - 11a b d e + 55a b d e + 4455a b d e + 4950a b d )x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 5 5 4 10 4 +--R (- a b e + 11a b d e - 55a b d e + 165a b d e + 1980a b d )x + a e +--R + +--R 9 3 8 2 2 2 7 3 3 6 4 4 +--R - 11a b d e + 55a b d e - 165a b d e + 330a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 +--R 2310b +--R Type: Expression(Integer) +--E 317 + +--S 318 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 of 765 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 765 +r0:=1/840*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^4+1/120*(b*d-a*e)^2*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+1/30*(b*d-a*e)*(d+e*x)^2*(a^2+_ + 2*a*b*x+b^2*x^2)^(7/2)/b^2+1/10*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 9 3 9 8 3 9 2 8 +--R 84b e x + (476a b e + 280b d e )x +--R + +--R 2 7 3 8 2 9 2 7 +--R (1099a b e + 1610a b d e + 315b d e)x +--R + +--R 3 6 3 2 7 2 8 2 9 3 6 +--R (1301a b e + 3790a b d e + 1845a b d e + 120b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (799a b e + 4610a b d e + 4455a b d e + 720a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 4 +--R (209a b e + 2950a b d e + 5625a b d e + 1800a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (a b e + 830a b d e + 3825a b d e + 2400a b d )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (- a b e + 10a b d e + 1215a b d e + 1800a b d )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 8 2 +--R (a b e - 10a b d e + 45a b d e + 720a b d )x - a e + 10a b d e +--R + +--R 7 2 2 6 3 3 +--R - 45a b d e + 120a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 +--R 840b +--R Type: Expression(Integer) +--E 320 + +--S 321 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 765 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 765 +r0:=1/252*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^3+1/36*(b*d-a*e)*_ + (d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2+1/9*(d+e*x)^2*(a^2+2*a*b*x+_ + b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 8 2 8 7 2 8 7 +--R 28b e x + (161a b e + 63b d e)x +--R + +--R 2 6 2 7 8 2 6 +--R (379a b e + 369a b d e + 36b d )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (461a b e + 891a b d e + 216a b d )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (295a b e + 1125a b d e + 540a b d )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (83a b e + 765a b d e + 720a b d )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (a b e + 243a b d e + 540a b d )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- a b e + 9a b d e + 216a b d )x + a e - 9a b d e + 36a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 +--R 252b +--R Type: Expression(Integer) +--E 323 + +--S 324 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 of 765 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 765 +r0:=1/56*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2+1/8*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 7 7 6 7 6 2 5 6 5 +--R 7b e x + (41a b e + 8b d)x + (99a b e + 48a b d)x +--R + +--R 3 4 2 5 4 4 3 3 4 3 +--R (125a b e + 120a b d)x + (85a b e + 160a b d)x +--R + +--R 5 2 4 3 2 6 5 2 7 6 +--R (27a b e + 120a b d)x + (a b e + 48a b d)x - a e + 8a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 +--R 56b +--R Type: Expression(Integer) +--E 326 + +--S 327 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 765 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7b +--R Type: Expression(Integer) +--E 329 + +--S 330 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 331 + +--S 332 of 765 +r0:=-1/3*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+1/4*(b*d-a*e)^2*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-1/5*(b*d-a*e)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/e^2+1/6*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-(b*d-_ + a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+1/2*(b*d-a*e)^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+(b*d-a*e)^6*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 60a e - 360a b d e + 900a b d e - 1200a b d e + 900a b d e +--R + +--R 5 5 6 6 +--R - 360a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (72a b e - 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (225a b e - 90a b d e + 15b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b e - 300a b d e + 120a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (450a b e - 600a b d e + 450a b d e - 180a b d e + 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 360a b e - 900a b d e + 1200a b d e - 900a b d e + 360a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 147a e - 522a b d e + 855a b d e - 740a b d e + 330a b d e +--R + +--R 5 5 +--R - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +--R 60b e x + 60a e +--R Type: Expression(Integer) +--E 332 + +--S 333 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 334 + +--S 335 of 765 +r0:=2*b*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-3/2*b*(b*d-a*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3+6/5*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/e^2-(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x))+_ + 6*b*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-3*b*(b*d-a*e)^3*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-6*b*(b*d-a*e)^5*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e +--R + +--R 5 4 2 6 5 +--R 300a b d e - 60b d e +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 60a b d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 6 6 +--R - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 2b e x + (15a b e - 3b d e )x + (50a b e - 25a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b e - 100a b d e + 50a b d e - 10b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (150a b e - 300a b d e + 300a b d e - 150a b d e + 30b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 77a b e - 85a b d e - 130a b d e + 330a b d e - 240a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e + 137a b d e - 385a b d e + 470a b d e - 270a b d e +--R + +--R 5 5 +--R 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +--R 10b e x + (10a e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 335 + +--S 336 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 336 + +)clear all + +--S 337 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 337 + +--S 338 of 765 +r0:=-5*b^2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+15/4*b^2*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-1/2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e*(d+e*x)^2)-3*b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e^2*(d+e*x))-15*b^2*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+_ + 15/2*b^2*(b*d-a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+_ + 15*b^2*(b*d-a*e)^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b e - 240a b d e + 360a b d e - 240a b d e + 60b d e )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b d e - 480a b d e + 720a b d e - 480a b d e + 120b d e)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b d e - 240a b d e + 360a b d e - 240a b d e + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (8a b e - 2b d e )x + (30a b e - 20a b d e + 5b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b e - 120a b d e + 80a b d e - 20b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (35a b e + 100a b d e - 330a b d e + 300a b d e - 90b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b e + 190a b d e - 280a b d e + 60a b d e + 120a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a e - 12a b d e + 125a b d e - 260a b d e + 210a b d e +--R + +--R 5 5 +--R - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R 4b e x + (4a e + 8b d e )x + (8a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 338 + +--S 339 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 339 + +)clear all + +--S 340 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^4 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 340 + +--S 341 of 765 +r0:=20/3*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4-5*b^2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*(d+e*x))-1/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/_ + (e*(d+e*x)^3)-b*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^2)+20*b^3*_ + (b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-10*b^3*(b*d-a*e)*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-20*b^3*(b*d-a*e)^3*log(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (60a b e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e )x +--R + +--R 3 3 2 4 2 4 3 3 5 4 2 6 5 3 3 3 3 +--R (180a b d e - 540a b d e + 540a b d e - 180b d e)x + 60a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 180a b d e + 180a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b e x + (9a b e - 3b d e )x + (45a b e - 45a b d e + 15b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (180a b d e - 270a b d e + 110b d e )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 2 +--R (- 45a b e + 180a b d e - 270a b d e + 150b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 6 5 6 6 +--R (- 9a b e - 45a b d e + 270a b d e - 270a b d e + 60b d e)x - a e +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 3a b d e - 15a b d e + 110a b d e - 150a b d e + 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 3b e x + (3a e + 9b d e )x + (9a d e + 9b d e )x +--R + +--R 2 8 3 7 3 7 +--R (9a d e + 3b d e )x + 3a d e +--R Type: Expression(Integer) +--E 341 + +--S 342 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^5 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Expression(Integer) +--E 343 + +--S 344 of 765 +r0:=-5/4*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^2)-_ + 5*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x))-1/4*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^4)-1/2*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^3)-15*b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6+15/2*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5+_ + 15*b^4*(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 2 4 6 5 5 6 2 4 4 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 2 4 5 5 2 4 6 3 3 3 +--R (240a b d e - 480a b d e + 240b d e )x +--R + +--R 2 4 2 4 5 3 3 6 4 2 2 +--R (360a b d e - 720a b d e + 360b d e )x +--R + +--R 2 4 3 3 5 4 2 6 5 2 4 4 2 5 5 +--R (240a b d e - 480a b d e + 240b d e)x + 60a b d e - 120a b d e +--R + +--R 6 6 +--R 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 2b e x + (24a b e - 12b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 35a b e + 190a b d e - 125b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 80a b e + 100a b d e + 280a b d e - 260b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 30a b e - 120a b d e + 330a b d e + 60a b d e - 210b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 8a b e - 20a b d e - 80a b d e + 300a b d e - 120a b d e +--R + +--R 6 5 +--R - 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - a e - 2a b d e - 5a b d e - 20a b d e + 90a b d e - 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 4b e x + (4a e + 16b d e )x + (16a d e + 24b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (24a d e + 16b d e )x + (16a d e + 4b d e )x + 4a d e +--R Type: Expression(Integer) +--E 344 + +--S 345 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^6 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Expression(Integer) +--E 346 + +--S 347 of 765 +r0:=-1/2*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^3)-_ + b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^2)-1/5*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^5)-3/10*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^4)+6*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-_ + 3*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x))-_ + 6*b^5*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 5 6 6 5 5 5 5 6 2 4 4 +--R (60a b e - 60b d e )x + (300a b d e - 300b d e )x +--R + +--R 5 2 4 6 3 3 3 5 3 3 6 4 2 2 +--R (600a b d e - 600b d e )x + (600a b d e - 600b d e )x +--R + +--R 5 4 2 6 5 5 5 6 6 +--R (300a b d e - 300b d e)x + 60a b d e - 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (- 77a b e + 137b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 150a b e - 85a b d e + 385b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 100a b e - 300a b d e + 130a b d e + 470b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 50a b e - 100a b d e - 300a b d e + 330a b d e + 270b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 15a b e - 25a b d e - 50a b d e - 150a b d e + 240a b d e +--R + +--R 6 5 +--R 60b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R - 2a e - 3a b d e - 5a b d e - 10a b d e - 30a b d e + 60a b d e +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 10b e x + (10a e + 50b d e )x + (50a d e + 100b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (100a d e + 100b d e )x + (100a d e + 50b d e )x +--R + +--R 4 8 5 7 5 7 +--R (50a d e + 10b d e )x + 10a d e +--R Type: Expression(Integer) +--E 347 + +--S 348 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^7 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Expression(Integer) +--E 349 + +--S 350 of 765 +r0:=-1/4*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^4)-_ + 1/3*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^3)-1/6*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^6)-1/5*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^5)-1/2*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^2)+b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x))+b^6*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 6 6 5 5 6 2 4 4 6 3 3 3 6 4 2 2 +--R 60b e x + 360b d e x + 900b d e x + 1200b d e x + 900b d e x +--R + +--R 6 5 6 6 +--R 360b d e x + 60b d +--R * +--R log(e x + d) +--R + +--R 6 6 6 5 6 6 5 5 +--R - 87b e x + (- 360a b e - 162b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 450a b e - 900a b d e + 45b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 400a b e - 600a b d e - 1200a b d e + 460b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 225a b e - 300a b d e - 450a b d e - 900a b d e + 570b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 72a b e - 90a b d e - 120a b d e - 180a b d e - 360a b d e +--R + +--R 6 5 +--R 300b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e - 12a b d e - 15a b d e - 20a b d e - 30a b d e +--R + +--R 5 5 6 6 +--R - 60a b d e + 60b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 7 13 12 6 12 2 11 5 +--R 60b e x + (60a e + 360b d e )x + (360a d e + 900b d e )x +--R + +--R 2 11 3 10 4 3 10 4 9 3 +--R (900a d e + 1200b d e )x + (1200a d e + 900b d e )x +--R + +--R 4 9 5 8 2 5 8 6 7 6 7 +--R (900a d e + 360b d e )x + (360a d e + 60b d e )x + 60a d e +--R Type: Expression(Integer) +--E 350 + +--S 351 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^8 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Expression(Integer) +--E 352 + +--S 353 of 765 +r0:=1/7*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^7) +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- b x - 6a b x - 15a b x - 20a b x - 15a b x - 6a b x - a ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 7 7 7 2 6 6 2 6 3 5 5 +--R (7a e - 7b d e )x + (49a d e - 49b d e )x + (147a d e - 147b d e )x +--R + +--R 3 5 4 4 4 4 4 5 3 3 +--R (245a d e - 245b d e )x + (245a d e - 245b d e )x +--R + +--R 5 3 6 2 2 6 2 7 7 8 +--R (147a d e - 147b d e )x + (49a d e - 49b d e)x + 7a d e - 7b d +--R Type: Expression(Integer) +--E 353 + +--S 354 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^9 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Expression(Integer) +--E 355 + +--S 356 of 765 +r0:=1/8*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^8)+_ + 1/56*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^7) +--R +--R +--R (2) +--R 7 7 6 7 6 2 5 6 5 +--R b e x + (- a b e + 8b d)x + (- 27a b e + 48a b d)x +--R + +--R 3 4 2 5 4 4 3 3 4 3 +--R (- 85a b e + 120a b d)x + (- 125a b e + 160a b d)x +--R + +--R 5 2 4 3 2 6 5 2 7 6 +--R (- 99a b e + 120a b d)x + (- 41a b e + 48a b d)x - 7a e + 8a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 10 9 2 2 8 8 +--R (56a e - 112a b d e + 56b d e )x +--R + +--R 2 9 2 8 2 3 7 7 +--R (448a d e - 896a b d e + 448b d e )x +--R + +--R 2 2 8 3 7 2 4 6 6 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 3 7 4 6 2 5 5 5 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 4 6 5 5 2 6 4 4 +--R (3920a d e - 7840a b d e + 3920b d e )x +--R + +--R 2 5 5 6 4 2 7 3 3 +--R (3136a d e - 6272a b d e + 3136b d e )x +--R + +--R 2 6 4 7 3 2 8 2 2 +--R (1568a d e - 3136a b d e + 1568b d e )x +--R + +--R 2 7 3 8 2 2 9 2 8 2 9 2 10 +--R (448a d e - 896a b d e + 448b d e)x + 56a d e - 112a b d e + 56b d +--R Type: Expression(Integer) +--E 356 + +--S 357 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^10 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Expression(Integer) +--E 358 + +--S 359 of 765 +r0:=1/9*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^9)+_ + 1/36*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^8)+_ + 1/252*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^7) +--R +--R +--R (2) +--R 8 2 8 7 2 8 7 2 6 2 7 8 2 6 +--R - b e x + (a b e - 9b d e)x + (- a b e + 9a b d e - 36b d )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 83a b e + 243a b d e - 216a b d )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 295a b e + 765a b d e - 540a b d )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 461a b e + 1125a b d e - 720a b d )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 379a b e + 891a b d e - 540a b d )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 161a b e + 369a b d e - 216a b d )x - 28a e + 63a b d e - 36a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 12 2 11 2 2 10 3 3 9 9 +--R (252a e - 756a b d e + 756a b d e - 252b d e )x +--R + +--R 3 11 2 2 10 2 3 9 3 4 8 8 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e )x +--R + +--R 3 2 10 2 3 9 2 4 8 3 5 7 7 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 3 9 2 4 8 2 5 7 3 6 6 6 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 4 8 2 5 7 2 6 6 3 7 5 5 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 5 7 2 6 6 2 7 5 3 8 4 4 +--R (31752a d e - 95256a b d e + 95256a b d e - 31752b d e )x +--R + +--R 3 6 6 2 7 5 2 8 4 3 9 3 3 +--R (21168a d e - 63504a b d e + 63504a b d e - 21168b d e )x +--R + +--R 3 7 5 2 8 4 2 9 3 3 10 2 2 +--R (9072a d e - 27216a b d e + 27216a b d e - 9072b d e )x +--R + +--R 3 8 4 2 9 3 2 10 2 3 11 3 9 3 +--R (2268a d e - 6804a b d e + 6804a b d e - 2268b d e)x + 252a d e +--R + +--R 2 10 2 2 11 3 12 +--R - 756a b d e + 756a b d e - 252b d +--R Type: Expression(Integer) +--E 359 + +--S 360 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^11 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Expression(Integer) +--E 361 + +--S 362 of 765 +r0:=1/10*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^10)+_ + 1/30*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^9)+_ + 1/120*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^8)+_ + 1/840*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^7) +--R +--R +--R (2) +--R 9 3 9 8 3 9 2 8 2 7 3 8 2 9 2 7 +--R b e x + (- a b e + 10b d e )x + (a b e - 10a b d e + 45b d e)x +--R + +--R 3 6 3 2 7 2 8 2 9 3 6 +--R (- a b e + 10a b d e - 45a b d e + 120b d )x +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (- 209a b e + 830a b d e - 1215a b d e + 720a b d )x +--R + +--R 5 4 3 4 5 2 3 6 2 2 7 3 4 +--R (- 799a b e + 2950a b d e - 3825a b d e + 1800a b d )x +--R + +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (- 1301a b e + 4610a b d e - 5625a b d e + 2400a b d )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (- 1099a b e + 3790a b d e - 4455a b d e + 1800a b d )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 +--R (- 476a b e + 1610a b d e - 1845a b d e + 720a b d )x - 84a e +--R + +--R 8 2 7 2 2 6 3 3 +--R 280a b d e - 315a b d e + 120a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 14 3 13 2 2 2 12 3 3 11 4 4 10 +--R (840a e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d e ) +--R * +--R 10 +--R x +--R + +--R 4 13 3 2 12 2 2 3 11 3 4 10 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 5 9 +--R 8400b d e +--R * +--R 9 +--R x +--R + +--R 4 2 12 3 3 11 2 2 4 10 3 5 9 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 6 8 +--R 37800b d e +--R * +--R 8 +--R x +--R + +--R 4 3 11 3 4 10 2 2 5 9 3 6 8 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 7 7 +--R 100800b d e +--R * +--R 7 +--R x +--R + +--R 4 4 10 3 5 9 2 2 6 8 3 7 7 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 8 6 +--R 176400b d e +--R * +--R 6 +--R x +--R + +--R 4 5 9 3 6 8 2 2 7 7 3 8 6 +--R 211680a d e - 846720a b d e + 1270080a b d e - 846720a b d e +--R + +--R 4 9 5 +--R 211680b d e +--R * +--R 5 +--R x +--R + +--R 4 6 8 3 7 7 2 2 8 6 3 9 5 +--R 176400a d e - 705600a b d e + 1058400a b d e - 705600a b d e +--R + +--R 4 10 4 +--R 176400b d e +--R * +--R 4 +--R x +--R + +--R 4 7 7 3 8 6 2 2 9 5 3 10 4 +--R 100800a d e - 403200a b d e + 604800a b d e - 403200a b d e +--R + +--R 4 11 3 +--R 100800b d e +--R * +--R 3 +--R x +--R + +--R 4 8 6 3 9 5 2 2 10 4 3 11 3 +--R 37800a d e - 151200a b d e + 226800a b d e - 151200a b d e +--R + +--R 4 12 2 +--R 37800b d e +--R * +--R 2 +--R x +--R + +--R 4 9 5 3 10 4 2 2 11 3 3 12 2 +--R 8400a d e - 33600a b d e + 50400a b d e - 33600a b d e +--R + +--R 4 13 +--R 8400b d e +--R * +--R x +--R + +--R 4 10 4 3 11 3 2 2 12 2 3 13 4 14 +--R 840a d e - 3360a b d e + 5040a b d e - 3360a b d e + 840b d +--R Type: Expression(Integer) +--E 362 + +--S 363 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^12 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R e x + 12d e x + 66d e x + 220d e x + 495d e x + 792d e x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924d e x + 792d e x + 495d e x + 220d e x + 66d e x + 12d e x + d +--R Type: Expression(Integer) +--E 364 + +--S 365 of 765 +r0:=1/11*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^11)+_ + 2/55*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^10)+_ + 2/165*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^9)+_ + 1/330*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^8)+_ + 1/2310*b^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^7) +--R +--R +--R (2) +--R 10 4 10 9 4 10 3 9 +--R - b e x + (a b e - 11b d e )x +--R + +--R 2 8 4 9 3 10 2 2 8 +--R (- a b e + 11a b d e - 55b d e )x +--R + +--R 3 7 4 2 8 3 9 2 2 10 3 7 +--R (a b e - 11a b d e + 55a b d e - 165b d e)x +--R + +--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 6 +--R (- a b e + 11a b d e - 55a b d e + 165a b d e - 330b d )x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R - 461a b e + 2299a b d e - 4565a b d e + 4455a b d e +--R + +--R 9 4 +--R - 1980a b d +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 +--R - 1849a b e + 8789a b d e - 16225a b d e + 14025a b d e +--R + +--R 2 8 4 +--R - 4950a b d +--R * +--R 4 +--R x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 +--R - 3101a b e + 14311a b d e - 25355a b d e + 20625a b d e +--R + +--R 3 7 4 +--R - 6600a b d +--R * +--R 3 +--R x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 +--R - 2674a b e + 12089a b d e - 20845a b d e + 16335a b d e +--R + +--R 4 6 4 +--R - 4950a b d +--R * +--R 2 +--R x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 +--R - 1176a b e + 5236a b d e - 8855a b d e + 6765a b d e +--R + +--R 5 5 4 +--R - 1980a b d +--R * +--R x +--R + +--R 10 4 9 3 8 2 2 2 7 3 3 6 4 4 +--R - 210a e + 924a b d e - 1540a b d e + 1155a b d e - 330a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 16 4 15 3 2 2 14 2 3 3 13 +--R 2310a e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 4 12 5 5 11 +--R 11550a b d e - 2310b d e +--R * +--R 11 +--R x +--R + +--R 5 15 4 2 14 3 2 3 13 2 3 4 12 +--R 25410a d e - 127050a b d e + 254100a b d e - 254100a b d e +--R + +--R 4 5 11 5 6 10 +--R 127050a b d e - 25410b d e +--R * +--R 10 +--R x +--R + +--R 5 2 14 4 3 13 3 2 4 12 2 3 5 11 +--R 127050a d e - 635250a b d e + 1270500a b d e - 1270500a b d e +--R + +--R 4 6 10 5 7 9 +--R 635250a b d e - 127050b d e +--R * +--R 9 +--R x +--R + +--R 5 3 13 4 4 12 3 2 5 11 +--R 381150a d e - 1905750a b d e + 3811500a b d e +--R + +--R 2 3 6 10 4 7 9 5 8 8 +--R - 3811500a b d e + 1905750a b d e - 381150b d e +--R * +--R 8 +--R x +--R + +--R 5 4 12 4 5 11 3 2 6 10 2 3 7 9 +--R 762300a d e - 3811500a b d e + 7623000a b d e - 7623000a b d e +--R + +--R 4 8 8 5 9 7 +--R 3811500a b d e - 762300b d e +--R * +--R 7 +--R x +--R + +--R 5 5 11 4 6 10 3 2 7 9 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 8 8 4 9 7 5 10 6 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 6 +--R x +--R + +--R 5 6 10 4 7 9 3 2 8 8 +--R 1067220a d e - 5336100a b d e + 10672200a b d e +--R + +--R 2 3 9 7 4 10 6 5 11 5 +--R - 10672200a b d e + 5336100a b d e - 1067220b d e +--R * +--R 5 +--R x +--R + +--R 5 7 9 4 8 8 3 2 9 7 2 3 10 6 +--R 762300a d e - 3811500a b d e + 7623000a b d e - 7623000a b d e +--R + +--R 4 11 5 5 12 4 +--R 3811500a b d e - 762300b d e +--R * +--R 4 +--R x +--R + +--R 5 8 8 4 9 7 3 2 10 6 2 3 11 5 +--R 381150a d e - 1905750a b d e + 3811500a b d e - 3811500a b d e +--R + +--R 4 12 4 5 13 3 +--R 1905750a b d e - 381150b d e +--R * +--R 3 +--R x +--R + +--R 5 9 7 4 10 6 3 2 11 5 2 3 12 4 +--R 127050a d e - 635250a b d e + 1270500a b d e - 1270500a b d e +--R + +--R 4 13 3 5 14 2 +--R 635250a b d e - 127050b d e +--R * +--R 2 +--R x +--R + +--R 5 10 6 4 11 5 3 2 12 4 2 3 13 3 +--R 25410a d e - 127050a b d e + 254100a b d e - 254100a b d e +--R + +--R 4 14 2 5 15 +--R 127050a b d e - 25410b d e +--R * +--R x +--R + +--R 5 11 5 4 12 4 3 2 13 3 2 3 14 2 +--R 2310a d e - 11550a b d e + 23100a b d e - 23100a b d e +--R + +--R 4 15 5 16 +--R 11550a b d e - 2310b d +--R Type: Expression(Integer) +--E 365 + +--S 366 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^13 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R e x + 13d e x + 78d e x + 286d e x + 715d e x + 1287d e x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 +--R 1716d e x + 1716d e x + 1287d e x + 715d e x + 286d e x + 78d e x +--R + +--R 12 13 +--R 13d e x + d +--R Type: Expression(Integer) +--E 367 + +--S 368 of 765 +r0:=1/12*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^12)+_ + 5/132*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^11)+_ + 1/66*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^10)+_ + 1/198*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^9)+_ + 1/792*b^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^8)+_ + 1/5544*b^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^6*(d+e*x)^7) +--R +--R +--R (2) +--R 11 5 11 10 5 11 4 10 +--R b e x + (- a b e + 12b d e )x +--R + +--R 2 9 5 10 4 11 2 3 9 +--R (a b e - 12a b d e + 66b d e )x +--R + +--R 3 8 5 2 9 4 10 2 3 11 3 2 8 +--R (- a b e + 12a b d e - 66a b d e + 220b d e )x +--R + +--R 4 7 5 3 8 4 2 9 2 3 10 3 2 11 4 7 +--R (a b e - 12a b d e + 66a b d e - 220a b d e + 495b d e)x +--R + +--R 5 6 5 4 7 4 3 8 2 3 2 9 3 2 10 4 +--R - a b e + 12a b d e - 66a b d e + 220a b d e - 495a b d e +--R + +--R 11 5 +--R 792b d +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 7 2 3 3 8 3 2 +--R - 923a b e + 5532a b d e - 13794a b d e + 18260a b d e +--R + +--R 2 9 4 10 5 +--R - 13365a b d e + 4752a b d +--R * +--R 5 +--R x +--R + +--R 7 4 5 6 5 4 5 6 2 3 4 7 3 2 +--R - 3829a b e + 22188a b d e - 52734a b d e + 64900a b d e +--R + +--R 3 8 4 2 9 5 +--R - 42075a b d e + 11880a b d +--R * +--R 4 +--R x +--R + +--R 8 3 5 7 4 4 6 5 2 3 5 6 3 2 +--R - 6566a b e + 37212a b d e - 85866a b d e + 101420a b d e +--R + +--R 4 7 4 3 8 5 +--R - 61875a b d e + 15840a b d +--R * +--R 3 +--R x +--R + +--R 9 2 5 8 3 4 7 4 2 3 6 5 3 2 +--R - 5754a b e + 32088a b d e - 72534a b d e + 83380a b d e +--R + +--R 5 6 4 4 7 5 +--R - 49005a b d e + 11880a b d +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 3 2 3 7 4 3 2 +--R - 2562a b e + 14112a b d e - 31416a b d e + 35420a b d e +--R + +--R 6 5 4 5 6 5 +--R - 20295a b d e + 4752a b d +--R * +--R x +--R + +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 +--R - 462a e + 2520a b d e - 5544a b d e + 6160a b d e - 3465a b d e +--R + +--R 6 5 5 +--R 792a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 18 5 17 4 2 2 16 3 3 3 15 +--R 5544a e - 33264a b d e + 83160a b d e - 110880a b d e +--R + +--R 2 4 4 14 5 5 13 6 6 12 +--R 83160a b d e - 33264a b d e + 5544b d e +--R * +--R 12 +--R x +--R + +--R 6 17 5 2 16 4 2 3 15 3 3 4 14 +--R 66528a d e - 399168a b d e + 997920a b d e - 1330560a b d e +--R + +--R 2 4 5 13 5 6 12 6 7 11 +--R 997920a b d e - 399168a b d e + 66528b d e +--R * +--R 11 +--R x +--R + +--R 6 2 16 5 3 15 4 2 4 14 +--R 365904a d e - 2195424a b d e + 5488560a b d e +--R + +--R 3 3 5 13 2 4 6 12 5 7 11 +--R - 7318080a b d e + 5488560a b d e - 2195424a b d e +--R + +--R 6 8 10 +--R 365904b d e +--R * +--R 10 +--R x +--R + +--R 6 3 15 5 4 14 4 2 5 13 +--R 1219680a d e - 7318080a b d e + 18295200a b d e +--R + +--R 3 3 6 12 2 4 7 11 5 8 10 +--R - 24393600a b d e + 18295200a b d e - 7318080a b d e +--R + +--R 6 9 9 +--R 1219680b d e +--R * +--R 9 +--R x +--R + +--R 6 4 14 5 5 13 4 2 6 12 +--R 2744280a d e - 16465680a b d e + 41164200a b d e +--R + +--R 3 3 7 11 2 4 8 10 5 9 9 +--R - 54885600a b d e + 41164200a b d e - 16465680a b d e +--R + +--R 6 10 8 +--R 2744280b d e +--R * +--R 8 +--R x +--R + +--R 6 5 13 5 6 12 4 2 7 11 +--R 4390848a d e - 26345088a b d e + 65862720a b d e +--R + +--R 3 3 8 10 2 4 9 9 5 10 8 +--R - 87816960a b d e + 65862720a b d e - 26345088a b d e +--R + +--R 6 11 7 +--R 4390848b d e +--R * +--R 7 +--R x +--R + +--R 6 6 12 5 7 11 4 2 8 10 +--R 5122656a d e - 30735936a b d e + 76839840a b d e +--R + +--R 3 3 9 9 2 4 10 8 5 11 7 +--R - 102453120a b d e + 76839840a b d e - 30735936a b d e +--R + +--R 6 12 6 +--R 5122656b d e +--R * +--R 6 +--R x +--R + +--R 6 7 11 5 8 10 4 2 9 9 +--R 4390848a d e - 26345088a b d e + 65862720a b d e +--R + +--R 3 3 10 8 2 4 11 7 5 12 6 +--R - 87816960a b d e + 65862720a b d e - 26345088a b d e +--R + +--R 6 13 5 +--R 4390848b d e +--R * +--R 5 +--R x +--R + +--R 6 8 10 5 9 9 4 2 10 8 +--R 2744280a d e - 16465680a b d e + 41164200a b d e +--R + +--R 3 3 11 7 2 4 12 6 5 13 5 +--R - 54885600a b d e + 41164200a b d e - 16465680a b d e +--R + +--R 6 14 4 +--R 2744280b d e +--R * +--R 4 +--R x +--R + +--R 6 9 9 5 10 8 4 2 11 7 +--R 1219680a d e - 7318080a b d e + 18295200a b d e +--R + +--R 3 3 12 6 2 4 13 5 5 14 4 +--R - 24393600a b d e + 18295200a b d e - 7318080a b d e +--R + +--R 6 15 3 +--R 1219680b d e +--R * +--R 3 +--R x +--R + +--R 6 10 8 5 11 7 4 2 12 6 +--R 365904a d e - 2195424a b d e + 5488560a b d e +--R + +--R 3 3 13 5 2 4 14 4 5 15 3 +--R - 7318080a b d e + 5488560a b d e - 2195424a b d e +--R + +--R 6 16 2 +--R 365904b d e +--R * +--R 2 +--R x +--R + +--R 6 11 7 5 12 6 4 2 13 5 3 3 14 4 +--R 66528a d e - 399168a b d e + 997920a b d e - 1330560a b d e +--R + +--R 2 4 15 3 5 16 2 6 17 +--R 997920a b d e - 399168a b d e + 66528b d e +--R * +--R x +--R + +--R 6 12 6 5 13 5 4 2 14 4 3 3 15 3 +--R 5544a d e - 33264a b d e + 83160a b d e - 110880a b d e +--R + +--R 2 4 16 2 5 17 6 18 +--R 83160a b d e - 33264a b d e + 5544b d +--R Type: Expression(Integer) +--E 368 + +--S 369 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^14 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R e x + 14d e x + 91d e x + 364d e x + 1001d e x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002d e x + 3003d e x + 3432d e x + 3003d e x + 2002d e x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001d e x + 364d e x + 91d e x + 14d e x + d +--R Type: Expression(Integer) +--E 370 + +--S 371 of 765 +r0:=1/13*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^13)+_ + 1/26*b*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^12)+_ + 5/286*b^2*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^3*(d+e*x)^11)+_ + 1/143*b^3*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^4*(d+e*x)^10)+_ + 1/429*b^4*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^5*(d+e*x)^9)+_ + 1/1716*b^5*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^6*(d+e*x)^8)+_ + 1/12012*b^6*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^7*(d+e*x)^7) +--R +--R +--R (2) +--R 12 6 12 11 6 12 5 11 +--R - b e x + (a b e - 13b d e )x +--R + +--R 2 10 6 11 5 12 2 4 10 +--R (- a b e + 13a b d e - 78b d e )x +--R + +--R 3 9 6 2 10 5 11 2 4 12 3 3 9 +--R (a b e - 13a b d e + 78a b d e - 286b d e )x +--R + +--R 4 8 6 3 9 5 2 10 2 4 11 3 3 12 4 2 8 +--R (- a b e + 13a b d e - 78a b d e + 286a b d e - 715b d e )x +--R + +--R 5 7 6 4 8 5 3 9 2 4 2 10 3 3 11 4 2 +--R a b e - 13a b d e + 78a b d e - 286a b d e + 715a b d e +--R + +--R 12 5 +--R - 1287b d e +--R * +--R 7 +--R x +--R + +--R 6 6 6 5 7 5 4 8 2 4 3 9 3 3 2 10 4 2 +--R - a b e + 13a b d e - 78a b d e + 286a b d e - 715a b d e +--R + +--R 11 5 12 6 +--R 1287a b d e - 1716b d +--R * +--R 6 +--R x +--R + +--R 7 5 6 6 6 5 5 7 2 4 4 8 3 3 +--R - 1715a b e + 11999a b d e - 35958a b d e + 59774a b d e +--R + +--R 3 9 4 2 2 10 5 11 6 +--R - 59345a b d e + 34749a b d e - 10296a b d +--R * +--R 5 +--R x +--R + +--R 8 4 6 7 5 5 6 6 2 4 5 7 3 3 +--R - 7294a b e + 49777a b d e - 144222a b d e + 228514a b d e +--R + +--R 4 8 4 2 3 9 5 2 10 6 +--R - 210925a b d e + 109395a b d e - 25740a b d +--R * +--R 4 +--R x +--R + +--R 9 3 6 8 4 5 7 5 2 4 6 6 3 3 +--R - 12726a b e + 85358a b d e - 241878a b d e + 372086a b d e +--R + +--R 5 7 4 2 4 8 5 3 9 6 +--R - 329615a b d e + 160875a b d e - 34320a b d +--R * +--R 3 +--R x +--R + +--R 10 2 6 9 3 5 8 4 2 4 7 5 3 3 +--R - 11298a b e + 74802a b d e - 208572a b d e + 314314a b d e +--R + +--R 6 6 4 2 5 7 5 4 8 6 +--R - 270985a b d e + 127413a b d e - 25740a b d +--R * +--R 2 +--R x +--R + +--R 11 6 10 2 5 9 3 2 4 8 4 3 3 +--R - 5082a b e + 33306a b d e - 91728a b d e + 136136a b d e +--R + +--R 7 5 4 2 6 6 5 5 7 6 +--R - 115115a b d e + 52767a b d e - 10296a b d +--R * +--R x +--R + +--R 12 6 11 5 10 2 2 4 9 3 3 3 +--R - 924a e + 6006a b d e - 16380a b d e + 24024a b d e +--R + +--R 8 4 4 2 7 5 5 6 6 6 +--R - 20020a b d e + 9009a b d e - 1716a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 20 6 19 5 2 2 18 4 3 3 17 +--R 12012a e - 84084a b d e + 252252a b d e - 420420a b d e +--R + +--R 3 4 4 16 2 5 5 15 6 6 14 7 7 13 +--R 420420a b d e - 252252a b d e + 84084a b d e - 12012b d e +--R * +--R 13 +--R x +--R + +--R 7 19 6 2 18 5 2 3 17 +--R 156156a d e - 1093092a b d e + 3279276a b d e +--R + +--R 4 3 4 16 3 4 5 15 2 5 6 14 +--R - 5465460a b d e + 5465460a b d e - 3279276a b d e +--R + +--R 6 7 13 7 8 12 +--R 1093092a b d e - 156156b d e +--R * +--R 12 +--R x +--R + +--R 7 2 18 6 3 17 5 2 4 16 +--R 936936a d e - 6558552a b d e + 19675656a b d e +--R + +--R 4 3 5 15 3 4 6 14 2 5 7 13 +--R - 32792760a b d e + 32792760a b d e - 19675656a b d e +--R + +--R 6 8 12 7 9 11 +--R 6558552a b d e - 936936b d e +--R * +--R 11 +--R x +--R + +--R 7 3 17 6 4 16 5 2 5 15 +--R 3435432a d e - 24048024a b d e + 72144072a b d e +--R + +--R 4 3 6 14 3 4 7 13 2 5 8 12 +--R - 120240120a b d e + 120240120a b d e - 72144072a b d e +--R + +--R 6 9 11 7 10 10 +--R 24048024a b d e - 3435432b d e +--R * +--R 10 +--R x +--R + +--R 7 4 16 6 5 15 5 2 6 14 +--R 8588580a d e - 60120060a b d e + 180360180a b d e +--R + +--R 4 3 7 13 3 4 8 12 2 5 9 11 +--R - 300600300a b d e + 300600300a b d e - 180360180a b d e +--R + +--R 6 10 10 7 11 9 +--R 60120060a b d e - 8588580b d e +--R * +--R 9 +--R x +--R + +--R 7 5 15 6 6 14 5 2 7 13 +--R 15459444a d e - 108216108a b d e + 324648324a b d e +--R + +--R 4 3 8 12 3 4 9 11 2 5 10 10 +--R - 541080540a b d e + 541080540a b d e - 324648324a b d e +--R + +--R 6 11 9 7 12 8 +--R 108216108a b d e - 15459444b d e +--R * +--R 8 +--R x +--R + +--R 7 6 14 6 7 13 5 2 8 12 +--R 20612592a d e - 144288144a b d e + 432864432a b d e +--R + +--R 4 3 9 11 3 4 10 10 2 5 11 9 +--R - 721440720a b d e + 721440720a b d e - 432864432a b d e +--R + +--R 6 12 8 7 13 7 +--R 144288144a b d e - 20612592b d e +--R * +--R 7 +--R x +--R + +--R 7 7 13 6 8 12 5 2 9 11 +--R 20612592a d e - 144288144a b d e + 432864432a b d e +--R + +--R 4 3 10 10 3 4 11 9 2 5 12 8 +--R - 721440720a b d e + 721440720a b d e - 432864432a b d e +--R + +--R 6 13 7 7 14 6 +--R 144288144a b d e - 20612592b d e +--R * +--R 6 +--R x +--R + +--R 7 8 12 6 9 11 5 2 10 10 +--R 15459444a d e - 108216108a b d e + 324648324a b d e +--R + +--R 4 3 11 9 3 4 12 8 2 5 13 7 +--R - 541080540a b d e + 541080540a b d e - 324648324a b d e +--R + +--R 6 14 6 7 15 5 +--R 108216108a b d e - 15459444b d e +--R * +--R 5 +--R x +--R + +--R 7 9 11 6 10 10 5 2 11 9 +--R 8588580a d e - 60120060a b d e + 180360180a b d e +--R + +--R 4 3 12 8 3 4 13 7 2 5 14 6 +--R - 300600300a b d e + 300600300a b d e - 180360180a b d e +--R + +--R 6 15 5 7 16 4 +--R 60120060a b d e - 8588580b d e +--R * +--R 4 +--R x +--R + +--R 7 10 10 6 11 9 5 2 12 8 +--R 3435432a d e - 24048024a b d e + 72144072a b d e +--R + +--R 4 3 13 7 3 4 14 6 2 5 15 5 +--R - 120240120a b d e + 120240120a b d e - 72144072a b d e +--R + +--R 6 16 4 7 17 3 +--R 24048024a b d e - 3435432b d e +--R * +--R 3 +--R x +--R + +--R 7 11 9 6 12 8 5 2 13 7 +--R 936936a d e - 6558552a b d e + 19675656a b d e +--R + +--R 4 3 14 6 3 4 15 5 2 5 16 4 +--R - 32792760a b d e + 32792760a b d e - 19675656a b d e +--R + +--R 6 17 3 7 18 2 +--R 6558552a b d e - 936936b d e +--R * +--R 2 +--R x +--R + +--R 7 12 8 6 13 7 5 2 14 6 +--R 156156a d e - 1093092a b d e + 3279276a b d e +--R + +--R 4 3 15 5 3 4 16 4 2 5 17 3 +--R - 5465460a b d e + 5465460a b d e - 3279276a b d e +--R + +--R 6 18 2 7 19 +--R 1093092a b d e - 156156b d e +--R * +--R x +--R + +--R 7 13 7 6 14 6 5 2 15 5 4 3 16 4 +--R 12012a d e - 84084a b d e + 252252a b d e - 420420a b d e +--R + +--R 3 4 17 3 2 5 18 2 6 19 7 20 +--R 420420a b d e - 252252a b d e + 84084a b d e - 12012b d +--R Type: Expression(Integer) +--E 371 + +--S 372 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^15 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 15 15 14 14 2 13 13 3 12 12 4 11 11 +--R e x + 15d e x + 105d e x + 455d e x + 1365d e x +--R + +--R 5 10 10 6 9 9 7 8 8 8 7 7 9 6 6 +--R 3003d e x + 5005d e x + 6435d e x + 6435d e x + 5005d e x +--R + +--R 10 5 5 11 4 4 12 3 3 13 2 2 14 15 +--R 3003d e x + 1365d e x + 455d e x + 105d e x + 15d e x + d +--R Type: Expression(Integer) +--E 373 + +--S 374 of 765 +r0:=-5/364*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^12)-_ + 5/1001*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^11)-1/14*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^14)-3/91*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^13)-3/2002*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^10)-3/8008*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^6*(d+e*x)^9)-1/24024*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x)^9) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 3003b e x + (- 16016a b e - 2002b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 36036a b e - 8008a b d e - 1001b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 43680a b e - 13104a b d e - 2912a b d e - 364b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 30030a b e - 10920a b d e - 3276a b d e - 728a b d e +--R + +--R 6 4 2 +--R - 91b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 11088a b e - 4620a b d e - 1680a b d e - 504a b d e +--R + +--R 5 4 2 6 5 +--R - 112a b d e - 14b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 1716a e - 792a b d e - 330a b d e - 120a b d e - 36a b d e +--R + +--R 5 5 6 6 +--R - 8a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 21 15 21 20 14 +--R 24024b e x + (24024a e + 336336b d e )x +--R + +--R 20 2 19 13 +--R (336336a d e + 2186184b d e )x +--R + +--R 2 19 3 18 12 +--R (2186184a d e + 8744736b d e )x +--R + +--R 3 18 4 17 11 +--R (8744736a d e + 24048024b d e )x +--R + +--R 4 17 5 16 10 +--R (24048024a d e + 48096048b d e )x +--R + +--R 5 16 6 15 9 +--R (48096048a d e + 72144072b d e )x +--R + +--R 6 15 7 14 8 +--R (72144072a d e + 82450368b d e )x +--R + +--R 7 14 8 13 7 +--R (82450368a d e + 72144072b d e )x +--R + +--R 8 13 9 12 6 +--R (72144072a d e + 48096048b d e )x +--R + +--R 9 12 10 11 5 +--R (48096048a d e + 24048024b d e )x +--R + +--R 10 11 11 10 4 +--R (24048024a d e + 8744736b d e )x +--R + +--R 11 10 12 9 3 12 9 13 8 2 +--R (8744736a d e + 2186184b d e )x + (2186184a d e + 336336b d e )x +--R + +--R 13 8 14 7 14 7 +--R (336336a d e + 24024b d e )x + 24024a d e +--R Type: Expression(Integer) +--E 374 + +--S 375 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^16 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 16 16 15 15 2 14 14 3 13 13 4 12 12 +--R e x + 16d e x + 120d e x + 560d e x + 1820d e x +--R + +--R 5 11 11 6 10 10 7 9 9 8 8 8 9 7 7 +--R 4368d e x + 8008d e x + 11440d e x + 12870d e x + 11440d e x +--R + +--R 10 6 6 11 5 5 12 4 4 13 3 3 14 2 2 +--R 8008d e x + 4368d e x + 1820d e x + 560d e x + 120d e x +--R + +--R 15 16 +--R 16d e x + d +--R Type: Expression(Integer) +--E 376 + +--S 377 of 765 +r0:=-1/91*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^13)-_ + 1/273*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^12)-1/15*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^15)-1/35*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^14)-1/1001*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^11)-2/9009*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^6*(d+e*x)^10)-1/45045*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x)^10) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 5005b e x + (- 27027a b e - 3003b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 61425a b e - 12285a b d e - 1365b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 75075a b e - 20475a b d e - 4095a b d e - 455b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 51975a b e - 17325a b d e - 4725a b d e - 945a b d e +--R + +--R 6 4 2 +--R - 105b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 19305a b e - 7425a b d e - 2475a b d e - 675a b d e +--R + +--R 5 4 2 6 5 +--R - 135a b d e - 15b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 3003a e - 1287a b d e - 495a b d e - 165a b d e - 45a b d e +--R + +--R 5 5 6 6 +--R - 9a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 22 16 22 21 15 +--R 45045b e x + (45045a e + 675675b d e )x +--R + +--R 21 2 20 14 +--R (675675a d e + 4729725b d e )x +--R + +--R 2 20 3 19 13 +--R (4729725a d e + 20495475b d e )x +--R + +--R 3 19 4 18 12 +--R (20495475a d e + 61486425b d e )x +--R + +--R 4 18 5 17 11 +--R (61486425a d e + 135270135b d e )x +--R + +--R 5 17 6 16 10 +--R (135270135a d e + 225450225b d e )x +--R + +--R 6 16 7 15 9 +--R (225450225a d e + 289864575b d e )x +--R + +--R 7 15 8 14 8 +--R (289864575a d e + 289864575b d e )x +--R + +--R 8 14 9 13 7 +--R (289864575a d e + 225450225b d e )x +--R + +--R 9 13 10 12 6 +--R (225450225a d e + 135270135b d e )x +--R + +--R 10 12 11 11 5 +--R (135270135a d e + 61486425b d e )x +--R + +--R 11 11 12 10 4 +--R (61486425a d e + 20495475b d e )x +--R + +--R 12 10 13 9 3 +--R (20495475a d e + 4729725b d e )x +--R + +--R 13 9 14 8 2 14 8 15 7 +--R (4729725a d e + 675675b d e )x + (675675a d e + 45045b d e )x +--R + +--R 15 7 +--R 45045a d e +--R Type: Expression(Integer) +--E 377 + +--S 378 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^17 +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 17 17 16 16 2 15 15 3 14 14 4 13 13 +--R e x + 17d e x + 136d e x + 680d e x + 2380d e x +--R + +--R 5 12 12 6 11 11 7 10 10 8 9 9 9 8 8 +--R 6188d e x + 12376d e x + 19448d e x + 24310d e x + 24310d e x +--R + +--R 10 7 7 11 6 6 12 5 5 13 4 4 14 3 3 +--R 19448d e x + 12376d e x + 6188d e x + 2380d e x + 680d e x +--R + +--R 15 2 2 16 17 +--R 136d e x + 17d e x + d +--R Type: Expression(Integer) +--E 379 + +--S 380 of 765 +r0:=-1/112*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^14)-_ + 1/364*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^13)-1/16*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^16)-1/40*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^15)-1/1456*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*(d+e*x)^12)-1/7280*b^5*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^6*(d+e*x)^11)-1/80080*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/_ + (e^7*(a+b*x)*(d+e*x)^11) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 8008b e x + (- 43680a b e - 4368b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 100100a b e - 18200a b d e - 1820b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 123200a b e - 30800a b d e - 5600a b d e - 560b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 85800a b e - 26400a b d e - 6600a b d e - 1200a b d e +--R + +--R 6 4 2 +--R - 120b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 32032a b e - 11440a b d e - 3520a b d e - 880a b d e +--R + +--R 5 4 2 6 5 +--R - 160a b d e - 16b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 5005a e - 2002a b d e - 715a b d e - 220a b d e - 55a b d e +--R + +--R 5 5 6 6 +--R - 10a b d e - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 23 17 23 22 16 +--R 80080b e x + (80080a e + 1281280b d e )x +--R + +--R 22 2 21 15 +--R (1281280a d e + 9609600b d e )x +--R + +--R 2 21 3 20 14 +--R (9609600a d e + 44844800b d e )x +--R + +--R 3 20 4 19 13 +--R (44844800a d e + 145745600b d e )x +--R + +--R 4 19 5 18 12 +--R (145745600a d e + 349789440b d e )x +--R + +--R 5 18 6 17 11 +--R (349789440a d e + 641280640b d e )x +--R + +--R 6 17 7 16 10 +--R (641280640a d e + 916115200b d e )x +--R + +--R 7 16 8 15 9 +--R (916115200a d e + 1030629600b d e )x +--R + +--R 8 15 9 14 8 +--R (1030629600a d e + 916115200b d e )x +--R + +--R 9 14 10 13 7 +--R (916115200a d e + 641280640b d e )x +--R + +--R 10 13 11 12 6 +--R (641280640a d e + 349789440b d e )x +--R + +--R 11 12 12 11 5 +--R (349789440a d e + 145745600b d e )x +--R + +--R 12 11 13 10 4 +--R (145745600a d e + 44844800b d e )x +--R + +--R 13 10 14 9 3 +--R (44844800a d e + 9609600b d e )x +--R + +--R 14 9 15 8 2 15 8 16 7 +--R (9609600a d e + 1281280b d e )x + (1281280a d e + 80080b d e )x +--R + +--R 16 7 +--R 80080a d e +--R Type: Expression(Integer) +--E 380 + +--S 381 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 of 765 +t0:=(a+b*x)*(d+e*x)^m/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R m +--R (b x + a)(e x + d) +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 382 + +--S 383 of 765 +r0:=(a+b*x)*(d+e*x)^(1+m)/(e*(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R m + 1 +--R (b x + a)(e x + d) +--R (2) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e m + e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 383 + +--S 384 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 of 765 +t0:=(a+b*x)*(d+e*x)^4/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 385 + +--S 386 of 765 +r0:=1/5*(a+b*x)*(d+e*x)^5/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 6 5 4 5 4 2 3 4 +--R b e x + (a e + 5b d e )x + (5a d e + 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a d e + 10b d e )x + (10a d e + 5b d e)x + (5a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 386 + +--S 387 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 765 +t0:=(a+b*x)*(d+e*x)^3/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 388 + +--S 389 of 765 +r0:=1/4*(a+b*x)*(d+e*x)^4/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R / +--R +------------------+ +--R | 2 2 2 +--R 4e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 389 + +--S 390 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 765 +t0:=(a+b*x)*(d+e*x)^2/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R b e x + (a e + 2b d e)x + (2a d e + b d )x + a d +--R (1) ---------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 391 + +--S 392 of 765 +r0:=1/3*(a+b*x)*(d+e*x)^3/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R ---------------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 392 + +--S 393 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 765 +t0:=(a+b*x)*(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +--R b e x + (a e + b d)x + a d +--R (1) --------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 765 +r0:=d*x*(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2)+1/2*e*x^2*(a+b*x)/_ + sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 2 +--R b e x + (a e + 2b d)x + 2a d x +--R (2) -------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 2\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 395 + +--S 396 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 of 765 +t0:=(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R b x + a +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 765 +r0:=sqrt(a^2+2*a*b*x+b^2*x^2)/b +--R +--R +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (2) --------------------- +--R b +--R Type: Expression(Integer) +--E 398 + +--S 399 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 of 765 +t0:=(a+b*x)/((d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (e x + d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 400 + +--S 401 of 765 +r0:=(a+b*x)*log(d+e*x)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b x + a)log(e x + d) +--R (2) ---------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 765 +t0:=(a+b*x)/((d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (e x + 2d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 765 +r0:=(-a-b*x)/(e*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) -------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (e x + d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 404 + +--S 405 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 765 +t0:=(a+b*x)/((d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 765 +r0:=1/2*(-a-b*x)/(e*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) -------------------------------------------- +--R +------------------+ +--R 3 2 2 2 | 2 2 2 +--R (2e x + 4d e x + 2d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 407 + +--S 408 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 765 +t0:=(a+b*x)/((d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 4 4 3 3 2 2 2 3 4 | 2 2 2 +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 765 +r0:=1/3*(-a-b*x)/(e*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) ------------------------------------------------------ +--R +------------------+ +--R 4 3 3 2 2 2 3 | 2 2 2 +--R (3e x + 9d e x + 9d e x + 3d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 of 765 +t0:=(a+b*x)/((d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R b x + a +--R ------------------------------------------------------------------------- +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 412 + +--S 413 of 765 +r0:=1/4*(-a-b*x)/(e*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - b x - a +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R 5 4 4 3 2 3 2 3 2 4 | 2 2 2 +--R (4e x + 16d e x + 24d e x + 16d e x + 4d e)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 765 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 415 + +--S 416 of 765 +r0:=2*e*(b*d-a*e)*(a+b*x)*(d+e*x)^2/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 4/3*e*(a+b*x)*(d+e*x)^3/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^4/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+4*e*(b*d-a*e)^3*(a+b*x)*_ + log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^2*(b*d-a*e)^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 12a b e + 36a b d e - 36a b d e + 12b d e)x - 12a e +--R + +--R 3 3 2 2 2 2 3 3 +--R 36a b d e - 36a b d e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b e x + (- 2a b e + 6b d e )x + (6a b e - 18a b d e + 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (24a b e - 60a b d e + 42a b d e - 2b d e)x + 12a e - 24a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 6a b d e + 10a b d e - 3b d +--R / +--R +------------------+ +--R 5 | 2 2 2 +--R 3b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 416 + +--S 417 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 765 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 418 + +--S 419 of 765 +r0:=3/2*e*(a+b*x)*(d+e*x)^2/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-(d+e*x)^3/_ + (b*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/_ + (b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b e - 12a b d e + 6b d e)x + 6a e - 12a b d e + 6a b d e) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R b e x + (- 3a b e + 6b d e )x + (- 12a b e + 18a b d e - 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 6a e + 6a b d e + 3a b d e - 2b d +--R / +--R +------------------+ +--R 4 | 2 2 2 +--R 2b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 765 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 765 +r0:=-(d+e*x)^2/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)*(a+b*x)*_ + log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((- 2a b e + 2b d e)x - 2a e + 2a b d e)log(b x + a) + b e x +--R + +--R 2 2 2 2 2 2 +--R (4a b e - 2b d e)x + 2a e - b d +--R / +--R +------------------+ +--R 3 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 765 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 765 +r0:=(-d-e*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(a+b*x)*log(a+b*x)/_ + (b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b e x + a e)log(b x + a) - b e x - b d +--R (2) --------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 425 + +--S 426 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 of 765 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 765 +r0:=(-1)/(b*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (2) - ---------------------- +--R +------------------+ +--R | 2 2 2 +--R b\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 428 + +--S 429 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 of 765 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R +------------------+ +--R 2 | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 430 + +--S 431 of 765 +r0:=(-1)/((b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(a+b*x)*log(a+b*x)/_ + ((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(a+b*x)*log(d+e*x)/_ + ((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (b e x + a e)log(e x + d) + (- b e x - a e)log(b x + a) + a e - b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R 2 2 2 2 | 2 2 2 +--R (a e - 2a b d e + b d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 765 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R +------------------+ +--R 2 3 2 2 2 2 | 2 2 2 +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 433 + +--S 434 of 765 +r0:=-2*b/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/((b*d-a*e)*(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-2*b*e*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+2*b*e*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (- 2b e x + (- 2a b e - 2b d e)x - 2a b d e)log(e x + d) +--R + +--R 2 2 2 2 2 +--R (2b e x + (2a b e + 2b d e)x + 2a b d e)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b e + 2b d e)x - a e + b d +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 2 3 +--R (a e - 3a b d e + 3a b d e - b d e)x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 765 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 765 +r0:=-3*b^2/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2/((b*d-a*e)*(d+e*x)^2*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+3/2*b/((b*d-a*e)^2*(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-3*b^2*e*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*b^2*e*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 2 2 2 +--R (6b e x + (6a b e + 12b d e )x + (12a b d e + 6b d e)x + 6a b d e) +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b e x + (- 6a b e - 12b d e )x + (- 12a b d e - 6b d e)x +--R + +--R 2 2 +--R - 6a b d e +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (3a b e + 6a b d e - 9b d e)x - a e +--R + +--R 2 2 2 2 3 3 +--R 6a b d e - 3a b d e - 2b d +--R / +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (2a e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4 2 4 +--R (4a d e - 16a b d e + 24a b d e - 16a b d e + 4b d e)x + 2a d e +--R + +--R 3 3 3 2 2 4 2 3 5 4 6 +--R - 8a b d e + 12a b d e - 8a b d e + 2b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 765 +t0:=(a+b*x)*(d+e*x)^5/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 765 +r0:=-5/6*e*(a+b*x)*(d+e*x)^4/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^5/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5*e^3*(a+b*x)*_ + (d+e*x)^2/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-10/3*e^2*(d+e*x)^3/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10*e^3*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^6*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10*e^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6 +--R +--R +--R (2) +--R 2 3 5 4 4 5 2 3 3 +--R (60a b e - 120a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (180a b e - 360a b d e + 180a b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 5 5 4 4 +--R (180a b e - 360a b d e + 180a b d e )x + 60a e - 120a b d e +--R + +--R 3 2 2 3 +--R 60a b d e +--R * +--R log(b x + a) +--R + +--R 5 5 5 4 5 5 4 4 +--R 3b e x + (- 15a b e + 30b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 170a b e + 280a b d e - 80b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 330a b e + 480a b d e - 60a b d e - 60b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 240a b e + 300a b d e + 30a b d e - 60a b d e - 15b d e)x - 60a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b d e + 30a b d e - 20a b d e - 5a b d e - 2b d +--R / +--R +------------------+ +--R 8 2 7 2 6 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 440 + +--S 441 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 441 + +)clear all + +--S 442 of 765 +t0:=(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 765 +r0:=-2/3*e*(a+b*x)*(d+e*x)^3/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^4/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-2*e^2*(d+e*x)^2/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^3*(b*d-a*e)*(a+b*x)*log(a+b*x)/(b^5*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5 +--R +--R +--R (2) +--R 3 4 4 3 3 2 2 4 3 3 2 +--R (- 12a b e + 12b d e )x + (- 36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 4 4 3 3 +--R (- 36a b e + 36a b d e )x - 12a e + 12a b d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b e x + (34a b e - 22b d e )x + (66a b e - 30a b d e - 18b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 2 2 2 2 +--R (48a b e - 12a b d e - 18a b d e - 6b d e)x + 12a e - 6a b d e +--R + +--R 3 3 4 4 +--R - 2a b d e - b d +--R / +--R +------------------+ +--R 7 2 6 2 5 | 2 2 2 +--R (3b x + 6a b x + 3a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 443 + +--S 444 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 765 +t0:=(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 765 +r0:=-1/2*e*(a+b*x)*(d+e*x)^2/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^3/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2*(d+e*x)/(b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(b x + a) - 11b e x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (- 15a b e - 18b d e )x + (- 6a b e - 18a b d e - 9b d e)x +--R + +--R 2 2 2 2 3 3 +--R - 6a b d e - 3a b d e - 2b d +--R / +--R +------------------+ +--R 6 2 5 2 4 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 446 + +--S 447 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 765 +t0:=(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 448 + +--S 449 of 765 +r0:=-1/3*(d+e*x)^3/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R ----------------------------------------------------------------------------- +--R +------------------+ +--R 2 3 2 2 2 3 2 | 2 2 2 +--R ((3a b e - 3b d)x + (6a b e - 6a b d)x + 3a e - 3a b d)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 765 +t0:=(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 765 +r0:=-1/6*e*(a+b*x)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 1/3*(-d-e*x)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R - 3b e x - a e - 2b d +--R (2) ---------------------------------------------- +--R +------------------+ +--R 4 2 3 2 2 | 2 2 2 +--R (6b x + 12a b x + 6a b )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 765 +t0:=(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 1 +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 765 +r0:=(-1/3)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (2) - -------------------------------------------- +--R +------------------+ +--R 3 2 2 2 | 2 2 2 +--R (3b x + 6a b x + 3a b)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 455 + +--S 456 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 456 + +)clear all + +--S 457 of 765 +t0:=(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 765 +r0:=(-1/3)/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2*e*(a+b*x)/_ + ((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-e^2/((b*d-a*e)^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b e x + 18a b e x + 18a b e x + 6a e )log(e x + d) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (- 6b e x - 18a b e x - 18a b e x - 6a e )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b e - 6b d e )x + (15a b e - 18a b d e + 3b d e)x + 11a e +--R + +--R 2 2 2 2 3 3 +--R - 18a b d e + 9a b d e - 2b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (6a b e - 24a b d e + 36a b d e - 24a b d e + 6b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 6 4 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12a b d )x + 6a e +--R + +--R 5 3 4 2 2 2 3 3 3 2 4 4 +--R - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 458 + +--S 459 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 765 +t0:=(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 460 + +--S 461 of 765 +r0:=-4/3*b/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+2*b*e*(a+b*x)/_ + ((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/((b*d-a*e)*(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))-4*b*e^2/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-4*b*e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+4*b*e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R - 12b e x + (- 36a b e - 12b d e )x + (- 36a b e - 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (- 12a b e - 36a b d e )x - 12a b d e +--R * +--R log(e x + d) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 12b e x + (36a b e + 12b d e )x + (36a b e + 36a b d e )x +--R + +--R 3 4 2 2 3 3 3 +--R (12a b e + 36a b d e )x + 12a b d e +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R (- 12a b e + 12b d e )x + (- 30a b e + 24a b d e + 6b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 22a b e + 6a b d e + 18a b d e - 2b d e)x - 3a e - 10a b d e +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b d e - 6a b d e + b d +--R / +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 3a b e - 15a b d e + 30a b d e - 30a b d e + 15a b d e +--R + +--R 7 5 +--R - 3b d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 6 5 7 6 2 +--R (6a b e - 27a b d e + 45a b d e - 30a b d e + 9a b d e - 3b d )x +--R + +--R 7 6 6 5 4 3 3 3 3 4 4 2 2 5 5 6 6 +--R (3a e - 9a b d e + 30a b d e - 45a b d e + 27a b d e - 6a b d )x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 2 5 6 +--R 3a d e - 15a b d e + 30a b d e - 30a b d e + 15a b d e - 3a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 765 +t0:=(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 463 + +--S 464 of 765 +r0:=-10/3*b^2/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+5*b^2*e*(a+b*x)/_ + ((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/2/((b*d-a*e)*(d+e*x)^2*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2))+5/2*b/((b*d-a*e)^2*(d+e*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2))-10*b^2*e^2/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 10*b^2*e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 10*b^2*e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 60b e x + (180a b e + 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (180a b e + 360a b d e + 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (60a b e + 360a b d e + 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (120a b d e + 180a b d e )x + 60a b d e +--R * +--R log(e x + d) +--R + +--R 5 5 5 4 5 5 4 4 +--R - 60b e x + (- 180a b e - 120b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 180a b e - 360a b d e - 60b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (- 60a b e - 360a b d e - 180a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (- 120a b d e - 180a b d e )x - 60a b d e +--R * +--R log(b x + a) +--R + +--R 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R (60a b e - 60b d e )x + (150a b e - 60a b d e - 90b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (110a b e + 120a b d e - 210a b d e - 20b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (15a b e + 160a b d e - 120a b d e - 60a b d e + 5b d e)x - 3a e +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 30a b d e + 20a b d e - 60a b d e + 15a b d e - 2b d +--R / +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 2 6 4 4 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 3 8 6 2 +--R - 36a b d e + 6b d e +--R * +--R 4 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R 12a b e - 60a b d e + 108a b d e - 60a b d e - 60a b d e +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 108a b d e - 60a b d e + 12b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R 6a e - 12a b d e - 48a b d e + 204a b d e - 300a b d e +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R 204a b d e - 48a b d e - 12a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R 12a d e - 60a b d e + 108a b d e - 60a b d e - 60a b d e +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 108a b d e - 60a b d e + 12a b d +--R * +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 3 5 7 2 6 8 +--R - 36a b d e + 6a b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 464 + +--S 465 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 466 + +--S 467 of 765 +r0:=-2/9*(b*d-a*e)^3*(d+e*x)^(9/2)/e^4+6/11*b*(b*d-a*e)^2*(d+e*x)^(11/2)/e^4-_ + 6/13*b^2*(b*d-a*e)*(d+e*x)^(13/2)/e^4+2/15*b^3*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 3 7 7 2 7 3 6 6 +--R 858b e x + (2970a b e + 3036b d e )x +--R + +--R 2 7 2 6 3 2 5 5 +--R (3510a b e + 10800a b d e + 3708b d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (1430a e + 13260a b d e + 13740a b d e + 1600b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (5720a d e + 17940a b d e + 6360a b d e + 10b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (8580a d e + 9360a b d e + 90a b d e - 12b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 3 4 3 +--R (5720a d e + 390a b d e - 120a b d e + 16b d e)x + 1430a d e +--R + +--R 2 5 2 2 6 3 7 +--R - 780a b d e + 240a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 467 + +--S 468 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 469 + +--S 470 of 765 +r0:=-2/7*(b*d-a*e)^3*(d+e*x)^(7/2)/e^4+2/3*b*(b*d-a*e)^2*(d+e*x)^(9/2)/e^4-_ + 6/11*b^2*(b*d-a*e)*(d+e*x)^(11/2)/e^4+2/13*b^3*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 462b e x + (1638a b e + 1134b d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (2002a b e + 4186a b d e + 742b d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (858a e + 5434a b d e + 2938a b d e + 10b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (2574a d e + 4290a b d e + 78a b d e - 12b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (2574a d e + 286a b d e - 104a b d e + 16b d e)x + 858a d e +--R + +--R 2 4 2 2 5 3 6 +--R - 572a b d e + 208a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3003e +--R Type: Expression(Integer) +--E 470 + +--S 471 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 471 + +)clear all + +--S 472 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 472 + +--S 473 of 765 +r0:=-2/5*(b*d-a*e)^3*(d+e*x)^(5/2)/e^4+6/7*b*(b*d-a*e)^2*(d+e*x)^(7/2)/e^4-_ + 2/3*b^2*(b*d-a*e)*(d+e*x)^(9/2)/e^4+2/11*b^3*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 210b e x + (770a b e + 280b d e )x +--R + +--R 2 5 2 4 3 2 3 3 +--R (990a b e + 1100a b d e + 10b d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (462a e + 1584a b d e + 66a b d e - 12b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (924a d e + 198a b d e - 88a b d e + 16b d e)x + 462a d e +--R + +--R 2 3 2 2 4 3 5 +--R - 396a b d e + 176a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 1155e +--R Type: Expression(Integer) +--E 473 + +--S 474 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 474 + +)clear all + +--S 475 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (1) (b x + 3a b x + 3a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 475 + +--S 476 of 765 +r0:=-2/3*(b*d-a*e)^3*(d+e*x)^(3/2)/e^4+6/5*b*(b*d-a*e)^2*(d+e*x)^(5/2)/e^4-_ + 6/7*b^2*(b*d-a*e)*(d+e*x)^(7/2)/e^4+2/9*b^3*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 3 4 4 2 4 3 3 3 +--R 70b e x + (270a b e + 10b d e )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (378a b e + 54a b d e - 12b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 +--R (210a e + 126a b d e - 72a b d e + 16b d e)x + 210a d e +--R + +--R 2 2 2 2 3 3 4 +--R - 252a b d e + 144a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 476 + +--S 477 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 478 + +--S 479 of 765 +r0:=2*b*(b*d-a*e)^2*(d+e*x)^(3/2)/e^4-6/5*b^2*(b*d-a*e)*(d+e*x)^(5/2)/e^4+_ + 2/7*b^3*(d+e*x)^(7/2)/e^4-2*(b*d-a*e)^3*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 10b e x + (42a b e - 12b d e )x + (70a b e - 56a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R 70a e - 140a b d e + 112a b d e - 32b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 35e +--R Type: Expression(Integer) +--E 479 + +--S 480 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 481 + +--S 482 of 765 +r0:=-2*b^2*(b*d-a*e)*(d+e*x)^(3/2)/e^4+2/5*b^3*(d+e*x)^(5/2)/e^4+_ + 2*(b*d-a*e)^3/(e^4*sqrt(d+e*x))+6*b*(b*d-a*e)^2*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (10a b e - 4b d e )x + (30a b e - 40a b d e + 16b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 10a e + 60a b d e - 80a b d e + 32b d +--R / +--R 4 +-------+ +--R 5e \|e x + d +--R Type: Expression(Integer) +--E 482 + +--S 483 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 484 + +--S 485 of 765 +r0:=2/3*(b*d-a*e)^3/(e^4*(d+e*x)^(3/2))+2/3*b^3*(d+e*x)^(3/2)/e^4-_ + 6*b*(b*d-a*e)^2/(e^4*sqrt(d+e*x))-6*b^2*(b*d-a*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b e x + (18a b e - 12b d e )x + (- 18a b e + 72a b d e - 48b d e)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a e - 12a b d e + 48a b d e - 32b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 485 + +--S 486 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 486 + +)clear all + +--S 487 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 487 + +--S 488 of 765 +r0:=2/5*(b*d-a*e)^3/(e^4*(d+e*x)^(5/2))-2*b*(b*d-a*e)^2/(e^4*(d+e*x)^(3/2))+_ + 6*b^2*(b*d-a*e)/(e^4*sqrt(d+e*x))+2*b^3*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R 10b e x + (- 30a b e + 60b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 10a b e - 40a b d e + 80b d e)x - 2a e - 4a b d e - 16a b d e +--R + +--R 3 3 +--R 32b d +--R / +--R 6 2 5 2 4 +-------+ +--R (5e x + 10d e x + 5d e )\|e x + d +--R Type: Expression(Integer) +--E 488 + +--S 489 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 489 + +)clear all + +--S 490 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b e x + (5a b e + 3b d e )x + (10a b e + 15a b d e + 3b d e)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b e + 30a b d e + 15a b d e + b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b e + 30a b d e + 30a b d e + 5a b d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a e + 15a b d e + 30a b d e + 10a b d )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a d e + 15a b d e + 10a b d )x + (3a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 490 + +--S 491 of 765 +r0:=-2/9*(b*d-a*e)^5*(d+e*x)^(9/2)/e^6+10/11*b*(b*d-a*e)^4*(d+e*x)^(11/2)/_ + e^6-20/13*b^2*(b*d-a*e)^3*(d+e*x)^(13/2)/e^6+4/3*b^3*(b*d-a*e)^2*(d+_ + e*x)^(15/2)/e^6-10/17*b^4*(b*d-a*e)*(d+e*x)^(17/2)/e^6+2/19*b^5*(d+_ + e*x)^(19/2)/e^6 +--R +--R +--R (2) +--R 5 9 9 4 9 5 8 8 +--R 43758b e x + (244530a b e + 149292b d e )x +--R + +--R 2 3 9 4 8 5 2 7 7 +--R (554268a b e + 847704a b d e + 173316b d e )x +--R + +--R 3 2 9 2 3 8 4 2 7 5 3 6 6 +--R (639540a b e + 1961256a b d e + 1005708a b d e + 69168b d e )x +--R + +--R 4 9 3 2 8 2 3 2 7 4 3 6 +--R 377910a b e + 2325600a b d e + 2395368a b d e + 414504a b d e +--R + +--R 5 4 5 +--R 126b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 8 3 2 2 7 2 3 3 6 +--R 92378a e + 1427660a b d e + 2958680a b d e + 1033600a b d e +--R + +--R 4 4 5 5 5 4 +--R 1330a b d e - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 +--R 369512a d e + 1931540a b d e + 1369520a b d e + 6460a b d e +--R + +--R 4 5 4 5 6 3 +--R - 1520a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 +--R 554268a d e + 1007760a b d e + 19380a b d e - 7752a b d e +--R + +--R 4 6 3 5 7 2 +--R 1824a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 +--R 369512a d e + 41990a b d e - 25840a b d e + 10336a b d e +--R + +--R 4 7 2 5 8 +--R - 2432a b d e + 256b d e +--R * +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 +--R 92378a d e - 83980a b d e + 51680a b d e - 20672a b d e +--R + +--R 4 8 5 9 +--R 4864a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 415701e +--R Type: Expression(Integer) +--E 491 + +--S 492 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 493 + +--S 494 of 765 +r0:=-2/7*(b*d-a*e)^5*(d+e*x)^(7/2)/e^6+10/9*b*(b*d-a*e)^4*(d+e*x)^(9/2)/e^6-_ + 20/11*b^2*(b*d-a*e)^3*(d+e*x)^(11/2)/e^6+20/13*b^3*(b*d-a*e)^2*(d+_ + e*x)^(13/2)/e^6-2/3*b^4*(b*d-a*e)*(d+e*x)^(15/2)/e^6+2/17*b^5*(d+_ + e*x)^(17/2)/e^6 +--R +--R +--R (2) +--R 5 8 8 4 8 5 7 7 +--R 18018b e x + (102102a b e + 42042b d e )x +--R + +--R 2 3 8 4 7 5 2 6 6 +--R (235620a b e + 243474a b d e + 25410b d e )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 5 +--R (278460a b e + 578340a b d e + 152082a b d e + 126b d e )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 +--R 170170a b e + 711620a b d e + 378420a b d e + 1190a b d e +--R + +--R 5 4 4 +--R - 140b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 +--R 43758a e + 461890a b d e + 499460a b d e + 5100a b d e +--R + +--R 4 4 4 5 5 3 +--R - 1360a b d e + 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 +--R 131274a d e + 364650a b d e + 13260a b d e - 6120a b d e +--R + +--R 4 5 3 5 6 2 +--R 1632a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 +--R 131274a d e + 24310a b d e - 17680a b d e + 8160a b d e +--R + +--R 4 6 2 5 7 +--R - 2176a b d e + 256b d e +--R * +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 +--R 43758a d e - 48620a b d e + 35360a b d e - 16320a b d e +--R + +--R 4 7 5 8 +--R 4352a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 153153e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 496 + +--S 497 of 765 +r0:=-2/5*(b*d-a*e)^5*(d+e*x)^(5/2)/e^6+10/7*b*(b*d-a*e)^4*(d+e*x)^(7/2)/e^6-_ + 20/9*b^2*(b*d-a*e)^3*(d+e*x)^(9/2)/e^6+20/11*b^3*(b*d-a*e)^2*(d+_ + e*x)^(11/2)/e^6-10/13*b^4*(b*d-a*e)*(d+e*x)^(13/2)/e^6+2/15*b^5*(d+_ + e*x)^(15/2)/e^6 +--R +--R +--R (2) +--R 5 7 7 4 7 5 6 6 +--R 6006b e x + (34650a b e + 7392b d e )x +--R + +--R 2 3 7 4 6 5 2 5 5 +--R (81900a b e + 44100a b d e + 126b d e )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (100100a b e + 109200a b d e + 1050a b d e - 140b d e )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 +--R 64350a b e + 143000a b d e + 3900a b d e - 1200a b d e +--R + +--R 5 4 3 +--R 160b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 18018a e + 102960a b d e + 8580a b d e - 4680a b d e +--R + +--R 4 4 3 5 5 2 +--R 1440a b d e - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 +--R 36036a d e + 12870a b d e - 11440a b d e + 6240a b d e +--R + +--R 4 5 2 5 6 +--R - 1920a b d e + 256b d e +--R * +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 +--R 18018a d e - 25740a b d e + 22880a b d e - 12480a b d e +--R + +--R 4 6 5 7 +--R 3840a b d e - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 45045e +--R Type: Expression(Integer) +--E 497 + +--S 498 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 499 + +--S 500 of 765 +r0:=-2/3*(b*d-a*e)^5*(d+e*x)^(3/2)/e^6+2*b*(b*d-a*e)^4*(d+e*x)^(5/2)/e^6-_ + 20/7*b^2*(b*d-a*e)^3*(d+e*x)^(7/2)/e^6+20/9*b^3*(b*d-a*e)^2*(d+_ + e*x)^(9/2)/e^6-10/11*b^4*(b*d-a*e)*(d+e*x)^(11/2)/e^6+2/13*b^5*(d+_ + e*x)^(13/2)/e^6 +--R +--R +--R (2) +--R 5 6 6 4 6 5 5 5 +--R 1386b e x + (8190a b e + 126b d e )x +--R + +--R 2 3 6 4 5 5 2 4 4 +--R (20020a b e + 910a b d e - 140b d e )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (25740a b e + 2860a b d e - 1040a b d e + 160b d e )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 18018a b e + 5148a b d e - 3432a b d e + 1248a b d e +--R + +--R 5 4 2 +--R - 192b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 6006a e + 6006a b d e - 6864a b d e + 4576a b d e +--R + +--R 4 4 2 5 5 +--R - 1664a b d e + 256b d e +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 6006a d e - 12012a b d e + 13728a b d e - 9152a b d e + 3328a b d e +--R + +--R 5 6 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 9009e +--R Type: Expression(Integer) +--E 500 + +--S 501 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 501 + +)clear all + +--S 502 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(d+e*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 502 + +--S 503 of 765 +r0:=10/3*b*(b*d-a*e)^4*(d+e*x)^(3/2)/e^6-4*b^2*(b*d-a*e)^3*(d+e*x)^(5/2)/e^6+_ + 20/7*b^3*(b*d-a*e)^2*(d+e*x)^(7/2)/e^6-10/9*b^4*(b*d-a*e)*_ + (d+e*x)^(9/2)/e^6+2/11*b^5*(d+e*x)^(11/2)/e^6-2*(b*d-a*e)^5*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 126b e x + (770a b e - 140b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (1980a b e - 880a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (2772a b e - 2376a b d e + 1056a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 1386a e - 4620a b d e + 7392a b d e - 6336a b d e + 2816a b d e +--R + +--R 5 5 +--R - 512b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 +--R 693e +--R Type: Expression(Integer) +--E 503 + +--S 504 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 504 + +)clear all + +--S 505 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 505 + +--S 506 of 765 +r0:=-20/3*b^2*(b*d-a*e)^3*(d+e*x)^(3/2)/e^6+4*b^3*(b*d-a*e)^2*_ + (d+e*x)^(5/2)/e^6-10/7*b^4*(b*d-a*e)*(d+e*x)^(7/2)/e^6+2/9*b^5*_ + (d+e*x)^(9/2)/e^6+2*(b*d-a*e)^5/(e^6*sqrt(d+e*x))+10*b*(b*d-a*e)^4*_ + sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 14b e x + (90a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (252a b e - 144a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 504a b d e + 288a b d e - 64b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (630a b e - 1680a b d e + 2016a b d e - 1152a b d e + 256b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 126a e + 1260a b d e - 3360a b d e + 4032a b d e - 2304a b d e +--R + +--R 5 5 +--R 512b d +--R / +--R 6 +-------+ +--R 63e \|e x + d +--R Type: Expression(Integer) +--E 506 + +--S 507 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 508 + +--S 509 of 765 +r0:=2/3*(b*d-a*e)^5/(e^6*(d+e*x)^(3/2))+20/3*b^3*(b*d-a*e)^2*_ + (d+e*x)^(3/2)/e^6-2*b^4*(b*d-a*e)*(d+e*x)^(5/2)/e^6+2/7*b^5*_ + (d+e*x)^(7/2)/e^6-10*b*(b*d-a*e)^4/(e^6*sqrt(d+e*x))-20*b^2*_ + (b*d-a*e)^3*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (42a b e - 12b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b e - 840a b d e + 672a b d e - 192b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b e + 1680a b d e - 3360a b d e + 2688a b d e - 768b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 14a e - 140a b d e + 1120a b d e - 2240a b d e + 1792a b d e +--R + +--R 5 5 +--R - 512b d +--R / +--R 7 6 +-------+ +--R (21e x + 21d e )\|e x + d +--R Type: Expression(Integer) +--E 509 + +--S 510 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 511 + +--S 512 of 765 +r0:=2/5*(b*d-a*e)^5/(e^6*(d+e*x)^(5/2))-10/3*b*(b*d-a*e)^4/(e^6*_ + (d+e*x)^(3/2))-10/3*b^4*(b*d-a*e)*(d+e*x)^(3/2)/e^6+2/5*b^5*_ + (d+e*x)^(5/2)/e^6+20*b^2*(b*d-a*e)^3/(e^6*sqrt(d+e*x))+20*b^3*_ + (b*d-a*e)^2*sqrt(d+e*x)/e^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 6b e x + (50a b e - 20b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (300a b e - 400a b d e + 160b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 300a b e + 1800a b d e - 2400a b d e + 960b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 50a b e - 400a b d e + 2400a b d e - 3200a b d e + 1280b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 6a e - 20a b d e - 160a b d e + 960a b d e - 1280a b d e + 512b d +--R / +--R 8 2 7 2 6 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 512 + +--S 513 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 3 10 6 3 7 2 9 2 5 3 6 2 7 2 8 +--R b e x + (7a b e + 3b d e )x + (21a b e + 21a b d e + 3b d e)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 7 +--R (35a b e + 63a b d e + 21a b d e + b d )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 6 +--R (35a b e + 105a b d e + 63a b d e + 7a b d )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 5 +--R (21a b e + 105a b d e + 105a b d e + 21a b d )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 4 +--R (7a b e + 63a b d e + 105a b d e + 35a b d )x +--R + +--R 7 3 6 2 5 2 2 4 3 3 3 +--R (a e + 21a b d e + 63a b d e + 35a b d )x +--R + +--R 7 2 6 2 5 2 3 2 7 2 6 3 7 3 +--R (3a d e + 21a b d e + 21a b d )x + (3a d e + 7a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 514 + +--S 515 of 765 +r0:=-2/9*(b*d-a*e)^7*(d+e*x)^(9/2)/e^8+14/11*b*(b*d-a*e)^6*_ + (d+e*x)^(11/2)/e^8-42/13*b^2*(b*d-a*e)^5*(d+e*x)^(13/2)/e^8+_ + 14/3*b^3*(b*d-a*e)^4*(d+e*x)^(15/2)/e^8-70/17*b^4*(b*d-a*e)^3*_ + (d+e*x)^(17/2)/e^8+42/19*b^5*(b*d-a*e)^2*(d+e*x)^(19/2)/e^8-_ + 2/3*b^6*(b*d-a*e)*(d+e*x)^(21/2)/e^8+2/23*b^7*(d+e*x)^(23/2)/e^8 +--R +--R +--R (2) +--R 7 11 11 6 11 7 10 10 +--R 831402b e x + (6374082a b e + 2771340b d e )x +--R + +--R 2 5 11 6 10 7 2 9 9 +--R (21135114a b e + 21470592a b d e + 3121404b d e )x +--R + +--R 3 4 11 2 5 10 6 2 9 +--R 39369330a b e + 72108036a b d e + 24509628a b d e +--R + +--R 7 3 8 +--R 1194336b d e +--R * +--R 8 +--R x +--R + +--R 4 3 11 3 4 10 2 5 2 9 +--R 44618574a b e + 136480344a b d e + 83711628a b d e +--R + +--R 6 3 8 7 4 7 +--R 9551256a b d e + 858b d e +--R * +--R 7 +--R x +--R + +--R 5 2 11 4 3 10 3 4 2 9 +--R 30889782a b e + 157881108a b d e + 161918988a b d e +--R + +--R 2 5 3 8 6 4 7 7 5 6 +--R 33408144a b d e + 10626a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 6 11 5 2 10 4 3 2 9 +--R 12168702a b e + 112326480a b d e + 192827124a b d e +--R + +--R 3 4 3 8 2 5 4 7 6 5 6 7 6 5 +--R 66735144a b d e + 60858a b d e - 11592a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 7 11 6 10 5 2 2 9 +--R 2124694a e + 45970652a b d e + 142904244a b d e +--R + +--R 4 3 3 8 3 4 4 7 2 5 5 6 6 6 5 +--R 83204800a b d e + 214130a b d e - 67620a b d e + 12880a b d e +--R + +--R 7 7 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 2 9 5 2 3 8 +--R 8498776a d e + 62195588a b d e + 66147816a b d e +--R + +--R 4 3 4 7 3 4 5 6 2 5 6 5 6 7 4 +--R 520030a b d e - 244720a b d e + 77280a b d e - 14720a b d e +--R + +--R 7 8 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 2 4 7 4 3 5 6 +--R 12748164a d e + 32449872a b d e + 936054a b d e - 624036a b d e +--R + +--R 3 4 6 5 2 5 7 4 6 8 3 7 9 2 +--R 293664a b d e - 92736a b d e + 17664a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 3 8 6 4 7 5 2 5 6 4 3 6 5 +--R 8498776a d e + 1352078a b d e - 1248072a b d e + 832048a b d e +--R + +--R 3 4 7 4 2 5 8 3 6 9 2 7 10 +--R - 391552a b d e + 123648a b d e - 23552a b d e + 2048b d e +--R * +--R x +--R + +--R 7 4 7 6 5 6 5 2 6 5 4 3 7 4 +--R 2124694a d e - 2704156a b d e + 2496144a b d e - 1664096a b d e +--R + +--R 3 4 8 3 2 5 9 2 6 10 7 11 +--R 783104a b d e - 247296a b d e + 47104a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 9561123e +--R Type: Expression(Integer) +--E 515 + +--S 516 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 516 + +)clear all + +--S 517 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 2 9 6 2 7 8 2 5 2 6 7 2 7 +--R b e x + (7a b e + 2b d e)x + (21a b e + 14a b d e + b d )x +--R + +--R 3 4 2 2 5 6 2 6 4 3 2 3 4 2 5 2 5 +--R (35a b e + 42a b d e + 7a b d )x + (35a b e + 70a b d e + 21a b d )x +--R + +--R 5 2 2 4 3 3 4 2 4 6 2 5 2 4 3 2 3 +--R (21a b e + 70a b d e + 35a b d )x + (7a b e + 42a b d e + 35a b d )x +--R + +--R 7 2 6 5 2 2 2 7 6 2 7 2 +--R (a e + 14a b d e + 21a b d )x + (2a d e + 7a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 517 + +--S 518 of 765 +r0:=-2/7*(b*d-a*e)^7*(d+e*x)^(7/2)/e^8+14/9*b*(b*d-a*e)^6*_ + (d+e*x)^(9/2)/e^8-42/11*b^2*(b*d-a*e)^5*(d+e*x)^(11/2)/e^8+_ + 70/13*b^3*(b*d-a*e)^4*(d+e*x)^(13/2)/e^8-14/3*b^4*(b*d-a*e)^3*_ + (d+e*x)^(15/2)/e^8+42/17*b^5*(b*d-a*e)^2*(d+e*x)^(17/2)/e^8-_ + 14/19*b^6*(b*d-a*e)*(d+e*x)^(19/2)/e^8+2/21*b^7*(d+e*x)^(21/2)/e^8 +--R +--R +--R (2) +--R 7 10 10 6 10 7 9 9 +--R 277134b e x + (2144142a b e + 627198b d e )x +--R + +--R 2 5 10 6 9 7 2 8 8 +--R (7189182a b e + 4918914a b d e + 362934b d e )x +--R + +--R 3 4 10 2 5 9 6 2 8 7 3 7 7 +--R (13579566a b e + 16774758a b d e + 2900898a b d e + 858b d e )x +--R + +--R 4 3 10 3 4 9 2 5 2 8 +--R 15668730a b e + 32382042a b d e + 10138590a b d e +--R + +--R 6 3 7 7 4 6 +--R 9702a b d e - 924b d e +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 4 2 8 +--R 11110554a b e + 38459610a b d e + 20226906a b d e +--R + +--R 2 5 3 7 6 4 6 7 5 5 +--R 50274a b d e - 10584a b d e + 1008b d e +--R * +--R 5 +--R x +--R + +--R 6 10 5 2 9 4 3 2 8 +--R 4526522a b e + 28393638a b d e + 25164930a b d e +--R + +--R 3 4 3 7 2 5 4 6 6 5 5 7 6 4 +--R 158270a b d e - 55860a b d e + 11760a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 +--R 831402a e + 12286274a b d e + 19928454a b d e + 339150a b d e +--R + +--R 3 4 4 6 2 5 5 5 6 6 4 7 7 3 +--R - 180880a b d e + 63840a b d e - 13440a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 +--R 2494206a d e + 9699690a b d e + 529074a b d e - 406980a b d e +--R + +--R 3 4 5 5 2 5 6 4 6 7 3 7 8 2 +--R 217056a b d e - 76608a b d e + 16128a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 +--R 2494206a d e + 646646a b d e - 705432a b d e + 542640a b d e +--R + +--R 3 4 6 4 2 5 7 3 6 8 2 7 9 +--R - 289408a b d e + 102144a b d e - 21504a b d e + 2048b d e +--R * +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 +--R 831402a d e - 1293292a b d e + 1410864a b d e - 1085280a b d e +--R + +--R 3 4 7 3 2 5 8 2 6 9 7 10 +--R 578816a b d e - 204288a b d e + 43008a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 2909907e +--R Type: Expression(Integer) +--E 518 + +--S 519 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 519 + +)clear all + +--S 520 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 8 6 7 7 2 5 6 6 3 4 2 5 5 +--R b e x + (7a b e + b d)x + (21a b e + 7a b d)x + (35a b e + 21a b d)x +--R + +--R 4 3 3 4 4 5 2 4 3 3 6 5 2 2 +--R (35a b e + 35a b d)x + (21a b e + 35a b d)x + (7a b e + 21a b d)x +--R + +--R 7 6 7 +--R (a e + 7a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 520 + +--S 521 of 765 +r0:=-2/5*(b*d-a*e)^7*(d+e*x)^(5/2)/e^8+2*b*(b*d-a*e)^6*(d+e*x)^(7/2)/e^8-_ + 14/3*b^2*(b*d-a*e)^5*(d+e*x)^(9/2)/e^8+70/11*b^3*(b*d-a*e)^4*_ + (d+e*x)^(11/2)/e^8-70/13*b^4*(b*d-a*e)^3*(d+e*x)^(13/2)/e^8+_ + 14/5*b^5*(b*d-a*e)^2*(d+e*x)^(15/2)/e^8-14/17*b^6*(b*d-a*e)*_ + (d+e*x)^(17/2)/e^8+2/19*b^7*(d+e*x)^(19/2)/e^8 +--R +--R +--R (2) +--R 7 9 9 6 9 7 8 8 +--R 72930b e x + (570570a b e + 85800b d e )x +--R + +--R 2 5 9 6 8 7 2 7 7 +--R (1939938a b e + 684684a b d e + 858b d e )x +--R + +--R 3 4 9 2 5 8 6 2 7 7 3 6 6 +--R (3730650a b e + 2387616a b d e + 8778a b d e - 924b d e )x +--R + +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 +--R 4408950a b e + 4748100a b d e + 40698a b d e - 9576a b d e +--R + +--R 7 4 5 +--R 1008b d e +--R * +--R 5 +--R x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 +--R 3233230a b e + 5878600a b d e + 113050a b d e - 45220a b d e +--R + +--R 6 4 5 7 5 4 +--R 10640a b d e - 1120b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 2 8 4 3 2 7 3 4 3 6 +--R 1385670a b e + 4618900a b d e + 209950a b d e - 129200a b d e +--R + +--R 2 5 4 5 6 5 4 7 6 3 +--R 51680a b d e - 12160a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 +--R 277134a e + 2217072a b d e + 277134a b d e - 251940a b d e +--R + +--R 3 4 4 5 2 5 5 4 6 6 3 7 7 2 +--R 155040a b d e - 62016a b d e + 14592a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 +--R 554268a d e + 277134a b d e - 369512a b d e + 335920a b d e +--R + +--R 3 4 5 4 2 5 6 3 6 7 2 7 8 +--R - 206720a b d e + 82688a b d e - 19456a b d e + 2048b d e +--R * +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 +--R 277134a d e - 554268a b d e + 739024a b d e - 671840a b d e +--R + +--R 3 4 6 3 2 5 7 2 6 8 7 9 +--R 413440a b d e - 165376a b d e + 38912a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 692835e +--R Type: Expression(Integer) +--E 521 + +--S 522 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 522 + +)clear all + +--S 523 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 523 + +--S 524 of 765 +r0:=-2/3*(b*d-a*e)^7*(d+e*x)^(3/2)/e^8+14/5*b*(b*d-a*e)^6*(d+e*x)^(5/2)/e^8-_ + 6*b^2*(b*d-a*e)^5*(d+e*x)^(7/2)/e^8+70/9*b^3*(b*d-a*e)^4*_ + (d+e*x)^(9/2)/e^8-70/11*b^4*(b*d-a*e)^3*(d+e*x)^(11/2)/e^8+42/13*b^5*_ + (b*d-a*e)^2*(d+e*x)^(13/2)/e^8-14/15*b^6*(b*d-a*e)*(d+e*x)^(15/2)/e^8+_ + 2/17*b^7*(d+e*x)^(17/2)/e^8 +--R +--R +--R (2) +--R 7 8 8 6 8 7 7 7 +--R 12870b e x + (102102a b e + 858b d e )x +--R + +--R 2 5 8 6 7 7 2 6 6 +--R (353430a b e + 7854a b d e - 924b d e )x +--R + +--R 3 4 8 2 5 7 6 2 6 7 3 5 5 +--R (696150a b e + 32130a b d e - 8568a b d e + 1008b d e )x +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 +--R 850850a b e + 77350a b d e - 35700a b d e + 9520a b d e +--R + +--R 7 4 4 +--R - 1120b d e +--R * +--R 4 +--R x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 +--R 656370a b e + 121550a b d e - 88400a b d e + 40800a b d e +--R + +--R 6 4 4 7 5 3 +--R - 10880a b d e + 1280b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 +--R 306306a b e + 131274a b d e - 145860a b d e + 106080a b d e +--R + +--R 2 5 4 4 6 5 3 7 6 2 +--R - 48960a b d e + 13056a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 +--R 72930a e + 102102a b d e - 175032a b d e + 194480a b d e +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 +--R - 141440a b d e + 65280a b d e - 17408a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 +--R 72930a d e - 204204a b d e + 350064a b d e - 388960a b d e +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 +--R 282880a b d e - 130560a b d e + 34816a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 109395e +--R Type: Expression(Integer) +--E 524 + +--S 525 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/sqrt(d+e*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 526 + +--S 527 of 765 +r0:=14/3*b*(b*d-a*e)^6*(d+e*x)^(3/2)/e^8-42/5*b^2*(b*d-a*e)^5*_ + (d+e*x)^(5/2)/e^8+10*b^3*(b*d-a*e)^4*(d+e*x)^(7/2)/e^8-70/9*b^4*_ + (b*d-a*e)^3*(d+e*x)^(9/2)/e^8+42/11*b^5*(b*d-a*e)^2*(d+e*x)^(11/2)/e^8-_ + 14/13*b^6*(b*d-a*e)*(d+e*x)^(13/2)/e^8+2/15*b^7*(d+e*x)^(15/2)/e^8-_ + 2*(b*d-a*e)^7*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 858b e x + (6930a b e - 924b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (24570a b e - 7560a b d e + 1008b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (50050a b e - 27300a b d e + 8400a b d e - 1120b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 64350a b e - 57200a b d e + 31200a b d e - 9600a b d e +--R + +--R 7 4 3 +--R 1280b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 54054a b e - 77220a b d e + 68640a b d e - 37440a b d e +--R + +--R 6 4 3 7 5 2 +--R 11520a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 30030a b e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 49920a b d e - 15360a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 12870a e - 60060a b d e + 144144a b d e - 205920a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 183040a b d e - 99840a b d e + 30720a b d e - 4096b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 8 +--R 6435e +--R Type: Expression(Integer) +--E 527 + +--S 528 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 528 + +)clear all + +--S 529 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 529 + +--S 530 of 765 +r0:=-14*b^2*(b*d-a*e)^5*(d+e*x)^(3/2)/e^8+14*b^3*(b*d-a*e)^4*_ + (d+e*x)^(5/2)/e^8-10*b^4*(b*d-a*e)^3*(d+e*x)^(7/2)/e^8+14/3*b^5*_ + (b*d-a*e)^2*(d+e*x)^(9/2)/e^8-14/11*b^6*(b*d-a*e)*(d+e*x)^(11/2)/e^8+_ + 2/13*b^7*(d+e*x)^(13/2)/e^8+2*(b*d-a*e)^7/(e^8*sqrt(d+e*x))+_ + 14*b*(b*d-a*e)^6*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 66b e x + (546a b e - 84b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (2002a b e - 728a b d e + 112b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (4290a b e - 2860a b d e + 1040a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (6006a b e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 6006a b e - 12012a b d e + 13728a b d e - 9152a b d e +--R + +--R 6 4 3 7 5 2 +--R 3328a b d e - 512b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 6006a b e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 36608a b d e - 13312a b d e + 2048b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 858a e + 12012a b d e - 48048a b d e + 96096a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 109824a b d e + 73216a b d e - 26624a b d e + 4096b d +--R / +--R 8 +-------+ +--R 429e \|e x + d +--R Type: Expression(Integer) +--E 530 + +--S 531 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 531 + +)clear all + +--S 532 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 532 + +--S 533 of 765 +r0:=2/3*(b*d-a*e)^7/(e^8*(d+e*x)^(3/2))+70/3*b^3*(b*d-a*e)^4*_ + (d+e*x)^(3/2)/e^8-14*b^4*(b*d-a*e)^3*(d+e*x)^(5/2)/e^8+6*b^5*_ + (b*d-a*e)^2*(d+e*x)^(7/2)/e^8-14/9*b^6*(b*d-a*e)*(d+e*x)^(9/2)/e^8+_ + 2/11*b^7*(d+e*x)^(11/2)/e^8-14*b*(b*d-a*e)^6/(e^8*sqrt(d+e*x))-_ + 42*b^2*(b*d-a*e)^5*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 18b e x + (154a b e - 28b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (594a b e - 264a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1386a b e - 1188a b d e + 528a b d e - 96b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4158a b e - 13860a b d e + 22176a b d e - 19008a b d e +--R + +--R 6 4 3 7 5 2 +--R 8448a b d e - 1536b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 1386a b e + 16632a b d e - 55440a b d e + 88704a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 76032a b d e + 33792a b d e - 6144b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 66a e - 924a b d e + 11088a b d e - 36960a b d e + 59136a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R - 50688a b d e + 22528a b d e - 4096b d +--R / +--R 9 8 +-------+ +--R (99e x + 99d e )\|e x + d +--R Type: Expression(Integer) +--E 533 + +--S 534 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 534 + +)clear all + +--S 535 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 535 + +--S 536 of 765 +r0:=2/5*(b*d-a*e)^7/(e^8*(d+e*x)^(5/2))-14/3*b*(b*d-a*e)^6/(e^8*_ + (d+e*x)^(3/2))-70/3*b^4*(b*d-a*e)^3*(d+e*x)^(3/2)/e^8+42/5*b^5*_ + (b*d-a*e)^2*(d+e*x)^(5/2)/e^8-2*b^6*(b*d-a*e)*(d+e*x)^(7/2)/e^8+_ + 2/9*b^7*(d+e*x)^(9/2)/e^8+42*b^2*(b*d-a*e)^5/(e^8*sqrt(d+e*x))+_ + 70*b^3*(b*d-a*e)^4*sqrt(d+e*x)/e^8 +--R +--R +--R (2) +--R 7 7 7 6 7 7 6 6 +--R 10b e x + (90a b e - 20b d e )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (1050a b e - 1260a b d e + 720a b d e - 160b d e )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (3150a b e - 8400a b d e + 10080a b d e - 5760a b d e + 1280b d e )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1890a b e + 18900a b d e - 50400a b d e + 60480a b d e +--R + +--R 6 4 3 7 5 2 +--R - 34560a b d e + 7680b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 210a b e - 2520a b d e + 25200a b d e - 67200a b d e +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 80640a b d e - 46080a b d e + 10240b d e +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 18a e - 84a b d e - 1008a b d e + 10080a b d e - 26880a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 32256a b d e - 18432a b d e + 4096b d +--R / +--R 10 2 9 2 8 +-------+ +--R (45e x + 90d e x + 45d e )\|e x + d +--R Type: Expression(Integer) +--E 536 + +--S 537 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 538 + +--S 539 of 765 +r0:=2/3*(b*d-a*e)^2*(d+e*x)^(3/2)/b^3+2/5*(b*d-a*e)*(d+e*x)^(5/2)/b^2+_ + 2/7*(d+e*x)^(7/2)/b-2*(b*d-a*e)^(7/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/b^(9/2)+2*(b*d-a*e)^3*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (210a e - 630a b d e + 630a b d e - 210b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b e x + (- 42a b e + 132b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 224a b d e + 244b d e)x - 210a e + 700a b d e +--R + +--R 2 2 3 3 +--R - 812a b d e + 352b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 +-+ +--R 105b \|b +--R Type: Expression(Integer) +--E 539 + +--S 540 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R b x + a +--R Type: Expression(Integer) +--E 541 + +--S 542 of 765 +r0:=2/3*(b*d-a*e)*(d+e*x)^(3/2)/b^2+2/5*(d+e*x)^(5/2)/b-2*(b*d-a*e)^(5/2)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(7/2)+2*(b*d-a*e)^2*_ + sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|e x + d +--R (- 30a e + 60a b d e - 30b d )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (6b e x + (- 10a b e + 22b d e)x + 30a e - 70a b d e + 46b d )\|b +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 542 + +--S 543 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------- +--R b x + a +--R Type: Expression(Integer) +--E 544 + +--S 545 of 765 +r0:=2/3*(d+e*x)^(3/2)/b-2*(b*d-a*e)^(3/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/b^(5/2)+2*(b*d-a*e)*sqrt(d+e*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (6a e - 6b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-+ +-------+ +--R (2b e x - 6a e + 8b d)\|b \|e x + d +--R / +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 545 + +--S 546 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 546 + +)clear all + +--S 547 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ---------- +--R b x + a +--R Type: Expression(Integer) +--E 547 + +--S 548 of 765 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(3/2)+_ + 2*sqrt(d+e*x)/b +--R +--R +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +-+ +-------+ +--R - 2\|- a e + b d atanh(--------------) + 2\|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) -------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 548 + +--S 549 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 765 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|e x + d +--R Type: Expression(Integer) +--E 550 + +--S 551 of 765 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(sqrt(b)*sqrt(b*d-a*e)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +--R 2atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R (2) - ---------------------- +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 551 + +--S 552 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 765 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) --------------------------------------- +--R 2 +-------+ +--R (b e x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 553 + +--S 554 of 765 +r0:=-2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(3/2)+_ + 2/((b*d-a*e)*sqrt(d+e*x)) +--R +--R +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +-----------+ +--R 2\|b \|e x + d atanh(--------------) - 2\|- a e + b d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------ +--R +-----------+ +-------+ +--R (a e - b d)\|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 554 + +--S 555 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 765 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R Type: Expression(Integer) +--E 556 + +--S 557 of 765 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2))-2*b^(3/2)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b*d-a*e)^(5/2)+2*b/((b*d-a*e)^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R (- 6b e x - 6b d)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R (6b e x - 2a e + 8b d)\|- a e + b d +--R / +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e)x + 3a d e - 6a b d e + 3b d ) +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 557 + +--S 558 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 of 765 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 559 + +--S 560 of 765 +r0:=2/5/((b*d-a*e)*(d+e*x)^(5/2))+2/3*b/((b*d-a*e)^2*(d+e*x)^(3/2))-_ + 2*b^(5/2)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(7/2)+_ + 2*b^2/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-+ +-------+ \|b \|e x + d +--R (30b e x + 60b d e x + 30b d )\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 30b e x + (10a b e - 70b d e)x - 6a e + 22a b d e - 46b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (30a d e - 90a b d e + 90a b d e - 30b d e)x + 15a d e - 45a b d e +--R + +--R 2 4 3 5 +--R 45a b d e - 15b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 560 + +--S 561 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 561 + +)clear all + +--S 562 of 765 +t0:=(a+b*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 562 + +--S 563 of 765 +r0:=21/4*e^2*(b*d-a*e)*(d+e*x)^(3/2)/b^4+63/20*e^2*(d+e*x)^(5/2)/b^3-_ + 9/4*e*(d+e*x)^(7/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(9/2)/(b*(a+b*x)^2)-_ + 63/4*e^2*(b*d-a*e)^(5/2)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + b^(11/2)+63/4*e^2*(b*d-a*e)^2*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (- 315a b e + 630a b d e - 315b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 4 3 3 +--R (- 630a b e + 1260a b d e - 630a b d e )x - 315a e + 630a b d e +--R + +--R 2 2 2 2 +--R - 315a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 8b e x + (- 24a b e + 56b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (168a b e - 408a b d e + 288b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (525a b e - 1239a b d e + 831a b d e - 85b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 735a b d e + 483a b d e - 45a b d e - 10b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 7 2 6 2 5 +-+ +--R (20b x + 40a b x + 20a b )\|b +--R Type: Expression(Integer) +--E 563 + +--S 564 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 565 + +--S 566 of 765 +r0:=35/12*e^2*(d+e*x)^(3/2)/b^3-7/4*e*(d+e*x)^(5/2)/(b^2*(a+b*x))-_ + 1/2*(d+e*x)^(7/2)/(b*(a+b*x)^2)-35/4*e^2*(b*d-a*e)^(3/2)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+35/4*e^2*(b*d-a*e)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (105a b e - 105b d e )x + (210a b e - 210a b d e )x + 105a e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 8b e x + (- 56a b e + 80b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 175a b e + 238a b d e - 39b d e)x - 105a e + 140a b d e +--R + +--R 2 2 3 3 +--R - 21a b d e - 6b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 2 5 2 4 +-+ +--R (12b x + 24a b x + 12a b )\|b +--R Type: Expression(Integer) +--E 566 + +--S 567 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 568 + +--S 569 of 765 +r0:=-5/4*e*(d+e*x)^(3/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(5/2)/(b*(a+b*x)^2)-_ + 15/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+_ + 15/4*e^2*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-----------+ \|b \|e x + d +--R (- 15b e x - 30a b e x - 15a e )\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-------+ +--R (8b e x + (25a b e - 9b d e)x + 15a e - 5a b d e - 2b d )\|b \|e x + d +--R / +--R 5 2 4 2 3 +-+ +--R (4b x + 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 569 + +--S 570 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 765 +r0:=-1/2*(d+e*x)^(3/2)/(b*(a+b*x)^2)-3/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))-3/4*e*sqrt(d+e*x)/(b^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- 3b e x - 6a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (- 5b e x - 3a e - 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 4 2 3 2 2 +-----------+ +-+ +--R (4b x + 8a b x + 4a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 572 + +--S 573 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2 +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 574 + +--S 575 of 765 +r0:=1/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + (b*d-a*e)^(3/2))-1/2*sqrt(d+e*x)/(b*(a+b*x)^2)-1/4*e*_ + sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- b e x - 2a b e x - a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (b e x - a e + 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 3 4 2 2 2 3 3 2 2 +-----------+ +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|- a e + b d +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 575 + +--S 576 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 576 + +)clear all + +--S 577 of 765 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 577 + +--S 578 of 765 +r0:=-3/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(5/2)*_ + sqrt(b))-1/2*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^2)+3/4*e*sqrt(d+e*x)/_ + ((b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|e x + d +--R (- 3b e x - 6a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (3b e x + 5a e - 2b d)\|- a e + b d \|b \|e x + d +--R / +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 2 +--R 4a e - 8a b d e + 4a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 578 + +--S 579 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 of 765 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 580 + +--S 581 of 765 +r0:=-15/4*e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/_ + (b*d-a*e)^(7/2)+15/4*e^2/((b*d-a*e)^3*sqrt(d+e*x))+(-1/2)/((b*d-a*e)*_ + (a+b*x)^2*sqrt(d+e*x))+5/4*e/((b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-+ +-------+ \|b \|e x + d +--R (15b e x + 30a b e x + 15a e )\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 15b e x + (- 25a b e - 5b d e)x - 8a e - 9a b d e + 2b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 581 + +--S 582 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 of 765 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 583 + +--S 584 of 765 +r0:=35/12*e^2/((b*d-a*e)^3*(d+e*x)^(3/2))+(-1/2)/((b*d-a*e)*(a+b*x)^2*_ + (d+e*x)^(3/2))+7/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2))-35/4*b^(3/2)*_ + e^2*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+35/4*b*_ + e^2/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 210a b e - 105b d e )x +--R + +--R 2 3 2 2 2 2 +--R (- 105a b e - 210a b d e )x - 105a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (175a b e + 140b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (56a b e + 238a b d e + 21b d e)x - 8a e + 80a b d e + 39a b d e +--R + +--R 3 3 +--R - 6b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e + 24a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 584 + +--S 585 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 765 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 586 + +--S 587 of 765 +r0:=63/20*e^2/((b*d-a*e)^3*(d+e*x)^(5/2))+(-1/2)/((b*d-a*e)*(a+b*x)^2*_ + (d+e*x)^(5/2))+9/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2))+21/4*b*_ + e^2/((b*d-a*e)^4*(d+e*x)^(3/2))-63/4*b^(5/2)*e^2*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(11/2)+63/4*b^2*e^2/((b*d-a*e)^5*_ + sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (630a b e + 630b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (315a b e + 1260a b d e + 315b d e )x +--R + +--R 2 2 3 3 2 2 2 2 2 2 +--R (630a b d e + 630a b d e )x + 315a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 525a b e - 735b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 168a b e - 1239a b d e - 483b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (24a b e - 408a b d e - 831a b d e - 45b d e)x - 8a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 56a b d e - 288a b d e - 85a b d e + 10b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 20a b e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 7 5 2 +--R - 20b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 40a b e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 7 6 +--R - 40b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 20a e - 20a b d e - 180a b d e + 500a b d e - 500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 180a b d e + 20a b d e - 20b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 40a d e - 160a b d e + 200a b d e - 200a b d e + 160a b d e +--R + +--R 6 7 +--R - 40a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 20a d e - 100a b d e + 200a b d e - 200a b d e + 100a b d e +--R + +--R 2 5 7 +--R - 20a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 587 + +--S 588 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 of 765 +t0:=(a+b*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 589 + +--S 590 of 765 +r0:=385/64*e^4*(d+e*x)^(3/2)/b^5-231/64*e^3*(d+e*x)^(5/2)/(b^4*(a+b*x))-_ + 33/32*e^2*(d+e*x)^(7/2)/(b^3*(a+b*x)^2)-11/24*e*(d+e*x)^(9/2)/(b^2*_ + (a+b*x)^3)-1/4*(d+e*x)^(11/2)/(b*(a+b*x)^4)-1155/64*e^4*(b*d-a*e)^(3/2)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(13/2)+1155/64*e^4*(b*d-_ + a*e)*sqrt(d+e*x)/b^6 +--R +--R +--R (2) +--R 4 5 5 4 4 2 3 5 4 4 3 +--R (3465a b e - 3465b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 3 2 5 2 3 4 2 4 5 3 2 4 +--R (20790a b e - 20790a b d e )x + (13860a b e - 13860a b d e )x +--R + +--R 5 5 4 4 +--R 3465a e - 3465a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R 128b e x + (- 1408a b e + 2048b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 9207a b e + 12782a b d e - 2295b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 16863a b e + 22968a b d e - 3795a b d e - 1030b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 +--R - 12705a b e + 17094a b d e - 2673a b d e - 748a b d e +--R + +--R 5 4 +--R - 328b d e +--R * +--R x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 3465a e + 4620a b d e - 693a b d e - 198a b d e - 88a b d e +--R + +--R 5 5 +--R - 48b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|b +--R Type: Expression(Integer) +--E 590 + +--S 591 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 591 + +)clear all + +--S 592 of 765 +t0:=(a+b*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 592 + +--S 593 of 765 +r0:=-105/64*e^3*(d+e*x)^(3/2)/(b^4*(a+b*x))-21/32*e^2*(d+e*x)^(5/2)/_ + (b^3*(a+b*x)^2)-3/8*e*(d+e*x)^(7/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(9/2)/_ + (b*(a+b*x)^4)-315/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b*d-a*e)/b^(11/2)+315/64*e^4*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 315b e x - 1260a b e x - 1890a b e x - 1260a b e x - 315a e ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 128b e x + (837a b e - 325b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1533a b e - 555a b d e - 210b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1155a b e - 399a b d e - 156a b d e - 88b d e)x + 315a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 105a b d e - 42a b d e - 24a b d e - 16b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +-+ +--R (64b x + 256a b x + 384a b x + 256a b x + 64a b )\|b +--R Type: Expression(Integer) +--E 593 + +--S 594 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 595 + +--S 596 of 765 +r0:=-35/96*e^2*(d+e*x)^(3/2)/(b^3*(a+b*x)^2)-7/24*e*(d+e*x)^(5/2)/_ + (b^2*(a+b*x)^3)-1/4*(d+e*x)^(7/2)/(b*(a+b*x)^4)-35/64*e^4*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(b*d-a*e))-_ + 35/64*e^3*sqrt(d+e*x)/(b^4*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 105b e x - 420a b e x - 630a b e x - 420a b e x - 105a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 279b e x + (- 511a b e - 326b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 385a b e - 252a b d e - 200b d e)x - 105a e - 70a b d e +--R + +--R 2 2 3 3 +--R - 56a b d e - 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +-----------+ +-+ +--R (192b x + 768a b x + 1152a b x + 768a b x + 192a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 596 + +--S 597 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 598 + +--S 599 of 765 +r0:=-5/24*e*(d+e*x)^(3/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(5/2)/(b*(a+b*x)^4)+_ + 5/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*_ + (b*d-a*e)^(3/2))-5/32*e^2*sqrt(d+e*x)/(b^3*(a+b*x)^2)-5/64*e^3*_ + sqrt(d+e*x)/(b^3*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 15b e x - 60a b e x - 90a b e x - 60a b e x - 15a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (- 73a b e + 118b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 55a b e - 36a b d e + 136b d e)x - 15a e - 10a b d e +--R + +--R 2 2 3 3 +--R - 8a b d e + 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 7 8 4 2 6 7 3 +--R (192a b e - 192b d)x + (768a b e - 768a b d)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 4 4 +--R (1152a b e - 1152a b d)x + (768a b e - 768a b d)x + 192a b e - 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 599 + +--S 600 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 601 + +--S 602 of 765 +r0:=-1/4*(d+e*x)^(3/2)/(b*(a+b*x)^4)-3/64*e^4*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(5/2))-1/8*e*_ + sqrt(d+e*x)/(b^2*(a+b*x)^3)-1/32*e^2*sqrt(d+e*x)/(b^2*(b*d-a*e)*_ + (a+b*x)^2)+3/64*e^3*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 3b e x - 12a b e x - 18a b e x - 12a b e x - 3a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 3b e x + (11a b e - 2b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 11a b e + 44a b d e - 24b d e)x - 3a e - 2a b d e + 24a b d e +--R + +--R 3 3 +--R - 16b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 6 2 7 8 2 4 +--R (64a b e - 128a b d e + 64b d )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (256a b e - 512a b d e + 256a b d )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (384a b e - 768a b d e + 384a b d )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 4 4 2 +--R (256a b e - 512a b d e + 256a b d )x + 64a b e - 128a b d e + 64a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 602 + +--S 603 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R +-------+ +--R \|e x + d +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 604 + +--S 605 of 765 +r0:=5/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + (b*d-a*e)^(7/2))-1/4*sqrt(d+e*x)/(b*(a+b*x)^4)-1/24*e*sqrt(d+e*x)/_ + (b*(b*d-a*e)*(a+b*x)^3)+5/96*e^2*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x)^2)-_ + 5/64*e^3*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 15b e x - 60a b e x - 90a b e x - 60a b e x - 15a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b e x + (55a b e - 10b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (73a b e - 36a b d e + 8b d e)x - 15a e + 118a b d e - 136a b d e +--R + +--R 3 3 +--R 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (192a b e - 576a b d e + 576a b d e - 192b d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (1152a b e - 3456a b d e + 3456a b d e - 1152a b d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (768a b e - 2304a b d e + 2304a b d e - 768a b d )x + 192a b e +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 576a b d e + 576a b d e - 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 605 + +--S 606 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 606 + +)clear all + +--S 607 of 765 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 607 + +--S 608 of 765 +r0:=-35/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*_ + sqrt(b))-1/4*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^4)+7/24*e*sqrt(d+e*x)/_ + ((b*d-a*e)^2*(a+b*x)^3)-35/96*e^2*sqrt(d+e*x)/((b*d-a*e)^3*(a+b*x)^2)+_ + 35/64*e^3*sqrt(d+e*x)/((b*d-a*e)^4*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 105b e x - 420a b e x - 630a b e x - 420a b e x - 105a e ) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b e x + (385a b e - 70b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (511a b e - 252a b d e + 56b d e)x + 279a e - 326a b d e +--R + +--R 2 2 3 3 +--R 200a b d e - 48b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (192a b e - 768a b d e + 1152a b d e - 768a b d e + 192b d )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (1152a b e - 4608a b d e + 6912a b d e - 4608a b d e + 1152a b d )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (768a b e - 3072a b d e + 4608a b d e - 3072a b d e + 768a b d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 192a e - 768a b d e + 1152a b d e - 768a b d e + 192a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 608 + +--S 609 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 765 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 6 4 5 5 2 3 4 4 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (10a b e + 10a b d)x + (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 610 + +--S 611 of 765 +r0:=-315/64*e^4*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-_ + a*e)^(11/2)+315/64*e^4/((b*d-a*e)^5*sqrt(d+e*x))+(-1/4)/((b*d-a*e)*_ + (a+b*x)^4*sqrt(d+e*x))+3/8*e/((b*d-a*e)^2*(a+b*x)^3*sqrt(d+e*x))-_ + 21/32*e^2/((b*d-a*e)^3*(a+b*x)^2*sqrt(d+e*x))+105/64*e^3/((b*d-a*e)^4*_ + (a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +-+ +--R (315b e x + 1260a b e x + 1890a b e x + 1260a b e x + 315a e )\|b +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 1155a b e - 105b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1533a b e - 399a b d e + 42b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 837a b e - 555a b d e + 156a b d e - 24b d e)x - 128a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 325a b d e + 210a b d e - 88a b d e + 16b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 8 4 +--R 64a b e - 320a b d e + 640a b d e - 640a b d e + 320a b d e +--R + +--R 9 5 +--R - 64b d +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 2 7 4 8 5 +--R 1280a b d e - 256a b d +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 384a b e - 1920a b d e + 3840a b d e - 3840a b d e +--R + +--R 3 6 4 2 7 5 +--R 1920a b d e - 384a b d +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 256a b e - 1280a b d e + 2560a b d e - 2560a b d e +--R + +--R 4 5 4 3 6 5 +--R 1280a b d e - 256a b d +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 4 5 5 +--R 64a e - 320a b d e + 640a b d e - 640a b d e + 320a b d e - 64a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 611 + +--S 612 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 765 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 613 + +--S 614 of 765 +r0:=385/64*e^4/((b*d-a*e)^5*(d+e*x)^(3/2))+(-1/4)/((b*d-a*e)*(a+b*x)^4*_ + (d+e*x)^(3/2))+11/24*e/((b*d-a*e)^2*(a+b*x)^3*(d+e*x)^(3/2))-_ + 33/32*e^2/((b*d-a*e)^3*(a+b*x)^2*(d+e*x)^(3/2))+231/64*e^3/((b*d-a*e)^4*_ + (a+b*x)*(d+e*x)^(3/2))-1155/64*b^(3/2)*e^4*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b*d-a*e)^(13/2)+1155/64*b*e^4/((b*d-a*e)^6*sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 3465b e x + (- 13860a b e - 3465b d e )x +--R + +--R 2 3 5 4 4 3 3 2 5 2 3 4 2 +--R (- 20790a b e - 13860a b d e )x + (- 13860a b e - 20790a b d e )x +--R + +--R 4 5 3 2 4 4 4 +--R (- 3465a b e - 13860a b d e )x - 3465a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (12705a b e + 4620b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (16863a b e + 17094a b d e + 693b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (9207a b e + 22968a b d e + 2673a b d e - 198b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (1408a b e + 12782a b d e + 3795a b d e - 748a b d e + 88b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 128a e + 2048a b d e + 2295a b d e - 1030a b d e + 328a b d e +--R + +--R 5 5 +--R - 48b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 4 7 5 5 6 4 6 2 5 3 7 3 4 +--R 192a b e - 1152a b d e + 2880a b d e - 3840a b d e +--R + +--R 2 8 4 3 9 5 2 10 6 +--R 2880a b d e - 1152a b d e + 192b d e +--R * +--R 5 +--R x +--R + +--R 7 3 7 6 4 6 5 5 2 5 4 6 3 4 +--R 768a b e - 4416a b d e + 10368a b d e - 12480a b d e +--R + +--R 3 7 4 3 2 8 5 2 9 6 10 7 +--R 7680a b d e - 1728a b d e - 384a b d e + 192b d +--R * +--R 4 +--R x +--R + +--R 8 2 7 7 3 6 6 4 2 5 5 5 3 4 +--R 1152a b e - 6144a b d e + 12672a b d e - 11520a b d e +--R + +--R 4 6 4 3 3 7 5 2 2 8 6 9 7 +--R 1920a b d e + 4608a b d e - 3456a b d e + 768a b d +--R * +--R 3 +--R x +--R + +--R 9 7 8 2 6 7 3 2 5 6 4 3 4 +--R 768a b e - 3456a b d e + 4608a b d e + 1920a b d e +--R + +--R 5 5 4 3 4 6 5 2 3 7 6 2 8 7 +--R - 11520a b d e + 12672a b d e - 6144a b d e + 1152a b d +--R * +--R 2 +--R x +--R + +--R 10 7 9 6 8 2 2 5 7 3 3 4 +--R 192a e - 384a b d e - 1728a b d e + 7680a b d e +--R + +--R 6 4 4 3 5 5 5 2 4 6 6 3 7 7 +--R - 12480a b d e + 10368a b d e - 4416a b d e + 768a b d +--R * +--R x +--R + +--R 10 6 9 2 5 8 2 3 4 7 3 4 3 6 4 5 2 +--R 192a d e - 1152a b d e + 2880a b d e - 3840a b d e + 2880a b d e +--R + +--R 5 5 6 4 6 7 +--R - 1152a b d e + 192a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 614 + +--S 615 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 616 + +--S 617 of 765 +r0:=-8/143*(b*d-a*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/1287*(b*d-a*e)^2*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+_ + b*x))+2/13*(a+b*x)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 +--R 198b e x + (468a b e + 720b d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (286a e + 1768a b d e + 916b d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (1144a d e + 2392a b d e + 424b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (1716a d e + 1248a b d e + 6b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (1144a d e + 52a b d e - 8b d e)x + 286a d e - 104a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 1287b e x + 1287a e +--R Type: Expression(Integer) +--E 617 + +--S 618 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 619 + +--S 620 of 765 +r0:=-8/99*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/693*(b*d-a*e)^2*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+_ + b*x))+2/11*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 +--R 126b e x + (308a b e + 322b d e )x +--R + +--R 2 5 4 2 2 3 3 +--R (198a e + 836a b d e + 226b d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (594a d e + 660a b d e + 6b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (594a d e + 44a b d e - 8b d e)x + 198a d e - 88a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 693b e x + 693a e +--R Type: Expression(Integer) +--E 620 + +--S 621 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (1) (b e x + (a e + b d)x + a d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 622 + +--S 623 of 765 +r0:=-8/63*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/315*(b*d-a*e)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 2/9*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 70b e x + (180a b e + 100b d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (126a e + 288a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (252a d e + 36a b d e - 8b d e)x + 126a d e - 72a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 623 + +--S 624 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 of 765 +t0:=(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +------------------+ +--R +-------+ | 2 2 2 +--R (1) (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 625 + +--S 626 of 765 +r0:=-8/35*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+_ + 16/105*(b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+_ + 2/7*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 30b e x + (84a b e + 6b d e )x + (70a e + 28a b d e - 8b d e)x +--R + +--R 2 2 2 2 3 +--R 70a d e - 56a b d e + 16b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 3 3 +--R 105b e x + 105a e +--R Type: Expression(Integer) +--E 626 + +--S 627 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 628 + +--S 629 of 765 +r0:=-8/15*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+16/15*(b*d-_ + a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/5*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (6b e x + (20a b e - 8b d e)x + 30a e - 40a b d e + 16b d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +--R 15b e x + 15a e +--R Type: Expression(Integer) +--E 629 + +--S 630 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 631 + +--S 632 of 765 +r0:=-2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*sqrt(d+e*x))+8/3*b*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^2-16/3*b*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2b e x + (12a b e - 8b d e)x - 6a e + 24a b d e - 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 3 3 +-------+ +--R (3b e x + 3a e )\|e x + d +--R Type: Expression(Integer) +--E 632 + +--S 633 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 634 + +--S 635 of 765 +r0:=-2/3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^(3/2))+8/3*b*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*sqrt(d+e*x))+16/3*b*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (6b e x + (- 12a b e + 24b d e)x - 2a e - 8a b d e + 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 4 2 4 3 3 +-------+ +--R (3b e x + (3a e + 3b d e )x + 3a d e )\|e x + d +--R Type: Expression(Integer) +--E 635 + +--S 636 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 of 765 +t0:=(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 637 + +--S 638 of 765 +r0:=-2/5*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(d+e*x)^(5/2))-8/5*b*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(d+e*x)^(3/2))-16/15*b*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 30b e x + (- 20a b e - 40b d e)x - 6a e - 8a b d e - 16b d ) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 3 5 4 2 4 2 3 2 3 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 638 + +--S 639 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 640 + +--S 641 of 765 +r0:=-16/195*(b*d-a*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/15*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/6435*(b*d-_ + a*e)^3*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/45045*(b*d-_ + a*e)^4*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/715*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 6006b e x + (27720a b e + 14322b d e )x +--R + +--R 2 2 7 3 6 4 2 5 5 +--R (49140a b e + 68040a b d e + 8946b d e )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 4 +--R (40040a b e + 125580a b d e + 44520a b d e + 70b d e )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (12870a e + 108680a b d e + 88140a b d e + 600a b d e - 80b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (38610a d e + 85800a b d e + 2340a b d e - 720a b d e + 96b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 +--R (38610a d e + 5720a b d e - 3120a b d e + 960a b d e - 128b d e)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 12870a d e - 11440a b d e + 6240a b d e - 1920a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 641 + +--S 642 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 643 + +--S 644 of 765 +r0:=-16/143*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/13*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/3003*_ + (b*d-a*e)^3*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/15015*_ + (b*d-a*e)^4*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/429*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 6 6 3 6 4 5 5 +--R 2310b e x + (10920a b e + 2940b d e )x +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (20020a b e + 14560a b d e + 70b d e )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (17160a b e + 28600a b d e + 520a b d e - 80b d e )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (6006a e + 27456a b d e + 1716a b d e - 624a b d e + 96b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (12012a d e + 3432a b d e - 2288a b d e + 832a b d e - 128b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 6006a d e - 6864a b d e + 4576a b d e - 1664a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 15015b e x + 15015a e +--R Type: Expression(Integer) +--E 644 + +--S 645 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (1) (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 765 +r0:=-16/99*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^2+_ + 2/11*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e-128/1155*_ + (b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+256/3465*_ + (b*d-a*e)^4*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/231*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 5 5 3 5 4 4 4 +--R 630b e x + (3080a b e + 70b d e )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (5940a b e + 440a b d e - 80b d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (5544a b e + 1188a b d e - 528a b d e + 96b d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (2310a e + 1848a b d e - 1584a b d e + 704a b d e - 128b d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 2310a d e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 3465b e x + 3465a e +--R Type: Expression(Integer) +--E 647 + +--S 648 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 649 + +--S 650 of 765 +r0:=-16/63*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^2+_ + 2/9*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e-_ + 128/315*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+_ + 256/315*(b*d-a*e)^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+_ + 32/105*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (360a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (756a b e - 432a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e)x + 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1680a b d e + 2016a b d e - 1152a b d e + 256b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 5 5 +--R 315b e x + 315a e +--R Type: Expression(Integer) +--E 650 + +--S 651 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 652 + +--S 653 of 765 +r0:=-2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*sqrt(d+e*x))+16/7*b*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^2+128/35*b*(b*d-a*e)^2*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-256/35*b*(b*d-a*e)^3*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-96/35*b*(b*d-a*e)*_ + (a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (56a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (140a b e - 112a b d e + 32b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (280a b e - 560a b d e + 448a b d e - 128b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 560a b d e - 1120a b d e + 896a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 5 5 +-------+ +--R (35b e x + 35a e )\|e x + d +--R Type: Expression(Integer) +--E 653 + +--S 654 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 655 + +--S 656 of 765 +r0:=-2/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(3/2))-_ + 16/3*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*sqrt(d+e*x))-_ + 128/15*b^2*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+_ + 256/15*b^2*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*_ + (a+b*x))+32/5*b^2*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 6b e x + (40a b e - 16b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (180a b e - 240a b d e + 96b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 120a b e + 720a b d e - 960a b d e + 384b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e + 480a b d e - 640a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 6 2 6 5 5 +-------+ +--R (15b e x + (15a e + 15b d e )x + 15a d e )\|e x + d +--R Type: Expression(Integer) +--E 656 + +--S 657 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 658 + +--S 659 of 765 +r0:=-2/5*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(5/2))-_ + 16/15*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-32/5*b^2*_ + (a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*sqrt(d+e*x))+128/15*b^3*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4-256/15*b^3*(b*d-a*e)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 10b e x + (120a b e - 80b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 180a b e + 720a b d e - 480b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 40a b e - 240a b d e + 960a b d e - 640b d e)x - 6a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 96a b d e + 384a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 3 7 6 2 6 2 5 2 5 +--R (15b e x + (15a e + 30b d e )x + (30a d e + 15b d e )x + 15a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 659 + +--S 660 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(9/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) --------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 661 + +--S 662 of 765 +r0:=-2/7*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(7/2))-_ + 16/35*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(5/2))-_ + 32/35*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(3/2))+_ + 128/35*b^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*sqrt(d+e*x))+_ + 256/35*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 70b e x + (- 280a b e + 560b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 140a b e - 560a b d e + 1120b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 56a b e - 112a b d e - 448a b d e + 896b d e)x - 10a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 16a b d e - 32a b d e - 128a b d e + 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 4 8 7 3 7 2 6 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 6 3 5 3 5 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 662 + +--S 663 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(11/2) +--R +--R +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 664 + +--S 665 of 765 +r0:=-2/9*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(9/2))-_ + 16/63*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(7/2))-_ + 32/105*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(5/2))-_ + 128/105*b^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(d+e*x)^(3/2))-_ + 256/315*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 630b e x + (- 840a b e - 1680b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 756a b e - 1008a b d e - 2016b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 360a b e - 432a b d e - 576a b d e - 1152b d e)x - 70a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b d e - 96a b d e - 128a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 5 9 8 4 8 2 7 3 +--R 315b e x + (315a e + 1260b d e )x + (1260a d e + 1890b d e )x +--R + +--R 2 7 3 6 2 3 6 4 5 4 5 +--R (1890a d e + 1260b d e )x + (1260a d e + 315b d e )x + 315a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 665 + +--S 666 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 667 + +--S 668 of 765 +r0:=-2/11*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e*(d+e*x)^(11/2))-_ + 16/99*b*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^2*(d+e*x)^(9/2))-32/231*b^2*_ + (a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(d+e*x)^(7/2))-128/693*b^3*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(d+e*x)^(5/2))-256/3465*b^3*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 2310b e x + (- 5544a b e - 3696b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 5940a b e - 4752a b d e - 3168b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 3080a b e - 2640a b d e - 2112a b d e - 1408b d e)x - 630a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 560a b d e - 480a b d e - 384a b d e - 256b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 6 10 9 5 +--R 3465b e x + (3465a e + 17325b d e )x +--R + +--R 9 2 8 4 2 8 3 7 3 +--R (17325a d e + 34650b d e )x + (34650a d e + 34650b d e )x +--R + +--R 3 7 4 6 2 4 6 5 5 5 5 +--R (34650a d e + 17325b d e )x + (17325a d e + 3465b d e )x + 3465a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 668 + +--S 669 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b e x + (5a b e + 2b d e)x + (10a b e + 10a b d e + b d )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b e + 20a b d e + 5a b d )x + (5a b e + 20a b d e + 10a b d )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a e + 10a b d e + 10a b d )x + (2a d e + 5a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 670 + +--S 671 of 765 +r0:=-128/4199*(b*d-a*e)^3*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/323*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 24/323*(b*d-a*e)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/19*_ + (a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/138567*(b*d-_ + a*e)^5*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/969969*(b*d-_ + a*e)^6*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+768/46189*_ + (b*d-a*e)^4*(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 9 9 5 9 6 8 8 +--R 102102b e x + (684684a b e + 234234b d e )x +--R + +--R 2 4 9 5 8 6 2 7 7 +--R (1939938a b e + 1597596a b d e + 138138b d e )x +--R + +--R 3 3 9 2 4 8 5 2 7 6 3 6 6 +--R (2984520a b e + 4626006a b d e + 965580a b d e + 462b d e )x +--R + +--R 4 2 9 3 3 8 2 4 2 7 5 3 6 +--R 2645370a b e + 7325640a b d e + 2889558a b d e + 4788a b d e +--R + +--R 6 4 5 +--R - 504b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 2 8 3 3 2 7 2 4 3 6 +--R 1293292a b e + 6760390a b d e + 4793320a b d e + 22610a b d e +--R + +--R 5 4 5 6 5 4 +--R - 5320a b d e + 560b d e +--R * +--R 4 +--R x +--R + +--R 6 9 5 8 4 2 2 7 3 3 3 6 +--R 277134a e + 3510364a b d e + 4744870a b d e + 64600a b d e +--R + +--R 2 4 4 5 5 5 4 6 6 3 +--R - 25840a b d e + 6080a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 2 7 4 2 3 6 3 3 4 5 +--R 831402a d e + 2771340a b d e + 125970a b d e - 77520a b d e +--R + +--R 2 4 5 4 5 6 3 6 7 2 +--R 31008a b d e - 7296a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 2 7 5 3 6 4 2 4 5 3 3 5 4 +--R 831402a d e + 184756a b d e - 167960a b d e + 103360a b d e +--R + +--R 2 4 6 3 5 7 2 6 8 +--R - 41344a b d e + 9728a b d e - 1024b d e +--R * +--R x +--R + +--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 +--R 277134a d e - 369512a b d e + 335920a b d e - 206720a b d e +--R + +--R 2 4 7 2 5 8 6 9 +--R 82688a b d e - 19456a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 969969b e x + 969969a e +--R Type: Expression(Integer) +--E 671 + +--S 672 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b e x + (5a b e + b d)x + (10a b e + 5a b d)x + (10a b e + 10a b d)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b e + 10a b d)x + (a e + 5a b d)x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 673 + +--S 674 of 765 +r0:=-128/2431*(b*d-a*e)^3*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/221*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 8/85*(b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/17*(a+_ + b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/51051*(b*d-a*e)^5*_ + (d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/255255*(b*d-a*e)^6*(d+_ + e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/7293*(b*d-a*e)^4*_ + (a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 8 8 5 8 6 7 7 +--R 30030b e x + (204204a b e + 36036b d e )x +--R + +--R 2 4 8 5 7 6 2 6 6 +--R (589050a b e + 251328a b d e + 462b d e )x +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (928200a b e + 749700a b d e + 4284a b d e - 504b d e )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 +--R 850850a b e + 1237600a b d e + 17850a b d e - 4760a b d e +--R + +--R 6 4 4 +--R 560b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 +--R 437580a b e + 1215500a b d e + 44200a b d e - 20400a b d e +--R + +--R 5 4 4 6 5 3 +--R 5440a b d e - 640b d e +--R * +--R 3 +--R x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 +--R 102102a e + 700128a b d e + 72930a b d e - 53040a b d e +--R + +--R 2 4 4 4 5 5 3 6 6 2 +--R 24480a b d e - 6528a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 3 3 4 4 +--R 204204a d e + 87516a b d e - 97240a b d e + 70720a b d e +--R + +--R 2 4 5 3 5 6 2 6 7 +--R - 32640a b d e + 8704a b d e - 1024b d e +--R * +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 +--R 102102a d e - 175032a b d e + 194480a b d e - 141440a b d e +--R + +--R 2 4 6 2 5 7 6 8 +--R 65280a b d e - 17408a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 255255b e x + 255255a e +--R Type: Expression(Integer) +--E 674 + +--S 675 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x) +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 765 +r0:=-128/1287*(b*d-a*e)^3*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^4+_ + 16/143*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/e^3-_ + 8/65*(b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e^2+2/15*(a+_ + b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/e-1024/15015*(b*d-_ + a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/45045*(b*d-_ + a*e)^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+_ + 256/3003*(b*d-a*e)^4*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 7 7 5 7 6 6 6 +--R 6006b e x + (41580a b e + 462b d e )x +--R + +--R 2 4 7 5 6 6 2 5 5 +--R (122850a b e + 3780a b d e - 504b d e )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 4 +--R (200200a b e + 13650a b d e - 4200a b d e + 560b d e )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 +--R 193050a b e + 28600a b d e - 15600a b d e + 4800a b d e +--R + +--R 6 4 3 +--R - 640b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 108108a b e + 38610a b d e - 34320a b d e + 18720a b d e +--R + +--R 5 4 3 6 5 2 +--R - 5760a b d e + 768b d e +--R * +--R 2 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 30030a e + 36036a b d e - 51480a b d e + 45760a b d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 24960a b d e + 7680a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 30030a d e - 72072a b d e + 102960a b d e - 91520a b d e +--R + +--R 2 4 5 2 5 6 6 7 +--R 49920a b d e - 15360a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 45045b e x + 45045a e +--R Type: Expression(Integer) +--E 677 + +--S 678 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 678 + +)clear all + +--S 679 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(d+e*x) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 679 + +--S 680 of 765 +r0:=-640/3003*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+_ + 80/429*(b*d-a*e)^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3-_ + 24/143*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e^2+2/13*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e-1024/3003*(b*d-a*e)^5*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/3003*(b*d-a*e)^6*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/1001*(b*d-_ + a*e)^4*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (3276a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (10010a b e - 3640a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (17160a b e - 11440a b d e + 4160a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R 18018a b e - 20592a b d e + 13728a b d e - 4992a b d e +--R + +--R 6 4 2 +--R 768b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 12012a b e - 24024a b d e + 27456a b d e - 18304a b d e +--R + +--R 5 4 2 6 5 +--R 6656a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R 6006a e - 24024a b d e + 48048a b d e - 54912a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R 36608a b d e - 13312a b d e + 2048b d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R / +--R 7 7 +--R 3003b e x + 3003a e +--R Type: Expression(Integer) +--E 680 + +--S 681 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 682 + +--S 683 of 765 +r0:=-2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*sqrt(d+e*x))+640/231*b*(b*d-_ + a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4-80/33*b*(b*d-a*e)*_ + (a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3+24/11*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)/e^2+1024/231*b*(b*d-a*e)^4*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6-2048/231*b*(b*d-a*e)^5*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-256/77*b*(b*d-a*e)^3*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (308a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (990a b e - 440a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1848a b e - 1584a b d e + 704a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (2310a b e - 3696a b d e + 3168a b d e - 1408a b d e + 256b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 2772a b e - 9240a b d e + 14784a b d e - 12672a b d e +--R + +--R 5 4 2 6 5 +--R 5632a b d e - 1024b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 +--R - 462a e + 5544a b d e - 18480a b d e + 29568a b d e +--R + +--R 2 4 4 2 5 5 6 6 +--R - 25344a b d e + 11264a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 7 7 +-------+ +--R (231b e x + 231a e )\|e x + d +--R Type: Expression(Integer) +--E 683 + +--S 684 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 685 + +--S 686 of 765 +r0:=-2/3*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(3/2))-8*b*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e^2*sqrt(d+e*x))-640/63*b^2*(b*d-a*e)*_ + (a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^4+80/9*b^2*(a+b*x)*(a^2+_ + 2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)/e^3-1024/63*b^2*(b*d-a*e)^3*sqrt(d+_ + e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/63*b^2*(b*d-a*e)^4*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+256/21*b^2*(b*d-a*e)^2*(a+b*x)*_ + sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (108a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (378a b e - 216a b d e + 48b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (840a b e - 1008a b d e + 576a b d e - 128b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (1890a b e - 5040a b d e + 6048a b d e - 3456a b d e + 768b d e )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 756a b e + 7560a b d e - 20160a b d e + 24192a b d e +--R + +--R 5 4 2 6 5 +--R - 13824a b d e + 3072b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 504a b d e + 5040a b d e - 13440a b d e + 16128a b d e +--R + +--R 5 5 6 6 +--R - 9216a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 8 2 8 7 7 +-------+ +--R (63b e x + (63a e + 63b d e )x + 63a d e )\|e x + d +--R Type: Expression(Integer) +--E 686 + +--S 687 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 688 + +--S 689 of 765 +r0:=-2/5*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(5/2))-8/5*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(3/2))-16*b^2*(a+b*x)*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^3*sqrt(d+e*x))+128/7*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*_ + sqrt(d+e*x)/e^4+1024/35*b^3*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6-2048/35*b^3*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x))-768/35*b^3*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 10b e x + (84a b e - 24b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (350a b e - 280a b d e + 80b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1400a b e - 2800a b d e + 2240a b d e - 640b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1050a b e + 8400a b d e - 16800a b d e + 13440a b d e +--R + +--R 6 4 2 +--R - 3840b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 140a b e - 1400a b d e + 11200a b d e - 22400a b d e +--R + +--R 5 4 2 6 5 +--R 17920a b d e - 5120b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 56a b d e - 560a b d e + 4480a b d e - 8960a b d e +--R + +--R 5 5 6 6 +--R 7168a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 9 3 9 8 2 8 2 7 2 7 +--R (35b e x + (35a e + 70b d e )x + (70a d e + 35b d e )x + 35a d e ) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 689 + +--S 690 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(9/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 691 + +--S 692 of 765 +r0:=-16/7*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(3/2))-_ + 2/7*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(7/2))-24/35*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(5/2))-128/7*b^3*(a^2+2*a*b*x+_ + b^2*x^2)^(3/2)/(e^4*sqrt(d+e*x))-1024/35*b^4*(b*d-a*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^6+2048/35*b^4*(b*d-a*e)^2*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+768/35*b^4*(a+b*x)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/e^5 +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 14b e x + (140a b e - 56b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (1050a b e - 1400a b d e + 560b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1400a b e + 8400a b d e - 11200a b d e + 4480b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 350a b e - 2800a b d e + 16800a b d e - 22400a b d e +--R + +--R 6 4 2 +--R 8960b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 84a b e - 280a b d e - 2240a b d e + 13440a b d e +--R + +--R 5 4 2 6 5 +--R - 17920a b d e + 7168b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a e - 24a b d e - 80a b d e - 640a b d e + 3840a b d e +--R + +--R 5 5 6 6 +--R - 5120a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 10 4 10 9 3 9 2 8 2 +--R 35b e x + (35a e + 105b d e )x + (105a d e + 105b d e )x +--R + +--R 2 8 3 7 3 7 +--R (105a d e + 35b d e )x + 35a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 692 + +--S 693 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(11/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 694 + +--S 695 of 765 +r0:=-16/21*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(5/2))-_ + 128/63*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(3/2))-2/9*(a+b*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(9/2))-8/21*b*(a^2+2*a*b*x+_ + b^2*x^2)^(5/2)/(e^2*(d+e*x)^(7/2))-256/21*b^4*(a+b*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^5*sqrt(d+e*x))+1024/63*b^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/e^6-2048/63*b^5*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2)/(e^7*(a+b*x)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 42b e x + (756a b e - 504b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1890a b e + 7560a b d e - 5040b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 840a b e - 5040a b d e + 20160a b d e - 13440b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 378a b e - 1008a b d e - 6048a b d e + 24192a b d e +--R + +--R 6 4 2 +--R - 16128b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 108a b e - 216a b d e - 576a b d e - 3456a b d e +--R + +--R 5 4 2 6 5 +--R 13824a b d e - 9216b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 14a e - 24a b d e - 48a b d e - 128a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R 3072a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 11 5 11 10 4 10 2 9 3 +--R 63b e x + (63a e + 252b d e )x + (252a d e + 378b d e )x +--R + +--R 2 9 3 8 2 3 8 4 7 4 7 +--R (378a d e + 252b d e )x + (252a d e + 63b d e )x + 63a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 695 + +--S 696 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 697 + +--S 698 of 765 +r0:=-80/231*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(7/2))-_ + 128/231*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(5/2))-2/11*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(11/2))-8/33*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(9/2))-256/231*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(3/2))+1024/231*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*sqrt(d+e*x))+2048/231*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R 462b e x + (- 2772a b e + 5544b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 2310a b e - 9240a b d e + 18480b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 1848a b e - 3696a b d e - 14784a b d e + 29568b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 990a b e - 1584a b d e - 3168a b d e - 12672a b d e +--R + +--R 6 4 2 +--R 25344b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 308a b e - 440a b d e - 704a b d e - 1408a b d e +--R + +--R 5 4 2 6 5 +--R - 5632a b d e + 11264b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 42a e - 56a b d e - 80a b d e - 128a b d e - 256a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e + 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 12 6 12 11 5 11 2 10 4 +--R 231b e x + (231a e + 1155b d e )x + (1155a d e + 2310b d e )x +--R + +--R 2 10 3 9 3 3 9 4 8 2 +--R (2310a d e + 2310b d e )x + (2310a d e + 1155b d e )x +--R + +--R 4 8 5 7 5 7 +--R (1155a d e + 231b d e )x + 231a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 698 + +--S 699 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(15/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 700 + +--S 701 of 765 +r0:=-80/429*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(9/2))-_ + 640/3003*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(7/2))-2/13*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(13/2))-24/143*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(11/2))-256/1001*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(5/2))-1024/1001*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(d+e*x)^(3/2))-2048/3003*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 6006b e x + (- 12012a b e - 24024b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 18018a b e - 24024a b d e - 48048b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 17160a b e - 20592a b d e - 27456a b d e - 54912b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 10010a b e - 11440a b d e - 13728a b d e - 18304a b d e +--R + +--R 6 4 2 +--R - 36608b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 3276a b e - 3640a b d e - 4160a b d e - 4992a b d e +--R + +--R 5 4 2 6 5 +--R - 6656a b d e - 13312b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 462a e - 504a b d e - 560a b d e - 640a b d e - 768a b d e +--R + +--R 5 5 6 6 +--R - 1024a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 13 7 13 12 6 +--R 3003b e x + (3003a e + 18018b d e )x +--R + +--R 12 2 11 5 2 11 3 10 4 +--R (18018a d e + 45045b d e )x + (45045a d e + 60060b d e )x +--R + +--R 3 10 4 9 3 4 9 5 8 2 +--R (60060a d e + 45045b d e )x + (45045a d e + 18018b d e )x +--R + +--R 5 8 6 7 6 7 +--R (18018a d e + 3003b d e )x + 3003a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 701 + +--S 702 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 765 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(17/2) +--R +--R +--R (1) +--R +------------------+ +--R 5 5 4 4 2 3 3 3 2 2 4 5 | 2 2 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 703 + +--S 704 of 765 +r0:=-16/143*b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^3*(d+e*x)^(11/2))-_ + 128/1287*b^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(e^4*(d+e*x)^(9/2))-2/15*(a+_ + b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(e*(d+e*x)^(15/2))-8/65*b*(a^2+_ + 2*a*b*x+b^2*x^2)^(5/2)/(e^2*(d+e*x)^(13/2))-256/3003*b^4*(a+b*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(d+e*x)^(7/2))-1024/9009*b^5*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^6*(d+e*x)^(5/2))-2048/45045*b^5*(b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 6 6 6 5 6 6 5 5 +--R - 30030b e x + (- 108108a b e - 72072b d e )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 193050a b e - 154440a b d e - 102960b d e )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 200200a b e - 171600a b d e - 137280a b d e - 91520b d e )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 122850a b e - 109200a b d e - 93600a b d e - 74880a b d e +--R + +--R 6 4 2 +--R - 49920b d e +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R - 41580a b e - 37800a b d e - 33600a b d e - 28800a b d e +--R + +--R 5 4 2 6 5 +--R - 23040a b d e - 15360b d e +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 6006a e - 5544a b d e - 5040a b d e - 4480a b d e - 3840a b d e +--R + +--R 5 5 6 6 +--R - 3072a b d e - 2048b d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 14 8 14 13 7 +--R 45045b e x + (45045a e + 315315b d e )x +--R + +--R 13 2 12 6 2 12 3 11 5 +--R (315315a d e + 945945b d e )x + (945945a d e + 1576575b d e )x +--R + +--R 3 11 4 10 4 4 10 5 9 3 +--R (1576575a d e + 1576575b d e )x + (1576575a d e + 945945b d e )x +--R + +--R 5 9 6 8 2 6 8 7 7 +--R (945945a d e + 315315b d e )x + (315315a d e + 45045b d e )x +--R + +--R 7 7 +--R 45045a d e +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 704 + +--S 705 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 765 +r0:=2/9*(a+b*x)*(d+e*x)^(9/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 5 4 3 4 3 2 2 3 +--R 2b e x + (2a e + 8b d e )x + (8a d e + 12b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (12a d e + 8b d e)x + (8a d e + 2b d )x + 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 9e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 707 + +--S 708 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 709 + +--S 710 of 765 +r0:=2/7*(a+b*x)*(d+e*x)^(7/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 4 3 2 3 2 2 2 +--R 2b e x + (2a e + 6b d e )x + (6a d e + 6b d e)x +--R + +--R 2 3 3 +--R (6a d e + 2b d )x + 2a d +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R | 2 2 2 +--R 7e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 710 + +--S 711 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 711 + +)clear all + +--S 712 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R 2 +-------+ +--R (b e x + (a e + b d)x + a d)\|e x + d +--R (1) --------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 712 + +--S 713 of 765 +r0:=2/5*(a+b*x)*(d+e*x)^(5/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (2b e x + (2a e + 4b d e)x + (4a d e + 2b d )x + 2a d )\|e x + d +--R (2) -------------------------------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 5e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 713 + +--S 714 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2) +--R +--R +--R +-------+ +--R (b x + a)\|e x + d +--R (1) --------------------- +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 715 + +--S 716 of 765 +r0:=2/3*(a+b*x)*(d+e*x)^(3/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R 2 +-------+ +--R (2b e x + (2a e + 2b d)x + 2a d)\|e x + d +--R (2) ------------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R 3e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 765 +t0:=(a+b*x)/(sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 718 + +--S 719 of 765 +r0:=2*(a+b*x)*sqrt(d+e*x)/(e*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R +-------+ +--R (2b x + 2a)\|e x + d +--R (2) ---------------------- +--R +------------------+ +--R | 2 2 2 +--R e\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 719 + +--S 720 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 765 +t0:=(a+b*x)/((d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (e x + d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 721 + +--S 722 of 765 +r0:=-2*(a+b*x)/(e*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) -------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R e\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 722 + +--S 723 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 of 765 +t0:=(a+b*x)/((d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) --------------------------------------------------- +--R +------------------+ +--R 2 2 2 +-------+ | 2 2 2 +--R (e x + 2d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 765 +r0:=-2/3*(a+b*x)/(e*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) -------------------------------------------- +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (3e x + 3d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 725 + +--S 726 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 726 + +)clear all + +--S 727 of 765 +t0:=(a+b*x)/((d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R b x + a +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 727 + +--S 728 of 765 +r0:=-2/5*(a+b*x)/(e*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R - 2b x - 2a +--R (2) ------------------------------------------------------- +--R +------------------+ +--R 3 2 2 2 +-------+ | 2 2 2 +--R (5e x + 10d e x + 5d e)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 728 + +--S 729 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 730 + +--S 731 of 765 +r0:=7/3*e*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+_ + 7/5*e*(a+b*x)*(d+e*x)^(5/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^(7/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-7*e*(b*d-a*e)^(5/2)*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+7*e*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 105a b e + 210a b d e - 105b d e)x - 105a e + 210a b d e +--R + +--R 2 2 +--R - 105a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b e x + (- 14a b e + 32b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b e - 168a b d e + 116b d e)x + 105a e - 245a b d e +--R + +--R 2 2 3 3 +--R 161a b d e - 15b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 4 +-+ | 2 2 2 +--R 15b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 731 + +--S 732 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 732 + +)clear all + +--S 733 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 765 +r0:=5/3*e*(a+b*x)*(d+e*x)^(3/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + (d+e*x)^(5/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-5*e*(b*d-a*e)^(3/2)*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+5*e*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)/(b^3*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 +-----------+ +--R ((15a b e - 15b d e)x + 15a e - 15a b d e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (2b e x + (- 10a b e + 14b d e)x - 15a e + 20a b d e - 3b d )\|b +--R * +--R +-------+ +--R \|e x + d +--R / +--R +------------------+ +--R 3 +-+ | 2 2 2 +--R 3b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 734 + +--S 735 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 736 + +--S 737 of 765 +r0:=-(d+e*x)^(3/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-3*e*(a+b*x)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(5/2)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))+3*e*(a+b*x)*sqrt(d+e*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (- 3b e x - 3a e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-+ +-------+ +--R (2b e x + 3a e - b d)\|b \|e x + d +--R / +--R +------------------+ +--R 2 +-+ | 2 2 2 +--R b \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 737 + +--S 738 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 738 + +)clear all + +--S 739 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ------------------------------ +--R +------------------+ +--R | 2 2 2 +--R (b x + a)\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 739 + +--S 740 of 765 +r0:=-e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-sqrt(d+e*x)/(b*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +-----------+ +-+ +-------+ +--R (- b e x - a e)atanh(--------------) - \|- a e + b d \|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R b\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 740 + +--S 741 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 741 + +)clear all + +--S 742 of 765 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R +------------------+ +--R +-------+ | 2 2 2 +--R (b x + a)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 742 + +--S 743 of 765 +r0:=e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(3/2)*_ + sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-sqrt(d+e*x)/((b*d-a*e)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R +-+ +-------+ +--R \|b \|e x + d +-----------+ +-+ +-------+ +--R (- b e x - a e)atanh(--------------) + \|- a e + b d \|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R (2) ------------------------------------------------------------------- +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R (a e - b d)\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 743 + +--S 744 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 744 + +)clear all + +--S 745 of 765 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------ +--R +------------------+ +--R 2 +-------+ | 2 2 2 +--R (b e x + (a e + b d)x + a d)\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 745 + +--S 746 of 765 +r0:=3*e*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-_ + a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2/((b*d-a*e)*sqrt(d+e*x)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-3*b*sqrt(d+e*x)/((b*d-a*e)^2*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R (3b e x + 3a e)\|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R (- 3b e x - 2a e - b d)\|- a e + b d +--R / +--R +------------------+ +--R 2 2 2 2 +-----------+ +-------+ | 2 2 2 +--R (a e - 2a b d e + b d )\|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 746 + +--S 747 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 747 + +)clear all + +--S 748 of 765 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 748 + +--S 749 of 765 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5*b^(3/2)*e*_ + (a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+10/3*b/((b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))-5*b^2*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 2 2 2 2 2 +-+ +-------+ +--R (- 15b e x + (- 15a b e - 15b d e)x - 15a b d e)\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (10a b e + 20b d e)x - 2a e + 14a b d e + 3b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a e - 9a b d e + 9a b d e - 3b d e)x + 3a d e - 9a b d e +--R + +--R 2 3 3 4 +--R 9a b d e - 3b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 749 + +--S 750 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 765 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 751 + +--S 752 of 765 +r0:=2/5/((b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+14/15*b/((b*d-_ + a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7*b^(5/2)*e*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(a^2+_ + 2*a*b*x+b^2*x^2))+14/3*b^2/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+_ + b^2*x^2))-7*b^3*sqrt(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R 105b e x + (105a b e + 210b d e )x + (210a b d e + 105b d e)x +--R + +--R 2 2 +--R 105a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 70a b e - 245b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (14a b e - 168a b d e - 161b d e)x - 6a e + 32a b d e +--R + +--R 2 2 3 3 +--R - 116a b d e - 15b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (15a e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (30a d e - 120a b d e + 180a b d e - 120a b d e + 30b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 752 + +--S 753 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 of 765 +t0:=(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 754 + +--S 755 of 765 +r0:=-7/12*e*(a+b*x)*(d+e*x)^(5/2)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^(7/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-35/24*e^2*_ + (d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-35/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(9/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+35/8*e^3*(a+b*x)*sqrt(d+e*x)/(b^4*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-----------+ +--R (- 105b e x - 315a b e x - 315a b e x - 105a e )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b e x + (231a b e - 87b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (280a b e - 98a b d e - 38b d e)x + 105a e - 35a b d e +--R + +--R 2 2 3 3 +--R - 14a b d e - 8b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R +------------------+ +--R 6 2 5 2 4 +-+ | 2 2 2 +--R (24b x + 48a b x + 24a b )\|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 755 + +--S 756 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 756 + +)clear all + +--S 757 of 765 +t0:=(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 757 + +--S 758 of 765 +r0:=-5/12*e*(a+b*x)*(d+e*x)^(3/2)/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + 1/3*(d+e*x)^(5/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))-5/8*e^2*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+_ + b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 15b e x - 45a b e x - 45a b e x - 15a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 33b e x + (- 40a b e - 26b d e)x - 15a e - 10a b d e - 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R +------------------+ +--R 5 2 4 2 3 +-----------+ +-+ | 2 2 2 +--R (24b x + 48a b x + 24a b )\|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 758 + +--S 759 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 759 + +)clear all + +--S 760 of 765 +t0:=(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 760 + +--S 761 of 765 +r0:=-1/3*(d+e*x)^(3/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/4*e*(a+b*x)*_ + (d+e*x)^(3/2)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/8*e^3*(a+_ + b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+1/8*e^2*sqrt(d+e*x)/(b^2*(b*d-a*e)*_ + sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 3b e x - 9a b e x - 9a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (- 8a b e + 14b d e)x - 3a e - 2a b d e + 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +--R ((24a b e - 24b d)x + (48a b e - 48a b d)x + 24a b e - 24a b d) +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 761 + +--S 762 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 762 + +)clear all + +--S 763 of 765 +t0:=(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) --------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 763 + +--S 764 of 765 +r0:=-1/3*sqrt(d+e*x)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/12*e*(a+b*x)*_ + sqrt(d+e*x)/(b*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/8*e^3*(a+b*x)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2)*_ + sqrt(a^2+2*a*b*x+b^2*x^2))+1/8*e^2*sqrt(d+e*x)/(b*(b*d-a*e)^2*sqrt(a^2+_ + 2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 3b e x - 9a b e x - 9a b e x - 3a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b e x + (8a b e - 2b d e)x - 3a e + 14a b d e - 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (24a b e - 48a b d e + 24b d )x + (48a b e - 96a b d e + 48a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 24a b e - 48a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 764 + +--S 765 of 765 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 765 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/richder12f.input.pamphlet b/src/input/richder12f.input.pamphlet new file mode 100644 index 0000000..05cc5d5 --- /dev/null +++ b/src/input/richder12f.input.pamphlet @@ -0,0 +1,20523 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richder12f.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p| +There are 3 derivatives that did not match +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richder12f.output +)spool richder12f.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1035 +t0:=(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------- +--R +------------------+ +--R 3 3 2 2 2 3 +-------+ | 2 2 2 +--R (b x + 3a b x + 3a b x + a )\|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1035 +r0:=-1/3*sqrt(d+e*x)/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 5/12*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 5/8*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 5/8*e^2*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|e x + d +--R (- 15b e x - 45a b e x - 45a b e x - 15a e )atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b e x + (40a b e - 10b d e)x + 33a e - 26a b d e + 8b d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (24a b e - 72a b d e + 72a b d e - 24b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (48a b e - 144a b d e + 144a b d e - 48a b d )x + 24a e - 72a b d e +--R + +--R 3 2 2 2 3 3 +--R 72a b d e - 24a b d +--R * +--R +------------------+ +--R +-----------+ +-+ | 2 2 2 +--R \|- a e + b d \|b \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 3 + +)clear all + +--S 4 of 1035 +t0:=(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1035 +r0:=2/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))-_ + 7/3*b*sqrt(d+e*x)/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/12*b*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/8*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b)/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 35/8*b*e^2*sqrt(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-+ +-------+ +--R (105b e x + 315a b e x + 315a b e x + 105a e )\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b e x + (- 280a b e - 35b d e )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 231a b e - 98a b d e + 14b d e)x - 48a e - 87a b d e +--R + +--R 2 2 3 3 +--R 38a b d e - 8b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 +--R (48a b e - 192a b d e + 288a b d e - 192a b d e + 48a b d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R 24a e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 5 + +--S 6 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 6 + +)clear all + +--S 7 of 1035 +t0:=(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1035 +r0:=2/3/((b*d-a*e)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 6*b/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))-_ + 7*b^2*sqrt(d+e*x)/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 35/4*b^2*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 105/8*b^(3/2)*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 105/8*b^2*e^2*sqrt(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 315b e x + (- 945a b e - 315b d e )x +--R + +--R 2 2 4 3 3 2 3 4 2 2 3 +--R (- 945a b e - 945a b d e )x + (- 315a b e - 945a b d e )x +--R + +--R 3 3 +--R - 315a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 3 4 4 3 3 +--R 315b e x + (840a b e + 420b d e )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (693a b e + 1134a b d e + 63b d e )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (144a b e + 954a b d e + 180a b d e - 18b d e)x - 16a e +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 208a b d e + 165a b d e - 50a b d e + 8b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 24a b e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 7 5 +--R - 24b d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 6 5 +--R 48a b e - 216a b d e + 360a b d e - 240a b d e + 72a b d e +--R + +--R 7 6 +--R - 24b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 5 4 3 3 3 3 4 4 2 2 5 5 +--R 24a e - 72a b d e + 240a b d e - 360a b d e + 216a b d e +--R + +--R 6 6 +--R - 48a b d +--R * +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 +--R 24a d e - 120a b d e + 240a b d e - 240a b d e + 120a b d e +--R + +--R 2 5 6 +--R - 24a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 8 + +--S 9 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 9 + +)clear all + +--S 10 of 1035 +t0:=(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +------------------+ +--R +-------+ | 2 2 2 +--R \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 10 + +--S 11 of 1035 +r0:=2/5/((b*d-a*e)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 22/15*b/((b*d-a*e)^2*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 66/5*b^2/((b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x))-_ + 77/5*b^3*sqrt(d+e*x)/((b*d-a*e)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 77/4*b^3*e*(a+b*x)*sqrt(d+e*x)/((b*d-a*e)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2))+_ + 231/8*b^(5/2)*e^3*(a+b*x)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-_ + 231/8*b^3*e^2*sqrt(d+e*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 3465b e x + (10395a b e + 6930b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (10395a b e + 20790a b d e + 3465b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 2 +--R (3465a b e + 20790a b d e + 10395a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 2 3 +--R (6930a b d e + 10395a b d e )x + 3465a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 5 5 5 4 5 5 4 4 +--R - 3465b e x + (- 9240a b e - 8085b d e )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 7623a b e - 21714a b d e - 5313b d e )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 1584a b e - 18117a b d e - 14454a b d e - 495b d e )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (176a b e - 3872a b d e - 12309a b d e - 1430a b d e + 110b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 48a e + 416a b d e - 2768a b d e - 1335a b d e + 310a b d e +--R + +--R 5 5 +--R - 40b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 +--R 120a b e - 720a b d e + 1800a b d e - 2400a b d e +--R + +--R 2 6 4 4 7 5 3 8 6 2 +--R 1800a b d e - 720a b d e + 120b d e +--R * +--R 4 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 +--R 240a b e - 1200a b d e + 2160a b d e - 1200a b d e +--R + +--R 3 5 4 4 2 6 5 3 7 6 2 8 7 +--R - 1200a b d e + 2160a b d e - 1200a b d e + 240b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R 120a e - 240a b d e - 960a b d e + 4080a b d e - 6000a b d e +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R 4080a b d e - 960a b d e - 240a b d e + 120b d +--R * +--R 2 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 +--R 240a d e - 1200a b d e + 2160a b d e - 1200a b d e +--R + +--R 4 4 5 3 3 5 6 2 2 6 7 7 8 +--R - 1200a b d e + 2160a b d e - 1200a b d e + 240a b d +--R * +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 +--R 120a d e - 720a b d e + 1800a b d e - 2400a b d e + 1800a b d e +--R + +--R 3 5 7 2 6 8 +--R - 720a b d e + 120a b d +--R * +--R +------------------+ +--R +-----------+ +-------+ | 2 2 2 +--R \|- a e + b d \|e x + d \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 1035 +t0:=(a+b*x)*(d+e*x)^(-3-2*p)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R - 2p - 3 2 2 2 p +--R (1) (b x + a)(e x + d) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 13 + +--S 14 of 1035 +r0:=1/2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/((b*d-a*e)*(1+p)*(d+e*x)^(2*(1+p))) +--R +--R +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R (2) - --------------------------------------------- +--R 2p + 2 +--R ((2a e - 2b d)p + 2a e - 2b d)(e x + d) +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1035 +t0:=(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R 2 2 2 p +--R (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1035 +r0:=3/2*(b*d-a*e)^3*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^4*(1+p)*(2+p)*(3+2*p)*_ + (5+2*p))+3*(b*d-a*e)^2*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^3*(2+p)*_ + (3+2*p)*(5+2*p))+3/2*(b*d-a*e)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/_ + (b^2*(2+p)*(5+2*p))+(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(5+2*p)) +--R +--R +--R (2) +--R 3 3 3 3 3 2 3 3 3 3 3 +--R (4b e p + 18b e p + 26b e p + 12b e )x +--R + +--R 3 2 3 2 3 3 2 2 2 3 3 2 +--R 12b d e p + (- 6a b e + 60b d e )p + (- 15a b e + 93b d e )p +--R + +--R 2 3 3 2 +--R - 9a b e + 45b d e +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 3 2 2 +--R 12b d e p + (- 12a b d e + 66b d e)p +--R + +--R 2 3 2 2 3 2 2 3 2 2 3 2 +--R (6a b e - 42a b d e + 114b d e)p + 6a b e - 30a b d e + 60b d e +--R * +--R x +--R + +--R 3 3 3 2 2 3 3 2 2 2 2 2 3 3 +--R 4b d p + (- 6a b d e + 24b d )p + (6a b d e - 27a b d e + 47b d )p +--R + +--R 3 3 2 2 2 2 3 3 +--R - 3a e + 15a b d e - 30a b d e + 30b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 4 4 4 3 4 2 4 4 +--R 8b p + 56b p + 142b p + 154b p + 60b +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 18 + +)clear all + +--S 19 of 1035 +t0:=(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R (1) +--R 2 3 2 2 2 2 2 2 2 p +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1035 +r0:=1/2*(b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^3*(1+p)*(2+p)*(3+2*p))+_ + (b*d-a*e)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^2*(2+p)*(3+2*p))+_ + 1/2*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(2+p)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (2b e p + 5b e p + 3b e )x +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4b d e p + (- 2a b e + 12b d e)p - 2a b e + 8b d e)x + 2b d p +--R + +--R 2 2 2 2 2 2 +--R (- 2a b d e + 7b d )p + a e - 4a b d e + 6b d +--R * +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R / +--R 3 3 3 2 3 3 +--R 4b p + 18b p + 26b p + 12b +--R Type: Expression(Integer) +--E 20 + +--S 21 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 of 1035 +t0:=(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R 2 2 2 2 p +--R (1) (b e x + (a e + b d)x + a d)(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1035 +r0:=1/2*(b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b^2*(1+p)*(3+2*p))+(d+e*x)*_ + (a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(3+2*p)) +--R +--R +--R 2 2 2 p + 1 +--R ((2b e p + 2b e)x + 2b d p - a e + 3b d)(b x + 2a b x + a ) +--R (2) ----------------------------------------------------------------- +--R 2 2 2 2 +--R 4b p + 10b p + 6b +--R Type: Expression(Integer) +--E 23 + +--S 24 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 24 + +)clear all + +--S 25 of 1035 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R 2 2 2 p +--R (1) (b x + a)(b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 25 + +--S 26 of 1035 +r0:=1/2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(1+p)) +--R +--R +--R 2 2 2 p + 1 +--R (b x + 2a b x + a ) +--R (2) ------------------------- +--R 2b p + 2b +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 27 + +)clear all + +--S 28 of 1035 +t0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p/(d+e*x) +--R +--R +--R 2 2 2 p +--R (b x + a)(b x + 2a b x + a ) +--R (1) ------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 28 + +--S 29 of 1035 +--r0:=(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p/(e*(1+2*p))-(a+b*x)*_ +-- (a^2+2*a*b*x+b^2*x^2)^p*hypergeometric(1,1+2*p,2*(1+p),_ +-- -e*(a+b*x)/(b*d-a*e))/(e*(1+2*p)) +--E 29 + +--S 30 of 1035 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 1035 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 6 7 6 5 6 5 2 4 5 +--R B b x + (A b + 6B a b )x + (6A a b + 15B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 4 2 5 2 +--R (15A a b + 20B a b )x + (20A a b + 15B a b )x + (15A a b + 6B a b)x +--R + +--R 5 6 6 +--R (6A a b + B a )x + A a +--R * +--R m +--R (b c x + a c) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1035 +r0:=(A*b-a*B)*(a*c+b*c*x)^(7+m)/(b^2*c^7*(7+m))+B*(a*c+b*c*x)^(8+m)/_ + (b^2*c^8*(8+m)) +--R +--R +--R (2) +--R m + 8 +--R (B m + 7B)(b c x + a c) +--R + +--R m + 7 +--R ((A b - B a)c m + (8A b - 8B a)c)(b c x + a c) +--R / +--R 2 8 2 2 8 2 8 +--R b c m + 15b c m + 56b c +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 of 1035 +t0:=(A+B*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R m +--R (B x + A)(b c x + a c) +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1035 +r0:=-(A*b-a*B)*c^5*(a*c+b*c*x)^(-5+m)/(b^2*(5-m))-B*c^4*(a*c+b*c*x)^(-4+m)/_ + (b^2*(4-m)) +--R +--R +--R (2) +--R 4 4 m - 4 +--R (B c m - 5B c )(b c x + a c) +--R + +--R 5 5 m - 5 +--R ((A b - B a)c m + (- 4A b + 4B a)c )(b c x + a c) +--R / +--R 2 2 2 2 +--R b m - 9b m + 20b +--R Type: Expression(Integer) +--E 35 + +--S 36 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 36 + +)clear all + +--S 37 of 1035 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 m +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )(b c x + a c) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1035 +r0:=(A*b-a*B)*(a*c+b*c*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*c*(4+m))+_ + B*(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(b^2*c^2*(5+m)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R ((B b m + 4B b )x + (2B a b m + 8B a b)x + B a m + 4B a ) +--R * +--R m + 2 +--R (b c x + a c) +--R + +--R 3 2 3 2 2 +--R ((A b - B a b )c m + (5A b - 5B a b )c)x +--R + +--R 2 2 2 2 +--R ((2A a b - 2B a b)c m + (10A a b - 10B a b)c)x +--R + +--R 2 3 2 3 +--R (A a b - B a )c m + (5A a b - 5B a )c +--R * +--R m + 1 +--R (b c x + a c) +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R 2 2 2 2 2 2 2 +--R b c m + 9b c m + 20b c +--R Type: Expression(Integer) +--E 38 + +--S 39 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 39 + +)clear all + +--S 40 of 1035 +t0:=(A+B*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^(3/2) +--R +--R +--R m +--R (B x + A)(b c x + a c) +--R (1) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + 2a b x + a )\|b x + 2a b x + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1035 +r0:=-(A*b-a*B)*(a*c+b*c*x)^(1+m)/(b^2*c*(2-m)*(a^2+2*a*b*x+b^2*x^2)^(3/2))-_ + B*(a*c+b*c*x)^(2+m)/(b^2*c^2*(1-m)*(a^2+2*a*b*x+b^2*x^2)^(3/2)) +--R +--R +--R (2) +--R m + 2 +--R (B m - 2B)(b c x + a c) +--R + +--R m + 1 +--R ((A b - B a)c m + (- A b + B a)c)(b c x + a c) +--R / +--R 4 2 2 4 2 4 2 2 3 2 2 3 2 3 2 +--R (b c m - 3b c m + 2b c )x + (2a b c m - 6a b c m + 4a b c )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R a b c m - 3a b c m + 2a b c +--R * +--R +------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 42 + +)clear all + +--S 43 of 1035 +t0:=(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R m 2 2 2 p +--R (1) (B x + A)(b c x + a c) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 43 + +--S 44 of 1035 +r0:=(A*b-a*B)*(a*c+b*c*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*c*(1+m+2*p))+_ + B*(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*c^2*(2+m+2*p)) +--R +--R +--R (2) +--R m + 2 +--R (2B p + B m + B)(b c x + a c) +--R + +--R m + 1 +--R ((2A b - 2B a)c p + (A b - B a)c m + (2A b - 2B a)c)(b c x + a c) +--R * +--R 2 2 2 p +--R (b x + 2a b x + a ) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +--R 4b c p + (4b c m + 6b c )p + b c m + 3b c m + 2b c +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1035 +t0:=(a+b*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^p +--R +--R +--R m 2 2 2 p +--R (1) (b x + a)(b c x + a c) (b x + 2a b x + a ) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1035 +r0:=(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b*c^2*(2+m+2*p)) +--R +--R +--R m + 2 2 2 2 p +--R (b c x + a c) (b x + 2a b x + a ) +--R (2) --------------------------------------- +--R 2 2 2 +--R 2b c p + b c m + 2b c +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 48 + +)clear all + +--S 49 of 1035 +t0:=(a+b*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a ) +--R * +--R m +--R (b c x + a c) +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1035 +r0:=(a*c+b*c*x)^(8+m)/(b*c^8*(8+m)) +--R +--R +--R m + 8 +--R (b c x + a c) +--R (2) ------------------ +--R 8 8 +--R b c m + 8b c +--R Type: Expression(Integer) +--E 50 + +--S 51 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 51 + +)clear all + +--S 52 of 1035 +t0:=(a+b*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^3 +--R +--R +--R m +--R (b c x + a c) +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1035 +r0:=-c^4*(a*c+b*c*x)^(-4+m)/(b*(4-m)) +--R +--R +--R 4 m - 4 +--R c (b c x + a c) +--R (2) -------------------- +--R b m - 4b +--R Type: Expression(Integer) +--E 53 + +--S 54 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 54 + +)clear all + +--S 55 of 1035 +t0:=x*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (c x + b x + a x)(e x + d) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1035 +r0:=-d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(3*c*d^2-_ + e*(2*b*d-a*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*c*d-b*e)*(d+e*x)^(3+m)/_ + (e^4*(3+m))+c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (c m + 6c m + 11c m + 6c)(e x + d) +--R + +--R 3 2 +--R ((b e - 3c d)m + (7b e - 21c d)m + (14b e - 42c d)m + 8b e - 24c d) +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 2 2 2 +--R (a e - 2b d e + 3c d )m + (8a e - 16b d e + 24c d )m +--R + +--R 2 2 2 2 +--R (19a e - 38b d e + 57c d )m + 12a e - 24b d e + 36c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 3 3 2 2 3 2 +--R (- a d e + b d e - c d )m + (- 9a d e + 9b d e - 9c d )m +--R + +--R 2 2 3 2 2 3 +--R (- 26a d e + 26b d e - 26c d )m - 24a d e + 24b d e - 24c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 1035 +t0:=x*(d+e*x)^5*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 5 8 5 4 7 5 4 2 3 6 +--R c e x + (b e + 5c d e )x + (a e + 5b d e + 10c d e )x +--R + +--R 4 2 3 3 2 5 2 3 3 2 4 4 +--R (5a d e + 10b d e + 10c d e )x + (10a d e + 10b d e + 5c d e)x +--R + +--R 3 2 4 5 3 4 5 2 5 +--R (10a d e + 5b d e + c d )x + (5a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 58 + +--S 59 of 1035 +r0:=-1/6*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^6/e^4+1/7*(3*c*d^2-e*(2*b*d-a*e))*_ + (d+e*x)^7/e^4-1/8*(3*c*d-b*e)*(d+e*x)^8/e^4+1/9*c*(d+e*x)^9/e^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 1 9 5 8 10 2 7 7 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + -- c d e )x +--R 9 8 8 7 7 7 +--R + +--R 5 8 5 2 7 5 3 6 6 2 7 3 6 4 5 5 +--R (- a d e + - b d e + - c d e )x + (2a d e + 2b d e + c d e )x +--R 6 3 3 +--R + +--R 5 3 6 5 4 5 1 5 4 4 5 4 5 1 5 4 3 1 5 4 2 +--R (- a d e + - b d e + - c d e )x + (- a d e + - b d e )x + - a d e x +--R 2 4 4 3 3 2 +--R + +--R 1 7 2 1 8 1 9 +--R - -- a d e + --- b d e - --- c d +--R 42 168 504 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 59 + +--S 60 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1035 +t0:=x*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 4 3 2 2 5 +--R c e x + (b e + 4c d e )x + (a e + 4b d e + 6c d e )x +--R + +--R 3 2 2 3 4 2 2 3 4 3 +--R (4a d e + 6b d e + 4c d e)x + (6a d e + 4b d e + c d )x +--R + +--R 3 4 2 4 +--R (4a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 61 + +--S 62 of 1035 +r0:=-1/5*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4+1/6*(3*c*d^2-e*(2*b*d-a*e))*_ + (d+e*x)^6/e^4-1/7*(3*c*d-b*e)*(d+e*x)^7/e^4+1/8*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 8 4 7 7 1 8 2 7 2 6 6 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + c d e )x +--R 8 7 7 6 3 +--R + +--R 4 7 6 2 6 4 3 5 5 3 2 6 3 5 1 4 4 4 +--R (- a d e + - b d e + - c d e )x + (- a d e + b d e + - c d e )x +--R 5 5 5 2 4 +--R + +--R 4 3 5 1 4 4 3 1 4 4 2 1 6 2 1 7 1 8 +--R (- a d e + - b d e )x + - a d e x - -- a d e + --- b d e - --- c d +--R 3 3 2 30 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 1035 +t0:=x*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 3 2 2 4 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 3 2 3 2 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d x +--R Type: Polynomial(Integer) +--E 64 + +--S 65 of 1035 +r0:=1/2*a*d^3*x^2+1/3*d^2*(b*d+3*a*e)*x^3+1/4*d*(c*d^2+3*e*(b*d+a*e))*x^4+_ + 1/5*e*(3*c*d^2+e*(3*b*d+a*e))*x^5+1/6*e^2*(3*c*d+b*e)*x^6+1/7*c*e^3*x^7 +--R +--R +--R (2) +--R 1 3 7 1 3 1 2 6 1 3 3 2 3 2 5 +--R - c e x + (- b e + - c d e )x + (- a e + - b d e + - c d e)x +--R 7 6 2 5 5 5 +--R + +--R 3 2 3 2 1 3 4 2 1 3 3 1 3 2 +--R (- a d e + - b d e + - c d )x + (a d e + - b d )x + - a d x +--R 4 4 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 65 + +--S 66 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 66 + +)clear all + +--S 67 of 1035 +t0:=x*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 2 2 3 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d x +--R Type: Polynomial(Integer) +--E 67 + +--S 68 of 1035 +r0:=1/2*a*d^2*x^2+1/3*d*(b*d+2*a*e)*x^3+1/4*(c*d^2+e*(2*b*d+a*e))*x^4+_ + 1/5*e*(2*c*d+b*e)*x^5+1/6*c*e^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 2 1 1 2 4 +--R - c e x + (- b e + - c d e)x + (- a e + - b d e + - c d )x +--R 6 5 5 4 2 4 +--R + +--R 2 1 2 3 1 2 2 +--R (- a d e + - b d )x + - a d x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 68 + +--S 69 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 69 + +)clear all + +--S 70 of 1035 +t0:=x*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R 4 3 2 +--R (1) c e x + (b e + c d)x + (a e + b d)x + a d x +--R Type: Polynomial(Integer) +--E 70 + +--S 71 of 1035 +r0:=1/2*a*d*x^2+1/3*(b*d+a*e)*x^3+1/4*(c*d+b*e)*x^4+1/5*c*e*x^5 +--R +--R +--R 1 5 1 1 4 1 1 3 1 2 +--R (2) - c e x + (- b e + - c d)x + (- a e + - b d)x + - a d x +--R 5 4 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 71 + +--S 72 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 of 1035 +t0:=x*(a+b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) c x + b x + a x +--R Type: Polynomial(Integer) +--E 73 + +--S 74 of 1035 +r0:=1/2*a*x^2+1/3*b*x^3+1/4*c*x^4 +--R +--R +--R 1 4 1 3 1 2 +--R (2) - c x + - b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ----------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 1035 +r0:=(c*d^2-b*d*e+a*e^2)*x/e^3-1/2*(c*d-b*e)*x^2/e^2+1/3*c*x^3/e-_ + d*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 2 3 3 3 3 2 2 +--R (- 6a d e + 6b d e - 6c d )log(e x + d) + 2c e x + (3b e - 3c d e )x +--R + +--R 3 2 2 +--R (6a e - 6b d e + 6c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 79 + +--S 80 of 1035 +r0:=-(2*c*d-b*e)*x/e^3+1/2*c*x^2/e^2+d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))+_ + (3*c*d^2-e*(2*b*d-a*e))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 +--R ((2a e - 4b d e + 6c d e)x + 2a d e - 4b d e + 6c d )log(e x + d) +--R + +--R 3 3 3 2 2 2 2 2 2 +--R c e x + (2b e - 3c d e )x + (2b d e - 4c d e)x + 2a d e - 2b d e +--R + +--R 3 +--R 2c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 80 + +--S 81 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 81 + +)clear all + +--S 82 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 82 + +--S 83 of 1035 +r0:=c*x/e^3+1/2*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (-3*c*d^2+e*(2*b*d-a*e))/(e^4*(d+e*x))-(3*c*d-b*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 +--R ((2b e - 6c d e )x + (4b d e - 12c d e)x + 2b d e - 6c d )log(e x + d) +--R + +--R 3 3 2 2 3 2 2 2 2 +--R 2c e x + 4c d e x + (- 2a e + 4b d e - 4c d e)x - a d e + 3b d e +--R + +--R 3 +--R - 5c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 83 + +--S 84 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 85 + +--S 86 of 1035 +r0:=1/3*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-3*c*d^2+_ + e*(2*b*d-a*e))/(e^4*(d+e*x)^2)+(3*c*d-b*e)/(e^4*(d+e*x))+c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6c e x + 18c d e x + 18c d e x + 6c d )log(e x + d) +--R + +--R 3 2 2 3 2 2 2 2 +--R (- 6b e + 18c d e )x + (- 3a e - 6b d e + 27c d e)x - a d e - 2b d e +--R + +--R 3 +--R 11c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 88 + +--S 89 of 1035 +r0:=1/4*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^3)+1/2*(3*c*d-b*e)/(e^4*(d+e*x)^2)-c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 3 3 2 2 1 3 1 2 2 +--R - c e x + (- - b e - - c d e )x + (- - a e - - b d e - c d e)x +--R 2 2 3 3 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - - c d +--R 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R c x + b x + a x +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 1035 +r0:=1/5*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^5)+1/4*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^4)+1/3*(3*c*d-b*e)/(e^4*(d+e*x)^3)-1/2*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 1 3 1 2 1 2 +--R - - c e x + (- - b e - - c d e )x + (- - a e - - b d e - - c d e)x +--R 2 3 2 4 6 4 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - -- c d +--R 20 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 1035 +t0:=x*(a+b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R c x + b x + a x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 94 + +--S 95 of 1035 +r0:=1/6*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^6)+1/5*(-3*c*d^2+e*(2*b*d-a*e))/_ + (e^4*(d+e*x)^5)+1/4*(3*c*d-b*e)/(e^4*(d+e*x)^4)-1/3*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 3 1 2 2 1 3 1 2 1 2 +--R - - c e x + (- - b e - - c d e )x + (- - a e - -- b d e - -- c d e)x +--R 3 4 4 5 10 10 +--R + +--R 1 2 1 2 1 3 +--R - -- a d e - -- b d e - -- c d +--R 30 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 95 + +--S 96 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 96 + +)clear all + +--S 97 of 1035 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + (A b + B a)x + A a)(e x + d) +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1035 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))-_ + (A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^(2+m)/(e^4*(2+m))-_ + (3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3+m)/(e^4*(3+m))+_ + B*c*(d+e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x + d) +--R + +--R 3 2 +--R ((A c + B b)e - 3B c d)m + ((7A c + 7B b)e - 21B c d)m +--R + +--R ((14A c + 14B b)e - 42B c d)m + (8A c + 8B b)e - 24B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 +--R ((A b + B a)e + (- 2A c - 2B b)d e + 3B c d )m +--R + +--R 2 2 2 +--R ((8A b + 8B a)e + (- 16A c - 16B b)d e + 24B c d )m +--R + +--R 2 2 +--R ((19A b + 19B a)e + (- 38A c - 38B b)d e + 57B c d )m +--R + +--R 2 2 +--R (12A b + 12B a)e + (- 24A c - 24B b)d e + 36B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 2 2 3 3 +--R (A a e + (- A b - B a)d e + (A c + B b)d e - B c d )m +--R + +--R 3 2 2 3 2 +--R (9A a e + (- 9A b - 9B a)d e + (9A c + 9B b)d e - 9B c d )m +--R + +--R 3 2 2 3 +--R (26A a e + (- 26A b - 26B a)d e + (26A c + 26B b)d e - 26B c d )m +--R + +--R 3 2 2 3 +--R 24A a e + (- 24A b - 24B a)d e + (24A c + 24B b)d e - 24B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 98 + +--S 99 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 1035 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 7 4 3 6 +--R B c e x + ((A c + B b)e + 4B c d e )x +--R + +--R 4 3 2 2 5 +--R ((A b + B a)e + (4A c + 4B b)d e + 6B c d e )x +--R + +--R 4 3 2 2 3 4 +--R (A a e + (4A b + 4B a)d e + (6A c + 6B b)d e + 4B c d e)x +--R + +--R 3 2 2 3 4 3 +--R (4A a d e + (6A b + 6B a)d e + (4A c + 4B b)d e + B c d )x +--R + +--R 2 2 3 4 2 +--R (6A a d e + (4A b + 4B a)d e + (A c + B b)d )x +--R + +--R 3 4 4 +--R (4A a d e + (A b + B a)d )x + A a d +--R Type: Polynomial(Integer) +--E 100 + +--S 101 of 1035 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4-1/6*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^7/e^4+1/8*B*c*(d+e*x)^8/e^4 +--R +--R +--R (2) +--R 1 8 8 1 1 8 4 7 7 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 1 8 2 2 7 2 6 6 +--R ((- A b + - B a)e + (- A c + - B b)d e + B c d e )x +--R 6 6 3 3 +--R + +--R 1 8 4 4 7 6 6 2 6 4 3 5 5 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 5 5 +--R + +--R 7 3 3 2 6 3 5 1 4 4 4 +--R (A a d e + (- A b + - B a)d e + (A c + B b)d e + - B c d e )x +--R 2 2 4 +--R + +--R 2 6 4 4 3 5 1 1 4 4 3 +--R (2A a d e + (- A b + - B a)d e + (- A c + - B b)d e )x +--R 3 3 3 3 +--R + +--R 3 5 1 1 4 4 2 4 4 1 5 3 +--R (2A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 5 +--R + +--R 1 1 6 2 1 1 7 1 8 +--R (- -- A b - -- B a)d e + (--- A c + --- B b)d e - --- B c d +--R 30 30 105 105 280 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 101 + +--S 102 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 1035 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 3 6 3 2 5 +--R B c e x + ((A c + B b)e + 3B c d e )x +--R + +--R 3 2 2 4 +--R ((A b + B a)e + (3A c + 3B b)d e + 3B c d e)x +--R + +--R 3 2 2 3 3 +--R (A a e + (3A b + 3B a)d e + (3A c + 3B b)d e + B c d )x +--R + +--R 2 2 3 2 +--R (3A a d e + (3A b + 3B a)d e + (A c + B b)d )x +--R + +--R 2 3 3 +--R (3A a d e + (A b + B a)d )x + A a d +--R Type: Polynomial(Integer) +--E 103 + +--S 104 of 1035 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4-1/5*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^6/e^4+1/7*B*c*(d+e*x)^7/e^4 +--R +--R +--R (2) +--R 1 7 7 1 1 7 1 6 6 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 7 6 6 2 +--R + +--R 1 1 7 3 3 6 3 2 5 5 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d e )x +--R 5 5 5 5 5 +--R + +--R 1 7 3 3 6 3 3 2 5 1 3 4 4 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e + - B c d e )x +--R 4 4 4 4 4 4 +--R + +--R 6 2 5 1 1 3 4 3 +--R (A a d e + (A b + B a)d e + (- A c + - B b)d e )x +--R 3 3 +--R + +--R 3 2 5 1 1 3 4 2 3 4 1 4 3 +--R (- A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 2 4 +--R + +--R 1 1 5 2 1 1 6 1 7 +--R (- -- A b - -- B a)d e + (-- A c + -- B b)d e - --- B c d +--R 20 20 60 60 140 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 104 + +--S 105 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1035 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 2 5 2 4 +--R B c e x + ((A c + B b)e + 2B c d e)x +--R + +--R 2 2 3 +--R ((A b + B a)e + (2A c + 2B b)d e + B c d )x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + (A c + B b)d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 1035 +r0:=-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3/e^4-1/4*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^4/e^4-1/5*(3*B*c*d-b*B*e-A*c*e)*_ + (d+e*x)^5/e^4+1/6*B*c*(d+e*x)^6/e^4 +--R +--R +--R (2) +--R 1 6 6 1 1 6 2 5 5 +--R - B c e x + ((- A c + - B b)e + - B c d e )x +--R 6 5 5 5 +--R + +--R 1 1 6 1 1 5 1 2 4 4 +--R ((- A b + - B a)e + (- A c + - B b)d e + - B c d e )x +--R 4 4 2 2 4 +--R + +--R 1 6 2 2 5 1 1 2 4 3 +--R (- A a e + (- A b + - B a)d e + (- A c + - B b)d e )x +--R 3 3 3 3 3 +--R + +--R 5 1 1 2 4 2 2 4 1 3 3 +--R (A a d e + (- A b + - B a)d e )x + A a d e x + - A a d e +--R 2 2 3 +--R + +--R 1 1 4 2 1 1 5 1 6 +--R (- -- A b - -- B a)d e + (-- A c + -- B b)d e - -- B c d +--R 12 12 30 30 60 +--R / +--R 4 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 107 + +--S 108 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 1035 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2) +--R +--R +--R (1) +--R 4 3 2 +--R B c e x + ((A c + B b)e + B c d)x + ((A b + B a)e + (A c + B b)d)x +--R + +--R (A a e + (A b + B a)d)x + A a d +--R Type: Polynomial(Integer) +--E 109 + +--S 110 of 1035 +r0:=a*A*d*x+1/2*(A*b*d+a*B*d+a*A*e)*x^2+1/3*(b*B*d+A*c*d+A*b*e+a*B*e)*x^3+_ + 1/4*(B*c*d+b*B*e+A*c*e)*x^4+1/5*B*c*e*x^5 +--R +--R +--R (2) +--R 1 5 1 1 1 4 +--R - B c e x + ((- A c + - B b)e + - B c d)x +--R 5 4 4 4 +--R + +--R 1 1 1 1 3 1 1 1 2 +--R ((- A b + - B a)e + (- A c + - B b)d)x + (- A a e + (- A b + - B a)d)x +--R 3 3 3 3 2 2 2 +--R + +--R A a d x +--R Type: Polynomial(Fraction(Integer)) +--E 110 + +--S 111 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) B c x + (A c + B b)x + (A b + B a)x + A a +--R Type: Polynomial(Integer) +--E 112 + +--S 113 of 1035 +r0:=a*A*x+1/2*(A*b+a*B)*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4 +--R +--R +--R 1 4 1 1 3 1 1 2 +--R (2) - B c x + (- A c + - B b)x + (- A b + - B a)x + A a x +--R 4 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x) +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 of 1035 +r0:=-(A*e*(c*d-b*e)-B*(c*d^2-e*(b*d-a*e)))*x/e^3-_ + 1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+1/3*B*c*x^3/e-_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 3 +--R (6A a e + (- 6A b - 6B a)d e + (6A c + 6B b)d e - 6B c d )log(e x + d) +--R + +--R 3 3 3 2 2 +--R 2B c e x + ((3A c + 3B b)e - 3B c d e )x +--R + +--R 3 2 2 +--R ((6A b + 6B a)e + (- 6A c - 6B b)d e + 6B c d e)x +--R / +--R 4 +--R 6e +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 118 + +--S 119 of 1035 +r0:=-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))-(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 +--R ((2A b + 2B a)e + (- 4A c - 4B b)d e + 6B c d e)x +--R + +--R 2 2 3 +--R (2A b + 2B a)d e + (- 4A c - 4B b)d e + 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 3 2 2 +--R B c e x + ((2A c + 2B b)e - 3B c d e )x +--R + +--R 2 2 3 2 +--R ((2A c + 2B b)d e - 4B c d e)x - 2A a e + (2A b + 2B a)d e +--R + +--R 2 3 +--R (- 2A c - 2B b)d e + 2B c d +--R / +--R 5 4 +--R 2e x + 2d e +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 1035 +r0:=B*c*x/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+_ + (A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x))-_ + (3*B*c*d-b*B*e-A*c*e)*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 2 2 2 2 +--R ((2A c + 2B b)e - 6B c d e )x + ((4A c + 4B b)d e - 12B c d e)x +--R + +--R 2 3 +--R (2A c + 2B b)d e - 6B c d +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 +--R 2B c e x + 4B c d e x +--R + +--R 3 2 2 3 +--R ((- 2A b - 2B a)e + (4A c + 4B b)d e - 4B c d e)x - A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (3A c + 3B b)d e - 5B c d +--R / +--R 6 2 5 2 4 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 124 + +--S 125 of 1035 +r0:=1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+_ + 1/2*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^2)+_ + (3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (6B c e x + 18B c d e x + 18B c d e x + 6B c d )log(e x + d) +--R + +--R 3 2 2 +--R ((- 6A c - 6B b)e + 18B c d e )x +--R + +--R 3 2 2 3 +--R ((- 3A b - 3B a)e + (- 6A c - 6B b)d e + 27B c d e)x - 2A a e +--R + +--R 2 2 3 +--R (- A b - B a)d e + (- 2A c - 2B b)d e + 11B c d +--R / +--R 7 3 6 2 2 5 3 4 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 125 + +--S 126 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 126 + +)clear all + +--S 127 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 127 + +--S 128 of 1035 +r0:=1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^2)-B*c/(e^4*(d+e*x)) +--R +--R +--R (2) +--R 3 3 1 1 3 3 2 2 +--R - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 2 2 +--R + +--R 1 1 3 1 1 2 2 1 3 +--R ((- - A b - - B a)e + (- - A c - - B b)d e - B c d e)x - - A a e +--R 3 3 3 3 4 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - - B c d +--R 12 12 12 12 4 +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 128 + +--S 129 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^6 +--R +--R +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 130 + +--S 131 of 1035 +r0:=1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^5)+1/4*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 2 3 3 2 +--R + +--R 1 1 3 1 1 2 1 2 1 3 +--R ((- - A b - - B a)e + (- - A c - - B b)d e - - B c d e)x - - A a e +--R 4 4 6 6 4 5 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - -- B c d +--R 20 20 30 30 20 +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 131 + +--S 132 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^7 +--R +--R +--R (1) +--R 3 2 +--R B c x + (A c + B b)x + (A b + B a)x + A a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 133 + +--S 134 of 1035 +r0:=1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^6)+1/5*(A*e*(2*c*d-b*e)-_ + B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^5)+1/4*(3*B*c*d-b*B*e-A*c*e)/_ + (e^4*(d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 3 1 1 3 1 2 2 +--R - - B c e x + ((- - A c - - B b)e - - B c d e )x +--R 3 4 4 4 +--R + +--R 1 1 3 1 1 2 1 2 1 3 +--R ((- - A b - - B a)e + (- -- A c - -- B b)d e - -- B c d e)x - - A a e +--R 5 5 10 10 10 6 +--R + +--R 1 1 2 1 1 2 1 3 +--R (- -- A b - -- B a)d e + (- -- A c - -- B b)d e - -- B c d +--R 30 30 60 60 60 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 134 + +--S 135 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1035 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1035 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))-_ + (c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^(2+m)/(e^6*(2+m))-(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^(4+m)/(e^6*(4+m))-c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c ) +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 5 2 2 4 +--R ((A c + 2B b c)e - 5B c d)m + ((16A c + 32B b c)e - 80B c d)m +--R + +--R 2 2 3 +--R ((95A c + 190B b c)e - 475B c d)m +--R + +--R 2 2 2 +--R ((260A c + 520B b c)e - 1300B c d)m +--R + +--R 2 2 2 2 +--R ((324A c + 648B b c)e - 1620B c d)m + (144A c + 288B b c)e - 720B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 2 2 2 5 +--R (((2A b + 2B a)c + B b )e + (- 4A c - 8B b c)d e + 10B c d )m +--R + +--R 2 2 2 +--R ((34A b + 34B a)c + 17B b )e + (- 68A c - 136B b c)d e +--R + +--R 2 2 +--R 170B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 +--R ((214A b + 214B a)c + 107B b )e + (- 428A c - 856B b c)d e +--R + +--R 2 2 +--R 1070B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 +--R ((614A b + 614B a)c + 307B b )e + (- 1228A c - 2456B b c)d e +--R + +--R 2 2 +--R 3070B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 +--R ((792A b + 792B a)c + 396B b )e + (- 1584A c - 3168B b c)d e +--R + +--R 2 2 +--R 3960B c d +--R * +--R m +--R + +--R 2 2 2 +--R ((360A b + 360B a)c + 180B b )e + (- 720A c - 1440B b c)d e +--R + +--R 2 2 +--R 1800B c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 3 2 2 +--R (2A a c + A b + 2B a b)e + ((- 6A b - 6B a)c - 3B b )d e +--R + +--R 2 2 2 3 +--R (6A c + 12B b c)d e - 10B c d +--R * +--R 5 +--R m +--R + +--R 2 3 +--R (36A a c + 18A b + 36B a b)e +--R + +--R 2 2 2 2 +--R ((- 108A b - 108B a)c - 54B b )d e + (108A c + 216B b c)d e +--R + +--R 2 3 +--R - 180B c d +--R * +--R 4 +--R m +--R + +--R 2 3 +--R (242A a c + 121A b + 242B a b)e +--R + +--R 2 2 2 2 +--R ((- 726A b - 726B a)c - 363B b )d e + (726A c + 1452B b c)d e +--R + +--R 2 3 +--R - 1210B c d +--R * +--R 3 +--R m +--R + +--R 2 3 +--R (744A a c + 372A b + 744B a b)e +--R + +--R 2 2 +--R ((- 2232A b - 2232B a)c - 1116B b )d e +--R + +--R 2 2 2 3 +--R (2232A c + 4464B b c)d e - 3720B c d +--R * +--R 2 +--R m +--R + +--R 2 3 +--R (1016A a c + 508A b + 1016B a b)e +--R + +--R 2 2 +--R ((- 3048A b - 3048B a)c - 1524B b )d e +--R + +--R 2 2 2 3 +--R (3048A c + 6096B b c)d e - 5080B c d +--R * +--R m +--R + +--R 2 3 +--R (480A a c + 240A b + 480B a b)e +--R + +--R 2 2 2 2 +--R ((- 1440A b - 1440B a)c - 720B b )d e + (1440A c + 2880B b c)d e +--R + +--R 2 3 +--R - 2400B c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 2 3 +--R (2A a b + B a )e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 2 2 2 3 2 4 +--R ((6A b + 6B a)c + 3B b )d e + (- 4A c - 8B b c)d e + 5B c d +--R * +--R 5 +--R m +--R + +--R 2 4 2 3 +--R (38A a b + 19B a )e + (- 76A a c - 38A b - 76B a b)d e +--R + +--R 2 2 2 2 3 +--R ((114A b + 114B a)c + 57B b )d e + (- 76A c - 152B b c)d e +--R + +--R 2 4 +--R 95B c d +--R * +--R 4 +--R m +--R + +--R 2 4 2 3 +--R (274A a b + 137B a )e + (- 548A a c - 274A b - 548B a b)d e +--R + +--R 2 2 2 2 3 +--R ((822A b + 822B a)c + 411B b )d e + (- 548A c - 1096B b c)d e +--R + +--R 2 4 +--R 685B c d +--R * +--R 3 +--R m +--R + +--R 2 4 2 3 +--R (922A a b + 461B a )e + (- 1844A a c - 922A b - 1844B a b)d e +--R + +--R 2 2 2 +--R ((2766A b + 2766B a)c + 1383B b )d e +--R + +--R 2 3 2 4 +--R (- 1844A c - 3688B b c)d e + 2305B c d +--R * +--R 2 +--R m +--R + +--R 2 4 +--R (1404A a b + 702B a )e +--R + +--R 2 3 +--R (- 2808A a c - 1404A b - 2808B a b)d e +--R + +--R 2 2 2 +--R ((4212A b + 4212B a)c + 2106B b )d e +--R + +--R 2 3 2 4 +--R (- 2808A c - 5616B b c)d e + 3510B c d +--R * +--R m +--R + +--R 2 4 2 3 +--R (720A a b + 360B a )e + (- 1440A a c - 720A b - 1440B a b)d e +--R + +--R 2 2 2 2 3 +--R ((2160A b + 2160B a)c + 1080B b )d e + (- 1440A c - 2880B b c)d e +--R + +--R 2 4 +--R 1800B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (- 2A a b - B a )d e + (2A a c + A b + 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 2A b - 2B a)c - B b )d e + (A c + 2B b c)d e - B c d +--R * +--R 5 +--R m +--R + +--R 2 5 2 4 +--R 20A a e + (- 40A a b - 20B a )d e +--R + +--R 2 2 3 +--R (40A a c + 20A b + 40B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 40A b - 40B a)c - 20B b )d e + (20A c + 40B b c)d e +--R + +--R 2 5 +--R - 20B c d +--R * +--R 4 +--R m +--R + +--R 2 5 2 4 +--R 155A a e + (- 310A a b - 155B a )d e +--R + +--R 2 2 3 +--R (310A a c + 155A b + 310B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 310A b - 310B a)c - 155B b )d e + (155A c + 310B b c)d e +--R + +--R 2 5 +--R - 155B c d +--R * +--R 3 +--R m +--R + +--R 2 5 2 4 +--R 580A a e + (- 1160A a b - 580B a )d e +--R + +--R 2 2 3 +--R (1160A a c + 580A b + 1160B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 1160A b - 1160B a)c - 580B b )d e + (580A c + 1160B b c)d e +--R + +--R 2 5 +--R - 580B c d +--R * +--R 2 +--R m +--R + +--R 2 5 2 4 +--R 1044A a e + (- 2088A a b - 1044B a )d e +--R + +--R 2 2 3 +--R (2088A a c + 1044A b + 2088B a b)d e +--R + +--R 2 3 2 +--R ((- 2088A b - 2088B a)c - 1044B b )d e +--R + +--R 2 4 2 5 +--R (1044A c + 2088B b c)d e - 1044B c d +--R * +--R m +--R + +--R 2 5 2 4 +--R 720A a e + (- 1440A a b - 720B a )d e +--R + +--R 2 2 3 +--R (1440A a c + 720A b + 1440B a b)d e +--R + +--R 2 3 2 2 4 +--R ((- 1440A b - 1440B a)c - 720B b )d e + (720A c + 1440B b c)d e +--R + +--R 2 5 +--R - 720B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 138 + +)clear all + +--S 139 of 1035 +t0:=(A+B*x)*(d+e*x)^5*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 10 2 5 2 4 9 +--R B c e x + ((A c + 2B b c)e + 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 8 +--R (((2A b + 2B a)c + B b )e + (5A c + 10B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 +--R (2A a c + A b + 2B a b)e + ((10A b + 10B a)c + 5B b )d e +--R + +--R 2 2 3 2 3 2 +--R (10A c + 20B b c)d e + 10B c d e +--R * +--R 7 +--R x +--R + +--R 2 5 2 4 +--R (2A a b + B a )e + (10A a c + 5A b + 10B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((20A b + 20B a)c + 10B b )d e + (10A c + 20B b c)d e + 5B c d e +--R * +--R 6 +--R x +--R + +--R 2 5 2 4 2 2 3 +--R A a e + (10A a b + 5B a )d e + (20A a c + 10A b + 20B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((20A b + 20B a)c + 10B b )d e + (5A c + 10B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 5A a d e + (20A a b + 10B a )d e + (20A a c + 10A b + 20B a b)d e +--R + +--R 2 4 2 5 +--R ((10A b + 10B a)c + 5B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 10A a d e + (20A a b + 10B a )d e + (10A a c + 5A b + 10B a b)d e +--R + +--R 2 5 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 4 2 5 2 +--R (10A a d e + (10A a b + 5B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 4 2 5 2 5 +--R (5A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 139 + +--S 140 of 1035 +r0:=-1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^6/e^6-_ + 1/7*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-_ + e*(3*b*d-a*e)))*(d+e*x)^7/e^6-1/8*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^8/e^6-1/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^9/e^6-1/10*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^10/e^6+1/11*B*c^2*(d+e*x)^11/e^6 +--R +--R +--R (2) +--R 1 2 11 11 1 2 1 11 1 2 10 10 +--R -- B c e x + ((-- A c + - B b c)e + - B c d e )x +--R 11 10 5 2 +--R + +--R 2 2 1 2 11 5 2 10 10 +--R ((- A b + - B a)c + - B b )e + (- A c + -- B b c)d e +--R 9 9 9 9 9 +--R + +--R 10 2 2 9 +--R -- B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 1 1 2 1 11 5 5 5 2 10 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 4 8 4 4 4 8 +--R + +--R 5 2 5 2 9 5 2 3 8 +--R (- A c + - B b c)d e + - B c d e +--R 4 2 4 +--R * +--R 8 +--R x +--R + +--R 2 1 2 11 10 5 2 10 10 +--R (- A a b + - B a )e + (-- A a c + - A b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 20 20 10 2 2 9 10 2 20 3 8 +--R ((-- A b + -- B a)c + -- B b )d e + (-- A c + -- B b c)d e +--R 7 7 7 7 7 +--R + +--R 5 2 4 7 +--R - B c d e +--R 7 +--R * +--R 7 +--R x +--R + +--R 1 2 11 5 5 2 10 +--R - A a e + (- A a b + - B a )d e +--R 6 3 6 +--R + +--R 10 5 2 10 2 9 +--R (-- A a c + - A b + -- B a b)d e +--R 3 3 3 +--R + +--R 10 10 5 2 3 8 5 2 5 4 7 1 2 5 6 +--R ((-- A b + -- B a)c + - B b )d e + (- A c + - B b c)d e + - B c d e +--R 3 3 3 6 3 6 +--R * +--R 6 +--R x +--R + +--R 2 10 2 2 9 2 3 8 +--R A a d e + (4A a b + 2B a )d e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 4 7 1 2 2 5 6 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 5 2 2 9 5 2 3 8 5 5 2 5 4 7 +--R - A a d e + (5A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 2 2 2 4 2 +--R + +--R 1 1 1 2 5 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 10 2 3 8 10 5 2 4 7 +--R -- A a d e + (-- A a b + - B a )d e +--R 3 3 3 +--R + +--R 2 1 2 2 5 6 +--R (- A a c + - A b + - B a b)d e +--R 3 3 3 +--R * +--R 3 +--R x +--R + +--R 5 2 4 7 1 2 5 6 2 2 5 6 1 2 6 5 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 6 +--R + +--R 1 1 2 7 4 1 1 2 1 8 3 +--R (- -- A a b - -- B a )d e + (-- A a c + --- A b + -- B a b)d e +--R 21 42 84 168 84 +--R + +--R 1 1 1 2 9 2 1 2 1 10 +--R ((- --- A b - --- B a)c - --- B b )d e + (---- A c + --- B b c)d e +--R 252 252 504 1260 630 +--R + +--R 1 2 11 +--R - ---- B c d +--R 2772 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 140 + +--S 141 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 141 + +)clear all + +--S 142 of 1035 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 9 2 4 2 3 8 +--R B c e x + ((A c + 2B b c)e + 4B c d e )x +--R + +--R 2 4 2 3 2 2 2 7 +--R (((2A b + 2B a)c + B b )e + (4A c + 8B b c)d e + 6B c d e )x +--R + +--R 2 4 2 3 +--R (2A a c + A b + 2B a b)e + ((8A b + 8B a)c + 4B b )d e +--R + +--R 2 2 2 2 3 +--R (6A c + 12B b c)d e + 4B c d e +--R * +--R 6 +--R x +--R + +--R 2 4 2 3 +--R (2A a b + B a )e + (8A a c + 4A b + 8B a b)d e +--R + +--R 2 2 2 2 3 2 4 +--R ((12A b + 12B a)c + 6B b )d e + (4A c + 8B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 4 2 3 2 2 2 +--R A a e + (8A a b + 4B a )d e + (12A a c + 6A b + 12B a b)d e +--R + +--R 2 3 2 4 +--R ((8A b + 8B a)c + 4B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 4A a d e + (12A a b + 6B a )d e + (8A a c + 4A b + 8B a b)d e +--R + +--R 2 4 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 3 2 4 2 +--R (6A a d e + (8A a b + 4B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 3 2 4 2 4 +--R (4A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 142 + +--S 143 of 1035 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^5/e^6-_ + 1/6*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^7/e^6-_ + 1/8*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*_ + (d+e*x)^8/e^6-1/9*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^9/e^6+_ + 1/10*B*c^2*(d+e*x)^10/e^6 +--R +--R +--R (2) +--R 1 2 10 10 1 2 2 10 4 2 9 9 +--R -- B c e x + ((- A c + - B b c)e + - B c d e )x +--R 10 9 9 9 +--R + +--R 1 1 1 2 10 1 2 9 3 2 2 8 8 +--R (((- A b + - B a)c + - B b )e + (- A c + B b c)d e + - B c d e )x +--R 4 4 8 2 4 +--R + +--R 2 1 2 2 10 8 8 4 2 9 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 7 7 7 7 7 7 +--R + +--R 6 2 12 2 8 4 2 3 7 +--R (- A c + -- B b c)d e + - B c d e +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 1 2 10 4 2 2 4 9 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 3 6 3 3 3 +--R + +--R 2 2 8 2 2 4 3 7 1 2 4 6 +--R ((2A b + 2B a)c + B b )d e + (- A c + - B b c)d e + - B c d e +--R 3 3 6 +--R * +--R 6 +--R x +--R + +--R 1 2 10 8 4 2 9 +--R - A a e + (- A a b + - B a )d e +--R 5 5 5 +--R + +--R 12 6 2 12 2 8 8 8 4 2 3 7 +--R (-- A a c + - A b + -- B a b)d e + ((- A b + - B a)c + - B b )d e +--R 5 5 5 5 5 5 +--R + +--R 1 2 2 4 6 +--R (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 2 9 3 2 2 8 2 3 7 +--R A a d e + (3A a b + - B a )d e + (2A a c + A b + 2B a b)d e +--R 2 +--R + +--R 1 1 1 2 4 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 2 8 8 4 2 3 7 2 1 2 2 4 6 3 +--R (2A a d e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 3 3 +--R + +--R 2 3 7 1 2 4 6 2 2 4 6 1 2 5 5 +--R (2A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 5 +--R + +--R 1 1 2 6 4 2 1 2 2 7 3 +--R (- -- A a b - -- B a )d e + (--- A a c + --- A b + --- B a b)d e +--R 15 30 105 105 105 +--R + +--R 1 1 1 2 8 2 1 2 1 9 +--R ((- --- A b - --- B a)c - --- B b )d e + (--- A c + --- B b c)d e +--R 140 140 280 630 315 +--R + +--R 1 2 10 +--R - ---- B c d +--R 1260 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 143 + +--S 144 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 1035 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 8 2 3 2 2 7 +--R B c e x + ((A c + 2B b c)e + 3B c d e )x +--R + +--R 2 3 2 2 2 2 6 +--R (((2A b + 2B a)c + B b )e + (3A c + 6B b c)d e + 3B c d e)x +--R + +--R 2 3 2 2 +--R (2A a c + A b + 2B a b)e + ((6A b + 6B a)c + 3B b )d e +--R + +--R 2 2 2 3 +--R (3A c + 6B b c)d e + B c d +--R * +--R 5 +--R x +--R + +--R 2 3 2 2 +--R (2A a b + B a )e + (6A a c + 3A b + 6B a b)d e +--R + +--R 2 2 2 3 +--R ((6A b + 6B a)c + 3B b )d e + (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 +--R A a e + (6A a b + 3B a )d e + (6A a c + 3A b + 6B a b)d e +--R + +--R 2 3 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 145 + +--S 146 of 1035 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4/e^6-_ + 1/5*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + (d+e*x)^5/e^6-1/6*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-_ + 6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(4*b*d-a*e)))*(d+e*x)^7/e^6-1/8*c*(5*B*c*d-2*b*B*e-A*c*e)*_ + (d+e*x)^8/e^6+1/9*B*c^2*(d+e*x)^9/e^6 +--R +--R +--R (2) +--R 1 2 9 9 1 2 1 9 3 2 8 8 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 9 8 4 8 +--R + +--R 2 2 1 2 9 3 2 6 8 3 2 2 7 7 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d e )x +--R 7 7 7 7 7 7 +--R + +--R 1 1 2 1 9 1 2 8 +--R (- A a c + - A b + - B a b)e + ((A b + B a)c + - B b )d e +--R 3 6 3 2 +--R + +--R 1 2 2 7 1 2 3 6 +--R (- A c + B b c)d e + - B c d e +--R 2 6 +--R * +--R 6 +--R x +--R + +--R 2 1 2 9 6 3 2 6 8 +--R (- A a b + - B a )e + (- A a c + - A b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 6 6 3 2 2 7 1 2 2 3 6 +--R ((- A b + - B a)c + - B b )d e + (- A c + - B b c)d e +--R 5 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 2 9 3 3 2 8 3 3 2 3 2 7 +--R - A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e +--R 4 2 4 2 4 2 +--R + +--R 1 1 1 2 3 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 2 8 2 2 7 2 1 2 2 3 6 3 +--R (A a d e + (2A a b + B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 +--R + +--R 3 2 2 7 1 2 3 6 2 2 3 6 1 2 4 5 +--R (- A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 4 +--R + +--R 1 1 2 5 4 1 1 2 1 6 3 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A b + -- B a b)d e +--R 10 20 30 60 30 +--R + +--R 1 1 1 2 7 2 1 2 1 8 +--R ((- -- A b - -- B a)c - --- B b )d e + (--- A c + --- B b c)d e +--R 70 70 140 280 140 +--R + +--R 1 2 9 +--R - --- B c d +--R 504 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 146 + +--S 147 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 1035 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 7 2 2 2 6 +--R B c e x + ((A c + 2B b c)e + 2B c d e)x +--R + +--R 2 2 2 2 2 5 +--R (((2A b + 2B a)c + B b )e + (2A c + 4B b c)d e + B c d )x +--R + +--R 2 2 2 +--R (2A a c + A b + 2B a b)e + ((4A b + 4B a)c + 2B b )d e +--R + +--R 2 2 +--R (A c + 2B b c)d +--R * +--R 4 +--R x +--R + +--R 2 2 2 +--R (2A a b + B a )e + (4A a c + 2A b + 4B a b)d e +--R + +--R 2 2 +--R ((2A b + 2B a)c + B b )d +--R * +--R 3 +--R x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (2A a c + A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 148 + +--S 149 of 1035 +r0:=-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^3/e^6-1/4*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*(d+e*x)^4/e^6-_ + 1/5*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^5/e^6-_ + 1/6*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*_ + (d+e*x)^6/e^6-1/7*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^7/e^6+_ + 1/8*B*c^2*(d+e*x)^8/e^6 +--R +--R +--R (2) +--R 1 2 8 8 1 2 2 8 2 2 7 7 +--R - B c e x + ((- A c + - B b c)e + - B c d e )x +--R 8 7 7 7 +--R + +--R 1 1 1 2 8 1 2 2 7 1 2 2 6 6 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d e + - B c d e )x +--R 3 3 6 3 3 6 +--R + +--R 2 1 2 2 8 4 4 2 2 7 +--R (- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d e +--R 5 5 5 5 5 5 +--R + +--R 1 2 2 2 6 +--R (- A c + - B b c)d e +--R 5 5 +--R * +--R 5 +--R x +--R + +--R 1 1 2 8 1 2 7 +--R (- A a b + - B a )e + (A a c + - A b + B a b)d e +--R 2 4 2 +--R + +--R 1 1 1 2 2 6 +--R ((- A b + - B a)c + - B b )d e +--R 2 2 4 +--R * +--R 4 +--R x +--R + +--R 1 2 8 4 2 2 7 2 1 2 2 2 6 3 +--R (- A a e + (- A a b + - B a )d e + (- A a c + - A b + - B a b)d e )x +--R 3 3 3 3 3 3 +--R + +--R 2 7 1 2 2 6 2 2 2 6 1 2 3 5 +--R (A a d e + (A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 3 +--R + +--R 1 1 2 4 4 1 1 2 1 5 3 +--R (- - A a b - -- B a )d e + (-- A a c + -- A b + -- B a b)d e +--R 6 12 15 30 15 +--R + +--R 1 1 1 2 6 2 1 2 2 7 +--R ((- -- A b - -- B a)c - -- B b )d e + (--- A c + --- B b c)d e +--R 30 30 60 105 105 +--R + +--R 1 2 8 +--R - --- B c d +--R 168 +--R / +--R 6 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1035 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 6 2 2 5 +--R B c e x + ((A c + 2B b c)e + B c d)x +--R + +--R 2 2 4 +--R (((2A b + 2B a)c + B b )e + (A c + 2B b c)d)x +--R + +--R 2 2 3 +--R ((2A a c + A b + 2B a b)e + ((2A b + 2B a)c + B b )d)x +--R + +--R 2 2 2 +--R ((2A a b + B a )e + (2A a c + A b + 2B a b)d)x +--R + +--R 2 2 2 +--R (A a e + (2A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 151 + +--S 152 of 1035 +r0:=a^2*A*d*x+1/2*a*(2*A*b*d+a*B*d+a*A*e)*x^2+1/3*(a*B*(2*b*d+a*e)+_ + A*(b^2*d+2*a*c*d+2*a*b*e))*x^3+1/4*(b^2*(B*d+A*e)+2*a*c*(B*d+A*e)+_ + 2*b*(A*c*d+a*B*e))*x^4+1/5*(b^2*B*e+2*b*c*(B*d+A*e)+_ + c*(A*c*d+2*a*B*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7 +--R +--R +--R (2) +--R 1 2 7 1 2 1 1 2 6 +--R - B c e x + ((- A c + - B b c)e + - B c d)x +--R 7 6 3 6 +--R + +--R 2 2 1 2 1 2 2 5 +--R (((- A b + - B a)c + - B b )e + (- A c + - B b c)d)x +--R 5 5 5 5 5 +--R + +--R 1 1 2 1 1 1 1 2 4 +--R ((- A a c + - A b + - B a b)e + ((- A b + - B a)c + - B b )d)x +--R 2 4 2 2 2 4 +--R + +--R 2 1 2 2 1 2 2 3 +--R ((- A a b + - B a )e + (- A a c + - A b + - B a b)d)x +--R 3 3 3 3 3 +--R + +--R 1 2 1 2 2 2 +--R (- A a e + (A a b + - B a )d)x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 152 + +--S 153 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 154 + +--S 155 of 1035 +r0:=a^2*A*x+1/2*a*(2*A*b+a*B)*x^2+1/3*(2*a*b*B+A*(b^2+2*a*c))*x^3+_ + 1/4*(b^2*B+2*A*b*c+2*a*B*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6 +--R +--R +--R (2) +--R 1 2 6 1 2 2 5 1 1 1 2 4 +--R - B c x + (- A c + - B b c)x + ((- A b + - B a)c + - B b )x +--R 6 5 5 2 2 4 +--R + +--R 2 1 2 2 3 1 2 2 2 +--R (- A a c + - A b + - B a b)x + (A a b + - B a )x + A a x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 155 + +--S 156 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x) +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 157 + +--S 158 of 1035 +r0:=-(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + x/e^5-1/2*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^2/e^6-1/3*(2*A*c*e*_ + (2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*(d+e*x)^3/e^6-_ + 1/4*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^4/e^6+1/5*B*c^2*(d+e*x)^5/e^6-_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R 60A a e + (- 120A a b - 60B a )d e +--R + +--R 2 2 3 +--R (120A a c + 60A b + 120B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 120A b - 120B a)c - 60B b )d e + (60A c + 120B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 12B c e x + ((15A c + 30B b c)e - 15B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((40A b + 40B a)c + 20B b )e + (- 20A c - 40B b c)d e + 20B c d e )x +--R + +--R 2 5 2 4 +--R (60A a c + 30A b + 60B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (30A c + 60B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (120A a b + 60B a )e + (- 120A a c - 60A b - 120B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((120A b + 120B a)c + 60B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 +--R (60A a c + 30A b + 60B a b)d e + ((- 140A b - 140B a)c - 70B b )d e +--R + +--R 2 4 2 5 +--R (115A c + 230B b c)d e - 163B c d +--R / +--R 6 +--R 60e +--R Type: Expression(Integer) +--E 158 + +--S 159 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 of 1035 +r0:=-(2*B*(2*c*d-b*e)*(c*d^2-e*(b*d-a*e))-A*e*(3*c^2*d^2+b^2*e^2-_ + 2*c*e*(2*b*d-a*e)))*x/e^5-1/2*(2*A*c*e*(c*d-b*e)-B*(3*c^2*d^2+b^2*e^2-_ + 2*c*e*(2*b*d-a*e)))*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+_ + 1/4*B*c^2*x^4/e^2+(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x))-_ + (c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*_ + log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R (24A a b + 12B a )e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e +--R + +--R 2 4 +--R 60B c d e +--R * +--R x +--R + +--R 2 4 2 2 3 +--R (24A a b + 12B a )d e + (- 48A a c - 24A b - 48B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((72A b + 72B a)c + 36B b )d e + (- 48A c - 96B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((4A c + 8B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 8A c - 16B b c)d e + 10B c d e )x +--R + +--R 2 5 2 4 +--R (24A a c + 12A b + 24B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (24A c + 48B b c)d e - 30B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 +--R (24A a c + 12A b + 24B a b)d e + ((- 48A b - 48B a)c - 24B b )d e +--R + +--R 2 3 2 2 4 +--R (36A c + 72B b c)d e - 48B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (24A a b + 12B a )d e + (- 24A a c - 12A b - 24B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((24A b + 24B a)c + 12B b )d e + (- 12A c - 24B b c)d e + 12B c d +--R / +--R 7 6 +--R 12e x + 12d e +--R Type: Expression(Integer) +--E 161 + +--S 162 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 163 + +--S 164 of 1035 +r0:=-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*x/e^5-_ + 1/2*c*(3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^2)+(c*d^2-b*d*e+a*e^2)*(2*A*e*_ + (2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x))-(B*(10*c^2*d^3+_ + b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-_ + 2*c*e*(3*b*d-a*e)))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R (12A a c + 6A b + 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (36A c + 72B b c)d e - 60B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 +--R (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 72A b - 72B a)c - 36B b )d e + (72A c + 144B b c)d e +--R + +--R 2 4 +--R - 120B c d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 +--R (12A a c + 6A b + 12B a b)d e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 4 2 5 +--R (36A c + 72B b c)d e - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 2B c e x + ((3A c + 6B b c)e - 5B c d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((12A b + 12B a)c + 6B b )e + (- 12A c - 24B b c)d e + 20B c d e )x +--R + +--R 2 4 2 2 3 +--R ((24A b + 24B a)c + 12B b )d e + (- 33A c - 66B b c)d e +--R + +--R 2 3 2 +--R 63B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 12A a b - 6B a )e + (24A a c + 12A b + 24B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((- 24A b - 24B a)c - 12B b )d e + (6A c + 12B b c)d e + 6B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 6A a b - 3B a )d e + (18A a c + 9A b + 18B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 30A b - 30B a)c - 15B b )d e + (21A c + 42B b c)d e - 27B c d +--R / +--R 8 2 7 2 6 +--R 6e x + 12d e x + 6d e +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1035 +r0:=-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^3)+1/2*(c*d^2-b*d*e+a*e^2)*(2*A*e*_ + (2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^2)+(B*(10*c^2*d^3+_ + b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-_ + 2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(4*b*d-a*e)))*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 +--R ((12A b + 12B a)c + 6B b )e + (- 24A c - 48B b c)d e +--R + +--R 2 2 3 +--R 60B c d e +--R * +--R 3 +--R x +--R + +--R 2 4 2 2 3 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 3 2 +--R 180B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 3 2 +--R ((36A b + 36B a)c + 18B b )d e + (- 72A c - 144B b c)d e +--R + +--R 2 4 +--R 180B c d e +--R * +--R x +--R + +--R 2 3 2 2 4 2 5 +--R ((12A b + 12B a)c + 6B b )d e + (- 24A c - 48B b c)d e + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 5 2 4 4 +--R 3B c e x + ((6A c + 12B b c)e - 15B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((18A c + 36B b c)d e - 63B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((36A b + 36B a)c + 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 18A c - 36B b c)d e - 9B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 6A a b - 3B a )e + (- 12A a c - 6A b - 12B a b)d e +--R + +--R 2 2 3 2 3 2 2 4 +--R ((54A b + 54B a)c + 27B b )d e + (- 54A c - 108B b c)d e + 81B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 2A a e + (- 2A a b - B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((22A b + 22B a)c + 11B b )d e + (- 26A c - 52B b c)d e + 47B c d +--R / +--R 9 3 8 2 2 7 3 6 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 168 + +)clear all + +--S 169 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^5 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 169 + +--S 170 of 1035 +r0:=B*c^2*x/e^5+1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^4)+_ + 1/3*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/_ + (e^6*(d+e*x)^3)+1/2*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-_ + a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^2)+_ + (2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*_ + (d+e*x))-c*(5*B*c*d-2*b*B*e-A*c*e)*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 2 4 4 +--R ((12A c + 24B b c)e - 60B c d e )x +--R + +--R 2 4 2 2 3 3 +--R ((48A c + 96B b c)d e - 240B c d e )x +--R + +--R 2 2 3 2 3 2 2 +--R ((72A c + 144B b c)d e - 360B c d e )x +--R + +--R 2 3 2 2 4 2 4 +--R ((48A c + 96B b c)d e - 240B c d e)x + (12A c + 24B b c)d e +--R + +--R 2 5 +--R - 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 5 2 4 4 +--R 12B c e x + 48B c d e x +--R + +--R 2 5 2 4 2 2 3 3 +--R (((- 24A b - 24B a)c - 12B b )e + (48A c + 96B b c)d e - 48B c d e )x +--R + +--R 2 5 2 4 +--R (- 12A a c - 6A b - 12B a b)e + ((- 36A b - 36B a)c - 18B b )d e +--R + +--R 2 2 3 2 3 2 +--R (108A c + 216B b c)d e - 252B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 8A a b - 4B a )e + (- 8A a c - 4A b - 8B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 24A b - 24B a)c - 12B b )d e + (88A c + 176B b c)d e +--R + +--R 2 4 +--R - 248B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 3A a e + (- 2A a b - B a )d e + (- 2A a c - A b - 2B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (25A c + 50B b c)d e - 77B c d +--R / +--R 10 4 9 3 2 8 2 3 7 4 6 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^6 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 172 + +--S 173 of 1035 +r0:=1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^5)+1/4*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^4)+_ + 1/3*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^3)+_ + 1/2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^2)+c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x))+B*c^2*log(d+e*x)/e^6 +--R +--R +--R (2) +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 +--R 60B c e x + 300B c d e x + 600B c d e x + 600B c d e x +--R + +--R 2 4 2 5 +--R 300B c d e x + 60B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 4 +--R ((- 60A c - 120B b c)e + 300B c d e )x +--R + +--R 2 5 2 4 +--R ((- 60A b - 60B a)c - 30B b )e + (- 120A c - 240B b c)d e +--R + +--R 2 2 3 +--R 900B c d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 4 +--R (- 40A a c - 20A b - 40B a b)e + ((- 60A b - 60B a)c - 30B b )d e +--R + +--R 2 2 3 2 3 2 +--R (- 120A c - 240B b c)d e + 1100B c d e +--R * +--R 2 +--R x +--R + +--R 2 5 2 4 +--R (- 30A a b - 15B a )e + (- 20A a c - 10A b - 20B a b)d e +--R + +--R 2 2 3 2 3 2 +--R ((- 30A b - 30B a)c - 15B b )d e + (- 60A c - 120B b c)d e +--R + +--R 2 4 +--R 625B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - 12A a e + (- 6A a b - 3B a )d e + (- 4A a c - 2A b - 4B a b)d e +--R + +--R 2 3 2 2 4 2 5 +--R ((- 6A b - 6B a)c - 3B b )d e + (- 12A c - 24B b c)d e + 137B c d +--R / +--R 11 5 10 4 2 9 3 3 8 2 4 7 5 6 +--R 60e x + 300d e x + 600d e x + 600d e x + 300d e x + 60d e +--R Type: Expression(Integer) +--E 173 + +--S 174 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 of 1035 +r0:=1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^6)+1/5*(c*d^2-_ + b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+_ + e*x)^5)+1/4*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^4)+_ + 1/3*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^3)+1/2*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^2)-_ + B*c^2/(e^6*(d+e*x)) +--R +--R +--R (2) +--R 2 5 5 1 2 5 5 2 4 4 +--R - B c e x + ((- - A c - B b c)e - - B c d e )x +--R 2 2 +--R + +--R 2 2 1 2 5 2 2 4 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 3 3 3 3 3 +--R + +--R 10 2 2 3 +--R - -- B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 1 1 2 1 5 1 1 1 2 4 +--R (- - A a c - - A b - - B a b)e + ((- - A b - - B a)c - - B b )d e +--R 2 4 2 2 2 4 +--R + +--R 1 2 2 3 5 2 3 2 +--R (- - A c - B b c)d e - - B c d e +--R 2 2 +--R * +--R 2 +--R x +--R + +--R 2 1 2 5 1 1 2 1 4 +--R (- - A a b - - B a )e + (- - A a c - -- A b - - B a b)d e +--R 5 5 5 10 5 +--R + +--R 1 1 1 2 2 3 1 2 2 3 2 2 4 +--R ((- - A b - - B a)c - -- B b )d e + (- - A c - - B b c)d e - B c d e +--R 5 5 10 5 5 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 6 15 30 +--R + +--R 1 1 2 1 2 3 +--R (- -- A a c - -- A b - -- B a b)d e +--R 30 60 30 +--R + +--R 1 1 1 2 3 2 1 2 1 4 1 2 5 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e - - B c d +--R 30 30 60 30 15 6 +--R / +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 176 + +--S 177 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 178 + +--S 179 of 1035 +r0:=1/7*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^7)+1/6*(c*d^2-_ + b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*_ + (d+e*x)^6)+1/5*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-_ + A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^5)+_ + 1/4*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/_ + (e^6*(d+e*x)^4)+1/3*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^3)-_ + 1/2*B*c^2/(e^6*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 5 5 1 2 2 5 5 2 4 4 +--R - - B c e x + ((- - A c - - B b c)e - - B c d e )x +--R 2 3 3 6 +--R + +--R 1 1 1 2 5 1 2 2 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 2 2 4 3 3 +--R + +--R 5 2 2 3 +--R - - B c d e +--R 6 +--R * +--R 3 +--R x +--R + +--R 2 1 2 2 5 +--R (- - A a c - - A b - - B a b)e +--R 5 5 5 +--R + +--R 3 3 3 2 4 1 2 2 2 3 +--R ((- -- A b - -- B a)c - -- B b )d e + (- - A c - - B b c)d e +--R 10 10 20 5 5 +--R + +--R 1 2 3 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 1 1 2 5 2 1 2 2 4 +--R (- - A a b - - B a )e + (- -- A a c - -- A b - -- B a b)d e +--R 3 6 15 15 15 +--R + +--R 1 1 1 2 2 3 1 2 2 3 2 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e +--R 10 10 20 15 15 +--R + +--R 1 2 4 +--R - - B c d e +--R 6 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 7 21 42 +--R + +--R 2 1 2 2 2 3 +--R (- --- A a c - --- A b - --- B a b)d e +--R 105 105 105 +--R + +--R 1 1 1 2 3 2 1 2 2 4 +--R ((- -- A b - -- B a)c - --- B b )d e + (- --- A c - --- B b c)d e +--R 70 70 140 105 105 +--R + +--R 1 2 5 +--R - -- B c d +--R 42 +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 6 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 179 + +--S 180 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^9 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1035 +r0:=1/8*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^8)+1/7*(c*d^2-b*d*e+_ + a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^7)+_ + 1/6*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*_ + d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^6)+1/5*(2*A*c*e*(2*c*d-_ + b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*(d+e*x)^5)+_ + 1/4*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^4)-1/3*B*c^2/(e^6*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 5 5 1 2 1 5 5 2 4 4 +--R - - B c e x + ((- - A c - - B b c)e - -- B c d e )x +--R 3 4 2 12 +--R + +--R 2 2 1 2 5 1 2 2 4 +--R ((- - A b - - B a)c - - B b )e + (- - A c - - B b c)d e +--R 5 5 5 5 5 +--R + +--R 1 2 2 3 +--R - - B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 1 1 2 1 5 1 1 1 2 4 +--R (- - A a c - - A b - - B a b)e + ((- - A b - - B a)c - -- B b )d e +--R 3 6 3 5 5 10 +--R + +--R 1 2 1 2 3 1 2 3 2 +--R (- -- A c - - B b c)d e - - B c d e +--R 10 5 6 +--R * +--R 2 +--R x +--R + +--R 2 1 2 5 2 1 2 2 4 +--R (- - A a b - - B a )e + (- -- A a c - -- A b - -- B a b)d e +--R 7 7 21 21 21 +--R + +--R 2 2 1 2 2 3 1 2 2 3 2 +--R ((- -- A b - -- B a)c - -- B b )d e + (- -- A c - -- B b c)d e +--R 35 35 35 35 35 +--R + +--R 1 2 4 +--R - -- B c d e +--R 21 +--R * +--R x +--R + +--R 1 2 5 1 1 2 4 +--R - - A a e + (- -- A a b - -- B a )d e +--R 8 28 56 +--R + +--R 1 1 2 1 2 3 +--R (- -- A a c - --- A b - -- B a b)d e +--R 84 168 84 +--R + +--R 1 1 1 2 3 2 1 2 1 4 +--R ((- --- A b - --- B a)c - --- B b )d e + (- --- A c - --- B b c)d e +--R 140 140 280 280 140 +--R + +--R 1 2 5 +--R - --- B c d +--R 168 +--R / +--R 14 8 13 7 2 12 6 3 11 5 4 10 4 5 9 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 8 2 7 7 8 6 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 182 + +--S 183 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 183 + +)clear all + +--S 184 of 1035 +t0:=(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R m +--R (e x + d) +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1035 +r0:=-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))-_ + (c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*_ + (d+e*x)^(2+m)/(e^8*(2+m))-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*(d+e*x)^(3+m)/(e^8*(3+m))-(A*e*(2*c*d-b*e)*_ + (10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*_ + (4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+_ + a^2*e^2)))*(d+e*x)^(4+m)/(e^8*(4+m))-(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*_ + (5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^(6+m)/(e^8*(6+m))-_ + c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*_ + (d+e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x + d) +--R + +--R 3 2 3 7 3 2 3 6 +--R ((A c + 3B b c )e - 7B c d)m + ((29A c + 87B b c )e - 203B c d)m +--R + +--R 3 2 3 5 +--R ((343A c + 1029B b c )e - 2401B c d)m +--R + +--R 3 2 3 4 +--R ((2135A c + 6405B b c )e - 14945B c d)m +--R + +--R 3 2 3 3 +--R ((7504A c + 22512B b c )e - 52528B c d)m +--R + +--R 3 2 3 2 +--R ((14756A c + 44268B b c )e - 103292B c d)m +--R + +--R 3 2 3 +--R ((14832A c + 44496B b c )e - 103824B c d)m +--R + +--R 3 2 3 +--R (5760A c + 17280B b c )e - 40320B c d +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 2 2 3 2 3 2 7 +--R (((3A b + 3B a)c + 3B b c)e + (- 6A c - 18B b c )d e + 21B c d )m +--R + +--R 2 2 2 3 2 +--R ((90A b + 90B a)c + 90B b c)e + (- 180A c - 540B b c )d e +--R + +--R 3 2 +--R 630B c d +--R * +--R 6 +--R m +--R + +--R 2 2 2 +--R ((1098A b + 1098B a)c + 1098B b c)e +--R + +--R 3 2 3 2 +--R (- 2196A c - 6588B b c )d e + 7686B c d +--R * +--R 5 +--R m +--R + +--R 2 2 2 +--R ((7020A b + 7020B a)c + 7020B b c)e +--R + +--R 3 2 3 2 +--R (- 14040A c - 42120B b c )d e + 49140B c d +--R * +--R 4 +--R m +--R + +--R 2 2 2 +--R ((25227A b + 25227B a)c + 25227B b c)e +--R + +--R 3 2 3 2 +--R (- 50454A c - 151362B b c )d e + 176589B c d +--R * +--R 3 +--R m +--R + +--R 2 2 2 +--R ((50490A b + 50490B a)c + 50490B b c)e +--R + +--R 3 2 3 2 +--R (- 100980A c - 302940B b c )d e + 353430B c d +--R * +--R 2 +--R m +--R + +--R 2 2 2 +--R ((51432A b + 51432B a)c + 51432B b c)e +--R + +--R 3 2 3 2 +--R (- 102864A c - 308592B b c )d e + 360024B c d +--R * +--R m +--R + +--R 2 2 2 +--R ((20160A b + 20160B a)c + 20160B b c)e +--R + +--R 3 2 3 2 +--R (- 40320A c - 120960B b c )d e + 141120B c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 3 3 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 2 3 2 2 +--R ((- 15A b - 15B a)c - 15B b c)d e + (15A c + 45B b c )d e +--R + +--R 3 3 +--R - 35B c d +--R * +--R 7 +--R m +--R + +--R 2 2 3 3 +--R (93A a c + (93A b + 186B a b)c + 31B b )e +--R + +--R 2 2 2 +--R ((- 465A b - 465B a)c - 465B b c)d e +--R + +--R 3 2 2 3 3 +--R (465A c + 1395B b c )d e - 1085B c d +--R * +--R 6 +--R m +--R + +--R 2 2 3 3 +--R (1173A a c + (1173A b + 2346B a b)c + 391B b )e +--R + +--R 2 2 2 +--R ((- 5865A b - 5865B a)c - 5865B b c)d e +--R + +--R 3 2 2 3 3 +--R (5865A c + 17595B b c )d e - 13685B c d +--R * +--R 5 +--R m +--R + +--R 2 2 3 3 +--R (7743A a c + (7743A b + 15486B a b)c + 2581B b )e +--R + +--R 2 2 2 +--R ((- 38715A b - 38715B a)c - 38715B b c)d e +--R + +--R 3 2 2 3 3 +--R (38715A c + 116145B b c )d e - 90335B c d +--R * +--R 4 +--R m +--R + +--R 2 2 3 3 +--R (28632A a c + (28632A b + 57264B a b)c + 9544B b )e +--R + +--R 2 2 2 +--R ((- 143160A b - 143160B a)c - 143160B b c)d e +--R + +--R 3 2 2 3 3 +--R (143160A c + 429480B b c )d e - 334040B c d +--R * +--R 3 +--R m +--R + +--R 2 2 3 3 +--R (58692A a c + (58692A b + 117384B a b)c + 19564B b )e +--R + +--R 2 2 2 +--R ((- 293460A b - 293460B a)c - 293460B b c)d e +--R + +--R 3 2 2 3 3 +--R (293460A c + 880380B b c )d e - 684740B c d +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 +--R (60912A a c + (60912A b + 121824B a b)c + 20304B b )e +--R + +--R 2 2 2 +--R ((- 304560A b - 304560B a)c - 304560B b c)d e +--R + +--R 3 2 2 3 3 +--R (304560A c + 913680B b c )d e - 710640B c d +--R * +--R m +--R + +--R 2 2 3 3 +--R (24192A a c + (24192A b + 48384B a b)c + 8064B b )e +--R + +--R 2 2 2 +--R ((- 120960A b - 120960B a)c - 120960B b c)d e +--R + +--R 3 2 2 3 3 +--R (120960A c + 362880B b c )d e - 282240B c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 2 2 3 2 3 +--R ((30A b + 30B a)c + 30B b c)d e + (- 20A c - 60B b c )d e +--R + +--R 3 4 +--R 35B c d +--R * +--R 7 +--R m +--R + +--R 2 3 2 4 +--R ((192A a b + 96B a )c + 32A b + 96B a b )e +--R + +--R 2 2 3 3 +--R (- 384A a c + (- 384A b - 768B a b)c - 128B b )d e +--R + +--R 2 2 2 2 +--R ((960A b + 960B a)c + 960B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 640A c - 1920B b c )d e + 1120B c d +--R * +--R 6 +--R m +--R + +--R 2 3 2 4 +--R ((2508A a b + 1254B a )c + 418A b + 1254B a b )e +--R + +--R 2 2 3 3 +--R (- 5016A a c + (- 5016A b - 10032B a b)c - 1672B b )d e +--R + +--R 2 2 2 2 +--R ((12540A b + 12540B a)c + 12540B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 8360A c - 25080B b c )d e + 14630B c d +--R * +--R 5 +--R m +--R + +--R 2 3 2 4 +--R ((17184A a b + 8592B a )c + 2864A b + 8592B a b )e +--R + +--R 2 2 3 3 +--R (- 34368A a c + (- 34368A b - 68736B a b)c - 11456B b )d e +--R + +--R 2 2 2 2 +--R ((85920A b + 85920B a)c + 85920B b c)d e +--R + +--R 3 2 3 3 4 +--R (- 57280A c - 171840B b c )d e + 100240B c d +--R * +--R 4 +--R m +--R + +--R 2 3 2 4 +--R ((65958A a b + 32979B a )c + 10993A b + 32979B a b )e +--R + +--R 2 2 3 3 +--R (- 131916A a c + (- 131916A b - 263832B a b)c - 43972B b )d e +--R + +--R 2 2 2 2 +--R ((329790A b + 329790B a)c + 329790B b c)d e +--R + +--R 3 2 3 3 4 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366936B a b)c - 61156B b )d e +--R + +--R 2 2 4 2 +--R ((229335A b + 229335B a)c + 229335B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 91734A c - 275202B b c )d e + 107023B c d +--R * +--R 3 +--R m +--R + +--R 2 3 6 +--R (110118A a b + 36706B a )e +--R + +--R 2 2 2 5 +--R (- 220236A a c - 220236A a b - 220236B a b)d e +--R + +--R 2 3 2 2 4 +--R ((660708A a b + 330354B a )c + 110118A b + 330354B a b )d e +--R + +--R 2 2 3 3 3 +--R (- 440472A a c + (- 440472A b - 880944B a b)c - 146824B b )d e +--R + +--R 2 2 4 2 +--R ((550590A b + 550590B a)c + 550590B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 220236A c - 660708B b c )d e + 256942B c d +--R * +--R 2 +--R m +--R + +--R 2 3 6 +--R (134136A a b + 44712B a )e +--R + +--R 2 2 2 5 +--R (- 268272A a c - 268272A a b - 268272B a b)d e +--R + +--R 2 3 2 2 4 +--R ((804816A a b + 402408B a )c + 134136A b + 402408B a b )d e +--R + +--R 2 2 3 +--R (- 536544A a c + (- 536544A b - 1073088B a b)c - 178848B b ) +--R * +--R 3 3 +--R d e +--R + +--R 2 2 4 2 +--R ((670680A b + 670680B a)c + 670680B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 268272A c - 804816B b c )d e + 312984B c d +--R * +--R m +--R + +--R 2 3 6 +--R (60480A a b + 20160B a )e +--R + +--R 2 2 2 5 +--R (- 120960A a c - 120960A a b - 120960B a b)d e +--R + +--R 2 3 2 2 4 +--R ((362880A a b + 181440B a )c + 60480A b + 181440B a b )d e +--R + +--R 2 2 3 3 3 +--R (- 241920A a c + (- 241920A b - 483840B a b)c - 80640B b )d e +--R + +--R 2 2 4 2 +--R ((302400A b + 302400B a)c + 302400B b c)d e +--R + +--R 3 2 5 3 6 +--R (- 120960A c - 362880B b c )d e + 141120B c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R A a e + (- 3A a b - B a )d e + (3A a c + 3A a b + 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (3A a c + (3A b + 6B a b)c + B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 3A b - 3B a)c - 3B b c)d e + (A c + 3B b c )d e - B c d +--R * +--R 7 +--R m +--R + +--R 3 7 2 3 6 +--R 35A a e + (- 105A a b - 35B a )d e +--R + +--R 2 2 2 2 5 +--R (105A a c + 105A a b + 105B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 210A a b - 105B a )c - 35A b - 105B a b )d e +--R + +--R 2 2 3 4 3 +--R (105A a c + (105A b + 210B a b)c + 35B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 105A b - 105B a)c - 105B b c)d e + (35A c + 105B b c )d e +--R + +--R 3 7 +--R - 35B c d +--R * +--R 6 +--R m +--R + +--R 3 7 2 3 6 +--R 511A a e + (- 1533A a b - 511B a )d e +--R + +--R 2 2 2 2 5 +--R (1533A a c + 1533A a b + 1533B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 3066A a b - 1533B a )c - 511A b - 1533B a b )d e +--R + +--R 2 2 3 4 3 +--R (1533A a c + (1533A b + 3066B a b)c + 511B b )d e +--R + +--R 2 2 5 2 +--R ((- 1533A b - 1533B a)c - 1533B b c)d e +--R + +--R 3 2 6 3 7 +--R (511A c + 1533B b c )d e - 511B c d +--R * +--R 5 +--R m +--R + +--R 3 7 2 3 6 +--R 4025A a e + (- 12075A a b - 4025B a )d e +--R + +--R 2 2 2 2 5 +--R (12075A a c + 12075A a b + 12075B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 24150A a b - 12075B a )c - 4025A b - 12075B a b )d e +--R + +--R 2 2 3 4 3 +--R (12075A a c + (12075A b + 24150B a b)c + 4025B b )d e +--R + +--R 2 2 5 2 +--R ((- 12075A b - 12075B a)c - 12075B b c)d e +--R + +--R 3 2 6 3 7 +--R (4025A c + 12075B b c )d e - 4025B c d +--R * +--R 4 +--R m +--R + +--R 3 7 2 3 6 +--R 18424A a e + (- 55272A a b - 18424B a )d e +--R + +--R 2 2 2 2 5 +--R (55272A a c + 55272A a b + 55272B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 110544A a b - 55272B a )c - 18424A b - 55272B a b )d e +--R + +--R 2 2 3 4 3 +--R (55272A a c + (55272A b + 110544B a b)c + 18424B b )d e +--R + +--R 2 2 5 2 +--R ((- 55272A b - 55272B a)c - 55272B b c)d e +--R + +--R 3 2 6 3 7 +--R (18424A c + 55272B b c )d e - 18424B c d +--R * +--R 3 +--R m +--R + +--R 3 7 2 3 6 +--R 48860A a e + (- 146580A a b - 48860B a )d e +--R + +--R 2 2 2 2 5 +--R (146580A a c + 146580A a b + 146580B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 293160A a b - 146580B a )c - 48860A b - 146580B a b )d e +--R + +--R 2 2 3 4 3 +--R (146580A a c + (146580A b + 293160B a b)c + 48860B b )d e +--R + +--R 2 2 5 2 +--R ((- 146580A b - 146580B a)c - 146580B b c)d e +--R + +--R 3 2 6 3 7 +--R (48860A c + 146580B b c )d e - 48860B c d +--R * +--R 2 +--R m +--R + +--R 3 7 2 3 6 +--R 69264A a e + (- 207792A a b - 69264B a )d e +--R + +--R 2 2 2 2 5 +--R (207792A a c + 207792A a b + 207792B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 415584A a b - 207792B a )c - 69264A b - 207792B a b )d e +--R + +--R 2 2 3 4 3 +--R (207792A a c + (207792A b + 415584B a b)c + 69264B b )d e +--R + +--R 2 2 5 2 +--R ((- 207792A b - 207792B a)c - 207792B b c)d e +--R + +--R 3 2 6 3 7 +--R (69264A c + 207792B b c )d e - 69264B c d +--R * +--R m +--R + +--R 3 7 2 3 6 +--R 40320A a e + (- 120960A a b - 40320B a )d e +--R + +--R 2 2 2 2 5 +--R (120960A a c + 120960A a b + 120960B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 241920A a b - 120960B a )c - 40320A b - 120960B a b )d e +--R + +--R 2 2 3 4 3 +--R (120960A a c + (120960A b + 241920B a b)c + 40320B b )d e +--R + +--R 2 2 5 2 +--R ((- 120960A b - 120960B a)c - 120960B b c)d e +--R + +--R 3 2 6 3 7 +--R (40320A c + 120960B b c )d e - 40320B c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 185 + +--S 186 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 1035 +t0:=(A+B*x)*(d+e*x)^5*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 5 12 3 2 5 3 4 11 +--R B c e x + ((A c + 3B b c )e + 5B c d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 10 +--R (((3A b + 3B a)c + 3B b c)e + (5A c + 15B b c )d e + 10B c d e )x +--R + +--R 2 2 3 5 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 4 3 2 2 3 3 3 2 +--R ((15A b + 15B a)c + 15B b c)d e + (10A c + 30B b c )d e + 10B c d e +--R * +--R 9 +--R x +--R + +--R 2 3 2 5 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 4 +--R (15A a c + (15A b + 30B a b)c + 5B b )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R ((30A b + 30B a)c + 30B b c)d e + (10A c + 30B b c )d e + 5B c d e +--R * +--R 8 +--R x +--R + +--R 2 2 2 5 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 4 +--R ((30A a b + 15B a )c + 5A b + 15B a b )d e +--R + +--R 2 2 3 2 3 +--R (30A a c + (30A b + 60B a b)c + 10B b )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R ((30A b + 30B a)c + 30B b c)d e + (5A c + 15B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 3 5 2 2 2 4 +--R (3A a b + B a )e + (15A a c + 15A a b + 15B a b)d e +--R + +--R 2 3 2 2 3 +--R ((60A a b + 30B a )c + 10A b + 30B a b )d e +--R + +--R 2 2 3 3 2 +--R (30A a c + (30A b + 60B a b)c + 10B b )d e +--R + +--R 2 2 4 3 2 5 +--R ((15A b + 15B a)c + 15B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 3 5 2 3 4 2 2 2 2 3 +--R A a e + (15A a b + 5B a )d e + (30A a c + 30A a b + 30B a b)d e +--R + +--R 2 3 2 3 2 +--R ((60A a b + 30B a )c + 10A b + 30B a b )d e +--R + +--R 2 2 3 4 +--R (15A a c + (15A b + 30B a b)c + 5B b )d e +--R + +--R 2 2 5 +--R ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 2 3 2 2 2 3 2 +--R 5A a d e + (30A a b + 10B a )d e + (30A a c + 30A a b + 30B a b)d e +--R + +--R 2 3 2 4 +--R ((30A a b + 15B a )c + 5A b + 15B a b )d e +--R + +--R 2 2 3 5 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 2 3 2 3 3 2 2 2 2 4 +--R 10A a d e + (30A a b + 10B a )d e + (15A a c + 15A a b + 15B a b)d e +--R + +--R 2 3 2 5 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 4 2 2 2 5 2 +--R (10A a d e + (15A a b + 5B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 4 2 3 5 3 5 +--R (5A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 187 + +--S 188 of 1035 +r0:=-1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^6/e^8-_ + 1/7*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-_ + e*(4*b*d-a*e)))*(d+e*x)^7/e^8-3/8*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*(d+e*x)^8/e^8-1/9*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*_ + (d+e*x)^9/e^8-1/10*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + (d+e*x)^10/e^8-3/11*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-_ + c*e*(6*b*d-a*e)))*(d+e*x)^11/e^8-1/12*c^2*(7*B*c*d-3*b*B*e-A*c*e)*_ + (d+e*x)^12/e^8+1/13*B*c^3*(d+e*x)^13/e^8 +--R +--R +--R (2) +--R 1 3 13 13 1 3 1 2 13 5 3 12 12 +--R -- B c e x + ((-- A c + - B b c )e + -- B c d e )x +--R 13 12 4 12 +--R + +--R 3 3 2 3 2 13 5 3 15 2 12 +--R ((-- A b + -- B a)c + -- B b c)e + (-- A c + -- B b c )d e +--R 11 11 11 11 11 +--R + +--R 10 3 2 11 +--R -- B c d e +--R 11 +--R * +--R 11 +--R x +--R + +--R 3 2 3 2 3 1 3 13 +--R (-- A a c + (-- A b + - B a b)c + -- B b )e +--R 10 10 5 10 +--R + +--R 3 3 2 3 2 12 3 2 2 11 3 3 10 +--R ((- A b + - B a)c + - B b c)d e + (A c + 3B b c )d e + B c d e +--R 2 2 2 +--R * +--R 10 +--R x +--R + +--R 2 1 2 1 3 1 2 13 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 3 3 9 3 +--R + +--R 5 2 5 2 10 5 3 12 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 3 3 3 9 +--R + +--R 10 10 2 10 2 2 11 10 3 10 2 3 10 +--R ((-- A b + -- B a)c + -- B b c)d e + (-- A c + -- B b c )d e +--R 3 3 3 9 3 +--R + +--R 5 3 4 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 2 3 2 3 2 13 +--R (- A a c + - A a b + - B a b)e +--R 8 8 8 +--R + +--R 15 15 2 5 3 15 2 12 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 4 8 8 8 +--R + +--R 15 2 15 2 15 5 3 2 11 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 4 4 2 4 +--R + +--R 15 15 2 15 2 3 10 5 3 15 2 4 9 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + -- B b c )d e +--R 4 4 4 8 8 +--R + +--R 1 3 5 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 3 2 1 3 13 15 2 15 2 15 2 12 +--R (- A a b + - B a )e + (-- A a c + -- A a b + -- B a b)d e +--R 7 7 7 7 7 +--R + +--R 60 30 2 10 3 30 2 2 11 +--R ((-- A a b + -- B a )c + -- A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 30 2 30 2 60 10 3 3 10 +--R (-- A a c + (-- A b + -- B a b)c + -- B b )d e +--R 7 7 7 7 +--R + +--R 15 15 2 15 2 4 9 1 3 3 2 5 8 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 3 13 5 2 5 3 12 +--R - A a e + (- A a b + - B a )d e +--R 6 2 6 +--R + +--R 2 2 2 2 11 +--R (5A a c + 5A a b + 5B a b)d e +--R + +--R 2 5 3 2 3 10 +--R ((10A a b + 5B a )c + - A b + 5B a b )d e +--R 3 +--R + +--R 5 2 5 2 5 3 4 9 +--R (- A a c + (- A b + 5B a b)c + - B b )d e +--R 2 2 6 +--R + +--R 1 1 2 1 2 5 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 12 2 3 2 11 2 2 2 3 10 +--R A a d e + (6A a b + 2B a )d e + (6A a c + 6A a b + 6B a b)d e +--R + +--R 2 3 2 4 9 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 3 2 3 2 6 1 3 5 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 5 3 2 11 15 2 5 3 3 10 +--R - A a d e + (-- A a b + - B a )d e +--R 2 2 2 +--R + +--R 15 2 15 2 15 2 4 9 +--R (-- A a c + -- A a b + -- B a b)d e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 5 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 10 3 3 10 2 5 3 4 9 2 2 2 5 8 3 +--R (-- A a d e + (5A a b + - B a )d e + (A a c + A a b + B a b)d e )x +--R 3 3 +--R + +--R 5 3 4 9 3 2 1 3 5 8 2 3 5 8 1 3 6 7 +--R (- A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 2 6 +--R + +--R 1 2 1 3 7 6 1 2 1 2 1 2 8 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 14 42 56 56 56 +--R + +--R 1 1 2 1 3 1 2 9 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 84 168 504 168 +--R + +--R 1 2 1 2 1 1 3 10 3 +--R (--- A a c + (--- A b + --- B a b)c + ---- B b )d e +--R 420 420 210 1260 +--R + +--R 1 1 2 1 2 11 2 +--R ((- --- A b - --- B a)c - --- B b c)d e +--R 924 924 924 +--R + +--R 1 3 1 2 12 1 3 13 +--R (---- A c + ---- B b c )d e - ----- B c d +--R 5544 1848 10296 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 188 + +--S 189 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 1035 +t0:=(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 11 3 2 4 3 3 10 +--R B c e x + ((A c + 3B b c )e + 4B c d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 9 +--R (((3A b + 3B a)c + 3B b c)e + (4A c + 12B b c )d e + 6B c d e )x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )e +--R + +--R 2 2 3 3 2 2 2 3 3 +--R ((12A b + 12B a)c + 12B b c)d e + (6A c + 18B b c )d e + 4B c d e +--R * +--R 8 +--R x +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 3 +--R (12A a c + (12A b + 24B a b)c + 4B b )d e +--R + +--R 2 2 2 2 3 2 3 3 4 +--R ((18A b + 18B a)c + 18B b c)d e + (4A c + 12B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 2 2 4 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 3 +--R ((24A a b + 12B a )c + 4A b + 12B a b )d e +--R + +--R 2 2 3 2 2 +--R (18A a c + (18A b + 36B a b)c + 6B b )d e +--R + +--R 2 2 3 3 2 4 +--R ((12A b + 12B a)c + 12B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 3 4 2 2 2 3 +--R (3A a b + B a )e + (12A a c + 12A a b + 12B a b)d e +--R + +--R 2 3 2 2 2 +--R ((36A a b + 18B a )c + 6A b + 18B a b )d e +--R + +--R 2 2 3 3 +--R (12A a c + (12A b + 24B a b)c + 4B b )d e +--R + +--R 2 2 4 +--R ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 2 +--R A a e + (12A a b + 4B a )d e + (18A a c + 18A a b + 18B a b)d e +--R + +--R 2 3 2 3 +--R ((24A a b + 12B a )c + 4A b + 12B a b )d e +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 3 +--R 4A a d e + (18A a b + 6B a )d e + (12A a c + 12A a b + 12B a b)d e +--R + +--R 2 3 2 4 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 2 3 3 2 2 2 4 2 +--R (6A a d e + (12A a b + 4B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 3 2 3 4 3 4 +--R (4A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 190 + +--S 191 of 1035 +r0:=-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^5/e^8-1/6*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^6/e^8-_ + 3/7*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^7/e^8-_ + 1/8*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^8/e^8-1/9*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*_ + d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^9/e^8-3/10*c*(A*c*e*(2*c*d-b*e)-_ + B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^10/e^8-1/11*c^2*(7*B*c*d-_ + 3*b*B*e-A*c*e)*(d+e*x)^11/e^8+1/12*B*c^3*(d+e*x)^12/e^8 +--R +--R +--R (2) +--R 1 3 12 12 1 3 3 2 12 4 3 11 11 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 12 11 11 11 +--R + +--R 3 3 2 3 2 12 2 3 6 2 11 +--R ((-- A b + -- B a)c + -- B b c)e + (- A c + - B b c )d e +--R 10 10 10 5 5 +--R + +--R 3 3 2 10 +--R - B c d e +--R 5 +--R * +--R 10 +--R x +--R + +--R 1 2 1 2 2 1 3 12 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 3 3 3 9 +--R + +--R 4 4 2 4 2 11 2 3 2 2 10 +--R ((- A b + - B a)c + - B b c)d e + (- A c + 2B b c )d e +--R 3 3 3 3 +--R + +--R 4 3 3 9 +--R - B c d e +--R 9 +--R * +--R 9 +--R x +--R + +--R 3 3 2 1 3 3 2 12 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 4 8 8 8 +--R + +--R 3 2 3 2 1 3 11 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 9 9 2 9 2 2 10 1 3 3 2 3 9 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 4 4 4 2 2 +--R + +--R 1 3 4 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 3 2 3 2 3 2 12 +--R (- A a c + - A a b + - B a b)e +--R 7 7 7 +--R + +--R 24 12 2 4 3 12 2 11 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 7 7 7 7 +--R + +--R 18 2 18 2 36 6 3 2 10 +--R (-- A a c + (-- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 12 12 2 12 2 3 9 1 3 3 2 4 8 +--R ((-- A b + -- B a)c + -- B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 12 2 2 2 11 +--R (- A a b + - B a )e + (2A a c + 2A a b + 2B a b)d e +--R 2 6 +--R + +--R 2 3 2 2 10 +--R ((6A a b + 3B a )c + A b + 3B a b )d e +--R + +--R 2 2 2 3 3 9 +--R (2A a c + (2A b + 4B a b)c + - B b )d e +--R 3 +--R + +--R 1 1 2 1 2 4 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 1 3 12 12 2 4 3 11 +--R - A a e + (-- A a b + - B a )d e +--R 5 5 5 +--R + +--R 18 2 18 2 18 2 2 10 +--R (-- A a c + -- A a b + -- B a b)d e +--R 5 5 5 +--R + +--R 24 12 2 4 3 12 2 3 9 +--R ((-- A a b + -- B a )c + - A b + -- B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 4 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 11 9 2 3 3 2 10 2 2 2 3 9 +--R A a d e + (- A a b + - B a )d e + (3A a c + 3A a b + 3B a b)d e +--R 2 2 +--R + +--R 3 3 2 1 3 3 2 4 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 2 10 2 4 3 3 9 2 2 2 4 8 3 +--R (2A a d e + (4A a b + - B a )d e + (A a c + A a b + B a b)d e )x +--R 3 +--R + +--R 3 3 9 3 2 1 3 4 8 2 3 4 8 1 3 5 7 +--R (2A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 5 +--R + +--R 1 2 1 3 6 6 1 2 1 2 1 2 7 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 10 30 35 35 35 +--R + +--R 3 3 2 1 3 3 2 8 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 280 280 +--R + +--R 1 2 1 2 1 1 3 9 3 +--R (--- A a c + (--- A b + --- B a b)c + --- B b )d e +--R 210 210 105 630 +--R + +--R 1 1 2 1 2 10 2 1 3 1 2 11 +--R ((- --- A b - --- B a)c - --- B b c)d e + (---- A c + --- B b c )d e +--R 420 420 420 2310 770 +--R + +--R 1 3 12 +--R - ---- B c d +--R 3960 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 191 + +--S 192 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 1035 +t0:=(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 10 3 2 3 3 2 9 +--R B c e x + ((A c + 3B b c )e + 3B c d e )x +--R + +--R 2 2 3 3 2 2 3 2 8 +--R (((3A b + 3B a)c + 3B b c)e + (3A c + 9B b c )d e + 3B c d e)x +--R + +--R 2 2 3 3 2 2 2 +--R (3A a c + (3A b + 6B a b)c + B b )e + ((9A b + 9B a)c + 9B b c)d e +--R + +--R 3 2 2 3 3 +--R (3A c + 9B b c )d e + B c d +--R * +--R 7 +--R x +--R + +--R 2 3 2 3 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 2 +--R (9A a c + (9A b + 18B a b)c + 3B b )d e +--R + +--R 2 2 2 3 2 3 +--R ((9A b + 9B a)c + 9B b c)d e + (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 2 2 3 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 2 +--R ((18A a b + 9B a )c + 3A b + 9B a b )d e +--R + +--R 2 2 3 2 2 2 3 +--R (9A a c + (9A b + 18B a b)c + 3B b )d e + ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 2 2 2 +--R (3A a b + B a )e + (9A a c + 9A a b + 9B a b)d e +--R + +--R 2 3 2 2 +--R ((18A a b + 9B a )c + 3A b + 9B a b )d e +--R + +--R 2 2 3 3 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 2 +--R A a e + (9A a b + 3B a )d e + (9A a c + 9A a b + 9B a b)d e +--R + +--R 2 3 2 3 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 2 3 2 +--R (3A a d e + (9A a b + 3B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 2 2 3 3 3 3 +--R (3A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 193 + +--S 194 of 1035 +r0:=-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^4/e^8-1/5*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^5/e^8-_ + 1/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^6/e^8-_ + 1/7*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^7/e^8-1/8*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^8/e^8-1/3*c*(A*c*e*(2*c*d-_ + b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^9/e^8-1/10*c^2*_ + (7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^10/e^8+1/11*B*c^3*(d+e*x)^11/e^8 +--R +--R +--R (2) +--R 1 3 11 11 1 3 3 2 11 3 3 10 10 +--R -- B c e x + ((-- A c + -- B b c )e + -- B c d e )x +--R 11 10 10 10 +--R + +--R 1 1 2 1 2 11 1 3 2 10 +--R ((- A b + - B a)c + - B b c)e + (- A c + B b c )d e +--R 3 3 3 3 +--R + +--R 1 3 2 9 +--R - B c d e +--R 3 +--R * +--R 9 +--R x +--R + +--R 3 2 3 2 3 1 3 11 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 8 8 4 8 +--R + +--R 9 9 2 9 2 10 3 3 9 2 2 9 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 8 8 8 8 8 +--R + +--R 1 3 3 8 +--R - B c d e +--R 8 +--R * +--R 8 +--R x +--R + +--R 6 3 2 1 3 3 2 11 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 7 7 7 7 +--R + +--R 9 2 9 2 18 3 3 10 +--R (- A a c + (- A b + -- B a b)c + - B b )d e +--R 7 7 7 7 +--R + +--R 9 9 2 9 2 2 9 1 3 3 2 3 8 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d e +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 2 1 2 11 +--R (- A a c + - A a b + - B a b)e +--R 2 2 2 +--R + +--R 3 2 1 3 3 2 10 +--R ((3A a b + - B a )c + - A b + - B a b )d e +--R 2 2 2 +--R + +--R 3 2 3 2 1 3 2 9 +--R (- A a c + (- A b + 3B a b)c + - B b )d e +--R 2 2 2 +--R + +--R 1 1 2 1 2 3 8 +--R ((- A b + - B a)c + - B b c)d e +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 1 3 11 9 2 9 2 9 2 10 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 5 5 5 5 5 +--R + +--R 18 9 2 3 3 9 2 2 9 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 3 8 +--R (- A a c + (- A b + - B a b)c + - B b )d e +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 1 3 11 9 2 3 3 10 +--R - A a e + (- A a b + - B a )d e +--R 4 4 4 +--R + +--R 9 2 9 2 9 2 2 9 +--R (- A a c + - A a b + - B a b)d e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 3 8 +--R ((- A a b + - B a )c + - A b + - B a b )d e +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 3 10 2 3 2 9 2 2 2 3 8 3 +--R (A a d e + (3A a b + B a )d e + (A a c + A a b + B a b)d e )x +--R + +--R 3 3 2 9 3 2 1 3 3 8 2 3 3 8 1 3 4 7 +--R (- A a d e + (- A a b + - B a )d e )x + A a d e x + - A a d e +--R 2 2 2 4 +--R + +--R 3 2 1 3 5 6 1 2 1 2 1 2 6 5 +--R (- -- A a b - -- B a )d e + (-- A a c + -- A a b + -- B a b)d e +--R 20 20 20 20 20 +--R + +--R 3 3 2 1 3 3 2 7 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 70 140 140 140 +--R + +--R 3 2 3 2 3 1 3 8 3 +--R (--- A a c + (--- A b + --- B a b)c + --- B b )d e +--R 280 280 140 280 +--R + +--R 1 1 2 1 2 9 2 1 3 1 2 10 +--R ((- --- A b - --- B a)c - --- B b c)d e + (--- A c + --- B b c )d e +--R 168 168 168 840 280 +--R + +--R 1 3 11 +--R - ---- B c d +--R 1320 +--R / +--R 8 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 194 + +--S 195 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1035 +t0:=(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 9 3 2 2 3 8 +--R B c e x + ((A c + 3B b c )e + 2B c d e)x +--R + +--R 2 2 2 3 2 3 2 7 +--R (((3A b + 3B a)c + 3B b c)e + (2A c + 6B b c )d e + B c d )x +--R + +--R 2 2 3 2 2 2 +--R (3A a c + (3A b + 6B a b)c + B b )e + ((6A b + 6B a)c + 6B b c)d e +--R + +--R 3 2 2 +--R (A c + 3B b c )d +--R * +--R 6 +--R x +--R + +--R 2 3 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 2 2 2 +--R (6A a c + (6A b + 12B a b)c + 2B b )d e + ((3A b + 3B a)c + 3B b c)d +--R * +--R 5 +--R x +--R + +--R 2 2 2 2 +--R (3A a c + 3A a b + 3B a b)e +--R + +--R 2 3 2 +--R ((12A a b + 6B a )c + 2A b + 6B a b )d e +--R + +--R 2 2 3 2 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 2 3 2 2 2 2 +--R (3A a b + B a )e + (6A a c + 6A a b + 6B a b)d e +--R + +--R 2 3 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (A a e + (6A a b + 2B a )d e + (3A a c + 3A a b + 3B a b)d )x +--R + +--R 3 2 3 2 3 2 +--R (2A a d e + (3A a b + B a )d )x + A a d +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 1035 +r0:=a^3*A*d^2*x+1/2*a^2*d*(3*A*b*d+a*B*d+2*a*A*e)*x^2+1/3*a*(a*B*d*_ + (3*b*d+2*a*e)+A*(3*b^2*d^2+6*a*b*d*e+a*(3*c*d^2+a*e^2)))*x^3+1/4*(A*_ + (b^3*d^2+6*a*b^2*d*e+6*a^2*c*d*e+3*a*b*(2*c*d^2+a*e^2))+a*B*_ + (3*b^2*d^2+6*a*b*d*e+a*(3*c*d^2+a*e^2)))*x^4+1/5*(b^3*d*(B*d+2*A*e)+_ + 3*b^2*(A*c*d^2+2*a*B*d*e+a*A*e^2)+3*a*c*(A*c*d^2+2*a*B*d*e+a*A*e^2)+_ + 3*a*b*(2*B*c*d^2+4*A*c*d*e+a*B*e^2))*x^5+1/6*(b^3*e*(2*B*d+A*e)+_ + 3*b*c*(A*c*d^2+4*a*B*d*e+2*a*A*e^2)+3*b^2*(B*c*d^2+2*A*c*d*e+a*B*e^2)+_ + 3*a*c*(B*c*d^2+2*A*c*d*e+a*B*e^2))*x^6+1/7*(b^3*B*e^2+3*b^2*c*e*_ + (2*B*d+A*e)+c^2*(A*c*d^2+6*a*B*d*e+3*a*A*e^2)+3*b*c*(B*c*d^2+2*A*c*d*e+_ + 2*a*B*e^2))*x^7+1/8*c*(A*c*e*(2*c*d+3*b*e)+B*(c^2*d^2+3*b^2*e^2+_ + 3*c*e*(2*b*d+a*e)))*x^8+1/9*c^2*e*(2*B*c*d+3*b*B*e+A*c*e)*x^9+_ + 1/10*B*c^3*e^2*x^10 +--R +--R +--R (2) +--R 1 3 2 10 1 3 1 2 2 2 3 9 +--R -- B c e x + ((- A c + - B b c )e + - B c d e)x +--R 10 9 3 9 +--R + +--R 3 3 2 3 2 2 1 3 3 2 1 3 2 8 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d e + - B c d )x +--R 8 8 8 4 4 8 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )e +--R 7 7 7 7 +--R + +--R 6 6 2 6 2 1 3 3 2 2 +--R ((- A b + - B a)c + - B b c)d e + (- A c + - B b c )d +--R 7 7 7 7 7 +--R * +--R 7 +--R x +--R + +--R 1 2 1 3 1 2 2 +--R ((A a b + - B a )c + - A b + - B a b )e +--R 2 6 2 +--R + +--R 2 2 1 3 1 1 2 1 2 2 +--R (A a c + (A b + 2B a b)c + - B b )d e + ((- A b + - B a)c + - B b c)d +--R 3 2 2 2 +--R * +--R 6 +--R x +--R + +--R 3 2 3 2 3 2 2 +--R (- A a c + - A a b + - B a b)e +--R 5 5 5 +--R + +--R 12 6 2 2 3 6 2 +--R ((-- A a b + - B a )c + - A b + - B a b )d e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 2 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 1 3 2 3 2 3 2 3 2 +--R (- A a b + - B a )e + (- A a c + - A a b + - B a b)d e +--R 4 4 2 2 2 +--R + +--R 3 3 2 1 3 3 2 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 1 3 2 2 2 3 2 2 2 2 3 +--R (- A a e + (2A a b + - B a )d e + (A a c + A a b + B a b)d )x +--R 3 3 +--R + +--R 3 3 2 1 3 2 2 3 2 +--R (A a d e + (- A a b + - B a )d )x + A a d x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 1035 +t0:=(A+B*x)*(d+e*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 8 3 2 3 7 +--R B c e x + ((A c + 3B b c )e + B c d)x +--R + +--R 2 2 3 2 6 +--R (((3A b + 3B a)c + 3B b c)e + (A c + 3B b c )d)x +--R + +--R 2 2 3 2 2 5 +--R ((3A a c + (3A b + 6B a b)c + B b )e + ((3A b + 3B a)c + 3B b c)d)x +--R + +--R 2 3 2 +--R ((6A a b + 3B a )c + A b + 3B a b )e +--R + +--R 2 2 3 +--R (3A a c + (3A b + 6B a b)c + B b )d +--R * +--R 4 +--R x +--R + +--R 2 2 2 2 3 2 3 +--R ((3A a c + 3A a b + 3B a b)e + ((6A a b + 3B a )c + A b + 3B a b )d)x +--R + +--R 2 3 2 2 2 2 +--R ((3A a b + B a )e + (3A a c + 3A a b + 3B a b)d)x +--R + +--R 3 2 3 3 +--R (A a e + (3A a b + B a )d)x + A a d +--R Type: Polynomial(Integer) +--E 199 + +--S 200 of 1035 +r0:=a^3*A*d*x+1/2*a^2*(3*A*b*d+a*B*d+a*A*e)*x^2+1/3*a*(a*B*(3*b*d+a*e)+_ + 3*A*(b^2*d+a*c*d+a*b*e))*x^3+1/4*(3*a*B*(b^2*d+a*c*d+a*b*e)+A*(b^3*d+_ + 6*a*b*c*d+3*a*b^2*e+3*a^2*c*e))*x^4+1/5*(b^3*(B*d+A*e)+6*a*b*c*(B*d+_ + A*e)+3*b^2*(A*c*d+a*B*e)+3*a*c*(A*c*d+a*B*e))*x^5+1/6*(b^3*B*e+_ + 3*b^2*c*(B*d+A*e)+3*a*c^2*(B*d+A*e)+3*b*c*(A*c*d+2*a*B*e))*x^6+_ + 1/7*c*(3*b^2*B*e+3*b*c*(B*d+A*e)+c*(A*c*d+3*a*B*e))*x^7+_ + 1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 3 2 1 3 8 +--R - B c e x + ((- A c + - B b c )e + - B c d)x +--R 9 8 8 8 +--R + +--R 3 3 2 3 2 1 3 3 2 7 +--R (((- A b + - B a)c + - B b c)e + (- A c + - B b c )d)x +--R 7 7 7 7 7 +--R + +--R 1 2 1 2 1 3 +--R (- A a c + (- A b + B a b)c + - B b )e +--R 2 2 6 +--R + +--R 1 1 2 1 2 +--R ((- A b + - B a)c + - B b c)d +--R 2 2 2 +--R * +--R 6 +--R x +--R + +--R 6 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 +--R (- A a c + (- A b + - B a b)c + - B b )d +--R 5 5 5 5 +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 3 2 +--R (- A a c + - A a b + - B a b)e +--R 4 4 4 +--R + +--R 3 3 2 1 3 3 2 +--R ((- A a b + - B a )c + - A b + - B a b )d +--R 2 4 4 4 +--R * +--R 4 +--R x +--R + +--R 2 1 3 2 2 2 3 +--R ((A a b + - B a )e + (A a c + A a b + B a b)d)x +--R 3 +--R + +--R 1 3 3 2 1 3 2 3 +--R (- A a e + (- A a b + - B a )d)x + A a d x +--R 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 200 + +--S 201 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 202 + +--S 203 of 1035 +r0:=a^3*A*x+1/2*a^2*(3*A*b+a*B)*x^2+a*(a*b*B+A*(b^2+a*c))*x^3+_ + 1/4*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^4+1/5*(b^3*B+3*A*b^2*c+_ + 6*a*b*B*c+3*a*A*c^2)*x^5+1/2*c*(b^2*B+A*b*c+a*B*c)*x^6+_ + 1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8 +--R +--R +--R (2) +--R 1 3 8 1 3 3 2 7 1 1 2 1 2 6 +--R - B c x + (- A c + - B b c )x + ((- A b + - B a)c + - B b c)x +--R 8 7 7 2 2 2 +--R + +--R 3 2 3 2 6 1 3 5 +--R (- A a c + (- A b + - B a b)c + - B b )x +--R 5 5 5 5 +--R + +--R 3 3 2 1 3 3 2 4 2 2 2 3 +--R ((- A a b + - B a )c + - A b + - B a b )x + (A a c + A a b + B a b)x +--R 2 4 4 4 +--R + +--R 3 2 1 3 2 3 +--R (- A a b + - B a )x + A a x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 203 + +--S 204 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x) +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 205 + +--S 206 of 1035 +r0:=-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*_ + (4*b*d-a*e)))*x/e^7-3/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*_ + (8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))*(d+e*x)^2/e^8-1/3*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^3/e^8-_ + 1/4*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^4/e^8-_ + 3/5*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*_ + (d+e*x)^5/e^8-1/6*c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^6/e^8+1/7*B*c^3*_ + (d+e*x)^7/e^8-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 2 3 6 +--R 420A a e + (- 1260A a b - 420B a )d e +--R + +--R 2 2 2 2 5 +--R (1260A a c + 1260A a b + 1260B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 2520A a b - 1260B a )c - 420A b - 1260B a b )d e +--R + +--R 2 2 3 4 3 +--R (1260A a c + (1260A b + 2520B a b)c + 420B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 1260A b - 1260B a)c - 1260B b c)d e + (420A c + 1260B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 60B c e x + ((70A c + 210B b c )e - 70B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((252A b + 252B a)c + 252B b c)e + (- 84A c - 252B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (315A a c + (315A b + 630B a b)c + 105B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 315A b - 315B a)c - 315B b c)d e + (105A c + 315B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((840A a b + 420B a )c + 140A b + 420B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((420A b + 420B a)c + 420B b c)d e + (- 140A c - 420B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (630A a c + 630A a b + 630B a b)e +--R + +--R 2 3 2 6 +--R ((- 1260A a b - 630B a )c - 210A b - 630B a b )d e +--R + +--R 2 2 3 2 5 +--R (630A a c + (630A b + 1260B a b)c + 210B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 630A b - 630B a)c - 630B b c)d e + (210A c + 630B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (1260A a b + 420B a )e + (- 1260A a c - 1260A a b - 1260B a b)d e +--R + +--R 2 3 2 2 5 +--R ((2520A a b + 1260B a )c + 420A b + 1260B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 1260A a c + (- 1260A b - 2520B a b)c - 420B b )d e +--R + +--R 2 2 4 3 +--R ((1260A b + 1260B a)c + 1260B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 420A c - 1260B b c )d e + 420B c d e +--R * +--R x +--R + +--R 2 2 2 2 5 +--R (630A a c + 630A a b + 630B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 2940A a b - 1470B a )c - 490A b - 1470B a b )d e +--R + +--R 2 2 3 4 3 +--R (2415A a c + (2415A b + 4830B a b)c + 805B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 3423A b - 3423B a)c - 3423B b c)d e + (1491A c + 4473B b c )d e +--R + +--R 3 7 +--R - 1851B c d +--R / +--R 8 +--R 420e +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 208 + +--S 209 of 1035 +r0:=-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*_ + (2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*x/e^7+(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x))-1/2*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*_ + (d+e*x)^2/e^8-1/3*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + (d+e*x)^3/e^8-3/4*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))*(d+e*x)^4/e^8-1/5*c^2*(7*B*c*d-3*b*B*e-A*c*e)*_ + (d+e*x)^5/e^8+1/6*B*c^3*(d+e*x)^6/e^8-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*_ + (2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 7 2 2 2 6 +--R (180A a b + 60B a )e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 2 5 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 4 3 +--R ((900A b + 900B a)c + 900B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 360A c - 1080B b c )d e + 420B c d e +--R * +--R x +--R + +--R 2 3 6 2 2 2 2 5 +--R (180A a b + 60B a )d e + (- 360A a c - 360A a b - 360B a b)d e +--R + +--R 2 3 2 3 4 +--R ((1080A a b + 540B a )c + 180A b + 540B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 720A a c + (- 720A b - 1440B a b)c - 240B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((900A b + 900B a)c + 900B b c)d e + (- 360A c - 1080B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((12A c + 36B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((45A b + 45B a)c + 45B b c)e + (- 18A c - 54B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (60A a c + (60A b + 120B a b)c + 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 75A b - 75B a)c - 75B b c)d e + (30A c + 90B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((180A a b + 90B a )c + 30A b + 90B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((150A b + 150B a)c + 150B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 4 3 +--R 70B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (180A a c + 180A a b + 180B a b)e +--R + +--R 2 3 2 6 +--R ((- 540A a b - 270B a )c - 90A b - 270B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 5 2 +--R - 210B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (180A a c + 180A a b + 180B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 540A a b - 270B a )c - 90A b - 270B a b )d e +--R + +--R 2 2 3 3 4 +--R (240A a c + (240A b + 480B a b)c + 80B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 75A b - 75B a)c - 75B b c)d e + (- 78A c - 234B b c )d e +--R + +--R 3 6 +--R 231B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (180A a b + 60B a )d e +--R + +--R 2 2 2 2 5 +--R (- 180A a c - 180A a b - 180B a b)d e +--R + +--R 2 3 2 3 4 +--R ((540A a b + 270B a )c + 90A b + 270B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 480A a c + (- 480A b - 960B a b)c - 160B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((825A b + 825B a)c + 825B b c)d e + (- 438A c - 1314B b c )d e +--R + +--R 3 7 +--R 651B c d +--R / +--R 9 8 +--R 60e x + 60d e +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1035 +r0:=-(A*e*(10*c^3*d^3-b^3*e^3+3*b*c*e^2*(3*b*d-2*a*e)-9*c^2*d*e*(2*b*d-a*e))-_ + 3*B*(5*c^3*d^4-2*c^2*d^2*e*(5*b*d-3*a*e)-b^2*e^3*(b*d-a*e)+c*e^2*_ + (6*b^2*d^2-6*a*b*d*e+a^2*e^2)))*x/e^7-1/2*(B*(10*c^3*d^3-b^3*e^3+_ + 3*b*c*e^2*(3*b*d-2*a*e)-9*c^2*d*e*(2*b*d-a*e))-3*A*c*e*(2*c^2*d^2+_ + b^2*e^2-c*e*(3*b*d-a*e)))*x^2/e^6-c*(A*c*e*(c*d-b*e)-B*(2*c^2*d^2+_ + b^2*e^2-c*e*(3*b*d-a*e)))*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*_ + x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*_ + (d+e*x)^2)+(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-_ + e*(4*b*d-a*e)))/(e^8*(d+e*x))-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 2 7 +--R (60A a c + 60A a b + 60B a b)e +--R + +--R 2 3 2 6 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 2 5 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (300A c + 900B b c )d e - 420B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 6 +--R (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 720A a b - 360B a )c - 120A b - 360B a b )d e +--R + +--R 2 2 3 3 4 +--R (720A a c + (720A b + 1440B a b)c + 240B b )d e +--R + +--R 2 2 4 3 +--R ((- 1200A b - 1200B a)c - 1200B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (600A c + 1800B b c )d e - 840B c d e +--R * +--R x +--R + +--R 2 2 2 2 5 +--R (60A a c + 60A a b + 60B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 360A a b - 180B a )c - 60A b - 180B a b )d e +--R + +--R 2 2 3 4 3 +--R (360A a c + (360A b + 720B a b)c + 120B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 600A b - 600B a)c - 600B b c)d e + (300A c + 900B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((5A c + 15B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((20A b + 20B a)c + 20B b c)e + (- 10A c - 30B b c )d e +--R + +--R 3 2 5 +--R 14B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (30A a c + (30A b + 60B a b)c + 10B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 50A b - 50B a)c - 50B b c)d e + (25A c + 75B b c )d e +--R + +--R 3 3 4 +--R - 35B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((120A a b + 60B a )c + 20A b + 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((200A b + 200B a)c + 200B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 4 3 +--R 140B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((240A a b + 120B a )c + 40A b + 120B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 330A a c + (- 330A b - 660B a b)c - 110B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((630A b + 630B a)c + 630B b c)d e + (- 340A c - 1020B b c )d e +--R + +--R 3 5 2 +--R 500B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 60A a b - 20B a )e + (120A a c + 120A a b + 120B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 240A a b - 120B a )c - 40A b - 120B a b )d e +--R + +--R 2 2 3 3 4 +--R (60A a c + (60A b + 120B a b)c + 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((60A b + 60B a)c + 60B b c)d e + (- 80A c - 240B b c )d e +--R + +--R 3 6 +--R 160B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 10A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (90A a c + 90A a b + 90B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 300A a b - 150B a )c - 50A b - 150B a b )d e +--R + +--R 2 2 3 4 3 +--R (210A a c + (210A b + 420B a b)c + 70B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 270A b - 270B a)c - 270B b c)d e + (110A c + 330B b c )d e +--R + +--R 3 7 +--R - 130B c d +--R / +--R 10 2 9 2 8 +--R 20e x + 40d e x + 20d e +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 214 + +--S 215 of 1035 +r0:=-(B*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + A*c*e*(10*c^2*d^2+3*b^2*e^2-3*c*e*(4*b*d-a*e)))*x/e^7-1/2*c*(A*c*e*_ + (4*c*d-3*b*e)-B*(10*c^2*d^2+3*b^2*e^2-3*c*e*(4*b*d-a*e)))*x^2/e^6-_ + 1/3*c^2*(4*B*c*d-3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+_ + 1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^3)+1/2*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^2)+3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x))-(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+_ + 3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 3 2 7 +--R ((72A a b + 36B a )c + 12A b + 36B a b )e +--R + +--R 2 2 3 6 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 2 5 +--R ((360A b + 360B a)c + 360B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 240A c - 720B b c )d e + 420B c d e +--R * +--R 3 +--R x +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 3 4 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 5 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 432A a c + (- 432A b - 864B a b)c - 144B b )d e +--R + +--R 2 2 4 3 +--R ((1080A b + 1080B a)c + 1080B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 720A c - 2160B b c )d e + 1260B c d e +--R * +--R x +--R + +--R 2 3 2 3 4 +--R ((72A a b + 36B a )c + 12A b + 36B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 144A a c + (- 144A b - 288B a b)c - 48B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((360A b + 360B a)c + 360B b c)d e + (- 240A c - 720B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 3B c e x + ((4A c + 12B b c )e - 7B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((18A b + 18B a)c + 18B b c)e + (- 12A c - 36B b c )d e +--R + +--R 3 2 5 +--R 21B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 90A b - 90B a)c - 90B b c)d e + (60A c + 180B b c )d e +--R + +--R 3 3 4 +--R - 105B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (108A a c + (108A b + 216B a b)c + 36B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 378A b - 378B a)c - 378B b c)d e + (292A c + 876B b c )d e +--R + +--R 3 4 3 +--R - 556B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 36A a c - 36A a b - 36B a b)e +--R + +--R 2 3 2 6 +--R ((216A a b + 108B a )c + 36A b + 108B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 108A a c + (- 108A b - 216B a b)c - 36B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 54A b - 54B a)c - 54B b c)d e + (156A c + 468B b c )d e +--R + +--R 3 5 2 +--R - 408B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 18A a b - 6B a )e + (- 36A a c - 36A a b - 36B a b)d e +--R + +--R 2 3 2 2 5 +--R ((324A a b + 162B a )c + 54A b + 162B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 324A a c + (- 324A b - 648B a b)c - 108B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((486A b + 486B a)c + 486B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 6 +--R 222B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 6A a b - 2B a )d e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((132A a b + 66B a )c + 22A b + 66B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 156A a c + (- 156A b - 312B a b)c - 52B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((282A b + 282B a)c + 282B b c)d e + (- 148A c - 444B b c )d e +--R + +--R 3 7 +--R 214B c d +--R / +--R 11 3 10 2 2 9 3 8 +--R 12e x + 36d e x + 36d e x + 12d e +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^5 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 217 + +--S 218 of 1035 +r0:=-c*(A*c*e*(5*c*d-3*b*e)-3*B*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*x/e^7-_ + 1/2*c^2*(5*B*c*d-3*b*B*e-A*c*e)*x^2/e^6+1/3*B*c^3*x^3/e^5+1/4*_ + (B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^4)+1/3*_ + (c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/_ + (e^8*(d+e*x)^3)+3/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*_ + (8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*_ + (5*b*d-a*e)))/(e^8*(d+e*x)^2)+(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-_ + 2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/_ + (e^8*(d+e*x))-(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 3 7 +--R (36A a c + (36A b + 72B a b)c + 12B b )e +--R + +--R 2 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (180A c + 540B b c )d e - 420B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 2 5 +--R (216A a c + (216A b + 432B a b)c + 72B b )d e +--R + +--R 2 2 3 4 +--R ((- 1080A b - 1080B a)c - 1080B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (1080A c + 3240B b c )d e - 2520B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 4 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 4 3 +--R ((- 720A b - 720B a)c - 720B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (720A c + 2160B b c )d e - 1680B c d e +--R * +--R x +--R + +--R 2 2 3 4 3 +--R (36A a c + (36A b + 72B a b)c + 12B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)d e + (180A c + 540B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 4B c e x + ((6A c + 18B b c )e - 14B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((36A b + 36B a)c + 36B b c)e + (- 36A c - 108B b c )d e +--R + +--R 3 2 5 +--R 84B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 3 2 2 5 +--R ((144A b + 144B a)c + 144B b c)d e + (- 204A c - 612B b c )d e +--R + +--R 3 3 4 +--R 556B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )e +--R + +--R 2 2 3 6 +--R (144A a c + (144A b + 288B a b)c + 48B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 144A b - 144B a)c - 144B b c)d e + (- 96A c - 288B b c )d e +--R + +--R 3 4 3 +--R 544B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 18A a c - 18A a b - 18B a b)e +--R + +--R 2 3 2 6 +--R ((- 108A a b - 54B a )c - 18A b - 54B a b )d e +--R + +--R 2 2 3 2 5 +--R (324A a c + (324A b + 648B a b)c + 108B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 756A b - 756B a)c - 756B b c)d e + (396A c + 1188B b c )d e +--R + +--R 3 5 2 +--R - 444B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 12A a b - 4B a )e + (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 72A a b - 36B a )c - 12A b - 36B a b )d e +--R + +--R 2 2 3 3 4 +--R (264A a c + (264A b + 528B a b)c + 88B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 744A b - 744B a)c - 744B b c)d e + (504A c + 1512B b c )d e +--R + +--R 3 6 +--R - 856B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 3A a e + (- 3A a b - B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (75A a c + (75A b + 150B a b)c + 25B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 231A b - 231B a)c - 231B b c)d e + (171A c + 513B b c )d e +--R + +--R 3 7 +--R - 319B c d +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^6 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 220 + +--S 221 of 1035 +r0:=-c^2*(6*B*c*d-3*b*B*e-A*c*e)*x/e^7+1/2*B*c^3*x^2/e^6+1/5*(B*d-A*e)*_ + (c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^5)+1/4*(c*d^2-b*d*e+a*e^2)^2*_ + (3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^4)+_ + (c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*_ + (2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^3)+_ + 1/2*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+_ + 3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^2)+_ + (B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-_ + 3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x))-_ + 3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*_ + log(d+e*x)/e^8 +--R +--R +--R (2) +--R 2 2 7 3 2 6 +--R ((60A b + 60B a)c + 60B b c)e + (- 120A c - 360B b c )d e +--R + +--R 3 2 5 +--R 420B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 6 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R 4 +--R x +--R + +--R 2 2 2 5 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 +--R ((600A b + 600B a)c + 600B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 4200B c d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 3 +--R ((300A b + 300B a)c + 300B b c)d e +--R + +--R 3 2 5 2 3 6 +--R (- 600A c - 1800B b c )d e + 2100B c d e +--R * +--R x +--R + +--R 2 2 5 2 3 2 6 +--R ((60A b + 60B a)c + 60B b c)d e + (- 120A c - 360B b c )d e +--R + +--R 3 7 +--R 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 2 7 3 6 6 +--R 10B c e x + ((20A c + 60B b c )e - 70B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((100A c + 300B b c )d e - 500B c d e )x +--R + +--R 2 2 3 7 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((300A b + 300B a)c + 300B b c)d e + (- 100A c - 300B b c )d e +--R + +--R 3 3 4 +--R - 400B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((900A b + 900B a)c + 900B b c)d e + (- 800A c - 2400B b c )d e +--R + +--R 3 4 3 +--R 1300B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 20A a c - 20A a b - 20B a b)e +--R + +--R 2 3 2 6 +--R ((- 60A a b - 30B a )c - 10A b - 30B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 3 4 +--R ((1100A b + 1100B a)c + 1100B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1200A c - 3600B b c )d e + 2700B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 15A a b - 5B a )e + (- 10A a c - 10A a b - 10B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 30A a b - 15B a )c - 5A b - 15B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 60A a c + (- 60A b - 120B a b)c - 20B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((625A b + 625B a)c + 625B b c)d e + (- 750A c - 2250B b c )d e +--R + +--R 3 6 +--R 1875B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 4A a e + (- 3A a b - B a )d e + (- 2A a c - 2A a b - 2B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((137A b + 137B a)c + 137B b c)d e + (- 174A c - 522B b c )d e +--R + +--R 3 7 +--R 459B c d +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20e x + 100d e x + 200d e x + 200d e x + 100d e x + 20d e +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^7 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 223 + +--S 224 of 1035 +r0:=B*c^3*x/e^7+1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^6)+_ + 1/5*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-_ + a*e)))/(e^8*(d+e*x)^5)+3/4*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-_ + c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-_ + c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^4)+1/3*(A*e*(2*c*d-b*e)*(10*c^2*d^2+_ + b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-_ + 30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/_ + (e^8*(d+e*x)^3)+1/2*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-_ + 15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/_ + (e^8*(d+e*x)^2)+3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x))-c^2*(7*B*c*d-3*b*B*e-A*c*e)*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 2 7 3 6 6 +--R ((60A c + 180B b c )e - 420B c d e )x +--R + +--R 3 2 6 3 2 5 5 +--R ((360A c + 1080B b c )d e - 2520B c d e )x +--R + +--R 3 2 2 5 3 3 4 4 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 3 4 3 4 3 3 +--R ((1200A c + 3600B b c )d e - 8400B c d e )x +--R + +--R 3 2 4 3 3 5 2 2 +--R ((900A c + 2700B b c )d e - 6300B c d e )x +--R + +--R 3 2 5 2 3 6 3 2 6 +--R ((360A c + 1080B b c )d e - 2520B c d e)x + (60A c + 180B b c )d e +--R + +--R 3 7 +--R - 420B c d +--R * +--R log(e x + d) +--R + +--R 3 7 7 3 6 6 +--R 60B c e x + 360B c d e x +--R + +--R 2 2 7 3 2 6 +--R ((- 180A b - 180B a)c - 180B b c)e + (360A c + 1080B b c )d e +--R + +--R 3 2 5 +--R - 360B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )e +--R + +--R 2 2 6 3 2 2 5 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1350A c + 4050B b c )d e +--R + +--R 3 3 4 +--R - 4050B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 120A a b - 60B a )c - 20A b - 60B a b )e +--R + +--R 2 2 3 6 +--R (- 120A a c + (- 120A b - 240B a b)c - 40B b )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R ((- 600A b - 600B a)c - 600B b c)d e + (2200A c + 6600B b c )d e +--R + +--R 3 4 3 +--R - 8200B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 45A a c - 45A a b - 45B a b)e +--R + +--R 2 3 2 6 +--R ((- 90A a b - 45B a )c - 15A b - 45B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 90A a c + (- 90A b - 180B a b)c - 30B b )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R ((- 450A b - 450B a)c - 450B b c)d e + (1875A c + 5625B b c )d e +--R + +--R 3 5 2 +--R - 7725B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 36A a b - 12B a )e + (- 18A a c - 18A a b - 18B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 36A a b - 18B a )c - 6A b - 18B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 36A a c + (- 36A b - 72B a b)c - 12B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 180A b - 180B a)c - 180B b c)d e + (822A c + 2466B b c )d e +--R + +--R 3 6 +--R - 3594B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 2 2 2 2 5 +--R - 10A a e + (- 6A a b - 2B a )d e + (- 3A a c - 3A a b - 3B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 6A a b - 3B a )c - A b - 3B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 6A a c + (- 6A b - 12B a b)c - 2B b )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R ((- 30A b - 30B a)c - 30B b c)d e + (147A c + 441B b c )d e - 669B c d +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 8 +--R 60d e +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^8 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 1035 +r0:=1/7*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^7)+1/6*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+3/5*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^5)+1/4*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^4)+_ + 1/3*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^3)+3/2*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x)^2)+c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*_ + (d+e*x))+B*c^3*log(d+e*x)/e^8 +--R +--R +--R (2) +--R 3 7 7 3 6 6 3 2 5 5 3 3 4 4 +--R 420B c e x + 2940B c d e x + 8820B c d e x + 14700B c d e x +--R + +--R 3 4 3 3 3 5 2 2 3 6 3 7 +--R 14700B c d e x + 8820B c d e x + 2940B c d e x + 420B c d +--R * +--R log(e x + d) +--R + +--R 3 2 7 3 6 6 +--R ((- 420A c - 1260B b c )e + 2940B c d e )x +--R + +--R 2 2 7 3 2 6 +--R ((- 630A b - 630B a)c - 630B b c)e + (- 1260A c - 3780B b c )d e +--R + +--R 3 2 5 +--R 13230B c d e +--R * +--R 5 +--R x +--R + +--R 2 2 3 7 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )e +--R + +--R 2 2 6 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 2 5 3 3 4 +--R (- 2100A c - 6300B b c )d e + 26950B c d e +--R * +--R 4 +--R x +--R + +--R 2 3 2 7 +--R ((- 630A a b - 315B a )c - 105A b - 315B a b )e +--R + +--R 2 2 3 6 +--R (- 420A a c + (- 420A b - 840B a b)c - 140B b )d e +--R + +--R 2 2 2 5 +--R ((- 1050A b - 1050B a)c - 1050B b c)d e +--R + +--R 3 2 3 4 3 4 3 +--R (- 2100A c - 6300B b c )d e + 30625B c d e +--R * +--R 3 +--R x +--R + +--R 2 2 2 7 +--R (- 252A a c - 252A a b - 252B a b)e +--R + +--R 2 3 2 6 +--R ((- 378A a b - 189B a )c - 63A b - 189B a b )d e +--R + +--R 2 2 3 2 5 +--R (- 252A a c + (- 252A b - 504B a b)c - 84B b )d e +--R + +--R 2 2 3 4 +--R ((- 630A b - 630B a)c - 630B b c)d e +--R + +--R 3 2 4 3 3 5 2 +--R (- 1260A c - 3780B b c )d e + 20139B c d e +--R * +--R 2 +--R x +--R + +--R 2 3 7 2 2 2 6 +--R (- 210A a b - 70B a )e + (- 84A a c - 84A a b - 84B a b)d e +--R + +--R 2 3 2 2 5 +--R ((- 126A a b - 63B a )c - 21A b - 63B a b )d e +--R + +--R 2 2 3 3 4 +--R (- 84A a c + (- 84A b - 168B a b)c - 28B b )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R ((- 210A b - 210B a)c - 210B b c)d e + (- 420A c - 1260B b c )d e +--R + +--R 3 6 +--R 7203B c d e +--R * +--R x +--R + +--R 3 7 2 3 6 +--R - 60A a e + (- 30A a b - 10B a )d e +--R + +--R 2 2 2 2 5 +--R (- 12A a c - 12A a b - 12B a b)d e +--R + +--R 2 3 2 3 4 +--R ((- 18A a b - 9B a )c - 3A b - 9B a b )d e +--R + +--R 2 2 3 4 3 +--R (- 12A a c + (- 12A b - 24B a b)c - 4B b )d e +--R + +--R 2 2 5 2 3 2 6 +--R ((- 30A b - 30B a)c - 30B b c)d e + (- 60A c - 180B b c )d e +--R + +--R 3 7 +--R 1089B c d +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420e x + 2940d e x + 8820d e x + 14700d e x + 14700d e x +--R + +--R 5 10 2 6 9 7 8 +--R 8820d e x + 2940d e x + 420d e +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^9 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 229 + +--S 230 of 1035 +r0:=1/8*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^8)+1/7*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^7)+1/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+1/5*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^5)+_ + 1/4*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-_ + a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^4)+c*_ + (A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*_ + (d+e*x)^3)+1/2*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^2)-B*c^3/_ + (e^8*(d+e*x)) +--R +--R +--R (2) +--R 3 7 7 1 3 3 2 7 7 3 6 6 +--R - B c e x + ((- - A c - - B b c )e - - B c d e )x +--R 2 2 2 +--R + +--R 2 2 7 3 2 6 3 2 5 5 +--R (((- A b - B a)c - B b c)e + (- A c - 3B b c )d e - 7B c d e )x +--R + +--R 3 2 3 2 3 1 3 7 +--R (- - A a c + (- - A b - - B a b)c - - B b )e +--R 4 4 2 4 +--R + +--R 5 5 2 5 2 6 5 3 15 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - -- B b c )d e +--R 4 4 4 4 4 +--R + +--R 35 3 3 4 +--R - -- B c d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 6 3 2 1 3 3 2 7 +--R ((- - A a b - - B a )c - - A b - - B a b )e +--R 5 5 5 5 +--R + +--R 3 2 3 2 6 1 3 6 +--R (- - A a c + (- - A b - - B a b)c - - B b )d e +--R 5 5 5 5 +--R + +--R 2 2 2 5 3 2 3 4 3 4 3 +--R ((- A b - B a)c - B b c)d e + (- A c - 3B b c )d e - 7B c d e +--R * +--R 3 +--R x +--R + +--R 1 2 1 2 1 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 2 2 2 +--R + +--R 3 3 2 1 3 3 2 6 +--R ((- - A a b - -- B a )c - -- A b - -- B a b )d e +--R 5 10 10 10 +--R + +--R 3 2 3 2 3 1 3 2 5 +--R (- -- A a c + (- -- A b - - B a b)c - -- B b )d e +--R 10 10 5 10 +--R + +--R 1 1 2 1 2 3 4 1 3 3 2 4 3 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 2 2 2 2 2 +--R + +--R 7 3 5 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 3 2 1 3 7 1 2 1 2 1 2 6 +--R (- - A a b - - B a )e + (- - A a c - - A a b - - B a b)d e +--R 7 7 7 7 7 +--R + +--R 6 3 2 1 3 3 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 35 35 35 35 +--R + +--R 3 2 3 2 6 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 35 35 35 35 +--R + +--R 1 1 2 1 2 4 3 1 3 3 2 5 2 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 7 7 7 7 7 +--R + +--R 3 6 +--R - B c d e +--R * +--R x +--R + +--R 1 3 7 3 2 1 3 6 +--R - - A a e + (- -- A a b - -- B a )d e +--R 8 56 56 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 56 56 56 +--R + +--R 3 3 2 1 3 3 2 3 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 280 280 +--R + +--R 3 2 3 2 3 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 280 280 140 280 +--R + +--R 1 1 2 1 2 5 2 1 3 3 2 6 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 56 56 56 56 56 +--R + +--R 1 3 7 +--R - - B c d +--R 8 +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 10 2 7 9 8 8 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 230 + +--S 231 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 231 + +)clear all + +--S 232 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^10 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 232 + +--S 233 of 1035 +r0:=1/9*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^9)+1/8*(c*d^2-b*d*e+_ + a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^8)+_ + 3/7*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-_ + a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^7)+_ + 1/6*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-_ + B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*_ + (10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^6)+1/5*(B*(35*c^3*d^3-_ + b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*_ + (5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^5)+3/4*c*(A*c*e*_ + (2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*(d+e*x)^4)+_ + 1/3*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^3)-1/2*B*c^3/(e^8*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 7 7 1 3 2 7 7 3 6 6 +--R - - B c e x + ((- - A c - B b c )e - - B c d e )x +--R 2 3 6 +--R + +--R 3 3 2 3 2 7 1 3 3 2 6 +--R ((- - A b - - B a)c - - B b c)e + (- - A c - - B b c )d e +--R 4 4 4 2 2 +--R + +--R 7 3 2 5 +--R - - B c d e +--R 4 +--R * +--R 5 +--R x +--R + +--R 3 2 3 2 6 1 3 7 +--R (- - A a c + (- - A b - - B a b)c - - B b )e +--R 5 5 5 5 +--R + +--R 3 3 2 3 2 6 1 3 3 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 4 4 4 2 2 +--R + +--R 7 3 3 4 +--R - - B c d e +--R 4 +--R * +--R 4 +--R x +--R + +--R 1 2 1 3 1 2 7 +--R ((- A a b - - B a )c - - A b - - B a b )e +--R 2 6 2 +--R + +--R 2 2 2 2 4 2 3 6 +--R (- - A a c + (- - A b - - B a b)c - -- B b )d e +--R 5 5 5 15 +--R + +--R 1 1 2 1 2 2 5 1 3 2 3 4 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - B b c )d e +--R 2 2 2 3 +--R + +--R 7 3 4 3 +--R - - B c d e +--R 6 +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 3 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 7 7 7 +--R + +--R 3 3 2 1 3 3 2 6 +--R ((- - A a b - -- B a )c - -- A b - -- B a b )d e +--R 7 14 14 14 +--R + +--R 6 2 6 2 12 2 3 2 5 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 35 35 35 35 +--R + +--R 3 3 2 3 2 3 4 1 3 3 2 4 3 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- - A c - - B b c )d e +--R 14 14 14 7 7 +--R + +--R 1 3 5 2 +--R - - B c d e +--R 2 +--R * +--R 2 +--R x +--R + +--R 3 2 1 3 7 3 2 3 2 3 2 6 +--R (- - A a b - - B a )e + (- -- A a c - -- A a b - -- B a b)d e +--R 8 8 28 28 28 +--R + +--R 3 3 2 1 3 3 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 28 56 56 56 +--R + +--R 3 2 3 2 3 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 70 70 35 70 +--R + +--R 3 3 2 3 2 4 3 1 3 3 2 5 2 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 56 56 56 28 28 +--R + +--R 1 3 6 +--R - - B c d e +--R 8 +--R * +--R x +--R + +--R 1 3 7 1 2 1 3 6 +--R - - A a e + (- -- A a b - -- B a )d e +--R 9 24 72 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- -- A a c - -- A a b - -- B a b)d e +--R 84 84 84 +--R + +--R 1 1 2 1 3 1 2 3 4 +--R ((- -- A a b - --- B a )c - --- A b - --- B a b )d e +--R 84 168 504 168 +--R + +--R 1 2 1 2 1 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - --- B b )d e +--R 210 210 105 630 +--R + +--R 1 1 2 1 2 5 2 1 3 1 2 6 +--R ((- --- A b - --- B a)c - --- B b c)d e + (- --- A c - -- B b c )d e +--R 168 168 168 252 84 +--R + +--R 1 3 7 +--R - -- B c d +--R 72 +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 5 12 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R 6 11 3 7 10 2 8 9 9 8 +--R 84d e x + 36d e x + 9d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 233 + +--S 234 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 1035 +t0:=(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^11 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R e x + 11d e x + 55d e x + 165d e x + 330d e x + 462d e x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462d e x + 330d e x + 165d e x + 55d e x + 11d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 235 + +--S 236 of 1035 +r0:=1/10*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^10)+1/9*(c*d^2-_ + b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*_ + (d+e*x)^9)+3/8*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+_ + b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^8)+1/7*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*_ + (5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*_ + (2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^7)+_ + 1/6*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*_ + (3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*_ + (d+e*x)^6)+3/5*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*_ + (6*b*d-a*e)))/(e^8*(d+e*x)^5)+1/4*c^2*(7*B*c*d-3*b*B*e-A*c*e)/_ + (e^8*(d+e*x)^4)-1/3*B*c^3/(e^8*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 7 7 1 3 3 2 7 7 3 6 6 +--R - - B c e x + ((- - A c - - B b c )e - -- B c d e )x +--R 3 4 4 12 +--R + +--R 3 3 2 3 2 7 3 3 9 2 6 +--R ((- - A b - - B a)c - - B b c)e + (- -- A c - -- B b c )d e +--R 5 5 5 10 10 +--R + +--R 7 3 2 5 +--R - -- B c d e +--R 10 +--R * +--R 5 +--R x +--R + +--R 1 2 1 2 1 3 7 +--R (- - A a c + (- - A b - B a b)c - - B b )e +--R 2 2 6 +--R + +--R 1 1 2 1 2 6 1 3 3 2 2 5 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 2 2 2 4 4 +--R + +--R 7 3 3 4 +--R - -- B c d e +--R 12 +--R * +--R 4 +--R x +--R + +--R 6 3 2 1 3 3 2 7 +--R ((- - A a b - - B a )c - - A b - - B a b )e +--R 7 7 7 7 +--R + +--R 2 2 2 2 4 2 3 6 +--R (- - A a c + (- - A b - - B a b)c - -- B b )d e +--R 7 7 7 21 +--R + +--R 2 2 2 2 2 2 5 1 3 3 2 3 4 +--R ((- - A b - - B a)c - - B b c)d e + (- - A c - - B b c )d e +--R 7 7 7 7 7 +--R + +--R 1 3 4 3 +--R - - B c d e +--R 3 +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 3 2 7 +--R (- - A a c - - A a b - - B a b)e +--R 8 8 8 +--R + +--R 9 9 2 3 3 9 2 6 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 28 56 56 56 +--R + +--R 3 2 3 2 3 1 3 2 5 +--R (- -- A a c + (- -- A b - -- B a b)c - -- B b )d e +--R 28 28 14 28 +--R + +--R 3 3 2 3 2 3 4 3 3 9 2 4 3 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 28 28 28 56 56 +--R + +--R 1 3 5 2 +--R - - B c d e +--R 8 +--R * +--R 2 +--R x +--R + +--R 1 2 1 3 7 1 2 1 2 1 2 6 +--R (- - A a b - - B a )e + (- -- A a c - -- A a b - -- B a b)d e +--R 3 9 12 12 12 +--R + +--R 1 1 2 1 3 1 2 2 5 +--R ((- -- A a b - -- B a )c - -- A b - -- B a b )d e +--R 14 28 84 28 +--R + +--R 1 2 1 2 1 1 3 3 4 +--R (- -- A a c + (- -- A b - -- B a b)c - --- B b )d e +--R 42 42 21 126 +--R + +--R 1 1 2 1 2 4 3 1 3 1 2 5 2 +--R ((- -- A b - -- B a)c - -- B b c)d e + (- -- A c - -- B b c )d e +--R 42 42 42 84 28 +--R + +--R 1 3 6 +--R - -- B c d e +--R 36 +--R * +--R x +--R + +--R 1 3 7 1 2 1 3 6 +--R - -- A a e + (- -- A a b - -- B a )d e +--R 10 30 90 +--R + +--R 1 2 1 2 1 2 2 5 +--R (- --- A a c - --- A a b - --- B a b)d e +--R 120 120 120 +--R + +--R 1 1 2 1 3 1 2 3 4 +--R ((- --- A a b - --- B a )c - --- A b - --- B a b )d e +--R 140 280 840 280 +--R + +--R 1 2 1 2 1 1 3 4 3 +--R (- --- A a c + (- --- A b - --- B a b)c - ---- B b )d e +--R 420 420 210 1260 +--R + +--R 1 1 2 1 2 5 2 1 3 1 2 6 +--R ((- --- A b - --- B a)c - --- B b c)d e + (- --- A c - --- B b c )d e +--R 420 420 420 840 280 +--R + +--R 1 3 7 +--R - --- B c d +--R 360 +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 5 13 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 12 4 7 11 3 8 10 2 9 9 10 8 +--R 210d e x + 120d e x + 45d e x + 10d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 236 + +--S 237 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 1035 +t0:=(e*x)^m*(A+B*x) +--R +--R +--R m +--R (1) (B x + A)(e x) +--R Type: Expression(Integer) +--E 238 + +--S 239 of 1035 +r0:=A*(e*x)^(1+m)/(e*(1+m))+B*(e*x)^(2+m)/(e^2*(2+m)) +--R +--R +--R m + 2 m + 1 +--R (B m + B)(e x) + (A e m + 2A e)(e x) +--R (2) ---------------------------------------------- +--R 2 2 2 2 +--R e m + 3e m + 2e +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1035 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2) +--R +--R +--R 3 2 m +--R (1) (B c x + (A c + B b)x + (A b + B a)x + A a)(e x) +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1035 +r0:=a*A*(e*x)^(1+m)/(e*(1+m))+(A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+(b*B+A*c)*_ + (e*x)^(3+m)/(e^3*(3+m))+B*c*(e*x)^(4+m)/(e^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (B c m + 6B c m + 11B c m + 6B c)(e x) +--R + +--R 3 2 +--R (A c + B b)e m + (7A c + 7B b)e m + (14A c + 14B b)e m +--R + +--R (8A c + 8B b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 2 2 2 +--R (A b + B a)e m + (8A b + 8B a)e m + (19A b + 19B a)e m +--R + +--R 2 +--R (12A b + 12B a)e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 3 3 2 3 3 m + 1 +--R (A a e m + 9A a e m + 26A a e m + 24A a e )(e x) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 10e m + 35e m + 50e m + 24e +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 1035 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 5 2 4 2 3 +--R B c x + (A c + 2B b c)x + ((2A b + 2B a)c + B b )x +--R + +--R 2 2 2 2 +--R (2A a c + A b + 2B a b)x + (2A a b + B a )x + A a +--R * +--R m +--R (e x) +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1035 +r0:=a^2*A*(e*x)^(1+m)/(e*(1+m))+a*(2*A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+_ + (2*a*b*B+A*(b^2+2*a*c))*(e*x)^(3+m)/(e^3*(3+m))+(b^2*B+2*A*b*c+2*a*B*c)*_ + (e*x)^(4+m)/(e^4*(4+m))+c*(2*b*B+A*c)*(e*x)^(5+m)/(e^5*(5+m))+_ + B*c^2*(e*x)^(6+m)/(e^6*(6+m)) +--R +--R +--R (2) +--R 2 5 2 4 2 3 2 2 2 2 m + 6 +--R (B c m + 15B c m + 85B c m + 225B c m + 274B c m + 120B c )(e x) +--R + +--R 2 5 2 4 +--R (A c + 2B b c)e m + (16A c + 32B b c)e m +--R + +--R 2 3 2 2 +--R (95A c + 190B b c)e m + (260A c + 520B b c)e m +--R + +--R 2 2 +--R (324A c + 648B b c)e m + (144A c + 288B b c)e +--R * +--R m + 5 +--R (e x) +--R + +--R 2 2 5 2 2 4 +--R ((2A b + 2B a)c + B b )e m + ((34A b + 34B a)c + 17B b )e m +--R + +--R 2 2 3 +--R ((214A b + 214B a)c + 107B b )e m +--R + +--R 2 2 2 +--R ((614A b + 614B a)c + 307B b )e m +--R + +--R 2 2 2 2 +--R ((792A b + 792B a)c + 396B b )e m + ((360A b + 360B a)c + 180B b )e +--R * +--R m + 4 +--R (e x) +--R + +--R 2 3 5 2 3 4 +--R (2A a c + A b + 2B a b)e m + (36A a c + 18A b + 36B a b)e m +--R + +--R 2 3 3 +--R (242A a c + 121A b + 242B a b)e m +--R + +--R 2 3 2 +--R (744A a c + 372A b + 744B a b)e m +--R + +--R 2 3 +--R (1016A a c + 508A b + 1016B a b)e m +--R + +--R 2 3 +--R (480A a c + 240A b + 480B a b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 4 5 2 4 4 +--R (2A a b + B a )e m + (38A a b + 19B a )e m +--R + +--R 2 4 3 2 4 2 +--R (274A a b + 137B a )e m + (922A a b + 461B a )e m +--R + +--R 2 4 2 4 +--R (1404A a b + 702B a )e m + (720A a b + 360B a )e +--R * +--R m + 2 +--R (e x) +--R + +--R 2 5 5 2 5 4 2 5 3 2 5 2 2 5 +--R A a e m + 20A a e m + 155A a e m + 580A a e m + 1044A a e m +--R + +--R 2 5 +--R 720A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R e m + 21e m + 175e m + 735e m + 1624e m + 1764e m + 720e +--R Type: Expression(Integer) +--E 245 + +--S 246 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 246 + +)clear all + +--S 247 of 1035 +t0:=(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 +--R B c x + (A c + 3B b c )x + ((3A b + 3B a)c + 3B b c)x +--R + +--R 2 2 3 4 +--R (3A a c + (3A b + 6B a b)c + B b )x +--R + +--R 2 3 2 3 2 2 2 2 +--R ((6A a b + 3B a )c + A b + 3B a b )x + (3A a c + 3A a b + 3B a b)x +--R + +--R 2 3 3 +--R (3A a b + B a )x + A a +--R * +--R m +--R (e x) +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1035 +r0:=a^3*A*(e*x)^(1+m)/(e*(1+m))+a^2*(3*A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+_ + 3*a*(a*b*B+A*(b^2+a*c))*(e*x)^(3+m)/(e^3*(3+m))+(3*a*B*(b^2+a*c)+A*_ + (b^3+6*a*b*c))*(e*x)^(4+m)/(e^4*(4+m))+(b^3*B+3*A*b^2*c+6*a*b*B*c+_ + 3*a*A*c^2)*(e*x)^(5+m)/(e^5*(5+m))+3*c*(b^2*B+A*b*c+a*B*c)*_ + (e*x)^(6+m)/(e^6*(6+m))+c^2*(3*b*B+A*c)*(e*x)^(7+m)/(e^7*(7+m))+_ + B*c^3*(e*x)^(8+m)/(e^8*(8+m)) +--R +--R +--R (2) +--R 3 7 3 6 3 5 3 4 3 3 3 2 +--R B c m + 28B c m + 322B c m + 1960B c m + 6769B c m + 13132B c m +--R + +--R 3 3 +--R 13068B c m + 5040B c +--R * +--R m + 8 +--R (e x) +--R + +--R 3 2 7 3 2 6 +--R (A c + 3B b c )e m + (29A c + 87B b c )e m +--R + +--R 3 2 5 3 2 4 +--R (343A c + 1029B b c )e m + (2135A c + 6405B b c )e m +--R + +--R 3 2 3 3 2 2 +--R (7504A c + 22512B b c )e m + (14756A c + 44268B b c )e m +--R + +--R 3 2 3 2 +--R (14832A c + 44496B b c )e m + (5760A c + 17280B b c )e +--R * +--R m + 7 +--R (e x) +--R + +--R 2 2 2 7 2 2 2 6 +--R ((3A b + 3B a)c + 3B b c)e m + ((90A b + 90B a)c + 90B b c)e m +--R + +--R 2 2 2 5 +--R ((1098A b + 1098B a)c + 1098B b c)e m +--R + +--R 2 2 2 4 +--R ((7020A b + 7020B a)c + 7020B b c)e m +--R + +--R 2 2 2 3 +--R ((25227A b + 25227B a)c + 25227B b c)e m +--R + +--R 2 2 2 2 +--R ((50490A b + 50490B a)c + 50490B b c)e m +--R + +--R 2 2 2 +--R ((51432A b + 51432B a)c + 51432B b c)e m +--R + +--R 2 2 2 +--R ((20160A b + 20160B a)c + 20160B b c)e +--R * +--R m + 6 +--R (e x) +--R + +--R 2 2 3 3 7 +--R (3A a c + (3A b + 6B a b)c + B b )e m +--R + +--R 2 2 3 3 6 +--R (93A a c + (93A b + 186B a b)c + 31B b )e m +--R + +--R 2 2 3 3 5 +--R (1173A a c + (1173A b + 2346B a b)c + 391B b )e m +--R + +--R 2 2 3 3 4 +--R (7743A a c + (7743A b + 15486B a b)c + 2581B b )e m +--R + +--R 2 2 3 3 3 +--R (28632A a c + (28632A b + 57264B a b)c + 9544B b )e m +--R + +--R 2 2 3 3 2 +--R (58692A a c + (58692A b + 117384B a b)c + 19564B b )e m +--R + +--R 2 2 3 3 +--R (60912A a c + (60912A b + 121824B a b)c + 20304B b )e m +--R + +--R 2 2 3 3 +--R (24192A a c + (24192A b + 48384B a b)c + 8064B b )e +--R * +--R m + 5 +--R (e x) +--R + +--R 2 3 2 4 7 +--R ((6A a b + 3B a )c + A b + 3B a b )e m +--R + +--R 2 3 2 4 6 +--R ((192A a b + 96B a )c + 32A b + 96B a b )e m +--R + +--R 2 3 2 4 5 +--R ((2508A a b + 1254B a )c + 418A b + 1254B a b )e m +--R + +--R 2 3 2 4 4 +--R ((17184A a b + 8592B a )c + 2864A b + 8592B a b )e m +--R + +--R 2 3 2 4 3 +--R ((65958A a b + 32979B a )c + 10993A b + 32979B a b )e m +--R + +--R 2 3 2 4 2 +--R ((139872A a b + 69936B a )c + 23312A b + 69936B a b )e m +--R + +--R 2 3 2 4 +--R ((149256A a b + 74628B a )c + 24876A b + 74628B a b )e m +--R + +--R 2 3 2 4 +--R ((60480A a b + 30240B a )c + 10080A b + 30240B a b )e +--R * +--R m + 4 +--R (e x) +--R + +--R 2 2 2 5 7 2 2 2 5 6 +--R (3A a c + 3A a b + 3B a b)e m + (99A a c + 99A a b + 99B a b)e m +--R + +--R 2 2 2 5 5 +--R (1341A a c + 1341A a b + 1341B a b)e m +--R + +--R 2 2 2 5 4 +--R (9585A a c + 9585A a b + 9585B a b)e m +--R + +--R 2 2 2 5 3 +--R (38592A a c + 38592A a b + 38592B a b)e m +--R + +--R 2 2 2 5 2 +--R (86076A a c + 86076A a b + 86076B a b)e m +--R + +--R 2 2 2 5 +--R (96144A a c + 96144A a b + 96144B a b)e m +--R + +--R 2 2 2 5 +--R (40320A a c + 40320A a b + 40320B a b)e +--R * +--R m + 3 +--R (e x) +--R + +--R 2 3 6 7 2 3 6 6 +--R (3A a b + B a )e m + (102A a b + 34B a )e m +--R + +--R 2 3 6 5 2 3 6 4 +--R (1434A a b + 478B a )e m + (10740A a b + 3580B a )e m +--R + +--R 2 3 6 3 2 3 6 2 +--R (45867A a b + 15289B a )e m + (110118A a b + 36706B a )e m +--R + +--R 2 3 6 2 3 6 +--R (134136A a b + 44712B a )e m + (60480A a b + 20160B a )e +--R * +--R m + 2 +--R (e x) +--R + +--R 3 7 7 3 7 6 3 7 5 3 7 4 3 7 3 +--R A a e m + 35A a e m + 511A a e m + 4025A a e m + 18424A a e m +--R + +--R 3 7 2 3 7 3 7 +--R 48860A a e m + 69264A a e m + 40320A a e +--R * +--R m + 1 +--R (e x) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R e m + 36e m + 546e m + 4536e m + 22449e m + 67284e m + 118124e m +--R + +--R 8 8 +--R 109584e m + 40320e +--R Type: Expression(Integer) +--E 248 + +--S 249 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 1035 +t0:=(A+B*x)*(d+e*x)^m/(a+b*x+c*x^2) +--R +--R +--R m +--R (B x + A)(e x + d) +--R (1) ------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1035 +--r0:=-(d+e*x)^(1+m)*hypergeometric(1,1+m,2+m,2*c*(d+e*x)/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/((1+m)*_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))-(d+e*x)^(1+m)*hypergeometric(1,1+m,_ +-- 2+m,2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(B+(b*B-2*A*c)/_ +-- sqrt(b^2-4*a*c))/((1+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--E 251 + +--S 252 of 1035 +--d0:=D(m0,x) +--E 252 + +)clear all + +--S 253 of 1035 +t0:=(A+B*x)*(d+e*x)^(1+m)/(a+b*x+c*x^2) +--R +--R +--R m + 1 +--R (B x + A)(e x + d) +--R (1) ----------------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 1035 +--r0:=-(d+e*x)^(2+m)*hypergeometric(1,2+m,3+m,2*c*(d+e*x)/(2*c*d-b*e+_ +-- e*sqrt(b^2-4*a*c)))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/((2+m)*_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))-(d+e*x)^(2+m)*_ +-- hypergeometric(1,2+m,3+m,2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- (B+(b*B-2*A*c)/sqrt(b^2-4*a*c))/((2+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c)))) +--E 254 + +--S 255 of 1035 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 1035 +t0:=(A+B*x)*(d+e*x)^2/(a+b*x+c*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1035 +r0:=e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+1/2*(A*c*e*(2*c*d-b*e)+_ + B*(c^2*d^2+b^2*e^2-c*e*(2*b*d+a*e)))*log(a+b*x+c*x^2)/c^3+(b^3*B*e^2-_ + b^2*c*e*(2*B*d+A*e)-2*c^2*(A*c*d^2-2*a*B*d*e-a*A*e^2)+b*c*(B*c*d^2+_ + 2*A*c*d*e-3*a*B*e^2))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-_ + 4*a*c)) +--R +--R +--R (2) +--R 2 2 3 2 +--R (4A a c + (- 2A b - 6B a b)c + 2B b )e +--R + +--R 2 2 3 2 2 +--R ((4A b + 8B a)c - 4B b c)d e + (- 4A c + 2B b c )d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 +--R (((- A b - B a)c + B b )e + (2A c - 2B b c)d e + B c d ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 2 2 2 2 +--R B c e x + ((2A c - 2B b c)e + 4B c d e)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 1035 +t0:=(A+B*x)*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 259 + +--S 260 of 1035 +r0:=B*e*x/c+1/2*(B*c*d-b*B*e+A*c*e)*log(a+b*x+c*x^2)/c^2-(b^2*B*e-b*c*_ + (B*d+A*e)+2*c*(A*c*d-a*B*e))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (c^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2c x + b +--R (((2A b + 4B a)c - 2B b )e + (- 4A c + 2B b c)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R (((A c - B b)e + B c d)log(c x + b x + a) + 2B c e x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 1035 +t0:=(A+B*x)/(a+b*x+c*x^2) +--R +--R +--R B x + A +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 262 + +--S 263 of 1035 +r0:=1/2*B*log(a+b*x+c*x^2)/c+(b*B-2*A*c)*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + (c*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R +-----------+ +--R 2c x + b 2 | 2 +--R (- 4A c + 2B b)atanh(--------------) + B log(c x + b x + a)\|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R -------------------------------------------------------------------------- +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 1035 +t0:=(A+B*x)/((d+e*x)*(a+b*x+c*x^2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 265 + +--S 266 of 1035 +r0:=-(B*d-A*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)+1/2*(B*d-A*e)*_ + log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)+(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2c x + b +--R ((2A b - 4B a)e + (- 4A c + 2B b)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R ((- A e + B d)log(c x + b x + a) + (2A e - 2B d)log(e x + d)) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 1035 +t0:=(A+B*x)/((d+e*x)^2*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R Type: Fraction(Polynomial(Integer)) +--E 268 + +--S 269 of 1035 +r0:=(B*d-A*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x))+(A*e*(2*c*d-b*e)-_ + B*(c*d^2-a*e^2))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2-1/2*(A*e*(2*c*d-b*e)-_ + B*(c*d^2-a*e^2))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2-(A*b^2*e^2+_ + 2*c*(A*c*d^2+2*a*B*d*e-a*A*e^2)-b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*_ + atanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 2 +--R (4A a c - 2A b + 2B a b)e + (4A b - 8B a)c d e +--R + +--R 2 2 +--R (- 4A c + 2B b c)d e +--R * +--R x +--R + +--R 2 2 2 +--R (4A a c - 2A b + 2B a b)d e + (4A b - 8B a)c d e +--R + +--R 2 3 +--R (- 4A c + 2B b c)d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 +--R ((A b - B a)e - 2A c d e + B c d e)x + (A b - B a)d e +--R + +--R 2 3 +--R - 2A c d e + B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 +--R ((- 2A b + 2B a)e + 4A c d e - 2B c d e)x + (- 2A b + 2B a)d e +--R + +--R 2 3 +--R 4A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 3 2 2 3 +--R - 2A a e + (2A b + 2B a)d e + (- 2A c - 2B b)d e + 2B c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1035 +t0:=(A+B*x)/((d+e*x)^3*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1035 +r0:=1/2*(B*d-A*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+(-A*e*(2*c*d-b*e)+_ + B*(c*d^2-a*e^2))/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))-(B*(c^2*d^3-_ + 3*a*c*d*e^2+a*b*e^3)-A*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*_ + log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*(B*(c^2*d^3-3*a*c*d*e^2+a*b*e^3)-_ + A*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*log(a+b*x+c*x^2)/(c*d^2-_ + b*d*e+a*e^2)^3+(A*b^3*e^3-b^2*e^2*(3*A*c*d+a*B*e)+b*c*(B*c*d^3+_ + 3*A*c*d^2*e+3*a*B*d*e^2-3*a*A*e^3)-2*c*(A*c*d*(c*d^2-3*a*e^2)+_ + a*B*e*(3*c*d^2-a*e^2)))*atanh((b+2*c*x)/sqrt(b^2-4*a*c))/_ + ((c*d^2-b*d*e+a*e^2)^3*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 3 2 5 +--R ((- 6A a b + 4B a )c + 2A b - 2B a b )e +--R + +--R 2 2 4 2 2 3 +--R (12A a c + (- 6A b + 6B a b)c)d e + (6A b - 12B a)c d e +--R + +--R 3 2 3 2 +--R (- 4A c + 2B b c )d e +--R * +--R 2 +--R x +--R + +--R 2 3 2 4 +--R ((- 12A a b + 8B a )c + 4A b - 4B a b )d e +--R + +--R 2 2 2 3 2 3 2 +--R (24A a c + (- 12A b + 12B a b)c)d e + (12A b - 24B a)c d e +--R + +--R 3 2 4 +--R (- 8A c + 4B b c )d e +--R * +--R x +--R + +--R 2 3 2 2 3 +--R ((- 6A a b + 4B a )c + 2A b - 2B a b )d e +--R + +--R 2 2 3 2 2 4 +--R (12A a c + (- 6A b + 6B a b)c)d e + (6A b - 12B a)c d e +--R + +--R 3 2 5 +--R (- 4A c + 2B b c )d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 5 4 2 2 3 +--R (A a c - A b + B a b)e + (3A b - 3B a)c d e - 3A c d e +--R + +--R 2 3 2 +--R B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 +--R (2A a c - 2A b + 2B a b)d e + (6A b - 6B a)c d e +--R + +--R 2 3 2 2 4 +--R - 6A c d e + 2B c d e +--R * +--R x +--R + +--R 2 2 3 3 2 2 4 +--R (A a c - A b + B a b)d e + (3A b - 3B a)c d e - 3A c d e +--R + +--R 2 5 +--R B c d +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 5 4 +--R (- 2A a c + 2A b - 2B a b)e + (- 6A b + 6B a)c d e +--R + +--R 2 2 3 2 3 2 +--R 6A c d e - 2B c d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 3 +--R (- 4A a c + 4A b - 4B a b)d e + (- 12A b + 12B a)c d e +--R + +--R 2 3 2 2 4 +--R 12A c d e - 4B c d e +--R * +--R x +--R + +--R 2 2 3 3 2 +--R (- 2A a c + 2A b - 2B a b)d e + (- 6A b + 6B a)c d e +--R + +--R 2 4 2 5 +--R 6A c d e - 2B c d +--R * +--R log(e x + d) +--R + +--R 2 5 2 4 +--R (2A a b - 2B a )e + (- 4A a c - 2A b + 2B a b)d e +--R + +--R 2 3 2 3 2 2 4 +--R 6A b c d e + (- 4A c - 2B b c)d e + 2B c d e +--R * +--R x +--R + +--R 2 5 2 4 2 2 3 +--R - A a e + (4A a b - B a )d e + (- 6A a c - 3A b )d e +--R + +--R 2 3 2 2 4 2 5 +--R ((8A b + 2B a)c + B b )d e + (- 5A c - 4B b c)d e + 3B c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 8 2 7 2 2 2 6 3 3 5 +--R 2a e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 4 4 2 5 3 3 6 2 +--R (6a c + 6b c)d e - 6b c d e + 2c d e +--R * +--R 2 +--R x +--R + +--R 3 7 2 2 6 2 2 3 5 3 4 4 +--R 4a d e - 12a b d e + (12a c + 12a b )d e + (- 24a b c - 4b )d e +--R + +--R 2 2 5 3 2 6 2 3 7 +--R (12a c + 12b c)d e - 12b c d e + 4c d e +--R * +--R x +--R + +--R 3 2 6 2 3 5 2 2 4 4 3 5 3 +--R 2a d e - 6a b d e + (6a c + 6a b )d e + (- 12a b c - 2b )d e +--R + +--R 2 2 6 2 2 7 3 8 +--R (6a c + 6b c)d e - 6b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 273 + +)clear all + +--S 274 of 1035 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 274 + +--S 275 of 1035 +r0:=11576/81*x+1156/27*x^2+32/27*x^3-4/3*x^4-6*log(1+x)+10625/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R 10625log(3x + 2) - 1458log(x + 1) - 324x + 288x + 10404x + 34728x +--R (2) -------------------------------------------------------------------- +--R 243 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 1035 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 277 + +--S 278 of 1035 +r0:=922/27*x+26/9*x^2-8/9*x^3-6*log(1+x)+2125/81*log(2+3*x) +--R +--R +--R 3 2 +--R 2125log(3x + 2) - 486log(x + 1) - 72x + 234x + 2766x +--R (2) ------------------------------------------------------ +--R 81 +--R Type: Expression(Integer) +--E 278 + +--S 279 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 1035 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 280 + +--S 281 of 1035 +r0:=44/9*x-2/3*x^2-6*log(1+x)+425/27*log(2+3*x) +--R +--R +--R 2 +--R 425log(3x + 2) - 162log(x + 1) - 18x + 132x +--R (2) -------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 1035 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 283 + +--S 284 of 1035 +r0:=-2/3*x-6*log(1+x)+85/9*log(2+3*x) +--R +--R +--R 85log(3x + 2) - 54log(x + 1) - 6x +--R (2) --------------------------------- +--R 9 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1035 +t0:=(5-x)/(2+5*x+3*x^2) +--R +--R +--R - x + 5 +--R (1) ------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1035 +r0:=-6*log(1+x)+17/3*log(2+3*x) +--R +--R +--R 17log(3x + 2) - 18log(x + 1) +--R (2) ---------------------------- +--R 3 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 1035 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) -------------------- +--R 3 2 +--R 6x + 19x + 19x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 289 + +--S 290 of 1035 +r0:=-6*log(1+x)+13/5*log(3+2*x)+17/5*log(2+3*x) +--R +--R +--R 17log(3x + 2) + 13log(2x + 3) - 30log(x + 1) +--R (2) -------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 1035 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------- +--R 4 3 2 +--R 12x + 56x + 95x + 69x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 292 + +--S 293 of 1035 +r0:=(-13/5)/(3+2*x)-6*log(1+x)+99/25*log(3+2*x)+51/25*log(2+3*x) +--R +--R +--R (2) +--R (102x + 153)log(3x + 2) + (198x + 297)log(2x + 3) +--R + +--R (- 300x - 450)log(x + 1) - 65 +--R / +--R 50x + 75 +--R Type: Expression(Integer) +--E 293 + +--S 294 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 1035 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 24x + 148x + 358x + 423x + 243x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 295 + +--S 296 of 1035 +r0:=(-13/10)/(3+2*x)^2+(-99/25)/(3+2*x)-6*log(1+x)+597/125*log(3+2*x)+_ + 153/125*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (1224x + 3672x + 2754)log(3x + 2) + (4776x + 14328x + 10746)log(2x + 3) +--R + +--R 2 +--R (- 6000x - 18000x - 13500)log(x + 1) - 1980x - 3295 +--R / +--R 2 +--R 1000x + 3000x + 2250 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 1035 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------- +--R 6 5 4 3 2 +--R 48x + 368x + 1160x + 1920x + 1755x + 837x + 162 +--R Type: Fraction(Polynomial(Integer)) +--E 298 + +--S 299 of 1035 +r0:=(-13/15)/(3+2*x)^3+(-99/50)/(3+2*x)^2+(-597/125)/(3+2*x)-6*log(1+x)+_ + 3291/625*log(3+2*x)+459/625*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (22032x + 99144x + 148716x + 74358)log(3x + 2) +--R + +--R 3 2 +--R (157968x + 710856x + 1066284x + 533142)log(2x + 3) +--R + +--R 3 2 2 +--R (- 180000x - 810000x - 1215000x - 607500)log(x + 1) - 71640x - 229770x +--R + +--R - 186715 +--R / +--R 3 2 +--R 30000x + 135000x + 202500x + 101250 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1035 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^2 +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1035 +r0:=15496/9*x+2888/3*x^2+560/3*x^3-(3+2*x)^4*(29+35*x)/(2+5*x+3*x^2)+_ + 83*log(1+x)-1625/27*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 4875x - 8125x - 3250)log(3x + 2) + (6723x + 11205x + 4482)log(x + 1) +--R + +--R 4 3 2 +--R - 72x + 216x - 88824x - 152697x - 63423 +--R / +--R 2 +--R 81x + 135x + 54 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 1035 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^2 +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 304 + +--S 305 of 1035 +r0:=3068/9*x+280/3*x^2-(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)+71*log(1+x)-_ + 1825/27*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 5475x - 9125x - 3650)log(3x + 2) + (5751x + 9585x + 3834)log(x + 1) +--R + +--R 3 2 +--R - 72x - 28158x - 49389x - 21141 +--R / +--R 2 +--R 81x + 135x + 54 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 1035 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^2 +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 307 + +--S 308 of 1035 +r0:=140/3*x-(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)+59*log(1+x)-535/9*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 1605x - 2675x - 1070)log(3x + 2) + (1593x + 2655x + 1062)log(x + 1) +--R + +--R 2 +--R - 2724x - 5127x - 2349 +--R / +--R 2 +--R 27x + 45x + 18 +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 1035 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^2 +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 310 + +--S 311 of 1035 +r0:=-(3+2*x)*(29+35*x)/(2+5*x+3*x^2)+94*atanh(5+6*x) +--R +--R +--R 2 2 +--R (282x + 470x + 188)atanh(6x + 5) - 70x - 163x - 87 +--R (2) ---------------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 1035 +t0:=(5-x)/(2+5*x+3*x^2)^2 +--R +--R +--R - x + 5 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 313 + +--S 314 of 1035 +r0:=(-29-35*x)/(2+5*x+3*x^2)+70*atanh(5+6*x) +--R +--R +--R 2 +--R (210x + 350x + 140)atanh(6x + 5) - 35x - 29 +--R (2) -------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1035 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R 5 4 3 2 +--R 18x + 87x + 164x + 151x + 68x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1035 +r0:=-3/5*(37+47*x)/(2+5*x+3*x^2)+23*log(1+x)+52/25*log(3+2*x)-627/25*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 1881x - 3135x - 1254)log(3x + 2) + (156x + 260x + 104)log(2x + 3) +--R + +--R 2 +--R (1725x + 2875x + 1150)log(x + 1) - 705x - 555 +--R / +--R 2 +--R 75x + 125x + 50 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 318 + +)clear all + +--S 319 of 1035 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------ +--R 6 5 4 3 2 +--R 36x + 228x + 589x + 794x + 589x + 228x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 319 + +--S 320 of 1035 +r0:=(-454/25)/(3+2*x)-3/5*(37+47*x)/((3+2*x)*(2+5*x+3*x^2))+11*log(1+x)+_ + 812/125*log(3+2*x)-2187/125*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (- 13122x - 41553x - 41553x - 13122)log(3x + 2) +--R + +--R 3 2 +--R (4872x + 15428x + 15428x + 4872)log(2x + 3) +--R + +--R 3 2 2 +--R (8250x + 26125x + 26125x + 8250)log(x + 1) - 6810x - 14875x - 7315 +--R / +--R 3 2 +--R 750x + 2375x + 2375x + 750 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 1035 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 322 + +--S 323 of 1035 +r0:=(-428/25)/(3+2*x)^2+(-2618/125)/(3+2*x)-3/5*(37+47*x)/((3+2*x)^2*_ + (2+5*x+3*x^2))-log(1+x)+8104/625*log(3+2*x)-7479/625*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 89748x - 418824x - 710505x - 516051x - 134622)log(3x + 2) +--R + +--R 4 3 2 +--R (97248x + 453824x + 769880x + 559176x + 145872)log(2x + 3) +--R + +--R 4 3 2 3 +--R (- 7500x - 35000x - 59375x - 43125x - 11250)log(x + 1) - 78540x +--R + +--R 2 +--R - 280810x - 319835x - 113815 +--R / +--R 4 3 2 +--R 7500x + 35000x + 59375x + 43125x + 11250 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 of 1035 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^2) +--R +--R +--R (1) +--R - x + 5 +--R ---------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 144x + 1344x + 5416x + 12296x + 17185x + 15126x + 8181x + 2484x + 324 +--R Type: Fraction(Polynomial(Integer)) +--E 325 + +--S 326 of 1035 +r0:=(-1258/75)/(3+2*x)^3+(-2212/125)/(3+2*x)^2+(-16522/625)/(3+2*x)-_ + 3/5*(37+47*x)/((3+2*x)^3*(2+5*x+3*x^2))-13*log(1+x)+65816/3125*_ + log(3+2*x)-25191/3125*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 1813752x - 11184804x - 27055134x - 31967379x - 18364239x +--R + +--R - 4080942 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 4738752x + 29222304x + 70686384x + 83520504x + 47979864x +--R + +--R 10662192 +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 2925000x - 18037500x - 43631250x - 51553125x - 29615625x +--R + +--R - 6581250 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R - 2973960x - 14873880x - 27167700x - 21302995x - 5978965 +--R / +--R 5 4 3 2 +--R 225000x + 1387500x + 3356250x + 3965625x + 2278125x + 506250 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 1035 +t0:=(5-x)*(3+2*x)^5/(2+5*x+3*x^2)^3 +--R +--R +--R 6 5 4 3 2 +--R - 32x - 80x + 480x + 2520x + 4590x + 3807x + 1215 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 328 + +--S 329 of 1035 +r0:=-182920/9*x-34760/3*x^2-6800/3*x^3-1/2*(3+2*x)^5*(29+35*x)/_ + (2+5*x+3*x^2)^2+5/2*(3+2*x)^4*(137+170*x)/(2+5*x+3*x^2)-_ + 1085*log(1+x)+29375/27*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (528750x + 1762500x + 2173750x + 1175000x + 235000)log(3x + 2) +--R + +--R 4 3 2 +--R (- 527310x - 1757700x - 2167830x - 1171800x - 234360)log(x + 1) +--R + +--R 5 4 3 2 +--R - 576x + 6126120x + 20591850x + 25603665x + 13944270x + 2805921 +--R / +--R 4 3 2 +--R 486x + 1620x + 1998x + 1080x + 216 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1035 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^3 +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1035 +r0:=-36892/9*x-3392/3*x^2-1/2*(3+2*x)^4*(29+35*x)/(2+5*x+3*x^2)^2+_ + 1/2*(3+2*x)^3*(695+848*x)/(2+5*x+3*x^2)-883*log(1+x)+23825/27*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (428850x + 1429500x + 1763050x + 953000x + 190600)log(3x + 2) +--R + +--R 4 3 2 +--R (- 429138x - 1430460x - 1764234x - 953640x - 190728)log(x + 1) +--R + +--R 4 3 2 +--R 1971108x + 6712446x + 8456811x + 4665198x + 949887 +--R / +--R 4 3 2 +--R 486x + 1620x + 1998x + 1080x + 216 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 1035 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^3 +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 334 + +--S 335 of 1035 +r0:=-1/2*(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)^2+141/2*(3+2*x)*(7+8*x)/_ + (2+5*x+3*x^2)-1410*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 4 +--R (- 25380x - 84600x - 104340x - 56400x - 11280)atanh(6x + 5) + 6488x +--R + +--R 3 2 +--R 25862x + 37251x + 23010x + 5139 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 336 + +)clear all + +--S 337 of 1035 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^3 +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 337 + +--S 338 of 1035 +r0:=-1/2*(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)^2+1/2*(7+8*x)*(199+70*x)/_ + (2+5*x+3*x^2)-1102*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 4 +--R (- 19836x - 66120x - 81548x - 44080x - 8816)atanh(6x + 5) + 1680x +--R + +--R 3 2 +--R 8906x + 15173x + 10466x + 2525 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 338 + +--S 339 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 339 + +)clear all + +--S 340 of 1035 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^3 +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 340 + +--S 341 of 1035 +r0:=-1/2*(3+2*x)*(29+35*x)/(2+5*x+3*x^2)^2+1/2*(725+842*x)/(2+5*x+3*x^2)-_ + 842*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (- 15156x - 50520x - 62308x - 33680x - 6736)atanh(6x + 5) + 2526x +--R + +--R 2 +--R 6315x + 5146x + 1363 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 1035 +t0:=(5-x)/(2+5*x+3*x^2)^3 +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 343 + +--S 344 of 1035 +r0:=1/2*(-29-35*x)/(2+5*x+3*x^2)^2+105/2*(5+6*x)/(2+5*x+3*x^2)-630*atanh(5+6*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (- 11340x - 37800x - 46620x - 25200x - 5040)atanh(6x + 5) + 1890x +--R + +--R 2 +--R 4725x + 3850x + 1021 +--R / +--R 4 3 2 +--R 18x + 60x + 74x + 40x + 8 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1035 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 54x + 351x + 963x + 1447x + 1287x + 678x + 196x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 1035 +r0:=-3/10*(37+47*x)/(2+5*x+3*x^2)^2+1/50*(9587+11442*x)/(2+5*x+3*x^2)-_ + 233*log(1+x)+208/125*log(3+2*x)+28917/125*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (520506x + 1735020x + 2139858x + 1156680x + 231336)log(3x + 2) +--R + +--R 4 3 2 +--R (3744x + 12480x + 15392x + 8320x + 1664)log(2x + 3) +--R + +--R 4 3 2 +--R (- 524250x - 1747500x - 2155250x - 1165000x - 233000)log(x + 1) +--R + +--R 3 2 +--R 171630x + 429855x + 350570x + 93095 +--R / +--R 4 3 2 +--R 2250x + 7500x + 9250x + 5000x + 1000 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 1035 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 108x + 864x + 2979x + 5783x + 6915x + 5217x + 2426x + 636x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 349 + +--S 350 of 1035 +r0:=12946/125/(3+2*x)-3/10*(37+47*x)/((3+2*x)*(2+5*x+3*x^2)^2)+_ + 1/50*(9293+10848*x)/((3+2*x)*(2+5*x+3*x^2))-175*log(1+x)+_ + 4912/625*log(3+2*x)+104463/625*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3760668x + 18176562x + 34263864x + 31547826x + 14206968x +--R + +--R 2507112 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (176832x + 854688x + 1611136x + 1483424x + 668032x + 117888) +--R * +--R log(2x + 3) +--R + +--R 5 4 3 2 +--R - 3937500x - 19031250x - 35875000x - 33031250x - 14875000x +--R + +--R - 2625000 +--R * +--R log(x + 1) +--R + +--R 4 3 2 +--R 1165140x + 4697400x + 6842995x + 4275600x + 968615 +--R / +--R 5 4 3 2 +--R 22500x + 108750x + 205000x + 188750x + 85000x + 15000 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 351 + +)clear all + +--S 352 of 1035 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 9 8 7 6 5 4 3 2 +--R 216x + 2052x + 8550x + 20503x + 31179x + 31179x + 20503x + 8550x +--R + +--R 2052x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 352 + +--S 353 of 1035 +r0:=11856/125/(3+2*x)^2+35886/625/(3+2*x)-3/10*(37+47*x)/((3+2*x)^2*_ + (2+5*x+3*x^2)^2)+1/50*(8999+10254*x)/((3+2*x)^2*(2+5*x+3*x^2))-_ + 141*log(1+x)+68592/3125*log(3+2*x)+372033/3125*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 26786376x + 169647048x + 438254874x + 590788404x + 438254874x +--R + +--R 169647048x + 26786376 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R 4938624x + 31277952x + 80801376x + 108924096x + 80801376x +--R + +--R 31277952x + 4938624 +--R * +--R log(2x + 3) +--R + +--R 6 5 4 3 2 +--R - 31725000x - 200925000x - 519056250x - 699712500x - 519056250x +--R + +--R - 200925000x - 31725000 +--R * +--R log(x + 1) +--R + +--R 5 4 3 2 +--R 6459480x + 36556020x + 80482290x + 85904835x + 44358230x + 8857895 +--R / +--R 6 5 4 3 2 +--R 225000x + 1425000x + 3681250x + 4962500x + 3681250x + 1425000x +--R + +--R 225000 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 1035 +t0:=x/((-1+x)^3*(3+5*x+4*x^2)^2) +--R +--R +--R x +--R (1) ----------------------------------------------- +--R 7 6 5 4 3 2 +--R 16x - 8x - 23x - 13x + 26x + 14x - 3x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 355 + +--S 356 of 1035 +r0:=(-21/736)/(1-x)^2+(-97/4416)/(1-x)+1/276*(39+44*x)/((1-x)^2*_ + (3+5*x+4*x^2))+11/2304*log(1-x)-11/4608*log(3+5*x+4*x^2)+_ + 6023/52992*atan((5+8*x)/sqrt(23))/sqrt(23) +--R +--R +--R (2) +--R 4 3 2 +--+ 2 +--R (- 1012x + 759x + 759x + 253x - 759)\|23 log(4x + 5x + 3) +--R + +--R 4 3 2 +--+ +--R (2024x - 1518x - 1518x - 506x + 1518)\|23 log(- x + 1) +--R + +--R +--+ +--R 4 3 2 (8x + 5)\|23 +--R (48184x - 36138x - 36138x - 12046x + 36138)atan(-------------) +--R 23 +--R + +--R 3 2 +--+ +--R (9312x - 9768x - 2880x - 1080)\|23 +--R / +--R 4 3 2 +--+ +--R (423936x - 317952x - 317952x - 105984x + 317952)\|23 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 1035 +t0:=(x^2+x^3)/(-2+x+x^2) +--R +--R +--R 3 2 +--R x + x +--R (1) ---------- +--R 2 +--R x + x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 358 + +--S 359 of 1035 +r0:=1/2*x^2+2/3*log(1-x)+4/3*log(2+x) +--R +--R +--R 2 +--R 8log(x + 2) + 4log(- x + 1) + 3x +--R (2) --------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1035 +t0:=(5-x)*(3+2*x)^4*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (1) (- 16x - 16x + 264x + 864x + 999x + 405)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1035 +r0:=19609/3402*(2+5*x+3*x^2)^(3/2)+478/315*(3+2*x)^2*(2+5*x+3*x^2)^(3/2)+_ + 229/378*(3+2*x)^3*(2+5*x+3*x^2)^(3/2)-1/21*(3+2*x)^4*(2+5*x+3*x^2)^(3/2)+_ + 1/7560*(53569+42086*x)*(2+5*x+3*x^2)^(3/2)-25969/31104*atanh(1/2*_ + (5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+25969/15552*(5+6*x)*_ + sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 908915atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R - 2488320x - 3248640x + 57298176x + 247266720x + 417203088x +--R + +--R 323830900x + 94018206 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 1088640\|3 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 1035 +t0:=(5-x)*(3+2*x)^3*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 4 3 2 | 2 +--R (1) (- 8x + 4x + 126x + 243x + 135)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1035 +r0:=304/81*(2+5*x+3*x^2)^(3/2)+11/15*(3+2*x)^2*(2+5*x+3*x^2)^(3/2)-_ + 1/18*(3+2*x)^3*(2+5*x+3*x^2)^(3/2)+1/360*(1703+1282*x)*_ + (2+5*x+3*x^2)^(3/2)-6221/10368*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)+6221/5184*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 31105atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 69120x + 29952x + 1651680x + 4635696x + 4864700x + 1719402)\|3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R +-+ +--R 51840\|3 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 of 1035 +t0:=(5-x)*(3+2*x)^2*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (1) (- 4x + 8x + 51x + 45)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1035 +r0:=337/162*(2+5*x+3*x^2)^(3/2)-1/15*(3+2*x)^2*(2+5*x+3*x^2)^(3/2)+_ + 1/180*(511+334*x)*(2+5*x+3*x^2)^(3/2)-2267/5184*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+2267/2592*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 11335atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (- 20736x + 47520x + 458832x + 750500x + 337254)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 25920\|3 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 1035 +t0:=(5-x)*(3+2*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (1) (- 2x + 7x + 15)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1035 +r0:=34/27*(2+5*x+3*x^2)^(3/2)-1/12*(3+2*x)*(2+5*x+3*x^2)^(3/2)-_ + 559/1728*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 559/864*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 559atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 864x + 3792x + 14852x + 9078)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 1728\|3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 +--R (1) (- x + 5)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1035 +r0:=-1/9*(2+5*x+3*x^2)^(3/2)-35/144*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)+35/72*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 6x + 5 2 +-+ | 2 +--R - 35atanh(--------------------) + (- 48x + 340x + 318)\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R -------------------------------------------------------------------------- +--R +-+ +--R 144\|3 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1035 +r0:=-311/48*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 13/8*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+_ + 1/24*(73-6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +-+ +-+ 8x + 7 +--R - 311atanh(--------------------) + 78\|3 \|5 atanh(--------------------) +--R +------------+ +------------+ +--R +-+ | 2 +-+ | 2 +--R 2\|3 \|3x + 5x + 2 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (- 12x + 146)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 48\|3 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1035 +r0:=43/8*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 57/8*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/2*(8+x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +-+ 6x + 5 +--R (86x + 129)\|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ 8x + 7 +--R (- 114x - 171)\|3 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ +-+ | 2 +--R (- 4x - 32)\|3 \|5 \|3x + 5x + 2 +--R / +--R +-+ +-+ +--R (16x + 24)\|3 \|5 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^3 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1035 +r0:=-13/10*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/8*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+27/80*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3/40*(25+26*x)*sqrt(2+5*x+3*x^2)/_ + (3+2*x) +--R +--R +--R (2) +--R 2 +-+ +-+ 6x + 5 +--R (- 40x - 120x - 90)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 2 8x + 7 +--R (108x + 324x + 243)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (248x + 242)\|5 \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (320x + 960x + 720)\|5 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^4 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------------- +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1035 +r0:=-47/400*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/6*(2-3*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^3+37/120*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2+29/100*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 8x + 7 +--R (- 1128x - 5076x - 7614x - 3807)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 2 +-+ | 2 +--R (1392x + 5516x + 3842)\|5 \|3x + 5x + 2 +--R / +--R 3 2 +-+ +--R (9600x + 43200x + 64800x + 32400)\|5 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^5 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1035 +r0:=-153/1600*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/16*(7-4*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^4+7/40*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^3+5/32*sqrt(2+5*x+3*x^2)/(3+2*x)^2+33/200*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 2448x - 14688x - 33048x - 33048x - 12393) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (2112x + 10504x + 18216x + 9518)\|5 \|3x + 5x + 2 +--R / +--R 4 3 2 +-+ +--R (25600x + 153600x + 345600x + 345600x + 129600)\|5 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^6 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1035 +r0:=-3159/40000*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/30*(12-5*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^5+131/1200*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^4+12/125*sqrt(2+5*x+3*x^2)/(3+2*x)^3+3/32*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2+549/5000*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (- 101088x - 758160x - 2274480x - 3411720x - 2558790x - 767637) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (70272x + 451632x + 1099032x + 1212652x + 488662)\|5 \|3x + 5x + 2 +--R / +--R 5 4 3 2 +-+ +--R (1280000x + 9600000x + 28800000x + 43200000x + 32400000x + 9720000)\|5 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^7 +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1035 +r0:=-26453/400000*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 1/48*(17-6*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^6+89/1200*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^5+259/4000*sqrt(2+5*x+3*x^2)/(3+2*x)^4+923/15000*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^3+311/4800*sqrt(2+5*x+3*x^2)/(3+2*x)^2+_ + 4083/50000*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 5078976x - 45710784x - 171415440x - 342830880x - 385684740x +--R + +--R - 231410844x - 57852711 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R 3135744x + 24762080x + 78608960x + 125594400x + 101415280x +--R + +--R 32644786 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R / +--R 6 5 4 3 2 +--R 76800000x + 691200000x + 2592000000x + 5184000000x + 5832000000x +--R + +--R 3499200000x + 874800000 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 396 + +)clear all + +--S 397 of 1035 +t0:=(5-x)*(3+2*x)^4*(2+5*x+3*x^2)^(3/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (- 48x - 128x + 680x + 3880x + 7845x + 7938x + 4023x + 810) +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1035 +r0:=454969/559872*(5+6*x)*(2+5*x+3*x^2)^(3/2)+127367/43740*_ + (2+5*x+3*x^2)^(5/2)+487/486*(3+2*x)^2*(2+5*x+3*x^2)^(5/2)+299/648*_ + (3+2*x)^3*(2+5*x+3*x^2)^(5/2)-1/27*(3+2*x)^4*(2+5*x+3*x^2)^(5/2)+_ + 1/34992*(150539+113346*x)*(2+5*x+3*x^2)^(5/2)+454969/8957952*_ + atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 454969/4478976*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 2274845atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 8 7 6 5 +--R - 238878720x - 741519360x + 4287375360x + 29622965760x +--R + +--R 4 3 2 +--R 74525490432x + 99834752160x + 75301381776x + 30098597300x +--R + +--R 4943976702 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 44789760\|3 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 of 1035 +t0:=(5-x)*(3+2*x)^3*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 6 5 4 3 2 | 2 +--R (1) (- 24x - 28x + 382x + 1367x + 1872x + 1161x + 270)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1035 +r0:=12277/20736*(5+6*x)*(2+5*x+3*x^2)^(3/2)+22577/11340*(2+5*x+_ + 3*x^2)^(5/2)+67/126*(3+2*x)^2*(2+5*x+3*x^2)^(5/2)-1/24*(3+2*x)^3*_ + (2+5*x+3*x^2)^(5/2)+1/9072*(27209+19926*x)*(2+5*x+3*x^2)^(5/2)+_ + 12277/331776*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 12277/165888*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 429695atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 7 6 5 4 3 +--R - 34836480x - 50595840x + 736473600x + 3300302592x + 5986095840x +--R + +--R 2 +--R 5524835376x + 2552224700x + 466274922 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 11612160\|3 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 1035 +t0:=(5-x)*(3+2*x)^2*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (1) (- 12x + 4x + 185x + 406x + 327x + 90)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1035 +r0:=1129/2592*(5+6*x)*(2+5*x+3*x^2)^(3/2)+1111/945*(2+5*x+3*x^2)^(5/2)-_ + 1/21*(3+2*x)^2*(2+5*x+3*x^2)^(5/2)+1/378*(721+474*x)*(2+5*x+_ + 3*x^2)^(5/2)+1129/41472*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+_ + 3*x^2)))/sqrt(3)-1129/20736*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 39515atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R - 2488320x + 622080x + 54169344x + 158099040x + 189722352x +--R + +--R 103942700x + 21339474 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 1451520\|3 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1035 +t0:=(5-x)*(3+2*x)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 4 3 2 | 2 +--R (1) (- 6x + 11x + 76x + 89x + 30)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1035 +r0:=839/2592*(5+6*x)*(2+5*x+3*x^2)^(3/2)+103/135*(2+5*x+3*x^2)^(5/2)-_ + 1/18*(3+2*x)*(2+5*x+3*x^2)^(5/2)+839/41472*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-839/20736*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 4195atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R (- 207360x + 421632x + 4065120x + 7134576x + 4813900x + 1123842) +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 207360\|3 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (1) (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1035 +r0:=35/144*(5+6*x)*(2+5*x+3*x^2)^(3/2)-1/15*(2+5*x+3*x^2)^(5/2)+_ + 35/2304*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 35/1152*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 175atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (- 6912x + 27360x + 97584x + 86140x + 23178)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 11520\|3 +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1035 +r0:=1/48*(47-6*x)*(2+5*x+3*x^2)^(3/2)-2011/256*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+65/32*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+1/128*(175-414*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 6033atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R 1560\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 288x + 1776x + 1084x + 2554)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 768\|3 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1035 +r0:=-1/6*(21+x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)+3743/192*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-161/32*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)-1/96*(361-726*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R (7486x + 11229)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R (- 1932x - 2898)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 96x + 728x - 512x - 3510)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R (384x + 576)\|3 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1035 +r0:=-1/4*(8+x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-343/64*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+1329/64*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3/16*(93+43*x)*sqrt(2+5*x+3*x^2)/_ + (3+2*x) +--R +--R +--R (2) +--R 2 +-+ +-+ 6x + 5 +--R (- 1372x - 4116x - 3087)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 2 8x + 7 +--R (5316x + 15948x + 11961)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 48x + 568x + 3108x + 3092)\|5 \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (256x + 768x + 576)\|5 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1035 +r0:=67/40*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/6*(11+3*x)*(2+5*x+3*x^2)^(3/2)/_ + (3+2*x)^3+51/32*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*_ + sqrt(3)-1973/320*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/_ + sqrt(5)-1/160*(845+402*x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 +-+ +-+ 6x + 5 +--R (12240x + 55080x + 82620x + 41310)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 3 2 8x + 7 +--R (- 47352x - 213084x - 319626x - 159813)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 1440x - 26352x - 61756x - 39502)\|5 \|3x + 5x + 2 +--R / +--R 3 2 +-+ +--R (7680x + 34560x + 51840x + 25920)\|5 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^5 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1035 +r0:=-41/800*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2+1/240*(215+234*x)*_ + (2+5*x+3*x^2)^(3/2)/(3+2*x)^3-13/20*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4-_ + 3/32*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+_ + 2359/6400*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+_ + 1/3200*(805+246*x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +-+ +--R (- 28800x - 172800x - 388800x - 388800x - 145800)\|3 \|5 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R (113232x + 679392x + 1528632x + 1528632x + 573237) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (121152x + 380824x + 422296x + 165978)\|5 \|3x + 5x + 2 +--R / +--R 4 3 2 +-+ +--R (307200x + 1843200x + 4147200x + 4147200x + 1555200)\|5 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^6 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1035 +r0:=1/10*(1+5*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^5+141/32000*atanh(1/2*_ + (7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+41/800*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^3+23/640*sqrt(2+5*x+3*x^2)/(3+2*x)^2+99/4000*sqrt(2+5*x+3*x^2)/_ + (3+2*x)-3/320*(87+76*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^4 +--R +--R +--R (2) +--R 5 4 3 2 +--R (4512x + 33840x + 101520x + 152280x + 114210x + 34263) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (12672x + 133232x + 263032x + 180252x + 38062)\|5 \|3x + 5x + 2 +--R / +--R 5 4 3 2 +-+ +--R (1024000x + 7680000x + 23040000x + 34560000x + 25920000x + 7776000)\|5 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^7 +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1035 +r0:=-1/12*(2-3*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^6+1141/320000*atanh(1/2*_ + (7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+77/3200*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^4+97/6000*sqrt(2+5*x+3*x^2)/(3+2*x)^3+41/3840*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2+249/40000*sqrt(2+5*x+3*x^2)/(3+2*x)-1/80*(49+45*x)*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^5 +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 219072x + 1971648x + 7393680x + 14787360x + 16635780x + 9981468x +--R + +--R 2495367 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (191232x + 1598240x + 6130880x + 8959200x + 5053840x + 825358)\|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R 6 5 4 3 2 +--R 61440000x + 552960000x + 2073600000x + 4147200000x + 4665600000x +--R + +--R 2799360000x + 699840000 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^8 +--R +--R +--R (1) +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R / +--R 8 7 6 5 4 3 2 +--R 256x + 3072x + 16128x + 48384x + 90720x + 108864x + 81648x +--R + +--R 34992x + 6561 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1035 +r0:=-1/42*(9-7*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^7+4663/1600000*atanh(1/2*_ + (7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+367/33600*sqrt(2+5*x+_ + 3*x^2)/(3+2*x)^5+111/16000*sqrt(2+5*x+3*x^2)/(3+2*x)^4+1769/420000*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^3+293/134400*sqrt(2+5*x+3*x^2)/(3+2*x)^2+_ + 249/1400000*sqrt(2+5*x+3*x^2)/(3+2*x)-1/1344*(559+534*x)*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^6 +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 12534144x + 131608512x + 592238304x + 1480595760x + 2220893640x +--R + +--R 2 +--R 1998804276x + 999402138x + 214157601 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R 382464x + 5786176x + 32752480x + 110807040x + 128281280x +--R + +--R 31518236x - 13108926 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R / +--R 7 6 5 4 +--R 4300800000x + 45158400000x + 203212800000x + 508032000000x +--R + +--R 3 2 +--R 762048000000x + 685843200000x + 342921600000x + 73483200000 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1035 +t0:=(5-x)*(3+2*x)^4*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 144x - 624x + 1304x + 14784x + 44295x + 70799x + 67449x +--R + +--R 2 +--R 38421x + 12096x + 1620 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1035 +r0:=-249299/4478976*(5+6*x)*(2+5*x+3*x^2)^(3/2)+249299/466560*(5+6*x)*_ + (2+5*x+3*x^2)^(5/2)+64067/34020*(2+5*x+3*x^2)^(7/2)+_ + 3298/4455*(3+2*x)^2*(2+5*x+3*x^2)^(7/2)+41/110*(3+2*x)^3*(2+5*x+_ + 3*x^2)^(7/2)-1/33*(3+2*x)^4*(2+5*x+3*x^2)^(7/2)+1/213840*(655267+_ + 480818*x)*(2+5*x+3*x^2)^(7/2)-249299/71663616*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+249299/35831808*(5+6*x)*_ + sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 95980115atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 10 9 8 +--R - 361184624640x - 1751745429504x + 3864341053440x +--R + +--R 7 6 5 +--R 51518646079488x + 180191859517440x + 344946733733376x +--R + +--R 4 3 2 +--R 409710253190400x + 310310741757600x + 146139720113040x +--R + +--R 39043400722420x + 4522595653470 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 27590492160\|3 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 1035 +t0:=(5-x)*(3+2*x)^3*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 72x - 204x + 958x + 5955x + 13215x + 15577x + 10359x + 3672x +--R + +--R 540 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1035 +r0:=-182917/4478976*(5+6*x)*(2+5*x+3*x^2)^(3/2)+182917/466560*(5+6*x)*_ + (2+5*x+3*x^2)^(5/2)+22493/17010*(2+5*x+3*x^2)^(7/2)+169/405*(3+2*x)^2*_ + (2+5*x+3*x^2)^(7/2)-1/30*(3+2*x)^3*(2+5*x+3*x^2)^(7/2)+1/19440*_ + (42451+30554*x)*(2+5*x+3*x^2)^(7/2)-182917/71663616*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+182917/35831808*(5+6*x)*_ + sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 6402095atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 9 8 7 6 +--R - 18059231232x - 58525286400x + 295894093824x + 2173375825920x +--R + +--R 5 4 3 2 +--R 5786089901568x + 8507866763520x + 7525492434720x + 3991828554960x +--R + +--R 1171498832260x + 146357368950 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 2508226560\|3 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 441 + +)clear all + +--S 442 of 1035 +t0:=(5-x)*(3+2*x)^2*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (- 36x - 48x + 551x + 2151x + 3381x + 2717x + 1104x + 180) +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1035 +r0:=-22535/746496*(5+6*x)*(2+5*x+3*x^2)^(3/2)+4507/15552*(5+6*x)*_ + (2+5*x+3*x^2)^(5/2)+1847/2268*(2+5*x+3*x^2)^(7/2)-1/27*(3+2*x)^2*_ + (2+5*x+3*x^2)^(7/2)+1/648*(931+614*x)*(2+5*x+3*x^2)^(7/2)-_ + 22535/11943936*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 22535/5971968*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 157745atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 8 7 6 5 +--R - 334430208x - 536481792x + 6551746560x + 30911721984x +--R + +--R 4 3 2 +--R 60711522048x + 64952003808x + 39524314416x + 12869874940x +--R + +--R 1743650634 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 83607552\|3 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 1035 +t0:=(5-x)*(3+2*x)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R +------------+ +--R 6 5 4 3 2 | 2 +--R (1) (- 18x + 3x + 271x + 669x + 687x + 328x + 60)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1035 +r0:=-1865/82944*(5+6*x)*(2+5*x+3*x^2)^(3/2)+373/1728*(5+6*x)*_ + (2+5*x+3*x^2)^(5/2)+23/42*(2+5*x+3*x^2)^(7/2)-1/24*(3+2*x)*_ + (2+5*x+3*x^2)^(7/2)-1865/1327104*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)+1865/663552*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 13055atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 7 6 5 4 3 +--R - 20901888x + 1492992x + 422309376x + 1310425344x + 1795636512x +--R + +--R 2 +--R 1285991376x + 470446660x + 69554838 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 9289728\|3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (1) (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1035 +r0:=-175/10368*(5+6*x)*(2+5*x+3*x^2)^(3/2)+35/216*(5+6*x)*_ + (2+5*x+3*x^2)^(5/2)-1/21*(2+5*x+3*x^2)^(7/2)-175/165888*_ + atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 175/82944*(5+6*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 1225atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R - 1492992x + 2695680x + 26908416x + 52777440x + 46221744x +--R + +--R 19303580x + 3137082 +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 1161216\|3 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 2x + 3 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1035 +r0:=1/3456*(25-5586*x)*(2+5*x+3*x^2)^(3/2)+1/360*(209-30*x)*_ + (2+5*x+3*x^2)^(5/2)-543811/55296*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)+325/128*atanh(1/2*(7+8*x)/(sqrt(5)*_ + sqrt(2+5*x+3*x^2)))*sqrt(5)+1/27648*(51455-106734*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R - 2719055atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R 702000\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R (- 207360x + 753408x + 2622240x + 3249744x + 1166980x + 1160598) +--R * +--R +------------+ +--R +-+ | 2 +--R \|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 276480\|3 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^2 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 2 +--R 4x + 12x + 9 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1035 +r0:=-1/192*(65-1194*x)*(2+5*x+3*x^2)^(3/2)-1/10*(34+x)*_ + (2+5*x+3*x^2)^(5/2)/(3+2*x)+41053/1024*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)-1325/128*atanh(1/2*(7+8*x)/(sqrt(5)*_ + sqrt(2+5*x+3*x^2)))*sqrt(5)-1/512*(3865-8082*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R (1231590x + 1847385)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +-+ +-+ 8x + 7 +--R (- 318000x - 477000)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 13824x + 57024x + 160128x + 237992x - 80824x - 587946)\|3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R +-+ +--R (30720x + 46080)\|3 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 456 + +)clear all + +--S 457 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^3 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 3 2 +--R 8x + 36x + 54x + 27 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1035 +r0:=5/192*(573+164*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)-1/16*(29+2*x)*_ + (2+5*x+3*x^2)^(5/2)/(3+2*x)^2-199615/3072*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+4295/256*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+5/1536*(3763-7854*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 2 6x + 5 +--R (- 798460x - 2395380x - 1796535)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 2 +-+ +-+ 8x + 7 +--R (206160x + 618480x + 463860)\|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 3456x + 17088x + 28912x + 114584x + 581484x + 591438)\|3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (12288x + 36864x + 27648)\|3 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 4 3 2 +--R 16x + 96x + 216x + 216x + 81 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1035 +r0:=5/48*(93+43*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/6*(8+x)*_ + (2+5*x+3*x^2)^(5/2)/(3+2*x)^3+13505/256*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))/sqrt(3)-3487/256*atanh(1/2*(7+8*x)/(sqrt(5)*_ + sqrt(2+5*x+3*x^2)))*sqrt(5)-5/64*(736+343*x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 6x + 5 +--R (324120x + 1458540x + 2187810x + 1093905)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +-+ +--R (- 83688x - 376596x - 564894x - 282447)\|3 \|5 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 1152x + 7584x - 7776x - 257328x - 574132x - 356896)\|3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R 3 2 +-+ +--R (6144x + 27648x + 41472x + 20736)\|3 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 5 4 3 2 +--R 32x + 240x + 720x + 1080x + 810x + 243 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1035 +r0:=-953/128*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2+5/192*(485+282*x)*_ + (2+5*x+3*x^2)^(3/2)/(3+2*x)^3-1/16*(19+4*x)*(2+5*x+3*x^2)^(5/2)/_ + (3+2*x)^4-1875/256*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*_ + sqrt(3)+29047/1024*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/_ + sqrt(5)+1/512*(12265+5718*x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +-+ +--R (- 360000x - 2160000x - 4860000x - 4860000x - 1822500)\|3 \|5 +--R * +--R 6x + 5 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +--R (1394256x + 8365536x + 18822456x + 18822456x + 7058421) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (- 6912x + 79488x + 1066560x + 3344536x + 4118536x + 1793442)\|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R 4 3 2 +-+ +--R (49152x + 294912x + 663552x + 663552x + 248832)\|5 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 6 5 4 3 2 +--R 64x + 576x + 2160x + 4320x + 4860x + 2916x + 729 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1035 +r0:=4489/3200*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/960*(2335+1386*x)*_ + (2+5*x+3*x^2)^(3/2)/(3+2*x)^3+77/80*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4-_ + 1/10*(14+5*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5+177/128*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-137111/25600*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-1/12800*(57845+26934*x)*_ + sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3398400x + 25488000x + 76464000x + 114696000x + 86022000x +--R + +--R 25806600 +--R * +--R +-+ +-+ 6x + 5 +--R \|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 13162656x - 98719920x - 296159760x - 444239640x - 333179730x +--R + +--R - 99953919 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 345600x - 9261696x - 43173616x - 83282296x - 74039676x +--R + +--R - 25200366 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R / +--R 5 4 3 2 +--R (2457600x + 18432000x + 55296000x + 82944000x + 62208000x + 18662400) +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^7 +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 128x + 1344x + 6048x + 15120x + 22680x + 20412x + 10206x + 2187 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1035 +r0:=-469/6400*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2+1/1920*(175+66*x)*_ + (2+5*x+3*x^2)^(3/2)/(3+2*x)^3-11/480*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4+_ + 1/120*(71+78*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5-13/30*(2+5*x+_ + 3*x^2)^(7/2)/(3+2*x)^6-9/128*atanh(1/2*(5+6*x)/(sqrt(3)*_ + sqrt(2+5*x+3*x^2)))*sqrt(3)+13931/51200*atanh(1/2*(7+8*x)/(sqrt(5)*_ + sqrt(2+5*x+3*x^2)))/sqrt(5)+1/25600*(5945+2814*x)*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 691200x - 6220800x - 23328000x - 46656000x - 52488000x +--R + +--R - 31492800x - 7873200 +--R * +--R +-+ +-+ 6x + 5 +--R \|3 \|5 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R 2674752x + 24072768x + 90272880x + 180545760x + 203113980x +--R + +--R 121868388x + 30467097 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R 2702592x + 15259360x + 36435520x + 45708960x + 29843120x +--R + +--R 8031698 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R / +--R 6 5 4 3 2 +--R 9830400x + 88473600x + 331776000x + 663552000x + 746496000x +--R + +--R 447897600x + 111974400 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 471 + +)clear all + +--S 472 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^8 +--R +--R +--R (1) +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R / +--R 8 7 6 5 4 3 2 +--R 256x + 3072x + 16128x + 48384x + 90720x + 108864x + 81648x +--R + +--R 34992x + 6561 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1035 +r0:=-5/336*(41+33*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^6+1/14*(4+7*x)*_ + (2+5*x+3*x^2)^(5/2)/(3+2*x)^7-47/256000*atanh(1/2*(7+8*x)/(sqrt(5)*_ + sqrt(2+5*x+3*x^2)))/sqrt(5)+41/2560*sqrt(2+5*x+3*x^2)/(3+2*x)^4+_ + 191/16800*sqrt(2+5*x+3*x^2)/(3+2*x)^3+179/21504*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2+1419/224000*sqrt(2+5*x+3*x^2)/(3+2*x)-1/448*(154+135*x)*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^5 +--R +--R +--R (2) +--R 7 6 5 4 3 +--R - 126336x - 1326528x - 5969376x - 14923440x - 22385160x +--R + +--R 2 +--R - 20146644x - 10073322x - 2158569 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R 2179584x + 45240256x + 163902880x + 255114240x + 201423680x +--R + +--R 79962116x + 12808494 +--R * +--R +------------+ +--R +-+ | 2 +--R \|5 \|3x + 5x + 2 +--R / +--R 7 6 5 4 +--R 688128000x + 7225344000x + 32514048000x + 81285120000x +--R + +--R 3 2 +--R 121927680000x + 109734912000x + 54867456000x + 11757312000 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 474 + +)clear all + +--S 475 of 1035 +t0:=(5-x)*(3+2*x)^4/sqrt(2+5*x+3*x^2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1035 +r0:=28051/1296*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 4043/162*sqrt(2+5*x+3*x^2)+391/135*(3+2*x)^2*sqrt(2+5*x+3*x^2)+_ + 53/60*(3+2*x)^3*sqrt(2+5*x+3*x^2)-1/15*(3+2*x)^4*sqrt(2+5*x+3*x^2)+_ + 1/648*(11347+9650*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 140255atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (- 6912x + 4320x + 187824x + 537500x + 563658)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 6480\|3 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 1035 +t0:=(5-x)*(3+2*x)^3/sqrt(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1035 +r0:=19405/1296*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 2375/162*sqrt(2+5*x+3*x^2)+32/27*(3+2*x)^2*sqrt(2+5*x+3*x^2)-_ + 1/12*(3+2*x)^3*sqrt(2+5*x+3*x^2)+5/648*(1361+1078*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R 6x + 5 +--R 19405atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 864x + 2256x + 23380x + 43518)\|3 \|3x + 5x + 2 +--R / +--R +-+ +--R 1296\|3 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1035 +t0:=(5-x)*(3+2*x)^2/sqrt(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ---------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1035 +r0:=1147/108*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 199/27*sqrt(2+5*x+3*x^2)-1/9*(3+2*x)^2*sqrt(2+5*x+3*x^2)+1/54*_ + (301+194*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 6x + 5 2 +-+ | 2 +--R 1147atanh(--------------------) + (- 48x + 244x + 1290)\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R --------------------------------------------------------------------------- +--R +-+ +--R 108\|3 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1035 +t0:=(5-x)*(3+2*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) --------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1035 +r0:=31/4*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 11/3*sqrt(2+5*x+3*x^2)-1/6*(3+2*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 6x + 5 +-+ | 2 +--R 93atanh(--------------------) + (- 4x + 38)\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 486 + +)clear all + +--S 487 of 1035 +t0:=(5-x)/sqrt(2+5*x+3*x^2) +--R +--R +--R - x + 5 +--R (1) --------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1035 +r0:=35/6*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 1/3*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 6x + 5 +-+ | 2 +--R 35atanh(--------------------) - 2\|3 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ---------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 489 + +)clear all + +--S 490 of 1035 +t0:=(5-x)/((3+2*x)*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ----------------------- +--R +------------+ +--R | 2 +--R (2x + 3)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1035 +r0:=-1/2*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+_ + 13/2*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5) +--R +--R +--R +-+ 6x + 5 +-+ 8x + 7 +--R - \|5 atanh(--------------------) + 13\|3 atanh(--------------------) +--R +------------+ +------------+ +--R +-+ | 2 +-+ | 2 +--R 2\|3 \|3x + 5x + 2 2\|5 \|3x + 5x + 2 +--R (2) --------------------------------------------------------------------- +--R +-+ +-+ +--R 2\|3 \|5 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 1035 +t0:=(5-x)/((3+2*x)^2*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------ +--R +------------+ +--R 2 | 2 +--R (4x + 12x + 9)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1035 +r0:=47/10*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/5*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R +------------+ +--R 8x + 7 +-+ | 2 +--R (94x + 141)atanh(--------------------) - 26\|5 \|3x + 5x + 2 +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R (2) -------------------------------------------------------------- +--R +-+ +--R (20x + 30)\|5 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1035 +t0:=(5-x)/((3+2*x)^3*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R +------------+ +--R 3 2 | 2 +--R (8x + 36x + 54x + 27)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1035 +r0:=389/100*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/10*sqrt(2+5*x+3*x^2)/(3+2*x)^2-73/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 2 8x + 7 +--R (1556x + 4668x + 3501)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R +-+ | 2 +--R (- 584x - 1006)\|5 \|3x + 5x + 2 +--R / +--R 2 +-+ +--R (400x + 1200x + 900)\|5 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 1035 +t0:=(5-x)/((3+2*x)^4*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------ +--R +------------+ +--R 4 3 2 | 2 +--R (16x + 96x + 216x + 216x + 81)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1035 +r0:=331/100*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/15*sqrt(2+5*x+3*x^2)/(3+2*x)^3-49/30*sqrt(2+5*x+3*x^2)/(3+2*x)^2-_ + 72/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 3 2 8x + 7 +--R (7944x + 35748x + 53622x + 26811)atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 2 +-+ | 2 +--R (- 3456x - 11348x - 9506)\|5 \|3x + 5x + 2 +--R / +--R 3 2 +-+ +--R (2400x + 10800x + 16200x + 8100)\|5 +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 501 + +)clear all + +--S 502 of 1035 +t0:=(5-x)/((3+2*x)^5*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 | 2 +--R (32x + 240x + 720x + 1080x + 810x + 243)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1035 +r0:=5771/2000*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/20*sqrt(2+5*x+3*x^2)/(3+2*x)^4-86/75*sqrt(2+5*x+3*x^2)/(3+2*x)^3-_ + 41/24*sqrt(2+5*x+3*x^2)/(3+2*x)^2-681/250*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (277008x + 1662048x + 3739608x + 3739608x + 1402353) +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R +------------+ +--R 3 2 +-+ | 2 +--R (- 130752x - 629384x - 1019336x - 558078)\|5 \|3x + 5x + 2 +--R / +--R 4 3 2 +-+ +--R (96000x + 576000x + 1296000x + 1296000x + 486000)\|5 +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 504 + +)clear all + +--S 505 of 1035 +t0:=(5-x)/((3+2*x)^6*sqrt(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------------------- +--R +------------+ +--R 6 5 4 3 2 | 2 +--R (64x + 576x + 2160x + 4320x + 4860x + 2916x + 729)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 1035 +r0:=128381/50000*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 13/25*sqrt(2+5*x+3*x^2)/(3+2*x)^5-443/500*sqrt(2+5*x+3*x^2)/(3+2*x)^4-_ + 2321/1875*sqrt(2+5*x+3*x^2)/(3+2*x)^3-1007/600*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2-15891/6250*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 12324576x + 92434320x + 277302960x + 415954440x + 311965830x +--R + +--R 93589749 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 6102144x - 38626864x - 92184664x - 98467404x - 39837174)\|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R / +--R 5 4 3 2 +--R 4800000x + 36000000x + 108000000x + 162000000x + 121500000x +--R + +--R 36450000 +--R * +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 1035 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) ------------------------------------------ +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1035 +r0:=6265/81*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 2*(3+2*x)^4*(29+35*x)/sqrt(2+5*x+3*x^2)+4040/27*sqrt(2+5*x+3*x^2)+_ + 7190/81*(3+2*x)*sqrt(2+5*x+3*x^2)+1664/27*(3+2*x)^2*sqrt(2+5*x+3*x^2)+_ + 140/3*(3+2*x)^3*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R | 2 6x + 5 +--R 6265\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 144x + 204x + 6662x - 13840x - 19182)\|3 +--R / +--R +------------+ +--R +-+ | 2 +--R 81\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1035 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1035 +r0:=247/9*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 2*(3+2*x)^3*(29+35*x)/sqrt(2+5*x+3*x^2)+272/3*sqrt(2+5*x+3*x^2)+_ + 554/9*(3+2*x)*sqrt(2+5*x+3*x^2)+140/3*(3+2*x)^2*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R | 2 6x + 5 +--R 247\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 12x + 62x - 1612x - 1578)\|3 +--R / +--R +------------+ +--R +-+ | 2 +--R 9\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 1035 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1035 +r0:=2*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-2*(3+2*x)^2*_ + (29+35*x)/sqrt(2+5*x+3*x^2)+184/3*sqrt(2+5*x+3*x^2)+140/3*(3+2*x)*_ + sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R +-+ | 2 6x + 5 2 +--R 6\|3 \|3x + 5x + 2 atanh(--------------------) - 4x - 398x - 358 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ------------------------------------------------------------------ +--R +------------+ +--R | 2 +--R 3\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 516 + +)clear all + +--S 517 of 1035 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1035 +r0:=-2/3*atanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-_ + 2*(3+2*x)*(29+35*x)/sqrt(2+5*x+3*x^2)+140/3*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 6x + 5 +-+ +--R - 2\|3x + 5x + 2 atanh(--------------------) + (- 278x - 242)\|3 +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R (2) ------------------------------------------------------------------ +--R +------------+ +--R +-+ | 2 +--R 3\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 519 + +)clear all + +--S 520 of 1035 +t0:=(5-x)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R - x + 5 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1035 +r0:=-2*(29+35*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R - 70x - 58 +--R (2) --------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 522 + +)clear all + +--S 523 of 1035 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------- +--R +------------+ +--R 3 2 | 2 +--R (6x + 19x + 19x + 6)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1035 +r0:=26/5*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R | 2 8x + 7 +-+ +--R 26\|3x + 5x + 2 atanh(--------------------) + (- 282x - 222)\|5 +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R (2) ----------------------------------------------------------------- +--R +------------+ +--R +-+ | 2 +--R 5\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1035 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (12x + 56x + 95x + 69x + 18)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1035 +r0:=302/25*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/((3+2*x)*sqrt(2+5*x+3*x^2))-856/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R | 2 8x + 7 +--R (604x + 906)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 2 +-+ +--R (- 2568x - 5690x - 2822)\|5 +--R / +--R +------------+ +--R +-+ | 2 +--R (50x + 75)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 528 + +)clear all + +--S 529 of 1035 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 | 2 +--R (24x + 148x + 358x + 423x + 243x + 54)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1035 +r0:=483/25*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/((3+2*x)^2*sqrt(2+5*x+3*x^2))-166/5*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^2-864/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R 2 | 2 8x + 7 +--R (1932x + 5796x + 4347)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (- 5184x - 18906x - 21976x - 7954)\|5 +--R / +--R +------------+ +--R 2 +-+ | 2 +--R (100x + 300x + 225)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 531 + +)clear all + +--S 532 of 1035 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------------------- +--R +------------+ +--R 6 5 4 3 2 | 2 +--R (48x + 368x + 1160x + 1920x + 1755x + 837x + 162)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1035 +r0:=3289/125*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/((3+2*x)^3*sqrt(2+5*x+3*x^2))-2464/75*_ + sqrt(2+5*x+3*x^2)/(3+2*x)^3-478/15*sqrt(2+5*x+3*x^2)/(3+2*x)^2-_ + 4632/125*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R 3 2 | 2 +--R (78936x + 355212x + 532818x + 266409)\|3x + 5x + 2 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 166752x - 849876x - 1584130x - 1268624x - 363118)\|5 +--R / +--R +------------+ +--R 3 2 +-+ | 2 +--R (3000x + 13500x + 20250x + 10125)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 534 + +)clear all + +--S 535 of 1035 +t0:=(5-x)/((3+2*x)^5*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 7 6 5 4 3 2 +--R (96x + 880x + 3424x + 7320x + 9270x + 6939x + 2835x + 486) +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1035 +r0:=82039/2500*atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-_ + 6/5*(37+47*x)/((3+2*x)^4*sqrt(2+5*x+3*x^2))-817/25*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^4-11596/375*sqrt(2+5*x+3*x^2)/(3+2*x)^3-973/30*sqrt(2+5*x+_ + 3*x^2)/(3+2*x)^2-25458/625*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (3937872x + 23627232x + 53161272x + 53161272x + 19935477) +--R * +--R +------------+ +--R | 2 8x + 7 +--R \|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +--R - 7331904x - 48132408x - 124381088x - 157475338x - 97074758x +--R + +--R - 23090004 +--R * +--R +-+ +--R \|5 +--R / +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (120000x + 720000x + 1620000x + 1620000x + 607500)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1035 +t0:=(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 5 4 3 2 +--R - 16x - 16x + 264x + 864x + 999x + 405 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1035 +r0:=-2/3*(3+2*x)^4*(29+35*x)/(2+5*x+3*x^2)^(3/2)+152/27*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+8/3*(3+2*x)^3*(225+284*x)/_ + sqrt(2+5*x+3*x^2)-6848/9*sqrt(2+5*x+3*x^2)-16496/27*(3+2*x)*_ + sqrt(2+5*x+3*x^2)-4544/9*(3+2*x)^2*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 2 | 2 6x + 5 +--R (456x + 760x + 304)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (- 144x + 117440x + 292360x + 236306x + 61638)\|3 +--R / +--R +------------+ +--R 2 +-+ | 2 +--R (81x + 135x + 54)\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1035 +t0:=(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 4 3 2 +--R - 8x + 4x + 126x + 243x + 135 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1035 +r0:=-2/3*(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)^(3/2)-8/9*atanh(1/2*(5+6*x)/_ + (sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+8/3*(3+2*x)^2*(230+283*x)/_ + sqrt(2+5*x+3*x^2)-1888/3*sqrt(2+5*x+3*x^2)-4528/9*(3+2*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 2 | 2 6x + 5 +--R (- 24x - 40x - 16)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|3 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (32896x + 82148x + 66886x + 17670)\|3 +--R / +--R +------------+ +--R 2 +-+ | 2 +--R (27x + 45x + 18)\|3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 of 1035 +t0:=(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 3 2 +--R - 4x + 8x + 51x + 45 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1035 +r0:=-2/3*(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)^(3/2)+376/3*(7+8*x)/_ + sqrt(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R 8744x + 21864x + 17850x + 4742 +--R (2) -------------------------------- +--R +------------+ +--R 2 | 2 +--R (9x + 15x + 6)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 546 + +)clear all + +--S 547 of 1035 +t0:=(5-x)*(3+2*x)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 2 +--R - 2x + 7x + 15 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1035 +r0:=-2/3*(3+2*x)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+8/3*(240+281*x)/_ + sqrt(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R 2248x + 5620x + 4590x + 1222 +--R (2) ------------------------------ +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 1035 +t0:=(5-x)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R - x + 5 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1035 +r0:=-2/3*(29+35*x)/(2+5*x+3*x^2)^(3/2)+280/3*(5+6*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R 3 2 +--R 1680x + 4200x + 3430x + 914 +--R (2) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 1035 +t0:=(5-x)/((3+2*x)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 | 2 +--R (18x + 87x + 164x + 151x + 68x + 12)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1035 +r0:=-2/5*(37+47*x)/(2+5*x+3*x^2)^(3/2)+104/25*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+12/25*(701+836*x)/sqrt(2+5*x+3*x^2) +--R +--R +--R (2) +--R +------------+ +--R 2 | 2 8x + 7 +--R (312x + 520x + 208)\|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 3 2 +-+ +--R (30096x + 75396x + 61654x + 16454)\|5 +--R / +--R +------------+ +--R 2 +-+ | 2 +--R (75x + 125x + 50)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1035 +t0:=(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------------- +--R +------------+ +--R 6 5 4 3 2 | 2 +--R (36x + 228x + 589x + 794x + 589x + 228x + 36)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1035 +r0:=-2/5*(37+47*x)/((3+2*x)*(2+5*x+3*x^2)^(3/2))+408/25*atanh(1/2*(7+8*x)/_ + (sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+4/5*(401+462*x)/((3+2*x)*_ + sqrt(2+5*x+3*x^2))+4416/25*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R 3 2 | 2 +--R (2448x + 7752x + 7752x + 2448)\|3x + 5x + 2 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 4 3 2 +-+ +--R (39744x + 160200x + 233652x + 146430x + 33334)\|5 +--R / +--R +------------+ +--R 3 2 +-+ | 2 +--R (150x + 475x + 475x + 150)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 of 1035 +t0:=(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 7 6 5 4 3 2 +--R (72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108) +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1035 +r0:=-2/5*(37+47*x)/((3+2*x)^2*(2+5*x+3*x^2)^(3/2))+4884/125*_ + atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+4/25*(1907+_ + 2112*x)/((3+2*x)^2*sqrt(2+5*x+3*x^2))+152*sqrt(2+5*x+3*x^2)/(3+2*x)^2+_ + 11808/125*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R +------------+ +--R 4 3 2 | 2 +--R (58608x + 273504x + 463980x + 336996x + 87912)\|3x + 5x + 2 +--R * +--R 8x + 7 +--R atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 5 4 3 2 +-+ +--R (212544x + 1198296x + 2633232x + 2811628x + 1455774x + 292126)\|5 +--R / +--R +------------+ +--R 4 3 2 +-+ | 2 +--R (1500x + 7000x + 11875x + 8625x + 2250)\|5 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 561 + +)clear all + +--S 562 of 1035 +t0:=(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 8 7 6 5 4 3 2 +--R 144x + 1344x + 5416x + 12296x + 17185x + 15126x + 8181x + 2484x +--R + +--R 324 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1035 +r0:=-2/5*(37+47*x)/((3+2*x)^3*(2+5*x+3*x^2)^(3/2))+46108/625*_ + atanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+12/25*_ + (603+638*x)/((3+2*x)^3*sqrt(2+5*x+3*x^2))+47552/375*sqrt(2+5*x+3*x^2)/_ + (3+2*x)^3+1048/15*sqrt(2+5*x+3*x^2)/(3+2*x)^2+_ + 9696/625*sqrt(2+5*x+3*x^2)/(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3319776x + 20471952x + 49519992x + 58511052x + 33612732x +--R + +--R 7469496 +--R * +--R +------------+ +--R | 2 8x + 7 +--R \|3x + 5x + 2 atanh(--------------------) +--R +------------+ +--R +-+ | 2 +--R 2\|5 \|3x + 5x + 2 +--R + +--R 6 5 4 3 2 +--R 1047168x + 8990064x + 30669672x + 53435272x + 50210052x +--R + +--R 24121914x + 4627858 +--R * +--R +-+ +--R \|5 +--R / +--R 5 4 3 2 +-+ +--R (45000x + 277500x + 671250x + 793125x + 455625x + 101250)\|5 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2) +--R +--R +--R 6 5 4 3 2 +------+ +--R (1) (- 24x - 28x + 382x + 1367x + 1872x + 1161x + 270)\|2x + 3 +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1035 +r0:=65/72*(3+2*x)^(9/2)-109/88*(3+2*x)^(11/2)+47/104*(3+2*x)^(13/2)-_ + 1/40*(3+2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 20592x - 30096x + 447048x + 2029120x + 3733305x + 3496257x +--R + +--R 1636821x + 301887 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 6435 +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2) +--R +--R +--R 5 4 3 2 +------+ +--R (1) (- 12x + 4x + 185x + 406x + 327x + 90)\|2x + 3 +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1035 +r0:=65/56*(3+2*x)^(7/2)-109/72*(3+2*x)^(9/2)+47/88*(3+2*x)^(11/2)-_ + 3/104*(3+2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 16632x + 4284x + 375242x + 1116057x + 1364067x + 758349x +--R + +--R 157383 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 9009 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +------+ +--R (1) (- 6x + 11x + 76x + 89x + 30)\|2x + 3 +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1035 +r0:=13/8*(3+2*x)^(5/2)-109/56*(3+2*x)^(7/2)+47/72*(3+2*x)^(9/2)-_ + 3/88*(3+2*x)^(11/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 756x + 1568x + 15627x + 28143x + 19251x + 4617)\|2x + 3 +--R (2) --------------------------------------------------------------- +--R 693 +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)*sqrt(3+2*x) +--R +--R +--R 3 2 +------+ +--R (1) (- 3x + 10x + 23x + 10)\|2x + 3 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1035 +r0:=65/24*(3+2*x)^(3/2)-109/40*(3+2*x)^(5/2)+47/56*(3+2*x)^(7/2)-_ + 1/24*(3+2*x)^(9/2) +--R +--R +--R 4 3 2 +------+ +--R (- 70x + 285x + 1083x + 949x + 303)\|2x + 3 +--R (2) ----------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 576 + +)clear all + +--S 577 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)/sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ----------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1035 +r0:=-109/24*(3+2*x)^(3/2)+47/40*(3+2*x)^(5/2)-3/56*(3+2*x)^(7/2)+_ + 65/8*sqrt(3+2*x) +--R +--R +--R 3 2 +------+ +--R (- 45x + 291x + 223x + 381)\|2x + 3 +--R (2) -------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(3/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ----------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1035 +r0:=47/24*(3+2*x)^(3/2)-3/40*(3+2*x)^(5/2)+(-65/8)/sqrt(3+2*x)-_ + 109/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 9x + 77x - 117x - 501 +--R (2) ------------------------- +--R +------+ +--R 15\|2x + 3 +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(5/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) ------------------------ +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1035 +r0:=(-65/24)/(3+2*x)^(3/2)-1/8*(3+2*x)^(3/2)+109/8/sqrt(3+2*x)+_ + 47/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 3x + 57x + 273x + 263 +--R (2) ------------------------- +--R +------+ +--R (6x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)/(3+2*x)^(7/2) +--R +--R +--R 3 2 +--R - 3x + 10x + 23x + 10 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1035 +r0:=(-13/8)/(3+2*x)^(5/2)+109/24/(3+2*x)^(3/2)+(-47/8)/sqrt(3+2*x)-_ + 3/8*sqrt(3+2*x) +--R +--R +--R 3 2 +--R - 9x - 111x - 245x - 153 +--R (2) -------------------------- +--R 2 +------+ +--R (12x + 36x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 72x - 204x + 958x + 5955x + 13215x + 15577x + 10359x + 3672x +--R + +--R 540 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1035 +r0:=325/288*(3+2*x)^(9/2)-1065/352*(3+2*x)^(11/2)+651/208*(3+2*x)^(13/2)-_ + 359/240*(3+2*x)^(15/2)+165/544*(3+2*x)^(17/2)-9/608*(3+2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R - 15752880x - 51274080x + 262729896x + 1939330008x + 5196312621x +--R + +--R 4 3 2 +--R 7690154020x + 6844462215x + 3651616134x + 1077299892x + 135278424 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 2078505 +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 591 + +)clear all + +--S 592 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^2 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +------+ +--R (- 36x - 48x + 551x + 2151x + 3381x + 2717x + 1104x + 180)\|2x + 3 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1035 +r0:=325/224*(3+2*x)^(7/2)-355/96*(3+2*x)^(9/2)+651/176*(3+2*x)^(11/2)-_ + 359/208*(3+2*x)^(13/2)+11/32*(3+2*x)^(15/2)-9/544*(3+2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 216216x - 348348x + 4324782x + 20560239x + 40692820x +--R + +--R 3 2 +--R 43843941x + 26848368x + 8789688x + 1198476 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 51051 +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^2 +--R +--R +--R 6 5 4 3 2 +------+ +--R (1) (- 18x + 3x + 271x + 669x + 687x + 328x + 60)\|2x + 3 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1035 +r0:=65/32*(3+2*x)^(5/2)-1065/224*(3+2*x)^(7/2)+217/48*(3+2*x)^(9/2)-_ + 359/176*(3+2*x)^(11/2)+165/416*(3+2*x)^(13/2)-3/160*(3+2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 36036x + 2772x + 747579x + 2342620x + 3236325x + 2333766x +--R + +--R 857988x + 128736 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15015 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^2*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +------+ +--R (1) (- 9x + 15x + 113x + 165x + 96x + 20)\|2x + 3 +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1035 +r0:=325/96*(3+2*x)^(3/2)-213/32*(3+2*x)^(5/2)+93/16*(3+2*x)^(7/2)-_ + 359/144*(3+2*x)^(9/2)+15/32*(3+2*x)^(11/2)-9/416*(3+2*x)^(13/2) +--R +--R +--R 6 5 4 3 2 +------+ +--R (- 162x + 297x + 3028x + 5991x + 5292x + 2208x + 396)\|2x + 3 +--R (2) ------------------------------------------------------------------- +--R 117 +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^2/sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1035 +r0:=-355/32*(3+2*x)^(3/2)+651/80*(3+2*x)^(5/2)-359/112*(3+2*x)^(7/2)+_ + 55/96*(3+2*x)^(9/2)-9/352*(3+2*x)^(11/2)+325/32*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +------+ +--R (- 945x + 3500x + 12645x + 15354x + 6252x + 4344)\|2x + 3 +--R (2) -------------------------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1035 +r0:=217/16*(3+2*x)^(3/2)-359/80*(3+2*x)^(5/2)+165/224*(3+2*x)^(7/2)-_ + 1/32*(3+2*x)^(9/2)+(-325/32)/sqrt(3+2*x)-1065/32*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 35x + 150x + 431x + 632x - 432x - 1996 +--R (2) -------------------------------------------- +--R +------+ +--R 35\|2x + 3 +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 606 + +)clear all + +--S 607 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(5/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1035 +r0:=(-325/96)/(3+2*x)^(3/2)-359/48*(3+2*x)^(3/2)+33/32*(3+2*x)^(5/2)-_ + 9/224*(3+2*x)^(7/2)+1065/32/sqrt(3+2*x)+651/16*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 27x + 144x + 215x + 1530x + 7164x + 7024 +--R (2) ---------------------------------------------- +--R +------+ +--R (42x + 63)\|2x + 3 +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(7/2) +--R +--R +--R 5 4 3 2 +--R - 9x + 15x + 113x + 165x + 96x + 20 +--R (1) --------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1035 +r0:=(-65/32)/(3+2*x)^(5/2)+355/32/(3+2*x)^(3/2)+55/32*(3+2*x)^(3/2)-_ + 9/160*(3+2*x)^(5/2)+(-651/16)/sqrt(3+2*x)-359/16*sqrt(3+2*x) +--R +--R +--R 5 4 3 2 +--R - 9x + 70x - 275x - 3300x - 6760x - 4076 +--R (2) -------------------------------------------- +--R 2 +------+ +--R (20x + 60x + 45)\|2x + 3 +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 216x - 972x + 1710x + 22247x + 71336x + 124716x + 135392x +--R + +--R 3 2 +--R 93965x + 40698x + 10044x + 1080 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1035 +r0:=1625/1152*(3+2*x)^(9/2)-7925/1408*(3+2*x)^(11/2)+_ + 16005/1664*(3+2*x)^(13/2)-17201/1920*(3+2*x)^(15/2)+_ + 10475/2176*(3+2*x)^(17/2)-3519/2432*(3+2*x)^(19/2)+_ + 27/128*(3+2*x)^(21/2)-27/2944*(3+2*x)^(23/2) +--R +--R +--R (2) +--R 11 10 9 8 +--R - 897914160x - 4489570800x + 8356902840x + 126274674240x +--R + +--R 7 6 5 4 +--R 465368338149x + 952484547267x + 1244240822034x + 1081998930520x +--R + +--R 3 2 +--R 626194644675x + 232269229971x + 50041179918x + 4766652846 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 47805615 +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 108x - 324x + 1341x + 9112x + 22000x + 29358x + 23659x + 11494x +--R + +--R 3108x + 360 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1035 +r0:=1625/896*(3+2*x)^(7/2)-7925/1152*(3+2*x)^(9/2)+_ + 1455/128*(3+2*x)^(11/2)-17201/1664*(3+2*x)^(13/2)+_ + 2095/384*(3+2*x)^(15/2)-207/128*(3+2*x)^(17/2)+_ + 567/2432*(3+2*x)^(19/2)-9/896*(3+2*x)^(21/2) +--R +--R +--R (2) +--R 10 9 8 7 6 +--R - 160056x - 543348x + 2428218x + 19193889x + 54383679x +--R + +--R 5 4 3 2 +--R 87436314x + 88365578x + 57400347x + 23339691x + 5418846x + 549342 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 15561 +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (- 54x - 81x + 792x + 3368x + 5948x + 5757x + 3194x + 956x + 120) +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1035 +r0:=325/128*(3+2*x)^(5/2)-7925/896*(3+2*x)^(7/2)+_ + 5335/384*(3+2*x)^(9/2)-17201/1408*(3+2*x)^(11/2)+_ + 10475/1664*(3+2*x)^(13/2)-1173/640*(3+2*x)^(15/2)+_ + 567/2176*(3+2*x)^(17/2)-27/2432*(3+2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R - 27567540x - 48648600x + 511413903x + 2573238129x + 5488936698x +--R + +--R 4 3 2 +--R 6671966560x + 4954126305x + 2231396337x + 561646746x + 61003962 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 4849845 +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^3*sqrt(3+2*x) +--R +--R +--R 7 5 4 3 2 +------+ +--R (1) (- 27x + 396x + 1090x + 1339x + 870x + 292x + 40)\|2x + 3 +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1035 +r0:=1625/384*(3+2*x)^(3/2)-1585/128*(3+2*x)^(5/2)+_ + 16005/896*(3+2*x)^(7/2)-17201/1152*(3+2*x)^(9/2)+_ + 10475/1408*(3+2*x)^(11/2)-3519/1664*(3+2*x)^(13/2)+_ + 189/640*(3+2*x)^(15/2)-27/2176*(3+2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 2432430x - 243243x + 47045691x + 157479462x + 243619810x +--R + +--R 3 2 +--R 212153055x + 107295183x + 29433414x + 3591558 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 765765 +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^3/sqrt(3+2*x) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1035 +r0:=-7925/384*(3+2*x)^(3/2)+3201/128*(3+2*x)^(5/2)-17201/896*(3+2*x)^(7/2)+_ + 10475/1152*(3+2*x)^(9/2)-3519/1408*(3+2*x)^(11/2)+567/1664*(3+2*x)^(13/2)-_ + 9/640*(3+2*x)^(15/2)+1625/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 81081x + 130977x + 1407294x + 3109960x + 3285105x + 1924641x +--R + +--R 535098x + 196506 +--R * +--R +------+ +--R \|2x + 3 +--R / +--R 45045 +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(3/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1035 +r0:=5335/128*(3+2*x)^(3/2)-17201/640*(3+2*x)^(5/2)+10475/896*(3+2*x)^(7/2)-_ + 391/128*(3+2*x)^(9/2)+567/1408*(3+2*x)^(11/2)-27/1664*(3+2*x)^(13/2)+_ + (-1625/128)/sqrt(3+2*x)-7925/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 10395x + 19845x + 180530x + 392500x + 398339x + 256433x - 77138x +--R + +--R - 431614 +--R / +--R +------+ +--R 5005\|2x + 3 +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(5/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1035 +r0:=(-1625/384)/(3+2*x)^(3/2)-17201/384*(3+2*x)^(3/2)+2095/128*(3+2*x)^(5/2)-_ + 3519/896*(3+2*x)^(7/2)+63/128*(3+2*x)^(9/2)-27/1408*(3+2*x)^(11/2)+_ + 7925/128/sqrt(3+2*x)+16005/128*sqrt(3+2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 567x + 1323x + 9666x + 21360x + 17663x + 42003x + 184566x + 181486 +--R -------------------------------------------------------------------------- +--R +------+ +--R (462x + 693)\|2x + 3 +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(7/2) +--R +--R +--R 7 5 4 3 2 +--R - 27x + 396x + 1090x + 1339x + 870x + 292x + 40 +--R (1) ---------------------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1035 +r0:=(-325/128)/(3+2*x)^(5/2)+7925/384/(3+2*x)^(3/2)+10475/384*(3+2*x)^(3/2)-_ + 3519/640*(3+2*x)^(5/2)+81/128*(3+2*x)^(7/2)-3/128*(3+2*x)^(9/2)+_ + (-16005/128)/sqrt(3+2*x)-17201/128*sqrt(3+2*x) +--R +--R +--R 7 6 5 4 3 2 +--R - 45x + 135x + 702x + 1940x - 3195x - 41805x - 85070x - 51162 +--R (2) ------------------------------------------------------------------- +--R 2 +------+ +--R (60x + 180x + 135)\|2x + 3 +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1035 +r0:=526/81*(3+2*x)^(3/2)+62/45*(3+2*x)^(5/2)-2/21*(3+2*x)^(7/2)+_ + 12*atanh(sqrt(3+2*x))-4250/81*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+_ + 3278/81*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 34020\|3 atanh(\|2x + 3 ) - 148750\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (- 2160x + 5904x + 69112x + 197824)\|3 \|2x + 3 +--R / +--R +-+ +--R 2835\|3 +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1035 +r0:=62/27*(3+2*x)^(3/2)-2/15*(3+2*x)^(5/2)+12*atanh(sqrt(3+2*x))-_ + 850/27*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+526/27*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 1620\|3 atanh(\|2x + 3 ) - 4250\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +------+ +--R (- 72x + 404x + 3398)\|3 \|2x + 3 +--R / +--R +-+ +--R 135\|3 +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------- +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1035 +r0:=-2/9*(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-170/9*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(5/3)+62/9*sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +--R 108\|3 atanh(\|2x + 3 ) - 170\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +------+ +--R (- 4x + 56)\|3 \|2x + 3 +--R / +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1035 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ------------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1035 +r0:=12*atanh(sqrt(3+2*x))-34/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-_ + 2/3*sqrt(3+2*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ +-+ \|3 \|2x + 3 +-+ +------+ +--R 36\|3 atanh(\|2x + 3 ) - 34\|5 atanh(-------------) - 2\|3 \|2x + 3 +--R +-+ +--R \|5 +--R (2) -------------------------------------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 1035 +t0:=(5-x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) ----------------------- +--R 2 +------+ +--R (3x + 5x + 2)\|2x + 3 +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1035 +r0:=12*atanh(sqrt(3+2*x))-34*atanh(sqrt(3/5)*sqrt(3+2*x))/sqrt(15) +--R +--R +--R +-+ +------+ +--R +--+ +------+ \|3 \|2x + 3 +--R 12\|15 atanh(\|2x + 3 ) - 34atanh(-------------) +--R +-+ +--R \|5 +--R (2) ------------------------------------------------ +--R +--+ +--R \|15 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R +-+ +-+ +--+ +--R - 17\|3 \|5 \|15 + 255 +--R (3) ----------------------- +--R +------+ +--R (45x + 30)\|2x + 3 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------- +--R 3 2 +------+ +--R (6x + 19x + 19x + 6)\|2x + 3 +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1035 +r0:=12*atanh(sqrt(3+2*x))-34/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-26/5)/sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ +------+ +-+ +------+ \|3 \|2x + 3 +--R 60\|5 \|2x + 3 atanh(\|2x + 3 ) - 34\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +--R - 26\|5 +--R / +--R +-+ +------+ +--R 5\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------- +--R 4 3 2 +------+ +--R (12x + 56x + 95x + 69x + 18)\|2x + 3 +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1035 +r0:=(-26/15)/(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-102/25*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(3/5)+(-198/25)/sqrt(3+2*x) +--R +--R +--R (2) +--R +-+ +------+ +------+ +--R (1800x + 2700)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +-+ +--R (- 612x - 918)\|3 \|2x + 3 atanh(-------------) + (- 1188x - 1912)\|5 +--R +-+ +--R \|5 +--R / +--R +-+ +------+ +--R (150x + 225)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------- +--R 5 4 3 2 +------+ +--R (24x + 148x + 358x + 423x + 243x + 54)\|2x + 3 +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1035 +r0:=(-26/25)/(3+2*x)^(5/2)+(-66/25)/(3+2*x)^(3/2)+12*atanh(sqrt(3+2*x))-_ + 306/125*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-1194/125)/sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +------+ +--R (6000x + 18000x + 13500)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ +------+ \|3 \|2x + 3 +--R (- 1224x - 3672x - 2754)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +--R (- 4776x - 14988x - 11866)\|5 +--R / +--R 2 +-+ +------+ +--R (500x + 1500x + 1125)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1035 +r0:=826/27*(3+2*x)^(3/2)+70/3*(3+2*x)^(5/2)-(3+2*x)^(7/2)*(29+35*x)/_ + (2+5*x+3*x^2)-154*atanh(sqrt(3+2*x))+2800/27*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(5/3)+1358/27*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 12474x - 20790x - 8316)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (8400x + 14000x + 5600)\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (- 48x + 400x - 1843x - 2129)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (81x + 135x + 54)\|3 +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1035 +r0:=70/3*(3+2*x)^(3/2)-(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)-_ + 130*atanh(sqrt(3+2*x))+100*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+_ + 30*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 1170x - 1950x - 780)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (900x + 1500x + 600)\|5 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +------+ +--R (- 8x - 209x - 183)\|3 \|2x + 3 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^2 +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1035 +r0:=-(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)-106*atanh(sqrt(3+2*x))+_ + 248/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+70/3*sqrt(3+2*x) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 954x - 1590x - 636)\|3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +-+ +------+ +--R (744x + 1240x + 496)\|5 atanh(-------------) + (- 139x - 121)\|3 \|2x + 3 +--R +-+ +--R \|5 +--R / +--R 2 +-+ +--R (9x + 15x + 6)\|3 +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1035 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2 +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) --------------------------- +--R 4 3 2 +--R 9x + 30x + 37x + 20x + 4 +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1035 +r0:=-82*atanh(sqrt(3+2*x))+316*atanh(sqrt(3/5)*sqrt(3+2*x))/sqrt(15)-_ + (29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 2 +--+ +------+ +--R (- 246x - 410x - 164)\|15 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 \|3 \|2x + 3 +--+ +------+ +--R (948x + 1580x + 632)atanh(-------------) + (- 35x - 29)\|15 \|2x + 3 +--R +-+ +--R \|5 +--R / +--R 2 +--+ +--R (3x + 5x + 2)\|15 +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R +-+ +-+ +--+ +--R 158\|3 \|5 \|15 - 2370 +--R (3) ----------------------- +--R +------+ +--R (45x + 30)\|2x + 3 +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 1035 +t0:=(5-x)/((2+5*x+3*x^2)^2*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R 4 3 2 +------+ +--R (9x + 30x + 37x + 20x + 4)\|2x + 3 +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1035 +r0:=-58*atanh(sqrt(3+2*x))+384/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 3/5*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 2 +-+ +------+ +--R (- 870x - 1450x - 580)\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ \|3 \|2x + 3 +--R (1152x + 1920x + 768)\|3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R +-+ +------+ +--R (- 141x - 111)\|5 \|2x + 3 +--R / +--R 2 +-+ +--R (15x + 25x + 10)\|5 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +------+ +--R (18x + 87x + 164x + 151x + 68x + 12)\|2x + 3 +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1035 +r0:=-34*atanh(sqrt(3+2*x))+1356/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-506/25)/sqrt(3+2*x)-3/5*(37+47*x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R (2) +--R 2 +-+ +------+ +------+ +--R (- 2550x - 4250x - 1700)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 2 +-+ +------+ \|3 \|2x + 3 +--R (4068x + 6780x + 2712)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 2 +-+ +--R (- 1518x - 3235x - 1567)\|5 +--R / +--R 2 +-+ +------+ +--R (75x + 125x + 50)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 678 + +)clear all + +--S 679 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^2) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (36x + 228x + 589x + 794x + 589x + 228x + 36)\|2x + 3 +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1035 +r0:=(-262/15)/(3+2*x)^(3/2)-3/5*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2))-_ + 10*atanh(sqrt(3+2*x))+936/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + (-686/25)/sqrt(3+2*x) +--R +--R +--R (2) +--R 3 2 +-+ +------+ +------+ +--R (- 4500x - 14250x - 14250x - 4500)\|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 3 2 +-+ +------+ \|3 \|2x + 3 +--R (16848x + 53352x + 53352x + 16848)\|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +--R (- 12348x - 43032x - 47767x - 16633)\|5 +--R / +--R 3 2 +-+ +------+ +--R (450x + 1425x + 1425x + 450)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^2) +--R +--R +--R (1) +--R - x + 5 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +------+ +--R (72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108)\|2x + 3 +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1035 +r0:=(-2114/125)/(3+2*x)^(5/2)+(-7042/375)/(3+2*x)^(3/2)-3/5*(37+47*x)/_ + ((3+2*x)^(5/2)*(2+5*x+3*x^2))+14*atanh(sqrt(3+2*x))+_ + 15876/625*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-24626/625)/sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (315000x + 1470000x + 2493750x + 1811250x + 472500)\|5 \|2x + 3 +--R * +--R +------+ +--R atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +------+ +--R (571536x + 2667168x + 4524660x + 3286332x + 857304)\|3 \|2x + 3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +--R (- 886536x - 4348428x - 7782530x - 5977997x - 1646109)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (22500x + 105000x + 178125x + 129375x + 33750)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 1035 +t0:=(5-x)*(3+2*x)^(9/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 5 4 3 2 +------+ +--R (- 16x - 16x + 264x + 864x + 999x + 405)\|2x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1035 +r0:=-3151/9*(3+2*x)^(3/2)-283*(3+2*x)^(5/2)-1/2*(3+2*x)^(9/2)*(29+35*x)/_ + (2+5*x+3*x^2)^2+3/2*(3+2*x)^(7/2)*(230+283*x)/(2+5*x+3*x^2)+_ + 1962*atanh(sqrt(3+2*x))-13675/9*atanh(sqrt(3/5)*sqrt(3+2*x))*_ + sqrt(5/3)-3983/9*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (317844x + 1059480x + 1306692x + 706320x + 141264)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 246150x - 820500x - 1011950x - 547000x - 109400)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +------+ +--R (- 192x + 45083x + 112467x + 90465x + 23327)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (162x + 540x + 666x + 360x + 72)\|3 +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1035 +r0:=-847/3*(3+2*x)^(3/2)-1/2*(3+2*x)^(7/2)*(29+35*x)/(2+5*x+3*x^2)^2+_ + 7/2*(3+2*x)^(5/2)*(100+121*x)/(2+5*x+3*x^2)+1582*atanh(sqrt(3+2*x))-_ + 1225*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-357*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (85428x + 284760x + 351204x + 189840x + 37968)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 66150x - 220500x - 271950x - 147000x - 29400)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (12443x + 30979x + 25073x + 6555)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1035 +r0:=-1/2*(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)^2+5/2*(3+2*x)^(3/2)*_ + (142+169*x)/(2+5*x+3*x^2)+1250*atanh(sqrt(3+2*x))-_ + 2905/3*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-845/3*sqrt(3+2*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (67500x + 225000x + 277500x + 150000x + 30000)\|3 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 52290x - 174300x - 214970x - 116200x - 23240)\|5 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (9825x + 24497x + 19891x + 5237)\|3 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (54x + 180x + 222x + 120x + 24)\|3 +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^3 +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1035 +r0:=-1/2*(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)^2+966*atanh(sqrt(3+2*x))-_ + 1247*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+3/2*(240+281*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (17388x + 57960x + 71484x + 38640x + 7728)\|5 atanh(\|2x + 3 ) +--R + +--R +-+ +------+ +--R 4 3 2 +-+ \|3 \|2x + 3 +--R (- 22446x - 74820x - 92278x - 49880x - 9976)\|3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (2529x + 6305x + 5123x + 1353)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (18x + 60x + 74x + 40x + 8)\|5 +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 of 1035 +t0:=(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^3 +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ---------------------------------------------- +--R 6 5 4 3 2 +--R 27x + 135x + 279x + 305x + 186x + 60x + 8 +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1035 +r0:=730*atanh(sqrt(3+2*x))-4713/5*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 1/2*(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+3/10*(878+1063*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (65700x + 219000x + 270100x + 146000x + 29200)\|5 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 84834x - 282780x - 348762x - 188520x - 37704)\|3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (9567x + 23847x + 19373x + 5123)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (90x + 300x + 370x + 200x + 40)\|5 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 1035 +t0:=(5-x)/((2+5*x+3*x^2)^3*sqrt(3+2*x)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (27x + 135x + 279x + 305x + 186x + 60x + 8)\|2x + 3 +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1035 +r0:=542*atanh(sqrt(3+2*x))-17463/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-_ + 3/10*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+1/50*(9734+11739*x)*_ + sqrt(3+2*x)/(2+5*x+3*x^2) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (243900x + 813000x + 1002700x + 542000x + 108400)\|5 atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +--R (- 314334x - 1047780x - 1292262x - 698520x - 139704)\|3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 3 2 +-+ +------+ +--R (35217x + 87897x + 71443x + 18913)\|5 \|2x + 3 +--R / +--R 4 3 2 +-+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^3) +--R +--R +--R - x + 5 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +------+ +--R (54x + 351x + 963x + 1447x + 1287x + 678x + 196x + 24)\|2x + 3 +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1035 +r0:=402*atanh(sqrt(3+2*x))-12717/25*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + 2667/25/sqrt(3+2*x)-3/10*(37+47*x)/((2+5*x+3*x^2)^2*sqrt(3+2*x))+_ + 1/10*(1888+2229*x)/((2+5*x+3*x^2)*sqrt(3+2*x)) +--R +--R +--R (2) +--R 4 3 2 +-+ +------+ +--R (180900x + 603000x + 743700x + 402000x + 80400)\|5 \|2x + 3 +--R * +--R +------+ +--R atanh(\|2x + 3 ) +--R + +--R 4 3 2 +-+ +------+ +--R (- 228906x - 763020x - 941058x - 508680x - 101736)\|3 \|2x + 3 +--R * +--R +-+ +------+ +--R \|3 \|2x + 3 +--R atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 4 3 2 +-+ +--R (48006x + 193455x + 281403x + 175465x + 39661)\|5 +--R / +--R 4 3 2 +-+ +------+ +--R (450x + 1500x + 1850x + 1000x + 200)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 8 7 6 5 4 3 2 +--R (108x + 864x + 2979x + 5783x + 6915x + 5217x + 2426x + 636x + 72) +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1035 +r0:=7451/75/(3+2*x)^(3/2)-3/10*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^2)+_ + 1/50*(9146+10551*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2))+310*_ + atanh(sqrt(3+2*x))-45603/125*atanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+_ + 6853/125/sqrt(3+2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 4185000x + 20227500x + 38130000x + 35107500x + 15810000x +--R + +--R 2790000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R 5 4 3 2 +--R - 4925124x - 23804766x - 44873352x - 41316318x - 18606024x +--R + +--R - 3283416 +--R * +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +--R \|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 5 4 3 2 +-+ +--R (740124x + 4247856x + 9453447x + 10168583x + 5278129x + 1057511)\|5 +--R / +--R 5 4 3 2 +-+ +------+ +--R (13500x + 65250x + 123000x + 113250x + 51000x + 9000)\|5 \|2x + 3 +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^3) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 9 8 7 6 5 4 3 +--R 216x + 2052x + 8550x + 20503x + 31179x + 31179x + 20503x +--R + +--R 2 +--R 8550x + 2052x + 216 +--R * +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1035 +r0:=56399/625/(3+2*x)^(5/2)+102697/1875/(3+2*x)^(3/2)-3/10*(37+47*x)/_ + ((3+2*x)^(5/2)*(2+5*x+3*x^2)^2)+1/50*(8852+9957*x)/((3+2*x)^(5/2)*_ + (2+5*x+3*x^2))+266*atanh(sqrt(3+2*x))-806841/3125*atanh(sqrt(3/5)*_ + sqrt(3+2*x))*sqrt(3/5)+(-24409/3125)/sqrt(3+2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 179550000x + 1137150000x + 2937637500x + 3960075000x +--R + +--R 2 +--R 2937637500x + 1137150000x + 179550000 +--R * +--R +-+ +------+ +------+ +--R \|5 \|2x + 3 atanh(\|2x + 3 ) +--R + +--R 6 5 4 3 +--R - 174277656x - 1103758488x - 2851376094x - 3843790524x +--R + +--R 2 +--R - 2851376094x - 1103758488x - 174277656 +--R * +--R +-+ +------+ +--R +-+ +------+ \|3 \|2x + 3 +--R \|3 \|2x + 3 atanh(-------------) +--R +-+ +--R \|5 +--R + +--R 6 5 4 3 2 +--R - 5272344x - 14906052x + 18312714x + 114099329x + 160041829x +--R + +--R 94082723x + 20250051 +--R * +--R +-+ +--R \|5 +--R / +--R 6 5 4 3 2 +--R 675000x + 4275000x + 11043750x + 14887500x + 11043750x + 4275000x +--R + +--R 675000 +--R * +--R +-+ +------+ +--R \|5 \|2x + 3 +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 711 + +)clear all + +--S 712 of 1035 +t0:=(5+10*x+sqrt(35))/((2+3*x+5*x^2)*sqrt(1+2*x)) +--R +--R +--R +--+ +--R \|35 + 10x + 5 +--R (1) ----------------------- +--R 2 +------+ +--R (5x + 3x + 2)\|2x + 1 +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1035 +r0:=-2*atan((-sqrt(10+20*x)+sqrt(2+sqrt(35)))/sqrt(-2+sqrt(35)))*_ + sqrt(10/(-2+sqrt(35)))+2*atan((sqrt(10+20*x)+sqrt(2+sqrt(35)))/_ + sqrt(-2+sqrt(35)))*sqrt(10/(-2+sqrt(35))),-2*atan((-10*sqrt(1+2*x)+_ + sqrt(10*(2+sqrt(35))))/sqrt(10*(-2+sqrt(35))))*sqrt(10/(-2+sqrt(35)))+_ + 2*atan((10*sqrt(1+2*x)+sqrt(10*(2+sqrt(35))))/sqrt(10*(-2+sqrt(35))))*_ + sqrt(10/(-2+sqrt(35))) +--R +--R +--R (2) +--R [ +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 + \|20x + 10 +--R 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R + +--R +---------+ +--R +------------+ | +--+ +--------+ +--R | +--+ \|\|35 + 2 - \|20x + 10 +--R - 2\|10\|35 + 20 atan(--------------------------) +--R +---------+ +--R | +--+ +--R \|\|35 - 2 +--R / +--R +--+ +--R \|31 +--R , +--R +--R +------------+ +--R +------------+ | +--+ +------+ +--R | +--+ \|10\|35 + 20 + 10\|2x + 1 +--R 2\|10\|35 + 20 atan(-----------------------------) +--R +------------+ +--R | +--+ +--R \|10\|35 - 20 +--R + +--R +------------+ +--R +------------+ | +--+ +------+ +--R | +--+ \|10\|35 + 20 - 10\|2x + 1 +--R - 2\|10\|35 + 20 atan(-----------------------------) +--R +------------+ +--R | +--+ +--R \|10\|35 - 20 +--R / +--R +--+ +--R \|31 +--R ] +--R Type: Tuple(Expression(Integer)) +--E 713 + +--S 714 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) +--R +---------+ +--R +--+ +--+ +--+ +------+ +--------+ | +--+ +--R (- \|31 \|35 + (- 10x - 5)\|31 )\|2x + 1 \|20x + 10 \|\|35 - 2 +--R * +--R +------------+ +--R | +--+ +--R \|10\|35 + 20 +--R + +--R +--+ 2 +--R (620x + 310)\|35 + 6200x + 6200x + 1550 +--R / +--R 3 2 +------+ +--R (3100x + 3410x + 2170x + 620)\|2x + 1 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 3 2 +------+ | 2 +--R (1) (- 4x + 8x + 51x + 45)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1035 +--r0:=730/891*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)-2/33*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(3/2)+12130/6237*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 32567/48114*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-63541/168399*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+_ +-- 1/56133*(250447+280359*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 716 + +--S 717 of 1035 +--d0:=D(m0,x) +--E 717 + +)clear all + +--S 718 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R 2 +------+ | 2 +--R (1) (- 2x + 7x + 15)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1035 +--r0:=-2/27*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)+202/189*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+4729/1458*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-7892/5103*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+1/8505*(27914+30033*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 719 + +--S 720 of 1035 +--d0:=D(m0,x) +--E 720 + +)clear all + +--S 721 of 1035 +t0:=(5-x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--R +--R +--R +------------+ +--R +------+ | 2 +--R (1) (- x + 5)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1035 +--r0:=-2/21*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+697/162*elliptic_e(asin(sqrt(3+_ +-- 2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 881/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1/945*(2327+2169*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 722 + +--S 723 of 1035 +--d0:=D(m0,x) +--E 723 + +)clear all + +--S 724 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1035 +--r0:=761/54*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-94/27*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/45*(88-9*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 725 + +--S 726 of 1035 +--d0:=D(m0,x) +--E 726 + +)clear all + +--S 727 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1035 +--r0:=61/9*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-121/18*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-1/3*(21+x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 728 + +--S 729 of 1035 +--d0:=D(m0,x) +--E 729 + +)clear all + +--S 730 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) ------------------------ +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1035 +--r0:=67/6*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-8/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-1/3*(11+3*x)*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+67/15*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 731 + +--S 732 of 1035 +--d0:=D(m0,x) +--E 732 + +)clear all + +--S 733 of 1035 +t0:=(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R | 2 +--R (- x + 5)\|3x + 5x + 2 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1035 +--r0:=49/50*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-11/25*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+9/25*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+1/5*(1+5*x)*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(5/2)+49/125*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 734 + +--S 735 of 1035 +--d0:=D(m0,x) +--E 735 + +)clear all + +--S 736 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R (1) +--R 6 5 4 3 2 +------+ +--R (- 24x - 28x + 382x + 1367x + 1872x + 1161x + 270)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1035 +--r0:=2086/1989*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)+42/85*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(5/2)-2/51*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2)+_ +-- 1/196911*(591064+699377*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 108934/65637*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-2200387/21266388*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1284593/10633194*elliptic_f(asin(sqrt(3+_ +-- 2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/17721990*(6668831+8076357*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 737 + +--S 738 of 1035 +--d0:=D(m0,x) +--E 738 + +)clear all + +--S 739 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (1) (- 12x + 4x + 185x + 406x + 327x + 90)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1035 +--r0:=202/351*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)-2/45*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(5/2)+1/243243*(534271+629153*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+13318/11583*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+_ +-- 207851/3752892*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+397651/6567561*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-1/21891870*(6006884+7817373*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 740 + +--S 741 of 1035 +--d0:=D(m0,x) +--E 741 + +)clear all + +--S 742 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (1) (- 6x + 11x + 76x + 89x + 30)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1035 +--r0:=-2/39*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)+1/27027*(43822+50771*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+886/1287*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+152657/416988*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 35611/1459458*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-1/2432430*(486863+783711*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 743 + +--S 744 of 1035 +--d0:=D(m0,x) +--E 744 + +)clear all + +--S 745 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x) +--R +--R +--R +------------+ +--R 3 2 +------+ | 2 +--R (1) (- 3x + 10x + 23x + 10)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1035 +--r0:=1/99*(119+127*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-_ +-- 2/33*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+15283/10692*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-706/2673*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/8910*(1246+3987*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 746 + +--S 747 of 1035 +--d0:=D(m0,x) +--E 747 + +)clear all + +--S 748 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1035 +--r0:=1/63*(52-7*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+11123/972*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-8179/3402*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/5670*(107+12429*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 749 + +--S 750 of 1035 +--d0:=D(m0,x) +--E 750 + +)clear all + +--S 751 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1035 +--r0:=-1/7*(47+x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x)-2411/36*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+899/63*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 1/210*(136-2493*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 752 + +--S 753 of 1035 +--d0:=D(m0,x) +--E 753 + +)clear all + +--S 754 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1035 +--r0:=-1/15*(37+3*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2)+367/4*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-39/2*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/10*(241+69*x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 755 + +--S 756 of 1035 +--d0:=D(m0,x) +--E 756 + +)clear all + +--S 757 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R 3 2 | 2 +--R (- 3x + 10x + 23x + 10)\|3x + 5x + 2 +--R (1) ---------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1035 +--r0:=-1/15*(27+5*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2)-2779/60*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+148/15*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1/30*(707+411*x)*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-2779/150*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 758 + +--S 759 of 1035 +--d0:=D(m0,x) +--E 759 + +)clear all + +--S 760 of 1035 +t0:=(5-x)*(3+2*x)^(9/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 144x - 624x + 1304x + 14784x + 44295x + 70799x + 67449x +--R + +--R 2 +--R 38421x + 12096x + 1620 +--R * +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1035 +--r0:=222422/200583*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)+25418/35397*_ +-- (3+2*x)^(5/2)*(2+5*x+3*x^2)^(7/2)+1538/4347*(3+2*x)^(7/2)*_ +-- (2+5*x+3*x^2)^(7/2)-2/69*(3+2*x)^(9/2)*(2+5*x+3*x^2)^(7/2)-_ +-- 5/97580821338*(5514025312+6580844291*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+1/2323352889*(6295010279+7506271641*x)*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+8515726/5415741*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+_ +-- 12104518303/1505532672072*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-18804590219/5269364352252*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1/1756454784084*(62607985973+_ +-- 65705093631*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 761 + +--S 762 of 1035 +--d0:=D(m0,x) +--E 762 + +)clear all + +--S 763 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 72x - 204x + 958x + 5955x + 13215x + 15577x + 10359x + 3672x +--R + +--R 540 +--R * +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1035 +--r0:=2218/2907*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)+202/513*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(7/2)-2/63*(3+2*x)^(7/2)*(2+5*x+3*x^2)^(7/2)-_ +-- 5/108785754*(4498331+5420233*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 1/2590137*(5130052+6113283*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+_ +-- 89294/78489*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+18269789/1678408776*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-10791761/2937215358*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1/1958143572*(51436624+44779653*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 764 + +--S 765 of 1035 +--d0:=D(m0,x) +--E 765 + +)clear all + +--S 766 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +------+ +--R (- 36x - 48x + 551x + 2151x + 3381x + 2717x + 1104x + 180)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1035 +--r0:=430/969*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)-2/57*(3+2*x)^(5/2)*_ +-- (2+5*x+3*x^2)^(7/2)-125/52378326*(64006+79583*x)*(2+5*x+3*x^2)^(3/2)*_ +-- sqrt(3+2*x)+25/1247103*(72737+86493*x)*(2+5*x+3*x^2)^(5/2)*_ +-- sqrt(3+2*x)+2350/2907*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+_ +-- 16503475/808122744*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-15117425/2828429604*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+25/942809868*(749099+216603*x)*_ +-- sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 767 + +--S 768 of 1035 +--d0:=D(m0,x) +--E 768 + +)clear all + +--S 769 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2) +--R +--R +--R (1) +--R +------------+ +--R 6 5 4 3 2 +------+ | 2 +--R (- 18x + 3x + 271x + 669x + 687x + 328x + 60)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1035 +--r0:=-2/51*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)-1/8270262*(949997+1332121*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/984555*(1063774+1253571*x)*_ +-- (2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+1166/2295*(2+5*x+3*x^2)^(7/2)*_ +-- sqrt(3+2*x)+34355693/127598328*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6809266/111648537*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+1/744323580*(12174838-22593339*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 770 + +--S 771 of 1035 +--d0:=D(m0,x) +--E 771 + +)clear all + +--S 772 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x) +--R +--R +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (1) (- 9x + 15x + 113x + 165x + 96x + 20)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1035 +--r0:=-1/162162*(15076+34643*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/19305*_ +-- (15467+17193*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-_ +-- 2/45*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)+2742319/2501928*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-2066087/8756748*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 1/14594580*(287729-2667537*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 773 + +--S 774 of 1035 +--d0:=D(m0,x) +--E 774 + +)clear all + +--S 775 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/sqrt(3+2*x) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R +------+ +--R \|2x + 3 +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1035 +--r0:=-5/18018*(563+4669*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+_ +-- 1/429*(224-33*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+651617/277992*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-242783/486486*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+_ +-- 1/324324*(34372-676791*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 776 + +--S 777 of 1035 +--d0:=D(m0,x) +--E 777 + +)clear all + +--S 778 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(3/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R +------+ +--R (2x + 3)\|2x + 3 +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1035 +--r0:=-1/11*(73+x)*(2+5*x+3*x^2)^(5/2)/sqrt(3+2*x)+5/1386*(218+3031*x)*_ +-- (2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-451331/21384*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+336013/74844*elliptic_f(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-_ +-- 1/24948*(21871-471213*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 779 + +--S 780 of 1035 +--d0:=D(m0,x) +--E 780 + +)clear all + +--S 781 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(5/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 2 +------+ +--R (4x + 12x + 9)\|2x + 3 +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1035 +--r0:=-1/9*(21+x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(3/2)+5/126*(745+121*x)*_ +-- (2+5*x+3*x^2)^(3/2)/sqrt(3+2*x)+33335/648*elliptic_e(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-_ +-- 6205/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+5/756*(326-6957*x)*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 782 + +--S 783 of 1035 +--d0:=D(m0,x) +--E 783 + +)clear all + +--S 784 of 1035 +t0:=(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(7/2) +--R +--R +--R +------------+ +--R 5 4 3 2 | 2 +--R (- 9x + 15x + 113x + 165x + 96x + 20)\|3x + 5x + 2 +--R (1) -------------------------------------------------------- +--R 3 2 +------+ +--R (8x + 36x + 54x + 27)\|2x + 3 +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1035 +--r0:=1/210*(2291+879*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2)-1/35*(53+5*x)*_ +-- (2+5*x+3*x^2)^(5/2)/(3+2*x)^(5/2)-2333/8*elliptic_e(asin(sqrt(3+2*x)),_ +-- 3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+1737/28*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-1/140*(10763+3117*x)*_ +-- sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 785 + +--S 786 of 1035 +--d0:=D(m0,x) +--E 786 + +)clear all + +--S 787 of 1035 +t0:=(A+B*x)*(d+e*x)^(1/2)/(a+b*x+c*x^2)^(1/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1035 +--r0:=2/3*B*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c-1/3*elliptic_f(asin(sqrt(2)*_ +-- sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*_ +-- (b*B*d-3*A*c*d+a*B*e)+(B*c*d-2*b*B*e+3*A*c*e)*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^(5/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- 1/3*(B*c*d-2*b*B*e+3*A*c*e)*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*_ +-- sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (c^(5/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 788 + +--S 789 of 1035 +--d0:=D(m0,x) +--E 789 + +)clear all + +--S 790 of 1035 +t0:=(A+B*x)/((d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)) +--R +--R +--R B x + A +--R (1) --------------------------- +--R +--------------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1035 +--r0:=-elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*(b+_ +-- sqrt(b^2-4*a*c))))*(b*B-2*A*c-B*sqrt(b^2-4*a*c))*sqrt(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c))))/(c^(3/2)*e*sqrt(2)*sqrt(a+b*x+c*x^2))-_ +-- B*elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*e^2*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 791 + +--S 792 of 1035 +--d0:=D(m0,x) +--E 792 + +)clear all + +--S 793 of 1035 +t0:=(A+B*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^(1/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------ +--R +--------------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1035 +--r0:=2*(B*d-A*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))+_ +-- elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-_ +-- sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c))))*(-2*(b*B*d-A*c*d-a*B*e)+(B*d-A*e)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-_ +-- b*e+e*sqrt(b^2-4*a*c)))*sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (e*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(B*d-A*e)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*_ +-- (b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*_ +-- (b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*_ +-- (b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(e^2*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 794 + +--S 795 of 1035 +--d0:=D(m0,x) +--E 795 + +)clear all + +--S 796 of 1035 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1035 +--r0:=-2*(A*b-2*a*B-(b*B-2*A*c)*x)*(d+e*x)^(3/2)/((b^2-4*a*c)*_ +-- sqrt(a+b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/_ +-- (c*(b^2-4*a*c))+elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*(b^2*B*d-2*a*c*(3*B*d+A*e)+_ +-- b*(A*c*d+a*B*e))+(b*B*c*d-2*A*c^2*d-2*b^2*B*e+A*b*c*e+6*a*B*c*e)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(5/2)*(b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))-(2*b^2*B*e-_ +-- b*c*(B*d+A*e)+2*c*(A*c*d-3*a*B*e))*elliptic_e(asin(sqrt(2)*sqrt(c)*_ +-- sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))),(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/_ +-- (2*c*d-b*e+e*sqrt(b^2-4*a*c)))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (c^(5/2)*(b^2-4*a*c)*e*sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 797 + +--S 798 of 1035 +--d0:=D(m0,x) +--E 798 + +)clear all + +--S 799 of 1035 +t0:=(A+B*x)*(d+e*x)^(1/2)/(a+b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) --------------------------------- +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1035 +--r0:=-2*(A*b-2*a*B-(b*B-2*A*c)*x)*sqrt(d+e*x)/((b^2-4*a*c)*_ +-- sqrt(a+b*x+c*x^2))+elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*A*b*c-4*a*B*c+(b*B-2*A*c)*_ +-- (b-sqrt(b^2-4*a*c)))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/_ +-- (c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(a+b*x+c*x^2))+(b*B-2*A*c)*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(c^(3/2)*(b^2-4*a*c)*e*_ +-- sqrt(2)*sqrt(a+b*x+c*x^2)) +--E 800 + +--S 801 of 1035 +--d0:=D(m0,x) +--E 801 + +)clear all + +--S 802 of 1035 +t0:=(A+B*x)/((d+e*x)^(1/2)*(a+b*x+c*x^2)^(3/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------- +--R +--------------+ +--R 2 +-------+ | 2 +--R (c x + b x + a)\|e x + d \|c x + b x + a +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1035 +--r0:=2*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-_ +-- 2*a*B*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(a+b*x+c*x^2))-elliptic_f(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/_ +-- sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))),(2*c*d-e*(b-sqrt(b^2-4*a*c)))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*b^2*B*d-4*a*c*(B*d-A*e)-_ +-- 2*b*(A*c*d+a*B*e)-(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(2*c*d-b*e+e*sqrt(b^2-4*a*c))*sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/_ +-- (2*c*d-e*(b+sqrt(b^2-4*a*c))))/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2))+(b*(B*d+A*e)-2*(A*c*d+a*B*e))*_ +-- elliptic_e(asin(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-_ +-- e*(b+sqrt(b^2-4*a*c)))),(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(2*c*d-_ +-- e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x-sqrt(b^2-4*a*c))/(2*c*d-b*e+e*sqrt(b^2-4*a*c)))*_ +-- sqrt(-e*(b+2*c*x+sqrt(b^2-4*a*c))/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*_ +-- sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)*e*(c*d^2-e*(b*d-a*e))*_ +-- sqrt(2)*sqrt(c)*sqrt(a+b*x+c*x^2)) +--E 803 + +--S 804 of 1035 +--d0:=D(m0,x) +--E 804 + +)clear all + +--S 805 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1035 +--r0:=-865/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+4540/567*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+10/7*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)-2/21*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)+_ +-- 1010/189*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 806 + +--S 807 of 1035 +--d0:=D(m0,x) +--E 807 + +)clear all + +--S 808 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------- +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1035 +--r0:=-2743/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+2254/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2/15*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+326/135*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 809 + +--S 810 of 1035 +--d0:=D(m0,x) +--E 810 + +)clear all + +--S 811 of 1035 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(1/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ------------------ +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1035 +--r0:=-101/27*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+104/27*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-2/9*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 812 + +--S 813 of 1035 +--d0:=D(m0,x) +--E 813 + +)clear all + +--S 814 of 1035 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------ +--R +------------+ +--R +------+ | 2 +--R \|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1035 +--r0:=34/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+1/3*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2) +--E 815 + +--S 816 of 1035 +--d0:=D(m0,x) +--E 816 + +)clear all + +--S 817 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------- +--R +------------+ +--R +------+ | 2 +--R (2x + 3)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1035 +--r0:=-13*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+12*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 26/5*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 818 + +--S 819 of 1035 +--d0:=D(m0,x) +--E 819 + +)clear all + +--S 820 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) --------------------------------------- +--R +------------+ +--R 2 +------+ | 2 +--R (4x + 12x + 9)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1035 +--r0:=-193/15*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+154/15*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-_ +-- 26/15*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-386/75*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 821 + +--S 822 of 1035 +--d0:=D(m0,x) +--E 822 + +)clear all + +--S 823 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(1/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------- +--R +------------+ +--R 3 2 +------+ | 2 +--R (8x + 36x + 54x + 27)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1035 +--r0:=-4501/375*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+3328/375*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-26/25*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-_ +-- 782/375*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-9002/1875*sqrt(2+5*x+3*x^2)/_ +-- sqrt(3+2*x) +--E 824 + +--S 825 of 1035 +--d0:=D(m0,x) +--E 825 + +)clear all + +--S 826 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) ------------------------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1035 +--r0:=-2*(3+2*x)^(7/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-34174/81*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+16072/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+308/5*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+140/3*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)+_ +-- 12068/135*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 827 + +--S 828 of 1035 +--d0:=D(m0,x) +--E 828 + +)clear all + +--S 829 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) --------------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1035 +--r0:=-2*(3+2*x)^(5/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-3830/81*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)+1340/81*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+140/3*(3+2*x)^(3/2)*_ +-- sqrt(2+5*x+3*x^2)+1660/27*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 830 + +--S 831 of 1035 +--d0:=D(m0,x) +--E 831 + +)clear all + +--S 832 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1035 +--r0:=-2*(3+2*x)^(3/2)*(29+35*x)/sqrt(2+5*x+3*x^2)-274/9*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- sqrt(2+5*x+3*x^2)+64/9*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+140/3*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 833 + +--S 834 of 1035 +--d0:=D(m0,x) +--E 834 + +)clear all + +--S 835 of 1035 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(3/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) ----------------------------- +--R +------------+ +--R 2 | 2 +--R (3x + 5x + 2)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1035 +--r0:=68/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-70/3*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-2*(29+35*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 836 + +--S 837 of 1035 +--d0:=D(m0,x) +--E 837 + +)clear all + +--S 838 of 1035 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) -------------------------------------- +--R +------------+ +--R 2 +------+ | 2 +--R (3x + 5x + 2)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1035 +--r0:=-94*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+24*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6/5*(37+47*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 839 + +--S 840 of 1035 +--d0:=D(m0,x) +--E 840 + +)clear all + +--S 841 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------- +--R +------------+ +--R 3 2 +------+ | 2 +--R (6x + 19x + 19x + 6)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1035 +--r0:=-454/5*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+172/5*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-6/5*(37+47*x)/_ +-- (sqrt(3+2*x)*sqrt(2+5*x+3*x^2))-908/25*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 842 + +--S 843 of 1035 +--d0:=D(m0,x) +--E 843 + +)clear all + +--S 844 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------- +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (12x + 56x + 95x + 69x + 18)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1035 +--r0:=-6/5*(37+47*x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2))-7438/75*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+3664/75*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2516/75*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-14876/375*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 845 + +--S 846 of 1035 +--d0:=D(m0,x) +--E 846 + +)clear all + +--S 847 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(3/2)) +--R +--R +--R - x + 5 +--R (1) ------------------------------------------------------------------ +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (24x + 148x + 358x + 423x + 243x + 54)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1035 +--r0:=-6/5*(37+47*x)/((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2))-213374/1875*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))+121172/1875*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-4124/125*_ +-- sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-61468/1875*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(3/2)-426748/9375*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 848 + +--S 849 of 1035 +--d0:=D(m0,x) +--E 849 + +)clear all + +--S 850 of 1035 +t0:=(5-x)*(3+2*x)^(9/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 16x - 16x + 264x + 864x + 999x + 405)\|2x + 3 +--R (1) ----------------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1035 +--r0:=-2/3*(3+2*x)^(9/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+4/3*(3+2*x)^(7/2)*_ +-- (445+569*x)/sqrt(2+5*x+3*x^2)+110516/243*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-21248/243*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-5416/9*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)-_ +-- 4552/9*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)-59512/81*sqrt(3+2*x)*_ +-- sqrt(2+5*x+3*x^2) +--E 851 + +--S 852 of 1035 +--d0:=D(m0,x) +--E 852 + +)clear all + +--S 853 of 1035 +t0:=(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 4 3 2 +------+ +--R (- 8x + 4x + 126x + 243x + 135)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1035 +--r0:=-2/3*(3+2*x)^(7/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+28/3*(3+2*x)^(5/2)*_ +-- (65+81*x)/sqrt(2+5*x+3*x^2)+31892/81*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-6776/81*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/sqrt(2+5*x+3*x^2)-504*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)-_ +-- 16744/27*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 854 + +--S 855 of 1035 +--d0:=D(m0,x) +--E 855 + +)clear all + +--S 856 of 1035 +t0:=(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 3 2 +------+ +--R (- 4x + 8x + 51x + 45)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1035 +--r0:=-2/3*(3+2*x)^(5/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)+20/3*(3+2*x)^(3/2)*_ +-- (93+113*x)/sqrt(2+5*x+3*x^2)+8620/27*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)-1840/27*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- sqrt(2+5*x+3*x^2)-4520/9*sqrt(3+2*x)*sqrt(2+5*x+3*x^2) +--E 857 + +--S 858 of 1035 +--d0:=D(m0,x) +--E 858 + +)clear all + +--S 859 of 1035 +t0:=(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R 2 +------+ +--R (- 2x + 7x + 15)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1035 +--r0:=-2/3*(3+2*x)^(3/2)*(29+35*x)/(2+5*x+3*x^2)^(3/2)-2392/9*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+2252/9*elliptic_e(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(5)*sqrt(-2-3*x)*sqrt(-1-x)/sqrt(2+5*x+3*x^2)+4/3*(475+563*x)*_ +-- sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 860 + +--S 861 of 1035 +--d0:=D(m0,x) +--E 861 + +)clear all + +--S 862 of 1035 +t0:=(5-x)*(3+2*x)^(1/2)/(2+5*x+3*x^2)^(5/2) +--R +--R +--R +------+ +--R (- x + 5)\|2x + 3 +--R (1) -------------------------------------------- +--R +------------+ +--R 4 3 2 | 2 +--R (9x + 30x + 37x + 20x + 4)\|3x + 5x + 2 +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1035 +--r0:=-2/3*(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+2852/3*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-608/3*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/15*(1759+2139*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 863 + +--S 864 of 1035 +--d0:=D(m0,x) +--E 864 + +)clear all + +--S 865 of 1035 +t0:=(5-x)/((3+2*x)^(1/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ----------------------------------------------------- +--R +------------+ +--R 4 3 2 +------+ | 2 +--R (9x + 30x + 37x + 20x + 4)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1035 +--r0:=-2/5*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+3476/5*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*_ +-- sqrt(2+5*x+3*x^2))-728/5*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/25*(2152+2607*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2) +--E 866 + +--S 867 of 1035 +--d0:=D(m0,x) +--E 867 + +)clear all + +--S 868 of 1035 +t0:=(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R - x + 5 +--R (1) ---------------------------------------------------------------- +--R +------------+ +--R 5 4 3 2 +------+ | 2 +--R (18x + 87x + 164x + 151x + 68x + 12)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1035 +--r0:=-2/5*(37+47*x)/((2+5*x+3*x^2)^(3/2)*sqrt(3+2*x))+11732/25*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))-2096/25*elliptic_f(asin(sqrt(3+2*x)),3/5)*_ +-- sqrt(-2-3*x)*sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))+_ +-- 4/25*(2054+2409*x)/(sqrt(3+2*x)*sqrt(2+5*x+3*x^2))+_ +-- 23464/125*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 869 + +--S 870 of 1035 +--d0:=D(m0,x) +--E 870 + +)clear all + +--S 871 of 1035 +t0:=(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R -------------------------------------------------------------------------- +--R +------------+ +--R 6 5 4 3 2 +------+ | 2 +--R (36x + 228x + 589x + 794x + 589x + 228x + 36)\|2x + 3 \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1035 +--r0:=-2/5*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2))+_ +-- 12/25*(652+737*x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2))+_ +-- 95396/375*elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*_ +-- sqrt(-1-x)/(sqrt(5)*sqrt(2+5*x+3*x^2))-2888/375*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+61672/375*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(3/2)+190792/1875*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 872 + +--S 873 of 1035 +--d0:=D(m0,x) +--E 873 + +)clear all + +--S 874 of 1035 +t0:=(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2)) +--R +--R +--R (1) +--R - x + 5 +--R / +--R 7 6 5 4 3 2 +------+ +--R (72x + 564x + 1862x + 3355x + 3560x + 2223x + 756x + 108)\|2x + 3 +--R * +--R +------------+ +--R | 2 +--R \|3x + 5x + 2 +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1035 +--r0:=-2/5*(37+47*x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2))+4/25*(1858+2013*x)/_ +-- ((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2))+107548/3125*_ +-- elliptic_e(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+280256/3125*_ +-- elliptic_f(asin(sqrt(3+2*x)),3/5)*sqrt(-2-3*x)*sqrt(-1-x)/_ +-- (sqrt(5)*sqrt(2+5*x+3*x^2))+87144/625*sqrt(2+5*x+3*x^2)/_ +-- (3+2*x)^(5/2)+258536/3125*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+_ +-- 215096/15625*sqrt(2+5*x+3*x^2)/sqrt(3+2*x) +--E 875 + +--S 876 of 1035 +--d0:=D(m0,x) +--E 876 + +)clear all + +--S 877 of 1035 +t0:=sqrt(x)/((1+x^2)*sqrt(1+x)) +--R +--R +--R +-+ +--R \|x +--R (1) ---------------- +--R 2 +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1035 +r0:=-1/2*(1-%i)^(3/2)*atanh(sqrt(1-%i)*sqrt(x)/sqrt(1+x))-_ + 1/2*(1+%i)^(3/2)*atanh(sqrt(1+%i)*sqrt(x)/sqrt(1+x)) +--R +--R +--R +------+ +-+ +------+ +-+ +--R +------+ \|1 + %i \|x +------+ \|1 - %i \|x +--R - %i\|1 + %i atanh(-------------) - \|1 - %i atanh(-------------) +--R +-----+ +-----+ +--R \|x + 1 \|x + 1 +--R (2) ----------------------------------------------------------------- +--R 1 + %i +--R Type: Expression(Complex(Integer)) +--E 878 + +--S 879 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Complex(Integer)) +--E 879 + +)clear all + +--S 880 of 1035 +t0:=(-1+2*x^2)/(sqrt(-1+x)*sqrt(1+x)) +--R +--R +--R 2 +--R 2x - 1 +--R (1) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1035 +r0:=x*sqrt(-1+x)*sqrt(1+x) +--R +--R +--R +-----+ +-----+ +--R (2) x\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 882 + +)clear all + +--S 883 of 1035 +t0:=(a+c*x^2)/(sqrt(d+e*x)*sqrt(f+g*x)) +--R +--R +--R 2 +--R c x + a +--R (1) -------------------- +--R +-------+ +-------+ +--R \|e x + d \|g x + f +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1035 +r0:=-1/4*c*(4*d*e*f*g-3*(e*f+d*g)^2)*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*_ + sqrt(f+g*x)))/(e^(5/2)*g^(5/2))+2*a*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*_ + sqrt(f+g*x)))/(sqrt(e)*sqrt(g))-3/4*c*(e*f+d*g)*sqrt(d+e*x)*_ + sqrt(f+g*x)/(e^2*g^2)+1/2*c*x*sqrt(d+e*x)*sqrt(f+g*x)/(e*g) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 \|g \|e x + d +--R ((8a e + 3c d )g + 2c d e f g + 3c e f )atanh(--------------) +--R +-+ +-------+ +--R \|e \|g x + f +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2c e g x - 3c d g - 3c e f)\|e \|g \|e x + d \|g x + f +--R / +--R 2 2 +-+ +-+ +--R 4e g \|e \|g +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1035 +--d0:=D(m0,x) +--E 885 + +)clear all + +--S 886 of 1035 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - e g x + (- 3d e g - 2e f g)x + (- 3d e g - 6d e f g - e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- d g - 6d e f g - 3d e f )x + (- 2d f g - 3d e f )x - d f +--R / +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 886 + +--S 887 of 1035 +r0:=-d^2*(7*e^2*f^2+16*d*e*f*g+8*d^2*g^2)*x/e^2-d*(2*e^2*f^2+7*d*e*f*g+_ + 4*d^2*g^2)*x^2/e-1/3*(e*f+d*g)*(e*f+7*d*g)*x^3-1/2*e*g*(e*f+2*d*g)*x^4-_ + 1/5*e^2*g^2*x^5-8*d^3*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 5 2 4 3 2 2 5 2 5 +--R (- 240d g - 480d e f g - 240d e f )log(- e x + d) - 6e g x +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (- 30d e g - 15e f g)x + (- 70d e g - 80d e f g - 10e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 120d e g - 210d e f g - 60d e f )x +--R + +--R 4 2 3 2 2 3 2 +--R (- 240d e g - 480d e f g - 210d e f )x +--R / +--R 3 +--R 30e +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 888 + +)clear all + +--S 889 of 1035 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R - e g x + (- 2d e g - 2e f g)x + (- d g - 4d e f g - e f )x +--R + +--R 2 2 2 2 +--R (- 2d f g - 2d e f )x - d f +--R / +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 889 + +--S 890 of 1035 +r0:=-d*(e*f+2*d*g)*(3*e*f+2*d*g)*x/e^2-1/2*(e^2*f^2+6*d*e*f*g+_ + 4*d^2*g^2)*x^2/e-1/3*g*(2*e*f+3*d*g)*x^3-1/4*e*g^2*x^4-_ + 4*d^2*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 3 2 2 2 4 2 4 +--R (- 48d g - 96d e f g - 48d e f )log(- e x + d) - 3e g x +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (- 12d e g - 8e f g)x + (- 24d e g - 36d e f g - 6e f )x +--R + +--R 3 2 2 2 3 2 +--R (- 48d e g - 96d e f g - 36d e f )x +--R / +--R 3 +--R 12e +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 891 + +)clear all + +--S 892 of 1035 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 3 2 2 2 2 +--R - e g x + (- d g - 2e f g)x + (- 2d f g - e f )x - d f +--R (1) ---------------------------------------------------------- +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 892 + +--S 893 of 1035 +r0:=-2*d*g*(e*f+d*g)*x/e^2-d*(f+g*x)^2/e-1/3*(f+g*x)^3/g-_ + 2*d*(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 +--R (- 6d g - 12d e f g - 6d e f g)log(- e x + d) - e g x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 2 2 +--R (- 3d e g - 3e f g )x + (- 6d e g - 12d e f g - 3e f g)x - 3d e f g +--R + +--R 3 3 +--R - e f +--R / +--R 3 +--R 3e g +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 894 + +)clear all + +--S 895 of 1035 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------- +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 895 + +--S 896 of 1035 +r0:=-g*(e*f+d*g)*x/e^2-1/2*(f+g*x)^2/e-(e*f+d*g)^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (- 2d g - 4d e f g - 2e f )log(- e x + d) - e g x +--R + +--R 2 2 2 2 +--R (- 2d e g - 4e f g)x - e f +--R / +--R 3 +--R 2e +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 897 + +)clear all + +--S 898 of 1035 +t0:=(f+g*x)^2/(d^2-e^2*x^2) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------- +--R 2 2 2 +--R e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 898 + +--S 899 of 1035 +r0:=-g^2*x/e^2-1/2*(e*f+d*g)^2*log(d-e*x)/(d*e^3)+_ + 1/2*(e*f-d*g)^2*log(d+e*x)/(d*e^3) +--R +--R +--R (2) +--R 2 2 2 2 +--R (d g - 2d e f g + e f )log(e x + d) +--R + +--R 2 2 2 2 2 +--R (- d g - 2d e f g - e f )log(- e x + d) - 2d e g x +--R / +--R 3 +--R 2d e +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 900 + +)clear all + +--S 901 of 1035 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------------- +--R 3 3 2 2 2 3 +--R e x + d e x - d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 901 + +--S 902 of 1035 +r0:=-1/2*(e*f-d*g)^2/(d*e^3*(d+e*x))-1/4*(e*f+d*g)^2*log(d-e*x)/(d^2*e^3)+_ + 1/4*(e*f-d*g)*(e*f+3*d*g)*log(d+e*x)/(d^2*e^3) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3d e g + 2d e f g + e f )x - 3d g + 2d e f g + d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- d e g - 2d e f g - e f )x - d g - 2d e f g - d e f )log(- e x + d) +--R + +--R 3 2 2 2 2 +--R - 2d g + 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x + 4d e +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 903 + +)clear all + +--S 904 of 1035 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 4 4 3 3 3 4 +--R e x + 2d e x - 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 904 + +--S 905 of 1035 +r0:=-1/4*(e*f-d*g)^2/(d*e^3*(d+e*x)^2)-1/4*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x))+1/4*(e*f+d*g)^2*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 4 2 +--R (d e g + 2d e f g + e f )x + (2d e g + 4d e f g + 2d e f )x + d g +--R + +--R 3 2 2 2 +--R 2d e f g + d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (3d e g - 2d e f g - d e f )x + 2d g - 2d e f +--R / +--R 3 5 2 4 4 5 3 +--R 4d e x + 8d e x + 4d e +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 906 + +)clear all + +--S 907 of 1035 +t0:=(f+g*x)^2/((d+e*x)^3*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 3d e x + 2d e x - 2d e x - 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 907 + +--S 908 of 1035 +r0:=-1/6*(e*f-d*g)^2/(d*e^3*(d+e*x)^3)-1/8*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x)^2)-1/8*(e*f+d*g)^2/(d^3*e^3*(d+e*x))+_ + 1/8*(e*f+d*g)^2*atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (3d e g + 6d e f g + 3e f )x + (9d e g + 18d e f g + 9d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (9d e g + 18d e f g + 9d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (- 3d e g - 6d e f g - 3d e f )x + (3d e g - 18d e f g - 9d e f )x +--R + +--R 5 2 4 3 2 2 +--R 2d g - 4d e f g - 10d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 24d e x + 72d e x + 72d e x + 24d e +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 909 + +)clear all + +--S 910 of 1035 +t0:=(f+g*x)^2/((d+e*x)^4*(d^2-e^2*x^2)) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------ +--R 6 6 5 5 2 4 4 4 2 2 5 6 +--R e x + 4d e x + 5d e x - 5d e x - 4d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 910 + +--S 911 of 1035 +r0:=-1/8*(e*f-d*g)^2/(d*e^3*(d+e*x)^4)-1/12*(e*f-d*g)*(e*f+3*d*g)/_ + (d^2*e^3*(d+e*x)^3)-1/16*(e*f+d*g)^2/(d^3*e^3*(d+e*x)^2)-_ + 1/16*(e*f+d*g)^2/(d^4*e^3*(d+e*x))+1/16*(e*f+d*g)^2*atanh(e*x/d)/(d^5*e^3) +--R +--R +--R (2) +--R 2 4 2 5 6 2 4 3 3 2 2 4 5 2 3 +--R (3d e g + 6d e f g + 3e f )x + (12d e g + 24d e f g + 12d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (18d e g + 36d e f g + 18d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (12d e g + 24d e f g + 12d e f )x + 3d g + 6d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 3d e g - 6d e f g - 3d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- 12d e g - 24d e f g - 12d e f )x +--R + +--R 5 2 4 2 3 3 2 5 4 2 2 +--R (- 3d e g - 38d e f g - 19d e f )x - 8d e f g - 16d e f +--R / +--R 5 7 4 6 6 3 7 5 2 8 4 9 3 +--R 48d e x + 192d e x + 288d e x + 192d e x + 48d e +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 912 + +)clear all + +--S 913 of 1035 +t0:=(d+e*x)^7*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R e g x + (5d e g + 2e f g)x + (10d e g + 10d e f g + e f )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10d e g + 20d e f g + 5d e f )x + (5d e g + 20d e f g + 10d e f )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (d g + 10d e f g + 10d e f )x + (2d f g + 5d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 913 + +--S 914 of 1035 +r0:=d^3*(49*e^2*f^2+160*d*e*f*g+112*d^2*g^2)*x/e^2+1/2*d^2*(23*e^2*f^2+_ + 98*d*e*f*g+80*d^2*g^2)*x^2/e+1/3*d*(7*e^2*f^2+46*d*e*f*g+49*d^2*g^2)*_ + x^3+1/4*e*(e^2*f^2+14*d*e*f*g+23*d^2*g^2)*x^4+1/5*e^2*g*(2*e*f+7*d*g)*_ + x^5+1/6*e^3*g^2*x^6+32*d^5*(e*f+d*g)^2/(e^3*(d-e*x))+_ + 16*d^4*(e*f+d*g)*(5*e*f+9*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 6 2 5 2 4 3 2 7 2 6 +--R (8640d e g + 13440d e f g + 4800d e f )x - 8640d g - 13440d e f g +--R + +--R 5 2 2 +--R - 4800d e f +--R * +--R log(- e x + d) +--R + +--R 7 2 7 6 2 7 6 2 5 2 6 7 2 5 +--R 10e g x + (74d e g + 24e f g)x + (261d e g + 186d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (635d e g + 710d e f g + 125d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (1420d e g + 2020d e f g + 550d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (4320d e g + 6660d e f g + 2250d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 +--R (- 6720d e g - 9600d e f g - 2940d e f )x - 1920d g - 3840d e f g +--R + +--R 5 2 2 +--R - 1920d e f +--R / +--R 4 3 +--R 60e x - 60d e +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 915 + +)clear all + +--S 916 of 1035 +t0:=(d+e*x)^6*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R e g x + (4d e g + 2e f g)x + (6d e g + 8d e f g + e f )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4d e g + 12d e f g + 4d e f )x + (d g + 8d e f g + 6d e f )x +--R + +--R 4 3 2 4 2 +--R (2d f g + 4d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 916 + +--S 917 of 1035 +r0:=d^2*(17*e^2*f^2+64*d*e*f*g+48*d^2*g^2)*x/e^2+d*(3*e^2*f^2+17*d*e*f*g+_ + 16*d^2*g^2)*x^2/e+1/3*(e^2*f^2+12*d*e*f*g+17*d^2*g^2)*x^3+_ + 1/2*e*g*(e*f+3*d*g)*x^4+1/5*e^2*g^2*x^5+16*d^4*(e*f+d*g)^2/(e^3*(d-e*x))+_ + 32*d^3*(e*f+d*g)*(e*f+2*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 5 2 4 2 3 3 2 6 2 5 +--R (1920d e g + 2880d e f g + 960d e f )x - 1920d g - 2880d e f g +--R + +--R 4 2 2 +--R - 960d e f +--R * +--R log(- e x + d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 6e g x + (39d e g + 15e f g)x + (125d e g + 105d e f g + 10e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (310d e g + 390d e f g + 80d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (960d e g + 1410d e f g + 420d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (- 1440d e g - 1920d e f g - 510d e f )x - 480d g - 960d e f g +--R + +--R 4 2 2 +--R - 480d e f +--R / +--R 4 3 +--R 30e x - 30d e +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 918 + +)clear all + +--S 919 of 1035 +t0:=(d+e*x)^5*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R e g x + (3d e g + 2e f g)x + (3d e g + 6d e f g + e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (d g + 6d e f g + 3d e f )x + (2d f g + 3d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 919 + +--S 920 of 1035 +r0:=d*(5*e^2*f^2+24*d*e*f*g+20*d^2*g^2)*x/e^2+1/2*(e^2*f^2+_ + 10*d*e*f*g+12*d^2*g^2)*x^2/e+1/3*g*(2*e*f+5*d*g)*x^3+1/4*e*g^2*x^4+_ + 8*d^3*(e*f+d*g)^2/(e^3*(d-e*x))+4*d^2*(e*f+d*g)*(3*e*f+7*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 3 2 2 3 2 5 2 4 +--R (336d e g + 480d e f g + 144d e f )x - 336d g - 480d e f g +--R + +--R 3 2 2 +--R - 144d e f +--R * +--R log(- e x + d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 3e g x + (17d e g + 8e f g)x + (52d e g + 52d e f g + 6e f )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (168d e g + 228d e f g + 54d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 240d e g - 288d e f g - 60d e f )x - 96d g - 192d e f g - 96d e f +--R / +--R 4 3 +--R 12e x - 12d e +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 921 + +)clear all + +--S 922 of 1035 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R e g x + (2d e g + 2e f g)x + (d g + 4d e f g + e f )x +--R + +--R 2 2 2 2 +--R (2d f g + 2d e f )x + d f +--R / +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 922 + +--S 923 of 1035 +r0:=(e^2*f^2+8*d*e*f*g+8*d^2*g^2)*x/e^2+g*(e*f+2*d*g)*x^2/e+1/3*g^2*x^3+_ + 4*d^2*(e*f+d*g)^2/(e^3*(d-e*x))+4*d*(e*f+d*g)*(e*f+3*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R ((36d e g + 48d e f g + 12d e f )x - 36d g - 48d e f g - 12d e f ) +--R * +--R log(- e x + d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R e g x + (5d e g + 3e f g)x + (18d e g + 21d e f g + 3e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (- 24d e g - 24d e f g - 3d e f )x - 12d g - 24d e f g - 12d e f +--R / +--R 4 3 +--R 3e x - 3d e +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 924 + +)clear all + +--S 925 of 1035 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 3 2 2 2 2 +--R e g x + (d g + 2e f g)x + (2d f g + e f )x + d f +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 925 + +--S 926 of 1035 +r0:=g*(2*e*f+3*d*g)*x/e^2+1/2*g^2*x^2/e+2*d*(e*f+d*g)^2/(e^3*(d-e*x))+_ + (e*f+d*g)*(e*f+5*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((10d e g + 12d e f g + 2e f )x - 10d g - 12d e f g - 2d e f ) +--R * +--R log(- e x + d) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R e g x + (5d e g + 4e f g)x + (- 6d e g - 4d e f g)x - 4d g +--R + +--R 2 2 2 +--R - 8d e f g - 4d e f +--R / +--R 4 3 +--R 2e x - 2d e +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 927 + +)clear all + +--S 928 of 1035 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------ +--R 2 2 2 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 928 + +--S 929 of 1035 +r0:=g^2*x/e^2+(e*f+d*g)^2/(e^3*(d-e*x))+2*g*(e*f+d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R ((2d e g + 2e f g)x - 2d g - 2d e f g)log(- e x + d) + e g x - d e g x +--R + +--R 2 2 2 2 +--R - d g - 2d e f g - e f +--R / +--R 4 3 +--R e x - d e +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 930 + +)clear all + +--S 931 of 1035 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) -------------------------- +--R 3 3 2 2 2 3 +--R e x - d e x - d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 931 + +--S 932 of 1035 +r0:=1/2*(e*f+d*g)^2/(d*e^3*(d-e*x))-1/4*(e*f-3*d*g)*(e*f+d*g)*_ + log(d-e*x)/(d^2*e^3)+1/4*(e*f-d*g)^2*log(d+e*x)/(d^2*e^3) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((d e g - 2d e f g + e f )x - d g + 2d e f g - d e f )log(e x + d) +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((3d e g + 2d e f g - e f )x - 3d g - 2d e f g + d e f )log(- e x + d) +--R + +--R 3 2 2 2 2 +--R - 2d g - 4d e f g - 2d e f +--R / +--R 2 4 3 3 +--R 4d e x - 4d e +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 933 + +)clear all + +--S 934 of 1035 +t0:=(f+g*x)^2/(d^2-e^2*x^2)^2 +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------- +--R 4 4 2 2 2 4 +--R e x - 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 934 + +--S 935 of 1035 +r0:=1/2*(d^2*g+e^2*f*x)*(f+g*x)/(d^2*e^2*(d^2-e^2*x^2))+1/2*(e*f-d*g)*_ + (e*f+d*g)*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 4 2 2 4 2 2 2 2 e x 3 2 +--R ((- d e g + e f )x + d g - d e f )atanh(---) - d e f g x +--R d +--R + +--R 3 2 3 2 3 +--R (- d e g - d e f )x - d e f g +--R / +--R 3 5 2 5 3 +--R 2d e x - 2d e +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 936 + +)clear all + +--S 937 of 1035 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ---------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + d e x - 2d e x - 2d e x + d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 937 + +--S 938 of 1035 +r0:=1/8*(e*f+d*g)^2/(d^3*e^3*(d-e*x))-1/8*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^2)+_ + 1/4*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x))+1/8*(3*e*f-d*g)*(e*f+d*g)*_ + atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g + 2d e f g + 3e f )x + (- d e g + 2d e f g + 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g - 2d e f g - 3d e f )x + d g - 2d e f g - 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (d e g - 2d e f g - 3d e f )x + (- 3d e g - 2d e f g - 3d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 2d g - 4d e f g + 2d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 8d e x + 8d e x - 8d e x - 8d e +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 939 + +)clear all + +--S 940 of 1035 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) -------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 2d e x - d e x - 4d e x - d e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 940 + +--S 941 of 1035 +r0:=1/16*(e*f+d*g)^2/(d^4*e^3*(d-e*x))-1/12*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^3)+_ + 1/8*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^2)-1/16*(3*e*f-d*g)*(e*f+d*g)/_ + (d^4*e^3*(d+e*x))+1/4*f*(e*f+d*g)*atanh(e*x/d)/(d^5*e^2) +--R +--R +--R (2) +--R 5 6 2 4 2 4 5 2 3 +--R (3d e f g + 3e f )x + (6d e f g + 6d e f )x +--R + +--R 4 2 3 3 2 5 4 2 2 +--R (- 6d e f g - 6d e f )x - 3d e f g - 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 2 4 5 2 3 3 3 2 4 2 2 +--R (- 3d e f g - 3d e f )x + (- 6d e f g - 6d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (- 4d e g - d e f g - d e f )x - 2d g - 2d e f g + 4d e f +--R / +--R 5 7 4 6 6 3 8 4 9 3 +--R 12d e x + 24d e x - 24d e x - 12d e +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 942 + +)clear all + +--S 943 of 1035 +t0:=(f+g*x)^2/((d+e*x)^3*(d^2-e^2*x^2)^2) +--R +--R +--R 2 2 2 +--R g x + 2f g x + f +--R (1) ------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 3d e x + d e x - 5d e x - 5d e x + d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 943 + +--S 944 of 1035 +r0:=1/32*(e*f+d*g)^2/(d^5*e^3*(d-e*x))-1/16*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^4)+_ + 1/12*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^3)-1/32*(3*e*f-d*g)*(e*f+d*g)/_ + (d^4*e^3*(d+e*x)^2)-1/8*f*(e*f+d*g)/(d^5*e^2*(d+e*x))+1/32*(e*f+d*g)*_ + (5*e*f+d*g)*atanh(e*x/d)/(d^6*e^3) +--R +--R +--R (2) +--R 2 5 2 6 7 2 5 3 4 2 2 5 6 2 4 +--R (3d e g + 18d e f g + 15e f )x + (9d e g + 54d e f g + 45d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g + 36d e f g + 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 6d e g - 36d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 9d e g - 54d e f g - 45d e f )x - 3d g - 18d e f g - 15d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 3d e g - 18d e f g - 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 9d e g - 54d e f g - 45d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (- 7d e g - 42d e f g - 35d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 5 2 2 +--R (- 21d e g + 18d e f g + 15d e f )x - 8d g + 32d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 96d e x + 288d e x + 192d e x - 192d e x - 288d e x - 96d e +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 945 + +)clear all + +--S 946 of 1035 +t0:=(f+g*x)^2/((d+e*x)^4*(d^2-e^2*x^2)^2) +--R +--R +--R (1) +--R 2 2 2 +--R g x + 2f g x + f +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 4d e x + 4d e x - 4d e x - 10d e x - 4d e x + 4d e x +--R + +--R 7 8 +--R 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 946 + +--S 947 of 1035 +r0:=1/64*(e*f+d*g)^2/(d^6*e^3*(d-e*x))-1/20*(e*f-d*g)^2/(d^2*e^3*(d+e*x)^5)+_ + 1/16*(-e^2*f^2+d^2*g^2)/(d^3*e^3*(d+e*x)^4)-1/48*(3*e*f-d*g)*_ + (e*f+d*g)/(d^4*e^3*(d+e*x)^3)-1/16*f*(e*f+d*g)/(d^5*e^2*(d+e*x)^2)-_ + 1/64*(e*f+d*g)*(5*e*f+d*g)/(d^6*e^3*(d+e*x))+1/32*(e*f+d*g)*_ + (3*e*f+d*g)*atanh(e*x/d)/(d^7*e^3) +--R +--R +--R (2) +--R 2 6 2 7 8 2 6 +--R (15d e g + 60d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (60d e g + 240d e f g + 180d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (75d e g + 300d e f g + 225d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 75d e g - 300d e f g - 225d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 60d e g - 240d e f g - 180d e f )x - 15d g - 60d e f g - 45d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 15d e g - 60d e f g - 45d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (- 60d e g - 240d e f g - 180d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 80d e g - 320d e f g - 240d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 20d e g - 80d e f g - 60d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 49d e g + 188d e f g + 141d e f )x - 16d g + 32d e f g + 144d e f +--R / +--R 7 9 6 8 8 5 9 7 4 11 5 2 12 4 13 3 +--R 480d e x + 1920d e x + 2400d e x - 2400d e x - 1920d e x - 480d e +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 948 + +)clear all + +--S 949 of 1035 +t0:=(d+e*x)^7*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R - e g x + (- 4d e g - 2e f g)x + (- 6d e g - 8d e f g - e f )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (- 4d e g - 12d e f g - 4d e f )x + (- d g - 8d e f g - 6d e f )x +--R + +--R 4 3 2 4 2 +--R (- 2d f g - 4d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 949 + +--S 950 of 1035 +r0:=-d*(7*e^2*f^2+48*d*e*f*g+56*d^2*g^2)*x/e^2-1/2*(e*f+2*d*g)*(e*f+12*d*g)*_ + x^2/e-1/3*g*(2*e*f+7*d*g)*x^3-1/4*e*g^2*x^4+8*d^4*(e*f+d*g)^2/(e^3*_ + (d-e*x)^2)-32*d^3*(e*f+d*g)*(e*f+2*d*g)/(e^3*(d-e*x))-8*d^2*(3*e^2*f^2+_ + 14*d*e*f*g+13*d^2*g^2)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 4 2 2 3 3 2 4 2 2 +--R (- 1248d e g - 1344d e f g - 288d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 +--R (2496d e g + 2688d e f g + 576d e f )x - 1248d g - 1344d e f g +--R + +--R 4 2 2 +--R - 288d e f +--R * +--R log(- e x + d) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R - 3e g x + (- 22d e g - 8e f g)x + (- 91d e g - 68d e f g - 6e f )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 412d e g - 416d e f g - 72d e f )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (1200d e g + 1068d e f g + 162d e f )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (96d e g + 576d e f g + 300d e f )x - 672d g - 960d e f g - 288d e f +--R / +--R 5 2 4 2 3 +--R 12e x - 24d e x + 12d e +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 951 + +)clear all + +--S 952 of 1035 +t0:=(d+e*x)^6*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R - e g x + (- 3d e g - 2e f g)x + (- 3d e g - 6d e f g - e f )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- d g - 6d e f g - 3d e f )x + (- 2d f g - 3d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 952 + +--S 953 of 1035 +r0:=-(e^2*f^2+12*d*e*f*g+18*d^2*g^2)*x/e^2-g*(e*f+3*d*g)*x^2/e-1/3*g^2*x^3+_ + 4*d^3*(e*f+d*g)^2/(e^3*(d-e*x)^2)-4*d^2*(e*f+d*g)*(3*e*f+7*d*g)/(e^3*_ + (d-e*x))-2*d*(3*e^2*f^2+18*d*e*f*g+19*d^2*g^2)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 3 2 2 2 3 4 2 2 +--R (- 114d e g - 108d e f g - 18d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (228d e g + 216d e f g + 36d e f )x - 114d g - 108d e f g - 18d e f +--R * +--R log(- e x + d) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R - e g x + (- 7d e g - 3e f g)x + (- 37d e g - 30d e f g - 3e f )x +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (99d e g + 69d e f g + 6d e f )x + (30d e g + 84d e f g + 33d e f )x +--R + +--R 5 2 4 3 2 2 +--R - 72d g - 96d e f g - 24d e f +--R / +--R 5 2 4 2 3 +--R 3e x - 6d e x + 3d e +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 954 + +)clear all + +--S 955 of 1035 +t0:=(d+e*x)^5*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R - e g x + (- 2d e g - 2e f g)x + (- d g - 4d e f g - e f )x +--R + +--R 2 2 2 2 +--R (- 2d f g - 2d e f )x - d f +--R / +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 955 + +--S 956 of 1035 +r0:=-g*(2*e*f+5*d*g)*x/e^2-1/2*g^2*x^2/e+2*d^2*(e*f+d*g)^2/(e^3*(d-e*x)^2)-_ + 4*d*(e*f+d*g)*(e*f+3*d*g)/(e^3*(d-e*x))-(e^2*f^2+10*d*e*f*g+13*d^2*g^2)*_ + log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 +--R (- 26d e g - 20d e f g - 2e f )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (52d e g + 40d e f g + 4d e f )x - 26d g - 20d e f g - 2d e f +--R * +--R log(- e x + d) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 2 +--R - e g x + (- 8d e g - 4e f g)x + (19d e g + 8d e f g)x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (14d e g + 28d e f g + 8d e f )x - 20d g - 24d e f g - 4d e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 957 + +)clear all + +--S 958 of 1035 +t0:=(d+e*x)^4*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 3 2 2 2 2 +--R - e g x + (- d g - 2e f g)x + (- 2d f g - e f )x - d f +--R (1) ---------------------------------------------------------- +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 958 + +--S 959 of 1035 +r0:=-g^2*x/e^2+d*(e*f+d*g)^2/(e^3*(d-e*x)^2)-(e*f+d*g)*(e*f+5*d*g)/(e^3*_ + (d-e*x))-2*g*(e*f+2*d*g)*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 3 2 2 2 2 3 2 2 +--R ((- 4d e g - 2e f g)x + (8d e g + 4d e f g)x - 4d g - 2d e f g) +--R * +--R log(- e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 3 2 3 2 2 +--R - e g x + 2d e g x + (4d e g + 6d e f g + e f )x - 4d g - 4d e f g +--R / +--R 5 2 4 2 3 +--R e x - 2d e x + d e +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1035 +t0:=(d+e*x)^3*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 961 + +--S 962 of 1035 +r0:=1/2*(e*f+d*g)^2/(e^3*(d-e*x)^2)-2*g*(e*f+d*g)/(e^3*(d-e*x))-_ + g^2*log(d-e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R (- 2e g x + 4d e g x - 2d g )log(- e x + d) + (4d e g + 4e f g)x +--R + +--R 2 2 2 2 +--R - 3d g - 2d e f g + e f +--R / +--R 5 2 4 2 3 +--R 2e x - 4d e x + 2d e +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 963 + +)clear all + +--S 964 of 1035 +t0:=(d+e*x)^2*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------- +--R 4 4 3 3 3 4 +--R e x - 2d e x + 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 964 + +--S 965 of 1035 +r0:=1/4*(e*f+d*g)^2/(d*e^3*(d-e*x)^2)+1/4*(e*f-3*d*g)*(e*f+d*g)/_ + (d^2*e^3*(d-e*x))+1/4*(e*f-d*g)^2*atanh(e*x/d)/(d^3*e^3) +--R +--R +--R (2) +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (d e g - 2d e f g + e f )x + (- 2d e g + 4d e f g - 2d e f )x +--R + +--R 4 2 3 2 2 2 +--R d g - 2d e f g + d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 2 4 2 2 2 2 +--R (3d e g + 2d e f g - d e f )x - 2d g + 2d e f +--R / +--R 3 5 2 4 4 5 3 +--R 4d e x - 8d e x + 4d e +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 966 + +)clear all + +--S 967 of 1035 +t0:=(d+e*x)*(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ---------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x - d e x - 2d e x + 2d e x + d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 967 + +--S 968 of 1035 +r0:=1/8*(e*f+d*g)^2/(d^2*e^3*(d-e*x)^2)+1/4*(e^2*f^2-d^2*g^2)/(d^3*e^3*_ + (d-e*x))-1/8*(e*f-d*g)^2/(d^3*e^3*(d+e*x))+1/8*(e*f-d*g)*(3*e*f+d*g)*_ + atanh(e*x/d)/(d^4*e^3) +--R +--R +--R (2) +--R 2 3 2 4 5 2 3 3 2 2 2 3 4 2 2 +--R (- d e g - 2d e f g + 3e f )x + (d e g + 2d e f g - 3d e f )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (d e g + 2d e f g - 3d e f )x - d g - 2d e f g + 3d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 5 2 +--R (d e g + 2d e f g - 3d e f )x + (3d e g - 2d e f g + 3d e f )x - 2d g +--R + +--R 4 3 2 2 +--R 4d e f g + 2d e f +--R / +--R 4 6 3 5 5 2 6 4 7 3 +--R 8d e x - 8d e x - 8d e x + 8d e +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 969 + +)clear all + +--S 970 of 1035 +t0:=(f+g*x)^2/(d^2-e^2*x^2)^3 +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ----------------------------- +--R 6 6 2 4 4 4 2 2 6 +--R e x - 3d e x + 3d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 970 + +--S 971 of 1035 +r0:=-1/4*(d^2*g-e^2*f*x)*(f+g*x)^3/(d^2*(e^2*f^2-d^2*g^2)*(d^2-e^2*x^2)^2)+_ + 1/8*(3*e^2*f^2-d^2*g^2)*(d^2*g+e^2*f*x)*(f+g*x)/(d^4*e^2*_ + (e^2*f^2-d^2*g^2)*(d^2-e^2*x^2))+1/8*(3*e^2*f^2-d^2*g^2)*atanh(e*x/d)/_ + (d^5*e^3) +--R +--R +--R (2) +--R 2 4 2 6 2 4 4 2 2 2 4 2 2 6 2 4 2 2 e x +--R ((- d e g + 3e f )x + (2d e g - 6d e f )x - d g + 3d e f )atanh(---) +--R d +--R + +--R 5 4 3 3 2 5 2 3 3 3 2 5 2 3 3 2 +--R - 3d e f g x + (d e g - 3d e f )x + 6d e f g x + (d e g + 5d e f )x +--R + +--R 5 +--R d e f g +--R / +--R 5 7 4 7 5 2 9 3 +--R 8d e x - 16d e x + 8d e +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 972 + +)clear all + +--S 973 of 1035 +t0:=(f+g*x)^2/((d+e*x)*(d^2-e^2*x^2)^3) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) ------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + d e x - 3d e x - 3d e x + 3d e x + 3d e x - d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 973 + +--S 974 of 1035 +r0:=1/32*(e*f+d*g)^2/(d^4*e^3*(d-e*x)^2)+1/8*f*(e*f+d*g)/(d^5*e^2*(d-e*x))-_ + 1/24*(e*f-d*g)^2/(d^3*e^3*(d+e*x)^3)-1/32*(e*f-d*g)*(3*e*f+d*g)/_ + (d^4*e^3*(d+e*x)^2)+1/16*(-3*e^2*f^2+d^2*g^2)/(d^5*e^3*(d+e*x))+_ + 1/16*(5*e^2*f^2+2*d*e*f*g-d^2*g^2)*atanh(e*x/d)/(d^6*e^3) +--R +--R +--R (2) +--R 2 5 2 6 7 2 5 +--R (- 3d e g + 6d e f g + 15e f )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (- 3d e g + 6d e f g + 15d e f )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (6d e g - 12d e f g - 30d e f )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (- 3d e g + 6d e f g + 15d e f )x - 3d g + 6d e f g + 15d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 4 2 2 5 6 2 4 4 3 2 3 4 2 5 2 3 +--R (3d e g - 6d e f g - 15d e f )x + (3d e g - 6d e f g - 15d e f )x +--R + +--R 5 2 2 4 3 3 4 2 2 6 2 5 2 4 3 2 +--R (- 5d e g + 10d e f g + 25d e f )x + (7d e g + 10d e f g + 25d e f )x +--R + +--R 7 2 6 5 2 2 +--R 4d g + 16d e f g - 8d e f +--R / +--R 6 8 5 7 7 4 8 6 3 9 5 2 10 4 11 3 +--R 48d e x + 48d e x - 96d e x - 96d e x + 48d e x + 48d e +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1035 +t0:=(f+g*x)^2/((d+e*x)^2*(d^2-e^2*x^2)^3) +--R +--R +--R 2 2 2 +--R - g x - 2f g x - f +--R (1) -------------------------------------------------------------------- +--R 8 8 7 7 2 6 6 3 5 5 5 3 3 6 2 2 7 8 +--R e x + 2d e x - 2d e x - 6d e x + 6d e x + 2d e x - 2d e x - d +--R Type: Fraction(Polynomial(Integer)) +--E 976 + +--S 977 of 1035 +r0:=1/64*(e*f+d*g)^2/(d^5*e^3*(d-e*x)^2)+1/64*(e*f+d*g)*(5*e*f+d*g)/_ + (d^6*e^3*(d-e*x))-1/32*(e*f-d*g)^2/(d^3*e^3*(d+e*x)^4)-1/48*(e*f-d*g)*_ + (3*e*f+d*g)/(d^4*e^3*(d+e*x)^3)+1/32*(-3*e^2*f^2+d^2*g^2)/(d^5*e^3*_ + (d+e*x)^2)+1/32*(-5*e^2*f^2-2*d*e*f*g+d^2*g^2)/(d^6*e^3*(d+e*x))+_ + 1/64*(15*e^2*f^2+10*d*e*f*g-d^2*g^2)*atanh(e*x/d)/(d^7*e^3) +--R +--R +--R (2) +--R 2 6 2 7 8 2 6 +--R (- 3d e g + 30d e f g + 45e f )x +--R + +--R 3 5 2 2 6 7 2 5 +--R (- 6d e g + 60d e f g + 90d e f )x +--R + +--R 4 4 2 3 5 2 6 2 4 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (12d e g - 120d e f g - 180d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (3d e g - 30d e f g - 45d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (- 6d e g + 60d e f g + 90d e f )x - 3d g + 30d e f g + 45d e f +--R * +--R e x +--R atanh(---) +--R d +--R + +--R 3 5 2 2 6 7 2 5 4 4 2 3 5 2 6 2 4 +--R (3d e g - 30d e f g - 45d e f )x + (6d e g - 60d e f g - 90d e f )x +--R + +--R 5 3 2 4 4 3 5 2 3 +--R (- 2d e g + 20d e f g + 30d e f )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (- 10d e g + 100d e f g + 150d e f )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (35d e g + 34d e f g + 51d e f )x + 16d g + 32d e f g - 48d e f +--R / +--R 7 9 6 8 8 5 9 7 4 10 6 3 11 5 2 12 4 +--R 192d e x + 384d e x - 192d e x - 768d e x - 192d e x + 384d e x +--R + +--R 13 3 +--R 192d e +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 978 + +)clear all + +--S 979 of 1035 +t0:=(a+b*x+c*x^2)/((d+e*x)*(f+g*x)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) --------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 979 + +--S 980 of 1035 +r0:=c*x/(e*g)+(c*d^2-b*d*e+a*e^2)*log(d+e*x)/(e^2*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))*log(f+g*x)/(g^2*(e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (a e g - b e f g + c e f )log(g x + f) +--R + +--R 2 2 2 2 2 +--R (- a e + b d e - c d )g log(e x + d) + (c d e g - c e f g)x +--R / +--R 2 3 3 2 +--R d e g - e f g +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 981 + +)clear all + +--S 982 of 1035 +t0:=(a+b*x+c*x^2)^2/((d+e*x)*(f+g*x)) +--R +--R +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R (1) -------------------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 982 + +--S 983 of 1035 +r0:=(b^2*e^2*g^2-2*c*e*g*(b*e*f+b*d*g-a*e*g)+c^2*(e^2*f^2+d*e*f*g+_ + d^2*g^2))*x/(e^3*g^3)-1/2*c*(c*e*f+c*d*g-2*b*e*g)*x^2/(e^2*g^2)+_ + 1/3*c^2*x^3/(e*g)+(c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/(e^4*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))^2*log(f+g*x)/(g^4*(e*f-d*g)) +--R +--R +--R (2) +--R 2 4 4 4 3 2 4 2 2 4 3 2 4 4 +--R (6a e g - 12a b e f g + (12a c + 6b )e f g - 12b c e f g + 6c e f ) +--R * +--R log(g x + f) +--R + +--R 2 4 3 2 2 2 3 2 4 4 +--R (- 6a e + 12a b d e + (- 12a c - 6b )d e + 12b c d e - 6c d )g +--R * +--R log(e x + d) +--R + +--R 2 3 4 2 4 3 3 +--R (2c d e g - 2c e f g )x +--R + +--R 3 2 2 2 4 4 3 2 4 2 2 2 +--R ((6b c d e - 3c d e )g - 6b c e f g + 3c e f g )x +--R + +--R 2 3 2 2 2 3 4 2 4 3 +--R ((12a c + 6b )d e - 12b c d e + 6c d e)g + (- 12a c - 6b )e f g +--R + +--R 4 2 2 2 4 3 +--R 12b c e f g - 6c e f g +--R * +--R x +--R / +--R 4 5 5 4 +--R 6d e g - 6e f g +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 984 + +)clear all + +--S 985 of 1035 +t0:=(a+b*x+c*x^2)^3/((d+e*x)*(f+g*x)) +--R +--R +--R (1) +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R / +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Fraction(Polynomial(Integer)) +--E 985 + +--S 986 of 1035 +r0:=-(b^2*e^3*g^3*(b*e*f+b*d*g-3*a*e*g)-c^3*(e^4*f^4+d*e^3*f^3*g+_ + d^2*e^2*f^2*g^2+d^3*e*f*g^3+d^4*g^4)-3*c*e^2*g^2*(a^2*e^2*g^2-_ + 2*a*b*e*g*(e*f+d*g)+b^2*(e^2*f^2+d*e*f*g+d^2*g^2))-3*c^2*e*g*(a*e*g*_ + (e^2*f^2+d*e*f*g+d^2*g^2)-b*(e^3*f^3+d*e^2*f^2*g+d^2*e*f*g^2+d^3*g^3)))*_ + x/(e^5*g^5)+1/2*(b^3*e^3*g^3-3*b*c*e^2*g^2*(b*e*f+b*d*g-2*a*e*g)-c^3*_ + (e^3*f^3+d*e^2*f^2*g+d^2*e*f*g^2+d^3*g^3)-3*c^2*e*g*(a*e*g*(e*f+d*g)-_ + b*(e^2*f^2+d*e*f*g+d^2*g^2)))*x^2/(e^4*g^4)+1/3*c*(3*b^2*e^2*g^2-_ + 3*c*e*g*(b*e*f+b*d*g-a*e*g)+c^2*(e^2*f^2+d*e*f*g+d^2*g^2))*_ + x^3/(e^3*g^3)-1/4*c^2*(c*e*f+c*d*g-3*b*e*g)*x^4/(e^2*g^2)+_ + 1/5*c^3*x^5/(e*g)+(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/(e^6*(e*f-d*g))-_ + (c*f^2-g*(b*f-a*g))^3*log(f+g*x)/(g^6*(e*f-d*g)) +--R +--R +--R (2) +--R 3 6 6 2 6 5 2 2 6 2 4 +--R 60a e g - 180a b e f g + (180a c + 180a b )e f g +--R + +--R 3 6 3 3 2 2 6 4 2 2 6 5 +--R (- 360a b c - 60b )e f g + (180a c + 180b c)e f g - 180b c e f g +--R + +--R 3 6 6 +--R 60c e f +--R * +--R log(g x + f) +--R + +--R 3 6 2 5 2 2 2 4 +--R - 60a e + 180a b d e + (- 180a c - 180a b )d e +--R + +--R 3 3 3 2 2 4 2 2 5 3 6 +--R (360a b c + 60b )d e + (- 180a c - 180b c)d e + 180b c d e - 60c d +--R * +--R 6 +--R g log(e x + d) +--R + +--R 3 5 6 3 6 5 5 +--R (12c d e g - 12c e f g )x +--R + +--R 2 5 3 2 4 6 2 6 5 3 6 2 4 4 +--R ((45b c d e - 15c d e )g - 45b c e f g + 15c e f g )x +--R + +--R 2 2 5 2 2 4 3 3 3 6 +--R ((60a c + 60b c)d e - 60b c d e + 20c d e )g +--R + +--R 2 2 6 5 2 6 2 4 3 6 3 3 +--R (- 60a c - 60b c)e f g + 60b c e f g - 20c e f g +--R * +--R 3 +--R x +--R + +--R 3 5 2 2 2 4 2 3 3 +--R (180a b c + 30b )d e + (- 90a c - 90b c)d e + 90b c d e +--R + +--R 3 4 2 +--R - 30c d e +--R * +--R 6 +--R g +--R + +--R 3 6 5 2 2 6 2 4 2 6 3 3 +--R (- 180a b c - 30b )e f g + (90a c + 90b c)e f g - 90b c e f g +--R + +--R 3 6 4 2 +--R 30c e f g +--R * +--R 2 +--R x +--R + +--R 2 2 5 3 2 4 +--R (180a c + 180a b )d e + (- 360a b c - 60b )d e +--R + +--R 2 2 3 3 2 4 2 3 5 +--R (180a c + 180b c)d e - 180b c d e + 60c d e +--R * +--R 6 +--R g +--R + +--R 2 2 6 5 3 6 2 4 +--R (- 180a c - 180a b )e f g + (360a b c + 60b )e f g +--R + +--R 2 2 6 3 3 2 6 4 2 3 6 5 +--R (- 180a c - 180b c)e f g + 180b c e f g - 60c e f g +--R * +--R x +--R / +--R 6 7 7 6 +--R 60d e g - 60e f g +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 987 + +)clear all + +--S 988 of 1035 +t0:=1/((d+e*x)*(f+g*x)*(a+b*x+c*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 3 2 +--R c e g x + ((b e + c d)g + c e f)x + ((a e + b d)g + (b e + c d)f)x +--R + +--R (a d g + (a e + b d)f)x + a d f +--R Type: Fraction(Polynomial(Integer)) +--E 988 + +--S 989 of 1035 +r0:=e^2*log(d+e*x)/((c*d^2-b*d*e+a*e^2)*(e*f-d*g))-g^2*log(f+g*x)/_ + ((e*f-d*g)*(c*f^2-g*(b*f-a*g)))-1/2*(c*e*f+c*d*g-b*e*g)*_ + log(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g)))-_ + (2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g))*sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((4a c - 2b )d e + 2b c d )g + ((- 4a c + 2b )e - 4c d )f g +--R + +--R 2 2 2 +--R (- 2b c e + 4c d e)f +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 +--R ((b d e - c d )g - b e f g + c e f )log(c x + b x + a) +--R + +--R 2 2 2 +--R (2a e - 2b d e + 2c d )g log(g x + f) +--R + +--R 2 2 2 2 2 +--R (- 2a e g + 2b e f g - 2c e f )log(e x + d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 2 2 3 3 +--R (2a d e - 2a b d e + 2a c d )g +--R + +--R 2 3 2 2 3 2 +--R (- 2a e + (- 2a c + 2b )d e - 2b c d )f g +--R + +--R 3 2 2 2 3 2 +--R (2a b e + (2a c - 2b )d e + 2c d )f g +--R + +--R 3 2 2 2 3 +--R (- 2a c e + 2b c d e - 2c d e)f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1035 +--d0:=D(m0,x) +--E 990 + +)clear all + +--S 991 of 1035 +t0:=1/((d+e*x)*(f+g*x)*(a+b*x+c*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 6 2 2 5 +--R c e g x + ((2b c e + c d)g + c e f)x +--R + +--R 2 2 4 +--R (((2a c + b )e + 2b c d)g + (2b c e + c d)f)x +--R + +--R 2 2 3 +--R ((2a b e + (2a c + b )d)g + ((2a c + b )e + 2b c d)f)x +--R + +--R 2 2 2 +--R ((a e + 2a b d)g + (2a b e + (2a c + b )d)f)x +--R + +--R 2 2 2 +--R (a d g + (a e + 2a b d)f)x + a d f +--R Type: Fraction(Polynomial(Integer)) +--E 991 + +--S 992 of 1035 +r0:=(-b^3*e*g+b^2*c*(e*f+d*g)-2*a*c^2*(e*f+d*g)-b*c*(c*d*f-3*a*e*g)-_ + c*(2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*x)/((b^2-4*a*c)*_ + (c*d^2-b*d*e+a*e^2)*(c*f^2-g*(b*f-a*g))*(a+b*x+c*x^2))+2*c*_ + (2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)*(c*f^2-_ + g*(b*f-a*g)))+e^4*log(d+e*x)/((c*d^2-b*d*e+a*e^2)^2*(e*f-d*g))-_ + g^4*log(f+g*x)/((e*f-d*g)*(c*f^2-g*(b*f-a*g))^2)-1/2*(c*e*f+c*d*g-_ + b*e*g)*(c*(e^2*f^2+d^2*g^2)+e*g*(2*a*e*g-b*(e*f+d*g)))*log(a+b*x+_ + c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(c*f^2-g*(b*f-a*g))^2)+(b^2*e^2*g^2*_ + (b*e*f+b*d*g-2*a*e*g)-2*c^3*d*f*(e^2*f^2+d*e*f*g+d^2*g^2)+2*c*e*g*_ + (a^2*e^2*g^2+a*b*e*g*(e*f+d*g)-b^2*(e*f+d*g)^2)-c^2*(4*a*d*e^2*f*g^2-_ + b*(e^3*f^3+5*d*e^2*f^2*g+5*d^2*e*f*g^2+d^3*g^3)))*atanh((b+2*c*x)/_ + sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*(c*f^2-g*(b*f-a*g))^2*_ + sqrt(b^2-4*a*c)) +--R +--R +--R (2) +--R 3 3 2 2 2 4 3 +--R (24a c - 24a b c + 4a b c)d e +--R + +--R 2 3 3 2 5 2 2 +--R (12a b c + 8a b c - 2b c)d e +--R + +--R 2 4 2 3 4 2 3 4 3 3 4 +--R (8a c - 24a b c + 4b c )d e + (12a b c - 2b c )d +--R * +--R 4 +--R g +--R + +--R 3 3 2 2 2 4 4 2 4 2 2 4 3 +--R (- 24a c + 24a b c - 4a b c)e - 48a c d e + 32a b c d e +--R + +--R 5 4 +--R - 24a c d +--R * +--R 3 +--R f g +--R + +--R 2 3 3 2 5 4 2 4 3 +--R (- 12a b c - 8a b c + 2b c)e + 48a c d e +--R + +--R 5 2 4 3 5 4 +--R (16a c - 16b c )d e + 12b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 4 2 3 4 2 4 4 3 +--R (- 8a c + 24a b c - 4b c )e - 32a b c d e +--R + +--R 5 2 4 2 2 6 4 +--R (- 16a c + 16b c )d e - 8c d +--R * +--R 3 +--R f g +--R + +--R 4 3 3 4 5 3 5 2 2 6 3 4 +--R ((- 12a b c + 2b c )e + 24a c d e - 12b c d e + 8c d e)f +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 5 3 +--R (24a b c - 24a b c + 4a b )d e +--R + +--R 2 2 2 4 6 2 2 +--R (12a b c + 8a b c - 2b )d e +--R + +--R 2 3 3 2 5 3 2 3 4 2 4 +--R (8a b c - 24a b c + 4b c)d e + (12a b c - 2b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 2 3 5 4 2 3 2 2 2 3 3 +--R (- 24a b c + 24a b c - 4a b )e - 48a b c d e + 32a b c d e +--R + +--R 4 4 +--R - 24a b c d +--R * +--R 3 +--R f g +--R + +--R 2 2 2 4 6 4 2 3 3 +--R (- 12a b c - 8a b c + 2b )e + 48a b c d e +--R + +--R 4 3 3 3 2 4 4 +--R (16a b c - 16b c )d e + 12b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 3 3 2 5 4 2 3 3 +--R (- 8a b c + 24a b c - 4b c)e - 32a b c d e +--R + +--R 4 3 3 2 2 5 4 +--R (- 16a b c + 16b c )d e - 8b c d +--R * +--R 3 +--R f g +--R + +--R 2 3 4 2 4 4 3 2 4 2 2 5 3 4 +--R ((- 12a b c + 2b c )e + 24a b c d e - 12b c d e + 8b c d e)f +--R * +--R x +--R + +--R 4 2 3 2 2 4 3 3 2 2 3 5 2 2 +--R (24a c - 24a b c + 4a b )d e + (12a b c + 8a b c - 2a b )d e +--R + +--R 3 3 2 2 2 4 3 2 3 3 2 4 +--R (8a c - 24a b c + 4a b c)d e + (12a b c - 2a b c )d +--R * +--R 4 +--R g +--R + +--R 4 2 3 2 2 4 4 3 3 2 2 2 3 3 +--R (- 24a c + 24a b c - 4a b )e - 48a c d e + 32a b c d e +--R + +--R 2 4 4 +--R - 24a c d +--R * +--R 3 +--R f g +--R + +--R 3 2 2 3 5 4 3 3 3 +--R (- 12a b c - 8a b c + 2a b )e + 48a c d e +--R + +--R 2 4 2 3 3 4 4 +--R (16a c - 16a b c )d e + 12a b c d +--R * +--R 2 2 +--R f g +--R + +--R 3 3 2 2 2 4 4 2 3 3 +--R (- 8a c + 24a b c - 4a b c)e - 32a b c d e +--R + +--R 2 4 2 3 2 2 5 4 +--R (- 16a c + 16a b c )d e - 8a c d +--R * +--R 3 +--R f g +--R + +--R 2 3 3 2 4 2 4 3 4 2 2 5 3 4 +--R ((- 12a b c + 2a b c )e + 24a c d e - 12a b c d e + 8a c d e)f +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 3 2 3 2 2 4 2 2 +--R (8a b c - 2a b c)d e + (- 8a c - 2a b c + b c)d e +--R + +--R 3 3 2 3 4 2 3 4 +--R (8a b c - 2b c )d e + (- 4a c + b c )d +--R * +--R 4 +--R g +--R + +--R 2 2 3 4 3 2 3 2 2 4 4 2 2 +--R (- 8a b c + 2a b c)e f g + (8a c + 2a b c - b c)e f g +--R + +--R 3 3 2 4 3 4 2 3 4 4 +--R (- 8a b c + 2b c )e f g + (4a c - b c )e f +--R * +--R 2 +--R x +--R + +--R 2 2 4 3 2 2 3 5 2 2 +--R (8a b c - 2a b )d e + (- 8a b c - 2a b c + b )d e +--R + +--R 2 2 4 3 3 3 2 4 +--R (8a b c - 2b c)d e + (- 4a b c + b c )d +--R * +--R 4 +--R g +--R + +--R 2 2 4 4 3 2 2 3 5 4 2 2 +--R (- 8a b c + 2a b )e f g + (8a b c + 2a b c - b )e f g +--R + +--R 2 2 4 4 3 3 3 2 4 4 +--R (- 8a b c + 2b c)e f g + (4a b c - b c )e f +--R * +--R x +--R + +--R 3 2 3 3 3 2 2 2 4 2 2 +--R (8a b c - 2a b )d e + (- 8a c - 2a b c + a b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (8a b c - 2a b c)d e + (- 4a c + a b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 3 4 3 3 2 2 2 4 4 2 2 +--R (- 8a b c + 2a b )e f g + (8a c + 2a b c - a b )e f g +--R + +--R 2 2 3 4 3 2 3 2 2 4 4 +--R (- 8a b c + 2a b c)e f g + (4a c - a b c )e f +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 4 2 2 3 3 +--R (8a c - 2a b c)e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (16a c + 4a b c - 2b c)d e + (- 16a b c + 4b c )d e +--R + +--R 4 2 3 4 +--R (8a c - 2b c )d +--R * +--R 4 2 +--R g x +--R + +--R 3 2 3 4 2 2 4 3 +--R (8a b c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (16a b c + 4a b c - 2b )d e + (- 16a b c + 4b c)d e +--R + +--R 3 3 2 4 +--R (8a b c - 2b c )d +--R * +--R 4 +--R g x +--R + +--R 4 3 2 4 3 2 3 3 +--R (8a c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 +--R (8a c - 2a b c )d +--R * +--R 4 +--R g +--R * +--R log(g x + f) +--R + +--R 3 2 2 2 4 4 2 2 3 4 3 +--R (- 8a c + 2a b c)e g + (16a b c - 4a b c)e f g +--R + +--R 2 3 2 2 4 4 2 2 3 3 2 4 3 +--R (- 16a c - 4a b c + 2b c)e f g + (16a b c - 4b c )e f g +--R + +--R 4 2 3 4 4 +--R (- 8a c + 2b c )e f +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 4 2 2 4 4 3 +--R (- 8a b c + 2a b )e g + (16a b c - 4a b )e f g +--R + +--R 2 2 3 5 4 2 2 2 2 4 4 3 +--R (- 16a b c - 4a b c + 2b )e f g + (16a b c - 4b c)e f g +--R + +--R 3 3 2 4 4 +--R (- 8a b c + 2b c )e f +--R * +--R x +--R + +--R 4 3 2 4 4 3 2 3 4 3 +--R (- 8a c + 2a b )e g + (16a b c - 4a b )e f g +--R + +--R 3 2 2 2 4 4 2 2 2 2 3 4 3 +--R (- 16a c - 4a b c + 2a b )e f g + (16a b c - 4a b c)e f g +--R + +--R 2 3 2 2 4 4 +--R (- 8a c + 2a b c )e f +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 3 2 2 3 2 2 +--R (- 4a c + 2a b c)d e + (2a b c - 2a b c)d e +--R + +--R 2 3 2 2 3 3 4 +--R (- 4a c + 4a b c )d e - 2a b c d +--R * +--R 4 +--R g +--R + +--R 3 2 2 2 4 2 3 2 2 4 2 2 3 2 3 +--R (4a c - 2a b c)e + (8a c - 4a b c + 2b c)d e - 4b c d e +--R + +--R 4 2 3 4 +--R (4a c + 2b c )d +--R * +--R 3 +--R f g +--R + +--R 2 2 3 4 2 3 2 2 4 3 +--R (- 2a b c + 2a b c)e + (- 8a c + 4a b c - 2b c)d e +--R + +--R 4 2 3 3 4 4 +--R (- 8a c + 8b c )d e - 6b c d +--R * +--R 2 2 +--R f g +--R + +--R 2 3 2 2 4 3 2 3 4 2 3 2 2 5 4 +--R ((4a c - 4a b c )e + 4b c d e + (8a c - 8b c )d e + 4c d ) +--R * +--R 3 +--R f g +--R + +--R 3 4 4 2 3 3 4 2 2 5 3 4 +--R (2a b c e + (- 4a c - 2b c )d e + 6b c d e - 4c d e)f +--R * +--R x +--R + +--R 3 2 3 3 3 2 2 2 4 2 2 +--R (- 6a b c + 2a b )d e + (4a c + 4a b c - 2a b )d e +--R + +--R 2 2 3 3 2 3 2 2 4 +--R (- 10a b c + 4a b c)d e + (4a c - 2a b c )d +--R * +--R 4 +--R g +--R + +--R 3 2 3 4 2 2 3 5 2 2 +--R (6a b c - 2a b )e + (4a b c - 6a b c + 2b )d e +--R + +--R 2 2 4 3 3 3 2 4 +--R (8a b c - 4b c)d e + (- 2a b c + 2b c )d +--R * +--R 3 +--R f g +--R + +--R 3 2 2 2 4 4 2 2 3 5 3 +--R (- 4a c - 4a b c + 2a b )e + (- 4a b c + 6a b c - 2b )d e +--R + +--R 3 3 2 3 4 2 3 4 +--R (- 12a b c + 6b c )d e + (4a c - 4b c )d +--R * +--R 2 2 +--R f g +--R + +--R 2 2 3 4 2 2 4 3 +--R (10a b c - 4a b c)e + (- 8a b c + 4b c)d e +--R + +--R 3 3 2 2 2 4 4 +--R (12a b c - 6b c )d e + 2b c d +--R * +--R 3 +--R f g +--R + +--R 2 3 2 2 4 3 3 2 3 +--R (- 4a c + 2a b c )e + (2a b c - 2b c )d e +--R + +--R 4 2 3 2 2 4 3 +--R (- 4a c + 4b c )d e - 2b c d e +--R * +--R 4 +--R f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 2 4 4 2 3 3 2 3 +--R (8a c - 2a b c)d e + (- 16a b c + 4a b c)d e +--R + +--R 4 3 3 2 2 2 4 3 2 3 3 2 3 2 4 +--R (16a c + 4a b c - 2a b c)d e + (- 16a b c + 4a b c )d e +--R + +--R 3 4 2 2 3 5 +--R (8a c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 5 2 4 2 5 4 3 3 2 2 2 4 2 3 +--R (- 8a c + 2a b c)e + (- 16a c + 28a b c - 6a b c)d e +--R + +--R 3 3 2 3 2 5 3 2 +--R (- 16a b c - 12a b c + 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 4 2 4 3 3 5 +--R (- 8a c + 34a b c - 8a b c )d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 2 3 3 5 4 3 3 2 2 2 4 4 +--R (16a b c - 4a b c)e + (16a c - 28a b c + 6a b c)d e +--R + +--R 3 4 2 2 3 4 2 6 3 2 +--R (32a c - 8a b c + 8a b c - 2b c)d e +--R + +--R 2 4 3 3 5 2 4 2 5 2 4 4 3 5 +--R (- 16a b c - 12a b c + 4b c )d e + (16a c + 4a b c - 2b c )d +--R * +--R 2 3 +--R f g +--R + +--R 4 3 3 2 2 2 4 5 +--R (- 16a c - 4a b c + 2a b c)e +--R + +--R 3 3 2 3 2 5 4 +--R (16a b c + 12a b c - 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 6 2 3 +--R (- 32a c + 8a b c - 8a b c + 2b c)d e +--R + +--R 2 5 2 4 4 3 4 5 3 4 5 +--R (- 16a c + 28a b c - 6b c )d e + (- 16a b c + 4b c )d +--R * +--R 3 2 +--R f g +--R + +--R 3 3 2 3 2 5 3 4 2 2 3 4 2 4 +--R (16a b c - 4a b c )e + (8a c - 34a b c + 8a b c )d e +--R + +--R 2 4 3 3 5 2 2 3 +--R (16a b c + 12a b c - 4b c )d e +--R + +--R 2 5 2 4 4 3 3 2 6 2 5 5 +--R (16a c - 28a b c + 6b c )d e + (8a c - 2b c )d +--R * +--R 4 +--R f g +--R + +--R 3 4 2 2 3 5 2 4 3 3 4 +--R (- 8a c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 2 5 2 4 4 3 2 3 5 3 4 3 2 +--R (- 16a c - 4a b c + 2b c )d e + (16a b c - 4b c )d e +--R + +--R 6 2 5 4 +--R (- 8a c + 2b c )d e +--R * +--R 5 +--R f +--R * +--R 2 +--R x +--R + +--R 5 4 3 4 4 2 3 4 2 3 +--R (8a b c - 2a b )d e + (- 16a b c + 4a b )d e +--R + +--R 4 2 3 3 2 5 3 2 3 2 2 2 4 4 +--R (16a b c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 3 3 2 3 2 5 +--R (8a b c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 5 4 3 5 4 2 3 3 2 5 2 3 +--R (- 8a b c + 2a b )e + (- 16a b c + 28a b c - 6a b )d e +--R + +--R 3 2 2 2 4 6 3 2 +--R (- 16a b c - 12a b c + 4a b )d e +--R + +--R 3 3 2 3 2 5 4 2 2 3 4 2 5 +--R (- 8a b c + 34a b c - 8a b c)d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 2 3 4 5 4 2 3 3 2 5 4 +--R (16a b c - 4a b )e + (16a b c - 28a b c + 6a b )d e +--R + +--R 3 3 2 3 2 5 7 3 2 +--R (32a b c - 8a b c + 8a b c - 2b )d e +--R + +--R 2 2 3 4 2 6 4 +--R (- 16a b c - 12a b c + 4b c)d e +--R + +--R 2 4 3 3 5 2 5 +--R (16a b c + 4a b c - 2b c )d +--R * +--R 2 3 +--R f g +--R + +--R 4 2 3 3 2 5 5 +--R (- 16a b c - 4a b c + 2a b )e +--R + +--R 3 2 2 2 4 6 4 +--R (16a b c + 12a b c - 4a b )d e +--R + +--R 3 3 2 3 2 5 7 2 3 +--R (- 32a b c + 8a b c - 8a b c + 2b )d e +--R + +--R 2 4 3 3 5 2 4 2 4 4 3 5 +--R (- 16a b c + 28a b c - 6b c )d e + (- 16a b c + 4b c )d +--R * +--R 3 2 +--R f g +--R + +--R 3 2 2 2 4 5 3 3 2 3 2 5 4 +--R (16a b c - 4a b c)e + (8a b c - 34a b c + 8a b c)d e +--R + +--R 2 2 3 4 2 6 2 3 +--R (16a b c + 12a b c - 4b c)d e +--R + +--R 2 4 3 3 5 2 3 2 5 3 4 5 +--R (16a b c - 28a b c + 6b c )d e + (8a b c - 2b c )d +--R * +--R 4 +--R f g +--R + +--R 3 3 2 3 2 5 2 2 3 4 2 4 +--R (- 8a b c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 2 4 3 3 5 2 2 3 2 4 4 3 3 2 +--R (- 16a b c - 4a b c + 2b c )d e + (16a b c - 4b c )d e +--R + +--R 5 3 4 4 +--R (- 8a b c + 2b c )d e +--R * +--R 5 +--R f +--R * +--R x +--R + +--R 6 5 2 4 5 4 3 2 3 +--R (8a c - 2a b )d e + (- 16a b c + 4a b )d e +--R + +--R 5 2 4 2 3 4 3 2 4 2 3 3 4 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 4 3 3 2 2 5 +--R (8a c - 2a b c )d +--R * +--R 5 +--R g +--R + +--R 6 5 2 5 5 2 4 2 3 4 2 3 +--R (- 8a c + 2a b )e + (- 16a c + 28a b c - 6a b )d e +--R + +--R 4 2 3 3 2 5 3 2 +--R (- 16a b c - 12a b c + 4a b )d e +--R + +--R 4 3 3 2 2 2 4 4 3 3 2 3 2 5 +--R (- 8a c + 34a b c - 8a b c)d e + (- 16a b c + 4a b c )d +--R * +--R 4 +--R f g +--R + +--R 5 4 3 5 5 2 4 2 3 4 4 +--R (16a b c - 4a b )e + (16a c - 28a b c + 6a b )d e +--R + +--R 4 3 3 2 2 2 4 6 3 2 +--R (32a c - 8a b c + 8a b c - 2a b )d e +--R + +--R 3 3 2 3 2 5 4 3 4 2 2 3 4 2 5 +--R (- 16a b c - 12a b c + 4a b c)d e + (16a c + 4a b c - 2a b c )d +--R * +--R 2 3 +--R f g +--R + +--R 5 2 4 2 3 4 5 4 2 3 3 2 5 4 +--R (- 16a c - 4a b c + 2a b )e + (16a b c + 12a b c - 4a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 3 +--R (- 32a c + 8a b c - 8a b c + 2a b )d e +--R + +--R 3 4 2 2 3 4 2 4 2 4 3 3 5 +--R (- 16a c + 28a b c - 6a b c )d e + (- 16a b c + 4a b c )d +--R * +--R 3 2 +--R f g +--R + +--R 4 2 3 3 5 4 3 3 2 2 2 4 4 +--R (16a b c - 4a b c)e + (8a c - 34a b c + 8a b c)d e +--R + +--R 3 3 2 3 2 5 2 3 +--R (16a b c + 12a b c - 4a b c)d e +--R + +--R 3 4 2 2 3 4 2 3 2 2 5 2 4 5 +--R (16a c - 28a b c + 6a b c )d e + (8a c - 2a b c )d +--R * +--R 4 +--R f g +--R + +--R 4 3 3 2 2 5 3 3 2 3 2 4 +--R (- 8a c + 2a b c )e + (16a b c - 4a b c )d e +--R + +--R 3 4 2 2 3 4 2 2 3 2 4 3 3 3 2 +--R (- 16a c - 4a b c + 2a b c )d e + (16a b c - 4a b c )d e +--R + +--R 2 5 2 4 4 +--R (- 8a c + 2a b c )d e +--R * +--R 5 +--R f +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1035 +--d0:=D(m0,x) +--E 993 + +)clear all + +--S 994 of 1035 +t0:=sqrt(a+b*x+c*x^2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R (1) --------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1035 +r0:=atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/(e*g)+_ + atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*_ + sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/(e*(e*f-d*g))-atanh(1/2*_ + (b*f-2*a*g+(2*c*f-b*g)*x)/(sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))*_ + sqrt(c*f^2-b*f*g+a*g^2)/(g*(e*f-d*g)) +--R +--R +--R (2) +--R +-+ 2c x + b +--R (d g - e f)\|c atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 (b e - 2c d)x + 2a e - b d +--R g\|a e - b d e + c d atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R | 2 2 (b g - 2c f)x + 2a g - b f +--R - e\|a g - b f g + c f atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R / +--R 2 2 +--R d e g - e f g +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1035 +--d0:=D(m0,x) +--E 996 + +)clear all + +--S 997 of 1035 +t0:=(a+b*x+c*x^2)^(3/2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (c x + b x + a)\|c x + b x + a +--R (1) --------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1035 +r0:=(c*d^2-b*d*e+a*e^2)^(3/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^3*(e*f-d*g))-_ + (c*f^2-b*f*g+a*g^2)^(3/2)*atanh(1/2*(b*f-2*a*g+(2*c*f-b*g)*x)/_ + (sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))/(g^3*(e*f-d*g))-_ + 1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*atanh(1/2*(b+2*c*x)/(sqrt(c)*_ + sqrt(a+b*x+c*x^2)))/(e^3*(e*f-d*g)*sqrt(c))+1/8*(8*c^2*e*f^3+b*g^2*_ + (3*b*e*f+b*d*g-4*a*e*g)-4*c*g*(3*b*e*f^2-a*g*(3*e*f-d*g)))*_ + atanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e*g^3*(e*f-d*g)*_ + sqrt(c))+(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)/(e^2*(e*f-d*g))-_ + 1/4*(4*c*e*f^2-g*(5*b*e*f-b*d*g-4*a*e*g)-2*c*g*(e*f-d*g)*x)*_ + sqrt(a+b*x+c*x^2)/(e*g^2*(e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 2 3 3 2 3 2 +--R ((12a c + 3b )d e - 12b c d e + 8c d )g + (- 12a c - 3b )e f g +--R + +--R 3 2 2 3 3 +--R 12b c e f g - 8c e f +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R +-------------------+ +--R 2 2 3 +-+ | 2 2 +--R (8a e - 8b d e + 8c d )g \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R +-------------------+ +--R 3 2 3 3 2 +-+ | 2 2 +--R (- 8a e g + 8b e f g - 8c e f )\|c \|a g - b f g + c f +--R * +--R (b g - 2c f)x + 2a g - b f +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (4c d e g - 4c e f g )x + (10b d e - 8c d e)g - 10b e f g +--R + +--R 3 2 +--R 8c e f g +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 3 4 4 3 +-+ +--R (8d e g - 8e f g )\|c +--R Type: Expression(Integer) +--E 998 + +--S 999 of 1035 +--d0:=D(m0,x) +--E 999 + +)clear all + +--S 1000 of 1035 +t0:=(a+b*x+c*x^2)^(5/2)/((d+e*x)*(f+g*x)) +--R +--R +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (c x + 2b c x + (2a c + b )x + 2a b x + a )\|c x + b x + a +--R (1) --------------------------------------------------------------- +--R 2 +--R e g x + (d g + e f)x + d f +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1035 +r0:=1/3*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2)/(e^2*(e*f-d*g))-_ + 1/24*(8*c*e*f^2-g*(11*b*e*f-3*b*d*g-8*a*e*g)-6*c*g*(e*f-d*g)*x)*_ + (a+b*x+c*x^2)^(3/2)/(e*g^2*(e*f-d*g))-1/16*(2*c*d-b*e)*(c*d^2-b*d*e+_ + a*e^2)*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*atanh(1/2*(b+2*c*x)/_ + (sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*e^5*(e*f-d*g))+1/128*_ + (128*c^4*e*f^5-320*c^3*e*f^3*g*(b*f-a*g)-b^3*g^4*(5*b*e*f+3*b*d*g-_ + 8*a*e*g)+48*c^2*g^2*(5*b^2*e*f^3-10*a*b*e*f^2*g+a^2*g^2*(5*e*f-d*g))-_ + 8*b*c*g^3*(5*b^2*e*f^2+12*a^2*e*g^2-3*a*b*g*(5*e*f+d*g)))*atanh(1/2*_ + (b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*e*g^5*(e*f-d*g))+_ + (c*d^2-b*d*e+a*e^2)^(5/2)*atanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/_ + (sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*(e*f-d*g))-_ + (c*f^2-b*f*g+a*g^2)^(5/2)*atanh(1/2*(b*f-2*a*g+(2*c*f-b*g)*x)/_ + (sqrt(c*f^2-g*(b*f-a*g))*sqrt(a+b*x+c*x^2)))/(g^5*(e*f-d*g))+_ + 1/8*(c*d^2-b*d*e+a*e^2)*(8*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-4*a*e)-_ + 2*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(c*e^4*(e*f-d*g))-_ + 1/64*(64*c^3*e*f^4-16*c^2*e*f^2*g*(9*b*f-8*a*g)-b^2*g^3*(5*b*e*f+_ + 3*b*d*g-8*a*e*g)+4*c*g^2*(22*b^2*e*f^2+16*a^2*e*g^2-3*a*b*g*(13*e*f-_ + d*g))-2*c*g*(16*c^2*e*f^3+b*g^2*(5*b*e*f+3*b*d*g-8*a*e*g)-_ + 4*c*g*(6*b*e*f^2-a*g*(7*e*f-3*d*g)))*x)*sqrt(a+b*x+c*x^2)/(c*e*g^4*_ + (e*f-d*g)) +--R +--R +--R (2) +--R 2 2 2 4 4 2 3 2 3 +--R (720a c + 360a b c - 15b )d e + (- 1440a b c - 120b c)d e +--R + +--R 3 2 2 3 2 3 4 4 5 +--R (960a c + 720b c )d e - 960b c d e + 384c d +--R * +--R 5 +--R g +--R + +--R 2 2 2 4 5 4 2 3 5 2 3 +--R (- 720a c - 360a b c + 15b )e f g + (1440a b c + 120b c)e f g +--R + +--R 3 2 2 5 3 2 3 5 4 4 5 5 +--R (- 960a c - 720b c )e f g + 960b c e f g - 384c e f +--R * +--R 2c x + b +--R atanh(----------------------) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R + +--R 2 4 3 2 2 2 2 2 3 +--R 384a c e - 768a b c d e + (768a c + 384b c)d e - 768b c d e +--R + +--R 3 4 +--R 384c d +--R * +--R +-------------------+ +--R 5 +-+ | 2 2 +--R g \|c \|a e - b d e + c d +--R * +--R (b e - 2c d)x + 2a e - b d +--R atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a e - b d e + c d \|c x + b x + a +--R + +--R 2 5 4 5 3 2 2 5 2 2 +--R - 384a c e g + 768a b c e f g + (- 768a c - 384b c)e f g +--R + +--R 2 5 3 3 5 4 +--R 768b c e f g - 384c e f +--R * +--R +-------------------+ +--R +-+ | 2 2 (b g - 2c f)x + 2a g - b f +--R \|c \|a g - b f g + c f atanh(----------------------------------------) +--R +-------------------+ +--------------+ +--R | 2 2 | 2 +--R 2\|a g - b f g + c f \|c x + b x + a +--R + +--R 3 4 5 3 5 4 3 +--R (96c d e g - 96c e f g )x +--R + +--R 2 4 3 2 3 5 2 5 4 3 5 2 3 2 +--R ((272b c d e - 128c d e )g - 272b c e f g + 128c e f g )x +--R + +--R 2 2 4 2 2 3 3 3 2 5 +--R ((432a c + 236b c)d e - 416b c d e + 192c d e )g +--R + +--R 2 2 5 4 2 5 2 3 3 5 3 2 +--R (- 432a c - 236b c)e f g + 416b c e f g - 192c e f g +--R * +--R x +--R + +--R 3 4 2 2 2 3 2 3 2 +--R (1112a b c + 30b )d e + (- 896a c - 528b c)d e + 864b c d e +--R + +--R 3 4 +--R - 384c d e +--R * +--R 5 +--R g +--R + +--R 3 5 4 2 2 5 2 3 2 5 3 2 +--R (- 1112a b c - 30b )e f g + (896a c + 528b c)e f g - 864b c e f g +--R + +--R 3 5 4 +--R 384c e f g +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 5 6 6 5 +-+ +--R (384c d e g - 384c e f g )\|c +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1035 +--d0:=D(m0,x) +--E 1002 + +)clear all + +--S 1003 of 1035 +t0:=(d+e*x)^m*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 2 m +--R (c x + b x + a)(e x + d) +--R (1) -------------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1035 +--r0:=2*a*(d+e*x)^(1+m)/((e^2-d*f)*sqrt(e+f*x))+2*c*e^2*(d+e*x)^(1+m)/_ +-- (f^2*(e^2-d*f)*sqrt(e+f*x))-2*b*e*(d+e*x)^(1+m)/(f*(e^2-d*f)*_ +-- sqrt(e+f*x))+2*c*(d+e*x)^(1+m)*sqrt(e+f*x)/(e*f^2*(3+2*m))-_ +-- 2*a*e*(1+2*m)*(d+e*x)^m*hypergeometric(1/2,-m,3/2,e*(e+f*x)/_ +-- (e^2-d*f))*sqrt(e+f*x)/(f*(e^2-d*f)*(-f*(d+e*x)/(e^2-d*f))^m)-_ +-- 2*b*(d*f-2*e^2*(1+m))*(d+e*x)^m*hypergeometric(1/2,-m,3/2,_ +-- e*(e+f*x)/(e^2-d*f))*sqrt(e+f*x)/(f^2*(e^2-d*f)*(-f*(d+e*x)/_ +-- (e^2-d*f))^m)+2*c*(d^2*f^2+4*d*e^2*f*(1+m)-4*e^4*(2+3*m+m^2))*_ +-- (d+e*x)^m*hypergeometric(1/2,-m,3/2,e*(e+f*x)/(e^2-d*f))*_ +-- sqrt(e+f*x)/(e*f^3*(e^2-d*f)*(3+2*m)*(-f*(d+e*x)/(e^2-d*f))^m) +--E 1004 + +--S 1005 of 1035 +--d0:=D(m0,x) +--E 1005 + +)clear all + +--S 1006 of 1035 +t0:=(d+e*x)^3*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R (1) +--R 3 5 3 2 4 3 2 2 3 +--R c e x + (b e + 3c d e )x + (a e + 3b d e + 3c d e)x +--R + +--R 2 2 3 2 2 3 3 +--R (3a d e + 3b d e + c d )x + (3a d e + b d )x + a d +--R / +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1035 +r0:=2/3*(e^2-d*f)*(3*e*f*(2*b*e^2-b*d*f-a*e*f)-c*(10*e^4-8*d*e^2*f+_ + d^2*f^2))*(e+f*x)^(3/2)/f^6-2/5*e*(e*f*(4*b*e^2-3*b*d*f-a*e*f)-_ + c*(10*e^4-12*d*e^2*f+3*d^2*f^2))*(e+f*x)^(5/2)/f^6-2/7*e^2*(5*c*e^2-_ + 3*c*d*f-b*e*f)*(e+f*x)^(7/2)/f^6+2/9*c*e^3*(e+f*x)^(9/2)/f^6+_ + 2*(e^2-d*f)^3*(c*e^2-f*(b*e-a*f))/(f^6*sqrt(e+f*x))-2*(e^2-d*f)^2*_ + (f*(4*b*e^2-b*d*f-3*a*e*f)-c*(5*e^3-2*d*e*f))*sqrt(e+f*x)/f^6 +--R +--R +--R (2) +--R 3 5 5 3 2 5 4 4 4 +--R 70c e f x + ((90b e + 270c d e )f - 100c e f )x +--R + +--R 3 2 2 5 4 3 4 +--R (126a e + 378b d e + 378c d e)f + (- 144b e - 432c d e )f +--R + +--R 5 3 +--R 160c e f +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 +--R (630a d e + 630b d e + 210c d )f +--R + +--R 4 3 2 2 4 5 4 3 +--R (- 252a e - 756b d e - 756c d e )f + (288b e + 864c d e )f +--R + +--R 6 2 +--R - 320c e f +--R * +--R 2 +--R x +--R + +--R 2 3 5 3 2 2 3 4 +--R (1890a d e + 630b d )f + (- 2520a d e - 2520b d e - 840c d e)f +--R + +--R 5 4 2 3 3 6 5 2 +--R (1008a e + 3024b d e + 3024c d e )f + (- 1152b e - 3456c d e )f +--R + +--R 7 +--R 1280c e f +--R * +--R x +--R + +--R 3 5 2 2 3 4 +--R - 630a d f + (3780a d e + 1260b d e)f +--R + +--R 4 2 3 3 2 3 +--R (- 5040a d e - 5040b d e - 1680c d e )f +--R + +--R 6 5 2 4 2 7 6 +--R (2016a e + 6048b d e + 6048c d e )f + (- 2304b e - 6912c d e )f +--R + +--R 8 +--R 2560c e +--R / +--R 6 +-------+ +--R 315f \|f x + e +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1008 + +)clear all + +--S 1009 of 1035 +t0:=(d+e*x)^2*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R (1) +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R / +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1035 +r0:=-2/3*(e*f*(3*b*e^2-2*b*d*f-a*e*f)-c*(6*e^4-6*d*e^2*f+d^2*f^2))*_ + (e+f*x)^(3/2)/f^5-2/5*e*(4*c*e^2-2*c*d*f-b*e*f)*(e+f*x)^(5/2)/f^5+_ + 2/7*c*e^2*(e+f*x)^(7/2)/f^5-2*(e^2-d*f)^2*(c*e^2-f*(b*e-a*f))/_ + (f^5*sqrt(e+f*x))+2*(e^2-d*f)*(f*(3*b*e^2-b*d*f-2*a*e*f)-_ + c*(4*e^3-2*d*e*f))*sqrt(e+f*x)/f^5 +--R +--R +--R (2) +--R 2 4 4 2 4 3 3 3 +--R 30c e f x + ((42b e + 84c d e)f - 48c e f )x +--R + +--R 2 2 4 3 2 3 4 2 2 +--R ((70a e + 140b d e + 70c d )f + (- 84b e - 168c d e )f + 96c e f )x +--R + +--R 2 4 3 2 2 3 +--R (420a d e + 210b d )f + (- 280a e - 560b d e - 280c d e)f +--R + +--R 4 3 2 5 +--R (336b e + 672c d e )f - 384c e f +--R * +--R x +--R + +--R 2 4 2 2 3 +--R - 210a d f + (840a d e + 420b d e)f +--R + +--R 4 3 2 2 2 5 4 6 +--R (- 560a e - 1120b d e - 560c d e )f + (672b e + 1344c d e )f - 768c e +--R / +--R 5 +-------+ +--R 105f \|f x + e +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1011 + +)clear all + +--S 1012 of 1035 +t0:=(d+e*x)*(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 3 2 +--R c e x + (b e + c d)x + (a e + b d)x + a d +--R (1) ------------------------------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1035 +r0:=-2/3*(3*c*e^2-c*d*f-b*e*f)*(e+f*x)^(3/2)/f^4+2/5*c*e*(e+f*x)^(5/2)/f^4+_ + 2*(e^2-d*f)*(c*e^2-f*(b*e-a*f))/(f^4*sqrt(e+f*x))-2*(f*(2*b*e^2-_ + b*d*f-a*e*f)-c*(3*e^3-2*d*e*f))*sqrt(e+f*x)/f^4 +--R +--R +--R (2) +--R 3 3 3 2 2 2 +--R 6c e f x + ((10b e + 10c d)f - 12c e f )x +--R + +--R 3 2 2 3 3 +--R ((30a e + 30b d)f + (- 40b e - 40c d e)f + 48c e f)x - 30a d f +--R + +--R 2 2 3 2 4 +--R (60a e + 60b d e)f + (- 80b e - 80c d e )f + 96c e +--R / +--R 4 +-------+ +--R 15f \|f x + e +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1014 + +)clear all + +--S 1015 of 1035 +t0:=(a+b*x+c*x^2)/(e+f*x)^(3/2) +--R +--R +--R 2 +--R c x + b x + a +--R (1) ------------------- +--R +-------+ +--R (f x + e)\|f x + e +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1035 +r0:=2/3*c*(e+f*x)^(3/2)/f^3-2*(c*e^2-f*(b*e-a*f))/(f^3*sqrt(e+f*x))-_ + 2*(2*c*e-b*f)*sqrt(e+f*x)/f^3 +--R +--R +--R 2 2 2 2 2 +--R 2c f x + (6b f - 8c e f)x - 6a f + 12b e f - 16c e +--R (2) ------------------------------------------------------ +--R 3 +-------+ +--R 3f \|f x + e +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1017 + +)clear all + +--S 1018 of 1035 +t0:=(a+b*x+c*x^2)/((d+e*x)*(e+f*x)^(3/2)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) -------------------------------------- +--R 2 2 +-------+ +--R (e f x + (d f + e )x + d e)\|f x + e +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1035 +r0:=-2*(c*d^2-b*d*e+a*e^2)*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(3/2))+2*(c*e^2-f*(b*e-a*f))/(f^2*(e^2-d*f)*_ + sqrt(e+f*x))+2*c*sqrt(e+f*x)/(e*f^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-------+ \|e \|f x + e +--R (2a e - 2b d e + 2c d )f \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 2 2 2 2 3 +--R ((2c d f - 2c e f)x - 2a e f + (2b e + 2c d e)f - 4c e ) +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R +----------+ +--R 3 3 2 | 2 +-+ +-------+ +--R (d e f - e f )\|- d f + e \|e \|f x + e +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 1035 +t0:=(a+b*x+c*x^2)/((d+e*x)^2*(e+f*x)^(3/2)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) ----------------------------------------------------------- +--R 2 3 3 2 2 2 2 +-------+ +--R (e f x + (2d e f + e )x + (d f + 2d e )x + d e)\|f x + e +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1035 +r0:=(c*d^2-b*d*e+a*e^2)*f*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(5/2))-2*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/(e^(3/2)*(e^2-d*f)^(5/2))-_ + 2*(c*e^2-f*(b*e-a*f))/(f*(e^2-d*f)^2*sqrt(e+f*x))+(c*d^2-b*d*e+a*e^2)*_ + f*sqrt(e+f*x)/(e*(e^2-d*f)^2*(e^2-d*f-e*(e+f*x))) +--R +--R +--R (2) +--R 3 2 2 2 4 3 +--R ((3a e - b d e - c d e)f + (- 2b e + 4c d e )f)x +--R + +--R 2 2 3 2 3 2 2 +--R (3a d e - b d e - c d )f + (- 2b d e + 4c d e )f +--R * +--R +-+ +-------+ +--R +-------+ \|e \|f x + e +--R \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 2 2 2 3 4 2 +--R ((- 3a e + b d e - c d )f + 2b e f - 2c e )x - 2a d e f +--R + +--R 3 2 2 3 +--R (- a e + 3b d e - c d e)f - 2c d e +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R +----------+ +--R 2 2 3 4 2 6 3 3 2 3 2 5 | 2 +-+ +--R ((d e f - 2d e f + e f)x + d e f - 2d e f + d e f)\|- d f + e \|e +--R * +--R +-------+ +--R \|f x + e +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1023 + +)clear all + +--S 1024 of 1035 +t0:=(a+b*x+c*x^2)/((d+e*x)^3*(e+f*x)^(3/2)) +--R +--R +--R (1) +--R 2 +--R c x + b x + a +--R / +--R 3 4 2 4 3 2 3 2 3 2 2 3 +--R (e f x + (3d e f + e )x + (3d e f + 3d e )x + (d f + 3d e )x + d e) +--R * +--R +-------+ +--R \|f x + e +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1035 +r0:=-3/4*(c*d^2-b*d*e+a*e^2)*f^2*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/_ + (e^(3/2)*(e^2-d*f)^(7/2))+f*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))/(e^(3/2)*(e^2-d*f)^(7/2))-_ + 2*(c*e^2-f*(b*e-a*f))*atanh(sqrt(e)*sqrt(e+f*x)/sqrt(e^2-d*f))*_ + sqrt(e)/(e^2-d*f)^(7/2)+2*(c*e^2-f*(b*e-a*f))/((e^2-d*f)^3*_ + sqrt(e+f*x))-1/2*(c*d^2-b*d*e+a*e^2)*f^2*sqrt(e+f*x)/(e*(e^2-d*f)^2*_ + (e^2-d*f-e*(e+f*x))^2)-3/4*(c*d^2-b*d*e+a*e^2)*f^2*sqrt(e+f*x)/_ + (e*(e^2-d*f)^3*(e^2-d*f-e*(e+f*x)))+f*(e^2*(b*e-a*f)-c*d*(2*e^2-d*f))*_ + sqrt(e+f*x)/(e*(e^2-d*f)^3*(e^2-d*f-e*(e+f*x))) +--R +--R +--R (2) +--R 4 3 2 2 2 5 4 6 2 +--R ((15a e - 3b d e - c d e )f + (- 12b e + 8c d e )f + 8c e )x +--R + +--R 3 2 2 3 2 4 2 3 +--R (30a d e - 6b d e - 2c d e)f + (- 24b d e + 16c d e )f +--R + +--R 5 +--R 16c d e +--R * +--R x +--R + +--R 2 2 3 4 2 2 3 3 2 2 4 +--R (15a d e - 3b d e - c d )f + (- 12b d e + 8c d e )f + 8c d e +--R * +--R +-+ +-------+ +--R +-------+ \|e \|f x + e +--R \|f x + e atanh(--------------) +--R +----------+ +--R | 2 +--R \|- d f + e +--R + +--R 3 2 2 2 4 3 5 2 +--R ((- 15a e + 3b d e + c d e)f + (12b e - 8c d e )f - 8c e )x +--R + +--R 2 2 3 2 4 3 2 2 +--R (- 25a d e + 5b d e - c d )f + (- 5a e + 21b d e - 5c d e )f +--R + +--R 5 4 +--R 4b e - 24c d e +--R * +--R x +--R + +--R 2 2 3 2 2 3 5 4 +--R - 8a d e f + (- 9a d e + 13b d e - c d e)f + 2a e + 2b d e +--R + +--R 2 3 +--R - 14c d e +--R * +--R +----------+ +--R | 2 +-+ +--R \|- d f + e \|e +--R / +--R 3 3 3 2 5 2 7 9 2 +--R (4d e f - 12d e f + 12d e f - 4e )x +--R + +--R 4 2 3 3 4 2 2 6 8 5 3 4 3 2 3 5 +--R (8d e f - 24d e f + 24d e f - 8d e )x + 4d e f - 12d e f + 12d e f +--R + +--R 2 7 +--R - 4d e +--R * +--R +----------+ +--R | 2 +-+ +-------+ +--R \|- d f + e \|e \|f x + e +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1035 +d0:=normalize(t0-D(r0,x)) +--R +--R +--R (3) 0 +--R Type: Expression(Integer) +--E 1026 + +)clear all + +--S 1027 of 1035 +t0:=x^m*(1-a^2*x^2)^p/(1+a*x) +--R +--R +--R 2 2 p m +--R (- a x + 1) x +--R (1) --------------- +--R a x + 1 +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1035 +--r0:=x^(1+m)*AppellF1(1+m,-p,1-p,2+m,a*x,-a*x)/(1+m) +--E 1028 + +--S 1029 of 1035 +--d0:=D(m0,x) +--E 1029 + +)clear all + +--S 1030 of 1035 +t0:=sqrt(-1+x)*sqrt(1+x)/(1+x-x^2) +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (1) - ---------------- +--R 2 +--R x - x - 1 +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1035 +r0:=-acosh(x)-atan(sqrt(-1+x)*sqrt(-2+sqrt(5))/sqrt(1+x))*_ + sqrt(2/5*(-1+sqrt(5)))+atanh(sqrt(-1+x)*sqrt(2+sqrt(5))/sqrt(1+x))*_ + sqrt(2/5*(1+sqrt(5))) +--R +--R +--R (2) +--R +--------+ +--R +---------+ +-----+ | +-+ +--R | +-+ \|x - 1 \|\|5 + 2 +--R \|2\|5 + 2 atanh(-------------------) +--R +-----+ +--R \|x + 1 +--R + +--R +--------+ +--R +---------+ +-----+ | +-+ +--R | +-+ \|x - 1 \|\|5 - 2 +-+ +--R - \|2\|5 - 2 atan(-------------------) - \|5 acosh(x) +--R +-----+ +--R \|x + 1 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1035 +--d0:=D(m0,x) +--E 1032 + +)clear all + +--S 1033 of 1035 +t0:=(a+b*x+c*x^2)/(sqrt(d+e*x)*sqrt(f+g*x)) +--R +--R +--R 2 +--R c x + b x + a +--R (1) -------------------- +--R +-------+ +-------+ +--R \|e x + d \|g x + f +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1035 +r0:=-b*(e*f+d*g)*atanh(sqrt(g)*sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/_ + (e^(3/2)*g^(3/2))-1/4*c*(4*d*e*f*g-3*(e*f+d*g)^2)*atanh(sqrt(g)*_ + sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/(e^(5/2)*g^(5/2))+2*a*atanh(sqrt(g)*_ + sqrt(d+e*x)/(sqrt(e)*sqrt(f+g*x)))/(sqrt(e)*sqrt(g))+b*sqrt(d+e*x)*_ + sqrt(f+g*x)/(e*g)-3/4*c*(e*f+d*g)*sqrt(d+e*x)*sqrt(f+g*x)/(e^2*g^2)+_ + 1/2*c*x*sqrt(d+e*x)*sqrt(f+g*x)/(e*g) +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R ((8a e - 4b d e + 3c d )g + (- 4b e + 2c d e)f g + 3c e f ) +--R * +--R +-+ +-------+ +--R \|g \|e x + d +--R atanh(--------------) +--R +-+ +-------+ +--R \|e \|g x + f +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2c e g x + (4b e - 3c d)g - 3c e f)\|e \|g \|e x + d \|g x + f +--R / +--R 2 2 +-+ +-+ +--R 4e g \|e \|g +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1035 +--d0:=D(m0,x) +--E 1035 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document}